Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(1049,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.1049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 4x^{8} - 30x^{6} + 36x^{4} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.9 | ||
Root | \(1.06864 + 1.36309i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.1049 |
Dual form | 1050.2.d.g.1049.10 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.36309 | − | 1.06864i | 0.786979 | − | 0.616980i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.36309 | + | 1.06864i | −0.556478 | + | 0.436271i | ||||
\(7\) | 0.294447 | − | 2.62932i | 0.111290 | − | 0.993788i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.716015 | − | 2.91330i | 0.238672 | − | 0.971100i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.43203i | 0.431773i | 0.976418 | + | 0.215887i | \(0.0692641\pi\) | ||||
−0.976418 | + | 0.215887i | \(0.930736\pi\) | |||||||
\(12\) | 1.36309 | − | 1.06864i | 0.393489 | − | 0.308490i | ||||
\(13\) | 4.73625 | 1.31360 | 0.656799 | − | 0.754066i | \(-0.271910\pi\) | ||||
0.656799 | + | 0.754066i | \(0.271910\pi\) | |||||||
\(14\) | −0.294447 | + | 2.62932i | −0.0786942 | + | 0.702714i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.59897i | − | 0.630342i | −0.949035 | − | 0.315171i | \(-0.897938\pi\) | ||
0.949035 | − | 0.315171i | \(-0.102062\pi\) | |||||||
\(18\) | −0.716015 | + | 2.91330i | −0.168766 | + | 0.686672i | ||||
\(19\) | 2.72617i | 0.625427i | 0.949847 | + | 0.312714i | \(0.101238\pi\) | ||||
−0.949847 | + | 0.312714i | \(0.898762\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.40844 | − | 3.89865i | −0.525564 | − | 0.850754i | ||||
\(22\) | − | 1.43203i | − | 0.305310i | ||||||
\(23\) | 2.82660 | 0.589387 | 0.294694 | − | 0.955592i | \(-0.404782\pi\) | ||||
0.294694 | + | 0.955592i | \(0.404782\pi\) | |||||||
\(24\) | −1.36309 | + | 1.06864i | −0.278239 | + | 0.218135i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.73625 | −0.928854 | ||||||||
\(27\) | −2.13728 | − | 4.73625i | −0.411320 | − | 0.911491i | ||||
\(28\) | 0.294447 | − | 2.62932i | 0.0556452 | − | 0.496894i | ||||
\(29\) | 2.82660i | 0.524887i | 0.964947 | + | 0.262443i | \(0.0845283\pi\) | ||||
−0.964947 | + | 0.262443i | \(0.915472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.91403i | − | 1.06219i | −0.847312 | − | 0.531096i | \(-0.821780\pi\) | ||
0.847312 | − | 0.531096i | \(-0.178220\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.53032 | + | 1.95198i | 0.266395 | + | 0.339796i | ||||
\(34\) | 2.59897i | 0.445719i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.716015 | − | 2.91330i | 0.119336 | − | 0.485550i | ||||
\(37\) | − | 2.39457i | − | 0.393665i | −0.980437 | − | 0.196833i | \(-0.936934\pi\) | ||
0.980437 | − | 0.196833i | \(-0.0630656\pi\) | |||||||
\(38\) | − | 2.72617i | − | 0.442244i | ||||||
\(39\) | 6.45592 | − | 5.06134i | 1.03377 | − | 0.810464i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1481 | −1.74104 | −0.870520 | − | 0.492134i | \(-0.836217\pi\) | ||||
−0.870520 | + | 0.492134i | \(0.836217\pi\) | |||||||
\(42\) | 2.40844 | + | 3.89865i | 0.371630 | + | 0.601574i | ||||
\(43\) | − | 0.432029i | − | 0.0658838i | −0.999457 | − | 0.0329419i | \(-0.989512\pi\) | ||
0.999457 | − | 0.0329419i | \(-0.0104876\pi\) | |||||||
\(44\) | 1.43203i | 0.215887i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.82660 | −0.416760 | ||||||||
\(47\) | − | 10.3158i | − | 1.50471i | −0.658755 | − | 0.752357i | \(-0.728917\pi\) | ||
0.658755 | − | 0.752357i | \(-0.271083\pi\) | |||||||
\(48\) | 1.36309 | − | 1.06864i | 0.196745 | − | 0.154245i | ||||
\(49\) | −6.82660 | − | 1.54839i | −0.975229 | − | 0.221198i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.77736 | − | 3.54262i | −0.388908 | − | 0.496066i | ||||
\(52\) | 4.73625 | 0.656799 | ||||||||
\(53\) | 5.69066 | 0.781672 | 0.390836 | − | 0.920460i | \(-0.372186\pi\) | ||||
0.390836 | + | 0.920460i | \(0.372186\pi\) | |||||||
\(54\) | 2.13728 | + | 4.73625i | 0.290847 | + | 0.644521i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.294447 | + | 2.62932i | −0.0393471 | + | 0.351357i | ||||
\(57\) | 2.91330 | + | 3.71601i | 0.385876 | + | 0.492198i | ||||
\(58\) | − | 2.82660i | − | 0.371151i | ||||||
\(59\) | 10.7775 | 1.40311 | 0.701555 | − | 0.712615i | \(-0.252490\pi\) | ||||
0.701555 | + | 0.712615i | \(0.252490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.05058i | − | 0.134513i | −0.997736 | − | 0.0672563i | \(-0.978575\pi\) | ||
0.997736 | − | 0.0672563i | \(-0.0214245\pi\) | |||||||
\(62\) | 5.91403i | 0.751083i | ||||||||
\(63\) | −7.44916 | − | 2.74044i | −0.938506 | − | 0.345263i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.53032 | − | 1.95198i | −0.188370 | − | 0.240272i | ||||
\(67\) | 9.82660i | 1.20051i | 0.799808 | + | 0.600255i | \(0.204934\pi\) | ||||
−0.799808 | + | 0.600255i | \(0.795066\pi\) | |||||||
\(68\) | − | 2.59897i | − | 0.315171i | ||||||
\(69\) | 3.85291 | − | 3.02062i | 0.463835 | − | 0.363640i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2586i | 1.57351i | 0.617265 | + | 0.786755i | \(0.288240\pi\) | ||||
−0.617265 | + | 0.786755i | \(0.711760\pi\) | |||||||
\(72\) | −0.716015 | + | 2.91330i | −0.0843831 | + | 0.343336i | ||||
\(73\) | 7.58963 | 0.888299 | 0.444150 | − | 0.895953i | \(-0.353506\pi\) | ||||
0.444150 | + | 0.895953i | \(0.353506\pi\) | |||||||
\(74\) | 2.39457i | 0.278363i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.72617i | 0.312714i | ||||||||
\(77\) | 3.76526 | + | 0.421657i | 0.429091 | + | 0.0480522i | ||||
\(78\) | −6.45592 | + | 5.06134i | −0.730989 | + | 0.573084i | ||||
\(79\) | −16.5173 | −1.85834 | −0.929169 | − | 0.369656i | \(-0.879475\pi\) | ||||
−0.929169 | + | 0.369656i | \(0.879475\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.97465 | − | 4.17193i | −0.886072 | − | 0.463548i | ||||
\(82\) | 11.1481 | 1.23110 | ||||||||
\(83\) | − | 12.9148i | − | 1.41758i | −0.705419 | − | 0.708790i | \(-0.749241\pi\) | ||
0.705419 | − | 0.708790i | \(-0.250759\pi\) | |||||||
\(84\) | −2.40844 | − | 3.89865i | −0.262782 | − | 0.425377i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.432029i | 0.0465869i | ||||||||
\(87\) | 3.02062 | + | 3.85291i | 0.323845 | + | 0.413075i | ||||
\(88\) | − | 1.43203i | − | 0.152655i | ||||||
\(89\) | 3.90396 | 0.413819 | 0.206910 | − | 0.978360i | \(-0.433659\pi\) | ||||
0.206910 | + | 0.978360i | \(0.433659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.39457 | − | 12.4531i | 0.146191 | − | 1.30544i | ||||
\(92\) | 2.82660 | 0.294694 | ||||||||
\(93\) | −6.31998 | − | 8.06134i | −0.655351 | − | 0.835923i | ||||
\(94\) | 10.3158i | 1.06399i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.36309 | + | 1.06864i | −0.139120 | + | 0.109068i | ||||
\(97\) | −14.0015 | −1.42163 | −0.710817 | − | 0.703377i | \(-0.751675\pi\) | ||||
−0.710817 | + | 0.703377i | \(0.751675\pi\) | |||||||
\(98\) | 6.82660 | + | 1.54839i | 0.689591 | + | 0.156411i | ||||
\(99\) | 4.17193 | + | 1.02535i | 0.419295 | + | 0.103052i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3158 | 1.02646 | 0.513231 | − | 0.858251i | \(-0.328449\pi\) | ||||
0.513231 | + | 0.858251i | \(0.328449\pi\) | |||||||
\(102\) | 2.77736 | + | 3.54262i | 0.275000 | + | 0.350771i | ||||
\(103\) | −13.8743 | −1.36707 | −0.683536 | − | 0.729917i | \(-0.739559\pi\) | ||||
−0.683536 | + | 0.729917i | \(0.739559\pi\) | |||||||
\(104\) | −4.73625 | −0.464427 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.69066 | −0.552726 | ||||||||
\(107\) | −15.9493 | −1.54188 | −0.770938 | − | 0.636910i | \(-0.780212\pi\) | ||||
−0.770938 | + | 0.636910i | \(0.780212\pi\) | |||||||
\(108\) | −2.13728 | − | 4.73625i | −0.205660 | − | 0.455746i | ||||
\(109\) | 10.7891 | 1.03341 | 0.516706 | − | 0.856163i | \(-0.327158\pi\) | ||||
0.516706 | + | 0.856163i | \(0.327158\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.55894 | − | 3.26401i | −0.242884 | − | 0.309806i | ||||
\(112\) | 0.294447 | − | 2.62932i | 0.0278226 | − | 0.248447i | ||||
\(113\) | 14.3439 | 1.34936 | 0.674679 | − | 0.738112i | \(-0.264282\pi\) | ||||
0.674679 | + | 0.738112i | \(0.264282\pi\) | |||||||
\(114\) | −2.91330 | − | 3.71601i | −0.272856 | − | 0.348037i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.82660i | 0.262443i | ||||||||
\(117\) | 3.39122 | − | 13.7981i | 0.313519 | − | 1.27564i | ||||
\(118\) | −10.7775 | −0.992148 | ||||||||
\(119\) | −6.83350 | − | 0.765257i | −0.626426 | − | 0.0701510i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.94929 | 0.813572 | ||||||||
\(122\) | 1.05058i | 0.0951148i | ||||||||
\(123\) | −15.1958 | + | 11.9133i | −1.37016 | + | 1.07419i | ||||
\(124\) | − | 5.91403i | − | 0.531096i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.44916 | + | 2.74044i | 0.663624 | + | 0.244138i | ||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.461684 | − | 0.588894i | −0.0406490 | − | 0.0518492i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2804 | 1.50980 | 0.754899 | − | 0.655842i | \(-0.227686\pi\) | ||||
0.754899 | + | 0.655842i | \(0.227686\pi\) | |||||||
\(132\) | 1.53032 | + | 1.95198i | 0.133198 | + | 0.169898i | ||||
\(133\) | 7.16797 | + | 0.802714i | 0.621542 | + | 0.0696041i | ||||
\(134\) | − | 9.82660i | − | 0.848889i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.59897i | 0.222859i | ||||||||
\(137\) | 3.03746 | 0.259507 | 0.129754 | − | 0.991546i | \(-0.458581\pi\) | ||||
0.129754 | + | 0.991546i | \(0.458581\pi\) | |||||||
\(138\) | −3.85291 | + | 3.02062i | −0.327981 | + | 0.257132i | ||||
\(139\) | − | 20.7478i | − | 1.75980i | −0.475155 | − | 0.879902i | \(-0.657608\pi\) | ||
0.475155 | − | 0.879902i | \(-0.342392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0239 | − | 14.0613i | −0.928379 | − | 1.18418i | ||||
\(142\) | − | 13.2586i | − | 1.11264i | ||||||
\(143\) | 6.78244i | 0.567176i | ||||||||
\(144\) | 0.716015 | − | 2.91330i | 0.0596679 | − | 0.242775i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.58963 | −0.628122 | ||||||||
\(147\) | −10.9599 | + | 5.18460i | −0.903959 | + | 0.427618i | ||||
\(148\) | − | 2.39457i | − | 0.196833i | ||||||
\(149\) | 18.9493i | 1.55239i | 0.630495 | + | 0.776193i | \(0.282852\pi\) | ||||
−0.630495 | + | 0.776193i | \(0.717148\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.25863 | 0.427941 | 0.213971 | − | 0.976840i | \(-0.431360\pi\) | ||||
0.213971 | + | 0.976840i | \(0.431360\pi\) | |||||||
\(152\) | − | 2.72617i | − | 0.221122i | ||||||
\(153\) | −7.57157 | − | 1.86090i | −0.612125 | − | 0.150445i | ||||
\(154\) | −3.76526 | − | 0.421657i | −0.303413 | − | 0.0339781i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.45592 | − | 5.06134i | 0.516887 | − | 0.405232i | ||||
\(157\) | 6.29566 | 0.502449 | 0.251224 | − | 0.967929i | \(-0.419167\pi\) | ||||
0.251224 | + | 0.967929i | \(0.419167\pi\) | |||||||
\(158\) | 16.5173 | 1.31404 | ||||||||
\(159\) | 7.75687 | − | 6.08127i | 0.615160 | − | 0.482276i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.832284 | − | 7.43203i | 0.0655932 | − | 0.585726i | ||||
\(162\) | 7.97465 | + | 4.17193i | 0.626547 | + | 0.327778i | ||||
\(163\) | 0.605427i | 0.0474207i | 0.999719 | + | 0.0237104i | \(0.00754795\pi\) | ||||
−0.999719 | + | 0.0237104i | \(0.992452\pi\) | |||||||
\(164\) | −11.1481 | −0.870520 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.9148i | 1.00238i | ||||||||
\(167\) | 12.0825i | 0.934971i | 0.884001 | + | 0.467485i | \(0.154840\pi\) | ||||
−0.884001 | + | 0.467485i | \(0.845160\pi\) | |||||||
\(168\) | 2.40844 | + | 3.89865i | 0.185815 | + | 0.300787i | ||||
\(169\) | 9.43203 | 0.725541 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.94217 | + | 1.95198i | 0.607353 | + | 0.149272i | ||||
\(172\) | − | 0.432029i | − | 0.0329419i | ||||||
\(173\) | 15.5137i | 1.17949i | 0.807590 | + | 0.589744i | \(0.200771\pi\) | ||||
−0.807590 | + | 0.589744i | \(0.799229\pi\) | |||||||
\(174\) | −3.02062 | − | 3.85291i | −0.228993 | − | 0.292088i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.43203i | 0.107943i | ||||||||
\(177\) | 14.6907 | − | 11.5173i | 1.10422 | − | 0.865690i | ||||
\(178\) | −3.90396 | −0.292614 | ||||||||
\(179\) | 4.56797i | 0.341426i | 0.985321 | + | 0.170713i | \(0.0546071\pi\) | ||||
−0.985321 | + | 0.170713i | \(0.945393\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.80792i | 0.580358i | 0.956972 | + | 0.290179i | \(0.0937149\pi\) | ||||
−0.956972 | + | 0.290179i | \(0.906285\pi\) | |||||||
\(182\) | −1.39457 | + | 12.4531i | −0.103373 | + | 0.923084i | ||||
\(183\) | −1.12269 | − | 1.43203i | −0.0829916 | − | 0.105859i | ||||
\(184\) | −2.82660 | −0.208380 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.31998 | + | 8.06134i | 0.463403 | + | 0.591086i | ||||
\(187\) | 3.72179 | 0.272165 | ||||||||
\(188\) | − | 10.3158i | − | 0.752357i | ||||||
\(189\) | −13.0824 | + | 4.22501i | −0.951605 | + | 0.307325i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.22117i | 0.522506i | 0.965270 | + | 0.261253i | \(0.0841357\pi\) | ||||
−0.965270 | + | 0.261253i | \(0.915864\pi\) | |||||||
\(192\) | 1.36309 | − | 1.06864i | 0.0983724 | − | 0.0771225i | ||||
\(193\) | 7.60250i | 0.547240i | 0.961838 | + | 0.273620i | \(0.0882210\pi\) | ||||
−0.961838 | + | 0.273620i | \(0.911779\pi\) | |||||||
\(194\) | 14.0015 | 1.00525 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.82660 | − | 1.54839i | −0.487614 | − | 0.110599i | ||||
\(197\) | −21.7384 | −1.54880 | −0.774400 | − | 0.632697i | \(-0.781948\pi\) | ||||
−0.774400 | + | 0.632697i | \(0.781948\pi\) | |||||||
\(198\) | −4.17193 | − | 1.02535i | −0.296486 | − | 0.0728687i | ||||
\(199\) | − | 6.04124i | − | 0.428252i | −0.976806 | − | 0.214126i | \(-0.931310\pi\) | ||
0.976806 | − | 0.214126i | \(-0.0686904\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5011 | + | 13.3945i | 0.740691 | + | 0.944776i | ||||
\(202\) | −10.3158 | −0.725818 | ||||||||
\(203\) | 7.43203 | + | 0.832284i | 0.521626 | + | 0.0584149i | ||||
\(204\) | −2.77736 | − | 3.54262i | −0.194454 | − | 0.248033i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.8743 | 0.966666 | ||||||||
\(207\) | 2.02389 | − | 8.23474i | 0.140670 | − | 0.572354i | ||||
\(208\) | 4.73625 | 0.328400 | ||||||||
\(209\) | −3.90396 | −0.270043 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.7759 | 1.15490 | 0.577450 | − | 0.816426i | \(-0.304048\pi\) | ||||
0.577450 | + | 0.816426i | \(0.304048\pi\) | |||||||
\(212\) | 5.69066 | 0.390836 | ||||||||
\(213\) | 14.1687 | + | 18.0727i | 0.970824 | + | 1.23832i | ||||
\(214\) | 15.9493 | 1.09027 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.13728 | + | 4.73625i | 0.145424 | + | 0.322261i | ||||
\(217\) | −15.5499 | − | 1.74137i | −1.05559 | − | 0.118212i | ||||
\(218\) | −10.7891 | −0.730733 | ||||||||
\(219\) | 10.3453 | − | 8.11059i | 0.699073 | − | 0.548063i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.3093i | − | 0.828016i | ||||||
\(222\) | 2.55894 | + | 3.26401i | 0.171745 | + | 0.219066i | ||||
\(223\) | −11.1120 | −0.744112 | −0.372056 | − | 0.928210i | \(-0.621347\pi\) | ||||
−0.372056 | + | 0.928210i | \(0.621347\pi\) | |||||||
\(224\) | −0.294447 | + | 2.62932i | −0.0196736 | + | 0.175679i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.3439 | −0.954140 | ||||||||
\(227\) | 7.24413i | 0.480810i | 0.970673 | + | 0.240405i | \(0.0772802\pi\) | ||||
−0.970673 | + | 0.240405i | \(0.922720\pi\) | |||||||
\(228\) | 2.91330 | + | 3.71601i | 0.192938 | + | 0.246099i | ||||
\(229\) | 27.1596i | 1.79476i | 0.441259 | + | 0.897380i | \(0.354532\pi\) | ||||
−0.441259 | + | 0.897380i | \(0.645468\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.58297 | − | 3.44895i | 0.367333 | − | 0.226924i | ||||
\(232\) | − | 2.82660i | − | 0.185576i | ||||||
\(233\) | 5.38132 | 0.352542 | 0.176271 | − | 0.984342i | \(-0.443596\pi\) | ||||
0.176271 | + | 0.984342i | \(0.443596\pi\) | |||||||
\(234\) | −3.39122 | + | 13.7981i | −0.221691 | + | 0.902011i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.7775 | 0.701555 | ||||||||
\(237\) | −22.5145 | + | 17.6510i | −1.46247 | + | 1.14656i | ||||
\(238\) | 6.83350 | + | 0.765257i | 0.442950 | + | 0.0496043i | ||||
\(239\) | 2.51726i | 0.162828i | 0.996680 | + | 0.0814141i | \(0.0259436\pi\) | ||||
−0.996680 | + | 0.0814141i | \(0.974056\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.8077i | 1.08268i | 0.840804 | + | 0.541340i | \(0.182083\pi\) | ||||
−0.840804 | + | 0.541340i | \(0.817917\pi\) | |||||||
\(242\) | −8.94929 | −0.575282 | ||||||||
\(243\) | −15.3284 | + | 2.83532i | −0.983320 | + | 0.181886i | ||||
\(244\) | − | 1.05058i | − | 0.0672563i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.1958 | − | 11.9133i | 0.968850 | − | 0.759564i | ||||
\(247\) | 12.9118i | 0.821560i | ||||||||
\(248\) | 5.91403i | 0.375542i | ||||||||
\(249\) | −13.8012 | − | 17.6040i | −0.874619 | − | 1.11561i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.75565 | 0.110816 | 0.0554079 | − | 0.998464i | \(-0.482354\pi\) | ||||
0.0554079 | + | 0.998464i | \(0.482354\pi\) | |||||||
\(252\) | −7.44916 | − | 2.74044i | −0.469253 | − | 0.172632i | ||||
\(253\) | 4.04778i | 0.254482i | ||||||||
\(254\) | 2.00000i | 0.125491i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 21.9366i | − | 1.36837i | −0.729309 | − | 0.684184i | \(-0.760159\pi\) | ||
0.729309 | − | 0.684184i | \(-0.239841\pi\) | |||||||
\(258\) | 0.461684 | + | 0.588894i | 0.0287432 | + | 0.0366629i | ||||
\(259\) | −6.29609 | − | 0.705074i | −0.391220 | − | 0.0438112i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.23474 | + | 2.02389i | 0.509718 | + | 0.125276i | ||||
\(262\) | −17.2804 | −1.06759 | ||||||||
\(263\) | −4.08523 | −0.251906 | −0.125953 | − | 0.992036i | \(-0.540199\pi\) | ||||
−0.125953 | + | 0.992036i | \(0.540199\pi\) | |||||||
\(264\) | −1.53032 | − | 1.95198i | −0.0941850 | − | 0.120136i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.16797 | − | 0.802714i | −0.439497 | − | 0.0492175i | ||||
\(267\) | 5.32144 | − | 4.17193i | 0.325667 | − | 0.255318i | ||||
\(268\) | 9.82660i | 0.600255i | ||||||||
\(269\) | −6.96461 | −0.424640 | −0.212320 | − | 0.977200i | \(-0.568102\pi\) | ||||
−0.212320 | + | 0.977200i | \(0.568102\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4740i | 1.42594i | 0.701194 | + | 0.712971i | \(0.252651\pi\) | ||||
−0.701194 | + | 0.712971i | \(0.747349\pi\) | |||||||
\(272\) | − | 2.59897i | − | 0.157585i | ||||||
\(273\) | −11.4069 | − | 18.4649i | −0.690380 | − | 1.11755i | ||||
\(274\) | −3.03746 | −0.183499 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.85291 | − | 3.02062i | 0.231918 | − | 0.181820i | ||||
\(277\) | 14.1227i | 0.848550i | 0.905533 | + | 0.424275i | \(0.139471\pi\) | ||||
−0.905533 | + | 0.424275i | \(0.860529\pi\) | |||||||
\(278\) | 20.7478i | 1.24437i | ||||||||
\(279\) | −17.2294 | − | 4.23453i | −1.03149 | − | 0.253515i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.6532i | 1.41103i | 0.708694 | + | 0.705516i | \(0.249285\pi\) | ||||
−0.708694 | + | 0.705516i | \(0.750715\pi\) | |||||||
\(282\) | 11.0239 | + | 14.0613i | 0.656463 | + | 0.837341i | ||||
\(283\) | 0.807187 | 0.0479823 | 0.0239912 | − | 0.999712i | \(-0.492363\pi\) | ||||
0.0239912 | + | 0.999712i | \(0.492363\pi\) | |||||||
\(284\) | 13.2586i | 0.786755i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 6.78244i | − | 0.401054i | ||||||
\(287\) | −3.28252 | + | 29.3118i | −0.193761 | + | 1.73022i | ||||
\(288\) | −0.716015 | + | 2.91330i | −0.0421916 | + | 0.171668i | ||||
\(289\) | 10.2454 | 0.602669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.0852 | + | 14.9625i | −1.11880 | + | 0.877120i | ||||
\(292\) | 7.58963 | 0.444150 | ||||||||
\(293\) | 14.6704i | 0.857055i | 0.903529 | + | 0.428528i | \(0.140968\pi\) | ||||
−0.903529 | + | 0.428528i | \(0.859032\pi\) | |||||||
\(294\) | 10.9599 | − | 5.18460i | 0.639196 | − | 0.302372i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.39457i | 0.139182i | ||||||||
\(297\) | 6.78244 | − | 3.06065i | 0.393557 | − | 0.177597i | ||||
\(298\) | − | 18.9493i | − | 1.09770i | ||||||
\(299\) | 13.3875 | 0.774218 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.13594 | − | 0.127210i | −0.0654746 | − | 0.00733224i | ||||
\(302\) | −5.25863 | −0.302600 | ||||||||
\(303\) | 14.0613 | − | 11.0239i | 0.807803 | − | 0.633306i | ||||
\(304\) | 2.72617i | 0.156357i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.57157 | + | 1.86090i | 0.432838 | + | 0.106380i | ||||
\(307\) | −10.0975 | −0.576295 | −0.288148 | − | 0.957586i | \(-0.593039\pi\) | ||||
−0.288148 | + | 0.957586i | \(0.593039\pi\) | |||||||
\(308\) | 3.76526 | + | 0.421657i | 0.214545 | + | 0.0240261i | ||||
\(309\) | −18.9118 | + | 14.8266i | −1.07586 | + | 0.843456i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.27456 | −0.242388 | −0.121194 | − | 0.992629i | \(-0.538672\pi\) | ||||
−0.121194 | + | 0.992629i | \(0.538672\pi\) | |||||||
\(312\) | −6.45592 | + | 5.06134i | −0.365494 | + | 0.286542i | ||||
\(313\) | 0.923368 | 0.0521918 | 0.0260959 | − | 0.999659i | \(-0.491692\pi\) | ||||
0.0260959 | + | 0.999659i | \(0.491692\pi\) | |||||||
\(314\) | −6.29566 | −0.355285 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.5173 | −0.929169 | ||||||||
\(317\) | 15.7384 | 0.883959 | 0.441979 | − | 0.897025i | \(-0.354276\pi\) | ||||
0.441979 | + | 0.897025i | \(0.354276\pi\) | |||||||
\(318\) | −7.75687 | + | 6.08127i | −0.434984 | + | 0.341021i | ||||
\(319\) | −4.04778 | −0.226632 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.7403 | + | 17.0441i | −1.21342 | + | 0.951307i | ||||
\(322\) | −0.832284 | + | 7.43203i | −0.0463814 | + | 0.414171i | ||||
\(323\) | 7.08523 | 0.394233 | ||||||||
\(324\) | −7.97465 | − | 4.17193i | −0.443036 | − | 0.231774i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 0.605427i | − | 0.0335315i | ||||||
\(327\) | 14.7065 | − | 11.5297i | 0.813274 | − | 0.637595i | ||||
\(328\) | 11.1481 | 0.615550 | ||||||||
\(329\) | −27.1235 | − | 3.03746i | −1.49537 | − | 0.167460i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.6054 | −0.692857 | −0.346428 | − | 0.938076i | \(-0.612606\pi\) | ||||
−0.346428 | + | 0.938076i | \(0.612606\pi\) | |||||||
\(332\) | − | 12.9148i | − | 0.708790i | ||||||
\(333\) | −6.97611 | − | 1.71455i | −0.382289 | − | 0.0939567i | ||||
\(334\) | − | 12.0825i | − | 0.661124i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.40844 | − | 3.89865i | −0.131391 | − | 0.212689i | ||||
\(337\) | 18.8986i | 1.02947i | 0.857349 | + | 0.514736i | \(0.172110\pi\) | ||||
−0.857349 | + | 0.514736i | \(0.827890\pi\) | |||||||
\(338\) | −9.43203 | −0.513035 | ||||||||
\(339\) | 19.5519 | − | 15.3284i | 1.06192 | − | 0.832526i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.46907 | 0.458626 | ||||||||
\(342\) | −7.94217 | − | 1.95198i | −0.429463 | − | 0.105551i | ||||
\(343\) | −6.08127 | + | 17.4934i | −0.328358 | + | 0.944553i | ||||
\(344\) | 0.432029i | 0.0232935i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 15.5137i | − | 0.834024i | ||||||
\(347\) | 30.7384 | 1.65013 | 0.825063 | − | 0.565041i | \(-0.191140\pi\) | ||||
0.825063 | + | 0.565041i | \(0.191140\pi\) | |||||||
\(348\) | 3.02062 | + | 3.85291i | 0.161922 | + | 0.206537i | ||||
\(349\) | − | 0.970523i | − | 0.0519509i | −0.999663 | − | 0.0259754i | \(-0.991731\pi\) | ||
0.999663 | − | 0.0259754i | \(-0.00826917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.1227 | − | 22.4320i | −0.540309 | − | 1.19733i | ||||
\(352\) | − | 1.43203i | − | 0.0763274i | ||||||
\(353\) | 16.3570i | 0.870598i | 0.900286 | + | 0.435299i | \(0.143357\pi\) | ||||
−0.900286 | + | 0.435299i | \(0.856643\pi\) | |||||||
\(354\) | −14.6907 | + | 11.5173i | −0.780800 | + | 0.612136i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.90396 | 0.206910 | ||||||||
\(357\) | −10.1324 | + | 6.25944i | −0.536266 | + | 0.331285i | ||||
\(358\) | − | 4.56797i | − | 0.241425i | ||||||
\(359\) | − | 9.81335i | − | 0.517929i | −0.965887 | − | 0.258964i | \(-0.916619\pi\) | ||
0.965887 | − | 0.258964i | \(-0.0833812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.5680 | 0.608841 | ||||||||
\(362\) | − | 7.80792i | − | 0.410375i | ||||||
\(363\) | 12.1987 | − | 9.56358i | 0.640264 | − | 0.501958i | ||||
\(364\) | 1.39457 | − | 12.4531i | 0.0730955 | − | 0.652719i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.12269 | + | 1.43203i | 0.0586839 | + | 0.0748534i | ||||
\(367\) | 33.9970 | 1.77463 | 0.887315 | − | 0.461163i | \(-0.152568\pi\) | ||||
0.887315 | + | 0.461163i | \(0.152568\pi\) | |||||||
\(368\) | 2.82660 | 0.147347 | ||||||||
\(369\) | −7.98220 | + | 32.4777i | −0.415537 | + | 1.69072i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.67560 | − | 14.9625i | 0.0869927 | − | 0.776817i | ||||
\(372\) | −6.31998 | − | 8.06134i | −0.327676 | − | 0.417961i | ||||
\(373\) | 26.5650i | 1.37549i | 0.725954 | + | 0.687743i | \(0.241398\pi\) | ||||
−0.725954 | + | 0.687743i | \(0.758602\pi\) | |||||||
\(374\) | −3.72179 | −0.192449 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3158i | 0.531997i | ||||||||
\(377\) | 13.3875i | 0.689490i | ||||||||
\(378\) | 13.0824 | − | 4.22501i | 0.672886 | − | 0.217311i | ||||
\(379\) | −8.25863 | −0.424217 | −0.212109 | − | 0.977246i | \(-0.568033\pi\) | ||||
−0.212109 | + | 0.977246i | \(0.568033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.13728 | − | 2.72617i | −0.109496 | − | 0.139666i | ||||
\(382\) | − | 7.22117i | − | 0.369467i | ||||||
\(383\) | − | 32.6920i | − | 1.67049i | −0.549882 | − | 0.835243i | \(-0.685327\pi\) | ||
0.549882 | − | 0.835243i | \(-0.314673\pi\) | |||||||
\(384\) | −1.36309 | + | 1.06864i | −0.0695598 | + | 0.0545338i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 7.60250i | − | 0.386957i | ||||||
\(387\) | −1.25863 | − | 0.309339i | −0.0639798 | − | 0.0157246i | ||||
\(388\) | −14.0015 | −0.710817 | ||||||||
\(389\) | 1.33354i | 0.0676134i | 0.999428 | + | 0.0338067i | \(0.0107631\pi\) | ||||
−0.999428 | + | 0.0338067i | \(0.989237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.34624i | − | 0.371515i | ||||||
\(392\) | 6.82660 | + | 1.54839i | 0.344795 | + | 0.0782054i | ||||
\(393\) | 23.5547 | − | 18.4666i | 1.18818 | − | 0.931514i | ||||
\(394\) | 21.7384 | 1.09517 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.17193 | + | 1.02535i | 0.209647 | + | 0.0515260i | ||||
\(397\) | 23.0123 | 1.15495 | 0.577477 | − | 0.816407i | \(-0.304037\pi\) | ||||
0.577477 | + | 0.816407i | \(0.304037\pi\) | |||||||
\(398\) | 6.04124i | 0.302820i | ||||||||
\(399\) | 10.6284 | − | 6.56582i | 0.532085 | − | 0.328702i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5547i | 0.876641i | 0.898819 | + | 0.438320i | \(0.144426\pi\) | ||||
−0.898819 | + | 0.438320i | \(0.855574\pi\) | |||||||
\(402\) | −10.5011 | − | 13.3945i | −0.523748 | − | 0.668058i | ||||
\(403\) | − | 28.0103i | − | 1.39529i | ||||||
\(404\) | 10.3158 | 0.513231 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.43203 | − | 0.832284i | −0.368845 | − | 0.0413056i | ||||
\(407\) | 3.42910 | 0.169974 | ||||||||
\(408\) | 2.77736 | + | 3.54262i | 0.137500 | + | 0.175386i | ||||
\(409\) | − | 9.94521i | − | 0.491759i | −0.969300 | − | 0.245879i | \(-0.920923\pi\) | ||
0.969300 | − | 0.245879i | \(-0.0790767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.14032 | − | 3.24595i | 0.204227 | − | 0.160111i | ||||
\(412\) | −13.8743 | −0.683536 | ||||||||
\(413\) | 3.17340 | − | 28.3374i | 0.156153 | − | 1.39439i | ||||
\(414\) | −2.02389 | + | 8.23474i | −0.0994687 | + | 0.404716i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.73625 | −0.232214 | ||||||||
\(417\) | −22.1719 | − | 28.2811i | −1.08576 | − | 1.38493i | ||||
\(418\) | 3.90396 | 0.190949 | ||||||||
\(419\) | −7.71684 | −0.376992 | −0.188496 | − | 0.982074i | \(-0.560361\pi\) | ||||
−0.188496 | + | 0.982074i | \(0.560361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.2109 | 0.546384 | 0.273192 | − | 0.961960i | \(-0.411921\pi\) | ||||
0.273192 | + | 0.961960i | \(0.411921\pi\) | |||||||
\(422\) | −16.7759 | −0.816638 | ||||||||
\(423\) | −30.0530 | − | 7.38627i | −1.46123 | − | 0.359133i | ||||
\(424\) | −5.69066 | −0.276363 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.1687 | − | 18.0727i | −0.686476 | − | 0.875624i | ||||
\(427\) | −2.76230 | − | 0.309339i | −0.133677 | − | 0.0149700i | ||||
\(428\) | −15.9493 | −0.770938 | ||||||||
\(429\) | 7.24799 | + | 9.24506i | 0.349936 | + | 0.446356i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 26.2079i | − | 1.26239i | −0.775624 | − | 0.631196i | \(-0.782565\pi\) | ||
0.775624 | − | 0.631196i | \(-0.217435\pi\) | |||||||
\(432\) | −2.13728 | − | 4.73625i | −0.102830 | − | 0.227873i | ||||
\(433\) | 23.4378 | 1.12635 | 0.563175 | − | 0.826337i | \(-0.309580\pi\) | ||||
0.563175 | + | 0.826337i | \(0.309580\pi\) | |||||||
\(434\) | 15.5499 | + | 1.74137i | 0.746417 | + | 0.0835884i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.7891 | 0.516706 | ||||||||
\(437\) | 7.70581i | 0.368619i | ||||||||
\(438\) | −10.3453 | + | 8.11059i | −0.494319 | + | 0.387539i | ||||
\(439\) | 25.0334i | 1.19478i | 0.801952 | + | 0.597389i | \(0.203795\pi\) | ||||
−0.801952 | + | 0.597389i | \(0.796205\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.39887 | + | 18.7793i | −0.447565 | + | 0.894251i | ||||
\(442\) | 12.3093i | 0.585496i | ||||||||
\(443\) | −18.4666 | −0.877373 | −0.438686 | − | 0.898640i | \(-0.644556\pi\) | ||||
−0.438686 | + | 0.898640i | \(0.644556\pi\) | |||||||
\(444\) | −2.55894 | − | 3.26401i | −0.121442 | − | 0.154903i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.1120 | 0.526167 | ||||||||
\(447\) | 20.2500 | + | 25.8295i | 0.957791 | + | 1.22170i | ||||
\(448\) | 0.294447 | − | 2.62932i | 0.0139113 | − | 0.124223i | ||||
\(449\) | − | 32.3439i | − | 1.52640i | −0.646162 | − | 0.763201i | \(-0.723627\pi\) | ||
0.646162 | − | 0.763201i | \(-0.276373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.9644i | − | 0.751734i | ||||||
\(452\) | 14.3439 | 0.674679 | ||||||||
\(453\) | 7.16797 | − | 5.61959i | 0.336781 | − | 0.264031i | ||||
\(454\) | − | 7.24413i | − | 0.339984i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.91330 | − | 3.71601i | −0.136428 | − | 0.174018i | ||||
\(457\) | 10.9251i | 0.511054i | 0.966802 | + | 0.255527i | \(0.0822490\pi\) | ||||
−0.966802 | + | 0.255527i | \(0.917751\pi\) | |||||||
\(458\) | − | 27.1596i | − | 1.26909i | ||||||
\(459\) | −12.3093 | + | 5.55472i | −0.574551 | + | 0.259272i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.6729 | −1.24228 | −0.621139 | − | 0.783700i | \(-0.713330\pi\) | ||||
−0.621139 | + | 0.783700i | \(0.713330\pi\) | |||||||
\(462\) | −5.58297 | + | 3.44895i | −0.259743 | + | 0.160460i | ||||
\(463\) | 8.07491i | 0.375273i | 0.982239 | + | 0.187637i | \(0.0600827\pi\) | ||||
−0.982239 | + | 0.187637i | \(0.939917\pi\) | |||||||
\(464\) | 2.82660i | 0.131222i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.38132 | −0.249285 | ||||||||
\(467\) | − | 41.6228i | − | 1.92607i | −0.269371 | − | 0.963037i | \(-0.586816\pi\) | ||
0.269371 | − | 0.963037i | \(-0.413184\pi\) | |||||||
\(468\) | 3.39122 | − | 13.7981i | 0.156759 | − | 0.637818i | ||||
\(469\) | 25.8372 | + | 2.89341i | 1.19305 | + | 0.133605i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.58154 | − | 6.72780i | 0.395416 | − | 0.310001i | ||||
\(472\) | −10.7775 | −0.496074 | ||||||||
\(473\) | 0.618679 | 0.0284469 | ||||||||
\(474\) | 22.5145 | − | 17.6510i | 1.03412 | − | 0.810738i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.83350 | − | 0.765257i | −0.313213 | − | 0.0350755i | ||||
\(477\) | 4.07460 | − | 16.5786i | 0.186563 | − | 0.759082i | ||||
\(478\) | − | 2.51726i | − | 0.115137i | ||||||
\(479\) | 21.3728 | 0.976549 | 0.488274 | − | 0.872690i | \(-0.337627\pi\) | ||||
0.488274 | + | 0.872690i | \(0.337627\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 11.3413i | − | 0.517118i | ||||||
\(482\) | − | 16.8077i | − | 0.765570i | ||||||
\(483\) | −6.80769 | − | 11.0199i | −0.309761 | − | 0.501424i | ||||
\(484\) | 8.94929 | 0.406786 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.3284 | − | 2.83532i | 0.695312 | − | 0.128613i | ||||
\(487\) | − | 27.1094i | − | 1.22845i | −0.789133 | − | 0.614223i | \(-0.789470\pi\) | ||
0.789133 | − | 0.614223i | \(-0.210530\pi\) | |||||||
\(488\) | 1.05058i | 0.0475574i | ||||||||
\(489\) | 0.646984 | + | 0.825250i | 0.0292576 | + | 0.0373191i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0000i | 1.35388i | 0.736038 | + | 0.676941i | \(0.236695\pi\) | ||||
−0.736038 | + | 0.676941i | \(0.763305\pi\) | |||||||
\(492\) | −15.1958 | + | 11.9133i | −0.685081 | + | 0.537093i | ||||
\(493\) | 7.34624 | 0.330858 | ||||||||
\(494\) | − | 12.9118i | − | 0.580931i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.91403i | − | 0.265548i | ||||||
\(497\) | 34.8611 | + | 3.90396i | 1.56374 | + | 0.175117i | ||||
\(498\) | 13.8012 | + | 17.6040i | 0.618449 | + | 0.788852i | ||||
\(499\) | −8.50694 | −0.380823 | −0.190412 | − | 0.981704i | \(-0.560982\pi\) | ||||
−0.190412 | + | 0.981704i | \(0.560982\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.9118 | + | 16.4695i | 0.576858 | + | 0.735802i | ||||
\(502\) | −1.75565 | −0.0783586 | ||||||||
\(503\) | − | 12.1625i | − | 0.542301i | −0.962537 | − | 0.271150i | \(-0.912596\pi\) | ||
0.962537 | − | 0.271150i | \(-0.0874041\pi\) | |||||||
\(504\) | 7.44916 | + | 2.74044i | 0.331812 | + | 0.122069i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 4.04778i | − | 0.179946i | ||||||
\(507\) | 12.8567 | − | 10.0794i | 0.570985 | − | 0.447644i | ||||
\(508\) | − | 2.00000i | − | 0.0887357i | ||||||
\(509\) | 6.12130 | 0.271322 | 0.135661 | − | 0.990755i | \(-0.456684\pi\) | ||||
0.135661 | + | 0.990755i | \(0.456684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.23474 | − | 19.9555i | 0.0988592 | − | 0.882781i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 12.9118 | − | 5.82660i | 0.570071 | − | 0.257251i | ||||
\(514\) | 21.9366i | 0.967582i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.461684 | − | 0.588894i | −0.0203245 | − | 0.0259246i | ||||
\(517\) | 14.7725 | 0.649695 | ||||||||
\(518\) | 6.29609 | + | 0.705074i | 0.276634 | + | 0.0309792i | ||||
\(519\) | 16.5786 | + | 21.1466i | 0.727720 | + | 0.928232i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.7031 | −1.43275 | −0.716374 | − | 0.697717i | \(-0.754199\pi\) | ||||
−0.716374 | + | 0.697717i | \(0.754199\pi\) | |||||||
\(522\) | −8.23474 | − | 2.02389i | −0.360425 | − | 0.0885832i | ||||
\(523\) | −28.5557 | −1.24865 | −0.624327 | − | 0.781163i | \(-0.714627\pi\) | ||||
−0.624327 | + | 0.781163i | \(0.714627\pi\) | |||||||
\(524\) | 17.2804 | 0.754899 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.08523 | 0.178125 | ||||||||
\(527\) | −15.3704 | −0.669544 | ||||||||
\(528\) | 1.53032 | + | 1.95198i | 0.0665988 | + | 0.0849491i | ||||
\(529\) | −15.0103 | −0.652623 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.71684 | − | 31.3981i | 0.334882 | − | 1.36256i | ||||
\(532\) | 7.16797 | + | 0.802714i | 0.310771 | + | 0.0348020i | ||||
\(533\) | −52.8001 | −2.28703 | ||||||||
\(534\) | −5.32144 | + | 4.17193i | −0.230281 | + | 0.180537i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 9.82660i | − | 0.424445i | ||||||
\(537\) | 4.88152 | + | 6.22654i | 0.210653 | + | 0.268695i | ||||
\(538\) | 6.96461 | 0.300266 | ||||||||
\(539\) | 2.21734 | − | 9.77589i | 0.0955074 | − | 0.421078i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.2932 | −1.47438 | −0.737189 | − | 0.675687i | \(-0.763847\pi\) | ||||
−0.737189 | + | 0.675687i | \(0.763847\pi\) | |||||||
\(542\) | − | 23.4740i | − | 1.00829i | ||||||
\(543\) | 8.34386 | + | 10.6429i | 0.358070 | + | 0.456730i | ||||
\(544\) | 2.59897i | 0.111430i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.4069 | + | 18.4649i | 0.488172 | + | 0.790227i | ||||
\(547\) | − | 26.7759i | − | 1.14485i | −0.819955 | − | 0.572427i | \(-0.806002\pi\) | ||
0.819955 | − | 0.572427i | \(-0.193998\pi\) | |||||||
\(548\) | 3.03746 | 0.129754 | ||||||||
\(549\) | −3.06065 | − | 0.752229i | −0.130625 | − | 0.0321044i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.70581 | −0.328279 | ||||||||
\(552\) | −3.85291 | + | 3.02062i | −0.163991 | + | 0.128566i | ||||
\(553\) | −4.86346 | + | 43.4291i | −0.206815 | + | 1.84679i | ||||
\(554\) | − | 14.1227i | − | 0.600016i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 20.7478i | − | 0.879902i | ||||||
\(557\) | −40.4158 | −1.71247 | −0.856237 | − | 0.516583i | \(-0.827204\pi\) | ||||
−0.856237 | + | 0.516583i | \(0.827204\pi\) | |||||||
\(558\) | 17.2294 | + | 4.23453i | 0.729377 | + | 0.179262i | ||||
\(559\) | − | 2.04620i | − | 0.0865449i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.07313 | − | 3.97726i | 0.214188 | − | 0.167920i | ||||
\(562\) | − | 23.6532i | − | 0.997750i | ||||||
\(563\) | − | 8.16750i | − | 0.344219i | −0.985078 | − | 0.172109i | \(-0.944942\pi\) | ||
0.985078 | − | 0.172109i | \(-0.0550583\pi\) | |||||||
\(564\) | −11.0239 | − | 14.0613i | −0.464189 | − | 0.592089i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.807187 | −0.0339286 | ||||||||
\(567\) | −13.3174 | + | 19.7394i | −0.559280 | + | 0.828979i | ||||
\(568\) | − | 13.2586i | − | 0.556320i | ||||||
\(569\) | − | 15.0375i | − | 0.630403i | −0.949025 | − | 0.315201i | \(-0.897928\pi\) | ||
0.949025 | − | 0.315201i | \(-0.102072\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.6025 | 1.61546 | 0.807732 | − | 0.589550i | \(-0.200695\pi\) | ||||
0.807732 | + | 0.589550i | \(0.200695\pi\) | |||||||
\(572\) | 6.78244i | 0.283588i | ||||||||
\(573\) | 7.71684 | + | 9.84309i | 0.322376 | + | 0.411201i | ||||
\(574\) | 3.28252 | − | 29.3118i | 0.137010 | − | 1.22345i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.716015 | − | 2.91330i | 0.0298339 | − | 0.121388i | ||||
\(577\) | 23.9467 | 0.996913 | 0.498457 | − | 0.866915i | \(-0.333900\pi\) | ||||
0.498457 | + | 0.866915i | \(0.333900\pi\) | |||||||
\(578\) | −10.2454 | −0.426152 | ||||||||
\(579\) | 8.12434 | + | 10.3629i | 0.337636 | + | 0.430666i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.9570 | − | 3.80271i | −1.40877 | − | 0.157763i | ||||
\(582\) | 19.0852 | − | 14.9625i | 0.791108 | − | 0.620217i | ||||
\(583\) | 8.14919i | 0.337505i | ||||||||
\(584\) | −7.58963 | −0.314061 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 14.6704i | − | 0.606030i | ||||||
\(587\) | 17.9305i | 0.740072i | 0.929017 | + | 0.370036i | \(0.120655\pi\) | ||||
−0.929017 | + | 0.370036i | \(0.879345\pi\) | |||||||
\(588\) | −10.9599 | + | 5.18460i | −0.451980 | + | 0.213809i | ||||
\(589\) | 16.1227 | 0.664324 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.6314 | + | 23.2306i | −1.21887 | + | 0.955578i | ||||
\(592\) | − | 2.39457i | − | 0.0984163i | ||||||
\(593\) | 18.5744i | 0.762759i | 0.924419 | + | 0.381379i | \(0.124551\pi\) | ||||
−0.924419 | + | 0.381379i | \(0.875449\pi\) | |||||||
\(594\) | −6.78244 | + | 3.06065i | −0.278287 | + | 0.125580i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.9493i | 0.776193i | ||||||||
\(597\) | −6.45592 | − | 8.23474i | −0.264223 | − | 0.337026i | ||||
\(598\) | −13.3875 | −0.547455 | ||||||||
\(599\) | 29.3439i | 1.19896i | 0.800391 | + | 0.599479i | \(0.204625\pi\) | ||||
−0.800391 | + | 0.599479i | \(0.795375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.5145i | − | 0.918385i | −0.888337 | − | 0.459192i | \(-0.848139\pi\) | ||
0.888337 | − | 0.459192i | \(-0.151861\pi\) | |||||||
\(602\) | 1.13594 | + | 0.127210i | 0.0462975 | + | 0.00518468i | ||||
\(603\) | 28.6279 | + | 7.03599i | 1.16582 | + | 0.286528i | ||||
\(604\) | 5.25863 | 0.213971 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.0613 | + | 11.0239i | −0.571203 | + | 0.447815i | ||||
\(607\) | 17.5128 | 0.710822 | 0.355411 | − | 0.934710i | \(-0.384341\pi\) | ||||
0.355411 | + | 0.934710i | \(0.384341\pi\) | |||||||
\(608\) | − | 2.72617i | − | 0.110561i | ||||||
\(609\) | 11.0199 | − | 6.80769i | 0.446550 | − | 0.275862i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 48.8582i | − | 1.97659i | ||||||
\(612\) | −7.57157 | − | 1.86090i | −0.306062 | − | 0.0752223i | ||||
\(613\) | − | 32.7626i | − | 1.32327i | −0.749826 | − | 0.661635i | \(-0.769863\pi\) | ||
0.749826 | − | 0.661635i | \(-0.230137\pi\) | |||||||
\(614\) | 10.0975 | 0.407502 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.76526 | − | 0.421657i | −0.151707 | − | 0.0169890i | ||||
\(617\) | −0.693592 | −0.0279229 | −0.0139615 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139615 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(618\) | 18.9118 | − | 14.8266i | 0.760746 | − | 0.596413i | ||||
\(619\) | − | 18.5305i | − | 0.744802i | −0.928072 | − | 0.372401i | \(-0.878535\pi\) | ||
0.928072 | − | 0.372401i | \(-0.121465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.04124 | − | 13.3875i | −0.242427 | − | 0.537221i | ||||
\(622\) | 4.27456 | 0.171394 | ||||||||
\(623\) | 1.14951 | − | 10.2647i | 0.0460541 | − | 0.411248i | ||||
\(624\) | 6.45592 | − | 5.06134i | 0.258444 | − | 0.202616i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.923368 | −0.0369052 | ||||||||
\(627\) | −5.32144 | + | 4.17193i | −0.212518 | + | 0.166611i | ||||
\(628\) | 6.29566 | 0.251224 | ||||||||
\(629\) | −6.22341 | −0.248144 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.39457 | −0.334183 | −0.167091 | − | 0.985941i | \(-0.553437\pi\) | ||||
−0.167091 | + | 0.985941i | \(0.553437\pi\) | |||||||
\(632\) | 16.5173 | 0.657021 | ||||||||
\(633\) | 22.8670 | − | 17.9274i | 0.908882 | − | 0.712550i | ||||
\(634\) | −15.7384 | −0.625053 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.75687 | − | 6.08127i | 0.307580 | − | 0.241138i | ||||
\(637\) | −32.3325 | − | 7.33354i | −1.28106 | − | 0.290566i | ||||
\(638\) | 4.04778 | 0.160253 | ||||||||
\(639\) | 38.6264 | + | 9.49337i | 1.52804 | + | 0.375552i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.6532i | − | 0.934245i | −0.884193 | − | 0.467123i | \(-0.845291\pi\) | ||
0.884193 | − | 0.467123i | \(-0.154709\pi\) | |||||||
\(642\) | 21.7403 | − | 17.0441i | 0.858020 | − | 0.672675i | ||||
\(643\) | 2.60999 | 0.102928 | 0.0514641 | − | 0.998675i | \(-0.483611\pi\) | ||||
0.0514641 | + | 0.998675i | \(0.483611\pi\) | |||||||
\(644\) | 0.832284 | − | 7.43203i | 0.0327966 | − | 0.292863i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.08523 | −0.278765 | ||||||||
\(647\) | 4.45673i | 0.175212i | 0.996155 | + | 0.0876061i | \(0.0279217\pi\) | ||||
−0.996155 | + | 0.0876061i | \(0.972078\pi\) | |||||||
\(648\) | 7.97465 | + | 4.17193i | 0.313274 | + | 0.163889i | ||||
\(649\) | 15.4337i | 0.605825i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.0567 | + | 14.2436i | −0.903664 | + | 0.558250i | ||||
\(652\) | 0.605427i | 0.0237104i | ||||||||
\(653\) | −30.9118 | −1.20967 | −0.604837 | − | 0.796349i | \(-0.706762\pi\) | ||||
−0.604837 | + | 0.796349i | \(0.706762\pi\) | |||||||
\(654\) | −14.7065 | + | 11.5297i | −0.575072 | + | 0.450848i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.1481 | −0.435260 | ||||||||
\(657\) | 5.43429 | − | 22.1109i | 0.212012 | − | 0.862628i | ||||
\(658\) | 27.1235 | + | 3.03746i | 1.05738 | + | 0.118412i | ||||
\(659\) | 4.56797i | 0.177943i | 0.996034 | + | 0.0889714i | \(0.0283580\pi\) | ||||
−0.996034 | + | 0.0889714i | \(0.971642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.0643i | 1.48053i | 0.672315 | + | 0.740266i | \(0.265300\pi\) | ||||
−0.672315 | + | 0.740266i | \(0.734700\pi\) | |||||||
\(662\) | 12.6054 | 0.489924 | ||||||||
\(663\) | −13.1543 | − | 16.7787i | −0.510869 | − | 0.651631i | ||||
\(664\) | 12.9148i | 0.501190i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.97611 | + | 1.71455i | 0.270319 | + | 0.0664374i | ||||
\(667\) | 7.98968i | 0.309362i | ||||||||
\(668\) | 12.0825i | 0.467485i | ||||||||
\(669\) | −15.1466 | + | 11.8747i | −0.585601 | + | 0.459102i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.50446 | 0.0580790 | ||||||||
\(672\) | 2.40844 | + | 3.89865i | 0.0929075 | + | 0.150393i | ||||
\(673\) | − | 21.2212i | − | 0.818016i | −0.912531 | − | 0.409008i | \(-0.865875\pi\) | ||
0.912531 | − | 0.409008i | \(-0.134125\pi\) | |||||||
\(674\) | − | 18.8986i | − | 0.727946i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.43203 | 0.362770 | ||||||||
\(677\) | − | 3.53336i | − | 0.135798i | −0.997692 | − | 0.0678991i | \(-0.978370\pi\) | ||
0.997692 | − | 0.0678991i | \(-0.0216296\pi\) | |||||||
\(678\) | −19.5519 | + | 15.3284i | −0.750888 | + | 0.588685i | ||||
\(679\) | −4.12269 | + | 36.8143i | −0.158214 | + | 1.41280i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.74137 | + | 9.87438i | 0.296650 | + | 0.378387i | ||||
\(682\) | −8.46907 | −0.324297 | ||||||||
\(683\) | 1.70391 | 0.0651984 | 0.0325992 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325992 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(684\) | 7.94217 | + | 1.95198i | 0.303676 | + | 0.0746359i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.08127 | − | 17.4934i | 0.232184 | − | 0.667900i | ||||
\(687\) | 29.0239 | + | 37.0210i | 1.10733 | + | 1.41244i | ||||
\(688\) | − | 0.432029i | − | 0.0164710i | ||||||
\(689\) | 26.9524 | 1.02680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.21734i | − | 0.0843514i | −0.999110 | − | 0.0421757i | \(-0.986571\pi\) | ||
0.999110 | − | 0.0421757i | \(-0.0134289\pi\) | |||||||
\(692\) | 15.5137i | 0.589744i | ||||||||
\(693\) | 3.92439 | − | 10.6674i | 0.149075 | − | 0.405222i | ||||
\(694\) | −30.7384 | −1.16682 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.02062 | − | 3.85291i | −0.114496 | − | 0.146044i | ||||
\(697\) | 28.9735i | 1.09745i | ||||||||
\(698\) | 0.970523i | 0.0367348i | ||||||||
\(699\) | 7.33521 | − | 5.75070i | 0.277443 | − | 0.217511i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.11976i | − | 0.117832i | −0.998263 | − | 0.0589158i | \(-0.981236\pi\) | ||
0.998263 | − | 0.0589158i | \(-0.0187644\pi\) | |||||||
\(702\) | 10.1227 | + | 22.4320i | 0.382056 | + | 0.846642i | ||||
\(703\) | 6.52802 | 0.246209 | ||||||||
\(704\) | 1.43203i | 0.0539716i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 16.3570i | − | 0.615606i | ||||||
\(707\) | 3.03746 | − | 27.1235i | 0.114235 | − | 1.02008i | ||||
\(708\) | 14.6907 | − | 11.5173i | 0.552109 | − | 0.432845i | ||||
\(709\) | −12.8641 | −0.483120 | −0.241560 | − | 0.970386i | \(-0.577659\pi\) | ||||
−0.241560 | + | 0.970386i | \(0.577659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.8266 | + | 48.1198i | −0.443532 | + | 1.80463i | ||||
\(712\) | −3.90396 | −0.146307 | ||||||||
\(713\) | − | 16.7166i | − | 0.626042i | ||||||
\(714\) | 10.1324 | − | 6.25944i | 0.379197 | − | 0.234254i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.56797i | 0.170713i | ||||||||
\(717\) | 2.69005 | + | 3.43125i | 0.100462 | + | 0.128142i | ||||
\(718\) | 9.81335i | 0.366231i | ||||||||
\(719\) | −28.5196 | −1.06360 | −0.531801 | − | 0.846870i | \(-0.678484\pi\) | ||||
−0.531801 | + | 0.846870i | \(0.678484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.08523 | + | 36.4798i | −0.152142 | + | 1.35858i | ||||
\(722\) | −11.5680 | −0.430515 | ||||||||
\(723\) | 17.9614 | + | 22.9104i | 0.667991 | + | 0.852046i | ||||
\(724\) | 7.80792i | 0.290179i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.1987 | + | 9.56358i | −0.452735 | + | 0.354938i | ||||
\(727\) | 18.9921 | 0.704379 | 0.352190 | − | 0.935929i | \(-0.385437\pi\) | ||||
0.352190 | + | 0.935929i | \(0.385437\pi\) | |||||||
\(728\) | −1.39457 | + | 12.4531i | −0.0516863 | + | 0.461542i | ||||
\(729\) | −17.8641 | + | 20.2454i | −0.661632 | + | 0.749829i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.12283 | −0.0415293 | ||||||||
\(732\) | −1.12269 | − | 1.43203i | −0.0414958 | − | 0.0529293i | ||||
\(733\) | 27.1345 | 1.00224 | 0.501119 | − | 0.865379i | \(-0.332922\pi\) | ||||
0.501119 | + | 0.865379i | \(0.332922\pi\) | |||||||
\(734\) | −33.9970 | −1.25485 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.82660 | −0.104190 | ||||||||
\(737\) | −14.0720 | −0.518348 | ||||||||
\(738\) | 7.98220 | − | 32.4777i | 0.293829 | − | 1.19552i | ||||
\(739\) | −8.67741 | −0.319204 | −0.159602 | − | 0.987181i | \(-0.551021\pi\) | ||||
−0.159602 | + | 0.987181i | \(0.551021\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.7981 | + | 17.6000i | 0.506886 | + | 0.646551i | ||||
\(742\) | −1.67560 | + | 14.9625i | −0.0615131 | + | 0.549292i | ||||
\(743\) | −52.5754 | −1.92880 | −0.964401 | − | 0.264443i | \(-0.914812\pi\) | ||||
−0.964401 | + | 0.264443i | \(0.914812\pi\) | |||||||
\(744\) | 6.31998 | + | 8.06134i | 0.231702 | + | 0.295543i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 26.5650i | − | 0.972615i | ||||||
\(747\) | −37.6246 | − | 9.24717i | −1.37661 | − | 0.338336i | ||||
\(748\) | 3.72179 | 0.136082 | ||||||||
\(749\) | −4.69622 | + | 41.9357i | −0.171596 | + | 1.53230i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.77589 | 0.0648033 | 0.0324016 | − | 0.999475i | \(-0.489684\pi\) | ||||
0.0324016 | + | 0.999475i | \(0.489684\pi\) | |||||||
\(752\) | − | 10.3158i | − | 0.376179i | ||||||
\(753\) | 2.39311 | − | 1.87616i | 0.0872097 | − | 0.0683711i | ||||
\(754\) | − | 13.3875i | − | 0.487543i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.0824 | + | 4.22501i | −0.475802 | + | 0.153662i | ||||
\(757\) | − | 4.63995i | − | 0.168642i | −0.996439 | − | 0.0843210i | \(-0.973128\pi\) | ||
0.996439 | − | 0.0843210i | \(-0.0268721\pi\) | |||||||
\(758\) | 8.25863 | 0.299967 | ||||||||
\(759\) | 4.32562 | + | 5.51747i | 0.157010 | + | 0.200272i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.6884 | 1.47495 | 0.737477 | − | 0.675373i | \(-0.236017\pi\) | ||||
0.737477 | + | 0.675373i | \(0.236017\pi\) | |||||||
\(762\) | 2.13728 | + | 2.72617i | 0.0774255 | + | 0.0987589i | ||||
\(763\) | 3.17683 | − | 28.3681i | 0.115009 | − | 1.02699i | ||||
\(764\) | 7.22117i | 0.261253i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.6920i | 1.18121i | ||||||||
\(767\) | 51.0448 | 1.84312 | ||||||||
\(768\) | 1.36309 | − | 1.06864i | 0.0491862 | − | 0.0385612i | ||||
\(769\) | 19.2355i | 0.693651i | 0.937930 | + | 0.346825i | \(0.112740\pi\) | ||||
−0.937930 | + | 0.346825i | \(0.887260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.4423 | − | 29.9015i | −0.844256 | − | 1.07688i | ||||
\(772\) | 7.60250i | 0.273620i | ||||||||
\(773\) | 28.4175i | 1.02211i | 0.859549 | + | 0.511053i | \(0.170744\pi\) | ||||
−0.859549 | + | 0.511053i | \(0.829256\pi\) | |||||||
\(774\) | 1.25863 | + | 0.309339i | 0.0452406 | + | 0.0111190i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.0015 | 0.502624 | ||||||||
\(777\) | −9.33559 | + | 5.76718i | −0.334912 | + | 0.206896i | ||||
\(778\) | − | 1.33354i | − | 0.0478099i | ||||||
\(779\) | − | 30.3916i | − | 1.08889i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.9867 | −0.679399 | ||||||||
\(782\) | 7.34624i | 0.262701i | ||||||||
\(783\) | 13.3875 | − | 6.04124i | 0.478430 | − | 0.215896i | ||||
\(784\) | −6.82660 | − | 1.54839i | −0.243807 | − | 0.0552996i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.5547 | + | 18.4666i | −0.840169 | + | 0.658680i | ||||
\(787\) | −41.6778 | −1.48565 | −0.742826 | − | 0.669485i | \(-0.766515\pi\) | ||||
−0.742826 | + | 0.669485i | \(0.766515\pi\) | |||||||
\(788\) | −21.7384 | −0.774400 | ||||||||
\(789\) | −5.56853 | + | 4.36565i | −0.198245 | + | 0.155421i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.22351 | − | 37.7145i | 0.150171 | − | 1.34097i | ||||
\(792\) | −4.17193 | − | 1.02535i | −0.148243 | − | 0.0364344i | ||||
\(793\) | − | 4.97579i | − | 0.176696i | ||||||
\(794\) | −23.0123 | −0.816675 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 6.04124i | − | 0.214126i | ||||||
\(797\) | 10.2137i | 0.361788i | 0.983503 | + | 0.180894i | \(0.0578990\pi\) | ||||
−0.983503 | + | 0.180894i | \(0.942101\pi\) | |||||||
\(798\) | −10.6284 | + | 6.56582i | −0.376241 | + | 0.232427i | ||||
\(799\) | −26.8104 | −0.948484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.79529 | − | 11.3734i | 0.0987669 | − | 0.401860i | ||||
\(802\) | − | 17.5547i | − | 0.619879i | ||||||
\(803\) | 10.8686i | 0.383544i | ||||||||
\(804\) | 10.5011 | + | 13.3945i | 0.370345 | + | 0.472388i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28.0103i | 0.986621i | ||||||||
\(807\) | −9.49337 | + | 7.44267i | −0.334183 | + | 0.261994i | ||||
\(808\) | −10.3158 | −0.362909 | ||||||||
\(809\) | − | 40.0691i | − | 1.40875i | −0.709827 | − | 0.704376i | \(-0.751227\pi\) | ||
0.709827 | − | 0.704376i | \(-0.248773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 34.8875i | − | 1.22507i | −0.790445 | − | 0.612533i | \(-0.790151\pi\) | ||
0.790445 | − | 0.612533i | \(-0.209849\pi\) | |||||||
\(812\) | 7.43203 | + | 0.832284i | 0.260813 | + | 0.0292074i | ||||
\(813\) | 25.0852 | + | 31.9971i | 0.879778 | + | 1.12219i | ||||
\(814\) | −3.42910 | −0.120190 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.77736 | − | 3.54262i | −0.0972270 | − | 0.124016i | ||||
\(817\) | 1.17779 | 0.0412056 | ||||||||
\(818\) | 9.94521i | 0.347726i | ||||||||
\(819\) | −35.2811 | − | 12.9794i | −1.23282 | − | 0.453537i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.4291i | 1.16668i | 0.812227 | + | 0.583342i | \(0.198255\pi\) | ||||
−0.812227 | + | 0.583342i | \(0.801745\pi\) | |||||||
\(822\) | −4.14032 | + | 3.24595i | −0.144410 | + | 0.113215i | ||||
\(823\) | − | 20.7414i | − | 0.722999i | −0.932372 | − | 0.361499i | \(-0.882265\pi\) | ||
0.932372 | − | 0.361499i | \(-0.117735\pi\) | |||||||
\(824\) | 13.8743 | 0.483333 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.17340 | + | 28.3374i | −0.110417 | + | 0.985985i | ||||
\(827\) | −41.8479 | −1.45519 | −0.727597 | − | 0.686005i | \(-0.759363\pi\) | ||||
−0.727597 | + | 0.686005i | \(0.759363\pi\) | |||||||
\(828\) | 2.02389 | − | 8.23474i | 0.0703350 | − | 0.286177i | ||||
\(829\) | − | 19.7632i | − | 0.686404i | −0.939262 | − | 0.343202i | \(-0.888488\pi\) | ||
0.939262 | − | 0.343202i | \(-0.111512\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.0921 | + | 19.2505i | 0.523538 | + | 0.667791i | ||||
\(832\) | 4.73625 | 0.164200 | ||||||||
\(833\) | −4.02421 | + | 17.7421i | −0.139430 | + | 0.614727i | ||||
\(834\) | 22.1719 | + | 28.2811i | 0.767751 | + | 0.979293i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.90396 | −0.135021 | ||||||||
\(837\) | −28.0103 | + | 12.6400i | −0.968178 | + | 0.436901i | ||||
\(838\) | 7.71684 | 0.266574 | ||||||||
\(839\) | −6.78244 | −0.234156 | −0.117078 | − | 0.993123i | \(-0.537353\pi\) | ||||
−0.117078 | + | 0.993123i | \(0.537353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0103 | 0.724494 | ||||||||
\(842\) | −11.2109 | −0.386352 | ||||||||
\(843\) | 25.2768 | + | 32.2414i | 0.870578 | + | 1.11045i | ||||
\(844\) | 16.7759 | 0.577450 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 30.0530 | + | 7.38627i | 1.03325 | + | 0.253945i | ||||
\(847\) | 2.63509 | − | 23.5305i | 0.0905428 | − | 0.808518i | ||||
\(848\) | 5.69066 | 0.195418 | ||||||||
\(849\) | 1.10027 | − | 0.862593i | 0.0377611 | − | 0.0296041i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.76850i | − | 0.232021i | ||||||
\(852\) | 14.1687 | + | 18.0727i | 0.485412 | + | 0.619160i | ||||
\(853\) | −2.22837 | −0.0762978 | −0.0381489 | − | 0.999272i | \(-0.512146\pi\) | ||||
−0.0381489 | + | 0.999272i | \(0.512146\pi\) | |||||||
\(854\) | 2.76230 | + | 0.309339i | 0.0945240 | + | 0.0105854i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.9493 | 0.545136 | ||||||||
\(857\) | − | 5.75070i | − | 0.196440i | −0.995165 | − | 0.0982201i | \(-0.968685\pi\) | ||
0.995165 | − | 0.0982201i | \(-0.0313149\pi\) | |||||||
\(858\) | −7.24799 | − | 9.24506i | −0.247442 | − | 0.315621i | ||||
\(859\) | − | 46.1407i | − | 1.57430i | −0.616760 | − | 0.787151i | \(-0.711555\pi\) | ||
0.616760 | − | 0.787151i | \(-0.288445\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.8495 | + | 43.4624i | 0.915027 | + | 1.48120i | ||||
\(862\) | 26.2079i | 0.892645i | ||||||||
\(863\) | 17.5783 | 0.598372 | 0.299186 | − | 0.954195i | \(-0.403285\pi\) | ||||
0.299186 | + | 0.954195i | \(0.403285\pi\) | |||||||
\(864\) | 2.13728 | + | 4.73625i | 0.0727118 | + | 0.161130i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.4378 | −0.796450 | ||||||||
\(867\) | 13.9653 | − | 10.9486i | 0.474288 | − | 0.371835i | ||||
\(868\) | −15.5499 | − | 1.74137i | −0.527797 | − | 0.0591059i | ||||
\(869\) | − | 23.6532i | − | 0.802380i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.5412i | 1.57699i | ||||||||
\(872\) | −10.7891 | −0.365367 | ||||||||
\(873\) | −10.0253 | + | 40.7905i | −0.339304 | + | 1.38055i | ||||
\(874\) | − | 7.70581i | − | 0.260653i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.3453 | − | 8.11059i | 0.349536 | − | 0.274031i | ||||
\(877\) | 41.8237i | 1.41229i | 0.708070 | + | 0.706143i | \(0.249566\pi\) | ||||
−0.708070 | + | 0.706143i | \(0.750434\pi\) | |||||||
\(878\) | − | 25.0334i | − | 0.844836i | ||||||
\(879\) | 15.6774 | + | 19.9971i | 0.528786 | + | 0.674484i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.8757 | 0.939158 | 0.469579 | − | 0.882891i | \(-0.344406\pi\) | ||||
0.469579 | + | 0.882891i | \(0.344406\pi\) | |||||||
\(882\) | 9.39887 | − | 18.7793i | 0.316476 | − | 0.632331i | ||||
\(883\) | − | 11.6400i | − | 0.391716i | −0.980632 | − | 0.195858i | \(-0.937251\pi\) | ||
0.980632 | − | 0.195858i | \(-0.0627491\pi\) | |||||||
\(884\) | − | 12.3093i | − | 0.414008i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.4666 | 0.620396 | ||||||||
\(887\) | 38.7333i | 1.30054i | 0.759705 | + | 0.650268i | \(0.225343\pi\) | ||||
−0.759705 | + | 0.650268i | \(0.774657\pi\) | |||||||
\(888\) | 2.55894 | + | 3.26401i | 0.0858723 | + | 0.109533i | ||||
\(889\) | −5.25863 | − | 0.588894i | −0.176369 | − | 0.0197509i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.97433 | − | 11.4199i | 0.200148 | − | 0.382582i | ||||
\(892\) | −11.1120 | −0.372056 | ||||||||
\(893\) | 28.1227 | 0.941090 | ||||||||
\(894\) | −20.2500 | − | 25.8295i | −0.677261 | − | 0.863869i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.294447 | + | 2.62932i | −0.00983678 | + | 0.0878393i | ||||
\(897\) | 18.2483 | − | 14.3064i | 0.609293 | − | 0.477677i | ||||
\(898\) | 32.3439i | 1.07933i | ||||||||
\(899\) | 16.7166 | 0.557530 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.7898i | − | 0.492721i | ||||||
\(902\) | 15.9644i | 0.531556i | ||||||||
\(903\) | −1.68433 | + | 1.04052i | −0.0560510 | + | 0.0346262i | ||||
\(904\) | −14.3439 | −0.477070 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.16797 | + | 5.61959i | −0.238140 | + | 0.186698i | ||||
\(907\) | − | 18.7730i | − | 0.623346i | −0.950189 | − | 0.311673i | \(-0.899111\pi\) | ||
0.950189 | − | 0.311673i | \(-0.100889\pi\) | |||||||
\(908\) | 7.24413i | 0.240405i | ||||||||
\(909\) | 7.38627 | − | 30.0530i | 0.244987 | − | 0.996797i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.73844i | − | 0.123860i | −0.998080 | − | 0.0619300i | \(-0.980274\pi\) | ||
0.998080 | − | 0.0619300i | \(-0.0197255\pi\) | |||||||
\(912\) | 2.91330 | + | 3.71601i | 0.0964690 | + | 0.123050i | ||||
\(913\) | 18.4943 | 0.612073 | ||||||||
\(914\) | − | 10.9251i | − | 0.361370i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.1596i | 0.897380i | ||||||||
\(917\) | 5.08816 | − | 45.4357i | 0.168026 | − | 1.50042i | ||||
\(918\) | 12.3093 | − | 5.55472i | 0.406269 | − | 0.183333i | ||||
\(919\) | −24.4423 | −0.806279 | −0.403139 | − | 0.915139i | \(-0.632081\pi\) | ||||
−0.403139 | + | 0.915139i | \(0.632081\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.7638 | + | 10.7906i | −0.453532 | + | 0.355563i | ||||
\(922\) | 26.6729 | 0.878424 | ||||||||
\(923\) | 62.7961i | 2.06696i | ||||||||
\(924\) | 5.58297 | − | 3.44895i | 0.183666 | − | 0.113462i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 8.07491i | − | 0.265358i | ||||||
\(927\) | −9.93418 | + | 40.4199i | −0.326281 | + | 1.32756i | ||||
\(928\) | − | 2.82660i | − | 0.0927878i | ||||||
\(929\) | −45.8974 | −1.50584 | −0.752922 | − | 0.658110i | \(-0.771356\pi\) | ||||
−0.752922 | + | 0.658110i | \(0.771356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.22117 | − | 18.6105i | 0.138343 | − | 0.609935i | ||||
\(932\) | 5.38132 | 0.176271 | ||||||||
\(933\) | −5.82660 | + | 4.56797i | −0.190754 | + | 0.149549i | ||||
\(934\) | 41.6228i | 1.36194i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.39122 | + | 13.7981i | −0.110846 | + | 0.451005i | ||||
\(937\) | −13.2241 | −0.432014 | −0.216007 | − | 0.976392i | \(-0.569303\pi\) | ||||
−0.216007 | + | 0.976392i | \(0.569303\pi\) | |||||||
\(938\) | −25.8372 | − | 2.89341i | −0.843616 | − | 0.0944733i | ||||
\(939\) | 1.25863 | − | 0.986749i | 0.0410739 | − | 0.0322013i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.3408 | 0.956484 | 0.478242 | − | 0.878228i | \(-0.341274\pi\) | ||||
0.478242 | + | 0.878228i | \(0.341274\pi\) | |||||||
\(942\) | −8.58154 | + | 6.72780i | −0.279602 | + | 0.219204i | ||||
\(943\) | −31.5112 | −1.02615 | ||||||||
\(944\) | 10.7775 | 0.350777 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.618679 | −0.0201150 | ||||||||
\(947\) | 47.1094 | 1.53085 | 0.765426 | − | 0.643524i | \(-0.222529\pi\) | ||||
0.765426 | + | 0.643524i | \(0.222529\pi\) | |||||||
\(948\) | −22.5145 | + | 17.6510i | −0.731236 | + | 0.573278i | ||||
\(949\) | 35.9464 | 1.16687 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.4529 | − | 16.8187i | 0.695657 | − | 0.545385i | ||||
\(952\) | 6.83350 | + | 0.765257i | 0.221475 | + | 0.0248021i | ||||
\(953\) | −20.8876 | −0.676617 | −0.338308 | − | 0.941035i | \(-0.609855\pi\) | ||||
−0.338308 | + | 0.941035i | \(0.609855\pi\) | |||||||
\(954\) | −4.07460 | + | 16.5786i | −0.131920 | + | 0.536752i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.51726i | 0.0814141i | ||||||||
\(957\) | −5.51747 | + | 4.32562i | −0.178355 | + | 0.139827i | ||||
\(958\) | −21.3728 | −0.690524 | ||||||||
\(959\) | 0.894369 | − | 7.98643i | 0.0288807 | − | 0.257895i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.97579 | −0.128251 | ||||||||
\(962\) | 11.3413i | 0.365658i | ||||||||
\(963\) | −11.4199 | + | 46.4651i | −0.368002 | + | 1.49732i | ||||
\(964\) | 16.8077i | 0.541340i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.80769 | + | 11.0199i | 0.219034 | + | 0.354560i | ||||
\(967\) | − | 27.3335i | − | 0.878988i | −0.898246 | − | 0.439494i | \(-0.855158\pi\) | ||
0.898246 | − | 0.439494i | \(-0.144842\pi\) | |||||||
\(968\) | −8.94929 | −0.287641 | ||||||||
\(969\) | 9.65779 | − | 7.57157i | 0.310253 | − | 0.243234i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4555 | −0.784815 | −0.392407 | − | 0.919791i | \(-0.628358\pi\) | ||||
−0.392407 | + | 0.919791i | \(0.628358\pi\) | |||||||
\(972\) | −15.3284 | + | 2.83532i | −0.491660 | + | 0.0909430i | ||||
\(973\) | −54.5525 | − | 6.10912i | −1.74887 | − | 0.195849i | ||||
\(974\) | 27.1094i | 0.868642i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 1.05058i | − | 0.0336282i | ||||||
\(977\) | 15.1124 | 0.483488 | 0.241744 | − | 0.970340i | \(-0.422281\pi\) | ||||
0.241744 | + | 0.970340i | \(0.422281\pi\) | |||||||
\(978\) | −0.646984 | − | 0.825250i | −0.0206883 | − | 0.0263886i | ||||
\(979\) | 5.59059i | 0.178676i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.72519 | − | 31.4320i | 0.246646 | − | 1.00355i | ||||
\(982\) | − | 30.0000i | − | 0.957338i | ||||||
\(983\) | − | 13.6670i | − | 0.435910i | −0.975959 | − | 0.217955i | \(-0.930061\pi\) | ||
0.975959 | − | 0.217955i | \(-0.0699385\pi\) | |||||||
\(984\) | 15.1958 | − | 11.9133i | 0.484425 | − | 0.379782i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.34624 | −0.233952 | ||||||||
\(987\) | −40.2177 | + | 24.8450i | −1.28014 | + | 0.790824i | ||||
\(988\) | 12.9118i | 0.410780i | ||||||||
\(989\) | − | 1.22117i | − | 0.0388311i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.45560 | −0.109771 | −0.0548854 | − | 0.998493i | \(-0.517479\pi\) | ||||
−0.0548854 | + | 0.998493i | \(0.517479\pi\) | |||||||
\(992\) | 5.91403i | 0.187771i | ||||||||
\(993\) | −17.1823 | + | 13.4707i | −0.545264 | + | 0.427479i | ||||
\(994\) | −34.8611 | − | 3.90396i | −1.10573 | − | 0.123826i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.8012 | − | 17.6040i | −0.437309 | − | 0.557803i | ||||
\(997\) | −40.4199 | −1.28011 | −0.640056 | − | 0.768329i | \(-0.721089\pi\) | ||||
−0.640056 | + | 0.768329i | \(0.721089\pi\) | |||||||
\(998\) | 8.50694 | 0.269283 | ||||||||
\(999\) | −11.3413 | + | 5.11788i | −0.358822 | + | 0.161922i |
(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 | 1050.2.d.g.1049.9 | 12 | ||
3.2 | odd | 2 | 1050.2.d.h.1049.10 | 12 | |||
5.2 | odd | 4 | 1050.2.b.d.251.2 | ✓ | 12 | ||
5.3 | odd | 4 | 1050.2.b.e.251.11 | yes | 12 | ||
5.4 | even | 2 | 1050.2.d.h.1049.4 | 12 | |||
7.6 | odd | 2 | inner | 1050.2.d.g.1049.4 | 12 | ||
15.2 | even | 4 | 1050.2.b.d.251.11 | yes | 12 | ||
15.8 | even | 4 | 1050.2.b.e.251.2 | yes | 12 | ||
15.14 | odd | 2 | inner | 1050.2.d.g.1049.3 | 12 | ||
21.20 | even | 2 | 1050.2.d.h.1049.3 | 12 | |||
35.13 | even | 4 | 1050.2.b.e.251.8 | yes | 12 | ||
35.27 | even | 4 | 1050.2.b.d.251.5 | yes | 12 | ||
35.34 | odd | 2 | 1050.2.d.h.1049.9 | 12 | |||
105.62 | odd | 4 | 1050.2.b.d.251.8 | yes | 12 | ||
105.83 | odd | 4 | 1050.2.b.e.251.5 | yes | 12 | ||
105.104 | even | 2 | inner | 1050.2.d.g.1049.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.b.d.251.2 | ✓ | 12 | 5.2 | odd | 4 | ||
1050.2.b.d.251.5 | yes | 12 | 35.27 | even | 4 | ||
1050.2.b.d.251.8 | yes | 12 | 105.62 | odd | 4 | ||
1050.2.b.d.251.11 | yes | 12 | 15.2 | even | 4 | ||
1050.2.b.e.251.2 | yes | 12 | 15.8 | even | 4 | ||
1050.2.b.e.251.5 | yes | 12 | 105.83 | odd | 4 | ||
1050.2.b.e.251.8 | yes | 12 | 35.13 | even | 4 | ||
1050.2.b.e.251.11 | yes | 12 | 5.3 | odd | 4 | ||
1050.2.d.g.1049.3 | 12 | 15.14 | odd | 2 | inner | ||
1050.2.d.g.1049.4 | 12 | 7.6 | odd | 2 | inner | ||
1050.2.d.g.1049.9 | 12 | 1.1 | even | 1 | trivial | ||
1050.2.d.g.1049.10 | 12 | 105.104 | even | 2 | inner | ||
1050.2.d.h.1049.3 | 12 | 21.20 | even | 2 | |||
1050.2.d.h.1049.4 | 12 | 5.4 | even | 2 | |||
1050.2.d.h.1049.9 | 12 | 35.34 | odd | 2 | |||
1050.2.d.h.1049.10 | 12 | 3.2 | odd | 2 |