Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(361,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.k (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(104.079369250\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.361 |
Dual form | 1764.4.k.j.1549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | + | 3.46410i | 0.178885 | + | 0.309839i | 0.941499 | − | 0.337016i | \(-0.109418\pi\) |
−0.762614 | + | 0.646854i | \(0.776084\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.0000 | + | 17.3205i | −0.274101 | + | 0.474757i | −0.969908 | − | 0.243472i | \(-0.921714\pi\) |
0.695807 | + | 0.718229i | \(0.255047\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −0.0853385 | −0.0426692 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426692 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.0000 | − | 20.7846i | 0.171202 | − | 0.296530i | −0.767639 | − | 0.640883i | \(-0.778568\pi\) |
0.938840 | + | 0.344353i | \(0.111902\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.0000 | − | 38.1051i | −0.265639 | − | 0.460101i | 0.702092 | − | 0.712087i | \(-0.252250\pi\) |
−0.967731 | + | 0.251986i | \(0.918916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 36.0000 | + | 62.3538i | 0.326370 | + | 0.565290i | 0.981789 | − | 0.189976i | \(-0.0608410\pi\) |
−0.655418 | + | 0.755266i | \(0.727508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 54.5000 | − | 94.3968i | 0.436000 | − | 0.755174i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 38.0000 | 0.243325 | 0.121662 | − | 0.992572i | \(-0.461177\pi\) | ||||
0.121662 | + | 0.992572i | \(0.461177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −92.0000 | + | 159.349i | −0.533022 | + | 0.923222i | 0.466234 | + | 0.884661i | \(0.345610\pi\) |
−0.999256 | + | 0.0385601i | \(0.987723\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.0000 | + | 25.9808i | 0.0666482 | + | 0.115438i | 0.897424 | − | 0.441169i | \(-0.145436\pi\) |
−0.830776 | + | 0.556607i | \(0.812103\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 216.000 | 0.822769 | 0.411385 | − | 0.911462i | \(-0.365045\pi\) | ||||
0.411385 | + | 0.911462i | \(0.365045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 260.000 | + | 450.333i | 0.806913 | + | 1.39761i | 0.914992 | + | 0.403472i | \(0.132197\pi\) |
−0.108079 | + | 0.994142i | \(0.534470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −73.0000 | + | 126.440i | −0.189195 | + | 0.327695i | −0.944982 | − | 0.327122i | \(-0.893921\pi\) |
0.755787 | + | 0.654817i | \(0.227254\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −80.0000 | −0.196131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 230.000 | − | 398.372i | 0.507516 | − | 0.879044i | −0.492446 | − | 0.870343i | \(-0.663897\pi\) |
0.999962 | − | 0.00870069i | \(-0.00276955\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −314.000 | − | 543.864i | −0.659075 | − | 1.14155i | −0.980855 | − | 0.194737i | \(-0.937615\pi\) |
0.321780 | − | 0.946814i | \(-0.395719\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.00000 | − | 13.8564i | −0.0152658 | − | 0.0264412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −278.000 | + | 481.510i | −0.506912 | + | 0.877997i | 0.493056 | + | 0.869998i | \(0.335880\pi\) |
−0.999968 | + | 0.00799979i | \(0.997454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −592.000 | −0.989542 | −0.494771 | − | 0.869023i | \(-0.664748\pi\) | ||||
−0.494771 | + | 0.869023i | \(0.664748\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −512.000 | + | 886.810i | −0.820891 | + | 1.42183i | 0.0841280 | + | 0.996455i | \(0.473190\pi\) |
−0.905019 | + | 0.425371i | \(0.860144\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 52.0000 | + | 90.0666i | 0.0740564 | + | 0.128269i | 0.900676 | − | 0.434492i | \(-0.143072\pi\) |
−0.826619 | + | 0.562762i | \(0.809739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 324.000 | 0.428477 | 0.214239 | − | 0.976781i | \(-0.431273\pi\) | ||||
0.214239 | + | 0.976781i | \(0.431273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 96.0000 | 0.122502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 448.000 | + | 775.959i | 0.533572 | + | 0.924174i | 0.999231 | + | 0.0392095i | \(0.0124840\pi\) |
−0.465659 | + | 0.884964i | \(0.654183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 88.0000 | − | 152.420i | 0.0950380 | − | 0.164611i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −920.000 | −0.963009 | −0.481504 | − | 0.876444i | \(-0.659909\pi\) | ||||
−0.481504 | + | 0.876444i | \(0.659909\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 554.000 | − | 959.556i | 0.545793 | − | 0.945341i | −0.452764 | − | 0.891630i | \(-0.649562\pi\) |
0.998557 | − | 0.0537102i | \(-0.0171047\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −724.000 | − | 1254.00i | −0.692600 | − | 1.19962i | −0.970983 | − | 0.239149i | \(-0.923132\pi\) |
0.278383 | − | 0.960470i | \(-0.410202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 658.000 | + | 1139.69i | 0.594498 | + | 1.02970i | 0.993618 | + | 0.112802i | \(0.0359824\pi\) |
−0.399120 | + | 0.916899i | \(0.630684\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 43.0000 | − | 74.4782i | 0.0377858 | − | 0.0654469i | −0.846514 | − | 0.532366i | \(-0.821303\pi\) |
0.884300 | + | 0.466919i | \(0.154636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1778.00 | −1.48018 | −0.740089 | − | 0.672509i | \(-0.765217\pi\) | ||||
−0.740089 | + | 0.672509i | \(0.765217\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −144.000 | + | 249.415i | −0.116766 | + | 0.202244i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 465.500 | + | 806.270i | 0.349737 | + | 0.605762i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 936.000 | 0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −928.000 | −0.648399 | −0.324200 | − | 0.945989i | \(-0.605095\pi\) | ||||
−0.324200 | + | 0.945989i | \(0.605095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 702.000 | + | 1215.90i | 0.468199 | + | 0.810944i | 0.999339 | − | 0.0363397i | \(-0.0115698\pi\) |
−0.531141 | + | 0.847284i | \(0.678236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −685.000 | + | 1186.45i | −0.427179 | + | 0.739895i | −0.996621 | − | 0.0821359i | \(-0.973826\pi\) |
0.569442 | + | 0.822031i | \(0.307159\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 516.000 | 0.314867 | 0.157434 | − | 0.987530i | \(-0.449678\pi\) | ||||
0.157434 | + | 0.987530i | \(0.449678\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 40.0000 | − | 69.2820i | 0.0233914 | − | 0.0405151i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 76.0000 | + | 131.636i | 0.0435273 | + | 0.0753915i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 695.000 | + | 1203.78i | 0.382125 | + | 0.661860i | 0.991366 | − | 0.131125i | \(-0.0418591\pi\) |
−0.609241 | + | 0.792985i | \(0.708526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −68.0000 | + | 117.779i | −0.0366474 | + | 0.0634752i | −0.883767 | − | 0.467927i | \(-0.845001\pi\) |
0.847120 | + | 0.531402i | \(0.178335\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −736.000 | −0.381400 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 74.0000 | − | 128.172i | 0.0376168 | − | 0.0651543i | −0.846604 | − | 0.532223i | \(-0.821357\pi\) |
0.884221 | + | 0.467069i | \(0.154690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 606.000 | + | 1049.62i | 0.291200 | + | 0.504373i | 0.974094 | − | 0.226145i | \(-0.0726122\pi\) |
−0.682894 | + | 0.730518i | \(0.739279\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1976.00 | −0.915614 | −0.457807 | − | 0.889052i | \(-0.651365\pi\) | ||||
−0.457807 | + | 0.889052i | \(0.651365\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2181.00 | −0.992717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1346.00 | − | 2331.34i | −0.591529 | − | 1.02456i | −0.994027 | − | 0.109137i | \(-0.965191\pi\) |
0.402498 | − | 0.915421i | \(-0.368142\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1290.00 | + | 2234.35i | −0.538654 | + | 0.932977i | 0.460322 | + | 0.887752i | \(0.347734\pi\) |
−0.998977 | + | 0.0452249i | \(0.985600\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2036.00 | −0.836103 | −0.418052 | − | 0.908423i | \(-0.637287\pi\) | ||||
−0.418052 | + | 0.908423i | \(0.637287\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −60.0000 | + | 103.923i | −0.0238448 | + | 0.0413004i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 240.000 | + | 415.692i | 0.0938531 | + | 0.162558i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1980.00 | + | 3429.46i | 0.750093 | + | 1.29920i | 0.947777 | + | 0.318933i | \(0.103325\pi\) |
−0.197684 | + | 0.980266i | \(0.563342\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | + | 1.73205i | −0.000372962 | + | 0.000645988i | −0.866212 | − | 0.499677i | \(-0.833452\pi\) |
0.865839 | + | 0.500323i | \(0.166785\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3774.00 | −1.36491 | −0.682453 | − | 0.730930i | \(-0.739087\pi\) | ||||
−0.682453 | + | 0.730930i | \(0.739087\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1780.00 | − | 3083.05i | 0.634075 | − | 1.09825i | −0.352636 | − | 0.935761i | \(-0.614715\pi\) |
0.986710 | − | 0.162489i | \(-0.0519521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 432.000 | + | 748.246i | 0.147181 | + | 0.254926i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 880.000 | 0.291248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2692.00 | −0.878317 | −0.439159 | − | 0.898410i | \(-0.644723\pi\) | ||||
−0.439159 | + | 0.898410i | \(0.644723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −328.000 | − | 568.113i | −0.104044 | − | 0.180209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −48.0000 | + | 83.1384i | −0.0146101 | + | 0.0253054i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4528.00 | 1.35972 | 0.679859 | − | 0.733342i | \(-0.262041\pi\) | ||||
0.679859 | + | 0.733342i | \(0.262041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1826.00 | + | 3162.72i | −0.533903 | + | 0.924746i | 0.465313 | + | 0.885146i | \(0.345942\pi\) |
−0.999216 | + | 0.0396002i | \(0.987392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2402.00 | + | 4160.39i | 0.693138 | + | 1.20055i | 0.970804 | + | 0.239873i | \(0.0771057\pi\) |
−0.277666 | + | 0.960678i | \(0.589561\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1379.00 | + | 2388.50i | 0.387731 | + | 0.671570i | 0.992144 | − | 0.125102i | \(-0.0399257\pi\) |
−0.604413 | + | 0.796671i | \(0.706592\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1040.00 | + | 1801.33i | −0.288690 | + | 0.500026i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6528.00 | −1.76678 | −0.883392 | − | 0.468635i | \(-0.844746\pi\) | ||||
−0.883392 | + | 0.468635i | \(0.844746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.0000 | − | 48.4974i | 0.00748398 | − | 0.0129626i | −0.862259 | − | 0.506467i | \(-0.830951\pi\) |
0.869743 | + | 0.493505i | \(0.164284\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 88.0000 | + | 152.420i | 0.0226693 | + | 0.0392643i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4900.00 | −1.23221 | −0.616106 | − | 0.787663i | \(-0.711291\pi\) | ||||
−0.616106 | + | 0.787663i | \(0.711291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1440.00 | −0.357834 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3392.00 | − | 5875.12i | −0.823296 | − | 1.42599i | −0.903214 | − | 0.429190i | \(-0.858799\pi\) |
0.0799181 | − | 0.996801i | \(-0.474534\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2272.00 | + | 3935.22i | −0.532690 | + | 0.922646i | 0.466581 | + | 0.884478i | \(0.345486\pi\) |
−0.999271 | + | 0.0381681i | \(0.987848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −584.000 | −0.135377 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2026.00 | + | 3509.13i | −0.459210 | + | 0.795374i | −0.998919 | − | 0.0464767i | \(-0.985201\pi\) |
0.539710 | + | 0.841851i | \(0.318534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1376.00 | + | 2383.30i | 0.308436 | + | 0.534226i | 0.978020 | − | 0.208510i | \(-0.0668612\pi\) |
−0.669585 | + | 0.742736i | \(0.733528\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1090.00 | + | 1887.94i | 0.239016 | + | 0.413988i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2183.00 | + | 3781.07i | −0.473515 | + | 0.820153i | −0.999540 | − | 0.0303164i | \(-0.990348\pi\) |
0.526025 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7734.00 | −1.64189 | −0.820946 | − | 0.571006i | \(-0.806553\pi\) | ||||
−0.820946 | + | 0.571006i | \(0.806553\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2026.00 | − | 3509.13i | 0.425559 | − | 0.737090i | −0.570913 | − | 0.821010i | \(-0.693411\pi\) |
0.996472 | + | 0.0839204i | \(0.0267442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2168.50 | + | 3755.95i | 0.441380 | + | 0.764493i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3420.00 | 0.681906 | 0.340953 | − | 0.940080i | \(-0.389250\pi\) | ||||
0.340953 | + | 0.940080i | \(0.389250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1840.00 | 0.363149 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −144.000 | − | 249.415i | −0.0278520 | − | 0.0482410i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1256.00 | − | 2175.46i | 0.235798 | − | 0.408414i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7324.00 | 1.36157 | 0.680786 | − | 0.732482i | \(-0.261638\pi\) | ||||
0.680786 | + | 0.732482i | \(0.261638\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2096.00 | + | 3630.38i | −0.382165 | + | 0.661929i | −0.991371 | − | 0.131083i | \(-0.958155\pi\) |
0.609207 | + | 0.793012i | \(0.291488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3420.00 | + | 5923.61i | 0.617603 | + | 1.06972i | 0.989922 | + | 0.141615i | \(0.0452296\pi\) |
−0.372318 | + | 0.928105i | \(0.621437\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3315.00 | + | 5741.75i | 0.587347 | + | 1.01731i | 0.994578 | + | 0.103990i | \(0.0331609\pi\) |
−0.407232 | + | 0.913325i | \(0.633506\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −380.000 | + | 658.179i | −0.0666957 | + | 0.115520i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1056.00 | −0.181911 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −218.000 | + | 377.587i | −0.0372076 | + | 0.0644454i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3434.00 | + | 5947.86i | 0.570241 | + | 0.987686i | 0.996541 | + | 0.0831042i | \(0.0264834\pi\) |
−0.426300 | + | 0.904582i | \(0.640183\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2224.00 | −0.362717 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7378.00 | −1.19260 | −0.596299 | − | 0.802763i | \(-0.703363\pi\) | ||||
−0.596299 | + | 0.802763i | \(0.703363\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1840.00 | − | 3186.97i | −0.292204 | − | 0.506112i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1338.00 | + | 2317.48i | −0.206996 | + | 0.358528i | −0.950767 | − | 0.309907i | \(-0.899702\pi\) |
0.743771 | + | 0.668435i | \(0.233035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5124.00 | −0.785907 | −0.392953 | − | 0.919558i | \(-0.628547\pi\) | ||||
−0.392953 | + | 0.919558i | \(0.628547\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2280.00 | − | 3949.08i | 0.343774 | − | 0.595434i | −0.641356 | − | 0.767243i | \(-0.721628\pi\) |
0.985130 | + | 0.171809i | \(0.0549613\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1184.00 | − | 2050.75i | −0.177015 | − | 0.306598i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1828.00 | + | 3166.19i | 0.268741 | + | 0.465474i | 0.968537 | − | 0.248869i | \(-0.0800590\pi\) |
−0.699796 | + | 0.714343i | \(0.746726\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2461.50 | − | 4263.44i | 0.358872 | − | 0.621584i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4096.00 | −0.587382 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 808.000 | − | 1399.50i | 0.114924 | − | 0.199055i | −0.802825 | − | 0.596215i | \(-0.796671\pi\) |
0.917750 | + | 0.397160i | \(0.130004\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1367.00 | − | 2367.71i | −0.189760 | − | 0.328674i | 0.755410 | − | 0.655252i | \(-0.227438\pi\) |
−0.945170 | + | 0.326578i | \(0.894104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −152.000 | −0.0207650 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1380.00 | −0.187034 | −0.0935169 | − | 0.995618i | \(-0.529811\pi\) | ||||
−0.0935169 | + | 0.995618i | \(0.529811\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3444.00 | + | 5965.18i | 0.459478 | + | 0.795840i | 0.998933 | − | 0.0461746i | \(-0.0147031\pi\) |
−0.539455 | + | 0.842014i | \(0.681370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1023.00 | + | 1771.89i | −0.133337 | + | 0.230947i | −0.924961 | − | 0.380062i | \(-0.875903\pi\) |
0.791624 | + | 0.611009i | \(0.209236\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1728.00 | 0.223501 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −208.000 | + | 360.267i | −0.0264952 | + | 0.0458911i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1558.00 | − | 2698.54i | −0.196962 | − | 0.341148i | 0.750580 | − | 0.660779i | \(-0.229774\pi\) |
−0.947542 | + | 0.319632i | \(0.896441\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1479.00 | + | 2561.70i | 0.184184 | + | 0.319016i | 0.943301 | − | 0.331938i | \(-0.107702\pi\) |
−0.759117 | + | 0.650954i | \(0.774369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 368.000 | − | 637.395i | 0.0454873 | − | 0.0787863i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −600.000 | −0.0730735 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3972.00 | + | 6879.71i | −0.480202 | + | 0.831735i | −0.999742 | − | 0.0227114i | \(-0.992770\pi\) |
0.519540 | + | 0.854446i | \(0.326103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 648.000 | + | 1122.37i | 0.0766484 | + | 0.132759i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4084.00 | −0.476173 | −0.238086 | − | 0.971244i | \(-0.576520\pi\) | ||||
−0.238086 | + | 0.971244i | \(0.576520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6306.00 | −0.730013 | −0.365007 | − | 0.931005i | \(-0.618933\pi\) | ||||
−0.365007 | + | 0.931005i | \(0.618933\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1308.00 | − | 2265.52i | −0.149288 | − | 0.258574i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5912.00 | + | 10239.9i | −0.660722 | + | 1.14440i | 0.319705 | + | 0.947517i | \(0.396416\pi\) |
−0.980426 | + | 0.196886i | \(0.936917\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4504.00 | −0.499881 | −0.249940 | − | 0.968261i | \(-0.580411\pi\) | ||||
−0.249940 | + | 0.968261i | \(0.580411\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1584.00 | − | 2743.57i | 0.173394 | − | 0.300326i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6528.00 | − | 11306.8i | −0.709714 | − | 1.22926i | −0.964963 | − | 0.262385i | \(-0.915491\pi\) |
0.255249 | − | 0.966875i | \(-0.417842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 66.0000 | + | 114.315i | 0.00707845 | + | 0.0122602i | 0.869543 | − | 0.493857i | \(-0.164414\pi\) |
−0.862464 | + | 0.506118i | \(0.831080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1792.00 | + | 3103.84i | −0.190897 | + | 0.330642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4866.00 | −0.511449 | −0.255725 | − | 0.966750i | \(-0.582314\pi\) | ||||
−0.255725 | + | 0.966750i | \(0.582314\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2160.00 | + | 3741.23i | −0.225522 | + | 0.390616i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5053.00 | − | 8752.05i | −0.517220 | − | 0.895851i | −0.999800 | − | 0.0199990i | \(-0.993634\pi\) |
0.482580 | − | 0.875852i | \(-0.339700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18036.0 | 1.82217 | 0.911085 | − | 0.412219i | \(-0.135246\pi\) | ||||
0.911085 | + | 0.412219i | \(0.135246\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5288.00 | 0.530787 | 0.265393 | − | 0.964140i | \(-0.414498\pi\) | ||||
0.265393 | + | 0.964140i | \(0.414498\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7582.00 | + | 13132.4i | 0.751291 | + | 1.30128i | 0.947197 | + | 0.320652i | \(0.103902\pi\) |
−0.195906 | + | 0.980623i | \(0.562765\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1640.00 | − | 2840.56i | 0.159423 | − | 0.276129i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4796.00 | −0.463275 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3948.00 | − | 6838.14i | 0.376594 | − | 0.652281i | −0.613970 | − | 0.789329i | \(-0.710428\pi\) |
0.990564 | + | 0.137049i | \(0.0437617\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −60.0000 | − | 103.923i | −0.00568766 | − | 0.00985132i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1840.00 | − | 3186.97i | −0.172268 | − | 0.298377i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1460.00 | + | 2528.79i | −0.135850 | + | 0.235299i | −0.925922 | − | 0.377715i | \(-0.876710\pi\) |
0.790072 | + | 0.613014i | \(0.210043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7932.00 | 0.729055 | 0.364528 | − | 0.931193i | \(-0.381230\pi\) | ||||
0.364528 | + | 0.931193i | \(0.381230\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 456.000 | − | 789.815i | 0.0416576 | − | 0.0721531i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1002.00 | + | 1735.51i | 0.0898911 | + | 0.155696i | 0.907465 | − | 0.420128i | \(-0.138015\pi\) |
−0.817574 | + | 0.575824i | \(0.804681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4496.00 | −0.398542 | −0.199271 | − | 0.979944i | \(-0.563857\pi\) | ||||
−0.199271 | + | 0.979944i | \(0.563857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4432.00 | 0.390537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6310.00 | + | 10929.2i | 0.549481 | + | 0.951729i | 0.998310 | + | 0.0581114i | \(0.0185079\pi\) |
−0.448829 | + | 0.893618i | \(0.648159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2896.00 | − | 5016.02i | 0.247792 | − | 0.429189i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10400.0 | −0.884703 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9004.00 | − | 15595.4i | 0.757145 | − | 1.31141i | −0.187156 | − | 0.982330i | \(-0.559927\pi\) |
0.944301 | − | 0.329083i | \(-0.106740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6646.00 | − | 11511.2i | −0.555658 | − | 0.962428i | −0.997852 | − | 0.0655088i | \(-0.979133\pi\) |
0.442194 | − | 0.896920i | \(-0.354200\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2208.00 | + | 3824.37i | 0.182509 | + | 0.316114i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3491.50 | − | 6047.46i | 0.286965 | − | 0.497038i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −864.000 | −0.0702139 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2632.00 | + | 4558.76i | −0.212694 | + | 0.368397i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4285.00 | + | 7421.84i | 0.340530 | + | 0.589815i | 0.984531 | − | 0.175210i | \(-0.0560603\pi\) |
−0.644002 | + | 0.765024i | \(0.722727\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 344.000 | 0.0270373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1916.00 | −0.149766 | −0.0748832 | − | 0.997192i | \(-0.523858\pi\) | ||||
−0.0748832 | + | 0.997192i | \(0.523858\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −836.000 | − | 1447.99i | −0.0646367 | − | 0.111954i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9963.00 | − | 17256.4i | 0.757892 | − | 1.31271i | −0.186032 | − | 0.982544i | \(-0.559563\pi\) |
0.943924 | − | 0.330164i | \(-0.107104\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 656.000 | 0.0496348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2122.00 | − | 3675.41i | 0.158848 | − | 0.275133i | −0.775605 | − | 0.631218i | \(-0.782555\pi\) |
0.934454 | + | 0.356085i | \(0.115889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3556.00 | − | 6159.17i | −0.264782 | − | 0.458617i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11397.0 | − | 19740.2i | −0.839696 | − | 1.45440i | −0.890149 | − | 0.455670i | \(-0.849400\pi\) |
0.0504527 | − | 0.998726i | \(-0.483934\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7014.00 | + | 12148.6i | −0.514057 | + | 0.890374i | 0.485810 | + | 0.874065i | \(0.338525\pi\) |
−0.999867 | + | 0.0163089i | \(0.994809\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7848.00 | 0.569190 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4184.00 | + | 7246.90i | −0.301876 | + | 0.522864i | −0.976561 | − | 0.215242i | \(-0.930946\pi\) |
0.674685 | + | 0.738106i | \(0.264279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1460.00 | − | 2528.79i | −0.103717 | − | 0.179643i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −52.0000 | −0.00365634 | −0.00182817 | − | 0.999998i | \(-0.500582\pi\) | ||||
−0.00182817 | + | 0.999998i | \(0.500582\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8096.00 | 0.566366 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2904.00 | + | 5029.88i | 0.201101 | + | 0.348317i | 0.948883 | − | 0.315627i | \(-0.102215\pi\) |
−0.747782 | + | 0.663944i | \(0.768881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5232.00 | + | 9062.09i | −0.356884 | + | 0.618142i | −0.987439 | − | 0.158003i | \(-0.949494\pi\) |
0.630554 | + | 0.776145i | \(0.282828\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1184.00 | 0.0803600 | 0.0401800 | − | 0.999192i | \(-0.487207\pi\) | ||||
0.0401800 | + | 0.999192i | \(0.487207\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1862.00 | + | 3225.08i | −0.125126 | + | 0.216724i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6576.00 | − | 11390.0i | −0.439723 | − | 0.761622i | 0.557945 | − | 0.829878i | \(-0.311590\pi\) |
−0.997668 | + | 0.0682559i | \(0.978257\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1040.00 | − | 1801.33i | −0.0688607 | − | 0.119270i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9167.00 | − | 15877.7i | 0.603999 | − | 1.04616i | −0.388209 | − | 0.921571i | \(-0.626906\pi\) |
0.992209 | − | 0.124586i | \(-0.0397604\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8122.00 | 0.529950 | 0.264975 | − | 0.964255i | \(-0.414636\pi\) | ||||
0.264975 | + | 0.964255i | \(0.414636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2990.00 | + | 5178.83i | −0.194149 | + | 0.336276i | −0.946621 | − | 0.322348i | \(-0.895528\pi\) |
0.752472 | + | 0.658624i | \(0.228861\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4940.50 | − | 8557.20i | −0.316192 | − | 0.547661i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 720.000 | 0.0456411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12528.0 | 0.790383 | 0.395192 | − | 0.918599i | \(-0.370678\pi\) | ||||
0.395192 | + | 0.918599i | \(0.370678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1856.00 | − | 3214.69i | −0.115989 | − | 0.200899i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10399.0 | − | 18011.6i | 0.640773 | − | 1.10985i | −0.344487 | − | 0.938791i | \(-0.611947\pi\) |
0.985260 | − | 0.171061i | \(-0.0547196\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1932.00 | −0.118492 | −0.0592462 | − | 0.998243i | \(-0.518870\pi\) | ||||
−0.0592462 | + | 0.998243i | \(0.518870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4212.00 | + | 7295.40i | −0.255936 | + | 0.443295i | −0.965149 | − | 0.261699i | \(-0.915717\pi\) |
0.709213 | + | 0.704994i | \(0.249050\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4600.00 | + | 7967.43i | 0.278222 | + | 0.481894i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8875.00 | − | 15372.0i | −0.531862 | − | 0.921211i | −0.999308 | − | 0.0371899i | \(-0.988159\pi\) |
0.467447 | − | 0.884021i | \(-0.345174\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2808.00 | + | 4863.60i | −0.167508 | + | 0.290132i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27580.0 | 1.63029 | 0.815147 | − | 0.579254i | \(-0.196656\pi\) | ||||
0.815147 | + | 0.579254i | \(0.196656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4646.00 | − | 8047.11i | 0.273386 | − | 0.473519i | −0.696340 | − | 0.717712i | \(-0.745190\pi\) |
0.969727 | + | 0.244193i | \(0.0785229\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1368.00 | + | 2369.45i | 0.0794141 | + | 0.137549i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12560.0 | 0.722613 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11486.0 | 0.657879 | 0.328940 | − | 0.944351i | \(-0.393309\pi\) | ||||
0.328940 | + | 0.944351i | \(0.393309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3558.00 | + | 6162.64i | 0.201987 | + | 0.349851i | 0.949168 | − | 0.314768i | \(-0.101927\pi\) |
−0.747182 | + | 0.664620i | \(0.768594\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3806.00 | + | 6592.19i | −0.213225 | + | 0.369316i | −0.952722 | − | 0.303843i | \(-0.901730\pi\) |
0.739497 | + | 0.673160i | \(0.235063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5480.00 | −0.305664 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 292.000 | − | 505.759i | 0.0161456 | − | 0.0279650i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10786.0 | + | 18681.9i | 0.593804 | + | 1.02850i | 0.993714 | + | 0.111945i | \(0.0357080\pi\) |
−0.399910 | + | 0.916554i | \(0.630959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1032.00 | + | 1787.48i | 0.0563252 | + | 0.0975581i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2592.00 | − | 4489.48i | 0.140859 | − | 0.243976i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1702.00 | 0.0917028 | 0.0458514 | − | 0.998948i | \(-0.485400\pi\) | ||||
0.0458514 | + | 0.998948i | \(0.485400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 660.000 | − | 1143.15i | 0.0354088 | − | 0.0613298i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3185.00 | − | 5516.58i | −0.168710 | − | 0.292214i | 0.769257 | − | 0.638940i | \(-0.220627\pi\) |
−0.937966 | + | 0.346726i | \(0.887293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13248.0 | −0.695851 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 320.000 | 0.0167375 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4404.00 | − | 7627.95i | −0.228430 | − | 0.395653i | 0.728913 | − | 0.684607i | \(-0.240026\pi\) |
−0.957343 | + | 0.288954i | \(0.906693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2071.00 | − | 3587.08i | 0.106090 | − | 0.183753i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17768.0 | 0.906436 | 0.453218 | − | 0.891400i | \(-0.350276\pi\) | ||||
0.453218 | + | 0.891400i | \(0.350276\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1968.00 | + | 3408.68i | −0.0995747 | + | 0.172468i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2782.00 | + | 4818.57i | 0.140185 | + | 0.242807i | 0.927566 | − | 0.373659i | \(-0.121897\pi\) |
−0.787381 | + | 0.616466i | \(0.788564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5560.00 | − | 9630.20i | −0.277890 | − | 0.481320i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8782.00 | − | 15210.9i | 0.437146 | − | 0.757160i | −0.560322 | − | 0.828275i | \(-0.689323\pi\) |
0.997468 | + | 0.0711154i | \(0.0226559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38280.0 | 1.89012 | 0.945059 | − | 0.326901i | \(-0.106004\pi\) | ||||
0.945059 | + | 0.326901i | \(0.106004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2780.00 | + | 4815.10i | −0.136713 | + | 0.236794i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18096.0 | − | 31343.2i | −0.879271 | − | 1.52294i | −0.852142 | − | 0.523310i | \(-0.824697\pi\) |
−0.0271284 | − | 0.999632i | \(-0.508636\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −544.000 | −0.0262228 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.000672178 | −0.000336089 | − | 1.00000i | \(-0.500107\pi\) | ||||
−0.000336089 | 1.00000i | \(0.500107\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13252.0 | − | 22953.1i | −0.631254 | − | 1.09336i | −0.987296 | − | 0.158894i | \(-0.949207\pi\) |
0.356041 | − | 0.934470i | \(-0.384126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −920.000 | + | 1593.49i | −0.0433107 | + | 0.0750163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40184.0 | 1.88436 | 0.942180 | − | 0.335109i | \(-0.108773\pi\) | ||||
0.942180 | + | 0.335109i | \(0.108773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17670.0 | + | 30605.3i | −0.822181 | + | 1.42406i | 0.0818742 | + | 0.996643i | \(0.473909\pi\) |
−0.904055 | + | 0.427416i | \(0.859424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10028.0 | + | 17369.0i | 0.464795 | + | 0.805049i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4752.00 | − | 8230.71i | −0.218560 | − | 0.378557i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5920.00 | − | 10253.7i | 0.271235 | − | 0.469792i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 592.000 | 0.0269164 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7426.00 | − | 12862.2i | 0.336351 | − | 0.582577i | −0.647392 | − | 0.762157i | \(-0.724140\pi\) |
0.983743 | + | 0.179580i | \(0.0574738\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1256.00 | + | 2175.46i | 0.0562445 | + | 0.0974183i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19788.0 | −0.879457 | −0.439728 | − | 0.898131i | \(-0.644925\pi\) | ||||
−0.439728 | + | 0.898131i | \(0.644925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12480.0 | 0.552579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10240.0 | − | 17736.2i | −0.450015 | − | 0.779448i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8493.00 | − | 14710.3i | 0.369095 | − | 0.639292i | −0.620329 | − | 0.784342i | \(-0.713001\pi\) |
0.989424 | + | 0.145050i | \(0.0463343\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26596.0 | −1.15156 | −0.575778 | − | 0.817606i | \(-0.695301\pi\) | ||||
−0.575778 | + | 0.817606i | \(0.695301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2424.00 | + | 4198.49i | −0.104183 | + | 0.180450i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3608.00 | + | 6249.24i | 0.154502 | + | 0.267605i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17449.0 | − | 30222.6i | −0.741747 | − | 1.28474i | −0.951699 | − | 0.307032i | \(-0.900664\pi\) |
0.209952 | − | 0.977712i | \(-0.432669\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6464.00 | + | 11196.0i | −0.273780 | + | 0.474201i | −0.969827 | − | 0.243796i | \(-0.921607\pi\) |
0.696047 | + | 0.717997i | \(0.254941\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43164.0 | 1.81494 | 0.907472 | − | 0.420112i | \(-0.138009\pi\) | ||||
0.907472 | + | 0.420112i | \(0.138009\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20614.0 | − | 35704.5i | 0.863635 | − | 1.49586i | −0.00476022 | − | 0.999989i | \(-0.501515\pi\) |
0.868396 | − | 0.495872i | \(-0.165151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3952.00 | − | 6845.06i | −0.163790 | − | 0.283692i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1368.00 | 0.0562915 | 0.0281458 | − | 0.999604i | \(-0.491040\pi\) | ||||
0.0281458 | + | 0.999604i | \(0.491040\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22945.0 | −0.940793 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4362.00 | − | 7555.21i | −0.177583 | − | 0.307582i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1080.00 | + | 1870.61i | −0.0435040 | + | 0.0753512i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5276.00 | 0.211778 | 0.105889 | − | 0.994378i | \(-0.466231\pi\) | ||||
0.105889 | + | 0.994378i | \(0.466231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 420.000 | − | 727.461i | 0.0167409 | − | 0.0289960i | −0.857534 | − | 0.514428i | \(-0.828004\pi\) |
0.874274 | + | 0.485432i | \(0.161338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13014.0 | + | 22540.9i | 0.516917 | + | 0.895327i | 0.999807 | + | 0.0196458i | \(0.00625386\pi\) |
−0.482890 | + | 0.875681i | \(0.660413\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14724.0 | − | 25502.7i | −0.580777 | − | 1.00594i | −0.995387 | − | 0.0959366i | \(-0.969415\pi\) |
0.414610 | − | 0.909999i | \(-0.363918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5384.00 | − | 9325.36i | 0.211632 | − | 0.366557i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2080.00 | −0.0811958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1112.00 | − | 1926.04i | 0.0432591 | − | 0.0749270i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12933.0 | − | 22400.6i | −0.497966 | − | 0.862503i | 0.502031 | − | 0.864850i | \(-0.332586\pi\) |
−0.999997 | + | 0.00234681i | \(0.999253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9472.00 | −0.362225 | −0.181112 | − | 0.983462i | \(-0.557970\pi\) | ||||
−0.181112 | + | 0.983462i | \(0.557970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49372.0 | 1.88165 | 0.940827 | − | 0.338888i | \(-0.110051\pi\) | ||||
0.940827 | + | 0.338888i | \(0.110051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5580.00 | − | 9664.84i | −0.211227 | − | 0.365855i | 0.740872 | − | 0.671646i | \(-0.234412\pi\) |
−0.952099 | + | 0.305791i | \(0.901079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11440.0 | − | 19814.7i | 0.428695 | − | 0.742522i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10320.0 | −0.385430 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3496.00 | + | 6055.25i | −0.129698 | + | 0.224643i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1752.00 | + | 3034.55i | 0.0647809 | + | 0.112204i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4072.00 | − | 7052.91i | −0.149567 | − | 0.259057i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11354.0 | + | 19665.7i | −0.415660 | + | 0.719944i | −0.995497 | − | 0.0947882i | \(-0.969783\pi\) |
0.579838 | + | 0.814732i | \(0.303116\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16192.0 | 0.588875 | 0.294437 | − | 0.955671i | \(-0.404868\pi\) | ||||
0.294437 | + | 0.955671i | \(0.404868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3240.00 | + | 5611.84i | −0.117446 | + | 0.203423i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23160.0 | + | 40114.3i | 0.831314 | + | 1.43988i | 0.896996 | + | 0.442038i | \(0.145744\pi\) |
−0.0656819 | + | 0.997841i | \(0.520922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2368.00 | 0.0844460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3270.00 | 0.116235 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1140.00 | − | 1974.54i | −0.0402607 | − | 0.0697336i | 0.845193 | − | 0.534461i | \(-0.179486\pi\) |
−0.885454 | + | 0.464728i | \(0.846152\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −960.000 | + | 1662.77i | −0.0335779 | + | 0.0581587i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49056.0 | 1.71034 | 0.855171 | − | 0.518347i | \(-0.173452\pi\) | ||||
0.855171 | + | 0.518347i | \(0.173452\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12438.0 | + | 21543.2i | −0.430890 | + | 0.746323i | −0.996950 | − | 0.0780409i | \(-0.975134\pi\) |
0.566060 | + | 0.824364i | \(0.308467\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7776.00 | + | 13468.4i | 0.268527 | + | 0.465103i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11714.0 | + | 20289.2i | 0.401958 | + | 0.696211i | 0.993962 | − | 0.109724i | \(-0.0349966\pi\) |
−0.592005 | + | 0.805935i | \(0.701663\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2048.00 | − | 3547.24i | 0.0700536 | − | 0.121336i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6678.00 | 0.226990 | 0.113495 | − | 0.993539i | \(-0.463795\pi\) | ||||
0.113495 | + | 0.993539i | \(0.463795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7920.00 | + | 13717.8i | −0.268361 | + | 0.464816i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2032.50 | − | 3520.39i | −0.0682253 | − | 0.118170i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.00000 | −0.000266870 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15544.0 | 0.516920 | 0.258460 | − | 0.966022i | \(-0.416785\pi\) | ||||
0.258460 | + | 0.966022i | \(0.416785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15562.0 | − | 26954.2i | −0.514324 | − | 0.890835i | −0.999862 | − | 0.0166194i | \(-0.994710\pi\) |
0.485538 | − | 0.874215i | \(-0.338624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25031.0 | − | 43355.0i | 0.819665 | − | 1.41970i | −0.0862643 | − | 0.996272i | \(-0.527493\pi\) |
0.905929 | − | 0.423429i | \(-0.139174\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17920.0 | −0.585011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 164.000 | − | 284.056i | 0.00532125 | − | 0.00921667i | −0.863353 | − | 0.504601i | \(-0.831640\pi\) |
0.868674 | + | 0.495385i | \(0.164973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7548.00 | − | 13073.5i | −0.244162 | − | 0.422900i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5904.00 | − | 10226.0i | −0.189824 | − | 0.328785i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10436.0 | − | 18075.7i | 0.334521 | − | 0.579408i | −0.648872 | − | 0.760898i | \(-0.724759\pi\) |
0.983393 | + | 0.181490i | \(0.0580921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14240.0 | 0.453707 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23462.0 | − | 40637.4i | 0.745285 | − | 1.29087i | −0.204777 | − | 0.978809i | \(-0.565647\pi\) |
0.950062 | − | 0.312063i | \(-0.101020\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.4.k.j.361.1 | 2 | ||
3.2 | odd | 2 | 588.4.i.g.361.1 | 2 | |||
7.2 | even | 3 | inner | 1764.4.k.j.1549.1 | 2 | ||
7.3 | odd | 6 | 1764.4.a.i.1.1 | 1 | |||
7.4 | even | 3 | 1764.4.a.d.1.1 | 1 | |||
7.5 | odd | 6 | 1764.4.k.g.1549.1 | 2 | |||
7.6 | odd | 2 | 1764.4.k.g.361.1 | 2 | |||
21.2 | odd | 6 | 588.4.i.g.373.1 | 2 | |||
21.5 | even | 6 | 588.4.i.b.373.1 | 2 | |||
21.11 | odd | 6 | 588.4.a.b.1.1 | ✓ | 1 | ||
21.17 | even | 6 | 588.4.a.e.1.1 | yes | 1 | ||
21.20 | even | 2 | 588.4.i.b.361.1 | 2 | |||
84.11 | even | 6 | 2352.4.a.be.1.1 | 1 | |||
84.59 | odd | 6 | 2352.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.b.1.1 | ✓ | 1 | 21.11 | odd | 6 | ||
588.4.a.e.1.1 | yes | 1 | 21.17 | even | 6 | ||
588.4.i.b.361.1 | 2 | 21.20 | even | 2 | |||
588.4.i.b.373.1 | 2 | 21.5 | even | 6 | |||
588.4.i.g.361.1 | 2 | 3.2 | odd | 2 | |||
588.4.i.g.373.1 | 2 | 21.2 | odd | 6 | |||
1764.4.a.d.1.1 | 1 | 7.4 | even | 3 | |||
1764.4.a.i.1.1 | 1 | 7.3 | odd | 6 | |||
1764.4.k.g.361.1 | 2 | 7.6 | odd | 2 | |||
1764.4.k.g.1549.1 | 2 | 7.5 | odd | 6 | |||
1764.4.k.j.361.1 | 2 | 1.1 | even | 1 | trivial | ||
1764.4.k.j.1549.1 | 2 | 7.2 | even | 3 | inner | ||
2352.4.a.g.1.1 | 1 | 84.59 | odd | 6 | |||
2352.4.a.be.1.1 | 1 | 84.11 | even | 6 |