Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,4,Mod(49,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.j (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.3283667211\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Character | \(\chi\) | \(=\) | 192.49 |
Dual form | 192.4.j.a.145.4 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | −2.12132 | + | 2.12132i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.706564 | + | 0.706564i | 0.0631970 | + | 0.0631970i | 0.737999 | − | 0.674802i | \(-0.235771\pi\) |
−0.674802 | + | 0.737999i | \(0.735771\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.44122i | 0.239803i | 0.992786 | + | 0.119902i | \(0.0382579\pi\) | ||||
−0.992786 | + | 0.119902i | \(0.961742\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 9.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.7126 | + | 17.7126i | 0.485506 | + | 0.485506i | 0.906885 | − | 0.421379i | \(-0.138454\pi\) |
−0.421379 | + | 0.906885i | \(0.638454\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.7078 | + | 17.7078i | −0.377789 | + | 0.377789i | −0.870304 | − | 0.492515i | \(-0.836078\pi\) |
0.492515 | + | 0.870304i | \(0.336078\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.99770 | −0.0516001 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −105.640 | −1.50715 | −0.753576 | − | 0.657361i | \(-0.771673\pi\) | ||||
−0.753576 | + | 0.657361i | \(0.771673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.2862 | + | 40.2862i | −0.486436 | + | 0.486436i | −0.907180 | − | 0.420743i | \(-0.861769\pi\) |
0.420743 | + | 0.907180i | \(0.361769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.42125 | − | 9.42125i | −0.0978993 | − | 0.0978993i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 42.9921i | 0.389759i | 0.980827 | + | 0.194880i | \(0.0624316\pi\) | ||||
−0.980827 | + | 0.194880i | \(0.937568\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 124.002i | − | 0.992012i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19.0919 | + | 19.0919i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −185.646 | + | 185.646i | −1.18875 | + | 1.18875i | −0.211331 | + | 0.977415i | \(0.567780\pi\) |
−0.977415 | + | 0.211331i | \(0.932220\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −291.485 | −1.68878 | −0.844390 | − | 0.535729i | \(-0.820037\pi\) | ||||
−0.844390 | + | 0.535729i | \(0.820037\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −75.1483 | −0.396414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.13800 | + | 3.13800i | −0.0151548 | + | 0.0151548i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 151.040 | + | 151.040i | 0.671104 | + | 0.671104i | 0.957971 | − | 0.286867i | \(-0.0926137\pi\) |
−0.286867 | + | 0.957971i | \(0.592614\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 75.1278i | − | 0.308463i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 60.3918i | 0.230040i | 0.993363 | + | 0.115020i | \(0.0366931\pi\) | ||||
−0.993363 | + | 0.115020i | \(0.963307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −120.532 | − | 120.532i | −0.427464 | − | 0.427464i | 0.460300 | − | 0.887764i | \(-0.347742\pi\) |
−0.887764 | + | 0.460300i | \(0.847742\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.35907 | − | 6.35907i | 0.0210657 | − | 0.0210657i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −500.182 | −1.55232 | −0.776159 | − | 0.630537i | \(-0.782835\pi\) | ||||
−0.776159 | + | 0.630537i | \(0.782835\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 323.276 | 0.942494 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 224.097 | − | 224.097i | 0.615292 | − | 0.615292i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 192.407 | + | 192.407i | 0.498663 | + | 0.498663i | 0.911022 | − | 0.412359i | \(-0.135295\pi\) |
−0.412359 | + | 0.911022i | \(0.635295\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25.0302i | 0.0613650i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 170.920i | − | 0.397174i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 500.053 | + | 500.053i | 1.10341 | + | 1.10341i | 0.993996 | + | 0.109417i | \(0.0348985\pi\) |
0.109417 | + | 0.993996i | \(0.465102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −166.418 | + | 166.418i | −0.349306 | + | 0.349306i | −0.859851 | − | 0.510545i | \(-0.829444\pi\) |
0.510545 | + | 0.859851i | \(0.329444\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 39.9710 | 0.0799344 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −25.0234 | −0.0477502 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 575.426 | − | 575.426i | 1.04925 | − | 1.04925i | 0.0505233 | − | 0.998723i | \(-0.483911\pi\) |
0.998723 | − | 0.0505233i | \(-0.0160889\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −91.2000 | − | 91.2000i | −0.159119 | − | 0.159119i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 457.290i | 0.764371i | 0.924086 | + | 0.382186i | \(0.124828\pi\) | ||||
−0.924086 | + | 0.382186i | \(0.875172\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1082.59i | − | 1.73572i | −0.496812 | − | 0.867858i | \(-0.665496\pi\) | ||
0.496812 | − | 0.867858i | \(-0.334504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 263.047 | + | 263.047i | 0.404987 | + | 0.404987i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −78.6657 | + | 78.6657i | −0.116426 | + | 0.116426i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 544.309 | 0.775184 | 0.387592 | − | 0.921831i | \(-0.373307\pi\) | ||||
0.387592 | + | 0.921831i | \(0.373307\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −81.0000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −48.6931 | + | 48.6931i | −0.0643947 | + | 0.0643947i | −0.738571 | − | 0.674176i | \(-0.764499\pi\) |
0.674176 | + | 0.738571i | \(0.264499\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −74.6417 | − | 74.6417i | −0.0952474 | − | 0.0952474i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 787.630i | − | 0.970607i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 43.6714i | 0.0520131i | 0.999662 | + | 0.0260065i | \(0.00827907\pi\) | ||||
−0.999662 | + | 0.0260065i | \(0.991721\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −78.6442 | − | 78.6442i | −0.0905950 | − | 0.0905950i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 618.332 | − | 618.332i | 0.689442 | − | 0.689442i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −56.9295 | −0.0614826 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 690.537 | 0.722818 | 0.361409 | − | 0.932407i | \(-0.382296\pi\) | ||||
0.361409 | + | 0.932407i | \(0.382296\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 159.414 | − | 159.414i | 0.161835 | − | 0.161835i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 564.484 | + | 564.484i | 0.556121 | + | 0.556121i | 0.928201 | − | 0.372080i | \(-0.121355\pi\) |
−0.372080 | + | 0.928201i | \(0.621355\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 110.408i | 0.105620i | 0.998605 | + | 0.0528098i | \(0.0168177\pi\) | ||||
−0.998605 | + | 0.0528098i | \(0.983182\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 13.3134i | − | 0.0123739i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 254.357 | + | 254.357i | 0.229810 | + | 0.229810i | 0.812613 | − | 0.582803i | \(-0.198044\pi\) |
−0.582803 | + | 0.812613i | \(0.698044\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −205.025 | + | 205.025i | −0.180164 | + | 0.180164i | −0.791427 | − | 0.611263i | \(-0.790662\pi\) |
0.611263 | + | 0.791427i | \(0.290662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −640.809 | −0.547954 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −729.046 | −0.606928 | −0.303464 | − | 0.952843i | \(-0.598143\pi\) | ||||
−0.303464 | + | 0.952843i | \(0.598143\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −30.3766 | + | 30.3766i | −0.0246316 | + | 0.0246316i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 159.370 | + | 159.370i | 0.125930 | + | 0.125930i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 469.172i | − | 0.361420i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 703.525i | − | 0.528569i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −128.110 | − | 128.110i | −0.0939132 | − | 0.0939132i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 175.935 | − | 175.935i | 0.125889 | − | 0.125889i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2431.21 | 1.69870 | 0.849352 | − | 0.527827i | \(-0.176993\pi\) | ||||
0.849352 | + | 0.527827i | \(0.176993\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 511.374 | 0.349023 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −898.181 | + | 898.181i | −0.599042 | + | 0.599042i | −0.940058 | − | 0.341016i | \(-0.889229\pi\) |
0.341016 | + | 0.940058i | \(0.389229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −178.920 | − | 178.920i | −0.116649 | − | 0.116649i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 26.9793i | 0.0172000i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3061.79i | 1.90939i | 0.297590 | + | 0.954694i | \(0.403817\pi\) | ||||
−0.297590 | + | 0.954694i | \(0.596183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1811.69 | − | 1811.69i | −1.10551 | − | 1.10551i | −0.993733 | − | 0.111776i | \(-0.964346\pi\) |
−0.111776 | − | 0.993733i | \(-0.535654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1061.05 | − | 1061.05i | 0.633731 | − | 0.633731i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −627.303 | −0.366837 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −262.342 | −0.150250 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −685.771 | + | 685.771i | −0.384772 | + | 0.384772i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −869.143 | − | 869.143i | −0.477872 | − | 0.477872i | 0.426578 | − | 0.904451i | \(-0.359719\pi\) |
−0.904451 | + | 0.426578i | \(0.859719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1033.70i | 0.557097i | 0.960422 | + | 0.278549i | \(0.0898534\pi\) | ||||
−0.960422 | + | 0.278549i | \(0.910147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 950.764i | 0.502384i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −205.952 | − | 205.952i | −0.106726 | − | 0.106726i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2314.43 | + | 2314.43i | −1.17651 | + | 1.17651i | −0.195879 | + | 0.980628i | \(0.562756\pi\) |
−0.980628 | + | 0.195879i | \(0.937244\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −816.314 | −0.407157 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −190.937 | −0.0934656 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −737.872 | + | 737.872i | −0.354568 | + | 0.354568i | −0.861806 | − | 0.507238i | \(-0.830667\pi\) |
0.507238 | + | 0.861806i | \(0.330667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −53.0971 | − | 53.0971i | −0.0250521 | − | 0.0250521i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 468.664i | − | 0.217164i | −0.994088 | − | 0.108582i | \(-0.965369\pi\) | ||
0.994088 | − | 0.108582i | \(-0.0346309\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1569.87i | 0.714551i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 362.576 | + | 362.576i | 0.162145 | + | 0.162145i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1671.65 | − | 1671.65i | 0.734643 | − | 0.734643i | −0.236893 | − | 0.971536i | \(-0.576129\pi\) |
0.971536 | + | 0.236893i | \(0.0761290\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 550.718 | 0.237888 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2121.55 | −0.900933 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1413.56 | + | 1413.56i | −0.590247 | + | 0.590247i | −0.937698 | − | 0.347451i | \(-0.887047\pi\) |
0.347451 | + | 0.937698i | \(0.387047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2515.65 | − | 2515.65i | −1.03308 | − | 1.03308i | −0.999434 | − | 0.0336429i | \(-0.989289\pi\) |
−0.0336429 | − | 0.999434i | \(-0.510711\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 706.053i | − | 0.285207i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 213.439i | 0.0848235i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1871.17 | − | 1871.17i | −0.731730 | − | 0.731730i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −84.7912 | + | 84.7912i | −0.0326331 | + | 0.0326331i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.1653 | −0.00688165 | −0.00344082 | − | 0.999994i | \(-0.501095\pi\) | ||||
−0.00344082 | + | 0.999994i | \(0.501095\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1318.14 | 0.491616 | 0.245808 | − | 0.969319i | \(-0.420947\pi\) | ||||
0.245808 | + | 0.969319i | \(0.420947\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 53.0826 | − | 53.0826i | 0.0194940 | − | 0.0194940i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1818.15 | − | 1818.15i | −0.657551 | − | 0.657551i | 0.297249 | − | 0.954800i | \(-0.403931\pi\) |
−0.954800 | + | 0.297249i | \(0.903931\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4114.56i | 1.46570i | 0.680392 | + | 0.732849i | \(0.261810\pi\) | ||||
−0.680392 | + | 0.732849i | \(0.738190\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2441.33i | 0.856706i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −824.495 | − | 824.495i | −0.285065 | − | 0.285065i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −42.6707 | + | 42.6707i | −0.0145378 | + | 0.0145378i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 386.929 | 0.129920 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1427.15 | −0.472335 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1636.19 | + | 1636.19i | −0.533840 | + | 0.533840i | −0.921713 | − | 0.387873i | \(-0.873210\pi\) |
0.387873 | + | 0.921713i | \(0.373210\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −970.059 | − | 970.059i | −0.312053 | − | 0.312053i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 170.327i | − | 0.0540289i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1294.55i | − | 0.404975i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2296.51 | + | 2296.51i | 0.708603 | + | 0.708603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1870.66 | − | 1870.66i | 0.569385 | − | 0.569385i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3121.80 | 0.937450 | 0.468725 | − | 0.883344i | \(-0.344714\pi\) | ||||
0.468725 | + | 0.883344i | \(0.344714\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1116.01 | −0.330671 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3405.69 | − | 3405.69i | 0.995787 | − | 0.995787i | −0.00420438 | − | 0.999991i | \(-0.501338\pi\) |
0.999991 | + | 0.00420438i | \(0.00133830\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2566.84 | + | 2566.84i | 0.740706 | + | 0.740706i | 0.972714 | − | 0.232008i | \(-0.0745294\pi\) |
−0.232008 | + | 0.972714i | \(0.574529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 333.750i | − | 0.0950613i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1509.90i | − | 0.424534i | −0.977212 | − | 0.212267i | \(-0.931915\pi\) | ||
0.977212 | − | 0.212267i | \(-0.0680847\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −353.410 | − | 353.410i | −0.0981018 | − | 0.0981018i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1154.65 | + | 1154.65i | −0.316468 | + | 0.316468i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2608.05 | 0.705860 | 0.352930 | − | 0.935650i | \(-0.385185\pi\) | ||||
0.352930 | + | 0.935650i | \(0.385185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2222.20 | 0.593962 | 0.296981 | − | 0.954883i | \(-0.404020\pi\) | ||||
0.296981 | + | 0.954883i | \(0.404020\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 171.827 | − | 171.827i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 228.415 | + | 228.415i | 0.0595628 | + | 0.0595628i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1426.76i | − | 0.367541i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 206.587i | − | 0.0525781i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2551.97 | + | 2551.97i | 0.641749 | + | 0.641749i | 0.950985 | − | 0.309236i | \(-0.100073\pi\) |
−0.309236 | + | 0.950985i | \(0.600073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −761.503 | + | 761.503i | −0.189230 | + | 0.189230i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 316.678 | 0.0777692 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2203.05 | 0.534718 | 0.267359 | − | 0.963597i | \(-0.413849\pi\) | ||||
0.267359 | + | 0.963597i | \(0.413849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −670.802 | + | 670.802i | −0.160933 | + | 0.160933i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1670.81 | + | 1670.81i | 0.396248 | + | 0.396248i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7230.57i | − | 1.69527i | −0.530581 | − | 0.847635i | \(-0.678026\pi\) | ||
0.530581 | − | 0.847635i | \(-0.321974\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 271.896i | 0.0630280i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −92.6411 | − | 92.6411i | −0.0212342 | − | 0.0212342i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3750.63 | − | 3750.63i | 0.850112 | − | 0.850112i | −0.140035 | − | 0.990147i | \(-0.544721\pi\) |
0.990147 | + | 0.140035i | \(0.0447215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2751.65 | −0.616792 | −0.308396 | − | 0.951258i | \(-0.599792\pi\) | ||||
−0.308396 | + | 0.951258i | \(0.599792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 333.659 | 0.0739705 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2196.39 | − | 2196.39i | 0.481627 | − | 0.481627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3621.67 | + | 3621.67i | 0.785578 | + | 0.785578i | 0.980766 | − | 0.195188i | \(-0.0625318\pi\) |
−0.195188 | + | 0.980766i | \(0.562532\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2623.36i | 0.562927i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4989.59i | − | 1.05927i | −0.848227 | − | 0.529633i | \(-0.822330\pi\) | ||
0.848227 | − | 0.529633i | \(-0.177670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2426.42 | − | 2426.42i | −0.509667 | − | 0.509667i | 0.404757 | − | 0.914424i | \(-0.367356\pi\) |
−0.914424 | + | 0.404757i | \(0.867356\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 120.766 | − | 120.766i | 0.0251002 | − | 0.0251002i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −268.213 | −0.0551642 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6246.91 | 1.27151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1464.85 | + | 1464.85i | −0.295089 | + | 0.295089i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3379.84 | + | 3379.84i | 0.673899 | + | 0.673899i | 0.958613 | − | 0.284714i | \(-0.0918985\pi\) |
−0.284714 | + | 0.958613i | \(0.591899\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 706.639i | 0.139465i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 676.335i | 0.132138i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −761.294 | − | 761.294i | −0.147247 | − | 0.147247i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 535.309 | − | 535.309i | 0.102507 | − | 0.102507i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2394.90 | −0.454071 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −235.170 | −0.0441502 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2575.52 | − | 2575.52i | 0.478803 | − | 0.478803i | −0.425946 | − | 0.904749i | \(-0.640059\pi\) |
0.904749 | + | 0.425946i | \(0.140059\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −234.211 | − | 234.211i | −0.0431190 | − | 0.0431190i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2993.88i | − | 0.545875i | −0.962032 | − | 0.272938i | \(-0.912005\pi\) | ||
0.962032 | − | 0.272938i | \(-0.0879953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6133.96i | − | 1.10771i | −0.832614 | − | 0.553853i | \(-0.813157\pi\) | ||
0.832614 | − | 0.553853i | \(-0.186843\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 28.2420 | + | 28.2420i | 0.00505161 | + | 0.00505161i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6740.75 | + | 6740.75i | −1.19432 | + | 1.19432i | −0.218474 | + | 0.975843i | \(0.570108\pi\) |
−0.975843 | + | 0.218474i | \(0.929892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6576.56 | −1.15428 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1079.15 | −0.187639 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4255.85 | − | 4255.85i | 0.733133 | − | 0.733133i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2195.79 | + | 2195.79i | 0.374771 | + | 0.374771i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 869.848i | − | 0.147103i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2221.42i | − | 0.372251i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6485.75 | + | 6485.75i | 1.07701 | + | 1.07701i | 0.996776 | + | 0.0802296i | \(0.0255654\pi\) |
0.0802296 | + | 0.996776i | \(0.474435\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1359.36 | − | 1359.36i | 0.223701 | − | 0.223701i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 813.150 | 0.132618 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9405.38 | −1.52031 | −0.760154 | − | 0.649743i | \(-0.774877\pi\) | ||||
−0.760154 | + | 0.649743i | \(0.774877\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1546.54 | − | 1546.54i | 0.247777 | − | 0.247777i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5162.96 | − | 5162.96i | −0.819912 | − | 0.819912i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2959.08i | 0.465817i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 128.877i | − | 0.0201116i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1557.96 | + | 1557.96i | 0.241025 | + | 0.241025i | 0.817274 | − | 0.576249i | \(-0.195484\pi\) |
−0.576249 | + | 0.817274i | \(0.695484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3041.63 | + | 3041.63i | −0.466518 | + | 0.466518i | −0.900784 | − | 0.434266i | \(-0.857008\pi\) |
0.434266 | + | 0.900784i | \(0.357008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −676.150 | −0.102821 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1629.66 | 0.245717 | 0.122859 | − | 0.992424i | \(-0.460794\pi\) | ||||
0.122859 | + | 0.992424i | \(0.460794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −323.104 | + | 323.104i | −0.0483059 | + | 0.0483059i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 995.265 | + | 995.265i | 0.147549 | + | 0.147549i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9276.15i | 1.36372i | 0.731482 | + | 0.681861i | \(0.238829\pi\) | ||||
−0.731482 | + | 0.681861i | \(0.761171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3613.04i | 0.526759i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1492.40 | + | 1492.40i | 0.215787 | + | 0.215787i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 764.917 | − | 764.917i | 0.109692 | − | 0.109692i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1016.63 | −0.144599 | −0.0722994 | − | 0.997383i | \(-0.523034\pi\) | ||||
−0.0722994 | + | 0.997383i | \(0.523034\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 543.527 | 0.0766798 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −854.522 | + | 854.522i | −0.119581 | + | 0.119581i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8897.07 | − | 8897.07i | −1.23505 | − | 1.23505i | −0.962001 | − | 0.273047i | \(-0.911969\pi\) |
−0.273047 | − | 0.962001i | \(-0.588031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 746.431i | 0.102788i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6574.76i | − | 0.898190i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5154.79 | + | 5154.79i | 0.698638 | + | 0.698638i | 0.964117 | − | 0.265478i | \(-0.0855299\pi\) |
−0.265478 | + | 0.964117i | \(0.585530\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5157.39 | + | 5157.39i | −0.693493 | + | 0.693493i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10573.7 | −1.41068 | −0.705340 | − | 0.708870i | \(-0.749205\pi\) | ||||
−0.705340 | + | 0.708870i | \(0.749205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −111.165 | −0.0147155 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1084.79 | + | 1084.79i | −0.142488 | + | 0.142488i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7789.01 | + | 7789.01i | 1.01522 | + | 1.01522i | 0.999882 | + | 0.0153326i | \(0.00488071\pi\) |
0.0153326 | + | 0.999882i | \(0.495119\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4541.70i | − | 0.587426i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3810.66i | − | 0.489115i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 384.589 | + | 384.589i | 0.0489893 | + | 0.0489893i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1219.69 | + | 1219.69i | −0.154193 | + | 0.154193i | −0.779988 | − | 0.625795i | \(-0.784775\pi\) |
0.625795 | + | 0.779988i | \(0.284775\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 759.093 | 0.0952435 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5714.97 | −0.711701 | −0.355850 | − | 0.934543i | \(-0.615809\pi\) | ||||
−0.355850 | + | 0.934543i | \(0.615809\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5161.55 | − | 5161.55i | 0.638003 | − | 0.638003i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −57.2316 | − | 57.2316i | −0.00702189 | − | 0.00702189i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5350.64i | 0.651649i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1504.54i | − | 0.181894i | −0.995856 | − | 0.0909469i | \(-0.971011\pi\) | ||
0.995856 | − | 0.0909469i | \(-0.0289894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6495.03 | − | 6495.03i | −0.779504 | − | 0.779504i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2220.85 | + | 2220.85i | −0.264602 | + | 0.264602i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −68.8095 | −0.00813910 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7686.36 | 0.902644 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9630.38 | + | 9630.38i | −1.12285 | + | 1.12285i | −0.131541 | + | 0.991311i | \(0.541993\pi\) |
−0.991311 | + | 0.131541i | \(0.958007\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2831.19 | + | 2831.19i | 0.327752 | + | 0.327752i | 0.851731 | − | 0.523979i | \(-0.175553\pi\) |
−0.523979 | + | 0.851731i | \(0.675553\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4501.63i | 0.517440i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13099.6i | 1.49511i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −739.100 | − | 739.100i | −0.0837647 | − | 0.0837647i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1330.71 | − | 1330.71i | 0.149761 | − | 0.149761i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5555.36 | −0.620864 | −0.310432 | − | 0.950596i | \(-0.600474\pi\) | ||||
−0.310432 | + | 0.950596i | \(0.600474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14582.8 | −1.61848 | −0.809241 | − | 0.587476i | \(-0.800122\pi\) | ||||
−0.809241 | + | 0.587476i | \(0.800122\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 556.510 | − | 556.510i | 0.0613394 | − | 0.0613394i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1731.99 | − | 1731.99i | −0.189593 | − | 0.189593i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4862.86i | − | 0.528682i | −0.964429 | − | 0.264341i | \(-0.914846\pi\) | ||
0.964429 | − | 0.264341i | \(-0.0851545\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2909.48i | − | 0.314165i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9325.47 | − | 9325.47i | −1.00015 | − | 1.00015i | −1.00000 | 0.000149687i | \(-0.999952\pi\) | |
−0.000149687 | − | 1.00000i | \(-0.500048\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.8566 | + | 30.8566i | −0.00328707 | + | 0.00328707i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3687.46 | 0.390181 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11461.1 | 1.20464 | 0.602318 | − | 0.798256i | \(-0.294244\pi\) | ||||
0.602318 | + | 0.798256i | \(0.294244\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1069.70 | + | 1069.70i | −0.111685 | + | 0.111685i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2192.82 | − | 2192.82i | −0.227434 | − | 0.227434i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 111.134i | − | 0.0114507i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13856.7i | 1.41835i | 0.705031 | + | 0.709177i | \(0.250933\pi\) | ||||
−0.705031 | + | 0.709177i | \(0.749067\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2016.88 | − | 2016.88i | −0.205097 | − | 0.205097i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3166.73 | + | 3166.73i | −0.319934 | + | 0.319934i | −0.848741 | − | 0.528808i | \(-0.822639\pi\) |
0.528808 | + | 0.848741i | \(0.322639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1566.96 | −0.157285 | −0.0786426 | − | 0.996903i | \(-0.525059\pi\) | ||||
−0.0786426 | + | 0.996903i | \(0.525059\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 873.782 | 0.0871412 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5309.28 | + | 5309.28i | −0.526090 | + | 0.526090i | −0.919404 | − | 0.393314i | \(-0.871329\pi\) |
0.393314 | + | 0.919404i | \(0.371329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2555.59 | + | 2555.59i | 0.251613 | + | 0.251613i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 9819.30i | − | 0.960614i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4269.88i | − | 0.415072i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4995.55 | + | 4995.55i | 0.482551 | + | 0.482551i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1731.66 | − | 1731.66i | 0.166221 | − | 0.166221i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4034.12 | 0.384809 | 0.192405 | − | 0.981316i | \(-0.438371\pi\) | ||||
0.192405 | + | 0.981316i | \(0.438371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5349.17 | −0.507071 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 405.039 | − | 405.039i | 0.0381572 | − | 0.0381572i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 487.908 | + | 487.908i | 0.0456799 | + | 0.0456799i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16499.3i | − | 1.53522i | −0.640915 | − | 0.767612i | \(-0.721445\pi\) | ||
0.640915 | − | 0.767612i | \(-0.278555\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3130.53i | − | 0.289504i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1060.25 | − | 1060.25i | −0.0974506 | − | 0.0974506i | 0.656701 | − | 0.754151i | \(-0.271951\pi\) |
−0.754151 | + | 0.656701i | \(0.771951\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19611.7 | − | 19611.7i | 1.79162 | − | 1.79162i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 225.272 | 0.0204550 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2030.93 | −0.183299 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4275.19 | + | 4275.19i | −0.383534 | + | 0.383534i | −0.872374 | − | 0.488839i | \(-0.837420\pi\) |
0.488839 | + | 0.872374i | \(0.337420\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 994.187 | + | 994.187i | 0.0886567 | + | 0.0886567i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13976.3i | 1.23891i | 0.785031 | + | 0.619456i | \(0.212647\pi\) | ||||
−0.785031 | + | 0.619456i | \(0.787353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 797.687i | 0.0702903i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3330.19 | − | 3330.19i | −0.291714 | − | 0.291714i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9315.16 | + | 9315.16i | −0.811174 | + | 0.811174i | −0.984810 | − | 0.173636i | \(-0.944448\pi\) |
0.173636 | + | 0.984810i | \(0.444448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4808.01 | 0.416230 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1538.28 | −0.132391 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −78.0102 | + | 78.0102i | −0.00667484 | + | 0.00667484i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8859.53 | − | 8859.53i | −0.753659 | − | 0.753659i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7092.21i | 0.599834i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10404.0i | 0.874870i | 0.899250 | + | 0.437435i | \(0.144113\pi\) | ||||
−0.899250 | + | 0.437435i | \(0.855887\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2520.38 | − | 2520.38i | −0.210724 | − | 0.210724i | 0.593851 | − | 0.804575i | \(-0.297607\pi\) |
−0.804575 | + | 0.593851i | \(0.797607\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1168.25 | + | 1168.25i | −0.0971173 | + | 0.0971173i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30792.6 | 2.54525 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10318.7 | 0.848088 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4500.48 | − | 4500.48i | 0.367804 | − | 0.367804i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1069.41 | − | 1069.41i | −0.0869064 | − | 0.0869064i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 359.439i | 0.0290465i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5997.21i | − | 0.481935i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5726.06 | + | 5726.06i | 0.457586 | + | 0.457586i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13635.3 | − | 13635.3i | 1.08360 | − | 1.08360i | 0.0874292 | − | 0.996171i | \(-0.472135\pi\) |
0.996171 | − | 0.0874292i | \(-0.0278651\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10673.0 | 0.843504 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −289.726 | −0.0227716 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1729.49 | − | 1729.49i | 0.135188 | − | 0.135188i | −0.636275 | − | 0.771463i | \(-0.719526\pi\) |
0.771463 | + | 0.636275i | \(0.219526\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1497.76 | + | 1497.76i | 0.116435 | + | 0.116435i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 14958.0i | − | 1.15650i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2417.39i | 0.185892i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −452.772 | − | 452.772i | −0.0346290 | − | 0.0346290i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3758.29 | − | 3758.29i | 0.285896 | − | 0.285896i | −0.549559 | − | 0.835455i | \(-0.685204\pi\) |
0.835455 | + | 0.549559i | \(0.185204\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4268.71 | 0.322982 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7938.71 | 0.597455 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1676.08 | + | 1676.08i | −0.125468 | + | 0.125468i | −0.767052 | − | 0.641585i | \(-0.778277\pi\) |
0.641585 | + | 0.767052i | \(0.278277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −515.118 | − | 515.118i | −0.0383560 | − | 0.0383560i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 359.739i | − | 0.0266448i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11314.4i | 0.833611i | 0.908996 | + | 0.416805i | \(0.136850\pi\) | ||||
−0.908996 | + | 0.416805i | \(0.863150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4555.47 | − | 4555.47i | −0.333871 | − | 0.333871i | 0.520184 | − | 0.854055i | \(-0.325864\pi\) |
−0.854055 | + | 0.520184i | \(0.825864\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.5344 | − | 38.5344i | 0.00280942 | − | 0.00280942i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5331.08 | 0.386646 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15216.2 | 1.09785 | 0.548925 | − | 0.835872i | \(-0.315037\pi\) | ||||
0.548925 | + | 0.835872i | \(0.315037\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2796.20 | + | 2796.20i | −0.200701 | + | 0.200701i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −216.257 | − | 216.257i | −0.0154421 | − | 0.0154421i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6816.07i | 0.484207i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 225.210i | 0.0159167i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3111.52 | − | 3111.52i | −0.218784 | − | 0.218784i | 0.589202 | − | 0.807986i | \(-0.299442\pi\) |
−0.807986 | + | 0.589202i | \(0.799442\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11742.8 | − | 11742.8i | 0.821484 | − | 0.821484i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7713.74 | 0.536888 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7275.10 | −0.503799 | −0.251899 | − | 0.967753i | \(-0.581055\pi\) | ||||
−0.251899 | + | 0.967753i | \(0.581055\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 331.500 | − | 331.500i | 0.0228406 | − | 0.0228406i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8728.31 | − | 8728.31i | −0.598368 | − | 0.598368i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18975.0i | 1.29432i | 0.762355 | + | 0.647159i | \(0.224043\pi\) | ||||
−0.762355 | + | 0.647159i | \(0.775957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2493.99i | 0.169271i | 0.996412 | + | 0.0846357i | \(0.0269726\pi\) | ||||
−0.996412 | + | 0.0846357i | \(0.973027\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5178.84 | − | 5178.84i | −0.349749 | − | 0.349749i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 497.085 | − | 497.085i | 0.0334039 | − | 0.0334039i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13075.7 | −0.874341 | −0.437171 | − | 0.899379i | \(-0.644019\pi\) | ||||
−0.437171 | + | 0.899379i | \(0.644019\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3498.04 | 0.232755 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8857.11 | − | 8857.11i | 0.586449 | − | 0.586449i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10449.8 | + | 10449.8i | 0.688523 | + | 0.688523i | 0.961906 | − | 0.273382i | \(-0.0881423\pi\) |
−0.273382 | + | 0.961906i | \(0.588142\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 181.036i | − | 0.0118701i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6927.08i | − | 0.451983i | −0.974129 | − | 0.225992i | \(-0.927438\pi\) | ||
0.974129 | − | 0.225992i | \(-0.0725622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16635.4 | + | 16635.4i | 1.08018 | + | 1.08018i | 0.996492 | + | 0.0836922i | \(0.0266713\pi\) |
0.0836922 | + | 0.996492i | \(0.473329\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −820.800 | + | 820.800i | −0.0530395 | + | 0.0530395i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −193.954 | −0.0124729 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15251.6 | −0.976101 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3027.44 | − | 3027.44i | 0.192830 | − | 0.192830i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15955.9 | − | 15955.9i | −1.01146 | − | 1.01146i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22231.3i | − | 1.40256i | −0.712888 | − | 0.701278i | \(-0.752613\pi\) | ||
0.712888 | − | 0.701278i | \(-0.247387\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6941.78i | − | 0.435878i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1717.81 | + | 1717.81i | 0.107353 | + | 0.107353i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5724.50 | + | 5724.50i | −0.356064 | + | 0.356064i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4115.61 | 0.254790 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8447.90 | 0.520549 | 0.260274 | − | 0.965535i | \(-0.416187\pi\) | ||||
0.260274 | + | 0.965535i | \(0.416187\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5326.38 | + | 5326.38i | −0.326675 | + | 0.326675i | −0.851321 | − | 0.524646i | \(-0.824198\pi\) |
0.524646 | + | 0.851321i | \(0.324198\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 361.318 | + | 361.318i | 0.0220572 | + | 0.0220572i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7105.36i | 0.431747i | 0.976421 | + | 0.215874i | \(0.0692599\pi\) | ||||
−0.976421 | + | 0.215874i | \(0.930740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17714.5i | 1.07143i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2746.15 | + | 2746.15i | 0.165330 | + | 0.165330i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1518.80 | − | 1518.80i | 0.0910189 | − | 0.0910189i | −0.660131 | − | 0.751150i | \(-0.729499\pi\) |
0.751150 | + | 0.660131i | \(0.229499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1269.24 | −0.0757152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9743.29 | −0.578572 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5425.29 | + | 5425.29i | −0.320697 | + | 0.320697i | −0.849035 | − | 0.528337i | \(-0.822816\pi\) |
0.528337 | + | 0.849035i | \(0.322816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18128.4 | − | 18128.4i | −1.06674 | − | 1.06674i | −0.997608 | − | 0.0691300i | \(-0.977978\pi\) |
−0.0691300 | − | 0.997608i | \(-0.522022\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7936.53i | 0.464901i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 252.837i | − | 0.0147437i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7981.31 | − | 7981.31i | −0.463325 | − | 0.463325i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6622.34 | + | 6622.34i | −0.382712 | + | 0.382712i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5895.41 | −0.339180 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1072.11 | 0.0614071 | 0.0307036 | − | 0.999529i | \(-0.490225\pi\) | ||||
0.0307036 | + | 0.999529i | \(0.490225\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2367.42 | − | 2367.42i | 0.134996 | − | 0.134996i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4806.53 | + | 4806.53i | 0.272865 | + | 0.272865i | 0.830253 | − | 0.557387i | \(-0.188196\pi\) |
−0.557387 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3066.82i | 0.173334i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14449.1i | 0.813057i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21855.0 | − | 21855.0i | −1.22439 | − | 1.22439i | −0.966056 | − | 0.258334i | \(-0.916826\pi\) |
−0.258334 | − | 0.966056i | \(-0.583174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2163.35 | + | 2163.35i | −0.120667 | + | 0.120667i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10890.2 | −0.604784 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6814.21 | −0.376779 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 585.815 | − | 585.815i | 0.0322510 | − | 0.0322510i | −0.690797 | − | 0.723048i | \(-0.742740\pi\) |
0.723048 | + | 0.690797i | \(0.242740\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 707.991 | + | 707.991i | 0.0388086 | + | 0.0388086i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2560.15i | − | 0.139730i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6379.82i | − | 0.346704i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3202.97 | + | 3202.97i | 0.173315 | + | 0.173315i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7273.96 | + | 7273.96i | −0.391917 | + | 0.391917i | −0.875370 | − | 0.483453i | \(-0.839382\pi\) |
0.483453 | + | 0.875370i | \(0.339382\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12169.7 | −0.652899 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1499.39 | 0.0800998 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2507.00 | + | 2507.00i | −0.133360 | + | 0.133360i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17600.7 | + | 17600.7i | 0.932309 | + | 0.932309i | 0.997850 | − | 0.0655405i | \(-0.0208772\pi\) |
−0.0655405 | + | 0.997850i | \(0.520877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4898.78i | − | 0.258395i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12531.5i | − | 0.658218i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −443.230 | − | 443.230i | −0.0231830 | − | 0.0231830i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5532.50 | + | 5532.50i | −0.288166 | + | 0.288166i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14431.8 | −0.748562 | −0.374281 | − | 0.927315i | \(-0.622110\pi\) | ||||
−0.374281 | + | 0.927315i | \(0.622110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −490.346 | −0.0253279 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4714.01 | + | 4714.01i | −0.242484 | + | 0.242484i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23020.4 | + | 23020.4i | 1.17925 | + | 1.17925i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5802.18i | 0.295998i | 0.988987 | + | 0.147999i | \(0.0472833\pi\) | ||||
−0.988987 | + | 0.147999i | \(0.952717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12733.1 | + | 12733.1i | 0.644253 | + | 0.644253i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16743.4 | + | 16743.4i | −0.843699 | + | 0.843699i | −0.989338 | − | 0.145639i | \(-0.953476\pi\) |
0.145639 | + | 0.989338i | \(0.453476\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −969.082 | −0.0486328 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20384.6 | 1.01883 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5259.84 | + | 5259.84i | −0.261822 | + | 0.261822i | −0.825794 | − | 0.563972i | \(-0.809273\pi\) |
0.563972 | + | 0.825794i | \(0.309273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3026.61 | + | 3026.61i | 0.150048 | + | 0.150048i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 29413.6i | − | 1.45233i | −0.687522 | − | 0.726163i | \(-0.741302\pi\) | ||
0.687522 | − | 0.726163i | \(-0.258698\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1228.21i | − | 0.0604002i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 438.238 | + | 438.238i | 0.0214649 | + | 0.0214649i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1129.66 | + | 1129.66i | −0.0551091 | + | 0.0551091i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37261.5 | −1.81051 | −0.905254 | − | 0.424870i | \(-0.860320\pi\) | ||||
−0.905254 | + | 0.424870i | \(0.860320\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10827.1 | −0.523986 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −730.378 | + | 730.378i | −0.0352069 | + | 0.0352069i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4651.56 | + | 4651.56i | 0.223334 | + | 0.223334i | 0.809901 | − | 0.586567i | \(-0.199521\pi\) |
−0.586567 | + | 0.809901i | \(0.699521\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 3230.78i | − | 0.154506i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25144.7i | − | 1.19776i | −0.800839 | − | 0.598879i | \(-0.795613\pi\) | ||
0.800839 | − | 0.598879i | \(-0.204387\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −910.561 | − | 910.561i | −0.0432038 | − | 0.0432038i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −671.775 | + | 671.775i | −0.0317491 | + | 0.0317491i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17709.7 | −0.833715 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29241.9 | −1.37125 | −0.685625 | − | 0.727955i | \(-0.740471\pi\) | ||||
−0.685625 | + | 0.727955i | \(0.740471\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4673.38 | + | 4673.38i | −0.218298 | + | 0.218298i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6698.95 | − | 6698.95i | −0.311700 | − | 0.311700i | 0.533868 | − | 0.845568i | \(-0.320738\pi\) |
−0.845568 | + | 0.533868i | \(0.820738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36144.5i | 1.67529i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2845.97i | − | 0.131401i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2432.96 | − | 2432.96i | −0.111900 | − | 0.111900i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8099.81 | + | 8099.81i | −0.371106 | + | 0.371106i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7088.67 | −0.323536 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3270.58 | −0.148703 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4317.53 | − | 4317.53i | 0.195557 | − | 0.195557i | −0.602535 | − | 0.798092i | \(-0.705843\pi\) |
0.798092 | + | 0.602535i | \(0.205843\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15338.3 | + | 15338.3i | 0.692091 | + | 0.692091i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3237.85i | − | 0.145543i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5893.80i | − | 0.263928i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −576.778 | − | 576.778i | −0.0257311 | − | 0.0257311i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12492.2 | − | 12492.2i | 0.555201 | − | 0.555201i | −0.372736 | − | 0.927937i | \(-0.621580\pi\) |
0.927937 | + | 0.372736i | \(0.121580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52839.4 | 2.33958 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 393.043 | 0.0173377 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19175.5 | − | 19175.5i | 0.842700 | − | 0.842700i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −134.909 | − | 134.909i | −0.00590674 | − | 0.00590674i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15912.6i | 0.694113i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4276.80i | 0.185864i | 0.995672 | + | 0.0929321i | \(0.0296239\pi\) | ||||
−0.995672 | + | 0.0929321i | \(0.970376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15331.3 | + | 15331.3i | 0.663817 | + | 0.663817i | 0.956277 | − | 0.292461i | \(-0.0944741\pi\) |
−0.292461 | + | 0.956277i | \(0.594474\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5837.13 | − | 5837.13i | 0.251804 | − | 0.251804i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1042.71 | −0.0448152 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9711.55 | 0.415868 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −707.797 | + | 707.797i | −0.0301983 | + | 0.0301983i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12527.1 | − | 12527.1i | −0.532521 | − | 0.532521i | 0.388801 | − | 0.921322i | \(-0.372890\pi\) |
−0.921322 | + | 0.388801i | \(0.872890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 15241.1i | − | 0.645532i | −0.946479 | − | 0.322766i | \(-0.895387\pi\) | ||
0.946479 | − | 0.322766i | \(-0.104613\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9318.51i | 0.393247i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25529.5 | + | 25529.5i | 1.07345 | + | 1.07345i | 0.997079 | + | 0.0763756i | \(0.0243348\pi\) |
0.0763756 | + | 0.997079i | \(0.475665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23542.4 | + | 23542.4i | −0.986322 | + | 0.986322i | −0.999908 | − | 0.0135854i | \(-0.995676\pi\) |
0.0135854 | + | 0.999908i | \(0.495676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15365.4 | −0.641421 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34151.0 | −1.42048 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 331.141 | − | 331.141i | 0.0137241 | − | 0.0137241i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5564.99 | − | 5564.99i | −0.229814 | − | 0.229814i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3385.26i | − | 0.139299i | −0.997572 | − | 0.0696497i | \(-0.977812\pi\) | ||
0.997572 | − | 0.0696497i | \(-0.0221882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 44540.0i | − | 1.82623i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10584.5 | + | 10584.5i | 0.432444 | + | 0.432444i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1109.21 | + | 1109.21i | −0.0451575 | + | 0.0451575i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3124.51 | 0.126753 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10294.4 | 0.416141 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6493.53 | + | 6493.53i | −0.261569 | + | 0.261569i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4371.94 | + | 4371.94i | 0.175489 | + | 0.175489i | 0.789386 | − | 0.613897i | \(-0.210399\pi\) |
−0.613897 | + | 0.789386i | \(0.710399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 512.366i | 0.0204942i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 32205.4i | − | 1.28368i | −0.766838 | − | 0.641840i | \(-0.778171\pi\) | ||
0.766838 | − | 0.641840i | \(-0.221829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2875.17 | − | 2875.17i | −0.114202 | − | 0.114202i | 0.647696 | − | 0.761898i | \(-0.275732\pi\) |
−0.761898 | + | 0.647696i | \(0.775732\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 568.966 | − | 568.966i | 0.0225207 | − | 0.0225207i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18181.9 | −0.717173 | −0.358586 | − | 0.933497i | \(-0.616741\pi\) | ||||
−0.358586 | + | 0.933497i | \(0.616741\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2362.26 | 0.0928544 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13251.7 | + | 13251.7i | −0.519090 | + | 0.519090i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9641.15 | + | 9641.15i | 0.376356 | + | 0.376356i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20379.0i | 0.792787i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6214.83i | − | 0.240939i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 781.368 | + | 781.368i | 0.0301886 | + | 0.0301886i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26665.8 | + | 26665.8i | −1.02673 | + | 1.02673i | −0.0270950 | + | 0.999633i | \(0.508626\pi\) |
−0.999633 | + | 0.0270950i | \(0.991374\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14339.4 | −0.550236 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26033.2 | 0.995552 | 0.497776 | − | 0.867305i | \(-0.334150\pi\) | ||||
0.497776 | + | 0.867305i | \(0.334150\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27917.9 | − | 27917.9i | 1.06400 | − | 1.06400i | 0.0661953 | − | 0.997807i | \(-0.478914\pi\) |
0.997807 | − | 0.0661953i | \(-0.0210860\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1499.01 | − | 1499.01i | −0.0569362 | − | 0.0569362i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 28947.2i | − | 1.09577i | −0.836553 | − | 0.547887i | \(-0.815433\pi\) | ||
0.836553 | − | 0.547887i | \(-0.184567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10797.6i | 0.407355i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1434.72 | − | 1434.72i | −0.0539451 | − | 0.0539451i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20150.4 | − | 20150.4i | 0.755104 | − | 0.755104i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1997.54 | −0.0746036 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3229.90 | 0.120227 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54113.0 | − | 54113.0i | 2.00753 | − | 2.00753i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20326.0 | − | 20326.0i | −0.751561 | − | 0.751561i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2271.12i | 0.0836968i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3554.94i | − | 0.130575i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3191.29 | − | 3191.29i | −0.116830 | − | 0.116830i | 0.646275 | − | 0.763105i | \(-0.276326\pi\) |
−0.763105 | + | 0.646275i | \(0.776326\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5080.35 | − | 5080.35i | 0.185374 | − | 0.185374i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40016.6 | 1.45534 | 0.727668 | − | 0.685930i | \(-0.240604\pi\) | ||||
0.727668 | + | 0.685930i | \(0.240604\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1724.97 | −0.0625280 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 498.871 | − | 498.871i | 0.0180242 | − | 0.0180242i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3989.02 | − | 3989.02i | −0.143652 | − | 0.143652i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15342.1i | 0.550694i | 0.961345 | + | 0.275347i | \(0.0887928\pi\) | ||||
−0.961345 | + | 0.275347i | \(0.911207\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10927.0i | 0.390941i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8097.60 | − | 8097.60i | −0.288771 | − | 0.288771i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18729.2 | − | 18729.2i | 0.665743 | − | 0.665743i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 993.671 | 0.0352065 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −104.186 | −0.00367946 | −0.00183973 | − | 0.999998i | \(-0.500586\pi\) | ||||
−0.00183973 | + | 0.999998i | \(0.500586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13023.5 | + | 13023.5i | −0.458464 | + | 0.458464i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6350.97 | + | 6350.97i | 0.222853 | + | 0.222853i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2644.20i | − | 0.0924863i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3137.81i | − | 0.109400i | −0.998503 | − | 0.0547001i | \(-0.982580\pi\) | ||
0.998503 | − | 0.0547001i | \(-0.0174203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13012.1 | + | 13012.1i | 0.452219 | + | 0.452219i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7984.14 | − | 7984.14i | 0.276595 | − | 0.276595i | −0.555153 | − | 0.831748i | \(-0.687340\pi\) |
0.831748 | + | 0.555153i | \(0.187340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2596.37 | −0.0896601 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −119.821 | −0.00412462 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20247.7 | + | 20247.7i | −0.694787 | + | 0.694787i | −0.963281 | − | 0.268495i | \(-0.913474\pi\) |
0.268495 | + | 0.963281i | \(0.413474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19170.2 | + | 19170.2i | 0.655734 | + | 0.655734i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 28598.6i | − | 0.975155i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34966.0i | 1.18852i | 0.804272 | + | 0.594261i | \(0.202555\pi\) | ||||
−0.804272 | + | 0.594261i | \(0.797445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.8349 | − | 12.8349i | −0.000434899 | − | 0.000434899i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13951.0 | − | 13951.0i | 0.471235 | − | 0.471235i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13598.1 | −0.457877 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55172.3 | 1.85198 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2289.21 | − | 2289.21i | 0.0766032 | − | 0.0766032i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 931.351 | + | 931.351i | 0.0310686 | + | 0.0310686i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15161.3i | − | 0.504194i | −0.967702 | − | 0.252097i | \(-0.918880\pi\) | ||
0.967702 | − | 0.252097i | \(-0.0811201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18056.1i | 0.598601i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13515.9 | − | 13515.9i | −0.446701 | − | 0.446701i | 0.447555 | − | 0.894256i | \(-0.352295\pi\) |
−0.894256 | + | 0.447555i | \(0.852295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8046.12 | − | 8046.12i | 0.265105 | − | 0.265105i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9315.96 | −0.305999 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22582.6 | 0.739490 | 0.369745 | − | 0.929133i | \(-0.379445\pi\) | ||||
0.369745 | + | 0.929133i | \(0.379445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −773.536 | + | 773.536i | −0.0252526 | + | 0.0252526i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1845.23 | + | 1845.23i | 0.0600546 | + | 0.0600546i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39898.2i | 1.29456i | 0.762252 | + | 0.647281i | \(0.224094\pi\) | ||||
−0.762252 | + | 0.647281i | \(0.775906\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2569.27i | − | 0.0831105i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4712.33 | + | 4712.33i | 0.151971 | + | 0.151971i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5181.92 | − | 5181.92i | 0.166608 | − | 0.166608i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36767.4 | 1.17856 | 0.589281 | − | 0.807928i | \(-0.299411\pi\) | ||||
0.589281 | + | 0.807928i | \(0.299411\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27516.7 | −0.879372 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2907.20 | + | 2907.20i | −0.0926276 | + | 0.0926276i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6130.71 | + | 6130.71i | 0.194746 | + | 0.194746i | 0.797743 | − | 0.602997i | \(-0.206027\pi\) |
−0.602997 | + | 0.797743i | \(0.706027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5767.28i | 0.182651i |
(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 | 192.4.j.a.49.4 | 24 | ||
3.2 | odd | 2 | 576.4.k.b.433.6 | 24 | |||
4.3 | odd | 2 | 48.4.j.a.37.11 | yes | 24 | ||
8.3 | odd | 2 | 384.4.j.b.97.3 | 24 | |||
8.5 | even | 2 | 384.4.j.a.97.10 | 24 | |||
12.11 | even | 2 | 144.4.k.b.37.2 | 24 | |||
16.3 | odd | 4 | 48.4.j.a.13.11 | ✓ | 24 | ||
16.5 | even | 4 | 384.4.j.a.289.10 | 24 | |||
16.11 | odd | 4 | 384.4.j.b.289.3 | 24 | |||
16.13 | even | 4 | inner | 192.4.j.a.145.4 | 24 | ||
48.29 | odd | 4 | 576.4.k.b.145.6 | 24 | |||
48.35 | even | 4 | 144.4.k.b.109.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.4.j.a.13.11 | ✓ | 24 | 16.3 | odd | 4 | ||
48.4.j.a.37.11 | yes | 24 | 4.3 | odd | 2 | ||
144.4.k.b.37.2 | 24 | 12.11 | even | 2 | |||
144.4.k.b.109.2 | 24 | 48.35 | even | 4 | |||
192.4.j.a.49.4 | 24 | 1.1 | even | 1 | trivial | ||
192.4.j.a.145.4 | 24 | 16.13 | even | 4 | inner | ||
384.4.j.a.97.10 | 24 | 8.5 | even | 2 | |||
384.4.j.a.289.10 | 24 | 16.5 | even | 4 | |||
384.4.j.b.97.3 | 24 | 8.3 | odd | 2 | |||
384.4.j.b.289.3 | 24 | 16.11 | odd | 4 | |||
576.4.k.b.145.6 | 24 | 48.29 | odd | 4 | |||
576.4.k.b.433.6 | 24 | 3.2 | odd | 2 |