Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 28x^{14} + 290x^{12} + 1396x^{10} + 3263x^{8} + 3508x^{6} + 1442x^{4} + 128x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.4 | ||
Root | \(0.328628i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.737 |
Dual form | 2070.2.j.i.323.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.80260 | + | 1.32312i | 0.806147 | + | 0.591716i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.949464 | + | 0.949464i | 0.358864 | + | 0.358864i | 0.863394 | − | 0.504530i | \(-0.168334\pi\) |
−0.504530 | + | 0.863394i | \(0.668334\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.21021 | + | 0.339045i | −0.698931 | + | 0.107215i | ||||
\(11\) | 2.64623i | 0.797870i | 0.916979 | + | 0.398935i | \(0.130620\pi\) | ||||
−0.916979 | + | 0.398935i | \(0.869380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 2.00000i | 0.554700 | − | 0.554700i | −0.373094 | − | 0.927794i | \(-0.621703\pi\) |
0.927794 | + | 0.373094i | \(0.121703\pi\) | |||||||
\(14\) | −1.34274 | −0.358864 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.94794 | + | 4.94794i | −1.20005 | + | 1.20005i | −0.225902 | + | 0.974150i | \(0.572533\pi\) |
−0.974150 | + | 0.225902i | \(0.927467\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.42043i | 0.555285i | 0.960685 | + | 0.277642i | \(0.0895530\pi\) | ||||
−0.960685 | + | 0.277642i | \(0.910447\pi\) | |||||||
\(20\) | 1.32312 | − | 1.80260i | 0.295858 | − | 0.403073i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.87117 | − | 1.87117i | −0.398935 | − | 0.398935i | ||||
\(23\) | −0.707107 | − | 0.707107i | −0.147442 | − | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.49872 | + | 4.77010i | 0.299745 | + | 0.954019i | ||||
\(26\) | 2.82843i | 0.554700i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.949464 | − | 0.949464i | 0.179432 | − | 0.179432i | ||||
\(29\) | 0.383781 | 0.0712664 | 0.0356332 | − | 0.999365i | \(-0.488655\pi\) | ||||
0.0356332 | + | 0.999365i | \(0.488655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.99745 | −1.25678 | −0.628389 | − | 0.777899i | \(-0.716285\pi\) | ||||
−0.628389 | + | 0.777899i | \(0.716285\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.99745i | − | 1.20005i | ||||||
\(35\) | 0.455250 | + | 2.96775i | 0.0769514 | + | 0.501642i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.820634 | − | 0.820634i | −0.134911 | − | 0.134911i | 0.636426 | − | 0.771338i | \(-0.280412\pi\) |
−0.771338 | + | 0.636426i | \(0.780412\pi\) | |||||||
\(38\) | −1.71150 | − | 1.71150i | −0.277642 | − | 0.277642i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.339045 | + | 2.21021i | 0.0536077 | + | 0.349466i | ||||
\(41\) | 5.41240i | 0.845275i | 0.906299 | + | 0.422637i | \(0.138896\pi\) | ||||
−0.906299 | + | 0.422637i | \(0.861104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.82063 | + | 2.82063i | −0.430143 | + | 0.430143i | −0.888677 | − | 0.458534i | \(-0.848375\pi\) |
0.458534 | + | 0.888677i | \(0.348375\pi\) | |||||||
\(44\) | 2.64623 | 0.398935 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.19098 | − | 2.19098i | 0.319588 | − | 0.319588i | −0.529021 | − | 0.848609i | \(-0.677441\pi\) |
0.848609 | + | 0.529021i | \(0.177441\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.19704i | − | 0.742434i | ||||||
\(50\) | −4.43273 | − | 2.31321i | −0.626882 | − | 0.327137i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | − | 2.00000i | −0.277350 | − | 0.277350i | ||||
\(53\) | 7.11469 | + | 7.11469i | 0.977278 | + | 0.977278i | 0.999748 | − | 0.0224692i | \(-0.00715276\pi\) |
−0.0224692 | + | 0.999748i | \(0.507153\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.50128 | + | 4.77010i | −0.472112 | + | 0.643200i | ||||
\(56\) | 1.34274i | 0.179432i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.271374 | + | 0.271374i | −0.0356332 | + | 0.0356332i | ||||
\(59\) | 1.93732 | 0.252218 | 0.126109 | − | 0.992016i | \(-0.459751\pi\) | ||||
0.126109 | + | 0.992016i | \(0.459751\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.31936 | −1.06518 | −0.532592 | − | 0.846372i | \(-0.678782\pi\) | ||||
−0.532592 | + | 0.846372i | \(0.678782\pi\) | |||||||
\(62\) | 4.94794 | − | 4.94794i | 0.628389 | − | 0.628389i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 6.25143 | − | 0.958963i | 0.775395 | − | 0.118945i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.59724 | − | 2.59724i | −0.317304 | − | 0.317304i | 0.530427 | − | 0.847731i | \(-0.322032\pi\) |
−0.847731 | + | 0.530427i | \(0.822032\pi\) | |||||||
\(68\) | 4.94794 | + | 4.94794i | 0.600026 | + | 0.600026i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.42043 | − | 1.77661i | −0.289297 | − | 0.212345i | ||||
\(71\) | 8.76755i | 1.04052i | 0.854009 | + | 0.520258i | \(0.174164\pi\) | ||||
−0.854009 | + | 0.520258i | \(0.825836\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.26882 | − | 8.26882i | 0.967792 | − | 0.967792i | −0.0317050 | − | 0.999497i | \(-0.510094\pi\) |
0.999497 | + | 0.0317050i | \(0.0100937\pi\) | |||||||
\(74\) | 1.16055 | 0.134911 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.42043 | 0.277642 | ||||||||
\(77\) | −2.51250 | + | 2.51250i | −0.286326 | + | 0.286326i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.2526i | − | 1.37852i | −0.724514 | − | 0.689260i | \(-0.757936\pi\) | ||
0.724514 | − | 0.689260i | \(-0.242064\pi\) | |||||||
\(80\) | −1.80260 | − | 1.32312i | −0.201537 | − | 0.147929i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.82714 | − | 3.82714i | −0.422637 | − | 0.422637i | ||||
\(83\) | 5.56115 | + | 5.56115i | 0.610416 | + | 0.610416i | 0.943054 | − | 0.332638i | \(-0.107939\pi\) |
−0.332638 | + | 0.943054i | \(0.607939\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.4659 | + | 2.37245i | −1.67751 | + | 0.257328i | ||||
\(86\) | − | 3.98898i | − | 0.430143i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.87117 | + | 1.87117i | −0.199467 | + | 0.199467i | ||||
\(89\) | −5.34093 | −0.566137 | −0.283069 | − | 0.959100i | \(-0.591352\pi\) | ||||
−0.283069 | + | 0.959100i | \(0.591352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.79785 | 0.398123 | ||||||||
\(92\) | −0.707107 | + | 0.707107i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.09852i | 0.319588i | ||||||||
\(95\) | −3.20251 | + | 4.36306i | −0.328571 | + | 0.447641i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.46841 | + | 4.46841i | 0.453698 | + | 0.453698i | 0.896580 | − | 0.442882i | \(-0.146044\pi\) |
−0.442882 | + | 0.896580i | \(0.646044\pi\) | |||||||
\(98\) | 3.67486 | + | 3.67486i | 0.371217 | + | 0.371217i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.77010 | − | 1.49872i | 0.477010 | − | 0.149872i | ||||
\(101\) | − | 4.62281i | − | 0.459987i | −0.973192 | − | 0.229993i | \(-0.926130\pi\) | ||
0.973192 | − | 0.229993i | \(-0.0738705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.949464 | + | 0.949464i | −0.0935534 | + | 0.0935534i | −0.752335 | − | 0.658781i | \(-0.771072\pi\) |
0.658781 | + | 0.752335i | \(0.271072\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0617 | −0.977278 | ||||||||
\(107\) | 1.18839 | − | 1.18839i | 0.114886 | − | 0.114886i | −0.647326 | − | 0.762213i | \(-0.724113\pi\) |
0.762213 | + | 0.647326i | \(0.224113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5138i | 1.29439i | 0.762324 | + | 0.647196i | \(0.224058\pi\) | ||||
−0.762324 | + | 0.647196i | \(0.775942\pi\) | |||||||
\(110\) | −0.897192 | − | 5.84874i | −0.0855439 | − | 0.557656i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.949464 | − | 0.949464i | −0.0897159 | − | 0.0897159i | ||||
\(113\) | 3.74814 | + | 3.74814i | 0.352595 | + | 0.352595i | 0.861074 | − | 0.508479i | \(-0.169792\pi\) |
−0.508479 | + | 0.861074i | \(0.669792\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.339045 | − | 2.21021i | −0.0316161 | − | 0.206104i | ||||
\(116\) | − | 0.383781i | − | 0.0356332i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.36989 | + | 1.36989i | −0.126109 | + | 0.126109i | ||||
\(119\) | −9.39578 | −0.861310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.99745 | 0.363404 | ||||||||
\(122\) | 5.88267 | − | 5.88267i | 0.532592 | − | 0.532592i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.99745i | 0.628389i | ||||||||
\(125\) | −3.60980 | + | 10.5816i | −0.322870 | + | 0.946443i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.79785 | − | 6.79785i | −0.603212 | − | 0.603212i | 0.337951 | − | 0.941164i | \(-0.390266\pi\) |
−0.941164 | + | 0.337951i | \(0.890266\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.74234 | + | 5.09852i | −0.328225 | + | 0.447170i | ||||
\(131\) | − | 3.08769i | − | 0.269772i | −0.990861 | − | 0.134886i | \(-0.956933\pi\) | ||
0.990861 | − | 0.134886i | \(-0.0430669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.29811 | + | 2.29811i | −0.199271 | + | 0.199271i | ||||
\(134\) | 3.67305 | 0.317304 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.99745 | −0.600026 | ||||||||
\(137\) | 2.43544 | − | 2.43544i | 0.208074 | − | 0.208074i | −0.595375 | − | 0.803448i | \(-0.702996\pi\) |
0.803448 | + | 0.595375i | \(0.202996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.9368i | 1.77584i | 0.460000 | + | 0.887919i | \(0.347850\pi\) | ||||
−0.460000 | + | 0.887919i | \(0.652150\pi\) | |||||||
\(140\) | 2.96775 | − | 0.455250i | 0.250821 | − | 0.0384757i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.19959 | − | 6.19959i | −0.520258 | − | 0.520258i | ||||
\(143\) | 5.29247 | + | 5.29247i | 0.442578 | + | 0.442578i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.691804 | + | 0.507788i | 0.0574512 | + | 0.0421695i | ||||
\(146\) | 11.6939i | 0.967792i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.820634 | + | 0.820634i | −0.0674557 | + | 0.0674557i | ||||
\(149\) | −13.0494 | −1.06905 | −0.534526 | − | 0.845152i | \(-0.679510\pi\) | ||||
−0.534526 | + | 0.845152i | \(0.679510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9394 | −0.971613 | −0.485806 | − | 0.874066i | \(-0.661474\pi\) | ||||
−0.485806 | + | 0.874066i | \(0.661474\pi\) | |||||||
\(152\) | −1.71150 | + | 1.71150i | −0.138821 | + | 0.138821i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 3.55322i | − | 0.286326i | ||||||
\(155\) | −12.6136 | − | 9.25844i | −1.01315 | − | 0.743656i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.4593 | + | 15.4593i | 1.23379 | + | 1.23379i | 0.962497 | + | 0.271294i | \(0.0874514\pi\) |
0.271294 | + | 0.962497i | \(0.412549\pi\) | |||||||
\(158\) | 8.66386 | + | 8.66386i | 0.689260 | + | 0.689260i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.21021 | − | 0.339045i | 0.174733 | − | 0.0268038i | ||||
\(161\) | − | 1.34274i | − | 0.105823i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.19704 | + | 2.19704i | −0.172085 | + | 0.172085i | −0.787895 | − | 0.615810i | \(-0.788829\pi\) |
0.615810 | + | 0.787895i | \(0.288829\pi\) | |||||||
\(164\) | 5.41240 | 0.422637 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.86466 | −0.610416 | ||||||||
\(167\) | 2.05166 | − | 2.05166i | 0.158762 | − | 0.158762i | −0.623256 | − | 0.782018i | \(-0.714191\pi\) |
0.782018 | + | 0.623256i | \(0.214191\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 9.25844 | − | 12.6136i | 0.710090 | − | 0.967418i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.82063 | + | 2.82063i | 0.215071 | + | 0.215071i | ||||
\(173\) | −2.75696 | − | 2.75696i | −0.209608 | − | 0.209608i | 0.594493 | − | 0.804101i | \(-0.297353\pi\) |
−0.804101 | + | 0.594493i | \(0.797353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.10605 | + | 5.95202i | −0.234795 | + | 0.449930i | ||||
\(176\) | − | 2.64623i | − | 0.199467i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.77661 | − | 3.77661i | 0.283069 | − | 0.283069i | ||||
\(179\) | −12.2620 | −0.916506 | −0.458253 | − | 0.888822i | \(-0.651525\pi\) | ||||
−0.458253 | + | 0.888822i | \(0.651525\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.77661 | 0.280713 | 0.140357 | − | 0.990101i | \(-0.455175\pi\) | ||||
0.140357 | + | 0.990101i | \(0.455175\pi\) | |||||||
\(182\) | −2.68549 | + | 2.68549i | −0.199062 | + | 0.199062i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | −0.393479 | − | 2.56507i | −0.0289291 | − | 0.188588i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.0934 | − | 13.0934i | −0.957485 | − | 0.957485i | ||||
\(188\) | −2.19098 | − | 2.19098i | −0.159794 | − | 0.159794i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.820634 | − | 5.34967i | −0.0595350 | − | 0.388106i | ||||
\(191\) | 17.0094i | 1.23075i | 0.788233 | + | 0.615377i | \(0.210996\pi\) | ||||
−0.788233 | + | 0.615377i | \(0.789004\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8964 | − | 17.8964i | 1.28821 | − | 1.28821i | 0.352335 | − | 0.935874i | \(-0.385388\pi\) |
0.935874 | − | 0.352335i | \(-0.114612\pi\) | |||||||
\(194\) | −6.31929 | −0.453698 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.19704 | −0.371217 | ||||||||
\(197\) | −2.70850 | + | 2.70850i | −0.192972 | + | 0.192972i | −0.796979 | − | 0.604007i | \(-0.793570\pi\) |
0.604007 | + | 0.796979i | \(0.293570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.19448i | − | 0.510003i | −0.966941 | − | 0.255002i | \(-0.917924\pi\) | ||
0.966941 | − | 0.255002i | \(-0.0820760\pi\) | |||||||
\(200\) | −2.31321 | + | 4.43273i | −0.163569 | + | 0.313441i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.26882 | + | 3.26882i | 0.229993 | + | 0.229993i | ||||
\(203\) | 0.364386 | + | 0.364386i | 0.0255749 | + | 0.0255749i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.16124 | + | 9.75638i | −0.500163 | + | 0.681415i | ||||
\(206\) | − | 1.34274i | − | 0.0935534i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.00000 | + | 2.00000i | −0.138675 | + | 0.138675i | ||||
\(209\) | −6.40502 | −0.443045 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0685362 | −0.00471823 | −0.00235911 | − | 0.999997i | \(-0.500751\pi\) | ||||
−0.00235911 | + | 0.999997i | \(0.500751\pi\) | |||||||
\(212\) | 7.11469 | − | 7.11469i | 0.488639 | − | 0.488639i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.68064i | 0.114886i | ||||||||
\(215\) | −8.81650 | + | 1.35244i | −0.601280 | + | 0.0922358i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.64382 | − | 6.64382i | −0.451012 | − | 0.451012i | ||||
\(218\) | −9.55573 | − | 9.55573i | −0.647196 | − | 0.647196i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.77010 | + | 3.50128i | 0.321600 | + | 0.236056i | ||||
\(221\) | 19.7918i | 1.33134i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.6524 | + | 19.6524i | −1.31602 | + | 1.31602i | −0.399129 | + | 0.916895i | \(0.630688\pi\) |
−0.916895 | + | 0.399129i | \(0.869312\pi\) | |||||||
\(224\) | 1.34274 | 0.0897159 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.30066 | −0.352595 | ||||||||
\(227\) | −2.83984 | + | 2.83984i | −0.188487 | + | 0.188487i | −0.795042 | − | 0.606555i | \(-0.792551\pi\) |
0.606555 | + | 0.795042i | \(0.292551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.42554i | − | 0.292448i | −0.989252 | − | 0.146224i | \(-0.953288\pi\) | ||
0.989252 | − | 0.146224i | \(-0.0467120\pi\) | |||||||
\(230\) | 1.80260 | + | 1.32312i | 0.118860 | + | 0.0872437i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.271374 | + | 0.271374i | 0.0178166 | + | 0.0178166i | ||||
\(233\) | 0.799777 | + | 0.799777i | 0.0523951 | + | 0.0523951i | 0.732819 | − | 0.680424i | \(-0.238204\pi\) |
−0.680424 | + | 0.732819i | \(0.738204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.84839 | − | 1.05054i | 0.446740 | − | 0.0685294i | ||||
\(236\) | − | 1.93732i | − | 0.126109i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.64382 | − | 6.64382i | 0.430655 | − | 0.430655i | ||||
\(239\) | −17.2078 | −1.11308 | −0.556540 | − | 0.830821i | \(-0.687871\pi\) | ||||
−0.556540 | + | 0.830821i | \(0.687871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.25511 | 0.338511 | 0.169256 | − | 0.985572i | \(-0.445864\pi\) | ||||
0.169256 | + | 0.985572i | \(0.445864\pi\) | |||||||
\(242\) | −2.82662 | + | 2.82662i | −0.181702 | + | 0.181702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.31936i | 0.532592i | ||||||||
\(245\) | 6.87629 | − | 9.36817i | 0.439310 | − | 0.598511i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.84086 | + | 4.84086i | 0.308016 | + | 0.308016i | ||||
\(248\) | −4.94794 | − | 4.94794i | −0.314195 | − | 0.314195i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.92978 | − | 10.0348i | −0.311786 | − | 0.634657i | ||||
\(251\) | 16.1381i | 1.01863i | 0.860581 | + | 0.509314i | \(0.170101\pi\) | ||||
−0.860581 | + | 0.509314i | \(0.829899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.87117 | − | 1.87117i | 0.117639 | − | 0.117639i | ||||
\(254\) | 9.61362 | 0.603212 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.8720 | − | 21.8720i | 1.36434 | − | 1.36434i | 0.496040 | − | 0.868300i | \(-0.334787\pi\) |
0.868300 | − | 0.496040i | \(-0.165213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.55832i | − | 0.0968295i | ||||||
\(260\) | −0.958963 | − | 6.25143i | −0.0594724 | − | 0.387697i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.18332 | + | 2.18332i | 0.134886 | + | 0.134886i | ||||
\(263\) | −19.9541 | − | 19.9541i | −1.23042 | − | 1.23042i | −0.963801 | − | 0.266621i | \(-0.914093\pi\) |
−0.266621 | − | 0.963801i | \(-0.585907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.41136 | + | 22.2385i | 0.209558 | + | 1.36610i | ||||
\(266\) | − | 3.25002i | − | 0.199271i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.59724 | + | 2.59724i | −0.158652 | + | 0.158652i | ||||
\(269\) | −28.0750 | −1.71176 | −0.855881 | − | 0.517172i | \(-0.826985\pi\) | ||||
−0.855881 | + | 0.517172i | \(0.826985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.6766 | 1.43825 | 0.719126 | − | 0.694880i | \(-0.244542\pi\) | ||||
0.719126 | + | 0.694880i | \(0.244542\pi\) | |||||||
\(272\) | 4.94794 | − | 4.94794i | 0.300013 | − | 0.300013i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.44423i | 0.208074i | ||||||||
\(275\) | −12.6228 | + | 3.96597i | −0.761183 | + | 0.239157i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.55577 | − | 6.55577i | −0.393898 | − | 0.393898i | 0.482176 | − | 0.876074i | \(-0.339846\pi\) |
−0.876074 | + | 0.482176i | \(0.839846\pi\) | |||||||
\(278\) | −14.8046 | − | 14.8046i | −0.887919 | − | 0.887919i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.77661 | + | 2.42043i | −0.106173 | + | 0.144648i | ||||
\(281\) | 20.6150i | 1.22979i | 0.788610 | + | 0.614894i | \(0.210801\pi\) | ||||
−0.788610 | + | 0.614894i | \(0.789199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.59980 | − | 5.59980i | 0.332873 | − | 0.332873i | −0.520803 | − | 0.853677i | \(-0.674368\pi\) |
0.853677 | + | 0.520803i | \(0.174368\pi\) | |||||||
\(284\) | 8.76755 | 0.520258 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.48468 | −0.442578 | ||||||||
\(287\) | −5.13888 | + | 5.13888i | −0.303338 | + | 0.303338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 31.9643i | − | 1.88025i | ||||||
\(290\) | −0.848239 | + | 0.130119i | −0.0498103 | + | 0.00764085i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.26882 | − | 8.26882i | −0.483896 | − | 0.483896i | ||||
\(293\) | 15.4662 | + | 15.4662i | 0.903548 | + | 0.903548i | 0.995741 | − | 0.0921935i | \(-0.0293878\pi\) |
−0.0921935 | + | 0.995741i | \(0.529388\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.49221 | + | 2.56330i | 0.203324 | + | 0.149241i | ||||
\(296\) | − | 1.16055i | − | 0.0674557i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.22735 | − | 9.22735i | 0.534526 | − | 0.534526i | ||||
\(299\) | −2.82843 | −0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.35618 | −0.308725 | ||||||||
\(302\) | 8.44241 | − | 8.44241i | 0.485806 | − | 0.485806i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 2.42043i | − | 0.138821i | ||||||
\(305\) | −14.9965 | − | 11.0075i | −0.858695 | − | 0.630287i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.58575 | + | 7.58575i | 0.432942 | + | 0.432942i | 0.889628 | − | 0.456686i | \(-0.150964\pi\) |
−0.456686 | + | 0.889628i | \(0.650964\pi\) | |||||||
\(308\) | 2.51250 | + | 2.51250i | 0.143163 | + | 0.143163i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.4659 | − | 2.37245i | 0.878402 | − | 0.134746i | ||||
\(311\) | − | 3.89765i | − | 0.221015i | −0.993875 | − | 0.110508i | \(-0.964752\pi\) | ||
0.993875 | − | 0.110508i | \(-0.0352477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9231 | − | 14.9231i | 0.843504 | − | 0.843504i | −0.145809 | − | 0.989313i | \(-0.546578\pi\) |
0.989313 | + | 0.145809i | \(0.0465784\pi\) | |||||||
\(314\) | −21.8628 | −1.23379 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.2526 | −0.689260 | ||||||||
\(317\) | 19.2202 | − | 19.2202i | 1.07951 | − | 1.07951i | 0.0829610 | − | 0.996553i | \(-0.473562\pi\) |
0.996553 | − | 0.0829610i | \(-0.0264377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.01558i | 0.0568613i | ||||||||
\(320\) | −1.32312 | + | 1.80260i | −0.0739645 | + | 0.100768i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.949464 | + | 0.949464i | 0.0529115 | + | 0.0529115i | ||||
\(323\) | −11.9761 | − | 11.9761i | −0.666370 | − | 0.666370i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5376 | + | 6.54275i | 0.695463 | + | 0.362926i | ||||
\(326\) | − | 3.10708i | − | 0.172085i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.82714 | + | 3.82714i | −0.211319 | + | 0.211319i | ||||
\(329\) | 4.16052 | 0.229377 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0960 | 1.10457 | 0.552287 | − | 0.833654i | \(-0.313755\pi\) | ||||
0.552287 | + | 0.833654i | \(0.313755\pi\) | |||||||
\(332\) | 5.56115 | − | 5.56115i | 0.305208 | − | 0.305208i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.90148i | 0.158762i | ||||||||
\(335\) | −1.24533 | − | 8.11824i | −0.0680396 | − | 0.443547i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6706 | + | 10.6706i | 0.581262 | + | 0.581262i | 0.935250 | − | 0.353988i | \(-0.115175\pi\) |
−0.353988 | + | 0.935250i | \(0.615175\pi\) | |||||||
\(338\) | −3.53553 | − | 3.53553i | −0.192308 | − | 0.192308i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.37245 | + | 15.4659i | 0.128664 | + | 0.838754i | ||||
\(341\) | − | 18.5169i | − | 1.00275i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5806 | − | 11.5806i | 0.625296 | − | 0.625296i | ||||
\(344\) | −3.98898 | −0.215071 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.89893 | 0.209608 | ||||||||
\(347\) | 25.3808 | − | 25.3808i | 1.36251 | − | 1.36251i | 0.491806 | − | 0.870705i | \(-0.336337\pi\) |
0.870705 | − | 0.491806i | \(-0.163663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.45725i | − | 0.0780049i | −0.999239 | − | 0.0390024i | \(-0.987582\pi\) | ||
0.999239 | − | 0.0390024i | \(-0.0124180\pi\) | |||||||
\(350\) | −2.01240 | − | 6.40502i | −0.107567 | − | 0.342363i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.87117 | + | 1.87117i | 0.0997337 | + | 0.0997337i | ||||
\(353\) | 6.53153 | + | 6.53153i | 0.347638 | + | 0.347638i | 0.859229 | − | 0.511591i | \(-0.170944\pi\) |
−0.511591 | + | 0.859229i | \(0.670944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.6005 | + | 15.8044i | −0.615690 | + | 0.838809i | ||||
\(356\) | 5.34093i | 0.283069i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.67056 | − | 8.67056i | 0.458253 | − | 0.458253i | ||||
\(359\) | −13.9135 | −0.734325 | −0.367162 | − | 0.930157i | \(-0.619671\pi\) | ||||
−0.367162 | + | 0.930157i | \(0.619671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.1415 | 0.691659 | ||||||||
\(362\) | −2.67047 | + | 2.67047i | −0.140357 | + | 0.140357i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 3.79785i | − | 0.199062i | ||||||
\(365\) | 25.8460 | − | 3.96475i | 1.35284 | − | 0.207524i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.87837 | − | 5.87837i | −0.306849 | − | 0.306849i | 0.536837 | − | 0.843686i | \(-0.319619\pi\) |
−0.843686 | + | 0.536837i | \(0.819619\pi\) | |||||||
\(368\) | 0.707107 | + | 0.707107i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.09201 | + | 1.53555i | 0.108758 | + | 0.0798292i | ||||
\(371\) | 13.5103i | 0.701419i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5049 | − | 13.5049i | 0.699257 | − | 0.699257i | −0.264993 | − | 0.964250i | \(-0.585370\pi\) |
0.964250 | + | 0.264993i | \(0.0853696\pi\) | |||||||
\(374\) | 18.5169 | 0.957485 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.09852 | 0.159794 | ||||||||
\(377\) | 0.767563 | − | 0.767563i | 0.0395315 | − | 0.0395315i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2692i | 1.09253i | 0.837614 | + | 0.546263i | \(0.183950\pi\) | ||||
−0.837614 | + | 0.546263i | \(0.816050\pi\) | |||||||
\(380\) | 4.36306 | + | 3.20251i | 0.223820 | + | 0.164285i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0274 | − | 12.0274i | −0.615377 | − | 0.615377i | ||||
\(383\) | 13.5403 | + | 13.5403i | 0.691879 | + | 0.691879i | 0.962645 | − | 0.270766i | \(-0.0872771\pi\) |
−0.270766 | + | 0.962645i | \(0.587277\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.85337 | + | 1.20470i | −0.400245 | + | 0.0613971i | ||||
\(386\) | 25.3093i | 1.28821i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.46841 | − | 4.46841i | 0.226849 | − | 0.226849i | ||||
\(389\) | 21.2504 | 1.07744 | 0.538718 | − | 0.842486i | \(-0.318909\pi\) | ||||
0.538718 | + | 0.842486i | \(0.318909\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.99745 | 0.353876 | ||||||||
\(392\) | 3.67486 | − | 3.67486i | 0.185608 | − | 0.185608i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 3.83039i | − | 0.192972i | ||||||
\(395\) | 16.2116 | − | 22.0864i | 0.815692 | − | 1.11129i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.48468 | − | 3.48468i | −0.174891 | − | 0.174891i | 0.614233 | − | 0.789124i | \(-0.289465\pi\) |
−0.789124 | + | 0.614233i | \(0.789465\pi\) | |||||||
\(398\) | 5.08727 | + | 5.08727i | 0.255002 | + | 0.255002i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.49872 | − | 4.77010i | −0.0749362 | − | 0.238505i | ||||
\(401\) | 31.1927i | 1.55769i | 0.627216 | + | 0.778845i | \(0.284194\pi\) | ||||
−0.627216 | + | 0.778845i | \(0.715806\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.9949 | + | 13.9949i | −0.697135 | + | 0.697135i | ||||
\(404\) | −4.62281 | −0.229993 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.515320 | −0.0255749 | ||||||||
\(407\) | 2.17159 | − | 2.17159i | 0.107642 | − | 0.107642i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.57529i | − | 0.226233i | −0.993582 | − | 0.113117i | \(-0.963917\pi\) | ||
0.993582 | − | 0.113117i | \(-0.0360834\pi\) | |||||||
\(410\) | −1.83505 | − | 11.9626i | −0.0906264 | − | 0.590789i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.949464 | + | 0.949464i | 0.0467767 | + | 0.0467767i | ||||
\(413\) | 1.83942 | + | 1.83942i | 0.0905118 | + | 0.0905118i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.66647 | + | 17.3826i | 0.130892 | + | 0.853278i | ||||
\(416\) | − | 2.82843i | − | 0.138675i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.52903 | − | 4.52903i | 0.221522 | − | 0.221522i | ||||
\(419\) | 9.80817 | 0.479160 | 0.239580 | − | 0.970877i | \(-0.422990\pi\) | ||||
0.239580 | + | 0.970877i | \(0.422990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0512 | 0.831026 | 0.415513 | − | 0.909587i | \(-0.363602\pi\) | ||||
0.415513 | + | 0.909587i | \(0.363602\pi\) | |||||||
\(422\) | 0.0484624 | − | 0.0484624i | 0.00235911 | − | 0.00235911i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.0617i | 0.488639i | ||||||||
\(425\) | −31.0178 | − | 16.1866i | −1.50458 | − | 0.785164i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.89893 | − | 7.89893i | −0.382256 | − | 0.382256i | ||||
\(428\) | −1.18839 | − | 1.18839i | −0.0574432 | − | 0.0574432i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.27788 | − | 7.19053i | 0.254522 | − | 0.346758i | ||||
\(431\) | − | 2.20380i | − | 0.106153i | −0.998590 | − | 0.0530767i | \(-0.983097\pi\) | ||
0.998590 | − | 0.0530767i | \(-0.0169028\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8571 | − | 11.8571i | 0.569817 | − | 0.569817i | −0.362260 | − | 0.932077i | \(-0.617995\pi\) |
0.932077 | + | 0.362260i | \(0.117995\pi\) | |||||||
\(434\) | 9.39578 | 0.451012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.5138 | 0.647196 | ||||||||
\(437\) | 1.71150 | − | 1.71150i | 0.0818722 | − | 0.0818722i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.0255i | − | 0.621675i | −0.950463 | − | 0.310837i | \(-0.899391\pi\) | ||
0.950463 | − | 0.310837i | \(-0.100609\pi\) | |||||||
\(440\) | −5.84874 | + | 0.897192i | −0.278828 | + | 0.0427719i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.9949 | − | 13.9949i | −0.665669 | − | 0.665669i | ||||
\(443\) | −16.5990 | − | 16.5990i | −0.788640 | − | 0.788640i | 0.192631 | − | 0.981271i | \(-0.438298\pi\) |
−0.981271 | + | 0.192631i | \(0.938298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.62755 | − | 7.06668i | −0.456390 | − | 0.334993i | ||||
\(446\) | − | 27.7927i | − | 1.31602i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.949464 | + | 0.949464i | −0.0448579 | + | 0.0448579i | ||||
\(449\) | 13.8119 | 0.651826 | 0.325913 | − | 0.945400i | \(-0.394328\pi\) | ||||
0.325913 | + | 0.945400i | \(0.394328\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.3225 | −0.674419 | ||||||||
\(452\) | 3.74814 | − | 3.74814i | 0.176297 | − | 0.176297i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.01614i | − | 0.188487i | ||||||
\(455\) | 6.84601 | + | 5.02501i | 0.320946 | + | 0.235576i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0822505 | + | 0.0822505i | 0.00384751 | + | 0.00384751i | 0.709028 | − | 0.705180i | \(-0.249134\pi\) |
−0.705180 | + | 0.709028i | \(0.749134\pi\) | |||||||
\(458\) | 3.12933 | + | 3.12933i | 0.146224 | + | 0.146224i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.21021 | + | 0.339045i | −0.103052 | + | 0.0158080i | ||||
\(461\) | − | 31.1893i | − | 1.45263i | −0.687362 | − | 0.726315i | \(-0.741231\pi\) | ||
0.687362 | − | 0.726315i | \(-0.258769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.05552 | + | 9.05552i | −0.420845 | + | 0.420845i | −0.885495 | − | 0.464649i | \(-0.846180\pi\) |
0.464649 | + | 0.885495i | \(0.346180\pi\) | |||||||
\(464\) | −0.383781 | −0.0178166 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.13105 | −0.0523951 | ||||||||
\(467\) | −9.87526 | + | 9.87526i | −0.456973 | + | 0.456973i | −0.897660 | − | 0.440688i | \(-0.854735\pi\) |
0.440688 | + | 0.897660i | \(0.354735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.93197i | − | 0.227737i | ||||||
\(470\) | −4.09970 | + | 5.58539i | −0.189105 | + | 0.257635i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.36989 | + | 1.36989i | 0.0630544 | + | 0.0630544i | ||||
\(473\) | −7.46406 | − | 7.46406i | −0.343198 | − | 0.343198i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.5457 | + | 3.62755i | −0.529752 | + | 0.166444i | ||||
\(476\) | 9.39578i | 0.430655i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.1677 | − | 12.1677i | 0.556540 | − | 0.556540i | ||||
\(479\) | −21.3913 | −0.977394 | −0.488697 | − | 0.872453i | \(-0.662528\pi\) | ||||
−0.488697 | + | 0.872453i | \(0.662528\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.28253 | −0.149671 | ||||||||
\(482\) | −3.71592 | + | 3.71592i | −0.169256 | + | 0.169256i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 3.99745i | − | 0.181702i | ||||||
\(485\) | 2.14252 | + | 13.9670i | 0.0972869 | + | 0.634208i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.6336 | + | 25.6336i | 1.16157 | + | 1.16157i | 0.984132 | + | 0.177437i | \(0.0567808\pi\) |
0.177437 | + | 0.984132i | \(0.443219\pi\) | |||||||
\(488\) | −5.88267 | − | 5.88267i | −0.266296 | − | 0.266296i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.76203 | + | 11.4866i | 0.0796003 | + | 0.518910i | ||||
\(491\) | − | 32.3925i | − | 1.46185i | −0.682455 | − | 0.730927i | \(-0.739088\pi\) | ||
0.682455 | − | 0.730927i | \(-0.260912\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.89893 | + | 1.89893i | −0.0855234 | + | 0.0855234i | ||||
\(494\) | −6.84601 | −0.308016 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.99745 | 0.314195 | ||||||||
\(497\) | −8.32447 | + | 8.32447i | −0.373403 | + | 0.373403i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 15.0379i | − | 0.673189i | −0.941650 | − | 0.336594i | \(-0.890725\pi\) | ||
0.941650 | − | 0.336594i | \(-0.109275\pi\) | |||||||
\(500\) | 10.5816 | + | 3.60980i | 0.473222 | + | 0.161435i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.4114 | − | 11.4114i | −0.509314 | − | 0.509314i | ||||
\(503\) | 17.7115 | + | 17.7115i | 0.789717 | + | 0.789717i | 0.981448 | − | 0.191731i | \(-0.0614100\pi\) |
−0.191731 | + | 0.981448i | \(0.561410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.11652 | − | 8.33307i | 0.272182 | − | 0.370817i | ||||
\(506\) | 2.64623i | 0.117639i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.79785 | + | 6.79785i | −0.301606 | + | 0.301606i | ||||
\(509\) | 40.5779 | 1.79858 | 0.899291 | − | 0.437351i | \(-0.144083\pi\) | ||||
0.899291 | + | 0.437351i | \(0.144083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.7019 | 0.694611 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.9317i | 1.36434i | ||||||||
\(515\) | −2.96775 | + | 0.455250i | −0.130775 | + | 0.0200607i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.79785 | + | 5.79785i | 0.254989 | + | 0.254989i | ||||
\(518\) | 1.10190 | + | 1.10190i | 0.0484148 | + | 0.0484148i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.09852 | + | 3.74234i | 0.223585 | + | 0.164112i | ||||
\(521\) | 17.7938i | 0.779561i | 0.920908 | + | 0.389781i | \(0.127449\pi\) | ||||
−0.920908 | + | 0.389781i | \(0.872551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.7300 | + | 13.7300i | −0.600372 | + | 0.600372i | −0.940411 | − | 0.340039i | \(-0.889560\pi\) |
0.340039 | + | 0.940411i | \(0.389560\pi\) | |||||||
\(524\) | −3.08769 | −0.134886 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.2194 | 1.23042 | ||||||||
\(527\) | 34.6230 | − | 34.6230i | 1.50820 | − | 1.50820i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | −18.1372 | − | 13.3128i | −0.787830 | − | 0.578271i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.29811 | + | 2.29811i | 0.0996357 | + | 0.0996357i | ||||
\(533\) | 10.8248 | + | 10.8248i | 0.468874 | + | 0.468874i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.71458 | − | 0.569813i | 0.160595 | − | 0.0246352i | ||||
\(536\) | − | 3.67305i | − | 0.158652i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.8520 | − | 19.8520i | 0.855881 | − | 0.855881i | ||||
\(539\) | 13.7526 | 0.592365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | −16.7419 | + | 16.7419i | −0.719126 | + | 0.719126i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.99745i | 0.300013i | ||||||||
\(545\) | −17.8804 | + | 24.3600i | −0.765912 | + | 1.04347i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.1894 | + | 21.1894i | 0.905992 | + | 0.905992i | 0.995946 | − | 0.0899537i | \(-0.0286719\pi\) |
−0.0899537 | + | 0.995946i | \(0.528672\pi\) | |||||||
\(548\) | −2.43544 | − | 2.43544i | −0.104037 | − | 0.104037i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.12130 | − | 11.7300i | 0.261013 | − | 0.500170i | ||||
\(551\) | 0.928915i | 0.0395731i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6334 | − | 11.6334i | 0.494701 | − | 0.494701i | ||||
\(554\) | 9.27126 | 0.393898 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.9368 | 0.887919 | ||||||||
\(557\) | −10.8857 | + | 10.8857i | −0.461240 | + | 0.461240i | −0.899062 | − | 0.437822i | \(-0.855750\pi\) |
0.437822 | + | 0.899062i | \(0.355750\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.2825i | 0.477200i | ||||||||
\(560\) | −0.455250 | − | 2.96775i | −0.0192378 | − | 0.125410i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.5770 | − | 14.5770i | −0.614894 | − | 0.614894i | ||||
\(563\) | 2.95418 | + | 2.95418i | 0.124504 | + | 0.124504i | 0.766613 | − | 0.642109i | \(-0.221941\pi\) |
−0.642109 | + | 0.766613i | \(0.721941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.79716 | + | 11.7156i | 0.0756072 | + | 0.492879i | ||||
\(566\) | 7.91931i | 0.332873i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.19959 | + | 6.19959i | −0.260129 | + | 0.260129i | ||||
\(569\) | −29.1503 | −1.22204 | −0.611022 | − | 0.791614i | \(-0.709241\pi\) | ||||
−0.611022 | + | 0.791614i | \(0.709241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.2706 | 1.72712 | 0.863560 | − | 0.504246i | \(-0.168229\pi\) | ||||
0.863560 | + | 0.504246i | \(0.168229\pi\) | |||||||
\(572\) | 5.29247 | − | 5.29247i | 0.221289 | − | 0.221289i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 7.26747i | − | 0.303338i | ||||||
\(575\) | 2.31321 | − | 4.43273i | 0.0964676 | − | 0.184857i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.0061 | − | 16.0061i | −0.666341 | − | 0.666341i | 0.290526 | − | 0.956867i | \(-0.406170\pi\) |
−0.956867 | + | 0.290526i | \(0.906170\pi\) | |||||||
\(578\) | 22.6021 | + | 22.6021i | 0.940125 | + | 0.940125i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.507788 | − | 0.691804i | 0.0210847 | − | 0.0287256i | ||||
\(581\) | 10.5602i | 0.438112i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.8271 | + | 18.8271i | −0.779741 | + | 0.779741i | ||||
\(584\) | 11.6939 | 0.483896 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.8726 | −0.903548 | ||||||||
\(587\) | 18.5920 | − | 18.5920i | 0.767372 | − | 0.767372i | −0.210271 | − | 0.977643i | \(-0.567435\pi\) |
0.977643 | + | 0.210271i | \(0.0674346\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 16.9368i | − | 0.697870i | ||||||
\(590\) | −4.28190 | + | 0.656838i | −0.176283 | + | 0.0270416i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.820634 | + | 0.820634i | 0.0337278 | + | 0.0337278i | ||||
\(593\) | 5.19456 | + | 5.19456i | 0.213315 | + | 0.213315i | 0.805674 | − | 0.592359i | \(-0.201803\pi\) |
−0.592359 | + | 0.805674i | \(0.701803\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.9368 | − | 12.4317i | −0.694342 | − | 0.509651i | ||||
\(596\) | 13.0494i | 0.534526i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.00000 | − | 2.00000i | 0.0817861 | − | 0.0817861i | ||||
\(599\) | −4.12632 | −0.168597 | −0.0842985 | − | 0.996441i | \(-0.526865\pi\) | ||||
−0.0842985 | + | 0.996441i | \(0.526865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1364 | 0.739800 | 0.369900 | − | 0.929072i | \(-0.379392\pi\) | ||||
0.369900 | + | 0.929072i | \(0.379392\pi\) | |||||||
\(602\) | 3.78739 | − | 3.78739i | 0.154363 | − | 0.154363i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.9394i | 0.485806i | ||||||||
\(605\) | 7.20579 | + | 5.28909i | 0.292957 | + | 0.215032i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.70794 | + | 7.70794i | 0.312856 | + | 0.312856i | 0.846015 | − | 0.533159i | \(-0.178995\pi\) |
−0.533159 | + | 0.846015i | \(0.678995\pi\) | |||||||
\(608\) | 1.71150 | + | 1.71150i | 0.0694106 | + | 0.0694106i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.3876 | − | 2.82063i | 0.744491 | − | 0.114204i | ||||
\(611\) | − | 8.76393i | − | 0.354551i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.8073 | − | 14.8073i | 0.598061 | − | 0.598061i | −0.341735 | − | 0.939796i | \(-0.611015\pi\) |
0.939796 | + | 0.341735i | \(0.111015\pi\) | |||||||
\(614\) | −10.7279 | −0.432942 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.55322 | −0.143163 | ||||||||
\(617\) | 8.08164 | − | 8.08164i | 0.325355 | − | 0.325355i | −0.525462 | − | 0.850817i | \(-0.676108\pi\) |
0.850817 | + | 0.525462i | \(0.176108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23.4100i | − | 0.940926i | −0.882420 | − | 0.470463i | \(-0.844087\pi\) | ||
0.882420 | − | 0.470463i | \(-0.155913\pi\) | |||||||
\(620\) | −9.25844 | + | 12.6136i | −0.371828 | + | 0.506574i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.75605 | + | 2.75605i | 0.110508 | + | 0.110508i | ||||
\(623\) | −5.07102 | − | 5.07102i | −0.203166 | − | 0.203166i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5077 | + | 14.2981i | −0.820306 | + | 0.571924i | ||||
\(626\) | 21.1045i | 0.843504i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.4593 | − | 15.4593i | 0.616895 | − | 0.616895i | ||||
\(629\) | 8.12089 | 0.323801 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.4977 | 1.33352 | 0.666761 | − | 0.745271i | \(-0.267680\pi\) | ||||
0.666761 | + | 0.745271i | \(0.267680\pi\) | |||||||
\(632\) | 8.66386 | − | 8.66386i | 0.344630 | − | 0.344630i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.1815i | 1.07951i | ||||||||
\(635\) | −3.25945 | − | 21.2482i | −0.129347 | − | 0.843208i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.3941 | − | 10.3941i | −0.411828 | − | 0.411828i | ||||
\(638\) | −0.718120 | − | 0.718120i | −0.0284306 | − | 0.0284306i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.339045 | − | 2.21021i | −0.0134019 | − | 0.0873664i | ||||
\(641\) | 6.17292i | 0.243816i | 0.992541 | + | 0.121908i | \(0.0389012\pi\) | ||||
−0.992541 | + | 0.121908i | \(0.961099\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5947 | − | 21.5947i | 0.851611 | − | 0.851611i | −0.138720 | − | 0.990332i | \(-0.544299\pi\) |
0.990332 | + | 0.138720i | \(0.0442989\pi\) | |||||||
\(644\) | −1.34274 | −0.0529115 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.9368 | 0.666370 | ||||||||
\(647\) | 16.9863 | − | 16.9863i | 0.667802 | − | 0.667802i | −0.289405 | − | 0.957207i | \(-0.593457\pi\) |
0.957207 | + | 0.289405i | \(0.0934573\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.12661i | 0.201237i | ||||||||
\(650\) | −13.4919 | + | 4.23903i | −0.529195 | + | 0.166268i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.19704 | + | 2.19704i | 0.0860426 | + | 0.0860426i | ||||
\(653\) | 34.5321 | + | 34.5321i | 1.35135 | + | 1.35135i | 0.884159 | + | 0.467186i | \(0.154732\pi\) |
0.467186 | + | 0.884159i | \(0.345268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.08537 | − | 5.56586i | 0.159629 | − | 0.217476i | ||||
\(656\) | − | 5.41240i | − | 0.211319i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.94193 | + | 2.94193i | −0.114688 | + | 0.114688i | ||||
\(659\) | −44.6066 | −1.73762 | −0.868812 | − | 0.495142i | \(-0.835116\pi\) | ||||
−0.868812 | + | 0.495142i | \(0.835116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6200 | 0.685339 | 0.342670 | − | 0.939456i | \(-0.388669\pi\) | ||||
0.342670 | + | 0.939456i | \(0.388669\pi\) | |||||||
\(662\) | −14.2100 | + | 14.2100i | −0.552287 | + | 0.552287i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.86466i | 0.305208i | ||||||||
\(665\) | −7.18324 | + | 1.10190i | −0.278554 | + | 0.0427299i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.271374 | − | 0.271374i | −0.0105077 | − | 0.0105077i | ||||
\(668\) | −2.05166 | − | 2.05166i | −0.0793810 | − | 0.0793810i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.62104 | + | 4.85988i | 0.255793 | + | 0.187754i | ||||
\(671\) | − | 22.0150i | − | 0.849878i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.66545 | − | 3.66545i | 0.141293 | − | 0.141293i | −0.632922 | − | 0.774215i | \(-0.718145\pi\) |
0.774215 | + | 0.632922i | \(0.218145\pi\) | |||||||
\(674\) | −15.0904 | −0.581262 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | 12.1377 | − | 12.1377i | 0.466490 | − | 0.466490i | −0.434285 | − | 0.900775i | \(-0.642999\pi\) |
0.900775 | + | 0.434285i | \(0.142999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.48519i | 0.325632i | ||||||||
\(680\) | −12.6136 | − | 9.25844i | −0.483709 | − | 0.355045i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.0934 | + | 13.0934i | 0.501373 | + | 0.501373i | ||||
\(683\) | −27.4988 | − | 27.4988i | −1.05221 | − | 1.05221i | −0.998560 | − | 0.0536540i | \(-0.982913\pi\) |
−0.0536540 | − | 0.998560i | \(-0.517087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.61249 | − | 1.16775i | 0.290858 | − | 0.0446174i | ||||
\(686\) | 16.3775i | 0.625296i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.82063 | − | 2.82063i | 0.107536 | − | 0.107536i | ||||
\(689\) | 28.4588 | 1.08419 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.04300 | −0.191845 | −0.0959224 | − | 0.995389i | \(-0.530580\pi\) | ||||
−0.0959224 | + | 0.995389i | \(0.530580\pi\) | |||||||
\(692\) | −2.75696 | + | 2.75696i | −0.104804 | + | 0.104804i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.8938i | 1.36251i | ||||||||
\(695\) | −27.7019 | + | 37.7407i | −1.05079 | + | 1.43159i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.7802 | − | 26.7802i | −1.01437 | − | 1.01437i | ||||
\(698\) | 1.03043 | + | 1.03043i | 0.0390024 | + | 0.0390024i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.95202 | + | 3.10605i | 0.224965 | + | 0.117398i | ||||
\(701\) | − | 35.4022i | − | 1.33712i | −0.743657 | − | 0.668561i | \(-0.766911\pi\) | ||
0.743657 | − | 0.668561i | \(-0.233089\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.98629 | − | 1.98629i | 0.0749142 | − | 0.0749142i | ||||
\(704\) | −2.64623 | −0.0997337 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.23698 | −0.347638 | ||||||||
\(707\) | 4.38919 | − | 4.38919i | 0.165073 | − | 0.165073i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 32.8245i | − | 1.23275i | −0.787453 | − | 0.616374i | \(-0.788601\pi\) | ||
0.787453 | − | 0.616374i | \(-0.211399\pi\) | |||||||
\(710\) | −2.97259 | − | 19.3782i | −0.111559 | − | 0.727249i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.77661 | − | 3.77661i | −0.141534 | − | 0.141534i | ||||
\(713\) | 4.94794 | + | 4.94794i | 0.185302 | + | 0.185302i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.53764 | + | 16.5427i | 0.0949024 | + | 0.618664i | ||||
\(716\) | 12.2620i | 0.458253i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.83830 | − | 9.83830i | 0.367162 | − | 0.367162i | ||||
\(719\) | −6.08304 | −0.226859 | −0.113430 | − | 0.993546i | \(-0.536184\pi\) | ||||
−0.113430 | + | 0.993546i | \(0.536184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.80296 | −0.0671458 | ||||||||
\(722\) | −9.29246 | + | 9.29246i | −0.345830 | + | 0.345830i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3.77661i | − | 0.140357i | ||||||
\(725\) | 0.575182 | + | 1.83067i | 0.0213617 | + | 0.0679895i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.6416 | − | 35.6416i | −1.32188 | − | 1.32188i | −0.912257 | − | 0.409619i | \(-0.865662\pi\) |
−0.409619 | − | 0.912257i | \(-0.634338\pi\) | |||||||
\(728\) | 2.68549 | + | 2.68549i | 0.0995308 | + | 0.0995308i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.4724 | + | 21.0794i | −0.572658 | + | 0.780182i | ||||
\(731\) | − | 27.9127i | − | 1.03239i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.6247 | + | 12.6247i | −0.466303 | + | 0.466303i | −0.900714 | − | 0.434412i | \(-0.856956\pi\) |
0.434412 | + | 0.900714i | \(0.356956\pi\) | |||||||
\(734\) | 8.31328 | 0.306849 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 6.87291 | − | 6.87291i | 0.253167 | − | 0.253167i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 26.0758i | − | 0.959213i | −0.877484 | − | 0.479607i | \(-0.840779\pi\) | ||
0.877484 | − | 0.479607i | \(-0.159221\pi\) | |||||||
\(740\) | −2.56507 | + | 0.393479i | −0.0942938 | + | 0.0144646i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.55322 | − | 9.55322i | −0.350710 | − | 0.350710i | ||||
\(743\) | −37.8958 | − | 37.8958i | −1.39026 | − | 1.39026i | −0.824719 | − | 0.565543i | \(-0.808666\pi\) |
−0.565543 | − | 0.824719i | \(-0.691334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.5229 | − | 17.2659i | −0.861813 | − | 0.632575i | ||||
\(746\) | 19.0988i | 0.699257i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13.0934 | + | 13.0934i | −0.478743 | + | 0.478743i | ||||
\(749\) | 2.25667 | 0.0824571 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.0249 | −0.767209 | −0.383604 | − | 0.923498i | \(-0.625317\pi\) | ||||
−0.383604 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(752\) | −2.19098 | + | 2.19098i | −0.0798969 | + | 0.0798969i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.08550i | 0.0395315i | ||||||||
\(755\) | −21.5219 | − | 15.7972i | −0.783262 | − | 0.574919i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.8472 | + | 23.8472i | 0.866743 | + | 0.866743i | 0.992110 | − | 0.125368i | \(-0.0400110\pi\) |
−0.125368 | + | 0.992110i | \(0.540011\pi\) | |||||||
\(758\) | −15.0396 | − | 15.0396i | −0.546263 | − | 0.546263i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.34967 | + | 0.820634i | −0.194053 | + | 0.0297675i | ||||
\(761\) | 25.7309i | 0.932744i | 0.884589 | + | 0.466372i | \(0.154439\pi\) | ||||
−0.884589 | + | 0.466372i | \(0.845561\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.8309 | + | 12.8309i | −0.464510 | + | 0.464510i | ||||
\(764\) | 17.0094 | 0.615377 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.1489 | −0.691879 | ||||||||
\(767\) | 3.87464 | − | 3.87464i | 0.139905 | − | 0.139905i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.80807i | 0.0652007i | 0.999468 | + | 0.0326003i | \(0.0103789\pi\) | ||||
−0.999468 | + | 0.0326003i | \(0.989621\pi\) | |||||||
\(770\) | 4.70132 | − | 6.40502i | 0.169424 | − | 0.230821i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.8964 | − | 17.8964i | −0.644105 | − | 0.644105i | ||||
\(773\) | −10.6612 | − | 10.6612i | −0.383458 | − | 0.383458i | 0.488888 | − | 0.872346i | \(-0.337403\pi\) |
−0.872346 | + | 0.488888i | \(0.837403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.4872 | − | 33.3785i | −0.376713 | − | 1.19899i | ||||
\(776\) | 6.31929i | 0.226849i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.0263 | + | 15.0263i | −0.538718 | + | 0.538718i | ||||
\(779\) | −13.1003 | −0.469368 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.2010 | −0.830196 | ||||||||
\(782\) | −4.94794 | + | 4.94794i | −0.176938 | + | 0.176938i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.19704i | 0.185608i | ||||||||
\(785\) | 7.41247 | + | 48.3215i | 0.264562 | + | 1.72467i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.39510 | − | 4.39510i | −0.156668 | − | 0.156668i | 0.624420 | − | 0.781089i | \(-0.285335\pi\) |
−0.781089 | + | 0.624420i | \(0.785335\pi\) | |||||||
\(788\) | 2.70850 | + | 2.70850i | 0.0964862 | + | 0.0964862i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.15416 | + | 27.0808i | 0.147798 | + | 0.963491i | ||||
\(791\) | 7.11744i | 0.253067i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.6387 | + | 16.6387i | −0.590858 | + | 0.590858i | ||||
\(794\) | 4.92808 | 0.174891 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.19448 | −0.255002 | ||||||||
\(797\) | 29.1863 | − | 29.1863i | 1.03383 | − | 1.03383i | 0.0344254 | − | 0.999407i | \(-0.489040\pi\) |
0.999407 | − | 0.0344254i | \(-0.0109601\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.6817i | 0.767044i | ||||||||
\(800\) | 4.43273 | + | 2.31321i | 0.156721 | + | 0.0817844i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.0566 | − | 22.0566i | −0.778845 | − | 0.778845i | ||||
\(803\) | 21.8812 | + | 21.8812i | 0.772172 | + | 0.772172i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.77661 | − | 2.42043i | 0.0626172 | − | 0.0853089i | ||||
\(806\) | − | 19.7918i | − | 0.697135i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.26882 | − | 3.26882i | 0.114997 | − | 0.114997i | ||||
\(809\) | −28.8768 | −1.01525 | −0.507626 | − | 0.861577i | \(-0.669477\pi\) | ||||
−0.507626 | + | 0.861577i | \(0.669477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.9696 | −1.19283 | −0.596417 | − | 0.802675i | \(-0.703410\pi\) | ||||
−0.596417 | + | 0.802675i | \(0.703410\pi\) | |||||||
\(812\) | 0.364386 | − | 0.364386i | 0.0127875 | − | 0.0127875i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.07109i | 0.107642i | ||||||||
\(815\) | −6.86731 | + | 1.05344i | −0.240551 | + | 0.0369004i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.82714 | − | 6.82714i | −0.238852 | − | 0.238852i | ||||
\(818\) | 3.23522 | + | 3.23522i | 0.113117 | + | 0.113117i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.75638 | + | 7.16124i | 0.340708 | + | 0.250081i | ||||
\(821\) | 43.0419i | 1.50217i | 0.660204 | + | 0.751086i | \(0.270470\pi\) | ||||
−0.660204 | + | 0.751086i | \(0.729530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.7261 | − | 17.7261i | 0.617892 | − | 0.617892i | −0.327098 | − | 0.944990i | \(-0.606071\pi\) |
0.944990 | + | 0.327098i | \(0.106071\pi\) | |||||||
\(824\) | −1.34274 | −0.0467767 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.60133 | −0.0905118 | ||||||||
\(827\) | −9.45223 | + | 9.45223i | −0.328686 | + | 0.328686i | −0.852087 | − | 0.523401i | \(-0.824663\pi\) |
0.523401 | + | 0.852087i | \(0.324663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 17.1064i | − | 0.594131i | −0.954857 | − | 0.297065i | \(-0.903992\pi\) | ||
0.954857 | − | 0.297065i | \(-0.0960080\pi\) | |||||||
\(830\) | −14.1768 | − | 10.4059i | −0.492085 | − | 0.361193i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | + | 2.00000i | 0.0693375 | + | 0.0693375i | ||||
\(833\) | 25.7146 | + | 25.7146i | 0.890959 | + | 0.890959i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.41290 | − | 0.983732i | 0.221927 | − | 0.0340434i | ||||
\(836\) | 6.40502i | 0.221522i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.93542 | + | 6.93542i | −0.239580 | + | 0.239580i | ||||
\(839\) | −40.4615 | −1.39689 | −0.698444 | − | 0.715665i | \(-0.746124\pi\) | ||||
−0.698444 | + | 0.715665i | \(0.746124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8527 | −0.994921 | ||||||||
\(842\) | −12.0570 | + | 12.0570i | −0.415513 | + | 0.415513i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.0685362i | 0.00235911i | ||||||||
\(845\) | −6.61558 | + | 9.01299i | −0.227583 | + | 0.310056i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.79543 | + | 3.79543i | 0.130413 | + | 0.130413i | ||||
\(848\) | −7.11469 | − | 7.11469i | −0.244320 | − | 0.244320i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 33.3785 | − | 10.4872i | 1.14487 | − | 0.359709i | ||||
\(851\) | 1.16055i | 0.0397832i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.0274 | + | 24.0274i | −0.822683 | + | 0.822683i | −0.986492 | − | 0.163809i | \(-0.947622\pi\) |
0.163809 | + | 0.986492i | \(0.447622\pi\) | |||||||
\(854\) | 11.1708 | 0.382256 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.68064 | 0.0574432 | ||||||||
\(857\) | 18.0066 | − | 18.0066i | 0.615093 | − | 0.615093i | −0.329175 | − | 0.944269i | \(-0.606771\pi\) |
0.944269 | + | 0.329175i | \(0.106771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.2742i | 1.92005i | 0.279912 | + | 0.960026i | \(0.409695\pi\) | ||||
−0.279912 | + | 0.960026i | \(0.590305\pi\) | |||||||
\(860\) | 1.35244 | + | 8.81650i | 0.0461179 | + | 0.300640i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.55832 | + | 1.55832i | 0.0530767 | + | 0.0530767i | ||||
\(863\) | 34.5743 | + | 34.5743i | 1.17692 | + | 1.17692i | 0.980524 | + | 0.196399i | \(0.0629248\pi\) |
0.196399 | + | 0.980524i | \(0.437075\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.32191 | − | 8.61747i | −0.0449463 | − | 0.293003i | ||||
\(866\) | 16.7685i | 0.569817i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.64382 | + | 6.64382i | −0.225506 | + | 0.225506i | ||||
\(869\) | 32.4231 | 1.09988 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3890 | −0.352017 | ||||||||
\(872\) | −9.55573 | + | 9.55573i | −0.323598 | + | 0.323598i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.42043i | 0.0818722i | ||||||||
\(875\) | −13.4742 | + | 6.61943i | −0.455510 | + | 0.223778i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.46516 | + | 7.46516i | 0.252081 | + | 0.252081i | 0.821823 | − | 0.569743i | \(-0.192957\pi\) |
−0.569743 | + | 0.821823i | \(0.692957\pi\) | |||||||
\(878\) | 9.21044 | + | 9.21044i | 0.310837 | + | 0.310837i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.50128 | − | 4.77010i | 0.118028 | − | 0.160800i | ||||
\(881\) | − | 6.96179i | − | 0.234549i | −0.993100 | − | 0.117274i | \(-0.962584\pi\) | ||
0.993100 | − | 0.117274i | \(-0.0374157\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.4066 | − | 11.4066i | 0.383862 | − | 0.383862i | −0.488629 | − | 0.872491i | \(-0.662503\pi\) |
0.872491 | + | 0.488629i | \(0.162503\pi\) | |||||||
\(884\) | 19.7918 | 0.665669 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.4745 | 0.788640 | ||||||||
\(887\) | 4.39479 | − | 4.39479i | 0.147562 | − | 0.147562i | −0.629466 | − | 0.777028i | \(-0.716726\pi\) |
0.777028 | + | 0.629466i | \(0.216726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 12.9086i | − | 0.432942i | ||||||
\(890\) | 11.8046 | − | 1.81081i | 0.395691 | − | 0.0606986i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.6524 | + | 19.6524i | 0.658012 | + | 0.658012i | ||||
\(893\) | 5.30312 | + | 5.30312i | 0.177462 | + | 0.177462i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.1035 | − | 16.2241i | −0.738838 | − | 0.542311i | ||||
\(896\) | − | 1.34274i | − | 0.0448579i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.76652 | + | 9.76652i | −0.325913 | + | 0.325913i | ||||
\(899\) | −2.68549 | −0.0895661 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.4062 | −2.34557 | ||||||||
\(902\) | 10.1275 | − | 10.1275i | 0.337209 | − | 0.337209i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.30066i | 0.176297i | ||||||||
\(905\) | 6.80771 | + | 4.99689i | 0.226296 | + | 0.166102i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.6034 | − | 32.6034i | −1.08258 | − | 1.08258i | −0.996268 | − | 0.0863106i | \(-0.972492\pi\) |
−0.0863106 | − | 0.996268i | \(-0.527508\pi\) | |||||||
\(908\) | 2.83984 | + | 2.83984i | 0.0942434 | + | 0.0942434i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.39407 | + | 1.28764i | −0.278261 | + | 0.0426849i | ||||
\(911\) | − | 54.2830i | − | 1.79848i | −0.437461 | − | 0.899238i | \(-0.644122\pi\) | ||
0.437461 | − | 0.899238i | \(-0.355878\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.7161 | + | 14.7161i | −0.487032 | + | 0.487032i | ||||
\(914\) | −0.116320 | −0.00384751 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.42554 | −0.146224 | ||||||||
\(917\) | 2.93164 | − | 2.93164i | 0.0968114 | − | 0.0968114i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 52.6590i | − | 1.73706i | −0.495637 | − | 0.868530i | \(-0.665065\pi\) | ||
0.495637 | − | 0.868530i | \(-0.334935\pi\) | |||||||
\(920\) | 1.32312 | − | 1.80260i | 0.0436219 | − | 0.0594299i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.0542 | + | 22.0542i | 0.726315 | + | 0.726315i | ||||
\(923\) | 17.5351 | + | 17.5351i | 0.577175 | + | 0.577175i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.68460 | − | 5.14441i | 0.0882691 | − | 0.169147i | ||||
\(926\) | − | 12.8064i | − | 0.420845i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.271374 | − | 0.271374i | 0.00890830 | − | 0.00890830i | ||||
\(929\) | −13.6515 | −0.447892 | −0.223946 | − | 0.974602i | \(-0.571894\pi\) | ||||
−0.223946 | + | 0.974602i | \(0.571894\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5791 | 0.412262 | ||||||||
\(932\) | 0.799777 | − | 0.799777i | 0.0261976 | − | 0.0261976i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 13.9657i | − | 0.456973i | ||||||
\(935\) | −6.27805 | − | 40.9263i | −0.205314 | − | 1.33843i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.6980 | + | 28.6980i | 0.937522 | + | 0.937522i | 0.998160 | − | 0.0606375i | \(-0.0193134\pi\) |
−0.0606375 | + | 0.998160i | \(0.519313\pi\) | |||||||
\(938\) | 3.48743 | + | 3.48743i | 0.113869 | + | 0.113869i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.05054 | − | 6.84839i | −0.0342647 | − | 0.223370i | ||||
\(941\) | 9.58042i | 0.312313i | 0.987732 | + | 0.156156i | \(0.0499104\pi\) | ||||
−0.987732 | + | 0.156156i | \(0.950090\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.82714 | − | 3.82714i | 0.124629 | − | 0.124629i | ||||
\(944\) | −1.93732 | −0.0630544 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.5558 | 0.343198 | ||||||||
\(947\) | −21.3347 | + | 21.3347i | −0.693283 | + | 0.693283i | −0.962953 | − | 0.269670i | \(-0.913085\pi\) |
0.269670 | + | 0.962953i | \(0.413085\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 33.0753i | − | 1.07367i | ||||||
\(950\) | 5.59896 | − | 10.7291i | 0.181654 | − | 0.348098i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.64382 | − | 6.64382i | −0.215327 | − | 0.215327i | ||||
\(953\) | −17.9775 | − | 17.9775i | −0.582349 | − | 0.582349i | 0.353199 | − | 0.935548i | \(-0.385094\pi\) |
−0.935548 | + | 0.353199i | \(0.885094\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.5054 | + | 30.6610i | −0.728256 | + | 0.992168i | ||||
\(956\) | 17.2078i | 0.556540i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.1259 | − | 15.1259i | 0.488697 | − | 0.488697i | ||||
\(959\) | 4.62472 | 0.149340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.9643 | 0.579492 | ||||||||
\(962\) | 2.32110 | − | 2.32110i | 0.0748353 | − | 0.0748353i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 5.25511i | − | 0.169256i | ||||||
\(965\) | 55.9390 | − | 8.58098i | 1.80074 | − | 0.276232i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.2356 | + | 14.2356i | 0.457787 | + | 0.457787i | 0.897928 | − | 0.440142i | \(-0.145072\pi\) |
−0.440142 | + | 0.897928i | \(0.645072\pi\) | |||||||
\(968\) | 2.82662 | + | 2.82662i | 0.0908510 | + | 0.0908510i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.3911 | − | 8.36116i | −0.365747 | − | 0.268461i | ||||
\(971\) | − | 14.5361i | − | 0.466486i | −0.972419 | − | 0.233243i | \(-0.925066\pi\) | ||
0.972419 | − | 0.233243i | \(-0.0749337\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.8788 | + | 19.8788i | −0.637284 | + | 0.637284i | ||||
\(974\) | −36.2514 | −1.16157 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.31936 | 0.266296 | ||||||||
\(977\) | −3.29748 | + | 3.29748i | −0.105496 | + | 0.105496i | −0.757884 | − | 0.652389i | \(-0.773767\pi\) |
0.652389 | + | 0.757884i | \(0.273767\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 14.1334i | − | 0.451704i | ||||||
\(980\) | −9.36817 | − | 6.87629i | −0.299255 | − | 0.219655i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.9050 | + | 22.9050i | 0.730927 | + | 0.730927i | ||||
\(983\) | 16.4632 | + | 16.4632i | 0.525096 | + | 0.525096i | 0.919106 | − | 0.394010i | \(-0.128913\pi\) |
−0.394010 | + | 0.919106i | \(0.628913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.46599 | + | 1.29867i | −0.269749 | + | 0.0413792i | ||||
\(986\) | − | 2.68549i | − | 0.0855234i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.84086 | − | 4.84086i | 0.154008 | − | 0.154008i | ||||
\(989\) | 3.98898 | 0.126842 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.1262 | −1.46525 | −0.732623 | − | 0.680634i | \(-0.761704\pi\) | ||||
−0.732623 | + | 0.680634i | \(0.761704\pi\) | |||||||
\(992\) | −4.94794 | + | 4.94794i | −0.157097 | + | 0.157097i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 11.7726i | − | 0.373403i | ||||||
\(995\) | 9.51914 | − | 12.9688i | 0.301777 | − | 0.411137i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.42727 | − | 2.42727i | −0.0768724 | − | 0.0768724i | 0.667625 | − | 0.744498i | \(-0.267311\pi\) |
−0.744498 | + | 0.667625i | \(0.767311\pi\) | |||||||
\(998\) | 10.6334 | + | 10.6334i | 0.336594 | + | 0.336594i | ||||
\(999\) | 0 | 0 |
(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 | 2070.2.j.i.737.4 | yes | 16 | |
3.2 | odd | 2 | inner | 2070.2.j.i.737.5 | yes | 16 | |
5.3 | odd | 4 | inner | 2070.2.j.i.323.5 | yes | 16 | |
15.8 | even | 4 | inner | 2070.2.j.i.323.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.i.323.4 | ✓ | 16 | 15.8 | even | 4 | inner | |
2070.2.j.i.323.5 | yes | 16 | 5.3 | odd | 4 | inner | |
2070.2.j.i.737.4 | yes | 16 | 1.1 | even | 1 | trivial | |
2070.2.j.i.737.5 | yes | 16 | 3.2 | odd | 2 | inner |