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: | \(\Q(\sqrt{-3}, \sqrt{58})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 58x^{2} + 3364 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(-3.80789 + 6.59545i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.bb.361.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||
\(5\) | −7.61577 | + | 13.1909i | −0.681175 | + | 1.17983i | 0.293447 | + | 0.955975i | \(0.405198\pi\) |
−0.974622 | + | 0.223855i | \(0.928136\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −15.2315 | − | 26.3818i | −0.481664 | − | 0.834266i | ||||
\(11\) | −1.00000 | − | 1.73205i | −0.0274101 | − | 0.0474757i | 0.851995 | − | 0.523550i | \(-0.175393\pi\) |
−0.879405 | + | 0.476074i | \(0.842059\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.4631 | −0.649919 | −0.324959 | − | 0.945728i | \(-0.605351\pi\) | ||||
−0.324959 | + | 0.945728i | \(0.605351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 22.8473 | + | 39.5727i | 0.325958 | + | 0.564576i | 0.981706 | − | 0.190404i | \(-0.0609798\pi\) |
−0.655748 | + | 0.754980i | \(0.727646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −76.1577 | + | 131.909i | −0.919567 | + | 1.59274i | −0.119494 | + | 0.992835i | \(0.538127\pi\) |
−0.800073 | + | 0.599903i | \(0.795206\pi\) | |||||||
\(20\) | 60.9262 | 0.681175 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.0387638 | ||||||||
\(23\) | −15.0000 | + | 25.9808i | −0.135988 | + | 0.235538i | −0.925974 | − | 0.377586i | \(-0.876754\pi\) |
0.789987 | + | 0.613124i | \(0.210087\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −53.5000 | − | 92.6647i | −0.428000 | − | 0.741318i | ||||
\(26\) | 30.4631 | − | 52.7636i | 0.229781 | − | 0.397992i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 212.000 | 1.35750 | 0.678748 | − | 0.734371i | \(-0.262523\pi\) | ||||
0.678748 | + | 0.734371i | \(0.262523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −106.621 | − | 184.673i | −0.617731 | − | 1.06994i | −0.989899 | − | 0.141776i | \(-0.954719\pi\) |
0.372168 | − | 0.928166i | \(-0.378615\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −91.3893 | −0.460974 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −123.000 | + | 213.042i | −0.546516 | + | 0.946593i | 0.451994 | + | 0.892021i | \(0.350713\pi\) |
−0.998510 | + | 0.0545719i | \(0.982621\pi\) | |||||||
\(38\) | −152.315 | − | 263.818i | −0.650232 | − | 1.12624i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −60.9262 | + | 105.527i | −0.240832 | + | 0.417133i | ||||
\(41\) | −319.862 | −1.21839 | −0.609197 | − | 0.793019i | \(-0.708508\pi\) | ||||
−0.609197 | + | 0.793019i | \(0.708508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −284.000 | −1.00720 | −0.503600 | − | 0.863937i | \(-0.667991\pi\) | ||||
−0.503600 | + | 0.863937i | \(0.667991\pi\) | |||||||
\(44\) | −4.00000 | + | 6.92820i | −0.0137051 | + | 0.0237379i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −30.0000 | − | 51.9615i | −0.0961578 | − | 0.166550i | ||||
\(47\) | −30.4631 | + | 52.7636i | −0.0945425 | + | 0.163752i | −0.909418 | − | 0.415884i | \(-0.863472\pi\) |
0.814875 | + | 0.579637i | \(0.196805\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 214.000 | 0.605283 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 60.9262 | + | 105.527i | 0.162480 | + | 0.281423i | ||||
\(53\) | −274.000 | − | 474.582i | −0.710128 | − | 1.22998i | −0.964809 | − | 0.262953i | \(-0.915304\pi\) |
0.254680 | − | 0.967025i | \(-0.418030\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30.4631 | 0.0746844 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −212.000 | + | 367.195i | −0.479948 | + | 0.831294i | ||||
\(59\) | 335.094 | + | 580.400i | 0.739416 | + | 1.28071i | 0.952759 | + | 0.303728i | \(0.0982315\pi\) |
−0.213343 | + | 0.976977i | \(0.568435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 258.936 | − | 448.491i | 0.543498 | − | 0.941367i | −0.455202 | − | 0.890388i | \(-0.650433\pi\) |
0.998700 | − | 0.0509782i | \(-0.0162339\pi\) | |||||||
\(62\) | 426.483 | 0.873604 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 232.000 | − | 401.836i | 0.442709 | − | 0.766794i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −326.000 | − | 564.649i | −0.594436 | − | 1.02959i | −0.993626 | − | 0.112726i | \(-0.964042\pi\) |
0.399190 | − | 0.916868i | \(-0.369291\pi\) | |||||||
\(68\) | 91.3893 | − | 158.291i | 0.162979 | − | 0.282288i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 770.000 | 1.28707 | 0.643537 | − | 0.765415i | \(-0.277466\pi\) | ||||
0.643537 | + | 0.765415i | \(0.277466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 487.409 | + | 844.218i | 0.781465 | + | 1.35354i | 0.931088 | + | 0.364794i | \(0.118861\pi\) |
−0.149623 | + | 0.988743i | \(0.547806\pi\) | |||||||
\(74\) | −246.000 | − | 426.084i | −0.386445 | − | 0.669342i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 609.262 | 0.919567 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −236.000 | + | 408.764i | −0.336102 | + | 0.582146i | −0.983696 | − | 0.179840i | \(-0.942442\pi\) |
0.647594 | + | 0.761986i | \(0.275775\pi\) | |||||||
\(80\) | −121.852 | − | 211.054i | −0.170294 | − | 0.294958i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 319.862 | − | 554.018i | 0.430767 | − | 0.746110i | ||||
\(83\) | 182.779 | 0.241718 | 0.120859 | − | 0.992670i | \(-0.461435\pi\) | ||||
0.120859 | + | 0.992670i | \(0.461435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −696.000 | −0.888139 | ||||||||
\(86\) | 284.000 | − | 491.902i | 0.356099 | − | 0.616781i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.00000 | − | 13.8564i | −0.00969094 | − | 0.0167852i | ||||
\(89\) | −357.941 | + | 619.973i | −0.426311 | + | 0.738393i | −0.996542 | − | 0.0830918i | \(-0.973521\pi\) |
0.570231 | + | 0.821485i | \(0.306854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 120.000 | 0.135988 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −60.9262 | − | 105.527i | −0.0668517 | − | 0.115790i | ||||
\(95\) | −1160.00 | − | 2009.18i | −1.25277 | − | 2.16987i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 304.631 | 0.318872 | 0.159436 | − | 0.987208i | \(-0.449032\pi\) | ||||
0.159436 | + | 0.987208i | \(0.449032\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −214.000 | + | 370.659i | −0.214000 | + | 0.370659i | ||||
\(101\) | −510.257 | − | 883.791i | −0.502698 | − | 0.870698i | −0.999995 | − | 0.00311763i | \(-0.999008\pi\) |
0.497298 | − | 0.867580i | \(-0.334326\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 289.399 | − | 501.254i | 0.276848 | − | 0.479515i | −0.693752 | − | 0.720214i | \(-0.744043\pi\) |
0.970600 | + | 0.240699i | \(0.0773767\pi\) | |||||||
\(104\) | −243.705 | −0.229781 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1096.00 | 1.00427 | ||||||||
\(107\) | 823.000 | − | 1425.48i | 0.743574 | − | 1.28791i | −0.207284 | − | 0.978281i | \(-0.566462\pi\) |
0.950858 | − | 0.309627i | \(-0.100204\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −491.000 | − | 850.437i | −0.431461 | − | 0.747313i | 0.565538 | − | 0.824722i | \(-0.308668\pi\) |
−0.996999 | + | 0.0774094i | \(0.975335\pi\) | |||||||
\(110\) | −30.4631 | + | 52.7636i | −0.0264049 | + | 0.0457347i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1288.00 | 1.07226 | 0.536128 | − | 0.844137i | \(-0.319887\pi\) | ||||
0.536128 | + | 0.844137i | \(0.319887\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −228.473 | − | 395.727i | −0.185263 | − | 0.320885i | ||||
\(116\) | −424.000 | − | 734.390i | −0.339374 | − | 0.587813i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1340.38 | −1.04569 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 663.500 | − | 1149.22i | 0.498497 | − | 0.863423i | ||||
\(122\) | 517.873 | + | 896.982i | 0.384311 | + | 0.665647i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −426.483 | + | 738.691i | −0.308866 | + | 0.534971i | ||||
\(125\) | −274.168 | −0.196179 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1072.00 | −0.749013 | −0.374506 | − | 0.927224i | \(-0.622188\pi\) | ||||
−0.374506 | + | 0.927224i | \(0.622188\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 464.000 | + | 803.672i | 0.313042 | + | 0.542205i | ||||
\(131\) | 1370.84 | − | 2374.36i | 0.914281 | − | 1.58358i | 0.106330 | − | 0.994331i | \(-0.466090\pi\) |
0.807951 | − | 0.589250i | \(-0.200577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1304.00 | 0.840660 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 182.779 | + | 316.582i | 0.115244 | + | 0.199608i | ||||
\(137\) | −1468.00 | − | 2542.65i | −0.915472 | − | 1.58564i | −0.806208 | − | 0.591632i | \(-0.798484\pi\) |
−0.109264 | − | 0.994013i | \(-0.534849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 182.779 | 0.111533 | 0.0557665 | − | 0.998444i | \(-0.482240\pi\) | ||||
0.0557665 | + | 0.998444i | \(0.482240\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −770.000 | + | 1333.68i | −0.455049 | + | 0.788168i | ||||
\(143\) | 30.4631 | + | 52.7636i | 0.0178143 | + | 0.0308554i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1614.54 | + | 2796.47i | −0.924694 | + | 1.60162i | ||||
\(146\) | −1949.64 | −1.10516 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 984.000 | 0.546516 | ||||||||
\(149\) | 482.000 | − | 834.848i | 0.265013 | − | 0.459016i | −0.702554 | − | 0.711631i | \(-0.747957\pi\) |
0.967567 | + | 0.252614i | \(0.0812903\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 844.000 | + | 1461.85i | 0.454859 | + | 0.787839i | 0.998680 | − | 0.0513620i | \(-0.0163562\pi\) |
−0.543821 | + | 0.839201i | \(0.683023\pi\) | |||||||
\(152\) | −609.262 | + | 1055.27i | −0.325116 | + | 0.563118i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3248.00 | 1.68313 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1721.16 | − | 2981.14i | −0.874929 | − | 1.51542i | −0.856838 | − | 0.515586i | \(-0.827574\pi\) |
−0.0180912 | − | 0.999836i | \(-0.505759\pi\) | |||||||
\(158\) | −472.000 | − | 817.528i | −0.237660 | − | 0.411639i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 487.409 | 0.240832 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1662.00 | − | 2878.67i | 0.798637 | − | 1.38328i | −0.121866 | − | 0.992547i | \(-0.538888\pi\) |
0.920504 | − | 0.390734i | \(-0.127779\pi\) | |||||||
\(164\) | 639.725 | + | 1108.04i | 0.304598 | + | 0.527580i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −182.779 | + | 316.582i | −0.0854600 | + | 0.148021i | ||||
\(167\) | 3046.31 | 1.41156 | 0.705780 | − | 0.708431i | \(-0.250597\pi\) | ||||
0.705780 | + | 0.708431i | \(0.250597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1269.00 | −0.577606 | ||||||||
\(170\) | 696.000 | − | 1205.51i | 0.314004 | − | 0.543872i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 568.000 | + | 983.805i | 0.251800 | + | 0.436130i | ||||
\(173\) | −1637.39 | + | 2836.04i | −0.719587 | + | 1.24636i | 0.241577 | + | 0.970382i | \(0.422336\pi\) |
−0.961164 | + | 0.275979i | \(0.910998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 32.0000 | 0.0137051 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −715.883 | − | 1239.95i | −0.301448 | − | 0.522123i | ||||
\(179\) | −627.000 | − | 1086.00i | −0.261811 | − | 0.453470i | 0.704912 | − | 0.709295i | \(-0.250986\pi\) |
−0.966723 | + | 0.255825i | \(0.917653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3076.77 | −1.26351 | −0.631753 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631753 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −120.000 | + | 207.846i | −0.0480789 | + | 0.0832751i | ||||
\(185\) | −1873.48 | − | 3244.96i | −0.744546 | − | 1.28959i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 45.6946 | − | 79.1454i | 0.0178691 | − | 0.0309502i | ||||
\(188\) | 243.705 | 0.0945425 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4640.00 | 1.77169 | ||||||||
\(191\) | −453.000 | + | 784.619i | −0.171612 | + | 0.297241i | −0.938984 | − | 0.343962i | \(-0.888231\pi\) |
0.767371 | + | 0.641203i | \(0.221564\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −91.0000 | − | 157.617i | −0.0339395 | − | 0.0587849i | 0.848557 | − | 0.529104i | \(-0.177472\pi\) |
−0.882496 | + | 0.470319i | \(0.844139\pi\) | |||||||
\(194\) | −304.631 | + | 527.636i | −0.112738 | + | 0.195268i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3468.00 | 1.25424 | 0.627119 | − | 0.778924i | \(-0.284234\pi\) | ||||
0.627119 | + | 0.778924i | \(0.284234\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1949.64 | + | 3376.87i | 0.694503 | + | 1.20292i | 0.970348 | + | 0.241713i | \(0.0777092\pi\) |
−0.275844 | + | 0.961202i | \(0.588957\pi\) | |||||||
\(200\) | −428.000 | − | 741.318i | −0.151321 | − | 0.262095i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2041.03 | 0.710922 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2436.00 | − | 4219.28i | 0.829940 | − | 1.43750i | ||||
\(206\) | 578.799 | + | 1002.51i | 0.195761 | + | 0.339068i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 243.705 | − | 422.109i | 0.0812398 | − | 0.140712i | ||||
\(209\) | 304.631 | 0.100822 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2620.00 | −0.854826 | −0.427413 | − | 0.904057i | \(-0.640575\pi\) | ||||
−0.427413 | + | 0.904057i | \(0.640575\pi\) | |||||||
\(212\) | −1096.00 | + | 1898.33i | −0.355064 | + | 0.614989i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1646.00 | + | 2850.96i | 0.525786 | + | 0.910688i | ||||
\(215\) | 2162.88 | − | 3746.22i | 0.686080 | − | 1.18833i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1964.00 | 0.610178 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −60.9262 | − | 105.527i | −0.0186711 | − | 0.0323393i | ||||
\(221\) | −696.000 | − | 1205.51i | −0.211846 | − | 0.366929i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1401.30 | 0.420799 | 0.210399 | − | 0.977616i | \(-0.432524\pi\) | ||||
0.210399 | + | 0.977616i | \(0.432524\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1288.00 | + | 2230.88i | −0.379099 | + | 0.656620i | ||||
\(227\) | 1949.64 | + | 3376.87i | 0.570053 | + | 0.987361i | 0.996560 | + | 0.0828763i | \(0.0264106\pi\) |
−0.426507 | + | 0.904484i | \(0.640256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2756.91 | − | 4775.11i | 0.795553 | − | 1.37794i | −0.126934 | − | 0.991911i | \(-0.540514\pi\) |
0.922487 | − | 0.386028i | \(-0.126153\pi\) | |||||||
\(230\) | 913.893 | 0.262001 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1696.00 | 0.479948 | ||||||||
\(233\) | 356.000 | − | 616.610i | 0.100096 | − | 0.173371i | −0.811628 | − | 0.584174i | \(-0.801418\pi\) |
0.911724 | + | 0.410803i | \(0.134752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −464.000 | − | 803.672i | −0.128800 | − | 0.223088i | ||||
\(236\) | 1340.38 | − | 2321.60i | 0.369708 | − | 0.640353i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2586.00 | −0.699893 | −0.349947 | − | 0.936770i | \(-0.613800\pi\) | ||||
−0.349947 | + | 0.936770i | \(0.613800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1127.13 | + | 1952.25i | 0.301266 | + | 0.521808i | 0.976423 | − | 0.215866i | \(-0.0692574\pi\) |
−0.675157 | + | 0.737674i | \(0.735924\pi\) | |||||||
\(242\) | 1327.00 | + | 2298.43i | 0.352491 | + | 0.610532i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2071.49 | −0.543498 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2320.00 | − | 4018.36i | 0.597644 | − | 1.03515i | ||||
\(248\) | −852.967 | − | 1477.38i | −0.218401 | − | 0.378282i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 274.168 | − | 474.873i | 0.0693596 | − | 0.120134i | ||||
\(251\) | −4508.54 | −1.13377 | −0.566885 | − | 0.823797i | \(-0.691852\pi\) | ||||
−0.566885 | + | 0.823797i | \(0.691852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 60.0000 | 0.0149098 | ||||||||
\(254\) | 1072.00 | − | 1856.76i | 0.264816 | − | 0.458675i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2277.12 | + | 3944.08i | −0.552695 | + | 0.957296i | 0.445384 | + | 0.895340i | \(0.353067\pi\) |
−0.998079 | + | 0.0619561i | \(0.980266\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1856.00 | −0.442709 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2741.68 | + | 4748.73i | 0.646494 | + | 1.11976i | ||||
\(263\) | 1289.00 | + | 2232.61i | 0.302217 | + | 0.523456i | 0.976638 | − | 0.214892i | \(-0.0689399\pi\) |
−0.674421 | + | 0.738347i | \(0.735607\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8346.89 | 1.93489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1304.00 | + | 2258.59i | −0.297218 | + | 0.514797i | ||||
\(269\) | −464.562 | − | 804.645i | −0.105297 | − | 0.182380i | 0.808563 | − | 0.588410i | \(-0.200246\pi\) |
−0.913859 | + | 0.406031i | \(0.866913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 563.567 | − | 976.127i | 0.126326 | − | 0.218803i | −0.795925 | − | 0.605396i | \(-0.793015\pi\) |
0.922250 | + | 0.386593i | \(0.126348\pi\) | |||||||
\(272\) | −731.114 | −0.162979 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5872.00 | 1.29467 | ||||||||
\(275\) | −107.000 | + | 185.329i | −0.0234631 | + | 0.0406392i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −755.000 | − | 1307.70i | −0.163767 | − | 0.283653i | 0.772450 | − | 0.635076i | \(-0.219031\pi\) |
−0.936217 | + | 0.351423i | \(0.885698\pi\) | |||||||
\(278\) | −182.779 | + | 316.582i | −0.0394328 | + | 0.0682997i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4008.00 | −0.850880 | −0.425440 | − | 0.904987i | \(-0.639881\pi\) | ||||
−0.425440 | + | 0.904987i | \(0.639881\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1203.29 | − | 2084.16i | −0.252750 | − | 0.437776i | 0.711532 | − | 0.702654i | \(-0.248002\pi\) |
−0.964282 | + | 0.264878i | \(0.914668\pi\) | |||||||
\(284\) | −1540.00 | − | 2667.36i | −0.321768 | − | 0.557319i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −121.852 | −0.0251933 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1412.50 | − | 2446.52i | 0.287503 | − | 0.497969i | ||||
\(290\) | −3229.09 | − | 5592.94i | −0.653857 | − | 1.13251i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1949.64 | − | 3376.87i | 0.390733 | − | 0.676769i | ||||
\(293\) | −5254.88 | −1.04776 | −0.523880 | − | 0.851792i | \(-0.675516\pi\) | ||||
−0.523880 | + | 0.851792i | \(0.675516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10208.0 | −2.01469 | ||||||||
\(296\) | −984.000 | + | 1704.34i | −0.193222 | + | 0.334671i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 964.000 | + | 1669.70i | 0.187393 | + | 0.324574i | ||||
\(299\) | 456.946 | − | 791.454i | 0.0883809 | − | 0.153080i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3376.00 | −0.643268 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1218.52 | − | 2110.54i | −0.229892 | − | 0.398184i | ||||
\(305\) | 3944.00 | + | 6831.21i | 0.740435 | + | 1.28247i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6366.79 | −1.18362 | −0.591811 | − | 0.806077i | \(-0.701587\pi\) | ||||
−0.591811 | + | 0.806077i | \(0.701587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3248.00 | + | 5625.70i | −0.595077 | + | 1.03070i | ||||
\(311\) | 3686.03 | + | 6384.40i | 0.672077 | + | 1.16407i | 0.977314 | + | 0.211795i | \(0.0679308\pi\) |
−0.305238 | + | 0.952276i | \(0.598736\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −274.168 | + | 474.873i | −0.0495108 | + | 0.0857552i | −0.889719 | − | 0.456509i | \(-0.849100\pi\) |
0.840208 | + | 0.542264i | \(0.182433\pi\) | |||||||
\(314\) | 6884.66 | 1.23734 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1888.00 | 0.336102 | ||||||||
\(317\) | −1890.00 | + | 3273.58i | −0.334867 | + | 0.580007i | −0.983459 | − | 0.181129i | \(-0.942025\pi\) |
0.648592 | + | 0.761136i | \(0.275358\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −212.000 | − | 367.195i | −0.0372092 | − | 0.0644482i | ||||
\(320\) | −487.409 | + | 844.218i | −0.0851469 | + | 0.147479i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6960.00 | −1.19896 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1629.78 | + | 2822.85i | 0.278165 | + | 0.481796i | ||||
\(326\) | 3324.00 | + | 5757.34i | 0.564722 | + | 0.978127i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2558.90 | −0.430767 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3130.00 | + | 5421.32i | −0.519759 | + | 0.900250i | 0.479977 | + | 0.877281i | \(0.340645\pi\) |
−0.999736 | + | 0.0229685i | \(0.992688\pi\) | |||||||
\(332\) | −365.557 | − | 633.163i | −0.0604294 | − | 0.104667i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3046.31 | + | 5276.36i | −0.499062 | + | 0.864400i | ||||
\(335\) | 9930.97 | 1.61966 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3166.00 | −0.511760 | −0.255880 | − | 0.966709i | \(-0.582365\pi\) | ||||
−0.255880 | + | 0.966709i | \(0.582365\pi\) | |||||||
\(338\) | 1269.00 | − | 2197.97i | 0.204214 | − | 0.353710i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1392.00 | + | 2411.01i | 0.222035 | + | 0.384575i | ||||
\(341\) | −213.242 | + | 369.345i | −0.0338642 | + | 0.0586545i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2272.00 | −0.356099 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3274.78 | − | 5672.09i | −0.508825 | − | 0.881310i | ||||
\(347\) | 1809.00 | + | 3133.28i | 0.279862 | + | 0.484736i | 0.971350 | − | 0.237652i | \(-0.0763779\pi\) |
−0.691488 | + | 0.722388i | \(0.743045\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4478.07 | −0.686836 | −0.343418 | − | 0.939183i | \(-0.611585\pi\) | ||||
−0.343418 | + | 0.939183i | \(0.611585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −32.0000 | + | 55.4256i | −0.00484547 | + | 0.00839260i | ||||
\(353\) | 1850.63 | + | 3205.39i | 0.279035 | + | 0.483302i | 0.971145 | − | 0.238489i | \(-0.0766522\pi\) |
−0.692110 | + | 0.721792i | \(0.743319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5864.15 | + | 10157.0i | −0.876723 | + | 1.51853i | ||||
\(356\) | 2863.53 | 0.426311 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2508.00 | 0.370257 | ||||||||
\(359\) | −65.0000 | + | 112.583i | −0.00955590 | + | 0.0165513i | −0.870764 | − | 0.491702i | \(-0.836375\pi\) |
0.861208 | + | 0.508253i | \(0.169708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8170.50 | − | 14151.7i | −1.19121 | − | 2.06323i | ||||
\(362\) | 3076.77 | − | 5329.13i | 0.446717 | − | 0.773737i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14848.0 | −2.12926 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3899.28 | − | 6753.74i | −0.554606 | − | 0.960606i | −0.997934 | − | 0.0642468i | \(-0.979536\pi\) |
0.443328 | − | 0.896360i | \(-0.353798\pi\) | |||||||
\(368\) | −240.000 | − | 415.692i | −0.0339969 | − | 0.0588844i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7493.92 | 1.05295 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.0000 | − | 43.3013i | 0.00347038 | − | 0.00601087i | −0.864285 | − | 0.503002i | \(-0.832229\pi\) |
0.867755 | + | 0.496992i | \(0.165562\pi\) | |||||||
\(374\) | 91.3893 | + | 158.291i | 0.0126354 | + | 0.0218851i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −243.705 | + | 422.109i | −0.0334258 | + | 0.0578952i | ||||
\(377\) | −6458.18 | −0.882263 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4956.00 | −0.671696 | −0.335848 | − | 0.941916i | \(-0.609023\pi\) | ||||
−0.335848 | + | 0.941916i | \(0.609023\pi\) | |||||||
\(380\) | −4640.00 | + | 8036.72i | −0.626387 | + | 1.08493i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −906.000 | − | 1569.24i | −0.121348 | − | 0.210181i | ||||
\(383\) | −3381.40 | + | 5856.76i | −0.451127 | + | 0.781375i | −0.998456 | − | 0.0555425i | \(-0.982311\pi\) |
0.547329 | + | 0.836917i | \(0.315645\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 364.000 | 0.0479977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −609.262 | − | 1055.27i | −0.0797180 | − | 0.138076i | ||||
\(389\) | 6570.00 | + | 11379.6i | 0.856330 | + | 1.48321i | 0.875406 | + | 0.483388i | \(0.160594\pi\) |
−0.0190764 | + | 0.999818i | \(0.506073\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1370.84 | −0.177305 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3468.00 | + | 6006.75i | −0.443440 | + | 0.768060i | ||||
\(395\) | −3594.64 | − | 6226.11i | −0.457889 | − | 0.793087i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1903.94 | + | 3297.73i | −0.240696 | + | 0.416897i | −0.960913 | − | 0.276852i | \(-0.910709\pi\) |
0.720217 | + | 0.693749i | \(0.244042\pi\) | |||||||
\(398\) | −7798.55 | −0.982176 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1712.00 | 0.214000 | ||||||||
\(401\) | −2412.00 | + | 4177.71i | −0.300373 | + | 0.520261i | −0.976220 | − | 0.216780i | \(-0.930444\pi\) |
0.675848 | + | 0.737041i | \(0.263778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3248.00 | + | 5625.70i | 0.401475 | + | 0.695375i | ||||
\(404\) | −2041.03 | + | 3535.16i | −0.251349 | + | 0.435349i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 492.000 | 0.0599202 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2650.29 | − | 4590.44i | −0.320412 | − | 0.554969i | 0.660161 | − | 0.751124i | \(-0.270488\pi\) |
−0.980573 | + | 0.196155i | \(0.937155\pi\) | |||||||
\(410\) | 4872.00 | + | 8438.55i | 0.586856 | + | 1.01646i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2315.20 | −0.276848 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1392.00 | + | 2411.01i | −0.164652 | + | 0.285186i | ||||
\(416\) | 487.409 | + | 844.218i | 0.0574452 | + | 0.0994981i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −304.631 | + | 527.636i | −0.0356459 | + | 0.0617405i | ||||
\(419\) | −10540.2 | −1.22894 | −0.614468 | − | 0.788942i | \(-0.710629\pi\) | ||||
−0.614468 | + | 0.788942i | \(0.710629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4458.00 | −0.516080 | −0.258040 | − | 0.966134i | \(-0.583077\pi\) | ||||
−0.258040 | + | 0.966134i | \(0.583077\pi\) | |||||||
\(422\) | 2620.00 | − | 4537.97i | 0.302227 | − | 0.523472i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2192.00 | − | 3796.66i | −0.251068 | − | 0.434863i | ||||
\(425\) | 2444.66 | − | 4234.28i | 0.279020 | − | 0.483277i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6584.00 | −0.743574 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4325.76 | + | 7492.43i | 0.485132 | + | 0.840273i | ||||
\(431\) | 8107.00 | + | 14041.7i | 0.906034 | + | 1.56930i | 0.819524 | + | 0.573045i | \(0.194238\pi\) |
0.0865097 | + | 0.996251i | \(0.472429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3594.64 | −0.398955 | −0.199478 | − | 0.979902i | \(-0.563925\pi\) | ||||
−0.199478 | + | 0.979902i | \(0.563925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1964.00 | + | 3401.75i | −0.215731 | + | 0.373656i | ||||
\(437\) | −2284.73 | − | 3957.27i | −0.250100 | − | 0.433185i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4295.30 | − | 7439.67i | 0.466978 | − | 0.808829i | −0.532310 | − | 0.846549i | \(-0.678676\pi\) |
0.999288 | + | 0.0377198i | \(0.0120094\pi\) | |||||||
\(440\) | 243.705 | 0.0264049 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2784.00 | 0.299596 | ||||||||
\(443\) | −7503.00 | + | 12995.6i | −0.804691 | + | 1.39377i | 0.111808 | + | 0.993730i | \(0.464336\pi\) |
−0.916499 | + | 0.400037i | \(0.868997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5452.00 | − | 9443.14i | −0.580786 | − | 1.00595i | ||||
\(446\) | −1401.30 | + | 2427.13i | −0.148775 | + | 0.257686i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1824.00 | 0.191715 | 0.0958573 | − | 0.995395i | \(-0.469441\pi\) | ||||
0.0958573 | + | 0.995395i | \(0.469441\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 319.862 | + | 554.018i | 0.0333963 | + | 0.0578441i | ||||
\(452\) | −2576.00 | − | 4461.76i | −0.268064 | − | 0.464300i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7798.55 | −0.806177 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 293.000 | − | 507.491i | 0.0299912 | − | 0.0519462i | −0.850640 | − | 0.525748i | \(-0.823785\pi\) |
0.880631 | + | 0.473802i | \(0.157119\pi\) | |||||||
\(458\) | 5513.82 | + | 9550.22i | 0.562541 | + | 0.974350i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −913.893 | + | 1582.91i | −0.0926315 | + | 0.160442i | ||||
\(461\) | 15399.1 | 1.55576 | 0.777882 | − | 0.628410i | \(-0.216294\pi\) | ||||
0.777882 | + | 0.628410i | \(0.216294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −88.0000 | −0.00883306 | −0.00441653 | − | 0.999990i | \(-0.501406\pi\) | ||||
−0.00441653 | + | 0.999990i | \(0.501406\pi\) | |||||||
\(464\) | −1696.00 | + | 2937.56i | −0.169687 | + | 0.293907i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 712.000 | + | 1233.22i | 0.0707785 | + | 0.122592i | ||||
\(467\) | 4874.09 | − | 8442.18i | 0.482968 | − | 0.836526i | −0.516840 | − | 0.856082i | \(-0.672892\pi\) |
0.999809 | + | 0.0195561i | \(0.00622529\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1856.00 | 0.182151 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2680.75 | + | 4643.20i | 0.261423 | + | 0.452798i | ||||
\(473\) | 284.000 | + | 491.902i | 0.0276075 | + | 0.0478175i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16297.8 | 1.57430 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2586.00 | − | 4479.08i | 0.247450 | − | 0.428595i | ||||
\(479\) | −2467.51 | − | 4273.85i | −0.235373 | − | 0.407677i | 0.724008 | − | 0.689791i | \(-0.242298\pi\) |
−0.959381 | + | 0.282114i | \(0.908964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3746.96 | − | 6489.93i | 0.355191 | − | 0.615208i | ||||
\(482\) | −4508.54 | −0.426054 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5308.00 | −0.498497 | ||||||||
\(485\) | −2320.00 | + | 4018.36i | −0.217208 | + | 0.376215i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 412.000 | + | 713.605i | 0.0383357 | + | 0.0663994i | 0.884557 | − | 0.466433i | \(-0.154461\pi\) |
−0.846221 | + | 0.532832i | \(0.821128\pi\) | |||||||
\(488\) | 2071.49 | − | 3587.93i | 0.192156 | − | 0.332823i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15426.0 | −1.41785 | −0.708926 | − | 0.705283i | \(-0.750820\pi\) | ||||
−0.708926 | + | 0.705283i | \(0.750820\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4843.63 | + | 8389.42i | 0.442487 | + | 0.766410i | ||||
\(494\) | 4640.00 | + | 8036.72i | 0.422598 | + | 0.731961i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3411.87 | 0.308866 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2922.00 | + | 5061.05i | −0.262138 | + | 0.454036i | −0.966810 | − | 0.255497i | \(-0.917761\pi\) |
0.704672 | + | 0.709533i | \(0.251094\pi\) | |||||||
\(500\) | 548.336 | + | 949.745i | 0.0490446 | + | 0.0849478i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4508.54 | − | 7809.02i | 0.400848 | − | 0.694290i | ||||
\(503\) | 10174.7 | 0.901921 | 0.450960 | − | 0.892544i | \(-0.351082\pi\) | ||||
0.450960 | + | 0.892544i | \(0.351082\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15544.0 | 1.36970 | ||||||||
\(506\) | −60.0000 | + | 103.923i | −0.00527139 | + | 0.00913032i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2144.00 | + | 3713.52i | 0.187253 | + | 0.324332i | ||||
\(509\) | 5902.22 | − | 10223.0i | 0.513971 | − | 0.890225i | −0.485897 | − | 0.874016i | \(-0.661507\pi\) |
0.999869 | − | 0.0162087i | \(-0.00515962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4554.23 | − | 7888.16i | −0.390814 | − | 0.676910i | ||||
\(515\) | 4408.00 | + | 7634.88i | 0.377164 | + | 0.653268i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 121.852 | 0.0103657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1856.00 | − | 3214.69i | 0.156521 | − | 0.271103i | ||||
\(521\) | 784.425 | + | 1358.66i | 0.0659621 | + | 0.114250i | 0.897120 | − | 0.441786i | \(-0.145655\pi\) |
−0.831158 | + | 0.556036i | \(0.812322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9565.41 | − | 16567.8i | 0.799744 | − | 1.38520i | −0.120038 | − | 0.992769i | \(-0.538302\pi\) |
0.919783 | − | 0.392428i | \(-0.128365\pi\) | |||||||
\(524\) | −10966.7 | −0.914281 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5156.00 | −0.427400 | ||||||||
\(527\) | 4872.00 | − | 8438.55i | 0.402709 | − | 0.697512i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5633.50 | + | 9757.51i | 0.463015 | + | 0.801965i | ||||
\(530\) | −8346.89 | + | 14457.2i | −0.684086 | + | 1.18487i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9744.00 | 0.791856 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12535.6 | + | 21712.2i | 1.01301 | + | 1.75458i | ||||
\(536\) | −2608.00 | − | 4517.19i | −0.210165 | − | 0.364016i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1858.25 | 0.148912 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3313.00 | − | 5738.28i | 0.263285 | − | 0.456022i | −0.703828 | − | 0.710370i | \(-0.748527\pi\) |
0.967113 | + | 0.254348i | \(0.0818608\pi\) | |||||||
\(542\) | 1127.13 | + | 1952.25i | 0.0893258 | + | 0.154717i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 731.114 | − | 1266.33i | 0.0576218 | − | 0.0998039i | ||||
\(545\) | 14957.4 | 1.17560 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19964.0 | −1.56051 | −0.780255 | − | 0.625462i | \(-0.784911\pi\) | ||||
−0.780255 | + | 0.625462i | \(0.784911\pi\) | |||||||
\(548\) | −5872.00 | + | 10170.6i | −0.457736 | + | 0.792822i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −214.000 | − | 370.659i | −0.0165909 | − | 0.0287363i | ||||
\(551\) | −16145.4 | + | 27964.7i | −1.24831 | + | 2.16214i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3020.00 | 0.231602 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −365.557 | − | 633.163i | −0.0278832 | − | 0.0482952i | ||||
\(557\) | −3390.00 | − | 5871.65i | −0.257880 | − | 0.446660i | 0.707794 | − | 0.706419i | \(-0.249690\pi\) |
−0.965674 | + | 0.259758i | \(0.916357\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8651.52 | 0.654598 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4008.00 | − | 6942.06i | 0.300831 | − | 0.521055i | ||||
\(563\) | −9474.02 | − | 16409.5i | −0.709205 | − | 1.22838i | −0.965152 | − | 0.261688i | \(-0.915721\pi\) |
0.255947 | − | 0.966691i | \(-0.417613\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9809.12 | + | 16989.9i | −0.730394 | + | 1.26508i | ||||
\(566\) | 4813.17 | 0.357443 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6160.00 | 0.455049 | ||||||||
\(569\) | 96.0000 | − | 166.277i | 0.00707299 | − | 0.0122508i | −0.862467 | − | 0.506113i | \(-0.831082\pi\) |
0.869540 | + | 0.493862i | \(0.164415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11514.0 | + | 19942.8i | 0.843863 | + | 1.46161i | 0.886605 | + | 0.462528i | \(0.153057\pi\) |
−0.0427415 | + | 0.999086i | \(0.513609\pi\) | |||||||
\(572\) | 121.852 | − | 211.054i | 0.00890717 | − | 0.0154277i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3210.00 | 0.232811 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5361.50 | − | 9286.40i | −0.386832 | − | 0.670014i | 0.605189 | − | 0.796082i | \(-0.293098\pi\) |
−0.992022 | + | 0.126068i | \(0.959764\pi\) | |||||||
\(578\) | 2825.00 | + | 4893.04i | 0.203295 | + | 0.352117i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12916.4 | 0.924694 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −548.000 | + | 949.164i | −0.0389294 | + | 0.0674277i | ||||
\(584\) | 3899.28 | + | 6753.74i | 0.276290 | + | 0.478548i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5254.88 | − | 9101.73i | 0.370439 | − | 0.641619i | ||||
\(587\) | −19496.4 | −1.37087 | −0.685436 | − | 0.728133i | \(-0.740388\pi\) | ||||
−0.685436 | + | 0.728133i | \(0.740388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32480.0 | 2.27218 | ||||||||
\(590\) | 10208.0 | − | 17680.8i | 0.712300 | − | 1.23374i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1968.00 | − | 3408.68i | −0.136629 | − | 0.236648i | ||||
\(593\) | 6694.26 | − | 11594.8i | 0.463576 | − | 0.802937i | −0.535560 | − | 0.844497i | \(-0.679899\pi\) |
0.999136 | + | 0.0415601i | \(0.0132328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3856.00 | −0.265013 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 913.893 | + | 1582.91i | 0.0624947 | + | 0.108244i | ||||
\(599\) | −9033.00 | − | 15645.6i | −0.616158 | − | 1.06722i | −0.990180 | − | 0.139797i | \(-0.955355\pi\) |
0.374023 | − | 0.927420i | \(-0.377978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19861.9 | −1.34806 | −0.674031 | − | 0.738703i | \(-0.735439\pi\) | ||||
−0.674031 | + | 0.738703i | \(0.735439\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3376.00 | − | 5847.40i | 0.227430 | − | 0.393920i | ||||
\(605\) | 10106.1 | + | 17504.3i | 0.679128 | + | 1.17628i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2650.29 | + | 4590.44i | −0.177219 | + | 0.306952i | −0.940927 | − | 0.338610i | \(-0.890043\pi\) |
0.763708 | + | 0.645562i | \(0.223377\pi\) | |||||||
\(608\) | 4874.09 | 0.325116 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15776.0 | −1.04713 | ||||||||
\(611\) | 928.000 | − | 1607.34i | 0.0614449 | − | 0.106426i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7969.00 | − | 13802.7i | −0.525065 | − | 0.909439i | −0.999574 | − | 0.0291886i | \(-0.990708\pi\) |
0.474509 | − | 0.880251i | \(-0.342626\pi\) | |||||||
\(614\) | 6366.79 | − | 11027.6i | 0.418473 | − | 0.724817i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11696.0 | −0.763149 | −0.381575 | − | 0.924338i | \(-0.624618\pi\) | ||||
−0.381575 | + | 0.924338i | \(0.624618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6732.34 | − | 11660.8i | −0.437150 | − | 0.757166i | 0.560319 | − | 0.828277i | \(-0.310679\pi\) |
−0.997468 | + | 0.0711115i | \(0.977345\pi\) | |||||||
\(620\) | −6496.00 | − | 11251.4i | −0.420783 | − | 0.728818i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14744.1 | −0.950460 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8775.50 | − | 15199.6i | 0.561632 | − | 0.972775i | ||||
\(626\) | −548.336 | − | 949.745i | −0.0350094 | − | 0.0606381i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6884.66 | + | 11924.6i | −0.437465 | + | 0.757711i | ||||
\(629\) | −11240.9 | −0.712565 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11856.0 | 0.747987 | 0.373994 | − | 0.927431i | \(-0.377988\pi\) | ||||
0.373994 | + | 0.927431i | \(0.377988\pi\) | |||||||
\(632\) | −1888.00 | + | 3270.11i | −0.118830 | + | 0.205820i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3780.00 | − | 6547.15i | −0.236787 | − | 0.410127i | ||||
\(635\) | 8164.11 | − | 14140.7i | 0.510209 | − | 0.883708i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 848.000 | 0.0526217 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −974.819 | − | 1688.44i | −0.0602080 | − | 0.104283i | ||||
\(641\) | −2804.00 | − | 4856.67i | −0.172779 | − | 0.299262i | 0.766611 | − | 0.642111i | \(-0.221941\pi\) |
−0.939390 | + | 0.342849i | \(0.888608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25314.8 | −1.55260 | −0.776298 | − | 0.630366i | \(-0.782905\pi\) | ||||
−0.776298 | + | 0.630366i | \(0.782905\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6960.00 | − | 12055.1i | 0.423897 | − | 0.734211i | ||||
\(647\) | −2924.46 | − | 5065.31i | −0.177701 | − | 0.307786i | 0.763392 | − | 0.645936i | \(-0.223533\pi\) |
−0.941093 | + | 0.338149i | \(0.890199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 670.188 | − | 1160.80i | 0.0405349 | − | 0.0702086i | ||||
\(650\) | −6519.10 | −0.393385 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13296.0 | −0.798637 | ||||||||
\(653\) | 14318.0 | − | 24799.5i | 0.858050 | − | 1.48619i | −0.0157364 | − | 0.999876i | \(-0.505009\pi\) |
0.873786 | − | 0.486310i | \(-0.161657\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20880.0 | + | 36165.2i | 1.24557 | + | 2.15739i | ||||
\(656\) | 2558.90 | − | 4432.14i | 0.152299 | − | 0.263790i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31786.0 | 1.87892 | 0.939459 | − | 0.342662i | \(-0.111328\pi\) | ||||
0.939459 | + | 0.342662i | \(0.111328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4737.01 | − | 8204.74i | −0.278742 | − | 0.482795i | 0.692330 | − | 0.721581i | \(-0.256584\pi\) |
−0.971072 | + | 0.238786i | \(0.923251\pi\) | |||||||
\(662\) | −6260.00 | − | 10842.6i | −0.367525 | − | 0.636573i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1462.23 | 0.0854600 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3180.00 | + | 5507.92i | −0.184603 | + | 0.319741i | ||||
\(668\) | −6092.62 | − | 10552.7i | −0.352890 | − | 0.611223i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9930.97 | + | 17200.9i | −0.572637 | + | 0.991836i | ||||
\(671\) | −1035.75 | −0.0595894 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24986.0 | 1.43111 | 0.715557 | − | 0.698555i | \(-0.246173\pi\) | ||||
0.715557 | + | 0.698555i | \(0.246173\pi\) | |||||||
\(674\) | 3166.00 | − | 5483.67i | 0.180934 | − | 0.313388i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2538.00 | + | 4395.94i | 0.144401 | + | 0.250111i | ||||
\(677\) | −22.8473 | + | 39.5727i | −0.00129704 | + | 0.00224653i | −0.866673 | − | 0.498876i | \(-0.833746\pi\) |
0.865376 | + | 0.501123i | \(0.167080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5568.00 | −0.314004 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −426.483 | − | 738.691i | −0.0239456 | − | 0.0414750i | ||||
\(683\) | −15047.0 | − | 26062.2i | −0.842983 | − | 1.46009i | −0.887361 | − | 0.461075i | \(-0.847464\pi\) |
0.0443782 | − | 0.999015i | \(-0.485869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44719.8 | 2.49439 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2272.00 | − | 3935.22i | 0.125900 | − | 0.218065i | ||||
\(689\) | 8346.89 | + | 14457.2i | 0.461526 | + | 0.799386i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8468.74 | + | 14668.3i | −0.466232 | + | 0.807537i | −0.999256 | − | 0.0385629i | \(-0.987722\pi\) |
0.533025 | + | 0.846100i | \(0.321055\pi\) | |||||||
\(692\) | 13099.1 | 0.719587 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7236.00 | −0.395785 | ||||||||
\(695\) | −1392.00 | + | 2411.01i | −0.0759735 | + | 0.131590i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7308.00 | − | 12657.8i | −0.397145 | − | 0.687876i | ||||
\(698\) | 4478.07 | − | 7756.25i | 0.242833 | − | 0.420600i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7660.00 | 0.412716 | 0.206358 | − | 0.978477i | \(-0.433839\pi\) | ||||
0.206358 | + | 0.978477i | \(0.433839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18734.8 | − | 32449.6i | −1.00512 | − | 1.74091i | ||||
\(704\) | −64.0000 | − | 110.851i | −0.00342627 | − | 0.00593447i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7402.53 | −0.394615 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5327.00 | + | 9226.63i | −0.282172 | + | 0.488736i | −0.971919 | − | 0.235314i | \(-0.924388\pi\) |
0.689748 | + | 0.724050i | \(0.257721\pi\) | |||||||
\(710\) | −11728.3 | − | 20314.0i | −0.619936 | − | 1.07376i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2863.53 | + | 4959.78i | −0.150724 | + | 0.261061i | ||||
\(713\) | 6397.25 | 0.336015 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −928.000 | −0.0485388 | ||||||||
\(716\) | −2508.00 | + | 4343.98i | −0.130906 | + | 0.226735i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −130.000 | − | 225.167i | −0.00675704 | − | 0.0117035i | ||||
\(719\) | −18552.0 | + | 32133.0i | −0.962272 | + | 1.66670i | −0.245500 | + | 0.969396i | \(0.578952\pi\) |
−0.716772 | + | 0.697308i | \(0.754381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 32682.0 | 1.68462 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6153.54 | + | 10658.3i | 0.315877 | + | 0.547114i | ||||
\(725\) | −11342.0 | − | 19644.9i | −0.581009 | − | 1.00634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17760.0 | −0.906027 | −0.453013 | − | 0.891504i | \(-0.649651\pi\) | ||||
−0.453013 | + | 0.891504i | \(0.649651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14848.0 | − | 25717.5i | 0.752807 | − | 1.30390i | ||||
\(731\) | −6488.64 | − | 11238.7i | −0.328305 | − | 0.568641i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1264.22 | − | 2189.69i | 0.0637039 | − | 0.110338i | −0.832414 | − | 0.554154i | \(-0.813042\pi\) |
0.896118 | + | 0.443815i | \(0.146375\pi\) | |||||||
\(734\) | 15597.1 | 0.784332 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 960.000 | 0.0480789 | ||||||||
\(737\) | −652.000 | + | 1129.30i | −0.0325871 | + | 0.0564426i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4078.00 | + | 7063.30i | 0.202993 | + | 0.351594i | 0.949491 | − | 0.313793i | \(-0.101600\pi\) |
−0.746499 | + | 0.665387i | \(0.768267\pi\) | |||||||
\(740\) | −7493.92 | + | 12979.9i | −0.372273 | + | 0.644796i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2910.00 | −0.143684 | −0.0718422 | − | 0.997416i | \(-0.522888\pi\) | ||||
−0.0718422 | + | 0.997416i | \(0.522888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7341.61 | + | 12716.0i | 0.361041 | + | 0.625341i | ||||
\(746\) | 50.0000 | + | 86.6025i | 0.00245393 | + | 0.00425033i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −365.557 | −0.0178691 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6792.00 | + | 11764.1i | −0.330018 | + | 0.571608i | −0.982515 | − | 0.186183i | \(-0.940388\pi\) |
0.652497 | + | 0.757791i | \(0.273722\pi\) | |||||||
\(752\) | −487.409 | − | 844.218i | −0.0236356 | − | 0.0409381i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6458.18 | − | 11185.9i | 0.311927 | − | 0.540273i | ||||
\(755\) | −25710.9 | −1.23936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19054.0 | 0.914834 | 0.457417 | − | 0.889252i | \(-0.348775\pi\) | ||||
0.457417 | + | 0.889252i | \(0.348775\pi\) | |||||||
\(758\) | 4956.00 | − | 8584.04i | 0.237480 | − | 0.411328i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9280.00 | − | 16073.4i | −0.442922 | − | 0.767164i | ||||
\(761\) | 2505.59 | − | 4339.81i | 0.119353 | − | 0.206725i | −0.800159 | − | 0.599789i | \(-0.795251\pi\) |
0.919511 | + | 0.393063i | \(0.128585\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3624.00 | 0.171612 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6762.81 | − | 11713.5i | −0.318995 | − | 0.552515i | ||||
\(767\) | −10208.0 | − | 17680.8i | −0.480560 | − | 0.832354i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21506.9 | −1.00853 | −0.504265 | − | 0.863549i | \(-0.668237\pi\) | ||||
−0.504265 | + | 0.863549i | \(0.668237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −364.000 | + | 630.466i | −0.0169697 | + | 0.0293925i | ||||
\(773\) | 11857.8 | + | 20538.2i | 0.551739 | + | 0.955639i | 0.998149 | + | 0.0608111i | \(0.0193687\pi\) |
−0.446411 | + | 0.894828i | \(0.647298\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11408.4 | + | 19760.0i | −0.528778 | + | 0.915870i | ||||
\(776\) | 2437.05 | 0.112738 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26280.0 | −1.21103 | ||||||||
\(779\) | 24360.0 | − | 42192.8i | 1.12039 | − | 1.94058i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −770.000 | − | 1333.68i | −0.0352788 | − | 0.0611047i | ||||
\(782\) | 1370.84 | − | 2374.36i | 0.0626868 | − | 0.108577i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52432.0 | 2.38392 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18491.1 | + | 32027.5i | 0.837530 | + | 1.45065i | 0.891953 | + | 0.452127i | \(0.149335\pi\) |
−0.0544230 | + | 0.998518i | \(0.517332\pi\) | |||||||
\(788\) | −6936.00 | − | 12013.5i | −0.313559 | − | 0.543101i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14378.6 | 0.647553 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7888.00 | + | 13662.4i | −0.353230 | + | 0.611812i | ||||
\(794\) | −3807.89 | − | 6595.45i | −0.170198 | − | 0.294791i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7798.55 | − | 13507.5i | 0.347252 | − | 0.601458i | ||||
\(797\) | 5346.27 | 0.237609 | 0.118805 | − | 0.992918i | \(-0.462094\pi\) | ||||
0.118805 | + | 0.992918i | \(0.462094\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2784.00 | −0.123268 | ||||||||
\(800\) | −1712.00 | + | 2965.27i | −0.0756604 | + | 0.131048i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4824.00 | − | 8355.41i | −0.212396 | − | 0.367880i | ||||
\(803\) | 974.819 | − | 1688.44i | 0.0428401 | − | 0.0742013i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12992.0 | −0.567771 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4082.05 | − | 7070.33i | −0.177730 | − | 0.307838i | ||||
\(809\) | −9888.00 | − | 17126.5i | −0.429720 | − | 0.744297i | 0.567128 | − | 0.823630i | \(-0.308054\pi\) |
−0.996848 | + | 0.0793325i | \(0.974721\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15962.7 | 0.691153 | 0.345576 | − | 0.938391i | \(-0.387683\pi\) | ||||
0.345576 | + | 0.938391i | \(0.387683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −492.000 | + | 852.169i | −0.0211850 | + | 0.0366935i | ||||
\(815\) | 25314.8 | + | 43846.6i | 1.08802 | + | 1.88451i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21628.8 | − | 37462.2i | 0.926188 | − | 1.60421i | ||||
\(818\) | 10601.2 | 0.453130 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19488.0 | −0.829940 | ||||||||
\(821\) | −14986.0 | + | 25956.5i | −0.637046 | + | 1.10340i | 0.349031 | + | 0.937111i | \(0.386511\pi\) |
−0.986078 | + | 0.166286i | \(0.946823\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19408.0 | + | 33615.6i | 0.822017 | + | 1.42378i | 0.904178 | + | 0.427157i | \(0.140485\pi\) |
−0.0821601 | + | 0.996619i | \(0.526182\pi\) | |||||||
\(824\) | 2315.20 | − | 4010.04i | 0.0978806 | − | 0.169534i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34386.0 | 1.44585 | 0.722925 | − | 0.690926i | \(-0.242797\pi\) | ||||
0.722925 | + | 0.690926i | \(0.242797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6564.80 | + | 11370.6i | 0.275036 | + | 0.476376i | 0.970144 | − | 0.242529i | \(-0.0779769\pi\) |
−0.695108 | + | 0.718905i | \(0.744644\pi\) | |||||||
\(830\) | −2784.00 | − | 4822.03i | −0.116427 | − | 0.201657i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1949.64 | −0.0812398 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23200.0 | + | 40183.6i | −0.961520 | + | 1.66540i | ||||
\(836\) | −609.262 | − | 1055.27i | −0.0252055 | − | 0.0436571i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10540.2 | − | 18256.2i | 0.434494 | − | 0.752566i | ||||
\(839\) | 27051.2 | 1.11313 | 0.556563 | − | 0.830806i | \(-0.312120\pi\) | ||||
0.556563 | + | 0.830806i | \(0.312120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20555.0 | 0.842798 | ||||||||
\(842\) | 4458.00 | − | 7721.48i | 0.182462 | − | 0.316033i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5240.00 | + | 9075.95i | 0.213706 | + | 0.370150i | ||||
\(845\) | 9664.42 | − | 16739.3i | 0.393451 | − | 0.681477i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8768.00 | 0.355064 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4889.33 | + | 8468.56i | 0.197297 | + | 0.341729i | ||||
\(851\) | −3690.00 | − | 6391.27i | −0.148639 | − | 0.257450i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14774.6 | 0.593051 | 0.296526 | − | 0.955025i | \(-0.404172\pi\) | ||||
0.296526 | + | 0.955025i | \(0.404172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6584.00 | − | 11403.8i | 0.262893 | − | 0.455344i | ||||
\(857\) | −9801.50 | − | 16976.7i | −0.390680 | − | 0.676678i | 0.601859 | − | 0.798602i | \(-0.294427\pi\) |
−0.992539 | + | 0.121924i | \(0.961093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6260.17 | − | 10842.9i | 0.248654 | − | 0.430682i | −0.714498 | − | 0.699637i | \(-0.753345\pi\) |
0.963153 | + | 0.268955i | \(0.0866783\pi\) | |||||||
\(860\) | −17303.0 | −0.686080 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32428.0 | −1.28132 | ||||||||
\(863\) | −15387.0 | + | 26651.1i | −0.606929 | + | 1.05123i | 0.384815 | + | 0.922994i | \(0.374265\pi\) |
−0.991743 | + | 0.128238i | \(0.959068\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24940.0 | − | 43197.3i | −0.980330 | − | 1.69798i | ||||
\(866\) | 3594.64 | − | 6226.11i | 0.141052 | − | 0.244309i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 944.000 | 0.0368504 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9930.97 | + | 17200.9i | 0.386335 | + | 0.669152i | ||||
\(872\) | −3928.00 | − | 6803.50i | −0.152545 | − | 0.264215i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9138.93 | 0.353694 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8379.00 | − | 14512.9i | 0.322621 | − | 0.558796i | −0.658407 | − | 0.752662i | \(-0.728769\pi\) |
0.981028 | + | 0.193866i | \(0.0621027\pi\) | |||||||
\(878\) | 8590.59 | + | 14879.3i | 0.330203 | + | 0.571929i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −243.705 | + | 422.109i | −0.00933555 | + | 0.0161696i | ||||
\(881\) | −25208.2 | −0.964002 | −0.482001 | − | 0.876171i | \(-0.660090\pi\) | ||||
−0.482001 | + | 0.876171i | \(0.660090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5468.00 | −0.208395 | −0.104198 | − | 0.994557i | \(-0.533227\pi\) | ||||
−0.104198 | + | 0.994557i | \(0.533227\pi\) | |||||||
\(884\) | −2784.00 | + | 4822.03i | −0.105923 | + | 0.183464i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15006.0 | − | 25991.2i | −0.569003 | − | 0.985542i | ||||
\(887\) | −13525.6 | + | 23427.0i | −0.512002 | + | 0.886813i | 0.487901 | + | 0.872899i | \(0.337763\pi\) |
−0.999903 | + | 0.0139144i | \(0.995571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 21808.0 | 0.821355 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2802.60 | − | 4854.25i | −0.105200 | − | 0.182211i | ||||
\(893\) | −4640.00 | − | 8036.72i | −0.173876 | − | 0.301163i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19100.4 | 0.713357 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1824.00 | + | 3159.26i | −0.0677814 | + | 0.117401i | ||||
\(899\) | −22603.6 | − | 39150.6i | −0.838568 | − | 1.45244i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12520.3 | − | 21685.8i | 0.462944 | − | 0.801843i | ||||
\(902\) | −1279.45 | −0.0472295 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10304.0 | 0.379099 | ||||||||
\(905\) | 23432.0 | − | 40585.4i | 0.860670 | − | 1.49072i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2938.00 | + | 5088.77i | 0.107558 | + | 0.186295i | 0.914780 | − | 0.403952i | \(-0.132364\pi\) |
−0.807223 | + | 0.590247i | \(0.799030\pi\) | |||||||
\(908\) | 7798.55 | − | 13507.5i | 0.285026 | − | 0.493680i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17962.0 | 0.653247 | 0.326623 | − | 0.945155i | \(-0.394089\pi\) | ||||
0.326623 | + | 0.945155i | \(0.394089\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −182.779 | − | 316.582i | −0.00662551 | − | 0.0114757i | ||||
\(914\) | 586.000 | + | 1014.98i | 0.0212070 | + | 0.0367315i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22055.3 | −0.795553 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26712.0 | + | 46266.5i | −0.958811 | + | 1.66071i | −0.233416 | + | 0.972377i | \(0.574991\pi\) |
−0.725395 | + | 0.688333i | \(0.758343\pi\) | |||||||
\(920\) | −1827.79 | − | 3165.82i | −0.0655003 | − | 0.113450i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15399.1 | + | 26672.0i | −0.550046 | + | 0.952707i | ||||
\(923\) | −23456.6 | −0.836493 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26322.0 | 0.935635 | ||||||||
\(926\) | 88.0000 | − | 152.420i | 0.00312296 | − | 0.00540912i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3392.00 | − | 5875.12i | −0.119987 | − | 0.207823i | ||||
\(929\) | 2993.00 | − | 5184.03i | 0.105702 | − | 0.183081i | −0.808323 | − | 0.588739i | \(-0.799624\pi\) |
0.914025 | + | 0.405658i | \(0.132958\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2848.00 | −0.100096 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9748.19 | + | 16884.4i | 0.341510 | + | 0.591513i | ||||
\(935\) | 696.000 | + | 1205.51i | 0.0243440 | + | 0.0421650i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3655.57 | 0.127452 | 0.0637259 | − | 0.997967i | \(-0.479702\pi\) | ||||
0.0637259 | + | 0.997967i | \(0.479702\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1856.00 | + | 3214.69i | −0.0644000 | + | 0.111544i | ||||
\(941\) | −26571.4 | − | 46023.1i | −0.920514 | − | 1.59438i | −0.798621 | − | 0.601834i | \(-0.794437\pi\) |
−0.121893 | − | 0.992543i | \(-0.538897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4797.94 | − | 8310.27i | 0.165686 | − | 0.286977i | ||||
\(944\) | −10723.0 | −0.369708 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1136.00 | −0.0390429 | ||||||||
\(947\) | −5101.00 | + | 8835.19i | −0.175037 | + | 0.303173i | −0.940174 | − | 0.340694i | \(-0.889338\pi\) |
0.765137 | + | 0.643868i | \(0.222671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14848.0 | − | 25717.5i | −0.507889 | − | 0.879689i | ||||
\(950\) | −16297.8 | + | 28228.5i | −0.556599 | + | 0.964058i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8856.00 | −0.301022 | −0.150511 | − | 0.988608i | \(-0.548092\pi\) | ||||
−0.150511 | + | 0.988608i | \(0.548092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6899.89 | − | 11951.0i | −0.233796 | − | 0.404947i | ||||
\(956\) | 5172.00 | + | 8958.17i | 0.174973 | + | 0.303063i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9870.04 | 0.332867 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7840.50 | + | 13580.1i | −0.263184 | + | 0.455847i | ||||
\(962\) | 7493.92 | + | 12979.9i | 0.251158 | + | 0.435018i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4508.54 | − | 7809.02i | 0.150633 | − | 0.260904i | ||||
\(965\) | 2772.14 | 0.0924750 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40760.0 | −1.35548 | −0.677742 | − | 0.735300i | \(-0.737041\pi\) | ||||
−0.677742 | + | 0.735300i | \(0.737041\pi\) | |||||||
\(968\) | 5308.00 | − | 9193.73i | 0.176245 | − | 0.305266i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4640.00 | − | 8036.72i | −0.153589 | − | 0.266024i | ||||
\(971\) | 23091.0 | − | 39994.8i | 0.763158 | − | 1.32183i | −0.178057 | − | 0.984020i | \(-0.556981\pi\) |
0.941215 | − | 0.337808i | \(-0.109685\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1648.00 | −0.0542149 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4142.98 | + | 7175.85i | 0.135875 | + | 0.235342i | ||||
\(977\) | −11680.0 | − | 20230.4i | −0.382473 | − | 0.662463i | 0.608942 | − | 0.793215i | \(-0.291594\pi\) |
−0.991415 | + | 0.130752i | \(0.958261\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1431.77 | 0.0467410 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15426.0 | − | 26718.6i | 0.501287 | − | 0.868254i | ||||
\(983\) | 6275.40 | + | 10869.3i | 0.203616 | + | 0.352672i | 0.949691 | − | 0.313189i | \(-0.101397\pi\) |
−0.746075 | + | 0.665862i | \(0.768064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26411.5 | + | 45746.1i | −0.854356 | + | 1.47979i | ||||
\(986\) | −19374.5 | −0.625771 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18560.0 | −0.597644 | ||||||||
\(989\) | 4260.00 | − | 7378.54i | 0.136967 | − | 0.237233i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9740.00 | + | 16870.2i | 0.312211 | + | 0.540766i | 0.978841 | − | 0.204624i | \(-0.0655970\pi\) |
−0.666630 | + | 0.745389i | \(0.732264\pi\) | |||||||
\(992\) | −3411.87 | + | 5909.53i | −0.109200 | + | 0.189141i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −59392.0 | −1.89231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18262.6 | − | 31631.8i | −0.580123 | − | 1.00480i | −0.995464 | − | 0.0951374i | \(-0.969671\pi\) |
0.415341 | − | 0.909666i | \(-0.363662\pi\) | |||||||
\(998\) | −5844.00 | − | 10122.1i | −0.185359 | − | 0.321052i | ||||
\(999\) | 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.bb.667.1 | 4 | ||
3.2 | odd | 2 | 882.4.g.bh.667.2 | 4 | |||
7.2 | even | 3 | 882.4.a.bf.1.2 | yes | 2 | ||
7.3 | odd | 6 | inner | 882.4.g.bb.361.2 | 4 | ||
7.4 | even | 3 | inner | 882.4.g.bb.361.1 | 4 | ||
7.5 | odd | 6 | 882.4.a.bf.1.1 | yes | 2 | ||
7.6 | odd | 2 | inner | 882.4.g.bb.667.2 | 4 | ||
21.2 | odd | 6 | 882.4.a.x.1.1 | ✓ | 2 | ||
21.5 | even | 6 | 882.4.a.x.1.2 | yes | 2 | ||
21.11 | odd | 6 | 882.4.g.bh.361.2 | 4 | |||
21.17 | even | 6 | 882.4.g.bh.361.1 | 4 | |||
21.20 | even | 2 | 882.4.g.bh.667.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.4.a.x.1.1 | ✓ | 2 | 21.2 | odd | 6 | ||
882.4.a.x.1.2 | yes | 2 | 21.5 | even | 6 | ||
882.4.a.bf.1.1 | yes | 2 | 7.5 | odd | 6 | ||
882.4.a.bf.1.2 | yes | 2 | 7.2 | even | 3 | ||
882.4.g.bb.361.1 | 4 | 7.4 | even | 3 | inner | ||
882.4.g.bb.361.2 | 4 | 7.3 | odd | 6 | inner | ||
882.4.g.bb.667.1 | 4 | 1.1 | even | 1 | trivial | ||
882.4.g.bb.667.2 | 4 | 7.6 | odd | 2 | inner | ||
882.4.g.bh.361.1 | 4 | 21.17 | even | 6 | |||
882.4.g.bh.361.2 | 4 | 21.11 | odd | 6 | |||
882.4.g.bh.667.1 | 4 | 21.20 | even | 2 | |||
882.4.g.bh.667.2 | 4 | 3.2 | odd | 2 |