Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,3,Mod(7,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.f (of order \(4\), degree \(2\), 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: | \(4.08720396540\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.7 |
Dual form | 150.3.f.c.43.1 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 7.22474 | + | 7.22474i | 1.03211 | + | 1.03211i | 0.999467 | + | 0.0326392i | \(0.0103912\pi\) |
0.0326392 | + | 0.999467i | \(0.489609\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.69694 | −0.790631 | −0.395315 | − | 0.918545i | \(-0.629365\pi\) | ||||
−0.395315 | + | 0.918545i | \(0.629365\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | −15.6742 | + | 15.6742i | −1.20571 | + | 1.20571i | −0.233307 | + | 0.972403i | \(0.574955\pi\) |
−0.972403 | + | 0.233307i | \(0.925045\pi\) | |||||||
\(14\) | 14.4495i | 1.03211i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 13.3485 | + | 13.3485i | 0.785204 | + | 0.785204i | 0.980704 | − | 0.195500i | \(-0.0626329\pi\) |
−0.195500 | + | 0.980704i | \(0.562633\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | − | 4.30306i | − | 0.226477i | −0.993568 | − | 0.113238i | \(-0.963878\pi\) | ||
0.993568 | − | 0.113238i | \(-0.0361224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −17.6969 | −0.842711 | ||||||||
\(22\) | −8.69694 | − | 8.69694i | −0.395315 | − | 0.395315i | ||||
\(23\) | 28.0454 | − | 28.0454i | 1.21937 | − | 1.21937i | 0.251511 | − | 0.967854i | \(-0.419072\pi\) |
0.967854 | − | 0.251511i | \(-0.0809275\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −31.3485 | −1.20571 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −14.4495 | + | 14.4495i | −0.516053 | + | 0.516053i | ||||
\(29\) | − | 20.6969i | − | 0.713688i | −0.934164 | − | 0.356844i | \(-0.883853\pi\) | ||
0.934164 | − | 0.356844i | \(-0.116147\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.0908 | 1.26099 | 0.630497 | − | 0.776192i | \(-0.282851\pi\) | ||||
0.630497 | + | 0.776192i | \(0.282851\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 10.6515 | − | 10.6515i | 0.322774 | − | 0.322774i | ||||
\(34\) | 26.6969i | 0.785204i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 12.4949 | + | 12.4949i | 0.337700 | + | 0.337700i | 0.855501 | − | 0.517801i | \(-0.173249\pi\) |
−0.517801 | + | 0.855501i | \(0.673249\pi\) | |||||||
\(38\) | 4.30306 | − | 4.30306i | 0.113238 | − | 0.113238i | ||||
\(39\) | − | 38.3939i | − | 0.984458i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 62.6969 | 1.52919 | 0.764597 | − | 0.644509i | \(-0.222938\pi\) | ||||
0.764597 | + | 0.644509i | \(0.222938\pi\) | |||||||
\(42\) | −17.6969 | − | 17.6969i | −0.421356 | − | 0.421356i | ||||
\(43\) | −11.8763 | + | 11.8763i | −0.276192 | + | 0.276192i | −0.831587 | − | 0.555395i | \(-0.812567\pi\) |
0.555395 | + | 0.831587i | \(0.312567\pi\) | |||||||
\(44\) | − | 17.3939i | − | 0.395315i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 56.0908 | 1.21937 | ||||||||
\(47\) | −58.0454 | − | 58.0454i | −1.23501 | − | 1.23501i | −0.962016 | − | 0.272993i | \(-0.911987\pi\) |
−0.272993 | − | 0.962016i | \(-0.588013\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 55.3939i | 1.13049i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −32.6969 | −0.641116 | ||||||||
\(52\) | −31.3485 | − | 31.3485i | −0.602855 | − | 0.602855i | ||||
\(53\) | 0.606123 | − | 0.606123i | 0.0114363 | − | 0.0114363i | −0.701366 | − | 0.712802i | \(-0.747426\pi\) |
0.712802 | + | 0.701366i | \(0.247426\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −28.8990 | −0.516053 | ||||||||
\(57\) | 5.27015 | + | 5.27015i | 0.0924588 | + | 0.0924588i | ||||
\(58\) | 20.6969 | − | 20.6969i | 0.356844 | − | 0.356844i | ||||
\(59\) | − | 30.0000i | − | 0.508475i | −0.967142 | − | 0.254237i | \(-0.918176\pi\) | ||
0.967142 | − | 0.254237i | \(-0.0818244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 69.7878 | 1.14406 | 0.572031 | − | 0.820232i | \(-0.306156\pi\) | ||||
0.572031 | + | 0.820232i | \(0.306156\pi\) | |||||||
\(62\) | 39.0908 | + | 39.0908i | 0.630497 | + | 0.630497i | ||||
\(63\) | 21.6742 | − | 21.6742i | 0.344035 | − | 0.344035i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 21.3031 | 0.322774 | ||||||||
\(67\) | −5.02270 | − | 5.02270i | −0.0749657 | − | 0.0749657i | 0.668630 | − | 0.743595i | \(-0.266881\pi\) |
−0.743595 | + | 0.668630i | \(0.766881\pi\) | |||||||
\(68\) | −26.6969 | + | 26.6969i | −0.392602 | + | 0.392602i | ||||
\(69\) | 68.6969i | 0.995608i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −38.6969 | −0.545027 | −0.272514 | − | 0.962152i | \(-0.587855\pi\) | ||||
−0.272514 | + | 0.962152i | \(0.587855\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −46.2929 | + | 46.2929i | −0.634149 | + | 0.634149i | −0.949106 | − | 0.314957i | \(-0.898010\pi\) |
0.314957 | + | 0.949106i | \(0.398010\pi\) | |||||||
\(74\) | 24.9898i | 0.337700i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.60612 | 0.113238 | ||||||||
\(77\) | −62.8332 | − | 62.8332i | −0.816015 | − | 0.816015i | ||||
\(78\) | 38.3939 | − | 38.3939i | 0.492229 | − | 0.492229i | ||||
\(79\) | − | 31.3939i | − | 0.397391i | −0.980061 | − | 0.198695i | \(-0.936330\pi\) | ||
0.980061 | − | 0.198695i | \(-0.0636705\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 62.6969 | + | 62.6969i | 0.764597 | + | 0.764597i | ||||
\(83\) | 39.4393 | − | 39.4393i | 0.475172 | − | 0.475172i | −0.428412 | − | 0.903584i | \(-0.640927\pi\) |
0.903584 | + | 0.428412i | \(0.140927\pi\) | |||||||
\(84\) | − | 35.3939i | − | 0.421356i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −23.7526 | −0.276192 | ||||||||
\(87\) | 25.3485 | + | 25.3485i | 0.291362 | + | 0.291362i | ||||
\(88\) | 17.3939 | − | 17.3939i | 0.197658 | − | 0.197658i | ||||
\(89\) | − | 41.3939i | − | 0.465100i | −0.972584 | − | 0.232550i | \(-0.925293\pi\) | ||
0.972584 | − | 0.232550i | \(-0.0747069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −226.485 | −2.48884 | ||||||||
\(92\) | 56.0908 | + | 56.0908i | 0.609683 | + | 0.609683i | ||||
\(93\) | −47.8763 | + | 47.8763i | −0.514799 | + | 0.514799i | ||||
\(94\) | − | 116.091i | − | 1.23501i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 54.1237 | + | 54.1237i | 0.557977 | + | 0.557977i | 0.928731 | − | 0.370754i | \(-0.120901\pi\) |
−0.370754 | + | 0.928731i | \(0.620901\pi\) | |||||||
\(98\) | −55.3939 | + | 55.3939i | −0.565244 | + | 0.565244i | ||||
\(99\) | 26.0908i | 0.263544i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −42.8786 | −0.424540 | −0.212270 | − | 0.977211i | \(-0.568086\pi\) | ||||
−0.212270 | + | 0.977211i | \(0.568086\pi\) | |||||||
\(102\) | −32.6969 | − | 32.6969i | −0.320558 | − | 0.320558i | ||||
\(103\) | 60.9898 | − | 60.9898i | 0.592134 | − | 0.592134i | −0.346073 | − | 0.938207i | \(-0.612485\pi\) |
0.938207 | + | 0.346073i | \(0.112485\pi\) | |||||||
\(104\) | − | 62.6969i | − | 0.602855i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.21225 | 0.0114363 | ||||||||
\(107\) | 45.9092 | + | 45.9092i | 0.429058 | + | 0.429058i | 0.888307 | − | 0.459250i | \(-0.151882\pi\) |
−0.459250 | + | 0.888307i | \(0.651882\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 145.000i | 1.33028i | 0.746721 | + | 0.665138i | \(0.231627\pi\) | ||||
−0.746721 | + | 0.665138i | \(0.768373\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30.6061 | −0.275731 | ||||||||
\(112\) | −28.8990 | − | 28.8990i | −0.258027 | − | 0.258027i | ||||
\(113\) | −130.788 | + | 130.788i | −1.15741 | + | 1.15741i | −0.172384 | + | 0.985030i | \(0.555147\pi\) |
−0.985030 | + | 0.172384i | \(0.944853\pi\) | |||||||
\(114\) | 10.5403i | 0.0924588i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 41.3939 | 0.356844 | ||||||||
\(117\) | 47.0227 | + | 47.0227i | 0.401903 | + | 0.401903i | ||||
\(118\) | 30.0000 | − | 30.0000i | 0.254237 | − | 0.254237i | ||||
\(119\) | 192.879i | 1.62083i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −45.3633 | −0.374903 | ||||||||
\(122\) | 69.7878 | + | 69.7878i | 0.572031 | + | 0.572031i | ||||
\(123\) | −76.7878 | + | 76.7878i | −0.624291 | + | 0.624291i | ||||
\(124\) | 78.1816i | 0.630497i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 43.3485 | 0.344035 | ||||||||
\(127\) | −21.3031 | − | 21.3031i | −0.167741 | − | 0.167741i | 0.618245 | − | 0.785986i | \(-0.287844\pi\) |
−0.785986 | + | 0.618245i | \(0.787844\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 29.0908i | − | 0.225510i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 108.272 | 0.826507 | 0.413254 | − | 0.910616i | \(-0.364392\pi\) | ||||
0.413254 | + | 0.910616i | \(0.364392\pi\) | |||||||
\(132\) | 21.3031 | + | 21.3031i | 0.161387 | + | 0.161387i | ||||
\(133\) | 31.0885 | − | 31.0885i | 0.233748 | − | 0.233748i | ||||
\(134\) | − | 10.0454i | − | 0.0749657i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −53.3939 | −0.392602 | ||||||||
\(137\) | −76.6515 | − | 76.6515i | −0.559500 | − | 0.559500i | 0.369665 | − | 0.929165i | \(-0.379472\pi\) |
−0.929165 | + | 0.369665i | \(0.879472\pi\) | |||||||
\(138\) | −68.6969 | + | 68.6969i | −0.497804 | + | 0.497804i | ||||
\(139\) | − | 152.788i | − | 1.09919i | −0.835430 | − | 0.549596i | \(-0.814782\pi\) | ||
0.835430 | − | 0.549596i | \(-0.185218\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 142.182 | 1.00838 | ||||||||
\(142\) | −38.6969 | − | 38.6969i | −0.272514 | − | 0.272514i | ||||
\(143\) | 136.318 | − | 136.318i | 0.953272 | − | 0.953272i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −92.5857 | −0.634149 | ||||||||
\(147\) | −67.8434 | − | 67.8434i | −0.461520 | − | 0.461520i | ||||
\(148\) | −24.9898 | + | 24.9898i | −0.168850 | + | 0.168850i | ||||
\(149\) | 112.788i | 0.756965i | 0.925608 | + | 0.378482i | \(0.123554\pi\) | ||||
−0.925608 | + | 0.378482i | \(0.876446\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −167.879 | −1.11178 | −0.555889 | − | 0.831256i | \(-0.687622\pi\) | ||||
−0.555889 | + | 0.831256i | \(0.687622\pi\) | |||||||
\(152\) | 8.60612 | + | 8.60612i | 0.0566192 | + | 0.0566192i | ||||
\(153\) | 40.0454 | − | 40.0454i | 0.261735 | − | 0.261735i | ||||
\(154\) | − | 125.666i | − | 0.816015i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 76.7878 | 0.492229 | ||||||||
\(157\) | −114.866 | − | 114.866i | −0.731631 | − | 0.731631i | 0.239312 | − | 0.970943i | \(-0.423078\pi\) |
−0.970943 | + | 0.239312i | \(0.923078\pi\) | |||||||
\(158\) | 31.3939 | − | 31.3939i | 0.198695 | − | 0.198695i | ||||
\(159\) | 1.48469i | 0.00933769i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 405.242 | 2.51703 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 10.1441 | − | 10.1441i | 0.0622340 | − | 0.0622340i | −0.675305 | − | 0.737539i | \(-0.735988\pi\) |
0.737539 | + | 0.675305i | \(0.235988\pi\) | |||||||
\(164\) | 125.394i | 0.764597i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 78.8786 | 0.475172 | ||||||||
\(167\) | 155.666 | + | 155.666i | 0.932134 | + | 0.932134i | 0.997839 | − | 0.0657054i | \(-0.0209298\pi\) |
−0.0657054 | + | 0.997839i | \(0.520930\pi\) | |||||||
\(168\) | 35.3939 | − | 35.3939i | 0.210678 | − | 0.210678i | ||||
\(169\) | − | 322.363i | − | 1.90747i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.9092 | −0.0754923 | ||||||||
\(172\) | −23.7526 | − | 23.7526i | −0.138096 | − | 0.138096i | ||||
\(173\) | −86.8332 | + | 86.8332i | −0.501926 | + | 0.501926i | −0.912036 | − | 0.410110i | \(-0.865490\pi\) |
0.410110 | + | 0.912036i | \(0.365490\pi\) | |||||||
\(174\) | 50.6969i | 0.291362i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 34.7878 | 0.197658 | ||||||||
\(177\) | 36.7423 | + | 36.7423i | 0.207584 | + | 0.207584i | ||||
\(178\) | 41.3939 | − | 41.3939i | 0.232550 | − | 0.232550i | ||||
\(179\) | − | 241.151i | − | 1.34721i | −0.739090 | − | 0.673606i | \(-0.764744\pi\) | ||
0.739090 | − | 0.673606i | \(-0.235256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 41.1816 | 0.227523 | 0.113761 | − | 0.993508i | \(-0.463710\pi\) | ||||
0.113761 | + | 0.993508i | \(0.463710\pi\) | |||||||
\(182\) | −226.485 | − | 226.485i | −1.24442 | − | 1.24442i | ||||
\(183\) | −85.4722 | + | 85.4722i | −0.467061 | + | 0.467061i | ||||
\(184\) | 112.182i | 0.609683i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −95.7526 | −0.514799 | ||||||||
\(187\) | −116.091 | − | 116.091i | −0.620806 | − | 0.620806i | ||||
\(188\) | 116.091 | − | 116.091i | 0.617504 | − | 0.617504i | ||||
\(189\) | 53.0908i | 0.280904i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −110.091 | −0.576392 | −0.288196 | − | 0.957571i | \(-0.593055\pi\) | ||||
−0.288196 | + | 0.957571i | \(0.593055\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 266.487 | − | 266.487i | 1.38076 | − | 1.38076i | 0.537494 | − | 0.843268i | \(-0.319371\pi\) |
0.843268 | − | 0.537494i | \(-0.180629\pi\) | |||||||
\(194\) | 108.247i | 0.557977i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −110.788 | −0.565244 | ||||||||
\(197\) | −39.4393 | − | 39.4393i | −0.200199 | − | 0.200199i | 0.599886 | − | 0.800085i | \(-0.295213\pi\) |
−0.800085 | + | 0.599886i | \(0.795213\pi\) | |||||||
\(198\) | −26.0908 | + | 26.0908i | −0.131772 | + | 0.131772i | ||||
\(199\) | − | 92.9092i | − | 0.466880i | −0.972371 | − | 0.233440i | \(-0.925002\pi\) | ||
0.972371 | − | 0.233440i | \(-0.0749983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.3031 | 0.0612093 | ||||||||
\(202\) | −42.8786 | − | 42.8786i | −0.212270 | − | 0.212270i | ||||
\(203\) | 149.530 | − | 149.530i | 0.736601 | − | 0.736601i | ||||
\(204\) | − | 65.3939i | − | 0.320558i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 121.980 | 0.592134 | ||||||||
\(207\) | −84.1362 | − | 84.1362i | −0.406455 | − | 0.406455i | ||||
\(208\) | 62.6969 | − | 62.6969i | 0.301428 | − | 0.301428i | ||||
\(209\) | 37.4235i | 0.179060i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 293.272 | 1.38992 | 0.694958 | − | 0.719050i | \(-0.255423\pi\) | ||||
0.694958 | + | 0.719050i | \(0.255423\pi\) | |||||||
\(212\) | 1.21225 | + | 1.21225i | 0.00571814 | + | 0.00571814i | ||||
\(213\) | 47.3939 | − | 47.3939i | 0.222506 | − | 0.222506i | ||||
\(214\) | 91.8184i | 0.429058i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 282.421 | + | 282.421i | 1.30148 | + | 1.30148i | ||||
\(218\) | −145.000 | + | 145.000i | −0.665138 | + | 0.665138i | ||||
\(219\) | − | 113.394i | − | 0.517780i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −418.454 | −1.89346 | ||||||||
\(222\) | −30.6061 | − | 30.6061i | −0.137865 | − | 0.137865i | ||||
\(223\) | −74.8207 | + | 74.8207i | −0.335519 | + | 0.335519i | −0.854678 | − | 0.519159i | \(-0.826245\pi\) |
0.519159 | + | 0.854678i | \(0.326245\pi\) | |||||||
\(224\) | − | 57.7980i | − | 0.258027i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −261.576 | −1.15741 | ||||||||
\(227\) | −47.1214 | − | 47.1214i | −0.207583 | − | 0.207583i | 0.595656 | − | 0.803240i | \(-0.296892\pi\) |
−0.803240 | + | 0.595656i | \(0.796892\pi\) | |||||||
\(228\) | −10.5403 | + | 10.5403i | −0.0462294 | + | 0.0462294i | ||||
\(229\) | 275.000i | 1.20087i | 0.799672 | + | 0.600437i | \(0.205007\pi\) | ||||
−0.799672 | + | 0.600437i | \(0.794993\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 153.909 | 0.666274 | ||||||||
\(232\) | 41.3939 | + | 41.3939i | 0.178422 | + | 0.178422i | ||||
\(233\) | −187.757 | + | 187.757i | −0.805825 | + | 0.805825i | −0.983999 | − | 0.178174i | \(-0.942981\pi\) |
0.178174 | + | 0.983999i | \(0.442981\pi\) | |||||||
\(234\) | 94.0454i | 0.401903i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 60.0000 | 0.254237 | ||||||||
\(237\) | 38.4495 | + | 38.4495i | 0.162234 | + | 0.162234i | ||||
\(238\) | −192.879 | + | 192.879i | −0.810414 | + | 0.810414i | ||||
\(239\) | − | 17.6663i | − | 0.0739177i | −0.999317 | − | 0.0369588i | \(-0.988233\pi\) | ||
0.999317 | − | 0.0369588i | \(-0.0117670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 167.000 | 0.692946 | 0.346473 | − | 0.938060i | \(-0.387379\pi\) | ||||
0.346473 | + | 0.938060i | \(0.387379\pi\) | |||||||
\(242\) | −45.3633 | − | 45.3633i | −0.187451 | − | 0.187451i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 139.576i | 0.572031i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −153.576 | −0.624291 | ||||||||
\(247\) | 67.4472 | + | 67.4472i | 0.273066 | + | 0.273066i | ||||
\(248\) | −78.1816 | + | 78.1816i | −0.315249 | + | 0.315249i | ||||
\(249\) | 96.6061i | 0.387976i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.4245 | 0.105277 | 0.0526384 | − | 0.998614i | \(-0.483237\pi\) | ||||
0.0526384 | + | 0.998614i | \(0.483237\pi\) | |||||||
\(252\) | 43.3485 | + | 43.3485i | 0.172018 | + | 0.172018i | ||||
\(253\) | −243.909 | + | 243.909i | −0.964068 | + | 0.964068i | ||||
\(254\) | − | 42.6061i | − | 0.167741i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 241.485 | + | 241.485i | 0.939629 | + | 0.939629i | 0.998279 | − | 0.0586495i | \(-0.0186794\pi\) |
−0.0586495 | + | 0.998279i | \(0.518679\pi\) | |||||||
\(258\) | 29.0908 | − | 29.0908i | 0.112755 | − | 0.112755i | ||||
\(259\) | 180.545i | 0.697085i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −62.0908 | −0.237896 | ||||||||
\(262\) | 108.272 | + | 108.272i | 0.413254 | + | 0.413254i | ||||
\(263\) | −142.182 | + | 142.182i | −0.540615 | + | 0.540615i | −0.923709 | − | 0.383095i | \(-0.874858\pi\) |
0.383095 | + | 0.923709i | \(0.374858\pi\) | |||||||
\(264\) | 42.6061i | 0.161387i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 62.1770 | 0.233748 | ||||||||
\(267\) | 50.6969 | + | 50.6969i | 0.189876 | + | 0.189876i | ||||
\(268\) | 10.0454 | − | 10.0454i | 0.0374829 | − | 0.0374829i | ||||
\(269\) | − | 521.605i | − | 1.93905i | −0.244988 | − | 0.969526i | \(-0.578784\pi\) | ||
0.244988 | − | 0.969526i | \(-0.421216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 39.2122 | 0.144695 | 0.0723473 | − | 0.997379i | \(-0.476951\pi\) | ||||
0.0723473 | + | 0.997379i | \(0.476951\pi\) | |||||||
\(272\) | −53.3939 | − | 53.3939i | −0.196301 | − | 0.196301i | ||||
\(273\) | 277.386 | − | 277.386i | 1.01607 | − | 1.01607i | ||||
\(274\) | − | 153.303i | − | 0.559500i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −137.394 | −0.497804 | ||||||||
\(277\) | −69.5880 | − | 69.5880i | −0.251220 | − | 0.251220i | 0.570251 | − | 0.821471i | \(-0.306846\pi\) |
−0.821471 | + | 0.570251i | \(0.806846\pi\) | |||||||
\(278\) | 152.788 | − | 152.788i | 0.549596 | − | 0.549596i | ||||
\(279\) | − | 117.272i | − | 0.420331i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −519.848 | −1.84999 | −0.924996 | − | 0.379976i | \(-0.875932\pi\) | ||||
−0.924996 | + | 0.379976i | \(0.875932\pi\) | |||||||
\(282\) | 142.182 | + | 142.182i | 0.504190 | + | 0.504190i | ||||
\(283\) | −153.427 | + | 153.427i | −0.542144 | + | 0.542144i | −0.924157 | − | 0.382013i | \(-0.875231\pi\) |
0.382013 | + | 0.924157i | \(0.375231\pi\) | |||||||
\(284\) | − | 77.3939i | − | 0.272514i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 272.636 | 0.953272 | ||||||||
\(287\) | 452.969 | + | 452.969i | 1.57829 | + | 1.57829i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 67.3633i | 0.233091i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −132.576 | −0.455586 | ||||||||
\(292\) | −92.5857 | − | 92.5857i | −0.317074 | − | 0.317074i | ||||
\(293\) | −19.6209 | + | 19.6209i | −0.0669656 | + | 0.0669656i | −0.739796 | − | 0.672831i | \(-0.765078\pi\) |
0.672831 | + | 0.739796i | \(0.265078\pi\) | |||||||
\(294\) | − | 135.687i | − | 0.461520i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −49.9796 | −0.168850 | ||||||||
\(297\) | −31.9546 | − | 31.9546i | −0.107591 | − | 0.107591i | ||||
\(298\) | −112.788 | + | 112.788i | −0.378482 | + | 0.378482i | ||||
\(299\) | 879.181i | 2.94040i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −171.606 | −0.570120 | ||||||||
\(302\) | −167.879 | − | 167.879i | −0.555889 | − | 0.555889i | ||||
\(303\) | 52.5153 | − | 52.5153i | 0.173318 | − | 0.173318i | ||||
\(304\) | 17.2122i | 0.0566192i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 80.0908 | 0.261735 | ||||||||
\(307\) | −10.9115 | − | 10.9115i | −0.0355423 | − | 0.0355423i | 0.689112 | − | 0.724655i | \(-0.258001\pi\) |
−0.724655 | + | 0.689112i | \(0.758001\pi\) | |||||||
\(308\) | 125.666 | − | 125.666i | 0.408008 | − | 0.408008i | ||||
\(309\) | 149.394i | 0.483475i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 64.7878 | 0.208321 | 0.104160 | − | 0.994561i | \(-0.466784\pi\) | ||||
0.104160 | + | 0.994561i | \(0.466784\pi\) | |||||||
\(312\) | 76.7878 | + | 76.7878i | 0.246115 | + | 0.246115i | ||||
\(313\) | −25.4472 | + | 25.4472i | −0.0813009 | + | 0.0813009i | −0.746588 | − | 0.665287i | \(-0.768309\pi\) |
0.665287 | + | 0.746588i | \(0.268309\pi\) | |||||||
\(314\) | − | 229.732i | − | 0.731631i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 62.7878 | 0.198695 | ||||||||
\(317\) | −431.060 | − | 431.060i | −1.35981 | − | 1.35981i | −0.874143 | − | 0.485668i | \(-0.838576\pi\) |
−0.485668 | − | 0.874143i | \(-0.661424\pi\) | |||||||
\(318\) | −1.48469 | + | 1.48469i | −0.00466884 | + | 0.00466884i | ||||
\(319\) | 180.000i | 0.564263i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −112.454 | −0.350324 | ||||||||
\(322\) | 405.242 | + | 405.242i | 1.25852 | + | 1.25852i | ||||
\(323\) | 57.4393 | − | 57.4393i | 0.177831 | − | 0.177831i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.2883 | 0.0622340 | ||||||||
\(327\) | −177.588 | − | 177.588i | −0.543083 | − | 0.543083i | ||||
\(328\) | −125.394 | + | 125.394i | −0.382298 | + | 0.382298i | ||||
\(329\) | − | 838.727i | − | 2.54932i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 295.939 | 0.894075 | 0.447037 | − | 0.894515i | \(-0.352479\pi\) | ||||
0.447037 | + | 0.894515i | \(0.352479\pi\) | |||||||
\(332\) | 78.8786 | + | 78.8786i | 0.237586 | + | 0.237586i | ||||
\(333\) | 37.4847 | − | 37.4847i | 0.112567 | − | 0.112567i | ||||
\(334\) | 311.333i | 0.932134i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 70.7878 | 0.210678 | ||||||||
\(337\) | −141.538 | − | 141.538i | −0.419994 | − | 0.419994i | 0.465208 | − | 0.885202i | \(-0.345980\pi\) |
−0.885202 | + | 0.465208i | \(0.845980\pi\) | |||||||
\(338\) | 322.363 | − | 322.363i | 0.953737 | − | 0.953737i | ||||
\(339\) | − | 320.363i | − | 0.945024i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −339.970 | −0.996981 | ||||||||
\(342\) | −12.9092 | − | 12.9092i | −0.0377462 | − | 0.0377462i | ||||
\(343\) | −46.1941 | + | 46.1941i | −0.134677 | + | 0.134677i | ||||
\(344\) | − | 47.5051i | − | 0.138096i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −173.666 | −0.501926 | ||||||||
\(347\) | −362.227 | − | 362.227i | −1.04388 | − | 1.04388i | −0.998992 | − | 0.0448900i | \(-0.985706\pi\) |
−0.0448900 | − | 0.998992i | \(-0.514294\pi\) | |||||||
\(348\) | −50.6969 | + | 50.6969i | −0.145681 | + | 0.145681i | ||||
\(349\) | 403.939i | 1.15742i | 0.815534 | + | 0.578709i | \(0.196443\pi\) | ||||
−0.815534 | + | 0.578709i | \(0.803557\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −115.182 | −0.328153 | ||||||||
\(352\) | 34.7878 | + | 34.7878i | 0.0988288 | + | 0.0988288i | ||||
\(353\) | 18.7423 | − | 18.7423i | 0.0530945 | − | 0.0530945i | −0.680061 | − | 0.733156i | \(-0.738047\pi\) |
0.733156 | + | 0.680061i | \(0.238047\pi\) | |||||||
\(354\) | 73.4847i | 0.207584i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 82.7878 | 0.232550 | ||||||||
\(357\) | −236.227 | − | 236.227i | −0.661700 | − | 0.661700i | ||||
\(358\) | 241.151 | − | 241.151i | 0.673606 | − | 0.673606i | ||||
\(359\) | 383.728i | 1.06888i | 0.845207 | + | 0.534439i | \(0.179477\pi\) | ||||
−0.845207 | + | 0.534439i | \(0.820523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 342.484 | 0.948708 | ||||||||
\(362\) | 41.1816 | + | 41.1816i | 0.113761 | + | 0.113761i | ||||
\(363\) | 55.5584 | − | 55.5584i | 0.153054 | − | 0.153054i | ||||
\(364\) | − | 452.969i | − | 1.24442i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −170.944 | −0.467061 | ||||||||
\(367\) | −387.341 | − | 387.341i | −1.05542 | − | 1.05542i | −0.998371 | − | 0.0570527i | \(-0.981830\pi\) |
−0.0570527 | − | 0.998371i | \(-0.518170\pi\) | |||||||
\(368\) | −112.182 | + | 112.182i | −0.304841 | + | 0.304841i | ||||
\(369\) | − | 188.091i | − | 0.509731i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.75817 | 0.0236069 | ||||||||
\(372\) | −95.7526 | − | 95.7526i | −0.257399 | − | 0.257399i | ||||
\(373\) | 419.815 | − | 419.815i | 1.12551 | − | 1.12551i | 0.134611 | − | 0.990899i | \(-0.457022\pi\) |
0.990899 | − | 0.134611i | \(-0.0429785\pi\) | |||||||
\(374\) | − | 232.182i | − | 0.620806i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 232.182 | 0.617504 | ||||||||
\(377\) | 324.409 | + | 324.409i | 0.860500 | + | 0.860500i | ||||
\(378\) | −53.0908 | + | 53.0908i | −0.140452 | + | 0.140452i | ||||
\(379\) | − | 472.181i | − | 1.24586i | −0.782278 | − | 0.622930i | \(-0.785942\pi\) | ||
0.782278 | − | 0.622930i | \(-0.214058\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52.1816 | 0.136960 | ||||||||
\(382\) | −110.091 | − | 110.091i | −0.288196 | − | 0.288196i | ||||
\(383\) | 67.8184 | − | 67.8184i | 0.177071 | − | 0.177071i | −0.613006 | − | 0.790078i | \(-0.710040\pi\) |
0.790078 | + | 0.613006i | \(0.210040\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 532.974 | 1.38076 | ||||||||
\(387\) | 35.6288 | + | 35.6288i | 0.0920642 | + | 0.0920642i | ||||
\(388\) | −108.247 | + | 108.247i | −0.278988 | + | 0.278988i | ||||
\(389\) | 603.242i | 1.55075i | 0.631501 | + | 0.775375i | \(0.282439\pi\) | ||||
−0.631501 | + | 0.775375i | \(0.717561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 748.727 | 1.91490 | ||||||||
\(392\) | −110.788 | − | 110.788i | −0.282622 | − | 0.282622i | ||||
\(393\) | −132.606 | + | 132.606i | −0.337420 | + | 0.337420i | ||||
\(394\) | − | 78.8786i | − | 0.200199i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −52.1816 | −0.131772 | ||||||||
\(397\) | −188.648 | − | 188.648i | −0.475184 | − | 0.475184i | 0.428403 | − | 0.903588i | \(-0.359076\pi\) |
−0.903588 | + | 0.428403i | \(0.859076\pi\) | |||||||
\(398\) | 92.9092 | − | 92.9092i | 0.233440 | − | 0.233440i | ||||
\(399\) | 76.1510i | 0.190855i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 302.697 | 0.754855 | 0.377428 | − | 0.926039i | \(-0.376809\pi\) | ||||
0.377428 | + | 0.926039i | \(0.376809\pi\) | |||||||
\(402\) | 12.3031 | + | 12.3031i | 0.0306046 | + | 0.0306046i | ||||
\(403\) | −612.719 | + | 612.719i | −1.52039 | + | 1.52039i | ||||
\(404\) | − | 85.7571i | − | 0.212270i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 299.060 | 0.736601 | ||||||||
\(407\) | −108.667 | − | 108.667i | −0.266996 | − | 0.266996i | ||||
\(408\) | 65.3939 | − | 65.3939i | 0.160279 | − | 0.160279i | ||||
\(409\) | − | 20.8184i | − | 0.0509007i | −0.999676 | − | 0.0254503i | \(-0.991898\pi\) | ||
0.999676 | − | 0.0254503i | \(-0.00810197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 187.757 | 0.456830 | ||||||||
\(412\) | 121.980 | + | 121.980i | 0.296067 | + | 0.296067i | ||||
\(413\) | 216.742 | − | 216.742i | 0.524800 | − | 0.524800i | ||||
\(414\) | − | 168.272i | − | 0.406455i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 125.394 | 0.301428 | ||||||||
\(417\) | 187.126 | + | 187.126i | 0.448743 | + | 0.448743i | ||||
\(418\) | −37.4235 | + | 37.4235i | −0.0895298 | + | 0.0895298i | ||||
\(419\) | 466.515i | 1.11340i | 0.830713 | + | 0.556701i | \(0.187933\pi\) | ||||
−0.830713 | + | 0.556701i | \(0.812067\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −636.120 | −1.51097 | −0.755487 | − | 0.655163i | \(-0.772600\pi\) | ||||
−0.755487 | + | 0.655163i | \(0.772600\pi\) | |||||||
\(422\) | 293.272 | + | 293.272i | 0.694958 | + | 0.694958i | ||||
\(423\) | −174.136 | + | 174.136i | −0.411670 | + | 0.411670i | ||||
\(424\) | 2.42449i | 0.00571814i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 94.7878 | 0.222506 | ||||||||
\(427\) | 504.199 | + | 504.199i | 1.18079 | + | 1.18079i | ||||
\(428\) | −91.8184 | + | 91.8184i | −0.214529 | + | 0.214529i | ||||
\(429\) | 333.909i | 0.778343i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 165.242 | 0.383392 | 0.191696 | − | 0.981454i | \(-0.438601\pi\) | ||||
0.191696 | + | 0.981454i | \(0.438601\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 282.619 | − | 282.619i | 0.652699 | − | 0.652699i | −0.300943 | − | 0.953642i | \(-0.597301\pi\) |
0.953642 | + | 0.300943i | \(0.0973015\pi\) | |||||||
\(434\) | 564.842i | 1.30148i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −290.000 | −0.665138 | ||||||||
\(437\) | −120.681 | − | 120.681i | −0.276158 | − | 0.276158i | ||||
\(438\) | 113.394 | − | 113.394i | 0.258890 | − | 0.258890i | ||||
\(439\) | − | 272.909i | − | 0.621661i | −0.950465 | − | 0.310831i | \(-0.899393\pi\) | ||
0.950465 | − | 0.310831i | \(-0.100607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 166.182 | 0.376829 | ||||||||
\(442\) | −418.454 | − | 418.454i | −0.946729 | − | 0.946729i | ||||
\(443\) | 176.636 | − | 176.636i | 0.398726 | − | 0.398726i | −0.479057 | − | 0.877784i | \(-0.659021\pi\) |
0.877784 | + | 0.479057i | \(0.159021\pi\) | |||||||
\(444\) | − | 61.2122i | − | 0.137865i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −149.641 | −0.335519 | ||||||||
\(447\) | −138.136 | − | 138.136i | −0.309030 | − | 0.309030i | ||||
\(448\) | 57.7980 | − | 57.7980i | 0.129013 | − | 0.129013i | ||||
\(449\) | − | 751.151i | − | 1.67294i | −0.548011 | − | 0.836471i | \(-0.684615\pi\) | ||
0.548011 | − | 0.836471i | \(-0.315385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −545.271 | −1.20903 | ||||||||
\(452\) | −261.576 | − | 261.576i | −0.578707 | − | 0.578707i | ||||
\(453\) | 205.608 | − | 205.608i | 0.453882 | − | 0.453882i | ||||
\(454\) | − | 94.2429i | − | 0.207583i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.0806 | −0.0462294 | ||||||||
\(457\) | −26.4245 | − | 26.4245i | −0.0578216 | − | 0.0578216i | 0.677605 | − | 0.735426i | \(-0.263018\pi\) |
−0.735426 | + | 0.677605i | \(0.763018\pi\) | |||||||
\(458\) | −275.000 | + | 275.000i | −0.600437 | + | 0.600437i | ||||
\(459\) | 98.0908i | 0.213705i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.6969 | −0.0839413 | −0.0419706 | − | 0.999119i | \(-0.513364\pi\) | ||||
−0.0419706 | + | 0.999119i | \(0.513364\pi\) | |||||||
\(462\) | 153.909 | + | 153.909i | 0.333137 | + | 0.333137i | ||||
\(463\) | −203.505 | + | 203.505i | −0.439536 | + | 0.439536i | −0.891856 | − | 0.452320i | \(-0.850597\pi\) |
0.452320 | + | 0.891856i | \(0.350597\pi\) | |||||||
\(464\) | 82.7878i | 0.178422i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −375.514 | −0.805825 | ||||||||
\(467\) | 557.530 | + | 557.530i | 1.19385 | + | 1.19385i | 0.975976 | + | 0.217879i | \(0.0699137\pi\) |
0.217879 | + | 0.975976i | \(0.430086\pi\) | |||||||
\(468\) | −94.0454 | + | 94.0454i | −0.200952 | + | 0.200952i | ||||
\(469\) | − | 72.5755i | − | 0.154745i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 281.363 | 0.597374 | ||||||||
\(472\) | 60.0000 | + | 60.0000i | 0.127119 | + | 0.127119i | ||||
\(473\) | 103.287 | − | 103.287i | 0.218366 | − | 0.218366i | ||||
\(474\) | 76.8990i | 0.162234i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −385.757 | −0.810414 | ||||||||
\(477\) | −1.81837 | − | 1.81837i | −0.00381209 | − | 0.00381209i | ||||
\(478\) | 17.6663 | − | 17.6663i | 0.0369588 | − | 0.0369588i | ||||
\(479\) | − | 265.818i | − | 0.554944i | −0.960734 | − | 0.277472i | \(-0.910503\pi\) | ||
0.960734 | − | 0.277472i | \(-0.0894966\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −391.696 | −0.814337 | ||||||||
\(482\) | 167.000 | + | 167.000i | 0.346473 | + | 0.346473i | ||||
\(483\) | −496.318 | + | 496.318i | −1.02757 | + | 1.02757i | ||||
\(484\) | − | 90.7265i | − | 0.187451i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −304.083 | − | 304.083i | −0.624400 | − | 0.624400i | 0.322253 | − | 0.946653i | \(-0.395560\pi\) |
−0.946653 | + | 0.322253i | \(0.895560\pi\) | |||||||
\(488\) | −139.576 | + | 139.576i | −0.286015 | + | 0.286015i | ||||
\(489\) | 24.8480i | 0.0508138i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 169.212 | 0.344628 | 0.172314 | − | 0.985042i | \(-0.444876\pi\) | ||||
0.172314 | + | 0.985042i | \(0.444876\pi\) | |||||||
\(492\) | −153.576 | − | 153.576i | −0.312145 | − | 0.312145i | ||||
\(493\) | 276.272 | − | 276.272i | 0.560390 | − | 0.560390i | ||||
\(494\) | 134.894i | 0.273066i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −156.363 | −0.315249 | ||||||||
\(497\) | −279.576 | − | 279.576i | −0.562526 | − | 0.562526i | ||||
\(498\) | −96.6061 | + | 96.6061i | −0.193988 | + | 0.193988i | ||||
\(499\) | 699.636i | 1.40208i | 0.713124 | + | 0.701038i | \(0.247280\pi\) | ||||
−0.713124 | + | 0.701038i | \(0.752720\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −381.303 | −0.761084 | ||||||||
\(502\) | 26.4245 | + | 26.4245i | 0.0526384 | + | 0.0526384i | ||||
\(503\) | −279.848 | + | 279.848i | −0.556358 | + | 0.556358i | −0.928268 | − | 0.371911i | \(-0.878703\pi\) |
0.371911 | + | 0.928268i | \(0.378703\pi\) | |||||||
\(504\) | 86.6969i | 0.172018i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −487.818 | −0.964068 | ||||||||
\(507\) | 394.813 | + | 394.813i | 0.778723 | + | 0.778723i | ||||
\(508\) | 42.6061 | − | 42.6061i | 0.0838703 | − | 0.0838703i | ||||
\(509\) | 193.696i | 0.380542i | 0.981732 | + | 0.190271i | \(0.0609367\pi\) | ||||
−0.981732 | + | 0.190271i | \(0.939063\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −668.908 | −1.30902 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 15.8105 | − | 15.8105i | 0.0308196 | − | 0.0308196i | ||||
\(514\) | 482.969i | 0.939629i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 58.1816 | 0.112755 | ||||||||
\(517\) | 504.817 | + | 504.817i | 0.976436 | + | 0.976436i | ||||
\(518\) | −180.545 | + | 180.545i | −0.348542 | + | 0.348542i | ||||
\(519\) | − | 212.697i | − | 0.409821i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 167.121 | 0.320771 | 0.160385 | − | 0.987054i | \(-0.448726\pi\) | ||||
0.160385 | + | 0.987054i | \(0.448726\pi\) | |||||||
\(522\) | −62.0908 | − | 62.0908i | −0.118948 | − | 0.118948i | ||||
\(523\) | 675.860 | − | 675.860i | 1.29228 | − | 1.29228i | 0.358900 | − | 0.933376i | \(-0.383152\pi\) |
0.933376 | − | 0.358900i | \(-0.116848\pi\) | |||||||
\(524\) | 216.545i | 0.413254i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −284.363 | −0.540615 | ||||||||
\(527\) | 521.803 | + | 521.803i | 0.990138 | + | 0.990138i | ||||
\(528\) | −42.6061 | + | 42.6061i | −0.0806934 | + | 0.0806934i | ||||
\(529\) | − | 1044.09i | − | 1.97370i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −90.0000 | −0.169492 | ||||||||
\(532\) | 62.1770 | + | 62.1770i | 0.116874 | + | 0.116874i | ||||
\(533\) | −982.727 | + | 982.727i | −1.84376 | + | 1.84376i | ||||
\(534\) | 101.394i | 0.189876i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.0908 | 0.0374829 | ||||||||
\(537\) | 295.348 | + | 295.348i | 0.549997 | + | 0.549997i | ||||
\(538\) | 521.605 | − | 521.605i | 0.969526 | − | 0.969526i | ||||
\(539\) | − | 481.757i | − | 0.893798i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −131.120 | −0.242367 | −0.121183 | − | 0.992630i | \(-0.538669\pi\) | ||||
−0.121183 | + | 0.992630i | \(0.538669\pi\) | |||||||
\(542\) | 39.2122 | + | 39.2122i | 0.0723473 | + | 0.0723473i | ||||
\(543\) | −50.4370 | + | 50.4370i | −0.0928858 | + | 0.0928858i | ||||
\(544\) | − | 106.788i | − | 0.196301i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 554.772 | 1.01607 | ||||||||
\(547\) | 423.959 | + | 423.959i | 0.775062 | + | 0.775062i | 0.978987 | − | 0.203924i | \(-0.0653696\pi\) |
−0.203924 | + | 0.978987i | \(0.565370\pi\) | |||||||
\(548\) | 153.303 | − | 153.303i | 0.279750 | − | 0.279750i | ||||
\(549\) | − | 209.363i | − | 0.381354i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −89.0602 | −0.161634 | ||||||||
\(552\) | −137.394 | − | 137.394i | −0.248902 | − | 0.248902i | ||||
\(553\) | 226.813 | − | 226.813i | 0.410150 | − | 0.410150i | ||||
\(554\) | − | 139.176i | − | 0.251220i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 305.576 | 0.549596 | ||||||||
\(557\) | −341.741 | − | 341.741i | −0.613539 | − | 0.613539i | 0.330327 | − | 0.943866i | \(-0.392841\pi\) |
−0.943866 | + | 0.330327i | \(0.892841\pi\) | |||||||
\(558\) | 117.272 | − | 117.272i | 0.210166 | − | 0.210166i | ||||
\(559\) | − | 372.303i | − | 0.666016i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 284.363 | 0.506886 | ||||||||
\(562\) | −519.848 | − | 519.848i | −0.924996 | − | 0.924996i | ||||
\(563\) | 13.6209 | − | 13.6209i | 0.0241935 | − | 0.0241935i | −0.694907 | − | 0.719100i | \(-0.744554\pi\) |
0.719100 | + | 0.694907i | \(0.244554\pi\) | |||||||
\(564\) | 284.363i | 0.504190i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −306.854 | −0.542144 | ||||||||
\(567\) | −65.0227 | − | 65.0227i | −0.114678 | − | 0.114678i | ||||
\(568\) | 77.3939 | − | 77.3939i | 0.136257 | − | 0.136257i | ||||
\(569\) | 22.9990i | 0.0404200i | 0.999796 | + | 0.0202100i | \(0.00643348\pi\) | ||||
−0.999796 | + | 0.0202100i | \(0.993567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −660.666 | −1.15703 | −0.578517 | − | 0.815670i | \(-0.696368\pi\) | ||||
−0.578517 | + | 0.815670i | \(0.696368\pi\) | |||||||
\(572\) | 272.636 | + | 272.636i | 0.476636 | + | 0.476636i | ||||
\(573\) | 134.833 | − | 134.833i | 0.235311 | − | 0.235311i | ||||
\(574\) | 905.939i | 1.57829i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 421.547 | + | 421.547i | 0.730584 | + | 0.730584i | 0.970736 | − | 0.240151i | \(-0.0771970\pi\) |
−0.240151 | + | 0.970736i | \(0.577197\pi\) | |||||||
\(578\) | −67.3633 | + | 67.3633i | −0.116545 | + | 0.116545i | ||||
\(579\) | 652.757i | 1.12739i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 569.878 | 0.980856 | ||||||||
\(582\) | −132.576 | − | 132.576i | −0.227793 | − | 0.227793i | ||||
\(583\) | −5.27142 | + | 5.27142i | −0.00904188 | + | 0.00904188i | ||||
\(584\) | − | 185.171i | − | 0.317074i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.2418 | −0.0669656 | ||||||||
\(587\) | −441.514 | − | 441.514i | −0.752154 | − | 0.752154i | 0.222727 | − | 0.974881i | \(-0.428504\pi\) |
−0.974881 | + | 0.222727i | \(0.928504\pi\) | |||||||
\(588\) | 135.687 | − | 135.687i | 0.230760 | − | 0.230760i | ||||
\(589\) | − | 168.210i | − | 0.285586i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 96.6061 | 0.163462 | ||||||||
\(592\) | −49.9796 | − | 49.9796i | −0.0844250 | − | 0.0844250i | ||||
\(593\) | 171.303 | − | 171.303i | 0.288875 | − | 0.288875i | −0.547760 | − | 0.836635i | \(-0.684519\pi\) |
0.836635 | + | 0.547760i | \(0.184519\pi\) | |||||||
\(594\) | − | 63.9092i | − | 0.107591i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −225.576 | −0.378482 | ||||||||
\(597\) | 113.790 | + | 113.790i | 0.190603 | + | 0.190603i | ||||
\(598\) | −879.181 | + | 879.181i | −1.47020 | + | 1.47020i | ||||
\(599\) | 64.1816i | 0.107148i | 0.998564 | + | 0.0535740i | \(0.0170613\pi\) | ||||
−0.998564 | + | 0.0535740i | \(0.982939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 469.545 | 0.781273 | 0.390636 | − | 0.920545i | \(-0.372255\pi\) | ||||
0.390636 | + | 0.920545i | \(0.372255\pi\) | |||||||
\(602\) | −171.606 | − | 171.606i | −0.285060 | − | 0.285060i | ||||
\(603\) | −15.0681 | + | 15.0681i | −0.0249886 | + | 0.0249886i | ||||
\(604\) | − | 335.757i | − | 0.555889i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 105.031 | 0.173318 | ||||||||
\(607\) | −121.930 | − | 121.930i | −0.200872 | − | 0.200872i | 0.599501 | − | 0.800374i | \(-0.295366\pi\) |
−0.800374 | + | 0.599501i | \(0.795366\pi\) | |||||||
\(608\) | −17.2122 | + | 17.2122i | −0.0283096 | + | 0.0283096i | ||||
\(609\) | 366.272i | 0.601433i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1819.63 | 2.97813 | ||||||||
\(612\) | 80.0908 | + | 80.0908i | 0.130867 | + | 0.130867i | ||||
\(613\) | −542.252 | + | 542.252i | −0.884587 | + | 0.884587i | −0.993997 | − | 0.109409i | \(-0.965104\pi\) |
0.109409 | + | 0.993997i | \(0.465104\pi\) | |||||||
\(614\) | − | 21.8230i | − | 0.0355423i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 251.333 | 0.408008 | ||||||||
\(617\) | −117.364 | − | 117.364i | −0.190218 | − | 0.190218i | 0.605572 | − | 0.795790i | \(-0.292944\pi\) |
−0.795790 | + | 0.605572i | \(0.792944\pi\) | |||||||
\(618\) | −149.394 | + | 149.394i | −0.241738 | + | 0.241738i | ||||
\(619\) | − | 295.697i | − | 0.477701i | −0.971056 | − | 0.238851i | \(-0.923229\pi\) | ||
0.971056 | − | 0.238851i | \(-0.0767706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 206.091 | 0.331869 | ||||||||
\(622\) | 64.7878 | + | 64.7878i | 0.104160 | + | 0.104160i | ||||
\(623\) | 299.060 | − | 299.060i | 0.480032 | − | 0.480032i | ||||
\(624\) | 153.576i | 0.246115i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −50.8944 | −0.0813009 | ||||||||
\(627\) | −45.8342 | − | 45.8342i | −0.0731008 | − | 0.0731008i | ||||
\(628\) | 229.732 | − | 229.732i | 0.365816 | − | 0.365816i | ||||
\(629\) | 333.576i | 0.530327i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 897.454 | 1.42227 | 0.711136 | − | 0.703054i | \(-0.248181\pi\) | ||||
0.711136 | + | 0.703054i | \(0.248181\pi\) | |||||||
\(632\) | 62.7878 | + | 62.7878i | 0.0993477 | + | 0.0993477i | ||||
\(633\) | −359.184 | + | 359.184i | −0.567431 | + | 0.567431i | ||||
\(634\) | − | 862.120i | − | 1.35981i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.96938 | −0.00466884 | ||||||||
\(637\) | −868.257 | − | 868.257i | −1.36304 | − | 1.36304i | ||||
\(638\) | −180.000 | + | 180.000i | −0.282132 | + | 0.282132i | ||||
\(639\) | 116.091i | 0.181676i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −226.120 | −0.352762 | −0.176381 | − | 0.984322i | \(-0.556439\pi\) | ||||
−0.176381 | + | 0.984322i | \(0.556439\pi\) | |||||||
\(642\) | −112.454 | − | 112.454i | −0.175162 | − | 0.175162i | ||||
\(643\) | 472.454 | − | 472.454i | 0.734765 | − | 0.734765i | −0.236794 | − | 0.971560i | \(-0.576097\pi\) |
0.971560 | + | 0.236794i | \(0.0760968\pi\) | |||||||
\(644\) | 810.484i | 1.25852i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 114.879 | 0.177831 | ||||||||
\(647\) | −583.151 | − | 583.151i | −0.901315 | − | 0.901315i | 0.0942347 | − | 0.995550i | \(-0.469960\pi\) |
−0.995550 | + | 0.0942347i | \(0.969960\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 260.908i | 0.402016i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −691.788 | −1.06265 | ||||||||
\(652\) | 20.2883 | + | 20.2883i | 0.0311170 | + | 0.0311170i | ||||
\(653\) | 36.1975 | − | 36.1975i | 0.0554325 | − | 0.0554325i | −0.678847 | − | 0.734280i | \(-0.737520\pi\) |
0.734280 | + | 0.678847i | \(0.237520\pi\) | |||||||
\(654\) | − | 355.176i | − | 0.543083i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −250.788 | −0.382298 | ||||||||
\(657\) | 138.879 | + | 138.879i | 0.211383 | + | 0.211383i | ||||
\(658\) | 838.727 | − | 838.727i | 1.27466 | − | 1.27466i | ||||
\(659\) | − | 615.787i | − | 0.934426i | −0.884145 | − | 0.467213i | \(-0.845258\pi\) | ||
0.884145 | − | 0.467213i | \(-0.154742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −426.849 | −0.645762 | −0.322881 | − | 0.946439i | \(-0.604651\pi\) | ||||
−0.322881 | + | 0.946439i | \(0.604651\pi\) | |||||||
\(662\) | 295.939 | + | 295.939i | 0.447037 | + | 0.447037i | ||||
\(663\) | 512.499 | − | 512.499i | 0.773001 | − | 0.773001i | ||||
\(664\) | 157.757i | 0.237586i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 74.9694 | 0.112567 | ||||||||
\(667\) | −580.454 | − | 580.454i | −0.870246 | − | 0.870246i | ||||
\(668\) | −311.333 | + | 311.333i | −0.466067 | + | 0.466067i | ||||
\(669\) | − | 183.272i | − | 0.273950i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −606.940 | −0.904530 | ||||||||
\(672\) | 70.7878 | + | 70.7878i | 0.105339 | + | 0.105339i | ||||
\(673\) | −350.474 | + | 350.474i | −0.520764 | + | 0.520764i | −0.917802 | − | 0.397038i | \(-0.870038\pi\) |
0.397038 | + | 0.917802i | \(0.370038\pi\) | |||||||
\(674\) | − | 283.076i | − | 0.419994i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 644.727 | 0.953737 | ||||||||
\(677\) | −208.985 | − | 208.985i | −0.308693 | − | 0.308693i | 0.535709 | − | 0.844402i | \(-0.320044\pi\) |
−0.844402 | + | 0.535709i | \(0.820044\pi\) | |||||||
\(678\) | 320.363 | − | 320.363i | 0.472512 | − | 0.472512i | ||||
\(679\) | 782.060i | 1.15178i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 115.423 | 0.169491 | ||||||||
\(682\) | −339.970 | − | 339.970i | −0.498490 | − | 0.498490i | ||||
\(683\) | 701.271 | − | 701.271i | 1.02675 | − | 1.02675i | 0.0271195 | − | 0.999632i | \(-0.491367\pi\) |
0.999632 | − | 0.0271195i | \(-0.00863347\pi\) | |||||||
\(684\) | − | 25.8184i | − | 0.0377462i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −92.3883 | −0.134677 | ||||||||
\(687\) | −336.805 | − | 336.805i | −0.490254 | − | 0.490254i | ||||
\(688\) | 47.5051 | − | 47.5051i | 0.0690481 | − | 0.0690481i | ||||
\(689\) | 19.0010i | 0.0275777i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −132.910 | −0.192345 | −0.0961724 | − | 0.995365i | \(-0.530660\pi\) | ||||
−0.0961724 | + | 0.995365i | \(0.530660\pi\) | |||||||
\(692\) | −173.666 | − | 173.666i | −0.250963 | − | 0.250963i | ||||
\(693\) | −188.499 | + | 188.499i | −0.272005 | + | 0.272005i | ||||
\(694\) | − | 724.454i | − | 1.04388i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −101.394 | −0.145681 | ||||||||
\(697\) | 836.908 | + | 836.908i | 1.20073 | + | 1.20073i | ||||
\(698\) | −403.939 | + | 403.939i | −0.578709 | + | 0.578709i | ||||
\(699\) | − | 459.909i | − | 0.657953i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 158.758 | 0.226474 | 0.113237 | − | 0.993568i | \(-0.463878\pi\) | ||||
0.113237 | + | 0.993568i | \(0.463878\pi\) | |||||||
\(702\) | −115.182 | − | 115.182i | −0.164076 | − | 0.164076i | ||||
\(703\) | 53.7663 | − | 53.7663i | 0.0764812 | − | 0.0764812i | ||||
\(704\) | 69.5755i | 0.0988288i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 37.4847 | 0.0530945 | ||||||||
\(707\) | −309.787 | − | 309.787i | −0.438171 | − | 0.438171i | ||||
\(708\) | −73.4847 | + | 73.4847i | −0.103792 | + | 0.103792i | ||||
\(709\) | 674.514i | 0.951360i | 0.879618 | + | 0.475680i | \(0.157798\pi\) | ||||
−0.879618 | + | 0.475680i | \(0.842202\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −94.1816 | −0.132464 | ||||||||
\(712\) | 82.7878 | + | 82.7878i | 0.116275 | + | 0.116275i | ||||
\(713\) | 1096.32 | − | 1096.32i | 1.53761 | − | 1.53761i | ||||
\(714\) | − | 472.454i | − | 0.661700i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 482.302 | 0.673606 | ||||||||
\(717\) | 21.6367 | + | 21.6367i | 0.0301768 | + | 0.0301768i | ||||
\(718\) | −383.728 | + | 383.728i | −0.534439 | + | 0.534439i | ||||
\(719\) | − | 103.485i | − | 0.143929i | −0.997407 | − | 0.0719643i | \(-0.977073\pi\) | ||
0.997407 | − | 0.0719643i | \(-0.0229268\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 881.271 | 1.22229 | ||||||||
\(722\) | 342.484 | + | 342.484i | 0.474354 | + | 0.474354i | ||||
\(723\) | −204.532 | + | 204.532i | −0.282894 | + | 0.282894i | ||||
\(724\) | 82.3633i | 0.113761i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 111.117 | 0.153054 | ||||||||
\(727\) | 658.392 | + | 658.392i | 0.905628 | + | 0.905628i | 0.995916 | − | 0.0902877i | \(-0.0287787\pi\) |
−0.0902877 | + | 0.995916i | \(0.528779\pi\) | |||||||
\(728\) | 452.969 | − | 452.969i | 0.622211 | − | 0.622211i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −317.060 | −0.433735 | ||||||||
\(732\) | −170.944 | − | 170.944i | −0.233531 | − | 0.233531i | ||||
\(733\) | 165.970 | − | 165.970i | 0.226426 | − | 0.226426i | −0.584772 | − | 0.811198i | \(-0.698816\pi\) |
0.811198 | + | 0.584772i | \(0.198816\pi\) | |||||||
\(734\) | − | 774.681i | − | 1.05542i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −224.363 | −0.304841 | ||||||||
\(737\) | 43.6821 | + | 43.6821i | 0.0592702 | + | 0.0592702i | ||||
\(738\) | 188.091 | − | 188.091i | 0.254866 | − | 0.254866i | ||||
\(739\) | 122.545i | 0.165825i | 0.996557 | + | 0.0829126i | \(0.0264222\pi\) | ||||
−0.996557 | + | 0.0829126i | \(0.973578\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −165.211 | −0.222957 | ||||||||
\(742\) | 8.75817 | + | 8.75817i | 0.0118035 | + | 0.0118035i | ||||
\(743\) | −541.485 | + | 541.485i | −0.728782 | + | 0.728782i | −0.970377 | − | 0.241595i | \(-0.922329\pi\) |
0.241595 | + | 0.970377i | \(0.422329\pi\) | |||||||
\(744\) | − | 191.505i | − | 0.257399i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 839.630 | 1.12551 | ||||||||
\(747\) | −118.318 | − | 118.318i | −0.158391 | − | 0.158391i | ||||
\(748\) | 232.182 | − | 232.182i | 0.310403 | − | 0.310403i | ||||
\(749\) | 663.364i | 0.885667i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −495.212 | −0.659404 | −0.329702 | − | 0.944085i | \(-0.606948\pi\) | ||||
−0.329702 | + | 0.944085i | \(0.606948\pi\) | |||||||
\(752\) | 232.182 | + | 232.182i | 0.308752 | + | 0.308752i | ||||
\(753\) | −32.3633 | + | 32.3633i | −0.0429791 | + | 0.0429791i | ||||
\(754\) | 648.817i | 0.860500i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −106.182 | −0.140452 | ||||||||
\(757\) | −565.547 | − | 565.547i | −0.747090 | − | 0.747090i | 0.226842 | − | 0.973932i | \(-0.427160\pi\) |
−0.973932 | + | 0.226842i | \(0.927160\pi\) | |||||||
\(758\) | 472.181 | − | 472.181i | 0.622930 | − | 0.622930i | ||||
\(759\) | − | 597.453i | − | 0.787158i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −737.271 | −0.968819 | −0.484410 | − | 0.874841i | \(-0.660966\pi\) | ||||
−0.484410 | + | 0.874841i | \(0.660966\pi\) | |||||||
\(762\) | 52.1816 | + | 52.1816i | 0.0684798 | + | 0.0684798i | ||||
\(763\) | −1047.59 | + | 1047.59i | −1.37299 | + | 1.37299i | ||||
\(764\) | − | 220.182i | − | 0.288196i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 135.637 | 0.177071 | ||||||||
\(767\) | 470.227 | + | 470.227i | 0.613073 | + | 0.613073i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 1014.27i | 1.31895i | 0.751727 | + | 0.659474i | \(0.229221\pi\) | ||||
−0.751727 | + | 0.659474i | \(0.770779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −591.514 | −0.767204 | ||||||||
\(772\) | 532.974 | + | 532.974i | 0.690381 | + | 0.690381i | ||||
\(773\) | −6.39491 | + | 6.39491i | −0.00827284 | + | 0.00827284i | −0.711231 | − | 0.702958i | \(-0.751862\pi\) |
0.702958 | + | 0.711231i | \(0.251862\pi\) | |||||||
\(774\) | 71.2577i | 0.0920642i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −216.495 | −0.278988 | ||||||||
\(777\) | −221.121 | − | 221.121i | −0.284584 | − | 0.284584i | ||||
\(778\) | −603.242 | + | 603.242i | −0.775375 | + | 0.775375i | ||||
\(779\) | − | 269.789i | − | 0.346327i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 336.545 | 0.430915 | ||||||||
\(782\) | 748.727 | + | 748.727i | 0.957451 | + | 0.957451i | ||||
\(783\) | 76.0454 | − | 76.0454i | 0.0971206 | − | 0.0971206i | ||||
\(784\) | − | 221.576i | − | 0.282622i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −265.212 | −0.337420 | ||||||||
\(787\) | −565.806 | − | 565.806i | −0.718940 | − | 0.718940i | 0.249448 | − | 0.968388i | \(-0.419751\pi\) |
−0.968388 | + | 0.249448i | \(0.919751\pi\) | |||||||
\(788\) | 78.8786 | − | 78.8786i | 0.100100 | − | 0.100100i | ||||
\(789\) | − | 348.272i | − | 0.441410i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1889.82 | −2.38915 | ||||||||
\(792\) | −52.1816 | − | 52.1816i | −0.0658859 | − | 0.0658859i | ||||
\(793\) | −1093.87 | + | 1093.87i | −1.37941 | + | 1.37941i | ||||
\(794\) | − | 377.296i | − | 0.475184i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 185.818 | 0.233440 | ||||||||
\(797\) | 352.182 | + | 352.182i | 0.441884 | + | 0.441884i | 0.892645 | − | 0.450761i | \(-0.148847\pi\) |
−0.450761 | + | 0.892645i | \(0.648847\pi\) | |||||||
\(798\) | −76.1510 | + | 76.1510i | −0.0954273 | + | 0.0954273i | ||||
\(799\) | − | 1549.63i | − | 1.93947i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −124.182 | −0.155033 | ||||||||
\(802\) | 302.697 | + | 302.697i | 0.377428 | + | 0.377428i | ||||
\(803\) | 402.606 | − | 402.606i | 0.501377 | − | 0.501377i | ||||
\(804\) | 24.6061i | 0.0306046i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1225.44 | −1.52039 | ||||||||
\(807\) | 638.833 | + | 638.833i | 0.791615 | + | 0.791615i | ||||
\(808\) | 85.7571 | − | 85.7571i | 0.106135 | − | 0.106135i | ||||
\(809\) | 563.728i | 0.696820i | 0.937342 | + | 0.348410i | \(0.113278\pi\) | ||||
−0.937342 | + | 0.348410i | \(0.886722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −205.091 | −0.252886 | −0.126443 | − | 0.991974i | \(-0.540356\pi\) | ||||
−0.126443 | + | 0.991974i | \(0.540356\pi\) | |||||||
\(812\) | 299.060 | + | 299.060i | 0.368301 | + | 0.368301i | ||||
\(813\) | −48.0250 | + | 48.0250i | −0.0590713 | + | 0.0590713i | ||||
\(814\) | − | 217.335i | − | 0.266996i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 130.788 | 0.160279 | ||||||||
\(817\) | 51.1043 | + | 51.1043i | 0.0625512 | + | 0.0625512i | ||||
\(818\) | 20.8184 | − | 20.8184i | 0.0254503 | − | 0.0254503i | ||||
\(819\) | 679.454i | 0.829614i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 867.576 | 1.05673 | 0.528365 | − | 0.849017i | \(-0.322805\pi\) | ||||
0.528365 | + | 0.849017i | \(0.322805\pi\) | |||||||
\(822\) | 187.757 | + | 187.757i | 0.228415 | + | 0.228415i | ||||
\(823\) | 80.8094 | − | 80.8094i | 0.0981889 | − | 0.0981889i | −0.656306 | − | 0.754495i | \(-0.727882\pi\) |
0.754495 | + | 0.656306i | \(0.227882\pi\) | |||||||
\(824\) | 243.959i | 0.296067i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 433.485 | 0.524800 | ||||||||
\(827\) | −935.939 | − | 935.939i | −1.13173 | − | 1.13173i | −0.989890 | − | 0.141838i | \(-0.954699\pi\) |
−0.141838 | − | 0.989890i | \(-0.545301\pi\) | |||||||
\(828\) | 168.272 | − | 168.272i | 0.203228 | − | 0.203228i | ||||
\(829\) | 1097.39i | 1.32375i | 0.749613 | + | 0.661877i | \(0.230240\pi\) | ||||
−0.749613 | + | 0.661877i | \(0.769760\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 170.455 | 0.205120 | ||||||||
\(832\) | 125.394 | + | 125.394i | 0.150714 | + | 0.150714i | ||||
\(833\) | −739.423 | + | 739.423i | −0.887663 | + | 0.887663i | ||||
\(834\) | 374.252i | 0.448743i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −74.8469 | −0.0895298 | ||||||||
\(837\) | 143.629 | + | 143.629i | 0.171600 | + | 0.171600i | ||||
\(838\) | −466.515 | + | 466.515i | −0.556701 | + | 0.556701i | ||||
\(839\) | 1047.18i | 1.24813i | 0.781373 | + | 0.624065i | \(0.214520\pi\) | ||||
−0.781373 | + | 0.624065i | \(0.785480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 412.637 | 0.490650 | ||||||||
\(842\) | −636.120 | − | 636.120i | −0.755487 | − | 0.755487i | ||||
\(843\) | 636.681 | − | 636.681i | 0.755256 | − | 0.755256i | ||||
\(844\) | 586.545i | 0.694958i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −348.272 | −0.411670 | ||||||||
\(847\) | −327.738 | − | 327.738i | −0.386940 | − | 0.386940i | ||||
\(848\) | −2.42449 | + | 2.42449i | −0.00285907 | + | 0.00285907i | ||||
\(849\) | − | 375.817i | − | 0.442659i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 700.849 | 0.823559 | ||||||||
\(852\) | 94.7878 | + | 94.7878i | 0.111253 | + | 0.111253i | ||||
\(853\) | −902.612 | + | 902.612i | −1.05816 | + | 1.05816i | −0.0599610 | + | 0.998201i | \(0.519098\pi\) |
−0.998201 | + | 0.0599610i | \(0.980902\pi\) | |||||||
\(854\) | 1008.40i | 1.18079i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −183.637 | −0.214529 | ||||||||
\(857\) | 928.454 | + | 928.454i | 1.08338 | + | 1.08338i | 0.996192 | + | 0.0871848i | \(0.0277871\pi\) |
0.0871848 | + | 0.996192i | \(0.472213\pi\) | |||||||
\(858\) | −333.909 | + | 333.909i | −0.389172 | + | 0.389172i | ||||
\(859\) | 581.151i | 0.676544i | 0.941048 | + | 0.338272i | \(0.109842\pi\) | ||||
−0.941048 | + | 0.338272i | \(0.890158\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1109.54 | −1.28867 | ||||||||
\(862\) | 165.242 | + | 165.242i | 0.191696 | + | 0.191696i | ||||
\(863\) | −317.271 | + | 317.271i | −0.367638 | + | 0.367638i | −0.866615 | − | 0.498977i | \(-0.833709\pi\) |
0.498977 | + | 0.866615i | \(0.333709\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 565.237 | 0.652699 | ||||||||
\(867\) | −82.5028 | − | 82.5028i | −0.0951589 | − | 0.0951589i | ||||
\(868\) | −564.842 | + | 564.842i | −0.650740 | + | 0.650740i | ||||
\(869\) | 273.031i | 0.314189i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 157.454 | 0.180774 | ||||||||
\(872\) | −290.000 | − | 290.000i | −0.332569 | − | 0.332569i | ||||
\(873\) | 162.371 | − | 162.371i | 0.185992 | − | 0.185992i | ||||
\(874\) | − | 241.362i | − | 0.276158i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 226.788 | 0.258890 | ||||||||
\(877\) | 1109.75 | + | 1109.75i | 1.26540 | + | 1.26540i | 0.948439 | + | 0.316958i | \(0.102662\pi\) |
0.316958 | + | 0.948439i | \(0.397338\pi\) | |||||||
\(878\) | 272.909 | − | 272.909i | 0.310831 | − | 0.310831i | ||||
\(879\) | − | 48.0612i | − | 0.0546772i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 119.455 | 0.135590 | 0.0677952 | − | 0.997699i | \(-0.478404\pi\) | ||||
0.0677952 | + | 0.997699i | \(0.478404\pi\) | |||||||
\(882\) | 166.182 | + | 166.182i | 0.188415 | + | 0.188415i | ||||
\(883\) | 252.619 | − | 252.619i | 0.286091 | − | 0.286091i | −0.549441 | − | 0.835532i | \(-0.685159\pi\) |
0.835532 | + | 0.549441i | \(0.185159\pi\) | |||||||
\(884\) | − | 836.908i | − | 0.946729i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 353.271 | 0.398726 | ||||||||
\(887\) | 516.347 | + | 516.347i | 0.582128 | + | 0.582128i | 0.935488 | − | 0.353360i | \(-0.114961\pi\) |
−0.353360 | + | 0.935488i | \(0.614961\pi\) | |||||||
\(888\) | 61.2122 | − | 61.2122i | 0.0689327 | − | 0.0689327i | ||||
\(889\) | − | 307.818i | − | 0.346252i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 78.2724 | 0.0878479 | ||||||||
\(892\) | −149.641 | − | 149.641i | −0.167759 | − | 0.167759i | ||||
\(893\) | −249.773 | + | 249.773i | −0.279701 | + | 0.279701i | ||||
\(894\) | − | 276.272i | − | 0.309030i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 115.596 | 0.129013 | ||||||||
\(897\) | −1076.77 | − | 1076.77i | −1.20041 | − | 1.20041i | ||||
\(898\) | 751.151 | − | 751.151i | 0.836471 | − | 0.836471i | ||||
\(899\) | − | 809.060i | − | 0.899956i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.1816 | 0.0179596 | ||||||||
\(902\) | −545.271 | − | 545.271i | −0.604514 | − | 0.604514i | ||||
\(903\) | 210.174 | − | 210.174i | 0.232751 | − | 0.232751i | ||||
\(904\) | − | 523.151i | − | 0.578707i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 411.217 | 0.453882 | ||||||||
\(907\) | 983.160 | + | 983.160i | 1.08397 | + | 1.08397i | 0.996135 | + | 0.0878342i | \(0.0279946\pi\) |
0.0878342 | + | 0.996135i | \(0.472005\pi\) | |||||||
\(908\) | 94.2429 | − | 94.2429i | 0.103792 | − | 0.103792i | ||||
\(909\) | 128.636i | 0.141513i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1698.00 | −1.86389 | −0.931943 | − | 0.362605i | \(-0.881887\pi\) | ||||
−0.931943 | + | 0.362605i | \(0.881887\pi\) | |||||||
\(912\) | −21.0806 | − | 21.0806i | −0.0231147 | − | 0.0231147i | ||||
\(913\) | −343.001 | + | 343.001i | −0.375686 | + | 0.375686i | ||||
\(914\) | − | 52.8490i | − | 0.0578216i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −550.000 | −0.600437 | ||||||||
\(917\) | 782.241 | + | 782.241i | 0.853043 | + | 0.853043i | ||||
\(918\) | −98.0908 | + | 98.0908i | −0.106853 | + | 0.106853i | ||||
\(919\) | 581.272i | 0.632505i | 0.948675 | + | 0.316253i | \(0.102425\pi\) | ||||
−0.948675 | + | 0.316253i | \(0.897575\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.7276 | 0.0290201 | ||||||||
\(922\) | −38.6969 | − | 38.6969i | −0.0419706 | − | 0.0419706i | ||||
\(923\) | 606.545 | − | 606.545i | 0.657145 | − | 0.657145i | ||||
\(924\) | 307.818i | 0.333137i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −407.010 | −0.439536 | ||||||||
\(927\) | −182.969 | − | 182.969i | −0.197378 | − | 0.197378i | ||||
\(928\) | −82.7878 | + | 82.7878i | −0.0892109 | + | 0.0892109i | ||||
\(929\) | − | 1328.57i | − | 1.43011i | −0.699067 | − | 0.715056i | \(-0.746401\pi\) | ||
0.699067 | − | 0.715056i | \(-0.253599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 238.363 | 0.256029 | ||||||||
\(932\) | −375.514 | − | 375.514i | −0.402912 | − | 0.402912i | ||||
\(933\) | −79.3485 | + | 79.3485i | −0.0850466 | + | 0.0850466i | ||||
\(934\) | 1115.06i | 1.19385i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −188.091 | −0.200952 | ||||||||
\(937\) | −626.487 | − | 626.487i | −0.668609 | − | 0.668609i | 0.288785 | − | 0.957394i | \(-0.406749\pi\) |
−0.957394 | + | 0.288785i | \(0.906749\pi\) | |||||||
\(938\) | 72.5755 | − | 72.5755i | 0.0773726 | − | 0.0773726i | ||||
\(939\) | − | 62.3326i | − | 0.0663819i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 762.422 | 0.810226 | 0.405113 | − | 0.914267i | \(-0.367232\pi\) | ||||
0.405113 | + | 0.914267i | \(0.367232\pi\) | |||||||
\(942\) | 281.363 | + | 281.363i | 0.298687 | + | 0.298687i | ||||
\(943\) | 1758.36 | − | 1758.36i | 1.86465 | − | 1.86465i | ||||
\(944\) | 120.000i | 0.127119i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 206.574 | 0.218366 | ||||||||
\(947\) | −614.983 | − | 614.983i | −0.649401 | − | 0.649401i | 0.303447 | − | 0.952848i | \(-0.401862\pi\) |
−0.952848 | + | 0.303447i | \(0.901862\pi\) | |||||||
\(948\) | −76.8990 | + | 76.8990i | −0.0811171 | + | 0.0811171i | ||||
\(949\) | − | 1451.21i | − | 1.52920i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1055.88 | 1.11028 | ||||||||
\(952\) | −385.757 | − | 385.757i | −0.405207 | − | 0.405207i | ||||
\(953\) | −328.454 | + | 328.454i | −0.344653 | + | 0.344653i | −0.858113 | − | 0.513460i | \(-0.828363\pi\) |
0.513460 | + | 0.858113i | \(0.328363\pi\) | |||||||
\(954\) | − | 3.63674i | − | 0.00381209i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 35.3326 | 0.0369588 | ||||||||
\(957\) | −220.454 | − | 220.454i | −0.230360 | − | 0.230360i | ||||
\(958\) | 265.818 | − | 265.818i | 0.277472 | − | 0.277472i | ||||
\(959\) | − | 1107.58i | − | 1.15493i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 567.092 | 0.590106 | ||||||||
\(962\) | −391.696 | − | 391.696i | −0.407168 | − | 0.407168i | ||||
\(963\) | 137.728 | − | 137.728i | 0.143019 | − | 0.143019i | ||||
\(964\) | 334.000i | 0.346473i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −992.636 | −1.02757 | ||||||||
\(967\) | 172.009 | + | 172.009i | 0.177879 | + | 0.177879i | 0.790431 | − | 0.612551i | \(-0.209857\pi\) |
−0.612551 | + | 0.790431i | \(0.709857\pi\) | |||||||
\(968\) | 90.7265 | − | 90.7265i | 0.0937257 | − | 0.0937257i | ||||
\(969\) | 140.697i | 0.145198i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1273.82 | −1.31186 | −0.655931 | − | 0.754821i | \(-0.727724\pi\) | ||||
−0.655931 | + | 0.754821i | \(0.727724\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 1103.85 | − | 1103.85i | 1.13448 | − | 1.13448i | ||||
\(974\) | − | 608.166i | − | 0.624400i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −279.151 | −0.286015 | ||||||||
\(977\) | −1013.86 | − | 1013.86i | −1.03773 | − | 1.03773i | −0.999260 | − | 0.0384719i | \(-0.987751\pi\) |
−0.0384719 | − | 0.999260i | \(-0.512249\pi\) | |||||||
\(978\) | −24.8480 | + | 24.8480i | −0.0254069 | + | 0.0254069i | ||||
\(979\) | 360.000i | 0.367722i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 435.000 | 0.443425 | ||||||||
\(982\) | 169.212 | + | 169.212i | 0.172314 | + | 0.172314i | ||||
\(983\) | −856.332 | + | 856.332i | −0.871141 | + | 0.871141i | −0.992597 | − | 0.121456i | \(-0.961244\pi\) |
0.121456 | + | 0.992597i | \(0.461244\pi\) | |||||||
\(984\) | − | 307.151i | − | 0.312145i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 552.545 | 0.560390 | ||||||||
\(987\) | 1027.23 | + | 1027.23i | 1.04076 | + | 1.04076i | ||||
\(988\) | −134.894 | + | 134.894i | −0.136533 | + | 0.136533i | ||||
\(989\) | 666.150i | 0.673559i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 688.605 | 0.694859 | 0.347429 | − | 0.937706i | \(-0.387055\pi\) | ||||
0.347429 | + | 0.937706i | \(0.387055\pi\) | |||||||
\(992\) | −156.363 | − | 156.363i | −0.157624 | − | 0.157624i | ||||
\(993\) | −362.449 | + | 362.449i | −0.365005 | + | 0.365005i | ||||
\(994\) | − | 559.151i | − | 0.562526i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −193.212 | −0.193988 | ||||||||
\(997\) | −1260.82 | − | 1260.82i | −1.26461 | − | 1.26461i | −0.948833 | − | 0.315778i | \(-0.897734\pi\) |
−0.315778 | − | 0.948833i | \(-0.602266\pi\) | |||||||
\(998\) | −699.636 | + | 699.636i | −0.701038 | + | 0.701038i | ||||
\(999\) | 91.8184i | 0.0919103i |
(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 | 150.3.f.c.7.1 | yes | 4 | |
3.2 | odd | 2 | 450.3.g.g.307.2 | 4 | |||
4.3 | odd | 2 | 1200.3.bg.a.1057.2 | 4 | |||
5.2 | odd | 4 | 150.3.f.a.43.2 | yes | 4 | ||
5.3 | odd | 4 | inner | 150.3.f.c.43.1 | yes | 4 | |
5.4 | even | 2 | 150.3.f.a.7.2 | ✓ | 4 | ||
15.2 | even | 4 | 450.3.g.h.343.1 | 4 | |||
15.8 | even | 4 | 450.3.g.g.343.2 | 4 | |||
15.14 | odd | 2 | 450.3.g.h.307.1 | 4 | |||
20.3 | even | 4 | 1200.3.bg.a.193.2 | 4 | |||
20.7 | even | 4 | 1200.3.bg.p.193.1 | 4 | |||
20.19 | odd | 2 | 1200.3.bg.p.1057.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.3.f.a.7.2 | ✓ | 4 | 5.4 | even | 2 | ||
150.3.f.a.43.2 | yes | 4 | 5.2 | odd | 4 | ||
150.3.f.c.7.1 | yes | 4 | 1.1 | even | 1 | trivial | |
150.3.f.c.43.1 | yes | 4 | 5.3 | odd | 4 | inner | |
450.3.g.g.307.2 | 4 | 3.2 | odd | 2 | |||
450.3.g.g.343.2 | 4 | 15.8 | even | 4 | |||
450.3.g.h.307.1 | 4 | 15.14 | odd | 2 | |||
450.3.g.h.343.1 | 4 | 15.2 | even | 4 | |||
1200.3.bg.a.193.2 | 4 | 20.3 | even | 4 | |||
1200.3.bg.a.1057.2 | 4 | 4.3 | odd | 2 | |||
1200.3.bg.p.193.1 | 4 | 20.7 | even | 4 | |||
1200.3.bg.p.1057.1 | 4 | 20.19 | odd | 2 |