Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(104,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11, 9, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.104");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.cs (of order \(18\), degree \(6\), 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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 419.3 | ||
Character | \(\chi\) | \(=\) | 945.419 |
Dual form | 945.2.cs.a.839.3 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{17}{18}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(3\) | 0.306808 | − | 1.70466i | 0.177136 | − | 0.984186i | ||||
\(4\) | 1.87939 | − | 0.684040i | 0.939693 | − | 0.342020i | ||||
\(5\) | −1.43732 | + | 1.71293i | −0.642788 | + | 0.766044i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.48619 | − | 0.904900i | −0.939693 | − | 0.342020i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.81174 | − | 1.04601i | −0.937246 | − | 0.348669i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.55941 | − | 3.05019i | −0.771692 | − | 0.919667i | 0.226834 | − | 0.973933i | \(-0.427162\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | −0.589446 | − | 3.41358i | −0.170158 | − | 0.985417i | ||||
\(13\) | −1.10071 | + | 6.24241i | −0.305281 | + | 1.73133i | 0.316898 | + | 0.948459i | \(0.397359\pi\) |
−0.622179 | + | 0.782875i | \(0.713753\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.47898 | + | 2.97568i | 0.640070 | + | 0.768317i | ||||
\(16\) | 3.06418 | − | 2.57115i | 0.766044 | − | 0.642788i | ||||
\(17\) | −4.17071 | − | 2.40796i | −1.01154 | − | 0.584016i | −0.0999013 | − | 0.994997i | \(-0.531853\pi\) |
−0.911644 | + | 0.410982i | \(0.865186\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | −1.52956 | + | 4.20243i | −0.342020 | + | 0.939693i | ||||
\(21\) | −2.30533 | + | 3.96049i | −0.503065 | + | 0.864249i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.868241 | − | 4.92404i | −0.173648 | − | 0.984808i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.64575 | + | 4.47214i | −0.509175 | + | 0.860663i | ||||
\(28\) | −5.29150 | −1.00000 | ||||||||
\(29\) | −10.5889 | + | 1.86711i | −1.96631 | + | 0.346714i | −0.973104 | + | 0.230366i | \(0.926008\pi\) |
−0.993208 | + | 0.116348i | \(0.962881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.98479 | + | 3.42711i | −1.04182 | + | 0.596583i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.12348 | − | 2.95804i | 0.866025 | − | 0.500000i | ||||
\(36\) | −5.99985 | − | 0.0425087i | −0.999975 | − | 0.00708479i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.3035 | + | 3.79155i | 1.64988 | + | 0.607134i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(44\) | −6.89658 | − | 3.98174i | −1.03970 | − | 0.600270i | ||||
\(45\) | 5.83309 | − | 3.31286i | 0.869546 | − | 0.493852i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.67425 | − | 12.8424i | 0.681810 | − | 1.87326i | 0.265086 | − | 0.964225i | \(-0.414600\pi\) |
0.416724 | − | 0.909033i | \(-0.363178\pi\) | |||||||
\(48\) | −3.44283 | − | 6.01223i | −0.496929 | − | 0.867791i | ||||
\(49\) | 5.36231 | + | 4.49951i | 0.766044 | + | 0.642788i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.38436 | + | 6.37086i | −0.753961 | + | 0.892099i | ||||
\(52\) | 2.20141 | + | 12.4848i | 0.305281 | + | 1.73133i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.90344 | 1.20054 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(60\) | 6.69444 | + | 3.89672i | 0.864249 | + | 0.503065i | ||||
\(61\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.04399 | + | 5.14492i | 0.761471 | + | 0.648199i | ||||
\(64\) | 4.00000 | − | 6.92820i | 0.500000 | − | 0.866025i | ||||
\(65\) | −9.11074 | − | 10.8578i | −1.13005 | − | 1.34674i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(68\) | −9.48551 | − | 1.67255i | −1.15029 | − | 0.202827i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.07461 | + | 3.50718i | 0.720923 | + | 0.416225i | 0.815092 | − | 0.579331i | \(-0.196686\pi\) |
−0.0941692 | + | 0.995556i | \(0.530019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.26673 | − | 12.5863i | −0.850506 | − | 1.47312i | −0.880752 | − | 0.473577i | \(-0.842962\pi\) |
0.0302463 | − | 0.999542i | \(-0.490371\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.66020 | − | 0.0306782i | −0.999994 | − | 0.00354242i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.60308 | + | 9.89937i | 0.410609 | + | 1.12814i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00497 | + | 17.0421i | 0.338086 | + | 1.91738i | 0.394340 | + | 0.918964i | \(0.370973\pi\) |
−0.0562544 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(80\) | 8.94427i | 1.00000i | ||||||||
\(81\) | 6.81174 | + | 5.88220i | 0.756860 | + | 0.653577i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8663 | + | 2.44500i | −1.52202 | + | 0.268373i | −0.871227 | − | 0.490881i | \(-0.836675\pi\) |
−0.650794 | + | 0.759254i | \(0.725564\pi\) | |||||||
\(84\) | −1.62348 | + | 9.02022i | −0.177136 | + | 0.984186i | ||||
\(85\) | 10.1193 | − | 3.68312i | 1.09759 | − | 0.399490i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0659721 | + | 18.6234i | −0.00707295 | + | 1.99663i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.38533 | − | 14.5238i | 0.879021 | − | 1.52251i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.5742 | − | 9.71188i | 1.17518 | − | 0.986092i | 0.175180 | − | 0.984536i | \(-0.443949\pi\) |
0.999999 | − | 0.00155612i | \(-0.000495328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00588 | + | 11.2535i | 0.402606 | + | 1.13102i | ||||
\(100\) | −5.00000 | − | 8.66025i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3376 | − | 10.3524i | −1.21566 | − | 1.02006i | −0.999040 | − | 0.0438001i | \(-0.986054\pi\) |
−0.216616 | − | 0.976257i | \(-0.569502\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.47053 | − | 9.64134i | −0.338689 | − | 0.940898i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −1.91326 | + | 10.2147i | −0.184104 | + | 0.982907i | ||||
\(109\) | −2.98186 | −0.285610 | −0.142805 | − | 0.989751i | \(-0.545612\pi\) | ||||
−0.142805 | + | 0.989751i | \(0.545612\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.94477 | + | 3.61960i | −0.939693 | + | 0.342020i | ||||
\(113\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −18.6235 | + | 10.7523i | −1.72915 | + | 0.998323i | ||||
\(117\) | 9.62451 | − | 16.4007i | 0.889786 | − | 1.51624i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.19022 | + | 9.76072i | 0.750796 | + | 0.894764i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.842932 | + | 4.78050i | −0.0766302 | + | 0.434591i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.68246 | + | 5.59017i | 0.866025 | + | 0.500000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(132\) | −8.90344 | + | 10.5347i | −0.774945 | + | 0.916927i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.85766 | − | 10.9599i | −0.332015 | − | 0.943274i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(140\) | 7.60557 | − | 9.06396i | 0.642788 | − | 0.766044i | ||||
\(141\) | −20.4579 | − | 11.9082i | −1.72286 | − | 1.00285i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.8577 | − | 12.6196i | 1.82783 | − | 1.05530i | ||||
\(144\) | −11.3051 | + | 4.02425i | −0.942092 | + | 0.335354i | ||||
\(145\) | 12.0214 | − | 20.8217i | 0.998323 | − | 1.72915i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.31534 | − | 7.76044i | 0.768317 | − | 0.640070i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.6506 | − | 3.81759i | −1.77369 | − | 0.312749i | −0.811343 | − | 0.584571i | \(-0.801263\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.6508 | − | 13.1326i | 1.27364 | − | 1.06871i | 0.279554 | − | 0.960130i | \(-0.409814\pi\) |
0.994088 | − | 0.108582i | \(-0.0346309\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.20819 | + | 11.1331i | 0.744438 | + | 0.900061i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21.9578 | + | 0.0777842i | 1.75803 | + | 0.00622772i | ||||
\(157\) | −7.30588 | − | 6.13036i | −0.583072 | − | 0.489256i | 0.302882 | − | 0.953028i | \(-0.402051\pi\) |
−0.885954 | + | 0.463772i | \(0.846496\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.73165 | − | 15.1773i | 0.212658 | − | 1.18155i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.27900 | − | 2.71600i | 0.176354 | − | 0.210171i | −0.670625 | − | 0.741796i | \(-0.733974\pi\) |
0.846979 | + | 0.531626i | \(0.178419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −25.5402 | − | 9.29586i | −1.96463 | − | 0.715066i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.66201 | + | 11.5147i | 0.734589 | + | 0.875449i | 0.995961 | − | 0.0897890i | \(-0.0286193\pi\) |
−0.261372 | + | 0.965238i | \(0.584175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.29715 | + | 13.0278i | −0.173648 | + | 0.984808i | ||||
\(176\) | −15.6850 | − | 2.76569i | −1.18230 | − | 0.208472i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.51047 | + | 3.18147i | 0.411872 | + | 0.237794i | 0.691594 | − | 0.722287i | \(-0.256909\pi\) |
−0.279722 | + | 0.960081i | \(0.590242\pi\) | |||||||
\(180\) | 8.69650 | − | 10.2162i | 0.648199 | − | 0.761471i | ||||
\(181\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.32983 | + | 18.8844i | 0.243501 | + | 1.38096i | ||||
\(188\) | − | 27.3332i | − | 1.99348i | ||||||
\(189\) | 10.6247 | − | 8.72445i | 0.772832 | − | 0.634611i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.82620 | − | 1.02732i | 0.421569 | − | 0.0743340i | 0.0411606 | − | 0.999153i | \(-0.486894\pi\) |
0.380409 | + | 0.924819i | \(0.375783\pi\) | |||||||
\(192\) | −10.5830 | − | 8.94427i | −0.763763 | − | 0.645497i | ||||
\(193\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −21.3040 | + | 12.1995i | −1.52561 | + | 0.873623i | ||||
\(196\) | 13.1557 | + | 4.78828i | 0.939693 | + | 0.342020i | ||||
\(197\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.0156 | + | 4.93991i | 1.96631 | + | 0.346714i | ||||
\(204\) | −5.76136 | + | 15.6564i | −0.403376 | + | 1.09617i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.6774 | + | 21.9579i | 0.879021 | + | 1.52251i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.2066 | − | 17.7944i | −1.45992 | − | 1.22502i | −0.924918 | − | 0.380166i | \(-0.875867\pi\) |
−0.535001 | − | 0.844851i | \(-0.679689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.84228 | − | 9.27911i | 0.537344 | − | 0.635794i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.6849 | + | 8.52572i | −1.60048 | + | 0.576114i | ||||
\(220\) | 16.7330 | − | 6.09031i | 1.12814 | − | 0.410609i | ||||
\(221\) | 19.6222 | − | 23.3848i | 1.31993 | − | 1.57303i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.8548 | + | 10.1383i | 1.86530 | + | 0.678912i | 0.974449 | + | 0.224607i | \(0.0721099\pi\) |
0.890846 | + | 0.454305i | \(0.150112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.70931 | + | 14.7533i | −0.180621 | + | 0.983553i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.0341 | − | 13.1500i | −0.732362 | − | 0.872795i | 0.263407 | − | 0.964685i | \(-0.415154\pi\) |
−0.995769 | + | 0.0918895i | \(0.970709\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.9805 | − | 3.10482i | 1.18303 | − | 0.204282i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.2797 | + | 26.4653i | 0.996740 | + | 1.72640i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 29.9729 | + | 0.106177i | 1.94695 | + | 0.00689694i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.39276 | + | 6.57406i | 0.154775 | + | 0.425241i | 0.992710 | − | 0.120530i | \(-0.0384593\pi\) |
−0.837935 | + | 0.545770i | \(0.816237\pi\) | |||||||
\(240\) | 15.2470 | + | 2.74417i | 0.984186 | + | 0.177136i | ||||
\(241\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.1170 | − | 9.80700i | 0.777309 | − | 0.629119i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.4147 | + | 2.71802i | −0.984808 | + | 0.173648i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0863910 | + | 24.3874i | −0.00547481 | + | 1.54549i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | 14.8783 | + | 5.53495i | 0.937246 | + | 0.348669i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.17379 | − | 18.3800i | −0.198750 | − | 1.15100i | ||||
\(256\) | 2.77837 | − | 15.7569i | 0.173648 | − | 0.984808i | ||||
\(257\) | 23.4716 | + | 4.13868i | 1.46412 | + | 0.258164i | 0.848213 | − | 0.529655i | \(-0.177678\pi\) |
0.615907 | + | 0.787819i | \(0.288790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −24.5497 | − | 14.1738i | −1.52251 | − | 0.879021i | ||||
\(261\) | 31.7263 | + | 5.82626i | 1.96381 | + | 0.360636i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −18.9710 | + | 3.34510i | −1.15029 | + | 0.202827i | ||||
\(273\) | −22.1855 | − | 18.7502i | −1.34273 | − | 1.13481i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.7971 | + | 15.2509i | −0.771692 | + | 0.919667i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.68148 | − | 4.38742i | −0.219619 | − | 0.261731i | 0.644974 | − | 0.764204i | \(-0.276868\pi\) |
−0.864593 | + | 0.502473i | \(0.832424\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.42376 | − | 13.7458i | 0.144078 | − | 0.817106i | −0.824025 | − | 0.566553i | \(-0.808277\pi\) |
0.968103 | − | 0.250553i | \(-0.0806123\pi\) | |||||||
\(284\) | 13.8156 | + | 2.43606i | 0.819804 | + | 0.144553i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.09653 | + | 5.36335i | 0.182149 | + | 0.315491i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.0044 | − | 22.7097i | −0.762333 | − | 1.33127i | ||||
\(292\) | −22.2665 | − | 18.6838i | −1.30305 | − | 1.09339i | ||||
\(293\) | −2.84671 | − | 7.82127i | −0.166306 | − | 0.456923i | 0.828344 | − | 0.560220i | \(-0.189283\pi\) |
−0.994651 | + | 0.103296i | \(0.967061\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.4124 | − | 3.37600i | 1.18445 | − | 0.195895i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −16.2968 | + | 5.86627i | −0.940898 | + | 0.338689i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.316851 | + | 0.548803i | −0.0180837 | + | 0.0313218i | −0.874926 | − | 0.484257i | \(-0.839090\pi\) |
0.856842 | + | 0.515579i | \(0.172423\pi\) | |||||||
\(308\) | 13.5431 | + | 16.1401i | 0.771692 | + | 0.919667i | ||||
\(309\) | −21.4327 | + | 17.8552i | −1.21926 | + | 1.01574i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.4981 | + | 20.5564i | −1.38472 | + | 1.16192i | −0.417288 | + | 0.908774i | \(0.637019\pi\) |
−0.967429 | + | 0.253141i | \(0.918536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.5000 | + | 2.95804i | −0.986013 | + | 0.166667i | ||||
\(316\) | 17.3050 | + | 29.9731i | 0.973480 | + | 1.68612i | ||||
\(317\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.7965 | + | 27.5195i | 1.83625 | + | 1.54080i | ||||
\(320\) | 6.11824 | + | 16.8097i | 0.342020 | + | 0.939693i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 16.8255 | + | 6.39541i | 0.934752 | + | 0.355301i | ||||
\(325\) | 31.6936 | 1.75804 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.914858 | + | 5.08306i | −0.0505918 | + | 0.281094i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.2422 | + | 27.6990i | −1.28138 | + | 1.52709i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.34417 | − | 1.58115i | −0.238777 | − | 0.0869078i | 0.219860 | − | 0.975531i | \(-0.429440\pi\) |
−0.458637 | + | 0.888624i | \(0.651662\pi\) | |||||||
\(332\) | −24.3876 | + | 14.0802i | −1.33844 | + | 0.772750i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.11906 | + | 18.0630i | 0.170158 | + | 0.985417i | ||||
\(337\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.4986 | − | 13.8440i | 0.894764 | − | 0.750796i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.26013 | − | 16.0390i | −0.500000 | − | 0.866025i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(348\) | 12.6151 | + | 35.0456i | 0.676243 | + | 1.87864i | ||||
\(349\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.0047 | − | 21.4384i | −1.33465 | − | 1.14430i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.6219 | + | 6.10478i | −1.84274 | + | 0.324925i | −0.982686 | − | 0.185279i | \(-0.940681\pi\) |
−0.860054 | + | 0.510204i | \(0.829570\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.7387 | + | 5.36444i | −0.782247 | + | 0.284715i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.1515 | − | 10.9669i | 1.01361 | − | 0.580429i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.8765 | − | 12.6304i | 1.15460 | − | 0.666608i | 0.204595 | − | 0.978847i | \(-0.434412\pi\) |
0.950004 | + | 0.312239i | \(0.101079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.89052 | + | 2.90361i | 0.414145 | + | 0.152400i | ||||
\(364\) | 5.82439 | − | 33.0318i | 0.305281 | − | 1.73133i | ||||
\(365\) | 32.0041 | + | 5.64318i | 1.67517 | + | 0.295378i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.7672 | + | 23.2994i | −1.44943 | + | 1.21622i | −0.516443 | + | 0.856322i | \(0.672744\pi\) |
−0.932992 | + | 0.359898i | \(0.882811\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.5000 | − | 14.7902i | 0.645497 | − | 0.763763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 68.1555i | − | 3.51019i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.7356 | −1.93835 | −0.969173 | − | 0.246380i | \(-0.920759\pi\) | ||||
−0.969173 | + | 0.246380i | \(0.920759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1202 | + | 21.5948i | −0.925900 | + | 1.10344i | 0.0684880 | + | 0.997652i | \(0.478183\pi\) |
−0.994388 | + | 0.105793i | \(0.966262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.1357 | − | 8.05673i | −1.12814 | − | 0.410609i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.1090 | − | 26.1696i | 0.767044 | − | 1.32856i | ||||
\(389\) | 13.2008 | + | 15.7321i | 0.669305 | + | 0.797647i | 0.988689 | − | 0.149979i | \(-0.0479205\pi\) |
−0.319384 | + | 0.947625i | \(0.603476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33.5109 | − | 19.3475i | −1.68612 | − | 0.973480i | ||||
\(396\) | 15.2264 | + | 18.4095i | 0.765157 | + | 0.925111i | ||||
\(397\) | 0.115521 | + | 0.200088i | 0.00579782 | + | 0.0100421i | 0.868910 | − | 0.494971i | \(-0.164821\pi\) |
−0.863112 | + | 0.505013i | \(0.831488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.3209 | − | 12.8558i | −0.766044 | − | 0.642788i | ||||
\(401\) | −10.1171 | − | 27.7965i | −0.505223 | − | 1.38809i | −0.886113 | − | 0.463469i | \(-0.846604\pi\) |
0.380889 | − | 0.924621i | \(-0.375618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.8664 | + | 3.21343i | −0.987169 | + | 0.159677i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −30.2685 | − | 11.0168i | −1.49122 | − | 0.542761i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.7421 | − | 27.2662i | 0.772750 | − | 1.33844i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(420\) | −13.1175 | − | 15.7458i | −0.640070 | − | 0.768317i | ||||
\(421\) | 8.46757 | − | 7.10513i | 0.412684 | − | 0.346283i | −0.412688 | − | 0.910872i | \(-0.635410\pi\) |
0.825372 | + | 0.564590i | \(0.190966\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.5760 | + | 31.2202i | −1.29217 | + | 1.51798i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.23570 | + | 22.6274i | −0.399490 | + | 1.09759i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.8059 | − | 41.1318i | −0.714838 | − | 1.98586i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 29.7955i | − | 1.43520i | −0.696456 | − | 0.717599i | \(-0.745241\pi\) | ||
0.696456 | − | 0.717599i | \(-0.254759\pi\) | |||||||
\(432\) | 3.39148 | + | 20.5060i | 0.163173 | + | 0.986598i | ||||
\(433\) | 40.1484 | 1.92941 | 0.964703 | − | 0.263339i | \(-0.0848238\pi\) | ||||
0.964703 | + | 0.263339i | \(0.0848238\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.8056 | − | 26.8807i | −1.52496 | − | 1.28883i | ||||
\(436\) | −5.60406 | + | 2.03971i | −0.268386 | + | 0.0976845i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.3709 | − | 18.2605i | −0.493852 | − | 0.869546i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.1503 | + | 35.7357i | −0.621988 | + | 1.69024i | ||||
\(448\) | −16.2141 | + | 13.6052i | −0.766044 | + | 0.642788i | ||||
\(449\) | −24.6822 | − | 14.2503i | −1.16482 | − | 0.672511i | −0.212368 | − | 0.977190i | \(-0.568118\pi\) |
−0.952455 | + | 0.304679i | \(0.901451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.5848 | − | 30.7084i | −0.826204 | − | 1.44281i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.8259 | + | 35.2388i | 0.601286 | + | 1.65202i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.8034 | − | 12.2811i | 1.01769 | − | 0.573233i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(464\) | −27.6457 | + | 32.9469i | −1.28342 | + | 1.52952i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.9254 | − | 21.3189i | 1.70871 | − | 0.986521i | 0.772536 | − | 0.634970i | \(-0.218988\pi\) |
0.936169 | − | 0.351551i | \(-0.114346\pi\) | |||||||
\(468\) | 6.86943 | − | 37.4068i | 0.317539 | − | 1.72913i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.6917 | + | 10.5732i | −0.584802 | + | 0.487187i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.0693 | + | 12.7417i | 1.01154 | + | 0.584016i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.68586 | + | 9.56101i | 0.0766302 | + | 0.434591i | ||||
\(485\) | 33.7848i | 1.53409i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.930698 | + | 1.10916i | −0.0420018 | + | 0.0500558i | −0.786636 | − | 0.617417i | \(-0.788179\pi\) |
0.744635 | + | 0.667472i | \(0.232624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.6592 | + | 17.7105i | 2.19150 | + | 0.797641i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −25.0341 | − | 9.31306i | −1.12520 | − | 0.418591i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.9290 | − | 14.2164i | −0.535089 | − | 0.637694i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.74430 | + | 43.9201i | −0.346683 | + | 1.96613i | −0.114816 | + | 0.993387i | \(0.536628\pi\) |
−0.231867 | + | 0.972748i | \(0.574483\pi\) | |||||||
\(500\) | 22.0210 | + | 3.88289i | 0.984808 | + | 0.173648i | ||||
\(501\) | −3.93065 | − | 4.71821i | −0.175608 | − | 0.210794i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.39864 | − | 0.807506i | −0.0623624 | − | 0.0360049i | 0.468495 | − | 0.883466i | \(-0.344797\pi\) |
−0.530857 | + | 0.847461i | \(0.678130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.6822 | + | 40.6853i | −1.05176 | + | 1.80690i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.67710 | + | 37.8677i | 0.295378 | + | 1.67517i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.4660 | − | 6.25361i | 1.56282 | − | 0.275567i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.1351 | + | 18.6117i | −2.24892 | + | 0.818540i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.5931 | − | 12.9376i | 0.991727 | − | 0.567899i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.56344 | + | 9.63616i | −0.243272 | + | 0.421360i | −0.961644 | − | 0.274299i | \(-0.911554\pi\) |
0.718372 | + | 0.695659i | \(0.244888\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.5032 | + | 7.91289i | 0.938475 | + | 0.345347i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −9.52684 | + | 25.8891i | −0.414603 | + | 1.12668i | ||||
\(529\) | −17.6190 | + | 14.7841i | −0.766044 | + | 0.642788i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.11399 | − | 8.41738i | 0.306991 | − | 0.363237i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 27.8722i | − | 1.20054i | ||||||
\(540\) | −14.7470 | − | 17.9590i | −0.634611 | − | 0.772832i | ||||
\(541\) | −44.3483 | −1.90668 | −0.953340 | − | 0.301898i | \(-0.902380\pi\) | ||||
−0.953340 | + | 0.301898i | \(0.902380\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.28588 | − | 5.10771i | 0.183587 | − | 0.218790i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.95041 | − | 45.0890i | 0.338086 | − | 1.91738i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.09367 | − | 22.2372i | 0.342020 | − | 0.939693i | ||||
\(561\) | 33.2131 | + | 0.117655i | 1.40226 | + | 0.00496742i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.2301 | + | 44.5919i | 0.684019 | + | 1.87933i | 0.349503 | + | 0.936935i | \(0.386350\pi\) |
0.334515 | + | 0.942390i | \(0.391427\pi\) | |||||||
\(564\) | −46.5939 | − | 8.38605i | −1.96196 | − | 0.353116i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.6125 | − | 20.7882i | −0.487679 | − | 0.873023i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.8197 | − | 8.07924i | 1.92086 | − | 0.338699i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
0.998827 | + | 0.0484135i | \(0.0154165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.4758 | + | 16.1879i | −1.86125 | + | 0.677441i | −0.883231 | + | 0.468938i | \(0.844637\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | 32.4468 | − | 38.6686i | 1.35667 | − | 1.61681i | ||||
\(573\) | 0.0362990 | − | 10.2469i | 0.00151641 | − | 0.428070i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −18.4939 | + | 15.2963i | −0.770579 | + | 0.637344i | ||||
\(577\) | 2.39408 | − | 4.14668i | 0.0996670 | − | 0.172628i | −0.811880 | − | 0.583825i | \(-0.801556\pi\) |
0.911547 | + | 0.411196i | \(0.134889\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.34998 | − | 47.3551i | 0.346714 | − | 1.96631i | ||||
\(581\) | 36.6867 | + | 6.46886i | 1.52202 | + | 0.268373i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.2597 | + | 40.0591i | 0.589567 | + | 1.65624i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5764 | + | 34.5535i | −0.519085 | + | 1.42617i | 0.352445 | + | 0.935833i | \(0.385350\pi\) |
−0.871530 | + | 0.490342i | \(0.836872\pi\) | |||||||
\(588\) | 12.1987 | − | 20.9569i | 0.503065 | − | 0.864249i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.8642i | 1.71916i | 0.511003 | + | 0.859579i | \(0.329274\pi\) | ||||
−0.511003 | + | 0.859579i | \(0.670726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.4914 | −1.16803 | ||||||||
\(596\) | −43.3013 | + | 7.63519i | −1.77369 | + | 0.312749i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.3861 | − | 25.4870i | 0.873814 | − | 1.04137i | −0.124975 | − | 0.992160i | \(-0.539885\pi\) |
0.998788 | − | 0.0492108i | \(-0.0156706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.4306 | − | 35.3869i | 0.831310 | − | 1.43987i | ||||
\(605\) | −6.97710 | − | 8.31498i | −0.283659 | − | 0.338052i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.93157 | + | 39.3109i | −0.281344 | + | 1.59558i | 0.436717 | + | 0.899599i | \(0.356141\pi\) |
−0.718061 | + | 0.695980i | \(0.754970\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.0163 | − | 46.2416i | 0.689535 | − | 1.87380i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 75.0227 | + | 43.3143i | 3.03509 | + | 1.75231i | ||||
\(612\) | 24.9213 | + | 14.6247i | 1.00738 | + | 0.591168i | ||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 41.3204 | − | 14.8738i | 1.65414 | − | 0.595430i | ||||
\(625\) | −23.4923 | + | 8.55050i | −0.939693 | + | 0.342020i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.9240 | − | 6.52379i | −0.715244 | − | 0.260328i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.2979 | + | 21.3005i | −0.489570 | + | 0.847961i | −0.999928 | − | 0.0120014i | \(-0.996180\pi\) |
0.510357 | + | 0.859962i | \(0.329513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −36.8398 | + | 30.6905i | −1.46425 | + | 1.21984i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.9902 | + | 28.5211i | −1.34674 | + | 1.13005i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.4117 | − | 16.2153i | −0.530557 | − | 0.641469i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.4252 | + | 36.8855i | −0.530265 | + | 1.45689i | 0.328491 | + | 0.944507i | \(0.393460\pi\) |
−0.858756 | + | 0.512384i | \(0.828762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.8024 | − | 27.5245i | −1.29360 | − | 1.08546i | −0.991213 | − | 0.132273i | \(-0.957772\pi\) |
−0.302386 | − | 0.953186i | \(-0.597783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 50.1875i | − | 1.97307i | −0.163543 | − | 0.986536i | \(-0.552292\pi\) | ||
0.163543 | − | 0.986536i | \(-0.447708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.26673 | + | 42.9905i | 0.283502 | + | 1.67722i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.6238 | + | 37.6878i | 1.23189 | + | 1.46811i | 0.835009 | + | 0.550236i | \(0.185462\pi\) |
0.396878 | + | 0.917871i | \(0.370093\pi\) | |||||||
\(660\) | −5.24810 | − | 30.3926i | −0.204282 | − | 1.18303i | ||||
\(661\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.8429 | − | 40.6238i | −1.31435 | − | 1.57770i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 2.42526 | − | 6.66334i | 0.0938360 | − | 0.257812i | ||||
\(669\) | 25.8285 | − | 44.3725i | 0.998587 | − | 1.71554i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.3181 | + | 9.14489i | 0.936005 | + | 0.351987i | ||||
\(676\) | −54.3586 | −2.09071 | ||||||||
\(677\) | −43.8233 | + | 7.72722i | −1.68426 | + | 0.296981i | −0.932156 | − | 0.362058i | \(-0.882074\pi\) |
−0.752109 | + | 0.659039i | \(0.770963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.5639 | + | 13.6721i | −1.44157 | + | 0.524689i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.8016 | + | 14.7750i | −0.988721 | + | 0.566178i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(692\) | 26.0352 | + | 15.0314i | 0.989709 | + | 0.571409i | ||||
\(693\) | 0.223908 | − | 31.6033i | 0.00850557 | − | 1.20051i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.59430 | + | 26.0556i | 0.173648 | + | 0.984808i | ||||
\(701\) | 25.3074i | 0.955849i | 0.878401 | + | 0.477924i | \(0.158611\pi\) | ||||
−0.878401 | + | 0.477924i | \(0.841389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −31.3700 | + | 5.53137i | −1.18230 | + | 0.208472i | ||||
\(705\) | 49.8023 | − | 17.9270i | 1.87566 | − | 0.675170i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.8606 | + | 15.6000i | 1.60966 | + | 0.585869i | 0.981373 | − | 0.192110i | \(-0.0615331\pi\) |
0.628290 | + | 0.777980i | \(0.283755\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.37691 | − | 51.0610i | 0.351662 | − | 1.91494i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.80007 | + | 55.5790i | −0.366502 | + | 2.07854i | ||||
\(716\) | 12.5326 | + | 2.20983i | 0.468363 | + | 0.0825851i | ||||
\(717\) | 11.9407 | − | 2.06187i | 0.445932 | − | 0.0770021i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 9.35577 | − | 25.1489i | 0.348669 | − | 0.937246i | ||||
\(721\) | 21.3056 | + | 36.9024i | 0.793463 | + | 1.37432i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.3875 | + | 50.5191i | 0.682893 | + | 1.87623i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.32382 | + | 13.1790i | 0.0861857 | + | 0.488783i | 0.997094 | + | 0.0761754i | \(0.0242709\pi\) |
−0.910909 | + | 0.412608i | \(0.864618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | − | 23.6643i | −0.481481 | − | 0.876456i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.24147 | + | 2.63568i | −0.267470 | + | 0.0973511i | −0.472274 | − | 0.881452i | \(-0.656567\pi\) |
0.204804 | + | 0.978803i | \(0.434344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.0960380 | + | 27.1107i | −0.00354242 | + | 0.999994i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.8056 | − | 44.6967i | 0.949276 | − | 1.64419i | 0.202321 | − | 0.979319i | \(-0.435152\pi\) |
0.746955 | − | 0.664875i | \(-0.231515\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.6581 | − | 31.5989i | 1.37969 | − | 1.15769i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.5458 | + | 7.62953i | 1.52008 | + | 0.279150i | ||||
\(748\) | 19.1757 | + | 33.2133i | 0.701134 | + | 1.21440i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.3440 | − | 25.4616i | −1.10727 | − | 0.929108i | −0.109376 | − | 0.994000i | \(-0.534885\pi\) |
−0.997892 | + | 0.0648920i | \(0.979330\pi\) | |||||||
\(752\) | −18.6970 | − | 51.3696i | −0.681810 | − | 1.87326i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.6843i | 1.66262i | ||||||||
\(756\) | 14.0000 | − | 23.6643i | 0.509175 | − | 0.860663i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.41348 | + | 2.69829i | 0.268386 | + | 0.0976845i | ||||
\(764\) | 10.2470 | − | 5.91608i | 0.370722 | − | 0.214036i | ||||
\(765\) | −32.3053 | − | 0.228882i | −1.16800 | − | 0.00827525i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −26.0078 | − | 9.57053i | −0.938475 | − | 0.345347i | ||||
\(769\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2563 | − | 38.7414i | 0.513430 | − | 1.39524i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.4456 | − | 17.0004i | −1.05908 | − | 0.611463i | −0.133906 | − | 0.990994i | \(-0.542752\pi\) |
−0.925179 | + | 0.379531i | \(0.876085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −31.6936 | + | 37.5003i | −1.13481 | + | 1.34273i | ||||
\(781\) | −4.84988 | − | 27.5050i | −0.173542 | − | 0.984207i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.6657 | − | 52.2950i | 0.702794 | − | 1.86887i | ||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 21.0017 | − | 3.70317i | 0.749583 | − | 0.132172i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.9365 | − | 10.5320i | 1.03147 | − | 0.375426i | 0.229832 | − | 0.973230i | \(-0.426182\pi\) |
0.801642 | + | 0.597804i | \(0.203960\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.2577 | − | 3.04299i | −0.611298 | − | 0.107788i | −0.140576 | − | 0.990070i | \(-0.544895\pi\) |
−0.470722 | + | 0.882282i | \(0.656007\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.4189 | + | 42.3065i | −1.78369 | + | 1.49670i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.7922 | + | 54.3785i | −0.698450 | + | 1.91898i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.2539i | 1.83715i | 0.395249 | + | 0.918574i | \(0.370658\pi\) | ||||
−0.395249 | + | 0.918574i | \(0.629342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 56.0313 | − | 9.87983i | 1.96631 | − | 0.346714i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.118195 | + | 33.3654i | −0.00413765 | + | 1.16802i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.7694 | + | 32.0660i | −1.35471 | + | 1.12048i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.7426 | − | 43.7881i | −1.28233 | − | 1.52822i | −0.695592 | − | 0.718437i | \(-0.744858\pi\) |
−0.586734 | − | 0.809780i | \(-0.699586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22.0715 | + | 26.4938i | 0.768429 | + | 0.922395i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 38.8459 | + | 32.5956i | 1.34674 | + | 1.13005i | ||||
\(833\) | −11.5300 | − | 31.6784i | −0.399490 | − | 1.09759i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.37667 | + | 7.80751i | 0.0476418 | + | 0.270190i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 81.3880 | − | 29.6228i | 2.80648 | − | 1.02148i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.60857 | + | 4.92958i | −0.296495 | + | 0.169784i | ||||
\(844\) | −52.0274 | − | 18.9364i | −1.79086 | − | 0.651818i | ||||
\(845\) | 52.6325 | − | 30.3874i | 1.81061 | − | 1.04536i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.42157 | − | 11.1225i | 0.220648 | − | 0.382173i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.6884 | − | 8.34903i | −0.778663 | − | 0.286538i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 8.39138 | − | 22.8035i | 0.287484 | − | 0.781234i | ||||
\(853\) | 42.9160 | − | 36.0108i | 1.46942 | − | 1.23299i | 0.552741 | − | 0.833353i | \(-0.313582\pi\) |
0.916675 | − | 0.399633i | \(-0.130862\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5244 | − | 53.6429i | 0.666941 | − | 1.83241i | 0.124678 | − | 0.992197i | \(-0.460210\pi\) |
0.542263 | − | 0.840209i | \(-0.317568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.6113 | −1.14282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.0927 | − | 3.63302i | 0.342767 | − | 0.123384i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.2905 | − | 52.7834i | 1.50245 | − | 1.79055i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.7022 | + | 15.2006i | −1.44525 | + | 0.514462i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.0139 | − | 22.6599i | −0.642788 | − | 0.766044i | ||||
\(876\) | −38.6812 | + | 32.2246i | −1.30692 | + | 1.08877i | ||||
\(877\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.2060 | + | 2.45304i | −0.479156 | + | 0.0827391i | ||||
\(880\) | 27.2817 | − | 22.8921i | 0.919667 | − | 0.771692i | ||||
\(881\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(884\) | 20.8815 | − | 57.3715i | 0.702321 | − | 1.92961i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.98776 | + | 21.9462i | 0.268203 | + | 0.736881i | 0.998551 | + | 0.0538062i | \(0.0171353\pi\) |
−0.730349 | + | 0.683074i | \(0.760642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.507763 | − | 35.8321i | 0.0170107 | − | 1.20042i | ||||
\(892\) | 59.2849 | 1.98501 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.3699 | + | 4.86625i | −0.446907 | + | 0.162661i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | + | 29.5804i | 0.166667 | + | 0.986013i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(908\) | −29.7325 | − | 17.1661i | −0.986709 | − | 0.569677i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.8621 | + | 35.3384i | −0.426141 | + | 1.17081i | 0.521995 | + | 0.852949i | \(0.325188\pi\) |
−0.948136 | + | 0.317865i | \(0.897034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.9472 | + | 36.0370i | 1.42135 | + | 1.19265i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −60.6113 | −1.99938 | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) | ||||
−0.999691 | + | 0.0248659i | \(0.992084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.838310 | + | 0.708501i | 0.0276232 | + | 0.0233459i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.5796 | + | 34.0598i | −0.940709 | + | 1.12109i | ||||
\(924\) | 31.6685 | − | 18.1346i | 1.04182 | − | 0.596583i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.8613 | + | 42.0136i | 0.783707 | + | 1.37991i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −37.1336 | − | 21.4391i | −1.21440 | − | 0.701134i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.58659 | − | 14.8724i | −0.280512 | − | 0.485860i | 0.690999 | − | 0.722856i | \(-0.257171\pi\) |
−0.971511 | + | 0.236995i | \(0.923837\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.5254 | + | 48.0679i | 0.898259 | + | 1.56864i | ||||
\(940\) | 46.8198 | + | 39.2865i | 1.52709 | + | 1.28138i | ||||
\(941\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.326685 | + | 30.7391i | −0.0106271 | + | 0.999944i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(948\) | 56.4032 | − | 20.3031i | 1.83189 | − | 0.659414i | ||||
\(949\) | 86.5677 | − | 31.5081i | 2.81011 | − | 1.02279i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.61438 | + | 11.4564i | −0.214036 | + | 0.370722i | ||||
\(956\) | 8.99385 | + | 10.7184i | 0.290882 | + | 0.346659i | ||||
\(957\) | 56.9736 | − | 47.4636i | 1.84170 | − | 1.53428i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.5320 | − | 5.27217i | 0.985417 | − | 0.170158i | ||||
\(961\) | 23.7474 | − | 19.9264i | 0.766044 | − | 0.642788i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 16.0642 | − | 26.7197i | 0.515260 | − | 0.857034i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.72384 | − | 54.0268i | 0.311412 | − | 1.73024i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −27.1109 | + | 15.6525i | −0.866025 | + | 0.500000i | ||||
\(981\) | 8.38421 | + | 3.11905i | 0.267687 | + | 0.0995835i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.4158 | − | 45.7822i | −1.22528 | − | 1.46023i | −0.844498 | − | 0.535559i | \(-0.820101\pi\) |
−0.380778 | − | 0.924667i | \(-0.624344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 40.0865 | + | 48.1183i | 1.27597 | + | 1.53162i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.9935 | + | 38.0938i | 0.698645 | + | 1.21009i | 0.968936 | + | 0.247310i | \(0.0795467\pi\) |
−0.270291 | + | 0.962779i | \(0.587120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.02815 | + | 6.92023i | −0.127829 | + | 0.219607i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.5196 | + | 45.8925i | 0.523444 | + | 1.45416i | ||||
\(997\) | −3.21601 | − | 18.2389i | −0.101852 | − | 0.577632i | −0.992431 | − | 0.122803i | \(-0.960812\pi\) |
0.890579 | − | 0.454829i | \(-0.150299\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 945.2.cs.a.419.3 | yes | 24 | |
5.4 | even | 2 | inner | 945.2.cs.a.419.2 | ✓ | 24 | |
7.6 | odd | 2 | inner | 945.2.cs.a.419.2 | ✓ | 24 | |
27.2 | odd | 18 | inner | 945.2.cs.a.839.3 | yes | 24 | |
35.34 | odd | 2 | CM | 945.2.cs.a.419.3 | yes | 24 | |
135.29 | odd | 18 | inner | 945.2.cs.a.839.2 | yes | 24 | |
189.83 | even | 18 | inner | 945.2.cs.a.839.2 | yes | 24 | |
945.839 | even | 18 | inner | 945.2.cs.a.839.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.cs.a.419.2 | ✓ | 24 | 5.4 | even | 2 | inner | |
945.2.cs.a.419.2 | ✓ | 24 | 7.6 | odd | 2 | inner | |
945.2.cs.a.419.3 | yes | 24 | 1.1 | even | 1 | trivial | |
945.2.cs.a.419.3 | yes | 24 | 35.34 | odd | 2 | CM | |
945.2.cs.a.839.2 | yes | 24 | 135.29 | odd | 18 | inner | |
945.2.cs.a.839.2 | yes | 24 | 189.83 | even | 18 | inner | |
945.2.cs.a.839.3 | yes | 24 | 27.2 | odd | 18 | inner | |
945.2.cs.a.839.3 | yes | 24 | 945.839 | even | 18 | inner |