Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(257,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.p (of order \(12\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.293 |
Dual form | 450.2.p.f.407.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | − | 0.965926i | 0.183013 | − | 0.683013i | ||||
\(3\) | −0.448288 | + | 1.67303i | −0.258819 | + | 0.965926i | ||||
\(4\) | −0.866025 | − | 0.500000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | 3.34607 | + | 0.896575i | 1.26469 | + | 0.338874i | 0.827996 | − | 0.560734i | \(-0.189481\pi\) |
0.436698 | + | 0.899608i | \(0.356148\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.59808 | − | 1.50000i | −0.866025 | − | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 0.866025i | −0.452267 | + | 0.261116i | −0.708787 | − | 0.705422i | \(-0.750757\pi\) |
0.256520 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(12\) | 1.22474 | − | 1.22474i | 0.353553 | − | 0.353553i | ||||
\(13\) | 3.34607 | − | 0.896575i | 0.928032 | − | 0.248665i | 0.237016 | − | 0.971506i | \(-0.423830\pi\) |
0.691015 | + | 0.722840i | \(0.257164\pi\) | |||||||
\(14\) | 1.73205 | − | 3.00000i | 0.462910 | − | 0.801784i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 2.12132 | + | 2.12132i | 0.514496 | + | 0.514496i | 0.915901 | − | 0.401405i | \(-0.131478\pi\) |
−0.401405 | + | 0.915901i | \(0.631478\pi\) | |||||||
\(18\) | −2.12132 | + | 2.12132i | −0.500000 | + | 0.500000i | ||||
\(19\) | 7.00000i | 1.60591i | 0.596040 | + | 0.802955i | \(0.296740\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | + | 5.19615i | −0.654654 | + | 1.13389i | ||||
\(22\) | 0.448288 | + | 1.67303i | 0.0955753 | + | 0.356692i | ||||
\(23\) | 1.55291 | + | 5.79555i | 0.323805 | + | 1.20846i | 0.915508 | + | 0.402300i | \(0.131789\pi\) |
−0.591703 | + | 0.806156i | \(0.701544\pi\) | |||||||
\(24\) | −0.866025 | − | 1.50000i | −0.176777 | − | 0.306186i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.46410i | − | 0.679366i | ||||||
\(27\) | 3.67423 | − | 3.67423i | 0.707107 | − | 0.707107i | ||||
\(28\) | −2.44949 | − | 2.44949i | −0.462910 | − | 0.462910i | ||||
\(29\) | 1.73205 | + | 3.00000i | 0.321634 | + | 0.557086i | 0.980825 | − | 0.194889i | \(-0.0624347\pi\) |
−0.659192 | + | 0.751975i | \(0.729101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.718421 | − | 1.24434i | −0.243204 | − | 0.969975i | \(-0.578198\pi\) |
0.961625 | − | 0.274367i | \(-0.0884683\pi\) | |||||||
\(32\) | 0.965926 | − | 0.258819i | 0.170753 | − | 0.0457532i | ||||
\(33\) | −0.776457 | − | 2.89778i | −0.135164 | − | 0.504438i | ||||
\(34\) | 2.59808 | − | 1.50000i | 0.445566 | − | 0.257248i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | 4.89898 | − | 4.89898i | 0.805387 | − | 0.805387i | −0.178545 | − | 0.983932i | \(-0.557139\pi\) |
0.983932 | + | 0.178545i | \(0.0571389\pi\) | |||||||
\(38\) | 6.76148 | + | 1.81173i | 1.09686 | + | 0.293902i | ||||
\(39\) | 6.00000i | 0.960769i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.5000 | − | 6.06218i | −1.63982 | − | 0.946753i | −0.980892 | − | 0.194551i | \(-0.937675\pi\) |
−0.658932 | − | 0.752202i | \(-0.728992\pi\) | |||||||
\(42\) | 4.24264 | + | 4.24264i | 0.654654 | + | 0.654654i | ||||
\(43\) | −1.34486 | + | 5.01910i | −0.205090 | + | 0.765405i | 0.784332 | + | 0.620341i | \(0.213006\pi\) |
−0.989422 | + | 0.145065i | \(0.953661\pi\) | |||||||
\(44\) | 1.73205 | 0.261116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −1.55291 | + | 5.79555i | −0.226516 | + | 0.845369i | 0.755276 | + | 0.655407i | \(0.227503\pi\) |
−0.981792 | + | 0.189961i | \(0.939164\pi\) | |||||||
\(48\) | −1.67303 | + | 0.448288i | −0.241481 | + | 0.0647048i | ||||
\(49\) | 4.33013 | + | 2.50000i | 0.618590 | + | 0.357143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | + | 2.59808i | −0.630126 | + | 0.363803i | ||||
\(52\) | −3.34607 | − | 0.896575i | −0.464016 | − | 0.124333i | ||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | −2.59808 | − | 4.50000i | −0.353553 | − | 0.612372i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | + | 1.73205i | −0.400892 | + | 0.231455i | ||||
\(57\) | −11.7112 | − | 3.13801i | −1.55119 | − | 0.415640i | ||||
\(58\) | 3.34607 | − | 0.896575i | 0.439360 | − | 0.117726i | ||||
\(59\) | 6.06218 | − | 10.5000i | 0.789228 | − | 1.36698i | −0.137212 | − | 0.990542i | \(-0.543814\pi\) |
0.926440 | − | 0.376442i | \(-0.122853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | −5.65685 | − | 5.65685i | −0.718421 | − | 0.718421i | ||||
\(63\) | −7.34847 | − | 7.34847i | −0.925820 | − | 0.925820i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | 0.448288 | + | 1.67303i | 0.0547671 | + | 0.204393i | 0.987888 | − | 0.155170i | \(-0.0495924\pi\) |
−0.933121 | + | 0.359563i | \(0.882926\pi\) | |||||||
\(68\) | −0.776457 | − | 2.89778i | −0.0941593 | − | 0.351407i | ||||
\(69\) | −10.3923 | −1.25109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.8564i | − | 1.64445i | −0.569160 | − | 0.822226i | \(-0.692732\pi\) | ||
0.569160 | − | 0.822226i | \(-0.307268\pi\) | |||||||
\(72\) | 2.89778 | − | 0.776457i | 0.341506 | − | 0.0915064i | ||||
\(73\) | −6.12372 | − | 6.12372i | −0.716728 | − | 0.716728i | 0.251206 | − | 0.967934i | \(-0.419173\pi\) |
−0.967934 | + | 0.251206i | \(0.919173\pi\) | |||||||
\(74\) | −3.46410 | − | 6.00000i | −0.402694 | − | 0.697486i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.50000 | − | 6.06218i | 0.401478 | − | 0.695379i | ||||
\(77\) | −5.79555 | + | 1.55291i | −0.660465 | + | 0.176971i | ||||
\(78\) | 5.79555 | + | 1.55291i | 0.656217 | + | 0.175833i | ||||
\(79\) | −3.46410 | + | 2.00000i | −0.389742 | + | 0.225018i | −0.682048 | − | 0.731307i | \(-0.738911\pi\) |
0.292306 | + | 0.956325i | \(0.405577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | −8.57321 | + | 8.57321i | −0.946753 | + | 0.946753i | ||||
\(83\) | −11.5911 | − | 3.10583i | −1.27229 | − | 0.340909i | −0.441382 | − | 0.897319i | \(-0.645512\pi\) |
−0.830908 | + | 0.556410i | \(0.812178\pi\) | |||||||
\(84\) | 5.19615 | − | 3.00000i | 0.566947 | − | 0.327327i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.50000 | + | 2.59808i | 0.485247 | + | 0.280158i | ||||
\(87\) | −5.79555 | + | 1.55291i | −0.621349 | + | 0.166490i | ||||
\(88\) | 0.448288 | − | 1.67303i | 0.0477876 | − | 0.178346i | ||||
\(89\) | −6.92820 | −0.734388 | −0.367194 | − | 0.930144i | \(-0.619682\pi\) | ||||
−0.367194 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 1.25794 | ||||||||
\(92\) | 1.55291 | − | 5.79555i | 0.161903 | − | 0.604228i | ||||
\(93\) | 9.79796 | + | 9.79796i | 1.01600 | + | 1.01600i | ||||
\(94\) | 5.19615 | + | 3.00000i | 0.535942 | + | 0.309426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.73205i | 0.176777i | ||||||||
\(97\) | −8.36516 | − | 2.24144i | −0.849354 | − | 0.227584i | −0.192215 | − | 0.981353i | \(-0.561567\pi\) |
−0.657139 | + | 0.753769i | \(0.728234\pi\) | |||||||
\(98\) | 3.53553 | − | 3.53553i | 0.357143 | − | 0.357143i | ||||
\(99\) | 5.19615 | 0.522233 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 3.46410i | −0.597022 | + | 0.344691i | −0.767869 | − | 0.640607i | \(-0.778683\pi\) |
0.170847 | + | 0.985298i | \(0.445350\pi\) | |||||||
\(102\) | 1.34486 | + | 5.01910i | 0.133161 | + | 0.496965i | ||||
\(103\) | 16.7303 | − | 4.48288i | 1.64849 | − | 0.441711i | 0.689299 | − | 0.724477i | \(-0.257919\pi\) |
0.959189 | + | 0.282766i | \(0.0912520\pi\) | |||||||
\(104\) | −1.73205 | + | 3.00000i | −0.169842 | + | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.12132 | + | 2.12132i | 0.205076 | + | 0.205076i | 0.802171 | − | 0.597095i | \(-0.203678\pi\) |
−0.597095 | + | 0.802171i | \(0.703678\pi\) | |||||||
\(108\) | −5.01910 | + | 1.34486i | −0.482963 | + | 0.129410i | ||||
\(109\) | − | 4.00000i | − | 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | + | 10.3923i | 0.569495 | + | 0.986394i | ||||
\(112\) | 0.896575 | + | 3.34607i | 0.0847184 | + | 0.316173i | ||||
\(113\) | −4.65874 | − | 17.3867i | −0.438258 | − | 1.63560i | −0.733148 | − | 0.680069i | \(-0.761950\pi\) |
0.294891 | − | 0.955531i | \(-0.404717\pi\) | |||||||
\(114\) | −6.06218 | + | 10.5000i | −0.567775 | + | 0.983415i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.46410i | − | 0.321634i | ||||||
\(117\) | −10.0382 | − | 2.68973i | −0.928032 | − | 0.248665i | ||||
\(118\) | −8.57321 | − | 8.57321i | −0.789228 | − | 0.789228i | ||||
\(119\) | 5.19615 | + | 9.00000i | 0.476331 | + | 0.825029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | + | 6.92820i | −0.363636 | + | 0.629837i | ||||
\(122\) | 3.86370 | − | 1.03528i | 0.349803 | − | 0.0937295i | ||||
\(123\) | 14.8492 | − | 14.8492i | 1.33891 | − | 1.33891i | ||||
\(124\) | −6.92820 | + | 4.00000i | −0.622171 | + | 0.359211i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.00000 | + | 5.19615i | −0.801784 | + | 0.462910i | ||||
\(127\) | 7.34847 | − | 7.34847i | 0.652071 | − | 0.652071i | −0.301420 | − | 0.953491i | \(-0.597461\pi\) |
0.953491 | + | 0.301420i | \(0.0974607\pi\) | |||||||
\(128\) | −0.965926 | − | 0.258819i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | −7.79423 | − | 4.50000i | −0.686244 | − | 0.396203i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 1.73205i | 0.262111 | + | 0.151330i | 0.625297 | − | 0.780387i | \(-0.284978\pi\) |
−0.363186 | + | 0.931717i | \(0.618311\pi\) | |||||||
\(132\) | −0.776457 | + | 2.89778i | −0.0675819 | + | 0.252219i | ||||
\(133\) | −6.27603 | + | 23.4225i | −0.544201 | + | 2.03098i | ||||
\(134\) | 1.73205 | 0.149626 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | −0.776457 | + | 2.89778i | −0.0663372 | + | 0.247574i | −0.991130 | − | 0.132898i | \(-0.957572\pi\) |
0.924793 | + | 0.380472i | \(0.124238\pi\) | |||||||
\(138\) | −2.68973 | + | 10.0382i | −0.228965 | + | 0.854508i | ||||
\(139\) | 4.33013 | + | 2.50000i | 0.367277 | + | 0.212047i | 0.672268 | − | 0.740308i | \(-0.265320\pi\) |
−0.304991 | + | 0.952355i | \(0.598654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.00000 | − | 5.19615i | −0.757937 | − | 0.437595i | ||||
\(142\) | −13.3843 | − | 3.58630i | −1.12318 | − | 0.300956i | ||||
\(143\) | −4.24264 | + | 4.24264i | −0.354787 | + | 0.354787i | ||||
\(144\) | − | 3.00000i | − | 0.250000i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.50000 | + | 4.33013i | −0.620704 | + | 0.358364i | ||||
\(147\) | −6.12372 | + | 6.12372i | −0.505076 | + | 0.505076i | ||||
\(148\) | −6.69213 | + | 1.79315i | −0.550090 | + | 0.147396i | ||||
\(149\) | 5.19615 | − | 9.00000i | 0.425685 | − | 0.737309i | −0.570799 | − | 0.821090i | \(-0.693366\pi\) |
0.996484 | + | 0.0837813i | \(0.0266997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | −4.94975 | − | 4.94975i | −0.401478 | − | 0.401478i | ||||
\(153\) | −2.32937 | − | 8.69333i | −0.188319 | − | 0.702814i | ||||
\(154\) | 6.00000i | 0.483494i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(158\) | 1.03528 | + | 3.86370i | 0.0823622 | + | 0.307380i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.7846i | 1.63806i | ||||||||
\(162\) | 8.69333 | − | 2.32937i | 0.683013 | − | 0.183013i | ||||
\(163\) | 2.44949 | + | 2.44949i | 0.191859 | + | 0.191859i | 0.796499 | − | 0.604640i | \(-0.206683\pi\) |
−0.604640 | + | 0.796499i | \(0.706683\pi\) | |||||||
\(164\) | 6.06218 | + | 10.5000i | 0.473377 | + | 0.819912i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(168\) | −1.55291 | − | 5.79555i | −0.119810 | − | 0.447137i | ||||
\(169\) | −0.866025 | + | 0.500000i | −0.0666173 | + | 0.0384615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5000 | − | 18.1865i | 0.802955 | − | 1.39076i | ||||
\(172\) | 3.67423 | − | 3.67423i | 0.280158 | − | 0.280158i | ||||
\(173\) | 5.79555 | + | 1.55291i | 0.440628 | + | 0.118066i | 0.472311 | − | 0.881432i | \(-0.343420\pi\) |
−0.0316829 | + | 0.999498i | \(0.510087\pi\) | |||||||
\(174\) | 6.00000i | 0.454859i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | − | 0.866025i | −0.113067 | − | 0.0652791i | ||||
\(177\) | 14.8492 | + | 14.8492i | 1.11614 | + | 1.11614i | ||||
\(178\) | −1.79315 | + | 6.69213i | −0.134402 | + | 0.501596i | ||||
\(179\) | −3.46410 | −0.258919 | −0.129460 | − | 0.991585i | \(-0.541324\pi\) | ||||
−0.129460 | + | 0.991585i | \(0.541324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 3.10583 | − | 11.5911i | 0.230219 | − | 0.859190i | ||||
\(183\) | −6.69213 | + | 1.79315i | −0.494697 | + | 0.132554i | ||||
\(184\) | −5.19615 | − | 3.00000i | −0.383065 | − | 0.221163i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.0000 | − | 6.92820i | 0.879883 | − | 0.508001i | ||||
\(187\) | −5.01910 | − | 1.34486i | −0.367033 | − | 0.0983461i | ||||
\(188\) | 4.24264 | − | 4.24264i | 0.309426 | − | 0.309426i | ||||
\(189\) | 15.5885 | − | 9.00000i | 1.13389 | − | 0.654654i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.0000 | − | 12.1244i | 1.51951 | − | 0.877288i | 0.519771 | − | 0.854306i | \(-0.326017\pi\) |
0.999736 | − | 0.0229818i | \(-0.00731599\pi\) | |||||||
\(192\) | 1.67303 | + | 0.448288i | 0.120741 | + | 0.0323524i | ||||
\(193\) | −8.36516 | + | 2.24144i | −0.602138 | + | 0.161342i | −0.546995 | − | 0.837136i | \(-0.684228\pi\) |
−0.0551431 | + | 0.998478i | \(0.517561\pi\) | |||||||
\(194\) | −4.33013 | + | 7.50000i | −0.310885 | + | 0.538469i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.50000 | − | 4.33013i | −0.178571 | − | 0.309295i | ||||
\(197\) | 16.9706 | + | 16.9706i | 1.20910 | + | 1.20910i | 0.971318 | + | 0.237785i | \(0.0764212\pi\) |
0.237785 | + | 0.971318i | \(0.423579\pi\) | |||||||
\(198\) | 1.34486 | − | 5.01910i | 0.0955753 | − | 0.356692i | ||||
\(199\) | − | 10.0000i | − | 0.708881i | −0.935079 | − | 0.354441i | \(-0.884671\pi\) | ||
0.935079 | − | 0.354441i | \(-0.115329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.00000 | −0.211604 | ||||||||
\(202\) | 1.79315 | + | 6.69213i | 0.126166 | + | 0.470857i | ||||
\(203\) | 3.10583 | + | 11.5911i | 0.217986 | + | 0.813536i | ||||
\(204\) | 5.19615 | 0.363803 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 17.3205i | − | 1.20678i | ||||||
\(207\) | 4.65874 | − | 17.3867i | 0.323805 | − | 1.20846i | ||||
\(208\) | 2.44949 | + | 2.44949i | 0.169842 | + | 0.169842i | ||||
\(209\) | −6.06218 | − | 10.5000i | −0.419330 | − | 0.726300i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.1822 | + | 6.21166i | 1.58842 | + | 0.425616i | ||||
\(214\) | 2.59808 | − | 1.50000i | 0.177601 | − | 0.102538i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 19.5959 | − | 19.5959i | 1.33026 | − | 1.33026i | ||||
\(218\) | −3.86370 | − | 1.03528i | −0.261683 | − | 0.0701178i | ||||
\(219\) | 12.9904 | − | 7.50000i | 0.877809 | − | 0.506803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.00000 | + | 5.19615i | 0.605406 | + | 0.349531i | ||||
\(222\) | 11.5911 | − | 3.10583i | 0.777944 | − | 0.208450i | ||||
\(223\) | −2.68973 | + | 10.0382i | −0.180117 | + | 0.672207i | 0.815506 | + | 0.578749i | \(0.196459\pi\) |
−0.995623 | + | 0.0934584i | \(0.970208\pi\) | |||||||
\(224\) | 3.46410 | 0.231455 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | −0.776457 | + | 2.89778i | −0.0515353 | + | 0.192332i | −0.986894 | − | 0.161367i | \(-0.948410\pi\) |
0.935359 | + | 0.353699i | \(0.115076\pi\) | |||||||
\(228\) | 8.57321 | + | 8.57321i | 0.567775 | + | 0.567775i | ||||
\(229\) | −19.0526 | − | 11.0000i | −1.25903 | − | 0.726900i | −0.286143 | − | 0.958187i | \(-0.592373\pi\) |
−0.972886 | + | 0.231287i | \(0.925707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 10.3923i | − | 0.683763i | ||||||
\(232\) | −3.34607 | − | 0.896575i | −0.219680 | − | 0.0588631i | ||||
\(233\) | −2.12132 | + | 2.12132i | −0.138972 | + | 0.138972i | −0.773171 | − | 0.634198i | \(-0.781330\pi\) |
0.634198 | + | 0.773171i | \(0.281330\pi\) | |||||||
\(234\) | −5.19615 | + | 9.00000i | −0.339683 | + | 0.588348i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.5000 | + | 6.06218i | −0.683492 | + | 0.394614i | ||||
\(237\) | −1.79315 | − | 6.69213i | −0.116478 | − | 0.434701i | ||||
\(238\) | 10.0382 | − | 2.68973i | 0.650680 | − | 0.174349i | ||||
\(239\) | −5.19615 | + | 9.00000i | −0.336111 | + | 0.582162i | −0.983698 | − | 0.179830i | \(-0.942445\pi\) |
0.647586 | + | 0.761992i | \(0.275778\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 5.65685 | + | 5.65685i | 0.363636 | + | 0.363636i | ||||
\(243\) | −15.0573 | + | 4.03459i | −0.965926 | + | 0.258819i | ||||
\(244\) | − | 4.00000i | − | 0.256074i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.5000 | − | 18.1865i | −0.669456 | − | 1.15953i | ||||
\(247\) | 6.27603 | + | 23.4225i | 0.399334 | + | 1.49034i | ||||
\(248\) | 2.07055 | + | 7.72741i | 0.131480 | + | 0.490691i | ||||
\(249\) | 10.3923 | − | 18.0000i | 0.658586 | − | 1.14070i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9808i | 1.63989i | 0.572441 | + | 0.819946i | \(0.305996\pi\) | ||||
−0.572441 | + | 0.819946i | \(0.694004\pi\) | |||||||
\(252\) | 2.68973 | + | 10.0382i | 0.169437 | + | 0.632347i | ||||
\(253\) | −7.34847 | − | 7.34847i | −0.461994 | − | 0.461994i | ||||
\(254\) | −5.19615 | − | 9.00000i | −0.326036 | − | 0.564710i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 26.0800 | − | 6.98811i | 1.62683 | − | 0.435907i | 0.673829 | − | 0.738887i | \(-0.264648\pi\) |
0.952997 | + | 0.302981i | \(0.0979818\pi\) | |||||||
\(258\) | −6.36396 | + | 6.36396i | −0.396203 | + | 0.396203i | ||||
\(259\) | 20.7846 | − | 12.0000i | 1.29149 | − | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 10.3923i | − | 0.643268i | ||||||
\(262\) | 2.44949 | − | 2.44949i | 0.151330 | − | 0.151330i | ||||
\(263\) | −5.79555 | − | 1.55291i | −0.357369 | − | 0.0957568i | 0.0756674 | − | 0.997133i | \(-0.475891\pi\) |
−0.433037 | + | 0.901376i | \(0.642558\pi\) | |||||||
\(264\) | 2.59808 | + | 1.50000i | 0.159901 | + | 0.0923186i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.0000 | + | 12.1244i | 1.28759 | + | 0.743392i | ||||
\(267\) | 3.10583 | − | 11.5911i | 0.190074 | − | 0.709364i | ||||
\(268\) | 0.448288 | − | 1.67303i | 0.0273835 | − | 0.102197i | ||||
\(269\) | −6.92820 | −0.422420 | −0.211210 | − | 0.977441i | \(-0.567740\pi\) | ||||
−0.211210 | + | 0.977441i | \(0.567740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | −0.776457 | + | 2.89778i | −0.0470796 | + | 0.175704i | ||||
\(273\) | −5.37945 | + | 20.0764i | −0.325579 | + | 1.21508i | ||||
\(274\) | 2.59808 | + | 1.50000i | 0.156956 | + | 0.0906183i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.00000 | + | 5.19615i | 0.541736 | + | 0.312772i | ||||
\(277\) | 10.0382 | + | 2.68973i | 0.603137 | + | 0.161610i | 0.547450 | − | 0.836838i | \(-0.315599\pi\) |
0.0556866 | + | 0.998448i | \(0.482265\pi\) | |||||||
\(278\) | 3.53553 | − | 3.53553i | 0.212047 | − | 0.212047i | ||||
\(279\) | −20.7846 | + | 12.0000i | −1.24434 | + | 0.718421i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | − | 10.3923i | 1.07379 | − | 0.619953i | 0.144575 | − | 0.989494i | \(-0.453818\pi\) |
0.929214 | + | 0.369541i | \(0.120485\pi\) | |||||||
\(282\) | −7.34847 | + | 7.34847i | −0.437595 | + | 0.437595i | ||||
\(283\) | 30.1146 | − | 8.06918i | 1.79013 | − | 0.479663i | 0.797759 | − | 0.602977i | \(-0.206019\pi\) |
0.992368 | + | 0.123314i | \(0.0393522\pi\) | |||||||
\(284\) | −6.92820 | + | 12.0000i | −0.411113 | + | 0.712069i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | + | 5.19615i | 0.177394 | + | 0.307255i | ||||
\(287\) | −29.6985 | − | 29.6985i | −1.75305 | − | 1.75305i | ||||
\(288\) | −2.89778 | − | 0.776457i | −0.170753 | − | 0.0457532i | ||||
\(289\) | − | 8.00000i | − | 0.470588i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.50000 | − | 12.9904i | 0.439658 | − | 0.761510i | ||||
\(292\) | 2.24144 | + | 8.36516i | 0.131170 | + | 0.489534i | ||||
\(293\) | −1.55291 | − | 5.79555i | −0.0907222 | − | 0.338580i | 0.905614 | − | 0.424103i | \(-0.139411\pi\) |
−0.996336 | + | 0.0855230i | \(0.972744\pi\) | |||||||
\(294\) | 4.33013 | + | 7.50000i | 0.252538 | + | 0.437409i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.92820i | 0.402694i | ||||||||
\(297\) | −2.32937 | + | 8.69333i | −0.135164 | + | 0.504438i | ||||
\(298\) | −7.34847 | − | 7.34847i | −0.425685 | − | 0.425685i | ||||
\(299\) | 10.3923 | + | 18.0000i | 0.601003 | + | 1.04097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.00000 | + | 15.5885i | −0.518751 | + | 0.898504i | ||||
\(302\) | −9.65926 | + | 2.58819i | −0.555828 | + | 0.148934i | ||||
\(303\) | −3.10583 | − | 11.5911i | −0.178425 | − | 0.665892i | ||||
\(304\) | −6.06218 | + | 3.50000i | −0.347690 | + | 0.200739i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.00000 | −0.514496 | ||||||||
\(307\) | −3.67423 | + | 3.67423i | −0.209700 | + | 0.209700i | −0.804140 | − | 0.594440i | \(-0.797374\pi\) |
0.594440 | + | 0.804140i | \(0.297374\pi\) | |||||||
\(308\) | 5.79555 | + | 1.55291i | 0.330232 | + | 0.0884855i | ||||
\(309\) | 30.0000i | 1.70664i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | − | 1.73205i | −0.170114 | − | 0.0982156i | 0.412525 | − | 0.910946i | \(-0.364647\pi\) |
−0.582640 | + | 0.812731i | \(0.697980\pi\) | |||||||
\(312\) | −4.24264 | − | 4.24264i | −0.240192 | − | 0.240192i | ||||
\(313\) | 2.24144 | − | 8.36516i | 0.126694 | − | 0.472827i | −0.873201 | − | 0.487361i | \(-0.837960\pi\) |
0.999894 | + | 0.0145337i | \(0.00462638\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | −1.55291 | + | 5.79555i | −0.0872204 | + | 0.325511i | −0.995725 | − | 0.0923631i | \(-0.970558\pi\) |
0.908505 | + | 0.417874i | \(0.137225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.19615 | − | 3.00000i | −0.290929 | − | 0.167968i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | + | 2.59808i | −0.251166 | + | 0.145010i | ||||
\(322\) | 20.0764 | + | 5.37945i | 1.11881 | + | 0.299785i | ||||
\(323\) | −14.8492 | + | 14.8492i | −0.826234 | + | 0.826234i | ||||
\(324\) | − | 9.00000i | − | 0.500000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.00000 | − | 1.73205i | 0.166155 | − | 0.0959294i | ||||
\(327\) | 6.69213 | + | 1.79315i | 0.370076 | + | 0.0991615i | ||||
\(328\) | 11.7112 | − | 3.13801i | 0.646644 | − | 0.173268i | ||||
\(329\) | −10.3923 | + | 18.0000i | −0.572946 | + | 0.992372i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | + | 24.2487i | 0.769510 | + | 1.33283i | 0.937829 | + | 0.347097i | \(0.112833\pi\) |
−0.168320 | + | 0.985732i | \(0.553834\pi\) | |||||||
\(332\) | 8.48528 | + | 8.48528i | 0.465690 | + | 0.465690i | ||||
\(333\) | −20.0764 | + | 5.37945i | −1.10018 | + | 0.294792i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.00000 | −0.327327 | ||||||||
\(337\) | −3.13801 | − | 11.7112i | −0.170939 | − | 0.637951i | −0.997208 | − | 0.0746760i | \(-0.976208\pi\) |
0.826269 | − | 0.563275i | \(-0.190459\pi\) | |||||||
\(338\) | 0.258819 | + | 0.965926i | 0.0140779 | + | 0.0525394i | ||||
\(339\) | 31.1769 | 1.69330 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8564i | 0.750366i | ||||||||
\(342\) | −14.8492 | − | 14.8492i | −0.802955 | − | 0.802955i | ||||
\(343\) | −4.89898 | − | 4.89898i | −0.264520 | − | 0.264520i | ||||
\(344\) | −2.59808 | − | 4.50000i | −0.140079 | − | 0.242624i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | −14.4889 | + | 3.88229i | −0.777804 | + | 0.208412i | −0.625816 | − | 0.779970i | \(-0.715234\pi\) |
−0.151988 | + | 0.988382i | \(0.548567\pi\) | |||||||
\(348\) | 5.79555 | + | 1.55291i | 0.310674 | + | 0.0832449i | ||||
\(349\) | −6.92820 | + | 4.00000i | −0.370858 | + | 0.214115i | −0.673833 | − | 0.738883i | \(-0.735353\pi\) |
0.302975 | + | 0.952998i | \(0.402020\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | − | 15.5885i | 0.480384 | − | 0.832050i | ||||
\(352\) | −1.22474 | + | 1.22474i | −0.0652791 | + | 0.0652791i | ||||
\(353\) | 20.2844 | + | 5.43520i | 1.07963 | + | 0.289287i | 0.754445 | − | 0.656363i | \(-0.227906\pi\) |
0.325187 | + | 0.945650i | \(0.394573\pi\) | |||||||
\(354\) | 18.1865 | − | 10.5000i | 0.966603 | − | 0.558069i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | + | 3.46410i | 0.317999 | + | 0.183597i | ||||
\(357\) | −17.3867 | + | 4.65874i | −0.920200 | + | 0.246567i | ||||
\(358\) | −0.896575 | + | 3.34607i | −0.0473855 | + | 0.176845i | ||||
\(359\) | −24.2487 | −1.27980 | −0.639899 | − | 0.768459i | \(-0.721024\pi\) | ||||
−0.639899 | + | 0.768459i | \(0.721024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.0000 | −1.57895 | ||||||||
\(362\) | −0.517638 | + | 1.93185i | −0.0272065 | + | 0.101536i | ||||
\(363\) | −9.79796 | − | 9.79796i | −0.514259 | − | 0.514259i | ||||
\(364\) | −10.3923 | − | 6.00000i | −0.544705 | − | 0.314485i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.92820i | 0.362143i | ||||||||
\(367\) | −13.3843 | − | 3.58630i | −0.698653 | − | 0.187203i | −0.108026 | − | 0.994148i | \(-0.534453\pi\) |
−0.590627 | + | 0.806945i | \(0.701120\pi\) | |||||||
\(368\) | −4.24264 | + | 4.24264i | −0.221163 | + | 0.221163i | ||||
\(369\) | 18.1865 | + | 31.5000i | 0.946753 | + | 1.63982i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.58630 | − | 13.3843i | −0.185941 | − | 0.693942i | ||||
\(373\) | −16.7303 | + | 4.48288i | −0.866263 | + | 0.232115i | −0.664471 | − | 0.747314i | \(-0.731343\pi\) |
−0.201792 | + | 0.979428i | \(0.564677\pi\) | |||||||
\(374\) | −2.59808 | + | 4.50000i | −0.134343 | + | 0.232689i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | 8.48528 | + | 8.48528i | 0.437014 | + | 0.437014i | ||||
\(378\) | −4.65874 | − | 17.3867i | −0.239620 | − | 0.894274i | ||||
\(379\) | 1.00000i | 0.0513665i | 0.999670 | + | 0.0256833i | \(0.00817614\pi\) | ||||
−0.999670 | + | 0.0256833i | \(0.991824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.00000 | + | 15.5885i | 0.461084 | + | 0.798621i | ||||
\(382\) | −6.27603 | − | 23.4225i | −0.321110 | − | 1.19840i | ||||
\(383\) | 3.10583 | + | 11.5911i | 0.158700 | + | 0.592278i | 0.998760 | + | 0.0497839i | \(0.0158533\pi\) |
−0.840060 | + | 0.542494i | \(0.817480\pi\) | |||||||
\(384\) | 0.866025 | − | 1.50000i | 0.0441942 | − | 0.0765466i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.66025i | 0.440795i | ||||||||
\(387\) | 11.0227 | − | 11.0227i | 0.560316 | − | 0.560316i | ||||
\(388\) | 6.12372 | + | 6.12372i | 0.310885 | + | 0.310885i | ||||
\(389\) | −5.19615 | − | 9.00000i | −0.263455 | − | 0.456318i | 0.703702 | − | 0.710495i | \(-0.251529\pi\) |
−0.967158 | + | 0.254177i | \(0.918196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | −4.82963 | + | 1.29410i | −0.243933 | + | 0.0653617i | ||||
\(393\) | −4.24264 | + | 4.24264i | −0.214013 | + | 0.214013i | ||||
\(394\) | 20.7846 | − | 12.0000i | 1.04711 | − | 0.604551i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.50000 | − | 2.59808i | −0.226134 | − | 0.130558i | ||||
\(397\) | −14.6969 | + | 14.6969i | −0.737618 | + | 0.737618i | −0.972117 | − | 0.234498i | \(-0.924655\pi\) |
0.234498 | + | 0.972117i | \(0.424655\pi\) | |||||||
\(398\) | −9.65926 | − | 2.58819i | −0.484175 | − | 0.129734i | ||||
\(399\) | −36.3731 | − | 21.0000i | −1.82093 | − | 1.05131i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.50000 | − | 2.59808i | −0.224719 | − | 0.129742i | 0.383414 | − | 0.923576i | \(-0.374748\pi\) |
−0.608134 | + | 0.793835i | \(0.708081\pi\) | |||||||
\(402\) | −0.776457 | + | 2.89778i | −0.0387262 | + | 0.144528i | ||||
\(403\) | 7.17260 | − | 26.7685i | 0.357293 | − | 1.33344i | ||||
\(404\) | 6.92820 | 0.344691 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | −3.10583 | + | 11.5911i | −0.153950 | + | 0.574550i | ||||
\(408\) | 1.34486 | − | 5.01910i | 0.0665807 | − | 0.248482i | ||||
\(409\) | −6.06218 | − | 3.50000i | −0.299755 | − | 0.173064i | 0.342578 | − | 0.939490i | \(-0.388700\pi\) |
−0.642333 | + | 0.766426i | \(0.722033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.50000 | − | 2.59808i | −0.221969 | − | 0.128154i | ||||
\(412\) | −16.7303 | − | 4.48288i | −0.824244 | − | 0.220856i | ||||
\(413\) | 29.6985 | − | 29.6985i | 1.46137 | − | 1.46137i | ||||
\(414\) | −15.5885 | − | 9.00000i | −0.766131 | − | 0.442326i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.00000 | − | 1.73205i | 0.147087 | − | 0.0849208i | ||||
\(417\) | −6.12372 | + | 6.12372i | −0.299880 | + | 0.299880i | ||||
\(418\) | −11.7112 | + | 3.13801i | −0.572815 | + | 0.153485i | ||||
\(419\) | 5.19615 | − | 9.00000i | 0.253849 | − | 0.439679i | −0.710734 | − | 0.703461i | \(-0.751637\pi\) |
0.964582 | + | 0.263783i | \(0.0849701\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0000 | − | 24.2487i | −0.682318 | − | 1.18181i | −0.974272 | − | 0.225377i | \(-0.927639\pi\) |
0.291953 | − | 0.956433i | \(-0.405695\pi\) | |||||||
\(422\) | −2.82843 | − | 2.82843i | −0.137686 | − | 0.137686i | ||||
\(423\) | 12.7279 | − | 12.7279i | 0.618853 | − | 0.618853i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.0000 | − | 20.7846i | 0.581402 | − | 1.00702i | ||||
\(427\) | 3.58630 | + | 13.3843i | 0.173553 | + | 0.647710i | ||||
\(428\) | −0.776457 | − | 2.89778i | −0.0375315 | − | 0.140069i | ||||
\(429\) | −5.19615 | − | 9.00000i | −0.250873 | − | 0.434524i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.46410i | − | 0.166860i | −0.996514 | − | 0.0834300i | \(-0.973413\pi\) | ||
0.996514 | − | 0.0834300i | \(-0.0265875\pi\) | |||||||
\(432\) | 5.01910 | + | 1.34486i | 0.241481 | + | 0.0647048i | ||||
\(433\) | −18.3712 | − | 18.3712i | −0.882862 | − | 0.882862i | 0.110962 | − | 0.993825i | \(-0.464607\pi\) |
−0.993825 | + | 0.110962i | \(0.964607\pi\) | |||||||
\(434\) | −13.8564 | − | 24.0000i | −0.665129 | − | 1.15204i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | + | 3.46410i | −0.0957826 | + | 0.165900i | ||||
\(437\) | −40.5689 | + | 10.8704i | −1.94067 | + | 0.520002i | ||||
\(438\) | −3.88229 | − | 14.4889i | −0.185503 | − | 0.692306i | ||||
\(439\) | −13.8564 | + | 8.00000i | −0.661330 | + | 0.381819i | −0.792784 | − | 0.609503i | \(-0.791369\pi\) |
0.131453 | + | 0.991322i | \(0.458036\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.50000 | − | 12.9904i | −0.357143 | − | 0.618590i | ||||
\(442\) | 7.34847 | − | 7.34847i | 0.349531 | − | 0.349531i | ||||
\(443\) | 26.0800 | + | 6.98811i | 1.23910 | + | 0.332015i | 0.818116 | − | 0.575054i | \(-0.195019\pi\) |
0.420982 | + | 0.907069i | \(0.361685\pi\) | |||||||
\(444\) | − | 12.0000i | − | 0.569495i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.00000 | + | 5.19615i | 0.426162 | + | 0.246045i | ||||
\(447\) | 12.7279 | + | 12.7279i | 0.602010 | + | 0.602010i | ||||
\(448\) | 0.896575 | − | 3.34607i | 0.0423592 | − | 0.158087i | ||||
\(449\) | 39.8372 | 1.88003 | 0.940016 | − | 0.341130i | \(-0.110810\pi\) | ||||
0.940016 | + | 0.341130i | \(0.110810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0000 | 0.988851 | ||||||||
\(452\) | −4.65874 | + | 17.3867i | −0.219129 | + | 0.817800i | ||||
\(453\) | 16.7303 | − | 4.48288i | 0.786059 | − | 0.210624i | ||||
\(454\) | 2.59808 | + | 1.50000i | 0.121934 | + | 0.0703985i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.5000 | − | 6.06218i | 0.491708 | − | 0.283887i | ||||
\(457\) | −25.0955 | − | 6.72432i | −1.17392 | − | 0.314550i | −0.381406 | − | 0.924408i | \(-0.624560\pi\) |
−0.792511 | + | 0.609857i | \(0.791227\pi\) | |||||||
\(458\) | −15.5563 | + | 15.5563i | −0.726900 | + | 0.726900i | ||||
\(459\) | 15.5885 | 0.727607 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | − | 8.66025i | 0.698620 | − | 0.403348i | −0.108213 | − | 0.994128i | \(-0.534513\pi\) |
0.806833 | + | 0.590779i | \(0.201180\pi\) | |||||||
\(462\) | −10.0382 | − | 2.68973i | −0.467019 | − | 0.125137i | ||||
\(463\) | 13.3843 | − | 3.58630i | 0.622019 | − | 0.166670i | 0.0659737 | − | 0.997821i | \(-0.478985\pi\) |
0.556046 | + | 0.831152i | \(0.312318\pi\) | |||||||
\(464\) | −1.73205 | + | 3.00000i | −0.0804084 | + | 0.139272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.50000 | + | 2.59808i | 0.0694862 | + | 0.120354i | ||||
\(467\) | −6.36396 | − | 6.36396i | −0.294489 | − | 0.294489i | 0.544362 | − | 0.838851i | \(-0.316772\pi\) |
−0.838851 | + | 0.544362i | \(0.816772\pi\) | |||||||
\(468\) | 7.34847 | + | 7.34847i | 0.339683 | + | 0.339683i | ||||
\(469\) | 6.00000i | 0.277054i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.13801 | + | 11.7112i | 0.144439 | + | 0.539053i | ||||
\(473\) | −2.32937 | − | 8.69333i | −0.107105 | − | 0.399720i | ||||
\(474\) | −6.92820 | −0.318223 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 10.3923i | − | 0.476331i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.34847 | + | 7.34847i | 0.336111 | + | 0.336111i | ||||
\(479\) | 8.66025 | + | 15.0000i | 0.395697 | + | 0.685367i | 0.993190 | − | 0.116507i | \(-0.0371697\pi\) |
−0.597493 | + | 0.801874i | \(0.703836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | − | 20.7846i | 0.547153 | − | 0.947697i | ||||
\(482\) | 0.965926 | − | 0.258819i | 0.0439967 | − | 0.0117889i | ||||
\(483\) | −34.7733 | − | 9.31749i | −1.58224 | − | 0.423960i | ||||
\(484\) | 6.92820 | − | 4.00000i | 0.314918 | − | 0.181818i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.5885i | 0.707107i | ||||||||
\(487\) | −17.1464 | + | 17.1464i | −0.776979 | + | 0.776979i | −0.979316 | − | 0.202337i | \(-0.935146\pi\) |
0.202337 | + | 0.979316i | \(0.435146\pi\) | |||||||
\(488\) | −3.86370 | − | 1.03528i | −0.174902 | − | 0.0468648i | ||||
\(489\) | −5.19615 | + | 3.00000i | −0.234978 | + | 0.135665i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.5000 | − | 11.2583i | −0.880023 | − | 0.508081i | −0.00935679 | − | 0.999956i | \(-0.502978\pi\) |
−0.870666 | + | 0.491875i | \(0.836312\pi\) | |||||||
\(492\) | −20.2844 | + | 5.43520i | −0.914493 | + | 0.245038i | ||||
\(493\) | −2.68973 | + | 10.0382i | −0.121139 | + | 0.452098i | ||||
\(494\) | 24.2487 | 1.09100 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 12.4233 | − | 46.3644i | 0.557262 | − | 2.07973i | ||||
\(498\) | −14.6969 | − | 14.6969i | −0.658586 | − | 0.658586i | ||||
\(499\) | 16.4545 | + | 9.50000i | 0.736604 | + | 0.425278i | 0.820833 | − | 0.571168i | \(-0.193510\pi\) |
−0.0842294 | + | 0.996446i | \(0.526843\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.0955 | + | 6.72432i | 1.12007 | + | 0.300121i | ||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | 10.3923 | 0.462910 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00000 | + | 5.19615i | −0.400099 | + | 0.230997i | ||||
\(507\) | −0.448288 | − | 1.67303i | −0.0199092 | − | 0.0743020i | ||||
\(508\) | −10.0382 | + | 2.68973i | −0.445373 | + | 0.119337i | ||||
\(509\) | −10.3923 | + | 18.0000i | −0.460631 | + | 0.797836i | −0.998992 | − | 0.0448779i | \(-0.985710\pi\) |
0.538362 | + | 0.842714i | \(0.319043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0000 | − | 25.9808i | −0.663561 | − | 1.14932i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 25.7196 | + | 25.7196i | 1.13555 | + | 1.13555i | ||||
\(514\) | − | 27.0000i | − | 1.19092i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.50000 | + | 7.79423i | 0.198101 | + | 0.343122i | ||||
\(517\) | −2.68973 | − | 10.0382i | −0.118294 | − | 0.441479i | ||||
\(518\) | −6.21166 | − | 23.1822i | −0.272925 | − | 1.01857i | ||||
\(519\) | −5.19615 | + | 9.00000i | −0.228086 | + | 0.395056i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.19615i | 0.227648i | 0.993501 | + | 0.113824i | \(0.0363099\pi\) | ||||
−0.993501 | + | 0.113824i | \(0.963690\pi\) | |||||||
\(522\) | −10.0382 | − | 2.68973i | −0.439360 | − | 0.117726i | ||||
\(523\) | 12.2474 | + | 12.2474i | 0.535544 | + | 0.535544i | 0.922217 | − | 0.386673i | \(-0.126376\pi\) |
−0.386673 | + | 0.922217i | \(0.626376\pi\) | |||||||
\(524\) | −1.73205 | − | 3.00000i | −0.0756650 | − | 0.131056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | + | 5.19615i | −0.130806 | + | 0.226563i | ||||
\(527\) | 23.1822 | − | 6.21166i | 1.00983 | − | 0.270584i | ||||
\(528\) | 2.12132 | − | 2.12132i | 0.0923186 | − | 0.0923186i | ||||
\(529\) | −11.2583 | + | 6.50000i | −0.489493 | + | 0.282609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.5000 | + | 18.1865i | −1.36698 | + | 0.789228i | ||||
\(532\) | 17.1464 | − | 17.1464i | 0.743392 | − | 0.743392i | ||||
\(533\) | −40.5689 | − | 10.8704i | −1.75723 | − | 0.470849i | ||||
\(534\) | −10.3923 | − | 6.00000i | −0.449719 | − | 0.259645i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.50000 | − | 0.866025i | −0.0647901 | − | 0.0374066i | ||||
\(537\) | 1.55291 | − | 5.79555i | 0.0670132 | − | 0.250097i | ||||
\(538\) | −1.79315 | + | 6.69213i | −0.0773082 | + | 0.288518i | ||||
\(539\) | −8.66025 | −0.373024 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | −7.24693 | + | 27.0459i | −0.311282 | + | 1.16172i | ||||
\(543\) | 0.896575 | − | 3.34607i | 0.0384757 | − | 0.143593i | ||||
\(544\) | 2.59808 | + | 1.50000i | 0.111392 | + | 0.0643120i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 18.0000 | + | 10.3923i | 0.770329 | + | 0.444750i | ||||
\(547\) | 21.7494 | + | 5.82774i | 0.929938 | + | 0.249176i | 0.691828 | − | 0.722062i | \(-0.256805\pi\) |
0.238110 | + | 0.971238i | \(0.423472\pi\) | |||||||
\(548\) | 2.12132 | − | 2.12132i | 0.0906183 | − | 0.0906183i | ||||
\(549\) | − | 12.0000i | − | 0.512148i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.0000 | + | 12.1244i | −0.894630 | + | 0.516515i | ||||
\(552\) | 7.34847 | − | 7.34847i | 0.312772 | − | 0.312772i | ||||
\(553\) | −13.3843 | + | 3.58630i | −0.569157 | + | 0.152505i | ||||
\(554\) | 5.19615 | − | 9.00000i | 0.220763 | − | 0.382373i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.50000 | − | 4.33013i | −0.106024 | − | 0.183638i | ||||
\(557\) | −12.7279 | − | 12.7279i | −0.539299 | − | 0.539299i | 0.384024 | − | 0.923323i | \(-0.374538\pi\) |
−0.923323 | + | 0.384024i | \(0.874538\pi\) | |||||||
\(558\) | 6.21166 | + | 23.1822i | 0.262960 | + | 0.981382i | ||||
\(559\) | 18.0000i | 0.761319i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.50000 | − | 7.79423i | 0.189990 | − | 0.329073i | ||||
\(562\) | −5.37945 | − | 20.0764i | −0.226919 | − | 0.846871i | ||||
\(563\) | 3.88229 | + | 14.4889i | 0.163619 | + | 0.610634i | 0.998212 | + | 0.0597675i | \(0.0190359\pi\) |
−0.834593 | + | 0.550866i | \(0.814297\pi\) | |||||||
\(564\) | 5.19615 | + | 9.00000i | 0.218797 | + | 0.378968i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 31.1769i | − | 1.31046i | ||||||
\(567\) | 8.06918 | + | 30.1146i | 0.338874 | + | 1.26469i | ||||
\(568\) | 9.79796 | + | 9.79796i | 0.411113 | + | 0.411113i | ||||
\(569\) | −9.52628 | − | 16.5000i | −0.399362 | − | 0.691716i | 0.594285 | − | 0.804255i | \(-0.297435\pi\) |
−0.993647 | + | 0.112539i | \(0.964102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | + | 4.33013i | −0.104622 | + | 0.181210i | −0.913584 | − | 0.406651i | \(-0.866697\pi\) |
0.808962 | + | 0.587861i | \(0.200030\pi\) | |||||||
\(572\) | 5.79555 | − | 1.55291i | 0.242324 | − | 0.0649306i | ||||
\(573\) | 10.8704 | + | 40.5689i | 0.454117 | + | 1.69479i | ||||
\(574\) | −36.3731 | + | 21.0000i | −1.51818 | + | 0.876523i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.50000 | + | 2.59808i | −0.0625000 | + | 0.108253i | ||||
\(577\) | −23.2702 | + | 23.2702i | −0.968749 | + | 0.968749i | −0.999526 | − | 0.0307771i | \(-0.990202\pi\) |
0.0307771 | + | 0.999526i | \(0.490202\pi\) | |||||||
\(578\) | −7.72741 | − | 2.07055i | −0.321418 | − | 0.0861236i | ||||
\(579\) | − | 15.0000i | − | 0.623379i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36.0000 | − | 20.7846i | −1.49353 | − | 0.862291i | ||||
\(582\) | −10.6066 | − | 10.6066i | −0.439658 | − | 0.439658i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.66025 | 0.358364 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 8.54103 | − | 31.8756i | 0.352526 | − | 1.31564i | −0.531043 | − | 0.847345i | \(-0.678200\pi\) |
0.883569 | − | 0.468300i | \(-0.155133\pi\) | |||||||
\(588\) | 8.36516 | − | 2.24144i | 0.344974 | − | 0.0924354i | ||||
\(589\) | 48.4974 | + | 28.0000i | 1.99830 | + | 1.15372i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.0000 | + | 20.7846i | −1.48084 | + | 0.854965i | ||||
\(592\) | 6.69213 | + | 1.79315i | 0.275045 | + | 0.0736980i | ||||
\(593\) | 12.7279 | − | 12.7279i | 0.522673 | − | 0.522673i | −0.395705 | − | 0.918378i | \(-0.629500\pi\) |
0.918378 | + | 0.395705i | \(0.129500\pi\) | |||||||
\(594\) | 7.79423 | + | 4.50000i | 0.319801 | + | 0.184637i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.00000 | + | 5.19615i | −0.368654 | + | 0.212843i | ||||
\(597\) | 16.7303 | + | 4.48288i | 0.684727 | + | 0.183472i | ||||
\(598\) | 20.0764 | − | 5.37945i | 0.820985 | − | 0.219982i | ||||
\(599\) | 6.92820 | − | 12.0000i | 0.283079 | − | 0.490307i | −0.689063 | − | 0.724702i | \(-0.741978\pi\) |
0.972141 | + | 0.234395i | \(0.0753109\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5000 | + | 25.1147i | 0.591467 | + | 1.02445i | 0.994035 | + | 0.109061i | \(0.0347845\pi\) |
−0.402568 | + | 0.915390i | \(0.631882\pi\) | |||||||
\(602\) | 12.7279 | + | 12.7279i | 0.518751 | + | 0.518751i | ||||
\(603\) | 1.34486 | − | 5.01910i | 0.0547671 | − | 0.204393i | ||||
\(604\) | 10.0000i | 0.406894i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.0000 | −0.487467 | ||||||||
\(607\) | −3.58630 | − | 13.3843i | −0.145564 | − | 0.543250i | −0.999730 | − | 0.0232502i | \(-0.992599\pi\) |
0.854166 | − | 0.520000i | \(-0.174068\pi\) | |||||||
\(608\) | 1.81173 | + | 6.76148i | 0.0734755 | + | 0.274214i | ||||
\(609\) | −20.7846 | −0.842235 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7846i | 0.840855i | ||||||||
\(612\) | −2.32937 | + | 8.69333i | −0.0941593 | + | 0.351407i | ||||
\(613\) | −4.89898 | − | 4.89898i | −0.197868 | − | 0.197868i | 0.601218 | − | 0.799085i | \(-0.294683\pi\) |
−0.799085 | + | 0.601218i | \(0.794683\pi\) | |||||||
\(614\) | 2.59808 | + | 4.50000i | 0.104850 | + | 0.181605i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | − | 5.19615i | 0.120873 | − | 0.209359i | ||||
\(617\) | 43.4667 | − | 11.6469i | 1.74990 | − | 0.468885i | 0.765297 | − | 0.643678i | \(-0.222592\pi\) |
0.984605 | + | 0.174793i | \(0.0559256\pi\) | |||||||
\(618\) | 28.9778 | + | 7.76457i | 1.16566 | + | 0.312337i | ||||
\(619\) | −11.2583 | + | 6.50000i | −0.452510 | + | 0.261257i | −0.708890 | − | 0.705319i | \(-0.750804\pi\) |
0.256379 | + | 0.966576i | \(0.417470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.0000 | + | 15.5885i | 1.08347 | + | 0.625543i | ||||
\(622\) | −2.44949 | + | 2.44949i | −0.0982156 | + | 0.0982156i | ||||
\(623\) | −23.1822 | − | 6.21166i | −0.928776 | − | 0.248865i | ||||
\(624\) | −5.19615 | + | 3.00000i | −0.208013 | + | 0.120096i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.50000 | − | 4.33013i | −0.299760 | − | 0.173067i | ||||
\(627\) | 20.2844 | − | 5.43520i | 0.810083 | − | 0.217061i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.7846 | 0.828737 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 1.03528 | − | 3.86370i | 0.0411811 | − | 0.153690i | ||||
\(633\) | 4.89898 | + | 4.89898i | 0.194717 | + | 0.194717i | ||||
\(634\) | 5.19615 | + | 3.00000i | 0.206366 | + | 0.119145i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.7303 | + | 4.48288i | 0.662880 | + | 0.177618i | ||||
\(638\) | −4.24264 | + | 4.24264i | −0.167968 | + | 0.167968i | ||||
\(639\) | −20.7846 | + | 36.0000i | −0.822226 | + | 1.42414i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.5000 | − | 11.2583i | 0.770204 | − | 0.444677i | −0.0627436 | − | 0.998030i | \(-0.519985\pi\) |
0.832947 | + | 0.553352i | \(0.186652\pi\) | |||||||
\(642\) | 1.34486 | + | 5.01910i | 0.0530775 | + | 0.198088i | ||||
\(643\) | −35.1337 | + | 9.41404i | −1.38554 | + | 0.371254i | −0.873129 | − | 0.487489i | \(-0.837913\pi\) |
−0.512408 | + | 0.858742i | \(0.671246\pi\) | |||||||
\(644\) | 10.3923 | − | 18.0000i | 0.409514 | − | 0.709299i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.5000 | + | 18.1865i | 0.413117 | + | 0.715540i | ||||
\(647\) | 21.2132 | + | 21.2132i | 0.833977 | + | 0.833977i | 0.988058 | − | 0.154081i | \(-0.0492417\pi\) |
−0.154081 | + | 0.988058i | \(0.549242\pi\) | |||||||
\(648\) | −8.69333 | − | 2.32937i | −0.341506 | − | 0.0915064i | ||||
\(649\) | 21.0000i | 0.824322i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.0000 | + | 41.5692i | 0.940634 | + | 1.62923i | ||||
\(652\) | −0.896575 | − | 3.34607i | −0.0351126 | − | 0.131042i | ||||
\(653\) | −4.65874 | − | 17.3867i | −0.182311 | − | 0.680393i | −0.995190 | − | 0.0979610i | \(-0.968768\pi\) |
0.812880 | − | 0.582432i | \(-0.197899\pi\) | |||||||
\(654\) | 3.46410 | − | 6.00000i | 0.135457 | − | 0.234619i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 12.1244i | − | 0.473377i | ||||||
\(657\) | 6.72432 | + | 25.0955i | 0.262341 | + | 0.979068i | ||||
\(658\) | 14.6969 | + | 14.6969i | 0.572946 | + | 0.572946i | ||||
\(659\) | −5.19615 | − | 9.00000i | −0.202413 | − | 0.350590i | 0.746892 | − | 0.664945i | \(-0.231545\pi\) |
−0.949306 | + | 0.314355i | \(0.898212\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0000 | − | 27.7128i | 0.622328 | − | 1.07790i | −0.366723 | − | 0.930330i | \(-0.619520\pi\) |
0.989051 | − | 0.147573i | \(-0.0471463\pi\) | |||||||
\(662\) | 27.0459 | − | 7.24693i | 1.05117 | − | 0.281660i | ||||
\(663\) | −12.7279 | + | 12.7279i | −0.494312 | + | 0.494312i | ||||
\(664\) | 10.3923 | − | 6.00000i | 0.403300 | − | 0.232845i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 20.7846i | 0.805387i | ||||||||
\(667\) | −14.6969 | + | 14.6969i | −0.569068 | + | 0.569068i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.5885 | − | 9.00000i | −0.602685 | − | 0.347960i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | − | 3.46410i | −0.231627 | − | 0.133730i | ||||
\(672\) | −1.55291 | + | 5.79555i | −0.0599050 | + | 0.223568i | ||||
\(673\) | 1.79315 | − | 6.69213i | 0.0691209 | − | 0.257963i | −0.922715 | − | 0.385483i | \(-0.874035\pi\) |
0.991836 | + | 0.127520i | \(0.0407017\pi\) | |||||||
\(674\) | −12.1244 | −0.467013 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −3.10583 | + | 11.5911i | −0.119367 | + | 0.445483i | −0.999576 | − | 0.0291023i | \(-0.990735\pi\) |
0.880210 | + | 0.474585i | \(0.157402\pi\) | |||||||
\(678\) | 8.06918 | − | 30.1146i | 0.309895 | − | 1.15654i | ||||
\(679\) | −25.9808 | − | 15.0000i | −0.997050 | − | 0.575647i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | 13.3843 | + | 3.58630i | 0.512510 | + | 0.137327i | ||||
\(683\) | −23.3345 | + | 23.3345i | −0.892871 | + | 0.892871i | −0.994792 | − | 0.101922i | \(-0.967501\pi\) |
0.101922 | + | 0.994792i | \(0.467501\pi\) | |||||||
\(684\) | −18.1865 | + | 10.5000i | −0.695379 | + | 0.401478i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.00000 | + | 3.46410i | −0.229081 | + | 0.132260i | ||||
\(687\) | 26.9444 | − | 26.9444i | 1.02799 | − | 1.02799i | ||||
\(688\) | −5.01910 | + | 1.34486i | −0.191351 | + | 0.0512724i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | + | 6.92820i | 0.152167 | + | 0.263561i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | −4.24264 | − | 4.24264i | −0.161281 | − | 0.161281i | ||||
\(693\) | 17.3867 | + | 4.65874i | 0.660465 | + | 0.176971i | ||||
\(694\) | 15.0000i | 0.569392i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.00000 | − | 5.19615i | 0.113715 | − | 0.196960i | ||||
\(697\) | −9.41404 | − | 35.1337i | −0.356582 | − | 1.33078i | ||||
\(698\) | 2.07055 | + | 7.72741i | 0.0783716 | + | 0.292487i | ||||
\(699\) | −2.59808 | − | 4.50000i | −0.0982683 | − | 0.170206i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 17.3205i | − | 0.654187i | −0.944992 | − | 0.327093i | \(-0.893931\pi\) | ||
0.944992 | − | 0.327093i | \(-0.106069\pi\) | |||||||
\(702\) | −12.7279 | − | 12.7279i | −0.480384 | − | 0.480384i | ||||
\(703\) | 34.2929 | + | 34.2929i | 1.29338 | + | 1.29338i | ||||
\(704\) | 0.866025 | + | 1.50000i | 0.0326396 | + | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.5000 | − | 18.1865i | 0.395173 | − | 0.684459i | ||||
\(707\) | −23.1822 | + | 6.21166i | −0.871857 | + | 0.233613i | ||||
\(708\) | −5.43520 | − | 20.2844i | −0.204267 | − | 0.762336i | ||||
\(709\) | 34.6410 | − | 20.0000i | 1.30097 | − | 0.751116i | 0.320400 | − | 0.947282i | \(-0.396183\pi\) |
0.980571 | + | 0.196167i | \(0.0628493\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 4.89898 | − | 4.89898i | 0.183597 | − | 0.183597i | ||||
\(713\) | 46.3644 | + | 12.4233i | 1.73636 | + | 0.465257i | ||||
\(714\) | 18.0000i | 0.673633i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.00000 | + | 1.73205i | 0.112115 | + | 0.0647298i | ||||
\(717\) | −12.7279 | − | 12.7279i | −0.475333 | − | 0.475333i | ||||
\(718\) | −6.27603 | + | 23.4225i | −0.234219 | + | 0.874118i | ||||
\(719\) | −27.7128 | −1.03351 | −0.516757 | − | 0.856132i | \(-0.672861\pi\) | ||||
−0.516757 | + | 0.856132i | \(0.672861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 60.0000 | 2.23452 | ||||||||
\(722\) | −7.76457 | + | 28.9778i | −0.288967 | + | 1.07844i | ||||
\(723\) | −1.67303 | + | 0.448288i | −0.0622208 | + | 0.0166720i | ||||
\(724\) | 1.73205 | + | 1.00000i | 0.0643712 | + | 0.0371647i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.0000 | + | 6.92820i | −0.445362 | + | 0.257130i | ||||
\(727\) | 10.0382 | + | 2.68973i | 0.372296 | + | 0.0997564i | 0.440115 | − | 0.897941i | \(-0.354938\pi\) |
−0.0678194 | + | 0.997698i | \(0.521604\pi\) | |||||||
\(728\) | −8.48528 | + | 8.48528i | −0.314485 | + | 0.314485i | ||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.5000 | + | 7.79423i | −0.499316 | + | 0.288280i | ||||
\(732\) | 6.69213 | + | 1.79315i | 0.247348 | + | 0.0662768i | ||||
\(733\) | −50.1910 | + | 13.4486i | −1.85385 | + | 0.496737i | −0.999728 | − | 0.0233418i | \(-0.992569\pi\) |
−0.854119 | + | 0.520078i | \(0.825903\pi\) | |||||||
\(734\) | −6.92820 | + | 12.0000i | −0.255725 | + | 0.442928i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | −2.12132 | − | 2.12132i | −0.0781398 | − | 0.0781398i | ||||
\(738\) | 35.1337 | − | 9.41404i | 1.29329 | − | 0.346536i | ||||
\(739\) | − | 41.0000i | − | 1.50821i | −0.656754 | − | 0.754105i | \(-0.728071\pi\) | ||
0.656754 | − | 0.754105i | \(-0.271929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −42.0000 | −1.54291 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.65874 | + | 17.3867i | 0.170913 | + | 0.637855i | 0.997212 | + | 0.0746233i | \(0.0237754\pi\) |
−0.826299 | + | 0.563232i | \(0.809558\pi\) | |||||||
\(744\) | −13.8564 | −0.508001 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.3205i | 0.634149i | ||||||||
\(747\) | 25.4558 | + | 25.4558i | 0.931381 | + | 0.931381i | ||||
\(748\) | 3.67423 | + | 3.67423i | 0.134343 | + | 0.134343i | ||||
\(749\) | 5.19615 | + | 9.00000i | 0.189863 | + | 0.328853i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000 | − | 17.3205i | 0.364905 | − | 0.632034i | −0.623856 | − | 0.781540i | \(-0.714435\pi\) |
0.988761 | + | 0.149505i | \(0.0477681\pi\) | |||||||
\(752\) | −5.79555 | + | 1.55291i | −0.211342 | + | 0.0566290i | ||||
\(753\) | −43.4667 | − | 11.6469i | −1.58401 | − | 0.424435i | ||||
\(754\) | 10.3923 | − | 6.00000i | 0.378465 | − | 0.218507i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.0000 | −0.654654 | ||||||||
\(757\) | 26.9444 | − | 26.9444i | 0.979310 | − | 0.979310i | −0.0204799 | − | 0.999790i | \(-0.506519\pi\) |
0.999790 | + | 0.0204799i | \(0.00651940\pi\) | |||||||
\(758\) | 0.965926 | + | 0.258819i | 0.0350840 | + | 0.00940073i | ||||
\(759\) | 15.5885 | − | 9.00000i | 0.565825 | − | 0.326679i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | − | 17.3205i | −1.08750 | − | 0.627868i | −0.154590 | − | 0.987979i | \(-0.549406\pi\) |
−0.932910 | + | 0.360111i | \(0.882739\pi\) | |||||||
\(762\) | 17.3867 | − | 4.65874i | 0.629852 | − | 0.168768i | ||||
\(763\) | 3.58630 | − | 13.3843i | 0.129833 | − | 0.484543i | ||||
\(764\) | −24.2487 | −0.877288 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | 10.8704 | − | 40.5689i | 0.392507 | − | 1.46486i | ||||
\(768\) | −1.22474 | − | 1.22474i | −0.0441942 | − | 0.0441942i | ||||
\(769\) | −12.1244 | − | 7.00000i | −0.437215 | − | 0.252426i | 0.265200 | − | 0.964193i | \(-0.414562\pi\) |
−0.702416 | + | 0.711767i | \(0.747895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 46.7654i | 1.68421i | ||||||||
\(772\) | 8.36516 | + | 2.24144i | 0.301069 | + | 0.0806711i | ||||
\(773\) | 38.1838 | − | 38.1838i | 1.37337 | − | 1.37337i | 0.517985 | − | 0.855390i | \(-0.326682\pi\) |
0.855390 | − | 0.517985i | \(-0.173318\pi\) | |||||||
\(774\) | −7.79423 | − | 13.5000i | −0.280158 | − | 0.485247i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.50000 | − | 4.33013i | 0.269234 | − | 0.155443i | ||||
\(777\) | 10.7589 | + | 40.1528i | 0.385974 | + | 1.44047i | ||||
\(778\) | −10.0382 | + | 2.68973i | −0.359887 | + | 0.0964314i | ||||
\(779\) | 42.4352 | − | 73.5000i | 1.52040 | − | 2.63341i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.0000 | + | 20.7846i | 0.429394 | + | 0.743732i | ||||
\(782\) | 12.7279 | + | 12.7279i | 0.455150 | + | 0.455150i | ||||
\(783\) | 17.3867 | + | 4.65874i | 0.621349 | + | 0.166490i | ||||
\(784\) | 5.00000i | 0.178571i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.00000 | + | 5.19615i | 0.107006 | + | 0.185341i | ||||
\(787\) | 4.48288 | + | 16.7303i | 0.159797 | + | 0.596372i | 0.998647 | + | 0.0520081i | \(0.0165622\pi\) |
−0.838849 | + | 0.544364i | \(0.816771\pi\) | |||||||
\(788\) | −6.21166 | − | 23.1822i | −0.221281 | − | 0.825832i | ||||
\(789\) | 5.19615 | − | 9.00000i | 0.184988 | − | 0.320408i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 62.3538i | − | 2.21705i | ||||||
\(792\) | −3.67423 | + | 3.67423i | −0.130558 | + | 0.130558i | ||||
\(793\) | 9.79796 | + | 9.79796i | 0.347936 | + | 0.347936i | ||||
\(794\) | 10.3923 | + | 18.0000i | 0.368809 | + | 0.638796i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.00000 | + | 8.66025i | −0.177220 | + | 0.306955i | ||||
\(797\) | 23.1822 | − | 6.21166i | 0.821156 | − | 0.220028i | 0.176304 | − | 0.984336i | \(-0.443586\pi\) |
0.644852 | + | 0.764308i | \(0.276919\pi\) | |||||||
\(798\) | −29.6985 | + | 29.6985i | −1.05131 | + | 1.05131i | ||||
\(799\) | −15.5885 | + | 9.00000i | −0.551480 | + | 0.318397i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.0000 | + | 10.3923i | 0.635999 | + | 0.367194i | ||||
\(802\) | −3.67423 | + | 3.67423i | −0.129742 | + | 0.129742i | ||||
\(803\) | 14.4889 | + | 3.88229i | 0.511302 | + | 0.137003i | ||||
\(804\) | 2.59808 | + | 1.50000i | 0.0916271 | + | 0.0529009i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.0000 | − | 13.8564i | −0.845364 | − | 0.488071i | ||||
\(807\) | 3.10583 | − | 11.5911i | 0.109330 | − | 0.408026i | ||||
\(808\) | 1.79315 | − | 6.69213i | 0.0630828 | − | 0.235428i | ||||
\(809\) | 12.1244 | 0.426270 | 0.213135 | − | 0.977023i | \(-0.431633\pi\) | ||||
0.213135 | + | 0.977023i | \(0.431633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.0000 | −1.43970 | −0.719852 | − | 0.694127i | \(-0.755791\pi\) | ||||
−0.719852 | + | 0.694127i | \(0.755791\pi\) | |||||||
\(812\) | 3.10583 | − | 11.5911i | 0.108993 | − | 0.406768i | ||||
\(813\) | 12.5521 | − | 46.8449i | 0.440220 | − | 1.64292i | ||||
\(814\) | 10.3923 | + | 6.00000i | 0.364250 | + | 0.210300i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.50000 | − | 2.59808i | −0.157532 | − | 0.0909509i | ||||
\(817\) | −35.1337 | − | 9.41404i | −1.22917 | − | 0.329356i | ||||
\(818\) | −4.94975 | + | 4.94975i | −0.173064 | + | 0.173064i | ||||
\(819\) | −31.1769 | − | 18.0000i | −1.08941 | − | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.0000 | − | 8.66025i | 0.523504 | − | 0.302245i | −0.214863 | − | 0.976644i | \(-0.568931\pi\) |
0.738367 | + | 0.674399i | \(0.235597\pi\) | |||||||
\(822\) | −3.67423 | + | 3.67423i | −0.128154 | + | 0.128154i | ||||
\(823\) | −13.3843 | + | 3.58630i | −0.466546 | + | 0.125011i | −0.484431 | − | 0.874829i | \(-0.660973\pi\) |
0.0178851 | + | 0.999840i | \(0.494307\pi\) | |||||||
\(824\) | −8.66025 | + | 15.0000i | −0.301694 | + | 0.522550i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.0000 | − | 36.3731i | −0.730683 | − | 1.26558i | ||||
\(827\) | −25.4558 | − | 25.4558i | −0.885186 | − | 0.885186i | 0.108870 | − | 0.994056i | \(-0.465277\pi\) |
−0.994056 | + | 0.108870i | \(0.965277\pi\) | |||||||
\(828\) | −12.7279 | + | 12.7279i | −0.442326 | + | 0.442326i | ||||
\(829\) | 34.0000i | 1.18087i | 0.807086 | + | 0.590434i | \(0.201044\pi\) | ||||
−0.807086 | + | 0.590434i | \(0.798956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.00000 | + | 15.5885i | −0.312207 | + | 0.540758i | ||||
\(832\) | −0.896575 | − | 3.34607i | −0.0310832 | − | 0.116004i | ||||
\(833\) | 3.88229 | + | 14.4889i | 0.134513 | + | 0.502010i | ||||
\(834\) | 4.33013 | + | 7.50000i | 0.149940 | + | 0.259704i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.1244i | 0.419330i | ||||||||
\(837\) | −10.7589 | − | 40.1528i | −0.371882 | − | 1.38788i | ||||
\(838\) | −7.34847 | − | 7.34847i | −0.253849 | − | 0.253849i | ||||
\(839\) | −17.3205 | − | 30.0000i | −0.597970 | − | 1.03572i | −0.993120 | − | 0.117098i | \(-0.962641\pi\) |
0.395150 | − | 0.918617i | \(-0.370693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.50000 | − | 14.7224i | 0.293103 | − | 0.507670i | ||||
\(842\) | −27.0459 | + | 7.24693i | −0.932064 | + | 0.249746i | ||||
\(843\) | 9.31749 | + | 34.7733i | 0.320911 | + | 1.19766i | ||||
\(844\) | −3.46410 | + | 2.00000i | −0.119239 | + | 0.0688428i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | − | 15.5885i | −0.309426 | − | 0.535942i | ||||
\(847\) | −19.5959 | + | 19.5959i | −0.673324 | + | 0.673324i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 54.0000i | 1.85328i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.0000 | + | 20.7846i | 1.23406 | + | 0.712487i | ||||
\(852\) | −16.9706 | − | 16.9706i | −0.581402 | − | 0.581402i | ||||
\(853\) | 9.86233 | − | 36.8067i | 0.337680 | − | 1.26024i | −0.563255 | − | 0.826283i | \(-0.690451\pi\) |
0.900935 | − | 0.433955i | \(-0.142882\pi\) | |||||||
\(854\) | 13.8564 | 0.474156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | −10.8704 | + | 40.5689i | −0.371326 | + | 1.38581i | 0.487314 | + | 0.873227i | \(0.337977\pi\) |
−0.858640 | + | 0.512580i | \(0.828690\pi\) | |||||||
\(858\) | −10.0382 | + | 2.68973i | −0.342698 | + | 0.0918257i | ||||
\(859\) | 11.2583 | + | 6.50000i | 0.384129 | + | 0.221777i | 0.679613 | − | 0.733571i | \(-0.262148\pi\) |
−0.295484 | + | 0.955348i | \(0.595481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 63.0000 | − | 36.3731i | 2.14703 | − | 1.23959i | ||||
\(862\) | −3.34607 | − | 0.896575i | −0.113967 | − | 0.0305375i | ||||
\(863\) | −16.9706 | + | 16.9706i | −0.577685 | + | 0.577685i | −0.934265 | − | 0.356580i | \(-0.883943\pi\) |
0.356580 | + | 0.934265i | \(0.383943\pi\) | |||||||
\(864\) | 2.59808 | − | 4.50000i | 0.0883883 | − | 0.153093i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −22.5000 | + | 12.9904i | −0.764581 | + | 0.441431i | ||||
\(867\) | 13.3843 | + | 3.58630i | 0.454553 | + | 0.121797i | ||||
\(868\) | −26.7685 | + | 7.17260i | −0.908583 | + | 0.243454i | ||||
\(869\) | 3.46410 | − | 6.00000i | 0.117512 | − | 0.203536i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.00000 | + | 5.19615i | 0.101651 | + | 0.176065i | ||||
\(872\) | 2.82843 | + | 2.82843i | 0.0957826 | + | 0.0957826i | ||||
\(873\) | 18.3712 | + | 18.3712i | 0.621770 | + | 0.621770i | ||||
\(874\) | 42.0000i | 1.42067i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.0000 | −0.506803 | ||||||||
\(877\) | 7.17260 | + | 26.7685i | 0.242202 | + | 0.903909i | 0.974769 | + | 0.223215i | \(0.0716551\pi\) |
−0.732568 | + | 0.680694i | \(0.761678\pi\) | |||||||
\(878\) | 4.14110 | + | 15.4548i | 0.139756 | + | 0.521575i | ||||
\(879\) | 10.3923 | 0.350524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.92820i | − | 0.233417i | −0.993166 | − | 0.116709i | \(-0.962766\pi\) | ||
0.993166 | − | 0.116709i | \(-0.0372343\pi\) | |||||||
\(882\) | −14.4889 | + | 3.88229i | −0.487866 | + | 0.130723i | ||||
\(883\) | 8.57321 | + | 8.57321i | 0.288512 | + | 0.288512i | 0.836492 | − | 0.547980i | \(-0.184603\pi\) |
−0.547980 | + | 0.836492i | \(0.684603\pi\) | |||||||
\(884\) | −5.19615 | − | 9.00000i | −0.174766 | − | 0.302703i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.5000 | − | 23.3827i | 0.453541 | − | 0.785557i | ||||
\(887\) | −46.3644 | + | 12.4233i | −1.55677 | + | 0.417134i | −0.931638 | − | 0.363388i | \(-0.881620\pi\) |
−0.625128 | + | 0.780522i | \(0.714953\pi\) | |||||||
\(888\) | −11.5911 | − | 3.10583i | −0.388972 | − | 0.104225i | ||||
\(889\) | 31.1769 | − | 18.0000i | 1.04564 | − | 0.603701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | − | 7.79423i | −0.452267 | − | 0.261116i | ||||
\(892\) | 7.34847 | − | 7.34847i | 0.246045 | − | 0.246045i | ||||
\(893\) | −40.5689 | − | 10.8704i | −1.35759 | − | 0.363764i | ||||
\(894\) | 15.5885 | − | 9.00000i | 0.521356 | − | 0.301005i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.00000 | − | 1.73205i | −0.100223 | − | 0.0578638i | ||||
\(897\) | −34.7733 | + | 9.31749i | −1.16105 | + | 0.311102i | ||||
\(898\) | 10.3106 | − | 38.4797i | 0.344070 | − | 1.28409i | ||||
\(899\) | 27.7128 | 0.924274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 5.43520 | − | 20.2844i | 0.180972 | − | 0.675398i | ||||
\(903\) | −22.0454 | − | 22.0454i | −0.733625 | − | 0.733625i | ||||
\(904\) | 15.5885 | + | 9.00000i | 0.518464 | + | 0.299336i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 17.3205i | − | 0.575435i | ||||||
\(907\) | 8.36516 | + | 2.24144i | 0.277761 | + | 0.0744257i | 0.395010 | − | 0.918677i | \(-0.370741\pi\) |
−0.117250 | + | 0.993102i | \(0.537408\pi\) | |||||||
\(908\) | 2.12132 | − | 2.12132i | 0.0703985 | − | 0.0703985i | ||||
\(909\) | 20.7846 | 0.689382 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0000 | + | 17.3205i | −0.993944 | + | 0.573854i | −0.906451 | − | 0.422311i | \(-0.861219\pi\) |
−0.0874934 | + | 0.996165i | \(0.527886\pi\) | |||||||
\(912\) | −3.13801 | − | 11.7112i | −0.103910 | − | 0.387798i | ||||
\(913\) | 20.0764 | − | 5.37945i | 0.664432 | − | 0.178034i | ||||
\(914\) | −12.9904 | + | 22.5000i | −0.429684 | + | 0.744234i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.0000 | + | 19.0526i | 0.363450 | + | 0.629514i | ||||
\(917\) | 8.48528 | + | 8.48528i | 0.280209 | + | 0.280209i | ||||
\(918\) | 4.03459 | − | 15.0573i | 0.133161 | − | 0.496965i | ||||
\(919\) | 22.0000i | 0.725713i | 0.931845 | + | 0.362857i | \(0.118198\pi\) | ||||
−0.931845 | + | 0.362857i | \(0.881802\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.50000 | − | 7.79423i | −0.148280 | − | 0.256829i | ||||
\(922\) | −4.48288 | − | 16.7303i | −0.147636 | − | 0.550984i | ||||
\(923\) | −12.4233 | − | 46.3644i | −0.408918 | − | 1.52610i | ||||
\(924\) | −5.19615 | + | 9.00000i | −0.170941 | + | 0.296078i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 13.8564i | − | 0.455350i | ||||||
\(927\) | −50.1910 | − | 13.4486i | −1.64849 | − | 0.441711i | ||||
\(928\) | 2.44949 | + | 2.44949i | 0.0804084 | + | 0.0804084i | ||||
\(929\) | 17.3205 | + | 30.0000i | 0.568267 | + | 0.984268i | 0.996737 | + | 0.0807121i | \(0.0257194\pi\) |
−0.428470 | + | 0.903556i | \(0.640947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5000 | + | 30.3109i | −0.573539 | + | 0.993399i | ||||
\(932\) | 2.89778 | − | 0.776457i | 0.0949199 | − | 0.0254337i | ||||
\(933\) | 4.24264 | − | 4.24264i | 0.138898 | − | 0.138898i | ||||
\(934\) | −7.79423 | + | 4.50000i | −0.255035 | + | 0.147244i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.00000 | − | 5.19615i | 0.294174 | − | 0.169842i | ||||
\(937\) | −24.4949 | + | 24.4949i | −0.800213 | + | 0.800213i | −0.983129 | − | 0.182915i | \(-0.941447\pi\) |
0.182915 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(938\) | 5.79555 | + | 1.55291i | 0.189232 | + | 0.0507044i | ||||
\(939\) | 12.9904 | + | 7.50000i | 0.423925 | + | 0.244753i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.0000 | − | 10.3923i | −0.586783 | − | 0.338779i | 0.177041 | − | 0.984203i | \(-0.443347\pi\) |
−0.763825 | + | 0.645424i | \(0.776681\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.8281 | − | 70.2674i | 0.613127 | − | 2.28822i | ||||
\(944\) | 12.1244 | 0.394614 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.00000 | −0.292615 | ||||||||
\(947\) | −6.98811 | + | 26.0800i | −0.227083 | + | 0.847486i | 0.754476 | + | 0.656328i | \(0.227891\pi\) |
−0.981559 | + | 0.191158i | \(0.938776\pi\) | |||||||
\(948\) | −1.79315 | + | 6.69213i | −0.0582388 | + | 0.217350i | ||||
\(949\) | −25.9808 | − | 15.0000i | −0.843371 | − | 0.486921i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.00000 | − | 5.19615i | −0.291845 | − | 0.168497i | ||||
\(952\) | −10.0382 | − | 2.68973i | −0.325340 | − | 0.0871745i | ||||
\(953\) | −23.3345 | + | 23.3345i | −0.755879 | + | 0.755879i | −0.975570 | − | 0.219690i | \(-0.929495\pi\) |
0.219690 | + | 0.975570i | \(0.429495\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.00000 | − | 5.19615i | 0.291081 | − | 0.168056i | ||||
\(957\) | 7.34847 | − | 7.34847i | 0.237542 | − | 0.237542i | ||||
\(958\) | 16.7303 | − | 4.48288i | 0.540532 | − | 0.144835i | ||||
\(959\) | −5.19615 | + | 9.00000i | −0.167793 | + | 0.290625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | −16.9706 | − | 16.9706i | −0.547153 | − | 0.547153i | ||||
\(963\) | −2.32937 | − | 8.69333i | −0.0750629 | − | 0.280139i | ||||
\(964\) | − | 1.00000i | − | 0.0322078i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.0000 | + | 31.1769i | −0.579141 | + | 1.00310i | ||||
\(967\) | −0.896575 | − | 3.34607i | −0.0288319 | − | 0.107602i | 0.950010 | − | 0.312218i | \(-0.101072\pi\) |
−0.978842 | + | 0.204616i | \(0.934405\pi\) | |||||||
\(968\) | −2.07055 | − | 7.72741i | −0.0665501 | − | 0.248368i | ||||
\(969\) | −18.1865 | − | 31.5000i | −0.584236 | − | 1.01193i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.46410i | 0.111168i | 0.998454 | + | 0.0555842i | \(0.0177021\pi\) | ||||
−0.998454 | + | 0.0555842i | \(0.982298\pi\) | |||||||
\(972\) | 15.0573 | + | 4.03459i | 0.482963 | + | 0.129410i | ||||
\(973\) | 12.2474 | + | 12.2474i | 0.392635 | + | 0.392635i | ||||
\(974\) | 12.1244 | + | 21.0000i | 0.388489 | + | 0.672883i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | + | 3.46410i | −0.0640184 | + | 0.110883i | ||||
\(977\) | 2.89778 | − | 0.776457i | 0.0927081 | − | 0.0248411i | −0.212167 | − | 0.977233i | \(-0.568052\pi\) |
0.304875 | + | 0.952392i | \(0.401385\pi\) | |||||||
\(978\) | 1.55291 | + | 5.79555i | 0.0496567 | + | 0.185321i | ||||
\(979\) | 10.3923 | − | 6.00000i | 0.332140 | − | 0.191761i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | + | 10.3923i | −0.191565 | + | 0.331801i | ||||
\(982\) | −15.9217 | + | 15.9217i | −0.508081 | + | 0.508081i | ||||
\(983\) | 34.7733 | + | 9.31749i | 1.10910 | + | 0.297182i | 0.766464 | − | 0.642288i | \(-0.222015\pi\) |
0.342633 | + | 0.939469i | \(0.388681\pi\) | |||||||
\(984\) | 21.0000i | 0.669456i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.00000 | + | 5.19615i | 0.286618 | + | 0.165479i | ||||
\(987\) | −25.4558 | − | 25.4558i | −0.810268 | − | 0.810268i | ||||
\(988\) | 6.27603 | − | 23.4225i | 0.199667 | − | 0.745168i | ||||
\(989\) | −31.1769 | −0.991368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 2.07055 | − | 7.72741i | 0.0657401 | − | 0.245345i | ||||
\(993\) | −46.8449 | + | 12.5521i | −1.48658 | + | 0.398327i | ||||
\(994\) | −41.5692 | − | 24.0000i | −1.31850 | − | 0.761234i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.0000 | + | 10.3923i | −0.570352 | + | 0.329293i | ||||
\(997\) | 40.1528 | + | 10.7589i | 1.27165 | + | 0.340738i | 0.830663 | − | 0.556775i | \(-0.187961\pi\) |
0.440988 | + | 0.897513i | \(0.354628\pi\) | |||||||
\(998\) | 13.4350 | − | 13.4350i | 0.425278 | − | 0.425278i | ||||
\(999\) | − | 36.0000i | − | 1.13899i |
(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 | 450.2.p.f.293.2 | yes | 8 | |
3.2 | odd | 2 | 1350.2.q.f.1043.1 | 8 | |||
5.2 | odd | 4 | inner | 450.2.p.f.257.2 | yes | 8 | |
5.3 | odd | 4 | inner | 450.2.p.f.257.1 | ✓ | 8 | |
5.4 | even | 2 | inner | 450.2.p.f.293.1 | yes | 8 | |
9.2 | odd | 6 | inner | 450.2.p.f.443.2 | yes | 8 | |
9.7 | even | 3 | 1350.2.q.f.143.1 | 8 | |||
15.2 | even | 4 | 1350.2.q.f.557.1 | 8 | |||
15.8 | even | 4 | 1350.2.q.f.557.2 | 8 | |||
15.14 | odd | 2 | 1350.2.q.f.1043.2 | 8 | |||
45.2 | even | 12 | inner | 450.2.p.f.407.2 | yes | 8 | |
45.7 | odd | 12 | 1350.2.q.f.1007.1 | 8 | |||
45.29 | odd | 6 | inner | 450.2.p.f.443.1 | yes | 8 | |
45.34 | even | 6 | 1350.2.q.f.143.2 | 8 | |||
45.38 | even | 12 | inner | 450.2.p.f.407.1 | yes | 8 | |
45.43 | odd | 12 | 1350.2.q.f.1007.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.f.257.1 | ✓ | 8 | 5.3 | odd | 4 | inner | |
450.2.p.f.257.2 | yes | 8 | 5.2 | odd | 4 | inner | |
450.2.p.f.293.1 | yes | 8 | 5.4 | even | 2 | inner | |
450.2.p.f.293.2 | yes | 8 | 1.1 | even | 1 | trivial | |
450.2.p.f.407.1 | yes | 8 | 45.38 | even | 12 | inner | |
450.2.p.f.407.2 | yes | 8 | 45.2 | even | 12 | inner | |
450.2.p.f.443.1 | yes | 8 | 45.29 | odd | 6 | inner | |
450.2.p.f.443.2 | yes | 8 | 9.2 | odd | 6 | inner | |
1350.2.q.f.143.1 | 8 | 9.7 | even | 3 | |||
1350.2.q.f.143.2 | 8 | 45.34 | even | 6 | |||
1350.2.q.f.557.1 | 8 | 15.2 | even | 4 | |||
1350.2.q.f.557.2 | 8 | 15.8 | even | 4 | |||
1350.2.q.f.1007.1 | 8 | 45.7 | odd | 12 | |||
1350.2.q.f.1007.2 | 8 | 45.43 | odd | 12 | |||
1350.2.q.f.1043.1 | 8 | 3.2 | odd | 2 | |||
1350.2.q.f.1043.2 | 8 | 15.14 | odd | 2 |