Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1690,2,Mod(1,1690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1690.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1690 = 2 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1690.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: | \(13.4947179416\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.20439713.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 15x^{4} + 22x^{3} + 70x^{2} - 56x - 91 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.57254\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1690.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.57254 | 1.48526 | 0.742629 | − | 0.669703i | \(-0.233579\pi\) | ||||
0.742629 | + | 0.669703i | \(0.233579\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.57254 | −1.05024 | ||||||||
\(7\) | −1.90403 | −0.719655 | −0.359827 | − | 0.933019i | \(-0.617164\pi\) | ||||
−0.359827 | + | 0.933019i | \(0.617164\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.61798 | 1.20599 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.17658 | −1.56080 | −0.780398 | − | 0.625283i | \(-0.784984\pi\) | ||||
−0.780398 | + | 0.625283i | \(0.784984\pi\) | |||||||
\(12\) | 2.57254 | 0.742629 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.90403 | 0.508873 | ||||||||
\(15\) | −2.57254 | −0.664228 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.89037 | −1.42862 | −0.714312 | − | 0.699827i | \(-0.753260\pi\) | ||||
−0.714312 | + | 0.699827i | \(0.753260\pi\) | |||||||
\(18\) | −3.61798 | −0.852765 | ||||||||
\(19\) | 8.09045 | 1.85608 | 0.928038 | − | 0.372485i | \(-0.121494\pi\) | ||||
0.928038 | + | 0.372485i | \(0.121494\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −4.89819 | −1.06887 | ||||||||
\(22\) | 5.17658 | 1.10365 | ||||||||
\(23\) | −0.908568 | −0.189449 | −0.0947247 | − | 0.995504i | \(-0.530197\pi\) | ||||
−0.0947247 | + | 0.995504i | \(0.530197\pi\) | |||||||
\(24\) | −2.57254 | −0.525118 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.58977 | 0.305952 | ||||||||
\(28\) | −1.90403 | −0.359827 | ||||||||
\(29\) | −5.29954 | −0.984099 | −0.492050 | − | 0.870567i | \(-0.663752\pi\) | ||||
−0.492050 | + | 0.870567i | \(0.663752\pi\) | |||||||
\(30\) | 2.57254 | 0.469680 | ||||||||
\(31\) | 0.0626650 | 0.0112550 | 0.00562748 | − | 0.999984i | \(-0.498209\pi\) | ||||
0.00562748 | + | 0.999984i | \(0.498209\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −13.3170 | −2.31819 | ||||||||
\(34\) | 5.89037 | 1.01019 | ||||||||
\(35\) | 1.90403 | 0.321839 | ||||||||
\(36\) | 3.61798 | 0.602996 | ||||||||
\(37\) | −1.63865 | −0.269393 | −0.134696 | − | 0.990887i | \(-0.543006\pi\) | ||||
−0.134696 | + | 0.990887i | \(0.543006\pi\) | |||||||
\(38\) | −8.09045 | −1.31244 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.77061 | −0.276522 | −0.138261 | − | 0.990396i | \(-0.544151\pi\) | ||||
−0.138261 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(42\) | 4.89819 | 0.755808 | ||||||||
\(43\) | −8.58977 | −1.30993 | −0.654964 | − | 0.755660i | \(-0.727316\pi\) | ||||
−0.654964 | + | 0.755660i | \(0.727316\pi\) | |||||||
\(44\) | −5.17658 | −0.780398 | ||||||||
\(45\) | −3.61798 | −0.539336 | ||||||||
\(46\) | 0.908568 | 0.133961 | ||||||||
\(47\) | 11.2024 | 1.63404 | 0.817018 | − | 0.576612i | \(-0.195626\pi\) | ||||
0.817018 | + | 0.576612i | \(0.195626\pi\) | |||||||
\(48\) | 2.57254 | 0.371315 | ||||||||
\(49\) | −3.37468 | −0.482097 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −15.1532 | −2.12188 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.92525 | −1.22598 | −0.612989 | − | 0.790092i | \(-0.710033\pi\) | ||||
−0.612989 | + | 0.790092i | \(0.710033\pi\) | |||||||
\(54\) | −1.58977 | −0.216341 | ||||||||
\(55\) | 5.17658 | 0.698009 | ||||||||
\(56\) | 1.90403 | 0.254436 | ||||||||
\(57\) | 20.8130 | 2.75675 | ||||||||
\(58\) | 5.29954 | 0.695863 | ||||||||
\(59\) | −10.6767 | −1.38999 | −0.694997 | − | 0.719013i | \(-0.744594\pi\) | ||||
−0.694997 | + | 0.719013i | \(0.744594\pi\) | |||||||
\(60\) | −2.57254 | −0.332114 | ||||||||
\(61\) | −0.681193 | −0.0872179 | −0.0436089 | − | 0.999049i | \(-0.513886\pi\) | ||||
−0.0436089 | + | 0.999049i | \(0.513886\pi\) | |||||||
\(62\) | −0.0626650 | −0.00795846 | ||||||||
\(63\) | −6.88873 | −0.867898 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.3170 | 1.63921 | ||||||||
\(67\) | −14.1492 | −1.72860 | −0.864301 | − | 0.502975i | \(-0.832239\pi\) | ||||
−0.864301 | + | 0.502975i | \(0.832239\pi\) | |||||||
\(68\) | −5.89037 | −0.714312 | ||||||||
\(69\) | −2.33733 | −0.281381 | ||||||||
\(70\) | −1.90403 | −0.227575 | ||||||||
\(71\) | −15.7017 | −1.86345 | −0.931725 | − | 0.363164i | \(-0.881696\pi\) | ||||
−0.931725 | + | 0.363164i | \(0.881696\pi\) | |||||||
\(72\) | −3.61798 | −0.426383 | ||||||||
\(73\) | −0.163089 | −0.0190881 | −0.00954407 | − | 0.999954i | \(-0.503038\pi\) | ||||
−0.00954407 | + | 0.999954i | \(0.503038\pi\) | |||||||
\(74\) | 1.63865 | 0.190489 | ||||||||
\(75\) | 2.57254 | 0.297052 | ||||||||
\(76\) | 8.09045 | 0.928038 | ||||||||
\(77\) | 9.85635 | 1.12323 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7178 | 1.65589 | 0.827943 | − | 0.560813i | \(-0.189511\pi\) | ||||
0.827943 | + | 0.560813i | \(0.189511\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −6.76417 | −0.751575 | ||||||||
\(82\) | 1.77061 | 0.195531 | ||||||||
\(83\) | 1.89246 | 0.207724 | 0.103862 | − | 0.994592i | \(-0.466880\pi\) | ||||
0.103862 | + | 0.994592i | \(0.466880\pi\) | |||||||
\(84\) | −4.89819 | −0.534437 | ||||||||
\(85\) | 5.89037 | 0.638900 | ||||||||
\(86\) | 8.58977 | 0.926259 | ||||||||
\(87\) | −13.6333 | −1.46164 | ||||||||
\(88\) | 5.17658 | 0.551825 | ||||||||
\(89\) | 0.541298 | 0.0573775 | 0.0286887 | − | 0.999588i | \(-0.490867\pi\) | ||||
0.0286887 | + | 0.999588i | \(0.490867\pi\) | |||||||
\(90\) | 3.61798 | 0.381368 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.908568 | −0.0947247 | ||||||||
\(93\) | 0.161208 | 0.0167165 | ||||||||
\(94\) | −11.2024 | −1.15544 | ||||||||
\(95\) | −8.09045 | −0.830063 | ||||||||
\(96\) | −2.57254 | −0.262559 | ||||||||
\(97\) | −12.8001 | −1.29966 | −0.649829 | − | 0.760081i | \(-0.725159\pi\) | ||||
−0.649829 | + | 0.760081i | \(0.725159\pi\) | |||||||
\(98\) | 3.37468 | 0.340894 | ||||||||
\(99\) | −18.7287 | −1.88231 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.59059 | 0.257773 | 0.128886 | − | 0.991659i | \(-0.458860\pi\) | ||||
0.128886 | + | 0.991659i | \(0.458860\pi\) | |||||||
\(102\) | 15.1532 | 1.50039 | ||||||||
\(103\) | −1.77799 | −0.175191 | −0.0875953 | − | 0.996156i | \(-0.527918\pi\) | ||||
−0.0875953 | + | 0.996156i | \(0.527918\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.89819 | 0.478015 | ||||||||
\(106\) | 8.92525 | 0.866897 | ||||||||
\(107\) | 3.56829 | 0.344959 | 0.172480 | − | 0.985013i | \(-0.444822\pi\) | ||||
0.172480 | + | 0.985013i | \(0.444822\pi\) | |||||||
\(108\) | 1.58977 | 0.152976 | ||||||||
\(109\) | 11.4449 | 1.09622 | 0.548112 | − | 0.836405i | \(-0.315347\pi\) | ||||
0.548112 | + | 0.836405i | \(0.315347\pi\) | |||||||
\(110\) | −5.17658 | −0.493567 | ||||||||
\(111\) | −4.21550 | −0.400118 | ||||||||
\(112\) | −1.90403 | −0.179914 | ||||||||
\(113\) | 11.2334 | 1.05675 | 0.528373 | − | 0.849012i | \(-0.322802\pi\) | ||||
0.528373 | + | 0.849012i | \(0.322802\pi\) | |||||||
\(114\) | −20.8130 | −1.94932 | ||||||||
\(115\) | 0.908568 | 0.0847244 | ||||||||
\(116\) | −5.29954 | −0.492050 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.6767 | 0.982874 | ||||||||
\(119\) | 11.2154 | 1.02812 | ||||||||
\(120\) | 2.57254 | 0.234840 | ||||||||
\(121\) | 15.7969 | 1.43609 | ||||||||
\(122\) | 0.681193 | 0.0616724 | ||||||||
\(123\) | −4.55496 | −0.410707 | ||||||||
\(124\) | 0.0626650 | 0.00562748 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.88873 | 0.613697 | ||||||||
\(127\) | 10.8735 | 0.964870 | 0.482435 | − | 0.875932i | \(-0.339752\pi\) | ||||
0.482435 | + | 0.875932i | \(0.339752\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −22.0976 | −1.94558 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.13042 | 0.0987653 | 0.0493827 | − | 0.998780i | \(-0.484275\pi\) | ||||
0.0493827 | + | 0.998780i | \(0.484275\pi\) | |||||||
\(132\) | −13.3170 | −1.15909 | ||||||||
\(133\) | −15.4044 | −1.33573 | ||||||||
\(134\) | 14.1492 | 1.22231 | ||||||||
\(135\) | −1.58977 | −0.136826 | ||||||||
\(136\) | 5.89037 | 0.505095 | ||||||||
\(137\) | 10.9390 | 0.934584 | 0.467292 | − | 0.884103i | \(-0.345230\pi\) | ||||
0.467292 | + | 0.884103i | \(0.345230\pi\) | |||||||
\(138\) | 2.33733 | 0.198967 | ||||||||
\(139\) | −4.30562 | −0.365198 | −0.182599 | − | 0.983188i | \(-0.558451\pi\) | ||||
−0.182599 | + | 0.983188i | \(0.558451\pi\) | |||||||
\(140\) | 1.90403 | 0.160920 | ||||||||
\(141\) | 28.8186 | 2.42697 | ||||||||
\(142\) | 15.7017 | 1.31766 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.61798 | 0.301498 | ||||||||
\(145\) | 5.29954 | 0.440103 | ||||||||
\(146\) | 0.163089 | 0.0134974 | ||||||||
\(147\) | −8.68150 | −0.716038 | ||||||||
\(148\) | −1.63865 | −0.134696 | ||||||||
\(149\) | 19.2499 | 1.57701 | 0.788505 | − | 0.615029i | \(-0.210856\pi\) | ||||
0.788505 | + | 0.615029i | \(0.210856\pi\) | |||||||
\(150\) | −2.57254 | −0.210047 | ||||||||
\(151\) | 7.91349 | 0.643990 | 0.321995 | − | 0.946741i | \(-0.395646\pi\) | ||||
0.321995 | + | 0.946741i | \(0.395646\pi\) | |||||||
\(152\) | −8.09045 | −0.656222 | ||||||||
\(153\) | −21.3112 | −1.72291 | ||||||||
\(154\) | −9.85635 | −0.794247 | ||||||||
\(155\) | −0.0626650 | −0.00503337 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.946176 | −0.0755131 | −0.0377565 | − | 0.999287i | \(-0.512021\pi\) | ||||
−0.0377565 | + | 0.999287i | \(0.512021\pi\) | |||||||
\(158\) | −14.7178 | −1.17089 | ||||||||
\(159\) | −22.9606 | −1.82089 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.72994 | 0.136338 | ||||||||
\(162\) | 6.76417 | 0.531444 | ||||||||
\(163\) | −4.51269 | −0.353461 | −0.176731 | − | 0.984259i | \(-0.556552\pi\) | ||||
−0.176731 | + | 0.984259i | \(0.556552\pi\) | |||||||
\(164\) | −1.77061 | −0.138261 | ||||||||
\(165\) | 13.3170 | 1.03672 | ||||||||
\(166\) | −1.89246 | −0.146883 | ||||||||
\(167\) | 1.96336 | 0.151929 | 0.0759647 | − | 0.997111i | \(-0.475796\pi\) | ||||
0.0759647 | + | 0.997111i | \(0.475796\pi\) | |||||||
\(168\) | 4.89819 | 0.377904 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −5.89037 | −0.451771 | ||||||||
\(171\) | 29.2711 | 2.23841 | ||||||||
\(172\) | −8.58977 | −0.654964 | ||||||||
\(173\) | 10.2747 | 0.781171 | 0.390585 | − | 0.920567i | \(-0.372273\pi\) | ||||
0.390585 | + | 0.920567i | \(0.372273\pi\) | |||||||
\(174\) | 13.6333 | 1.03354 | ||||||||
\(175\) | −1.90403 | −0.143931 | ||||||||
\(176\) | −5.17658 | −0.390199 | ||||||||
\(177\) | −27.4664 | −2.06450 | ||||||||
\(178\) | −0.541298 | −0.0405720 | ||||||||
\(179\) | 11.3293 | 0.846790 | 0.423395 | − | 0.905945i | \(-0.360838\pi\) | ||||
0.423395 | + | 0.905945i | \(0.360838\pi\) | |||||||
\(180\) | −3.61798 | −0.269668 | ||||||||
\(181\) | 16.6110 | 1.23468 | 0.617342 | − | 0.786695i | \(-0.288209\pi\) | ||||
0.617342 | + | 0.786695i | \(0.288209\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.75240 | −0.129541 | ||||||||
\(184\) | 0.908568 | 0.0669805 | ||||||||
\(185\) | 1.63865 | 0.120476 | ||||||||
\(186\) | −0.161208 | −0.0118204 | ||||||||
\(187\) | 30.4919 | 2.22979 | ||||||||
\(188\) | 11.2024 | 0.817018 | ||||||||
\(189\) | −3.02697 | −0.220180 | ||||||||
\(190\) | 8.09045 | 0.586943 | ||||||||
\(191\) | 21.7130 | 1.57110 | 0.785550 | − | 0.618798i | \(-0.212380\pi\) | ||||
0.785550 | + | 0.618798i | \(0.212380\pi\) | |||||||
\(192\) | 2.57254 | 0.185657 | ||||||||
\(193\) | −11.3641 | −0.818006 | −0.409003 | − | 0.912533i | \(-0.634123\pi\) | ||||
−0.409003 | + | 0.912533i | \(0.634123\pi\) | |||||||
\(194\) | 12.8001 | 0.918997 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.37468 | −0.241048 | ||||||||
\(197\) | −17.6398 | −1.25678 | −0.628390 | − | 0.777898i | \(-0.716286\pi\) | ||||
−0.628390 | + | 0.777898i | \(0.716286\pi\) | |||||||
\(198\) | 18.7287 | 1.33099 | ||||||||
\(199\) | −23.6305 | −1.67512 | −0.837562 | − | 0.546342i | \(-0.816020\pi\) | ||||
−0.837562 | + | 0.546342i | \(0.816020\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −36.3995 | −2.56742 | ||||||||
\(202\) | −2.59059 | −0.182273 | ||||||||
\(203\) | 10.0905 | 0.708212 | ||||||||
\(204\) | −15.1532 | −1.06094 | ||||||||
\(205\) | 1.77061 | 0.123664 | ||||||||
\(206\) | 1.77799 | 0.123878 | ||||||||
\(207\) | −3.28718 | −0.228475 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.8808 | −2.89696 | ||||||||
\(210\) | −4.89819 | −0.338007 | ||||||||
\(211\) | −15.2360 | −1.04889 | −0.524445 | − | 0.851444i | \(-0.675727\pi\) | ||||
−0.524445 | + | 0.851444i | \(0.675727\pi\) | |||||||
\(212\) | −8.92525 | −0.612989 | ||||||||
\(213\) | −40.3933 | −2.76770 | ||||||||
\(214\) | −3.56829 | −0.243923 | ||||||||
\(215\) | 8.58977 | 0.585818 | ||||||||
\(216\) | −1.58977 | −0.108170 | ||||||||
\(217\) | −0.119316 | −0.00809969 | ||||||||
\(218\) | −11.4449 | −0.775148 | ||||||||
\(219\) | −0.419554 | −0.0283508 | ||||||||
\(220\) | 5.17658 | 0.349005 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.21550 | 0.282926 | ||||||||
\(223\) | 2.78265 | 0.186340 | 0.0931699 | − | 0.995650i | \(-0.470300\pi\) | ||||
0.0931699 | + | 0.995650i | \(0.470300\pi\) | |||||||
\(224\) | 1.90403 | 0.127218 | ||||||||
\(225\) | 3.61798 | 0.241198 | ||||||||
\(226\) | −11.2334 | −0.747232 | ||||||||
\(227\) | 3.94347 | 0.261737 | 0.130869 | − | 0.991400i | \(-0.458223\pi\) | ||||
0.130869 | + | 0.991400i | \(0.458223\pi\) | |||||||
\(228\) | 20.8130 | 1.37838 | ||||||||
\(229\) | −10.3809 | −0.685986 | −0.342993 | − | 0.939338i | \(-0.611441\pi\) | ||||
−0.342993 | + | 0.939338i | \(0.611441\pi\) | |||||||
\(230\) | −0.908568 | −0.0599092 | ||||||||
\(231\) | 25.3559 | 1.66829 | ||||||||
\(232\) | 5.29954 | 0.347932 | ||||||||
\(233\) | −13.2410 | −0.867449 | −0.433725 | − | 0.901045i | \(-0.642801\pi\) | ||||
−0.433725 | + | 0.901045i | \(0.642801\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2024 | −0.730763 | ||||||||
\(236\) | −10.6767 | −0.694997 | ||||||||
\(237\) | 37.8623 | 2.45942 | ||||||||
\(238\) | −11.2154 | −0.726988 | ||||||||
\(239\) | −24.3290 | −1.57371 | −0.786856 | − | 0.617137i | \(-0.788292\pi\) | ||||
−0.786856 | + | 0.617137i | \(0.788292\pi\) | |||||||
\(240\) | −2.57254 | −0.166057 | ||||||||
\(241\) | 11.1983 | 0.721349 | 0.360674 | − | 0.932692i | \(-0.382547\pi\) | ||||
0.360674 | + | 0.932692i | \(0.382547\pi\) | |||||||
\(242\) | −15.7969 | −1.01547 | ||||||||
\(243\) | −22.1704 | −1.42223 | ||||||||
\(244\) | −0.681193 | −0.0436089 | ||||||||
\(245\) | 3.37468 | 0.215600 | ||||||||
\(246\) | 4.55496 | 0.290414 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.0626650 | −0.00397923 | ||||||||
\(249\) | 4.86843 | 0.308524 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 5.81385 | 0.366967 | 0.183483 | − | 0.983023i | \(-0.441263\pi\) | ||||
0.183483 | + | 0.983023i | \(0.441263\pi\) | |||||||
\(252\) | −6.88873 | −0.433949 | ||||||||
\(253\) | 4.70327 | 0.295692 | ||||||||
\(254\) | −10.8735 | −0.682266 | ||||||||
\(255\) | 15.1532 | 0.948932 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.1850 | −1.82051 | −0.910254 | − | 0.414050i | \(-0.864114\pi\) | ||||
−0.910254 | + | 0.414050i | \(0.864114\pi\) | |||||||
\(258\) | 22.0976 | 1.37573 | ||||||||
\(259\) | 3.12004 | 0.193870 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.1736 | −1.18682 | ||||||||
\(262\) | −1.13042 | −0.0698376 | ||||||||
\(263\) | 27.5544 | 1.69908 | 0.849538 | − | 0.527527i | \(-0.176881\pi\) | ||||
0.849538 | + | 0.527527i | \(0.176881\pi\) | |||||||
\(264\) | 13.3170 | 0.819603 | ||||||||
\(265\) | 8.92525 | 0.548274 | ||||||||
\(266\) | 15.4044 | 0.944507 | ||||||||
\(267\) | 1.39251 | 0.0852204 | ||||||||
\(268\) | −14.1492 | −0.864301 | ||||||||
\(269\) | 3.97887 | 0.242596 | 0.121298 | − | 0.992616i | \(-0.461294\pi\) | ||||
0.121298 | + | 0.992616i | \(0.461294\pi\) | |||||||
\(270\) | 1.58977 | 0.0967505 | ||||||||
\(271\) | −13.6399 | −0.828567 | −0.414283 | − | 0.910148i | \(-0.635968\pi\) | ||||
−0.414283 | + | 0.910148i | \(0.635968\pi\) | |||||||
\(272\) | −5.89037 | −0.357156 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.9390 | −0.660851 | ||||||||
\(275\) | −5.17658 | −0.312159 | ||||||||
\(276\) | −2.33733 | −0.140691 | ||||||||
\(277\) | −2.30543 | −0.138520 | −0.0692600 | − | 0.997599i | \(-0.522064\pi\) | ||||
−0.0692600 | + | 0.997599i | \(0.522064\pi\) | |||||||
\(278\) | 4.30562 | 0.258234 | ||||||||
\(279\) | 0.226720 | 0.0135734 | ||||||||
\(280\) | −1.90403 | −0.113787 | ||||||||
\(281\) | 21.0557 | 1.25608 | 0.628038 | − | 0.778183i | \(-0.283858\pi\) | ||||
0.628038 | + | 0.778183i | \(0.283858\pi\) | |||||||
\(282\) | −28.8186 | −1.71612 | ||||||||
\(283\) | −2.60164 | −0.154652 | −0.0773258 | − | 0.997006i | \(-0.524638\pi\) | ||||
−0.0773258 | + | 0.997006i | \(0.524638\pi\) | |||||||
\(284\) | −15.7017 | −0.931725 | ||||||||
\(285\) | −20.8130 | −1.23286 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.37128 | 0.199000 | ||||||||
\(288\) | −3.61798 | −0.213191 | ||||||||
\(289\) | 17.6964 | 1.04097 | ||||||||
\(290\) | −5.29954 | −0.311200 | ||||||||
\(291\) | −32.9289 | −1.93033 | ||||||||
\(292\) | −0.163089 | −0.00954407 | ||||||||
\(293\) | −6.46826 | −0.377880 | −0.188940 | − | 0.981989i | \(-0.560505\pi\) | ||||
−0.188940 | + | 0.981989i | \(0.560505\pi\) | |||||||
\(294\) | 8.68150 | 0.506316 | ||||||||
\(295\) | 10.6767 | 0.621624 | ||||||||
\(296\) | 1.63865 | 0.0952447 | ||||||||
\(297\) | −8.22958 | −0.477529 | ||||||||
\(298\) | −19.2499 | −1.11511 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.57254 | 0.148526 | ||||||||
\(301\) | 16.3552 | 0.942696 | ||||||||
\(302\) | −7.91349 | −0.455370 | ||||||||
\(303\) | 6.66439 | 0.382859 | ||||||||
\(304\) | 8.09045 | 0.464019 | ||||||||
\(305\) | 0.681193 | 0.0390050 | ||||||||
\(306\) | 21.3112 | 1.21828 | ||||||||
\(307\) | 11.7707 | 0.671789 | 0.335894 | − | 0.941900i | \(-0.390961\pi\) | ||||
0.335894 | + | 0.941900i | \(0.390961\pi\) | |||||||
\(308\) | 9.85635 | 0.561617 | ||||||||
\(309\) | −4.57395 | −0.260203 | ||||||||
\(310\) | 0.0626650 | 0.00355913 | ||||||||
\(311\) | 2.09362 | 0.118718 | 0.0593591 | − | 0.998237i | \(-0.481094\pi\) | ||||
0.0593591 | + | 0.998237i | \(0.481094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.7645 | −1.39977 | −0.699885 | − | 0.714256i | \(-0.746765\pi\) | ||||
−0.699885 | + | 0.714256i | \(0.746765\pi\) | |||||||
\(314\) | 0.946176 | 0.0533958 | ||||||||
\(315\) | 6.88873 | 0.388136 | ||||||||
\(316\) | 14.7178 | 0.827943 | ||||||||
\(317\) | −20.9473 | −1.17652 | −0.588259 | − | 0.808672i | \(-0.700186\pi\) | ||||
−0.588259 | + | 0.808672i | \(0.700186\pi\) | |||||||
\(318\) | 22.9606 | 1.28757 | ||||||||
\(319\) | 27.4335 | 1.53598 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 9.17957 | 0.512354 | ||||||||
\(322\) | −1.72994 | −0.0964057 | ||||||||
\(323\) | −47.6557 | −2.65164 | ||||||||
\(324\) | −6.76417 | −0.375787 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.51269 | 0.249935 | ||||||||
\(327\) | 29.4426 | 1.62818 | ||||||||
\(328\) | 1.77061 | 0.0977653 | ||||||||
\(329\) | −21.3297 | −1.17594 | ||||||||
\(330\) | −13.3170 | −0.733075 | ||||||||
\(331\) | 21.2478 | 1.16789 | 0.583944 | − | 0.811794i | \(-0.301509\pi\) | ||||
0.583944 | + | 0.811794i | \(0.301509\pi\) | |||||||
\(332\) | 1.89246 | 0.103862 | ||||||||
\(333\) | −5.92861 | −0.324886 | ||||||||
\(334\) | −1.96336 | −0.107430 | ||||||||
\(335\) | 14.1492 | 0.773054 | ||||||||
\(336\) | −4.89819 | −0.267218 | ||||||||
\(337\) | 11.8333 | 0.644603 | 0.322301 | − | 0.946637i | \(-0.395544\pi\) | ||||
0.322301 | + | 0.946637i | \(0.395544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.8983 | 1.56954 | ||||||||
\(340\) | 5.89037 | 0.319450 | ||||||||
\(341\) | −0.324390 | −0.0175667 | ||||||||
\(342\) | −29.2711 | −1.58280 | ||||||||
\(343\) | 19.7537 | 1.06660 | ||||||||
\(344\) | 8.58977 | 0.463130 | ||||||||
\(345\) | 2.33733 | 0.125838 | ||||||||
\(346\) | −10.2747 | −0.552371 | ||||||||
\(347\) | −21.3904 | −1.14830 | −0.574149 | − | 0.818751i | \(-0.694667\pi\) | ||||
−0.574149 | + | 0.818751i | \(0.694667\pi\) | |||||||
\(348\) | −13.6333 | −0.730821 | ||||||||
\(349\) | 18.5446 | 0.992670 | 0.496335 | − | 0.868131i | \(-0.334679\pi\) | ||||
0.496335 | + | 0.868131i | \(0.334679\pi\) | |||||||
\(350\) | 1.90403 | 0.101775 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.17658 | 0.275912 | ||||||||
\(353\) | −11.2265 | −0.597527 | −0.298764 | − | 0.954327i | \(-0.596574\pi\) | ||||
−0.298764 | + | 0.954327i | \(0.596574\pi\) | |||||||
\(354\) | 27.4664 | 1.45982 | ||||||||
\(355\) | 15.7017 | 0.833360 | ||||||||
\(356\) | 0.541298 | 0.0286887 | ||||||||
\(357\) | 28.8522 | 1.52702 | ||||||||
\(358\) | −11.3293 | −0.598771 | ||||||||
\(359\) | 7.97148 | 0.420719 | 0.210359 | − | 0.977624i | \(-0.432537\pi\) | ||||
0.210359 | + | 0.977624i | \(0.432537\pi\) | |||||||
\(360\) | 3.61798 | 0.190684 | ||||||||
\(361\) | 46.4554 | 2.44502 | ||||||||
\(362\) | −16.6110 | −0.873054 | ||||||||
\(363\) | 40.6383 | 2.13296 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.163089 | 0.00853648 | ||||||||
\(366\) | 1.75240 | 0.0915994 | ||||||||
\(367\) | −20.4864 | −1.06938 | −0.534690 | − | 0.845048i | \(-0.679572\pi\) | ||||
−0.534690 | + | 0.845048i | \(0.679572\pi\) | |||||||
\(368\) | −0.908568 | −0.0473624 | ||||||||
\(369\) | −6.40601 | −0.333484 | ||||||||
\(370\) | −1.63865 | −0.0851895 | ||||||||
\(371\) | 16.9939 | 0.882281 | ||||||||
\(372\) | 0.161208 | 0.00835826 | ||||||||
\(373\) | 14.4319 | 0.747254 | 0.373627 | − | 0.927579i | \(-0.378114\pi\) | ||||
0.373627 | + | 0.927579i | \(0.378114\pi\) | |||||||
\(374\) | −30.4919 | −1.57670 | ||||||||
\(375\) | −2.57254 | −0.132846 | ||||||||
\(376\) | −11.2024 | −0.577719 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.02697 | 0.155691 | ||||||||
\(379\) | −0.607528 | −0.0312066 | −0.0156033 | − | 0.999878i | \(-0.504967\pi\) | ||||
−0.0156033 | + | 0.999878i | \(0.504967\pi\) | |||||||
\(380\) | −8.09045 | −0.415031 | ||||||||
\(381\) | 27.9726 | 1.43308 | ||||||||
\(382\) | −21.7130 | −1.11094 | ||||||||
\(383\) | −14.6778 | −0.749998 | −0.374999 | − | 0.927025i | \(-0.622357\pi\) | ||||
−0.374999 | + | 0.927025i | \(0.622357\pi\) | |||||||
\(384\) | −2.57254 | −0.131280 | ||||||||
\(385\) | −9.85635 | −0.502326 | ||||||||
\(386\) | 11.3641 | 0.578418 | ||||||||
\(387\) | −31.0776 | −1.57976 | ||||||||
\(388\) | −12.8001 | −0.649829 | ||||||||
\(389\) | 18.6299 | 0.944572 | 0.472286 | − | 0.881445i | \(-0.343429\pi\) | ||||
0.472286 | + | 0.881445i | \(0.343429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.35180 | 0.270652 | ||||||||
\(392\) | 3.37468 | 0.170447 | ||||||||
\(393\) | 2.90806 | 0.146692 | ||||||||
\(394\) | 17.6398 | 0.888678 | ||||||||
\(395\) | −14.7178 | −0.740535 | ||||||||
\(396\) | −18.7287 | −0.941154 | ||||||||
\(397\) | −7.96619 | −0.399811 | −0.199906 | − | 0.979815i | \(-0.564064\pi\) | ||||
−0.199906 | + | 0.979815i | \(0.564064\pi\) | |||||||
\(398\) | 23.6305 | 1.18449 | ||||||||
\(399\) | −39.6286 | −1.98391 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 4.76351 | 0.237878 | 0.118939 | − | 0.992902i | \(-0.462051\pi\) | ||||
0.118939 | + | 0.992902i | \(0.462051\pi\) | |||||||
\(402\) | 36.3995 | 1.81544 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.59059 | 0.128886 | ||||||||
\(405\) | 6.76417 | 0.336114 | ||||||||
\(406\) | −10.0905 | −0.500782 | ||||||||
\(407\) | 8.48261 | 0.420467 | ||||||||
\(408\) | 15.1532 | 0.750196 | ||||||||
\(409\) | 9.59521 | 0.474452 | 0.237226 | − | 0.971454i | \(-0.423762\pi\) | ||||
0.237226 | + | 0.971454i | \(0.423762\pi\) | |||||||
\(410\) | −1.77061 | −0.0874440 | ||||||||
\(411\) | 28.1411 | 1.38810 | ||||||||
\(412\) | −1.77799 | −0.0875953 | ||||||||
\(413\) | 20.3288 | 1.00032 | ||||||||
\(414\) | 3.28718 | 0.161556 | ||||||||
\(415\) | −1.89246 | −0.0928971 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.0764 | −0.542413 | ||||||||
\(418\) | 41.8808 | 2.04846 | ||||||||
\(419\) | 17.0041 | 0.830707 | 0.415353 | − | 0.909660i | \(-0.363658\pi\) | ||||
0.415353 | + | 0.909660i | \(0.363658\pi\) | |||||||
\(420\) | 4.89819 | 0.239007 | ||||||||
\(421\) | 11.3647 | 0.553882 | 0.276941 | − | 0.960887i | \(-0.410679\pi\) | ||||
0.276941 | + | 0.960887i | \(0.410679\pi\) | |||||||
\(422\) | 15.2360 | 0.741677 | ||||||||
\(423\) | 40.5300 | 1.97064 | ||||||||
\(424\) | 8.92525 | 0.433449 | ||||||||
\(425\) | −5.89037 | −0.285725 | ||||||||
\(426\) | 40.3933 | 1.95706 | ||||||||
\(427\) | 1.29701 | 0.0627668 | ||||||||
\(428\) | 3.56829 | 0.172480 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.58977 | −0.414236 | ||||||||
\(431\) | −22.6058 | −1.08888 | −0.544441 | − | 0.838799i | \(-0.683258\pi\) | ||||
−0.544441 | + | 0.838799i | \(0.683258\pi\) | |||||||
\(432\) | 1.58977 | 0.0764880 | ||||||||
\(433\) | 2.99497 | 0.143929 | 0.0719645 | − | 0.997407i | \(-0.477073\pi\) | ||||
0.0719645 | + | 0.997407i | \(0.477073\pi\) | |||||||
\(434\) | 0.119316 | 0.00572734 | ||||||||
\(435\) | 13.6333 | 0.653666 | ||||||||
\(436\) | 11.4449 | 0.548112 | ||||||||
\(437\) | −7.35072 | −0.351633 | ||||||||
\(438\) | 0.419554 | 0.0200471 | ||||||||
\(439\) | 13.4489 | 0.641881 | 0.320940 | − | 0.947099i | \(-0.396001\pi\) | ||||
0.320940 | + | 0.947099i | \(0.396001\pi\) | |||||||
\(440\) | −5.17658 | −0.246784 | ||||||||
\(441\) | −12.2095 | −0.581405 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.6206 | −0.789671 | −0.394835 | − | 0.918752i | \(-0.629198\pi\) | ||||
−0.394835 | + | 0.918752i | \(0.629198\pi\) | |||||||
\(444\) | −4.21550 | −0.200059 | ||||||||
\(445\) | −0.541298 | −0.0256600 | ||||||||
\(446\) | −2.78265 | −0.131762 | ||||||||
\(447\) | 49.5211 | 2.34227 | ||||||||
\(448\) | −1.90403 | −0.0899569 | ||||||||
\(449\) | −14.0974 | −0.665298 | −0.332649 | − | 0.943051i | \(-0.607942\pi\) | ||||
−0.332649 | + | 0.943051i | \(0.607942\pi\) | |||||||
\(450\) | −3.61798 | −0.170553 | ||||||||
\(451\) | 9.16567 | 0.431595 | ||||||||
\(452\) | 11.2334 | 0.528373 | ||||||||
\(453\) | 20.3578 | 0.956492 | ||||||||
\(454\) | −3.94347 | −0.185076 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.8130 | −0.974660 | ||||||||
\(457\) | 26.2785 | 1.22926 | 0.614628 | − | 0.788817i | \(-0.289306\pi\) | ||||
0.614628 | + | 0.788817i | \(0.289306\pi\) | |||||||
\(458\) | 10.3809 | 0.485066 | ||||||||
\(459\) | −9.36435 | −0.437090 | ||||||||
\(460\) | 0.908568 | 0.0423622 | ||||||||
\(461\) | 2.52721 | 0.117704 | 0.0588520 | − | 0.998267i | \(-0.481256\pi\) | ||||
0.0588520 | + | 0.998267i | \(0.481256\pi\) | |||||||
\(462\) | −25.3559 | −1.17966 | ||||||||
\(463\) | −20.9477 | −0.973522 | −0.486761 | − | 0.873535i | \(-0.661822\pi\) | ||||
−0.486761 | + | 0.873535i | \(0.661822\pi\) | |||||||
\(464\) | −5.29954 | −0.246025 | ||||||||
\(465\) | −0.161208 | −0.00747586 | ||||||||
\(466\) | 13.2410 | 0.613379 | ||||||||
\(467\) | −19.2552 | −0.891023 | −0.445511 | − | 0.895276i | \(-0.646978\pi\) | ||||
−0.445511 | + | 0.895276i | \(0.646978\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.9405 | 1.24400 | ||||||||
\(470\) | 11.2024 | 0.516728 | ||||||||
\(471\) | −2.43408 | −0.112156 | ||||||||
\(472\) | 10.6767 | 0.491437 | ||||||||
\(473\) | 44.4656 | 2.04453 | ||||||||
\(474\) | −37.8623 | −1.73907 | ||||||||
\(475\) | 8.09045 | 0.371215 | ||||||||
\(476\) | 11.2154 | 0.514058 | ||||||||
\(477\) | −32.2914 | −1.47852 | ||||||||
\(478\) | 24.3290 | 1.11278 | ||||||||
\(479\) | 22.9230 | 1.04738 | 0.523689 | − | 0.851910i | \(-0.324555\pi\) | ||||
0.523689 | + | 0.851910i | \(0.324555\pi\) | |||||||
\(480\) | 2.57254 | 0.117420 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −11.1983 | −0.510071 | ||||||||
\(483\) | 4.45034 | 0.202498 | ||||||||
\(484\) | 15.7969 | 0.718043 | ||||||||
\(485\) | 12.8001 | 0.581225 | ||||||||
\(486\) | 22.1704 | 1.00567 | ||||||||
\(487\) | 27.0722 | 1.22676 | 0.613379 | − | 0.789789i | \(-0.289810\pi\) | ||||
0.613379 | + | 0.789789i | \(0.289810\pi\) | |||||||
\(488\) | 0.681193 | 0.0308362 | ||||||||
\(489\) | −11.6091 | −0.524981 | ||||||||
\(490\) | −3.37468 | −0.152452 | ||||||||
\(491\) | −14.7213 | −0.664363 | −0.332182 | − | 0.943215i | \(-0.607785\pi\) | ||||
−0.332182 | + | 0.943215i | \(0.607785\pi\) | |||||||
\(492\) | −4.55496 | −0.205353 | ||||||||
\(493\) | 31.2162 | 1.40591 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.7287 | 0.841794 | ||||||||
\(496\) | 0.0626650 | 0.00281374 | ||||||||
\(497\) | 29.8965 | 1.34104 | ||||||||
\(498\) | −4.86843 | −0.218160 | ||||||||
\(499\) | 4.24391 | 0.189984 | 0.0949918 | − | 0.995478i | \(-0.469718\pi\) | ||||
0.0949918 | + | 0.995478i | \(0.469718\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 5.05083 | 0.225654 | ||||||||
\(502\) | −5.81385 | −0.259485 | ||||||||
\(503\) | −9.57492 | −0.426925 | −0.213462 | − | 0.976951i | \(-0.568474\pi\) | ||||
−0.213462 | + | 0.976951i | \(0.568474\pi\) | |||||||
\(504\) | 6.88873 | 0.306848 | ||||||||
\(505\) | −2.59059 | −0.115280 | ||||||||
\(506\) | −4.70327 | −0.209086 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.8735 | 0.482435 | ||||||||
\(509\) | −33.5783 | −1.48833 | −0.744165 | − | 0.667995i | \(-0.767153\pi\) | ||||
−0.744165 | + | 0.667995i | \(0.767153\pi\) | |||||||
\(510\) | −15.1532 | −0.670996 | ||||||||
\(511\) | 0.310526 | 0.0137369 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.8620 | 0.567870 | ||||||||
\(514\) | 29.1850 | 1.28729 | ||||||||
\(515\) | 1.77799 | 0.0783476 | ||||||||
\(516\) | −22.0976 | −0.972791 | ||||||||
\(517\) | −57.9900 | −2.55040 | ||||||||
\(518\) | −3.12004 | −0.137087 | ||||||||
\(519\) | 26.4321 | 1.16024 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.45328 | 0.107480 | 0.0537400 | − | 0.998555i | \(-0.482886\pi\) | ||||
0.0537400 | + | 0.998555i | \(0.482886\pi\) | |||||||
\(522\) | 19.1736 | 0.839206 | ||||||||
\(523\) | −28.1579 | −1.23126 | −0.615630 | − | 0.788035i | \(-0.711098\pi\) | ||||
−0.615630 | + | 0.788035i | \(0.711098\pi\) | |||||||
\(524\) | 1.13042 | 0.0493827 | ||||||||
\(525\) | −4.89819 | −0.213775 | ||||||||
\(526\) | −27.5544 | −1.20143 | ||||||||
\(527\) | −0.369120 | −0.0160791 | ||||||||
\(528\) | −13.3170 | −0.579546 | ||||||||
\(529\) | −22.1745 | −0.964109 | ||||||||
\(530\) | −8.92525 | −0.387688 | ||||||||
\(531\) | −38.6282 | −1.67632 | ||||||||
\(532\) | −15.4044 | −0.667867 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.39251 | −0.0602599 | ||||||||
\(535\) | −3.56829 | −0.154271 | ||||||||
\(536\) | 14.1492 | 0.611153 | ||||||||
\(537\) | 29.1450 | 1.25770 | ||||||||
\(538\) | −3.97887 | −0.171541 | ||||||||
\(539\) | 17.4693 | 0.752455 | ||||||||
\(540\) | −1.58977 | −0.0684130 | ||||||||
\(541\) | −21.4643 | −0.922820 | −0.461410 | − | 0.887187i | \(-0.652656\pi\) | ||||
−0.461410 | + | 0.887187i | \(0.652656\pi\) | |||||||
\(542\) | 13.6399 | 0.585885 | ||||||||
\(543\) | 42.7325 | 1.83383 | ||||||||
\(544\) | 5.89037 | 0.252547 | ||||||||
\(545\) | −11.4449 | −0.490247 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0076 | 0.727192 | 0.363596 | − | 0.931557i | \(-0.381549\pi\) | ||||
0.363596 | + | 0.931557i | \(0.381549\pi\) | |||||||
\(548\) | 10.9390 | 0.467292 | ||||||||
\(549\) | −2.46454 | −0.105184 | ||||||||
\(550\) | 5.17658 | 0.220730 | ||||||||
\(551\) | −42.8756 | −1.82656 | ||||||||
\(552\) | 2.33733 | 0.0994834 | ||||||||
\(553\) | −28.0232 | −1.19167 | ||||||||
\(554\) | 2.30543 | 0.0979484 | ||||||||
\(555\) | 4.21550 | 0.178938 | ||||||||
\(556\) | −4.30562 | −0.182599 | ||||||||
\(557\) | −3.62480 | −0.153588 | −0.0767938 | − | 0.997047i | \(-0.524468\pi\) | ||||
−0.0767938 | + | 0.997047i | \(0.524468\pi\) | |||||||
\(558\) | −0.226720 | −0.00959784 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.90403 | 0.0804599 | ||||||||
\(561\) | 78.4418 | 3.31182 | ||||||||
\(562\) | −21.0557 | −0.888180 | ||||||||
\(563\) | −40.7538 | −1.71757 | −0.858783 | − | 0.512339i | \(-0.828779\pi\) | ||||
−0.858783 | + | 0.512339i | \(0.828779\pi\) | |||||||
\(564\) | 28.8186 | 1.21348 | ||||||||
\(565\) | −11.2334 | −0.472591 | ||||||||
\(566\) | 2.60164 | 0.109355 | ||||||||
\(567\) | 12.8792 | 0.540874 | ||||||||
\(568\) | 15.7017 | 0.658829 | ||||||||
\(569\) | 31.7297 | 1.33018 | 0.665089 | − | 0.746764i | \(-0.268394\pi\) | ||||
0.665089 | + | 0.746764i | \(0.268394\pi\) | |||||||
\(570\) | 20.8130 | 0.871762 | ||||||||
\(571\) | −14.5697 | −0.609722 | −0.304861 | − | 0.952397i | \(-0.598610\pi\) | ||||
−0.304861 | + | 0.952397i | \(0.598610\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 55.8577 | 2.33349 | ||||||||
\(574\) | −3.37128 | −0.140715 | ||||||||
\(575\) | −0.908568 | −0.0378899 | ||||||||
\(576\) | 3.61798 | 0.150749 | ||||||||
\(577\) | 5.78013 | 0.240630 | 0.120315 | − | 0.992736i | \(-0.461610\pi\) | ||||
0.120315 | + | 0.992736i | \(0.461610\pi\) | |||||||
\(578\) | −17.6964 | −0.736075 | ||||||||
\(579\) | −29.2347 | −1.21495 | ||||||||
\(580\) | 5.29954 | 0.220051 | ||||||||
\(581\) | −3.60329 | −0.149490 | ||||||||
\(582\) | 32.9289 | 1.36495 | ||||||||
\(583\) | 46.2023 | 1.91350 | ||||||||
\(584\) | 0.163089 | 0.00674868 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.46826 | 0.267201 | ||||||||
\(587\) | 1.46614 | 0.0605139 | 0.0302570 | − | 0.999542i | \(-0.490367\pi\) | ||||
0.0302570 | + | 0.999542i | \(0.490367\pi\) | |||||||
\(588\) | −8.68150 | −0.358019 | ||||||||
\(589\) | 0.506988 | 0.0208901 | ||||||||
\(590\) | −10.6767 | −0.439554 | ||||||||
\(591\) | −45.3790 | −1.86664 | ||||||||
\(592\) | −1.63865 | −0.0673482 | ||||||||
\(593\) | −25.7264 | −1.05646 | −0.528228 | − | 0.849103i | \(-0.677143\pi\) | ||||
−0.528228 | + | 0.849103i | \(0.677143\pi\) | |||||||
\(594\) | 8.22958 | 0.337664 | ||||||||
\(595\) | −11.2154 | −0.459788 | ||||||||
\(596\) | 19.2499 | 0.788505 | ||||||||
\(597\) | −60.7906 | −2.48799 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7207 | −1.09178 | −0.545890 | − | 0.837857i | \(-0.683808\pi\) | ||||
−0.545890 | + | 0.837857i | \(0.683808\pi\) | |||||||
\(600\) | −2.57254 | −0.105024 | ||||||||
\(601\) | 26.9562 | 1.09956 | 0.549782 | − | 0.835308i | \(-0.314711\pi\) | ||||
0.549782 | + | 0.835308i | \(0.314711\pi\) | |||||||
\(602\) | −16.3552 | −0.666587 | ||||||||
\(603\) | −51.1915 | −2.08468 | ||||||||
\(604\) | 7.91349 | 0.321995 | ||||||||
\(605\) | −15.7969 | −0.642237 | ||||||||
\(606\) | −6.66439 | −0.270722 | ||||||||
\(607\) | −32.3286 | −1.31218 | −0.656088 | − | 0.754684i | \(-0.727790\pi\) | ||||
−0.656088 | + | 0.754684i | \(0.727790\pi\) | |||||||
\(608\) | −8.09045 | −0.328111 | ||||||||
\(609\) | 25.9582 | 1.05188 | ||||||||
\(610\) | −0.681193 | −0.0275807 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −21.3112 | −0.861455 | ||||||||
\(613\) | −10.2117 | −0.412447 | −0.206224 | − | 0.978505i | \(-0.566117\pi\) | ||||
−0.206224 | + | 0.978505i | \(0.566117\pi\) | |||||||
\(614\) | −11.7707 | −0.475027 | ||||||||
\(615\) | 4.55496 | 0.183674 | ||||||||
\(616\) | −9.85635 | −0.397123 | ||||||||
\(617\) | 32.6071 | 1.31271 | 0.656356 | − | 0.754452i | \(-0.272097\pi\) | ||||
0.656356 | + | 0.754452i | \(0.272097\pi\) | |||||||
\(618\) | 4.57395 | 0.183991 | ||||||||
\(619\) | 8.49492 | 0.341440 | 0.170720 | − | 0.985320i | \(-0.445391\pi\) | ||||
0.170720 | + | 0.985320i | \(0.445391\pi\) | |||||||
\(620\) | −0.0626650 | −0.00251669 | ||||||||
\(621\) | −1.44442 | −0.0579625 | ||||||||
\(622\) | −2.09362 | −0.0839465 | ||||||||
\(623\) | −1.03065 | −0.0412920 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.7645 | 0.989787 | ||||||||
\(627\) | −107.740 | −4.30273 | ||||||||
\(628\) | −0.946176 | −0.0377565 | ||||||||
\(629\) | 9.65226 | 0.384861 | ||||||||
\(630\) | −6.88873 | −0.274454 | ||||||||
\(631\) | −41.4992 | −1.65206 | −0.826029 | − | 0.563628i | \(-0.809405\pi\) | ||||
−0.826029 | + | 0.563628i | \(0.809405\pi\) | |||||||
\(632\) | −14.7178 | −0.585444 | ||||||||
\(633\) | −39.1953 | −1.55787 | ||||||||
\(634\) | 20.9473 | 0.831924 | ||||||||
\(635\) | −10.8735 | −0.431503 | ||||||||
\(636\) | −22.9606 | −0.910447 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −27.4335 | −1.08610 | ||||||||
\(639\) | −56.8084 | −2.24731 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 17.9976 | 0.710862 | 0.355431 | − | 0.934703i | \(-0.384334\pi\) | ||||
0.355431 | + | 0.934703i | \(0.384334\pi\) | |||||||
\(642\) | −9.17957 | −0.362289 | ||||||||
\(643\) | −24.9350 | −0.983342 | −0.491671 | − | 0.870781i | \(-0.663614\pi\) | ||||
−0.491671 | + | 0.870781i | \(0.663614\pi\) | |||||||
\(644\) | 1.72994 | 0.0681691 | ||||||||
\(645\) | 22.0976 | 0.870091 | ||||||||
\(646\) | 47.6557 | 1.87499 | ||||||||
\(647\) | −31.5515 | −1.24042 | −0.620209 | − | 0.784437i | \(-0.712952\pi\) | ||||
−0.620209 | + | 0.784437i | \(0.712952\pi\) | |||||||
\(648\) | 6.76417 | 0.265722 | ||||||||
\(649\) | 55.2690 | 2.16950 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.306945 | −0.0120301 | ||||||||
\(652\) | −4.51269 | −0.176731 | ||||||||
\(653\) | 8.31180 | 0.325266 | 0.162633 | − | 0.986687i | \(-0.448001\pi\) | ||||
0.162633 | + | 0.986687i | \(0.448001\pi\) | |||||||
\(654\) | −29.4426 | −1.15130 | ||||||||
\(655\) | −1.13042 | −0.0441692 | ||||||||
\(656\) | −1.77061 | −0.0691305 | ||||||||
\(657\) | −0.590053 | −0.0230202 | ||||||||
\(658\) | 21.3297 | 0.831517 | ||||||||
\(659\) | −4.11647 | −0.160355 | −0.0801774 | − | 0.996781i | \(-0.525549\pi\) | ||||
−0.0801774 | + | 0.996781i | \(0.525549\pi\) | |||||||
\(660\) | 13.3170 | 0.518362 | ||||||||
\(661\) | 39.4880 | 1.53591 | 0.767953 | − | 0.640506i | \(-0.221276\pi\) | ||||
0.767953 | + | 0.640506i | \(0.221276\pi\) | |||||||
\(662\) | −21.2478 | −0.825821 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.89246 | −0.0734416 | ||||||||
\(665\) | 15.4044 | 0.597359 | ||||||||
\(666\) | 5.92861 | 0.229729 | ||||||||
\(667\) | 4.81499 | 0.186437 | ||||||||
\(668\) | 1.96336 | 0.0759647 | ||||||||
\(669\) | 7.15847 | 0.276763 | ||||||||
\(670\) | −14.1492 | −0.546632 | ||||||||
\(671\) | 3.52625 | 0.136129 | ||||||||
\(672\) | 4.89819 | 0.188952 | ||||||||
\(673\) | −30.1004 | −1.16028 | −0.580142 | − | 0.814515i | \(-0.697003\pi\) | ||||
−0.580142 | + | 0.814515i | \(0.697003\pi\) | |||||||
\(674\) | −11.8333 | −0.455803 | ||||||||
\(675\) | 1.58977 | 0.0611904 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8446 | 0.608959 | 0.304479 | − | 0.952519i | \(-0.401518\pi\) | ||||
0.304479 | + | 0.952519i | \(0.401518\pi\) | |||||||
\(678\) | −28.8983 | −1.10983 | ||||||||
\(679\) | 24.3718 | 0.935305 | ||||||||
\(680\) | −5.89037 | −0.225885 | ||||||||
\(681\) | 10.1447 | 0.388747 | ||||||||
\(682\) | 0.324390 | 0.0124215 | ||||||||
\(683\) | −3.74741 | −0.143391 | −0.0716954 | − | 0.997427i | \(-0.522841\pi\) | ||||
−0.0716954 | + | 0.997427i | \(0.522841\pi\) | |||||||
\(684\) | 29.2711 | 1.11921 | ||||||||
\(685\) | −10.9390 | −0.417959 | ||||||||
\(686\) | −19.7537 | −0.754199 | ||||||||
\(687\) | −26.7052 | −1.01887 | ||||||||
\(688\) | −8.58977 | −0.327482 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2.33733 | −0.0889806 | ||||||||
\(691\) | −49.7932 | −1.89422 | −0.947111 | − | 0.320905i | \(-0.896013\pi\) | ||||
−0.947111 | + | 0.320905i | \(0.896013\pi\) | |||||||
\(692\) | 10.2747 | 0.390585 | ||||||||
\(693\) | 35.6600 | 1.35461 | ||||||||
\(694\) | 21.3904 | 0.811969 | ||||||||
\(695\) | 4.30562 | 0.163321 | ||||||||
\(696\) | 13.6333 | 0.516768 | ||||||||
\(697\) | 10.4295 | 0.395046 | ||||||||
\(698\) | −18.5446 | −0.701924 | ||||||||
\(699\) | −34.0631 | −1.28839 | ||||||||
\(700\) | −1.90403 | −0.0719655 | ||||||||
\(701\) | 32.9089 | 1.24295 | 0.621476 | − | 0.783434i | \(-0.286534\pi\) | ||||
0.621476 | + | 0.783434i | \(0.286534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.2574 | −0.500014 | ||||||||
\(704\) | −5.17658 | −0.195100 | ||||||||
\(705\) | −28.8186 | −1.08537 | ||||||||
\(706\) | 11.2265 | 0.422515 | ||||||||
\(707\) | −4.93255 | −0.185508 | ||||||||
\(708\) | −27.4664 | −1.03225 | ||||||||
\(709\) | 23.1678 | 0.870083 | 0.435042 | − | 0.900410i | \(-0.356734\pi\) | ||||
0.435042 | + | 0.900410i | \(0.356734\pi\) | |||||||
\(710\) | −15.7017 | −0.589275 | ||||||||
\(711\) | 53.2488 | 1.99699 | ||||||||
\(712\) | −0.541298 | −0.0202860 | ||||||||
\(713\) | −0.0569354 | −0.00213225 | ||||||||
\(714\) | −28.8522 | −1.07977 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.3293 | 0.423395 | ||||||||
\(717\) | −62.5874 | −2.33737 | ||||||||
\(718\) | −7.97148 | −0.297493 | ||||||||
\(719\) | 4.76483 | 0.177698 | 0.0888491 | − | 0.996045i | \(-0.471681\pi\) | ||||
0.0888491 | + | 0.996045i | \(0.471681\pi\) | |||||||
\(720\) | −3.61798 | −0.134834 | ||||||||
\(721\) | 3.38534 | 0.126077 | ||||||||
\(722\) | −46.4554 | −1.72889 | ||||||||
\(723\) | 28.8082 | 1.07139 | ||||||||
\(724\) | 16.6110 | 0.617342 | ||||||||
\(725\) | −5.29954 | −0.196820 | ||||||||
\(726\) | −40.6383 | −1.50823 | ||||||||
\(727\) | 42.5004 | 1.57625 | 0.788127 | − | 0.615513i | \(-0.211051\pi\) | ||||
0.788127 | + | 0.615513i | \(0.211051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.7419 | −1.36081 | ||||||||
\(730\) | −0.163089 | −0.00603620 | ||||||||
\(731\) | 50.5969 | 1.87139 | ||||||||
\(732\) | −1.75240 | −0.0647705 | ||||||||
\(733\) | 10.3609 | 0.382689 | 0.191345 | − | 0.981523i | \(-0.438715\pi\) | ||||
0.191345 | + | 0.981523i | \(0.438715\pi\) | |||||||
\(734\) | 20.4864 | 0.756166 | ||||||||
\(735\) | 8.68150 | 0.320222 | ||||||||
\(736\) | 0.908568 | 0.0334903 | ||||||||
\(737\) | 73.2445 | 2.69800 | ||||||||
\(738\) | 6.40601 | 0.235808 | ||||||||
\(739\) | 25.9157 | 0.953324 | 0.476662 | − | 0.879087i | \(-0.341846\pi\) | ||||
0.476662 | + | 0.879087i | \(0.341846\pi\) | |||||||
\(740\) | 1.63865 | 0.0602380 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.9939 | −0.623867 | ||||||||
\(743\) | −9.84397 | −0.361140 | −0.180570 | − | 0.983562i | \(-0.557794\pi\) | ||||
−0.180570 | + | 0.983562i | \(0.557794\pi\) | |||||||
\(744\) | −0.161208 | −0.00591018 | ||||||||
\(745\) | −19.2499 | −0.705260 | ||||||||
\(746\) | −14.4319 | −0.528388 | ||||||||
\(747\) | 6.84687 | 0.250514 | ||||||||
\(748\) | 30.4919 | 1.11490 | ||||||||
\(749\) | −6.79412 | −0.248252 | ||||||||
\(750\) | 2.57254 | 0.0939360 | ||||||||
\(751\) | −48.3807 | −1.76544 | −0.882718 | − | 0.469903i | \(-0.844289\pi\) | ||||
−0.882718 | + | 0.469903i | \(0.844289\pi\) | |||||||
\(752\) | 11.2024 | 0.408509 | ||||||||
\(753\) | 14.9564 | 0.545041 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.91349 | −0.288001 | ||||||||
\(756\) | −3.02697 | −0.110090 | ||||||||
\(757\) | −10.3630 | −0.376649 | −0.188324 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188324 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(758\) | 0.607528 | 0.0220664 | ||||||||
\(759\) | 12.0994 | 0.439179 | ||||||||
\(760\) | 8.09045 | 0.293471 | ||||||||
\(761\) | 24.0420 | 0.871521 | 0.435760 | − | 0.900063i | \(-0.356480\pi\) | ||||
0.435760 | + | 0.900063i | \(0.356480\pi\) | |||||||
\(762\) | −27.9726 | −1.01334 | ||||||||
\(763\) | −21.7915 | −0.788904 | ||||||||
\(764\) | 21.7130 | 0.785550 | ||||||||
\(765\) | 21.3112 | 0.770509 | ||||||||
\(766\) | 14.6778 | 0.530329 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.57254 | 0.0928286 | ||||||||
\(769\) | −11.4605 | −0.413277 | −0.206639 | − | 0.978417i | \(-0.566252\pi\) | ||||
−0.206639 | + | 0.978417i | \(0.566252\pi\) | |||||||
\(770\) | 9.85635 | 0.355198 | ||||||||
\(771\) | −75.0796 | −2.70393 | ||||||||
\(772\) | −11.3641 | −0.409003 | ||||||||
\(773\) | 0.507988 | 0.0182711 | 0.00913553 | − | 0.999958i | \(-0.497092\pi\) | ||||
0.00913553 | + | 0.999958i | \(0.497092\pi\) | |||||||
\(774\) | 31.0776 | 1.11706 | ||||||||
\(775\) | 0.0626650 | 0.00225099 | ||||||||
\(776\) | 12.8001 | 0.459498 | ||||||||
\(777\) | 8.02643 | 0.287947 | ||||||||
\(778\) | −18.6299 | −0.667914 | ||||||||
\(779\) | −14.3250 | −0.513246 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 81.2811 | 2.90847 | ||||||||
\(782\) | −5.35180 | −0.191380 | ||||||||
\(783\) | −8.42506 | −0.301087 | ||||||||
\(784\) | −3.37468 | −0.120524 | ||||||||
\(785\) | 0.946176 | 0.0337705 | ||||||||
\(786\) | −2.90806 | −0.103727 | ||||||||
\(787\) | 27.4018 | 0.976769 | 0.488384 | − | 0.872629i | \(-0.337586\pi\) | ||||
0.488384 | + | 0.872629i | \(0.337586\pi\) | |||||||
\(788\) | −17.6398 | −0.628390 | ||||||||
\(789\) | 70.8849 | 2.52357 | ||||||||
\(790\) | 14.7178 | 0.523637 | ||||||||
\(791\) | −21.3886 | −0.760493 | ||||||||
\(792\) | 18.7287 | 0.665497 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 7.96619 | 0.282709 | ||||||||
\(795\) | 22.9606 | 0.814328 | ||||||||
\(796\) | −23.6305 | −0.837562 | ||||||||
\(797\) | −2.46568 | −0.0873388 | −0.0436694 | − | 0.999046i | \(-0.513905\pi\) | ||||
−0.0436694 | + | 0.999046i | \(0.513905\pi\) | |||||||
\(798\) | 39.6286 | 1.40284 | ||||||||
\(799\) | −65.9862 | −2.33442 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 1.95840 | 0.0691968 | ||||||||
\(802\) | −4.76351 | −0.168205 | ||||||||
\(803\) | 0.844244 | 0.0297927 | ||||||||
\(804\) | −36.3995 | −1.28371 | ||||||||
\(805\) | −1.72994 | −0.0609723 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.2358 | 0.360318 | ||||||||
\(808\) | −2.59059 | −0.0911365 | ||||||||
\(809\) | 1.54477 | 0.0543112 | 0.0271556 | − | 0.999631i | \(-0.491355\pi\) | ||||
0.0271556 | + | 0.999631i | \(0.491355\pi\) | |||||||
\(810\) | −6.76417 | −0.237669 | ||||||||
\(811\) | −26.1714 | −0.919003 | −0.459502 | − | 0.888177i | \(-0.651972\pi\) | ||||
−0.459502 | + | 0.888177i | \(0.651972\pi\) | |||||||
\(812\) | 10.0905 | 0.354106 | ||||||||
\(813\) | −35.0893 | −1.23064 | ||||||||
\(814\) | −8.48261 | −0.297315 | ||||||||
\(815\) | 4.51269 | 0.158073 | ||||||||
\(816\) | −15.1532 | −0.530469 | ||||||||
\(817\) | −69.4951 | −2.43133 | ||||||||
\(818\) | −9.59521 | −0.335489 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.77061 | 0.0618322 | ||||||||
\(821\) | −41.5128 | −1.44881 | −0.724403 | − | 0.689377i | \(-0.757884\pi\) | ||||
−0.724403 | + | 0.689377i | \(0.757884\pi\) | |||||||
\(822\) | −28.1411 | −0.981534 | ||||||||
\(823\) | −17.6447 | −0.615056 | −0.307528 | − | 0.951539i | \(-0.599502\pi\) | ||||
−0.307528 | + | 0.951539i | \(0.599502\pi\) | |||||||
\(824\) | 1.77799 | 0.0619392 | ||||||||
\(825\) | −13.3170 | −0.463637 | ||||||||
\(826\) | −20.3288 | −0.707330 | ||||||||
\(827\) | −30.1723 | −1.04919 | −0.524596 | − | 0.851351i | \(-0.675784\pi\) | ||||
−0.524596 | + | 0.851351i | \(0.675784\pi\) | |||||||
\(828\) | −3.28718 | −0.114237 | ||||||||
\(829\) | 19.3250 | 0.671185 | 0.335593 | − | 0.942007i | \(-0.391063\pi\) | ||||
0.335593 | + | 0.942007i | \(0.391063\pi\) | |||||||
\(830\) | 1.89246 | 0.0656882 | ||||||||
\(831\) | −5.93082 | −0.205738 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.8781 | 0.688735 | ||||||||
\(834\) | 11.0764 | 0.383544 | ||||||||
\(835\) | −1.96336 | −0.0679449 | ||||||||
\(836\) | −41.8808 | −1.44848 | ||||||||
\(837\) | 0.0996231 | 0.00344348 | ||||||||
\(838\) | −17.0041 | −0.587398 | ||||||||
\(839\) | 3.98927 | 0.137725 | 0.0688625 | − | 0.997626i | \(-0.478063\pi\) | ||||
0.0688625 | + | 0.997626i | \(0.478063\pi\) | |||||||
\(840\) | −4.89819 | −0.169004 | ||||||||
\(841\) | −0.914902 | −0.0315483 | ||||||||
\(842\) | −11.3647 | −0.391654 | ||||||||
\(843\) | 54.1666 | 1.86560 | ||||||||
\(844\) | −15.2360 | −0.524445 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −40.5300 | −1.39345 | ||||||||
\(847\) | −30.0778 | −1.03349 | ||||||||
\(848\) | −8.92525 | −0.306494 | ||||||||
\(849\) | −6.69283 | −0.229697 | ||||||||
\(850\) | 5.89037 | 0.202038 | ||||||||
\(851\) | 1.48883 | 0.0510363 | ||||||||
\(852\) | −40.3933 | −1.38385 | ||||||||
\(853\) | −0.0825760 | −0.00282735 | −0.00141367 | − | 0.999999i | \(-0.500450\pi\) | ||||
−0.00141367 | + | 0.999999i | \(0.500450\pi\) | |||||||
\(854\) | −1.29701 | −0.0443828 | ||||||||
\(855\) | −29.2711 | −1.00105 | ||||||||
\(856\) | −3.56829 | −0.121962 | ||||||||
\(857\) | −33.2315 | −1.13517 | −0.567584 | − | 0.823316i | \(-0.692122\pi\) | ||||
−0.567584 | + | 0.823316i | \(0.692122\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0394 | −0.376658 | −0.188329 | − | 0.982106i | \(-0.560307\pi\) | ||||
−0.188329 | + | 0.982106i | \(0.560307\pi\) | |||||||
\(860\) | 8.58977 | 0.292909 | ||||||||
\(861\) | 8.67277 | 0.295567 | ||||||||
\(862\) | 22.6058 | 0.769957 | ||||||||
\(863\) | −22.7798 | −0.775432 | −0.387716 | − | 0.921779i | \(-0.626736\pi\) | ||||
−0.387716 | + | 0.921779i | \(0.626736\pi\) | |||||||
\(864\) | −1.58977 | −0.0540852 | ||||||||
\(865\) | −10.2747 | −0.349350 | ||||||||
\(866\) | −2.99497 | −0.101773 | ||||||||
\(867\) | 45.5248 | 1.54610 | ||||||||
\(868\) | −0.119316 | −0.00404984 | ||||||||
\(869\) | −76.1880 | −2.58450 | ||||||||
\(870\) | −13.6333 | −0.462212 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11.4449 | −0.387574 | ||||||||
\(873\) | −46.3106 | −1.56738 | ||||||||
\(874\) | 7.35072 | 0.248642 | ||||||||
\(875\) | 1.90403 | 0.0643679 | ||||||||
\(876\) | −0.419554 | −0.0141754 | ||||||||
\(877\) | 33.3282 | 1.12541 | 0.562706 | − | 0.826657i | \(-0.309760\pi\) | ||||
0.562706 | + | 0.826657i | \(0.309760\pi\) | |||||||
\(878\) | −13.4489 | −0.453878 | ||||||||
\(879\) | −16.6399 | −0.561249 | ||||||||
\(880\) | 5.17658 | 0.174502 | ||||||||
\(881\) | 20.8588 | 0.702750 | 0.351375 | − | 0.936235i | \(-0.385714\pi\) | ||||
0.351375 | + | 0.936235i | \(0.385714\pi\) | |||||||
\(882\) | 12.2095 | 0.411115 | ||||||||
\(883\) | −38.2565 | −1.28743 | −0.643716 | − | 0.765264i | \(-0.722608\pi\) | ||||
−0.643716 | + | 0.765264i | \(0.722608\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.4664 | 0.923272 | ||||||||
\(886\) | 16.6206 | 0.558382 | ||||||||
\(887\) | 42.9534 | 1.44223 | 0.721117 | − | 0.692814i | \(-0.243629\pi\) | ||||
0.721117 | + | 0.692814i | \(0.243629\pi\) | |||||||
\(888\) | 4.21550 | 0.141463 | ||||||||
\(889\) | −20.7035 | −0.694373 | ||||||||
\(890\) | 0.541298 | 0.0181444 | ||||||||
\(891\) | 35.0152 | 1.17305 | ||||||||
\(892\) | 2.78265 | 0.0931699 | ||||||||
\(893\) | 90.6324 | 3.03290 | ||||||||
\(894\) | −49.5211 | −1.65623 | ||||||||
\(895\) | −11.3293 | −0.378696 | ||||||||
\(896\) | 1.90403 | 0.0636091 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.0974 | 0.470437 | ||||||||
\(899\) | −0.332095 | −0.0110760 | ||||||||
\(900\) | 3.61798 | 0.120599 | ||||||||
\(901\) | 52.5730 | 1.75146 | ||||||||
\(902\) | −9.16567 | −0.305184 | ||||||||
\(903\) | 42.0744 | 1.40015 | ||||||||
\(904\) | −11.2334 | −0.373616 | ||||||||
\(905\) | −16.6110 | −0.552168 | ||||||||
\(906\) | −20.3578 | −0.676342 | ||||||||
\(907\) | −15.3490 | −0.509656 | −0.254828 | − | 0.966986i | \(-0.582019\pi\) | ||||
−0.254828 | + | 0.966986i | \(0.582019\pi\) | |||||||
\(908\) | 3.94347 | 0.130869 | ||||||||
\(909\) | 9.37268 | 0.310872 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.48652 | −0.248040 | −0.124020 | − | 0.992280i | \(-0.539579\pi\) | ||||
−0.124020 | + | 0.992280i | \(0.539579\pi\) | |||||||
\(912\) | 20.8130 | 0.689188 | ||||||||
\(913\) | −9.79646 | −0.324215 | ||||||||
\(914\) | −26.2785 | −0.869216 | ||||||||
\(915\) | 1.75240 | 0.0579325 | ||||||||
\(916\) | −10.3809 | −0.342993 | ||||||||
\(917\) | −2.15235 | −0.0710769 | ||||||||
\(918\) | 9.36435 | 0.309070 | ||||||||
\(919\) | −12.4412 | −0.410396 | −0.205198 | − | 0.978720i | \(-0.565784\pi\) | ||||
−0.205198 | + | 0.978720i | \(0.565784\pi\) | |||||||
\(920\) | −0.908568 | −0.0299546 | ||||||||
\(921\) | 30.2806 | 0.997780 | ||||||||
\(922\) | −2.52721 | −0.0832293 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 25.3559 | 0.834147 | ||||||||
\(925\) | −1.63865 | −0.0538785 | ||||||||
\(926\) | 20.9477 | 0.688384 | ||||||||
\(927\) | −6.43273 | −0.211278 | ||||||||
\(928\) | 5.29954 | 0.173966 | ||||||||
\(929\) | −22.5855 | −0.741007 | −0.370504 | − | 0.928831i | \(-0.620815\pi\) | ||||
−0.370504 | + | 0.928831i | \(0.620815\pi\) | |||||||
\(930\) | 0.161208 | 0.00528623 | ||||||||
\(931\) | −27.3027 | −0.894809 | ||||||||
\(932\) | −13.2410 | −0.433725 | ||||||||
\(933\) | 5.38592 | 0.176327 | ||||||||
\(934\) | 19.2552 | 0.630048 | ||||||||
\(935\) | −30.4919 | −0.997193 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.5615 | −0.671714 | −0.335857 | − | 0.941913i | \(-0.609026\pi\) | ||||
−0.335857 | + | 0.941913i | \(0.609026\pi\) | |||||||
\(938\) | −26.9405 | −0.879639 | ||||||||
\(939\) | −63.7076 | −2.07902 | ||||||||
\(940\) | −11.2024 | −0.365382 | ||||||||
\(941\) | −35.6763 | −1.16301 | −0.581506 | − | 0.813542i | \(-0.697536\pi\) | ||||
−0.581506 | + | 0.813542i | \(0.697536\pi\) | |||||||
\(942\) | 2.43408 | 0.0793066 | ||||||||
\(943\) | 1.60871 | 0.0523870 | ||||||||
\(944\) | −10.6767 | −0.347498 | ||||||||
\(945\) | 3.02697 | 0.0984674 | ||||||||
\(946\) | −44.4656 | −1.44570 | ||||||||
\(947\) | 16.0381 | 0.521167 | 0.260584 | − | 0.965451i | \(-0.416085\pi\) | ||||
0.260584 | + | 0.965451i | \(0.416085\pi\) | |||||||
\(948\) | 37.8623 | 1.22971 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.09045 | −0.262489 | ||||||||
\(951\) | −53.8879 | −1.74743 | ||||||||
\(952\) | −11.2154 | −0.363494 | ||||||||
\(953\) | −35.6022 | −1.15327 | −0.576634 | − | 0.817002i | \(-0.695634\pi\) | ||||
−0.576634 | + | 0.817002i | \(0.695634\pi\) | |||||||
\(954\) | 32.2914 | 1.04547 | ||||||||
\(955\) | −21.7130 | −0.702617 | ||||||||
\(956\) | −24.3290 | −0.786856 | ||||||||
\(957\) | 70.5738 | 2.28133 | ||||||||
\(958\) | −22.9230 | −0.740608 | ||||||||
\(959\) | −20.8282 | −0.672578 | ||||||||
\(960\) | −2.57254 | −0.0830285 | ||||||||
\(961\) | −30.9961 | −0.999873 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.9100 | 0.416018 | ||||||||
\(964\) | 11.1983 | 0.360674 | ||||||||
\(965\) | 11.3641 | 0.365824 | ||||||||
\(966\) | −4.45034 | −0.143187 | ||||||||
\(967\) | −8.36719 | −0.269071 | −0.134535 | − | 0.990909i | \(-0.542954\pi\) | ||||
−0.134535 | + | 0.990909i | \(0.542954\pi\) | |||||||
\(968\) | −15.7969 | −0.507733 | ||||||||
\(969\) | −122.596 | −3.93836 | ||||||||
\(970\) | −12.8001 | −0.410988 | ||||||||
\(971\) | 29.0504 | 0.932270 | 0.466135 | − | 0.884714i | \(-0.345646\pi\) | ||||
0.466135 | + | 0.884714i | \(0.345646\pi\) | |||||||
\(972\) | −22.1704 | −0.711117 | ||||||||
\(973\) | 8.19802 | 0.262816 | ||||||||
\(974\) | −27.0722 | −0.867449 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.681193 | −0.0218045 | ||||||||
\(977\) | 14.1557 | 0.452880 | 0.226440 | − | 0.974025i | \(-0.427291\pi\) | ||||
0.226440 | + | 0.974025i | \(0.427291\pi\) | |||||||
\(978\) | 11.6091 | 0.371218 | ||||||||
\(979\) | −2.80207 | −0.0895546 | ||||||||
\(980\) | 3.37468 | 0.107800 | ||||||||
\(981\) | 41.4075 | 1.32204 | ||||||||
\(982\) | 14.7213 | 0.469776 | ||||||||
\(983\) | 7.74156 | 0.246917 | 0.123459 | − | 0.992350i | \(-0.460601\pi\) | ||||
0.123459 | + | 0.992350i | \(0.460601\pi\) | |||||||
\(984\) | 4.55496 | 0.145207 | ||||||||
\(985\) | 17.6398 | 0.562049 | ||||||||
\(986\) | −31.2162 | −0.994127 | ||||||||
\(987\) | −54.8715 | −1.74658 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.80439 | 0.248165 | ||||||||
\(990\) | −18.7287 | −0.595238 | ||||||||
\(991\) | −20.8876 | −0.663517 | −0.331759 | − | 0.943364i | \(-0.607642\pi\) | ||||
−0.331759 | + | 0.943364i | \(0.607642\pi\) | |||||||
\(992\) | −0.0626650 | −0.00198961 | ||||||||
\(993\) | 54.6610 | 1.73461 | ||||||||
\(994\) | −29.8965 | −0.948259 | ||||||||
\(995\) | 23.6305 | 0.749138 | ||||||||
\(996\) | 4.86843 | 0.154262 | ||||||||
\(997\) | −33.3691 | −1.05681 | −0.528406 | − | 0.848992i | \(-0.677210\pi\) | ||||
−0.528406 | + | 0.848992i | \(0.677210\pi\) | |||||||
\(998\) | −4.24391 | −0.134339 | ||||||||
\(999\) | −2.60509 | −0.0824213 |
(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 | 1690.2.a.v.1.6 | ✓ | 6 | |
5.4 | even | 2 | 8450.2.a.cq.1.1 | 6 | |||
13.2 | odd | 12 | 1690.2.l.n.1161.6 | 24 | |||
13.3 | even | 3 | 1690.2.e.v.191.1 | 12 | |||
13.4 | even | 6 | 1690.2.e.u.991.1 | 12 | |||
13.5 | odd | 4 | 1690.2.d.l.1351.12 | 12 | |||
13.6 | odd | 12 | 1690.2.l.n.361.10 | 24 | |||
13.7 | odd | 12 | 1690.2.l.n.361.6 | 24 | |||
13.8 | odd | 4 | 1690.2.d.l.1351.6 | 12 | |||
13.9 | even | 3 | 1690.2.e.v.991.1 | 12 | |||
13.10 | even | 6 | 1690.2.e.u.191.1 | 12 | |||
13.11 | odd | 12 | 1690.2.l.n.1161.10 | 24 | |||
13.12 | even | 2 | 1690.2.a.w.1.6 | yes | 6 | ||
65.64 | even | 2 | 8450.2.a.cp.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1690.2.a.v.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1690.2.a.w.1.6 | yes | 6 | 13.12 | even | 2 | ||
1690.2.d.l.1351.6 | 12 | 13.8 | odd | 4 | |||
1690.2.d.l.1351.12 | 12 | 13.5 | odd | 4 | |||
1690.2.e.u.191.1 | 12 | 13.10 | even | 6 | |||
1690.2.e.u.991.1 | 12 | 13.4 | even | 6 | |||
1690.2.e.v.191.1 | 12 | 13.3 | even | 3 | |||
1690.2.e.v.991.1 | 12 | 13.9 | even | 3 | |||
1690.2.l.n.361.6 | 24 | 13.7 | odd | 12 | |||
1690.2.l.n.361.10 | 24 | 13.6 | odd | 12 | |||
1690.2.l.n.1161.6 | 24 | 13.2 | odd | 12 | |||
1690.2.l.n.1161.10 | 24 | 13.11 | odd | 12 | |||
8450.2.a.cp.1.1 | 6 | 65.64 | even | 2 | |||
8450.2.a.cq.1.1 | 6 | 5.4 | even | 2 |