Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(524,525)]
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, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.524");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 524.1 | ||
Root | \(-1.26217 + 1.18614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.524 |
Dual form | 525.2.g.e.524.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52434 | −1.78498 | −0.892488 | − | 0.451071i | \(-0.851042\pi\) | ||||
−0.892488 | + | 0.451071i | \(0.851042\pi\) | |||||||
\(3\) | −0.396143 | − | 1.68614i | −0.228714 | − | 0.973494i | ||||
\(4\) | 4.37228 | 2.18614 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | + | 4.25639i | 0.408248 | + | 1.73766i | ||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | −5.98844 | −2.11723 | ||||||||
\(9\) | −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 | \(-0.0381105\pi\) | |||||||
\(12\) | −1.73205 | − | 7.37228i | −0.500000 | − | 2.12819i | ||||
\(13\) | 5.84096 | 1.61999 | 0.809996 | − | 0.586436i | \(-0.199469\pi\) | ||||
0.809996 | + | 0.586436i | \(0.199469\pi\) | |||||||
\(14\) | 4.37228 | − | 5.04868i | 1.16854 | − | 1.34932i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.37228 | 1.59307 | ||||||||
\(17\) | − | 1.37228i | − | 0.332827i | −0.986056 | − | 0.166414i | \(-0.946781\pi\) | ||
0.986056 | − | 0.166414i | \(-0.0532187\pi\) | |||||||
\(18\) | 6.78073 | − | 3.37228i | 1.59823 | − | 0.794854i | ||||
\(19\) | − | 3.46410i | − | 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.05842 | + | 2.12819i | 0.885620 | + | 0.464410i | ||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | 1.87953 | 0.391909 | 0.195954 | − | 0.980613i | \(-0.437220\pi\) | ||||
0.195954 | + | 0.980613i | \(0.437220\pi\) | |||||||
\(24\) | 2.37228 | + | 10.0974i | 0.484240 | + | 2.06111i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −14.7446 | −2.89165 | ||||||||
\(27\) | 3.31662 | + | 4.00000i | 0.638285 | + | 0.769800i | ||||
\(28\) | −7.57301 | + | 8.74456i | −1.43117 | + | 1.65257i | ||||
\(29\) | 4.25639i | 0.790392i | 0.918597 | + | 0.395196i | \(0.129323\pi\) | ||||
−0.918597 | + | 0.395196i | \(0.870677\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | −4.10891 | −0.726360 | ||||||||
\(33\) | −1.33591 | + | 0.313859i | −0.232552 | + | 0.0546359i | ||||
\(34\) | 3.46410i | 0.594089i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.7446 | + | 5.84096i | −1.95743 | + | 0.973494i | ||||
\(37\) | − | 4.74456i | − | 0.780001i | −0.920815 | − | 0.390001i | \(-0.872475\pi\) | ||
0.920815 | − | 0.390001i | \(-0.127525\pi\) | |||||||
\(38\) | 8.74456i | 1.41856i | ||||||||
\(39\) | −2.31386 | − | 9.84868i | −0.370514 | − | 1.57705i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | −10.2448 | − | 5.37228i | −1.58081 | − | 0.828961i | ||||
\(43\) | − | 6.74456i | − | 1.02854i | −0.857629 | − | 0.514268i | \(-0.828064\pi\) | ||
0.857629 | − | 0.514268i | \(-0.171936\pi\) | |||||||
\(44\) | − | 3.46410i | − | 0.522233i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.74456 | −0.699548 | ||||||||
\(47\) | − | 7.37228i | − | 1.07536i | −0.843150 | − | 0.537679i | \(-0.819301\pi\) | ||
0.843150 | − | 0.537679i | \(-0.180699\pi\) | |||||||
\(48\) | −2.52434 | − | 10.7446i | −0.364357 | − | 1.55084i | ||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.31386 | + | 0.543620i | −0.324005 | + | 0.0761221i | ||||
\(52\) | 25.5383 | 3.54153 | ||||||||
\(53\) | −8.51278 | −1.16932 | −0.584660 | − | 0.811278i | \(-0.698772\pi\) | ||||
−0.584660 | + | 0.811278i | \(0.698772\pi\) | |||||||
\(54\) | −8.37228 | − | 10.0974i | −1.13932 | − | 1.37408i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.3723 | − | 11.9769i | 1.38605 | − | 1.60048i | ||||
\(57\) | −5.84096 | + | 1.37228i | −0.773654 | + | 0.181763i | ||||
\(58\) | − | 10.7446i | − | 1.41083i | ||||||
\(59\) | 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 | \(-0.853725\pi\) | ||
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | 8.74456i | 1.11056i | ||||||||
\(63\) | 1.98072 | − | 7.68614i | 0.249547 | − | 0.968363i | ||||
\(64\) | −2.37228 | −0.296535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.37228 | − | 0.792287i | 0.415099 | − | 0.0975238i | ||||
\(67\) | 6.74456i | 0.823979i | 0.911188 | + | 0.411990i | \(0.135166\pi\) | ||||
−0.911188 | + | 0.411990i | \(0.864834\pi\) | |||||||
\(68\) | − | 6.00000i | − | 0.727607i | ||||||
\(69\) | −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 | \(-0.297687\pi\) | |||||||
\(72\) | 16.0858 | − | 8.00000i | 1.89573 | − | 0.942809i | ||||
\(73\) | 6.92820 | 0.810885 | 0.405442 | − | 0.914121i | \(-0.367117\pi\) | ||||
0.405442 | + | 0.914121i | \(0.367117\pi\) | |||||||
\(74\) | 11.9769i | 1.39228i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 15.1460i | − | 1.73737i | ||||||
\(77\) | 1.58457 | + | 1.37228i | 0.180579 | + | 0.156386i | ||||
\(78\) | 5.84096 | + | 24.8614i | 0.661359 | + | 2.81500i | ||||
\(79\) | −3.37228 | −0.379411 | −0.189706 | − | 0.981841i | \(-0.560753\pi\) | ||||
−0.189706 | + | 0.981841i | \(0.560753\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.43070 | − | 7.17687i | 0.603411 | − | 0.797430i | ||||
\(82\) | −15.1460 | −1.67260 | ||||||||
\(83\) | − | 5.48913i | − | 0.602510i | −0.953544 | − | 0.301255i | \(-0.902594\pi\) | ||
0.953544 | − | 0.301255i | \(-0.0974055\pi\) | |||||||
\(84\) | 17.7446 | + | 9.30506i | 1.93609 | + | 1.01527i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 17.0256i | 1.83591i | ||||||||
\(87\) | 7.17687 | − | 1.68614i | 0.769441 | − | 0.180773i | ||||
\(88\) | 4.74456i | 0.505772i | ||||||||
\(89\) | 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 | ||||
\(92\) | 8.21782 | 0.856767 | ||||||||
\(93\) | −5.84096 | + | 1.37228i | −0.605680 | + | 0.142299i | ||||
\(94\) | 18.6101i | 1.91949i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.62772 | + | 6.92820i | 0.166128 | + | 0.707107i | ||||
\(97\) | 1.08724 | 0.110393 | 0.0551963 | − | 0.998476i | \(-0.482422\pi\) | ||||
0.0551963 | + | 0.998476i | \(0.482422\pi\) | |||||||
\(98\) | 2.52434 | + | 17.4891i | 0.254997 | + | 1.76667i | ||||
\(99\) | 1.05842 | + | 2.12819i | 0.106375 | + | 0.213892i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 5.84096 | − | 1.37228i | 0.578341 | − | 0.135876i | ||||
\(103\) | −16.2333 | −1.59951 | −0.799756 | − | 0.600326i | \(-0.795038\pi\) | ||||
−0.799756 | + | 0.600326i | \(0.795038\pi\) | |||||||
\(104\) | −34.9783 | −3.42990 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.4891 | 2.08721 | ||||||||
\(107\) | −6.63325 | −0.641260 | −0.320630 | − | 0.947204i | \(-0.603895\pi\) | ||||
−0.320630 | + | 0.947204i | \(0.603895\pi\) | |||||||
\(108\) | 14.5012 | + | 17.4891i | 1.39538 | + | 1.68289i | ||||
\(109\) | −0.116844 | −0.0111916 | −0.00559581 | − | 0.999984i | \(-0.501781\pi\) | ||||
−0.00559581 | + | 0.999984i | \(0.501781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | + | 1.87953i | −0.759326 | + | 0.178397i | ||||
\(112\) | −11.0371 | + | 12.7446i | −1.04291 | + | 1.20425i | ||||
\(113\) | 10.0974 | 0.949879 | 0.474939 | − | 0.880018i | \(-0.342470\pi\) | ||||
0.474939 | + | 0.880018i | \(0.342470\pi\) | |||||||
\(114\) | 14.7446 | − | 3.46410i | 1.38095 | − | 0.324443i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 18.6101i | 1.72791i | ||||||||
\(117\) | −15.6896 | + | 7.80298i | −1.45051 | + | 0.721386i | ||||
\(118\) | −6.92820 | −0.637793 | ||||||||
\(119\) | 2.74456 | + | 2.37686i | 0.251594 | + | 0.217886i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3723 | 0.942935 | ||||||||
\(122\) | 17.4891i | 1.58339i | ||||||||
\(123\) | −2.37686 | − | 10.1168i | −0.214314 | − | 0.912205i | ||||
\(124\) | − | 15.1460i | − | 1.36015i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.00000 | + | 19.4024i | −0.445435 | + | 1.72850i | ||||
\(127\) | − | 10.7446i | − | 0.953426i | −0.879059 | − | 0.476713i | \(-0.841828\pi\) | ||
0.879059 | − | 0.476713i | \(-0.158172\pi\) | |||||||
\(128\) | 14.2063 | 1.25567 | ||||||||
\(129\) | −11.3723 | + | 2.67181i | −1.00127 | + | 0.235240i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4891 | 1.52803 | 0.764016 | − | 0.645197i | \(-0.223225\pi\) | ||||
0.764016 | + | 0.645197i | \(0.223225\pi\) | |||||||
\(132\) | −5.84096 | + | 1.37228i | −0.508391 | + | 0.119442i | ||||
\(133\) | 6.92820 | + | 6.00000i | 0.600751 | + | 0.520266i | ||||
\(134\) | − | 17.0256i | − | 1.47078i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.21782i | 0.704673i | ||||||||
\(137\) | 13.2665 | 1.13343 | 0.566717 | − | 0.823913i | \(-0.308213\pi\) | ||||
0.566717 | + | 0.823913i | \(0.308213\pi\) | |||||||
\(138\) | 1.87953 | + | 8.00000i | 0.159996 | + | 0.681005i | ||||
\(139\) | − | 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 | ||||
\(142\) | 34.2337i | 2.87283i | ||||||||
\(143\) | − | 4.62772i | − | 0.386989i | ||||||
\(144\) | −17.1168 | + | 8.51278i | −1.42640 | + | 0.709398i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.4891 | −1.44741 | ||||||||
\(147\) | −11.2858 | + | 4.43070i | −0.930836 | + | 0.365438i | ||||
\(148\) | − | 20.7446i | − | 1.70519i | ||||||
\(149\) | 10.0974i | 0.827207i | 0.910457 | + | 0.413604i | \(0.135730\pi\) | ||||
−0.910457 | + | 0.413604i | \(0.864270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.37228 | 0.274432 | 0.137216 | − | 0.990541i | \(-0.456184\pi\) | ||||
0.137216 | + | 0.990541i | \(0.456184\pi\) | |||||||
\(152\) | 20.7446i | 1.68261i | ||||||||
\(153\) | 1.83324 | + | 3.68614i | 0.148209 | + | 0.298007i | ||||
\(154\) | −4.00000 | − | 3.46410i | −0.322329 | − | 0.279145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10.1168 | − | 43.0612i | −0.809996 | − | 3.44766i | ||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | 8.51278 | 0.677240 | ||||||||
\(159\) | 3.37228 | + | 14.3537i | 0.267439 | + | 1.13833i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.25544 | + | 3.75906i | −0.256564 | + | 0.296255i | ||||
\(162\) | −13.7089 | + | 18.1168i | −1.07708 | + | 1.42339i | ||||
\(163\) | 8.00000i | 0.626608i | 0.949653 | + | 0.313304i | \(0.101436\pi\) | ||||
−0.949653 | + | 0.313304i | \(0.898564\pi\) | |||||||
\(164\) | 26.2337 | 2.04851 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.8564i | 1.07547i | ||||||||
\(167\) | − | 22.1168i | − | 1.71145i | −0.517429 | − | 0.855726i | \(-0.673111\pi\) | ||
0.517429 | − | 0.855726i | \(-0.326889\pi\) | |||||||
\(168\) | −24.3036 | − | 12.7446i | −1.87506 | − | 0.983264i | ||||
\(169\) | 21.1168 | 1.62437 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.62772 | + | 9.30506i | 0.353890 | + | 0.711576i | ||||
\(172\) | − | 29.4891i | − | 2.24852i | ||||||
\(173\) | − | 16.1168i | − | 1.22534i | −0.790338 | − | 0.612670i | \(-0.790095\pi\) | ||
0.790338 | − | 0.612670i | \(-0.209905\pi\) | |||||||
\(174\) | −18.1168 | + | 4.25639i | −1.37343 | + | 0.322676i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.04868i | − | 0.380558i | ||||||
\(177\) | −1.08724 | − | 4.62772i | −0.0817220 | − | 0.347841i | ||||
\(178\) | −8.21782 | −0.615952 | ||||||||
\(179\) | 6.63325i | 0.495792i | 0.968787 | + | 0.247896i | \(0.0797392\pi\) | ||||
−0.968787 | + | 0.247896i | \(0.920261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6101i | 1.38328i | 0.722242 | + | 0.691640i | \(0.243111\pi\) | ||||
−0.722242 | + | 0.691640i | \(0.756889\pi\) | |||||||
\(182\) | 25.5383 | − | 29.4891i | 1.89303 | − | 2.18588i | ||||
\(183\) | −11.6819 | + | 2.74456i | −0.863553 | + | 0.202884i | ||||
\(184\) | −11.2554 | −0.829762 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.7446 | − | 3.46410i | 1.08112 | − | 0.254000i | ||||
\(187\) | −1.08724 | −0.0795069 | ||||||||
\(188\) | − | 32.2337i | − | 2.35088i | ||||||
\(189\) | −13.7446 | − | 0.294954i | −0.999770 | − | 0.0214547i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.6434i | 1.13191i | 0.824435 | + | 0.565957i | \(0.191493\pi\) | ||||
−0.824435 | + | 0.565957i | \(0.808507\pi\) | |||||||
\(192\) | 0.939764 | + | 4.00000i | 0.0678216 | + | 0.288675i | ||||
\(193\) | 22.2337i | 1.60042i | 0.599723 | + | 0.800208i | \(0.295278\pi\) | ||||
−0.599723 | + | 0.800208i | \(0.704722\pi\) | |||||||
\(194\) | −2.74456 | −0.197048 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.37228 | − | 30.2921i | −0.312306 | − | 2.16372i | ||||
\(197\) | 22.3692 | 1.59374 | 0.796869 | − | 0.604152i | \(-0.206488\pi\) | ||||
0.796869 | + | 0.604152i | \(0.206488\pi\) | |||||||
\(198\) | −2.67181 | − | 5.37228i | −0.189878 | − | 0.381791i | ||||
\(199\) | 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 | ||||
\(202\) | 15.1460 | 1.06567 | ||||||||
\(203\) | −8.51278 | − | 7.37228i | −0.597480 | − | 0.517433i | ||||
\(204\) | −10.1168 | + | 2.37686i | −0.708321 | + | 0.166414i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 40.9783 | 2.85509 | ||||||||
\(207\) | −5.04868 | + | 2.51087i | −0.350907 | + | 0.174518i | ||||
\(208\) | 37.2203 | 2.58076 | ||||||||
\(209\) | −2.74456 | −0.189845 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.11684 | 0.421101 | 0.210550 | − | 0.977583i | \(-0.432474\pi\) | ||||
0.210550 | + | 0.977583i | \(0.432474\pi\) | |||||||
\(212\) | −37.2203 | −2.55630 | ||||||||
\(213\) | −22.8665 | + | 5.37228i | −1.56679 | + | 0.368103i | ||||
\(214\) | 16.7446 | 1.14463 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −19.8614 | − | 23.9538i | −1.35140 | − | 1.62985i | ||||
\(217\) | 6.92820 | + | 6.00000i | 0.470317 | + | 0.407307i | ||||
\(218\) | 0.294954 | 0.0199768 | ||||||||
\(219\) | −2.74456 | − | 11.6819i | −0.185460 | − | 0.789391i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.01544i | − | 0.539177i | ||||||
\(222\) | 20.1947 | − | 4.74456i | 1.35538 | − | 0.318434i | ||||
\(223\) | 20.9870 | 1.40539 | 0.702696 | − | 0.711490i | \(-0.251979\pi\) | ||||
0.702696 | + | 0.711490i | \(0.251979\pi\) | |||||||
\(224\) | 7.11684 | − | 8.21782i | 0.475514 | − | 0.549076i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.4891 | −1.69551 | ||||||||
\(227\) | − | 15.6060i | − | 1.03580i | −0.855440 | − | 0.517902i | \(-0.826713\pi\) | ||
0.855440 | − | 0.517902i | \(-0.173287\pi\) | |||||||
\(228\) | −25.5383 | + | 6.00000i | −1.69132 | + | 0.397360i | ||||
\(229\) | − | 4.75372i | − | 0.314135i | −0.987588 | − | 0.157067i | \(-0.949796\pi\) | ||
0.987588 | − | 0.157067i | \(-0.0502040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.68614 | − | 3.21543i | 0.110940 | − | 0.211560i | ||||
\(232\) | − | 25.4891i | − | 1.67344i | ||||||
\(233\) | −3.75906 | −0.246264 | −0.123132 | − | 0.992390i | \(-0.539294\pi\) | ||||
−0.123132 | + | 0.992390i | \(0.539294\pi\) | |||||||
\(234\) | 39.6060 | − | 19.6974i | 2.58912 | − | 1.28766i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 1.33591 | + | 5.68614i | 0.0867765 | + | 0.369355i | ||||
\(238\) | −6.92820 | − | 6.00000i | −0.449089 | − | 0.388922i | ||||
\(239\) | − | 15.6434i | − | 1.01188i | −0.862567 | − | 0.505942i | \(-0.831145\pi\) | ||
0.862567 | − | 0.505942i | \(-0.168855\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.3639i | − | 1.50500i | −0.658593 | − | 0.752499i | \(-0.728848\pi\) | ||
0.658593 | − | 0.752499i | \(-0.271152\pi\) | |||||||
\(242\) | −26.1831 | −1.68312 | ||||||||
\(243\) | −14.2525 | − | 6.31386i | −0.914302 | − | 0.405034i | ||||
\(244\) | − | 30.2921i | − | 1.93925i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.00000 | + | 25.5383i | 0.382546 | + | 1.62826i | ||||
\(247\) | − | 20.2337i | − | 1.28744i | ||||||
\(248\) | 20.7446i | 1.31728i | ||||||||
\(249\) | −9.25544 | + | 2.17448i | −0.586540 | + | 0.137802i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.4891 | −1.10390 | −0.551952 | − | 0.833876i | \(-0.686117\pi\) | ||||
−0.551952 | + | 0.833876i | \(0.686117\pi\) | |||||||
\(252\) | 8.66025 | − | 33.6060i | 0.545545 | − | 2.11698i | ||||
\(253\) | − | 1.48913i | − | 0.0936205i | ||||||
\(254\) | 27.1229i | 1.70184i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.1168 | −1.94480 | ||||||||
\(257\) | 23.4891i | 1.46521i | 0.680653 | + | 0.732606i | \(0.261696\pi\) | ||||
−0.680653 | + | 0.732606i | \(0.738304\pi\) | |||||||
\(258\) | 28.7075 | − | 6.74456i | 1.78725 | − | 0.419898i | ||||
\(259\) | 9.48913 | + | 8.21782i | 0.589626 | + | 0.510631i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.68614 | − | 11.4333i | −0.351963 | − | 0.707701i | ||||
\(262\) | −44.1485 | −2.72750 | ||||||||
\(263\) | 13.5615 | 0.836235 | 0.418118 | − | 0.908393i | \(-0.362690\pi\) | ||||
0.418118 | + | 0.908393i | \(0.362690\pi\) | |||||||
\(264\) | 8.00000 | − | 1.87953i | 0.492366 | − | 0.115677i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −17.4891 | − | 15.1460i | −1.07233 | − | 0.928662i | ||||
\(267\) | −1.28962 | − | 5.48913i | −0.0789235 | − | 0.335929i | ||||
\(268\) | 29.4891i | 1.80134i | ||||||||
\(269\) | −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 | \(-0.847839\pi\) | ||
0.887905 | − | 0.460028i | \(-0.152161\pi\) | |||||||
\(272\) | − | 8.74456i | − | 0.530217i | ||||||
\(273\) | 23.7051 | + | 12.4307i | 1.43470 | + | 0.752340i | ||||
\(274\) | −33.4891 | −2.02315 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.25544 | − | 13.8564i | −0.195954 | − | 0.834058i | ||||
\(277\) | 6.23369i | 0.374546i | 0.982308 | + | 0.187273i | \(0.0599649\pi\) | ||||
−0.982308 | + | 0.187273i | \(0.940035\pi\) | |||||||
\(278\) | 3.25544i | 0.195248i | ||||||||
\(279\) | 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 | \(0.953826\pi\) | |||||||
\(282\) | 31.3793 | − | 7.37228i | 1.86861 | − | 0.439013i | ||||
\(283\) | −9.30506 | −0.553129 | −0.276564 | − | 0.960995i | \(-0.589196\pi\) | ||||
−0.276564 | + | 0.960995i | \(0.589196\pi\) | |||||||
\(284\) | − | 59.2945i | − | 3.51848i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.6819i | 0.690767i | ||||||||
\(287\) | −10.3923 | + | 12.0000i | −0.613438 | + | 0.708338i | ||||
\(288\) | 11.0371 | − | 5.48913i | 0.650368 | − | 0.323450i | ||||
\(289\) | 15.1168 | 0.889226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.430703 | − | 1.83324i | −0.0252483 | − | 0.107466i | ||||
\(292\) | 30.2921 | 1.77271 | ||||||||
\(293\) | 28.1168i | 1.64260i | 0.570494 | + | 0.821302i | \(0.306752\pi\) | ||||
−0.570494 | + | 0.821302i | \(0.693248\pi\) | |||||||
\(294\) | 28.4891 | − | 11.1846i | 1.66152 | − | 0.652299i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 28.4125i | 1.65144i | ||||||||
\(297\) | 3.16915 | − | 2.62772i | 0.183893 | − | 0.152476i | ||||
\(298\) | − | 25.4891i | − | 1.47655i | ||||||
\(299\) | 10.9783 | 0.634889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.4891 | + | 11.6819i | 0.777500 | + | 0.673335i | ||||
\(302\) | −8.51278 | −0.489855 | ||||||||
\(303\) | 2.37686 | + | 10.1168i | 0.136547 | + | 0.581198i | ||||
\(304\) | − | 22.0742i | − | 1.26604i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.62772 | − | 9.30506i | −0.264549 | − | 0.531935i | ||||
\(307\) | 7.13058 | 0.406964 | 0.203482 | − | 0.979079i | \(-0.434774\pi\) | ||||
0.203482 | + | 0.979079i | \(0.434774\pi\) | |||||||
\(308\) | 6.92820 | + | 6.00000i | 0.394771 | + | 0.341882i | ||||
\(309\) | 6.43070 | + | 27.3716i | 0.365830 | + | 1.55711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.2337 | −1.14735 | −0.573674 | − | 0.819084i | \(-0.694482\pi\) | ||||
−0.573674 | + | 0.819084i | \(0.694482\pi\) | |||||||
\(312\) | 13.8564 | + | 58.9783i | 0.784465 | + | 3.33899i | ||||
\(313\) | −24.4511 | −1.38206 | −0.691029 | − | 0.722827i | \(-0.742842\pi\) | ||||
−0.691029 | + | 0.722827i | \(0.742842\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.7446 | −0.829446 | ||||||||
\(317\) | 8.51278 | 0.478125 | 0.239063 | − | 0.971004i | \(-0.423160\pi\) | ||||
0.239063 | + | 0.971004i | \(0.423160\pi\) | |||||||
\(318\) | −8.51278 | − | 36.2337i | −0.477373 | − | 2.03188i | ||||
\(319\) | 3.37228 | 0.188812 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.62772 | + | 11.1846i | 0.146665 | + | 0.624263i | ||||
\(322\) | 8.21782 | − | 9.48913i | 0.457961 | − | 0.528808i | ||||
\(323\) | −4.75372 | −0.264504 | ||||||||
\(324\) | 23.7446 | − | 31.3793i | 1.31914 | − | 1.74329i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 20.1947i | − | 1.11848i | ||||||
\(327\) | 0.0462870 | + | 0.197015i | 0.00255968 | + | 0.0108950i | ||||
\(328\) | −35.9306 | −1.98394 | ||||||||
\(329\) | 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 | \(0.535063\pi\) | |||||||
\(332\) | − | 24.0000i | − | 1.31717i | ||||||
\(333\) | 6.33830 | + | 12.7446i | 0.347336 | + | 0.698398i | ||||
\(334\) | 55.8304i | 3.05490i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 25.8614 | + | 13.5615i | 1.41086 | + | 0.739838i | ||||
\(337\) | 18.2337i | 0.993252i | 0.867965 | + | 0.496626i | \(0.165428\pi\) | ||||
−0.867965 | + | 0.496626i | \(0.834572\pi\) | |||||||
\(338\) | −53.3060 | −2.89947 | ||||||||
\(339\) | −4.00000 | − | 17.0256i | −0.217250 | − | 0.924701i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.74456 | −0.148626 | ||||||||
\(342\) | −11.6819 | − | 23.4891i | −0.631686 | − | 1.27015i | ||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 40.3894i | 2.17765i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 40.6844i | 2.18720i | ||||||||
\(347\) | −18.3152 | −0.983210 | −0.491605 | − | 0.870818i | \(-0.663590\pi\) | ||||
−0.491605 | + | 0.870818i | \(0.663590\pi\) | |||||||
\(348\) | 31.3793 | − | 7.37228i | 1.68211 | − | 0.395196i | ||||
\(349\) | 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 | ||||
\(352\) | 3.25544i | 0.173515i | ||||||||
\(353\) | − | 7.88316i | − | 0.419578i | −0.977747 | − | 0.209789i | \(-0.932722\pi\) | ||
0.977747 | − | 0.209789i | \(-0.0672777\pi\) | |||||||
\(354\) | 2.74456 | + | 11.6819i | 0.145872 | + | 0.620887i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.2337 | 0.754384 | ||||||||
\(357\) | 2.92048 | − | 5.56930i | 0.154568 | − | 0.294758i | ||||
\(358\) | − | 16.7446i | − | 0.884978i | ||||||
\(359\) | − | 9.80240i | − | 0.517351i | −0.965964 | − | 0.258675i | \(-0.916714\pi\) | ||
0.965964 | − | 0.258675i | \(-0.0832860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | − | 46.9783i | − | 2.46912i | ||||||
\(363\) | −4.10891 | − | 17.4891i | −0.215662 | − | 0.917941i | ||||
\(364\) | −44.2337 | + | 51.0767i | −2.31848 | + | 2.67714i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 29.4891 | − | 6.92820i | 1.54142 | − | 0.362143i | ||||
\(367\) | −25.3360 | −1.32253 | −0.661263 | − | 0.750154i | \(-0.729979\pi\) | ||||
−0.661263 | + | 0.750154i | \(0.729979\pi\) | |||||||
\(368\) | 11.9769 | 0.624338 | ||||||||
\(369\) | −16.1168 | + | 8.01544i | −0.839009 | + | 0.417267i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.7446 | − | 17.0256i | 0.765500 | − | 0.883923i | ||||
\(372\) | −25.5383 | + | 6.00000i | −1.32410 | + | 0.311086i | ||||
\(373\) | − | 24.7446i | − | 1.28122i | −0.767864 | − | 0.640612i | \(-0.778681\pi\) | ||
0.767864 | − | 0.640612i | \(-0.221319\pi\) | |||||||
\(374\) | 2.74456 | 0.141918 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 44.1485i | 2.27678i | ||||||||
\(377\) | 24.8614i | 1.28043i | ||||||||
\(378\) | 34.6959 | + | 0.744563i | 1.78457 | + | 0.0382962i | ||||
\(379\) | −1.48913 | −0.0764912 | −0.0382456 | − | 0.999268i | \(-0.512177\pi\) | ||||
−0.0382456 | + | 0.999268i | \(0.512177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.1168 | + | 4.25639i | −0.928154 | + | 0.218061i | ||||
\(382\) | − | 39.4891i | − | 2.02044i | ||||||
\(383\) | 17.4891i | 0.893653i | 0.894621 | + | 0.446826i | \(0.147446\pi\) | ||||
−0.894621 | + | 0.446826i | \(0.852554\pi\) | |||||||
\(384\) | −5.62772 | − | 23.9538i | −0.287188 | − | 1.22239i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 56.1253i | − | 2.85670i | ||||||
\(387\) | 9.01011 | + | 18.1168i | 0.458010 | + | 0.920931i | ||||
\(388\) | 4.75372 | 0.241334 | ||||||||
\(389\) | 13.7638i | 0.697854i | 0.937150 | + | 0.348927i | \(0.113454\pi\) | ||||
−0.937150 | + | 0.348927i | \(0.886546\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.57924i | − | 0.130438i | ||||||
\(392\) | 5.98844 | + | 41.4891i | 0.302462 | + | 2.09552i | ||||
\(393\) | −6.92820 | − | 29.4891i | −0.349482 | − | 1.48753i | ||||
\(394\) | −56.4674 | −2.84479 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.62772 | + | 9.30506i | 0.232552 | + | 0.467597i | ||||
\(397\) | −3.66648 | −0.184015 | −0.0920077 | − | 0.995758i | \(-0.529328\pi\) | ||||
−0.0920077 | + | 0.995758i | \(0.529328\pi\) | |||||||
\(398\) | − | 32.7446i | − | 1.64134i | ||||||
\(399\) | 7.37228 | − | 14.0588i | 0.369076 | − | 0.703820i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.67181i | 0.133424i | 0.997772 | + | 0.0667120i | \(0.0212509\pi\) | ||||
−0.997772 | + | 0.0667120i | \(0.978749\pi\) | |||||||
\(402\) | −28.7075 | + | 6.74456i | −1.43180 | + | 0.336388i | ||||
\(403\) | − | 20.2337i | − | 1.00791i | ||||||
\(404\) | −26.2337 | −1.30517 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.4891 | + | 18.6101i | 1.06649 | + | 0.923605i | ||||
\(407\) | −3.75906 | −0.186329 | ||||||||
\(408\) | 13.8564 | − | 3.25544i | 0.685994 | − | 0.161168i | ||||
\(409\) | − | 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 | ||||
\(412\) | −70.9764 | −3.49676 | ||||||||
\(413\) | −4.75372 | + | 5.48913i | −0.233915 | + | 0.270102i | ||||
\(414\) | 12.7446 | − | 6.33830i | 0.626361 | − | 0.311510i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −24.0000 | −1.17670 | ||||||||
\(417\) | −2.17448 | + | 0.510875i | −0.106485 | + | 0.0250176i | ||||
\(418\) | 6.92820 | 0.338869 | ||||||||
\(419\) | −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 | \(0.714485\pi\) | |||||||
\(422\) | −15.4410 | −0.751655 | ||||||||
\(423\) | 9.84868 | + | 19.8030i | 0.478859 | + | 0.962854i | ||||
\(424\) | 50.9783 | 2.47572 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 57.7228 | − | 13.5615i | 2.79668 | − | 0.657055i | ||||
\(427\) | 13.8564 | + | 12.0000i | 0.670559 | + | 0.580721i | ||||
\(428\) | −29.0024 | −1.40189 | ||||||||
\(429\) | −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 | \(0.723801\pi\) | |||||||
\(432\) | 21.1345 | + | 25.4891i | 1.01683 | + | 1.22635i | ||||
\(433\) | −2.57924 | −0.123950 | −0.0619752 | − | 0.998078i | \(-0.519740\pi\) | ||||
−0.0619752 | + | 0.998078i | \(0.519740\pi\) | |||||||
\(434\) | −17.4891 | − | 15.1460i | −0.839505 | − | 0.727033i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.510875 | −0.0244665 | ||||||||
\(437\) | − | 6.51087i | − | 0.311457i | ||||||
\(438\) | 6.92820 | + | 29.4891i | 0.331042 | + | 1.40904i | ||||
\(439\) | 1.28962i | 0.0615502i | 0.999526 | + | 0.0307751i | \(0.00979757\pi\) | ||||
−0.999526 | + | 0.0307751i | \(0.990202\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.9416 | + | 17.2742i | 0.568647 | + | 0.822582i | ||||
\(442\) | 20.2337i | 0.962418i | ||||||||
\(443\) | 6.63325 | 0.315155 | 0.157578 | − | 0.987507i | \(-0.449632\pi\) | ||||
0.157578 | + | 0.987507i | \(0.449632\pi\) | |||||||
\(444\) | −34.9783 | + | 8.21782i | −1.65999 | + | 0.390001i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −52.9783 | −2.50859 | ||||||||
\(447\) | 17.0256 | − | 4.00000i | 0.805281 | − | 0.189194i | ||||
\(448\) | 4.10891 | − | 4.74456i | 0.194128 | − | 0.224160i | ||||
\(449\) | − | 28.2101i | − | 1.33132i | −0.746256 | − | 0.665660i | \(-0.768150\pi\) | ||
0.746256 | − | 0.665660i | \(-0.231850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.75372i | − | 0.223844i | ||||||
\(452\) | 44.1485 | 2.07657 | ||||||||
\(453\) | −1.33591 | − | 5.68614i | −0.0627664 | − | 0.267158i | ||||
\(454\) | 39.3947i | 1.84889i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 34.9783 | − | 8.21782i | 1.63801 | − | 0.384835i | ||||
\(457\) | 32.9783i | 1.54266i | 0.636437 | + | 0.771329i | \(0.280408\pi\) | ||||
−0.636437 | + | 0.771329i | \(0.719592\pi\) | |||||||
\(458\) | 12.0000i | 0.560723i | ||||||||
\(459\) | 5.48913 | − | 4.55134i | 0.256210 | − | 0.212438i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.74456 | 0.407275 | 0.203637 | − | 0.979046i | \(-0.434724\pi\) | ||||
0.203637 | + | 0.979046i | \(0.434724\pi\) | |||||||
\(462\) | −4.25639 | + | 8.11684i | −0.198025 | + | 0.377630i | ||||
\(463\) | 36.4674i | 1.69478i | 0.530969 | + | 0.847391i | \(0.321828\pi\) | ||||
−0.530969 | + | 0.847391i | \(0.678172\pi\) | |||||||
\(464\) | 27.1229i | 1.25915i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.48913 | 0.439575 | ||||||||
\(467\) | − | 13.8832i | − | 0.642436i | −0.947005 | − | 0.321218i | \(-0.895908\pi\) | ||
0.947005 | − | 0.321218i | \(-0.104092\pi\) | |||||||
\(468\) | −68.5996 | + | 34.1168i | −3.17102 | + | 1.57705i | ||||
\(469\) | −13.4891 | − | 11.6819i | −0.622870 | − | 0.539421i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.4356 | −0.756512 | ||||||||
\(473\) | −5.34363 | −0.245700 | ||||||||
\(474\) | −3.37228 | − | 14.3537i | −0.154894 | − | 0.659289i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | + | 10.3923i | 0.550019 | + | 0.476331i | ||||
\(477\) | 22.8665 | − | 11.3723i | 1.04699 | − | 0.520701i | ||||
\(478\) | 39.4891i | 1.80619i | ||||||||
\(479\) | 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 | ||||||
\(482\) | 58.9783i | 2.68639i | ||||||||
\(483\) | 7.62792 | + | 4.00000i | 0.347082 | + | 0.182006i | ||||
\(484\) | 45.3505 | 2.06139 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 35.9783 | + | 15.9383i | 1.63201 | + | 0.722977i | ||||
\(487\) | − | 14.5109i | − | 0.657550i | −0.944408 | − | 0.328775i | \(-0.893364\pi\) | ||
0.944408 | − | 0.328775i | \(-0.106636\pi\) | |||||||
\(488\) | 41.4891i | 1.87812i | ||||||||
\(489\) | 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 | \(0.920975\pi\) | |||||||
\(492\) | −10.3923 | − | 44.2337i | −0.468521 | − | 1.99421i | ||||
\(493\) | 5.84096 | 0.263064 | ||||||||
\(494\) | 51.0767i | 2.29805i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 22.0742i | − | 0.991162i | ||||||
\(497\) | 27.1229 | + | 23.4891i | 1.21663 | + | 1.05363i | ||||
\(498\) | 23.3639 | − | 5.48913i | 1.04696 | − | 0.245974i | ||||
\(499\) | 10.3505 | 0.463353 | 0.231677 | − | 0.972793i | \(-0.425579\pi\) | ||||
0.231677 | + | 0.972793i | \(0.425579\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −37.2921 | + | 8.76144i | −1.66609 | + | 0.391432i | ||||
\(502\) | 44.1485 | 1.97044 | ||||||||
\(503\) | 27.6060i | 1.23089i | 0.788180 | + | 0.615445i | \(0.211024\pi\) | ||||
−0.788180 | + | 0.615445i | \(0.788976\pi\) | |||||||
\(504\) | −11.8614 | + | 46.0280i | −0.528349 | + | 2.05025i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.75906i | 0.167110i | ||||||||
\(507\) | −8.36530 | − | 35.6060i | −0.371516 | − | 1.58132i | ||||
\(508\) | − | 46.9783i | − | 2.08432i | ||||||
\(509\) | −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 | ||||
\(512\) | 50.1369 | 2.21576 | ||||||||
\(513\) | 13.8564 | − | 11.4891i | 0.611775 | − | 0.507257i | ||||
\(514\) | − | 59.2945i | − | 2.61537i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −49.7228 | + | 11.6819i | −2.18892 | + | 0.514268i | ||||
\(517\) | −5.84096 | −0.256885 | ||||||||
\(518\) | −23.9538 | − | 20.7446i | −1.05247 | − | 0.911464i | ||||
\(519\) | −27.1753 | + | 6.38458i | −1.19286 | + | 0.280252i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.4674 | −1.51004 | −0.755022 | − | 0.655700i | \(-0.772374\pi\) | ||||
−0.755022 | + | 0.655700i | \(0.772374\pi\) | |||||||
\(522\) | 14.3537 | + | 28.8614i | 0.628246 | + | 1.26323i | ||||
\(523\) | 10.3923 | 0.454424 | 0.227212 | − | 0.973845i | \(-0.427039\pi\) | ||||
0.227212 | + | 0.973845i | \(0.427039\pi\) | |||||||
\(524\) | 76.4674 | 3.34049 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.2337 | −1.49266 | ||||||||
\(527\) | −4.75372 | −0.207075 | ||||||||
\(528\) | −8.51278 | + | 2.00000i | −0.370471 | + | 0.0870388i | ||||
\(529\) | −19.4674 | −0.846408 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.37228 | + | 3.66648i | −0.319930 | + | 0.159112i | ||||
\(532\) | 30.2921 | + | 26.2337i | 1.31333 | + | 1.13737i | ||||
\(533\) | 35.0458 | 1.51800 | ||||||||
\(534\) | 3.25544 | + | 13.8564i | 0.140877 | + | 0.599625i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 40.3894i | − | 1.74456i | ||||||
\(537\) | 11.1846 | − | 2.62772i | 0.482651 | − | 0.113394i | ||||
\(538\) | 22.0742 | 0.951688 | ||||||||
\(539\) | −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 | \(0.368859\pi\) | |||||||
\(542\) | 38.2337i | 1.64228i | ||||||||
\(543\) | 31.3793 | − | 7.37228i | 1.34661 | − | 0.316375i | ||||
\(544\) | 5.63858i | 0.241752i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −59.8397 | − | 31.3793i | −2.56090 | − | 1.34291i | ||||
\(547\) | − | 42.9783i | − | 1.83762i | −0.394703 | − | 0.918809i | \(-0.629153\pi\) | ||
0.394703 | − | 0.918809i | \(-0.370847\pi\) | |||||||
\(548\) | 58.0049 | 2.47785 | ||||||||
\(549\) | 9.25544 | + | 18.6101i | 0.395012 | + | 0.794261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.7446 | 0.628139 | ||||||||
\(552\) | 4.45877 | + | 18.9783i | 0.189778 | + | 0.807768i | ||||
\(553\) | 5.84096 | − | 6.74456i | 0.248383 | − | 0.286808i | ||||
\(554\) | − | 15.7359i | − | 0.668556i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 5.63858i | − | 0.239129i | ||||||
\(557\) | −30.8820 | −1.30851 | −0.654255 | − | 0.756274i | \(-0.727018\pi\) | ||||
−0.654255 | + | 0.756274i | \(0.727018\pi\) | |||||||
\(558\) | −11.6819 | − | 23.4891i | −0.494535 | − | 0.994374i | ||||
\(559\) | − | 39.3947i | − | 1.66622i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.430703 | + | 1.83324i | 0.0181843 | + | 0.0773995i | ||||
\(562\) | − | 12.2337i | − | 0.516047i | ||||||
\(563\) | − | 5.48913i | − | 0.231339i | −0.993288 | − | 0.115670i | \(-0.963099\pi\) | ||
0.993288 | − | 0.115670i | \(-0.0369014\pi\) | |||||||
\(564\) | −54.3505 | + | 12.7692i | −2.28857 | + | 0.537679i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 23.4891 | 0.987322 | ||||||||
\(567\) | 4.94749 | + | 23.2921i | 0.207775 | + | 0.978177i | ||||
\(568\) | 81.2119i | 3.40758i | ||||||||
\(569\) | − | 10.6873i | − | 0.448033i | −0.974585 | − | 0.224017i | \(-0.928083\pi\) | ||
0.974585 | − | 0.224017i | \(-0.0719170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | − | 20.2337i | − | 0.846013i | ||||||
\(573\) | 26.3769 | − | 6.19702i | 1.10191 | − | 0.258884i | ||||
\(574\) | 26.2337 | − | 30.2921i | 1.09497 | − | 1.26437i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.37228 | − | 3.16915i | 0.265512 | − | 0.132048i | ||||
\(577\) | 12.7692 | 0.531587 | 0.265794 | − | 0.964030i | \(-0.414366\pi\) | ||||
0.265794 | + | 0.964030i | \(0.414366\pi\) | |||||||
\(578\) | −38.1600 | −1.58725 | ||||||||
\(579\) | 37.4891 | − | 8.80773i | 1.55799 | − | 0.366037i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.9783 | + | 9.50744i | 0.455455 | + | 0.394435i | ||||
\(582\) | 1.08724 | + | 4.62772i | 0.0450676 | + | 0.191825i | ||||
\(583\) | 6.74456i | 0.279331i | ||||||||
\(584\) | −41.4891 | −1.71683 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 70.9764i | − | 2.93201i | ||||||
\(587\) | − | 5.48913i | − | 0.226560i | −0.993563 | − | 0.113280i | \(-0.963864\pi\) | ||
0.993563 | − | 0.113280i | \(-0.0361358\pi\) | |||||||
\(588\) | −49.3446 | + | 19.3723i | −2.03494 | + | 0.798899i | ||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.86141 | − | 37.7176i | −0.364510 | − | 1.55149i | ||||
\(592\) | − | 30.2337i | − | 1.24260i | ||||||
\(593\) | 1.37228i | 0.0563528i | 0.999603 | + | 0.0281764i | \(0.00897002\pi\) | ||||
−0.999603 | + | 0.0281764i | \(0.991030\pi\) | |||||||
\(594\) | −8.00000 | + | 6.63325i | −0.328244 | + | 0.272166i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 44.1485i | 1.80839i | ||||||||
\(597\) | 21.8719 | − | 5.13859i | 0.895155 | − | 0.210309i | ||||
\(598\) | −27.7128 | −1.13326 | ||||||||
\(599\) | − | 1.78695i | − | 0.0730129i | −0.999333 | − | 0.0365065i | \(-0.988377\pi\) | ||
0.999333 | − | 0.0365065i | \(-0.0116230\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.17448i | − | 0.0886989i | −0.999016 | − | 0.0443495i | \(-0.985878\pi\) | ||
0.999016 | − | 0.0443495i | \(-0.0141215\pi\) | |||||||
\(602\) | −34.0511 | − | 29.4891i | −1.38782 | − | 1.20189i | ||||
\(603\) | −9.01011 | − | 18.1168i | −0.366920 | − | 0.737775i | ||||
\(604\) | 14.7446 | 0.599948 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.00000 | − | 25.5383i | −0.243733 | − | 1.03742i | ||||
\(607\) | −20.9870 | −0.851836 | −0.425918 | − | 0.904762i | \(-0.640049\pi\) | ||||
−0.425918 | + | 0.904762i | \(0.640049\pi\) | |||||||
\(608\) | 14.2337i | 0.577252i | ||||||||
\(609\) | −9.05842 | + | 17.2742i | −0.367066 | + | 0.699987i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 43.0612i | − | 1.74207i | ||||||
\(612\) | 8.01544 | + | 16.1168i | 0.324005 | + | 0.651485i | ||||
\(613\) | − | 4.51087i | − | 0.182193i | −0.995842 | − | 0.0910963i | \(-0.970963\pi\) | ||
0.995842 | − | 0.0910963i | \(-0.0290371\pi\) | |||||||
\(614\) | −18.0000 | −0.726421 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.48913 | − | 8.21782i | −0.382328 | − | 0.331106i | ||||
\(617\) | −37.8102 | −1.52218 | −0.761090 | − | 0.648646i | \(-0.775335\pi\) | ||||
−0.761090 | + | 0.648646i | \(0.775335\pi\) | |||||||
\(618\) | −16.2333 | − | 69.0951i | −0.652998 | − | 2.77941i | ||||
\(619\) | − | 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 | ||||
\(622\) | 51.0767 | 2.04799 | ||||||||
\(623\) | −5.63858 | + | 6.51087i | −0.225905 | + | 0.260853i | ||||
\(624\) | −14.7446 | − | 62.7586i | −0.590255 | − | 2.51235i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 61.7228 | 2.46694 | ||||||||
\(627\) | 1.08724 | + | 4.62772i | 0.0434202 | + | 0.184813i | ||||
\(628\) | 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 | \(0.537361\pi\) | |||||||
\(632\) | 20.1947 | 0.803302 | ||||||||
\(633\) | −2.42315 | − | 10.3139i | −0.0963115 | − | 0.409939i | ||||
\(634\) | −21.4891 | −0.853442 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.7446 | + | 62.7586i | 0.584660 | + | 2.48854i | ||||
\(637\) | −5.84096 | − | 40.4674i | −0.231427 | − | 1.60338i | ||||
\(638\) | −8.51278 | −0.337024 | ||||||||
\(639\) | 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 | \(0.800473\pi\) | |||||||
\(642\) | −6.63325 | − | 28.2337i | −0.261793 | − | 1.11429i | ||||
\(643\) | 39.5971 | 1.56156 | 0.780779 | − | 0.624807i | \(-0.214822\pi\) | ||||
0.780779 | + | 0.624807i | \(0.214822\pi\) | |||||||
\(644\) | −14.2337 | + | 16.4356i | −0.560886 | + | 0.647655i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | 12.0000i | 0.471769i | 0.971781 | + | 0.235884i | \(0.0757987\pi\) | ||||
−0.971781 | + | 0.235884i | \(0.924201\pi\) | |||||||
\(648\) | −32.5214 | + | 42.9783i | −1.27756 | + | 1.68835i | ||||
\(649\) | − | 2.17448i | − | 0.0853559i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.37228 | − | 14.0588i | 0.288942 | − | 0.551007i | ||||
\(652\) | 34.9783i | 1.36985i | ||||||||
\(653\) | 33.0564 | 1.29360 | 0.646799 | − | 0.762660i | \(-0.276107\pi\) | ||||
0.646799 | + | 0.762660i | \(0.276107\pi\) | |||||||
\(654\) | −0.116844 | − | 0.497333i | −0.00456896 | − | 0.0194473i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 38.2337 | 1.49277 | ||||||||
\(657\) | −18.6101 | + | 9.25544i | −0.726050 | + | 0.361089i | ||||
\(658\) | −37.2203 | − | 32.2337i | −1.45100 | − | 1.25660i | ||||
\(659\) | − | 20.3971i | − | 0.794558i | −0.917698 | − | 0.397279i | \(-0.869955\pi\) | ||
0.917698 | − | 0.397279i | \(-0.130045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.92820i | 0.269476i | 0.990881 | + | 0.134738i | \(0.0430193\pi\) | ||||
−0.990881 | + | 0.134738i | \(0.956981\pi\) | |||||||
\(662\) | 10.0974 | 0.392445 | ||||||||
\(663\) | −13.5152 | + | 3.17527i | −0.524886 | + | 0.123317i | ||||
\(664\) | 32.8713i | 1.27565i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.0000 | − | 32.1716i | −0.619987 | − | 1.24662i | ||||
\(667\) | 8.00000i | 0.309761i | ||||||||
\(668\) | − | 96.7011i | − | 3.74148i | ||||||
\(669\) | −8.31386 | − | 35.3870i | −0.321432 | − | 1.36814i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.48913 | −0.211905 | ||||||||
\(672\) | −16.6757 | − | 8.74456i | −0.643279 | − | 0.337329i | ||||
\(673\) | 22.2337i | 0.857046i | 0.903531 | + | 0.428523i | \(0.140966\pi\) | ||||
−0.903531 | + | 0.428523i | \(0.859034\pi\) | |||||||
\(674\) | − | 46.0280i | − | 1.77293i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 92.3288 | 3.55111 | ||||||||
\(677\) | 21.6060i | 0.830385i | 0.909734 | + | 0.415192i | \(0.136286\pi\) | ||||
−0.909734 | + | 0.415192i | \(0.863714\pi\) | |||||||
\(678\) | 10.0974 | + | 42.9783i | 0.387786 | + | 1.65057i | ||||
\(679\) | −1.88316 | + | 2.17448i | −0.0722689 | + | 0.0834489i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.3139 | + | 6.18220i | −1.00835 | + | 0.236903i | ||||
\(682\) | 6.92820 | 0.265295 | ||||||||
\(683\) | −51.7764 | −1.98117 | −0.990584 | − | 0.136906i | \(-0.956284\pi\) | ||||
−0.990584 | + | 0.136906i | \(0.956284\pi\) | |||||||
\(684\) | 20.2337 | + | 40.6844i | 0.773654 | + | 1.55561i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −39.3505 | − | 25.2434i | −1.50241 | − | 0.963797i | ||||
\(687\) | −8.01544 | + | 1.88316i | −0.305808 | + | 0.0718469i | ||||
\(688\) | − | 42.9783i | − | 1.63853i | ||||||
\(689\) | −49.7228 | −1.89429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.5099i | 1.46498i | 0.680775 | + | 0.732492i | \(0.261643\pi\) | ||||
−0.680775 | + | 0.732492i | \(0.738357\pi\) | |||||||
\(692\) | − | 70.4674i | − | 2.67877i | ||||||
\(693\) | −6.08963 | − | 1.56930i | −0.231326 | − | 0.0596127i | ||||
\(694\) | 46.2337 | 1.75501 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −42.9783 | + | 10.0974i | −1.62909 | + | 0.382739i | ||||
\(697\) | − | 8.23369i | − | 0.311873i | ||||||
\(698\) | − | 12.0000i | − | 0.454207i | ||||||
\(699\) | 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 | \(-0.332939\pi\) | |||||||
\(702\) | −48.9022 | − | 58.9783i | −1.84569 | − | 2.22599i | ||||
\(703\) | −16.4356 | −0.619882 | ||||||||
\(704\) | 1.87953i | 0.0708374i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.8997i | 0.748937i | ||||||||
\(707\) | 10.3923 | − | 12.0000i | 0.390843 | − | 0.451306i | ||||
\(708\) | −4.75372 | − | 20.2337i | −0.178656 | − | 0.760429i | ||||
\(709\) | −24.1168 | −0.905727 | −0.452864 | − | 0.891580i | \(-0.649598\pi\) | ||||
−0.452864 | + | 0.891580i | \(0.649598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.05842 | − | 4.50506i | 0.339717 | − | 0.168953i | ||||
\(712\) | −19.4950 | −0.730606 | ||||||||
\(713\) | − | 6.51087i | − | 0.243834i | ||||||
\(714\) | −7.37228 | + | 14.0588i | −0.275901 | + | 0.526137i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.0024i | 1.08387i | ||||||||
\(717\) | −26.3769 | + | 6.19702i | −0.985064 | + | 0.231432i | ||||
\(718\) | 24.7446i | 0.923459i | ||||||||
\(719\) | 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 | ||||
\(722\) | −17.6704 | −0.657623 | ||||||||
\(723\) | −39.3947 | + | 9.25544i | −1.46511 | + | 0.344213i | ||||
\(724\) | 81.3687i | 3.02404i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.3723 | + | 44.1485i | 0.384951 | + | 1.63850i | ||||
\(727\) | −3.46410 | −0.128476 | −0.0642382 | − | 0.997935i | \(-0.520462\pi\) | ||||
−0.0642382 | + | 0.997935i | \(0.520462\pi\) | |||||||
\(728\) | 60.5841 | − | 69.9565i | 2.24540 | − | 2.59276i | ||||
\(729\) | −5.00000 | + | 26.5330i | −0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.25544 | −0.342325 | ||||||||
\(732\) | −51.0767 | + | 12.0000i | −1.88785 | + | 0.443533i | ||||
\(733\) | −10.1899 | −0.376373 | −0.188187 | − | 0.982133i | \(-0.560261\pi\) | ||||
−0.188187 | + | 0.982133i | \(0.560261\pi\) | |||||||
\(734\) | 63.9565 | 2.36068 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.72281 | −0.284667 | ||||||||
\(737\) | 5.34363 | 0.196835 | ||||||||
\(738\) | 40.6844 | − | 20.2337i | 1.49761 | − | 0.744812i | ||||
\(739\) | 8.62772 | 0.317376 | 0.158688 | − | 0.987329i | \(-0.449274\pi\) | ||||
0.158688 | + | 0.987329i | \(0.449274\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34.1168 | + | 8.01544i | −1.25331 | + | 0.294455i | ||||
\(742\) | −37.2203 | + | 42.9783i | −1.36640 | + | 1.57778i | ||||
\(743\) | 36.9253 | 1.35466 | 0.677329 | − | 0.735680i | \(-0.263137\pi\) | ||||
0.677329 | + | 0.735680i | \(0.263137\pi\) | |||||||
\(744\) | 34.9783 | − | 8.21782i | 1.28236 | − | 0.301280i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 62.4636i | 2.28696i | ||||||||
\(747\) | 7.33296 | + | 14.7446i | 0.268299 | + | 0.539475i | ||||
\(748\) | −4.75372 | −0.173813 | ||||||||
\(749\) | 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 | \(0.633701\pi\) | |||||||
\(752\) | − | 46.9783i | − | 1.71312i | ||||||
\(753\) | 6.92820 | + | 29.4891i | 0.252478 | + | 1.07464i | ||||
\(754\) | − | 62.7586i | − | 2.28553i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −60.0951 | − | 1.28962i | −2.18564 | − | 0.0469030i | ||||
\(757\) | 54.2337i | 1.97116i | 0.169219 | + | 0.985578i | \(0.445875\pi\) | ||||
−0.169219 | + | 0.985578i | \(0.554125\pi\) | |||||||
\(758\) | 3.75906 | 0.136535 | ||||||||
\(759\) | −2.51087 | + | 0.589907i | −0.0911390 | + | 0.0214123i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.2337 | 0.950970 | 0.475485 | − | 0.879724i | \(-0.342273\pi\) | ||||
0.475485 | + | 0.879724i | \(0.342273\pi\) | |||||||
\(762\) | 45.7330 | − | 10.7446i | 1.65673 | − | 0.389234i | ||||
\(763\) | 0.202380 | − | 0.233688i | 0.00732664 | − | 0.00846007i | ||||
\(764\) | 68.3972i | 2.47452i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 44.1485i | − | 1.59515i | ||||||
\(767\) | 16.0309 | 0.578842 | ||||||||
\(768\) | 12.3267 | + | 52.4674i | 0.444803 | + | 1.89325i | ||||
\(769\) | 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 | ||||
\(772\) | 97.2119i | 3.49873i | ||||||||
\(773\) | 46.6277i | 1.67708i | 0.544838 | + | 0.838541i | \(0.316591\pi\) | ||||
−0.544838 | + | 0.838541i | \(0.683409\pi\) | |||||||
\(774\) | −22.7446 | − | 45.7330i | −0.817536 | − | 1.64384i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.51087 | −0.233727 | ||||||||
\(777\) | 10.0974 | − | 19.2554i | 0.362240 | − | 0.690785i | ||||
\(778\) | − | 34.7446i | − | 1.24565i | ||||||
\(779\) | − | 20.7846i | − | 0.744686i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7446 | −0.384471 | ||||||||
\(782\) | 6.51087i | 0.232828i | ||||||||
\(783\) | −17.0256 | + | 14.1168i | −0.608444 | + | 0.504495i | ||||
\(784\) | −6.37228 | − | 44.1485i | −0.227581 | − | 1.57673i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.4891 | + | 74.4405i | 0.623816 | + | 2.65521i | ||||
\(787\) | 46.5253 | 1.65845 | 0.829224 | − | 0.558916i | \(-0.188783\pi\) | ||||
0.829224 | + | 0.558916i | \(0.188783\pi\) | |||||||
\(788\) | 97.8044 | 3.48414 | ||||||||
\(789\) | −5.37228 | − | 22.8665i | −0.191258 | − | 0.814070i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.4891 | + | 20.1947i | −0.621842 | + | 0.718041i | ||||
\(792\) | −6.33830 | − | 12.7446i | −0.225222 | − | 0.452858i | ||||
\(793\) | − | 40.4674i | − | 1.43704i | ||||||
\(794\) | 9.25544 | 0.328463 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 56.7152i | 2.01022i | ||||||||
\(797\) | − | 42.8614i | − | 1.51823i | −0.650957 | − | 0.759114i | \(-0.725632\pi\) | ||
0.650957 | − | 0.759114i | \(-0.274368\pi\) | |||||||
\(798\) | −18.6101 | + | 35.4891i | −0.658791 | + | 1.25630i | ||||
\(799\) | −10.1168 | −0.357908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.74456 | + | 4.34896i | −0.308974 | + | 0.153663i | ||||
\(802\) | − | 6.74456i | − | 0.238159i | ||||||
\(803\) | − | 5.48913i | − | 0.193707i | ||||||
\(804\) | 49.7228 | − | 11.6819i | 1.75359 | − | 0.411990i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 51.0767i | 1.79910i | ||||||||
\(807\) | 3.46410 | + | 14.7446i | 0.121942 | + | 0.519033i | ||||
\(808\) | 35.9306 | 1.26404 | ||||||||
\(809\) | 36.7229i | 1.29111i | 0.763714 | + | 0.645555i | \(0.223374\pi\) | ||||
−0.763714 | + | 0.645555i | \(0.776626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.28962i | 0.0452847i | 0.999744 | + | 0.0226423i | \(0.00720790\pi\) | ||||
−0.999744 | + | 0.0226423i | \(0.992792\pi\) | |||||||
\(812\) | −37.2203 | − | 32.2337i | −1.30617 | − | 1.13118i | ||||
\(813\) | −25.5383 | + | 6.00000i | −0.895668 | + | 0.210429i | ||||
\(814\) | 9.48913 | 0.332594 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.7446 | + | 3.46410i | −0.516163 | + | 0.121268i | ||||
\(817\) | −23.3639 | −0.817398 | ||||||||
\(818\) | 88.4674i | 3.09319i | ||||||||
\(819\) | 11.5693 | − | 44.8945i | 0.404264 | − | 1.56874i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7745i | 0.410933i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(822\) | 13.2665 | + | 56.4674i | 0.462722 | + | 1.96953i | ||||
\(823\) | − | 48.2337i | − | 1.68132i | −0.541563 | − | 0.840660i | \(-0.682167\pi\) | ||
0.541563 | − | 0.840660i | \(-0.317833\pi\) | |||||||
\(824\) | 97.2119 | 3.38654 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | − | 13.8564i | 0.417533 | − | 0.482126i | ||||
\(827\) | −18.3152 | −0.636881 | −0.318441 | − | 0.947943i | \(-0.603159\pi\) | ||||
−0.318441 | + | 0.947943i | \(0.603159\pi\) | |||||||
\(828\) | −22.0742 | + | 10.9783i | −0.767133 | + | 0.381521i | ||||
\(829\) | 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 | ||||
\(832\) | −13.8564 | −0.480384 | ||||||||
\(833\) | −9.50744 | + | 1.37228i | −0.329413 | + | 0.0475467i | ||||
\(834\) | 5.48913 | − | 1.28962i | 0.190073 | − | 0.0446559i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | 13.8564 | − | 11.4891i | 0.478947 | − | 0.397122i | ||||
\(838\) | 6.92820 | 0.239331 | ||||||||
\(839\) | −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 | ||||||||
\(842\) | 64.6381 | 2.22758 | ||||||||
\(843\) | 8.17154 | − | 1.91983i | 0.281443 | − | 0.0661224i | ||||
\(844\) | 26.7446 | 0.920586 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −24.8614 | − | 49.9894i | −0.854753 | − | 1.71867i | ||||
\(847\) | −17.9653 | + | 20.7446i | −0.617296 | + | 0.712792i | ||||
\(848\) | −54.2458 | −1.86281 | ||||||||
\(849\) | 3.68614 | + | 15.6896i | 0.126508 | + | 0.538467i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 8.91754i | − | 0.305689i | ||||||
\(852\) | −99.9788 | + | 23.4891i | −3.42522 | + | 0.804724i | ||||
\(853\) | −46.7277 | −1.59993 | −0.799963 | − | 0.600049i | \(-0.795148\pi\) | ||||
−0.799963 | + | 0.600049i | \(0.795148\pi\) | |||||||
\(854\) | −34.9783 | − | 30.2921i | −1.19693 | − | 1.03657i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.7228 | 1.35770 | ||||||||
\(857\) | − | 22.4674i | − | 0.767471i | −0.923443 | − | 0.383735i | \(-0.874637\pi\) | ||
0.923443 | − | 0.383735i | \(-0.125363\pi\) | |||||||
\(858\) | 19.6974 | − | 4.62772i | 0.672457 | − | 0.157988i | ||||
\(859\) | 45.4381i | 1.55033i | 0.631760 | + | 0.775164i | \(0.282333\pi\) | ||||
−0.631760 | + | 0.775164i | \(0.717667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.3505 | + | 12.7692i | 0.829864 | + | 0.435172i | ||||
\(862\) | − | 79.9565i | − | 2.72333i | ||||||
\(863\) | −28.0078 | −0.953395 | −0.476698 | − | 0.879067i | \(-0.658166\pi\) | ||||
−0.476698 | + | 0.879067i | \(0.658166\pi\) | |||||||
\(864\) | −13.6277 | − | 16.4356i | −0.463624 | − | 0.559152i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.51087 | 0.221249 | ||||||||
\(867\) | −5.98844 | − | 25.4891i | −0.203378 | − | 0.865656i | ||||
\(868\) | 30.2921 | + | 26.2337i | 1.02818 | + | 0.890429i | ||||
\(869\) | 2.67181i | 0.0906351i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.3947i | 1.33484i | ||||||||
\(872\) | 0.699713 | 0.0236953 | ||||||||
\(873\) | −2.92048 | + | 1.45245i | −0.0988433 | + | 0.0491581i | ||||
\(874\) | 16.4356i | 0.555944i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | − | 51.0767i | −0.405442 | − | 1.72572i | ||||
\(877\) | − | 30.4674i | − | 1.02881i | −0.857547 | − | 0.514405i | \(-0.828013\pi\) | ||
0.857547 | − | 0.514405i | \(-0.171987\pi\) | |||||||
\(878\) | − | 3.25544i | − | 0.109866i | ||||||
\(879\) | 47.4090 | − | 11.1383i | 1.59906 | − | 0.375686i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.23369 | 0.0752549 | 0.0376274 | − | 0.999292i | \(-0.488020\pi\) | ||||
0.0376274 | + | 0.999292i | \(0.488020\pi\) | |||||||
\(882\) | −30.1446 | − | 43.6060i | −1.01502 | − | 1.46829i | ||||
\(883\) | 26.5109i | 0.892162i | 0.894993 | + | 0.446081i | \(0.147181\pi\) | ||||
−0.894993 | + | 0.446081i | \(0.852819\pi\) | |||||||
\(884\) | − | 35.0458i | − | 1.17872i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.7446 | −0.562545 | ||||||||
\(887\) | 41.4891i | 1.39307i | 0.717524 | + | 0.696534i | \(0.245276\pi\) | ||||
−0.717524 | + | 0.696534i | \(0.754724\pi\) | |||||||
\(888\) | 47.9075 | − | 11.2554i | 1.60767 | − | 0.377708i | ||||
\(889\) | 21.4891 | + | 18.6101i | 0.720722 | + | 0.624164i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.68614 | − | 4.30268i | −0.190493 | − | 0.144145i | ||||
\(892\) | 91.7610 | 3.07239 | ||||||||
\(893\) | −25.5383 | −0.854608 | ||||||||
\(894\) | −42.9783 | + | 10.0974i | −1.43741 | + | 0.337706i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24.6060 | + | 28.4125i | −0.822028 | + | 0.949196i | ||||
\(897\) | −4.34896 | − | 18.5109i | −0.145208 | − | 0.618060i | ||||
\(898\) | 71.2119i | 2.37637i | ||||||||
\(899\) | 14.7446 | 0.491759 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.6819i | 0.389181i | ||||||||
\(902\) | 12.0000i | 0.399556i | ||||||||
\(903\) | 14.3537 | − | 27.3723i | 0.477663 | − | 0.910892i | ||||
\(904\) | −60.4674 | −2.01112 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.37228 | + | 14.3537i | 0.112037 | + | 0.476871i | ||||
\(907\) | − | 8.00000i | − | 0.265636i | −0.991140 | − | 0.132818i | \(-0.957597\pi\) | ||
0.991140 | − | 0.132818i | \(-0.0424025\pi\) | |||||||
\(908\) | − | 68.2337i | − | 2.26441i | ||||||
\(909\) | 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 | \(0.871809\pi\) | |||||||
\(912\) | −37.2203 | + | 8.74456i | −1.23249 | + | 0.289561i | ||||
\(913\) | −4.34896 | −0.143930 | ||||||||
\(914\) | − | 83.2482i | − | 2.75361i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 20.7846i | − | 0.686743i | ||||||
\(917\) | −30.2921 | + | 34.9783i | −1.00033 | + | 1.15508i | ||||
\(918\) | −13.8564 | + | 11.4891i | −0.457330 | + | 0.379198i | ||||
\(919\) | 11.3723 | 0.375137 | 0.187568 | − | 0.982252i | \(-0.439939\pi\) | ||||
0.187568 | + | 0.982252i | \(0.439939\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.82473 | − | 12.0232i | −0.0930782 | − | 0.396177i | ||||
\(922\) | −22.0742 | −0.726976 | ||||||||
\(923\) | − | 79.2119i | − | 2.60729i | ||||||
\(924\) | 7.37228 | − | 14.0588i | 0.242530 | − | 0.462500i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 92.0560i | − | 3.02515i | ||||||
\(927\) | 43.6048 | − | 21.6861i | 1.43217 | − | 0.712266i | ||||
\(928\) | − | 17.4891i | − | 0.574109i | ||||||
\(929\) | 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 | ||||
\(932\) | −16.4356 | −0.538368 | ||||||||
\(933\) | 8.01544 | + | 34.1168i | 0.262414 | + | 1.11694i | ||||
\(934\) | 35.0458i | 1.14673i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 93.9565 | − | 46.7277i | 3.07106 | − | 1.52734i | ||||
\(937\) | 49.9894 | 1.63308 | 0.816542 | − | 0.577287i | \(-0.195888\pi\) | ||||
0.816542 | + | 0.577287i | \(0.195888\pi\) | |||||||
\(938\) | 34.0511 | + | 29.4891i | 1.11181 | + | 0.962854i | ||||
\(939\) | 9.68614 | + | 41.2280i | 0.316095 | + | 1.34542i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.2554 | 0.888502 | 0.444251 | − | 0.895902i | \(-0.353470\pi\) | ||||
0.444251 | + | 0.895902i | \(0.353470\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.2772 | 0.367235 | ||||||||
\(944\) | 17.4891 | 0.569223 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.4891 | 0.438569 | ||||||||
\(947\) | −48.2025 | −1.56637 | −0.783185 | − | 0.621789i | \(-0.786406\pi\) | ||||
−0.783185 | + | 0.621789i | \(0.786406\pi\) | |||||||
\(948\) | 5.84096 | + | 24.8614i | 0.189706 | + | 0.807461i | ||||
\(949\) | 40.4674 | 1.31363 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.37228 | − | 14.3537i | −0.109354 | − | 0.465452i | ||||
\(952\) | −16.4356 | − | 14.2337i | −0.532682 | − | 0.461316i | ||||
\(953\) | −38.8048 | −1.25701 | −0.628506 | − | 0.777805i | \(-0.716333\pi\) | ||||
−0.628506 | + | 0.777805i | \(0.716333\pi\) | |||||||
\(954\) | −57.7228 | + | 28.7075i | −1.86885 | + | 0.929439i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 68.3972i | − | 2.21212i | ||||||
\(957\) | −1.33591 | − | 5.68614i | −0.0431838 | − | 0.183807i | ||||
\(958\) | −46.7277 | −1.50970 | ||||||||
\(959\) | −22.9783 | + | 26.5330i | −0.742006 | + | 0.856795i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 69.9565i | 2.25549i | ||||||||
\(963\) | 17.8178 | − | 8.86141i | 0.574172 | − | 0.285555i | ||||
\(964\) | − | 102.153i | − | 3.29014i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −19.2554 | − | 10.0974i | −0.619534 | − | 0.324877i | ||||
\(967\) | 24.2337i | 0.779303i | 0.920962 | + | 0.389651i | \(0.127405\pi\) | ||||
−0.920962 | + | 0.389651i | \(0.872595\pi\) | |||||||
\(968\) | −62.1138 | −1.99641 | ||||||||
\(969\) | 1.88316 | + | 8.01544i | 0.0604957 | + | 0.257493i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.2119 | 1.38674 | 0.693369 | − | 0.720583i | \(-0.256126\pi\) | ||||
0.693369 | + | 0.720583i | \(0.256126\pi\) | |||||||
\(972\) | −62.3162 | − | 27.6060i | −1.99879 | − | 0.885462i | ||||
\(973\) | 2.57924 | + | 2.23369i | 0.0826867 | + | 0.0716087i | ||||
\(974\) | 36.6303i | 1.17371i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 44.1485i | − | 1.41316i | ||||||
\(977\) | 38.8048 | 1.24148 | 0.620738 | − | 0.784018i | \(-0.286833\pi\) | ||||
0.620738 | + | 0.784018i | \(0.286833\pi\) | |||||||
\(978\) | −34.0511 | + | 8.00000i | −1.08883 | + | 0.255812i | ||||
\(979\) | − | 2.57924i | − | 0.0824329i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.313859 | − | 0.156093i | 0.0100208 | − | 0.00498366i | ||||
\(982\) | − | 27.4891i | − | 0.877213i | ||||||
\(983\) | − | 11.1386i | − | 0.355266i | −0.984097 | − | 0.177633i | \(-0.943156\pi\) | ||
0.984097 | − | 0.177633i | \(-0.0568440\pi\) | |||||||
\(984\) | 14.2337 | + | 60.5841i | 0.453753 | + | 1.93135i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −14.7446 | −0.469563 | ||||||||
\(987\) | 15.6896 | − | 29.9198i | 0.499407 | − | 0.952359i | ||||
\(988\) | − | 88.4674i | − | 2.81452i | ||||||
\(989\) | − | 12.6766i | − | 0.403092i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.51087 | 0.0797606 | 0.0398803 | − | 0.999204i | \(-0.487302\pi\) | ||||
0.0398803 | + | 0.999204i | \(0.487302\pi\) | |||||||
\(992\) | 14.2337i | 0.451920i | ||||||||
\(993\) | 1.58457 | + | 6.74456i | 0.0502849 | + | 0.214032i | ||||
\(994\) | −68.4674 | − | 59.2945i | −2.17165 | − | 1.88071i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −40.4674 | + | 9.50744i | −1.28226 | + | 0.301255i | ||||
\(997\) | 21.8719 | 0.692688 | 0.346344 | − | 0.938107i | \(-0.387423\pi\) | ||||
0.346344 | + | 0.938107i | \(0.387423\pi\) | |||||||
\(998\) | −26.1282 | −0.827075 | ||||||||
\(999\) | 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.g.e.524.1 | 8 | ||
3.2 | odd | 2 | 525.2.g.d.524.8 | 8 | |||
5.2 | odd | 4 | 105.2.b.c.41.1 | ✓ | 4 | ||
5.3 | odd | 4 | 525.2.b.g.251.4 | 4 | |||
5.4 | even | 2 | inner | 525.2.g.e.524.8 | 8 | ||
7.6 | odd | 2 | 525.2.g.d.524.2 | 8 | |||
15.2 | even | 4 | 105.2.b.d.41.4 | yes | 4 | ||
15.8 | even | 4 | 525.2.b.e.251.1 | 4 | |||
15.14 | odd | 2 | 525.2.g.d.524.1 | 8 | |||
20.7 | even | 4 | 1680.2.f.h.881.3 | 4 | |||
21.20 | even | 2 | inner | 525.2.g.e.524.7 | 8 | ||
35.2 | odd | 12 | 735.2.s.h.521.1 | 4 | |||
35.12 | even | 12 | 735.2.s.g.521.1 | 4 | |||
35.13 | even | 4 | 525.2.b.e.251.4 | 4 | |||
35.17 | even | 12 | 735.2.s.j.656.2 | 4 | |||
35.27 | even | 4 | 105.2.b.d.41.1 | yes | 4 | ||
35.32 | odd | 12 | 735.2.s.i.656.2 | 4 | |||
35.34 | odd | 2 | 525.2.g.d.524.7 | 8 | |||
60.47 | odd | 4 | 1680.2.f.g.881.1 | 4 | |||
105.2 | even | 12 | 735.2.s.j.521.2 | 4 | |||
105.17 | odd | 12 | 735.2.s.h.656.1 | 4 | |||
105.32 | even | 12 | 735.2.s.g.656.1 | 4 | |||
105.47 | odd | 12 | 735.2.s.i.521.2 | 4 | |||
105.62 | odd | 4 | 105.2.b.c.41.4 | yes | 4 | ||
105.83 | odd | 4 | 525.2.b.g.251.1 | 4 | |||
105.104 | even | 2 | inner | 525.2.g.e.524.2 | 8 | ||
140.27 | odd | 4 | 1680.2.f.g.881.2 | 4 | |||
420.167 | even | 4 | 1680.2.f.h.881.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.b.c.41.1 | ✓ | 4 | 5.2 | odd | 4 | ||
105.2.b.c.41.4 | yes | 4 | 105.62 | odd | 4 | ||
105.2.b.d.41.1 | yes | 4 | 35.27 | even | 4 | ||
105.2.b.d.41.4 | yes | 4 | 15.2 | even | 4 | ||
525.2.b.e.251.1 | 4 | 15.8 | even | 4 | |||
525.2.b.e.251.4 | 4 | 35.13 | even | 4 | |||
525.2.b.g.251.1 | 4 | 105.83 | odd | 4 | |||
525.2.b.g.251.4 | 4 | 5.3 | odd | 4 | |||
525.2.g.d.524.1 | 8 | 15.14 | odd | 2 | |||
525.2.g.d.524.2 | 8 | 7.6 | odd | 2 | |||
525.2.g.d.524.7 | 8 | 35.34 | odd | 2 | |||
525.2.g.d.524.8 | 8 | 3.2 | odd | 2 | |||
525.2.g.e.524.1 | 8 | 1.1 | even | 1 | trivial | ||
525.2.g.e.524.2 | 8 | 105.104 | even | 2 | inner | ||
525.2.g.e.524.7 | 8 | 21.20 | even | 2 | inner | ||
525.2.g.e.524.8 | 8 | 5.4 | even | 2 | inner | ||
735.2.s.g.521.1 | 4 | 35.12 | even | 12 | |||
735.2.s.g.656.1 | 4 | 105.32 | even | 12 | |||
735.2.s.h.521.1 | 4 | 35.2 | odd | 12 | |||
735.2.s.h.656.1 | 4 | 105.17 | odd | 12 | |||
735.2.s.i.521.2 | 4 | 105.47 | odd | 12 | |||
735.2.s.i.656.2 | 4 | 35.32 | odd | 12 | |||
735.2.s.j.521.2 | 4 | 105.2 | even | 12 | |||
735.2.s.j.656.2 | 4 | 35.17 | even | 12 | |||
1680.2.f.g.881.1 | 4 | 60.47 | odd | 4 | |||
1680.2.f.g.881.2 | 4 | 140.27 | odd | 4 | |||
1680.2.f.h.881.3 | 4 | 20.7 | even | 4 | |||
1680.2.f.h.881.4 | 4 | 420.167 | even | 4 |