Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{15})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.33826\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.82709 | 1.29195 | 0.645974 | − | 0.763359i | \(-0.276451\pi\) | ||||
0.645974 | + | 0.763359i | \(0.276451\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.33826 | 0.669131 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.82709 | 0.745907 | ||||||||
\(7\) | 1.74724 | 0.660394 | 0.330197 | − | 0.943912i | \(-0.392885\pi\) | ||||
0.330197 | + | 0.943912i | \(0.392885\pi\) | |||||||
\(8\) | −1.20906 | −0.427466 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.33826 | 0.386323 | ||||||||
\(13\) | −5.35772 | −1.48596 | −0.742981 | − | 0.669312i | \(-0.766589\pi\) | ||||
−0.742981 | + | 0.669312i | \(0.766589\pi\) | |||||||
\(14\) | 3.19236 | 0.853195 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.88558 | −1.22139 | ||||||||
\(17\) | 7.33070 | 1.77796 | 0.888978 | − | 0.457949i | \(-0.151416\pi\) | ||||
0.888978 | + | 0.457949i | \(0.151416\pi\) | |||||||
\(18\) | 1.82709 | 0.430649 | ||||||||
\(19\) | −6.01478 | −1.37989 | −0.689943 | − | 0.723864i | \(-0.742364\pi\) | ||||
−0.689943 | + | 0.723864i | \(0.742364\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.74724 | 0.381279 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.35772 | −1.74270 | −0.871352 | − | 0.490658i | \(-0.836756\pi\) | ||||
−0.871352 | + | 0.490658i | \(0.836756\pi\) | |||||||
\(24\) | −1.20906 | −0.246798 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.78903 | −1.91979 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.33826 | 0.441890 | ||||||||
\(29\) | −5.53818 | −1.02841 | −0.514207 | − | 0.857666i | \(-0.671914\pi\) | ||||
−0.514207 | + | 0.857666i | \(0.671914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0213642 | −0.00383712 | −0.00191856 | − | 0.999998i | \(-0.500611\pi\) | ||||
−0.00191856 | + | 0.999998i | \(0.500611\pi\) | |||||||
\(32\) | −6.50828 | −1.15051 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.3939 | 2.29703 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.33826 | 0.223044 | ||||||||
\(37\) | 1.12165 | 0.184398 | 0.0921988 | − | 0.995741i | \(-0.470610\pi\) | ||||
0.0921988 | + | 0.995741i | \(0.470610\pi\) | |||||||
\(38\) | −10.9896 | −1.78274 | ||||||||
\(39\) | −5.35772 | −0.857921 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.65983 | 0.571569 | 0.285785 | − | 0.958294i | \(-0.407746\pi\) | ||||
0.285785 | + | 0.958294i | \(0.407746\pi\) | |||||||
\(42\) | 3.19236 | 0.492592 | ||||||||
\(43\) | −1.96950 | −0.300346 | −0.150173 | − | 0.988660i | \(-0.547983\pi\) | ||||
−0.150173 | + | 0.988660i | \(0.547983\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −15.2703 | −2.25148 | ||||||||
\(47\) | −3.81953 | −0.557136 | −0.278568 | − | 0.960416i | \(-0.589860\pi\) | ||||
−0.278568 | + | 0.960416i | \(0.589860\pi\) | |||||||
\(48\) | −4.88558 | −0.705173 | ||||||||
\(49\) | −3.94716 | −0.563880 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.33070 | 1.02650 | ||||||||
\(52\) | −7.17002 | −0.994303 | ||||||||
\(53\) | −1.67088 | −0.229512 | −0.114756 | − | 0.993394i | \(-0.536609\pi\) | ||||
−0.114756 | + | 0.993394i | \(0.536609\pi\) | |||||||
\(54\) | 1.82709 | 0.248636 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.11251 | −0.282296 | ||||||||
\(57\) | −6.01478 | −0.796678 | ||||||||
\(58\) | −10.1188 | −1.32866 | ||||||||
\(59\) | 5.66332 | 0.737301 | 0.368651 | − | 0.929568i | \(-0.379820\pi\) | ||||
0.368651 | + | 0.929568i | \(0.379820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.27977 | −1.18815 | −0.594077 | − | 0.804408i | \(-0.702482\pi\) | ||||
−0.594077 | + | 0.804408i | \(0.702482\pi\) | |||||||
\(62\) | −0.0390343 | −0.00495737 | ||||||||
\(63\) | 1.74724 | 0.220131 | ||||||||
\(64\) | −2.12007 | −0.265008 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.350489 | −0.0428190 | −0.0214095 | − | 0.999771i | \(-0.506815\pi\) | ||||
−0.0214095 | + | 0.999771i | \(0.506815\pi\) | |||||||
\(68\) | 9.81040 | 1.18969 | ||||||||
\(69\) | −8.35772 | −1.00615 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.53818 | 0.538583 | 0.269292 | − | 0.963059i | \(-0.413210\pi\) | ||||
0.269292 | + | 0.963059i | \(0.413210\pi\) | |||||||
\(72\) | −1.20906 | −0.142489 | ||||||||
\(73\) | 10.1395 | 1.18674 | 0.593371 | − | 0.804929i | \(-0.297797\pi\) | ||||
0.593371 | + | 0.804929i | \(0.297797\pi\) | |||||||
\(74\) | 2.04935 | 0.238232 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.04935 | −0.923324 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.78903 | −1.10839 | ||||||||
\(79\) | −2.56401 | −0.288474 | −0.144237 | − | 0.989543i | \(-0.546073\pi\) | ||||
−0.144237 | + | 0.989543i | \(0.546073\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.68684 | 0.738438 | ||||||||
\(83\) | −16.0805 | −1.76506 | −0.882532 | − | 0.470252i | \(-0.844163\pi\) | ||||
−0.882532 | + | 0.470252i | \(0.844163\pi\) | |||||||
\(84\) | 2.33826 | 0.255125 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.59845 | −0.388031 | ||||||||
\(87\) | −5.53818 | −0.593755 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5062 | −1.53765 | −0.768825 | − | 0.639459i | \(-0.779159\pi\) | ||||
−0.768825 | + | 0.639459i | \(0.779159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.36121 | −0.981321 | ||||||||
\(92\) | −11.1848 | −1.16610 | ||||||||
\(93\) | −0.0213642 | −0.00221536 | ||||||||
\(94\) | −6.97864 | −0.719791 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.50828 | −0.664249 | ||||||||
\(97\) | 1.89972 | 0.192887 | 0.0964435 | − | 0.995338i | \(-0.469253\pi\) | ||||
0.0964435 | + | 0.995338i | \(0.469253\pi\) | |||||||
\(98\) | −7.21182 | −0.728504 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.71011 | −0.667681 | −0.333841 | − | 0.942630i | \(-0.608345\pi\) | ||||
−0.333841 | + | 0.942630i | \(0.608345\pi\) | |||||||
\(102\) | 13.3939 | 1.32619 | ||||||||
\(103\) | 4.24678 | 0.418448 | 0.209224 | − | 0.977868i | \(-0.432906\pi\) | ||||
0.209224 | + | 0.977868i | \(0.432906\pi\) | |||||||
\(104\) | 6.47778 | 0.635199 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.05284 | −0.296518 | ||||||||
\(107\) | −15.7230 | −1.52000 | −0.759999 | − | 0.649924i | \(-0.774801\pi\) | ||||
−0.759999 | + | 0.649924i | \(0.774801\pi\) | |||||||
\(108\) | 1.33826 | 0.128774 | ||||||||
\(109\) | −4.23895 | −0.406018 | −0.203009 | − | 0.979177i | \(-0.565072\pi\) | ||||
−0.203009 | + | 0.979177i | \(0.565072\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.12165 | 0.106462 | ||||||||
\(112\) | −8.53627 | −0.806602 | ||||||||
\(113\) | 7.19643 | 0.676983 | 0.338492 | − | 0.940969i | \(-0.390083\pi\) | ||||
0.338492 | + | 0.940969i | \(0.390083\pi\) | |||||||
\(114\) | −10.9896 | −1.02927 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.41153 | −0.688144 | ||||||||
\(117\) | −5.35772 | −0.495321 | ||||||||
\(118\) | 10.3474 | 0.952555 | ||||||||
\(119\) | 12.8085 | 1.17415 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −16.9550 | −1.53503 | ||||||||
\(123\) | 3.65983 | 0.329996 | ||||||||
\(124\) | −0.0285909 | −0.00256754 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.19236 | 0.284398 | ||||||||
\(127\) | 12.6870 | 1.12579 | 0.562897 | − | 0.826527i | \(-0.309687\pi\) | ||||
0.562897 | + | 0.826527i | \(0.309687\pi\) | |||||||
\(128\) | 9.14301 | 0.808136 | ||||||||
\(129\) | −1.96950 | −0.173405 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.970102 | 0.0847582 | 0.0423791 | − | 0.999102i | \(-0.486506\pi\) | ||||
0.0423791 | + | 0.999102i | \(0.486506\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.5093 | −0.911268 | ||||||||
\(134\) | −0.640375 | −0.0553199 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.86324 | −0.760016 | ||||||||
\(137\) | −4.22035 | −0.360569 | −0.180284 | − | 0.983615i | \(-0.557702\pi\) | ||||
−0.180284 | + | 0.983615i | \(0.557702\pi\) | |||||||
\(138\) | −15.2703 | −1.29989 | ||||||||
\(139\) | −8.84846 | −0.750516 | −0.375258 | − | 0.926920i | \(-0.622446\pi\) | ||||
−0.375258 | + | 0.926920i | \(0.622446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.81953 | −0.321663 | ||||||||
\(142\) | 8.29167 | 0.695821 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.88558 | −0.407132 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 18.5258 | 1.53321 | ||||||||
\(147\) | −3.94716 | −0.325556 | ||||||||
\(148\) | 1.50106 | 0.123386 | ||||||||
\(149\) | −9.55357 | −0.782659 | −0.391329 | − | 0.920251i | \(-0.627985\pi\) | ||||
−0.391329 | + | 0.920251i | \(0.627985\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.75158 | 0.549436 | 0.274718 | − | 0.961525i | \(-0.411416\pi\) | ||||
0.274718 | + | 0.961525i | \(0.411416\pi\) | |||||||
\(152\) | 7.27222 | 0.589855 | ||||||||
\(153\) | 7.33070 | 0.592652 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.17002 | −0.574061 | ||||||||
\(157\) | 12.6604 | 1.01041 | 0.505206 | − | 0.862999i | \(-0.331416\pi\) | ||||
0.505206 | + | 0.862999i | \(0.331416\pi\) | |||||||
\(158\) | −4.68468 | −0.372693 | ||||||||
\(159\) | −1.67088 | −0.132509 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.6029 | −1.15087 | ||||||||
\(162\) | 1.82709 | 0.143550 | ||||||||
\(163\) | 23.4058 | 1.83328 | 0.916640 | − | 0.399713i | \(-0.130890\pi\) | ||||
0.916640 | + | 0.399713i | \(0.130890\pi\) | |||||||
\(164\) | 4.89781 | 0.382454 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.3805 | −2.28037 | ||||||||
\(167\) | 3.05191 | 0.236164 | 0.118082 | − | 0.993004i | \(-0.462325\pi\) | ||||
0.118082 | + | 0.993004i | \(0.462325\pi\) | |||||||
\(168\) | −2.11251 | −0.162984 | ||||||||
\(169\) | 15.7051 | 1.20809 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.01478 | −0.459962 | ||||||||
\(172\) | −2.63570 | −0.200971 | ||||||||
\(173\) | 16.0074 | 1.21702 | 0.608511 | − | 0.793545i | \(-0.291767\pi\) | ||||
0.608511 | + | 0.793545i | \(0.291767\pi\) | |||||||
\(174\) | −10.1188 | −0.767101 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.66332 | 0.425681 | ||||||||
\(178\) | −26.5041 | −1.98657 | ||||||||
\(179\) | −19.2991 | −1.44248 | −0.721241 | − | 0.692684i | \(-0.756428\pi\) | ||||
−0.721241 | + | 0.692684i | \(0.756428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1911 | −0.906154 | −0.453077 | − | 0.891471i | \(-0.649674\pi\) | ||||
−0.453077 | + | 0.891471i | \(0.649674\pi\) | |||||||
\(182\) | −17.1038 | −1.26782 | ||||||||
\(183\) | −9.27977 | −0.685981 | ||||||||
\(184\) | 10.1050 | 0.744947 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0390343 | −0.00286214 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.11153 | −0.372797 | ||||||||
\(189\) | 1.74724 | 0.127093 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4244 | −0.971353 | −0.485676 | − | 0.874139i | \(-0.661427\pi\) | ||||
−0.485676 | + | 0.874139i | \(0.661427\pi\) | |||||||
\(192\) | −2.12007 | −0.153003 | ||||||||
\(193\) | 7.57782 | 0.545463 | 0.272732 | − | 0.962090i | \(-0.412073\pi\) | ||||
0.272732 | + | 0.962090i | \(0.412073\pi\) | |||||||
\(194\) | 3.47096 | 0.249200 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.28233 | −0.377309 | ||||||||
\(197\) | −6.89118 | −0.490976 | −0.245488 | − | 0.969400i | \(-0.578948\pi\) | ||||
−0.245488 | + | 0.969400i | \(0.578948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.639398 | 0.0453257 | 0.0226629 | − | 0.999743i | \(-0.492786\pi\) | ||||
0.0226629 | + | 0.999743i | \(0.492786\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.350489 | −0.0247216 | ||||||||
\(202\) | −12.2600 | −0.862610 | ||||||||
\(203\) | −9.67652 | −0.679159 | ||||||||
\(204\) | 9.81040 | 0.686865 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.75926 | 0.540613 | ||||||||
\(207\) | −8.35772 | −0.580901 | ||||||||
\(208\) | 26.1755 | 1.81495 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.82149 | 0.263082 | 0.131541 | − | 0.991311i | \(-0.458008\pi\) | ||||
0.131541 | + | 0.991311i | \(0.458008\pi\) | |||||||
\(212\) | −2.23607 | −0.153574 | ||||||||
\(213\) | 4.53818 | 0.310951 | ||||||||
\(214\) | −28.7273 | −1.96376 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.20906 | −0.0822659 | ||||||||
\(217\) | −0.0373284 | −0.00253401 | ||||||||
\(218\) | −7.74496 | −0.524555 | ||||||||
\(219\) | 10.1395 | 0.685165 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.2758 | −2.64198 | ||||||||
\(222\) | 2.04935 | 0.137543 | ||||||||
\(223\) | 26.7201 | 1.78931 | 0.894657 | − | 0.446755i | \(-0.147420\pi\) | ||||
0.894657 | + | 0.446755i | \(0.147420\pi\) | |||||||
\(224\) | −11.3715 | −0.759792 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.1485 | 0.874627 | ||||||||
\(227\) | 12.2373 | 0.812219 | 0.406110 | − | 0.913824i | \(-0.366885\pi\) | ||||
0.406110 | + | 0.913824i | \(0.366885\pi\) | |||||||
\(228\) | −8.04935 | −0.533081 | ||||||||
\(229\) | −6.68664 | −0.441865 | −0.220933 | − | 0.975289i | \(-0.570910\pi\) | ||||
−0.220933 | + | 0.975289i | \(0.570910\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.69598 | 0.439612 | ||||||||
\(233\) | −6.51742 | −0.426970 | −0.213485 | − | 0.976946i | \(-0.568482\pi\) | ||||
−0.213485 | + | 0.976946i | \(0.568482\pi\) | |||||||
\(234\) | −9.78903 | −0.639929 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.57900 | 0.493351 | ||||||||
\(237\) | −2.56401 | −0.166550 | ||||||||
\(238\) | 23.4023 | 1.51694 | ||||||||
\(239\) | 10.8419 | 0.701303 | 0.350651 | − | 0.936506i | \(-0.385960\pi\) | ||||
0.350651 | + | 0.936506i | \(0.385960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.1803 | −1.75084 | −0.875420 | − | 0.483363i | \(-0.839415\pi\) | ||||
−0.875420 | + | 0.483363i | \(0.839415\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.4188 | −0.795030 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.68684 | 0.426337 | ||||||||
\(247\) | 32.2255 | 2.05046 | ||||||||
\(248\) | 0.0258305 | 0.00164024 | ||||||||
\(249\) | −16.0805 | −1.01906 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.54443 | 0.349961 | 0.174981 | − | 0.984572i | \(-0.444014\pi\) | ||||
0.174981 | + | 0.984572i | \(0.444014\pi\) | |||||||
\(252\) | 2.33826 | 0.147297 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 23.1804 | 1.45447 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9452 | 1.30908 | ||||||||
\(257\) | 18.9439 | 1.18169 | 0.590845 | − | 0.806785i | \(-0.298794\pi\) | ||||
0.590845 | + | 0.806785i | \(0.298794\pi\) | |||||||
\(258\) | −3.59845 | −0.224030 | ||||||||
\(259\) | 1.95979 | 0.121775 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.53818 | −0.342805 | ||||||||
\(262\) | 1.77247 | 0.109503 | ||||||||
\(263\) | 3.20873 | 0.197859 | 0.0989293 | − | 0.995094i | \(-0.468458\pi\) | ||||
0.0989293 | + | 0.995094i | \(0.468458\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −19.2014 | −1.17731 | ||||||||
\(267\) | −14.5062 | −0.887763 | ||||||||
\(268\) | −0.469045 | −0.0286515 | ||||||||
\(269\) | −3.24423 | −0.197804 | −0.0989020 | − | 0.995097i | \(-0.531533\pi\) | ||||
−0.0989020 | + | 0.995097i | \(0.531533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.02977 | 0.123300 | 0.0616499 | − | 0.998098i | \(-0.480364\pi\) | ||||
0.0616499 | + | 0.998098i | \(0.480364\pi\) | |||||||
\(272\) | −35.8147 | −2.17159 | ||||||||
\(273\) | −9.36121 | −0.566566 | ||||||||
\(274\) | −7.71096 | −0.465836 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.1848 | −0.673246 | ||||||||
\(277\) | 11.3166 | 0.679947 | 0.339973 | − | 0.940435i | \(-0.389582\pi\) | ||||
0.339973 | + | 0.940435i | \(0.389582\pi\) | |||||||
\(278\) | −16.1669 | −0.969628 | ||||||||
\(279\) | −0.0213642 | −0.00127904 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3177 | 0.615503 | 0.307751 | − | 0.951467i | \(-0.400424\pi\) | ||||
0.307751 | + | 0.951467i | \(0.400424\pi\) | |||||||
\(282\) | −6.97864 | −0.415572 | ||||||||
\(283\) | −2.10589 | −0.125182 | −0.0625910 | − | 0.998039i | \(-0.519936\pi\) | ||||
−0.0625910 | + | 0.998039i | \(0.519936\pi\) | |||||||
\(284\) | 6.07327 | 0.360382 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.39459 | 0.377461 | ||||||||
\(288\) | −6.50828 | −0.383504 | ||||||||
\(289\) | 36.7392 | 2.16113 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.89972 | 0.111363 | ||||||||
\(292\) | 13.5693 | 0.794085 | ||||||||
\(293\) | −23.3755 | −1.36561 | −0.682805 | − | 0.730601i | \(-0.739240\pi\) | ||||
−0.682805 | + | 0.730601i | \(0.739240\pi\) | |||||||
\(294\) | −7.21182 | −0.420602 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.35614 | −0.0788238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.4552 | −1.01115 | ||||||||
\(299\) | 44.7783 | 2.58959 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.44118 | −0.198347 | ||||||||
\(302\) | 12.3357 | 0.709843 | ||||||||
\(303\) | −6.71011 | −0.385486 | ||||||||
\(304\) | 29.3857 | 1.68539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.3939 | 0.765676 | ||||||||
\(307\) | −32.0518 | −1.82929 | −0.914646 | − | 0.404256i | \(-0.867531\pi\) | ||||
−0.914646 | + | 0.404256i | \(0.867531\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.24678 | 0.241591 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.63433 | 0.0926743 | 0.0463371 | − | 0.998926i | \(-0.485245\pi\) | ||||
0.0463371 | + | 0.998926i | \(0.485245\pi\) | |||||||
\(312\) | 6.47778 | 0.366732 | ||||||||
\(313\) | −30.4130 | −1.71904 | −0.859522 | − | 0.511099i | \(-0.829239\pi\) | ||||
−0.859522 | + | 0.511099i | \(0.829239\pi\) | |||||||
\(314\) | 23.1318 | 1.30540 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.43132 | −0.193027 | ||||||||
\(317\) | 29.4340 | 1.65318 | 0.826590 | − | 0.562805i | \(-0.190278\pi\) | ||||
0.826590 | + | 0.562805i | \(0.190278\pi\) | |||||||
\(318\) | −3.05284 | −0.171195 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.7230 | −0.877572 | ||||||||
\(322\) | −26.6809 | −1.48687 | ||||||||
\(323\) | −44.0926 | −2.45338 | ||||||||
\(324\) | 1.33826 | 0.0743478 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 42.7645 | 2.36850 | ||||||||
\(327\) | −4.23895 | −0.234415 | ||||||||
\(328\) | −4.42494 | −0.244327 | ||||||||
\(329\) | −6.67364 | −0.367929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.7902 | −1.25266 | −0.626332 | − | 0.779557i | \(-0.715444\pi\) | ||||
−0.626332 | + | 0.779557i | \(0.715444\pi\) | |||||||
\(332\) | −21.5199 | −1.18106 | ||||||||
\(333\) | 1.12165 | 0.0614659 | ||||||||
\(334\) | 5.57611 | 0.305111 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8.53627 | −0.465692 | ||||||||
\(337\) | −14.4901 | −0.789325 | −0.394662 | − | 0.918826i | \(-0.629138\pi\) | ||||
−0.394662 | + | 0.918826i | \(0.629138\pi\) | |||||||
\(338\) | 28.6947 | 1.56078 | ||||||||
\(339\) | 7.19643 | 0.390856 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.9896 | −0.594247 | ||||||||
\(343\) | −19.1273 | −1.03278 | ||||||||
\(344\) | 2.38124 | 0.128388 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.2470 | 1.57233 | ||||||||
\(347\) | 4.38728 | 0.235522 | 0.117761 | − | 0.993042i | \(-0.462428\pi\) | ||||
0.117761 | + | 0.993042i | \(0.462428\pi\) | |||||||
\(348\) | −7.41153 | −0.397300 | ||||||||
\(349\) | −14.4061 | −0.771140 | −0.385570 | − | 0.922679i | \(-0.625995\pi\) | ||||
−0.385570 | + | 0.922679i | \(0.625995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.35772 | −0.285974 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.01065 | 0.319914 | 0.159957 | − | 0.987124i | \(-0.448864\pi\) | ||||
0.159957 | + | 0.987124i | \(0.448864\pi\) | |||||||
\(354\) | 10.3474 | 0.549958 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −19.4130 | −1.02889 | ||||||||
\(357\) | 12.8085 | 0.677897 | ||||||||
\(358\) | −35.2612 | −1.86361 | ||||||||
\(359\) | 2.45715 | 0.129683 | 0.0648417 | − | 0.997896i | \(-0.479346\pi\) | ||||
0.0648417 | + | 0.997896i | \(0.479346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1776 | 0.904085 | ||||||||
\(362\) | −22.2742 | −1.17070 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.5277 | −0.656632 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −16.9550 | −0.886251 | ||||||||
\(367\) | −1.47990 | −0.0772500 | −0.0386250 | − | 0.999254i | \(-0.512298\pi\) | ||||
−0.0386250 | + | 0.999254i | \(0.512298\pi\) | |||||||
\(368\) | 40.8323 | 2.12853 | ||||||||
\(369\) | 3.65983 | 0.190523 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.91942 | −0.151569 | ||||||||
\(372\) | −0.0285909 | −0.00148237 | ||||||||
\(373\) | −24.3331 | −1.25992 | −0.629961 | − | 0.776627i | \(-0.716929\pi\) | ||||
−0.629961 | + | 0.776627i | \(0.716929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.61803 | 0.238157 | ||||||||
\(377\) | 29.6720 | 1.52819 | ||||||||
\(378\) | 3.19236 | 0.164197 | ||||||||
\(379\) | 15.9311 | 0.818328 | 0.409164 | − | 0.912461i | \(-0.365820\pi\) | ||||
0.409164 | + | 0.912461i | \(0.365820\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6870 | 0.649977 | ||||||||
\(382\) | −24.5275 | −1.25494 | ||||||||
\(383\) | 3.91994 | 0.200300 | 0.100150 | − | 0.994972i | \(-0.468068\pi\) | ||||
0.100150 | + | 0.994972i | \(0.468068\pi\) | |||||||
\(384\) | 9.14301 | 0.466577 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8454 | 0.704710 | ||||||||
\(387\) | −1.96950 | −0.100115 | ||||||||
\(388\) | 2.54232 | 0.129067 | ||||||||
\(389\) | −35.2910 | −1.78933 | −0.894663 | − | 0.446742i | \(-0.852584\pi\) | ||||
−0.894663 | + | 0.446742i | \(0.852584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −61.2679 | −3.09845 | ||||||||
\(392\) | 4.77234 | 0.241040 | ||||||||
\(393\) | 0.970102 | 0.0489352 | ||||||||
\(394\) | −12.5908 | −0.634316 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.2231 | −1.16553 | −0.582767 | − | 0.812639i | \(-0.698030\pi\) | ||||
−0.582767 | + | 0.812639i | \(0.698030\pi\) | |||||||
\(398\) | 1.16824 | 0.0585585 | ||||||||
\(399\) | −10.5093 | −0.526121 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.69460 | 0.284375 | 0.142187 | − | 0.989840i | \(-0.454586\pi\) | ||||
0.142187 | + | 0.989840i | \(0.454586\pi\) | |||||||
\(402\) | −0.640375 | −0.0319390 | ||||||||
\(403\) | 0.114463 | 0.00570182 | ||||||||
\(404\) | −8.97989 | −0.446766 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.6799 | −0.877438 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −8.86324 | −0.438796 | ||||||||
\(409\) | −25.4530 | −1.25857 | −0.629284 | − | 0.777176i | \(-0.716652\pi\) | ||||
−0.629284 | + | 0.777176i | \(0.716652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.22035 | −0.208175 | ||||||||
\(412\) | 5.68331 | 0.279996 | ||||||||
\(413\) | 9.89517 | 0.486909 | ||||||||
\(414\) | −15.2703 | −0.750495 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 34.8695 | 1.70962 | ||||||||
\(417\) | −8.84846 | −0.433311 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4850 | −0.658786 | −0.329393 | − | 0.944193i | \(-0.606844\pi\) | ||||
−0.329393 | + | 0.944193i | \(0.606844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.94967 | 0.143758 | 0.0718791 | − | 0.997413i | \(-0.477100\pi\) | ||||
0.0718791 | + | 0.997413i | \(0.477100\pi\) | |||||||
\(422\) | 6.98220 | 0.339888 | ||||||||
\(423\) | −3.81953 | −0.185712 | ||||||||
\(424\) | 2.02018 | 0.0981088 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.29167 | 0.401733 | ||||||||
\(427\) | −16.2140 | −0.784649 | ||||||||
\(428\) | −21.0415 | −1.01708 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.5227 | −0.555031 | −0.277515 | − | 0.960721i | \(-0.589511\pi\) | ||||
−0.277515 | + | 0.960721i | \(0.589511\pi\) | |||||||
\(432\) | −4.88558 | −0.235058 | ||||||||
\(433\) | −11.1638 | −0.536500 | −0.268250 | − | 0.963349i | \(-0.586445\pi\) | ||||
−0.268250 | + | 0.963349i | \(0.586445\pi\) | |||||||
\(434\) | −0.0682023 | −0.00327382 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.67283 | −0.271679 | ||||||||
\(437\) | 50.2698 | 2.40473 | ||||||||
\(438\) | 18.5258 | 0.885198 | ||||||||
\(439\) | −0.993624 | −0.0474231 | −0.0237115 | − | 0.999719i | \(-0.507548\pi\) | ||||
−0.0237115 | + | 0.999719i | \(0.507548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.94716 | −0.187960 | ||||||||
\(442\) | −71.7605 | −3.41330 | ||||||||
\(443\) | 10.9825 | 0.521796 | 0.260898 | − | 0.965366i | \(-0.415981\pi\) | ||||
0.260898 | + | 0.965366i | \(0.415981\pi\) | |||||||
\(444\) | 1.50106 | 0.0712370 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 48.8201 | 2.31170 | ||||||||
\(447\) | −9.55357 | −0.451868 | ||||||||
\(448\) | −3.70426 | −0.175010 | ||||||||
\(449\) | 29.0203 | 1.36955 | 0.684776 | − | 0.728753i | \(-0.259900\pi\) | ||||
0.684776 | + | 0.728753i | \(0.259900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.63070 | 0.452990 | ||||||||
\(453\) | 6.75158 | 0.317217 | ||||||||
\(454\) | 22.3587 | 1.04935 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.27222 | 0.340553 | ||||||||
\(457\) | −3.55670 | −0.166375 | −0.0831877 | − | 0.996534i | \(-0.526510\pi\) | ||||
−0.0831877 | + | 0.996534i | \(0.526510\pi\) | |||||||
\(458\) | −12.2171 | −0.570867 | ||||||||
\(459\) | 7.33070 | 0.342168 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.1829 | −1.17288 | −0.586441 | − | 0.809992i | \(-0.699472\pi\) | ||||
−0.586441 | + | 0.809992i | \(0.699472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8743 | 0.830690 | 0.415345 | − | 0.909664i | \(-0.363661\pi\) | ||||
0.415345 | + | 0.909664i | \(0.363661\pi\) | |||||||
\(464\) | 27.0572 | 1.25610 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.9079 | −0.551624 | ||||||||
\(467\) | 25.2252 | 1.16728 | 0.583642 | − | 0.812011i | \(-0.301627\pi\) | ||||
0.583642 | + | 0.812011i | \(0.301627\pi\) | |||||||
\(468\) | −7.17002 | −0.331434 | ||||||||
\(469\) | −0.612387 | −0.0282774 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6604 | 0.583362 | ||||||||
\(472\) | −6.84727 | −0.315171 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4.68468 | −0.215175 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.1411 | 0.785661 | ||||||||
\(477\) | −1.67088 | −0.0765041 | ||||||||
\(478\) | 19.8091 | 0.906047 | ||||||||
\(479\) | 5.23574 | 0.239227 | 0.119613 | − | 0.992821i | \(-0.461834\pi\) | ||||
0.119613 | + | 0.992821i | \(0.461834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00947 | −0.274008 | ||||||||
\(482\) | −49.6610 | −2.26199 | ||||||||
\(483\) | −14.6029 | −0.664456 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.82709 | 0.0828785 | ||||||||
\(487\) | −9.04508 | −0.409872 | −0.204936 | − | 0.978775i | \(-0.565699\pi\) | ||||
−0.204936 | + | 0.978775i | \(0.565699\pi\) | |||||||
\(488\) | 11.2198 | 0.507895 | ||||||||
\(489\) | 23.4058 | 1.05845 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.8112 | 1.57101 | 0.785505 | − | 0.618856i | \(-0.212403\pi\) | ||||
0.785505 | + | 0.618856i | \(0.212403\pi\) | |||||||
\(492\) | 4.89781 | 0.220810 | ||||||||
\(493\) | −40.5988 | −1.82848 | ||||||||
\(494\) | 58.8789 | 2.64909 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.104377 | 0.00468664 | ||||||||
\(497\) | 7.92928 | 0.355677 | ||||||||
\(498\) | −29.3805 | −1.31657 | ||||||||
\(499\) | 19.5992 | 0.877380 | 0.438690 | − | 0.898638i | \(-0.355443\pi\) | ||||
0.438690 | + | 0.898638i | \(0.355443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.05191 | 0.136349 | ||||||||
\(502\) | 10.1302 | 0.452132 | ||||||||
\(503\) | 18.4160 | 0.821129 | 0.410564 | − | 0.911832i | \(-0.365332\pi\) | ||||
0.410564 | + | 0.911832i | \(0.365332\pi\) | |||||||
\(504\) | −2.11251 | −0.0940987 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.7051 | 0.697489 | ||||||||
\(508\) | 16.9786 | 0.753303 | ||||||||
\(509\) | 1.23838 | 0.0548901 | 0.0274451 | − | 0.999623i | \(-0.491263\pi\) | ||||
0.0274451 | + | 0.999623i | \(0.491263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7162 | 0.783717 | ||||||||
\(512\) | 19.9828 | 0.883126 | ||||||||
\(513\) | −6.01478 | −0.265559 | ||||||||
\(514\) | 34.6123 | 1.52668 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.63570 | −0.116030 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.58071 | 0.157327 | ||||||||
\(519\) | 16.0074 | 0.702648 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.1850 | 1.45386 | 0.726931 | − | 0.686711i | \(-0.240946\pi\) | ||||
0.726931 | + | 0.686711i | \(0.240946\pi\) | |||||||
\(522\) | −10.1188 | −0.442886 | ||||||||
\(523\) | 13.1508 | 0.575046 | 0.287523 | − | 0.957774i | \(-0.407168\pi\) | ||||
0.287523 | + | 0.957774i | \(0.407168\pi\) | |||||||
\(524\) | 1.29825 | 0.0567143 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.86264 | 0.255623 | ||||||||
\(527\) | −0.156615 | −0.00682224 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.8514 | 2.03702 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.66332 | 0.245767 | ||||||||
\(532\) | −14.0641 | −0.609758 | ||||||||
\(533\) | −19.6083 | −0.849331 | ||||||||
\(534\) | −26.5041 | −1.14694 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.423761 | 0.0183037 | ||||||||
\(537\) | −19.2991 | −0.832818 | ||||||||
\(538\) | −5.92750 | −0.255553 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.6519 | −1.40381 | −0.701907 | − | 0.712269i | \(-0.747668\pi\) | ||||
−0.701907 | + | 0.712269i | \(0.747668\pi\) | |||||||
\(542\) | 3.70858 | 0.159297 | ||||||||
\(543\) | −12.1911 | −0.523168 | ||||||||
\(544\) | −47.7103 | −2.04556 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −17.1038 | −0.731974 | ||||||||
\(547\) | 27.7048 | 1.18457 | 0.592285 | − | 0.805728i | \(-0.298226\pi\) | ||||
0.592285 | + | 0.805728i | \(0.298226\pi\) | |||||||
\(548\) | −5.64793 | −0.241268 | ||||||||
\(549\) | −9.27977 | −0.396051 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.3110 | 1.41909 | ||||||||
\(552\) | 10.1050 | 0.430095 | ||||||||
\(553\) | −4.47994 | −0.190506 | ||||||||
\(554\) | 20.6764 | 0.878456 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.8415 | −0.502193 | ||||||||
\(557\) | −23.4252 | −0.992558 | −0.496279 | − | 0.868163i | \(-0.665301\pi\) | ||||
−0.496279 | + | 0.868163i | \(0.665301\pi\) | |||||||
\(558\) | −0.0390343 | −0.00165246 | ||||||||
\(559\) | 10.5520 | 0.446303 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.8514 | 0.795198 | ||||||||
\(563\) | 22.0856 | 0.930796 | 0.465398 | − | 0.885101i | \(-0.345911\pi\) | ||||
0.465398 | + | 0.885101i | \(0.345911\pi\) | |||||||
\(564\) | −5.11153 | −0.215234 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.84765 | −0.161729 | ||||||||
\(567\) | 1.74724 | 0.0733771 | ||||||||
\(568\) | −5.48692 | −0.230226 | ||||||||
\(569\) | 13.7351 | 0.575805 | 0.287902 | − | 0.957660i | \(-0.407042\pi\) | ||||
0.287902 | + | 0.957660i | \(0.407042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.5201 | 1.10983 | 0.554915 | − | 0.831907i | \(-0.312751\pi\) | ||||
0.554915 | + | 0.831907i | \(0.312751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.4244 | −0.560811 | ||||||||
\(574\) | 11.6835 | 0.487660 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.12007 | −0.0883361 | ||||||||
\(577\) | −5.68765 | −0.236780 | −0.118390 | − | 0.992967i | \(-0.537773\pi\) | ||||
−0.118390 | + | 0.992967i | \(0.537773\pi\) | |||||||
\(578\) | 67.1259 | 2.79207 | ||||||||
\(579\) | 7.57782 | 0.314923 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.0965 | −1.16564 | ||||||||
\(582\) | 3.47096 | 0.143876 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −12.2593 | −0.507292 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −42.7091 | −1.76430 | ||||||||
\(587\) | −13.5460 | −0.559104 | −0.279552 | − | 0.960131i | \(-0.590186\pi\) | ||||
−0.279552 | + | 0.960131i | \(0.590186\pi\) | |||||||
\(588\) | −5.28233 | −0.217840 | ||||||||
\(589\) | 0.128501 | 0.00529479 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.89118 | −0.283465 | ||||||||
\(592\) | −5.47990 | −0.225222 | ||||||||
\(593\) | 21.1786 | 0.869702 | 0.434851 | − | 0.900502i | \(-0.356801\pi\) | ||||
0.434851 | + | 0.900502i | \(0.356801\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.7852 | −0.523701 | ||||||||
\(597\) | 0.639398 | 0.0261688 | ||||||||
\(598\) | 81.8140 | 3.34562 | ||||||||
\(599\) | −33.8404 | −1.38268 | −0.691341 | − | 0.722528i | \(-0.742980\pi\) | ||||
−0.691341 | + | 0.722528i | \(0.742980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.3177 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(602\) | −6.28736 | −0.256254 | ||||||||
\(603\) | −0.350489 | −0.0142730 | ||||||||
\(604\) | 9.03538 | 0.367644 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.2600 | −0.498028 | ||||||||
\(607\) | 7.17486 | 0.291219 | 0.145609 | − | 0.989342i | \(-0.453486\pi\) | ||||
0.145609 | + | 0.989342i | \(0.453486\pi\) | |||||||
\(608\) | 39.1459 | 1.58758 | ||||||||
\(609\) | −9.67652 | −0.392112 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.4640 | 0.827884 | ||||||||
\(612\) | 9.81040 | 0.396562 | ||||||||
\(613\) | −27.5044 | −1.11089 | −0.555447 | − | 0.831552i | \(-0.687453\pi\) | ||||
−0.555447 | + | 0.831552i | \(0.687453\pi\) | |||||||
\(614\) | −58.5615 | −2.36335 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.0712 | −0.969068 | −0.484534 | − | 0.874772i | \(-0.661011\pi\) | ||||
−0.484534 | + | 0.874772i | \(0.661011\pi\) | |||||||
\(618\) | 7.75926 | 0.312123 | ||||||||
\(619\) | 26.9729 | 1.08413 | 0.542067 | − | 0.840335i | \(-0.317642\pi\) | ||||
0.542067 | + | 0.840335i | \(0.317642\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.35772 | −0.335384 | ||||||||
\(622\) | 2.98607 | 0.119730 | ||||||||
\(623\) | −25.3457 | −1.01546 | ||||||||
\(624\) | 26.1755 | 1.04786 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −55.5673 | −2.22092 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.9430 | 0.676098 | ||||||||
\(629\) | 8.22246 | 0.327851 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.73627 | 0.387595 | 0.193797 | − | 0.981042i | \(-0.437920\pi\) | ||||
0.193797 | + | 0.981042i | \(0.437920\pi\) | |||||||
\(632\) | 3.10004 | 0.123313 | ||||||||
\(633\) | 3.82149 | 0.151890 | ||||||||
\(634\) | 53.7786 | 2.13582 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.23607 | −0.0886659 | ||||||||
\(637\) | 21.1478 | 0.837904 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.53818 | 0.179528 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.1165 | 0.992040 | 0.496020 | − | 0.868311i | \(-0.334794\pi\) | ||||
0.496020 | + | 0.868311i | \(0.334794\pi\) | |||||||
\(642\) | −28.7273 | −1.13378 | ||||||||
\(643\) | 26.9257 | 1.06185 | 0.530924 | − | 0.847420i | \(-0.321845\pi\) | ||||
0.530924 | + | 0.847420i | \(0.321845\pi\) | |||||||
\(644\) | −19.5425 | −0.770083 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −80.5612 | −3.16964 | ||||||||
\(647\) | 26.8011 | 1.05366 | 0.526829 | − | 0.849971i | \(-0.323381\pi\) | ||||
0.526829 | + | 0.849971i | \(0.323381\pi\) | |||||||
\(648\) | −1.20906 | −0.0474962 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0373284 | −0.00146301 | ||||||||
\(652\) | 31.3230 | 1.22670 | ||||||||
\(653\) | −28.7633 | −1.12559 | −0.562797 | − | 0.826595i | \(-0.690275\pi\) | ||||
−0.562797 | + | 0.826595i | \(0.690275\pi\) | |||||||
\(654\) | −7.74496 | −0.302852 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.8804 | −0.698112 | ||||||||
\(657\) | 10.1395 | 0.395580 | ||||||||
\(658\) | −12.1933 | −0.475346 | ||||||||
\(659\) | −36.5327 | −1.42311 | −0.711556 | − | 0.702629i | \(-0.752009\pi\) | ||||
−0.711556 | + | 0.702629i | \(0.752009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7750 | −1.39149 | −0.695743 | − | 0.718291i | \(-0.744925\pi\) | ||||
−0.695743 | + | 0.718291i | \(0.744925\pi\) | |||||||
\(662\) | −41.6398 | −1.61838 | ||||||||
\(663\) | −39.2758 | −1.52535 | ||||||||
\(664\) | 19.4422 | 0.754505 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.04935 | 0.0794108 | ||||||||
\(667\) | 46.2865 | 1.79222 | ||||||||
\(668\) | 4.08425 | 0.158024 | ||||||||
\(669\) | 26.7201 | 1.03306 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.3715 | −0.438666 | ||||||||
\(673\) | −11.2915 | −0.435254 | −0.217627 | − | 0.976032i | \(-0.569832\pi\) | ||||
−0.217627 | + | 0.976032i | \(0.569832\pi\) | |||||||
\(674\) | −26.4747 | −1.01977 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.0175 | 0.808367 | ||||||||
\(677\) | −43.8574 | −1.68558 | −0.842788 | − | 0.538246i | \(-0.819087\pi\) | ||||
−0.842788 | + | 0.538246i | \(0.819087\pi\) | |||||||
\(678\) | 13.1485 | 0.504966 | ||||||||
\(679\) | 3.31926 | 0.127381 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.2373 | 0.468935 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.5355 | 0.709241 | 0.354620 | − | 0.935010i | \(-0.384610\pi\) | ||||
0.354620 | + | 0.935010i | \(0.384610\pi\) | |||||||
\(684\) | −8.04935 | −0.307775 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −34.9473 | −1.33429 | ||||||||
\(687\) | −6.68664 | −0.255111 | ||||||||
\(688\) | 9.62214 | 0.366841 | ||||||||
\(689\) | 8.95208 | 0.341047 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.2055 | −1.07299 | −0.536494 | − | 0.843904i | \(-0.680251\pi\) | ||||
−0.536494 | + | 0.843904i | \(0.680251\pi\) | |||||||
\(692\) | 21.4221 | 0.814347 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.01596 | 0.304282 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.69598 | 0.253810 | ||||||||
\(697\) | 26.8291 | 1.01623 | ||||||||
\(698\) | −26.3212 | −0.996274 | ||||||||
\(699\) | −6.51742 | −0.246511 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.315386 | −0.0119120 | −0.00595599 | − | 0.999982i | \(-0.501896\pi\) | ||||
−0.00595599 | + | 0.999982i | \(0.501896\pi\) | |||||||
\(702\) | −9.78903 | −0.369463 | ||||||||
\(703\) | −6.74647 | −0.254448 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.9820 | 0.413313 | ||||||||
\(707\) | −11.7242 | −0.440933 | ||||||||
\(708\) | 7.57900 | 0.284836 | ||||||||
\(709\) | 39.0246 | 1.46560 | 0.732800 | − | 0.680444i | \(-0.238213\pi\) | ||||
0.732800 | + | 0.680444i | \(0.238213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.56401 | −0.0961580 | ||||||||
\(712\) | 17.5388 | 0.657294 | ||||||||
\(713\) | 0.178556 | 0.00668697 | ||||||||
\(714\) | 23.4023 | 0.875808 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.8272 | −0.965209 | ||||||||
\(717\) | 10.8419 | 0.404897 | ||||||||
\(718\) | 4.48943 | 0.167544 | ||||||||
\(719\) | 28.4691 | 1.06172 | 0.530859 | − | 0.847460i | \(-0.321869\pi\) | ||||
0.530859 | + | 0.847460i | \(0.321869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.42014 | 0.276341 | ||||||||
\(722\) | 31.3851 | 1.16803 | ||||||||
\(723\) | −27.1803 | −1.01085 | ||||||||
\(724\) | −16.3148 | −0.606335 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.8400 | −1.70011 | −0.850057 | − | 0.526691i | \(-0.823432\pi\) | ||||
−0.850057 | + | 0.526691i | \(0.823432\pi\) | |||||||
\(728\) | 11.3182 | 0.419482 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.4378 | −0.534002 | ||||||||
\(732\) | −12.4188 | −0.459011 | ||||||||
\(733\) | 37.9681 | 1.40239 | 0.701193 | − | 0.712972i | \(-0.252651\pi\) | ||||
0.701193 | + | 0.712972i | \(0.252651\pi\) | |||||||
\(734\) | −2.70391 | −0.0998030 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 54.3944 | 2.00500 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 6.68684 | 0.246146 | ||||||||
\(739\) | −21.1226 | −0.777008 | −0.388504 | − | 0.921447i | \(-0.627008\pi\) | ||||
−0.388504 | + | 0.921447i | \(0.627008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.2255 | 1.18383 | ||||||||
\(742\) | −5.33404 | −0.195819 | ||||||||
\(743\) | 7.98035 | 0.292771 | 0.146385 | − | 0.989228i | \(-0.453236\pi\) | ||||
0.146385 | + | 0.989228i | \(0.453236\pi\) | |||||||
\(744\) | 0.0258305 | 0.000946993 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −44.4588 | −1.62775 | ||||||||
\(747\) | −16.0805 | −0.588355 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.4718 | −1.00380 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.62482 | −0.351215 | −0.175607 | − | 0.984460i | \(-0.556189\pi\) | ||||
−0.175607 | + | 0.984460i | \(0.556189\pi\) | |||||||
\(752\) | 18.6606 | 0.680483 | ||||||||
\(753\) | 5.54443 | 0.202050 | ||||||||
\(754\) | 54.2134 | 1.97434 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.33826 | 0.0850417 | ||||||||
\(757\) | 46.6153 | 1.69426 | 0.847130 | − | 0.531385i | \(-0.178328\pi\) | ||||
0.847130 | + | 0.531385i | \(0.178328\pi\) | |||||||
\(758\) | 29.1076 | 1.05724 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.9943 | 0.797293 | 0.398646 | − | 0.917105i | \(-0.369480\pi\) | ||||
0.398646 | + | 0.917105i | \(0.369480\pi\) | |||||||
\(762\) | 23.1804 | 0.839737 | ||||||||
\(763\) | −7.40646 | −0.268132 | ||||||||
\(764\) | −17.9653 | −0.649962 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.16209 | 0.258777 | ||||||||
\(767\) | −30.3424 | −1.09560 | ||||||||
\(768\) | 20.9452 | 0.755797 | ||||||||
\(769\) | −48.0330 | −1.73211 | −0.866057 | − | 0.499946i | \(-0.833353\pi\) | ||||
−0.866057 | + | 0.499946i | \(0.833353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9439 | 0.682249 | ||||||||
\(772\) | 10.1411 | 0.364986 | ||||||||
\(773\) | 17.0851 | 0.614509 | 0.307255 | − | 0.951627i | \(-0.400590\pi\) | ||||
0.307255 | + | 0.951627i | \(0.400590\pi\) | |||||||
\(774\) | −3.59845 | −0.129344 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.29687 | −0.0824527 | ||||||||
\(777\) | 1.95979 | 0.0703069 | ||||||||
\(778\) | −64.4799 | −2.31172 | ||||||||
\(779\) | −22.0131 | −0.788700 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −111.942 | −4.00304 | ||||||||
\(783\) | −5.53818 | −0.197918 | ||||||||
\(784\) | 19.2842 | 0.688720 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.77247 | 0.0632217 | ||||||||
\(787\) | −22.4918 | −0.801746 | −0.400873 | − | 0.916134i | \(-0.631293\pi\) | ||||
−0.400873 | + | 0.916134i | \(0.631293\pi\) | |||||||
\(788\) | −9.22220 | −0.328527 | ||||||||
\(789\) | 3.20873 | 0.114234 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.5739 | 0.447076 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.7184 | 1.76555 | ||||||||
\(794\) | −42.4307 | −1.50581 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.855682 | 0.0303288 | ||||||||
\(797\) | 3.41778 | 0.121064 | 0.0605321 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605321 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(798\) | −19.2014 | −0.679721 | ||||||||
\(799\) | −27.9999 | −0.990564 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.5062 | −0.512550 | ||||||||
\(802\) | 10.4046 | 0.367398 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.469045 | −0.0165420 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.209135 | 0.00736646 | ||||||||
\(807\) | −3.24423 | −0.114202 | ||||||||
\(808\) | 8.11291 | 0.285411 | ||||||||
\(809\) | 10.1185 | 0.355748 | 0.177874 | − | 0.984053i | \(-0.443078\pi\) | ||||
0.177874 | + | 0.984053i | \(0.443078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.3749 | −0.891034 | −0.445517 | − | 0.895273i | \(-0.646980\pi\) | ||||
−0.445517 | + | 0.895273i | \(0.646980\pi\) | |||||||
\(812\) | −12.9497 | −0.454446 | ||||||||
\(813\) | 2.02977 | 0.0711872 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −35.8147 | −1.25377 | ||||||||
\(817\) | 11.8461 | 0.414443 | ||||||||
\(818\) | −46.5049 | −1.62600 | ||||||||
\(819\) | −9.36121 | −0.327107 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.49915 | −0.0523206 | −0.0261603 | − | 0.999658i | \(-0.508328\pi\) | ||||
−0.0261603 | + | 0.999658i | \(0.508328\pi\) | |||||||
\(822\) | −7.71096 | −0.268951 | ||||||||
\(823\) | 19.1246 | 0.666641 | 0.333320 | − | 0.942814i | \(-0.391831\pi\) | ||||
0.333320 | + | 0.942814i | \(0.391831\pi\) | |||||||
\(824\) | −5.13460 | −0.178872 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0794 | 0.629062 | ||||||||
\(827\) | −16.6305 | −0.578298 | −0.289149 | − | 0.957284i | \(-0.593372\pi\) | ||||
−0.289149 | + | 0.957284i | \(0.593372\pi\) | |||||||
\(828\) | −11.1848 | −0.388699 | ||||||||
\(829\) | 25.6955 | 0.892442 | 0.446221 | − | 0.894923i | \(-0.352769\pi\) | ||||
0.446221 | + | 0.894923i | \(0.352769\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.3166 | 0.392567 | ||||||||
\(832\) | 11.3587 | 0.393793 | ||||||||
\(833\) | −28.9355 | −1.00255 | ||||||||
\(834\) | −16.1669 | −0.559815 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.0213642 | −0.000738455 0 | ||||||||
\(838\) | −24.6383 | −0.851117 | ||||||||
\(839\) | −28.3971 | −0.980376 | −0.490188 | − | 0.871617i | \(-0.663072\pi\) | ||||
−0.490188 | + | 0.871617i | \(0.663072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.67145 | 0.0576363 | ||||||||
\(842\) | 5.38932 | 0.185728 | ||||||||
\(843\) | 10.3177 | 0.355361 | ||||||||
\(844\) | 5.11415 | 0.176036 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.97864 | −0.239930 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.16320 | 0.280325 | ||||||||
\(849\) | −2.10589 | −0.0722739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.37441 | −0.321351 | ||||||||
\(852\) | 6.07327 | 0.208067 | ||||||||
\(853\) | 15.1072 | 0.517260 | 0.258630 | − | 0.965976i | \(-0.416729\pi\) | ||||
0.258630 | + | 0.965976i | \(0.416729\pi\) | |||||||
\(854\) | −29.6244 | −1.01373 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.0100 | 0.649748 | ||||||||
\(857\) | 2.37040 | 0.0809713 | 0.0404856 | − | 0.999180i | \(-0.487109\pi\) | ||||
0.0404856 | + | 0.999180i | \(0.487109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.0423 | 1.53682 | 0.768411 | − | 0.639956i | \(-0.221048\pi\) | ||||
0.768411 | + | 0.639956i | \(0.221048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.39459 | 0.217927 | ||||||||
\(862\) | −21.0531 | −0.717071 | ||||||||
\(863\) | 25.0210 | 0.851724 | 0.425862 | − | 0.904788i | \(-0.359971\pi\) | ||||
0.425862 | + | 0.904788i | \(0.359971\pi\) | |||||||
\(864\) | −6.50828 | −0.221416 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.3974 | −0.693130 | ||||||||
\(867\) | 36.7392 | 1.24773 | ||||||||
\(868\) | −0.0499551 | −0.00169559 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.87782 | 0.0636274 | ||||||||
\(872\) | 5.12514 | 0.173559 | ||||||||
\(873\) | 1.89972 | 0.0642957 | ||||||||
\(874\) | 91.8476 | 3.10679 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.5693 | 0.458465 | ||||||||
\(877\) | −48.8755 | −1.65041 | −0.825203 | − | 0.564836i | \(-0.808940\pi\) | ||||
−0.825203 | + | 0.564836i | \(0.808940\pi\) | |||||||
\(878\) | −1.81544 | −0.0612682 | ||||||||
\(879\) | −23.3755 | −0.788435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.5530 | 1.50103 | 0.750515 | − | 0.660853i | \(-0.229805\pi\) | ||||
0.750515 | + | 0.660853i | \(0.229805\pi\) | |||||||
\(882\) | −7.21182 | −0.242835 | ||||||||
\(883\) | 44.0547 | 1.48256 | 0.741279 | − | 0.671197i | \(-0.234220\pi\) | ||||
0.741279 | + | 0.671197i | \(0.234220\pi\) | |||||||
\(884\) | −52.5613 | −1.76783 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.0661 | 0.674133 | ||||||||
\(887\) | −12.1293 | −0.407261 | −0.203631 | − | 0.979048i | \(-0.565274\pi\) | ||||
−0.203631 | + | 0.979048i | \(0.565274\pi\) | |||||||
\(888\) | −1.35614 | −0.0455089 | ||||||||
\(889\) | 22.1673 | 0.743467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 35.7585 | 1.19728 | ||||||||
\(893\) | 22.9737 | 0.768785 | ||||||||
\(894\) | −17.4552 | −0.583790 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.9750 | 0.533688 | ||||||||
\(897\) | 44.7783 | 1.49510 | ||||||||
\(898\) | 53.0227 | 1.76939 | ||||||||
\(899\) | 0.118319 | 0.00394615 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.2487 | −0.408063 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.44118 | −0.114515 | ||||||||
\(904\) | −8.70089 | −0.289387 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.3357 | 0.409828 | ||||||||
\(907\) | −32.8672 | −1.09134 | −0.545670 | − | 0.838000i | \(-0.683725\pi\) | ||||
−0.545670 | + | 0.838000i | \(0.683725\pi\) | |||||||
\(908\) | 16.3767 | 0.543481 | ||||||||
\(909\) | −6.71011 | −0.222560 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.7054 | −1.54742 | −0.773710 | − | 0.633540i | \(-0.781601\pi\) | ||||
−0.773710 | + | 0.633540i | \(0.781601\pi\) | |||||||
\(912\) | 29.3857 | 0.973058 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6.49842 | −0.214949 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.94847 | −0.295666 | ||||||||
\(917\) | 1.69500 | 0.0559738 | ||||||||
\(918\) | 13.3939 | 0.442063 | ||||||||
\(919\) | −7.33826 | −0.242067 | −0.121033 | − | 0.992648i | \(-0.538621\pi\) | ||||
−0.121033 | + | 0.992648i | \(0.538621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.0518 | −1.05614 | ||||||||
\(922\) | −46.0114 | −1.51530 | ||||||||
\(923\) | −24.3143 | −0.800314 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32.6580 | 1.07321 | ||||||||
\(927\) | 4.24678 | 0.139483 | ||||||||
\(928\) | 36.0441 | 1.18320 | ||||||||
\(929\) | 12.7285 | 0.417609 | 0.208804 | − | 0.977957i | \(-0.433043\pi\) | ||||
0.208804 | + | 0.977957i | \(0.433043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.7413 | 0.778090 | ||||||||
\(932\) | −8.72201 | −0.285699 | ||||||||
\(933\) | 1.63433 | 0.0535055 | ||||||||
\(934\) | 46.0888 | 1.50807 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.47778 | 0.211733 | ||||||||
\(937\) | 19.2533 | 0.628979 | 0.314490 | − | 0.949261i | \(-0.398167\pi\) | ||||
0.314490 | + | 0.949261i | \(0.398167\pi\) | |||||||
\(938\) | −1.11889 | −0.0365330 | ||||||||
\(939\) | −30.4130 | −0.992490 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.2694 | 1.34535 | 0.672673 | − | 0.739940i | \(-0.265146\pi\) | ||||
0.672673 | + | 0.739940i | \(0.265146\pi\) | |||||||
\(942\) | 23.1318 | 0.753673 | ||||||||
\(943\) | −30.5878 | −0.996076 | ||||||||
\(944\) | −27.6686 | −0.900536 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.3012 | 1.63457 | 0.817285 | − | 0.576233i | \(-0.195478\pi\) | ||||
0.817285 | + | 0.576233i | \(0.195478\pi\) | |||||||
\(948\) | −3.43132 | −0.111444 | ||||||||
\(949\) | −54.3247 | −1.76345 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.4340 | 0.954464 | ||||||||
\(952\) | −15.4862 | −0.501910 | ||||||||
\(953\) | −9.02580 | −0.292374 | −0.146187 | − | 0.989257i | \(-0.546700\pi\) | ||||
−0.146187 | + | 0.989257i | \(0.546700\pi\) | |||||||
\(954\) | −3.05284 | −0.0988394 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.5093 | 0.469263 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.56617 | 0.309069 | ||||||||
\(959\) | −7.37396 | −0.238118 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9995 | −0.999985 | ||||||||
\(962\) | −10.9798 | −0.354004 | ||||||||
\(963\) | −15.7230 | −0.506666 | ||||||||
\(964\) | −36.3744 | −1.17154 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −26.6809 | −0.858443 | ||||||||
\(967\) | −30.2503 | −0.972785 | −0.486392 | − | 0.873740i | \(-0.661687\pi\) | ||||
−0.486392 | + | 0.873740i | \(0.661687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44.0926 | −1.41646 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.8285 | 0.411686 | 0.205843 | − | 0.978585i | \(-0.434006\pi\) | ||||
0.205843 | + | 0.978585i | \(0.434006\pi\) | |||||||
\(972\) | 1.33826 | 0.0429247 | ||||||||
\(973\) | −15.4604 | −0.495636 | ||||||||
\(974\) | −16.5262 | −0.529533 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 45.3371 | 1.45120 | ||||||||
\(977\) | 13.1592 | 0.420999 | 0.210500 | − | 0.977594i | \(-0.432491\pi\) | ||||
0.210500 | + | 0.977594i | \(0.432491\pi\) | |||||||
\(978\) | 42.7645 | 1.36746 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.23895 | −0.135339 | ||||||||
\(982\) | 63.6033 | 2.02966 | ||||||||
\(983\) | −22.4369 | −0.715627 | −0.357813 | − | 0.933793i | \(-0.616478\pi\) | ||||
−0.357813 | + | 0.933793i | \(0.616478\pi\) | |||||||
\(984\) | −4.42494 | −0.141062 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −74.1776 | −2.36230 | ||||||||
\(987\) | −6.67364 | −0.212424 | ||||||||
\(988\) | 43.1261 | 1.37203 | ||||||||
\(989\) | 16.4605 | 0.523414 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.9146 | 0.727907 | 0.363953 | − | 0.931417i | \(-0.381427\pi\) | ||||
0.363953 | + | 0.931417i | \(0.381427\pi\) | |||||||
\(992\) | 0.139044 | 0.00441466 | ||||||||
\(993\) | −22.7902 | −0.723226 | ||||||||
\(994\) | 14.4875 | 0.459516 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.5199 | −0.681884 | ||||||||
\(997\) | −16.8394 | −0.533309 | −0.266654 | − | 0.963792i | \(-0.585918\pi\) | ||||
−0.266654 | + | 0.963792i | \(0.585918\pi\) | |||||||
\(998\) | 35.8095 | 1.13353 | ||||||||
\(999\) | 1.12165 | 0.0354874 |
(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 | 9075.2.a.df.1.4 | 4 | ||
5.4 | even | 2 | 1815.2.a.q.1.1 | 4 | |||
11.7 | odd | 10 | 825.2.n.j.676.1 | 8 | |||
11.8 | odd | 10 | 825.2.n.j.526.1 | 8 | |||
11.10 | odd | 2 | 9075.2.a.co.1.1 | 4 | |||
15.14 | odd | 2 | 5445.2.a.bq.1.4 | 4 | |||
55.7 | even | 20 | 825.2.bx.e.49.4 | 16 | |||
55.8 | even | 20 | 825.2.bx.e.724.4 | 16 | |||
55.18 | even | 20 | 825.2.bx.e.49.1 | 16 | |||
55.19 | odd | 10 | 165.2.m.c.31.2 | yes | 8 | ||
55.29 | odd | 10 | 165.2.m.c.16.2 | ✓ | 8 | ||
55.52 | even | 20 | 825.2.bx.e.724.1 | 16 | |||
55.54 | odd | 2 | 1815.2.a.u.1.4 | 4 | |||
165.29 | even | 10 | 495.2.n.c.181.1 | 8 | |||
165.74 | even | 10 | 495.2.n.c.361.1 | 8 | |||
165.164 | even | 2 | 5445.2.a.bj.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.c.16.2 | ✓ | 8 | 55.29 | odd | 10 | ||
165.2.m.c.31.2 | yes | 8 | 55.19 | odd | 10 | ||
495.2.n.c.181.1 | 8 | 165.29 | even | 10 | |||
495.2.n.c.361.1 | 8 | 165.74 | even | 10 | |||
825.2.n.j.526.1 | 8 | 11.8 | odd | 10 | |||
825.2.n.j.676.1 | 8 | 11.7 | odd | 10 | |||
825.2.bx.e.49.1 | 16 | 55.18 | even | 20 | |||
825.2.bx.e.49.4 | 16 | 55.7 | even | 20 | |||
825.2.bx.e.724.1 | 16 | 55.52 | even | 20 | |||
825.2.bx.e.724.4 | 16 | 55.8 | even | 20 | |||
1815.2.a.q.1.1 | 4 | 5.4 | even | 2 | |||
1815.2.a.u.1.4 | 4 | 55.54 | odd | 2 | |||
5445.2.a.bj.1.1 | 4 | 165.164 | even | 2 | |||
5445.2.a.bq.1.4 | 4 | 15.14 | odd | 2 | |||
9075.2.a.co.1.1 | 4 | 11.10 | odd | 2 | |||
9075.2.a.df.1.4 | 4 | 1.1 | even | 1 | trivial |