Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.53121.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} - x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2300) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.631352\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | −0.631352 | −0.364511 | −0.182256 | − | 0.983251i | \(-0.558340\pi\) | ||||
−0.182256 | + | 0.983251i | \(0.558340\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.16780 | −1.19732 | −0.598659 | − | 0.801004i | \(-0.704299\pi\) | ||||
−0.598659 | + | 0.801004i | \(0.704299\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.60139 | −0.867132 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.90510 | 0.574409 | 0.287205 | − | 0.957869i | \(-0.407274\pi\) | ||||
0.287205 | + | 0.957869i | \(0.407274\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.76920 | 1.87744 | 0.938719 | − | 0.344683i | \(-0.112014\pi\) | ||||
0.938719 | + | 0.344683i | \(0.112014\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.737296 | −0.178820 | −0.0894102 | − | 0.995995i | \(-0.528498\pi\) | ||||
−0.0894102 | + | 0.995995i | \(0.528498\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.90510 | −0.895891 | −0.447946 | − | 0.894061i | \(-0.647844\pi\) | ||||
−0.447946 | + | 0.894061i | \(0.647844\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.53645 | 0.680591 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.935058 | −0.173636 | −0.0868179 | − | 0.996224i | \(-0.527670\pi\) | ||||
−0.0868179 | + | 0.996224i | \(0.527670\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02996 | −0.184986 | −0.0924929 | − | 0.995713i | \(-0.529484\pi\) | ||||
−0.0924929 | + | 0.995713i | \(0.529484\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.20279 | −0.209379 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.94008 | −0.976544 | −0.488272 | − | 0.872692i | \(-0.662373\pi\) | ||||
−0.488272 | + | 0.872692i | \(0.662373\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.27375 | −0.684347 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.0019 | 1.71822 | 0.859108 | − | 0.511795i | \(-0.171019\pi\) | ||||
0.859108 | + | 0.511795i | \(0.171019\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.90510 | −0.595522 | −0.297761 | − | 0.954640i | \(-0.596240\pi\) | ||||
−0.297761 | + | 0.954640i | \(0.596240\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.47151 | 0.798102 | 0.399051 | − | 0.916929i | \(-0.369340\pi\) | ||||
0.399051 | + | 0.916929i | \(0.369340\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.03498 | 0.433569 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.465493 | 0.0651821 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.07290 | −0.422096 | −0.211048 | − | 0.977476i | \(-0.567688\pi\) | ||||
−0.211048 | + | 0.977476i | \(0.567688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.46549 | 0.326563 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.90510 | −0.638590 | −0.319295 | − | 0.947655i | \(-0.603446\pi\) | ||||
−0.319295 | + | 0.947655i | \(0.603446\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0729 | 1.41774 | 0.708870 | − | 0.705339i | \(-0.249205\pi\) | ||||
0.708870 | + | 0.705339i | \(0.249205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.24071 | 1.03823 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.20279 | −0.391283 | −0.195641 | − | 0.980675i | \(-0.562679\pi\) | ||||
−0.195641 | + | 0.980675i | \(0.562679\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.631352 | 0.0760059 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.86410 | −1.05197 | −0.525987 | − | 0.850492i | \(-0.676304\pi\) | ||||
−0.525987 | + | 0.850492i | \(0.676304\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.40055 | 1.10025 | 0.550126 | − | 0.835082i | \(-0.314580\pi\) | ||||
0.550126 | + | 0.835082i | \(0.314580\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.03498 | −0.687750 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.56949 | −0.176582 | −0.0882908 | − | 0.996095i | \(-0.528140\pi\) | ||||
−0.0882908 | + | 0.996095i | \(0.528140\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.57144 | 0.619049 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.64240 | −0.290041 | −0.145020 | − | 0.989429i | \(-0.546325\pi\) | ||||
−0.145020 | + | 0.989429i | \(0.546325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.590351 | 0.0632922 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.6113 | −1.97279 | −0.986397 | − | 0.164380i | \(-0.947438\pi\) | ||||
−0.986397 | + | 0.164380i | \(0.947438\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.4435 | −2.24789 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.650266 | 0.0674294 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.3486 | 1.55841 | 0.779207 | − | 0.626767i | \(-0.215622\pi\) | ||||
0.779207 | + | 0.626767i | \(0.215622\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.95592 | −0.498088 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.18079 | −0.913523 | −0.456762 | − | 0.889589i | \(-0.650991\pi\) | ||||
−0.456762 | + | 0.889589i | \(0.650991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.50341 | 0.739333 | 0.369667 | − | 0.929164i | \(-0.379472\pi\) | ||||
0.369667 | + | 0.929164i | \(0.379472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5384 | 1.50215 | 0.751077 | − | 0.660215i | \(-0.229535\pi\) | ||||
0.751077 | + | 0.660215i | \(0.229535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.13282 | 0.300070 | 0.150035 | − | 0.988681i | \(-0.452061\pi\) | ||||
0.150035 | + | 0.988681i | \(0.452061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.75029 | 0.355961 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.0130 | 1.60045 | 0.800224 | − | 0.599702i | \(-0.204714\pi\) | ||||
0.800224 | + | 0.599702i | \(0.204714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.6094 | −1.62799 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.33561 | 0.214105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.37059 | −0.670054 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.94610 | −0.626309 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.97004 | −0.263549 | −0.131774 | − | 0.991280i | \(-0.542067\pi\) | ||||
−0.131774 | + | 0.991280i | \(0.542067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.46549 | 0.217075 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.22967 | 0.369548 | 0.184774 | − | 0.982781i | \(-0.440845\pi\) | ||||
0.184774 | + | 0.982781i | \(0.440845\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.3706 | 1.07267 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.52541 | −0.386632 | −0.193316 | − | 0.981137i | \(-0.561924\pi\) | ||||
−0.193316 | + | 0.981137i | \(0.561924\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.00991 | 0.594573 | 0.297286 | − | 0.954788i | \(-0.403918\pi\) | ||||
0.297286 | + | 0.954788i | \(0.403918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.45445 | −0.290917 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.8960 | 1.07842 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.91614 | −0.158041 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.73113 | 0.715282 | 0.357641 | − | 0.933859i | \(-0.383581\pi\) | ||||
0.357641 | + | 0.933859i | \(0.383581\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2697 | −1.56814 | −0.784072 | − | 0.620670i | \(-0.786861\pi\) | ||||
−0.784072 | + | 0.620670i | \(0.786861\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.91800 | 0.155061 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.65529 | −0.531150 | −0.265575 | − | 0.964090i | \(-0.585562\pi\) | ||||
−0.265575 | + | 0.964090i | \(0.585562\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.94008 | 0.153859 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.16780 | 0.249658 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.11585 | −0.714009 | −0.357004 | − | 0.934103i | \(-0.616202\pi\) | ||||
−0.357004 | + | 0.934103i | \(0.616202\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.6463 | 1.67504 | 0.837520 | − | 0.546407i | \(-0.184005\pi\) | ||||
0.837520 | + | 0.546407i | \(0.184005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.8221 | 2.52477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.1587 | 0.776856 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8102 | 0.973941 | 0.486971 | − | 0.873418i | \(-0.338102\pi\) | ||||
0.486971 | + | 0.873418i | \(0.338102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.09685 | 0.232773 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.9769 | −1.94160 | −0.970801 | − | 0.239886i | \(-0.922890\pi\) | ||||
−0.970801 | + | 0.239886i | \(0.922890\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.1966 | −0.980897 | −0.490449 | − | 0.871470i | \(-0.663167\pi\) | ||||
−0.490449 | + | 0.871470i | \(0.663167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.99090 | −0.516782 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.40462 | −0.102716 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.2028 | −0.814883 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.3136 | −1.39748 | −0.698742 | − | 0.715374i | \(-0.746256\pi\) | ||||
−0.698742 | + | 0.715374i | \(0.746256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.70132 | −0.482372 | −0.241186 | − | 0.970479i | \(-0.577536\pi\) | ||||
−0.241186 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.9320 | −0.778871 | −0.389436 | − | 0.921054i | \(-0.627330\pi\) | ||||
−0.389436 | + | 0.921054i | \(0.627330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.77228 | −0.621850 | −0.310925 | − | 0.950434i | \(-0.600639\pi\) | ||||
−0.310925 | + | 0.950434i | \(0.600639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.02209 | 0.142627 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.96208 | 0.207897 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.60139 | 0.180809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.43961 | −0.514608 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.71530 | 0.462300 | 0.231150 | − | 0.972918i | \(-0.425751\pi\) | ||||
0.231150 | + | 0.972918i | \(0.425751\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.59637 | 0.383457 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.26270 | 0.221487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.93506 | −0.401054 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.99090 | −0.335724 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7661 | 1.45757 | 0.728784 | − | 0.684744i | \(-0.240086\pi\) | ||||
0.728784 | + | 0.684744i | \(0.240086\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.5485 | −1.56297 | −0.781483 | − | 0.623927i | \(-0.785536\pi\) | ||||
−0.781483 | + | 0.623927i | \(0.785536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6204 | −0.767898 | −0.383949 | − | 0.923354i | \(-0.625436\pi\) | ||||
−0.383949 | + | 0.923354i | \(0.625436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.81020 | 0.250693 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1178 | −0.793863 | −0.396932 | − | 0.917848i | \(-0.629925\pi\) | ||||
−0.396932 | + | 0.917848i | \(0.629925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.990902 | 0.0643660 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.63429 | 0.364452 | 0.182226 | − | 0.983257i | \(-0.441670\pi\) | ||||
0.182226 | + | 0.983257i | \(0.441670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.07907 | −0.327172 | −0.163586 | − | 0.986529i | \(-0.552306\pi\) | ||||
−0.163586 | + | 0.986529i | \(0.552306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1269 | −0.906241 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.4344 | −1.68198 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.66828 | 0.105723 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.4186 | −1.22569 | −0.612845 | − | 0.790203i | \(-0.709975\pi\) | ||||
−0.612845 | + | 0.790203i | \(0.709975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.90510 | −0.119773 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.75507 | −0.546126 | −0.273063 | − | 0.961996i | \(-0.588037\pi\) | ||||
−0.273063 | + | 0.961996i | \(0.588037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.8170 | 1.16923 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.43245 | 0.150565 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.3457 | −1.00792 | −0.503958 | − | 0.863728i | \(-0.668124\pi\) | ||||
−0.503958 | + | 0.863728i | \(0.668124\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.7503 | 0.719106 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.14880 | −0.191986 | −0.0959928 | − | 0.995382i | \(-0.530603\pi\) | ||||
−0.0959928 | + | 0.995382i | \(0.530603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.1525 | −1.52791 | −0.763954 | − | 0.645271i | \(-0.776745\pi\) | ||||
−0.763954 | + | 0.645271i | \(0.776745\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.5384 | 0.819381 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8630 | −0.953113 | −0.476557 | − | 0.879144i | \(-0.658115\pi\) | ||||
−0.476557 | + | 0.879144i | \(0.658115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.67933 | 0.160407 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.2057 | −0.966752 | −0.483376 | − | 0.875413i | \(-0.660590\pi\) | ||||
−0.483376 | + | 0.875413i | \(0.660590\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.4814 | 1.81193 | 0.905966 | − | 0.423350i | \(-0.139146\pi\) | ||||
0.905966 | + | 0.423350i | \(0.139146\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.8520 | −2.05725 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4564 | −0.968023 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.69037 | −0.568060 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.9339 | −0.930870 | −0.465435 | − | 0.885082i | \(-0.654102\pi\) | ||||
−0.465435 | + | 0.885082i | \(0.654102\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.73730 | 0.390938 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.76920 | −0.391473 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.3706 | 0.713029 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.79631 | 0.332990 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.93003 | −0.452591 | −0.226295 | − | 0.974059i | \(-0.572661\pi\) | ||||
−0.226295 | + | 0.974059i | \(0.572661\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.73730 | −0.269495 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.9960 | 1.64421 | 0.822107 | − | 0.569333i | \(-0.192799\pi\) | ||||
0.822107 | + | 0.569333i | \(0.192799\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.4564 | −1.21279 | −0.606394 | − | 0.795165i | \(-0.707384\pi\) | ||||
−0.606394 | + | 0.795165i | \(0.707384\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.70620 | 0.264327 | 0.132163 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132163 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.78138 | −0.0997381 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.81020 | −0.547552 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.87921 | 0.160204 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.97791 | −0.109379 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.3327 | −0.955581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.98611 | 0.329027 | 0.164513 | − | 0.986375i | \(-0.447395\pi\) | ||||
0.164513 | + | 0.986375i | \(0.447395\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.4525 | 0.846792 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.82319 | −0.371683 | −0.185841 | − | 0.982580i | \(-0.559501\pi\) | ||||
−0.185841 | + | 0.982580i | \(0.559501\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.7412 | −0.583381 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.96217 | −0.106258 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.5604 | 0.678197 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.50048 | 0.187915 | 0.0939577 | − | 0.995576i | \(-0.470048\pi\) | ||||
0.0939577 | + | 0.995576i | \(0.470048\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.44042 | −0.398276 | −0.199138 | − | 0.979971i | \(-0.563814\pi\) | ||||
−0.199138 | + | 0.979971i | \(0.563814\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.9389 | 1.27777 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.87822 | 0.259642 | 0.129821 | − | 0.991537i | \(-0.458560\pi\) | ||||
0.129821 | + | 0.991537i | \(0.458560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.47459 | −0.0780437 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.0570722 | −0.00301216 | −0.00150608 | − | 0.999999i | \(-0.500479\pi\) | ||||
−0.00150608 | + | 0.999999i | \(0.500479\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.75019 | −0.197379 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.65344 | 0.244242 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.11082 | 0.214583 | 0.107292 | − | 0.994228i | \(-0.465782\pi\) | ||||
0.107292 | + | 0.994228i | \(0.465782\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.6204 | −1.48992 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.73436 | 0.505383 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.2057 | −1.35688 | −0.678440 | − | 0.734655i | \(-0.737344\pi\) | ||||
−0.678440 | + | 0.734655i | \(0.737344\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.32959 | −0.325991 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.9938 | −1.43795 | −0.718973 | − | 0.695038i | \(-0.755388\pi\) | ||||
−0.718973 | + | 0.695038i | \(0.755388\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.87514 | 0.0960665 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.16487 | 0.212815 | 0.106407 | − | 0.994323i | \(-0.466065\pi\) | ||||
0.106407 | + | 0.994323i | \(0.466065\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.1587 | 0.516396 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.4593 | −1.34154 | −0.670771 | − | 0.741665i | \(-0.734037\pi\) | ||||
−0.670771 | + | 0.741665i | \(0.734037\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.737296 | 0.0372866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.67041 | −0.134704 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.65036 | −0.233395 | −0.116697 | − | 0.993168i | \(-0.537231\pi\) | ||||
−0.116697 | + | 0.993168i | \(0.537231\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.81020 | −0.390999 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.1328 | −1.25507 | −0.627537 | − | 0.778587i | \(-0.715937\pi\) | ||||
−0.627537 | + | 0.778587i | \(0.715937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.97199 | −0.347299 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.3165 | −0.560936 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.8659 | 0.833965 | 0.416982 | − | 0.908915i | \(-0.363088\pi\) | ||||
0.416982 | + | 0.908915i | \(0.363088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.85713 | 0.140932 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.5384 | 0.764595 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.42572 | −0.216728 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.4594 | −0.950655 | −0.475328 | − | 0.879809i | \(-0.657670\pi\) | ||||
−0.475328 | + | 0.879809i | \(0.657670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.41761 | −0.215301 | −0.107651 | − | 0.994189i | \(-0.534333\pi\) | ||||
−0.107651 | + | 0.994189i | \(0.534333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.2336 | −0.692059 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.0768 | −1.69749 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.14192 | −0.393096 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.89220 | −0.0911442 | −0.0455721 | − | 0.998961i | \(-0.514511\pi\) | ||||
−0.0455721 | + | 0.998961i | \(0.514511\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.4147 | −1.22135 | −0.610676 | − | 0.791881i | \(-0.709102\pi\) | ||||
−0.610676 | + | 0.791881i | \(0.709102\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.90510 | 0.186806 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.8979 | 0.758768 | 0.379384 | − | 0.925239i | \(-0.376136\pi\) | ||||
0.379384 | + | 0.925239i | \(0.376136\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.89519 | −0.375962 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.34485 | 0.111407 | 0.0557037 | − | 0.998447i | \(-0.482260\pi\) | ||||
0.0557037 | + | 0.998447i | \(0.482260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.51242 | −0.260728 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.3774 | −1.71676 | −0.858378 | − | 0.513017i | \(-0.828528\pi\) | ||||
−0.858378 | + | 0.513017i | \(0.828528\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.9598 | 0.986959 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.1660 | 0.571606 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.5035 | −0.865557 | −0.432779 | − | 0.901500i | \(-0.642467\pi\) | ||||
−0.432779 | + | 0.901500i | \(0.642467\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.60741 | −0.121704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.0296 | 1.58492 | 0.792459 | − | 0.609925i | \(-0.208801\pi\) | ||||
0.792459 | + | 0.609925i | \(0.208801\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.7153 | −0.776826 | −0.388413 | − | 0.921485i | \(-0.626977\pi\) | ||||
−0.388413 | + | 0.921485i | \(0.626977\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.0480 | −0.511239 | −0.255620 | − | 0.966777i | \(-0.582279\pi\) | ||||
−0.255620 | + | 0.966777i | \(0.582279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.1458 | 0.468490 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.20183 | 0.193610 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.43961 | −0.342073 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.99384 | 0.366013 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.2508 | 1.38219 | 0.691096 | − | 0.722763i | \(-0.257128\pi\) | ||||
0.691096 | + | 0.722763i | \(0.257128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.2096 | −1.83340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.00000 | −0.0910032 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.9211 | −0.812082 | −0.406041 | − | 0.913855i | \(-0.633091\pi\) | ||||
−0.406041 | + | 0.913855i | \(0.633091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.75531 | 0.260264 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.5861 | 1.56085 | 0.780425 | − | 0.625249i | \(-0.215003\pi\) | ||||
0.780425 | + | 0.625249i | \(0.215003\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.689414 | 0.0310497 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.0797 | 1.25955 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.653440 | 0.0292520 | 0.0146260 | − | 0.999893i | \(-0.495344\pi\) | ||||
0.0146260 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6664 | −0.610571 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.50048 | 0.289842 | 0.144921 | − | 0.989443i | \(-0.453707\pi\) | ||||
0.144921 | + | 0.989443i | \(0.453707\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.7223 | −0.920308 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.6612 | 1.53633 | 0.768166 | − | 0.640251i | \(-0.221170\pi\) | ||||
0.768166 | + | 0.640251i | \(0.221170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.7791 | −1.31735 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.8102 | −0.609735 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4238 | 0.458437 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.08775 | −0.355013 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.8073 | −0.561096 | −0.280548 | − | 0.959840i | \(-0.590516\pi\) | ||||
−0.280548 | + | 0.959840i | \(0.590516\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.9689 | 1.66026 | 0.830132 | − | 0.557567i | \(-0.188265\pi\) | ||||
0.830132 | + | 0.557567i | \(0.188265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.759383 | 0.0330793 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.7601 | 0.553741 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 74.4744 | 3.22584 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.4006 | 0.707736 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.78195 | 0.249046 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.3088 | 0.529198 | 0.264599 | − | 0.964359i | \(-0.414760\pi\) | ||||
0.264599 | + | 0.964359i | \(0.414760\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.33172 | 0.357548 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.3009 | −0.868002 | −0.434001 | − | 0.900912i | \(-0.642899\pi\) | ||||
−0.434001 | + | 0.900912i | \(0.642899\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.8050 | −1.22937 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.65149 | 0.155559 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.97184 | 0.211424 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.59149 | −0.279290 | −0.139645 | − | 0.990202i | \(-0.544596\pi\) | ||||
−0.139645 | + | 0.990202i | \(0.544596\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.4344 | −1.11806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.886811 | 0.0374412 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.08191 | −0.214177 | −0.107088 | − | 0.994249i | \(-0.534153\pi\) | ||||
−0.107088 | + | 0.994249i | \(0.534153\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.6492 | −0.741198 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.8672 | −0.707109 | −0.353554 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353554 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3174 | −1.60353 | −0.801767 | − | 0.597637i | \(-0.796106\pi\) | ||||
−0.801767 | + | 0.597637i | \(0.796106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.1937 | 0.509399 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.0240 | 0.791981 | 0.395990 | − | 0.918255i | \(-0.370401\pi\) | ||||
0.395990 | + | 0.918255i | \(0.370401\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.23089 | 0.175830 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.37059 | 0.347271 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.85419 | −0.242456 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.66747 | −0.233922 | −0.116961 | − | 0.993137i | \(-0.537315\pi\) | ||||
−0.116961 | + | 0.993137i | \(0.537315\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.02209 | 0.165727 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.90193 | 0.283907 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.7130 | −1.46656 | −0.733279 | − | 0.679928i | \(-0.762011\pi\) | ||||
−0.733279 | + | 0.679928i | \(0.762011\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.53840 | 0.226672 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.1717 | −0.824193 | −0.412097 | − | 0.911140i | \(-0.635203\pi\) | ||||
−0.412097 | + | 0.911140i | \(0.635203\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.9069 | −1.70942 | −0.854709 | − | 0.519107i | \(-0.826264\pi\) | ||||
−0.854709 | + | 0.519107i | \(0.826264\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.33172 | 0.339294 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.8678 | 1.45583 | 0.727915 | − | 0.685667i | \(-0.240489\pi\) | ||||
0.727915 | + | 0.685667i | \(0.240489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.87012 | −0.0757809 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.0377 | 1.49839 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.7819 | −0.879765 | −0.439882 | − | 0.898055i | \(-0.644980\pi\) | ||||
−0.439882 | + | 0.898055i | \(0.644980\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.8480 | −0.557501 | −0.278750 | − | 0.960364i | \(-0.589920\pi\) | ||||
−0.278750 | + | 0.960364i | \(0.589920\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.6113 | −1.55192 | −0.775960 | − | 0.630783i | \(-0.782734\pi\) | ||||
−0.775960 | + | 0.630783i | \(0.782734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.53645 | −0.141913 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 58.9570 | 2.36206 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.69701 | 0.187581 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.37960 | 0.174626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.598221 | 0.0238148 | 0.0119074 | − | 0.999929i | \(-0.496210\pi\) | ||||
0.0119074 | + | 0.999929i | \(0.496210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.23972 | −0.168514 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.5444 | 0.813999 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.0590 | 0.912201 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.5254 | −0.889700 | −0.444850 | − | 0.895605i | \(-0.646743\pi\) | ||||
−0.444850 | + | 0.895605i | \(0.646743\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.1908 | 1.42723 | 0.713614 | − | 0.700539i | \(-0.247057\pi\) | ||||
0.713614 | + | 0.700539i | \(0.247057\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.33067 | 0.248884 | 0.124442 | − | 0.992227i | \(-0.460286\pi\) | ||||
0.124442 | + | 0.992227i | \(0.460286\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.34471 | −0.366812 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.05992 | −0.0807344 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.3057 | −0.559827 | −0.279914 | − | 0.960025i | \(-0.590306\pi\) | ||||
−0.279914 | + | 0.960025i | \(0.590306\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.4545 | −0.954063 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.6563 | 1.50584 | 0.752919 | − | 0.658114i | \(-0.228645\pi\) | ||||
0.752919 | + | 0.658114i | \(0.228645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5954 | 0.489903 | 0.244952 | − | 0.969535i | \(-0.421228\pi\) | ||||
0.244952 | + | 0.969535i | \(0.421228\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.15102 | 0.122375 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.935058 | 0.0362056 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.7421 | −0.531300 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.0950 | 0.814363 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.356707 | 0.0137500 | 0.00687501 | − | 0.999976i | \(-0.497812\pi\) | ||||
0.00687501 | + | 0.999976i | \(0.497812\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.8831 | −0.725737 | −0.362868 | − | 0.931840i | \(-0.618203\pi\) | ||||
−0.362868 | + | 0.931840i | \(0.618203\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48.6214 | −1.86592 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.8674 | 0.569719 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.7520 | 0.717525 | 0.358763 | − | 0.933429i | \(-0.383199\pi\) | ||||
0.358763 | + | 0.933429i | \(0.383199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.33656 | 0.279907 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.8011 | −0.792459 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3175 | 0.696831 | 0.348415 | − | 0.937340i | \(-0.386720\pi\) | ||||
0.348415 | + | 0.937340i | \(0.386720\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.6994 | 0.596370 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.11169 | −0.307252 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.65060 | 0.289372 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.0007 | 1.01980 | 0.509900 | − | 0.860233i | \(-0.329682\pi\) | ||||
0.509900 | + | 0.860233i | \(0.329682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.1966 | 0.874877 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.0830 | 1.09378 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1875 | 0.607935 | 0.303968 | − | 0.952682i | \(-0.401689\pi\) | ||||
0.303968 | + | 0.952682i | \(0.401689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.08287 | 0.153119 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.02996 | 0.0385722 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.55722 | −0.132847 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.2926 | 1.83830 | 0.919151 | − | 0.393904i | \(-0.128876\pi\) | ||||
0.919151 | + | 0.393904i | \(0.128876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.7693 | −0.885217 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.20668 | 0.119258 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.2447 | 0.862098 | 0.431049 | − | 0.902329i | \(-0.358144\pi\) | ||||
0.431049 | + | 0.902329i | \(0.358144\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.79527 | −0.288714 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.87921 | 0.106492 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.8203 | 0.953693 | 0.476846 | − | 0.878987i | \(-0.341780\pi\) | ||||
0.476846 | + | 0.878987i | \(0.341780\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.10163 | −0.224757 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.6853 | −0.797705 | −0.398852 | − | 0.917015i | \(-0.630591\pi\) | ||||
−0.398852 | + | 0.917015i | \(0.630591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.6894 | 0.613101 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.5932 | −1.01230 | −0.506148 | − | 0.862447i | \(-0.668931\pi\) | ||||
−0.506148 | + | 0.862447i | \(0.668931\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.87391 | 0.251503 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.2226 | −1.79855 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.2644 | 1.76119 | 0.880597 | − | 0.473866i | \(-0.157142\pi\) | ||||
0.880597 | + | 0.473866i | \(0.157142\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.2600 | 0.446778 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.87012 | −0.213353 | −0.106676 | − | 0.994294i | \(-0.534021\pi\) | ||||
−0.106676 | + | 0.994294i | \(0.534021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.20279 | 0.0436585 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.67624 | −0.205764 | −0.102882 | − | 0.994694i | \(-0.532806\pi\) | ||||
−0.102882 | + | 0.994694i | \(0.532806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.92416 | −0.359279 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.2036 | −1.19891 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.3226 | 0.624670 | 0.312335 | − | 0.949972i | \(-0.398889\pi\) | ||||
0.312335 | + | 0.949972i | \(0.398889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.52753 | 0.199069 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.3773 | −1.02066 | −0.510331 | − | 0.859978i | \(-0.670477\pi\) | ||||
−0.510331 | + | 0.859978i | \(0.670477\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.8802 | −0.426199 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.9637 | −1.53933 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.8870 | −0.604264 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.30679 | −0.118175 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.3995 | 1.11927 | 0.559636 | − | 0.828739i | \(-0.310941\pi\) | ||||
0.559636 | + | 0.828739i | \(0.310941\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.3199 | 0.367397 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −53.8938 | −1.91624 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 74.9547 | 2.66172 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.0169 | 0.744456 | 0.372228 | − | 0.928141i | \(-0.378594\pi\) | ||||
0.372228 | + | 0.928141i | \(0.378594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.03412 | −0.142717 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.4153 | 1.71067 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.9090 | 0.631995 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.98800 | 0.0699809 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.6712 | 0.902552 | 0.451276 | − | 0.892384i | \(-0.350969\pi\) | ||||
0.451276 | + | 0.892384i | \(0.350969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.3647 | −1.41740 | −0.708698 | − | 0.705512i | \(-0.750717\pi\) | ||||
−0.708698 | + | 0.705512i | \(0.750717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.8801 | 0.556940 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.2498 | 0.533523 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 55.7830 | 1.94922 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.6396 | 0.894827 | 0.447413 | − | 0.894327i | \(-0.352345\pi\) | ||||
0.447413 | + | 0.894327i | \(0.352345\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.6726 | 0.546312 | 0.273156 | − | 0.961970i | \(-0.411932\pi\) | ||||
0.273156 | + | 0.961970i | \(0.411932\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.8429 | 1.59411 | 0.797057 | − | 0.603904i | \(-0.206389\pi\) | ||||
0.797057 | + | 0.603904i | \(0.206389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.6214 | −0.542552 | −0.271276 | − | 0.962502i | \(-0.587446\pi\) | ||||
−0.271276 | + | 0.962502i | \(0.587446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.0151 | 0.347420 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.23768 | −0.0775311 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.64240 | −0.125900 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.7853 | −1.23544 | −0.617722 | − | 0.786396i | \(-0.711944\pi\) | ||||
−0.617722 | + | 0.786396i | \(0.711944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1257 | −0.969851 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.2315 | 0.352392 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.3486 | 0.802267 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.2445 | −0.660470 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.94008 | 0.203623 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.0350 | −0.959900 | −0.479950 | − | 0.877296i | \(-0.659345\pi\) | ||||
−0.479950 | + | 0.877296i | \(0.659345\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.37562 | 0.320265 | 0.160133 | − | 0.987096i | \(-0.448808\pi\) | ||||
0.160133 | + | 0.987096i | \(0.448808\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.85704 | 0.336318 | 0.168159 | − | 0.985760i | \(-0.446218\pi\) | ||||
0.168159 | + | 0.985760i | \(0.446218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.0039 | 0.749891 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.1607 | −1.80961 | −0.904805 | − | 0.425827i | \(-0.859983\pi\) | ||||
−0.904805 | + | 0.425827i | \(0.859983\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.3898 | 0.352855 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.99004 | −0.101430 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.6803 | −0.734609 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.9278 | −1.35135 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.8780 | 1.88687 | 0.943433 | − | 0.331564i | \(-0.107576\pi\) | ||||
0.943433 | + | 0.331564i | \(0.107576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.0599 | 0.339313 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.8961 | 1.20937 | 0.604685 | − | 0.796465i | \(-0.293299\pi\) | ||||
0.604685 | + | 0.796465i | \(0.293299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.2225 | −1.05072 | −0.525361 | − | 0.850880i | \(-0.676070\pi\) | ||||
−0.525361 | + | 0.850880i | \(0.676070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.3094 | −1.48776 | −0.743882 | − | 0.668311i | \(-0.767018\pi\) | ||||
−0.743882 | + | 0.668311i | \(0.767018\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.40851 | 0.315551 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.6141 | 0.355587 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.3668 | −0.715013 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.27375 | 0.142696 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.963070 | 0.0321202 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.26564 | 0.0754794 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.81020 | −0.259907 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.5424 | −1.67823 | −0.839116 | − | 0.543952i | \(-0.816927\pi\) | ||||
−0.839116 | + | 0.543952i | \(0.816927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.8829 | 0.792145 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.446726 | −0.0148007 | −0.00740034 | − | 0.999973i | \(-0.502356\pi\) | ||||
−0.00740034 | + | 0.999973i | \(0.502356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.03403 | −0.166602 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.3988 | −0.442466 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.6373 | −1.20855 | −0.604276 | − | 0.796775i | \(-0.706538\pi\) | ||||
−0.604276 | + | 0.796775i | \(0.706538\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.00664 | 0.164974 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.0028 | −1.97502 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.5193 | −0.641099 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.8243 | −0.584797 | −0.292399 | − | 0.956297i | \(-0.594453\pi\) | ||||
−0.292399 | + | 0.956297i | \(0.594453\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.8519 | −0.388431 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.3067 | −0.599334 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.503505 | −0.0164488 | −0.00822440 | − | 0.999966i | \(-0.502618\pi\) | ||||
−0.00822440 | + | 0.999966i | \(0.502618\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.5465 | 0.442075 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.3593 | −1.38087 | −0.690437 | − | 0.723392i | \(-0.742582\pi\) | ||||
−0.690437 | + | 0.723392i | \(0.742582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.0019 | −0.358273 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.89002 | −0.158904 | −0.0794521 | − | 0.996839i | \(-0.525317\pi\) | ||||
−0.0794521 | + | 0.996839i | \(0.525317\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.6342 | 2.06565 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.97127 | −0.0963501 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.04399 | 0.260570 | 0.130285 | − | 0.991477i | \(-0.458411\pi\) | ||||
0.130285 | + | 0.991477i | \(0.458411\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.12468 | 0.0363557 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.3356 | 0.462921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9392 | −0.965780 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.4215 | −1.30256 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.1938 | 0.681548 | 0.340774 | − | 0.940145i | \(-0.389311\pi\) | ||||
0.340774 | + | 0.940145i | \(0.389311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.81780 | −0.0583961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −61.5773 | −1.97611 | −0.988054 | − | 0.154106i | \(-0.950750\pi\) | ||||
−0.988054 | + | 0.154106i | \(0.950750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.2060 | −0.711892 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.8339 | −1.40237 | −0.701185 | − | 0.712979i | \(-0.747346\pi\) | ||||
−0.701185 | + | 0.712979i | \(0.747346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.4564 | −1.13319 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.14970 | −0.260200 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.6752 | −1.20165 | −0.600826 | − | 0.799380i | \(-0.705162\pi\) | ||||
−0.600826 | + | 0.799380i | \(0.705162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.9430 | 0.348320 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.90510 | 0.124175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.1831 | −0.545838 | −0.272919 | − | 0.962037i | \(-0.587989\pi\) | ||||
−0.272919 | + | 0.962037i | \(0.587989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.77935 | −0.119934 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.3297 | 0.422157 | 0.211079 | − | 0.977469i | \(-0.432302\pi\) | ||||
0.211079 | + | 0.977469i | \(0.432302\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.0068 | −0.664627 |
(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 | 9200.2.a.co.1.2 | 4 | ||
4.3 | odd | 2 | 2300.2.a.l.1.3 | ✓ | 4 | ||
5.4 | even | 2 | 9200.2.a.cm.1.3 | 4 | |||
20.3 | even | 4 | 2300.2.c.j.1749.6 | 8 | |||
20.7 | even | 4 | 2300.2.c.j.1749.3 | 8 | |||
20.19 | odd | 2 | 2300.2.a.m.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2300.2.a.l.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
2300.2.a.m.1.2 | yes | 4 | 20.19 | odd | 2 | ||
2300.2.c.j.1749.3 | 8 | 20.7 | even | 4 | |||
2300.2.c.j.1749.6 | 8 | 20.3 | even | 4 | |||
9200.2.a.cm.1.3 | 4 | 5.4 | even | 2 | |||
9200.2.a.co.1.2 | 4 | 1.1 | even | 1 | trivial |