Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(419,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.b (of order \(2\), degree \(1\), 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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 26 x^{18} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + 2753 x^{4} + 276 x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.5 | ||
Root | \(-1.51095i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.419 |
Dual form | 1045.2.b.c.419.16 |
$q$-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 \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.51095i | − | 1.06841i | −0.845356 | − | 0.534203i | \(-0.820612\pi\) | ||
0.845356 | − | 0.534203i | \(-0.179388\pi\) | |||||||
\(3\) | 0.900785i | 0.520069i | 0.965599 | + | 0.260034i | \(0.0837339\pi\) | ||||
−0.965599 | + | 0.260034i | \(0.916266\pi\) | |||||||
\(4\) | −0.282982 | −0.141491 | ||||||||
\(5\) | 0.672383 | − | 2.13258i | 0.300699 | − | 0.953719i | ||||
\(6\) | 1.36104 | 0.555644 | ||||||||
\(7\) | 0.603482i | 0.228095i | 0.993475 | + | 0.114047i | \(0.0363816\pi\) | ||||
−0.993475 | + | 0.114047i | \(0.963618\pi\) | |||||||
\(8\) | − | 2.59434i | − | 0.917236i | ||||||
\(9\) | 2.18859 | 0.729529 | ||||||||
\(10\) | −3.22223 | − | 1.01594i | −1.01896 | − | 0.321268i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − | 0.254906i | − | 0.0735850i | ||||||
\(13\) | 3.06772i | 0.850833i | 0.904998 | + | 0.425417i | \(0.139872\pi\) | ||||
−0.904998 | + | 0.425417i | \(0.860128\pi\) | |||||||
\(14\) | 0.911833 | 0.243698 | ||||||||
\(15\) | 1.92100 | + | 0.605673i | 0.495999 | + | 0.156384i | ||||
\(16\) | −4.48589 | −1.12147 | ||||||||
\(17\) | − | 4.08319i | − | 0.990318i | −0.868802 | − | 0.495159i | \(-0.835110\pi\) | ||
0.868802 | − | 0.495159i | \(-0.164890\pi\) | |||||||
\(18\) | − | 3.30685i | − | 0.779433i | ||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.190272 | + | 0.603482i | −0.0425462 | + | 0.134943i | ||||
\(21\) | −0.543607 | −0.118625 | ||||||||
\(22\) | − | 1.51095i | − | 0.322136i | ||||||
\(23\) | − | 6.19344i | − | 1.29142i | −0.763582 | − | 0.645710i | \(-0.776561\pi\) | ||
0.763582 | − | 0.645710i | \(-0.223439\pi\) | |||||||
\(24\) | 2.33694 | 0.477026 | ||||||||
\(25\) | −4.09580 | − | 2.86782i | −0.819160 | − | 0.573564i | ||||
\(26\) | 4.63519 | 0.909035 | ||||||||
\(27\) | 4.67380i | 0.899473i | ||||||||
\(28\) | − | 0.170774i | − | 0.0322733i | ||||||
\(29\) | 2.92797 | 0.543711 | 0.271855 | − | 0.962338i | \(-0.412363\pi\) | ||||
0.271855 | + | 0.962338i | \(0.412363\pi\) | |||||||
\(30\) | 0.915143 | − | 2.90254i | 0.167082 | − | 0.529929i | ||||
\(31\) | 7.98044 | 1.43333 | 0.716665 | − | 0.697418i | \(-0.245668\pi\) | ||||
0.716665 | + | 0.697418i | \(0.245668\pi\) | |||||||
\(32\) | 1.58930i | 0.280950i | ||||||||
\(33\) | 0.900785i | 0.156807i | ||||||||
\(34\) | −6.16951 | −1.05806 | ||||||||
\(35\) | 1.28697 | + | 0.405771i | 0.217538 | + | 0.0685878i | ||||
\(36\) | −0.619330 | −0.103222 | ||||||||
\(37\) | 10.2773i | 1.68957i | 0.535106 | + | 0.844785i | \(0.320272\pi\) | ||||
−0.535106 | + | 0.844785i | \(0.679728\pi\) | |||||||
\(38\) | − | 1.51095i | − | 0.245109i | ||||||
\(39\) | −2.76336 | −0.442492 | ||||||||
\(40\) | −5.53263 | − | 1.74439i | −0.874786 | − | 0.275812i | ||||
\(41\) | −7.31303 | −1.14210 | −0.571052 | − | 0.820914i | \(-0.693465\pi\) | ||||
−0.571052 | + | 0.820914i | \(0.693465\pi\) | |||||||
\(42\) | 0.821366i | 0.126740i | ||||||||
\(43\) | − | 0.0821817i | − | 0.0125326i | −0.999980 | − | 0.00626629i | \(-0.998005\pi\) | ||
0.999980 | − | 0.00626629i | \(-0.00199464\pi\) | |||||||
\(44\) | −0.282982 | −0.0426611 | ||||||||
\(45\) | 1.47157 | − | 4.66734i | 0.219368 | − | 0.695765i | ||||
\(46\) | −9.35800 | −1.37976 | ||||||||
\(47\) | − | 2.77574i | − | 0.404883i | −0.979294 | − | 0.202442i | \(-0.935112\pi\) | ||
0.979294 | − | 0.202442i | \(-0.0648877\pi\) | |||||||
\(48\) | − | 4.04082i | − | 0.583242i | ||||||
\(49\) | 6.63581 | 0.947973 | ||||||||
\(50\) | −4.33315 | + | 6.18857i | −0.612800 | + | 0.875196i | ||||
\(51\) | 3.67807 | 0.515033 | ||||||||
\(52\) | − | 0.868110i | − | 0.120385i | ||||||
\(53\) | − | 8.01831i | − | 1.10140i | −0.834703 | − | 0.550700i | \(-0.814361\pi\) | ||
0.834703 | − | 0.550700i | \(-0.185639\pi\) | |||||||
\(54\) | 7.06190 | 0.961003 | ||||||||
\(55\) | 0.672383 | − | 2.13258i | 0.0906641 | − | 0.287557i | ||||
\(56\) | 1.56563 | 0.209217 | ||||||||
\(57\) | 0.900785i | 0.119312i | ||||||||
\(58\) | − | 4.42403i | − | 0.580904i | ||||||
\(59\) | −3.21020 | −0.417933 | −0.208966 | − | 0.977923i | \(-0.567010\pi\) | ||||
−0.208966 | + | 0.977923i | \(0.567010\pi\) | |||||||
\(60\) | −0.543607 | − | 0.171394i | −0.0701794 | − | 0.0221269i | ||||
\(61\) | −11.1879 | −1.43247 | −0.716233 | − | 0.697862i | \(-0.754135\pi\) | ||||
−0.716233 | + | 0.697862i | \(0.754135\pi\) | |||||||
\(62\) | − | 12.0581i | − | 1.53138i | ||||||
\(63\) | 1.32077i | 0.166402i | ||||||||
\(64\) | −6.57042 | −0.821302 | ||||||||
\(65\) | 6.54217 | + | 2.06269i | 0.811456 | + | 0.255845i | ||||
\(66\) | 1.36104 | 0.167533 | ||||||||
\(67\) | − | 3.52951i | − | 0.431198i | −0.976482 | − | 0.215599i | \(-0.930830\pi\) | ||
0.976482 | − | 0.215599i | \(-0.0691704\pi\) | |||||||
\(68\) | 1.15547i | 0.140121i | ||||||||
\(69\) | 5.57896 | 0.671627 | ||||||||
\(70\) | 0.613101 | − | 1.94456i | 0.0732796 | − | 0.232419i | ||||
\(71\) | 1.51928 | 0.180305 | 0.0901525 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901525 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(72\) | − | 5.67793i | − | 0.669150i | ||||||
\(73\) | 3.04579i | 0.356483i | 0.983987 | + | 0.178242i | \(0.0570409\pi\) | ||||
−0.983987 | + | 0.178242i | \(0.942959\pi\) | |||||||
\(74\) | 15.5285 | 1.80515 | ||||||||
\(75\) | 2.58329 | − | 3.68944i | 0.298293 | − | 0.426020i | ||||
\(76\) | −0.282982 | −0.0324603 | ||||||||
\(77\) | 0.603482i | 0.0687731i | ||||||||
\(78\) | 4.17531i | 0.472761i | ||||||||
\(79\) | 3.57318 | 0.402014 | 0.201007 | − | 0.979590i | \(-0.435579\pi\) | ||||
0.201007 | + | 0.979590i | \(0.435579\pi\) | |||||||
\(80\) | −3.01623 | + | 9.56651i | −0.337225 | + | 1.06957i | ||||
\(81\) | 2.35567 | 0.261741 | ||||||||
\(82\) | 11.0497i | 1.22023i | ||||||||
\(83\) | − | 9.37109i | − | 1.02861i | −0.857607 | − | 0.514305i | \(-0.828050\pi\) | ||
0.857607 | − | 0.514305i | \(-0.171950\pi\) | |||||||
\(84\) | 0.153831 | 0.0167843 | ||||||||
\(85\) | −8.70772 | − | 2.74546i | −0.944485 | − | 0.297787i | ||||
\(86\) | −0.124173 | −0.0133899 | ||||||||
\(87\) | 2.63747i | 0.282767i | ||||||||
\(88\) | − | 2.59434i | − | 0.276557i | ||||||
\(89\) | 0.629618 | 0.0667394 | 0.0333697 | − | 0.999443i | \(-0.489376\pi\) | ||||
0.0333697 | + | 0.999443i | \(0.489376\pi\) | |||||||
\(90\) | −7.05213 | − | 2.22347i | −0.743360 | − | 0.234374i | ||||
\(91\) | −1.85132 | −0.194071 | ||||||||
\(92\) | 1.75263i | 0.182724i | ||||||||
\(93\) | 7.18867i | 0.745430i | ||||||||
\(94\) | −4.19402 | −0.432580 | ||||||||
\(95\) | 0.672383 | − | 2.13258i | 0.0689850 | − | 0.218798i | ||||
\(96\) | −1.43161 | −0.146113 | ||||||||
\(97\) | − | 5.71214i | − | 0.579980i | −0.957030 | − | 0.289990i | \(-0.906348\pi\) | ||
0.957030 | − | 0.289990i | \(-0.0936520\pi\) | |||||||
\(98\) | − | 10.0264i | − | 1.01282i | ||||||
\(99\) | 2.18859 | 0.219961 | ||||||||
\(100\) | 1.15904 | + | 0.811542i | 0.115904 | + | 0.0811542i | ||||
\(101\) | −15.0319 | −1.49573 | −0.747865 | − | 0.663850i | \(-0.768921\pi\) | ||||
−0.747865 | + | 0.663850i | \(0.768921\pi\) | |||||||
\(102\) | − | 5.55740i | − | 0.550264i | ||||||
\(103\) | − | 15.9710i | − | 1.57367i | −0.617162 | − | 0.786836i | \(-0.711718\pi\) | ||
0.617162 | − | 0.786836i | \(-0.288282\pi\) | |||||||
\(104\) | 7.95870 | 0.780415 | ||||||||
\(105\) | −0.365512 | + | 1.15929i | −0.0356704 | + | 0.113135i | ||||
\(106\) | −12.1153 | −1.17674 | ||||||||
\(107\) | 0.124523i | 0.0120381i | 0.999982 | + | 0.00601903i | \(0.00191593\pi\) | ||||
−0.999982 | + | 0.00601903i | \(0.998084\pi\) | |||||||
\(108\) | − | 1.32260i | − | 0.127267i | ||||||
\(109\) | 14.3549 | 1.37495 | 0.687477 | − | 0.726206i | \(-0.258718\pi\) | ||||
0.687477 | + | 0.726206i | \(0.258718\pi\) | |||||||
\(110\) | −3.22223 | − | 1.01594i | −0.307228 | − | 0.0968661i | ||||
\(111\) | −9.25760 | −0.878692 | ||||||||
\(112\) | − | 2.70715i | − | 0.255802i | ||||||
\(113\) | 11.5904i | 1.09033i | 0.838328 | + | 0.545166i | \(0.183533\pi\) | ||||
−0.838328 | + | 0.545166i | \(0.816467\pi\) | |||||||
\(114\) | 1.36104 | 0.127474 | ||||||||
\(115\) | −13.2080 | − | 4.16436i | −1.23165 | − | 0.388329i | ||||
\(116\) | −0.828563 | −0.0769302 | ||||||||
\(117\) | 6.71398i | 0.620707i | ||||||||
\(118\) | 4.85047i | 0.446522i | ||||||||
\(119\) | 2.46413 | 0.225886 | ||||||||
\(120\) | 1.57132 | − | 4.98371i | 0.143441 | − | 0.454948i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 16.9044i | 1.53045i | ||||||||
\(123\) | − | 6.58747i | − | 0.593972i | ||||||
\(124\) | −2.25832 | −0.202803 | ||||||||
\(125\) | −8.86981 | + | 6.80635i | −0.793340 | + | 0.608779i | ||||
\(126\) | 1.99563 | 0.177784 | ||||||||
\(127\) | 18.8000i | 1.66823i | 0.551591 | + | 0.834115i | \(0.314021\pi\) | ||||
−0.551591 | + | 0.834115i | \(0.685979\pi\) | |||||||
\(128\) | 13.1062i | 1.15843i | ||||||||
\(129\) | 0.0740280 | 0.00651780 | ||||||||
\(130\) | 3.11662 | − | 9.88492i | 0.273346 | − | 0.866965i | ||||
\(131\) | 16.2223 | 1.41735 | 0.708674 | − | 0.705537i | \(-0.249294\pi\) | ||||
0.708674 | + | 0.705537i | \(0.249294\pi\) | |||||||
\(132\) | − | 0.254906i | − | 0.0221867i | ||||||
\(133\) | 0.603482i | 0.0523285i | ||||||||
\(134\) | −5.33292 | −0.460694 | ||||||||
\(135\) | 9.96726 | + | 3.14258i | 0.857845 | + | 0.270471i | ||||
\(136\) | −10.5932 | −0.908355 | ||||||||
\(137\) | 21.2561i | 1.81603i | 0.418932 | + | 0.908017i | \(0.362404\pi\) | ||||
−0.418932 | + | 0.908017i | \(0.637596\pi\) | |||||||
\(138\) | − | 8.42955i | − | 0.717571i | ||||||
\(139\) | −21.9041 | −1.85788 | −0.928942 | − | 0.370226i | \(-0.879280\pi\) | ||||
−0.928942 | + | 0.370226i | \(0.879280\pi\) | |||||||
\(140\) | −0.364190 | − | 0.114826i | −0.0307797 | − | 0.00970455i | ||||
\(141\) | 2.50035 | 0.210567 | ||||||||
\(142\) | − | 2.29556i | − | 0.192639i | ||||||
\(143\) | 3.06772i | 0.256536i | ||||||||
\(144\) | −9.81775 | −0.818145 | ||||||||
\(145\) | 1.96872 | − | 6.24414i | 0.163493 | − | 0.518547i | ||||
\(146\) | 4.60206 | 0.380869 | ||||||||
\(147\) | 5.97744i | 0.493011i | ||||||||
\(148\) | − | 2.90828i | − | 0.239059i | ||||||
\(149\) | −11.0150 | −0.902388 | −0.451194 | − | 0.892426i | \(-0.649002\pi\) | ||||
−0.451194 | + | 0.892426i | \(0.649002\pi\) | |||||||
\(150\) | −5.57457 | − | 3.90323i | −0.455162 | − | 0.318698i | ||||
\(151\) | 15.7653 | 1.28296 | 0.641481 | − | 0.767139i | \(-0.278320\pi\) | ||||
0.641481 | + | 0.767139i | \(0.278320\pi\) | |||||||
\(152\) | − | 2.59434i | − | 0.210428i | ||||||
\(153\) | − | 8.93640i | − | 0.722465i | ||||||
\(154\) | 0.911833 | 0.0734776 | ||||||||
\(155\) | 5.36591 | − | 17.0189i | 0.431001 | − | 1.36699i | ||||
\(156\) | 0.781981 | 0.0626086 | ||||||||
\(157\) | 23.8820i | 1.90599i | 0.302981 | + | 0.952997i | \(0.402018\pi\) | ||||
−0.302981 | + | 0.952997i | \(0.597982\pi\) | |||||||
\(158\) | − | 5.39890i | − | 0.429514i | ||||||
\(159\) | 7.22277 | 0.572803 | ||||||||
\(160\) | 3.38930 | + | 1.06862i | 0.267948 | + | 0.0844814i | ||||
\(161\) | 3.73763 | 0.294566 | ||||||||
\(162\) | − | 3.55930i | − | 0.279645i | ||||||
\(163\) | 18.1018i | 1.41784i | 0.705290 | + | 0.708919i | \(0.250817\pi\) | ||||
−0.705290 | + | 0.708919i | \(0.749183\pi\) | |||||||
\(164\) | 2.06946 | 0.161597 | ||||||||
\(165\) | 1.92100 | + | 0.605673i | 0.149549 | + | 0.0471515i | ||||
\(166\) | −14.1593 | −1.09897 | ||||||||
\(167\) | 8.11307i | 0.627808i | 0.949455 | + | 0.313904i | \(0.101637\pi\) | ||||
−0.949455 | + | 0.313904i | \(0.898363\pi\) | |||||||
\(168\) | 1.41030i | 0.108807i | ||||||||
\(169\) | 3.58907 | 0.276082 | ||||||||
\(170\) | −4.14827 | + | 13.1570i | −0.318158 | + | 1.00909i | ||||
\(171\) | 2.18859 | 0.167365 | ||||||||
\(172\) | 0.0232559i | 0.00177325i | ||||||||
\(173\) | 17.9368i | 1.36371i | 0.731489 | + | 0.681853i | \(0.238826\pi\) | ||||
−0.731489 | + | 0.681853i | \(0.761174\pi\) | |||||||
\(174\) | 3.98510 | 0.302110 | ||||||||
\(175\) | 1.73068 | − | 2.47174i | 0.130827 | − | 0.186846i | ||||
\(176\) | −4.48589 | −0.338136 | ||||||||
\(177\) | − | 2.89170i | − | 0.217354i | ||||||
\(178\) | − | 0.951324i | − | 0.0713048i | ||||||
\(179\) | 22.6454 | 1.69260 | 0.846300 | − | 0.532707i | \(-0.178825\pi\) | ||||
0.846300 | + | 0.532707i | \(0.178825\pi\) | |||||||
\(180\) | −0.416427 | + | 1.32077i | −0.0310386 | + | 0.0984445i | ||||
\(181\) | −2.12283 | −0.157789 | −0.0788943 | − | 0.996883i | \(-0.525139\pi\) | ||||
−0.0788943 | + | 0.996883i | \(0.525139\pi\) | |||||||
\(182\) | 2.79725i | 0.207346i | ||||||||
\(183\) | − | 10.0779i | − | 0.744980i | ||||||
\(184\) | −16.0679 | −1.18454 | ||||||||
\(185\) | 21.9171 | + | 6.91025i | 1.61138 | + | 0.508052i | ||||
\(186\) | 10.8617 | 0.796422 | ||||||||
\(187\) | − | 4.08319i | − | 0.298592i | ||||||
\(188\) | 0.785485i | 0.0572873i | ||||||||
\(189\) | −2.82055 | −0.205165 | ||||||||
\(190\) | −3.22223 | − | 1.01594i | −0.233765 | − | 0.0737040i | ||||
\(191\) | −5.41877 | −0.392088 | −0.196044 | − | 0.980595i | \(-0.562810\pi\) | ||||
−0.196044 | + | 0.980595i | \(0.562810\pi\) | |||||||
\(192\) | − | 5.91854i | − | 0.427133i | ||||||
\(193\) | 2.89582i | 0.208446i | 0.994554 | + | 0.104223i | \(0.0332356\pi\) | ||||
−0.994554 | + | 0.104223i | \(0.966764\pi\) | |||||||
\(194\) | −8.63078 | −0.619654 | ||||||||
\(195\) | −1.85804 | + | 5.89309i | −0.133057 | + | 0.422013i | ||||
\(196\) | −1.87781 | −0.134130 | ||||||||
\(197\) | 3.06581i | 0.218430i | 0.994018 | + | 0.109215i | \(0.0348337\pi\) | ||||
−0.994018 | + | 0.109215i | \(0.965166\pi\) | |||||||
\(198\) | − | 3.30685i | − | 0.235008i | ||||||
\(199\) | 23.6145 | 1.67399 | 0.836993 | − | 0.547214i | \(-0.184312\pi\) | ||||
0.836993 | + | 0.547214i | \(0.184312\pi\) | |||||||
\(200\) | −7.44009 | + | 10.6259i | −0.526094 | + | 0.751363i | ||||
\(201\) | 3.17933 | 0.224252 | ||||||||
\(202\) | 22.7125i | 1.59805i | ||||||||
\(203\) | 1.76698i | 0.124018i | ||||||||
\(204\) | −1.04083 | −0.0728725 | ||||||||
\(205\) | −4.91716 | + | 15.5956i | −0.343429 | + | 1.08925i | ||||
\(206\) | −24.1315 | −1.68132 | ||||||||
\(207\) | − | 13.5549i | − | 0.942129i | ||||||
\(208\) | − | 13.7615i | − | 0.954185i | ||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 1.75163 | + | 0.552272i | 0.120874 | + | 0.0381104i | ||||
\(211\) | −11.5535 | −0.795377 | −0.397688 | − | 0.917521i | \(-0.630187\pi\) | ||||
−0.397688 | + | 0.917521i | \(0.630187\pi\) | |||||||
\(212\) | 2.26904i | 0.155838i | ||||||||
\(213\) | 1.36854i | 0.0937709i | ||||||||
\(214\) | 0.188148 | 0.0128615 | ||||||||
\(215\) | −0.175259 | − | 0.0552576i | −0.0119526 | − | 0.00376853i | ||||
\(216\) | 12.1254 | 0.825030 | ||||||||
\(217\) | 4.81605i | 0.326935i | ||||||||
\(218\) | − | 21.6897i | − | 1.46901i | ||||||
\(219\) | −2.74361 | −0.185396 | ||||||||
\(220\) | −0.190272 | + | 0.603482i | −0.0128282 | + | 0.0406867i | ||||
\(221\) | 12.5261 | 0.842596 | ||||||||
\(222\) | 13.9878i | 0.938800i | ||||||||
\(223\) | − | 9.59966i | − | 0.642841i | −0.946937 | − | 0.321420i | \(-0.895840\pi\) | ||
0.946937 | − | 0.321420i | \(-0.104160\pi\) | |||||||
\(224\) | −0.959111 | −0.0640833 | ||||||||
\(225\) | −8.96402 | − | 6.27648i | −0.597601 | − | 0.418432i | ||||
\(226\) | 17.5125 | 1.16492 | ||||||||
\(227\) | 5.29283i | 0.351298i | 0.984453 | + | 0.175649i | \(0.0562023\pi\) | ||||
−0.984453 | + | 0.175649i | \(0.943798\pi\) | |||||||
\(228\) | − | 0.254906i | − | 0.0168816i | ||||||
\(229\) | 1.45160 | 0.0959243 | 0.0479622 | − | 0.998849i | \(-0.484727\pi\) | ||||
0.0479622 | + | 0.998849i | \(0.484727\pi\) | |||||||
\(230\) | −6.29216 | + | 19.9567i | −0.414893 | + | 1.31591i | ||||
\(231\) | −0.543607 | −0.0357667 | ||||||||
\(232\) | − | 7.59614i | − | 0.498711i | ||||||
\(233\) | 25.0472i | 1.64090i | 0.571721 | + | 0.820448i | \(0.306276\pi\) | ||||
−0.571721 | + | 0.820448i | \(0.693724\pi\) | |||||||
\(234\) | 10.1445 | 0.663167 | ||||||||
\(235\) | −5.91949 | − | 1.86636i | −0.386145 | − | 0.121748i | ||||
\(236\) | 0.908429 | 0.0591337 | ||||||||
\(237\) | 3.21866i | 0.209075i | ||||||||
\(238\) | − | 3.72318i | − | 0.241338i | ||||||
\(239\) | −1.53900 | −0.0995499 | −0.0497749 | − | 0.998760i | \(-0.515850\pi\) | ||||
−0.0497749 | + | 0.998760i | \(0.515850\pi\) | |||||||
\(240\) | −8.61737 | − | 2.71698i | −0.556249 | − | 0.175380i | ||||
\(241\) | −4.82341 | −0.310703 | −0.155352 | − | 0.987859i | \(-0.549651\pi\) | ||||
−0.155352 | + | 0.987859i | \(0.549651\pi\) | |||||||
\(242\) | − | 1.51095i | − | 0.0971278i | ||||||
\(243\) | 16.1434i | 1.03560i | ||||||||
\(244\) | 3.16598 | 0.202681 | ||||||||
\(245\) | 4.46181 | − | 14.1514i | 0.285054 | − | 0.904100i | ||||
\(246\) | −9.95337 | −0.634603 | ||||||||
\(247\) | 3.06772i | 0.195195i | ||||||||
\(248\) | − | 20.7039i | − | 1.31470i | ||||||
\(249\) | 8.44134 | 0.534948 | ||||||||
\(250\) | 10.2841 | + | 13.4019i | 0.650423 | + | 0.847609i | ||||
\(251\) | −11.4453 | −0.722423 | −0.361211 | − | 0.932484i | \(-0.617637\pi\) | ||||
−0.361211 | + | 0.932484i | \(0.617637\pi\) | |||||||
\(252\) | − | 0.373755i | − | 0.0235443i | ||||||
\(253\) | − | 6.19344i | − | 0.389378i | ||||||
\(254\) | 28.4059 | 1.78235 | ||||||||
\(255\) | 2.47307 | − | 7.84379i | 0.154870 | − | 0.491197i | ||||
\(256\) | 6.66201 | 0.416376 | ||||||||
\(257\) | 4.14766i | 0.258724i | 0.991597 | + | 0.129362i | \(0.0412929\pi\) | ||||
−0.991597 | + | 0.129362i | \(0.958707\pi\) | |||||||
\(258\) | − | 0.111853i | − | 0.00696366i | ||||||
\(259\) | −6.20214 | −0.385382 | ||||||||
\(260\) | −1.85132 | − | 0.583703i | −0.114814 | − | 0.0361997i | ||||
\(261\) | 6.40812 | 0.396653 | ||||||||
\(262\) | − | 24.5111i | − | 1.51430i | ||||||
\(263\) | 4.43431i | 0.273431i | 0.990610 | + | 0.136716i | \(0.0436546\pi\) | ||||
−0.990610 | + | 0.136716i | \(0.956345\pi\) | |||||||
\(264\) | 2.33694 | 0.143829 | ||||||||
\(265\) | −17.0997 | − | 5.39137i | −1.05043 | − | 0.331189i | ||||
\(266\) | 0.911833 | 0.0559081 | ||||||||
\(267\) | 0.567151i | 0.0347091i | ||||||||
\(268\) | 0.998787i | 0.0610106i | ||||||||
\(269\) | −4.65270 | −0.283680 | −0.141840 | − | 0.989890i | \(-0.545302\pi\) | ||||
−0.141840 | + | 0.989890i | \(0.545302\pi\) | |||||||
\(270\) | 4.74830 | − | 15.0601i | 0.288972 | − | 0.916527i | ||||
\(271\) | −19.7128 | −1.19746 | −0.598732 | − | 0.800949i | \(-0.704329\pi\) | ||||
−0.598732 | + | 0.800949i | \(0.704329\pi\) | |||||||
\(272\) | 18.3167i | 1.11061i | ||||||||
\(273\) | − | 1.66764i | − | 0.100930i | ||||||
\(274\) | 32.1171 | 1.94026 | ||||||||
\(275\) | −4.09580 | − | 2.86782i | −0.246986 | − | 0.172936i | ||||
\(276\) | −1.57874 | −0.0950292 | ||||||||
\(277\) | − | 21.9425i | − | 1.31840i | −0.751970 | − | 0.659198i | \(-0.770896\pi\) | ||
0.751970 | − | 0.659198i | \(-0.229104\pi\) | |||||||
\(278\) | 33.0961i | 1.98497i | ||||||||
\(279\) | 17.4659 | 1.04566 | ||||||||
\(280\) | 1.05271 | − | 3.33884i | 0.0629112 | − | 0.199534i | ||||
\(281\) | −4.67060 | −0.278625 | −0.139312 | − | 0.990248i | \(-0.544489\pi\) | ||||
−0.139312 | + | 0.990248i | \(0.544489\pi\) | |||||||
\(282\) | − | 3.77791i | − | 0.224971i | ||||||
\(283\) | 10.2046i | 0.606598i | 0.952895 | + | 0.303299i | \(0.0980881\pi\) | ||||
−0.952895 | + | 0.303299i | \(0.901912\pi\) | |||||||
\(284\) | −0.429928 | −0.0255115 | ||||||||
\(285\) | 1.92100 | + | 0.605673i | 0.113790 | + | 0.0358769i | ||||
\(286\) | 4.63519 | 0.274084 | ||||||||
\(287\) | − | 4.41328i | − | 0.260508i | ||||||
\(288\) | 3.47831i | 0.204961i | ||||||||
\(289\) | 0.327596 | 0.0192703 | ||||||||
\(290\) | −9.43461 | − | 2.97464i | −0.554019 | − | 0.174677i | ||||
\(291\) | 5.14541 | 0.301629 | ||||||||
\(292\) | − | 0.861905i | − | 0.0504392i | ||||||
\(293\) | 19.0508i | 1.11296i | 0.830862 | + | 0.556478i | \(0.187848\pi\) | ||||
−0.830862 | + | 0.556478i | \(0.812152\pi\) | |||||||
\(294\) | 9.03164 | 0.526736 | ||||||||
\(295\) | −2.15848 | + | 6.84601i | −0.125672 | + | 0.398590i | ||||
\(296\) | 26.6626 | 1.54973 | ||||||||
\(297\) | 4.67380i | 0.271201i | ||||||||
\(298\) | 16.6432i | 0.964117i | ||||||||
\(299\) | 18.9998 | 1.09878 | ||||||||
\(300\) | −0.731025 | + | 1.04404i | −0.0422057 | + | 0.0602779i | ||||
\(301\) | 0.0495951 | 0.00285862 | ||||||||
\(302\) | − | 23.8206i | − | 1.37072i | ||||||
\(303\) | − | 13.5405i | − | 0.777883i | ||||||
\(304\) | −4.48589 | −0.257283 | ||||||||
\(305\) | −7.52256 | + | 23.8591i | −0.430741 | + | 1.36617i | ||||
\(306\) | −13.5025 | −0.771886 | ||||||||
\(307\) | 1.26498i | 0.0721961i | 0.999348 | + | 0.0360981i | \(0.0114929\pi\) | ||||
−0.999348 | + | 0.0360981i | \(0.988507\pi\) | |||||||
\(308\) | − | 0.170774i | − | 0.00973078i | ||||||
\(309\) | 14.3865 | 0.818417 | ||||||||
\(310\) | −25.7148 | − | 8.10765i | −1.46050 | − | 0.460484i | ||||
\(311\) | 34.2924 | 1.94455 | 0.972273 | − | 0.233849i | \(-0.0751322\pi\) | ||||
0.972273 | + | 0.233849i | \(0.0751322\pi\) | |||||||
\(312\) | 7.16908i | 0.405869i | ||||||||
\(313\) | − | 0.755401i | − | 0.0426978i | −0.999772 | − | 0.0213489i | \(-0.993204\pi\) | ||
0.999772 | − | 0.0213489i | \(-0.00679608\pi\) | |||||||
\(314\) | 36.0846 | 2.03637 | ||||||||
\(315\) | 2.81665 | + | 0.888065i | 0.158700 | + | 0.0500368i | ||||
\(316\) | −1.01114 | −0.0568813 | ||||||||
\(317\) | − | 19.4248i | − | 1.09101i | −0.838108 | − | 0.545504i | \(-0.816338\pi\) | ||
0.838108 | − | 0.545504i | \(-0.183662\pi\) | |||||||
\(318\) | − | 10.9133i | − | 0.611986i | ||||||
\(319\) | 2.92797 | 0.163935 | ||||||||
\(320\) | −4.41784 | + | 14.0119i | −0.246965 | + | 0.783292i | ||||
\(321\) | −0.112168 | −0.00626062 | ||||||||
\(322\) | − | 5.64738i | − | 0.314716i | ||||||
\(323\) | − | 4.08319i | − | 0.227195i | ||||||
\(324\) | −0.666611 | −0.0370340 | ||||||||
\(325\) | 8.79769 | − | 12.5648i | 0.488008 | − | 0.696969i | ||||
\(326\) | 27.3509 | 1.51483 | ||||||||
\(327\) | 12.9307i | 0.715071i | ||||||||
\(328\) | 18.9725i | 1.04758i | ||||||||
\(329\) | 1.67511 | 0.0923518 | ||||||||
\(330\) | 0.915143 | − | 2.90254i | 0.0503770 | − | 0.159779i | ||||
\(331\) | 26.3233 | 1.44686 | 0.723429 | − | 0.690399i | \(-0.242565\pi\) | ||||
0.723429 | + | 0.690399i | \(0.242565\pi\) | |||||||
\(332\) | 2.65185i | 0.145539i | ||||||||
\(333\) | 22.4927i | 1.23259i | ||||||||
\(334\) | 12.2585 | 0.670754 | ||||||||
\(335\) | −7.52696 | − | 2.37318i | −0.411242 | − | 0.129661i | ||||
\(336\) | 2.43856 | 0.133034 | ||||||||
\(337\) | − | 28.4082i | − | 1.54749i | −0.633495 | − | 0.773746i | \(-0.718380\pi\) | ||
0.633495 | − | 0.773746i | \(-0.281620\pi\) | |||||||
\(338\) | − | 5.42292i | − | 0.294968i | ||||||
\(339\) | −10.4404 | −0.567047 | ||||||||
\(340\) | 2.46413 | + | 0.776917i | 0.133636 | + | 0.0421342i | ||||
\(341\) | 7.98044 | 0.432165 | ||||||||
\(342\) | − | 3.30685i | − | 0.178814i | ||||||
\(343\) | 8.22896i | 0.444322i | ||||||||
\(344\) | −0.213207 | −0.0114953 | ||||||||
\(345\) | 3.75120 | − | 11.8976i | 0.201958 | − | 0.640544i | ||||
\(346\) | 27.1016 | 1.45699 | ||||||||
\(347\) | − | 15.4328i | − | 0.828475i | −0.910169 | − | 0.414237i | \(-0.864048\pi\) | ||
0.910169 | − | 0.414237i | \(-0.135952\pi\) | |||||||
\(348\) | − | 0.746358i | − | 0.0400090i | ||||||
\(349\) | −9.55388 | −0.511408 | −0.255704 | − | 0.966755i | \(-0.582307\pi\) | ||||
−0.255704 | + | 0.966755i | \(0.582307\pi\) | |||||||
\(350\) | −3.73469 | − | 2.61498i | −0.199628 | − | 0.139776i | ||||
\(351\) | −14.3379 | −0.765302 | ||||||||
\(352\) | 1.58930i | 0.0847097i | ||||||||
\(353\) | 6.07556i | 0.323370i | 0.986842 | + | 0.161685i | \(0.0516928\pi\) | ||||
−0.986842 | + | 0.161685i | \(0.948307\pi\) | |||||||
\(354\) | −4.36923 | −0.232222 | ||||||||
\(355\) | 1.02154 | − | 3.23998i | 0.0542175 | − | 0.171960i | ||||
\(356\) | −0.178171 | −0.00944302 | ||||||||
\(357\) | 2.21965i | 0.117476i | ||||||||
\(358\) | − | 34.2162i | − | 1.80838i | ||||||
\(359\) | −19.9636 | −1.05364 | −0.526820 | − | 0.849977i | \(-0.676616\pi\) | ||||
−0.526820 | + | 0.849977i | \(0.676616\pi\) | |||||||
\(360\) | −12.1086 | − | 3.81774i | −0.638181 | − | 0.201213i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 3.20750i | 0.168582i | ||||||||
\(363\) | 0.900785i | 0.0472790i | ||||||||
\(364\) | 0.523889 | 0.0274592 | ||||||||
\(365\) | 6.49540 | + | 2.04794i | 0.339985 | + | 0.107194i | ||||
\(366\) | −15.2273 | −0.795941 | ||||||||
\(367\) | − | 0.193444i | − | 0.0100977i | −0.999987 | − | 0.00504886i | \(-0.998393\pi\) | ||
0.999987 | − | 0.00504886i | \(-0.00160711\pi\) | |||||||
\(368\) | 27.7830i | 1.44829i | ||||||||
\(369\) | −16.0052 | −0.833198 | ||||||||
\(370\) | 10.4411 | − | 33.1157i | 0.542805 | − | 1.72160i | ||||
\(371\) | 4.83890 | 0.251223 | ||||||||
\(372\) | − | 2.03426i | − | 0.105472i | ||||||
\(373\) | 33.8918i | 1.75485i | 0.479712 | + | 0.877426i | \(0.340741\pi\) | ||||
−0.479712 | + | 0.877426i | \(0.659259\pi\) | |||||||
\(374\) | −6.16951 | −0.319018 | ||||||||
\(375\) | −6.13106 | − | 7.98979i | −0.316607 | − | 0.412591i | ||||
\(376\) | −7.20120 | −0.371374 | ||||||||
\(377\) | 8.98221i | 0.462607i | ||||||||
\(378\) | 4.26173i | 0.219200i | ||||||||
\(379\) | 9.70742 | 0.498637 | 0.249318 | − | 0.968422i | \(-0.419793\pi\) | ||||
0.249318 | + | 0.968422i | \(0.419793\pi\) | |||||||
\(380\) | −0.190272 | + | 0.603482i | −0.00976076 | + | 0.0309580i | ||||
\(381\) | −16.9348 | −0.867594 | ||||||||
\(382\) | 8.18751i | 0.418909i | ||||||||
\(383\) | − | 12.2664i | − | 0.626783i | −0.949624 | − | 0.313391i | \(-0.898535\pi\) | ||
0.949624 | − | 0.313391i | \(-0.101465\pi\) | |||||||
\(384\) | −11.8059 | −0.602465 | ||||||||
\(385\) | 1.28697 | + | 0.405771i | 0.0655903 | + | 0.0206800i | ||||
\(386\) | 4.37546 | 0.222705 | ||||||||
\(387\) | − | 0.179862i | − | 0.00914288i | ||||||
\(388\) | 1.61643i | 0.0820619i | ||||||||
\(389\) | −22.1011 | −1.12057 | −0.560285 | − | 0.828300i | \(-0.689308\pi\) | ||||
−0.560285 | + | 0.828300i | \(0.689308\pi\) | |||||||
\(390\) | 8.90419 | + | 2.80741i | 0.450881 | + | 0.142159i | ||||
\(391\) | −25.2890 | −1.27892 | ||||||||
\(392\) | − | 17.2155i | − | 0.869515i | ||||||
\(393\) | 14.6128i | 0.737118i | ||||||||
\(394\) | 4.63229 | 0.233372 | ||||||||
\(395\) | 2.40254 | − | 7.62009i | 0.120885 | − | 0.383408i | ||||
\(396\) | −0.619330 | −0.0311225 | ||||||||
\(397\) | 1.76411i | 0.0885380i | 0.999020 | + | 0.0442690i | \(0.0140959\pi\) | ||||
−0.999020 | + | 0.0442690i | \(0.985904\pi\) | |||||||
\(398\) | − | 35.6804i | − | 1.78850i | ||||||
\(399\) | −0.543607 | −0.0272144 | ||||||||
\(400\) | 18.3733 | + | 12.8647i | 0.918665 | + | 0.643236i | ||||
\(401\) | −37.7407 | −1.88468 | −0.942339 | − | 0.334659i | \(-0.891379\pi\) | ||||
−0.942339 | + | 0.334659i | \(0.891379\pi\) | |||||||
\(402\) | − | 4.80382i | − | 0.239593i | ||||||
\(403\) | 24.4818i | 1.21953i | ||||||||
\(404\) | 4.25376 | 0.211632 | ||||||||
\(405\) | 1.58391 | − | 5.02365i | 0.0787051 | − | 0.249627i | ||||
\(406\) | 2.66982 | 0.132501 | ||||||||
\(407\) | 10.2773i | 0.509425i | ||||||||
\(408\) | − | 9.54215i | − | 0.472407i | ||||||
\(409\) | 15.2172 | 0.752440 | 0.376220 | − | 0.926530i | \(-0.377224\pi\) | ||||
0.376220 | + | 0.926530i | \(0.377224\pi\) | |||||||
\(410\) | 23.5643 | + | 7.42960i | 1.16376 | + | 0.366922i | ||||
\(411\) | −19.1472 | −0.944463 | ||||||||
\(412\) | 4.51951i | 0.222660i | ||||||||
\(413\) | − | 1.93730i | − | 0.0953282i | ||||||
\(414\) | −20.4808 | −1.00658 | ||||||||
\(415\) | −19.9846 | − | 6.30096i | −0.981005 | − | 0.309302i | ||||
\(416\) | −4.87552 | −0.239042 | ||||||||
\(417\) | − | 19.7309i | − | 0.966227i | ||||||
\(418\) | − | 1.51095i | − | 0.0739032i | ||||||
\(419\) | 23.6883 | 1.15725 | 0.578624 | − | 0.815595i | \(-0.303590\pi\) | ||||
0.578624 | + | 0.815595i | \(0.303590\pi\) | |||||||
\(420\) | 0.103433 | − | 0.328057i | 0.00504703 | − | 0.0160076i | ||||
\(421\) | −14.2242 | −0.693244 | −0.346622 | − | 0.938005i | \(-0.612671\pi\) | ||||
−0.346622 | + | 0.938005i | \(0.612671\pi\) | |||||||
\(422\) | 17.4568i | 0.849785i | ||||||||
\(423\) | − | 6.07495i | − | 0.295374i | ||||||
\(424\) | −20.8022 | −1.01024 | ||||||||
\(425\) | −11.7098 | + | 16.7239i | −0.568011 | + | 0.811229i | ||||
\(426\) | 2.06780 | 0.100185 | ||||||||
\(427\) | − | 6.75170i | − | 0.326738i | ||||||
\(428\) | − | 0.0352377i | − | 0.00170328i | ||||||
\(429\) | −2.76336 | −0.133416 | ||||||||
\(430\) | −0.0834916 | + | 0.264808i | −0.00402632 | + | 0.0127702i | ||||
\(431\) | −23.9472 | −1.15350 | −0.576749 | − | 0.816922i | \(-0.695679\pi\) | ||||
−0.576749 | + | 0.816922i | \(0.695679\pi\) | |||||||
\(432\) | − | 20.9661i | − | 1.00873i | ||||||
\(433\) | 26.4436i | 1.27080i | 0.772185 | + | 0.635398i | \(0.219164\pi\) | ||||
−0.772185 | + | 0.635398i | \(0.780836\pi\) | |||||||
\(434\) | 7.27683 | 0.349299 | ||||||||
\(435\) | 5.62463 | + | 1.77339i | 0.269680 | + | 0.0850277i | ||||
\(436\) | −4.06219 | −0.194544 | ||||||||
\(437\) | − | 6.19344i | − | 0.296272i | ||||||
\(438\) | 4.14546i | 0.198078i | ||||||||
\(439\) | −22.3823 | −1.06825 | −0.534124 | − | 0.845406i | \(-0.679359\pi\) | ||||
−0.534124 | + | 0.845406i | \(0.679359\pi\) | |||||||
\(440\) | −5.53263 | − | 1.74439i | −0.263758 | − | 0.0831604i | ||||
\(441\) | 14.5230 | 0.691573 | ||||||||
\(442\) | − | 18.9263i | − | 0.900234i | ||||||
\(443\) | 10.3295i | 0.490771i | 0.969426 | + | 0.245386i | \(0.0789146\pi\) | ||||
−0.969426 | + | 0.245386i | \(0.921085\pi\) | |||||||
\(444\) | 2.61973 | 0.124327 | ||||||||
\(445\) | 0.423345 | − | 1.34271i | 0.0200685 | − | 0.0636506i | ||||
\(446\) | −14.5046 | −0.686815 | ||||||||
\(447\) | − | 9.92219i | − | 0.469304i | ||||||
\(448\) | − | 3.96513i | − | 0.187335i | ||||||
\(449\) | 14.4952 | 0.684068 | 0.342034 | − | 0.939687i | \(-0.388884\pi\) | ||||
0.342034 | + | 0.939687i | \(0.388884\pi\) | |||||||
\(450\) | −9.48347 | + | 13.5442i | −0.447055 | + | 0.638480i | ||||
\(451\) | −7.31303 | −0.344357 | ||||||||
\(452\) | − | 3.27987i | − | 0.154272i | ||||||
\(453\) | 14.2012i | 0.667228i | ||||||||
\(454\) | 7.99723 | 0.375328 | ||||||||
\(455\) | −1.24479 | + | 3.94808i | −0.0583568 | + | 0.185089i | ||||
\(456\) | 2.33694 | 0.109437 | ||||||||
\(457\) | − | 16.8399i | − | 0.787737i | −0.919167 | − | 0.393869i | \(-0.871136\pi\) | ||
0.919167 | − | 0.393869i | \(-0.128864\pi\) | |||||||
\(458\) | − | 2.19330i | − | 0.102486i | ||||||
\(459\) | 19.0840 | 0.890765 | ||||||||
\(460\) | 3.73763 | + | 1.17844i | 0.174268 | + | 0.0549450i | ||||
\(461\) | 10.7768 | 0.501928 | 0.250964 | − | 0.967996i | \(-0.419252\pi\) | ||||
0.250964 | + | 0.967996i | \(0.419252\pi\) | |||||||
\(462\) | 0.821366i | 0.0382134i | ||||||||
\(463\) | − | 13.0560i | − | 0.606764i | −0.952869 | − | 0.303382i | \(-0.901884\pi\) | ||
0.952869 | − | 0.303382i | \(-0.0981159\pi\) | |||||||
\(464\) | −13.1345 | −0.609756 | ||||||||
\(465\) | 15.3304 | + | 4.83354i | 0.710931 | + | 0.224150i | ||||
\(466\) | 37.8451 | 1.75314 | ||||||||
\(467\) | 13.1491i | 0.608470i | 0.952597 | + | 0.304235i | \(0.0984008\pi\) | ||||
−0.952597 | + | 0.304235i | \(0.901599\pi\) | |||||||
\(468\) | − | 1.89993i | − | 0.0878245i | ||||||
\(469\) | 2.12999 | 0.0983540 | ||||||||
\(470\) | −2.81999 | + | 8.94408i | −0.130076 | + | 0.412560i | ||||
\(471\) | −21.5126 | −0.991247 | ||||||||
\(472\) | 8.32834i | 0.383343i | ||||||||
\(473\) | − | 0.0821817i | − | 0.00377872i | ||||||
\(474\) | 4.86325 | 0.223377 | ||||||||
\(475\) | −4.09580 | − | 2.86782i | −0.187928 | − | 0.131585i | ||||
\(476\) | −0.697304 | −0.0319609 | ||||||||
\(477\) | − | 17.5488i | − | 0.803502i | ||||||
\(478\) | 2.32536i | 0.106360i | ||||||||
\(479\) | −6.76244 | −0.308984 | −0.154492 | − | 0.987994i | \(-0.549374\pi\) | ||||
−0.154492 | + | 0.987994i | \(0.549374\pi\) | |||||||
\(480\) | −0.962593 | + | 3.05303i | −0.0439361 | + | 0.139351i | ||||
\(481\) | −31.5278 | −1.43754 | ||||||||
\(482\) | 7.28795i | 0.331957i | ||||||||
\(483\) | 3.36680i | 0.153195i | ||||||||
\(484\) | −0.282982 | −0.0128628 | ||||||||
\(485\) | −12.1816 | − | 3.84074i | −0.553138 | − | 0.174399i | ||||
\(486\) | 24.3919 | 1.10644 | ||||||||
\(487\) | − | 28.4833i | − | 1.29070i | −0.763886 | − | 0.645351i | \(-0.776711\pi\) | ||
0.763886 | − | 0.645351i | \(-0.223289\pi\) | |||||||
\(488\) | 29.0252i | 1.31391i | ||||||||
\(489\) | −16.3058 | −0.737373 | ||||||||
\(490\) | −21.3821 | − | 6.74158i | −0.965946 | − | 0.304554i | ||||
\(491\) | −0.746198 | −0.0336754 | −0.0168377 | − | 0.999858i | \(-0.505360\pi\) | ||||
−0.0168377 | + | 0.999858i | \(0.505360\pi\) | |||||||
\(492\) | 1.86414i | 0.0840417i | ||||||||
\(493\) | − | 11.9555i | − | 0.538447i | ||||||
\(494\) | 4.63519 | 0.208547 | ||||||||
\(495\) | 1.47157 | − | 4.66734i | 0.0661421 | − | 0.209781i | ||||
\(496\) | −35.7994 | −1.60744 | ||||||||
\(497\) | 0.916856i | 0.0411266i | ||||||||
\(498\) | − | 12.7545i | − | 0.571541i | ||||||
\(499\) | 10.7995 | 0.483452 | 0.241726 | − | 0.970345i | \(-0.422287\pi\) | ||||
0.241726 | + | 0.970345i | \(0.422287\pi\) | |||||||
\(500\) | 2.51000 | − | 1.92608i | 0.112250 | − | 0.0861367i | ||||
\(501\) | −7.30813 | −0.326503 | ||||||||
\(502\) | 17.2934i | 0.771841i | ||||||||
\(503\) | − | 23.2195i | − | 1.03530i | −0.855591 | − | 0.517652i | \(-0.826806\pi\) | ||
0.855591 | − | 0.517652i | \(-0.173194\pi\) | |||||||
\(504\) | 3.42653 | 0.152630 | ||||||||
\(505\) | −10.1072 | + | 32.0568i | −0.449764 | + | 1.42651i | ||||
\(506\) | −9.35800 | −0.416014 | ||||||||
\(507\) | 3.23298i | 0.143582i | ||||||||
\(508\) | − | 5.32006i | − | 0.236039i | ||||||
\(509\) | −35.1577 | −1.55834 | −0.779169 | − | 0.626814i | \(-0.784359\pi\) | ||||
−0.779169 | + | 0.626814i | \(0.784359\pi\) | |||||||
\(510\) | −11.8516 | − | 3.73670i | −0.524798 | − | 0.165464i | ||||
\(511\) | −1.83808 | −0.0813119 | ||||||||
\(512\) | 16.1464i | 0.713576i | ||||||||
\(513\) | 4.67380i | 0.206353i | ||||||||
\(514\) | 6.26692 | 0.276422 | ||||||||
\(515\) | −34.0595 | − | 10.7386i | −1.50084 | − | 0.473201i | ||||
\(516\) | −0.0209486 | −0.000922211 | ||||||||
\(517\) | − | 2.77574i | − | 0.122077i | ||||||
\(518\) | 9.37114i | 0.411744i | ||||||||
\(519\) | −16.1572 | −0.709221 | ||||||||
\(520\) | 5.35130 | − | 16.9726i | 0.234670 | − | 0.744297i | ||||
\(521\) | −6.74136 | −0.295344 | −0.147672 | − | 0.989036i | \(-0.547178\pi\) | ||||
−0.147672 | + | 0.989036i | \(0.547178\pi\) | |||||||
\(522\) | − | 9.68237i | − | 0.423786i | ||||||
\(523\) | − | 17.7769i | − | 0.777329i | −0.921379 | − | 0.388664i | \(-0.872937\pi\) | ||
0.921379 | − | 0.388664i | \(-0.127063\pi\) | |||||||
\(524\) | −4.59061 | −0.200542 | ||||||||
\(525\) | 2.22651 | + | 1.55897i | 0.0971728 | + | 0.0680390i | ||||
\(526\) | 6.70004 | 0.292135 | ||||||||
\(527\) | − | 32.5856i | − | 1.41945i | ||||||
\(528\) | − | 4.04082i | − | 0.175854i | ||||||
\(529\) | −15.3587 | −0.667768 | ||||||||
\(530\) | −8.14612 | + | 25.8368i | −0.353845 | + | 1.12228i | ||||
\(531\) | −7.02580 | −0.304894 | ||||||||
\(532\) | − | 0.170774i | − | 0.00740401i | ||||||
\(533\) | − | 22.4344i | − | 0.971740i | ||||||
\(534\) | 0.856939 | 0.0370834 | ||||||||
\(535\) | 0.265555 | + | 0.0837270i | 0.0114809 | + | 0.00361983i | ||||
\(536\) | −9.15673 | −0.395510 | ||||||||
\(537\) | 20.3987i | 0.880268i | ||||||||
\(538\) | 7.03001i | 0.303085i | ||||||||
\(539\) | 6.63581 | 0.285825 | ||||||||
\(540\) | −2.82055 | − | 0.889295i | −0.121377 | − | 0.0382691i | ||||
\(541\) | 8.59351 | 0.369464 | 0.184732 | − | 0.982789i | \(-0.440858\pi\) | ||||
0.184732 | + | 0.982789i | \(0.440858\pi\) | |||||||
\(542\) | 29.7851i | 1.27938i | ||||||||
\(543\) | − | 1.91221i | − | 0.0820609i | ||||||
\(544\) | 6.48939 | 0.278230 | ||||||||
\(545\) | 9.65202 | − | 30.6131i | 0.413447 | − | 1.31132i | ||||
\(546\) | −2.51972 | −0.107834 | ||||||||
\(547\) | − | 8.81086i | − | 0.376725i | −0.982100 | − | 0.188363i | \(-0.939682\pi\) | ||
0.982100 | − | 0.188363i | \(-0.0603180\pi\) | |||||||
\(548\) | − | 6.01510i | − | 0.256953i | ||||||
\(549\) | −24.4857 | −1.04502 | ||||||||
\(550\) | −4.33315 | + | 6.18857i | −0.184766 | + | 0.263881i | ||||
\(551\) | 2.92797 | 0.124736 | ||||||||
\(552\) | − | 14.4737i | − | 0.616041i | ||||||
\(553\) | 2.15635i | 0.0916972i | ||||||||
\(554\) | −33.1541 | −1.40858 | ||||||||
\(555\) | −6.22465 | + | 19.7426i | −0.264222 | + | 0.838026i | ||||
\(556\) | 6.19847 | 0.262874 | ||||||||
\(557\) | − | 27.6651i | − | 1.17221i | −0.810235 | − | 0.586105i | \(-0.800661\pi\) | ||
0.810235 | − | 0.586105i | \(-0.199339\pi\) | |||||||
\(558\) | − | 26.3902i | − | 1.11718i | ||||||
\(559\) | 0.252111 | 0.0106631 | ||||||||
\(560\) | −5.77322 | − | 1.82024i | −0.243963 | − | 0.0769192i | ||||
\(561\) | 3.67807 | 0.155288 | ||||||||
\(562\) | 7.05707i | 0.297684i | ||||||||
\(563\) | 9.49474i | 0.400156i | 0.979780 | + | 0.200078i | \(0.0641195\pi\) | ||||
−0.979780 | + | 0.200078i | \(0.935880\pi\) | |||||||
\(564\) | −0.707553 | −0.0297933 | ||||||||
\(565\) | 24.7174 | + | 7.79318i | 1.03987 | + | 0.327861i | ||||
\(566\) | 15.4186 | 0.648093 | ||||||||
\(567\) | 1.42160i | 0.0597017i | ||||||||
\(568\) | − | 3.94151i | − | 0.165382i | ||||||
\(569\) | −0.862737 | −0.0361678 | −0.0180839 | − | 0.999836i | \(-0.505757\pi\) | ||||
−0.0180839 | + | 0.999836i | \(0.505757\pi\) | |||||||
\(570\) | 0.915143 | − | 2.90254i | 0.0383311 | − | 0.121574i | ||||
\(571\) | −31.5625 | −1.32085 | −0.660424 | − | 0.750892i | \(-0.729624\pi\) | ||||
−0.660424 | + | 0.750892i | \(0.729624\pi\) | |||||||
\(572\) | − | 0.868110i | − | 0.0362975i | ||||||
\(573\) | − | 4.88114i | − | 0.203913i | ||||||
\(574\) | −6.66827 | −0.278328 | ||||||||
\(575\) | −17.7617 | + | 25.3671i | −0.740713 | + | 1.05788i | ||||
\(576\) | −14.3799 | −0.599164 | ||||||||
\(577\) | − | 19.9673i | − | 0.831250i | −0.909536 | − | 0.415625i | \(-0.863563\pi\) | ||
0.909536 | − | 0.415625i | \(-0.136437\pi\) | |||||||
\(578\) | − | 0.494982i | − | 0.0205886i | ||||||
\(579\) | −2.60851 | −0.108406 | ||||||||
\(580\) | −0.557112 | + | 1.76698i | −0.0231328 | + | 0.0733698i | ||||
\(581\) | 5.65528 | 0.234621 | ||||||||
\(582\) | − | 7.77448i | − | 0.322262i | ||||||
\(583\) | − | 8.01831i | − | 0.332084i | ||||||
\(584\) | 7.90181 | 0.326979 | ||||||||
\(585\) | 14.3181 | + | 4.51436i | 0.591981 | + | 0.186646i | ||||
\(586\) | 28.7848 | 1.18909 | ||||||||
\(587\) | 33.3785i | 1.37768i | 0.724913 | + | 0.688840i | \(0.241880\pi\) | ||||
−0.724913 | + | 0.688840i | \(0.758120\pi\) | |||||||
\(588\) | − | 1.69151i | − | 0.0697566i | ||||||
\(589\) | 7.98044 | 0.328828 | ||||||||
\(590\) | 10.3440 | + | 3.26137i | 0.425856 | + | 0.134268i | ||||
\(591\) | −2.76163 | −0.113598 | ||||||||
\(592\) | − | 46.1026i | − | 1.89480i | ||||||
\(593\) | − | 30.5439i | − | 1.25429i | −0.778904 | − | 0.627143i | \(-0.784224\pi\) | ||
0.778904 | − | 0.627143i | \(-0.215776\pi\) | |||||||
\(594\) | 7.06190 | 0.289753 | ||||||||
\(595\) | 1.65684 | − | 5.25495i | 0.0679237 | − | 0.215432i | ||||
\(596\) | 3.11706 | 0.127680 | ||||||||
\(597\) | 21.2716i | 0.870587i | ||||||||
\(598\) | − | 28.7078i | − | 1.17395i | ||||||
\(599\) | 0.919784 | 0.0375814 | 0.0187907 | − | 0.999823i | \(-0.494018\pi\) | ||||
0.0187907 | + | 0.999823i | \(0.494018\pi\) | |||||||
\(600\) | −9.57164 | − | 6.70192i | −0.390761 | − | 0.273605i | ||||
\(601\) | −21.5390 | −0.878592 | −0.439296 | − | 0.898342i | \(-0.644772\pi\) | ||||
−0.439296 | + | 0.898342i | \(0.644772\pi\) | |||||||
\(602\) | − | 0.0749360i | − | 0.00305416i | ||||||
\(603\) | − | 7.72463i | − | 0.314571i | ||||||
\(604\) | −4.46130 | −0.181528 | ||||||||
\(605\) | 0.672383 | − | 2.13258i | 0.0273363 | − | 0.0867017i | ||||
\(606\) | −20.4591 | −0.831094 | ||||||||
\(607\) | − | 21.9638i | − | 0.891485i | −0.895161 | − | 0.445742i | \(-0.852940\pi\) | ||
0.895161 | − | 0.445742i | \(-0.147060\pi\) | |||||||
\(608\) | 1.58930i | 0.0644544i | ||||||||
\(609\) | −1.59167 | −0.0644976 | ||||||||
\(610\) | 36.0500 | + | 11.3662i | 1.45962 | + | 0.460206i | ||||
\(611\) | 8.51521 | 0.344488 | ||||||||
\(612\) | 2.52884i | 0.102222i | ||||||||
\(613\) | − | 34.6490i | − | 1.39946i | −0.714408 | − | 0.699730i | \(-0.753304\pi\) | ||
0.714408 | − | 0.699730i | \(-0.246696\pi\) | |||||||
\(614\) | 1.91132 | 0.0771347 | ||||||||
\(615\) | −14.0483 | − | 4.42930i | −0.566483 | − | 0.178607i | ||||
\(616\) | 1.56563 | 0.0630812 | ||||||||
\(617\) | − | 10.0214i | − | 0.403448i | −0.979442 | − | 0.201724i | \(-0.935346\pi\) | ||
0.979442 | − | 0.201724i | \(-0.0646544\pi\) | |||||||
\(618\) | − | 21.7373i | − | 0.874402i | ||||||
\(619\) | 41.5032 | 1.66815 | 0.834077 | − | 0.551648i | \(-0.186001\pi\) | ||||
0.834077 | + | 0.551648i | \(0.186001\pi\) | |||||||
\(620\) | −1.51846 | + | 4.81605i | −0.0609827 | + | 0.193417i | ||||
\(621\) | 28.9469 | 1.16160 | ||||||||
\(622\) | − | 51.8143i | − | 2.07756i | ||||||
\(623\) | 0.379963i | 0.0152229i | ||||||||
\(624\) | 12.3961 | 0.496242 | ||||||||
\(625\) | 8.55119 | + | 23.4921i | 0.342048 | + | 0.939683i | ||||
\(626\) | −1.14138 | −0.0456186 | ||||||||
\(627\) | 0.900785i | 0.0359739i | ||||||||
\(628\) | − | 6.75818i | − | 0.269681i | ||||||
\(629\) | 41.9639 | 1.67321 | ||||||||
\(630\) | 1.34182 | − | 4.25583i | 0.0534596 | − | 0.169556i | ||||
\(631\) | −38.1373 | −1.51822 | −0.759112 | − | 0.650960i | \(-0.774367\pi\) | ||||
−0.759112 | + | 0.650960i | \(0.774367\pi\) | |||||||
\(632\) | − | 9.27002i | − | 0.368741i | ||||||
\(633\) | − | 10.4072i | − | 0.413650i | ||||||
\(634\) | −29.3500 | −1.16564 | ||||||||
\(635\) | 40.0925 | + | 12.6408i | 1.59102 | + | 0.501635i | ||||
\(636\) | −2.04391 | −0.0810465 | ||||||||
\(637\) | 20.3568i | 0.806567i | ||||||||
\(638\) | − | 4.42403i | − | 0.175149i | ||||||
\(639\) | 3.32507 | 0.131538 | ||||||||
\(640\) | 27.9500 | + | 8.81238i | 1.10482 | + | 0.348340i | ||||
\(641\) | 35.1370 | 1.38783 | 0.693914 | − | 0.720058i | \(-0.255885\pi\) | ||||
0.693914 | + | 0.720058i | \(0.255885\pi\) | |||||||
\(642\) | 0.169481i | 0.00668888i | ||||||||
\(643\) | 32.6958i | 1.28940i | 0.764437 | + | 0.644698i | \(0.223017\pi\) | ||||
−0.764437 | + | 0.644698i | \(0.776983\pi\) | |||||||
\(644\) | −1.05768 | −0.0416785 | ||||||||
\(645\) | 0.0497752 | − | 0.157871i | 0.00195990 | − | 0.00621616i | ||||
\(646\) | −6.16951 | −0.242736 | ||||||||
\(647\) | − | 6.81340i | − | 0.267863i | −0.990991 | − | 0.133931i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133931i | \(-0.0427601\pi\) | |||||||
\(648\) | − | 6.11139i | − | 0.240078i | ||||||
\(649\) | −3.21020 | −0.126011 | ||||||||
\(650\) | −18.9848 | − | 13.2929i | −0.744646 | − | 0.521390i | ||||
\(651\) | −4.33823 | −0.170029 | ||||||||
\(652\) | − | 5.12247i | − | 0.200611i | ||||||
\(653\) | 19.1447i | 0.749190i | 0.927188 | + | 0.374595i | \(0.122218\pi\) | ||||
−0.927188 | + | 0.374595i | \(0.877782\pi\) | |||||||
\(654\) | 19.5377 | 0.763986 | ||||||||
\(655\) | 10.9076 | − | 34.5953i | 0.426195 | − | 1.35175i | ||||
\(656\) | 32.8054 | 1.28084 | ||||||||
\(657\) | 6.66598i | 0.260065i | ||||||||
\(658\) | − | 2.53101i | − | 0.0986692i | ||||||
\(659\) | 10.4111 | 0.405559 | 0.202779 | − | 0.979224i | \(-0.435003\pi\) | ||||
0.202779 | + | 0.979224i | \(0.435003\pi\) | |||||||
\(660\) | −0.543607 | − | 0.171394i | −0.0211599 | − | 0.00667152i | ||||
\(661\) | −18.8172 | −0.731903 | −0.365951 | − | 0.930634i | \(-0.619256\pi\) | ||||
−0.365951 | + | 0.930634i | \(0.619256\pi\) | |||||||
\(662\) | − | 39.7733i | − | 1.54583i | ||||||
\(663\) | 11.2833i | 0.438208i | ||||||||
\(664\) | −24.3117 | −0.943479 | ||||||||
\(665\) | 1.28697 | + | 0.405771i | 0.0499067 | + | 0.0157351i | ||||
\(666\) | 33.9854 | 1.31691 | ||||||||
\(667\) | − | 18.1342i | − | 0.702160i | ||||||
\(668\) | − | 2.29585i | − | 0.0888292i | ||||||
\(669\) | 8.64723 | 0.334321 | ||||||||
\(670\) | −3.58577 | + | 11.3729i | −0.138530 | + | 0.439373i | ||||
\(671\) | −11.1879 | −0.431905 | ||||||||
\(672\) | − | 0.863953i | − | 0.0333277i | ||||||
\(673\) | 48.1251i | 1.85508i | 0.373718 | + | 0.927542i | \(0.378083\pi\) | ||||
−0.373718 | + | 0.927542i | \(0.621917\pi\) | |||||||
\(674\) | −42.9235 | −1.65335 | ||||||||
\(675\) | 13.4036 | − | 19.1430i | 0.515906 | − | 0.736813i | ||||
\(676\) | −1.01564 | −0.0390632 | ||||||||
\(677\) | 35.9017i | 1.37981i | 0.723898 | + | 0.689907i | \(0.242349\pi\) | ||||
−0.723898 | + | 0.689907i | \(0.757651\pi\) | |||||||
\(678\) | 15.7750i | 0.605837i | ||||||||
\(679\) | 3.44717 | 0.132290 | ||||||||
\(680\) | −7.12266 | + | 22.5908i | −0.273141 | + | 0.866316i | ||||
\(681\) | −4.76771 | −0.182699 | ||||||||
\(682\) | − | 12.0581i | − | 0.461728i | ||||||
\(683\) | − | 10.6585i | − | 0.407837i | −0.978988 | − | 0.203918i | \(-0.934632\pi\) | ||
0.978988 | − | 0.203918i | \(-0.0653677\pi\) | |||||||
\(684\) | −0.619330 | −0.0236807 | ||||||||
\(685\) | 45.3304 | + | 14.2923i | 1.73199 | + | 0.546080i | ||||
\(686\) | 12.4336 | 0.474716 | ||||||||
\(687\) | 1.30758i | 0.0498872i | ||||||||
\(688\) | 0.368658i | 0.0140549i | ||||||||
\(689\) | 24.5980 | 0.937108 | ||||||||
\(690\) | −17.9767 | − | 5.66788i | −0.684361 | − | 0.215773i | ||||
\(691\) | −4.88607 | −0.185875 | −0.0929375 | − | 0.995672i | \(-0.529626\pi\) | ||||
−0.0929375 | + | 0.995672i | \(0.529626\pi\) | |||||||
\(692\) | − | 5.07578i | − | 0.192952i | ||||||
\(693\) | 1.32077i | 0.0501720i | ||||||||
\(694\) | −23.3182 | −0.885147 | ||||||||
\(695\) | −14.7280 | + | 46.7123i | −0.558663 | + | 1.77190i | ||||
\(696\) | 6.84249 | 0.259364 | ||||||||
\(697\) | 29.8605i | 1.13105i | ||||||||
\(698\) | 14.4355i | 0.546391i | ||||||||
\(699\) | −22.5621 | −0.853378 | ||||||||
\(700\) | −0.489751 | + | 0.699458i | −0.0185108 | + | 0.0264370i | ||||
\(701\) | 22.9415 | 0.866490 | 0.433245 | − | 0.901276i | \(-0.357368\pi\) | ||||
0.433245 | + | 0.901276i | \(0.357368\pi\) | |||||||
\(702\) | 21.6640i | 0.817653i | ||||||||
\(703\) | 10.2773i | 0.387614i | ||||||||
\(704\) | −6.57042 | −0.247632 | ||||||||
\(705\) | 1.68119 | − | 5.33219i | 0.0633173 | − | 0.200822i | ||||
\(706\) | 9.17990 | 0.345490 | ||||||||
\(707\) | − | 9.07148i | − | 0.341168i | ||||||
\(708\) | 0.818299i | 0.0307536i | ||||||||
\(709\) | 35.0072 | 1.31472 | 0.657361 | − | 0.753576i | \(-0.271673\pi\) | ||||
0.657361 | + | 0.753576i | \(0.271673\pi\) | |||||||
\(710\) | −4.89546 | − | 1.54349i | −0.183723 | − | 0.0579263i | ||||
\(711\) | 7.82020 | 0.293281 | ||||||||
\(712\) | − | 1.63344i | − | 0.0612158i | ||||||
\(713\) | − | 49.4264i | − | 1.85103i | ||||||
\(714\) | 3.35379 | 0.125512 | ||||||||
\(715\) | 6.54217 | + | 2.06269i | 0.244663 | + | 0.0771401i | ||||
\(716\) | −6.40825 | −0.239487 | ||||||||
\(717\) | − | 1.38631i | − | 0.0517728i | ||||||
\(718\) | 30.1641i | 1.12571i | ||||||||
\(719\) | −48.2732 | −1.80029 | −0.900144 | − | 0.435592i | \(-0.856539\pi\) | ||||
−0.900144 | + | 0.435592i | \(0.856539\pi\) | |||||||
\(720\) | −6.60128 | + | 20.9371i | −0.246015 | + | 0.780281i | ||||
\(721\) | 9.63822 | 0.358946 | ||||||||
\(722\) | − | 1.51095i | − | 0.0562319i | ||||||
\(723\) | − | 4.34486i | − | 0.161587i | ||||||
\(724\) | 0.600722 | 0.0223257 | ||||||||
\(725\) | −11.9924 | − | 8.39690i | −0.445386 | − | 0.311853i | ||||
\(726\) | 1.36104 | 0.0505131 | ||||||||
\(727\) | − | 14.0424i | − | 0.520803i | −0.965500 | − | 0.260402i | \(-0.916145\pi\) | ||
0.965500 | − | 0.260402i | \(-0.0838550\pi\) | |||||||
\(728\) | 4.80293i | 0.178009i | ||||||||
\(729\) | −7.47469 | −0.276840 | ||||||||
\(730\) | 3.09434 | − | 9.81426i | 0.114527 | − | 0.363242i | ||||
\(731\) | −0.335563 | −0.0124112 | ||||||||
\(732\) | 2.85186i | 0.105408i | ||||||||
\(733\) | − | 41.9169i | − | 1.54824i | −0.633040 | − | 0.774119i | \(-0.718193\pi\) | ||
0.633040 | − | 0.774119i | \(-0.281807\pi\) | |||||||
\(734\) | −0.292286 | −0.0107885 | ||||||||
\(735\) | 12.7474 | + | 4.01913i | 0.470194 | + | 0.148248i | ||||
\(736\) | 9.84320 | 0.362825 | ||||||||
\(737\) | − | 3.52951i | − | 0.130011i | ||||||
\(738\) | 24.1831i | 0.890193i | ||||||||
\(739\) | 43.9013 | 1.61493 | 0.807467 | − | 0.589912i | \(-0.200838\pi\) | ||||
0.807467 | + | 0.589912i | \(0.200838\pi\) | |||||||
\(740\) | −6.20214 | − | 1.95548i | −0.227995 | − | 0.0718847i | ||||
\(741\) | −2.76336 | −0.101515 | ||||||||
\(742\) | − | 7.31136i | − | 0.268409i | ||||||
\(743\) | 16.7953i | 0.616161i | 0.951360 | + | 0.308080i | \(0.0996866\pi\) | ||||
−0.951360 | + | 0.308080i | \(0.900313\pi\) | |||||||
\(744\) | 18.6498 | 0.683735 | ||||||||
\(745\) | −7.40633 | + | 23.4905i | −0.271347 | + | 0.860625i | ||||
\(746\) | 51.2090 | 1.87489 | ||||||||
\(747\) | − | 20.5094i | − | 0.750401i | ||||||
\(748\) | 1.15547i | 0.0422481i | ||||||||
\(749\) | −0.0751472 | −0.00274582 | ||||||||
\(750\) | −12.0722 | + | 9.26375i | −0.440815 | + | 0.338264i | ||||
\(751\) | −31.0266 | −1.13218 | −0.566089 | − | 0.824344i | \(-0.691544\pi\) | ||||
−0.566089 | + | 0.824344i | \(0.691544\pi\) | |||||||
\(752\) | 12.4517i | 0.454065i | ||||||||
\(753\) | − | 10.3098i | − | 0.375709i | ||||||
\(754\) | 13.5717 | 0.494252 | ||||||||
\(755\) | 10.6003 | − | 33.6208i | 0.385785 | − | 1.22359i | ||||
\(756\) | 0.798166 | 0.0290290 | ||||||||
\(757\) | − | 37.0243i | − | 1.34567i | −0.739793 | − | 0.672835i | \(-0.765076\pi\) | ||
0.739793 | − | 0.672835i | \(-0.234924\pi\) | |||||||
\(758\) | − | 14.6675i | − | 0.532746i | ||||||
\(759\) | 5.57896 | 0.202503 | ||||||||
\(760\) | −5.53263 | − | 1.74439i | −0.200690 | − | 0.0632756i | ||||
\(761\) | −5.37641 | −0.194895 | −0.0974473 | − | 0.995241i | \(-0.531068\pi\) | ||||
−0.0974473 | + | 0.995241i | \(0.531068\pi\) | |||||||
\(762\) | 25.5876i | 0.926942i | ||||||||
\(763\) | 8.66295i | 0.313620i | ||||||||
\(764\) | 1.53341 | 0.0554769 | ||||||||
\(765\) | −19.0576 | − | 6.00869i | −0.689029 | − | 0.217244i | ||||
\(766\) | −18.5339 | −0.669658 | ||||||||
\(767\) | − | 9.84801i | − | 0.355591i | ||||||
\(768\) | 6.00104i | 0.216544i | ||||||||
\(769\) | 45.0438 | 1.62432 | 0.812161 | − | 0.583433i | \(-0.198291\pi\) | ||||
0.812161 | + | 0.583433i | \(0.198291\pi\) | |||||||
\(770\) | 0.613101 | − | 1.94456i | 0.0220946 | − | 0.0700770i | ||||
\(771\) | −3.73615 | −0.134554 | ||||||||
\(772\) | − | 0.819466i | − | 0.0294932i | ||||||
\(773\) | 8.86055i | 0.318692i | 0.987223 | + | 0.159346i | \(0.0509385\pi\) | ||||
−0.987223 | + | 0.159346i | \(0.949061\pi\) | |||||||
\(774\) | −0.271763 | −0.00976831 | ||||||||
\(775\) | −32.6863 | − | 22.8865i | −1.17413 | − | 0.822107i | ||||
\(776\) | −14.8192 | −0.531978 | ||||||||
\(777\) | − | 5.58679i | − | 0.200425i | ||||||
\(778\) | 33.3937i | 1.19722i | ||||||||
\(779\) | −7.31303 | −0.262017 | ||||||||
\(780\) | 0.525791 | − | 1.66764i | 0.0188263 | − | 0.0597110i | ||||
\(781\) | 1.51928 | 0.0543640 | ||||||||
\(782\) | 38.2104i | 1.36640i | ||||||||
\(783\) | 13.6848i | 0.489054i | ||||||||
\(784\) | −29.7675 | −1.06312 | ||||||||
\(785\) | 50.9303 | + | 16.0579i | 1.81778 | + | 0.573130i | ||||
\(786\) | 22.0793 | 0.787541 | ||||||||
\(787\) | − | 7.51142i | − | 0.267753i | −0.990998 | − | 0.133877i | \(-0.957257\pi\) | ||
0.990998 | − | 0.133877i | \(-0.0427426\pi\) | |||||||
\(788\) | − | 0.867568i | − | 0.0309058i | ||||||
\(789\) | −3.99436 | −0.142203 | ||||||||
\(790\) | −11.5136 | − | 3.63013i | −0.409636 | − | 0.129154i | ||||
\(791\) | −6.99459 | −0.248699 | ||||||||
\(792\) | − | 5.67793i | − | 0.201756i | ||||||
\(793\) | − | 34.3214i | − | 1.21879i | ||||||
\(794\) | 2.66548 | 0.0945945 | ||||||||
\(795\) | 4.85647 | − | 15.4031i | 0.172241 | − | 0.546293i | ||||
\(796\) | −6.68247 | −0.236854 | ||||||||
\(797\) | 20.2219i | 0.716295i | 0.933665 | + | 0.358148i | \(0.116592\pi\) | ||||
−0.933665 | + | 0.358148i | \(0.883408\pi\) | |||||||
\(798\) | 0.821366i | 0.0290760i | ||||||||
\(799\) | −11.3339 | −0.400963 | ||||||||
\(800\) | 4.55782 | − | 6.50944i | 0.161143 | − | 0.230143i | ||||
\(801\) | 1.37797 | 0.0486883 | ||||||||
\(802\) | 57.0244i | 2.01360i | ||||||||
\(803\) | 3.04579i | 0.107484i | ||||||||
\(804\) | −0.899692 | −0.0317297 | ||||||||
\(805\) | 2.51312 | − | 7.97079i | 0.0885757 | − | 0.280933i | ||||
\(806\) | 36.9909 | 1.30295 | ||||||||
\(807\) | − | 4.19108i | − | 0.147533i | ||||||
\(808\) | 38.9978i | 1.37194i | ||||||||
\(809\) | 27.4034 | 0.963453 | 0.481727 | − | 0.876322i | \(-0.340010\pi\) | ||||
0.481727 | + | 0.876322i | \(0.340010\pi\) | |||||||
\(810\) | −7.59051 | − | 2.39322i | −0.266703 | − | 0.0840890i | ||||
\(811\) | −27.4966 | −0.965535 | −0.482768 | − | 0.875748i | \(-0.660368\pi\) | ||||
−0.482768 | + | 0.875748i | \(0.660368\pi\) | |||||||
\(812\) | − | 0.500023i | − | 0.0175474i | ||||||
\(813\) | − | 17.7570i | − | 0.622764i | ||||||
\(814\) | 15.5285 | 0.544272 | ||||||||
\(815\) | 38.6034 | + | 12.1713i | 1.35222 | + | 0.426342i | ||||
\(816\) | −16.4994 | −0.577595 | ||||||||
\(817\) | − | 0.0821817i | − | 0.00287517i | ||||||
\(818\) | − | 22.9924i | − | 0.803911i | ||||||
\(819\) | −4.05176 | −0.141580 | ||||||||
\(820\) | 1.39147 | − | 4.41328i | 0.0485921 | − | 0.154119i | ||||
\(821\) | 24.3693 | 0.850495 | 0.425247 | − | 0.905077i | \(-0.360187\pi\) | ||||
0.425247 | + | 0.905077i | \(0.360187\pi\) | |||||||
\(822\) | 28.9306i | 1.00907i | ||||||||
\(823\) | − | 38.8757i | − | 1.35512i | −0.735467 | − | 0.677561i | \(-0.763037\pi\) | ||
0.735467 | − | 0.677561i | \(-0.236963\pi\) | |||||||
\(824\) | −41.4342 | −1.44343 | ||||||||
\(825\) | 2.58329 | − | 3.68944i | 0.0899387 | − | 0.128450i | ||||
\(826\) | −2.92717 | −0.101849 | ||||||||
\(827\) | − | 33.7426i | − | 1.17335i | −0.809824 | − | 0.586673i | \(-0.800437\pi\) | ||
0.809824 | − | 0.586673i | \(-0.199563\pi\) | |||||||
\(828\) | 3.83578i | 0.133303i | ||||||||
\(829\) | −0.348062 | −0.0120887 | −0.00604435 | − | 0.999982i | \(-0.501924\pi\) | ||||
−0.00604435 | + | 0.999982i | \(0.501924\pi\) | |||||||
\(830\) | −9.52046 | + | 30.1958i | −0.330460 | + | 1.04811i | ||||
\(831\) | 19.7655 | 0.685656 | ||||||||
\(832\) | − | 20.1562i | − | 0.698791i | ||||||
\(833\) | − | 27.0952i | − | 0.938794i | ||||||
\(834\) | −29.8125 | −1.03232 | ||||||||
\(835\) | 17.3018 | + | 5.45509i | 0.598753 | + | 0.188781i | ||||
\(836\) | −0.282982 | −0.00978713 | ||||||||
\(837\) | 37.2990i | 1.28924i | ||||||||
\(838\) | − | 35.7919i | − | 1.23641i | ||||||
\(839\) | −16.5097 | −0.569979 | −0.284989 | − | 0.958531i | \(-0.591990\pi\) | ||||
−0.284989 | + | 0.958531i | \(0.591990\pi\) | |||||||
\(840\) | 3.00758 | + | 0.948262i | 0.103771 | + | 0.0327181i | ||||
\(841\) | −20.4270 | −0.704378 | ||||||||
\(842\) | 21.4921i | 0.740666i | ||||||||
\(843\) | − | 4.20721i | − | 0.144904i | ||||||
\(844\) | 3.26944 | 0.112539 | ||||||||
\(845\) | 2.41323 | − | 7.65398i | 0.0830176 | − | 0.263305i | ||||
\(846\) | −9.17897 | −0.315579 | ||||||||
\(847\) | 0.603482i | 0.0207359i | ||||||||
\(848\) | 35.9692i | 1.23519i | ||||||||
\(849\) | −9.19212 | −0.315473 | ||||||||
\(850\) | 25.2691 | + | 17.6930i | 0.866722 | + | 0.606866i | ||||
\(851\) | 63.6515 | 2.18195 | ||||||||
\(852\) | − | 0.387273i | − | 0.0132677i | ||||||
\(853\) | 7.46786i | 0.255695i | 0.991794 | + | 0.127847i | \(0.0408068\pi\) | ||||
−0.991794 | + | 0.127847i | \(0.959193\pi\) | |||||||
\(854\) | −10.2015 | −0.349088 | ||||||||
\(855\) | 1.47157 | − | 4.66734i | 0.0503266 | − | 0.159620i | ||||
\(856\) | 0.323054 | 0.0110418 | ||||||||
\(857\) | 11.9526i | 0.408294i | 0.978940 | + | 0.204147i | \(0.0654421\pi\) | ||||
−0.978940 | + | 0.204147i | \(0.934558\pi\) | |||||||
\(858\) | 4.17531i | 0.142543i | ||||||||
\(859\) | −33.9395 | −1.15800 | −0.579001 | − | 0.815327i | \(-0.696557\pi\) | ||||
−0.579001 | + | 0.815327i | \(0.696557\pi\) | |||||||
\(860\) | 0.0495951 | + | 0.0156369i | 0.00169118 | + | 0.000533214i | ||||
\(861\) | 3.97542 | 0.135482 | ||||||||
\(862\) | 36.1832i | 1.23240i | ||||||||
\(863\) | 42.3256i | 1.44078i | 0.693569 | + | 0.720391i | \(0.256037\pi\) | ||||
−0.693569 | + | 0.720391i | \(0.743963\pi\) | |||||||
\(864\) | −7.42805 | −0.252707 | ||||||||
\(865\) | 38.2516 | + | 12.0604i | 1.30059 | + | 0.410065i | ||||
\(866\) | 39.9550 | 1.35773 | ||||||||
\(867\) | 0.295094i | 0.0100219i | ||||||||
\(868\) | − | 1.36286i | − | 0.0462583i | ||||||
\(869\) | 3.57318 | 0.121212 | ||||||||
\(870\) | 2.67951 | − | 8.49855i | 0.0908441 | − | 0.288128i | ||||
\(871\) | 10.8276 | 0.366878 | ||||||||
\(872\) | − | 37.2416i | − | 1.26116i | ||||||
\(873\) | − | 12.5015i | − | 0.423112i | ||||||
\(874\) | −9.35800 | −0.316539 | ||||||||
\(875\) | −4.10751 | − | 5.35277i | −0.138859 | − | 0.180957i | ||||
\(876\) | 0.776391 | 0.0262318 | ||||||||
\(877\) | 24.5946i | 0.830501i | 0.909707 | + | 0.415251i | \(0.136306\pi\) | ||||
−0.909707 | + | 0.415251i | \(0.863694\pi\) | |||||||
\(878\) | 33.8186i | 1.14132i | ||||||||
\(879\) | −17.1606 | −0.578814 | ||||||||
\(880\) | −3.01623 | + | 9.56651i | −0.101677 | + | 0.322487i | ||||
\(881\) | −11.3838 | −0.383529 | −0.191765 | − | 0.981441i | \(-0.561421\pi\) | ||||
−0.191765 | + | 0.981441i | \(0.561421\pi\) | |||||||
\(882\) | − | 21.9436i | − | 0.738881i | ||||||
\(883\) | 32.2722i | 1.08605i | 0.839717 | + | 0.543024i | \(0.182721\pi\) | ||||
−0.839717 | + | 0.543024i | \(0.817279\pi\) | |||||||
\(884\) | −3.54466 | −0.119220 | ||||||||
\(885\) | −6.16679 | − | 1.94433i | −0.207294 | − | 0.0653580i | ||||
\(886\) | 15.6075 | 0.524343 | ||||||||
\(887\) | 29.2459i | 0.981980i | 0.871165 | + | 0.490990i | \(0.163365\pi\) | ||||
−0.871165 | + | 0.490990i | \(0.836635\pi\) | |||||||
\(888\) | 24.0173i | 0.805968i | ||||||||
\(889\) | −11.3455 | −0.380514 | ||||||||
\(890\) | −2.02878 | − | 0.639654i | −0.0680047 | − | 0.0214413i | ||||
\(891\) | 2.35567 | 0.0789178 | ||||||||
\(892\) | 2.71653i | 0.0909562i | ||||||||
\(893\) | − | 2.77574i | − | 0.0928866i | ||||||
\(894\) | −14.9920 | −0.501407 | ||||||||
\(895\) | 15.2264 | − | 48.2932i | 0.508963 | − | 1.61426i | ||||
\(896\) | −7.90935 | −0.264233 | ||||||||
\(897\) | 17.1147i | 0.571443i | ||||||||
\(898\) | − | 21.9015i | − | 0.730863i | ||||||
\(899\) | 23.3665 | 0.779317 | ||||||||
\(900\) | 2.53665 | + | 1.77613i | 0.0845551 | + | 0.0592043i | ||||
\(901\) | −32.7402 | −1.09074 | ||||||||
\(902\) | 11.0497i | 0.367913i | ||||||||
\(903\) | 0.0446746i | 0.00148668i | ||||||||
\(904\) | 30.0693 | 1.00009 | ||||||||
\(905\) | −1.42735 | + | 4.52710i | −0.0474468 | + | 0.150486i | ||||
\(906\) | 21.4573 | 0.712871 | ||||||||
\(907\) | − | 24.0627i | − | 0.798990i | −0.916735 | − | 0.399495i | \(-0.869185\pi\) | ||
0.916735 | − | 0.399495i | \(-0.130815\pi\) | |||||||
\(908\) | − | 1.49778i | − | 0.0497054i | ||||||
\(909\) | −32.8986 | −1.09118 | ||||||||
\(910\) | 5.96537 | + | 1.88083i | 0.197750 | + | 0.0623487i | ||||
\(911\) | −8.77047 | −0.290579 | −0.145289 | − | 0.989389i | \(-0.546411\pi\) | ||||
−0.145289 | + | 0.989389i | \(0.546411\pi\) | |||||||
\(912\) | − | 4.04082i | − | 0.133805i | ||||||
\(913\) | − | 9.37109i | − | 0.310138i | ||||||
\(914\) | −25.4443 | −0.841623 | ||||||||
\(915\) | −21.4919 | − | 6.77621i | −0.710502 | − | 0.224015i | ||||
\(916\) | −0.410776 | −0.0135724 | ||||||||
\(917\) | 9.78985i | 0.323289i | ||||||||
\(918\) | − | 28.8350i | − | 0.951698i | ||||||
\(919\) | 9.19702 | 0.303382 | 0.151691 | − | 0.988428i | \(-0.451528\pi\) | ||||
0.151691 | + | 0.988428i | \(0.451528\pi\) | |||||||
\(920\) | −10.8038 | + | 34.2660i | −0.356189 | + | 1.12972i | ||||
\(921\) | −1.13947 | −0.0375469 | ||||||||
\(922\) | − | 16.2833i | − | 0.536263i | ||||||
\(923\) | 4.66072i | 0.153410i | ||||||||
\(924\) | 0.153831 | 0.00506067 | ||||||||
\(925\) | 29.4733 | − | 42.0936i | 0.969077 | − | 1.38403i | ||||
\(926\) | −19.7270 | −0.648270 | ||||||||
\(927\) | − | 34.9540i | − | 1.14804i | ||||||
\(928\) | 4.65341i | 0.152756i | ||||||||
\(929\) | −40.7749 | −1.33778 | −0.668891 | − | 0.743360i | \(-0.733231\pi\) | ||||
−0.668891 | + | 0.743360i | \(0.733231\pi\) | |||||||
\(930\) | 7.30325 | − | 23.1635i | 0.239483 | − | 0.759563i | ||||
\(931\) | 6.63581 | 0.217480 | ||||||||
\(932\) | − | 7.08790i | − | 0.232172i | ||||||
\(933\) | 30.8901i | 1.01130i | ||||||||
\(934\) | 19.8678 | 0.650093 | ||||||||
\(935\) | −8.70772 | − | 2.74546i | −0.284773 | − | 0.0897863i | ||||
\(936\) | 17.4183 | 0.569335 | ||||||||
\(937\) | − | 18.4291i | − | 0.602052i | −0.953616 | − | 0.301026i | \(-0.902671\pi\) | ||
0.953616 | − | 0.301026i | \(-0.0973291\pi\) | |||||||
\(938\) | − | 3.21832i | − | 0.105082i | ||||||
\(939\) | 0.680454 | 0.0222058 | ||||||||
\(940\) | 1.67511 | + | 0.528146i | 0.0546360 | + | 0.0172262i | ||||
\(941\) | −36.4393 | −1.18789 | −0.593943 | − | 0.804507i | \(-0.702430\pi\) | ||||
−0.593943 | + | 0.804507i | \(0.702430\pi\) | |||||||
\(942\) | 32.5045i | 1.05905i | ||||||||
\(943\) | 45.2928i | 1.47494i | ||||||||
\(944\) | 14.4006 | 0.468699 | ||||||||
\(945\) | −1.89649 | + | 6.01506i | −0.0616929 | + | 0.195670i | ||||
\(946\) | −0.124173 | −0.00403720 | ||||||||
\(947\) | − | 35.2476i | − | 1.14539i | −0.819767 | − | 0.572697i | \(-0.805897\pi\) | ||
0.819767 | − | 0.572697i | \(-0.194103\pi\) | |||||||
\(948\) | − | 0.910824i | − | 0.0295822i | ||||||
\(949\) | −9.34366 | −0.303308 | ||||||||
\(950\) | −4.33315 | + | 6.18857i | −0.140586 | + | 0.200784i | ||||
\(951\) | 17.4976 | 0.567399 | ||||||||
\(952\) | − | 6.39278i | − | 0.207191i | ||||||
\(953\) | − | 21.0701i | − | 0.682527i | −0.939968 | − | 0.341263i | \(-0.889145\pi\) | ||
0.939968 | − | 0.341263i | \(-0.110855\pi\) | |||||||
\(954\) | −26.5154 | −0.858467 | ||||||||
\(955\) | −3.64349 | + | 11.5560i | −0.117900 | + | 0.373942i | ||||
\(956\) | 0.435510 | 0.0140854 | ||||||||
\(957\) | 2.63747i | 0.0852574i | ||||||||
\(958\) | 10.2177i | 0.330120i | ||||||||
\(959\) | −12.8277 | −0.414228 | ||||||||
\(960\) | −12.6218 | − | 3.97952i | −0.407365 | − | 0.128439i | ||||
\(961\) | 32.6875 | 1.05443 | ||||||||
\(962\) | 47.6370i | 1.53588i | ||||||||
\(963\) | 0.272529i | 0.00878212i | ||||||||
\(964\) | 1.36494 | 0.0439617 | ||||||||
\(965\) | 6.17558 | + | 1.94710i | 0.198799 | + | 0.0626794i | ||||
\(966\) | 5.08708 | 0.163674 | ||||||||
\(967\) | 3.18321i | 0.102365i | 0.998689 | + | 0.0511826i | \(0.0162991\pi\) | ||||
−0.998689 | + | 0.0511826i | \(0.983701\pi\) | |||||||
\(968\) | − | 2.59434i | − | 0.0833851i | ||||||
\(969\) | 3.67807 | 0.118157 | ||||||||
\(970\) | −5.80319 | + | 18.4058i | −0.186329 | + | 0.590976i | ||||
\(971\) | −3.50130 | −0.112362 | −0.0561810 | − | 0.998421i | \(-0.517892\pi\) | ||||
−0.0561810 | + | 0.998421i | \(0.517892\pi\) | |||||||
\(972\) | − | 4.56828i | − | 0.146528i | ||||||
\(973\) | − | 13.2187i | − | 0.423773i | ||||||
\(974\) | −43.0370 | −1.37899 | ||||||||
\(975\) | 11.3182 | + | 7.92483i | 0.362472 | + | 0.253798i | ||||
\(976\) | 50.1877 | 1.60647 | ||||||||
\(977\) | − | 19.0989i | − | 0.611027i | −0.952188 | − | 0.305514i | \(-0.901172\pi\) | ||
0.952188 | − | 0.305514i | \(-0.0988282\pi\) | |||||||
\(978\) | 24.6373i | 0.787814i | ||||||||
\(979\) | 0.629618 | 0.0201227 | ||||||||
\(980\) | −1.26261 | + | 4.00459i | −0.0403326 | + | 0.127922i | ||||
\(981\) | 31.4170 | 1.00307 | ||||||||
\(982\) | 1.12747i | 0.0359790i | ||||||||
\(983\) | − | 48.2760i | − | 1.53976i | −0.638186 | − | 0.769882i | \(-0.720315\pi\) | ||
0.638186 | − | 0.769882i | \(-0.279685\pi\) | |||||||
\(984\) | −17.0901 | −0.544813 | ||||||||
\(985\) | 6.53808 | + | 2.06140i | 0.208321 | + | 0.0656816i | ||||
\(986\) | −18.0641 | −0.575280 | ||||||||
\(987\) | 1.50891i | 0.0480293i | ||||||||
\(988\) | − | 0.868110i | − | 0.0276183i | ||||||
\(989\) | −0.508987 | −0.0161848 | ||||||||
\(990\) | −7.05213 | − | 2.22347i | −0.224131 | − | 0.0706666i | ||||
\(991\) | 23.8140 | 0.756477 | 0.378238 | − | 0.925708i | \(-0.376530\pi\) | ||||
0.378238 | + | 0.925708i | \(0.376530\pi\) | |||||||
\(992\) | 12.6833i | 0.402695i | ||||||||
\(993\) | 23.7116i | 0.752465i | ||||||||
\(994\) | 1.38533 | 0.0439399 | ||||||||
\(995\) | 15.8780 | − | 50.3598i | 0.503365 | − | 1.59651i | ||||
\(996\) | −2.38875 | −0.0756903 | ||||||||
\(997\) | − | 1.80923i | − | 0.0572988i | −0.999590 | − | 0.0286494i | \(-0.990879\pi\) | ||
0.999590 | − | 0.0286494i | \(-0.00912063\pi\) | |||||||
\(998\) | − | 16.3175i | − | 0.516522i | ||||||
\(999\) | −48.0338 | −1.51972 |
(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 | 1045.2.b.c.419.5 | ✓ | 20 | |
5.2 | odd | 4 | 5225.2.a.ba.1.16 | 20 | |||
5.3 | odd | 4 | 5225.2.a.ba.1.5 | 20 | |||
5.4 | even | 2 | inner | 1045.2.b.c.419.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.b.c.419.5 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1045.2.b.c.419.16 | yes | 20 | 5.4 | even | 2 | inner | |
5225.2.a.ba.1.5 | 20 | 5.3 | odd | 4 | |||
5225.2.a.ba.1.16 | 20 | 5.2 | odd | 4 |