Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(143,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([2, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.q (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7798042729\) |
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: | no (minimal twist has level 450) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 143.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.143 |
Dual form | 1350.2.q.f.557.2 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 0.258819i | 0.683013 | − | 0.183013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.896575 | + | 3.34607i | 0.338874 | + | 1.26469i | 0.899608 | + | 0.436698i | \(0.143852\pi\) |
−0.560734 | + | 0.827996i | \(0.689481\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 0.866025i | 0.452267 | + | 0.261116i | 0.708787 | − | 0.705422i | \(-0.249243\pi\) |
−0.256520 | + | 0.966539i | \(0.582576\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.896575 | − | 3.34607i | 0.248665 | − | 0.928032i | −0.722840 | − | 0.691015i | \(-0.757164\pi\) |
0.971506 | − | 0.237016i | \(-0.0761695\pi\) | |||||||
\(14\) | 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 | 0.401405 | − | 0.915901i | \(-0.368522\pi\) |
−0.915901 | + | 0.401405i | \(0.868522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000i | 1.60591i | 0.596040 | + | 0.802955i | \(0.296740\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.67303 | + | 0.448288i | 0.356692 | + | 0.0955753i | ||||
\(23\) | 5.79555 | + | 1.55291i | 1.20846 | + | 0.323805i | 0.806156 | − | 0.591703i | \(-0.201544\pi\) |
0.402300 | + | 0.915508i | \(0.368211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 3.46410i | − | 0.679366i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.44949 | + | 2.44949i | 0.462910 | + | 0.462910i | ||||
\(29\) | 1.73205 | − | 3.00000i | 0.321634 | − | 0.557086i | −0.659192 | − | 0.751975i | \(-0.729101\pi\) |
0.980825 | + | 0.194889i | \(0.0624347\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | 0.258819 | − | 0.965926i | 0.0457532 | − | 0.170753i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.59808 | − | 1.50000i | −0.445566 | − | 0.257248i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.89898 | + | 4.89898i | −0.805387 | + | 0.805387i | −0.983932 | − | 0.178545i | \(-0.942861\pi\) |
0.178545 | + | 0.983932i | \(0.442861\pi\) | |||||||
\(38\) | 1.81173 | + | 6.76148i | 0.293902 | + | 1.09686i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5000 | − | 6.06218i | 1.63982 | − | 0.946753i | 0.658932 | − | 0.752202i | \(-0.271008\pi\) |
0.980892 | − | 0.194551i | \(-0.0623249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.01910 | + | 1.34486i | −0.765405 | + | 0.205090i | −0.620341 | − | 0.784332i | \(-0.713006\pi\) |
−0.145065 | + | 0.989422i | \(0.546339\pi\) | |||||||
\(44\) | 1.73205 | 0.261116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −5.79555 | + | 1.55291i | −0.845369 | + | 0.226516i | −0.655407 | − | 0.755276i | \(-0.727503\pi\) |
−0.189961 | + | 0.981792i | \(0.560836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.33013 | + | 2.50000i | −0.618590 | + | 0.357143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.896575 | − | 3.34607i | −0.124333 | − | 0.464016i | ||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | + | 1.73205i | 0.400892 | + | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.896575 | − | 3.34607i | 0.117726 | − | 0.439360i | ||||
\(59\) | 6.06218 | + | 10.5000i | 0.789228 | + | 1.36698i | 0.926440 | + | 0.376442i | \(0.122853\pi\) |
−0.137212 | + | 0.990542i | \(0.543814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | − | 3.46410i | 0.256074 | − | 0.443533i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) |
0.965187 | + | 0.261562i | \(0.0842377\pi\) | |||||||
\(62\) | 5.65685 | + | 5.65685i | 0.718421 | + | 0.718421i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.67303 | + | 0.448288i | 0.204393 | + | 0.0547671i | 0.359563 | − | 0.933121i | \(-0.382926\pi\) |
−0.155170 | + | 0.987888i | \(0.549592\pi\) | |||||||
\(68\) | −2.89778 | − | 0.776457i | −0.351407 | − | 0.0941593i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.8564i | − | 1.64445i | −0.569160 | − | 0.822226i | \(-0.692732\pi\) | ||
0.569160 | − | 0.822226i | \(-0.307268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.12372 | + | 6.12372i | 0.716728 | + | 0.716728i | 0.967934 | − | 0.251206i | \(-0.0808271\pi\) |
−0.251206 | + | 0.967934i | \(0.580827\pi\) | |||||||
\(74\) | −3.46410 | + | 6.00000i | −0.402694 | + | 0.697486i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.50000 | + | 6.06218i | 0.401478 | + | 0.695379i | ||||
\(77\) | −1.55291 | + | 5.79555i | −0.176971 | + | 0.660465i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46410 | + | 2.00000i | 0.389742 | + | 0.225018i | 0.682048 | − | 0.731307i | \(-0.261089\pi\) |
−0.292306 | + | 0.956325i | \(0.594423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.57321 | − | 8.57321i | 0.946753 | − | 0.946753i | ||||
\(83\) | −3.10583 | − | 11.5911i | −0.340909 | − | 1.27229i | −0.897319 | − | 0.441382i | \(-0.854488\pi\) |
0.556410 | − | 0.830908i | \(-0.312178\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.50000 | + | 2.59808i | −0.485247 | + | 0.280158i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.67303 | − | 0.448288i | 0.178346 | − | 0.0477876i | ||||
\(89\) | −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 | ||||||||
\(92\) | 5.79555 | − | 1.55291i | 0.604228 | − | 0.161903i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.19615 | + | 3.00000i | −0.535942 | + | 0.309426i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.24144 | − | 8.36516i | −0.227584 | − | 0.849354i | −0.981353 | − | 0.192215i | \(-0.938433\pi\) |
0.753769 | − | 0.657139i | \(-0.228234\pi\) | |||||||
\(98\) | −3.53553 | + | 3.53553i | −0.357143 | + | 0.357143i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 3.46410i | 0.597022 | + | 0.344691i | 0.767869 | − | 0.640607i | \(-0.221317\pi\) |
−0.170847 | + | 0.985298i | \(0.554650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.48288 | − | 16.7303i | 0.441711 | − | 1.64849i | −0.282766 | − | 0.959189i | \(-0.591252\pi\) |
0.724477 | − | 0.689299i | \(-0.242081\pi\) | |||||||
\(104\) | −1.73205 | − | 3.00000i | −0.169842 | − | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.12132 | − | 2.12132i | −0.205076 | − | 0.205076i | 0.597095 | − | 0.802171i | \(-0.296322\pi\) |
−0.802171 | + | 0.597095i | \(0.796322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.00000i | − | 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.34607 | + | 0.896575i | 0.316173 | + | 0.0847184i | ||||
\(113\) | −17.3867 | − | 4.65874i | −1.63560 | − | 0.438258i | −0.680069 | − | 0.733148i | \(-0.738050\pi\) |
−0.955531 | + | 0.294891i | \(0.904717\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.46410i | − | 0.321634i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||
\(122\) | 1.03528 | − | 3.86370i | 0.0937295 | − | 0.349803i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.92820 | + | 4.00000i | 0.622171 | + | 0.359211i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | + | 7.34847i | −0.652071 | + | 0.652071i | −0.953491 | − | 0.301420i | \(-0.902539\pi\) |
0.301420 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(128\) | −0.258819 | − | 0.965926i | −0.0228766 | − | 0.0853766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | + | 1.73205i | −0.262111 | + | 0.151330i | −0.625297 | − | 0.780387i | \(-0.715022\pi\) |
0.363186 | + | 0.931717i | \(0.381689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.4225 | + | 6.27603i | −2.03098 | + | 0.544201i | ||||
\(134\) | 1.73205 | 0.149626 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | −2.89778 | + | 0.776457i | −0.247574 | + | 0.0663372i | −0.380472 | − | 0.924793i | \(-0.624238\pi\) |
0.132898 | + | 0.991130i | \(0.457572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.33013 | + | 2.50000i | −0.367277 | + | 0.212047i | −0.672268 | − | 0.740308i | \(-0.734680\pi\) |
0.304991 | + | 0.952355i | \(0.401346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.58630 | − | 13.3843i | −0.300956 | − | 1.12318i | ||||
\(143\) | 4.24264 | − | 4.24264i | 0.354787 | − | 0.354787i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.50000 | + | 4.33013i | 0.620704 | + | 0.358364i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.79315 | + | 6.69213i | −0.147396 | + | 0.550090i | ||||
\(149\) | 5.19615 | + | 9.00000i | 0.425685 | + | 0.737309i | 0.996484 | − | 0.0837813i | \(-0.0266997\pi\) |
−0.570799 | + | 0.821090i | \(0.693366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | + | 8.66025i | −0.406894 | + | 0.704761i | −0.994540 | − | 0.104357i | \(-0.966722\pi\) |
0.587646 | + | 0.809118i | \(0.300055\pi\) | |||||||
\(152\) | 4.94975 | + | 4.94975i | 0.401478 | + | 0.401478i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000i | 0.483494i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(158\) | 3.86370 | + | 1.03528i | 0.307380 | + | 0.0823622i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.7846i | 1.63806i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.44949 | − | 2.44949i | −0.191859 | − | 0.191859i | 0.604640 | − | 0.796499i | \(-0.293317\pi\) |
−0.796499 | + | 0.604640i | \(0.793317\pi\) | |||||||
\(164\) | 6.06218 | − | 10.5000i | 0.473377 | − | 0.819912i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | − | 10.3923i | −0.465690 | − | 0.806599i | ||||
\(167\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.866025 | + | 0.500000i | 0.0666173 | + | 0.0384615i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.67423 | + | 3.67423i | −0.280158 | + | 0.280158i | ||||
\(173\) | 1.55291 | + | 5.79555i | 0.118066 | + | 0.440628i | 0.999498 | − | 0.0316829i | \(-0.0100867\pi\) |
−0.881432 | + | 0.472311i | \(0.843420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.50000 | − | 0.866025i | 0.113067 | − | 0.0652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.69213 | + | 1.79315i | −0.501596 | + | 0.134402i | ||||
\(179\) | −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 | \(0.523682\pi\) | |||||||
\(182\) | 11.5911 | − | 3.10583i | 0.859190 | − | 0.230219i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.19615 | − | 3.00000i | 0.383065 | − | 0.221163i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.34486 | − | 5.01910i | −0.0983461 | − | 0.367033i | ||||
\(188\) | −4.24264 | + | 4.24264i | −0.309426 | + | 0.309426i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.0000 | − | 12.1244i | −1.51951 | − | 0.877288i | −0.999736 | − | 0.0229818i | \(-0.992684\pi\) |
−0.519771 | − | 0.854306i | \(-0.673983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.24144 | + | 8.36516i | −0.161342 | + | 0.602138i | 0.837136 | + | 0.546995i | \(0.184228\pi\) |
−0.998478 | + | 0.0551431i | \(0.982439\pi\) | |||||||
\(194\) | −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 | \(-0.923579\pi\) |
−0.237785 | − | 0.971318i | \(-0.576421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.0000i | − | 0.708881i | −0.935079 | − | 0.354441i | \(-0.884671\pi\) | ||
0.935079 | − | 0.354441i | \(-0.115329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.69213 | + | 1.79315i | 0.470857 | + | 0.126166i | ||||
\(203\) | 11.5911 | + | 3.10583i | 0.813536 | + | 0.217986i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 17.3205i | − | 1.20678i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.59808 | − | 1.50000i | −0.177601 | − | 0.102538i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.5959 | + | 19.5959i | −1.33026 | + | 1.33026i | ||||
\(218\) | −1.03528 | − | 3.86370i | −0.0701178 | − | 0.261683i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.00000 | + | 5.19615i | −0.605406 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0382 | + | 2.68973i | −0.672207 | + | 0.180117i | −0.578749 | − | 0.815506i | \(-0.696459\pi\) |
−0.0934584 | + | 0.995623i | \(0.529792\pi\) | |||||||
\(224\) | 3.46410 | 0.231455 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | −2.89778 | + | 0.776457i | −0.192332 | + | 0.0515353i | −0.353699 | − | 0.935359i | \(-0.615076\pi\) |
0.161367 | + | 0.986894i | \(0.448410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.0526 | − | 11.0000i | 1.25903 | − | 0.726900i | 0.286143 | − | 0.958187i | \(-0.407627\pi\) |
0.972886 | + | 0.231287i | \(0.0742935\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.896575 | − | 3.34607i | −0.0588631 | − | 0.219680i | ||||
\(233\) | 2.12132 | − | 2.12132i | 0.138972 | − | 0.138972i | −0.634198 | − | 0.773171i | \(-0.718670\pi\) |
0.773171 | + | 0.634198i | \(0.218670\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.5000 | + | 6.06218i | 0.683492 | + | 0.394614i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.68973 | − | 10.0382i | 0.174349 | − | 0.650680i | ||||
\(239\) | −5.19615 | − | 9.00000i | −0.336111 | − | 0.582162i | 0.647586 | − | 0.761992i | \(-0.275778\pi\) |
−0.983698 | + | 0.179830i | \(0.942445\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | −5.65685 | − | 5.65685i | −0.363636 | − | 0.363636i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 4.00000i | − | 0.256074i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.4225 | + | 6.27603i | 1.49034 | + | 0.399334i | ||||
\(248\) | 7.72741 | + | 2.07055i | 0.490691 | + | 0.131480i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9808i | 1.63989i | 0.572441 | + | 0.819946i | \(0.305996\pi\) | ||||
−0.572441 | + | 0.819946i | \(0.694004\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | ||||
\(257\) | 6.98811 | − | 26.0800i | 0.435907 | − | 1.62683i | −0.302981 | − | 0.952997i | \(-0.597982\pi\) |
0.738887 | − | 0.673829i | \(-0.235352\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.7846 | − | 12.0000i | −1.29149 | − | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.44949 | + | 2.44949i | −0.151330 | + | 0.151330i | ||||
\(263\) | −1.55291 | − | 5.79555i | −0.0957568 | − | 0.357369i | 0.901376 | − | 0.433037i | \(-0.142558\pi\) |
−0.997133 | + | 0.0756674i | \(0.975891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −21.0000 | + | 12.1244i | −1.28759 | + | 0.743392i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.67303 | − | 0.448288i | 0.102197 | − | 0.0273835i | ||||
\(269\) | −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 | \(0.823664\pi\) | |||||||
\(272\) | −2.89778 | + | 0.776457i | −0.175704 | + | 0.0470796i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.59808 | + | 1.50000i | −0.156956 | + | 0.0906183i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.68973 | + | 10.0382i | 0.161610 | + | 0.603137i | 0.998448 | + | 0.0556866i | \(0.0177348\pi\) |
−0.836838 | + | 0.547450i | \(0.815599\pi\) | |||||||
\(278\) | −3.53553 | + | 3.53553i | −0.212047 | + | 0.212047i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | − | 10.3923i | −1.07379 | − | 0.619953i | −0.144575 | − | 0.989494i | \(-0.546182\pi\) |
−0.929214 | + | 0.369541i | \(0.879515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.06918 | − | 30.1146i | 0.479663 | − | 1.79013i | −0.123314 | − | 0.992368i | \(-0.539352\pi\) |
0.602977 | − | 0.797759i | \(-0.293981\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 8.00000i | − | 0.470588i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.36516 | + | 2.24144i | 0.489534 | + | 0.131170i | ||||
\(293\) | −5.79555 | − | 1.55291i | −0.338580 | − | 0.0907222i | 0.0855230 | − | 0.996336i | \(-0.472744\pi\) |
−0.424103 | + | 0.905614i | \(0.639411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.92820i | 0.402694i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||
\(302\) | −2.58819 | + | 9.65926i | −0.148934 | + | 0.555828i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.06218 | + | 3.50000i | 0.347690 | + | 0.200739i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.67423 | − | 3.67423i | 0.209700 | − | 0.209700i | −0.594440 | − | 0.804140i | \(-0.702626\pi\) |
0.804140 | + | 0.594440i | \(0.202626\pi\) | |||||||
\(308\) | 1.55291 | + | 5.79555i | 0.0884855 | + | 0.330232i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000 | − | 1.73205i | 0.170114 | − | 0.0982156i | −0.412525 | − | 0.910946i | \(-0.635353\pi\) |
0.582640 | + | 0.812731i | \(0.302020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.36516 | − | 2.24144i | 0.472827 | − | 0.126694i | −0.0145337 | − | 0.999894i | \(-0.504626\pi\) |
0.487361 | + | 0.873201i | \(0.337960\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | −5.79555 | + | 1.55291i | −0.325511 | + | 0.0872204i | −0.417874 | − | 0.908505i | \(-0.637225\pi\) |
0.0923631 | + | 0.995725i | \(0.470558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.19615 | − | 3.00000i | 0.290929 | − | 0.167968i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.37945 | + | 20.0764i | 0.299785 | + | 1.11881i | ||||
\(323\) | 14.8492 | − | 14.8492i | 0.826234 | − | 0.826234i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.00000 | − | 1.73205i | −0.166155 | − | 0.0959294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.13801 | − | 11.7112i | 0.173268 | − | 0.646644i | ||||
\(329\) | −10.3923 | − | 18.0000i | −0.572946 | − | 0.992372i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | −8.48528 | − | 8.48528i | −0.465690 | − | 0.465690i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7112 | − | 3.13801i | −0.637951 | − | 0.170939i | −0.0746760 | − | 0.997208i | \(-0.523792\pi\) |
−0.563275 | + | 0.826269i | \(0.690459\pi\) | |||||||
\(338\) | 0.965926 | + | 0.258819i | 0.0525394 | + | 0.0140779i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.8564i | 0.750366i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 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 | ||||
\(347\) | −3.88229 | + | 14.4889i | −0.208412 | + | 0.777804i | 0.779970 | + | 0.625816i | \(0.215234\pi\) |
−0.988382 | + | 0.151988i | \(0.951433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.92820 | + | 4.00000i | 0.370858 | + | 0.214115i | 0.673833 | − | 0.738883i | \(-0.264647\pi\) |
−0.302975 | + | 0.952998i | \(0.597980\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.22474 | − | 1.22474i | 0.0652791 | − | 0.0652791i | ||||
\(353\) | 5.43520 | + | 20.2844i | 0.289287 | + | 1.07963i | 0.945650 | + | 0.325187i | \(0.105427\pi\) |
−0.656363 | + | 0.754445i | \(0.727906\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | + | 3.46410i | −0.317999 | + | 0.183597i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.34607 | + | 0.896575i | −0.176845 | + | 0.0473855i | ||||
\(359\) | −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 | ||||||||
\(362\) | −1.93185 | + | 0.517638i | −0.101536 | + | 0.0272065i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.3923 | − | 6.00000i | 0.544705 | − | 0.314485i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.58630 | − | 13.3843i | −0.187203 | − | 0.698653i | −0.994148 | − | 0.108026i | \(-0.965547\pi\) |
0.806945 | − | 0.590627i | \(-0.201120\pi\) | |||||||
\(368\) | 4.24264 | − | 4.24264i | 0.221163 | − | 0.221163i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.48288 | + | 16.7303i | −0.232115 | + | 0.866263i | 0.747314 | + | 0.664471i | \(0.231343\pi\) |
−0.979428 | + | 0.201792i | \(0.935323\pi\) | |||||||
\(374\) | −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 | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000i | 0.0513665i | 0.999670 | + | 0.0256833i | \(0.00817614\pi\) | ||||
−0.999670 | + | 0.0256833i | \(0.991824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −23.4225 | − | 6.27603i | −1.19840 | − | 0.321110i | ||||
\(383\) | 11.5911 | + | 3.10583i | 0.592278 | + | 0.158700i | 0.542494 | − | 0.840060i | \(-0.317480\pi\) |
0.0497839 | + | 0.998760i | \(0.484147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.66025i | 0.440795i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.12372 | − | 6.12372i | −0.310885 | − | 0.310885i | ||||
\(389\) | −5.19615 | + | 9.00000i | −0.263455 | + | 0.456318i | −0.967158 | − | 0.254177i | \(-0.918196\pi\) |
0.703702 | + | 0.710495i | \(0.251529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | − | 15.5885i | −0.455150 | − | 0.788342i | ||||
\(392\) | −1.29410 | + | 4.82963i | −0.0653617 | + | 0.243933i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.7846 | − | 12.0000i | −1.04711 | − | 0.604551i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.6969 | − | 14.6969i | 0.737618 | − | 0.737618i | −0.234498 | − | 0.972117i | \(-0.575345\pi\) |
0.972117 | + | 0.234498i | \(0.0753447\pi\) | |||||||
\(398\) | −2.58819 | − | 9.65926i | −0.129734 | − | 0.484175i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.50000 | − | 2.59808i | 0.224719 | − | 0.129742i | −0.383414 | − | 0.923576i | \(-0.625252\pi\) |
0.608134 | + | 0.793835i | \(0.291919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.7685 | − | 7.17260i | 1.33344 | − | 0.357293i | ||||
\(404\) | 6.92820 | 0.344691 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | −11.5911 | + | 3.10583i | −0.574550 | + | 0.153950i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.06218 | − | 3.50000i | 0.299755 | − | 0.173064i | −0.342578 | − | 0.939490i | \(-0.611300\pi\) |
0.642333 | + | 0.766426i | \(0.277967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.48288 | − | 16.7303i | −0.220856 | − | 0.824244i | ||||
\(413\) | −29.6985 | + | 29.6985i | −1.46137 | + | 1.46137i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.00000 | − | 1.73205i | −0.147087 | − | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.13801 | + | 11.7112i | −0.153485 | + | 0.572815i | ||||
\(419\) | 5.19615 | + | 9.00000i | 0.253849 | + | 0.439679i | 0.964582 | − | 0.263783i | \(-0.0849701\pi\) |
−0.710734 | + | 0.703461i | \(0.751637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0000 | + | 24.2487i | −0.682318 | + | 1.18181i | 0.291953 | + | 0.956433i | \(0.405695\pi\) |
−0.974272 | + | 0.225377i | \(0.927639\pi\) | |||||||
\(422\) | 2.82843 | + | 2.82843i | 0.137686 | + | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.3843 | + | 3.58630i | 0.647710 | + | 0.173553i | ||||
\(428\) | −2.89778 | − | 0.776457i | −0.140069 | − | 0.0375315i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.46410i | − | 0.166860i | −0.996514 | − | 0.0834300i | \(-0.973413\pi\) | ||
0.996514 | − | 0.0834300i | \(-0.0265875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.3712 | + | 18.3712i | 0.882862 | + | 0.882862i | 0.993825 | − | 0.110962i | \(-0.0353933\pi\) |
−0.110962 | + | 0.993825i | \(0.535393\pi\) | |||||||
\(434\) | −13.8564 | + | 24.0000i | −0.665129 | + | 1.15204i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | − | 3.46410i | −0.0957826 | − | 0.165900i | ||||
\(437\) | −10.8704 | + | 40.5689i | −0.520002 | + | 1.94067i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8564 | + | 8.00000i | 0.661330 | + | 0.381819i | 0.792784 | − | 0.609503i | \(-0.208631\pi\) |
−0.131453 | + | 0.991322i | \(0.541964\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.34847 | + | 7.34847i | −0.349531 | + | 0.349531i | ||||
\(443\) | 6.98811 | + | 26.0800i | 0.332015 | + | 1.23910i | 0.907069 | + | 0.420982i | \(0.138315\pi\) |
−0.575054 | + | 0.818116i | \(0.695019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.00000 | + | 5.19615i | −0.426162 | + | 0.246045i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.34607 | − | 0.896575i | 0.158087 | − | 0.0423592i | ||||
\(449\) | 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 | ||||||||
\(452\) | −17.3867 | + | 4.65874i | −0.817800 | + | 0.219129i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.59808 | + | 1.50000i | −0.121934 | + | 0.0703985i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.72432 | − | 25.0955i | −0.314550 | − | 1.17392i | −0.924408 | − | 0.381406i | \(-0.875440\pi\) |
0.609857 | − | 0.792511i | \(-0.291227\pi\) | |||||||
\(458\) | 15.5563 | − | 15.5563i | 0.726900 | − | 0.726900i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0000 | − | 8.66025i | −0.698620 | − | 0.403348i | 0.108213 | − | 0.994128i | \(-0.465487\pi\) |
−0.806833 | + | 0.590779i | \(0.798820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.58630 | − | 13.3843i | 0.166670 | − | 0.622019i | −0.831152 | − | 0.556046i | \(-0.812318\pi\) |
0.997821 | − | 0.0659737i | \(-0.0210154\pi\) | |||||||
\(464\) | −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 | 0.838851 | − | 0.544362i | \(-0.183228\pi\) |
−0.544362 | + | 0.838851i | \(0.683228\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.00000i | 0.277054i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.7112 | + | 3.13801i | 0.539053 | + | 0.144439i | ||||
\(473\) | −8.69333 | − | 2.32937i | −0.399720 | − | 0.107105i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 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 | −0.597493 | − | 0.801874i | \(-0.703836\pi\) |
0.993190 | + | 0.116507i | \(0.0371697\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 20.7846i | 0.547153 | + | 0.947697i | ||||
\(482\) | 0.258819 | − | 0.965926i | 0.0117889 | − | 0.0439967i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.92820 | − | 4.00000i | −0.314918 | − | 0.181818i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.1464 | − | 17.1464i | 0.776979 | − | 0.776979i | −0.202337 | − | 0.979316i | \(-0.564854\pi\) |
0.979316 | + | 0.202337i | \(0.0648537\pi\) | |||||||
\(488\) | −1.03528 | − | 3.86370i | −0.0468648 | − | 0.174902i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.5000 | − | 11.2583i | 0.880023 | − | 0.508081i | 0.00935679 | − | 0.999956i | \(-0.497022\pi\) |
0.870666 | + | 0.491875i | \(0.163688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0382 | + | 2.68973i | −0.452098 | + | 0.121139i | ||||
\(494\) | 24.2487 | 1.09100 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 46.3644 | − | 12.4233i | 2.07973 | − | 0.557262i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.4545 | + | 9.50000i | −0.736604 | + | 0.425278i | −0.820833 | − | 0.571168i | \(-0.806490\pi\) |
0.0842294 | + | 0.996446i | \(0.473157\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.72432 | + | 25.0955i | 0.300121 | + | 1.12007i | ||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | + | 5.19615i | 0.400099 | + | 0.230997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.68973 | + | 10.0382i | −0.119337 | + | 0.445373i | ||||
\(509\) | −10.3923 | − | 18.0000i | −0.460631 | − | 0.797836i | 0.538362 | − | 0.842714i | \(-0.319043\pi\) |
−0.998992 | + | 0.0448779i | \(0.985710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0000 | + | 25.9808i | −0.663561 | + | 1.14932i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 27.0000i | − | 1.19092i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0382 | − | 2.68973i | −0.441479 | − | 0.118294i | ||||
\(518\) | −23.1822 | − | 6.21166i | −1.01857 | − | 0.272925i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.19615i | 0.227648i | 0.993501 | + | 0.113824i | \(0.0363099\pi\) | ||||
−0.993501 | + | 0.113824i | \(0.963690\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.2474 | − | 12.2474i | −0.535544 | − | 0.535544i | 0.386673 | − | 0.922217i | \(-0.373624\pi\) |
−0.922217 | + | 0.386673i | \(0.873624\pi\) | |||||||
\(524\) | −1.73205 | + | 3.00000i | −0.0756650 | + | 0.131056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | − | 5.19615i | −0.130806 | − | 0.226563i | ||||
\(527\) | 6.21166 | − | 23.1822i | 0.270584 | − | 1.00983i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2583 | + | 6.50000i | 0.489493 | + | 0.282609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.1464 | + | 17.1464i | −0.743392 | + | 0.743392i | ||||
\(533\) | −10.8704 | − | 40.5689i | −0.470849 | − | 1.75723i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.50000 | − | 0.866025i | 0.0647901 | − | 0.0374066i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.69213 | + | 1.79315i | −0.288518 | + | 0.0773082i | ||||
\(539\) | −8.66025 | −0.373024 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | −27.0459 | + | 7.24693i | −1.16172 | + | 0.311282i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.59808 | + | 1.50000i | −0.111392 | + | 0.0643120i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.82774 | + | 21.7494i | 0.249176 | + | 0.929938i | 0.971238 | + | 0.238110i | \(0.0765278\pi\) |
−0.722062 | + | 0.691828i | \(0.756805\pi\) | |||||||
\(548\) | −2.12132 | + | 2.12132i | −0.0906183 | + | 0.0906183i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.0000 | + | 12.1244i | 0.894630 | + | 0.516515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.58630 | + | 13.3843i | −0.152505 | + | 0.569157i | ||||
\(554\) | 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 | 0.923323 | − | 0.384024i | \(-0.125462\pi\) |
−0.384024 | + | 0.923323i | \(0.625462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.0000i | 0.761319i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.0764 | − | 5.37945i | −0.846871 | − | 0.226919i | ||||
\(563\) | 14.4889 | + | 3.88229i | 0.610634 | + | 0.163619i | 0.550866 | − | 0.834593i | \(-0.314297\pi\) |
0.0597675 | + | 0.998212i | \(0.480964\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 31.1769i | − | 1.31046i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.79796 | − | 9.79796i | −0.411113 | − | 0.411113i | ||||
\(569\) | −9.52628 | + | 16.5000i | −0.399362 | + | 0.691716i | −0.993647 | − | 0.112539i | \(-0.964102\pi\) |
0.594285 | + | 0.804255i | \(0.297435\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.50000 | − | 4.33013i | −0.104622 | − | 0.181210i | 0.808962 | − | 0.587861i | \(-0.200030\pi\) |
−0.913584 | + | 0.406651i | \(0.866697\pi\) | |||||||
\(572\) | 1.55291 | − | 5.79555i | 0.0649306 | − | 0.242324i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 36.3731 | + | 21.0000i | 1.51818 | + | 0.876523i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2702 | − | 23.2702i | 0.968749 | − | 0.968749i | −0.0307771 | − | 0.999526i | \(-0.509798\pi\) |
0.999526 | + | 0.0307771i | \(0.00979822\pi\) | |||||||
\(578\) | −2.07055 | − | 7.72741i | −0.0861236 | − | 0.321418i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0000 | − | 20.7846i | 1.49353 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.66025 | 0.358364 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 31.8756 | − | 8.54103i | 1.31564 | − | 0.352526i | 0.468300 | − | 0.883569i | \(-0.344867\pi\) |
0.847345 | + | 0.531043i | \(0.178200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.4974 | + | 28.0000i | −1.99830 | + | 1.15372i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.79315 | + | 6.69213i | 0.0736980 | + | 0.275045i | ||||
\(593\) | −12.7279 | + | 12.7279i | −0.522673 | + | 0.522673i | −0.918378 | − | 0.395705i | \(-0.870500\pi\) |
0.395705 | + | 0.918378i | \(0.370500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.00000 | + | 5.19615i | 0.368654 | + | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.37945 | − | 20.0764i | 0.219982 | − | 0.820985i | ||||
\(599\) | 6.92820 | + | 12.0000i | 0.283079 | + | 0.490307i | 0.972141 | − | 0.234395i | \(-0.0753109\pi\) |
−0.689063 | + | 0.724702i | \(0.741978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5000 | − | 25.1147i | 0.591467 | − | 1.02445i | −0.402568 | − | 0.915390i | \(-0.631882\pi\) |
0.994035 | − | 0.109061i | \(-0.0347845\pi\) | |||||||
\(602\) | −12.7279 | − | 12.7279i | −0.518751 | − | 0.518751i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000i | 0.406894i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.3843 | − | 3.58630i | −0.543250 | − | 0.145564i | −0.0232502 | − | 0.999730i | \(-0.507401\pi\) |
−0.520000 | + | 0.854166i | \(0.674068\pi\) | |||||||
\(608\) | 6.76148 | + | 1.81173i | 0.274214 | + | 0.0734755i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7846i | 0.840855i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.89898 | + | 4.89898i | 0.197868 | + | 0.197868i | 0.799085 | − | 0.601218i | \(-0.205317\pi\) |
−0.601218 | + | 0.799085i | \(0.705317\pi\) | |||||||
\(614\) | 2.59808 | − | 4.50000i | 0.104850 | − | 0.181605i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | + | 5.19615i | 0.120873 | + | 0.209359i | ||||
\(617\) | 11.6469 | − | 43.4667i | 0.468885 | − | 1.74990i | −0.174793 | − | 0.984605i | \(-0.555926\pi\) |
0.643678 | − | 0.765297i | \(-0.277408\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.2583 | + | 6.50000i | 0.452510 | + | 0.261257i | 0.708890 | − | 0.705319i | \(-0.249196\pi\) |
−0.256379 | + | 0.966576i | \(0.582530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.44949 | − | 2.44949i | 0.0982156 | − | 0.0982156i | ||||
\(623\) | −6.21166 | − | 23.1822i | −0.248865 | − | 0.928776i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.50000 | − | 4.33013i | 0.299760 | − | 0.173067i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | \(0.369672\pi\) | |||||||
\(632\) | 3.86370 | − | 1.03528i | 0.153690 | − | 0.0411811i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.19615 | + | 3.00000i | −0.206366 | + | 0.119145i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.48288 | + | 16.7303i | 0.177618 | + | 0.662880i | ||||
\(638\) | 4.24264 | − | 4.24264i | 0.167968 | − | 0.167968i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.5000 | − | 11.2583i | −0.770204 | − | 0.444677i | 0.0627436 | − | 0.998030i | \(-0.480015\pi\) |
−0.832947 | + | 0.553352i | \(0.813348\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.41404 | + | 35.1337i | −0.371254 | + | 1.38554i | 0.487489 | + | 0.873129i | \(0.337913\pi\) |
−0.858742 | + | 0.512408i | \(0.828754\pi\) | |||||||
\(644\) | 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 | 0.154081 | − | 0.988058i | \(-0.450758\pi\) |
−0.988058 | + | 0.154081i | \(0.950758\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.0000i | 0.824322i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.34607 | − | 0.896575i | −0.131042 | − | 0.0351126i | ||||
\(653\) | −17.3867 | − | 4.65874i | −0.680393 | − | 0.182311i | −0.0979610 | − | 0.995190i | \(-0.531232\pi\) |
−0.582432 | + | 0.812880i | \(0.697899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 12.1244i | − | 0.473377i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.6969 | − | 14.6969i | −0.572946 | − | 0.572946i | ||||
\(659\) | −5.19615 | + | 9.00000i | −0.202413 | + | 0.350590i | −0.949306 | − | 0.314355i | \(-0.898212\pi\) |
0.746892 | + | 0.664945i | \(0.231545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0000 | + | 27.7128i | 0.622328 | + | 1.07790i | 0.989051 | + | 0.147573i | \(0.0471463\pi\) |
−0.366723 | + | 0.930330i | \(0.619520\pi\) | |||||||
\(662\) | 7.24693 | − | 27.0459i | 0.281660 | − | 1.05117i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.3923 | − | 6.00000i | −0.403300 | − | 0.232845i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6969 | − | 14.6969i | 0.569068 | − | 0.569068i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.00000 | − | 3.46410i | 0.231627 | − | 0.133730i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.69213 | − | 1.79315i | 0.257963 | − | 0.0691209i | −0.127520 | − | 0.991836i | \(-0.540702\pi\) |
0.385483 | + | 0.922715i | \(0.374035\pi\) | |||||||
\(674\) | −12.1244 | −0.467013 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −11.5911 | + | 3.10583i | −0.445483 | + | 0.119367i | −0.474585 | − | 0.880210i | \(-0.657402\pi\) |
0.0291023 | + | 0.999576i | \(0.490735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.9808 | − | 15.0000i | 0.997050 | − | 0.575647i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.58630 | + | 13.3843i | 0.137327 | + | 0.512510i | ||||
\(683\) | 23.3345 | − | 23.3345i | 0.892871 | − | 0.892871i | −0.101922 | − | 0.994792i | \(-0.532499\pi\) |
0.994792 | + | 0.101922i | \(0.0324991\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.00000 | + | 3.46410i | 0.229081 | + | 0.132260i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.34486 | + | 5.01910i | −0.0512724 | + | 0.191351i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | − | 6.92820i | 0.152167 | − | 0.263561i | −0.779857 | − | 0.625958i | \(-0.784708\pi\) |
0.932024 | + | 0.362397i | \(0.118041\pi\) | |||||||
\(692\) | 4.24264 | + | 4.24264i | 0.161281 | + | 0.161281i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.0000i | 0.569392i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.1337 | − | 9.41404i | −1.33078 | − | 0.356582i | ||||
\(698\) | 7.72741 | + | 2.07055i | 0.292487 | + | 0.0783716i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 17.3205i | − | 0.654187i | −0.944992 | − | 0.327093i | \(-0.893931\pi\) | ||
0.944992 | − | 0.327093i | \(-0.106069\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −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 | ||||
\(707\) | −6.21166 | + | 23.1822i | −0.233613 | + | 0.871857i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.6410 | − | 20.0000i | −1.30097 | − | 0.751116i | −0.320400 | − | 0.947282i | \(-0.603817\pi\) |
−0.980571 | + | 0.196167i | \(0.937151\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.89898 | + | 4.89898i | −0.183597 | + | 0.183597i | ||||
\(713\) | 12.4233 | + | 46.3644i | 0.465257 | + | 1.73636i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.00000 | + | 1.73205i | −0.112115 | + | 0.0647298i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −23.4225 | + | 6.27603i | −0.874118 | + | 0.234219i | ||||
\(719\) | −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 | ||||||||
\(722\) | −28.9778 | + | 7.76457i | −1.07844 | + | 0.288967i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.73205 | + | 1.00000i | −0.0643712 | + | 0.0371647i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.68973 | + | 10.0382i | 0.0997564 | + | 0.372296i | 0.997698 | − | 0.0678194i | \(-0.0216042\pi\) |
−0.897941 | + | 0.440115i | \(0.854938\pi\) | |||||||
\(728\) | 8.48528 | − | 8.48528i | 0.314485 | − | 0.314485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5000 | + | 7.79423i | 0.499316 | + | 0.288280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.4486 | + | 50.1910i | −0.496737 | + | 1.85385i | 0.0233418 | + | 0.999728i | \(0.492569\pi\) |
−0.520078 | + | 0.854119i | \(0.674097\pi\) | |||||||
\(734\) | −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 | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 41.0000i | − | 1.50821i | −0.656754 | − | 0.754105i | \(-0.728071\pi\) | ||
0.656754 | − | 0.754105i | \(-0.271929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.3867 | + | 4.65874i | 0.637855 | + | 0.170913i | 0.563232 | − | 0.826299i | \(-0.309558\pi\) |
0.0746233 | + | 0.997212i | \(0.476225\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.3205i | 0.634149i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −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 | 0.988761 | − | 0.149505i | \(-0.0477681\pi\) |
−0.623856 | + | 0.781540i | \(0.714435\pi\) | |||||||
\(752\) | −1.55291 | + | 5.79555i | −0.0566290 | + | 0.211342i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.3923 | − | 6.00000i | −0.378465 | − | 0.218507i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.9444 | + | 26.9444i | −0.979310 | + | 0.979310i | −0.999790 | − | 0.0204799i | \(-0.993481\pi\) |
0.0204799 | + | 0.999790i | \(0.493481\pi\) | |||||||
\(758\) | 0.258819 | + | 0.965926i | 0.00940073 | + | 0.0350840i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | − | 17.3205i | 1.08750 | − | 0.627868i | 0.154590 | − | 0.987979i | \(-0.450594\pi\) |
0.932910 | + | 0.360111i | \(0.117261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.3843 | − | 3.58630i | 0.484543 | − | 0.129833i | ||||
\(764\) | −24.2487 | −0.877288 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | 40.5689 | − | 10.8704i | 1.46486 | − | 0.392507i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1244 | − | 7.00000i | 0.437215 | − | 0.252426i | −0.265200 | − | 0.964193i | \(-0.585438\pi\) |
0.702416 | + | 0.711767i | \(0.252105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.24144 | + | 8.36516i | 0.0806711 | + | 0.301069i | ||||
\(773\) | −38.1838 | + | 38.1838i | −1.37337 | + | 1.37337i | −0.517985 | + | 0.855390i | \(0.673318\pi\) |
−0.855390 | + | 0.517985i | \(0.826682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.50000 | − | 4.33013i | −0.269234 | − | 0.155443i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.68973 | + | 10.0382i | −0.0964314 | + | 0.359887i | ||||
\(779\) | 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 | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.00000i | 0.178571i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.7303 | + | 4.48288i | 0.596372 | + | 0.159797i | 0.544364 | − | 0.838849i | \(-0.316771\pi\) |
0.0520081 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(788\) | −23.1822 | − | 6.21166i | −0.825832 | − | 0.221281i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 62.3538i | − | 2.21705i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −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 | ||||
\(797\) | 6.21166 | − | 23.1822i | 0.220028 | − | 0.821156i | −0.764308 | − | 0.644852i | \(-0.776919\pi\) |
0.984336 | − | 0.176304i | \(-0.0564143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.5885 | + | 9.00000i | 0.551480 | + | 0.318397i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.67423 | − | 3.67423i | 0.129742 | − | 0.129742i | ||||
\(803\) | 3.88229 | + | 14.4889i | 0.137003 | + | 0.511302i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.0000 | − | 13.8564i | 0.845364 | − | 0.488071i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.69213 | − | 1.79315i | 0.235428 | − | 0.0630828i | ||||
\(809\) | 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 | \(0.755791\pi\) | |||||||
\(812\) | 11.5911 | − | 3.10583i | 0.406768 | − | 0.108993i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.3923 | + | 6.00000i | −0.364250 | + | 0.210300i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.41404 | − | 35.1337i | −0.329356 | − | 1.22917i | ||||
\(818\) | 4.94975 | − | 4.94975i | 0.173064 | − | 0.173064i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | − | 8.66025i | −0.523504 | − | 0.302245i | 0.214863 | − | 0.976644i | \(-0.431069\pi\) |
−0.738367 | + | 0.674399i | \(0.764403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.58630 | + | 13.3843i | −0.125011 | + | 0.466546i | −0.999840 | − | 0.0178851i | \(-0.994307\pi\) |
0.874829 | + | 0.484431i | \(0.160973\pi\) | |||||||
\(824\) | −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 | 0.994056 | − | 0.108870i | \(-0.0347231\pi\) |
−0.108870 | + | 0.994056i | \(0.534723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0000i | 1.18087i | 0.807086 | + | 0.590434i | \(0.201044\pi\) | ||||
−0.807086 | + | 0.590434i | \(0.798956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.34607 | − | 0.896575i | −0.116004 | − | 0.0310832i | ||||
\(833\) | 14.4889 | + | 3.88229i | 0.502010 | + | 0.134513i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.1244i | 0.419330i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.34847 | + | 7.34847i | 0.253849 | + | 0.253849i | ||||
\(839\) | −17.3205 | + | 30.0000i | −0.597970 | + | 1.03572i | 0.395150 | + | 0.918617i | \(0.370693\pi\) |
−0.993120 | + | 0.117098i | \(0.962641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.50000 | + | 14.7224i | 0.293103 | + | 0.507670i | ||||
\(842\) | −7.24693 | + | 27.0459i | −0.249746 | + | 0.932064i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.46410 | + | 2.00000i | 0.119239 | + | 0.0688428i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.5959 | − | 19.5959i | 0.673324 | − | 0.673324i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0000 | + | 20.7846i | −1.23406 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.8067 | − | 9.86233i | 1.26024 | − | 0.337680i | 0.433955 | − | 0.900935i | \(-0.357118\pi\) |
0.826283 | + | 0.563255i | \(0.190451\pi\) | |||||||
\(854\) | 13.8564 | 0.474156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | −40.5689 | + | 10.8704i | −1.38581 | + | 0.371326i | −0.873227 | − | 0.487314i | \(-0.837977\pi\) |
−0.512580 | + | 0.858640i | \(0.671310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.2583 | + | 6.50000i | −0.384129 | + | 0.221777i | −0.679613 | − | 0.733571i | \(-0.737852\pi\) |
0.295484 | + | 0.955348i | \(0.404519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.896575 | − | 3.34607i | −0.0305375 | − | 0.113967i | ||||
\(863\) | 16.9706 | − | 16.9706i | 0.577685 | − | 0.577685i | −0.356580 | − | 0.934265i | \(-0.616057\pi\) |
0.934265 | + | 0.356580i | \(0.116057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.5000 | + | 12.9904i | 0.764581 | + | 0.441431i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.17260 | + | 26.7685i | −0.243454 | + | 0.908583i | ||||
\(869\) | 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 | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 42.0000i | 1.42067i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.7685 | + | 7.17260i | 0.903909 | + | 0.242202i | 0.680694 | − | 0.732568i | \(-0.261678\pi\) |
0.223215 | + | 0.974769i | \(0.428345\pi\) | |||||||
\(878\) | 15.4548 | + | 4.14110i | 0.521575 | + | 0.139756i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.92820i | − | 0.233417i | −0.993166 | − | 0.116709i | \(-0.962766\pi\) | ||
0.993166 | − | 0.116709i | \(-0.0372343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.57321 | − | 8.57321i | −0.288512 | − | 0.288512i | 0.547980 | − | 0.836492i | \(-0.315397\pi\) |
−0.836492 | + | 0.547980i | \(0.815397\pi\) | |||||||
\(884\) | −5.19615 | + | 9.00000i | −0.174766 | + | 0.302703i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.5000 | + | 23.3827i | 0.453541 | + | 0.785557i | ||||
\(887\) | −12.4233 | + | 46.3644i | −0.417134 | + | 1.55677i | 0.363388 | + | 0.931638i | \(0.381620\pi\) |
−0.780522 | + | 0.625128i | \(0.785047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.1769 | − | 18.0000i | −1.04564 | − | 0.603701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.34847 | + | 7.34847i | −0.246045 | + | 0.246045i | ||||
\(893\) | −10.8704 | − | 40.5689i | −0.363764 | − | 1.35759i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.00000 | − | 1.73205i | 0.100223 | − | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 38.4797 | − | 10.3106i | 1.28409 | − | 0.344070i | ||||
\(899\) | 27.7128 | 0.924274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 20.2844 | − | 5.43520i | 0.675398 | − | 0.180972i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.5885 | + | 9.00000i | −0.518464 | + | 0.299336i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.24144 | + | 8.36516i | 0.0744257 | + | 0.277761i | 0.993102 | − | 0.117250i | \(-0.0374077\pi\) |
−0.918677 | + | 0.395010i | \(0.870741\pi\) | |||||||
\(908\) | −2.12132 | + | 2.12132i | −0.0703985 | + | 0.0703985i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | + | 17.3205i | 0.993944 | + | 0.573854i | 0.906451 | − | 0.422311i | \(-0.138781\pi\) |
0.0874934 | + | 0.996165i | \(0.472114\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.37945 | − | 20.0764i | 0.178034 | − | 0.664432i | ||||
\(914\) | −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 | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.0000i | 0.725713i | 0.931845 | + | 0.362857i | \(0.118198\pi\) | ||||
−0.931845 | + | 0.362857i | \(0.881802\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.7303 | − | 4.48288i | −0.550984 | − | 0.147636i | ||||
\(923\) | −46.3644 | − | 12.4233i | −1.52610 | − | 0.408918i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 13.8564i | − | 0.455350i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.44949 | − | 2.44949i | −0.0804084 | − | 0.0804084i | ||||
\(929\) | 17.3205 | − | 30.0000i | 0.568267 | − | 0.984268i | −0.428470 | − | 0.903556i | \(-0.640947\pi\) |
0.996737 | − | 0.0807121i | \(-0.0257194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.5000 | − | 30.3109i | −0.573539 | − | 0.993399i | ||||
\(932\) | 0.776457 | − | 2.89778i | 0.0254337 | − | 0.0949199i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.79423 | + | 4.50000i | 0.255035 | + | 0.147244i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.4949 | − | 24.4949i | 0.800213 | − | 0.800213i | −0.182915 | − | 0.983129i | \(-0.558553\pi\) |
0.983129 | + | 0.182915i | \(0.0585534\pi\) | |||||||
\(938\) | 1.55291 | + | 5.79555i | 0.0507044 | + | 0.189232i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0000 | − | 10.3923i | 0.586783 | − | 0.338779i | −0.177041 | − | 0.984203i | \(-0.556653\pi\) |
0.763825 | + | 0.645424i | \(0.223319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70.2674 | − | 18.8281i | 2.28822 | − | 0.613127i | ||||
\(944\) | 12.1244 | 0.394614 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.00000 | −0.292615 | ||||||||
\(947\) | −26.0800 | + | 6.98811i | −0.847486 | + | 0.227083i | −0.656328 | − | 0.754476i | \(-0.727891\pi\) |
−0.191158 | + | 0.981559i | \(0.561224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.9808 | − | 15.0000i | 0.843371 | − | 0.486921i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.68973 | − | 10.0382i | −0.0871745 | − | 0.325340i | ||||
\(953\) | 23.3345 | − | 23.3345i | 0.755879 | − | 0.755879i | −0.219690 | − | 0.975570i | \(-0.570505\pi\) |
0.975570 | + | 0.219690i | \(0.0705047\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.00000 | − | 5.19615i | −0.291081 | − | 0.168056i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.48288 | − | 16.7303i | 0.144835 | − | 0.540532i | ||||
\(959\) | −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 | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 1.00000i | − | 0.0322078i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.34607 | − | 0.896575i | −0.107602 | − | 0.0288319i | 0.204616 | − | 0.978842i | \(-0.434405\pi\) |
−0.312218 | + | 0.950010i | \(0.601072\pi\) | |||||||
\(968\) | −7.72741 | − | 2.07055i | −0.248368 | − | 0.0665501i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.46410i | 0.111168i | 0.998454 | + | 0.0555842i | \(0.0177021\pi\) | ||||
−0.998454 | + | 0.0555842i | \(0.982298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −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 | ||||
\(977\) | 0.776457 | − | 2.89778i | 0.0248411 | − | 0.0927081i | −0.952392 | − | 0.304875i | \(-0.901385\pi\) |
0.977233 | + | 0.212167i | \(0.0680520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.3923 | − | 6.00000i | −0.332140 | − | 0.191761i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.9217 | − | 15.9217i | 0.508081 | − | 0.508081i | ||||
\(983\) | 9.31749 | + | 34.7733i | 0.297182 | + | 1.10910i | 0.939469 | + | 0.342633i | \(0.111319\pi\) |
−0.642288 | + | 0.766464i | \(0.722015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.00000 | + | 5.19615i | −0.286618 | + | 0.165479i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.4225 | − | 6.27603i | 0.745168 | − | 0.199667i | ||||
\(989\) | −31.1769 | −0.991368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 7.72741 | − | 2.07055i | 0.245345 | − | 0.0657401i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 41.5692 | − | 24.0000i | 1.31850 | − | 0.761234i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.7589 | + | 40.1528i | 0.340738 | + | 1.27165i | 0.897513 | + | 0.440988i | \(0.145372\pi\) |
−0.556775 | + | 0.830663i | \(0.687961\pi\) | |||||||
\(998\) | −13.4350 | + | 13.4350i | −0.425278 | + | 0.425278i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.2.q.f.143.2 | 8 | ||
3.2 | odd | 2 | 450.2.p.f.443.1 | yes | 8 | ||
5.2 | odd | 4 | inner | 1350.2.q.f.1007.2 | 8 | ||
5.3 | odd | 4 | inner | 1350.2.q.f.1007.1 | 8 | ||
5.4 | even | 2 | inner | 1350.2.q.f.143.1 | 8 | ||
9.4 | even | 3 | 450.2.p.f.293.1 | yes | 8 | ||
9.5 | odd | 6 | inner | 1350.2.q.f.1043.2 | 8 | ||
15.2 | even | 4 | 450.2.p.f.407.1 | yes | 8 | ||
15.8 | even | 4 | 450.2.p.f.407.2 | yes | 8 | ||
15.14 | odd | 2 | 450.2.p.f.443.2 | yes | 8 | ||
45.4 | even | 6 | 450.2.p.f.293.2 | yes | 8 | ||
45.13 | odd | 12 | 450.2.p.f.257.2 | yes | 8 | ||
45.14 | odd | 6 | inner | 1350.2.q.f.1043.1 | 8 | ||
45.22 | odd | 12 | 450.2.p.f.257.1 | ✓ | 8 | ||
45.23 | even | 12 | inner | 1350.2.q.f.557.1 | 8 | ||
45.32 | even | 12 | inner | 1350.2.q.f.557.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.p.f.257.1 | ✓ | 8 | 45.22 | odd | 12 | ||
450.2.p.f.257.2 | yes | 8 | 45.13 | odd | 12 | ||
450.2.p.f.293.1 | yes | 8 | 9.4 | even | 3 | ||
450.2.p.f.293.2 | yes | 8 | 45.4 | even | 6 | ||
450.2.p.f.407.1 | yes | 8 | 15.2 | even | 4 | ||
450.2.p.f.407.2 | yes | 8 | 15.8 | even | 4 | ||
450.2.p.f.443.1 | yes | 8 | 3.2 | odd | 2 | ||
450.2.p.f.443.2 | yes | 8 | 15.14 | odd | 2 | ||
1350.2.q.f.143.1 | 8 | 5.4 | even | 2 | inner | ||
1350.2.q.f.143.2 | 8 | 1.1 | even | 1 | trivial | ||
1350.2.q.f.557.1 | 8 | 45.23 | even | 12 | inner | ||
1350.2.q.f.557.2 | 8 | 45.32 | even | 12 | inner | ||
1350.2.q.f.1007.1 | 8 | 5.3 | odd | 4 | inner | ||
1350.2.q.f.1007.2 | 8 | 5.2 | odd | 4 | inner | ||
1350.2.q.f.1043.1 | 8 | 45.14 | odd | 6 | inner | ||
1350.2.q.f.1043.2 | 8 | 9.5 | odd | 6 | inner |