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 84) |
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.n.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 | ||||||||
\(5\) | 7.00000 | + | 12.1244i | 0.626099 | + | 1.08444i | 0.988327 | + | 0.152346i | \(0.0486828\pi\) |
−0.362228 | + | 0.932089i | \(0.617984\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | − | 3.46410i | 0.0548202 | − | 0.0949514i | −0.837313 | − | 0.546724i | \(-0.815875\pi\) |
0.892133 | + | 0.451772i | \(0.149208\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.0000 | 1.15207 | 0.576035 | − | 0.817425i | \(-0.304599\pi\) | ||||
0.576035 | + | 0.817425i | \(0.304599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.00000 | + | 12.1244i | −0.0998676 | + | 0.172976i | −0.911630 | − | 0.411012i | \(-0.865175\pi\) |
0.811762 | + | 0.583988i | \(0.198509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −46.0000 | − | 79.6743i | −0.555428 | − | 0.962029i | −0.997870 | − | 0.0652319i | \(-0.979221\pi\) |
0.442443 | − | 0.896797i | \(-0.354112\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −76.0000 | − | 131.636i | −0.689004 | − | 1.19339i | −0.972160 | − | 0.234316i | \(-0.924715\pi\) |
0.283156 | − | 0.959074i | \(-0.408619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −35.5000 | + | 61.4878i | −0.284000 | + | 0.491902i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 106.000 | 0.678748 | 0.339374 | − | 0.940651i | \(-0.389785\pi\) | ||||
0.339374 | + | 0.940651i | \(0.389785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72.0000 | − | 124.708i | 0.417148 | − | 0.722521i | −0.578503 | − | 0.815680i | \(-0.696363\pi\) |
0.995651 | + | 0.0931587i | \(0.0296964\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −79.0000 | − | 136.832i | −0.351014 | − | 0.607974i | 0.635413 | − | 0.772172i | \(-0.280830\pi\) |
−0.986427 | + | 0.164198i | \(0.947496\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 390.000 | 1.48556 | 0.742778 | − | 0.669538i | \(-0.233508\pi\) | ||||
0.742778 | + | 0.669538i | \(0.233508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −508.000 | −1.80161 | −0.900806 | − | 0.434223i | \(-0.857023\pi\) | ||||
−0.900806 | + | 0.434223i | \(0.857023\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −264.000 | − | 457.261i | −0.819327 | − | 1.41912i | −0.906179 | − | 0.422894i | \(-0.861014\pi\) |
0.0868522 | − | 0.996221i | \(-0.472319\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 303.000 | − | 524.811i | 0.785288 | − | 1.36016i | −0.143539 | − | 0.989645i | \(-0.545848\pi\) |
0.928827 | − | 0.370514i | \(-0.120818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 56.0000 | 0.137292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −182.000 | + | 315.233i | −0.401600 | + | 0.695591i | −0.993919 | − | 0.110112i | \(-0.964879\pi\) |
0.592319 | + | 0.805703i | \(0.298212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −339.000 | − | 587.165i | −0.711549 | − | 1.23244i | −0.964275 | − | 0.264902i | \(-0.914661\pi\) |
0.252726 | − | 0.967538i | \(-0.418673\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 378.000 | + | 654.715i | 0.721310 | + | 1.24935i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −422.000 | + | 730.925i | −0.769485 | + | 1.33279i | 0.168357 | + | 0.985726i | \(0.446154\pi\) |
−0.937842 | + | 0.347061i | \(0.887180\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.0133722 | 0.00668609 | − | 0.999978i | \(-0.497872\pi\) | ||||
0.00668609 | + | 0.999978i | \(0.497872\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 211.000 | − | 365.463i | 0.338297 | − | 0.585948i | −0.645816 | − | 0.763494i | \(-0.723482\pi\) |
0.984113 | + | 0.177546i | \(0.0568158\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −192.000 | − | 332.554i | −0.273439 | − | 0.473610i | 0.696301 | − | 0.717750i | \(-0.254828\pi\) |
−0.969740 | + | 0.244139i | \(0.921495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 548.000 | 0.724709 | 0.362354 | − | 0.932040i | \(-0.381973\pi\) | ||||
0.362354 | + | 0.932040i | \(0.381973\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −196.000 | −0.250108 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 597.000 | + | 1034.03i | 0.711032 | + | 1.23154i | 0.964470 | + | 0.264192i | \(0.0851054\pi\) |
−0.253438 | + | 0.967352i | \(0.581561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 644.000 | − | 1115.44i | 0.695505 | − | 1.20465i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1502.00 | −1.57222 | −0.786108 | − | 0.618089i | \(-0.787907\pi\) | ||||
−0.786108 | + | 0.618089i | \(0.787907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 199.000 | − | 344.678i | 0.196052 | − | 0.339572i | −0.751193 | − | 0.660083i | \(-0.770521\pi\) |
0.947245 | + | 0.320511i | \(0.103855\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −580.000 | − | 1004.59i | −0.554846 | − | 0.961021i | −0.997916 | − | 0.0645337i | \(-0.979444\pi\) |
0.443070 | − | 0.896487i | \(-0.353889\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 162.000 | + | 280.592i | 0.146366 | + | 0.253513i | 0.929882 | − | 0.367859i | \(-0.119909\pi\) |
−0.783516 | + | 0.621372i | \(0.786576\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 469.000 | − | 812.332i | 0.412129 | − | 0.713828i | −0.582993 | − | 0.812477i | \(-0.698119\pi\) |
0.995122 | + | 0.0986487i | \(0.0314520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 622.000 | 0.517813 | 0.258906 | − | 0.965902i | \(-0.416638\pi\) | ||||
0.258906 | + | 0.965902i | \(0.416638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1064.00 | − | 1842.90i | 0.862770 | − | 1.49436i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 657.500 | + | 1138.82i | 0.493989 | + | 0.855615i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 756.000 | 0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1200.00 | 0.838447 | 0.419224 | − | 0.907883i | \(-0.362302\pi\) | ||||
0.419224 | + | 0.907883i | \(0.362302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −698.000 | − | 1208.97i | −0.465531 | − | 0.806323i | 0.533694 | − | 0.845677i | \(-0.320803\pi\) |
−0.999225 | + | 0.0393543i | \(0.987470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1405.00 | − | 2433.53i | 0.876184 | − | 1.51760i | 0.0206885 | − | 0.999786i | \(-0.493414\pi\) |
0.855496 | − | 0.517810i | \(-0.173253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.00244083 | 0.00122042 | − | 0.999999i | \(-0.499612\pi\) | ||||
0.00122042 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 108.000 | − | 187.061i | 0.0631567 | − | 0.109391i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 742.000 | + | 1285.18i | 0.424964 | + | 0.736059i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 687.000 | + | 1189.92i | 0.377726 | + | 0.654241i | 0.990731 | − | 0.135838i | \(-0.0433727\pi\) |
−0.613005 | + | 0.790079i | \(0.710039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1052.00 | + | 1822.12i | −0.566957 | + | 0.981999i | 0.429907 | + | 0.902873i | \(0.358546\pi\) |
−0.996865 | + | 0.0791258i | \(0.974787\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2016.00 | 1.04470 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1603.00 | + | 2776.48i | −0.814862 | + | 1.41138i | 0.0945650 | + | 0.995519i | \(0.469854\pi\) |
−0.909427 | + | 0.415864i | \(0.863479\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −166.000 | − | 287.520i | −0.0797676 | − | 0.138162i | 0.823382 | − | 0.567488i | \(-0.192084\pi\) |
−0.903150 | + | 0.429326i | \(0.858751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1496.00 | −0.693197 | −0.346599 | − | 0.938014i | \(-0.612663\pi\) | ||||
−0.346599 | + | 0.938014i | \(0.612663\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719.000 | 0.327264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1661.00 | − | 2876.94i | −0.729962 | − | 1.26433i | −0.956899 | − | 0.290422i | \(-0.906204\pi\) |
0.226936 | − | 0.973910i | \(-0.427129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −450.000 | + | 779.423i | −0.187903 | + | 0.325457i | −0.944551 | − | 0.328365i | \(-0.893502\pi\) |
0.756648 | + | 0.653822i | \(0.226836\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1902.00 | 0.781075 | 0.390537 | − | 0.920587i | \(-0.372289\pi\) | ||||
0.390537 | + | 0.920587i | \(0.372289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1106.00 | − | 1915.65i | 0.439539 | − | 0.761304i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.0000 | + | 48.4974i | 0.0109495 | + | 0.0189651i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2064.00 | + | 3574.95i | 0.781915 | + | 1.35432i | 0.930825 | + | 0.365466i | \(0.119090\pi\) |
−0.148910 | + | 0.988851i | \(0.547576\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 671.000 | − | 1162.21i | 0.250257 | − | 0.433458i | −0.713339 | − | 0.700819i | \(-0.752818\pi\) |
0.963597 | + | 0.267361i | \(0.0861515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3506.00 | 1.26798 | 0.633990 | − | 0.773341i | \(-0.281416\pi\) | ||||
0.633990 | + | 0.773341i | \(0.281416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −340.000 | + | 588.897i | −0.121115 | + | 0.209778i | −0.920208 | − | 0.391430i | \(-0.871980\pi\) |
0.799092 | + | 0.601208i | \(0.205314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2730.00 | + | 4728.50i | 0.930105 | + | 1.61099i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −368.000 | −0.121795 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5372.00 | 1.75272 | 0.876360 | − | 0.481657i | \(-0.159965\pi\) | ||||
0.876360 | + | 0.481657i | \(0.159965\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3556.00 | − | 6159.17i | −1.12799 | − | 1.95373i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −378.000 | + | 654.715i | −0.115054 | + | 0.199280i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1072.00 | −0.321912 | −0.160956 | − | 0.986962i | \(-0.551458\pi\) | ||||
−0.160956 | + | 0.986962i | \(0.551458\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1434.00 | + | 2483.76i | −0.419286 | + | 0.726225i | −0.995868 | − | 0.0908148i | \(-0.971053\pi\) |
0.576582 | + | 0.817039i | \(0.304386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2399.00 | − | 4155.19i | −0.692272 | − | 1.19905i | −0.971092 | − | 0.238707i | \(-0.923276\pi\) |
0.278819 | − | 0.960344i | \(-0.410057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2563.00 | − | 4439.25i | −0.720634 | − | 1.24817i | −0.960746 | − | 0.277429i | \(-0.910518\pi\) |
0.240112 | − | 0.970745i | \(-0.422816\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3696.00 | − | 6401.66i | 1.02596 | − | 1.77701i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 528.000 | 0.142902 | 0.0714508 | − | 0.997444i | \(-0.477237\pi\) | ||||
0.0714508 | + | 0.997444i | \(0.477237\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 407.000 | − | 704.945i | 0.108785 | − | 0.188421i | −0.806493 | − | 0.591243i | \(-0.798637\pi\) |
0.915278 | + | 0.402822i | \(0.131971\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2484.00 | − | 4302.41i | −0.639891 | − | 1.10832i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1932.00 | 0.485844 | 0.242922 | − | 0.970046i | \(-0.421894\pi\) | ||||
0.242922 | + | 0.970046i | \(0.421894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −608.000 | −0.151086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1647.00 | − | 2852.69i | −0.399755 | − | 0.692396i | 0.593940 | − | 0.804509i | \(-0.297571\pi\) |
−0.993695 | + | 0.112113i | \(0.964238\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3540.00 | + | 6131.46i | −0.829984 | + | 1.43757i | 0.0680662 | + | 0.997681i | \(0.478317\pi\) |
−0.898050 | + | 0.439893i | \(0.855016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8484.00 | 1.96667 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3907.00 | − | 6767.12i | 0.885554 | − | 1.53382i | 0.0404764 | − | 0.999180i | \(-0.487112\pi\) |
0.845078 | − | 0.534644i | \(-0.179554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1584.00 | − | 2743.57i | −0.355060 | − | 0.614981i | 0.632069 | − | 0.774912i | \(-0.282206\pi\) |
−0.987128 | + | 0.159931i | \(0.948873\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 142.000 | + | 245.951i | 0.0311379 | + | 0.0539324i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3929.00 | − | 6805.23i | 0.852241 | − | 1.47612i | −0.0269403 | − | 0.999637i | \(-0.508576\pi\) |
0.879181 | − | 0.476488i | \(-0.158090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6730.00 | −1.42875 | −0.714374 | − | 0.699764i | \(-0.753288\pi\) | ||||
−0.714374 | + | 0.699764i | \(0.753288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1510.00 | − | 2615.40i | 0.317174 | − | 0.549361i | −0.662723 | − | 0.748864i | \(-0.730599\pi\) |
0.979897 | + | 0.199503i | \(0.0639328\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2358.50 | + | 4085.04i | 0.480053 | + | 0.831476i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6834.00 | 1.36262 | 0.681308 | − | 0.731997i | \(-0.261411\pi\) | ||||
0.681308 | + | 0.731997i | \(0.261411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5096.00 | −1.00576 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4104.00 | − | 7108.34i | −0.793781 | − | 1.37487i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4746.00 | − | 8220.31i | 0.891001 | − | 1.54326i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2332.00 | 0.433532 | 0.216766 | − | 0.976224i | \(-0.430449\pi\) | ||||
0.216766 | + | 0.976224i | \(0.430449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4420.00 | − | 7655.66i | 0.805901 | − | 1.39586i | −0.109780 | − | 0.993956i | \(-0.535015\pi\) |
0.915681 | − | 0.401906i | \(-0.131652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 523.000 | + | 905.863i | 0.0944464 | + | 0.163586i | 0.909377 | − | 0.415972i | \(-0.136559\pi\) |
−0.814931 | + | 0.579558i | \(0.803225\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3771.00 | + | 6531.56i | 0.668140 | + | 1.15725i | 0.978424 | + | 0.206609i | \(0.0662427\pi\) |
−0.310283 | + | 0.950644i | \(0.600424\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 212.000 | − | 367.195i | 0.0372092 | − | 0.0644482i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1288.00 | 0.221877 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1917.00 | + | 3320.34i | −0.327188 | + | 0.566706i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1378.00 | − | 2386.77i | −0.228827 | − | 0.396340i | 0.728634 | − | 0.684904i | \(-0.240156\pi\) |
−0.957461 | + | 0.288564i | \(0.906822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11816.0 | −1.92710 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3954.00 | 0.639134 | 0.319567 | − | 0.947564i | \(-0.396463\pi\) | ||||
0.319567 | + | 0.947564i | \(0.396463\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −288.000 | − | 498.831i | −0.0457363 | − | 0.0792176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3450.00 | − | 5975.58i | 0.533734 | − | 0.924454i | −0.465489 | − | 0.885053i | \(-0.654122\pi\) |
0.999223 | − | 0.0394010i | \(-0.0125450\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2426.00 | −0.372094 | −0.186047 | − | 0.982541i | \(-0.559568\pi\) | ||||
−0.186047 | + | 0.982541i | \(0.559568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −735.000 | + | 1273.06i | −0.110822 | + | 0.191949i | −0.916102 | − | 0.400946i | \(-0.868682\pi\) |
0.805280 | + | 0.592895i | \(0.202015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 56.0000 | + | 96.9948i | 0.00837231 | + | 0.0145013i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3436.00 | + | 5951.33i | 0.505140 | + | 0.874928i | 0.999982 | + | 0.00594499i | \(0.00189236\pi\) |
−0.494843 | + | 0.868983i | \(0.664774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −802.500 | + | 1389.97i | −0.117000 | + | 0.202649i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5908.00 | 0.847230 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3536.00 | − | 6124.53i | 0.502937 | − | 0.871112i | −0.497058 | − | 0.867717i | \(-0.665586\pi\) |
0.999994 | − | 0.00339411i | \(-0.00108038\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 409.000 | + | 708.409i | 0.0567754 | + | 0.0983378i | 0.893016 | − | 0.450025i | \(-0.148585\pi\) |
−0.836241 | + | 0.548362i | \(0.815251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5724.00 | 0.781966 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5132.00 | −0.695549 | −0.347775 | − | 0.937578i | \(-0.613063\pi\) | ||||
−0.347775 | + | 0.937578i | \(0.613063\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4288.00 | − | 7427.03i | −0.572080 | − | 0.990871i | −0.996352 | − | 0.0853367i | \(-0.972803\pi\) |
0.424272 | − | 0.905535i | \(-0.360530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1865.00 | + | 3230.27i | −0.243083 | + | 0.421032i | −0.961591 | − | 0.274487i | \(-0.911492\pi\) |
0.718508 | + | 0.695519i | \(0.244825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2128.00 | 0.275237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2688.00 | − | 4655.75i | 0.342400 | − | 0.593054i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3339.00 | − | 5783.32i | −0.422115 | − | 0.731124i | 0.574031 | − | 0.818833i | \(-0.305379\pi\) |
−0.996146 | + | 0.0877090i | \(0.972045\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1527.00 | − | 2644.84i | −0.190161 | − | 0.329369i | 0.755142 | − | 0.655561i | \(-0.227568\pi\) |
−0.945304 | + | 0.326192i | \(0.894234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3888.00 | − | 6734.21i | 0.480583 | − | 0.832395i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −632.000 | −0.0769707 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −133.000 | + | 230.363i | −0.0160793 | + | 0.0278501i | −0.873953 | − | 0.486010i | \(-0.838452\pi\) |
0.857874 | + | 0.513860i | \(0.171785\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3836.00 | + | 6644.15i | 0.453739 | + | 0.785900i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8844.00 | −1.03116 | −0.515582 | − | 0.856840i | \(-0.672424\pi\) | ||||
−0.515582 | + | 0.856840i | \(0.672424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4482.00 | −0.518858 | −0.259429 | − | 0.965762i | \(-0.583534\pi\) | ||||
−0.259429 | + | 0.965762i | \(0.583534\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −497.000 | − | 860.829i | −0.0567248 | − | 0.0982502i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4968.00 | − | 8604.83i | 0.555221 | − | 0.961671i | −0.442666 | − | 0.896687i | \(-0.645967\pi\) |
0.997886 | − | 0.0649838i | \(-0.0206996\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11758.0 | −1.30497 | −0.652487 | − | 0.757800i | \(-0.726274\pi\) | ||||
−0.652487 | + | 0.757800i | \(0.726274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6992.00 | + | 12110.5i | −0.765384 | + | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2052.00 | + | 3554.17i | 0.223090 | + | 0.386404i | 0.955745 | − | 0.294197i | \(-0.0950522\pi\) |
−0.732655 | + | 0.680601i | \(0.761719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4874.00 | + | 8442.02i | 0.522733 | + | 0.905400i | 0.999650 | + | 0.0264519i | \(0.00842087\pi\) |
−0.476917 | + | 0.878948i | \(0.658246\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8358.00 | + | 14476.5i | −0.890353 | + | 1.54214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 478.000 | 0.0502410 | 0.0251205 | − | 0.999684i | \(-0.492003\pi\) | ||||
0.0251205 | + | 0.999684i | \(0.492003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 780.000 | − | 1351.00i | 0.0814385 | − | 0.141056i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5587.00 | + | 9676.97i | 0.571879 | + | 0.990524i | 0.996373 | + | 0.0850931i | \(0.0271188\pi\) |
−0.424494 | + | 0.905431i | \(0.639548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11674.0 | 1.17942 | 0.589710 | − | 0.807615i | \(-0.299242\pi\) | ||||
0.589710 | + | 0.807615i | \(0.299242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10528.0 | 1.05676 | 0.528378 | − | 0.849009i | \(-0.322801\pi\) | ||||
0.528378 | + | 0.849009i | \(0.322801\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8302.00 | + | 14379.5i | 0.822635 | + | 1.42485i | 0.903713 | + | 0.428139i | \(0.140830\pi\) |
−0.0810777 | + | 0.996708i | \(0.525836\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1016.00 | + | 1759.76i | −0.0987648 | + | 0.171066i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6532.00 | 0.630966 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4288.00 | + | 7427.03i | −0.409027 | + | 0.708455i | −0.994781 | − | 0.102034i | \(-0.967465\pi\) |
0.585754 | + | 0.810489i | \(0.300798\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4266.00 | − | 7388.93i | −0.404393 | − | 0.700429i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10514.0 | − | 18210.8i | −0.984363 | − | 1.70497i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4852.00 | + | 8403.91i | −0.451468 | + | 0.781966i | −0.998478 | − | 0.0551605i | \(-0.982433\pi\) |
0.547009 | + | 0.837127i | \(0.315766\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4092.00 | 0.376109 | 0.188054 | − | 0.982159i | \(-0.439782\pi\) | ||||
0.188054 | + | 0.982159i | \(0.439782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −742.000 | + | 1285.18i | −0.0677850 | + | 0.117407i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8942.00 | − | 15488.0i | −0.802202 | − | 1.38945i | −0.918164 | − | 0.396201i | \(-0.870328\pi\) |
0.115961 | − | 0.993254i | \(-0.463005\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7704.00 | 0.682911 | 0.341456 | − | 0.939898i | \(-0.389080\pi\) | ||||
0.341456 | + | 0.939898i | \(0.389080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5572.00 | 0.490992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7179.00 | + | 12434.4i | 0.625154 | + | 1.08280i | 0.988511 | + | 0.151149i | \(0.0482973\pi\) |
−0.363357 | + | 0.931650i | \(0.618369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8120.00 | − | 14064.3i | 0.694777 | − | 1.20339i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2112.00 | −0.179663 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2541.00 | − | 4401.14i | 0.213672 | − | 0.370091i | −0.739189 | − | 0.673498i | \(-0.764791\pi\) |
0.952861 | + | 0.303407i | \(0.0981242\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 878.000 | + | 1520.74i | 0.0734078 | + | 0.127146i | 0.900393 | − | 0.435078i | \(-0.143279\pi\) |
−0.826985 | + | 0.562224i | \(0.809946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1008.00 | + | 1745.91i | 0.0833191 | + | 0.144313i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5468.50 | + | 9471.72i | −0.449453 | + | 0.778476i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21060.0 | 1.71146 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2268.00 | + | 3928.29i | −0.183279 | + | 0.317448i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8115.00 | − | 14055.6i | −0.644900 | − | 1.11700i | −0.984325 | − | 0.176367i | \(-0.943566\pi\) |
0.339424 | − | 0.940633i | \(-0.389768\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13132.0 | 1.03213 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17676.0 | 1.38167 | 0.690833 | − | 0.723014i | \(-0.257244\pi\) | ||||
0.690833 | + | 0.723014i | \(0.257244\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4876.00 | − | 8445.48i | −0.376996 | − | 0.652976i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6125.00 | + | 10608.8i | −0.465933 | + | 0.807019i | −0.999243 | − | 0.0389004i | \(-0.987614\pi\) |
0.533310 | + | 0.845920i | \(0.320948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27432.0 | −2.07558 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5026.00 | + | 8705.29i | −0.376236 | + | 0.651659i | −0.990511 | − | 0.137432i | \(-0.956115\pi\) |
0.614276 | + | 0.789092i | \(0.289448\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4354.00 | + | 7541.35i | 0.324202 | + | 0.561534i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12837.0 | + | 22234.3i | 0.945791 | + | 1.63816i | 0.754160 | + | 0.656691i | \(0.228044\pi\) |
0.191631 | + | 0.981467i | \(0.438622\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1866.00 | + | 3232.01i | −0.136759 | + | 0.236874i | −0.926268 | − | 0.376865i | \(-0.877002\pi\) |
0.789509 | + | 0.613739i | \(0.210335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10792.0 | 0.782709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 607.000 | − | 1051.35i | 0.0437950 | − | 0.0758552i | −0.843297 | − | 0.537448i | \(-0.819388\pi\) |
0.887092 | + | 0.461593i | \(0.152722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1212.00 | − | 2099.25i | −0.0860993 | − | 0.149128i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7108.00 | −0.499793 | −0.249897 | − | 0.968273i | \(-0.580397\pi\) | ||||
−0.249897 | + | 0.968273i | \(0.580397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13248.0 | −0.926782 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3081.00 | + | 5336.45i | 0.213358 | + | 0.369548i | 0.952763 | − | 0.303713i | \(-0.0982265\pi\) |
−0.739405 | + | 0.673261i | \(0.764893\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1236.00 | − | 2140.81i | 0.0843098 | − | 0.146029i | −0.820787 | − | 0.571234i | \(-0.806465\pi\) |
0.905097 | + | 0.425205i | \(0.139798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13750.0 | −0.933235 | −0.466617 | − | 0.884459i | \(-0.654528\pi\) | ||||
−0.466617 | + | 0.884459i | \(0.654528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9205.00 | + | 15943.5i | −0.618573 | + | 1.07140i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5688.00 | + | 9851.90i | 0.380344 | + | 0.658775i | 0.991111 | − | 0.133035i | \(-0.0424723\pi\) |
−0.610767 | + | 0.791810i | \(0.709139\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14256.0 | − | 24692.1i | −0.943921 | − | 1.63492i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10191.0 | + | 17651.3i | −0.671469 | + | 1.16302i | 0.306018 | + | 0.952026i | \(0.401003\pi\) |
−0.977488 | + | 0.210993i | \(0.932330\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21178.0 | −1.38184 | −0.690919 | − | 0.722932i | \(-0.742794\pi\) | ||||
−0.690919 | + | 0.722932i | \(0.742794\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2350.00 | − | 4070.32i | 0.152592 | − | 0.264297i | −0.779588 | − | 0.626293i | \(-0.784571\pi\) |
0.932180 | + | 0.361996i | \(0.117905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9729.50 | + | 16852.0i | 0.622688 | + | 1.07853i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2212.00 | 0.140220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21736.0 | −1.37131 | −0.685655 | − | 0.727927i | \(-0.740484\pi\) | ||||
−0.685655 | + | 0.727927i | \(0.740484\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8400.00 | + | 14549.2i | 0.524951 | + | 0.909242i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6511.00 | + | 11277.4i | −0.401200 | + | 0.694898i | −0.993871 | − | 0.110546i | \(-0.964740\pi\) |
0.592671 | + | 0.805444i | \(0.298073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3308.00 | 0.202885 | 0.101442 | − | 0.994841i | \(-0.467654\pi\) | ||||
0.101442 | + | 0.994841i | \(0.467654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6900.00 | + | 11951.2i | −0.419269 | + | 0.726195i | −0.995866 | − | 0.0908335i | \(-0.971047\pi\) |
0.576597 | + | 0.817029i | \(0.304380\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 728.000 | + | 1260.93i | 0.0440316 | + | 0.0762649i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1341.00 | − | 2322.68i | −0.0803635 | − | 0.139194i | 0.823043 | − | 0.567980i | \(-0.192275\pi\) |
−0.903406 | + | 0.428786i | \(0.858941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9772.00 | − | 16925.6i | 0.582937 | − | 1.00968i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23836.0 | −1.40898 | −0.704491 | − | 0.709713i | \(-0.748825\pi\) | ||||
−0.704491 | + | 0.709713i | \(0.748825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5641.00 | − | 9770.50i | 0.331936 | − | 0.574929i | −0.650956 | − | 0.759116i | \(-0.725632\pi\) |
0.982891 | + | 0.184186i | \(0.0589650\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8056.00 | − | 13953.4i | −0.467661 | − | 0.810012i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2712.00 | −0.156029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13726.0 | −0.786179 | −0.393089 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393089 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2487.00 | + | 4307.61i | 0.141186 | + | 0.244542i | 0.927944 | − | 0.372721i | \(-0.121575\pi\) |
−0.786757 | + | 0.617263i | \(0.788242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4494.00 | + | 7783.84i | −0.251769 | + | 0.436076i | −0.964013 | − | 0.265855i | \(-0.914346\pi\) |
0.712244 | + | 0.701932i | \(0.247679\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39340.0 | 2.19431 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16362.0 | − | 28339.8i | 0.904706 | − | 1.56700i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5086.00 | − | 8809.21i | −0.280001 | − | 0.484976i | 0.691384 | − | 0.722488i | \(-0.257001\pi\) |
−0.971385 | + | 0.237512i | \(0.923668\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.0000 | + | 48.4974i | 0.00152820 | + | 0.00264692i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2730.00 | + | 4728.50i | −0.148359 | + | 0.256965i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27446.0 | −1.47877 | −0.739387 | − | 0.673280i | \(-0.764885\pi\) | ||||
−0.739387 | + | 0.673280i | \(0.764885\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7268.00 | + | 12588.5i | −0.389926 | + | 0.675371i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1999.00 | − | 3462.37i | −0.105887 | − | 0.183402i | 0.808213 | − | 0.588890i | \(-0.200435\pi\) |
−0.914100 | + | 0.405488i | \(0.867102\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21888.0 | −1.14967 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3024.00 | 0.158169 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12936.0 | + | 22405.8i | 0.670976 | + | 1.16216i | 0.977628 | + | 0.210342i | \(0.0674578\pi\) |
−0.306652 | + | 0.951822i | \(0.599209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3763.00 | + | 6517.71i | −0.192765 | + | 0.333878i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12088.0 | 0.616670 | 0.308335 | − | 0.951278i | \(-0.400228\pi\) | ||||
0.308335 | + | 0.951278i | \(0.400228\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3556.00 | − | 6159.17i | 0.179923 | − | 0.311635i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3987.00 | − | 6905.69i | −0.200905 | − | 0.347977i | 0.747915 | − | 0.663794i | \(-0.231055\pi\) |
−0.948820 | + | 0.315817i | \(0.897722\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1688.00 | + | 2923.70i | 0.0843667 | + | 0.146127i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15882.0 | − | 27508.4i | 0.790567 | − | 1.36930i | −0.135050 | − | 0.990839i | \(-0.543119\pi\) |
0.925616 | − | 0.378463i | \(-0.123547\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −888.000 | −0.0438460 | −0.0219230 | − | 0.999760i | \(-0.506979\pi\) | ||||
−0.0219230 | + | 0.999760i | \(0.506979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9618.00 | + | 16658.9i | −0.472988 | + | 0.819240i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17328.0 | + | 30013.0i | 0.841954 | + | 1.45831i | 0.888240 | + | 0.459379i | \(0.151928\pi\) |
−0.0462858 | + | 0.998928i | \(0.514738\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29456.0 | −1.41989 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22866.0 | −1.09786 | −0.548929 | − | 0.835869i | \(-0.684964\pi\) | ||||
−0.548929 | + | 0.835869i | \(0.684964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11285.0 | + | 19546.2i | 0.537557 | + | 0.931076i | 0.999035 | + | 0.0439244i | \(0.0139861\pi\) |
−0.461478 | + | 0.887152i | \(0.652681\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9828.00 | + | 17022.6i | −0.462671 | + | 0.801369i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1790.00 | −0.0839389 | −0.0419695 | − | 0.999119i | \(-0.513363\pi\) | ||||
−0.0419695 | + | 0.999119i | \(0.513363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1495.00 | − | 2589.42i | 0.0695620 | − | 0.120485i | −0.829147 | − | 0.559031i | \(-0.811173\pi\) |
0.898709 | + | 0.438546i | \(0.144507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5112.00 | + | 8854.24i | 0.236940 | + | 0.410392i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17940.0 | − | 31073.0i | −0.825118 | − | 1.42915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.000733067 | − | 0.00126971i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44884.0 | −2.04074 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15378.0 | − | 26635.5i | 0.696527 | − | 1.20642i | −0.273137 | − | 0.961975i | \(-0.588061\pi\) |
0.969663 | − | 0.244444i | \(-0.0786056\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18306.0 | − | 31706.9i | −0.819754 | − | 1.41986i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15126.0 | −0.672259 | −0.336129 | − | 0.941816i | \(-0.609118\pi\) | ||||
−0.336129 | + | 0.941816i | \(0.609118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7392.00 | 0.327297 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −844.000 | − | 1461.85i | −0.0370911 | − | 0.0642436i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3251.00 | + | 5630.90i | −0.141284 | + | 0.244712i | −0.927981 | − | 0.372629i | \(-0.878457\pi\) |
0.786696 | + | 0.617340i | \(0.211790\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8252.00 | −0.357296 | −0.178648 | − | 0.983913i | \(-0.557172\pi\) | ||||
−0.178648 | + | 0.983913i | \(0.557172\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2324.00 | − | 4025.29i | 0.0998849 | − | 0.173006i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23368.0 | + | 40474.6i | 1.00066 | + | 1.73320i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10993.0 | − | 19040.4i | −0.467306 | − | 0.809398i | 0.531996 | − | 0.846747i | \(-0.321442\pi\) |
−0.999302 | + | 0.0373488i | \(0.988109\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1868.00 | + | 3235.47i | −0.0791183 | + | 0.137037i | −0.902870 | − | 0.429914i | \(-0.858544\pi\) |
0.823751 | + | 0.566951i | \(0.191877\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23820.0 | 1.00158 | 0.500788 | − | 0.865570i | \(-0.333044\pi\) | ||||
0.500788 | + | 0.865570i | \(0.333044\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3971.00 | + | 6877.97i | −0.166367 | + | 0.288157i | −0.937140 | − | 0.348954i | \(-0.886537\pi\) |
0.770773 | + | 0.637110i | \(0.219870\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10472.0 | − | 18138.0i | −0.434010 | − | 0.751728i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21016.0 | −0.864783 | −0.432391 | − | 0.901686i | \(-0.642330\pi\) | ||||
−0.432391 | + | 0.901686i | \(0.642330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13153.0 | −0.539301 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5033.00 | + | 8717.41i | 0.204900 | + | 0.354897i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12008.0 | + | 20798.5i | −0.483700 | + | 0.837793i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24878.0 | 0.998601 | 0.499300 | − | 0.866429i | \(-0.333590\pi\) | ||||
0.499300 | + | 0.866429i | \(0.333590\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3195.00 | + | 5533.90i | −0.127350 | + | 0.220577i | −0.922649 | − | 0.385640i | \(-0.873981\pi\) |
0.795299 | + | 0.606217i | \(0.207314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23222.0 | + | 40221.7i | 0.922380 | + | 1.59761i | 0.795722 | + | 0.605663i | \(0.207092\pi\) |
0.126658 | + | 0.991946i | \(0.459575\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12704.0 | − | 22004.0i | −0.501100 | − | 0.867930i | −0.999999 | − | 0.00127049i | \(-0.999596\pi\) |
0.498899 | − | 0.866660i | \(-0.333738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23254.0 | − | 40277.1i | 0.914057 | − | 1.58319i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1536.00 | −0.0599600 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22788.0 | + | 39470.0i | −0.886500 | + | 1.53546i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −539.000 | − | 933.575i | −0.0207534 | − | 0.0359460i | 0.855462 | − | 0.517865i | \(-0.173273\pi\) |
−0.876216 | + | 0.481919i | \(0.839940\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45006.0 | 1.72110 | 0.860551 | − | 0.509364i | \(-0.170119\pi\) | ||||
0.860551 | + | 0.509364i | \(0.170119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4028.00 | 0.153514 | 0.0767571 | − | 0.997050i | \(-0.475543\pi\) | ||||
0.0767571 | + | 0.997050i | \(0.475543\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14652.0 | − | 25378.0i | −0.554640 | − | 0.960665i | −0.997931 | − | 0.0642876i | \(-0.979523\pi\) |
0.443291 | − | 0.896378i | \(-0.353811\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24288.0 | + | 42068.1i | −0.910153 | + | 1.57643i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12600.0 | −0.470583 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7632.00 | − | 13219.0i | 0.283138 | − | 0.490410i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4242.00 | + | 7347.36i | 0.156850 | + | 0.271672i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13314.0 | + | 23060.5i | 0.489030 | + | 0.847025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25458.0 | + | 44094.5i | −0.931995 | + | 1.61426i | −0.152087 | + | 0.988367i | \(0.548599\pi\) |
−0.779908 | + | 0.625895i | \(0.784734\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24432.0 | 0.888549 | 0.444275 | − | 0.895891i | \(-0.353461\pi\) | ||||
0.444275 | + | 0.895891i | \(0.353461\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1096.00 | − | 1898.33i | 0.0397287 | − | 0.0688121i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10180.0 | + | 17632.3i | 0.365405 | + | 0.632900i | 0.988841 | − | 0.148974i | \(-0.0475972\pi\) |
−0.623436 | + | 0.781874i | \(0.714264\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 432.000 | 0.0154057 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11218.0 | 0.398752 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11601.0 | + | 20093.5i | 0.409706 | + | 0.709631i | 0.994857 | − | 0.101293i | \(-0.0322981\pi\) |
−0.585151 | + | 0.810924i | \(0.698965\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −392.000 | + | 678.964i | −0.0137110 | + | 0.0237481i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1990.00 | −0.0693815 | −0.0346908 | − | 0.999398i | \(-0.511045\pi\) | ||||
−0.0346908 | + | 0.999398i | \(0.511045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25565.0 | + | 44279.9i | −0.885648 | + | 1.53399i | −0.0406798 | + | 0.999172i | \(0.512952\pi\) |
−0.844969 | + | 0.534816i | \(0.820381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29640.0 | − | 51338.0i | −1.02355 | − | 1.77285i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23522.0 | − | 40741.3i | −0.807141 | − | 1.39801i | −0.914836 | − | 0.403825i | \(-0.867681\pi\) |
0.107696 | − | 0.994184i | \(-0.465653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11394.0 | − | 19735.0i | 0.389742 | − | 0.675052i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46858.0 | −1.59274 | −0.796369 | − | 0.604811i | \(-0.793249\pi\) | ||||
−0.796369 | + | 0.604811i | \(0.793249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28896.0 | + | 50049.3i | −0.979113 | + | 1.69587i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4527.50 | + | 7841.86i | 0.151975 | + | 0.263229i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18788.0 | 0.626743 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30632.0 | 1.01867 | 0.509337 | − | 0.860567i | \(-0.329890\pi\) | ||||
0.509337 | + | 0.860567i | \(0.329890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1902.00 | − | 3294.36i | −0.0628611 | − | 0.108879i | 0.832882 | − | 0.553450i | \(-0.186689\pi\) |
−0.895743 | + | 0.444572i | \(0.853356\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24663.0 | + | 42717.6i | −0.807614 | + | 1.39883i | 0.106897 | + | 0.994270i | \(0.465908\pi\) |
−0.914512 | + | 0.404559i | \(0.867425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4776.00 | 0.155916 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5556.00 | − | 9623.27i | 0.180274 | − | 0.312243i | −0.761700 | − | 0.647930i | \(-0.775635\pi\) |
0.941974 | + | 0.335687i | \(0.108968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24542.0 | + | 42508.0i | 0.793881 | + | 1.37504i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38608.0 | + | 66871.0i | 1.24132 | + | 2.15002i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6808.00 | + | 11791.8i | −0.218227 | + | 0.377981i | −0.954266 | − | 0.298959i | \(-0.903361\pi\) |
0.736039 | + | 0.676939i | \(0.236694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9520.00 | −0.303321 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28337.0 | − | 49081.1i | 0.900142 | − | 1.55909i | 0.0728338 | − | 0.997344i | \(-0.476796\pi\) |
0.827308 | − | 0.561748i | \(-0.189871\pi\) | |||||||
\(998\) | 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.n.361.1 | 2 | ||
3.2 | odd | 2 | 588.4.i.a.361.1 | 2 | |||
7.2 | even | 3 | inner | 1764.4.k.n.1549.1 | 2 | ||
7.3 | odd | 6 | 1764.4.a.l.1.1 | 1 | |||
7.4 | even | 3 | 252.4.a.a.1.1 | 1 | |||
7.5 | odd | 6 | 1764.4.k.c.1549.1 | 2 | |||
7.6 | odd | 2 | 1764.4.k.c.361.1 | 2 | |||
21.2 | odd | 6 | 588.4.i.a.373.1 | 2 | |||
21.5 | even | 6 | 588.4.i.h.373.1 | 2 | |||
21.11 | odd | 6 | 84.4.a.b.1.1 | ✓ | 1 | ||
21.17 | even | 6 | 588.4.a.a.1.1 | 1 | |||
21.20 | even | 2 | 588.4.i.h.361.1 | 2 | |||
28.11 | odd | 6 | 1008.4.a.d.1.1 | 1 | |||
84.11 | even | 6 | 336.4.a.e.1.1 | 1 | |||
84.59 | odd | 6 | 2352.4.a.v.1.1 | 1 | |||
105.32 | even | 12 | 2100.4.k.g.1849.1 | 2 | |||
105.53 | even | 12 | 2100.4.k.g.1849.2 | 2 | |||
105.74 | odd | 6 | 2100.4.a.g.1.1 | 1 | |||
168.11 | even | 6 | 1344.4.a.p.1.1 | 1 | |||
168.53 | odd | 6 | 1344.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.a.b.1.1 | ✓ | 1 | 21.11 | odd | 6 | ||
252.4.a.a.1.1 | 1 | 7.4 | even | 3 | |||
336.4.a.e.1.1 | 1 | 84.11 | even | 6 | |||
588.4.a.a.1.1 | 1 | 21.17 | even | 6 | |||
588.4.i.a.361.1 | 2 | 3.2 | odd | 2 | |||
588.4.i.a.373.1 | 2 | 21.2 | odd | 6 | |||
588.4.i.h.361.1 | 2 | 21.20 | even | 2 | |||
588.4.i.h.373.1 | 2 | 21.5 | even | 6 | |||
1008.4.a.d.1.1 | 1 | 28.11 | odd | 6 | |||
1344.4.a.b.1.1 | 1 | 168.53 | odd | 6 | |||
1344.4.a.p.1.1 | 1 | 168.11 | even | 6 | |||
1764.4.a.l.1.1 | 1 | 7.3 | odd | 6 | |||
1764.4.k.c.361.1 | 2 | 7.6 | odd | 2 | |||
1764.4.k.c.1549.1 | 2 | 7.5 | odd | 6 | |||
1764.4.k.n.361.1 | 2 | 1.1 | even | 1 | trivial | ||
1764.4.k.n.1549.1 | 2 | 7.2 | even | 3 | inner | ||
2100.4.a.g.1.1 | 1 | 105.74 | odd | 6 | |||
2100.4.k.g.1849.1 | 2 | 105.32 | even | 12 | |||
2100.4.k.g.1849.2 | 2 | 105.53 | even | 12 | |||
2352.4.a.v.1.1 | 1 | 84.59 | odd | 6 |