Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,4,Mod(165,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("196.165");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.e (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: | \(11.5643743611\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.165 |
Dual form | 196.4.e.e.177.1 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 2.00000 | − | 3.46410i | 0.384900 | − | 0.666667i | −0.606855 | − | 0.794812i | \(-0.707569\pi\) |
0.991755 | + | 0.128146i | \(0.0409025\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.0000 | + | 17.3205i | 0.894427 | + | 1.54919i | 0.834512 | + | 0.550990i | \(0.185750\pi\) |
0.0599153 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.50000 | + | 9.52628i | 0.203704 | + | 0.352825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −22.0000 | + | 38.1051i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −44.0000 | −0.938723 | −0.469362 | − | 0.883006i | \(-0.655516\pi\) | ||||
−0.469362 | + | 0.883006i | \(0.655516\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 80.0000 | 1.37706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −36.0000 | + | 62.3538i | −0.513605 | + | 0.889590i | 0.486271 | + | 0.873808i | \(0.338357\pi\) |
−0.999875 | + | 0.0157814i | \(0.994976\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.0000 | − | 86.6025i | −0.603726 | − | 1.04568i | −0.992251 | − | 0.124246i | \(-0.960349\pi\) |
0.388526 | − | 0.921438i | \(-0.372984\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 60.0000 | + | 103.923i | 0.543951 | + | 0.942150i | 0.998672 | + | 0.0515165i | \(0.0164055\pi\) |
−0.454721 | + | 0.890634i | \(0.650261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −137.500 | + | 238.157i | −1.10000 | + | 1.90526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.000 | 1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 218.000 | 1.39592 | 0.697958 | − | 0.716138i | \(-0.254092\pi\) | ||||
0.697958 | + | 0.716138i | \(0.254092\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 140.000 | − | 242.487i | 0.811121 | − | 1.40490i | −0.100960 | − | 0.994891i | \(-0.532191\pi\) |
0.912080 | − | 0.410012i | \(-0.134475\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 88.0000 | + | 152.420i | 0.464207 | + | 0.804030i | ||||
\(34\) | 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 | ||||||||
\(39\) | −88.0000 | + | 152.420i | −0.361315 | + | 0.625816i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 120.000 | 0.457094 | 0.228547 | − | 0.973533i | \(-0.426603\pi\) | ||||
0.228547 | + | 0.973533i | \(0.426603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 220.000 | 0.780225 | 0.390113 | − | 0.920767i | \(-0.372436\pi\) | ||||
0.390113 | + | 0.920767i | \(0.372436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −110.000 | + | 190.526i | −0.364396 | + | 0.631153i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −44.0000 | − | 76.2102i | −0.136554 | − | 0.236519i | 0.789636 | − | 0.613576i | \(-0.210270\pi\) |
−0.926190 | + | 0.377057i | \(0.876936\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 144.000 | + | 249.415i | 0.395373 | + | 0.684806i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −55.0000 | + | 95.2628i | −0.142544 | + | 0.246893i | −0.928454 | − | 0.371448i | \(-0.878862\pi\) |
0.785910 | + | 0.618341i | \(0.212195\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −880.000 | −2.15744 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −400.000 | −0.929496 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −290.000 | + | 502.295i | −0.639912 | + | 1.10836i | 0.345540 | + | 0.938404i | \(0.387696\pi\) |
−0.985452 | + | 0.169955i | \(0.945638\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −190.000 | − | 329.090i | −0.398803 | − | 0.690748i | 0.594775 | − | 0.803892i | \(-0.297241\pi\) |
−0.993579 | + | 0.113144i | \(0.963908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −440.000 | − | 762.102i | −0.839620 | − | 1.45426i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 490.000 | − | 848.705i | 0.893478 | − | 1.54755i | 0.0578010 | − | 0.998328i | \(-0.481591\pi\) |
0.835677 | − | 0.549221i | \(-0.185076\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 480.000 | 0.837467 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −112.000 | −0.187211 | −0.0936053 | − | 0.995609i | \(-0.529839\pi\) | ||||
−0.0936053 | + | 0.995609i | \(0.529839\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 320.000 | − | 554.256i | 0.513057 | − | 0.888641i | −0.486828 | − | 0.873498i | \(-0.661846\pi\) |
0.999885 | − | 0.0151432i | \(-0.00482042\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 550.000 | + | 952.628i | 0.846780 | + | 1.46667i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 244.000 | + | 422.620i | 0.347496 | + | 0.601880i | 0.985804 | − | 0.167901i | \(-0.0536989\pi\) |
−0.638308 | + | 0.769781i | \(0.720366\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 155.500 | − | 269.334i | 0.213306 | − | 0.369457i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 660.000 | 0.872824 | 0.436412 | − | 0.899747i | \(-0.356249\pi\) | ||||
0.436412 | + | 0.899747i | \(0.356249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1440.00 | −1.83753 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 436.000 | − | 755.174i | 0.537289 | − | 0.930611i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −160.000 | − | 277.128i | −0.190561 | − | 0.330062i | 0.754875 | − | 0.655869i | \(-0.227697\pi\) |
−0.945436 | + | 0.325807i | \(0.894364\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −560.000 | − | 969.948i | −0.624401 | − | 1.08149i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1000.00 | − | 1732.05i | 1.07998 | − | 1.87058i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 248.000 | 0.259594 | 0.129797 | − | 0.991541i | \(-0.458567\pi\) | ||||
0.129797 | + | 0.991541i | \(0.458567\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −484.000 | −0.491352 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −110.000 | + | 190.526i | −0.108370 | + | 0.187703i | −0.915110 | − | 0.403204i | \(-0.867897\pi\) |
0.806740 | + | 0.590907i | \(0.201230\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −668.000 | − | 1157.01i | −0.639029 | − | 1.10683i | −0.985646 | − | 0.168824i | \(-0.946003\pi\) |
0.346617 | − | 0.938007i | \(-0.387330\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −50.0000 | − | 86.6025i | −0.0451746 | − | 0.0782447i | 0.842554 | − | 0.538612i | \(-0.181051\pi\) |
−0.887729 | + | 0.460367i | \(0.847718\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −341.000 | + | 590.629i | −0.299650 | + | 0.519009i | −0.976056 | − | 0.217520i | \(-0.930203\pi\) |
0.676406 | + | 0.736529i | \(0.263537\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 120.000 | 0.102612 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 370.000 | 0.308024 | 0.154012 | − | 0.988069i | \(-0.450781\pi\) | ||||
0.154012 | + | 0.988069i | \(0.450781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1200.00 | + | 2078.46i | −0.973048 | + | 1.68537i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −242.000 | − | 419.156i | −0.191221 | − | 0.331205i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −302.500 | − | 523.945i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 240.000 | − | 415.692i | 0.175936 | − | 0.304729i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3000.00 | −2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −160.000 | −0.111793 | −0.0558965 | − | 0.998437i | \(-0.517802\pi\) | ||||
−0.0558965 | + | 0.998437i | \(0.517802\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 440.000 | − | 762.102i | 0.300309 | − | 0.520150i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 150.000 | + | 259.808i | 0.100042 | + | 0.173279i | 0.911702 | − | 0.410852i | \(-0.134769\pi\) |
−0.811659 | + | 0.584131i | \(0.801435\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1520.00 | + | 2632.72i | 0.969043 | + | 1.67843i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −595.000 | + | 1030.57i | −0.371053 | + | 0.642683i | −0.989728 | − | 0.142964i | \(-0.954337\pi\) |
0.618675 | + | 0.785647i | \(0.287670\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2220.00 | 1.35466 | 0.677331 | − | 0.735679i | \(-0.263137\pi\) | ||||
0.677331 | + | 0.735679i | \(0.263137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −352.000 | −0.210239 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 968.000 | − | 1676.63i | 0.566072 | − | 0.980465i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2180.00 | + | 3775.87i | 1.24855 | + | 2.16254i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1207.00 | − | 2090.59i | −0.663633 | − | 1.14945i | −0.979654 | − | 0.200694i | \(-0.935680\pi\) |
0.316021 | − | 0.948752i | \(-0.397653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1028.00 | + | 1780.55i | −0.554023 | + | 0.959596i | 0.443956 | + | 0.896049i | \(0.353575\pi\) |
−0.997979 | + | 0.0635472i | \(0.979759\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −792.000 | −0.418493 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5600.00 | 2.90195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −530.000 | + | 917.987i | −0.269418 | + | 0.466645i | −0.968712 | − | 0.248189i | \(-0.920165\pi\) |
0.699294 | + | 0.714834i | \(0.253498\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 220.000 | + | 381.051i | 0.109730 | + | 0.190059i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 990.000 | + | 1714.73i | 0.475723 | + | 0.823976i | 0.999613 | − | 0.0278098i | \(-0.00885328\pi\) |
−0.523891 | + | 0.851786i | \(0.675520\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1760.00 | + | 3048.41i | −0.830399 | + | 1.43829i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 488.000 | 0.226123 | 0.113062 | − | 0.993588i | \(-0.463934\pi\) | ||||
0.113062 | + | 0.993588i | \(0.463934\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −261.000 | −0.118798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 550.000 | − | 952.628i | 0.245962 | − | 0.426019i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1738.00 | − | 3010.30i | −0.763802 | − | 1.32294i | −0.940878 | − | 0.338746i | \(-0.889997\pi\) |
0.177076 | − | 0.984197i | \(-0.443336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1160.00 | + | 2009.18i | 0.492604 | + | 0.853215i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 42.0000 | − | 72.7461i | 0.0175376 | − | 0.0303760i | −0.857123 | − | 0.515111i | \(-0.827751\pi\) |
0.874661 | + | 0.484735i | \(0.161084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2180.00 | 0.895238 | 0.447619 | − | 0.894224i | \(-0.352272\pi\) | ||||
0.447619 | + | 0.894224i | \(0.352272\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1520.00 | −0.613998 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −300.000 | + | 519.615i | −0.119224 | + | 0.206502i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1584.00 | − | 2743.57i | −0.619431 | − | 1.07289i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −348.000 | − | 602.754i | −0.131835 | − | 0.228344i | 0.792549 | − | 0.609808i | \(-0.208753\pi\) |
−0.924384 | + | 0.381464i | \(0.875420\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1345.00 | + | 2329.61i | −0.501633 | + | 0.868854i | 0.498365 | + | 0.866967i | \(0.333934\pi\) |
−0.999998 | + | 0.00188695i | \(0.999399\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3520.00 | −1.29268 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5310.00 | 1.92042 | 0.960208 | − | 0.279287i | \(-0.0900980\pi\) | ||||
0.960208 | + | 0.279287i | \(0.0900980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1540.00 | + | 2667.36i | −0.548581 | + | 0.950171i | 0.449791 | + | 0.893134i | \(0.351499\pi\) |
−0.998372 | + | 0.0570369i | \(0.981835\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1960.00 | − | 3394.82i | −0.687800 | − | 1.19130i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1200.00 | + | 2078.46i | 0.408837 | + | 0.708127i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −660.000 | + | 1143.15i | −0.221610 | + | 0.383839i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4400.00 | 1.45624 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.00130508 | −0.000652539 | − | 1.00000i | \(-0.500208\pi\) | ||||
−0.000652539 | 1.00000i | \(0.500208\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −224.000 | + | 387.979i | −0.0720574 | + | 0.124807i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2200.00 | + | 3810.51i | 0.697855 | + | 1.20872i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1280.00 | − | 2217.03i | −0.394952 | − | 0.684076i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1584.00 | − | 2743.57i | 0.482133 | − | 0.835079i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2416.00 | −0.725504 | −0.362752 | − | 0.931886i | \(-0.618163\pi\) | ||||
−0.362752 | + | 0.931886i | \(0.618163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3025.00 | −0.896296 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2486.00 | − | 4305.88i | 0.726879 | − | 1.25899i | −0.231316 | − | 0.972879i | \(-0.574303\pi\) |
0.958196 | − | 0.286113i | \(-0.0923634\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2230.00 | + | 3862.47i | 0.643505 | + | 1.11458i | 0.984645 | + | 0.174570i | \(0.0558536\pi\) |
−0.341140 | + | 0.940012i | \(0.610813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2275.00 | − | 3940.42i | −0.639658 | − | 1.10792i | −0.985508 | − | 0.169630i | \(-0.945743\pi\) |
0.345850 | − | 0.938290i | \(-0.387590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 880.000 | − | 1524.20i | 0.244276 | − | 0.423099i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1952.00 | 0.535004 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2112.00 | −0.571606 | −0.285803 | − | 0.958288i | \(-0.592260\pi\) | ||||
−0.285803 | + | 0.958288i | \(0.592260\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2420.00 | − | 4191.56i | 0.646829 | − | 1.12034i | −0.337046 | − | 0.941488i | \(-0.609428\pi\) |
0.983876 | − | 0.178853i | \(-0.0572388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1430.00 | + | 2476.83i | 0.377508 | + | 0.653864i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2200.00 | + | 3810.51i | 0.566731 | + | 0.981608i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1320.00 | − | 2286.31i | 0.335950 | − | 0.581883i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4340.00 | −1.09139 | −0.545694 | − | 0.837985i | \(-0.683734\pi\) | ||||
−0.545694 | + | 0.837985i | \(0.683734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5280.00 | −1.31206 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2880.00 | + | 4988.31i | −0.707265 | + | 1.22502i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1760.00 | + | 3048.41i | 0.427182 | + | 0.739901i | 0.996621 | − | 0.0821323i | \(-0.0261730\pi\) |
−0.569439 | + | 0.822033i | \(0.692840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1199.00 | + | 2076.73i | 0.284353 | + | 0.492515i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1280.00 | − | 2217.03i | 0.300107 | − | 0.519801i | −0.676053 | − | 0.736853i | \(-0.736311\pi\) |
0.976160 | + | 0.217052i | \(0.0696442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2200.00 | −0.509981 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1280.00 | −0.293388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3410.00 | + | 5906.29i | −0.772905 | + | 1.33871i | 0.163060 | + | 0.986616i | \(0.447864\pi\) |
−0.935965 | + | 0.352094i | \(0.885470\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1760.00 | − | 3048.41i | −0.394511 | − | 0.683312i | 0.598528 | − | 0.801102i | \(-0.295753\pi\) |
−0.993039 | + | 0.117789i | \(0.962419\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6050.00 | − | 10478.9i | −1.32665 | − | 2.29783i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4345.00 | − | 7525.76i | 0.942476 | − | 1.63242i | 0.181747 | − | 0.983345i | \(-0.441825\pi\) |
0.760728 | − | 0.649070i | \(-0.224842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3080.00 | 0.660913 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3894.00 | 0.826678 | 0.413339 | − | 0.910577i | \(-0.364362\pi\) | ||||
0.413339 | + | 0.910577i | \(0.364362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3278.00 | − | 5677.66i | 0.688540 | − | 1.19259i | −0.283770 | − | 0.958892i | \(-0.591585\pi\) |
0.972310 | − | 0.233694i | \(-0.0750815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4000.00 | − | 6928.20i | −0.831367 | − | 1.43997i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −135.500 | − | 234.693i | −0.0275799 | − | 0.0477698i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 496.000 | − | 859.097i | 0.0999176 | − | 0.173062i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2484.00 | −0.495279 | −0.247640 | − | 0.968852i | \(-0.579655\pi\) | ||||
−0.247640 | + | 0.968852i | \(0.579655\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11600.0 | −2.28942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3344.00 | + | 5791.98i | −0.653328 | + | 1.13160i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2640.00 | − | 4572.61i | −0.510619 | − | 0.884418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 440.000 | + | 762.102i | 0.0834236 | + | 0.144494i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3800.00 | − | 6581.79i | 0.713401 | − | 1.23565i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 308.000 | 0.0572589 | 0.0286295 | − | 0.999590i | \(-0.490886\pi\) | ||||
0.0286295 | + | 0.999590i | \(0.490886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5344.00 | −0.983850 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −880.000 | + | 1524.20i | −0.160451 | + | 0.277909i | −0.935030 | − | 0.354567i | \(-0.884628\pi\) |
0.774580 | + | 0.632476i | \(0.217961\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0000 | − | 20.7846i | −0.00216703 | − | 0.00375340i | 0.864940 | − | 0.501876i | \(-0.167356\pi\) |
−0.867107 | + | 0.498122i | \(0.834023\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2445.00 | + | 4234.86i | 0.433202 | + | 0.750327i | 0.997147 | − | 0.0754850i | \(-0.0240505\pi\) |
−0.563945 | + | 0.825812i | \(0.690717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4796.00 | + | 8306.92i | −0.841769 | + | 1.45799i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −400.000 | −0.0695509 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7200.00 | 1.24031 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6050.00 | − | 10478.9i | 1.03260 | − | 1.78851i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1364.00 | + | 2362.52i | 0.230671 | + | 0.399534i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4054.00 | − | 7021.73i | −0.673196 | − | 1.16601i | −0.976993 | − | 0.213273i | \(-0.931588\pi\) |
0.303796 | − | 0.952737i | \(-0.401746\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −165.000 | + | 285.788i | −0.0271530 | + | 0.0470304i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19600.0 | 3.19660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2990.00 | 0.483311 | 0.241655 | − | 0.970362i | \(-0.422310\pi\) | ||||
0.241655 | + | 0.970362i | \(0.422310\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 740.000 | − | 1281.72i | 0.118558 | − | 0.205349i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6160.00 | + | 10669.4i | 0.978248 | + | 1.69438i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4800.00 | + | 8313.84i | 0.749053 | + | 1.29740i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3930.00 | − | 6806.96i | 0.607993 | − | 1.05307i | −0.383578 | − | 0.923508i | \(-0.625308\pi\) |
0.991571 | − | 0.129566i | \(-0.0413583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6060.00 | −0.929468 | −0.464734 | − | 0.885450i | \(-0.653850\pi\) | ||||
−0.464734 | + | 0.885450i | \(0.653850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6688.00 | −1.01703 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1512.00 | − | 2618.86i | 0.227976 | − | 0.394867i | −0.729232 | − | 0.684267i | \(-0.760122\pi\) |
0.957208 | + | 0.289400i | \(0.0934558\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1120.00 | − | 1939.90i | −0.167446 | − | 0.290025i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2948.00 | − | 5106.09i | −0.433397 | − | 0.750665i | 0.563766 | − | 0.825934i | \(-0.309352\pi\) |
−0.997163 | + | 0.0752688i | \(0.976019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1570.50 | + | 2720.19i | −0.228969 | + | 0.396586i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2420.00 | −0.349909 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12800.0 | 1.83557 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1096.00 | + | 1898.33i | −0.155888 | + | 0.270005i | −0.933382 | − | 0.358885i | \(-0.883157\pi\) |
0.777494 | + | 0.628890i | \(0.216490\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 660.000 | + | 1143.15i | 0.0931117 | + | 0.161274i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1705.00 | + | 2953.15i | 0.236680 | + | 0.409941i | 0.959760 | − | 0.280823i | \(-0.0906074\pi\) |
−0.723080 | + | 0.690765i | \(0.757274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6000.00 | + | 10392.3i | −0.826236 | + | 1.43108i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9592.00 | −1.31038 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5916.00 | 0.801806 | 0.400903 | − | 0.916120i | \(-0.368696\pi\) | ||||
0.400903 | + | 0.916120i | \(0.368696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −320.000 | + | 554.256i | −0.0430291 | + | 0.0745286i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1020.00 | − | 1766.69i | −0.136082 | − | 0.235702i | 0.789928 | − | 0.613200i | \(-0.210118\pi\) |
−0.926010 | + | 0.377498i | \(0.876785\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1210.00 | + | 2095.78i | 0.158935 | + | 0.275283i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5889.00 | + | 10200.0i | −0.767569 | + | 1.32947i | 0.171309 | + | 0.985217i | \(0.445200\pi\) |
−0.938878 | + | 0.344250i | \(0.888133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8640.00 | −1.11750 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1200.00 | 0.154025 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4880.00 | + | 8452.41i | −0.621619 | + | 1.07668i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2354.00 | − | 4077.25i | −0.297592 | − | 0.515444i | 0.677993 | − | 0.735069i | \(-0.262850\pi\) |
−0.975584 | + | 0.219625i | \(0.929517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2937.00 | + | 5087.03i | 0.365753 | + | 0.633502i | 0.988897 | − | 0.148605i | \(-0.0474783\pi\) |
−0.623144 | + | 0.782107i | \(0.714145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6160.00 | + | 10669.4i | −0.761418 | + | 1.31881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6220.00 | 0.763146 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1320.00 | −0.160762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7020.00 | + | 12159.0i | −0.848696 | + | 1.46998i | 0.0336764 | + | 0.999433i | \(0.489278\pi\) |
−0.882372 | + | 0.470552i | \(0.844055\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2380.00 | + | 4122.28i | 0.285637 | + | 0.494738i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6600.00 | + | 11431.5i | 0.780678 | + | 1.35217i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4440.00 | − | 7690.31i | 0.521409 | − | 0.903108i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7940.00 | −0.925762 | −0.462881 | − | 0.886420i | \(-0.653184\pi\) | ||||
−0.462881 | + | 0.886420i | \(0.653184\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5214.00 | 0.603598 | 0.301799 | − | 0.953372i | \(-0.402413\pi\) | ||||
0.301799 | + | 0.953372i | \(0.402413\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 484.000 | − | 838.313i | 0.0556333 | − | 0.0963597i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9900.00 | − | 17147.3i | −1.12993 | − | 1.95710i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3872.00 | − | 6706.50i | −0.435762 | − | 0.754762i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5192.00 | + | 8992.81i | −0.580255 | + | 1.00503i | 0.415194 | + | 0.909733i | \(0.363714\pi\) |
−0.995449 | + | 0.0952980i | \(0.969620\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6520.00 | 0.723629 | 0.361814 | − | 0.932250i | \(-0.382157\pi\) | ||||
0.361814 | + | 0.932250i | \(0.382157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17440.0 | 1.92226 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6000.00 | − | 10392.3i | 0.656794 | − | 1.13760i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5760.00 | + | 9976.61i | 0.626218 | + | 1.08464i | 0.988304 | + | 0.152497i | \(0.0487314\pi\) |
−0.362086 | + | 0.932145i | \(0.617935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6690.00 | − | 11587.4i | −0.717498 | − | 1.24274i | −0.961988 | − | 0.273091i | \(-0.911954\pi\) |
0.244491 | − | 0.969652i | \(-0.421379\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3200.00 | − | 5542.56i | 0.340887 | − | 0.590433i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9656.00 | −1.02173 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4098.00 | 0.430727 | 0.215364 | − | 0.976534i | \(-0.430906\pi\) | ||||
0.215364 | + | 0.976534i | \(0.430906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2640.00 | + | 4572.61i | −0.275638 | + | 0.477419i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4112.00 | + | 7122.19i | 0.426487 | + | 0.738697i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8195.00 | + | 14194.2i | 0.838831 | + | 1.45290i | 0.890872 | + | 0.454254i | \(0.150094\pi\) |
−0.0520411 | + | 0.998645i | \(0.516573\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5472.00 | + | 9477.78i | −0.556451 | + | 0.963802i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9540.00 | 0.963822 | 0.481911 | − | 0.876220i | \(-0.339943\pi\) | ||||
0.481911 | + | 0.876220i | \(0.339943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8920.00 | −0.895351 | −0.447676 | − | 0.894196i | \(-0.647748\pi\) | ||||
−0.447676 | + | 0.894196i | \(0.647748\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11200.0 | − | 19399.0i | 1.11696 | − | 1.93464i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4214.00 | + | 7298.86i | 0.417560 | + | 0.723236i | 0.995693 | − | 0.0927068i | \(-0.0295519\pi\) |
−0.578133 | + | 0.815942i | \(0.696219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2120.00 | + | 3671.95i | 0.207398 | + | 0.359224i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4840.00 | + | 8383.13i | −0.470494 | + | 0.814919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27500.0 | 2.65639 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1210.00 | −0.116147 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7260.00 | − | 12574.7i | 0.692522 | − | 1.19948i | −0.278487 | − | 0.960440i | \(-0.589833\pi\) |
0.971009 | − | 0.239043i | \(-0.0768336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −660.000 | − | 1143.15i | −0.0625643 | − | 0.108364i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2480.00 | + | 4295.49i | 0.232188 | + | 0.402161i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5260.00 | − | 9110.59i | 0.489432 | − | 0.847721i | −0.510494 | − | 0.859881i | \(-0.670537\pi\) |
0.999926 | + | 0.0121603i | \(0.00387083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7920.00 | 0.732423 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5436.00 | −0.499640 | −0.249820 | − | 0.968292i | \(-0.580371\pi\) | ||||
−0.249820 | + | 0.968292i | \(0.580371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7848.00 | + | 13593.1i | −0.716950 | + | 1.24179i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4840.00 | − | 8383.13i | −0.439478 | − | 0.761199i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9174.00 | − | 15889.8i | −0.823015 | − | 1.42550i | −0.903427 | − | 0.428743i | \(-0.858957\pi\) |
0.0804114 | − | 0.996762i | \(-0.474377\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 976.000 | − | 1690.48i | 0.0870349 | − | 0.150749i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20944.0 | −1.85655 | −0.928277 | − | 0.371889i | \(-0.878710\pi\) | ||||
−0.928277 | + | 0.371889i | \(0.878710\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4400.00 | −0.387718 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −522.000 | + | 904.131i | −0.0457255 | + | 0.0791989i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −130.000 | − | 225.167i | −0.0113205 | − | 0.0196077i | 0.860310 | − | 0.509772i | \(-0.170270\pi\) |
−0.871630 | + | 0.490164i | \(0.836937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7600.00 | − | 13163.6i | −0.654090 | − | 1.13292i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13360.0 | − | 23140.2i | 1.14313 | − | 1.97996i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3872.00 | 0.329382 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13904.0 | −1.17595 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7300.00 | + | 12644.0i | −0.613856 | + | 1.06323i | 0.376728 | + | 0.926324i | \(0.377049\pi\) |
−0.990584 | + | 0.136905i | \(0.956284\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3410.00 | − | 5906.29i | −0.285103 | − | 0.493813i | 0.687531 | − | 0.726155i | \(-0.258694\pi\) |
−0.972634 | + | 0.232342i | \(0.925361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10080.0 | + | 17459.1i | 0.833191 | + | 1.44313i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1116.50 | + | 1933.83i | −0.0917646 | + | 0.158941i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6380.00 | −0.521409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5280.00 | −0.429085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1000.00 | − | 1732.05i | 0.0808108 | − | 0.139968i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −168.000 | − | 290.985i | −0.0135004 | − | 0.0233834i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6083.00 | − | 10536.1i | −0.483417 | − | 0.837303i | 0.516402 | − | 0.856347i | \(-0.327271\pi\) |
−0.999819 | + | 0.0190437i | \(0.993938\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4360.00 | − | 7551.74i | 0.344577 | − | 0.596826i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13640.0 | −1.07206 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22660.0 | 1.77125 | 0.885623 | − | 0.464405i | \(-0.153732\pi\) | ||||
0.885623 | + | 0.464405i | \(0.153732\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2090.00 | − | 3619.99i | 0.162475 | − | 0.281416i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10900.0 | − | 18879.4i | −0.842751 | − | 1.45969i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1200.00 | + | 2078.46i | 0.0917787 | + | 0.158965i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4245.00 | − | 7352.56i | 0.322920 | − | 0.559314i | −0.658169 | − | 0.752870i | \(-0.728669\pi\) |
0.981089 | + | 0.193556i | \(0.0620022\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9680.00 | −0.732416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12672.0 | −0.953676 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7150.00 | + | 12384.2i | −0.535234 | + | 0.927052i | 0.463918 | + | 0.885878i | \(0.346443\pi\) |
−0.999152 | + | 0.0411740i | \(0.986890\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3700.00 | + | 6408.59i | 0.275505 | + | 0.477188i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9147.00 | − | 15843.1i | −0.673923 | − | 1.16727i | −0.976782 | − | 0.214234i | \(-0.931275\pi\) |
0.302859 | − | 0.953035i | \(-0.402059\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7194.00 | − | 12460.4i | 0.527250 | − | 0.913223i | −0.472246 | − | 0.881467i | \(-0.656557\pi\) |
0.999496 | − | 0.0317563i | \(-0.0101101\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2784.00 | −0.202973 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33000.0 | −2.39338 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12616.0 | + | 21851.6i | −0.910244 | + | 1.57659i | −0.0965256 | + | 0.995331i | \(0.530773\pi\) |
−0.813719 | + | 0.581259i | \(0.802560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5380.00 | + | 9318.43i | 0.386157 | + | 0.668844i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2420.00 | − | 4191.56i | −0.171915 | − | 0.297765i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4840.00 | − | 8383.13i | 0.342067 | − | 0.592478i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16060.0 | 1.12925 | 0.564623 | − | 0.825349i | \(-0.309022\pi\) | ||||
0.564623 | + | 0.825349i | \(0.309022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28000.0 | −1.95878 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10620.0 | − | 18394.4i | 0.739168 | − | 1.28028i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11928.0 | + | 20659.9i | 0.826011 | + | 1.43069i | 0.901145 | + | 0.433519i | \(0.142728\pi\) |
−0.0751340 | + | 0.997173i | \(0.523938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6160.00 | + | 10669.4i | 0.422298 | + | 0.731442i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1584.00 | + | 2743.57i | −0.108048 | + | 0.187144i | −0.914979 | − | 0.403501i | \(-0.867793\pi\) |
0.806932 | + | 0.590645i | \(0.201127\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12320.0 | −0.836179 | −0.418089 | − | 0.908406i | \(-0.637300\pi\) | ||||
−0.418089 | + | 0.908406i | \(0.637300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10780.0 | 0.728019 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6050.00 | − | 10478.9i | 0.406558 | − | 0.704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4464.00 | + | 7731.87i | 0.298498 | + | 0.517013i | 0.975792 | − | 0.218698i | \(-0.0701811\pi\) |
−0.677295 | + | 0.735712i | \(0.736848\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1936.00 | + | 3353.25i | 0.128187 | + | 0.222026i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2255.00 | − | 3905.77i | 0.148578 | − | 0.257345i | −0.782124 | − | 0.623123i | \(-0.785864\pi\) |
0.930702 | + | 0.365778i | \(0.119197\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9600.00 | 0.629446 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5830.00 | 0.380400 | 0.190200 | − | 0.981745i | \(-0.439086\pi\) | ||||
0.190200 | + | 0.981745i | \(0.439086\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12230.0 | − | 21183.0i | 0.794128 | − | 1.37547i | −0.129263 | − | 0.991610i | \(-0.541261\pi\) |
0.923391 | − | 0.383860i | \(-0.125405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9120.00 | + | 15796.3i | 0.589328 | + | 1.02075i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12812.5 | − | 22191.9i | −0.820000 | − | 1.42028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8800.00 | − | 15242.0i | 0.560507 | − | 0.970827i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2160.00 | −0.136923 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15216.0 | 0.959967 | 0.479984 | − | 0.877277i | \(-0.340643\pi\) | ||||
0.479984 | + | 0.877277i | \(0.340643\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.00000 | + | 13.8564i | −0.000502325 | + | 0.000870052i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1600.00 | − | 2771.28i | −0.0999907 | − | 0.173189i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −616.000 | − | 1066.94i | −0.0381355 | − | 0.0660526i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6239.00 | + | 10806.3i | −0.384439 | + | 0.665869i | −0.991691 | − | 0.128641i | \(-0.958939\pi\) |
0.607252 | + | 0.794509i | \(0.292272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15996.0 | 0.981059 | 0.490529 | − | 0.871425i | \(-0.336803\pi\) | ||||
0.490529 | + | 0.871425i | \(0.336803\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17600.0 | 1.07442 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2940.00 | − | 5092.23i | 0.178645 | − | 0.309422i | −0.762772 | − | 0.646668i | \(-0.776162\pi\) |
0.941417 | + | 0.337246i | \(0.109495\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12760.0 | − | 22101.0i | −0.771762 | − | 1.33673i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3755.00 | + | 6503.85i | 0.225030 | + | 0.389763i | 0.956328 | − | 0.292294i | \(-0.0944187\pi\) |
−0.731299 | + | 0.682058i | \(0.761085\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3000.00 | + | 5196.15i | −0.178961 | + | 0.309970i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7040.00 | 0.418047 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16508.0 | −0.975812 | −0.487906 | − | 0.872896i | \(-0.662239\pi\) | ||||
−0.487906 | + | 0.872896i | \(0.662239\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 610.000 | − | 1056.55i | 0.0358945 | − | 0.0621711i | −0.847520 | − | 0.530763i | \(-0.821905\pi\) |
0.883415 | + | 0.468592i | \(0.155239\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6336.00 | − | 10974.3i | −0.371146 | − | 0.642844i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13080.0 | + | 22655.2i | 0.759310 | + | 1.31516i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4832.00 | + | 8369.27i | −0.279247 | + | 0.483669i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16720.0 | 0.961950 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13090.0 | −0.749751 | −0.374875 | − | 0.927075i | \(-0.622315\pi\) | ||||
−0.374875 | + | 0.927075i | \(0.622315\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20900.0 | + | 36199.9i | −1.19177 | + | 2.06420i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7554.00 | − | 13083.9i | −0.428839 | − | 0.742770i | 0.567932 | − | 0.823076i | \(-0.307744\pi\) |
−0.996770 | + | 0.0803053i | \(0.974410\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9944.00 | − | 17223.5i | −0.559552 | − | 0.969172i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −770.000 | + | 1333.68i | −0.0431380 | + | 0.0747171i | −0.886788 | − | 0.462176i | \(-0.847069\pi\) |
0.843650 | + | 0.536893i | \(0.180402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23800.0 | −1.32752 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17840.0 | 0.990740 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2420.00 | − | 4191.56i | 0.133809 | − | 0.231765i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2890.00 | − | 5005.63i | −0.159104 | − | 0.275576i | 0.775442 | − | 0.631419i | \(-0.217527\pi\) |
−0.934546 | + | 0.355843i | \(0.884194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22200.0 | + | 38451.5i | 1.21165 | + | 2.09863i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4320.00 | + | 7482.46i | −0.234766 | + | 0.406626i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18200.0 | −0.984817 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10406.0 | −0.560669 | −0.280335 | − | 0.959902i | \(-0.590445\pi\) | ||||
−0.280335 | + | 0.959902i | \(0.590445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1500.00 | − | 2598.08i | 0.0804745 | − | 0.139386i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3520.00 | − | 6096.82i | −0.188044 | − | 0.325701i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14321.0 | − | 24804.7i | −0.758585 | − | 1.31391i | −0.943572 | − | 0.331166i | \(-0.892558\pi\) |
0.184988 | − | 0.982741i | \(-0.440775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2684.00 | + | 4648.82i | −0.141572 | + | 0.245210i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33600.0 | 1.76484 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38720.0 | 2.02524 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4224.00 | + | 7316.18i | −0.220011 | + | 0.381071i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3780.00 | − | 6547.15i | −0.196064 | − | 0.339593i | 0.751185 | − | 0.660092i | \(-0.229483\pi\) |
−0.947249 | + | 0.320499i | \(0.896149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9680.00 | − | 16766.3i | −0.497930 | − | 0.862439i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29975.0 | + | 51918.2i | −1.53551 | + | 2.65958i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20360.0 | −1.03867 | −0.519333 | − | 0.854572i | \(-0.673820\pi\) | ||||
−0.519333 | + | 0.854572i | \(0.673820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7920.00 | + | 13717.8i | −0.400727 | + | 0.694080i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11638.0 | − | 20157.6i | −0.586438 | − | 1.01574i | −0.994694 | − | 0.102874i | \(-0.967196\pi\) |
0.408256 | − | 0.912867i | \(-0.366137\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21560.0 | + | 37343.0i | 1.07758 | + | 1.86641i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1586.00 | + | 2747.03i | −0.0789472 | + | 0.136740i | −0.902796 | − | 0.430069i | \(-0.858489\pi\) |
0.823849 | + | 0.566810i | \(0.191823\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17600.0 | 0.872540 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6600.00 | −0.325882 | −0.162941 | − | 0.986636i | \(-0.552098\pi\) | ||||
−0.162941 | + | 0.986636i | \(0.552098\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24140.0 | − | 41811.7i | 1.18714 | − | 2.05619i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3630.00 | + | 6287.34i | 0.177798 | + | 0.307954i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8208.00 | + | 14216.7i | 0.398820 | + | 0.690777i | 0.993581 | − | 0.113126i | \(-0.0360863\pi\) |
−0.594760 | + | 0.803903i | \(0.702753\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8680.00 | + | 15034.2i | −0.420075 | + | 0.727592i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41120.0 | −1.98213 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36850.0 | 1.76927 | 0.884634 | − | 0.466286i | \(-0.154408\pi\) | ||||
0.884634 | + | 0.466286i | \(0.154408\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10560.0 | + | 18290.5i | −0.505011 | + | 0.874706i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18700.0 | + | 32389.4i | 0.890768 | + | 1.54286i | 0.838956 | + | 0.544199i | \(0.183166\pi\) |
0.0518116 | + | 0.998657i | \(0.483500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7920.00 | − | 13717.8i | −0.374311 | − | 0.648326i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12760.0 | − | 22101.0i | 0.600700 | − | 1.04044i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5720.00 | −0.268229 | −0.134115 | − | 0.990966i | \(-0.542819\pi\) | ||||
−0.134115 | + | 0.990966i | \(0.542819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14080.0 | 0.657690 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3678.00 | + | 6370.48i | −0.171136 | + | 0.296417i | −0.938817 | − | 0.344415i | \(-0.888077\pi\) |
0.767681 | + | 0.640832i | \(0.221411\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38500.0 | + | 66684.0i | 1.78447 | + | 3.09079i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6000.00 | − | 10392.3i | −0.275959 | − | 0.477976i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2464.00 | − | 4267.77i | 0.112892 | − | 0.195535i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33136.0 | 1.51237 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21200.0 | −0.963899 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19286.0 | − | 33404.3i | 0.873535 | − | 1.51301i | 0.0152188 | − | 0.999884i | \(-0.495156\pi\) |
0.858316 | − | 0.513122i | \(-0.171511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5120.00 | − | 8868.10i | −0.231023 | − | 0.400143i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8360.00 | + | 14479.9i | 0.374366 | + | 0.648421i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4400.00 | + | 7621.02i | −0.196292 | + | 0.339987i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7812.00 | 0.347196 | 0.173598 | − | 0.984817i | \(-0.444461\pi\) | ||||
0.173598 | + | 0.984817i | \(0.444461\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6336.00 | 0.280540 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1760.00 | − | 3048.41i | 0.0776361 | − | 0.134470i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14080.0 | + | 24387.3i | 0.618770 | + | 1.07174i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13640.0 | + | 23625.2i | 0.594982 | + | 1.03054i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22509.0 | + | 38986.7i | −0.978213 | + | 1.69431i | −0.309316 | + | 0.950959i | \(0.600100\pi\) |
−0.668897 | + | 0.743355i | \(0.733233\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2740.00 | 0.118637 | 0.0593184 | − | 0.998239i | \(-0.481107\pi\) | ||||
0.0593184 | + | 0.998239i | \(0.481107\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14080.0 | −0.607389 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19800.0 | + | 34294.6i | −0.850998 | + | 1.47397i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11000.0 | − | 19052.6i | −0.471042 | − | 0.815869i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −727.000 | − | 1259.20i | −0.0309044 | − | 0.0535279i | 0.850160 | − | 0.526525i | \(-0.176505\pi\) |
−0.881064 | + | 0.472997i | \(0.843172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18560.0 | + | 32146.9i | −0.786101 | + | 1.36157i | 0.142239 | + | 0.989832i | \(0.454570\pi\) |
−0.928339 | + | 0.371734i | \(0.878763\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −48400.0 | −2.04251 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7260.00 | −0.305266 | −0.152633 | − | 0.988283i | \(-0.548775\pi\) | ||||
−0.152633 | + | 0.988283i | \(0.548775\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5570.00 | − | 9647.52i | 0.233358 | − | 0.404189i | −0.725436 | − | 0.688290i | \(-0.758362\pi\) |
0.958794 | + | 0.284101i | \(0.0916951\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17380.0 | − | 30103.0i | −0.725518 | − | 1.25663i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4880.00 | + | 8452.41i | 0.202251 | + | 0.350309i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21280.0 | − | 36858.0i | 0.878787 | − | 1.52210i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8760.00 | 0.360463 | 0.180232 | − | 0.983624i | \(-0.442315\pi\) | ||||
0.180232 | + | 0.983624i | \(0.442315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23135.0 | 0.948583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7788.00 | − | 13489.2i | 0.318189 | − | 0.551119i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2610.00 | − | 4520.65i | −0.106256 | − | 0.184042i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13112.0 | − | 22710.7i | −0.530038 | − | 0.918054i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1800.00 | + | 3117.69i | −0.0725067 | + | 0.125585i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 820.000 | 0.0329147 | 0.0164574 | − | 0.999865i | \(-0.494761\pi\) | ||||
0.0164574 | + | 0.999865i | \(0.494761\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22000.0 | 0.879981 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 660.000 | − | 1143.15i | 0.0263071 | − | 0.0455652i | −0.852572 | − | 0.522610i | \(-0.824959\pi\) |
0.878879 | + | 0.477044i | \(0.158292\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21390.0 | − | 37048.6i | −0.849613 | − | 1.47157i | −0.881554 | − | 0.472083i | \(-0.843502\pi\) |
0.0319414 | − | 0.999490i | \(-0.489831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14940.0 | − | 25876.8i | −0.589297 | − | 1.02069i | −0.994325 | − | 0.106388i | \(-0.966071\pi\) |
0.405027 | − | 0.914305i | \(-0.367262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34760.0 | − | 60206.1i | 1.36633 | − | 2.36655i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1084.00 | −0.0424620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21472.0 | −0.838191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21560.0 | + | 37343.0i | −0.838729 | + | 1.45272i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1364.00 | + | 2362.52i | 0.0528802 | + | 0.0915912i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14085.0 | − | 24395.9i | −0.542322 | − | 0.939330i | −0.998770 | − | 0.0495796i | \(-0.984212\pi\) |
0.456448 | − | 0.889750i | \(-0.349121\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4968.00 | + | 8604.83i | −0.190633 | + | 0.330186i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20800.0 | 0.795425 | 0.397713 | − | 0.917510i | \(-0.369804\pi\) | ||||
0.397713 | + | 0.917510i | \(0.369804\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20900.0 | −0.796536 | −0.398268 | − | 0.917269i | \(-0.630389\pi\) | ||||
−0.398268 | + | 0.917269i | \(0.630389\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23200.0 | + | 40183.6i | −0.881197 | + | 1.52628i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5820.00 | − | 10080.5i | −0.220312 | − | 0.381591i | 0.734591 | − | 0.678510i | \(-0.237374\pi\) |
−0.954903 | + | 0.296919i | \(0.904041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6842.00 | + | 11850.7i | 0.257257 | + | 0.445581i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4400.00 | + | 7621.02i | −0.164883 | + | 0.285585i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1680.00 | 0.0627444 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21120.0 | −0.786150 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30520.0 | − | 52862.2i | 1.13226 | − | 1.96113i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3960.00 | − | 6858.92i | −0.146423 | − | 0.253611i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21800.0 | + | 37758.7i | 0.800725 | + | 1.38690i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18790.0 | − | 32545.2i | 0.687885 | − | 1.19145i | −0.284636 | − | 0.958636i | \(-0.591873\pi\) |
0.972521 | − | 0.232816i | \(-0.0747940\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2420.00 | −0.0883018 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40832.0 | −1.48499 | −0.742494 | − | 0.669852i | \(-0.766357\pi\) | ||||
−0.742494 | + | 0.669852i | \(0.766357\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14520.0 | + | 25149.4i | −0.526333 | + | 0.911635i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15200.0 | − | 26327.2i | −0.549177 | − | 0.951202i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21384.0 | − | 37038.2i | −0.767566 | − | 1.32946i | −0.938879 | − | 0.344247i | \(-0.888134\pi\) |
0.171313 | − | 0.985217i | \(-0.445199\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 616.000 | − | 1066.94i | 0.0220390 | − | 0.0381726i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4928.00 | 0.175739 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8250.00 | −0.293252 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7348.00 | − | 12727.1i | 0.260345 | − | 0.450931i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4380.00 | + | 7586.38i | 0.154686 | + | 0.267924i | 0.932945 | − | 0.360020i | \(-0.117230\pi\) |
−0.778259 | + | 0.627944i | \(0.783897\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3520.00 | + | 6096.82i | 0.123515 | + | 0.213934i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31680.0 | − | 54871.4i | 1.10807 | − | 1.91924i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49632.0 | 1.73042 | 0.865212 | − | 0.501407i | \(-0.167184\pi\) | ||||
0.865212 | + | 0.501407i | \(0.167184\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −96.0000 | −0.00333636 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18450.0 | − | 31956.3i | 0.639163 | − | 1.10706i | −0.346453 | − | 0.938067i | \(-0.612614\pi\) |
0.985617 | − | 0.168996i | \(-0.0540526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7200.00 | + | 12470.8i | 0.248637 | + | 0.430651i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16670.0 | + | 28873.3i | 0.572019 | + | 0.990766i | 0.996358 | + | 0.0852631i | \(0.0271731\pi\) |
−0.424339 | + | 0.905503i | \(0.639494\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14080.0 | + | 24387.3i | −0.481619 | + | 0.834188i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19560.0 | 0.666957 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5610.00 | 0.190688 | 0.0953440 | − | 0.995444i | \(-0.469605\pi\) | ||||
0.0953440 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6960.00 | − | 12055.1i | 0.235833 | − | 0.408474i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19184.0 | + | 33227.7i | 0.647994 | + | 1.12236i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24304.5 | − | 42096.6i | −0.815834 | − | 1.41307i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 550.000 | − | 952.628i | 0.0184045 | − | 0.0318775i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −53800.0 | −1.79470 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25160.0 | −0.836702 | −0.418351 | − | 0.908285i | \(-0.637392\pi\) | ||||
−0.418351 | + | 0.908285i | \(0.637392\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14400.0 | − | 24941.5i | 0.477394 | − | 0.826870i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −530.000 | − | 917.987i | −0.0175165 | − | 0.0303394i | 0.857134 | − | 0.515093i | \(-0.172243\pi\) |
−0.874651 | + | 0.484754i | \(0.838909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24200.0 | − | 41915.6i | −0.794893 | − | 1.37679i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19385.0 | − | 33575.8i | 0.634781 | − | 1.09947i | −0.351780 | − | 0.936083i | \(-0.614424\pi\) |
0.986561 | − | 0.163390i | \(-0.0522430\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14080.0 | 0.459651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7502.00 | −0.244159 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12148.0 | − | 21041.0i | 0.394162 | − | 0.682708i | −0.598832 | − | 0.800875i | \(-0.704368\pi\) |
0.992994 | + | 0.118166i | \(0.0377016\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53100.0 | + | 91971.9i | 1.71767 | + | 2.97509i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13200.0 | + | 22863.1i | 0.424404 | + | 0.735089i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 836.000 | − | 1447.99i | 0.0267976 | − | 0.0464148i | −0.852316 | − | 0.523028i | \(-0.824802\pi\) |
0.879113 | + | 0.476613i | \(0.158136\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32432.0 | −1.03645 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −61600.0 | −1.96266 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22814.0 | + | 39515.0i | −0.724701 | + | 1.25522i | 0.234396 | + | 0.972141i | \(0.424689\pi\) |
−0.959097 | + | 0.283077i | \(0.908645\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2280.00 | + | 3949.08i | 0.0722082 | + | 0.125068i |
(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 | 196.4.e.e.165.1 | 2 | ||
3.2 | odd | 2 | 1764.4.k.a.361.1 | 2 | |||
7.2 | even | 3 | inner | 196.4.e.e.177.1 | 2 | ||
7.3 | odd | 6 | 196.4.a.c.1.1 | yes | 1 | ||
7.4 | even | 3 | 196.4.a.a.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | 196.4.e.b.177.1 | 2 | |||
7.6 | odd | 2 | 196.4.e.b.165.1 | 2 | |||
21.2 | odd | 6 | 1764.4.k.a.1549.1 | 2 | |||
21.5 | even | 6 | 1764.4.k.p.1549.1 | 2 | |||
21.11 | odd | 6 | 1764.4.a.m.1.1 | 1 | |||
21.17 | even | 6 | 1764.4.a.a.1.1 | 1 | |||
21.20 | even | 2 | 1764.4.k.p.361.1 | 2 | |||
28.3 | even | 6 | 784.4.a.f.1.1 | 1 | |||
28.11 | odd | 6 | 784.4.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.4.a.a.1.1 | ✓ | 1 | 7.4 | even | 3 | ||
196.4.a.c.1.1 | yes | 1 | 7.3 | odd | 6 | ||
196.4.e.b.165.1 | 2 | 7.6 | odd | 2 | |||
196.4.e.b.177.1 | 2 | 7.5 | odd | 6 | |||
196.4.e.e.165.1 | 2 | 1.1 | even | 1 | trivial | ||
196.4.e.e.177.1 | 2 | 7.2 | even | 3 | inner | ||
784.4.a.f.1.1 | 1 | 28.3 | even | 6 | |||
784.4.a.m.1.1 | 1 | 28.11 | odd | 6 | |||
1764.4.a.a.1.1 | 1 | 21.17 | even | 6 | |||
1764.4.a.m.1.1 | 1 | 21.11 | odd | 6 | |||
1764.4.k.a.361.1 | 2 | 3.2 | odd | 2 | |||
1764.4.k.a.1549.1 | 2 | 21.2 | odd | 6 | |||
1764.4.k.p.361.1 | 2 | 21.20 | even | 2 | |||
1764.4.k.p.1549.1 | 2 | 21.5 | even | 6 |