Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(89,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.r (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1277.2 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.1277 |
Dual form | 1386.2.r.c.89.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.96593 | + | 3.40508i | 0.879189 | + | 1.52280i | 0.852233 | + | 0.523163i | \(0.175248\pi\) |
0.0269561 | + | 0.999637i | \(0.491419\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.19067 | − | 1.48356i | 0.827996 | − | 0.560734i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.40508 | − | 1.96593i | −1.07678 | − | 0.621680i | ||||
\(11\) | −0.866025 | − | 0.500000i | −0.261116 | − | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | −1.15539 | + | 2.38014i | −0.308792 | + | 0.636119i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.64626 | + | 6.31552i | −0.884349 | + | 1.53174i | −0.0378910 | + | 0.999282i | \(0.512064\pi\) |
−0.846458 | + | 0.532456i | \(0.821269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.17914 | − | 1.83548i | 0.729344 | − | 0.421087i | −0.0888382 | − | 0.996046i | \(-0.528315\pi\) |
0.818182 | + | 0.574959i | \(0.194982\pi\) | |||||||
\(20\) | 3.93185 | 0.879189 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 2.94098 | − | 1.69798i | 0.613237 | − | 0.354053i | −0.160994 | − | 0.986955i | \(-0.551470\pi\) |
0.774231 | + | 0.632903i | \(0.218137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.22973 | + | 9.05816i | −1.04595 | + | 1.81163i | ||||
\(26\) | −1.22474 | − | 2.12132i | −0.240192 | − | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.189469 | − | 2.63896i | −0.0358062 | − | 0.498716i | ||||
\(29\) | 5.16088i | 0.958351i | 0.877719 | + | 0.479175i | \(0.159064\pi\) | ||||
−0.877719 | + | 0.479175i | \(0.840936\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.99465 | − | 1.15161i | −0.358250 | − | 0.206836i | 0.310063 | − | 0.950716i | \(-0.399650\pi\) |
−0.668313 | + | 0.743880i | \(0.732983\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 7.29253i | − | 1.25066i | ||||||
\(35\) | 9.35835 | + | 4.54284i | 1.58185 | + | 0.767880i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.98709 | + | 3.44174i | 0.326675 | + | 0.565818i | 0.981850 | − | 0.189659i | \(-0.0607383\pi\) |
−0.655175 | + | 0.755477i | \(0.727405\pi\) | |||||||
\(38\) | −1.83548 | + | 3.17914i | −0.297753 | + | 0.515724i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.40508 | + | 1.96593i | −0.538391 | + | 0.310840i | ||||
\(41\) | 5.92480 | 0.925299 | 0.462649 | − | 0.886541i | \(-0.346899\pi\) | ||||
0.462649 | + | 0.886541i | \(0.346899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7128 | −1.63369 | −0.816843 | − | 0.576860i | \(-0.804278\pi\) | ||||
−0.816843 | + | 0.576860i | \(0.804278\pi\) | |||||||
\(44\) | −0.866025 | + | 0.500000i | −0.130558 | + | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.69798 | + | 2.94098i | −0.250353 | + | 0.433624i | ||||
\(47\) | −4.31199 | − | 7.46859i | −0.628969 | − | 1.08941i | −0.987759 | − | 0.155987i | \(-0.950144\pi\) |
0.358791 | − | 0.933418i | \(-0.383189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.59808 | − | 6.50000i | 0.371154 | − | 0.928571i | ||||
\(50\) | − | 10.4595i | − | 1.47919i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.12132 | + | 1.22474i | 0.294174 | + | 0.169842i | ||||
\(53\) | 11.5854 | + | 6.68885i | 1.59138 | + | 0.918784i | 0.993071 | + | 0.117519i | \(0.0374940\pi\) |
0.598309 | + | 0.801265i | \(0.295839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.93185i | − | 0.530171i | ||||||
\(56\) | 1.48356 | + | 2.19067i | 0.198250 | + | 0.292741i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.58044 | − | 4.46945i | −0.338828 | − | 0.586868i | ||||
\(59\) | 0.975056 | − | 1.68885i | 0.126941 | − | 0.219869i | −0.795549 | − | 0.605890i | \(-0.792817\pi\) |
0.922490 | + | 0.386021i | \(0.126151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.16813 | − | 2.98382i | 0.661711 | − | 0.382039i | −0.131217 | − | 0.991354i | \(-0.541889\pi\) |
0.792929 | + | 0.609314i | \(0.208555\pi\) | |||||||
\(62\) | 2.30323 | 0.292510 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −8.34072 | + | 4.81552i | −1.03454 | + | 0.597291i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.33378 | + | 4.04222i | −0.285116 | + | 0.493835i | −0.972637 | − | 0.232329i | \(-0.925365\pi\) |
0.687521 | + | 0.726164i | \(0.258699\pi\) | |||||||
\(68\) | 3.64626 | + | 6.31552i | 0.442175 | + | 0.765869i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.3760 | + | 0.744963i | −1.24017 | + | 0.0890401i | ||||
\(71\) | − | 8.90754i | − | 1.05713i | −0.848893 | − | 0.528565i | \(-0.822730\pi\) | ||
0.848893 | − | 0.528565i | \(-0.177270\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.37466 | − | 1.37101i | −0.277933 | − | 0.160464i | 0.354554 | − | 0.935035i | \(-0.384633\pi\) |
−0.632487 | + | 0.774571i | \(0.717966\pi\) | |||||||
\(74\) | −3.44174 | − | 1.98709i | −0.400094 | − | 0.230994i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.67095i | − | 0.421087i | ||||||
\(77\) | −2.63896 | + | 0.189469i | −0.300737 | + | 0.0215920i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.69798 | + | 13.3333i | 0.866090 | + | 1.50011i | 0.865961 | + | 0.500112i | \(0.166708\pi\) |
0.000129281 | 1.00000i | \(0.499959\pi\) | ||||||||
\(80\) | 1.96593 | − | 3.40508i | 0.219797 | − | 0.380700i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.13103 | + | 2.96240i | −0.566628 | + | 0.327143i | ||||
\(83\) | −6.05521 | −0.664646 | −0.332323 | − | 0.943166i | \(-0.607832\pi\) | ||||
−0.332323 | + | 0.943166i | \(0.607832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.6731 | −3.11004 | ||||||||
\(86\) | 9.27755 | − | 5.35640i | 1.00042 | − | 0.577595i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −5.87404 | − | 10.1741i | −0.622647 | − | 1.07846i | −0.988991 | − | 0.147976i | \(-0.952724\pi\) |
0.366344 | − | 0.930479i | \(-0.380609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.63397 | + | 5.36603i | 0.380944 | + | 0.562512i | ||||
\(92\) | − | 3.39595i | − | 0.354053i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.46859 | + | 4.31199i | 0.770326 | + | 0.444748i | ||||
\(95\) | 12.4999 | + | 7.21682i | 1.28246 | + | 0.740430i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.85765i | − | 0.594754i | −0.954760 | − | 0.297377i | \(-0.903888\pi\) | ||
0.954760 | − | 0.297377i | \(-0.0961119\pi\) | |||||||
\(98\) | 1.00000 | + | 6.92820i | 0.101015 | + | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.22973 | + | 9.05816i | 0.522973 | + | 0.905816i | ||||
\(101\) | −7.76028 | + | 13.4412i | −0.772177 | + | 1.33745i | 0.164191 | + | 0.986429i | \(0.447499\pi\) |
−0.936368 | + | 0.351021i | \(0.885835\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7413 | − | 6.20150i | 1.05837 | − | 0.611052i | 0.133391 | − | 0.991063i | \(-0.457413\pi\) |
0.924982 | + | 0.380011i | \(0.124080\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.3777 | −1.29936 | ||||||||
\(107\) | −11.9441 | + | 6.89595i | −1.15468 | + | 0.666657i | −0.950024 | − | 0.312176i | \(-0.898942\pi\) |
−0.204660 | + | 0.978833i | \(0.565609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.45534 | + | 4.25277i | −0.235179 | + | 0.407341i | −0.959325 | − | 0.282306i | \(-0.908901\pi\) |
0.724146 | + | 0.689647i | \(0.242234\pi\) | |||||||
\(110\) | 1.96593 | + | 3.40508i | 0.187444 | + | 0.324662i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.38014 | − | 1.15539i | −0.224902 | − | 0.109175i | ||||
\(113\) | 16.1270i | 1.51710i | 0.651614 | + | 0.758551i | \(0.274092\pi\) | ||||
−0.651614 | + | 0.758551i | \(0.725908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.5635 | + | 6.67619i | 1.07830 | + | 0.622558i | ||||
\(116\) | 4.46945 | + | 2.58044i | 0.414978 | + | 0.239588i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.95011i | 0.179522i | ||||||||
\(119\) | 1.38171 | + | 19.2447i | 0.126661 | + | 1.76416i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | −2.98382 | + | 5.16813i | −0.270143 | + | 0.467901i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.99465 | + | 1.15161i | −0.179125 | + | 0.103418i | ||||
\(125\) | −21.4658 | −1.91996 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.94522 | 0.882495 | 0.441248 | − | 0.897385i | \(-0.354536\pi\) | ||||
0.441248 | + | 0.897385i | \(0.354536\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.81552 | − | 8.34072i | 0.422349 | − | 0.731529i | ||||
\(131\) | 9.24264 | + | 16.0087i | 0.807533 | + | 1.39869i | 0.914567 | + | 0.404433i | \(0.132531\pi\) |
−0.107034 | + | 0.994255i | \(0.534135\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.24140 | − | 8.73737i | 0.367776 | − | 0.757626i | ||||
\(134\) | − | 4.66755i | − | 0.403215i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.31552 | − | 3.64626i | −0.541551 | − | 0.312665i | ||||
\(137\) | −2.41786 | − | 1.39595i | −0.206572 | − | 0.119264i | 0.393145 | − | 0.919476i | \(-0.371387\pi\) |
−0.599717 | + | 0.800212i | \(0.704720\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.10583i | 0.433071i | 0.976275 | + | 0.216535i | \(0.0694757\pi\) | ||||
−0.976275 | + | 0.216535i | \(0.930524\pi\) | |||||||
\(140\) | 8.61339 | − | 5.83315i | 0.727965 | − | 0.492991i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.45377 | + | 7.71415i | 0.373752 | + | 0.647358i | ||||
\(143\) | 1.22474 | − | 2.12132i | 0.102418 | − | 0.177394i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.5732 | + | 10.1459i | −1.45938 | + | 0.842571i | ||||
\(146\) | 2.74202 | 0.226931 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.97418 | 0.326675 | ||||||||
\(149\) | 5.93596 | − | 3.42713i | 0.486292 | − | 0.280761i | −0.236743 | − | 0.971572i | \(-0.576080\pi\) |
0.723035 | + | 0.690811i | \(0.242746\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.23351 | − | 12.5288i | 0.588655 | − | 1.01958i | −0.405754 | − | 0.913982i | \(-0.632991\pi\) |
0.994409 | − | 0.105598i | \(-0.0336756\pi\) | |||||||
\(152\) | 1.83548 | + | 3.17914i | 0.148877 | + | 0.257862i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.19067 | − | 1.48356i | 0.176529 | − | 0.119549i | ||||
\(155\) | − | 9.05594i | − | 0.727391i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.4305 | + | 8.33145i | 1.15168 | + | 0.664922i | 0.949296 | − | 0.314384i | \(-0.101798\pi\) |
0.202383 | + | 0.979306i | \(0.435131\pi\) | |||||||
\(158\) | −13.3333 | − | 7.69798i | −1.06074 | − | 0.612418i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.93185i | 0.310840i | ||||||||
\(161\) | 3.92367 | − | 8.08284i | 0.309228 | − | 0.637017i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.481740 | − | 0.834398i | −0.0377328 | − | 0.0653551i | 0.846542 | − | 0.532321i | \(-0.178680\pi\) |
−0.884275 | + | 0.466966i | \(0.845347\pi\) | |||||||
\(164\) | 2.96240 | − | 5.13103i | 0.231325 | − | 0.400666i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.24397 | − | 3.02761i | 0.407011 | − | 0.234988i | ||||
\(167\) | −1.93426 | −0.149677 | −0.0748386 | − | 0.997196i | \(-0.523844\pi\) | ||||
−0.0748386 | + | 0.997196i | \(0.523844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 24.8317 | − | 14.3366i | 1.90450 | − | 1.09956i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.35640 | + | 9.27755i | −0.408421 | + | 0.707407i | ||||
\(173\) | −9.87902 | − | 17.1110i | −0.751088 | − | 1.30092i | −0.947296 | − | 0.320360i | \(-0.896196\pi\) |
0.196208 | − | 0.980562i | \(-0.437137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.98174 | + | 27.6021i | 0.149805 | + | 2.08652i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.1741 | + | 5.87404i | 0.762583 | + | 0.440278i | ||||
\(179\) | −9.13593 | − | 5.27463i | −0.682852 | − | 0.394245i | 0.118077 | − | 0.993004i | \(-0.462327\pi\) |
−0.800929 | + | 0.598760i | \(0.795660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.12560i | − | 0.306653i | −0.988176 | − | 0.153327i | \(-0.951001\pi\) | ||
0.988176 | − | 0.153327i | \(-0.0489987\pi\) | |||||||
\(182\) | −5.83013 | − | 2.83013i | −0.432158 | − | 0.209783i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.69798 | + | 2.94098i | 0.125176 | + | 0.216812i | ||||
\(185\) | −7.81294 | + | 13.5324i | −0.574418 | + | 0.994922i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.31552 | − | 3.64626i | 0.461836 | − | 0.266641i | ||||
\(188\) | −8.62398 | −0.628969 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.4336 | −1.04713 | ||||||||
\(191\) | −19.9354 | + | 11.5097i | −1.44248 | + | 0.832813i | −0.998014 | − | 0.0629850i | \(-0.979938\pi\) |
−0.444461 | + | 0.895798i | \(0.646605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.60708 | + | 7.97970i | −0.331625 | + | 0.574391i | −0.982831 | − | 0.184510i | \(-0.940930\pi\) |
0.651206 | + | 0.758901i | \(0.274264\pi\) | |||||||
\(194\) | 2.92883 | + | 5.07287i | 0.210277 | + | 0.364211i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.33013 | − | 5.50000i | −0.309295 | − | 0.392857i | ||||
\(197\) | − | 6.52180i | − | 0.464659i | −0.972637 | − | 0.232330i | \(-0.925365\pi\) | ||
0.972637 | − | 0.232330i | \(-0.0746348\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9813 | − | 7.49473i | −0.920217 | − | 0.531288i | −0.0365128 | − | 0.999333i | \(-0.511625\pi\) |
−0.883704 | + | 0.468046i | \(0.844958\pi\) | |||||||
\(200\) | −9.05816 | − | 5.22973i | −0.640508 | − | 0.369798i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 15.5206i | − | 1.09202i | ||||||
\(203\) | 7.65649 | + | 11.3058i | 0.537380 | + | 0.793510i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6477 | + | 20.1744i | 0.813512 | + | 1.40904i | ||||
\(206\) | −6.20150 | + | 10.7413i | −0.432079 | + | 0.748383i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.12132 | − | 1.22474i | 0.147087 | − | 0.0849208i | ||||
\(209\) | −3.67095 | −0.253925 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.10759 | −0.626992 | −0.313496 | − | 0.949589i | \(-0.601500\pi\) | ||||
−0.313496 | + | 0.949589i | \(0.601500\pi\) | |||||||
\(212\) | 11.5854 | − | 6.68885i | 0.795690 | − | 0.459392i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.89595 | − | 11.9441i | 0.471398 | − | 0.816485i | ||||
\(215\) | −21.0606 | − | 36.4780i | −1.43632 | − | 2.48778i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.07812 | + | 0.436389i | −0.412609 | + | 0.0296240i | ||||
\(218\) | − | 4.91067i | − | 0.332593i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.40508 | − | 1.96593i | −0.229571 | − | 0.132543i | ||||
\(221\) | −15.4698 | − | 8.93149i | −1.04061 | − | 0.600797i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.28788i | 0.488033i | 0.969771 | + | 0.244016i | \(0.0784651\pi\) | ||||
−0.969771 | + | 0.244016i | \(0.921535\pi\) | |||||||
\(224\) | 2.63896 | − | 0.189469i | 0.176323 | − | 0.0126594i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.06350 | − | 13.9664i | −0.536376 | − | 0.929031i | ||||
\(227\) | −0.465428 | + | 0.806145i | −0.0308915 | + | 0.0535057i | −0.881058 | − | 0.473009i | \(-0.843168\pi\) |
0.850166 | + | 0.526514i | \(0.176501\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.8048 | − | 12.0117i | 1.37482 | − | 0.793753i | 0.383291 | − | 0.923628i | \(-0.374791\pi\) |
0.991530 | + | 0.129874i | \(0.0414574\pi\) | |||||||
\(230\) | −13.3524 | −0.880430 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.16088 | −0.338828 | ||||||||
\(233\) | 15.1427 | − | 8.74264i | 0.992031 | − | 0.572749i | 0.0861503 | − | 0.996282i | \(-0.472543\pi\) |
0.905881 | + | 0.423533i | \(0.139210\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9541 | − | 29.3654i | 1.10596 | − | 1.91559i | ||||
\(236\) | −0.975056 | − | 1.68885i | −0.0634707 | − | 0.109935i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.8189 | − | 15.9755i | −0.701287 | − | 1.03554i | ||||
\(239\) | − | 0.712115i | − | 0.0460629i | −0.999735 | − | 0.0230315i | \(-0.992668\pi\) | ||
0.999735 | − | 0.0230315i | \(-0.00733179\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5097 | − | 7.79983i | −0.870237 | − | 0.502432i | −0.00280996 | − | 0.999996i | \(-0.500894\pi\) |
−0.867427 | + | 0.497565i | \(0.834228\pi\) | |||||||
\(242\) | −0.866025 | − | 0.500000i | −0.0556702 | − | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5.96764i | − | 0.382039i | ||||||
\(245\) | 27.2407 | − | 3.93185i | 1.74034 | − | 0.251197i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.49598 | + | 7.78726i | 0.286072 | + | 0.495492i | ||||
\(248\) | 1.15161 | − | 1.99465i | 0.0731275 | − | 0.126661i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.5899 | − | 10.7329i | 1.17573 | − | 0.678807i | ||||
\(251\) | 22.2326 | 1.40331 | 0.701655 | − | 0.712516i | \(-0.252445\pi\) | ||||
0.701655 | + | 0.712516i | \(0.252445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.39595 | −0.213502 | ||||||||
\(254\) | −8.61281 | + | 4.97261i | −0.540416 | + | 0.312009i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.47443 | − | 2.55379i | −0.0919727 | − | 0.159301i | 0.816368 | − | 0.577531i | \(-0.195984\pi\) |
−0.908341 | + | 0.418230i | \(0.862651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.45909 | + | 4.59174i | 0.587759 | + | 0.285317i | ||||
\(260\) | 9.63103i | 0.597291i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.0087 | − | 9.24264i | −0.989022 | − | 0.571012i | ||||
\(263\) | −16.4066 | − | 9.47237i | −1.01168 | − | 0.584091i | −0.0999939 | − | 0.994988i | \(-0.531882\pi\) |
−0.911682 | + | 0.410897i | \(0.865216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 52.5991i | 3.23114i | ||||||||
\(266\) | 0.695530 | + | 9.68749i | 0.0426457 | + | 0.593978i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.33378 | + | 4.04222i | 0.142558 | + | 0.246918i | ||||
\(269\) | 12.1165 | − | 20.9863i | 0.738754 | − | 1.27956i | −0.214302 | − | 0.976767i | \(-0.568748\pi\) |
0.953057 | − | 0.302792i | \(-0.0979189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4275 | − | 11.2165i | 1.18013 | − | 0.681351i | 0.224089 | − | 0.974569i | \(-0.428059\pi\) |
0.956046 | + | 0.293218i | \(0.0947261\pi\) | |||||||
\(272\) | 7.29253 | 0.442175 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.79191 | 0.168665 | ||||||||
\(275\) | 9.05816 | − | 5.22973i | 0.546227 | − | 0.315365i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.92392 | − | 8.52849i | 0.295850 | − | 0.512427i | −0.679332 | − | 0.733831i | \(-0.737731\pi\) |
0.975182 | + | 0.221404i | \(0.0710638\pi\) | |||||||
\(278\) | −2.55291 | − | 4.42178i | −0.153114 | − | 0.265201i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.54284 | + | 9.35835i | −0.271487 | + | 0.559269i | ||||
\(281\) | − | 10.8623i | − | 0.647990i | −0.946059 | − | 0.323995i | \(-0.894974\pi\) | ||
0.946059 | − | 0.323995i | \(-0.105026\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.32792 | − | 4.80813i | −0.495044 | − | 0.285814i | 0.231621 | − | 0.972806i | \(-0.425597\pi\) |
−0.726664 | + | 0.686993i | \(0.758930\pi\) | |||||||
\(284\) | −7.71415 | − | 4.45377i | −0.457751 | − | 0.264283i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.44949i | 0.144841i | ||||||||
\(287\) | 12.9793 | − | 8.78982i | 0.766143 | − | 0.518847i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.0905 | − | 31.3336i | −1.06415 | − | 1.84316i | ||||
\(290\) | 10.1459 | − | 17.5732i | 0.595788 | − | 1.03193i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.37466 | + | 1.37101i | −0.138966 | + | 0.0802322i | ||||
\(293\) | −14.4546 | −0.844450 | −0.422225 | − | 0.906491i | \(-0.638751\pi\) | ||||
−0.422225 | + | 0.906491i | \(0.638751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.66755 | 0.446422 | ||||||||
\(296\) | −3.44174 | + | 1.98709i | −0.200047 | + | 0.115497i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.42713 | + | 5.93596i | −0.198528 | + | 0.343861i | ||||
\(299\) | 4.15918 | + | 7.20390i | 0.240531 | + | 0.416613i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.4682 | + | 15.8931i | −1.35268 | + | 0.916064i | ||||
\(302\) | 14.4670i | 0.832484i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.17914 | − | 1.83548i | −0.182336 | − | 0.105272i | ||||
\(305\) | 20.3203 | + | 11.7319i | 1.16354 | + | 0.671769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.928932i | 0.0530170i | 0.999649 | + | 0.0265085i | \(0.00843890\pi\) | ||||
−0.999649 | + | 0.0265085i | \(0.991561\pi\) | |||||||
\(308\) | −1.15539 | + | 2.38014i | −0.0658347 | + | 0.135621i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.52797 | + | 7.84267i | 0.257171 | + | 0.445434i | ||||
\(311\) | 13.3841 | − | 23.1819i | 0.758940 | − | 1.31452i | −0.184451 | − | 0.982842i | \(-0.559051\pi\) |
0.943392 | − | 0.331681i | \(-0.107616\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.88437 | − | 3.97469i | 0.389127 | − | 0.224663i | −0.292655 | − | 0.956218i | \(-0.594539\pi\) |
0.681782 | + | 0.731555i | \(0.261205\pi\) | |||||||
\(314\) | −16.6629 | −0.940342 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.3960 | 0.866090 | ||||||||
\(317\) | 14.4394 | − | 8.33657i | 0.810995 | − | 0.468228i | −0.0363060 | − | 0.999341i | \(-0.511559\pi\) |
0.847301 | + | 0.531112i | \(0.178226\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.58044 | − | 4.46945i | 0.144477 | − | 0.250241i | ||||
\(320\) | −1.96593 | − | 3.40508i | −0.109899 | − | 0.190350i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.643427 | + | 8.96178i | 0.0358568 | + | 0.499420i | ||||
\(323\) | 26.7705i | 1.48955i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.1879 | − | 12.8102i | −1.23076 | − | 0.710580i | ||||
\(326\) | 0.834398 | + | 0.481740i | 0.0462130 | + | 0.0266811i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.92480i | 0.327143i | ||||||||
\(329\) | −20.5263 | − | 9.96410i | −1.13165 | − | 0.549339i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.58933 | + | 2.75280i | 0.0873574 | + | 0.151307i | 0.906393 | − | 0.422435i | \(-0.138824\pi\) |
−0.819036 | + | 0.573742i | \(0.805491\pi\) | |||||||
\(332\) | −3.02761 | + | 5.24397i | −0.166161 | + | 0.287800i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.67511 | − | 0.967128i | 0.0916582 | − | 0.0529189i | ||||
\(335\) | −18.3521 | −1.00268 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7473 | 0.857812 | 0.428906 | − | 0.903349i | \(-0.358899\pi\) | ||||
0.428906 | + | 0.903349i | \(0.358899\pi\) | |||||||
\(338\) | −6.06218 | + | 3.50000i | −0.329739 | + | 0.190375i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.3366 | + | 24.8317i | −0.777510 | + | 1.34669i | ||||
\(341\) | 1.15161 | + | 1.99465i | 0.0623633 | + | 0.108016i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.95164 | − | 18.0938i | −0.213368 | − | 0.976972i | ||||
\(344\) | − | 10.7128i | − | 0.577595i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.1110 | + | 9.87902i | 0.919891 | + | 0.531099i | ||||
\(347\) | 22.7976 | + | 13.1622i | 1.22384 | + | 0.706584i | 0.965734 | − | 0.259533i | \(-0.0835686\pi\) |
0.258105 | + | 0.966117i | \(0.416902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 32.9044i | − | 1.76133i | −0.473737 | − | 0.880666i | \(-0.657095\pi\) | ||
0.473737 | − | 0.880666i | \(-0.342905\pi\) | |||||||
\(350\) | −15.5173 | − | 22.9132i | −0.829433 | − | 1.22476i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 4.74943 | − | 8.22626i | 0.252787 | − | 0.437839i | −0.711505 | − | 0.702681i | \(-0.751986\pi\) |
0.964292 | + | 0.264841i | \(0.0853196\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.3309 | − | 17.5116i | 1.60980 | − | 0.929417i | ||||
\(356\) | −11.7481 | −0.622647 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.5493 | 0.557546 | ||||||||
\(359\) | −2.59578 | + | 1.49867i | −0.137000 | + | 0.0790970i | −0.566933 | − | 0.823764i | \(-0.691870\pi\) |
0.429933 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.76206 | + | 4.78403i | −0.145372 | + | 0.251791i | ||||
\(362\) | 2.06280 | + | 3.57287i | 0.108418 | + | 0.187786i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.46410 | − | 0.464102i | 0.338811 | − | 0.0243255i | ||||
\(365\) | − | 10.7812i | − | 0.564314i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.3336 | + | 8.27551i | 0.748208 | + | 0.431978i | 0.825046 | − | 0.565065i | \(-0.191149\pi\) |
−0.0768379 | + | 0.997044i | \(0.524482\pi\) | |||||||
\(368\) | −2.94098 | − | 1.69798i | −0.153309 | − | 0.0885132i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 15.6259i | − | 0.812350i | ||||||
\(371\) | 35.3032 | − | 2.53465i | 1.83285 | − | 0.131593i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.73753 | + | 16.8659i | 0.504190 | + | 0.873283i | 0.999988 | + | 0.00484535i | \(0.00154233\pi\) |
−0.495798 | + | 0.868438i | \(0.665124\pi\) | |||||||
\(374\) | −3.64626 | + | 6.31552i | −0.188544 | + | 0.326568i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.46859 | − | 4.31199i | 0.385163 | − | 0.222374i | ||||
\(377\) | −12.6415 | −0.651071 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.20809 | 0.113422 | 0.0567111 | − | 0.998391i | \(-0.481939\pi\) | ||||
0.0567111 | + | 0.998391i | \(0.481939\pi\) | |||||||
\(380\) | 12.4999 | − | 7.21682i | 0.641231 | − | 0.370215i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.5097 | − | 19.9354i | 0.588888 | − | 1.01998i | ||||
\(383\) | −1.41849 | − | 2.45690i | −0.0724816 | − | 0.125542i | 0.827507 | − | 0.561456i | \(-0.189759\pi\) |
−0.899988 | + | 0.435914i | \(0.856425\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.83315 | − | 8.61339i | −0.297285 | − | 0.438979i | ||||
\(386\) | − | 9.21416i | − | 0.468989i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.07287 | − | 2.92883i | −0.257536 | − | 0.148689i | ||||
\(389\) | 16.4686 | + | 9.50814i | 0.834991 | + | 0.482082i | 0.855558 | − | 0.517706i | \(-0.173214\pi\) |
−0.0205678 | + | 0.999788i | \(0.506547\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.7651i | 1.25242i | ||||||||
\(392\) | 6.50000 | + | 2.59808i | 0.328300 | + | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.26090 | + | 5.64805i | 0.164282 | + | 0.284544i | ||||
\(395\) | −30.2673 | + | 52.4245i | −1.52291 | + | 2.63776i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.23729 | − | 5.33315i | 0.463606 | − | 0.267663i | −0.249953 | − | 0.968258i | \(-0.580415\pi\) |
0.713559 | + | 0.700595i | \(0.247082\pi\) | |||||||
\(398\) | 14.9895 | 0.751354 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.4595 | 0.522973 | ||||||||
\(401\) | 28.4216 | − | 16.4092i | 1.41931 | − | 0.819437i | 0.423068 | − | 0.906098i | \(-0.360953\pi\) |
0.996238 | + | 0.0866614i | \(0.0276198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.82086 | − | 4.88588i | 0.140517 | − | 0.243383i | ||||
\(404\) | 7.76028 | + | 13.4412i | 0.386088 | + | 0.668725i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.2836 | − | 5.96285i | −0.609625 | − | 0.295931i | ||||
\(407\) | − | 3.97418i | − | 0.196993i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.25334 | − | 3.61037i | −0.309208 | − | 0.178521i | 0.337364 | − | 0.941374i | \(-0.390465\pi\) |
−0.646572 | + | 0.762853i | \(0.723798\pi\) | |||||||
\(410\) | −20.1744 | − | 11.6477i | −0.996345 | − | 0.575240i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 12.4030i | − | 0.611052i | ||||||
\(413\) | −0.369485 | − | 5.14626i | −0.0181812 | − | 0.253231i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.9041 | − | 20.6185i | −0.584349 | − | 1.01212i | ||||
\(416\) | −1.22474 | + | 2.12132i | −0.0600481 | + | 0.104006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.17914 | − | 1.83548i | 0.155497 | − | 0.0897760i | ||||
\(419\) | −15.9184 | −0.777665 | −0.388832 | − | 0.921309i | \(-0.627121\pi\) | ||||
−0.388832 | + | 0.921309i | \(0.627121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.23889 | 0.206591 | 0.103295 | − | 0.994651i | \(-0.467061\pi\) | ||||
0.103295 | + | 0.994651i | \(0.467061\pi\) | |||||||
\(422\) | 7.88740 | − | 4.55379i | 0.383953 | − | 0.221675i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.68885 | + | 11.5854i | −0.324839 | + | 0.562638i | ||||
\(425\) | −38.1379 | − | 66.0569i | −1.84996 | − | 3.20423i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.89498 | − | 14.2038i | 0.333672 | − | 0.687371i | ||||
\(428\) | 13.7919i | 0.666657i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 36.4780 | + | 21.0606i | 1.75912 | + | 1.01563i | ||||
\(431\) | −17.4567 | − | 10.0786i | −0.840860 | − | 0.485471i | 0.0166966 | − | 0.999861i | \(-0.494685\pi\) |
−0.857556 | + | 0.514390i | \(0.828018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.81292i | 0.279351i | 0.990197 | + | 0.139676i | \(0.0446060\pi\) | ||||
−0.990197 | + | 0.139676i | \(0.955394\pi\) | |||||||
\(434\) | 5.04561 | − | 3.41698i | 0.242197 | − | 0.164020i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.45534 | + | 4.25277i | 0.117589 | + | 0.203671i | ||||
\(437\) | 6.23319 | − | 10.7962i | 0.298174 | − | 0.516452i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0204 | − | 13.8682i | 1.14643 | − | 0.661893i | 0.198416 | − | 0.980118i | \(-0.436420\pi\) |
0.948015 | + | 0.318225i | \(0.103087\pi\) | |||||||
\(440\) | 3.93185 | 0.187444 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.8630 | 0.849655 | ||||||||
\(443\) | 11.4746 | − | 6.62486i | 0.545175 | − | 0.314757i | −0.201999 | − | 0.979386i | \(-0.564744\pi\) |
0.747173 | + | 0.664629i | \(0.231410\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.0958 | − | 40.0032i | 1.09485 | − | 1.89633i | ||||
\(446\) | −3.64394 | − | 6.31149i | −0.172546 | − | 0.298858i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.19067 | + | 1.48356i | −0.103499 | + | 0.0700918i | ||||
\(449\) | − | 21.9232i | − | 1.03462i | −0.855798 | − | 0.517310i | \(-0.826933\pi\) | ||
0.855798 | − | 0.517310i | \(-0.173067\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.13103 | − | 2.96240i | −0.241611 | − | 0.139494i | ||||
\(452\) | 13.9664 | + | 8.06350i | 0.656924 | + | 0.379275i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 0.930856i | − | 0.0436872i | ||||||
\(455\) | −11.1276 | + | 22.9232i | −0.521672 | + | 1.07466i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.3092 | + | 28.2483i | 0.762911 | + | 1.32140i | 0.941344 | + | 0.337449i | \(0.109564\pi\) |
−0.178433 | + | 0.983952i | \(0.557103\pi\) | |||||||
\(458\) | −12.0117 | + | 20.8048i | −0.561268 | + | 0.972145i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.5635 | − | 6.67619i | 0.539151 | − | 0.311279i | ||||
\(461\) | −31.6262 | −1.47298 | −0.736489 | − | 0.676450i | \(-0.763518\pi\) | ||||
−0.736489 | + | 0.676450i | \(0.763518\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.5687 | 0.537642 | 0.268821 | − | 0.963190i | \(-0.413366\pi\) | ||||
0.268821 | + | 0.963190i | \(0.413366\pi\) | |||||||
\(464\) | 4.46945 | − | 2.58044i | 0.207489 | − | 0.119794i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.74264 | + | 15.1427i | −0.404995 | + | 0.701472i | ||||
\(467\) | 3.92392 | + | 6.79643i | 0.181578 | + | 0.314501i | 0.942418 | − | 0.334438i | \(-0.108546\pi\) |
−0.760840 | + | 0.648939i | \(0.775213\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.884355 | + | 12.3175i | 0.0408357 | + | 0.568768i | ||||
\(470\) | 33.9082i | 1.56407i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.68885 | + | 0.975056i | 0.0777355 | + | 0.0448806i | ||||
\(473\) | 9.27755 | + | 5.35640i | 0.426582 | + | 0.246287i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.3962i | 1.76174i | ||||||||
\(476\) | 17.3572 | + | 8.42575i | 0.795568 | + | 0.386194i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.356058 | + | 0.616710i | 0.0162857 | + | 0.0282077i | ||||
\(479\) | −20.3161 | + | 35.1885i | −0.928267 | + | 1.60781i | −0.142046 | + | 0.989860i | \(0.545368\pi\) |
−0.786221 | + | 0.617945i | \(0.787965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.43050 | + | 4.86735i | −0.384398 | + | 0.221932i | ||||
\(482\) | 15.5997 | 0.710545 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 19.9458 | − | 11.5157i | 0.905692 | − | 0.522901i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.6074 | − | 21.8367i | 0.571297 | − | 0.989515i | −0.425136 | − | 0.905129i | \(-0.639774\pi\) |
0.996433 | − | 0.0843858i | \(-0.0268928\pi\) | |||||||
\(488\) | 2.98382 | + | 5.16813i | 0.135071 | + | 0.233950i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.6252 | + | 17.0254i | −0.976926 | + | 0.769130i | ||||
\(491\) | 2.83551i | 0.127965i | 0.997951 | + | 0.0639824i | \(0.0203802\pi\) | ||||
−0.997951 | + | 0.0639824i | \(0.979620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.5936 | − | 18.8179i | −1.46794 | − | 0.847516i | ||||
\(494\) | −7.78726 | − | 4.49598i | −0.350365 | − | 0.202284i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.30323i | 0.103418i | ||||||||
\(497\) | −13.2149 | − | 19.5135i | −0.592769 | − | 0.875299i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.29858 | − | 12.6415i | −0.326729 | − | 0.565912i | 0.655131 | − | 0.755515i | \(-0.272613\pi\) |
−0.981861 | + | 0.189603i | \(0.939280\pi\) | |||||||
\(500\) | −10.7329 | + | 18.5899i | −0.479989 | + | 0.831366i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.2540 | + | 11.1163i | −0.859349 | + | 0.496145i | ||||
\(503\) | −14.4955 | −0.646322 | −0.323161 | − | 0.946344i | \(-0.604745\pi\) | ||||
−0.323161 | + | 0.946344i | \(0.604745\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −61.0245 | −2.71556 | ||||||||
\(506\) | 2.94098 | − | 1.69798i | 0.130743 | − | 0.0754843i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.97261 | − | 8.61281i | 0.220624 | − | 0.382132i | ||||
\(509\) | 14.4421 | + | 25.0144i | 0.640134 | + | 1.10874i | 0.985403 | + | 0.170240i | \(0.0544544\pi\) |
−0.345269 | + | 0.938504i | \(0.612212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.23607 | + | 0.519527i | −0.320105 | + | 0.0229825i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.55379 | + | 1.47443i | 0.112643 | + | 0.0650345i | ||||
\(515\) | 42.2333 | + | 24.3834i | 1.86102 | + | 1.07446i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.62398i | 0.379282i | ||||||||
\(518\) | −10.4877 | + | 0.752982i | −0.460802 | + | 0.0330841i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.81552 | − | 8.34072i | −0.211174 | − | 0.365765i | ||||
\(521\) | −2.96937 | + | 5.14310i | −0.130090 | + | 0.225323i | −0.923711 | − | 0.383090i | \(-0.874860\pi\) |
0.793621 | + | 0.608413i | \(0.208193\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.6424 | + | 9.03115i | −0.683995 | + | 0.394905i | −0.801358 | − | 0.598184i | \(-0.795889\pi\) |
0.117364 | + | 0.993089i | \(0.462556\pi\) | |||||||
\(524\) | 18.4853 | 0.807533 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.9447 | 0.826030 | ||||||||
\(527\) | 14.5461 | − | 8.39817i | 0.633636 | − | 0.365830i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.73375 | + | 9.93115i | −0.249294 | + | 0.431789i | ||||
\(530\) | −26.2996 | − | 45.5522i | −1.14238 | − | 1.97866i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.44609 | − | 8.04184i | −0.236118 | − | 0.348658i | ||||
\(533\) | 14.5127i | 0.628617i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.9626 | − | 27.1139i | −2.03037 | − | 1.17223i | ||||
\(536\) | −4.04222 | − | 2.33378i | −0.174597 | − | 0.100804i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.2329i | 1.04476i | ||||||||
\(539\) | −5.50000 | + | 4.33013i | −0.236902 | + | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.59039 | + | 13.1469i | 0.326336 | + | 0.565231i | 0.981782 | − | 0.190011i | \(-0.0608525\pi\) |
−0.655446 | + | 0.755242i | \(0.727519\pi\) | |||||||
\(542\) | −11.2165 | + | 19.4275i | −0.481788 | + | 0.834481i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.31552 | + | 3.64626i | −0.270775 | + | 0.156332i | ||||
\(545\) | −19.3080 | −0.827065 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.6498 | 0.540865 | 0.270433 | − | 0.962739i | \(-0.412833\pi\) | ||||
0.270433 | + | 0.962739i | \(0.412833\pi\) | |||||||
\(548\) | −2.41786 | + | 1.39595i | −0.103286 | + | 0.0596322i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.22973 | + | 9.05816i | −0.222996 | + | 0.386241i | ||||
\(551\) | 9.47266 | + | 16.4071i | 0.403549 | + | 0.698967i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.6445 | + | 17.7884i | 1.55828 | + | 0.756440i | ||||
\(554\) | 9.84785i | 0.418395i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.42178 | + | 2.55291i | 0.187525 | + | 0.108268i | ||||
\(557\) | 2.43639 | + | 1.40665i | 0.103233 | + | 0.0596017i | 0.550728 | − | 0.834685i | \(-0.314350\pi\) |
−0.447495 | + | 0.894287i | \(0.647684\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 26.2409i | − | 1.10987i | ||||||
\(560\) | −0.744963 | − | 10.3760i | −0.0314804 | − | 0.438466i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.43115 | + | 9.40702i | 0.229099 | + | 0.396811i | ||||
\(563\) | −2.94887 | + | 5.10759i | −0.124280 | + | 0.215259i | −0.921451 | − | 0.388494i | \(-0.872995\pi\) |
0.797171 | + | 0.603753i | \(0.206329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −54.9138 | + | 31.7045i | −2.31024 | + | 1.33382i | ||||
\(566\) | 9.61625 | 0.404201 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.90754 | 0.373752 | ||||||||
\(569\) | 24.4687 | − | 14.1270i | 1.02578 | − | 0.592235i | 0.110008 | − | 0.993931i | \(-0.464912\pi\) |
0.915773 | + | 0.401696i | \(0.131579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.6142 | − | 28.7766i | 0.695281 | − | 1.20426i | −0.274805 | − | 0.961500i | \(-0.588613\pi\) |
0.970086 | − | 0.242762i | \(-0.0780535\pi\) | |||||||
\(572\) | −1.22474 | − | 2.12132i | −0.0512092 | − | 0.0886969i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.84549 | + | 14.1019i | −0.285725 | + | 0.588600i | ||||
\(575\) | 35.5198i | 1.48128i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.80012 | − | 4.50340i | −0.324723 | − | 0.187479i | 0.328773 | − | 0.944409i | \(-0.393365\pi\) |
−0.653496 | + | 0.756930i | \(0.726698\pi\) | |||||||
\(578\) | 31.3336 | + | 18.0905i | 1.30331 | + | 0.752465i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.2918i | 0.842571i | ||||||||
\(581\) | −13.2650 | + | 8.98329i | −0.550324 | + | 0.372690i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.68885 | − | 11.5854i | −0.277024 | − | 0.479819i | ||||
\(584\) | 1.37101 | − | 2.37466i | 0.0567328 | − | 0.0982640i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.5181 | − | 7.22732i | 0.517118 | − | 0.298558i | ||||
\(587\) | 39.5783 | 1.63357 | 0.816785 | − | 0.576942i | \(-0.195754\pi\) | ||||
0.816785 | + | 0.576942i | \(0.195754\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.45503 | −0.348383 | ||||||||
\(590\) | −6.64029 | + | 3.83378i | −0.273377 | + | 0.157834i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.98709 | − | 3.44174i | 0.0816688 | − | 0.141455i | ||||
\(593\) | −17.9542 | − | 31.0976i | −0.737290 | − | 1.27702i | −0.953711 | − | 0.300724i | \(-0.902772\pi\) |
0.216421 | − | 0.976300i | \(-0.430562\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −62.8134 | + | 42.5384i | −2.57510 | + | 1.74391i | ||||
\(596\) | − | 6.85425i | − | 0.280761i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.20390 | − | 4.15918i | −0.294590 | − | 0.170081i | ||||
\(599\) | −28.9870 | − | 16.7357i | −1.18438 | − | 0.683800i | −0.227354 | − | 0.973812i | \(-0.573007\pi\) |
−0.957023 | + | 0.290012i | \(0.906341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27.5546i | − | 1.12398i | −0.827146 | − | 0.561988i | \(-0.810037\pi\) | ||
0.827146 | − | 0.561988i | \(-0.189963\pi\) | |||||||
\(602\) | 12.3775 | − | 25.4979i | 0.504469 | − | 1.03922i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.23351 | − | 12.5288i | −0.294327 | − | 0.509790i | ||||
\(605\) | −1.96593 | + | 3.40508i | −0.0799263 | + | 0.138436i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.1116 | + | 22.5811i | −1.58749 | + | 0.916539i | −0.593773 | + | 0.804633i | \(0.702362\pi\) |
−0.993719 | + | 0.111906i | \(0.964305\pi\) | |||||||
\(608\) | 3.67095 | 0.148877 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.4639 | −0.950025 | ||||||||
\(611\) | 18.2942 | − | 10.5622i | 0.740105 | − | 0.427300i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4202 | − | 23.2445i | 0.542037 | − | 0.938836i | −0.456750 | − | 0.889595i | \(-0.650987\pi\) |
0.998787 | − | 0.0492407i | \(-0.0156802\pi\) | |||||||
\(614\) | −0.464466 | − | 0.804479i | −0.0187443 | − | 0.0324661i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.189469 | − | 2.63896i | −0.00763391 | − | 0.106327i | ||||
\(617\) | 37.4317i | 1.50694i | 0.657481 | + | 0.753471i | \(0.271622\pi\) | ||||
−0.657481 | + | 0.753471i | \(0.728378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.7567 | − | 6.21039i | −0.432349 | − | 0.249617i | 0.267998 | − | 0.963419i | \(-0.413638\pi\) |
−0.700347 | + | 0.713803i | \(0.746971\pi\) | |||||||
\(620\) | −7.84267 | − | 4.52797i | −0.314969 | − | 0.181848i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.7681i | 1.07330i | ||||||||
\(623\) | −27.9620 | − | 13.5737i | −1.12028 | − | 0.543817i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.0515 | − | 27.8020i | −0.642059 | − | 1.11208i | ||||
\(626\) | −3.97469 | + | 6.88437i | −0.158861 | + | 0.275155i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.4305 | − | 8.33145i | 0.575840 | − | 0.332461i | ||||
\(629\) | −28.9818 | −1.15558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.57938 | −0.222112 | −0.111056 | − | 0.993814i | \(-0.535423\pi\) | ||||
−0.111056 | + | 0.993814i | \(0.535423\pi\) | |||||||
\(632\) | −13.3333 | + | 7.69798i | −0.530370 | + | 0.306209i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.33657 | + | 14.4394i | −0.331088 | + | 0.573460i | ||||
\(635\) | 19.5516 | + | 33.8643i | 0.775880 | + | 1.34386i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.9217 | + | 6.36396i | 0.630840 | + | 0.252149i | ||||
\(638\) | 5.16088i | 0.204321i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.40508 | + | 1.96593i | 0.134598 | + | 0.0777100i | ||||
\(641\) | −29.7432 | − | 17.1723i | −1.17479 | − | 0.678263i | −0.219984 | − | 0.975504i | \(-0.570600\pi\) |
−0.954803 | + | 0.297240i | \(0.903934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 21.2432i | − | 0.837748i | −0.908044 | − | 0.418874i | \(-0.862425\pi\) | ||
0.908044 | − | 0.418874i | \(-0.137575\pi\) | |||||||
\(644\) | −5.03811 | − | 7.43942i | −0.198529 | − | 0.293154i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.3853 | − | 23.1839i | −0.526636 | − | 0.912160i | ||||
\(647\) | −12.0354 | + | 20.8459i | −0.473160 | + | 0.819537i | −0.999528 | − | 0.0307199i | \(-0.990220\pi\) |
0.526368 | + | 0.850257i | \(0.323553\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.68885 | + | 0.975056i | −0.0662930 | + | 0.0382743i | ||||
\(650\) | 25.6203 | 1.00491 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.963479 | −0.0377328 | ||||||||
\(653\) | 25.2388 | − | 14.5716i | 0.987672 | − | 0.570233i | 0.0830943 | − | 0.996542i | \(-0.473520\pi\) |
0.904578 | + | 0.426309i | \(0.140186\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.3407 | + | 62.9439i | −1.41995 | + | 2.45942i | ||||
\(656\) | −2.96240 | − | 5.13103i | −0.115662 | − | 0.200333i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.7583 | − | 1.63397i | 0.887212 | − | 0.0636990i | ||||
\(659\) | − | 39.4790i | − | 1.53788i | −0.639318 | − | 0.768942i | \(-0.720783\pi\) | ||
0.639318 | − | 0.768942i | \(-0.279217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0582 | − | 19.0861i | −1.28581 | − | 0.742365i | −0.307909 | − | 0.951416i | \(-0.599629\pi\) |
−0.977905 | + | 0.209051i | \(0.932962\pi\) | |||||||
\(662\) | −2.75280 | − | 1.58933i | −0.106990 | − | 0.0617710i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.05521i | − | 0.234988i | ||||||
\(665\) | 38.0898 | − | 2.73472i | 1.47706 | − | 0.106048i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.76305 | + | 15.1780i | 0.339307 | + | 0.587696i | ||||
\(668\) | −0.967128 | + | 1.67511i | −0.0374193 | + | 0.0648121i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.8934 | − | 9.17606i | 0.614016 | − | 0.354502i | ||||
\(671\) | −5.96764 | −0.230378 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.7014 | −0.412509 | −0.206255 | − | 0.978498i | \(-0.566128\pi\) | ||||
−0.206255 | + | 0.978498i | \(0.566128\pi\) | |||||||
\(674\) | −13.6376 | + | 7.87367i | −0.525301 | + | 0.303282i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | − | 6.06218i | 0.134615 | − | 0.233161i | ||||
\(677\) | 8.12925 | + | 14.0803i | 0.312432 | + | 0.541149i | 0.978888 | − | 0.204396i | \(-0.0655229\pi\) |
−0.666456 | + | 0.745544i | \(0.732190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.69020 | − | 12.8322i | −0.333499 | − | 0.492454i | ||||
\(680\) | − | 28.6731i | − | 1.09956i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.99465 | − | 1.15161i | −0.0763792 | − | 0.0440975i | ||||
\(683\) | −0.845958 | − | 0.488414i | −0.0323697 | − | 0.0186887i | 0.483728 | − | 0.875218i | \(-0.339282\pi\) |
−0.516098 | + | 0.856530i | \(0.672616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10.9774i | − | 0.419423i | ||||||
\(686\) | 12.4691 | + | 13.6938i | 0.476073 | + | 0.522834i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.35640 | + | 9.27755i | 0.204211 | + | 0.353703i | ||||
\(689\) | −16.3843 | + | 28.3784i | −0.624191 | + | 1.08113i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3783 | − | 8.87869i | 0.585020 | − | 0.337761i | −0.178106 | − | 0.984011i | \(-0.556997\pi\) |
0.763126 | + | 0.646250i | \(0.223664\pi\) | |||||||
\(692\) | −19.7580 | −0.751088 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.3244 | −0.999261 | ||||||||
\(695\) | −17.3858 | + | 10.0377i | −0.659480 | + | 0.380751i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.6034 | + | 37.4182i | −0.818287 | + | 1.41731i | ||||
\(698\) | 16.4522 | + | 28.4961i | 0.622725 | + | 1.07859i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.8950 | + | 12.0848i | 0.940941 | + | 0.456762i | ||||
\(701\) | 9.85160i | 0.372090i | 0.982541 | + | 0.186045i | \(0.0595670\pi\) | ||||
−0.982541 | + | 0.186045i | \(0.940433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.6344 | + | 7.29450i | 0.476517 | + | 0.275117i | ||||
\(704\) | 0.866025 | + | 0.500000i | 0.0326396 | + | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.49886i | 0.357494i | ||||||||
\(707\) | 2.94066 | + | 40.9581i | 0.110595 | + | 1.54039i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.4994 | + | 33.7739i | 0.732314 | + | 1.26840i | 0.955892 | + | 0.293718i | \(0.0948928\pi\) |
−0.223578 | + | 0.974686i | \(0.571774\pi\) | |||||||
\(710\) | −17.5116 | + | 30.3309i | −0.657197 | + | 1.13830i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.1741 | − | 5.87404i | 0.381292 | − | 0.220139i | ||||
\(713\) | −7.82165 | −0.292923 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.63103 | 0.360180 | ||||||||
\(716\) | −9.13593 | + | 5.27463i | −0.341426 | + | 0.197122i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.49867 | − | 2.59578i | 0.0559300 | − | 0.0968736i | ||||
\(719\) | −6.32864 | − | 10.9615i | −0.236019 | − | 0.408796i | 0.723550 | − | 0.690272i | \(-0.242509\pi\) |
−0.959568 | + | 0.281476i | \(0.909176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3304 | − | 29.5209i | 0.533690 | − | 1.09941i | ||||
\(722\) | − | 5.52412i | − | 0.205587i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.57287 | − | 2.06280i | −0.132785 | − | 0.0766634i | ||||
\(725\) | −46.7480 | − | 26.9900i | −1.73618 | − | 1.00238i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.8671i | 0.588478i | 0.955732 | + | 0.294239i | \(0.0950662\pi\) | ||||
−0.955732 | + | 0.294239i | \(0.904934\pi\) | |||||||
\(728\) | −5.36603 | + | 3.63397i | −0.198878 | + | 0.134684i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.39060 | + | 9.33680i | 0.199515 | + | 0.345571i | ||||
\(731\) | 39.0617 | − | 67.6568i | 1.44475 | − | 2.50238i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.8797 | + | 12.6322i | −0.808144 | + | 0.466582i | −0.846311 | − | 0.532689i | \(-0.821181\pi\) |
0.0381669 | + | 0.999271i | \(0.487848\pi\) | |||||||
\(734\) | −16.5510 | −0.610910 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.39595 | 0.125176 | ||||||||
\(737\) | 4.04222 | − | 2.33378i | 0.148897 | − | 0.0859657i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.35023 | − | 4.07072i | 0.0864546 | − | 0.149744i | −0.819556 | − | 0.573000i | \(-0.805780\pi\) |
0.906010 | + | 0.423256i | \(0.139113\pi\) | |||||||
\(740\) | 7.81294 | + | 13.5324i | 0.287209 | + | 0.497461i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −29.3061 | + | 19.8467i | −1.07586 | + | 0.728594i | ||||
\(743\) | − | 37.5807i | − | 1.37870i | −0.724427 | − | 0.689352i | \(-0.757895\pi\) | ||
0.724427 | − | 0.689352i | \(-0.242105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.3393 | + | 13.4749i | 0.855086 | + | 0.493684i | ||||
\(746\) | −16.8659 | − | 9.73753i | −0.617505 | − | 0.356516i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 7.29253i | − | 0.266641i | ||||||
\(749\) | −15.9351 | + | 32.8267i | −0.582256 | + | 1.19946i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6493 | + | 23.6413i | 0.498070 | + | 0.862682i | 0.999998 | − | 0.00222750i | \(-0.000709036\pi\) |
−0.501928 | + | 0.864910i | \(0.667376\pi\) | |||||||
\(752\) | −4.31199 | + | 7.46859i | −0.157242 | + | 0.272351i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.9479 | − | 6.32076i | 0.398698 | − | 0.230188i | ||||
\(755\) | 56.8822 | 2.07015 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.76874 | −0.0642858 | −0.0321429 | − | 0.999483i | \(-0.510233\pi\) | ||||
−0.0321429 | + | 0.999483i | \(0.510233\pi\) | |||||||
\(758\) | −1.91227 | + | 1.10405i | −0.0694566 | + | 0.0401008i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.21682 | + | 12.4999i | −0.261781 | + | 0.453419i | ||||
\(761\) | −15.4241 | − | 26.7153i | −0.559122 | − | 0.968428i | −0.997570 | − | 0.0696715i | \(-0.977805\pi\) |
0.438448 | − | 0.898757i | \(-0.355528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.930419 | + | 12.9591i | 0.0336834 | + | 0.469149i | ||||
\(764\) | 23.0194i | 0.832813i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.45690 | + | 1.41849i | 0.0887715 | + | 0.0512522i | ||||
\(767\) | 4.13681 | + | 2.38839i | 0.149372 | + | 0.0862398i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.1842i | 1.41302i | 0.707704 | + | 0.706509i | \(0.249731\pi\) | ||||
−0.707704 | + | 0.706509i | \(0.750269\pi\) | |||||||
\(770\) | 9.35835 | + | 4.54284i | 0.337252 | + | 0.163713i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.60708 | + | 7.97970i | 0.165813 | + | 0.287196i | ||||
\(773\) | 27.0296 | − | 46.8166i | 0.972186 | − | 1.68388i | 0.283263 | − | 0.959042i | \(-0.408583\pi\) |
0.688924 | − | 0.724834i | \(-0.258084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.8630 | − | 12.0452i | 0.749420 | − | 0.432678i | ||||
\(776\) | 5.85765 | 0.210277 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.0163 | −0.681767 | ||||||||
\(779\) | 18.8358 | − | 10.8748i | 0.674861 | − | 0.389631i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.45377 | + | 7.71415i | −0.159368 | + | 0.276034i | ||||
\(782\) | −12.3825 | − | 21.4472i | −0.442799 | − | 0.766950i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.92820 | + | 1.00000i | −0.247436 | + | 0.0357143i | ||||
\(785\) | 65.5161i | 2.33837i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.76131 | − | 5.05834i | −0.312307 | − | 0.180311i | 0.335651 | − | 0.941986i | \(-0.391044\pi\) |
−0.647958 | + | 0.761676i | \(0.724377\pi\) | |||||||
\(788\) | −5.64805 | − | 3.26090i | −0.201203 | − | 0.116165i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 60.5346i | − | 2.15372i | ||||||
\(791\) | 23.9254 | + | 35.3290i | 0.850691 | + | 1.25615i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.30884 | + | 12.6593i | 0.259545 | + | 0.449544i | ||||
\(794\) | −5.33315 | + | 9.23729i | −0.189267 | + | 0.327819i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.9813 | + | 7.49473i | −0.460109 | + | 0.265644i | ||||
\(797\) | 44.4401 | 1.57415 | 0.787075 | − | 0.616858i | \(-0.211595\pi\) | ||||
0.787075 | + | 0.616858i | \(0.211595\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.8906 | 2.22491 | ||||||||
\(800\) | −9.05816 | + | 5.22973i | −0.320254 | + | 0.184899i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.4092 | + | 28.4216i | −0.579429 | + | 1.00360i | ||||
\(803\) | 1.37101 | + | 2.37466i | 0.0483819 | + | 0.0837998i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.2364 | − | 2.52986i | 1.24192 | − | 0.0891658i | ||||
\(806\) | 5.64173i | 0.198721i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.4412 | − | 7.76028i | −0.472860 | − | 0.273006i | ||||
\(809\) | 42.6703 | + | 24.6357i | 1.50021 | + | 0.866146i | 1.00000 | 0.000241636i | \(7.69150e-5\pi\) | |
0.500209 | + | 0.865905i | \(0.333256\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 21.4369i | − | 0.752750i | −0.926467 | − | 0.376375i | \(-0.877170\pi\) | ||
0.926467 | − | 0.376375i | \(-0.122830\pi\) | |||||||
\(812\) | 13.6193 | − | 0.977824i | 0.477945 | − | 0.0343149i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.98709 | + | 3.44174i | 0.0696474 | + | 0.120633i | ||||
\(815\) | 1.89413 | − | 3.28073i | 0.0663484 | − | 0.114919i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.0574 | + | 19.6631i | −1.19152 | + | 0.687924i | ||||
\(818\) | 7.22073 | 0.252467 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.2954 | 0.813512 | ||||||||
\(821\) | 18.7461 | − | 10.8231i | 0.654244 | − | 0.377728i | −0.135836 | − | 0.990731i | \(-0.543372\pi\) |
0.790080 | + | 0.613003i | \(0.210039\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.93650 | − | 6.81821i | 0.137218 | − | 0.237668i | −0.789225 | − | 0.614104i | \(-0.789517\pi\) |
0.926442 | + | 0.376437i | \(0.122851\pi\) | |||||||
\(824\) | 6.20150 | + | 10.7413i | 0.216040 | + | 0.374191i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.89312 | + | 4.27205i | 0.100664 | + | 0.148644i | ||||
\(827\) | 21.5865i | 0.750635i | 0.926896 | + | 0.375317i | \(0.122466\pi\) | ||||
−0.926896 | + | 0.375317i | \(0.877534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.04678 | + | 3.49111i | 0.210013 | + | 0.121251i | 0.601318 | − | 0.799010i | \(-0.294643\pi\) |
−0.391304 | + | 0.920261i | \(0.627976\pi\) | |||||||
\(830\) | 20.6185 | + | 11.9041i | 0.715679 | + | 0.413197i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.44949i | − | 0.0849208i | ||||||
\(833\) | 31.5776 | + | 40.1089i | 1.09410 | + | 1.38969i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.80260 | − | 6.58630i | −0.131595 | − | 0.227928i | ||||
\(836\) | −1.83548 | + | 3.17914i | −0.0634812 | + | 0.109953i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.7857 | − | 7.95920i | 0.476220 | − | 0.274946i | ||||
\(839\) | −9.03111 | −0.311789 | −0.155894 | − | 0.987774i | \(-0.549826\pi\) | ||||
−0.155894 | + | 0.987774i | \(0.549826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.36536 | 0.0815640 | ||||||||
\(842\) | −3.67099 | + | 2.11944i | −0.126511 | + | 0.0730409i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.55379 | + | 7.88740i | −0.156748 | + | 0.271496i | ||||
\(845\) | 13.7615 | + | 23.8356i | 0.473409 | + | 0.819969i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.38014 | + | 1.15539i | 0.0817826 | + | 0.0396998i | ||||
\(848\) | − | 13.3777i | − | 0.459392i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 66.0569 | + | 38.1379i | 2.26573 | + | 1.30812i | ||||
\(851\) | 11.6880 | + | 6.74806i | 0.400659 | + | 0.231320i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.1105i | − | 0.859768i | −0.902884 | − | 0.429884i | \(-0.858554\pi\) | ||
0.902884 | − | 0.429884i | \(-0.141446\pi\) | |||||||
\(854\) | 1.13068 | + | 15.7484i | 0.0386911 | + | 0.538898i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.89595 | − | 11.9441i | −0.235699 | − | 0.408242i | ||||
\(857\) | 25.9758 | − | 44.9914i | 0.887315 | − | 1.53688i | 0.0442787 | − | 0.999019i | \(-0.485901\pi\) |
0.843037 | − | 0.537856i | \(-0.180766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.7954 | − | 9.69686i | 0.573053 | − | 0.330852i | −0.185315 | − | 0.982679i | \(-0.559330\pi\) |
0.758368 | + | 0.651827i | \(0.225997\pi\) | |||||||
\(860\) | −42.1211 | −1.43632 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.1573 | 0.686559 | ||||||||
\(863\) | −49.7575 | + | 28.7275i | −1.69377 | + | 0.977896i | −0.742337 | + | 0.670027i | \(0.766283\pi\) |
−0.951429 | + | 0.307869i | \(0.900384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.8428 | − | 67.2778i | 1.32070 | − | 2.28751i | ||||
\(866\) | −2.90646 | − | 5.03414i | −0.0987656 | − | 0.171067i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.66113 | + | 5.48200i | −0.0903248 | + | 0.186071i | ||||
\(869\) | − | 15.3960i | − | 0.522272i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.90137 | − | 5.71656i | −0.335495 | − | 0.193698i | ||||
\(872\) | −4.25277 | − | 2.45534i | −0.144017 | − | 0.0831482i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.4664i | 0.421681i | ||||||||
\(875\) | −47.0244 | + | 31.8459i | −1.58972 | + | 1.07659i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.9828 | + | 22.4869i | 0.438399 | + | 0.759329i | 0.997566 | − | 0.0697257i | \(-0.0222124\pi\) |
−0.559167 | + | 0.829055i | \(0.688879\pi\) | |||||||
\(878\) | −13.8682 | + | 24.0204i | −0.468029 | + | 0.810650i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.40508 | + | 1.96593i | −0.114785 | + | 0.0662713i | ||||
\(881\) | −11.9446 | −0.402423 | −0.201211 | − | 0.979548i | \(-0.564488\pi\) | ||||
−0.201211 | + | 0.979548i | \(0.564488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.7238 | −1.77430 | −0.887149 | − | 0.461483i | \(-0.847318\pi\) | ||||
−0.887149 | + | 0.461483i | \(0.847318\pi\) | |||||||
\(884\) | −15.4698 | + | 8.93149i | −0.520305 | + | 0.300398i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.62486 | + | 11.4746i | −0.222567 | + | 0.385497i | ||||
\(887\) | 13.8518 | + | 23.9921i | 0.465099 | + | 0.805575i | 0.999206 | − | 0.0398422i | \(-0.0126855\pi\) |
−0.534107 | + | 0.845417i | \(0.679352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.7867 | − | 14.7544i | 0.730702 | − | 0.494846i | ||||
\(890\) | 46.1917i | 1.54835i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.31149 | + | 3.64394i | 0.211324 | + | 0.122008i | ||||
\(893\) | −27.4168 | − | 15.8291i | −0.917469 | − | 0.529701i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 41.4781i | − | 1.38646i | ||||||
\(896\) | 1.15539 | − | 2.38014i | 0.0385990 | − | 0.0795149i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.9616 | + | 18.9861i | 0.365793 | + | 0.633573i | ||||
\(899\) | 5.94333 | − | 10.2942i | 0.198221 | − | 0.343329i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −84.4870 | + | 48.7786i | −2.81467 | + | 1.62505i | ||||
\(902\) | 5.92480 | 0.197274 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.1270 | −0.536376 | ||||||||
\(905\) | 14.0480 | − | 8.11062i | 0.466972 | − | 0.269606i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7674 | + | 27.3100i | −0.523548 | + | 0.906812i | 0.476076 | + | 0.879404i | \(0.342059\pi\) |
−0.999624 | + | 0.0274080i | \(0.991275\pi\) | |||||||
\(908\) | 0.465428 | + | 0.806145i | 0.0154458 | + | 0.0267529i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.82478 | − | 25.4159i | −0.0604908 | − | 0.842529i | ||||
\(911\) | 0.137644i | 0.00456035i | 0.999997 | + | 0.00228018i | \(0.000725803\pi\) | ||||
−0.999997 | + | 0.00228018i | \(0.999274\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.24397 | + | 3.02761i | 0.173550 | + | 0.100199i | ||||
\(914\) | −28.2483 | − | 16.3092i | −0.934372 | − | 0.539460i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 24.0233i | − | 0.793753i | ||||||
\(917\) | 43.9975 | + | 21.3578i | 1.45293 | + | 0.705296i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.7828 | + | 41.1930i | 0.784521 | + | 1.35883i | 0.929285 | + | 0.369365i | \(0.120425\pi\) |
−0.144763 | + | 0.989466i | \(0.546242\pi\) | |||||||
\(920\) | −6.67619 | + | 11.5635i | −0.220108 | + | 0.381237i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.3891 | − | 15.8131i | 0.902011 | − | 0.520776i | ||||
\(923\) | 21.8189 | 0.718179 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.5677 | −1.36674 | ||||||||
\(926\) | −10.0188 | + | 5.78434i | −0.329237 | + | 0.190085i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.58044 | + | 4.46945i | −0.0847070 | + | 0.146717i | ||||
\(929\) | 3.76320 | + | 6.51805i | 0.123467 | + | 0.213850i | 0.921132 | − | 0.389249i | \(-0.127266\pi\) |
−0.797666 | + | 0.603100i | \(0.793932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.67095 | − | 25.4331i | −0.120311 | − | 0.833536i | ||||
\(932\) | − | 17.4853i | − | 0.572749i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.79643 | − | 3.92392i | −0.222386 | − | 0.128395i | ||||
\(935\) | 24.8317 | + | 14.3366i | 0.812082 | + | 0.468856i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.64372i | 0.249709i | 0.992175 | + | 0.124855i | \(0.0398465\pi\) | ||||
−0.992175 | + | 0.124855i | \(0.960154\pi\) | |||||||
\(938\) | −6.92461 | − | 10.2251i | −0.226097 | − | 0.333860i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.9541 | − | 29.3654i | −0.552982 | − | 0.957793i | ||||
\(941\) | 3.92910 | − | 6.80539i | 0.128085 | − | 0.221850i | −0.794850 | − | 0.606806i | \(-0.792450\pi\) |
0.922935 | + | 0.384957i | \(0.125784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.4247 | − | 10.0602i | 0.567428 | − | 0.327604i | ||||
\(944\) | −1.95011 | −0.0634707 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.7128 | −0.348303 | ||||||||
\(947\) | −33.1290 | + | 19.1270i | −1.07655 | + | 0.621544i | −0.929963 | − | 0.367654i | \(-0.880161\pi\) |
−0.146584 | + | 0.989198i | \(0.546828\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.35827 | − | 5.81670i | 0.109014 | − | 0.188818i | ||||
\(950\) | −19.1981 | − | 33.2520i | −0.622868 | − | 1.07884i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.2447 | + | 1.38171i | −0.623724 | + | 0.0447813i | ||||
\(953\) | − | 12.6569i | − | 0.409996i | −0.978762 | − | 0.204998i | \(-0.934281\pi\) | ||
0.978762 | − | 0.204998i | \(-0.0657187\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −78.3830 | − | 45.2545i | −2.53642 | − | 1.46440i | ||||
\(956\) | −0.616710 | − | 0.356058i | −0.0199458 | − | 0.0115157i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 40.6322i | − | 1.31277i | ||||||
\(959\) | −7.36773 | + | 0.528979i | −0.237916 | + | 0.0170816i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.8476 | − | 22.2527i | −0.414438 | − | 0.717828i | ||||
\(962\) | 4.86735 | − | 8.43050i | 0.156930 | − | 0.271810i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.5097 | + | 7.79983i | −0.435118 | + | 0.251216i | ||||
\(965\) | −36.2287 | −1.16624 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.2489 | 1.19784 | 0.598922 | − | 0.800807i | \(-0.295596\pi\) | ||||
0.598922 | + | 0.800807i | \(0.295596\pi\) | |||||||
\(968\) | −0.866025 | + | 0.500000i | −0.0278351 | + | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.5157 | + | 19.9458i | −0.369747 | + | 0.640421i | ||||
\(971\) | −28.9586 | − | 50.1577i | −0.929325 | − | 1.60964i | −0.784453 | − | 0.620188i | \(-0.787056\pi\) |
−0.144872 | − | 0.989450i | \(-0.546277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.57482 | + | 11.1852i | 0.242838 | + | 0.358581i | ||||
\(974\) | 25.2148i | 0.807936i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.16813 | − | 2.98382i | −0.165428 | − | 0.0955098i | ||||
\(977\) | 11.2435 | + | 6.49145i | 0.359712 | + | 0.207680i | 0.668954 | − | 0.743303i | \(-0.266742\pi\) |
−0.309242 | + | 0.950983i | \(0.600075\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.7481i | 0.375470i | ||||||||
\(980\) | 10.2153 | − | 25.5570i | 0.326314 | − | 0.816390i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.41776 | − | 2.45562i | −0.0452424 | − | 0.0783621i | ||||
\(983\) | 9.60828 | − | 16.6420i | 0.306457 | − | 0.530799i | −0.671128 | − | 0.741342i | \(-0.734190\pi\) |
0.977585 | + | 0.210543i | \(0.0675232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.2073 | − | 12.8214i | 0.707583 | − | 0.408523i | ||||
\(986\) | 37.6358 | 1.19857 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.99196 | 0.286072 | ||||||||
\(989\) | −31.5061 | + | 18.1901i | −1.00184 | + | 0.578411i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.7408 | − | 27.2639i | 0.500024 | − | 0.866067i | −0.499976 | − | 0.866039i | \(-0.666658\pi\) |
1.00000 | 2.77966e-5i | \(-8.84792e-6\pi\) | ||||||||
\(992\) | −1.15161 | − | 1.99465i | −0.0365637 | − | 0.0633303i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.2012 | + | 10.2917i | 0.672461 | + | 0.326434i | ||||
\(995\) | − | 58.9364i | − | 1.86841i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.6287 | + | 21.1476i | 1.16004 | + | 0.669750i | 0.951314 | − | 0.308223i | \(-0.0997344\pi\) |
0.208728 | + | 0.977974i | \(0.433068\pi\) | |||||||
\(998\) | 12.6415 | + | 7.29858i | 0.400160 | + | 0.231033i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.r.c.1277.2 | yes | 8 | |
3.2 | odd | 2 | 1386.2.r.a.1277.3 | yes | 8 | ||
7.5 | odd | 6 | 1386.2.r.a.89.3 | ✓ | 8 | ||
21.5 | even | 6 | inner | 1386.2.r.c.89.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.a.89.3 | ✓ | 8 | 7.5 | odd | 6 | ||
1386.2.r.a.1277.3 | yes | 8 | 3.2 | odd | 2 | ||
1386.2.r.c.89.2 | yes | 8 | 21.5 | even | 6 | inner | |
1386.2.r.c.1277.2 | yes | 8 | 1.1 | even | 1 | trivial |