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 | 383.3 | ||
Root | \(-3.14286i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.4.c.b.383.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −4.12202 | − | 3.16369i | −0.793283 | − | 0.608853i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 21.4043i | 1.91446i | 0.289323 | + | 0.957232i | \(0.406570\pi\) | ||||
−0.289323 | + | 0.957232i | \(0.593430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 20.9034i | − | 1.12868i | −0.825543 | − | 0.564339i | \(-0.809131\pi\) | ||
0.825543 | − | 0.564339i | \(-0.190869\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.98212 | + | 26.0816i | 0.258597 | + | 0.965985i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.94564 | −0.272611 | −0.136306 | − | 0.990667i | \(-0.543523\pi\) | ||||
−0.136306 | + | 0.990667i | \(0.543523\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 67.8290 | 1.44711 | 0.723554 | − | 0.690268i | \(-0.242507\pi\) | ||||
0.723554 | + | 0.690268i | \(0.242507\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 67.7167 | − | 88.2292i | 1.16563 | − | 1.51871i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.97348i | − | 0.113756i | −0.998381 | − | 0.0568780i | \(-0.981885\pi\) | ||
0.998381 | − | 0.0568780i | \(-0.0181146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 62.4014i | 0.753466i | 0.926322 | + | 0.376733i | \(0.122953\pi\) | ||||
−0.926322 | + | 0.376733i | \(0.877047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −66.1320 | + | 86.1644i | −0.687199 | + | 0.895362i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −101.816 | −0.923049 | −0.461525 | − | 0.887127i | \(-0.652697\pi\) | ||||
−0.461525 | + | 0.887127i | \(0.652697\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −333.146 | −2.66517 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 53.7337 | − | 129.598i | 0.383002 | − | 0.923748i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 122.445i | − | 0.784051i | −0.919954 | − | 0.392025i | \(-0.871775\pi\) | ||
0.919954 | − | 0.392025i | \(-0.128225\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 87.5072i | 0.506992i | 0.967336 | + | 0.253496i | \(0.0815805\pi\) | ||||
−0.967336 | + | 0.253496i | \(0.918419\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 40.9961 | + | 31.4649i | 0.216258 | + | 0.165980i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 447.424 | 2.16081 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −106.136 | −0.471587 | −0.235794 | − | 0.971803i | \(-0.575769\pi\) | ||||
−0.235794 | + | 0.971803i | \(0.575769\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −279.593 | − | 214.590i | −1.14797 | − | 0.881075i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 90.3818i | 0.344275i | 0.985073 | + | 0.172137i | \(0.0550673\pi\) | ||||
−0.985073 | + | 0.172137i | \(0.944933\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 451.366i | 1.60076i | 0.599494 | + | 0.800380i | \(0.295369\pi\) | ||||
−0.599494 | + | 0.800380i | \(0.704631\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −558.260 | + | 149.448i | −1.84934 | + | 0.495075i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −428.890 | −1.33106 | −0.665532 | − | 0.746369i | \(-0.731795\pi\) | ||||
−0.665532 | + | 0.746369i | \(0.731795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −93.9530 | −0.273916 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −25.2256 | + | 32.8669i | −0.0692607 | + | 0.0902408i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 362.452i | 0.939370i | 0.882834 | + | 0.469685i | \(0.155633\pi\) | ||||
−0.882834 | + | 0.469685i | \(0.844367\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 212.880i | − | 0.521904i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 197.419 | − | 257.220i | 0.458750 | − | 0.597712i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −801.483 | −1.76855 | −0.884273 | − | 0.466970i | \(-0.845346\pi\) | ||||
−0.884273 | + | 0.466970i | \(0.845346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −647.903 | −1.35993 | −0.679963 | − | 0.733247i | \(-0.738004\pi\) | ||||
−0.679963 | + | 0.733247i | \(0.738004\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 545.195 | − | 145.950i | 1.09029 | − | 0.291873i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1451.84i | 2.77043i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 957.240i | 1.74545i | 0.488208 | + | 0.872727i | \(0.337651\pi\) | ||||
−0.488208 | + | 0.872727i | \(0.662349\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 419.688 | + | 322.115i | 0.732240 | + | 0.562001i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 224.090 | 0.374572 | 0.187286 | − | 0.982305i | \(-0.440031\pi\) | ||||
0.187286 | + | 0.982305i | \(0.440031\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −108.474 | −0.173916 | −0.0869582 | − | 0.996212i | \(-0.527715\pi\) | ||||
−0.0869582 | + | 0.996212i | \(0.527715\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1373.24 | + | 1053.97i | 2.11423 | + | 1.62269i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 207.898i | 0.307690i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 615.569i | − | 0.876670i | −0.898812 | − | 0.438335i | \(-0.855568\pi\) | ||
0.898812 | − | 0.438335i | \(-0.144432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −631.500 | + | 364.210i | −0.866255 | + | 0.499602i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −204.385 | −0.270291 | −0.135145 | − | 0.990826i | \(-0.543150\pi\) | ||||
−0.135145 | + | 0.990826i | \(0.543150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 170.667 | 0.217782 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −387.378 | + | 504.721i | −0.477371 | + | 0.621974i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 454.067i | − | 0.540798i | −0.962748 | − | 0.270399i | \(-0.912844\pi\) | ||
0.962748 | − | 0.270399i | \(-0.0871556\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1417.86i | − | 1.63332i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 276.846 | − | 360.707i | 0.308684 | − | 0.402189i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1335.66 | −1.44248 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 740.490 | 0.775106 | 0.387553 | − | 0.921847i | \(-0.373320\pi\) | ||||
0.387553 | + | 0.921847i | \(0.373320\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −69.4417 | − | 259.398i | −0.0704965 | − | 0.263338i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 52.9454i | 0.0521610i | 0.999660 | + | 0.0260805i | \(0.00830263\pi\) | ||||
−0.999660 | + | 0.0260805i | \(0.991697\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 808.292i | − | 0.773236i | −0.922240 | − | 0.386618i | \(-0.873643\pi\) | ||
0.922240 | − | 0.386618i | \(-0.126357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1844.29 | − | 1415.51i | −1.71414 | − | 1.31562i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 728.059 | 0.657796 | 0.328898 | − | 0.944366i | \(-0.393323\pi\) | ||||
0.328898 | + | 0.944366i | \(0.393323\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1488.85 | −1.30831 | −0.654157 | − | 0.756358i | \(-0.726977\pi\) | ||||
−0.654157 | + | 0.756358i | \(0.726977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 437.497 | + | 335.783i | 0.374102 | + | 0.287127i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 38.0071i | − | 0.0316408i | −0.999875 | − | 0.0158204i | \(-0.994964\pi\) | ||
0.999875 | − | 0.0158204i | \(-0.00503600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2179.31i | − | 1.76714i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 473.591 | + | 1769.09i | 0.374218 | + | 1.39788i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −166.673 | −0.128394 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1232.08 | −0.925683 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 285.940 | − | 372.556i | 0.209613 | − | 0.273107i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4455.23i | − | 3.18790i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 226.671i | − | 0.158376i | −0.996860 | − | 0.0791882i | \(-0.974767\pi\) | ||
0.996860 | − | 0.0791882i | \(-0.0252328\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1427.98 | − | 1860.54i | 0.974626 | − | 1.26986i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1580.10 | −1.05385 | −0.526925 | − | 0.849912i | \(-0.676655\pi\) | ||||
−0.526925 | + | 0.849912i | \(0.676655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1304.40 | 0.850421 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2773.96 | + | 1150.13i | 1.76848 | + | 0.733243i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 543.435i | 0.338896i | 0.985539 | + | 0.169448i | \(0.0541985\pi\) | ||||
−0.985539 | + | 0.169448i | \(0.945801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 29.7527i | 0.0181554i | 0.999959 | + | 0.00907768i | \(0.00288955\pi\) | ||||
−0.999959 | + | 0.00907768i | \(0.997110\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1767.89 | + | 1356.87i | 1.05591 | + | 0.810422i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −674.603 | −0.394498 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2620.86 | 1.50104 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 387.276 | + | 297.238i | 0.217293 | + | 0.166774i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 489.426i | 0.269096i | 0.990907 | + | 0.134548i | \(0.0429583\pi\) | ||||
−0.990907 | + | 0.134548i | \(0.957042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 396.852i | 0.213877i | 0.994266 | + | 0.106938i | \(0.0341047\pi\) | ||||
−0.994266 | + | 0.106938i | \(0.965895\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 207.961 | − | 55.6718i | 0.109887 | − | 0.0294170i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1873.04 | −0.970618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2542.51 | 1.29245 | 0.646224 | − | 0.763148i | \(-0.276347\pi\) | ||||
0.646224 | + | 0.763148i | \(0.276347\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1146.69 | − | 1494.03i | 0.571938 | − | 0.745187i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2128.31i | 1.04183i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1807.94i | 0.868765i | 0.900728 | + | 0.434383i | \(0.143033\pi\) | ||||
−0.900728 | + | 0.434383i | \(0.856967\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −673.486 | + | 877.496i | −0.317763 | + | 0.414018i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.5944 | −0.0118596 | −0.00592980 | − | 0.999982i | \(-0.501888\pi\) | ||||
−0.00592980 | + | 0.999982i | \(0.501888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2403.78 | 1.09412 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1627.53 | + | 435.694i | −0.727837 | + | 0.194844i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 677.278i | − | 0.297644i | −0.988864 | − | 0.148822i | \(-0.952452\pi\) | ||
0.988864 | − | 0.148822i | \(-0.0475482\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6963.89i | 3.00812i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3303.73 | + | 2535.64i | 1.40296 | + | 1.07678i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3240.41 | −1.35307 | −0.676535 | − | 0.736411i | \(-0.736519\pi\) | ||||
−0.676535 | + | 0.736411i | \(0.736519\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2123.69 | 0.872114 | 0.436057 | − | 0.899919i | \(-0.356375\pi\) | ||||
0.436057 | + | 0.899919i | \(0.356375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2670.67 | + | 2049.76i | 1.07881 | + | 0.827994i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2271.78i | − | 0.902836i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 79.3014i | 0.0310112i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2709.05 | − | 1123.22i | −1.04261 | − | 0.432286i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3080.73 | 1.16709 | 0.583543 | − | 0.812082i | \(-0.301666\pi\) | ||||
0.583543 | + | 0.812082i | \(0.301666\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2614.09 | −0.974955 | −0.487478 | − | 0.873135i | \(-0.662083\pi\) | ||||
−0.487478 | + | 0.873135i | \(0.662083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4593.16 | − | 5984.50i | 1.68679 | − | 2.19774i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4223.51i | − | 1.52748i | −0.645527 | − | 0.763738i | \(-0.723362\pi\) | ||
0.645527 | − | 0.763738i | \(-0.276638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 783.071i | − | 0.278947i | −0.990226 | − | 0.139474i | \(-0.955459\pi\) | ||
0.990226 | − | 0.139474i | \(-0.0445410\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3028.41 | − | 3945.76i | 1.06272 | − | 1.38464i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2559.52 | −0.884941 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1934.56 | −0.659101 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −710.893 | − | 2655.53i | −0.238698 | − | 0.891652i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 620.622i | − | 0.205403i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3515.60i | 1.14703i | 0.819195 | + | 0.573516i | \(0.194421\pi\) | ||||
−0.819195 | + | 0.573516i | \(0.805579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −923.705 | − | 708.952i | −0.297142 | − | 0.228059i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9661.19 | −3.06459 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1829.20 | 0.572232 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 447.131 | + | 343.177i | 0.137965 | + | 0.105889i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 540.834i | − | 0.164617i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1864.10i | 0.559772i | 0.960033 | + | 0.279886i | \(0.0902967\pi\) | ||||
−0.960033 | + | 0.279886i | \(0.909703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2326.07 | − | 8688.98i | −0.689205 | − | 2.57451i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2871.51 | −0.839600 | −0.419800 | − | 0.907617i | \(-0.637900\pi\) | ||||
−0.419800 | + | 0.907617i | \(0.637900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3048.58 | 0.879720 | 0.439860 | − | 0.898066i | \(-0.355028\pi\) | ||||
0.439860 | + | 0.898066i | \(0.355028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 657.725 | − | 856.960i | 0.187338 | − | 0.244086i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2078.46i | 0.584398i | 0.956358 | + | 0.292199i | \(0.0943870\pi\) | ||||
−0.956358 | + | 0.292199i | \(0.905613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9180.11i | − | 2.54827i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1947.47 | + | 2537.39i | −0.533763 | + | 0.695448i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2778.79 | 0.752072 | 0.376036 | − | 0.926605i | \(-0.377287\pi\) | ||||
0.376036 | + | 0.926605i | \(0.377287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2838.97 | −0.758815 | −0.379408 | − | 0.925230i | \(-0.623872\pi\) | ||||
−0.379408 | + | 0.925230i | \(0.623872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3755.30 | + | 496.589i | 0.991370 | + | 0.131095i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2011.00i | − | 0.524401i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4232.63i | 1.09035i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 842.478 | + | 646.610i | 0.214417 | + | 0.164567i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5339.24 | 1.34267 | 0.671334 | − | 0.741155i | \(-0.265722\pi\) | ||||
0.671334 | + | 0.741155i | \(0.265722\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1012.63 | 0.251634 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −703.494 | − | 539.938i | −0.172763 | − | 0.132597i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6223.99i | 1.51067i | 0.655339 | + | 0.755335i | \(0.272526\pi\) | ||||
−0.655339 | + | 0.755335i | \(0.727474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2218.61i | 0.532270i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3193.56 | − | 854.926i | 0.757381 | − | 0.202753i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4779.81 | 1.12067 | 0.560334 | − | 0.828267i | \(-0.310673\pi\) | ||||
0.560334 | + | 0.828267i | \(0.310673\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7758.05 | −1.79839 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1436.53 | + | 1871.67i | −0.329266 | + | 0.429006i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3916.03i | 0.887601i | 0.896126 | + | 0.443800i | \(0.146370\pi\) | ||||
−0.896126 | + | 0.443800i | \(0.853630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6412.78i | − | 1.43745i | −0.695295 | − | 0.718725i | \(-0.744726\pi\) | ||
0.695295 | − | 0.718725i | \(-0.255274\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4485.67 | + | 5844.45i | −0.994450 | + | 1.29568i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3313.35 | 0.726555 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3745.22 | −0.812376 | −0.406188 | − | 0.913789i | \(-0.633142\pi\) | ||||
−0.406188 | + | 0.913789i | \(0.633142\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2282.33 | + | 610.986i | −0.489747 | + | 0.131107i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6656.43i | 1.41313i | 0.707648 | + | 0.706565i | \(0.249756\pi\) | ||||
−0.707648 | + | 0.706565i | \(0.750244\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6460.77i | 1.35708i | 0.734564 | + | 0.678539i | \(0.237387\pi\) | ||||
−0.734564 | + | 0.678539i | \(0.762613\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5505.62 | + | 4225.62i | 1.14430 | + | 0.878260i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1889.29 | 0.388576 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4849.42 | 0.987060 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3052.31 | − | 2342.68i | −0.614879 | − | 0.471925i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2620.84i | 0.522564i | 0.965263 | + | 0.261282i | \(0.0841453\pi\) | ||||
−0.965263 | + | 0.261282i | \(0.915855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 17155.2i | − | 3.38582i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −534.416 | + | 1288.94i | −0.104411 | + | 0.251824i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6906.09 | −1.33575 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9435.09 | 1.80674 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 167.503 | − | 218.242i | 0.0317584 | − | 0.0413785i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 13867.9i | − | 2.60353i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 952.063i | 0.176994i | 0.996076 | + | 0.0884969i | \(0.0282063\pi\) | ||||
−0.996076 | + | 0.0884969i | \(0.971794\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2557.18 | + | 3331.80i | −0.470787 | + | 0.613395i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −464.965 | −0.0847773 | −0.0423887 | − | 0.999101i | \(-0.513497\pi\) | ||||
−0.0423887 | + | 0.999101i | \(0.513497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5656.16 | 1.02142 | 0.510711 | − | 0.859752i | \(-0.329382\pi\) | ||||
0.510711 | + | 0.859752i | \(0.329382\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3123.97 | + | 11669.5i | 0.558780 | + | 2.08731i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4593.57i | 0.813883i | 0.913454 | + | 0.406941i | \(0.133405\pi\) | ||||
−0.913454 | + | 0.406941i | \(0.866595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1217.79i | 0.213741i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3001.08 | − | 2303.35i | −0.521818 | − | 0.400501i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 497.556 | 0.0857113 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22597.0 | −3.85678 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6137.09 | + | 4710.27i | 1.03786 | + | 0.796571i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8965.26i | 1.50234i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6709.02i | − | 1.11408i | −0.830485 | − | 0.557041i | \(-0.811937\pi\) | ||
0.830485 | − | 0.557041i | \(-0.188063\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −741.058 | − | 2768.21i | −0.121951 | − | 0.455546i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20489.1 | −3.34161 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3712.30 | −0.600064 | −0.300032 | − | 0.953929i | \(-0.596997\pi\) | ||||
−0.300032 | + | 0.953929i | \(0.596997\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −120.243 | + | 156.666i | −0.0192646 | + | 0.0251001i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 870.316i | − | 0.138212i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 5205.93i | − | 0.819516i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6894.66 | + | 8983.16i | −1.07593 | + | 1.40185i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6331.12 | 0.979459 | 0.489729 | − | 0.871874i | \(-0.337096\pi\) | ||||
0.489729 | + | 0.871874i | \(0.337096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8328.66 | −1.27743 | −0.638714 | − | 0.769444i | \(-0.720533\pi\) | ||||
−0.638714 | + | 0.769444i | \(0.720533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3644.70 | − | 8790.52i | 0.554245 | − | 1.33676i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1494.95i | 0.225406i | 0.993629 | + | 0.112703i | \(0.0359508\pi\) | ||||
−0.993629 | + | 0.112703i | \(0.964049\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4796.51i | 0.717104i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 687.030 | + | 527.302i | 0.101853 | + | 0.0781730i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2701.95 | 0.397223 | 0.198612 | − | 0.980078i | \(-0.436357\pi\) | ||||
0.198612 | + | 0.980078i | \(0.436357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2965.07 | 0.432289 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5078.68 | + | 3897.93i | 0.734329 | + | 0.563605i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2321.81i | − | 0.332956i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11089.3i | 1.57727i | 0.614861 | + | 0.788636i | \(0.289212\pi\) | ||||
−0.614861 | + | 0.788636i | \(0.710788\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2357.30 | + | 631.057i | −0.332564 | + | 0.0890285i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7576.49 | 1.06025 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1299.98 | −0.180456 | −0.0902282 | − | 0.995921i | \(-0.528760\pi\) | ||||
−0.0902282 | + | 0.995921i | \(0.528760\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14095.0 | + | 18364.6i | −1.94096 | + | 2.52891i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8305.33i | − | 1.13461i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2953.18i | − | 0.400250i | −0.979770 | − | 0.200125i | \(-0.935865\pi\) | ||
0.979770 | − | 0.200125i | \(-0.0641348\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −717.117 | + | 934.343i | −0.0964279 | + | 0.125637i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2647.22 | −0.353176 | −0.176588 | − | 0.984285i | \(-0.556506\pi\) | ||||
−0.176588 | + | 0.984285i | \(0.556506\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4449.92 | −0.589062 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11772.3 | + | 3151.49i | −1.54631 | + | 0.413952i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3585.34i | − | 0.467310i | −0.972320 | − | 0.233655i | \(-0.924931\pi\) | ||
0.972320 | − | 0.233655i | \(-0.0750687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 811.829i | 0.105002i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6513.22 | + | 4998.96i | 0.836001 | + | 0.641639i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13175.9 | 1.67835 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6502.91 | −0.822094 | −0.411047 | − | 0.911614i | \(-0.634837\pi\) | ||||
−0.411047 | + | 0.911614i | \(0.634837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5376.77 | − | 4126.73i | −0.674625 | − | 0.517781i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 6673.49i | − | 0.831068i | −0.909578 | − | 0.415534i | \(-0.863595\pi\) | ||
0.909578 | − | 0.415534i | \(-0.136405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5935.53i | 0.733672i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7795.68 | − | 13516.8i | −0.956470 | − | 1.65841i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1055.59 | 0.128560 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2660.34 | −0.321627 | −0.160814 | − | 0.986985i | \(-0.551412\pi\) | ||||
−0.160814 | + | 0.986985i | \(0.551412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1719.26 | − | 2240.05i | 0.206338 | − | 0.268841i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16753.7i | 1.99612i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4374.72i | − | 0.517461i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 94.1285 | − | 122.641i | 0.0110539 | − | 0.0144023i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8957.94 | 1.04445 | 0.522224 | − | 0.852808i | \(-0.325102\pi\) | ||||
0.522224 | + | 0.852808i | \(0.325102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12070.2 | 1.39730 | 0.698652 | − | 0.715461i | \(-0.253783\pi\) | ||||
0.698652 | + | 0.715461i | \(0.253783\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2994.56 | − | 11186.1i | −0.344209 | − | 1.28579i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2656.33i | 0.303179i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13543.4i | 1.53492i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2780.73 | + | 2134.24i | 0.312948 | + | 0.240191i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14197.2 | 1.58667 | 0.793334 | − | 0.608787i | \(-0.208344\pi\) | ||||
0.793334 | + | 0.608787i | \(0.208344\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7129.67 | −0.791294 | −0.395647 | − | 0.918403i | \(-0.629480\pi\) | ||||
−0.395647 | + | 0.918403i | \(0.629480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10803.2 | − | 8291.58i | −1.19075 | − | 0.913909i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6353.47i | − | 0.695487i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5206.56i | 0.566049i | 0.959113 | + | 0.283025i | \(0.0913378\pi\) | ||||
−0.959113 | + | 0.283025i | \(0.908662\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −655.992 | − | 2450.45i | −0.0708338 | − | 0.264598i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17034.3 | −1.82692 | −0.913459 | − | 0.406930i | \(-0.866599\pi\) | ||||
−0.913459 | + | 0.406930i | \(0.866599\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9719.01 | 1.03534 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1548.39 | − | 2017.42i | 0.163840 | − | 0.213470i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9312.78i | 0.978836i | 0.872049 | + | 0.489418i | \(0.162791\pi\) | ||||
−0.872049 | + | 0.489418i | \(0.837209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 898.905i | − | 0.0938532i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1255.52 | − | 1635.83i | 0.130219 | − | 0.169665i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30348.4 | 3.12693 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13276.6 | 1.35898 | 0.679488 | − | 0.733687i | \(-0.262202\pi\) | ||||
0.679488 | + | 0.733687i | \(0.262202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1033.35 | − | 428.444i | −0.105082 | − | 0.0435688i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 507.329i | 0.0512552i | 0.999672 | + | 0.0256276i | \(0.00815842\pi\) | ||||
−0.999672 | + | 0.0256276i | \(0.991842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4468.90i | 0.448569i | 0.974524 | + | 0.224284i | \(0.0720044\pi\) | ||||
−0.974524 | + | 0.224284i | \(0.927996\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7720.69 | + | 5925.70i | 0.769975 | + | 0.590963i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12258.9 | −1.21472 | −0.607358 | − | 0.794428i | \(-0.707771\pi\) | ||||
−0.607358 | + | 0.794428i | \(0.707771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20009.6 | 1.97006 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10480.3 | − | 8043.71i | −1.02528 | − | 0.786910i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 4489.12i | − | 0.436385i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 20788.8i | − | 2.00811i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9453.33 | + | 2530.68i | −0.907418 | + | 0.242918i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5781.56 | 0.551495 | 0.275747 | − | 0.961230i | \(-0.411075\pi\) | ||||
0.275747 | + | 0.961230i | \(0.411075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7199.13 | −0.682437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6733.30 | − | 8772.92i | 0.634318 | − | 0.826463i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15849.7i | 1.48391i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8699.77i | − | 0.809495i | −0.914429 | − | 0.404747i | \(-0.867359\pi\) | ||
0.914429 | − | 0.404747i | \(-0.132641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5719.76 | − | 7452.36i | 0.528950 | − | 0.689177i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6084.95 | −0.559287 | −0.279643 | − | 0.960104i | \(-0.590216\pi\) | ||||
−0.279643 | + | 0.960104i | \(0.590216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −976.313 | −0.0891905 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5552.25 | − | 1486.35i | 0.504152 | − | 0.134963i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4684.25i | − | 0.422772i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6970.12i | 0.625301i | 0.949868 | + | 0.312651i | \(0.101217\pi\) | ||||
−0.949868 | + | 0.312651i | \(0.898783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 105.501 | + | 80.9728i | 0.00940803 | + | 0.00722075i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15721.2 | −1.39359 | −0.696795 | − | 0.717271i | \(-0.745391\pi\) | ||||
−0.696795 | + | 0.717271i | \(0.745391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1133.26 | −0.0998604 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9908.43 | − | 7604.82i | −0.867947 | − | 0.666157i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11249.3i | 0.979602i | 0.871834 | + | 0.489801i | \(0.162931\pi\) | ||||
−0.871834 | + | 0.489801i | \(0.837069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2267.47i | 0.196296i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8087.11 | + | 3353.05i | 0.696013 | + | 0.288579i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17301.0 | 1.48033 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4265.58 | 0.362863 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2142.70 | + | 2791.75i | −0.181222 | + | 0.236116i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12276.2i | − | 1.03231i | −0.856496 | − | 0.516153i | \(-0.827364\pi\) | ||
0.856496 | − | 0.516153i | \(-0.172636\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 770.278i | − | 0.0644013i | −0.999481 | − | 0.0322007i | \(-0.989748\pi\) | ||
0.999481 | − | 0.0322007i | \(-0.0102516\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22031.6 | − | 28705.3i | 1.83150 | − | 2.38629i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 697.737 | 0.0576735 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1800.47 | −0.147980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5596.05 | − | 20904.0i | −0.457341 | − | 1.70839i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6130.51i | 0.498202i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15583.6i | 1.25933i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13357.0 | + | 10251.6i | 1.07337 | + | 0.823820i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 934.423 | 0.0746725 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14469.7 | 1.14991 | 0.574956 | − | 0.818184i | \(-0.305019\pi\) | ||||
0.574956 | + | 0.818184i | \(0.305019\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8753.90 | − | 6718.70i | −0.691834 | − | 0.530989i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 31867.9i | − | 2.50472i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1150.14i | 0.0899021i | 0.998989 | + | 0.0449511i | \(0.0143132\pi\) | ||||
−0.998989 | + | 0.0449511i | \(0.985687\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4523.74 | − | 16898.3i | −0.351673 | − | 1.31367i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7640.74 | 0.590756 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12867.5 | −0.989479 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7187.21 | + | 9364.33i | −0.549694 | + | 0.716205i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 24347.5i | − | 1.85213i | −0.377361 | − | 0.926066i | \(-0.623168\pi\) | ||
0.377361 | − | 0.926066i | \(-0.376832\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30615.7i | 2.31647i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 250.885 | − | 326.882i | 0.0188812 | − | 0.0246007i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15515.2 | 1.16144 | 0.580718 | − | 0.814105i | \(-0.302772\pi\) | ||||
0.580718 | + | 0.814105i | \(0.302772\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 813.518 | 0.0605752 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7613.23 | + | 13200.5i | 0.563890 | + | 0.977724i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 10960.4i | − | 0.807531i | −0.914863 | − | 0.403765i | \(-0.867701\pi\) | ||
0.914863 | − | 0.403765i | \(-0.132299\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24367.3i | − | 1.78588i | −0.450174 | − | 0.892941i | \(-0.648638\pi\) | ||
0.450174 | − | 0.892941i | \(-0.351362\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12698.8 | − | 9746.46i | −0.925830 | − | 0.710583i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33919.7 | 2.46008 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17109.4 | 1.23445 | 0.617223 | − | 0.786788i | \(-0.288258\pi\) | ||||
0.617223 | + | 0.786788i | \(0.288258\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10775.3 | + | 8270.17i | 0.773416 | + | 0.593604i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4272.34i | 0.305071i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3604.82i | − | 0.256083i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −37866.2 | + | 10136.9i | −2.67620 | + | 0.716426i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13267.9 | 0.932921 | 0.466460 | − | 0.884542i | \(-0.345529\pi\) | ||||
0.466460 | + | 0.884542i | \(0.345529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5460.57 | −0.382002 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13361.9 | + | 17409.4i | −0.930007 | + | 1.21172i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16312.5i | 1.12963i | 0.825216 | + | 0.564817i | \(0.191053\pi\) | ||||
−0.825216 | + | 0.564817i | \(0.808947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3567.53i | − | 0.245806i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2477.40 | + | 3227.84i | −0.169838 | + | 0.221284i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15038.9 | −1.02583 | −0.512915 | − | 0.858440i | \(-0.671434\pi\) | ||||
−0.512915 | + | 0.858440i | \(0.671434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4408.70 | −0.299226 | −0.149613 | − | 0.988745i | \(-0.547803\pi\) | ||||
−0.149613 | + | 0.988745i | \(0.547803\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24966.3 | + | 6683.57i | −1.68608 | + | 0.451370i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 26372.0i | − | 1.77219i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1271.09i | 0.0849950i | 0.999097 | + | 0.0424975i | \(0.0135315\pi\) | ||||
−0.999097 | + | 0.0424975i | \(0.986469\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10550.4 | + | 8097.53i | 0.702009 | + | 0.538799i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29091.2 | −1.92619 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21306.8 | −1.40387 | −0.701937 | − | 0.712239i | \(-0.747681\pi\) | ||||
−0.701937 | + | 0.712239i | \(0.747681\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7974.31 | + | 6120.36i | 0.522854 | + | 0.401295i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 26964.4i | − | 1.75940i | −0.475533 | − | 0.879698i | \(-0.657745\pi\) | ||
0.475533 | − | 0.879698i | \(-0.342255\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17633.6i | 1.14500i | 0.819905 | + | 0.572500i | \(0.194026\pi\) | ||||
−0.819905 | + | 0.572500i | \(0.805974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5470.95 | + | 13195.2i | −0.353529 | + | 0.852665i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9491.56 | −0.610387 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 53718.1 | 3.43796 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1963.46 | + | 2558.22i | −0.125060 | + | 0.162943i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 846.277i | 0.0536459i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 168.115i | 0.0106062i | 0.999986 | + | 0.00530312i | \(0.00168804\pi\) | ||||
−0.999986 | + | 0.00530312i | \(0.998312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11122.3 | − | 14491.4i | 0.698373 | − | 0.909921i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4851.75 | 0.303206 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6372.74 | −0.396385 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1564.63 | + | 5844.63i | 0.0968633 | + | 0.361831i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 823.334i | − | 0.0507328i | −0.999678 | − | 0.0253664i | \(-0.991925\pi\) | ||
0.999678 | − | 0.0253664i | \(-0.00807525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17860.7i | − | 1.09543i | −0.836666 | − | 0.547713i | \(-0.815499\pi\) | ||
0.836666 | − | 0.547713i | \(-0.184501\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 39823.6 | + | 30565.0i | 2.43109 | + | 1.86589i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2518.14 | −0.153011 | −0.0765057 | − | 0.997069i | \(-0.524376\pi\) | ||||
−0.0765057 | + | 0.997069i | \(0.524376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7971.26 | 0.482126 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7540.01 | − | 5787.03i | −0.453942 | − | 0.348405i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18937.3i | 1.13488i | 0.823416 | + | 0.567439i | \(0.192066\pi\) | ||||
−0.823416 | + | 0.567439i | \(0.807934\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 33821.1i | − | 2.01756i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −757.377 | − | 2829.17i | −0.0449743 | − | 0.168001i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10400.8 | −0.614807 | −0.307404 | − | 0.951579i | \(-0.599460\pi\) | ||||
−0.307404 | + | 0.951579i | \(0.599460\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3225.88 | 0.189822 | 0.0949108 | − | 0.995486i | \(-0.469743\pi\) | ||||
0.0949108 | + | 0.995486i | \(0.469743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1711.03 | + | 2229.33i | −0.100228 | + | 0.130588i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27919.9i | 1.62810i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12466.9i | 0.723717i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5897.43 | − | 7683.85i | 0.340819 | − | 0.444058i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6443.81 | 0.370731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1215.38 | 0.0696128 | 0.0348064 | − | 0.999394i | \(-0.488919\pi\) | ||||
0.0348064 | + | 0.999394i | \(0.488919\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17901.2 | + | 43175.1i | −1.02076 | + | 2.46194i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3901.92i | − | 0.221511i | −0.993848 | − | 0.110755i | \(-0.964673\pi\) | ||
0.993848 | − | 0.110755i | \(-0.0353270\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 15478.8i | − | 0.874846i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11836.4 | + | 9084.58i | 0.666040 | + | 0.511192i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31547.8 | 1.76742 | 0.883708 | − | 0.468039i | \(-0.155040\pi\) | ||||
0.883708 | + | 0.468039i | \(0.155040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11631.9 | −0.648805 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12566.3 | − | 9644.76i | −0.697867 | − | 0.535620i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24584.8i | 1.35937i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2791.51i | − | 0.153682i | −0.997043 | − | 0.0768408i | \(-0.975517\pi\) | ||
0.997043 | − | 0.0768408i | \(-0.0244833\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5422.31 | + | 1451.57i | −0.297224 | + | 0.0795679i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −636.838 | −0.0347578 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 720.657 | 0.0391633 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6575.62 | − | 8567.48i | 0.355812 | − | 0.463593i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9830.35i | 0.529653i | 0.964296 | + | 0.264827i | \(0.0853148\pi\) | ||||
−0.964296 | + | 0.264827i | \(0.914685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6623.06i | − | 0.355325i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29043.0 | + | 37840.6i | −1.55152 | + | 2.02150i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1106.74 | 0.0588730 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3029.84 | 0.160491 | 0.0802455 | − | 0.996775i | \(-0.474430\pi\) | ||||
0.0802455 | + | 0.996775i | \(0.474430\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16055.0 | − | 4297.98i | 0.846850 | − | 0.226704i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 8909.65i | − | 0.467979i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 14439.4i | − | 0.755251i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11454.2 | − | 8791.24i | −0.596606 | − | 0.457901i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28359.2 | 1.47096 | 0.735479 | − | 0.677548i | \(-0.236957\pi\) | ||||
0.735479 | + | 0.677548i | \(0.236957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16896.1 | −0.872735 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11702.3 | + | 8981.64i | 0.601955 | + | 0.462006i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40792.1i | 2.08963i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24702.5i | 1.26020i | 0.776514 | + | 0.630100i | \(0.216986\pi\) | ||||
−0.776514 | + | 0.630100i | \(0.783014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13908.4 | − | 13927.6i | −0.706619 | − | 0.707594i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3598.96 | 0.182096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30507.1 | −1.53725 | −0.768627 | − | 0.639698i | \(-0.779060\pi\) | ||||
−0.768627 | + | 0.639698i | \(0.779060\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6362.19 | + | 8289.40i | −0.319283 | + | 0.415999i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 9520.36i | − | 0.475831i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 4105.52i | − | 0.204363i | −0.994766 | − | 0.102181i | \(-0.967418\pi\) | ||
0.994766 | − | 0.102181i | \(-0.0325822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13390.7 | − | 17447.0i | 0.663860 | − | 0.864954i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4140.87 | 0.204460 | 0.102230 | − | 0.994761i | \(-0.467402\pi\) | ||||
0.102230 | + | 0.994761i | \(0.467402\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10475.8 | −0.515175 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1427.04 | − | 5330.68i | −0.0698964 | − | 0.261097i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 15218.9i | − | 0.742440i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 22033.0i | − | 1.07057i | −0.844672 | − | 0.535284i | \(-0.820204\pi\) | ||
0.844672 | − | 0.535284i | \(-0.179796\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22008.5 | − | 16891.7i | −1.06512 | − | 0.817487i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8494.36 | −0.409459 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37525.3 | 1.80169 | 0.900847 | − | 0.434137i | \(-0.142947\pi\) | ||||
0.900847 | + | 0.434137i | \(0.142947\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4174.07 | − | 3203.64i | −0.199617 | − | 0.153208i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32680.8i | − | 1.55674i | −0.627806 | − | 0.778369i | \(-0.716047\pi\) | ||
0.627806 | − | 0.778369i | \(-0.283953\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31122.1i | 1.47667i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1191.62 | + | 4451.27i | 0.0563177 | + | 0.210374i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −54363.8 | −2.55928 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27457.2 | −1.28756 | −0.643779 | − | 0.765212i | \(-0.722634\pi\) | ||||
−0.643779 | + | 0.765212i | \(0.722634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19690.8 | − | 25655.4i | 0.919775 | − | 1.19839i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8851.25i | 0.411847i | 0.978568 | + | 0.205923i | \(0.0660197\pi\) | ||||
−0.978568 | + | 0.205923i | \(0.933980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 29152.7i | − | 1.35122i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7019.01 | − | 9145.18i | 0.324074 | − | 0.422241i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5639.95 | −0.259399 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2228.72 | −0.102113 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15868.7 | − | 6579.42i | −0.724265 | − | 0.300293i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54420.8i | 2.47434i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3892.16i | − | 0.176290i | −0.996108 | − | 0.0881452i | \(-0.971906\pi\) | ||
0.996108 | − | 0.0881452i | \(-0.0280939\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19702.5 | − | 15121.8i | −0.889007 | − | 0.682321i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −794.479 | −0.0357123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −43946.6 | −1.96796 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31978.8 | + | 24544.1i | 1.42663 | + | 1.09495i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 16462.8i | − | 0.731672i | −0.930679 | − | 0.365836i | \(-0.880783\pi\) | ||
0.930679 | − | 0.365836i | \(-0.119217\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3419.74i | 0.151417i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11842.8 | − | 3170.35i | 0.522403 | − | 0.139849i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1078.84 | 0.0474116 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45555.0 | −1.99454 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12389.1 | − | 16142.0i | 0.540418 | − | 0.704119i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2287.89i | − | 0.0994287i | −0.998763 | − | 0.0497144i | \(-0.984169\pi\) | ||
0.998763 | − | 0.0497144i | \(-0.0158311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2892.28i | 0.125230i | 0.998038 | + | 0.0626150i | \(0.0199440\pi\) | ||||
−0.998038 | + | 0.0626150i | \(0.980056\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20288.1 | + | 26433.6i | −0.875195 | + | 1.14031i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38697.8 | −1.66322 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28165.8 | −1.20612 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 36980.0 | − | 9899.67i | 1.57776 | − | 0.422372i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 37351.7i | − | 1.58780i | −0.608049 | − | 0.793899i | \(-0.708048\pi\) | ||
0.608049 | − | 0.793899i | \(-0.291952\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25859.6i | − | 1.09527i | −0.836717 | − | 0.547636i | \(-0.815528\pi\) | ||
0.836717 | − | 0.547636i | \(-0.184472\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13657.7 | − | 10482.4i | −0.576364 | − | 0.442365i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32182.0 | 1.35318 | 0.676589 | − | 0.736361i | \(-0.263457\pi\) | ||||
0.676589 | + | 0.736361i | \(0.263457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16710.7 | 0.700105 | 0.350053 | − | 0.936730i | \(-0.386164\pi\) | ||||
0.350053 | + | 0.936730i | \(0.386164\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15437.9 | + | 11848.7i | 0.644445 | + | 0.494617i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 749.133i | 0.0311595i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 547.831i | − | 0.0227048i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11340.8 | + | 4702.08i | 0.468333 | + | 0.194179i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19182.4 | −0.789334 | −0.394667 | − | 0.918824i | \(-0.629140\pi\) | ||||
−0.394667 | + | 0.918824i | \(0.629140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9396.22 | 0.385265 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21058.9 | − | 27438.0i | 0.860388 | − | 1.12101i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 51451.3i | 2.09465i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25754.8i | 1.04480i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20439.9 | − | 26631.4i | 0.826260 | − | 1.07655i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10806.4 | 0.435298 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16306.8 | 0.654552 | 0.327276 | − | 0.944929i | \(-0.393869\pi\) | ||||
0.327276 | + | 0.944929i | \(0.393869\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9325.75 | − | 34836.2i | −0.373022 | − | 1.39342i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42374.8i | 1.68903i | 0.535534 | + | 0.844514i | \(0.320110\pi\) | ||||
−0.535534 | + | 0.844514i | \(0.679890\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21561.9i | 0.856442i | 0.903674 | + | 0.428221i | \(0.140860\pi\) | ||||
−0.903674 | + | 0.428221i | \(0.859140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7787.69 | − | 5977.12i | −0.308251 | − | 0.236585i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16679.1 | 0.657894 | 0.328947 | − | 0.944348i | \(-0.393306\pi\) | ||||
0.328947 | + | 0.944348i | \(0.393306\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14496.7 | 0.569829 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19989.4 | − | 15342.1i | −0.783018 | − | 0.600974i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6122.23i | 0.238990i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64928.7i | 2.52586i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5170.19 | + | 19313.2i | 0.200440 | + | 0.748741i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −93129.6 | −3.59812 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14094.6 | −0.542690 | −0.271345 | − | 0.962482i | \(-0.587468\pi\) | ||||
−0.271345 | + | 0.962482i | \(0.587468\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8291.53 | − | 10803.2i | 0.318164 | − | 0.414541i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 12553.3i | − | 0.480057i | −0.970766 | − | 0.240028i | \(-0.922843\pi\) | ||
0.970766 | − | 0.240028i | \(-0.0771568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43192.3i | 1.64613i | 0.567944 | + | 0.823067i | \(0.307739\pi\) | ||||
−0.567944 | + | 0.823067i | \(0.692261\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −54273.8 | + | 70714.2i | −2.06146 | + | 2.68591i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17930.0 | 0.678725 | 0.339362 | − | 0.940656i | \(-0.389789\pi\) | ||||
0.339362 | + | 0.940656i | \(0.389789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4738.20 | −0.178756 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6280.67 | − | 3622.30i | 0.236151 | − | 0.136197i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 26763.3i | − | 1.00291i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 69358.8i | − | 2.59040i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28467.1 | + | 21848.7i | 1.05963 | + | 0.813276i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10714.8 | 0.397508 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2890.00 | 0.106859 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −38891.6 | − | 29849.7i | −1.43326 | − | 1.10004i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45456.2i | 1.66963i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5289.85i | − | 0.193657i | −0.995301 | − | 0.0968283i | \(-0.969130\pi\) | ||
0.995301 | − | 0.0968283i | \(-0.0308698\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1380.90 | + | 369.671i | −0.0503868 | + | 0.0134887i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4585.72 | −0.166774 | −0.0833872 | − | 0.996517i | \(-0.526574\pi\) | ||||
−0.0833872 | + | 0.996517i | \(0.526574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2032.74 | 0.0736843 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −43873.9 | + | 57163.9i | −1.58516 | + | 2.06533i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33029.6i | 1.18946i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43234.5i | 1.55188i | 0.630809 | + | 0.775939i | \(0.282723\pi\) | ||||
−0.630809 | + | 0.775939i | \(0.717277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3012.03 | − | 3924.42i | 0.107763 | − | 0.140406i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15199.8 | 0.542046 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35358.9 | 1.25686 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21081.5 | − | 5643.59i | 0.746935 | − | 0.199957i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 695.704i | 0.0245697i | 0.999925 | + | 0.0122849i | \(0.00391050\pi\) | ||||
−0.999925 | + | 0.0122849i | \(0.996090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 5862.80i | − | 0.206386i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1916.60 | + | 1471.01i | 0.0672525 | + | 0.0516169i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1697.39 | −0.0593698 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21092.2 | −0.735381 | −0.367691 | − | 0.929948i | \(-0.619851\pi\) | ||||
−0.367691 | + | 0.929948i | \(0.619851\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23314.8 | − | 17894.3i | −0.810277 | − | 0.621896i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 11392.6i | − | 0.394676i | −0.980336 | − | 0.197338i | \(-0.936770\pi\) | ||
0.980336 | − | 0.197338i | \(-0.0632296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 9202.33i | − | 0.317783i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24041.7 | − | 57985.4i | 0.827595 | − | 1.99605i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3540.41 | 0.121487 | 0.0607433 | − | 0.998153i | \(-0.480653\pi\) | ||||
0.0607433 | + | 0.998153i | \(0.480653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7357.67 | −0.251676 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14532.6 | − | 18934.8i | 0.495535 | − | 0.645640i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29360.7i | 0.997992i | 0.866604 | + | 0.498996i | \(0.166298\pi\) | ||||
−0.866604 | + | 0.498996i | \(0.833702\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 65940.9i | 2.23434i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3852.72 | − | 5019.77i | 0.130137 | − | 0.169557i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11359.7 | 0.382505 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22133.5 | 0.742959 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5083.40 | + | 18989.0i | 0.170104 | + | 0.635421i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 55952.9i | − | 1.86652i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27094.7i | 0.901043i | 0.892766 | + | 0.450521i | \(0.148762\pi\) | ||||
−0.892766 | + | 0.450521i | \(0.851238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2050.94 | − | 1574.11i | −0.0679934 | − | 0.0521856i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10806.5 | −0.357154 | −0.178577 | − | 0.983926i | \(-0.557149\pi\) | ||||
−0.178577 | + | 0.983926i | \(0.557149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 621.934 | 0.0204916 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 93145.2 | + | 71489.9i | 3.05952 | + | 2.34821i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 14327.6i | − | 0.469172i | −0.972095 | − | 0.234586i | \(-0.924627\pi\) | ||
0.972095 | − | 0.234586i | \(-0.0753734\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4515.99i | 0.147428i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10395.4 | − | 38831.7i | −0.338327 | − | 1.26381i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25691.9 | −0.833617 | −0.416808 | − | 0.908994i | \(-0.636851\pi\) | ||||
−0.416808 | + | 0.908994i | \(0.636851\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 90401.5 | 2.92430 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28363.3 | − | 36955.0i | 0.914706 | − | 1.19178i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 45956.3i | − | 1.47758i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49378.3i | 1.58280i | 0.611300 | + | 0.791399i | \(0.290647\pi\) | ||||
−0.611300 | + | 0.791399i | \(0.709353\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21225.3 | + | 27654.7i | −0.678311 | + | 0.883782i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16761.1 | 0.534034 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22705.1 | −0.721241 | −0.360621 | − | 0.932713i | \(-0.617435\pi\) | ||||
−0.360621 | + | 0.932713i | \(0.617435\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5703.10 | + | 13755.1i | −0.180619 | + | 0.435627i |
(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.b.383.3 | yes | 12 | |
3.2 | odd | 2 | 384.4.c.c.383.9 | yes | 12 | ||
4.3 | odd | 2 | 384.4.c.c.383.10 | yes | 12 | ||
8.3 | odd | 2 | 384.4.c.a.383.3 | ✓ | 12 | ||
8.5 | even | 2 | 384.4.c.d.383.10 | yes | 12 | ||
12.11 | even | 2 | inner | 384.4.c.b.383.4 | yes | 12 | |
16.3 | odd | 4 | 768.4.f.h.383.4 | 12 | |||
16.5 | even | 4 | 768.4.f.g.383.4 | 12 | |||
16.11 | odd | 4 | 768.4.f.e.383.9 | 12 | |||
16.13 | even | 4 | 768.4.f.f.383.9 | 12 | |||
24.5 | odd | 2 | 384.4.c.a.383.4 | yes | 12 | ||
24.11 | even | 2 | 384.4.c.d.383.9 | yes | 12 | ||
48.5 | odd | 4 | 768.4.f.h.383.3 | 12 | |||
48.11 | even | 4 | 768.4.f.f.383.10 | 12 | |||
48.29 | odd | 4 | 768.4.f.e.383.10 | 12 | |||
48.35 | even | 4 | 768.4.f.g.383.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.c.a.383.3 | ✓ | 12 | 8.3 | odd | 2 | ||
384.4.c.a.383.4 | yes | 12 | 24.5 | odd | 2 | ||
384.4.c.b.383.3 | yes | 12 | 1.1 | even | 1 | trivial | |
384.4.c.b.383.4 | yes | 12 | 12.11 | even | 2 | inner | |
384.4.c.c.383.9 | yes | 12 | 3.2 | odd | 2 | ||
384.4.c.c.383.10 | yes | 12 | 4.3 | odd | 2 | ||
384.4.c.d.383.9 | yes | 12 | 24.11 | even | 2 | ||
384.4.c.d.383.10 | yes | 12 | 8.5 | even | 2 | ||
768.4.f.e.383.9 | 12 | 16.11 | odd | 4 | |||
768.4.f.e.383.10 | 12 | 48.29 | odd | 4 | |||
768.4.f.f.383.9 | 12 | 16.13 | even | 4 | |||
768.4.f.f.383.10 | 12 | 48.11 | even | 4 | |||
768.4.f.g.383.3 | 12 | 48.35 | even | 4 | |||
768.4.f.g.383.4 | 12 | 16.5 | even | 4 | |||
768.4.f.h.383.3 | 12 | 48.5 | odd | 4 | |||
768.4.f.h.383.4 | 12 | 16.3 | odd | 4 |