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 | 361.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.4.g.bc.667.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0.663470 | − | 0.748203i | \(-0.269083\pi\) |
−0.979698 | + | 0.200480i | \(0.935750\pi\) | |||||||
\(6\) | 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 | \(-0.648646\pi\) |
0.998398 | − | 0.0565844i | \(-0.0180210\pi\) | |||||||
\(12\) | 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 | −0.860937 | − | 0.508711i | \(-0.830122\pi\) |
0.871025 | + | 0.491238i | \(0.163455\pi\) | |||||||
\(18\) | 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 | 0.977977 | − | 0.208712i | \(-0.0669271\pi\) |
−0.669738 | + | 0.742597i | \(0.733594\pi\) | |||||||
\(24\) | 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 | \(-0.614560\pi\) | ||||
−0.352181 | + | 0.935932i | \(0.614560\pi\) | |||||||
\(30\) | 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 | \(-0.469948\pi\) | ||||
0.0942708 | + | 0.995547i | \(0.469948\pi\) | |||||||
\(42\) | 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 | 0.927666 | − | 0.373412i | \(-0.121812\pi\) |
−0.787217 | + | 0.616676i | \(0.788479\pi\) | |||||||
\(48\) | 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 | \(-0.530730\pi\) |
0.910189 | − | 0.414194i | \(-0.135936\pi\) | |||||||
\(54\) | 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 | \(0.585145\pi\) |
−0.703070 | + | 0.711121i | \(0.748188\pi\) | |||||||
\(60\) | 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 | \(-0.385835\pi\) | ||||
0.351020 | + | 0.936368i | \(0.385835\pi\) | |||||||
\(72\) | 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 | \(-0.714763\pi\) | ||||
−0.624661 | + | 0.780896i | \(0.714763\pi\) | |||||||
\(84\) | 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 | \(0.0741298\pi\) |
−0.286636 | + | 0.958040i | \(0.592537\pi\) | |||||||
\(90\) | 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 | \(0.500817\pi\) |
−0.864739 | + | 0.502221i | \(0.832516\pi\) | |||||||
\(102\) | 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 | \(0.200618\pi\) |
0.106460 | + | 0.994317i | \(0.466048\pi\) | |||||||
\(108\) | 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 | \(-0.637822\pi\) | ||||
−0.419578 | + | 0.907719i | \(0.637822\pi\) | |||||||
\(114\) | 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 | 0.879827 | − | 0.475294i | \(-0.157658\pi\) |
−0.851530 | + | 0.524305i | \(0.824325\pi\) | |||||||
\(132\) | 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 | \(-0.614655\pi\) |
0.986680 | − | 0.162675i | \(-0.0520121\pi\) | |||||||
\(138\) | 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 | \(0.0335389\pi\) |
−0.406147 | + | 0.913808i | \(0.633128\pi\) | |||||||
\(150\) | 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 | \(-0.527149\pi\) | ||||
−0.0851890 | + | 0.996365i | \(0.527149\pi\) | |||||||
\(168\) | 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 | \(0.100825\pi\) |
−0.205377 | + | 0.978683i | \(0.565842\pi\) | |||||||
\(174\) | 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 | −0.781024 | − | 0.624501i | \(-0.785302\pi\) |
0.931346 | + | 0.364136i | \(0.118636\pi\) | |||||||
\(180\) | 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 | \(0.105154\pi\) |
−0.192047 | + | 0.981386i | \(0.561513\pi\) | |||||||
\(192\) | 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 | \(-0.555305\pi\) | ||||
−0.172874 | + | 0.984944i | \(0.555305\pi\) | |||||||
\(198\) | 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 | −0.878164 | − | 0.478360i | \(-0.841231\pi\) |
0.853354 | + | 0.521332i | \(0.174565\pi\) | |||||||
\(228\) | 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 | \(-0.949681\pi\) |
0.357433 | − | 0.933939i | \(-0.383652\pi\) | |||||||
\(234\) | 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 | \(-0.424339\pi\) | ||||
0.235463 | + | 0.971883i | \(0.424339\pi\) | |||||||
\(240\) | 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 | \(-0.238303\pi\) | ||||
0.732608 | + | 0.680651i | \(0.238303\pi\) | |||||||
\(252\) | 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 | \(-0.974019\pi\) |
0.427728 | − | 0.903908i | \(-0.359314\pi\) | |||||||
\(258\) | 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 | −0.710171 | − | 0.704030i | \(-0.751382\pi\) |
0.964793 | + | 0.263011i | \(0.0847156\pi\) | |||||||
\(264\) | 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 | −0.977687 | − | 0.210067i | \(-0.932632\pi\) |
0.670767 | + | 0.741668i | \(0.265965\pi\) | |||||||
\(270\) | 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 | \(-0.432943\pi\) | ||||
0.209111 | + | 0.977892i | \(0.432943\pi\) | |||||||
\(282\) | 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 | \(-0.777891\pi\) | ||||
−0.766272 | + | 0.642516i | \(0.777891\pi\) | |||||||
\(294\) | 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 | \(-0.590482\pi\) |
0.971494 | − | 0.237063i | \(-0.0761847\pi\) | |||||||
\(312\) | 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 | 0.744532 | − | 0.667587i | \(-0.232673\pi\) |
−0.950413 | + | 0.310990i | \(0.899339\pi\) | |||||||
\(318\) | 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 | \(0.334475\pi\) |
−0.999994 | + | 0.00358597i | \(0.998859\pi\) | |||||||
\(348\) | 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 | \(-0.461009\pi\) |
0.798442 | − | 0.602072i | \(-0.205658\pi\) | |||||||
\(354\) | 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 | \(-0.985264\pi\) |
0.459388 | − | 0.888236i | \(-0.348069\pi\) | |||||||
\(360\) | 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 | \(-0.942308\pi\) |
0.335707 | − | 0.941967i | \(-0.391025\pi\) | |||||||
\(384\) | 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 | −0.787425 | − | 0.616411i | \(-0.788586\pi\) |
0.927540 | + | 0.373725i | \(0.121919\pi\) | |||||||
\(390\) | 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 | \(-0.895369\pi\) |
0.193660 | − | 0.981069i | \(-0.437964\pi\) | |||||||
\(402\) | 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 | \(-0.480568\pi\) | ||||
0.0610093 | + | 0.998137i | \(0.480568\pi\) | |||||||
\(420\) | 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 | −0.931549 | − | 0.363615i | \(-0.881542\pi\) |
0.780674 | + | 0.624938i | \(0.214876\pi\) | |||||||
\(432\) | 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 | 0.618287 | − | 0.785953i | \(-0.287827\pi\) |
−0.989798 | + | 0.142476i | \(0.954494\pi\) | |||||||
\(444\) | 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 | \(-0.477901\pi\) | ||||
0.0693704 | + | 0.997591i | \(0.477901\pi\) | |||||||
\(450\) | 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 | \(-0.149866\pi\) | ||||
0.891198 | + | 0.453615i | \(0.149866\pi\) | |||||||
\(462\) | 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 | 0.991229 | − | 0.132159i | \(-0.0421910\pi\) |
−0.610067 | + | 0.792350i | \(0.708858\pi\) | |||||||
\(468\) | 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 | \(-0.544545\pi\) |
0.927303 | − | 0.374313i | \(-0.122121\pi\) | |||||||
\(480\) | 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 | \(-0.533414\pi\) | ||||
−0.104781 | + | 0.994495i | \(0.533414\pi\) | |||||||
\(492\) | 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 | \(-0.581740\pi\) | ||||
−0.253982 | + | 0.967209i | \(0.581740\pi\) | |||||||
\(504\) | 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 | 0.948468 | − | 0.316874i | \(-0.102633\pi\) |
−0.748655 | + | 0.662960i | \(0.769300\pi\) | |||||||
\(510\) | 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 | \(-0.623161\pi\) |
0.990674 | − | 0.136252i | \(-0.0435057\pi\) | |||||||
\(522\) | 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 | −0.599065 | − | 0.800700i | \(-0.704461\pi\) |
0.992959 | + | 0.118456i | \(0.0377944\pi\) | |||||||
\(558\) | 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 | \(0.501729\pi\) |
−0.863297 | + | 0.504696i | \(0.831605\pi\) | |||||||
\(564\) | 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 | 0.953883 | − | 0.300179i | \(-0.0970465\pi\) |
−0.736904 | + | 0.675997i | \(0.763713\pi\) | |||||||
\(570\) | 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 | \(-0.590078\pi\) | ||||
−0.279225 | + | 0.960226i | \(0.590078\pi\) | |||||||
\(588\) | 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 | 0.512430 | − | 0.858729i | \(-0.328745\pi\) |
−0.999896 | + | 0.0144132i | \(0.995412\pi\) | |||||||
\(594\) | 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 | −0.963241 | − | 0.268638i | \(-0.913426\pi\) |
0.714268 | + | 0.699872i | \(0.246760\pi\) | |||||||
\(600\) | 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 | \(-0.472405\pi\) | ||||
0.0865851 | + | 0.996244i | \(0.472405\pi\) | |||||||
\(618\) | 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 | −0.526596 | − | 0.850116i | \(-0.676532\pi\) |
0.999520 | + | 0.0309874i | \(0.00986518\pi\) | |||||||
\(642\) | 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 | −0.996455 | − | 0.0841319i | \(-0.973188\pi\) |
0.571088 | + | 0.820889i | \(0.306522\pi\) | |||||||
\(648\) | 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 | \(0.123518\pi\) |
−0.135140 | + | 0.990827i | \(0.543148\pi\) | |||||||
\(654\) | 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 | \(-0.639938\pi\) | ||||
−0.425603 | + | 0.904910i | \(0.639938\pi\) | |||||||
\(660\) | 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 | \(0.00191112\pi\) |
−0.494791 | + | 0.869012i | \(0.664756\pi\) | |||||||
\(678\) | 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 | −0.840808 | − | 0.541333i | \(-0.817920\pi\) |
0.889212 | + | 0.457495i | \(0.151253\pi\) | |||||||
\(684\) | 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 | \(-0.617654\pi\) | ||||
−0.361262 | + | 0.932465i | \(0.617654\pi\) | |||||||
\(702\) | 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 | \(0.0681786\pi\) |
−0.304496 | + | 0.952514i | \(0.598488\pi\) | |||||||
\(720\) | 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 | \(-0.244774\pi\) | ||||
0.718620 | + | 0.695403i | \(0.244774\pi\) | |||||||
\(744\) | 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 | 0.917521 | − | 0.397687i | \(-0.130187\pi\) |
−0.803168 | + | 0.595753i | \(0.796854\pi\) | |||||||
\(762\) | 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 | −0.998528 | − | 0.0542330i | \(-0.982729\pi\) |
0.546231 | + | 0.837634i | \(0.316062\pi\) | |||||||
\(774\) | 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 | \(-0.719067\pi\) | ||||
−0.635163 | + | 0.772378i | \(0.719067\pi\) | |||||||
\(798\) | 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 | −0.515703 | − | 0.856767i | \(-0.672469\pi\) |
0.999834 | + | 0.0182286i | \(0.00580268\pi\) | |||||||
\(810\) | 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 | 0.825950 | − | 0.563744i | \(-0.190639\pi\) |
−0.901191 | + | 0.433421i | \(0.857306\pi\) | |||||||
\(822\) | 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 | \(-0.802922\pi\) | ||||
−0.814379 | + | 0.580334i | \(0.802922\pi\) | |||||||
\(828\) | 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 | \(-0.293322\pi\) | ||||
0.604627 | + | 0.796509i | \(0.293322\pi\) | |||||||
\(840\) | 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 | −0.970305 | − | 0.241884i | \(-0.922235\pi\) |
0.694630 | + | 0.719367i | \(0.255568\pi\) | |||||||
\(858\) | 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 | \(0.0506358\pi\) |
−0.356502 | + | 0.934294i | \(0.616031\pi\) | |||||||
\(864\) | 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 | \(-0.578652\pi\) | ||||
−0.244585 | + | 0.969628i | \(0.578652\pi\) | |||||||
\(882\) | 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 | 0.974327 | − | 0.225138i | \(-0.0722832\pi\) |
−0.682138 | + | 0.731223i | \(0.738950\pi\) | |||||||
\(888\) | 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 | \(-0.756067\pi\) | ||||
−0.720455 | + | 0.693502i | \(0.756067\pi\) | |||||||
\(912\) | 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 | \(0.137408\pi\) |
−0.0917893 | + | 0.995778i | \(0.529259\pi\) | |||||||
\(930\) | 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 | −0.767700 | − | 0.640809i | \(-0.778599\pi\) |
0.938807 | + | 0.344444i | \(0.111932\pi\) | |||||||
\(942\) | 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 | \(0.00681305\pi\) |
−0.481351 | + | 0.876528i | \(0.659854\pi\) | |||||||
\(948\) | 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 | \(-0.706243\pi\) | ||||
−0.603540 | + | 0.797333i | \(0.706243\pi\) | |||||||
\(954\) | 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 | 0.710431 | − | 0.703767i | \(-0.248500\pi\) |
−0.964695 | + | 0.263368i | \(0.915167\pi\) | |||||||
\(972\) | 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 | \(0.404987\pi\) |
−0.974770 | + | 0.223210i | \(0.928346\pi\) | |||||||
\(978\) | 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 | \(-0.578544\pi\) |
0.961923 | − | 0.273321i | \(-0.0881222\pi\) | |||||||
\(984\) | 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.bc.361.1 | 4 | ||
3.2 | odd | 2 | 882.4.g.bg.361.2 | 4 | |||
7.2 | even | 3 | inner | 882.4.g.bc.667.1 | 4 | ||
7.3 | odd | 6 | 882.4.a.be.1.1 | yes | 2 | ||
7.4 | even | 3 | 882.4.a.be.1.2 | yes | 2 | ||
7.5 | odd | 6 | inner | 882.4.g.bc.667.2 | 4 | ||
7.6 | odd | 2 | inner | 882.4.g.bc.361.2 | 4 | ||
21.2 | odd | 6 | 882.4.g.bg.667.2 | 4 | |||
21.5 | even | 6 | 882.4.g.bg.667.1 | 4 | |||
21.11 | odd | 6 | 882.4.a.y.1.1 | ✓ | 2 | ||
21.17 | even | 6 | 882.4.a.y.1.2 | yes | 2 | ||
21.20 | even | 2 | 882.4.g.bg.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.4.a.y.1.1 | ✓ | 2 | 21.11 | odd | 6 | ||
882.4.a.y.1.2 | yes | 2 | 21.17 | even | 6 | ||
882.4.a.be.1.1 | yes | 2 | 7.3 | odd | 6 | ||
882.4.a.be.1.2 | yes | 2 | 7.4 | even | 3 | ||
882.4.g.bc.361.1 | 4 | 1.1 | even | 1 | trivial | ||
882.4.g.bc.361.2 | 4 | 7.6 | odd | 2 | inner | ||
882.4.g.bc.667.1 | 4 | 7.2 | even | 3 | inner | ||
882.4.g.bc.667.2 | 4 | 7.5 | odd | 6 | inner | ||
882.4.g.bg.361.1 | 4 | 21.20 | even | 2 | |||
882.4.g.bg.361.2 | 4 | 3.2 | odd | 2 | |||
882.4.g.bg.667.1 | 4 | 21.5 | even | 6 | |||
882.4.g.bg.667.2 | 4 | 21.2 | odd | 6 |