Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,5,Mod(145,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.145");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bh (of order \(6\), 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: | \(34.7323075962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.145 |
Dual form | 336.5.bh.d.241.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.50000 | − | 2.59808i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −20.7426 | − | 11.9758i | −0.829706 | − | 0.479031i | 0.0240462 | − | 0.999711i | \(-0.492345\pi\) |
−0.853752 | + | 0.520680i | \(0.825678\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 47.1985 | + | 13.1645i | 0.963234 | + | 0.268662i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.5000 | − | 23.3827i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.9853 | + | 84.8450i | 0.404837 | + | 0.701198i | 0.994302 | − | 0.106595i | \(-0.0339949\pi\) |
−0.589465 | + | 0.807794i | \(0.700662\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 104.211i | 0.616636i | 0.951283 | + | 0.308318i | \(0.0997661\pi\) | ||||
−0.951283 | + | 0.308318i | \(0.900234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −124.456 | −0.553137 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 93.2498 | − | 53.8378i | 0.322664 | − | 0.186290i | −0.329916 | − | 0.944010i | \(-0.607020\pi\) |
0.652579 | + | 0.757721i | \(0.273687\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −33.2498 | − | 19.1968i | −0.0921047 | − | 0.0531767i | 0.453240 | − | 0.891388i | \(-0.350268\pi\) |
−0.545345 | + | 0.838212i | \(0.683601\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 246.595 | − | 63.3852i | 0.559173 | − | 0.143731i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −510.749 | + | 884.644i | −0.965500 | + | 1.67229i | −0.257233 | + | 0.966349i | \(0.582811\pi\) |
−0.708266 | + | 0.705945i | \(0.750522\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.6619 | − | 44.4477i | −0.0410590 | − | 0.0711164i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 621.603 | 0.739124 | 0.369562 | − | 0.929206i | \(-0.379508\pi\) | ||||
0.369562 | + | 0.929206i | \(0.379508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1315.61 | − | 759.568i | 1.36900 | − | 0.790393i | 0.378200 | − | 0.925724i | \(-0.376543\pi\) |
0.990800 | + | 0.135331i | \(0.0432097\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 440.868 | + | 254.535i | 0.404837 | + | 0.233733i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −821.367 | − | 838.304i | −0.670503 | − | 0.684330i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 281.118 | − | 486.910i | 0.205345 | − | 0.355669i | −0.744897 | − | 0.667179i | \(-0.767502\pi\) |
0.950243 | + | 0.311511i | \(0.100835\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 270.749 | + | 468.952i | 0.178007 | + | 0.308318i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1023.20i | 0.608684i | 0.952563 | + | 0.304342i | \(0.0984365\pi\) | ||||
−0.952563 | + | 0.304342i | \(0.901563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3382.41 | 1.82932 | 0.914658 | − | 0.404228i | \(-0.132460\pi\) | ||||
0.914658 | + | 0.404228i | \(0.132460\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −560.051 | + | 323.346i | −0.276569 | + | 0.159677i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3416.50 | + | 1972.52i | 1.54663 | + | 0.892945i | 0.998396 | + | 0.0566179i | \(0.0180317\pi\) |
0.548231 | + | 0.836327i | \(0.315302\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2054.39 | + | 1242.69i | 0.855641 | + | 0.517570i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 279.749 | − | 484.540i | 0.107555 | − | 0.186290i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1095.30 | − | 1897.12i | −0.389925 | − | 0.675370i | 0.602514 | − | 0.798108i | \(-0.294166\pi\) |
−0.992439 | + | 0.122738i | \(0.960833\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2346.55i | − | 0.775718i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −199.499 | −0.0614031 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2541.67 | + | 1467.44i | −0.730156 | + | 0.421556i | −0.818479 | − | 0.574536i | \(-0.805182\pi\) |
0.0883234 | + | 0.996092i | \(0.471849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 576.207 | + | 332.673i | 0.154853 | + | 0.0894043i | 0.575424 | − | 0.817855i | \(-0.304837\pi\) |
−0.420571 | + | 0.907259i | \(0.638170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 945.000 | − | 925.907i | 0.238095 | − | 0.233285i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1248.01 | − | 2161.62i | 0.295388 | − | 0.511626i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2962.69 | − | 5131.53i | −0.659989 | − | 1.14314i | −0.980618 | − | 0.195930i | \(-0.937227\pi\) |
0.320629 | − | 0.947205i | \(-0.396106\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5307.86i | 1.11486i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4494.41 | 0.891571 | 0.445785 | − | 0.895140i | \(-0.352924\pi\) | ||||
0.445785 | + | 0.895140i | \(0.352924\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7767.32 | − | 4484.46i | 1.45756 | − | 0.841521i | 0.458666 | − | 0.888609i | \(-0.348327\pi\) |
0.998891 | + | 0.0470879i | \(0.0149941\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −230.957 | − | 133.343i | −0.0410590 | − | 0.0237055i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1195.09 | + | 4649.42i | 0.201567 | + | 0.784183i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5223.41 | + | 9047.22i | −0.836951 | + | 1.44964i | 0.0554805 | + | 0.998460i | \(0.482331\pi\) |
−0.892432 | + | 0.451182i | \(0.851002\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −364.500 | − | 631.333i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1269.28i | 0.184247i | 0.995748 | + | 0.0921234i | \(0.0293654\pi\) | ||||
−0.995748 | + | 0.0921234i | \(0.970635\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2579.00 | −0.356954 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2797.21 | − | 1614.97i | 0.369562 | − | 0.213367i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3121.46 | − | 1802.18i | −0.394074 | − | 0.227519i | 0.289850 | − | 0.957072i | \(-0.406395\pi\) |
−0.683924 | + | 0.729553i | \(0.739728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1371.89 | + | 4918.62i | −0.165667 | + | 0.593965i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3946.83 | − | 6836.11i | 0.456334 | − | 0.790393i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 459.792 | + | 796.383i | 0.0509465 | + | 0.0882419i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1950.53i | 0.207304i | 0.994614 | + | 0.103652i | \(0.0330529\pi\) | ||||
−0.994614 | + | 0.103652i | \(0.966947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2645.21 | 0.269891 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9808.81 | − | 5663.12i | 0.961554 | − | 0.555153i | 0.0649030 | − | 0.997892i | \(-0.479326\pi\) |
0.896651 | + | 0.442738i | \(0.145993\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14141.2 | + | 8164.43i | 1.33294 | + | 0.769576i | 0.985750 | − | 0.168217i | \(-0.0538010\pi\) |
0.347195 | + | 0.937793i | \(0.387134\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5874.13 | − | 1638.39i | −0.532801 | − | 0.148607i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2198.23 | − | 3807.45i | 0.192002 | − | 0.332557i | −0.753912 | − | 0.656976i | \(-0.771835\pi\) |
0.945914 | + | 0.324419i | \(0.105169\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7348.89 | + | 12728.6i | 0.618541 | + | 1.07134i | 0.989752 | + | 0.142796i | \(0.0456093\pi\) |
−0.371211 | + | 0.928548i | \(0.621057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2921.46i | − | 0.237112i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2124.36 | 0.166368 | 0.0831842 | − | 0.996534i | \(-0.473491\pi\) | ||||
0.0831842 | + | 0.996534i | \(0.473491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21188.6 | − | 12233.2i | 1.60216 | − | 0.925008i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2436.74 | + | 1406.85i | 0.178007 | + | 0.102773i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5109.99 | − | 1313.48i | 0.360850 | − | 0.0927533i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2521.38 | − | 4367.17i | 0.172214 | − | 0.298283i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2658.35 | + | 4604.39i | 0.175712 | + | 0.304342i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16199.0i | 1.03674i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8498.07 | −0.526881 | −0.263441 | − | 0.964676i | \(-0.584857\pi\) | ||||
−0.263441 | + | 0.964676i | \(0.584857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15220.8 | − | 8787.75i | 0.914658 | − | 0.528078i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12533.4 | − | 7236.14i | −0.730340 | − | 0.421662i | 0.0882063 | − | 0.996102i | \(-0.471887\pi\) |
−0.818547 | + | 0.574440i | \(0.805220\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1316.62 | − | 1343.77i | −0.0744318 | − | 0.0759666i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1680.15 | + | 2910.11i | −0.0921895 | + | 0.159677i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6427.59 | − | 11132.9i | −0.342458 | − | 0.593154i | 0.642431 | − | 0.766344i | \(-0.277926\pi\) |
−0.984888 | + | 0.173190i | \(0.944593\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5009.46i | 0.259275i | 0.991561 | + | 0.129638i | \(0.0413814\pi\) | ||||
−0.991561 | + | 0.129638i | \(0.958619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20499.0 | 1.03108 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8841.82 | + | 5104.83i | −0.432384 | + | 0.249637i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12893.7 | − | 7444.17i | −0.613255 | − | 0.354063i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12473.4 | + | 254.611i | 0.577230 | + | 0.0117827i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12699.5 | + | 21996.1i | −0.572022 | + | 0.990771i | 0.424336 | + | 0.905505i | \(0.360507\pi\) |
−0.996358 | + | 0.0852664i | \(0.972826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9154.39 | − | 15855.9i | −0.401491 | − | 0.695402i | 0.592415 | − | 0.805633i | \(-0.298174\pi\) |
−0.993906 | + | 0.110230i | \(0.964841\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2907.24i | − | 0.124193i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −36385.6 | −1.51449 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −30522.6 | + | 17622.2i | −1.23829 | + | 0.714926i | −0.968744 | − | 0.248062i | \(-0.920206\pi\) |
−0.269544 | + | 0.962988i | \(0.586873\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9857.70 | − | 5691.35i | −0.389925 | − | 0.225123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −35752.5 | + | 35030.1i | −1.37929 | + | 1.35142i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 72.9693 | − | 126.386i | 0.00274641 | − | 0.00475691i | −0.864649 | − | 0.502377i | \(-0.832459\pi\) |
0.867395 | + | 0.497620i | \(0.165792\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6096.50 | − | 10559.5i | −0.223930 | − | 0.387859i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 31314.1i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17701.0 | 0.619760 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −897.744 | + | 518.313i | −0.0307016 | + | 0.0177256i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −34741.3 | − | 20057.9i | −1.16079 | − | 0.670183i | −0.209298 | − | 0.977852i | \(-0.567118\pi\) |
−0.951494 | + | 0.307669i | \(0.900451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −626.073 | − | 2435.69i | −0.0204432 | − | 0.0795327i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7625.02 | + | 13206.9i | −0.243385 | + | 0.421556i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25077.2 | − | 43435.0i | −0.782661 | − | 1.35561i | −0.930387 | − | 0.366580i | \(-0.880529\pi\) |
0.147726 | − | 0.989028i | \(-0.452805\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 63974.3i | − | 1.95276i | −0.216069 | − | 0.976378i | \(-0.569323\pi\) | ||
0.216069 | − | 0.976378i | \(-0.430677\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3457.24 | 0.103235 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11662.2 | + | 6733.20i | −0.340752 | + | 0.196733i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9135.73 | + | 5274.52i | 0.261252 | + | 0.150834i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1846.92 | − | 6621.76i | 0.0517041 | − | 0.185375i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21384.4 | + | 37039.0i | −0.586180 | + | 1.01529i | 0.408547 | + | 0.912737i | \(0.366036\pi\) |
−0.994727 | + | 0.102557i | \(0.967298\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4386.29 | + | 7597.28i | 0.117756 | + | 0.203959i | 0.918878 | − | 0.394542i | \(-0.129097\pi\) |
−0.801122 | + | 0.598501i | \(0.795763\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 12969.7i | − | 0.341084i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −32825.0 | −0.845808 | −0.422904 | − | 0.906174i | \(-0.638989\pi\) | ||||
−0.422904 | + | 0.906174i | \(0.638989\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22918.7 | − | 13232.1i | 0.578740 | − | 0.334136i | −0.181893 | − | 0.983318i | \(-0.558222\pi\) |
0.760632 | + | 0.649183i | \(0.224889\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26664.2 | − | 15394.6i | −0.659989 | − | 0.381045i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29338.7 | + | 8183.07i | 0.711949 | + | 0.198575i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12253.6 | − | 21223.8i | 0.291578 | − | 0.505028i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13790.2 | + | 23885.4i | 0.321833 | + | 0.557432i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3761.44i | − | 0.0861115i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −67056.3 | −1.50617 | −0.753087 | − | 0.657921i | \(-0.771436\pi\) | ||||
−0.753087 | + | 0.657921i | \(0.771436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20224.8 | − | 11676.8i | 0.445785 | − | 0.257374i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −70160.1 | − | 40506.9i | −1.51779 | − | 0.876299i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 72094.1 | − | 18531.1i | 1.53102 | − | 0.393535i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23302.0 | − | 40360.2i | 0.485852 | − | 0.841521i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5610.52 | + | 9717.70i | 0.114873 | + | 0.198966i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 56260.1i | 1.13133i | 0.824634 | + | 0.565666i | \(0.191381\pi\) | ||||
−0.824634 | + | 0.565666i | \(0.808619\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1385.74 | −0.0273727 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −52955.8 | + | 30574.1i | −1.02769 | + | 0.593337i | −0.916322 | − | 0.400442i | \(-0.868857\pi\) |
−0.111368 | + | 0.993779i | \(0.535523\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29274.9 | + | 16901.9i | 0.558244 | + | 0.322303i | 0.752441 | − | 0.658660i | \(-0.228877\pi\) |
−0.194196 | + | 0.980963i | \(0.562210\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17457.5 | + | 17817.4i | 0.327158 | + | 0.333904i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4343.63 | + | 7523.39i | −0.0800094 | + | 0.138580i | −0.903254 | − | 0.429107i | \(-0.858828\pi\) |
0.823244 | + | 0.567687i | \(0.192162\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −47244.8 | − | 81830.4i | −0.855496 | − | 1.48176i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 54283.3i | 0.966428i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15715.0 | 0.275118 | 0.137559 | − | 0.990494i | \(-0.456074\pi\) | ||||
0.137559 | + | 0.990494i | \(0.456074\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4744.80 | + | 2739.41i | −0.0816928 | + | 0.0471654i | −0.540290 | − | 0.841479i | \(-0.681685\pi\) |
0.458597 | + | 0.888644i | \(0.348352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3280.50 | − | 1894.00i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −27731.4 | − | 50379.5i | −0.461998 | − | 0.839309i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2000.52 | − | 3465.01i | 0.0327906 | − | 0.0567950i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3297.68 | + | 5711.74i | 0.0531875 | + | 0.0921234i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 24350.9i | − | 0.386516i | −0.981148 | − | 0.193258i | \(-0.938095\pi\) | ||
0.981148 | − | 0.193258i | \(-0.0619054\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −100077. | −1.56348 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11605.5 | + | 6700.43i | −0.178477 | + | 0.103044i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10051.7 | + | 5803.37i | 0.152186 | + | 0.0878647i | 0.574159 | − | 0.818744i | \(-0.305329\pi\) |
−0.421973 | + | 0.906608i | \(0.638662\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19678.2 | − | 19280.7i | 0.293350 | − | 0.287424i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8391.64 | − | 14534.7i | 0.123187 | − | 0.213367i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 60333.8 | + | 104501.i | 0.872266 | + | 1.51081i | 0.859646 | + | 0.510889i | \(0.170684\pi\) |
0.0126200 | + | 0.999920i | \(0.495983\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 52468.3i | 0.747145i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18728.8 | −0.262716 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23596.3 | + | 13623.3i | −0.326091 | + | 0.188269i | −0.654104 | − | 0.756404i | \(-0.726954\pi\) |
0.328013 | + | 0.944673i | \(0.393621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 84041.9 | + | 48521.6i | 1.14435 | + | 0.660689i | 0.947503 | − | 0.319746i | \(-0.103598\pi\) |
0.196843 | + | 0.980435i | \(0.436931\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6605.46 | + | 25698.1i | 0.0886294 | + | 0.344806i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2514.11 | − | 4354.57i | 0.0332444 | − | 0.0575811i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14876.4 | − | 25766.7i | −0.193882 | − | 0.335814i | 0.752651 | − | 0.658419i | \(-0.228775\pi\) |
−0.946534 | + | 0.322605i | \(0.895441\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 41016.7i | − | 0.526929i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −122275. | −1.54855 | −0.774276 | − | 0.632849i | \(-0.781886\pi\) | ||||
−0.774276 | + | 0.632849i | \(0.781886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 52568.4 | − | 30350.4i | 0.656374 | − | 0.378958i | −0.134520 | − | 0.990911i | \(-0.542949\pi\) |
0.790894 | + | 0.611953i | \(0.209616\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4138.13 | + | 2389.15i | 0.0509465 | + | 0.0294140i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13469.8 | + | 48293.4i | −0.163531 | + | 0.586305i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −35963.5 | + | 62290.6i | −0.430592 | + | 0.745807i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5067.62 | + | 8777.37i | 0.0598436 | + | 0.103652i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29557.4i | 0.344296i | 0.985071 | + | 0.172148i | \(0.0550707\pi\) | ||||
−0.985071 | + | 0.172148i | \(0.944929\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 70294.7 | 0.807752 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11903.4 | − | 6872.44i | 0.134946 | − | 0.0779109i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −92190.0 | − | 53225.9i | −1.03120 | − | 0.595362i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 159644. | + | 44527.6i | 1.76206 | + | 0.491469i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29426.4 | − | 50968.1i | 0.320518 | − | 0.555153i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7968.04 | − | 13801.0i | −0.0856548 | − | 0.148358i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 107567.i | − | 1.14131i | −0.821191 | − | 0.570654i | \(-0.806690\pi\) | ||
0.821191 | − | 0.570654i | \(-0.193310\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 84847.3 | 0.888630 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −37561.0 | + | 21685.9i | −0.388344 | + | 0.224211i | −0.681442 | − | 0.731872i | \(-0.738647\pi\) |
0.293098 | + | 0.956082i | \(0.405314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −93311.1 | − | 53873.2i | −0.952455 | − | 0.549900i | −0.0586125 | − | 0.998281i | \(-0.518668\pi\) |
−0.893843 | + | 0.448381i | \(0.852001\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30690.2 | + | 7888.66i | −0.309300 | + | 0.0795027i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 77996.9 | − | 135095.i | 0.776174 | − | 1.34437i | −0.157959 | − | 0.987446i | \(-0.550491\pi\) |
0.934133 | − | 0.356926i | \(-0.116175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30449.4 | + | 52739.9i | 0.299225 | + | 0.518272i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 22844.7i | − | 0.221705i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4134.05 | −0.0396251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4631.96 | − | 2674.26i | 0.0438529 | − | 0.0253185i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 66140.0 | + | 38185.9i | 0.618541 | + | 0.357115i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 135286. | + | 138076.i | 1.24986 | + | 1.27564i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20109.4 | − | 34830.4i | 0.183545 | − | 0.317909i | −0.759540 | − | 0.650460i | \(-0.774576\pi\) |
0.943085 | + | 0.332551i | \(0.107909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7590.18 | − | 13146.6i | −0.0684484 | − | 0.118556i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 141922.i | 1.26462i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 90476.4 | 0.796665 | 0.398332 | − | 0.917241i | \(-0.369589\pi\) | ||||
0.398332 | + | 0.917241i | \(0.369589\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9559.61 | − | 5519.25i | 0.0831842 | − | 0.0480264i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 128891. | + | 74415.3i | 1.10844 | + | 0.639961i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 80605.0 | + | 85697.8i | 0.685131 | + | 0.728420i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 63565.7 | − | 110099.i | 0.534054 | − | 0.925008i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16037.2 | + | 27777.3i | 0.133190 | + | 0.230691i | 0.924904 | − | 0.380200i | \(-0.124145\pi\) |
−0.791715 | + | 0.610891i | \(0.790811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 116783.i | 0.958805i | 0.877595 | + | 0.479402i | \(0.159147\pi\) | ||||
−0.877595 | + | 0.479402i | \(0.840853\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14620.5 | 0.118672 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 107957. | − | 62329.1i | 0.866367 | − | 0.500197i | 0.000227639 | − | 1.00000i | \(-0.499928\pi\) |
0.866139 | + | 0.499803i | \(0.166594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −93225.9 | − | 53824.0i | −0.739741 | − | 0.427090i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19582.5 | − | 19186.8i | 0.153649 | − | 0.150545i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 49721.0 | − | 86119.4i | 0.385790 | − | 0.668208i | −0.606088 | − | 0.795397i | \(-0.707262\pi\) |
0.991878 | + | 0.127189i | \(0.0405955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −64423.5 | − | 111585.i | −0.494344 | − | 0.856230i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 26203.0i | − | 0.198856i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −214820. | −1.61246 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −77002.3 | + | 44457.3i | −0.571704 | + | 0.330074i | −0.757830 | − | 0.652452i | \(-0.773740\pi\) |
0.186126 | + | 0.982526i | \(0.440407\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 23925.1 | + | 13813.2i | 0.175712 | + | 0.101447i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26722.0 | − | 103960.i | −0.194143 | − | 0.755298i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 45676.4 | − | 79113.9i | 0.328303 | − | 0.568637i | −0.653872 | − | 0.756605i | \(-0.726857\pi\) |
0.982175 | + | 0.187968i | \(0.0601900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 42086.2 | + | 72895.5i | 0.299280 | + | 0.518368i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 64778.2i | 0.455770i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6328.51 | −0.0440578 | −0.0220289 | − | 0.999757i | \(-0.507013\pi\) | ||||
−0.0220289 | + | 0.999757i | \(0.507013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38241.3 | + | 22078.6i | −0.263441 | + | 0.152097i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11635.9 | + | 6717.98i | 0.0793235 | + | 0.0457974i | 0.539137 | − | 0.842218i | \(-0.318750\pi\) |
−0.459814 | + | 0.888015i | \(0.652084\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30891.0 | − | 110753.i | 0.208406 | − | 0.747198i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 45662.5 | − | 79089.8i | 0.304886 | − | 0.528078i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −44148.1 | − | 76466.8i | −0.291752 | − | 0.505328i | 0.682472 | − | 0.730911i | \(-0.260905\pi\) |
−0.974224 | + | 0.225583i | \(0.927571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 109990.i | 0.719451i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −75200.2 | −0.486894 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 216695. | − | 125109.i | 1.38885 | − | 0.801851i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 187570. | + | 108294.i | 1.19010 | + | 0.687103i | 0.958329 | − | 0.285668i | \(-0.0922155\pi\) |
0.231769 | + | 0.972771i | \(0.425549\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9416.04 | − | 2626.29i | −0.0591456 | − | 0.0164967i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2583.42 | − | 4474.61i | 0.0160659 | − | 0.0278270i | −0.857881 | − | 0.513849i | \(-0.828219\pi\) |
0.873947 | + | 0.486022i | \(0.161553\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 79155.7 | + | 137102.i | 0.487385 | + | 0.844175i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17460.7i | 0.106451i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 55082.5 | 0.332526 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33697.7 | − | 19455.3i | 0.201443 | − | 0.116303i | −0.395885 | − | 0.918300i | \(-0.629562\pi\) |
0.597329 | + | 0.801997i | \(0.296229\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −57848.3 | − | 33398.7i | −0.342458 | − | 0.197718i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −139281. | + | 35801.0i | −0.816567 | + | 0.209891i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15200.6 | − | 26328.1i | 0.0882599 | − | 0.152871i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13015.0 | + | 22542.6i | 0.0748463 | + | 0.129638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 263425.i | 1.50048i | 0.661167 | + | 0.750239i | \(0.270062\pi\) | ||||
−0.661167 | + | 0.750239i | \(0.729938\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16375.1 | −0.0923889 | −0.0461944 | − | 0.998932i | \(-0.514709\pi\) | ||||
−0.0461944 | + | 0.998932i | \(0.514709\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 92245.4 | − | 53257.9i | 0.515542 | − | 0.297648i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4785.93 | − | 2763.16i | −0.0264965 | − | 0.0152978i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22816.6 | + | 23287.1i | 0.125140 | + | 0.127720i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −26525.5 | + | 45943.5i | −0.144128 | + | 0.249637i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −125208. | − | 216867.i | −0.674028 | − | 1.16745i | −0.976752 | − | 0.214373i | \(-0.931229\pi\) |
0.302724 | − | 0.953078i | \(-0.402104\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 91495.1i | 0.488002i | 0.969775 | + | 0.244001i | \(0.0784601\pi\) | ||||
−0.969775 | + | 0.244001i | \(0.921540\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −77362.1 | −0.408837 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33964.6 | − | 19609.5i | 0.177854 | − | 0.102684i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7672.44 | − | 4429.69i | −0.0398111 | − | 0.0229850i | 0.479962 | − | 0.877289i | \(-0.340650\pi\) |
−0.519773 | + | 0.854304i | \(0.673984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 56791.6 | − | 31261.0i | 0.292016 | − | 0.160741i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 150105. | − | 259989.i | 0.764868 | − | 1.32479i | −0.175448 | − | 0.984489i | \(-0.556137\pi\) |
0.940316 | − | 0.340302i | \(-0.110529\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 43164.9 | + | 74763.9i | 0.217977 | + | 0.377548i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 131977.i | 0.660514i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 116866. | 0.579691 | 0.289846 | − | 0.957073i | \(-0.406396\pi\) | ||||
0.289846 | + | 0.957073i | \(0.406396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −86813.2 | + | 50121.6i | −0.426808 | + | 0.246418i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −82389.5 | − | 47567.6i | −0.401491 | − | 0.231801i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 87360.9 | − | 85595.8i | 0.421982 | − | 0.413456i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36872.9 | + | 63865.7i | −0.176553 | + | 0.305798i | −0.940698 | − | 0.339246i | \(-0.889828\pi\) |
0.764145 | + | 0.645045i | \(0.223161\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7553.23 | − | 13082.6i | −0.0358515 | − | 0.0620966i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 88219.1i | 0.415108i | 0.978224 | + | 0.207554i | \(0.0665502\pi\) | ||||
−0.978224 | + | 0.207554i | \(0.933450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −297880. | −1.38957 | −0.694784 | − | 0.719219i | \(-0.744500\pi\) | ||||
−0.694784 | + | 0.719219i | \(0.744500\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −163735. | + | 94532.6i | −0.757245 | + | 0.437196i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 162353. | + | 93734.8i | 0.744436 | + | 0.429801i | 0.823680 | − | 0.567055i | \(-0.191917\pi\) |
−0.0792437 | + | 0.996855i | \(0.525251\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −72280.7 | − | 281203.i | −0.328607 | − | 1.27842i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −91567.7 | + | 158600.i | −0.412763 | + | 0.714926i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 165688. | + | 286980.i | 0.740575 | + | 1.28271i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1970.50i | 0.00873353i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −59146.2 | −0.259950 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 104347. | − | 60244.5i | 0.454786 | − | 0.262571i | −0.255063 | − | 0.966924i | \(-0.582096\pi\) |
0.709849 | + | 0.704354i | \(0.248763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50741.6 | + | 29295.7i | 0.219318 | + | 0.126623i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −69875.2 | + | 250523.i | −0.299522 | + | 1.07387i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23359.1 | − | 40459.1i | 0.0993052 | − | 0.172002i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −133697. | − | 231570.i | −0.563721 | − | 0.976393i | −0.997167 | − | 0.0752136i | \(-0.976036\pi\) |
0.433447 | − | 0.901179i | \(-0.357297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 758.319i | − | 0.00317128i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −178364. | −0.739851 | −0.369926 | − | 0.929061i | \(-0.620617\pi\) | ||||
−0.369926 | + | 0.929061i | \(0.620617\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 57964.3 | − | 33465.7i | 0.238488 | − | 0.137691i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −54868.5 | − | 31678.4i | −0.223930 | − | 0.129286i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 212129. | + | 59166.5i | 0.858792 | + | 0.239532i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 131873. | − | 228411.i | 0.529610 | − | 0.917311i | −0.469794 | − | 0.882776i | \(-0.655672\pi\) |
0.999403 | − | 0.0345349i | \(-0.0109950\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 81356.3 | + | 140913.i | 0.324128 | + | 0.561405i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 480056.i | 1.89739i | 0.316197 | + | 0.948694i | \(0.397594\pi\) | ||||
−0.316197 | + | 0.948694i | \(0.602406\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −271281. | −1.06374 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 79654.4 | − | 45988.5i | 0.309880 | − | 0.178909i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −52192.6 | − | 30133.4i | −0.201453 | − | 0.116309i | 0.395880 | − | 0.918302i | \(-0.370440\pi\) |
−0.597333 | + | 0.801993i | \(0.703773\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 425641. | − | 109407.i | 1.63005 | − | 0.418991i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2693.23 | + | 4664.82i | −0.0102339 | + | 0.0177256i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −195551. | − | 338704.i | −0.737301 | − | 1.27704i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 386497.i | 1.44599i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −208448. | −0.773861 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 248823. | − | 143658.i | 0.916674 | − | 0.529242i | 0.0341018 | − | 0.999418i | \(-0.489143\pi\) |
0.882573 | + | 0.470176i | \(0.155810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 239407. | + | 138222.i | 0.875254 | + | 0.505328i | 0.869091 | − | 0.494653i | \(-0.164705\pi\) |
0.00616355 | + | 0.999981i | \(0.498038\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9145.44 | − | 9334.02i | −0.0331807 | − | 0.0338649i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 81786.9 | − | 141659.i | 0.294484 | − | 0.510062i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −381809. | − | 661313.i | −1.36438 | − | 2.36317i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 79241.5i | 0.281037i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −106629. | −0.375336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −91194.3 | + | 52651.0i | −0.318610 | + | 0.183950i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −225695. | − | 130305.i | −0.782661 | − | 0.451869i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4800.56 | + | 235178.i | −0.0165240 | + | 0.809505i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29832.0 | − | 51670.6i | 0.101927 | − | 0.176542i | −0.810552 | − | 0.585667i | \(-0.800833\pi\) |
0.912478 | + | 0.409125i | \(0.134166\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −166210. | − | 287884.i | −0.563712 | − | 0.976378i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 352034.i | − | 1.18520i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −489585. | −1.63627 | −0.818133 | − | 0.575030i | \(-0.804990\pi\) | ||||
−0.818133 | + | 0.575030i | \(0.804990\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15557.6 | − | 8982.18i | 0.0516176 | − | 0.0298014i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20668.2 | − | 11932.8i | −0.0680767 | − | 0.0393041i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −365639. | + | 358251.i | −1.19564 | + | 1.17149i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −34986.7 | + | 60598.8i | −0.113584 | + | 0.196733i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −254267. | − | 440404.i | −0.819558 | − | 1.41952i | −0.906008 | − | 0.423261i | \(-0.860885\pi\) |
0.0864495 | − | 0.996256i | \(-0.472448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 352486.i | 1.12802i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 54814.4 | 0.174168 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −103765. | + | 59908.5i | −0.327365 | + | 0.189004i | −0.654671 | − | 0.755914i | \(-0.727193\pi\) |
0.327306 | + | 0.944919i | \(0.393859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −44064.8 | − | 25440.8i | −0.138037 | − | 0.0796956i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8892.70 | − | 34596.4i | −0.0276610 | − | 0.107613i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 48829.7 | − | 84575.5i | 0.150820 | − | 0.261228i | −0.780709 | − | 0.624895i | \(-0.785142\pi\) |
0.931529 | + | 0.363667i | \(0.118475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23825.7 | + | 41267.3i | 0.0730757 | + | 0.126571i | 0.900248 | − | 0.435378i | \(-0.143385\pi\) |
−0.827172 | + | 0.561949i | \(0.810052\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 222234.i | 0.676863i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 52427.2 | 0.158570 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −113845. | + | 65728.4i | −0.341949 | + | 0.197425i | −0.661134 | − | 0.750268i | \(-0.729924\pi\) |
0.319184 | + | 0.947693i | \(0.396591\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39476.6 | + | 22791.8i | 0.117756 | + | 0.0679864i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16709.3 | + | 59907.9i | −0.0495002 | + | 0.177473i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 107307. | − | 185861.i | 0.315712 | − | 0.546830i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −33696.3 | − | 58363.8i | −0.0984625 | − | 0.170542i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 135493.i | − | 0.393224i | −0.980481 | − | 0.196612i | \(-0.937006\pi\) | ||
0.980481 | − | 0.196612i | \(-0.0629940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −58325.0 | −0.168122 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −147712. | + | 85281.8i | −0.422904 | + | 0.244164i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 162993. | + | 94104.0i | 0.463510 | + | 0.267608i | 0.713519 | − | 0.700636i | \(-0.247100\pi\) |
−0.250009 | + | 0.968244i | \(0.580433\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −121725. | − | 33951.1i | −0.343831 | − | 0.0959003i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 68756.0 | − | 119089.i | 0.192913 | − | 0.334136i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39202.4 | − | 67900.5i | −0.109259 | − | 0.189243i | 0.806211 | − | 0.591628i | \(-0.201515\pi\) |
−0.915470 | + | 0.402385i | \(0.868181\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 254898.i | 0.705695i | 0.935681 | + | 0.352848i | \(0.114787\pi\) | ||||
−0.935681 | + | 0.352848i | \(0.885213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −159985. | −0.439993 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −104600. | + | 60391.0i | −0.285774 | + | 0.164992i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −489896. | − | 282842.i | −1.32962 | − | 0.767655i | −0.344378 | − | 0.938831i | \(-0.611910\pi\) |
−0.985241 | + | 0.171176i | \(0.945243\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 153284. | − | 39400.4i | 0.413298 | − | 0.106235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −205559. | + | 356038.i | −0.550622 | + | 0.953705i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 207111. | + | 358726.i | 0.551164 | + | 0.954645i | 0.998191 | + | 0.0601241i | \(0.0191496\pi\) |
−0.447026 | + | 0.894521i | \(0.647517\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 127343.i | − | 0.336686i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22896.0 | 0.0601435 | 0.0300717 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300717 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −139564. | + | 80577.4i | −0.364244 | + | 0.210296i | −0.670941 | − | 0.741511i | \(-0.734110\pi\) |
0.306697 | + | 0.951807i | \(0.400776\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 124112. | + | 71656.1i | 0.321833 | + | 0.185811i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −123604. | − | 126152.i | −0.318460 | − | 0.325027i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 177957. | − | 308230.i | 0.455569 | − | 0.789069i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9772.50 | − | 16926.5i | −0.0248583 | − | 0.0430558i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 60539.0i | − | 0.153015i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −489038. | −1.22824 | −0.614121 | − | 0.789212i | \(-0.710489\pi\) | ||||
−0.614121 | + | 0.789212i | \(0.710489\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −301754. | + | 174217.i | −0.753087 | + | 0.434795i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 176272. | + | 101771.i | 0.437156 | + | 0.252392i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −129502. | + | 214091.i | −0.319152 | + | 0.527619i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 60674.5 | − | 105091.i | 0.148595 | − | 0.257374i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −59669.8 | − | 103351.i | −0.145224 | − | 0.251536i | 0.784232 | − | 0.620467i | \(-0.213057\pi\) |
−0.929457 | + | 0.368932i | \(0.879724\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 324224.i | − | 0.784194i | −0.919924 | − | 0.392097i | \(-0.871750\pi\) | ||
0.919924 | − | 0.392097i | \(-0.128250\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −420960. | −1.01186 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 399048. | − | 230391.i | 0.953272 | − | 0.550372i | 0.0591759 | − | 0.998248i | \(-0.481153\pi\) |
0.894096 | + | 0.447876i | \(0.147819\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −249009. | − | 143765.i | −0.591188 | − | 0.341323i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 276278. | − | 270696.i | 0.651905 | − | 0.638734i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 279562. | − | 484216.i | 0.655620 | − | 1.13557i | −0.326118 | − | 0.945329i | \(-0.605741\pi\) |
0.981738 | − | 0.190238i | \(-0.0609260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 173317. | + | 300193.i | 0.403978 | + | 0.699711i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 242161.i | − | 0.561014i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 184372. | 0.424546 | 0.212273 | − | 0.977210i | \(-0.431913\pi\) | ||||
0.212273 | + | 0.977210i | \(0.431913\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 68612.1 | − | 39613.2i | 0.157035 | − | 0.0906645i | −0.419423 | − | 0.907791i | \(-0.637768\pi\) |
0.576458 | + | 0.817126i | \(0.304434\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 50494.6 | + | 29153.1i | 0.114873 | + | 0.0663220i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11217.5 | + | 43641.0i | 0.0253661 | + | 0.0986851i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −317483. | + | 549897.i | −0.713624 | + | 1.23603i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 146168. | + | 253170.i | 0.326588 | + | 0.565666i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 65184.4i | 0.144777i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −482896. | −1.06616 | −0.533082 | − | 0.846064i | \(-0.678966\pi\) | ||||
−0.533082 | + | 0.846064i | \(0.678966\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6235.84 | + | 3600.27i | −0.0136863 | + | 0.00790182i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −329375. | − | 190165.i | −0.718642 | − | 0.414908i | 0.0956105 | − | 0.995419i | \(-0.469520\pi\) |
−0.814253 | + | 0.580511i | \(0.802853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25677.6 | + | 92061.9i | −0.0556949 | + | 0.199683i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −158868. | + | 275167.i | −0.342563 | + | 0.593337i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −171034. | − | 296240.i | −0.366642 | − | 0.635042i | 0.622396 | − | 0.782702i | \(-0.286159\pi\) |
−0.989038 | + | 0.147660i | \(0.952826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 307901.i | 0.656191i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 175649. | 0.372163 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 197701. | − | 114143.i | 0.416458 | − | 0.240442i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −63274.0 | − | 36531.3i | −0.132516 | − | 0.0765084i | 0.432276 | − | 0.901741i | \(-0.357711\pi\) |
−0.564793 | + | 0.825233i | \(0.691044\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 124850. | + | 34822.7i | 0.259969 | + | 0.0725097i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 59992.1 | − | 103909.i | 0.124201 | − | 0.215122i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55086.7 | + | 95413.0i | 0.113392 | + | 0.196400i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 45140.3i | 0.0923869i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −288287. | −0.586664 | −0.293332 | − | 0.956011i | \(-0.594764\pi\) | ||||
−0.293332 | + | 0.956011i | \(0.594764\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18694.2 | + | 10793.1i | −0.0378265 | + | 0.0218392i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −425203. | − | 245491.i | −0.855496 | − | 0.493921i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 537513. | − | 138163.i | 1.07535 | − | 0.276409i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 155256. | − | 268911.i | 0.308856 | − | 0.534954i | −0.669257 | − | 0.743031i | \(-0.733387\pi\) |
0.978112 | + | 0.208078i | \(0.0667206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 141032. | + | 244275.i | 0.278984 | + | 0.483214i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.55179e6i | 3.05250i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 244537. | 0.478335 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 70717.6 | − | 40828.8i | 0.137559 | − | 0.0794198i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8733.60 | − | 5042.35i | −0.0168941 | − | 0.00975383i | 0.491529 | − | 0.870861i | \(-0.336438\pi\) |
−0.508423 | + | 0.861107i | \(0.669771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 559963. | + | 571510.i | 1.07718 | + | 1.09939i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14234.4 | + | 24654.7i | −0.0272309 | + | 0.0471654i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15951.5 | − | 27628.8i | −0.0303477 | − | 0.0525638i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 638552.i | − | 1.20817i | −0.796921 | − | 0.604084i | \(-0.793539\pi\) | ||
0.796921 | − | 0.604084i | \(-0.206461\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 315409. | − | 182101.i | 0.590254 | − | 0.340783i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −715410. | − | 413042.i | −1.33152 | − | 0.768752i | −0.345985 | − | 0.938240i | \(-0.612455\pi\) |
−0.985532 | + | 0.169488i | \(0.945789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −255681. | − | 154659.i | −0.473287 | − | 0.286287i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 290257. | − | 502739.i | 0.534376 | − | 0.925567i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 384995. | + | 666831.i | 0.704962 | + | 1.22103i | 0.966705 | + | 0.255893i | \(0.0823695\pi\) |
−0.261743 | + | 0.965138i | \(0.584297\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 20790.1i | − | 0.0378634i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 611777. | 1.10819 | 0.554097 | − | 0.832452i | \(-0.313064\pi\) | ||||
0.554097 | + | 0.832452i | \(0.313064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 526841. | − | 304172.i | 0.949220 | − | 0.548032i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 29679.1 | + | 17135.2i | 0.0531875 | + | 0.0307078i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 153876. | − | 150767.i | 0.274289 | − | 0.268747i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 185311. | − | 320968.i | 0.328565 | − | 0.569091i | −0.653663 | − | 0.756786i | \(-0.726768\pi\) |
0.982227 | + | 0.187695i | \(0.0601018\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −63265.5 | − | 109579.i | −0.111578 | − | 0.193258i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 438523.i | 0.769305i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 298778. | 0.521384 | 0.260692 | − | 0.965422i | \(-0.416049\pi\) | ||||
0.260692 | + | 0.965422i | \(0.416049\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −450346. | + | 260007.i | −0.781740 | + | 0.451338i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 695541. | + | 401571.i | 1.20103 | + | 0.693414i | 0.960784 | − | 0.277298i | \(-0.0894389\pi\) |
0.240245 | + | 0.970712i | \(0.422772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 179291. | + | 697517.i | 0.307970 | + | 1.19813i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −34816.4 | + | 60303.8i | −0.0594924 | + | 0.103044i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −152924. | − | 264871.i | −0.259946 | − | 0.450240i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 452541.i | − | 0.765253i | −0.923903 | − | 0.382626i | \(-0.875020\pi\) | ||
0.923903 | − | 0.382626i | \(-0.124980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60310.4 | 0.101457 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 908057. | − | 524267.i | 1.51969 | − | 0.877392i | 0.519957 | − | 0.854193i | \(-0.325948\pi\) |
0.999731 | − | 0.0231996i | \(-0.00738531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −67522.1 | − | 38983.9i | −0.112420 | − | 0.0649056i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 38459.5 | − | 137889.i | 0.0637032 | − | 0.228395i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19642.1 | − | 34021.1i | 0.0323678 | − | 0.0560626i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 220160. | + | 381328.i | 0.360941 | + | 0.625168i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 87208.5i | − | 0.142244i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 844159. | 1.36989 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −169712. | + | 97983.5i | −0.274009 | + | 0.158199i | −0.630708 | − | 0.776020i | \(-0.717235\pi\) |
0.356699 | + | 0.934219i | \(0.383902\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 543004. | + | 313504.i | 0.872266 | + | 0.503603i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 100266. | + | 27966.0i | 0.160252 | + | 0.0446970i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34668.4 | + | 60047.4i | −0.0551299 | + | 0.0954877i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 136317. | + | 236107.i | 0.215682 | + | 0.373572i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 66453.8i | − | 0.104617i | −0.998631 | − | 0.0523086i | \(-0.983342\pi\) | ||
0.998631 | − | 0.0523086i | \(-0.0166579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 424784. | 0.665387 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −84279.5 | + | 48658.8i | −0.131358 | + | 0.0758397i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 760969. | + | 439346.i | 1.18015 | + | 0.681358i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.16111e6 | − | 298454.i | 1.79177 | − | 0.460559i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −70788.8 | + | 122610.i | −0.108697 | + | 0.188269i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41152.3 | − | 71277.9i | −0.0628777 | − | 0.108907i | 0.832873 | − | 0.553464i | \(-0.186694\pi\) |
−0.895751 | + | 0.444557i | \(0.853361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 469097.i | 0.713215i | 0.934254 | + | 0.356608i | \(0.116067\pi\) | ||||
−0.934254 | + | 0.356608i | \(0.883933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 504252. | 0.762898 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3027.15 | + | 1747.73i | −0.00455742 | + | 0.00263123i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −112464. | − | 64931.3i | −0.168489 | − | 0.0972769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 96490.1 | + | 98479.8i | 0.143852 | + | 0.146818i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2689.76 | − | 4658.80i | 0.00399050 | − | 0.00691174i | −0.864023 | − | 0.503452i | \(-0.832063\pi\) |
0.868014 | + | 0.496540i | \(0.165396\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −484903. | − | 839877.i | −0.715905 | − | 1.23998i | −0.962609 | − | 0.270893i | \(-0.912681\pi\) |
0.246704 | − | 0.969091i | \(-0.420652\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 26127.4i | − | 0.0383874i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −838747. | −1.22637 | −0.613183 | − | 0.789941i | \(-0.710111\pi\) | ||||
−0.613183 | + | 0.789941i | \(0.710111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −765309. | + | 441852.i | −1.11360 | + | 0.642935i | −0.939759 | − | 0.341839i | \(-0.888950\pi\) |
−0.173838 | + | 0.984774i | \(0.555617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −133888. | − | 77300.0i | −0.193882 | − | 0.111938i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 258475. | + | 5276.10i | 0.372502 | + | 0.00760367i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 375010. | − | 649536.i | 0.537861 | − | 0.931602i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −106564. | − | 184575.i | −0.152111 | − | 0.263464i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1.12626e6i | − | 1.59998i | −0.600011 | − | 0.799992i | \(-0.704837\pi\) | ||
0.600011 | − | 0.799992i | \(-0.295163\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −320891. | −0.453696 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −550238. | + | 317680.i | −0.774276 | + | 0.447028i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −367165. | − | 211983.i | −0.514218 | − | 0.296884i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 176497. | − | 172931.i | 0.246020 | − | 0.241049i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 157705. | − | 273153.i | 0.218791 | − | 0.378958i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 287161. | + | 497378.i | 0.396522 | + | 0.686796i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 805486.i | − | 1.10703i | −0.832839 | − | 0.553516i | \(-0.813286\pi\) | ||
0.832839 | − | 0.553516i | \(-0.186714\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24828.8 | 0.0339643 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −849118. | + | 490238.i | −1.15613 | + | 0.667491i | −0.950373 | − | 0.311112i | \(-0.899299\pi\) |
−0.205756 | + | 0.978603i | \(0.565965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 375665. | + | 216890.i | 0.509113 | + | 0.293936i | 0.732469 | − | 0.680800i | \(-0.238368\pi\) |
−0.223356 | + | 0.974737i | \(0.571701\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 64855.6 | + | 252316.i | 0.0874865 | + | 0.340360i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −151578. | + | 262542.i | −0.203524 | + | 0.352514i | −0.949661 | − | 0.313278i | \(-0.898573\pi\) |
0.746137 | + | 0.665792i | \(0.231906\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 480418. | + | 832108.i | 0.642077 | + | 1.11211i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 373744.i | 0.497205i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.02348e6 | −1.35532 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 534765. | − | 308747.i | 0.704898 | − | 0.406973i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 45608.6 | + | 26332.1i | 0.0598436 | + | 0.0345507i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −213251. | + | 764568.i | −0.278532 | + | 0.998619i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −177500. | + | 307439.i | −0.230781 | + | 0.399724i | −0.958038 | − | 0.286641i | \(-0.907461\pi\) |
0.727257 | + | 0.686365i | \(0.240795\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 76792.5 | + | 133008.i | 0.0993896 | + | 0.172148i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 320002.i | 0.412288i | 0.978522 | + | 0.206144i | \(0.0660915\pi\) | ||||
−0.978522 | + | 0.206144i | \(0.933909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.08605e6 | 1.39293 | 0.696467 | − | 0.717589i | \(-0.254754\pi\) | ||||
0.696467 | + | 0.717589i | \(0.254754\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 316326. | − | 182631.i | 0.403876 | − | 0.233178i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.11218e6 | − | 642117.i | −1.41360 | − | 0.816144i | −0.417878 | − | 0.908503i | \(-0.637226\pi\) |
−0.995726 | + | 0.0923591i | \(0.970559\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −401096. | − | 111872.i | −0.507510 | − | 0.141553i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35710.3 | − | 61852.0i | 0.0449819 | − | 0.0779109i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −75731.9 | − | 131171.i | −0.0949677 | − | 0.164489i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.20128e6i | 1.49967i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −553140. | −0.687465 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 817787. | − | 472150.i | 1.01186 | − | 0.584198i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −204273. | − | 117937.i | −0.251629 | − | 0.145278i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 834086. | − | 214394.i | 1.02291 | − | 0.262929i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −766141. | + | 1.32699e6i | −0.935430 | + | 1.62021i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24217.8 | + | 41946.4i | 0.0294388 | + | 0.0509894i | 0.880369 | − | 0.474289i | \(-0.157295\pi\) |
−0.850931 | + | 0.525278i | \(0.823961\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 305808.i | − | 0.370102i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −727675. | −0.876801 | −0.438400 | − | 0.898780i | \(-0.644455\pi\) | ||||
−0.438400 | + | 0.898780i | \(0.644455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −107692. | + | 62175.8i | −0.129194 | + | 0.0745899i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −71712.3 | − | 41403.1i | −0.0856548 | − | 0.0494528i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −496296. | − | 506530.i | −0.590204 | − | 0.602375i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43858.0 | − | 75964.2i | 0.0519299 | − | 0.0899452i | −0.838892 | − | 0.544298i | \(-0.816796\pi\) |
0.890822 | + | 0.454353i | \(0.150129\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −279468. | − | 484052.i | −0.329467 | − | 0.570654i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 468369.i | 0.549775i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28856.1 | −0.0337251 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 381813. | − | 220440.i | 0.444315 | − | 0.256525i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 781079. | + | 450956.i | 0.905032 | + | 0.522520i | 0.878829 | − | 0.477136i | \(-0.158325\pi\) |
0.0262024 | + | 0.999657i | \(0.491659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44452.6 | − | 80756.7i | −0.0512859 | − | 0.0931707i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −112683. | + | 195173.i | −0.129448 | + | 0.224211i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −126333. | − | 218815.i | −0.144508 | − | 0.250296i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.24186e6i | − | 1.41447i | −0.706978 | − | 0.707236i | \(-0.749942\pi\) | ||
0.706978 | − | 0.707236i | \(-0.250058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −559867. | −0.634970 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 369139. | − | 213122.i | 0.416879 | − | 0.240685i | −0.276862 | − | 0.960910i | \(-0.589294\pi\) |
0.693741 | + | 0.720224i | \(0.255961\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −905165. | − | 522598.i | −1.01790 | − | 0.587684i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −117611. | + | 115235.i | −0.131699 | + | 0.129038i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13665.2 | − | 23668.9i | 0.0152376 | − | 0.0263923i | −0.858306 | − | 0.513138i | \(-0.828483\pi\) |
0.873544 | + | 0.486746i | \(0.161816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 467333. | + | 809444.i | 0.518912 | + | 0.898782i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 810568.i | − | 0.896248i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.30093e6 | 1.43242 | 0.716208 | − | 0.697887i | \(-0.245876\pi\) | ||||
0.716208 | + | 0.697887i | \(0.245876\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 887140. | − | 512190.i | 0.972714 | − | 0.561597i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 274045. | + | 158220.i | 0.299225 | + | 0.172757i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −156814. | − | 610072.i | −0.170509 | − | 0.663352i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 692125. | − | 1.19880e6i | 0.749442 | − | 1.29807i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −59352.3 | − | 102801.i | −0.0640007 | − | 0.110852i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 210117.i | − | 0.225635i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −463079. | −0.495225 | −0.247612 | − | 0.968859i | \(-0.579646\pi\) | ||||
−0.247612 | + | 0.968859i | \(0.579646\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18603.2 | + | 10740.6i | −0.0198125 | + | 0.0114388i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54723.1 | − | 31594.4i | −0.0580406 | − | 0.0335098i | 0.470699 | − | 0.882294i | \(-0.344002\pi\) |
−0.528739 | + | 0.848784i | \(0.677335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −65946.8 | + | 236439.i | −0.0696575 | + | 0.249743i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13895.9 | − | 24068.4i | 0.0146176 | − | 0.0253185i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −719497. | − | 1.24621e6i | −0.753772 | − | 1.30557i | −0.945982 | − | 0.324218i | \(-0.894899\pi\) |
0.192210 | − | 0.981354i | \(-0.438434\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 353121.i | − | 0.368432i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 396840. | 0.412361 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −346926. | + | 200298.i | −0.359030 | + | 0.207286i | −0.668655 | − | 0.743573i | \(-0.733130\pi\) |
0.309625 | + | 0.950859i | \(0.399796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 680877. | + | 393104.i | 0.701772 | + | 0.405168i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 967521. | + | 269858.i | 0.993176 | + | 0.277014i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.72756e6 | + | 2.99223e6i | −1.76620 | + | 3.05916i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 99274.5 | + | 171949.i | 0.101086 | + | 0.175086i | 0.912132 | − | 0.409896i | \(-0.134435\pi\) |
−0.811046 | + | 0.584982i | \(0.801102\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 208983.i | − | 0.211939i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −633858. | −0.640245 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 792228. | − | 457393.i | 0.797003 | − | 0.460150i | −0.0454194 | − | 0.998968i | \(-0.514462\pi\) |
0.842422 | + | 0.538818i | \(0.181129\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −68311.6 | − | 39439.7i | −0.0684484 | − | 0.0395187i |
(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 | 336.5.bh.d.145.1 | 4 | ||
4.3 | odd | 2 | 42.5.g.a.19.2 | ✓ | 4 | ||
7.3 | odd | 6 | inner | 336.5.bh.d.241.1 | 4 | ||
12.11 | even | 2 | 126.5.n.b.19.1 | 4 | |||
28.3 | even | 6 | 42.5.g.a.31.2 | yes | 4 | ||
28.11 | odd | 6 | 294.5.g.c.31.2 | 4 | |||
28.19 | even | 6 | 294.5.c.a.97.2 | 4 | |||
28.23 | odd | 6 | 294.5.c.a.97.1 | 4 | |||
28.27 | even | 2 | 294.5.g.c.19.2 | 4 | |||
84.23 | even | 6 | 882.5.c.a.685.3 | 4 | |||
84.47 | odd | 6 | 882.5.c.a.685.4 | 4 | |||
84.59 | odd | 6 | 126.5.n.b.73.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.5.g.a.19.2 | ✓ | 4 | 4.3 | odd | 2 | ||
42.5.g.a.31.2 | yes | 4 | 28.3 | even | 6 | ||
126.5.n.b.19.1 | 4 | 12.11 | even | 2 | |||
126.5.n.b.73.1 | 4 | 84.59 | odd | 6 | |||
294.5.c.a.97.1 | 4 | 28.23 | odd | 6 | |||
294.5.c.a.97.2 | 4 | 28.19 | even | 6 | |||
294.5.g.c.19.2 | 4 | 28.27 | even | 2 | |||
294.5.g.c.31.2 | 4 | 28.11 | odd | 6 | |||
336.5.bh.d.145.1 | 4 | 1.1 | even | 1 | trivial | ||
336.5.bh.d.241.1 | 4 | 7.3 | odd | 6 | inner | ||
882.5.c.a.685.3 | 4 | 84.23 | even | 6 | |||
882.5.c.a.685.4 | 4 | 84.47 | odd | 6 |