Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,3,Mod(701,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.q (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: | \(30.8992619785\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1079.3 | ||
Root | \(-1.00781 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1079 |
Dual form | 1134.3.q.c.701.3 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 0.707107i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | −5.25600 | + | 3.03455i | −1.05120 | + | 0.606910i | −0.922985 | − | 0.384836i | \(-0.874258\pi\) |
−0.128214 | + | 0.991746i | \(0.540925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32288 | − | 2.29129i | 0.188982 | − | 0.327327i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.58301 | −0.858301 | ||||||||
\(11\) | 10.5120 | + | 6.06910i | 0.955636 | + | 0.551736i | 0.894827 | − | 0.446413i | \(-0.147299\pi\) |
0.0608086 | + | 0.998149i | \(0.480632\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.29150 | + | 16.0934i | 0.714731 | + | 1.23795i | 0.963063 | + | 0.269275i | \(0.0867842\pi\) |
−0.248332 | + | 0.968675i | \(0.579882\pi\) | |||||||
\(14\) | 3.24037 | − | 1.87083i | 0.231455 | − | 0.133631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | − | 10.9015i | − | 0.641262i | −0.947204 | − | 0.320631i | \(-0.896105\pi\) | ||
0.947204 | − | 0.320631i | \(-0.103895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.0000 | 1.05263 | 0.526316 | − | 0.850289i | \(-0.323573\pi\) | ||||
0.526316 | + | 0.850289i | \(0.323573\pi\) | |||||||
\(20\) | −10.5120 | − | 6.06910i | −0.525600 | − | 0.303455i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.58301 | + | 14.8662i | 0.390137 | + | 0.675736i | ||||
\(23\) | −10.5120 | + | 6.06910i | −0.457043 | + | 0.263874i | −0.710800 | − | 0.703394i | \(-0.751667\pi\) |
0.253757 | + | 0.967268i | \(0.418334\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.91699 | − | 10.2485i | 0.236680 | − | 0.409941i | ||||
\(26\) | 26.2803i | 1.01078i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.29150 | 0.188982 | ||||||||
\(29\) | −36.2316 | − | 20.9183i | −1.24937 | − | 0.721322i | −0.278384 | − | 0.960470i | \(-0.589799\pi\) |
−0.970983 | + | 0.239148i | \(0.923132\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.5830 | − | 21.7944i | −0.405903 | − | 0.703045i | 0.588523 | − | 0.808481i | \(-0.299710\pi\) |
−0.994426 | + | 0.105435i | \(0.966376\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.70850 | − | 13.3515i | 0.226721 | − | 0.392691i | ||||
\(35\) | 16.0573i | 0.458781i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.0000 | 1.02703 | 0.513514 | − | 0.858082i | \(-0.328344\pi\) | ||||
0.513514 | + | 0.858082i | \(0.328344\pi\) | |||||||
\(38\) | 24.4949 | + | 14.1421i | 0.644603 | + | 0.372161i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.58301 | − | 14.8662i | −0.214575 | − | 0.371655i | ||||
\(41\) | −52.5103 | + | 30.3169i | −1.28074 | + | 0.739435i | −0.976984 | − | 0.213314i | \(-0.931574\pi\) |
−0.303756 | + | 0.952750i | \(0.598241\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −41.7490 | + | 72.3114i | −0.970907 | + | 1.68166i | −0.278079 | + | 0.960558i | \(0.589698\pi\) |
−0.692828 | + | 0.721103i | \(0.743636\pi\) | |||||||
\(44\) | 24.2764i | 0.551736i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.1660 | −0.373174 | ||||||||
\(47\) | 14.6969 | + | 8.48528i | 0.312701 | + | 0.180538i | 0.648134 | − | 0.761526i | \(-0.275549\pi\) |
−0.335434 | + | 0.942064i | \(0.608883\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | − | 6.06218i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 14.4936 | − | 8.36789i | 0.289872 | − | 0.167358i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −18.5830 | + | 32.1867i | −0.357365 | + | 0.618975i | ||||
\(53\) | 94.0424i | 1.77439i | 0.461399 | + | 0.887193i | \(0.347348\pi\) | ||||
−0.461399 | + | 0.887193i | \(0.652652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −73.6680 | −1.33942 | ||||||||
\(56\) | 6.48074 | + | 3.74166i | 0.115728 | + | 0.0668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −29.5830 | − | 51.2393i | −0.510052 | − | 0.883436i | ||||
\(59\) | −50.4179 | + | 29.1088i | −0.854540 | + | 0.493369i | −0.862180 | − | 0.506602i | \(-0.830901\pi\) |
0.00764008 | + | 0.999971i | \(0.497568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.83399 | + | 13.5689i | −0.128426 | + | 0.222440i | −0.923067 | − | 0.384639i | \(-0.874326\pi\) |
0.794641 | + | 0.607080i | \(0.207659\pi\) | |||||||
\(62\) | − | 35.5901i | − | 0.574034i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −97.6722 | − | 56.3911i | −1.50265 | − | 0.867555i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66.3320 | + | 114.890i | 0.990030 | + | 1.71478i | 0.617000 | + | 0.786964i | \(0.288348\pi\) |
0.373031 | + | 0.927819i | \(0.378319\pi\) | |||||||
\(68\) | 18.8819 | − | 10.9015i | 0.277675 | − | 0.160316i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.3542 | + | 19.6661i | −0.162204 | + | 0.280945i | ||||
\(71\) | − | 12.1382i | − | 0.170961i | −0.996340 | − | 0.0854803i | \(-0.972758\pi\) | ||
0.996340 | − | 0.0854803i | \(-0.0272425\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76.9150 | −1.05363 | −0.526815 | − | 0.849980i | \(-0.676614\pi\) | ||||
−0.526815 | + | 0.849980i | \(0.676614\pi\) | |||||||
\(74\) | 46.5403 | + | 26.8701i | 0.628923 | + | 0.363109i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.0000 | + | 34.6410i | 0.263158 | + | 0.455803i | ||||
\(77\) | 27.8121 | − | 16.0573i | 0.361196 | − | 0.208537i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.8340 | + | 29.1573i | −0.213088 | + | 0.369080i | −0.952680 | − | 0.303976i | \(-0.901686\pi\) |
0.739591 | + | 0.673056i | \(0.235019\pi\) | |||||||
\(80\) | − | 24.2764i | − | 0.303455i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −85.7490 | −1.04572 | ||||||||
\(83\) | 52.4607 | + | 30.2882i | 0.632057 | + | 0.364918i | 0.781548 | − | 0.623845i | \(-0.214430\pi\) |
−0.149491 | + | 0.988763i | \(0.547764\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 33.0810 | + | 57.2980i | 0.389189 | + | 0.674095i | ||||
\(86\) | −102.264 | + | 59.0420i | −1.18911 | + | 0.686535i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −17.1660 | + | 29.7324i | −0.195068 | + | 0.337868i | ||||
\(89\) | − | 4.77506i | − | 0.0536523i | −0.999640 | − | 0.0268262i | \(-0.991460\pi\) | ||
0.999640 | − | 0.0268262i | \(-0.00854006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.1660 | 0.540286 | ||||||||
\(92\) | −21.0240 | − | 12.1382i | −0.228522 | − | 0.131937i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.0000 | + | 20.7846i | 0.127660 | + | 0.221113i | ||||
\(95\) | −105.120 | + | 60.6910i | −1.10653 | + | 0.638853i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 94.2065 | − | 163.170i | 0.971201 | − | 1.68217i | 0.279261 | − | 0.960215i | \(-0.409910\pi\) |
0.691940 | − | 0.721955i | \(-0.256756\pi\) | |||||||
\(98\) | − | 9.89949i | − | 0.101015i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 23.6680 | 0.236680 | ||||||||
\(101\) | −92.4162 | − | 53.3565i | −0.915012 | − | 0.528282i | −0.0329716 | − | 0.999456i | \(-0.510497\pi\) |
−0.882040 | + | 0.471174i | \(0.843830\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −65.7490 | − | 113.881i | −0.638340 | − | 1.10564i | −0.985797 | − | 0.167941i | \(-0.946288\pi\) |
0.347457 | − | 0.937696i | \(-0.387045\pi\) | |||||||
\(104\) | −45.5189 | + | 26.2803i | −0.437682 | + | 0.252696i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −66.4980 | + | 115.178i | −0.627340 | + | 1.08658i | ||||
\(107\) | 82.3793i | 0.769900i | 0.922937 | + | 0.384950i | \(0.125781\pi\) | ||||
−0.922937 | + | 0.384950i | \(0.874219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 33.8301 | 0.310367 | 0.155184 | − | 0.987886i | \(-0.450403\pi\) | ||||
0.155184 | + | 0.987886i | \(0.450403\pi\) | |||||||
\(110\) | −90.2245 | − | 52.0911i | −0.820223 | − | 0.473556i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.29150 | + | 9.16515i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | −24.6982 | + | 14.2595i | −0.218568 | + | 0.126190i | −0.605287 | − | 0.796007i | \(-0.706942\pi\) |
0.386719 | + | 0.922198i | \(0.373608\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 36.8340 | − | 63.7983i | 0.320296 | − | 0.554768i | ||||
\(116\) | − | 83.6734i | − | 0.721322i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −82.3320 | −0.697729 | ||||||||
\(119\) | −24.9784 | − | 14.4213i | −0.209902 | − | 0.121187i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.1680 | + | 22.8076i | 0.108826 | + | 0.188493i | ||||
\(122\) | −19.1893 | + | 11.0789i | −0.157289 | + | 0.0908109i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 25.1660 | − | 43.5888i | 0.202952 | − | 0.351523i | ||||
\(125\) | − | 79.9059i | − | 0.639247i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 129.668 | 1.02101 | 0.510504 | − | 0.859875i | \(-0.329459\pi\) | ||||
0.510504 | + | 0.859875i | \(0.329459\pi\) | |||||||
\(128\) | −9.79796 | − | 5.65685i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −79.7490 | − | 138.129i | −0.613454 | − | 1.06253i | ||||
\(131\) | −128.187 | + | 74.0087i | −0.978525 | + | 0.564952i | −0.901824 | − | 0.432103i | \(-0.857772\pi\) |
−0.0767004 | + | 0.997054i | \(0.524438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.4575 | − | 45.8258i | 0.198929 | − | 0.344555i | ||||
\(134\) | 187.615i | 1.40011i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 30.8340 | 0.226721 | ||||||||
\(137\) | 66.6469 | + | 38.4786i | 0.486474 | + | 0.280866i | 0.723111 | − | 0.690732i | \(-0.242712\pi\) |
−0.236637 | + | 0.971598i | \(0.576045\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −108.664 | − | 188.212i | −0.781756 | − | 1.35404i | −0.930918 | − | 0.365228i | \(-0.880991\pi\) |
0.149162 | − | 0.988813i | \(-0.452342\pi\) | |||||||
\(140\) | −27.8121 | + | 16.0573i | −0.198658 | + | 0.114695i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.58301 | − | 14.8662i | 0.0604437 | − | 0.104692i | ||||
\(143\) | 225.564i | 1.57737i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 253.911 | 1.75111 | ||||||||
\(146\) | −94.2013 | − | 54.3871i | −0.645214 | − | 0.372515i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 38.0000 | + | 65.8179i | 0.256757 | + | 0.444716i | ||||
\(149\) | 140.231 | − | 80.9623i | 0.941147 | − | 0.543371i | 0.0508272 | − | 0.998707i | \(-0.483814\pi\) |
0.890320 | + | 0.455336i | \(0.150481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 46.5830 | − | 80.6841i | 0.308497 | − | 0.534332i | −0.669537 | − | 0.742779i | \(-0.733507\pi\) |
0.978034 | + | 0.208447i | \(0.0668408\pi\) | |||||||
\(152\) | 56.5685i | 0.372161i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 45.4170 | 0.294916 | ||||||||
\(155\) | 132.272 | + | 76.3675i | 0.853371 | + | 0.492694i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 92.4980 | + | 160.211i | 0.589159 | + | 1.02045i | 0.994343 | + | 0.106219i | \(0.0338743\pi\) |
−0.405183 | + | 0.914235i | \(0.632792\pi\) | |||||||
\(158\) | −41.2347 | + | 23.8069i | −0.260979 | + | 0.150676i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.1660 | − | 29.7324i | 0.107288 | − | 0.185828i | ||||
\(161\) | 32.1147i | 0.199470i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 86.9961 | 0.533718 | 0.266859 | − | 0.963736i | \(-0.414014\pi\) | ||||
0.266859 | + | 0.963736i | \(0.414014\pi\) | |||||||
\(164\) | −105.021 | − | 60.6337i | −0.640370 | − | 0.369718i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 42.8340 | + | 74.1906i | 0.258036 | + | 0.446932i | ||||
\(167\) | 52.4607 | − | 30.2882i | 0.314136 | − | 0.181366i | −0.334640 | − | 0.942346i | \(-0.608615\pi\) |
0.648776 | + | 0.760980i | \(0.275281\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −88.1640 | + | 152.705i | −0.521681 | + | 0.903578i | ||||
\(170\) | 93.5673i | 0.550396i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −166.996 | −0.970907 | ||||||||
\(173\) | −140.791 | − | 81.2858i | −0.813822 | − | 0.469860i | 0.0344594 | − | 0.999406i | \(-0.489029\pi\) |
−0.848281 | + | 0.529546i | \(0.822362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.6549 | − | 27.1151i | −0.0894566 | − | 0.154943i | ||||
\(176\) | −42.0480 | + | 24.2764i | −0.238909 | + | 0.137934i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.37648 | − | 5.84823i | 0.0189690 | − | 0.0328552i | ||||
\(179\) | 223.091i | 1.24632i | 0.782095 | + | 0.623159i | \(0.214151\pi\) | ||||
−0.782095 | + | 0.623159i | \(0.785849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 188.915 | 1.04373 | 0.521865 | − | 0.853028i | \(-0.325237\pi\) | ||||
0.521865 | + | 0.853028i | \(0.325237\pi\) | |||||||
\(182\) | 60.2158 | + | 34.7656i | 0.330856 | + | 0.191020i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.1660 | − | 29.7324i | −0.0932935 | − | 0.161589i | ||||
\(185\) | −199.728 | + | 115.313i | −1.07961 | + | 0.623313i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 66.1621 | − | 114.596i | 0.353808 | − | 0.612813i | ||||
\(188\) | 33.9411i | 0.180538i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −171.660 | −0.903474 | ||||||||
\(191\) | 197.486 | + | 114.019i | 1.03396 | + | 0.596957i | 0.918117 | − | 0.396310i | \(-0.129709\pi\) |
0.115844 | + | 0.993267i | \(0.463043\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −67.0000 | − | 116.047i | −0.347150 | − | 0.601282i | 0.638592 | − | 0.769546i | \(-0.279517\pi\) |
−0.985742 | + | 0.168264i | \(0.946184\pi\) | |||||||
\(194\) | 230.758 | − | 133.228i | 1.18947 | − | 0.686743i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.00000 | − | 12.1244i | 0.0357143 | − | 0.0618590i | ||||
\(197\) | − | 188.560i | − | 0.957157i | −0.878045 | − | 0.478579i | \(-0.841152\pi\) | ||
0.878045 | − | 0.478579i | \(-0.158848\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 102.494 | 0.515046 | 0.257523 | − | 0.966272i | \(-0.417094\pi\) | ||||
0.257523 | + | 0.966272i | \(0.417094\pi\) | |||||||
\(200\) | 28.9872 | + | 16.7358i | 0.144936 | + | 0.0836789i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −75.4575 | − | 130.696i | −0.373552 | − | 0.647011i | ||||
\(203\) | −95.8599 | + | 55.3447i | −0.472216 | + | 0.272634i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 183.996 | − | 318.691i | 0.897542 | − | 1.55459i | ||||
\(206\) | − | 185.966i | − | 0.902749i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −74.3320 | −0.357365 | ||||||||
\(209\) | 210.240 | + | 121.382i | 1.00593 | + | 0.580775i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 42.2510 | + | 73.1809i | 0.200242 | + | 0.346829i | 0.948606 | − | 0.316459i | \(-0.102494\pi\) |
−0.748365 | + | 0.663288i | \(0.769161\pi\) | |||||||
\(212\) | −162.886 | + | 94.0424i | −0.768331 | + | 0.443596i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −58.2510 | + | 100.894i | −0.272201 | + | 0.471466i | ||||
\(215\) | − | 506.758i | − | 2.35701i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −66.5830 | −0.306834 | ||||||||
\(218\) | 41.4332 | + | 23.9215i | 0.190060 | + | 0.109731i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −73.6680 | − | 127.597i | −0.334854 | − | 0.579985i | ||||
\(221\) | 175.441 | − | 101.291i | 0.793851 | − | 0.458330i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 79.2470 | − | 137.260i | 0.355368 | − | 0.615515i | −0.631813 | − | 0.775121i | \(-0.717689\pi\) |
0.987181 | + | 0.159606i | \(0.0510222\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −40.3320 | −0.178460 | ||||||||
\(227\) | −88.1816 | − | 50.9117i | −0.388465 | − | 0.224281i | 0.293030 | − | 0.956103i | \(-0.405337\pi\) |
−0.681495 | + | 0.731823i | \(0.738670\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 134.458 | + | 232.887i | 0.587151 | + | 1.01697i | 0.994604 | + | 0.103749i | \(0.0330837\pi\) |
−0.407453 | + | 0.913226i | \(0.633583\pi\) | |||||||
\(230\) | 90.2245 | − | 52.0911i | 0.392280 | − | 0.226483i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 59.1660 | − | 102.479i | 0.255026 | − | 0.441718i | ||||
\(233\) | − | 26.2748i | − | 0.112767i | −0.998409 | − | 0.0563836i | \(-0.982043\pi\) | ||
0.998409 | − | 0.0563836i | \(-0.0179570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −102.996 | −0.438281 | ||||||||
\(236\) | −100.836 | − | 58.2175i | −0.427270 | − | 0.246684i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −20.3948 | − | 35.3248i | −0.0856923 | − | 0.148423i | ||||
\(239\) | 79.9110 | − | 46.1366i | 0.334356 | − | 0.193040i | −0.323418 | − | 0.946256i | \(-0.604832\pi\) |
0.657773 | + | 0.753216i | \(0.271499\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −171.624 | + | 297.261i | −0.712131 | + | 1.23345i | 0.251925 | + | 0.967747i | \(0.418936\pi\) |
−0.964056 | + | 0.265700i | \(0.914397\pi\) | |||||||
\(242\) | 37.2447i | 0.153904i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −31.3360 | −0.128426 | ||||||||
\(245\) | 36.7920 | + | 21.2419i | 0.150171 | + | 0.0867014i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 185.830 | + | 321.867i | 0.752348 | + | 1.30311i | ||||
\(248\) | 61.6439 | − | 35.5901i | 0.248564 | − | 0.143509i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 56.5020 | − | 97.8643i | 0.226008 | − | 0.391457i | ||||
\(251\) | 356.382i | 1.41985i | 0.704278 | + | 0.709924i | \(0.251271\pi\) | ||||
−0.704278 | + | 0.709924i | \(0.748729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −147.336 | −0.582356 | ||||||||
\(254\) | 158.810 | + | 91.6891i | 0.625237 | + | 0.360981i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −220.603 | + | 127.365i | −0.858377 | + | 0.495584i | −0.863469 | − | 0.504403i | \(-0.831713\pi\) |
0.00509129 | + | 0.999987i | \(0.498379\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 50.2693 | − | 87.0689i | 0.194090 | − | 0.336174i | ||||
\(260\) | − | 225.564i | − | 0.867555i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −209.328 | −0.798962 | ||||||||
\(263\) | −226.880 | − | 130.989i | −0.862663 | − | 0.498059i | 0.00224015 | − | 0.999997i | \(-0.499287\pi\) |
−0.864903 | + | 0.501939i | \(0.832620\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −285.376 | − | 494.287i | −1.07689 | − | 1.86523i | ||||
\(266\) | 64.8074 | − | 37.4166i | 0.243637 | − | 0.140664i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −132.664 | + | 229.781i | −0.495015 | + | 0.857391i | ||||
\(269\) | 93.6246i | 0.348047i | 0.984742 | + | 0.174023i | \(0.0556768\pi\) | ||||
−0.984742 | + | 0.174023i | \(0.944323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.16601 | 0.00430262 | 0.00215131 | − | 0.999998i | \(-0.499315\pi\) | ||||
0.00215131 | + | 0.999998i | \(0.499315\pi\) | |||||||
\(272\) | 37.7638 | + | 21.8029i | 0.138837 | + | 0.0801578i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 54.4170 | + | 94.2530i | 0.198602 | + | 0.343989i | ||||
\(275\) | 124.399 | − | 71.8217i | 0.452359 | − | 0.261170i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0000 | + | 27.7128i | −0.0577617 | + | 0.100046i | −0.893460 | − | 0.449142i | \(-0.851730\pi\) |
0.835699 | + | 0.549188i | \(0.185063\pi\) | |||||||
\(278\) | − | 307.348i | − | 1.10557i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −45.4170 | −0.162204 | ||||||||
\(281\) | −144.416 | − | 83.3785i | −0.513935 | − | 0.296721i | 0.220514 | − | 0.975384i | \(-0.429226\pi\) |
−0.734450 | + | 0.678663i | \(0.762560\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.16995 | − | 14.1508i | −0.0288691 | − | 0.0500027i | 0.851230 | − | 0.524793i | \(-0.175857\pi\) |
−0.880099 | + | 0.474790i | \(0.842524\pi\) | |||||||
\(284\) | 21.0240 | − | 12.1382i | 0.0740281 | − | 0.0427401i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −159.498 | + | 276.259i | −0.557685 | + | 0.965939i | ||||
\(287\) | 160.422i | 0.558961i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 170.158 | 0.588782 | ||||||||
\(290\) | 310.976 | + | 179.542i | 1.07233 | + | 0.619111i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −76.9150 | − | 133.221i | −0.263408 | − | 0.456235i | ||||
\(293\) | 319.495 | − | 184.461i | 1.09043 | − | 0.629558i | 0.156737 | − | 0.987640i | \(-0.449903\pi\) |
0.933690 | + | 0.358082i | \(0.116569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 176.664 | − | 305.991i | 0.598861 | − | 1.03726i | ||||
\(296\) | 107.480i | 0.363109i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 228.996 | 0.768443 | ||||||||
\(299\) | −195.344 | − | 112.782i | −0.653326 | − | 0.377198i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 110.458 | + | 191.318i | 0.366968 | + | 0.635608i | ||||
\(302\) | 114.105 | − | 65.8783i | 0.377830 | − | 0.218140i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −40.0000 | + | 69.2820i | −0.131579 | + | 0.227901i | ||||
\(305\) | − | 95.0906i | − | 0.311772i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −192.664 | −0.627570 | −0.313785 | − | 0.949494i | \(-0.601597\pi\) | ||||
−0.313785 | + | 0.949494i | \(0.601597\pi\) | |||||||
\(308\) | 55.6242 | + | 32.1147i | 0.180598 | + | 0.104268i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 108.000 | + | 187.061i | 0.348387 | + | 0.603424i | ||||
\(311\) | 113.688 | − | 65.6380i | 0.365557 | − | 0.211055i | −0.305959 | − | 0.952045i | \(-0.598977\pi\) |
0.671516 | + | 0.740990i | \(0.265644\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.6640 | + | 37.5232i | −0.0692142 | + | 0.119882i | −0.898556 | − | 0.438860i | \(-0.855383\pi\) |
0.829341 | + | 0.558742i | \(0.188716\pi\) | |||||||
\(314\) | 261.624i | 0.833197i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −67.3360 | −0.213088 | ||||||||
\(317\) | 218.000 | + | 125.862i | 0.687696 | + | 0.397042i | 0.802748 | − | 0.596318i | \(-0.203370\pi\) |
−0.115052 | + | 0.993359i | \(0.536703\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −253.911 | − | 439.787i | −0.795960 | − | 1.37864i | ||||
\(320\) | 42.0480 | − | 24.2764i | 0.131400 | − | 0.0758638i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.7085 | + | 39.3323i | −0.0705233 | + | 0.122150i | ||||
\(323\) | − | 218.029i | − | 0.675013i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 219.911 | 0.676650 | ||||||||
\(326\) | 106.548 | + | 61.5155i | 0.326834 | + | 0.188698i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −85.7490 | − | 148.522i | −0.261430 | − | 0.452810i | ||||
\(329\) | 38.8844 | − | 22.4499i | 0.118190 | − | 0.0682369i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −180.745 | + | 313.060i | −0.546058 | + | 0.945800i | 0.452482 | + | 0.891774i | \(0.350539\pi\) |
−0.998540 | + | 0.0540260i | \(0.982795\pi\) | |||||||
\(332\) | 121.153i | 0.364918i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 85.6680 | 0.256491 | ||||||||
\(335\) | −697.282 | − | 402.576i | −2.08144 | − | 1.20172i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 149.417 | + | 258.798i | 0.443374 | + | 0.767946i | 0.997937 | − | 0.0641954i | \(-0.0204481\pi\) |
−0.554563 | + | 0.832141i | \(0.687115\pi\) | |||||||
\(338\) | −215.957 | + | 124.683i | −0.638926 | + | 0.368884i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −66.1621 | + | 114.596i | −0.194594 | + | 0.337047i | ||||
\(341\) | − | 305.470i | − | 0.895807i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | −204.528 | − | 118.084i | −0.594557 | − | 0.343268i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −114.956 | − | 199.109i | −0.332241 | − | 0.575459i | ||||
\(347\) | 178.505 | − | 103.060i | 0.514425 | − | 0.297003i | −0.220226 | − | 0.975449i | \(-0.570679\pi\) |
0.734651 | + | 0.678446i | \(0.237346\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −217.162 | + | 376.136i | −0.622241 | + | 1.07775i | 0.366827 | + | 0.930289i | \(0.380444\pi\) |
−0.989067 | + | 0.147464i | \(0.952889\pi\) | |||||||
\(350\) | − | 44.2787i | − | 0.126511i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −68.6640 | −0.195068 | ||||||||
\(353\) | 160.595 | + | 92.7197i | 0.454944 | + | 0.262662i | 0.709916 | − | 0.704286i | \(-0.248733\pi\) |
−0.254972 | + | 0.966948i | \(0.582066\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.8340 | + | 63.7983i | 0.103758 | + | 0.179714i | ||||
\(356\) | 8.27064 | − | 4.77506i | 0.0232321 | − | 0.0134131i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −157.749 | + | 273.229i | −0.440640 | + | 0.763210i | ||||
\(359\) | − | 516.767i | − | 1.43946i | −0.694254 | − | 0.719731i | \(-0.744265\pi\) | ||
0.694254 | − | 0.719731i | \(-0.255735\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.0000 | 0.108033 | ||||||||
\(362\) | 231.373 | + | 133.583i | 0.639151 | + | 0.369014i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 49.1660 | + | 85.1580i | 0.135071 | + | 0.233951i | ||||
\(365\) | 404.265 | − | 233.403i | 1.10758 | − | 0.639459i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 58.7451 | − | 101.749i | 0.160068 | − | 0.277246i | −0.774825 | − | 0.632176i | \(-0.782162\pi\) |
0.934893 | + | 0.354930i | \(0.115495\pi\) | |||||||
\(368\) | − | 48.5528i | − | 0.131937i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −326.154 | −0.881498 | ||||||||
\(371\) | 215.478 | + | 124.406i | 0.580804 | + | 0.335327i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 201.332 | + | 348.717i | 0.539764 | + | 0.934899i | 0.998916 | + | 0.0465413i | \(0.0148199\pi\) |
−0.459152 | + | 0.888358i | \(0.651847\pi\) | |||||||
\(374\) | 162.063 | − | 93.5673i | 0.433324 | − | 0.250180i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | + | 41.5692i | −0.0638298 | + | 0.110556i | ||||
\(377\) | − | 777.451i | − | 2.06221i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 398.834 | 1.05233 | 0.526166 | − | 0.850382i | \(-0.323629\pi\) | ||||
0.526166 | + | 0.850382i | \(0.323629\pi\) | |||||||
\(380\) | −210.240 | − | 121.382i | −0.553263 | − | 0.319426i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 161.247 | + | 279.288i | 0.422113 | + | 0.731121i | ||||
\(383\) | 645.019 | − | 372.402i | 1.68412 | − | 0.972329i | 0.725255 | − | 0.688481i | \(-0.241722\pi\) |
0.958869 | − | 0.283849i | \(-0.0916114\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −97.4536 | + | 168.795i | −0.253126 | + | 0.438427i | ||||
\(386\) | − | 189.505i | − | 0.490945i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 376.826 | 0.971201 | ||||||||
\(389\) | 463.464 | + | 267.581i | 1.19142 | + | 0.687869i | 0.958630 | − | 0.284656i | \(-0.0918795\pi\) |
0.232795 | + | 0.972526i | \(0.425213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 66.1621 | + | 114.596i | 0.169212 | + | 0.293085i | ||||
\(392\) | 17.1464 | − | 9.89949i | 0.0437409 | − | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 133.332 | − | 230.938i | 0.338406 | − | 0.586137i | ||||
\(395\) | − | 204.334i | − | 0.517302i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −94.3241 | −0.237592 | −0.118796 | − | 0.992919i | \(-0.537904\pi\) | ||||
−0.118796 | + | 0.992919i | \(0.537904\pi\) | |||||||
\(398\) | 125.529 | + | 72.4743i | 0.315400 | + | 0.182096i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 23.6680 | + | 40.9941i | 0.0591699 | + | 0.102485i | ||||
\(401\) | −89.7138 | + | 51.7963i | −0.223725 | + | 0.129168i | −0.607674 | − | 0.794187i | \(-0.707897\pi\) |
0.383949 | + | 0.923354i | \(0.374564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 233.830 | − | 405.006i | 0.580223 | − | 1.00498i | ||||
\(404\) | − | 213.426i | − | 0.528282i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −156.539 | −0.385563 | ||||||||
\(407\) | 399.456 | + | 230.626i | 0.981464 | + | 0.566648i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.87844 | + | 8.44971i | 0.0119277 | + | 0.0206594i | 0.871928 | − | 0.489635i | \(-0.162870\pi\) |
−0.860000 | + | 0.510294i | \(0.829537\pi\) | |||||||
\(410\) | 450.696 | − | 260.210i | 1.09926 | − | 0.634658i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 131.498 | − | 227.761i | 0.319170 | − | 0.552819i | ||||
\(413\) | 154.029i | 0.372952i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −367.644 | −0.885890 | ||||||||
\(416\) | −91.0378 | − | 52.5607i | −0.218841 | − | 0.126348i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 171.660 | + | 297.324i | 0.410670 | + | 0.711301i | ||||
\(419\) | 293.939 | − | 169.706i | 0.701525 | − | 0.405025i | −0.106390 | − | 0.994324i | \(-0.533929\pi\) |
0.807915 | + | 0.589299i | \(0.200596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 299.660 | − | 519.027i | 0.711782 | − | 1.23284i | −0.252406 | − | 0.967621i | \(-0.581222\pi\) |
0.964188 | − | 0.265221i | \(-0.0854448\pi\) | |||||||
\(422\) | 119.504i | 0.283184i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −265.992 | −0.627340 | ||||||||
\(425\) | −111.724 | − | 64.5039i | −0.262880 | − | 0.151774i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.7268 | + | 35.8998i | 0.0485405 | + | 0.0840746i | ||||
\(428\) | −142.685 | + | 82.3793i | −0.333377 | + | 0.192475i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 358.332 | − | 620.649i | 0.833330 | − | 1.44337i | ||||
\(431\) | 710.978i | 1.64960i | 0.565424 | + | 0.824800i | \(0.308712\pi\) | ||||
−0.565424 | + | 0.824800i | \(0.691288\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 377.984 | 0.872943 | 0.436471 | − | 0.899718i | \(-0.356228\pi\) | ||||
0.436471 | + | 0.899718i | \(0.356228\pi\) | |||||||
\(434\) | −81.5472 | − | 47.0813i | −0.187897 | − | 0.108482i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.8301 | + | 58.5954i | 0.0775919 | + | 0.134393i | ||||
\(437\) | −210.240 | + | 121.382i | −0.481098 | + | 0.277762i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −264.073 | + | 457.388i | −0.601533 | + | 1.04189i | 0.391056 | + | 0.920367i | \(0.372110\pi\) |
−0.992589 | + | 0.121519i | \(0.961223\pi\) | |||||||
\(440\) | − | 208.365i | − | 0.473556i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 286.494 | 0.648177 | ||||||||
\(443\) | −31.7345 | − | 18.3219i | −0.0716354 | − | 0.0413587i | 0.463754 | − | 0.885964i | \(-0.346502\pi\) |
−0.535390 | + | 0.844605i | \(0.679835\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.4902 | + | 25.0977i | 0.0325622 | + | 0.0563993i | ||||
\(446\) | 194.115 | − | 112.072i | 0.435235 | − | 0.251283i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.5830 | + | 18.3303i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | − | 397.612i | − | 0.885550i | −0.896633 | − | 0.442775i | \(-0.853994\pi\) | ||
0.896633 | − | 0.442775i | \(-0.146006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −735.984 | −1.63189 | ||||||||
\(452\) | −49.3964 | − | 28.5190i | −0.109284 | − | 0.0630952i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −72.0000 | − | 124.708i | −0.158590 | − | 0.274686i | ||||
\(455\) | −258.416 | + | 149.197i | −0.567948 | + | 0.327905i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −172.162 | + | 298.193i | −0.376722 | + | 0.652502i | −0.990583 | − | 0.136912i | \(-0.956282\pi\) |
0.613861 | + | 0.789414i | \(0.289616\pi\) | |||||||
\(458\) | 380.303i | 0.830357i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 147.336 | 0.320296 | ||||||||
\(461\) | 321.240 | + | 185.468i | 0.696833 | + | 0.402317i | 0.806167 | − | 0.591688i | \(-0.201538\pi\) |
−0.109334 | + | 0.994005i | \(0.534872\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.1660 | − | 67.8375i | −0.0845918 | − | 0.146517i | 0.820625 | − | 0.571467i | \(-0.193625\pi\) |
−0.905217 | + | 0.424949i | \(0.860292\pi\) | |||||||
\(464\) | 144.927 | − | 83.6734i | 0.312342 | − | 0.180331i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.5791 | − | 32.1799i | 0.0398692 | − | 0.0690556i | ||||
\(467\) | − | 399.758i | − | 0.856014i | −0.903775 | − | 0.428007i | \(-0.859216\pi\) | ||
0.903775 | − | 0.428007i | \(-0.140784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 350.996 | 0.748392 | ||||||||
\(470\) | −126.144 | − | 72.8292i | −0.268391 | − | 0.154956i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −82.3320 | − | 142.603i | −0.174432 | − | 0.302126i | ||||
\(473\) | −877.731 | + | 506.758i | −1.85567 | + | 1.07137i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 118.340 | − | 204.971i | 0.249137 | − | 0.431517i | ||||
\(476\) | − | 57.6851i | − | 0.121187i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 130.494 | 0.273000 | ||||||||
\(479\) | 609.100 | + | 351.664i | 1.27161 | + | 0.734163i | 0.975290 | − | 0.220927i | \(-0.0709081\pi\) |
0.296317 | + | 0.955090i | \(0.404241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 353.077 | + | 611.547i | 0.734048 | + | 1.27141i | ||||
\(482\) | −420.390 | + | 242.712i | −0.872179 | + | 0.503553i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.3360 | + | 45.6152i | −0.0544131 | + | 0.0942463i | ||||
\(485\) | 1143.50i | 2.35773i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −82.5098 | −0.169425 | −0.0847124 | − | 0.996405i | \(-0.526997\pi\) | ||||
−0.0847124 | + | 0.996405i | \(0.526997\pi\) | |||||||
\(488\) | −38.3786 | − | 22.1579i | −0.0786446 | − | 0.0454055i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 30.0405 | + | 52.0317i | 0.0613072 | + | 0.106187i | ||||
\(491\) | −159.524 | + | 92.1014i | −0.324897 | + | 0.187579i | −0.653573 | − | 0.756863i | \(-0.726731\pi\) |
0.328676 | + | 0.944443i | \(0.393397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −228.041 | + | 394.978i | −0.462557 | + | 0.801172i | ||||
\(494\) | 525.607i | 1.06398i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 100.664 | 0.202952 | ||||||||
\(497\) | −27.8121 | − | 16.0573i | −0.0559600 | − | 0.0323085i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −376.405 | − | 651.953i | −0.754319 | − | 1.30652i | −0.945712 | − | 0.325005i | \(-0.894634\pi\) |
0.191393 | − | 0.981513i | \(-0.438699\pi\) | |||||||
\(500\) | 138.401 | − | 79.9059i | 0.276802 | − | 0.159812i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −252.000 | + | 436.477i | −0.501992 | + | 0.869476i | ||||
\(503\) | − | 662.540i | − | 1.31718i | −0.752504 | − | 0.658588i | \(-0.771154\pi\) | ||
0.752504 | − | 0.658588i | \(-0.228846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 647.652 | 1.28248 | ||||||||
\(506\) | −180.449 | − | 104.182i | −0.356618 | − | 0.205894i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 129.668 | + | 224.592i | 0.255252 | + | 0.442109i | ||||
\(509\) | 821.958 | − | 474.557i | 1.61485 | − | 0.932333i | 0.626623 | − | 0.779322i | \(-0.284437\pi\) |
0.988225 | − | 0.153010i | \(-0.0488968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −101.749 | + | 176.234i | −0.199117 | + | 0.344882i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −360.243 | −0.700862 | ||||||||
\(515\) | 691.153 | + | 399.037i | 1.34204 | + | 0.774830i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 102.996 | + | 178.394i | 0.199219 | + | 0.345057i | ||||
\(518\) | 123.134 | − | 71.0915i | 0.237711 | − | 0.137242i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 159.498 | − | 276.259i | 0.306727 | − | 0.531267i | ||||
\(521\) | 714.344i | 1.37110i | 0.728025 | + | 0.685551i | \(0.240439\pi\) | ||||
−0.728025 | + | 0.685551i | \(0.759561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −232.000 | −0.443595 | −0.221797 | − | 0.975093i | \(-0.571192\pi\) | ||||
−0.221797 | + | 0.975093i | \(0.571192\pi\) | |||||||
\(524\) | −256.373 | − | 148.017i | −0.489262 | − | 0.282476i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −185.247 | − | 320.857i | −0.352181 | − | 0.609995i | ||||
\(527\) | −237.591 | + | 137.173i | −0.450837 | + | 0.260291i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −190.832 | + | 330.531i | −0.360741 | + | 0.624822i | ||||
\(530\) | − | 807.167i | − | 1.52296i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 105.830 | 0.198929 | ||||||||
\(533\) | −975.800 | − | 563.378i | −1.83077 | − | 1.05699i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −249.984 | − | 432.985i | −0.467260 | − | 0.809319i | ||||
\(536\) | −324.959 | + | 187.615i | −0.606267 | + | 0.350029i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −66.2026 | + | 114.666i | −0.123053 | + | 0.213134i | ||||
\(539\) | − | 84.9674i | − | 0.157639i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 165.668 | 0.306225 | 0.153113 | − | 0.988209i | \(-0.451070\pi\) | ||||
0.153113 | + | 0.988209i | \(0.451070\pi\) | |||||||
\(542\) | 1.42807 | + | 0.824494i | 0.00263481 | + | 0.00152121i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 30.8340 | + | 53.4060i | 0.0566801 | + | 0.0981729i | ||||
\(545\) | −177.811 | + | 102.659i | −0.326258 | + | 0.188365i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −147.838 | + | 256.063i | −0.270270 | + | 0.468122i | −0.968931 | − | 0.247331i | \(-0.920446\pi\) |
0.698661 | + | 0.715453i | \(0.253780\pi\) | |||||||
\(548\) | 153.915i | 0.280866i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 203.142 | 0.369350 | ||||||||
\(551\) | −724.633 | − | 418.367i | −1.31512 | − | 0.759287i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.5385 | + | 77.1430i | 0.0805399 | + | 0.139499i | ||||
\(554\) | −39.1918 | + | 22.6274i | −0.0707434 | + | 0.0408437i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 217.328 | − | 376.423i | 0.390878 | − | 0.677020i | ||||
\(557\) | 76.8426i | 0.137958i | 0.997618 | + | 0.0689790i | \(0.0219742\pi\) | ||||
−0.997618 | + | 0.0689790i | \(0.978026\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1551.64 | −2.77575 | ||||||||
\(560\) | −55.6242 | − | 32.1147i | −0.0993290 | − | 0.0573476i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −117.915 | − | 204.235i | −0.209813 | − | 0.363407i | ||||
\(563\) | 880.170 | − | 508.167i | 1.56336 | − | 0.902605i | 0.566444 | − | 0.824100i | \(-0.308319\pi\) |
0.996914 | − | 0.0785049i | \(-0.0250146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 86.5425 | − | 149.896i | 0.153173 | − | 0.265303i | ||||
\(566\) | − | 23.1081i | − | 0.0408270i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 34.3320 | 0.0604437 | ||||||||
\(569\) | 507.952 | + | 293.266i | 0.892710 | + | 0.515406i | 0.874828 | − | 0.484434i | \(-0.160974\pi\) |
0.0178822 | + | 0.999840i | \(0.494308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −475.822 | − | 824.148i | −0.833314 | − | 1.44334i | −0.895396 | − | 0.445271i | \(-0.853107\pi\) |
0.0620822 | − | 0.998071i | \(-0.480226\pi\) | |||||||
\(572\) | −390.689 | + | 225.564i | −0.683022 | + | 0.394343i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −113.435 | + | 196.476i | −0.197622 | + | 0.342292i | ||||
\(575\) | 143.643i | 0.249815i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −148.672 | −0.257664 | −0.128832 | − | 0.991666i | \(-0.541123\pi\) | ||||
−0.128832 | + | 0.991666i | \(0.541123\pi\) | |||||||
\(578\) | 208.400 | + | 120.320i | 0.360554 | + | 0.208166i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 253.911 | + | 439.787i | 0.437778 | + | 0.758253i | ||||
\(581\) | 138.798 | − | 80.1351i | 0.238895 | − | 0.137926i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −570.753 | + | 988.573i | −0.978993 | + | 1.69567i | ||||
\(584\) | − | 217.549i | − | 0.372515i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 521.733 | 0.890330 | ||||||||
\(587\) | −288.009 | − | 166.282i | −0.490645 | − | 0.283274i | 0.234197 | − | 0.972189i | \(-0.424754\pi\) |
−0.724842 | + | 0.688915i | \(0.758087\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −251.660 | − | 435.888i | −0.427267 | − | 0.740048i | ||||
\(590\) | 432.737 | − | 249.841i | 0.733452 | − | 0.423459i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −76.0000 | + | 131.636i | −0.128378 | + | 0.222358i | ||||
\(593\) | 217.251i | 0.366359i | 0.983079 | + | 0.183180i | \(0.0586390\pi\) | ||||
−0.983079 | + | 0.183180i | \(0.941361\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 175.048 | 0.294199 | ||||||||
\(596\) | 280.462 | + | 161.925i | 0.470573 | + | 0.271686i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −159.498 | − | 276.259i | −0.266719 | − | 0.461971i | ||||
\(599\) | −149.111 | + | 86.0896i | −0.248934 | + | 0.143722i | −0.619276 | − | 0.785173i | \(-0.712574\pi\) |
0.370342 | + | 0.928895i | \(0.379240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 209.000 | − | 361.999i | 0.347754 | − | 0.602327i | −0.638096 | − | 0.769957i | \(-0.720278\pi\) |
0.985850 | + | 0.167629i | \(0.0536112\pi\) | |||||||
\(602\) | 312.421i | 0.518972i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 186.332 | 0.308497 | ||||||||
\(605\) | −138.422 | − | 79.9178i | −0.228796 | − | 0.132096i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −313.579 | − | 543.135i | −0.516605 | − | 0.894786i | −0.999814 | − | 0.0192808i | \(-0.993862\pi\) |
0.483209 | − | 0.875505i | \(-0.339471\pi\) | |||||||
\(608\) | −97.9796 | + | 56.5685i | −0.161151 | + | 0.0930404i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 67.2392 | − | 116.462i | 0.110228 | − | 0.190921i | ||||
\(611\) | 315.364i | 0.516144i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −279.328 | −0.455674 | −0.227837 | − | 0.973699i | \(-0.573165\pi\) | ||||
−0.227837 | + | 0.973699i | \(0.573165\pi\) | |||||||
\(614\) | −235.964 | − | 136.234i | −0.384307 | − | 0.221880i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 45.4170 | + | 78.6645i | 0.0737289 | + | 0.127702i | ||||
\(617\) | 310.366 | − | 179.190i | 0.503025 | − | 0.290422i | −0.226937 | − | 0.973909i | \(-0.572871\pi\) |
0.729962 | + | 0.683488i | \(0.239538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 491.822 | − | 851.861i | 0.794543 | − | 1.37619i | −0.128586 | − | 0.991698i | \(-0.541044\pi\) |
0.923129 | − | 0.384491i | \(-0.125623\pi\) | |||||||
\(620\) | 305.470i | 0.492694i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 185.652 | 0.298476 | ||||||||
\(623\) | −10.9410 | − | 6.31681i | −0.0175619 | − | 0.0101393i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390.403 | + | 676.198i | 0.624645 | + | 1.08192i | ||||
\(626\) | −53.0658 | + | 30.6376i | −0.0847697 | + | 0.0489418i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −184.996 | + | 320.423i | −0.294580 | + | 0.510227i | ||||
\(629\) | − | 414.256i | − | 0.658594i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −298.996 | −0.473845 | −0.236922 | − | 0.971529i | \(-0.576139\pi\) | ||||
−0.236922 | + | 0.971529i | \(0.576139\pi\) | |||||||
\(632\) | −82.4694 | − | 47.6137i | −0.130490 | − | 0.0753382i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 177.996 | + | 308.298i | 0.280751 | + | 0.486275i | ||||
\(635\) | −681.534 | + | 393.484i | −1.07328 | + | 0.619660i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 65.0405 | − | 112.653i | 0.102104 | − | 0.176850i | ||||
\(638\) | − | 718.169i | − | 1.12566i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 68.6640 | 0.107288 | ||||||||
\(641\) | 270.163 | + | 155.979i | 0.421471 | + | 0.243336i | 0.695706 | − | 0.718326i | \(-0.255091\pi\) |
−0.274236 | + | 0.961663i | \(0.588425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 302.000 | + | 523.079i | 0.469673 | + | 0.813498i | 0.999399 | − | 0.0346710i | \(-0.0110383\pi\) |
−0.529725 | + | 0.848169i | \(0.677705\pi\) | |||||||
\(644\) | −55.6242 | + | 32.1147i | −0.0863730 | + | 0.0498675i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 154.170 | − | 267.030i | 0.238653 | − | 0.413359i | ||||
\(647\) | 179.600i | 0.277588i | 0.990321 | + | 0.138794i | \(0.0443226\pi\) | ||||
−0.990321 | + | 0.138794i | \(0.955677\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −706.656 | −1.08884 | ||||||||
\(650\) | 269.335 | + | 155.501i | 0.414362 | + | 0.239232i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 86.9961 | + | 150.682i | 0.133430 | + | 0.231107i | ||||
\(653\) | 417.331 | − | 240.946i | 0.639097 | − | 0.368983i | −0.145169 | − | 0.989407i | \(-0.546373\pi\) |
0.784267 | + | 0.620424i | \(0.213039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 449.166 | − | 777.978i | 0.685750 | − | 1.18775i | ||||
\(656\) | − | 242.535i | − | 0.369718i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 63.4980 | 0.0965016 | ||||||||
\(659\) | −759.857 | − | 438.704i | −1.15305 | − | 0.665711i | −0.203418 | − | 0.979092i | \(-0.565205\pi\) |
−0.949628 | + | 0.313380i | \(0.898538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 260.822 | + | 451.757i | 0.394587 | + | 0.683445i | 0.993048 | − | 0.117707i | \(-0.0375543\pi\) |
−0.598461 | + | 0.801152i | \(0.704221\pi\) | |||||||
\(662\) | −442.733 | + | 255.612i | −0.668781 | + | 0.386121i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −85.6680 | + | 148.381i | −0.129018 | + | 0.223466i | ||||
\(665\) | 321.147i | 0.482927i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 507.822 | 0.761353 | ||||||||
\(668\) | 104.921 | + | 60.5764i | 0.157068 | + | 0.0906832i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −569.328 | − | 986.105i | −0.849743 | − | 1.47180i | ||||
\(671\) | −164.702 | + | 95.0906i | −0.245457 | + | 0.141715i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 329.996 | − | 571.570i | 0.490336 | − | 0.849287i | −0.509602 | − | 0.860410i | \(-0.670207\pi\) |
0.999938 | + | 0.0111234i | \(0.00354077\pi\) | |||||||
\(674\) | 422.615i | 0.627025i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −352.656 | −0.521681 | ||||||||
\(677\) | −880.121 | − | 508.138i | −1.30003 | − | 0.750573i | −0.319622 | − | 0.947545i | \(-0.603556\pi\) |
−0.980409 | + | 0.196972i | \(0.936889\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −249.247 | − | 431.709i | −0.367080 | − | 0.635801i | ||||
\(680\) | −162.063 | + | 93.5673i | −0.238328 | + | 0.137599i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 216.000 | − | 374.123i | 0.316716 | − | 0.548567i | ||||
\(683\) | − | 235.114i | − | 0.344238i | −0.985076 | − | 0.172119i | \(-0.944939\pi\) | ||
0.985076 | − | 0.172119i | \(-0.0550613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −467.061 | −0.681841 | ||||||||
\(686\) | −22.6826 | − | 13.0958i | −0.0330650 | − | 0.0190901i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −166.996 | − | 289.246i | −0.242727 | − | 0.420415i | ||||
\(689\) | −1513.46 | + | 873.795i | −2.19660 | + | 1.26821i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.4902 | − | 44.1502i | 0.0368888 | − | 0.0638933i | −0.846992 | − | 0.531606i | \(-0.821589\pi\) |
0.883880 | + | 0.467713i | \(0.154922\pi\) | |||||||
\(692\) | − | 325.143i | − | 0.469860i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 291.498 | 0.420026 | ||||||||
\(695\) | 1142.28 | + | 659.493i | 1.64356 | + | 0.948911i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 330.498 | + | 572.439i | 0.474172 | + | 0.821290i | ||||
\(698\) | −531.936 | + | 307.114i | −0.762086 | + | 0.439991i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 31.3098 | − | 54.2302i | 0.0447283 | − | 0.0774716i | ||||
\(701\) | 141.530i | 0.201898i | 0.994892 | + | 0.100949i | \(0.0321879\pi\) | ||||
−0.994892 | + | 0.100949i | \(0.967812\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 760.000 | 1.08108 | ||||||||
\(704\) | −84.0959 | − | 48.5528i | −0.119454 | − | 0.0689671i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 131.125 | + | 227.116i | 0.185730 | + | 0.321694i | ||||
\(707\) | −244.510 | + | 141.168i | −0.345842 | + | 0.199672i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.7490 | − | 48.0627i | 0.0391382 | − | 0.0677894i | −0.845793 | − | 0.533512i | \(-0.820872\pi\) |
0.884931 | + | 0.465722i | \(0.154205\pi\) | |||||||
\(710\) | 104.182i | 0.146736i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.5059 | 0.0189690 | ||||||||
\(713\) | 264.545 | + | 152.735i | 0.371031 | + | 0.214215i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −684.486 | − | 1185.56i | −0.957323 | − | 1.65813i | ||||
\(716\) | −386.405 | + | 223.091i | −0.539671 | + | 0.311579i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 365.409 | − | 632.907i | 0.508926 | − | 0.881486i | ||||
\(719\) | − | 1009.03i | − | 1.40338i | −0.712484 | − | 0.701688i | \(-0.752430\pi\) | ||
0.712484 | − | 0.701688i | \(-0.247570\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −347.911 | −0.482540 | ||||||||
\(722\) | 47.7650 | + | 27.5772i | 0.0661566 | + | 0.0381955i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 188.915 | + | 327.210i | 0.260932 | + | 0.451948i | ||||
\(725\) | −428.765 | + | 247.547i | −0.591400 | + | 0.341445i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 182.591 | − | 316.257i | 0.251157 | − | 0.435016i | −0.712688 | − | 0.701481i | \(-0.752522\pi\) |
0.963845 | + | 0.266465i | \(0.0858557\pi\) | |||||||
\(728\) | 139.062i | 0.191020i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 660.162 | 0.904332 | ||||||||
\(731\) | 788.300 | + | 455.125i | 1.07839 | + | 0.622606i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 176.539 | + | 305.774i | 0.240844 | + | 0.417154i | 0.960955 | − | 0.276705i | \(-0.0892425\pi\) |
−0.720111 | + | 0.693859i | \(0.755909\pi\) | |||||||
\(734\) | 143.895 | − | 83.0781i | 0.196043 | − | 0.113185i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.3320 | − | 59.4648i | 0.0466468 | − | 0.0807946i | ||||
\(737\) | 1610.30i | 2.18494i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 329.684 | 0.446121 | 0.223061 | − | 0.974805i | \(-0.428395\pi\) | ||||
0.223061 | + | 0.974805i | \(0.428395\pi\) | |||||||
\(740\) | −399.456 | − | 230.626i | −0.539805 | − | 0.311657i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 175.937 | + | 304.732i | 0.237112 | + | 0.410690i | ||||
\(743\) | −97.0478 | + | 56.0306i | −0.130616 | + | 0.0754112i | −0.563884 | − | 0.825854i | \(-0.690694\pi\) |
0.433268 | + | 0.901265i | \(0.357360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −491.369 | + | 851.075i | −0.659555 | + | 1.14238i | ||||
\(746\) | 569.453i | 0.763342i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 264.648 | 0.353808 | ||||||||
\(749\) | 188.755 | + | 108.978i | 0.252009 | + | 0.145497i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 72.4131 | + | 125.423i | 0.0964222 | + | 0.167008i | 0.910201 | − | 0.414166i | \(-0.135927\pi\) |
−0.813779 | + | 0.581174i | \(0.802593\pi\) | |||||||
\(752\) | −58.7878 | + | 33.9411i | −0.0781752 | + | 0.0451345i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 549.741 | − | 952.180i | 0.729100 | − | 1.26284i | ||||
\(755\) | 565.434i | 0.748919i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 78.1699 | 0.103263 | 0.0516314 | − | 0.998666i | \(-0.483558\pi\) | ||||
0.0516314 | + | 0.998666i | \(0.483558\pi\) | |||||||
\(758\) | 488.470 | + | 282.018i | 0.644419 | + | 0.372056i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −171.660 | − | 297.324i | −0.225869 | − | 0.391216i | ||||
\(761\) | 1269.16 | − | 732.752i | 1.66776 | − | 0.962880i | 0.698915 | − | 0.715205i | \(-0.253667\pi\) |
0.968843 | − | 0.247676i | \(-0.0796667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.7530 | − | 77.5144i | 0.0586539 | − | 0.101592i | ||||
\(764\) | 456.076i | 0.596957i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1053.31 | 1.37508 | ||||||||
\(767\) | −936.915 | − | 540.928i | −1.22153 | − | 0.705252i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −364.660 | − | 631.610i | −0.474200 | − | 0.821339i | 0.525363 | − | 0.850878i | \(-0.323929\pi\) |
−0.999564 | + | 0.0295389i | \(0.990596\pi\) | |||||||
\(770\) | −238.712 | + | 137.820i | −0.310015 | + | 0.178987i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 134.000 | − | 232.095i | 0.173575 | − | 0.300641i | ||||
\(773\) | − | 434.559i | − | 0.562172i | −0.959683 | − | 0.281086i | \(-0.909305\pi\) | ||
0.959683 | − | 0.281086i | \(-0.0906947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −297.814 | −0.384277 | ||||||||
\(776\) | 461.516 | + | 266.456i | 0.594737 | + | 0.343372i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 378.417 | + | 655.437i | 0.486397 | + | 0.842465i | ||||
\(779\) | −1050.21 | + | 606.337i | −1.34815 | + | 0.778353i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 73.6680 | − | 127.597i | 0.0943252 | − | 0.163376i | ||||
\(782\) | 187.135i | 0.239303i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | −972.339 | − | 561.380i | −1.23865 | − | 0.715134i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.67585 | + | 13.2950i | 0.00975331 | + | 0.0168932i | 0.870861 | − | 0.491530i | \(-0.163562\pi\) |
−0.861108 | + | 0.508423i | \(0.830229\pi\) | |||||||
\(788\) | 326.595 | − | 188.560i | 0.414461 | − | 0.239289i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 144.486 | − | 250.257i | 0.182894 | − | 0.316782i | ||||
\(791\) | 75.4543i | 0.0953910i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −291.158 | −0.367160 | ||||||||
\(794\) | −115.523 | − | 66.6972i | −0.145495 | − | 0.0840016i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 102.494 | + | 177.525i | 0.128761 | + | 0.223021i | ||||
\(797\) | −903.684 | + | 521.742i | −1.13386 | + | 0.654633i | −0.944902 | − | 0.327353i | \(-0.893843\pi\) |
−0.188955 | + | 0.981986i | \(0.560510\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 92.5020 | − | 160.218i | 0.115772 | − | 0.200523i | ||||
\(800\) | 66.9432i | 0.0836789i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −146.502 | −0.182671 | ||||||||
\(803\) | −808.530 | − | 466.805i | −1.00689 | − | 0.581326i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −97.4536 | − | 168.795i | −0.121060 | − | 0.209683i | ||||
\(806\) | 572.764 | − | 330.686i | 0.710626 | − | 0.410280i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 150.915 | − | 261.392i | 0.186776 | − | 0.323506i | ||||
\(809\) | 1041.31i | 1.28716i | 0.765378 | + | 0.643581i | \(0.222552\pi\) | ||||
−0.765378 | + | 0.643581i | \(0.777448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 502.316 | 0.619379 | 0.309689 | − | 0.950838i | \(-0.399775\pi\) | ||||
0.309689 | + | 0.950838i | \(0.399775\pi\) | |||||||
\(812\) | −191.720 | − | 110.689i | −0.236108 | − | 0.136317i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 326.154 | + | 564.916i | 0.400681 | + | 0.694000i | ||||
\(815\) | −457.251 | + | 263.994i | −0.561044 | + | 0.323919i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −834.980 | + | 1446.23i | −1.02201 | + | 1.77017i | ||||
\(818\) | 13.7983i | 0.0168684i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 735.984 | 0.897542 | ||||||||
\(821\) | 20.0170 | + | 11.5568i | 0.0243813 | + | 0.0140765i | 0.512141 | − | 0.858901i | \(-0.328852\pi\) |
−0.487760 | + | 0.872978i | \(0.662186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 300.332 | + | 520.190i | 0.364923 | + | 0.632066i | 0.988764 | − | 0.149486i | \(-0.0477618\pi\) |
−0.623840 | + | 0.781552i | \(0.714428\pi\) | |||||||
\(824\) | 322.103 | − | 185.966i | 0.390902 | − | 0.225687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −108.915 | + | 188.646i | −0.131858 | + | 0.228385i | ||||
\(827\) | − | 1309.21i | − | 1.58308i | −0.611118 | − | 0.791540i | \(-0.709280\pi\) | ||
0.611118 | − | 0.791540i | \(-0.290720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −621.919 | −0.750204 | −0.375102 | − | 0.926984i | \(-0.622392\pi\) | ||||
−0.375102 | + | 0.926984i | \(0.622392\pi\) | |||||||
\(830\) | −450.271 | − | 259.964i | −0.542495 | − | 0.313209i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −74.3320 | − | 128.747i | −0.0893414 | − | 0.154744i | ||||
\(833\) | −66.0866 | + | 38.1551i | −0.0793357 | + | 0.0458045i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −183.822 | + | 318.389i | −0.220146 | + | 0.381305i | ||||
\(836\) | 485.528i | 0.580775i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 480.000 | 0.572792 | ||||||||
\(839\) | −1030.83 | − | 595.149i | −1.22864 | − | 0.709355i | −0.261894 | − | 0.965097i | \(-0.584347\pi\) |
−0.966745 | + | 0.255741i | \(0.917680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 454.654 | + | 787.484i | 0.540611 | + | 0.936366i | ||||
\(842\) | 734.014 | − | 423.783i | 0.871751 | − | 0.503306i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −84.5020 | + | 146.362i | −0.100121 | + | 0.173414i | ||||
\(845\) | − | 1070.15i | − | 1.26645i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 69.6784 | 0.0822649 | ||||||||
\(848\) | −325.772 | − | 188.085i | −0.384166 | − | 0.221798i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −91.2223 | − | 158.002i | −0.107320 | − | 0.185884i | ||||
\(851\) | −399.456 | + | 230.626i | −0.469396 | + | 0.271006i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −68.5059 | + | 118.656i | −0.0803117 | + | 0.139104i | −0.903384 | − | 0.428833i | \(-0.858925\pi\) |
0.823072 | + | 0.567937i | \(0.192258\pi\) | |||||||
\(854\) | 58.6242i | 0.0686466i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −233.004 | −0.272201 | ||||||||
\(857\) | −403.690 | − | 233.071i | −0.471050 | − | 0.271961i | 0.245629 | − | 0.969364i | \(-0.421006\pi\) |
−0.716679 | + | 0.697403i | \(0.754339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.9921 | − | 20.7710i | −0.0139606 | − | 0.0241804i | 0.858961 | − | 0.512041i | \(-0.171111\pi\) |
−0.872921 | + | 0.487861i | \(0.837777\pi\) | |||||||
\(860\) | 877.731 | − | 506.758i | 1.02062 | − | 0.589253i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −502.737 | + | 870.766i | −0.583222 | + | 1.01017i | ||||
\(863\) | 0.114603i | 0.000132796i | 1.00000 | 6.63982e-5i | \(2.11352e-5\pi\) | |||||
−1.00000 | 6.63982e-5i | \(0.999979\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 986.664 | 1.14065 | ||||||||
\(866\) | 462.934 | + | 267.275i | 0.534566 | + | 0.308632i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −66.5830 | − | 115.325i | −0.0767085 | − | 0.132863i | ||||
\(869\) | −353.918 | + | 204.334i | −0.407270 | + | 0.235137i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1232.65 | + | 2135.01i | −1.41521 | + | 2.45122i | ||||
\(872\) | 95.6858i | 0.109731i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −343.320 | −0.392815 | ||||||||
\(875\) | −183.087 | − | 105.706i | −0.209243 | − | 0.120806i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −498.652 | − | 863.691i | −0.568589 | − | 0.984824i | −0.996706 | − | 0.0811012i | \(-0.974156\pi\) |
0.428117 | − | 0.903723i | \(-0.359177\pi\) | |||||||
\(878\) | −646.845 | + | 373.456i | −0.736725 | + | 0.425348i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 147.336 | − | 255.193i | 0.167427 | − | 0.289992i | ||||
\(881\) | 935.649i | 1.06203i | 0.847362 | + | 0.531015i | \(0.178189\pi\) | ||||
−0.847362 | + | 0.531015i | \(0.821811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1549.47 | −1.75478 | −0.877392 | − | 0.479774i | \(-0.840719\pi\) | ||||
−0.877392 | + | 0.479774i | \(0.840719\pi\) | |||||||
\(884\) | 350.882 | + | 202.582i | 0.396926 | + | 0.229165i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.9111 | − | 44.8793i | −0.0292450 | − | 0.0506539i | ||||
\(887\) | −774.654 | + | 447.246i | −0.873341 | + | 0.504224i | −0.868457 | − | 0.495764i | \(-0.834888\pi\) |
−0.00488401 | + | 0.999988i | \(0.501555\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 171.535 | − | 297.107i | 0.192952 | − | 0.334203i | ||||
\(890\) | 40.9844i | 0.0460498i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 316.988 | 0.355368 | ||||||||
\(893\) | 293.939 | + | 169.706i | 0.329159 | + | 0.190040i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −676.980 | − | 1172.56i | −0.756403 | − | 1.31013i | ||||
\(896\) | −25.9230 | + | 14.9666i | −0.0289319 | + | 0.0167038i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 281.154 | − | 486.973i | 0.313089 | − | 0.542287i | ||||
\(899\) | 1052.86i | 1.17115i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1025.20 | 1.13785 | ||||||||
\(902\) | −901.393 | − | 520.419i | −0.999327 | − | 0.576962i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −40.3320 | − | 69.8571i | −0.0446151 | − | 0.0772756i | ||||
\(905\) | −992.937 | + | 573.272i | −1.09717 | + | 0.633450i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 67.9190 | − | 117.639i | 0.0748831 | − | 0.129701i | −0.826152 | − | 0.563447i | \(-0.809475\pi\) |
0.901035 | + | 0.433746i | \(0.142808\pi\) | |||||||
\(908\) | − | 203.647i | − | 0.224281i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −421.992 | −0.463728 | ||||||||
\(911\) | 1075.61 | + | 621.006i | 1.18070 | + | 0.681675i | 0.956175 | − | 0.292794i | \(-0.0945851\pi\) |
0.224521 | + | 0.974469i | \(0.427918\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 367.644 | + | 636.779i | 0.402677 | + | 0.697458i | ||||
\(914\) | −421.709 | + | 243.474i | −0.461389 | + | 0.266383i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −268.915 | + | 465.774i | −0.293575 | + | 0.508487i | ||||
\(917\) | 391.617i | 0.427063i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −388.162 | −0.422374 | −0.211187 | − | 0.977446i | \(-0.567733\pi\) | ||||
−0.211187 | + | 0.977446i | \(0.567733\pi\) | |||||||
\(920\) | 180.449 | + | 104.182i | 0.196140 | + | 0.113242i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 262.292 | + | 454.302i | 0.284481 | + | 0.492736i | ||||
\(923\) | 195.344 | − | 112.782i | 0.211641 | − | 0.122191i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 224.846 | − | 389.444i | 0.243077 | − | 0.421021i | ||||
\(926\) | − | 110.778i | − | 0.119631i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 236.664 | 0.255026 | ||||||||
\(929\) | 538.403 | + | 310.847i | 0.579551 | + | 0.334604i | 0.760955 | − | 0.648805i | \(-0.224731\pi\) |
−0.181404 | + | 0.983409i | \(0.558064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −70.0000 | − | 121.244i | −0.0751880 | − | 0.130229i | ||||
\(932\) | 45.5092 | − | 26.2748i | 0.0488297 | − | 0.0281918i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 282.672 | − | 489.602i | 0.302647 | − | 0.524199i | ||||
\(935\) | 803.089i | 0.858918i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1262.00 | 1.34685 | 0.673426 | − | 0.739255i | \(-0.264822\pi\) | ||||
0.673426 | + | 0.739255i | \(0.264822\pi\) | |||||||
\(938\) | 429.881 | + | 248.192i | 0.458295 | + | 0.264597i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −102.996 | − | 178.394i | −0.109570 | − | 0.189781i | ||||
\(941\) | 582.324 | − | 336.205i | 0.618835 | − | 0.357285i | −0.157580 | − | 0.987506i | \(-0.550369\pi\) |
0.776415 | + | 0.630222i | \(0.217036\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 367.992 | − | 637.381i | 0.390236 | − | 0.675908i | ||||
\(944\) | − | 232.870i | − | 0.246684i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1433.33 | −1.51515 | ||||||||
\(947\) | −1004.37 | − | 579.874i | −1.06058 | − | 0.612327i | −0.134989 | − | 0.990847i | \(-0.543100\pi\) |
−0.925593 | + | 0.378520i | \(0.876433\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −714.656 | − | 1237.82i | −0.753062 | − | 1.30434i | ||||
\(950\) | 289.872 | − | 167.358i | 0.305129 | − | 0.176166i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 40.7895 | − | 70.6495i | 0.0428461 | − | 0.0742117i | ||||
\(953\) | − | 163.104i | − | 0.171148i | −0.996332 | − | 0.0855740i | \(-0.972728\pi\) | ||
0.996332 | − | 0.0855740i | \(-0.0272724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1383.98 | −1.44920 | ||||||||
\(956\) | 159.822 | + | 92.2733i | 0.167178 | + | 0.0965201i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 497.328 | + | 861.398i | 0.519132 | + | 0.899162i | ||||
\(959\) | 176.331 | − | 101.805i | 0.183870 | − | 0.106157i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 163.836 | − | 283.772i | 0.170485 | − | 0.295288i | ||||
\(962\) | 998.653i | 1.03810i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −686.494 | −0.712131 | ||||||||
\(965\) | 704.303 | + | 406.630i | 0.729848 | + | 0.421378i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −443.506 | − | 768.175i | −0.458641 | − | 0.794390i | 0.540248 | − | 0.841506i | \(-0.318330\pi\) |
−0.998889 | + | 0.0471160i | \(0.984997\pi\) | |||||||
\(968\) | −64.5097 | + | 37.2447i | −0.0666422 | + | 0.0384759i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −808.575 | + | 1400.49i | −0.833583 | + | 1.44381i | ||||
\(971\) | − | 1416.32i | − | 1.45862i | −0.684183 | − | 0.729310i | \(-0.739841\pi\) | ||
0.684183 | − | 0.729310i | \(-0.260159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −574.996 | −0.590952 | ||||||||
\(974\) | −101.054 | − | 58.3433i | −0.103751 | − | 0.0599007i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.3360 | − | 54.2755i | −0.0321065 | − | 0.0556101i | ||||
\(977\) | 293.627 | − | 169.525i | 0.300539 | − | 0.173516i | −0.342146 | − | 0.939647i | \(-0.611154\pi\) |
0.642685 | + | 0.766131i | \(0.277820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.9803 | − | 50.1954i | 0.0296020 | − | 0.0512721i | ||||
\(980\) | 84.9674i | 0.0867014i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −260.502 | −0.265277 | ||||||||
\(983\) | 422.523 | + | 243.943i | 0.429830 | + | 0.248162i | 0.699274 | − | 0.714854i | \(-0.253507\pi\) |
−0.269444 | + | 0.963016i | \(0.586840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 572.195 | + | 991.070i | 0.580908 | + | 1.00616i | ||||
\(986\) | −558.583 | + | 322.498i | −0.566514 | + | 0.327077i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −371.660 | + | 643.734i | −0.376174 | + | 0.651553i | ||||
\(989\) | − | 1013.52i | − | 1.02479i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −937.474 | −0.945988 | −0.472994 | − | 0.881066i | \(-0.656827\pi\) | ||||
−0.472994 | + | 0.881066i | \(0.656827\pi\) | |||||||
\(992\) | 123.288 | + | 71.1802i | 0.124282 | + | 0.0717543i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.7085 | − | 39.3323i | −0.0228456 | − | 0.0395697i | ||||
\(995\) | −538.709 | + | 311.024i | −0.541416 | + | 0.312586i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −230.506 | + | 399.248i | −0.231200 | + | 0.400449i | −0.958161 | − | 0.286229i | \(-0.907598\pi\) |
0.726962 | + | 0.686678i | \(0.240932\pi\) | |||||||
\(998\) | − | 1064.63i | − | 1.06677i | ||||||
\(999\) | 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 | 1134.3.q.c.1079.3 | 8 | ||
3.2 | odd | 2 | inner | 1134.3.q.c.1079.2 | 8 | ||
9.2 | odd | 6 | 126.3.b.a.71.4 | yes | 4 | ||
9.4 | even | 3 | inner | 1134.3.q.c.701.2 | 8 | ||
9.5 | odd | 6 | inner | 1134.3.q.c.701.3 | 8 | ||
9.7 | even | 3 | 126.3.b.a.71.1 | ✓ | 4 | ||
36.7 | odd | 6 | 1008.3.d.a.449.2 | 4 | |||
36.11 | even | 6 | 1008.3.d.a.449.3 | 4 | |||
45.2 | even | 12 | 3150.3.c.b.449.1 | 8 | |||
45.7 | odd | 12 | 3150.3.c.b.449.6 | 8 | |||
45.29 | odd | 6 | 3150.3.e.e.701.2 | 4 | |||
45.34 | even | 6 | 3150.3.e.e.701.4 | 4 | |||
45.38 | even | 12 | 3150.3.c.b.449.7 | 8 | |||
45.43 | odd | 12 | 3150.3.c.b.449.4 | 8 | |||
63.2 | odd | 6 | 882.3.s.e.557.4 | 8 | |||
63.11 | odd | 6 | 882.3.s.e.863.1 | 8 | |||
63.16 | even | 3 | 882.3.s.e.557.1 | 8 | |||
63.20 | even | 6 | 882.3.b.f.197.3 | 4 | |||
63.25 | even | 3 | 882.3.s.e.863.4 | 8 | |||
63.34 | odd | 6 | 882.3.b.f.197.2 | 4 | |||
63.38 | even | 6 | 882.3.s.i.863.2 | 8 | |||
63.47 | even | 6 | 882.3.s.i.557.3 | 8 | |||
63.52 | odd | 6 | 882.3.s.i.863.3 | 8 | |||
63.61 | odd | 6 | 882.3.s.i.557.2 | 8 | |||
72.11 | even | 6 | 4032.3.d.j.449.2 | 4 | |||
72.29 | odd | 6 | 4032.3.d.i.449.2 | 4 | |||
72.43 | odd | 6 | 4032.3.d.j.449.3 | 4 | |||
72.61 | even | 6 | 4032.3.d.i.449.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.b.a.71.1 | ✓ | 4 | 9.7 | even | 3 | ||
126.3.b.a.71.4 | yes | 4 | 9.2 | odd | 6 | ||
882.3.b.f.197.2 | 4 | 63.34 | odd | 6 | |||
882.3.b.f.197.3 | 4 | 63.20 | even | 6 | |||
882.3.s.e.557.1 | 8 | 63.16 | even | 3 | |||
882.3.s.e.557.4 | 8 | 63.2 | odd | 6 | |||
882.3.s.e.863.1 | 8 | 63.11 | odd | 6 | |||
882.3.s.e.863.4 | 8 | 63.25 | even | 3 | |||
882.3.s.i.557.2 | 8 | 63.61 | odd | 6 | |||
882.3.s.i.557.3 | 8 | 63.47 | even | 6 | |||
882.3.s.i.863.2 | 8 | 63.38 | even | 6 | |||
882.3.s.i.863.3 | 8 | 63.52 | odd | 6 | |||
1008.3.d.a.449.2 | 4 | 36.7 | odd | 6 | |||
1008.3.d.a.449.3 | 4 | 36.11 | even | 6 | |||
1134.3.q.c.701.2 | 8 | 9.4 | even | 3 | inner | ||
1134.3.q.c.701.3 | 8 | 9.5 | odd | 6 | inner | ||
1134.3.q.c.1079.2 | 8 | 3.2 | odd | 2 | inner | ||
1134.3.q.c.1079.3 | 8 | 1.1 | even | 1 | trivial | ||
3150.3.c.b.449.1 | 8 | 45.2 | even | 12 | |||
3150.3.c.b.449.4 | 8 | 45.43 | odd | 12 | |||
3150.3.c.b.449.6 | 8 | 45.7 | odd | 12 | |||
3150.3.c.b.449.7 | 8 | 45.38 | even | 12 | |||
3150.3.e.e.701.2 | 4 | 45.29 | odd | 6 | |||
3150.3.e.e.701.4 | 4 | 45.34 | even | 6 | |||
4032.3.d.i.449.2 | 4 | 72.29 | odd | 6 | |||
4032.3.d.i.449.3 | 4 | 72.61 | even | 6 | |||
4032.3.d.j.449.2 | 4 | 72.11 | even | 6 | |||
4032.3.d.j.449.3 | 4 | 72.43 | odd | 6 |