Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (of order \(2\), degree \(1\), 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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 39x^{10} + 549x^{8} + 3500x^{6} + 10236x^{4} + 11952x^{2} + 4624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.6 | ||
Root | \(2.36157i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.4.c.d.383.5 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.556921 | + | 5.16622i | 0.107180 | + | 0.994240i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.6077i | 0.948781i | 0.880315 | + | 0.474390i | \(0.157332\pi\) | ||||
−0.880315 | + | 0.474390i | \(0.842668\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.90379i | 0.426764i | 0.976969 | + | 0.213382i | \(0.0684480\pi\) | ||||
−0.976969 | + | 0.213382i | \(0.931552\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.3797 | + | 5.75435i | −0.977025 | + | 0.213124i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.7652 | 0.322487 | 0.161243 | − | 0.986915i | \(-0.448450\pi\) | ||||
0.161243 | + | 0.986915i | \(0.448450\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 30.5992 | 0.652823 | 0.326412 | − | 0.945228i | \(-0.394160\pi\) | ||||
0.326412 | + | 0.945228i | \(0.394160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −54.8017 | + | 5.90765i | −0.943316 | + | 0.101690i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 118.124i | 1.68526i | 0.538495 | + | 0.842629i | \(0.318993\pi\) | ||||
−0.538495 | + | 0.842629i | \(0.681007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 66.4680i | 0.802568i | 0.915954 | + | 0.401284i | \(0.131436\pi\) | ||||
−0.915954 | + | 0.401284i | \(0.868564\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −40.8327 | + | 4.40179i | −0.424306 | + | 0.0457404i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −166.335 | −1.50797 | −0.753985 | − | 0.656891i | \(-0.771871\pi\) | ||||
−0.753985 | + | 0.656891i | \(0.771871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.4768 | 0.0998147 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −44.4197 | − | 133.079i | −0.316614 | − | 0.948555i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 111.999i | − | 0.717159i | −0.933499 | − | 0.358580i | \(-0.883261\pi\) | ||
0.933499 | − | 0.358580i | \(-0.116739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 224.770i | − | 1.30226i | −0.758968 | − | 0.651128i | \(-0.774296\pi\) | ||
0.758968 | − | 0.651128i | \(-0.225704\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.55231 | + | 60.7818i | 0.0345640 | + | 0.320629i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −83.8410 | −0.404906 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −70.6099 | −0.313735 | −0.156868 | − | 0.987620i | \(-0.550140\pi\) | ||||
−0.156868 | + | 0.987620i | \(0.550140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17.0414 | + | 158.082i | 0.0699693 | + | 0.649063i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 247.184i | 0.941551i | 0.882253 | + | 0.470775i | \(0.156026\pi\) | ||||
−0.882253 | + | 0.470775i | \(0.843974\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 98.7603i | − | 0.350251i | −0.984546 | − | 0.175126i | \(-0.943967\pi\) | ||
0.984546 | − | 0.175126i | \(-0.0560332\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −61.0404 | − | 279.828i | −0.202208 | − | 0.926983i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −189.577 | −0.588355 | −0.294178 | − | 0.955751i | \(-0.595046\pi\) | ||||
−0.294178 | + | 0.955751i | \(0.595046\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 280.530 | 0.817872 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −610.257 | + | 65.7860i | −1.67555 | + | 0.180625i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 529.370i | − | 1.37197i | −0.727614 | − | 0.685987i | \(-0.759371\pi\) | ||
0.727614 | − | 0.685987i | \(-0.240629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 124.802i | 0.305969i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −343.388 | + | 37.0174i | −0.797945 | + | 0.0860189i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −811.889 | −1.79151 | −0.895753 | − | 0.444551i | \(-0.853363\pi\) | ||||
−0.895753 | + | 0.444551i | \(0.853363\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 833.410 | 1.74930 | 0.874650 | − | 0.484756i | \(-0.161091\pi\) | ||||
0.874650 | + | 0.484756i | \(0.161091\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −45.4812 | − | 208.499i | −0.0909538 | − | 0.416960i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 324.587i | 0.619386i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.83446i | − | 0.00516843i | −0.999997 | − | 0.00258421i | \(-0.999177\pi\) | ||
0.999997 | − | 0.00258421i | \(-0.000822582\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −92.6357 | − | 859.325i | −0.161624 | − | 1.49928i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −796.627 | −1.33158 | −0.665790 | − | 0.746139i | \(-0.731905\pi\) | ||||
−0.665790 | + | 0.746139i | \(0.731905\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −875.489 | −1.40367 | −0.701837 | − | 0.712338i | \(-0.747637\pi\) | ||||
−0.701837 | + | 0.712338i | \(0.747637\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.94861 | + | 64.4581i | 0.0106981 | + | 0.0992397i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 92.9900i | 0.137626i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 656.826i | 0.935427i | 0.883880 | + | 0.467713i | \(0.154922\pi\) | ||||
−0.883880 | + | 0.467713i | \(0.845078\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 662.775 | − | 303.596i | 0.909156 | − | 0.416455i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 237.058 | 0.313500 | 0.156750 | − | 0.987638i | \(-0.449898\pi\) | ||||
0.156750 | + | 0.987638i | \(0.449898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1253.03 | −1.59894 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 578.610 | − | 62.3744i | 0.713028 | − | 0.0768648i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 868.956i | 1.03493i | 0.855703 | + | 0.517467i | \(0.173125\pi\) | ||||
−0.855703 | + | 0.517467i | \(0.826875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 241.850i | 0.278602i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1161.21 | − | 125.179i | 1.29476 | − | 0.139575i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −705.072 | −0.761461 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 755.048 | 0.790345 | 0.395173 | − | 0.918607i | \(-0.370685\pi\) | ||||
0.395173 | + | 0.918607i | \(0.370685\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −310.363 | + | 67.7014i | −0.315078 | + | 0.0687297i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1159.48i | 1.14230i | 0.820846 | + | 0.571149i | \(0.193502\pi\) | ||||
−0.820846 | + | 0.571149i | \(0.806498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1426.76i | − | 1.36488i | −0.730942 | − | 0.682440i | \(-0.760919\pi\) | ||
0.730942 | − | 0.682440i | \(-0.239081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −46.6928 | − | 433.141i | −0.0433976 | − | 0.402574i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1503.34 | 1.35826 | 0.679128 | − | 0.734020i | \(-0.262358\pi\) | ||||
0.679128 | + | 0.734020i | \(0.262358\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −446.011 | −0.391928 | −0.195964 | − | 0.980611i | \(-0.562784\pi\) | ||||
−0.195964 | + | 0.980611i | \(0.562784\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −39.3242 | − | 364.787i | −0.0336260 | − | 0.311928i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1413.62i | 1.17684i | 0.808557 | + | 0.588418i | \(0.200249\pi\) | ||||
−0.808557 | + | 0.588418i | \(0.799751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1764.44i | − | 1.43073i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −807.198 | + | 176.079i | −0.637825 | + | 0.139132i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −933.630 | −0.719208 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1192.58 | −0.896002 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1277.00 | + | 137.662i | −0.936127 | + | 0.100915i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1458.31i | 1.04348i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1315.32i | 0.919020i | 0.888173 | + | 0.459510i | \(0.151975\pi\) | ||||
−0.888173 | + | 0.459510i | \(0.848025\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 510.218 | − | 55.0017i | 0.348234 | − | 0.0375398i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2183.27 | 1.45613 | 0.728067 | − | 0.685506i | \(-0.240419\pi\) | ||||
0.728067 | + | 0.685506i | \(0.240419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −525.349 | −0.342508 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1411.66 | − | 471.190i | 0.899971 | − | 0.300397i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 751.608i | − | 0.468717i | −0.972150 | − | 0.234359i | \(-0.924701\pi\) | ||
0.972150 | − | 0.234359i | \(-0.0752990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1745.14i | 1.06490i | 0.846463 | + | 0.532448i | \(0.178728\pi\) | ||||
−0.846463 | + | 0.532448i | \(0.821272\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −105.580 | − | 979.399i | −0.0630596 | − | 0.584966i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 360.008 | 0.210527 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1188.05 | 0.680427 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 156.233 | + | 1449.28i | 0.0876591 | + | 0.813161i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1859.32i | 1.02229i | 0.859494 | + | 0.511145i | \(0.170779\pi\) | ||||
−0.859494 | + | 0.511145i | \(0.829221\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 967.660i | 0.521504i | 0.965406 | + | 0.260752i | \(0.0839704\pi\) | ||||
−0.965406 | + | 0.260752i | \(0.916030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −679.730 | − | 3116.08i | −0.359169 | − | 1.64654i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2384.30 | 1.23556 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3639.08 | 1.84987 | 0.924936 | − | 0.380123i | \(-0.124118\pi\) | ||||
0.924936 | + | 0.380123i | \(0.124118\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2734.84 | − | 294.817i | 1.36407 | − | 0.147047i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1314.68i | − | 0.643548i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 337.359i | − | 0.162110i | −0.996710 | − | 0.0810551i | \(-0.974171\pi\) | ||
0.996710 | − | 0.0810551i | \(-0.0258290\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −644.755 | + | 69.5049i | −0.304207 | + | 0.0327936i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2686.84 | 1.24499 | 0.622497 | − | 0.782622i | \(-0.286118\pi\) | ||||
0.622497 | + | 0.782622i | \(0.286118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1260.69 | −0.573822 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −382.480 | − | 1753.40i | −0.171047 | − | 0.784129i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1970.03i | 0.865773i | 0.901449 | + | 0.432886i | \(0.142505\pi\) | ||||
−0.901449 | + | 0.432886i | \(0.857495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 98.6143i | 0.0425974i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −452.158 | − | 4194.40i | −0.192013 | − | 1.78119i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 836.542 | 0.349308 | 0.174654 | − | 0.984630i | \(-0.444119\pi\) | ||||
0.174654 | + | 0.984630i | \(0.444119\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1716.39 | −0.704853 | −0.352426 | − | 0.935840i | \(-0.614643\pi\) | ||||
−0.352426 | + | 0.935840i | \(0.614643\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 464.144 | + | 4305.58i | 0.187489 | + | 1.73922i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 749.009i | − | 0.297666i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1389.76i | 0.543473i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1051.82 | − | 351.084i | 0.404809 | − | 0.135119i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −358.884 | −0.135958 | −0.0679788 | − | 0.997687i | \(-0.521655\pi\) | ||||
−0.0679788 | + | 0.997687i | \(0.521655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2670.56 | 0.996015 | 0.498007 | − | 0.867173i | \(-0.334065\pi\) | ||||
0.498007 | + | 0.867173i | \(0.334065\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1676.89 | + | 180.770i | −0.615819 | + | 0.0663855i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 597.410i | 0.216059i | 0.994148 | + | 0.108030i | \(0.0344542\pi\) | ||||
−0.994148 | + | 0.108030i | \(0.965546\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3336.44i | − | 1.18851i | −0.804276 | − | 0.594256i | \(-0.797447\pi\) | ||
0.804276 | − | 0.594256i | \(-0.202553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.6435 | − | 1.57857i | 0.00513865 | − | 0.000553949i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 885.213 | 0.306058 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2622.05 | −0.893326 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4387.87 | − | 957.153i | 1.47333 | − | 0.321385i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 782.012i | 0.258818i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1234.24i | 0.402695i | 0.979520 | + | 0.201348i | \(0.0645321\pi\) | ||||
−0.979520 | + | 0.201348i | \(0.935468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −443.658 | − | 4115.55i | −0.142718 | − | 1.32391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1047.62 | 0.332312 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1776.54 | 0.555757 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −487.578 | − | 4522.97i | −0.150445 | − | 1.39559i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3614.52i | 1.10018i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1647.48i | − | 0.494723i | −0.968923 | − | 0.247362i | \(-0.920436\pi\) | ||
0.968923 | − | 0.247362i | \(-0.0795635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −329.135 | + | 71.7962i | −0.0975215 | + | 0.0212729i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 340.265 | 0.0994897 | 0.0497449 | − | 0.998762i | \(-0.484159\pi\) | ||||
0.0497449 | + | 0.998762i | \(0.484159\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4031.94 | 1.16349 | 0.581743 | − | 0.813373i | \(-0.302371\pi\) | ||||
0.581743 | + | 0.813373i | \(0.302371\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −480.407 | + | 51.7881i | −0.136833 | + | 0.0147507i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1464.29i | 0.411710i | 0.978582 | + | 0.205855i | \(0.0659976\pi\) | ||||
−0.978582 | + | 0.205855i | \(0.934002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2010.98i | − | 0.558220i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3393.31 | + | 365.800i | −0.930038 | + | 0.100259i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3357.75 | −0.908765 | −0.454382 | − | 0.890807i | \(-0.650140\pi\) | ||||
−0.454382 | + | 0.890807i | \(0.650140\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2736.93 | −0.731541 | −0.365771 | − | 0.930705i | \(-0.619195\pi\) | ||||
−0.365771 | + | 0.930705i | \(0.619195\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1937.56 | + | 3254.96i | 0.511499 | + | 0.859284i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2975.78i | 0.775981i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2033.87i | 0.523935i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 132.023 | + | 1224.70i | 0.0336008 | + | 0.311694i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5959.74 | 1.49871 | 0.749354 | − | 0.662170i | \(-0.230364\pi\) | ||||
0.749354 | + | 0.662170i | \(0.230364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1956.98 | −0.486301 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −697.837 | − | 6473.42i | −0.171374 | − | 1.58973i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1384.26i | − | 0.335982i | −0.985788 | − | 0.167991i | \(-0.946272\pi\) | ||
0.985788 | − | 0.167991i | \(-0.0537280\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 558.086i | − | 0.133891i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 644.480 | + | 2954.49i | 0.152844 | + | 0.700683i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6426.06 | −1.50664 | −0.753322 | − | 0.657651i | \(-0.771550\pi\) | ||||
−0.753322 | + | 0.657651i | \(0.771550\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5615.40 | 1.30170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4489.22 | + | 483.940i | −1.02897 | + | 0.110924i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1594.21i | − | 0.361341i | −0.983544 | − | 0.180671i | \(-0.942173\pi\) | ||
0.983544 | − | 0.180671i | \(-0.0578268\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7502.42i | 1.68170i | 0.541271 | + | 0.840848i | \(0.317943\pi\) | ||||
−0.541271 | + | 0.840848i | \(0.682057\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1249.45 | + | 134.691i | −0.276997 | + | 0.0298604i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 146.793 | 0.0321889 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1099.05 | 0.238395 | 0.119198 | − | 0.992871i | \(-0.461968\pi\) | ||||
0.119198 | + | 0.992871i | \(0.461968\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1293.41 | + | 5929.37i | 0.277542 | + | 1.27234i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6848.46i | 1.45390i | 0.686692 | + | 0.726949i | \(0.259062\pi\) | ||||
−0.686692 | + | 0.726949i | \(0.740938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4354.29i | 0.914614i | 0.889309 | + | 0.457307i | \(0.151186\pi\) | ||||
−0.889309 | + | 0.457307i | \(0.848814\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −392.669 | − | 3642.56i | −0.0816131 | − | 0.757075i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1953.69 | −0.401820 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9040.37 | −1.84009 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 420.502 | + | 3900.74i | 0.0847088 | + | 0.785793i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2845.10i | − | 0.567278i | −0.958931 | − | 0.283639i | \(-0.908458\pi\) | ||
0.958931 | − | 0.283639i | \(-0.0915417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8612.27i | − | 1.69975i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −522.608 | − | 1565.70i | −0.102104 | − | 0.305896i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5089.74 | −0.984439 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 780.581 | 0.149475 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5990.11 | + | 645.737i | −1.13572 | + | 0.122431i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8840.56i | 1.65970i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7798.95i | − | 1.44987i | −0.688819 | − | 0.724934i | \(-0.741870\pi\) | ||
0.688819 | − | 0.724934i | \(-0.258130\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7370.95 | − | 794.592i | 1.35702 | − | 0.146287i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4799.43 | −0.875084 | −0.437542 | − | 0.899198i | \(-0.644151\pi\) | ||||
−0.437542 | + | 0.899198i | \(0.644151\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2400.65 | −0.433524 | −0.216762 | − | 0.976224i | \(-0.569550\pi\) | ||||
−0.216762 | + | 0.976224i | \(0.569550\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2211.70 | − | 482.451i | 0.395603 | − | 0.0862953i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5599.88i | − | 0.992179i | −0.868271 | − | 0.496090i | \(-0.834769\pi\) | ||
0.868271 | − | 0.496090i | \(-0.165231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1317.69i | − | 0.231274i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 837.242 | + | 7766.59i | 0.145577 | + | 1.35043i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7851.49 | −1.35253 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 381.782 | 0.0651614 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −248.393 | − | 2304.19i | −0.0420067 | − | 0.389670i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1498.38i | − | 0.251089i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5568.28i | 0.924654i | 0.886709 | + | 0.462327i | \(0.152985\pi\) | ||||
−0.886709 | + | 0.462327i | \(0.847015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1862.67 | − | 406.315i | 0.306527 | − | 0.0668646i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 30.0671 | 0.00490370 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1366.22 | −0.220839 | −0.110420 | − | 0.993885i | \(-0.535220\pi\) | ||||
−0.110420 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7303.09 | + | 787.276i | −1.17006 | + | 0.126133i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2644.48i | − | 0.419961i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4928.25i | 0.775803i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9115.46 | − | 982.651i | 1.42249 | − | 0.153345i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9688.05 | −1.49879 | −0.749397 | − | 0.662121i | \(-0.769657\pi\) | ||||
−0.749397 | + | 0.662121i | \(0.769657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11427.5 | −1.75272 | −0.876361 | − | 0.481654i | \(-0.840036\pi\) | ||||
−0.876361 | + | 0.481654i | \(0.840036\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1359.21 | − | 4072.10i | −0.206693 | − | 0.619239i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 630.357i | − | 0.0950440i | −0.998870 | − | 0.0475220i | \(-0.984868\pi\) | ||
0.998870 | − | 0.0475220i | \(-0.0151324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 8450.37i | − | 1.26338i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −519.958 | − | 4823.34i | −0.0770843 | − | 0.715065i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7429.40 | 1.09222 | 0.546112 | − | 0.837712i | \(-0.316107\pi\) | ||||
0.546112 | + | 0.837712i | \(0.316107\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2441.01 | 0.355884 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −664.172 | − | 6161.13i | −0.0960331 | − | 0.890841i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9286.92i | − | 1.33178i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11698.9i | 1.66397i | 0.554797 | + | 0.831986i | \(0.312796\pi\) | ||||
−0.554797 | + | 0.831986i | \(0.687204\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1422.38 | − | 6520.62i | −0.200667 | − | 0.919919i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4184.03 | 0.585510 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5197.32 | 0.721466 | 0.360733 | − | 0.932669i | \(-0.382527\pi\) | ||||
0.360733 | + | 0.932669i | \(0.382527\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7533.96 | + | 812.165i | −1.03747 | + | 0.111840i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3427.07i | − | 0.468178i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2510.74i | 0.340284i | 0.985420 | + | 0.170142i | \(0.0544227\pi\) | ||||
−0.985420 | + | 0.170142i | \(0.945577\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6795.22 | + | 732.528i | −0.913726 | + | 0.0985001i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4920.99 | 0.656530 | 0.328265 | − | 0.944586i | \(-0.393536\pi\) | ||||
0.328265 | + | 0.944586i | \(0.393536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −986.409 | −0.130577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 568.302 | + | 2605.27i | 0.0746471 | + | 0.342204i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3477.90i | − | 0.453308i | −0.973975 | − | 0.226654i | \(-0.927221\pi\) | ||
0.973975 | − | 0.226654i | \(-0.0727786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19648.3i | − | 2.54132i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1215.91 | + | 11279.3i | 0.156068 | + | 1.44775i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6967.41 | −0.887515 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2710.55 | 0.342667 | 0.171333 | − | 0.985213i | \(-0.445192\pi\) | ||||
0.171333 | + | 0.985213i | \(0.445192\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −292.578 | − | 2714.07i | −0.0367098 | − | 0.340535i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4661.17i | − | 0.580468i | −0.956956 | − | 0.290234i | \(-0.906267\pi\) | ||
0.956956 | − | 0.290234i | \(-0.0937331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6877.80i | − | 0.850144i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3220.45 | + | 7030.51i | 0.395125 | + | 0.862590i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −830.743 | −0.101175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12349.9 | 1.49307 | 0.746533 | − | 0.665348i | \(-0.231717\pi\) | ||||
0.746533 | + | 0.665348i | \(0.231717\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3882.97 | − | 418.586i | 0.466017 | − | 0.0502369i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6417.00i | − | 0.764551i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2514.64i | 0.297443i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9015.76 | + | 971.903i | −1.05876 | + | 0.114135i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −528.053 | −0.0615682 | −0.0307841 | − | 0.999526i | \(-0.509800\pi\) | ||||
−0.0307841 | + | 0.999526i | \(0.509800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8788.97 | 1.01745 | 0.508727 | − | 0.860928i | \(-0.330116\pi\) | ||||
0.508727 | + | 0.860928i | \(0.330116\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5000.99 | − | 1090.90i | 0.574838 | − | 0.125393i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1473.82i | 0.168213i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6587.10i | 0.746539i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 200.496 | + | 1859.88i | 0.0225642 | + | 0.209314i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3660.00 | −0.409040 | −0.204520 | − | 0.978862i | \(-0.565563\pi\) | ||||
−0.204520 | + | 0.978862i | \(0.565563\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4322.55 | −0.479742 | −0.239871 | − | 0.970805i | \(-0.577105\pi\) | ||||
−0.239871 | + | 0.970805i | \(0.577105\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 661.648 | + | 6137.71i | 0.0729278 | + | 0.676508i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 11056.0i | − | 1.21025i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12788.3i | 1.39032i | 0.718854 | + | 0.695161i | \(0.244667\pi\) | ||||
−0.718854 | + | 0.695161i | \(0.755333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7400.29 | + | 1614.27i | −0.799082 | + | 0.174308i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5382.41 | −0.577259 | −0.288630 | − | 0.957441i | \(-0.593200\pi\) | ||||
−0.288630 | + | 0.957441i | \(0.593200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9217.62 | −0.981926 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9605.65 | + | 1035.49i | −1.01640 | + | 0.109569i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9465.38i | − | 0.994875i | −0.867500 | − | 0.497437i | \(-0.834274\pi\) | ||
0.867500 | − | 0.497437i | \(-0.165726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2908.17i | 0.303638i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4999.15 | + | 538.910i | −0.518500 | + | 0.0558945i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2565.47 | −0.264332 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −716.322 | −0.0733219 | −0.0366610 | − | 0.999328i | \(-0.511672\pi\) | ||||
−0.0366610 | + | 0.999328i | \(0.511672\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15719.8 | − | 5247.05i | 1.59856 | − | 0.533575i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19191.7i | 1.93893i | 0.245226 | + | 0.969466i | \(0.421138\pi\) | ||||
−0.245226 | + | 0.969466i | \(0.578862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 222.541i | − | 0.0223377i | −0.999938 | − | 0.0111689i | \(-0.996445\pi\) | ||
0.999938 | − | 0.0111689i | \(-0.00355523\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1327.86 | + | 12317.8i | 0.132426 | + | 1.22844i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5784.61 | −0.573190 | −0.286595 | − | 0.958052i | \(-0.592523\pi\) | ||||
−0.286595 | + | 0.958052i | \(0.592523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.4030 | 0.00220570 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2026.68 | + | 18800.3i | 0.198268 | + | 1.83922i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1161.94i | − | 0.112951i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 829.310i | 0.0801081i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3046.18 | + | 13964.6i | 0.292401 | + | 1.34045i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9218.02 | 0.879294 | 0.439647 | − | 0.898171i | \(-0.355103\pi\) | ||||
0.439647 | + | 0.898171i | \(0.355103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2160.61 | −0.204814 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6791.93 | − | 732.173i | 0.639841 | − | 0.0689752i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8009.32i | 0.749864i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17851.9i | − | 1.66109i | −0.556955 | − | 0.830543i | \(-0.688030\pi\) | ||
0.556955 | − | 0.830543i | \(-0.311970\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1742.87 | − | 187.882i | 0.161176 | − | 0.0173749i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12979.1 | 1.19295 | 0.596473 | − | 0.802633i | \(-0.296568\pi\) | ||||
0.596473 | + | 0.802633i | \(0.296568\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13229.8 | 1.20860 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −718.155 | − | 3292.24i | −0.0652095 | − | 0.298940i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6296.37i | − | 0.568271i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17513.6i | 1.57117i | 0.618752 | + | 0.785586i | \(0.287639\pi\) | ||||
−0.618752 | + | 0.785586i | \(0.712361\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1496.36 | + | 13880.8i | 0.133438 | + | 1.23782i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7405.59 | 0.656459 | 0.328230 | − | 0.944598i | \(-0.393548\pi\) | ||||
0.328230 | + | 0.944598i | \(0.393548\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12299.4 | −1.08379 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −702.103 | − | 6512.98i | −0.0615019 | − | 0.570516i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2162.88i | 0.188346i | 0.995556 | + | 0.0941728i | \(0.0300206\pi\) | ||||
−0.995556 | + | 0.0941728i | \(0.969979\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6919.68i | − | 0.599038i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8845.46 | − | 2952.48i | 0.761280 | − | 0.254104i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15134.6 | 1.29497 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2230.42 | −0.189737 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10177.6 | + | 1097.15i | −0.860786 | + | 0.0927931i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13662.4i | − | 1.14887i | −0.818550 | − | 0.574435i | \(-0.805222\pi\) | ||
0.818550 | − | 0.574435i | \(-0.194778\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3574.54i | 0.298860i | 0.988772 | + | 0.149430i | \(0.0477438\pi\) | ||||
−0.988772 | + | 0.149430i | \(0.952256\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −509.463 | + | 54.9204i | −0.0423520 | + | 0.00456556i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26550.9 | 2.19464 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15500.5 | 1.27398 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21417.4 | − | 4671.89i | 1.75035 | − | 0.381813i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7563.63i | 0.614666i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15947.0i | 1.28869i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 465.888 | + | 4321.76i | 0.0374386 | + | 0.347295i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3300.51 | 0.263753 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5965.93 | −0.474114 | −0.237057 | − | 0.971496i | \(-0.576183\pi\) | ||||
−0.237057 | + | 0.971496i | \(0.576183\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −955.895 | − | 8867.26i | −0.0755458 | − | 0.700793i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4731.15i | − | 0.371854i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6960.57i | − | 0.544081i | −0.962286 | − | 0.272040i | \(-0.912302\pi\) | ||
0.962286 | − | 0.272040i | \(-0.0876985\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21985.1 | + | 4795.74i | −1.70911 | + | 0.372818i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7444.32 | 0.575569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5191.41 | −0.399207 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3869.54 | − | 417.139i | 0.295951 | − | 0.0319037i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 6929.11i | − | 0.527102i | −0.964645 | − | 0.263551i | \(-0.915106\pi\) | ||
0.964645 | − | 0.263551i | \(-0.0848937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3021.99i | − | 0.228652i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7179.82 | + | 773.988i | −0.540343 | + | 0.0582492i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20207.5 | −1.51269 | −0.756344 | − | 0.654175i | \(-0.773016\pi\) | ||||
−0.756344 | + | 0.654175i | \(0.773016\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14995.3 | −1.11656 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2399.56 | + | 5238.43i | 0.177728 | + | 0.387995i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 14954.6i | − | 1.10181i | −0.834567 | − | 0.550906i | \(-0.814282\pi\) | ||
0.834567 | − | 0.550906i | \(-0.185718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11065.5i | − | 0.810996i | −0.914096 | − | 0.405498i | \(-0.867098\pi\) | ||
0.914096 | − | 0.405498i | \(-0.132902\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −199.870 | − | 1854.07i | −0.0145719 | − | 0.135174i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2075.34 | −0.150518 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20741.1 | 1.49647 | 0.748235 | − | 0.663433i | \(-0.230901\pi\) | ||||
0.748235 | + | 0.663433i | \(0.230901\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1487.29 | + | 13796.7i | 0.106752 | + | 0.990277i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1873.66i | 0.133791i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6228.17i | − | 0.442443i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1867.79 | − | 8562.51i | −0.132006 | − | 0.605156i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8044.96 | 0.565675 | 0.282837 | − | 0.959168i | \(-0.408724\pi\) | ||||
0.282837 | + | 0.959168i | \(0.408724\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14940.0 | 1.04515 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3086.35 | + | 332.710i | −0.214815 | + | 0.0231571i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11007.3i | − | 0.762255i | −0.924522 | − | 0.381128i | \(-0.875536\pi\) | ||
0.924522 | − | 0.381128i | \(-0.124464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 9903.66i | − | 0.682371i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17236.8 | − | 1858.13i | 1.18167 | − | 0.127384i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15693.5 | 1.07048 | 0.535242 | − | 0.844699i | \(-0.320220\pi\) | ||||
0.535242 | + | 0.844699i | \(0.320220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6984.08 | 0.474021 | 0.237010 | − | 0.971507i | \(-0.423832\pi\) | ||||
0.237010 | + | 0.971507i | \(0.423832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.3105 | + | 74.7722i | 0.00110152 | + | 0.00504968i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 12650.5i | − | 0.850110i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2251.13i | − | 0.150528i | −0.997164 | − | 0.0752641i | \(-0.976020\pi\) | ||
0.997164 | − | 0.0752641i | \(-0.0239800\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 492.994 | + | 4573.21i | 0.0328032 | + | 0.304295i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5800.93 | −0.384092 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4638.50 | −0.305624 | −0.152812 | − | 0.988255i | \(-0.548833\pi\) | ||||
−0.152812 | + | 0.988255i | \(0.548833\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1460.27 | − | 13546.1i | −0.0957462 | − | 0.888180i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 16218.9i | − | 1.05826i | −0.848540 | − | 0.529132i | \(-0.822518\pi\) | ||
0.848540 | − | 0.529132i | \(-0.177482\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 11838.8i | − | 0.768727i | −0.923182 | − | 0.384363i | \(-0.874421\pi\) | ||
0.923182 | − | 0.384363i | \(-0.125579\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7388.56 | + | 22135.7i | 0.477444 | + | 1.43039i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6868.05 | −0.441673 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13909.7 | −0.890222 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4040.04 | + | 435.519i | −0.257327 | + | 0.0277399i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 8340.76i | − | 0.528724i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14214.6i | 0.896791i | 0.893835 | + | 0.448395i | \(0.148004\pi\) | ||||
−0.893835 | + | 0.448395i | \(0.851996\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6376.36 | + | 687.375i | −0.400375 | + | 0.0431607i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13952.5 | −0.871949 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8584.01 | 0.533926 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21014.8 | − | 4584.07i | 1.30099 | − | 0.283792i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13075.6i | 0.805704i | 0.915265 | + | 0.402852i | \(0.131981\pi\) | ||||
−0.915265 | + | 0.402852i | \(0.868019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5272.61i | 0.323377i | 0.986842 | + | 0.161689i | \(0.0516940\pi\) | ||||
−0.986842 | + | 0.161689i | \(0.948306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 583.441 | + | 5412.23i | 0.0356170 | + | 0.330398i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32739.3 | 1.98936 | 0.994679 | − | 0.103027i | \(-0.0328527\pi\) | ||||
0.994679 | + | 0.103027i | \(0.0328527\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9552.07 | −0.577737 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 989.391 | + | 9177.99i | 0.0595657 | + | 0.552555i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 14895.3i | − | 0.892649i | −0.894871 | − | 0.446324i | \(-0.852733\pi\) | ||
0.894871 | − | 0.446324i | \(-0.147267\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23159.5i | 1.38155i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23095.1 | − | 5037.87i | 1.37142 | − | 0.299157i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13070.1 | 0.772595 | 0.386297 | − | 0.922374i | \(-0.373754\pi\) | ||||
0.386297 | + | 0.922374i | \(0.373754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24322.7 | −1.43123 | −0.715616 | − | 0.698494i | \(-0.753854\pi\) | ||||
−0.715616 | + | 0.698494i | \(0.753854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18673.4 | + | 2013.00i | −1.09384 | + | 0.117916i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 5572.74i | − | 0.324965i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18629.3i | 1.08146i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8511.23 | − | 917.515i | 0.491873 | − | 0.0530242i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9805.27 | 0.564126 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1854.52 | −0.106221 | −0.0531104 | − | 0.998589i | \(-0.516914\pi\) | ||||
−0.0531104 | + | 0.998589i | \(0.516914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −554.217 | − | 1660.40i | −0.0316027 | − | 0.0946797i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 6481.24i | − | 0.367938i | −0.982932 | − | 0.183969i | \(-0.941105\pi\) | ||
0.982932 | − | 0.183969i | \(-0.0588946\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5967.74i | 0.337291i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 189.501 | + | 1757.88i | 0.0106633 | + | 0.0989166i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7618.89 | −0.426836 | −0.213418 | − | 0.976961i | \(-0.568460\pi\) | ||||
−0.213418 | + | 0.976961i | \(0.568460\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7972.83 | 0.444710 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2245.47 | + | 20829.9i | 0.124702 | + | 1.15678i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 16198.3i | − | 0.895657i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8461.55i | 0.465836i | 0.972496 | + | 0.232918i | \(0.0748273\pi\) | ||||
−0.972496 | + | 0.232918i | \(0.925173\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −535.097 | − | 2453.05i | −0.0293314 | − | 0.134464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18511.9 | −1.01035 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29198.4 | −1.58676 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7564.82 | + | 815.492i | −0.409339 | + | 0.0441269i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19113.8i | 1.02984i | 0.857238 | + | 0.514921i | \(0.172179\pi\) | ||||
−0.857238 | + | 0.514921i | \(0.827821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4693.30i | − | 0.251794i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10389.2 | − | 1119.96i | 0.555005 | − | 0.0598298i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9164.25 | −0.487493 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7854.59 | 0.416058 | 0.208029 | − | 0.978123i | \(-0.433295\pi\) | ||||
0.208029 | + | 0.978123i | \(0.433295\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3779.61 | − | 17326.9i | −0.199362 | − | 0.913935i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37387.3i | 1.96377i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3818.85i | 0.199744i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1870.00 | − | 17346.9i | −0.0974010 | − | 0.903530i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27011.1 | −1.40103 | −0.700517 | − | 0.713635i | \(-0.747047\pi\) | ||||
−0.700517 | + | 0.713635i | \(0.747047\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11276.8 | 0.582482 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1524.26 | − | 14139.6i | −0.0784062 | − | 0.727327i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1397.39i | − | 0.0715830i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22178.9i | − | 1.13146i | −0.824591 | − | 0.565729i | \(-0.808595\pi\) | ||
0.824591 | − | 0.565729i | \(-0.191405\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15736.8 | + | 11822.6i | −0.799512 | + | 0.600651i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11666.0 | 0.590264 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9103.17 | 0.458708 | 0.229354 | − | 0.973343i | \(-0.426339\pi\) | ||||
0.229354 | + | 0.973343i | \(0.426339\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15373.5 | + | 1657.27i | −0.771512 | + | 0.0831693i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 33.3481i | − | 0.00166675i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19226.3i | − | 0.957036i | −0.878078 | − | 0.478518i | \(-0.841174\pi\) | ||
0.878078 | − | 0.478518i | \(-0.158826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10507.4 | + | 1132.70i | −0.520917 | + | 0.0561551i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22501.9 | −1.11106 | −0.555528 | − | 0.831498i | \(-0.687484\pi\) | ||||
−0.555528 | + | 0.831498i | \(0.687484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19723.1 | −0.969930 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6253.52 | + | 1364.12i | −0.306298 | + | 0.0668145i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11882.1i | 0.579655i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2080.69i | − | 0.101099i | −0.998722 | − | 0.0505495i | \(-0.983903\pi\) | ||
0.998722 | − | 0.0505495i | \(-0.0160973\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3319.10 | + | 30789.3i | 0.160631 | + | 1.49007i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10264.6 | −0.494793 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26222.3 | −1.25900 | −0.629501 | − | 0.777000i | \(-0.716741\pi\) | ||||
−0.629501 | + | 0.777000i | \(0.716741\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1089.88 | − | 10110.2i | −0.0521215 | − | 0.483499i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11443.7i | 0.545118i | 0.962139 | + | 0.272559i | \(0.0878700\pi\) | ||||
−0.962139 | + | 0.272559i | \(0.912130\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3525.18i | − | 0.167261i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33054.5 | − | 7210.36i | 1.56220 | − | 0.340773i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24843.2 | −1.16954 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18991.7 | 0.890582 | 0.445291 | − | 0.895386i | \(-0.353100\pi\) | ||||
0.445291 | + | 0.895386i | \(0.353100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7151.37 | − | 770.921i | 0.334047 | − | 0.0360104i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 36956.6i | − | 1.71958i | −0.510645 | − | 0.859791i | \(-0.670593\pi\) | ||
0.510645 | − | 0.859791i | \(-0.329407\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2804.42i | − | 0.129984i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2883.20 | − | 310.810i | 0.133120 | − | 0.0143504i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16429.8 | −0.755659 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9372.51 | −0.429417 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14904.6 | + | 4974.94i | −0.680265 | + | 0.227062i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38602.2i | 1.75512i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 19962.2i | − | 0.904162i | −0.891977 | − | 0.452081i | \(-0.850682\pi\) | ||
0.891977 | − | 0.452081i | \(-0.149318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3578.81 | − | 33198.4i | −0.161481 | − | 1.49797i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11173.0 | −0.502232 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25501.7 | 1.14198 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3127.33 | + | 29010.4i | 0.139516 | + | 1.29420i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6131.27i | 0.272498i | 0.990675 | + | 0.136249i | \(0.0435047\pi\) | ||||
−0.990675 | + | 0.136249i | \(0.956495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 22393.7i | − | 0.991530i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5000.28 | − | 22922.8i | −0.220570 | − | 1.01116i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10300.3 | −0.452666 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13945.7 | 0.610586 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8236.05 | − | 887.850i | 0.359260 | − | 0.0387284i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18915.6i | 0.822050i | 0.911624 | + | 0.411025i | \(0.134829\pi\) | ||||
−0.911624 | + | 0.411025i | \(0.865171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8699.98i | − | 0.376692i | −0.982103 | − | 0.188346i | \(-0.939687\pi\) | ||
0.982103 | − | 0.188346i | \(-0.0603127\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38759.2 | + | 4178.26i | −1.67201 | + | 0.180243i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3578.60 | 0.153807 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6564.40 | 0.281101 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1391.69 | − | 6379.92i | −0.0593768 | − | 0.272201i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21629.4i | 0.919453i | 0.888061 | + | 0.459726i | \(0.152052\pi\) | ||||
−0.888061 | + | 0.459726i | \(0.847948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17966.4i | 0.760960i | 0.924789 | + | 0.380480i | \(0.124241\pi\) | ||||
−0.924789 | + | 0.380480i | \(0.875759\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 81.7521 | + | 758.365i | 0.00344999 | + | 0.0320035i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19001.1 | 0.798951 | 0.399475 | − | 0.916744i | \(-0.369192\pi\) | ||||
0.399475 | + | 0.916744i | \(0.369192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25624.2 | 1.07354 | 0.536770 | − | 0.843728i | \(-0.319644\pi\) | ||||
0.536770 | + | 0.843728i | \(0.319644\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 612.083 | + | 5677.93i | 0.0255511 | + | 0.237022i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33137.4i | 1.37832i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28501.2i | 1.18123i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29912.1 | + | 9984.23i | −1.23526 | + | 0.412312i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39037.6 | −1.60635 | −0.803176 | − | 0.595742i | \(-0.796858\pi\) | ||||
−0.803176 | + | 0.595742i | \(0.796858\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11845.3 | 0.485683 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35380.7 | + | 3814.05i | −1.44552 | + | 0.155828i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 13373.0i | − | 0.544431i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9425.89i | − | 0.382382i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22495.2 | + | 2425.00i | −0.909346 | + | 0.0980279i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11744.9 | 0.473104 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10697.0 | −0.429377 | −0.214688 | − | 0.976683i | \(-0.568874\pi\) | ||||
−0.214688 | + | 0.976683i | \(0.568874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18599.6 | − | 4057.23i | 0.743967 | − | 0.162286i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3546.91i | 0.141377i | 0.997498 | + | 0.0706886i | \(0.0225197\pi\) | ||||
−0.997498 | + | 0.0706886i | \(0.977480\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 37273.1i | − | 1.48049i | −0.672336 | − | 0.740246i | \(-0.734709\pi\) | ||
0.672336 | − | 0.740246i | \(-0.265291\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1088.05 | − | 10093.2i | −0.0430669 | − | 0.399506i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12710.9 | −0.501372 | −0.250686 | − | 0.968068i | \(-0.580656\pi\) | ||||
−0.250686 | + | 0.968068i | \(0.580656\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20897.5 | −0.821429 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5034.77 | − | 46704.5i | −0.197220 | − | 1.82949i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7727.72i | 0.301663i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 86.7324i | − | 0.00337407i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19917.9 | + | 4344.81i | −0.772187 | + | 0.168442i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11526.2 | −0.445322 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13273.5 | −0.511078 | −0.255539 | − | 0.966799i | \(-0.582253\pi\) | ||||
−0.255539 | + | 0.966799i | \(0.582253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14698.4 | − | 1584.49i | 0.564010 | − | 0.0608005i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 24760.3i | − | 0.946875i | −0.880828 | − | 0.473437i | \(-0.843013\pi\) | ||
0.880828 | − | 0.473437i | \(-0.156987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46347.6i | 1.76639i | 0.469009 | + | 0.883193i | \(0.344611\pi\) | ||||
−0.469009 | + | 0.883193i | \(0.655389\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 44492.9 | − | 4796.35i | 1.68996 | − | 0.182178i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12454.7 | 0.471461 | 0.235731 | − | 0.971818i | \(-0.424252\pi\) | ||||
0.235731 | + | 0.971818i | \(0.424252\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10396.0 | −0.392205 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7797.71 | − | 3571.88i | 0.293191 | − | 0.134301i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 12600.8i | − | 0.472195i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8873.78i | 0.331416i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2834.58 | − | 26294.7i | −0.105512 | − | 0.978768i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25174.0 | −0.933925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62531.5 | 2.31213 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 434.722 | + | 4032.65i | 0.0160206 | + | 0.148614i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18207.0i | − | 0.668751i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31110.3i | 1.13892i | 0.822020 | + | 0.569459i | \(0.192847\pi\) | ||||
−0.822020 | + | 0.569459i | \(0.807153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6672.04 | − | 30586.6i | −0.243452 | − | 1.11605i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2882.81 | 0.104843 | 0.0524214 | − | 0.998625i | \(-0.483306\pi\) | ||||
0.0524214 | + | 0.998625i | \(0.483306\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2789.05 | 0.101100 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −45672.3 | + | 4923.49i | −1.65014 | + | 0.177886i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17256.1i | 0.621426i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6249.30i | 0.224315i | 0.993690 | + | 0.112157i | \(0.0357761\pi\) | ||||
−0.993690 | + | 0.112157i | \(0.964224\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40291.1 | − | 4343.40i | 1.44152 | − | 0.155396i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24376.2 | −0.869287 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −880.989 | −0.0313154 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8210.07 | + | 37637.4i | 0.290889 | + | 1.33352i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32605.2i | 1.15150i | 0.817627 | + | 0.575749i | \(0.195289\pi\) | ||||
−0.817627 | + | 0.575749i | \(0.804711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18646.3i | 0.656398i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2672.91 | − | 24794.9i | −0.0937910 | − | 0.870043i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14742.2 | −0.515637 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15176.1 | 0.529116 | 0.264558 | − | 0.964370i | \(-0.414774\pi\) | ||||
0.264558 | + | 0.964370i | \(0.414774\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1336.97 | − | 12402.3i | −0.0464649 | − | 0.431027i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 37892.6i | − | 1.31271i | −0.754450 | − | 0.656357i | \(-0.772096\pi\) | ||
0.754450 | − | 0.656357i | \(-0.227904\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 41115.4i | − | 1.41983i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3724.19 | + | 11157.4i | 0.128199 | + | 0.384075i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54773.3 | 1.87951 | 0.939754 | − | 0.341853i | \(-0.111054\pi\) | ||||
0.939754 | + | 0.341853i | \(0.111054\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26789.3 | −0.916351 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28930.2 | − | 3118.69i | 0.986464 | − | 0.106341i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5158.12i | 0.175328i | 0.996150 | + | 0.0876642i | \(0.0279403\pi\) | ||||
−0.996150 | + | 0.0876642i | \(0.972060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 3806.93i | − | 0.128994i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6807.48 | − | 733.850i | 0.229942 | − | 0.0247879i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5940.55 | 0.200032 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20730.7 | −0.695872 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39657.6 | + | 8650.76i | −1.32705 | + | 0.289477i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28328.4i | 0.945000i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46108.3i | 1.53334i | 0.642039 | + | 0.766672i | \(0.278089\pi\) | ||||
−0.642039 | + | 0.766672i | \(0.721911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4372.66 | − | 40562.5i | −0.144964 | − | 1.34474i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5437.59 | 0.179712 | 0.0898561 | − | 0.995955i | \(-0.471359\pi\) | ||||
0.0898561 | + | 0.995955i | \(0.471359\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13793.2 | −0.454460 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 212.622 | + | 1972.37i | 0.00698396 | + | 0.0647860i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 21599.2i | − | 0.707288i | −0.935380 | − | 0.353644i | \(-0.884942\pi\) | ||
0.935380 | − | 0.353644i | \(-0.115058\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10223.5i | 0.333753i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11765.6 | − | 2566.51i | 0.382924 | − | 0.0835294i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37178.0 | −1.20630 | −0.603151 | − | 0.797627i | \(-0.706088\pi\) | ||||
−0.603151 | + | 0.797627i | \(0.706088\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6337.14 | −0.204993 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7740.96 | − | 834.479i | 0.249643 | − | 0.0269116i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16427.3i | 0.528169i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 8124.54i | − | 0.260428i | −0.991486 | − | 0.130214i | \(-0.958434\pi\) | ||
0.991486 | − | 0.130214i | \(-0.0415665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28767.0 | + | 3101.09i | −0.919328 | + | 0.0991040i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35391.9 | 1.12764 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32053.1 | 1.01819 | 0.509093 | − | 0.860711i | \(-0.329981\pi\) | ||||
0.509093 | + | 0.860711i | \(0.329981\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3136.47 | + | 9396.67i | 0.0993328 | + | 0.297595i |
(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 | 384.4.c.d.383.6 | yes | 12 | |
3.2 | odd | 2 | 384.4.c.a.383.8 | yes | 12 | ||
4.3 | odd | 2 | 384.4.c.a.383.7 | ✓ | 12 | ||
8.3 | odd | 2 | 384.4.c.c.383.6 | yes | 12 | ||
8.5 | even | 2 | 384.4.c.b.383.7 | yes | 12 | ||
12.11 | even | 2 | inner | 384.4.c.d.383.5 | yes | 12 | |
16.3 | odd | 4 | 768.4.f.e.383.11 | 12 | |||
16.5 | even | 4 | 768.4.f.f.383.11 | 12 | |||
16.11 | odd | 4 | 768.4.f.h.383.2 | 12 | |||
16.13 | even | 4 | 768.4.f.g.383.2 | 12 | |||
24.5 | odd | 2 | 384.4.c.c.383.5 | yes | 12 | ||
24.11 | even | 2 | 384.4.c.b.383.8 | yes | 12 | ||
48.5 | odd | 4 | 768.4.f.e.383.12 | 12 | |||
48.11 | even | 4 | 768.4.f.g.383.1 | 12 | |||
48.29 | odd | 4 | 768.4.f.h.383.1 | 12 | |||
48.35 | even | 4 | 768.4.f.f.383.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.7 | ✓ | 12 | 4.3 | odd | 2 | ||
384.4.c.a.383.8 | yes | 12 | 3.2 | odd | 2 | ||
384.4.c.b.383.7 | yes | 12 | 8.5 | even | 2 | ||
384.4.c.b.383.8 | yes | 12 | 24.11 | even | 2 | ||
384.4.c.c.383.5 | yes | 12 | 24.5 | odd | 2 | ||
384.4.c.c.383.6 | yes | 12 | 8.3 | odd | 2 | ||
384.4.c.d.383.5 | yes | 12 | 12.11 | even | 2 | inner | |
384.4.c.d.383.6 | yes | 12 | 1.1 | even | 1 | trivial | |
768.4.f.e.383.11 | 12 | 16.3 | odd | 4 | |||
768.4.f.e.383.12 | 12 | 48.5 | odd | 4 | |||
768.4.f.f.383.11 | 12 | 16.5 | even | 4 | |||
768.4.f.f.383.12 | 12 | 48.35 | even | 4 | |||
768.4.f.g.383.1 | 12 | 48.11 | even | 4 | |||
768.4.f.g.383.2 | 12 | 16.13 | even | 4 | |||
768.4.f.h.383.1 | 12 | 48.29 | odd | 4 | |||
768.4.f.h.383.2 | 12 | 16.11 | odd | 4 |