Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), degree \(2\), not 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: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.3 | ||
Character | \(\chi\) | \(=\) | 1008.593 |
Dual form | 1008.4.bt.d.17.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −8.48442 | + | 14.6954i | −0.758869 | + | 1.31440i | 0.184558 | + | 0.982822i | \(0.440914\pi\) |
−0.943428 | + | 0.331578i | \(0.892419\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.52711 | − | 18.1813i | −0.190446 | − | 0.981698i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −60.3894 | + | 34.8658i | −1.65528 | + | 0.955677i | −0.680431 | + | 0.732812i | \(0.738208\pi\) |
−0.974849 | + | 0.222865i | \(0.928459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 38.2009i | − | 0.815001i | −0.913205 | − | 0.407501i | \(-0.866400\pi\) | ||
0.913205 | − | 0.407501i | \(-0.133600\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 52.9872 | + | 91.7766i | 0.755958 | + | 1.30936i | 0.944897 | + | 0.327369i | \(0.106162\pi\) |
−0.188938 | + | 0.981989i | \(0.560505\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.3954 | − | 29.0958i | −0.608499 | − | 0.351317i | 0.163879 | − | 0.986481i | \(-0.447599\pi\) |
−0.772378 | + | 0.635163i | \(0.780933\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −107.941 | − | 62.3199i | −0.978578 | − | 0.564982i | −0.0767375 | − | 0.997051i | \(-0.524450\pi\) |
−0.901841 | + | 0.432069i | \(0.857784\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −81.4706 | − | 141.111i | −0.651765 | − | 1.12889i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 66.5957i | 0.426431i | 0.977005 | + | 0.213216i | \(0.0683937\pi\) | ||||
−0.977005 | + | 0.213216i | \(0.931606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 136.580 | − | 78.8547i | 0.791309 | − | 0.456862i | −0.0491145 | − | 0.998793i | \(-0.515640\pi\) |
0.840423 | + | 0.541931i | \(0.182307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 297.108 | + | 102.425i | 1.43487 | + | 0.494658i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −107.191 | + | 185.660i | −0.476271 | + | 0.824926i | −0.999630 | − | 0.0271864i | \(-0.991345\pi\) |
0.523359 | + | 0.852112i | \(0.324679\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −448.509 | −1.70842 | −0.854212 | − | 0.519925i | \(-0.825960\pi\) | ||||
−0.854212 | + | 0.519925i | \(0.825960\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 320.784 | 1.13765 | 0.568827 | − | 0.822457i | \(-0.307397\pi\) | ||||
0.568827 | + | 0.822457i | \(0.307397\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 87.8142 | − | 152.099i | 0.272532 | − | 0.472040i | −0.696977 | − | 0.717093i | \(-0.745472\pi\) |
0.969510 | + | 0.245054i | \(0.0788056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −318.119 | + | 128.255i | −0.927461 | + | 0.373921i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 585.770 | − | 338.194i | 1.51815 | − | 0.876502i | 0.518373 | − | 0.855155i | \(-0.326538\pi\) |
0.999772 | − | 0.0213470i | \(-0.00679548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1183.26i | − | 2.90093i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −343.373 | − | 594.740i | −0.757685 | − | 1.31235i | −0.944028 | − | 0.329864i | \(-0.892997\pi\) |
0.186344 | − | 0.982485i | \(-0.440336\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −91.1567 | − | 52.6294i | −0.191335 | − | 0.110467i | 0.401272 | − | 0.915959i | \(-0.368568\pi\) |
−0.592607 | + | 0.805492i | \(0.701901\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 561.379 | + | 324.112i | 1.07124 | + | 0.618479i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 426.641 | + | 738.964i | 0.777948 | + | 1.34745i | 0.933122 | + | 0.359559i | \(0.117073\pi\) |
−0.155174 | + | 0.987887i | \(0.549594\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 21.6022i | 0.0361086i | 0.999837 | + | 0.0180543i | \(0.00574718\pi\) | ||||
−0.999837 | + | 0.0180543i | \(0.994253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 296.300 | − | 171.069i | 0.475059 | − | 0.274276i | −0.243296 | − | 0.969952i | \(-0.578229\pi\) |
0.718355 | + | 0.695676i | \(0.244895\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 846.906 | + | 974.982i | 1.25343 | + | 1.44298i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 156.927 | − | 271.805i | 0.223489 | − | 0.387095i | −0.732376 | − | 0.680901i | \(-0.761589\pi\) |
0.955865 | + | 0.293806i | \(0.0949219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 627.751 | 0.830176 | 0.415088 | − | 0.909781i | \(-0.363751\pi\) | ||||
0.415088 | + | 0.909781i | \(0.363751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1798.26 | −2.29469 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 207.480 | − | 359.367i | 0.247111 | − | 0.428009i | −0.715612 | − | 0.698498i | \(-0.753852\pi\) |
0.962723 | + | 0.270489i | \(0.0871854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −694.541 | + | 134.739i | −0.800085 | + | 0.155214i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 855.150 | − | 493.721i | 0.923543 | − | 0.533208i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 223.956i | 0.234426i | 0.993107 | + | 0.117213i | \(0.0373960\pi\) | ||||
−0.993107 | + | 0.117213i | \(0.962604\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 974.570 | + | 1688.01i | 0.960133 | + | 1.66300i | 0.722160 | + | 0.691727i | \(0.243150\pi\) |
0.237973 | + | 0.971272i | \(0.423517\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 755.905 | + | 436.422i | 0.723122 | + | 0.417495i | 0.815901 | − | 0.578192i | \(-0.196242\pi\) |
−0.0927787 | + | 0.995687i | \(0.529575\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −490.143 | − | 282.984i | −0.442840 | − | 0.255674i | 0.261961 | − | 0.965078i | \(-0.415631\pi\) |
−0.704802 | + | 0.709404i | \(0.748964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 781.523 | + | 1353.64i | 0.686755 | + | 1.18949i | 0.972882 | + | 0.231303i | \(0.0742988\pi\) |
−0.286127 | + | 0.958192i | \(0.592368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1609.24i | − | 1.33969i | −0.742502 | − | 0.669844i | \(-0.766361\pi\) | ||
0.742502 | − | 0.669844i | \(-0.233639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1831.64 | − | 1057.50i | 1.48523 | − | 0.857495i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1481.72 | − | 1287.08i | 1.14142 | − | 0.991484i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1765.75 | − | 3058.37i | 1.32664 | − | 2.29780i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 643.818 | 0.460679 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 741.194 | 0.517877 | 0.258938 | − | 0.965894i | \(-0.416627\pi\) | ||||
0.258938 | + | 0.965894i | \(0.416627\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −132.345 | + | 229.229i | −0.0882676 | + | 0.152884i | −0.906779 | − | 0.421606i | \(-0.861466\pi\) |
0.818511 | + | 0.574490i | \(0.194800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −351.249 | + | 1018.88i | −0.229001 | + | 0.664269i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1028.68 | − | 593.907i | 0.641502 | − | 0.370372i | −0.143691 | − | 0.989623i | \(-0.545897\pi\) |
0.785193 | + | 0.619251i | \(0.212564\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1080.39i | − | 0.659262i | −0.944110 | − | 0.329631i | \(-0.893076\pi\) | ||
0.944110 | − | 0.329631i | \(-0.106924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1331.91 | + | 2306.93i | 0.778878 | + | 1.34906i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −978.653 | − | 565.026i | −0.560501 | − | 0.323606i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.97793 | + | 4.60606i | 0.00438643 | + | 0.00253251i | 0.502192 | − | 0.864756i | \(-0.332527\pi\) |
−0.497805 | + | 0.867289i | \(0.665861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −978.571 | − | 1694.94i | −0.527384 | − | 0.913456i | −0.999491 | − | 0.0319147i | \(-0.989840\pi\) |
0.472106 | − | 0.881542i | \(-0.343494\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2676.15i | 1.38679i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −188.970 | + | 109.102i | −0.0960600 | + | 0.0554603i | −0.547260 | − | 0.836962i | \(-0.684329\pi\) |
0.451200 | + | 0.892423i | \(0.350996\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −752.336 | + | 2182.32i | −0.368276 | + | 1.06827i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1095.52 | − | 1897.50i | 0.526430 | − | 0.911803i | −0.473096 | − | 0.881011i | \(-0.656864\pi\) |
0.999526 | − | 0.0307921i | \(-0.00980298\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1567.81 | 0.726471 | 0.363235 | − | 0.931697i | \(-0.381672\pi\) | ||||
0.363235 | + | 0.931697i | \(0.381672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 737.693 | 0.335773 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 388.338 | − | 672.621i | 0.170664 | − | 0.295598i | −0.767989 | − | 0.640464i | \(-0.778742\pi\) |
0.938652 | + | 0.344866i | \(0.112076\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2278.23 | + | 1978.96i | −0.984103 | + | 0.854829i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1513.06 | − | 873.568i | 0.631797 | − | 0.364768i | −0.149650 | − | 0.988739i | \(-0.547815\pi\) |
0.781448 | + | 0.623971i | \(0.214482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1787.57i | − | 0.734085i | −0.930204 | − | 0.367042i | \(-0.880370\pi\) | ||
0.930204 | − | 0.367042i | \(-0.119630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1818.90 | − | 3150.43i | −0.722855 | − | 1.25202i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6399.73 | − | 3694.89i | −2.50265 | − | 1.44490i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −588.184 | − | 339.588i | −0.222825 | − | 0.128648i | 0.384433 | − | 0.923153i | \(-0.374397\pi\) |
−0.607258 | + | 0.794505i | \(0.707730\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1698.73 | − | 2942.29i | −0.633562 | − | 1.09736i | −0.986818 | − | 0.161835i | \(-0.948259\pi\) |
0.353255 | − | 0.935527i | \(-0.385075\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3407.09i | 1.23221i | 0.787665 | + | 0.616104i | \(0.211290\pi\) | ||||
−0.787665 | + | 0.616104i | \(0.788710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −181.152 | + | 104.588i | −0.0645302 | + | 0.0372565i | −0.531918 | − | 0.846796i | \(-0.678529\pi\) |
0.467388 | + | 0.884052i | \(0.345195\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1210.80 | − | 234.890i | 0.418627 | − | 0.0812122i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3805.34 | − | 6591.04i | 1.29647 | − | 2.24555i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4057.79 | 1.34298 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2275.52 | −0.742434 | −0.371217 | − | 0.928546i | \(-0.621059\pi\) | ||||
−0.371217 | + | 0.928546i | \(0.621059\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2721.67 | + | 4714.06i | −0.863331 | + | 1.49533i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1915.42 | − | 2205.08i | −0.599202 | − | 0.689818i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3505.94 | − | 2024.16i | 1.06713 | − | 0.616107i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3401.49i | 1.02144i | 0.859747 | + | 0.510719i | \(0.170621\pi\) | ||||
−0.859747 | + | 0.510719i | \(0.829379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1502.78 | − | 2602.90i | −0.439397 | − | 0.761058i | 0.558246 | − | 0.829676i | \(-0.311475\pi\) |
−0.997643 | + | 0.0686172i | \(0.978141\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −397.955 | − | 229.759i | −0.114837 | − | 0.0663009i | 0.441482 | − | 0.897270i | \(-0.354453\pi\) |
−0.556318 | + | 0.830969i | \(0.687786\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5044.86 | − | 2912.65i | −1.41845 | − | 0.818944i | −0.422290 | − | 0.906461i | \(-0.638774\pi\) |
−0.996163 | + | 0.0875166i | \(0.972107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1490.10 | + | 2580.94i | 0.413633 | + | 0.716433i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4219.42i | − | 1.14197i | −0.820959 | − | 0.570987i | \(-0.806561\pi\) | ||
0.820959 | − | 0.570987i | \(-0.193439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2837.81 | − | 1638.41i | 0.758503 | − | 0.437922i | −0.0702548 | − | 0.997529i | \(-0.522381\pi\) |
0.828758 | + | 0.559607i | \(0.189048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 814.292 | − | 5763.07i | 0.212340 | − | 1.50281i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1111.48 | + | 1925.15i | −0.286324 | + | 0.495928i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3221.43 | 0.810100 | 0.405050 | − | 0.914294i | \(-0.367254\pi\) | ||||
0.405050 | + | 0.914294i | \(0.367254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8691.34 | 2.15976 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −411.892 | + | 713.418i | −0.0999732 | + | 0.173159i | −0.911673 | − | 0.410916i | \(-0.865209\pi\) |
0.811700 | + | 0.584074i | \(0.198542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3753.61 | + | 1294.02i | 0.900532 | + | 0.310450i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2955.61 | − | 1706.42i | 0.692969 | − | 0.400086i | −0.111754 | − | 0.993736i | \(-0.535647\pi\) |
0.804723 | + | 0.593650i | \(0.202314\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11477.5i | 2.66060i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3209.91 | + | 5559.73i | 0.727553 | + | 1.26016i | 0.957914 | + | 0.287054i | \(0.0926758\pi\) |
−0.230361 | + | 0.973105i | \(0.573991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7375.18 | − | 4258.06i | −1.65317 | − | 0.954461i | −0.975756 | − | 0.218863i | \(-0.929765\pi\) |
−0.677419 | − | 0.735597i | \(-0.736902\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9839.92 | + | 5681.08i | 2.15771 | + | 1.24575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3028.50 | + | 5245.52i | 0.656914 | + | 1.13781i | 0.981410 | + | 0.191921i | \(0.0614717\pi\) |
−0.324497 | + | 0.945887i | \(0.605195\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4217.81i | − | 0.895421i | −0.894179 | − | 0.447710i | \(-0.852240\pi\) | ||
0.894179 | − | 0.447710i | \(-0.147760\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 708.451 | − | 409.024i | 0.148809 | − | 0.0859151i | −0.423747 | − | 0.905781i | \(-0.639285\pi\) |
0.572556 | + | 0.819866i | \(0.305952\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1581.94 | + | 8154.48i | 0.325363 | + | 1.67716i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3158.79 | + | 5471.19i | −0.642945 | + | 1.11361i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −699.920 | −0.139556 | −0.0697778 | − | 0.997563i | \(-0.522229\pi\) | ||||
−0.0697778 | + | 0.997563i | \(0.522229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11653.3 | 2.29993 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2380.67 | + | 4123.45i | −0.460461 | + | 0.797542i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1131.44 | − | 5832.27i | −0.216662 | − | 1.11683i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1546.82 | − | 893.059i | 0.290396 | − | 0.167660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8523.88i | 1.58464i | 0.610108 | + | 0.792319i | \(0.291126\pi\) | ||||
−0.610108 | + | 0.792319i | \(0.708874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1170.89 | − | 2028.04i | −0.213489 | − | 0.369774i | 0.739315 | − | 0.673360i | \(-0.235149\pi\) |
−0.952804 | + | 0.303586i | \(0.901816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3462.94 | + | 1999.33i | 0.625357 | + | 0.361050i | 0.778952 | − | 0.627084i | \(-0.215752\pi\) |
−0.153595 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6056.74 | − | 3496.86i | −1.07312 | − | 0.619569i | −0.144091 | − | 0.989564i | \(-0.546026\pi\) |
−0.929034 | + | 0.369996i | \(0.879359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2321.91 | − | 4021.67i | −0.407531 | − | 0.705864i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6166.82i | − | 1.06232i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5390.57 | + | 3112.25i | −0.920047 | + | 0.531189i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3075.08 | − | 1060.11i | −0.515303 | − | 0.177646i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2095.81 | + | 3630.05i | −0.348025 | + | 0.602797i | −0.985899 | − | 0.167344i | \(-0.946481\pi\) |
0.637874 | + | 0.770141i | \(0.279814\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14479.2 | −2.36144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2226.74 | 0.359936 | 0.179968 | − | 0.983672i | \(-0.442401\pi\) | ||||
0.179968 | + | 0.983672i | \(0.442401\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5498.67 | + | 9523.98i | −0.873225 | + | 1.51247i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3453.88 | + | 5331.45i | 0.543708 | + | 0.839274i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1073.31 | − | 619.673i | 0.166046 | − | 0.0958668i | −0.414674 | − | 0.909970i | \(-0.636104\pi\) |
0.580720 | + | 0.814103i | \(0.302771\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8806.73i | − | 1.35075i | −0.737473 | − | 0.675377i | \(-0.763981\pi\) | ||
0.737473 | − | 0.675377i | \(-0.236019\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2424.56 | + | 4199.45i | 0.365570 | + | 0.633185i | 0.988867 | − | 0.148799i | \(-0.0475409\pi\) |
−0.623298 | + | 0.781985i | \(0.714208\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −317.454 | − | 183.282i | −0.0474612 | − | 0.0274017i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1691.26 | − | 976.450i | −0.248639 | − | 0.143552i | 0.370502 | − | 0.928832i | \(-0.379186\pi\) |
−0.619141 | + | 0.785280i | \(0.712519\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1736.37 | − | 3007.49i | −0.253152 | − | 0.438473i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5805.69i | 0.832557i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1159.84 | − | 669.633i | 0.164968 | − | 0.0952440i | −0.415243 | − | 0.909710i | \(-0.636304\pi\) |
0.580211 | + | 0.814466i | \(0.302970\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8214.89 | − | 9457.21i | −1.14958 | − | 1.32343i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3493.37 | − | 6050.69i | 0.484933 | − | 0.839928i | −0.514918 | − | 0.857240i | \(-0.672177\pi\) |
0.999850 | + | 0.0173119i | \(0.00551082\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2544.01 | 0.347542 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5328.03 | −0.722117 | −0.361059 | − | 0.932543i | \(-0.617585\pi\) | ||||
−0.361059 | + | 0.932543i | \(0.617585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2600.62 | + | 4504.40i | −0.346959 | + | 0.600951i | −0.985708 | − | 0.168465i | \(-0.946119\pi\) |
0.638749 | + | 0.769416i | \(0.279452\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21513.3 | + | 4173.51i | −2.84784 | + | 0.552472i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2739.35 | − | 1581.56i | 0.357045 | − | 0.206140i | −0.310739 | − | 0.950495i | \(-0.600576\pi\) |
0.667784 | + | 0.744355i | \(0.267243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 13208.6i | − | 1.70841i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2662.87 | + | 4612.22i | 0.339198 | + | 0.587509i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6689.56 | + | 3862.22i | 0.845692 | + | 0.488260i | 0.859195 | − | 0.511649i | \(-0.170965\pi\) |
−0.0135032 | + | 0.999909i | \(0.504298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8214.37 | − | 4742.57i | −1.02296 | − | 0.590605i | −0.107999 | − | 0.994151i | \(-0.534444\pi\) |
−0.914959 | + | 0.403546i | \(0.867778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3012.32 | − | 5217.49i | −0.372343 | − | 0.644917i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14949.2i | − | 1.82064i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13564.1 | + | 7831.22i | −1.63985 | + | 0.946770i | −0.658971 | + | 0.752168i | \(0.729008\pi\) |
−0.980882 | + | 0.194602i | \(0.937659\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9602.03 | + | 8340.69i | −1.14403 | + | 0.993749i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5326.10 | + | 9225.07i | −0.629995 | + | 1.09118i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13214.3 | −1.54071 | −0.770357 | − | 0.637613i | \(-0.779922\pi\) | ||||
−0.770357 | + | 0.637613i | \(0.779922\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3985.81 | −0.461417 | −0.230709 | − | 0.973023i | \(-0.574104\pi\) | ||||
−0.230709 | + | 0.973023i | \(0.574104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8633.80 | − | 14954.2i | 0.985414 | − | 1.70679i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −635.350 | + | 1842.98i | −0.0720064 | + | 0.208871i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −875.377 | + | 505.399i | −0.0978316 | + | 0.0564831i | −0.548118 | − | 0.836401i | \(-0.684655\pi\) |
0.450286 | + | 0.892884i | \(0.351322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10704.5i | 1.18805i | 0.804446 | + | 0.594026i | \(0.202462\pi\) | ||||
−0.804446 | + | 0.594026i | \(0.797538\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3626.49 | + | 6281.26i | 0.396976 | + | 0.687583i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5935.42 | + | 3426.82i | 0.645289 | + | 0.372558i | 0.786649 | − | 0.617400i | \(-0.211814\pi\) |
−0.141360 | + | 0.989958i | \(0.545147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13821.3 | − | 7979.76i | −1.48233 | − | 0.855823i | −0.482531 | − | 0.875879i | \(-0.660282\pi\) |
−0.999799 | + | 0.0200558i | \(0.993616\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3520.70 | + | 6098.03i | 0.375050 | + | 0.649605i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2486.47i | 0.261345i | 0.991426 | + | 0.130673i | \(0.0417137\pi\) | ||||
−0.991426 | + | 0.130673i | \(0.958286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27085.2 | − | 15637.6i | 2.82792 | − | 1.63270i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3912.73 | − | 11349.8i | 0.403147 | − | 1.16942i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2649.67 | + | 4589.36i | −0.271217 | + | 0.469762i | −0.969174 | − | 0.246378i | \(-0.920759\pi\) |
0.697957 | + | 0.716140i | \(0.254093\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −633.711 | −0.0640236 | −0.0320118 | − | 0.999487i | \(-0.510191\pi\) | ||||
−0.0320118 | + | 0.999487i | \(0.510191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1208.19 | −0.121273 | −0.0606366 | − | 0.998160i | \(-0.519313\pi\) | ||||
−0.0606366 | + | 0.998160i | \(0.519313\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2211.57 | + | 3830.55i | −0.219142 | + | 0.379564i | −0.954546 | − | 0.298064i | \(-0.903659\pi\) |
0.735404 | + | 0.677629i | \(0.236992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11930.5 | − | 10363.3i | 1.17463 | − | 1.02033i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19372.0 | + | 11184.4i | −1.88314 | + | 1.08723i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9481.80i | 0.915905i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1210.61 | + | 2096.84i | 0.115479 | + | 0.200015i | 0.917971 | − | 0.396648i | \(-0.129827\pi\) |
−0.802492 | + | 0.596662i | \(0.796493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7092.36 | + | 4094.78i | 0.672315 | + | 0.388162i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3291.14 | − | 1900.14i | −0.308130 | − | 0.177899i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5304.79 | + | 9188.16i | 0.493599 | + | 0.854939i | 0.999973 | − | 0.00737514i | \(-0.00234760\pi\) |
−0.506373 | + | 0.862314i | \(0.669014\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16314.2i | 1.49949i | 0.661728 | + | 0.749744i | \(0.269824\pi\) | ||||
−0.661728 | + | 0.749744i | \(0.730176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6111.92 | + | 3528.72i | −0.558351 | + | 0.322364i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 392.756 | − | 76.1934i | 0.0354478 | − | 0.00687675i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1876.73 | + | 3250.60i | −0.168365 | + | 0.291617i | −0.937845 | − | 0.347054i | \(-0.887182\pi\) |
0.769480 | + | 0.638671i | \(0.220515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9135.50 | −0.809805 | −0.404903 | − | 0.914360i | \(-0.632695\pi\) | ||||
−0.404903 | + | 0.914360i | \(0.632695\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33074.6 | −2.91446 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.73217 | + | 3.00021i | −0.000150839 | + | 0.000261261i | −0.866101 | − | 0.499869i | \(-0.833381\pi\) |
0.865950 | + | 0.500131i | \(0.166715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4155.34 | − | 4783.75i | −0.359729 | − | 0.414130i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12826.8 | + | 7405.57i | −1.09751 | + | 0.633648i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12246.9i | 1.04181i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5027.11 | − | 8707.20i | −0.422728 | − | 0.732187i | 0.573477 | − | 0.819222i | \(-0.305594\pi\) |
−0.996205 | + | 0.0870347i | \(0.972261\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1142.12 | + | 659.405i | 0.0954905 | + | 0.0551314i | 0.546985 | − | 0.837143i | \(-0.315776\pi\) |
−0.451494 | + | 0.892274i | \(0.649109\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14474.0 | + | 8356.59i | 1.19639 | + | 0.690737i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1684.04 | + | 2916.83i | 0.138410 | + | 0.239733i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17133.4i | 1.39237i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8317.16 | − | 4801.91i | 0.672116 | − | 0.388046i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14739.3 | − | 18836.7i | 1.17786 | − | 1.50530i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2144.41 | − | 3714.23i | 0.170417 | − | 0.295170i | −0.768149 | − | 0.640271i | \(-0.778822\pi\) |
0.938566 | + | 0.345101i | \(0.112155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26523.1 | −2.08463 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8456.92 | 0.661045 | 0.330523 | − | 0.943798i | \(-0.392775\pi\) | ||||
0.330523 | + | 0.943798i | \(0.392775\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1937.65 | − | 3356.11i | 0.149813 | − | 0.259483i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5495.27 | − | 1894.45i | −0.422573 | − | 0.145678i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12043.6 | − | 6953.36i | 0.916163 | − | 0.528947i | 0.0337539 | − | 0.999430i | \(-0.489254\pi\) |
0.882409 | + | 0.470483i | \(0.155920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 12254.2i | − | 0.927190i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9052.19 | − | 15678.8i | −0.677627 | − | 1.17369i | −0.975693 | − | 0.219140i | \(-0.929675\pi\) |
0.298066 | − | 0.954545i | \(-0.403658\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23648.5 | + | 13653.5i | 1.76089 | + | 1.01665i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 664.706 | + | 383.768i | 0.0489735 | + | 0.0282749i | 0.524287 | − | 0.851542i | \(-0.324332\pi\) |
−0.475313 | + | 0.879817i | \(0.657665\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10674.7 | − | 18489.2i | −0.782354 | − | 1.35508i | −0.930567 | − | 0.366121i | \(-0.880686\pi\) |
0.148213 | − | 0.988955i | \(-0.452648\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20309.0i | 1.47294i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14315.8 | − | 8265.21i | 1.03288 | − | 0.596335i | 0.115073 | − | 0.993357i | \(-0.463290\pi\) |
0.917809 | + | 0.397022i | \(0.129956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2214.15 | − | 11413.3i | −0.158104 | − | 0.814982i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23582.9 | + | 40846.7i | −1.67530 | + | 2.90171i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10940.7 | −0.769286 | −0.384643 | − | 0.923065i | \(-0.625675\pi\) | ||||
−0.384643 | + | 0.923065i | \(0.625675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9177.36 | −0.642014 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11096.9 | − | 19220.4i | 0.768459 | − | 1.33101i | −0.169940 | − | 0.985454i | \(-0.554357\pi\) |
0.938398 | − | 0.345555i | \(-0.112309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6342.67 | + | 32694.7i | 0.437015 | + | 2.25270i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11509.9 | − | 6645.23i | 0.785110 | − | 0.453283i | −0.0531284 | − | 0.998588i | \(-0.516919\pi\) |
0.838238 | + | 0.545304i | \(0.183586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9590.78i | 0.650942i | 0.945552 | + | 0.325471i | \(0.105523\pi\) | ||||
−0.945552 | + | 0.325471i | \(0.894477\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29962.8 | + | 51897.0i | 2.01349 | + | 3.48746i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3936.82 | + | 2272.93i | 0.263247 | + | 0.151985i | 0.625815 | − | 0.779972i | \(-0.284767\pi\) |
−0.362568 | + | 0.931957i | \(0.618100\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5810.30 | − | 3354.58i | −0.384713 | − | 0.222114i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10676.4 | − | 18492.1i | −0.703451 | − | 1.21841i | −0.967248 | − | 0.253835i | \(-0.918308\pi\) |
0.263796 | − | 0.964578i | \(-0.415025\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9496.27i | − | 0.619620i | −0.950798 | − | 0.309810i | \(-0.899735\pi\) | ||
0.950798 | − | 0.309810i | \(-0.100265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15773.7 | + | 9106.96i | −1.02423 | + | 0.591340i | −0.915327 | − | 0.402712i | \(-0.868068\pi\) |
−0.108905 | + | 0.994052i | \(0.534734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7265.56 | − | 2504.74i | −0.467237 | − | 0.161076i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4721.41 | − | 8177.71i | 0.302170 | − | 0.523374i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22718.9 | −1.44016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6711.25 | 0.423409 | 0.211704 | − | 0.977334i | \(-0.432099\pi\) | ||||
0.211704 | + | 0.977334i | \(0.432099\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6288.60 | + | 10892.2i | −0.393001 | + | 0.680697i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4899.45 | + | 12152.4i | 0.304746 | + | 0.755882i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25619.6 | − | 14791.5i | 1.57865 | − | 0.911434i | 0.583602 | − | 0.812040i | \(-0.301643\pi\) |
0.995048 | − | 0.0993938i | \(-0.0316904\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3793.02i | 0.232631i | 0.993212 | + | 0.116316i | \(0.0371084\pi\) | ||||
−0.993212 | + | 0.116316i | \(0.962892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5797.58 | − | 10041.7i | −0.352282 | − | 0.610170i | 0.634367 | − | 0.773032i | \(-0.281261\pi\) |
−0.986649 | + | 0.162862i | \(0.947927\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41472.2 | + | 23944.0i | 2.50836 | + | 1.44820i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18076.2 | + | 10436.3i | 1.08327 | + | 0.625427i | 0.931777 | − | 0.363031i | \(-0.118258\pi\) |
0.151494 | + | 0.988458i | \(0.451591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2245.74 | − | 3889.74i | −0.133967 | − | 0.232038i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26007.1i | 1.53732i | 0.639659 | + | 0.768658i | \(0.279075\pi\) | ||||
−0.639659 | + | 0.768658i | \(0.720925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14619.8 | − | 8440.73i | 0.860277 | − | 0.496681i | −0.00382819 | − | 0.999993i | \(-0.501219\pi\) |
0.864105 | + | 0.503312i | \(0.167885\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11992.7 | − | 13806.3i | −0.699334 | − | 0.805092i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4150.24 | − | 7188.42i | 0.240926 | − | 0.417296i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7339.87 | 0.422284 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2688.00 | 0.153960 | 0.0769799 | − | 0.997033i | \(-0.475472\pi\) | ||||
0.0769799 | + | 0.997033i | \(0.475472\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10001.4 | − | 17323.0i | 0.567779 | − | 0.983422i | −0.429006 | − | 0.903301i | \(-0.641136\pi\) |
0.996785 | − | 0.0801203i | \(-0.0255305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4071.82 | − | 789.919i | 0.230135 | − | 0.0446455i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9088.08 | − | 5247.00i | 0.509144 | − | 0.293955i | −0.223337 | − | 0.974741i | \(-0.571695\pi\) |
0.732482 | + | 0.680787i | \(0.238362\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20155.8i | 1.12425i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12919.3 | − | 22376.9i | −0.714350 | − | 1.23729i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2514.74 | − | 1451.88i | −0.138444 | − | 0.0799310i | 0.429178 | − | 0.903220i | \(-0.358803\pi\) |
−0.567622 | + | 0.823289i | \(0.692137\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15876.8 | + | 9166.47i | 0.866534 | + | 0.500294i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23765.3 | − | 41162.6i | −1.29150 | − | 2.23694i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5829.71i | − | 0.314102i | −0.987591 | − | 0.157051i | \(-0.949801\pi\) | ||
0.987591 | − | 0.157051i | \(-0.0501986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10803.8 | − | 6237.59i | 0.579621 | − | 0.334644i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27252.7 | − | 23672.7i | 1.44971 | − | 1.25927i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7940.28 | − | 13753.0i | 0.420597 | − | 0.728495i | −0.575401 | − | 0.817872i | \(-0.695154\pi\) |
0.995998 | + | 0.0893760i | \(0.0284873\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19656.9 | −1.03248 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45201.7 | −2.36427 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2601.36 | − | 4505.68i | 0.134929 | − | 0.233705i | −0.790641 | − | 0.612280i | \(-0.790253\pi\) |
0.925570 | + | 0.378575i | \(0.123586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5268.56 | − | 15282.6i | 0.272138 | − | 0.789397i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9397.40 | − | 5425.59i | 0.481394 | − | 0.277933i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 37948.0i | − | 1.93592i | −0.251107 | − | 0.967959i | \(-0.580794\pi\) | ||
0.251107 | − | 0.967959i | \(-0.419206\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16997.5 | + | 29440.5i | 0.860019 | + | 1.48960i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15869.6 | − | 9162.32i | −0.799669 | − | 0.461689i | 0.0436864 | − | 0.999045i | \(-0.486090\pi\) |
−0.843355 | + | 0.537356i | \(0.819423\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −51529.2 | − | 29750.4i | −2.57545 | − | 1.48693i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9963.10 | − | 17256.6i | −0.495939 | − | 0.858991i | 0.504050 | − | 0.863674i | \(-0.331843\pi\) |
−0.999989 | + | 0.00468324i | \(0.998509\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7621.89i | − | 0.376339i | −0.982137 | − | 0.188170i | \(-0.939745\pi\) | ||
0.982137 | − | 0.188170i | \(-0.0602555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −135.376 | + | 78.1595i | −0.00665745 | + | 0.00384368i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3416.23 | + | 9909.55i | −0.166657 | + | 0.483428i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17180.8 | + | 29758.1i | −0.834803 | + | 1.44592i | 0.0593874 | + | 0.998235i | \(0.481085\pi\) |
−0.894191 | + | 0.447687i | \(0.852248\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33210.4 | 1.60086 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13327.2 | 0.639874 | 0.319937 | − | 0.947439i | \(-0.396338\pi\) | ||||
0.319937 | + | 0.947439i | \(0.396338\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11743.9 | + | 20341.0i | −0.559414 | + | 0.968934i | 0.438131 | + | 0.898911i | \(0.355641\pi\) |
−0.997545 | + | 0.0700230i | \(0.977693\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21854.4 | − | 18983.5i | 1.03693 | − | 0.900720i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22719.6 | + | 13117.2i | −1.06957 | + | 0.617514i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27145.7i | − | 1.27295i | −0.771297 | − | 0.636476i | \(-0.780391\pi\) | ||
0.771297 | − | 0.636476i | \(-0.219609\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10441.9 | + | 18085.9i | 0.485859 | + | 0.841532i | 0.999868 | − | 0.0162524i | \(-0.00517352\pi\) |
−0.514009 | + | 0.857785i | \(0.671840\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22254.6 | − | 12848.7i | −1.03149 | − | 0.595533i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22602.8 | + | 13049.7i | 1.03957 | + | 0.600199i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −753.180 | − | 1304.55i | −0.0345082 | − | 0.0597699i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 3702.66i | − | 0.168348i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 690.527 | − | 398.676i | 0.0312766 | − | 0.0180575i | −0.484280 | − | 0.874913i | \(-0.660918\pi\) |
0.515557 | + | 0.856855i | \(0.327585\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29258.1 | + | 5675.97i | −1.31517 | + | 0.255138i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2010.49 | + | 3482.27i | −0.0900309 | + | 0.155938i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14974.0 | 0.665504 | 0.332752 | − | 0.943014i | \(-0.392023\pi\) | ||||
0.332752 | + | 0.943014i | \(0.392023\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18612.1 | 0.824092 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11928.9 | + | 20661.5i | −0.524238 | + | 0.908006i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25687.0 | − | 29571.6i | −1.12466 | − | 1.29474i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35121.5 | − | 20277.4i | 1.52634 | − | 0.881231i | 0.526825 | − | 0.849974i | \(-0.323382\pi\) |
0.999511 | − | 0.0312567i | \(-0.00995093\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17327.0i | 0.750227i | 0.926979 | + | 0.375113i | \(0.122396\pi\) | ||||
−0.926979 | + | 0.375113i | \(0.877604\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18589.8 | + | 32198.4i | 0.798982 | + | 1.38388i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16166.0 | − | 9333.46i | −0.692262 | − | 0.399678i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34173.6 | + | 19730.1i | 1.45270 | + | 0.838717i | 0.998634 | − | 0.0522514i | \(-0.0166397\pi\) |
0.454066 | + | 0.890968i | \(0.349973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14242.4 | − | 24668.6i | −0.603232 | − | 1.04483i | −0.992328 | − | 0.123631i | \(-0.960546\pi\) |
0.389096 | − | 0.921197i | \(-0.372787\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 23460.2i | − | 0.986446i | −0.869903 | − | 0.493223i | \(-0.835819\pi\) | ||
0.869903 | − | 0.493223i | \(-0.164181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7503.24 | − | 4332.00i | 0.314353 | − | 0.181492i | −0.334520 | − | 0.942389i | \(-0.608574\pi\) |
0.648873 | + | 0.760897i | \(0.275241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28627.0 | − | 22400.0i | −1.19072 | − | 0.931709i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13301.9 | + | 23039.6i | −0.551296 | + | 0.954873i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45107.5 | −1.85612 | −0.928060 | − | 0.372430i | \(-0.878525\pi\) | ||||
−0.928060 | + | 0.372430i | \(0.878525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19954.0 | 0.818156 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6258.90 | + | 10840.7i | −0.254808 | + | 0.441340i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −61833.2 | − | 21316.4i | −2.50840 | − | 0.864748i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23140.6 | − | 13360.2i | 0.932137 | − | 0.538170i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8466.89i | − | 0.339860i | −0.985456 | − | 0.169930i | \(-0.945646\pi\) | ||
0.985456 | − | 0.169930i | \(-0.0543542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18419.2 | + | 31902.9i | 0.734173 | + | 1.27163i | 0.955085 | + | 0.296332i | \(0.0957635\pi\) |
−0.220912 | + | 0.975294i | \(0.570903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2523.02 | + | 1456.67i | 0.100215 | + | 0.0578589i | 0.549270 | − | 0.835645i | \(-0.314906\pi\) |
−0.449055 | + | 0.893504i | \(0.648239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6013.10 | + | 3471.67i | 0.237182 | + | 0.136937i | 0.613881 | − | 0.789399i | \(-0.289607\pi\) |
−0.376699 | + | 0.926336i | \(0.622941\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6589.64 | + | 11413.6i | 0.259023 | + | 0.448640i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21885.5i | 0.854334i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28229.1 | − | 16298.1i | 1.09817 | − | 0.634029i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2270.82 | − | 11705.4i | −0.0877344 | − | 0.452247i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6098.71 | − | 10563.3i | 0.234822 | − | 0.406723i | −0.724399 | − | 0.689381i | \(-0.757883\pi\) |
0.959221 | + | 0.282658i | \(0.0912160\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49702.0 | 1.90068 | 0.950341 | − | 0.311210i | \(-0.100734\pi\) | ||||
0.950341 | + | 0.311210i | \(0.100734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45661.4 | 1.74024 | 0.870118 | − | 0.492843i | \(-0.164042\pi\) | ||||
0.870118 | + | 0.492843i | \(0.164042\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13631.5 | + | 23610.4i | −0.516009 | + | 0.893754i | 0.483818 | + | 0.875169i | \(0.339250\pi\) |
−0.999827 | + | 0.0185857i | \(0.994084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2614.27 | − | 13475.9i | −0.0986276 | − | 0.508398i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8850.85 | + | 5110.04i | −0.331671 | + | 0.191490i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29646.9i | 1.10725i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5251.39 | + | 9095.67i | 0.194820 | + | 0.337439i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62076.6 | + | 35840.0i | 2.29531 | + | 1.32520i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26269.2 | + | 15166.5i | 0.964881 | + | 0.557074i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24726.1 | − | 42826.9i | −0.905200 | − | 1.56785i | −0.820648 | − | 0.571434i | \(-0.806387\pi\) |
−0.0845520 | − | 0.996419i | \(-0.526946\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18037.2i | − | 0.655982i | −0.944681 | − | 0.327991i | \(-0.893628\pi\) | ||
0.944681 | − | 0.327991i | \(-0.106372\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37909.5 | + | 21887.0i | −1.37417 | + | 0.793380i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4634.47 | + | 1597.69i | 0.166896 | + | 0.0575359i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10193.8 | − | 17656.2i | 0.365900 | − | 0.633757i | −0.623020 | − | 0.782206i | \(-0.714095\pi\) |
0.988920 | + | 0.148448i | \(0.0474279\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 825.224 | 0.0294286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34931.5 | 1.24167 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2997.17 | − | 5191.26i | 0.105849 | − | 0.183337i | −0.808236 | − | 0.588859i | \(-0.799577\pi\) |
0.914085 | + | 0.405523i | \(0.132911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19763.4 | + | 2792.47i | 0.695724 | + | 0.0983023i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 108596. | − | 62697.9i | 3.79836 | − | 2.19299i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6529.41i | 0.227648i | 0.993501 | + | 0.113824i | \(0.0363101\pi\) | ||||
−0.993501 | + | 0.113824i | \(0.963690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14309.7 | − | 24785.2i | −0.495732 | − | 0.858634i | 0.504256 | − | 0.863554i | \(-0.331767\pi\) |
−0.999988 | + | 0.00492088i | \(0.998434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48412.6 | + | 27951.0i | 1.67183 | + | 0.965229i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5709.78 | − | 3296.54i | −0.195927 | − | 0.113119i | 0.398827 | − | 0.917026i | \(-0.369417\pi\) |
−0.594754 | + | 0.803908i | \(0.702751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6534.99 | − | 11318.9i | −0.223535 | − | 0.387174i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 168.973i | − | 0.00574351i | −0.999996 | − | 0.00287175i | \(-0.999086\pi\) | ||
0.999996 | − | 0.00287175i | \(-0.000914109\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9980.80 | − | 5762.42i | 0.338190 | − | 0.195254i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14426.3 | − | 16607.9i | −0.485765 | − | 0.559226i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2459.36 | + | 4259.74i | −0.0825539 | + | 0.142988i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57651.1 | 1.92316 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37762.6 | 1.25580 | 0.627902 | − | 0.778292i | \(-0.283914\pi\) | ||||
0.627902 | + | 0.778292i | \(0.283914\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12773.5 | − | 22124.4i | 0.422165 | − | 0.731212i | −0.573986 | − | 0.818865i | \(-0.694603\pi\) |
0.996151 | + | 0.0876535i | \(0.0279368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19642.9 | + | 3810.65i | −0.647196 | + | 0.125554i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5397.11 | − | 3116.02i | 0.176734 | − | 0.102037i | −0.409023 | − | 0.912524i | \(-0.634131\pi\) |
0.585757 | + | 0.810487i | \(0.300797\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28935.9i | 0.944633i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22199.8 | + | 38451.1i | 0.720308 | + | 1.24761i | 0.960876 | + | 0.276978i | \(0.0893330\pi\) |
−0.240568 | + | 0.970632i | \(0.577334\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50068.6 | − | 28907.1i | −1.61961 | − | 0.935084i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34625.8 | − | 19991.2i | −1.11328 | − | 0.642755i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23356.8 | + | 40455.2i | 0.748693 | + | 1.29677i | 0.948449 | + | 0.316929i | \(0.102652\pi\) |
−0.199756 | + | 0.979846i | \(0.564015\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3549.47i | − | 0.113091i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26568.0 | − | 15339.0i | 0.843949 | − | 0.487254i | −0.0146559 | − | 0.999893i | \(-0.504665\pi\) |
0.858604 | + | 0.512639i | \(0.171332\pi\) | |||||||
\(998\) | 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 | 1008.4.bt.d.593.3 | 48 | ||
3.2 | odd | 2 | inner | 1008.4.bt.d.593.22 | 48 | ||
4.3 | odd | 2 | 504.4.bl.a.89.3 | yes | 48 | ||
7.3 | odd | 6 | inner | 1008.4.bt.d.17.22 | 48 | ||
12.11 | even | 2 | 504.4.bl.a.89.22 | yes | 48 | ||
21.17 | even | 6 | inner | 1008.4.bt.d.17.3 | 48 | ||
28.3 | even | 6 | 504.4.bl.a.17.22 | yes | 48 | ||
84.59 | odd | 6 | 504.4.bl.a.17.3 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.4.bl.a.17.3 | ✓ | 48 | 84.59 | odd | 6 | ||
504.4.bl.a.17.22 | yes | 48 | 28.3 | even | 6 | ||
504.4.bl.a.89.3 | yes | 48 | 4.3 | odd | 2 | ||
504.4.bl.a.89.22 | yes | 48 | 12.11 | even | 2 | ||
1008.4.bt.d.17.3 | 48 | 21.17 | even | 6 | inner | ||
1008.4.bt.d.17.22 | 48 | 7.3 | odd | 6 | inner | ||
1008.4.bt.d.593.3 | 48 | 1.1 | even | 1 | trivial | ||
1008.4.bt.d.593.22 | 48 | 3.2 | odd | 2 | inner |