Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
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, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
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.bc (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
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 | 751.3 | ||
Root | \(3.17270 + 3.17270i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.751 |
Dual form | 1950.2.bc.g.901.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −1.14539 | − | 0.661290i | −0.432916 | − | 0.249944i | 0.267672 | − | 0.963510i | \(-0.413746\pi\) |
−0.700588 | + | 0.713566i | \(0.747079\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.99528 | + | 2.30668i | −1.20462 | + | 0.695489i | −0.961580 | − | 0.274526i | \(-0.911479\pi\) |
−0.243043 | + | 0.970015i | \(0.578146\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.20002 | − | 1.66129i | −0.887525 | − | 0.460759i | ||||
\(14\) | −1.32258 | −0.353474 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.98387 | + | 1.14539i | 0.455131 | + | 0.262770i | 0.709995 | − | 0.704207i | \(-0.248697\pi\) |
−0.254864 | + | 0.966977i | \(0.582031\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.32258i | − | 0.288611i | ||||||
\(22\) | −2.30668 | + | 3.99528i | −0.491785 | + | 0.851797i | ||||
\(23\) | −4.33399 | − | 7.50670i | −0.903700 | − | 1.56525i | −0.822653 | − | 0.568544i | \(-0.807507\pi\) |
−0.0810471 | − | 0.996710i | \(-0.525826\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.60194 | + | 0.161290i | −0.706399 | + | 0.0316315i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.14539 | + | 0.661290i | −0.216458 | + | 0.124972i | ||||
\(29\) | 1.01141 | + | 1.75182i | 0.187815 | + | 0.325305i | 0.944521 | − | 0.328450i | \(-0.106526\pi\) |
−0.756707 | + | 0.653755i | \(0.773193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1321i | 1.81978i | 0.414853 | + | 0.909888i | \(0.363833\pi\) | ||||
−0.414853 | + | 0.909888i | \(0.636167\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −3.99528 | − | 2.30668i | −0.695489 | − | 0.401541i | ||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −5.89721 | + | 3.40475i | −0.969495 | + | 0.559738i | −0.899082 | − | 0.437780i | \(-0.855765\pi\) |
−0.0704126 | + | 0.997518i | \(0.522432\pi\) | |||||||
\(38\) | 2.29078 | 0.371613 | ||||||||
\(39\) | −0.161290 | − | 3.60194i | −0.0258270 | − | 0.576772i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.02283 | + | 2.32258i | −0.628260 | + | 0.362726i | −0.780078 | − | 0.625682i | \(-0.784821\pi\) |
0.151818 | + | 0.988408i | \(0.451487\pi\) | |||||||
\(42\) | −0.661290 | − | 1.14539i | −0.102039 | − | 0.176737i | ||||
\(43\) | −4.30281 | + | 7.45269i | −0.656173 | + | 1.13652i | 0.325426 | + | 0.945568i | \(0.394492\pi\) |
−0.981598 | + | 0.190957i | \(0.938841\pi\) | |||||||
\(44\) | 4.61335i | 0.695489i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.50670 | − | 4.33399i | −1.10680 | − | 0.639012i | ||||
\(47\) | − | 9.10926i | − | 1.32872i | −0.747412 | − | 0.664361i | \(-0.768704\pi\) | ||
0.747412 | − | 0.664361i | \(-0.231296\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −2.62539 | − | 4.54731i | −0.375056 | − | 0.649616i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −3.03873 | + | 1.94065i | −0.421396 | + | 0.269120i | ||||
\(53\) | −0.826674 | −0.113552 | −0.0567762 | − | 0.998387i | \(-0.518082\pi\) | ||||
−0.0567762 | + | 0.998387i | \(0.518082\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.661290 | + | 1.14539i | −0.0883686 | + | 0.153059i | ||||
\(57\) | 2.29078i | 0.303421i | ||||||||
\(58\) | 1.75182 | + | 1.01141i | 0.230025 | + | 0.132805i | ||||
\(59\) | 2.72064 | + | 1.57076i | 0.354197 | + | 0.204496i | 0.666532 | − | 0.745476i | \(-0.267778\pi\) |
−0.312335 | + | 0.949972i | \(0.601111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.267949 | + | 0.464102i | −0.0343074 | + | 0.0594221i | −0.882669 | − | 0.469995i | \(-0.844256\pi\) |
0.848362 | + | 0.529417i | \(0.177589\pi\) | |||||||
\(62\) | 5.06604 | + | 8.77464i | 0.643388 | + | 1.11438i | ||||
\(63\) | 1.14539 | − | 0.661290i | 0.144305 | − | 0.0833147i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.61335 | −0.567865 | ||||||||
\(67\) | 2.75488 | − | 1.59053i | 0.336562 | − | 0.194314i | −0.322189 | − | 0.946675i | \(-0.604419\pi\) |
0.658751 | + | 0.752361i | \(0.271085\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | 4.33399 | − | 7.50670i | 0.521751 | − | 0.903700i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.81724 | − | 5.66799i | −1.16509 | − | 0.672666i | −0.212573 | − | 0.977145i | \(-0.568184\pi\) |
−0.952519 | + | 0.304479i | \(0.901518\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | − | 6.28304i | − | 0.735375i | −0.929949 | − | 0.367687i | \(-0.880150\pi\) | ||
0.929949 | − | 0.367687i | \(-0.119850\pi\) | |||||||
\(74\) | −3.40475 | + | 5.89721i | −0.395795 | + | 0.685536i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.98387 | − | 1.14539i | 0.227565 | − | 0.131385i | ||||
\(77\) | 6.10153 | 0.695334 | ||||||||
\(78\) | −1.94065 | − | 3.03873i | −0.219736 | − | 0.344068i | ||||
\(79\) | 2.96774 | 0.333897 | 0.166948 | − | 0.985966i | \(-0.446609\pi\) | ||||
0.166948 | + | 0.985966i | \(0.446609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.32258 | + | 4.02283i | −0.256486 | + | 0.444247i | ||||
\(83\) | 15.8719i | 1.74216i | 0.491138 | + | 0.871082i | \(0.336581\pi\) | ||||
−0.491138 | + | 0.871082i | \(0.663419\pi\) | |||||||
\(84\) | −1.14539 | − | 0.661290i | −0.124972 | − | 0.0721526i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.60562i | 0.927968i | ||||||||
\(87\) | −1.01141 | + | 1.75182i | −0.108435 | + | 0.187815i | ||||
\(88\) | 2.30668 | + | 3.99528i | 0.245893 | + | 0.425899i | ||||
\(89\) | 10.2746 | − | 5.93207i | 1.08911 | − | 0.628798i | 0.155771 | − | 0.987793i | \(-0.450214\pi\) |
0.933339 | + | 0.358995i | \(0.116881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.56667 | + | 4.01896i | 0.269060 | + | 0.421302i | ||||
\(92\) | −8.66799 | −0.903700 | ||||||||
\(93\) | −8.77464 | + | 5.06604i | −0.909888 | + | 0.525324i | ||||
\(94\) | −4.55463 | − | 7.88885i | −0.469774 | − | 0.813673i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 7.63743 | + | 4.40947i | 0.775463 | + | 0.447714i | 0.834820 | − | 0.550523i | \(-0.185572\pi\) |
−0.0593568 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(98\) | −4.54731 | − | 2.62539i | −0.459348 | − | 0.265205i | ||||
\(99\) | − | 4.61335i | − | 0.463660i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.61335 | − | 6.25851i | −0.359542 | − | 0.622745i | 0.628342 | − | 0.777937i | \(-0.283734\pi\) |
−0.987884 | + | 0.155192i | \(0.950400\pi\) | |||||||
\(102\) | −3.46410 | + | 2.00000i | −0.342997 | + | 0.198030i | ||||
\(103\) | 18.4000 | 1.81301 | 0.906505 | − | 0.422196i | \(-0.138740\pi\) | ||||
0.906505 | + | 0.422196i | \(0.138740\pi\) | |||||||
\(104\) | −1.66129 | + | 3.20002i | −0.162903 | + | 0.313788i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.715920 | + | 0.413337i | −0.0695363 | + | 0.0401468i | ||||
\(107\) | 1.53590 | + | 2.66025i | 0.148481 | + | 0.257176i | 0.930666 | − | 0.365869i | \(-0.119228\pi\) |
−0.782185 | + | 0.623046i | \(0.785895\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | − | 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 | ||||
\(112\) | 1.32258i | 0.124972i | ||||||||
\(113\) | −4.04322 | + | 7.00306i | −0.380354 | + | 0.658792i | −0.991113 | − | 0.133024i | \(-0.957531\pi\) |
0.610759 | + | 0.791817i | \(0.290864\pi\) | |||||||
\(114\) | 1.14539 | + | 1.98387i | 0.107275 | + | 0.185806i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.02283 | 0.187815 | ||||||||
\(117\) | 3.03873 | − | 1.94065i | 0.280931 | − | 0.179413i | ||||
\(118\) | 3.14152 | 0.289201 | ||||||||
\(119\) | 4.58155 | − | 2.64516i | 0.419990 | − | 0.242481i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.14152 | − | 8.90538i | 0.467411 | − | 0.809580i | ||||
\(122\) | 0.535898i | 0.0485180i | ||||||||
\(123\) | −4.02283 | − | 2.32258i | −0.362726 | − | 0.209420i | ||||
\(124\) | 8.77464 | + | 5.06604i | 0.787986 | + | 0.454944i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.661290 | − | 1.14539i | 0.0589124 | − | 0.102039i | ||||
\(127\) | −5.73592 | − | 9.93490i | −0.508980 | − | 0.881580i | −0.999946 | − | 0.0104008i | \(-0.996689\pi\) |
0.490966 | − | 0.871179i | \(-0.336644\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −8.60562 | −0.757683 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.9906 | −1.39710 | −0.698551 | − | 0.715560i | \(-0.746172\pi\) | ||||
−0.698551 | + | 0.715560i | \(0.746172\pi\) | |||||||
\(132\) | −3.99528 | + | 2.30668i | −0.347745 | + | 0.200771i | ||||
\(133\) | −1.51487 | − | 2.62383i | −0.131356 | − | 0.227515i | ||||
\(134\) | 1.59053 | − | 2.75488i | 0.137401 | − | 0.237985i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | + | 2.00000i | 0.297044 | + | 0.171499i | ||||
\(137\) | −13.9168 | − | 8.03486i | −1.18899 | − | 0.686465i | −0.230914 | − | 0.972974i | \(-0.574172\pi\) |
−0.958077 | + | 0.286509i | \(0.907505\pi\) | |||||||
\(138\) | − | 8.66799i | − | 0.737868i | ||||||
\(139\) | −4.66129 | + | 8.07359i | −0.395365 | + | 0.684793i | −0.993148 | − | 0.116865i | \(-0.962715\pi\) |
0.597782 | + | 0.801658i | \(0.296049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.88885 | − | 4.55463i | 0.664361 | − | 0.383569i | ||||
\(142\) | −11.3360 | −0.951294 | ||||||||
\(143\) | 16.6170 | − | 0.744087i | 1.38959 | − | 0.0622237i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.14152 | − | 5.44128i | −0.259994 | − | 0.450323i | ||||
\(147\) | 2.62539 | − | 4.54731i | 0.216539 | − | 0.375056i | ||||
\(148\) | 6.80951i | 0.559738i | ||||||||
\(149\) | 3.53788 | + | 2.04259i | 0.289834 | + | 0.167336i | 0.637867 | − | 0.770146i | \(-0.279817\pi\) |
−0.348033 | + | 0.937482i | \(0.613150\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.9811i | 1.62604i | 0.582235 | + | 0.813021i | \(0.302178\pi\) | ||||
−0.582235 | + | 0.813021i | \(0.697822\pi\) | |||||||
\(152\) | 1.14539 | − | 1.98387i | 0.0929032 | − | 0.160913i | ||||
\(153\) | −2.00000 | − | 3.46410i | −0.161690 | − | 0.280056i | ||||
\(154\) | 5.28408 | − | 3.05076i | 0.425803 | − | 0.245838i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.20002 | − | 1.66129i | −0.256206 | − | 0.133010i | ||||
\(157\) | −7.13379 | −0.569338 | −0.284669 | − | 0.958626i | \(-0.591884\pi\) | ||||
−0.284669 | + | 0.958626i | \(0.591884\pi\) | |||||||
\(158\) | 2.57014 | − | 1.48387i | 0.204469 | − | 0.118050i | ||||
\(159\) | −0.413337 | − | 0.715920i | −0.0327797 | − | 0.0567762i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.4641i | 0.903498i | ||||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 8.56906 | + | 4.94735i | 0.671180 | + | 0.387506i | 0.796524 | − | 0.604607i | \(-0.206670\pi\) |
−0.125343 | + | 0.992113i | \(0.540003\pi\) | |||||||
\(164\) | 4.64516i | 0.362726i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.93593 | + | 13.7454i | 0.615948 | + | 1.06685i | ||||
\(167\) | −20.8171 | + | 12.0187i | −1.61087 | + | 0.930037i | −0.621704 | + | 0.783253i | \(0.713559\pi\) |
−0.989168 | + | 0.146785i | \(0.953108\pi\) | |||||||
\(168\) | −1.32258 | −0.102039 | ||||||||
\(169\) | 7.48023 | + | 10.6323i | 0.575402 | + | 0.817870i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.98387 | + | 1.14539i | −0.151710 | + | 0.0875900i | ||||
\(172\) | 4.30281 | + | 7.45269i | 0.328086 | + | 0.568262i | ||||
\(173\) | −1.26408 | + | 2.18946i | −0.0961065 | + | 0.166461i | −0.910070 | − | 0.414455i | \(-0.863972\pi\) |
0.813963 | + | 0.580916i | \(0.197306\pi\) | |||||||
\(174\) | 2.02283i | 0.153350i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.99528 | + | 2.30668i | 0.301156 | + | 0.173872i | ||||
\(177\) | 3.14152i | 0.236131i | ||||||||
\(178\) | 5.93207 | − | 10.2746i | 0.444627 | − | 0.770117i | ||||
\(179\) | −3.13784 | − | 5.43490i | −0.234533 | − | 0.406223i | 0.724604 | − | 0.689166i | \(-0.242023\pi\) |
−0.959137 | + | 0.282942i | \(0.908689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2830 | −0.912991 | −0.456496 | − | 0.889726i | \(-0.650896\pi\) | ||||
−0.456496 | + | 0.889726i | \(0.650896\pi\) | |||||||
\(182\) | 4.23228 | + | 2.19719i | 0.313717 | + | 0.162866i | ||||
\(183\) | −0.535898 | −0.0396147 | ||||||||
\(184\) | −7.50670 | + | 4.33399i | −0.553401 | + | 0.319506i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.06604 | + | 8.77464i | −0.371460 | + | 0.643388i | ||||
\(187\) | − | 18.4534i | − | 1.34945i | ||||||
\(188\) | −7.88885 | − | 4.55463i | −0.575354 | − | 0.332181i | ||||
\(189\) | 1.14539 | + | 0.661290i | 0.0833147 | + | 0.0481018i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.87357 | − | 8.44128i | 0.352639 | − | 0.610789i | −0.634072 | − | 0.773274i | \(-0.718618\pi\) |
0.986711 | + | 0.162485i | \(0.0519509\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 11.9188 | − | 6.88130i | 0.857932 | − | 0.495327i | −0.00538741 | − | 0.999985i | \(-0.501715\pi\) |
0.863319 | + | 0.504658i | \(0.168382\pi\) | |||||||
\(194\) | 8.81894 | 0.633163 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.25078 | −0.375056 | ||||||||
\(197\) | 8.78282 | − | 5.07076i | 0.625750 | − | 0.361277i | −0.153354 | − | 0.988171i | \(-0.549008\pi\) |
0.779104 | + | 0.626894i | \(0.215674\pi\) | |||||||
\(198\) | −2.30668 | − | 3.99528i | −0.163928 | − | 0.283932i | ||||
\(199\) | 4.78668 | − | 8.29078i | 0.339319 | − | 0.587717i | −0.644986 | − | 0.764194i | \(-0.723137\pi\) |
0.984305 | + | 0.176477i | \(0.0564701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.75488 | + | 1.59053i | 0.194314 | + | 0.112187i | ||||
\(202\) | −6.25851 | − | 3.61335i | −0.440348 | − | 0.254235i | ||||
\(203\) | − | 2.67535i | − | 0.187773i | ||||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.9349 | − | 9.20002i | 1.11024 | − | 0.640996i | ||||
\(207\) | 8.66799 | 0.602467 | ||||||||
\(208\) | 0.161290 | + | 3.60194i | 0.0111834 | + | 0.249750i | ||||
\(209\) | −10.5682 | −0.731015 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.542594 | + | 0.939800i | 0.0373537 | + | 0.0646985i | 0.884098 | − | 0.467302i | \(-0.154774\pi\) |
−0.846744 | + | 0.532000i | \(0.821441\pi\) | |||||||
\(212\) | −0.413337 | + | 0.715920i | −0.0283881 | + | 0.0491696i | ||||
\(213\) | − | 11.3360i | − | 0.776728i | ||||||
\(214\) | 2.66025 | + | 1.53590i | 0.181851 | + | 0.104992i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 6.70025 | − | 11.6052i | 0.454842 | − | 0.787810i | ||||
\(218\) | −6.61335 | − | 11.4547i | −0.447913 | − | 0.775808i | ||||
\(219\) | 5.44128 | − | 3.14152i | 0.367687 | − | 0.212284i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.1549 | − | 7.76261i | 0.817628 | − | 0.522170i | ||||
\(222\) | −6.80951 | −0.457024 | ||||||||
\(223\) | −21.6001 | + | 12.4708i | −1.44645 | + | 0.835106i | −0.998268 | − | 0.0588375i | \(-0.981261\pi\) |
−0.448179 | + | 0.893944i | \(0.647927\pi\) | |||||||
\(224\) | 0.661290 | + | 1.14539i | 0.0441843 | + | 0.0765294i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.08643i | 0.537902i | ||||||||
\(227\) | 16.7321 | + | 9.66025i | 1.11055 | + | 0.641174i | 0.938971 | − | 0.343998i | \(-0.111781\pi\) |
0.171575 | + | 0.985171i | \(0.445115\pi\) | |||||||
\(228\) | 1.98387 | + | 1.14539i | 0.131385 | + | 0.0758551i | ||||
\(229\) | − | 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 | ||||
\(232\) | 1.75182 | − | 1.01141i | 0.115013 | − | 0.0664025i | ||||
\(233\) | −16.9665 | −1.11151 | −0.555756 | − | 0.831346i | \(-0.687571\pi\) | ||||
−0.555756 | + | 0.831346i | \(0.687571\pi\) | |||||||
\(234\) | 1.66129 | − | 3.20002i | 0.108602 | − | 0.209192i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.72064 | − | 1.57076i | 0.177098 | − | 0.102248i | ||||
\(237\) | 1.48387 | + | 2.57014i | 0.0963877 | + | 0.166948i | ||||
\(238\) | 2.64516 | − | 4.58155i | 0.171460 | − | 0.296978i | ||||
\(239\) | 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 | 0.988136 | − | 0.153579i | \(-0.0490800\pi\) |
0.361065 | + | 0.932541i | \(0.382413\pi\) | |||||||
\(242\) | − | 10.2830i | − | 0.661019i | ||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0.267949 | + | 0.464102i | 0.0171537 | + | 0.0297111i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.64516 | −0.296165 | ||||||||
\(247\) | −4.44560 | − | 6.96104i | −0.282867 | − | 0.442921i | ||||
\(248\) | 10.1321 | 0.643388 | ||||||||
\(249\) | −13.7454 | + | 7.93593i | −0.871082 | + | 0.502919i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.41249 | − | 7.64265i | 0.278514 | − | 0.482400i | −0.692502 | − | 0.721416i | \(-0.743492\pi\) |
0.971016 | + | 0.239016i | \(0.0768249\pi\) | |||||||
\(252\) | − | 1.32258i | − | 0.0833147i | ||||||
\(253\) | 34.6311 | + | 19.9942i | 2.17724 | + | 1.25703i | ||||
\(254\) | −9.93490 | − | 5.73592i | −0.623371 | − | 0.359903i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −4.19247 | − | 7.26157i | −0.261519 | − | 0.452964i | 0.705127 | − | 0.709081i | \(-0.250890\pi\) |
−0.966646 | + | 0.256117i | \(0.917557\pi\) | |||||||
\(258\) | −7.45269 | + | 4.30281i | −0.463984 | + | 0.267881i | ||||
\(259\) | 9.00612 | 0.559613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.02283 | −0.125210 | ||||||||
\(262\) | −13.8482 | + | 7.99528i | −0.855547 | + | 0.493950i | ||||
\(263\) | 0.960648 | + | 1.66389i | 0.0592361 | + | 0.102600i | 0.894123 | − | 0.447822i | \(-0.147800\pi\) |
−0.834887 | + | 0.550422i | \(0.814467\pi\) | |||||||
\(264\) | −2.30668 | + | 3.99528i | −0.141966 | + | 0.245893i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.62383 | − | 1.51487i | −0.160877 | − | 0.0928824i | ||||
\(267\) | 10.2746 | + | 5.93207i | 0.628798 | + | 0.363037i | ||||
\(268\) | − | 3.18106i | − | 0.194314i | ||||||
\(269\) | 16.1549 | − | 27.9811i | 0.984982 | − | 1.70604i | 0.342968 | − | 0.939347i | \(-0.388568\pi\) |
0.642014 | − | 0.766693i | \(-0.278099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3105 | − | 11.7263i | 1.23378 | − | 0.712322i | 0.265962 | − | 0.963983i | \(-0.414310\pi\) |
0.967815 | + | 0.251662i | \(0.0809770\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | −2.19719 | + | 4.23228i | −0.132980 | + | 0.256149i | ||||
\(274\) | −16.0697 | −0.970808 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.33399 | − | 7.50670i | −0.260876 | − | 0.451850i | ||||
\(277\) | 4.50283 | − | 7.79913i | 0.270549 | − | 0.468604i | −0.698454 | − | 0.715655i | \(-0.746128\pi\) |
0.969002 | + | 0.247051i | \(0.0794615\pi\) | |||||||
\(278\) | 9.32258i | 0.559131i | ||||||||
\(279\) | −8.77464 | − | 5.06604i | −0.525324 | − | 0.303296i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.71696i | − | 0.102425i | −0.998688 | − | 0.0512125i | \(-0.983691\pi\) | ||
0.998688 | − | 0.0512125i | \(-0.0163086\pi\) | |||||||
\(282\) | 4.55463 | − | 7.88885i | 0.271224 | − | 0.469774i | ||||
\(283\) | 0.774645 | + | 1.34172i | 0.0460479 | + | 0.0797572i | 0.888131 | − | 0.459591i | \(-0.152004\pi\) |
−0.842083 | + | 0.539348i | \(0.818671\pi\) | |||||||
\(284\) | −9.81724 | + | 5.66799i | −0.582546 | + | 0.336333i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.0187 | − | 8.95292i | 0.828945 | − | 0.529397i | ||||
\(287\) | 6.14359 | 0.362645 | ||||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.81894i | 0.516976i | ||||||||
\(292\) | −5.44128 | − | 3.14152i | −0.318427 | − | 0.183844i | ||||
\(293\) | −26.3321 | − | 15.2028i | −1.53834 | − | 0.888160i | −0.998936 | − | 0.0461113i | \(-0.985317\pi\) |
−0.539402 | − | 0.842049i | \(-0.681350\pi\) | |||||||
\(294\) | − | 5.25078i | − | 0.306232i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.40475 | + | 5.89721i | 0.197897 | + | 0.342768i | ||||
\(297\) | 3.99528 | − | 2.30668i | 0.231830 | − | 0.133847i | ||||
\(298\) | 4.08519 | 0.236649 | ||||||||
\(299\) | 1.39806 | + | 31.2216i | 0.0808518 | + | 1.80559i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.85677 | − | 5.69081i | 0.568135 | − | 0.328013i | ||||
\(302\) | 9.99057 | + | 17.3042i | 0.574892 | + | 0.995743i | ||||
\(303\) | 3.61335 | − | 6.25851i | 0.207582 | − | 0.359542i | ||||
\(304\) | − | 2.29078i | − | 0.131385i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.46410 | − | 2.00000i | −0.198030 | − | 0.114332i | ||||
\(307\) | 9.82622i | 0.560812i | 0.959882 | + | 0.280406i | \(0.0904691\pi\) | ||||
−0.959882 | + | 0.280406i | \(0.909531\pi\) | |||||||
\(308\) | 3.05076 | − | 5.28408i | 0.173833 | − | 0.301088i | ||||
\(309\) | 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 | \(0.530737\pi\) | |||||||
\(312\) | −3.60194 | + | 0.161290i | −0.203920 | + | 0.00913124i | ||||
\(313\) | 16.2340 | 0.917599 | 0.458800 | − | 0.888540i | \(-0.348280\pi\) | ||||
0.458800 | + | 0.888540i | \(0.348280\pi\) | |||||||
\(314\) | −6.17804 | + | 3.56690i | −0.348647 | + | 0.201292i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.48387 | − | 2.57014i | 0.0834742 | − | 0.144582i | ||||
\(317\) | 23.5231i | 1.32119i | 0.750742 | + | 0.660596i | \(0.229696\pi\) | ||||
−0.750742 | + | 0.660596i | \(0.770304\pi\) | |||||||
\(318\) | −0.715920 | − | 0.413337i | −0.0401468 | − | 0.0231788i | ||||
\(319\) | −8.08176 | − | 4.66601i | −0.452492 | − | 0.261246i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.53590 | + | 2.66025i | −0.0857255 | + | 0.148481i | ||||
\(322\) | 5.73205 | + | 9.92820i | 0.319435 | + | 0.553277i | ||||
\(323\) | −7.93548 | + | 4.58155i | −0.441542 | + | 0.254924i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.89470 | 0.548016 | ||||||||
\(327\) | 11.4547 | − | 6.61335i | 0.633445 | − | 0.365719i | ||||
\(328\) | 2.32258 | + | 4.02283i | 0.128243 | + | 0.222123i | ||||
\(329\) | −6.02386 | + | 10.4336i | −0.332106 | + | 0.575225i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.6667 | + | 9.04520i | 0.861122 | + | 0.497169i | 0.864388 | − | 0.502826i | \(-0.167706\pi\) |
−0.00326597 | + | 0.999995i | \(0.501040\pi\) | |||||||
\(332\) | 13.7454 | + | 7.93593i | 0.754379 | + | 0.435541i | ||||
\(333\) | − | 6.80951i | − | 0.373159i | ||||||
\(334\) | −12.0187 | + | 20.8171i | −0.657636 | + | 1.13906i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.14539 | + | 0.661290i | −0.0624860 | + | 0.0360763i | ||||
\(337\) | 5.69900 | 0.310444 | 0.155222 | − | 0.987880i | \(-0.450391\pi\) | ||||
0.155222 | + | 0.987880i | \(0.450391\pi\) | |||||||
\(338\) | 11.7942 | + | 5.46774i | 0.641521 | + | 0.297406i | ||||
\(339\) | −8.08643 | −0.439195 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.3715 | − | 40.4806i | −1.26564 | − | 2.19214i | ||||
\(342\) | −1.14539 | + | 1.98387i | −0.0619355 | + | 0.107275i | ||||
\(343\) | 16.2026i | 0.874860i | ||||||||
\(344\) | 7.45269 | + | 4.30281i | 0.401822 | + | 0.231992i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.52817i | 0.135915i | ||||||||
\(347\) | −7.87357 | + | 13.6374i | −0.422676 | + | 0.732095i | −0.996200 | − | 0.0870928i | \(-0.972242\pi\) |
0.573525 | + | 0.819188i | \(0.305576\pi\) | |||||||
\(348\) | 1.01141 | + | 1.75182i | 0.0542174 | + | 0.0939073i | ||||
\(349\) | 13.2679 | − | 7.66025i | 0.710217 | − | 0.410044i | −0.100924 | − | 0.994894i | \(-0.532180\pi\) |
0.811141 | + | 0.584850i | \(0.198847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.20002 | + | 1.66129i | 0.170804 | + | 0.0886731i | ||||
\(352\) | 4.61335 | 0.245893 | ||||||||
\(353\) | −1.03917 | + | 0.599964i | −0.0553093 | + | 0.0319328i | −0.527400 | − | 0.849617i | \(-0.676833\pi\) |
0.472090 | + | 0.881550i | \(0.343500\pi\) | |||||||
\(354\) | 1.57076 | + | 2.72064i | 0.0834850 | + | 0.144600i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 11.8641i | − | 0.628798i | ||||||
\(357\) | 4.58155 | + | 2.64516i | 0.242481 | + | 0.139997i | ||||
\(358\) | −5.43490 | − | 3.13784i | −0.287243 | − | 0.165840i | ||||
\(359\) | − | 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 | ||||
\(362\) | −10.6374 | + | 6.14152i | −0.559091 | + | 0.322791i | ||||
\(363\) | 10.2830 | 0.539720 | ||||||||
\(364\) | 4.76386 | − | 0.213319i | 0.249694 | − | 0.0111809i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.464102 | + | 0.267949i | −0.0242590 | + | 0.0140059i | ||||
\(367\) | −9.81724 | − | 17.0040i | −0.512456 | − | 0.887599i | −0.999896 | − | 0.0144428i | \(-0.995403\pi\) |
0.487440 | − | 0.873156i | \(-0.337931\pi\) | |||||||
\(368\) | −4.33399 | + | 7.50670i | −0.225925 | + | 0.391314i | ||||
\(369\) | − | 4.64516i | − | 0.241817i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.946862 | + | 0.546671i | 0.0491586 | + | 0.0283817i | ||||
\(372\) | 10.1321i | 0.525324i | ||||||||
\(373\) | −1.27874 | + | 2.21484i | −0.0662106 | + | 0.114680i | −0.897230 | − | 0.441563i | \(-0.854424\pi\) |
0.831020 | + | 0.556243i | \(0.187758\pi\) | |||||||
\(374\) | −9.22671 | − | 15.9811i | −0.477102 | − | 0.826365i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.10926 | −0.469774 | ||||||||
\(377\) | −0.326261 | − | 7.28610i | −0.0168033 | − | 0.375253i | ||||
\(378\) | 1.32258 | 0.0680262 | ||||||||
\(379\) | −13.0846 | + | 7.55440i | −0.672111 | + | 0.388044i | −0.796876 | − | 0.604143i | \(-0.793516\pi\) |
0.124765 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.73592 | − | 9.93490i | 0.293860 | − | 0.508980i | ||||
\(382\) | − | 9.74715i | − | 0.498707i | ||||||
\(383\) | 16.2210 | + | 9.36517i | 0.828852 | + | 0.478538i | 0.853459 | − | 0.521159i | \(-0.174500\pi\) |
−0.0246073 | + | 0.999697i | \(0.507834\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.88130 | − | 11.9188i | 0.350249 | − | 0.606649i | ||||
\(387\) | −4.30281 | − | 7.45269i | −0.218724 | − | 0.378841i | ||||
\(388\) | 7.63743 | − | 4.40947i | 0.387732 | − | 0.223857i | ||||
\(389\) | 6.96899 | 0.353342 | 0.176671 | − | 0.984270i | \(-0.443467\pi\) | ||||
0.176671 | + | 0.984270i | \(0.443467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.6719 | 1.75344 | ||||||||
\(392\) | −4.54731 | + | 2.62539i | −0.229674 | + | 0.132602i | ||||
\(393\) | −7.99528 | − | 13.8482i | −0.403309 | − | 0.698551i | ||||
\(394\) | 5.07076 | − | 8.78282i | 0.255461 | − | 0.442472i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.99528 | − | 2.30668i | −0.200771 | − | 0.115915i | ||||
\(397\) | 16.0839 | + | 9.28606i | 0.807229 | + | 0.466054i | 0.845993 | − | 0.533195i | \(-0.179009\pi\) |
−0.0387637 | + | 0.999248i | \(0.512342\pi\) | |||||||
\(398\) | − | 9.57336i | − | 0.479869i | ||||||
\(399\) | 1.51487 | − | 2.62383i | 0.0758382 | − | 0.131356i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.7126 | + | 14.8452i | −1.28403 | + | 0.741333i | −0.977582 | − | 0.210556i | \(-0.932473\pi\) |
−0.306444 | + | 0.951889i | \(0.599139\pi\) | |||||||
\(402\) | 3.18106 | 0.158657 | ||||||||
\(403\) | 16.8323 | − | 32.4229i | 0.838478 | − | 1.61510i | ||||
\(404\) | −7.22671 | −0.359542 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.33767 | − | 2.31692i | −0.0663877 | − | 0.114987i | ||||
\(407\) | 15.7073 | − | 27.2059i | 0.778584 | − | 1.34855i | ||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | −21.0752 | − | 12.1678i | −1.04210 | − | 0.601657i | −0.121673 | − | 0.992570i | \(-0.538826\pi\) |
−0.920427 | + | 0.390913i | \(0.872159\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 16.0697i | − | 0.792661i | ||||||
\(412\) | 9.20002 | − | 15.9349i | 0.453252 | − | 0.785056i | ||||
\(413\) | −2.07746 | − | 3.59826i | −0.102225 | − | 0.177059i | ||||
\(414\) | 7.50670 | − | 4.33399i | 0.368934 | − | 0.213004i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.94065 | + | 3.03873i | 0.0951483 | + | 0.148986i | ||||
\(417\) | −9.32258 | −0.456529 | ||||||||
\(418\) | −9.15229 | + | 5.28408i | −0.447653 | + | 0.258453i | ||||
\(419\) | 1.44128 | + | 2.49636i | 0.0704109 | + | 0.121955i | 0.899081 | − | 0.437781i | \(-0.144236\pi\) |
−0.828671 | + | 0.559737i | \(0.810902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.94707i | 0.241106i | 0.992707 | + | 0.120553i | \(0.0384667\pi\) | ||||
−0.992707 | + | 0.120553i | \(0.961533\pi\) | |||||||
\(422\) | 0.939800 | + | 0.542594i | 0.0457488 | + | 0.0264131i | ||||
\(423\) | 7.88885 | + | 4.55463i | 0.383569 | + | 0.221454i | ||||
\(424\) | 0.826674i | 0.0401468i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.66799 | − | 9.81724i | −0.274615 | − | 0.475647i | ||||
\(427\) | 0.613811 | − | 0.354384i | 0.0297044 | − | 0.0171499i | ||||
\(428\) | 3.07180 | 0.148481 | ||||||||
\(429\) | 8.95292 | + | 14.0187i | 0.432251 | + | 0.676831i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3829 | + | 8.88130i | −0.740967 | + | 0.427797i | −0.822421 | − | 0.568880i | \(-0.807377\pi\) |
0.0814539 | + | 0.996677i | \(0.474044\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −17.9188 | + | 31.0362i | −0.861121 | + | 1.49151i | 0.00972676 | + | 0.999953i | \(0.496904\pi\) |
−0.870848 | + | 0.491553i | \(0.836430\pi\) | |||||||
\(434\) | − | 13.4005i | − | 0.643244i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.4547 | − | 6.61335i | −0.548579 | − | 0.316722i | ||||
\(437\) | − | 19.8564i | − | 0.949861i | ||||||
\(438\) | 3.14152 | − | 5.44128i | 0.150108 | − | 0.259994i | ||||
\(439\) | 5.04520 | + | 8.73854i | 0.240794 | + | 0.417068i | 0.960941 | − | 0.276754i | \(-0.0892588\pi\) |
−0.720147 | + | 0.693822i | \(0.755925\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.25078 | 0.250037 | ||||||||
\(442\) | 6.64516 | − | 12.8001i | 0.316078 | − | 0.608837i | ||||
\(443\) | −13.6981 | −0.650816 | −0.325408 | − | 0.945574i | \(-0.605502\pi\) | ||||
−0.325408 | + | 0.945574i | \(0.605502\pi\) | |||||||
\(444\) | −5.89721 | + | 3.40475i | −0.279869 | + | 0.161582i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.4708 | + | 21.6001i | −0.590509 | + | 1.02279i | ||||
\(447\) | 4.08519i | 0.193223i | ||||||||
\(448\) | 1.14539 | + | 0.661290i | 0.0541145 | + | 0.0312430i | ||||
\(449\) | 13.2613 | + | 7.65639i | 0.625837 | + | 0.361327i | 0.779138 | − | 0.626852i | \(-0.215657\pi\) |
−0.153301 | + | 0.988180i | \(0.548990\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.7149 | − | 18.5587i | 0.504544 | − | 0.873896i | ||||
\(452\) | 4.04322 | + | 7.00306i | 0.190177 | + | 0.329396i | ||||
\(453\) | −17.3042 | + | 9.99057i | −0.813021 | + | 0.469398i | ||||
\(454\) | 19.3205 | 0.906756 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.29078 | 0.107275 | ||||||||
\(457\) | 13.4714 | − | 7.77770i | 0.630164 | − | 0.363826i | −0.150651 | − | 0.988587i | \(-0.548137\pi\) |
0.780816 | + | 0.624761i | \(0.214804\pi\) | |||||||
\(458\) | −2.07746 | − | 3.59826i | −0.0970732 | − | 0.168136i | ||||
\(459\) | 2.00000 | − | 3.46410i | 0.0933520 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.5473 | + | 7.82154i | 0.630961 | + | 0.364286i | 0.781124 | − | 0.624376i | \(-0.214647\pi\) |
−0.150163 | + | 0.988661i | \(0.547980\pi\) | |||||||
\(462\) | 5.28408 | + | 3.05076i | 0.245838 | + | 0.141934i | ||||
\(463\) | 13.7170i | 0.637481i | 0.947842 | + | 0.318741i | \(0.103260\pi\) | ||||
−0.947842 | + | 0.318741i | \(0.896740\pi\) | |||||||
\(464\) | 1.01141 | − | 1.75182i | 0.0469537 | − | 0.0813261i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.6934 | + | 8.48325i | −0.680659 | + | 0.392979i | ||||
\(467\) | 0.943666 | 0.0436677 | 0.0218338 | − | 0.999762i | \(-0.493050\pi\) | ||||
0.0218338 | + | 0.999762i | \(0.493050\pi\) | |||||||
\(468\) | −0.161290 | − | 3.60194i | −0.00745563 | − | 0.166500i | ||||
\(469\) | −4.20720 | −0.194271 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.56690 | − | 6.17804i | −0.164354 | − | 0.284669i | ||||
\(472\) | 1.57076 | − | 2.72064i | 0.0723001 | − | 0.125228i | ||||
\(473\) | − | 39.7008i | − | 1.82544i | ||||||
\(474\) | 2.57014 | + | 1.48387i | 0.118050 | + | 0.0681564i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 5.29032i | − | 0.242481i | ||||||
\(477\) | 0.413337 | − | 0.715920i | 0.0189254 | − | 0.0327797i | ||||
\(478\) | 3.17208 | + | 5.49420i | 0.145088 | + | 0.251299i | ||||
\(479\) | −9.61460 | + | 5.55099i | −0.439302 | + | 0.253631i | −0.703302 | − | 0.710892i | \(-0.748292\pi\) |
0.263999 | + | 0.964523i | \(0.414958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5275 | − | 1.09830i | 1.11836 | − | 0.0500784i | ||||
\(482\) | 24.1855 | 1.10162 | ||||||||
\(483\) | −9.92820 | + | 5.73205i | −0.451749 | + | 0.260817i | ||||
\(484\) | −5.14152 | − | 8.90538i | −0.233706 | − | 0.404790i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 28.5283 | + | 16.4708i | 1.29274 | + | 0.746363i | 0.979139 | − | 0.203192i | \(-0.0651316\pi\) |
0.313600 | + | 0.949555i | \(0.398465\pi\) | |||||||
\(488\) | 0.464102 | + | 0.267949i | 0.0210089 | + | 0.0121295i | ||||
\(489\) | 9.89470i | 0.447454i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2257 | + | 24.6396i | 0.641996 | + | 1.11197i | 0.984987 | + | 0.172630i | \(0.0552266\pi\) |
−0.342991 | + | 0.939339i | \(0.611440\pi\) | |||||||
\(492\) | −4.02283 | + | 2.32258i | −0.181363 | + | 0.104710i | ||||
\(493\) | −8.09130 | −0.364414 | ||||||||
\(494\) | −7.33052 | − | 3.80564i | −0.329816 | − | 0.171224i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.77464 | − | 5.06604i | 0.393993 | − | 0.227472i | ||||
\(497\) | 7.49636 | + | 12.9841i | 0.336258 | + | 0.582416i | ||||
\(498\) | −7.93593 | + | 13.7454i | −0.355618 | + | 0.615948i | ||||
\(499\) | 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 | ||||
\(502\) | − | 8.82497i | − | 0.393878i | ||||||
\(503\) | 2.86800 | − | 4.96753i | 0.127878 | − | 0.221491i | −0.794976 | − | 0.606641i | \(-0.792517\pi\) |
0.922854 | + | 0.385149i | \(0.125850\pi\) | |||||||
\(504\) | −0.661290 | − | 1.14539i | −0.0294562 | − | 0.0510196i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 39.9885 | 1.77771 | ||||||||
\(507\) | −5.46774 | + | 11.7942i | −0.242831 | + | 0.523800i | ||||
\(508\) | −11.4718 | −0.508980 | ||||||||
\(509\) | −13.1129 | + | 7.57076i | −0.581221 | + | 0.335568i | −0.761618 | − | 0.648026i | \(-0.775595\pi\) |
0.180397 | + | 0.983594i | \(0.442262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.15491 | + | 7.19652i | −0.183803 | + | 0.318355i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.98387 | − | 1.14539i | −0.0875900 | − | 0.0505701i | ||||
\(514\) | −7.26157 | − | 4.19247i | −0.320294 | − | 0.184922i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.30281 | + | 7.45269i | −0.189421 | + | 0.328086i | ||||
\(517\) | 21.0121 | + | 36.3941i | 0.924112 | + | 1.60061i | ||||
\(518\) | 7.79953 | − | 4.50306i | 0.342691 | − | 0.197853i | ||||
\(519\) | −2.52817 | −0.110974 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.93027 | 0.391242 | 0.195621 | − | 0.980680i | \(-0.437328\pi\) | ||||
0.195621 | + | 0.980680i | \(0.437328\pi\) | |||||||
\(522\) | −1.75182 | + | 1.01141i | −0.0766750 | + | 0.0442683i | ||||
\(523\) | −4.90844 | − | 8.50166i | −0.214631 | − | 0.371752i | 0.738527 | − | 0.674223i | \(-0.235522\pi\) |
−0.953158 | + | 0.302472i | \(0.902188\pi\) | |||||||
\(524\) | −7.99528 | + | 13.8482i | −0.349276 | + | 0.604963i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.66389 | + | 0.960648i | 0.0725491 | + | 0.0418863i | ||||
\(527\) | −35.0986 | − | 20.2642i | −1.52892 | − | 0.882721i | ||||
\(528\) | 4.61335i | 0.200771i | ||||||||
\(529\) | −26.0670 | + | 45.1493i | −1.13335 | + | 1.96301i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.72064 | + | 1.57076i | −0.118066 | + | 0.0681652i | ||||
\(532\) | −3.02973 | −0.131356 | ||||||||
\(533\) | 16.7316 | − | 0.749217i | 0.724726 | − | 0.0324522i | ||||
\(534\) | 11.8641 | 0.513411 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.59053 | − | 2.75488i | −0.0687004 | − | 0.118993i | ||||
\(537\) | 3.13784 | − | 5.43490i | 0.135408 | − | 0.234533i | ||||
\(538\) | − | 32.3098i | − | 1.39298i | ||||||
\(539\) | 20.9784 | + | 12.1119i | 0.903602 | + | 0.521695i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 3.80826i | − | 0.163730i | −0.996643 | − | 0.0818650i | \(-0.973912\pi\) | ||
0.996643 | − | 0.0818650i | \(-0.0260876\pi\) | |||||||
\(542\) | 11.7263 | − | 20.3105i | 0.503688 | − | 0.872413i | ||||
\(543\) | −6.14152 | − | 10.6374i | −0.263558 | − | 0.456496i | ||||
\(544\) | 3.46410 | − | 2.00000i | 0.148522 | − | 0.0857493i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.213319 | + | 4.76386i | 0.00912920 | + | 0.203874i | ||||
\(547\) | −45.5847 | −1.94906 | −0.974530 | − | 0.224257i | \(-0.928005\pi\) | ||||
−0.974530 | + | 0.224257i | \(0.928005\pi\) | |||||||
\(548\) | −13.9168 | + | 8.03486i | −0.594496 | + | 0.343232i | ||||
\(549\) | −0.267949 | − | 0.464102i | −0.0114358 | − | 0.0198074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.63384i | 0.197408i | ||||||||
\(552\) | −7.50670 | − | 4.33399i | −0.319506 | − | 0.184467i | ||||
\(553\) | −3.39921 | − | 1.96254i | −0.144549 | − | 0.0834555i | ||||
\(554\) | − | 9.00566i | − | 0.382614i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.66129 | + | 8.07359i | 0.197683 | + | 0.342397i | ||||
\(557\) | 31.9209 | − | 18.4296i | 1.35253 | − | 0.780885i | 0.363929 | − | 0.931427i | \(-0.381435\pi\) |
0.988604 | + | 0.150541i | \(0.0481016\pi\) | |||||||
\(558\) | −10.1321 | −0.428925 | ||||||||
\(559\) | 26.1502 | − | 16.7005i | 1.10603 | − | 0.706357i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.9811 | − | 9.22671i | 0.674724 | − | 0.389552i | ||||
\(562\) | −0.858478 | − | 1.48693i | −0.0362127 | − | 0.0627223i | ||||
\(563\) | −16.8870 | + | 29.2491i | −0.711701 | + | 1.23270i | 0.252518 | + | 0.967592i | \(0.418741\pi\) |
−0.964218 | + | 0.265109i | \(0.914592\pi\) | |||||||
\(564\) | − | 9.10926i | − | 0.383569i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.34172 | + | 0.774645i | 0.0563969 | + | 0.0325607i | ||||
\(567\) | 1.32258i | 0.0555431i | ||||||||
\(568\) | −5.66799 | + | 9.81724i | −0.237823 | + | 0.411922i | ||||
\(569\) | −12.7159 | − | 22.0246i | −0.533079 | − | 0.923320i | −0.999254 | − | 0.0386274i | \(-0.987701\pi\) |
0.466175 | − | 0.884693i | \(-0.345632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.3682 | 0.559443 | 0.279722 | − | 0.960081i | \(-0.409758\pi\) | ||||
0.279722 | + | 0.960081i | \(0.409758\pi\) | |||||||
\(572\) | 7.66412 | − | 14.7628i | 0.320453 | − | 0.617264i | ||||
\(573\) | 9.74715 | 0.407193 | ||||||||
\(574\) | 5.32051 | − | 3.07180i | 0.222074 | − | 0.128214i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 9.57428i | − | 0.398582i | −0.979940 | − | 0.199291i | \(-0.936136\pi\) | ||
0.979940 | − | 0.199291i | \(-0.0638639\pi\) | |||||||
\(578\) | 0.866025 | + | 0.500000i | 0.0360219 | + | 0.0207973i | ||||
\(579\) | 11.9188 | + | 6.88130i | 0.495327 | + | 0.285977i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.4959 | − | 18.1794i | 0.435444 | − | 0.754210i | ||||
\(582\) | 4.40947 | + | 7.63743i | 0.182778 | + | 0.316582i | ||||
\(583\) | 3.30279 | − | 1.90687i | 0.136788 | − | 0.0789745i | ||||
\(584\) | −6.28304 | −0.259994 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.4057 | −1.25605 | ||||||||
\(587\) | −1.21286 | + | 0.700246i | −0.0500602 | + | 0.0289023i | −0.524821 | − | 0.851212i | \(-0.675868\pi\) |
0.474761 | + | 0.880115i | \(0.342534\pi\) | |||||||
\(588\) | −2.62539 | − | 4.54731i | −0.108269 | − | 0.187528i | ||||
\(589\) | −11.6052 | + | 20.1007i | −0.478183 | + | 0.828237i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.78282 | + | 5.07076i | 0.361277 | + | 0.208583i | ||||
\(592\) | 5.89721 | + | 3.40475i | 0.242374 | + | 0.139935i | ||||
\(593\) | − | 10.7303i | − | 0.440643i | −0.975427 | − | 0.220321i | \(-0.929289\pi\) | ||
0.975427 | − | 0.220321i | \(-0.0707106\pi\) | |||||||
\(594\) | 2.30668 | − | 3.99528i | 0.0946441 | − | 0.163928i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.53788 | − | 2.04259i | 0.144917 | − | 0.0836679i | ||||
\(597\) | 9.57336 | 0.391812 | ||||||||
\(598\) | 16.8215 | + | 26.3397i | 0.687884 | + | 1.07711i | ||||
\(599\) | −40.7967 | −1.66691 | −0.833453 | − | 0.552590i | \(-0.813640\pi\) | ||||
−0.833453 | + | 0.552590i | \(0.813640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.4416 | − | 37.1379i | −0.874621 | − | 1.51489i | −0.857166 | − | 0.515040i | \(-0.827777\pi\) |
−0.0174548 | − | 0.999848i | \(-0.505556\pi\) | |||||||
\(602\) | 5.69081 | − | 9.85677i | 0.231940 | − | 0.401732i | ||||
\(603\) | 3.18106i | 0.129543i | ||||||||
\(604\) | 17.3042 | + | 9.99057i | 0.704097 | + | 0.406510i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 7.22671i | − | 0.293565i | ||||||
\(607\) | −3.43616 | + | 5.95161i | −0.139470 | + | 0.241568i | −0.927296 | − | 0.374329i | \(-0.877873\pi\) |
0.787826 | + | 0.615897i | \(0.211206\pi\) | |||||||
\(608\) | −1.14539 | − | 1.98387i | −0.0464516 | − | 0.0804565i | ||||
\(609\) | 2.31692 | − | 1.33767i | 0.0938863 | − | 0.0542053i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.1331 | + | 29.1498i | −0.612221 | + | 1.17927i | ||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | 0.659358 | − | 0.380681i | 0.0266312 | − | 0.0153755i | −0.486625 | − | 0.873611i | \(-0.661772\pi\) |
0.513257 | + | 0.858235i | \(0.328439\pi\) | |||||||
\(614\) | 4.91311 | + | 8.50975i | 0.198277 | + | 0.343426i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 6.10153i | − | 0.245838i | ||||||
\(617\) | −21.3061 | − | 12.3011i | −0.857753 | − | 0.495224i | 0.00550613 | − | 0.999985i | \(-0.498247\pi\) |
−0.863259 | + | 0.504761i | \(0.831581\pi\) | |||||||
\(618\) | 15.9349 | + | 9.20002i | 0.640996 | + | 0.370079i | ||||
\(619\) | − | 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 | ||||
\(622\) | −2.94491 | + | 1.70025i | −0.118080 | + | 0.0681737i | ||||
\(623\) | −15.6913 | −0.628657 | ||||||||
\(624\) | −3.03873 | + | 1.94065i | −0.121646 | + | 0.0776883i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.0590 | − | 8.11699i | 0.561912 | − | 0.324420i | ||||
\(627\) | −5.28408 | − | 9.15229i | −0.211026 | − | 0.365507i | ||||
\(628\) | −3.56690 | + | 6.17804i | −0.142335 | + | 0.246531i | ||||
\(629\) | − | 27.2380i | − | 1.08605i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.08519 | + | 1.20388i | 0.0830100 | + | 0.0479259i | 0.540930 | − | 0.841067i | \(-0.318072\pi\) |
−0.457920 | + | 0.888993i | \(0.651406\pi\) | |||||||
\(632\) | − | 2.96774i | − | 0.118050i | ||||||
\(633\) | −0.542594 | + | 0.939800i | −0.0215662 | + | 0.0373537i | ||||
\(634\) | 11.7616 | + | 20.3716i | 0.467112 | + | 0.809061i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.826674 | −0.0327797 | ||||||||
\(637\) | 0.846898 | + | 18.9130i | 0.0335553 | + | 0.749361i | ||||
\(638\) | −9.33201 | −0.369458 | ||||||||
\(639\) | 9.81724 | − | 5.66799i | 0.388364 | − | 0.224222i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.73875 | + | 16.8680i | −0.384657 | + | 0.666246i | −0.991722 | − | 0.128407i | \(-0.959014\pi\) |
0.607064 | + | 0.794653i | \(0.292347\pi\) | |||||||
\(642\) | 3.07180i | 0.121234i | ||||||||
\(643\) | 20.7451 | + | 11.9772i | 0.818106 | + | 0.472334i | 0.849763 | − | 0.527165i | \(-0.176745\pi\) |
−0.0316570 | + | 0.999499i | \(0.510078\pi\) | |||||||
\(644\) | 9.92820 | + | 5.73205i | 0.391226 | + | 0.225874i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.58155 | + | 7.93548i | −0.180259 | + | 0.312217i | ||||
\(647\) | −9.10540 | − | 15.7710i | −0.357970 | − | 0.620022i | 0.629652 | − | 0.776878i | \(-0.283198\pi\) |
−0.987622 | + | 0.156855i | \(0.949864\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −14.4930 | −0.568898 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.4005 | 0.525207 | ||||||||
\(652\) | 8.56906 | − | 4.94735i | 0.335590 | − | 0.193753i | ||||
\(653\) | −24.0793 | − | 41.7065i | −0.942294 | − | 1.63210i | −0.761081 | − | 0.648657i | \(-0.775331\pi\) |
−0.181213 | − | 0.983444i | \(-0.558002\pi\) | |||||||
\(654\) | 6.61335 | − | 11.4547i | 0.258603 | − | 0.447913i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.02283 | + | 2.32258i | 0.157065 | + | 0.0906815i | ||||
\(657\) | 5.44128 | + | 3.14152i | 0.212284 | + | 0.122562i | ||||
\(658\) | 12.0477i | 0.469669i | ||||||||
\(659\) | 18.4127 | − | 31.8917i | 0.717257 | − | 1.24233i | −0.244826 | − | 0.969567i | \(-0.578731\pi\) |
0.962083 | − | 0.272758i | \(-0.0879359\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5131 | + | 11.2659i | −0.758971 | + | 0.438192i | −0.828926 | − | 0.559358i | \(-0.811048\pi\) |
0.0699555 | + | 0.997550i | \(0.477714\pi\) | |||||||
\(662\) | 18.0904 | 0.703103 | ||||||||
\(663\) | 12.8001 | + | 6.64516i | 0.497114 | + | 0.258077i | ||||
\(664\) | 15.8719 | 0.615948 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.40475 | − | 5.89721i | −0.131932 | − | 0.228512i | ||||
\(667\) | 8.76691 | − | 15.1847i | 0.339456 | − | 0.587955i | ||||
\(668\) | 24.0375i | 0.930037i | ||||||||
\(669\) | −21.6001 | − | 12.4708i | −0.835106 | − | 0.482149i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.47229i | − | 0.0954417i | ||||||
\(672\) | −0.661290 | + | 1.14539i | −0.0255098 | + | 0.0441843i | ||||
\(673\) | −11.8719 | − | 20.5627i | −0.457627 | − | 0.792633i | 0.541208 | − | 0.840889i | \(-0.317967\pi\) |
−0.998835 | + | 0.0482556i | \(0.984634\pi\) | |||||||
\(674\) | 4.93548 | − | 2.84950i | 0.190108 | − | 0.109759i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.9480 | − | 1.16191i | 0.497999 | − | 0.0446890i | ||||
\(677\) | −1.16559 | −0.0447975 | −0.0223987 | − | 0.999749i | \(-0.507130\pi\) | ||||
−0.0223987 | + | 0.999749i | \(0.507130\pi\) | |||||||
\(678\) | −7.00306 | + | 4.04322i | −0.268951 | + | 0.155279i | ||||
\(679\) | −5.83188 | − | 10.1011i | −0.223807 | − | 0.387645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.3205i | 0.740363i | ||||||||
\(682\) | −40.4806 | − | 23.3715i | −1.55008 | − | 0.894939i | ||||
\(683\) | −12.0134 | − | 6.93593i | −0.459680 | − | 0.265396i | 0.252230 | − | 0.967667i | \(-0.418836\pi\) |
−0.711910 | + | 0.702271i | \(0.752169\pi\) | |||||||
\(684\) | 2.29078i | 0.0875900i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.10132 | + | 14.0319i | 0.309310 | + | 0.535740i | ||||
\(687\) | 3.59826 | − | 2.07746i | 0.137282 | − | 0.0792599i | ||||
\(688\) | 8.60562 | 0.328086 | ||||||||
\(689\) | 2.64537 | + | 1.37334i | 0.100781 | + | 0.0523203i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.6967 | + | 20.6095i | −1.35797 | + | 0.784022i | −0.989349 | − | 0.145560i | \(-0.953502\pi\) |
−0.368616 | + | 0.929582i | \(0.620168\pi\) | |||||||
\(692\) | 1.26408 | + | 2.18946i | 0.0480532 | + | 0.0832307i | ||||
\(693\) | −3.05076 | + | 5.28408i | −0.115889 | + | 0.200726i | ||||
\(694\) | 15.7471i | 0.597753i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.75182 | + | 1.01141i | 0.0664025 | + | 0.0383375i | ||||
\(697\) | − | 18.5806i | − | 0.703792i | ||||||
\(698\) | 7.66025 | − | 13.2679i | 0.289945 | − | 0.502199i | ||||
\(699\) | −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 | \(0.643096\pi\) | |||||||
\(702\) | 3.60194 | − | 0.161290i | 0.135947 | − | 0.00608749i | ||||
\(703\) | −15.5991 | −0.588329 | ||||||||
\(704\) | 3.99528 | − | 2.30668i | 0.150578 | − | 0.0869362i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.599964 | + | 1.03917i | −0.0225799 | + | 0.0391096i | ||||
\(707\) | 9.55790i | 0.359462i | ||||||||
\(708\) | 2.72064 | + | 1.57076i | 0.102248 | + | 0.0590328i | ||||
\(709\) | −14.7944 | − | 8.54156i | −0.555616 | − | 0.320785i | 0.195768 | − | 0.980650i | \(-0.437280\pi\) |
−0.751384 | + | 0.659865i | \(0.770613\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.48387 | + | 2.57014i | −0.0556495 | + | 0.0963877i | ||||
\(712\) | −5.93207 | − | 10.2746i | −0.222314 | − | 0.385059i | ||||
\(713\) | 76.0585 | − | 43.9124i | 2.84841 | − | 1.64453i | ||||
\(714\) | 5.29032 | 0.197985 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.27568 | −0.234533 | ||||||||
\(717\) | −5.49420 | + | 3.17208i | −0.205185 | + | 0.118463i | ||||
\(718\) | −8.14152 | − | 14.1015i | −0.303839 | − | 0.526264i | ||||
\(719\) | −21.8564 | + | 37.8564i | −0.815106 | + | 1.41181i | 0.0941451 | + | 0.995558i | \(0.469988\pi\) |
−0.909251 | + | 0.416247i | \(0.863345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.0752 | − | 12.1678i | −0.784880 | − | 0.453151i | ||||
\(722\) | −11.9099 | − | 6.87617i | −0.443240 | − | 0.255905i | ||||
\(723\) | 24.1855i | 0.899467i | ||||||||
\(724\) | −6.14152 | + | 10.6374i | −0.228248 | + | 0.395337i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.90538 | − | 5.14152i | 0.330510 | − | 0.190820i | ||||
\(727\) | −31.8453 | −1.18108 | −0.590538 | − | 0.807010i | \(-0.701084\pi\) | ||||
−0.590538 | + | 0.807010i | \(0.701084\pi\) | |||||||
\(728\) | 4.01896 | − | 2.56667i | 0.148953 | − | 0.0951270i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.2112 | − | 29.8108i | −0.636581 | − | 1.10259i | ||||
\(732\) | −0.267949 | + | 0.464102i | −0.00990369 | + | 0.0171537i | ||||
\(733\) | − | 5.96774i | − | 0.220423i | −0.993908 | − | 0.110212i | \(-0.964847\pi\) | ||
0.993908 | − | 0.110212i | \(-0.0351529\pi\) | |||||||
\(734\) | −17.0040 | − | 9.81724i | −0.627627 | − | 0.362361i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.66799i | 0.319506i | ||||||||
\(737\) | −7.33767 | + | 12.7092i | −0.270287 | + | 0.468150i | ||||
\(738\) | −2.32258 | − | 4.02283i | −0.0854953 | − | 0.148082i | ||||
\(739\) | 9.37833 | − | 5.41458i | 0.344988 | − | 0.199179i | −0.317488 | − | 0.948262i | \(-0.602839\pi\) |
0.662475 | + | 0.749084i | \(0.269506\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.80564 | − | 7.33052i | 0.139804 | − | 0.269293i | ||||
\(742\) | 1.09334 | 0.0401378 | ||||||||
\(743\) | −17.1909 | + | 9.92515i | −0.630671 | + | 0.364118i | −0.781012 | − | 0.624516i | \(-0.785296\pi\) |
0.150341 | + | 0.988634i | \(0.451963\pi\) | |||||||
\(744\) | 5.06604 | + | 8.77464i | 0.185730 | + | 0.321694i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.55748i | 0.0936359i | ||||||||
\(747\) | −13.7454 | − | 7.93593i | −0.502919 | − | 0.290361i | ||||
\(748\) | −15.9811 | − | 9.22671i | −0.584328 | − | 0.337362i | ||||
\(749\) | − | 4.06270i | − | 0.148448i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.66538 | − | 13.2768i | −0.279714 | − | 0.484479i | 0.691600 | − | 0.722281i | \(-0.256906\pi\) |
−0.971314 | + | 0.237802i | \(0.923573\pi\) | |||||||
\(752\) | −7.88885 | + | 4.55463i | −0.287677 | + | 0.166090i | ||||
\(753\) | 8.82497 | 0.321600 | ||||||||
\(754\) | −3.92560 | − | 6.14682i | −0.142962 | − | 0.223854i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.14539 | − | 0.661290i | 0.0416573 | − | 0.0240509i | ||||
\(757\) | 22.5816 | + | 39.1125i | 0.820744 | + | 1.42157i | 0.905129 | + | 0.425137i | \(0.139774\pi\) |
−0.0843855 | + | 0.996433i | \(0.526893\pi\) | |||||||
\(758\) | −7.55440 | + | 13.0846i | −0.274388 | + | 0.475254i | ||||
\(759\) | 39.9885i | 1.45149i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.7978 | − | 10.8529i | −0.681419 | − | 0.393418i | 0.118970 | − | 0.992898i | \(-0.462041\pi\) |
−0.800390 | + | 0.599480i | \(0.795374\pi\) | |||||||
\(762\) | − | 11.4718i | − | 0.415581i | ||||||
\(763\) | −8.74669 | + | 15.1497i | −0.316651 | + | 0.548456i | ||||
\(764\) | −4.87357 | − | 8.44128i | −0.176320 | − | 0.305395i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.7303 | 0.676755 | ||||||||
\(767\) | −6.09660 | − | 9.54623i | −0.220136 | − | 0.344694i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 36.4711 | − | 21.0566i | 1.31518 | − | 0.759321i | 0.332233 | − | 0.943197i | \(-0.392198\pi\) |
0.982949 | + | 0.183877i | \(0.0588647\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.19247 | − | 7.26157i | 0.150988 | − | 0.261519i | ||||
\(772\) | − | 13.7626i | − | 0.495327i | ||||||
\(773\) | −25.7734 | − | 14.8803i | −0.927004 | − | 0.535206i | −0.0411413 | − | 0.999153i | \(-0.513099\pi\) |
−0.885863 | + | 0.463947i | \(0.846433\pi\) | |||||||
\(774\) | −7.45269 | − | 4.30281i | −0.267881 | − | 0.154661i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.40947 | − | 7.63743i | 0.158291 | − | 0.274168i | ||||
\(777\) | 4.50306 | + | 7.79953i | 0.161546 | + | 0.279806i | ||||
\(778\) | 6.03532 | − | 3.48449i | 0.216377 | − | 0.124925i | ||||
\(779\) | −10.6410 | −0.381254 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.2969 | 1.87133 | ||||||||
\(782\) | 30.0268 | − | 17.3360i | 1.07376 | − | 0.619933i | ||||
\(783\) | −1.01141 | − | 1.75182i | −0.0361450 | − | 0.0626049i | ||||
\(784\) | −2.62539 | + | 4.54731i | −0.0937640 | + | 0.162404i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.8482 | − | 7.99528i | −0.493950 | − | 0.285182i | ||||
\(787\) | 35.5459 | + | 20.5224i | 1.26707 | + | 0.731545i | 0.974433 | − | 0.224678i | \(-0.0721329\pi\) |
0.292640 | + | 0.956223i | \(0.405466\pi\) | |||||||
\(788\) | − | 10.1415i | − | 0.361277i | ||||||
\(789\) | −0.960648 | + | 1.66389i | −0.0342000 | + | 0.0592361i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.26210 | − | 5.34748i | 0.329322 | − | 0.190134i | ||||
\(792\) | −4.61335 | −0.163928 | ||||||||
\(793\) | 1.62845 | − | 1.03999i | 0.0578279 | − | 0.0369312i | ||||
\(794\) | 18.5721 | 0.659100 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.78668 | − | 8.29078i | −0.169659 | − | 0.293859i | ||||
\(797\) | −22.6263 | + | 39.1899i | −0.801464 | + | 1.38818i | 0.117188 | + | 0.993110i | \(0.462612\pi\) |
−0.918652 | + | 0.395067i | \(0.870721\pi\) | |||||||
\(798\) | − | 3.02973i | − | 0.107251i | ||||||
\(799\) | 31.5554 | + | 18.2185i | 1.11635 | + | 0.644525i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.8641i | 0.419199i | ||||||||
\(802\) | −14.8452 | + | 25.7126i | −0.524201 | + | 0.907944i | ||||
\(803\) | 14.4930 | + | 25.1025i | 0.511445 | + | 0.885849i | ||||
\(804\) | 2.75488 | − | 1.59053i | 0.0971570 | − | 0.0560936i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.63420 | − | 36.4952i | −0.0575623 | − | 1.28549i | ||||
\(807\) | 32.3098 | 1.13736 | ||||||||
\(808\) | −6.25851 | + | 3.61335i | −0.220174 | + | 0.127117i | ||||
\(809\) | 14.2267 | + | 24.6414i | 0.500184 | + | 0.866345i | 1.00000 | 0.000213036i | \(6.78113e-5\pi\) | |
−0.499815 | + | 0.866132i | \(0.666599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.4114i | 1.55949i | 0.626095 | + | 0.779747i | \(0.284652\pi\) | ||||
−0.626095 | + | 0.779747i | \(0.715348\pi\) | |||||||
\(812\) | −2.31692 | − | 1.33767i | −0.0813079 | − | 0.0469432i | ||||
\(813\) | 20.3105 | + | 11.7263i | 0.712322 | + | 0.411259i | ||||
\(814\) | − | 31.4147i | − | 1.10108i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | −17.0724 | + | 9.85677i | −0.597289 | + | 0.344845i | ||||
\(818\) | −24.3355 | −0.850871 | ||||||||
\(819\) | −4.76386 | + | 0.213319i | −0.166463 | + | 0.00745396i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.1169 | + | 22.5842i | −1.36519 | + | 0.788192i | −0.990309 | − | 0.138881i | \(-0.955649\pi\) |
−0.374880 | + | 0.927073i | \(0.622316\pi\) | |||||||
\(822\) | −8.03486 | − | 13.9168i | −0.280248 | − | 0.485404i | ||||
\(823\) | −1.20900 | + | 2.09404i | −0.0421430 | + | 0.0729938i | −0.886328 | − | 0.463059i | \(-0.846752\pi\) |
0.844185 | + | 0.536053i | \(0.180085\pi\) | |||||||
\(824\) | − | 18.4000i | − | 0.640996i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.59826 | − | 2.07746i | −0.125199 | − | 0.0722840i | ||||
\(827\) | 4.26832i | 0.148424i | 0.997242 | + | 0.0742120i | \(0.0236441\pi\) | ||||
−0.997242 | + | 0.0742120i | \(0.976356\pi\) | |||||||
\(828\) | 4.33399 | − | 7.50670i | 0.150617 | − | 0.260876i | ||||
\(829\) | −21.4926 | − | 37.2263i | −0.746468 | − | 1.29292i | −0.949506 | − | 0.313750i | \(-0.898415\pi\) |
0.203037 | − | 0.979171i | \(-0.434919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.00566 | 0.312403 | ||||||||
\(832\) | 3.20002 | + | 1.66129i | 0.110941 | + | 0.0575949i | ||||
\(833\) | 21.0031 | 0.727715 | ||||||||
\(834\) | −8.07359 | + | 4.66129i | −0.279566 | + | 0.161407i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.28408 | + | 9.15229i | −0.182754 | + | 0.316539i | ||||
\(837\) | − | 10.1321i | − | 0.350216i | ||||||
\(838\) | 2.49636 | + | 1.44128i | 0.0862354 | + | 0.0497880i | ||||
\(839\) | −20.1798 | − | 11.6508i | −0.696684 | − | 0.402231i | 0.109427 | − | 0.993995i | \(-0.465098\pi\) |
−0.806111 | + | 0.591764i | \(0.798432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4541 | − | 21.5711i | 0.429451 | − | 0.743831i | ||||
\(842\) | 2.47354 | + | 4.28429i | 0.0852437 | + | 0.147646i | ||||
\(843\) | 1.48693 | − | 0.858478i | 0.0512125 | − | 0.0295676i | ||||
\(844\) | 1.08519 | 0.0373537 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.10926 | 0.313183 | ||||||||
\(847\) | −11.7781 | + | 6.80007i | −0.404699 | + | 0.233653i | ||||
\(848\) | 0.413337 | + | 0.715920i | 0.0141940 | + | 0.0245848i | ||||
\(849\) | −0.774645 | + | 1.34172i | −0.0265857 | + | 0.0460479i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.1169 | + | 29.5124i | 1.75226 | + | 1.01167i | ||||
\(852\) | −9.81724 | − | 5.66799i | −0.336333 | − | 0.194182i | ||||
\(853\) | 20.8418i | 0.713609i | 0.934179 | + | 0.356804i | \(0.116134\pi\) | ||||
−0.934179 | + | 0.356804i | \(0.883866\pi\) | |||||||
\(854\) | 0.354384 | − | 0.613811i | 0.0121268 | − | 0.0210042i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.66025 | − | 1.53590i | 0.0909256 | − | 0.0524959i | ||||
\(857\) | −36.7250 | −1.25450 | −0.627250 | − | 0.778818i | \(-0.715820\pi\) | ||||
−0.627250 | + | 0.778818i | \(0.715820\pi\) | |||||||
\(858\) | 14.7628 | + | 7.66412i | 0.503994 | + | 0.261649i | ||||
\(859\) | 0.914812 | 0.0312130 | 0.0156065 | − | 0.999878i | \(-0.495032\pi\) | ||||
0.0156065 | + | 0.999878i | \(0.495032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.07180 | + | 5.32051i | 0.104687 | + | 0.181322i | ||||
\(862\) | −8.88130 | + | 15.3829i | −0.302498 | + | 0.523943i | ||||
\(863\) | 33.6104i | 1.14411i | 0.820215 | + | 0.572056i | \(0.193854\pi\) | ||||
−0.820215 | + | 0.572056i | \(0.806146\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.8375i | 1.21781i | ||||||||
\(867\) | −0.500000 | + | 0.866025i | −0.0169809 | + | 0.0294118i | ||||
\(868\) | −6.70025 | − | 11.6052i | −0.227421 | − | 0.393905i | ||||
\(869\) | −11.8570 | + | 6.84562i | −0.402220 | + | 0.232222i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.4580 | + | 0.513072i | −0.388239 | + | 0.0173848i | ||||
\(872\) | −13.2267 | −0.447913 | ||||||||
\(873\) | −7.63743 | + | 4.40947i | −0.258488 | + | 0.149238i | ||||
\(874\) | −9.92820 | − | 17.1962i | −0.335826 | − | 0.581669i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 6.28304i | − | 0.212284i | ||||||
\(877\) | 21.0629 | + | 12.1607i | 0.711243 | + | 0.410637i | 0.811521 | − | 0.584323i | \(-0.198640\pi\) |
−0.100278 | + | 0.994959i | \(0.531973\pi\) | |||||||
\(878\) | 8.73854 | + | 5.04520i | 0.294911 | + | 0.170267i | ||||
\(879\) | − | 30.4057i | − | 1.02556i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.95207 | − | 8.57723i | −0.166839 | − | 0.288974i | 0.770468 | − | 0.637479i | \(-0.220023\pi\) |
−0.937307 | + | 0.348505i | \(0.886689\pi\) | |||||||
\(882\) | 4.54731 | − | 2.62539i | 0.153116 | − | 0.0884015i | ||||
\(883\) | 43.9718 | 1.47977 | 0.739884 | − | 0.672734i | \(-0.234880\pi\) | ||||
0.739884 | + | 0.672734i | \(0.234880\pi\) | |||||||
\(884\) | −0.645159 | − | 14.4078i | −0.0216991 | − | 0.484586i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.8629 | + | 6.84904i | −0.398542 | + | 0.230098i | ||||
\(887\) | 25.2807 | + | 43.7875i | 0.848843 | + | 1.47024i | 0.882242 | + | 0.470797i | \(0.156034\pi\) |
−0.0333988 | + | 0.999442i | \(0.510633\pi\) | |||||||
\(888\) | −3.40475 | + | 5.89721i | −0.114256 | + | 0.197897i | ||||
\(889\) | 15.1724i | 0.508866i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.99528 | + | 2.30668i | 0.133847 | + | 0.0772766i | ||||
\(892\) | 24.9416i | 0.835106i | ||||||||
\(893\) | 10.4336 | − | 18.0716i | 0.349148 | − | 0.604743i | ||||
\(894\) | 2.04259 | + | 3.53788i | 0.0683146 | + | 0.118324i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.32258 | 0.0441843 | ||||||||
\(897\) | −26.3397 | + | 16.8215i | −0.879455 | + | 0.561655i | ||||
\(898\) | 15.3128 | 0.510994 | ||||||||
\(899\) | −17.7496 | + | 10.2477i | −0.591982 | + | 0.341781i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.65335 | − | 2.86368i | 0.0550810 | − | 0.0954031i | ||||
\(902\) | − | 21.4298i | − | 0.713533i | ||||||
\(903\) | 9.85677 | + | 5.69081i | 0.328013 | + | 0.189378i | ||||
\(904\) | 7.00306 | + | 4.04322i | 0.232918 | + | 0.134475i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.99057 | + | 17.3042i | −0.331914 | + | 0.574892i | ||||
\(907\) | −7.12175 | − | 12.3352i | −0.236474 | − | 0.409585i | 0.723226 | − | 0.690611i | \(-0.242658\pi\) |
−0.959700 | + | 0.281026i | \(0.909325\pi\) | |||||||
\(908\) | 16.7321 | − | 9.66025i | 0.555273 | − | 0.320587i | ||||
\(909\) | 7.22671 | 0.239695 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.8108 | 0.722623 | 0.361311 | − | 0.932445i | \(-0.382329\pi\) | ||||
0.361311 | + | 0.932445i | \(0.382329\pi\) | |||||||
\(912\) | 1.98387 | − | 1.14539i | 0.0656925 | − | 0.0379276i | ||||
\(913\) | −36.6113 | − | 63.4126i | −1.21166 | − | 2.09865i | ||||
\(914\) | 7.77770 | − | 13.4714i | 0.257264 | − | 0.445594i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.59826 | − | 2.07746i | −0.118890 | − | 0.0686411i | ||||
\(917\) | 18.3154 | + | 10.5744i | 0.604828 | + | 0.349197i | ||||
\(918\) | − | 4.00000i | − | 0.132020i | ||||||
\(919\) | 2.65289 | − | 4.59494i | 0.0875108 | − | 0.151573i | −0.818948 | − | 0.573868i | \(-0.805442\pi\) |
0.906458 | + | 0.422295i | \(0.138775\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.50975 | + | 4.91311i | −0.280406 | + | 0.161892i | ||||
\(922\) | 15.6431 | 0.515178 | ||||||||
\(923\) | 21.9992 | + | 34.4469i | 0.724112 | + | 1.13383i | ||||
\(924\) | 6.10153 | 0.200726 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.85848 | + | 11.8792i | 0.225384 | + | 0.390376i | ||||
\(927\) | −9.20002 | + | 15.9349i | −0.302168 | + | 0.523371i | ||||
\(928\) | − | 2.02283i | − | 0.0664025i | ||||||
\(929\) | −38.4002 | − | 22.1704i | −1.25987 | − | 0.727386i | −0.286821 | − | 0.957984i | \(-0.592599\pi\) |
−0.973049 | + | 0.230598i | \(0.925932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 12.0284i | − | 0.394214i | ||||||
\(932\) | −8.48325 | + | 14.6934i | −0.277878 | + | 0.481299i | ||||
\(933\) | −1.70025 | − | 2.94491i | −0.0556636 | − | 0.0964121i | ||||
\(934\) | 0.817239 | − | 0.471833i | 0.0267409 | − | 0.0154388i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.94065 | − | 3.03873i | −0.0634322 | − | 0.0993239i | ||||
\(937\) | −38.5283 | −1.25867 | −0.629333 | − | 0.777136i | \(-0.716672\pi\) | ||||
−0.629333 | + | 0.777136i | \(0.716672\pi\) | |||||||
\(938\) | −3.64354 | + | 2.10360i | −0.118966 | + | 0.0686850i | ||||
\(939\) | 8.11699 | + | 14.0590i | 0.264888 | + | 0.458800i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 28.8637i | − | 0.940929i | −0.882419 | − | 0.470465i | \(-0.844086\pi\) | ||
0.882419 | − | 0.470465i | \(-0.155914\pi\) | |||||||
\(942\) | −6.17804 | − | 3.56690i | −0.201292 | − | 0.116216i | ||||
\(943\) | 34.8698 | + | 20.1321i | 1.13552 | + | 0.655591i | ||||
\(944\) | − | 3.14152i | − | 0.102248i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −19.8504 | − | 34.3819i | −0.645392 | − | 1.11785i | ||||
\(947\) | −42.6384 | + | 24.6173i | −1.38556 | + | 0.799955i | −0.992811 | − | 0.119689i | \(-0.961810\pi\) |
−0.392752 | + | 0.919645i | \(0.628477\pi\) | |||||||
\(948\) | 2.96774 | 0.0963877 | ||||||||
\(949\) | −10.4380 | + | 20.1059i | −0.338830 | + | 0.652664i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.3716 | + | 11.7616i | −0.660596 | + | 0.381395i | ||||
\(952\) | −2.64516 | − | 4.58155i | −0.0857301 | − | 0.148489i | ||||
\(953\) | 13.2548 | − | 22.9580i | 0.429366 | − | 0.743684i | −0.567451 | − | 0.823407i | \(-0.692070\pi\) |
0.996817 | + | 0.0797233i | \(0.0254037\pi\) | |||||||
\(954\) | − | 0.826674i | − | 0.0267645i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.49420 | + | 3.17208i | 0.177695 | + | 0.102592i | ||||
\(957\) | − | 9.33201i | − | 0.301661i | ||||||
\(958\) | −5.55099 | + | 9.61460i | −0.179344 | + | 0.310634i | ||||
\(959\) | 10.6267 | + | 18.4061i | 0.343156 | + | 0.594363i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −71.6592 | −2.31159 | ||||||||
\(962\) | 20.6922 | − | 13.2149i | 0.667145 | − | 0.426065i | ||||
\(963\) | −3.07180 | −0.0989873 | ||||||||
\(964\) | 20.9452 | − | 12.0927i | 0.674600 | − | 0.389481i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.73205 | + | 9.92820i | −0.184426 | + | 0.319435i | ||||
\(967\) | 52.3877i | 1.68468i | 0.538950 | + | 0.842338i | \(0.318821\pi\) | ||||
−0.538950 | + | 0.842338i | \(0.681179\pi\) | |||||||
\(968\) | −8.90538 | − | 5.14152i | −0.286230 | − | 0.165255i | ||||
\(969\) | −7.93548 | − | 4.58155i | −0.254924 | − | 0.147181i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3215 | − | 24.8056i | 0.459600 | − | 0.796051i | −0.539339 | − | 0.842088i | \(-0.681326\pi\) |
0.998940 | + | 0.0460375i | \(0.0146594\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 10.6780 | − | 6.16493i | 0.342320 | − | 0.197638i | ||||
\(974\) | 32.9416 | 1.05552 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.535898 | 0.0171537 | ||||||||
\(977\) | −35.1173 | + | 20.2750i | −1.12350 | + | 0.648654i | −0.942292 | − | 0.334791i | \(-0.891334\pi\) |
−0.181209 | + | 0.983445i | \(0.558001\pi\) | |||||||
\(978\) | 4.94735 | + | 8.56906i | 0.158199 | + | 0.274008i | ||||
\(979\) | −27.3667 | + | 47.4006i | −0.874645 | + | 1.51493i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4547 | + | 6.61335i | 0.365719 | + | 0.211148i | ||||
\(982\) | 24.6396 | + | 14.2257i | 0.786281 | + | 0.453960i | ||||
\(983\) | 22.4160i | 0.714958i | 0.933921 | + | 0.357479i | \(0.116364\pi\) | ||||
−0.933921 | + | 0.357479i | \(0.883636\pi\) | |||||||
\(984\) | −2.32258 | + | 4.02283i | −0.0740411 | + | 0.128243i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.00727 | + | 4.04565i | −0.223157 | + | 0.128840i | ||||
\(987\) | −12.0477 | −0.383483 | ||||||||
\(988\) | −8.25124 | + | 0.369479i | −0.262507 | + | 0.0117547i | ||||
\(989\) | 74.5934 | 2.37193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.2844 | + | 24.7413i | 0.453759 | + | 0.785933i | 0.998616 | − | 0.0525955i | \(-0.0167494\pi\) |
−0.544857 | + | 0.838529i | \(0.683416\pi\) | |||||||
\(992\) | 5.06604 | − | 8.77464i | 0.160847 | − | 0.278595i | ||||
\(993\) | 18.0904i | 0.574081i | ||||||||
\(994\) | 12.9841 | + | 7.49636i | 0.411830 | + | 0.237770i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.8719i | 0.502919i | ||||||||
\(997\) | −17.2000 | + | 29.7913i | −0.544730 | + | 0.943500i | 0.453894 | + | 0.891056i | \(0.350035\pi\) |
−0.998624 | + | 0.0524443i | \(0.983299\pi\) | |||||||
\(998\) | 2.05463 | + | 3.55872i | 0.0650382 | + | 0.112649i | ||||
\(999\) | 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.bc.g.751.3 | 8 | ||
5.2 | odd | 4 | 1950.2.y.k.49.4 | 8 | |||
5.3 | odd | 4 | 1950.2.y.j.49.1 | 8 | |||
5.4 | even | 2 | 390.2.bb.c.361.2 | yes | 8 | ||
13.4 | even | 6 | inner | 1950.2.bc.g.901.3 | 8 | ||
15.14 | odd | 2 | 1170.2.bs.f.361.4 | 8 | |||
65.4 | even | 6 | 390.2.bb.c.121.2 | ✓ | 8 | ||
65.17 | odd | 12 | 1950.2.y.j.199.1 | 8 | |||
65.24 | odd | 12 | 5070.2.a.ca.1.2 | 4 | |||
65.29 | even | 6 | 5070.2.b.ba.1351.2 | 8 | |||
65.43 | odd | 12 | 1950.2.y.k.199.4 | 8 | |||
65.49 | even | 6 | 5070.2.b.ba.1351.7 | 8 | |||
65.54 | odd | 12 | 5070.2.a.bz.1.3 | 4 | |||
195.134 | odd | 6 | 1170.2.bs.f.901.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.2 | ✓ | 8 | 65.4 | even | 6 | ||
390.2.bb.c.361.2 | yes | 8 | 5.4 | even | 2 | ||
1170.2.bs.f.361.4 | 8 | 15.14 | odd | 2 | |||
1170.2.bs.f.901.4 | 8 | 195.134 | odd | 6 | |||
1950.2.y.j.49.1 | 8 | 5.3 | odd | 4 | |||
1950.2.y.j.199.1 | 8 | 65.17 | odd | 12 | |||
1950.2.y.k.49.4 | 8 | 5.2 | odd | 4 | |||
1950.2.y.k.199.4 | 8 | 65.43 | odd | 12 | |||
1950.2.bc.g.751.3 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.bc.g.901.3 | 8 | 13.4 | even | 6 | inner | ||
5070.2.a.bz.1.3 | 4 | 65.54 | odd | 12 | |||
5070.2.a.ca.1.2 | 4 | 65.24 | odd | 12 | |||
5070.2.b.ba.1351.2 | 8 | 65.29 | even | 6 | |||
5070.2.b.ba.1351.7 | 8 | 65.49 | even | 6 |