Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(3905,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4032.3905");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3905.1 | ||
Root | \(0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.3905 |
Dual form | 4032.2.k.e.3905.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.69552 | −1.65269 | −0.826343 | − | 0.563167i | \(-0.809583\pi\) | ||||
−0.826343 | + | 0.563167i | \(0.809583\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.41421 | − | 1.08239i | −0.912487 | − | 0.409106i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.41421i | 1.02942i | 0.857363 | + | 0.514712i | \(0.172101\pi\) | ||||
−0.857363 | + | 0.514712i | \(0.827899\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.22625i | 1.44950i | 0.689011 | + | 0.724751i | \(0.258045\pi\) | ||||
−0.689011 | + | 0.724751i | \(0.741955\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.75699 | −1.63881 | −0.819405 | − | 0.573215i | \(-0.805696\pi\) | ||||
−0.819405 | + | 0.573215i | \(0.805696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.16478i | 0.496636i | 0.968679 | + | 0.248318i | \(0.0798777\pi\) | ||||
−0.968679 | + | 0.248318i | \(0.920122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.24264i | − | 1.30168i | −0.759215 | − | 0.650840i | \(-0.774417\pi\) | ||
0.759215 | − | 0.650840i | \(-0.225583\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.65685 | 1.73137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.58579i | 0.480168i | 0.970752 | + | 0.240084i | \(0.0771751\pi\) | ||||
−0.970752 | + | 0.240084i | \(0.922825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4525i | 1.87733i | 0.344837 | + | 0.938663i | \(0.387934\pi\) | ||||
−0.344837 | + | 0.938663i | \(0.612066\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.92177 | + | 4.00000i | 1.50805 | + | 0.676123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.634051 | 0.0990221 | 0.0495110 | − | 0.998774i | \(-0.484234\pi\) | ||||
0.0495110 | + | 0.998774i | \(0.484234\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.48528 | −0.988996 | −0.494498 | − | 0.869179i | \(-0.664648\pi\) | ||||
−0.494498 | + | 0.869179i | \(0.664648\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.06147 | −0.446561 | −0.223280 | − | 0.974754i | \(-0.571677\pi\) | ||||
−0.223280 | + | 0.974754i | \(0.571677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.65685 | + | 5.22625i | 0.665265 | + | 0.746607i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.58579i | − | 0.355185i | −0.984104 | − | 0.177593i | \(-0.943169\pi\) | ||
0.984104 | − | 0.177593i | \(-0.0568309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 12.6173i | − | 1.70131i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 19.3137i | − | 2.39557i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.65685 | 0.202417 | 0.101208 | − | 0.994865i | \(-0.467729\pi\) | ||||
0.101208 | + | 0.994865i | \(0.467729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.41421i | 0.879905i | 0.898021 | + | 0.439953i | \(0.145005\pi\) | ||||
−0.898021 | + | 0.439953i | \(0.854995\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.896683i | 0.104949i | 0.998622 | + | 0.0524744i | \(0.0167108\pi\) | ||||
−0.998622 | + | 0.0524744i | \(0.983289\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.69552 | − | 8.24264i | 0.421143 | − | 0.939336i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6569 | 1.53652 | 0.768258 | − | 0.640140i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640140i | \(0.221124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.7206 | −1.28650 | −0.643252 | − | 0.765655i | \(-0.722415\pi\) | ||||
−0.643252 | + | 0.765655i | \(0.722415\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.9706 | 2.70844 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.75699 | −0.716239 | −0.358120 | − | 0.933676i | \(-0.616582\pi\) | ||||
−0.358120 | + | 0.933676i | \(0.616582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65685 | − | 12.6173i | 0.592999 | − | 1.32265i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 8.00000i | − | 0.820783i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.55582i | − | 0.970247i | −0.874446 | − | 0.485123i | \(-0.838775\pi\) | ||
0.874446 | − | 0.485123i | \(-0.161225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.42742 | −0.241537 | −0.120768 | − | 0.992681i | \(-0.538536\pi\) | ||||
−0.120768 | + | 0.992681i | \(0.538536\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6.12293i | − | 0.603311i | −0.953417 | − | 0.301655i | \(-0.902461\pi\) | ||
0.953417 | − | 0.301655i | \(-0.0975392\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.07107i | 0.103544i | 0.998659 | + | 0.0517720i | \(0.0164869\pi\) | ||||
−0.998659 | + | 0.0517720i | \(0.983513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.65685 | −0.158698 | −0.0793489 | − | 0.996847i | \(-0.525284\pi\) | ||||
−0.0793489 | + | 0.996847i | \(0.525284\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.7574i | − | 1.10604i | −0.833168 | − | 0.553020i | \(-0.813475\pi\) | ||
0.833168 | − | 0.553020i | \(-0.186525\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23.0698i | 2.15127i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.3128 | + | 7.31371i | 1.49539 | + | 0.670447i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.656854 | −0.0597140 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.5140 | −1.20873 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9706 | 1.50589 | 0.752947 | − | 0.658081i | \(-0.228632\pi\) | ||||
0.752947 | + | 0.658081i | \(0.228632\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.06147 | −0.267482 | −0.133741 | − | 0.991016i | \(-0.542699\pi\) | ||||
−0.133741 | + | 0.991016i | \(0.542699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.34315 | − | 5.22625i | 0.203177 | − | 0.453174i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.89949i | − | 0.845771i | −0.906183 | − | 0.422885i | \(-0.861017\pi\) | ||
0.906183 | − | 0.422885i | \(-0.138983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.32957i | − | 0.367229i | −0.982998 | − | 0.183615i | \(-0.941220\pi\) | ||
0.982998 | − | 0.183615i | \(-0.0587798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.8435 | −1.49215 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.55582i | − | 0.793568i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 7.75736i | − | 0.635508i | −0.948173 | − | 0.317754i | \(-0.897071\pi\) | ||
0.948173 | − | 0.317754i | \(-0.102929\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.1421 | −1.31363 | −0.656814 | − | 0.754052i | \(-0.728096\pi\) | ||||
−0.656814 | + | 0.754052i | \(0.728096\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 38.6274i | − | 3.10263i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.1116i | − | 1.52528i | −0.646826 | − | 0.762638i | \(-0.723904\pi\) | ||
0.646826 | − | 0.762638i | \(-0.276096\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.75699 | + | 15.0711i | −0.532525 | + | 1.18777i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6569 | −1.38299 | −0.691496 | − | 0.722380i | \(-0.743048\pi\) | ||||
−0.691496 | + | 0.722380i | \(0.743048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.7206 | −0.906968 | −0.453484 | − | 0.891265i | \(-0.649819\pi\) | ||||
−0.453484 | + | 0.891265i | \(0.649819\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.3137 | −1.10105 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3547 | 0.939307 | 0.469654 | − | 0.882851i | \(-0.344379\pi\) | ||||
0.469654 | + | 0.882851i | \(0.344379\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.8995 | − | 9.37011i | −1.57985 | − | 0.708314i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.8995i | 1.18838i | 0.804323 | + | 0.594192i | \(0.202528\pi\) | ||||
−0.804323 | + | 0.594192i | \(0.797472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.3379i | − | 1.80902i | −0.426451 | − | 0.904511i | \(-0.640236\pi\) | ||
0.426451 | − | 0.904511i | \(-0.359764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.7821 | 1.08680 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 23.0698i | − | 1.68703i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.72792i | − | 0.197386i | −0.995118 | − | 0.0986928i | \(-0.968534\pi\) | ||
0.995118 | − | 0.0986928i | \(-0.0314661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.65685 | 0.407189 | 0.203595 | − | 0.979055i | \(-0.434738\pi\) | ||||
0.203595 | + | 0.979055i | \(0.434738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22.3848i | − | 1.59485i | −0.603419 | − | 0.797425i | \(-0.706195\pi\) | ||
0.603419 | − | 0.797425i | \(-0.293805\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0698i | 1.63537i | 0.575663 | + | 0.817687i | \(0.304744\pi\) | ||||
−0.575663 | + | 0.817687i | \(0.695256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.79884 | − | 6.24264i | 0.196440 | − | 0.438147i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.34315 | −0.163652 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.39104 | −0.511249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.1716 | 1.31983 | 0.659913 | − | 0.751342i | \(-0.270593\pi\) | ||||
0.659913 | + | 0.751342i | \(0.270593\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.9665 | 1.63450 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3137 | − | 25.2346i | 0.768025 | − | 1.71303i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 35.3137i | − | 2.37546i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.0698i | 1.54487i | 0.635095 | + | 0.772434i | \(0.280961\pi\) | ||||
−0.635095 | + | 0.772434i | \(0.719039\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.7821 | −0.981121 | −0.490560 | − | 0.871407i | \(-0.663208\pi\) | ||||
−0.490560 | + | 0.871407i | \(0.663208\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.43289i | − | 0.226851i | −0.993546 | − | 0.113426i | \(-0.963818\pi\) | ||
0.993546 | − | 0.113426i | \(-0.0361824\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.7279i | − | 1.35793i | −0.734170 | − | 0.678966i | \(-0.762429\pi\) | ||
0.734170 | − | 0.678966i | \(-0.237571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3137 | 0.738025 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.92893i | 0.189457i | 0.995503 | + | 0.0947284i | \(0.0301983\pi\) | ||||
−0.995503 | + | 0.0947284i | \(0.969802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.3492i | − | 0.731065i | −0.930799 | − | 0.365533i | \(-0.880887\pi\) | ||
0.930799 | − | 0.365533i | \(-0.119113\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.2095 | − | 19.3137i | −1.09947 | − | 1.23391i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.3137 | −0.719874 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.59767 | 0.353322 | 0.176661 | − | 0.984272i | \(-0.443470\pi\) | ||||
0.176661 | + | 0.984272i | \(0.443470\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.3137 | 1.33998 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.8072 | 1.42267 | 0.711336 | − | 0.702852i | \(-0.248091\pi\) | ||||
0.711336 | + | 0.702852i | \(0.248091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.65685 | + | 4.32957i | 0.600048 | + | 0.269026i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.7279i | 1.15481i | 0.816457 | + | 0.577407i | \(0.195935\pi\) | ||||
−0.816457 | + | 0.577407i | \(0.804065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.55582i | 0.587009i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.0866 | −0.675959 | −0.337980 | − | 0.941153i | \(-0.609743\pi\) | ||||
−0.337980 | + | 0.941153i | \(0.609743\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.1116i | − | 1.16095i | −0.814278 | − | 0.580475i | \(-0.802867\pi\) | ||
0.814278 | − | 0.580475i | \(-0.197133\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 29.5563i | 1.78231i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.6569 | −1.18107 | −0.590533 | − | 0.807014i | \(-0.701082\pi\) | ||||
−0.590533 | + | 0.807014i | \(0.701082\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.89949i | 0.590554i | 0.955412 | + | 0.295277i | \(0.0954120\pi\) | ||||
−0.955412 | + | 0.295277i | \(0.904588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.4107i | 0.856624i | 0.903631 | + | 0.428312i | \(0.140892\pi\) | ||||
−0.903631 | + | 0.428312i | \(0.859108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.53073 | − | 0.686292i | −0.0903564 | − | 0.0405105i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.6569 | 1.68570 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.8686 | 1.51126 | 0.755631 | − | 0.654998i | \(-0.227331\pi\) | ||||
0.755631 | + | 0.654998i | \(0.227331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.6256 | 1.88679 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6569 | + | 7.01962i | 0.902446 | + | 0.404604i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8239i | 0.617754i | 0.951102 | + | 0.308877i | \(0.0999531\pi\) | ||||
−0.951102 | + | 0.308877i | \(0.900047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.2459 | 0.694400 | 0.347200 | − | 0.937791i | \(-0.387133\pi\) | ||||
0.347200 | + | 0.937791i | \(0.387133\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.9050i | 1.18162i | 0.806810 | + | 0.590810i | \(0.201192\pi\) | ||||
−0.806810 | + | 0.590810i | \(0.798808\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.3848i | 1.25725i | 0.777707 | + | 0.628627i | \(0.216383\pi\) | ||||
−0.777707 | + | 0.628627i | \(0.783617\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.82843 | −0.494297 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 14.6274i | − | 0.813891i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 45.2429i | 2.50962i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.39104 | + | 3.31371i | 0.407481 | + | 0.182691i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.82843 | 0.265394 | 0.132697 | − | 0.991157i | \(-0.457636\pi\) | ||||
0.132697 | + | 0.991157i | \(0.457636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.12293 | −0.334532 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | −0.435788 | −0.217894 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217894 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.6871 | −1.93256 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.58579 | − | 17.6578i | −0.301604 | − | 0.953433i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5563i | 0.727743i | 0.931449 | + | 0.363871i | \(0.118545\pi\) | ||||
−0.931449 | + | 0.363871i | \(0.881455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.1116i | 1.02302i | 0.859277 | + | 0.511511i | \(0.170914\pi\) | ||||
−0.859277 | + | 0.511511i | \(0.829086\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.5391 | −1.14641 | −0.573204 | − | 0.819413i | \(-0.694300\pi\) | ||||
−0.573204 | + | 0.819413i | \(0.694300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 27.3994i | − | 1.45421i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.38478i | − | 0.442532i | −0.975214 | − | 0.221266i | \(-0.928981\pi\) | ||
0.975214 | − | 0.221266i | \(-0.0710188\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.3137 | 0.753353 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.31371i | − | 0.173447i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.49435i | − | 0.339002i | −0.985530 | − | 0.169501i | \(-0.945784\pi\) | ||
0.985530 | − | 0.169501i | \(-0.0542157\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.79884 | + | 6.24264i | −0.145308 | + | 0.324102i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.3137 | 0.896470 | 0.448235 | − | 0.893916i | \(-0.352053\pi\) | ||||
0.448235 | + | 0.893916i | \(0.352053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.5140 | −0.696005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1716 | 0.573845 | 0.286923 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286923 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.59767 | 0.286028 | 0.143014 | − | 0.989721i | \(-0.454321\pi\) | ||||
0.143014 | + | 0.989721i | \(0.454321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.6569 | + | 30.4608i | −0.696018 | + | 1.55243i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.7279i | 1.25376i | 0.779118 | + | 0.626878i | \(0.215667\pi\) | ||||
−0.779118 | + | 0.626878i | \(0.784333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.1814i | 2.13321i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −50.4692 | −2.53938 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.9050i | − | 1.04919i | −0.851351 | − | 0.524596i | \(-0.824216\pi\) | ||
0.851351 | − | 0.524596i | \(-0.175784\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.443651i | 0.0221549i | 0.999939 | + | 0.0110774i | \(0.00352613\pi\) | ||||
−0.999939 | + | 0.0110774i | \(0.996474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −54.6274 | −2.72119 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 13.6569i | − | 0.676945i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.896683i | 0.0443381i | 0.999754 | + | 0.0221691i | \(0.00705721\pi\) | ||||
−0.999754 | + | 0.0221691i | \(0.992943\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 43.3137 | 2.12619 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.9050 | 1.02128 | 0.510638 | − | 0.859796i | \(-0.329409\pi\) | ||||
0.510638 | + | 0.859796i | \(0.329409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9706 | −0.924569 | −0.462284 | − | 0.886732i | \(-0.652970\pi\) | ||||
−0.462284 | + | 0.886732i | \(0.652970\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −58.4942 | −2.83739 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.75736i | − | 0.0846490i | −0.999104 | − | 0.0423245i | \(-0.986524\pi\) | ||
0.999104 | − | 0.0423245i | \(-0.0134763\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.6984i | 1.09081i | 0.838171 | + | 0.545407i | \(0.183625\pi\) | ||||
−0.838171 | + | 0.545407i | \(0.816375\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.5140 | 0.646461 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 23.0698i | − | 1.10106i | −0.834815 | − | 0.550531i | \(-0.814425\pi\) | ||
0.834815 | − | 0.550531i | \(-0.185575\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.4142i | − | 0.542306i | −0.962536 | − | 0.271153i | \(-0.912595\pi\) | ||
0.962536 | − | 0.271153i | \(-0.0874049\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.9706 | 1.18372 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.58579i | 0.310802i | 0.987851 | + | 0.155401i | \(0.0496670\pi\) | ||||
−0.987851 | + | 0.155401i | \(0.950333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.16478i | 0.101936i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.9050 | + | 46.6274i | −0.980042 | + | 2.18593i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3137 | 0.529233 | 0.264616 | − | 0.964354i | \(-0.414755\pi\) | ||||
0.264616 | + | 0.964354i | \(0.414755\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.8686 | −1.20482 | −0.602411 | − | 0.798186i | \(-0.705793\pi\) | ||||
−0.602411 | + | 0.798186i | \(0.705793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.3431 | 0.852478 | 0.426239 | − | 0.904611i | \(-0.359838\pi\) | ||||
0.426239 | + | 0.904611i | \(0.359838\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.0894 | 1.39237 | 0.696186 | − | 0.717862i | \(-0.254879\pi\) | ||||
0.696186 | + | 0.717862i | \(0.254879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | − | 1.79337i | −0.184703 | − | 0.0828100i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 22.1421i | − | 1.01810i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.7402i | 0.859860i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.0279 | −1.23494 | −0.617469 | − | 0.786595i | \(-0.711842\pi\) | ||||
−0.617469 | + | 0.786595i | \(0.711842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 20.9050i | − | 0.953186i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.3137i | 1.60351i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4558 | 0.519114 | 0.259557 | − | 0.965728i | \(-0.416423\pi\) | ||||
0.259557 | + | 0.965728i | \(0.416423\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 38.5269i | − | 1.73870i | −0.494201 | − | 0.869348i | \(-0.664539\pi\) | ||
0.494201 | − | 0.869348i | \(-0.335461\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 17.4721i | − | 0.786905i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.02509 | − | 17.8995i | 0.359974 | − | 0.802902i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.8284 | −0.574279 | −0.287140 | − | 0.957889i | \(-0.592704\pi\) | ||||
−0.287140 | + | 0.957889i | \(0.592704\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.5027 | 1.18170 | 0.590848 | − | 0.806783i | \(-0.298793\pi\) | ||||
0.590848 | + | 0.806783i | \(0.298793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.97056 | 0.399185 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.2095 | 0.762797 | 0.381399 | − | 0.924411i | \(-0.375443\pi\) | ||||
0.381399 | + | 0.924411i | \(0.375443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.970563 | − | 2.16478i | 0.0429352 | − | 0.0957644i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.6274i | 0.997083i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.4525i | − | 0.459701i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.75699 | 0.296029 | 0.148014 | − | 0.988985i | \(-0.452712\pi\) | ||||
0.148014 | + | 0.988985i | \(0.452712\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.9050i | 0.914112i | 0.889438 | + | 0.457056i | \(0.151096\pi\) | ||||
−0.889438 | + | 0.457056i | \(0.848904\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 70.6274i | − | 3.07658i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.9706 | −0.694372 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.31371i | 0.143533i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.95815i | − | 0.171126i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.8435 | + | 15.8995i | −0.768576 | + | 0.684840i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.6569 | −1.18906 | −0.594531 | − | 0.804073i | \(-0.702662\pi\) | ||||
−0.594531 | + | 0.804073i | \(0.702662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.12293 | 0.262278 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6569 | 0.754953 | 0.377476 | − | 0.926019i | \(-0.376792\pi\) | ||||
0.377476 | + | 0.926019i | \(0.376792\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.59767 | −0.238469 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.9706 | − | 14.7821i | −1.40205 | − | 0.628598i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 45.8995i | 1.94482i | 0.233270 | + | 0.972412i | \(0.425057\pi\) | ||||
−0.233270 | + | 0.972412i | \(0.574943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 33.8937i | − | 1.43355i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.2123 | 1.52617 | 0.763084 | − | 0.646299i | \(-0.223684\pi\) | ||||
0.763084 | + | 0.646299i | \(0.223684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.4495i | 1.82794i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.24264i | 0.177861i | 0.996038 | + | 0.0889304i | \(0.0283449\pi\) | ||||
−0.996038 | + | 0.0889304i | \(0.971655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9706 | 0.542801 | 0.271401 | − | 0.962466i | \(-0.412513\pi\) | ||||
0.271401 | + | 0.962466i | \(0.412513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 54.0416i | − | 2.25369i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4525i | 0.435143i | 0.976044 | + | 0.217572i | \(0.0698136\pi\) | ||||
−0.976044 | + | 0.217572i | \(0.930186\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.2960 | + | 12.6863i | 1.17392 | + | 0.526316i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.82843 | 0.365636 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.6256 | −1.34660 | −0.673302 | − | 0.739368i | \(-0.735124\pi\) | ||||
−0.673302 | + | 0.739368i | \(0.735124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.6274 | −0.932346 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.9301 | 1.18802 | 0.594008 | − | 0.804459i | \(-0.297545\pi\) | ||||
0.594008 | + | 0.804459i | \(0.297545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −60.2843 | − | 27.0279i | −2.47141 | − | 1.10804i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.2132i | 1.27534i | 0.770311 | + | 0.637668i | \(0.220101\pi\) | ||||
−0.770311 | + | 0.637668i | \(0.779899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.6984i | − | 0.925886i | −0.886388 | − | 0.462943i | \(-0.846793\pi\) | ||
0.886388 | − | 0.462943i | \(-0.153207\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.42742 | 0.0986885 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.16478i | − | 0.0878659i | −0.999034 | − | 0.0439329i | \(-0.986011\pi\) | ||
0.999034 | − | 0.0439329i | \(-0.0139888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 16.0000i | − | 0.647291i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3137 | 0.860853 | 0.430426 | − | 0.902626i | \(-0.358363\pi\) | ||||
0.430426 | + | 0.902626i | \(0.358363\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.75736i | − | 0.151266i | −0.997136 | − | 0.0756328i | \(-0.975902\pi\) | ||
0.997136 | − | 0.0756328i | \(-0.0240977\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16.5754i | − | 0.666223i | −0.942887 | − | 0.333112i | \(-0.891901\pi\) | ||
0.942887 | − | 0.333112i | \(-0.108099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.3128 | + | 7.31371i | 0.653559 | + | 0.293018i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.65685 | 0.266274 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.0279 | 1.07767 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.5980 | −1.57637 | −0.788185 | − | 0.615438i | \(-0.788979\pi\) | ||||
−0.788185 | + | 0.615438i | \(0.788979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −62.7150 | −2.48877 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.3137 | + | 24.3379i | −1.08221 | + | 0.964302i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.8701i | 1.37728i | 0.725101 | + | 0.688642i | \(0.241793\pi\) | ||||
−0.725101 | + | 0.688642i | \(0.758207\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.7402i | 0.739042i | 0.929222 | + | 0.369521i | \(0.120478\pi\) | ||||
−0.929222 | + | 0.369521i | \(0.879522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −50.4692 | −1.98415 | −0.992074 | − | 0.125658i | \(-0.959896\pi\) | ||||
−0.992074 | + | 0.125658i | \(0.959896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.21320i | 0.0474763i | 0.999718 | + | 0.0237382i | \(0.00755680\pi\) | ||||
−0.999718 | + | 0.0237382i | \(0.992443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.3137 | 0.442063 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.5858i | 1.73682i | 0.495851 | + | 0.868408i | \(0.334856\pi\) | ||||
−0.495851 | + | 0.868408i | \(0.665144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 27.7708i | − | 1.08016i | −0.841614 | − | 0.540079i | \(-0.818394\pi\) | ||
0.841614 | − | 0.540079i | \(-0.181606\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.65914 | + | 19.3137i | −0.335787 | + | 0.748953i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.1421 | 0.625026 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.34315 | −0.0903216 | −0.0451608 | − | 0.998980i | \(-0.514380\pi\) | ||||
−0.0451608 | + | 0.998980i | \(0.514380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.6733 | 0.563940 | 0.281970 | − | 0.959423i | \(-0.409012\pi\) | ||||
0.281970 | + | 0.959423i | \(0.409012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.3431 | + | 23.0698i | −0.396934 | + | 0.885337i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 9.27208i | − | 0.354786i | −0.984140 | − | 0.177393i | \(-0.943234\pi\) | ||
0.984140 | − | 0.177393i | \(-0.0567664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.5838i | 1.39779i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.5140 | 0.514841 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.9887i | 0.494114i | 0.969001 | + | 0.247057i | \(0.0794634\pi\) | ||||
−0.969001 | + | 0.247057i | \(0.920537\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0000i | 0.606915i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.28427 | −0.162278 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 43.0711i | − | 1.62677i | −0.581725 | − | 0.813386i | \(-0.697622\pi\) | ||
0.581725 | − | 0.813386i | \(-0.302378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.65914i | − | 0.326586i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.86030 | + | 2.62742i | 0.220399 | + | 0.0988142i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.2843 | −1.21246 | −0.606231 | − | 0.795289i | \(-0.707319\pi\) | ||||
−0.606231 | + | 0.795289i | \(0.707319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 65.2512 | 2.44368 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 65.9411 | 2.46606 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.65914 | 0.322931 | 0.161466 | − | 0.986878i | \(-0.448378\pi\) | ||||
0.161466 | + | 0.986878i | \(0.448378\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.62742 | + | 14.7821i | −0.246818 | + | 0.550513i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.3848i | 0.831350i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 14.7821i | − | 0.548237i | −0.961696 | − | 0.274118i | \(-0.911614\pi\) | ||
0.961696 | − | 0.274118i | \(-0.0883860\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.8210 | 1.62078 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 15.6788i | − | 0.579108i | −0.957162 | − | 0.289554i | \(-0.906493\pi\) | ||
0.957162 | − | 0.289554i | \(-0.0935070\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685i | 0.208373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.2843 | −0.599027 | −0.299513 | − | 0.954092i | \(-0.596824\pi\) | ||||
−0.299513 | + | 0.954092i | \(0.596824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.6985i | − | 0.429176i | −0.976705 | − | 0.214588i | \(-0.931159\pi\) | ||
0.976705 | − | 0.214588i | \(-0.0688408\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.6675i | 1.05029i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.15932 | − | 2.58579i | 0.0423605 | − | 0.0944826i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.4853 | −1.11242 | −0.556212 | − | 0.831041i | \(-0.687746\pi\) | ||||
−0.556212 | + | 0.831041i | \(0.687746\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 59.6536 | 2.17102 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.5980 | −1.87536 | −0.937680 | − | 0.347499i | \(-0.887031\pi\) | ||||
−0.937680 | + | 0.347499i | \(0.887031\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.7849 | 1.22470 | 0.612351 | − | 0.790586i | \(-0.290224\pi\) | ||||
0.612351 | + | 0.790586i | \(0.290224\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.00000 | + | 1.79337i | 0.144810 | + | 0.0649242i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 22.6984i | − | 0.818524i | −0.912417 | − | 0.409262i | \(-0.865786\pi\) | ||
0.912417 | − | 0.409262i | \(-0.134214\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.42742 | −0.0873081 | −0.0436541 | − | 0.999047i | \(-0.513900\pi\) | ||||
−0.0436541 | + | 0.999047i | \(0.513900\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 90.4858i | 3.25035i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.37258i | 0.0491779i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.3137 | −0.905796 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 70.6274i | 2.52080i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33.1509i | − | 1.18170i | −0.806781 | − | 0.590851i | \(-0.798792\pi\) | ||
0.806781 | − | 0.590851i | \(-0.201208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.7261 | + | 28.3848i | −0.452487 | + | 1.00925i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.3547 | −0.437624 | −0.218812 | − | 0.975767i | \(-0.570218\pi\) | ||||
−0.218812 | + | 0.975767i | \(0.570218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.6863 | 0.731828 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.06147 | −0.108037 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.9706 | − | 55.6954i | 0.880097 | − | 1.96301i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.07107i | 0.248606i | 0.992244 | + | 0.124303i | \(0.0396694\pi\) | ||||
−0.992244 | + | 0.124303i | \(0.960331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29.5641i | − | 1.03814i | −0.854732 | − | 0.519069i | \(-0.826279\pi\) | ||
0.854732 | − | 0.519069i | \(-0.173721\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 65.2512 | 2.28565 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.0392i | − | 0.491171i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 31.3553i | − | 1.09431i | −0.837032 | − | 0.547154i | \(-0.815711\pi\) | ||
0.837032 | − | 0.547154i | \(-0.184289\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3431 | −0.360539 | −0.180270 | − | 0.983617i | \(-0.557697\pi\) | ||||
−0.180270 | + | 0.983617i | \(0.557697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.0122i | − | 0.939306i | −0.882851 | − | 0.469653i | \(-0.844379\pi\) | ||
0.882851 | − | 0.469653i | \(-0.155621\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.1313i | − | 0.907576i | −0.891110 | − | 0.453788i | \(-0.850072\pi\) | ||
0.891110 | − | 0.453788i | \(-0.149928\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.4663 | − | 35.3137i | −1.09024 | − | 1.22355i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.3137 | 1.49893 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.4303 | 0.739855 | 0.369928 | − | 0.929061i | \(-0.379382\pi\) | ||||
0.369928 | + | 0.929061i | \(0.379382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.3137 | 0.769438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 52.8966 | 1.81970 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.58579 | + | 0.710974i | 0.0544883 | + | 0.0244294i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.9706i | 0.855980i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.2459i | − | 0.419291i | −0.977778 | − | 0.209645i | \(-0.932769\pi\) | ||
0.977778 | − | 0.209645i | \(-0.0672309\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.75699 | 0.230814 | 0.115407 | − | 0.993318i | \(-0.463183\pi\) | ||||
0.115407 | + | 0.993318i | \(0.463183\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.7402i | 0.639408i | 0.947517 | + | 0.319704i | \(0.103583\pi\) | ||||
−0.947517 | + | 0.319704i | \(0.896417\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.4142i | 0.797029i | 0.917162 | + | 0.398515i | \(0.130474\pi\) | ||||
−0.917162 | + | 0.398515i | \(0.869526\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.6569 | −1.55238 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.6274i | 1.58173i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.65914i | 0.293404i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.6256 | + | 14.6274i | 1.10295 | + | 0.494497i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.4663 | −1.06013 | −0.530063 | − | 0.847958i | \(-0.677832\pi\) | ||||
−0.530063 | + | 0.847958i | \(0.677832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.1421 | 0.812448 | 0.406224 | − | 0.913774i | \(-0.366845\pi\) | ||||
0.406224 | + | 0.913774i | \(0.366845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.9665 | −0.804715 | −0.402358 | − | 0.915483i | \(-0.631809\pi\) | ||||
−0.402358 | + | 0.915483i | \(0.631809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.9706 | − | 18.3688i | −1.37411 | − | 0.616070i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6.62742i | − | 0.221778i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 58.7569i | − | 1.96403i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.0279 | −0.901432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.4721i | 0.582081i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 89.9411i | 2.98974i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.7990 | −1.65355 | −0.826774 | − | 0.562534i | \(-0.809827\pi\) | ||||
−0.826774 | + | 0.562534i | \(0.809827\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 56.1838i | − | 1.86145i | −0.365718 | − | 0.930726i | \(-0.619177\pi\) | ||
0.365718 | − | 0.930726i | \(-0.380823\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 40.0166i | − | 1.32436i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.39104 | + | 3.31371i | 0.244074 | + | 0.109428i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.79899 | −0.0593432 | −0.0296716 | − | 0.999560i | \(-0.509446\pi\) | ||||
−0.0296716 | + | 0.999560i | \(0.509446\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.7485 | −1.27542 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.6274 | −1.13854 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 55.9580 | 1.83592 | 0.917962 | − | 0.396669i | \(-0.129834\pi\) | ||||
0.917962 | + | 0.396669i | \(0.129834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.3137 | + | 10.0811i | −0.370792 | + | 0.330394i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 85.2548i | 2.78813i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.4692i | − | 1.64876i | −0.566040 | − | 0.824378i | \(-0.691525\pi\) | ||
0.566040 | − | 0.824378i | \(-0.308475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3547 | 0.402750 | 0.201375 | − | 0.979514i | \(-0.435459\pi\) | ||||
0.201375 | + | 0.979514i | \(0.435459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.95815i | − | 0.128895i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.4142i | 0.890842i | 0.895321 | + | 0.445421i | \(0.146946\pi\) | ||||
−0.895321 | + | 0.445421i | \(0.853054\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.68629 | −0.152123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.7868i | 0.349419i | 0.984620 | + | 0.174709i | \(0.0558986\pi\) | ||||
−0.984620 | + | 0.174709i | \(0.944101\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0811i | 0.326216i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.7151 | + | 23.8995i | −0.346010 | + | 0.771755i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −78.2548 | −2.52435 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.9050 | −0.672956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3431 | 0.589876 | 0.294938 | − | 0.955516i | \(-0.404701\pi\) | ||||
0.294938 | + | 0.955516i | \(0.404701\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.0279 | −0.867368 | −0.433684 | − | 0.901065i | \(-0.642787\pi\) | ||||
−0.433684 | + | 0.901065i | \(0.642787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.68629 | + | 10.4525i | −0.150236 | + | 0.335092i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.89949i | 0.0607702i | 0.999538 | + | 0.0303851i | \(0.00967337\pi\) | ||||
−0.999538 | + | 0.0303851i | \(0.990327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 23.0698i | − | 0.737314i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.6536 | 1.90265 | 0.951326 | − | 0.308185i | \(-0.0997216\pi\) | ||||
0.951326 | + | 0.308185i | \(0.0997216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 82.7233i | 2.63578i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.4853i | 1.28736i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.1421 | −1.78341 | −0.891707 | − | 0.452613i | \(-0.850492\pi\) | ||||
−0.891707 | + | 0.452613i | \(0.850492\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 85.2548i | − | 2.70276i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.8824i | 1.48478i | 0.669967 | + | 0.742391i | \(0.266308\pi\) | ||||
−0.669967 | + | 0.742391i | \(0.733692\pi\) | |||||||
\(998\) | 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 | 4032.2.k.e.3905.1 | 8 | ||
3.2 | odd | 2 | inner | 4032.2.k.e.3905.7 | 8 | ||
4.3 | odd | 2 | 4032.2.k.f.3905.2 | 8 | |||
7.6 | odd | 2 | inner | 4032.2.k.e.3905.8 | 8 | ||
8.3 | odd | 2 | 504.2.k.a.377.8 | yes | 8 | ||
8.5 | even | 2 | 1008.2.k.c.881.7 | 8 | |||
12.11 | even | 2 | 4032.2.k.f.3905.8 | 8 | |||
21.20 | even | 2 | inner | 4032.2.k.e.3905.2 | 8 | ||
24.5 | odd | 2 | 1008.2.k.c.881.1 | 8 | |||
24.11 | even | 2 | 504.2.k.a.377.2 | yes | 8 | ||
28.27 | even | 2 | 4032.2.k.f.3905.7 | 8 | |||
56.3 | even | 6 | 3528.2.bl.b.1097.8 | 16 | |||
56.11 | odd | 6 | 3528.2.bl.b.1097.2 | 16 | |||
56.13 | odd | 2 | 1008.2.k.c.881.2 | 8 | |||
56.19 | even | 6 | 3528.2.bl.b.521.7 | 16 | |||
56.27 | even | 2 | 504.2.k.a.377.1 | ✓ | 8 | ||
56.51 | odd | 6 | 3528.2.bl.b.521.1 | 16 | |||
84.83 | odd | 2 | 4032.2.k.f.3905.1 | 8 | |||
168.11 | even | 6 | 3528.2.bl.b.1097.7 | 16 | |||
168.59 | odd | 6 | 3528.2.bl.b.1097.1 | 16 | |||
168.83 | odd | 2 | 504.2.k.a.377.7 | yes | 8 | ||
168.107 | even | 6 | 3528.2.bl.b.521.8 | 16 | |||
168.125 | even | 2 | 1008.2.k.c.881.8 | 8 | |||
168.131 | odd | 6 | 3528.2.bl.b.521.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.k.a.377.1 | ✓ | 8 | 56.27 | even | 2 | ||
504.2.k.a.377.2 | yes | 8 | 24.11 | even | 2 | ||
504.2.k.a.377.7 | yes | 8 | 168.83 | odd | 2 | ||
504.2.k.a.377.8 | yes | 8 | 8.3 | odd | 2 | ||
1008.2.k.c.881.1 | 8 | 24.5 | odd | 2 | |||
1008.2.k.c.881.2 | 8 | 56.13 | odd | 2 | |||
1008.2.k.c.881.7 | 8 | 8.5 | even | 2 | |||
1008.2.k.c.881.8 | 8 | 168.125 | even | 2 | |||
3528.2.bl.b.521.1 | 16 | 56.51 | odd | 6 | |||
3528.2.bl.b.521.2 | 16 | 168.131 | odd | 6 | |||
3528.2.bl.b.521.7 | 16 | 56.19 | even | 6 | |||
3528.2.bl.b.521.8 | 16 | 168.107 | even | 6 | |||
3528.2.bl.b.1097.1 | 16 | 168.59 | odd | 6 | |||
3528.2.bl.b.1097.2 | 16 | 56.11 | odd | 6 | |||
3528.2.bl.b.1097.7 | 16 | 168.11 | even | 6 | |||
3528.2.bl.b.1097.8 | 16 | 56.3 | even | 6 | |||
4032.2.k.e.3905.1 | 8 | 1.1 | even | 1 | trivial | ||
4032.2.k.e.3905.2 | 8 | 21.20 | even | 2 | inner | ||
4032.2.k.e.3905.7 | 8 | 3.2 | odd | 2 | inner | ||
4032.2.k.e.3905.8 | 8 | 7.6 | odd | 2 | inner | ||
4032.2.k.f.3905.1 | 8 | 84.83 | odd | 2 | |||
4032.2.k.f.3905.2 | 8 | 4.3 | odd | 2 | |||
4032.2.k.f.3905.7 | 8 | 28.27 | even | 2 | |||
4032.2.k.f.3905.8 | 8 | 12.11 | even | 2 |