Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.d.337.1 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.353553i | 0.984251 | + | 0.176777i | \(0.0565670\pi\) | ||||
−0.984251 | + | 0.176777i | \(0.943433\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 7.00000 | 0.875000 | ||||||||
\(5\) | − 7.00000i | − 0.626099i | −0.949737 | − | 0.313050i | \(-0.898649\pi\) | ||||
0.949737 | − | 0.313050i | \(-0.101351\pi\) | |||||||
\(6\) | 3.00000i | 0.204124i | ||||||||
\(7\) | − 10.0000i | − 0.539949i | −0.962867 | − | 0.269975i | \(-0.912985\pi\) | ||||
0.962867 | − | 0.269975i | \(-0.0870153\pi\) | |||||||
\(8\) | 15.0000i | 0.662913i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 7.00000 | 0.221359 | ||||||||
\(11\) | − 22.0000i | − 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 21.0000 | 0.505181 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 10.0000 | 0.190901 | ||||||||
\(15\) | − 21.0000i | − 0.361478i | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | −37.0000 | −0.527872 | −0.263936 | − | 0.964540i | \(-0.585021\pi\) | ||||
−0.263936 | + | 0.964540i | \(0.585021\pi\) | |||||||
\(18\) | 9.00000i | 0.117851i | ||||||||
\(19\) | − 30.0000i | − 0.362235i | −0.983461 | − | 0.181118i | \(-0.942029\pi\) | ||||
0.983461 | − | 0.181118i | \(-0.0579715\pi\) | |||||||
\(20\) | − 49.0000i | − 0.547837i | ||||||||
\(21\) | − 30.0000i | − 0.311740i | ||||||||
\(22\) | 22.0000 | 0.213201 | ||||||||
\(23\) | 162.000 | 1.46867 | 0.734333 | − | 0.678789i | \(-0.237495\pi\) | ||||
0.734333 | + | 0.678789i | \(0.237495\pi\) | |||||||
\(24\) | 45.0000i | 0.382733i | ||||||||
\(25\) | 76.0000 | 0.608000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | − 70.0000i | − 0.472456i | ||||||||
\(29\) | −113.000 | −0.723571 | −0.361786 | − | 0.932261i | \(-0.617833\pi\) | ||||
−0.361786 | + | 0.932261i | \(0.617833\pi\) | |||||||
\(30\) | 21.0000 | 0.127802 | ||||||||
\(31\) | − 196.000i | − 1.13557i | −0.823177 | − | 0.567785i | \(-0.807801\pi\) | ||||
0.823177 | − | 0.567785i | \(-0.192199\pi\) | |||||||
\(32\) | 161.000i | 0.889408i | ||||||||
\(33\) | − 66.0000i | − 0.348155i | ||||||||
\(34\) | − 37.0000i | − 0.186631i | ||||||||
\(35\) | −70.0000 | −0.338062 | ||||||||
\(36\) | 63.0000 | 0.291667 | ||||||||
\(37\) | 13.0000i | 0.0577618i | 0.999583 | + | 0.0288809i | \(0.00919436\pi\) | ||||
−0.999583 | + | 0.0288809i | \(0.990806\pi\) | |||||||
\(38\) | 30.0000 | 0.128070 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 105.000 | 0.415049 | ||||||||
\(41\) | − 285.000i | − 1.08560i | −0.839863 | − | 0.542799i | \(-0.817365\pi\) | ||||
0.839863 | − | 0.542799i | \(-0.182635\pi\) | |||||||
\(42\) | 30.0000 | 0.110217 | ||||||||
\(43\) | 246.000 | 0.872434 | 0.436217 | − | 0.899842i | \(-0.356318\pi\) | ||||
0.436217 | + | 0.899842i | \(0.356318\pi\) | |||||||
\(44\) | − 154.000i | − 0.527645i | ||||||||
\(45\) | − 63.0000i | − 0.208700i | ||||||||
\(46\) | 162.000i | 0.519252i | ||||||||
\(47\) | − 462.000i | − 1.43382i | −0.697165 | − | 0.716911i | \(-0.745555\pi\) | ||||
0.697165 | − | 0.716911i | \(-0.254445\pi\) | |||||||
\(48\) | 123.000 | 0.369865 | ||||||||
\(49\) | 243.000 | 0.708455 | ||||||||
\(50\) | 76.0000i | 0.214960i | ||||||||
\(51\) | −111.000 | −0.304767 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −537.000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(54\) | 27.0000i | 0.0680414i | ||||||||
\(55\) | −154.000 | −0.377552 | ||||||||
\(56\) | 150.000 | 0.357939 | ||||||||
\(57\) | − 90.0000i | − 0.209137i | ||||||||
\(58\) | − 113.000i | − 0.255821i | ||||||||
\(59\) | 576.000i | 1.27100i | 0.772102 | + | 0.635498i | \(0.219205\pi\) | ||||
−0.772102 | + | 0.635498i | \(0.780795\pi\) | |||||||
\(60\) | − 147.000i | − 0.316294i | ||||||||
\(61\) | −635.000 | −1.33284 | −0.666421 | − | 0.745575i | \(-0.732175\pi\) | ||||
−0.666421 | + | 0.745575i | \(0.732175\pi\) | |||||||
\(62\) | 196.000 | 0.401484 | ||||||||
\(63\) | − 90.0000i | − 0.179983i | ||||||||
\(64\) | 167.000 | 0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 66.0000 | 0.123091 | ||||||||
\(67\) | − 202.000i | − 0.368332i | −0.982895 | − | 0.184166i | \(-0.941042\pi\) | ||||
0.982895 | − | 0.184166i | \(-0.0589584\pi\) | |||||||
\(68\) | −259.000 | −0.461888 | ||||||||
\(69\) | 486.000 | 0.847935 | ||||||||
\(70\) | − 70.0000i | − 0.119523i | ||||||||
\(71\) | 1086.00i | 1.81527i | 0.419755 | + | 0.907637i | \(0.362116\pi\) | ||||
−0.419755 | + | 0.907637i | \(0.637884\pi\) | |||||||
\(72\) | 135.000i | 0.220971i | ||||||||
\(73\) | − 805.000i | − 1.29066i | −0.763904 | − | 0.645330i | \(-0.776720\pi\) | ||||
0.763904 | − | 0.645330i | \(-0.223280\pi\) | |||||||
\(74\) | −13.0000 | −0.0204219 | ||||||||
\(75\) | 228.000 | 0.351029 | ||||||||
\(76\) | − 210.000i | − 0.316956i | ||||||||
\(77\) | −220.000 | −0.325602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 884.000 | 1.25896 | 0.629480 | − | 0.777017i | \(-0.283268\pi\) | ||||
0.629480 | + | 0.777017i | \(0.283268\pi\) | |||||||
\(80\) | − 287.000i | − 0.401095i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 285.000 | 0.383817 | ||||||||
\(83\) | − 518.000i | − 0.685035i | −0.939511 | − | 0.342517i | \(-0.888720\pi\) | ||||
0.939511 | − | 0.342517i | \(-0.111280\pi\) | |||||||
\(84\) | − 210.000i | − 0.272772i | ||||||||
\(85\) | 259.000i | 0.330500i | ||||||||
\(86\) | 246.000i | 0.308452i | ||||||||
\(87\) | −339.000 | −0.417754 | ||||||||
\(88\) | 330.000 | 0.399751 | ||||||||
\(89\) | 194.000i | 0.231056i | 0.993304 | + | 0.115528i | \(0.0368560\pi\) | ||||
−0.993304 | + | 0.115528i | \(0.963144\pi\) | |||||||
\(90\) | 63.0000 | 0.0737865 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1134.00 | 1.28508 | ||||||||
\(93\) | − 588.000i | − 0.655621i | ||||||||
\(94\) | 462.000 | 0.506933 | ||||||||
\(95\) | −210.000 | −0.226795 | ||||||||
\(96\) | 483.000i | 0.513500i | ||||||||
\(97\) | 1202.00i | 1.25819i | 0.777328 | + | 0.629096i | \(0.216575\pi\) | ||||
−0.777328 | + | 0.629096i | \(0.783425\pi\) | |||||||
\(98\) | 243.000i | 0.250477i | ||||||||
\(99\) | − 198.000i | − 0.201008i | ||||||||
\(100\) | 532.000 | 0.532000 | ||||||||
\(101\) | 429.000 | 0.422645 | 0.211322 | − | 0.977416i | \(-0.432223\pi\) | ||||
0.211322 | + | 0.977416i | \(0.432223\pi\) | |||||||
\(102\) | − 111.000i | − 0.107751i | ||||||||
\(103\) | 1302.00 | 1.24553 | 0.622766 | − | 0.782408i | \(-0.286009\pi\) | ||||
0.622766 | + | 0.782408i | \(0.286009\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −210.000 | −0.195180 | ||||||||
\(106\) | − 537.000i | − 0.492057i | ||||||||
\(107\) | −1338.00 | −1.20887 | −0.604436 | − | 0.796654i | \(-0.706602\pi\) | ||||
−0.604436 | + | 0.796654i | \(0.706602\pi\) | |||||||
\(108\) | 189.000 | 0.168394 | ||||||||
\(109\) | 1034.00i | 0.908617i | 0.890844 | + | 0.454308i | \(0.150114\pi\) | ||||
−0.890844 | + | 0.454308i | \(0.849886\pi\) | |||||||
\(110\) | − 154.000i | − 0.133485i | ||||||||
\(111\) | 39.0000i | 0.0333488i | ||||||||
\(112\) | − 410.000i | − 0.345905i | ||||||||
\(113\) | 1077.00 | 0.896599 | 0.448299 | − | 0.893884i | \(-0.352030\pi\) | ||||
0.448299 | + | 0.893884i | \(0.352030\pi\) | |||||||
\(114\) | 90.0000 | 0.0739410 | ||||||||
\(115\) | − 1134.00i | − 0.919531i | ||||||||
\(116\) | −791.000 | −0.633125 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −576.000 | −0.449365 | ||||||||
\(119\) | 370.000i | 0.285024i | ||||||||
\(120\) | 315.000 | 0.239629 | ||||||||
\(121\) | 847.000 | 0.636364 | ||||||||
\(122\) | − 635.000i | − 0.471231i | ||||||||
\(123\) | − 855.000i | − 0.626770i | ||||||||
\(124\) | − 1372.00i | − 0.993623i | ||||||||
\(125\) | − 1407.00i | − 1.00677i | ||||||||
\(126\) | 90.0000 | 0.0636336 | ||||||||
\(127\) | 988.000 | 0.690321 | 0.345161 | − | 0.938544i | \(-0.387824\pi\) | ||||
0.345161 | + | 0.938544i | \(0.387824\pi\) | |||||||
\(128\) | 1455.00i | 1.00473i | ||||||||
\(129\) | 738.000 | 0.503700 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 560.000 | 0.373492 | 0.186746 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186746 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(132\) | − 462.000i | − 0.304636i | ||||||||
\(133\) | −300.000 | −0.195589 | ||||||||
\(134\) | 202.000 | 0.130225 | ||||||||
\(135\) | − 189.000i | − 0.120493i | ||||||||
\(136\) | − 555.000i | − 0.349933i | ||||||||
\(137\) | − 519.000i | − 0.323658i | −0.986819 | − | 0.161829i | \(-0.948261\pi\) | ||||
0.986819 | − | 0.161829i | \(-0.0517393\pi\) | |||||||
\(138\) | 486.000i | 0.299790i | ||||||||
\(139\) | −348.000 | −0.212352 | −0.106176 | − | 0.994347i | \(-0.533861\pi\) | ||||
−0.106176 | + | 0.994347i | \(0.533861\pi\) | |||||||
\(140\) | −490.000 | −0.295804 | ||||||||
\(141\) | − 1386.00i | − 0.827817i | ||||||||
\(142\) | −1086.00 | −0.641796 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 369.000 | 0.213542 | ||||||||
\(145\) | 791.000i | 0.453027i | ||||||||
\(146\) | 805.000 | 0.456317 | ||||||||
\(147\) | 729.000 | 0.409027 | ||||||||
\(148\) | 91.0000i | 0.0505416i | ||||||||
\(149\) | 645.000i | 0.354634i | 0.984154 | + | 0.177317i | \(0.0567418\pi\) | ||||
−0.984154 | + | 0.177317i | \(0.943258\pi\) | |||||||
\(150\) | 228.000i | 0.124107i | ||||||||
\(151\) | 2914.00i | 1.57045i | 0.619211 | + | 0.785225i | \(0.287453\pi\) | ||||
−0.619211 | + | 0.785225i | \(0.712547\pi\) | |||||||
\(152\) | 450.000 | 0.240130 | ||||||||
\(153\) | −333.000 | −0.175957 | ||||||||
\(154\) | − 220.000i | − 0.115118i | ||||||||
\(155\) | −1372.00 | −0.710979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2079.00 | −1.05683 | −0.528415 | − | 0.848986i | \(-0.677213\pi\) | ||||
−0.528415 | + | 0.848986i | \(0.677213\pi\) | |||||||
\(158\) | 884.000i | 0.445109i | ||||||||
\(159\) | −1611.00 | −0.803526 | ||||||||
\(160\) | 1127.00 | 0.556857 | ||||||||
\(161\) | − 1620.00i | − 0.793006i | ||||||||
\(162\) | 81.0000i | 0.0392837i | ||||||||
\(163\) | 1700.00i | 0.816897i | 0.912781 | + | 0.408449i | \(0.133930\pi\) | ||||
−0.912781 | + | 0.408449i | \(0.866070\pi\) | |||||||
\(164\) | − 1995.00i | − 0.949898i | ||||||||
\(165\) | −462.000 | −0.217980 | ||||||||
\(166\) | 518.000 | 0.242196 | ||||||||
\(167\) | 3680.00i | 1.70519i | 0.522571 | + | 0.852596i | \(0.324973\pi\) | ||||
−0.522571 | + | 0.852596i | \(0.675027\pi\) | |||||||
\(168\) | 450.000 | 0.206656 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −259.000 | −0.116849 | ||||||||
\(171\) | − 270.000i | − 0.120745i | ||||||||
\(172\) | 1722.00 | 0.763379 | ||||||||
\(173\) | −4146.00 | −1.82205 | −0.911025 | − | 0.412352i | \(-0.864707\pi\) | ||||
−0.911025 | + | 0.412352i | \(0.864707\pi\) | |||||||
\(174\) | − 339.000i | − 0.147698i | ||||||||
\(175\) | − 760.000i | − 0.328289i | ||||||||
\(176\) | − 902.000i | − 0.386311i | ||||||||
\(177\) | 1728.00i | 0.733810i | ||||||||
\(178\) | −194.000 | −0.0816905 | ||||||||
\(179\) | −3674.00 | −1.53412 | −0.767060 | − | 0.641575i | \(-0.778281\pi\) | ||||
−0.767060 | + | 0.641575i | \(0.778281\pi\) | |||||||
\(180\) | − 441.000i | − 0.182612i | ||||||||
\(181\) | 3283.00 | 1.34820 | 0.674098 | − | 0.738642i | \(-0.264533\pi\) | ||||
0.674098 | + | 0.738642i | \(0.264533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1905.00 | −0.769517 | ||||||||
\(184\) | 2430.00i | 0.973598i | ||||||||
\(185\) | 91.0000 | 0.0361646 | ||||||||
\(186\) | 588.000 | 0.231797 | ||||||||
\(187\) | 814.000i | 0.318319i | ||||||||
\(188\) | − 3234.00i | − 1.25459i | ||||||||
\(189\) | − 270.000i | − 0.103913i | ||||||||
\(190\) | − 210.000i | − 0.0801842i | ||||||||
\(191\) | −596.000 | −0.225786 | −0.112893 | − | 0.993607i | \(-0.536012\pi\) | ||||
−0.112893 | + | 0.993607i | \(0.536012\pi\) | |||||||
\(192\) | 501.000 | 0.188315 | ||||||||
\(193\) | − 393.000i | − 0.146574i | −0.997311 | − | 0.0732869i | \(-0.976651\pi\) | ||||
0.997311 | − | 0.0732869i | \(-0.0233489\pi\) | |||||||
\(194\) | −1202.00 | −0.444838 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1701.00 | 0.619898 | ||||||||
\(197\) | 3522.00i | 1.27377i | 0.770960 | + | 0.636884i | \(0.219777\pi\) | ||||
−0.770960 | + | 0.636884i | \(0.780223\pi\) | |||||||
\(198\) | 198.000 | 0.0710669 | ||||||||
\(199\) | −2018.00 | −0.718855 | −0.359428 | − | 0.933173i | \(-0.617028\pi\) | ||||
−0.359428 | + | 0.933173i | \(0.617028\pi\) | |||||||
\(200\) | 1140.00i | 0.403051i | ||||||||
\(201\) | − 606.000i | − 0.212656i | ||||||||
\(202\) | 429.000i | 0.149427i | ||||||||
\(203\) | 1130.00i | 0.390692i | ||||||||
\(204\) | −777.000 | −0.266671 | ||||||||
\(205\) | −1995.00 | −0.679692 | ||||||||
\(206\) | 1302.00i | 0.440362i | ||||||||
\(207\) | 1458.00 | 0.489556 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −660.000 | −0.218436 | ||||||||
\(210\) | − 210.000i | − 0.0690066i | ||||||||
\(211\) | 160.000 | 0.0522031 | 0.0261016 | − | 0.999659i | \(-0.491691\pi\) | ||||
0.0261016 | + | 0.999659i | \(0.491691\pi\) | |||||||
\(212\) | −3759.00 | −1.21778 | ||||||||
\(213\) | 3258.00i | 1.04805i | ||||||||
\(214\) | − 1338.00i | − 0.427401i | ||||||||
\(215\) | − 1722.00i | − 0.546230i | ||||||||
\(216\) | 405.000i | 0.127578i | ||||||||
\(217\) | −1960.00 | −0.613150 | ||||||||
\(218\) | −1034.00 | −0.321245 | ||||||||
\(219\) | − 2415.00i | − 0.745162i | ||||||||
\(220\) | −1078.00 | −0.330358 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −39.0000 | −0.0117906 | ||||||||
\(223\) | − 4072.00i | − 1.22279i | −0.791327 | − | 0.611393i | \(-0.790609\pi\) | ||||
0.791327 | − | 0.611393i | \(-0.209391\pi\) | |||||||
\(224\) | 1610.00 | 0.480235 | ||||||||
\(225\) | 684.000 | 0.202667 | ||||||||
\(226\) | 1077.00i | 0.316995i | ||||||||
\(227\) | 5794.00i | 1.69410i | 0.531511 | + | 0.847051i | \(0.321624\pi\) | ||||
−0.531511 | + | 0.847051i | \(0.678376\pi\) | |||||||
\(228\) | − 630.000i | − 0.182995i | ||||||||
\(229\) | 6482.00i | 1.87049i | 0.353999 | + | 0.935246i | \(0.384822\pi\) | ||||
−0.353999 | + | 0.935246i | \(0.615178\pi\) | |||||||
\(230\) | 1134.00 | 0.325103 | ||||||||
\(231\) | −660.000 | −0.187986 | ||||||||
\(232\) | − 1695.00i | − 0.479665i | ||||||||
\(233\) | −6890.00 | −1.93725 | −0.968624 | − | 0.248530i | \(-0.920053\pi\) | ||||
−0.968624 | + | 0.248530i | \(0.920053\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3234.00 | −0.897714 | ||||||||
\(236\) | 4032.00i | 1.11212i | ||||||||
\(237\) | 2652.00 | 0.726860 | ||||||||
\(238\) | −370.000 | −0.100771 | ||||||||
\(239\) | − 2466.00i | − 0.667415i | −0.942677 | − | 0.333708i | \(-0.891700\pi\) | ||||
0.942677 | − | 0.333708i | \(-0.108300\pi\) | |||||||
\(240\) | − 861.000i | − 0.231572i | ||||||||
\(241\) | − 3617.00i | − 0.966770i | −0.875408 | − | 0.483385i | \(-0.839407\pi\) | ||||
0.875408 | − | 0.483385i | \(-0.160593\pi\) | |||||||
\(242\) | 847.000i | 0.224989i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −4445.00 | −1.16624 | ||||||||
\(245\) | − 1701.00i | − 0.443563i | ||||||||
\(246\) | 855.000 | 0.221597 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2940.00 | 0.752783 | ||||||||
\(249\) | − 1554.00i | − 0.395505i | ||||||||
\(250\) | 1407.00 | 0.355946 | ||||||||
\(251\) | −4860.00 | −1.22215 | −0.611077 | − | 0.791571i | \(-0.709263\pi\) | ||||
−0.611077 | + | 0.791571i | \(0.709263\pi\) | |||||||
\(252\) | − 630.000i | − 0.157485i | ||||||||
\(253\) | − 3564.00i | − 0.885639i | ||||||||
\(254\) | 988.000i | 0.244065i | ||||||||
\(255\) | 777.000i | 0.190814i | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | −565.000 | −0.137135 | −0.0685676 | − | 0.997646i | \(-0.521843\pi\) | ||||
−0.0685676 | + | 0.997646i | \(0.521843\pi\) | |||||||
\(258\) | 738.000i | 0.178085i | ||||||||
\(259\) | 130.000 | 0.0311884 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1017.00 | −0.241190 | ||||||||
\(262\) | 560.000i | 0.132049i | ||||||||
\(263\) | −498.000 | −0.116760 | −0.0583802 | − | 0.998294i | \(-0.518594\pi\) | ||||
−0.0583802 | + | 0.998294i | \(0.518594\pi\) | |||||||
\(264\) | 990.000 | 0.230797 | ||||||||
\(265\) | 3759.00i | 0.871372i | ||||||||
\(266\) | − 300.000i | − 0.0691511i | ||||||||
\(267\) | 582.000i | 0.133400i | ||||||||
\(268\) | − 1414.00i | − 0.322290i | ||||||||
\(269\) | 5546.00 | 1.25705 | 0.628523 | − | 0.777791i | \(-0.283660\pi\) | ||||
0.628523 | + | 0.777791i | \(0.283660\pi\) | |||||||
\(270\) | 189.000 | 0.0426006 | ||||||||
\(271\) | − 2256.00i | − 0.505691i | −0.967507 | − | 0.252845i | \(-0.918634\pi\) | ||||
0.967507 | − | 0.252845i | \(-0.0813664\pi\) | |||||||
\(272\) | −1517.00 | −0.338168 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 519.000 | 0.114430 | ||||||||
\(275\) | − 1672.00i | − 0.366638i | ||||||||
\(276\) | 3402.00 | 0.741943 | ||||||||
\(277\) | −2309.00 | −0.500846 | −0.250423 | − | 0.968137i | \(-0.580570\pi\) | ||||
−0.250423 | + | 0.968137i | \(0.580570\pi\) | |||||||
\(278\) | − 348.000i | − 0.0750779i | ||||||||
\(279\) | − 1764.00i | − 0.378523i | ||||||||
\(280\) | − 1050.00i | − 0.224105i | ||||||||
\(281\) | 5833.00i | 1.23832i | 0.785265 | + | 0.619159i | \(0.212527\pi\) | ||||
−0.785265 | + | 0.619159i | \(0.787473\pi\) | |||||||
\(282\) | 1386.00 | 0.292678 | ||||||||
\(283\) | −1650.00 | −0.346581 | −0.173290 | − | 0.984871i | \(-0.555440\pi\) | ||||
−0.173290 | + | 0.984871i | \(0.555440\pi\) | |||||||
\(284\) | 7602.00i | 1.58837i | ||||||||
\(285\) | −630.000 | −0.130940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2850.00 | −0.586168 | ||||||||
\(288\) | 1449.00i | 0.296469i | ||||||||
\(289\) | −3544.00 | −0.721352 | ||||||||
\(290\) | −791.000 | −0.160169 | ||||||||
\(291\) | 3606.00i | 0.726417i | ||||||||
\(292\) | − 5635.00i | − 1.12933i | ||||||||
\(293\) | 2991.00i | 0.596369i | 0.954508 | + | 0.298184i | \(0.0963811\pi\) | ||||
−0.954508 | + | 0.298184i | \(0.903619\pi\) | |||||||
\(294\) | 729.000i | 0.144613i | ||||||||
\(295\) | 4032.00 | 0.795770 | ||||||||
\(296\) | −195.000 | −0.0382910 | ||||||||
\(297\) | − 594.000i | − 0.116052i | ||||||||
\(298\) | −645.000 | −0.125382 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1596.00 | 0.307150 | ||||||||
\(301\) | − 2460.00i | − 0.471070i | ||||||||
\(302\) | −2914.00 | −0.555238 | ||||||||
\(303\) | 1287.00 | 0.244014 | ||||||||
\(304\) | − 1230.00i | − 0.232057i | ||||||||
\(305\) | 4445.00i | 0.834492i | ||||||||
\(306\) | − 333.000i | − 0.0622103i | ||||||||
\(307\) | − 2422.00i | − 0.450263i | −0.974328 | − | 0.225132i | \(-0.927719\pi\) | ||||
0.974328 | − | 0.225132i | \(-0.0722812\pi\) | |||||||
\(308\) | −1540.00 | −0.284901 | ||||||||
\(309\) | 3906.00 | 0.719109 | ||||||||
\(310\) | − 1372.00i | − 0.251369i | ||||||||
\(311\) | 3402.00 | 0.620288 | 0.310144 | − | 0.950690i | \(-0.399623\pi\) | ||||
0.310144 | + | 0.950690i | \(0.399623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2310.00 | 0.417153 | 0.208577 | − | 0.978006i | \(-0.433117\pi\) | ||||
0.208577 | + | 0.978006i | \(0.433117\pi\) | |||||||
\(314\) | − 2079.00i | − 0.373646i | ||||||||
\(315\) | −630.000 | −0.112687 | ||||||||
\(316\) | 6188.00 | 1.10159 | ||||||||
\(317\) | 257.000i | 0.0455349i | 0.999741 | + | 0.0227674i | \(0.00724773\pi\) | ||||
−0.999741 | + | 0.0227674i | \(0.992752\pi\) | |||||||
\(318\) | − 1611.00i | − 0.284089i | ||||||||
\(319\) | 2486.00i | 0.436330i | ||||||||
\(320\) | − 1169.00i | − 0.204216i | ||||||||
\(321\) | −4014.00 | −0.697943 | ||||||||
\(322\) | 1620.00 | 0.280370 | ||||||||
\(323\) | 1110.00i | 0.191214i | ||||||||
\(324\) | 567.000 | 0.0972222 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1700.00 | −0.288817 | ||||||||
\(327\) | 3102.00i | 0.524590i | ||||||||
\(328\) | 4275.00 | 0.719657 | ||||||||
\(329\) | −4620.00 | −0.774191 | ||||||||
\(330\) | − 462.000i | − 0.0770675i | ||||||||
\(331\) | − 1028.00i | − 0.170707i | −0.996351 | − | 0.0853535i | \(-0.972798\pi\) | ||||
0.996351 | − | 0.0853535i | \(-0.0272019\pi\) | |||||||
\(332\) | − 3626.00i | − 0.599405i | ||||||||
\(333\) | 117.000i | 0.0192539i | ||||||||
\(334\) | −3680.00 | −0.602876 | ||||||||
\(335\) | −1414.00 | −0.230612 | ||||||||
\(336\) | − 1230.00i | − 0.199708i | ||||||||
\(337\) | −2487.00 | −0.402005 | −0.201002 | − | 0.979591i | \(-0.564420\pi\) | ||||
−0.201002 | + | 0.979591i | \(0.564420\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3231.00 | 0.517651 | ||||||||
\(340\) | 1813.00i | 0.289187i | ||||||||
\(341\) | −4312.00 | −0.684774 | ||||||||
\(342\) | 270.000 | 0.0426898 | ||||||||
\(343\) | − 5860.00i | − 0.922479i | ||||||||
\(344\) | 3690.00i | 0.578347i | ||||||||
\(345\) | − 3402.00i | − 0.530891i | ||||||||
\(346\) | − 4146.00i | − 0.644192i | ||||||||
\(347\) | −2850.00 | −0.440911 | −0.220455 | − | 0.975397i | \(-0.570754\pi\) | ||||
−0.220455 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(348\) | −2373.00 | −0.365535 | ||||||||
\(349\) | − 2018.00i | − 0.309516i | −0.987952 | − | 0.154758i | \(-0.950540\pi\) | ||||
0.987952 | − | 0.154758i | \(-0.0494598\pi\) | |||||||
\(350\) | 760.000 | 0.116068 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3542.00 | 0.536333 | ||||||||
\(353\) | 5287.00i | 0.797163i | 0.917133 | + | 0.398582i | \(0.130497\pi\) | ||||
−0.917133 | + | 0.398582i | \(0.869503\pi\) | |||||||
\(354\) | −1728.00 | −0.259441 | ||||||||
\(355\) | 7602.00 | 1.13654 | ||||||||
\(356\) | 1358.00i | 0.202174i | ||||||||
\(357\) | 1110.00i | 0.164559i | ||||||||
\(358\) | − 3674.00i | − 0.542394i | ||||||||
\(359\) | − 7278.00i | − 1.06997i | −0.844863 | − | 0.534983i | \(-0.820318\pi\) | ||||
0.844863 | − | 0.534983i | \(-0.179682\pi\) | |||||||
\(360\) | 945.000 | 0.138350 | ||||||||
\(361\) | 5959.00 | 0.868786 | ||||||||
\(362\) | 3283.00i | 0.476659i | ||||||||
\(363\) | 2541.00 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5635.00 | −0.808080 | ||||||||
\(366\) | − 1905.00i | − 0.272065i | ||||||||
\(367\) | −4202.00 | −0.597664 | −0.298832 | − | 0.954306i | \(-0.596597\pi\) | ||||
−0.298832 | + | 0.954306i | \(0.596597\pi\) | |||||||
\(368\) | 6642.00 | 0.940865 | ||||||||
\(369\) | − 2565.00i | − 0.361866i | ||||||||
\(370\) | 91.0000i | 0.0127861i | ||||||||
\(371\) | 5370.00i | 0.751473i | ||||||||
\(372\) | − 4116.00i | − 0.573668i | ||||||||
\(373\) | −1583.00 | −0.219744 | −0.109872 | − | 0.993946i | \(-0.535044\pi\) | ||||
−0.109872 | + | 0.993946i | \(0.535044\pi\) | |||||||
\(374\) | −814.000 | −0.112543 | ||||||||
\(375\) | − 4221.00i | − 0.581257i | ||||||||
\(376\) | 6930.00 | 0.950499 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 270.000 | 0.0367389 | ||||||||
\(379\) | 2052.00i | 0.278111i | 0.990285 | + | 0.139056i | \(0.0444067\pi\) | ||||
−0.990285 | + | 0.139056i | \(0.955593\pi\) | |||||||
\(380\) | −1470.00 | −0.198446 | ||||||||
\(381\) | 2964.00 | 0.398557 | ||||||||
\(382\) | − 596.000i | − 0.0798273i | ||||||||
\(383\) | 6872.00i | 0.916822i | 0.888740 | + | 0.458411i | \(0.151581\pi\) | ||||
−0.888740 | + | 0.458411i | \(0.848419\pi\) | |||||||
\(384\) | 4365.00i | 0.580079i | ||||||||
\(385\) | 1540.00i | 0.203859i | ||||||||
\(386\) | 393.000 | 0.0518217 | ||||||||
\(387\) | 2214.00 | 0.290811 | ||||||||
\(388\) | 8414.00i | 1.10092i | ||||||||
\(389\) | 11653.0 | 1.51884 | 0.759422 | − | 0.650598i | \(-0.225482\pi\) | ||||
0.759422 | + | 0.650598i | \(0.225482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5994.00 | −0.775268 | ||||||||
\(392\) | 3645.00i | 0.469644i | ||||||||
\(393\) | 1680.00 | 0.215636 | ||||||||
\(394\) | −3522.00 | −0.450345 | ||||||||
\(395\) | − 6188.00i | − 0.788233i | ||||||||
\(396\) | − 1386.00i | − 0.175882i | ||||||||
\(397\) | 6134.00i | 0.775458i | 0.921774 | + | 0.387729i | \(0.126740\pi\) | ||||
−0.921774 | + | 0.387729i | \(0.873260\pi\) | |||||||
\(398\) | − 2018.00i | − 0.254154i | ||||||||
\(399\) | −900.000 | −0.112923 | ||||||||
\(400\) | 3116.00 | 0.389500 | ||||||||
\(401\) | − 10795.0i | − 1.34433i | −0.740401 | − | 0.672165i | \(-0.765364\pi\) | ||||
0.740401 | − | 0.672165i | \(-0.234636\pi\) | |||||||
\(402\) | 606.000 | 0.0751854 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3003.00 | 0.369814 | ||||||||
\(405\) | − 567.000i | − 0.0695666i | ||||||||
\(406\) | −1130.00 | −0.138130 | ||||||||
\(407\) | 286.000 | 0.0348317 | ||||||||
\(408\) | − 1665.00i | − 0.202034i | ||||||||
\(409\) | 8489.00i | 1.02629i | 0.858301 | + | 0.513147i | \(0.171520\pi\) | ||||
−0.858301 | + | 0.513147i | \(0.828480\pi\) | |||||||
\(410\) | − 1995.00i | − 0.240307i | ||||||||
\(411\) | − 1557.00i | − 0.186864i | ||||||||
\(412\) | 9114.00 | 1.08984 | ||||||||
\(413\) | 5760.00 | 0.686274 | ||||||||
\(414\) | 1458.00i | 0.173084i | ||||||||
\(415\) | −3626.00 | −0.428900 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1044.00 | −0.122602 | ||||||||
\(418\) | − 660.000i | − 0.0772288i | ||||||||
\(419\) | 1496.00 | 0.174426 | 0.0872129 | − | 0.996190i | \(-0.472204\pi\) | ||||
0.0872129 | + | 0.996190i | \(0.472204\pi\) | |||||||
\(420\) | −1470.00 | −0.170783 | ||||||||
\(421\) | 11695.0i | 1.35387i | 0.736043 | + | 0.676935i | \(0.236692\pi\) | ||||
−0.736043 | + | 0.676935i | \(0.763308\pi\) | |||||||
\(422\) | 160.000i | 0.0184566i | ||||||||
\(423\) | − 4158.00i | − 0.477941i | ||||||||
\(424\) | − 8055.00i | − 0.922607i | ||||||||
\(425\) | −2812.00 | −0.320946 | ||||||||
\(426\) | −3258.00 | −0.370541 | ||||||||
\(427\) | 6350.00i | 0.719668i | ||||||||
\(428\) | −9366.00 | −1.05776 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1722.00 | 0.193121 | ||||||||
\(431\) | − 10590.0i | − 1.18353i | −0.806110 | − | 0.591766i | \(-0.798431\pi\) | ||||
0.806110 | − | 0.591766i | \(-0.201569\pi\) | |||||||
\(432\) | 1107.00 | 0.123288 | ||||||||
\(433\) | 13949.0 | 1.54814 | 0.774072 | − | 0.633098i | \(-0.218217\pi\) | ||||
0.774072 | + | 0.633098i | \(0.218217\pi\) | |||||||
\(434\) | − 1960.00i | − 0.216781i | ||||||||
\(435\) | 2373.00i | 0.261555i | ||||||||
\(436\) | 7238.00i | 0.795040i | ||||||||
\(437\) | − 4860.00i | − 0.532003i | ||||||||
\(438\) | 2415.00 | 0.263455 | ||||||||
\(439\) | 10726.0 | 1.16611 | 0.583057 | − | 0.812431i | \(-0.301856\pi\) | ||||
0.583057 | + | 0.812431i | \(0.301856\pi\) | |||||||
\(440\) | − 2310.00i | − 0.250284i | ||||||||
\(441\) | 2187.00 | 0.236152 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16228.0 | 1.74044 | 0.870221 | − | 0.492662i | \(-0.163976\pi\) | ||||
0.870221 | + | 0.492662i | \(0.163976\pi\) | |||||||
\(444\) | 273.000i | 0.0291802i | ||||||||
\(445\) | 1358.00 | 0.144664 | ||||||||
\(446\) | 4072.00 | 0.432320 | ||||||||
\(447\) | 1935.00i | 0.204748i | ||||||||
\(448\) | − 1670.00i | − 0.176116i | ||||||||
\(449\) | 7538.00i | 0.792294i | 0.918187 | + | 0.396147i | \(0.129653\pi\) | ||||
−0.918187 | + | 0.396147i | \(0.870347\pi\) | |||||||
\(450\) | 684.000i | 0.0716535i | ||||||||
\(451\) | −6270.00 | −0.654640 | ||||||||
\(452\) | 7539.00 | 0.784524 | ||||||||
\(453\) | 8742.00i | 0.906700i | ||||||||
\(454\) | −5794.00 | −0.598956 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1350.00 | 0.138639 | ||||||||
\(457\) | − 15539.0i | − 1.59056i | −0.606245 | − | 0.795278i | \(-0.707325\pi\) | ||||
0.606245 | − | 0.795278i | \(-0.292675\pi\) | |||||||
\(458\) | −6482.00 | −0.661319 | ||||||||
\(459\) | −999.000 | −0.101589 | ||||||||
\(460\) | − 7938.00i | − 0.804589i | ||||||||
\(461\) | − 4811.00i | − 0.486053i | −0.970020 | − | 0.243027i | \(-0.921860\pi\) | ||||
0.970020 | − | 0.243027i | \(-0.0781403\pi\) | |||||||
\(462\) | − 660.000i | − 0.0664632i | ||||||||
\(463\) | 562.000i | 0.0564111i | 0.999602 | + | 0.0282056i | \(0.00897930\pi\) | ||||
−0.999602 | + | 0.0282056i | \(0.991021\pi\) | |||||||
\(464\) | −4633.00 | −0.463538 | ||||||||
\(465\) | −4116.00 | −0.410484 | ||||||||
\(466\) | − 6890.00i | − 0.684921i | ||||||||
\(467\) | −4914.00 | −0.486922 | −0.243461 | − | 0.969911i | \(-0.578283\pi\) | ||||
−0.243461 | + | 0.969911i | \(0.578283\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2020.00 | −0.198880 | ||||||||
\(470\) | − 3234.00i | − 0.317390i | ||||||||
\(471\) | −6237.00 | −0.610161 | ||||||||
\(472\) | −8640.00 | −0.842560 | ||||||||
\(473\) | − 5412.00i | − 0.526097i | ||||||||
\(474\) | 2652.00i | 0.256984i | ||||||||
\(475\) | − 2280.00i | − 0.220239i | ||||||||
\(476\) | 2590.00i | 0.249396i | ||||||||
\(477\) | −4833.00 | −0.463916 | ||||||||
\(478\) | 2466.00 | 0.235967 | ||||||||
\(479\) | − 3600.00i | − 0.343399i | −0.985149 | − | 0.171700i | \(-0.945074\pi\) | ||||
0.985149 | − | 0.171700i | \(-0.0549258\pi\) | |||||||
\(480\) | 3381.00 | 0.321502 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3617.00 | 0.341805 | ||||||||
\(483\) | − 4860.00i | − 0.457842i | ||||||||
\(484\) | 5929.00 | 0.556818 | ||||||||
\(485\) | 8414.00 | 0.787753 | ||||||||
\(486\) | 243.000i | 0.0226805i | ||||||||
\(487\) | 17130.0i | 1.59391i | 0.604038 | + | 0.796955i | \(0.293557\pi\) | ||||
−0.604038 | + | 0.796955i | \(0.706443\pi\) | |||||||
\(488\) | − 9525.00i | − 0.883558i | ||||||||
\(489\) | 5100.00i | 0.471636i | ||||||||
\(490\) | 1701.00 | 0.156823 | ||||||||
\(491\) | 11838.0 | 1.08807 | 0.544034 | − | 0.839063i | \(-0.316896\pi\) | ||||
0.544034 | + | 0.839063i | \(0.316896\pi\) | |||||||
\(492\) | − 5985.00i | − 0.548424i | ||||||||
\(493\) | 4181.00 | 0.381953 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1386.00 | −0.125851 | ||||||||
\(496\) | − 8036.00i | − 0.727474i | ||||||||
\(497\) | 10860.0 | 0.980156 | ||||||||
\(498\) | 1554.00 | 0.139832 | ||||||||
\(499\) | − 8976.00i | − 0.805252i | −0.915364 | − | 0.402626i | \(-0.868097\pi\) | ||||
0.915364 | − | 0.402626i | \(-0.131903\pi\) | |||||||
\(500\) | − 9849.00i | − 0.880921i | ||||||||
\(501\) | 11040.0i | 0.984493i | ||||||||
\(502\) | − 4860.00i | − 0.432096i | ||||||||
\(503\) | 1682.00 | 0.149099 | 0.0745494 | − | 0.997217i | \(-0.476248\pi\) | ||||
0.0745494 | + | 0.997217i | \(0.476248\pi\) | |||||||
\(504\) | 1350.00 | 0.119313 | ||||||||
\(505\) | − 3003.00i | − 0.264617i | ||||||||
\(506\) | 3564.00 | 0.313121 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6916.00 | 0.604031 | ||||||||
\(509\) | − 15167.0i | − 1.32076i | −0.750933 | − | 0.660379i | \(-0.770396\pi\) | ||||
0.750933 | − | 0.660379i | \(-0.229604\pi\) | |||||||
\(510\) | −777.000 | −0.0674630 | ||||||||
\(511\) | −8050.00 | −0.696890 | ||||||||
\(512\) | 11521.0i | 0.994455i | ||||||||
\(513\) | − 810.000i | − 0.0697122i | ||||||||
\(514\) | − 565.000i | − 0.0484846i | ||||||||
\(515\) | − 9114.00i | − 0.779827i | ||||||||
\(516\) | 5166.00 | 0.440737 | ||||||||
\(517\) | −10164.0 | −0.864627 | ||||||||
\(518\) | 130.000i | 0.0110268i | ||||||||
\(519\) | −12438.0 | −1.05196 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6783.00 | −0.570381 | −0.285191 | − | 0.958471i | \(-0.592057\pi\) | ||||
−0.285191 | + | 0.958471i | \(0.592057\pi\) | |||||||
\(522\) | − 1017.00i | − 0.0852737i | ||||||||
\(523\) | −13918.0 | −1.16366 | −0.581828 | − | 0.813312i | \(-0.697662\pi\) | ||||
−0.581828 | + | 0.813312i | \(0.697662\pi\) | |||||||
\(524\) | 3920.00 | 0.326805 | ||||||||
\(525\) | − 2280.00i | − 0.189538i | ||||||||
\(526\) | − 498.000i | − 0.0412810i | ||||||||
\(527\) | 7252.00i | 0.599435i | ||||||||
\(528\) | − 2706.00i | − 0.223037i | ||||||||
\(529\) | 14077.0 | 1.15698 | ||||||||
\(530\) | −3759.00 | −0.308076 | ||||||||
\(531\) | 5184.00i | 0.423666i | ||||||||
\(532\) | −2100.00 | −0.171140 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −582.000 | −0.0471641 | ||||||||
\(535\) | 9366.00i | 0.756874i | ||||||||
\(536\) | 3030.00 | 0.244172 | ||||||||
\(537\) | −11022.0 | −0.885725 | ||||||||
\(538\) | 5546.00i | 0.444433i | ||||||||
\(539\) | − 5346.00i | − 0.427214i | ||||||||
\(540\) | − 1323.00i | − 0.105431i | ||||||||
\(541\) | − 1335.00i | − 0.106093i | −0.998592 | − | 0.0530463i | \(-0.983107\pi\) | ||||
0.998592 | − | 0.0530463i | \(-0.0168931\pi\) | |||||||
\(542\) | 2256.00 | 0.178789 | ||||||||
\(543\) | 9849.00 | 0.778381 | ||||||||
\(544\) | − 5957.00i | − 0.469493i | ||||||||
\(545\) | 7238.00 | 0.568884 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3806.00 | −0.297501 | −0.148750 | − | 0.988875i | \(-0.547525\pi\) | ||||
−0.148750 | + | 0.988875i | \(0.547525\pi\) | |||||||
\(548\) | − 3633.00i | − 0.283201i | ||||||||
\(549\) | −5715.00 | −0.444281 | ||||||||
\(550\) | 1672.00 | 0.129626 | ||||||||
\(551\) | 3390.00i | 0.262103i | ||||||||
\(552\) | 7290.00i | 0.562107i | ||||||||
\(553\) | − 8840.00i | − 0.679774i | ||||||||
\(554\) | − 2309.00i | − 0.177076i | ||||||||
\(555\) | 273.000 | 0.0208796 | ||||||||
\(556\) | −2436.00 | −0.185808 | ||||||||
\(557\) | − 1905.00i | − 0.144915i | −0.997372 | − | 0.0724573i | \(-0.976916\pi\) | ||||
0.997372 | − | 0.0724573i | \(-0.0230841\pi\) | |||||||
\(558\) | 1764.00 | 0.133828 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2870.00 | −0.216571 | ||||||||
\(561\) | 2442.00i | 0.183781i | ||||||||
\(562\) | −5833.00 | −0.437812 | ||||||||
\(563\) | 4800.00 | 0.359318 | 0.179659 | − | 0.983729i | \(-0.442501\pi\) | ||||
0.179659 | + | 0.983729i | \(0.442501\pi\) | |||||||
\(564\) | − 9702.00i | − 0.724340i | ||||||||
\(565\) | − 7539.00i | − 0.561359i | ||||||||
\(566\) | − 1650.00i | − 0.122535i | ||||||||
\(567\) | − 810.000i | − 0.0599944i | ||||||||
\(568\) | −16290.0 | −1.20337 | ||||||||
\(569\) | −14678.0 | −1.08143 | −0.540715 | − | 0.841206i | \(-0.681846\pi\) | ||||
−0.540715 | + | 0.841206i | \(0.681846\pi\) | |||||||
\(570\) | − 630.000i | − 0.0462944i | ||||||||
\(571\) | 586.000 | 0.0429481 | 0.0214740 | − | 0.999769i | \(-0.493164\pi\) | ||||
0.0214740 | + | 0.999769i | \(0.493164\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1788.00 | −0.130357 | ||||||||
\(574\) | − 2850.00i | − 0.207242i | ||||||||
\(575\) | 12312.0 | 0.892949 | ||||||||
\(576\) | 1503.00 | 0.108724 | ||||||||
\(577\) | − 8939.00i | − 0.644949i | −0.946578 | − | 0.322474i | \(-0.895485\pi\) | ||||
0.946578 | − | 0.322474i | \(-0.104515\pi\) | |||||||
\(578\) | − 3544.00i | − 0.255036i | ||||||||
\(579\) | − 1179.00i | − 0.0846245i | ||||||||
\(580\) | 5537.00i | 0.396399i | ||||||||
\(581\) | −5180.00 | −0.369884 | ||||||||
\(582\) | −3606.00 | −0.256827 | ||||||||
\(583\) | 11814.0i | 0.839255i | ||||||||
\(584\) | 12075.0 | 0.855594 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2991.00 | −0.210848 | ||||||||
\(587\) | 13792.0i | 0.969773i | 0.874577 | + | 0.484887i | \(0.161139\pi\) | ||||
−0.874577 | + | 0.484887i | \(0.838861\pi\) | |||||||
\(588\) | 5103.00 | 0.357898 | ||||||||
\(589\) | −5880.00 | −0.411343 | ||||||||
\(590\) | 4032.00i | 0.281347i | ||||||||
\(591\) | 10566.0i | 0.735410i | ||||||||
\(592\) | 533.000i | 0.0370037i | ||||||||
\(593\) | 9569.00i | 0.662650i | 0.943517 | + | 0.331325i | \(0.107496\pi\) | ||||
−0.943517 | + | 0.331325i | \(0.892504\pi\) | |||||||
\(594\) | 594.000 | 0.0410305 | ||||||||
\(595\) | 2590.00 | 0.178453 | ||||||||
\(596\) | 4515.00i | 0.310305i | ||||||||
\(597\) | −6054.00 | −0.415031 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5192.00 | −0.354156 | −0.177078 | − | 0.984197i | \(-0.556664\pi\) | ||||
−0.177078 | + | 0.984197i | \(0.556664\pi\) | |||||||
\(600\) | 3420.00i | 0.232702i | ||||||||
\(601\) | −3677.00 | −0.249564 | −0.124782 | − | 0.992184i | \(-0.539823\pi\) | ||||
−0.124782 | + | 0.992184i | \(0.539823\pi\) | |||||||
\(602\) | 2460.00 | 0.166548 | ||||||||
\(603\) | − 1818.00i | − 0.122777i | ||||||||
\(604\) | 20398.0i | 1.37414i | ||||||||
\(605\) | − 5929.00i | − 0.398427i | ||||||||
\(606\) | 1287.00i | 0.0862719i | ||||||||
\(607\) | −10960.0 | −0.732871 | −0.366435 | − | 0.930443i | \(-0.619422\pi\) | ||||
−0.366435 | + | 0.930443i | \(0.619422\pi\) | |||||||
\(608\) | 4830.00 | 0.322175 | ||||||||
\(609\) | 3390.00i | 0.225566i | ||||||||
\(610\) | −4445.00 | −0.295037 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2331.00 | −0.153963 | ||||||||
\(613\) | 26027.0i | 1.71488i | 0.514585 | + | 0.857439i | \(0.327946\pi\) | ||||
−0.514585 | + | 0.857439i | \(0.672054\pi\) | |||||||
\(614\) | 2422.00 | 0.159192 | ||||||||
\(615\) | −5985.00 | −0.392420 | ||||||||
\(616\) | − 3300.00i | − 0.215845i | ||||||||
\(617\) | − 17681.0i | − 1.15366i | −0.816863 | − | 0.576832i | \(-0.804289\pi\) | ||||
0.816863 | − | 0.576832i | \(-0.195711\pi\) | |||||||
\(618\) | 3906.00i | 0.254243i | ||||||||
\(619\) | 3192.00i | 0.207265i | 0.994616 | + | 0.103633i | \(0.0330467\pi\) | ||||
−0.994616 | + | 0.103633i | \(0.966953\pi\) | |||||||
\(620\) | −9604.00 | −0.622106 | ||||||||
\(621\) | 4374.00 | 0.282645 | ||||||||
\(622\) | 3402.00i | 0.219305i | ||||||||
\(623\) | 1940.00 | 0.124758 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −349.000 | −0.0223360 | ||||||||
\(626\) | 2310.00i | 0.147486i | ||||||||
\(627\) | −1980.00 | −0.126114 | ||||||||
\(628\) | −14553.0 | −0.924726 | ||||||||
\(629\) | − 481.000i | − 0.0304908i | ||||||||
\(630\) | − 630.000i | − 0.0398410i | ||||||||
\(631\) | 7580.00i | 0.478217i | 0.970993 | + | 0.239109i | \(0.0768552\pi\) | ||||
−0.970993 | + | 0.239109i | \(0.923145\pi\) | |||||||
\(632\) | 13260.0i | 0.834580i | ||||||||
\(633\) | 480.000 | 0.0301395 | ||||||||
\(634\) | −257.000 | −0.0160990 | ||||||||
\(635\) | − 6916.00i | − 0.432210i | ||||||||
\(636\) | −11277.0 | −0.703085 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2486.00 | −0.154266 | ||||||||
\(639\) | 9774.00i | 0.605091i | ||||||||
\(640\) | 10185.0 | 0.629059 | ||||||||
\(641\) | 27707.0 | 1.70727 | 0.853635 | − | 0.520871i | \(-0.174393\pi\) | ||||
0.853635 | + | 0.520871i | \(0.174393\pi\) | |||||||
\(642\) | − 4014.00i | − 0.246760i | ||||||||
\(643\) | − 11216.0i | − 0.687894i | −0.938989 | − | 0.343947i | \(-0.888236\pi\) | ||||
0.938989 | − | 0.343947i | \(-0.111764\pi\) | |||||||
\(644\) | − 11340.0i | − 0.693880i | ||||||||
\(645\) | − 5166.00i | − 0.315366i | ||||||||
\(646\) | −1110.00 | −0.0676043 | ||||||||
\(647\) | 2536.00 | 0.154097 | 0.0770483 | − | 0.997027i | \(-0.475450\pi\) | ||||
0.0770483 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(648\) | 1215.00i | 0.0736570i | ||||||||
\(649\) | 12672.0 | 0.766440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5880.00 | −0.354002 | ||||||||
\(652\) | 11900.0i | 0.714785i | ||||||||
\(653\) | 17730.0 | 1.06252 | 0.531262 | − | 0.847207i | \(-0.321718\pi\) | ||||
0.531262 | + | 0.847207i | \(0.321718\pi\) | |||||||
\(654\) | −3102.00 | −0.185471 | ||||||||
\(655\) | − 3920.00i | − 0.233843i | ||||||||
\(656\) | − 11685.0i | − 0.695461i | ||||||||
\(657\) | − 7245.00i | − 0.430220i | ||||||||
\(658\) | − 4620.00i | − 0.273718i | ||||||||
\(659\) | 18920.0 | 1.11839 | 0.559195 | − | 0.829036i | \(-0.311110\pi\) | ||||
0.559195 | + | 0.829036i | \(0.311110\pi\) | |||||||
\(660\) | −3234.00 | −0.190732 | ||||||||
\(661\) | 5241.00i | 0.308398i | 0.988040 | + | 0.154199i | \(0.0492797\pi\) | ||||
−0.988040 | + | 0.154199i | \(0.950720\pi\) | |||||||
\(662\) | 1028.00 | 0.0603540 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7770.00 | 0.454118 | ||||||||
\(665\) | 2100.00i | 0.122458i | ||||||||
\(666\) | −117.000 | −0.00680729 | ||||||||
\(667\) | −18306.0 | −1.06269 | ||||||||
\(668\) | 25760.0i | 1.49204i | ||||||||
\(669\) | − 12216.0i | − 0.705976i | ||||||||
\(670\) | − 1414.00i | − 0.0815337i | ||||||||
\(671\) | 13970.0i | 0.803735i | ||||||||
\(672\) | 4830.00 | 0.277264 | ||||||||
\(673\) | −20467.0 | −1.17228 | −0.586140 | − | 0.810210i | \(-0.699353\pi\) | ||||
−0.586140 | + | 0.810210i | \(0.699353\pi\) | |||||||
\(674\) | − 2487.00i | − 0.142130i | ||||||||
\(675\) | 2052.00 | 0.117010 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −70.0000 | −0.00397388 | −0.00198694 | − | 0.999998i | \(-0.500632\pi\) | ||||
−0.00198694 | + | 0.999998i | \(0.500632\pi\) | |||||||
\(678\) | 3231.00i | 0.183017i | ||||||||
\(679\) | 12020.0 | 0.679360 | ||||||||
\(680\) | −3885.00 | −0.219093 | ||||||||
\(681\) | 17382.0i | 0.978091i | ||||||||
\(682\) | − 4312.00i | − 0.242104i | ||||||||
\(683\) | 6432.00i | 0.360342i | 0.983635 | + | 0.180171i | \(0.0576651\pi\) | ||||
−0.983635 | + | 0.180171i | \(0.942335\pi\) | |||||||
\(684\) | − 1890.00i | − 0.105652i | ||||||||
\(685\) | −3633.00 | −0.202642 | ||||||||
\(686\) | 5860.00 | 0.326146 | ||||||||
\(687\) | 19446.0i | 1.07993i | ||||||||
\(688\) | 10086.0 | 0.558903 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3402.00 | 0.187698 | ||||||||
\(691\) | 6666.00i | 0.366985i | 0.983021 | + | 0.183492i | \(0.0587403\pi\) | ||||
−0.983021 | + | 0.183492i | \(0.941260\pi\) | |||||||
\(692\) | −29022.0 | −1.59429 | ||||||||
\(693\) | −1980.00 | −0.108534 | ||||||||
\(694\) | − 2850.00i | − 0.155885i | ||||||||
\(695\) | 2436.00i | 0.132954i | ||||||||
\(696\) | − 5085.00i | − 0.276935i | ||||||||
\(697\) | 10545.0i | 0.573056i | ||||||||
\(698\) | 2018.00 | 0.109430 | ||||||||
\(699\) | −20670.0 | −1.11847 | ||||||||
\(700\) | − 5320.00i | − 0.287253i | ||||||||
\(701\) | 14054.0 | 0.757221 | 0.378611 | − | 0.925556i | \(-0.376402\pi\) | ||||
0.378611 | + | 0.925556i | \(0.376402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 390.000 | 0.0209234 | ||||||||
\(704\) | − 3674.00i | − 0.196689i | ||||||||
\(705\) | −9702.00 | −0.518296 | ||||||||
\(706\) | −5287.00 | −0.281840 | ||||||||
\(707\) | − 4290.00i | − 0.228207i | ||||||||
\(708\) | 12096.0i | 0.642084i | ||||||||
\(709\) | − 71.0000i | − 0.00376088i | −0.999998 | − | 0.00188044i | \(-0.999401\pi\) | ||||
0.999998 | − | 0.00188044i | \(-0.000598562\pi\) | |||||||
\(710\) | 7602.00i | 0.401828i | ||||||||
\(711\) | 7956.00 | 0.419653 | ||||||||
\(712\) | −2910.00 | −0.153170 | ||||||||
\(713\) | − 31752.0i | − 1.66777i | ||||||||
\(714\) | −1110.00 | −0.0581803 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25718.0 | −1.34236 | ||||||||
\(717\) | − 7398.00i | − 0.385332i | ||||||||
\(718\) | 7278.00 | 0.378290 | ||||||||
\(719\) | −3936.00 | −0.204156 | −0.102078 | − | 0.994776i | \(-0.532549\pi\) | ||||
−0.102078 | + | 0.994776i | \(0.532549\pi\) | |||||||
\(720\) | − 2583.00i | − 0.133698i | ||||||||
\(721\) | − 13020.0i | − 0.672524i | ||||||||
\(722\) | 5959.00i | 0.307162i | ||||||||
\(723\) | − 10851.0i | − 0.558165i | ||||||||
\(724\) | 22981.0 | 1.17967 | ||||||||
\(725\) | −8588.00 | −0.439931 | ||||||||
\(726\) | 2541.00i | 0.129897i | ||||||||
\(727\) | −34202.0 | −1.74482 | −0.872409 | − | 0.488777i | \(-0.837443\pi\) | ||||
−0.872409 | + | 0.488777i | \(0.837443\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − 5635.00i | − 0.285700i | ||||||||
\(731\) | −9102.00 | −0.460533 | ||||||||
\(732\) | −13335.0 | −0.673328 | ||||||||
\(733\) | 27363.0i | 1.37882i | 0.724371 | + | 0.689410i | \(0.242130\pi\) | ||||
−0.724371 | + | 0.689410i | \(0.757870\pi\) | |||||||
\(734\) | − 4202.00i | − 0.211306i | ||||||||
\(735\) | − 5103.00i | − 0.256091i | ||||||||
\(736\) | 26082.0i | 1.30624i | ||||||||
\(737\) | −4444.00 | −0.222112 | ||||||||
\(738\) | 2565.00 | 0.127939 | ||||||||
\(739\) | 21776.0i | 1.08396i | 0.840393 | + | 0.541978i | \(0.182324\pi\) | ||||
−0.840393 | + | 0.541978i | \(0.817676\pi\) | |||||||
\(740\) | 637.000 | 0.0316440 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5370.00 | −0.265686 | ||||||||
\(743\) | − 2484.00i | − 0.122650i | −0.998118 | − | 0.0613251i | \(-0.980467\pi\) | ||||
0.998118 | − | 0.0613251i | \(-0.0195326\pi\) | |||||||
\(744\) | 8820.00 | 0.434619 | ||||||||
\(745\) | 4515.00 | 0.222036 | ||||||||
\(746\) | − 1583.00i | − 0.0776914i | ||||||||
\(747\) | − 4662.00i | − 0.228345i | ||||||||
\(748\) | 5698.00i | 0.278529i | ||||||||
\(749\) | 13380.0i | 0.652730i | ||||||||
\(750\) | 4221.00 | 0.205506 | ||||||||
\(751\) | −32906.0 | −1.59888 | −0.799439 | − | 0.600748i | \(-0.794870\pi\) | ||||
−0.799439 | + | 0.600748i | \(0.794870\pi\) | |||||||
\(752\) | − 18942.0i | − 0.918542i | ||||||||
\(753\) | −14580.0 | −0.705611 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20398.0 | 0.983257 | ||||||||
\(756\) | − 1890.00i | − 0.0909241i | ||||||||
\(757\) | −3914.00 | −0.187922 | −0.0939609 | − | 0.995576i | \(-0.529953\pi\) | ||||
−0.0939609 | + | 0.995576i | \(0.529953\pi\) | |||||||
\(758\) | −2052.00 | −0.0983272 | ||||||||
\(759\) | − 10692.0i | − 0.511324i | ||||||||
\(760\) | − 3150.00i | − 0.150345i | ||||||||
\(761\) | − 33038.0i | − 1.57375i | −0.617110 | − | 0.786877i | \(-0.711697\pi\) | ||||
0.617110 | − | 0.786877i | \(-0.288303\pi\) | |||||||
\(762\) | 2964.00i | 0.140911i | ||||||||
\(763\) | 10340.0 | 0.490607 | ||||||||
\(764\) | −4172.00 | −0.197562 | ||||||||
\(765\) | 2331.00i | 0.110167i | ||||||||
\(766\) | −6872.00 | −0.324145 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −357.000 | −0.0167736 | ||||||||
\(769\) | 17586.0i | 0.824665i | 0.911033 | + | 0.412332i | \(0.135286\pi\) | ||||
−0.911033 | + | 0.412332i | \(0.864714\pi\) | |||||||
\(770\) | −1540.00 | −0.0720750 | ||||||||
\(771\) | −1695.00 | −0.0791750 | ||||||||
\(772\) | − 2751.00i | − 0.128252i | ||||||||
\(773\) | − 18314.0i | − 0.852146i | −0.904689 | − | 0.426073i | \(-0.859897\pi\) | ||||
0.904689 | − | 0.426073i | \(-0.140103\pi\) | |||||||
\(774\) | 2214.00i | 0.102817i | ||||||||
\(775\) | − 14896.0i | − 0.690426i | ||||||||
\(776\) | −18030.0 | −0.834071 | ||||||||
\(777\) | 390.000 | 0.0180067 | ||||||||
\(778\) | 11653.0i | 0.536993i | ||||||||
\(779\) | −8550.00 | −0.393242 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23892.0 | 1.09465 | ||||||||
\(782\) | − 5994.00i | − 0.274098i | ||||||||
\(783\) | −3051.00 | −0.139251 | ||||||||
\(784\) | 9963.00 | 0.453854 | ||||||||
\(785\) | 14553.0i | 0.661680i | ||||||||
\(786\) | 1680.00i | 0.0762387i | ||||||||
\(787\) | − 42068.0i | − 1.90542i | −0.303888 | − | 0.952708i | \(-0.598285\pi\) | ||||
0.303888 | − | 0.952708i | \(-0.401715\pi\) | |||||||
\(788\) | 24654.0i | 1.11455i | ||||||||
\(789\) | −1494.00 | −0.0674117 | ||||||||
\(790\) | 6188.00 | 0.278682 | ||||||||
\(791\) | − 10770.0i | − 0.484118i | ||||||||
\(792\) | 2970.00 | 0.133250 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −6134.00 | −0.274166 | ||||||||
\(795\) | 11277.0i | 0.503087i | ||||||||
\(796\) | −14126.0 | −0.628998 | ||||||||
\(797\) | 4282.00 | 0.190309 | 0.0951545 | − | 0.995463i | \(-0.469665\pi\) | ||||
0.0951545 | + | 0.995463i | \(0.469665\pi\) | |||||||
\(798\) | − 900.000i | − 0.0399244i | ||||||||
\(799\) | 17094.0i | 0.756874i | ||||||||
\(800\) | 12236.0i | 0.540760i | ||||||||
\(801\) | 1746.00i | 0.0770186i | ||||||||
\(802\) | 10795.0 | 0.475293 | ||||||||
\(803\) | −17710.0 | −0.778297 | ||||||||
\(804\) | − 4242.00i | − 0.186074i | ||||||||
\(805\) | −11340.0 | −0.496500 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16638.0 | 0.725756 | ||||||||
\(808\) | 6435.00i | 0.280176i | ||||||||
\(809\) | 40221.0 | 1.74795 | 0.873977 | − | 0.485967i | \(-0.161532\pi\) | ||||
0.873977 | + | 0.485967i | \(0.161532\pi\) | |||||||
\(810\) | 567.000 | 0.0245955 | ||||||||
\(811\) | 7084.00i | 0.306724i | 0.988170 | + | 0.153362i | \(0.0490100\pi\) | ||||
−0.988170 | + | 0.153362i | \(0.950990\pi\) | |||||||
\(812\) | 7910.00i | 0.341855i | ||||||||
\(813\) | − 6768.00i | − 0.291961i | ||||||||
\(814\) | 286.000i | 0.0123149i | ||||||||
\(815\) | 11900.0 | 0.511459 | ||||||||
\(816\) | −4551.00 | −0.195241 | ||||||||
\(817\) | − 7380.00i | − 0.316026i | ||||||||
\(818\) | −8489.00 | −0.362850 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13965.0 | −0.594730 | ||||||||
\(821\) | − 17338.0i | − 0.737028i | −0.929622 | − | 0.368514i | \(-0.879867\pi\) | ||||
0.929622 | − | 0.368514i | \(-0.120133\pi\) | |||||||
\(822\) | 1557.00 | 0.0660664 | ||||||||
\(823\) | −35496.0 | −1.50342 | −0.751709 | − | 0.659495i | \(-0.770770\pi\) | ||||
−0.751709 | + | 0.659495i | \(0.770770\pi\) | |||||||
\(824\) | 19530.0i | 0.825679i | ||||||||
\(825\) | − 5016.00i | − 0.211678i | ||||||||
\(826\) | 5760.00i | 0.242634i | ||||||||
\(827\) | − 14992.0i | − 0.630378i | −0.949029 | − | 0.315189i | \(-0.897932\pi\) | ||||
0.949029 | − | 0.315189i | \(-0.102068\pi\) | |||||||
\(828\) | 10206.0 | 0.428361 | ||||||||
\(829\) | 20659.0 | 0.865521 | 0.432760 | − | 0.901509i | \(-0.357540\pi\) | ||||
0.432760 | + | 0.901509i | \(0.357540\pi\) | |||||||
\(830\) | − 3626.00i | − 0.151639i | ||||||||
\(831\) | −6927.00 | −0.289164 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8991.00 | −0.373973 | ||||||||
\(834\) | − 1044.00i | − 0.0433462i | ||||||||
\(835\) | 25760.0 | 1.06762 | ||||||||
\(836\) | −4620.00 | −0.191132 | ||||||||
\(837\) | − 5292.00i | − 0.218540i | ||||||||
\(838\) | 1496.00i | 0.0616688i | ||||||||
\(839\) | 28716.0i | 1.18163i | 0.806808 | + | 0.590814i | \(0.201193\pi\) | ||||
−0.806808 | + | 0.590814i | \(0.798807\pi\) | |||||||
\(840\) | − 3150.00i | − 0.129387i | ||||||||
\(841\) | −11620.0 | −0.476444 | ||||||||
\(842\) | −11695.0 | −0.478665 | ||||||||
\(843\) | 17499.0i | 0.714944i | ||||||||
\(844\) | 1120.00 | 0.0456777 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4158.00 | 0.168978 | ||||||||
\(847\) | − 8470.00i | − 0.343604i | ||||||||
\(848\) | −22017.0 | −0.891588 | ||||||||
\(849\) | −4950.00 | −0.200098 | ||||||||
\(850\) | − 2812.00i | − 0.113472i | ||||||||
\(851\) | 2106.00i | 0.0848328i | ||||||||
\(852\) | 22806.0i | 0.917043i | ||||||||
\(853\) | 13377.0i | 0.536952i | 0.963286 | + | 0.268476i | \(0.0865199\pi\) | ||||
−0.963286 | + | 0.268476i | \(0.913480\pi\) | |||||||
\(854\) | −6350.00 | −0.254441 | ||||||||
\(855\) | −1890.00 | −0.0755984 | ||||||||
\(856\) | − 20070.0i | − 0.801377i | ||||||||
\(857\) | 27419.0 | 1.09290 | 0.546450 | − | 0.837492i | \(-0.315979\pi\) | ||||
0.546450 | + | 0.837492i | \(0.315979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2422.00 | 0.0962021 | 0.0481010 | − | 0.998842i | \(-0.484683\pi\) | ||||
0.0481010 | + | 0.998842i | \(0.484683\pi\) | |||||||
\(860\) | − 12054.0i | − 0.477951i | ||||||||
\(861\) | −8550.00 | −0.338424 | ||||||||
\(862\) | 10590.0 | 0.418442 | ||||||||
\(863\) | 34522.0i | 1.36169i | 0.732425 | + | 0.680847i | \(0.238388\pi\) | ||||
−0.732425 | + | 0.680847i | \(0.761612\pi\) | |||||||
\(864\) | 4347.00i | 0.171167i | ||||||||
\(865\) | 29022.0i | 1.14078i | ||||||||
\(866\) | 13949.0i | 0.547351i | ||||||||
\(867\) | −10632.0 | −0.416472 | ||||||||
\(868\) | −13720.0 | −0.536506 | ||||||||
\(869\) | − 19448.0i | − 0.759181i | ||||||||
\(870\) | −2373.00 | −0.0924738 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15510.0 | −0.602334 | ||||||||
\(873\) | 10818.0i | 0.419397i | ||||||||
\(874\) | 4860.00 | 0.188091 | ||||||||
\(875\) | −14070.0 | −0.543603 | ||||||||
\(876\) | − 16905.0i | − 0.652017i | ||||||||
\(877\) | − 13733.0i | − 0.528769i | −0.964417 | − | 0.264385i | \(-0.914831\pi\) | ||||
0.964417 | − | 0.264385i | \(-0.0851688\pi\) | |||||||
\(878\) | 10726.0i | 0.412284i | ||||||||
\(879\) | 8973.00i | 0.344314i | ||||||||
\(880\) | −6314.00 | −0.241869 | ||||||||
\(881\) | 22759.0 | 0.870341 | 0.435170 | − | 0.900348i | \(-0.356688\pi\) | ||||
0.435170 | + | 0.900348i | \(0.356688\pi\) | |||||||
\(882\) | 2187.00i | 0.0834922i | ||||||||
\(883\) | 2168.00 | 0.0826263 | 0.0413131 | − | 0.999146i | \(-0.486846\pi\) | ||||
0.0413131 | + | 0.999146i | \(0.486846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12096.0 | 0.459438 | ||||||||
\(886\) | 16228.0i | 0.615339i | ||||||||
\(887\) | 15888.0 | 0.601428 | 0.300714 | − | 0.953714i | \(-0.402775\pi\) | ||||
0.300714 | + | 0.953714i | \(0.402775\pi\) | |||||||
\(888\) | −585.000 | −0.0221073 | ||||||||
\(889\) | − 9880.00i | − 0.372739i | ||||||||
\(890\) | 1358.00i | 0.0511464i | ||||||||
\(891\) | − 1782.00i | − 0.0670025i | ||||||||
\(892\) | − 28504.0i | − 1.06994i | ||||||||
\(893\) | −13860.0 | −0.519381 | ||||||||
\(894\) | −1935.00 | −0.0723894 | ||||||||
\(895\) | 25718.0i | 0.960512i | ||||||||
\(896\) | 14550.0 | 0.542502 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7538.00 | −0.280118 | ||||||||
\(899\) | 22148.0i | 0.821665i | ||||||||
\(900\) | 4788.00 | 0.177333 | ||||||||
\(901\) | 19869.0 | 0.734664 | ||||||||
\(902\) | − 6270.00i | − 0.231450i | ||||||||
\(903\) | − 7380.00i | − 0.271972i | ||||||||
\(904\) | 16155.0i | 0.594366i | ||||||||
\(905\) | − 22981.0i | − 0.844104i | ||||||||
\(906\) | −8742.00 | −0.320567 | ||||||||
\(907\) | 11628.0 | 0.425691 | 0.212845 | − | 0.977086i | \(-0.431727\pi\) | ||||
0.212845 | + | 0.977086i | \(0.431727\pi\) | |||||||
\(908\) | 40558.0i | 1.48234i | ||||||||
\(909\) | 3861.00 | 0.140882 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12584.0 | −0.457658 | −0.228829 | − | 0.973467i | \(-0.573490\pi\) | ||||
−0.228829 | + | 0.973467i | \(0.573490\pi\) | |||||||
\(912\) | − 3690.00i | − 0.133978i | ||||||||
\(913\) | −11396.0 | −0.413092 | ||||||||
\(914\) | 15539.0 | 0.562346 | ||||||||
\(915\) | 13335.0i | 0.481794i | ||||||||
\(916\) | 45374.0i | 1.63668i | ||||||||
\(917\) | − 5600.00i | − 0.201667i | ||||||||
\(918\) | − 999.000i | − 0.0359171i | ||||||||
\(919\) | 17184.0 | 0.616809 | 0.308405 | − | 0.951255i | \(-0.400205\pi\) | ||||
0.308405 | + | 0.951255i | \(0.400205\pi\) | |||||||
\(920\) | 17010.0 | 0.609569 | ||||||||
\(921\) | − 7266.00i | − 0.259960i | ||||||||
\(922\) | 4811.00 | 0.171846 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4620.00 | −0.164488 | ||||||||
\(925\) | 988.000i | 0.0351192i | ||||||||
\(926\) | −562.000 | −0.0199443 | ||||||||
\(927\) | 11718.0 | 0.415178 | ||||||||
\(928\) | − 18193.0i | − 0.643550i | ||||||||
\(929\) | − 12777.0i | − 0.451238i | −0.974216 | − | 0.225619i | \(-0.927560\pi\) | ||||
0.974216 | − | 0.225619i | \(-0.0724404\pi\) | |||||||
\(930\) | − 4116.00i | − 0.145128i | ||||||||
\(931\) | − 7290.00i | − 0.256627i | ||||||||
\(932\) | −48230.0 | −1.69509 | ||||||||
\(933\) | 10206.0 | 0.358124 | ||||||||
\(934\) | − 4914.00i | − 0.172153i | ||||||||
\(935\) | 5698.00 | 0.199299 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9191.00 | 0.320445 | 0.160222 | − | 0.987081i | \(-0.448779\pi\) | ||||
0.160222 | + | 0.987081i | \(0.448779\pi\) | |||||||
\(938\) | − 2020.00i | − 0.0703149i | ||||||||
\(939\) | 6930.00 | 0.240843 | ||||||||
\(940\) | −22638.0 | −0.785500 | ||||||||
\(941\) | − 50498.0i | − 1.74940i | −0.484662 | − | 0.874701i | \(-0.661058\pi\) | ||||
0.484662 | − | 0.874701i | \(-0.338942\pi\) | |||||||
\(942\) | − 6237.00i | − 0.215724i | ||||||||
\(943\) | − 46170.0i | − 1.59438i | ||||||||
\(944\) | 23616.0i | 0.814232i | ||||||||
\(945\) | −1890.00 | −0.0650600 | ||||||||
\(946\) | 5412.00 | 0.186003 | ||||||||
\(947\) | 1560.00i | 0.0535303i | 0.999642 | + | 0.0267651i | \(0.00852063\pi\) | ||||
−0.999642 | + | 0.0267651i | \(0.991479\pi\) | |||||||
\(948\) | 18564.0 | 0.636003 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2280.00 | 0.0778663 | ||||||||
\(951\) | 771.000i | 0.0262896i | ||||||||
\(952\) | −5550.00 | −0.188946 | ||||||||
\(953\) | 21498.0 | 0.730733 | 0.365366 | − | 0.930864i | \(-0.380944\pi\) | ||||
0.365366 | + | 0.930864i | \(0.380944\pi\) | |||||||
\(954\) | − 4833.00i | − 0.164019i | ||||||||
\(955\) | 4172.00i | 0.141364i | ||||||||
\(956\) | − 17262.0i | − 0.583988i | ||||||||
\(957\) | 7458.00i | 0.251915i | ||||||||
\(958\) | 3600.00 | 0.121410 | ||||||||
\(959\) | −5190.00 | −0.174759 | ||||||||
\(960\) | − 3507.00i | − 0.117904i | ||||||||
\(961\) | −8625.00 | −0.289517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12042.0 | −0.402957 | ||||||||
\(964\) | − 25319.0i | − 0.845923i | ||||||||
\(965\) | −2751.00 | −0.0917698 | ||||||||
\(966\) | 4860.00 | 0.161872 | ||||||||
\(967\) | 418.000i | 0.0139007i | 0.999976 | + | 0.00695035i | \(0.00221238\pi\) | ||||
−0.999976 | + | 0.00695035i | \(0.997788\pi\) | |||||||
\(968\) | 12705.0i | 0.421853i | ||||||||
\(969\) | 3330.00i | 0.110397i | ||||||||
\(970\) | 8414.00i | 0.278513i | ||||||||
\(971\) | 18132.0 | 0.599262 | 0.299631 | − | 0.954055i | \(-0.403136\pi\) | ||||
0.299631 | + | 0.954055i | \(0.403136\pi\) | |||||||
\(972\) | 1701.00 | 0.0561313 | ||||||||
\(973\) | 3480.00i | 0.114659i | ||||||||
\(974\) | −17130.0 | −0.563532 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26035.0 | −0.853853 | ||||||||
\(977\) | − 12501.0i | − 0.409358i | −0.978829 | − | 0.204679i | \(-0.934385\pi\) | ||||
0.978829 | − | 0.204679i | \(-0.0656150\pi\) | |||||||
\(978\) | −5100.00 | −0.166748 | ||||||||
\(979\) | 4268.00 | 0.139332 | ||||||||
\(980\) | − 11907.0i | − 0.388118i | ||||||||
\(981\) | 9306.00i | 0.302872i | ||||||||
\(982\) | 11838.0i | 0.384690i | ||||||||
\(983\) | − 43708.0i | − 1.41818i | −0.705119 | − | 0.709089i | \(-0.749106\pi\) | ||||
0.705119 | − | 0.709089i | \(-0.250894\pi\) | |||||||
\(984\) | 12825.0 | 0.415494 | ||||||||
\(985\) | 24654.0 | 0.797504 | ||||||||
\(986\) | 4181.00i | 0.135041i | ||||||||
\(987\) | −13860.0 | −0.446979 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39852.0 | 1.28131 | ||||||||
\(990\) | − 1386.00i | − 0.0444949i | ||||||||
\(991\) | −39614.0 | −1.26981 | −0.634904 | − | 0.772591i | \(-0.718960\pi\) | ||||
−0.634904 | + | 0.772591i | \(0.718960\pi\) | |||||||
\(992\) | 31556.0 | 1.00998 | ||||||||
\(993\) | − 3084.00i | − 0.0985577i | ||||||||
\(994\) | 10860.0i | 0.346538i | ||||||||
\(995\) | 14126.0i | 0.450075i | ||||||||
\(996\) | − 10878.0i | − 0.346067i | ||||||||
\(997\) | −36503.0 | −1.15954 | −0.579770 | − | 0.814780i | \(-0.696858\pi\) | ||||
−0.579770 | + | 0.814780i | \(0.696858\pi\) | |||||||
\(998\) | 8976.00 | 0.284700 | ||||||||
\(999\) | 351.000i | 0.0111163i |
(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 | 507.4.b.d.337.2 | 2 | ||
13.5 | odd | 4 | 507.4.a.d.1.1 | 1 | |||
13.7 | odd | 12 | 39.4.e.b.16.1 | ✓ | 2 | ||
13.8 | odd | 4 | 507.4.a.b.1.1 | 1 | |||
13.11 | odd | 12 | 39.4.e.b.22.1 | yes | 2 | ||
13.12 | even | 2 | inner | 507.4.b.d.337.1 | 2 | ||
39.5 | even | 4 | 1521.4.a.e.1.1 | 1 | |||
39.8 | even | 4 | 1521.4.a.h.1.1 | 1 | |||
39.11 | even | 12 | 117.4.g.a.100.1 | 2 | |||
39.20 | even | 12 | 117.4.g.a.55.1 | 2 | |||
52.7 | even | 12 | 624.4.q.c.289.1 | 2 | |||
52.11 | even | 12 | 624.4.q.c.529.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.b.16.1 | ✓ | 2 | 13.7 | odd | 12 | ||
39.4.e.b.22.1 | yes | 2 | 13.11 | odd | 12 | ||
117.4.g.a.55.1 | 2 | 39.20 | even | 12 | |||
117.4.g.a.100.1 | 2 | 39.11 | even | 12 | |||
507.4.a.b.1.1 | 1 | 13.8 | odd | 4 | |||
507.4.a.d.1.1 | 1 | 13.5 | odd | 4 | |||
507.4.b.d.337.1 | 2 | 13.12 | even | 2 | inner | ||
507.4.b.d.337.2 | 2 | 1.1 | even | 1 | trivial | ||
624.4.q.c.289.1 | 2 | 52.7 | even | 12 | |||
624.4.q.c.529.1 | 2 | 52.11 | even | 12 | |||
1521.4.a.e.1.1 | 1 | 39.5 | even | 4 | |||
1521.4.a.h.1.1 | 1 | 39.8 | even | 4 |