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: | no (minimal twist has level 294) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.be.361.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | −2.29289 | + | 3.97141i | −0.205083 | + | 0.355213i | −0.950159 | − | 0.311766i | \(-0.899080\pi\) |
0.745076 | + | 0.666979i | \(0.232413\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.58579 | + | 7.94282i | 0.145015 | + | 0.251174i | ||||
\(11\) | −3.24264 | − | 5.61642i | −0.0888812 | − | 0.153947i | 0.818157 | − | 0.574994i | \(-0.194996\pi\) |
−0.907038 | + | 0.421048i | \(0.861662\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −45.2132 | −0.964607 | −0.482303 | − | 0.876004i | \(-0.660200\pi\) | ||||
−0.482303 | + | 0.876004i | \(0.660200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −40.7782 | − | 70.6299i | −0.581774 | − | 1.00766i | −0.995269 | − | 0.0971560i | \(-0.969025\pi\) |
0.413495 | − | 0.910506i | \(-0.364308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.52691 | + | 4.37674i | −0.0305112 | + | 0.0528470i | −0.880878 | − | 0.473344i | \(-0.843047\pi\) |
0.850367 | + | 0.526191i | \(0.176380\pi\) | |||||||
\(20\) | 18.3431 | 0.205083 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.9706 | −0.125697 | ||||||||
\(23\) | 53.1249 | − | 92.0150i | 0.481622 | − | 0.834194i | −0.518156 | − | 0.855286i | \(-0.673381\pi\) |
0.999778 | + | 0.0210927i | \(0.00671450\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 51.9853 | + | 90.0411i | 0.415882 | + | 0.720329i | ||||
\(26\) | −45.2132 | + | 78.3116i | −0.341040 | + | 0.590699i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 268.132 | 1.71693 | 0.858463 | − | 0.512875i | \(-0.171420\pi\) | ||||
0.858463 | + | 0.512875i | \(0.171420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 146.184 | + | 253.198i | 0.846948 | + | 1.46696i | 0.883919 | + | 0.467640i | \(0.154896\pi\) |
−0.0369712 | + | 0.999316i | \(0.511771\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −163.113 | −0.822753 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −57.2792 | + | 99.2105i | −0.254504 | + | 0.440814i | −0.964761 | − | 0.263129i | \(-0.915246\pi\) |
0.710257 | + | 0.703943i | \(0.248579\pi\) | |||||||
\(38\) | 5.05382 | + | 8.75348i | 0.0215747 | + | 0.0373685i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 18.3431 | − | 31.7713i | 0.0725077 | − | 0.125587i | ||||
\(41\) | −161.605 | −0.615573 | −0.307786 | − | 0.951456i | \(-0.599588\pi\) | ||||
−0.307786 | + | 0.951456i | \(0.599588\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −471.294 | −1.67143 | −0.835716 | − | 0.549162i | \(-0.814947\pi\) | ||||
−0.835716 | + | 0.549162i | \(0.814947\pi\) | |||||||
\(44\) | −12.9706 | + | 22.4657i | −0.0444406 | + | 0.0769734i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −106.250 | − | 184.030i | −0.340558 | − | 0.589864i | ||||
\(47\) | −173.002 | + | 299.648i | −0.536914 | + | 0.929962i | 0.462154 | + | 0.886800i | \(0.347077\pi\) |
−0.999068 | + | 0.0431624i | \(0.986257\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 207.941 | 0.588146 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 90.4264 | + | 156.623i | 0.241152 | + | 0.417687i | ||||
\(53\) | 202.765 | + | 351.198i | 0.525507 | + | 0.910204i | 0.999559 | + | 0.0297072i | \(0.00945750\pi\) |
−0.474052 | + | 0.880497i | \(0.657209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29.7401 | 0.0729119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 268.132 | − | 464.418i | 0.607025 | − | 1.05140i | ||||
\(59\) | 126.718 | + | 219.482i | 0.279614 | + | 0.484307i | 0.971289 | − | 0.237903i | \(-0.0764600\pi\) |
−0.691674 | + | 0.722209i | \(0.743127\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −375.609 | + | 650.573i | −0.788390 | + | 1.36553i | 0.138563 | + | 0.990354i | \(0.455752\pi\) |
−0.926953 | + | 0.375177i | \(0.877582\pi\) | |||||||
\(62\) | 584.735 | 1.19776 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 103.669 | − | 179.560i | 0.197824 | − | 0.342641i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.82338 | − | 10.0864i | −0.0106185 | − | 0.0183918i | 0.860667 | − | 0.509168i | \(-0.170047\pi\) |
−0.871286 | + | 0.490776i | \(0.836713\pi\) | |||||||
\(68\) | −163.113 | + | 282.519i | −0.290887 | + | 0.503831i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 681.661 | 1.13941 | 0.569706 | − | 0.821848i | \(-0.307057\pi\) | ||||
0.569706 | + | 0.821848i | \(0.307057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 342.729 | + | 593.623i | 0.549498 | + | 0.951758i | 0.998309 | + | 0.0581315i | \(0.0185143\pi\) |
−0.448811 | + | 0.893627i | \(0.648152\pi\) | |||||||
\(74\) | 114.558 | + | 198.421i | 0.179961 | + | 0.311702i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.2153 | 0.0305112 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.132034 | + | 0.228690i | −0.000188038 | + | 0.000325692i | −0.866119 | − | 0.499837i | \(-0.833393\pi\) |
0.865931 | + | 0.500163i | \(0.166727\pi\) | |||||||
\(80\) | −36.6863 | − | 63.5425i | −0.0512707 | − | 0.0888034i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −161.605 | + | 279.908i | −0.217638 | + | 0.376960i | ||||
\(83\) | −437.137 | −0.578097 | −0.289048 | − | 0.957314i | \(-0.593339\pi\) | ||||
−0.289048 | + | 0.957314i | \(0.593339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 374.000 | 0.477247 | ||||||||
\(86\) | −471.294 | + | 816.304i | −0.590941 | + | 1.02354i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 25.9411 | + | 44.9313i | 0.0314242 | + | 0.0544284i | ||||
\(89\) | 29.2563 | − | 50.6734i | 0.0348445 | − | 0.0603525i | −0.848077 | − | 0.529873i | \(-0.822240\pi\) |
0.882922 | + | 0.469520i | \(0.155573\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −424.999 | −0.481622 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 346.004 | + | 599.297i | 0.379655 | + | 0.657582i | ||||
\(95\) | −11.5879 | − | 20.0708i | −0.0125146 | − | 0.0216760i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1280.09 | 1.33993 | 0.669966 | − | 0.742391i | \(-0.266308\pi\) | ||||
0.669966 | + | 0.742391i | \(0.266308\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 207.941 | − | 360.165i | 0.207941 | − | 0.360165i | ||||
\(101\) | 653.194 | + | 1131.37i | 0.643518 | + | 1.11461i | 0.984642 | + | 0.174587i | \(0.0558590\pi\) |
−0.341124 | + | 0.940018i | \(0.610808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −379.487 | + | 657.291i | −0.363029 | + | 0.628785i | −0.988458 | − | 0.151496i | \(-0.951591\pi\) |
0.625429 | + | 0.780281i | \(0.284924\pi\) | |||||||
\(104\) | 361.706 | 0.341040 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 811.058 | 0.743178 | ||||||||
\(107\) | 631.257 | − | 1093.37i | 0.570336 | − | 0.987850i | −0.426196 | − | 0.904631i | \(-0.640146\pi\) |
0.996531 | − | 0.0832192i | \(-0.0265202\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1052.76 | + | 1823.44i | 0.925105 | + | 1.60233i | 0.791392 | + | 0.611309i | \(0.209357\pi\) |
0.133713 | + | 0.991020i | \(0.457310\pi\) | |||||||
\(110\) | 29.7401 | − | 51.5114i | 0.0257783 | − | 0.0446493i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1535.76 | −1.27852 | −0.639258 | − | 0.768992i | \(-0.720759\pi\) | ||||
−0.639258 | + | 0.768992i | \(0.720759\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 243.619 | + | 421.961i | 0.197545 | + | 0.342157i | ||||
\(116\) | −536.264 | − | 928.837i | −0.429232 | − | 0.743451i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 506.871 | 0.395435 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 644.471 | − | 1116.26i | 0.484200 | − | 0.838659i | ||||
\(122\) | 751.217 | + | 1301.15i | 0.557476 | + | 0.965576i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 584.735 | − | 1012.79i | 0.423474 | − | 0.733478i | ||||
\(125\) | −1050.01 | −0.751326 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 24.1749 | 0.0168911 | 0.00844557 | − | 0.999964i | \(-0.497312\pi\) | ||||
0.00844557 | + | 0.999964i | \(0.497312\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −207.338 | − | 359.120i | −0.139883 | − | 0.242284i | ||||
\(131\) | −790.764 | + | 1369.64i | −0.527400 | + | 0.913483i | 0.472090 | + | 0.881550i | \(0.343500\pi\) |
−0.999490 | + | 0.0319327i | \(0.989834\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −23.2935 | −0.0150168 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 326.225 | + | 565.039i | 0.205688 | + | 0.356262i | ||||
\(137\) | −372.594 | − | 645.352i | −0.232357 | − | 0.402454i | 0.726144 | − | 0.687542i | \(-0.241310\pi\) |
−0.958501 | + | 0.285089i | \(0.907977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1373.60 | 0.838179 | 0.419090 | − | 0.907945i | \(-0.362349\pi\) | ||||
0.419090 | + | 0.907945i | \(0.362349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 681.661 | − | 1180.67i | 0.402843 | − | 0.697745i | ||||
\(143\) | 146.610 | + | 253.936i | 0.0857354 | + | 0.148498i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −614.798 | + | 1064.86i | −0.352112 | + | 0.609875i | ||||
\(146\) | 1370.91 | 0.777107 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 458.234 | 0.254504 | ||||||||
\(149\) | 310.265 | − | 537.395i | 0.170590 | − | 0.295470i | −0.768036 | − | 0.640406i | \(-0.778766\pi\) |
0.938626 | + | 0.344936i | \(0.112099\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 969.632 | + | 1679.45i | 0.522567 | + | 0.905112i | 0.999655 | + | 0.0262568i | \(0.00835877\pi\) |
−0.477089 | + | 0.878855i | \(0.658308\pi\) | |||||||
\(152\) | 20.2153 | − | 35.0139i | 0.0107873 | − | 0.0186842i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1340.74 | −0.694777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −206.422 | − | 357.533i | −0.104931 | − | 0.181747i | 0.808779 | − | 0.588113i | \(-0.200129\pi\) |
−0.913710 | + | 0.406366i | \(0.866796\pi\) | |||||||
\(158\) | 0.264069 | + | 0.457380i | 0.000132963 | + | 0.000230299i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −146.745 | −0.0725077 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1953.72 | − | 3383.94i | 0.938817 | − | 1.62608i | 0.171135 | − | 0.985248i | \(-0.445257\pi\) |
0.767682 | − | 0.640831i | \(-0.221410\pi\) | |||||||
\(164\) | 323.210 | + | 559.817i | 0.153893 | + | 0.266551i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −437.137 | + | 757.144i | −0.204388 | + | 0.354011i | ||||
\(167\) | −1286.41 | −0.596082 | −0.298041 | − | 0.954553i | \(-0.596333\pi\) | ||||
−0.298041 | + | 0.954553i | \(0.596333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −152.766 | −0.0695340 | ||||||||
\(170\) | 374.000 | − | 647.787i | 0.168732 | − | 0.292253i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 942.587 | + | 1632.61i | 0.417858 | + | 0.723751i | ||||
\(173\) | 625.628 | − | 1083.62i | 0.274946 | − | 0.476220i | −0.695176 | − | 0.718840i | \(-0.744673\pi\) |
0.970121 | + | 0.242620i | \(0.0780068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 103.765 | 0.0444406 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −58.5126 | − | 101.347i | −0.0246388 | − | 0.0426757i | ||||
\(179\) | 1811.76 | + | 3138.05i | 0.756520 | + | 1.31033i | 0.944615 | + | 0.328180i | \(0.106435\pi\) |
−0.188095 | + | 0.982151i | \(0.560231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −181.727 | −0.0746280 | −0.0373140 | − | 0.999304i | \(-0.511880\pi\) | ||||
−0.0373140 | + | 0.999304i | \(0.511880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −424.999 | + | 736.120i | −0.170279 | + | 0.294932i | ||||
\(185\) | −262.670 | − | 454.958i | −0.104389 | − | 0.180806i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −264.458 | + | 458.055i | −0.103418 | + | 0.179124i | ||||
\(188\) | 1384.02 | 0.536914 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −46.3515 | −0.0176984 | ||||||||
\(191\) | 740.640 | − | 1282.83i | 0.280580 | − | 0.485979i | −0.690948 | − | 0.722905i | \(-0.742806\pi\) |
0.971528 | + | 0.236926i | \(0.0761398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 178.354 | + | 308.918i | 0.0665192 | + | 0.115215i | 0.897367 | − | 0.441285i | \(-0.145477\pi\) |
−0.830848 | + | 0.556500i | \(0.812144\pi\) | |||||||
\(194\) | 1280.09 | − | 2217.18i | 0.473738 | − | 0.820538i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4890.53 | −1.76871 | −0.884355 | − | 0.466816i | \(-0.845401\pi\) | ||||
−0.884355 | + | 0.466816i | \(0.845401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1771.43 | + | 3068.20i | 0.631020 | + | 1.09296i | 0.987344 | + | 0.158596i | \(0.0506969\pi\) |
−0.356323 | + | 0.934363i | \(0.615970\pi\) | |||||||
\(200\) | −415.882 | − | 720.329i | −0.147037 | − | 0.254675i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2612.78 | 0.910071 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 370.543 | − | 641.800i | 0.126243 | − | 0.218660i | ||||
\(206\) | 758.975 | + | 1314.58i | 0.256700 | + | 0.444618i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 361.706 | − | 626.493i | 0.120576 | − | 0.208843i | ||||
\(209\) | 32.7755 | 0.0108475 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4289.50 | −1.39953 | −0.699765 | − | 0.714373i | \(-0.746712\pi\) | ||||
−0.699765 | + | 0.714373i | \(0.746712\pi\) | |||||||
\(212\) | 811.058 | − | 1404.79i | 0.262753 | − | 0.455102i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1262.51 | − | 2186.74i | −0.403288 | − | 0.698516i | ||||
\(215\) | 1080.63 | − | 1871.70i | 0.342782 | − | 0.593715i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4211.05 | 1.30830 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −59.4802 | − | 103.023i | −0.0182280 | − | 0.0315718i | ||||
\(221\) | 1843.71 | + | 3193.40i | 0.561183 | + | 0.971998i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5795.73 | −1.74041 | −0.870204 | − | 0.492692i | \(-0.836013\pi\) | ||||
−0.870204 | + | 0.492692i | \(0.836013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1535.76 | + | 2660.02i | −0.452024 | + | 0.782929i | ||||
\(227\) | −2052.02 | − | 3554.21i | −0.599989 | − | 1.03921i | −0.992822 | − | 0.119601i | \(-0.961838\pi\) |
0.392833 | − | 0.919610i | \(-0.371495\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −648.416 | + | 1123.09i | −0.187111 | + | 0.324086i | −0.944286 | − | 0.329126i | \(-0.893246\pi\) |
0.757175 | + | 0.653213i | \(0.226579\pi\) | |||||||
\(230\) | 974.478 | 0.279370 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2145.06 | −0.607025 | ||||||||
\(233\) | −739.167 | + | 1280.27i | −0.207830 | + | 0.359972i | −0.951031 | − | 0.309096i | \(-0.899973\pi\) |
0.743201 | + | 0.669069i | \(0.233307\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −793.351 | − | 1374.12i | −0.220223 | − | 0.381438i | ||||
\(236\) | 506.871 | − | 877.927i | 0.139807 | − | 0.242153i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3776.92 | 1.02221 | 0.511106 | − | 0.859518i | \(-0.329236\pi\) | ||||
0.511106 | + | 0.859518i | \(0.329236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1998.19 | − | 3460.97i | −0.534086 | − | 0.925065i | −0.999207 | − | 0.0398173i | \(-0.987322\pi\) |
0.465121 | − | 0.885247i | \(-0.346011\pi\) | |||||||
\(242\) | −1288.94 | − | 2232.51i | −0.342381 | − | 0.593022i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3004.87 | 0.788390 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 114.250 | − | 197.886i | 0.0294313 | − | 0.0509766i | ||||
\(248\) | −1169.47 | − | 2025.58i | −0.299441 | − | 0.518647i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1050.01 | + | 1818.67i | −0.265634 | + | 0.460091i | ||||
\(251\) | 5423.58 | 1.36388 | 0.681939 | − | 0.731409i | \(-0.261137\pi\) | ||||
0.681939 | + | 0.731409i | \(0.261137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −689.060 | −0.171229 | ||||||||
\(254\) | 24.1749 | − | 41.8721i | 0.00597192 | − | 0.0103437i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2982.11 | + | 5165.17i | −0.723809 | + | 1.25367i | 0.235653 | + | 0.971837i | \(0.424277\pi\) |
−0.959462 | + | 0.281837i | \(0.909056\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −829.352 | −0.197824 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1581.53 | + | 2739.29i | 0.372928 | + | 0.645930i | ||||
\(263\) | 2583.00 | + | 4473.89i | 0.605608 | + | 1.04894i | 0.991955 | + | 0.126590i | \(0.0404033\pi\) |
−0.386347 | + | 0.922353i | \(0.626263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1859.67 | −0.431089 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.2935 | + | 40.3455i | −0.00530924 | + | 0.00919588i | ||||
\(269\) | −1941.65 | − | 3363.03i | −0.440090 | − | 0.762259i | 0.557605 | − | 0.830106i | \(-0.311720\pi\) |
−0.997696 | + | 0.0678474i | \(0.978387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2763.83 | − | 4787.09i | 0.619522 | − | 1.07304i | −0.370051 | − | 0.929011i | \(-0.620660\pi\) |
0.989573 | − | 0.144032i | \(-0.0460069\pi\) | |||||||
\(272\) | 1304.90 | 0.290887 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1490.38 | −0.328602 | ||||||||
\(275\) | 337.139 | − | 583.942i | 0.0739282 | − | 0.128047i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1134.06 | − | 1964.25i | −0.245989 | − | 0.426066i | 0.716420 | − | 0.697669i | \(-0.245779\pi\) |
−0.962409 | + | 0.271603i | \(0.912446\pi\) | |||||||
\(278\) | 1373.60 | − | 2379.14i | 0.296341 | − | 0.513278i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −725.656 | −0.154053 | −0.0770267 | − | 0.997029i | \(-0.524543\pi\) | ||||
−0.0770267 | + | 0.997029i | \(0.524543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2118.50 | + | 3669.35i | 0.444988 | + | 0.770742i | 0.998051 | − | 0.0623972i | \(-0.0198745\pi\) |
−0.553063 | + | 0.833139i | \(0.686541\pi\) | |||||||
\(284\) | −1363.32 | − | 2361.34i | −0.284853 | − | 0.493380i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 586.441 | 0.121248 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −869.219 | + | 1505.53i | −0.176922 | + | 0.306438i | ||||
\(290\) | 1229.60 | + | 2129.72i | 0.248981 | + | 0.431247i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1370.91 | − | 2374.49i | 0.274749 | − | 0.475879i | ||||
\(293\) | −4373.78 | −0.872079 | −0.436039 | − | 0.899928i | \(-0.643619\pi\) | ||||
−0.436039 | + | 0.899928i | \(0.643619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1162.20 | −0.229376 | ||||||||
\(296\) | 458.234 | − | 793.684i | 0.0899807 | − | 0.155851i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −620.530 | − | 1074.79i | −0.120625 | − | 0.208929i | ||||
\(299\) | −2401.95 | + | 4160.29i | −0.464576 | + | 0.804669i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3878.53 | 0.739021 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −40.4306 | − | 70.0278i | −0.00762781 | − | 0.0132117i | ||||
\(305\) | −1722.46 | − | 2983.39i | −0.323370 | − | 0.560093i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4133.47 | −0.768435 | −0.384217 | − | 0.923243i | \(-0.625529\pi\) | ||||
−0.384217 | + | 0.923243i | \(0.625529\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1340.74 | + | 2322.22i | −0.245641 | + | 0.425462i | ||||
\(311\) | −2531.62 | − | 4384.89i | −0.461591 | − | 0.799499i | 0.537450 | − | 0.843296i | \(-0.319388\pi\) |
−0.999040 | + | 0.0437972i | \(0.986054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3705.78 | − | 6418.60i | 0.669211 | − | 1.15911i | −0.308914 | − | 0.951090i | \(-0.599966\pi\) |
0.978125 | − | 0.208017i | \(-0.0667011\pi\) | |||||||
\(314\) | −825.686 | −0.148395 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.05627 | 0.000188038 | ||||||||
\(317\) | −3368.53 | + | 5834.46i | −0.596831 | + | 1.03374i | 0.396455 | + | 0.918054i | \(0.370240\pi\) |
−0.993286 | + | 0.115687i | \(0.963093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −869.456 | − | 1505.94i | −0.152602 | − | 0.264315i | ||||
\(320\) | −146.745 | + | 254.170i | −0.0256353 | + | 0.0444017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 412.171 | 0.0710026 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2350.42 | − | 4071.05i | −0.401163 | − | 0.694834i | ||||
\(326\) | −3907.44 | − | 6767.88i | −0.663844 | − | 1.14981i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1292.84 | 0.217638 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5587.97 | + | 9678.65i | −0.927923 | + | 1.60721i | −0.141132 | + | 0.989991i | \(0.545074\pi\) |
−0.786791 | + | 0.617219i | \(0.788259\pi\) | |||||||
\(332\) | 874.274 | + | 1514.29i | 0.144524 | + | 0.250323i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1286.41 | + | 2228.14i | −0.210747 | + | 0.365024i | ||||
\(335\) | 53.4095 | 0.00871067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9379.78 | 1.51617 | 0.758085 | − | 0.652156i | \(-0.226135\pi\) | ||||
0.758085 | + | 0.652156i | \(0.226135\pi\) | |||||||
\(338\) | −152.766 | + | 264.599i | −0.0245840 | + | 0.0425807i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −748.000 | − | 1295.57i | −0.119312 | − | 0.206654i | ||||
\(341\) | 948.043 | − | 1642.06i | 0.150555 | − | 0.260770i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3770.35 | 0.590941 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1251.26 | − | 2167.24i | −0.194416 | − | 0.336738i | ||||
\(347\) | 2840.73 | + | 4920.29i | 0.439476 | + | 0.761195i | 0.997649 | − | 0.0685293i | \(-0.0218307\pi\) |
−0.558173 | + | 0.829725i | \(0.688497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 704.250 | 0.108016 | 0.0540080 | − | 0.998541i | \(-0.482800\pi\) | ||||
0.0540080 | + | 0.998541i | \(0.482800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 103.765 | − | 179.725i | 0.0157121 | − | 0.0272142i | ||||
\(353\) | 2142.48 | + | 3710.89i | 0.323039 | + | 0.559520i | 0.981114 | − | 0.193433i | \(-0.0619622\pi\) |
−0.658074 | + | 0.752953i | \(0.728629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1562.98 | + | 2707.15i | −0.233674 | + | 0.404735i | ||||
\(356\) | −234.051 | −0.0348445 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7247.03 | 1.06988 | ||||||||
\(359\) | 2330.64 | − | 4036.78i | 0.342636 | − | 0.593463i | −0.642285 | − | 0.766465i | \(-0.722014\pi\) |
0.984921 | + | 0.173003i | \(0.0553470\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3416.73 | + | 5917.95i | 0.498138 | + | 0.862801i | ||||
\(362\) | −181.727 | + | 314.760i | −0.0263850 | + | 0.0457001i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3143.36 | −0.450770 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3467.65 | − | 6006.15i | −0.493215 | − | 0.854274i | 0.506754 | − | 0.862091i | \(-0.330845\pi\) |
−0.999969 | + | 0.00781688i | \(0.997512\pi\) | |||||||
\(368\) | 849.998 | + | 1472.24i | 0.120405 | + | 0.208548i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1050.68 | −0.147628 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1540.55 | − | 2668.31i | 0.213852 | − | 0.370402i | −0.739065 | − | 0.673634i | \(-0.764732\pi\) |
0.952917 | + | 0.303232i | \(0.0980657\pi\) | |||||||
\(374\) | 528.916 | + | 916.109i | 0.0731272 | + | 0.126660i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1384.02 | − | 2397.19i | 0.189828 | − | 0.328791i | ||||
\(377\) | −12123.1 | −1.65616 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 941.827 | 0.127647 | 0.0638237 | − | 0.997961i | \(-0.479670\pi\) | ||||
0.0638237 | + | 0.997961i | \(0.479670\pi\) | |||||||
\(380\) | −46.3515 | + | 80.2832i | −0.00625732 | + | 0.0108380i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1481.28 | − | 2565.65i | −0.198400 | − | 0.343639i | ||||
\(383\) | 338.763 | − | 586.755i | 0.0451958 | − | 0.0782814i | −0.842543 | − | 0.538630i | \(-0.818942\pi\) |
0.887738 | + | 0.460348i | \(0.152276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 713.416 | 0.0940724 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2560.18 | − | 4434.36i | −0.334983 | − | 0.580208i | ||||
\(389\) | −5932.71 | − | 10275.8i | −0.773266 | − | 1.33934i | −0.935764 | − | 0.352627i | \(-0.885289\pi\) |
0.162498 | − | 0.986709i | \(-0.448045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8665.34 | −1.12078 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4890.53 | + | 8470.64i | −0.625333 | + | 1.08311i | ||||
\(395\) | −0.605481 | − | 1.04872i | −7.71268e−5 | − | 0.000133587i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2570.38 | + | 4452.03i | −0.324947 | + | 0.562824i | −0.981502 | − | 0.191454i | \(-0.938680\pi\) |
0.656555 | + | 0.754278i | \(0.272013\pi\) | |||||||
\(398\) | 7085.70 | 0.892397 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1663.53 | −0.207941 | ||||||||
\(401\) | −6190.99 | + | 10723.1i | −0.770981 | + | 1.33538i | 0.166045 | + | 0.986118i | \(0.446900\pi\) |
−0.937026 | + | 0.349260i | \(0.886433\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6609.44 | − | 11447.9i | −0.816971 | − | 1.41504i | ||||
\(404\) | 2612.78 | − | 4525.46i | 0.321759 | − | 0.557303i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 742.944 | 0.0904824 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7937.82 | − | 13748.7i | −0.959657 | − | 1.66217i | −0.723331 | − | 0.690501i | \(-0.757390\pi\) |
−0.236326 | − | 0.971674i | \(-0.575943\pi\) | |||||||
\(410\) | −741.087 | − | 1283.60i | −0.0892675 | − | 0.154616i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3035.90 | 0.363029 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1002.31 | − | 1736.05i | 0.118558 | − | 0.205348i | ||||
\(416\) | −723.411 | − | 1252.99i | −0.0852600 | − | 0.147675i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 32.7755 | − | 56.7688i | 0.00383517 | − | 0.00664271i | ||||
\(419\) | −16111.9 | −1.87857 | −0.939283 | − | 0.343145i | \(-0.888508\pi\) | ||||
−0.939283 | + | 0.343145i | \(0.888508\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8691.58 | 1.00618 | 0.503090 | − | 0.864234i | \(-0.332197\pi\) | ||||
0.503090 | + | 0.864234i | \(0.332197\pi\) | |||||||
\(422\) | −4289.50 | + | 7429.62i | −0.494809 | + | 0.857034i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1622.12 | − | 2809.59i | −0.185795 | − | 0.321806i | ||||
\(425\) | 4239.73 | − | 7343.43i | 0.483899 | − | 0.838138i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5050.06 | −0.570336 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2161.25 | − | 3743.40i | −0.242383 | − | 0.419820i | ||||
\(431\) | −2097.55 | − | 3633.07i | −0.234421 | − | 0.406029i | 0.724683 | − | 0.689082i | \(-0.241986\pi\) |
−0.959104 | + | 0.283053i | \(0.908653\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5426.54 | 0.602270 | 0.301135 | − | 0.953582i | \(-0.402635\pi\) | ||||
0.301135 | + | 0.953582i | \(0.402635\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4211.05 | − | 7293.76i | 0.462553 | − | 0.801165i | ||||
\(437\) | 268.484 | + | 465.028i | 0.0293898 | + | 0.0509046i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1885.62 | + | 3265.99i | −0.205002 | + | 0.355073i | −0.950133 | − | 0.311844i | \(-0.899053\pi\) |
0.745132 | + | 0.666917i | \(0.232387\pi\) | |||||||
\(440\) | −237.921 | −0.0257783 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7374.85 | 0.793633 | ||||||||
\(443\) | −2965.15 | + | 5135.79i | −0.318010 | + | 0.550810i | −0.980073 | − | 0.198639i | \(-0.936348\pi\) |
0.662063 | + | 0.749449i | \(0.269681\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 134.163 | + | 232.377i | 0.0142920 | + | 0.0247545i | ||||
\(446\) | −5795.73 | + | 10038.5i | −0.615327 | + | 1.06578i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 529.065 | 0.0556083 | 0.0278041 | − | 0.999613i | \(-0.491149\pi\) | ||||
0.0278041 | + | 0.999613i | \(0.491149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 524.027 | + | 907.642i | 0.0547128 | + | 0.0947654i | ||||
\(452\) | 3071.53 | + | 5320.04i | 0.319629 | + | 0.553614i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8208.09 | −0.848512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5028.59 | + | 8709.77i | −0.514721 | + | 0.891523i | 0.485133 | + | 0.874440i | \(0.338771\pi\) |
−0.999854 | + | 0.0170824i | \(0.994562\pi\) | |||||||
\(458\) | 1296.83 | + | 2246.18i | 0.132308 | + | 0.229164i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 974.478 | − | 1687.84i | 0.0987723 | − | 0.171079i | ||||
\(461\) | −5010.31 | −0.506190 | −0.253095 | − | 0.967441i | \(-0.581448\pi\) | ||||
−0.253095 | + | 0.967441i | \(0.581448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7124.38 | −0.715114 | −0.357557 | − | 0.933891i | \(-0.616390\pi\) | ||||
−0.357557 | + | 0.933891i | \(0.616390\pi\) | |||||||
\(464\) | −2145.06 | + | 3715.35i | −0.214616 | + | 0.371725i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1478.33 | + | 2560.55i | 0.146958 | + | 0.254539i | ||||
\(467\) | −3750.72 | + | 6496.44i | −0.371654 | + | 0.643724i | −0.989820 | − | 0.142323i | \(-0.954543\pi\) |
0.618166 | + | 0.786048i | \(0.287876\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3173.40 | −0.311443 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1013.74 | − | 1755.85i | −0.0988587 | − | 0.171228i | ||||
\(473\) | 1528.24 | + | 2646.98i | 0.148559 | + | 0.257312i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −525.449 | −0.0507563 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3776.92 | − | 6541.82i | 0.361406 | − | 0.625974i | ||||
\(479\) | 4086.90 | + | 7078.72i | 0.389844 | + | 0.675230i | 0.992428 | − | 0.122826i | \(-0.0391956\pi\) |
−0.602584 | + | 0.798055i | \(0.705862\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2589.78 | − | 4485.63i | 0.245496 | − | 0.425212i | ||||
\(482\) | −7992.76 | −0.755312 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5155.76 | −0.484200 | ||||||||
\(485\) | −2935.11 | + | 5083.76i | −0.274797 | + | 0.475962i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5984.39 | + | 10365.3i | 0.556835 | + | 0.964467i | 0.997758 | + | 0.0669221i | \(0.0213179\pi\) |
−0.440923 | + | 0.897545i | \(0.645349\pi\) | |||||||
\(488\) | 3004.87 | − | 5204.59i | 0.278738 | − | 0.482788i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2079.96 | −0.191176 | −0.0955878 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955878 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10933.9 | − | 18938.1i | −0.998863 | − | 1.73008i | ||||
\(494\) | −228.500 | − | 395.773i | −0.0208111 | − | 0.0360459i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4677.88 | −0.423474 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6417.21 | + | 11114.9i | −0.575699 | + | 0.997140i | 0.420266 | + | 0.907401i | \(0.361937\pi\) |
−0.995965 | + | 0.0897390i | \(0.971397\pi\) | |||||||
\(500\) | 2100.02 | + | 3637.34i | 0.187832 | + | 0.325334i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5423.58 | − | 9393.92i | 0.482204 | − | 0.835202i | ||||
\(503\) | 16808.8 | 1.48999 | 0.744997 | − | 0.667068i | \(-0.232451\pi\) | ||||
0.744997 | + | 0.667068i | \(0.232451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5990.82 | −0.527897 | ||||||||
\(506\) | −689.060 | + | 1193.49i | −0.0605384 | + | 0.104856i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −48.3498 | − | 83.7443i | −0.00422278 | − | 0.00731408i | ||||
\(509\) | 2135.13 | − | 3698.16i | 0.185929 | − | 0.322039i | −0.757960 | − | 0.652301i | \(-0.773804\pi\) |
0.943889 | + | 0.330262i | \(0.107137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5964.22 | + | 10330.3i | 0.511811 | + | 0.886482i | ||||
\(515\) | −1740.25 | − | 3014.20i | −0.148902 | − | 0.257906i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2243.93 | 0.190886 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −829.352 | + | 1436.48i | −0.0699414 | + | 0.121142i | ||||
\(521\) | −7641.64 | − | 13235.7i | −0.642584 | − | 1.11299i | −0.984854 | − | 0.173386i | \(-0.944529\pi\) |
0.342270 | − | 0.939602i | \(-0.388804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2249.66 | + | 3896.53i | −0.188090 | + | 0.325781i | −0.944613 | − | 0.328185i | \(-0.893563\pi\) |
0.756524 | + | 0.653966i | \(0.226896\pi\) | |||||||
\(524\) | 6326.11 | 0.527400 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10332.0 | 0.856459 | ||||||||
\(527\) | 11922.2 | − | 20649.9i | 0.985465 | − | 1.70687i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 438.992 | + | 760.356i | 0.0360805 | + | 0.0624933i | ||||
\(530\) | −1859.67 | + | 3221.04i | −0.152413 | + | 0.263987i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7306.69 | 0.593785 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2894.81 | + | 5013.96i | 0.233932 | + | 0.405182i | ||||
\(536\) | 46.5870 | + | 80.6911i | 0.00375420 | + | 0.00650247i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7766.59 | −0.622382 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1985.41 | + | 3438.83i | −0.157781 | + | 0.273284i | −0.934068 | − | 0.357095i | \(-0.883767\pi\) |
0.776287 | + | 0.630379i | \(0.217101\pi\) | |||||||
\(542\) | −5527.65 | − | 9574.18i | −0.438068 | − | 0.758757i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1304.90 | − | 2260.16i | 0.102844 | − | 0.178131i | ||||
\(545\) | −9655.50 | −0.758892 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2703.90 | −0.211353 | −0.105677 | − | 0.994401i | \(-0.533701\pi\) | ||||
−0.105677 | + | 0.994401i | \(0.533701\pi\) | |||||||
\(548\) | −1490.38 | + | 2581.41i | −0.116178 | + | 0.201227i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −674.278 | − | 1167.88i | −0.0522751 | − | 0.0905432i | ||||
\(551\) | −677.546 | + | 1173.54i | −0.0523855 | + | 0.0907344i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4536.24 | −0.347881 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2747.19 | − | 4758.28i | −0.209545 | − | 0.362942i | ||||
\(557\) | 395.412 | + | 684.874i | 0.0300793 | + | 0.0520988i | 0.880673 | − | 0.473724i | \(-0.157091\pi\) |
−0.850594 | + | 0.525823i | \(0.823757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21308.7 | 1.61227 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −725.656 | + | 1256.87i | −0.0544661 | + | 0.0943380i | ||||
\(563\) | −3758.58 | − | 6510.05i | −0.281359 | − | 0.487328i | 0.690361 | − | 0.723465i | \(-0.257452\pi\) |
−0.971720 | + | 0.236137i | \(0.924119\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3521.34 | − | 6099.14i | 0.262202 | − | 0.454146i | ||||
\(566\) | 8473.99 | 0.629308 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5453.29 | −0.402843 | ||||||||
\(569\) | 6972.72 | − | 12077.1i | 0.513728 | − | 0.889804i | −0.486145 | − | 0.873878i | \(-0.661597\pi\) |
0.999873 | − | 0.0159254i | \(-0.00506942\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1059.25 | + | 1834.67i | 0.0776323 | + | 0.134463i | 0.902228 | − | 0.431259i | \(-0.141931\pi\) |
−0.824596 | + | 0.565723i | \(0.808597\pi\) | |||||||
\(572\) | 586.441 | − | 1015.75i | 0.0428677 | − | 0.0742490i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11046.8 | 0.801192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11428.9 | + | 19795.4i | 0.824592 | + | 1.42823i | 0.902231 | + | 0.431253i | \(0.141928\pi\) |
−0.0776391 | + | 0.996982i | \(0.524738\pi\) | |||||||
\(578\) | 1738.44 | + | 3011.06i | 0.125103 | + | 0.216685i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4918.38 | 0.352112 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1314.98 | − | 2277.62i | 0.0934153 | − | 0.161800i | ||||
\(584\) | −2741.83 | − | 4748.99i | −0.194277 | − | 0.336497i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4373.78 | + | 7575.61i | −0.308326 | + | 0.534037i | ||||
\(587\) | 23955.3 | 1.68440 | 0.842199 | − | 0.539167i | \(-0.181261\pi\) | ||||
0.842199 | + | 0.539167i | \(0.181261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1477.57 | −0.103366 | ||||||||
\(590\) | −1162.20 | + | 2012.99i | −0.0810968 | + | 0.140464i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −916.468 | − | 1587.37i | −0.0636260 | − | 0.110203i | ||||
\(593\) | 5388.99 | − | 9334.01i | 0.373186 | − | 0.646378i | −0.616867 | − | 0.787067i | \(-0.711599\pi\) |
0.990054 | + | 0.140689i | \(0.0449319\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2482.12 | −0.170590 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4803.89 | + | 8320.59i | 0.328505 | + | 0.568987i | ||||
\(599\) | 3798.79 | + | 6579.69i | 0.259122 | + | 0.448813i | 0.966007 | − | 0.258516i | \(-0.0832334\pi\) |
−0.706885 | + | 0.707329i | \(0.749900\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19956.1 | −1.35445 | −0.677225 | − | 0.735776i | \(-0.736818\pi\) | ||||
−0.677225 | + | 0.735776i | \(0.736818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3878.53 | − | 6717.81i | 0.261283 | − | 0.452556i | ||||
\(605\) | 2955.40 | + | 5118.91i | 0.198602 | + | 0.343989i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −118.155 | + | 204.651i | −0.00790079 | + | 0.0136846i | −0.869949 | − | 0.493142i | \(-0.835848\pi\) |
0.862048 | + | 0.506827i | \(0.169182\pi\) | |||||||
\(608\) | −161.722 | −0.0107873 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6889.85 | −0.457314 | ||||||||
\(611\) | 7821.98 | − | 13548.1i | 0.517911 | − | 0.897048i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13207.5 | − | 22876.0i | −0.870219 | − | 1.50726i | −0.861770 | − | 0.507300i | \(-0.830644\pi\) |
−0.00844986 | − | 0.999964i | \(-0.502690\pi\) | |||||||
\(614\) | −4133.47 | + | 7159.38i | −0.271683 | + | 0.470568i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18473.6 | −1.20538 | −0.602689 | − | 0.797976i | \(-0.705904\pi\) | ||||
−0.602689 | + | 0.797976i | \(0.705904\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8023.96 | + | 13897.9i | 0.521018 | + | 0.902430i | 0.999701 | + | 0.0244421i | \(0.00778093\pi\) |
−0.478683 | + | 0.877988i | \(0.658886\pi\) | |||||||
\(620\) | 2681.47 | + | 4644.44i | 0.173694 | + | 0.300847i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10126.5 | −0.652788 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4090.60 | + | 7085.13i | −0.261798 | + | 0.453448i | ||||
\(626\) | −7411.56 | − | 12837.2i | −0.473204 | − | 0.819613i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −825.686 | + | 1430.13i | −0.0524657 | + | 0.0908733i | ||||
\(629\) | 9342.97 | 0.592255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15065.7 | −0.950487 | −0.475243 | − | 0.879854i | \(-0.657640\pi\) | ||||
−0.475243 | + | 0.879854i | \(0.657640\pi\) | |||||||
\(632\) | 1.05627 | − | 1.82952i | 6.64816e−5 | − | 0.000115149i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6737.05 | + | 11668.9i | 0.422023 | + | 0.730965i | ||||
\(635\) | −55.4304 | + | 96.0083i | −0.00346408 | + | 0.00599996i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3477.82 | −0.215812 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 293.490 | + | 508.340i | 0.0181269 | + | 0.0313967i | ||||
\(641\) | −15599.2 | − | 27018.6i | −0.961203 | − | 1.66485i | −0.719488 | − | 0.694505i | \(-0.755623\pi\) |
−0.241715 | − | 0.970347i | \(-0.577710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12497.9 | 0.766517 | 0.383259 | − | 0.923641i | \(-0.374802\pi\) | ||||
0.383259 | + | 0.923641i | \(0.374802\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 412.171 | − | 713.902i | 0.0251032 | − | 0.0434800i | ||||
\(647\) | 4964.86 | + | 8599.39i | 0.301683 | + | 0.522530i | 0.976517 | − | 0.215439i | \(-0.0691183\pi\) |
−0.674834 | + | 0.737969i | \(0.735785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 821.801 | − | 1423.40i | 0.0497049 | − | 0.0860915i | ||||
\(650\) | −9401.68 | −0.567330 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15629.8 | −0.938817 | ||||||||
\(653\) | −4072.79 | + | 7054.28i | −0.244075 | + | 0.422750i | −0.961871 | − | 0.273503i | \(-0.911817\pi\) |
0.717796 | + | 0.696253i | \(0.245151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3626.27 | − | 6280.89i | −0.216321 | − | 0.374679i | ||||
\(656\) | 1292.84 | − | 2239.27i | 0.0769466 | − | 0.133275i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16975.8 | 1.00347 | 0.501733 | − | 0.865022i | \(-0.332696\pi\) | ||||
0.501733 | + | 0.865022i | \(0.332696\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10318.9 | + | 17872.8i | 0.607199 | + | 1.05170i | 0.991700 | + | 0.128574i | \(0.0410401\pi\) |
−0.384501 | + | 0.923124i | \(0.625627\pi\) | |||||||
\(662\) | 11175.9 | + | 19357.3i | 0.656141 | + | 1.13647i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3497.10 | 0.204388 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14244.5 | − | 24672.2i | 0.826910 | − | 1.43225i | ||||
\(668\) | 2572.83 | + | 4456.27i | 0.149021 | + | 0.258111i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 53.4095 | − | 92.5080i | 0.00307969 | − | 0.00533417i | ||||
\(671\) | 4871.86 | 0.280292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2150.29 | −0.123161 | −0.0615807 | − | 0.998102i | \(-0.519614\pi\) | ||||
−0.0615807 | + | 0.998102i | \(0.519614\pi\) | |||||||
\(674\) | 9379.78 | − | 16246.3i | 0.536047 | − | 0.928461i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 305.532 | + | 529.198i | 0.0173835 | + | 0.0301091i | ||||
\(677\) | 13891.7 | − | 24061.1i | 0.788628 | − | 1.36594i | −0.138180 | − | 0.990407i | \(-0.544125\pi\) |
0.926808 | − | 0.375536i | \(-0.122541\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2992.00 | −0.168732 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1896.09 | − | 3284.12i | −0.106459 | − | 0.184392i | ||||
\(683\) | 9090.89 | + | 15745.9i | 0.509302 | + | 0.882137i | 0.999942 | + | 0.0107743i | \(0.00342962\pi\) |
−0.490640 | + | 0.871362i | \(0.663237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3417.27 | 0.190609 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3770.35 | − | 6530.43i | 0.208929 | − | 0.361876i | ||||
\(689\) | −9167.63 | − | 15878.8i | −0.506907 | − | 0.877989i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11967.6 | − | 20728.4i | 0.658853 | − | 1.14117i | −0.322060 | − | 0.946719i | \(-0.604375\pi\) |
0.980913 | − | 0.194447i | \(-0.0622912\pi\) | |||||||
\(692\) | −5005.02 | −0.274946 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11362.9 | 0.621513 | ||||||||
\(695\) | −3149.51 | + | 5455.11i | −0.171896 | + | 0.297733i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6589.96 | + | 11414.1i | 0.358124 | + | 0.620289i | ||||
\(698\) | 704.250 | − | 1219.80i | 0.0381895 | − | 0.0661461i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20627.2 | 1.11138 | 0.555691 | − | 0.831389i | \(-0.312454\pi\) | ||||
0.555691 | + | 0.831389i | \(0.312454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −289.479 | − | 501.392i | −0.0155305 | − | 0.0268995i | ||||
\(704\) | −207.529 | − | 359.451i | −0.0111101 | − | 0.0192433i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8569.93 | 0.456846 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3292.32 | − | 5702.46i | 0.174394 | − | 0.302060i | −0.765557 | − | 0.643368i | \(-0.777537\pi\) |
0.939952 | + | 0.341308i | \(0.110870\pi\) | |||||||
\(710\) | 3125.95 | + | 5414.31i | 0.165232 | + | 0.286191i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −234.051 | + | 405.387i | −0.0123194 | + | 0.0213378i | ||||
\(713\) | 31064.0 | 1.63163 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1344.65 | −0.0703313 | ||||||||
\(716\) | 7247.03 | − | 12552.2i | 0.378260 | − | 0.655165i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4661.27 | − | 8073.56i | −0.242280 | − | 0.419642i | ||||
\(719\) | −85.4430 | + | 147.992i | −0.00443183 | + | 0.00767616i | −0.868233 | − | 0.496157i | \(-0.834744\pi\) |
0.863801 | + | 0.503833i | \(0.168077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13666.9 | 0.704474 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 363.454 | + | 629.521i | 0.0186570 | + | 0.0323149i | ||||
\(725\) | 13938.9 | + | 24142.9i | 0.714039 | + | 1.23675i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11127.5 | 0.567671 | 0.283836 | − | 0.958873i | \(-0.408393\pi\) | ||||
0.283836 | + | 0.958873i | \(0.408393\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3143.36 | + | 5444.46i | −0.159371 | + | 0.276039i | ||||
\(731\) | 19218.5 | + | 33287.4i | 0.972396 | + | 1.68424i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11288.0 | + | 19551.3i | −0.568800 | + | 0.985191i | 0.427885 | + | 0.903833i | \(0.359259\pi\) |
−0.996685 | + | 0.0813578i | \(0.974074\pi\) | |||||||
\(734\) | −13870.6 | −0.697511 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3399.99 | 0.170279 | ||||||||
\(737\) | −37.7662 | + | 65.4130i | −0.00188757 | + | 0.00326936i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11468.2 | + | 19863.5i | 0.570860 | + | 0.988758i | 0.996478 | + | 0.0838550i | \(0.0267233\pi\) |
−0.425618 | + | 0.904903i | \(0.639943\pi\) | |||||||
\(740\) | −1050.68 | + | 1819.83i | −0.0521943 | + | 0.0904032i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16973.4 | −0.838081 | −0.419041 | − | 0.907967i | \(-0.637634\pi\) | ||||
−0.419041 | + | 0.907967i | \(0.637634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1422.81 | + | 2464.38i | 0.0699700 | + | 0.121192i | ||||
\(746\) | −3081.10 | − | 5336.63i | −0.151216 | − | 0.261914i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2115.66 | 0.103418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10598.9 | − | 18357.9i | 0.514994 | − | 0.891995i | −0.484855 | − | 0.874595i | \(-0.661128\pi\) |
0.999849 | − | 0.0174007i | \(-0.00553909\pi\) | |||||||
\(752\) | −2768.03 | − | 4794.37i | −0.134228 | − | 0.232490i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12123.1 | + | 20997.8i | −0.585541 | + | 1.01419i | ||||
\(755\) | −8893.05 | −0.428677 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7962.24 | −0.382289 | −0.191144 | − | 0.981562i | \(-0.561220\pi\) | ||||
−0.191144 | + | 0.981562i | \(0.561220\pi\) | |||||||
\(758\) | 941.827 | − | 1631.29i | 0.0451302 | − | 0.0781678i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 92.7030 | + | 160.566i | 0.00442460 | + | 0.00766362i | ||||
\(761\) | −13428.1 | + | 23258.1i | −0.639642 | + | 1.10789i | 0.345869 | + | 0.938283i | \(0.387584\pi\) |
−0.985511 | + | 0.169610i | \(0.945749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5925.12 | −0.280580 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −677.526 | − | 1173.51i | −0.0319582 | − | 0.0553533i | ||||
\(767\) | −5729.32 | − | 9923.47i | −0.269718 | − | 0.467165i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12183.6 | 0.571331 | 0.285666 | − | 0.958329i | \(-0.407785\pi\) | ||||
0.285666 | + | 0.958329i | \(0.407785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 713.416 | − | 1235.67i | 0.0332596 | − | 0.0576073i | ||||
\(773\) | 8727.61 | + | 15116.7i | 0.406093 | + | 0.703374i | 0.994448 | − | 0.105229i | \(-0.0335574\pi\) |
−0.588355 | + | 0.808603i | \(0.700224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15198.8 | + | 26325.1i | −0.704461 | + | 1.22016i | ||||
\(776\) | −10240.7 | −0.473738 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23730.8 | −1.09356 | ||||||||
\(779\) | 408.362 | − | 707.304i | 0.0187819 | − | 0.0325312i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2210.38 | − | 3828.49i | −0.101272 | − | 0.175409i | ||||
\(782\) | −8665.34 | + | 15008.8i | −0.396256 | + | 0.686335i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1893.21 | 0.0860785 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15490.5 | + | 26830.3i | 0.701622 | + | 1.21524i | 0.967897 | + | 0.251348i | \(0.0808738\pi\) |
−0.266275 | + | 0.963897i | \(0.585793\pi\) | |||||||
\(788\) | 9781.06 | + | 16941.3i | 0.442177 | + | 0.765874i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.42193 | −0.000109074 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16982.5 | − | 29414.5i | 0.760486 | − | 1.31720i | ||||
\(794\) | 5140.76 | + | 8904.07i | 0.229772 | + | 0.397977i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7085.70 | − | 12272.8i | 0.315510 | − | 0.546480i | ||||
\(797\) | −10517.6 | −0.467446 | −0.233723 | − | 0.972303i | \(-0.575091\pi\) | ||||
−0.233723 | + | 0.972303i | \(0.575091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28218.8 | 1.24945 | ||||||||
\(800\) | −1663.53 | + | 2881.32i | −0.0735183 | + | 0.127337i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12382.0 | + | 21446.2i | 0.545166 | + | 0.944255i | ||||
\(803\) | 2222.69 | − | 3849.81i | 0.0976800 | − | 0.169187i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26437.7 | −1.15537 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5225.56 | − | 9050.93i | −0.227518 | − | 0.394072i | ||||
\(809\) | −20889.2 | − | 36181.2i | −0.907819 | − | 1.57239i | −0.817087 | − | 0.576514i | \(-0.804413\pi\) |
−0.0907320 | − | 0.995875i | \(-0.528921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12935.4 | 0.560079 | 0.280039 | − | 0.959988i | \(-0.409652\pi\) | ||||
0.280039 | + | 0.959988i | \(0.409652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 742.944 | − | 1286.82i | 0.0319904 | − | 0.0554090i | ||||
\(815\) | 8959.34 | + | 15518.0i | 0.385070 | + | 0.666961i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1190.92 | − | 2062.73i | 0.0509975 | − | 0.0883302i | ||||
\(818\) | −31751.3 | −1.35716 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2964.35 | −0.126243 | ||||||||
\(821\) | −7249.61 | + | 12556.7i | −0.308177 | + | 0.533778i | −0.977964 | − | 0.208776i | \(-0.933052\pi\) |
0.669787 | + | 0.742554i | \(0.266386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5988.57 | + | 10372.5i | 0.253643 | + | 0.439323i | 0.964526 | − | 0.263987i | \(-0.0850377\pi\) |
−0.710883 | + | 0.703310i | \(0.751704\pi\) | |||||||
\(824\) | 3035.90 | − | 5258.33i | 0.128350 | − | 0.222309i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27613.5 | −1.16108 | −0.580541 | − | 0.814231i | \(-0.697159\pi\) | ||||
−0.580541 | + | 0.814231i | \(0.697159\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −338.918 | − | 587.023i | −0.0141992 | − | 0.0245937i | 0.858839 | − | 0.512246i | \(-0.171187\pi\) |
−0.873038 | + | 0.487653i | \(0.837853\pi\) | |||||||
\(830\) | −2004.62 | − | 3472.10i | −0.0838329 | − | 0.145203i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2893.65 | −0.120576 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2949.61 | − | 5108.88i | 0.122246 | − | 0.211736i | ||||
\(836\) | −65.5509 | − | 113.538i | −0.00271187 | − | 0.00469710i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16111.9 | + | 27906.7i | −0.664173 | + | 1.15038i | ||||
\(839\) | 42209.6 | 1.73687 | 0.868436 | − | 0.495801i | \(-0.165126\pi\) | ||||
0.868436 | + | 0.495801i | \(0.165126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47505.8 | 1.94784 | ||||||||
\(842\) | 8691.58 | − | 15054.3i | 0.355738 | − | 0.616157i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8578.99 | + | 14859.2i | 0.349883 | + | 0.606015i | ||||
\(845\) | 350.277 | − | 606.697i | 0.0142602 | − | 0.0246994i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6488.46 | −0.262753 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8479.46 | − | 14686.9i | −0.342168 | − | 0.592653i | ||||
\(851\) | 6085.90 | + | 10541.1i | 0.245149 | + | 0.424611i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2796.45 | 0.112249 | 0.0561247 | − | 0.998424i | \(-0.482126\pi\) | ||||
0.0561247 | + | 0.998424i | \(0.482126\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5050.06 | + | 8746.95i | −0.201644 | + | 0.349258i | ||||
\(857\) | −11590.5 | − | 20075.4i | −0.461989 | − | 0.800189i | 0.537071 | − | 0.843537i | \(-0.319531\pi\) |
−0.999060 | + | 0.0433483i | \(0.986197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5948.75 | + | 10303.5i | −0.236285 | + | 0.409257i | −0.959645 | − | 0.281213i | \(-0.909263\pi\) |
0.723361 | + | 0.690471i | \(0.242596\pi\) | |||||||
\(860\) | −8645.01 | −0.342782 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8390.21 | −0.331521 | ||||||||
\(863\) | −14907.9 | + | 25821.3i | −0.588033 | + | 1.01850i | 0.406457 | + | 0.913670i | \(0.366764\pi\) |
−0.994490 | + | 0.104833i | \(0.966569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2869.00 | + | 4969.25i | 0.112773 | + | 0.195329i | ||||
\(866\) | 5426.54 | − | 9399.04i | 0.212934 | − | 0.368813i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.71256 | 6.68523e−5 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 263.294 | + | 456.038i | 0.0102427 | + | 0.0177408i | ||||
\(872\) | −8422.11 | − | 14587.5i | −0.327074 | − | 0.566509i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1073.94 | 0.0415634 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5169.42 | − | 8953.70i | 0.199041 | − | 0.344749i | −0.749177 | − | 0.662370i | \(-0.769551\pi\) |
0.948218 | + | 0.317621i | \(0.102884\pi\) | |||||||
\(878\) | 3771.24 | + | 6531.98i | 0.144958 | + | 0.251075i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −237.921 | + | 412.091i | −0.00911399 | + | 0.0157859i | ||||
\(881\) | 24140.2 | 0.923160 | 0.461580 | − | 0.887099i | \(-0.347283\pi\) | ||||
0.461580 | + | 0.887099i | \(0.347283\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12997.6 | 0.495361 | 0.247681 | − | 0.968842i | \(-0.420332\pi\) | ||||
0.247681 | + | 0.968842i | \(0.420332\pi\) | |||||||
\(884\) | 7374.85 | − | 12773.6i | 0.280592 | − | 0.485999i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5930.30 | + | 10271.6i | 0.224867 | + | 0.389481i | ||||
\(887\) | −22633.3 | + | 39202.0i | −0.856766 | + | 1.48396i | 0.0182306 | + | 0.999834i | \(0.494197\pi\) |
−0.874997 | + | 0.484129i | \(0.839137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 536.653 | 0.0202120 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11591.5 | + | 20077.0i | 0.435102 | + | 0.753619i | ||||
\(893\) | −874.322 | − | 1514.37i | −0.0327638 | − | 0.0567486i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16616.7 | −0.620596 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 529.065 | − | 916.367i | 0.0196605 | − | 0.0340530i | ||||
\(899\) | 39196.6 | + | 67890.4i | 1.45415 | + | 2.51866i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16536.7 | − | 28642.5i | 0.611452 | − | 1.05907i | ||||
\(902\) | 2096.11 | 0.0773756 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12286.1 | 0.452024 | ||||||||
\(905\) | 416.681 | − | 721.712i | 0.0153049 | − | 0.0265089i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13883.2 | + | 24046.5i | 0.508253 | + | 0.880319i | 0.999954 | + | 0.00955575i | \(0.00304174\pi\) |
−0.491702 | + | 0.870764i | \(0.663625\pi\) | |||||||
\(908\) | −8208.09 | + | 14216.8i | −0.299994 | + | 0.519605i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18531.2 | −0.673948 | −0.336974 | − | 0.941514i | \(-0.609403\pi\) | ||||
−0.336974 | + | 0.941514i | \(0.609403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1417.48 | + | 2455.14i | 0.0513819 | + | 0.0889961i | ||||
\(914\) | 10057.2 | + | 17419.5i | 0.363963 | + | 0.630402i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5187.33 | 0.187111 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9046.70 | − | 15669.3i | 0.324726 | − | 0.562442i | −0.656731 | − | 0.754125i | \(-0.728061\pi\) |
0.981457 | + | 0.191683i | \(0.0613947\pi\) | |||||||
\(920\) | −1948.96 | − | 3375.69i | −0.0698426 | − | 0.120971i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5010.31 | + | 8678.11i | −0.178965 | + | 0.309977i | ||||
\(923\) | −30820.1 | −1.09908 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11910.7 | −0.423375 | ||||||||
\(926\) | −7124.38 | + | 12339.8i | −0.252831 | + | 0.437916i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4290.11 | + | 7430.69i | 0.151756 | + | 0.262850i | ||||
\(929\) | −5311.26 | + | 9199.37i | −0.187574 | + | 0.324888i | −0.944441 | − | 0.328681i | \(-0.893396\pi\) |
0.756867 | + | 0.653569i | \(0.226729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5913.34 | 0.207830 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7501.44 | + | 12992.9i | 0.262799 | + | 0.455182i | ||||
\(935\) | −1212.75 | − | 2100.54i | −0.0424183 | − | 0.0734706i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16057.6 | −0.559851 | −0.279925 | − | 0.960022i | \(-0.590310\pi\) | ||||
−0.279925 | + | 0.960022i | \(0.590310\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3173.40 | + | 5496.49i | −0.110112 | + | 0.190719i | ||||
\(941\) | −27576.6 | − | 47764.1i | −0.955338 | − | 1.65469i | −0.733593 | − | 0.679589i | \(-0.762158\pi\) |
−0.221745 | − | 0.975105i | \(-0.571175\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8585.25 | + | 14870.1i | −0.296473 | + | 0.513507i | ||||
\(944\) | −4054.97 | −0.139807 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6112.94 | 0.210094 | ||||||||
\(947\) | 9392.86 | − | 16268.9i | 0.322309 | − | 0.558256i | −0.658655 | − | 0.752445i | \(-0.728874\pi\) |
0.980964 | + | 0.194189i | \(0.0622075\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15495.9 | − | 26839.6i | −0.530049 | − | 0.918072i | ||||
\(950\) | −525.449 | + | 910.104i | −0.0179451 | + | 0.0310818i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36499.4 | 1.24064 | 0.620321 | − | 0.784348i | \(-0.287002\pi\) | ||||
0.620321 | + | 0.784348i | \(0.287002\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3396.42 | + | 5882.76i | 0.115084 | + | 0.199332i | ||||
\(956\) | −7553.84 | − | 13083.6i | −0.255553 | − | 0.442631i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16347.6 | 0.551323 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27843.9 | + | 48227.0i | −0.934641 | + | 1.61885i | ||||
\(962\) | −5179.55 | − | 8971.25i | −0.173592 | − | 0.300670i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7992.76 | + | 13843.9i | −0.267043 | + | 0.462532i | ||||
\(965\) | −1635.79 | −0.0545677 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26059.9 | 0.866627 | 0.433314 | − | 0.901243i | \(-0.357344\pi\) | ||||
0.433314 | + | 0.901243i | \(0.357344\pi\) | |||||||
\(968\) | −5155.76 | + | 8930.05i | −0.171191 | + | 0.296511i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5870.22 | + | 10167.5i | 0.194311 | + | 0.336556i | ||||
\(971\) | −10844.5 | + | 18783.2i | −0.358410 | + | 0.620785i | −0.987695 | − | 0.156390i | \(-0.950014\pi\) |
0.629285 | + | 0.777174i | \(0.283348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23937.6 | 0.787484 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6009.74 | − | 10409.2i | −0.197097 | − | 0.341383i | ||||
\(977\) | 1059.59 | + | 1835.27i | 0.0346975 | + | 0.0600978i | 0.882853 | − | 0.469650i | \(-0.155620\pi\) |
−0.848155 | + | 0.529748i | \(0.822287\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −379.471 | −0.0123881 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2079.96 | + | 3602.59i | −0.0675908 | + | 0.117071i | ||||
\(983\) | 24252.1 | + | 42005.8i | 0.786898 | + | 1.36295i | 0.927859 | + | 0.372932i | \(0.121648\pi\) |
−0.140960 | + | 0.990015i | \(0.545019\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11213.5 | − | 19422.3i | 0.362731 | − | 0.628269i | ||||
\(986\) | −43735.7 | −1.41261 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −913.998 | −0.0294313 | ||||||||
\(989\) | −25037.4 | + | 43366.1i | −0.804999 | + | 1.39430i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1021.92 | − | 1770.02i | −0.0327572 | − | 0.0567372i | 0.849182 | − | 0.528100i | \(-0.177095\pi\) |
−0.881939 | + | 0.471363i | \(0.843762\pi\) | |||||||
\(992\) | −4677.88 | + | 8102.33i | −0.149721 | + | 0.259324i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16246.8 | −0.517645 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13369.5 | − | 23156.6i | −0.424689 | − | 0.735583i | 0.571702 | − | 0.820461i | \(-0.306283\pi\) |
−0.996391 | + | 0.0848782i | \(0.972950\pi\) | |||||||
\(998\) | 12834.4 | + | 22229.9i | 0.407081 | + | 0.705084i | ||||
\(999\) | 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.be.667.2 | 4 | ||
3.2 | odd | 2 | 294.4.e.m.79.1 | 4 | |||
7.2 | even | 3 | 882.4.a.bb.1.1 | 2 | |||
7.3 | odd | 6 | 882.4.g.bk.361.1 | 4 | |||
7.4 | even | 3 | inner | 882.4.g.be.361.2 | 4 | ||
7.5 | odd | 6 | 882.4.a.t.1.2 | 2 | |||
7.6 | odd | 2 | 882.4.g.bk.667.1 | 4 | |||
21.2 | odd | 6 | 294.4.a.l.1.2 | ✓ | 2 | ||
21.5 | even | 6 | 294.4.a.o.1.1 | yes | 2 | ||
21.11 | odd | 6 | 294.4.e.m.67.1 | 4 | |||
21.17 | even | 6 | 294.4.e.k.67.2 | 4 | |||
21.20 | even | 2 | 294.4.e.k.79.2 | 4 | |||
84.23 | even | 6 | 2352.4.a.bw.1.2 | 2 | |||
84.47 | odd | 6 | 2352.4.a.bu.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.l.1.2 | ✓ | 2 | 21.2 | odd | 6 | ||
294.4.a.o.1.1 | yes | 2 | 21.5 | even | 6 | ||
294.4.e.k.67.2 | 4 | 21.17 | even | 6 | |||
294.4.e.k.79.2 | 4 | 21.20 | even | 2 | |||
294.4.e.m.67.1 | 4 | 21.11 | odd | 6 | |||
294.4.e.m.79.1 | 4 | 3.2 | odd | 2 | |||
882.4.a.t.1.2 | 2 | 7.5 | odd | 6 | |||
882.4.a.bb.1.1 | 2 | 7.2 | even | 3 | |||
882.4.g.be.361.2 | 4 | 7.4 | even | 3 | inner | ||
882.4.g.be.667.2 | 4 | 1.1 | even | 1 | trivial | ||
882.4.g.bk.361.1 | 4 | 7.3 | odd | 6 | |||
882.4.g.bk.667.1 | 4 | 7.6 | odd | 2 | |||
2352.4.a.bu.1.1 | 2 | 84.47 | odd | 6 | |||
2352.4.a.bw.1.2 | 2 | 84.23 | even | 6 |