Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(406,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.406");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.k (of order \(3\), 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: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 406.6 | ||
Root | \(1.50733 + 2.61078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.406 |
Dual form | 855.2.k.j.676.6 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00733 | + | 1.74475i | 0.712293 | + | 1.23373i | 0.963994 | + | 0.265922i | \(0.0856765\pi\) |
−0.251702 | + | 0.967805i | \(0.580990\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.02944 | + | 1.78305i | −0.514722 | + | 0.891525i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.66469 | 0.629193 | 0.314596 | − | 0.949226i | \(-0.398131\pi\) | ||||
0.314596 | + | 0.949226i | \(0.398131\pi\) | |||||||
\(8\) | −0.118641 | −0.0419458 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00733 | − | 1.74475i | 0.318547 | − | 0.551740i | ||||
\(11\) | 0.745446 | 0.224760 | 0.112380 | − | 0.993665i | \(-0.464153\pi\) | ||||
0.112380 | + | 0.993665i | \(0.464153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.269815 | − | 0.467333i | 0.0748332 | − | 0.129615i | −0.826181 | − | 0.563405i | \(-0.809491\pi\) |
0.901014 | + | 0.433791i | \(0.142824\pi\) | |||||||
\(14\) | 1.67690 | + | 2.90447i | 0.448170 | + | 0.776252i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.93938 | + | 3.35910i | 0.484844 | + | 0.839775i | ||||
\(17\) | 0.705067 | + | 1.22121i | 0.171004 | + | 0.296187i | 0.938771 | − | 0.344542i | \(-0.111966\pi\) |
−0.767767 | + | 0.640729i | \(0.778632\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.17330 | + | 1.25841i | 0.957420 | + | 0.288700i | ||||
\(20\) | 2.05889 | 0.460381 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.750913 | + | 1.30062i | 0.160095 | + | 0.277293i | ||||
\(23\) | 0.437471 | − | 0.757722i | 0.0912190 | − | 0.157996i | −0.816805 | − | 0.576913i | \(-0.804257\pi\) |
0.908024 | + | 0.418917i | \(0.137590\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 1.08718 | 0.213213 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.71370 | + | 2.96822i | −0.323859 | + | 0.560941i | ||||
\(29\) | −3.70083 | + | 6.41003i | −0.687228 | + | 1.19031i | 0.285504 | + | 0.958378i | \(0.407839\pi\) |
−0.972731 | + | 0.231935i | \(0.925494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.02934 | 1.26251 | 0.631253 | − | 0.775577i | \(-0.282541\pi\) | ||||
0.631253 | + | 0.775577i | \(0.282541\pi\) | |||||||
\(32\) | −4.02584 | + | 6.97297i | −0.711675 | + | 1.23266i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.42048 | + | 2.46034i | −0.243610 | + | 0.421944i | ||||
\(35\) | −0.832344 | − | 1.44166i | −0.140692 | − | 0.243685i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.84476 | 1.28967 | 0.644836 | − | 0.764321i | \(-0.276926\pi\) | ||||
0.644836 | + | 0.764321i | \(0.276926\pi\) | |||||||
\(38\) | 2.00828 | + | 8.54902i | 0.325787 | + | 1.38683i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0593204 | + | 0.102746i | 0.00937937 | + | 0.0162455i | ||||
\(41\) | −4.36591 | − | 7.56198i | −0.681841 | − | 1.18098i | −0.974418 | − | 0.224742i | \(-0.927846\pi\) |
0.292577 | − | 0.956242i | \(-0.405487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.93324 | − | 5.08052i | −0.447315 | − | 0.774772i | 0.550896 | − | 0.834574i | \(-0.314286\pi\) |
−0.998210 | + | 0.0598025i | \(0.980953\pi\) | |||||||
\(44\) | −0.767395 | + | 1.32917i | −0.115689 | + | 0.200380i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.76272 | 0.259899 | ||||||||
\(47\) | −3.29875 | + | 5.71360i | −0.481172 | + | 0.833414i | −0.999767 | − | 0.0216064i | \(-0.993122\pi\) |
0.518595 | + | 0.855020i | \(0.326455\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.22881 | −0.604116 | ||||||||
\(50\) | −2.01467 | −0.284917 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.555519 | + | 0.962187i | 0.0770366 | + | 0.133431i | ||||
\(53\) | −3.85018 | + | 6.66871i | −0.528863 | + | 0.916018i | 0.470570 | + | 0.882362i | \(0.344048\pi\) |
−0.999434 | + | 0.0336552i | \(0.989285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.372723 | − | 0.645575i | −0.0502580 | − | 0.0870494i | ||||
\(56\) | −0.197500 | −0.0263920 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −14.9119 | −1.95803 | ||||||||
\(59\) | −2.45356 | − | 4.24969i | −0.319426 | − | 0.553263i | 0.660942 | − | 0.750437i | \(-0.270157\pi\) |
−0.980368 | + | 0.197174i | \(0.936824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.60473 | − | 4.51153i | 0.333502 | − | 0.577643i | −0.649694 | − | 0.760196i | \(-0.725103\pi\) |
0.983196 | + | 0.182553i | \(0.0584362\pi\) | |||||||
\(62\) | 7.08089 | + | 12.2645i | 0.899274 | + | 1.55759i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.46397 | −1.05800 | ||||||||
\(65\) | −0.539630 | −0.0669329 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.443531 | + | 0.768219i | −0.0541860 | + | 0.0938528i | −0.891846 | − | 0.452339i | \(-0.850590\pi\) |
0.837660 | + | 0.546192i | \(0.183923\pi\) | |||||||
\(68\) | −2.90331 | −0.352078 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.67690 | − | 2.90447i | 0.200428 | − | 0.347151i | ||||
\(71\) | −1.41061 | − | 2.44324i | −0.167408 | − | 0.289959i | 0.770100 | − | 0.637923i | \(-0.220206\pi\) |
−0.937508 | + | 0.347964i | \(0.886873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.524369 | − | 0.908233i | −0.0613727 | − | 0.106301i | 0.833707 | − | 0.552208i | \(-0.186214\pi\) |
−0.895079 | + | 0.445907i | \(0.852881\pi\) | |||||||
\(74\) | 7.90230 | + | 13.6872i | 0.918624 | + | 1.59110i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.53999 | + | 6.14573i | −0.750188 | + | 0.704963i | ||||
\(77\) | 1.24094 | 0.141418 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.88624 | − | 4.99911i | −0.324727 | − | 0.562444i | 0.656730 | − | 0.754126i | \(-0.271939\pi\) |
−0.981457 | + | 0.191682i | \(0.938606\pi\) | |||||||
\(80\) | 1.93938 | − | 3.35910i | 0.216829 | − | 0.375559i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.79587 | − | 15.2349i | 0.971341 | − | 1.68241i | ||||
\(83\) | 3.61555 | 0.396858 | 0.198429 | − | 0.980115i | \(-0.436416\pi\) | ||||
0.198429 | + | 0.980115i | \(0.436416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.705067 | − | 1.22121i | 0.0764752 | − | 0.132459i | ||||
\(86\) | 5.90950 | − | 10.2356i | 0.637238 | − | 1.10373i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0884403 | −0.00942776 | ||||||||
\(89\) | 0.464416 | − | 0.804392i | 0.0492280 | − | 0.0852654i | −0.840361 | − | 0.542026i | \(-0.817657\pi\) |
0.889589 | + | 0.456761i | \(0.150991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.449158 | − | 0.777964i | 0.0470845 | − | 0.0815528i | ||||
\(92\) | 0.900704 | + | 1.56007i | 0.0939049 | + | 0.162648i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.2918 | −1.37094 | ||||||||
\(95\) | −0.996831 | − | 4.24339i | −0.102273 | − | 0.435362i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.00920110 | − | 0.0159368i | −0.000934230 | − | 0.00161813i | 0.865558 | − | 0.500809i | \(-0.166964\pi\) |
−0.866492 | + | 0.499191i | \(0.833631\pi\) | |||||||
\(98\) | −4.25983 | − | 7.37824i | −0.430308 | − | 0.745315i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.02944 | − | 1.78305i | −0.102944 | − | 0.178305i | ||||
\(101\) | 7.93725 | − | 13.7477i | 0.789786 | − | 1.36795i | −0.136312 | − | 0.990666i | \(-0.543525\pi\) |
0.926098 | − | 0.377284i | \(-0.123142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.55819 | −0.843264 | −0.421632 | − | 0.906767i | \(-0.638543\pi\) | ||||
−0.421632 | + | 0.906767i | \(0.638543\pi\) | |||||||
\(104\) | −0.0320110 | + | 0.0554448i | −0.00313894 | + | 0.00543681i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.5137 | −1.50682 | ||||||||
\(107\) | −11.6508 | −1.12632 | −0.563162 | − | 0.826347i | \(-0.690415\pi\) | ||||
−0.563162 | + | 0.826347i | \(0.690415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.12075 | + | 1.94119i | 0.107348 | + | 0.185932i | 0.914695 | − | 0.404145i | \(-0.132431\pi\) |
−0.807347 | + | 0.590077i | \(0.799097\pi\) | |||||||
\(110\) | 0.750913 | − | 1.30062i | 0.0715968 | − | 0.124009i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.22846 | + | 5.59185i | 0.305061 | + | 0.528380i | ||||
\(113\) | 8.94383 | 0.841364 | 0.420682 | − | 0.907208i | \(-0.361791\pi\) | ||||
0.420682 | + | 0.907208i | \(0.361791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.874942 | −0.0815888 | ||||||||
\(116\) | −7.61960 | − | 13.1975i | −0.707462 | − | 1.22536i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.94311 | − | 8.56172i | 0.455050 | − | 0.788170i | ||||
\(119\) | 1.17372 | + | 2.03294i | 0.107594 | + | 0.186359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4443 | −0.949483 | ||||||||
\(122\) | 10.4954 | 0.950205 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.23631 | + | 12.5337i | −0.649840 | + | 1.12556i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.91270 | − | 17.1693i | 0.879609 | − | 1.52353i | 0.0278395 | − | 0.999612i | \(-0.491137\pi\) |
0.851770 | − | 0.523916i | \(-0.175529\pi\) | |||||||
\(128\) | −0.474357 | − | 0.821611i | −0.0419276 | − | 0.0726208i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.543588 | − | 0.941522i | −0.0476758 | − | 0.0825769i | ||||
\(131\) | −0.917977 | − | 1.58998i | −0.0802040 | − | 0.138917i | 0.823133 | − | 0.567848i | \(-0.192224\pi\) |
−0.903337 | + | 0.428931i | \(0.858891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.94723 | + | 2.09486i | 0.602402 | + | 0.181648i | ||||
\(134\) | −1.78714 | −0.154385 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0836496 | − | 0.144885i | −0.00717290 | − | 0.0124238i | ||||
\(137\) | −1.98094 | + | 3.43109i | −0.169243 | + | 0.293138i | −0.938154 | − | 0.346218i | \(-0.887466\pi\) |
0.768911 | + | 0.639356i | \(0.220799\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.889046 | − | 1.53987i | 0.0754079 | − | 0.130610i | −0.825856 | − | 0.563882i | \(-0.809307\pi\) |
0.901264 | + | 0.433271i | \(0.142641\pi\) | |||||||
\(140\) | 3.42741 | 0.289669 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.84190 | − | 4.92232i | 0.238487 | − | 0.413072i | ||||
\(143\) | 0.201133 | − | 0.348372i | 0.0168196 | − | 0.0291323i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.40167 | 0.614675 | ||||||||
\(146\) | 1.05643 | − | 1.82979i | 0.0874307 | − | 0.151434i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.07575 | + | 13.9876i | −0.663822 | + | 1.14977i | ||||
\(149\) | −9.55320 | − | 16.5466i | −0.782629 | − | 1.35555i | −0.930405 | − | 0.366532i | \(-0.880545\pi\) |
0.147777 | − | 0.989021i | \(-0.452788\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.44644 | 0.199088 | 0.0995442 | − | 0.995033i | \(-0.468262\pi\) | ||||
0.0995442 | + | 0.995033i | \(0.468262\pi\) | |||||||
\(152\) | −0.495123 | − | 0.149299i | −0.0401598 | − | 0.0121097i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.25004 | + | 2.16513i | 0.100731 | + | 0.174471i | ||||
\(155\) | −3.51467 | − | 6.08758i | −0.282305 | − | 0.488967i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.60586 | − | 7.97759i | −0.367588 | − | 0.636681i | 0.621600 | − | 0.783335i | \(-0.286483\pi\) |
−0.989188 | + | 0.146654i | \(0.953150\pi\) | |||||||
\(158\) | 5.81481 | − | 10.0715i | 0.462601 | − | 0.801249i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.05169 | 0.636542 | ||||||||
\(161\) | 0.728253 | − | 1.26137i | 0.0573944 | − | 0.0994100i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.09691 | 0.0859164 | 0.0429582 | − | 0.999077i | \(-0.486322\pi\) | ||||
0.0429582 | + | 0.999077i | \(0.486322\pi\) | |||||||
\(164\) | 17.9779 | 1.40383 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.64207 | + | 6.30824i | 0.282679 | + | 0.489615i | ||||
\(167\) | −6.24438 | + | 10.8156i | −0.483205 | + | 0.836935i | −0.999814 | − | 0.0192861i | \(-0.993861\pi\) |
0.516609 | + | 0.856221i | \(0.327194\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.35440 | + | 11.0061i | 0.488800 | + | 0.846626i | ||||
\(170\) | 2.84095 | 0.217891 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.0784 | 0.920971 | ||||||||
\(173\) | −2.15558 | − | 3.73357i | −0.163886 | − | 0.283858i | 0.772373 | − | 0.635169i | \(-0.219069\pi\) |
−0.936259 | + | 0.351310i | \(0.885736\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.832344 | + | 1.44166i | −0.0629193 | + | 0.108979i | ||||
\(176\) | 1.44570 | + | 2.50403i | 0.108974 | + | 0.188748i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.87129 | 0.140259 | ||||||||
\(179\) | −12.6038 | −0.942052 | −0.471026 | − | 0.882119i | \(-0.656116\pi\) | ||||
−0.471026 | + | 0.882119i | \(0.656116\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.84534 | + | 3.19623i | −0.137163 | + | 0.237574i | −0.926422 | − | 0.376487i | \(-0.877132\pi\) |
0.789259 | + | 0.614061i | \(0.210465\pi\) | |||||||
\(182\) | 1.80981 | 0.134152 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.0519019 | + | 0.0898967i | −0.00382626 | + | 0.00662727i | ||||
\(185\) | −3.92238 | − | 6.79377i | −0.288379 | − | 0.499488i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.525589 | + | 0.910348i | 0.0384349 | + | 0.0665712i | ||||
\(188\) | −6.79175 | − | 11.7637i | −0.495339 | − | 0.857953i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.39952 | − | 6.01373i | 0.464270 | − | 0.436282i | ||||
\(191\) | −6.23634 | −0.451246 | −0.225623 | − | 0.974215i | \(-0.572442\pi\) | ||||
−0.225623 | + | 0.974215i | \(0.572442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.46275 | + | 16.3900i | 0.681143 | + | 1.17978i | 0.974632 | + | 0.223813i | \(0.0718503\pi\) |
−0.293489 | + | 0.955963i | \(0.594816\pi\) | |||||||
\(194\) | 0.0185372 | − | 0.0321073i | 0.00133089 | − | 0.00230517i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.35333 | − | 7.54019i | 0.310952 | − | 0.538585i | ||||
\(197\) | 6.85139 | 0.488141 | 0.244071 | − | 0.969757i | \(-0.421517\pi\) | ||||
0.244071 | + | 0.969757i | \(0.421517\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.99420 | + | 17.3105i | −0.708470 | + | 1.22711i | 0.256954 | + | 0.966424i | \(0.417281\pi\) |
−0.965424 | + | 0.260683i | \(0.916052\pi\) | |||||||
\(200\) | 0.0593204 | − | 0.102746i | 0.00419458 | − | 0.00726523i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 31.9819 | 2.25024 | ||||||||
\(203\) | −6.16073 | + | 10.6707i | −0.432399 | + | 0.748936i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.36591 | + | 7.56198i | −0.304929 | + | 0.528152i | ||||
\(206\) | −8.62096 | − | 14.9319i | −0.600651 | − | 1.04036i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.09309 | 0.145130 | ||||||||
\(209\) | 3.11097 | + | 0.938079i | 0.215190 | + | 0.0648883i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.41451 | − | 12.8423i | −0.510436 | − | 0.884101i | −0.999927 | − | 0.0120925i | \(-0.996151\pi\) |
0.489491 | − | 0.872008i | \(-0.337183\pi\) | |||||||
\(212\) | −7.92709 | − | 13.7301i | −0.544435 | − | 0.942989i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.7362 | − | 20.3278i | −0.802272 | − | 1.38958i | ||||
\(215\) | −2.93324 | + | 5.08052i | −0.200045 | + | 0.346488i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.7017 | 0.794360 | ||||||||
\(218\) | −2.25793 | + | 3.91085i | −0.152926 | + | 0.264876i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.53479 | 0.103476 | ||||||||
\(221\) | 0.760951 | 0.0511871 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.44388 | + | 16.3573i | 0.632409 | + | 1.09536i | 0.987058 | + | 0.160365i | \(0.0512670\pi\) |
−0.354649 | + | 0.934999i | \(0.615400\pi\) | |||||||
\(224\) | −6.70177 | + | 11.6078i | −0.447781 | + | 0.775579i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00942 | + | 15.6048i | 0.599298 | + | 1.03801i | ||||
\(227\) | 15.7322 | 1.04418 | 0.522090 | − | 0.852890i | \(-0.325152\pi\) | ||||
0.522090 | + | 0.852890i | \(0.325152\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.0417 | −1.25831 | −0.629157 | − | 0.777278i | \(-0.716600\pi\) | ||||
−0.629157 | + | 0.777278i | \(0.716600\pi\) | |||||||
\(230\) | −0.881359 | − | 1.52656i | −0.0581151 | − | 0.100658i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.439070 | − | 0.760491i | 0.0288263 | − | 0.0499287i | ||||
\(233\) | −0.594442 | − | 1.02960i | −0.0389432 | − | 0.0674515i | 0.845897 | − | 0.533346i | \(-0.179066\pi\) |
−0.884840 | + | 0.465895i | \(0.845732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.59749 | 0.430373 | ||||||||
\(236\) | 10.1032 | 0.657663 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.36465 | + | 4.09569i | −0.153277 | + | 0.265484i | ||||
\(239\) | −25.9446 | −1.67822 | −0.839108 | − | 0.543965i | \(-0.816922\pi\) | ||||
−0.839108 | + | 0.543965i | \(0.816922\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.52815 | − | 7.84299i | 0.291684 | − | 0.505211i | −0.682524 | − | 0.730863i | \(-0.739118\pi\) |
0.974208 | + | 0.225652i | \(0.0724512\pi\) | |||||||
\(242\) | −10.5209 | − | 18.2228i | −0.676310 | − | 1.17140i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.36286 | + | 9.28874i | 0.343322 | + | 0.594651i | ||||
\(245\) | 2.11441 | + | 3.66226i | 0.135085 | + | 0.233973i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.71412 | − | 1.61078i | 0.109067 | − | 0.102492i | ||||
\(248\) | −0.833966 | −0.0529569 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00733 | + | 1.74475i | 0.0637094 | + | 0.110348i | ||||
\(251\) | 1.46528 | − | 2.53794i | 0.0924876 | − | 0.160193i | −0.816070 | − | 0.577954i | \(-0.803851\pi\) |
0.908557 | + | 0.417760i | \(0.137185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.326111 | − | 0.564841i | 0.0205024 | − | 0.0355113i | ||||
\(254\) | 39.9416 | 2.50616 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.50830 | + | 13.0047i | −0.469268 | + | 0.812797i | ||||
\(257\) | 5.42535 | − | 9.39698i | 0.338424 | − | 0.586168i | −0.645712 | − | 0.763581i | \(-0.723439\pi\) |
0.984136 | + | 0.177413i | \(0.0567728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.0591 | 0.811452 | ||||||||
\(260\) | 0.555519 | − | 0.962187i | 0.0344518 | − | 0.0596723i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.84942 | − | 3.20329i | 0.114257 | − | 0.197900i | ||||
\(263\) | −8.42898 | − | 14.5994i | −0.519753 | − | 0.900239i | −0.999736 | − | 0.0229610i | \(-0.992691\pi\) |
0.479983 | − | 0.877278i | \(-0.340643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.70036 | 0.473029 | ||||||||
\(266\) | 3.34317 | + | 14.2314i | 0.204983 | + | 0.872586i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.913181 | − | 1.58168i | −0.0557814 | − | 0.0966163i | ||||
\(269\) | −14.7731 | − | 25.5878i | −0.900733 | − | 1.56012i | −0.826544 | − | 0.562872i | \(-0.809696\pi\) |
−0.0741891 | − | 0.997244i | \(-0.523637\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6224 | − | 18.3985i | −0.645262 | − | 1.11763i | −0.984241 | − | 0.176833i | \(-0.943415\pi\) |
0.338979 | − | 0.940794i | \(-0.389919\pi\) | |||||||
\(272\) | −2.73478 | + | 4.73678i | −0.165821 | + | 0.287210i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.98188 | −0.482203 | ||||||||
\(275\) | −0.372723 | + | 0.645575i | −0.0224760 | + | 0.0389297i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.3656 | −1.70432 | −0.852161 | − | 0.523279i | \(-0.824708\pi\) | ||||
−0.852161 | + | 0.523279i | \(0.824708\pi\) | |||||||
\(278\) | 3.58226 | 0.214850 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0987499 | + | 0.171040i | 0.00590143 | + | 0.0102216i | ||||
\(281\) | −8.80909 | + | 15.2578i | −0.525506 | + | 0.910204i | 0.474052 | + | 0.880497i | \(0.342791\pi\) |
−0.999559 | + | 0.0297069i | \(0.990543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.54552 | + | 14.8013i | 0.507978 | + | 0.879844i | 0.999957 | + | 0.00923712i | \(0.00294031\pi\) |
−0.491979 | + | 0.870607i | \(0.663726\pi\) | |||||||
\(284\) | 5.80856 | 0.344675 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.810431 | 0.0479218 | ||||||||
\(287\) | −7.26788 | − | 12.5883i | −0.429010 | − | 0.743066i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.50576 | − | 13.0004i | 0.441515 | − | 0.764727i | ||||
\(290\) | 7.45595 | + | 12.9141i | 0.437829 | + | 0.758341i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.15923 | 0.126360 | ||||||||
\(293\) | 22.2555 | 1.30018 | 0.650089 | − | 0.759858i | \(-0.274732\pi\) | ||||
0.650089 | + | 0.759858i | \(0.274732\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.45356 | + | 4.24969i | −0.142852 | + | 0.247427i | ||||
\(296\) | −0.930708 | −0.0540963 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.2465 | − | 33.3360i | 1.11492 | − | 1.93110i | ||||
\(299\) | −0.236073 | − | 0.408890i | −0.0136524 | − | 0.0236467i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.88293 | − | 8.45747i | −0.281447 | − | 0.487481i | ||||
\(302\) | 2.46438 | + | 4.26843i | 0.141809 | + | 0.245621i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.86646 | + | 16.4591i | 0.221757 | + | 0.943992i | ||||
\(305\) | −5.20947 | −0.298293 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.2964 | + | 23.0300i | 0.758863 | + | 1.31439i | 0.943431 | + | 0.331570i | \(0.107578\pi\) |
−0.184568 | + | 0.982820i | \(0.559088\pi\) | |||||||
\(308\) | −1.27747 | + | 2.21265i | −0.0727908 | + | 0.126077i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.08089 | − | 12.2645i | 0.402168 | − | 0.696575i | ||||
\(311\) | 11.1894 | 0.634493 | 0.317247 | − | 0.948343i | \(-0.397242\pi\) | ||||
0.317247 | + | 0.948343i | \(0.397242\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2321 | + | 17.7225i | −0.578351 | + | 1.00173i | 0.417317 | + | 0.908761i | \(0.362970\pi\) |
−0.995669 | + | 0.0929730i | \(0.970363\pi\) | |||||||
\(314\) | 9.27928 | − | 16.0722i | 0.523660 | − | 0.907006i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.8849 | 0.668577 | ||||||||
\(317\) | 7.76650 | − | 13.4520i | 0.436210 | − | 0.755538i | −0.561183 | − | 0.827692i | \(-0.689654\pi\) |
0.997394 | + | 0.0721532i | \(0.0229870\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.75877 | + | 4.77833i | −0.154462 | + | 0.267535i | ||||
\(320\) | 4.23198 | + | 7.33001i | 0.236575 | + | 0.409760i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.93438 | 0.163526 | ||||||||
\(323\) | 1.40567 | + | 5.98374i | 0.0782133 | + | 0.332944i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.269815 | + | 0.467333i | 0.0149666 | + | 0.0259230i | ||||
\(326\) | 1.10495 | + | 1.91383i | 0.0611976 | + | 0.105997i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.517975 | + | 0.897159i | 0.0286004 | + | 0.0495373i | ||||
\(329\) | −5.49138 | + | 9.51135i | −0.302750 | + | 0.524378i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3063 | −0.896278 | −0.448139 | − | 0.893964i | \(-0.647913\pi\) | ||||
−0.448139 | + | 0.893964i | \(0.647913\pi\) | |||||||
\(332\) | −3.72201 | + | 6.44670i | −0.204272 | + | 0.353809i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.1607 | −1.37673 | ||||||||
\(335\) | 0.887063 | 0.0484654 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5604 | − | 25.2193i | −0.793155 | − | 1.37378i | −0.924004 | − | 0.382382i | \(-0.875104\pi\) |
0.130849 | − | 0.991402i | \(-0.458230\pi\) | |||||||
\(338\) | −12.8020 | + | 22.1737i | −0.696337 | + | 1.20609i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.45165 | + | 2.51434i | 0.0787270 | + | 0.136359i | ||||
\(341\) | 5.23999 | 0.283761 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.6925 | −1.00930 | ||||||||
\(344\) | 0.348001 | + | 0.602756i | 0.0187630 | + | 0.0324984i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.34278 | − | 7.52191i | 0.233469 | − | 0.404381i | ||||
\(347\) | −1.36152 | − | 2.35823i | −0.0730904 | − | 0.126596i | 0.827164 | − | 0.561961i | \(-0.189953\pi\) |
−0.900254 | + | 0.435364i | \(0.856620\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.70995 | −0.305647 | −0.152823 | − | 0.988254i | \(-0.548837\pi\) | ||||
−0.152823 | + | 0.988254i | \(0.548837\pi\) | |||||||
\(350\) | −3.35379 | −0.179268 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.00105 | + | 5.19797i | −0.159956 | + | 0.277053i | ||||
\(353\) | 27.6435 | 1.47131 | 0.735657 | − | 0.677354i | \(-0.236874\pi\) | ||||
0.735657 | + | 0.677354i | \(0.236874\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.41061 | + | 2.44324i | −0.0748672 | + | 0.129674i | ||||
\(356\) | 0.956181 | + | 1.65615i | 0.0506775 | + | 0.0877760i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.6962 | − | 21.9905i | −0.671017 | − | 1.16224i | ||||
\(359\) | −2.11633 | − | 3.66559i | −0.111696 | − | 0.193463i | 0.804758 | − | 0.593603i | \(-0.202295\pi\) |
−0.916454 | + | 0.400140i | \(0.868962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8328 | + | 10.5035i | 0.833305 | + | 0.552813i | ||||
\(362\) | −7.43550 | −0.390801 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.924766 | + | 1.60174i | 0.0484709 | + | 0.0839540i | ||||
\(365\) | −0.524369 | + | 0.908233i | −0.0274467 | + | 0.0475391i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.769642 | + | 1.33306i | −0.0401750 | + | 0.0695852i | −0.885414 | − | 0.464804i | \(-0.846125\pi\) |
0.845239 | + | 0.534389i | \(0.179458\pi\) | |||||||
\(368\) | 3.39369 | 0.176908 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.90230 | − | 13.6872i | 0.410821 | − | 0.711563i | ||||
\(371\) | −6.40935 | + | 11.1013i | −0.332757 | + | 0.576352i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.490289 | 0.0253862 | 0.0126931 | − | 0.999919i | \(-0.495960\pi\) | ||||
0.0126931 | + | 0.999919i | \(0.495960\pi\) | |||||||
\(374\) | −1.05889 | + | 1.83405i | −0.0547538 | + | 0.0948364i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.391366 | − | 0.677865i | 0.0201831 | − | 0.0349582i | ||||
\(377\) | 1.99708 | + | 3.45905i | 0.102855 | + | 0.178150i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.6250 | −1.77857 | −0.889283 | − | 0.457358i | \(-0.848796\pi\) | ||||
−0.889283 | + | 0.457358i | \(0.848796\pi\) | |||||||
\(380\) | 8.59235 | + | 2.59093i | 0.440778 | + | 0.132912i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.28208 | − | 10.8809i | −0.321419 | − | 0.556714i | ||||
\(383\) | 11.9762 | + | 20.7433i | 0.611953 | + | 1.05993i | 0.990911 | + | 0.134520i | \(0.0429492\pi\) |
−0.378958 | + | 0.925414i | \(0.623717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.620468 | − | 1.07468i | −0.0316220 | − | 0.0547708i | ||||
\(386\) | −19.0643 | + | 33.0203i | −0.970347 | + | 1.68069i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.0378881 | 0.00192348 | ||||||||
\(389\) | 8.75864 | − | 15.1704i | 0.444081 | − | 0.769171i | −0.553907 | − | 0.832579i | \(-0.686864\pi\) |
0.997988 | + | 0.0634081i | \(0.0201970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.23379 | 0.0623952 | ||||||||
\(392\) | 0.501710 | 0.0253402 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.90164 | + | 11.9540i | 0.347699 | + | 0.602233i | ||||
\(395\) | −2.88624 | + | 4.99911i | −0.145222 | + | 0.251532i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.44472 | − | 7.69848i | −0.223074 | − | 0.386376i | 0.732666 | − | 0.680589i | \(-0.238276\pi\) |
−0.955740 | + | 0.294213i | \(0.904943\pi\) | |||||||
\(398\) | −40.2700 | −2.01855 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.87876 | −0.193938 | ||||||||
\(401\) | 18.1428 | + | 31.4242i | 0.906007 | + | 1.56925i | 0.819560 | + | 0.572994i | \(0.194218\pi\) |
0.0864475 | + | 0.996256i | \(0.472449\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.89662 | − | 3.28504i | 0.0944774 | − | 0.163640i | ||||
\(404\) | 16.3419 | + | 28.3050i | 0.813041 | + | 1.40823i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.8237 | −1.23198 | ||||||||
\(407\) | 5.84785 | 0.289867 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.69791 | − | 15.0652i | 0.430084 | − | 0.744928i | −0.566796 | − | 0.823858i | \(-0.691817\pi\) |
0.996880 | + | 0.0789306i | \(0.0251505\pi\) | |||||||
\(410\) | −17.5917 | −0.868794 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.81018 | − | 15.2597i | 0.434046 | − | 0.751790i | ||||
\(413\) | −4.08441 | − | 7.07441i | −0.200981 | − | 0.348109i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.80777 | − | 3.13116i | −0.0887402 | − | 0.153702i | ||||
\(416\) | 2.17247 | + | 3.76282i | 0.106514 | + | 0.184487i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.49707 | + | 6.37283i | 0.0732240 | + | 0.311705i | ||||
\(419\) | −30.9259 | −1.51083 | −0.755414 | − | 0.655248i | \(-0.772564\pi\) | ||||
−0.755414 | + | 0.655248i | \(0.772564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.81345 | + | 10.0692i | 0.283330 | + | 0.490742i | 0.972203 | − | 0.234140i | \(-0.0752275\pi\) |
−0.688873 | + | 0.724882i | \(0.741894\pi\) | |||||||
\(422\) | 14.9378 | − | 25.8730i | 0.727160 | − | 1.25948i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.456788 | − | 0.791180i | 0.0221836 | − | 0.0384231i | ||||
\(425\) | −1.41013 | −0.0684015 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.33607 | − | 7.51029i | 0.209837 | − | 0.363449i | ||||
\(428\) | 11.9938 | − | 20.7739i | 0.579744 | − | 1.00415i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.8190 | −0.569963 | ||||||||
\(431\) | −12.2150 | + | 21.1569i | −0.588374 | + | 1.01909i | 0.406072 | + | 0.913841i | \(0.366898\pi\) |
−0.994446 | + | 0.105252i | \(0.966435\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.4503 | + | 18.1004i | −0.502208 | + | 0.869851i | 0.497788 | + | 0.867299i | \(0.334146\pi\) |
−0.999997 | + | 0.00255203i | \(0.999188\pi\) | |||||||
\(434\) | 11.7875 | + | 20.4165i | 0.565817 | + | 0.980023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.61498 | −0.221017 | ||||||||
\(437\) | 2.77922 | − | 2.61168i | 0.132948 | − | 0.124934i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.21019 | − | 14.2205i | −0.391851 | − | 0.678706i | 0.600843 | − | 0.799367i | \(-0.294832\pi\) |
−0.992694 | + | 0.120661i | \(0.961498\pi\) | |||||||
\(440\) | 0.0442201 | + | 0.0765915i | 0.00210811 | + | 0.00365136i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.766531 | + | 1.32767i | 0.0364602 | + | 0.0631509i | ||||
\(443\) | −1.32291 | + | 2.29135i | −0.0628533 | + | 0.108865i | −0.895740 | − | 0.444579i | \(-0.853353\pi\) |
0.832886 | + | 0.553444i | \(0.186687\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.928832 | −0.0440309 | ||||||||
\(446\) | −19.0263 | + | 32.9545i | −0.900920 | + | 1.56044i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.0899 | −0.665683 | ||||||||
\(449\) | 8.17261 | 0.385689 | 0.192845 | − | 0.981229i | \(-0.438229\pi\) | ||||
0.192845 | + | 0.981229i | \(0.438229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.25455 | − | 5.63705i | −0.153251 | − | 0.265438i | ||||
\(452\) | −9.20717 | + | 15.9473i | −0.433069 | + | 0.750097i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.8476 | + | 27.4488i | 0.743763 | + | 1.28823i | ||||
\(455\) | −0.898315 | −0.0421137 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.94164 | −0.418272 | −0.209136 | − | 0.977887i | \(-0.567065\pi\) | ||||
−0.209136 | + | 0.977887i | \(0.567065\pi\) | |||||||
\(458\) | −19.1814 | − | 33.2232i | −0.896288 | − | 1.55242i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.900704 | − | 1.56007i | 0.0419956 | − | 0.0727384i | ||||
\(461\) | 8.82526 | + | 15.2858i | 0.411033 | + | 0.711930i | 0.995003 | − | 0.0998450i | \(-0.0318347\pi\) |
−0.583970 | + | 0.811775i | \(0.698501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.8670 | −0.969771 | −0.484885 | − | 0.874578i | \(-0.661139\pi\) | ||||
−0.484885 | + | 0.874578i | \(0.661139\pi\) | |||||||
\(464\) | −28.7093 | −1.33279 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.19760 | − | 2.07431i | 0.0554779 | − | 0.0960905i | ||||
\(467\) | −24.4820 | −1.13289 | −0.566445 | − | 0.824099i | \(-0.691682\pi\) | ||||
−0.566445 | + | 0.824099i | \(0.691682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.738341 | + | 1.27884i | −0.0340934 | + | 0.0590515i | ||||
\(470\) | 6.64588 | + | 11.5110i | 0.306552 | + | 0.530963i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.291092 | + | 0.504186i | 0.0133986 | + | 0.0232071i | ||||
\(473\) | −2.18657 | − | 3.78725i | −0.100539 | − | 0.174138i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.17646 | + | 2.98497i | −0.145746 | + | 0.136960i | ||||
\(476\) | −4.83310 | −0.221525 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −26.1349 | − | 45.2669i | −1.19538 | − | 2.07046i | ||||
\(479\) | −1.65218 | + | 2.86165i | −0.0754898 | + | 0.130752i | −0.901299 | − | 0.433197i | \(-0.857385\pi\) |
0.825809 | + | 0.563949i | \(0.190719\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.11664 | − | 3.66612i | 0.0965103 | − | 0.167161i | ||||
\(482\) | 18.2454 | 0.831057 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.7518 | − | 18.6227i | 0.488720 | − | 0.846487i | ||||
\(485\) | −0.00920110 | + | 0.0159368i | −0.000417800 | + | 0.000723652i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.6648 | 1.48019 | 0.740093 | − | 0.672505i | \(-0.234782\pi\) | ||||
0.740093 | + | 0.672505i | \(0.234782\pi\) | |||||||
\(488\) | −0.309028 | + | 0.535252i | −0.0139890 | + | 0.0242297i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.25983 | + | 7.37824i | −0.192439 | + | 0.333315i | ||||
\(491\) | 6.51626 | + | 11.2865i | 0.294075 | + | 0.509352i | 0.974769 | − | 0.223215i | \(-0.0716552\pi\) |
−0.680694 | + | 0.732567i | \(0.738322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.4373 | −0.470074 | ||||||||
\(494\) | 4.53710 | + | 1.36811i | 0.204134 | + | 0.0615544i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.6325 | + | 23.6122i | 0.612119 | + | 1.06022i | ||||
\(497\) | −2.34822 | − | 4.06723i | −0.105332 | − | 0.182440i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.1552 | − | 26.2496i | −0.678441 | − | 1.17509i | −0.975450 | − | 0.220220i | \(-0.929323\pi\) |
0.297009 | − | 0.954875i | \(-0.404011\pi\) | |||||||
\(500\) | −1.02944 | + | 1.78305i | −0.0460381 | + | 0.0797404i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.90411 | 0.263513 | ||||||||
\(503\) | −19.0259 | + | 32.9539i | −0.848324 | + | 1.46934i | 0.0343796 | + | 0.999409i | \(0.489054\pi\) |
−0.882703 | + | 0.469931i | \(0.844279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.8745 | −0.706406 | ||||||||
\(506\) | 1.31401 | 0.0584150 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.4091 | + | 35.3497i | 0.905509 | + | 1.56839i | ||||
\(509\) | 11.8719 | − | 20.5627i | 0.526212 | − | 0.911427i | −0.473321 | − | 0.880890i | \(-0.656945\pi\) |
0.999534 | − | 0.0305368i | \(-0.00972167\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.872910 | − | 1.51192i | −0.0386153 | − | 0.0668836i | ||||
\(512\) | −32.1509 | −1.42088 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.8606 | 0.964228 | ||||||||
\(515\) | 4.27910 | + | 7.41161i | 0.188559 | + | 0.326595i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.45904 | + | 4.25918i | −0.108148 | + | 0.187318i | ||||
\(518\) | 13.1549 | + | 22.7849i | 0.577991 | + | 1.00111i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0640221 | 0.00280755 | ||||||||
\(521\) | 29.8052 | 1.30579 | 0.652896 | − | 0.757448i | \(-0.273554\pi\) | ||||
0.652896 | + | 0.757448i | \(0.273554\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.97546 | + | 5.15365i | −0.130108 | + | 0.225353i | −0.923718 | − | 0.383073i | \(-0.874866\pi\) |
0.793610 | + | 0.608427i | \(0.208199\pi\) | |||||||
\(524\) | 3.78002 | 0.165131 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.9816 | − | 29.4130i | 0.740433 | − | 1.28247i | ||||
\(527\) | 4.95615 | + | 8.58431i | 0.215893 | + | 0.373938i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1172 | + | 19.2556i | 0.483358 | + | 0.837201i | ||||
\(530\) | 7.75684 | + | 13.4352i | 0.336936 | + | 0.583589i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.8870 | + | 10.2307i | −0.472013 | + | 0.443558i | ||||
\(533\) | −4.71196 | −0.204097 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.82539 | + | 10.0899i | 0.251854 | + | 0.436223i | ||||
\(536\) | 0.0526209 | − | 0.0911420i | 0.00227288 | − | 0.00393674i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.7629 | − | 51.5509i | 1.28317 | − | 2.22252i | ||||
\(539\) | −3.15235 | −0.135781 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.20614 | + | 3.82115i | −0.0948496 | + | 0.164284i | −0.909546 | − | 0.415604i | \(-0.863570\pi\) |
0.814696 | + | 0.579888i | \(0.196904\pi\) | |||||||
\(542\) | 21.4005 | − | 37.0668i | 0.919231 | − | 1.59216i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.3540 | −0.486797 | ||||||||
\(545\) | 1.12075 | − | 1.94119i | 0.0480075 | − | 0.0831514i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2986 | + | 38.6224i | −0.953421 | + | 1.65137i | −0.215479 | + | 0.976508i | \(0.569131\pi\) |
−0.737942 | + | 0.674865i | \(0.764202\pi\) | |||||||
\(548\) | −4.07854 | − | 7.06424i | −0.174227 | − | 0.301769i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.50183 | −0.0640381 | ||||||||
\(551\) | −23.5111 | + | 22.0938i | −1.00161 | + | 0.941227i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.80468 | − | 8.32195i | −0.204316 | − | 0.353885i | ||||
\(554\) | −28.5736 | − | 49.4910i | −1.21398 | − | 2.10267i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.83045 | + | 3.17043i | 0.0776282 | + | 0.134456i | ||||
\(557\) | 6.46476 | − | 11.1973i | 0.273921 | − | 0.474444i | −0.695942 | − | 0.718098i | \(-0.745013\pi\) |
0.969862 | + | 0.243654i | \(0.0783461\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.16573 | −0.133896 | ||||||||
\(560\) | 3.22846 | − | 5.59185i | 0.136427 | − | 0.236299i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.4948 | −1.49726 | ||||||||
\(563\) | 31.7105 | 1.33644 | 0.668219 | − | 0.743964i | \(-0.267057\pi\) | ||||
0.668219 | + | 0.743964i | \(0.267057\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.47191 | − | 7.74558i | −0.188135 | − | 0.325859i | ||||
\(566\) | −17.2164 | + | 29.8196i | −0.723659 | + | 1.25341i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.167355 | + | 0.289868i | 0.00702207 | + | 0.0121626i | ||||
\(569\) | 28.4382 | 1.19219 | 0.596095 | − | 0.802914i | \(-0.296718\pi\) | ||||
0.596095 | + | 0.802914i | \(0.296718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.32088 | −0.306369 | −0.153185 | − | 0.988198i | \(-0.548953\pi\) | ||||
−0.153185 | + | 0.988198i | \(0.548953\pi\) | |||||||
\(572\) | 0.414110 | + | 0.717259i | 0.0173148 | + | 0.0299901i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.6424 | − | 25.3613i | 0.611161 | − | 1.05856i | ||||
\(575\) | 0.437471 | + | 0.757722i | 0.0182438 | + | 0.0315992i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.8157 | −0.575156 | −0.287578 | − | 0.957757i | \(-0.592850\pi\) | ||||
−0.287578 | + | 0.957757i | \(0.592850\pi\) | |||||||
\(578\) | 30.2432 | 1.25795 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.61960 | + | 13.1975i | −0.316387 | + | 0.547998i | ||||
\(581\) | 6.01876 | 0.249700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.87010 | + | 4.97116i | −0.118868 | + | 0.205885i | ||||
\(584\) | 0.0622115 | + | 0.107753i | 0.00257433 | + | 0.00445887i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.4187 | + | 38.8303i | 0.926108 | + | 1.60407i | ||||
\(587\) | −9.94338 | − | 17.2224i | −0.410407 | − | 0.710846i | 0.584527 | − | 0.811374i | \(-0.301280\pi\) |
−0.994934 | + | 0.100528i | \(0.967947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.3355 | + | 8.84580i | 1.20875 | + | 0.364485i | ||||
\(590\) | −9.88622 | −0.407009 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.2140 | + | 26.3514i | 0.625290 | + | 1.08303i | ||||
\(593\) | 4.92452 | − | 8.52952i | 0.202226 | − | 0.350266i | −0.747019 | − | 0.664802i | \(-0.768516\pi\) |
0.949245 | + | 0.314537i | \(0.101849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.17372 | − | 2.03294i | 0.0481177 | − | 0.0833423i | ||||
\(596\) | 39.3380 | 1.61135 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.475608 | − | 0.823777i | 0.0194491 | − | 0.0336867i | ||||
\(599\) | 3.58661 | − | 6.21220i | 0.146545 | − | 0.253823i | −0.783403 | − | 0.621514i | \(-0.786518\pi\) |
0.929948 | + | 0.367690i | \(0.119851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.2040 | 1.59916 | 0.799582 | − | 0.600557i | \(-0.205054\pi\) | ||||
0.799582 | + | 0.600557i | \(0.205054\pi\) | |||||||
\(602\) | 9.83747 | − | 17.0390i | 0.400946 | − | 0.694458i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.51847 | + | 4.36212i | −0.102475 | + | 0.177492i | ||||
\(605\) | 5.22215 | + | 9.04504i | 0.212311 | + | 0.367733i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.1741 | 1.79297 | 0.896485 | − | 0.443074i | \(-0.146112\pi\) | ||||
0.896485 | + | 0.443074i | \(0.146112\pi\) | |||||||
\(608\) | −25.5759 | + | 24.0341i | −1.03724 | + | 0.974711i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.24768 | − | 9.08924i | −0.212472 | − | 0.368013i | ||||
\(611\) | 1.78010 | + | 3.08323i | 0.0720152 | + | 0.124734i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.75407 | + | 6.50224i | 0.151625 | + | 0.262623i | 0.931825 | − | 0.362907i | \(-0.118216\pi\) |
−0.780200 | + | 0.625531i | \(0.784883\pi\) | |||||||
\(614\) | −26.7877 | + | 46.3977i | −1.08107 | + | 1.87246i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.147225 | −0.00593188 | ||||||||
\(617\) | −7.53673 | + | 13.0540i | −0.303417 | + | 0.525534i | −0.976908 | − | 0.213662i | \(-0.931461\pi\) |
0.673490 | + | 0.739196i | \(0.264794\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.5536 | 1.75057 | 0.875283 | − | 0.483610i | \(-0.160675\pi\) | ||||
0.875283 | + | 0.483610i | \(0.160675\pi\) | |||||||
\(620\) | 14.4726 | 0.581234 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.2715 | + | 19.5228i | 0.451945 | + | 0.782792i | ||||
\(623\) | 0.773108 | − | 1.33906i | 0.0309739 | − | 0.0536484i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −41.2285 | −1.64782 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.9659 | 0.756822 | ||||||||
\(629\) | 5.53108 | + | 9.58012i | 0.220539 | + | 0.381984i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9200 | + | 24.1101i | −0.554146 | + | 0.959809i | 0.443823 | + | 0.896114i | \(0.353622\pi\) |
−0.997969 | + | 0.0636948i | \(0.979712\pi\) | |||||||
\(632\) | 0.342425 | + | 0.593098i | 0.0136209 | + | 0.0235922i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.2939 | 1.24284 | ||||||||
\(635\) | −19.8254 | −0.786747 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.14100 | + | 1.97627i | −0.0452080 | + | 0.0783025i | ||||
\(638\) | −11.1160 | −0.440088 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.474357 | + | 0.821611i | −0.0187506 | + | 0.0324770i | ||||
\(641\) | −2.21833 | − | 3.84226i | −0.0876187 | − | 0.151760i | 0.818885 | − | 0.573957i | \(-0.194592\pi\) |
−0.906504 | + | 0.422197i | \(0.861259\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.32952 | + | 5.76690i | 0.131304 | + | 0.227425i | 0.924179 | − | 0.381959i | \(-0.124750\pi\) |
−0.792876 | + | 0.609383i | \(0.791417\pi\) | |||||||
\(644\) | 1.49939 | + | 2.59702i | 0.0590843 | + | 0.102337i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.02418 | + | 8.48017i | −0.355052 | + | 0.333648i | ||||
\(647\) | 1.27795 | 0.0502415 | 0.0251208 | − | 0.999684i | \(-0.492003\pi\) | ||||
0.0251208 | + | 0.999684i | \(0.492003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.82900 | − | 3.16792i | −0.0717944 | − | 0.124352i | ||||
\(650\) | −0.543588 | + | 0.941522i | −0.0213213 | + | 0.0369295i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.12920 | + | 1.95584i | −0.0442231 | + | 0.0765966i | ||||
\(653\) | 45.2709 | 1.77159 | 0.885795 | − | 0.464078i | \(-0.153614\pi\) | ||||
0.885795 | + | 0.464078i | \(0.153614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.917977 | + | 1.58998i | −0.0358683 | + | 0.0621257i | ||||
\(656\) | 16.9343 | − | 29.3311i | 0.661174 | − | 1.14519i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.1266 | −0.862586 | ||||||||
\(659\) | 6.80538 | − | 11.7873i | 0.265100 | − | 0.459167i | −0.702490 | − | 0.711694i | \(-0.747928\pi\) |
0.967590 | + | 0.252527i | \(0.0812617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5259 | − | 25.1596i | 0.564991 | − | 0.978594i | −0.432059 | − | 0.901845i | \(-0.642213\pi\) |
0.997050 | − | 0.0767486i | \(-0.0244539\pi\) | |||||||
\(662\) | −16.4259 | − | 28.4506i | −0.638412 | − | 1.10576i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.428951 | −0.0166465 | ||||||||
\(665\) | −1.65941 | − | 7.06391i | −0.0643493 | − | 0.273927i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.23802 | + | 5.60841i | 0.125376 | + | 0.217158i | ||||
\(668\) | −12.8565 | − | 22.2681i | −0.497432 | − | 0.861578i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.893568 | + | 1.54771i | 0.0345216 | + | 0.0597931i | ||||
\(671\) | 1.94169 | − | 3.36311i | 0.0749581 | − | 0.129831i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.4534 | −0.518591 | −0.259296 | − | 0.965798i | \(-0.583490\pi\) | ||||
−0.259296 | + | 0.965798i | \(0.583490\pi\) | |||||||
\(674\) | 29.3344 | − | 50.8086i | 1.12992 | − | 1.95707i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.1660 | −1.00638 | ||||||||
\(677\) | 48.1048 | 1.84882 | 0.924409 | − | 0.381404i | \(-0.124559\pi\) | ||||
0.924409 | + | 0.381404i | \(0.124559\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0153170 | − | 0.0265298i | −0.000587811 | − | 0.00101812i | ||||
\(680\) | −0.0836496 | + | 0.144885i | −0.00320782 | + | 0.00555610i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.27842 | + | 9.14250i | 0.202121 | + | 0.350084i | ||||
\(683\) | −31.7434 | −1.21463 | −0.607314 | − | 0.794462i | \(-0.707753\pi\) | ||||
−0.607314 | + | 0.794462i | \(0.707753\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.96188 | 0.151376 | ||||||||
\(686\) | −18.8296 | − | 32.6138i | −0.718916 | − | 1.24520i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.3773 | − | 19.7061i | 0.433756 | − | 0.751287i | ||||
\(689\) | 2.07767 | + | 3.59864i | 0.0791530 | + | 0.137097i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.63348 | 0.214308 | 0.107154 | − | 0.994242i | \(-0.465826\pi\) | ||||
0.107154 | + | 0.994242i | \(0.465826\pi\) | |||||||
\(692\) | 8.87620 | 0.337422 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.74302 | − | 4.75105i | 0.104124 | − | 0.180347i | ||||
\(695\) | −1.77809 | −0.0674469 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.15652 | − | 10.6634i | 0.233195 | − | 0.403905i | ||||
\(698\) | −5.75183 | − | 9.96246i | −0.217710 | − | 0.377085i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.71370 | − | 2.96822i | −0.0647719 | − | 0.112188i | ||||
\(701\) | −14.9878 | − | 25.9596i | −0.566080 | − | 0.980480i | −0.996948 | − | 0.0780649i | \(-0.975126\pi\) |
0.430868 | − | 0.902415i | \(-0.358207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.7385 | + | 9.87195i | 1.23476 | + | 0.372328i | ||||
\(704\) | −6.30943 | −0.237796 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.8462 | + | 48.2311i | 1.04801 | + | 1.81520i | ||||
\(707\) | 13.2130 | − | 22.8857i | 0.496928 | − | 0.860704i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.14344 | + | 1.98050i | −0.0429429 | + | 0.0743793i | −0.886698 | − | 0.462349i | \(-0.847007\pi\) |
0.843755 | + | 0.536728i | \(0.180340\pi\) | |||||||
\(710\) | −5.68380 | −0.213309 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.0550987 | + | 0.0954337i | −0.00206491 | + | 0.00357653i | ||||
\(713\) | 3.07513 | − | 5.32628i | 0.115165 | − | 0.199471i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.402265 | −0.0150439 | ||||||||
\(716\) | 12.9749 | − | 22.4732i | 0.484895 | − | 0.839863i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.26370 | − | 7.38495i | 0.159120 | − | 0.275604i | ||||
\(719\) | 22.1981 | + | 38.4483i | 0.827850 | + | 1.43388i | 0.899722 | + | 0.436464i | \(0.143769\pi\) |
−0.0718716 | + | 0.997414i | \(0.522897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.2467 | −0.530575 | ||||||||
\(722\) | −2.37702 | + | 38.2048i | −0.0884636 | + | 1.42184i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.79935 | − | 6.58067i | −0.141202 | − | 0.244569i | ||||
\(725\) | −3.70083 | − | 6.41003i | −0.137446 | − | 0.238063i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.39956 | + | 7.62026i | 0.163171 | + | 0.282620i | 0.936004 | − | 0.351989i | \(-0.114495\pi\) |
−0.772834 | + | 0.634609i | \(0.781161\pi\) | |||||||
\(728\) | −0.0532884 | + | 0.0922982i | −0.00197500 | + | 0.00342080i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.11286 | −0.0782004 | ||||||||
\(731\) | 4.13626 | − | 7.16421i | 0.152985 | − | 0.264978i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.5385 | 1.05409 | 0.527047 | − | 0.849836i | \(-0.323299\pi\) | ||||
0.527047 | + | 0.849836i | \(0.323299\pi\) | |||||||
\(734\) | −3.10115 | −0.114465 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.52238 | + | 6.10094i | 0.129837 | + | 0.224884i | ||||
\(737\) | −0.330629 | + | 0.572666i | −0.0121789 | + | 0.0210944i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.16208 | + | 8.94099i | 0.189890 | + | 0.328900i | 0.945213 | − | 0.326453i | \(-0.105853\pi\) |
−0.755323 | + | 0.655352i | \(0.772520\pi\) | |||||||
\(740\) | 16.1515 | 0.593741 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.8254 | −0.948081 | ||||||||
\(743\) | 13.5295 | + | 23.4339i | 0.496351 | + | 0.859705i | 0.999991 | − | 0.00420839i | \(-0.00133958\pi\) |
−0.503640 | + | 0.863914i | \(0.668006\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.55320 | + | 16.5466i | −0.350002 | + | 0.606222i | ||||
\(746\) | 0.493885 | + | 0.855434i | 0.0180824 | + | 0.0313196i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.16426 | −0.0791332 | ||||||||
\(749\) | −19.3949 | −0.708675 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.9995 | − | 45.0325i | 0.948735 | − | 1.64326i | 0.200642 | − | 0.979665i | \(-0.435697\pi\) |
0.748093 | − | 0.663593i | \(-0.230969\pi\) | |||||||
\(752\) | −25.5901 | −0.933173 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.02346 | + | 6.96883i | −0.146526 | + | 0.253790i | ||||
\(755\) | −1.22322 | − | 2.11868i | −0.0445175 | − | 0.0771066i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.7487 | − | 46.3301i | −0.972199 | − | 1.68390i | −0.688886 | − | 0.724870i | \(-0.741900\pi\) |
−0.283313 | − | 0.959028i | \(-0.591433\pi\) | |||||||
\(758\) | −34.8789 | − | 60.4121i | −1.26686 | − | 2.19427i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.118265 | + | 0.503438i | 0.00428991 | + | 0.0182616i | ||||
\(761\) | 33.8123 | 1.22569 | 0.612847 | − | 0.790201i | \(-0.290024\pi\) | ||||
0.612847 | + | 0.790201i | \(0.290024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.86569 | + | 3.23147i | 0.0675426 | + | 0.116987i | ||||
\(764\) | 6.41996 | − | 11.1197i | 0.232266 | − | 0.402297i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.1280 | + | 41.7909i | −0.871780 | + | 1.50997i | ||||
\(767\) | −2.64803 | −0.0956148 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.09718 | − | 5.36447i | 0.111687 | − | 0.193448i | −0.804763 | − | 0.593596i | \(-0.797708\pi\) |
0.916451 | + | 0.400148i | \(0.131041\pi\) | |||||||
\(770\) | 1.25004 | − | 2.16513i | 0.0450482 | − | 0.0780257i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −38.9655 | −1.40240 | ||||||||
\(773\) | 4.36013 | − | 7.55197i | 0.156823 | − | 0.271626i | −0.776898 | − | 0.629626i | \(-0.783208\pi\) |
0.933721 | + | 0.358001i | \(0.116541\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.51467 | + | 6.08758i | −0.126251 | + | 0.218672i | ||||
\(776\) | 0.00109163 | + | 0.00189075i | 3.91871e−5 | + | 6.78740e-5i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.2915 | 1.26526 | ||||||||
\(779\) | −8.70416 | − | 37.0525i | −0.311859 | − | 1.32754i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.05153 | − | 1.82130i | −0.0376267 | − | 0.0651714i | ||||
\(782\) | 1.24283 | + | 2.15265i | 0.0444437 | + | 0.0769787i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.20127 | − | 14.2050i | −0.292902 | − | 0.507322i | ||||
\(785\) | −4.60586 | + | 7.97759i | −0.164390 | + | 0.284732i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.67992 | −0.0598826 | −0.0299413 | − | 0.999552i | \(-0.509532\pi\) | ||||
−0.0299413 | + | 0.999552i | \(0.509532\pi\) | |||||||
\(788\) | −7.05312 | + | 12.2164i | −0.251257 | + | 0.435190i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11.6296 | −0.413763 | ||||||||
\(791\) | 14.8887 | 0.529380 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.40559 | − | 2.43456i | −0.0499141 | − | 0.0864537i | ||||
\(794\) | 8.95464 | − | 15.5099i | 0.317788 | − | 0.550425i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.5769 | − | 35.6403i | −0.729331 | − | 1.26324i | ||||
\(797\) | −15.8793 | −0.562475 | −0.281237 | − | 0.959638i | \(-0.590745\pi\) | ||||
−0.281237 | + | 0.959638i | \(0.590745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.30335 | −0.329129 | ||||||||
\(800\) | −4.02584 | − | 6.97297i | −0.142335 | − | 0.246532i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −36.5517 | + | 63.3094i | −1.29068 | + | 2.23553i | ||||
\(803\) | −0.390889 | − | 0.677039i | −0.0137942 | − | 0.0238922i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.45651 | −0.0513351 | ||||||||
\(806\) | 7.64212 | 0.269182 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.941681 | + | 1.63104i | −0.0331282 | + | 0.0573798i | ||||
\(809\) | −47.8983 | −1.68402 | −0.842008 | − | 0.539465i | \(-0.818627\pi\) | ||||
−0.842008 | + | 0.539465i | \(0.818627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.1961 | − | 22.8564i | 0.463379 | − | 0.802596i | −0.535748 | − | 0.844378i | \(-0.679970\pi\) |
0.999127 | + | 0.0417821i | \(0.0133035\pi\) | |||||||
\(812\) | −12.6843 | − | 21.9698i | −0.445130 | − | 0.770988i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.89074 | + | 10.2031i | 0.206470 | + | 0.357617i | ||||
\(815\) | −0.548453 | − | 0.949949i | −0.0192115 | − | 0.0332753i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.84789 | − | 24.8937i | −0.204592 | − | 0.870921i | ||||
\(818\) | 35.0468 | 1.22538 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.98893 | − | 15.5693i | −0.313907 | − | 0.543703i | ||||
\(821\) | 0.411319 | − | 0.712425i | 0.0143551 | − | 0.0248638i | −0.858759 | − | 0.512380i | \(-0.828764\pi\) |
0.873114 | + | 0.487517i | \(0.162097\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.76958 | + | 13.4573i | −0.270831 | + | 0.469092i | −0.969075 | − | 0.246767i | \(-0.920632\pi\) |
0.698244 | + | 0.715860i | \(0.253965\pi\) | |||||||
\(824\) | 1.01535 | 0.0353714 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.22874 | − | 14.2526i | 0.286314 | − | 0.495911i | ||||
\(827\) | −14.1156 | + | 24.4490i | −0.490848 | + | 0.850174i | −0.999944 | − | 0.0105355i | \(-0.996646\pi\) |
0.509096 | + | 0.860710i | \(0.329980\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.85357 | 0.168571 | 0.0842857 | − | 0.996442i | \(-0.473139\pi\) | ||||
0.0842857 | + | 0.996442i | \(0.473139\pi\) | |||||||
\(830\) | 3.64207 | − | 6.30824i | 0.126418 | − | 0.218962i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.28371 | + | 3.95549i | −0.0791732 | + | 0.137132i | ||||
\(833\) | −2.98160 | − | 5.16428i | −0.103306 | − | 0.178932i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.4888 | 0.432191 | ||||||||
\(836\) | −4.87521 | + | 4.58131i | −0.168613 | + | 0.158448i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.1527 | − | 53.9581i | −1.07615 | − | 1.86395i | ||||
\(839\) | −10.4587 | − | 18.1151i | −0.361075 | − | 0.625401i | 0.627063 | − | 0.778969i | \(-0.284257\pi\) |
−0.988138 | + | 0.153568i | \(0.950924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.8923 | − | 22.3302i | −0.444563 | − | 0.770006i | ||||
\(842\) | −11.7122 | + | 20.2861i | −0.403628 | + | 0.699104i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30.5313 | 1.05093 | ||||||||
\(845\) | 6.35440 | − | 11.0061i | 0.218598 | − | 0.378623i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.3865 | −0.597408 | ||||||||
\(848\) | −29.8678 | −1.02567 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.42048 | − | 2.46034i | −0.0487219 | − | 0.0843889i | ||||
\(851\) | 3.43186 | − | 5.94415i | 0.117643 | − | 0.203763i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.9685 | + | 44.9788i | 0.889146 | + | 1.54005i | 0.840887 | + | 0.541211i | \(0.182034\pi\) |
0.0482595 | + | 0.998835i | \(0.484633\pi\) | |||||||
\(854\) | 17.4715 | 0.597862 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.38226 | 0.0472446 | ||||||||
\(857\) | −3.13726 | − | 5.43389i | −0.107167 | − | 0.185618i | 0.807455 | − | 0.589930i | \(-0.200845\pi\) |
−0.914621 | + | 0.404311i | \(0.867511\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.7479 | − | 39.4005i | 0.776148 | − | 1.34433i | −0.157999 | − | 0.987439i | \(-0.550504\pi\) |
0.934147 | − | 0.356888i | \(-0.116162\pi\) | |||||||
\(860\) | −6.03921 | − | 10.4602i | −0.205935 | − | 0.356690i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −49.2182 | −1.67638 | ||||||||
\(863\) | 36.0191 | 1.22611 | 0.613053 | − | 0.790042i | \(-0.289941\pi\) | ||||
0.613053 | + | 0.790042i | \(0.289941\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.15558 | + | 3.73357i | −0.0732919 | + | 0.126945i | ||||
\(866\) | −42.1077 | −1.43088 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.0462 | + | 20.8646i | −0.408875 | + | 0.708191i | ||||
\(869\) | −2.15153 | − | 3.72657i | −0.0729858 | − | 0.126415i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.239343 | + | 0.414554i | 0.00810982 | + | 0.0140466i | ||||
\(872\) | −0.132966 | − | 0.230304i | −0.00450280 | − | 0.00779907i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.35635 | + | 2.21823i | 0.248832 | + | 0.0750326i | ||||
\(875\) | 1.66469 | 0.0562767 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.5506 | + | 20.0063i | 0.390037 | + | 0.675564i | 0.992454 | − | 0.122617i | \(-0.0391288\pi\) |
−0.602417 | + | 0.798182i | \(0.705795\pi\) | |||||||
\(878\) | 16.5408 | − | 28.6495i | 0.558225 | − | 0.966875i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.44570 | − | 2.50403i | 0.0487346 | − | 0.0844108i | ||||
\(881\) | −14.4294 | −0.486141 | −0.243070 | − | 0.970009i | \(-0.578155\pi\) | ||||
−0.243070 | + | 0.970009i | \(0.578155\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.48691 | + | 12.9677i | −0.251955 | + | 0.436398i | −0.964064 | − | 0.265671i | \(-0.914407\pi\) |
0.712109 | + | 0.702069i | \(0.247740\pi\) | |||||||
\(884\) | −0.783356 | + | 1.35681i | −0.0263471 | + | 0.0456345i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.33045 | −0.179080 | ||||||||
\(887\) | −5.39733 | + | 9.34845i | −0.181225 | + | 0.313890i | −0.942298 | − | 0.334776i | \(-0.891339\pi\) |
0.761073 | + | 0.648666i | \(0.224673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.5015 | − | 28.5815i | 0.553444 | − | 0.958593i | ||||
\(890\) | −0.935644 | − | 1.62058i | −0.0313629 | − | 0.0543221i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −38.8878 | −1.30206 | ||||||||
\(893\) | −20.9567 | + | 19.6933i | −0.701289 | + | 0.659013i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.30190 | + | 10.9152i | 0.210649 | + | 0.364855i | ||||
\(896\) | −0.789656 | − | 1.36773i | −0.0263806 | − | 0.0456925i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.23255 | + | 14.2592i | 0.274724 | + | 0.475835i | ||||
\(899\) | −26.0144 | + | 45.0583i | −0.867629 | + | 1.50278i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.8585 | −0.361750 | ||||||||
\(902\) | 6.55685 | − | 11.3568i | 0.218319 | − | 0.378140i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.06110 | −0.0352917 | ||||||||
\(905\) | 3.69068 | 0.122682 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5290 | − | 42.4854i | −0.814471 | − | 1.41071i | −0.909707 | − | 0.415251i | \(-0.863694\pi\) |
0.0952355 | − | 0.995455i | \(-0.469640\pi\) | |||||||
\(908\) | −16.1954 | + | 28.0512i | −0.537463 | + | 0.930913i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.904904 | − | 1.56734i | −0.0299973 | − | 0.0519568i | ||||
\(911\) | −21.3969 | −0.708912 | −0.354456 | − | 0.935073i | \(-0.615334\pi\) | ||||
−0.354456 | + | 0.935073i | \(0.615334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.69520 | 0.0891980 | ||||||||
\(914\) | −9.00722 | − | 15.6010i | −0.297932 | − | 0.516034i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.6024 | − | 33.9524i | 0.647682 | − | 1.12182i | ||||
\(917\) | −1.52814 | − | 2.64682i | −0.0504638 | − | 0.0874058i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.9528 | −1.02104 | −0.510520 | − | 0.859866i | \(-0.670547\pi\) | ||||
−0.510520 | + | 0.859866i | \(0.670547\pi\) | |||||||
\(920\) | 0.103804 | 0.00342231 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.7800 | + | 30.7958i | −0.585552 | + | 1.01421i | ||||
\(923\) | −1.52241 | −0.0501107 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.92238 | + | 6.79377i | −0.128967 | + | 0.223378i | ||||
\(926\) | −21.0200 | − | 36.4077i | −0.690761 | − | 1.19643i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.7980 | − | 51.6116i | −0.978166 | − | 1.69423i | ||||
\(929\) | 25.8861 | + | 44.8361i | 0.849296 | + | 1.47102i | 0.881838 | + | 0.471553i | \(0.156306\pi\) |
−0.0325418 | + | 0.999470i | \(0.510360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.6481 | − | 5.32159i | −0.578393 | − | 0.174408i | ||||
\(932\) | 2.44778 | 0.0801796 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.6615 | − | 42.7150i | −0.806950 | − | 1.39768i | ||||
\(935\) | 0.525589 | − | 0.910348i | 0.0171886 | − | 0.0297716i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.5665 | + | 30.4261i | −0.573873 | + | 0.993977i | 0.422290 | + | 0.906461i | \(0.361226\pi\) |
−0.996163 | + | 0.0875161i | \(0.972107\pi\) | |||||||
\(938\) | −2.97502 | −0.0971380 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.79175 | + | 11.7637i | −0.221522 | + | 0.383688i | ||||
\(941\) | 26.0465 | − | 45.1139i | 0.849092 | − | 1.47067i | −0.0329279 | − | 0.999458i | \(-0.510483\pi\) |
0.882020 | − | 0.471212i | \(-0.156183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.63985 | −0.248788 | ||||||||
\(944\) | 9.51676 | − | 16.4835i | 0.309744 | − | 0.536493i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.40522 | − | 7.63006i | 0.143226 | − | 0.248075i | ||||
\(947\) | 25.0695 | + | 43.4217i | 0.814651 | + | 1.41102i | 0.909579 | + | 0.415532i | \(0.136405\pi\) |
−0.0949279 | + | 0.995484i | \(0.530262\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.565930 | −0.0183709 | ||||||||
\(950\) | −8.40781 | − | 2.53528i | −0.272785 | − | 0.0822554i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.139251 | − | 0.241189i | −0.00451314 | − | 0.00781698i | ||||
\(953\) | 20.3402 | + | 35.2303i | 0.658884 | + | 1.14122i | 0.980905 | + | 0.194488i | \(0.0623045\pi\) |
−0.322021 | + | 0.946732i | \(0.604362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.11817 | + | 5.40083i | 0.100902 | + | 0.174767i | ||||
\(956\) | 26.7085 | − | 46.2605i | 0.863815 | − | 1.49617i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.65717 | −0.215083 | ||||||||
\(959\) | −3.29765 | + | 5.71170i | −0.106487 | + | 0.184440i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.4116 | 0.593922 | ||||||||
\(962\) | 8.52864 | 0.274974 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.32296 | + | 16.1478i | 0.300272 | + | 0.520087i | ||||
\(965\) | 9.46275 | − | 16.3900i | 0.304617 | − | 0.527611i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.9627 | − | 34.5763i | −0.641956 | − | 1.11190i | −0.984996 | − | 0.172579i | \(-0.944790\pi\) |
0.343040 | − | 0.939321i | \(-0.388543\pi\) | |||||||
\(968\) | 1.23912 | 0.0398268 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.0370743 | −0.00119039 | ||||||||
\(971\) | −8.58195 | − | 14.8644i | −0.275408 | − | 0.477020i | 0.694830 | − | 0.719174i | \(-0.255480\pi\) |
−0.970238 | + | 0.242153i | \(0.922146\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.47998 | − | 2.56341i | 0.0474461 | − | 0.0821790i | ||||
\(974\) | 32.9044 | + | 56.9921i | 1.05433 | + | 1.82614i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.2063 | 0.646787 | ||||||||
\(977\) | 36.0150 | 1.15222 | 0.576111 | − | 0.817371i | \(-0.304569\pi\) | ||||
0.576111 | + | 0.817371i | \(0.304569\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.346197 | − | 0.599631i | 0.0110645 | − | 0.0191643i | ||||
\(980\) | −8.70666 | −0.278124 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.1281 | + | 22.7385i | −0.418935 | + | 0.725616i | ||||
\(983\) | −23.8054 | − | 41.2321i | −0.759273 | − | 1.31510i | −0.943222 | − | 0.332164i | \(-0.892221\pi\) |
0.183949 | − | 0.982936i | \(-0.441112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.42569 | − | 5.93348i | −0.109152 | − | 0.189056i | ||||
\(986\) | −10.5139 | − | 18.2106i | −0.334831 | − | 0.579943i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.10752 | + | 4.71456i | 0.0352348 | + | 0.149990i | ||||
\(989\) | −5.13283 | −0.163214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.5005 | − | 26.8477i | −0.492391 | − | 0.852845i | 0.507571 | − | 0.861610i | \(-0.330543\pi\) |
−0.999962 | + | 0.00876452i | \(0.997210\pi\) | |||||||
\(992\) | −28.2990 | + | 49.0153i | −0.898494 | + | 1.55624i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.73088 | − | 8.19412i | 0.150054 | − | 0.259902i | ||||
\(995\) | 19.9884 | 0.633675 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.8534 | − | 23.9948i | 0.438741 | − | 0.759921i | −0.558852 | − | 0.829268i | \(-0.688758\pi\) |
0.997593 | + | 0.0693461i | \(0.0220913\pi\) | |||||||
\(998\) | 30.5327 | − | 52.8843i | 0.966497 | − | 1.67402i | ||||
\(999\) | 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 | 855.2.k.j.406.6 | ✓ | 12 | |
3.2 | odd | 2 | 855.2.k.k.406.1 | yes | 12 | ||
19.11 | even | 3 | inner | 855.2.k.j.676.6 | yes | 12 | |
57.11 | odd | 6 | 855.2.k.k.676.1 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
855.2.k.j.406.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
855.2.k.j.676.6 | yes | 12 | 19.11 | even | 3 | inner | |
855.2.k.k.406.1 | yes | 12 | 3.2 | odd | 2 | ||
855.2.k.k.676.1 | yes | 12 | 57.11 | odd | 6 |