Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1063,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.1063");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1063.7 | ||
Character | \(\chi\) | \(=\) | 2394.1063 |
Dual form | 2394.2.e.d.1063.5 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.63913i | 0.733043i | 0.930410 | + | 0.366521i | \(0.119451\pi\) | ||||
−0.930410 | + | 0.366521i | \(0.880549\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.91223 | − | 1.82849i | 0.722755 | − | 0.691105i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.63913 | −0.518340 | ||||||||
\(11\) | −2.23105 | −0.672686 | −0.336343 | − | 0.941740i | \(-0.609190\pi\) | ||||
−0.336343 | + | 0.941740i | \(0.609190\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.801180 | 0.222207 | 0.111104 | − | 0.993809i | \(-0.464561\pi\) | ||||
0.111104 | + | 0.993809i | \(0.464561\pi\) | |||||||
\(14\) | 1.82849 | + | 1.91223i | 0.488685 | + | 0.511065i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.71542i | − | 0.658587i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.13440 | + | 3.02912i | 0.719080 | + | 0.694927i | ||||
\(20\) | − | 1.63913i | − | 0.366521i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.23105i | − | 0.475661i | ||||||
\(23\) | −6.49732 | −1.35478 | −0.677392 | − | 0.735622i | \(-0.736890\pi\) | ||||
−0.677392 | + | 0.735622i | \(0.736890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.31324 | 0.462648 | ||||||||
\(26\) | 0.801180i | 0.157124i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.91223 | + | 1.82849i | −0.361377 | + | 0.345552i | ||||
\(29\) | 3.82446i | 0.710184i | 0.934831 | + | 0.355092i | \(0.115550\pi\) | ||||
−0.934831 | + | 0.355092i | \(0.884450\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.19251 | 0.932602 | 0.466301 | − | 0.884626i | \(-0.345586\pi\) | ||||
0.466301 | + | 0.884626i | \(0.345586\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.71542 | 0.465691 | ||||||||
\(35\) | 2.99714 | + | 3.13440i | 0.506609 | + | 0.529810i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.19617i | 1.18304i | 0.806289 | + | 0.591522i | \(0.201473\pi\) | ||||
−0.806289 | + | 0.591522i | \(0.798527\pi\) | |||||||
\(38\) | −3.02912 | + | 3.13440i | −0.491387 | + | 0.508467i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.63913 | 0.259170 | ||||||||
\(41\) | 6.99299 | 1.09212 | 0.546061 | − | 0.837746i | \(-0.316127\pi\) | ||||
0.546061 | + | 0.837746i | \(0.316127\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.13770 | 1.08849 | 0.544244 | − | 0.838927i | \(-0.316816\pi\) | ||||
0.544244 | + | 0.838927i | \(0.316816\pi\) | |||||||
\(44\) | 2.23105 | 0.336343 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 6.49732i | − | 0.957977i | ||||||
\(47\) | 1.91424i | 0.279221i | 0.990207 | + | 0.139610i | \(0.0445850\pi\) | ||||
−0.990207 | + | 0.139610i | \(0.955415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.313241 | − | 6.99299i | 0.0447487 | − | 0.998998i | ||||
\(50\) | 2.31324i | 0.327142i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.801180 | −0.111104 | ||||||||
\(53\) | − | 1.19798i | − | 0.164555i | −0.996609 | − | 0.0822774i | \(-0.973781\pi\) | ||
0.996609 | − | 0.0822774i | \(-0.0262193\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.65698i | − | 0.493107i | ||||||
\(56\) | −1.82849 | − | 1.91223i | −0.244342 | − | 0.255532i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.82446 | −0.502176 | ||||||||
\(59\) | 4.59174 | 0.597793 | 0.298897 | − | 0.954285i | \(-0.403381\pi\) | ||||
0.298897 | + | 0.954285i | \(0.403381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.934757i | − | 0.119683i | −0.998208 | − | 0.0598417i | \(-0.980940\pi\) | ||
0.998208 | − | 0.0598417i | \(-0.0190596\pi\) | |||||||
\(62\) | 5.19251i | 0.659449i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.31324i | 0.162887i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.2257i | 1.86011i | 0.367417 | + | 0.930056i | \(0.380242\pi\) | ||||
−0.367417 | + | 0.930056i | \(0.619758\pi\) | |||||||
\(68\) | 2.71542i | 0.329293i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.13440 | + | 2.99714i | −0.374632 | + | 0.358227i | ||||
\(71\) | − | 1.19798i | − | 0.142174i | −0.997470 | − | 0.0710868i | \(-0.977353\pi\) | ||
0.997470 | − | 0.0710868i | \(-0.0226467\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.99299i | − | 0.818467i | −0.912430 | − | 0.409234i | \(-0.865796\pi\) | ||
0.912430 | − | 0.409234i | \(-0.134204\pi\) | |||||||
\(74\) | −7.19617 | −0.836538 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.13440 | − | 3.02912i | −0.359540 | − | 0.347463i | ||||
\(77\) | −4.26627 | + | 4.07945i | −0.486187 | + | 0.464896i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.503034i | 0.0565957i | 0.999600 | + | 0.0282979i | \(0.00900869\pi\) | ||||
−0.999600 | + | 0.0282979i | \(0.990991\pi\) | |||||||
\(80\) | 1.63913i | 0.183261i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.99299i | 0.772246i | ||||||||
\(83\) | 11.1494i | 1.22381i | 0.790932 | + | 0.611904i | \(0.209596\pi\) | ||||
−0.790932 | + | 0.611904i | \(0.790404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.45094 | 0.482772 | ||||||||
\(86\) | 7.13770i | 0.769678i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.23105i | 0.237830i | ||||||||
\(89\) | 13.9860 | 1.48251 | 0.741255 | − | 0.671223i | \(-0.234231\pi\) | ||||
0.741255 | + | 0.671223i | \(0.234231\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.53204 | − | 1.46495i | 0.160601 | − | 0.153569i | ||||
\(92\) | 6.49732 | 0.677392 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.91424 | −0.197439 | ||||||||
\(95\) | −4.96513 | + | 5.13770i | −0.509411 | + | 0.527117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.9811 | 1.82570 | 0.912850 | − | 0.408294i | \(-0.133876\pi\) | ||||
0.912850 | + | 0.408294i | \(0.133876\pi\) | |||||||
\(98\) | 6.99299 | + | 0.313241i | 0.706398 | + | 0.0316421i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.31324 | −0.231324 | ||||||||
\(101\) | − | 9.29610i | − | 0.924997i | −0.886620 | − | 0.462498i | \(-0.846953\pi\) | ||
0.886620 | − | 0.462498i | \(-0.153047\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0115 | −1.18353 | −0.591765 | − | 0.806110i | \(-0.701569\pi\) | ||||
−0.591765 | + | 0.806110i | \(0.701569\pi\) | |||||||
\(104\) | − | 0.801180i | − | 0.0785621i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.19798 | 0.116358 | ||||||||
\(107\) | 2.62648i | 0.253912i | 0.991908 | + | 0.126956i | \(0.0405206\pi\) | ||||
−0.991908 | + | 0.126956i | \(0.959479\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.26627i | 0.408635i | 0.978905 | + | 0.204317i | \(0.0654974\pi\) | ||||
−0.978905 | + | 0.204317i | \(0.934503\pi\) | |||||||
\(110\) | 3.65698 | 0.348680 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.91223 | − | 1.82849i | 0.180689 | − | 0.172776i | ||||
\(113\) | 11.5886i | 1.09017i | 0.838382 | + | 0.545084i | \(0.183502\pi\) | ||||
−0.838382 | + | 0.545084i | \(0.816498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 10.6500i | − | 0.993115i | ||||||
\(116\) | − | 3.82446i | − | 0.355092i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.59174i | 0.422704i | ||||||||
\(119\) | −4.96513 | − | 5.19251i | −0.455152 | − | 0.475997i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.02243 | −0.547494 | ||||||||
\(122\) | 0.934757 | 0.0846289 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.19251 | −0.466301 | ||||||||
\(125\) | 11.9874i | 1.07218i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.503034i | − | 0.0446370i | −0.999751 | − | 0.0223185i | \(-0.992895\pi\) | ||
0.999751 | − | 0.0223185i | \(-0.00710480\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.31324 | −0.115179 | ||||||||
\(131\) | 14.2135i | 1.24184i | 0.783874 | + | 0.620920i | \(0.213241\pi\) | ||||
−0.783874 | + | 0.620920i | \(0.786759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.5324 | + | 0.0611424i | 0.999986 | + | 0.00530172i | ||||
\(134\) | −15.2257 | −1.31530 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.71542 | −0.232846 | ||||||||
\(137\) | −1.53219 | −0.130904 | −0.0654520 | − | 0.997856i | \(-0.520849\pi\) | ||||
−0.0654520 | + | 0.997856i | \(0.520849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.33601i | − | 0.282956i | −0.989941 | − | 0.141478i | \(-0.954815\pi\) | ||
0.989941 | − | 0.141478i | \(-0.0451855\pi\) | |||||||
\(140\) | −2.99714 | − | 3.13440i | −0.253305 | − | 0.264905i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.19798 | 0.100532 | ||||||||
\(143\) | −1.78747 | −0.149476 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.26880 | −0.520595 | ||||||||
\(146\) | 6.99299 | 0.578744 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 7.19617i | − | 0.591522i | ||||||
\(149\) | −20.1908 | −1.65410 | −0.827048 | − | 0.562132i | \(-0.809981\pi\) | ||||
−0.827048 | + | 0.562132i | \(0.809981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.02951i | − | 0.653432i | −0.945123 | − | 0.326716i | \(-0.894058\pi\) | ||
0.945123 | − | 0.326716i | \(-0.105942\pi\) | |||||||
\(152\) | 3.02912 | − | 3.13440i | 0.245694 | − | 0.254233i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.07945 | − | 4.26627i | −0.328731 | − | 0.343786i | ||||
\(155\) | 8.51122i | 0.683637i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.33601i | − | 0.266242i | −0.991100 | − | 0.133121i | \(-0.957500\pi\) | ||
0.991100 | − | 0.133121i | \(-0.0424999\pi\) | |||||||
\(158\) | −0.503034 | −0.0400192 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.63913 | −0.129585 | ||||||||
\(161\) | −12.4244 | + | 11.8803i | −0.979177 | + | 0.936298i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.62648 | −0.205722 | −0.102861 | − | 0.994696i | \(-0.532800\pi\) | ||||
−0.102861 | + | 0.994696i | \(0.532800\pi\) | |||||||
\(164\) | −6.99299 | −0.546061 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.1494 | −0.865363 | ||||||||
\(167\) | 10.9709 | 0.848957 | 0.424479 | − | 0.905438i | \(-0.360457\pi\) | ||||
0.424479 | + | 0.905438i | \(0.360457\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3581 | −0.950624 | ||||||||
\(170\) | 4.45094i | 0.341372i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.13770 | −0.544244 | ||||||||
\(173\) | 20.3652 | 1.54834 | 0.774168 | − | 0.632980i | \(-0.218168\pi\) | ||||
0.774168 | + | 0.632980i | \(0.218168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.42345 | − | 4.22974i | 0.334381 | − | 0.319738i | ||||
\(176\) | −2.23105 | −0.168171 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.9860i | 1.04829i | ||||||||
\(179\) | 18.7866i | 1.40418i | 0.712089 | + | 0.702089i | \(0.247749\pi\) | ||||
−0.712089 | + | 0.702089i | \(0.752251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.250962 | −0.0186539 | −0.00932694 | − | 0.999957i | \(-0.502969\pi\) | ||||
−0.00932694 | + | 0.999957i | \(0.502969\pi\) | |||||||
\(182\) | 1.46495 | + | 1.53204i | 0.108589 | + | 0.113562i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.49732i | 0.478989i | ||||||||
\(185\) | −11.7955 | −0.867221 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.05823i | 0.443022i | ||||||||
\(188\) | − | 1.91424i | − | 0.139610i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.13770 | − | 4.96513i | −0.372728 | − | 0.360208i | ||||
\(191\) | 23.9540 | 1.73325 | 0.866627 | − | 0.498957i | \(-0.166283\pi\) | ||||
0.866627 | + | 0.498957i | \(0.166283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.4564i | − | 0.752666i | −0.926484 | − | 0.376333i | \(-0.877185\pi\) | ||
0.926484 | − | 0.376333i | \(-0.122815\pi\) | |||||||
\(194\) | 17.9811i | 1.29097i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.313241 | + | 6.99299i | −0.0223743 | + | 0.499499i | ||||
\(197\) | 0.195821 | 0.0139516 | 0.00697582 | − | 0.999976i | \(-0.497780\pi\) | ||||
0.00697582 | + | 0.999976i | \(0.497780\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9860i | 0.991440i | 0.868483 | + | 0.495720i | \(0.165096\pi\) | ||||
−0.868483 | + | 0.495720i | \(0.834904\pi\) | |||||||
\(200\) | − | 2.31324i | − | 0.163571i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.29610 | 0.654072 | ||||||||
\(203\) | 6.99299 | + | 7.31324i | 0.490812 | + | 0.513289i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.4624i | 0.800572i | ||||||||
\(206\) | − | 12.0115i | − | 0.836883i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.801180 | 0.0555518 | ||||||||
\(209\) | −6.99299 | − | 6.75810i | −0.483715 | − | 0.467467i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.69314i | 0.460775i | 0.973099 | + | 0.230387i | \(0.0739993\pi\) | ||||
−0.973099 | + | 0.230387i | \(0.926001\pi\) | |||||||
\(212\) | 1.19798i | 0.0822774i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.62648 | −0.179543 | ||||||||
\(215\) | 11.6996i | 0.797909i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.92927 | − | 9.49446i | 0.674043 | − | 0.644526i | ||||
\(218\) | −4.26627 | −0.288948 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.65698i | 0.246554i | ||||||||
\(221\) | − | 2.17554i | − | 0.146343i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.03993 | −0.203569 | −0.101784 | − | 0.994806i | \(-0.532455\pi\) | ||||
−0.101784 | + | 0.994806i | \(0.532455\pi\) | |||||||
\(224\) | 1.82849 | + | 1.91223i | 0.122171 | + | 0.127766i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.5886 | −0.770865 | ||||||||
\(227\) | −27.3582 | −1.81583 | −0.907913 | − | 0.419159i | \(-0.862325\pi\) | ||||
−0.907913 | + | 0.419159i | \(0.862325\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.84747i | − | 0.386412i | −0.981158 | − | 0.193206i | \(-0.938111\pi\) | ||
0.981158 | − | 0.193206i | \(-0.0618885\pi\) | |||||||
\(230\) | 10.6500 | 0.702238 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.82446 | 0.251088 | ||||||||
\(233\) | 3.06438 | 0.200754 | 0.100377 | − | 0.994949i | \(-0.467995\pi\) | ||||
0.100377 | + | 0.994949i | \(0.467995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.13770 | −0.204681 | ||||||||
\(236\) | −4.59174 | −0.298897 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.19251 | − | 4.96513i | 0.336580 | − | 0.321841i | ||||
\(239\) | −15.4215 | −0.997534 | −0.498767 | − | 0.866736i | \(-0.666214\pi\) | ||||
−0.498767 | + | 0.866736i | \(0.666214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.42769 | 0.156381 | 0.0781905 | − | 0.996938i | \(-0.475086\pi\) | ||||
0.0781905 | + | 0.996938i | \(0.475086\pi\) | |||||||
\(242\) | − | 6.02243i | − | 0.387137i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.934757i | 0.0598417i | ||||||||
\(245\) | 11.4624 | + | 0.513444i | 0.732309 | + | 0.0328027i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.51122 | + | 2.42687i | 0.159785 | + | 0.154418i | ||||
\(248\) | − | 5.19251i | − | 0.329725i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.9874 | −0.758148 | ||||||||
\(251\) | − | 9.90835i | − | 0.625409i | −0.949850 | − | 0.312705i | \(-0.898765\pi\) | ||
0.949850 | − | 0.312705i | \(-0.101235\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.4958 | 0.911344 | ||||||||
\(254\) | 0.503034 | 0.0315632 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.80250 | 0.299572 | 0.149786 | − | 0.988718i | \(-0.452142\pi\) | ||||
0.149786 | + | 0.988718i | \(0.452142\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.1581 | + | 13.7607i | 0.817607 | + | 0.855050i | ||||
\(260\) | − | 1.31324i | − | 0.0814437i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.2135 | −0.878113 | ||||||||
\(263\) | 7.89503 | 0.486828 | 0.243414 | − | 0.969922i | \(-0.421733\pi\) | ||||
0.243414 | + | 0.969922i | \(0.421733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.96364 | 0.120626 | ||||||||
\(266\) | −0.0611424 | + | 11.5324i | −0.00374888 | + | 0.707097i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 15.2257i | − | 0.930056i | ||||||
\(269\) | −8.78046 | −0.535354 | −0.267677 | − | 0.963509i | \(-0.586256\pi\) | ||||
−0.267677 | + | 0.963509i | \(0.586256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.9569i | 1.51603i | 0.652240 | + | 0.758013i | \(0.273829\pi\) | ||||
−0.652240 | + | 0.758013i | \(0.726171\pi\) | |||||||
\(272\) | − | 2.71542i | − | 0.164647i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1.53219i | − | 0.0925630i | ||||||
\(275\) | −5.16095 | −0.311217 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.62648 | 0.518315 | 0.259158 | − | 0.965835i | \(-0.416555\pi\) | ||||
0.259158 | + | 0.965835i | \(0.416555\pi\) | |||||||
\(278\) | 3.33601 | 0.200080 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.13440 | − | 2.99714i | 0.187316 | − | 0.179113i | ||||
\(281\) | − | 26.8865i | − | 1.60391i | −0.597383 | − | 0.801956i | \(-0.703793\pi\) | ||
0.597383 | − | 0.801956i | \(-0.296207\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.97796i | − | 0.236465i | −0.992986 | − | 0.118233i | \(-0.962277\pi\) | ||
0.992986 | − | 0.118233i | \(-0.0377228\pi\) | |||||||
\(284\) | 1.19798i | 0.0710868i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1.78747i | − | 0.105695i | ||||||
\(287\) | 13.3722 | − | 12.7866i | 0.789336 | − | 0.754770i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.62648 | 0.566264 | ||||||||
\(290\) | − | 6.26880i | − | 0.368117i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.99299i | 0.409234i | ||||||||
\(293\) | −3.97796 | −0.232395 | −0.116197 | − | 0.993226i | \(-0.537071\pi\) | ||||
−0.116197 | + | 0.993226i | \(0.537071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.52647i | 0.438208i | ||||||||
\(296\) | 7.19617 | 0.418269 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 20.1908i | − | 1.16962i | ||||||
\(299\) | −5.20552 | −0.301043 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.6489 | − | 13.0512i | 0.786710 | − | 0.752260i | ||||
\(302\) | 8.02951 | 0.462046 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.13440 | + | 3.02912i | 0.179770 | + | 0.173732i | ||||
\(305\) | 1.53219 | 0.0877330 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.8585 | −1.13339 | −0.566693 | − | 0.823929i | \(-0.691778\pi\) | ||||
−0.566693 | + | 0.823929i | \(0.691778\pi\) | |||||||
\(308\) | 4.26627 | − | 4.07945i | 0.243093 | − | 0.232448i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.51122 | −0.483405 | ||||||||
\(311\) | − | 22.3230i | − | 1.26582i | −0.774225 | − | 0.632911i | \(-0.781860\pi\) | ||
0.774225 | − | 0.632911i | \(-0.218140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.12347i | 0.289596i | 0.989461 | + | 0.144798i | \(0.0462532\pi\) | ||||
−0.989461 | + | 0.144798i | \(0.953747\pi\) | |||||||
\(314\) | 3.33601 | 0.188262 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 0.503034i | − | 0.0282979i | ||||||
\(317\) | − | 13.8794i | − | 0.779547i | −0.920911 | − | 0.389774i | \(-0.872553\pi\) | ||
0.920911 | − | 0.389774i | \(-0.127447\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.53254i | − | 0.477731i | ||||||
\(320\) | − | 1.63913i | − | 0.0916304i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.8803 | − | 12.4244i | −0.662062 | − | 0.692382i | ||||
\(323\) | 8.22533 | − | 8.51122i | 0.457670 | − | 0.473577i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.85332 | 0.102804 | ||||||||
\(326\) | − | 2.62648i | − | 0.145467i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.99299i | − | 0.386123i | ||||||
\(329\) | 3.50018 | + | 3.66047i | 0.192971 | + | 0.201808i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 25.6821i | − | 1.41161i | −0.708405 | − | 0.705807i | \(-0.750585\pi\) | ||
0.708405 | − | 0.705807i | \(-0.249415\pi\) | |||||||
\(332\) | − | 11.1494i | − | 0.611904i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.9709i | 0.600303i | ||||||||
\(335\) | −24.9569 | −1.36354 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.92383i | − | 0.104798i | −0.998626 | − | 0.0523989i | \(-0.983313\pi\) | ||
0.998626 | − | 0.0523989i | \(-0.0166867\pi\) | |||||||
\(338\) | − | 12.3581i | − | 0.672193i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.45094 | −0.241386 | ||||||||
\(341\) | −11.5847 | −0.627348 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.1876 | − | 13.9450i | −0.658070 | − | 0.752957i | ||||
\(344\) | − | 7.13770i | − | 0.384839i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.3652i | 1.09484i | ||||||||
\(347\) | 34.0801 | 1.82952 | 0.914758 | − | 0.404002i | \(-0.132381\pi\) | ||||
0.914758 | + | 0.404002i | \(0.132381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 31.9499i | − | 1.71024i | −0.518431 | − | 0.855120i | \(-0.673484\pi\) | ||
0.518431 | − | 0.855120i | \(-0.326516\pi\) | |||||||
\(350\) | 4.22974 | + | 4.42345i | 0.226089 | + | 0.236443i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 2.23105i | − | 0.118915i | ||||||
\(353\) | − | 19.2957i | − | 1.02701i | −0.858088 | − | 0.513503i | \(-0.828348\pi\) | ||
0.858088 | − | 0.513503i | \(-0.171652\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.96364 | 0.104219 | ||||||||
\(356\) | −13.9860 | −0.741255 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.7866 | −0.992904 | ||||||||
\(359\) | −9.56170 | −0.504647 | −0.252324 | − | 0.967643i | \(-0.581195\pi\) | ||||
−0.252324 | + | 0.967643i | \(0.581195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.648917 | + | 18.9889i | 0.0341535 | + | 0.999417i | ||||
\(362\) | − | 0.250962i | − | 0.0131903i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.53204 | + | 1.46495i | −0.0803007 | + | 0.0767843i | ||||
\(365\) | 11.4624 | 0.599972 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.9709i | 0.572679i | 0.958128 | + | 0.286339i | \(0.0924385\pi\) | ||||
−0.958128 | + | 0.286339i | \(0.907562\pi\) | |||||||
\(368\) | −6.49732 | −0.338696 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 11.7955i | − | 0.613218i | ||||||
\(371\) | −2.19049 | − | 2.29081i | −0.113725 | − | 0.118933i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.7116i | 1.74552i | 0.488151 | + | 0.872759i | \(0.337672\pi\) | ||||
−0.488151 | + | 0.872759i | \(0.662328\pi\) | |||||||
\(374\) | −6.05823 | −0.313264 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.91424 | 0.0987195 | ||||||||
\(377\) | 3.06408i | 0.157808i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 28.6120i | − | 1.46970i | −0.678231 | − | 0.734849i | \(-0.737253\pi\) | ||
0.678231 | − | 0.734849i | \(-0.262747\pi\) | |||||||
\(380\) | 4.96513 | − | 5.13770i | 0.254706 | − | 0.263558i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.9540i | 1.22560i | ||||||||
\(383\) | 18.7885 | 0.960046 | 0.480023 | − | 0.877256i | \(-0.340628\pi\) | ||||
0.480023 | + | 0.877256i | \(0.340628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.68676 | − | 6.99299i | −0.340789 | − | 0.356396i | ||||
\(386\) | 10.4564 | 0.532215 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.9811 | −0.912850 | ||||||||
\(389\) | 17.1264 | 0.868344 | 0.434172 | − | 0.900830i | \(-0.357041\pi\) | ||||
0.434172 | + | 0.900830i | \(0.357041\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.6430i | 0.892243i | ||||||||
\(392\) | −6.99299 | − | 0.313241i | −0.353199 | − | 0.0158211i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.195821i | 0.00986531i | ||||||||
\(395\) | −0.824540 | −0.0414871 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.57671i | − | 0.0791328i | −0.999217 | − | 0.0395664i | \(-0.987402\pi\) | ||
0.999217 | − | 0.0395664i | \(-0.0125977\pi\) | |||||||
\(398\) | −13.9860 | −0.701054 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.31324 | 0.115662 | ||||||||
\(401\) | − | 18.2600i | − | 0.911860i | −0.890016 | − | 0.455930i | \(-0.849307\pi\) | ||
0.890016 | − | 0.455930i | \(-0.150693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.16013 | 0.207231 | ||||||||
\(404\) | 9.29610i | 0.462498i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.31324 | + | 6.99299i | −0.362950 | + | 0.347056i | ||||
\(407\) | − | 16.0550i | − | 0.795816i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.3139 | 1.35059 | 0.675294 | − | 0.737549i | \(-0.264017\pi\) | ||||
0.675294 | + | 0.737549i | \(0.264017\pi\) | |||||||
\(410\) | −11.4624 | −0.566090 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.0115 | 0.591765 | ||||||||
\(413\) | 8.78046 | − | 8.39595i | 0.432058 | − | 0.413138i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2754 | −0.897104 | ||||||||
\(416\) | 0.801180i | 0.0392811i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.75810 | − | 6.99299i | 0.330549 | − | 0.342038i | ||||
\(419\) | 2.72805i | 0.133274i | 0.997777 | + | 0.0666370i | \(0.0212269\pi\) | ||||
−0.997777 | + | 0.0666370i | \(0.978773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1261i | 0.493515i | 0.969077 | + | 0.246757i | \(0.0793650\pi\) | ||||
−0.969077 | + | 0.246757i | \(0.920635\pi\) | |||||||
\(422\) | −6.69314 | −0.325817 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.19798 | −0.0581789 | ||||||||
\(425\) | − | 6.28143i | − | 0.304694i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.70919 | − | 1.78747i | −0.0827137 | − | 0.0865017i | ||||
\(428\) | − | 2.62648i | − | 0.126956i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.6996 | −0.564207 | ||||||||
\(431\) | 5.02243i | 0.241922i | 0.992657 | + | 0.120961i | \(0.0385976\pi\) | ||||
−0.992657 | + | 0.120961i | \(0.961402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5313 | −0.890557 | −0.445278 | − | 0.895392i | \(-0.646895\pi\) | ||||
−0.445278 | + | 0.895392i | \(0.646895\pi\) | |||||||
\(434\) | 9.49446 | + | 9.92927i | 0.455749 | + | 0.476620i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 4.26627i | − | 0.204317i | ||||||
\(437\) | −20.3652 | − | 19.6811i | −0.974199 | − | 0.941476i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.6534 | −1.27210 | −0.636049 | − | 0.771649i | \(-0.719432\pi\) | ||||
−0.636049 | + | 0.771649i | \(0.719432\pi\) | |||||||
\(440\) | −3.65698 | −0.174340 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.17554 | 0.103480 | ||||||||
\(443\) | 0.698855 | 0.0332036 | 0.0166018 | − | 0.999862i | \(-0.494715\pi\) | ||||
0.0166018 | + | 0.999862i | \(0.494715\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.9249i | 1.08674i | ||||||||
\(446\) | − | 3.03993i | − | 0.143945i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.91223 | + | 1.82849i | −0.0903443 | + | 0.0863881i | ||||
\(449\) | 26.3203i | 1.24213i | 0.783759 | + | 0.621065i | \(0.213300\pi\) | ||||
−0.783759 | + | 0.621065i | \(0.786700\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.6017 | −0.734654 | ||||||||
\(452\) | − | 11.5886i | − | 0.545084i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 27.3582i | − | 1.28398i | ||||||
\(455\) | 2.40125 | + | 2.51122i | 0.112572 | + | 0.117728i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.97757 | 0.139285 | 0.0696423 | − | 0.997572i | \(-0.477814\pi\) | ||||
0.0696423 | + | 0.997572i | \(0.477814\pi\) | |||||||
\(458\) | 5.84747 | 0.273234 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.6500i | 0.496557i | ||||||||
\(461\) | − | 38.0779i | − | 1.77347i | −0.462281 | − | 0.886733i | \(-0.652969\pi\) | ||
0.462281 | − | 0.886733i | \(-0.347031\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.72634 | −0.405547 | −0.202774 | − | 0.979226i | \(-0.564996\pi\) | ||||
−0.202774 | + | 0.979226i | \(0.564996\pi\) | |||||||
\(464\) | 3.82446i | 0.177546i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.06438i | 0.141955i | ||||||||
\(467\) | − | 3.63955i | − | 0.168418i | −0.996448 | − | 0.0842092i | \(-0.973164\pi\) | ||
0.996448 | − | 0.0842092i | \(-0.0268364\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.8400 | + | 29.1150i | 1.28553 | + | 1.34441i | ||||
\(470\) | − | 3.13770i | − | 0.144731i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 4.59174i | − | 0.211352i | ||||||
\(473\) | −15.9245 | −0.732211 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.25062 | + | 7.00707i | 0.332681 | + | 0.321507i | ||||
\(476\) | 4.96513 | + | 5.19251i | 0.227576 | + | 0.237998i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 15.4215i | − | 0.705363i | ||||||
\(479\) | − | 25.5277i | − | 1.16639i | −0.812332 | − | 0.583196i | \(-0.801802\pi\) | ||
0.812332 | − | 0.583196i | \(-0.198198\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.76543i | 0.262881i | ||||||||
\(482\) | 2.42769i | 0.110578i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.02243 | 0.273747 | ||||||||
\(485\) | 29.4734i | 1.33832i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.9605i | − | 1.44827i | −0.689660 | − | 0.724133i | \(-0.742240\pi\) | ||
0.689660 | − | 0.724133i | \(-0.257760\pi\) | |||||||
\(488\) | −0.934757 | −0.0423144 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.513444 | + | 11.4624i | −0.0231950 | + | 0.517820i | ||||
\(491\) | 0.307213 | 0.0138643 | 0.00693217 | − | 0.999976i | \(-0.497793\pi\) | ||||
0.00693217 | + | 0.999976i | \(0.497793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3850 | 0.467718 | ||||||||
\(494\) | −2.42687 | + | 2.51122i | −0.109190 | + | 0.112985i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.19251 | 0.233151 | ||||||||
\(497\) | −2.19049 | − | 2.29081i | −0.0982569 | − | 0.102757i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.4355 | 0.646223 | 0.323112 | − | 0.946361i | \(-0.395271\pi\) | ||||
0.323112 | + | 0.946361i | \(0.395271\pi\) | |||||||
\(500\) | − | 11.9874i | − | 0.536092i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.90835 | 0.442231 | ||||||||
\(503\) | 10.5751i | 0.471519i | 0.971811 | + | 0.235759i | \(0.0757577\pi\) | ||||
−0.971811 | + | 0.235759i | \(0.924242\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.2376 | 0.678062 | ||||||||
\(506\) | 14.4958i | 0.644417i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.503034i | 0.0223185i | ||||||||
\(509\) | 30.7223 | 1.36174 | 0.680872 | − | 0.732402i | \(-0.261601\pi\) | ||||
0.680872 | + | 0.732402i | \(0.261601\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7866 | − | 13.3722i | −0.565647 | − | 0.591551i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.80250i | 0.211829i | ||||||||
\(515\) | − | 19.6885i | − | 0.867579i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.27076i | − | 0.187828i | ||||||
\(518\) | −13.7607 | + | 13.1581i | −0.604612 | + | 0.578135i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.31324 | 0.0575894 | ||||||||
\(521\) | −40.7304 | −1.78443 | −0.892215 | − | 0.451611i | \(-0.850849\pi\) | ||||
−0.892215 | + | 0.451611i | \(0.850849\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.42138 | 0.368241 | 0.184121 | − | 0.982904i | \(-0.441056\pi\) | ||||
0.184121 | + | 0.982904i | \(0.441056\pi\) | |||||||
\(524\) | − | 14.2135i | − | 0.620920i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.89503i | 0.344239i | ||||||||
\(527\) | − | 14.0999i | − | 0.614199i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.2151 | 0.835440 | ||||||||
\(530\) | 1.96364i | 0.0852952i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.5324 | − | 0.0611424i | −0.499993 | − | 0.00265086i | ||||
\(533\) | 5.60264 | 0.242677 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.30515 | −0.186128 | ||||||||
\(536\) | 15.2257 | 0.657649 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 8.78046i | − | 0.378552i | ||||||
\(539\) | −0.698855 | + | 15.6017i | −0.0301018 | + | 0.672012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8245 | 0.508373 | 0.254187 | − | 0.967155i | \(-0.418192\pi\) | ||||
0.254187 | + | 0.967155i | \(0.418192\pi\) | |||||||
\(542\) | −24.9569 | −1.07199 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.71542 | 0.116423 | ||||||||
\(545\) | −6.99299 | −0.299547 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6291i | 0.454468i | 0.973840 | + | 0.227234i | \(0.0729682\pi\) | ||||
−0.973840 | + | 0.227234i | \(0.927032\pi\) | |||||||
\(548\) | 1.53219 | 0.0654520 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 5.16095i | − | 0.220063i | ||||||
\(551\) | −11.5847 | + | 11.9874i | −0.493526 | + | 0.510680i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.919793 | + | 0.961916i | 0.0391136 | + | 0.0409048i | ||||
\(554\) | 8.62648i | 0.366504i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.33601i | 0.141478i | ||||||||
\(557\) | −15.1143 | −0.640413 | −0.320206 | − | 0.947348i | \(-0.603752\pi\) | ||||
−0.320206 | + | 0.947348i | \(0.603752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.71858 | 0.241870 | ||||||||
\(560\) | 2.99714 | + | 3.13440i | 0.126652 | + | 0.132453i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.8865 | 1.13414 | ||||||||
\(563\) | −36.1386 | −1.52306 | −0.761531 | − | 0.648129i | \(-0.775552\pi\) | ||||
−0.761531 | + | 0.648129i | \(0.775552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.9953 | −0.799139 | ||||||||
\(566\) | 3.97796 | 0.167206 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.19798 | −0.0502660 | ||||||||
\(569\) | − | 17.2530i | − | 0.723282i | −0.932317 | − | 0.361641i | \(-0.882217\pi\) | ||
0.932317 | − | 0.361641i | \(-0.117783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.4580 | −1.65126 | −0.825632 | − | 0.564209i | \(-0.809181\pi\) | ||||
−0.825632 | + | 0.564209i | \(0.809181\pi\) | |||||||
\(572\) | 1.78747 | 0.0747378 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.7866 | + | 13.3722i | 0.533703 | + | 0.558145i | ||||
\(575\) | −15.0299 | −0.626788 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 28.6139i | − | 1.19121i | −0.803277 | − | 0.595606i | \(-0.796912\pi\) | ||
0.803277 | − | 0.595606i | \(-0.203088\pi\) | |||||||
\(578\) | 9.62648i | 0.400409i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.26880 | 0.260298 | ||||||||
\(581\) | 20.3866 | + | 21.3203i | 0.845780 | + | 0.884513i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.67274i | 0.110694i | ||||||||
\(584\) | −6.99299 | −0.289372 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 3.97796i | − | 0.164328i | ||||||
\(587\) | − | 42.3045i | − | 1.74609i | −0.487637 | − | 0.873046i | \(-0.662141\pi\) | ||
0.487637 | − | 0.873046i | \(-0.337859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.2754 | + | 15.7287i | 0.670616 | + | 0.648090i | ||||
\(590\) | −7.52647 | −0.309860 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.19617i | 0.295761i | ||||||||
\(593\) | 40.4270i | 1.66014i | 0.557660 | + | 0.830069i | \(0.311699\pi\) | ||||
−0.557660 | + | 0.830069i | \(0.688301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.51122 | − | 8.13850i | 0.348926 | − | 0.333646i | ||||
\(596\) | 20.1908 | 0.827048 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 5.20552i | − | 0.212870i | ||||||
\(599\) | − | 1.72460i | − | 0.0704653i | −0.999379 | − | 0.0352327i | \(-0.988783\pi\) | ||
0.999379 | − | 0.0352327i | \(-0.0112172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3384 | 0.951992 | 0.475996 | − | 0.879448i | \(-0.342088\pi\) | ||||
0.475996 | + | 0.879448i | \(0.342088\pi\) | |||||||
\(602\) | 13.0512 | + | 13.6489i | 0.531928 | + | 0.556288i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.02951i | 0.326716i | ||||||||
\(605\) | − | 9.87158i | − | 0.401337i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.9388 | −0.646936 | −0.323468 | − | 0.946239i | \(-0.604849\pi\) | ||||
−0.323468 | + | 0.946239i | \(0.604849\pi\) | |||||||
\(608\) | −3.02912 | + | 3.13440i | −0.122847 | + | 0.127117i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.53219i | 0.0620366i | ||||||||
\(611\) | 1.53365i | 0.0620449i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.9243 | 0.966294 | 0.483147 | − | 0.875539i | \(-0.339494\pi\) | ||||
0.483147 | + | 0.875539i | \(0.339494\pi\) | |||||||
\(614\) | − | 19.8585i | − | 0.801425i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.07945 | + | 4.26627i | 0.164366 | + | 0.171893i | ||||
\(617\) | 31.8491 | 1.28220 | 0.641098 | − | 0.767459i | \(-0.278479\pi\) | ||||
0.641098 | + | 0.767459i | \(0.278479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.67201i | − | 0.268171i | −0.990970 | − | 0.134085i | \(-0.957190\pi\) | ||
0.990970 | − | 0.134085i | \(-0.0428096\pi\) | |||||||
\(620\) | − | 8.51122i | − | 0.341819i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.3230 | 0.895071 | ||||||||
\(623\) | 26.7444 | − | 25.5732i | 1.07149 | − | 1.02457i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.08271 | −0.323308 | ||||||||
\(626\) | −5.12347 | −0.204775 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.33601i | 0.133121i | ||||||||
\(629\) | 19.5406 | 0.779136 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.7488 | −0.865805 | −0.432903 | − | 0.901441i | \(-0.642511\pi\) | ||||
−0.432903 | + | 0.901441i | \(0.642511\pi\) | |||||||
\(632\) | 0.503034 | 0.0200096 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.8794 | 0.551223 | ||||||||
\(635\) | 0.824540 | 0.0327209 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.250962 | − | 5.60264i | 0.00994349 | − | 0.221985i | ||||
\(638\) | 8.53254 | 0.337807 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.63913 | 0.0647924 | ||||||||
\(641\) | − | 18.9019i | − | 0.746579i | −0.927715 | − | 0.373290i | \(-0.878230\pi\) | ||
0.927715 | − | 0.373290i | \(-0.121770\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.3802i | 0.922026i | 0.887393 | + | 0.461013i | \(0.152514\pi\) | ||||
−0.887393 | + | 0.461013i | \(0.847486\pi\) | |||||||
\(644\) | 12.4244 | − | 11.8803i | 0.489588 | − | 0.468149i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.51122 | + | 8.22533i | 0.334869 | + | 0.323621i | ||||
\(647\) | − | 45.2456i | − | 1.77879i | −0.457141 | − | 0.889394i | \(-0.651126\pi\) | ||
0.457141 | − | 0.889394i | \(-0.348874\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2444 | −0.402127 | ||||||||
\(650\) | 1.85332i | 0.0726933i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.62648 | 0.102861 | ||||||||
\(653\) | 12.1844 | 0.476812 | 0.238406 | − | 0.971166i | \(-0.423375\pi\) | ||||
0.238406 | + | 0.971166i | \(0.423375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.2978 | −0.910322 | ||||||||
\(656\) | 6.99299 | 0.273030 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.66047 | + | 3.50018i | −0.142700 | + | 0.136451i | ||||
\(659\) | − | 11.8091i | − | 0.460015i | −0.973189 | − | 0.230008i | \(-0.926125\pi\) | ||
0.973189 | − | 0.230008i | \(-0.0738751\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.0811 | 1.13112 | 0.565562 | − | 0.824706i | \(-0.308659\pi\) | ||||
0.565562 | + | 0.824706i | \(0.308659\pi\) | |||||||
\(662\) | 25.6821 | 0.998161 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.1494 | 0.432682 | ||||||||
\(665\) | −0.100221 | + | 18.9031i | −0.00388639 | + | 0.733033i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 24.8487i | − | 0.962146i | ||||||
\(668\) | −10.9709 | −0.424479 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 24.9569i | − | 0.964170i | ||||||
\(671\) | 2.08548i | 0.0805092i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 10.4564i | − | 0.403064i | −0.979482 | − | 0.201532i | \(-0.935408\pi\) | ||
0.979482 | − | 0.201532i | \(-0.0645919\pi\) | |||||||
\(674\) | 1.92383 | 0.0741033 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.3581 | 0.475312 | ||||||||
\(677\) | −24.7462 | −0.951072 | −0.475536 | − | 0.879696i | \(-0.657746\pi\) | ||||
−0.475536 | + | 0.879696i | \(0.657746\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.3839 | − | 32.8782i | 1.31953 | − | 1.26175i | ||||
\(680\) | − | 4.45094i | − | 0.170686i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 11.5847i | − | 0.443602i | ||||||
\(683\) | 8.74175i | 0.334494i | 0.985915 | + | 0.167247i | \(0.0534877\pi\) | ||||
−0.985915 | + | 0.167247i | \(0.946512\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.51147i | − | 0.0959582i | ||||||
\(686\) | 13.9450 | − | 12.1876i | 0.532421 | − | 0.465326i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.13770 | 0.272122 | ||||||||
\(689\) | − | 0.959795i | − | 0.0365653i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 22.5557i | − | 0.858058i | −0.903291 | − | 0.429029i | \(-0.858856\pi\) | ||
0.903291 | − | 0.429029i | \(-0.141144\pi\) | |||||||
\(692\) | −20.3652 | −0.774168 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.0801i | 1.29366i | ||||||||
\(695\) | 5.46816 | 0.207419 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 18.9889i | − | 0.719256i | ||||||
\(698\) | 31.9499 | 1.20932 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.42345 | + | 4.22974i | −0.167191 | + | 0.159869i | ||||
\(701\) | −5.79846 | −0.219005 | −0.109502 | − | 0.993987i | \(-0.534926\pi\) | ||||
−0.109502 | + | 0.993987i | \(0.534926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.7980 | + | 22.5557i | −0.822128 | + | 0.850703i | ||||
\(704\) | 2.23105 | 0.0840857 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.2957 | 0.726203 | ||||||||
\(707\) | −16.9978 | − | 17.7763i | −0.639270 | − | 0.668546i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.0466 | 1.54154 | 0.770769 | − | 0.637115i | \(-0.219872\pi\) | ||||
0.770769 | + | 0.637115i | \(0.219872\pi\) | |||||||
\(710\) | 1.96364i | 0.0736942i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 13.9860i | − | 0.524147i | ||||||
\(713\) | −33.7374 | −1.26347 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.92990i | − | 0.109572i | ||||||
\(716\) | − | 18.7866i | − | 0.702089i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 9.56170i | − | 0.356839i | ||||||
\(719\) | 14.1894i | 0.529174i | 0.964362 | + | 0.264587i | \(0.0852356\pi\) | ||||
−0.964362 | + | 0.264587i | \(0.914764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.9688 | + | 21.9630i | −0.855402 | + | 0.817944i | ||||
\(722\) | −18.9889 | + | 0.648917i | −0.706694 | + | 0.0241502i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.250962 | 0.00932694 | ||||||||
\(725\) | 8.84689i | 0.328565i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.9429i | 1.44431i | 0.691730 | + | 0.722156i | \(0.256849\pi\) | ||||
−0.691730 | + | 0.722156i | \(0.743151\pi\) | |||||||
\(728\) | −1.46495 | − | 1.53204i | −0.0542947 | − | 0.0567812i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.4624i | 0.424244i | ||||||||
\(731\) | − | 19.3819i | − | 0.716864i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.7524i | 1.35748i | 0.734378 | + | 0.678741i | \(0.237474\pi\) | ||||
−0.734378 | + | 0.678741i | \(0.762526\pi\) | |||||||
\(734\) | −10.9709 | −0.404945 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.49732i | − | 0.239494i | ||||||
\(737\) | − | 33.9692i | − | 1.25127i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.29783 | −0.121313 | −0.0606564 | − | 0.998159i | \(-0.519319\pi\) | ||||
−0.0606564 | + | 0.998159i | \(0.519319\pi\) | |||||||
\(740\) | 11.7955 | 0.433611 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.29081 | − | 2.19049i | 0.0840981 | − | 0.0804154i | ||||
\(743\) | − | 37.8693i | − | 1.38929i | −0.719352 | − | 0.694645i | \(-0.755561\pi\) | ||
0.719352 | − | 0.694645i | \(-0.244439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 33.0954i | − | 1.21252i | ||||||
\(746\) | −33.7116 | −1.23427 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 6.05823i | − | 0.221511i | ||||||
\(749\) | 4.80250 | + | 5.02243i | 0.175479 | + | 0.183516i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 45.3467i | − | 1.65473i | −0.561668 | − | 0.827363i | \(-0.689840\pi\) | ||
0.561668 | − | 0.827363i | \(-0.310160\pi\) | |||||||
\(752\) | 1.91424i | 0.0698052i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.06408 | −0.111587 | ||||||||
\(755\) | 13.1614 | 0.478994 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.2978 | −0.774083 | −0.387041 | − | 0.922062i | \(-0.626503\pi\) | ||||
−0.387041 | + | 0.922062i | \(0.626503\pi\) | |||||||
\(758\) | 28.6120 | 1.03923 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.13770 | + | 4.96513i | 0.186364 | + | 0.180104i | ||||
\(761\) | 7.57079i | 0.274441i | 0.990541 | + | 0.137221i | \(0.0438169\pi\) | ||||
−0.990541 | + | 0.137221i | \(0.956183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.80084 | + | 8.15809i | 0.282409 | + | 0.295343i | ||||
\(764\) | −23.9540 | −0.866627 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.7885i | 0.678855i | ||||||||
\(767\) | 3.67881 | 0.132834 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9.50445i | − | 0.342739i | −0.985207 | − | 0.171370i | \(-0.945181\pi\) | ||
0.985207 | − | 0.171370i | \(-0.0548193\pi\) | |||||||
\(770\) | 6.99299 | − | 6.68676i | 0.252010 | − | 0.240974i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.4564i | 0.376333i | ||||||||
\(773\) | 0.403021 | 0.0144956 | 0.00724782 | − | 0.999974i | \(-0.497693\pi\) | ||||
0.00724782 | + | 0.999974i | \(0.497693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.0115 | 0.431467 | ||||||||
\(776\) | − | 17.9811i | − | 0.645483i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.1264i | 0.614012i | ||||||||
\(779\) | 21.9188 | + | 21.1826i | 0.785323 | + | 0.758944i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.67274i | 0.0956382i | ||||||||
\(782\) | −17.6430 | −0.630911 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.313241 | − | 6.99299i | 0.0111872 | − | 0.249750i | ||||
\(785\) | 5.46816 | 0.195167 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.3115 | −1.22307 | −0.611536 | − | 0.791216i | \(-0.709448\pi\) | ||||
−0.611536 | + | 0.791216i | \(0.709448\pi\) | |||||||
\(788\) | −0.195821 | −0.00697582 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 0.824540i | − | 0.0293358i | ||||||
\(791\) | 21.1897 | + | 22.1601i | 0.753420 | + | 0.787924i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.748908i | − | 0.0265945i | ||||||
\(794\) | 1.57671 | 0.0559553 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 13.9860i | − | 0.495720i | ||||||
\(797\) | −6.37921 | −0.225963 | −0.112982 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112982 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.19798 | 0.183891 | ||||||||
\(800\) | 2.31324i | 0.0817854i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.2600 | 0.644783 | ||||||||
\(803\) | 15.6017i | 0.550571i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.4734 | − | 20.3652i | −0.686346 | − | 0.717778i | ||||
\(806\) | 4.16013i | 0.146534i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.29610 | −0.327036 | ||||||||
\(809\) | 22.4449 | 0.789122 | 0.394561 | − | 0.918870i | \(-0.370897\pi\) | ||||
0.394561 | + | 0.918870i | \(0.370897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.3850 | −0.364667 | −0.182334 | − | 0.983237i | \(-0.558365\pi\) | ||||
−0.182334 | + | 0.983237i | \(0.558365\pi\) | |||||||
\(812\) | −6.99299 | − | 7.31324i | −0.245406 | − | 0.256644i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.0550 | 0.562727 | ||||||||
\(815\) | − | 4.30515i | − | 0.150803i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.3724 | + | 21.6209i | 0.782711 | + | 0.756420i | ||||
\(818\) | 27.3139i | 0.955010i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 11.4624i | − | 0.400286i | ||||||
\(821\) | 29.2495 | 1.02081 | 0.510407 | − | 0.859933i | \(-0.329495\pi\) | ||||
0.510407 | + | 0.859933i | \(0.329495\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.8143 | 0.760400 | 0.380200 | − | 0.924904i | \(-0.375855\pi\) | ||||
0.380200 | + | 0.924904i | \(0.375855\pi\) | |||||||
\(824\) | 12.0115i | 0.418441i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.39595 | + | 8.78046i | 0.292133 | + | 0.305511i | ||||
\(827\) | 13.5337i | 0.470611i | 0.971921 | + | 0.235306i | \(0.0756091\pi\) | ||||
−0.971921 | + | 0.235306i | \(0.924391\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.5989 | 0.923819 | 0.461910 | − | 0.886927i | \(-0.347164\pi\) | ||||
0.461910 | + | 0.886927i | \(0.347164\pi\) | |||||||
\(830\) | − | 18.2754i | − | 0.634348i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.801180 | −0.0277759 | ||||||||
\(833\) | −18.9889 | − | 0.850581i | −0.657927 | − | 0.0294709i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.9828i | 0.622322i | ||||||||
\(836\) | 6.99299 | + | 6.75810i | 0.241858 | + | 0.233734i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.72805 | −0.0942389 | ||||||||
\(839\) | −51.7013 | −1.78493 | −0.892464 | − | 0.451119i | \(-0.851025\pi\) | ||||
−0.892464 | + | 0.451119i | \(0.851025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.3735 | 0.495639 | ||||||||
\(842\) | −10.1261 | −0.348967 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 6.69314i | − | 0.230387i | ||||||
\(845\) | − | 20.2566i | − | 0.696848i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.5163 | + | 11.0120i | −0.395704 | + | 0.378376i | ||||
\(848\) | − | 1.19798i | − | 0.0411387i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.28143 | 0.215451 | ||||||||
\(851\) | − | 46.7558i | − | 1.60277i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.4093i | 0.424885i | 0.977174 | + | 0.212443i | \(0.0681419\pi\) | ||||
−0.977174 | + | 0.212443i | \(0.931858\pi\) | |||||||
\(854\) | 1.78747 | − | 1.70919i | 0.0611659 | − | 0.0584874i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.62648 | 0.0897713 | ||||||||
\(857\) | −6.03006 | −0.205983 | −0.102991 | − | 0.994682i | \(-0.532841\pi\) | ||||
−0.102991 | + | 0.994682i | \(0.532841\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.2999i | 0.726745i | 0.931644 | + | 0.363372i | \(0.118375\pi\) | ||||
−0.931644 | + | 0.363372i | \(0.881625\pi\) | |||||||
\(860\) | − | 11.6996i | − | 0.398955i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.02243 | −0.171065 | ||||||||
\(863\) | 44.9261i | 1.52930i | 0.644445 | + | 0.764650i | \(0.277088\pi\) | ||||
−0.644445 | + | 0.764650i | \(0.722912\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.3813i | 1.13500i | ||||||||
\(866\) | − | 18.5313i | − | 0.629719i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.92927 | + | 9.49446i | −0.337021 | + | 0.322263i | ||||
\(869\) | − | 1.12229i | − | 0.0380711i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.1985i | 0.413331i | ||||||||
\(872\) | 4.26627 | 0.144474 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.6811 | − | 20.3652i | 0.665724 | − | 0.688863i | ||||
\(875\) | 21.9188 | + | 22.9226i | 0.740991 | + | 0.774926i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 42.5013i | − | 1.43517i | −0.696473 | − | 0.717583i | \(-0.745248\pi\) | ||
0.696473 | − | 0.717583i | \(-0.254752\pi\) | |||||||
\(878\) | − | 26.6534i | − | 0.899509i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 3.65698i | − | 0.123277i | ||||||
\(881\) | − | 28.6286i | − | 0.964521i | −0.876028 | − | 0.482261i | \(-0.839816\pi\) | ||
0.876028 | − | 0.482261i | \(-0.160184\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0396 | −1.21283 | −0.606414 | − | 0.795149i | \(-0.707393\pi\) | ||||
−0.606414 | + | 0.795149i | \(0.707393\pi\) | |||||||
\(884\) | 2.17554i | 0.0731714i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.698855i | 0.0234785i | ||||||||
\(887\) | 17.5609 | 0.589638 | 0.294819 | − | 0.955553i | \(-0.404741\pi\) | ||||
0.294819 | + | 0.955553i | \(0.404741\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.919793 | − | 0.961916i | −0.0308489 | − | 0.0322616i | ||||
\(890\) | −22.9249 | −0.768444 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.03993 | 0.101784 | ||||||||
\(893\) | −5.79846 | + | 6.00000i | −0.194038 | + | 0.200782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.7938 | −1.02932 | ||||||||
\(896\) | −1.82849 | − | 1.91223i | −0.0610856 | − | 0.0638831i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.3203 | −0.878319 | ||||||||
\(899\) | 19.8585i | 0.662319i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.25301 | −0.108374 | ||||||||
\(902\) | − | 15.6017i | − | 0.519479i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.5886 | 0.385432 | ||||||||
\(905\) | − | 0.411361i | − | 0.0136741i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.6120i | 0.950044i | 0.879974 | + | 0.475022i | \(0.157560\pi\) | ||||
−0.879974 | + | 0.475022i | \(0.842440\pi\) | |||||||
\(908\) | 27.3582 | 0.907913 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.51122 | + | 2.40125i | −0.0832460 | + | 0.0796006i | ||||
\(911\) | − | 0.230528i | − | 0.00763775i | −0.999993 | − | 0.00381887i | \(-0.998784\pi\) | ||
0.999993 | − | 0.00381887i | \(-0.00121559\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 24.8749i | − | 0.823238i | ||||||
\(914\) | 2.97757i | 0.0984891i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.84747i | 0.193206i | ||||||||
\(917\) | 25.9893 | + | 27.1795i | 0.858241 | + | 0.897545i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.8038 | −1.24703 | −0.623515 | − | 0.781811i | \(-0.714296\pi\) | ||||
−0.623515 | + | 0.781811i | \(0.714296\pi\) | |||||||
\(920\) | −10.6500 | −0.351119 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 38.0779 | 1.25403 | ||||||||
\(923\) | − | 0.959795i | − | 0.0315920i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.6465i | 0.547333i | ||||||||
\(926\) | − | 8.72634i | − | 0.286765i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.82446 | −0.125544 | ||||||||
\(929\) | 32.3352i | 1.06088i | 0.847721 | + | 0.530442i | \(0.177974\pi\) | ||||
−0.847721 | + | 0.530442i | \(0.822026\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.1644 | − | 20.9700i | 0.726409 | − | 0.687263i | ||||
\(932\) | −3.06438 | −0.100377 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.63955 | 0.119090 | ||||||||
\(935\) | −9.93025 | −0.324754 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.6933i | 1.36206i | 0.732255 | + | 0.681030i | \(0.238468\pi\) | ||||
−0.732255 | + | 0.681030i | \(0.761532\pi\) | |||||||
\(938\) | −29.1150 | + | 27.8400i | −0.950638 | + | 0.909009i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.13770 | 0.102340 | ||||||||
\(941\) | −36.7524 | −1.19809 | −0.599047 | − | 0.800714i | \(-0.704454\pi\) | ||||
−0.599047 | + | 0.800714i | \(0.704454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.4357 | −1.47959 | ||||||||
\(944\) | 4.59174 | 0.149448 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 15.9245i | − | 0.517751i | ||||||
\(947\) | 21.6999 | 0.705152 | 0.352576 | − | 0.935783i | \(-0.385306\pi\) | ||||
0.352576 | + | 0.935783i | \(0.385306\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 5.60264i | − | 0.181869i | ||||||
\(950\) | −7.00707 | + | 7.25062i | −0.227340 | + | 0.235241i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.19251 | + | 4.96513i | −0.168290 | + | 0.160921i | ||||
\(953\) | 59.4373i | 1.92536i | 0.270639 | + | 0.962681i | \(0.412765\pi\) | ||||
−0.270639 | + | 0.962681i | \(0.587235\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.2639i | 1.27055i | ||||||||
\(956\) | 15.4215 | 0.498767 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.5277 | 0.824763 | ||||||||
\(959\) | −2.92990 | + | 2.80160i | −0.0946114 | + | 0.0904683i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.03784 | −0.130253 | ||||||||
\(962\) | −5.76543 | −0.185885 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.42769 | −0.0781905 | ||||||||
\(965\) | 17.1394 | 0.551737 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.0567 | −1.38461 | −0.692305 | − | 0.721605i | \(-0.743405\pi\) | ||||
−0.692305 | + | 0.721605i | \(0.743405\pi\) | |||||||
\(968\) | 6.02243i | 0.193568i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29.4734 | −0.946333 | ||||||||
\(971\) | 44.4976 | 1.42799 | 0.713997 | − | 0.700148i | \(-0.246883\pi\) | ||||
0.713997 | + | 0.700148i | \(0.246883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.09986 | − | 6.37921i | −0.195552 | − | 0.204508i | ||||
\(974\) | 31.9605 | 1.02408 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 0.934757i | − | 0.0299208i | ||||||
\(977\) | 37.0070i | 1.18396i | 0.805953 | + | 0.591980i | \(0.201654\pi\) | ||||
−0.805953 | + | 0.591980i | \(0.798346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.2034 | −0.997263 | ||||||||
\(980\) | −11.4624 | − | 0.513444i | −0.366154 | − | 0.0164014i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.307213i | 0.00980357i | ||||||||
\(983\) | 34.1404 | 1.08891 | 0.544455 | − | 0.838790i | \(-0.316737\pi\) | ||||
0.544455 | + | 0.838790i | \(0.316737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.320976i | 0.0102272i | ||||||||
\(986\) | 10.3850i | 0.330726i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.51122 | − | 2.42687i | −0.0798925 | − | 0.0772089i | ||||
\(989\) | −46.3759 | −1.47467 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 36.8142i | − | 1.16944i | −0.811235 | − | 0.584721i | \(-0.801204\pi\) | ||
0.811235 | − | 0.584721i | \(-0.198796\pi\) | |||||||
\(992\) | 5.19251i | 0.164862i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.29081 | − | 2.19049i | 0.0726600 | − | 0.0694781i | ||||
\(995\) | −22.9249 | −0.726768 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.1969i | − | 1.33639i | −0.743987 | − | 0.668194i | \(-0.767068\pi\) | ||
0.743987 | − | 0.668194i | \(-0.232932\pi\) | |||||||
\(998\) | 14.4355i | 0.456949i | ||||||||
\(999\) | 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 | 2394.2.e.d.1063.7 | yes | 24 | |
3.2 | odd | 2 | inner | 2394.2.e.d.1063.14 | yes | 24 | |
7.6 | odd | 2 | inner | 2394.2.e.d.1063.15 | yes | 24 | |
19.18 | odd | 2 | inner | 2394.2.e.d.1063.13 | yes | 24 | |
21.20 | even | 2 | inner | 2394.2.e.d.1063.6 | yes | 24 | |
57.56 | even | 2 | inner | 2394.2.e.d.1063.8 | yes | 24 | |
133.132 | even | 2 | inner | 2394.2.e.d.1063.5 | ✓ | 24 | |
399.398 | odd | 2 | inner | 2394.2.e.d.1063.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.e.d.1063.5 | ✓ | 24 | 133.132 | even | 2 | inner | |
2394.2.e.d.1063.6 | yes | 24 | 21.20 | even | 2 | inner | |
2394.2.e.d.1063.7 | yes | 24 | 1.1 | even | 1 | trivial | |
2394.2.e.d.1063.8 | yes | 24 | 57.56 | even | 2 | inner | |
2394.2.e.d.1063.13 | yes | 24 | 19.18 | odd | 2 | inner | |
2394.2.e.d.1063.14 | yes | 24 | 3.2 | odd | 2 | inner | |
2394.2.e.d.1063.15 | yes | 24 | 7.6 | odd | 2 | inner | |
2394.2.e.d.1063.16 | yes | 24 | 399.398 | odd | 2 | inner |