Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(269,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.t (of order \(6\), degree \(2\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.5 | ||
Root | \(-1.07992 + 0.623490i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.593 |
Dual form | 756.2.t.e.269.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.07992 | − | 1.87047i | 0.482953 | − | 0.836499i | −0.516855 | − | 0.856073i | \(-0.672897\pi\) |
0.999808 | + | 0.0195734i | \(0.00623081\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.167563 | − | 2.64044i | −0.0633328 | − | 0.997992i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.15625 | − | 0.667563i | 0.348623 | − | 0.201278i | −0.315455 | − | 0.948940i | \(-0.602157\pi\) |
0.664079 | + | 0.747663i | \(0.268824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.35021i | 0.651832i | 0.945399 | + | 0.325916i | \(0.105673\pi\) | ||||
−0.945399 | + | 0.325916i | \(0.894327\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.60166 | − | 6.23825i | −0.873530 | − | 1.51300i | −0.858321 | − | 0.513114i | \(-0.828492\pi\) |
−0.0152091 | − | 0.999884i | \(-0.504841\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.03803 | + | 0.599308i | 0.238141 | + | 0.137491i | 0.614322 | − | 0.789055i | \(-0.289430\pi\) |
−0.376181 | + | 0.926546i | \(0.622763\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.08350 | − | 1.20291i | −0.434439 | − | 0.250823i | 0.266797 | − | 0.963753i | \(-0.414035\pi\) |
−0.701236 | + | 0.712929i | \(0.747368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.167563 | + | 0.290227i | 0.0335126 | + | 0.0580455i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.14675i | − | 1.14142i | −0.821151 | − | 0.570712i | \(-0.806667\pi\) | ||
0.821151 | − | 0.570712i | \(-0.193333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.11141 | + | 4.10577i | −1.27725 | + | 0.737419i | −0.976341 | − | 0.216235i | \(-0.930622\pi\) |
−0.300905 | + | 0.953654i | \(0.597289\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.11982 | − | 2.53803i | −0.865407 | − | 0.429006i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.57338 | − | 4.45722i | 0.423060 | − | 0.732762i | −0.573177 | − | 0.819432i | \(-0.694289\pi\) |
0.996237 | + | 0.0866697i | \(0.0276225\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.47234 | 0.698462 | 0.349231 | − | 0.937037i | \(-0.386443\pi\) | ||||
0.349231 | + | 0.937037i | \(0.386443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.664874 | −0.101392 | −0.0506962 | − | 0.998714i | \(-0.516144\pi\) | ||||
−0.0506962 | + | 0.998714i | \(0.516144\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.07992 | − | 1.87047i | 0.157522 | − | 0.272836i | −0.776453 | − | 0.630176i | \(-0.782983\pi\) |
0.933974 | + | 0.357340i | \(0.116316\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94385 | + | 0.884879i | −0.991978 | + | 0.126411i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.0340 | − | 6.37047i | 1.51563 | − | 0.875051i | 0.515802 | − | 0.856708i | \(-0.327494\pi\) |
0.999832 | − | 0.0183431i | \(-0.00583913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.88365i | − | 0.388831i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.83424 | − | 8.37316i | −0.629365 | − | 1.09009i | −0.987679 | − | 0.156491i | \(-0.949982\pi\) |
0.358314 | − | 0.933601i | \(-0.383352\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6468 | + | 6.14691i | 1.36318 | + | 0.787031i | 0.990045 | − | 0.140748i | \(-0.0449507\pi\) |
0.373131 | + | 0.927778i | \(0.378284\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.39600 | + | 2.53803i | 0.545257 | + | 0.314804i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.86778 | + | 3.23509i | 0.228186 | + | 0.395229i | 0.957270 | − | 0.289194i | \(-0.0933873\pi\) |
−0.729085 | + | 0.684423i | \(0.760054\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4058i | 1.35362i | 0.736157 | + | 0.676810i | \(0.236638\pi\) | ||||
−0.736157 | + | 0.676810i | \(0.763362\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.07338 | − | 5.23852i | 1.06196 | − | 0.613122i | 0.135985 | − | 0.990711i | \(-0.456580\pi\) |
0.925973 | + | 0.377589i | \(0.123247\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.95640 | − | 2.94116i | −0.222953 | − | 0.335176i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.53803 | − | 7.86010i | 0.510569 | − | 0.884331i | −0.489356 | − | 0.872084i | \(-0.662768\pi\) |
0.999925 | − | 0.0122468i | \(-0.00389836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.7992 | −1.18536 | −0.592681 | − | 0.805437i | \(-0.701930\pi\) | ||||
−0.592681 | + | 0.805437i | \(0.701930\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.5579 | −1.68750 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.59808 | + | 4.50000i | −0.275396 | + | 0.476999i | −0.970235 | − | 0.242166i | \(-0.922142\pi\) |
0.694839 | + | 0.719165i | \(0.255475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.20560 | − | 0.393808i | 0.650523 | − | 0.0412823i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.24198 | − | 1.29440i | 0.230022 | − | 0.132803i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.23632i | − | 0.125530i | −0.998028 | − | 0.0627648i | \(-0.980008\pi\) | ||
0.998028 | − | 0.0627648i | \(-0.0199918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.95640 | − | 3.38859i | −0.194670 | − | 0.337177i | 0.752123 | − | 0.659023i | \(-0.229030\pi\) |
−0.946792 | + | 0.321846i | \(0.895697\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.57606 | − | 2.06464i | −0.352360 | − | 0.203435i | 0.313364 | − | 0.949633i | \(-0.398544\pi\) |
−0.665724 | + | 0.746198i | \(0.731877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.39823 | + | 1.96197i | 0.328519 | + | 0.189671i | 0.655183 | − | 0.755470i | \(-0.272591\pi\) |
−0.326664 | + | 0.945140i | \(0.605925\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.664874 | − | 1.15160i | −0.0636834 | − | 0.110303i | 0.832426 | − | 0.554137i | \(-0.186951\pi\) |
−0.896109 | + | 0.443834i | \(0.853618\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.4819i | 1.55048i | 0.631664 | + | 0.775242i | \(0.282372\pi\) | ||||
−0.631664 | + | 0.775242i | \(0.717628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.50000 | + | 2.59808i | −0.419627 | + | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.8682 | + | 10.5553i | −1.45464 | + | 0.967599i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.60872 | + | 7.98254i | −0.418975 | + | 0.725685i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5230 | 1.03065 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.8877 | 1.32107 | 0.660534 | − | 0.750796i | \(-0.270330\pi\) | ||||
0.660534 | + | 0.750796i | \(0.270330\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.92132 | + | 13.7201i | −0.692089 | + | 1.19873i | 0.279063 | + | 0.960273i | \(0.409976\pi\) |
−0.971152 | + | 0.238460i | \(0.923357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.40850 | − | 2.84128i | 0.122133 | − | 0.246371i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.7554 | − | 11.4058i | 1.68782 | − | 0.974464i | 0.731640 | − | 0.681691i | \(-0.238755\pi\) |
0.956182 | − | 0.292773i | \(-0.0945780\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3761i | 1.38900i | 0.719492 | + | 0.694500i | \(0.244374\pi\) | ||||
−0.719492 | + | 0.694500i | \(0.755626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.56891 | + | 2.71744i | 0.131199 | + | 0.227244i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.4973 | − | 6.63798i | −0.954800 | − | 0.551254i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.56522 | + | 4.36778i | 0.619767 | + | 0.357823i | 0.776778 | − | 0.629774i | \(-0.216853\pi\) |
−0.157011 | + | 0.987597i | \(0.550186\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.57338 | − | 6.18927i | −0.290797 | − | 0.503676i | 0.683201 | − | 0.730230i | \(-0.260587\pi\) |
−0.973998 | + | 0.226555i | \(0.927254\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.7356i | 1.42455i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.6060 | + | 6.12340i | −0.846453 | + | 0.488700i | −0.859453 | − | 0.511215i | \(-0.829195\pi\) |
0.0129992 | + | 0.999916i | \(0.495862\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.82709 | + | 5.70291i | −0.222806 | + | 0.449452i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.03803 | + | 13.9223i | −0.629587 | + | 1.09048i | 0.358047 | + | 0.933703i | \(0.383443\pi\) |
−0.987635 | + | 0.156774i | \(0.949891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3703 | 0.879860 | 0.439930 | − | 0.898032i | \(-0.355003\pi\) | ||||
0.439930 | + | 0.898032i | \(0.355003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.47650 | 0.575115 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.35241 | + | 11.0027i | −0.482964 | + | 0.836519i | −0.999809 | − | 0.0195605i | \(-0.993773\pi\) |
0.516844 | + | 0.856079i | \(0.327107\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.738250 | − | 0.491071i | 0.0558065 | − | 0.0371215i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.8862 | + | 8.01722i | −1.03791 | + | 0.599235i | −0.919239 | − | 0.393699i | \(-0.871195\pi\) |
−0.118666 | + | 0.992934i | \(0.537862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.0729i | − | 1.04603i | −0.852324 | − | 0.523015i | \(-0.824807\pi\) | ||
0.852324 | − | 0.523015i | \(-0.175193\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.55806 | − | 9.62684i | −0.408637 | − | 0.707780i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.32885 | − | 4.80866i | −0.609066 | − | 0.351644i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.7662 | + | 13.1441i | 1.64730 | + | 0.951071i | 0.978138 | + | 0.207958i | \(0.0666817\pi\) |
0.669166 | + | 0.743113i | \(0.266652\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.53803 | − | 2.66395i | −0.110710 | − | 0.191755i | 0.805347 | − | 0.592804i | \(-0.201979\pi\) |
−0.916057 | + | 0.401049i | \(0.868646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.08144i | 0.647026i | 0.946224 | + | 0.323513i | \(0.104864\pi\) | ||||
−0.946224 | + | 0.323513i | \(0.895136\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6468 | − | 11.3431i | 1.39272 | − | 0.804088i | 0.399106 | − | 0.916905i | \(-0.369321\pi\) |
0.993616 | + | 0.112817i | \(0.0359874\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.2301 | + | 1.02997i | −1.13913 | + | 0.0722895i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.82975 | − | 8.36537i | 0.337324 | − | 0.584263i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.60030 | 0.110695 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.81700 | 0.675830 | 0.337915 | − | 0.941177i | \(-0.390278\pi\) | ||||
0.337915 | + | 0.941177i | \(0.390278\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.718009 | + | 1.24363i | −0.0489678 | + | 0.0848147i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0327 | + | 18.0893i | 0.816830 | + | 1.22798i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6612 | − | 8.46466i | 0.986220 | − | 0.569394i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.05064i | 0.472146i | 0.971735 | + | 0.236073i | \(0.0758604\pi\) | ||||
−0.971735 | + | 0.236073i | \(0.924140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.87772 | − | 17.1087i | −0.655608 | − | 1.13555i | −0.981741 | − | 0.190222i | \(-0.939079\pi\) |
0.326134 | − | 0.945324i | \(-0.394254\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.88590 | + | 1.66618i | 0.190706 | + | 0.110104i | 0.592313 | − | 0.805708i | \(-0.298215\pi\) |
−0.401607 | + | 0.915812i | \(0.631548\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.48172 | − | 3.16487i | −0.359120 | − | 0.207338i | 0.309575 | − | 0.950875i | \(-0.399813\pi\) |
−0.668695 | + | 0.743537i | \(0.733147\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.33244 | − | 4.03990i | −0.152151 | − | 0.263534i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.8877i | 1.80390i | 0.431836 | + | 0.901952i | \(0.357866\pi\) | ||||
−0.431836 | + | 0.901952i | \(0.642134\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.79350 | − | 4.49958i | 0.502024 | − | 0.289844i | −0.227525 | − | 0.973772i | \(-0.573063\pi\) |
0.729549 | + | 0.683929i | \(0.239730\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.84363 | + | 13.9438i | −0.373336 | + | 0.890840i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.40850 | + | 2.43960i | −0.0896208 | + | 0.155228i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5230 | −0.727324 | −0.363662 | − | 0.931531i | \(-0.618474\pi\) | ||||
−0.363662 | + | 0.931531i | \(0.618474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.21206 | −0.201941 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.56891 | − | 2.71744i | 0.0978662 | − | 0.169509i | −0.812935 | − | 0.582354i | \(-0.802132\pi\) |
0.910801 | + | 0.412845i | \(0.135465\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2002 | − | 6.04798i | −0.758085 | − | 0.375803i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.87772 | − | 5.70291i | 0.609087 | − | 0.351656i | −0.163521 | − | 0.986540i | \(-0.552285\pi\) |
0.772608 | + | 0.634884i | \(0.218952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 27.5183i | − | 1.69043i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.6721 | − | 18.4846i | −0.650688 | − | 1.12702i | −0.982956 | − | 0.183839i | \(-0.941147\pi\) |
0.332269 | − | 0.943185i | \(-0.392186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5434 | − | 8.97399i | −0.944195 | − | 0.545131i | −0.0529220 | − | 0.998599i | \(-0.516853\pi\) |
−0.891273 | + | 0.453467i | \(0.850187\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.387490 | + | 0.223717i | 0.0233665 | + | 0.0134907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8850 | + | 27.5136i | 0.954437 | + | 1.65313i | 0.735651 | + | 0.677361i | \(0.236877\pi\) |
0.218787 | + | 0.975773i | \(0.429790\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.55794i | − | 0.212249i | −0.994353 | − | 0.106125i | \(-0.966156\pi\) | ||
0.994353 | − | 0.106125i | \(-0.0338442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.71475 | − | 3.87676i | 0.399151 | − | 0.230450i | −0.286967 | − | 0.957941i | \(-0.592647\pi\) |
0.686117 | + | 0.727491i | \(0.259314\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.749397 | − | 11.8089i | −0.0442355 | − | 0.697060i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.4438 | + | 30.2136i | −1.02611 | + | 1.77727i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.04348 | 0.294643 | 0.147322 | − | 0.989089i | \(-0.452935\pi\) | ||||
0.147322 | + | 0.989089i | \(0.452935\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.8823 | −1.21582 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.82709 | − | 4.89666i | 0.163495 | − | 0.283181i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.111408 | + | 1.75556i | 0.00642146 | + | 0.101189i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.9952 | − | 13.2763i | 1.31670 | − | 0.760198i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.0080i | − | 0.856552i | −0.903648 | − | 0.428276i | \(-0.859121\pi\) | ||
0.903648 | − | 0.428276i | \(-0.140879\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.04348 | − | 8.73556i | −0.285989 | − | 0.495348i | 0.686859 | − | 0.726791i | \(-0.258989\pi\) |
−0.972849 | + | 0.231442i | \(0.925656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.5761 | + | 8.99284i | 0.880411 | + | 0.508306i | 0.870794 | − | 0.491648i | \(-0.163605\pi\) |
0.00961724 | + | 0.999954i | \(0.496939\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.09646 | − | 2.36509i | −0.230080 | − | 0.132837i | 0.380529 | − | 0.924769i | \(-0.375742\pi\) |
−0.610609 | + | 0.791932i | \(0.709075\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.10334 | − | 7.10720i | −0.229743 | − | 0.397927i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.63401i | − | 0.480409i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.682096 | + | 0.393808i | −0.0378359 | + | 0.0218445i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.11982 | − | 2.53803i | −0.282265 | − | 0.139926i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.38859 | − | 2.40511i | 0.0763239 | − | 0.132197i | −0.825337 | − | 0.564640i | \(-0.809015\pi\) |
0.901661 | + | 0.432443i | \(0.142348\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.06819 | 0.440812 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.99462 | −0.381021 | −0.190511 | − | 0.981685i | \(-0.561014\pi\) | ||||
−0.190511 | + | 0.981685i | \(0.561014\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.48172 | + | 9.49462i | −0.296852 | + | 0.514163i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.50000 | + | 18.1865i | 0.188982 | + | 0.981981i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.5840 | − | 10.1521i | 0.943959 | − | 0.544995i | 0.0527597 | − | 0.998607i | \(-0.483198\pi\) |
0.891199 | + | 0.453612i | \(0.149865\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.77414i | 0.523198i | 0.965177 | + | 0.261599i | \(0.0842498\pi\) | ||||
−0.965177 | + | 0.261599i | \(0.915750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.42874 | − | 11.1349i | −0.342167 | − | 0.592651i | 0.642668 | − | 0.766145i | \(-0.277828\pi\) |
−0.984835 | + | 0.173494i | \(0.944494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.3342 | + | 12.3173i | 1.13230 | + | 0.653735i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.7447 | + | 9.66756i | 0.883752 | + | 0.510234i | 0.871894 | − | 0.489695i | \(-0.162892\pi\) |
0.0118583 | + | 0.999930i | \(0.496225\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.78166 | − | 15.2103i | −0.462193 | − | 0.800541i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 22.6286i | − | 1.18444i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.2881 | + | 13.4454i | −1.21563 | + | 0.701845i | −0.963980 | − | 0.265974i | \(-0.914307\pi\) |
−0.251650 | + | 0.967818i | \(0.580973\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.6697 | − | 28.0671i | −0.969284 | − | 1.45717i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.2228 | − | 33.2949i | 0.995320 | − | 1.72394i | 0.413970 | − | 0.910291i | \(-0.364142\pi\) |
0.581350 | − | 0.813654i | \(-0.302525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.4462 | 0.744016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.05993 | 0.157178 | 0.0785891 | − | 0.996907i | \(-0.474958\pi\) | ||||
0.0785891 | + | 0.996907i | \(0.474958\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.84140 | − | 11.8497i | 0.349579 | − | 0.605489i | −0.636595 | − | 0.771198i | \(-0.719658\pi\) |
0.986175 | + | 0.165709i | \(0.0529912\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.61410 | + | 0.483192i | −0.388050 | + | 0.0246257i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.768763 | + | 0.443845i | −0.0389778 | + | 0.0225039i | −0.519362 | − | 0.854554i | \(-0.673830\pi\) |
0.480384 | + | 0.877058i | \(0.340497\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.3298i | 0.876407i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.80139 | − | 16.9765i | −0.493161 | − | 0.854180i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.6114 | − | 17.0962i | −1.48615 | − | 0.858031i | −0.486278 | − | 0.873804i | \(-0.661646\pi\) |
−0.999876 | + | 0.0157726i | \(0.994979\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.1514 | − | 13.9438i | −1.20607 | − | 0.696322i | −0.244168 | − | 0.969733i | \(-0.578515\pi\) |
−0.961897 | + | 0.273410i | \(0.911848\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.64944 | − | 16.7133i | −0.480673 | − | 0.832550i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.87156i | − | 0.340611i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6848 | − | 6.74621i | 0.577775 | − | 0.333579i | −0.182473 | − | 0.983211i | \(-0.558410\pi\) |
0.760249 | + | 0.649632i | \(0.225077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.2988 | + | 14.1676i | −1.04804 | + | 0.697140i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.6622 | + | 20.1995i | −0.572474 | + | 0.991554i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.9368 | −1.36480 | −0.682400 | − | 0.730979i | \(-0.739064\pi\) | ||||
−0.682400 | + | 0.730979i | \(0.739064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5472 | 0.611513 | 0.305756 | − | 0.952110i | \(-0.401091\pi\) | ||||
0.305756 | + | 0.952110i | \(0.401091\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.20701 | − | 2.09060i | 0.0585484 | − | 0.101409i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.4465 | − | 29.1421i | 0.699117 | − | 1.41029i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.9720 | − | 8.64406i | 0.721174 | − | 0.416370i | −0.0940108 | − | 0.995571i | \(-0.529969\pi\) |
0.815185 | + | 0.579201i | \(0.196635\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.1920i | 1.30676i | 0.757028 | + | 0.653382i | \(0.226651\pi\) | ||||
−0.757028 | + | 0.653382i | \(0.773349\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.44182 | − | 2.49731i | −0.0689718 | − | 0.119463i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.49462 | + | 5.48172i | 0.453154 | + | 0.261628i | 0.709161 | − | 0.705046i | \(-0.249074\pi\) |
−0.256008 | + | 0.966675i | \(0.582407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.9697 | − | 9.22013i | −0.758745 | − | 0.438062i | 0.0701001 | − | 0.997540i | \(-0.477668\pi\) |
−0.828845 | + | 0.559478i | \(0.811001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.61141 | + | 9.71924i | 0.266006 | + | 0.460736i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.6179i | 1.11460i | 0.830312 | + | 0.557298i | \(0.188162\pi\) | ||||
−0.830312 | + | 0.557298i | \(0.811838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.17115 | − | 2.98557i | 0.243500 | − | 0.140585i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.96492 | − | 12.0327i | 0.279640 | − | 0.564100i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.6141 | − | 25.3124i | 0.683619 | − | 1.18406i | −0.290250 | − | 0.956951i | \(-0.593739\pi\) |
0.973869 | − | 0.227111i | \(-0.0729281\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.91997 | −0.275720 | −0.137860 | − | 0.990452i | \(-0.544022\pi\) | ||||
−0.137860 | + | 0.990452i | \(0.544022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.4349 | 1.60032 | 0.800162 | − | 0.599784i | \(-0.204747\pi\) | ||||
0.800162 | + | 0.599784i | \(0.204747\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3114 | − | 33.4483i | 0.893625 | − | 1.54780i | 0.0581276 | − | 0.998309i | \(-0.481487\pi\) |
0.835497 | − | 0.549495i | \(-0.185180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.22909 | − | 5.47384i | 0.379984 | − | 0.252759i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.768763 | + | 0.443845i | −0.0353478 | + | 0.0204080i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.401687i | 0.0184307i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.51816 | + | 2.62953i | 0.0693665 | + | 0.120146i | 0.898623 | − | 0.438722i | \(-0.144569\pi\) |
−0.829256 | + | 0.558869i | \(0.811236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.4754 | + | 6.04798i | 0.477638 | + | 0.275764i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.31251 | − | 1.33513i | −0.105005 | − | 0.0606249i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.3850 | + | 23.1835i | 0.606532 | + | 1.05054i | 0.991807 | + | 0.127743i | \(0.0407733\pi\) |
−0.385275 | + | 0.922802i | \(0.625893\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.9584i | − | 0.494545i | −0.968946 | − | 0.247272i | \(-0.920466\pi\) | ||
0.968946 | − | 0.247272i | \(-0.0795342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.3450 | + | 22.1385i | −1.72697 | + | 0.997067i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.1164 | − | 1.91119i | 1.35090 | − | 0.0857286i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0499 | − | 26.0672i | 0.673725 | − | 1.16693i | −0.303115 | − | 0.952954i | \(-0.598027\pi\) |
0.976840 | − | 0.213972i | \(-0.0686401\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0941 | 0.539250 | 0.269625 | − | 0.962965i | \(-0.413100\pi\) | ||||
0.269625 | + | 0.962965i | \(0.413100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.45101 | −0.376065 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.5266 | + | 21.6966i | −0.555230 | + | 0.961686i | 0.442656 | + | 0.896692i | \(0.354036\pi\) |
−0.997886 | + | 0.0649946i | \(0.979297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.3523 | − | 23.0799i | −0.679148 | − | 1.02100i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.72370 | + | 4.45928i | −0.340347 | + | 0.196499i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.88365i | − | 0.126823i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.35956 | − | 14.4792i | −0.366239 | − | 0.634345i | 0.622735 | − | 0.782433i | \(-0.286021\pi\) |
−0.988974 | + | 0.148088i | \(0.952688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.5327 | − | 13.0092i | −0.985284 | − | 0.568854i | −0.0814229 | − | 0.996680i | \(-0.525946\pi\) |
−0.903861 | + | 0.427826i | \(0.859280\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 51.2257 | + | 29.5752i | 2.23143 | + | 1.28831i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.60603 | − | 14.9061i | −0.374175 | − | 0.648091i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5109i | 0.455280i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.33960 | − | 4.23752i | 0.317319 | − | 0.183204i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.43813 | + | 5.65860i | −0.320383 | + | 0.243733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.4973 | + | 26.8421i | −0.666281 | + | 1.15403i | 0.312655 | + | 0.949867i | \(0.398782\pi\) |
−0.978936 | + | 0.204167i | \(0.934552\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.87203 | −0.123024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.3696 | −1.55505 | −0.777525 | − | 0.628852i | \(-0.783525\pi\) | ||||
−0.777525 | + | 0.628852i | \(0.783525\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.68380 | − | 6.38053i | 0.156935 | − | 0.271820i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.5145 | − | 10.6653i | −0.914891 | − | 0.453536i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.6697 | − | 10.7790i | 0.791062 | − | 0.456720i | −0.0492745 | − | 0.998785i | \(-0.515691\pi\) |
0.840336 | + | 0.542066i | \(0.182358\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.56260i | − | 0.0660908i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.356101 | − | 0.616785i | −0.0150079 | − | 0.0259944i | 0.858424 | − | 0.512941i | \(-0.171444\pi\) |
−0.873432 | + | 0.486946i | \(0.838111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.8288 | + | 17.7990i | 1.29698 | + | 0.748811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.7742 | − | 17.1902i | −1.24820 | − | 0.720649i | −0.277450 | − | 0.960740i | \(-0.589489\pi\) |
−0.970750 | + | 0.240091i | \(0.922823\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.7201 | + | 22.0319i | 0.532321 | + | 0.922007i | 0.999288 | + | 0.0377320i | \(0.0120133\pi\) |
−0.466967 | + | 0.884275i | \(0.654653\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.806250i | − | 0.0336229i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.45928 | − | 4.30662i | 0.310534 | − | 0.179287i | −0.336631 | − | 0.941636i | \(-0.609288\pi\) |
0.647165 | + | 0.762350i | \(0.275954\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.80954 | + | 28.5145i | 0.0750723 | + | 1.18298i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.50538 | − | 14.7317i | 0.352257 | − | 0.610127i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.6853 | 1.30779 | 0.653896 | − | 0.756585i | \(-0.273134\pi\) | ||||
0.653896 | + | 0.756585i | \(0.273134\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.84249 | −0.405553 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.1456 | + | 41.8215i | −0.991543 | + | 1.71740i | −0.383378 | + | 0.923592i | \(0.625239\pi\) |
−0.608165 | + | 0.793811i | \(0.708094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.60693 | + | 41.0798i | 0.106874 | + | 1.68411i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.6952 | + | 14.8351i | −1.04988 | + | 0.606147i | −0.922615 | − | 0.385722i | \(-0.873952\pi\) |
−0.127262 | + | 0.991869i | \(0.540619\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.0577i | 1.67478i | 0.546606 | + | 0.837390i | \(0.315920\pi\) | ||||
−0.546606 | + | 0.837390i | \(0.684080\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.95406 | + | 17.2409i | 0.404690 | + | 0.700944i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.8016 | + | 11.4324i | 0.803721 | + | 0.464028i | 0.844771 | − | 0.535129i | \(-0.179737\pi\) |
−0.0410497 | + | 0.999157i | \(0.513070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.39600 | + | 2.53803i | 0.177843 | + | 0.102678i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.7029 | − | 22.0021i | −0.513066 | − | 0.888656i | −0.999885 | − | 0.0151531i | \(-0.995176\pi\) |
0.486820 | − | 0.873503i | \(-0.338157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14.9638i | − | 0.602418i | −0.953558 | − | 0.301209i | \(-0.902610\pi\) | ||
0.953558 | − | 0.301209i | \(-0.0973902\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.6767 | + | 8.47361i | −0.589907 | + | 0.340583i | −0.765061 | − | 0.643958i | \(-0.777291\pi\) |
0.175154 | + | 0.984541i | \(0.443958\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.3173 | + | 6.10603i | 0.493483 | + | 0.244633i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.6060 | − | 20.1022i | 0.464241 | − | 0.804089i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.0737 | −1.47822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.3534 | −0.850067 | −0.425033 | − | 0.905178i | \(-0.639738\pi\) | ||||
−0.425033 | + | 0.905178i | \(0.639738\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0775 | − | 27.8470i | 0.638014 | − | 1.10507i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.07965 | − | 16.3195i | −0.0823989 | − | 0.646603i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.8064 | + | 22.4049i | −1.53276 | + | 0.884941i | −0.533529 | + | 0.845781i | \(0.679135\pi\) |
−0.999233 | + | 0.0391594i | \(0.987532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18.8487i | − | 0.743321i | −0.928369 | − | 0.371660i | \(-0.878789\pi\) | ||
0.928369 | − | 0.371660i | \(-0.121211\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5404 | + | 33.8450i | 0.768213 | + | 1.33058i | 0.938531 | + | 0.345194i | \(0.112187\pi\) |
−0.170319 | + | 0.985389i | \(0.554480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.1792 | − | 6.45432i | −0.438823 | − | 0.253354i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.2652 | − | 5.92662i | −0.401709 | − | 0.231927i | 0.285512 | − | 0.958375i | \(-0.407836\pi\) |
−0.687221 | + | 0.726448i | \(0.741170\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.1087 | + | 29.6332i | 0.668493 | + | 1.15786i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3226i | 1.29806i | 0.760762 | + | 0.649032i | \(0.224826\pi\) | ||||
−0.760762 | + | 0.649032i | \(0.775174\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.69285 | + | 1.55472i | −0.104740 | + | 0.0604715i | −0.551455 | − | 0.834205i | \(-0.685927\pi\) |
0.446715 | + | 0.894676i | \(0.352594\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.79347 | − | 5.70291i | −0.147104 | − | 0.221149i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.39397 | + | 12.8067i | −0.286296 | + | 0.495879i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.4138 | 0.633647 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.68100 | 0.103345 | 0.0516726 | − | 0.998664i | \(-0.483545\pi\) | ||||
0.0516726 | + | 0.998664i | \(0.483545\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2737 | + | 24.7228i | −0.548584 | + | 0.950175i | 0.449788 | + | 0.893135i | \(0.351500\pi\) |
−0.998372 | + | 0.0570397i | \(0.981834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.26444 | + | 0.207162i | −0.125278 | + | 0.00795014i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.0377 | + | 21.9611i | −1.45547 | + | 0.840317i | −0.998784 | − | 0.0493101i | \(-0.984298\pi\) |
−0.456688 | + | 0.889627i | \(0.650964\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 49.2693i | − | 1.88248i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.9720 | + | 25.9322i | 0.570386 | + | 0.987938i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.1060 | + | 15.6497i | 1.03116 | + | 0.595342i | 0.917317 | − | 0.398157i | \(-0.130350\pi\) |
0.113845 | + | 0.993499i | \(0.463683\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.6309 | + | 17.6848i | 1.16190 | + | 0.670822i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.1078 | − | 27.8996i | −0.610127 | − | 1.05677i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.2591i | − | 0.878483i | −0.898369 | − | 0.439241i | \(-0.855247\pi\) | ||
0.898369 | − | 0.439241i | \(-0.144753\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.34249 | − | 3.08449i | 0.201496 | − | 0.116334i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.61955 | + | 5.73357i | −0.324172 | + | 0.215633i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.2962 | + | 17.8335i | −0.386682 | + | 0.669752i | −0.992001 | − | 0.126231i | \(-0.959712\pi\) |
0.605319 | + | 0.795983i | \(0.293045\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.7554 | 0.739847 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.77718 | 0.253452 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.76014 | − | 6.51275i | 0.140229 | − | 0.242884i | −0.787354 | − | 0.616502i | \(-0.788549\pi\) |
0.927583 | + | 0.373617i | \(0.121883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.85235 | + | 9.78834i | −0.180711 | + | 0.364537i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.78396 | − | 1.02997i | 0.0662544 | − | 0.0382520i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.2949i | − | 1.23484i | −0.786634 | − | 0.617420i | \(-0.788178\pi\) | ||
0.786634 | − | 0.617420i | \(-0.211822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.39465 | + | 4.14765i | 0.0885693 | + | 0.153406i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.3859 | + | 7.72835i | 0.494420 | + | 0.285453i | 0.726406 | − | 0.687266i | \(-0.241189\pi\) |
−0.231986 | + | 0.972719i | \(0.574523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.31925 | + | 2.49372i | 0.159102 | + | 0.0918574i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.10872 | − | 5.38446i | −0.114356 | − | 0.198071i | 0.803166 | − | 0.595755i | \(-0.203147\pi\) |
−0.917522 | + | 0.397685i | \(0.869814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0291i | 0.441304i | 0.975353 | + | 0.220652i | \(0.0708184\pi\) | ||||
−0.975353 | + | 0.220652i | \(0.929182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.3396 | − | 9.43367i | 0.598637 | − | 0.345623i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.61104 | − | 9.30157i | 0.168484 | − | 0.339872i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.8877 | − | 29.2503i | 0.616241 | − | 1.06736i | −0.373925 | − | 0.927459i | \(-0.621988\pi\) |
0.990165 | − | 0.139901i | \(-0.0446784\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.4358 | −0.561766 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.5870 | 1.80227 | 0.901135 | − | 0.433538i | \(-0.142735\pi\) | ||||
0.901135 | + | 0.433538i | \(0.142735\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.9647 | + | 34.5798i | −0.723719 | + | 1.25352i | 0.235780 | + | 0.971806i | \(0.424236\pi\) |
−0.959499 | + | 0.281712i | \(0.909098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.92931 | + | 1.94853i | −0.106048 | + | 0.0705414i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.6787 | − | 11.3615i | 0.710557 | − | 0.410240i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.4693i | 0.557839i | 0.960315 | + | 0.278919i | \(0.0899762\pi\) | ||||
−0.960315 | + | 0.278919i | \(0.910024\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.3666 | + | 30.0798i | 0.624633 | + | 1.08190i | 0.988612 | + | 0.150489i | \(0.0480849\pi\) |
−0.363978 | + | 0.931407i | \(0.618582\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.38321 | − | 1.37595i | −0.0856076 | − | 0.0494256i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.64243 | + | 2.68031i | 0.166332 | + | 0.0960320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.61410 | + | 13.1880i | 0.272454 | + | 0.471904i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.4510i | 0.944077i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5814 | + | 13.0374i | −0.804941 | + | 0.464733i | −0.845196 | − | 0.534456i | \(-0.820516\pi\) |
0.0402547 | + | 0.999189i | \(0.487183\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.5194 | − | 2.76175i | 1.54737 | − | 0.0981965i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.4465 | + | 25.0221i | −0.513011 | + | 0.888562i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.1013 | −0.499493 | −0.249746 | − | 0.968311i | \(-0.580347\pi\) | ||||
−0.249746 | + | 0.968311i | \(0.580347\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.5579 | −0.550400 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.99408 | − | 12.1141i | 0.246816 | − | 0.427497i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.61410 | + | 11.4466i | 0.268362 | + | 0.403441i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.4791 | + | 15.8651i | −0.966115 | + | 0.557787i | −0.898050 | − | 0.439894i | \(-0.855016\pi\) |
−0.0680656 | + | 0.997681i | \(0.521683\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18.3590i | − | 0.644671i | −0.946625 | − | 0.322336i | \(-0.895532\pi\) | ||
0.946625 | − | 0.322336i | \(-0.104468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.3608 | + | 30.0698i | 0.608122 | + | 1.05330i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.690161 | − | 0.398465i | −0.0241457 | − | 0.0139405i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.8858 | − | 9.74900i | −0.589317 | − | 0.340243i | 0.175510 | − | 0.984478i | \(-0.443843\pi\) |
−0.764828 | + | 0.644235i | \(0.777176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.317904 | − | 0.550626i | −0.0110814 | − | 0.0191936i | 0.860432 | − | 0.509566i | \(-0.170194\pi\) |
−0.871513 | + | 0.490372i | \(0.836861\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 28.6939i | − | 0.997786i | −0.866664 | − | 0.498893i | \(-0.833740\pi\) | ||
0.866664 | − | 0.498893i | \(-0.166260\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5461 | − | 17.0584i | 1.02618 | − | 0.592464i | 0.110291 | − | 0.993899i | \(-0.464822\pi\) |
0.915888 | + | 0.401435i | \(0.131488\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.5294 | + | 40.1304i | 1.05778 | + | 1.39044i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.2790 | − | 21.2678i | 0.424931 | − | 0.736003i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.6105 | −0.504409 | −0.252205 | − | 0.967674i | \(-0.581156\pi\) | ||||
−0.252205 | + | 0.967674i | \(0.581156\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.78256 | −0.302847 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.07399 | − | 13.9846i | 0.277754 | − | 0.481084i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.8497 | + | 10.8315i | 0.750763 | + | 0.372174i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7232 | + | 6.19106i | −0.367588 | + | 0.212227i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.1794i | 0.930604i | 0.885152 | + | 0.465302i | \(0.154054\pi\) | ||||
−0.885152 | + | 0.465302i | \(0.845946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.30893 | + | 2.26713i | 0.0447121 | + | 0.0774436i | 0.887515 | − | 0.460778i | \(-0.152430\pi\) |
−0.842803 | + | 0.538222i | \(0.819096\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.9783 | − | 22.5041i | −1.32992 | − | 0.767831i | −0.344635 | − | 0.938737i | \(-0.611997\pi\) |
−0.985287 | + | 0.170906i | \(0.945331\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.8475 | − | 14.9230i | −0.879858 | − | 0.507986i | −0.00924613 | − | 0.999957i | \(-0.502943\pi\) |
−0.870611 | + | 0.491971i | \(0.836277\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7201 | + | 23.7640i | 0.466498 | + | 0.807999i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 12.1177i | − | 0.411064i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.60315 | + | 4.38968i | −0.257623 | + | 0.148739i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.93082 | − | 30.4257i | −0.0652737 | − | 1.02858i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3642 | + | 35.2718i | −0.687650 | + | 1.19104i | 0.284946 | + | 0.958543i | \(0.408024\pi\) |
−0.972596 | + | 0.232501i | \(0.925309\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.774980 | 0.0261097 | 0.0130549 | − | 0.999915i | \(-0.495844\pi\) | ||||
0.0130549 | + | 0.999915i | \(0.495844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.22819 | 0.243248 | 0.121624 | − | 0.992576i | \(-0.461190\pi\) | ||||
0.121624 | + | 0.992576i | \(0.461190\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.9588 | − | 46.6939i | 0.905187 | − | 1.56783i | 0.0845199 | − | 0.996422i | \(-0.473064\pi\) |
0.820667 | − | 0.571407i | \(-0.193602\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.49462 | − | 39.3101i | −0.0836670 | − | 1.31842i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.24198 | − | 1.29440i | 0.0750248 | − | 0.0433156i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.6317i | 1.15761i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.2372 | + | 43.7121i | 0.841707 | + | 1.45788i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −79.4812 | − | 45.8885i | −2.64790 | − | 1.52877i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.3229 | − | 15.1975i | −0.875003 | − | 0.505183i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1468 | − | 29.6990i | −0.569349 | − | 0.986141i | −0.996631 | − | 0.0820222i | \(-0.973862\pi\) |
0.427282 | − | 0.904118i | \(-0.359471\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.55794i | 0.117880i | 0.998262 | + | 0.0589399i | \(0.0187720\pi\) | ||||
−0.998262 | + | 0.0589399i | \(0.981228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4866 | + | 7.20912i | −0.413245 | + | 0.238587i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.5545 | + | 18.6168i | 1.24016 | + | 0.614780i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.3931 | + | 35.3218i | −0.672705 | + | 1.16516i | 0.304429 | + | 0.952535i | \(0.401534\pi\) |
−0.977134 | + | 0.212625i | \(0.931799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.8061 | −0.882333 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.72481 | 0.0567114 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.9356 | + | 20.6731i | −0.391596 | + | 0.678263i | −0.992660 | − | 0.120937i | \(-0.961410\pi\) |
0.601065 | + | 0.799200i | \(0.294743\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.73825 | − | 3.24297i | −0.253611 | − | 0.106284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.9889 | + | 10.3859i | −0.588300 | + | 0.339655i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.4063i | 1.58136i | 0.612228 | + | 0.790682i | \(0.290274\pi\) | ||||
−0.612228 | + | 0.790682i | \(0.709726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.44676 | − | 7.70201i | −0.144960 | − | 0.251078i | 0.784398 | − | 0.620258i | \(-0.212972\pi\) |
−0.929358 | + | 0.369180i | \(0.879639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.31809 | − | 5.37980i | −0.303439 | − | 0.175191i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.7559 | − | 9.67403i | −0.544494 | − | 0.314364i | 0.202404 | − | 0.979302i | \(-0.435124\pi\) |
−0.746898 | + | 0.664938i | \(0.768458\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.3116 | + | 21.3244i | 0.399652 | + | 0.692218i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21.7409i | − | 0.704258i | −0.935951 | − | 0.352129i | \(-0.885458\pi\) | ||
0.935951 | − | 0.352129i | \(-0.114542\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 49.1711 | − | 28.3890i | 1.59114 | − | 0.918645i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.4266 | − | 50.2519i | −1.07940 | − | 1.62272i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.2148 | − | 31.5489i | 0.587573 | − | 1.01771i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.64378 | −0.213871 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1866 | −0.391894 | −0.195947 | − | 0.980615i | \(-0.562778\pi\) | ||||
−0.195947 | + | 0.980615i | \(0.562778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.67441 | − | 4.63222i | 0.0858260 | − | 0.148655i | −0.819917 | − | 0.572483i | \(-0.805980\pi\) |
0.905743 | + | 0.423828i | \(0.139314\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43.2400 | − | 2.74402i | 1.38621 | − | 0.0879693i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.00851 | − | 2.31431i | 0.128244 | − | 0.0740415i | −0.434506 | − | 0.900669i | \(-0.643077\pi\) |
0.562749 | + | 0.826628i | \(0.309744\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.93752i | 0.221724i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.03274 | + | 3.52081i | 0.0648344 | + | 0.112296i | 0.896621 | − | 0.442800i | \(-0.146015\pi\) |
−0.831786 | + | 0.555096i | \(0.812681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.9866 | + | 9.80719i | 0.541237 | + | 0.312483i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.38526 | + | 0.799782i | 0.0440488 | + | 0.0254316i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.7582 | − | 44.6144i | −0.818235 | − | 1.41722i | −0.906982 | − | 0.421170i | \(-0.861619\pi\) |
0.0887467 | − | 0.996054i | \(-0.471714\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 48.9982i | − | 1.55335i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.49731 | + | 3.17387i | −0.174102 | + | 0.100518i | −0.584518 | − | 0.811380i | \(-0.698717\pi\) |
0.410417 | + | 0.911898i | \(0.365383\pi\) | |||||||
\(998\) | 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 | 756.2.t.e.593.5 | yes | 12 | |
3.2 | odd | 2 | inner | 756.2.t.e.593.2 | yes | 12 | |
7.2 | even | 3 | 5292.2.f.e.2645.4 | 12 | |||
7.3 | odd | 6 | inner | 756.2.t.e.269.2 | ✓ | 12 | |
7.5 | odd | 6 | 5292.2.f.e.2645.10 | 12 | |||
9.2 | odd | 6 | 2268.2.w.i.1349.2 | 12 | |||
9.4 | even | 3 | 2268.2.bm.i.593.2 | 12 | |||
9.5 | odd | 6 | 2268.2.bm.i.593.5 | 12 | |||
9.7 | even | 3 | 2268.2.w.i.1349.5 | 12 | |||
21.2 | odd | 6 | 5292.2.f.e.2645.9 | 12 | |||
21.5 | even | 6 | 5292.2.f.e.2645.3 | 12 | |||
21.17 | even | 6 | inner | 756.2.t.e.269.5 | yes | 12 | |
63.31 | odd | 6 | 2268.2.w.i.269.2 | 12 | |||
63.38 | even | 6 | 2268.2.bm.i.1025.2 | 12 | |||
63.52 | odd | 6 | 2268.2.bm.i.1025.5 | 12 | |||
63.59 | even | 6 | 2268.2.w.i.269.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.t.e.269.2 | ✓ | 12 | 7.3 | odd | 6 | inner | |
756.2.t.e.269.5 | yes | 12 | 21.17 | even | 6 | inner | |
756.2.t.e.593.2 | yes | 12 | 3.2 | odd | 2 | inner | |
756.2.t.e.593.5 | yes | 12 | 1.1 | even | 1 | trivial | |
2268.2.w.i.269.2 | 12 | 63.31 | odd | 6 | |||
2268.2.w.i.269.5 | 12 | 63.59 | even | 6 | |||
2268.2.w.i.1349.2 | 12 | 9.2 | odd | 6 | |||
2268.2.w.i.1349.5 | 12 | 9.7 | even | 3 | |||
2268.2.bm.i.593.2 | 12 | 9.4 | even | 3 | |||
2268.2.bm.i.593.5 | 12 | 9.5 | odd | 6 | |||
2268.2.bm.i.1025.2 | 12 | 63.38 | even | 6 | |||
2268.2.bm.i.1025.5 | 12 | 63.52 | odd | 6 | |||
5292.2.f.e.2645.3 | 12 | 21.5 | even | 6 | |||
5292.2.f.e.2645.4 | 12 | 7.2 | even | 3 | |||
5292.2.f.e.2645.9 | 12 | 21.2 | odd | 6 | |||
5292.2.f.e.2645.10 | 12 | 7.5 | odd | 6 |