Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.a (trivial) |
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: | yes |
Analytic conductor: | \(130.099211563\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.00000 | −1.06066 | −0.530330 | − | 0.847791i | \(-0.677932\pi\) | ||||
−0.530330 | + | 0.847791i | \(0.677932\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 21.0000 | 0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −15.0000 | −0.474342 | ||||||||
\(11\) | 45.0000 | 1.23346 | 0.616728 | − | 0.787177i | \(-0.288458\pi\) | ||||
0.616728 | + | 0.787177i | \(0.288458\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −59.0000 | −1.25874 | −0.629371 | − | 0.777105i | \(-0.716688\pi\) | ||||
−0.629371 | + | 0.777105i | \(0.716688\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | −54.0000 | −0.770407 | −0.385204 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385204 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 121.000 | 1.46102 | 0.730508 | − | 0.682904i | \(-0.239283\pi\) | ||||
0.730508 | + | 0.682904i | \(0.239283\pi\) | |||||||
\(20\) | 5.00000 | 0.0559017 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −135.000 | −1.30828 | ||||||||
\(23\) | −69.0000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 177.000 | 1.33510 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 162.000 | 1.03733 | 0.518666 | − | 0.854977i | \(-0.326429\pi\) | ||||
0.518666 | + | 0.854977i | \(0.326429\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 88.0000 | 0.509847 | 0.254924 | − | 0.966961i | \(-0.417950\pi\) | ||||
0.254924 | + | 0.966961i | \(0.417950\pi\) | |||||||
\(32\) | 45.0000 | 0.248592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 162.000 | 0.817140 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −259.000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | −363.000 | −1.54964 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 105.000 | 0.415049 | ||||||||
\(41\) | 195.000 | 0.742778 | 0.371389 | − | 0.928477i | \(-0.378882\pi\) | ||||
0.371389 | + | 0.928477i | \(0.378882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −286.000 | −1.01429 | −0.507146 | − | 0.861860i | \(-0.669300\pi\) | ||||
−0.507146 | + | 0.861860i | \(0.669300\pi\) | |||||||
\(44\) | 45.0000 | 0.154182 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 207.000 | 0.663489 | ||||||||
\(47\) | 45.0000 | 0.139658 | 0.0698290 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698290 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −75.0000 | −0.212132 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −59.0000 | −0.157343 | ||||||||
\(53\) | −597.000 | −1.54725 | −0.773625 | − | 0.633644i | \(-0.781559\pi\) | ||||
−0.773625 | + | 0.633644i | \(0.781559\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 225.000 | 0.551618 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −486.000 | −1.10026 | ||||||||
\(59\) | −360.000 | −0.794373 | −0.397187 | − | 0.917738i | \(-0.630013\pi\) | ||||
−0.397187 | + | 0.917738i | \(0.630013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −392.000 | −0.822794 | −0.411397 | − | 0.911456i | \(-0.634959\pi\) | ||||
−0.411397 | + | 0.911456i | \(0.634959\pi\) | |||||||
\(62\) | −264.000 | −0.540775 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | −295.000 | −0.562927 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −280.000 | −0.510559 | −0.255279 | − | 0.966867i | \(-0.582167\pi\) | ||||
−0.255279 | + | 0.966867i | \(0.582167\pi\) | |||||||
\(68\) | −54.0000 | −0.0963009 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −48.0000 | −0.0802331 | −0.0401166 | − | 0.999195i | \(-0.512773\pi\) | ||||
−0.0401166 | + | 0.999195i | \(0.512773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −668.000 | −1.07101 | −0.535503 | − | 0.844533i | \(-0.679878\pi\) | ||||
−0.535503 | + | 0.844533i | \(0.679878\pi\) | |||||||
\(74\) | 777.000 | 1.22060 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 121.000 | 0.182627 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 782.000 | 1.11369 | 0.556847 | − | 0.830615i | \(-0.312011\pi\) | ||||
0.556847 | + | 0.830615i | \(0.312011\pi\) | |||||||
\(80\) | −355.000 | −0.496128 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −585.000 | −0.787835 | ||||||||
\(83\) | 768.000 | 1.01565 | 0.507825 | − | 0.861460i | \(-0.330450\pi\) | ||||
0.507825 | + | 0.861460i | \(0.330450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −270.000 | −0.344537 | ||||||||
\(86\) | 858.000 | 1.07582 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 945.000 | 1.14474 | ||||||||
\(89\) | −1194.00 | −1.42206 | −0.711032 | − | 0.703159i | \(-0.751772\pi\) | ||||
−0.711032 | + | 0.703159i | \(0.751772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −69.0000 | −0.0781929 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −135.000 | −0.148130 | ||||||||
\(95\) | 605.000 | 0.653386 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −902.000 | −0.944167 | −0.472084 | − | 0.881554i | \(-0.656498\pi\) | ||||
−0.472084 | + | 0.881554i | \(0.656498\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 25.0000 | 0.0250000 | ||||||||
\(101\) | 684.000 | 0.673867 | 0.336933 | − | 0.941528i | \(-0.390610\pi\) | ||||
0.336933 | + | 0.941528i | \(0.390610\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1516.00 | 1.45025 | 0.725126 | − | 0.688616i | \(-0.241782\pi\) | ||||
0.725126 | + | 0.688616i | \(0.241782\pi\) | |||||||
\(104\) | −1239.00 | −1.16821 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1791.00 | 1.64111 | ||||||||
\(107\) | 732.000 | 0.661356 | 0.330678 | − | 0.943744i | \(-0.392723\pi\) | ||||
0.330678 | + | 0.943744i | \(0.392723\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1600.00 | −1.40598 | −0.702992 | − | 0.711198i | \(-0.748153\pi\) | ||||
−0.702992 | + | 0.711198i | \(0.748153\pi\) | |||||||
\(110\) | −675.000 | −0.585079 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1392.00 | 1.15883 | 0.579417 | − | 0.815031i | \(-0.303280\pi\) | ||||
0.579417 | + | 0.815031i | \(0.303280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −345.000 | −0.279751 | ||||||||
\(116\) | 162.000 | 0.129667 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1080.00 | 0.842560 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 694.000 | 0.521412 | ||||||||
\(122\) | 1176.00 | 0.872705 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 88.0000 | 0.0637309 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 803.000 | 0.561061 | 0.280530 | − | 0.959845i | \(-0.409490\pi\) | ||||
0.280530 | + | 0.959845i | \(0.409490\pi\) | |||||||
\(128\) | −1659.00 | −1.14560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 885.000 | 0.597074 | ||||||||
\(131\) | 2019.00 | 1.34657 | 0.673286 | − | 0.739382i | \(-0.264882\pi\) | ||||
0.673286 | + | 0.739382i | \(0.264882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 840.000 | 0.541529 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1134.00 | −0.714998 | ||||||||
\(137\) | −60.0000 | −0.0374171 | −0.0187086 | − | 0.999825i | \(-0.505955\pi\) | ||||
−0.0187086 | + | 0.999825i | \(0.505955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1708.00 | 1.04224 | 0.521118 | − | 0.853485i | \(-0.325515\pi\) | ||||
0.521118 | + | 0.853485i | \(0.325515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 144.000 | 0.0851001 | ||||||||
\(143\) | −2655.00 | −1.55260 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 810.000 | 0.463909 | ||||||||
\(146\) | 2004.00 | 1.13597 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −259.000 | −0.143849 | ||||||||
\(149\) | 1086.00 | 0.597105 | 0.298552 | − | 0.954393i | \(-0.403496\pi\) | ||||
0.298552 | + | 0.954393i | \(0.403496\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2866.00 | −1.54458 | −0.772291 | − | 0.635269i | \(-0.780889\pi\) | ||||
−0.772291 | + | 0.635269i | \(0.780889\pi\) | |||||||
\(152\) | 2541.00 | 1.35594 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 440.000 | 0.228011 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 229.000 | 0.116409 | 0.0582044 | − | 0.998305i | \(-0.481462\pi\) | ||||
0.0582044 | + | 0.998305i | \(0.481462\pi\) | |||||||
\(158\) | −2346.00 | −1.18125 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 225.000 | 0.111174 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1228.00 | −0.590088 | −0.295044 | − | 0.955484i | \(-0.595334\pi\) | ||||
−0.295044 | + | 0.955484i | \(0.595334\pi\) | |||||||
\(164\) | 195.000 | 0.0928472 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2304.00 | −1.07726 | ||||||||
\(167\) | −1929.00 | −0.893835 | −0.446918 | − | 0.894575i | \(-0.647478\pi\) | ||||
−0.446918 | + | 0.894575i | \(0.647478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1284.00 | 0.584433 | ||||||||
\(170\) | 810.000 | 0.365436 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −286.000 | −0.126787 | ||||||||
\(173\) | −699.000 | −0.307191 | −0.153595 | − | 0.988134i | \(-0.549085\pi\) | ||||
−0.153595 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3195.00 | −1.36836 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3582.00 | 1.50833 | ||||||||
\(179\) | −3117.00 | −1.30154 | −0.650770 | − | 0.759275i | \(-0.725554\pi\) | ||||
−0.650770 | + | 0.759275i | \(0.725554\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1798.00 | 0.738366 | 0.369183 | − | 0.929357i | \(-0.379638\pi\) | ||||
0.369183 | + | 0.929357i | \(0.379638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1449.00 | −0.580553 | ||||||||
\(185\) | −1295.00 | −0.514650 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2430.00 | −0.950263 | ||||||||
\(188\) | 45.0000 | 0.0174572 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1815.00 | −0.693021 | ||||||||
\(191\) | 2388.00 | 0.904658 | 0.452329 | − | 0.891851i | \(-0.350593\pi\) | ||||
0.452329 | + | 0.891851i | \(0.350593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 272.000 | 0.101446 | 0.0507228 | − | 0.998713i | \(-0.483848\pi\) | ||||
0.0507228 | + | 0.998713i | \(0.483848\pi\) | |||||||
\(194\) | 2706.00 | 1.00144 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2109.00 | 0.762741 | 0.381371 | − | 0.924422i | \(-0.375452\pi\) | ||||
0.381371 | + | 0.924422i | \(0.375452\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1424.00 | −0.507260 | −0.253630 | − | 0.967301i | \(-0.581625\pi\) | ||||
−0.253630 | + | 0.967301i | \(0.581625\pi\) | |||||||
\(200\) | 525.000 | 0.185616 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2052.00 | −0.714744 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 975.000 | 0.332180 | ||||||||
\(206\) | −4548.00 | −1.53822 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4189.00 | 1.39642 | ||||||||
\(209\) | 5445.00 | 1.80210 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3625.00 | −1.18273 | −0.591363 | − | 0.806405i | \(-0.701410\pi\) | ||||
−0.591363 | + | 0.806405i | \(0.701410\pi\) | |||||||
\(212\) | −597.000 | −0.193406 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2196.00 | −0.701474 | ||||||||
\(215\) | −1430.00 | −0.453606 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4800.00 | 1.49127 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 225.000 | 0.0689523 | ||||||||
\(221\) | 3186.00 | 0.969745 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4960.00 | 1.48944 | 0.744722 | − | 0.667374i | \(-0.232582\pi\) | ||||
0.744722 | + | 0.667374i | \(0.232582\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4176.00 | −1.22913 | ||||||||
\(227\) | −1500.00 | −0.438584 | −0.219292 | − | 0.975659i | \(-0.570375\pi\) | ||||
−0.219292 | + | 0.975659i | \(0.570375\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6092.00 | −1.75795 | −0.878975 | − | 0.476867i | \(-0.841772\pi\) | ||||
−0.878975 | + | 0.476867i | \(0.841772\pi\) | |||||||
\(230\) | 1035.00 | 0.296721 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3402.00 | 0.962725 | ||||||||
\(233\) | −138.000 | −0.0388012 | −0.0194006 | − | 0.999812i | \(-0.506176\pi\) | ||||
−0.0194006 | + | 0.999812i | \(0.506176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 225.000 | 0.0624569 | ||||||||
\(236\) | −360.000 | −0.0992966 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5502.00 | 1.48910 | 0.744550 | − | 0.667567i | \(-0.232664\pi\) | ||||
0.744550 | + | 0.667567i | \(0.232664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3551.00 | −0.949129 | −0.474564 | − | 0.880221i | \(-0.657394\pi\) | ||||
−0.474564 | + | 0.880221i | \(0.657394\pi\) | |||||||
\(242\) | −2082.00 | −0.553041 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −392.000 | −0.102849 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7139.00 | −1.83904 | ||||||||
\(248\) | 1848.00 | 0.473178 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −375.000 | −0.0948683 | ||||||||
\(251\) | 7065.00 | 1.77665 | 0.888324 | − | 0.459216i | \(-0.151870\pi\) | ||||
0.888324 | + | 0.459216i | \(0.151870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3105.00 | −0.771580 | ||||||||
\(254\) | −2409.00 | −0.595095 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | −4080.00 | −0.990286 | −0.495143 | − | 0.868812i | \(-0.664884\pi\) | ||||
−0.495143 | + | 0.868812i | \(0.664884\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −295.000 | −0.0703659 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6057.00 | −1.42825 | ||||||||
\(263\) | 3288.00 | 0.770900 | 0.385450 | − | 0.922729i | \(-0.374046\pi\) | ||||
0.385450 | + | 0.922729i | \(0.374046\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2985.00 | −0.691951 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −280.000 | −0.0638199 | ||||||||
\(269\) | −3264.00 | −0.739813 | −0.369906 | − | 0.929069i | \(-0.620610\pi\) | ||||
−0.369906 | + | 0.929069i | \(0.620610\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2752.00 | 0.616871 | 0.308436 | − | 0.951245i | \(-0.400195\pi\) | ||||
0.308436 | + | 0.951245i | \(0.400195\pi\) | |||||||
\(272\) | 3834.00 | 0.854671 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 180.000 | 0.0396869 | ||||||||
\(275\) | 1125.00 | 0.246691 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4690.00 | −1.01731 | −0.508655 | − | 0.860971i | \(-0.669857\pi\) | ||||
−0.508655 | + | 0.860971i | \(0.669857\pi\) | |||||||
\(278\) | −5124.00 | −1.10546 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7821.00 | −1.66036 | −0.830181 | − | 0.557494i | \(-0.811763\pi\) | ||||
−0.830181 | + | 0.557494i | \(0.811763\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 658.000 | 0.138212 | 0.0691061 | − | 0.997609i | \(-0.477985\pi\) | ||||
0.0691061 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(284\) | −48.0000 | −0.0100291 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7965.00 | 1.64678 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | −2430.00 | −0.492050 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −668.000 | −0.133876 | ||||||||
\(293\) | −5997.00 | −1.19573 | −0.597864 | − | 0.801597i | \(-0.703984\pi\) | ||||
−0.597864 | + | 0.801597i | \(0.703984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1800.00 | −0.355254 | ||||||||
\(296\) | −5439.00 | −1.06803 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3258.00 | −0.633325 | ||||||||
\(299\) | 4071.00 | 0.787398 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8598.00 | 1.63828 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8591.00 | −1.62081 | ||||||||
\(305\) | −1960.00 | −0.367965 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6226.00 | 1.15745 | 0.578724 | − | 0.815523i | \(-0.303551\pi\) | ||||
0.578724 | + | 0.815523i | \(0.303551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1320.00 | −0.241842 | ||||||||
\(311\) | 4680.00 | 0.853307 | 0.426653 | − | 0.904415i | \(-0.359692\pi\) | ||||
0.426653 | + | 0.904415i | \(0.359692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1028.00 | −0.185642 | −0.0928211 | − | 0.995683i | \(-0.529588\pi\) | ||||
−0.0928211 | + | 0.995683i | \(0.529588\pi\) | |||||||
\(314\) | −687.000 | −0.123470 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 782.000 | 0.139212 | ||||||||
\(317\) | −8622.00 | −1.52763 | −0.763817 | − | 0.645433i | \(-0.776677\pi\) | ||||
−0.763817 | + | 0.645433i | \(0.776677\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7290.00 | 1.27950 | ||||||||
\(320\) | 2165.00 | 0.378210 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6534.00 | −1.12558 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1475.00 | −0.251749 | ||||||||
\(326\) | 3684.00 | 0.625883 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4095.00 | 0.689355 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1999.00 | −0.331949 | −0.165974 | − | 0.986130i | \(-0.553077\pi\) | ||||
−0.165974 | + | 0.986130i | \(0.553077\pi\) | |||||||
\(332\) | 768.000 | 0.126956 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5787.00 | 0.948056 | ||||||||
\(335\) | −1400.00 | −0.228329 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5114.00 | 0.826639 | 0.413319 | − | 0.910586i | \(-0.364369\pi\) | ||||
0.413319 | + | 0.910586i | \(0.364369\pi\) | |||||||
\(338\) | −3852.00 | −0.619885 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −270.000 | −0.0430671 | ||||||||
\(341\) | 3960.00 | 0.628874 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6006.00 | −0.941342 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2097.00 | 0.325825 | ||||||||
\(347\) | −4320.00 | −0.668328 | −0.334164 | − | 0.942515i | \(-0.608454\pi\) | ||||
−0.334164 | + | 0.942515i | \(0.608454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7922.00 | −1.21506 | −0.607529 | − | 0.794298i | \(-0.707839\pi\) | ||||
−0.607529 | + | 0.794298i | \(0.707839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2025.00 | 0.306627 | ||||||||
\(353\) | 828.000 | 0.124844 | 0.0624221 | − | 0.998050i | \(-0.480118\pi\) | ||||
0.0624221 | + | 0.998050i | \(0.480118\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −240.000 | −0.0358813 | ||||||||
\(356\) | −1194.00 | −0.177758 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9351.00 | 1.38049 | ||||||||
\(359\) | 1350.00 | 0.198469 | 0.0992344 | − | 0.995064i | \(-0.468361\pi\) | ||||
0.0992344 | + | 0.995064i | \(0.468361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7782.00 | 1.13457 | ||||||||
\(362\) | −5394.00 | −0.783156 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3340.00 | −0.478969 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2801.00 | −0.398395 | −0.199198 | − | 0.979959i | \(-0.563834\pi\) | ||||
−0.199198 | + | 0.979959i | \(0.563834\pi\) | |||||||
\(368\) | 4899.00 | 0.693962 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3885.00 | 0.545869 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6602.00 | 0.916457 | 0.458229 | − | 0.888834i | \(-0.348484\pi\) | ||||
0.458229 | + | 0.888834i | \(0.348484\pi\) | |||||||
\(374\) | 7290.00 | 1.00791 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 945.000 | 0.129613 | ||||||||
\(377\) | −9558.00 | −1.30573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8305.00 | −1.12559 | −0.562796 | − | 0.826596i | \(-0.690274\pi\) | ||||
−0.562796 | + | 0.826596i | \(0.690274\pi\) | |||||||
\(380\) | 605.000 | 0.0816733 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7164.00 | −0.959534 | ||||||||
\(383\) | 945.000 | 0.126076 | 0.0630382 | − | 0.998011i | \(-0.479921\pi\) | ||||
0.0630382 | + | 0.998011i | \(0.479921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −816.000 | −0.107599 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −902.000 | −0.118021 | ||||||||
\(389\) | −12036.0 | −1.56876 | −0.784382 | − | 0.620278i | \(-0.787020\pi\) | ||||
−0.784382 | + | 0.620278i | \(0.787020\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3726.00 | 0.481923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6327.00 | −0.809009 | ||||||||
\(395\) | 3910.00 | 0.498059 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2698.00 | 0.341080 | 0.170540 | − | 0.985351i | \(-0.445449\pi\) | ||||
0.170540 | + | 0.985351i | \(0.445449\pi\) | |||||||
\(398\) | 4272.00 | 0.538030 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1775.00 | −0.221875 | ||||||||
\(401\) | −7053.00 | −0.878329 | −0.439165 | − | 0.898407i | \(-0.644726\pi\) | ||||
−0.439165 | + | 0.898407i | \(0.644726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5192.00 | −0.641767 | ||||||||
\(404\) | 684.000 | 0.0842333 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11655.0 | −1.41945 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10870.0 | 1.31415 | 0.657074 | − | 0.753826i | \(-0.271794\pi\) | ||||
0.657074 | + | 0.753826i | \(0.271794\pi\) | |||||||
\(410\) | −2925.00 | −0.352330 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1516.00 | 0.181281 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3840.00 | 0.454212 | ||||||||
\(416\) | −2655.00 | −0.312914 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16335.0 | −1.91141 | ||||||||
\(419\) | −9729.00 | −1.13435 | −0.567175 | − | 0.823597i | \(-0.691964\pi\) | ||||
−0.567175 | + | 0.823597i | \(0.691964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12550.0 | −1.45285 | −0.726425 | − | 0.687246i | \(-0.758819\pi\) | ||||
−0.726425 | + | 0.687246i | \(0.758819\pi\) | |||||||
\(422\) | 10875.0 | 1.25447 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12537.0 | −1.43597 | ||||||||
\(425\) | −1350.00 | −0.154081 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 732.000 | 0.0826695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4290.00 | 0.481121 | ||||||||
\(431\) | −2988.00 | −0.333937 | −0.166969 | − | 0.985962i | \(-0.553398\pi\) | ||||
−0.166969 | + | 0.985962i | \(0.553398\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16616.0 | −1.84414 | −0.922072 | − | 0.387019i | \(-0.873505\pi\) | ||||
−0.922072 | + | 0.387019i | \(0.873505\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1600.00 | −0.175748 | ||||||||
\(437\) | −8349.00 | −0.913929 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7346.00 | −0.798646 | −0.399323 | − | 0.916810i | \(-0.630755\pi\) | ||||
−0.399323 | + | 0.916810i | \(0.630755\pi\) | |||||||
\(440\) | 4725.00 | 0.511944 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9558.00 | −1.02857 | ||||||||
\(443\) | −12.0000 | −0.00128699 | −0.000643496 | − | 1.00000i | \(-0.500205\pi\) | ||||
−0.000643496 | 1.00000i | \(0.500205\pi\) | ||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5970.00 | −0.635967 | ||||||||
\(446\) | −14880.0 | −1.57979 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9669.00 | −1.01628 | −0.508138 | − | 0.861275i | \(-0.669666\pi\) | ||||
−0.508138 | + | 0.861275i | \(0.669666\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8775.00 | 0.916183 | ||||||||
\(452\) | 1392.00 | 0.144854 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4500.00 | 0.465188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9634.00 | −0.986126 | −0.493063 | − | 0.869994i | \(-0.664123\pi\) | ||||
−0.493063 | + | 0.869994i | \(0.664123\pi\) | |||||||
\(458\) | 18276.0 | 1.86459 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −345.000 | −0.0349689 | ||||||||
\(461\) | −342.000 | −0.0345521 | −0.0172761 | − | 0.999851i | \(-0.505499\pi\) | ||||
−0.0172761 | + | 0.999851i | \(0.505499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2411.00 | 0.242006 | 0.121003 | − | 0.992652i | \(-0.461389\pi\) | ||||
0.121003 | + | 0.992652i | \(0.461389\pi\) | |||||||
\(464\) | −11502.0 | −1.15079 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 414.000 | 0.0411549 | ||||||||
\(467\) | −1206.00 | −0.119501 | −0.0597506 | − | 0.998213i | \(-0.519031\pi\) | ||||
−0.0597506 | + | 0.998213i | \(0.519031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −675.000 | −0.0662456 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7560.00 | −0.737240 | ||||||||
\(473\) | −12870.0 | −1.25109 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3025.00 | 0.292203 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16506.0 | −1.57943 | ||||||||
\(479\) | −432.000 | −0.0412079 | −0.0206039 | − | 0.999788i | \(-0.506559\pi\) | ||||
−0.0206039 | + | 0.999788i | \(0.506559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15281.0 | 1.44855 | ||||||||
\(482\) | 10653.0 | 1.00670 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 694.000 | 0.0651766 | ||||||||
\(485\) | −4510.00 | −0.422244 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11896.0 | −1.10690 | −0.553449 | − | 0.832883i | \(-0.686689\pi\) | ||||
−0.553449 | + | 0.832883i | \(0.686689\pi\) | |||||||
\(488\) | −8232.00 | −0.763617 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12276.0 | 1.12833 | 0.564163 | − | 0.825663i | \(-0.309199\pi\) | ||||
0.564163 | + | 0.825663i | \(0.309199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8748.00 | −0.799169 | ||||||||
\(494\) | 21417.0 | 1.95060 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6248.00 | −0.565612 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10876.0 | −0.975705 | −0.487852 | − | 0.872926i | \(-0.662220\pi\) | ||||
−0.487852 | + | 0.872926i | \(0.662220\pi\) | |||||||
\(500\) | 125.000 | 0.0111803 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21195.0 | −1.88442 | ||||||||
\(503\) | 12000.0 | 1.06372 | 0.531862 | − | 0.846831i | \(-0.321492\pi\) | ||||
0.531862 | + | 0.846831i | \(0.321492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3420.00 | 0.301362 | ||||||||
\(506\) | 9315.00 | 0.818384 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 803.000 | 0.0701326 | ||||||||
\(509\) | −11682.0 | −1.01728 | −0.508640 | − | 0.860979i | \(-0.669852\pi\) | ||||
−0.508640 | + | 0.860979i | \(0.669852\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8733.00 | 0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12240.0 | 1.05036 | ||||||||
\(515\) | 7580.00 | 0.648572 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2025.00 | 0.172262 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6195.00 | −0.522440 | ||||||||
\(521\) | 9609.00 | 0.808019 | 0.404010 | − | 0.914755i | \(-0.367616\pi\) | ||||
0.404010 | + | 0.914755i | \(0.367616\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21188.0 | −1.77148 | −0.885742 | − | 0.464177i | \(-0.846350\pi\) | ||||
−0.885742 | + | 0.464177i | \(0.846350\pi\) | |||||||
\(524\) | 2019.00 | 0.168321 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9864.00 | −0.817663 | ||||||||
\(527\) | −4752.00 | −0.392790 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7406.00 | −0.608696 | ||||||||
\(530\) | 8955.00 | 0.733925 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11505.0 | −0.934966 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3660.00 | 0.295767 | ||||||||
\(536\) | −5880.00 | −0.473838 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9792.00 | 0.784690 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8072.00 | 0.641483 | 0.320742 | − | 0.947167i | \(-0.396068\pi\) | ||||
0.320742 | + | 0.947167i | \(0.396068\pi\) | |||||||
\(542\) | −8256.00 | −0.654291 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2430.00 | −0.191517 | ||||||||
\(545\) | −8000.00 | −0.628775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 344.000 | 0.0268892 | 0.0134446 | − | 0.999910i | \(-0.495720\pi\) | ||||
0.0134446 | + | 0.999910i | \(0.495720\pi\) | |||||||
\(548\) | −60.0000 | −0.00467714 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3375.00 | −0.261655 | ||||||||
\(551\) | 19602.0 | 1.51556 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14070.0 | 1.07902 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1708.00 | 0.130279 | ||||||||
\(557\) | −18363.0 | −1.39689 | −0.698443 | − | 0.715666i | \(-0.746123\pi\) | ||||
−0.698443 | + | 0.715666i | \(0.746123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16874.0 | 1.27673 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23463.0 | 1.76108 | ||||||||
\(563\) | −6294.00 | −0.471155 | −0.235578 | − | 0.971856i | \(-0.575698\pi\) | ||||
−0.235578 | + | 0.971856i | \(0.575698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6960.00 | 0.518247 | ||||||||
\(566\) | −1974.00 | −0.146596 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1008.00 | −0.0744626 | ||||||||
\(569\) | −11733.0 | −0.864452 | −0.432226 | − | 0.901765i | \(-0.642272\pi\) | ||||
−0.432226 | + | 0.901765i | \(0.642272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1052.00 | 0.0771013 | 0.0385506 | − | 0.999257i | \(-0.487726\pi\) | ||||
0.0385506 | + | 0.999257i | \(0.487726\pi\) | |||||||
\(572\) | −2655.00 | −0.194075 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1725.00 | −0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13156.0 | 0.949205 | 0.474603 | − | 0.880200i | \(-0.342592\pi\) | ||||
0.474603 | + | 0.880200i | \(0.342592\pi\) | |||||||
\(578\) | 5991.00 | 0.431129 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 810.000 | 0.0579887 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26865.0 | −1.90846 | ||||||||
\(584\) | −14028.0 | −0.993977 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17991.0 | 1.26826 | ||||||||
\(587\) | −13368.0 | −0.939960 | −0.469980 | − | 0.882677i | \(-0.655739\pi\) | ||||
−0.469980 | + | 0.882677i | \(0.655739\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10648.0 | 0.744895 | ||||||||
\(590\) | 5400.00 | 0.376804 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18389.0 | 1.27666 | ||||||||
\(593\) | 26664.0 | 1.84647 | 0.923237 | − | 0.384231i | \(-0.125533\pi\) | ||||
0.923237 | + | 0.384231i | \(0.125533\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1086.00 | 0.0746381 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12213.0 | −0.835162 | ||||||||
\(599\) | −7614.00 | −0.519365 | −0.259682 | − | 0.965694i | \(-0.583618\pi\) | ||||
−0.259682 | + | 0.965694i | \(0.583618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6410.00 | −0.435057 | −0.217529 | − | 0.976054i | \(-0.569800\pi\) | ||||
−0.217529 | + | 0.976054i | \(0.569800\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2866.00 | −0.193073 | ||||||||
\(605\) | 3470.00 | 0.233183 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21469.0 | 1.43558 | 0.717792 | − | 0.696257i | \(-0.245153\pi\) | ||||
0.717792 | + | 0.696257i | \(0.245153\pi\) | |||||||
\(608\) | 5445.00 | 0.363197 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5880.00 | 0.390286 | ||||||||
\(611\) | −2655.00 | −0.175793 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3737.00 | 0.246225 | 0.123113 | − | 0.992393i | \(-0.460712\pi\) | ||||
0.123113 | + | 0.992393i | \(0.460712\pi\) | |||||||
\(614\) | −18678.0 | −1.22766 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18078.0 | −1.17957 | −0.589784 | − | 0.807561i | \(-0.700787\pi\) | ||||
−0.589784 | + | 0.807561i | \(0.700787\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12287.0 | −0.797829 | −0.398915 | − | 0.916988i | \(-0.630613\pi\) | ||||
−0.398915 | + | 0.916988i | \(0.630613\pi\) | |||||||
\(620\) | 440.000 | 0.0285013 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14040.0 | −0.905069 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 3084.00 | 0.196903 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 229.000 | 0.0145511 | ||||||||
\(629\) | 13986.0 | 0.886579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9580.00 | −0.604396 | −0.302198 | − | 0.953245i | \(-0.597720\pi\) | ||||
−0.302198 | + | 0.953245i | \(0.597720\pi\) | |||||||
\(632\) | 16422.0 | 1.03360 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25866.0 | 1.62030 | ||||||||
\(635\) | 4015.00 | 0.250914 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21870.0 | −1.35712 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8295.00 | −0.512326 | ||||||||
\(641\) | −10779.0 | −0.664189 | −0.332094 | − | 0.943246i | \(-0.607755\pi\) | ||||
−0.332094 | + | 0.943246i | \(0.607755\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8882.00 | −0.544746 | −0.272373 | − | 0.962192i | \(-0.587809\pi\) | ||||
−0.272373 | + | 0.962192i | \(0.587809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19602.0 | 1.19386 | ||||||||
\(647\) | −11019.0 | −0.669554 | −0.334777 | − | 0.942297i | \(-0.608661\pi\) | ||||
−0.334777 | + | 0.942297i | \(0.608661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16200.0 | −0.979824 | ||||||||
\(650\) | 4425.00 | 0.267020 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1228.00 | −0.0737610 | ||||||||
\(653\) | −22323.0 | −1.33777 | −0.668887 | − | 0.743364i | \(-0.733229\pi\) | ||||
−0.668887 | + | 0.743364i | \(0.733229\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10095.0 | 0.602205 | ||||||||
\(656\) | −13845.0 | −0.824019 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11856.0 | 0.700826 | 0.350413 | − | 0.936595i | \(-0.386041\pi\) | ||||
0.350413 | + | 0.936595i | \(0.386041\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33244.0 | 1.95619 | 0.978095 | − | 0.208158i | \(-0.0667470\pi\) | ||||
0.978095 | + | 0.208158i | \(0.0667470\pi\) | |||||||
\(662\) | 5997.00 | 0.352085 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16128.0 | 0.942602 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11178.0 | −0.648896 | ||||||||
\(668\) | −1929.00 | −0.111729 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4200.00 | 0.242179 | ||||||||
\(671\) | −17640.0 | −1.01488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12322.0 | −0.705763 | −0.352881 | − | 0.935668i | \(-0.614798\pi\) | ||||
−0.352881 | + | 0.935668i | \(0.614798\pi\) | |||||||
\(674\) | −15342.0 | −0.876783 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1284.00 | 0.0730542 | ||||||||
\(677\) | −12597.0 | −0.715129 | −0.357564 | − | 0.933889i | \(-0.616393\pi\) | ||||
−0.357564 | + | 0.933889i | \(0.616393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5670.00 | −0.319757 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11880.0 | −0.667022 | ||||||||
\(683\) | 8340.00 | 0.467235 | 0.233617 | − | 0.972329i | \(-0.424944\pi\) | ||||
0.233617 | + | 0.972329i | \(0.424944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −300.000 | −0.0167334 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20306.0 | 1.12523 | ||||||||
\(689\) | 35223.0 | 1.94759 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20200.0 | 1.11208 | 0.556038 | − | 0.831157i | \(-0.312321\pi\) | ||||
0.556038 | + | 0.831157i | \(0.312321\pi\) | |||||||
\(692\) | −699.000 | −0.0383988 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12960.0 | 0.708869 | ||||||||
\(695\) | 8540.00 | 0.466102 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10530.0 | −0.572241 | ||||||||
\(698\) | 23766.0 | 1.28876 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −474.000 | −0.0255388 | −0.0127694 | − | 0.999918i | \(-0.504065\pi\) | ||||
−0.0127694 | + | 0.999918i | \(0.504065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31339.0 | −1.68133 | ||||||||
\(704\) | 19485.0 | 1.04314 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2484.00 | −0.132417 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25126.0 | −1.33093 | −0.665463 | − | 0.746431i | \(-0.731766\pi\) | ||||
−0.665463 | + | 0.746431i | \(0.731766\pi\) | |||||||
\(710\) | 720.000 | 0.0380579 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25074.0 | −1.31979 | ||||||||
\(713\) | −6072.00 | −0.318932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13275.0 | −0.694345 | ||||||||
\(716\) | −3117.00 | −0.162692 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4050.00 | −0.210508 | ||||||||
\(719\) | −7296.00 | −0.378435 | −0.189218 | − | 0.981935i | \(-0.560595\pi\) | ||||
−0.189218 | + | 0.981935i | \(0.560595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −23346.0 | −1.20339 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1798.00 | 0.0922958 | ||||||||
\(725\) | 4050.00 | 0.207467 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15421.0 | 0.786703 | 0.393352 | − | 0.919388i | \(-0.371316\pi\) | ||||
0.393352 | + | 0.919388i | \(0.371316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10020.0 | 0.508023 | ||||||||
\(731\) | 15444.0 | 0.781419 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29167.0 | 1.46972 | 0.734862 | − | 0.678217i | \(-0.237247\pi\) | ||||
0.734862 | + | 0.678217i | \(0.237247\pi\) | |||||||
\(734\) | 8403.00 | 0.422562 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3105.00 | −0.155505 | ||||||||
\(737\) | −12600.0 | −0.629752 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13381.0 | −0.666073 | −0.333037 | − | 0.942914i | \(-0.608073\pi\) | ||||
−0.333037 | + | 0.942914i | \(0.608073\pi\) | |||||||
\(740\) | −1295.00 | −0.0643313 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5487.00 | −0.270927 | −0.135463 | − | 0.990782i | \(-0.543252\pi\) | ||||
−0.135463 | + | 0.990782i | \(0.543252\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5430.00 | 0.267033 | ||||||||
\(746\) | −19806.0 | −0.972050 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2430.00 | −0.118783 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6638.00 | 0.322535 | 0.161268 | − | 0.986911i | \(-0.448442\pi\) | ||||
0.161268 | + | 0.986911i | \(0.448442\pi\) | |||||||
\(752\) | −3195.00 | −0.154933 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 28674.0 | 1.38494 | ||||||||
\(755\) | −14330.0 | −0.690758 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14846.0 | 0.712797 | 0.356398 | − | 0.934334i | \(-0.384005\pi\) | ||||
0.356398 | + | 0.934334i | \(0.384005\pi\) | |||||||
\(758\) | 24915.0 | 1.19387 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12705.0 | 0.606393 | ||||||||
\(761\) | −3651.00 | −0.173914 | −0.0869571 | − | 0.996212i | \(-0.527714\pi\) | ||||
−0.0869571 | + | 0.996212i | \(0.527714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2388.00 | 0.113082 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2835.00 | −0.133724 | ||||||||
\(767\) | 21240.0 | 0.999911 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29855.0 | −1.40000 | −0.699999 | − | 0.714144i | \(-0.746816\pi\) | ||||
−0.699999 | + | 0.714144i | \(0.746816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 272.000 | 0.0126807 | ||||||||
\(773\) | −6519.00 | −0.303327 | −0.151664 | − | 0.988432i | \(-0.548463\pi\) | ||||
−0.151664 | + | 0.988432i | \(0.548463\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2200.00 | 0.101969 | ||||||||
\(776\) | −18942.0 | −0.876261 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36108.0 | 1.66393 | ||||||||
\(779\) | 23595.0 | 1.08521 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2160.00 | −0.0989640 | ||||||||
\(782\) | −11178.0 | −0.511157 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1145.00 | 0.0520596 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35114.0 | −1.59044 | −0.795222 | − | 0.606319i | \(-0.792646\pi\) | ||||
−0.795222 | + | 0.606319i | \(0.792646\pi\) | |||||||
\(788\) | 2109.00 | 0.0953427 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11730.0 | −0.528272 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23128.0 | 1.03569 | ||||||||
\(794\) | −8094.00 | −0.361770 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1424.00 | −0.0634075 | ||||||||
\(797\) | 20910.0 | 0.929323 | 0.464661 | − | 0.885488i | \(-0.346176\pi\) | ||||
0.464661 | + | 0.885488i | \(0.346176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2430.00 | −0.107594 | ||||||||
\(800\) | 1125.00 | 0.0497184 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21159.0 | 0.931609 | ||||||||
\(803\) | −30060.0 | −1.32104 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15576.0 | 0.680696 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14364.0 | 0.625401 | ||||||||
\(809\) | −4431.00 | −0.192566 | −0.0962829 | − | 0.995354i | \(-0.530695\pi\) | ||||
−0.0962829 | + | 0.995354i | \(0.530695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9577.00 | 0.414666 | 0.207333 | − | 0.978270i | \(-0.433522\pi\) | ||||
0.207333 | + | 0.978270i | \(0.433522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 34965.0 | 1.50556 | ||||||||
\(815\) | −6140.00 | −0.263895 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34606.0 | −1.48190 | ||||||||
\(818\) | −32610.0 | −1.39387 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 975.000 | 0.0415225 | ||||||||
\(821\) | 10938.0 | 0.464968 | 0.232484 | − | 0.972600i | \(-0.425315\pi\) | ||||
0.232484 | + | 0.972600i | \(0.425315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11540.0 | 0.488772 | 0.244386 | − | 0.969678i | \(-0.421414\pi\) | ||||
0.244386 | + | 0.969678i | \(0.421414\pi\) | |||||||
\(824\) | 31836.0 | 1.34595 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18762.0 | 0.788898 | 0.394449 | − | 0.918918i | \(-0.370935\pi\) | ||||
0.394449 | + | 0.918918i | \(0.370935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39610.0 | 1.65948 | 0.829742 | − | 0.558147i | \(-0.188488\pi\) | ||||
0.829742 | + | 0.558147i | \(0.188488\pi\) | |||||||
\(830\) | −11520.0 | −0.481765 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −25547.0 | −1.06452 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9645.00 | −0.399735 | ||||||||
\(836\) | 5445.00 | 0.225262 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29187.0 | 1.20316 | ||||||||
\(839\) | 39162.0 | 1.61147 | 0.805734 | − | 0.592277i | \(-0.201771\pi\) | ||||
0.805734 | + | 0.592277i | \(0.201771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1855.00 | 0.0760589 | ||||||||
\(842\) | 37650.0 | 1.54098 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3625.00 | −0.147841 | ||||||||
\(845\) | 6420.00 | 0.261367 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 42387.0 | 1.71648 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4050.00 | 0.163428 | ||||||||
\(851\) | 17871.0 | 0.719871 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11527.0 | 0.462693 | 0.231346 | − | 0.972871i | \(-0.425687\pi\) | ||||
0.231346 | + | 0.972871i | \(0.425687\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15372.0 | 0.613790 | ||||||||
\(857\) | −41826.0 | −1.66715 | −0.833576 | − | 0.552405i | \(-0.813710\pi\) | ||||
−0.833576 | + | 0.552405i | \(0.813710\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35192.0 | −1.39783 | −0.698915 | − | 0.715205i | \(-0.746333\pi\) | ||||
−0.698915 | + | 0.715205i | \(0.746333\pi\) | |||||||
\(860\) | −1430.00 | −0.0567007 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8964.00 | 0.354194 | ||||||||
\(863\) | 9063.00 | 0.357483 | 0.178742 | − | 0.983896i | \(-0.442797\pi\) | ||||
0.178742 | + | 0.983896i | \(0.442797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3495.00 | −0.137380 | ||||||||
\(866\) | 49848.0 | 1.95601 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35190.0 | 1.37369 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16520.0 | 0.642662 | ||||||||
\(872\) | −33600.0 | −1.30486 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25047.0 | 0.969368 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28439.0 | 1.09500 | 0.547501 | − | 0.836805i | \(-0.315579\pi\) | ||||
0.547501 | + | 0.836805i | \(0.315579\pi\) | |||||||
\(878\) | 22038.0 | 0.847092 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15975.0 | −0.611951 | ||||||||
\(881\) | −9303.00 | −0.355762 | −0.177881 | − | 0.984052i | \(-0.556924\pi\) | ||||
−0.177881 | + | 0.984052i | \(0.556924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14728.0 | −0.561310 | −0.280655 | − | 0.959809i | \(-0.590552\pi\) | ||||
−0.280655 | + | 0.959809i | \(0.590552\pi\) | |||||||
\(884\) | 3186.00 | 0.121218 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.0000 | 0.00136506 | ||||||||
\(887\) | −17016.0 | −0.644128 | −0.322064 | − | 0.946718i | \(-0.604377\pi\) | ||||
−0.322064 | + | 0.946718i | \(0.604377\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 17910.0 | 0.674544 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4960.00 | 0.186181 | ||||||||
\(893\) | 5445.00 | 0.204043 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15585.0 | −0.582066 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29007.0 | 1.07792 | ||||||||
\(899\) | 14256.0 | 0.528881 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32238.0 | 1.19201 | ||||||||
\(902\) | −26325.0 | −0.971759 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29232.0 | 1.07549 | ||||||||
\(905\) | 8990.00 | 0.330207 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24922.0 | −0.912372 | −0.456186 | − | 0.889884i | \(-0.650785\pi\) | ||||
−0.456186 | + | 0.889884i | \(0.650785\pi\) | |||||||
\(908\) | −1500.00 | −0.0548230 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30714.0 | −1.11701 | −0.558507 | − | 0.829500i | \(-0.688626\pi\) | ||||
−0.558507 | + | 0.829500i | \(0.688626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34560.0 | 1.25276 | ||||||||
\(914\) | 28902.0 | 1.04594 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6092.00 | −0.219744 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17426.0 | 0.625496 | 0.312748 | − | 0.949836i | \(-0.398750\pi\) | ||||
0.312748 | + | 0.949836i | \(0.398750\pi\) | |||||||
\(920\) | −7245.00 | −0.259631 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1026.00 | 0.0366481 | ||||||||
\(923\) | 2832.00 | 0.100993 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6475.00 | −0.230159 | ||||||||
\(926\) | −7233.00 | −0.256686 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7290.00 | 0.257873 | ||||||||
\(929\) | 26649.0 | 0.941147 | 0.470573 | − | 0.882361i | \(-0.344047\pi\) | ||||
0.470573 | + | 0.882361i | \(0.344047\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −138.000 | −0.00485015 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3618.00 | 0.126750 | ||||||||
\(935\) | −12150.0 | −0.424971 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27686.0 | −0.965274 | −0.482637 | − | 0.875820i | \(-0.660321\pi\) | ||||
−0.482637 | + | 0.875820i | \(0.660321\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 225.000 | 0.00780712 | ||||||||
\(941\) | −17808.0 | −0.616923 | −0.308461 | − | 0.951237i | \(-0.599814\pi\) | ||||
−0.308461 | + | 0.951237i | \(0.599814\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13455.0 | −0.464640 | ||||||||
\(944\) | 25560.0 | 0.881258 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38610.0 | 1.32698 | ||||||||
\(947\) | 6906.00 | 0.236974 | 0.118487 | − | 0.992956i | \(-0.462196\pi\) | ||||
0.118487 | + | 0.992956i | \(0.462196\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39412.0 | 1.34812 | ||||||||
\(950\) | −9075.00 | −0.309928 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20940.0 | 0.711766 | 0.355883 | − | 0.934530i | \(-0.384180\pi\) | ||||
0.355883 | + | 0.934530i | \(0.384180\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11940.0 | 0.404575 | ||||||||
\(956\) | 5502.00 | 0.186137 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1296.00 | 0.0437076 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22047.0 | −0.740056 | ||||||||
\(962\) | −45843.0 | −1.53642 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3551.00 | −0.118641 | ||||||||
\(965\) | 1360.00 | 0.0453678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9176.00 | 0.305150 | 0.152575 | − | 0.988292i | \(-0.451243\pi\) | ||||
0.152575 | + | 0.988292i | \(0.451243\pi\) | |||||||
\(968\) | 14574.0 | 0.483911 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13530.0 | 0.447858 | ||||||||
\(971\) | 29763.0 | 0.983666 | 0.491833 | − | 0.870689i | \(-0.336327\pi\) | ||||
0.491833 | + | 0.870689i | \(0.336327\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 35688.0 | 1.17404 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27832.0 | 0.912788 | ||||||||
\(977\) | 38490.0 | 1.26039 | 0.630197 | − | 0.776436i | \(-0.282974\pi\) | ||||
0.630197 | + | 0.776436i | \(0.282974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53730.0 | −1.75405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −36828.0 | −1.19677 | ||||||||
\(983\) | −12609.0 | −0.409120 | −0.204560 | − | 0.978854i | \(-0.565576\pi\) | ||||
−0.204560 | + | 0.978854i | \(0.565576\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10545.0 | 0.341108 | ||||||||
\(986\) | 26244.0 | 0.847646 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7139.00 | −0.229880 | ||||||||
\(989\) | 19734.0 | 0.634484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19820.0 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 3960.00 | 0.126744 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7120.00 | −0.226853 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46034.0 | −1.46230 | −0.731149 | − | 0.682218i | \(-0.761016\pi\) | ||||
−0.731149 | + | 0.682218i | \(0.761016\pi\) | |||||||
\(998\) | 32628.0 | 1.03489 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2205.4.a.g.1.1 | 1 | ||
3.2 | odd | 2 | 245.4.a.f.1.1 | 1 | |||
7.3 | odd | 6 | 315.4.j.b.226.1 | 2 | |||
7.5 | odd | 6 | 315.4.j.b.46.1 | 2 | |||
7.6 | odd | 2 | 2205.4.a.e.1.1 | 1 | |||
15.14 | odd | 2 | 1225.4.a.a.1.1 | 1 | |||
21.2 | odd | 6 | 245.4.e.a.116.1 | 2 | |||
21.5 | even | 6 | 35.4.e.a.11.1 | ✓ | 2 | ||
21.11 | odd | 6 | 245.4.e.a.226.1 | 2 | |||
21.17 | even | 6 | 35.4.e.a.16.1 | yes | 2 | ||
21.20 | even | 2 | 245.4.a.e.1.1 | 1 | |||
84.47 | odd | 6 | 560.4.q.b.81.1 | 2 | |||
84.59 | odd | 6 | 560.4.q.b.401.1 | 2 | |||
105.17 | odd | 12 | 175.4.k.b.149.1 | 4 | |||
105.38 | odd | 12 | 175.4.k.b.149.2 | 4 | |||
105.47 | odd | 12 | 175.4.k.b.74.2 | 4 | |||
105.59 | even | 6 | 175.4.e.b.51.1 | 2 | |||
105.68 | odd | 12 | 175.4.k.b.74.1 | 4 | |||
105.89 | even | 6 | 175.4.e.b.151.1 | 2 | |||
105.104 | even | 2 | 1225.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.a.11.1 | ✓ | 2 | 21.5 | even | 6 | ||
35.4.e.a.16.1 | yes | 2 | 21.17 | even | 6 | ||
175.4.e.b.51.1 | 2 | 105.59 | even | 6 | |||
175.4.e.b.151.1 | 2 | 105.89 | even | 6 | |||
175.4.k.b.74.1 | 4 | 105.68 | odd | 12 | |||
175.4.k.b.74.2 | 4 | 105.47 | odd | 12 | |||
175.4.k.b.149.1 | 4 | 105.17 | odd | 12 | |||
175.4.k.b.149.2 | 4 | 105.38 | odd | 12 | |||
245.4.a.e.1.1 | 1 | 21.20 | even | 2 | |||
245.4.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
245.4.e.a.116.1 | 2 | 21.2 | odd | 6 | |||
245.4.e.a.226.1 | 2 | 21.11 | odd | 6 | |||
315.4.j.b.46.1 | 2 | 7.5 | odd | 6 | |||
315.4.j.b.226.1 | 2 | 7.3 | odd | 6 | |||
560.4.q.b.81.1 | 2 | 84.47 | odd | 6 | |||
560.4.q.b.401.1 | 2 | 84.59 | odd | 6 | |||
1225.4.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
1225.4.a.b.1.1 | 1 | 105.104 | even | 2 | |||
2205.4.a.e.1.1 | 1 | 7.6 | odd | 2 | |||
2205.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial |