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 | 323.4 | ||
Root | \(-0.328628i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.323 |
Dual form | 2070.2.j.i.737.4 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | −0.504530 | − | 0.863394i | \(-0.668334\pi\) |
0.863394 | + | 0.504530i | \(0.168334\pi\) | |||||||
\(8\) | 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 | \(-0.869380\pi\) | ||
0.916979 | − | 0.398935i | \(-0.130620\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 2.00000i | 0.554700 | + | 0.554700i | 0.927794 | − | 0.373094i | \(-0.121703\pi\) |
−0.373094 | + | 0.927794i | \(0.621703\pi\) | |||||||
\(14\) | −1.34274 | −0.358864 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.94794 | − | 4.94794i | −1.20005 | − | 1.20005i | −0.974150 | − | 0.225902i | \(-0.927467\pi\) |
−0.225902 | − | 0.974150i | \(-0.572533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.42043i | − | 0.555285i | −0.960685 | − | 0.277642i | \(-0.910447\pi\) | ||
0.960685 | − | 0.277642i | \(-0.0895530\pi\) | |||||||
\(20\) | 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 | −0.771338 | − | 0.636426i | \(-0.780412\pi\) |
0.636426 | + | 0.771338i | \(0.280412\pi\) | |||||||
\(38\) | −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 | \(-0.861104\pi\) | ||
0.906299 | − | 0.422637i | \(-0.138896\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.82063 | − | 2.82063i | −0.430143 | − | 0.430143i | 0.458534 | − | 0.888677i | \(-0.348375\pi\) |
−0.888677 | + | 0.458534i | \(0.848375\pi\) | |||||||
\(44\) | 2.64623 | 0.398935 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.19098 | + | 2.19098i | 0.319588 | + | 0.319588i | 0.848609 | − | 0.529021i | \(-0.177441\pi\) |
−0.529021 | + | 0.848609i | \(0.677441\pi\) | |||||||
\(48\) | 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 | −0.0224692 | − | 0.999748i | \(-0.507153\pi\) |
0.999748 | + | 0.0224692i | \(0.00715276\pi\) | |||||||
\(54\) | 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 | −0.847731 | − | 0.530427i | \(-0.822032\pi\) |
0.530427 | + | 0.847731i | \(0.322032\pi\) | |||||||
\(68\) | 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 | \(-0.825836\pi\) | ||
0.854009 | − | 0.520258i | \(-0.174164\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.26882 | + | 8.26882i | 0.967792 | + | 0.967792i | 0.999497 | − | 0.0317050i | \(-0.0100937\pi\) |
−0.0317050 | + | 0.999497i | \(0.510094\pi\) | |||||||
\(74\) | 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 | \(0.242064\pi\) | ||||
−0.724514 | + | 0.689260i | \(0.757936\pi\) | |||||||
\(80\) | −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 | −0.332638 | − | 0.943054i | \(-0.607939\pi\) |
0.943054 | + | 0.332638i | \(0.107939\pi\) | |||||||
\(84\) | 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 | −0.442882 | − | 0.896580i | \(-0.646044\pi\) |
0.896580 | + | 0.442882i | \(0.146044\pi\) | |||||||
\(98\) | 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 | \(0.0738705\pi\) | ||||
−0.973192 | + | 0.229993i | \(0.926130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.949464 | − | 0.949464i | −0.0935534 | − | 0.0935534i | 0.658781 | − | 0.752335i | \(-0.271072\pi\) |
−0.752335 | + | 0.658781i | \(0.771072\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0617 | −0.977278 | ||||||||
\(107\) | 1.18839 | + | 1.18839i | 0.114886 | + | 0.114886i | 0.762213 | − | 0.647326i | \(-0.224113\pi\) |
−0.647326 | + | 0.762213i | \(0.724113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.5138i | − | 1.29439i | −0.762324 | − | 0.647196i | \(-0.775942\pi\) | ||
0.762324 | − | 0.647196i | \(-0.224058\pi\) | |||||||
\(110\) | −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 | −0.508479 | − | 0.861074i | \(-0.669792\pi\) |
0.861074 | + | 0.508479i | \(0.169792\pi\) | |||||||
\(114\) | 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 | −0.941164 | − | 0.337951i | \(-0.890266\pi\) |
0.337951 | + | 0.941164i | \(0.390266\pi\) | |||||||
\(128\) | −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 | \(0.0430669\pi\) | ||||
−0.990861 | + | 0.134886i | \(0.956933\pi\) | |||||||
\(132\) | 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 | 0.803448 | − | 0.595375i | \(-0.202996\pi\) |
−0.595375 | + | 0.803448i | \(0.702996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.9368i | − | 1.77584i | −0.460000 | − | 0.887919i | \(-0.652150\pi\) | ||
0.460000 | − | 0.887919i | \(-0.347850\pi\) | |||||||
\(140\) | 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 | 0.271294 | − | 0.962497i | \(-0.412549\pi\) |
0.962497 | − | 0.271294i | \(-0.0874514\pi\) | |||||||
\(158\) | 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 | 0.615810 | − | 0.787895i | \(-0.288829\pi\) |
−0.787895 | + | 0.615810i | \(0.788829\pi\) | |||||||
\(164\) | 5.41240 | 0.422637 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.86466 | −0.610416 | ||||||||
\(167\) | 2.05166 | + | 2.05166i | 0.158762 | + | 0.158762i | 0.782018 | − | 0.623256i | \(-0.214191\pi\) |
−0.623256 | + | 0.782018i | \(0.714191\pi\) | |||||||
\(168\) | 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 | −0.804101 | − | 0.594493i | \(-0.797353\pi\) |
0.594493 | + | 0.804101i | \(0.297353\pi\) | |||||||
\(174\) | 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 | \(-0.789004\pi\) | ||
0.788233 | − | 0.615377i | \(-0.210996\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8964 | + | 17.8964i | 1.28821 | + | 1.28821i | 0.935874 | + | 0.352335i | \(0.114612\pi\) |
0.352335 | + | 0.935874i | \(0.385388\pi\) | |||||||
\(194\) | −6.31929 | −0.453698 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.19704 | −0.371217 | ||||||||
\(197\) | −2.70850 | − | 2.70850i | −0.192972 | − | 0.192972i | 0.604007 | − | 0.796979i | \(-0.293570\pi\) |
−0.796979 | + | 0.604007i | \(0.793570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.19448i | 0.510003i | 0.966941 | + | 0.255002i | \(0.0820760\pi\) | ||||
−0.966941 | + | 0.255002i | \(0.917924\pi\) | |||||||
\(200\) | −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 | −0.916895 | − | 0.399129i | \(-0.869312\pi\) |
−0.399129 | − | 0.916895i | \(-0.630688\pi\) | |||||||
\(224\) | 1.34274 | 0.0897159 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.30066 | −0.352595 | ||||||||
\(227\) | −2.83984 | − | 2.83984i | −0.188487 | − | 0.188487i | 0.606555 | − | 0.795042i | \(-0.292551\pi\) |
−0.795042 | + | 0.606555i | \(0.792551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.42554i | 0.292448i | 0.989252 | + | 0.146224i | \(0.0467120\pi\) | ||||
−0.989252 | + | 0.146224i | \(0.953288\pi\) | |||||||
\(230\) | 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 | −0.680424 | − | 0.732819i | \(-0.738204\pi\) |
0.732819 | + | 0.680424i | \(0.238204\pi\) | |||||||
\(234\) | 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 | \(-0.829899\pi\) | ||
0.860581 | − | 0.509314i | \(-0.170101\pi\) | |||||||
\(252\) | 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 | 0.868300 | + | 0.496040i | \(0.165213\pi\) |
0.496040 | + | 0.868300i | \(0.334787\pi\) | |||||||
\(258\) | 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 | −0.266621 | + | 0.963801i | \(0.585907\pi\) |
−0.963801 | + | 0.266621i | \(0.914093\pi\) | |||||||
\(264\) | 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 | −0.876074 | − | 0.482176i | \(-0.839846\pi\) |
0.482176 | + | 0.876074i | \(0.339846\pi\) | |||||||
\(278\) | −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 | \(-0.789199\pi\) | ||
0.788610 | − | 0.614894i | \(-0.210801\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.59980 | + | 5.59980i | 0.332873 | + | 0.332873i | 0.853677 | − | 0.520803i | \(-0.174368\pi\) |
−0.520803 | + | 0.853677i | \(0.674368\pi\) | |||||||
\(284\) | 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 | −0.0921935 | − | 0.995741i | \(-0.529388\pi\) |
0.995741 | + | 0.0921935i | \(0.0293878\pi\) | |||||||
\(294\) | 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 | −0.456686 | − | 0.889628i | \(-0.650964\pi\) |
0.889628 | + | 0.456686i | \(0.150964\pi\) | |||||||
\(308\) | 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 | \(0.0352477\pi\) | ||||
−0.993875 | + | 0.110508i | \(0.964752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9231 | + | 14.9231i | 0.843504 | + | 0.843504i | 0.989313 | − | 0.145809i | \(-0.0465784\pi\) |
−0.145809 | + | 0.989313i | \(0.546578\pi\) | |||||||
\(314\) | −21.8628 | −1.23379 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.2526 | −0.689260 | ||||||||
\(317\) | 19.2202 | + | 19.2202i | 1.07951 | + | 1.07951i | 0.996553 | + | 0.0829610i | \(0.0264377\pi\) |
0.0829610 | + | 0.996553i | \(0.473562\pi\) | |||||||
\(318\) | 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 | −0.353988 | − | 0.935250i | \(-0.615175\pi\) |
0.935250 | + | 0.353988i | \(0.115175\pi\) | |||||||
\(338\) | −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 | 0.870705 | + | 0.491806i | \(0.163663\pi\) |
0.491806 | + | 0.870705i | \(0.336337\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.45725i | 0.0780049i | 0.999239 | + | 0.0390024i | \(0.0124180\pi\) | ||||
−0.999239 | + | 0.0390024i | \(0.987582\pi\) | |||||||
\(350\) | −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 | −0.511591 | − | 0.859229i | \(-0.670944\pi\) |
0.859229 | + | 0.511591i | \(0.170944\pi\) | |||||||
\(354\) | 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 | −0.843686 | − | 0.536837i | \(-0.819619\pi\) |
0.536837 | + | 0.843686i | \(0.319619\pi\) | |||||||
\(368\) | 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 | 0.964250 | − | 0.264993i | \(-0.0853696\pi\) |
−0.264993 | + | 0.964250i | \(0.585370\pi\) | |||||||
\(374\) | 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 | \(-0.816050\pi\) | ||
0.837614 | − | 0.546263i | \(-0.183950\pi\) | |||||||
\(380\) | 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 | −0.270766 | − | 0.962645i | \(-0.587277\pi\) |
0.962645 | + | 0.270766i | \(0.0872771\pi\) | |||||||
\(384\) | 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 | −0.789124 | − | 0.614233i | \(-0.789465\pi\) |
0.614233 | + | 0.789124i | \(0.289465\pi\) | |||||||
\(398\) | 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 | \(-0.715806\pi\) | ||
0.627216 | − | 0.778845i | \(-0.284194\pi\) | |||||||
\(402\) | 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 | \(0.0360834\pi\) | ||||
−0.993582 | + | 0.113117i | \(0.963917\pi\) | |||||||
\(410\) | −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 | \(0.0169028\pi\) | ||||
−0.998590 | + | 0.0530767i | \(0.983097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8571 | + | 11.8571i | 0.569817 | + | 0.569817i | 0.932077 | − | 0.362260i | \(-0.117995\pi\) |
−0.362260 | + | 0.932077i | \(0.617995\pi\) | |||||||
\(434\) | 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 | \(0.100609\pi\) | ||||
−0.950463 | + | 0.310837i | \(0.899391\pi\) | |||||||
\(440\) | −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 | −0.981271 | − | 0.192631i | \(-0.938298\pi\) |
0.192631 | + | 0.981271i | \(0.438298\pi\) | |||||||
\(444\) | 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 | −0.705180 | − | 0.709028i | \(-0.749134\pi\) |
0.709028 | + | 0.705180i | \(0.249134\pi\) | |||||||
\(458\) | 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 | \(0.258769\pi\) | ||||
−0.687362 | + | 0.726315i | \(0.741231\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.05552 | − | 9.05552i | −0.420845 | − | 0.420845i | 0.464649 | − | 0.885495i | \(-0.346180\pi\) |
−0.885495 | + | 0.464649i | \(0.846180\pi\) | |||||||
\(464\) | −0.383781 | −0.0178166 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.13105 | −0.0523951 | ||||||||
\(467\) | −9.87526 | − | 9.87526i | −0.456973 | − | 0.456973i | 0.440688 | − | 0.897660i | \(-0.354735\pi\) |
−0.897660 | + | 0.440688i | \(0.854735\pi\) | |||||||
\(468\) | 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 | 0.177437 | − | 0.984132i | \(-0.443219\pi\) |
0.984132 | − | 0.177437i | \(-0.0567808\pi\) | |||||||
\(488\) | −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 | \(0.260912\pi\) | ||||
−0.682455 | + | 0.730927i | \(0.739088\pi\) | |||||||
\(492\) | 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 | \(0.109275\pi\) | ||||
−0.941650 | + | 0.336594i | \(0.890725\pi\) | |||||||
\(500\) | 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 | −0.191731 | − | 0.981448i | \(-0.561410\pi\) |
0.981448 | + | 0.191731i | \(0.0614100\pi\) | |||||||
\(504\) | 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 | \(-0.872551\pi\) | ||
0.920908 | − | 0.389781i | \(-0.127449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.7300 | − | 13.7300i | −0.600372 | − | 0.600372i | 0.340039 | − | 0.940411i | \(-0.389560\pi\) |
−0.940411 | + | 0.340039i | \(0.889560\pi\) | |||||||
\(524\) | −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 | −0.0899537 | − | 0.995946i | \(-0.528672\pi\) |
0.995946 | + | 0.0899537i | \(0.0286719\pi\) | |||||||
\(548\) | −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 | 0.437822 | − | 0.899062i | \(-0.355750\pi\) |
−0.899062 | + | 0.437822i | \(0.855750\pi\) | |||||||
\(558\) | 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 | −0.642109 | − | 0.766613i | \(-0.721941\pi\) |
0.766613 | + | 0.642109i | \(0.221941\pi\) | |||||||
\(564\) | 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 | −0.956867 | − | 0.290526i | \(-0.906170\pi\) |
0.290526 | + | 0.956867i | \(0.406170\pi\) | |||||||
\(578\) | 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 | 0.977643 | − | 0.210271i | \(-0.0674346\pi\) |
−0.210271 | + | 0.977643i | \(0.567435\pi\) | |||||||
\(588\) | 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 | −0.592359 | − | 0.805674i | \(-0.701803\pi\) |
0.805674 | + | 0.592359i | \(0.201803\pi\) | |||||||
\(594\) | 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 | −0.533159 | − | 0.846015i | \(-0.678995\pi\) |
0.846015 | + | 0.533159i | \(0.178995\pi\) | |||||||
\(608\) | 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 | 0.939796 | − | 0.341735i | \(-0.111015\pi\) |
−0.341735 | + | 0.939796i | \(0.611015\pi\) | |||||||
\(614\) | −10.7279 | −0.432942 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.55322 | −0.143163 | ||||||||
\(617\) | 8.08164 | + | 8.08164i | 0.325355 | + | 0.325355i | 0.850817 | − | 0.525462i | \(-0.176108\pi\) |
−0.525462 | + | 0.850817i | \(0.676108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.4100i | 0.940926i | 0.882420 | + | 0.470463i | \(0.155913\pi\) | ||||
−0.882420 | + | 0.470463i | \(0.844087\pi\) | |||||||
\(620\) | −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 | \(-0.961099\pi\) | ||
0.992541 | − | 0.121908i | \(-0.0389012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5947 | + | 21.5947i | 0.851611 | + | 0.851611i | 0.990332 | − | 0.138720i | \(-0.0442989\pi\) |
−0.138720 | + | 0.990332i | \(0.544299\pi\) | |||||||
\(644\) | −1.34274 | −0.0529115 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.9368 | 0.666370 | ||||||||
\(647\) | 16.9863 | + | 16.9863i | 0.667802 | + | 0.667802i | 0.957207 | − | 0.289405i | \(-0.0934573\pi\) |
−0.289405 | + | 0.957207i | \(0.593457\pi\) | |||||||
\(648\) | 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 | 0.467186 | − | 0.884159i | \(-0.345268\pi\) |
0.884159 | − | 0.467186i | \(-0.154732\pi\) | |||||||
\(654\) | 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 | 0.774215 | − | 0.632922i | \(-0.218145\pi\) |
−0.632922 | + | 0.774215i | \(0.718145\pi\) | |||||||
\(674\) | −15.0904 | −0.581262 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | 12.1377 | + | 12.1377i | 0.466490 | + | 0.466490i | 0.900775 | − | 0.434285i | \(-0.142999\pi\) |
−0.434285 | + | 0.900775i | \(0.642999\pi\) | |||||||
\(678\) | 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 | −0.0536540 | + | 0.998560i | \(0.517087\pi\) |
−0.998560 | + | 0.0536540i | \(0.982913\pi\) | |||||||
\(684\) | 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 | \(0.233089\pi\) | ||||
−0.743657 | + | 0.668561i | \(0.766911\pi\) | |||||||
\(702\) | 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 | \(0.211399\pi\) | ||||
−0.787453 | + | 0.616374i | \(0.788601\pi\) | |||||||
\(710\) | −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 | −0.409619 | + | 0.912257i | \(0.634338\pi\) |
−0.912257 | + | 0.409619i | \(0.865662\pi\) | |||||||
\(728\) | 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 | 0.434412 | − | 0.900714i | \(-0.356956\pi\) |
−0.900714 | + | 0.434412i | \(0.856956\pi\) | |||||||
\(734\) | 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 | \(0.159221\pi\) | ||||
−0.877484 | + | 0.479607i | \(0.840779\pi\) | |||||||
\(740\) | −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 | −0.565543 | + | 0.824719i | \(0.691334\pi\) |
−0.824719 | + | 0.565543i | \(0.808666\pi\) | |||||||
\(744\) | 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 | −0.125368 | − | 0.992110i | \(-0.540011\pi\) |
0.992110 | + | 0.125368i | \(0.0400110\pi\) | |||||||
\(758\) | −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 | \(-0.845561\pi\) | ||
0.884589 | − | 0.466372i | \(-0.154439\pi\) | |||||||
\(762\) | 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 | \(-0.989621\pi\) | ||
0.999468 | − | 0.0326003i | \(-0.0103789\pi\) | |||||||
\(770\) | 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 | −0.872346 | − | 0.488888i | \(-0.837403\pi\) |
0.488888 | + | 0.872346i | \(0.337403\pi\) | |||||||
\(774\) | 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 | −0.781089 | − | 0.624420i | \(-0.785335\pi\) |
0.624420 | + | 0.781089i | \(0.285335\pi\) | |||||||
\(788\) | 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 | 0.999407 | + | 0.0344254i | \(0.0109601\pi\) |
0.0344254 | + | 0.999407i | \(0.489040\pi\) | |||||||
\(798\) | 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 | \(-0.729530\pi\) | ||
0.660204 | − | 0.751086i | \(-0.270470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.7261 | + | 17.7261i | 0.617892 | + | 0.617892i | 0.944990 | − | 0.327098i | \(-0.106071\pi\) |
−0.327098 | + | 0.944990i | \(0.606071\pi\) | |||||||
\(824\) | −1.34274 | −0.0467767 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.60133 | −0.0905118 | ||||||||
\(827\) | −9.45223 | − | 9.45223i | −0.328686 | − | 0.328686i | 0.523401 | − | 0.852087i | \(-0.324663\pi\) |
−0.852087 | + | 0.523401i | \(0.824663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.1064i | 0.594131i | 0.954857 | + | 0.297065i | \(0.0960080\pi\) | ||||
−0.954857 | + | 0.297065i | \(0.903992\pi\) | |||||||
\(830\) | −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 | 0.163809 | − | 0.986492i | \(-0.447622\pi\) |
−0.986492 | + | 0.163809i | \(0.947622\pi\) | |||||||
\(854\) | 11.1708 | 0.382256 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.68064 | 0.0574432 | ||||||||
\(857\) | 18.0066 | + | 18.0066i | 0.615093 | + | 0.615093i | 0.944269 | − | 0.329175i | \(-0.106771\pi\) |
−0.329175 | + | 0.944269i | \(0.606771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 56.2742i | − | 1.92005i | −0.279912 | − | 0.960026i | \(-0.590305\pi\) | ||
0.279912 | − | 0.960026i | \(-0.409695\pi\) | |||||||
\(860\) | 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 | 0.196399 | − | 0.980524i | \(-0.437075\pi\) |
0.980524 | − | 0.196399i | \(-0.0629248\pi\) | |||||||
\(864\) | 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 | −0.569743 | − | 0.821823i | \(-0.692957\pi\) |
0.821823 | + | 0.569743i | \(0.192957\pi\) | |||||||
\(878\) | 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 | \(0.0374157\pi\) | ||||
−0.993100 | + | 0.117274i | \(0.962584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.4066 | + | 11.4066i | 0.383862 | + | 0.383862i | 0.872491 | − | 0.488629i | \(-0.162503\pi\) |
−0.488629 | + | 0.872491i | \(0.662503\pi\) | |||||||
\(884\) | 19.7918 | 0.665669 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.4745 | 0.788640 | ||||||||
\(887\) | 4.39479 | + | 4.39479i | 0.147562 | + | 0.147562i | 0.777028 | − | 0.629466i | \(-0.216726\pi\) |
−0.629466 | + | 0.777028i | \(0.716726\pi\) | |||||||
\(888\) | 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 | −0.0863106 | + | 0.996268i | \(0.527508\pi\) |
−0.996268 | + | 0.0863106i | \(0.972492\pi\) | |||||||
\(908\) | 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 | \(0.355878\pi\) | ||||
−0.437461 | + | 0.899238i | \(0.644122\pi\) | |||||||
\(912\) | 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 | \(0.334935\pi\) | ||||
−0.495637 | + | 0.868530i | \(0.665065\pi\) | |||||||
\(920\) | 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 | −0.0606375 | − | 0.998160i | \(-0.519313\pi\) |
0.998160 | + | 0.0606375i | \(0.0193134\pi\) | |||||||
\(938\) | 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 | \(-0.950090\pi\) | ||
0.987732 | − | 0.156156i | \(-0.0499104\pi\) | |||||||
\(942\) | 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 | 0.269670 | − | 0.962953i | \(-0.413085\pi\) |
−0.962953 | + | 0.269670i | \(0.913085\pi\) | |||||||
\(948\) | 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 | −0.935548 | − | 0.353199i | \(-0.885094\pi\) |
0.353199 | + | 0.935548i | \(0.385094\pi\) | |||||||
\(954\) | 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 | −0.440142 | − | 0.897928i | \(-0.645072\pi\) |
0.897928 | + | 0.440142i | \(0.145072\pi\) | |||||||
\(968\) | 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 | \(0.0749337\pi\) | ||||
−0.972419 | + | 0.233243i | \(0.925066\pi\) | |||||||
\(972\) | 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 | 0.652389 | − | 0.757884i | \(-0.273767\pi\) |
−0.757884 | + | 0.652389i | \(0.773767\pi\) | |||||||
\(978\) | 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 | −0.394010 | − | 0.919106i | \(-0.628913\pi\) |
0.919106 | + | 0.394010i | \(0.128913\pi\) | |||||||
\(984\) | 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 | −0.744498 | − | 0.667625i | \(-0.767311\pi\) |
0.667625 | + | 0.744498i | \(0.267311\pi\) | |||||||
\(998\) | 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.323.4 | ✓ | 16 | |
3.2 | odd | 2 | inner | 2070.2.j.i.323.5 | yes | 16 | |
5.2 | odd | 4 | inner | 2070.2.j.i.737.5 | yes | 16 | |
15.2 | even | 4 | inner | 2070.2.j.i.737.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.i.323.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2070.2.j.i.323.5 | yes | 16 | 3.2 | odd | 2 | inner | |
2070.2.j.i.737.4 | yes | 16 | 15.2 | even | 4 | inner | |
2070.2.j.i.737.5 | yes | 16 | 5.2 | odd | 4 | inner |