Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.17284886784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 30x^{5} + 185x^{4} + 36x^{3} + 8x^{2} + 208x + 2704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.80668 + 1.80668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.199 |
Dual form | 1950.2.y.j.49.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −0.661290 | − | 1.14539i | −0.249944 | − | 0.432916i | 0.713566 | − | 0.700588i | \(-0.247079\pi\) |
−0.963510 | + | 0.267672i | \(0.913746\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.99528 | − | 2.30668i | −1.20462 | − | 0.695489i | −0.243043 | − | 0.970015i | \(-0.578146\pi\) |
−0.961580 | + | 0.274526i | \(0.911479\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 1.66129 | + | 3.20002i | 0.460759 | + | 0.887525i | ||||
\(14\) | 1.32258 | 0.353474 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.46410 | − | 2.00000i | 0.840168 | − | 0.485071i | −0.0171533 | − | 0.999853i | \(-0.505460\pi\) |
0.857321 | + | 0.514782i | \(0.172127\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.98387 | + | 1.14539i | −0.455131 | + | 0.262770i | −0.709995 | − | 0.704207i | \(-0.751303\pi\) |
0.254864 | + | 0.966977i | \(0.417969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.32258i | 0.288611i | ||||||||
\(22\) | 3.99528 | − | 2.30668i | 0.851797 | − | 0.491785i | ||||
\(23\) | 7.50670 | + | 4.33399i | 1.56525 | + | 0.903700i | 0.996710 | + | 0.0810471i | \(0.0258264\pi\) |
0.568544 | + | 0.822653i | \(0.307507\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.60194 | − | 0.161290i | −0.706399 | − | 0.0316315i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.661290 | + | 1.14539i | −0.124972 | + | 0.216458i | ||||
\(29\) | −1.01141 | + | 1.75182i | −0.187815 | + | 0.325305i | −0.944521 | − | 0.328450i | \(-0.893474\pi\) |
0.756707 | + | 0.653755i | \(0.226807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.1321i | − | 1.81978i | −0.414853 | − | 0.909888i | \(-0.636167\pi\) | ||
0.414853 | − | 0.909888i | \(-0.363833\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 2.30668 | + | 3.99528i | 0.401541 | + | 0.695489i | ||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 3.40475 | − | 5.89721i | 0.559738 | − | 0.969495i | −0.437780 | − | 0.899082i | \(-0.644235\pi\) |
0.997518 | − | 0.0704126i | \(-0.0224316\pi\) | |||||||
\(38\) | − | 2.29078i | − | 0.371613i | ||||||
\(39\) | 0.161290 | − | 3.60194i | 0.0258270 | − | 0.576772i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.02283 | − | 2.32258i | −0.628260 | − | 0.362726i | 0.151818 | − | 0.988408i | \(-0.451487\pi\) |
−0.780078 | + | 0.625682i | \(0.784821\pi\) | |||||||
\(42\) | −1.14539 | − | 0.661290i | −0.176737 | − | 0.102039i | ||||
\(43\) | −7.45269 | + | 4.30281i | −1.13652 | + | 0.656173i | −0.945568 | − | 0.325426i | \(-0.894492\pi\) |
−0.190957 | + | 0.981598i | \(0.561159\pi\) | |||||||
\(44\) | 4.61335i | 0.695489i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.50670 | + | 4.33399i | −1.10680 | + | 0.639012i | ||||
\(47\) | −9.10926 | −1.32872 | −0.664361 | − | 0.747412i | \(-0.731296\pi\) | ||||
−0.664361 | + | 0.747412i | \(0.731296\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 2.62539 | − | 4.54731i | 0.375056 | − | 0.649616i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 1.94065 | − | 3.03873i | 0.269120 | − | 0.421396i | ||||
\(53\) | 0.826674i | 0.113552i | 0.998387 | + | 0.0567762i | \(0.0180821\pi\) | ||||
−0.998387 | + | 0.0567762i | \(0.981918\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.661290 | − | 1.14539i | −0.0883686 | − | 0.153059i | ||||
\(57\) | 2.29078 | 0.303421 | ||||||||
\(58\) | −1.01141 | − | 1.75182i | −0.132805 | − | 0.230025i | ||||
\(59\) | −2.72064 | + | 1.57076i | −0.354197 | + | 0.204496i | −0.666532 | − | 0.745476i | \(-0.732222\pi\) |
0.312335 | + | 0.949972i | \(0.398889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.267949 | − | 0.464102i | −0.0343074 | − | 0.0594221i | 0.848362 | − | 0.529417i | \(-0.177589\pi\) |
−0.882669 | + | 0.469995i | \(0.844256\pi\) | |||||||
\(62\) | 8.77464 | + | 5.06604i | 1.11438 | + | 0.643388i | ||||
\(63\) | 0.661290 | − | 1.14539i | 0.0833147 | − | 0.144305i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.61335 | −0.567865 | ||||||||
\(67\) | −1.59053 | + | 2.75488i | −0.194314 | + | 0.336562i | −0.946675 | − | 0.322189i | \(-0.895581\pi\) |
0.752361 | + | 0.658751i | \(0.228915\pi\) | |||||||
\(68\) | −3.46410 | − | 2.00000i | −0.420084 | − | 0.242536i | ||||
\(69\) | −4.33399 | − | 7.50670i | −0.521751 | − | 0.903700i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.81724 | + | 5.66799i | −1.16509 | + | 0.672666i | −0.952519 | − | 0.304479i | \(-0.901518\pi\) |
−0.212573 | + | 0.977145i | \(0.568184\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 6.28304 | 0.735375 | 0.367687 | − | 0.929949i | \(-0.380150\pi\) | ||||
0.367687 | + | 0.929949i | \(0.380150\pi\) | |||||||
\(74\) | 3.40475 | + | 5.89721i | 0.395795 | + | 0.685536i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.98387 | + | 1.14539i | 0.227565 | + | 0.131385i | ||||
\(77\) | 6.10153i | 0.695334i | ||||||||
\(78\) | 3.03873 | + | 1.94065i | 0.344068 | + | 0.219736i | ||||
\(79\) | −2.96774 | −0.333897 | −0.166948 | − | 0.985966i | \(-0.553391\pi\) | ||||
−0.166948 | + | 0.985966i | \(0.553391\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.02283 | − | 2.32258i | 0.444247 | − | 0.256486i | ||||
\(83\) | −15.8719 | −1.74216 | −0.871082 | − | 0.491138i | \(-0.836581\pi\) | ||||
−0.871082 | + | 0.491138i | \(0.836581\pi\) | |||||||
\(84\) | 1.14539 | − | 0.661290i | 0.124972 | − | 0.0721526i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 8.60562i | − | 0.927968i | ||||||
\(87\) | 1.75182 | − | 1.01141i | 0.187815 | − | 0.108435i | ||||
\(88\) | −3.99528 | − | 2.30668i | −0.425899 | − | 0.245893i | ||||
\(89\) | −10.2746 | − | 5.93207i | −1.08911 | − | 0.628798i | −0.155771 | − | 0.987793i | \(-0.549786\pi\) |
−0.933339 | + | 0.358995i | \(0.883119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.56667 | − | 4.01896i | 0.269060 | − | 0.421302i | ||||
\(92\) | − | 8.66799i | − | 0.903700i | ||||||
\(93\) | −5.06604 | + | 8.77464i | −0.525324 | + | 0.909888i | ||||
\(94\) | 4.55463 | − | 7.88885i | 0.469774 | − | 0.813673i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 4.40947 | + | 7.63743i | 0.447714 | + | 0.775463i | 0.998237 | − | 0.0593568i | \(-0.0189050\pi\) |
−0.550523 | + | 0.834820i | \(0.685572\pi\) | |||||||
\(98\) | 2.62539 | + | 4.54731i | 0.265205 | + | 0.459348i | ||||
\(99\) | − | 4.61335i | − | 0.463660i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.61335 | + | 6.25851i | −0.359542 | + | 0.622745i | −0.987884 | − | 0.155192i | \(-0.950400\pi\) |
0.628342 | + | 0.777937i | \(0.283734\pi\) | |||||||
\(102\) | 2.00000 | − | 3.46410i | 0.198030 | − | 0.342997i | ||||
\(103\) | − | 18.4000i | − | 1.81301i | −0.422196 | − | 0.906505i | \(-0.638740\pi\) | ||
0.422196 | − | 0.906505i | \(-0.361260\pi\) | |||||||
\(104\) | 1.66129 | + | 3.20002i | 0.162903 | + | 0.313788i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.715920 | − | 0.413337i | −0.0695363 | − | 0.0401468i | ||||
\(107\) | 2.66025 | + | 1.53590i | 0.257176 | + | 0.148481i | 0.623046 | − | 0.782185i | \(-0.285895\pi\) |
−0.365869 | + | 0.930666i | \(0.619228\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | − | 13.2267i | − | 1.26689i | −0.773788 | − | 0.633445i | \(-0.781640\pi\) | ||
0.773788 | − | 0.633445i | \(-0.218360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.89721 | + | 3.40475i | −0.559738 | + | 0.323165i | ||||
\(112\) | 1.32258 | 0.124972 | ||||||||
\(113\) | −7.00306 | + | 4.04322i | −0.658792 | + | 0.380354i | −0.791817 | − | 0.610759i | \(-0.790864\pi\) |
0.133024 | + | 0.991113i | \(0.457531\pi\) | |||||||
\(114\) | −1.14539 | + | 1.98387i | −0.107275 | + | 0.185806i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.02283 | 0.187815 | ||||||||
\(117\) | −1.94065 | + | 3.03873i | −0.179413 | + | 0.280931i | ||||
\(118\) | − | 3.14152i | − | 0.289201i | ||||||
\(119\) | −4.58155 | − | 2.64516i | −0.419990 | − | 0.242481i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.14152 | + | 8.90538i | 0.467411 | + | 0.809580i | ||||
\(122\) | 0.535898 | 0.0485180 | ||||||||
\(123\) | 2.32258 | + | 4.02283i | 0.209420 | + | 0.362726i | ||||
\(124\) | −8.77464 | + | 5.06604i | −0.787986 | + | 0.454944i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.661290 | + | 1.14539i | 0.0589124 | + | 0.102039i | ||||
\(127\) | −9.93490 | − | 5.73592i | −0.881580 | − | 0.508980i | −0.0104008 | − | 0.999946i | \(-0.503311\pi\) |
−0.871179 | + | 0.490966i | \(0.836644\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 8.60562 | 0.757683 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.9906 | −1.39710 | −0.698551 | − | 0.715560i | \(-0.746172\pi\) | ||||
−0.698551 | + | 0.715560i | \(0.746172\pi\) | |||||||
\(132\) | 2.30668 | − | 3.99528i | 0.200771 | − | 0.347745i | ||||
\(133\) | 2.62383 | + | 1.51487i | 0.227515 | + | 0.131356i | ||||
\(134\) | −1.59053 | − | 2.75488i | −0.137401 | − | 0.237985i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | − | 2.00000i | 0.297044 | − | 0.171499i | ||||
\(137\) | −8.03486 | − | 13.9168i | −0.686465 | − | 1.18899i | −0.972974 | − | 0.230914i | \(-0.925828\pi\) |
0.286509 | − | 0.958077i | \(-0.407505\pi\) | |||||||
\(138\) | 8.66799 | 0.737868 | ||||||||
\(139\) | 4.66129 | + | 8.07359i | 0.395365 | + | 0.684793i | 0.993148 | − | 0.116865i | \(-0.0372846\pi\) |
−0.597782 | + | 0.801658i | \(0.703951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.88885 | + | 4.55463i | 0.664361 | + | 0.383569i | ||||
\(142\) | − | 11.3360i | − | 0.951294i | ||||||
\(143\) | 0.744087 | − | 16.6170i | 0.0622237 | − | 1.38959i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.14152 | + | 5.44128i | −0.259994 | + | 0.450323i | ||||
\(147\) | −4.54731 | + | 2.62539i | −0.375056 | + | 0.216539i | ||||
\(148\) | −6.80951 | −0.559738 | ||||||||
\(149\) | −3.53788 | + | 2.04259i | −0.289834 | + | 0.167336i | −0.637867 | − | 0.770146i | \(-0.720183\pi\) |
0.348033 | + | 0.937482i | \(0.386850\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19.9811i | − | 1.62604i | −0.582235 | − | 0.813021i | \(-0.697822\pi\) | ||
0.582235 | − | 0.813021i | \(-0.302178\pi\) | |||||||
\(152\) | −1.98387 | + | 1.14539i | −0.160913 | + | 0.0929032i | ||||
\(153\) | 3.46410 | + | 2.00000i | 0.280056 | + | 0.161690i | ||||
\(154\) | −5.28408 | − | 3.05076i | −0.425803 | − | 0.245838i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.20002 | + | 1.66129i | −0.256206 | + | 0.133010i | ||||
\(157\) | − | 7.13379i | − | 0.569338i | −0.958626 | − | 0.284669i | \(-0.908116\pi\) | ||
0.958626 | − | 0.284669i | \(-0.0918838\pi\) | |||||||
\(158\) | 1.48387 | − | 2.57014i | 0.118050 | − | 0.204469i | ||||
\(159\) | 0.413337 | − | 0.715920i | 0.0327797 | − | 0.0567762i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.4641i | − | 0.903498i | ||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −4.94735 | − | 8.56906i | −0.387506 | − | 0.671180i | 0.604607 | − | 0.796524i | \(-0.293330\pi\) |
−0.992113 | + | 0.125343i | \(0.959997\pi\) | |||||||
\(164\) | 4.64516i | 0.362726i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.93593 | − | 13.7454i | 0.615948 | − | 1.06685i | ||||
\(167\) | 12.0187 | − | 20.8171i | 0.930037 | − | 1.61087i | 0.146785 | − | 0.989168i | \(-0.453108\pi\) |
0.783253 | − | 0.621704i | \(-0.213559\pi\) | |||||||
\(168\) | 1.32258i | 0.102039i | ||||||||
\(169\) | −7.48023 | + | 10.6323i | −0.575402 | + | 0.817870i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.98387 | − | 1.14539i | −0.151710 | − | 0.0875900i | ||||
\(172\) | 7.45269 | + | 4.30281i | 0.568262 | + | 0.328086i | ||||
\(173\) | −2.18946 | + | 1.26408i | −0.166461 | + | 0.0961065i | −0.580916 | − | 0.813963i | \(-0.697306\pi\) |
0.414455 | + | 0.910070i | \(0.363972\pi\) | |||||||
\(174\) | 2.02283i | 0.153350i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.99528 | − | 2.30668i | 0.301156 | − | 0.173872i | ||||
\(177\) | 3.14152 | 0.236131 | ||||||||
\(178\) | 10.2746 | − | 5.93207i | 0.770117 | − | 0.444627i | ||||
\(179\) | 3.13784 | − | 5.43490i | 0.234533 | − | 0.406223i | −0.724604 | − | 0.689166i | \(-0.757977\pi\) |
0.959137 | + | 0.282942i | \(0.0913105\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2830 | −0.912991 | −0.456496 | − | 0.889726i | \(-0.650896\pi\) | ||||
−0.456496 | + | 0.889726i | \(0.650896\pi\) | |||||||
\(182\) | 2.19719 | + | 4.23228i | 0.162866 | + | 0.313717i | ||||
\(183\) | 0.535898i | 0.0396147i | ||||||||
\(184\) | 7.50670 | + | 4.33399i | 0.553401 | + | 0.319506i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.06604 | − | 8.77464i | −0.371460 | − | 0.643388i | ||||
\(187\) | −18.4534 | −1.34945 | ||||||||
\(188\) | 4.55463 | + | 7.88885i | 0.332181 | + | 0.575354i | ||||
\(189\) | −1.14539 | + | 0.661290i | −0.0833147 | + | 0.0481018i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.87357 | + | 8.44128i | 0.352639 | + | 0.610789i | 0.986711 | − | 0.162485i | \(-0.0519509\pi\) |
−0.634072 | + | 0.773274i | \(0.718618\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 6.88130 | − | 11.9188i | 0.495327 | − | 0.857932i | −0.504658 | − | 0.863319i | \(-0.668382\pi\) |
0.999985 | + | 0.00538741i | \(0.00171487\pi\) | |||||||
\(194\) | −8.81894 | −0.633163 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.25078 | −0.375056 | ||||||||
\(197\) | −5.07076 | + | 8.78282i | −0.361277 | + | 0.625750i | −0.988171 | − | 0.153354i | \(-0.950992\pi\) |
0.626894 | + | 0.779104i | \(0.284326\pi\) | |||||||
\(198\) | 3.99528 | + | 2.30668i | 0.283932 | + | 0.163928i | ||||
\(199\) | −4.78668 | − | 8.29078i | −0.339319 | − | 0.587717i | 0.644986 | − | 0.764194i | \(-0.276863\pi\) |
−0.984305 | + | 0.176477i | \(0.943530\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.75488 | − | 1.59053i | 0.194314 | − | 0.112187i | ||||
\(202\) | −3.61335 | − | 6.25851i | −0.254235 | − | 0.440348i | ||||
\(203\) | 2.67535 | 0.187773 | ||||||||
\(204\) | 2.00000 | + | 3.46410i | 0.140028 | + | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.9349 | + | 9.20002i | 1.11024 | + | 0.640996i | ||||
\(207\) | 8.66799i | 0.602467i | ||||||||
\(208\) | −3.60194 | − | 0.161290i | −0.249750 | − | 0.0111834i | ||||
\(209\) | 10.5682 | 0.731015 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.542594 | − | 0.939800i | 0.0373537 | − | 0.0646985i | −0.846744 | − | 0.532000i | \(-0.821441\pi\) |
0.884098 | + | 0.467302i | \(0.154774\pi\) | |||||||
\(212\) | 0.715920 | − | 0.413337i | 0.0491696 | − | 0.0283881i | ||||
\(213\) | 11.3360 | 0.776728 | ||||||||
\(214\) | −2.66025 | + | 1.53590i | −0.181851 | + | 0.104992i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −11.6052 | + | 6.70025i | −0.787810 | + | 0.454842i | ||||
\(218\) | 11.4547 | + | 6.61335i | 0.775808 | + | 0.447913i | ||||
\(219\) | −5.44128 | − | 3.14152i | −0.367687 | − | 0.212284i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.1549 | + | 7.76261i | 0.817628 | + | 0.522170i | ||||
\(222\) | − | 6.80951i | − | 0.457024i | ||||||
\(223\) | −12.4708 | + | 21.6001i | −0.835106 | + | 1.44645i | 0.0588375 | + | 0.998268i | \(0.481261\pi\) |
−0.893944 | + | 0.448179i | \(0.852073\pi\) | |||||||
\(224\) | −0.661290 | + | 1.14539i | −0.0441843 | + | 0.0765294i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 8.08643i | − | 0.537902i | ||||||
\(227\) | 9.66025 | + | 16.7321i | 0.641174 | + | 1.11055i | 0.985171 | + | 0.171575i | \(0.0548855\pi\) |
−0.343998 | + | 0.938971i | \(0.611781\pi\) | |||||||
\(228\) | −1.14539 | − | 1.98387i | −0.0758551 | − | 0.131385i | ||||
\(229\) | − | 4.15491i | − | 0.274564i | −0.990532 | − | 0.137282i | \(-0.956163\pi\) | ||
0.990532 | − | 0.137282i | \(-0.0438367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.05076 | − | 5.28408i | 0.200726 | − | 0.347667i | ||||
\(232\) | −1.01141 | + | 1.75182i | −0.0664025 | + | 0.115013i | ||||
\(233\) | 16.9665i | 1.11151i | 0.831346 | + | 0.555756i | \(0.187571\pi\) | ||||
−0.831346 | + | 0.555756i | \(0.812429\pi\) | |||||||
\(234\) | −1.66129 | − | 3.20002i | −0.108602 | − | 0.209192i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.72064 | + | 1.57076i | 0.177098 | + | 0.102248i | ||||
\(237\) | 2.57014 | + | 1.48387i | 0.166948 | + | 0.0963877i | ||||
\(238\) | 4.58155 | − | 2.64516i | 0.296978 | − | 0.171460i | ||||
\(239\) | 6.34416i | 0.410370i | 0.978723 | + | 0.205185i | \(0.0657795\pi\) | ||||
−0.978723 | + | 0.205185i | \(0.934220\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.9452 | − | 12.0927i | 1.34920 | − | 0.778962i | 0.361065 | − | 0.932541i | \(-0.382413\pi\) |
0.988136 | + | 0.153579i | \(0.0490800\pi\) | |||||||
\(242\) | −10.2830 | −0.661019 | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −0.267949 | + | 0.464102i | −0.0171537 | + | 0.0297111i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.64516 | −0.296165 | ||||||||
\(247\) | −6.96104 | − | 4.44560i | −0.442921 | − | 0.282867i | ||||
\(248\) | − | 10.1321i | − | 0.643388i | ||||||
\(249\) | 13.7454 | + | 7.93593i | 0.871082 | + | 0.502919i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.41249 | + | 7.64265i | 0.278514 | + | 0.482400i | 0.971016 | − | 0.239016i | \(-0.0768249\pi\) |
−0.692502 | + | 0.721416i | \(0.743492\pi\) | |||||||
\(252\) | −1.32258 | −0.0833147 | ||||||||
\(253\) | −19.9942 | − | 34.6311i | −1.25703 | − | 2.17724i | ||||
\(254\) | 9.93490 | − | 5.73592i | 0.623371 | − | 0.359903i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −7.26157 | − | 4.19247i | −0.452964 | − | 0.261519i | 0.256117 | − | 0.966646i | \(-0.417557\pi\) |
−0.709081 | + | 0.705127i | \(0.750890\pi\) | |||||||
\(258\) | −4.30281 | + | 7.45269i | −0.267881 | + | 0.463984i | ||||
\(259\) | −9.00612 | −0.559613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.02283 | −0.125210 | ||||||||
\(262\) | 7.99528 | − | 13.8482i | 0.493950 | − | 0.855547i | ||||
\(263\) | −1.66389 | − | 0.960648i | −0.102600 | − | 0.0592361i | 0.447822 | − | 0.894123i | \(-0.352200\pi\) |
−0.550422 | + | 0.834887i | \(0.685533\pi\) | |||||||
\(264\) | 2.30668 | + | 3.99528i | 0.141966 | + | 0.245893i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.62383 | + | 1.51487i | −0.160877 | + | 0.0928824i | ||||
\(267\) | 5.93207 | + | 10.2746i | 0.363037 | + | 0.628798i | ||||
\(268\) | 3.18106 | 0.194314 | ||||||||
\(269\) | −16.1549 | − | 27.9811i | −0.984982 | − | 1.70604i | −0.642014 | − | 0.766693i | \(-0.721901\pi\) |
−0.342968 | − | 0.939347i | \(-0.611432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3105 | + | 11.7263i | 1.23378 | + | 0.712322i | 0.967815 | − | 0.251662i | \(-0.0809770\pi\) |
0.265962 | + | 0.963983i | \(0.414310\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | −4.23228 | + | 2.19719i | −0.256149 | + | 0.132980i | ||||
\(274\) | 16.0697 | 0.970808 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.33399 | + | 7.50670i | −0.260876 | + | 0.451850i | ||||
\(277\) | −7.79913 | + | 4.50283i | −0.468604 | + | 0.270549i | −0.715655 | − | 0.698454i | \(-0.753872\pi\) |
0.247051 | + | 0.969002i | \(0.420538\pi\) | |||||||
\(278\) | −9.32258 | −0.559131 | ||||||||
\(279\) | 8.77464 | − | 5.06604i | 0.525324 | − | 0.303296i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.71696i | 0.102425i | 0.998688 | + | 0.0512125i | \(0.0163086\pi\) | ||||
−0.998688 | + | 0.0512125i | \(0.983691\pi\) | |||||||
\(282\) | −7.88885 | + | 4.55463i | −0.469774 | + | 0.271224i | ||||
\(283\) | −1.34172 | − | 0.774645i | −0.0797572 | − | 0.0460479i | 0.459591 | − | 0.888131i | \(-0.347996\pi\) |
−0.539348 | + | 0.842083i | \(0.681329\pi\) | |||||||
\(284\) | 9.81724 | + | 5.66799i | 0.582546 | + | 0.336333i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.0187 | + | 8.95292i | 0.828945 | + | 0.529397i | ||||
\(287\) | 6.14359i | 0.362645i | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 8.81894i | − | 0.516976i | ||||||
\(292\) | −3.14152 | − | 5.44128i | −0.183844 | − | 0.318427i | ||||
\(293\) | 15.2028 | + | 26.3321i | 0.888160 | + | 1.53834i | 0.842049 | + | 0.539402i | \(0.181350\pi\) |
0.0461113 | + | 0.998936i | \(0.485317\pi\) | |||||||
\(294\) | − | 5.25078i | − | 0.306232i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.40475 | − | 5.89721i | 0.197897 | − | 0.342768i | ||||
\(297\) | −2.30668 | + | 3.99528i | −0.133847 | + | 0.231830i | ||||
\(298\) | − | 4.08519i | − | 0.236649i | ||||||
\(299\) | −1.39806 | + | 31.2216i | −0.0808518 | + | 1.80559i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.85677 | + | 5.69081i | 0.568135 | + | 0.328013i | ||||
\(302\) | 17.3042 | + | 9.99057i | 0.995743 | + | 0.574892i | ||||
\(303\) | 6.25851 | − | 3.61335i | 0.359542 | − | 0.207582i | ||||
\(304\) | − | 2.29078i | − | 0.131385i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.46410 | + | 2.00000i | −0.198030 | + | 0.114332i | ||||
\(307\) | 9.82622 | 0.560812 | 0.280406 | − | 0.959882i | \(-0.409531\pi\) | ||||
0.280406 | + | 0.959882i | \(0.409531\pi\) | |||||||
\(308\) | 5.28408 | − | 3.05076i | 0.301088 | − | 0.173833i | ||||
\(309\) | −9.20002 | + | 15.9349i | −0.523371 | + | 0.906505i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.40049 | −0.192824 | −0.0964121 | − | 0.995342i | \(-0.530737\pi\) | ||||
−0.0964121 | + | 0.995342i | \(0.530737\pi\) | |||||||
\(312\) | 0.161290 | − | 3.60194i | 0.00913124 | − | 0.203920i | ||||
\(313\) | − | 16.2340i | − | 0.917599i | −0.888540 | − | 0.458800i | \(-0.848280\pi\) | ||
0.888540 | − | 0.458800i | \(-0.151720\pi\) | |||||||
\(314\) | 6.17804 | + | 3.56690i | 0.348647 | + | 0.201292i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.48387 | + | 2.57014i | 0.0834742 | + | 0.144582i | ||||
\(317\) | 23.5231 | 1.32119 | 0.660596 | − | 0.750742i | \(-0.270304\pi\) | ||||
0.660596 | + | 0.750742i | \(0.270304\pi\) | |||||||
\(318\) | 0.413337 | + | 0.715920i | 0.0231788 | + | 0.0401468i | ||||
\(319\) | 8.08176 | − | 4.66601i | 0.452492 | − | 0.261246i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.53590 | − | 2.66025i | −0.0857255 | − | 0.148481i | ||||
\(322\) | 9.92820 | + | 5.73205i | 0.553277 | + | 0.319435i | ||||
\(323\) | −4.58155 | + | 7.93548i | −0.254924 | + | 0.441542i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.89470 | 0.548016 | ||||||||
\(327\) | −6.61335 | + | 11.4547i | −0.365719 | + | 0.633445i | ||||
\(328\) | −4.02283 | − | 2.32258i | −0.222123 | − | 0.128243i | ||||
\(329\) | 6.02386 | + | 10.4336i | 0.332106 | + | 0.575225i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.6667 | − | 9.04520i | 0.861122 | − | 0.497169i | −0.00326597 | − | 0.999995i | \(-0.501040\pi\) |
0.864388 | + | 0.502826i | \(0.167706\pi\) | |||||||
\(332\) | 7.93593 | + | 13.7454i | 0.435541 | + | 0.754379i | ||||
\(333\) | 6.80951 | 0.373159 | ||||||||
\(334\) | 12.0187 | + | 20.8171i | 0.657636 | + | 1.13906i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.14539 | − | 0.661290i | −0.0624860 | − | 0.0360763i | ||||
\(337\) | 5.69900i | 0.310444i | 0.987880 | + | 0.155222i | \(0.0496093\pi\) | ||||
−0.987880 | + | 0.155222i | \(0.950391\pi\) | |||||||
\(338\) | −5.46774 | − | 11.7942i | −0.297406 | − | 0.641521i | ||||
\(339\) | 8.08643 | 0.439195 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.3715 | + | 40.4806i | −1.26564 | + | 2.19214i | ||||
\(342\) | 1.98387 | − | 1.14539i | 0.107275 | − | 0.0619355i | ||||
\(343\) | −16.2026 | −0.874860 | ||||||||
\(344\) | −7.45269 | + | 4.30281i | −0.401822 | + | 0.231992i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 2.52817i | − | 0.135915i | ||||||
\(347\) | 13.6374 | − | 7.87357i | 0.732095 | − | 0.422676i | −0.0870928 | − | 0.996200i | \(-0.527758\pi\) |
0.819188 | + | 0.573525i | \(0.194424\pi\) | |||||||
\(348\) | −1.75182 | − | 1.01141i | −0.0939073 | − | 0.0542174i | ||||
\(349\) | −13.2679 | − | 7.66025i | −0.710217 | − | 0.410044i | 0.100924 | − | 0.994894i | \(-0.467820\pi\) |
−0.811141 | + | 0.584850i | \(0.801153\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.20002 | − | 1.66129i | 0.170804 | − | 0.0886731i | ||||
\(352\) | 4.61335i | 0.245893i | ||||||||
\(353\) | −0.599964 | + | 1.03917i | −0.0319328 | + | 0.0553093i | −0.881550 | − | 0.472090i | \(-0.843500\pi\) |
0.849617 | + | 0.527400i | \(0.176833\pi\) | |||||||
\(354\) | −1.57076 | + | 2.72064i | −0.0834850 | + | 0.144600i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.8641i | 0.628798i | ||||||||
\(357\) | 2.64516 | + | 4.58155i | 0.139997 | + | 0.242481i | ||||
\(358\) | 3.13784 | + | 5.43490i | 0.165840 | + | 0.287243i | ||||
\(359\) | − | 16.2830i | − | 0.859386i | −0.902975 | − | 0.429693i | \(-0.858622\pi\) | ||
0.902975 | − | 0.429693i | \(-0.141378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.87617 | + | 11.9099i | −0.361904 | + | 0.626836i | ||||
\(362\) | 6.14152 | − | 10.6374i | 0.322791 | − | 0.559091i | ||||
\(363\) | − | 10.2830i | − | 0.539720i | ||||||
\(364\) | −4.76386 | − | 0.213319i | −0.249694 | − | 0.0111809i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.464102 | − | 0.267949i | −0.0242590 | − | 0.0140059i | ||||
\(367\) | −17.0040 | − | 9.81724i | −0.887599 | − | 0.512456i | −0.0144428 | − | 0.999896i | \(-0.504597\pi\) |
−0.873156 | + | 0.487440i | \(0.837931\pi\) | |||||||
\(368\) | −7.50670 | + | 4.33399i | −0.391314 | + | 0.225925i | ||||
\(369\) | − | 4.64516i | − | 0.241817i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.946862 | − | 0.546671i | 0.0491586 | − | 0.0283817i | ||||
\(372\) | 10.1321 | 0.525324 | ||||||||
\(373\) | −2.21484 | + | 1.27874i | −0.114680 | + | 0.0662106i | −0.556243 | − | 0.831020i | \(-0.687758\pi\) |
0.441563 | + | 0.897230i | \(0.354424\pi\) | |||||||
\(374\) | 9.22671 | − | 15.9811i | 0.477102 | − | 0.826365i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.10926 | −0.469774 | ||||||||
\(377\) | −7.28610 | − | 0.326261i | −0.375253 | − | 0.0168033i | ||||
\(378\) | − | 1.32258i | − | 0.0680262i | ||||||
\(379\) | 13.0846 | + | 7.55440i | 0.672111 | + | 0.388044i | 0.796876 | − | 0.604143i | \(-0.206484\pi\) |
−0.124765 | + | 0.992186i | \(0.539818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.73592 | + | 9.93490i | 0.293860 | + | 0.508980i | ||||
\(382\) | −9.74715 | −0.498707 | ||||||||
\(383\) | −9.36517 | − | 16.2210i | −0.478538 | − | 0.828852i | 0.521159 | − | 0.853459i | \(-0.325500\pi\) |
−0.999697 | + | 0.0246073i | \(0.992166\pi\) | |||||||
\(384\) | 0.866025 | − | 0.500000i | 0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.88130 | + | 11.9188i | 0.350249 | + | 0.606649i | ||||
\(387\) | −7.45269 | − | 4.30281i | −0.378841 | − | 0.218724i | ||||
\(388\) | 4.40947 | − | 7.63743i | 0.223857 | − | 0.387732i | ||||
\(389\) | −6.96899 | −0.353342 | −0.176671 | − | 0.984270i | \(-0.556533\pi\) | ||||
−0.176671 | + | 0.984270i | \(0.556533\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.6719 | 1.75344 | ||||||||
\(392\) | 2.62539 | − | 4.54731i | 0.132602 | − | 0.229674i | ||||
\(393\) | 13.8482 | + | 7.99528i | 0.698551 | + | 0.403309i | ||||
\(394\) | −5.07076 | − | 8.78282i | −0.255461 | − | 0.442472i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.99528 | + | 2.30668i | −0.200771 | + | 0.115915i | ||||
\(397\) | 9.28606 | + | 16.0839i | 0.466054 | + | 0.807229i | 0.999248 | − | 0.0387637i | \(-0.0123420\pi\) |
−0.533195 | + | 0.845993i | \(0.679009\pi\) | |||||||
\(398\) | 9.57336 | 0.479869 | ||||||||
\(399\) | −1.51487 | − | 2.62383i | −0.0758382 | − | 0.131356i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.7126 | − | 14.8452i | −1.28403 | − | 0.741333i | −0.306444 | − | 0.951889i | \(-0.599139\pi\) |
−0.977582 | + | 0.210556i | \(0.932473\pi\) | |||||||
\(402\) | 3.18106i | 0.158657i | ||||||||
\(403\) | 32.4229 | − | 16.8323i | 1.61510 | − | 0.838478i | ||||
\(404\) | 7.22671 | 0.359542 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.33767 | + | 2.31692i | −0.0663877 | + | 0.114987i | ||||
\(407\) | −27.2059 | + | 15.7073i | −1.34855 | + | 0.778584i | ||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | 21.0752 | − | 12.1678i | 1.04210 | − | 0.601657i | 0.121673 | − | 0.992570i | \(-0.461174\pi\) |
0.920427 | + | 0.390913i | \(0.127841\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.0697i | 0.792661i | ||||||||
\(412\) | −15.9349 | + | 9.20002i | −0.785056 | + | 0.453252i | ||||
\(413\) | 3.59826 | + | 2.07746i | 0.177059 | + | 0.102225i | ||||
\(414\) | −7.50670 | − | 4.33399i | −0.368934 | − | 0.213004i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.94065 | − | 3.03873i | 0.0951483 | − | 0.148986i | ||||
\(417\) | − | 9.32258i | − | 0.456529i | ||||||
\(418\) | −5.28408 | + | 9.15229i | −0.258453 | + | 0.447653i | ||||
\(419\) | −1.44128 | + | 2.49636i | −0.0704109 | + | 0.121955i | −0.899081 | − | 0.437781i | \(-0.855764\pi\) |
0.828671 | + | 0.559737i | \(0.189098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.94707i | − | 0.241106i | −0.992707 | − | 0.120553i | \(-0.961533\pi\) | ||
0.992707 | − | 0.120553i | \(-0.0384667\pi\) | |||||||
\(422\) | 0.542594 | + | 0.939800i | 0.0264131 | + | 0.0457488i | ||||
\(423\) | −4.55463 | − | 7.88885i | −0.221454 | − | 0.383569i | ||||
\(424\) | 0.826674i | 0.0401468i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.66799 | + | 9.81724i | −0.274615 | + | 0.475647i | ||||
\(427\) | −0.354384 | + | 0.613811i | −0.0171499 | + | 0.0297044i | ||||
\(428\) | − | 3.07180i | − | 0.148481i | ||||||
\(429\) | −8.95292 | + | 14.0187i | −0.432251 | + | 0.676831i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3829 | − | 8.88130i | −0.740967 | − | 0.427797i | 0.0814539 | − | 0.996677i | \(-0.474044\pi\) |
−0.822421 | + | 0.568880i | \(0.807377\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | −31.0362 | + | 17.9188i | −1.49151 | + | 0.861121i | −0.999953 | − | 0.00972676i | \(-0.996904\pi\) |
−0.491553 | + | 0.870848i | \(0.663570\pi\) | |||||||
\(434\) | − | 13.4005i | − | 0.643244i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.4547 | + | 6.61335i | −0.548579 | + | 0.316722i | ||||
\(437\) | −19.8564 | −0.949861 | ||||||||
\(438\) | 5.44128 | − | 3.14152i | 0.259994 | − | 0.150108i | ||||
\(439\) | −5.04520 | + | 8.73854i | −0.240794 | + | 0.417068i | −0.960941 | − | 0.276754i | \(-0.910741\pi\) |
0.720147 | + | 0.693822i | \(0.244075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.25078 | 0.250037 | ||||||||
\(442\) | −12.8001 | + | 6.64516i | −0.608837 | + | 0.316078i | ||||
\(443\) | 13.6981i | 0.650816i | 0.945574 | + | 0.325408i | \(0.105502\pi\) | ||||
−0.945574 | + | 0.325408i | \(0.894498\pi\) | |||||||
\(444\) | 5.89721 | + | 3.40475i | 0.279869 | + | 0.161582i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.4708 | − | 21.6001i | −0.590509 | − | 1.02279i | ||||
\(447\) | 4.08519 | 0.193223 | ||||||||
\(448\) | −0.661290 | − | 1.14539i | −0.0312430 | − | 0.0541145i | ||||
\(449\) | −13.2613 | + | 7.65639i | −0.625837 | + | 0.361327i | −0.779138 | − | 0.626852i | \(-0.784343\pi\) |
0.153301 | + | 0.988180i | \(0.451010\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.7149 | + | 18.5587i | 0.504544 | + | 0.873896i | ||||
\(452\) | 7.00306 | + | 4.04322i | 0.329396 | + | 0.190177i | ||||
\(453\) | −9.99057 | + | 17.3042i | −0.469398 | + | 0.813021i | ||||
\(454\) | −19.3205 | −0.906756 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.29078 | 0.107275 | ||||||||
\(457\) | −7.77770 | + | 13.4714i | −0.363826 | + | 0.630164i | −0.988587 | − | 0.150651i | \(-0.951863\pi\) |
0.624761 | + | 0.780816i | \(0.285196\pi\) | |||||||
\(458\) | 3.59826 | + | 2.07746i | 0.168136 | + | 0.0970732i | ||||
\(459\) | −2.00000 | − | 3.46410i | −0.0933520 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.5473 | − | 7.82154i | 0.630961 | − | 0.364286i | −0.150163 | − | 0.988661i | \(-0.547980\pi\) |
0.781124 | + | 0.624376i | \(0.214647\pi\) | |||||||
\(462\) | 3.05076 | + | 5.28408i | 0.141934 | + | 0.245838i | ||||
\(463\) | −13.7170 | −0.637481 | −0.318741 | − | 0.947842i | \(-0.603260\pi\) | ||||
−0.318741 | + | 0.947842i | \(0.603260\pi\) | |||||||
\(464\) | −1.01141 | − | 1.75182i | −0.0469537 | − | 0.0813261i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.6934 | − | 8.48325i | −0.680659 | − | 0.392979i | ||||
\(467\) | 0.943666i | 0.0436677i | 0.999762 | + | 0.0218338i | \(0.00695048\pi\) | ||||
−0.999762 | + | 0.0218338i | \(0.993050\pi\) | |||||||
\(468\) | 3.60194 | + | 0.161290i | 0.166500 | + | 0.00745563i | ||||
\(469\) | 4.20720 | 0.194271 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.56690 | + | 6.17804i | −0.164354 | + | 0.284669i | ||||
\(472\) | −2.72064 | + | 1.57076i | −0.125228 | + | 0.0723001i | ||||
\(473\) | 39.7008 | 1.82544 | ||||||||
\(474\) | −2.57014 | + | 1.48387i | −0.118050 | + | 0.0681564i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.29032i | 0.242481i | ||||||||
\(477\) | −0.715920 | + | 0.413337i | −0.0327797 | + | 0.0189254i | ||||
\(478\) | −5.49420 | − | 3.17208i | −0.251299 | − | 0.145088i | ||||
\(479\) | 9.61460 | + | 5.55099i | 0.439302 | + | 0.253631i | 0.703302 | − | 0.710892i | \(-0.251708\pi\) |
−0.263999 | + | 0.964523i | \(0.585042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5275 | + | 1.09830i | 1.11836 | + | 0.0500784i | ||||
\(482\) | 24.1855i | 1.10162i | ||||||||
\(483\) | −5.73205 | + | 9.92820i | −0.260817 | + | 0.451749i | ||||
\(484\) | 5.14152 | − | 8.90538i | 0.233706 | − | 0.404790i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 16.4708 | + | 28.5283i | 0.746363 | + | 1.29274i | 0.949555 | + | 0.313600i | \(0.101535\pi\) |
−0.203192 | + | 0.979139i | \(0.565132\pi\) | |||||||
\(488\) | −0.267949 | − | 0.464102i | −0.0121295 | − | 0.0210089i | ||||
\(489\) | 9.89470i | 0.447454i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2257 | − | 24.6396i | 0.641996 | − | 1.11197i | −0.342991 | − | 0.939339i | \(-0.611440\pi\) |
0.984987 | − | 0.172630i | \(-0.0552266\pi\) | |||||||
\(492\) | 2.32258 | − | 4.02283i | 0.104710 | − | 0.181363i | ||||
\(493\) | 8.09130i | 0.364414i | ||||||||
\(494\) | 7.33052 | − | 3.80564i | 0.329816 | − | 0.171224i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.77464 | + | 5.06604i | 0.393993 | + | 0.227472i | ||||
\(497\) | 12.9841 | + | 7.49636i | 0.582416 | + | 0.336258i | ||||
\(498\) | −13.7454 | + | 7.93593i | −0.615948 | + | 0.355618i | ||||
\(499\) | 4.10926i | 0.183956i | 0.995761 | + | 0.0919779i | \(0.0293189\pi\) | ||||
−0.995761 | + | 0.0919779i | \(0.970681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.8171 | + | 12.0187i | −0.930037 | + | 0.536957i | ||||
\(502\) | −8.82497 | −0.393878 | ||||||||
\(503\) | 4.96753 | − | 2.86800i | 0.221491 | − | 0.127878i | −0.385149 | − | 0.922854i | \(-0.625850\pi\) |
0.606641 | + | 0.794976i | \(0.292517\pi\) | |||||||
\(504\) | 0.661290 | − | 1.14539i | 0.0294562 | − | 0.0510196i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 39.9885 | 1.77771 | ||||||||
\(507\) | 11.7942 | − | 5.46774i | 0.523800 | − | 0.242831i | ||||
\(508\) | 11.4718i | 0.508980i | ||||||||
\(509\) | 13.1129 | + | 7.57076i | 0.581221 | + | 0.335568i | 0.761618 | − | 0.648026i | \(-0.224405\pi\) |
−0.180397 | + | 0.983594i | \(0.557738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.15491 | − | 7.19652i | −0.183803 | − | 0.318355i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.14539 | + | 1.98387i | 0.0505701 | + | 0.0875900i | ||||
\(514\) | 7.26157 | − | 4.19247i | 0.320294 | − | 0.184922i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.30281 | − | 7.45269i | −0.189421 | − | 0.328086i | ||||
\(517\) | 36.3941 | + | 21.0121i | 1.60061 | + | 0.924112i | ||||
\(518\) | 4.50306 | − | 7.79953i | 0.197853 | − | 0.342691i | ||||
\(519\) | 2.52817 | 0.110974 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.93027 | 0.391242 | 0.195621 | − | 0.980680i | \(-0.437328\pi\) | ||||
0.195621 | + | 0.980680i | \(0.437328\pi\) | |||||||
\(522\) | 1.01141 | − | 1.75182i | 0.0442683 | − | 0.0766750i | ||||
\(523\) | 8.50166 | + | 4.90844i | 0.371752 | + | 0.214631i | 0.674223 | − | 0.738527i | \(-0.264478\pi\) |
−0.302472 | + | 0.953158i | \(0.597812\pi\) | |||||||
\(524\) | 7.99528 | + | 13.8482i | 0.349276 | + | 0.604963i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.66389 | − | 0.960648i | 0.0725491 | − | 0.0418863i | ||||
\(527\) | −20.2642 | − | 35.0986i | −0.882721 | − | 1.52892i | ||||
\(528\) | −4.61335 | −0.200771 | ||||||||
\(529\) | 26.0670 | + | 45.1493i | 1.13335 | + | 1.96301i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.72064 | − | 1.57076i | −0.118066 | − | 0.0681652i | ||||
\(532\) | − | 3.02973i | − | 0.131356i | ||||||
\(533\) | 0.749217 | − | 16.7316i | 0.0324522 | − | 0.724726i | ||||
\(534\) | −11.8641 | −0.513411 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.59053 | + | 2.75488i | −0.0687004 | + | 0.118993i | ||||
\(537\) | −5.43490 | + | 3.13784i | −0.234533 | + | 0.135408i | ||||
\(538\) | 32.3098 | 1.39298 | ||||||||
\(539\) | −20.9784 | + | 12.1119i | −0.903602 | + | 0.521695i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.80826i | 0.163730i | 0.996643 | + | 0.0818650i | \(0.0260876\pi\) | ||||
−0.996643 | + | 0.0818650i | \(0.973912\pi\) | |||||||
\(542\) | −20.3105 | + | 11.7263i | −0.872413 | + | 0.503688i | ||||
\(543\) | 10.6374 | + | 6.14152i | 0.456496 | + | 0.263558i | ||||
\(544\) | −3.46410 | − | 2.00000i | −0.148522 | − | 0.0857493i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.213319 | − | 4.76386i | 0.00912920 | − | 0.203874i | ||||
\(547\) | − | 45.5847i | − | 1.94906i | −0.224257 | − | 0.974530i | \(-0.571995\pi\) | ||
0.224257 | − | 0.974530i | \(-0.428005\pi\) | |||||||
\(548\) | −8.03486 | + | 13.9168i | −0.343232 | + | 0.594496i | ||||
\(549\) | 0.267949 | − | 0.464102i | 0.0114358 | − | 0.0198074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 4.63384i | − | 0.197408i | ||||||
\(552\) | −4.33399 | − | 7.50670i | −0.184467 | − | 0.319506i | ||||
\(553\) | 1.96254 | + | 3.39921i | 0.0834555 | + | 0.144549i | ||||
\(554\) | − | 9.00566i | − | 0.382614i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.66129 | − | 8.07359i | 0.197683 | − | 0.342397i | ||||
\(557\) | −18.4296 | + | 31.9209i | −0.780885 | + | 1.35253i | 0.150541 | + | 0.988604i | \(0.451898\pi\) |
−0.931427 | + | 0.363929i | \(0.881435\pi\) | |||||||
\(558\) | 10.1321i | 0.428925i | ||||||||
\(559\) | −26.1502 | − | 16.7005i | −1.10603 | − | 0.706357i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.9811 | + | 9.22671i | 0.674724 | + | 0.389552i | ||||
\(562\) | −1.48693 | − | 0.858478i | −0.0627223 | − | 0.0362127i | ||||
\(563\) | −29.2491 | + | 16.8870i | −1.23270 | + | 0.711701i | −0.967592 | − | 0.252518i | \(-0.918741\pi\) |
−0.265109 | + | 0.964218i | \(0.585408\pi\) | |||||||
\(564\) | − | 9.10926i | − | 0.383569i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.34172 | − | 0.774645i | 0.0563969 | − | 0.0325607i | ||||
\(567\) | 1.32258 | 0.0555431 | ||||||||
\(568\) | −9.81724 | + | 5.66799i | −0.411922 | + | 0.237823i | ||||
\(569\) | 12.7159 | − | 22.0246i | 0.533079 | − | 0.923320i | −0.466175 | − | 0.884693i | \(-0.654368\pi\) |
0.999254 | − | 0.0386274i | \(-0.0122985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.3682 | 0.559443 | 0.279722 | − | 0.960081i | \(-0.409758\pi\) | ||||
0.279722 | + | 0.960081i | \(0.409758\pi\) | |||||||
\(572\) | −14.7628 | + | 7.66412i | −0.617264 | + | 0.320453i | ||||
\(573\) | − | 9.74715i | − | 0.407193i | ||||||
\(574\) | −5.32051 | − | 3.07180i | −0.222074 | − | 0.128214i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −9.57428 | −0.398582 | −0.199291 | − | 0.979940i | \(-0.563864\pi\) | ||||
−0.199291 | + | 0.979940i | \(0.563864\pi\) | |||||||
\(578\) | −0.500000 | − | 0.866025i | −0.0207973 | − | 0.0360219i | ||||
\(579\) | −11.9188 | + | 6.88130i | −0.495327 | + | 0.285977i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.4959 | + | 18.1794i | 0.435444 | + | 0.754210i | ||||
\(582\) | 7.63743 | + | 4.40947i | 0.316582 | + | 0.182778i | ||||
\(583\) | 1.90687 | − | 3.30279i | 0.0789745 | − | 0.136788i | ||||
\(584\) | 6.28304 | 0.259994 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.4057 | −1.25605 | ||||||||
\(587\) | 0.700246 | − | 1.21286i | 0.0289023 | − | 0.0500602i | −0.851212 | − | 0.524821i | \(-0.824132\pi\) |
0.880115 | + | 0.474761i | \(0.157466\pi\) | |||||||
\(588\) | 4.54731 | + | 2.62539i | 0.187528 | + | 0.108269i | ||||
\(589\) | 11.6052 | + | 20.1007i | 0.478183 | + | 0.828237i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.78282 | − | 5.07076i | 0.361277 | − | 0.208583i | ||||
\(592\) | 3.40475 | + | 5.89721i | 0.139935 | + | 0.242374i | ||||
\(593\) | 10.7303 | 0.440643 | 0.220321 | − | 0.975427i | \(-0.429289\pi\) | ||||
0.220321 | + | 0.975427i | \(0.429289\pi\) | |||||||
\(594\) | −2.30668 | − | 3.99528i | −0.0946441 | − | 0.163928i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.53788 | + | 2.04259i | 0.144917 | + | 0.0836679i | ||||
\(597\) | 9.57336i | 0.391812i | ||||||||
\(598\) | −26.3397 | − | 16.8215i | −1.07711 | − | 0.687884i | ||||
\(599\) | 40.7967 | 1.66691 | 0.833453 | − | 0.552590i | \(-0.186360\pi\) | ||||
0.833453 | + | 0.552590i | \(0.186360\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.4416 | + | 37.1379i | −0.874621 | + | 1.51489i | −0.0174548 | + | 0.999848i | \(0.505556\pi\) |
−0.857166 | + | 0.515040i | \(0.827777\pi\) | |||||||
\(602\) | −9.85677 | + | 5.69081i | −0.401732 | + | 0.231940i | ||||
\(603\) | −3.18106 | −0.129543 | ||||||||
\(604\) | −17.3042 | + | 9.99057i | −0.704097 | + | 0.406510i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.22671i | 0.293565i | ||||||||
\(607\) | 5.95161 | − | 3.43616i | 0.241568 | − | 0.139470i | −0.374329 | − | 0.927296i | \(-0.622127\pi\) |
0.615897 | + | 0.787826i | \(0.288794\pi\) | |||||||
\(608\) | 1.98387 | + | 1.14539i | 0.0804565 | + | 0.0464516i | ||||
\(609\) | −2.31692 | − | 1.33767i | −0.0938863 | − | 0.0542053i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.1331 | − | 29.1498i | −0.612221 | − | 1.17927i | ||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | 0.380681 | − | 0.659358i | 0.0153755 | − | 0.0266312i | −0.858235 | − | 0.513257i | \(-0.828439\pi\) |
0.873611 | + | 0.486625i | \(0.161772\pi\) | |||||||
\(614\) | −4.91311 | + | 8.50975i | −0.198277 | + | 0.343426i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.10153i | 0.245838i | ||||||||
\(617\) | −12.3011 | − | 21.3061i | −0.495224 | − | 0.857753i | 0.504761 | − | 0.863259i | \(-0.331581\pi\) |
−0.999985 | + | 0.00550613i | \(0.998247\pi\) | |||||||
\(618\) | −9.20002 | − | 15.9349i | −0.370079 | − | 0.640996i | ||||
\(619\) | − | 17.2035i | − | 0.691468i | −0.938333 | − | 0.345734i | \(-0.887630\pi\) | ||
0.938333 | − | 0.345734i | \(-0.112370\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.33399 | − | 7.50670i | 0.173917 | − | 0.301233i | ||||
\(622\) | 1.70025 | − | 2.94491i | 0.0681737 | − | 0.118080i | ||||
\(623\) | 15.6913i | 0.628657i | ||||||||
\(624\) | 3.03873 | + | 1.94065i | 0.121646 | + | 0.0776883i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.0590 | + | 8.11699i | 0.561912 | + | 0.324420i | ||||
\(627\) | −9.15229 | − | 5.28408i | −0.365507 | − | 0.211026i | ||||
\(628\) | −6.17804 | + | 3.56690i | −0.246531 | + | 0.142335i | ||||
\(629\) | − | 27.2380i | − | 1.08605i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.08519 | − | 1.20388i | 0.0830100 | − | 0.0479259i | −0.457920 | − | 0.888993i | \(-0.651406\pi\) |
0.540930 | + | 0.841067i | \(0.318072\pi\) | |||||||
\(632\) | −2.96774 | −0.118050 | ||||||||
\(633\) | −0.939800 | + | 0.542594i | −0.0373537 | + | 0.0215662i | ||||
\(634\) | −11.7616 | + | 20.3716i | −0.467112 | + | 0.809061i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.826674 | −0.0327797 | ||||||||
\(637\) | 18.9130 | + | 0.846898i | 0.749361 | + | 0.0335553i | ||||
\(638\) | 9.33201i | 0.369458i | ||||||||
\(639\) | −9.81724 | − | 5.66799i | −0.388364 | − | 0.224222i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.73875 | − | 16.8680i | −0.384657 | − | 0.666246i | 0.607064 | − | 0.794653i | \(-0.292347\pi\) |
−0.991722 | + | 0.128407i | \(0.959014\pi\) | |||||||
\(642\) | 3.07180 | 0.121234 | ||||||||
\(643\) | −11.9772 | − | 20.7451i | −0.472334 | − | 0.818106i | 0.527165 | − | 0.849763i | \(-0.323255\pi\) |
−0.999499 | + | 0.0316570i | \(0.989922\pi\) | |||||||
\(644\) | −9.92820 | + | 5.73205i | −0.391226 | + | 0.225874i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.58155 | − | 7.93548i | −0.180259 | − | 0.312217i | ||||
\(647\) | −15.7710 | − | 9.10540i | −0.620022 | − | 0.357970i | 0.156855 | − | 0.987622i | \(-0.449864\pi\) |
−0.776878 | + | 0.629652i | \(0.783198\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 14.4930 | 0.568898 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.4005 | 0.525207 | ||||||||
\(652\) | −4.94735 | + | 8.56906i | −0.193753 | + | 0.335590i | ||||
\(653\) | 41.7065 | + | 24.0793i | 1.63210 | + | 0.942294i | 0.983444 | + | 0.181213i | \(0.0580024\pi\) |
0.648657 | + | 0.761081i | \(0.275331\pi\) | |||||||
\(654\) | −6.61335 | − | 11.4547i | −0.258603 | − | 0.447913i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.02283 | − | 2.32258i | 0.157065 | − | 0.0906815i | ||||
\(657\) | 3.14152 | + | 5.44128i | 0.122562 | + | 0.212284i | ||||
\(658\) | −12.0477 | −0.469669 | ||||||||
\(659\) | −18.4127 | − | 31.8917i | −0.717257 | − | 1.24233i | −0.962083 | − | 0.272758i | \(-0.912064\pi\) |
0.244826 | − | 0.969567i | \(-0.421269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5131 | − | 11.2659i | −0.758971 | − | 0.438192i | 0.0699555 | − | 0.997550i | \(-0.477714\pi\) |
−0.828926 | + | 0.559358i | \(0.811048\pi\) | |||||||
\(662\) | 18.0904i | 0.703103i | ||||||||
\(663\) | −6.64516 | − | 12.8001i | −0.258077 | − | 0.497114i | ||||
\(664\) | −15.8719 | −0.615948 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.40475 | + | 5.89721i | −0.131932 | + | 0.228512i | ||||
\(667\) | −15.1847 | + | 8.76691i | −0.587955 | + | 0.339456i | ||||
\(668\) | −24.0375 | −0.930037 | ||||||||
\(669\) | 21.6001 | − | 12.4708i | 0.835106 | − | 0.482149i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.47229i | 0.0954417i | ||||||||
\(672\) | 1.14539 | − | 0.661290i | 0.0441843 | − | 0.0255098i | ||||
\(673\) | 20.5627 | + | 11.8719i | 0.792633 | + | 0.457627i | 0.840889 | − | 0.541208i | \(-0.182033\pi\) |
−0.0482556 | + | 0.998835i | \(0.515366\pi\) | |||||||
\(674\) | −4.93548 | − | 2.84950i | −0.190108 | − | 0.109759i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.9480 | + | 1.16191i | 0.497999 | + | 0.0446890i | ||||
\(677\) | − | 1.16559i | − | 0.0447975i | −0.999749 | − | 0.0223987i | \(-0.992870\pi\) | ||
0.999749 | − | 0.0223987i | \(-0.00713033\pi\) | |||||||
\(678\) | −4.04322 | + | 7.00306i | −0.155279 | + | 0.268951i | ||||
\(679\) | 5.83188 | − | 10.1011i | 0.223807 | − | 0.387645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 19.3205i | − | 0.740363i | ||||||
\(682\) | −23.3715 | − | 40.4806i | −0.894939 | − | 1.55008i | ||||
\(683\) | 6.93593 | + | 12.0134i | 0.265396 | + | 0.459680i | 0.967667 | − | 0.252230i | \(-0.0811639\pi\) |
−0.702271 | + | 0.711910i | \(0.747831\pi\) | |||||||
\(684\) | 2.29078i | 0.0875900i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.10132 | − | 14.0319i | 0.309310 | − | 0.535740i | ||||
\(687\) | −2.07746 | + | 3.59826i | −0.0792599 | + | 0.137282i | ||||
\(688\) | − | 8.60562i | − | 0.328086i | ||||||
\(689\) | −2.64537 | + | 1.37334i | −0.100781 | + | 0.0523203i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.6967 | − | 20.6095i | −1.35797 | − | 0.784022i | −0.368616 | − | 0.929582i | \(-0.620168\pi\) |
−0.989349 | + | 0.145560i | \(0.953502\pi\) | |||||||
\(692\) | 2.18946 | + | 1.26408i | 0.0832307 | + | 0.0480532i | ||||
\(693\) | −5.28408 | + | 3.05076i | −0.200726 | + | 0.115889i | ||||
\(694\) | 15.7471i | 0.597753i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.75182 | − | 1.01141i | 0.0664025 | − | 0.0383375i | ||||
\(697\) | −18.5806 | −0.703792 | ||||||||
\(698\) | 13.2679 | − | 7.66025i | 0.502199 | − | 0.289945i | ||||
\(699\) | 8.48325 | − | 14.6934i | 0.320866 | − | 0.555756i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.0112 | −0.869122 | −0.434561 | − | 0.900642i | \(-0.643096\pi\) | ||||
−0.434561 | + | 0.900642i | \(0.643096\pi\) | |||||||
\(702\) | −0.161290 | + | 3.60194i | −0.00608749 | + | 0.135947i | ||||
\(703\) | 15.5991i | 0.588329i | ||||||||
\(704\) | −3.99528 | − | 2.30668i | −0.150578 | − | 0.0869362i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.599964 | − | 1.03917i | −0.0225799 | − | 0.0391096i | ||||
\(707\) | 9.55790 | 0.359462 | ||||||||
\(708\) | −1.57076 | − | 2.72064i | −0.0590328 | − | 0.102248i | ||||
\(709\) | 14.7944 | − | 8.54156i | 0.555616 | − | 0.320785i | −0.195768 | − | 0.980650i | \(-0.562720\pi\) |
0.751384 | + | 0.659865i | \(0.229387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.48387 | − | 2.57014i | −0.0556495 | − | 0.0963877i | ||||
\(712\) | −10.2746 | − | 5.93207i | −0.385059 | − | 0.222314i | ||||
\(713\) | 43.9124 | − | 76.0585i | 1.64453 | − | 2.84841i | ||||
\(714\) | −5.29032 | −0.197985 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.27568 | −0.234533 | ||||||||
\(717\) | 3.17208 | − | 5.49420i | 0.118463 | − | 0.205185i | ||||
\(718\) | 14.1015 | + | 8.14152i | 0.526264 | + | 0.303839i | ||||
\(719\) | 21.8564 | + | 37.8564i | 0.815106 | + | 1.41181i | 0.909251 | + | 0.416247i | \(0.136655\pi\) |
−0.0941451 | + | 0.995558i | \(0.530012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.0752 | + | 12.1678i | −0.784880 | + | 0.453151i | ||||
\(722\) | −6.87617 | − | 11.9099i | −0.255905 | − | 0.443240i | ||||
\(723\) | −24.1855 | −0.899467 | ||||||||
\(724\) | 6.14152 | + | 10.6374i | 0.228248 | + | 0.395337i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.90538 | + | 5.14152i | 0.330510 | + | 0.190820i | ||||
\(727\) | − | 31.8453i | − | 1.18108i | −0.807010 | − | 0.590538i | \(-0.798916\pi\) | ||
0.807010 | − | 0.590538i | \(-0.201084\pi\) | |||||||
\(728\) | 2.56667 | − | 4.01896i | 0.0951270 | − | 0.148953i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.2112 | + | 29.8108i | −0.636581 | + | 1.10259i | ||||
\(732\) | 0.464102 | − | 0.267949i | 0.0171537 | − | 0.00990369i | ||||
\(733\) | 5.96774 | 0.220423 | 0.110212 | − | 0.993908i | \(-0.464847\pi\) | ||||
0.110212 | + | 0.993908i | \(0.464847\pi\) | |||||||
\(734\) | 17.0040 | − | 9.81724i | 0.627627 | − | 0.362361i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 8.66799i | − | 0.319506i | ||||||
\(737\) | 12.7092 | − | 7.33767i | 0.468150 | − | 0.270287i | ||||
\(738\) | 4.02283 | + | 2.32258i | 0.148082 | + | 0.0854953i | ||||
\(739\) | −9.37833 | − | 5.41458i | −0.344988 | − | 0.199179i | 0.317488 | − | 0.948262i | \(-0.397161\pi\) |
−0.662475 | + | 0.749084i | \(0.730494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.80564 | + | 7.33052i | 0.139804 | + | 0.269293i | ||||
\(742\) | 1.09334i | 0.0401378i | ||||||||
\(743\) | −9.92515 | + | 17.1909i | −0.364118 | + | 0.630671i | −0.988634 | − | 0.150341i | \(-0.951963\pi\) |
0.624516 | + | 0.781012i | \(0.285296\pi\) | |||||||
\(744\) | −5.06604 | + | 8.77464i | −0.185730 | + | 0.321694i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 2.55748i | − | 0.0936359i | ||||||
\(747\) | −7.93593 | − | 13.7454i | −0.290361 | − | 0.502919i | ||||
\(748\) | 9.22671 | + | 15.9811i | 0.337362 | + | 0.584328i | ||||
\(749\) | − | 4.06270i | − | 0.148448i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.66538 | + | 13.2768i | −0.279714 | + | 0.484479i | −0.971314 | − | 0.237802i | \(-0.923573\pi\) |
0.691600 | + | 0.722281i | \(0.256906\pi\) | |||||||
\(752\) | 4.55463 | − | 7.88885i | 0.166090 | − | 0.287677i | ||||
\(753\) | − | 8.82497i | − | 0.321600i | ||||||
\(754\) | 3.92560 | − | 6.14682i | 0.142962 | − | 0.223854i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.14539 | + | 0.661290i | 0.0416573 | + | 0.0240509i | ||||
\(757\) | 39.1125 | + | 22.5816i | 1.42157 | + | 0.820744i | 0.996433 | − | 0.0843855i | \(-0.0268927\pi\) |
0.425137 | + | 0.905129i | \(0.360226\pi\) | |||||||
\(758\) | −13.0846 | + | 7.55440i | −0.475254 | + | 0.274388i | ||||
\(759\) | 39.9885i | 1.45149i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.7978 | + | 10.8529i | −0.681419 | + | 0.393418i | −0.800390 | − | 0.599480i | \(-0.795374\pi\) |
0.118970 | + | 0.992898i | \(0.462041\pi\) | |||||||
\(762\) | −11.4718 | −0.415581 | ||||||||
\(763\) | −15.1497 | + | 8.74669i | −0.548456 | + | 0.316651i | ||||
\(764\) | 4.87357 | − | 8.44128i | 0.176320 | − | 0.305395i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.7303 | 0.676755 | ||||||||
\(767\) | −9.54623 | − | 6.09660i | −0.344694 | − | 0.220136i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −36.4711 | − | 21.0566i | −1.31518 | − | 0.759321i | −0.332233 | − | 0.943197i | \(-0.607802\pi\) |
−0.982949 | + | 0.183877i | \(0.941135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.19247 | + | 7.26157i | 0.150988 | + | 0.261519i | ||||
\(772\) | −13.7626 | −0.495327 | ||||||||
\(773\) | 14.8803 | + | 25.7734i | 0.535206 | + | 0.927004i | 0.999153 | + | 0.0411413i | \(0.0130994\pi\) |
−0.463947 | + | 0.885863i | \(0.653567\pi\) | |||||||
\(774\) | 7.45269 | − | 4.30281i | 0.267881 | − | 0.154661i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.40947 | + | 7.63743i | 0.158291 | + | 0.274168i | ||||
\(777\) | 7.79953 | + | 4.50306i | 0.279806 | + | 0.161546i | ||||
\(778\) | 3.48449 | − | 6.03532i | 0.124925 | − | 0.216377i | ||||
\(779\) | 10.6410 | 0.381254 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.2969 | 1.87133 | ||||||||
\(782\) | −17.3360 | + | 30.0268i | −0.619933 | + | 1.07376i | ||||
\(783\) | 1.75182 | + | 1.01141i | 0.0626049 | + | 0.0361450i | ||||
\(784\) | 2.62539 | + | 4.54731i | 0.0937640 | + | 0.162404i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.8482 | + | 7.99528i | −0.493950 | + | 0.285182i | ||||
\(787\) | 20.5224 | + | 35.5459i | 0.731545 | + | 1.26707i | 0.956223 | + | 0.292640i | \(0.0945338\pi\) |
−0.224678 | + | 0.974433i | \(0.572133\pi\) | |||||||
\(788\) | 10.1415 | 0.361277 | ||||||||
\(789\) | 0.960648 | + | 1.66389i | 0.0342000 | + | 0.0592361i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.26210 | + | 5.34748i | 0.329322 | + | 0.190134i | ||||
\(792\) | − | 4.61335i | − | 0.163928i | ||||||
\(793\) | 1.03999 | − | 1.62845i | 0.0369312 | − | 0.0578279i | ||||
\(794\) | −18.5721 | −0.659100 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.78668 | + | 8.29078i | −0.169659 | + | 0.293859i | ||||
\(797\) | 39.1899 | − | 22.6263i | 1.38818 | − | 0.801464i | 0.395067 | − | 0.918652i | \(-0.370721\pi\) |
0.993110 | + | 0.117188i | \(0.0373880\pi\) | |||||||
\(798\) | 3.02973 | 0.107251 | ||||||||
\(799\) | −31.5554 | + | 18.2185i | −1.11635 | + | 0.644525i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 11.8641i | − | 0.419199i | ||||||
\(802\) | 25.7126 | − | 14.8452i | 0.907944 | − | 0.524201i | ||||
\(803\) | −25.1025 | − | 14.4930i | −0.885849 | − | 0.511445i | ||||
\(804\) | −2.75488 | − | 1.59053i | −0.0971570 | − | 0.0560936i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.63420 | + | 36.4952i | −0.0575623 | + | 1.28549i | ||||
\(807\) | 32.3098i | 1.13736i | ||||||||
\(808\) | −3.61335 | + | 6.25851i | −0.127117 | + | 0.220174i | ||||
\(809\) | −14.2267 | + | 24.6414i | −0.500184 | + | 0.866345i | 0.499815 | + | 0.866132i | \(0.333401\pi\) |
−1.00000 | 0.000213036i | \(0.999932\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 44.4114i | − | 1.55949i | −0.626095 | − | 0.779747i | \(-0.715348\pi\) | ||
0.626095 | − | 0.779747i | \(-0.284652\pi\) | |||||||
\(812\) | −1.33767 | − | 2.31692i | −0.0469432 | − | 0.0813079i | ||||
\(813\) | −11.7263 | − | 20.3105i | −0.411259 | − | 0.712322i | ||||
\(814\) | − | 31.4147i | − | 1.10108i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | − | 3.46410i | 0.0700140 | − | 0.121268i | ||||
\(817\) | 9.85677 | − | 17.0724i | 0.344845 | − | 0.597289i | ||||
\(818\) | 24.3355i | 0.850871i | ||||||||
\(819\) | 4.76386 | + | 0.213319i | 0.166463 | + | 0.00745396i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.1169 | − | 22.5842i | −1.36519 | − | 0.788192i | −0.374880 | − | 0.927073i | \(-0.622316\pi\) |
−0.990309 | + | 0.138881i | \(0.955649\pi\) | |||||||
\(822\) | −13.9168 | − | 8.03486i | −0.485404 | − | 0.280248i | ||||
\(823\) | −2.09404 | + | 1.20900i | −0.0729938 | + | 0.0421430i | −0.536053 | − | 0.844185i | \(-0.680085\pi\) |
0.463059 | + | 0.886328i | \(0.346752\pi\) | |||||||
\(824\) | − | 18.4000i | − | 0.640996i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.59826 | + | 2.07746i | −0.125199 | + | 0.0722840i | ||||
\(827\) | 4.26832 | 0.148424 | 0.0742120 | − | 0.997242i | \(-0.476356\pi\) | ||||
0.0742120 | + | 0.997242i | \(0.476356\pi\) | |||||||
\(828\) | 7.50670 | − | 4.33399i | 0.260876 | − | 0.150617i | ||||
\(829\) | 21.4926 | − | 37.2263i | 0.746468 | − | 1.29292i | −0.203037 | − | 0.979171i | \(-0.565081\pi\) |
0.949506 | − | 0.313750i | \(-0.101585\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.00566 | 0.312403 | ||||||||
\(832\) | 1.66129 | + | 3.20002i | 0.0575949 | + | 0.110941i | ||||
\(833\) | − | 21.0031i | − | 0.727715i | ||||||
\(834\) | 8.07359 | + | 4.66129i | 0.279566 | + | 0.161407i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.28408 | − | 9.15229i | −0.182754 | − | 0.316539i | ||||
\(837\) | −10.1321 | −0.350216 | ||||||||
\(838\) | −1.44128 | − | 2.49636i | −0.0497880 | − | 0.0862354i | ||||
\(839\) | 20.1798 | − | 11.6508i | 0.696684 | − | 0.402231i | −0.109427 | − | 0.993995i | \(-0.534902\pi\) |
0.806111 | + | 0.591764i | \(0.201568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4541 | + | 21.5711i | 0.429451 | + | 0.743831i | ||||
\(842\) | 4.28429 | + | 2.47354i | 0.147646 | + | 0.0852437i | ||||
\(843\) | 0.858478 | − | 1.48693i | 0.0295676 | − | 0.0512125i | ||||
\(844\) | −1.08519 | −0.0373537 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.10926 | 0.313183 | ||||||||
\(847\) | 6.80007 | − | 11.7781i | 0.233653 | − | 0.404699i | ||||
\(848\) | −0.715920 | − | 0.413337i | −0.0245848 | − | 0.0141940i | ||||
\(849\) | 0.774645 | + | 1.34172i | 0.0265857 | + | 0.0460479i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.1169 | − | 29.5124i | 1.75226 | − | 1.01167i | ||||
\(852\) | −5.66799 | − | 9.81724i | −0.194182 | − | 0.336333i | ||||
\(853\) | −20.8418 | −0.713609 | −0.356804 | − | 0.934179i | \(-0.616134\pi\) | ||||
−0.356804 | + | 0.934179i | \(0.616134\pi\) | |||||||
\(854\) | −0.354384 | − | 0.613811i | −0.0121268 | − | 0.0210042i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.66025 | + | 1.53590i | 0.0909256 | + | 0.0524959i | ||||
\(857\) | − | 36.7250i | − | 1.25450i | −0.778818 | − | 0.627250i | \(-0.784180\pi\) | ||
0.778818 | − | 0.627250i | \(-0.215820\pi\) | |||||||
\(858\) | −7.66412 | − | 14.7628i | −0.261649 | − | 0.503994i | ||||
\(859\) | −0.914812 | −0.0312130 | −0.0156065 | − | 0.999878i | \(-0.504968\pi\) | ||||
−0.0156065 | + | 0.999878i | \(0.504968\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.07180 | − | 5.32051i | 0.104687 | − | 0.181322i | ||||
\(862\) | 15.3829 | − | 8.88130i | 0.523943 | − | 0.302498i | ||||
\(863\) | −33.6104 | −1.14411 | −0.572056 | − | 0.820215i | \(-0.693854\pi\) | ||||
−0.572056 | + | 0.820215i | \(0.693854\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 35.8375i | − | 1.21781i | ||||||
\(867\) | 0.866025 | − | 0.500000i | 0.0294118 | − | 0.0169809i | ||||
\(868\) | 11.6052 | + | 6.70025i | 0.393905 | + | 0.227421i | ||||
\(869\) | 11.8570 | + | 6.84562i | 0.402220 | + | 0.232222i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.4580 | − | 0.513072i | −0.388239 | − | 0.0173848i | ||||
\(872\) | − | 13.2267i | − | 0.447913i | ||||||
\(873\) | −4.40947 | + | 7.63743i | −0.149238 | + | 0.258488i | ||||
\(874\) | 9.92820 | − | 17.1962i | 0.335826 | − | 0.581669i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.28304i | 0.212284i | ||||||||
\(877\) | 12.1607 | + | 21.0629i | 0.410637 | + | 0.711243i | 0.994959 | − | 0.100278i | \(-0.0319732\pi\) |
−0.584323 | + | 0.811521i | \(0.698640\pi\) | |||||||
\(878\) | −5.04520 | − | 8.73854i | −0.170267 | − | 0.294911i | ||||
\(879\) | − | 30.4057i | − | 1.02556i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.95207 | + | 8.57723i | −0.166839 | + | 0.288974i | −0.937307 | − | 0.348505i | \(-0.886689\pi\) |
0.770468 | + | 0.637479i | \(0.220023\pi\) | |||||||
\(882\) | −2.62539 | + | 4.54731i | −0.0884015 | + | 0.153116i | ||||
\(883\) | − | 43.9718i | − | 1.47977i | −0.672734 | − | 0.739884i | \(-0.734880\pi\) | ||
0.672734 | − | 0.739884i | \(-0.265120\pi\) | |||||||
\(884\) | 0.645159 | − | 14.4078i | 0.0216991 | − | 0.484586i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.8629 | − | 6.84904i | −0.398542 | − | 0.230098i | ||||
\(887\) | 43.7875 | + | 25.2807i | 1.47024 | + | 0.848843i | 0.999442 | − | 0.0333988i | \(-0.0106332\pi\) |
0.470797 | + | 0.882242i | \(0.343966\pi\) | |||||||
\(888\) | −5.89721 | + | 3.40475i | −0.197897 | + | 0.114256i | ||||
\(889\) | 15.1724i | 0.508866i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.99528 | − | 2.30668i | 0.133847 | − | 0.0772766i | ||||
\(892\) | 24.9416 | 0.835106 | ||||||||
\(893\) | 18.0716 | − | 10.4336i | 0.604743 | − | 0.349148i | ||||
\(894\) | −2.04259 | + | 3.53788i | −0.0683146 | + | 0.118324i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.32258 | 0.0441843 | ||||||||
\(897\) | 16.8215 | − | 26.3397i | 0.561655 | − | 0.879455i | ||||
\(898\) | − | 15.3128i | − | 0.510994i | ||||||
\(899\) | 17.7496 | + | 10.2477i | 0.591982 | + | 0.341781i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.65335 | + | 2.86368i | 0.0550810 | + | 0.0954031i | ||||
\(902\) | −21.4298 | −0.713533 | ||||||||
\(903\) | −5.69081 | − | 9.85677i | −0.189378 | − | 0.328013i | ||||
\(904\) | −7.00306 | + | 4.04322i | −0.232918 | + | 0.134475i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.99057 | − | 17.3042i | −0.331914 | − | 0.574892i | ||||
\(907\) | −12.3352 | − | 7.12175i | −0.409585 | − | 0.236474i | 0.281026 | − | 0.959700i | \(-0.409325\pi\) |
−0.690611 | + | 0.723226i | \(0.742658\pi\) | |||||||
\(908\) | 9.66025 | − | 16.7321i | 0.320587 | − | 0.555273i | ||||
\(909\) | −7.22671 | −0.239695 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.8108 | 0.722623 | 0.361311 | − | 0.932445i | \(-0.382329\pi\) | ||||
0.361311 | + | 0.932445i | \(0.382329\pi\) | |||||||
\(912\) | −1.14539 | + | 1.98387i | −0.0379276 | + | 0.0656925i | ||||
\(913\) | 63.4126 | + | 36.6113i | 2.09865 | + | 1.21166i | ||||
\(914\) | −7.77770 | − | 13.4714i | −0.257264 | − | 0.445594i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.59826 | + | 2.07746i | −0.118890 | + | 0.0686411i | ||||
\(917\) | 10.5744 | + | 18.3154i | 0.349197 | + | 0.604828i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | −2.65289 | − | 4.59494i | −0.0875108 | − | 0.151573i | 0.818948 | − | 0.573868i | \(-0.194558\pi\) |
−0.906458 | + | 0.422295i | \(0.861225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.50975 | − | 4.91311i | −0.280406 | − | 0.161892i | ||||
\(922\) | 15.6431i | 0.515178i | ||||||||
\(923\) | −34.4469 | − | 21.9992i | −1.13383 | − | 0.724112i | ||||
\(924\) | −6.10153 | −0.200726 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.85848 | − | 11.8792i | 0.225384 | − | 0.390376i | ||||
\(927\) | 15.9349 | − | 9.20002i | 0.523371 | − | 0.302168i | ||||
\(928\) | 2.02283 | 0.0664025 | ||||||||
\(929\) | 38.4002 | − | 22.1704i | 1.25987 | − | 0.727386i | 0.286821 | − | 0.957984i | \(-0.407401\pi\) |
0.973049 | + | 0.230598i | \(0.0740681\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0284i | 0.394214i | ||||||||
\(932\) | 14.6934 | − | 8.48325i | 0.481299 | − | 0.277878i | ||||
\(933\) | 2.94491 | + | 1.70025i | 0.0964121 | + | 0.0556636i | ||||
\(934\) | −0.817239 | − | 0.471833i | −0.0267409 | − | 0.0154388i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.94065 | + | 3.03873i | −0.0634322 | + | 0.0993239i | ||||
\(937\) | − | 38.5283i | − | 1.25867i | −0.777136 | − | 0.629333i | \(-0.783328\pi\) | ||
0.777136 | − | 0.629333i | \(-0.216672\pi\) | |||||||
\(938\) | −2.10360 | + | 3.64354i | −0.0686850 | + | 0.118966i | ||||
\(939\) | −8.11699 | + | 14.0590i | −0.264888 | + | 0.458800i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.8637i | 0.940929i | 0.882419 | + | 0.470465i | \(0.155914\pi\) | ||||
−0.882419 | + | 0.470465i | \(0.844086\pi\) | |||||||
\(942\) | −3.56690 | − | 6.17804i | −0.116216 | − | 0.201292i | ||||
\(943\) | −20.1321 | − | 34.8698i | −0.655591 | − | 1.13552i | ||||
\(944\) | − | 3.14152i | − | 0.102248i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −19.8504 | + | 34.3819i | −0.645392 | + | 1.11785i | ||||
\(947\) | 24.6173 | − | 42.6384i | 0.799955 | − | 1.38556i | −0.119689 | − | 0.992811i | \(-0.538190\pi\) |
0.919645 | − | 0.392752i | \(-0.128477\pi\) | |||||||
\(948\) | − | 2.96774i | − | 0.0963877i | ||||||
\(949\) | 10.4380 | + | 20.1059i | 0.338830 | + | 0.652664i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.3716 | − | 11.7616i | −0.660596 | − | 0.381395i | ||||
\(952\) | −4.58155 | − | 2.64516i | −0.148489 | − | 0.0857301i | ||||
\(953\) | 22.9580 | − | 13.2548i | 0.743684 | − | 0.429366i | −0.0797233 | − | 0.996817i | \(-0.525404\pi\) |
0.823407 | + | 0.567451i | \(0.192070\pi\) | |||||||
\(954\) | − | 0.826674i | − | 0.0267645i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.49420 | − | 3.17208i | 0.177695 | − | 0.102592i | ||||
\(957\) | −9.33201 | −0.301661 | ||||||||
\(958\) | −9.61460 | + | 5.55099i | −0.310634 | + | 0.179344i | ||||
\(959\) | −10.6267 | + | 18.4061i | −0.343156 | + | 0.594363i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −71.6592 | −2.31159 | ||||||||
\(962\) | −13.2149 | + | 20.6922i | −0.426065 | + | 0.667145i | ||||
\(963\) | 3.07180i | 0.0989873i | ||||||||
\(964\) | −20.9452 | − | 12.0927i | −0.674600 | − | 0.389481i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.73205 | − | 9.92820i | −0.184426 | − | 0.319435i | ||||
\(967\) | 52.3877 | 1.68468 | 0.842338 | − | 0.538950i | \(-0.181179\pi\) | ||||
0.842338 | + | 0.538950i | \(0.181179\pi\) | |||||||
\(968\) | 5.14152 | + | 8.90538i | 0.165255 | + | 0.286230i | ||||
\(969\) | 7.93548 | − | 4.58155i | 0.254924 | − | 0.147181i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3215 | + | 24.8056i | 0.459600 | + | 0.796051i | 0.998940 | − | 0.0460375i | \(-0.0146594\pi\) |
−0.539339 | + | 0.842088i | \(0.681326\pi\) | |||||||
\(972\) | −0.866025 | − | 0.500000i | −0.0277778 | − | 0.0160375i | ||||
\(973\) | 6.16493 | − | 10.6780i | 0.197638 | − | 0.342320i | ||||
\(974\) | −32.9416 | −1.05552 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.535898 | 0.0171537 | ||||||||
\(977\) | 20.2750 | − | 35.1173i | 0.648654 | − | 1.12350i | −0.334791 | − | 0.942292i | \(-0.608666\pi\) |
0.983445 | − | 0.181209i | \(-0.0580009\pi\) | |||||||
\(978\) | −8.56906 | − | 4.94735i | −0.274008 | − | 0.158199i | ||||
\(979\) | 27.3667 | + | 47.4006i | 0.874645 | + | 1.51493i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4547 | − | 6.61335i | 0.365719 | − | 0.211148i | ||||
\(982\) | 14.2257 | + | 24.6396i | 0.453960 | + | 0.786281i | ||||
\(983\) | −22.4160 | −0.714958 | −0.357479 | − | 0.933921i | \(-0.616364\pi\) | ||||
−0.357479 | + | 0.933921i | \(0.616364\pi\) | |||||||
\(984\) | 2.32258 | + | 4.02283i | 0.0740411 | + | 0.128243i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.00727 | − | 4.04565i | −0.223157 | − | 0.128840i | ||||
\(987\) | − | 12.0477i | − | 0.383483i | ||||||
\(988\) | −0.369479 | + | 8.25124i | −0.0117547 | + | 0.262507i | ||||
\(989\) | −74.5934 | −2.37193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.2844 | − | 24.7413i | 0.453759 | − | 0.785933i | −0.544857 | − | 0.838529i | \(-0.683416\pi\) |
0.998616 | + | 0.0525955i | \(0.0167494\pi\) | |||||||
\(992\) | −8.77464 | + | 5.06604i | −0.278595 | + | 0.160847i | ||||
\(993\) | −18.0904 | −0.574081 | ||||||||
\(994\) | −12.9841 | + | 7.49636i | −0.411830 | + | 0.237770i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 15.8719i | − | 0.502919i | ||||||
\(997\) | 29.7913 | − | 17.2000i | 0.943500 | − | 0.544730i | 0.0524443 | − | 0.998624i | \(-0.483299\pi\) |
0.891056 | + | 0.453894i | \(0.149965\pi\) | |||||||
\(998\) | −3.55872 | − | 2.05463i | −0.112649 | − | 0.0650382i | ||||
\(999\) | −5.89721 | − | 3.40475i | −0.186579 | − | 0.107722i |
(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 | 1950.2.y.j.199.1 | 8 | ||
5.2 | odd | 4 | 390.2.bb.c.121.2 | ✓ | 8 | ||
5.3 | odd | 4 | 1950.2.bc.g.901.3 | 8 | |||
5.4 | even | 2 | 1950.2.y.k.199.4 | 8 | |||
13.10 | even | 6 | 1950.2.y.k.49.4 | 8 | |||
15.2 | even | 4 | 1170.2.bs.f.901.4 | 8 | |||
65.7 | even | 12 | 5070.2.a.bz.1.3 | 4 | |||
65.17 | odd | 12 | 5070.2.b.ba.1351.2 | 8 | |||
65.22 | odd | 12 | 5070.2.b.ba.1351.7 | 8 | |||
65.23 | odd | 12 | 1950.2.bc.g.751.3 | 8 | |||
65.32 | even | 12 | 5070.2.a.ca.1.2 | 4 | |||
65.49 | even | 6 | inner | 1950.2.y.j.49.1 | 8 | ||
65.62 | odd | 12 | 390.2.bb.c.361.2 | yes | 8 | ||
195.62 | even | 12 | 1170.2.bs.f.361.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.2 | ✓ | 8 | 5.2 | odd | 4 | ||
390.2.bb.c.361.2 | yes | 8 | 65.62 | odd | 12 | ||
1170.2.bs.f.361.4 | 8 | 195.62 | even | 12 | |||
1170.2.bs.f.901.4 | 8 | 15.2 | even | 4 | |||
1950.2.y.j.49.1 | 8 | 65.49 | even | 6 | inner | ||
1950.2.y.j.199.1 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.y.k.49.4 | 8 | 13.10 | even | 6 | |||
1950.2.y.k.199.4 | 8 | 5.4 | even | 2 | |||
1950.2.bc.g.751.3 | 8 | 65.23 | odd | 12 | |||
1950.2.bc.g.901.3 | 8 | 5.3 | odd | 4 | |||
5070.2.a.bz.1.3 | 4 | 65.7 | even | 12 | |||
5070.2.a.ca.1.2 | 4 | 65.32 | even | 12 | |||
5070.2.b.ba.1351.2 | 8 | 65.17 | odd | 12 | |||
5070.2.b.ba.1351.7 | 8 | 65.22 | odd | 12 |