Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, 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("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 3x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.347296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | 0.347296 | 0.200512 | 0.100256 | − | 0.994962i | \(-0.468034\pi\) | ||||
0.100256 | + | 0.994962i | \(0.468034\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.41147 | −1.28942 | −0.644708 | − | 0.764429i | \(-0.723021\pi\) | ||||
−0.644708 | + | 0.764429i | \(0.723021\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.87939 | −0.959795 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41147 | 0.727087 | 0.363543 | − | 0.931577i | \(-0.381567\pi\) | ||||
0.363543 | + | 0.931577i | \(0.381567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.29086 | 1.74477 | 0.872385 | − | 0.488819i | \(-0.162572\pi\) | ||||
0.872385 | + | 0.488819i | \(0.162572\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.34730 | −0.569303 | −0.284651 | − | 0.958631i | \(-0.591878\pi\) | ||||
−0.284651 | + | 0.958631i | \(0.591878\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.18479 | −0.258543 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.49020 | 0.519243 | 0.259621 | − | 0.965711i | \(-0.416402\pi\) | ||||
0.259621 | + | 0.965711i | \(0.416402\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.04189 | −0.392962 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.17024 | −1.51718 | −0.758588 | − | 0.651570i | \(-0.774111\pi\) | ||||
−0.758588 | + | 0.651570i | \(0.774111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.77332 | −0.498103 | −0.249051 | − | 0.968490i | \(-0.580119\pi\) | ||||
−0.249051 | + | 0.968490i | \(0.580119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.837496 | 0.145789 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.977711 | −0.160735 | −0.0803674 | − | 0.996765i | \(-0.525609\pi\) | ||||
−0.0803674 | + | 0.996765i | \(0.525609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.18479 | 0.349847 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.49020 | −0.545078 | −0.272539 | − | 0.962145i | \(-0.587863\pi\) | ||||
−0.272539 | + | 0.962145i | \(0.587863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.75877 | −0.420709 | −0.210354 | − | 0.977625i | \(-0.567462\pi\) | ||||
−0.210354 | + | 0.977625i | \(0.567462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.29086 | 0.917616 | 0.458808 | − | 0.888535i | \(-0.348277\pi\) | ||||
0.458808 | + | 0.888535i | \(0.348277\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.63816 | 0.662594 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.815207 | −0.114152 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.38919 | 0.328180 | 0.164090 | − | 0.986445i | \(-0.447531\pi\) | ||||
0.164090 | + | 0.986445i | \(0.447531\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.347296 | 0.0460005 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.67499 | 0.478443 | 0.239222 | − | 0.970965i | \(-0.423108\pi\) | ||||
0.239222 | + | 0.970965i | \(0.423108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.7442 | −1.63173 | −0.815865 | − | 0.578242i | \(-0.803739\pi\) | ||||
−0.815865 | + | 0.578242i | \(0.803739\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.82295 | 1.23758 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.41147 | 0.294608 | 0.147304 | − | 0.989091i | \(-0.452940\pi\) | ||||
0.147304 | + | 0.989091i | \(0.452940\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.864837 | 0.104114 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.51754 | 0.536133 | 0.268067 | − | 0.963400i | \(-0.413615\pi\) | ||||
0.268067 | + | 0.963400i | \(0.413615\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.81521 | 0.212454 | 0.106227 | − | 0.994342i | \(-0.466123\pi\) | ||||
0.106227 | + | 0.994342i | \(0.466123\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.22668 | −0.937517 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.04189 | −0.567257 | −0.283628 | − | 0.958934i | \(-0.591538\pi\) | ||||
−0.283628 | + | 0.958934i | \(0.591538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.92902 | 0.881002 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.07192 | −0.886008 | −0.443004 | − | 0.896520i | \(-0.646087\pi\) | ||||
−0.443004 | + | 0.896520i | \(0.646087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.83750 | −0.304212 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.94356 | −0.312017 | −0.156009 | − | 0.987756i | \(-0.549863\pi\) | ||||
−0.156009 | + | 0.987756i | \(0.549863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.4611 | −2.24973 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.963163 | −0.0998754 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.09833 | −0.314587 | −0.157294 | − | 0.987552i | \(-0.550277\pi\) | ||||
−0.157294 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.94356 | −0.697854 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.02229 | −0.599240 | −0.299620 | − | 0.954059i | \(-0.596860\pi\) | ||||
−0.299620 | + | 0.954059i | \(0.596860\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.25402 | −0.714760 | −0.357380 | − | 0.933959i | \(-0.616330\pi\) | ||||
−0.357380 | + | 0.933959i | \(0.616330\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.94356 | 0.864607 | 0.432303 | − | 0.901728i | \(-0.357701\pi\) | ||||
0.432303 | + | 0.901728i | \(0.357701\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.81521 | −0.940126 | −0.470063 | − | 0.882633i | \(-0.655769\pi\) | ||||
−0.470063 | + | 0.882633i | \(0.655769\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.339556 | −0.0322292 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.57667 | −0.712753 | −0.356376 | − | 0.934342i | \(-0.615988\pi\) | ||||
−0.356376 | + | 0.934342i | \(0.615988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.1138 | −1.67462 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.00774 | 0.734068 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.18479 | −0.471345 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.21213 | −0.109294 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.33275 | 0.739412 | 0.369706 | − | 0.929149i | \(-0.379458\pi\) | ||||
0.369706 | + | 0.929149i | \(0.379458\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.958111 | −0.0843570 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0915 | −1.14381 | −0.571906 | − | 0.820319i | \(-0.693796\pi\) | ||||
−0.571906 | + | 0.820319i | \(0.693796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.41147 | −0.295812 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.3327 | −1.30997 | −0.654983 | − | 0.755644i | \(-0.727324\pi\) | ||||
−0.654983 | + | 0.755644i | \(0.727324\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.77837 | −0.659753 | −0.329876 | − | 0.944024i | \(-0.607007\pi\) | ||||
−0.329876 | + | 0.944024i | \(0.607007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.18479 | 0.183993 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.1702 | 1.26860 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.61081 | 0.132858 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.1361 | −1.40384 | −0.701922 | − | 0.712254i | \(-0.747674\pi\) | ||||
−0.701922 | + | 0.712254i | \(0.747674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.4638 | −1.74670 | −0.873349 | − | 0.487094i | \(-0.838057\pi\) | ||||
−0.873349 | + | 0.487094i | \(0.838057\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.75877 | 0.546414 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.5253 | −1.55829 | −0.779144 | − | 0.626846i | \(-0.784346\pi\) | ||||
−0.779144 | + | 0.626846i | \(0.784346\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.829755 | 0.0658039 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.49525 | −0.669520 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.59627 | −0.281681 | −0.140841 | − | 0.990032i | \(-0.544981\pi\) | ||||
−0.140841 | + | 0.990032i | \(0.544981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.1361 | −1.01650 | −0.508251 | − | 0.861209i | \(-0.669708\pi\) | ||||
−0.508251 | + | 0.861209i | \(0.669708\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.5749 | 2.04422 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.87939 | −0.220192 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.4757 | 1.25262 | 0.626310 | − | 0.779574i | \(-0.284564\pi\) | ||||
0.626310 | + | 0.779574i | \(0.284564\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.27631 | 0.0959334 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.1438 | −1.72985 | −0.864926 | − | 0.501900i | \(-0.832635\pi\) | ||||
−0.864926 | + | 0.501900i | \(0.832635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.1634 | 1.79605 | 0.898027 | − | 0.439940i | \(-0.145000\pi\) | ||||
0.898027 | + | 0.439940i | \(0.145000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.42602 | −0.327181 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.66044 | −0.413933 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.96585 | 0.506691 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.62361 | 0.189838 | 0.0949188 | − | 0.995485i | \(-0.469741\pi\) | ||||
0.0949188 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.5544 | −0.903684 | −0.451842 | − | 0.892098i | \(-0.649233\pi\) | ||||
−0.451842 | + | 0.892098i | \(0.649233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.9094 | −1.20475 | −0.602373 | − | 0.798215i | \(-0.705778\pi\) | ||||
−0.602373 | + | 0.798215i | \(0.705778\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.1607 | 1.35827 | 0.679135 | − | 0.734014i | \(-0.262355\pi\) | ||||
0.679135 | + | 0.734014i | \(0.262355\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.837496 | 0.0590724 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27.8726 | 1.95627 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.17024 | −0.498366 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.41147 | 0.166805 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4534 | −0.926168 | −0.463084 | − | 0.886314i | \(-0.653257\pi\) | ||||
−0.463084 | + | 0.886314i | \(0.653257\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.56893 | 0.107501 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.46110 | 0.642262 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.630415 | 0.0425995 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.7665 | −0.993303 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.9864 | 1.94107 | 0.970536 | − | 0.240956i | \(-0.0774610\pi\) | ||||
0.970536 | + | 0.240956i | \(0.0774610\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.6091 | 0.704148 | 0.352074 | − | 0.935972i | \(-0.385477\pi\) | ||||
0.352074 | + | 0.935972i | \(0.385477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.8375 | −0.848326 | −0.424163 | − | 0.905586i | \(-0.639432\pi\) | ||||
−0.424163 | + | 0.905586i | \(0.639432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.85710 | −0.187983 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.4953 | −0.687567 | −0.343783 | − | 0.939049i | \(-0.611709\pi\) | ||||
−0.343783 | + | 0.939049i | \(0.611709\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.75103 | −0.113742 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.07873 | 0.263831 | 0.131915 | − | 0.991261i | \(-0.457887\pi\) | ||||
0.131915 | + | 0.991261i | \(0.457887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.6382 | −0.942927 | −0.471463 | − | 0.881886i | \(-0.656274\pi\) | ||||
−0.471463 | + | 0.881886i | \(0.656274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.87939 | 0.569613 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.29086 | 0.400278 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.80335 | −0.177655 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0692 | −0.761803 | −0.380902 | − | 0.924616i | \(-0.624386\pi\) | ||||
−0.380902 | + | 0.924616i | \(0.624386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00505 | 0.377534 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.62361 | 0.101278 | 0.0506389 | − | 0.998717i | \(-0.483874\pi\) | ||||
0.0506389 | + | 0.998717i | \(0.483874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.33544 | 0.207254 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.5253 | 1.45618 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.2618 | 1.74269 | 0.871347 | − | 0.490666i | \(-0.163247\pi\) | ||||
0.871347 | + | 0.490666i | \(0.163247\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.02229 | −0.0625631 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.1138 | −0.616650 | −0.308325 | − | 0.951281i | \(-0.599768\pi\) | ||||
−0.308325 | + | 0.951281i | \(0.599768\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.9486 | −1.39403 | −0.697015 | − | 0.717057i | \(-0.745489\pi\) | ||||
−0.697015 | + | 0.717057i | \(0.745489\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.45336 | −0.451098 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.1634 | 0.850998 | 0.425499 | − | 0.904959i | \(-0.360099\pi\) | ||||
0.425499 | + | 0.904959i | \(0.360099\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.98545 | 0.478077 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.822948 | 0.0490930 | 0.0245465 | − | 0.999699i | \(-0.492186\pi\) | ||||
0.0245465 | + | 0.999699i | \(0.492186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.83481 | 0.287399 | 0.143700 | − | 0.989621i | \(-0.454100\pi\) | ||||
0.143700 | + | 0.989621i | \(0.454100\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.9067 | 0.702832 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4902 | −0.675894 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.07604 | −0.0630784 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5699 | −1.02644 | −0.513221 | − | 0.858256i | \(-0.671548\pi\) | ||||
−0.513221 | + | 0.858256i | \(0.671548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.92396 | −0.285717 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.6655 | 0.905959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.41147 | 0.542468 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.09152 | −0.120155 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.9632 | 1.02521 | 0.512606 | − | 0.858624i | \(-0.328680\pi\) | ||||
0.512606 | + | 0.858624i | \(0.328680\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.51930 | −0.143318 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.4543 | 1.55679 | 0.778395 | − | 0.627775i | \(-0.216034\pi\) | ||||
0.778395 | + | 0.627775i | \(0.216034\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.90941 | 0.164450 | 0.0822249 | − | 0.996614i | \(-0.473797\pi\) | ||||
0.0822249 | + | 0.996614i | \(0.473797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.1070 | 1.29782 | 0.648909 | − | 0.760866i | \(-0.275225\pi\) | ||||
0.648909 | + | 0.760866i | \(0.275225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.7023 | −1.10312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.10607 | 0.173364 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.34730 | −0.130607 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.40879 | −0.188506 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.4611 | −1.18319 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.89218 | 0.158969 | 0.0794843 | − | 0.996836i | \(-0.474673\pi\) | ||||
0.0794843 | + | 0.996836i | \(0.474673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.81521 | 0.154272 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.3901 | 1.54651 | 0.773254 | − | 0.634096i | \(-0.218628\pi\) | ||||
0.773254 | + | 0.634096i | \(0.218628\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.63135 | −0.142915 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.68779 | −0.362164 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.05737 | 0.435057 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.4175 | −1.25712 | −0.628558 | − | 0.777763i | \(-0.716354\pi\) | ||||
−0.628558 | + | 0.777763i | \(0.716354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.48751 | −0.293740 | −0.146870 | − | 0.989156i | \(-0.546920\pi\) | ||||
−0.146870 | + | 0.989156i | \(0.546920\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.8452 | −0.685628 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.8530 | 1.21634 | 0.608171 | − | 0.793806i | \(-0.291904\pi\) | ||||
0.608171 | + | 0.793806i | \(0.291904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.78106 | 0.147189 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.6604 | 1.09042 | 0.545208 | − | 0.838301i | \(-0.316451\pi\) | ||||
0.545208 | + | 0.838301i | \(0.316451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.80066 | −0.0945101 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.29767 | 0.328736 | 0.164368 | − | 0.986399i | \(-0.447442\pi\) | ||||
0.164368 | + | 0.986399i | \(0.447442\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0496 | 0.523163 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.15064 | −0.423160 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.0401 | 1.40009 | 0.700043 | − | 0.714101i | \(-0.253164\pi\) | ||||
0.700043 | + | 0.714101i | \(0.253164\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −51.3979 | −2.64712 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8375 | 0.608051 | 0.304026 | − | 0.952664i | \(-0.401669\pi\) | ||||
0.304026 | + | 0.952664i | \(0.401669\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.89393 | 0.148261 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.4252 | −1.50356 | −0.751779 | − | 0.659415i | \(-0.770804\pi\) | ||||
−0.751779 | + | 0.659415i | \(0.770804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.94356 | 0.403794 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.75877 | −0.342683 | −0.171342 | − | 0.985212i | \(-0.554810\pi\) | ||||
−0.171342 | + | 0.985212i | \(0.554810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.84524 | −0.295606 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.54664 | −0.229347 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.3158 | −1.01962 | −0.509811 | − | 0.860286i | \(-0.670285\pi\) | ||||
−0.509811 | + | 0.860286i | \(0.670285\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.18479 | −0.0593138 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.57903 | −0.278603 | −0.139302 | − | 0.990250i | \(-0.544486\pi\) | ||||
−0.139302 | + | 0.990250i | \(0.544486\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.4466 | −0.869075 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.35773 | −0.116868 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.3387 | −1.84628 | −0.923141 | − | 0.384462i | \(-0.874387\pi\) | ||||
−0.923141 | + | 0.384462i | \(0.874387\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.32501 | −0.262663 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.5371 | −0.616912 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.70140 | −0.132288 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.80840 | 0.234906 | 0.117453 | − | 0.993078i | \(-0.462527\pi\) | ||||
0.117453 | + | 0.993078i | \(0.462527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.0009 | 1.31594 | 0.657972 | − | 0.753042i | \(-0.271414\pi\) | ||||
0.657972 | + | 0.753042i | \(0.271414\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.1138 | −0.880723 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.4766 | 2.10398 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.26857 | 0.254369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.2249 | 1.74489 | 0.872447 | − | 0.488709i | \(-0.162532\pi\) | ||||
0.872447 | + | 0.488709i | \(0.162532\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.6382 | −1.52043 | −0.760216 | − | 0.649670i | \(-0.774907\pi\) | ||||
−0.760216 | + | 0.649670i | \(0.774907\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.49020 | 0.119122 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.88444 | 0.471758 | 0.235879 | − | 0.971782i | \(-0.424203\pi\) | ||||
0.235879 | + | 0.971782i | \(0.424203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.3550 | −0.635954 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.3191 | 1.39299 | 0.696497 | − | 0.717560i | \(-0.254741\pi\) | ||||
0.696497 | + | 0.717560i | \(0.254741\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.95130 | −0.281487 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.86247 | 0.135088 | 0.0675442 | − | 0.997716i | \(-0.478484\pi\) | ||||
0.0675442 | + | 0.997716i | \(0.478484\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.41653 | −0.396319 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.45430 | −0.350233 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.6664 | −1.20062 | −0.600312 | − | 0.799766i | \(-0.704957\pi\) | ||||
−0.600312 | + | 0.799766i | \(0.704957\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.79292 | 0.223714 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.77332 | 0.268890 | 0.134445 | − | 0.990921i | \(-0.457075\pi\) | ||||
0.134445 | + | 0.990921i | \(0.457075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.1097 | −1.44579 | −0.722895 | − | 0.690958i | \(-0.757189\pi\) | ||||
−0.722895 | + | 0.690958i | \(0.757189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.8408 | −1.75106 | −0.875532 | − | 0.483161i | \(-0.839489\pi\) | ||||
−0.875532 | + | 0.483161i | \(0.839489\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.22668 | −0.379873 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.78106 | −0.312455 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.65270 | −0.305892 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.87939 | −0.314985 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.10338 | 0.233179 | 0.116590 | − | 0.993180i | \(-0.462804\pi\) | ||||
0.116590 | + | 0.993180i | \(0.462804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.15064 | −0.280445 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.95037 | −0.134246 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.8503 | 0.854188 | 0.427094 | − | 0.904207i | \(-0.359537\pi\) | ||||
0.427094 | + | 0.904207i | \(0.359537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.24897 | −0.0564804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.593578 | 0.0267878 | 0.0133939 | − | 0.999910i | \(-0.495736\pi\) | ||||
0.0133939 | + | 0.999910i | \(0.495736\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.1780 | 0.863733 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.4115 | −0.691299 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.7965 | −1.33388 | −0.666938 | − | 0.745113i | \(-0.732395\pi\) | ||||
−0.666938 | + | 0.745113i | \(0.732395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.56212 | −0.203820 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.8357 | −0.973608 | −0.486804 | − | 0.873511i | \(-0.661837\pi\) | ||||
−0.486804 | + | 0.873511i | \(0.661837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.22937 | 0.409891 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.4861 | 0.553436 | 0.276718 | − | 0.960951i | \(-0.410753\pi\) | ||||
0.276718 | + | 0.960951i | \(0.410753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.19253 | −0.273942 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.04189 | −0.0901516 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.1702 | 0.667187 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.72193 | 0.251165 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.37908 | 0.148040 | 0.0740201 | − | 0.997257i | \(-0.476417\pi\) | ||||
0.0740201 | + | 0.997257i | \(0.476417\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.7419 | −0.688343 | −0.344172 | − | 0.938907i | \(-0.611840\pi\) | ||||
−0.344172 | + | 0.938907i | \(0.611840\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.50980 | 0.283571 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7989 | −0.730387 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.5817 | −0.459207 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.9564 | −0.951035 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.03777 | −0.346855 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.1848 | 0.481763 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.31820 | −0.0566739 | −0.0283369 | − | 0.999598i | \(-0.509021\pi\) | ||||
−0.0283369 | + | 0.999598i | \(0.509021\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.39187 | 0.360130 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.68954 | 0.414295 | 0.207147 | − | 0.978310i | \(-0.433582\pi\) | ||||
0.207147 | + | 0.978310i | \(0.433582\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.6955 | 1.56613 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.17024 | −0.348064 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.2003 | 0.731430 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.4757 | 0.613353 | 0.306677 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306677 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.3550 | −0.734040 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.96585 | −0.0829983 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.8898 | −1.09113 | −0.545563 | − | 0.838070i | \(-0.683684\pi\) | ||||
−0.545563 | + | 0.838070i | \(0.683684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.0496 | −1.13598 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.8384 | 1.46050 | 0.730251 | − | 0.683178i | \(-0.239403\pi\) | ||||
0.730251 | + | 0.683178i | \(0.239403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.8557 | 1.04018 | 0.520089 | − | 0.854112i | \(-0.325899\pi\) | ||||
0.520089 | + | 0.854112i | \(0.325899\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.911169 | 0.0380646 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.4620 | −1.51793 | −0.758967 | − | 0.651129i | \(-0.774296\pi\) | ||||
−0.758967 | + | 0.651129i | \(0.774296\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.36009 | −0.181199 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.5371 | 1.14243 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.76146 | 0.238615 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.9249 | 1.27641 | 0.638204 | − | 0.769868i | \(-0.279678\pi\) | ||||
0.638204 | + | 0.769868i | \(0.279678\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.77332 | −0.114273 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.87258 | −0.241566 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.2909 | −1.24390 | −0.621948 | − | 0.783058i | \(-0.713659\pi\) | ||||
−0.621948 | + | 0.783058i | \(0.713659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.65446 | 0.272349 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.3236 | 1.03469 | 0.517347 | − | 0.855776i | \(-0.326920\pi\) | ||||
0.517347 | + | 0.855776i | \(0.326920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.2894 | −1.39869 | −0.699347 | − | 0.714782i | \(-0.746526\pi\) | ||||
−0.699347 | + | 0.714782i | \(0.746526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.94356 | −0.282764 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.2550 | 1.71508 | 0.857538 | − | 0.514421i | \(-0.171993\pi\) | ||||
0.857538 | + | 0.514421i | \(0.171993\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.68004 | 0.392255 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.5749 | 1.60103 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.6759 | 0.956262 | 0.478131 | − | 0.878289i | \(-0.341314\pi\) | ||||
0.478131 | + | 0.878289i | \(0.341314\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.8425 | −0.879348 | −0.439674 | − | 0.898157i | \(-0.644906\pi\) | ||||
−0.439674 | + | 0.898157i | \(0.644906\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.2841 | 1.53877 | 0.769383 | − | 0.638788i | \(-0.220564\pi\) | ||||
0.769383 | + | 0.638788i | \(0.220564\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.08471 | −0.204042 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.0419 | 0.402320 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.837496 | 0.0334464 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.29498 | 0.0915068 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.28817 | 0.290138 | 0.145069 | − | 0.989422i | \(-0.453660\pi\) | ||||
0.145069 | + | 0.989422i | \(0.453660\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.67230 | −0.185707 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.1780 | 1.15607 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.0077 | −0.514578 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.2026 | 0.560970 | 0.280485 | − | 0.959858i | \(-0.409505\pi\) | ||||
0.280485 | + | 0.959858i | \(0.409505\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.867526 | 0.0342119 | 0.0171059 | − | 0.999854i | \(-0.494555\pi\) | ||||
0.0171059 | + | 0.999854i | \(0.494555\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.5503 | 1.83008 | 0.915040 | − | 0.403364i | \(-0.132159\pi\) | ||||
0.915040 | + | 0.403364i | \(0.132159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.86215 | 0.347870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.28581 | 0.128781 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.9050 | 1.09201 | 0.546003 | − | 0.837783i | \(-0.316149\pi\) | ||||
0.546003 | + | 0.837783i | \(0.316149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.22668 | −0.203912 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.5340 | 1.92957 | 0.964784 | − | 0.263042i | \(-0.0847257\pi\) | ||||
0.964784 | + | 0.263042i | \(0.0847257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.0164 | 1.55646 | 0.778229 | − | 0.627980i | \(-0.216118\pi\) | ||||
0.778229 | + | 0.627980i | \(0.216118\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.12836 | −0.199169 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.3455 | −0.787783 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.0669 | 0.389208 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.7324 | −1.18641 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.5449 | −1.02323 | −0.511615 | − | 0.859215i | \(-0.670953\pi\) | ||||
−0.511615 | + | 0.859215i | \(0.670953\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.5398 | 0.866276 | 0.433138 | − | 0.901328i | \(-0.357406\pi\) | ||||
0.433138 | + | 0.901328i | \(0.357406\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.5699 | 0.405634 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.68449 | 0.141190 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.2154 | 1.69186 | 0.845928 | − | 0.533297i | \(-0.179047\pi\) | ||||
0.845928 | + | 0.533297i | \(0.179047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.45842 | −0.170099 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0300 | 0.572599 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.0743 | 1.18212 | 0.591061 | − | 0.806627i | \(-0.298709\pi\) | ||||
0.591061 | + | 0.806627i | \(0.298709\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.6878 | 0.899825 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.19253 | 0.310314 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.64496 | −0.137865 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.8185 | 1.69277 | 0.846386 | − | 0.532570i | \(-0.178774\pi\) | ||||
0.846386 | + | 0.532570i | \(0.178774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.977711 | −0.0368751 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.5449 | 0.772670 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.1334 | −1.50724 | −0.753621 | − | 0.657309i | \(-0.771695\pi\) | ||||
−0.753621 | + | 0.657309i | \(0.771695\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.5175 | 0.544450 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.90612 | −0.258636 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.41653 | 0.0529012 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.8571 | 0.777838 | 0.388919 | − | 0.921272i | \(-0.372849\pi\) | ||||
0.388919 | + | 0.921272i | \(0.372849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.7469 | 0.921623 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.08378 | −0.189068 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.2540 | −0.417389 | −0.208694 | − | 0.977981i | \(-0.566921\pi\) | ||||
−0.208694 | + | 0.977981i | \(0.566921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7033 | −0.766788 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.47565 | 0.239511 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.3952 | −0.420890 | −0.210445 | − | 0.977606i | \(-0.567491\pi\) | ||||
−0.210445 | + | 0.977606i | \(0.567491\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.81521 | 0.214206 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.7015 | −1.68116 | −0.840579 | − | 0.541690i | \(-0.817785\pi\) | ||||
−0.840579 | + | 0.541690i | \(0.817785\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.18479 | 0.0802604 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.82470 | 0.140315 | 0.0701574 | − | 0.997536i | \(-0.477650\pi\) | ||||
0.0701574 | + | 0.997536i | \(0.477650\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.2422 | 0.850386 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30.5107 | −1.11484 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.5550 | 0.969005 | 0.484503 | − | 0.874790i | \(-0.339001\pi\) | ||||
0.484503 | + | 0.874790i | \(0.339001\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.19160 | −0.152750 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.64765 | 0.168922 | 0.0844609 | − | 0.996427i | \(-0.473083\pi\) | ||||
0.0844609 | + | 0.996427i | \(0.473083\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.08553 | 0.0757000 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.0327 | −0.943685 | −0.471843 | − | 0.881683i | \(-0.656411\pi\) | ||||
−0.471843 | + | 0.881683i | \(0.656411\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.4843 | 1.21221 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.1189 | 0.834774 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.10876 | 0.112105 | 0.0560523 | − | 0.998428i | \(-0.482149\pi\) | ||||
0.0560523 | + | 0.998428i | \(0.482149\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.563873 | 0.0203074 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.4516 | −0.699626 | −0.349813 | − | 0.936820i | \(-0.613755\pi\) | ||||
−0.349813 | + | 0.936820i | \(0.613755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.15839 | 0.0415568 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.49020 | −0.125049 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.8939 | 0.389816 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.6827 | 0.596192 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0496 | −0.500815 | −0.250408 | − | 0.968141i | \(-0.580565\pi\) | ||||
−0.250408 | + | 0.968141i | \(0.580565\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.81521 | 0.349431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.8476 | 0.919035 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −80.1721 | −2.84700 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.57810 | 0.0913209 | 0.0456604 | − | 0.998957i | \(-0.485461\pi\) | ||||
0.0456604 | + | 0.998957i | \(0.485461\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7665 | −0.522402 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.47565 | 0.299472 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.37733 | 0.154472 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.51249 | −0.123645 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.8220 | 0.696905 | 0.348452 | − | 0.937326i | \(-0.386707\pi\) | ||||
0.348452 | + | 0.937326i | \(0.386707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6563 | 0.795571 | 0.397786 | − | 0.917478i | \(-0.369779\pi\) | ||||
0.397786 | + | 0.917478i | \(0.369779\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.96997 | −0.279519 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.75877 | −0.0965172 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 61.7948 | 2.15928 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0570 | −0.804696 | −0.402348 | − | 0.915487i | \(-0.631806\pi\) | ||||
−0.402348 | + | 0.915487i | \(0.631806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.6563 | −1.55662 | −0.778311 | − | 0.627879i | \(-0.783923\pi\) | ||||
−0.778311 | + | 0.627879i | \(0.783923\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.4306 | −1.82319 | −0.911595 | − | 0.411090i | \(-0.865148\pi\) | ||||
−0.911595 | + | 0.411090i | \(0.865148\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.2412 | −1.39764 | −0.698818 | − | 0.715300i | \(-0.746290\pi\) | ||||
−0.698818 | + | 0.715300i | \(0.746290\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.91891 | 0.170635 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.8871 | −0.377217 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.66281 | 0.195735 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.5185 | −1.81314 | −0.906570 | − | 0.422056i | \(-0.861308\pi\) | ||||
−0.906570 | + | 0.422056i | \(0.861308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.7529 | 1.30182 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.285807 | 0.00984371 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.6878 | 0.607760 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.67911 | 0.0576269 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.43470 | −0.0834603 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2094 | 0.691958 | 0.345979 | − | 0.938242i | \(-0.387547\pi\) | ||||
0.345979 | + | 0.938242i | \(0.387547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.9522 | 0.510759 | 0.255379 | − | 0.966841i | \(-0.417800\pi\) | ||||
0.255379 | + | 0.966841i | \(0.417800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.3286 | −1.17128 | −0.585639 | − | 0.810572i | \(-0.699156\pi\) | ||||
−0.585639 | + | 0.810572i | \(0.699156\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.13516 | 0.140926 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.0392 | −0.920425 | −0.460213 | − | 0.887809i | \(-0.652227\pi\) | ||||
−0.460213 | + | 0.887809i | \(0.652227\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.99050 | −0.135525 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.1584 | −0.412445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1702 | 0.514024 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.92127 | 0.301939 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.2216 | 0.581533 | 0.290767 | − | 0.956794i | \(-0.406090\pi\) | ||||
0.290767 | + | 0.956794i | \(0.406090\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.10195 | −0.205814 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.2312 | 1.72602 | 0.863012 | − | 0.505183i | \(-0.168575\pi\) | ||||
0.863012 | + | 0.505183i | \(0.168575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.8939 | −0.938706 | −0.469353 | − | 0.883011i | \(-0.655513\pi\) | ||||
−0.469353 | + | 0.883011i | \(0.655513\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.5749 | −1.09376 | −0.546879 | − | 0.837211i | \(-0.684184\pi\) | ||||
−0.546879 | + | 0.837211i | \(0.684184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.4270 | −0.953409 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.1206 | 0.640565 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.29086 | 0.210516 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.44057 | 0.181655 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.6587 | 0.755710 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.60813 | −0.186834 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.26857 | 0.108771 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.6673 | 0.785858 | 0.392929 | − | 0.919569i | \(-0.371462\pi\) | ||||
0.392929 | + | 0.919569i | \(0.371462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.3405 | 0.575148 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4233 | 0.378472 | 0.189236 | − | 0.981932i | \(-0.439399\pi\) | ||||
0.189236 | + | 0.981932i | \(0.439399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.4652 | −0.644205 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.6614 | 1.47485 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.7401 | −1.14597 | −0.572985 | − | 0.819566i | \(-0.694215\pi\) | ||||
−0.572985 | + | 0.819566i | \(0.694215\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.23854 | 0.205567 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.4192 | 0.935430 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.8871 | 0.686023 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.1848 | 1.64651 | 0.823255 | − | 0.567672i | \(-0.192156\pi\) | ||||
0.823255 | + | 0.567672i | \(0.192156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.63816 | 0.152009 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.53478 | 0.312155 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.48927 | 0.146658 | 0.0733290 | − | 0.997308i | \(-0.476638\pi\) | ||||
0.0733290 | + | 0.997308i | \(0.476638\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.01043 | 0.0329741 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.70233 | −0.251089 | −0.125544 | − | 0.992088i | \(-0.540068\pi\) | ||||
−0.125544 | + | 0.992088i | \(0.540068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.69129 | −0.283028 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.4415 | −0.436790 | −0.218395 | − | 0.975860i | \(-0.570082\pi\) | ||||
−0.218395 | + | 0.975860i | \(0.570082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.4192 | 0.370683 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.02498 | 0.260228 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.1943 | −0.751337 | −0.375668 | − | 0.926754i | \(-0.622587\pi\) | ||||
−0.375668 | + | 0.926754i | \(0.622587\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.84255 | −0.221188 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 52.3073 | 1.68909 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3087 | −0.751894 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.7520 | −0.829845 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.1429 | −0.712068 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.815207 | −0.0261882 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.9804 | 0.865842 | 0.432921 | − | 0.901432i | \(-0.357483\pi\) | ||||
0.432921 | + | 0.901432i | \(0.357483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.5357 | 0.850696 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.64496 | −0.0846199 | −0.0423099 | − | 0.999105i | \(-0.513472\pi\) | ||||
−0.0423099 | + | 0.999105i | \(0.513472\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.09833 | −0.226863 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.2618 | 0.902329 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.4492 | 0.716020 | 0.358010 | − | 0.933718i | \(-0.383455\pi\) | ||||
0.358010 | + | 0.933718i | \(0.383455\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.45336 | −0.237243 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.86989 | −0.218450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.4570 | −0.840434 | −0.420217 | − | 0.907424i | \(-0.638046\pi\) | ||||
−0.420217 | + | 0.907424i | \(0.638046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.00444 | 0.0318750 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.17881 | 0.0690035 | 0.0345017 | − | 0.999405i | \(-0.489016\pi\) | ||||
0.0345017 | + | 0.999405i | \(0.489016\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.99638 | 0.0631626 |
(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 | 3800.2.a.t.1.2 | yes | 3 | |
4.3 | odd | 2 | 7600.2.a.bs.1.2 | 3 | |||
5.2 | odd | 4 | 3800.2.d.o.3649.3 | 6 | |||
5.3 | odd | 4 | 3800.2.d.o.3649.4 | 6 | |||
5.4 | even | 2 | 3800.2.a.s.1.2 | ✓ | 3 | ||
20.19 | odd | 2 | 7600.2.a.br.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3800.2.a.s.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
3800.2.a.t.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
3800.2.d.o.3649.3 | 6 | 5.2 | odd | 4 | |||
3800.2.d.o.3649.4 | 6 | 5.3 | odd | 4 | |||
7600.2.a.br.1.2 | 3 | 20.19 | odd | 2 | |||
7600.2.a.bs.1.2 | 3 | 4.3 | odd | 2 |