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 | 31.1 | ||
Root | \(-2.61524 + 4.52973i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.31 |
Dual form | 112.4.p.f.47.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −4.64712 | + | 8.04905i | −0.894339 | + | 1.54904i | −0.0597180 | + | 0.998215i | \(0.519020\pi\) |
−0.834621 | + | 0.550825i | \(0.814313\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.1915 | + | 9.92549i | −1.53765 | + | 0.887763i | −0.538675 | + | 0.842513i | \(0.681075\pi\) |
−0.998976 | + | 0.0452498i | \(0.985592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.3972 | + | 2.13127i | 0.993357 | + | 0.115078i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −29.6915 | − | 51.4271i | −1.09968 | − | 1.90471i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.2499 | + | 5.91778i | 0.280951 | + | 0.162207i | 0.633854 | − | 0.773453i | \(-0.281472\pi\) |
−0.352903 | + | 0.935660i | \(0.614805\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 19.9862i | − | 0.426398i | −0.977009 | − | 0.213199i | \(-0.931612\pi\) | ||
0.977009 | − | 0.213199i | \(-0.0683882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 184.500i | − | 3.17584i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.57359 | + | 0.908512i | 0.0224501 | + | 0.0129616i | 0.511183 | − | 0.859472i | \(-0.329207\pi\) |
−0.488733 | + | 0.872433i | \(0.662541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.66142 | + | 6.34176i | 0.0442098 | + | 0.0765737i | 0.887284 | − | 0.461224i | \(-0.152590\pi\) |
−0.843074 | + | 0.537798i | \(0.819256\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −102.649 | + | 138.176i | −1.06666 | + | 1.43583i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −92.2074 | + | 53.2360i | −0.835938 | + | 0.482629i | −0.855881 | − | 0.517172i | \(-0.826985\pi\) |
0.0199435 | + | 0.999801i | \(0.493651\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 134.531 | − | 233.014i | 1.07625 | − | 1.86411i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 300.975 | 2.14528 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −191.679 | −1.22737 | −0.613687 | − | 0.789549i | \(-0.710315\pi\) | ||||
−0.613687 | + | 0.789549i | \(0.710315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −62.5752 | + | 108.383i | −0.362543 | + | 0.627944i | −0.988379 | − | 0.152012i | \(-0.951425\pi\) |
0.625835 | + | 0.779955i | \(0.284758\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −95.2651 | + | 55.0013i | −0.502531 | + | 0.290136i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −337.429 | + | 145.962i | −1.62960 | + | 0.704916i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −158.414 | − | 274.381i | −0.703867 | − | 1.21913i | −0.967099 | − | 0.254401i | \(-0.918122\pi\) |
0.263232 | − | 0.964733i | \(-0.415211\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 160.870 | + | 92.8782i | 0.660507 | + | 0.381344i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 321.806i | 1.22580i | 0.790162 | + | 0.612898i | \(0.209997\pi\) | ||||
−0.790162 | + | 0.612898i | \(0.790003\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 74.3089i | 0.263535i | 0.991281 | + | 0.131767i | \(0.0420652\pi\) | ||||
−0.991281 | + | 0.131767i | \(0.957935\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1020.88 | + | 589.405i | 3.38186 | + | 1.95252i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −77.2810 | − | 133.855i | −0.239842 | − | 0.415419i | 0.720827 | − | 0.693116i | \(-0.243762\pi\) |
−0.960669 | + | 0.277696i | \(0.910429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 333.915 | + | 78.4187i | 0.973514 | + | 0.228626i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.6253 | + | 8.44393i | −0.0401560 | + | 0.0231841i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 159.711 | − | 276.627i | 0.413923 | − | 0.716936i | −0.581391 | − | 0.813624i | \(-0.697492\pi\) |
0.995315 | + | 0.0966878i | \(0.0308248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −234.948 | −0.576006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −68.0602 | −0.158154 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 30.5584 | − | 52.9288i | 0.0674300 | − | 0.116792i | −0.830339 | − | 0.557258i | \(-0.811853\pi\) |
0.897769 | + | 0.440466i | \(0.145187\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −267.882 | + | 154.662i | −0.562275 | + | 0.324630i | −0.754058 | − | 0.656808i | \(-0.771906\pi\) |
0.191783 | + | 0.981437i | \(0.438573\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −436.635 | − | 1009.40i | −0.873189 | − | 2.01860i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 198.373 | + | 343.592i | 0.378540 | + | 0.655651i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 514.507 | + | 297.051i | 0.938165 | + | 0.541650i | 0.889385 | − | 0.457160i | \(-0.151133\pi\) |
0.0487806 | + | 0.998810i | \(0.484466\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 989.576i | − | 1.72654i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48.6774i | 0.0813654i | 0.999172 | + | 0.0406827i | \(0.0129533\pi\) | ||||
−0.999172 | + | 0.0406827i | \(0.987047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −667.072 | − | 385.134i | −1.06952 | − | 0.617487i | −0.141469 | − | 0.989943i | \(-0.545183\pi\) |
−0.928050 | + | 0.372455i | \(0.878516\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1250.36 | + | 2165.69i | 1.92506 | + | 3.33430i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 175.957 | + | 130.716i | 0.260418 | + | 0.193461i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −831.564 | + | 480.103i | −1.18428 | + | 0.683745i | −0.957001 | − | 0.290084i | \(-0.906317\pi\) |
−0.227280 | + | 0.973829i | \(0.572983\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −596.996 | + | 1034.03i | −0.818925 | + | 1.41842i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1064.55 | −1.40782 | −0.703912 | − | 0.710288i | \(-0.748565\pi\) | ||||
−0.703912 | + | 0.710288i | \(0.748565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −36.0697 | −0.0460272 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 890.755 | − | 1542.83i | 1.09769 | − | 1.90125i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −567.737 | + | 327.783i | −0.676180 | + | 0.390393i | −0.798414 | − | 0.602108i | \(-0.794327\pi\) |
0.122234 | + | 0.992501i | \(0.460994\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 42.5959 | − | 367.690i | 0.0490688 | − | 0.423565i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −581.589 | − | 1007.34i | −0.648473 | − | 1.12319i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −125.890 | − | 72.6828i | −0.135959 | − | 0.0784957i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 704.225i | 0.737147i | 0.929599 | + | 0.368573i | \(0.120154\pi\) | ||||
−0.929599 | + | 0.368573i | \(0.879846\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 702.830i | − | 0.713506i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −597.608 | − | 345.029i | −0.588754 | − | 0.339918i | 0.175850 | − | 0.984417i | \(-0.443733\pi\) |
−0.764605 | + | 0.644499i | \(0.777066\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −699.136 | − | 1210.94i | −0.668814 | − | 1.15842i | −0.978236 | − | 0.207496i | \(-0.933469\pi\) |
0.309421 | − | 0.950925i | \(-0.399865\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 393.218 | − | 3394.29i | 0.365468 | − | 3.15475i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 26.9985 | − | 15.5876i | 0.0243929 | − | 0.0140832i | −0.487754 | − | 0.872981i | \(-0.662184\pi\) |
0.512147 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −239.079 | + | 414.096i | −0.210088 | + | 0.363883i | −0.951742 | − | 0.306900i | \(-0.900708\pi\) |
0.741654 | + | 0.670783i | \(0.234042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2944.67 | 2.51798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1861.07 | 1.54933 | 0.774666 | − | 0.632371i | \(-0.217918\pi\) | ||||
0.774666 | + | 0.632371i | \(0.217918\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1056.79 | − | 1830.41i | 0.856921 | − | 1.48423i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1027.83 | + | 593.419i | −0.812163 | + | 0.468903i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 27.0134 | + | 20.0678i | 0.0208094 | + | 0.0154590i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −595.460 | − | 1031.37i | −0.447378 | − | 0.774881i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2590.23 | − | 1495.47i | −1.89881 | − | 1.09628i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2859.77i | 2.04628i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1583.04i | 1.10608i | 0.833155 | + | 0.553040i | \(0.186532\pi\) | ||||
−0.833155 | + | 0.553040i | \(0.813468\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −598.116 | − | 345.323i | −0.408226 | − | 0.235690i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1098.60 | + | 1902.83i | 0.732712 | + | 1.26909i | 0.955720 | + | 0.294278i | \(0.0950791\pi\) |
−0.223008 | + | 0.974817i | \(0.571588\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 53.8439 | + | 124.474i | 0.0351042 | + | 0.0811525i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5174.19 | + | 2987.32i | −3.29869 | + | 1.90450i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1249.70 | + | 2164.54i | −0.779336 | + | 1.34985i | 0.152990 | + | 0.988228i | \(0.451110\pi\) |
−0.932325 | + | 0.361621i | \(0.882223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2709.21 | 1.65318 | 0.826591 | − | 0.562804i | \(-0.190277\pi\) | ||||
0.826591 | + | 0.562804i | \(0.190277\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1436.54 | 0.858001 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 118.274 | − | 204.856i | 0.0691647 | − | 0.119797i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3295.24 | − | 1902.51i | 1.88727 | − | 1.08962i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2182.94 | + | 2323.28i | −1.22480 | + | 1.30354i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 843.791 | + | 1461.49i | 0.463933 | + | 0.803556i | 0.999153 | − | 0.0411569i | \(-0.0131044\pi\) |
−0.535219 | + | 0.844713i | \(0.679771\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2212.49 | + | 1277.38i | 1.19239 | + | 0.688424i | 0.958847 | − | 0.283924i | \(-0.0916363\pi\) |
0.233538 | + | 0.972348i | \(0.424970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 107.900i | − | 0.0570145i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2484.36i | − | 1.28741i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −249.833 | − | 144.241i | −0.126999 | − | 0.0733230i | 0.435155 | − | 0.900356i | \(-0.356694\pi\) |
−0.562154 | + | 0.827033i | \(0.690027\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1484.39 | + | 2571.04i | 0.740375 | + | 1.28237i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1809.82 | + | 782.875i | −0.885924 | + | 0.383225i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −633.656 | + | 365.841i | −0.304489 | + | 0.175797i | −0.644458 | − | 0.764640i | \(-0.722917\pi\) |
0.339969 | + | 0.940437i | \(0.389584\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1091.83 | − | 1891.11i | 0.515145 | − | 0.892257i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2121.63 | −0.983092 | −0.491546 | − | 0.870852i | \(-0.663568\pi\) | ||||
−0.491546 | + | 0.870852i | \(0.663568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1797.55 | 0.818185 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 217.426 | − | 376.592i | 0.0972337 | − | 0.168414i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2753.74 | + | 1589.87i | −1.21019 | + | 0.698703i | −0.962800 | − | 0.270214i | \(-0.912906\pi\) |
−0.247388 | + | 0.968916i | \(0.579572\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2971.61 | − | 4000.10i | 1.28361 | − | 1.72788i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 284.018 | + | 491.933i | 0.120611 | + | 0.208904i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1903.63 | − | 1099.06i | −0.794881 | − | 0.458924i | 0.0467974 | − | 0.998904i | \(-0.485098\pi\) |
−0.841678 | + | 0.539980i | \(0.818432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1266.98i | − | 0.520299i | −0.965568 | − | 0.260150i | \(-0.916228\pi\) | ||
0.965568 | − | 0.260150i | \(-0.0837719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2874.93i | − | 1.16132i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5446.73 | + | 3144.67i | 2.16460 | + | 1.24973i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.7528 | + | 18.6243i | 0.00420492 | + | 0.00728313i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5537.10 | + | 641.457i | 2.13103 | + | 0.246874i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1508.17 | − | 870.745i | 0.571349 | − | 0.329869i | −0.186339 | − | 0.982486i | \(-0.559662\pi\) |
0.757688 | + | 0.652617i | \(0.226329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 639.307 | − | 1107.31i | 0.238437 | − | 0.412985i | −0.721829 | − | 0.692071i | \(-0.756698\pi\) |
0.960266 | + | 0.279087i | \(0.0900316\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3687.45 | −1.35417 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 760.622 | 0.275087 | 0.137543 | − | 0.990496i | \(-0.456079\pi\) | ||||
0.137543 | + | 0.990496i | \(0.456079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2219.45 | + | 3844.19i | −0.790615 | + | 1.36939i | 0.134971 | + | 0.990850i | \(0.456906\pi\) |
−0.925587 | + | 0.378536i | \(0.876428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4781.96 | + | 2760.86i | −1.67808 | + | 0.968837i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3526.36 | − | 408.519i | −1.21922 | − | 0.141243i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3194.08 | − | 5532.32i | −1.08822 | − | 1.88485i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5475.55 | + | 3161.31i | 1.83853 | + | 1.06148i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 86.6699i | 0.0286846i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2084.90i | 0.680239i | 0.940382 | + | 0.340119i | \(0.110467\pi\) | ||||
−0.940382 | + | 0.340119i | \(0.889533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −391.807 | − | 226.210i | −0.126038 | − | 0.0727683i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −737.553 | − | 1277.48i | −0.233957 | − | 0.405225i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1382.20 | + | 1860.59i | −0.432397 | + | 0.582051i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6199.93 | − | 3579.53i | 1.91303 | − | 1.10449i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.1577 | − | 31.4500i | 0.00552678 | − | 0.00957266i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 399.456 | 0.119953 | 0.0599766 | − | 0.998200i | \(-0.480897\pi\) | ||||
0.0599766 | + | 0.998200i | \(0.480897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15977.7 | −4.73413 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1466.31 | − | 2539.72i | 0.428733 | − | 0.742587i | −0.568028 | − | 0.823009i | \(-0.692294\pi\) |
0.996761 | + | 0.0804222i | \(0.0256269\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1303.58 | − | 752.621i | 0.376170 | − | 0.217182i | −0.299981 | − | 0.953945i | \(-0.596980\pi\) |
0.676150 | + | 0.736764i | \(0.263647\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1869.83 | + | 808.836i | −0.532580 | + | 0.230379i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −467.095 | − | 809.032i | −0.131332 | − | 0.227474i | 0.792858 | − | 0.609406i | \(-0.208592\pi\) |
−0.924190 | + | 0.381932i | \(0.875259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2657.15 | + | 1534.10i | 0.737588 | + | 0.425846i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 8924.39i | − | 2.44600i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6859.78i | 1.85658i | 0.371860 | + | 0.928289i | \(0.378720\pi\) | ||||
−0.371860 | + | 0.928289i | \(0.621280\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1120.85 | + | 647.123i | 0.299586 | + | 0.172966i | 0.642257 | − | 0.766489i | \(-0.277998\pi\) |
−0.342671 | + | 0.939456i | \(0.611331\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1485.47 | − | 2572.91i | −0.392152 | − | 0.679227i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6518.84 | + | 1966.14i | −1.69989 | + | 0.512703i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 126.748 | − | 73.1778i | 0.0326508 | − | 0.0188510i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4947.08 | − | 8568.60i | 1.25907 | − | 2.18077i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 178.426 | 0.0448691 | 0.0224345 | − | 0.999748i | \(-0.492858\pi\) | ||||
0.0224345 | + | 0.999748i | \(0.492858\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1260.16 | −0.313144 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 167.620 | − | 290.327i | 0.0411639 | − | 0.0712980i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5109.33 | − | 2949.87i | 1.24012 | − | 0.715984i | 0.271002 | − | 0.962579i | \(-0.412645\pi\) |
0.969119 | + | 0.246595i | \(0.0793116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2329.60 | − | 5385.47i | −0.558896 | − | 1.29203i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5691.23 | + | 9857.49i | 1.34972 | + | 2.33779i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1748.87 | − | 1009.71i | −0.410037 | − | 0.236735i | 0.280768 | − | 0.959776i | \(-0.409411\pi\) |
−0.690806 | + | 0.723040i | \(0.742744\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6340.83i | 1.46986i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6092.99i | − | 1.39657i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1601.94 | − | 924.883i | −0.363094 | − | 0.209632i | 0.307343 | − | 0.951599i | \(-0.400560\pi\) |
−0.670437 | + | 0.741966i | \(0.733893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3599.43 | − | 6234.39i | −0.806826 | − | 1.39746i | −0.915052 | − | 0.403337i | \(-0.867850\pi\) |
0.108226 | − | 0.994126i | \(-0.465483\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2761.61 | + | 2051.56i | 0.612235 | + | 0.454820i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2757.86 | − | 1592.25i | 0.604746 | − | 0.349150i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2767.41 | + | 4793.30i | −0.600281 | + | 1.03972i | 0.392498 | + | 0.919753i | \(0.371611\pi\) |
−0.992778 | + | 0.119964i | \(0.961722\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7431.80 | 1.59473 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 752.919 | 0.159841 | 0.0799207 | − | 0.996801i | \(-0.474533\pi\) | ||||
0.0799207 | + | 0.996801i | \(0.474533\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2811.79 | + | 4870.17i | −0.590614 | + | 1.02297i | 0.403536 | + | 0.914964i | \(0.367781\pi\) |
−0.994150 | + | 0.108009i | \(0.965552\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1170.05 | − | 675.531i | 0.243186 | − | 0.140404i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −685.854 | + | 5920.34i | −0.141062 | + | 1.21765i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2454.85 | − | 4251.92i | −0.499664 | − | 0.865443i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5668.34 | − | 3272.62i | −1.14187 | − | 0.659259i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 507.111i | − | 0.101112i | −0.998721 | − | 0.0505559i | \(-0.983901\pi\) | ||
0.998721 | − | 0.0505559i | \(-0.0160993\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1213.23i | 0.239447i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3084.96 | + | 1781.10i | 0.602719 | + | 0.347980i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1063.98 | + | 1842.87i | 0.205792 | + | 0.356442i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −158.372 | + | 1367.08i | −0.0303270 | + | 0.261784i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5554.31 | − | 3206.78i | 1.05309 | − | 0.608003i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3070.19 | − | 5317.73i | 0.576389 | − | 0.998335i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7402.96 | −1.37625 | −0.688126 | − | 0.725591i | \(-0.741566\pi\) | ||||
−0.688126 | + | 0.725591i | \(0.741566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12995.9 | 2.39259 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2142.39 | + | 3710.72i | −0.390623 | + | 0.676578i | −0.992532 | − | 0.121986i | \(-0.961074\pi\) |
0.601909 | + | 0.798565i | \(0.294407\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1300.77 | + | 750.998i | −0.234900 | + | 0.135620i | −0.612830 | − | 0.790214i | \(-0.709969\pi\) |
0.377930 | + | 0.925834i | \(0.376636\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17525.2 | + | 13019.2i | 3.13470 | + | 2.32872i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3548.77 | − | 6146.66i | −0.628767 | − | 1.08906i | −0.987800 | − | 0.155731i | \(-0.950227\pi\) |
0.359033 | − | 0.933325i | \(-0.383107\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1964.69 | − | 1134.31i | −0.344832 | − | 0.199089i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 289.749i | 0.0503808i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.3058i | 0.00229211i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4657.07 | − | 2688.76i | −0.794854 | − | 0.458909i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2222.05 | − | 3848.71i | −0.375779 | − | 0.650869i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1136.48 | − | 2627.26i | −0.190444 | − | 0.440260i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9956.85 | + | 5748.59i | −1.65341 | + | 0.954595i | −0.677750 | + | 0.735292i | \(0.737045\pi\) |
−0.975657 | + | 0.219303i | \(0.929622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9407.08 | + | 16293.5i | −1.54806 | + | 2.68132i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11793.5 | −1.92343 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6020.26 | 0.973128 | 0.486564 | − | 0.873645i | \(-0.338250\pi\) | ||||
0.486564 | + | 0.873645i | \(0.338250\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8648.60 | + | 14979.8i | −1.38563 | + | 2.39998i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1282.78 | + | 740.613i | −0.203714 | + | 0.117614i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5975.98 | + | 2154.35i | 0.940737 | + | 0.339137i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9822.03 | + | 17012.3i | 1.53275 | + | 2.65481i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7699.30 | + | 4445.19i | 1.19112 | + | 0.687696i | 0.958562 | − | 0.284886i | \(-0.0919556\pi\) |
0.232563 | + | 0.972581i | \(0.425289\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6396.47i | 0.981075i | 0.871420 | + | 0.490538i | \(0.163200\pi\) | ||||
−0.871420 | + | 0.490538i | \(0.836800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 6015.33i | − | 0.914743i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9935.50 | − | 5736.27i | −1.49806 | − | 0.864903i | −0.498058 | − | 0.867144i | \(-0.665953\pi\) |
−0.999997 | + | 0.00224128i | \(0.999287\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −483.147 | − | 836.836i | −0.0722332 | − | 0.125112i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −287.062 | + | 124.174i | −0.0425572 | + | 0.0184090i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 169.226 | − | 97.7025i | 0.0248785 | − | 0.0143636i | −0.487509 | − | 0.873118i | \(-0.662094\pi\) |
0.512388 | + | 0.858754i | \(0.328761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3402.69 | − | 5893.63i | 0.496091 | − | 0.859255i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11068.7 | 1.60043 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15290.6 | 2.19273 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5113.87 | − | 8857.49i | 0.727362 | − | 1.25983i | −0.230632 | − | 0.973041i | \(-0.574079\pi\) |
0.957994 | − | 0.286787i | \(-0.0925873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16549.6 | − | 9554.89i | 2.33479 | − | 1.34799i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3527.80 | − | 4748.78i | 0.493677 | − | 0.664540i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3867.07 | + | 6697.97i | 0.536808 | + | 0.929779i | 0.999073 | + | 0.0430373i | \(0.0137034\pi\) |
−0.462265 | + | 0.886742i | \(0.652963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23018.4 | − | 13289.7i | −3.16978 | − | 1.83007i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3830.93i | 0.523350i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9739.99i | 1.32008i | 0.751231 | + | 0.660039i | \(0.229460\pi\) | ||||
−0.751231 | + | 0.660039i | \(0.770540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12742.0 | − | 7356.58i | −1.71336 | − | 0.989211i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1262.59 | + | 2186.86i | 0.168447 | + | 0.291759i | 0.937874 | − | 0.346976i | \(-0.112791\pi\) |
−0.769427 | + | 0.638735i | \(0.779458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4322.38 | − | 500.736i | −0.572180 | − | 0.0662854i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3821.49 | − | 2206.34i | 0.501957 | − | 0.289805i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1332.63 | − | 2308.18i | 0.173694 | − | 0.300847i | −0.766014 | − | 0.642823i | \(-0.777763\pi\) |
0.939709 | + | 0.341976i | \(0.111096\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −193.462 | −0.0250225 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20421.3 | −2.62117 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9530.53 | − | 16507.4i | 1.21401 | − | 2.10272i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6899.43 | − | 3983.39i | 0.872223 | − | 0.503578i | 0.00413668 | − | 0.999991i | \(-0.498683\pi\) |
0.868086 | + | 0.496413i | \(0.165350\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1252.12 | − | 145.054i | −0.157104 | − | 0.0182000i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1303.95 | − | 2258.50i | −0.162384 | − | 0.281257i | 0.773339 | − | 0.633992i | \(-0.218585\pi\) |
−0.935723 | + | 0.352735i | \(0.885252\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2166.17 | + | 1250.64i | 0.267754 | + | 0.154588i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 23701.9i | − | 2.90805i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3749.83i | − | 0.456689i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7616.13 | − | 4397.17i | −0.920766 | − | 0.531605i | −0.0368867 | − | 0.999319i | \(-0.511744\pi\) |
−0.883879 | + | 0.467715i | \(0.845077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11615.0 | − | 20117.8i | −1.39398 | − | 2.41444i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 674.996 | − | 908.614i | 0.0804222 | − | 0.108257i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18301.1 | − | 10566.2i | 2.16474 | − | 1.24981i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12590.0 | + | 21806.6i | −1.47850 | + | 2.56084i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −333.409 | −0.0388737 | −0.0194368 | − | 0.999811i | \(-0.506187\pi\) | ||||
−0.0194368 | + | 0.999811i | \(0.506187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1186.07 | −0.137305 | −0.0686526 | − | 0.997641i | \(-0.521870\pi\) | ||||
−0.0686526 | + | 0.997641i | \(0.521870\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4589.17 | + | 7948.68i | −0.527502 | + | 0.913659i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 423.393 | − | 244.446i | 0.0483237 | − | 0.0278997i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5257.91 | + | 2274.42i | −0.595897 | + | 0.257768i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1099.27 | + | 1903.98i | 0.123713 | + | 0.214278i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10533.5 | + | 6081.53i | 1.17722 | + | 0.679669i | 0.955370 | − | 0.295412i | \(-0.0954570\pi\) |
0.221851 | + | 0.975081i | \(0.428790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14229.4i | 1.57926i | 0.613582 | + | 0.789631i | \(0.289728\pi\) | ||||
−0.613582 | + | 0.789631i | \(0.710272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 35364.7i | 3.89795i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −675.220 | − | 389.838i | −0.0739134 | − | 0.0426739i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3977.54 | + | 6889.31i | 0.432432 | + | 0.748995i | 0.997082 | − | 0.0763357i | \(-0.0243221\pi\) |
−0.564650 | + | 0.825331i | \(0.690989\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5881.59 | − | 19500.7i | −0.635092 | − | 2.10568i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5552.88 | − | 3205.96i | 0.595542 | − | 0.343837i | −0.171744 | − | 0.985142i | \(-0.554940\pi\) |
0.767286 | + | 0.641305i | \(0.221607\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6506.82 | − | 11270.1i | 0.693153 | − | 1.20058i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15684.8 | −1.65965 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5918.99 | −0.622125 | −0.311063 | − | 0.950389i | \(-0.600685\pi\) | ||||
−0.311063 | + | 0.950389i | \(0.600685\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1904.38 | + | 3298.48i | −0.198833 | + | 0.344389i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20563.4 | + | 11872.3i | −2.13279 | + | 1.23137i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2917.22 | + | 6743.92i | 0.300575 | + | 0.694856i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −434.306 | − | 752.241i | −0.0444551 | − | 0.0769986i | 0.842942 | − | 0.538005i | \(-0.180822\pi\) |
−0.887397 | + | 0.461006i | \(0.847489\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 473.611 | + | 273.439i | 0.0481618 | + | 0.0278062i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4645.89i | − | 0.469372i | −0.972071 | − | 0.234686i | \(-0.924594\pi\) | ||
0.972071 | − | 0.234686i | \(-0.0754062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 288.831i | 0.0289916i | 0.999895 | + | 0.0144958i | \(0.00461433\pi\) | ||||
−0.999895 | + | 0.0144958i | \(0.995386\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19996.7 | + | 11545.1i | 1.99425 | + | 1.15138i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5658.72 | − | 9801.20i | −0.560716 | − | 0.971189i | −0.997434 | − | 0.0715906i | \(-0.977192\pi\) |
0.436718 | − | 0.899599i | \(-0.356141\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8832.41 | + | 6561.46i | 0.869601 | + | 0.646013i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2322.01 | − | 1340.61i | 0.227161 | − | 0.131151i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −439.744 | + | 761.659i | −0.0427473 | + | 0.0740404i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1970.30 | 0.190323 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18968.2 | −1.82074 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2162.11 | − | 3744.89i | 0.206241 | − | 0.357220i | −0.744286 | − | 0.667860i | \(-0.767210\pi\) |
0.950527 | + | 0.310641i | \(0.100544\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5483.82 | + | 3166.09i | −0.519835 | + | 0.300127i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2109.05 | − | 18205.4i | 0.198685 | − | 1.71507i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6989.78 | − | 12106.7i | −0.654412 | − | 1.13347i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9942.41 | − | 5740.26i | −0.925121 | − | 0.534119i | −0.0398556 | − | 0.999205i | \(-0.512690\pi\) |
−0.885265 | + | 0.465087i | \(0.846023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6800.44i | − | 0.628888i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10052.9i | − | 0.923994i | −0.886881 | − | 0.461997i | \(-0.847133\pi\) | ||
0.886881 | − | 0.461997i | \(-0.152867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −301.624 | − | 174.143i | −0.0275547 | − | 0.0159087i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6975.94 | + | 12082.7i | 0.633425 | + | 1.09712i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −103.745 | + | 895.529i | −0.00936334 | + | 0.0808249i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6238.96 | − | 3602.06i | 0.559708 | − | 0.323147i | −0.193320 | − | 0.981136i | \(-0.561926\pi\) |
0.753028 | + | 0.657988i | \(0.228592\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9859.45 | − | 17077.1i | 0.879217 | − | 1.52285i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6434.36 | −0.570366 | −0.285183 | − | 0.958473i | \(-0.592054\pi\) | ||||
−0.285183 | + | 0.958473i | \(0.592054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13698.3 | 1.20707 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8353.44 | + | 14468.6i | −0.731735 | + | 1.26740i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11271.3 | − | 6507.49i | 0.981517 | − | 0.566679i | 0.0787889 | − | 0.996891i | \(-0.474895\pi\) |
0.902728 | + | 0.430213i | \(0.141561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11451.5 | − | 8507.11i | −0.991355 | − | 0.736463i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1101.99 | + | 1908.71i | 0.0948426 | + | 0.164272i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24038.3 | + | 13878.5i | 2.05681 | + | 1.18750i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1829.33i | − | 0.155617i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 29553.3i | − | 2.49951i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4455.62 | + | 2572.46i | 0.374673 | + | 0.216317i | 0.675498 | − | 0.737362i | \(-0.263929\pi\) |
−0.300825 | + | 0.953679i | \(0.597262\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5598.83 | + | 9697.46i | 0.468106 | + | 0.810784i | 0.999336 | − | 0.0364439i | \(-0.0116030\pi\) |
−0.531229 | + | 0.847228i | \(0.678270\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18387.5 | + | 42507.6i | 1.52857 | + | 3.53368i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −196.935 | + | 113.701i | −0.0162783 | + | 0.00939826i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −415.363 | + | 719.430i | −0.0341385 | + | 0.0591296i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3629.30 | −0.296607 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6431.67 | 0.522677 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −309.429 | + | 535.946i | −0.0250052 | + | 0.0433102i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17692.8 | − | 10214.9i | 1.42179 | − | 0.820868i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2958.53 | + | 2779.82i | 0.236425 | + | 0.222144i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10913.7 | + | 18903.1i | 0.867313 | + | 1.50223i | 0.864732 | + | 0.502234i | \(0.167488\pi\) |
0.00258182 | + | 0.999997i | \(0.499178\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10198.0 | + | 5887.82i | 0.805964 | + | 0.465324i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9491.89i | − | 0.746033i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20005.0i | − | 1.56371i | −0.623459 | − | 0.781856i | \(-0.714273\pi\) | ||
0.623459 | − | 0.781856i | \(-0.285727\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15907.6 | + | 9184.27i | 1.23665 | + | 0.713980i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −701.816 | − | 1215.58i | −0.0542620 | − | 0.0939846i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16321.7 | + | 7060.29i | −1.25510 | + | 0.542918i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −50623.2 | + | 29227.3i | −3.87178 | + | 2.23537i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3700.46 | − | 6409.38i | 0.281496 | − | 0.487566i | −0.690257 | − | 0.723564i | \(-0.742503\pi\) |
0.971753 | + | 0.235998i | \(0.0758360\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1485.15 | 0.112371 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −199.877 | −0.0150425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 540.397 | − | 935.995i | 0.0404529 | − | 0.0700666i | −0.845090 | − | 0.534624i | \(-0.820453\pi\) |
0.885543 | + | 0.464557i | \(0.153787\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31994.5 | + | 18472.0i | −2.38233 | + | 1.37544i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13186.9 | + | 17750.9i | −0.976713 | + | 1.31476i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2104.06 | − | 3644.35i | −0.155021 | − | 0.268504i | 0.778046 | − | 0.628208i | \(-0.216211\pi\) |
−0.933067 | + | 0.359703i | \(0.882878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11155.9 | − | 6440.87i | −0.817619 | − | 0.472052i | 0.0319758 | − | 0.999489i | \(-0.489820\pi\) |
−0.849595 | + | 0.527436i | \(0.823153\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16185.8i | 1.18006i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28647.5i | 2.07771i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11493.5 | + | 6635.80i | 0.829259 | + | 0.478773i | 0.853599 | − | 0.520931i | \(-0.174415\pi\) |
−0.0243396 | + | 0.999704i | \(0.507748\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5941.87 | + | 10291.6i | 0.426487 | + | 0.738697i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19584.7 | − | 2268.83i | −1.39847 | − | 0.162009i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3274.03 | − | 1890.26i | 0.232584 | − | 0.134283i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11780.0 | − | 20403.5i | 0.832549 | − | 1.44202i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16892.3 | 1.18777 | 0.593885 | − | 0.804550i | \(-0.297593\pi\) | ||||
0.593885 | + | 0.804550i | \(0.297593\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −916.456 | −0.0641119 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3534.70 | + | 6122.28i | −0.246021 | + | 0.426120i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9489.27 | − | 5478.63i | 0.657129 | − | 0.379394i | −0.134053 | − | 0.990974i | \(-0.542799\pi\) |
0.791182 | + | 0.611580i | \(0.209466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −663.583 | − | 76.8742i | −0.0457214 | − | 0.00529670i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20628.1 | − | 35728.9i | −1.41416 | − | 2.44939i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10024.8 | + | 5787.82i | 0.683810 | + | 0.394798i | 0.801289 | − | 0.598277i | \(-0.204148\pi\) |
−0.117479 | + | 0.993075i | \(0.537481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17612.6i | 1.19540i | 0.801721 | + | 0.597699i | \(0.203918\pi\) | ||||
−0.801721 | + | 0.597699i | \(0.796082\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 35279.5i | − | 2.38257i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20473.6 | + | 11820.5i | 1.37582 | + | 0.794331i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8181.52 | + | 14170.8i | 0.547080 | + | 0.947570i | 0.998473 | + | 0.0552449i | \(0.0175939\pi\) |
−0.451393 | + | 0.892325i | \(0.649073\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19675.6 | − | 26485.4i | 1.30919 | − | 1.76230i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2675.24 | + | 1544.55i | −0.177134 | + | 0.102268i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −503.862 | + | 872.715i | −0.0331987 | + | 0.0575018i | −0.882147 | − | 0.470973i | \(-0.843903\pi\) |
0.848949 | + | 0.528475i | \(0.177236\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 59373.2 | 3.89294 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14986.9 | −0.977876 | −0.488938 | − | 0.872318i | \(-0.662616\pi\) | ||||
−0.488938 | + | 0.872318i | \(0.662616\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8834.12 | + | 15301.2i | −0.573624 | + | 0.993546i | 0.422565 | + | 0.906332i | \(0.361130\pi\) |
−0.996190 | + | 0.0872139i | \(0.972204\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27752.1 | + | 16022.7i | −1.79332 | + | 1.03538i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11143.4 | + | 4820.30i | −0.716613 | + | 0.309986i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11568.3 | − | 20036.8i | −0.740369 | − | 1.28236i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −697.610 | − | 402.766i | −0.0444336 | − | 0.0256538i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 575.684i | − | 0.0364929i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3794.54i | 0.239395i | 0.992810 | + | 0.119698i | \(0.0381925\pi\) | ||||
−0.992810 | + | 0.119698i | \(0.961807\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16781.5 | − | 9688.78i | −1.05372 | − | 0.608364i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15712.5 | − | 27214.8i | −0.981937 | − | 1.70077i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1567.29 | − | 6673.69i | 0.0974856 | − | 0.415104i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2503.34 | − | 1445.30i | 0.154977 | − | 0.0894762i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7125.73 | + | 12342.1i | −0.439079 | + | 0.760507i | −0.997619 | − | 0.0689710i | \(-0.978028\pi\) |
0.558540 | + | 0.829478i | \(0.311362\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10643.5 | −0.652782 | −0.326391 | − | 0.945235i | \(-0.605833\pi\) | ||||
−0.326391 | + | 0.945235i | \(0.605833\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13710.0 | 0.836946 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9474.19 | − | 16409.8i | 0.575686 | − | 0.997118i | −0.420281 | − | 0.907394i | \(-0.638068\pi\) |
0.995967 | − | 0.0897234i | \(-0.0285983\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 626.442 | − | 361.676i | 0.0378891 | − | 0.0218753i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8552.71 | − | 19771.8i | −0.514911 | − | 1.19035i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10673.1 | − | 18486.4i | −0.639620 | − | 1.10785i | −0.985516 | − | 0.169582i | \(-0.945758\pi\) |
0.345896 | − | 0.938273i | \(-0.387575\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37773.1 | − | 21808.3i | −2.25331 | − | 1.30095i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 45740.8i | 2.71616i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3245.68i | − | 0.191857i | −0.995388 | − | 0.0959284i | \(-0.969418\pi\) | ||
0.995388 | − | 0.0959284i | \(-0.0305820\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13847.6 | + | 7994.93i | 0.814841 | + | 0.470449i | 0.848634 | − | 0.528980i | \(-0.177425\pi\) |
−0.0337929 | + | 0.999429i | \(0.510759\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 168.762 | + | 292.304i | 0.00988563 | + | 0.0171224i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2161.12 | − | 1605.47i | −0.126022 | − | 0.0936200i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17674.2 | − | 10204.2i | 1.02601 | − | 0.592367i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1856.32 | + | 3215.24i | −0.107279 | + | 0.185812i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3661.02 | −0.210629 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3473.65 | −0.198959 | −0.0994796 | − | 0.995040i | \(-0.531718\pi\) | ||||
−0.0994796 | + | 0.995040i | \(0.531718\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 40490.4 | − | 70131.4i | 2.30885 | − | 3.99905i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23449.5 | − | 13538.6i | 1.33122 | − | 0.768583i | 0.345737 | − | 0.938331i | \(-0.387629\pi\) |
0.985487 | + | 0.169748i | \(0.0542954\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1500.89 | + | 12955.8i | −0.0848290 | + | 0.732249i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13628.2 | + | 23604.8i | 0.766865 | + | 1.32825i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5728.91 | − | 3307.59i | −0.320952 | − | 0.185302i | 0.330865 | − | 0.943678i | \(-0.392660\pi\) |
−0.651817 | + | 0.758376i | \(0.725993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 49615.5i | − | 2.76746i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13990.1i | 0.776936i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5528.71 | − | 3192.00i | −0.305700 | − | 0.176496i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7904.11 | + | 13690.3i | 0.435147 | + | 0.753697i | 0.997308 | − | 0.0733313i | \(-0.0233631\pi\) |
−0.562161 | + | 0.827028i | \(0.690030\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1497.92 | − | 12930.1i | 0.0821086 | − | 0.708766i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46575.3 | + | 26890.2i | −2.54202 | + | 1.46763i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −292.365 | + | 506.391i | −0.0158882 | + | 0.0275192i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8682.59 | 0.469822 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9851.70 | 0.530804 | 0.265402 | − | 0.964138i | \(-0.414495\pi\) | ||||
0.265402 | + | 0.964138i | \(0.414495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1160.04 | − | 2009.25i | 0.0622357 | − | 0.107795i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24696.2 | + | 14258.3i | −1.31931 | + | 0.761702i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10259.0 | − | 7621.24i | −0.545726 | − | 0.405412i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5383.62 | + | 9324.70i | 0.285171 | + | 0.493930i | 0.972651 | − | 0.232273i | \(-0.0746163\pi\) |
−0.687480 | + | 0.726204i | \(0.741283\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 49380.7 | + | 28509.9i | 2.60467 | + | 1.50381i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 13325.0i | − | 0.699896i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4695.71i | 0.245608i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −55214.7 | − | 31878.2i | −2.87591 | − | 1.66041i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10369.0 | + | 17959.6i | 0.537827 | + | 0.931544i | 0.999021 | + | 0.0442447i | \(0.0140881\pi\) |
−0.461193 | + | 0.887300i | \(0.652579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10281.3 | − | 23767.9i | −0.531063 | − | 1.22769i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10417.5 | + | 6014.52i | −0.535864 | + | 0.309381i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25786.7 | + | 44663.9i | −1.32096 | + | 2.28797i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2738.00 | 0.139679 | 0.0698396 | − | 0.997558i | \(-0.477751\pi\) | ||||
0.0698396 | + | 0.997558i | \(0.477751\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4625.18 | −0.234984 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −67.5106 | + | 116.932i | −0.00341583 | + | 0.00591638i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14909.6 | − | 8608.06i | 0.751294 | − | 0.433760i | −0.0748673 | − | 0.997194i | \(-0.523853\pi\) |
0.826161 | + | 0.563434i | \(0.190520\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14468.3 | − | 61607.4i | 0.726081 | − | 3.09173i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3515.77 | + | 6089.49i | 0.175719 | + | 0.304354i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4783.71 | + | 2761.87i | 0.238121 | + | 0.137479i | 0.614313 | − | 0.789063i | \(-0.289433\pi\) |
−0.376192 | + | 0.926542i | \(0.622767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1360.26i | 0.0674366i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 20424.6i | − | 1.00849i | −0.863561 | − | 0.504244i | \(-0.831771\pi\) | ||
0.863561 | − | 0.504244i | \(-0.168229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29012.0 | − | 16750.1i | −1.42674 | − | 0.823726i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31608.0 | + | 54746.6i | 1.54816 | + | 2.68149i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 529.918 | − | 229.227i | 0.0258515 | − | 0.0111826i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9321.70 | + | 5381.88i | −0.452934 | + | 0.261502i | −0.709069 | − | 0.705140i | \(-0.750884\pi\) |
0.256134 | + | 0.966641i | \(0.417551\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −829.166 | + | 1436.16i | −0.0401281 | + | 0.0695040i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −50714.7 | −2.44463 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8591.14 | 0.412484 | 0.206242 | − | 0.978501i | \(-0.433877\pi\) | ||||
0.206242 | + | 0.978501i | \(0.433877\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5856.10 | − | 10143.1i | 0.280056 | − | 0.485072i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25875.0 | + | 14938.9i | −1.23254 | + | 0.711610i | −0.967560 | − | 0.252642i | \(-0.918700\pi\) |
−0.264985 | + | 0.964252i | \(0.585367\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5280.93 | + | 7108.68i | −0.250567 | + | 0.337289i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1070.96 | + | 1854.96i | 0.0506154 | + | 0.0876684i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1057.84 | − | 610.746i | −0.0497999 | − | 0.0287520i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3093.61i | − | 0.145070i | −0.997366 | − | 0.0725348i | \(-0.976891\pi\) | ||
0.997366 | − | 0.0725348i | \(-0.0231089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54833.6i | 2.56133i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20812.1 | + | 12015.9i | 0.968381 | + | 0.559095i | 0.898742 | − | 0.438477i | \(-0.144482\pi\) |
0.0696388 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16836.6 | + | 29161.9i | 0.780373 | + | 1.35164i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 54173.8 | + | 6275.88i | 2.50125 | + | 0.289763i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2040.82 | + | 1178.27i | −0.0938638 | + | 0.0541923i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −288.062 | + | 498.939i | −0.0131981 | + | 0.0228597i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −57690.5 | −2.63307 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5726.67 | 0.260374 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5796.60 | + | 10040.0i | −0.262550 | + | 0.454749i | −0.966919 | − | 0.255085i | \(-0.917897\pi\) |
0.704369 | + | 0.709834i | \(0.251230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16254.4 | − | 9384.48i | 0.733425 | − | 0.423443i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34238.5 | + | 3966.43i | 1.53904 | + | 0.178293i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3091.10 | + | 5353.94i | 0.138421 | + | 0.239753i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −51037.6 | − | 29466.6i | −2.27688 | − | 1.31456i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11467.4i | 0.509658i | 0.966986 | + | 0.254829i | \(0.0820192\pi\) | ||||
−0.966986 | + | 0.254829i | \(0.917981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 280.843i | − | 0.0124349i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33713.9 | + | 19464.7i | 1.48717 | + | 0.858617i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4558.28 | − | 7895.18i | −0.200322 | − | 0.346967i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23343.0 | − | 31422.1i | 1.02203 | − | 1.37576i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14888.9 | − | 8596.09i | 0.649458 | − | 0.374965i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18190.8 | + | 31507.5i | −0.790551 | + | 1.36928i | 0.135074 | + | 0.990835i | \(0.456873\pi\) |
−0.925626 | + | 0.378440i | \(0.876461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35717.1 | 1.54648 | 0.773241 | − | 0.634113i | \(-0.218634\pi\) | ||||
0.773241 | + | 0.634113i | \(0.218634\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 66907.9 | 2.88630 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7262.31 | − | 12578.7i | 0.312132 | − | 0.540629i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −471.250 | + | 272.076i | −0.0201798 | + | 0.0116508i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20174.0 | + | 8726.67i | −0.860728 | + | 0.372326i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15659.5 | + | 27123.1i | 0.665678 | + | 1.15299i | 0.979101 | + | 0.203375i | \(0.0651909\pi\) |
−0.313423 | + | 0.949614i | \(0.601476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3616.81 | + | 2088.17i | 0.153189 | + | 0.0884435i | 0.574635 | − | 0.818410i | \(-0.305144\pi\) |
−0.421446 | + | 0.906853i | \(0.638477\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29597.5i | 1.24903i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7930.70i | − | 0.333467i | −0.986002 | − | 0.166734i | \(-0.946678\pi\) | ||
0.986002 | − | 0.166734i | \(-0.0533220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2465.72 | + | 1423.58i | 0.103303 | + | 0.0596419i | 0.550761 | − | 0.834663i | \(-0.314337\pi\) |
−0.447459 | + | 0.894305i | \(0.647671\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25721.0 | − | 44550.1i | −1.07371 | − | 1.85972i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 454.201 | + | 426.765i | 0.0188921 | + | 0.0177509i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36473.9 | − | 21058.2i | 1.51165 | − | 0.872753i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18833.6 | + | 32620.7i | −0.777758 | + | 1.34712i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25648.9 | −1.05542 | −0.527711 | − | 0.849424i | \(-0.676949\pi\) | ||||
−0.527711 | + | 0.849424i | \(0.676949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12351.8 | 0.506449 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3498.91 | + | 6060.29i | −0.142952 | + | 0.247601i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30902.6 | + | 17841.6i | −1.25808 | + | 0.726355i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8756.69 | − | 20243.4i | −0.355234 | − | 0.821216i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26133.5 | − | 45264.5i | −1.05642 | − | 1.82977i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29213.9 | + | 16866.6i | 1.17678 | + | 0.679413i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1004.85i | − | 0.0403348i | −0.999797 | − | 0.0201674i | \(-0.993580\pi\) | ||
0.999797 | − | 0.0201674i | \(-0.00641991\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8632.23i | 0.345282i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30363.3 | + | 17530.2i | 1.21026 | + | 0.698742i | 0.962815 | − | 0.270161i | \(-0.0870770\pi\) |
0.247441 | + | 0.968903i | \(0.420410\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4503.21 | − | 7799.79i | −0.178868 | − | 0.309808i | 0.762625 | − | 0.646841i | \(-0.223910\pi\) |
−0.941493 | + | 0.337032i | \(0.890577\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −44465.8 | − | 33033.0i | −1.76004 | − | 1.30750i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37701.0 | + | 21766.7i | −1.48709 | + | 0.858570i | −0.999892 | − | 0.0147228i | \(-0.995313\pi\) |
−0.487195 | + | 0.873293i | \(0.661980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31560.5 | − | 54664.4i | 1.24057 | − | 2.14872i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45631.9 | 1.78748 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11364.6 | −0.443633 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5936.91 | − | 10283.0i | 0.230958 | − | 0.400031i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36216.3 | − | 20909.5i | 1.40405 | − | 0.810628i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6094.93 | + | 52611.8i | −0.235481 | + | 2.03269i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11768.8 | + | 20384.1i | 0.453140 | + | 0.784862i | 0.998579 | − | 0.0532888i | \(-0.0169704\pi\) |
−0.545439 | + | 0.838151i | \(0.683637\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4081.76 | + | 2356.61i | 0.156626 | + | 0.0904281i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 41234.7i | − | 1.57688i | −0.615111 | − | 0.788440i | \(-0.710889\pi\) | ||
0.615111 | − | 0.788440i | \(-0.289111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2981.04i | − | 0.113613i | −0.998385 | − | 0.0568063i | \(-0.981908\pi\) | ||
0.998385 | − | 0.0568063i | \(-0.0180917\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9765.35 | − | 5638.03i | −0.370914 | − | 0.214147i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11920.6 | − | 20647.1i | −0.451245 | − | 0.781580i | 0.547218 | − | 0.836990i | \(-0.315687\pi\) |
−0.998464 | + | 0.0554102i | \(0.982353\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3373.88 | + | 29123.6i | −0.127285 | + | 1.09873i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12238.3 | + | 7065.79i | −0.460156 | + | 0.265671i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 565.916 | − | 980.195i | 0.0212068 | − | 0.0367312i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43634.8 | 1.62967 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19777.8 | −0.736191 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11994.4 | − | 20774.8i | 0.444977 | − | 0.770722i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 502.638 | − | 290.198i | 0.0185852 | − | 0.0107302i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10267.7 | − | 7627.72i | −0.378392 | − | 0.281101i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12575.4 | + | 21781.3i | 0.461902 | + | 0.800038i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29395.0 | − | 16971.2i | −1.07612 | − | 0.621301i | −0.146276 | − | 0.989244i | \(-0.546729\pi\) |
−0.929848 | + | 0.367943i | \(0.880062\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 40977.7i | 1.49521i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18217.3i | 0.662531i | 0.943538 | + | 0.331265i | \(0.107476\pi\) | ||||
−0.943538 | + | 0.331265i | \(0.892524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10911.5 | − | 6299.76i | −0.395529 | − | 0.228359i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28535.1 | + | 49424.2i | 1.03097 | + | 1.78570i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16155.8 | + | 37348.3i | 0.581800 | + | 1.34498i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35386.4 | + | 20430.3i | −1.27017 | + | 0.733335i | −0.975021 | − | 0.222115i | \(-0.928704\pi\) |
−0.295153 | + | 0.955450i | \(0.595371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34402.5 | − | 59586.8i | 1.23084 | − | 2.13187i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 972.875 | 0.0346940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −85246.2 | −3.03014 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41516.7 | + | 71909.1i | −1.47097 | + | 2.54779i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26497.2 | − | 15298.2i | 0.935786 | − | 0.540276i | 0.0471490 | − | 0.998888i | \(-0.484986\pi\) |
0.888637 | + | 0.458612i | \(0.151653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 725.291 | + | 2404.74i | 0.0255322 | + | 0.0846531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19911.9 | − | 34488.4i | −0.698698 | − | 1.21018i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −369.711 | − | 213.453i | −0.0129314 | − | 0.00746594i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28125.2i | 0.980586i | 0.871558 | + | 0.490293i | \(0.163110\pi\) | ||||
−0.871558 | + | 0.490293i | \(0.836890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 13959.9i | − | 0.485159i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26065.7 | − | 15049.0i | −0.902994 | − | 0.521344i | −0.0248237 | − | 0.999692i | \(-0.507902\pi\) |
−0.878170 | + | 0.478348i | \(0.841236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17131.7 | − | 29672.9i | −0.591605 | − | 1.02469i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −101558. | + | 43930.8i | −3.49595 | + | 1.51224i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35865.6 | − | 20707.0i | 1.23070 | − | 0.710547i | 0.263526 | − | 0.964652i | \(-0.415114\pi\) |
0.967176 | + | 0.254106i | \(0.0817811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7697.36 | + | 13332.2i | −0.263295 | + | 0.456040i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 65966.3 | 2.24932 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33248.1 | −1.13013 | −0.565063 | − | 0.825047i | \(-0.691148\pi\) | ||||
−0.565063 | + | 0.825047i | \(0.691148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17285.1 | + | 29938.8i | −0.585690 | + | 1.01445i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18260.3 | − | 10542.6i | 0.616794 | − | 0.356106i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27604.2 | + | 37158.1i | −0.929495 | + | 1.25120i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7064.18 | + | 12235.5i | 0.237125 | + | 0.410712i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1603.25 | − | 925.635i | −0.0536489 | − | 0.0309742i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25381.8i | 0.846702i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39769.8i | − | 1.32255i | −0.750142 | − | 0.661277i | \(-0.770015\pi\) | ||
0.750142 | − | 0.661277i | \(-0.229985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −107.099 | − | 61.8335i | −0.00355058 | − | 0.00204993i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13406.3 | − | 23220.3i | −0.443077 | − | 0.767431i | 0.554839 | − | 0.831957i | \(-0.312780\pi\) |
−0.997916 | + | 0.0645263i | \(0.979446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49841.9 | + | 5774.05i | 1.64220 | + | 0.190244i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 43283.9 | − | 24990.0i | 1.42174 | − | 0.820841i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7910.98 | + | 13702.2i | −0.259053 | + | 0.448693i | −0.965988 | − | 0.258585i | \(-0.916744\pi\) |
0.706935 | + | 0.707278i | \(0.250077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7759.00 | −0.253298 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28394.4 | 0.924120 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17516.6 | − | 30339.7i | 0.568356 | − | 0.984421i | −0.428373 | − | 0.903602i | \(-0.640913\pi\) |
0.996729 | − | 0.0808192i | \(-0.0257536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13076.2 | + | 7549.55i | −0.422987 | + | 0.244212i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26428.3 | + | 3061.64i | 0.852301 | + | 0.0987367i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3955.91 | − | 6851.83i | −0.127190 | − | 0.220299i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22133.0 | + | 12778.5i | 0.709463 | + | 0.409608i | 0.810862 | − | 0.585237i | \(-0.198999\pi\) |
−0.101399 | + | 0.994846i | \(0.532332\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 106858.i | − | 3.41493i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 88116.4i | − | 2.80752i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25633.4 | − | 14799.4i | −0.814259 | − | 0.470113i | 0.0341734 | − | 0.999416i | \(-0.489120\pi\) |
−0.848433 | + | 0.529303i | \(0.822453\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −47678.6 | − | 82581.7i | −1.50999 | − | 2.61538i |
(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.31.1 | ✓ | 6 | |
4.3 | odd | 2 | 112.4.p.g.31.3 | yes | 6 | ||
7.3 | odd | 6 | 784.4.f.g.783.2 | 6 | |||
7.4 | even | 3 | 784.4.f.h.783.5 | 6 | |||
7.5 | odd | 6 | 112.4.p.g.47.3 | yes | 6 | ||
8.3 | odd | 2 | 448.4.p.f.255.1 | 6 | |||
8.5 | even | 2 | 448.4.p.g.255.3 | 6 | |||
28.3 | even | 6 | 784.4.f.h.783.6 | 6 | |||
28.11 | odd | 6 | 784.4.f.g.783.1 | 6 | |||
28.19 | even | 6 | inner | 112.4.p.f.47.1 | yes | 6 | |
56.5 | odd | 6 | 448.4.p.f.383.1 | 6 | |||
56.19 | even | 6 | 448.4.p.g.383.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.4.p.f.31.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
112.4.p.f.47.1 | yes | 6 | 28.19 | even | 6 | inner | |
112.4.p.g.31.3 | yes | 6 | 4.3 | odd | 2 | ||
112.4.p.g.47.3 | yes | 6 | 7.5 | odd | 6 | ||
448.4.p.f.255.1 | 6 | 8.3 | odd | 2 | |||
448.4.p.f.383.1 | 6 | 56.5 | odd | 6 | |||
448.4.p.g.255.3 | 6 | 8.5 | even | 2 | |||
448.4.p.g.383.3 | 6 | 56.19 | even | 6 | |||
784.4.f.g.783.1 | 6 | 28.11 | odd | 6 | |||
784.4.f.g.783.2 | 6 | 7.3 | odd | 6 | |||
784.4.f.h.783.5 | 6 | 7.4 | even | 3 | |||
784.4.f.h.783.6 | 6 | 28.3 | even | 6 |