Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, 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("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.4.g.bg.667.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 3.53553 | + | 6.12372i | 0.316228 | + | 0.547723i | 0.979698 | − | 0.200480i | \(-0.0642503\pi\) |
−0.663470 | + | 0.748203i | \(0.730917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.07107 | + | 12.2474i | −0.223607 | + | 0.387298i | ||||
\(11\) | −20.0000 | + | 34.6410i | −0.548202 | + | 0.949514i | 0.450195 | + | 0.892930i | \(0.351354\pi\) |
−0.998398 | + | 0.0565844i | \(0.981979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −63.6396 | −1.35773 | −0.678864 | − | 0.734264i | \(-0.737527\pi\) | ||||
−0.678864 | + | 0.734264i | \(0.737527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.707107 | + | 1.22474i | −0.0100882 | + | 0.0174732i | −0.871025 | − | 0.491238i | \(-0.836545\pi\) |
0.860937 | + | 0.508711i | \(0.169878\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | − | 9.79796i | −0.0683038 | − | 0.118306i | 0.829851 | − | 0.557985i | \(-0.188425\pi\) |
−0.898155 | + | 0.439679i | \(0.855092\pi\) | |||||||
\(20\) | −28.2843 | −0.316228 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −80.0000 | −0.775275 | ||||||||
\(23\) | −34.0000 | − | 58.8897i | −0.308239 | − | 0.533885i | 0.669738 | − | 0.742597i | \(-0.266406\pi\) |
−0.977977 | + | 0.208712i | \(0.933073\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 37.5000 | − | 64.9519i | 0.300000 | − | 0.519615i | ||||
\(26\) | −63.6396 | − | 110.227i | −0.480029 | − | 0.831435i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 110.000 | 0.704362 | 0.352181 | − | 0.935932i | \(-0.385440\pi\) | ||||
0.352181 | + | 0.935932i | \(0.385440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 59.3970 | − | 102.879i | 0.344129 | − | 0.596050i | −0.641066 | − | 0.767486i | \(-0.721507\pi\) |
0.985195 | + | 0.171436i | \(0.0548408\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.82843 | −0.0142668 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000 | + | 17.3205i | 0.0444322 | + | 0.0769588i | 0.887386 | − | 0.461027i | \(-0.152519\pi\) |
−0.842954 | + | 0.537986i | \(0.819185\pi\) | |||||||
\(38\) | 11.3137 | − | 19.5959i | 0.0482980 | − | 0.0836547i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −28.2843 | − | 48.9898i | −0.111803 | − | 0.193649i | ||||
\(41\) | −49.4975 | −0.188542 | −0.0942708 | − | 0.995547i | \(-0.530052\pi\) | ||||
−0.0942708 | + | 0.995547i | \(0.530052\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −340.000 | −1.20580 | −0.602901 | − | 0.797816i | \(-0.705989\pi\) | ||||
−0.602901 | + | 0.797816i | \(0.705989\pi\) | |||||||
\(44\) | −80.0000 | − | 138.564i | −0.274101 | − | 0.474757i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 68.0000 | − | 117.779i | 0.217958 | − | 0.377514i | ||||
\(47\) | −45.2548 | − | 78.3837i | −0.140449 | − | 0.243265i | 0.787217 | − | 0.616676i | \(-0.211521\pi\) |
−0.927666 | + | 0.373412i | \(0.878188\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 150.000 | 0.424264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 127.279 | − | 220.454i | 0.339432 | − | 0.587913i | ||||
\(53\) | −314.000 | + | 543.864i | −0.813797 | + | 1.40954i | 0.0963923 | + | 0.995343i | \(0.469270\pi\) |
−0.910189 | + | 0.414194i | \(0.864064\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −282.843 | −0.693427 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 110.000 | + | 190.526i | 0.249029 | + | 0.431332i | ||||
\(59\) | 438.406 | − | 759.342i | 0.967383 | − | 1.67556i | 0.264313 | − | 0.964437i | \(-0.414855\pi\) |
0.703070 | − | 0.711121i | \(-0.251812\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −458.912 | − | 794.859i | −0.963241 | − | 1.66838i | −0.714269 | − | 0.699872i | \(-0.753240\pi\) |
−0.248972 | − | 0.968511i | \(-0.580093\pi\) | |||||||
\(62\) | 237.588 | 0.486672 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −225.000 | − | 389.711i | −0.429351 | − | 0.743658i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −270.000 | + | 467.654i | −0.492325 | + | 0.852731i | −0.999961 | − | 0.00884020i | \(-0.997186\pi\) |
0.507636 | + | 0.861571i | \(0.330519\pi\) | |||||||
\(68\) | −2.82843 | − | 4.89898i | −0.00504408 | − | 0.00873660i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −420.000 | −0.702040 | −0.351020 | − | 0.936368i | \(-0.614165\pi\) | ||||
−0.351020 | + | 0.936368i | \(0.614165\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −144.957 | + | 251.073i | −0.232410 | + | 0.402546i | −0.958517 | − | 0.285036i | \(-0.907994\pi\) |
0.726107 | + | 0.687582i | \(0.241328\pi\) | |||||||
\(74\) | −20.0000 | + | 34.6410i | −0.0314183 | + | 0.0544181i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 45.2548 | 0.0683038 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 380.000 | + | 658.179i | 0.541182 | + | 0.937354i | 0.998837 | + | 0.0482240i | \(0.0153561\pi\) |
−0.457655 | + | 0.889130i | \(0.651311\pi\) | |||||||
\(80\) | 56.5685 | − | 97.9796i | 0.0790569 | − | 0.136931i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −49.4975 | − | 85.7321i | −0.0666595 | − | 0.115458i | ||||
\(83\) | 944.695 | 1.24932 | 0.624661 | − | 0.780896i | \(-0.285237\pi\) | ||||
0.624661 | + | 0.780896i | \(0.285237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0000 | −0.0127606 | ||||||||
\(86\) | −340.000 | − | 588.897i | −0.426316 | − | 0.738400i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 160.000 | − | 277.128i | 0.193819 | − | 0.335704i | ||||
\(89\) | −576.292 | − | 998.167i | −0.686369 | − | 1.18883i | −0.973005 | − | 0.230786i | \(-0.925870\pi\) |
0.286636 | − | 0.958040i | \(-0.407463\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 272.000 | 0.308239 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 90.5097 | − | 156.767i | 0.0993123 | − | 0.172014i | ||||
\(95\) | 40.0000 | − | 69.2820i | 0.0431991 | − | 0.0748230i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −502.046 | −0.525516 | −0.262758 | − | 0.964862i | \(-0.584632\pi\) | ||||
−0.262758 | + | 0.964862i | \(0.584632\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 150.000 | + | 259.808i | 0.150000 | + | 0.259808i | ||||
\(101\) | 880.348 | − | 1524.81i | 0.867306 | − | 1.50222i | 0.00256667 | − | 0.999997i | \(-0.499183\pi\) |
0.864739 | − | 0.502221i | \(-0.167484\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −113.137 | − | 195.959i | −0.108230 | − | 0.187461i | 0.806823 | − | 0.590793i | \(-0.201185\pi\) |
−0.915053 | + | 0.403333i | \(0.867852\pi\) | |||||||
\(104\) | 509.117 | 0.480029 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1256.00 | −1.15088 | ||||||||
\(107\) | −1012.00 | − | 1752.84i | −0.914334 | − | 1.58367i | −0.807874 | − | 0.589356i | \(-0.799382\pi\) |
−0.106460 | − | 0.994317i | \(-0.533952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 202.000 | − | 349.874i | 0.177505 | − | 0.307448i | −0.763520 | − | 0.645784i | \(-0.776531\pi\) |
0.941025 | + | 0.338336i | \(0.109864\pi\) | |||||||
\(110\) | −282.843 | − | 489.898i | −0.245164 | − | 0.424636i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1008.00 | 0.839156 | 0.419578 | − | 0.907719i | \(-0.362178\pi\) | ||||
0.419578 | + | 0.907719i | \(0.362178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 240.416 | − | 416.413i | 0.194947 | − | 0.337659i | ||||
\(116\) | −220.000 | + | 381.051i | −0.176090 | + | 0.304998i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1753.62 | 1.36809 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −134.500 | − | 232.961i | −0.101052 | − | 0.175027i | ||||
\(122\) | 917.825 | − | 1589.72i | 0.681114 | − | 1.17972i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 237.588 | + | 411.514i | 0.172065 | + | 0.298025i | ||||
\(125\) | 1414.21 | 1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1000.00 | 0.698706 | 0.349353 | − | 0.936991i | \(-0.386401\pi\) | ||||
0.349353 | + | 0.936991i | \(0.386401\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 450.000 | − | 779.423i | 0.303597 | − | 0.525845i | ||||
\(131\) | −42.4264 | − | 73.4847i | −0.0282963 | − | 0.0490106i | 0.851530 | − | 0.524305i | \(-0.175675\pi\) |
−0.879827 | + | 0.475294i | \(0.842342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1080.00 | −0.696252 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.65685 | − | 9.79796i | 0.00356670 | − | 0.00617771i | ||||
\(137\) | −1017.00 | + | 1761.50i | −0.634220 | + | 1.09850i | 0.352460 | + | 0.935827i | \(0.385345\pi\) |
−0.986680 | + | 0.162675i | \(0.947988\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1736.65 | −1.05972 | −0.529860 | − | 0.848085i | \(-0.677756\pi\) | ||||
−0.529860 | + | 0.848085i | \(0.677756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −420.000 | − | 727.461i | −0.248209 | − | 0.429910i | ||||
\(143\) | 1272.79 | − | 2204.54i | 0.744309 | − | 1.28918i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 388.909 | + | 673.610i | 0.222739 | + | 0.385795i | ||||
\(146\) | −579.828 | −0.328677 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −80.0000 | −0.0444322 | ||||||||
\(149\) | −1070.00 | − | 1853.29i | −0.588307 | − | 1.01898i | −0.994454 | − | 0.105171i | \(-0.966461\pi\) |
0.406147 | − | 0.913808i | \(-0.366872\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1060.00 | + | 1835.97i | −0.571269 | + | 0.989466i | 0.425167 | + | 0.905115i | \(0.360215\pi\) |
−0.996436 | + | 0.0843517i | \(0.973118\pi\) | |||||||
\(152\) | 45.2548 | + | 78.3837i | 0.0241490 | + | 0.0418273i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 840.000 | 0.435293 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −873.277 | + | 1512.56i | −0.443918 | + | 0.768888i | −0.997976 | − | 0.0635898i | \(-0.979745\pi\) |
0.554058 | + | 0.832478i | \(0.313078\pi\) | |||||||
\(158\) | −760.000 | + | 1316.36i | −0.382673 | + | 0.662809i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 226.274 | 0.111803 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1670.00 | − | 2892.52i | −0.802482 | − | 1.38994i | −0.917978 | − | 0.396631i | \(-0.870179\pi\) |
0.115497 | − | 0.993308i | \(-0.463154\pi\) | |||||||
\(164\) | 98.9949 | − | 171.464i | 0.0471354 | − | 0.0816409i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 944.695 | + | 1636.26i | 0.441702 | + | 0.765050i | ||||
\(167\) | 367.696 | 0.170378 | 0.0851890 | − | 0.996365i | \(-0.472851\pi\) | ||||
0.0851890 | + | 0.996365i | \(0.472851\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1853.00 | 0.843423 | ||||||||
\(170\) | −10.0000 | − | 17.3205i | −0.00451156 | − | 0.00781425i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 680.000 | − | 1177.79i | 0.301451 | − | 0.522128i | ||||
\(173\) | −1694.93 | − | 2935.71i | −0.744876 | − | 1.29016i | −0.950253 | − | 0.311480i | \(-0.899175\pi\) |
0.205377 | − | 0.978683i | \(-0.434158\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 640.000 | 0.274101 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1152.58 | − | 1996.33i | 0.485336 | − | 0.840627i | ||||
\(179\) | −360.000 | + | 623.538i | −0.150322 | + | 0.260366i | −0.931346 | − | 0.364136i | \(-0.881364\pi\) |
0.781024 | + | 0.624501i | \(0.214698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1854.03 | −0.761377 | −0.380689 | − | 0.924703i | \(-0.624313\pi\) | ||||
−0.380689 | + | 0.924703i | \(0.624313\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 272.000 | + | 471.118i | 0.108979 | + | 0.188757i | ||||
\(185\) | −70.7107 | + | 122.474i | −0.0281014 | + | 0.0486730i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.2843 | − | 48.9898i | −0.0110607 | − | 0.0191577i | ||||
\(188\) | 362.039 | 0.140449 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 160.000 | 0.0610927 | ||||||||
\(191\) | −1990.00 | − | 3446.78i | −0.753881 | − | 1.30576i | −0.945929 | − | 0.324375i | \(-0.894846\pi\) |
0.192047 | − | 0.981386i | \(-0.438487\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1855.00 | + | 3212.95i | −0.691844 | + | 1.19831i | 0.279390 | + | 0.960178i | \(0.409868\pi\) |
−0.971233 | + | 0.238130i | \(0.923465\pi\) | |||||||
\(194\) | −502.046 | − | 869.569i | −0.185798 | − | 0.321811i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 956.000 | 0.345747 | 0.172874 | − | 0.984944i | \(-0.444695\pi\) | ||||
0.172874 | + | 0.984944i | \(0.444695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2044.95 | + | 3541.96i | −0.728457 | + | 1.26172i | 0.229079 | + | 0.973408i | \(0.426429\pi\) |
−0.957535 | + | 0.288316i | \(0.906905\pi\) | |||||||
\(200\) | −300.000 | + | 519.615i | −0.106066 | + | 0.183712i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3521.39 | 1.22656 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −175.000 | − | 303.109i | −0.0596221 | − | 0.103269i | ||||
\(206\) | 226.274 | − | 391.918i | 0.0765304 | − | 0.132555i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 509.117 | + | 881.816i | 0.169716 | + | 0.293957i | ||||
\(209\) | 452.548 | 0.149777 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2868.00 | 0.935741 | 0.467870 | − | 0.883797i | \(-0.345021\pi\) | ||||
0.467870 | + | 0.883797i | \(0.345021\pi\) | |||||||
\(212\) | −1256.00 | − | 2175.46i | −0.406898 | − | 0.704768i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2024.00 | − | 3505.67i | 0.646532 | − | 1.11983i | ||||
\(215\) | −1202.08 | − | 2082.07i | −0.381308 | − | 0.660445i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 808.000 | 0.251031 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 565.685 | − | 979.796i | 0.173357 | − | 0.300263i | ||||
\(221\) | 45.0000 | − | 77.9423i | 0.0136970 | − | 0.0237238i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2630.44 | 0.789897 | 0.394949 | − | 0.918703i | \(-0.370762\pi\) | ||||
0.394949 | + | 0.918703i | \(0.370762\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1008.00 | + | 1745.91i | 0.296687 | + | 0.513876i | ||||
\(227\) | 84.8528 | − | 146.969i | 0.0248100 | − | 0.0429722i | −0.853354 | − | 0.521332i | \(-0.825435\pi\) |
0.878164 | + | 0.478360i | \(0.158769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1571.90 | + | 2722.61i | 0.453598 | + | 0.785655i | 0.998606 | − | 0.0527757i | \(-0.0168068\pi\) |
−0.545008 | + | 0.838431i | \(0.683473\pi\) | |||||||
\(230\) | 961.665 | 0.275697 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −880.000 | −0.249029 | ||||||||
\(233\) | 2241.00 | + | 3881.53i | 0.630098 | + | 1.09136i | 0.987531 | + | 0.157423i | \(0.0503186\pi\) |
−0.357433 | + | 0.933939i | \(0.616348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 320.000 | − | 554.256i | 0.0888277 | − | 0.153854i | ||||
\(236\) | 1753.62 | + | 3037.37i | 0.483692 | + | 0.837779i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1740.00 | −0.470926 | −0.235463 | − | 0.971883i | \(-0.575661\pi\) | ||||
−0.235463 | + | 0.971883i | \(0.575661\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −630.032 | + | 1091.25i | −0.168398 | + | 0.291674i | −0.937857 | − | 0.347023i | \(-0.887193\pi\) |
0.769459 | + | 0.638697i | \(0.220526\pi\) | |||||||
\(242\) | 269.000 | − | 465.922i | 0.0714544 | − | 0.123763i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3671.30 | 0.963241 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 360.000 | + | 623.538i | 0.0927379 | + | 0.160627i | ||||
\(248\) | −475.176 | + | 823.029i | −0.121668 | + | 0.210735i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1414.21 | + | 2449.49i | 0.357771 | + | 0.619677i | ||||
\(251\) | −5826.56 | −1.46522 | −0.732608 | − | 0.680651i | \(-0.761697\pi\) | ||||
−0.732608 | + | 0.680651i | \(0.761697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2720.00 | 0.675909 | ||||||||
\(254\) | 1000.00 | + | 1732.05i | 0.247030 | + | 0.427868i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2344.06 | + | 4060.03i | 0.568943 | + | 0.985438i | 0.996671 | + | 0.0815308i | \(0.0259809\pi\) |
−0.427728 | + | 0.903908i | \(0.640686\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1800.00 | 0.429351 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 84.8528 | − | 146.969i | 0.0200085 | − | 0.0346557i | ||||
\(263\) | −1086.00 | + | 1881.01i | −0.254622 | + | 0.441019i | −0.964793 | − | 0.263011i | \(-0.915284\pi\) |
0.710171 | + | 0.704030i | \(0.248618\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4440.63 | −1.02938 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1080.00 | − | 1870.61i | −0.246162 | − | 0.426366i | ||||
\(269\) | 1354.11 | − | 2345.39i | 0.306920 | − | 0.531601i | −0.670767 | − | 0.741668i | \(-0.734035\pi\) |
0.977687 | + | 0.210067i | \(0.0673682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3094.30 | − | 5359.48i | −0.693599 | − | 1.20135i | −0.970651 | − | 0.240494i | \(-0.922691\pi\) |
0.277052 | − | 0.960855i | \(-0.410643\pi\) | |||||||
\(272\) | 22.6274 | 0.00504408 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4068.00 | −0.896923 | ||||||||
\(275\) | 1500.00 | + | 2598.08i | 0.328921 | + | 0.569709i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3065.00 | + | 5308.74i | −0.664830 | + | 1.15152i | 0.314501 | + | 0.949257i | \(0.398163\pi\) |
−0.979331 | + | 0.202263i | \(0.935170\pi\) | |||||||
\(278\) | −1736.65 | − | 3007.97i | −0.374668 | − | 0.648943i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1970.00 | −0.418222 | −0.209111 | − | 0.977892i | \(-0.567057\pi\) | ||||
−0.209111 | + | 0.977892i | \(0.567057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 777.817 | − | 1347.22i | 0.163380 | − | 0.282982i | −0.772699 | − | 0.634773i | \(-0.781094\pi\) |
0.936079 | + | 0.351791i | \(0.114427\pi\) | |||||||
\(284\) | 840.000 | − | 1454.92i | 0.175510 | − | 0.303992i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5091.17 | 1.05261 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2455.50 | + | 4253.05i | 0.499796 | + | 0.865673i | ||||
\(290\) | −777.817 | + | 1347.22i | −0.157500 | + | 0.272798i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −579.828 | − | 1004.29i | −0.116205 | − | 0.201273i | ||||
\(293\) | 7686.25 | 1.53254 | 0.766272 | − | 0.642516i | \(-0.222109\pi\) | ||||
0.766272 | + | 0.642516i | \(0.222109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6200.00 | 1.22365 | ||||||||
\(296\) | −80.0000 | − | 138.564i | −0.0157091 | − | 0.0272090i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2140.00 | − | 3706.59i | 0.415996 | − | 0.720527i | ||||
\(299\) | 2163.75 | + | 3747.72i | 0.418504 | + | 0.724870i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4240.00 | −0.807896 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −90.5097 | + | 156.767i | −0.0170759 | + | 0.0295764i | ||||
\(305\) | 3245.00 | − | 5620.50i | 0.609207 | − | 1.05518i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8598.42 | −1.59849 | −0.799247 | − | 0.601003i | \(-0.794768\pi\) | ||||
−0.799247 | + | 0.601003i | \(0.794768\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 840.000 | + | 1454.92i | 0.153899 | + | 0.266561i | ||||
\(311\) | −3790.09 | + | 6564.63i | −0.691050 | + | 1.19693i | 0.280445 | + | 0.959870i | \(0.409518\pi\) |
−0.971494 | + | 0.237063i | \(0.923815\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1537.96 | − | 2663.82i | −0.277733 | − | 0.481048i | 0.693088 | − | 0.720853i | \(-0.256250\pi\) |
−0.970821 | + | 0.239805i | \(0.922916\pi\) | |||||||
\(314\) | −3493.11 | −0.627794 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3040.00 | −0.541182 | ||||||||
\(317\) | 1162.00 | + | 2012.64i | 0.205881 | + | 0.356597i | 0.950413 | − | 0.310990i | \(-0.100661\pi\) |
−0.744532 | + | 0.667587i | \(0.767327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2200.00 | + | 3810.51i | −0.386133 | + | 0.668802i | ||||
\(320\) | 226.274 | + | 391.918i | 0.0395285 | + | 0.0684653i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0000 | 0.00275623 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2386.49 | + | 4133.51i | −0.407318 | + | 0.705496i | ||||
\(326\) | 3340.00 | − | 5785.05i | 0.567440 | − | 0.982835i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 395.980 | 0.0666595 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4754.00 | − | 8234.17i | −0.789436 | − | 1.36734i | −0.926313 | − | 0.376756i | \(-0.877040\pi\) |
0.136876 | − | 0.990588i | \(-0.456294\pi\) | |||||||
\(332\) | −1889.39 | + | 3272.52i | −0.312330 | + | 0.540972i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 367.696 | + | 636.867i | 0.0602377 | + | 0.104335i | ||||
\(335\) | −3818.38 | −0.622747 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4720.00 | −0.762952 | −0.381476 | − | 0.924379i | \(-0.624584\pi\) | ||||
−0.381476 | + | 0.924379i | \(0.624584\pi\) | |||||||
\(338\) | 1853.00 | + | 3209.49i | 0.298195 | + | 0.516489i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20.0000 | − | 34.6410i | 0.00319015 | − | 0.00552551i | ||||
\(341\) | 2375.88 | + | 4115.14i | 0.377305 | + | 0.653512i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2720.00 | 0.426316 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3389.87 | − | 5871.43i | 0.526707 | − | 0.912283i | ||||
\(347\) | 3252.00 | − | 5632.63i | 0.503102 | − | 0.871399i | −0.496891 | − | 0.867813i | \(-0.665525\pi\) |
0.999994 | − | 0.00358597i | \(-0.00114145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5256.63 | −0.806249 | −0.403125 | − | 0.915145i | \(-0.632076\pi\) | ||||
−0.403125 | + | 0.915145i | \(0.632076\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 640.000 | + | 1108.51i | 0.0969094 | + | 0.167852i | ||||
\(353\) | −6105.87 | + | 10575.7i | −0.920630 | + | 1.59458i | −0.122188 | + | 0.992507i | \(0.538991\pi\) |
−0.798442 | + | 0.602072i | \(0.794342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1484.92 | − | 2571.96i | −0.222004 | − | 0.384523i | ||||
\(356\) | 4610.34 | 0.686369 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1440.00 | −0.212588 | ||||||||
\(359\) | 3670.00 | + | 6356.63i | 0.539541 | + | 0.934512i | 0.998929 | + | 0.0462765i | \(0.0147355\pi\) |
−0.459388 | + | 0.888236i | \(0.651931\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3365.50 | − | 5829.22i | 0.490669 | − | 0.849864i | ||||
\(362\) | −1854.03 | − | 3211.28i | −0.269187 | − | 0.466246i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2050.00 | −0.293978 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3832.52 | − | 6638.12i | 0.545111 | − | 0.944160i | −0.453489 | − | 0.891262i | \(-0.649821\pi\) |
0.998600 | − | 0.0528984i | \(-0.0168459\pi\) | |||||||
\(368\) | −544.000 | + | 942.236i | −0.0770597 | + | 0.133471i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −282.843 | −0.0397413 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1495.00 | + | 2589.42i | 0.207529 | + | 0.359450i | 0.950935 | − | 0.309389i | \(-0.100125\pi\) |
−0.743407 | + | 0.668840i | \(0.766791\pi\) | |||||||
\(374\) | 56.5685 | − | 97.9796i | 0.00782110 | − | 0.0135465i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 362.039 | + | 627.069i | 0.0496562 | + | 0.0860070i | ||||
\(377\) | −7000.36 | −0.956331 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11900.0 | −1.61283 | −0.806414 | − | 0.591351i | \(-0.798595\pi\) | ||||
−0.806414 | + | 0.591351i | \(0.798595\pi\) | |||||||
\(380\) | 160.000 | + | 277.128i | 0.0215995 | + | 0.0374115i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3980.00 | − | 6893.56i | 0.533075 | − | 0.923312i | ||||
\(383\) | 4856.41 | + | 8411.55i | 0.647914 | + | 1.12222i | 0.983620 | + | 0.180253i | \(0.0576916\pi\) |
−0.335707 | + | 0.941967i | \(0.608975\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7420.00 | −0.978415 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1004.09 | − | 1739.14i | 0.131379 | − | 0.227555i | ||||
\(389\) | −1075.00 | + | 1861.95i | −0.140115 | + | 0.242686i | −0.927540 | − | 0.373725i | \(-0.878081\pi\) |
0.787425 | + | 0.616411i | \(0.211414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 96.1665 | 0.0124382 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 956.000 | + | 1655.84i | 0.122240 | + | 0.211726i | ||||
\(395\) | −2687.01 | + | 4654.03i | −0.342273 | + | 0.592835i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1700.59 | − | 2945.51i | −0.214988 | − | 0.372370i | 0.738281 | − | 0.674493i | \(-0.235638\pi\) |
−0.953269 | + | 0.302123i | \(0.902305\pi\) | |||||||
\(398\) | −8179.81 | −1.03019 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1200.00 | −0.150000 | ||||||||
\(401\) | 6045.00 | + | 10470.2i | 0.752800 | + | 1.30389i | 0.946461 | + | 0.322820i | \(0.104631\pi\) |
−0.193660 | + | 0.981069i | \(0.562036\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3780.00 | + | 6547.15i | −0.467234 | + | 0.809273i | ||||
\(404\) | 3521.39 | + | 6099.23i | 0.433653 | + | 0.751109i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −800.000 | −0.0974313 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4096.27 | + | 7094.95i | −0.495226 | + | 0.857757i | −0.999985 | − | 0.00550362i | \(-0.998248\pi\) |
0.504759 | + | 0.863260i | \(0.331581\pi\) | |||||||
\(410\) | 350.000 | − | 606.218i | 0.0421592 | − | 0.0730219i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 905.097 | 0.108230 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3340.00 | + | 5785.05i | 0.395070 | + | 0.684282i | ||||
\(416\) | −1018.23 | + | 1763.63i | −0.120007 | + | 0.207859i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 452.548 | + | 783.837i | 0.0529542 | + | 0.0917194i | ||||
\(419\) | −1046.52 | −0.122019 | −0.0610093 | − | 0.998137i | \(-0.519432\pi\) | ||||
−0.0610093 | + | 0.998137i | \(0.519432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3870.00 | −0.448010 | −0.224005 | − | 0.974588i | \(-0.571913\pi\) | ||||
−0.224005 | + | 0.974588i | \(0.571913\pi\) | |||||||
\(422\) | 2868.00 | + | 4967.52i | 0.330834 | + | 0.573022i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2512.00 | − | 4350.91i | 0.287721 | − | 0.498347i | ||||
\(425\) | 53.0330 | + | 91.8559i | 0.00605289 | + | 0.0104839i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8096.00 | 0.914334 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2404.16 | − | 4164.13i | 0.269626 | − | 0.467005i | ||||
\(431\) | 1350.00 | − | 2338.27i | 0.150875 | − | 0.261324i | −0.780674 | − | 0.624938i | \(-0.785124\pi\) |
0.931549 | + | 0.363615i | \(0.118458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5876.06 | −0.652160 | −0.326080 | − | 0.945342i | \(-0.605728\pi\) | ||||
−0.326080 | + | 0.945342i | \(0.605728\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 808.000 | + | 1399.50i | 0.0887527 | + | 0.153724i | ||||
\(437\) | −384.666 | + | 666.261i | −0.0421077 | + | 0.0729327i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3173.50 | − | 5496.65i | −0.345017 | − | 0.597588i | 0.640339 | − | 0.768092i | \(-0.278794\pi\) |
−0.985357 | + | 0.170504i | \(0.945460\pi\) | |||||||
\(440\) | 2262.74 | 0.245164 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 180.000 | 0.0193704 | ||||||||
\(443\) | 3464.00 | + | 5999.82i | 0.371512 | + | 0.643477i | 0.989798 | − | 0.142476i | \(-0.0455063\pi\) |
−0.618287 | + | 0.785953i | \(0.712173\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4075.00 | − | 7058.11i | 0.434098 | − | 0.751879i | ||||
\(446\) | 2630.44 | + | 4556.05i | 0.279271 | + | 0.483711i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1320.00 | −0.138741 | −0.0693704 | − | 0.997591i | \(-0.522099\pi\) | ||||
−0.0693704 | + | 0.997591i | \(0.522099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 989.949 | − | 1714.64i | 0.103359 | − | 0.179023i | ||||
\(452\) | −2016.00 | + | 3491.81i | −0.209789 | + | 0.363365i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 339.411 | 0.0350867 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −645.000 | − | 1117.17i | −0.0660215 | − | 0.114353i | 0.831125 | − | 0.556085i | \(-0.187697\pi\) |
−0.897147 | + | 0.441733i | \(0.854364\pi\) | |||||||
\(458\) | −3143.80 | + | 5445.22i | −0.320742 | + | 0.555542i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 961.665 | + | 1665.65i | 0.0974736 | + | 0.168829i | ||||
\(461\) | −17642.3 | −1.78240 | −0.891198 | − | 0.453615i | \(-0.850134\pi\) | ||||
−0.891198 | + | 0.453615i | \(0.850134\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5680.00 | 0.570134 | 0.285067 | − | 0.958508i | \(-0.407984\pi\) | ||||
0.285067 | + | 0.958508i | \(0.407984\pi\) | |||||||
\(464\) | −880.000 | − | 1524.20i | −0.0880452 | − | 0.152499i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4482.00 | + | 7763.05i | −0.445546 | + | 0.771709i | ||||
\(467\) | −3846.66 | − | 6662.61i | −0.381161 | − | 0.660190i | 0.610067 | − | 0.792350i | \(-0.291142\pi\) |
−0.991229 | + | 0.132159i | \(0.957809\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1280.00 | 0.125621 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3507.25 | + | 6074.73i | −0.342022 | + | 0.592399i | ||||
\(473\) | 6800.00 | − | 11777.9i | 0.661024 | − | 1.14493i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −848.528 | −0.0819645 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1740.00 | − | 3013.77i | −0.166497 | − | 0.288382i | ||||
\(479\) | −8259.01 | + | 14305.0i | −0.787816 | + | 1.36454i | 0.139487 | + | 0.990224i | \(0.455455\pi\) |
−0.927303 | + | 0.374313i | \(0.877879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −636.396 | − | 1102.27i | −0.0603267 | − | 0.104489i | ||||
\(482\) | −2520.13 | −0.238151 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1076.00 | 0.101052 | ||||||||
\(485\) | −1775.00 | − | 3074.39i | −0.166183 | − | 0.287837i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6840.00 | + | 11847.2i | −0.636448 | + | 1.10236i | 0.349759 | + | 0.936840i | \(0.386264\pi\) |
−0.986206 | + | 0.165520i | \(0.947070\pi\) | |||||||
\(488\) | 3671.30 | + | 6358.88i | 0.340557 | + | 0.589862i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2280.00 | 0.209562 | 0.104781 | − | 0.994495i | \(-0.466586\pi\) | ||||
0.104781 | + | 0.994495i | \(0.466586\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −77.7817 | + | 134.722i | −0.00710571 | + | 0.0123074i | ||||
\(494\) | −720.000 | + | 1247.08i | −0.0655756 | + | 0.113580i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1900.70 | −0.172065 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −430.000 | − | 744.782i | −0.0385760 | − | 0.0668157i | 0.846093 | − | 0.533036i | \(-0.178949\pi\) |
−0.884669 | + | 0.466220i | \(0.845616\pi\) | |||||||
\(500\) | −2828.43 | + | 4898.98i | −0.252982 | + | 0.438178i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5826.56 | − | 10091.9i | −0.518032 | − | 0.897258i | ||||
\(503\) | 5730.39 | 0.507963 | 0.253982 | − | 0.967209i | \(-0.418260\pi\) | ||||
0.253982 | + | 0.967209i | \(0.418260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12450.0 | 1.09706 | ||||||||
\(506\) | 2720.00 | + | 4711.18i | 0.238970 | + | 0.413908i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2000.00 | + | 3464.10i | −0.174676 | + | 0.302549i | ||||
\(509\) | −2294.56 | − | 3974.30i | −0.199813 | − | 0.346086i | 0.748655 | − | 0.662960i | \(-0.230700\pi\) |
−0.948468 | + | 0.316874i | \(0.897367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4688.12 | + | 8120.06i | −0.402304 | + | 0.696810i | ||||
\(515\) | 800.000 | − | 1385.64i | 0.0684509 | − | 0.118560i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3620.39 | 0.307978 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1800.00 | + | 3117.69i | 0.151799 | + | 0.262923i | ||||
\(521\) | −7293.81 | + | 12633.2i | −0.613335 | + | 1.06233i | 0.377339 | + | 0.926075i | \(0.376839\pi\) |
−0.990674 | + | 0.136252i | \(0.956494\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3054.70 | + | 5290.90i | 0.255397 | + | 0.442361i | 0.965003 | − | 0.262238i | \(-0.0844604\pi\) |
−0.709606 | + | 0.704599i | \(0.751127\pi\) | |||||||
\(524\) | 339.411 | 0.0282963 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4344.00 | −0.360090 | ||||||||
\(527\) | 84.0000 | + | 145.492i | 0.00694326 | + | 0.0120261i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3771.50 | − | 6532.43i | 0.309978 | − | 0.536897i | ||||
\(530\) | −4440.63 | − | 7691.40i | −0.363941 | − | 0.630364i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3150.00 | 0.255988 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7155.92 | − | 12394.4i | 0.578276 | − | 1.00160i | ||||
\(536\) | 2160.00 | − | 3741.23i | 0.174063 | − | 0.301486i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5416.44 | 0.434051 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8605.00 | + | 14904.3i | 0.683841 | + | 1.18445i | 0.973800 | + | 0.227408i | \(0.0730250\pi\) |
−0.289959 | + | 0.957039i | \(0.593642\pi\) | |||||||
\(542\) | 6188.60 | − | 10719.0i | 0.490448 | − | 0.849482i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.6274 | + | 39.1918i | 0.00178335 | + | 0.00308885i | ||||
\(545\) | 2856.71 | 0.224529 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4060.00 | 0.317355 | 0.158677 | − | 0.987330i | \(-0.449277\pi\) | ||||
0.158677 | + | 0.987330i | \(0.449277\pi\) | |||||||
\(548\) | −4068.00 | − | 7045.98i | −0.317110 | − | 0.549251i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3000.00 | + | 5196.15i | −0.232583 | + | 0.402845i | ||||
\(551\) | −622.254 | − | 1077.78i | −0.0481105 | − | 0.0833299i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12260.0 | −0.940212 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3473.31 | − | 6015.95i | 0.264930 | − | 0.458872i | ||||
\(557\) | −5178.00 | + | 8968.56i | −0.393894 | + | 0.682244i | −0.992959 | − | 0.118456i | \(-0.962206\pi\) |
0.599065 | + | 0.800700i | \(0.295539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21637.5 | 1.63715 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1970.00 | − | 3412.14i | −0.147864 | − | 0.256108i | ||||
\(563\) | 11605.0 | − | 20100.5i | 0.868728 | − | 1.50468i | 0.00543113 | − | 0.999985i | \(-0.498271\pi\) |
0.863297 | − | 0.504696i | \(-0.168395\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3563.82 | + | 6172.71i | 0.265365 | + | 0.459625i | ||||
\(566\) | 3111.27 | 0.231054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3360.00 | 0.248209 | ||||||||
\(569\) | −2945.00 | − | 5100.89i | −0.216979 | − | 0.375818i | 0.736904 | − | 0.675997i | \(-0.236287\pi\) |
−0.953883 | + | 0.300179i | \(0.902954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2806.00 | − | 4860.13i | 0.205652 | − | 0.356200i | −0.744688 | − | 0.667413i | \(-0.767402\pi\) |
0.950340 | + | 0.311212i | \(0.100735\pi\) | |||||||
\(572\) | 5091.17 | + | 8818.16i | 0.372155 | + | 0.644591i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5100.00 | −0.369886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8898.94 | + | 15413.4i | −0.642058 | + | 1.11208i | 0.342914 | + | 0.939367i | \(0.388586\pi\) |
−0.984973 | + | 0.172711i | \(0.944747\pi\) | |||||||
\(578\) | −4911.00 | + | 8506.10i | −0.353409 | + | 0.612123i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3111.27 | −0.222739 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12560.0 | − | 21754.6i | −0.892251 | − | 1.54542i | ||||
\(584\) | 1159.66 | − | 2008.58i | 0.0821693 | − | 0.142321i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7686.25 | + | 13313.0i | 0.541836 | + | 0.938488i | ||||
\(587\) | 7942.22 | 0.558451 | 0.279225 | − | 0.960226i | \(-0.409922\pi\) | ||||
0.279225 | + | 0.960226i | \(0.409922\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1344.00 | −0.0940213 | ||||||||
\(590\) | 6200.00 | + | 10738.7i | 0.432627 | + | 0.749332i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 160.000 | − | 277.128i | 0.0111080 | − | 0.0192397i | ||||
\(593\) | 7039.25 | + | 12192.3i | 0.487466 | + | 0.844316i | 0.999896 | − | 0.0144132i | \(-0.00458802\pi\) |
−0.512430 | + | 0.858729i | \(0.671255\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8560.00 | 0.588307 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4327.49 | + | 7495.44i | −0.295927 | + | 0.512561i | ||||
\(599\) | 3650.00 | − | 6321.99i | 0.248973 | − | 0.431234i | −0.714268 | − | 0.699872i | \(-0.753240\pi\) |
0.963241 | + | 0.268638i | \(0.0865736\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8727.11 | 0.592323 | 0.296162 | − | 0.955138i | \(-0.404293\pi\) | ||||
0.296162 | + | 0.955138i | \(0.404293\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4240.00 | − | 7343.90i | −0.285634 | − | 0.494733i | ||||
\(605\) | 951.059 | − | 1647.28i | 0.0639108 | − | 0.110697i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5303.30 | + | 9185.59i | 0.354620 | + | 0.614220i | 0.987053 | − | 0.160395i | \(-0.0512769\pi\) |
−0.632433 | + | 0.774615i | \(0.717944\pi\) | |||||||
\(608\) | −362.039 | −0.0241490 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12980.0 | 0.861549 | ||||||||
\(611\) | 2880.00 | + | 4988.31i | 0.190691 | + | 0.330287i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6990.00 | − | 12107.0i | 0.460560 | − | 0.797714i | −0.538429 | − | 0.842671i | \(-0.680982\pi\) |
0.998989 | + | 0.0449573i | \(0.0143152\pi\) | |||||||
\(614\) | −8598.42 | − | 14892.9i | −0.565153 | − | 0.978874i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2654.00 | −0.173170 | −0.0865851 | − | 0.996244i | \(-0.527595\pi\) | ||||
−0.0865851 | + | 0.996244i | \(0.527595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11941.6 | − | 20683.5i | 0.775403 | − | 1.34304i | −0.159165 | − | 0.987252i | \(-0.550880\pi\) |
0.934568 | − | 0.355785i | \(-0.115786\pi\) | |||||||
\(620\) | −1680.00 | + | 2909.85i | −0.108823 | + | 0.188487i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15160.4 | −0.977292 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 312.500 | + | 541.266i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | 3075.91 | − | 5327.64i | 0.196387 | − | 0.340152i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3493.11 | − | 6050.24i | −0.221959 | − | 0.384444i | ||||
\(629\) | −28.2843 | −0.00179295 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6400.00 | −0.403772 | −0.201886 | − | 0.979409i | \(-0.564707\pi\) | ||||
−0.201886 | + | 0.979409i | \(0.564707\pi\) | |||||||
\(632\) | −3040.00 | − | 5265.43i | −0.191337 | − | 0.331405i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2324.00 | + | 4025.29i | −0.145580 | + | 0.252152i | ||||
\(635\) | 3535.53 | + | 6123.72i | 0.220950 | + | 0.382697i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8800.00 | −0.546074 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −452.548 | + | 783.837i | −0.0279508 | + | 0.0484123i | ||||
\(641\) | −7675.00 | + | 13293.5i | −0.472924 | + | 0.819128i | −0.999520 | − | 0.0309874i | \(-0.990135\pi\) |
0.526596 | + | 0.850116i | \(0.323468\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17847.4 | 1.09461 | 0.547303 | − | 0.836934i | \(-0.315655\pi\) | ||||
0.547303 | + | 0.836934i | \(0.315655\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.0000 | + | 27.7128i | 0.000974476 | + | 0.00168784i | ||||
\(647\) | 7000.36 | − | 12125.0i | 0.425367 | − | 0.736757i | −0.571088 | − | 0.820889i | \(-0.693478\pi\) |
0.996455 | + | 0.0841319i | \(0.0268117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17536.2 | + | 30373.7i | 1.06064 | + | 1.83709i | ||||
\(650\) | −9545.94 | −0.576035 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13360.0 | 0.802482 | ||||||||
\(653\) | −13191.0 | − | 22847.5i | −0.790511 | − | 1.36921i | −0.925651 | − | 0.378379i | \(-0.876482\pi\) |
0.135140 | − | 0.990827i | \(-0.456852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 300.000 | − | 519.615i | 0.0178961 | − | 0.0309970i | ||||
\(656\) | 395.980 | + | 685.857i | 0.0235677 | + | 0.0408205i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14400.0 | 0.851205 | 0.425603 | − | 0.904910i | \(-0.360062\pi\) | ||||
0.425603 | + | 0.904910i | \(0.360062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14291.3 | + | 24753.3i | −0.840951 | + | 1.45657i | 0.0481409 | + | 0.998841i | \(0.484670\pi\) |
−0.889092 | + | 0.457729i | \(0.848663\pi\) | |||||||
\(662\) | 9508.00 | − | 16468.3i | 0.558216 | − | 0.966858i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7557.56 | −0.441702 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3740.00 | − | 6477.87i | −0.217112 | − | 0.376048i | ||||
\(668\) | −735.391 | + | 1273.73i | −0.0425945 | + | 0.0737759i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3818.38 | − | 6613.62i | −0.220174 | − | 0.381353i | ||||
\(671\) | 36713.0 | 2.11220 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18120.0 | −1.03785 | −0.518926 | − | 0.854819i | \(-0.673668\pi\) | ||||
−0.518926 | + | 0.854819i | \(0.673668\pi\) | |||||||
\(674\) | −4720.00 | − | 8175.28i | −0.269744 | − | 0.467211i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3706.00 | + | 6418.98i | −0.210856 | + | 0.365213i | ||||
\(677\) | −8898.94 | − | 15413.4i | −0.505191 | − | 0.875016i | −0.999982 | − | 0.00600394i | \(-0.998089\pi\) |
0.494791 | − | 0.869012i | \(-0.335244\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 80.0000 | 0.00451156 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4751.76 | + | 8230.29i | −0.266795 | + | 0.462103i | ||||
\(683\) | −864.000 | + | 1496.49i | −0.0484042 | + | 0.0838385i | −0.889212 | − | 0.457495i | \(-0.848747\pi\) |
0.840808 | + | 0.541333i | \(0.182080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14382.6 | −0.802232 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2720.00 | + | 4711.18i | 0.150725 | + | 0.261064i | ||||
\(689\) | 19982.8 | − | 34611.3i | 1.10491 | − | 1.91377i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8544.68 | − | 14799.8i | −0.470412 | − | 0.814778i | 0.529015 | − | 0.848612i | \(-0.322561\pi\) |
−0.999427 | + | 0.0338344i | \(0.989228\pi\) | |||||||
\(692\) | 13559.5 | 0.744876 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13008.0 | 0.711494 | ||||||||
\(695\) | −6140.00 | − | 10634.8i | −0.335113 | − | 0.580433i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.0000 | − | 60.6218i | 0.00190204 | − | 0.00329442i | ||||
\(698\) | −5256.63 | − | 9104.75i | −0.285052 | − | 0.493725i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13410.0 | 0.722523 | 0.361262 | − | 0.932465i | \(-0.382346\pi\) | ||||
0.361262 | + | 0.932465i | \(0.382346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 113.137 | − | 195.959i | 0.00606977 | − | 0.0105131i | ||||
\(704\) | −1280.00 | + | 2217.03i | −0.0685253 | + | 0.118689i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24423.5 | −1.30197 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 70.0000 | + | 121.244i | 0.00370791 | + | 0.00642228i | 0.867873 | − | 0.496785i | \(-0.165486\pi\) |
−0.864165 | + | 0.503208i | \(0.832153\pi\) | |||||||
\(710\) | 2969.85 | − | 5143.93i | 0.156981 | − | 0.271899i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4610.34 | + | 7985.34i | 0.242668 | + | 0.420313i | ||||
\(713\) | −8077.99 | −0.424296 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18000.0 | 0.941485 | ||||||||
\(716\) | −1440.00 | − | 2494.15i | −0.0751611 | − | 0.130183i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7340.00 | + | 12713.3i | −0.381513 | + | 0.660800i | ||||
\(719\) | −12968.3 | − | 22461.8i | −0.672653 | − | 1.16507i | −0.977149 | − | 0.212555i | \(-0.931821\pi\) |
0.304496 | − | 0.952514i | \(-0.401512\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13462.0 | 0.693911 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3708.07 | − | 6422.56i | 0.190344 | − | 0.329686i | ||||
\(725\) | 4125.00 | − | 7144.71i | 0.211308 | − | 0.365997i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9277.24 | 0.473279 | 0.236639 | − | 0.971598i | \(-0.423954\pi\) | ||||
0.236639 | + | 0.971598i | \(0.423954\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2050.00 | − | 3550.70i | −0.103937 | − | 0.180024i | ||||
\(731\) | 240.416 | − | 416.413i | 0.0121643 | − | 0.0210692i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12738.5 | + | 22063.8i | 0.641894 | + | 1.11179i | 0.985010 | + | 0.172500i | \(0.0551844\pi\) |
−0.343116 | + | 0.939293i | \(0.611482\pi\) | |||||||
\(734\) | 15330.1 | 0.770904 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2176.00 | −0.108979 | ||||||||
\(737\) | −10800.0 | − | 18706.1i | −0.539787 | − | 0.934939i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3462.00 | − | 5996.36i | 0.172330 | − | 0.298484i | −0.766904 | − | 0.641762i | \(-0.778204\pi\) |
0.939234 | + | 0.343278i | \(0.111537\pi\) | |||||||
\(740\) | −282.843 | − | 489.898i | −0.0140507 | − | 0.0243365i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29108.0 | −1.43724 | −0.718620 | − | 0.695403i | \(-0.755226\pi\) | ||||
−0.718620 | + | 0.695403i | \(0.755226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7566.04 | − | 13104.8i | 0.372078 | − | 0.644459i | ||||
\(746\) | −2990.00 | + | 5178.83i | −0.146745 | + | 0.254170i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 226.274 | 0.0110607 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15724.0 | − | 27234.8i | −0.764017 | − | 1.32332i | −0.940765 | − | 0.339060i | \(-0.889891\pi\) |
0.176747 | − | 0.984256i | \(-0.443442\pi\) | |||||||
\(752\) | −724.077 | + | 1254.14i | −0.0351122 | + | 0.0608161i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7000.36 | − | 12125.0i | −0.338114 | − | 0.585631i | ||||
\(755\) | −14990.7 | −0.722604 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13300.0 | −0.638569 | −0.319284 | − | 0.947659i | \(-0.603443\pi\) | ||||
−0.319284 | + | 0.947659i | \(0.603443\pi\) | |||||||
\(758\) | −11900.0 | − | 20611.4i | −0.570221 | − | 0.987652i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −320.000 | + | 554.256i | −0.0152732 | + | 0.0264539i | ||||
\(761\) | −2400.63 | − | 4158.01i | −0.114353 | − | 0.198065i | 0.803168 | − | 0.595753i | \(-0.203146\pi\) |
−0.917521 | + | 0.397687i | \(0.869813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15920.0 | 0.753881 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9712.82 | + | 16823.1i | −0.458144 | + | 0.793529i | ||||
\(767\) | −27900.0 | + | 48324.2i | −1.31344 | + | 2.27495i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16932.4 | 0.794015 | 0.397007 | − | 0.917815i | \(-0.370049\pi\) | ||||
0.397007 | + | 0.917815i | \(0.370049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7420.00 | − | 12851.8i | −0.345922 | − | 0.599154i | ||||
\(773\) | 9720.60 | − | 16836.6i | 0.452297 | − | 0.783401i | −0.546231 | − | 0.837634i | \(-0.683938\pi\) |
0.998528 | + | 0.0542330i | \(0.0172714\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4454.77 | − | 7715.89i | −0.206478 | − | 0.357630i | ||||
\(776\) | 4016.37 | 0.185798 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4300.00 | −0.198152 | ||||||||
\(779\) | 280.000 | + | 484.974i | 0.0128781 | + | 0.0223055i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8400.00 | − | 14549.2i | 0.384860 | − | 0.666597i | ||||
\(782\) | 96.1665 | + | 166.565i | 0.00439758 | + | 0.00761683i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12350.0 | −0.561516 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10366.2 | − | 17954.8i | 0.469523 | − | 0.813238i | −0.529870 | − | 0.848079i | \(-0.677759\pi\) |
0.999393 | + | 0.0348413i | \(0.0110926\pi\) | |||||||
\(788\) | −1912.00 | + | 3311.68i | −0.0864368 | + | 0.149713i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10748.0 | −0.484047 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29205.0 | + | 50584.5i | 1.30782 | + | 2.26521i | ||||
\(794\) | 3401.18 | − | 5891.02i | 0.152020 | − | 0.263306i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8179.81 | − | 14167.8i | −0.364228 | − | 0.630862i | ||||
\(797\) | 28582.7 | 1.27033 | 0.635163 | − | 0.772378i | \(-0.280933\pi\) | ||||
0.635163 | + | 0.772378i | \(0.280933\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 128.000 | 0.00566748 | ||||||||
\(800\) | −1200.00 | − | 2078.46i | −0.0530330 | − | 0.0918559i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12090.0 | + | 20940.5i | −0.532310 | + | 0.921988i | ||||
\(803\) | −5798.28 | − | 10042.9i | −0.254815 | − | 0.441353i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15120.0 | −0.660768 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7042.78 | + | 12198.5i | −0.306639 | + | 0.531114i | ||||
\(809\) | −11140.0 | + | 19295.0i | −0.484130 | + | 0.838539i | −0.999834 | − | 0.0182286i | \(-0.994197\pi\) |
0.515703 | + | 0.856767i | \(0.327531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26100.7 | 1.13011 | 0.565056 | − | 0.825053i | \(-0.308855\pi\) | ||||
0.565056 | + | 0.825053i | \(0.308855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −800.000 | − | 1385.64i | −0.0344472 | − | 0.0596642i | ||||
\(815\) | 11808.7 | − | 20453.2i | 0.507534 | − | 0.879075i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1923.33 | + | 3331.31i | 0.0823609 | + | 0.142653i | ||||
\(818\) | −16385.1 | −0.700356 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1400.00 | 0.0596221 | ||||||||
\(821\) | 1770.00 | + | 3065.73i | 0.0752417 | + | 0.130322i | 0.901191 | − | 0.433421i | \(-0.142694\pi\) |
−0.825950 | + | 0.563744i | \(0.809361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14200.0 | − | 24595.1i | 0.601435 | − | 1.04172i | −0.391169 | − | 0.920319i | \(-0.627929\pi\) |
0.992604 | − | 0.121397i | \(-0.0387374\pi\) | |||||||
\(824\) | 905.097 | + | 1567.67i | 0.0382652 | + | 0.0662773i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38736.0 | 1.62876 | 0.814379 | − | 0.580334i | \(-0.197078\pi\) | ||||
0.814379 | + | 0.580334i | \(0.197078\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11704.7 | − | 20273.2i | 0.490377 | − | 0.849358i | −0.509562 | − | 0.860434i | \(-0.670192\pi\) |
0.999939 | + | 0.0110765i | \(0.00352583\pi\) | |||||||
\(830\) | −6680.00 | + | 11570.1i | −0.279357 | + | 0.483860i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4072.94 | −0.169716 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1300.00 | + | 2251.67i | 0.0538783 | + | 0.0933199i | ||||
\(836\) | −905.097 | + | 1567.67i | −0.0374443 | + | 0.0648554i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1046.52 | − | 1812.62i | −0.0431401 | − | 0.0747208i | ||||
\(839\) | −29387.4 | −1.20925 | −0.604627 | − | 0.796509i | \(-0.706678\pi\) | ||||
−0.604627 | + | 0.796509i | \(0.706678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12289.0 | −0.503875 | ||||||||
\(842\) | −3870.00 | − | 6703.04i | −0.158395 | − | 0.274349i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5736.00 | + | 9935.04i | −0.233935 | + | 0.405188i | ||||
\(845\) | 6551.34 | + | 11347.3i | 0.266714 | + | 0.461962i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10048.0 | 0.406898 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −106.066 | + | 183.712i | −0.00428004 | + | 0.00741325i | ||||
\(851\) | 680.000 | − | 1177.79i | 0.0273914 | − | 0.0474433i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22252.7 | 0.893220 | 0.446610 | − | 0.894729i | \(-0.352631\pi\) | ||||
0.446610 | + | 0.894729i | \(0.352631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8096.00 | + | 14022.7i | 0.323266 | + | 0.559913i | ||||
\(857\) | 6916.21 | − | 11979.2i | 0.275675 | − | 0.477483i | −0.694630 | − | 0.719367i | \(-0.744432\pi\) |
0.970305 | + | 0.241884i | \(0.0777654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19832.9 | − | 34351.6i | −0.787766 | − | 1.36445i | −0.927333 | − | 0.374238i | \(-0.877904\pi\) |
0.139567 | − | 0.990213i | \(-0.455429\pi\) | |||||||
\(860\) | 9616.65 | 0.381308 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5400.00 | 0.213370 | ||||||||
\(863\) | −15994.0 | − | 27702.4i | −0.630871 | − | 1.09270i | −0.987374 | − | 0.158407i | \(-0.949364\pi\) |
0.356502 | − | 0.934294i | \(-0.383969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11985.0 | − | 20758.6i | 0.471101 | − | 0.815971i | ||||
\(866\) | −5876.06 | − | 10177.6i | −0.230573 | − | 0.399365i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30400.0 | −1.18671 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17182.7 | − | 29761.3i | 0.668442 | − | 1.15778i | ||||
\(872\) | −1616.00 | + | 2798.99i | −0.0627576 | + | 0.108699i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1538.66 | −0.0595493 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16730.0 | + | 28977.2i | 0.644164 | + | 1.11573i | 0.984494 | + | 0.175419i | \(0.0561280\pi\) |
−0.340330 | + | 0.940306i | \(0.610539\pi\) | |||||||
\(878\) | 6346.99 | − | 10993.3i | 0.243964 | − | 0.422558i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2262.74 | + | 3919.18i | 0.0866784 | + | 0.150131i | ||||
\(881\) | 12791.6 | 0.489170 | 0.244585 | − | 0.969628i | \(-0.421348\pi\) | ||||
0.244585 | + | 0.969628i | \(0.421348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35260.0 | −1.34382 | −0.671910 | − | 0.740633i | \(-0.734526\pi\) | ||||
−0.671910 | + | 0.740633i | \(0.734526\pi\) | |||||||
\(884\) | 180.000 | + | 311.769i | 0.00684848 | + | 0.0118619i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6928.00 | + | 11999.6i | −0.262698 | + | 0.455007i | ||||
\(887\) | −7718.78 | − | 13369.3i | −0.292188 | − | 0.506085i | 0.682138 | − | 0.731223i | \(-0.261050\pi\) |
−0.974327 | + | 0.225138i | \(0.927717\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16300.0 | 0.613907 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5260.87 | + | 9112.10i | −0.197474 | + | 0.342036i | ||||
\(893\) | −512.000 | + | 886.810i | −0.0191864 | + | 0.0332318i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5091.17 | −0.190144 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1320.00 | − | 2286.31i | −0.0490523 | − | 0.0849611i | ||||
\(899\) | 6533.67 | − | 11316.6i | 0.242392 | − | 0.419834i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −444.063 | − | 769.140i | −0.0164194 | − | 0.0284392i | ||||
\(902\) | 3959.80 | 0.146172 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8064.00 | −0.296687 | ||||||||
\(905\) | −6555.00 | − | 11353.6i | −0.240769 | − | 0.417023i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16550.0 | + | 28665.4i | −0.605881 | + | 1.04942i | 0.386031 | + | 0.922486i | \(0.373846\pi\) |
−0.991912 | + | 0.126930i | \(0.959488\pi\) | |||||||
\(908\) | 339.411 | + | 587.878i | 0.0124050 | + | 0.0214861i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39620.0 | 1.44091 | 0.720455 | − | 0.693502i | \(-0.243933\pi\) | ||||
0.720455 | + | 0.693502i | \(0.243933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18893.9 | + | 32725.2i | −0.684881 | + | 1.18625i | ||||
\(914\) | 1290.00 | − | 2234.35i | 0.0466843 | − | 0.0808595i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12575.2 | −0.453598 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10472.0 | − | 18138.0i | −0.375886 | − | 0.651054i | 0.614573 | − | 0.788860i | \(-0.289328\pi\) |
−0.990459 | + | 0.137806i | \(0.955995\pi\) | |||||||
\(920\) | −1923.33 | + | 3331.31i | −0.0689243 | + | 0.119380i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17642.3 | − | 30557.4i | −0.630172 | − | 1.09149i | ||||
\(923\) | 26728.6 | 0.953179 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1500.00 | 0.0533186 | ||||||||
\(926\) | 5680.00 | + | 9838.05i | 0.201573 | + | 0.349134i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1760.00 | − | 3048.41i | 0.0622574 | − | 0.107833i | ||||
\(929\) | −23118.9 | − | 40043.0i | −0.816475 | − | 1.41418i | −0.908264 | − | 0.418397i | \(-0.862592\pi\) |
0.0917893 | − | 0.995778i | \(-0.470741\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17928.0 | −0.630098 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7693.32 | − | 13325.2i | 0.269522 | − | 0.466825i | ||||
\(935\) | 200.000 | − | 346.410i | 0.00699540 | − | 0.0121164i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50522.8 | −1.76148 | −0.880740 | − | 0.473600i | \(-0.842954\pi\) | ||||
−0.880740 | + | 0.473600i | \(0.842954\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1280.00 | + | 2217.03i | 0.0444138 | + | 0.0769270i | ||||
\(941\) | −4939.14 | + | 8554.84i | −0.171107 | + | 0.296365i | −0.938807 | − | 0.344444i | \(-0.888068\pi\) |
0.767700 | + | 0.640809i | \(0.221401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1682.91 | + | 2914.89i | 0.0581158 | + | 0.100660i | ||||
\(944\) | −14029.0 | −0.483692 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27200.0 | 0.934829 | ||||||||
\(947\) | −15108.0 | − | 26167.8i | −0.518420 | − | 0.897930i | −0.999771 | − | 0.0214022i | \(-0.993187\pi\) |
0.481351 | − | 0.876528i | \(-0.340146\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9225.00 | − | 15978.2i | 0.315549 | − | 0.546547i | ||||
\(950\) | −848.528 | − | 1469.69i | −0.0289788 | − | 0.0501928i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35512.0 | 1.20708 | 0.603540 | − | 0.797333i | \(-0.293757\pi\) | ||||
0.603540 | + | 0.797333i | \(0.293757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14071.4 | − | 24372.4i | 0.476796 | − | 0.825836i | ||||
\(956\) | 3480.00 | − | 6027.54i | 0.117731 | − | 0.203917i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33036.0 | −1.11414 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7839.50 | + | 13578.4i | 0.263150 | + | 0.455789i | ||||
\(962\) | 1272.79 | − | 2204.54i | 0.0426575 | − | 0.0738849i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2520.13 | − | 4364.99i | −0.0841990 | − | 0.145837i | ||||
\(965\) | −26233.7 | −0.875121 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −720.000 | −0.0239438 | −0.0119719 | − | 0.999928i | \(-0.503811\pi\) | ||||
−0.0119719 | + | 0.999928i | \(0.503811\pi\) | |||||||
\(968\) | 1076.00 | + | 1863.69i | 0.0357272 | + | 0.0618814i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3550.00 | − | 6148.78i | 0.117509 | − | 0.203531i | ||||
\(971\) | 7693.32 | + | 13325.2i | 0.254264 | + | 0.440398i | 0.964695 | − | 0.263368i | \(-0.0848334\pi\) |
−0.710431 | + | 0.703767i | \(0.751500\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27360.0 | −0.900073 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7342.60 | + | 12717.8i | −0.240810 | + | 0.417096i | ||||
\(977\) | 20787.0 | − | 36004.1i | 0.680691 | − | 1.17899i | −0.294079 | − | 0.955781i | \(-0.595013\pi\) |
0.974770 | − | 0.223210i | \(-0.0716537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46103.4 | 1.50508 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2280.00 | + | 3949.08i | 0.0740914 | + | 0.128330i | ||||
\(983\) | −22118.3 | + | 38310.0i | −0.717665 | + | 1.24303i | 0.244258 | + | 0.969710i | \(0.421456\pi\) |
−0.961923 | + | 0.273321i | \(0.911878\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3379.97 | + | 5854.28i | 0.109335 | + | 0.189373i | ||||
\(986\) | −311.127 | −0.0100490 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2880.00 | −0.0927379 | ||||||||
\(989\) | 11560.0 | + | 20022.5i | 0.371675 | + | 0.643760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6136.00 | + | 10627.9i | −0.196687 | + | 0.340671i | −0.947452 | − | 0.319898i | \(-0.896351\pi\) |
0.750765 | + | 0.660569i | \(0.229685\pi\) | |||||||
\(992\) | −1900.70 | − | 3292.11i | −0.0608341 | − | 0.105368i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28920.0 | −0.921433 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28846.4 | + | 49963.5i | −0.916324 | + | 1.58712i | −0.111374 | + | 0.993779i | \(0.535525\pi\) |
−0.804951 | + | 0.593342i | \(0.797808\pi\) | |||||||
\(998\) | 860.000 | − | 1489.56i | 0.0272774 | − | 0.0472458i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.4.g.bg.361.2 | 4 | ||
3.2 | odd | 2 | 882.4.g.bc.361.1 | 4 | |||
7.2 | even | 3 | inner | 882.4.g.bg.667.2 | 4 | ||
7.3 | odd | 6 | 882.4.a.y.1.2 | yes | 2 | ||
7.4 | even | 3 | 882.4.a.y.1.1 | ✓ | 2 | ||
7.5 | odd | 6 | inner | 882.4.g.bg.667.1 | 4 | ||
7.6 | odd | 2 | inner | 882.4.g.bg.361.1 | 4 | ||
21.2 | odd | 6 | 882.4.g.bc.667.1 | 4 | |||
21.5 | even | 6 | 882.4.g.bc.667.2 | 4 | |||
21.11 | odd | 6 | 882.4.a.be.1.2 | yes | 2 | ||
21.17 | even | 6 | 882.4.a.be.1.1 | yes | 2 | ||
21.20 | even | 2 | 882.4.g.bc.361.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.4.a.y.1.1 | ✓ | 2 | 7.4 | even | 3 | ||
882.4.a.y.1.2 | yes | 2 | 7.3 | odd | 6 | ||
882.4.a.be.1.1 | yes | 2 | 21.17 | even | 6 | ||
882.4.a.be.1.2 | yes | 2 | 21.11 | odd | 6 | ||
882.4.g.bc.361.1 | 4 | 3.2 | odd | 2 | |||
882.4.g.bc.361.2 | 4 | 21.20 | even | 2 | |||
882.4.g.bc.667.1 | 4 | 21.2 | odd | 6 | |||
882.4.g.bc.667.2 | 4 | 21.5 | even | 6 | |||
882.4.g.bg.361.1 | 4 | 7.6 | odd | 2 | inner | ||
882.4.g.bg.361.2 | 4 | 1.1 | even | 1 | trivial | ||
882.4.g.bg.667.1 | 4 | 7.5 | odd | 6 | inner | ||
882.4.g.bg.667.2 | 4 | 7.2 | even | 3 | inner |