Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(251,1050)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.251");
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.b (of order \(2\), degree \(1\), 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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.11 | ||
Root | \(1.06864 + 1.36309i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.251 |
Dual form | 1050.2.b.d.251.5 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.06864 | − | 1.36309i | 0.616980 | − | 0.786979i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.36309 | + | 1.06864i | 0.556478 | + | 0.436271i | ||||
\(7\) | 2.62932 | + | 0.294447i | 0.993788 | + | 0.111290i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.716015 | − | 2.91330i | −0.238672 | − | 0.971100i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.43203i | − | 0.431773i | −0.976418 | − | 0.215887i | \(-0.930736\pi\) | ||
0.976418 | − | 0.215887i | \(-0.0692641\pi\) | |||||||
\(12\) | −1.06864 | + | 1.36309i | −0.308490 | + | 0.393489i | ||||
\(13\) | − | 4.73625i | − | 1.31360i | −0.754066 | − | 0.656799i | \(-0.771910\pi\) | ||
0.754066 | − | 0.656799i | \(-0.228090\pi\) | |||||||
\(14\) | −0.294447 | + | 2.62932i | −0.0786942 | + | 0.702714i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.59897 | −0.630342 | −0.315171 | − | 0.949035i | \(-0.602062\pi\) | ||||
−0.315171 | + | 0.949035i | \(0.602062\pi\) | |||||||
\(18\) | 2.91330 | − | 0.716015i | 0.686672 | − | 0.168766i | ||||
\(19\) | − | 2.72617i | − | 0.625427i | −0.949847 | − | 0.312714i | \(-0.898762\pi\) | ||
0.949847 | − | 0.312714i | \(-0.101238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.21115 | − | 3.26933i | 0.700730 | − | 0.713426i | ||||
\(22\) | 1.43203 | 0.305310 | ||||||||
\(23\) | 2.82660i | 0.589387i | 0.955592 | + | 0.294694i | \(0.0952176\pi\) | ||||
−0.955592 | + | 0.294694i | \(0.904782\pi\) | |||||||
\(24\) | −1.36309 | − | 1.06864i | −0.278239 | − | 0.218135i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.73625 | 0.928854 | ||||||||
\(27\) | −4.73625 | − | 2.13728i | −0.911491 | − | 0.411320i | ||||
\(28\) | −2.62932 | − | 0.294447i | −0.496894 | − | 0.0556452i | ||||
\(29\) | 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 | \(-0.178220\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −1.95198 | − | 1.53032i | −0.339796 | − | 0.266395i | ||||
\(34\) | − | 2.59897i | − | 0.445719i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.716015 | + | 2.91330i | 0.119336 | + | 0.485550i | ||||
\(37\) | 2.39457 | 0.393665 | 0.196833 | − | 0.980437i | \(-0.436934\pi\) | ||||
0.196833 | + | 0.980437i | \(0.436934\pi\) | |||||||
\(38\) | 2.72617 | 0.442244 | ||||||||
\(39\) | −6.45592 | − | 5.06134i | −1.03377 | − | 0.810464i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.1481 | 1.74104 | 0.870520 | − | 0.492134i | \(-0.163783\pi\) | ||||
0.870520 | + | 0.492134i | \(0.163783\pi\) | |||||||
\(42\) | 3.26933 | + | 3.21115i | 0.504468 | + | 0.495491i | ||||
\(43\) | −0.432029 | −0.0658838 | −0.0329419 | − | 0.999457i | \(-0.510488\pi\) | ||||
−0.0329419 | + | 0.999457i | \(0.510488\pi\) | |||||||
\(44\) | 1.43203i | 0.215887i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.82660 | −0.416760 | ||||||||
\(47\) | −10.3158 | −1.50471 | −0.752357 | − | 0.658755i | \(-0.771083\pi\) | ||||
−0.752357 | + | 0.658755i | \(0.771083\pi\) | |||||||
\(48\) | 1.06864 | − | 1.36309i | 0.154245 | − | 0.196745i | ||||
\(49\) | 6.82660 | + | 1.54839i | 0.975229 | + | 0.221198i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.77736 | + | 3.54262i | −0.388908 | + | 0.496066i | ||||
\(52\) | 4.73625i | 0.656799i | ||||||||
\(53\) | 5.69066i | 0.781672i | 0.920460 | + | 0.390836i | \(0.127814\pi\) | ||||
−0.920460 | + | 0.390836i | \(0.872186\pi\) | |||||||
\(54\) | 2.13728 | − | 4.73625i | 0.290847 | − | 0.644521i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.294447 | − | 2.62932i | 0.0393471 | − | 0.351357i | ||||
\(57\) | −3.71601 | − | 2.91330i | −0.492198 | − | 0.385876i | ||||
\(58\) | −2.82660 | −0.371151 | ||||||||
\(59\) | 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 | \(-0.0214245\pi\) | |||||||
\(62\) | 5.91403 | 0.751083 | ||||||||
\(63\) | −1.02482 | − | 7.87082i | −0.129115 | − | 0.991630i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.53032 | − | 1.95198i | 0.188370 | − | 0.240272i | ||||
\(67\) | −9.82660 | −1.20051 | −0.600255 | − | 0.799808i | \(-0.704934\pi\) | ||||
−0.600255 | + | 0.799808i | \(0.704934\pi\) | |||||||
\(68\) | 2.59897 | 0.315171 | ||||||||
\(69\) | 3.85291 | + | 3.02062i | 0.463835 | + | 0.363640i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.2586i | − | 1.57351i | −0.617265 | − | 0.786755i | \(-0.711760\pi\) | ||
0.617265 | − | 0.786755i | \(-0.288240\pi\) | |||||||
\(72\) | −2.91330 | + | 0.716015i | −0.343336 | + | 0.0843831i | ||||
\(73\) | − | 7.58963i | − | 0.888299i | −0.895953 | − | 0.444150i | \(-0.853506\pi\) | ||
0.895953 | − | 0.444150i | \(-0.146494\pi\) | |||||||
\(74\) | 2.39457i | 0.278363i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.72617i | 0.312714i | ||||||||
\(77\) | 0.421657 | − | 3.76526i | 0.0480522 | − | 0.429091i | ||||
\(78\) | 5.06134 | − | 6.45592i | 0.573084 | − | 0.730989i | ||||
\(79\) | 16.5173 | 1.85834 | 0.929169 | − | 0.369656i | \(-0.120525\pi\) | ||||
0.929169 | + | 0.369656i | \(0.120525\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.97465 | + | 4.17193i | −0.886072 | + | 0.463548i | ||||
\(82\) | 11.1481i | 1.23110i | ||||||||
\(83\) | 12.9148 | 1.41758 | 0.708790 | − | 0.705419i | \(-0.249241\pi\) | ||||
0.708790 | + | 0.705419i | \(0.249241\pi\) | |||||||
\(84\) | −3.21115 | + | 3.26933i | −0.350365 | + | 0.356713i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 0.432029i | − | 0.0465869i | ||||||
\(87\) | 3.85291 | + | 3.02062i | 0.413075 | + | 0.323845i | ||||
\(88\) | −1.43203 | −0.152655 | ||||||||
\(89\) | 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 | ||||
\(92\) | − | 2.82660i | − | 0.294694i | ||||||
\(93\) | −8.06134 | − | 6.31998i | −0.835923 | − | 0.655351i | ||||
\(94\) | − | 10.3158i | − | 1.06399i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.36309 | + | 1.06864i | 0.139120 | + | 0.109068i | ||||
\(97\) | − | 14.0015i | − | 1.42163i | −0.703377 | − | 0.710817i | \(-0.748325\pi\) | ||
0.703377 | − | 0.710817i | \(-0.251675\pi\) | |||||||
\(98\) | −1.54839 | + | 6.82660i | −0.156411 | + | 0.689591i | ||||
\(99\) | −4.17193 | + | 1.02535i | −0.419295 | + | 0.103052i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3158 | −1.02646 | −0.513231 | − | 0.858251i | \(-0.671551\pi\) | ||||
−0.513231 | + | 0.858251i | \(0.671551\pi\) | |||||||
\(102\) | −3.54262 | − | 2.77736i | −0.350771 | − | 0.275000i | ||||
\(103\) | 13.8743i | 1.36707i | 0.729917 | + | 0.683536i | \(0.239559\pi\) | ||||
−0.729917 | + | 0.683536i | \(0.760441\pi\) | |||||||
\(104\) | −4.73625 | −0.464427 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.69066 | −0.552726 | ||||||||
\(107\) | 15.9493i | 1.54188i | 0.636910 | + | 0.770938i | \(0.280212\pi\) | ||||
−0.636910 | + | 0.770938i | \(0.719788\pi\) | |||||||
\(108\) | 4.73625 | + | 2.13728i | 0.455746 | + | 0.205660i | ||||
\(109\) | −10.7891 | −1.03341 | −0.516706 | − | 0.856163i | \(-0.672842\pi\) | ||||
−0.516706 | + | 0.856163i | \(0.672842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.55894 | − | 3.26401i | 0.242884 | − | 0.309806i | ||||
\(112\) | 2.62932 | + | 0.294447i | 0.248447 | + | 0.0278226i | ||||
\(113\) | 14.3439i | 1.34936i | 0.738112 | + | 0.674679i | \(0.235718\pi\) | ||||
−0.738112 | + | 0.674679i | \(0.764282\pi\) | |||||||
\(114\) | 2.91330 | − | 3.71601i | 0.272856 | − | 0.348037i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 2.82660i | − | 0.262443i | ||||||
\(117\) | −13.7981 | + | 3.39122i | −1.27564 | + | 0.313519i | ||||
\(118\) | 10.7775i | 0.992148i | ||||||||
\(119\) | −6.83350 | − | 0.765257i | −0.626426 | − | 0.0701510i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.94929 | 0.813572 | ||||||||
\(122\) | 1.05058 | 0.0951148 | ||||||||
\(123\) | 11.9133 | − | 15.1958i | 1.07419 | − | 1.37016i | ||||
\(124\) | 5.91403i | 0.531096i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.87082 | − | 1.02482i | 0.701188 | − | 0.0912979i | ||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −0.461684 | + | 0.588894i | −0.0406490 | + | 0.0518492i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.2804 | −1.50980 | −0.754899 | − | 0.655842i | \(-0.772314\pi\) | ||||
−0.754899 | + | 0.655842i | \(0.772314\pi\) | |||||||
\(132\) | 1.95198 | + | 1.53032i | 0.169898 | + | 0.133198i | ||||
\(133\) | 0.802714 | − | 7.16797i | 0.0696041 | − | 0.621542i | ||||
\(134\) | − | 9.82660i | − | 0.848889i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.59897i | 0.222859i | ||||||||
\(137\) | − | 3.03746i | − | 0.259507i | −0.991546 | − | 0.129754i | \(-0.958581\pi\) | ||
0.991546 | − | 0.129754i | \(-0.0414187\pi\) | |||||||
\(138\) | −3.02062 | + | 3.85291i | −0.257132 | + | 0.327981i | ||||
\(139\) | 20.7478i | 1.75980i | 0.475155 | + | 0.879902i | \(0.342392\pi\) | ||||
−0.475155 | + | 0.879902i | \(0.657608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0239 | + | 14.0613i | −0.928379 | + | 1.18418i | ||||
\(142\) | 13.2586 | 1.11264 | ||||||||
\(143\) | −6.78244 | −0.567176 | ||||||||
\(144\) | −0.716015 | − | 2.91330i | −0.0596679 | − | 0.242775i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.58963 | 0.628122 | ||||||||
\(147\) | 9.40577 | − | 7.65059i | 0.775775 | − | 0.631010i | ||||
\(148\) | −2.39457 | −0.196833 | ||||||||
\(149\) | 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 | \(0.431360\pi\) | |||||||
\(152\) | −2.72617 | −0.221122 | ||||||||
\(153\) | 1.86090 | + | 7.57157i | 0.150445 | + | 0.612125i | ||||
\(154\) | 3.76526 | + | 0.421657i | 0.303413 | + | 0.0339781i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.45592 | + | 5.06134i | 0.516887 | + | 0.405232i | ||||
\(157\) | 6.29566i | 0.502449i | 0.967929 | + | 0.251224i | \(0.0808332\pi\) | ||||
−0.967929 | + | 0.251224i | \(0.919167\pi\) | |||||||
\(158\) | 16.5173i | 1.31404i | ||||||||
\(159\) | 7.75687 | + | 6.08127i | 0.615160 | + | 0.482276i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.832284 | + | 7.43203i | −0.0655932 | + | 0.585726i | ||||
\(162\) | −4.17193 | − | 7.97465i | −0.327778 | − | 0.626547i | ||||
\(163\) | 0.605427 | 0.0474207 | 0.0237104 | − | 0.999719i | \(-0.492452\pi\) | ||||
0.0237104 | + | 0.999719i | \(0.492452\pi\) | |||||||
\(164\) | −11.1481 | −0.870520 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.9148i | 1.00238i | ||||||||
\(167\) | 12.0825 | 0.934971 | 0.467485 | − | 0.884001i | \(-0.345160\pi\) | ||||
0.467485 | + | 0.884001i | \(0.345160\pi\) | |||||||
\(168\) | −3.26933 | − | 3.21115i | −0.252234 | − | 0.247746i | ||||
\(169\) | −9.43203 | −0.725541 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.94217 | + | 1.95198i | −0.607353 | + | 0.149272i | ||||
\(172\) | 0.432029 | 0.0329419 | ||||||||
\(173\) | −15.5137 | −1.17949 | −0.589744 | − | 0.807590i | \(-0.700771\pi\) | ||||
−0.589744 | + | 0.807590i | \(0.700771\pi\) | |||||||
\(174\) | −3.02062 | + | 3.85291i | −0.228993 | + | 0.292088i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.43203i | − | 0.107943i | ||||||
\(177\) | 11.5173 | − | 14.6907i | 0.865690 | − | 1.10422i | ||||
\(178\) | 3.90396i | 0.292614i | ||||||||
\(179\) | 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 | \(0.906285\pi\) | |||||||
\(182\) | 12.4531 | + | 1.39457i | 0.923084 | + | 0.103373i | ||||
\(183\) | −1.43203 | − | 1.12269i | −0.105859 | − | 0.0829916i | ||||
\(184\) | 2.82660 | 0.208380 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.31998 | − | 8.06134i | 0.463403 | − | 0.591086i | ||||
\(187\) | 3.72179i | 0.272165i | ||||||||
\(188\) | 10.3158 | 0.752357 | ||||||||
\(189\) | −11.8238 | − | 7.01416i | −0.860053 | − | 0.510205i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.22117i | − | 0.522506i | −0.965270 | − | 0.261253i | \(-0.915864\pi\) | ||
0.965270 | − | 0.261253i | \(-0.0841357\pi\) | |||||||
\(192\) | −1.06864 | + | 1.36309i | −0.0771225 | + | 0.0983724i | ||||
\(193\) | 7.60250 | 0.547240 | 0.273620 | − | 0.961838i | \(-0.411779\pi\) | ||||
0.273620 | + | 0.961838i | \(0.411779\pi\) | |||||||
\(194\) | 14.0015 | 1.00525 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.82660 | − | 1.54839i | −0.487614 | − | 0.110599i | ||||
\(197\) | 21.7384i | 1.54880i | 0.632697 | + | 0.774400i | \(0.281948\pi\) | ||||
−0.632697 | + | 0.774400i | \(0.718052\pi\) | |||||||
\(198\) | −1.02535 | − | 4.17193i | −0.0728687 | − | 0.296486i | ||||
\(199\) | 6.04124i | 0.428252i | 0.976806 | + | 0.214126i | \(0.0686904\pi\) | ||||
−0.976806 | + | 0.214126i | \(0.931310\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.5011 | + | 13.3945i | −0.740691 | + | 0.944776i | ||||
\(202\) | − | 10.3158i | − | 0.725818i | ||||||
\(203\) | −0.832284 | + | 7.43203i | −0.0584149 | + | 0.521626i | ||||
\(204\) | 2.77736 | − | 3.54262i | 0.194454 | − | 0.248033i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.8743 | −0.966666 | ||||||||
\(207\) | 8.23474 | − | 2.02389i | 0.572354 | − | 0.140670i | ||||
\(208\) | − | 4.73625i | − | 0.328400i | ||||||
\(209\) | −3.90396 | −0.270043 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.7759 | 1.15490 | 0.577450 | − | 0.816426i | \(-0.304048\pi\) | ||||
0.577450 | + | 0.816426i | \(0.304048\pi\) | |||||||
\(212\) | − | 5.69066i | − | 0.390836i | ||||||
\(213\) | −18.0727 | − | 14.1687i | −1.23832 | − | 0.970824i | ||||
\(214\) | −15.9493 | −1.09027 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.13728 | + | 4.73625i | −0.145424 | + | 0.322261i | ||||
\(217\) | 1.74137 | − | 15.5499i | 0.118212 | − | 1.05559i | ||||
\(218\) | − | 10.7891i | − | 0.730733i | ||||||
\(219\) | −10.3453 | − | 8.11059i | −0.699073 | − | 0.548063i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.3093i | 0.828016i | ||||||||
\(222\) | 3.26401 | + | 2.55894i | 0.219066 | + | 0.171745i | ||||
\(223\) | 11.1120i | 0.744112i | 0.928210 | + | 0.372056i | \(0.121347\pi\) | ||||
−0.928210 | + | 0.372056i | \(0.878653\pi\) | |||||||
\(224\) | −0.294447 | + | 2.62932i | −0.0196736 | + | 0.175679i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.3439 | −0.954140 | ||||||||
\(227\) | 7.24413 | 0.480810 | 0.240405 | − | 0.970673i | \(-0.422720\pi\) | ||||
0.240405 | + | 0.970673i | \(0.422720\pi\) | |||||||
\(228\) | 3.71601 | + | 2.91330i | 0.246099 | + | 0.192938i | ||||
\(229\) | − | 27.1596i | − | 1.79476i | −0.441259 | − | 0.897380i | \(-0.645468\pi\) | ||
0.441259 | − | 0.897380i | \(-0.354532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.68178 | − | 4.59846i | −0.308038 | − | 0.302557i | ||||
\(232\) | 2.82660 | 0.185576 | ||||||||
\(233\) | 5.38132i | 0.352542i | 0.984342 | + | 0.176271i | \(0.0564035\pi\) | ||||
−0.984342 | + | 0.176271i | \(0.943596\pi\) | |||||||
\(234\) | −3.39122 | − | 13.7981i | −0.221691 | − | 0.902011i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.7775 | −0.701555 | ||||||||
\(237\) | 17.6510 | − | 22.5145i | 1.14656 | − | 1.46247i | ||||
\(238\) | 0.765257 | − | 6.83350i | 0.0496043 | − | 0.442950i | ||||
\(239\) | 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 | \(0.817917\pi\) | |||||||
\(242\) | 8.94929i | 0.575282i | ||||||||
\(243\) | −2.83532 | + | 15.3284i | −0.181886 | + | 0.983320i | ||||
\(244\) | 1.05058i | 0.0672563i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.1958 | + | 11.9133i | 0.968850 | + | 0.759564i | ||||
\(247\) | −12.9118 | −0.821560 | ||||||||
\(248\) | −5.91403 | −0.375542 | ||||||||
\(249\) | 13.8012 | − | 17.6040i | 0.874619 | − | 1.11561i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.75565 | −0.110816 | −0.0554079 | − | 0.998464i | \(-0.517646\pi\) | ||||
−0.0554079 | + | 0.998464i | \(0.517646\pi\) | |||||||
\(252\) | 1.02482 | + | 7.87082i | 0.0645574 | + | 0.495815i | ||||
\(253\) | 4.04778 | 0.254482 | ||||||||
\(254\) | 2.00000i | 0.125491i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.9366 | −1.36837 | −0.684184 | − | 0.729309i | \(-0.739841\pi\) | ||||
−0.684184 | + | 0.729309i | \(0.739841\pi\) | |||||||
\(258\) | −0.588894 | − | 0.461684i | −0.0366629 | − | 0.0287432i | ||||
\(259\) | 6.29609 | + | 0.705074i | 0.391220 | + | 0.0438112i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.23474 | − | 2.02389i | 0.509718 | − | 0.125276i | ||||
\(262\) | − | 17.2804i | − | 1.06759i | ||||||
\(263\) | − | 4.08523i | − | 0.251906i | −0.992036 | − | 0.125953i | \(-0.959801\pi\) | ||
0.992036 | − | 0.125953i | \(-0.0401989\pi\) | |||||||
\(264\) | −1.53032 | + | 1.95198i | −0.0941850 | + | 0.120136i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.16797 | + | 0.802714i | 0.439497 | + | 0.0492175i | ||||
\(267\) | 4.17193 | − | 5.32144i | 0.255318 | − | 0.325667i | ||||
\(268\) | 9.82660 | 0.600255 | ||||||||
\(269\) | −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 | \(0.747349\pi\) | |||||||
\(272\) | −2.59897 | −0.157585 | ||||||||
\(273\) | −15.4843 | − | 15.2088i | −0.937155 | − | 0.920478i | ||||
\(274\) | 3.03746 | 0.183499 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.85291 | − | 3.02062i | −0.231918 | − | 0.181820i | ||||
\(277\) | −14.1227 | −0.848550 | −0.424275 | − | 0.905533i | \(-0.639471\pi\) | ||||
−0.424275 | + | 0.905533i | \(0.639471\pi\) | |||||||
\(278\) | −20.7478 | −1.24437 | ||||||||
\(279\) | −17.2294 | + | 4.23453i | −1.03149 | + | 0.253515i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.6532i | − | 1.41103i | −0.708694 | − | 0.705516i | \(-0.750715\pi\) | ||
0.708694 | − | 0.705516i | \(-0.249285\pi\) | |||||||
\(282\) | −14.0613 | − | 11.0239i | −0.837341 | − | 0.656463i | ||||
\(283\) | − | 0.807187i | − | 0.0479823i | −0.999712 | − | 0.0239912i | \(-0.992363\pi\) | ||
0.999712 | − | 0.0239912i | \(-0.00763735\pi\) | |||||||
\(284\) | 13.2586i | 0.786755i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 6.78244i | − | 0.401054i | ||||||
\(287\) | 29.3118 | + | 3.28252i | 1.73022 | + | 0.193761i | ||||
\(288\) | 2.91330 | − | 0.716015i | 0.171668 | − | 0.0421916i | ||||
\(289\) | −10.2454 | −0.602669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.0852 | − | 14.9625i | −1.11880 | − | 0.877120i | ||||
\(292\) | 7.58963i | 0.444150i | ||||||||
\(293\) | −14.6704 | −0.857055 | −0.428528 | − | 0.903529i | \(-0.640968\pi\) | ||||
−0.428528 | + | 0.903529i | \(0.640968\pi\) | |||||||
\(294\) | 7.65059 | + | 9.40577i | 0.446191 | + | 0.548556i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.39457i | − | 0.139182i | ||||||
\(297\) | −3.06065 | + | 6.78244i | −0.177597 | + | 0.393557i | ||||
\(298\) | −18.9493 | −1.09770 | ||||||||
\(299\) | 13.3875 | 0.774218 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.13594 | − | 0.127210i | −0.0654746 | − | 0.00733224i | ||||
\(302\) | 5.25863i | 0.302600i | ||||||||
\(303\) | −11.0239 | + | 14.0613i | −0.633306 | + | 0.807803i | ||||
\(304\) | − | 2.72617i | − | 0.156357i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.57157 | + | 1.86090i | −0.432838 | + | 0.106380i | ||||
\(307\) | − | 10.0975i | − | 0.576295i | −0.957586 | − | 0.288148i | \(-0.906961\pi\) | ||
0.957586 | − | 0.288148i | \(-0.0930394\pi\) | |||||||
\(308\) | −0.421657 | + | 3.76526i | −0.0240261 | + | 0.214545i | ||||
\(309\) | 18.9118 | + | 14.8266i | 1.07586 | + | 0.843456i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.27456 | 0.242388 | 0.121194 | − | 0.992629i | \(-0.461328\pi\) | ||||
0.121194 | + | 0.992629i | \(0.461328\pi\) | |||||||
\(312\) | −5.06134 | + | 6.45592i | −0.286542 | + | 0.365494i | ||||
\(313\) | − | 0.923368i | − | 0.0521918i | −0.999659 | − | 0.0260959i | \(-0.991692\pi\) | ||
0.999659 | − | 0.0260959i | \(-0.00830753\pi\) | |||||||
\(314\) | −6.29566 | −0.355285 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.5173 | −0.929169 | ||||||||
\(317\) | − | 15.7384i | − | 0.883959i | −0.897025 | − | 0.441979i | \(-0.854276\pi\) | ||
0.897025 | − | 0.441979i | \(-0.145724\pi\) | |||||||
\(318\) | −6.08127 | + | 7.75687i | −0.341021 | + | 0.434984i | ||||
\(319\) | 4.04778 | 0.226632 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.7403 | + | 17.0441i | 1.21342 | + | 0.951307i | ||||
\(322\) | −7.43203 | − | 0.832284i | −0.414171 | − | 0.0463814i | ||||
\(323\) | 7.08523i | 0.394233i | ||||||||
\(324\) | 7.97465 | − | 4.17193i | 0.443036 | − | 0.231774i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.605427i | 0.0335315i | ||||||||
\(327\) | −11.5297 | + | 14.7065i | −0.637595 | + | 0.813274i | ||||
\(328\) | − | 11.1481i | − | 0.615550i | ||||||
\(329\) | −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 | \(0.612606\pi\) | |||||||
\(332\) | −12.9148 | −0.708790 | ||||||||
\(333\) | −1.71455 | − | 6.97611i | −0.0939567 | − | 0.382289i | ||||
\(334\) | 12.0825i | 0.661124i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.21115 | − | 3.26933i | 0.175183 | − | 0.178357i | ||||
\(337\) | −18.8986 | −1.02947 | −0.514736 | − | 0.857349i | \(-0.672110\pi\) | ||||
−0.514736 | + | 0.857349i | \(0.672110\pi\) | |||||||
\(338\) | − | 9.43203i | − | 0.513035i | ||||||
\(339\) | 19.5519 | + | 15.3284i | 1.06192 | + | 0.832526i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.46907 | −0.458626 | ||||||||
\(342\) | −1.95198 | − | 7.94217i | −0.105551 | − | 0.429463i | ||||
\(343\) | 17.4934 | + | 6.08127i | 0.944553 | + | 0.328358i | ||||
\(344\) | 0.432029i | 0.0232935i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 15.5137i | − | 0.834024i | ||||||
\(347\) | − | 30.7384i | − | 1.65013i | −0.565041 | − | 0.825063i | \(-0.691140\pi\) | ||
0.565041 | − | 0.825063i | \(-0.308860\pi\) | |||||||
\(348\) | −3.85291 | − | 3.02062i | −0.206537 | − | 0.161922i | ||||
\(349\) | 0.970523i | 0.0519509i | 0.999663 | + | 0.0259754i | \(0.00826917\pi\) | ||||
−0.999663 | + | 0.0259754i | \(0.991731\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.1227 | + | 22.4320i | −0.540309 | + | 1.19733i | ||||
\(352\) | 1.43203 | 0.0763274 | ||||||||
\(353\) | −16.3570 | −0.870598 | −0.435299 | − | 0.900286i | \(-0.643357\pi\) | ||||
−0.435299 | + | 0.900286i | \(0.643357\pi\) | |||||||
\(354\) | 14.6907 | + | 11.5173i | 0.780800 | + | 0.612136i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.90396 | −0.206910 | ||||||||
\(357\) | −8.34567 | + | 8.49687i | −0.441700 | + | 0.449702i | ||||
\(358\) | −4.56797 | −0.241425 | ||||||||
\(359\) | − | 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 | ||||||||
\(362\) | −7.80792 | −0.410375 | ||||||||
\(363\) | 9.56358 | − | 12.1987i | 0.501958 | − | 0.640264i | ||||
\(364\) | −1.39457 | + | 12.4531i | −0.0730955 | + | 0.652719i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.12269 | − | 1.43203i | 0.0586839 | − | 0.0748534i | ||||
\(367\) | 33.9970i | 1.77463i | 0.461163 | + | 0.887315i | \(0.347432\pi\) | ||||
−0.461163 | + | 0.887315i | \(0.652568\pi\) | |||||||
\(368\) | 2.82660i | 0.147347i | ||||||||
\(369\) | −7.98220 | − | 32.4777i | −0.415537 | − | 1.69072i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.67560 | + | 14.9625i | −0.0869927 | + | 0.776817i | ||||
\(372\) | 8.06134 | + | 6.31998i | 0.417961 | + | 0.327676i | ||||
\(373\) | 26.5650 | 1.37549 | 0.687743 | − | 0.725954i | \(-0.258602\pi\) | ||||
0.687743 | + | 0.725954i | \(0.258602\pi\) | |||||||
\(374\) | −3.72179 | −0.192449 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3158i | 0.531997i | ||||||||
\(377\) | 13.3875 | 0.689490 | ||||||||
\(378\) | 7.01416 | − | 11.8238i | 0.360769 | − | 0.608149i | ||||
\(379\) | 8.25863 | 0.424217 | 0.212109 | − | 0.977246i | \(-0.431967\pi\) | ||||
0.212109 | + | 0.977246i | \(0.431967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.13728 | − | 2.72617i | 0.109496 | − | 0.139666i | ||||
\(382\) | 7.22117 | 0.369467 | ||||||||
\(383\) | 32.6920 | 1.67049 | 0.835243 | − | 0.549882i | \(-0.185327\pi\) | ||||
0.835243 | + | 0.549882i | \(0.185327\pi\) | |||||||
\(384\) | −1.36309 | − | 1.06864i | −0.0695598 | − | 0.0545338i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.60250i | 0.386957i | ||||||||
\(387\) | 0.309339 | + | 1.25863i | 0.0157246 | + | 0.0639798i | ||||
\(388\) | 14.0015i | 0.710817i | ||||||||
\(389\) | 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 | ||||||
\(392\) | 1.54839 | − | 6.82660i | 0.0782054 | − | 0.344795i | ||||
\(393\) | −18.4666 | + | 23.5547i | −0.931514 | + | 1.18818i | ||||
\(394\) | −21.7384 | −1.09517 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.17193 | − | 1.02535i | 0.209647 | − | 0.0515260i | ||||
\(397\) | 23.0123i | 1.15495i | 0.816407 | + | 0.577477i | \(0.195963\pi\) | ||||
−0.816407 | + | 0.577477i | \(0.804037\pi\) | |||||||
\(398\) | −6.04124 | −0.302820 | ||||||||
\(399\) | −8.91276 | − | 8.75416i | −0.446196 | − | 0.438256i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 17.5547i | − | 0.876641i | −0.898819 | − | 0.438320i | \(-0.855574\pi\) | ||
0.898819 | − | 0.438320i | \(-0.144426\pi\) | |||||||
\(402\) | −13.3945 | − | 10.5011i | −0.668058 | − | 0.523748i | ||||
\(403\) | −28.0103 | −1.39529 | ||||||||
\(404\) | 10.3158 | 0.513231 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.43203 | − | 0.832284i | −0.368845 | − | 0.0413056i | ||||
\(407\) | − | 3.42910i | − | 0.169974i | ||||||
\(408\) | 3.54262 | + | 2.77736i | 0.175386 | + | 0.137500i | ||||
\(409\) | 9.94521i | 0.491759i | 0.969300 | + | 0.245879i | \(0.0790767\pi\) | ||||
−0.969300 | + | 0.245879i | \(0.920923\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.14032 | − | 3.24595i | −0.204227 | − | 0.160111i | ||||
\(412\) | − | 13.8743i | − | 0.683536i | ||||||
\(413\) | 28.3374 | + | 3.17340i | 1.39439 | + | 0.156153i | ||||
\(414\) | 2.02389 | + | 8.23474i | 0.0994687 | + | 0.404716i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.73625 | 0.232214 | ||||||||
\(417\) | 28.2811 | + | 22.1719i | 1.38493 | + | 1.08576i | ||||
\(418\) | − | 3.90396i | − | 0.190949i | ||||||
\(419\) | −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 | \(0.411921\pi\) | |||||||
\(422\) | 16.7759i | 0.816638i | ||||||||
\(423\) | 7.38627 | + | 30.0530i | 0.359133 | + | 1.46123i | ||||
\(424\) | 5.69066 | 0.276363 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 14.1687 | − | 18.0727i | 0.686476 | − | 0.875624i | ||||
\(427\) | 0.309339 | − | 2.76230i | 0.0149700 | − | 0.133677i | ||||
\(428\) | − | 15.9493i | − | 0.770938i | ||||||
\(429\) | −7.24799 | + | 9.24506i | −0.349936 | + | 0.446356i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.2079i | 1.26239i | 0.775624 | + | 0.631196i | \(0.217435\pi\) | ||||
−0.775624 | + | 0.631196i | \(0.782565\pi\) | |||||||
\(432\) | −4.73625 | − | 2.13728i | −0.227873 | − | 0.102830i | ||||
\(433\) | − | 23.4378i | − | 1.12635i | −0.826337 | − | 0.563175i | \(-0.809580\pi\) | ||
0.826337 | − | 0.563175i | \(-0.190420\pi\) | |||||||
\(434\) | 15.5499 | + | 1.74137i | 0.746417 | + | 0.0835884i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.7891 | 0.516706 | ||||||||
\(437\) | 7.70581 | 0.368619 | ||||||||
\(438\) | 8.11059 | − | 10.3453i | 0.387539 | − | 0.494319i | ||||
\(439\) | − | 25.0334i | − | 1.19478i | −0.801952 | − | 0.597389i | \(-0.796205\pi\) | ||
0.801952 | − | 0.597389i | \(-0.203795\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.377028 | − | 20.9966i | −0.0179537 | − | 0.999839i | ||||
\(442\) | −12.3093 | −0.585496 | ||||||||
\(443\) | − | 18.4666i | − | 0.877373i | −0.898640 | − | 0.438686i | \(-0.855444\pi\) | ||
0.898640 | − | 0.438686i | \(-0.144556\pi\) | |||||||
\(444\) | −2.55894 | + | 3.26401i | −0.121442 | + | 0.154903i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.1120 | −0.526167 | ||||||||
\(447\) | 25.8295 | + | 20.2500i | 1.22170 | + | 0.957791i | ||||
\(448\) | −2.62932 | − | 0.294447i | −0.124223 | − | 0.0139113i | ||||
\(449\) | − | 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 | ||||||
\(452\) | − | 14.3439i | − | 0.674679i | ||||||
\(453\) | 5.61959 | − | 7.16797i | 0.264031 | − | 0.336781i | ||||
\(454\) | 7.24413i | 0.339984i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.91330 | + | 3.71601i | −0.136428 | + | 0.174018i | ||||
\(457\) | −10.9251 | −0.511054 | −0.255527 | − | 0.966802i | \(-0.582249\pi\) | ||||
−0.255527 | + | 0.966802i | \(0.582249\pi\) | |||||||
\(458\) | 27.1596 | 1.26909 | ||||||||
\(459\) | 12.3093 | + | 5.55472i | 0.574551 | + | 0.259272i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.6729 | 1.24228 | 0.621139 | − | 0.783700i | \(-0.286670\pi\) | ||||
0.621139 | + | 0.783700i | \(0.286670\pi\) | |||||||
\(462\) | 4.59846 | − | 4.68178i | 0.213940 | − | 0.217816i | ||||
\(463\) | 8.07491 | 0.375273 | 0.187637 | − | 0.982239i | \(-0.439917\pi\) | ||||
0.187637 | + | 0.982239i | \(0.439917\pi\) | |||||||
\(464\) | 2.82660i | 0.131222i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.38132 | −0.249285 | ||||||||
\(467\) | −41.6228 | −1.92607 | −0.963037 | − | 0.269371i | \(-0.913184\pi\) | ||||
−0.963037 | + | 0.269371i | \(0.913184\pi\) | |||||||
\(468\) | 13.7981 | − | 3.39122i | 0.637818 | − | 0.156759i | ||||
\(469\) | −25.8372 | − | 2.89341i | −1.19305 | − | 0.133605i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.58154 | + | 6.72780i | 0.395416 | + | 0.310001i | ||||
\(472\) | − | 10.7775i | − | 0.496074i | ||||||
\(473\) | 0.618679i | 0.0284469i | ||||||||
\(474\) | 22.5145 | + | 17.6510i | 1.03412 | + | 0.810738i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.83350 | + | 0.765257i | 0.313213 | + | 0.0350755i | ||||
\(477\) | 16.5786 | − | 4.07460i | 0.759082 | − | 0.186563i | ||||
\(478\) | −2.51726 | −0.115137 | ||||||||
\(479\) | 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 | ||||||
\(482\) | −16.8077 | −0.765570 | ||||||||
\(483\) | 9.24109 | + | 9.07664i | 0.420484 | + | 0.413002i | ||||
\(484\) | −8.94929 | −0.406786 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −15.3284 | − | 2.83532i | −0.695312 | − | 0.128613i | ||||
\(487\) | 27.1094 | 1.22845 | 0.614223 | − | 0.789133i | \(-0.289470\pi\) | ||||
0.614223 | + | 0.789133i | \(0.289470\pi\) | |||||||
\(488\) | −1.05058 | −0.0475574 | ||||||||
\(489\) | 0.646984 | − | 0.825250i | 0.0292576 | − | 0.0373191i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 30.0000i | − | 1.35388i | −0.736038 | − | 0.676941i | \(-0.763305\pi\) | ||
0.736038 | − | 0.676941i | \(-0.236695\pi\) | |||||||
\(492\) | −11.9133 | + | 15.1958i | −0.537093 | + | 0.685081i | ||||
\(493\) | − | 7.34624i | − | 0.330858i | ||||||
\(494\) | − | 12.9118i | − | 0.580931i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.91403i | − | 0.265548i | ||||||
\(497\) | 3.90396 | − | 34.8611i | 0.175117 | − | 1.56374i | ||||
\(498\) | 17.6040 | + | 13.8012i | 0.788852 | + | 0.618449i | ||||
\(499\) | 8.50694 | 0.380823 | 0.190412 | − | 0.981704i | \(-0.439018\pi\) | ||||
0.190412 | + | 0.981704i | \(0.439018\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.9118 | − | 16.4695i | 0.576858 | − | 0.735802i | ||||
\(502\) | − | 1.75565i | − | 0.0783586i | ||||||
\(503\) | 12.1625 | 0.542301 | 0.271150 | − | 0.962537i | \(-0.412596\pi\) | ||||
0.271150 | + | 0.962537i | \(0.412596\pi\) | |||||||
\(504\) | −7.87082 | + | 1.02482i | −0.350594 | + | 0.0456489i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.04778i | 0.179946i | ||||||||
\(507\) | −10.0794 | + | 12.8567i | −0.447644 | + | 0.570985i | ||||
\(508\) | −2.00000 | −0.0887357 | ||||||||
\(509\) | 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 | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −5.82660 | + | 12.9118i | −0.257251 | + | 0.570071i | ||||
\(514\) | − | 21.9366i | − | 0.967582i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.461684 | − | 0.588894i | 0.0203245 | − | 0.0259246i | ||||
\(517\) | 14.7725i | 0.649695i | ||||||||
\(518\) | −0.705074 | + | 6.29609i | −0.0309792 | + | 0.276634i | ||||
\(519\) | −16.5786 | + | 21.1466i | −0.727720 | + | 0.928232i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.7031 | 1.43275 | 0.716374 | − | 0.697717i | \(-0.245801\pi\) | ||||
0.716374 | + | 0.697717i | \(0.245801\pi\) | |||||||
\(522\) | 2.02389 | + | 8.23474i | 0.0885832 | + | 0.360425i | ||||
\(523\) | 28.5557i | 1.24865i | 0.781163 | + | 0.624327i | \(0.214627\pi\) | ||||
−0.781163 | + | 0.624327i | \(0.785373\pi\) | |||||||
\(524\) | 17.2804 | 0.754899 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.08523 | 0.178125 | ||||||||
\(527\) | 15.3704i | 0.669544i | ||||||||
\(528\) | −1.95198 | − | 1.53032i | −0.0849491 | − | 0.0665988i | ||||
\(529\) | 15.0103 | 0.652623 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.71684 | − | 31.3981i | −0.334882 | − | 1.36256i | ||||
\(532\) | −0.802714 | + | 7.16797i | −0.0348020 | + | 0.310771i | ||||
\(533\) | − | 52.8001i | − | 2.28703i | ||||||
\(534\) | 5.32144 | + | 4.17193i | 0.230281 | + | 0.180537i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.82660i | 0.424445i | ||||||||
\(537\) | 6.22654 | + | 4.88152i | 0.268695 | + | 0.210653i | ||||
\(538\) | − | 6.96461i | − | 0.300266i | ||||||
\(539\) | 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 | \(0.763847\pi\) | |||||||
\(542\) | −23.4740 | −1.00829 | ||||||||
\(543\) | 10.6429 | + | 8.34386i | 0.456730 | + | 0.358070i | ||||
\(544\) | − | 2.59897i | − | 0.111430i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.2088 | − | 15.4843i | 0.650876 | − | 0.662669i | ||||
\(547\) | 26.7759 | 1.14485 | 0.572427 | − | 0.819955i | \(-0.306002\pi\) | ||||
0.572427 | + | 0.819955i | \(0.306002\pi\) | |||||||
\(548\) | 3.03746i | 0.129754i | ||||||||
\(549\) | −3.06065 | + | 0.752229i | −0.130625 | + | 0.0321044i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.70581 | 0.328279 | ||||||||
\(552\) | 3.02062 | − | 3.85291i | 0.128566 | − | 0.163991i | ||||
\(553\) | 43.4291 | + | 4.86346i | 1.84679 | + | 0.206815i | ||||
\(554\) | − | 14.1227i | − | 0.600016i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 20.7478i | − | 0.879902i | ||||||
\(557\) | 40.4158i | 1.71247i | 0.516583 | + | 0.856237i | \(0.327204\pi\) | ||||
−0.516583 | + | 0.856237i | \(0.672796\pi\) | |||||||
\(558\) | −4.23453 | − | 17.2294i | −0.179262 | − | 0.729377i | ||||
\(559\) | 2.04620i | 0.0865449i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.07313 | + | 3.97726i | 0.214188 | + | 0.167920i | ||||
\(562\) | 23.6532 | 0.997750 | ||||||||
\(563\) | 8.16750 | 0.344219 | 0.172109 | − | 0.985078i | \(-0.444942\pi\) | ||||
0.172109 | + | 0.985078i | \(0.444942\pi\) | |||||||
\(564\) | 11.0239 | − | 14.0613i | 0.464189 | − | 0.592089i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.807187 | 0.0339286 | ||||||||
\(567\) | −22.1963 | + | 8.62122i | −0.932156 | + | 0.362057i | ||||
\(568\) | −13.2586 | −0.556320 | ||||||||
\(569\) | − | 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 | \(0.200695\pi\) | |||||||
\(572\) | 6.78244 | 0.283588 | ||||||||
\(573\) | −9.84309 | − | 7.71684i | −0.411201 | − | 0.322376i | ||||
\(574\) | −3.28252 | + | 29.3118i | −0.137010 | + | 1.22345i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.716015 | + | 2.91330i | 0.0298339 | + | 0.121388i | ||||
\(577\) | 23.9467i | 0.996913i | 0.866915 | + | 0.498457i | \(0.166100\pi\) | ||||
−0.866915 | + | 0.498457i | \(0.833900\pi\) | |||||||
\(578\) | − | 10.2454i | − | 0.426152i | ||||||
\(579\) | 8.12434 | − | 10.3629i | 0.337636 | − | 0.430666i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.9570 | + | 3.80271i | 1.40877 | + | 0.157763i | ||||
\(582\) | 14.9625 | − | 19.0852i | 0.620217 | − | 0.791108i | ||||
\(583\) | 8.14919 | 0.337505 | ||||||||
\(584\) | −7.58963 | −0.314061 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 14.6704i | − | 0.606030i | ||||||
\(587\) | 17.9305 | 0.740072 | 0.370036 | − | 0.929017i | \(-0.379345\pi\) | ||||
0.370036 | + | 0.929017i | \(0.379345\pi\) | |||||||
\(588\) | −9.40577 | + | 7.65059i | −0.387887 | + | 0.315505i | ||||
\(589\) | −16.1227 | −0.664324 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.6314 | + | 23.2306i | 1.21887 | + | 0.955578i | ||||
\(592\) | 2.39457 | 0.0984163 | ||||||||
\(593\) | −18.5744 | −0.762759 | −0.381379 | − | 0.924419i | \(-0.624551\pi\) | ||||
−0.381379 | + | 0.924419i | \(0.624551\pi\) | |||||||
\(594\) | −6.78244 | − | 3.06065i | −0.278287 | − | 0.125580i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 18.9493i | − | 0.776193i | ||||||
\(597\) | 8.23474 | + | 6.45592i | 0.337026 | + | 0.264223i | ||||
\(598\) | 13.3875i | 0.547455i | ||||||||
\(599\) | 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 | \(-0.151861\pi\) | |||||||
\(602\) | 0.127210 | − | 1.13594i | 0.00518468 | − | 0.0462975i | ||||
\(603\) | 7.03599 | + | 28.6279i | 0.286528 | + | 1.16582i | ||||
\(604\) | −5.25863 | −0.213971 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.0613 | − | 11.0239i | −0.571203 | − | 0.447815i | ||||
\(607\) | 17.5128i | 0.710822i | 0.934710 | + | 0.355411i | \(0.115659\pi\) | ||||
−0.934710 | + | 0.355411i | \(0.884341\pi\) | |||||||
\(608\) | 2.72617 | 0.110561 | ||||||||
\(609\) | 9.24109 | + | 9.07664i | 0.374468 | + | 0.367804i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.8582i | 1.97659i | ||||||||
\(612\) | −1.86090 | − | 7.57157i | −0.0752223 | − | 0.306062i | ||||
\(613\) | −32.7626 | −1.32327 | −0.661635 | − | 0.749826i | \(-0.730137\pi\) | ||||
−0.661635 | + | 0.749826i | \(0.730137\pi\) | |||||||
\(614\) | 10.0975 | 0.407502 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.76526 | − | 0.421657i | −0.151707 | − | 0.0169890i | ||||
\(617\) | 0.693592i | 0.0279229i | 0.999903 | + | 0.0139615i | \(0.00444422\pi\) | ||||
−0.999903 | + | 0.0139615i | \(0.995556\pi\) | |||||||
\(618\) | −14.8266 | + | 18.9118i | −0.596413 | + | 0.760746i | ||||
\(619\) | 18.5305i | 0.744802i | 0.928072 | + | 0.372401i | \(0.121465\pi\) | ||||
−0.928072 | + | 0.372401i | \(0.878535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.04124 | − | 13.3875i | 0.242427 | − | 0.537221i | ||||
\(622\) | 4.27456i | 0.171394i | ||||||||
\(623\) | 10.2647 | + | 1.14951i | 0.411248 | + | 0.0460541i | ||||
\(624\) | −6.45592 | − | 5.06134i | −0.258444 | − | 0.202616i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.923368 | 0.0369052 | ||||||||
\(627\) | −4.17193 | + | 5.32144i | −0.166611 | + | 0.212518i | ||||
\(628\) | − | 6.29566i | − | 0.251224i | ||||||
\(629\) | −6.22341 | −0.248144 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.39457 | −0.334183 | −0.167091 | − | 0.985941i | \(-0.553437\pi\) | ||||
−0.167091 | + | 0.985941i | \(0.553437\pi\) | |||||||
\(632\) | − | 16.5173i | − | 0.657021i | ||||||
\(633\) | 17.9274 | − | 22.8670i | 0.712550 | − | 0.908882i | ||||
\(634\) | 15.7384 | 0.625053 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.75687 | − | 6.08127i | −0.307580 | − | 0.241138i | ||||
\(637\) | 7.33354 | − | 32.3325i | 0.290566 | − | 1.28106i | ||||
\(638\) | 4.04778i | 0.160253i | ||||||||
\(639\) | −38.6264 | + | 9.49337i | −1.52804 | + | 0.375552i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.6532i | 0.934245i | 0.884193 | + | 0.467123i | \(0.154709\pi\) | ||||
−0.884193 | + | 0.467123i | \(0.845291\pi\) | |||||||
\(642\) | −17.0441 | + | 21.7403i | −0.672675 | + | 0.858020i | ||||
\(643\) | − | 2.60999i | − | 0.102928i | −0.998675 | − | 0.0514641i | \(-0.983611\pi\) | ||
0.998675 | − | 0.0514641i | \(-0.0163888\pi\) | |||||||
\(644\) | 0.832284 | − | 7.43203i | 0.0327966 | − | 0.292863i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.08523 | −0.278765 | ||||||||
\(647\) | 4.45673 | 0.175212 | 0.0876061 | − | 0.996155i | \(-0.472078\pi\) | ||||
0.0876061 | + | 0.996155i | \(0.472078\pi\) | |||||||
\(648\) | 4.17193 | + | 7.97465i | 0.163889 | + | 0.313274i | ||||
\(649\) | − | 15.4337i | − | 0.605825i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.3349 | − | 18.9909i | −0.757795 | − | 0.744310i | ||||
\(652\) | −0.605427 | −0.0237104 | ||||||||
\(653\) | − | 30.9118i | − | 1.20967i | −0.796349 | − | 0.604837i | \(-0.793238\pi\) | ||
0.796349 | − | 0.604837i | \(-0.206762\pi\) | |||||||
\(654\) | −14.7065 | − | 11.5297i | −0.575072 | − | 0.450848i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.1481 | 0.435260 | ||||||||
\(657\) | −22.1109 | + | 5.43429i | −0.862628 | + | 0.212012i | ||||
\(658\) | 3.03746 | − | 27.1235i | 0.118412 | − | 1.05738i | ||||
\(659\) | 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 | \(0.734700\pi\) | |||||||
\(662\) | − | 12.6054i | − | 0.489924i | ||||||
\(663\) | 16.7787 | + | 13.1543i | 0.651631 | + | 0.510869i | ||||
\(664\) | − | 12.9148i | − | 0.501190i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.97611 | − | 1.71455i | 0.270319 | − | 0.0664374i | ||||
\(667\) | −7.98968 | −0.309362 | ||||||||
\(668\) | −12.0825 | −0.467485 | ||||||||
\(669\) | 15.1466 | + | 11.8747i | 0.585601 | + | 0.459102i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.50446 | −0.0580790 | ||||||||
\(672\) | 3.26933 | + | 3.21115i | 0.126117 | + | 0.123873i | ||||
\(673\) | −21.2212 | −0.818016 | −0.409008 | − | 0.912531i | \(-0.634125\pi\) | ||||
−0.409008 | + | 0.912531i | \(0.634125\pi\) | |||||||
\(674\) | − | 18.8986i | − | 0.727946i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.43203 | 0.362770 | ||||||||
\(677\) | −3.53336 | −0.135798 | −0.0678991 | − | 0.997692i | \(-0.521630\pi\) | ||||
−0.0678991 | + | 0.997692i | \(0.521630\pi\) | |||||||
\(678\) | −15.3284 | + | 19.5519i | −0.588685 | + | 0.750888i | ||||
\(679\) | 4.12269 | − | 36.8143i | 0.158214 | − | 1.41280i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.74137 | − | 9.87438i | 0.296650 | − | 0.378387i | ||||
\(682\) | − | 8.46907i | − | 0.324297i | ||||||
\(683\) | 1.70391i | 0.0651984i | 0.999469 | + | 0.0325992i | \(0.0103785\pi\) | ||||
−0.999469 | + | 0.0325992i | \(0.989622\pi\) | |||||||
\(684\) | 7.94217 | − | 1.95198i | 0.303676 | − | 0.0746359i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.08127 | + | 17.4934i | −0.232184 | + | 0.667900i | ||||
\(687\) | −37.0210 | − | 29.0239i | −1.41244 | − | 1.10733i | ||||
\(688\) | −0.432029 | −0.0164710 | ||||||||
\(689\) | 26.9524 | 1.02680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.21734i | − | 0.0843514i | −0.999110 | − | 0.0421757i | \(-0.986571\pi\) | ||
0.999110 | − | 0.0421757i | \(-0.0134289\pi\) | |||||||
\(692\) | 15.5137 | 0.589744 | ||||||||
\(693\) | −11.2712 | + | 1.46757i | −0.428159 | + | 0.0557483i | ||||
\(694\) | 30.7384 | 1.16682 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.02062 | − | 3.85291i | 0.114496 | − | 0.146044i | ||||
\(697\) | −28.9735 | −1.09745 | ||||||||
\(698\) | −0.970523 | −0.0367348 | ||||||||
\(699\) | 7.33521 | + | 5.75070i | 0.277443 | + | 0.217511i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.11976i | 0.117832i | 0.998263 | + | 0.0589158i | \(0.0187644\pi\) | ||||
−0.998263 | + | 0.0589158i | \(0.981236\pi\) | |||||||
\(702\) | −22.4320 | − | 10.1227i | −0.846642 | − | 0.382056i | ||||
\(703\) | − | 6.52802i | − | 0.246209i | ||||||
\(704\) | 1.43203i | 0.0539716i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 16.3570i | − | 0.615606i | ||||||
\(707\) | −27.1235 | − | 3.03746i | −1.02008 | − | 0.114235i | ||||
\(708\) | −11.5173 | + | 14.6907i | −0.432845 | + | 0.552109i | ||||
\(709\) | 12.8641 | 0.483120 | 0.241560 | − | 0.970386i | \(-0.422341\pi\) | ||||
0.241560 | + | 0.970386i | \(0.422341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.8266 | − | 48.1198i | −0.443532 | − | 1.80463i | ||||
\(712\) | − | 3.90396i | − | 0.146307i | ||||||
\(713\) | 16.7166 | 0.626042 | ||||||||
\(714\) | −8.49687 | − | 8.34567i | −0.317987 | − | 0.312329i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 4.56797i | − | 0.170713i | ||||||
\(717\) | 3.43125 | + | 2.69005i | 0.128142 | + | 0.100462i | ||||
\(718\) | 9.81335 | 0.366231 | ||||||||
\(719\) | −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 | ||||
\(722\) | 11.5680i | 0.430515i | ||||||||
\(723\) | 22.9104 | + | 17.9614i | 0.852046 | + | 0.667991i | ||||
\(724\) | − | 7.80792i | − | 0.290179i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.1987 | + | 9.56358i | 0.452735 | + | 0.354938i | ||||
\(727\) | 18.9921i | 0.704379i | 0.935929 | + | 0.352190i | \(0.114563\pi\) | ||||
−0.935929 | + | 0.352190i | \(0.885437\pi\) | |||||||
\(728\) | −12.4531 | − | 1.39457i | −0.461542 | − | 0.0516863i | ||||
\(729\) | 17.8641 | + | 20.2454i | 0.661632 | + | 0.749829i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.12283 | 0.0415293 | ||||||||
\(732\) | 1.43203 | + | 1.12269i | 0.0529293 | + | 0.0414958i | ||||
\(733\) | − | 27.1345i | − | 1.00224i | −0.865379 | − | 0.501119i | \(-0.832922\pi\) | ||
0.865379 | − | 0.501119i | \(-0.167078\pi\) | |||||||
\(734\) | −33.9970 | −1.25485 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.82660 | −0.104190 | ||||||||
\(737\) | 14.0720i | 0.518348i | ||||||||
\(738\) | 32.4777 | − | 7.98220i | 1.19552 | − | 0.293829i | ||||
\(739\) | 8.67741 | 0.319204 | 0.159602 | − | 0.987181i | \(-0.448979\pi\) | ||||
0.159602 | + | 0.987181i | \(0.448979\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.7981 | + | 17.6000i | −0.506886 | + | 0.646551i | ||||
\(742\) | −14.9625 | − | 1.67560i | −0.549292 | − | 0.0615131i | ||||
\(743\) | − | 52.5754i | − | 1.92880i | −0.264443 | − | 0.964401i | \(-0.585188\pi\) | ||
0.264443 | − | 0.964401i | \(-0.414812\pi\) | |||||||
\(744\) | −6.31998 | + | 8.06134i | −0.231702 | + | 0.295543i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.5650i | 0.972615i | ||||||||
\(747\) | −9.24717 | − | 37.6246i | −0.338336 | − | 1.37661i | ||||
\(748\) | − | 3.72179i | − | 0.136082i | ||||||
\(749\) | −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 | \(0.489684\pi\) | |||||||
\(752\) | −10.3158 | −0.376179 | ||||||||
\(753\) | −1.87616 | + | 2.39311i | −0.0683711 | + | 0.0872097i | ||||
\(754\) | 13.3875i | 0.487543i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.8238 | + | 7.01416i | 0.430026 | + | 0.255103i | ||||
\(757\) | 4.63995 | 0.168642 | 0.0843210 | − | 0.996439i | \(-0.473128\pi\) | ||||
0.0843210 | + | 0.996439i | \(0.473128\pi\) | |||||||
\(758\) | 8.25863i | 0.299967i | ||||||||
\(759\) | 4.32562 | − | 5.51747i | 0.157010 | − | 0.200272i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.6884 | −1.47495 | −0.737477 | − | 0.675373i | \(-0.763983\pi\) | ||||
−0.737477 | + | 0.675373i | \(0.763983\pi\) | |||||||
\(762\) | 2.72617 | + | 2.13728i | 0.0987589 | + | 0.0774255i | ||||
\(763\) | −28.3681 | − | 3.17683i | −1.02699 | − | 0.115009i | ||||
\(764\) | 7.22117i | 0.261253i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.6920i | 1.18121i | ||||||||
\(767\) | − | 51.0448i | − | 1.84312i | ||||||
\(768\) | 1.06864 | − | 1.36309i | 0.0385612 | − | 0.0491862i | ||||
\(769\) | − | 19.2355i | − | 0.693651i | −0.937930 | − | 0.346825i | \(-0.887260\pi\) | ||
0.937930 | − | 0.346825i | \(-0.112740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.4423 | + | 29.9015i | −0.844256 | + | 1.07688i | ||||
\(772\) | −7.60250 | −0.273620 | ||||||||
\(773\) | −28.4175 | −1.02211 | −0.511053 | − | 0.859549i | \(-0.670744\pi\) | ||||
−0.511053 | + | 0.859549i | \(0.670744\pi\) | |||||||
\(774\) | −1.25863 | + | 0.309339i | −0.0452406 | + | 0.0111190i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.0015 | −0.502624 | ||||||||
\(777\) | 7.68933 | − | 7.82865i | 0.275853 | − | 0.280851i | ||||
\(778\) | −1.33354 | −0.0478099 | ||||||||
\(779\) | − | 30.3916i | − | 1.08889i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.9867 | −0.679399 | ||||||||
\(782\) | 7.34624 | 0.262701 | ||||||||
\(783\) | 6.04124 | − | 13.3875i | 0.215896 | − | 0.478430i | ||||
\(784\) | 6.82660 | + | 1.54839i | 0.243807 | + | 0.0552996i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23.5547 | − | 18.4666i | −0.840169 | − | 0.658680i | ||||
\(787\) | − | 41.6778i | − | 1.48565i | −0.669485 | − | 0.742826i | \(-0.733485\pi\) | ||
0.669485 | − | 0.742826i | \(-0.266515\pi\) | |||||||
\(788\) | − | 21.7384i | − | 0.774400i | ||||||
\(789\) | −5.56853 | − | 4.36565i | −0.198245 | − | 0.155421i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.22351 | + | 37.7145i | −0.150171 | + | 1.34097i | ||||
\(792\) | 1.02535 | + | 4.17193i | 0.0364344 | + | 0.148243i | ||||
\(793\) | −4.97579 | −0.176696 | ||||||||
\(794\) | −23.0123 | −0.816675 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 6.04124i | − | 0.214126i | ||||||
\(797\) | 10.2137 | 0.361788 | 0.180894 | − | 0.983503i | \(-0.442101\pi\) | ||||
0.180894 | + | 0.983503i | \(0.442101\pi\) | |||||||
\(798\) | 8.75416 | − | 8.91276i | 0.309894 | − | 0.315508i | ||||
\(799\) | 26.8104 | 0.948484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.79529 | − | 11.3734i | −0.0987669 | − | 0.401860i | ||||
\(802\) | 17.5547 | 0.619879 | ||||||||
\(803\) | −10.8686 | −0.383544 | ||||||||
\(804\) | 10.5011 | − | 13.3945i | 0.370345 | − | 0.472388i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 28.0103i | − | 0.986621i | ||||||
\(807\) | −7.44267 | + | 9.49337i | −0.261994 | + | 0.334183i | ||||
\(808\) | 10.3158i | 0.362909i | ||||||||
\(809\) | − | 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 | \(-0.209849\pi\) | |||||||
\(812\) | 0.832284 | − | 7.43203i | 0.0292074 | − | 0.260813i | ||||
\(813\) | 31.9971 | + | 25.0852i | 1.12219 | + | 0.879778i | ||||
\(814\) | 3.42910 | 0.120190 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.77736 | + | 3.54262i | −0.0972270 | + | 0.124016i | ||||
\(817\) | 1.17779i | 0.0412056i | ||||||||
\(818\) | −9.94521 | −0.347726 | ||||||||
\(819\) | −37.2781 | + | 4.85378i | −1.30260 | + | 0.169605i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 33.4291i | − | 1.16668i | −0.812227 | − | 0.583342i | \(-0.801745\pi\) | ||
0.812227 | − | 0.583342i | \(-0.198255\pi\) | |||||||
\(822\) | 3.24595 | − | 4.14032i | 0.113215 | − | 0.144410i | ||||
\(823\) | −20.7414 | −0.722999 | −0.361499 | − | 0.932372i | \(-0.617735\pi\) | ||||
−0.361499 | + | 0.932372i | \(0.617735\pi\) | |||||||
\(824\) | 13.8743 | 0.483333 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.17340 | + | 28.3374i | −0.110417 | + | 0.985985i | ||||
\(827\) | 41.8479i | 1.45519i | 0.686005 | + | 0.727597i | \(0.259363\pi\) | ||||
−0.686005 | + | 0.727597i | \(0.740637\pi\) | |||||||
\(828\) | −8.23474 | + | 2.02389i | −0.286177 | + | 0.0703350i | ||||
\(829\) | 19.7632i | 0.686404i | 0.939262 | + | 0.343202i | \(0.111512\pi\) | ||||
−0.939262 | + | 0.343202i | \(0.888488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.0921 | + | 19.2505i | −0.523538 | + | 0.667791i | ||||
\(832\) | 4.73625i | 0.164200i | ||||||||
\(833\) | −17.7421 | − | 4.02421i | −0.614727 | − | 0.139430i | ||||
\(834\) | −22.1719 | + | 28.2811i | −0.767751 | + | 0.979293i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.90396 | 0.135021 | ||||||||
\(837\) | −12.6400 | + | 28.0103i | −0.436901 | + | 0.968178i | ||||
\(838\) | − | 7.71684i | − | 0.266574i | ||||||
\(839\) | −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 | ||||||||
\(842\) | 11.2109i | 0.386352i | ||||||||
\(843\) | −32.2414 | − | 25.2768i | −1.11045 | − | 0.870578i | ||||
\(844\) | −16.7759 | −0.577450 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −30.0530 | + | 7.38627i | −1.03325 | + | 0.253945i | ||||
\(847\) | 23.5305 | + | 2.63509i | 0.808518 | + | 0.0905428i | ||||
\(848\) | 5.69066i | 0.195418i | ||||||||
\(849\) | −1.10027 | − | 0.862593i | −0.0377611 | − | 0.0296041i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.76850i | 0.232021i | ||||||||
\(852\) | 18.0727 | + | 14.1687i | 0.619160 | + | 0.485412i | ||||
\(853\) | 2.22837i | 0.0762978i | 0.999272 | + | 0.0381489i | \(0.0121461\pi\) | ||||
−0.999272 | + | 0.0381489i | \(0.987854\pi\) | |||||||
\(854\) | 2.76230 | + | 0.309339i | 0.0945240 | + | 0.0105854i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.9493 | 0.545136 | ||||||||
\(857\) | −5.75070 | −0.196440 | −0.0982201 | − | 0.995165i | \(-0.531315\pi\) | ||||
−0.0982201 | + | 0.995165i | \(0.531315\pi\) | |||||||
\(858\) | −9.24506 | − | 7.24799i | −0.315621 | − | 0.247442i | ||||
\(859\) | 46.1407i | 1.57430i | 0.616760 | + | 0.787151i | \(0.288445\pi\) | ||||
−0.616760 | + | 0.787151i | \(0.711555\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.7982 | − | 36.4468i | 1.22000 | − | 1.24210i | ||||
\(862\) | −26.2079 | −0.892645 | ||||||||
\(863\) | 17.5783i | 0.598372i | 0.954195 | + | 0.299186i | \(0.0967151\pi\) | ||||
−0.954195 | + | 0.299186i | \(0.903285\pi\) | |||||||
\(864\) | 2.13728 | − | 4.73625i | 0.0727118 | − | 0.161130i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.4378 | 0.796450 | ||||||||
\(867\) | −10.9486 | + | 13.9653i | −0.371835 | + | 0.474288i | ||||
\(868\) | −1.74137 | + | 15.5499i | −0.0591059 | + | 0.527797i | ||||
\(869\) | − | 23.6532i | − | 0.802380i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.5412i | 1.57699i | ||||||||
\(872\) | 10.7891i | 0.365367i | ||||||||
\(873\) | −40.7905 | + | 10.0253i | −1.38055 | + | 0.339304i | ||||
\(874\) | 7.70581i | 0.260653i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.3453 | + | 8.11059i | 0.349536 | + | 0.274031i | ||||
\(877\) | −41.8237 | −1.41229 | −0.706143 | − | 0.708070i | \(-0.749566\pi\) | ||||
−0.706143 | + | 0.708070i | \(0.749566\pi\) | |||||||
\(878\) | 25.0334 | 0.844836 | ||||||||
\(879\) | −15.6774 | + | 19.9971i | −0.528786 | + | 0.674484i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.8757 | −0.939158 | −0.469579 | − | 0.882891i | \(-0.655594\pi\) | ||||
−0.469579 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(882\) | 20.9966 | − | 0.377028i | 0.706993 | − | 0.0126952i | ||||
\(883\) | −11.6400 | −0.391716 | −0.195858 | − | 0.980632i | \(-0.562749\pi\) | ||||
−0.195858 | + | 0.980632i | \(0.562749\pi\) | |||||||
\(884\) | − | 12.3093i | − | 0.414008i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.4666 | 0.620396 | ||||||||
\(887\) | 38.7333 | 1.30054 | 0.650268 | − | 0.759705i | \(-0.274657\pi\) | ||||
0.650268 | + | 0.759705i | \(0.274657\pi\) | |||||||
\(888\) | −3.26401 | − | 2.55894i | −0.109533 | − | 0.0858723i | ||||
\(889\) | 5.25863 | + | 0.588894i | 0.176369 | + | 0.0197509i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.97433 | + | 11.4199i | 0.200148 | + | 0.382582i | ||||
\(892\) | − | 11.1120i | − | 0.372056i | ||||||
\(893\) | 28.1227i | 0.941090i | ||||||||
\(894\) | −20.2500 | + | 25.8295i | −0.677261 | + | 0.863869i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.294447 | − | 2.62932i | 0.00983678 | − | 0.0878393i | ||||
\(897\) | 14.3064 | − | 18.2483i | 0.477677 | − | 0.609293i | ||||
\(898\) | 32.3439 | 1.07933 | ||||||||
\(899\) | 16.7166 | 0.557530 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.7898i | − | 0.492721i | ||||||
\(902\) | 15.9644 | 0.531556 | ||||||||
\(903\) | −1.38731 | + | 1.41245i | −0.0461668 | + | 0.0470033i | ||||
\(904\) | 14.3439 | 0.477070 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.16797 | + | 5.61959i | 0.238140 | + | 0.186698i | ||||
\(907\) | 18.7730 | 0.623346 | 0.311673 | − | 0.950189i | \(-0.399111\pi\) | ||||
0.311673 | + | 0.950189i | \(0.399111\pi\) | |||||||
\(908\) | −7.24413 | −0.240405 | ||||||||
\(909\) | 7.38627 | + | 30.0530i | 0.244987 | + | 0.996797i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.73844i | 0.123860i | 0.998080 | + | 0.0619300i | \(0.0197255\pi\) | ||||
−0.998080 | + | 0.0619300i | \(0.980274\pi\) | |||||||
\(912\) | −3.71601 | − | 2.91330i | −0.123050 | − | 0.0964690i | ||||
\(913\) | − | 18.4943i | − | 0.612073i | ||||||
\(914\) | − | 10.9251i | − | 0.361370i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.1596i | 0.897380i | ||||||||
\(917\) | −45.4357 | − | 5.08816i | −1.50042 | − | 0.168026i | ||||
\(918\) | −5.55472 | + | 12.3093i | −0.183333 | + | 0.406269i | ||||
\(919\) | 24.4423 | 0.806279 | 0.403139 | − | 0.915139i | \(-0.367919\pi\) | ||||
0.403139 | + | 0.915139i | \(0.367919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.7638 | − | 10.7906i | −0.453532 | − | 0.355563i | ||||
\(922\) | 26.6729i | 0.878424i | ||||||||
\(923\) | −62.7961 | −2.06696 | ||||||||
\(924\) | 4.68178 | + | 4.59846i | 0.154019 | + | 0.151278i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.07491i | 0.265358i | ||||||||
\(927\) | 40.4199 | − | 9.93418i | 1.32756 | − | 0.326281i | ||||
\(928\) | −2.82660 | −0.0927878 | ||||||||
\(929\) | −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 | ||||
\(932\) | − | 5.38132i | − | 0.176271i | ||||||
\(933\) | 4.56797 | − | 5.82660i | 0.149549 | − | 0.190754i | ||||
\(934\) | − | 41.6228i | − | 1.36194i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.39122 | + | 13.7981i | 0.110846 | + | 0.451005i | ||||
\(937\) | − | 13.2241i | − | 0.432014i | −0.976392 | − | 0.216007i | \(-0.930697\pi\) | ||
0.976392 | − | 0.216007i | \(-0.0693034\pi\) | |||||||
\(938\) | 2.89341 | − | 25.8372i | 0.0944733 | − | 0.843616i | ||||
\(939\) | −1.25863 | − | 0.986749i | −0.0410739 | − | 0.0322013i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.3408 | −0.956484 | −0.478242 | − | 0.878228i | \(-0.658726\pi\) | ||||
−0.478242 | + | 0.878228i | \(0.658726\pi\) | |||||||
\(942\) | −6.72780 | + | 8.58154i | −0.219204 | + | 0.279602i | ||||
\(943\) | 31.5112i | 1.02615i | ||||||||
\(944\) | 10.7775 | 0.350777 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.618679 | −0.0201150 | ||||||||
\(947\) | − | 47.1094i | − | 1.53085i | −0.643524 | − | 0.765426i | \(-0.722529\pi\) | ||
0.643524 | − | 0.765426i | \(-0.277471\pi\) | |||||||
\(948\) | −17.6510 | + | 22.5145i | −0.573278 | + | 0.731236i | ||||
\(949\) | −35.9464 | −1.16687 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.4529 | − | 16.8187i | −0.695657 | − | 0.545385i | ||||
\(952\) | −0.765257 | + | 6.83350i | −0.0248021 | + | 0.221475i | ||||
\(953\) | − | 20.8876i | − | 0.676617i | −0.941035 | − | 0.338308i | \(-0.890145\pi\) | ||
0.941035 | − | 0.338308i | \(-0.109855\pi\) | |||||||
\(954\) | 4.07460 | + | 16.5786i | 0.131920 | + | 0.536752i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 2.51726i | − | 0.0814141i | ||||||
\(957\) | 4.32562 | − | 5.51747i | 0.139827 | − | 0.178355i | ||||
\(958\) | 21.3728i | 0.690524i | ||||||||
\(959\) | 0.894369 | − | 7.98643i | 0.0288807 | − | 0.257895i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.97579 | −0.128251 | ||||||||
\(962\) | 11.3413 | 0.365658 | ||||||||
\(963\) | 46.4651 | − | 11.4199i | 1.49732 | − | 0.368002i | ||||
\(964\) | − | 16.8077i | − | 0.541340i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.07664 | + | 9.24109i | −0.292036 | + | 0.297327i | ||||
\(967\) | 27.3335 | 0.878988 | 0.439494 | − | 0.898246i | \(-0.355158\pi\) | ||||
0.439494 | + | 0.898246i | \(0.355158\pi\) | |||||||
\(968\) | − | 8.94929i | − | 0.287641i | ||||||
\(969\) | 9.65779 | + | 7.57157i | 0.310253 | + | 0.243234i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.4555 | 0.784815 | 0.392407 | − | 0.919791i | \(-0.371642\pi\) | ||||
0.392407 | + | 0.919791i | \(0.371642\pi\) | |||||||
\(972\) | 2.83532 | − | 15.3284i | 0.0909430 | − | 0.491660i | ||||
\(973\) | −6.10912 | + | 54.5525i | −0.195849 | + | 1.74887i | ||||
\(974\) | 27.1094i | 0.868642i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 1.05058i | − | 0.0336282i | ||||||
\(977\) | − | 15.1124i | − | 0.483488i | −0.970340 | − | 0.241744i | \(-0.922281\pi\) | ||
0.970340 | − | 0.241744i | \(-0.0777193\pi\) | |||||||
\(978\) | 0.825250 | + | 0.646984i | 0.0263886 | + | 0.0206883i | ||||
\(979\) | − | 5.59059i | − | 0.178676i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.72519 | + | 31.4320i | 0.246646 | + | 1.00355i | ||||
\(982\) | 30.0000 | 0.957338 | ||||||||
\(983\) | 13.6670 | 0.435910 | 0.217955 | − | 0.975959i | \(-0.430061\pi\) | ||||
0.217955 | + | 0.975959i | \(0.430061\pi\) | |||||||
\(984\) | −15.1958 | − | 11.9133i | −0.484425 | − | 0.379782i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.34624 | 0.233952 | ||||||||
\(987\) | −33.1256 | + | 33.7258i | −1.05440 | + | 1.07350i | ||||
\(988\) | 12.9118 | 0.410780 | ||||||||
\(989\) | − | 1.22117i | − | 0.0388311i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.45560 | −0.109771 | −0.0548854 | − | 0.998493i | \(-0.517479\pi\) | ||||
−0.0548854 | + | 0.998493i | \(0.517479\pi\) | |||||||
\(992\) | 5.91403 | 0.187771 | ||||||||
\(993\) | −13.4707 | + | 17.1823i | −0.427479 | + | 0.545264i | ||||
\(994\) | 34.8611 | + | 3.90396i | 1.10573 | + | 0.123826i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.8012 | + | 17.6040i | −0.437309 | + | 0.557803i | ||||
\(997\) | − | 40.4199i | − | 1.28011i | −0.768329 | − | 0.640056i | \(-0.778911\pi\) | ||
0.768329 | − | 0.640056i | \(-0.221089\pi\) | |||||||
\(998\) | 8.50694i | 0.269283i | ||||||||
\(999\) | −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.b.d.251.11 | yes | 12 | |
3.2 | odd | 2 | inner | 1050.2.b.d.251.2 | ✓ | 12 | |
5.2 | odd | 4 | 1050.2.d.g.1049.3 | 12 | |||
5.3 | odd | 4 | 1050.2.d.h.1049.10 | 12 | |||
5.4 | even | 2 | 1050.2.b.e.251.2 | yes | 12 | ||
7.6 | odd | 2 | inner | 1050.2.b.d.251.8 | yes | 12 | |
15.2 | even | 4 | 1050.2.d.h.1049.4 | 12 | |||
15.8 | even | 4 | 1050.2.d.g.1049.9 | 12 | |||
15.14 | odd | 2 | 1050.2.b.e.251.11 | yes | 12 | ||
21.20 | even | 2 | inner | 1050.2.b.d.251.5 | yes | 12 | |
35.13 | even | 4 | 1050.2.d.h.1049.3 | 12 | |||
35.27 | even | 4 | 1050.2.d.g.1049.10 | 12 | |||
35.34 | odd | 2 | 1050.2.b.e.251.5 | yes | 12 | ||
105.62 | odd | 4 | 1050.2.d.h.1049.9 | 12 | |||
105.83 | odd | 4 | 1050.2.d.g.1049.4 | 12 | |||
105.104 | even | 2 | 1050.2.b.e.251.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.b.d.251.2 | ✓ | 12 | 3.2 | odd | 2 | inner | |
1050.2.b.d.251.5 | yes | 12 | 21.20 | even | 2 | inner | |
1050.2.b.d.251.8 | yes | 12 | 7.6 | odd | 2 | inner | |
1050.2.b.d.251.11 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.2.b.e.251.2 | yes | 12 | 5.4 | even | 2 | ||
1050.2.b.e.251.5 | yes | 12 | 35.34 | odd | 2 | ||
1050.2.b.e.251.8 | yes | 12 | 105.104 | even | 2 | ||
1050.2.b.e.251.11 | yes | 12 | 15.14 | odd | 2 | ||
1050.2.d.g.1049.3 | 12 | 5.2 | odd | 4 | |||
1050.2.d.g.1049.4 | 12 | 105.83 | odd | 4 | |||
1050.2.d.g.1049.9 | 12 | 15.8 | even | 4 | |||
1050.2.d.g.1049.10 | 12 | 35.27 | even | 4 | |||
1050.2.d.h.1049.3 | 12 | 35.13 | even | 4 | |||
1050.2.d.h.1049.4 | 12 | 15.2 | even | 4 | |||
1050.2.d.h.1049.9 | 12 | 105.62 | odd | 4 | |||
1050.2.d.h.1049.10 | 12 | 5.3 | odd | 4 |