Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,2,Mod(73,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.bo (of order \(9\), degree \(6\), 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: | \(5.46176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(-0.173648 - 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.541 |
Dual form | 684.2.bo.a.397.1 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.826352 | − | 0.300767i | −0.369556 | − | 0.134507i | 0.150565 | − | 0.988600i | \(-0.451891\pi\) |
−0.520121 | + | 0.854093i | \(0.674113\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.09240 | − | 1.89209i | 0.412887 | − | 0.715141i | −0.582317 | − | 0.812962i | \(-0.697854\pi\) |
0.995204 | + | 0.0978205i | \(0.0311871\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0812519 | − | 0.140732i | −0.0244984 | − | 0.0424324i | 0.853516 | − | 0.521066i | \(-0.174466\pi\) |
−0.878015 | + | 0.478634i | \(0.841132\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.581252 | + | 0.487728i | 0.161210 | + | 0.135271i | 0.719824 | − | 0.694156i | \(-0.244222\pi\) |
−0.558614 | + | 0.829428i | \(0.688667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.539363 | − | 3.05888i | −0.130815 | − | 0.741887i | −0.977683 | − | 0.210085i | \(-0.932626\pi\) |
0.846868 | − | 0.531802i | \(-0.178485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.77719 | − | 3.35965i | 0.637131 | − | 0.770756i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.21301 | − | 0.441500i | 0.252930 | − | 0.0920591i | −0.212443 | − | 0.977173i | \(-0.568142\pi\) |
0.465374 | + | 0.885114i | \(0.345920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.23783 | − | 2.71686i | −0.647565 | − | 0.543372i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.13176 | − | 6.41852i | 0.210162 | − | 1.19189i | −0.678944 | − | 0.734190i | \(-0.737562\pi\) |
0.889107 | − | 0.457700i | \(-0.151327\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.479055 | + | 0.829748i | −0.0860409 | + | 0.149027i | −0.905834 | − | 0.423632i | \(-0.860755\pi\) |
0.819793 | + | 0.572659i | \(0.194088\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.47178 | + | 1.23497i | −0.248776 | + | 0.208748i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.16250 | −0.191114 | −0.0955572 | − | 0.995424i | \(-0.530463\pi\) | ||||
−0.0955572 | + | 0.995424i | \(0.530463\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.11721 | − | 6.81115i | 1.26770 | − | 1.06372i | 0.272878 | − | 0.962049i | \(-0.412025\pi\) |
0.994818 | − | 0.101674i | \(-0.0324199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.166374 | + | 0.0605553i | 0.0253718 | + | 0.00923459i | 0.354675 | − | 0.934990i | \(-0.384592\pi\) |
−0.329303 | + | 0.944224i | \(0.606814\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.602196 | − | 3.41523i | 0.0878394 | − | 0.498162i | −0.908868 | − | 0.417083i | \(-0.863052\pi\) |
0.996708 | − | 0.0810787i | \(-0.0258365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.11334 | + | 1.92836i | 0.159049 | + | 0.275480i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.83022 | − | 2.84997i | 1.07556 | − | 0.391473i | 0.257309 | − | 0.966329i | \(-0.417164\pi\) |
0.818255 | + | 0.574856i | \(0.194942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0248149 | + | 0.140732i | 0.00334604 | + | 0.0189764i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.482926 | + | 2.73881i | 0.0628716 | + | 0.356563i | 0.999972 | + | 0.00750222i | \(0.00238805\pi\) |
−0.937100 | + | 0.349060i | \(0.886501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.79086 | + | 2.47167i | −0.869480 | + | 0.316465i | −0.737957 | − | 0.674848i | \(-0.764209\pi\) |
−0.131524 | + | 0.991313i | \(0.541987\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.333626 | − | 0.577857i | −0.0413812 | − | 0.0716743i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.184793 | − | 1.04801i | 0.0225760 | − | 0.128035i | −0.971437 | − | 0.237298i | \(-0.923738\pi\) |
0.994013 | + | 0.109263i | \(0.0348492\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.77719 | + | 1.73875i | 0.566948 | + | 0.206352i | 0.609561 | − | 0.792739i | \(-0.291346\pi\) |
−0.0426126 | + | 0.999092i | \(0.513568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.72281 | − | 1.44561i | 0.201640 | − | 0.169196i | −0.536376 | − | 0.843979i | \(-0.680207\pi\) |
0.738016 | + | 0.674783i | \(0.235763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.355037 | −0.0404602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.01501 | + | 3.36900i | −0.451724 | + | 0.379042i | −0.840075 | − | 0.542470i | \(-0.817489\pi\) |
0.388351 | + | 0.921512i | \(0.373045\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.55690 | + | 14.8210i | −0.939242 | + | 1.62682i | −0.172353 | + | 0.985035i | \(0.555137\pi\) |
−0.766889 | + | 0.641780i | \(0.778196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.474308 | + | 2.68993i | −0.0514459 | + | 0.291764i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9684 | − | 10.0427i | −1.26865 | − | 1.06452i | −0.994705 | − | 0.102773i | \(-0.967228\pi\) |
−0.273941 | − | 0.961747i | \(-0.588327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.55778 | − | 0.566986i | 0.163300 | − | 0.0594363i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.30541 | + | 1.94096i | −0.339128 | + | 0.199138i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.63563 | − | 9.27612i | −0.166073 | − | 0.941847i | −0.947951 | − | 0.318416i | \(-0.896849\pi\) |
0.781878 | − | 0.623431i | \(-0.214262\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.83022 | + | 4.05304i | 0.480625 | + | 0.403292i | 0.850652 | − | 0.525729i | \(-0.176207\pi\) |
−0.370027 | + | 0.929021i | \(0.620652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.30793 | + | 7.46156i | 0.424473 | + | 0.735209i | 0.996371 | − | 0.0851156i | \(-0.0271259\pi\) |
−0.571898 | + | 0.820325i | \(0.693793\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.57398 | + | 11.3865i | −0.635530 | + | 1.10077i | 0.350872 | + | 0.936423i | \(0.385885\pi\) |
−0.986402 | + | 0.164348i | \(0.947448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.44356 | + | 3.43718i | 0.904529 | + | 0.329222i | 0.752066 | − | 0.659087i | \(-0.229057\pi\) |
0.152463 | + | 0.988309i | \(0.451280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.04458 | −0.756770 | −0.378385 | − | 0.925648i | \(-0.623520\pi\) | ||||
−0.378385 | + | 0.925648i | \(0.623520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.13516 | −0.105854 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.37686 | − | 2.32099i | −0.584566 | − | 0.212765i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.48680 | − | 9.50341i | 0.498800 | − | 0.863946i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.05690 | + | 7.02676i | 0.362861 | + | 0.628493i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3589 | + | 12.8877i | 1.36288 | + | 1.14359i | 0.975080 | + | 0.221852i | \(0.0712101\pi\) |
0.387802 | + | 0.921743i | \(0.373234\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.76264 | + | 15.6677i | 0.241373 | + | 1.36889i | 0.828767 | + | 0.559594i | \(0.189043\pi\) |
−0.587394 | + | 0.809301i | \(0.699846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.32295 | − | 8.92474i | −0.288136 | − | 0.773873i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.74035 | + | 1.72535i | −0.404996 | + | 0.147406i | −0.536482 | − | 0.843912i | \(-0.680247\pi\) |
0.131487 | + | 0.991318i | \(0.458025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.08512 | − | 6.78422i | −0.685771 | − | 0.575430i | 0.231915 | − | 0.972736i | \(-0.425501\pi\) |
−0.917686 | + | 0.397306i | \(0.869945\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0214114 | − | 0.121430i | 0.00179051 | − | 0.0101545i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.86571 | + | 4.96356i | −0.237985 | + | 0.412202i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5680 | + | 8.86765i | −0.865768 | + | 0.726466i | −0.963203 | − | 0.268776i | \(-0.913381\pi\) |
0.0974344 | + | 0.995242i | \(0.468936\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.2841 | −1.65069 | −0.825346 | − | 0.564627i | \(-0.809020\pi\) | ||||
−0.825346 | + | 0.564627i | \(0.809020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.645430 | − | 0.541580i | 0.0518422 | − | 0.0435007i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3807 | + | 4.50622i | 0.988090 | + | 0.359635i | 0.784980 | − | 0.619521i | \(-0.212673\pi\) |
0.203110 | + | 0.979156i | \(0.434895\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.489733 | − | 2.77741i | 0.0385964 | − | 0.218891i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.74510 | + | 15.1470i | 0.684969 | + | 1.18640i | 0.973447 | + | 0.228915i | \(0.0735176\pi\) |
−0.288477 | + | 0.957487i | \(0.593149\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.0077 | − | 5.09840i | 1.08395 | − | 0.394526i | 0.262574 | − | 0.964912i | \(-0.415428\pi\) |
0.821377 | + | 0.570386i | \(0.193206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.15745 | − | 12.2355i | −0.165958 | − | 0.941193i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.311804 | − | 1.76833i | −0.0237060 | − | 0.134443i | 0.970658 | − | 0.240465i | \(-0.0772999\pi\) |
−0.994364 | + | 0.106021i | \(0.966189\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.67752 | + | 3.15836i | −0.655959 | + | 0.238749i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.91740 | + | 6.78514i | 0.292801 | + | 0.507145i | 0.974471 | − | 0.224514i | \(-0.0720795\pi\) |
−0.681670 | + | 0.731659i | \(0.738746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0727959 | + | 0.412846i | −0.00541088 | + | 0.0306866i | −0.987394 | − | 0.158284i | \(-0.949404\pi\) |
0.981983 | + | 0.188970i | \(0.0605150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.960637 | + | 0.349643i | 0.0706274 | + | 0.0257063i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.386659 | + | 0.324446i | −0.0282753 | + | 0.0237258i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5398 | 1.41385 | 0.706926 | − | 0.707287i | \(-0.250081\pi\) | ||||
0.706926 | + | 0.707287i | \(0.250081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7476 | + | 10.6965i | −0.917594 | + | 0.769953i | −0.973549 | − | 0.228480i | \(-0.926624\pi\) |
0.0559543 | + | 0.998433i | \(0.482180\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.9979 | + | 19.0490i | −0.783571 | + | 1.35718i | 0.146278 | + | 0.989243i | \(0.453270\pi\) |
−0.929849 | + | 0.367941i | \(0.880063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.77584 | + | 21.4139i | −0.267663 | + | 1.51799i | 0.493682 | + | 0.869642i | \(0.335651\pi\) |
−0.761345 | + | 0.648347i | \(0.775461\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.9081 | − | 9.15296i | −0.765596 | − | 0.642412i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.75624 | + | 3.18701i | −0.611563 | + | 0.222591i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.698463 | − | 0.117863i | −0.0483137 | − | 0.00815275i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.49794 | − | 8.49524i | −0.103122 | − | 0.584837i | −0.991954 | − | 0.126602i | \(-0.959593\pi\) |
0.888831 | − | 0.458235i | \(-0.151518\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.119271 | − | 0.100080i | −0.00813419 | − | 0.00682539i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.04664 | + | 1.81283i | 0.0710503 | + | 0.123063i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.17840 | − | 2.04104i | 0.0792675 | − | 0.137295i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.2442 | − | 5.18447i | −0.953864 | − | 0.347178i | −0.182238 | − | 0.983255i | \(-0.558334\pi\) |
−0.771626 | + | 0.636077i | \(0.780556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.71419 | 0.379264 | 0.189632 | − | 0.981855i | \(-0.439270\pi\) | ||||
0.189632 | + | 0.981855i | \(0.439270\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.1634 | 1.46460 | 0.732301 | − | 0.680982i | \(-0.238447\pi\) | ||||
0.732301 | + | 0.680982i | \(0.238447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1750 | − | 3.70339i | −0.666586 | − | 0.242617i | −0.0135087 | − | 0.999909i | \(-0.504300\pi\) |
−0.653077 | + | 0.757291i | \(0.726522\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.52481 | + | 2.64106i | −0.0994680 | + | 0.172284i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.93107 | − | 8.54087i | −0.318965 | − | 0.552463i | 0.661308 | − | 0.750115i | \(-0.270002\pi\) |
−0.980272 | + | 0.197652i | \(0.936668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.29086 | − | 4.43956i | −0.340814 | − | 0.285977i | 0.456275 | − | 0.889839i | \(-0.349183\pi\) |
−0.797089 | + | 0.603862i | \(0.793628\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.340022 | − | 1.92836i | −0.0217232 | − | 0.123199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.25284 | − | 0.598287i | 0.206973 | − | 0.0380681i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.3910 | − | 8.51363i | 1.47643 | − | 0.537375i | 0.526589 | − | 0.850120i | \(-0.323471\pi\) |
0.949837 | + | 0.312744i | \(0.101248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.160693 | − | 0.134837i | −0.0101027 | − | 0.00847715i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.47565 | − | 14.0401i | 0.154427 | − | 0.875799i | −0.804881 | − | 0.593436i | \(-0.797771\pi\) |
0.959308 | − | 0.282362i | \(-0.0911180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.26991 | + | 2.19956i | −0.0789087 | + | 0.136674i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.5594 | + | 13.8950i | −1.02110 | + | 0.856803i | −0.989765 | − | 0.142706i | \(-0.954420\pi\) |
−0.0313331 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.32770 | −0.450137 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.14022 | − | 6.83045i | 0.496318 | − | 0.416460i | −0.359966 | − | 0.932965i | \(-0.617212\pi\) |
0.856284 | + | 0.516505i | \(0.172767\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.4179 | + | 4.15577i | 0.693586 | + | 0.252445i | 0.664670 | − | 0.747137i | \(-0.268572\pi\) |
0.0289163 | + | 0.999582i | \(0.490794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.119271 | + | 0.676417i | −0.00719229 | + | 0.0407895i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.90760 | − | 8.50022i | −0.294869 | − | 0.510729i | 0.680085 | − | 0.733133i | \(-0.261943\pi\) |
−0.974954 | + | 0.222404i | \(0.928609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.5133 | − | 9.65004i | 1.58165 | − | 0.575673i | 0.606087 | − | 0.795399i | \(-0.292738\pi\) |
0.975562 | + | 0.219726i | \(0.0705162\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.67752 | − | 15.1850i | −0.159162 | − | 0.902652i | −0.954882 | − | 0.296987i | \(-0.904018\pi\) |
0.795720 | − | 0.605665i | \(-0.207093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.02007 | − | 22.7989i | −0.237297 | − | 1.34578i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.90895 | − | 2.51465i | 0.406409 | − | 0.147921i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.8885 | + | 24.0555i | 0.811373 | + | 1.40534i | 0.911903 | + | 0.410405i | \(0.134613\pi\) |
−0.100530 | + | 0.994934i | \(0.532054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.424678 | − | 2.40847i | 0.0247257 | − | 0.140226i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.920397 | + | 0.334997i | 0.0532279 | + | 0.0193734i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.296322 | − | 0.248644i | 0.0170797 | − | 0.0143316i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.35504 | 0.363888 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.8293 | − | 17.4779i | 1.18879 | − | 0.997516i | 0.188914 | − | 0.981994i | \(-0.439503\pi\) |
0.999880 | − | 0.0155226i | \(-0.00494118\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.97178 | + | 5.14728i | −0.168514 | + | 0.291875i | −0.937898 | − | 0.346912i | \(-0.887230\pi\) |
0.769383 | + | 0.638787i | \(0.220564\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.24170 | − | 7.04201i | 0.0701848 | − | 0.398038i | −0.929396 | − | 0.369084i | \(-0.879671\pi\) |
0.999581 | − | 0.0289536i | \(-0.00921752\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.0758 | − | 14.3283i | −0.959072 | − | 0.804757i | 0.0217300 | − | 0.999764i | \(-0.493083\pi\) |
−0.980802 | + | 0.195007i | \(0.937527\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.995252 | + | 0.362242i | −0.0557234 | + | 0.0202817i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.7747 | − | 6.68302i | −0.655160 | − | 0.371853i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.556904 | − | 3.15836i | −0.0308915 | − | 0.175194i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.80406 | − | 4.87019i | −0.319988 | − | 0.268502i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.15183 | − | 5.45912i | −0.173240 | − | 0.300061i | 0.766311 | − | 0.642470i | \(-0.222090\pi\) |
−0.939551 | + | 0.342410i | \(0.888757\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.467911 | + | 0.810446i | −0.0255647 | + | 0.0442794i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.3123 | + | 8.84894i | 1.32437 | + | 0.482033i | 0.904857 | − | 0.425715i | \(-0.139977\pi\) |
0.419517 | + | 0.907748i | \(0.362200\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.155697 | 0.00843145 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1584 | 1.08845 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.4820 | − | 6.36295i | −0.938486 | − | 0.341581i | −0.172918 | − | 0.984936i | \(-0.555320\pi\) |
−0.765568 | + | 0.643355i | \(0.777542\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.871644 | − | 1.50973i | 0.0466581 | − | 0.0808141i | −0.841753 | − | 0.539863i | \(-0.818476\pi\) |
0.888411 | + | 0.459048i | \(0.151810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.33615 | − | 9.24249i | −0.284015 | − | 0.491928i | 0.688355 | − | 0.725374i | \(-0.258333\pi\) |
−0.972370 | + | 0.233446i | \(0.925000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.42468 | − | 2.87365i | −0.181763 | − | 0.152517i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.18298 | + | 6.70902i | 0.0624354 | + | 0.354089i | 0.999981 | + | 0.00622527i | \(0.00198158\pi\) |
−0.937545 | + | 0.347863i | \(0.886907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.57444 | − | 18.6607i | −0.188129 | − | 0.982144i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.85844 | + | 0.676417i | −0.0972752 | + | 0.0354053i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.7815 | − | 11.5641i | −0.719390 | − | 0.603640i | 0.207827 | − | 0.978166i | \(-0.433361\pi\) |
−0.927216 | + | 0.374526i | \(0.877805\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.16132 | − | 17.9287i | 0.164128 | − | 0.930814i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.68004 | + | 2.90992i | −0.0869894 | + | 0.150670i | −0.906237 | − | 0.422770i | \(-0.861058\pi\) |
0.819248 | + | 0.573440i | \(0.194391\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.78833 | − | 3.17879i | 0.195109 | − | 0.163716i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.1584 | 0.778634 | 0.389317 | − | 0.921104i | \(-0.372711\pi\) | ||||
0.389317 | + | 0.921104i | \(0.372711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.46585 | + | 4.58639i | −0.279292 | + | 0.234354i | −0.771663 | − | 0.636032i | \(-0.780575\pi\) |
0.492371 | + | 0.870385i | \(0.336130\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.293386 | + | 0.106784i | 0.0149523 | + | 0.00544220i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.33006 | + | 24.5570i | −0.219543 | + | 1.24509i | 0.653304 | + | 0.757095i | \(0.273382\pi\) |
−0.872847 | + | 0.487994i | \(0.837729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00475 | − | 3.47232i | −0.101384 | − | 0.175603i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.33110 | − | 1.57639i | 0.217921 | − | 0.0793169i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.58647 | + | 20.3399i | 0.180000 | + | 1.02083i | 0.932213 | + | 0.361909i | \(0.117875\pi\) |
−0.752214 | + | 0.658919i | \(0.771014\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.30722 | − | 35.7700i | −0.314967 | − | 1.78627i | −0.572402 | − | 0.819973i | \(-0.693988\pi\) |
0.257434 | − | 0.966296i | \(-0.417123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.683144 | + | 0.248644i | −0.0340298 | + | 0.0123858i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0944557 | + | 0.163602i | 0.00468199 | + | 0.00810945i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.860662 | − | 4.88106i | 0.0425570 | − | 0.241353i | −0.956108 | − | 0.293016i | \(-0.905341\pi\) |
0.998665 | + | 0.0516631i | \(0.0164522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.70961 | + | 2.07813i | 0.280951 | + | 0.102258i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.5287 | − | 9.67372i | 0.565921 | − | 0.474864i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.0966 | 1.71458 | 0.857290 | − | 0.514834i | \(-0.172146\pi\) | ||||
0.857290 | + | 0.514834i | \(0.172146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0967 | + | 11.8286i | −0.687033 | + | 0.576489i | −0.918052 | − | 0.396460i | \(-0.870238\pi\) |
0.231019 | + | 0.972949i | \(0.425794\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.56418 | + | 11.3695i | −0.318409 | + | 0.551501i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.74170 | + | 15.5489i | −0.132680 | + | 0.752466i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.73648 | − | 5.65258i | −0.324485 | − | 0.272275i | 0.465963 | − | 0.884804i | \(-0.345708\pi\) |
−0.790448 | + | 0.612529i | \(0.790152\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.3614 | + | 5.95507i | −0.786280 | + | 0.286183i | −0.703789 | − | 0.710409i | \(-0.748510\pi\) |
−0.0824914 | + | 0.996592i | \(0.526288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.88548 | − | 5.30142i | 0.0901946 | − | 0.253601i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.94743 | − | 28.0583i | −0.236128 | − | 1.33915i | −0.840225 | − | 0.542238i | \(-0.817577\pi\) |
0.604097 | − | 0.796911i | \(-0.293534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.8216 | − | 11.5977i | −0.656684 | − | 0.551023i | 0.252407 | − | 0.967621i | \(-0.418778\pi\) |
−0.909091 | + | 0.416598i | \(0.863222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.86959 | + | 11.8985i | 0.325650 | + | 0.564042i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.76739 | − | 8.25736i | 0.224987 | − | 0.389689i | −0.731329 | − | 0.682025i | \(-0.761099\pi\) |
0.956316 | + | 0.292336i | \(0.0944327\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.61809 | − | 0.588936i | −0.0761928 | − | 0.0277319i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.45781 | −0.0683430 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4584 | 0.489224 | 0.244612 | − | 0.969621i | \(-0.421339\pi\) | ||||
0.244612 | + | 0.969621i | \(0.421339\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.1489 | + | 14.2490i | 1.82335 | + | 0.663644i | 0.994571 | + | 0.104061i | \(0.0331837\pi\) |
0.828775 | + | 0.559583i | \(0.189039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.90895 | + | 11.9666i | −0.321086 | + | 0.556137i | −0.980712 | − | 0.195456i | \(-0.937381\pi\) |
0.659626 | + | 0.751594i | \(0.270715\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.72668 | − | 6.45480i | −0.172450 | − | 0.298693i | 0.766826 | − | 0.641855i | \(-0.221835\pi\) |
−0.939276 | + | 0.343163i | \(0.888502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.78106 | − | 1.49449i | −0.0822417 | − | 0.0690090i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.00499613 | − | 0.0283345i | −0.000229722 | − | 0.00130282i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.1197 | + | 3.33272i | −0.831391 | + | 0.152916i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.3525 | − | 8.13565i | 1.02131 | − | 0.371727i | 0.223546 | − | 0.974693i | \(-0.428237\pi\) |
0.797767 | + | 0.602966i | \(0.206015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.675708 | − | 0.566986i | −0.0308096 | − | 0.0258523i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.43835 | + | 8.15728i | −0.0653120 | + | 0.370403i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.42855 | + | 4.20637i | −0.110048 | + | 0.190609i | −0.915789 | − | 0.401659i | \(-0.868434\pi\) |
0.805741 | + | 0.592268i | \(0.201767\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.29632 | − | 1.92684i | 0.103632 | − | 0.0869572i | −0.589500 | − | 0.807769i | \(-0.700675\pi\) |
0.693131 | + | 0.720811i | \(0.256231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.2439 | −0.911740 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.50846 | − | 7.13944i | 0.381656 | − | 0.320248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.37211 | − | 0.863378i | −0.106190 | − | 0.0386501i | 0.288379 | − | 0.957516i | \(-0.406884\pi\) |
−0.394569 | + | 0.918866i | \(0.629106\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.18614 | + | 18.0695i | −0.142063 | + | 0.805678i | 0.827616 | + | 0.561295i | \(0.189697\pi\) |
−0.969679 | + | 0.244383i | \(0.921414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.77244 | − | 4.80201i | −0.123372 | − | 0.213687i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.2922 | − | 5.56591i | 0.677815 | − | 0.246704i | 0.0199059 | − | 0.999802i | \(-0.493663\pi\) |
0.657909 | + | 0.753097i | \(0.271441\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.853226 | − | 4.83889i | −0.0377445 | − | 0.214060i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.31567 | − | 7.46156i | −0.0579755 | − | 0.328796i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.529563 | + | 0.192745i | −0.0232901 | + | 0.00847692i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.1454 | + | 24.5006i | 0.619723 | + | 1.07339i | 0.989536 | + | 0.144285i | \(0.0460882\pi\) |
−0.369814 | + | 0.929106i | \(0.620578\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.841833 | − | 4.77427i | 0.0368108 | − | 0.208764i | −0.960855 | − | 0.277052i | \(-0.910642\pi\) |
0.997666 | + | 0.0682878i | \(0.0217536\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.79648 | + | 1.01784i | 0.121817 | + | 0.0443377i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.3425 | + | 13.7130i | −0.710546 | + | 0.596219i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.04013 | 0.348257 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.85710 | − | 7.43199i | 0.382926 | − | 0.321313i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.180922 | − | 0.313366i | 0.00779287 | − | 0.0134976i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.22193 | + | 23.9438i | −0.181515 | + | 1.02942i | 0.748837 | + | 0.662755i | \(0.230613\pi\) |
−0.930352 | + | 0.366669i | \(0.880498\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.76991 | − | 5.68063i | −0.289991 | − | 0.243332i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.3999 | − | 7.78893i | 0.914994 | − | 0.333031i | 0.158749 | − | 0.987319i | \(-0.449254\pi\) |
0.756245 | + | 0.654288i | \(0.227032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.4209 | − | 21.6278i | −0.784755 | − | 0.921374i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.98845 | + | 11.2770i | 0.0845573 | + | 0.479548i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.6578 | − | 12.2993i | −0.621069 | − | 0.521139i | 0.277070 | − | 0.960850i | \(-0.410636\pi\) |
−0.898139 | + | 0.439711i | \(0.855081\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0671708 | + | 0.116343i | 0.00284102 | + | 0.00492080i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.6741 | + | 18.4881i | −0.449860 | + | 0.779181i | −0.998377 | − | 0.0569590i | \(-0.981860\pi\) |
0.548516 | + | 0.836140i | \(0.315193\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.64765 | + | 2.41955i | 0.279669 | + | 0.101791i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.2121 | −1.64386 | −0.821929 | − | 0.569590i | \(-0.807102\pi\) | ||||
−0.821929 | + | 0.569590i | \(0.807102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.27900 | −0.304617 | −0.152308 | − | 0.988333i | \(-0.548671\pi\) | ||||
−0.152308 | + | 0.988333i | \(0.548671\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.12701 | − | 1.86608i | −0.213811 | − | 0.0778209i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.49613 | + | 12.9837i | −0.312068 | + | 0.540518i | −0.978810 | − | 0.204771i | \(-0.934355\pi\) |
0.666742 | + | 0.745289i | \(0.267688\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.6951 | + | 32.3808i | 0.775602 | + | 1.34338i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.03730 | − | 0.870401i | −0.0429607 | − | 0.0360483i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.08559 | + | 11.8280i | 0.0860815 | + | 0.488192i | 0.997118 | + | 0.0758666i | \(0.0241723\pi\) |
−0.911037 | + | 0.412326i | \(0.864717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.45723 | + | 3.91382i | 0.0600443 | + | 0.161266i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.1866 | + | 12.4429i | −1.40388 | + | 0.510969i | −0.929326 | − | 0.369260i | \(-0.879611\pi\) |
−0.474549 | + | 0.880229i | \(0.657389\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.57145 | + | 3.83590i | 0.187411 | + | 0.157257i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.39739 | + | 13.5963i | −0.0979548 | + | 0.555529i | 0.895847 | + | 0.444363i | \(0.146570\pi\) |
−0.993802 | + | 0.111167i | \(0.964541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.483803 | − | 0.837972i | 0.0197347 | − | 0.0341816i | −0.855989 | − | 0.516993i | \(-0.827051\pi\) |
0.875724 | + | 0.482812i | \(0.160384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.39234 | + | 6.20291i | −0.300541 | + | 0.252184i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.53890 | 0.0624619 | 0.0312309 | − | 0.999512i | \(-0.490057\pi\) | ||||
0.0312309 | + | 0.999512i | \(0.490057\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.01573 | − | 1.69140i | 0.0815477 | − | 0.0684266i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.6921 | − | 14.0828i | −1.56276 | − | 0.568798i | −0.591393 | − | 0.806383i | \(-0.701422\pi\) |
−0.971367 | + | 0.237585i | \(0.923644\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.32857 | + | 30.2198i | −0.214520 | + | 1.21660i | 0.667217 | + | 0.744864i | \(0.267485\pi\) |
−0.881737 | + | 0.471741i | \(0.843626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.97906 | + | 10.3560i | 0.240319 | + | 0.416244i | 0.960805 | − | 0.277225i | \(-0.0894148\pi\) |
−0.720486 | + | 0.693469i | \(0.756081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.0758 | + | 11.6746i | −1.28509 | + | 0.467734i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.43077 | + | 13.7856i | 0.0972308 | + | 0.551423i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.627011 | + | 3.55596i | 0.0250006 | + | 0.141785i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.2708 | − | 16.4772i | 1.80220 | − | 0.655949i | 0.804094 | − | 0.594503i | \(-0.202651\pi\) |
0.998110 | − | 0.0614459i | \(-0.0195712\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.81567 | − | 15.2692i | −0.349839 | − | 0.605940i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.293386 | + | 1.66387i | −0.0116244 | + | 0.0659250i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.32383 | + | 2.30168i | 0.249776 | + | 0.0909111i | 0.463874 | − | 0.885901i | \(-0.346459\pi\) |
−0.214098 | + | 0.976812i | \(0.568681\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.6819 | + | 16.5150i | −0.776177 | + | 0.651290i | −0.942283 | − | 0.334818i | \(-0.891325\pi\) |
0.166106 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 50.4380 | 1.98292 | 0.991461 | − | 0.130403i | \(-0.0416271\pi\) | ||||
0.991461 | + | 0.130403i | \(0.0416271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.346201 | − | 0.290497i | 0.0135896 | − | 0.0114030i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.9304 | + | 31.0563i | −0.701669 | + | 1.21533i | 0.266211 | + | 0.963915i | \(0.414228\pi\) |
−0.967880 | + | 0.251412i | \(0.919105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.42943 | − | 13.7780i | 0.0949255 | − | 0.538349i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.66044 | + | 8.10608i | 0.376317 | + | 0.315768i | 0.811255 | − | 0.584693i | \(-0.198785\pi\) |
−0.434937 | + | 0.900461i | \(0.643229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.8820 | − | 15.2438i | 1.62902 | − | 0.592915i | 0.643950 | − | 0.765068i | \(-0.277295\pi\) |
0.985070 | + | 0.172153i | \(0.0550724\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0616516 | + | 8.37441i | 0.00239074 | + | 0.324746i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.46094 | − | 8.28541i | −0.0565679 | − | 0.320812i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.899615 | + | 0.754866i | 0.0347292 | + | 0.0291413i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.41013 | + | 11.1027i | 0.247092 | + | 0.427977i | 0.962718 | − | 0.270508i | \(-0.0871916\pi\) |
−0.715625 | + | 0.698484i | \(0.753858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6844 | + | 25.4341i | −0.564367 | + | 0.977512i | 0.432742 | + | 0.901518i | \(0.357546\pi\) |
−0.997108 | + | 0.0759937i | \(0.975787\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.3380 | − | 7.03844i | −0.742123 | − | 0.270111i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.0033 | −1.45416 | −0.727078 | − | 0.686555i | \(-0.759122\pi\) | ||||
−0.727078 | + | 0.686555i | \(0.759122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.43613 | 0.169496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.94134 | + | 2.16247i | 0.226347 | + | 0.0823836i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.1459 | + | 27.9655i | −0.614219 | + | 1.06386i | 0.376302 | + | 0.926497i | \(0.377195\pi\) |
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.64068 | + | 8.03790i | 0.176031 | + | 0.304895i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.2126 | − | 21.1559i | −0.954995 | − | 0.801336i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.01367 | − | 22.7627i | −0.151594 | − | 0.859734i | −0.961834 | − | 0.273635i | \(-0.911774\pi\) |
0.810239 | − | 0.586099i | \(-0.199337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.22849 | + | 3.90560i | −0.121765 | + | 0.147303i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.9452 | − | 4.71167i | 0.486855 | − | 0.177201i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.1589 | + | 23.6281i | 1.05753 | + | 0.887371i | 0.993865 | − | 0.110600i | \(-0.0352773\pi\) |
0.0636629 | + | 0.997971i | \(0.479722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.214766 | + | 1.21800i | −0.00804304 | + | 0.0456143i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0542155 | + | 0.0939039i | −0.00202754 | + | 0.00351181i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.2414 | + | 21.1801i | −0.941347 | + | 0.789884i | −0.977819 | − | 0.209451i | \(-0.932832\pi\) |
0.0364721 | + | 0.999335i | \(0.488388\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8239 | 0.701038 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.1027 | + | 17.7072i | −0.783733 | + | 0.657630i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.44521 | + | 2.70984i | 0.276128 | + | 0.100502i | 0.476372 | − | 0.879244i | \(-0.341951\pi\) |
−0.200245 | + | 0.979746i | \(0.564174\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0954951 | − | 0.541580i | 0.00353202 | − | 0.0200311i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.71735 | + | 6.43864i | 0.137303 | + | 0.237816i | 0.926475 | − | 0.376356i | \(-0.122823\pi\) |
−0.789172 | + | 0.614173i | \(0.789490\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.162504 | + | 0.0591466i | −0.00598591 | + | 0.00217869i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.36009 | + | 19.0560i | 0.123603 | + | 0.700987i | 0.982128 | + | 0.188215i | \(0.0602702\pi\) |
−0.858525 | + | 0.512772i | \(0.828619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.44965 | − | 30.9065i | −0.199928 | − | 1.13385i | −0.905223 | − | 0.424936i | \(-0.860296\pi\) |
0.705295 | − | 0.708914i | \(-0.250815\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.4000 | − | 4.14927i | 0.417665 | − | 0.152017i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.3628 | + | 24.8771i | 0.524804 | + | 0.908988i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.906889 | − | 5.14322i | 0.0330928 | − | 0.187679i | −0.963780 | − | 0.266697i | \(-0.914068\pi\) |
0.996873 | + | 0.0790187i | \(0.0251787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.7618 | + | 6.10078i | 0.610023 | + | 0.222030i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.8063 | + | 19.1368i | −0.828911 | + | 0.695539i | −0.955041 | − | 0.296475i | \(-0.904189\pi\) |
0.126130 | + | 0.992014i | \(0.459744\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.35267 | 0.339034 | 0.169517 | − | 0.985527i | \(-0.445779\pi\) | ||||
0.169517 | + | 0.985527i | \(0.445779\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.8195 | − | 14.1133i | 0.608908 | − | 0.510935i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.05509 | + | 1.82747i | −0.0380972 | + | 0.0659863i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.74335 | − | 38.2434i | 0.243171 | − | 1.37909i | −0.581530 | − | 0.813525i | \(-0.697546\pi\) |
0.824702 | − | 0.565568i | \(-0.191343\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.2069 | + | 15.2774i | 0.654857 | + | 0.549491i | 0.908540 | − | 0.417797i | \(-0.137198\pi\) |
−0.253683 | + | 0.967287i | \(0.581642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.80541 | − | 1.38505i | 0.136694 | − | 0.0497526i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.340022 | − | 46.1868i | −0.0121826 | − | 1.65481i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.143457 | − | 0.813583i | −0.00513328 | − | 0.0291123i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.87551 | − | 7.44744i | −0.316781 | − | 0.265811i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.87804 | + | 11.9131i | 0.245176 | + | 0.424657i | 0.962181 | − | 0.272411i | \(-0.0878210\pi\) |
−0.717005 | + | 0.697068i | \(0.754488\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.78787 | + | 15.2210i | −0.312461 | + | 0.541198i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.15270 | − | 1.87543i | −0.182978 | − | 0.0665985i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.77238 | 0.275312 | 0.137656 | − | 0.990480i | \(-0.456043\pi\) | ||||
0.137656 | + | 0.990480i | \(0.456043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.7716 | −0.381071 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.343426 | − | 0.124997i | −0.0121192 | − | 0.00441104i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.24005 | + | 2.14783i | −0.0437059 | + | 0.0757009i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.84595 | + | 11.8575i | 0.240691 | + | 0.416889i | 0.960911 | − | 0.276857i | \(-0.0892927\pi\) |
−0.720220 | + | 0.693745i | \(0.755959\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.9360 | − | 14.2110i | −0.594705 | − | 0.499017i | 0.295034 | − | 0.955487i | \(-0.404669\pi\) |
−0.889739 | + | 0.456470i | \(0.849114\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.67082 | − | 15.1470i | −0.0935546 | − | 0.530575i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.665497 | − | 0.390785i | 0.0232828 | − | 0.0136718i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.2763 | + | 7.37997i | −0.707648 | + | 0.257563i | −0.670673 | − | 0.741753i | \(-0.733995\pi\) |
−0.0369753 | + | 0.999316i | \(0.511772\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.16431 | − | 6.01157i | −0.249732 | − | 0.209550i | 0.509325 | − | 0.860574i | \(-0.329895\pi\) |
−0.759057 | + | 0.651024i | \(0.774340\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.83110 | − | 33.0698i | 0.202767 | − | 1.14995i | −0.698148 | − | 0.715954i | \(-0.745992\pi\) |
0.900915 | − | 0.433996i | \(-0.142897\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.325170 | + | 0.563211i | −0.0112936 | + | 0.0195611i | −0.871617 | − | 0.490188i | \(-0.836928\pi\) |
0.860323 | + | 0.509749i | \(0.170262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.29813 | − | 4.44566i | 0.183569 | − | 0.154033i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.1088 | −0.453647 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.5483 | − | 14.7248i | 0.605834 | − | 0.508355i | −0.287481 | − | 0.957786i | \(-0.592818\pi\) |
0.893315 | + | 0.449431i | \(0.148373\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.6655 | − | 4.60986i | −0.436741 | − | 0.158961i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.89723 | + | 10.7597i | −0.0652667 | + | 0.370146i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.9875 | − | 20.7630i | −0.411896 | − | 0.713424i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.41013 | + | 0.513245i | −0.0483386 | + | 0.0175938i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.29901 | + | 30.0522i | 0.181435 | + | 1.02897i | 0.930451 | + | 0.366416i | \(0.119415\pi\) |
−0.749017 | + | 0.662551i | \(0.769474\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.13387 | − | 17.7731i | −0.107051 | − | 0.607117i | −0.990381 | − | 0.138366i | \(-0.955815\pi\) |
0.883330 | − | 0.468751i | \(-0.155296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.6612 | + | 12.6157i | −1.18263 | + | 0.430440i | −0.857129 | − | 0.515103i | \(-0.827754\pi\) |
−0.325497 | + | 0.945543i | \(0.605532\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.0856 | − | 24.3970i | −0.479479 | − | 0.830482i | 0.520244 | − | 0.854018i | \(-0.325841\pi\) |
−0.999723 | + | 0.0235356i | \(0.992508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.274196 | + | 1.55504i | −0.00932294 | + | 0.0528730i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.800355 | + | 0.291305i | 0.0271502 | + | 0.00988186i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.618555 | − | 0.519030i | 0.0209589 | − | 0.0175866i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.7270 | 0.599282 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.73758 | − | 8.17080i | 0.328815 | − | 0.275908i | −0.463402 | − | 0.886148i | \(-0.653371\pi\) |
0.792217 | + | 0.610240i | \(0.208927\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.4265 | − | 31.9156i | 0.620804 | − | 1.07526i | −0.368532 | − | 0.929615i | \(-0.620140\pi\) |
0.989336 | − | 0.145649i | \(-0.0465271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.88073 | + | 39.0226i | −0.231555 | + | 1.31321i | 0.618194 | + | 0.786026i | \(0.287865\pi\) |
−0.849749 | + | 0.527188i | \(0.823246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.3915 | + | 30.5361i | 1.22191 | + | 1.02530i | 0.998723 | + | 0.0505241i | \(0.0160892\pi\) |
0.223183 | + | 0.974777i | \(0.428355\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.1626 | − | 14.9819i | 1.38055 | − | 0.502478i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.80154 | − | 11.5079i | −0.327996 | − | 0.385097i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.19640 | − | 6.78514i | −0.0399914 | − | 0.226802i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.78359 | + | 4.01390i | 0.159542 | + | 0.133871i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.9410 | − | 22.4145i | −0.431128 | − | 0.746736i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.184326 | − | 0.319261i | 0.00612719 | − | 0.0106126i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.6186 | − | 7.86851i | −0.717832 | − | 0.261270i | −0.0428271 | − | 0.999083i | \(-0.513636\pi\) |
−0.675005 | + | 0.737813i | \(0.735859\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.7888 | −0.456843 | −0.228422 | − | 0.973562i | \(-0.573356\pi\) | ||||
−0.228422 | + | 0.973562i | \(0.573356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.78106 | 0.0920396 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 32.6626 | + | 11.8882i | 1.07861 | + | 0.392583i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.3312 | + | 47.3390i | −0.901572 | + | 1.56157i | −0.0761174 | + | 0.997099i | \(0.524252\pi\) |
−0.825454 | + | 0.564469i | \(0.809081\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.92871 | + | 3.34062i | 0.0634843 | + | 0.109958i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.76399 | + | 3.15836i | 0.123759 | + | 0.103846i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.12819 | − | 46.0973i | −0.266677 | − | 1.51240i | −0.764216 | − | 0.644961i | \(-0.776874\pi\) |
0.497538 | − | 0.867442i | \(-0.334237\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.57057 | + | 1.61500i | 0.313663 | + | 0.0529294i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.417099 | − | 0.151812i | 0.0136406 | − | 0.00496477i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.3555 | − | 24.6322i | −0.959003 | − | 0.804699i | 0.0217880 | − | 0.999763i | \(-0.493064\pi\) |
−0.980791 | + | 0.195064i | \(0.937509\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.11540 | − | 29.0109i | 0.166757 | − | 0.945728i | −0.780477 | − | 0.625185i | \(-0.785024\pi\) |
0.947234 | − | 0.320543i | \(-0.103865\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.83915 | − | 11.8457i | 0.222713 | − | 0.385751i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.0540 | − | 24.3792i | 0.944127 | − | 0.792217i | −0.0341717 | − | 0.999416i | \(-0.510879\pi\) |
0.978299 | + | 0.207199i | \(0.0664349\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.70645 | 0.0553938 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.30659 | − | 5.29186i | 0.204290 | − | 0.171420i | −0.534902 | − | 0.844914i | \(-0.679652\pi\) |
0.739193 | + | 0.673494i | \(0.235207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.1468 | − | 5.87695i | −0.522497 | − | 0.190173i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.91384 | + | 10.8539i | −0.0618011 | + | 0.350491i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0410 | + | 26.0518i | 0.485194 | + | 0.840381i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.7512 | − | 5.00502i | 0.442667 | − | 0.161117i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.81820 | − | 15.9828i | −0.0906272 | − | 0.513972i | −0.996000 | − | 0.0893546i | \(-0.971520\pi\) |
0.905373 | − | 0.424618i | \(-0.139592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.76445 | − | 32.6918i | −0.184990 | − | 1.04913i | −0.925968 | − | 0.377602i | \(-0.876749\pi\) |
0.740978 | − | 0.671529i | \(-0.234362\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.6685 | + | 7.88669i | −0.694660 | + | 0.252836i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.9966 | + | 20.7787i | 0.383805 | + | 0.664770i | 0.991603 | − | 0.129322i | \(-0.0412801\pi\) |
−0.607798 | + | 0.794092i | \(0.707947\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.440875 | + | 2.50032i | −0.0140904 | + | 0.0799107i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.6921 | + | 15.9026i | 1.39356 | + | 0.507215i | 0.926261 | − | 0.376883i | \(-0.123004\pi\) |
0.467301 | + | 0.884098i | \(0.345226\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.8175 | − | 12.4333i | 0.472124 | − | 0.396159i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.228549 | 0.00726743 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0041 | − | 22.6591i | 0.857813 | − | 0.719791i | −0.103683 | − | 0.994610i | \(-0.533063\pi\) |
0.961496 | + | 0.274820i | \(0.0886182\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.56077 | − | 16.5597i | 0.303097 | − | 0.524979i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.65270 | − | 54.7432i | 0.305704 | − | 1.73373i | −0.314467 | − | 0.949268i | \(-0.601826\pi\) |
0.620171 | − | 0.784466i | \(-0.287063\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 684.2.bo.a.541.1 | 6 | ||
3.2 | odd | 2 | 228.2.q.a.85.1 | ✓ | 6 | ||
12.11 | even | 2 | 912.2.bo.e.769.1 | 6 | |||
19.17 | even | 9 | inner | 684.2.bo.a.397.1 | 6 | ||
57.17 | odd | 18 | 228.2.q.a.169.1 | yes | 6 | ||
57.32 | even | 18 | 4332.2.a.n.1.1 | 3 | |||
57.44 | odd | 18 | 4332.2.a.o.1.1 | 3 | |||
228.131 | even | 18 | 912.2.bo.e.625.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.q.a.85.1 | ✓ | 6 | 3.2 | odd | 2 | ||
228.2.q.a.169.1 | yes | 6 | 57.17 | odd | 18 | ||
684.2.bo.a.397.1 | 6 | 19.17 | even | 9 | inner | ||
684.2.bo.a.541.1 | 6 | 1.1 | even | 1 | trivial | ||
912.2.bo.e.625.1 | 6 | 228.131 | even | 18 | |||
912.2.bo.e.769.1 | 6 | 12.11 | even | 2 | |||
4332.2.a.n.1.1 | 3 | 57.32 | even | 18 | |||
4332.2.a.o.1.1 | 3 | 57.44 | odd | 18 |