Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.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: | \(44.0774219157\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.561553 | −0.212247 | −0.106124 | − | 0.994353i | \(-0.533844\pi\) | ||||
−0.106124 | + | 0.994353i | \(0.533844\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.56155 | −0.621268 | −0.310634 | − | 0.950530i | \(-0.600541\pi\) | ||||
−0.310634 | + | 0.950530i | \(0.600541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12311 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.561553 | −0.122541 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.56155 | 0.847059 | 0.423530 | − | 0.905882i | \(-0.360791\pi\) | ||||
0.423530 | + | 0.905882i | \(0.360791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.68466 | 0.661784 | 0.330892 | − | 0.943669i | \(-0.392650\pi\) | ||||
0.330892 | + | 0.943669i | \(0.392650\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | −0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.561553 | 0.0949197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.68466 | 0.605754 | 0.302877 | − | 0.953030i | \(-0.402053\pi\) | ||||
0.302877 | + | 0.953030i | \(0.402053\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.68466 | 0.887794 | 0.443897 | − | 0.896078i | \(-0.353596\pi\) | ||||
0.443897 | + | 0.896078i | \(0.353596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.2462 | 1.49456 | 0.747282 | − | 0.664507i | \(-0.231359\pi\) | ||||
0.747282 | + | 0.664507i | \(0.231359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68466 | −0.954951 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.56155 | −0.358689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.43845 | −0.472307 | −0.236154 | − | 0.971716i | \(-0.575887\pi\) | ||||
−0.236154 | + | 0.971716i | \(0.575887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.12311 | 0.148759 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.56155 | −0.333486 | −0.166743 | − | 0.986000i | \(-0.553325\pi\) | ||||
−0.166743 | + | 0.986000i | \(0.553325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.2462 | −1.82404 | −0.912020 | − | 0.410145i | \(-0.865478\pi\) | ||||
−0.912020 | + | 0.410145i | \(0.865478\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.561553 | −0.0707490 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6847 | −1.42751 | −0.713754 | − | 0.700396i | \(-0.753007\pi\) | ||||
−0.713754 | + | 0.700396i | \(0.753007\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.9309 | −1.65329 | −0.826645 | − | 0.562724i | \(-0.809753\pi\) | ||||
−0.826645 | + | 0.562724i | \(0.809753\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.12311 | 0.127990 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.3693 | −1.50417 | −0.752083 | − | 0.659069i | \(-0.770951\pi\) | ||||
−0.752083 | + | 0.659069i | \(0.770951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.68466 | 0.623972 | 0.311986 | − | 0.950087i | \(-0.399006\pi\) | ||||
0.311986 | + | 0.950087i | \(0.399006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.56155 | 0.277839 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.56155 | 0.489050 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.24621 | −0.662097 | −0.331049 | − | 0.943614i | \(-0.607402\pi\) | ||||
−0.331049 | + | 0.943614i | \(0.607402\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.12311 | 0.117733 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.68466 | 0.382081 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.12311 | −0.115228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0000 | −1.42148 | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||||
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.43845 | −0.740153 | −0.370077 | − | 0.929001i | \(-0.620669\pi\) | ||||
−0.370077 | + | 0.929001i | \(0.620669\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1231 | 1.09599 | 0.547996 | − | 0.836481i | \(-0.315391\pi\) | ||||
0.547996 | + | 0.836481i | \(0.315391\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.561553 | 0.0548019 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.8078 | −1.43152 | −0.715760 | − | 0.698346i | \(-0.753920\pi\) | ||||
−0.715760 | + | 0.698346i | \(0.753920\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1231 | −1.25697 | −0.628483 | − | 0.777824i | \(-0.716324\pi\) | ||||
−0.628483 | + | 0.777824i | \(0.716324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.68466 | 0.349732 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.8078 | −1.20485 | −0.602427 | − | 0.798174i | \(-0.705799\pi\) | ||||
−0.602427 | + | 0.798174i | \(0.705799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.43845 | 0.131862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.68466 | 0.512568 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4924 | 1.46347 | 0.731733 | − | 0.681591i | \(-0.238712\pi\) | ||||
0.731733 | + | 0.681591i | \(0.238712\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2462 | 0.895216 | 0.447608 | − | 0.894230i | \(-0.352276\pi\) | ||||
0.447608 | + | 0.894230i | \(0.352276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.630683 | −0.0546872 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.87689 | 0.245790 | 0.122895 | − | 0.992420i | \(-0.460782\pi\) | ||||
0.122895 | + | 0.992420i | \(0.460782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.68466 | −0.651804 | −0.325902 | − | 0.945404i | \(-0.605668\pi\) | ||||
−0.325902 | + | 0.945404i | \(0.605668\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2462 | 0.862887 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.56155 | −0.378816 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.68466 | −0.551341 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.12311 | −0.255855 | −0.127927 | − | 0.991784i | \(-0.540832\pi\) | ||||
−0.127927 | + | 0.991784i | \(0.540832\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.56155 | −0.207089 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.68466 | −0.295959 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.43845 | −0.753270 | −0.376635 | − | 0.926362i | \(-0.622919\pi\) | ||||
−0.376635 | + | 0.926362i | \(0.622919\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.43845 | −0.272687 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.561553 | −0.0442566 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.12311 | 0.714577 | 0.357288 | − | 0.933994i | \(-0.383701\pi\) | ||||
0.357288 | + | 0.933994i | \(0.383701\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00000 | 0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.24621 | −0.173817 | −0.0869085 | − | 0.996216i | \(-0.527699\pi\) | ||||
−0.0869085 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.12311 | 0.0858860 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.12311 | −0.541560 | −0.270780 | − | 0.962641i | \(-0.587282\pi\) | ||||
−0.270780 | + | 0.962641i | \(0.587282\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.561553 | −0.0424494 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.56155 | −0.192538 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.00000 | −0.597948 | −0.298974 | − | 0.954261i | \(-0.596644\pi\) | ||||
−0.298974 | + | 0.954261i | \(0.596644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.24621 | 0.166960 | 0.0834798 | − | 0.996509i | \(-0.473397\pi\) | ||||
0.0834798 | + | 0.996509i | \(0.473397\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.2462 | −1.05311 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.68466 | −0.270901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.12311 | 0.374639 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.561553 | −0.0408470 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2462 | 1.32025 | 0.660125 | − | 0.751156i | \(-0.270503\pi\) | ||||
0.660125 | + | 0.751156i | \(0.270503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.1231 | −1.08858 | −0.544292 | − | 0.838896i | \(-0.683202\pi\) | ||||
−0.544292 | + | 0.838896i | \(0.683202\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.00000 | 0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.246211 | −0.0175418 | −0.00877091 | − | 0.999962i | \(-0.502792\pi\) | ||||
−0.00877091 | + | 0.999962i | \(0.502792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2462 | 0.868111 | 0.434055 | − | 0.900886i | \(-0.357082\pi\) | ||||
0.434055 | + | 0.900886i | \(0.357082\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.6847 | −0.824172 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.56155 | −0.179786 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.68466 | −0.397034 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.24621 | −0.155374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0540 | −1.58710 | −0.793551 | − | 0.608504i | \(-0.791770\pi\) | ||||
−0.793551 | + | 0.608504i | \(0.791770\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.9309 | −0.954527 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.06913 | −0.140462 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.0000 | −0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.12311 | 0.344617 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.8769 | 0.996231 | 0.498115 | − | 0.867111i | \(-0.334026\pi\) | ||||
0.498115 | + | 0.867111i | \(0.334026\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.876894 | −0.0582015 | −0.0291008 | − | 0.999576i | \(-0.509264\pi\) | ||||
−0.0291008 | + | 0.999576i | \(0.509264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.2462 | 1.20574 | 0.602872 | − | 0.797838i | \(-0.294023\pi\) | ||||
0.602872 | + | 0.797838i | \(0.294023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.12311 | 0.0738949 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1231 | 0.990748 | 0.495374 | − | 0.868680i | \(-0.335031\pi\) | ||||
0.495374 | + | 0.868680i | \(0.335031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2462 | −0.668389 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.3693 | −0.868430 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.43845 | 0.610522 | 0.305261 | − | 0.952269i | \(-0.401256\pi\) | ||||
0.305261 | + | 0.952269i | \(0.401256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.75379 | −0.241803 | −0.120901 | − | 0.992665i | \(-0.538578\pi\) | ||||
−0.120901 | + | 0.992665i | \(0.538578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.68466 | 0.427067 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.24621 | −0.142923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.68466 | 0.360251 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.246211 | 0.0155407 | 0.00777036 | − | 0.999970i | \(-0.497527\pi\) | ||||
0.00777036 | + | 0.999970i | \(0.497527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.56155 | 0.160411 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.6155 | 1.72261 | 0.861305 | − | 0.508089i | \(-0.169648\pi\) | ||||
0.861305 | + | 0.508089i | \(0.169648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.06913 | −0.128570 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.56155 | 0.282353 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.56155 | −0.157952 | −0.0789761 | − | 0.996877i | \(-0.525165\pi\) | ||||
−0.0789761 | + | 0.996877i | \(0.525165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.43845 | 0.211222 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.24621 | −0.382262 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.19224 | 0.0726919 | 0.0363460 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363460 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.43845 | −0.330362 | −0.165181 | − | 0.986263i | \(-0.552821\pi\) | ||||
−0.165181 | + | 0.986263i | \(0.552821\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.12311 | 0.0679734 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | −0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.7386 | −1.72674 | −0.863369 | − | 0.504574i | \(-0.831650\pi\) | ||||
−0.863369 | + | 0.504574i | \(0.831650\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.68466 | 0.220595 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.12311 | 0.0669989 | 0.0334994 | − | 0.999439i | \(-0.489335\pi\) | ||||
0.0334994 | + | 0.999439i | \(0.489335\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.4384 | 0.798833 | 0.399416 | − | 0.916770i | \(-0.369213\pi\) | ||||
0.399416 | + | 0.916770i | \(0.369213\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.12311 | −0.0665270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.19224 | −0.188432 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4384 | −0.614026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.0000 | −0.820695 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.06913 | −0.237721 | −0.118861 | − | 0.992911i | \(-0.537924\pi\) | ||||
−0.118861 | + | 0.992911i | \(0.537924\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.56155 | 0.149139 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.43845 | −0.427328 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.2462 | 0.815736 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.1231 | −1.43385 | −0.716926 | − | 0.697150i | \(-0.754451\pi\) | ||||
−0.716926 | + | 0.697150i | \(0.754451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.1231 | 0.632771 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.9848 | −1.87040 | −0.935199 | − | 0.354121i | \(-0.884780\pi\) | ||||
−0.935199 | + | 0.354121i | \(0.884780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.8078 | −0.610891 | −0.305445 | − | 0.952210i | \(-0.598805\pi\) | ||||
−0.305445 | + | 0.952210i | \(0.598805\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.561553 | 0.0316399 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.6155 | −1.10172 | −0.550859 | − | 0.834598i | \(-0.685700\pi\) | ||||
−0.550859 | + | 0.834598i | \(0.685700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.12311 | −0.510796 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.8078 | −0.826489 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.87689 | −0.160075 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.1231 | −0.725709 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.75379 | −0.317217 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.6847 | 1.30183 | 0.650913 | − | 0.759152i | \(-0.274386\pi\) | ||||
0.650913 | + | 0.759152i | \(0.274386\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.68466 | 0.201918 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.6847 | 0.638401 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.24621 | 0.449200 | 0.224600 | − | 0.974451i | \(-0.427892\pi\) | ||||
0.224600 | + | 0.974451i | \(0.427892\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.8078 | −0.695622 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.36932 | −0.399071 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.4924 | 0.670628 | 0.335314 | − | 0.942106i | \(-0.391158\pi\) | ||||
0.335314 | + | 0.942106i | \(0.391158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.80776 | 0.150296 | 0.0751481 | − | 0.997172i | \(-0.476057\pi\) | ||||
0.0751481 | + | 0.997172i | \(0.476057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.6307 | −0.565814 | −0.282907 | − | 0.959147i | \(-0.591299\pi\) | ||||
−0.282907 | + | 0.959147i | \(0.591299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.9309 | 0.739374 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.43845 | 0.0761307 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.7386 | 0.777875 | 0.388938 | − | 0.921264i | \(-0.372842\pi\) | ||||
0.388938 | + | 0.921264i | \(0.372842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.6847 | −1.34073 | −0.670364 | − | 0.742032i | \(-0.733862\pi\) | ||||
−0.670364 | + | 0.742032i | \(0.733862\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.68466 | 0.295931 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.93087 | 0.100246 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.3693 | 1.21002 | 0.605009 | − | 0.796219i | \(-0.293170\pi\) | ||||
0.605009 | + | 0.796219i | \(0.293170\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.12311 | −0.469864 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.2462 | −1.14271 | −0.571356 | − | 0.820703i | \(-0.693582\pi\) | ||||
−0.571356 | + | 0.820703i | \(0.693582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.4924 | 0.844932 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.4384 | 0.686673 | 0.343336 | − | 0.939213i | \(-0.388443\pi\) | ||||
0.343336 | + | 0.939213i | \(0.388443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.12311 | −0.0572388 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.4924 | 1.54603 | 0.773014 | − | 0.634389i | \(-0.218748\pi\) | ||||
0.773014 | + | 0.634389i | \(0.218748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.56155 | −0.129543 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.2462 | 0.516853 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.3693 | 0.672683 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.6155 | 0.783721 | 0.391860 | − | 0.920025i | \(-0.371832\pi\) | ||||
0.391860 | + | 0.920025i | \(0.371832\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.630683 | −0.0315736 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.1231 | −0.855087 | −0.427544 | − | 0.903995i | \(-0.640621\pi\) | ||||
−0.427544 | + | 0.903995i | \(0.640621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.36932 | −0.367092 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.36932 | −0.365283 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.561553 | −0.0277670 | −0.0138835 | − | 0.999904i | \(-0.504419\pi\) | ||||
−0.0138835 | + | 0.999904i | \(0.504419\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.87689 | 0.141907 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.43845 | 0.0707814 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.68466 | −0.279049 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.68466 | −0.376319 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.4924 | −0.903414 | −0.451707 | − | 0.892166i | \(-0.649185\pi\) | ||||
−0.451707 | + | 0.892166i | \(0.649185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.12311 | −0.444633 | −0.222316 | − | 0.974975i | \(-0.571362\pi\) | ||||
−0.222316 | + | 0.974975i | \(0.571362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.2462 | 0.498188 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.56155 | −0.124254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.00000 | 0.387147 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.75379 | 0.0844770 | 0.0422385 | − | 0.999108i | \(-0.486551\pi\) | ||||
0.0422385 | + | 0.999108i | \(0.486551\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8078 | 0.711616 | 0.355808 | − | 0.934559i | \(-0.384206\pi\) | ||||
0.355808 | + | 0.934559i | \(0.384206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.56155 | −0.218710 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.12311 | 0.0537254 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.9848 | −1.57428 | −0.787140 | − | 0.616774i | \(-0.788439\pi\) | ||||
−0.787140 | + | 0.616774i | \(0.788439\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.68466 | −0.318317 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.75379 | 0.0833250 | 0.0416625 | − | 0.999132i | \(-0.486735\pi\) | ||||
0.0416625 | + | 0.999132i | \(0.486735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.24621 | 0.296099 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.12311 | −0.147718 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.3002 | 1.47715 | 0.738574 | − | 0.674173i | \(-0.235500\pi\) | ||||
0.738574 | + | 0.674173i | \(0.235500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.3693 | −0.535360 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.12311 | −0.0526520 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.8078 | −1.44113 | −0.720563 | − | 0.693389i | \(-0.756117\pi\) | ||||
−0.720563 | + | 0.693389i | \(0.756117\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.56155 | −0.119563 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2462 | 0.570363 | 0.285181 | − | 0.958474i | \(-0.407946\pi\) | ||||
0.285181 | + | 0.958474i | \(0.407946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.3693 | 1.45786 | 0.728928 | − | 0.684590i | \(-0.240019\pi\) | ||||
0.728928 | + | 0.684590i | \(0.240019\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.68466 | −0.170872 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5616 | −0.766377 | −0.383189 | − | 0.923670i | \(-0.625174\pi\) | ||||
−0.383189 | + | 0.923670i | \(0.625174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.56155 | 0.302984 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.43845 | −0.434901 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.12311 | 0.0515316 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.43845 | −0.157436 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.4924 | −1.30185 | −0.650926 | − | 0.759141i | \(-0.725619\pi\) | ||||
−0.650926 | + | 0.759141i | \(0.725619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.36932 | −0.336012 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.561553 | −0.0255515 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.0000 | 0.635707 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7386 | 1.03039 | 0.515193 | − | 0.857074i | \(-0.327720\pi\) | ||||
0.515193 | + | 0.857074i | \(0.327720\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.12311 | 0.412561 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.0540 | 0.859894 | 0.429947 | − | 0.902854i | \(-0.358532\pi\) | ||||
0.429947 | + | 0.902854i | \(0.358532\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.6847 | −0.526251 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | 0.0898933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.82292 | 0.350906 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.4384 | −0.959717 | −0.479858 | − | 0.877346i | \(-0.659312\pi\) | ||||
−0.479858 | + | 0.877346i | \(0.659312\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.24621 | −0.100353 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.1771 | 1.61306 | 0.806528 | − | 0.591196i | \(-0.201344\pi\) | ||||
0.806528 | + | 0.591196i | \(0.201344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.43845 | 0.331007 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.7538 | 0.875571 | 0.437786 | − | 0.899079i | \(-0.355763\pi\) | ||||
0.437786 | + | 0.899079i | \(0.355763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.61553 | 0.248416 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.12311 | 0.0495863 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.1231 | −0.490143 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4924 | −0.901256 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.12311 | −0.312670 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.3693 | 0.673342 | 0.336671 | − | 0.941622i | \(-0.390699\pi\) | ||||
0.336671 | + | 0.941622i | \(0.390699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.75379 | 0.251596 | 0.125798 | − | 0.992056i | \(-0.459851\pi\) | ||||
0.125798 | + | 0.992056i | \(0.459851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.561553 | −0.0245082 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.43845 | −0.411145 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.56155 | −0.111162 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.3693 | −0.492460 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.8078 | 0.640195 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.3693 | 0.575857 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.24621 | −0.354532 | −0.177266 | − | 0.984163i | \(-0.556725\pi\) | ||||
−0.177266 | + | 0.984163i | \(0.556725\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.24621 | 0.0963942 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.1231 | 0.562132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.7386 | 0.459151 | 0.229575 | − | 0.973291i | \(-0.426266\pi\) | ||||
0.229575 | + | 0.973291i | \(0.426266\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.2462 | −0.608013 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.12311 | 0.218252 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.50758 | 0.319255 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.68466 | −0.156405 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.3153 | 0.945531 | 0.472766 | − | 0.881188i | \(-0.343256\pi\) | ||||
0.472766 | + | 0.881188i | \(0.343256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.12311 | 0.216298 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.5616 | 0.697986 | 0.348993 | − | 0.937125i | \(-0.386524\pi\) | ||||
0.348993 | + | 0.937125i | \(0.386524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.8078 | 0.538827 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.561553 | −0.0235830 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.12311 | −0.0470830 | −0.0235415 | − | 0.999723i | \(-0.507494\pi\) | ||||
−0.0235415 | + | 0.999723i | \(0.507494\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.4924 | −0.522792 | −0.261396 | − | 0.965232i | \(-0.584183\pi\) | ||||
−0.261396 | + | 0.965232i | \(0.584183\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.2462 | 0.762246 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.8617 | 0.577072 | 0.288536 | − | 0.957469i | \(-0.406832\pi\) | ||||
0.288536 | + | 0.957469i | \(0.406832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.1231 | −0.628495 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.19224 | −0.132436 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.87689 | 0.284812 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.8769 | −1.43952 | −0.719762 | − | 0.694221i | \(-0.755749\pi\) | ||||
−0.719762 | + | 0.694221i | \(0.755749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.13826 | 0.170514 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.246211 | −0.0101278 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.63068 | 0.108029 | 0.0540146 | − | 0.998540i | \(-0.482798\pi\) | ||||
0.0540146 | + | 0.998540i | \(0.482798\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.43845 | −0.0589706 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.2462 | 0.501204 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.49242 | 0.183555 | 0.0917777 | − | 0.995780i | \(-0.470745\pi\) | ||||
0.0917777 | + | 0.995780i | \(0.470745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.5464 | 1.04206 | 0.521030 | − | 0.853539i | \(-0.325548\pi\) | ||||
0.521030 | + | 0.853539i | \(0.325548\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.6847 | −0.475836 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | 0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.7538 | 0.720604 | 0.360302 | − | 0.932836i | \(-0.382674\pi\) | ||||
0.360302 | + | 0.932836i | \(0.382674\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.56155 | −0.103799 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.4924 | −0.829035 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.8617 | −0.640650 | −0.320325 | − | 0.947308i | \(-0.603792\pi\) | ||||
−0.320325 | + | 0.947308i | \(0.603792\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.68466 | −0.229228 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.5616 | 0.747260 | 0.373630 | − | 0.927578i | \(-0.378113\pi\) | ||||
0.373630 | + | 0.927578i | \(0.378113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.75379 | −0.392038 | −0.196019 | − | 0.980600i | \(-0.562801\pi\) | ||||
−0.196019 | + | 0.980600i | \(0.562801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.50758 | 0.140528 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.24621 | −0.0897050 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.43845 | −0.376336 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.38447 | −0.333781 | −0.166890 | − | 0.985975i | \(-0.553373\pi\) | ||||
−0.166890 | + | 0.985975i | \(0.553373\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.0540 | −0.916313 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.4924 | −0.654482 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.3693 | 0.529712 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.9309 | −0.551097 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.3693 | 1.39700 | 0.698502 | − | 0.715608i | \(-0.253850\pi\) | ||||
0.698502 | + | 0.715608i | \(0.253850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.43845 | −0.0567268 | −0.0283634 | − | 0.999598i | \(-0.509030\pi\) | ||||
−0.0283634 | + | 0.999598i | \(0.509030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.1231 | −1.14495 | −0.572474 | − | 0.819923i | \(-0.694016\pi\) | ||||
−0.572474 | + | 0.819923i | \(0.694016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.12311 | 0.201099 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.06913 | −0.0810956 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.75379 | −0.146897 | −0.0734486 | − | 0.997299i | \(-0.523400\pi\) | ||||
−0.0734486 | + | 0.997299i | \(0.523400\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.2462 | −0.400353 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.73863 | 0.184591 | 0.0922955 | − | 0.995732i | \(-0.470580\pi\) | ||||
0.0922955 | + | 0.995732i | \(0.470580\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.1231 | −0.977176 | −0.488588 | − | 0.872515i | \(-0.662488\pi\) | ||||
−0.488588 | + | 0.872515i | \(0.662488\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.12311 | 0.198965 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.630683 | 0.0244568 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.56155 | 0.176624 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.8769 | 0.575174 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.4924 | 1.09994 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.8769 | 0.804745 | 0.402373 | − | 0.915476i | \(-0.368186\pi\) | ||||
0.402373 | + | 0.915476i | \(0.368186\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.4233 | 0.784931 | 0.392465 | − | 0.919767i | \(-0.371622\pi\) | ||||
0.392465 | + | 0.919767i | \(0.371622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.86174 | 0.301706 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.876894 | −0.0336027 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.73863 | −0.257847 | −0.128923 | − | 0.991655i | \(-0.541152\pi\) | ||||
−0.128923 | + | 0.991655i | \(0.541152\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.87689 | −0.109920 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.2462 | 0.696136 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.87689 | 0.261989 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.50758 | 0.285602 | 0.142801 | − | 0.989751i | \(-0.454389\pi\) | ||||
0.142801 | + | 0.989751i | \(0.454389\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.12311 | 0.0426633 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.68466 | 0.291496 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.5616 | −0.551558 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.1231 | 0.572008 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.876894 | 0.0331198 | 0.0165599 | − | 0.999863i | \(-0.494729\pi\) | ||||
0.0165599 | + | 0.999863i | \(0.494729\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.13826 | 0.156077 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.2462 | −0.385895 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.17708 | 0.157095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.9848 | −0.788102 | −0.394051 | − | 0.919088i | \(-0.628927\pi\) | ||||
−0.394051 | + | 0.919088i | \(0.628927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.3693 | −0.501389 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.68466 | 0.137992 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.43845 | 0.352485 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.4384 | 0.650344 | 0.325172 | − | 0.945655i | \(-0.394578\pi\) | ||||
0.325172 | + | 0.945655i | \(0.394578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.24621 | −0.232621 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.75379 | −0.139605 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.56155 | 0.169412 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.0691 | 0.892675 | 0.446337 | − | 0.894865i | \(-0.352728\pi\) | ||||
0.446337 | + | 0.894865i | \(0.352728\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.43845 | 0.200874 | 0.100437 | − | 0.994943i | \(-0.467976\pi\) | ||||
0.100437 | + | 0.994943i | \(0.467976\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.68466 | 0.246567 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.3693 | 0.860820 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.0540 | −0.848054 | −0.424027 | − | 0.905650i | \(-0.639384\pi\) | ||||
−0.424027 | + | 0.905650i | \(0.639384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.24621 | −0.0825166 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.7386 | −0.393962 | −0.196981 | − | 0.980407i | \(-0.563114\pi\) | ||||
−0.196981 | + | 0.980407i | \(0.563114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.12311 | 0.114422 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.68466 | 0.207991 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.31534 | 0.303836 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.4924 | −0.674798 | −0.337399 | − | 0.941362i | \(-0.609547\pi\) | ||||
−0.337399 | + | 0.941362i | \(0.609547\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.246211 | 0.00897244 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.1771 | −1.75103 | −0.875513 | − | 0.483195i | \(-0.839476\pi\) | ||||
−0.875513 | + | 0.483195i | \(0.839476\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.00000 | −0.0725954 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3002 | −1.13463 | −0.567315 | − | 0.823501i | \(-0.692018\pi\) | ||||
−0.567315 | + | 0.823501i | \(0.692018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.36932 | 0.266787 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.56155 | 0.0926131 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.12311 | 0.184985 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.6155 | −0.995841 | −0.497921 | − | 0.867223i | \(-0.665903\pi\) | ||||
−0.497921 | + | 0.867223i | \(0.665903\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.6155 | 0.994549 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.4924 | 1.81609 | 0.908043 | − | 0.418877i | \(-0.137576\pi\) | ||||
0.908043 | + | 0.418877i | \(0.137576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.68466 | 0.132357 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.06913 | −0.0742296 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.38447 | 0.228747 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.8617 | 0.996971 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.56155 | 0.163017 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.43845 | 0.336873 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.94602 | −0.176307 | −0.0881534 | − | 0.996107i | \(-0.528097\pi\) | ||||
−0.0881534 | + | 0.996107i | \(0.528097\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.56155 | −0.0911937 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.19224 | 0.255726 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.4924 | 1.01180 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.43845 | 0.121949 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.5464 | −1.61334 | −0.806668 | − | 0.591005i | \(-0.798731\pi\) | ||||
−0.806668 | + | 0.591005i | \(0.798731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.2462 | −0.928524 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.24621 | −0.220699 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0000 | 0.705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.561553 | 0.0197921 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.19224 | 0.0419687 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.3002 | 1.52235 | 0.761177 | − | 0.648544i | \(-0.224622\pi\) | ||||
0.761177 | + | 0.648544i | \(0.224622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.946025 | 0.0332194 | 0.0166097 | − | 0.999862i | \(-0.494713\pi\) | ||||
0.0166097 | + | 0.999862i | \(0.494713\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.43845 | −0.190735 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.12311 | −0.319568 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.12311 | 0.0392445 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.49242 | 0.226587 | 0.113294 | − | 0.993562i | \(-0.463860\pi\) | ||||
0.113294 | + | 0.993562i | \(0.463860\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.73863 | −0.234894 | −0.117447 | − | 0.993079i | \(-0.537471\pi\) | ||||
−0.117447 | + | 0.993079i | \(0.537471\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.00000 | −0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.9309 | −0.832158 | −0.416079 | − | 0.909328i | \(-0.636596\pi\) | ||||
−0.416079 | + | 0.909328i | \(0.636596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.9309 | 1.66471 | 0.832354 | − | 0.554244i | \(-0.186993\pi\) | ||||
0.832354 | + | 0.554244i | \(0.186993\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.7386 | −0.996932 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.1231 | 0.593280 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.24621 | 0.0777333 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.68466 | 0.127360 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.1231 | −0.867346 | −0.433673 | − | 0.901070i | \(-0.642783\pi\) | ||||
−0.433673 | + | 0.901070i | \(0.642783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.19224 | −0.282491 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.12311 | 0.0386818 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.93087 | 0.135066 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.4384 | 0.461206 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.68466 | 0.126308 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.9848 | −0.923943 | −0.461972 | − | 0.886895i | \(-0.652858\pi\) | ||||
−0.461972 | + | 0.886895i | \(0.652858\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.12311 | −0.0384094 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −52.7386 | −1.80152 | −0.900759 | − | 0.434320i | \(-0.856989\pi\) | ||||
−0.900759 | + | 0.434320i | \(0.856989\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.8078 | −0.982908 | −0.491454 | − | 0.870903i | \(-0.663534\pi\) | ||||
−0.491454 | + | 0.870903i | \(0.663534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.19224 | −0.108791 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.3693 | 1.06782 | 0.533912 | − | 0.845540i | \(-0.320721\pi\) | ||||
0.533912 | + | 0.845540i | \(0.320721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.12311 | 0.242193 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.4384 | −0.354508 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.7386 | 0.907046 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.3693 | 0.791839 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.0000 | −0.473828 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.561553 | 0.0189839 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7386 | 0.565224 | 0.282612 | − | 0.959234i | \(-0.408799\pi\) | ||||
0.282612 | + | 0.959234i | \(0.408799\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.06913 | −0.137248 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.7386 | −0.361794 | −0.180897 | − | 0.983502i | \(-0.557900\pi\) | ||||
−0.180897 | + | 0.983502i | \(0.557900\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.2462 | 1.01787 | 0.508933 | − | 0.860806i | \(-0.330040\pi\) | ||||
0.508933 | + | 0.860806i | \(0.330040\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.56155 | 0.0861057 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.6307 | 0.558404 | 0.279202 | − | 0.960232i | \(-0.409930\pi\) | ||||
0.279202 | + | 0.960232i | \(0.409930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.26137 | −0.310616 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.5076 | 0.385086 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.8078 | 0.560570 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.80776 | 0.293429 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.24621 | −0.0746666 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.4233 | −1.27582 | −0.637912 | − | 0.770109i | \(-0.720202\pi\) | ||||
−0.637912 | + | 0.770109i | \(0.720202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.43845 | −0.246718 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9848 | 0.960311 | 0.480155 | − | 0.877183i | \(-0.340580\pi\) | ||||
0.480155 | + | 0.877183i | \(0.340580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3693 | −0.376269 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.2462 | 0.470965 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.75379 | −0.190007 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.36932 | 0.0451696 | 0.0225848 | − | 0.999745i | \(-0.492810\pi\) | ||||
0.0225848 | + | 0.999745i | \(0.492810\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.1231 | −0.827834 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.8617 | 0.917080 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.68466 | 0.121151 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.1231 | 0.365331 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.1771 | −1.77749 | −0.888746 | − | 0.458400i | \(-0.848423\pi\) | ||||
−0.888746 | + | 0.458400i | \(0.848423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.50758 | −0.246051 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.9848 | −1.07988 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.12311 | −0.167543 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0000 | −0.457360 | −0.228680 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228680 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.8078 | −0.352698 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.1231 | −1.40577 | −0.702887 | − | 0.711302i | \(-0.748106\pi\) | ||||
−0.702887 | + | 0.711302i | \(0.748106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.68466 | 0.185118 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.561553 | 0.0182673 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.2311 | −1.40482 | −0.702410 | − | 0.711772i | \(-0.747893\pi\) | ||||
−0.702410 | + | 0.711772i | \(0.747893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.0000 | 0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.6155 | −0.636077 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.8769 | 0.481910 | 0.240955 | − | 0.970536i | \(-0.422539\pi\) | ||||
0.240955 | + | 0.970536i | \(0.422539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.2462 | −0.590434 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.12311 | −0.294908 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.61553 | −0.0521681 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.4233 | −0.562042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.8078 | −0.477174 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.1231 | 0.486830 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.9848 | −0.546196 | −0.273098 | − | 0.961986i | \(-0.588048\pi\) | ||||
−0.273098 | + | 0.961986i | \(0.588048\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.87689 | −0.0924192 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.3542 | −1.23084 | −0.615422 | − | 0.788198i | \(-0.711014\pi\) | ||||
−0.615422 | + | 0.788198i | \(0.711014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.31534 | 0.138343 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.00000 | −0.0640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.5616 | 0.977751 | 0.488875 | − | 0.872354i | \(-0.337407\pi\) | ||||
0.488875 | + | 0.872354i | \(0.337407\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4924 | 0.399260 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.1231 | −0.418989 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.3002 | 1.06211 | 0.531056 | − | 0.847337i | \(-0.321796\pi\) | ||||
0.531056 | + | 0.847337i | \(0.321796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.246211 | 0.00784494 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.75379 | −0.183145 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.4233 | 1.34762 | 0.673810 | − | 0.738905i | \(-0.264657\pi\) | ||||
0.673810 | + | 0.738905i | \(0.264657\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.6847 | 0.751610 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.2462 | −0.388231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.1231 | −0.605635 | −0.302817 | − | 0.953049i | \(-0.597927\pi\) | ||||
−0.302817 | + | 0.953049i | \(0.597927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.68466 | 0.116577 |
(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 | 5520.2.a.bn.1.1 | 2 | ||
4.3 | odd | 2 | 2760.2.a.m.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 8280.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.m.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
5520.2.a.bn.1.1 | 2 | 1.1 | even | 1 | trivial | ||
8280.2.a.bd.1.2 | 2 | 12.11 | even | 2 |