Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(251,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.b (of order \(2\), degree \(1\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.4 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.251 |
Dual form | 525.2.b.e.251.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.52434i | 1.78498i | 0.451071 | + | 0.892488i | \(0.351042\pi\) | ||||
−0.451071 | + | 0.892488i | \(0.648958\pi\) | |||||||
\(3\) | −1.68614 | + | 0.396143i | −0.973494 | + | 0.228714i | ||||
\(4\) | −4.37228 | −2.18614 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | − | 4.25639i | −0.408248 | − | 1.73766i | ||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | − | 5.98844i | − | 2.11723i | ||||||
\(9\) | 2.68614 | − | 1.33591i | 0.895380 | − | 0.445302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.792287i | − | 0.238884i | −0.992841 | − | 0.119442i | \(-0.961890\pi\) | ||
0.992841 | − | 0.119442i | \(-0.0381105\pi\) | |||||||
\(12\) | 7.37228 | − | 1.73205i | 2.12819 | − | 0.500000i | ||||
\(13\) | − | 5.84096i | − | 1.61999i | −0.586436 | − | 0.809996i | \(-0.699469\pi\) | ||
0.586436 | − | 0.809996i | \(-0.300531\pi\) | |||||||
\(14\) | 4.37228 | + | 5.04868i | 1.16854 | + | 1.34932i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.37228 | 1.59307 | ||||||||
\(17\) | 1.37228 | 0.332827 | 0.166414 | − | 0.986056i | \(-0.446781\pi\) | ||||
0.166414 | + | 0.986056i | \(0.446781\pi\) | |||||||
\(18\) | 3.37228 | + | 6.78073i | 0.794854 | + | 1.59823i | ||||
\(19\) | − | 3.46410i | − | 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.68614 | + | 3.71277i | −0.586164 | + | 0.810192i | ||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 1.87953i | 0.391909i | 0.980613 | + | 0.195954i | \(0.0627804\pi\) | ||||
−0.980613 | + | 0.195954i | \(0.937220\pi\) | |||||||
\(24\) | 2.37228 | + | 10.0974i | 0.484240 | + | 2.06111i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.7446 | 2.89165 | ||||||||
\(27\) | −4.00000 | + | 3.31662i | −0.769800 | + | 0.638285i | ||||
\(28\) | −8.74456 | + | 7.57301i | −1.65257 | + | 1.43117i | ||||
\(29\) | − | 4.25639i | − | 0.790392i | −0.918597 | − | 0.395196i | \(-0.870677\pi\) | ||
0.918597 | − | 0.395196i | \(-0.129323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410i | 0.622171i | 0.950382 | + | 0.311086i | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | 4.10891i | 0.726360i | ||||||||
\(33\) | 0.313859 | + | 1.33591i | 0.0546359 | + | 0.232552i | ||||
\(34\) | 3.46410i | 0.594089i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.7446 | + | 5.84096i | −1.95743 | + | 0.973494i | ||||
\(37\) | −4.74456 | −0.780001 | −0.390001 | − | 0.920815i | \(-0.627525\pi\) | ||||
−0.390001 | + | 0.920815i | \(0.627525\pi\) | |||||||
\(38\) | 8.74456 | 1.41856 | ||||||||
\(39\) | 2.31386 | + | 9.84868i | 0.370514 | + | 1.57705i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | −9.37228 | − | 6.78073i | −1.44617 | − | 1.04629i | ||||
\(43\) | 6.74456 | 1.02854 | 0.514268 | − | 0.857629i | \(-0.328064\pi\) | ||||
0.514268 | + | 0.857629i | \(0.328064\pi\) | |||||||
\(44\) | 3.46410i | 0.522233i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.74456 | −0.699548 | ||||||||
\(47\) | 7.37228 | 1.07536 | 0.537679 | − | 0.843150i | \(-0.319301\pi\) | ||||
0.537679 | + | 0.843150i | \(0.319301\pi\) | |||||||
\(48\) | −10.7446 | + | 2.52434i | −1.55084 | + | 0.364357i | ||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.31386 | + | 0.543620i | −0.324005 | + | 0.0761221i | ||||
\(52\) | 25.5383i | 3.54153i | ||||||||
\(53\) | − | 8.51278i | − | 1.16932i | −0.811278 | − | 0.584660i | \(-0.801228\pi\) | ||
0.811278 | − | 0.584660i | \(-0.198772\pi\) | |||||||
\(54\) | −8.37228 | − | 10.0974i | −1.13932 | − | 1.37408i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.3723 | − | 11.9769i | −1.38605 | − | 1.60048i | ||||
\(57\) | 1.37228 | + | 5.84096i | 0.181763 | + | 0.773654i | ||||
\(58\) | 10.7446 | 1.41083 | ||||||||
\(59\) | 2.74456 | 0.357312 | 0.178656 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178656 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | −8.74456 | −1.11056 | ||||||||
\(63\) | 3.05842 | − | 7.32435i | 0.385325 | − | 0.922781i | ||||
\(64\) | 2.37228 | 0.296535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.37228 | + | 0.792287i | −0.415099 | + | 0.0975238i | ||||
\(67\) | 6.74456 | 0.823979 | 0.411990 | − | 0.911188i | \(-0.364834\pi\) | ||||
0.411990 | + | 0.911188i | \(0.364834\pi\) | |||||||
\(68\) | −6.00000 | −0.727607 | ||||||||
\(69\) | −0.744563 | − | 3.16915i | −0.0896348 | − | 0.381521i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.5615i | − | 1.60945i | −0.593649 | − | 0.804724i | \(-0.702313\pi\) | ||
0.593649 | − | 0.804724i | \(-0.297687\pi\) | |||||||
\(72\) | −8.00000 | − | 16.0858i | −0.942809 | − | 1.89573i | ||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | − | 11.9769i | − | 1.39228i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.1460i | 1.73737i | ||||||||
\(77\) | −1.37228 | − | 1.58457i | −0.156386 | − | 0.180579i | ||||
\(78\) | −24.8614 | + | 5.84096i | −2.81500 | + | 0.661359i | ||||
\(79\) | 3.37228 | 0.379411 | 0.189706 | − | 0.981841i | \(-0.439247\pi\) | ||||
0.189706 | + | 0.981841i | \(0.439247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.43070 | − | 7.17687i | 0.603411 | − | 0.797430i | ||||
\(82\) | − | 15.1460i | − | 1.67260i | ||||||
\(83\) | −5.48913 | −0.602510 | −0.301255 | − | 0.953544i | \(-0.597406\pi\) | ||||
−0.301255 | + | 0.953544i | \(0.597406\pi\) | |||||||
\(84\) | 11.7446 | − | 16.2333i | 1.28144 | − | 1.77119i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 17.0256i | 1.83591i | ||||||||
\(87\) | 1.68614 | + | 7.17687i | 0.180773 | + | 0.769441i | ||||
\(88\) | −4.74456 | −0.505772 | ||||||||
\(89\) | 3.25544 | 0.345076 | 0.172538 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172538 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.1168 | − | 11.6819i | −1.06053 | − | 1.22460i | ||||
\(92\) | − | 8.21782i | − | 0.856767i | ||||||
\(93\) | −1.37228 | − | 5.84096i | −0.142299 | − | 0.605680i | ||||
\(94\) | 18.6101i | 1.91949i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.62772 | − | 6.92820i | −0.166128 | − | 0.707107i | ||||
\(97\) | 1.08724i | 0.110393i | 0.998476 | + | 0.0551963i | \(0.0175785\pi\) | ||||
−0.998476 | + | 0.0551963i | \(0.982422\pi\) | |||||||
\(98\) | 17.4891 | + | 2.52434i | 1.76667 | + | 0.254997i | ||||
\(99\) | −1.05842 | − | 2.12819i | −0.106375 | − | 0.213892i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | −1.37228 | − | 5.84096i | −0.135876 | − | 0.578341i | ||||
\(103\) | 16.2333i | 1.59951i | 0.600326 | + | 0.799756i | \(0.295038\pi\) | ||||
−0.600326 | + | 0.799756i | \(0.704962\pi\) | |||||||
\(104\) | −34.9783 | −3.42990 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.4891 | 2.08721 | ||||||||
\(107\) | 6.63325i | 0.641260i | 0.947204 | + | 0.320630i | \(0.103895\pi\) | ||||
−0.947204 | + | 0.320630i | \(0.896105\pi\) | |||||||
\(108\) | 17.4891 | − | 14.5012i | 1.68289 | − | 1.39538i | ||||
\(109\) | 0.116844 | 0.0111916 | 0.00559581 | − | 0.999984i | \(-0.498219\pi\) | ||||
0.00559581 | + | 0.999984i | \(0.498219\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | − | 1.87953i | 0.759326 | − | 0.178397i | ||||
\(112\) | 12.7446 | − | 11.0371i | 1.20425 | − | 1.04291i | ||||
\(113\) | 10.0974i | 0.949879i | 0.880018 | + | 0.474939i | \(0.157530\pi\) | ||||
−0.880018 | + | 0.474939i | \(0.842470\pi\) | |||||||
\(114\) | −14.7446 | + | 3.46410i | −1.38095 | + | 0.324443i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 18.6101i | 1.72791i | ||||||||
\(117\) | −7.80298 | − | 15.6896i | −0.721386 | − | 1.45051i | ||||
\(118\) | 6.92820i | 0.637793i | ||||||||
\(119\) | 2.74456 | − | 2.37686i | 0.251594 | − | 0.217886i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3723 | 0.942935 | ||||||||
\(122\) | −17.4891 | −1.58339 | ||||||||
\(123\) | 10.1168 | − | 2.37686i | 0.912205 | − | 0.214314i | ||||
\(124\) | − | 15.1460i | − | 1.36015i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.4891 | + | 7.72049i | 1.64714 | + | 0.687796i | ||||
\(127\) | −10.7446 | −0.953426 | −0.476713 | − | 0.879059i | \(-0.658172\pi\) | ||||
−0.476713 | + | 0.879059i | \(0.658172\pi\) | |||||||
\(128\) | 14.2063i | 1.25567i | ||||||||
\(129\) | −11.3723 | + | 2.67181i | −1.00127 | + | 0.235240i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4891 | −1.52803 | −0.764016 | − | 0.645197i | \(-0.776775\pi\) | ||||
−0.764016 | + | 0.645197i | \(0.776775\pi\) | |||||||
\(132\) | −1.37228 | − | 5.84096i | −0.119442 | − | 0.508391i | ||||
\(133\) | −6.00000 | − | 6.92820i | −0.520266 | − | 0.600751i | ||||
\(134\) | 17.0256i | 1.47078i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 8.21782i | − | 0.704673i | ||||||
\(137\) | − | 13.2665i | − | 1.13343i | −0.823913 | − | 0.566717i | \(-0.808213\pi\) | ||
0.823913 | − | 0.566717i | \(-0.191787\pi\) | |||||||
\(138\) | 8.00000 | − | 1.87953i | 0.681005 | − | 0.159996i | ||||
\(139\) | − | 1.28962i | − | 0.109384i | −0.998503 | − | 0.0546921i | \(-0.982582\pi\) | ||
0.998503 | − | 0.0546921i | \(-0.0174177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.4307 | + | 2.92048i | −1.04685 | + | 0.245949i | ||||
\(142\) | 34.2337 | 2.87283 | ||||||||
\(143\) | −4.62772 | −0.386989 | ||||||||
\(144\) | 17.1168 | − | 8.51278i | 1.42640 | − | 0.709398i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.4891 | 1.44741 | ||||||||
\(147\) | 1.05842 | + | 12.0781i | 0.0872972 | + | 0.996182i | ||||
\(148\) | 20.7446 | 1.70519 | ||||||||
\(149\) | − | 10.0974i | − | 0.827207i | −0.910457 | − | 0.413604i | \(-0.864270\pi\) | ||
0.910457 | − | 0.413604i | \(-0.135730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.37228 | 0.274432 | 0.137216 | − | 0.990541i | \(-0.456184\pi\) | ||||
0.137216 | + | 0.990541i | \(0.456184\pi\) | |||||||
\(152\) | −20.7446 | −1.68261 | ||||||||
\(153\) | 3.68614 | − | 1.83324i | 0.298007 | − | 0.148209i | ||||
\(154\) | 4.00000 | − | 3.46410i | 0.322329 | − | 0.279145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.1168 | − | 43.0612i | −0.809996 | − | 3.44766i | ||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 8.51278i | 0.677240i | ||||||||
\(159\) | 3.37228 | + | 14.3537i | 0.267439 | + | 1.13833i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.25544 | + | 3.75906i | 0.256564 | + | 0.296255i | ||||
\(162\) | 18.1168 | + | 13.7089i | 1.42339 | + | 1.07708i | ||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | 26.2337 | 2.04851 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 13.8564i | − | 1.07547i | ||||||
\(167\) | 22.1168 | 1.71145 | 0.855726 | − | 0.517429i | \(-0.173111\pi\) | ||||
0.855726 | + | 0.517429i | \(0.173111\pi\) | |||||||
\(168\) | 22.2337 | + | 16.0858i | 1.71537 | + | 1.24105i | ||||
\(169\) | −21.1168 | −1.62437 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.62772 | − | 9.30506i | −0.353890 | − | 0.711576i | ||||
\(172\) | −29.4891 | −2.24852 | ||||||||
\(173\) | −16.1168 | −1.22534 | −0.612670 | − | 0.790338i | \(-0.709905\pi\) | ||||
−0.612670 | + | 0.790338i | \(0.709905\pi\) | |||||||
\(174\) | −18.1168 | + | 4.25639i | −1.37343 | + | 0.322676i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.04868i | − | 0.380558i | ||||||
\(177\) | −4.62772 | + | 1.08724i | −0.347841 | + | 0.0817220i | ||||
\(178\) | 8.21782i | 0.615952i | ||||||||
\(179\) | − | 6.63325i | − | 0.495792i | −0.968787 | − | 0.247896i | \(-0.920261\pi\) | ||
0.968787 | − | 0.247896i | \(-0.0797392\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.6101i | − | 1.38328i | −0.722242 | − | 0.691640i | \(-0.756889\pi\) | ||
0.722242 | − | 0.691640i | \(-0.243111\pi\) | |||||||
\(182\) | 29.4891 | − | 25.5383i | 2.18588 | − | 1.89303i | ||||
\(183\) | −2.74456 | − | 11.6819i | −0.202884 | − | 0.863553i | ||||
\(184\) | 11.2554 | 0.829762 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.7446 | − | 3.46410i | 1.08112 | − | 0.254000i | ||||
\(187\) | − | 1.08724i | − | 0.0795069i | ||||||
\(188\) | −32.2337 | −2.35088 | ||||||||
\(189\) | −2.25544 | + | 13.5615i | −0.164059 | + | 0.986451i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.6434i | 1.13191i | 0.824435 | + | 0.565957i | \(0.191493\pi\) | ||||
−0.824435 | + | 0.565957i | \(0.808507\pi\) | |||||||
\(192\) | −4.00000 | + | 0.939764i | −0.288675 | + | 0.0678216i | ||||
\(193\) | −22.2337 | −1.60042 | −0.800208 | − | 0.599723i | \(-0.795278\pi\) | ||||
−0.800208 | + | 0.599723i | \(0.795278\pi\) | |||||||
\(194\) | −2.74456 | −0.197048 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.37228 | + | 30.2921i | −0.312306 | + | 2.16372i | ||||
\(197\) | − | 22.3692i | − | 1.59374i | −0.604152 | − | 0.796869i | \(-0.706488\pi\) | ||
0.604152 | − | 0.796869i | \(-0.293512\pi\) | |||||||
\(198\) | 5.37228 | − | 2.67181i | 0.381791 | − | 0.189878i | ||||
\(199\) | 12.9715i | 0.919528i | 0.888041 | + | 0.459764i | \(0.152066\pi\) | ||||
−0.888041 | + | 0.459764i | \(0.847934\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3723 | + | 2.67181i | −0.802139 | + | 0.188455i | ||||
\(202\) | 15.1460i | 1.06567i | ||||||||
\(203\) | −7.37228 | − | 8.51278i | −0.517433 | − | 0.597480i | ||||
\(204\) | 10.1168 | − | 2.37686i | 0.708321 | − | 0.166414i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −40.9783 | −2.85509 | ||||||||
\(207\) | 2.51087 | + | 5.04868i | 0.174518 | + | 0.350907i | ||||
\(208\) | − | 37.2203i | − | 2.58076i | ||||||
\(209\) | −2.74456 | −0.189845 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.11684 | 0.421101 | 0.210550 | − | 0.977583i | \(-0.432474\pi\) | ||||
0.210550 | + | 0.977583i | \(0.432474\pi\) | |||||||
\(212\) | 37.2203i | 2.55630i | ||||||||
\(213\) | 5.37228 | + | 22.8665i | 0.368103 | + | 1.56679i | ||||
\(214\) | −16.7446 | −1.14463 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 19.8614 | + | 23.9538i | 1.35140 | + | 1.62985i | ||||
\(217\) | 6.00000 | + | 6.92820i | 0.407307 | + | 0.470317i | ||||
\(218\) | 0.294954i | 0.0199768i | ||||||||
\(219\) | 2.74456 | + | 11.6819i | 0.185460 | + | 0.789391i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.01544i | − | 0.539177i | ||||||
\(222\) | 4.74456 | + | 20.1947i | 0.318434 | + | 1.35538i | ||||
\(223\) | − | 20.9870i | − | 1.40539i | −0.711490 | − | 0.702696i | \(-0.751979\pi\) | ||
0.711490 | − | 0.702696i | \(-0.248021\pi\) | |||||||
\(224\) | 7.11684 | + | 8.21782i | 0.475514 | + | 0.549076i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.4891 | −1.69551 | ||||||||
\(227\) | 15.6060 | 1.03580 | 0.517902 | − | 0.855440i | \(-0.326713\pi\) | ||||
0.517902 | + | 0.855440i | \(0.326713\pi\) | |||||||
\(228\) | −6.00000 | − | 25.5383i | −0.397360 | − | 1.69132i | ||||
\(229\) | − | 4.75372i | − | 0.314135i | −0.987588 | − | 0.157067i | \(-0.949796\pi\) | ||
0.987588 | − | 0.157067i | \(-0.0502040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.94158 | + | 2.12819i | 0.193542 | + | 0.140025i | ||||
\(232\) | −25.4891 | −1.67344 | ||||||||
\(233\) | − | 3.75906i | − | 0.246264i | −0.992390 | − | 0.123132i | \(-0.960706\pi\) | ||
0.992390 | − | 0.123132i | \(-0.0392938\pi\) | |||||||
\(234\) | 39.6060 | − | 19.6974i | 2.58912 | − | 1.28766i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.0000 | −0.781133 | ||||||||
\(237\) | −5.68614 | + | 1.33591i | −0.369355 | + | 0.0867765i | ||||
\(238\) | 6.00000 | + | 6.92820i | 0.388922 | + | 0.449089i | ||||
\(239\) | 15.6434i | 1.01188i | 0.862567 | + | 0.505942i | \(0.168855\pi\) | ||||
−0.862567 | + | 0.505942i | \(0.831145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.3639i | 1.50500i | 0.658593 | + | 0.752499i | \(0.271152\pi\) | ||||
−0.658593 | + | 0.752499i | \(0.728848\pi\) | |||||||
\(242\) | 26.1831i | 1.68312i | ||||||||
\(243\) | −6.31386 | + | 14.2525i | −0.405034 | + | 0.914302i | ||||
\(244\) | − | 30.2921i | − | 1.93925i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.00000 | + | 25.5383i | 0.382546 | + | 1.62826i | ||||
\(247\) | −20.2337 | −1.28744 | ||||||||
\(248\) | 20.7446 | 1.31728 | ||||||||
\(249\) | 9.25544 | − | 2.17448i | 0.586540 | − | 0.137802i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4891 | 1.10390 | 0.551952 | − | 0.833876i | \(-0.313883\pi\) | ||||
0.551952 | + | 0.833876i | \(0.313883\pi\) | |||||||
\(252\) | −13.3723 | + | 32.0241i | −0.842375 | + | 2.01733i | ||||
\(253\) | 1.48913 | 0.0936205 | ||||||||
\(254\) | − | 27.1229i | − | 1.70184i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.1168 | −1.94480 | ||||||||
\(257\) | −23.4891 | −1.46521 | −0.732606 | − | 0.680653i | \(-0.761696\pi\) | ||||
−0.732606 | + | 0.680653i | \(0.761696\pi\) | |||||||
\(258\) | −6.74456 | − | 28.7075i | −0.419898 | − | 1.78725i | ||||
\(259\) | −9.48913 | + | 8.21782i | −0.589626 | + | 0.510631i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.68614 | − | 11.4333i | −0.351963 | − | 0.707701i | ||||
\(262\) | − | 44.1485i | − | 2.72750i | ||||||
\(263\) | 13.5615i | 0.836235i | 0.908393 | + | 0.418118i | \(0.137310\pi\) | ||||
−0.908393 | + | 0.418118i | \(0.862690\pi\) | |||||||
\(264\) | 8.00000 | − | 1.87953i | 0.492366 | − | 0.115677i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17.4891 | − | 15.1460i | 1.07233 | − | 0.928662i | ||||
\(267\) | −5.48913 | + | 1.28962i | −0.335929 | + | 0.0789235i | ||||
\(268\) | −29.4891 | −1.80134 | ||||||||
\(269\) | −8.74456 | −0.533165 | −0.266583 | − | 0.963812i | \(-0.585895\pi\) | ||||
−0.266583 | + | 0.963812i | \(0.585895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1460i | 0.920056i | 0.887905 | + | 0.460028i | \(0.152161\pi\) | ||||
−0.887905 | + | 0.460028i | \(0.847839\pi\) | |||||||
\(272\) | 8.74456 | 0.530217 | ||||||||
\(273\) | 21.6861 | + | 15.6896i | 1.31250 | + | 0.949581i | ||||
\(274\) | 33.4891 | 2.02315 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.25544 | + | 13.8564i | 0.195954 | + | 0.834058i | ||||
\(277\) | 6.23369 | 0.374546 | 0.187273 | − | 0.982308i | \(-0.440035\pi\) | ||||
0.187273 | + | 0.982308i | \(0.440035\pi\) | |||||||
\(278\) | 3.25544 | 0.195248 | ||||||||
\(279\) | 4.62772 | + | 9.30506i | 0.277054 | + | 0.557080i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.84630i | 0.289106i | 0.989497 | + | 0.144553i | \(0.0461744\pi\) | ||||
−0.989497 | + | 0.144553i | \(0.953826\pi\) | |||||||
\(282\) | −7.37228 | − | 31.3793i | −0.439013 | − | 1.86861i | ||||
\(283\) | 9.30506i | 0.553129i | 0.960995 | + | 0.276564i | \(0.0891959\pi\) | ||||
−0.960995 | + | 0.276564i | \(0.910804\pi\) | |||||||
\(284\) | 59.2945i | 3.51848i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 11.6819i | − | 0.690767i | ||||||
\(287\) | −12.0000 | + | 10.3923i | −0.708338 | + | 0.613438i | ||||
\(288\) | 5.48913 | + | 11.0371i | 0.323450 | + | 0.650368i | ||||
\(289\) | −15.1168 | −0.889226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.430703 | − | 1.83324i | −0.0252483 | − | 0.107466i | ||||
\(292\) | 30.2921i | 1.77271i | ||||||||
\(293\) | 28.1168 | 1.64260 | 0.821302 | − | 0.570494i | \(-0.193248\pi\) | ||||
0.821302 | + | 0.570494i | \(0.193248\pi\) | |||||||
\(294\) | −30.4891 | + | 2.67181i | −1.77816 | + | 0.155823i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 28.4125i | 1.65144i | ||||||||
\(297\) | 2.62772 | + | 3.16915i | 0.152476 | + | 0.183893i | ||||
\(298\) | 25.4891 | 1.47655 | ||||||||
\(299\) | 10.9783 | 0.634889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.4891 | − | 11.6819i | 0.777500 | − | 0.673335i | ||||
\(302\) | 8.51278i | 0.489855i | ||||||||
\(303\) | −10.1168 | + | 2.37686i | −0.581198 | + | 0.136547i | ||||
\(304\) | − | 22.0742i | − | 1.26604i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.62772 | + | 9.30506i | 0.264549 | + | 0.531935i | ||||
\(307\) | 7.13058i | 0.406964i | 0.979079 | + | 0.203482i | \(0.0652258\pi\) | ||||
−0.979079 | + | 0.203482i | \(0.934774\pi\) | |||||||
\(308\) | 6.00000 | + | 6.92820i | 0.341882 | + | 0.394771i | ||||
\(309\) | −6.43070 | − | 27.3716i | −0.365830 | − | 1.55711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.2337 | 1.14735 | 0.573674 | − | 0.819084i | \(-0.305518\pi\) | ||||
0.573674 | + | 0.819084i | \(0.305518\pi\) | |||||||
\(312\) | 58.9783 | − | 13.8564i | 3.33899 | − | 0.784465i | ||||
\(313\) | 24.4511i | 1.38206i | 0.722827 | + | 0.691029i | \(0.242842\pi\) | ||||
−0.722827 | + | 0.691029i | \(0.757158\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.7446 | −0.829446 | ||||||||
\(317\) | − | 8.51278i | − | 0.478125i | −0.971004 | − | 0.239063i | \(-0.923160\pi\) | ||
0.971004 | − | 0.239063i | \(-0.0768401\pi\) | |||||||
\(318\) | −36.2337 | + | 8.51278i | −2.03188 | + | 0.477373i | ||||
\(319\) | −3.37228 | −0.188812 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.62772 | − | 11.1846i | −0.146665 | − | 0.624263i | ||||
\(322\) | −9.48913 | + | 8.21782i | −0.528808 | + | 0.457961i | ||||
\(323\) | − | 4.75372i | − | 0.264504i | ||||||
\(324\) | −23.7446 | + | 31.3793i | −1.31914 | + | 1.74329i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 20.1947i | − | 1.11848i | ||||||
\(327\) | −0.197015 | + | 0.0462870i | −0.0108950 | + | 0.00255968i | ||||
\(328\) | 35.9306i | 1.98394i | ||||||||
\(329\) | 14.7446 | − | 12.7692i | 0.812894 | − | 0.703987i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 24.0000 | 1.31717 | ||||||||
\(333\) | −12.7446 | + | 6.33830i | −0.698398 | + | 0.347336i | ||||
\(334\) | 55.8304i | 3.05490i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −17.1168 | + | 23.6588i | −0.933800 | + | 1.29069i | ||||
\(337\) | 18.2337 | 0.993252 | 0.496626 | − | 0.867965i | \(-0.334572\pi\) | ||||
0.496626 | + | 0.867965i | \(0.334572\pi\) | |||||||
\(338\) | − | 53.3060i | − | 2.89947i | ||||||
\(339\) | −4.00000 | − | 17.0256i | −0.217250 | − | 0.924701i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.74456 | 0.148626 | ||||||||
\(342\) | 23.4891 | − | 11.6819i | 1.27015 | − | 0.631686i | ||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | − | 40.3894i | − | 2.17765i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 40.6844i | − | 2.18720i | ||||||
\(347\) | 18.3152i | 0.983210i | 0.870818 | + | 0.491605i | \(0.163590\pi\) | ||||
−0.870818 | + | 0.491605i | \(0.836410\pi\) | |||||||
\(348\) | −7.37228 | − | 31.3793i | −0.395196 | − | 1.68211i | ||||
\(349\) | 4.75372i | 0.254461i | 0.991873 | + | 0.127230i | \(0.0406088\pi\) | ||||
−0.991873 | + | 0.127230i | \(0.959391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.3723 | + | 23.3639i | 1.03402 | + | 1.24707i | ||||
\(352\) | 3.25544 | 0.173515 | ||||||||
\(353\) | −7.88316 | −0.419578 | −0.209789 | − | 0.977747i | \(-0.567278\pi\) | ||||
−0.209789 | + | 0.977747i | \(0.567278\pi\) | |||||||
\(354\) | −2.74456 | − | 11.6819i | −0.145872 | − | 0.620887i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.2337 | −0.754384 | ||||||||
\(357\) | −3.68614 | + | 5.09496i | −0.195091 | + | 0.269654i | ||||
\(358\) | 16.7446 | 0.884978 | ||||||||
\(359\) | 9.80240i | 0.517351i | 0.965964 | + | 0.258675i | \(0.0832860\pi\) | ||||
−0.965964 | + | 0.258675i | \(0.916714\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 46.9783 | 2.46912 | ||||||||
\(363\) | −17.4891 | + | 4.10891i | −0.917941 | + | 0.215662i | ||||
\(364\) | 44.2337 | + | 51.0767i | 2.31848 | + | 2.67714i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 29.4891 | − | 6.92820i | 1.54142 | − | 0.362143i | ||||
\(367\) | − | 25.3360i | − | 1.32253i | −0.750154 | − | 0.661263i | \(-0.770021\pi\) | ||
0.750154 | − | 0.661263i | \(-0.229979\pi\) | |||||||
\(368\) | 11.9769i | 0.624338i | ||||||||
\(369\) | −16.1168 | + | 8.01544i | −0.839009 | + | 0.417267i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.7446 | − | 17.0256i | −0.765500 | − | 0.883923i | ||||
\(372\) | 6.00000 | + | 25.5383i | 0.311086 | + | 1.32410i | ||||
\(373\) | 24.7446 | 1.28122 | 0.640612 | − | 0.767864i | \(-0.278681\pi\) | ||||
0.640612 | + | 0.767864i | \(0.278681\pi\) | |||||||
\(374\) | 2.74456 | 0.141918 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 44.1485i | − | 2.27678i | ||||||
\(377\) | −24.8614 | −1.28043 | ||||||||
\(378\) | −34.2337 | − | 5.69349i | −1.76079 | − | 0.292841i | ||||
\(379\) | 1.48913 | 0.0764912 | 0.0382456 | − | 0.999268i | \(-0.487823\pi\) | ||||
0.0382456 | + | 0.999268i | \(0.487823\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.1168 | − | 4.25639i | 0.928154 | − | 0.218061i | ||||
\(382\) | −39.4891 | −2.02044 | ||||||||
\(383\) | 17.4891 | 0.893653 | 0.446826 | − | 0.894621i | \(-0.352554\pi\) | ||||
0.446826 | + | 0.894621i | \(0.352554\pi\) | |||||||
\(384\) | −5.62772 | − | 23.9538i | −0.287188 | − | 1.22239i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 56.1253i | − | 2.85670i | ||||||
\(387\) | 18.1168 | − | 9.01011i | 0.920931 | − | 0.458010i | ||||
\(388\) | − | 4.75372i | − | 0.241334i | ||||||
\(389\) | − | 13.7638i | − | 0.697854i | −0.937150 | − | 0.348927i | \(-0.886546\pi\) | ||
0.937150 | − | 0.348927i | \(-0.113454\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.57924i | 0.130438i | ||||||||
\(392\) | −41.4891 | − | 5.98844i | −2.09552 | − | 0.302462i | ||||
\(393\) | 29.4891 | − | 6.92820i | 1.48753 | − | 0.349482i | ||||
\(394\) | 56.4674 | 2.84479 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.62772 | + | 9.30506i | 0.232552 | + | 0.467597i | ||||
\(397\) | − | 3.66648i | − | 0.184015i | −0.995758 | − | 0.0920077i | \(-0.970672\pi\) | ||
0.995758 | − | 0.0920077i | \(-0.0293284\pi\) | |||||||
\(398\) | −32.7446 | −1.64134 | ||||||||
\(399\) | 12.8614 | + | 9.30506i | 0.643876 | + | 0.465836i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.67181i | 0.133424i | 0.997772 | + | 0.0667120i | \(0.0212509\pi\) | ||||
−0.997772 | + | 0.0667120i | \(0.978749\pi\) | |||||||
\(402\) | −6.74456 | − | 28.7075i | −0.336388 | − | 1.43180i | ||||
\(403\) | 20.2337 | 1.00791 | ||||||||
\(404\) | −26.2337 | −1.30517 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.4891 | − | 18.6101i | 1.06649 | − | 0.923605i | ||||
\(407\) | 3.75906i | 0.186329i | ||||||||
\(408\) | 3.25544 | + | 13.8564i | 0.161168 | + | 0.685994i | ||||
\(409\) | − | 35.0458i | − | 1.73290i | −0.499262 | − | 0.866451i | \(-0.666396\pi\) | ||
0.499262 | − | 0.866451i | \(-0.333604\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.25544 | + | 22.3692i | 0.259232 | + | 1.10339i | ||||
\(412\) | − | 70.9764i | − | 3.49676i | ||||||
\(413\) | 5.48913 | − | 4.75372i | 0.270102 | − | 0.233915i | ||||
\(414\) | −12.7446 | + | 6.33830i | −0.626361 | + | 0.311510i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.0000 | 1.17670 | ||||||||
\(417\) | 0.510875 | + | 2.17448i | 0.0250176 | + | 0.106485i | ||||
\(418\) | − | 6.92820i | − | 0.338869i | ||||||
\(419\) | −2.74456 | −0.134081 | −0.0670403 | − | 0.997750i | \(-0.521356\pi\) | ||||
−0.0670403 | + | 0.997750i | \(0.521356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.6060 | −1.24796 | −0.623979 | − | 0.781441i | \(-0.714485\pi\) | ||||
−0.623979 | + | 0.781441i | \(0.714485\pi\) | |||||||
\(422\) | 15.4410i | 0.751655i | ||||||||
\(423\) | 19.8030 | − | 9.84868i | 0.962854 | − | 0.478859i | ||||
\(424\) | −50.9783 | −2.47572 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −57.7228 | + | 13.5615i | −2.79668 | + | 0.657055i | ||||
\(427\) | 12.0000 | + | 13.8564i | 0.580721 | + | 0.670559i | ||||
\(428\) | − | 29.0024i | − | 1.40189i | ||||||
\(429\) | 7.80298 | − | 1.83324i | 0.376732 | − | 0.0885097i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.6742i | 1.52569i | 0.646579 | + | 0.762847i | \(0.276199\pi\) | ||||
−0.646579 | + | 0.762847i | \(0.723801\pi\) | |||||||
\(432\) | −25.4891 | + | 21.1345i | −1.22635 | + | 1.01683i | ||||
\(433\) | 2.57924i | 0.123950i | 0.998078 | + | 0.0619752i | \(0.0197400\pi\) | ||||
−0.998078 | + | 0.0619752i | \(0.980260\pi\) | |||||||
\(434\) | −17.4891 | + | 15.1460i | −0.839505 | + | 0.727033i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.510875 | −0.0244665 | ||||||||
\(437\) | 6.51087 | 0.311457 | ||||||||
\(438\) | −29.4891 | + | 6.92820i | −1.40904 | + | 0.331042i | ||||
\(439\) | 1.28962i | 0.0615502i | 0.999526 | + | 0.0307751i | \(0.00979757\pi\) | ||||
−0.999526 | + | 0.0307751i | \(0.990202\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.56930 | − | 19.9460i | −0.312824 | − | 0.949811i | ||||
\(442\) | 20.2337 | 0.962418 | ||||||||
\(443\) | 6.63325i | 0.315155i | 0.987507 | + | 0.157578i | \(0.0503684\pi\) | ||||
−0.987507 | + | 0.157578i | \(0.949632\pi\) | |||||||
\(444\) | −34.9783 | + | 8.21782i | −1.65999 | + | 0.390001i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 52.9783 | 2.50859 | ||||||||
\(447\) | 4.00000 | + | 17.0256i | 0.189194 | + | 0.805281i | ||||
\(448\) | 4.74456 | − | 4.10891i | 0.224160 | − | 0.194128i | ||||
\(449\) | 28.2101i | 1.33132i | 0.746256 | + | 0.665660i | \(0.231850\pi\) | ||||
−0.746256 | + | 0.665660i | \(0.768150\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.75372i | 0.223844i | ||||||||
\(452\) | − | 44.1485i | − | 2.07657i | ||||||
\(453\) | −5.68614 | + | 1.33591i | −0.267158 | + | 0.0627664i | ||||
\(454\) | 39.3947i | 1.84889i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 34.9783 | − | 8.21782i | 1.63801 | − | 0.384835i | ||||
\(457\) | 32.9783 | 1.54266 | 0.771329 | − | 0.636437i | \(-0.219592\pi\) | ||||
0.771329 | + | 0.636437i | \(0.219592\pi\) | |||||||
\(458\) | 12.0000 | 0.560723 | ||||||||
\(459\) | −5.48913 | + | 4.55134i | −0.256210 | + | 0.212438i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.74456 | −0.407275 | −0.203637 | − | 0.979046i | \(-0.565276\pi\) | ||||
−0.203637 | + | 0.979046i | \(0.565276\pi\) | |||||||
\(462\) | −5.37228 | + | 7.42554i | −0.249941 | + | 0.345467i | ||||
\(463\) | −36.4674 | −1.69478 | −0.847391 | − | 0.530969i | \(-0.821828\pi\) | ||||
−0.847391 | + | 0.530969i | \(0.821828\pi\) | |||||||
\(464\) | − | 27.1229i | − | 1.25915i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.48913 | 0.439575 | ||||||||
\(467\) | 13.8832 | 0.642436 | 0.321218 | − | 0.947005i | \(-0.395908\pi\) | ||||
0.321218 | + | 0.947005i | \(0.395908\pi\) | |||||||
\(468\) | 34.1168 | + | 68.5996i | 1.57705 | + | 3.17102i | ||||
\(469\) | 13.4891 | − | 11.6819i | 0.622870 | − | 0.539421i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 16.4356i | − | 0.756512i | ||||||
\(473\) | − | 5.34363i | − | 0.245700i | ||||||
\(474\) | −3.37228 | − | 14.3537i | −0.154894 | − | 0.659289i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.0000 | + | 10.3923i | −0.550019 | + | 0.476331i | ||||
\(477\) | −11.3723 | − | 22.8665i | −0.520701 | − | 1.04699i | ||||
\(478\) | −39.4891 | −1.80619 | ||||||||
\(479\) | 18.5109 | 0.845783 | 0.422892 | − | 0.906180i | \(-0.361015\pi\) | ||||
0.422892 | + | 0.906180i | \(0.361015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7128i | 1.26360i | ||||||||
\(482\) | −58.9783 | −2.68639 | ||||||||
\(483\) | −6.97825 | − | 5.04868i | −0.317521 | − | 0.229723i | ||||
\(484\) | −45.3505 | −2.06139 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −35.9783 | − | 15.9383i | −1.63201 | − | 0.722977i | ||||
\(487\) | −14.5109 | −0.657550 | −0.328775 | − | 0.944408i | \(-0.606636\pi\) | ||||
−0.328775 | + | 0.944408i | \(0.606636\pi\) | |||||||
\(488\) | 41.4891 | 1.87812 | ||||||||
\(489\) | 13.4891 | − | 3.16915i | 0.609999 | − | 0.143314i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.8896i | 0.491442i | 0.969341 | + | 0.245721i | \(0.0790248\pi\) | ||||
−0.969341 | + | 0.245721i | \(0.920975\pi\) | |||||||
\(492\) | −44.2337 | + | 10.3923i | −1.99421 | + | 0.468521i | ||||
\(493\) | − | 5.84096i | − | 0.263064i | ||||||
\(494\) | − | 51.0767i | − | 2.29805i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.0742i | 0.991162i | ||||||||
\(497\) | −23.4891 | − | 27.1229i | −1.05363 | − | 1.21663i | ||||
\(498\) | 5.48913 | + | 23.3639i | 0.245974 | + | 1.04696i | ||||
\(499\) | −10.3505 | −0.463353 | −0.231677 | − | 0.972793i | \(-0.574421\pi\) | ||||
−0.231677 | + | 0.972793i | \(0.574421\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −37.2921 | + | 8.76144i | −1.66609 | + | 0.391432i | ||||
\(502\) | 44.1485i | 1.97044i | ||||||||
\(503\) | 27.6060 | 1.23089 | 0.615445 | − | 0.788180i | \(-0.288976\pi\) | ||||
0.615445 | + | 0.788180i | \(0.288976\pi\) | |||||||
\(504\) | −43.8614 | − | 18.3152i | −1.95374 | − | 0.815823i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.75906i | 0.167110i | ||||||||
\(507\) | 35.6060 | − | 8.36530i | 1.58132 | − | 0.371516i | ||||
\(508\) | 46.9783 | 2.08432 | ||||||||
\(509\) | −38.2337 | −1.69468 | −0.847339 | − | 0.531052i | \(-0.821797\pi\) | ||||
−0.847339 | + | 0.531052i | \(0.821797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | − | 13.8564i | −0.530849 | − | 0.612971i | ||||
\(512\) | − | 50.1369i | − | 2.21576i | ||||||
\(513\) | 11.4891 | + | 13.8564i | 0.507257 | + | 0.611775i | ||||
\(514\) | − | 59.2945i | − | 2.61537i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 49.7228 | − | 11.6819i | 2.18892 | − | 0.514268i | ||||
\(517\) | − | 5.84096i | − | 0.256885i | ||||||
\(518\) | −20.7446 | − | 23.9538i | −0.911464 | − | 1.05247i | ||||
\(519\) | 27.1753 | − | 6.38458i | 1.19286 | − | 0.280252i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4674 | 1.51004 | 0.755022 | − | 0.655700i | \(-0.227626\pi\) | ||||
0.755022 | + | 0.655700i | \(0.227626\pi\) | |||||||
\(522\) | 28.8614 | − | 14.3537i | 1.26323 | − | 0.628246i | ||||
\(523\) | − | 10.3923i | − | 0.454424i | −0.973845 | − | 0.227212i | \(-0.927039\pi\) | ||
0.973845 | − | 0.227212i | \(-0.0729610\pi\) | |||||||
\(524\) | 76.4674 | 3.34049 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.2337 | −1.49266 | ||||||||
\(527\) | 4.75372i | 0.207075i | ||||||||
\(528\) | 2.00000 | + | 8.51278i | 0.0870388 | + | 0.370471i | ||||
\(529\) | 19.4674 | 0.846408 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.37228 | − | 3.66648i | 0.319930 | − | 0.159112i | ||||
\(532\) | 26.2337 | + | 30.2921i | 1.13737 | + | 1.31333i | ||||
\(533\) | 35.0458i | 1.51800i | ||||||||
\(534\) | −3.25544 | − | 13.8564i | −0.140877 | − | 0.599625i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 40.3894i | − | 1.74456i | ||||||
\(537\) | 2.62772 | + | 11.1846i | 0.113394 | + | 0.482651i | ||||
\(538\) | − | 22.0742i | − | 0.951688i | ||||||
\(539\) | −5.48913 | − | 0.792287i | −0.236433 | − | 0.0341262i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6277 | 0.800868 | 0.400434 | − | 0.916326i | \(-0.368859\pi\) | ||||
0.400434 | + | 0.916326i | \(0.368859\pi\) | |||||||
\(542\) | −38.2337 | −1.64228 | ||||||||
\(543\) | 7.37228 | + | 31.3793i | 0.316375 | + | 1.34661i | ||||
\(544\) | 5.63858i | 0.241752i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −39.6060 | + | 54.7431i | −1.69498 | + | 2.34279i | ||||
\(547\) | −42.9783 | −1.83762 | −0.918809 | − | 0.394703i | \(-0.870847\pi\) | ||||
−0.918809 | + | 0.394703i | \(0.870847\pi\) | |||||||
\(548\) | 58.0049i | 2.47785i | ||||||||
\(549\) | 9.25544 | + | 18.6101i | 0.395012 | + | 0.794261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.7446 | −0.628139 | ||||||||
\(552\) | −18.9783 | + | 4.45877i | −0.807768 | + | 0.189778i | ||||
\(553\) | 6.74456 | − | 5.84096i | 0.286808 | − | 0.248383i | ||||
\(554\) | 15.7359i | 0.668556i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.63858i | 0.239129i | ||||||||
\(557\) | 30.8820i | 1.30851i | 0.756274 | + | 0.654255i | \(0.227018\pi\) | ||||
−0.756274 | + | 0.654255i | \(0.772982\pi\) | |||||||
\(558\) | −23.4891 | + | 11.6819i | −0.994374 | + | 0.494535i | ||||
\(559\) | − | 39.3947i | − | 1.66622i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.430703 | + | 1.83324i | 0.0181843 | + | 0.0773995i | ||||
\(562\) | −12.2337 | −0.516047 | ||||||||
\(563\) | −5.48913 | −0.231339 | −0.115670 | − | 0.993288i | \(-0.536901\pi\) | ||||
−0.115670 | + | 0.993288i | \(0.536901\pi\) | |||||||
\(564\) | 54.3505 | − | 12.7692i | 2.28857 | − | 0.537679i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.4891 | −0.987322 | ||||||||
\(567\) | −1.56930 | − | 23.7600i | −0.0659043 | − | 0.997826i | ||||
\(568\) | −81.2119 | −3.40758 | ||||||||
\(569\) | 10.6873i | 0.448033i | 0.974585 | + | 0.224017i | \(0.0719170\pi\) | ||||
−0.974585 | + | 0.224017i | \(0.928083\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 20.2337 | 0.846013 | ||||||||
\(573\) | −6.19702 | − | 26.3769i | −0.258884 | − | 1.10191i | ||||
\(574\) | −26.2337 | − | 30.2921i | −1.09497 | − | 1.26437i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.37228 | − | 3.16915i | 0.265512 | − | 0.132048i | ||||
\(577\) | 12.7692i | 0.531587i | 0.964030 | + | 0.265794i | \(0.0856340\pi\) | ||||
−0.964030 | + | 0.265794i | \(0.914366\pi\) | |||||||
\(578\) | − | 38.1600i | − | 1.58725i | ||||||
\(579\) | 37.4891 | − | 8.80773i | 1.55799 | − | 0.366037i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9783 | + | 9.50744i | −0.455455 | + | 0.394435i | ||||
\(582\) | 4.62772 | − | 1.08724i | 0.191825 | − | 0.0450676i | ||||
\(583\) | −6.74456 | −0.279331 | ||||||||
\(584\) | −41.4891 | −1.71683 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 70.9764i | 2.93201i | ||||||||
\(587\) | 5.48913 | 0.226560 | 0.113280 | − | 0.993563i | \(-0.463864\pi\) | ||||
0.113280 | + | 0.993563i | \(0.463864\pi\) | |||||||
\(588\) | −4.62772 | − | 52.8087i | −0.190844 | − | 2.17779i | ||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.86141 | + | 37.7176i | 0.364510 | + | 1.55149i | ||||
\(592\) | −30.2337 | −1.24260 | ||||||||
\(593\) | 1.37228 | 0.0563528 | 0.0281764 | − | 0.999603i | \(-0.491030\pi\) | ||||
0.0281764 | + | 0.999603i | \(0.491030\pi\) | |||||||
\(594\) | −8.00000 | + | 6.63325i | −0.328244 | + | 0.272166i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 44.1485i | 1.80839i | ||||||||
\(597\) | −5.13859 | − | 21.8719i | −0.210309 | − | 0.895155i | ||||
\(598\) | 27.7128i | 1.13326i | ||||||||
\(599\) | 1.78695i | 0.0730129i | 0.999333 | + | 0.0365065i | \(0.0116230\pi\) | ||||
−0.999333 | + | 0.0365065i | \(0.988377\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.17448i | 0.0886989i | 0.999016 | + | 0.0443495i | \(0.0141215\pi\) | ||||
−0.999016 | + | 0.0443495i | \(0.985878\pi\) | |||||||
\(602\) | 29.4891 | + | 34.0511i | 1.20189 | + | 1.38782i | ||||
\(603\) | 18.1168 | − | 9.01011i | 0.737775 | − | 0.366920i | ||||
\(604\) | −14.7446 | −0.599948 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.00000 | − | 25.5383i | −0.243733 | − | 1.03742i | ||||
\(607\) | − | 20.9870i | − | 0.851836i | −0.904762 | − | 0.425918i | \(-0.859951\pi\) | ||
0.904762 | − | 0.425918i | \(-0.140049\pi\) | |||||||
\(608\) | 14.2337 | 0.577252 | ||||||||
\(609\) | 15.8030 | + | 11.4333i | 0.640369 | + | 0.463299i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 43.0612i | − | 1.74207i | ||||||
\(612\) | −16.1168 | + | 8.01544i | −0.651485 | + | 0.324005i | ||||
\(613\) | 4.51087 | 0.182193 | 0.0910963 | − | 0.995842i | \(-0.470963\pi\) | ||||
0.0910963 | + | 0.995842i | \(0.470963\pi\) | |||||||
\(614\) | −18.0000 | −0.726421 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.48913 | + | 8.21782i | −0.382328 | + | 0.331106i | ||||
\(617\) | 37.8102i | 1.52218i | 0.648646 | + | 0.761090i | \(0.275335\pi\) | ||||
−0.648646 | + | 0.761090i | \(0.724665\pi\) | |||||||
\(618\) | 69.0951 | − | 16.2333i | 2.77941 | − | 0.652998i | ||||
\(619\) | − | 1.28962i | − | 0.0518342i | −0.999664 | − | 0.0259171i | \(-0.991749\pi\) | ||
0.999664 | − | 0.0259171i | \(-0.00825060\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.23369 | − | 7.51811i | −0.250149 | − | 0.301691i | ||||
\(622\) | 51.0767i | 2.04799i | ||||||||
\(623\) | 6.51087 | − | 5.63858i | 0.260853 | − | 0.225905i | ||||
\(624\) | 14.7446 | + | 62.7586i | 0.590255 | + | 2.51235i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −61.7228 | −2.46694 | ||||||||
\(627\) | 4.62772 | − | 1.08724i | 0.184813 | − | 0.0434202i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.51087 | −0.259606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.88316 | −0.234205 | −0.117102 | − | 0.993120i | \(-0.537361\pi\) | ||||
−0.117102 | + | 0.993120i | \(0.537361\pi\) | |||||||
\(632\) | − | 20.1947i | − | 0.803302i | ||||||
\(633\) | −10.3139 | + | 2.42315i | −0.409939 | + | 0.0963115i | ||||
\(634\) | 21.4891 | 0.853442 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −14.7446 | − | 62.7586i | −0.584660 | − | 2.48854i | ||||
\(637\) | −40.4674 | − | 5.84096i | −1.60338 | − | 0.231427i | ||||
\(638\) | − | 8.51278i | − | 0.337024i | ||||||
\(639\) | −18.1168 | − | 36.4280i | −0.716691 | − | 1.44107i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.7021i | 1.17316i | 0.809890 | + | 0.586582i | \(0.199527\pi\) | ||||
−0.809890 | + | 0.586582i | \(0.800473\pi\) | |||||||
\(642\) | 28.2337 | − | 6.63325i | 1.11429 | − | 0.261793i | ||||
\(643\) | − | 39.5971i | − | 1.56156i | −0.624807 | − | 0.780779i | \(-0.714822\pi\) | ||
0.624807 | − | 0.780779i | \(-0.285178\pi\) | |||||||
\(644\) | −14.2337 | − | 16.4356i | −0.560886 | − | 0.647655i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | −42.9783 | − | 32.5214i | −1.68835 | − | 1.27756i | ||||
\(649\) | − | 2.17448i | − | 0.0853559i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.8614 | − | 9.30506i | −0.504078 | − | 0.364694i | ||||
\(652\) | 34.9783 | 1.36985 | ||||||||
\(653\) | 33.0564i | 1.29360i | 0.762660 | + | 0.646799i | \(0.223893\pi\) | ||||
−0.762660 | + | 0.646799i | \(0.776107\pi\) | |||||||
\(654\) | −0.116844 | − | 0.497333i | −0.00456896 | − | 0.0194473i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −38.2337 | −1.49277 | ||||||||
\(657\) | −9.25544 | − | 18.6101i | −0.361089 | − | 0.726050i | ||||
\(658\) | 32.2337 | + | 37.2203i | 1.25660 | + | 1.45100i | ||||
\(659\) | 20.3971i | 0.794558i | 0.917698 | + | 0.397279i | \(0.130045\pi\) | ||||
−0.917698 | + | 0.397279i | \(0.869955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.92820i | − | 0.269476i | −0.990881 | − | 0.134738i | \(-0.956981\pi\) | ||
0.990881 | − | 0.134738i | \(-0.0430193\pi\) | |||||||
\(662\) | − | 10.0974i | − | 0.392445i | ||||||
\(663\) | 3.17527 | + | 13.5152i | 0.123317 | + | 0.524886i | ||||
\(664\) | 32.8713i | 1.27565i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.0000 | − | 32.1716i | −0.619987 | − | 1.24662i | ||||
\(667\) | 8.00000 | 0.309761 | ||||||||
\(668\) | −96.7011 | −3.74148 | ||||||||
\(669\) | 8.31386 | + | 35.3870i | 0.321432 | + | 1.36814i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.48913 | 0.211905 | ||||||||
\(672\) | −15.2554 | − | 11.0371i | −0.588491 | − | 0.425766i | ||||
\(673\) | −22.2337 | −0.857046 | −0.428523 | − | 0.903531i | \(-0.640966\pi\) | ||||
−0.428523 | + | 0.903531i | \(0.640966\pi\) | |||||||
\(674\) | 46.0280i | 1.77293i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 92.3288 | 3.55111 | ||||||||
\(677\) | −21.6060 | −0.830385 | −0.415192 | − | 0.909734i | \(-0.636286\pi\) | ||||
−0.415192 | + | 0.909734i | \(0.636286\pi\) | |||||||
\(678\) | 42.9783 | − | 10.0974i | 1.65057 | − | 0.387786i | ||||
\(679\) | 1.88316 | + | 2.17448i | 0.0722689 | + | 0.0834489i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.3139 | + | 6.18220i | −1.00835 | + | 0.236903i | ||||
\(682\) | 6.92820i | 0.265295i | ||||||||
\(683\) | − | 51.7764i | − | 1.98117i | −0.136906 | − | 0.990584i | \(-0.543716\pi\) | ||
0.136906 | − | 0.990584i | \(-0.456284\pi\) | |||||||
\(684\) | 20.2337 | + | 40.6844i | 0.773654 | + | 1.55561i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 39.3505 | − | 25.2434i | 1.50241 | − | 0.963797i | ||||
\(687\) | 1.88316 | + | 8.01544i | 0.0718469 | + | 0.305808i | ||||
\(688\) | 42.9783 | 1.63853 | ||||||||
\(689\) | −49.7228 | −1.89429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 38.5099i | − | 1.46498i | −0.680775 | − | 0.732492i | \(-0.738357\pi\) | ||
0.680775 | − | 0.732492i | \(-0.261643\pi\) | |||||||
\(692\) | 70.4674 | 2.67877 | ||||||||
\(693\) | −5.80298 | − | 2.42315i | −0.220437 | − | 0.0920478i | ||||
\(694\) | −46.2337 | −1.75501 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 42.9783 | − | 10.0974i | 1.62909 | − | 0.382739i | ||||
\(697\) | −8.23369 | −0.311873 | ||||||||
\(698\) | −12.0000 | −0.454207 | ||||||||
\(699\) | 1.48913 | + | 6.33830i | 0.0563239 | + | 0.239736i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 45.8256i | − | 1.73081i | −0.501074 | − | 0.865405i | \(-0.667061\pi\) | ||
0.501074 | − | 0.865405i | \(-0.332939\pi\) | |||||||
\(702\) | −58.9783 | + | 48.9022i | −2.22599 | + | 1.84569i | ||||
\(703\) | 16.4356i | 0.619882i | ||||||||
\(704\) | − | 1.87953i | − | 0.0708374i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 19.8997i | − | 0.748937i | ||||||
\(707\) | 12.0000 | − | 10.3923i | 0.451306 | − | 0.390843i | ||||
\(708\) | 20.2337 | − | 4.75372i | 0.760429 | − | 0.178656i | ||||
\(709\) | 24.1168 | 0.905727 | 0.452864 | − | 0.891580i | \(-0.350402\pi\) | ||||
0.452864 | + | 0.891580i | \(0.350402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.05842 | − | 4.50506i | 0.339717 | − | 0.168953i | ||||
\(712\) | − | 19.4950i | − | 0.730606i | ||||||
\(713\) | −6.51087 | −0.243834 | ||||||||
\(714\) | −12.8614 | − | 9.30506i | −0.481326 | − | 0.348233i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.0024i | 1.08387i | ||||||||
\(717\) | −6.19702 | − | 26.3769i | −0.231432 | − | 0.985064i | ||||
\(718\) | −24.7446 | −0.923459 | ||||||||
\(719\) | 40.4674 | 1.50918 | 0.754589 | − | 0.656197i | \(-0.227836\pi\) | ||||
0.754589 | + | 0.656197i | \(0.227836\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.1168 | + | 32.4665i | 1.04713 | + | 1.20912i | ||||
\(722\) | 17.6704i | 0.657623i | ||||||||
\(723\) | −9.25544 | − | 39.3947i | −0.344213 | − | 1.46511i | ||||
\(724\) | 81.3687i | 3.02404i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.3723 | − | 44.1485i | −0.384951 | − | 1.63850i | ||||
\(727\) | − | 3.46410i | − | 0.128476i | −0.997935 | − | 0.0642382i | \(-0.979538\pi\) | ||
0.997935 | − | 0.0642382i | \(-0.0204617\pi\) | |||||||
\(728\) | −69.9565 | + | 60.5841i | −2.59276 | + | 2.24540i | ||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.25544 | 0.342325 | ||||||||
\(732\) | 12.0000 | + | 51.0767i | 0.443533 | + | 1.88785i | ||||
\(733\) | 10.1899i | 0.376373i | 0.982133 | + | 0.188187i | \(0.0602610\pi\) | ||||
−0.982133 | + | 0.188187i | \(0.939739\pi\) | |||||||
\(734\) | 63.9565 | 2.36068 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.72281 | −0.284667 | ||||||||
\(737\) | − | 5.34363i | − | 0.196835i | ||||||
\(738\) | −20.2337 | − | 40.6844i | −0.744812 | − | 1.49761i | ||||
\(739\) | −8.62772 | −0.317376 | −0.158688 | − | 0.987329i | \(-0.550726\pi\) | ||||
−0.158688 | + | 0.987329i | \(0.550726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.1168 | − | 8.01544i | 1.25331 | − | 0.294455i | ||||
\(742\) | 42.9783 | − | 37.2203i | 1.57778 | − | 1.36640i | ||||
\(743\) | 36.9253i | 1.35466i | 0.735680 | + | 0.677329i | \(0.236863\pi\) | ||||
−0.735680 | + | 0.677329i | \(0.763137\pi\) | |||||||
\(744\) | −34.9783 | + | 8.21782i | −1.28236 | + | 0.301280i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 62.4636i | 2.28696i | ||||||||
\(747\) | −14.7446 | + | 7.33296i | −0.539475 | + | 0.268299i | ||||
\(748\) | 4.75372i | 0.173813i | ||||||||
\(749\) | 11.4891 | + | 13.2665i | 0.419804 | + | 0.484747i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.3505 | −0.815582 | −0.407791 | − | 0.913075i | \(-0.633701\pi\) | ||||
−0.407791 | + | 0.913075i | \(0.633701\pi\) | |||||||
\(752\) | 46.9783 | 1.71312 | ||||||||
\(753\) | −29.4891 | + | 6.92820i | −1.07464 | + | 0.252478i | ||||
\(754\) | − | 62.7586i | − | 2.28553i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 9.86141 | − | 59.2945i | 0.358656 | − | 2.15652i | ||||
\(757\) | 54.2337 | 1.97116 | 0.985578 | − | 0.169219i | \(-0.0541245\pi\) | ||||
0.985578 | + | 0.169219i | \(0.0541245\pi\) | |||||||
\(758\) | 3.75906i | 0.136535i | ||||||||
\(759\) | −2.51087 | + | 0.589907i | −0.0911390 | + | 0.0214123i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.2337 | −0.950970 | −0.475485 | − | 0.879724i | \(-0.657727\pi\) | ||||
−0.475485 | + | 0.879724i | \(0.657727\pi\) | |||||||
\(762\) | 10.7446 | + | 45.7330i | 0.389234 | + | 1.65673i | ||||
\(763\) | 0.233688 | − | 0.202380i | 0.00846007 | − | 0.00732664i | ||||
\(764\) | − | 68.3972i | − | 2.47452i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 44.1485i | 1.59515i | ||||||||
\(767\) | − | 16.0309i | − | 0.578842i | ||||||
\(768\) | 52.4674 | − | 12.3267i | 1.89325 | − | 0.444803i | ||||
\(769\) | 21.1894i | 0.764108i | 0.924140 | + | 0.382054i | \(0.124783\pi\) | ||||
−0.924140 | + | 0.382054i | \(0.875217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.6060 | − | 9.30506i | 1.42637 | − | 0.335114i | ||||
\(772\) | 97.2119 | 3.49873 | ||||||||
\(773\) | 46.6277 | 1.67708 | 0.838541 | − | 0.544838i | \(-0.183409\pi\) | ||||
0.838541 | + | 0.544838i | \(0.183409\pi\) | |||||||
\(774\) | 22.7446 | + | 45.7330i | 0.817536 | + | 1.64384i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.51087 | 0.233727 | ||||||||
\(777\) | 12.7446 | − | 17.6155i | 0.457209 | − | 0.631951i | ||||
\(778\) | 34.7446 | 1.24565 | ||||||||
\(779\) | 20.7846i | 0.744686i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7446 | −0.384471 | ||||||||
\(782\) | −6.51087 | −0.232828 | ||||||||
\(783\) | 14.1168 | + | 17.0256i | 0.504495 | + | 0.608444i | ||||
\(784\) | 6.37228 | − | 44.1485i | 0.227581 | − | 1.57673i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.4891 | + | 74.4405i | 0.623816 | + | 2.65521i | ||||
\(787\) | 46.5253i | 1.65845i | 0.558916 | + | 0.829224i | \(0.311217\pi\) | ||||
−0.558916 | + | 0.829224i | \(0.688783\pi\) | |||||||
\(788\) | 97.8044i | 3.48414i | ||||||||
\(789\) | −5.37228 | − | 22.8665i | −0.191258 | − | 0.814070i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.4891 | + | 20.1947i | 0.621842 | + | 0.718041i | ||||
\(792\) | −12.7446 | + | 6.33830i | −0.452858 | + | 0.225222i | ||||
\(793\) | 40.4674 | 1.43704 | ||||||||
\(794\) | 9.25544 | 0.328463 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 56.7152i | − | 2.01022i | ||||||
\(797\) | 42.8614 | 1.51823 | 0.759114 | − | 0.650957i | \(-0.225632\pi\) | ||||
0.759114 | + | 0.650957i | \(0.225632\pi\) | |||||||
\(798\) | −23.4891 | + | 32.4665i | −0.831506 | + | 1.14930i | ||||
\(799\) | 10.1168 | 0.357908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.74456 | − | 4.34896i | 0.308974 | − | 0.153663i | ||||
\(802\) | −6.74456 | −0.238159 | ||||||||
\(803\) | −5.48913 | −0.193707 | ||||||||
\(804\) | 49.7228 | − | 11.6819i | 1.75359 | − | 0.411990i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 51.0767i | 1.79910i | ||||||||
\(807\) | 14.7446 | − | 3.46410i | 0.519033 | − | 0.121942i | ||||
\(808\) | − | 35.9306i | − | 1.26404i | ||||||
\(809\) | − | 36.7229i | − | 1.29111i | −0.763714 | − | 0.645555i | \(-0.776626\pi\) | ||
0.763714 | − | 0.645555i | \(-0.223374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.28962i | − | 0.0452847i | −0.999744 | − | 0.0226423i | \(-0.992792\pi\) | ||
0.999744 | − | 0.0226423i | \(-0.00720790\pi\) | |||||||
\(812\) | 32.2337 | + | 37.2203i | 1.13118 | + | 1.30617i | ||||
\(813\) | −6.00000 | − | 25.5383i | −0.210429 | − | 0.895668i | ||||
\(814\) | −9.48913 | −0.332594 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.7446 | + | 3.46410i | −0.516163 | + | 0.121268i | ||||
\(817\) | − | 23.3639i | − | 0.817398i | ||||||
\(818\) | 88.4674 | 3.09319 | ||||||||
\(819\) | −42.7812 | − | 17.8641i | −1.49490 | − | 0.624223i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7745i | 0.410933i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(822\) | −56.4674 | + | 13.2665i | −1.96953 | + | 0.462722i | ||||
\(823\) | 48.2337 | 1.68132 | 0.840660 | − | 0.541563i | \(-0.182167\pi\) | ||||
0.840660 | + | 0.541563i | \(0.182167\pi\) | |||||||
\(824\) | 97.2119 | 3.38654 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | + | 13.8564i | 0.417533 | + | 0.482126i | ||||
\(827\) | 18.3152i | 0.636881i | 0.947943 | + | 0.318441i | \(0.103159\pi\) | ||||
−0.947943 | + | 0.318441i | \(0.896841\pi\) | |||||||
\(828\) | −10.9783 | − | 22.0742i | −0.381521 | − | 0.767133i | ||||
\(829\) | 32.4665i | 1.12761i | 0.825908 | + | 0.563805i | \(0.190663\pi\) | ||||
−0.825908 | + | 0.563805i | \(0.809337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.5109 | + | 2.46943i | −0.364618 | + | 0.0856637i | ||||
\(832\) | − | 13.8564i | − | 0.480384i | ||||||
\(833\) | 1.37228 | − | 9.50744i | 0.0475467 | − | 0.329413i | ||||
\(834\) | −5.48913 | + | 1.28962i | −0.190073 | + | 0.0446559i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.0000 | 0.415029 | ||||||||
\(837\) | −11.4891 | − | 13.8564i | −0.397122 | − | 0.478947i | ||||
\(838\) | − | 6.92820i | − | 0.239331i | ||||||
\(839\) | −53.4891 | −1.84665 | −0.923325 | − | 0.384020i | \(-0.874539\pi\) | ||||
−0.923325 | + | 0.384020i | \(0.874539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8832 | 0.375281 | ||||||||
\(842\) | − | 64.6381i | − | 2.22758i | ||||||
\(843\) | −1.91983 | − | 8.17154i | −0.0661224 | − | 0.281443i | ||||
\(844\) | −26.7446 | −0.920586 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 24.8614 | + | 49.9894i | 0.854753 | + | 1.71867i | ||||
\(847\) | 20.7446 | − | 17.9653i | 0.712792 | − | 0.617296i | ||||
\(848\) | − | 54.2458i | − | 1.86281i | ||||||
\(849\) | −3.68614 | − | 15.6896i | −0.126508 | − | 0.538467i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 8.91754i | − | 0.305689i | ||||||
\(852\) | −23.4891 | − | 99.9788i | −0.804724 | − | 3.42522i | ||||
\(853\) | 46.7277i | 1.59993i | 0.600049 | + | 0.799963i | \(0.295148\pi\) | ||||
−0.600049 | + | 0.799963i | \(0.704852\pi\) | |||||||
\(854\) | −34.9783 | + | 30.2921i | −1.19693 | + | 1.03657i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.7228 | 1.35770 | ||||||||
\(857\) | 22.4674 | 0.767471 | 0.383735 | − | 0.923443i | \(-0.374637\pi\) | ||||
0.383735 | + | 0.923443i | \(0.374637\pi\) | |||||||
\(858\) | 4.62772 | + | 19.6974i | 0.157988 | + | 0.672457i | ||||
\(859\) | 45.4381i | 1.55033i | 0.631760 | + | 0.775164i | \(0.282333\pi\) | ||||
−0.631760 | + | 0.775164i | \(0.717667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.1168 | − | 22.2766i | 0.549261 | − | 0.759185i | ||||
\(862\) | −79.9565 | −2.72333 | ||||||||
\(863\) | − | 28.0078i | − | 0.953395i | −0.879067 | − | 0.476698i | \(-0.841834\pi\) | ||
0.879067 | − | 0.476698i | \(-0.158166\pi\) | |||||||
\(864\) | −13.6277 | − | 16.4356i | −0.463624 | − | 0.559152i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.51087 | −0.221249 | ||||||||
\(867\) | 25.4891 | − | 5.98844i | 0.865656 | − | 0.203378i | ||||
\(868\) | −26.2337 | − | 30.2921i | −0.890429 | − | 1.02818i | ||||
\(869\) | − | 2.67181i | − | 0.0906351i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 39.3947i | − | 1.33484i | ||||||
\(872\) | − | 0.699713i | − | 0.0236953i | ||||||
\(873\) | 1.45245 | + | 2.92048i | 0.0491581 | + | 0.0988433i | ||||
\(874\) | 16.4356i | 0.555944i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | − | 51.0767i | −0.405442 | − | 1.72572i | ||||
\(877\) | −30.4674 | −1.02881 | −0.514405 | − | 0.857547i | \(-0.671987\pi\) | ||||
−0.514405 | + | 0.857547i | \(0.671987\pi\) | |||||||
\(878\) | −3.25544 | −0.109866 | ||||||||
\(879\) | −47.4090 | + | 11.1383i | −1.59906 | + | 0.375686i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.23369 | −0.0752549 | −0.0376274 | − | 0.999292i | \(-0.511980\pi\) | ||||
−0.0376274 | + | 0.999292i | \(0.511980\pi\) | |||||||
\(882\) | 50.3505 | − | 16.5831i | 1.69539 | − | 0.558383i | ||||
\(883\) | −26.5109 | −0.892162 | −0.446081 | − | 0.894993i | \(-0.647181\pi\) | ||||
−0.446081 | + | 0.894993i | \(0.647181\pi\) | |||||||
\(884\) | 35.0458i | 1.17872i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.7446 | −0.562545 | ||||||||
\(887\) | −41.4891 | −1.39307 | −0.696534 | − | 0.717524i | \(-0.745276\pi\) | ||||
−0.696534 | + | 0.717524i | \(0.745276\pi\) | |||||||
\(888\) | −11.2554 | − | 47.9075i | −0.377708 | − | 1.60767i | ||||
\(889\) | −21.4891 | + | 18.6101i | −0.720722 | + | 0.624164i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.68614 | − | 4.30268i | −0.190493 | − | 0.144145i | ||||
\(892\) | 91.7610i | 3.07239i | ||||||||
\(893\) | − | 25.5383i | − | 0.854608i | ||||||
\(894\) | −42.9783 | + | 10.0974i | −1.43741 | + | 0.337706i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.6060 | + | 28.4125i | 0.822028 | + | 0.949196i | ||||
\(897\) | −18.5109 | + | 4.34896i | −0.618060 | + | 0.145208i | ||||
\(898\) | −71.2119 | −2.37637 | ||||||||
\(899\) | 14.7446 | 0.491759 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 11.6819i | − | 0.389181i | ||||||
\(902\) | −12.0000 | −0.399556 | ||||||||
\(903\) | −18.1168 | + | 25.0410i | −0.602891 | + | 0.833312i | ||||
\(904\) | 60.4674 | 2.01112 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.37228 | − | 14.3537i | −0.112037 | − | 0.476871i | ||||
\(907\) | −8.00000 | −0.265636 | −0.132818 | − | 0.991140i | \(-0.542403\pi\) | ||||
−0.132818 | + | 0.991140i | \(0.542403\pi\) | |||||||
\(908\) | −68.2337 | −2.26441 | ||||||||
\(909\) | 16.1168 | − | 8.01544i | 0.534562 | − | 0.265855i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.6588i | 0.783851i | 0.919997 | + | 0.391926i | \(0.128191\pi\) | ||||
−0.919997 | + | 0.391926i | \(0.871809\pi\) | |||||||
\(912\) | 8.74456 | + | 37.2203i | 0.289561 | + | 1.23249i | ||||
\(913\) | 4.34896i | 0.143930i | ||||||||
\(914\) | 83.2482i | 2.75361i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.7846i | 0.686743i | ||||||||
\(917\) | −34.9783 | + | 30.2921i | −1.15508 | + | 1.00033i | ||||
\(918\) | −11.4891 | − | 13.8564i | −0.379198 | − | 0.457330i | ||||
\(919\) | −11.3723 | −0.375137 | −0.187568 | − | 0.982252i | \(-0.560061\pi\) | ||||
−0.187568 | + | 0.982252i | \(0.560061\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.82473 | − | 12.0232i | −0.0930782 | − | 0.396177i | ||||
\(922\) | − | 22.0742i | − | 0.726976i | ||||||
\(923\) | −79.2119 | −2.60729 | ||||||||
\(924\) | −12.8614 | − | 9.30506i | −0.423109 | − | 0.306114i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 92.0560i | − | 3.02515i | ||||||
\(927\) | 21.6861 | + | 43.6048i | 0.712266 | + | 1.43217i | ||||
\(928\) | 17.4891 | 0.574109 | ||||||||
\(929\) | 7.02175 | 0.230376 | 0.115188 | − | 0.993344i | \(-0.463253\pi\) | ||||
0.115188 | + | 0.993344i | \(0.463253\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0000 | − | 3.46410i | −0.786568 | − | 0.113531i | ||||
\(932\) | 16.4356i | 0.538368i | ||||||||
\(933\) | −34.1168 | + | 8.01544i | −1.11694 | + | 0.262414i | ||||
\(934\) | 35.0458i | 1.14673i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −93.9565 | + | 46.7277i | −3.07106 | + | 1.52734i | ||||
\(937\) | 49.9894i | 1.63308i | 0.577287 | + | 0.816542i | \(0.304112\pi\) | ||||
−0.577287 | + | 0.816542i | \(0.695888\pi\) | |||||||
\(938\) | 29.4891 | + | 34.0511i | 0.962854 | + | 1.11181i | ||||
\(939\) | −9.68614 | − | 41.2280i | −0.316095 | − | 1.34542i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.2554 | −0.888502 | −0.444251 | − | 0.895902i | \(-0.646530\pi\) | ||||
−0.444251 | + | 0.895902i | \(0.646530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 11.2772i | − | 0.367235i | ||||||
\(944\) | 17.4891 | 0.569223 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.4891 | 0.438569 | ||||||||
\(947\) | 48.2025i | 1.56637i | 0.621789 | + | 0.783185i | \(0.286406\pi\) | ||||
−0.621789 | + | 0.783185i | \(0.713594\pi\) | |||||||
\(948\) | 24.8614 | − | 5.84096i | 0.807461 | − | 0.189706i | ||||
\(949\) | −40.4674 | −1.31363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.37228 | + | 14.3537i | 0.109354 | + | 0.465452i | ||||
\(952\) | −14.2337 | − | 16.4356i | −0.461316 | − | 0.532682i | ||||
\(953\) | − | 38.8048i | − | 1.25701i | −0.777805 | − | 0.628506i | \(-0.783667\pi\) | ||
0.777805 | − | 0.628506i | \(-0.216333\pi\) | |||||||
\(954\) | 57.7228 | − | 28.7075i | 1.86885 | − | 0.929439i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 68.3972i | − | 2.21212i | ||||||
\(957\) | 5.68614 | − | 1.33591i | 0.183807 | − | 0.0431838i | ||||
\(958\) | 46.7277i | 1.50970i | ||||||||
\(959\) | −22.9783 | − | 26.5330i | −0.742006 | − | 0.856795i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | −69.9565 | −2.25549 | ||||||||
\(963\) | 8.86141 | + | 17.8178i | 0.285555 | + | 0.574172i | ||||
\(964\) | − | 102.153i | − | 3.29014i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12.7446 | − | 17.6155i | 0.410050 | − | 0.566768i | ||||
\(967\) | 24.2337 | 0.779303 | 0.389651 | − | 0.920962i | \(-0.372595\pi\) | ||||
0.389651 | + | 0.920962i | \(0.372595\pi\) | |||||||
\(968\) | − | 62.1138i | − | 1.99641i | ||||||
\(969\) | 1.88316 | + | 8.01544i | 0.0604957 | + | 0.257493i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.2119 | −1.38674 | −0.693369 | − | 0.720583i | \(-0.743874\pi\) | ||||
−0.693369 | + | 0.720583i | \(0.743874\pi\) | |||||||
\(972\) | 27.6060 | − | 62.3162i | 0.885462 | − | 1.99879i | ||||
\(973\) | −2.23369 | − | 2.57924i | −0.0716087 | − | 0.0826867i | ||||
\(974\) | − | 36.6303i | − | 1.17371i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.1485i | 1.41316i | ||||||||
\(977\) | − | 38.8048i | − | 1.24148i | −0.784018 | − | 0.620738i | \(-0.786833\pi\) | ||
0.784018 | − | 0.620738i | \(-0.213167\pi\) | |||||||
\(978\) | 8.00000 | + | 34.0511i | 0.255812 | + | 1.08883i | ||||
\(979\) | − | 2.57924i | − | 0.0824329i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.313859 | − | 0.156093i | 0.0100208 | − | 0.00498366i | ||||
\(982\) | −27.4891 | −0.877213 | ||||||||
\(983\) | −11.1386 | −0.355266 | −0.177633 | − | 0.984097i | \(-0.556844\pi\) | ||||
−0.177633 | + | 0.984097i | \(0.556844\pi\) | |||||||
\(984\) | −14.2337 | − | 60.5841i | −0.453753 | − | 1.93135i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.7446 | 0.469563 | ||||||||
\(987\) | −19.8030 | + | 27.3716i | −0.630336 | + | 0.871247i | ||||
\(988\) | 88.4674 | 2.81452 | ||||||||
\(989\) | 12.6766i | 0.403092i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.51087 | 0.0797606 | 0.0398803 | − | 0.999204i | \(-0.487302\pi\) | ||||
0.0398803 | + | 0.999204i | \(0.487302\pi\) | |||||||
\(992\) | −14.2337 | −0.451920 | ||||||||
\(993\) | 6.74456 | − | 1.58457i | 0.214032 | − | 0.0502849i | ||||
\(994\) | 68.4674 | − | 59.2945i | 2.17165 | − | 1.88071i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −40.4674 | + | 9.50744i | −1.28226 | + | 0.301255i | ||||
\(997\) | 21.8719i | 0.692688i | 0.938107 | + | 0.346344i | \(0.112577\pi\) | ||||
−0.938107 | + | 0.346344i | \(0.887423\pi\) | |||||||
\(998\) | − | 26.1282i | − | 0.827075i | ||||||
\(999\) | 18.9783 | − | 15.7359i | 0.600445 | − | 0.497863i |
(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 | 525.2.b.e.251.4 | 4 | ||
3.2 | odd | 2 | 525.2.b.g.251.1 | 4 | |||
5.2 | odd | 4 | 525.2.g.d.524.2 | 8 | |||
5.3 | odd | 4 | 525.2.g.d.524.7 | 8 | |||
5.4 | even | 2 | 105.2.b.d.41.1 | yes | 4 | ||
7.6 | odd | 2 | 525.2.b.g.251.4 | 4 | |||
15.2 | even | 4 | 525.2.g.e.524.7 | 8 | |||
15.8 | even | 4 | 525.2.g.e.524.2 | 8 | |||
15.14 | odd | 2 | 105.2.b.c.41.4 | yes | 4 | ||
20.19 | odd | 2 | 1680.2.f.g.881.2 | 4 | |||
21.20 | even | 2 | inner | 525.2.b.e.251.1 | 4 | ||
35.4 | even | 6 | 735.2.s.j.656.2 | 4 | |||
35.9 | even | 6 | 735.2.s.g.521.1 | 4 | |||
35.13 | even | 4 | 525.2.g.e.524.8 | 8 | |||
35.19 | odd | 6 | 735.2.s.h.521.1 | 4 | |||
35.24 | odd | 6 | 735.2.s.i.656.2 | 4 | |||
35.27 | even | 4 | 525.2.g.e.524.1 | 8 | |||
35.34 | odd | 2 | 105.2.b.c.41.1 | ✓ | 4 | ||
60.59 | even | 2 | 1680.2.f.h.881.4 | 4 | |||
105.44 | odd | 6 | 735.2.s.i.521.2 | 4 | |||
105.59 | even | 6 | 735.2.s.g.656.1 | 4 | |||
105.62 | odd | 4 | 525.2.g.d.524.8 | 8 | |||
105.74 | odd | 6 | 735.2.s.h.656.1 | 4 | |||
105.83 | odd | 4 | 525.2.g.d.524.1 | 8 | |||
105.89 | even | 6 | 735.2.s.j.521.2 | 4 | |||
105.104 | even | 2 | 105.2.b.d.41.4 | yes | 4 | ||
140.139 | even | 2 | 1680.2.f.h.881.3 | 4 | |||
420.419 | odd | 2 | 1680.2.f.g.881.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.b.c.41.1 | ✓ | 4 | 35.34 | odd | 2 | ||
105.2.b.c.41.4 | yes | 4 | 15.14 | odd | 2 | ||
105.2.b.d.41.1 | yes | 4 | 5.4 | even | 2 | ||
105.2.b.d.41.4 | yes | 4 | 105.104 | even | 2 | ||
525.2.b.e.251.1 | 4 | 21.20 | even | 2 | inner | ||
525.2.b.e.251.4 | 4 | 1.1 | even | 1 | trivial | ||
525.2.b.g.251.1 | 4 | 3.2 | odd | 2 | |||
525.2.b.g.251.4 | 4 | 7.6 | odd | 2 | |||
525.2.g.d.524.1 | 8 | 105.83 | odd | 4 | |||
525.2.g.d.524.2 | 8 | 5.2 | odd | 4 | |||
525.2.g.d.524.7 | 8 | 5.3 | odd | 4 | |||
525.2.g.d.524.8 | 8 | 105.62 | odd | 4 | |||
525.2.g.e.524.1 | 8 | 35.27 | even | 4 | |||
525.2.g.e.524.2 | 8 | 15.8 | even | 4 | |||
525.2.g.e.524.7 | 8 | 15.2 | even | 4 | |||
525.2.g.e.524.8 | 8 | 35.13 | even | 4 | |||
735.2.s.g.521.1 | 4 | 35.9 | even | 6 | |||
735.2.s.g.656.1 | 4 | 105.59 | even | 6 | |||
735.2.s.h.521.1 | 4 | 35.19 | odd | 6 | |||
735.2.s.h.656.1 | 4 | 105.74 | odd | 6 | |||
735.2.s.i.521.2 | 4 | 105.44 | odd | 6 | |||
735.2.s.i.656.2 | 4 | 35.24 | odd | 6 | |||
735.2.s.j.521.2 | 4 | 105.89 | even | 6 | |||
735.2.s.j.656.2 | 4 | 35.4 | even | 6 | |||
1680.2.f.g.881.1 | 4 | 420.419 | odd | 2 | |||
1680.2.f.g.881.2 | 4 | 20.19 | odd | 2 | |||
1680.2.f.h.881.3 | 4 | 140.139 | even | 2 | |||
1680.2.f.h.881.4 | 4 | 60.59 | even | 2 |