Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.599");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), 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: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} + 124x^{6} + 4272x^{4} + 28129x^{2} + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.8 | ||
Root | \(8.04090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.4.b.o.599.1 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 5.04090i | 0.970122i | 0.874480 | + | 0.485061i | \(0.161203\pi\) | ||||
−0.874480 | + | 0.485061i | \(0.838797\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −10.0818 | −0.685980 | ||||||||
\(7\) | 5.03071i | 0.271633i | 0.990734 | + | 0.135816i | \(0.0433657\pi\) | ||||
−0.990734 | + | 0.135816i | \(0.956634\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | 1.58932 | 0.0588637 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.58219 | −0.153008 | −0.0765042 | − | 0.997069i | \(-0.524376\pi\) | ||||
−0.0765042 | + | 0.997069i | \(0.524376\pi\) | |||||||
\(12\) | − 20.1636i | − 0.485061i | ||||||||
\(13\) | − 62.7277i | − 1.33827i | −0.743140 | − | 0.669136i | \(-0.766664\pi\) | ||||
0.743140 | − | 0.669136i | \(-0.233336\pi\) | |||||||
\(14\) | −10.0614 | −0.192073 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − 19.7435i | − 0.281677i | −0.990033 | − | 0.140838i | \(-0.955020\pi\) | ||||
0.990033 | − | 0.140838i | \(-0.0449798\pi\) | |||||||
\(18\) | 3.17864i | 0.0416229i | ||||||||
\(19\) | −158.545 | −1.91435 | −0.957177 | − | 0.289505i | \(-0.906509\pi\) | ||||
−0.957177 | + | 0.289505i | \(0.906509\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −25.3593 | −0.263517 | ||||||||
\(22\) | − 11.1644i | − 0.108193i | ||||||||
\(23\) | 23.0000i | 0.208514i | ||||||||
\(24\) | 40.3272 | 0.342990 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 125.455 | 0.946301 | ||||||||
\(27\) | 144.116i | 1.02723i | ||||||||
\(28\) | − 20.1228i | − 0.135816i | ||||||||
\(29\) | 35.5033 | 0.227338 | 0.113669 | − | 0.993519i | \(-0.463740\pi\) | ||||
0.113669 | + | 0.993519i | \(0.463740\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 282.041 | 1.63406 | 0.817032 | − | 0.576592i | \(-0.195618\pi\) | ||||
0.817032 | + | 0.576592i | \(0.195618\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | − 28.1393i | − 0.148437i | ||||||||
\(34\) | 39.4870 | 0.199175 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.35728 | −0.0294319 | ||||||||
\(37\) | − 139.981i | − 0.621967i | −0.950415 | − | 0.310984i | \(-0.899342\pi\) | ||||
0.950415 | − | 0.310984i | \(-0.100658\pi\) | |||||||
\(38\) | − 317.090i | − 1.35365i | ||||||||
\(39\) | 316.204 | 1.29829 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 227.680 | 0.867260 | 0.433630 | − | 0.901091i | \(-0.357232\pi\) | ||||
0.433630 | + | 0.901091i | \(0.357232\pi\) | |||||||
\(42\) | − 50.7186i | − 0.186335i | ||||||||
\(43\) | − 436.962i | − 1.54968i | −0.632159 | − | 0.774838i | \(-0.717831\pi\) | ||||
0.632159 | − | 0.774838i | \(-0.282169\pi\) | |||||||
\(44\) | 22.3288 | 0.0765042 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 90.2701i | 0.280154i | 0.990141 | + | 0.140077i | \(0.0447350\pi\) | ||||
−0.990141 | + | 0.140077i | \(0.955265\pi\) | |||||||
\(48\) | 80.6544i | 0.242530i | ||||||||
\(49\) | 317.692 | 0.926216 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 99.5250 | 0.273261 | ||||||||
\(52\) | 250.911i | 0.669136i | ||||||||
\(53\) | − 330.183i | − 0.855737i | −0.903841 | − | 0.427869i | \(-0.859265\pi\) | ||||
0.903841 | − | 0.427869i | \(-0.140735\pi\) | |||||||
\(54\) | −288.232 | −0.726359 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 40.2457 | 0.0960367 | ||||||||
\(57\) | − 799.209i | − 1.85716i | ||||||||
\(58\) | 71.0066i | 0.160752i | ||||||||
\(59\) | 796.203 | 1.75689 | 0.878447 | − | 0.477839i | \(-0.158580\pi\) | ||||
0.878447 | + | 0.477839i | \(0.158580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −568.580 | −1.19343 | −0.596715 | − | 0.802453i | \(-0.703528\pi\) | ||||
−0.596715 | + | 0.802453i | \(0.703528\pi\) | |||||||
\(62\) | 564.081i | 1.15546i | ||||||||
\(63\) | 7.99541i | 0.0159893i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 56.2785 | 0.104961 | ||||||||
\(67\) | 85.1419i | 0.155250i | 0.996983 | + | 0.0776250i | \(0.0247337\pi\) | ||||
−0.996983 | + | 0.0776250i | \(0.975266\pi\) | |||||||
\(68\) | 78.9740i | 0.140838i | ||||||||
\(69\) | −115.941 | −0.202284 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −369.578 | −0.617758 | −0.308879 | − | 0.951101i | \(-0.599954\pi\) | ||||
−0.308879 | + | 0.951101i | \(0.599954\pi\) | |||||||
\(72\) | − 12.7146i | − 0.0208115i | ||||||||
\(73\) | 310.188i | 0.497325i | 0.968590 | + | 0.248662i | \(0.0799910\pi\) | ||||
−0.968590 | + | 0.248662i | \(0.920009\pi\) | |||||||
\(74\) | 279.963 | 0.439797 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 634.180 | 0.957177 | ||||||||
\(77\) | − 28.0824i | − 0.0415621i | ||||||||
\(78\) | 632.408i | 0.918027i | ||||||||
\(79\) | 1325.46 | 1.88766 | 0.943832 | − | 0.330427i | \(-0.107193\pi\) | ||||
0.943832 | + | 0.330427i | \(0.107193\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −683.562 | −0.937671 | ||||||||
\(82\) | 455.360i | 0.613246i | ||||||||
\(83\) | 158.806i | 0.210014i | 0.994471 | + | 0.105007i | \(0.0334865\pi\) | ||||
−0.994471 | + | 0.105007i | \(0.966513\pi\) | |||||||
\(84\) | 101.437 | 0.131758 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 873.924 | 1.09579 | ||||||||
\(87\) | 178.969i | 0.220545i | ||||||||
\(88\) | 44.6575i | 0.0540967i | ||||||||
\(89\) | 1233.89 | 1.46957 | 0.734787 | − | 0.678298i | \(-0.237282\pi\) | ||||
0.734787 | + | 0.678298i | \(0.237282\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 315.565 | 0.363519 | ||||||||
\(92\) | − 92.0000i | − 0.104257i | ||||||||
\(93\) | 1421.74i | 1.58524i | ||||||||
\(94\) | −180.540 | −0.198099 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −161.309 | −0.171495 | ||||||||
\(97\) | − 106.389i | − 0.111363i | −0.998449 | − | 0.0556814i | \(-0.982267\pi\) | ||||
0.998449 | − | 0.0556814i | \(-0.0177331\pi\) | |||||||
\(98\) | 635.384i | 0.654933i | ||||||||
\(99\) | −8.87189 | −0.00900665 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 642.676 | 0.633155 | 0.316578 | − | 0.948567i | \(-0.397466\pi\) | ||||
0.316578 | + | 0.948567i | \(0.397466\pi\) | |||||||
\(102\) | 199.050i | 0.193224i | ||||||||
\(103\) | − 1621.99i | − 1.55165i | −0.630951 | − | 0.775823i | \(-0.717335\pi\) | ||||
0.630951 | − | 0.775823i | \(-0.282665\pi\) | |||||||
\(104\) | −501.822 | −0.473150 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 660.365 | 0.605098 | ||||||||
\(107\) | 1490.86i | 1.34698i | 0.739196 | + | 0.673490i | \(0.235205\pi\) | ||||
−0.739196 | + | 0.673490i | \(0.764795\pi\) | |||||||
\(108\) | − 576.464i | − 0.513613i | ||||||||
\(109\) | −1204.00 | −1.05800 | −0.529001 | − | 0.848621i | \(-0.677433\pi\) | ||||
−0.529001 | + | 0.848621i | \(0.677433\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 705.632 | 0.603384 | ||||||||
\(112\) | 80.4914i | 0.0679082i | ||||||||
\(113\) | − 276.771i | − 0.230411i | −0.993342 | − | 0.115206i | \(-0.963247\pi\) | ||||
0.993342 | − | 0.115206i | \(-0.0367527\pi\) | |||||||
\(114\) | 1598.42 | 1.31321 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −142.013 | −0.113669 | ||||||||
\(117\) | − 99.6944i | − 0.0787757i | ||||||||
\(118\) | 1592.41i | 1.24231i | ||||||||
\(119\) | 99.3239 | 0.0765126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1299.84 | −0.976588 | ||||||||
\(122\) | − 1137.16i | − 0.843883i | ||||||||
\(123\) | 1147.71i | 0.841348i | ||||||||
\(124\) | −1128.16 | −0.817032 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −15.9908 | −0.0113062 | ||||||||
\(127\) | 1552.79i | 1.08494i | 0.840075 | + | 0.542471i | \(0.182511\pi\) | ||||
−0.840075 | + | 0.542471i | \(0.817489\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | 2202.68 | 1.50338 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −313.873 | −0.209337 | −0.104669 | − | 0.994507i | \(-0.533378\pi\) | ||||
−0.104669 | + | 0.994507i | \(0.533378\pi\) | |||||||
\(132\) | 112.557i | 0.0742184i | ||||||||
\(133\) | − 797.594i | − 0.520001i | ||||||||
\(134\) | −170.284 | −0.109778 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −157.948 | −0.0995877 | ||||||||
\(137\) | − 1066.09i | − 0.664835i | −0.943132 | − | 0.332417i | \(-0.892136\pi\) | ||||
0.943132 | − | 0.332417i | \(-0.107864\pi\) | |||||||
\(138\) | − 231.881i | − 0.143037i | ||||||||
\(139\) | 1594.79 | 0.973152 | 0.486576 | − | 0.873638i | \(-0.338246\pi\) | ||||
0.486576 | + | 0.873638i | \(0.338246\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −455.043 | −0.271784 | ||||||||
\(142\) | − 739.155i | − 0.436821i | ||||||||
\(143\) | 350.158i | 0.204767i | ||||||||
\(144\) | 25.4291 | 0.0147159 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −620.375 | −0.351662 | ||||||||
\(147\) | 1601.45i | 0.898542i | ||||||||
\(148\) | 559.925i | 0.310984i | ||||||||
\(149\) | 1096.91 | 0.603102 | 0.301551 | − | 0.953450i | \(-0.402496\pi\) | ||||
0.301551 | + | 0.953450i | \(0.402496\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2734.41 | 1.47366 | 0.736832 | − | 0.676076i | \(-0.236321\pi\) | ||||
0.736832 | + | 0.676076i | \(0.236321\pi\) | |||||||
\(152\) | 1268.36i | 0.676826i | ||||||||
\(153\) | − 31.3788i | − 0.0165805i | ||||||||
\(154\) | 56.1647 | 0.0293889 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1264.82 | −0.649143 | ||||||||
\(157\) | − 1439.63i | − 0.731813i | −0.930652 | − | 0.365907i | \(-0.880759\pi\) | ||||
0.930652 | − | 0.365907i | \(-0.119241\pi\) | |||||||
\(158\) | 2650.91i | 1.33478i | ||||||||
\(159\) | 1664.42 | 0.830169 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −115.706 | −0.0566394 | ||||||||
\(162\) | − 1367.12i | − 0.663034i | ||||||||
\(163\) | 2995.82i | 1.43957i | 0.694195 | + | 0.719787i | \(0.255760\pi\) | ||||
−0.694195 | + | 0.719787i | \(0.744240\pi\) | |||||||
\(164\) | −910.721 | −0.433630 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −317.611 | −0.148503 | ||||||||
\(167\) | − 351.532i | − 0.162888i | −0.996678 | − | 0.0814442i | \(-0.974047\pi\) | ||||
0.996678 | − | 0.0814442i | \(-0.0259532\pi\) | |||||||
\(168\) | 202.874i | 0.0931673i | ||||||||
\(169\) | −1737.76 | −0.790971 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −251.979 | −0.112686 | ||||||||
\(172\) | 1747.85i | 0.774838i | ||||||||
\(173\) | 3701.77i | 1.62682i | 0.581690 | + | 0.813411i | \(0.302392\pi\) | ||||
−0.581690 | + | 0.813411i | \(0.697608\pi\) | |||||||
\(174\) | −357.937 | −0.155949 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −89.3150 | −0.0382521 | ||||||||
\(177\) | 4013.58i | 1.70440i | ||||||||
\(178\) | 2467.78i | 1.03915i | ||||||||
\(179\) | −3584.09 | −1.49658 | −0.748290 | − | 0.663372i | \(-0.769125\pi\) | ||||
−0.748290 | + | 0.663372i | \(0.769125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 783.672 | 0.321822 | 0.160911 | − | 0.986969i | \(-0.448557\pi\) | ||||
0.160911 | + | 0.986969i | \(0.448557\pi\) | |||||||
\(182\) | 631.130i | 0.257046i | ||||||||
\(183\) | − 2866.16i | − 1.15777i | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2843.48 | −1.12093 | ||||||||
\(187\) | 110.212i | 0.0430989i | ||||||||
\(188\) | − 361.080i | − 0.140077i | ||||||||
\(189\) | −725.005 | −0.279029 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1491.95 | 0.565201 | 0.282601 | − | 0.959238i | \(-0.408803\pi\) | ||||
0.282601 | + | 0.959238i | \(0.408803\pi\) | |||||||
\(192\) | − 322.618i | − 0.121265i | ||||||||
\(193\) | − 3091.09i | − 1.15286i | −0.817147 | − | 0.576430i | \(-0.804446\pi\) | ||||
0.817147 | − | 0.576430i | \(-0.195554\pi\) | |||||||
\(194\) | 212.778 | 0.0787454 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1270.77 | −0.463108 | ||||||||
\(197\) | 2820.30i | 1.01999i | 0.860178 | + | 0.509995i | \(0.170353\pi\) | ||||
−0.860178 | + | 0.509995i | \(0.829647\pi\) | |||||||
\(198\) | − 17.7438i | − 0.00636866i | ||||||||
\(199\) | −1316.11 | −0.468825 | −0.234413 | − | 0.972137i | \(-0.575317\pi\) | ||||
−0.234413 | + | 0.972137i | \(0.575317\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −429.192 | −0.150611 | ||||||||
\(202\) | 1285.35i | 0.447708i | ||||||||
\(203\) | 178.607i | 0.0617524i | ||||||||
\(204\) | −398.100 | −0.136630 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3243.98 | 1.09718 | ||||||||
\(207\) | 36.5544i | 0.0122739i | ||||||||
\(208\) | − 1003.64i | − 0.334568i | ||||||||
\(209\) | 885.028 | 0.292912 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3399.19 | −1.10905 | −0.554525 | − | 0.832167i | \(-0.687100\pi\) | ||||
−0.554525 | + | 0.832167i | \(0.687100\pi\) | |||||||
\(212\) | 1320.73i | 0.427869i | ||||||||
\(213\) | − 1863.00i | − 0.599300i | ||||||||
\(214\) | −2981.72 | −0.952458 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1152.93 | 0.363180 | ||||||||
\(217\) | 1418.86i | 0.443865i | ||||||||
\(218\) | − 2408.00i | − 0.748121i | ||||||||
\(219\) | −1563.62 | −0.482466 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1238.46 | −0.376960 | ||||||||
\(222\) | 1411.26i | 0.426657i | ||||||||
\(223\) | − 864.660i | − 0.259650i | −0.991537 | − | 0.129825i | \(-0.958558\pi\) | ||||
0.991537 | − | 0.129825i | \(-0.0414416\pi\) | |||||||
\(224\) | −160.983 | −0.0480184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 553.543 | 0.162925 | ||||||||
\(227\) | − 1979.40i | − 0.578754i | −0.957215 | − | 0.289377i | \(-0.906552\pi\) | ||||
0.957215 | − | 0.289377i | \(-0.0934481\pi\) | |||||||
\(228\) | 3196.84i | 0.928578i | ||||||||
\(229\) | 3113.53 | 0.898462 | 0.449231 | − | 0.893416i | \(-0.351698\pi\) | ||||
0.449231 | + | 0.893416i | \(0.351698\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 141.560 | 0.0403203 | ||||||||
\(232\) | − 284.026i | − 0.0803761i | ||||||||
\(233\) | − 6018.65i | − 1.69225i | −0.532983 | − | 0.846126i | \(-0.678929\pi\) | ||||
0.532983 | − | 0.846126i | \(-0.321071\pi\) | |||||||
\(234\) | 199.389 | 0.0557028 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3184.81 | −0.878447 | ||||||||
\(237\) | 6681.49i | 1.83126i | ||||||||
\(238\) | 198.648i | 0.0541026i | ||||||||
\(239\) | 4224.88 | 1.14345 | 0.571725 | − | 0.820445i | \(-0.306274\pi\) | ||||
0.571725 | + | 0.820445i | \(0.306274\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1394.24 | 0.372658 | 0.186329 | − | 0.982487i | \(-0.440341\pi\) | ||||
0.186329 | + | 0.982487i | \(0.440341\pi\) | |||||||
\(242\) | − 2599.68i | − 0.690552i | ||||||||
\(243\) | 445.360i | 0.117571i | ||||||||
\(244\) | 2274.32 | 0.596715 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2295.43 | −0.594923 | ||||||||
\(247\) | 9945.16i | 2.56192i | ||||||||
\(248\) | − 2256.32i | − 0.577729i | ||||||||
\(249\) | −800.523 | −0.203739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5968.83 | −1.50099 | −0.750497 | − | 0.660874i | \(-0.770186\pi\) | ||||
−0.750497 | + | 0.660874i | \(0.770186\pi\) | |||||||
\(252\) | − 31.9816i | − 0.00799466i | ||||||||
\(253\) | − 128.390i | − 0.0319045i | ||||||||
\(254\) | −3105.57 | −0.767169 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 1636.06i | − 0.397100i | −0.980091 | − | 0.198550i | \(-0.936377\pi\) | ||||
0.980091 | − | 0.198550i | \(-0.0636232\pi\) | |||||||
\(258\) | 4405.37i | 1.06305i | ||||||||
\(259\) | 704.206 | 0.168947 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 56.4261 | 0.0133820 | ||||||||
\(262\) | − 627.745i | − 0.148024i | ||||||||
\(263\) | − 2995.55i | − 0.702333i | −0.936313 | − | 0.351166i | \(-0.885785\pi\) | ||||
0.936313 | − | 0.351166i | \(-0.114215\pi\) | |||||||
\(264\) | −225.114 | −0.0524803 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1595.19 | 0.367696 | ||||||||
\(267\) | 6219.92i | 1.42567i | ||||||||
\(268\) | − 340.568i | − 0.0776250i | ||||||||
\(269\) | 5190.17 | 1.17640 | 0.588198 | − | 0.808717i | \(-0.299838\pi\) | ||||
0.588198 | + | 0.808717i | \(0.299838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6720.43 | 1.50641 | 0.753205 | − | 0.657786i | \(-0.228507\pi\) | ||||
0.753205 | + | 0.657786i | \(0.228507\pi\) | |||||||
\(272\) | − 315.896i | − 0.0704192i | ||||||||
\(273\) | 1590.73i | 0.352657i | ||||||||
\(274\) | 2132.18 | 0.470109 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 463.763 | 0.101142 | ||||||||
\(277\) | − 6114.74i | − 1.32635i | −0.748464 | − | 0.663176i | \(-0.769208\pi\) | ||||
0.748464 | − | 0.663176i | \(-0.230792\pi\) | |||||||
\(278\) | 3189.58i | 0.688123i | ||||||||
\(279\) | 448.253 | 0.0961871 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3549.07 | −0.753450 | −0.376725 | − | 0.926325i | \(-0.622950\pi\) | ||||
−0.376725 | + | 0.926325i | \(0.622950\pi\) | |||||||
\(282\) | − 910.085i | − 0.192180i | ||||||||
\(283\) | − 3103.11i | − 0.651806i | −0.945403 | − | 0.325903i | \(-0.894332\pi\) | ||||
0.945403 | − | 0.325903i | \(-0.105668\pi\) | |||||||
\(284\) | 1478.31 | 0.308879 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −700.316 | −0.144792 | ||||||||
\(287\) | 1145.39i | 0.235576i | ||||||||
\(288\) | 50.8583i | 0.0104057i | ||||||||
\(289\) | 4523.19 | 0.920658 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 536.297 | 0.108035 | ||||||||
\(292\) | − 1240.75i | − 0.248662i | ||||||||
\(293\) | − 1218.51i | − 0.242957i | −0.992594 | − | 0.121478i | \(-0.961237\pi\) | ||||
0.992594 | − | 0.121478i | \(-0.0387635\pi\) | |||||||
\(294\) | −3202.91 | −0.635365 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1119.85 | −0.219899 | ||||||||
\(297\) | − 804.482i | − 0.157174i | ||||||||
\(298\) | 2193.82i | 0.426458i | ||||||||
\(299\) | 1442.74 | 0.279049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2198.23 | 0.420943 | ||||||||
\(302\) | 5468.82i | 1.04204i | ||||||||
\(303\) | 3239.67i | 0.614238i | ||||||||
\(304\) | −2536.72 | −0.478588 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 62.7575 | 0.0117242 | ||||||||
\(307\) | 2564.45i | 0.476745i | 0.971174 | + | 0.238373i | \(0.0766140\pi\) | ||||
−0.971174 | + | 0.238373i | \(0.923386\pi\) | |||||||
\(308\) | 112.329i | 0.0207811i | ||||||||
\(309\) | 8176.30 | 1.50529 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −92.6253 | −0.0168884 | −0.00844421 | − | 0.999964i | \(-0.502688\pi\) | ||||
−0.00844421 | + | 0.999964i | \(0.502688\pi\) | |||||||
\(312\) | − 2529.63i | − 0.459014i | ||||||||
\(313\) | 4276.44i | 0.772263i | 0.922444 | + | 0.386132i | \(0.126189\pi\) | ||||
−0.922444 | + | 0.386132i | \(0.873811\pi\) | |||||||
\(314\) | 2879.25 | 0.517470 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5301.82 | −0.943832 | ||||||||
\(317\) | − 2964.24i | − 0.525199i | −0.964905 | − | 0.262600i | \(-0.915420\pi\) | ||||
0.964905 | − | 0.262600i | \(-0.0845798\pi\) | |||||||
\(318\) | 3328.84i | 0.587018i | ||||||||
\(319\) | −198.186 | −0.0347846 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7515.27 | −1.30673 | ||||||||
\(322\) | − 231.413i | − 0.0400501i | ||||||||
\(323\) | 3130.23i | 0.539229i | ||||||||
\(324\) | 2734.25 | 0.468836 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5991.63 | −1.01793 | ||||||||
\(327\) | − 6069.24i | − 1.02639i | ||||||||
\(328\) | − 1821.44i | − 0.306623i | ||||||||
\(329\) | −454.123 | −0.0760991 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1348.81 | −0.223979 | −0.111989 | − | 0.993709i | \(-0.535722\pi\) | ||||
−0.111989 | + | 0.993709i | \(0.535722\pi\) | |||||||
\(332\) | − 635.223i | − 0.105007i | ||||||||
\(333\) | − 222.475i | − 0.0366113i | ||||||||
\(334\) | 703.064 | 0.115180 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −405.749 | −0.0658792 | ||||||||
\(337\) | − 5764.30i | − 0.931755i | −0.884849 | − | 0.465878i | \(-0.845739\pi\) | ||||
0.884849 | − | 0.465878i | \(-0.154261\pi\) | |||||||
\(338\) | − 3475.53i | − 0.559301i | ||||||||
\(339\) | 1395.18 | 0.223527 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1574.40 | −0.250026 | ||||||||
\(342\) | − 503.958i | − 0.0796810i | ||||||||
\(343\) | 3323.75i | 0.523223i | ||||||||
\(344\) | −3495.70 | −0.547894 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7403.53 | −1.15034 | ||||||||
\(347\) | 4066.16i | 0.629057i | 0.949248 | + | 0.314528i | \(0.101846\pi\) | ||||
−0.949248 | + | 0.314528i | \(0.898154\pi\) | |||||||
\(348\) | − 715.875i | − 0.110273i | ||||||||
\(349\) | −8407.82 | −1.28957 | −0.644786 | − | 0.764363i | \(-0.723053\pi\) | ||||
−0.644786 | + | 0.764363i | \(0.723053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9040.06 | 1.37471 | ||||||||
\(352\) | − 178.630i | − 0.0270483i | ||||||||
\(353\) | − 256.068i | − 0.0386095i | −0.999814 | − | 0.0193047i | \(-0.993855\pi\) | ||||
0.999814 | − | 0.0193047i | \(-0.00614527\pi\) | |||||||
\(354\) | −8027.16 | −1.20519 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4935.56 | −0.734787 | ||||||||
\(357\) | 500.682i | 0.0742266i | ||||||||
\(358\) | − 7168.19i | − 1.05824i | ||||||||
\(359\) | 12052.5 | 1.77189 | 0.885943 | − | 0.463794i | \(-0.153512\pi\) | ||||
0.885943 | + | 0.463794i | \(0.153512\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18277.5 | 2.66475 | ||||||||
\(362\) | 1567.34i | 0.227563i | ||||||||
\(363\) | − 6552.36i | − 0.947410i | ||||||||
\(364\) | −1262.26 | −0.181759 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5732.31 | 0.818669 | ||||||||
\(367\) | − 9245.40i | − 1.31500i | −0.753453 | − | 0.657502i | \(-0.771613\pi\) | ||||
0.753453 | − | 0.657502i | \(-0.228387\pi\) | |||||||
\(368\) | 368.000i | 0.0521286i | ||||||||
\(369\) | 361.857 | 0.0510502 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1661.05 | 0.232446 | ||||||||
\(372\) | − 5686.96i | − 0.792621i | ||||||||
\(373\) | 869.265i | 0.120667i | 0.998178 | + | 0.0603335i | \(0.0192164\pi\) | ||||
−0.998178 | + | 0.0603335i | \(0.980784\pi\) | |||||||
\(374\) | −220.424 | −0.0304755 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 722.161 | 0.0990495 | ||||||||
\(377\) | − 2227.04i | − 0.304240i | ||||||||
\(378\) | − 1450.01i | − 0.197303i | ||||||||
\(379\) | −1278.76 | −0.173313 | −0.0866566 | − | 0.996238i | \(-0.527618\pi\) | ||||
−0.0866566 | + | 0.996238i | \(0.527618\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7827.44 | −1.05252 | ||||||||
\(382\) | 2983.89i | 0.399658i | ||||||||
\(383\) | 5343.75i | 0.712932i | 0.934308 | + | 0.356466i | \(0.116018\pi\) | ||||
−0.934308 | + | 0.356466i | \(0.883982\pi\) | |||||||
\(384\) | 645.235 | 0.0857475 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6182.19 | 0.815194 | ||||||||
\(387\) | − 694.473i | − 0.0912198i | ||||||||
\(388\) | 425.557i | 0.0556814i | ||||||||
\(389\) | 708.346 | 0.0923254 | 0.0461627 | − | 0.998934i | \(-0.485301\pi\) | ||||
0.0461627 | + | 0.998934i | \(0.485301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 454.101 | 0.0587336 | ||||||||
\(392\) | − 2541.54i | − 0.327467i | ||||||||
\(393\) | − 1582.20i | − 0.203083i | ||||||||
\(394\) | −5640.60 | −0.721241 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 35.4875 | 0.00450332 | ||||||||
\(397\) | − 5924.01i | − 0.748911i | −0.927245 | − | 0.374455i | \(-0.877830\pi\) | ||||
0.927245 | − | 0.374455i | \(-0.122170\pi\) | |||||||
\(398\) | − 2632.21i | − 0.331510i | ||||||||
\(399\) | 4020.59 | 0.504464 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11393.6 | −1.41888 | −0.709441 | − | 0.704765i | \(-0.751052\pi\) | ||||
−0.709441 | + | 0.704765i | \(0.751052\pi\) | |||||||
\(402\) | − 858.384i | − 0.106498i | ||||||||
\(403\) | − 17691.8i | − 2.18682i | ||||||||
\(404\) | −2570.71 | −0.316578 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −357.214 | −0.0436656 | ||||||||
\(407\) | 781.402i | 0.0951663i | ||||||||
\(408\) | − 796.200i | − 0.0966122i | ||||||||
\(409\) | −13804.4 | −1.66891 | −0.834457 | − | 0.551073i | \(-0.814218\pi\) | ||||
−0.834457 | + | 0.551073i | \(0.814218\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5374.06 | 0.644971 | ||||||||
\(412\) | 6487.96i | 0.775823i | ||||||||
\(413\) | 4005.47i | 0.477230i | ||||||||
\(414\) | −73.1087 | −0.00867898 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2007.29 | 0.236575 | ||||||||
\(417\) | 8039.17i | 0.944076i | ||||||||
\(418\) | 1770.06i | 0.207120i | ||||||||
\(419\) | 14795.8 | 1.72512 | 0.862558 | − | 0.505958i | \(-0.168861\pi\) | ||||
0.862558 | + | 0.505958i | \(0.168861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5804.66 | 0.671976 | 0.335988 | − | 0.941866i | \(-0.390930\pi\) | ||||
0.335988 | + | 0.941866i | \(0.390930\pi\) | |||||||
\(422\) | − 6798.37i | − 0.784217i | ||||||||
\(423\) | 143.468i | 0.0164909i | ||||||||
\(424\) | −2641.46 | −0.302549 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3726.01 | 0.423769 | ||||||||
\(427\) | − 2860.36i | − 0.324175i | ||||||||
\(428\) | − 5963.44i | − 0.673490i | ||||||||
\(429\) | −1765.11 | −0.198649 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15268.2 | 1.70636 | 0.853181 | − | 0.521615i | \(-0.174670\pi\) | ||||
0.853181 | + | 0.521615i | \(0.174670\pi\) | |||||||
\(432\) | 2305.85i | 0.256807i | ||||||||
\(433\) | − 2250.62i | − 0.249788i | −0.992170 | − | 0.124894i | \(-0.960141\pi\) | ||||
0.992170 | − | 0.124894i | \(-0.0398591\pi\) | |||||||
\(434\) | −2837.73 | −0.313860 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4816.00 | 0.529001 | ||||||||
\(437\) | − 3646.53i | − 0.399170i | ||||||||
\(438\) | − 3127.25i | − 0.341155i | ||||||||
\(439\) | −10366.2 | −1.12700 | −0.563499 | − | 0.826117i | \(-0.690545\pi\) | ||||
−0.563499 | + | 0.826117i | \(0.690545\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 504.914 | 0.0545205 | ||||||||
\(442\) | − 2476.93i | − 0.266551i | ||||||||
\(443\) | 3881.11i | 0.416246i | 0.978103 | + | 0.208123i | \(0.0667355\pi\) | ||||
−0.978103 | + | 0.208123i | \(0.933264\pi\) | |||||||
\(444\) | −2822.53 | −0.301692 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1729.32 | 0.183600 | ||||||||
\(447\) | 5529.41i | 0.585083i | ||||||||
\(448\) | − 321.965i | − 0.0339541i | ||||||||
\(449\) | 10146.5 | 1.06647 | 0.533233 | − | 0.845968i | \(-0.320977\pi\) | ||||
0.533233 | + | 0.845968i | \(0.320977\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1270.95 | −0.132698 | ||||||||
\(452\) | 1107.09i | 0.115206i | ||||||||
\(453\) | 13783.9i | 1.42963i | ||||||||
\(454\) | 3958.79 | 0.409241 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6393.68 | −0.656604 | ||||||||
\(457\) | − 4728.87i | − 0.484042i | −0.970271 | − | 0.242021i | \(-0.922190\pi\) | ||||
0.970271 | − | 0.242021i | \(-0.0778103\pi\) | |||||||
\(458\) | 6227.06i | 0.635308i | ||||||||
\(459\) | 2845.35 | 0.289346 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8380.69 | 0.846698 | 0.423349 | − | 0.905967i | \(-0.360854\pi\) | ||||
0.423349 | + | 0.905967i | \(0.360854\pi\) | |||||||
\(462\) | 283.121i | 0.0285108i | ||||||||
\(463\) | − 6845.17i | − 0.687089i | −0.939136 | − | 0.343545i | \(-0.888372\pi\) | ||||
0.939136 | − | 0.343545i | \(-0.111628\pi\) | |||||||
\(464\) | 568.053 | 0.0568345 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12037.3 | 1.19660 | ||||||||
\(467\) | − 14884.0i | − 1.47484i | −0.675436 | − | 0.737418i | \(-0.736045\pi\) | ||||
0.675436 | − | 0.737418i | \(-0.263955\pi\) | |||||||
\(468\) | 398.778i | 0.0393878i | ||||||||
\(469\) | −428.324 | −0.0421710 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7257.01 | 0.709948 | ||||||||
\(472\) | − 6369.62i | − 0.621156i | ||||||||
\(473\) | 2439.20i | 0.237114i | ||||||||
\(474\) | −13363.0 | −1.29490 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −397.295 | −0.0382563 | ||||||||
\(477\) | − 524.766i | − 0.0503719i | ||||||||
\(478\) | 8449.76i | 0.808542i | ||||||||
\(479\) | −6048.69 | −0.576976 | −0.288488 | − | 0.957483i | \(-0.593153\pi\) | ||||
−0.288488 | + | 0.957483i | \(0.593153\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8780.71 | −0.832361 | ||||||||
\(482\) | 2788.47i | 0.263509i | ||||||||
\(483\) | − 583.264i | − 0.0549471i | ||||||||
\(484\) | 5199.36 | 0.488294 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −890.720 | −0.0831355 | ||||||||
\(487\) | 3199.35i | 0.297693i | 0.988860 | + | 0.148846i | \(0.0475560\pi\) | ||||
−0.988860 | + | 0.148846i | \(0.952444\pi\) | |||||||
\(488\) | 4548.64i | 0.421941i | ||||||||
\(489\) | −15101.6 | −1.39656 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1614.41 | −0.148385 | −0.0741926 | − | 0.997244i | \(-0.523638\pi\) | ||||
−0.0741926 | + | 0.997244i | \(0.523638\pi\) | |||||||
\(492\) | − 4590.85i | − 0.420674i | ||||||||
\(493\) | − 700.960i | − 0.0640358i | ||||||||
\(494\) | −19890.3 | −1.81155 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4512.65 | 0.408516 | ||||||||
\(497\) | − 1859.24i | − 0.167803i | ||||||||
\(498\) | − 1601.05i | − 0.144066i | ||||||||
\(499\) | 5392.04 | 0.483729 | 0.241864 | − | 0.970310i | \(-0.422241\pi\) | ||||
0.241864 | + | 0.970310i | \(0.422241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1772.04 | 0.158022 | ||||||||
\(502\) | − 11937.7i | − 1.06136i | ||||||||
\(503\) | − 12625.4i | − 1.11917i | −0.828775 | − | 0.559583i | \(-0.810961\pi\) | ||||
0.828775 | − | 0.559583i | \(-0.189039\pi\) | |||||||
\(504\) | 63.9633 | 0.00565308 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 256.781 | 0.0225599 | ||||||||
\(507\) | − 8759.89i | − 0.767338i | ||||||||
\(508\) | − 6211.15i | − 0.542471i | ||||||||
\(509\) | −7065.76 | −0.615294 | −0.307647 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307647 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1560.46 | −0.135090 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | − 22848.9i | − 1.96647i | ||||||||
\(514\) | 3272.12 | 0.280792 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8810.73 | −0.751688 | ||||||||
\(517\) | − 503.905i | − 0.0428660i | ||||||||
\(518\) | 1408.41i | 0.119463i | ||||||||
\(519\) | −18660.2 | −1.57822 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8399.20 | −0.706287 | −0.353144 | − | 0.935569i | \(-0.614887\pi\) | ||||
−0.353144 | + | 0.935569i | \(0.614887\pi\) | |||||||
\(522\) | 112.852i | 0.00946247i | ||||||||
\(523\) | 7002.06i | 0.585428i | 0.956200 | + | 0.292714i | \(0.0945584\pi\) | ||||
−0.956200 | + | 0.292714i | \(0.905442\pi\) | |||||||
\(524\) | 1255.49 | 0.104669 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5991.10 | 0.496624 | ||||||||
\(527\) | − 5568.47i | − 0.460278i | ||||||||
\(528\) | − 450.228i | − 0.0371092i | ||||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1265.42 | 0.103417 | ||||||||
\(532\) | 3190.37i | 0.260001i | ||||||||
\(533\) | − 14281.9i | − 1.16063i | ||||||||
\(534\) | −12439.8 | −1.00810 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 681.136 | 0.0548891 | ||||||||
\(537\) | − 18067.1i | − 1.45186i | ||||||||
\(538\) | 10380.3i | 0.831838i | ||||||||
\(539\) | −1773.42 | −0.141719 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3338.13 | 0.265282 | 0.132641 | − | 0.991164i | \(-0.457654\pi\) | ||||
0.132641 | + | 0.991164i | \(0.457654\pi\) | |||||||
\(542\) | 13440.9i | 1.06519i | ||||||||
\(543\) | 3950.41i | 0.312207i | ||||||||
\(544\) | 631.792 | 0.0497939 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3181.46 | −0.249366 | ||||||||
\(547\) | 9609.09i | 0.751106i | 0.926801 | + | 0.375553i | \(0.122547\pi\) | ||||
−0.926801 | + | 0.375553i | \(0.877453\pi\) | |||||||
\(548\) | 4264.37i | 0.332417i | ||||||||
\(549\) | −903.656 | −0.0702497 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5628.87 | −0.435205 | ||||||||
\(552\) | 927.526i | 0.0715183i | ||||||||
\(553\) | 6667.98i | 0.512751i | ||||||||
\(554\) | 12229.5 | 0.937872 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6379.15 | −0.486576 | ||||||||
\(557\) | − 11931.1i | − 0.907608i | −0.891102 | − | 0.453804i | \(-0.850067\pi\) | ||||
0.891102 | − | 0.453804i | \(-0.149933\pi\) | |||||||
\(558\) | 896.506i | 0.0680146i | ||||||||
\(559\) | −27409.6 | −2.07389 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −555.567 | −0.0418112 | ||||||||
\(562\) | − 7098.13i | − 0.532770i | ||||||||
\(563\) | 10082.4i | 0.754746i | 0.926061 | + | 0.377373i | \(0.123173\pi\) | ||||
−0.926061 | + | 0.377373i | \(0.876827\pi\) | |||||||
\(564\) | 1820.17 | 0.135892 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6206.23 | 0.460896 | ||||||||
\(567\) | − 3438.80i | − 0.254702i | ||||||||
\(568\) | 2956.62i | 0.218410i | ||||||||
\(569\) | 18710.5 | 1.37853 | 0.689267 | − | 0.724507i | \(-0.257933\pi\) | ||||
0.689267 | + | 0.724507i | \(0.257933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13510.1 | 0.990159 | 0.495079 | − | 0.868848i | \(-0.335139\pi\) | ||||
0.495079 | + | 0.868848i | \(0.335139\pi\) | |||||||
\(572\) | − 1400.63i | − 0.102383i | ||||||||
\(573\) | 7520.75i | 0.548314i | ||||||||
\(574\) | −2290.79 | −0.166578 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −101.717 | −0.00735797 | ||||||||
\(577\) | 11582.3i | 0.835662i | 0.908525 | + | 0.417831i | \(0.137210\pi\) | ||||
−0.908525 | + | 0.417831i | \(0.862790\pi\) | |||||||
\(578\) | 9046.39i | 0.651004i | ||||||||
\(579\) | 15581.9 | 1.11841 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −798.905 | −0.0570468 | ||||||||
\(582\) | 1072.59i | 0.0763926i | ||||||||
\(583\) | 1843.14i | 0.130935i | ||||||||
\(584\) | 2481.50 | 0.175831 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2437.03 | 0.171796 | ||||||||
\(587\) | − 6019.34i | − 0.423245i | −0.977351 | − | 0.211623i | \(-0.932125\pi\) | ||||
0.977351 | − | 0.211623i | \(-0.0678747\pi\) | |||||||
\(588\) | − 6405.81i | − 0.449271i | ||||||||
\(589\) | −44716.1 | −3.12818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14216.8 | −0.989514 | ||||||||
\(592\) | − 2239.70i | − 0.155492i | ||||||||
\(593\) | − 26299.3i | − 1.82122i | −0.413270 | − | 0.910608i | \(-0.635613\pi\) | ||||
0.413270 | − | 0.910608i | \(-0.364387\pi\) | |||||||
\(594\) | 1608.96 | 0.111139 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4387.63 | −0.301551 | ||||||||
\(597\) | − 6634.36i | − 0.454818i | ||||||||
\(598\) | 2885.47i | 0.197317i | ||||||||
\(599\) | 27368.0 | 1.86682 | 0.933409 | − | 0.358813i | \(-0.116819\pi\) | ||||
0.933409 | + | 0.358813i | \(0.116819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3472.33 | −0.235673 | −0.117836 | − | 0.993033i | \(-0.537596\pi\) | ||||
−0.117836 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(602\) | 4396.46i | 0.297652i | ||||||||
\(603\) | 135.318i | 0.00913859i | ||||||||
\(604\) | −10937.6 | −0.736832 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6479.33 | −0.434332 | ||||||||
\(607\) | 5061.10i | 0.338425i | 0.985580 | + | 0.169212i | \(0.0541224\pi\) | ||||
−0.985580 | + | 0.169212i | \(0.945878\pi\) | |||||||
\(608\) | − 5073.44i | − 0.338413i | ||||||||
\(609\) | −900.339 | −0.0599074 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5662.44 | 0.374922 | ||||||||
\(612\) | 125.515i | 0.00829027i | ||||||||
\(613\) | 28272.6i | 1.86283i | 0.363953 | + | 0.931417i | \(0.381427\pi\) | ||||
−0.363953 | + | 0.931417i | \(0.618573\pi\) | |||||||
\(614\) | −5128.90 | −0.337110 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −224.659 | −0.0146944 | ||||||||
\(617\) | − 2222.47i | − 0.145013i | −0.997368 | − | 0.0725066i | \(-0.976900\pi\) | ||||
0.997368 | − | 0.0725066i | \(-0.0230999\pi\) | |||||||
\(618\) | 16352.6i | 1.06440i | ||||||||
\(619\) | 10498.2 | 0.681679 | 0.340840 | − | 0.940121i | \(-0.389289\pi\) | ||||
0.340840 | + | 0.940121i | \(0.389289\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3314.67 | −0.214192 | ||||||||
\(622\) | − 185.251i | − 0.0119419i | ||||||||
\(623\) | 6207.34i | 0.399185i | ||||||||
\(624\) | 5059.27 | 0.324572 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8552.87 | −0.546073 | ||||||||
\(627\) | 4461.34i | 0.284160i | ||||||||
\(628\) | 5758.51i | 0.365907i | ||||||||
\(629\) | −2763.72 | −0.175194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11402.2 | −0.719355 | −0.359678 | − | 0.933077i | \(-0.617113\pi\) | ||||
−0.359678 | + | 0.933077i | \(0.617113\pi\) | |||||||
\(632\) | − 10603.6i | − 0.667390i | ||||||||
\(633\) | − 17135.0i | − 1.07591i | ||||||||
\(634\) | 5928.47 | 0.371372 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6657.67 | −0.415085 | ||||||||
\(637\) | − 19928.1i | − 1.23953i | ||||||||
\(638\) | − 396.372i | − 0.0245964i | ||||||||
\(639\) | −587.377 | −0.0363635 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26128.3 | 1.60999 | 0.804996 | − | 0.593280i | \(-0.202167\pi\) | ||||
0.804996 | + | 0.593280i | \(0.202167\pi\) | |||||||
\(642\) | − 15030.5i | − 0.924001i | ||||||||
\(643\) | − 863.502i | − 0.0529599i | −0.999649 | − | 0.0264799i | \(-0.991570\pi\) | ||||
0.999649 | − | 0.0264799i | \(-0.00842981\pi\) | |||||||
\(644\) | 462.825 | 0.0283197 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6260.47 | −0.381292 | ||||||||
\(647\) | − 5477.43i | − 0.332828i | −0.986056 | − | 0.166414i | \(-0.946781\pi\) | ||||
0.986056 | − | 0.166414i | \(-0.0532188\pi\) | |||||||
\(648\) | 5468.50i | 0.331517i | ||||||||
\(649\) | −4444.55 | −0.268820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7152.36 | −0.430604 | ||||||||
\(652\) | − 11983.3i | − 0.719787i | ||||||||
\(653\) | − 19233.2i | − 1.15261i | −0.817235 | − | 0.576305i | \(-0.804494\pi\) | ||||
0.817235 | − | 0.576305i | \(-0.195506\pi\) | |||||||
\(654\) | 12138.5 | 0.725768 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3642.88 | 0.216815 | ||||||||
\(657\) | 492.987i | 0.0292744i | ||||||||
\(658\) | − 908.245i | − 0.0538102i | ||||||||
\(659\) | −9952.51 | −0.588307 | −0.294154 | − | 0.955758i | \(-0.595038\pi\) | ||||
−0.294154 | + | 0.955758i | \(0.595038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3047.96 | 0.179352 | 0.0896762 | − | 0.995971i | \(-0.471417\pi\) | ||||
0.0896762 | + | 0.995971i | \(0.471417\pi\) | |||||||
\(662\) | − 2697.61i | − 0.158377i | ||||||||
\(663\) | − 6242.98i | − 0.365697i | ||||||||
\(664\) | 1270.45 | 0.0742513 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 444.950 | 0.0258881 | ||||||||
\(667\) | 816.576i | 0.0474032i | ||||||||
\(668\) | 1406.13i | 0.0814442i | ||||||||
\(669\) | 4358.67 | 0.251892 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3173.92 | 0.182605 | ||||||||
\(672\) | − 811.498i | − 0.0465836i | ||||||||
\(673\) | − 16245.9i | − 0.930508i | −0.885177 | − | 0.465254i | \(-0.845963\pi\) | ||||
0.885177 | − | 0.465254i | \(-0.154037\pi\) | |||||||
\(674\) | 11528.6 | 0.658850 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6951.05 | 0.395486 | ||||||||
\(677\) | − 30056.6i | − 1.70631i | −0.521659 | − | 0.853154i | \(-0.674687\pi\) | ||||
0.521659 | − | 0.853154i | \(-0.325313\pi\) | |||||||
\(678\) | 2790.35i | 0.158057i | ||||||||
\(679\) | 535.213 | 0.0302498 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9977.94 | 0.561462 | ||||||||
\(682\) | − 3148.81i | − 0.176795i | ||||||||
\(683\) | − 10064.8i | − 0.563866i | −0.959434 | − | 0.281933i | \(-0.909024\pi\) | ||||
0.959434 | − | 0.281933i | \(-0.0909755\pi\) | |||||||
\(684\) | 1007.92 | 0.0563430 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6647.50 | −0.369975 | ||||||||
\(687\) | 15695.0i | 0.871617i | ||||||||
\(688\) | − 6991.39i | − 0.387419i | ||||||||
\(689\) | −20711.6 | −1.14521 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10260.7 | 0.564886 | 0.282443 | − | 0.959284i | \(-0.408855\pi\) | ||||
0.282443 | + | 0.959284i | \(0.408855\pi\) | |||||||
\(692\) | − 14807.1i | − 0.813411i | ||||||||
\(693\) | − 44.6319i | − 0.00244650i | ||||||||
\(694\) | −8132.31 | −0.444810 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1431.75 | 0.0779746 | ||||||||
\(697\) | − 4495.21i | − 0.244287i | ||||||||
\(698\) | − 16815.6i | − 0.911865i | ||||||||
\(699\) | 30339.4 | 1.64169 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19815.6 | −1.06766 | −0.533828 | − | 0.845593i | \(-0.679247\pi\) | ||||
−0.533828 | + | 0.845593i | \(0.679247\pi\) | |||||||
\(702\) | 18080.1i | 0.972066i | ||||||||
\(703\) | 22193.3i | 1.19067i | ||||||||
\(704\) | 357.260 | 0.0191261 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 512.136 | 0.0273010 | ||||||||
\(707\) | 3233.12i | 0.171986i | ||||||||
\(708\) | − 16054.3i | − 0.852201i | ||||||||
\(709\) | 30533.5 | 1.61736 | 0.808681 | − | 0.588247i | \(-0.200182\pi\) | ||||
0.808681 | + | 0.588247i | \(0.200182\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2106.57 | 0.111115 | ||||||||
\(712\) | − 9871.12i | − 0.519573i | ||||||||
\(713\) | 6486.93i | 0.340726i | ||||||||
\(714\) | −1001.36 | −0.0524861 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14336.4 | 0.748290 | ||||||||
\(717\) | 21297.2i | 1.10929i | ||||||||
\(718\) | 24105.0i | 1.25291i | ||||||||
\(719\) | −9125.45 | −0.473327 | −0.236663 | − | 0.971592i | \(-0.576054\pi\) | ||||
−0.236663 | + | 0.971592i | \(0.576054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8159.77 | 0.421478 | ||||||||
\(722\) | 36555.0i | 1.88426i | ||||||||
\(723\) | 7028.21i | 0.361524i | ||||||||
\(724\) | −3134.69 | −0.160911 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13104.7 | 0.669920 | ||||||||
\(727\) | 2635.53i | 0.134452i | 0.997738 | + | 0.0672259i | \(0.0214148\pi\) | ||||
−0.997738 | + | 0.0672259i | \(0.978585\pi\) | |||||||
\(728\) | − 2524.52i | − 0.128523i | ||||||||
\(729\) | −20701.2 | −1.05173 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8627.17 | −0.436508 | ||||||||
\(732\) | 11464.6i | 0.578886i | ||||||||
\(733\) | − 10778.0i | − 0.543102i | −0.962424 | − | 0.271551i | \(-0.912463\pi\) | ||||
0.962424 | − | 0.271551i | \(-0.0875366\pi\) | |||||||
\(734\) | 18490.8 | 0.929848 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | − 475.278i | − 0.0237545i | ||||||||
\(738\) | 723.714i | 0.0360979i | ||||||||
\(739\) | 1758.72 | 0.0875449 | 0.0437725 | − | 0.999042i | \(-0.486062\pi\) | ||||
0.0437725 | + | 0.999042i | \(0.486062\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −50132.6 | −2.48538 | ||||||||
\(742\) | 3322.11i | 0.164364i | ||||||||
\(743\) | − 9737.97i | − 0.480823i | −0.970671 | − | 0.240412i | \(-0.922718\pi\) | ||||
0.970671 | − | 0.240412i | \(-0.0772824\pi\) | |||||||
\(744\) | 11373.9 | 0.560467 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1738.53 | −0.0853245 | ||||||||
\(747\) | 252.393i | 0.0123622i | ||||||||
\(748\) | − 440.848i | − 0.0215495i | ||||||||
\(749\) | −7500.08 | −0.365884 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23795.7 | −1.15621 | −0.578107 | − | 0.815961i | \(-0.696208\pi\) | ||||
−0.578107 | + | 0.815961i | \(0.696208\pi\) | |||||||
\(752\) | 1444.32i | 0.0700385i | ||||||||
\(753\) | − 30088.3i | − 1.45615i | ||||||||
\(754\) | 4454.08 | 0.215130 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2900.02 | 0.139514 | ||||||||
\(757\) | 23647.6i | 1.13538i | 0.823241 | + | 0.567692i | \(0.192163\pi\) | ||||
−0.823241 | + | 0.567692i | \(0.807837\pi\) | |||||||
\(758\) | − 2557.53i | − 0.122551i | ||||||||
\(759\) | 647.203 | 0.0309512 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4606.09 | −0.219410 | −0.109705 | − | 0.993964i | \(-0.534991\pi\) | ||||
−0.109705 | + | 0.993964i | \(0.534991\pi\) | |||||||
\(762\) | − 15654.9i | − 0.744248i | ||||||||
\(763\) | − 6056.98i | − 0.287388i | ||||||||
\(764\) | −5967.79 | −0.282601 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10687.5 | −0.504119 | ||||||||
\(767\) | − 49944.0i | − 2.35120i | ||||||||
\(768\) | 1290.47i | 0.0606326i | ||||||||
\(769\) | −17760.9 | −0.832867 | −0.416433 | − | 0.909166i | \(-0.636720\pi\) | ||||
−0.416433 | + | 0.909166i | \(0.636720\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8247.22 | 0.385235 | ||||||||
\(772\) | 12364.4i | 0.576430i | ||||||||
\(773\) | − 7147.47i | − 0.332570i | −0.986078 | − | 0.166285i | \(-0.946823\pi\) | ||||
0.986078 | − | 0.166285i | \(-0.0531772\pi\) | |||||||
\(774\) | 1388.95 | 0.0645021 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −851.114 | −0.0393727 | ||||||||
\(777\) | 3549.83i | 0.163899i | ||||||||
\(778\) | 1416.69i | 0.0652839i | ||||||||
\(779\) | −36097.6 | −1.66024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2063.05 | 0.0945222 | ||||||||
\(782\) | 908.201i | 0.0415310i | ||||||||
\(783\) | 5116.59i | 0.233528i | ||||||||
\(784\) | 5083.07 | 0.231554 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3164.40 | 0.143601 | ||||||||
\(787\) | − 31719.1i | − 1.43668i | −0.695694 | − | 0.718338i | \(-0.744903\pi\) | ||||
0.695694 | − | 0.718338i | \(-0.255097\pi\) | |||||||
\(788\) | − 11281.2i | − 0.509995i | ||||||||
\(789\) | 15100.3 | 0.681348 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1392.36 | 0.0625872 | ||||||||
\(792\) | 70.9751i | 0.00318433i | ||||||||
\(793\) | 35665.7i | 1.59713i | ||||||||
\(794\) | 11848.0 | 0.529560 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5264.42 | 0.234413 | ||||||||
\(797\) | 30828.3i | 1.37013i | 0.728481 | + | 0.685066i | \(0.240227\pi\) | ||||
−0.728481 | + | 0.685066i | \(0.759773\pi\) | |||||||
\(798\) | 8041.18i | 0.356710i | ||||||||
\(799\) | 1782.25 | 0.0789129 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1961.05 | 0.0865046 | ||||||||
\(802\) | − 22787.3i | − 1.00330i | ||||||||
\(803\) | − 1731.53i | − 0.0760949i | ||||||||
\(804\) | 1716.77 | 0.0753057 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 35383.5 | 1.54632 | ||||||||
\(807\) | 26163.2i | 1.14125i | ||||||||
\(808\) | − 5141.41i | − 0.223854i | ||||||||
\(809\) | −36679.2 | −1.59403 | −0.797015 | − | 0.603959i | \(-0.793589\pi\) | ||||
−0.797015 | + | 0.603959i | \(0.793589\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12210.0 | −0.528672 | −0.264336 | − | 0.964431i | \(-0.585153\pi\) | ||||
−0.264336 | + | 0.964431i | \(0.585153\pi\) | |||||||
\(812\) | − 714.427i | − 0.0308762i | ||||||||
\(813\) | 33877.0i | 1.46140i | ||||||||
\(814\) | −1562.80 | −0.0672927 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1592.40 | 0.0683152 | ||||||||
\(817\) | 69278.2i | 2.96663i | ||||||||
\(818\) | − 27608.9i | − 1.18010i | ||||||||
\(819\) | 501.534 | 0.0213981 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9996.47 | −0.424944 | −0.212472 | − | 0.977167i | \(-0.568151\pi\) | ||||
−0.212472 | + | 0.977167i | \(0.568151\pi\) | |||||||
\(822\) | 10748.1i | 0.456063i | ||||||||
\(823\) | 42868.8i | 1.81569i | 0.419306 | + | 0.907845i | \(0.362273\pi\) | ||||
−0.419306 | + | 0.907845i | \(0.637727\pi\) | |||||||
\(824\) | −12975.9 | −0.548590 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8010.93 | −0.337453 | ||||||||
\(827\) | − 15833.4i | − 0.665759i | −0.942969 | − | 0.332880i | \(-0.891980\pi\) | ||||
0.942969 | − | 0.332880i | \(-0.108020\pi\) | |||||||
\(828\) | − 146.217i | − 0.00613697i | ||||||||
\(829\) | 17722.3 | 0.742484 | 0.371242 | − | 0.928536i | \(-0.378932\pi\) | ||||
0.371242 | + | 0.928536i | \(0.378932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30823.8 | 1.28672 | ||||||||
\(832\) | 4014.57i | 0.167284i | ||||||||
\(833\) | − 6272.35i | − 0.260893i | ||||||||
\(834\) | −16078.3 | −0.667563 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3540.11 | −0.146456 | ||||||||
\(837\) | 40646.5i | 1.67855i | ||||||||
\(838\) | 29591.7i | 1.21984i | ||||||||
\(839\) | 40528.4 | 1.66769 | 0.833847 | − | 0.551996i | \(-0.186134\pi\) | ||||
0.833847 | + | 0.551996i | \(0.186134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23128.5 | −0.948317 | ||||||||
\(842\) | 11609.3i | 0.475159i | ||||||||
\(843\) | − 17890.5i | − 0.730938i | ||||||||
\(844\) | 13596.7 | 0.554525 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −286.936 | −0.0116608 | ||||||||
\(847\) | − 6539.11i | − 0.265273i | ||||||||
\(848\) | − 5282.92i | − 0.213934i | ||||||||
\(849\) | 15642.5 | 0.632331 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3219.57 | 0.129689 | ||||||||
\(852\) | 7452.02i | 0.299650i | ||||||||
\(853\) | − 8116.97i | − 0.325814i | −0.986641 | − | 0.162907i | \(-0.947913\pi\) | ||||
0.986641 | − | 0.162907i | \(-0.0520871\pi\) | |||||||
\(854\) | 5720.73 | 0.229226 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11926.9 | 0.476229 | ||||||||
\(857\) | 16285.5i | 0.649126i | 0.945864 | + | 0.324563i | \(0.105217\pi\) | ||||
−0.945864 | + | 0.324563i | \(0.894783\pi\) | |||||||
\(858\) | − 3530.22i | − 0.140466i | ||||||||
\(859\) | 26487.5 | 1.05209 | 0.526043 | − | 0.850458i | \(-0.323675\pi\) | ||||
0.526043 | + | 0.850458i | \(0.323675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5773.81 | −0.228538 | ||||||||
\(862\) | 30536.3i | 1.20658i | ||||||||
\(863\) | − 40396.2i | − 1.59340i | −0.604376 | − | 0.796699i | \(-0.706578\pi\) | ||||
0.604376 | − | 0.796699i | \(-0.293422\pi\) | |||||||
\(864\) | −4611.71 | −0.181590 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4501.25 | 0.176627 | ||||||||
\(867\) | 22801.0i | 0.893151i | ||||||||
\(868\) | − 5675.46i | − 0.221933i | ||||||||
\(869\) | −7398.94 | −0.288828 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5340.76 | 0.207767 | ||||||||
\(872\) | 9632.00i | 0.374060i | ||||||||
\(873\) | − 169.087i | − 0.00655523i | ||||||||
\(874\) | 7293.07 | 0.282256 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6254.50 | 0.241233 | ||||||||
\(877\) | 10962.9i | 0.422109i | 0.977474 | + | 0.211054i | \(0.0676897\pi\) | ||||
−0.977474 | + | 0.211054i | \(0.932310\pi\) | |||||||
\(878\) | − 20732.4i | − 0.796908i | ||||||||
\(879\) | 6142.40 | 0.235698 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23906.5 | 0.914222 | 0.457111 | − | 0.889410i | \(-0.348884\pi\) | ||||
0.457111 | + | 0.889410i | \(0.348884\pi\) | |||||||
\(882\) | 1009.83i | 0.0385518i | ||||||||
\(883\) | 30509.1i | 1.16275i | 0.813634 | + | 0.581377i | \(0.197486\pi\) | ||||
−0.813634 | + | 0.581377i | \(0.802514\pi\) | |||||||
\(884\) | 4953.86 | 0.188480 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7762.22 | −0.294331 | ||||||||
\(887\) | − 40034.3i | − 1.51547i | −0.652565 | − | 0.757733i | \(-0.726307\pi\) | ||||
0.652565 | − | 0.757733i | \(-0.273693\pi\) | |||||||
\(888\) | − 5645.06i | − 0.213328i | ||||||||
\(889\) | −7811.62 | −0.294706 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3815.77 | 0.143472 | ||||||||
\(892\) | 3458.64i | 0.129825i | ||||||||
\(893\) | − 14311.9i | − 0.536314i | ||||||||
\(894\) | −11058.8 | −0.413716 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 643.931 | 0.0240092 | ||||||||
\(897\) | 7272.69i | 0.270711i | ||||||||
\(898\) | 20293.0i | 0.754106i | ||||||||
\(899\) | 10013.4 | 0.371485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6518.96 | −0.241041 | ||||||||
\(902\) | − 2541.91i | − 0.0938318i | ||||||||
\(903\) | 11081.1i | 0.408366i | ||||||||
\(904\) | −2214.17 | −0.0814626 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −27567.8 | −1.01090 | ||||||||
\(907\) | − 2843.48i | − 0.104097i | −0.998645 | − | 0.0520486i | \(-0.983425\pi\) | ||||
0.998645 | − | 0.0520486i | \(-0.0165751\pi\) | |||||||
\(908\) | 7917.58i | 0.289377i | ||||||||
\(909\) | 1021.42 | 0.0372699 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42268.6 | 1.53723 | 0.768617 | − | 0.639710i | \(-0.220945\pi\) | ||||
0.768617 | + | 0.639710i | \(0.220945\pi\) | |||||||
\(912\) | − 12787.4i | − 0.464289i | ||||||||
\(913\) | − 886.483i | − 0.0321340i | ||||||||
\(914\) | 9457.74 | 0.342269 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12454.1 | −0.449231 | ||||||||
\(917\) | − 1579.00i | − 0.0568629i | ||||||||
\(918\) | 5690.71i | 0.204598i | ||||||||
\(919\) | 12699.6 | 0.455844 | 0.227922 | − | 0.973679i | \(-0.426807\pi\) | ||||
0.227922 | + | 0.973679i | \(0.426807\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12927.1 | −0.462501 | ||||||||
\(922\) | 16761.4i | 0.598706i | ||||||||
\(923\) | 23182.8i | 0.826728i | ||||||||
\(924\) | −566.242 | −0.0201602 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13690.3 | 0.485845 | ||||||||
\(927\) | − 2577.86i | − 0.0913357i | ||||||||
\(928\) | 1136.11i | 0.0401880i | ||||||||
\(929\) | 24889.6 | 0.879011 | 0.439505 | − | 0.898240i | \(-0.355154\pi\) | ||||
0.439505 | + | 0.898240i | \(0.355154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50368.5 | −1.77310 | ||||||||
\(932\) | 24074.6i | 0.846126i | ||||||||
\(933\) | − 466.915i | − 0.0163838i | ||||||||
\(934\) | 29768.0 | 1.04287 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −797.555 | −0.0278514 | ||||||||
\(937\) | 9585.48i | 0.334199i | 0.985940 | + | 0.167099i | \(0.0534401\pi\) | ||||
−0.985940 | + | 0.167099i | \(0.946560\pi\) | |||||||
\(938\) | − 856.649i | − 0.0298194i | ||||||||
\(939\) | −21557.1 | −0.749189 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21146.9 | −0.732592 | −0.366296 | − | 0.930498i | \(-0.619374\pi\) | ||||
−0.366296 | + | 0.930498i | \(0.619374\pi\) | |||||||
\(942\) | 14514.0i | 0.502009i | ||||||||
\(943\) | 5236.65i | 0.180836i | ||||||||
\(944\) | 12739.2 | 0.439224 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4878.41 | −0.167665 | ||||||||
\(947\) | 48747.2i | 1.67272i | 0.548177 | + | 0.836362i | \(0.315322\pi\) | ||||
−0.548177 | + | 0.836362i | \(0.684678\pi\) | |||||||
\(948\) | − 26726.0i | − 0.915632i | ||||||||
\(949\) | 19457.3 | 0.665556 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14942.4 | 0.509507 | ||||||||
\(952\) | − 794.591i | − 0.0270513i | ||||||||
\(953\) | − 24925.9i | − 0.847249i | −0.905838 | − | 0.423625i | \(-0.860758\pi\) | ||||
0.905838 | − | 0.423625i | \(-0.139242\pi\) | |||||||
\(954\) | 1049.53 | 0.0356183 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −16899.5 | −0.571725 | ||||||||
\(957\) | − 999.036i | − 0.0337453i | ||||||||
\(958\) | − 12097.4i | − 0.407984i | ||||||||
\(959\) | 5363.20 | 0.180591 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49755.9 | 1.67017 | ||||||||
\(962\) | − 17561.4i | − 0.588568i | ||||||||
\(963\) | 2369.45i | 0.0792882i | ||||||||
\(964\) | −5576.95 | −0.186329 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1166.53 | 0.0388534 | ||||||||
\(967\) | − 1881.92i | − 0.0625838i | −0.999510 | − | 0.0312919i | \(-0.990038\pi\) | ||||
0.999510 | − | 0.0312919i | \(-0.00996215\pi\) | |||||||
\(968\) | 10398.7i | 0.345276i | ||||||||
\(969\) | −15779.2 | −0.523117 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14637.3 | −0.483763 | −0.241881 | − | 0.970306i | \(-0.577764\pi\) | ||||
−0.241881 | + | 0.970306i | \(0.577764\pi\) | |||||||
\(972\) | − 1781.44i | − 0.0587857i | ||||||||
\(973\) | 8022.92i | 0.264340i | ||||||||
\(974\) | −6398.70 | −0.210501 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9097.28 | −0.298358 | ||||||||
\(977\) | 42591.4i | 1.39470i | 0.716733 | + | 0.697348i | \(0.245637\pi\) | ||||
−0.716733 | + | 0.697348i | \(0.754363\pi\) | |||||||
\(978\) | − 30203.2i | − 0.987518i | ||||||||
\(979\) | −6887.81 | −0.224857 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1913.54 | −0.0622780 | ||||||||
\(982\) | − 3228.81i | − 0.104924i | ||||||||
\(983\) | 48858.3i | 1.58529i | 0.609684 | + | 0.792644i | \(0.291296\pi\) | ||||
−0.609684 | + | 0.792644i | \(0.708704\pi\) | |||||||
\(984\) | 9181.71 | 0.297462 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1401.92 | 0.0452801 | ||||||||
\(987\) | − 2289.19i | − 0.0738254i | ||||||||
\(988\) | − 39780.6i | − 1.28096i | ||||||||
\(989\) | 10050.1 | 0.323130 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56522.1 | −1.81179 | −0.905895 | − | 0.423502i | \(-0.860801\pi\) | ||||
−0.905895 | + | 0.423502i | \(0.860801\pi\) | |||||||
\(992\) | 9025.30i | 0.288864i | ||||||||
\(993\) | − 6799.19i | − 0.217287i | ||||||||
\(994\) | 3718.48 | 0.118655 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3202.09 | 0.101870 | ||||||||
\(997\) | − 20767.9i | − 0.659706i | −0.944032 | − | 0.329853i | \(-0.893001\pi\) | ||||
0.944032 | − | 0.329853i | \(-0.106999\pi\) | |||||||
\(998\) | 10784.1i | 0.342048i | ||||||||
\(999\) | 20173.5 | 0.638902 |
(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 | 1150.4.b.o.599.8 | 8 | ||
5.2 | odd | 4 | 1150.4.a.n.1.4 | 4 | |||
5.3 | odd | 4 | 230.4.a.j.1.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1150.4.b.o.599.1 | 8 | ||
15.8 | even | 4 | 2070.4.a.bg.1.3 | 4 | |||
20.3 | even | 4 | 1840.4.a.k.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.j.1.1 | ✓ | 4 | 5.3 | odd | 4 | ||
1150.4.a.n.1.4 | 4 | 5.2 | odd | 4 | |||
1150.4.b.o.599.1 | 8 | 5.4 | even | 2 | inner | ||
1150.4.b.o.599.8 | 8 | 1.1 | even | 1 | trivial | ||
1840.4.a.k.1.4 | 4 | 20.3 | even | 4 | |||
2070.4.a.bg.1.3 | 4 | 15.8 | even | 4 |