Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,4,Mod(31,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.31");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.60821392064\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.12258833328.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 29x^{4} - 20x^{3} + 808x^{2} - 672x + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.3 | ||
Root | \(0.426664 + 0.739004i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.47 |
Dual form | 112.4.p.f.31.3 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.53129 | + | 6.11637i | 0.679597 | + | 1.17710i | 0.975102 | + | 0.221755i | \(0.0711787\pi\) |
−0.295505 | + | 0.955341i | \(0.595488\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.05999 | + | 0.611983i | 0.0948080 | + | 0.0547374i | 0.546654 | − | 0.837358i | \(-0.315901\pi\) |
−0.451846 | + | 0.892096i | \(0.649234\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.5026 | + | 8.40621i | 0.891056 | + | 0.453893i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.4400 | + | 19.8147i | −0.423704 | + | 0.733877i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.96612 | − | 2.28984i | 0.108712 | − | 0.0627647i | −0.444658 | − | 0.895700i | \(-0.646675\pi\) |
0.553370 | + | 0.832936i | \(0.313342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 41.0611i | 0.876024i | 0.898969 | + | 0.438012i | \(0.144317\pi\) | ||||
−0.898969 | + | 0.438012i | \(0.855683\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.64436i | 0.148798i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −103.451 | + | 59.7275i | −1.47592 | + | 0.852120i | −0.999631 | − | 0.0271712i | \(-0.991350\pi\) |
−0.476284 | + | 0.879291i | \(0.658017\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.0913 | − | 52.1196i | 0.363337 | − | 0.629319i | −0.625170 | − | 0.780488i | \(-0.714971\pi\) |
0.988508 | + | 0.151169i | \(0.0483039\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.85991 | + | 130.621i | 0.0712836 | + | 1.35732i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.23396 | − | 4.17653i | −0.0655819 | − | 0.0378637i | 0.466850 | − | 0.884336i | \(-0.345389\pi\) |
−0.532432 | + | 0.846473i | \(0.678722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −61.7510 | − | 106.956i | −0.494008 | − | 0.855646i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.0976 | 0.207401 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 164.382 | 1.05258 | 0.526292 | − | 0.850304i | \(-0.323582\pi\) | ||||
0.526292 | + | 0.850304i | \(0.323582\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 143.780 | + | 249.034i | 0.833019 | + | 1.44283i | 0.895633 | + | 0.444793i | \(0.146723\pi\) |
−0.0626143 | + | 0.998038i | \(0.519944\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 28.0110 | + | 16.1722i | 0.147760 | + | 0.0853095i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.3481 | + | 19.0098i | 0.0596343 | + | 0.0918068i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 74.3709 | − | 128.814i | 0.330446 | − | 0.572349i | −0.652153 | − | 0.758087i | \(-0.726134\pi\) |
0.982599 | + | 0.185738i | \(0.0594675\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −251.145 | + | 144.999i | −1.03116 | + | 0.595343i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 358.778i | − | 1.36663i | −0.730125 | − | 0.683314i | \(-0.760538\pi\) | ||
0.730125 | − | 0.683314i | \(-0.239462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 360.388i | − | 1.27811i | −0.769161 | − | 0.639055i | \(-0.779326\pi\) | ||
0.769161 | − | 0.639055i | \(-0.220674\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −24.2525 | + | 14.0022i | −0.0803411 | + | 0.0463850i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 112.717 | − | 195.232i | 0.349819 | − | 0.605904i | −0.636398 | − | 0.771361i | \(-0.719577\pi\) |
0.986217 | + | 0.165457i | \(0.0529099\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 201.671 | + | 277.449i | 0.587963 | + | 0.808888i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −730.631 | − | 421.830i | −2.00606 | − | 1.15820i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −342.362 | − | 592.988i | −0.887302 | − | 1.53685i | −0.843052 | − | 0.537832i | \(-0.819244\pi\) |
−0.0442500 | − | 0.999020i | \(-0.514090\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.60537 | 0.0137423 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 425.044 | 0.987692 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 42.5261 | + | 73.6574i | 0.0938377 | + | 0.162532i | 0.909123 | − | 0.416528i | \(-0.136753\pi\) |
−0.815285 | + | 0.579060i | \(0.803420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −181.109 | − | 104.563i | −0.380141 | − | 0.219475i | 0.297738 | − | 0.954648i | \(-0.403768\pi\) |
−0.677880 | + | 0.735173i | \(0.737101\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −355.356 | + | 230.827i | −0.710646 | + | 0.461610i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −25.1287 | + | 43.5242i | −0.0479513 | + | 0.0830541i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 361.327 | − | 208.612i | 0.658853 | − | 0.380389i | −0.132987 | − | 0.991118i | \(-0.542457\pi\) |
0.791840 | + | 0.610729i | \(0.209123\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 58.9941i | − | 0.102928i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 982.974i | 1.64306i | 0.570162 | + | 0.821532i | \(0.306880\pi\) | ||||
−0.570162 | + | 0.821532i | \(0.693120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 295.770 | − | 170.763i | 0.474210 | − | 0.273785i | −0.243791 | − | 0.969828i | \(-0.578391\pi\) |
0.718000 | + | 0.696043i | \(0.245058\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 436.121 | − | 755.384i | 0.671452 | − | 1.16299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 84.7001 | − | 4.44826i | 0.125357 | − | 0.00658346i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 66.0721 | + | 38.1467i | 0.0940973 | + | 0.0543271i | 0.546310 | − | 0.837583i | \(-0.316032\pi\) |
−0.452213 | + | 0.891910i | \(0.649365\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 411.633 | + | 712.968i | 0.564654 | + | 0.978009i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 523.643 | 0.692498 | 0.346249 | − | 0.938143i | \(-0.387455\pi\) | ||||
0.346249 | + | 0.938143i | \(0.387455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −146.209 | −0.186571 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 580.480 | + | 1005.42i | 0.715334 | + | 1.23899i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −841.824 | − | 486.027i | −1.00262 | − | 0.578863i | −0.0935976 | − | 0.995610i | \(-0.529837\pi\) |
−0.909022 | + | 0.416747i | \(0.863170\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −345.169 | + | 677.615i | −0.397621 | + | 0.780587i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1015.46 | + | 1758.82i | −1.13223 | + | 1.96109i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 63.7926 | − | 36.8307i | 0.0688946 | − | 0.0397763i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 676.730i | 0.708367i | 0.935176 | + | 0.354183i | \(0.115241\pi\) | ||||
−0.935176 | + | 0.354183i | \(0.884759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 104.783i | 0.106375i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 726.410 | − | 419.393i | 0.715649 | − | 0.413180i | −0.0975005 | − | 0.995235i | \(-0.531085\pi\) |
0.813149 | + | 0.582056i | \(0.197751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 757.601 | − | 1312.20i | 0.724744 | − | 1.25529i | −0.234335 | − | 0.972156i | \(-0.575291\pi\) |
0.959079 | − | 0.283138i | \(-0.0913753\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −72.6663 | + | 142.654i | −0.0675381 | + | 0.132587i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1461.57 | − | 843.836i | −1.32051 | − | 0.762399i | −0.336704 | − | 0.941611i | \(-0.609312\pi\) |
−0.983811 | + | 0.179211i | \(0.942645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 788.117 | + | 1365.06i | 0.692550 | + | 1.19953i | 0.971000 | + | 0.239081i | \(0.0768460\pi\) |
−0.278450 | + | 0.960451i | \(0.589821\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1050.50 | 0.898281 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2192.01 | −1.82484 | −0.912422 | − | 0.409251i | \(-0.865790\pi\) | ||||
−0.912422 | + | 0.409251i | \(0.865790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.11193 | − | 8.85412i | −0.00414513 | − | 0.00717957i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −813.613 | − | 469.740i | −0.642894 | − | 0.371175i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2209.29 | + | 116.027i | −1.70189 | + | 0.0893797i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −655.013 | + | 1134.52i | −0.492121 | + | 0.852379i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2194.42 | − | 1266.95i | 1.60865 | − | 0.928756i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 304.158i | − | 0.217638i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1085.60i | 0.758515i | 0.925291 | + | 0.379258i | \(0.123821\pi\) | ||||
−0.925291 | + | 0.379258i | \(0.876179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2204.27 | − | 1272.64i | 1.50446 | − | 0.868599i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −766.676 | + | 1327.92i | −0.511334 | + | 0.885657i | 0.488580 | + | 0.872519i | \(0.337515\pi\) |
−0.999914 | + | 0.0131373i | \(0.995818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 934.713 | − | 607.155i | 0.609397 | − | 0.395842i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 30.8431 | + | 17.8072i | 0.0196633 | + | 0.0113526i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −460.087 | − | 796.895i | −0.286919 | − | 0.496958i | 0.686154 | − | 0.727457i | \(-0.259298\pi\) |
−0.973073 | + | 0.230498i | \(0.925964\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1424.66 | 0.869339 | 0.434669 | − | 0.900590i | \(-0.356865\pi\) | ||||
0.434669 | + | 0.900590i | \(0.356865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1592.15 | 0.950943 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 94.0234 | + | 162.853i | 0.0549834 | + | 0.0952341i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 174.242 | + | 100.599i | 0.0997934 | + | 0.0576158i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −984.820 | + | 2213.25i | −0.552562 | + | 1.24181i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 689.127 | − | 1193.60i | 0.378896 | − | 0.656267i | −0.612006 | − | 0.790853i | \(-0.709637\pi\) |
0.990902 | + | 0.134586i | \(0.0429706\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1155.09 | + | 666.890i | −0.622514 | + | 0.359409i | −0.777847 | − | 0.628453i | \(-0.783688\pi\) |
0.155333 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2733.13i | − | 1.44419i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 351.963i | 0.182389i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1087.64 | − | 627.947i | 0.552884 | − | 0.319208i | −0.197400 | − | 0.980323i | \(-0.563250\pi\) |
0.750285 | + | 0.661115i | \(0.229916\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2417.96 | − | 4188.03i | 1.20602 | − | 2.08888i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −84.2703 | − | 129.734i | −0.0412511 | − | 0.0635059i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2818.55 | − | 1627.29i | −1.35439 | − | 0.781959i | −0.365532 | − | 0.930799i | \(-0.619113\pi\) |
−0.988861 | + | 0.148840i | \(0.952446\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.7942 | + | 34.2845i | 0.00933924 | + | 0.0161760i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2736.24 | −1.26788 | −0.633941 | − | 0.773381i | \(-0.718564\pi\) | ||||
−0.633941 | + | 0.773381i | \(0.718564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 510.983 | 0.232582 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 688.489 | + | 1192.50i | 0.307895 | + | 0.533290i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2927.28 | − | 1690.07i | −1.28646 | − | 0.742737i | −0.308437 | − | 0.951245i | \(-0.599806\pi\) |
−0.978021 | + | 0.208508i | \(0.933139\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −119.958 | − | 2284.14i | −0.0518170 | − | 0.986656i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −300.344 | + | 520.211i | −0.127544 | + | 0.220912i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1054.81 | + | 608.992i | −0.440446 | + | 0.254292i | −0.703787 | − | 0.710411i | \(-0.748509\pi\) |
0.263341 | + | 0.964703i | \(0.415176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1757.61i | 0.721781i | 0.932608 | + | 0.360890i | \(0.117527\pi\) | ||||
−0.932608 | + | 0.360890i | \(0.882473\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1476.97i | − | 0.596618i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 157.664 | − | 91.0275i | 0.0626579 | − | 0.0361755i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −273.533 | + | 473.772i | −0.106966 | + | 0.185271i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 480.186 | + | 244.601i | 0.184806 | + | 0.0941380i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −828.295 | − | 478.217i | −0.313787 | − | 0.181165i | 0.334833 | − | 0.942278i | \(-0.391320\pi\) |
−0.648620 | + | 0.761112i | \(0.724654\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −666.774 | − | 1154.89i | −0.248681 | − | 0.430729i | 0.714479 | − | 0.699657i | \(-0.246664\pi\) |
−0.963160 | + | 0.268928i | \(0.913330\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −354.947 | −0.130350 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1098.75 | 0.397373 | 0.198686 | − | 0.980063i | \(-0.436332\pi\) | ||||
0.198686 | + | 0.980063i | \(0.436332\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −124.289 | − | 215.275i | −0.0442745 | − | 0.0766857i | 0.843039 | − | 0.537853i | \(-0.180764\pi\) |
−0.887313 | + | 0.461167i | \(0.847431\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2551.90 | + | 1473.34i | 0.895509 | + | 0.517023i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2712.73 | + | 1381.83i | 0.937912 | + | 0.477761i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 219.566 | − | 380.300i | 0.0748057 | − | 0.129567i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 165.513 | − | 95.5590i | 0.0555747 | − | 0.0320861i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 275.617i | − | 0.0912191i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2029.24i | 0.662078i | 0.943617 | + | 0.331039i | \(0.107399\pi\) | ||||
−0.943617 | + | 0.331039i | \(0.892601\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6012.24 | + | 3471.17i | −1.93405 | + | 1.11662i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 220.551 | − | 382.006i | 0.0699604 | − | 0.121175i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 279.308 | + | 5318.34i | 0.0873762 | + | 1.66375i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2088.90 | + | 1206.03i | 0.644543 | + | 0.372127i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2452.48 | − | 4247.82i | −0.746477 | − | 1.29294i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3904.24 | 1.17241 | 0.586204 | − | 0.810164i | \(-0.300622\pi\) | ||||
0.586204 | + | 0.810164i | \(0.300622\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2825.73 | 0.837253 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2127.88 | + | 3685.59i | 0.622168 | + | 1.07763i | 0.989081 | + | 0.147371i | \(0.0470811\pi\) |
−0.366914 | + | 0.930255i | \(0.619586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1500.18 | + | 866.127i | 0.432901 | + | 0.249936i | 0.700582 | − | 0.713572i | \(-0.252924\pi\) |
−0.267681 | + | 0.963508i | \(0.586257\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 326.308 | + | 502.349i | 0.0929414 | + | 0.143083i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 437.455 | − | 757.694i | 0.122998 | − | 0.213039i | −0.797950 | − | 0.602723i | \(-0.794082\pi\) |
0.920949 | + | 0.389684i | \(0.127416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 238.957 | − | 137.962i | 0.0663312 | − | 0.0382963i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 538.828i | 0.147682i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1842.84i | − | 0.498760i | −0.968406 | − | 0.249380i | \(-0.919773\pi\) | ||
0.968406 | − | 0.249380i | \(-0.0802269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4056.11 | + | 2341.80i | −1.08414 | + | 0.625927i | −0.932010 | − | 0.362433i | \(-0.881946\pi\) |
−0.152128 | + | 0.988361i | \(0.548613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2514.37 | + | 4355.02i | −0.663773 | + | 1.14969i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 43.9748 | + | 417.511i | 0.0114671 | + | 0.108873i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2140.09 | + | 1235.58i | 0.551298 | + | 0.318292i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1849.14 | + | 3202.80i | 0.470619 | + | 0.815137i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1015.59 | 0.255393 | 0.127696 | − | 0.991813i | \(-0.459242\pi\) | ||||
0.127696 | + | 0.991813i | \(0.459242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.2543 | −0.00950603 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −516.306 | − | 894.268i | −0.126793 | − | 0.219613i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2612.42 | + | 1508.28i | 0.634078 | + | 0.366085i | 0.782330 | − | 0.622864i | \(-0.214031\pi\) |
−0.148251 | + | 0.988950i | \(0.547365\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2310.15 | − | 1500.59i | 0.554231 | − | 0.360008i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1880.53 | + | 3257.18i | −0.445985 | + | 0.772468i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2295.87 | + | 1325.52i | −0.538287 | + | 0.310780i | −0.744385 | − | 0.667751i | \(-0.767257\pi\) |
0.206097 | + | 0.978532i | \(0.433924\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 838.078i | − | 0.194275i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6865.21i | − | 1.57357i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 391.947 | − | 226.291i | 0.0888381 | − | 0.0512907i | −0.454923 | − | 0.890531i | \(-0.650333\pi\) |
0.543761 | + | 0.839240i | \(0.317000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −82.3630 | + | 142.657i | −0.0184620 | + | 0.0319771i | −0.875109 | − | 0.483926i | \(-0.839210\pi\) |
0.856647 | + | 0.515903i | \(0.172544\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5363.44 | + | 281.676i | −1.18905 | + | 0.0624461i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −489.823 | − | 282.799i | −0.107409 | − | 0.0620125i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −969.804 | − | 1679.75i | −0.210360 | − | 0.364355i | 0.741467 | − | 0.670989i | \(-0.234130\pi\) |
−0.951827 | + | 0.306634i | \(0.900797\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6579.37 | −1.41181 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7152.79 | −1.51850 | −0.759252 | − | 0.650796i | \(-0.774435\pi\) | ||||
−0.759252 | + | 0.650796i | \(0.774435\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1647.77 | − | 2854.03i | −0.346113 | − | 0.599485i | 0.639442 | − | 0.768839i | \(-0.279165\pi\) |
−0.985555 | + | 0.169354i | \(0.945832\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 450.541 | + | 260.120i | 0.0936411 | + | 0.0540637i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3015.97 | − | 5920.77i | 0.620303 | − | 1.21774i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4678.24 | − | 8102.95i | 0.952217 | − | 1.64929i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4139.14 | + | 2389.73i | −0.833816 | + | 0.481404i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7368.65i | 1.46922i | 0.678491 | + | 0.734609i | \(0.262634\pi\) | ||||
−0.678491 | + | 0.734609i | \(0.737366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 104.101i | 0.0205457i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 115.405 | − | 66.6289i | 0.0225470 | − | 0.0130175i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 171.493 | − | 297.034i | 0.0331695 | − | 0.0574513i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3029.50 | − | 5947.34i | 0.580124 | − | 1.13887i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5130.33 | + | 2962.00i | 0.972705 | + | 0.561592i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −127.982 | − | 221.671i | −0.0240270 | − | 0.0416159i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2692.96 | −0.500636 | −0.250318 | − | 0.968164i | \(-0.580535\pi\) | ||||
−0.250318 | + | 0.968164i | \(0.580535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10701.2 | 1.97014 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1486.00 | − | 2573.82i | −0.270943 | − | 0.469286i | 0.698161 | − | 0.715941i | \(-0.254002\pi\) |
−0.969103 | + | 0.246655i | \(0.920669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −987.269 | − | 570.000i | −0.178287 | − | 0.102934i | 0.408201 | − | 0.912892i | \(-0.366156\pi\) |
−0.586487 | + | 0.809958i | \(0.699490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −517.935 | + | 27.2008i | −0.0926422 | + | 0.00486536i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2822.56 | − | 4888.81i | 0.500097 | − | 0.866193i | −0.499903 | − | 0.866081i | \(-0.666631\pi\) |
1.00000 | 0.000111477i | \(-3.54842e-5\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 651.958 | − | 376.408i | 0.114428 | − | 0.0660652i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 11919.3i | − | 2.07250i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7189.10i | 1.23843i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4391.73 | − | 2535.56i | 0.749567 | − | 0.432762i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5566.14 | + | 9640.83i | −0.941309 | + | 1.63040i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3501.28 | − | 2274.31i | 0.586723 | − | 0.381114i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6373.93 | + | 3679.99i | 1.05844 | + | 0.611089i | 0.925000 | − | 0.379968i | \(-0.124065\pi\) |
0.133438 | + | 0.991057i | \(0.457398\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1701.61 | + | 2947.27i | 0.280023 | + | 0.485014i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 510.669 | 0.0832861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10163.9 | −1.64292 | −0.821459 | − | 0.570268i | \(-0.806839\pi\) | ||||
−0.821459 | + | 0.570268i | \(0.806839\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7740.64 | − | 13407.2i | −1.24016 | − | 2.14802i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1140.49 | + | 658.464i | 0.181118 | + | 0.104568i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 995.807 | + | 6273.91i | 0.156759 | + | 0.987637i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 36.1034 | − | 62.5329i | 0.00563403 | − | 0.00975843i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9132.03 | − | 5272.38i | 1.41278 | − | 0.815666i | 0.417127 | − | 0.908848i | \(-0.363037\pi\) |
0.995649 | + | 0.0931819i | \(0.0297038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6048.02i | 0.927631i | 0.885932 | + | 0.463816i | \(0.153520\pi\) | ||||
−0.885932 | + | 0.463816i | \(0.846480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1194.78i | 0.181689i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5446.54 | − | 3144.56i | 0.821218 | − | 0.474131i | −0.0296180 | − | 0.999561i | \(-0.509429\pi\) |
0.850836 | + | 0.525431i | \(0.176096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −601.563 | + | 1041.94i | −0.0899371 | + | 0.155776i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8511.32 | − | 13103.1i | −1.26181 | − | 1.94255i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −133.941 | − | 77.3311i | −0.0196912 | − | 0.0113687i | 0.490122 | − | 0.871654i | \(-0.336952\pi\) |
−0.509813 | + | 0.860285i | \(0.670286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1618.53 | + | 2803.38i | 0.235972 | + | 0.408715i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9252.17 | −1.33778 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 418.016 | 0.0599451 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2945.21 | − | 5101.26i | −0.418907 | − | 0.725568i | 0.576923 | − | 0.816799i | \(-0.304253\pi\) |
−0.995830 | + | 0.0912308i | \(0.970920\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7109.08 | + | 4104.43i | 1.00294 | + | 0.579046i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −665.075 | − | 12663.8i | −0.0930700 | − | 1.77216i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −175.150 | + | 303.369i | −0.0243135 | + | 0.0421122i | −0.877926 | − | 0.478796i | \(-0.841073\pi\) |
0.853613 | + | 0.520908i | \(0.174407\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1860.34 | − | 1074.07i | 0.256181 | − | 0.147906i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6749.71i | 0.922089i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8247.17i | − | 1.11775i | −0.829251 | − | 0.558877i | \(-0.811233\pi\) | ||
0.829251 | − | 0.558877i | \(-0.188767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6639.93 | + | 3833.57i | −0.892845 | + | 0.515485i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6340.08 | + | 10981.3i | −0.845856 | + | 1.46507i | 0.0390189 | + | 0.999238i | \(0.487577\pi\) |
−0.884875 | + | 0.465828i | \(0.845757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 92.5031 | + | 47.1199i | 0.0122452 | + | 0.00623754i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7140.98 | + | 4122.85i | 0.937975 | + | 0.541540i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3863.76 | + | 6692.24i | 0.503601 | + | 0.872262i | 0.999991 | + | 0.00416264i | \(0.00132501\pi\) |
−0.496391 | + | 0.868099i | \(0.665342\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 997.814 | 0.129058 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10829.4 | −1.39000 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 46.6903 | + | 80.8699i | 0.00594745 | + | 0.0103013i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8743.56 | − | 5048.10i | −1.10536 | − | 0.638178i | −0.167734 | − | 0.985832i | \(-0.553645\pi\) |
−0.937623 | + | 0.347654i | \(0.886978\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7014.33 | + | 3573.01i | 0.880089 | + | 0.448306i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3839.25 | + | 6649.77i | −0.478112 | + | 0.828114i | −0.999685 | − | 0.0250922i | \(-0.992012\pi\) |
0.521573 | + | 0.853207i | \(0.325345\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10225.6 | + | 5903.76i | −1.26395 | + | 0.729744i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1007.65i | 0.123631i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 681.190i | − | 0.0829615i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3214.30 | − | 1855.78i | 0.388599 | − | 0.224358i | −0.292954 | − | 0.956127i | \(-0.594638\pi\) |
0.681553 | + | 0.731769i | \(0.261305\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3249.40 | − | 5628.13i | 0.389979 | − | 0.675463i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 82.6116 | + | 1573.02i | 0.00984273 | + | 0.187417i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 555.054 | + | 320.461i | 0.0656543 | + | 0.0379055i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5030.89 | + | 8713.75i | 0.590800 | + | 1.02330i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8868.09 | 1.03397 | 0.516986 | − | 0.855994i | \(-0.327054\pi\) | ||||
0.516986 | + | 0.855994i | \(0.327054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9571.99 | −1.10810 | −0.554050 | − | 0.832483i | \(-0.686919\pi\) | ||||
−0.554050 | + | 0.832483i | \(0.686919\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2578.97 | + | 4466.91i | 0.296439 | + | 0.513448i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12776.4 | + | 7376.46i | 1.45823 | + | 0.841908i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2109.79 | − | 3248.01i | −0.239109 | − | 0.368108i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −664.047 | + | 1150.16i | −0.0747331 | + | 0.129442i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6678.90 | − | 3856.06i | 0.746430 | − | 0.430952i | −0.0779726 | − | 0.996956i | \(-0.524845\pi\) |
0.824403 | + | 0.566004i | \(0.191511\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2222.71i | 0.246690i | 0.992364 | + | 0.123345i | \(0.0393622\pi\) | ||||
−0.992364 | + | 0.123345i | \(0.960638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1420.98i | 0.156622i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −435.358 | + | 251.354i | −0.0476567 | + | 0.0275146i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5306.28 | + | 9190.74i | −0.576890 | + | 0.999203i | 0.418943 | + | 0.908012i | \(0.362401\pi\) |
−0.995833 | + | 0.0911907i | \(0.970933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7804.68 | + | 822.036i | −0.842747 | + | 0.0887632i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13502.3 | + | 7795.53i | 1.44811 | + | 0.836065i | 0.998369 | − | 0.0570953i | \(-0.0181839\pi\) |
0.449738 | + | 0.893160i | \(0.351517\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −594.881 | − | 1030.36i | −0.0633709 | − | 0.109762i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9734.03 | 1.02999 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2759.74 | 0.290067 | 0.145033 | − | 0.989427i | \(-0.453671\pi\) | ||||
0.145033 | + | 0.989427i | \(0.453671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −821.544 | − | 1422.96i | −0.0857761 | − | 0.148569i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8157.89 | − | 4709.96i | −0.846117 | − | 0.488506i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −780.563 | + | 507.025i | −0.0804249 | + | 0.0522411i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3836.15 | − | 6644.40i | 0.392664 | − | 0.680113i | −0.600136 | − | 0.799898i | \(-0.704887\pi\) |
0.992800 | + | 0.119784i | \(0.0382203\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3010.18 | + | 1737.93i | −0.306107 | + | 0.176731i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13864.8i | 1.40076i | 0.713771 | + | 0.700379i | \(0.246986\pi\) | ||||
−0.713771 | + | 0.700379i | \(0.753014\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11518.3i | 1.15616i | 0.815981 | + | 0.578079i | \(0.196197\pi\) | ||||
−0.815981 | + | 0.578079i | \(0.803803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2152.74 | + | 1242.88i | −0.214690 | + | 0.123951i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1407.96 | − | 2438.66i | 0.139513 | − | 0.241644i | −0.787799 | − | 0.615932i | \(-0.788780\pi\) |
0.927312 | + | 0.374288i | \(0.122113\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7716.48 | − | 405.252i | 0.759731 | − | 0.0398994i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7681.52 | + | 4434.93i | 0.751477 | + | 0.433866i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −825.231 | − | 1429.34i | −0.0802202 | − | 0.138945i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7432.66 | −0.717966 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15666.5 | 1.50381 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1560.08 | − | 2702.13i | −0.148813 | − | 0.257753i | 0.781976 | − | 0.623309i | \(-0.214212\pi\) |
−0.930789 | + | 0.365556i | \(0.880879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5289.26 | + | 3053.75i | 0.501392 | + | 0.289479i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 495.917 | − | 973.556i | 0.0467184 | − | 0.0917149i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −414.147 | + | 717.324i | −0.0387742 | + | 0.0671588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1721.99 | − | 994.191i | 0.160227 | − | 0.0925074i | −0.417742 | − | 0.908566i | \(-0.637178\pi\) |
0.577970 | + | 0.816058i | \(0.303845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 22985.8i | − | 2.12567i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3035.51i | − | 0.279003i | −0.990222 | − | 0.139502i | \(-0.955450\pi\) | ||
0.990222 | − | 0.139502i | \(-0.0445501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17005.5 | + | 9818.12i | −1.55353 | + | 0.896929i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −64.1255 | + | 111.069i | −0.00582268 | + | 0.0100852i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8263.09 | + | 16221.6i | −0.745775 | + | 1.46406i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14306.5 | − | 8259.87i | −1.28346 | − | 0.741007i | −0.305982 | − | 0.952037i | \(-0.598985\pi\) |
−0.977479 | + | 0.211031i | \(0.932318\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9662.45 | − | 16735.8i | −0.861649 | − | 1.49242i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16446.0 | −1.45783 | −0.728917 | − | 0.684602i | \(-0.759976\pi\) | ||||
−0.728917 | + | 0.684602i | \(0.759976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1026.65 | 0.0904656 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1804.43 | + | 3125.36i | 0.158062 | + | 0.273772i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4057.43 | + | 2342.56i | 0.353325 | + | 0.203992i | 0.666149 | − | 0.745819i | \(-0.267942\pi\) |
−0.312824 | + | 0.949811i | \(0.601275\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6316.45 | − | 331.726i | 0.546817 | − | 0.0287176i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 875.585 | − | 1516.56i | 0.0753567 | − | 0.130522i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1606.09 | − | 927.278i | 0.137423 | − | 0.0793412i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1032.42i | − | 0.0878251i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 23872.5i | − | 2.01905i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1904.98 | − | 1099.84i | 0.160189 | − | 0.0924853i | −0.417762 | − | 0.908556i | \(-0.637186\pi\) |
0.577952 | + | 0.816071i | \(0.303852\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5232.69 | − | 9063.28i | 0.437494 | − | 0.757762i | −0.560001 | − | 0.828492i | \(-0.689199\pi\) |
0.997496 | + | 0.0707295i | \(0.0225327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13547.0 | − | 8799.67i | 1.12617 | − | 0.731522i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29748.3 | − | 17175.2i | −2.45893 | − | 1.41966i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6048.61 | − | 10476.5i | −0.497133 | − | 0.861059i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1946.00 | −0.159038 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14731.8 | 1.19720 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1032.83 | − | 1788.91i | −0.0834635 | − | 0.144563i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7449.65 | − | 4301.06i | −0.598652 | − | 0.345632i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1435.16 | + | 638.599i | 0.114688 | + | 0.0510323i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1467.47 | − | 2541.74i | 0.116620 | − | 0.201992i | −0.801806 | − | 0.597584i | \(-0.796127\pi\) |
0.918426 | + | 0.395592i | \(0.129461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10750.2 | + | 6206.64i | −0.849606 | + | 0.490520i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1929.26i | 0.151634i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9168.13i | 0.716638i | 0.933599 | + | 0.358319i | \(0.116650\pi\) | ||||
−0.933599 | + | 0.358319i | \(0.883350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4143.78 | − | 2392.41i | 0.322135 | − | 0.185985i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4946.46 | − | 8567.52i | 0.382444 | − | 0.662412i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 769.691 | + | 1184.94i | 0.0591873 | + | 0.0911186i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1113.52 | + | 642.889i | 0.0851642 | + | 0.0491696i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2309.07 | − | 3999.42i | −0.175652 | − | 0.304239i | 0.764734 | − | 0.644346i | \(-0.222870\pi\) |
−0.940387 | + | 0.340107i | \(0.889537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14797.9 | 1.11965 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3863.69 | −0.290776 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11894.8 | + | 20602.4i | 0.890418 | + | 1.54225i | 0.839375 | + | 0.543552i | \(0.182921\pi\) |
0.0510424 | + | 0.998696i | \(0.483746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2323.50 | − | 1341.48i | −0.173010 | − | 0.0998873i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 799.641 | + | 15226.1i | 0.0592271 | + | 1.12775i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7386.30 | − | 12793.4i | 0.544200 | − | 0.942582i | −0.454457 | − | 0.890769i | \(-0.650167\pi\) |
0.998657 | − | 0.0518134i | \(-0.0165001\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21040.7 | + | 12147.8i | −1.54208 | + | 0.890318i | −0.543369 | + | 0.839494i | \(0.682851\pi\) |
−0.998708 | + | 0.0508238i | \(0.983815\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6754.88i | − | 0.492477i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1031.62i | 0.0748199i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8681.56 | − | 5012.30i | 0.626375 | − | 0.361638i | −0.152972 | − | 0.988231i | \(-0.548884\pi\) |
0.779347 | + | 0.626593i | \(0.215551\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4709.15 | − | 8156.48i | 0.338006 | − | 0.585444i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8641.47 | + | 4401.86i | 0.617054 | + | 0.314320i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2715.69 | − | 1567.91i | −0.192920 | − | 0.111383i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −574.946 | − | 995.835i | −0.0406343 | − | 0.0703807i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10134.7 | −0.712613 | −0.356306 | − | 0.934369i | \(-0.615964\pi\) | ||||
−0.356306 | + | 0.934369i | \(0.615964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17306.1 | 1.21067 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3879.99 | + | 6720.34i | 0.270053 | + | 0.467746i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1903.10 | − | 1098.76i | −0.131789 | − | 0.0760885i | 0.432656 | − | 0.901559i | \(-0.357576\pi\) |
−0.564445 | + | 0.825471i | \(0.690910\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2412.82 | − | 1229.06i | −0.166246 | − | 0.0846834i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 877.803 | − | 1520.40i | 0.0601777 | − | 0.104231i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21359.3 | − | 12331.8i | 1.45696 | − | 0.841174i | 0.458095 | − | 0.888903i | \(-0.348532\pi\) |
0.998860 | + | 0.0477293i | \(0.0151985\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21532.0i | − | 1.46142i | −0.682691 | − | 0.730708i | \(-0.739190\pi\) | ||
0.682691 | − | 0.730708i | \(-0.260810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9546.12i | 0.644690i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1388.61 | + | 801.714i | −0.0933140 | + | 0.0538749i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 493.715 | − | 855.140i | 0.0330136 | − | 0.0571813i | −0.849047 | − | 0.528318i | \(-0.822823\pi\) |
0.882060 | + | 0.471137i | \(0.156156\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1127.65 | + | 21471.7i | 0.0750320 | + | 1.42870i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8016.43 | + | 4628.29i | 0.530786 | + | 0.306449i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3639.26 | − | 6303.38i | −0.239785 | − | 0.415320i | 0.720867 | − | 0.693073i | \(-0.243744\pi\) |
−0.960653 | + | 0.277753i | \(0.910410\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3101.41 | 0.203351 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2543.97 | −0.165991 | −0.0829953 | − | 0.996550i | \(-0.526449\pi\) | ||||
−0.0829953 | + | 0.996550i | \(0.526449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3926.57 | + | 6801.02i | 0.254963 | + | 0.441609i | 0.964886 | − | 0.262671i | \(-0.0846033\pi\) |
−0.709922 | + | 0.704280i | \(0.751270\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −210.491 | − | 121.527i | −0.0136018 | − | 0.00785300i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9806.63 | − | 15097.3i | −0.630649 | − | 0.970882i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7532.73 | + | 13047.1i | −0.482095 | + | 0.835013i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1685.77 | − | 973.282i | 0.107374 | − | 0.0619923i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17768.0i | 1.12632i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16369.0i | − | 1.03271i | −0.856375 | − | 0.516355i | \(-0.827289\pi\) | ||
0.856375 | − | 0.516355i | \(-0.172711\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12411.6 | + | 7165.83i | −0.779330 | + | 0.449946i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −664.369 | + | 1150.72i | −0.0415192 | + | 0.0719133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11392.4 | + | 8280.85i | −0.708605 | + | 0.515069i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19477.3 | − | 11245.2i | −1.20581 | − | 0.696173i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7248.62 | − | 12555.0i | −0.446651 | − | 0.773622i | 0.551515 | − | 0.834165i | \(-0.314050\pi\) |
−0.998166 | + | 0.0605431i | \(0.980717\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29771.6 | 1.82594 | 0.912969 | − | 0.408029i | \(-0.133784\pi\) | ||||
0.912969 | + | 0.408029i | \(0.133784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3115.32 | 0.190179 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5607.76 | + | 9712.93i | 0.340748 | + | 0.590193i | 0.984572 | − | 0.174981i | \(-0.0559864\pi\) |
−0.643824 | + | 0.765174i | \(0.722653\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 337.327 | + | 194.756i | 0.0204025 | + | 0.0117794i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31542.7 | + | 20489.0i | −1.89901 | + | 1.23353i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10200.5 | + | 17667.8i | −0.611295 | + | 1.05879i | 0.379727 | + | 0.925099i | \(0.376018\pi\) |
−0.991022 | + | 0.133696i | \(0.957315\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1625.33 | + | 938.385i | −0.0969571 | + | 0.0559782i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7814.13i | 0.464016i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13427.1i | 0.793693i | 0.917885 | + | 0.396846i | \(0.129895\pi\) | ||||
−0.917885 | + | 0.396846i | \(0.870105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2003.84 | + | 1156.92i | −0.117913 | + | 0.0680771i | −0.557797 | − | 0.829978i | \(-0.688353\pi\) |
0.439884 | + | 0.898055i | \(0.355020\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17320.8 | − | 30000.5i | 1.01461 | − | 1.75735i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1362.35 | − | 71.5476i | 0.0794431 | − | 0.00417218i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1189.13 | − | 686.546i | −0.0690305 | − | 0.0398548i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13787.0 | + | 23879.8i | 0.796765 | + | 1.38004i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −957.732 | −0.0551011 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16395.5 | −0.939081 | −0.469540 | − | 0.882911i | \(-0.655580\pi\) | ||||
−0.469540 | + | 0.882911i | \(0.655580\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1796.81 | − | 3112.16i | −0.102458 | − | 0.177462i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21618.4 | − | 12481.4i | −1.22727 | − | 0.708566i | −0.260814 | − | 0.965389i | \(-0.583991\pi\) |
−0.966458 | + | 0.256823i | \(0.917324\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5688.74 | + | 11167.8i | −0.321522 | + | 0.631195i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15028.3 | + | 26029.8i | −0.845647 | + | 1.46470i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17644.8 | − | 10187.3i | 0.988523 | − | 0.570724i | 0.0836904 | − | 0.996492i | \(-0.473329\pi\) |
0.904832 | + | 0.425768i | \(0.139996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1126.26i | − | 0.0628208i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12234.2i | 0.679422i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24348.8 | − | 14057.8i | 1.34632 | − | 0.777298i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3196.66 | − | 5536.78i | 0.175986 | − | 0.304817i | −0.764516 | − | 0.644605i | \(-0.777022\pi\) |
0.940502 | + | 0.339788i | \(0.110355\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −880.829 | + | 1729.19i | −0.0482827 | + | 0.0947859i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1510.12 | + | 871.868i | 0.0824203 | + | 0.0475854i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21428.9 | + | 37116.0i | 1.16453 | + | 2.01703i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6179.12 | 0.334357 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19401.6 | −1.04535 | −0.522674 | − | 0.852533i | \(-0.675066\pi\) | ||||
−0.522674 | + | 0.852533i | \(0.675066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4475.83 | − | 7752.37i | −0.240127 | − | 0.415912i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1687.65 | + | 974.367i | 0.0901570 | + | 0.0520521i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15513.2 | − | 814.716i | 0.825222 | − | 0.0433388i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7388.85 | + | 12797.9i | −0.391388 | + | 0.677904i | −0.992633 | − | 0.121161i | \(-0.961338\pi\) |
0.601245 | + | 0.799065i | \(0.294672\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1511.73 | + | 872.798i | −0.0797389 | + | 0.0460372i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2402.00i | − | 0.126165i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 230.163i | 0.0120386i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11271.5 | − | 6507.62i | 0.587089 | − | 0.338956i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3218.52 | + | 5574.64i | −0.166941 | + | 0.289150i | −0.937343 | − | 0.348408i | \(-0.886722\pi\) |
0.770402 | + | 0.637559i | \(0.220056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23533.0 | − | 15286.2i | 1.21556 | − | 0.789581i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28646.6 | − | 16539.1i | −1.47355 | − | 0.850757i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10150.7 | − | 17581.6i | −0.519985 | − | 0.900640i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13490.8 | 0.688235 | 0.344118 | − | 0.938927i | \(-0.388178\pi\) | ||||
0.344118 | + | 0.938927i | \(0.388178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13287.7 | −0.675086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21525.1 | + | 37282.5i | 1.08910 | + | 1.88638i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18019.0 | − | 10403.3i | −0.907978 | − | 0.524221i | −0.0281980 | − | 0.999602i | \(-0.508977\pi\) |
−0.879780 | + | 0.475381i | \(0.842310\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2398.36 | + | 1743.32i | −0.120361 | + | 0.0874874i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 955.377 | − | 1654.76i | 0.0477500 | − | 0.0827055i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14968.2 | − | 8641.87i | 0.745078 | − | 0.430171i | −0.0788348 | − | 0.996888i | \(-0.525120\pi\) |
0.823913 | + | 0.566717i | \(0.191787\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17452.8i | 0.865242i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11763.6i | 0.580839i | 0.956899 | + | 0.290420i | \(0.0937948\pi\) | ||||
−0.956899 | + | 0.290420i | \(0.906205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1460.93 | − | 843.468i | 0.0718447 | − | 0.0414795i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5990.49 | + | 10375.8i | −0.293414 | + | 0.508208i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17026.2 | − | 26211.7i | −0.830605 | − | 1.27871i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10719.5 | + | 6188.89i | 0.520851 | + | 0.300713i | 0.737283 | − | 0.675584i | \(-0.236109\pi\) |
−0.216432 | + | 0.976298i | \(0.569442\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3586.35 | + | 6211.74i | 0.173564 | + | 0.300622i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1632.50 | −0.0786924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18350.8 | 0.881071 | 0.440536 | − | 0.897735i | \(-0.354789\pi\) | ||||
0.440536 | + | 0.897735i | \(0.354789\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −135.087 | − | 233.977i | −0.00646027 | − | 0.0111895i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14340.0 | + | 8279.21i | 0.683081 | + | 0.394377i | 0.801015 | − | 0.598644i | \(-0.204294\pi\) |
−0.117934 | + | 0.993021i | \(0.537627\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1531.00 | + | 29152.1i | 0.0726422 | + | 1.38319i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1672.63 | − | 2897.08i | 0.0790511 | − | 0.136921i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3024.46 | + | 1746.17i | −0.142382 | + | 0.0822041i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3663.72i | − | 0.171804i | −0.996304 | − | 0.0859019i | \(-0.972623\pi\) | ||
0.996304 | − | 0.0859019i | \(-0.0273772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21304.7i | 0.995162i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34341.3 | − | 19827.0i | 1.59789 | − | 0.922544i | 0.606000 | − | 0.795465i | \(-0.292773\pi\) |
0.991893 | − | 0.127079i | \(-0.0405602\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17757.1 | − | 30756.1i | 0.823035 | − | 1.42554i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17336.0 | + | 8830.73i | 0.800419 | + | 0.407723i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18699.4 | − | 10796.1i | −0.860045 | − | 0.496547i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2250.85 | + | 3898.59i | 0.103126 | + | 0.178620i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4783.12 | 0.218308 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1537.17 | 0.0698905 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17734.3 | − | 30716.8i | −0.803254 | − | 1.39128i | −0.917464 | − | 0.397820i | \(-0.869767\pi\) |
0.114210 | − | 0.993457i | \(-0.463566\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16214.8 | − | 9361.61i | −0.731637 | − | 0.422411i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36173.9 | − | 18426.5i | −1.62604 | − | 0.828284i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4293.49 | − | 7436.54i | 0.192265 | − | 0.333013i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5126.00 | − | 2959.50i | 0.228680 | − | 0.132028i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 32026.0i | − | 1.42336i | −0.702503 | − | 0.711681i | \(-0.747934\pi\) | ||
0.702503 | − | 0.711681i | \(-0.252066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26929.2i | 1.19235i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19261.0 | − | 11120.3i | 0.849629 | − | 0.490533i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 782.040 | − | 1354.53i | 0.0343681 | − | 0.0595273i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.93047 | − | 189.088i | −0.000434786 | − | 0.00827884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2768.16 | + | 1598.20i | 0.120748 | + | 0.0697140i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1708.60 | − | 2959.39i | −0.0742537 | − | 0.128611i | 0.826508 | − | 0.562925i | \(-0.190324\pi\) |
−0.900761 | + | 0.434314i | \(0.856991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27667.8 | −1.19796 | −0.598982 | − | 0.800763i | \(-0.704428\pi\) | ||||
−0.598982 | + | 0.800763i | \(0.704428\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1163.39 | −0.0501868 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1991.75 | − | 3449.81i | −0.0856048 | − | 0.148272i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18783.3 | − | 10844.5i | −0.804338 | − | 0.464385i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9478.00 | − | 14591.3i | −0.404381 | − | 0.622543i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14342.5 | + | 24841.9i | −0.609690 | + | 1.05601i | 0.381601 | + | 0.924327i | \(0.375373\pi\) |
−0.991291 | + | 0.131687i | \(0.957960\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18633.9 | − | 10758.3i | 0.789231 | − | 0.455663i | −0.0504606 | − | 0.998726i | \(-0.516069\pi\) |
0.839692 | + | 0.543063i | \(0.182736\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3994.59i | − | 0.168574i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 28539.8i | − | 1.20003i | −0.799988 | − | 0.600016i | \(-0.795161\pi\) | ||
0.799988 | − | 0.600016i | \(-0.204839\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3778.09 | + | 2181.28i | −0.158285 | + | 0.0913862i | −0.577051 | − | 0.816708i | \(-0.695796\pi\) |
0.418765 | + | 0.908095i | \(0.362463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6849.32 | − | 11863.4i | 0.285921 | − | 0.495229i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37434.4 | − | 16657.0i | −1.55705 | − | 0.692835i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2900.37 | − | 1674.53i | −0.120205 | − | 0.0694006i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4183.65 | + | 7246.29i | 0.172769 | + | 0.299245i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34373.2 | −1.41442 | −0.707208 | − | 0.707006i | \(-0.750045\pi\) | ||||
−0.707208 | + | 0.707006i | \(0.750045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2632.42 | 0.107935 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25258.6 | − | 43749.2i | −1.03197 | − | 1.78743i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 541.635 | + | 312.713i | 0.0220507 | + | 0.0127310i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20346.4 | + | 13216.3i | −0.825396 | + | 0.536147i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11637.5 | − | 20156.8i | 0.470435 | − | 0.814816i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1075.99 | + | 621.224i | −0.0433426 | + | 0.0250238i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9468.45i | 0.380063i | 0.981778 | + | 0.190031i | \(0.0608590\pi\) | ||||
−0.981778 | + | 0.190031i | \(0.939141\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1685.37i | 0.0674136i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9863.17 | + | 5694.50i | −0.393138 | + | 0.226978i | −0.683519 | − | 0.729933i | \(-0.739551\pi\) |
0.290381 | + | 0.956911i | \(0.406218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4227.95 | + | 7323.02i | −0.167935 | + | 0.290871i | −0.937694 | − | 0.347464i | \(-0.887043\pi\) |
0.769759 | + | 0.638335i | \(0.220376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 46863.9 | − | 2461.19i | 1.85496 | − | 0.0974182i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6473.10 | − | 3737.24i | −0.255326 | − | 0.147413i | 0.366874 | − | 0.930271i | \(-0.380428\pi\) |
−0.622201 | + | 0.782858i | \(0.713761\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2068.58 | − | 3582.89i | −0.0813110 | − | 0.140835i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 66080.9 | 2.58850 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 349.399 | 0.0136393 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8565.86 | + | 14836.5i | 0.333230 | + | 0.577171i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13409.2 | − | 7741.81i | −0.519854 | − | 0.300138i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2556.82 | − | 5019.39i | 0.0987842 | − | 0.193927i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16028.3 | − | 27761.9i | 0.617147 | − | 1.06893i | −0.372857 | − | 0.927889i | \(-0.621622\pi\) |
0.990004 | − | 0.141041i | \(-0.0450449\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −45069.4 | + | 26020.8i | −1.72941 | + | 0.998476i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 27139.7i | − | 1.03787i | −0.854815 | − | 0.518933i | \(-0.826329\pi\) | ||
0.854815 | − | 0.518933i | \(-0.173671\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 43490.8i | − | 1.65751i | −0.559611 | − | 0.828755i | \(-0.689049\pi\) | ||
0.559611 | − | 0.828755i | \(-0.310951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −636.721 | + | 367.611i | −0.0241843 | + | 0.0139628i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16755.6 | + | 29021.6i | −0.634271 | + | 1.09859i | 0.352398 | + | 0.935850i | \(0.385366\pi\) |
−0.986669 | + | 0.162740i | \(0.947967\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9125.78 | + | 17915.2i | −0.344284 | + | 0.675880i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3265.16 | + | 1885.14i | 0.122769 | + | 0.0708807i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6783.60 | − | 11749.5i | −0.254204 | − | 0.440295i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1490.77 | −0.0556771 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2422.36 | 0.0901677 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23634.8 | + | 40936.6i | 0.876823 | + | 1.51870i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 70835.4 | + | 40896.8i | 2.61917 | + | 1.51218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 47074.2 | − | 2472.23i | 1.73481 | − | 0.0911082i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1075.63 | + | 1863.04i | −0.0395084 | + | 0.0684306i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6521.56 | + | 3765.22i | −0.238748 | + | 0.137841i | −0.614601 | − | 0.788838i | \(-0.710683\pi\) |
0.375853 | + | 0.926679i | \(0.377350\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19191.4i | 0.700264i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19971.6i | 0.726332i | 0.931724 | + | 0.363166i | \(0.118304\pi\) | ||||
−0.931724 | + | 0.363166i | \(0.881696\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2076.83 | − | 1199.06i | 0.0752826 | − | 0.0434644i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 903.882 | − | 1565.57i | 0.0326573 | − | 0.0565641i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23814.9 | + | 15469.3i | −0.857621 | + | 0.557079i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40488.0 | + | 23375.8i | 1.45329 | + | 0.839059i | 0.998667 | − | 0.0516235i | \(-0.0164396\pi\) |
0.454626 | + | 0.890682i | \(0.349773\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9509.61 | − | 16471.1i | −0.340230 | − | 0.589296i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40362.0 | −1.43936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18369.9 | −0.652972 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17333.9 | + | 30023.2i | 0.614154 | + | 1.06375i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16257.2 | − | 9386.12i | −0.574147 | − | 0.331484i | 0.184657 | − | 0.982803i | \(-0.440883\pi\) |
−0.758804 | + | 0.651319i | \(0.774216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20529.1 | − | 2162.24i | 0.722677 | − | 0.0761168i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10495.0 | − | 18177.8i | 0.368264 | − | 0.637851i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −579.881 | + | 334.794i | −0.0202825 | + | 0.0117101i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13717.6i | 0.478263i | 0.970987 | + | 0.239132i | \(0.0768628\pi\) | ||||
−0.970987 | + | 0.239132i | \(0.923137\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 8051.34i | − | 0.279814i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15972.8 | + | 9221.91i | −0.553346 | + | 0.319475i | −0.750471 | − | 0.660904i | \(-0.770173\pi\) |
0.197124 | + | 0.980379i | \(0.436840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1498.45 | + | 2595.39i | −0.0517456 | + | 0.0896261i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 359.299 | + | 553.139i | 0.0123683 | + | 0.0190409i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28785.9 | − | 16619.6i | −0.987769 | − | 0.570289i | −0.0831621 | − | 0.996536i | \(-0.526502\pi\) |
−0.904607 | + | 0.426247i | \(0.859835\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7011.73 | + | 12144.7i | 0.239842 | + | 0.415419i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39869.1 | 1.35946 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32914.7 | 1.11880 | 0.559398 | − | 0.828899i | \(-0.311033\pi\) | ||||
0.559398 | + | 0.828899i | \(0.311033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −585.321 | − | 1013.81i | −0.0198330 | − | 0.0343518i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4604.50 | + | 2658.41i | 0.155530 | + | 0.0897955i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −893.769 | − | 17018.4i | −0.0300952 | − | 0.573048i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26449.7 | + | 45812.2i | −0.887841 | + | 1.53779i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33440.7 | − | 19307.0i | 1.11902 | − | 0.646064i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1632.22i | − | 0.0544487i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 29368.7i | − | 0.976663i | −0.872658 | − | 0.488332i | \(-0.837606\pi\) | ||
0.872658 | − | 0.488332i | \(-0.162394\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43971.2 | + | 25386.8i | −1.45775 | + | 0.841632i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15783.6 | + | 27338.0i | −0.521647 | + | 0.903520i | 0.478035 | + | 0.878341i | \(0.341349\pi\) |
−0.999683 | + | 0.0251794i | \(0.991984\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23510.6 | + | 11976.0i | 0.774630 | + | 0.394587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 31016.9 | + | 17907.6i | 1.01881 | + | 0.588208i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11625.0 | − | 20135.1i | −0.380672 | − | 0.659343i | 0.610486 | − | 0.792027i | \(-0.290974\pi\) |
−0.991158 | + | 0.132683i | \(0.957641\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4451.70 | −0.145329 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −36064.3 | −1.17374 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2028.77 | + | 3513.93i | 0.0658268 | + | 0.114015i | 0.897060 | − | 0.441908i | \(-0.145698\pi\) |
−0.831234 | + | 0.555923i | \(0.812365\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1164.66 | + | 672.414i | 0.0376741 | + | 0.0217512i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26274.5 | + | 13383.9i | 0.847344 | + | 0.431626i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1505.17 | + | 2607.03i | −0.0483940 | + | 0.0838208i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36725.1 | + | 21203.3i | −1.17721 | + | 0.679661i | −0.955367 | − | 0.295422i | \(-0.904540\pi\) |
−0.221841 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 51980.4i | 1.66118i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 304.252i | − | 0.00969389i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49960.1 | + | 28844.5i | −1.58701 | + | 0.916263i | −0.593219 | + | 0.805041i | \(0.702143\pi\) |
−0.993796 | + | 0.111222i | \(0.964523\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2164.02 | − | 3748.19i | 0.0685350 | − | 0.118706i |
(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 | 112.4.p.f.47.3 | yes | 6 | |
4.3 | odd | 2 | 112.4.p.g.47.1 | yes | 6 | ||
7.2 | even | 3 | 784.4.f.h.783.1 | 6 | |||
7.3 | odd | 6 | 112.4.p.g.31.1 | yes | 6 | ||
7.5 | odd | 6 | 784.4.f.g.783.6 | 6 | |||
8.3 | odd | 2 | 448.4.p.f.383.3 | 6 | |||
8.5 | even | 2 | 448.4.p.g.383.1 | 6 | |||
28.3 | even | 6 | inner | 112.4.p.f.31.3 | ✓ | 6 | |
28.19 | even | 6 | 784.4.f.h.783.2 | 6 | |||
28.23 | odd | 6 | 784.4.f.g.783.5 | 6 | |||
56.3 | even | 6 | 448.4.p.g.255.1 | 6 | |||
56.45 | odd | 6 | 448.4.p.f.255.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.4.p.f.31.3 | ✓ | 6 | 28.3 | even | 6 | inner | |
112.4.p.f.47.3 | yes | 6 | 1.1 | even | 1 | trivial | |
112.4.p.g.31.1 | yes | 6 | 7.3 | odd | 6 | ||
112.4.p.g.47.1 | yes | 6 | 4.3 | odd | 2 | ||
448.4.p.f.255.3 | 6 | 56.45 | odd | 6 | |||
448.4.p.f.383.3 | 6 | 8.3 | odd | 2 | |||
448.4.p.g.255.1 | 6 | 56.3 | even | 6 | |||
448.4.p.g.383.1 | 6 | 8.5 | even | 2 | |||
784.4.f.g.783.5 | 6 | 28.23 | odd | 6 | |||
784.4.f.g.783.6 | 6 | 7.5 | odd | 6 | |||
784.4.f.h.783.1 | 6 | 7.2 | even | 3 | |||
784.4.f.h.783.2 | 6 | 28.19 | even | 6 |