Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(961,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.q (of order \(3\), degree \(2\), 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: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1176) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.961 |
Dual form | 2352.2.q.ba.1537.1 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.70711 | + | 2.95680i | −0.763441 | + | 1.32232i | 0.177625 | + | 0.984098i | \(0.443158\pi\) |
−0.941067 | + | 0.338221i | \(0.890175\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.414214 | + | 0.717439i | 0.124890 | + | 0.216316i | 0.921690 | − | 0.387927i | \(-0.126809\pi\) |
−0.796800 | + | 0.604243i | \(0.793476\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.70711 | − | 6.42090i | −0.899105 | − | 1.55730i | −0.828640 | − | 0.559782i | \(-0.810885\pi\) |
−0.0704656 | − | 0.997514i | \(-0.522449\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.41421 | − | 5.91359i | 0.783274 | − | 1.35667i | −0.146750 | − | 0.989174i | \(-0.546881\pi\) |
0.930025 | − | 0.367497i | \(-0.119785\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.41421 | + | 4.18154i | −0.503398 | + | 0.871911i | 0.496594 | + | 0.867983i | \(0.334584\pi\) |
−0.999992 | + | 0.00392850i | \(0.998750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.32843 | − | 5.76500i | −0.665685 | − | 1.15300i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.41421 | − | 2.44949i | −0.254000 | − | 0.439941i | 0.710623 | − | 0.703573i | \(-0.248413\pi\) |
−0.964623 | + | 0.263631i | \(0.915080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.414214 | − | 0.717439i | 0.0721053 | − | 0.124890i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.828427 | − | 1.43488i | 0.136193 | − | 0.235892i | −0.789860 | − | 0.613287i | \(-0.789847\pi\) |
0.926052 | + | 0.377395i | \(0.123180\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.12132 | + | 3.67423i | 0.339683 | + | 0.588348i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.2426 | 1.59963 | 0.799816 | − | 0.600245i | \(-0.204930\pi\) | ||||
0.799816 | + | 0.600245i | \(0.204930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3137 | 1.72532 | 0.862662 | − | 0.505781i | \(-0.168795\pi\) | ||||
0.862662 | + | 0.505781i | \(0.168795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.70711 | − | 2.95680i | −0.254480 | − | 0.440773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.24264 | + | 3.88437i | −0.327123 | + | 0.566593i | −0.981940 | − | 0.189194i | \(-0.939412\pi\) |
0.654817 | + | 0.755788i | \(0.272746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.70711 | + | 6.42090i | −0.519099 | + | 0.899105i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | + | 1.73205i | 0.137361 | + | 0.237915i | 0.926497 | − | 0.376303i | \(-0.122805\pi\) |
−0.789136 | + | 0.614218i | \(0.789471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82843 | −0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.82843 | −0.904447 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.24264 | + | 7.34847i | 0.552345 | + | 0.956689i | 0.998105 | + | 0.0615367i | \(0.0196001\pi\) |
−0.445760 | + | 0.895152i | \(0.647067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.53553 | + | 9.58783i | −0.708752 | + | 1.22760i | 0.256568 | + | 0.966526i | \(0.417408\pi\) |
−0.965320 | + | 0.261069i | \(0.915925\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.24264 | − | 12.5446i | 0.898339 | − | 1.55597i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.65685 | + | 9.79796i | 0.691095 | + | 1.19701i | 0.971480 | + | 0.237124i | \(0.0762046\pi\) |
−0.280385 | + | 0.959888i | \(0.590462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.82843 | 0.581274 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4853 | 1.24437 | 0.622187 | − | 0.782869i | \(-0.286244\pi\) | ||||
0.622187 | + | 0.782869i | \(0.286244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.87868 | − | 6.71807i | −0.453965 | − | 0.786291i | 0.544663 | − | 0.838655i | \(-0.316658\pi\) |
−0.998628 | + | 0.0523644i | \(0.983324\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.32843 | + | 5.76500i | −0.384334 | + | 0.665685i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.82843 | − | 11.8272i | 0.768258 | − | 1.33066i | −0.170249 | − | 0.985401i | \(-0.554457\pi\) |
0.938507 | − | 0.345261i | \(-0.112210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.3137 | 2.74566 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.41421 | − | 2.44949i | −0.151620 | − | 0.262613i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.87868 | + | 4.98602i | −0.305139 | + | 0.528517i | −0.977292 | − | 0.211895i | \(-0.932036\pi\) |
0.672153 | + | 0.740412i | \(0.265370\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.41421 | + | 2.44949i | −0.146647 | + | 0.254000i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.6569 | + | 20.1903i | 1.19597 | + | 2.07148i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.242641 | −0.0246364 | −0.0123182 | − | 0.999924i | \(-0.503921\pi\) | ||||
−0.0123182 | + | 0.999924i | \(0.503921\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.828427 | −0.0832601 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.36396 | + | 9.29065i | 0.533734 | + | 0.924455i | 0.999223 | + | 0.0394011i | \(0.0125450\pi\) |
−0.465489 | + | 0.885053i | \(0.654122\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.07107 | − | 12.2474i | 0.696733 | − | 1.20678i | −0.272860 | − | 0.962054i | \(-0.587970\pi\) |
0.969593 | − | 0.244723i | \(-0.0786971\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.41421 | − | 11.1097i | 0.620085 | − | 1.07402i | −0.369384 | − | 0.929277i | \(-0.620431\pi\) |
0.989469 | − | 0.144743i | \(-0.0462354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.65685 | + | 2.86976i | 0.158698 | + | 0.274873i | 0.934399 | − | 0.356227i | \(-0.115937\pi\) |
−0.775702 | + | 0.631100i | \(0.782604\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.65685 | −0.157262 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.24264 | − | 14.2767i | −0.768630 | − | 1.33131i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.12132 | − | 3.67423i | 0.196116 | − | 0.339683i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.15685 | − | 8.93193i | 0.468805 | − | 0.811994i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.12132 | − | 8.87039i | −0.461774 | − | 0.799816i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.0000 | −1.77471 | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.65685 | − | 9.79796i | −0.498058 | − | 0.862662i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.00000 | + | 3.46410i | −0.174741 | + | 0.302660i | −0.940072 | − | 0.340977i | \(-0.889242\pi\) |
0.765331 | + | 0.643637i | \(0.222575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.70711 | + | 2.95680i | −0.146924 | + | 0.254480i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.58579 | + | 7.94282i | 0.391790 | + | 0.678600i | 0.992686 | − | 0.120727i | \(-0.0385226\pi\) |
−0.600896 | + | 0.799328i | \(0.705189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.9706 | 1.77870 | 0.889350 | − | 0.457227i | \(-0.151157\pi\) | ||||
0.889350 | + | 0.457227i | \(0.151157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.48528 | 0.377729 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.75736 | − | 3.04384i | −0.146958 | − | 0.254538i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.82843 | + | 8.36308i | −0.400979 | + | 0.694516i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.656854 | + | 1.13770i | −0.0538116 | + | 0.0932044i | −0.891676 | − | 0.452673i | \(-0.850470\pi\) |
0.837865 | + | 0.545878i | \(0.183804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.82843 | − | 8.36308i | −0.392932 | − | 0.680578i | 0.599903 | − | 0.800073i | \(-0.295206\pi\) |
−0.992835 | + | 0.119495i | \(0.961872\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.41421 | 0.599404 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.65685 | 0.775657 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.121320 | − | 0.210133i | −0.00968242 | − | 0.0167704i | 0.861144 | − | 0.508362i | \(-0.169749\pi\) |
−0.870826 | + | 0.491591i | \(0.836415\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.00000 | − | 1.73205i | 0.0793052 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.82843 | − | 4.89898i | 0.221540 | − | 0.383718i | −0.733736 | − | 0.679435i | \(-0.762225\pi\) |
0.955276 | + | 0.295717i | \(0.0955585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.41421 | + | 2.44949i | 0.110096 | + | 0.190693i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.8284 | 1.14746 | 0.573729 | − | 0.819045i | \(-0.305496\pi\) | ||||
0.573729 | + | 0.819045i | \(0.305496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.41421 | + | 5.91359i | 0.261091 | + | 0.452224i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.29289 | − | 14.3637i | 0.630497 | − | 1.09205i | −0.356953 | − | 0.934122i | \(-0.616184\pi\) |
0.987450 | − | 0.157931i | \(-0.0504822\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.24264 | − | 7.34847i | 0.318896 | − | 0.552345i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.24264 | − | 5.61642i | −0.242366 | − | 0.419791i | 0.719022 | − | 0.694988i | \(-0.244590\pi\) |
−0.961388 | + | 0.275197i | \(0.911257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.07107 | −0.525588 | −0.262794 | − | 0.964852i | \(-0.584644\pi\) | ||||
−0.262794 | + | 0.964852i | \(0.584644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.0711 | 0.818397 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.82843 | + | 4.89898i | 0.207950 | + | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.07107 | − | 5.31925i | 0.224579 | − | 0.388982i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.07107 | − | 10.5154i | 0.439287 | − | 0.760867i | −0.558348 | − | 0.829607i | \(-0.688564\pi\) |
0.997635 | + | 0.0687396i | \(0.0218978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | − | 1.73205i | −0.0719816 | − | 0.124676i | 0.827788 | − | 0.561041i | \(-0.189599\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.4853 | −1.03731 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.68629 | −0.191390 | −0.0956952 | − | 0.995411i | \(-0.530507\pi\) | ||||
−0.0956952 | + | 0.995411i | \(0.530507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.82843 | − | 4.89898i | −0.200502 | − | 0.347279i | 0.748188 | − | 0.663486i | \(-0.230924\pi\) |
−0.948690 | + | 0.316207i | \(0.897591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.65685 | − | 9.79796i | 0.399004 | − | 0.691095i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.4853 | + | 30.2854i | −1.22123 | + | 2.11522i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.41421 | − | 4.18154i | −0.167799 | − | 0.290637i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.65685 | −0.114063 | −0.0570313 | − | 0.998372i | \(-0.518163\pi\) | ||||
−0.0570313 | + | 0.998372i | \(0.518163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.24264 | − | 9.08052i | −0.359220 | − | 0.622187i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.3137 | + | 33.4523i | −1.31718 | + | 2.28143i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.87868 | + | 6.71807i | −0.262097 | + | 0.453965i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.7279 | + | 27.2416i | 1.05797 | + | 1.83247i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6569 | −0.914531 | −0.457265 | − | 0.889330i | \(-0.651171\pi\) | ||||
−0.457265 | + | 0.889330i | \(0.651171\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.58579 | − | 4.47871i | −0.171625 | − | 0.297263i | 0.767363 | − | 0.641213i | \(-0.221568\pi\) |
−0.938988 | + | 0.343950i | \(0.888235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7071 | − | 22.0094i | 0.839709 | − | 1.45442i | −0.0504286 | − | 0.998728i | \(-0.516059\pi\) |
0.890138 | − | 0.455691i | \(-0.150608\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.41421 | − | 12.8418i | 0.485721 | − | 0.841294i | −0.514144 | − | 0.857704i | \(-0.671890\pi\) |
0.999865 | + | 0.0164099i | \(0.00522367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.65685 | − | 13.2621i | −0.499478 | − | 0.865121i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.6569 | −0.887108 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.8284 | 0.829802 | 0.414901 | − | 0.909867i | \(-0.363816\pi\) | ||||
0.414901 | + | 0.909867i | \(0.363816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.94975 | − | 12.0373i | −0.447673 | − | 0.775392i | 0.550561 | − | 0.834795i | \(-0.314414\pi\) |
−0.998234 | + | 0.0594029i | \(0.981080\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.4853 | + | 25.0892i | −0.921676 | + | 1.59639i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.00000 | − | 3.46410i | −0.126745 | − | 0.219529i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.14214 | 0.387688 | 0.193844 | − | 0.981032i | \(-0.437904\pi\) | ||||
0.193844 | + | 0.981032i | \(0.437904\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.6569 | − | 21.9223i | −0.792603 | − | 1.37283i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.70711 | − | 2.95680i | 0.106486 | − | 0.184440i | −0.807858 | − | 0.589377i | \(-0.799373\pi\) |
0.914345 | + | 0.404937i | \(0.132707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41421 | + | 2.44949i | −0.0875376 | + | 0.151620i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0711 | − | 17.4436i | −0.621009 | − | 1.07562i | −0.989298 | − | 0.145907i | \(-0.953390\pi\) |
0.368290 | − | 0.929711i | \(-0.379943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.82843 | −0.419467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.75736 | 0.352345 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.0502525 | + | 0.0870399i | 0.00306395 | + | 0.00530692i | 0.867553 | − | 0.497344i | \(-0.165691\pi\) |
−0.864489 | + | 0.502651i | \(0.832358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.07107 | − | 5.31925i | 0.186554 | − | 0.323121i | −0.757545 | − | 0.652783i | \(-0.773601\pi\) |
0.944099 | + | 0.329662i | \(0.106935\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.75736 | − | 4.77589i | 0.166275 | − | 0.287997i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3137 | + | 24.7921i | 0.860027 | + | 1.48961i | 0.871901 | + | 0.489682i | \(0.162887\pi\) |
−0.0118739 | + | 0.999930i | \(0.503780\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.82843 | 0.169334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.17157 | 0.0698902 | 0.0349451 | − | 0.999389i | \(-0.488874\pi\) | ||||
0.0349451 | + | 0.999389i | \(0.488874\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0711 | − | 22.6398i | −0.776994 | − | 1.34579i | −0.933667 | − | 0.358143i | \(-0.883410\pi\) |
0.156672 | − | 0.987651i | \(-0.449923\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.6569 | − | 20.1903i | 0.690492 | − | 1.19597i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.9853 | + | 32.8835i | −1.11678 | + | 1.93432i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.121320 | + | 0.210133i | 0.00711192 | + | 0.0123182i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.75736 | −0.102666 | −0.0513330 | − | 0.998682i | \(-0.516347\pi\) | ||||
−0.0513330 | + | 0.998682i | \(0.516347\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.9706 | −1.68673 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.414214 | + | 0.717439i | 0.0240351 | + | 0.0416300i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2426 | − | 17.7408i | 0.592347 | − | 1.02598i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.36396 | − | 9.29065i | 0.308152 | − | 0.533734i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.8995 | − | 32.7349i | −1.08218 | − | 1.87439i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5147 | 0.657180 | 0.328590 | − | 0.944473i | \(-0.393427\pi\) | ||||
0.328590 | + | 0.944473i | \(0.393427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.1421 | −0.804518 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.8995 | + | 20.6105i | 0.674758 | + | 1.16872i | 0.976539 | + | 0.215339i | \(0.0690855\pi\) |
−0.301781 | + | 0.953377i | \(0.597581\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3640 | + | 24.8791i | −0.811899 | + | 1.40625i | 0.0996342 | + | 0.995024i | \(0.468233\pi\) |
−0.911533 | + | 0.411226i | \(0.865101\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0000 | − | 19.0526i | 0.617822 | − | 1.07010i | −0.372061 | − | 0.928208i | \(-0.621349\pi\) |
0.989882 | − | 0.141890i | \(-0.0453179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.17157 | + | 2.02922i | 0.0655955 | + | 0.113615i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8284 | −0.716013 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −50.6274 | −2.81698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.1213 | + | 24.4588i | 0.783310 | + | 1.35673i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.65685 | − | 2.86976i | 0.0916242 | − | 0.158698i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.65685 | − | 6.33386i | 0.200999 | − | 0.348140i | −0.747852 | − | 0.663866i | \(-0.768915\pi\) |
0.948851 | + | 0.315726i | \(0.102248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.828427 | + | 1.43488i | 0.0453975 | + | 0.0786308i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −38.6274 | −2.11044 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3431 | 0.563427 | 0.281714 | − | 0.959499i | \(-0.409097\pi\) | ||||
0.281714 | + | 0.959499i | \(0.409097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.00000 | + | 8.66025i | 0.271563 | + | 0.470360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.17157 | − | 2.02922i | 0.0634442 | − | 0.109889i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.24264 | + | 14.2767i | −0.443769 | + | 0.768630i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.24264 | − | 2.15232i | −0.0667084 | − | 0.115542i | 0.830742 | − | 0.556657i | \(-0.187916\pi\) |
−0.897451 | + | 0.441115i | \(0.854583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.5858 | 0.566644 | 0.283322 | − | 0.959025i | \(-0.408563\pi\) | ||||
0.283322 | + | 0.959025i | \(0.408563\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.24264 | −0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.8492 | + | 23.9876i | 0.737121 | + | 1.27673i | 0.953787 | + | 0.300485i | \(0.0971485\pi\) |
−0.216666 | + | 0.976246i | \(0.569518\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.8995 | + | 31.0028i | −0.950007 | + | 1.64546i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.4142 | − | 24.9662i | 0.760753 | − | 1.31766i | −0.181710 | − | 0.983352i | \(-0.558163\pi\) |
0.942463 | − | 0.334311i | \(-0.108504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.8137 | − | 23.9260i | −0.727037 | − | 1.25927i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.3137 | −0.541329 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.4853 | 1.38630 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.34315 | + | 4.05845i | 0.122311 | + | 0.211849i | 0.920679 | − | 0.390321i | \(-0.127636\pi\) |
−0.798368 | + | 0.602171i | \(0.794303\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.12132 | + | 8.87039i | −0.266605 | + | 0.461774i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.65685 | + | 4.60181i | −0.137567 | + | 0.238273i | −0.926575 | − | 0.376110i | \(-0.877261\pi\) |
0.789008 | + | 0.614383i | \(0.210595\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.82843 | − | 4.89898i | −0.146059 | − | 0.252982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.3137 | 1.19754 | 0.598772 | − | 0.800919i | \(-0.295655\pi\) | ||||
0.598772 | + | 0.800919i | \(0.295655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.0000 | + | 17.3205i | 0.512316 | + | 0.887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.48528 | + | 7.76874i | −0.229187 | + | 0.396964i | −0.957567 | − | 0.288209i | \(-0.906940\pi\) |
0.728380 | + | 0.685173i | \(0.240273\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.65685 | + | 9.79796i | −0.287554 | + | 0.498058i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.8995 | + | 31.0028i | 0.907540 | + | 1.57191i | 0.817470 | + | 0.575971i | \(0.195376\pi\) |
0.0900701 | + | 0.995935i | \(0.471291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.7990 | 1.81043 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.3137 | + | 40.3805i | 1.17304 | + | 2.03176i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.12132 | − | 14.0665i | 0.407597 | − | 0.705979i | −0.587023 | − | 0.809571i | \(-0.699700\pi\) |
0.994620 | + | 0.103591i | \(0.0330334\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.585786 | + | 1.01461i | −0.0292528 | + | 0.0506673i | −0.880281 | − | 0.474452i | \(-0.842646\pi\) |
0.851028 | + | 0.525120i | \(0.175979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | + | 10.3923i | 0.298881 | + | 0.517678i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.41421 | 0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.37258 | 0.0680364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.12132 | + | 7.13834i | 0.203786 | + | 0.352968i | 0.949745 | − | 0.313024i | \(-0.101342\pi\) |
−0.745959 | + | 0.665992i | \(0.768009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.58579 | − | 7.94282i | 0.226200 | − | 0.391790i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.82843 | + | 11.8272i | −0.335194 | + | 0.580574i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.4853 | − | 18.1610i | −0.513466 | − | 0.889350i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.51472 | −0.367118 | −0.183559 | − | 0.983009i | \(-0.558762\pi\) | ||||
−0.183559 | + | 0.983009i | \(0.558762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.3137 | −1.23371 | −0.616857 | − | 0.787075i | \(-0.711594\pi\) | ||||
−0.616857 | + | 0.787075i | \(0.711594\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.24264 | − | 3.88437i | −0.109041 | − | 0.188864i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.6777 | + | 42.7430i | −1.19704 | + | 2.07334i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.75736 | + | 3.04384i | −0.0848461 | + | 0.146958i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.07107 | − | 7.05130i | −0.196096 | − | 0.339649i | 0.751163 | − | 0.660117i | \(-0.229493\pi\) |
−0.947259 | + | 0.320468i | \(0.896160\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.928932 | 0.0446416 | 0.0223208 | − | 0.999751i | \(-0.492894\pi\) | ||||
0.0223208 | + | 0.999751i | \(0.492894\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.65685 | 0.463011 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.4853 | + | 28.5533i | 0.788598 | + | 1.36589i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.34315 | − | 10.9867i | 0.302742 | − | 0.524364i | −0.674014 | − | 0.738718i | \(-0.735431\pi\) |
0.976756 | + | 0.214354i | \(0.0687647\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.58579 | + | 9.67487i | −0.265389 | + | 0.459667i | −0.967665 | − | 0.252237i | \(-0.918834\pi\) |
0.702277 | + | 0.711904i | \(0.252167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.82843 | − | 17.0233i | −0.465912 | − | 0.806983i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.31371 | 0.0621363 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.6274 | −0.784696 | −0.392348 | − | 0.919817i | \(-0.628337\pi\) | ||||
−0.392348 | + | 0.919817i | \(0.628337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.24264 | + | 7.34847i | 0.199778 | + | 0.346026i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.82843 | + | 8.36308i | −0.226859 | + | 0.392932i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.3137 | − | 21.3280i | 0.576011 | − | 0.997680i | −0.419920 | − | 0.907561i | \(-0.637942\pi\) |
0.995931 | − | 0.0901192i | \(-0.0287248\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.70711 | − | 6.42090i | −0.173033 | − | 0.299702i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.3848 | 0.763115 | 0.381558 | − | 0.924345i | \(-0.375388\pi\) | ||||
0.381558 | + | 0.924345i | \(0.375388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.65685 | −0.0770005 | −0.0385003 | − | 0.999259i | \(-0.512258\pi\) | ||||
−0.0385003 | + | 0.999259i | \(0.512258\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.82843 | − | 8.36308i | −0.223913 | − | 0.387829i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.41421 | + | 16.3059i | −0.435638 | + | 0.754547i | −0.997347 | − | 0.0727876i | \(-0.976810\pi\) |
0.561710 | + | 0.827334i | \(0.310144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.121320 | + | 0.210133i | −0.00559015 | + | 0.00968242i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.68629 | + | 8.11689i | 0.215476 | + | 0.373215i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −45.4558 | −2.08566 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.4142 | + | 19.7700i | 0.521529 | + | 0.903314i | 0.999686 | + | 0.0250403i | \(0.00797140\pi\) |
−0.478158 | + | 0.878274i | \(0.658695\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.51472 | + | 6.08767i | −0.160257 | + | 0.277574i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.414214 | − | 0.717439i | 0.0188085 | − | 0.0325772i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.48528 | + | 4.30463i | 0.112619 | + | 0.195062i | 0.916825 | − | 0.399288i | \(-0.130743\pi\) |
−0.804207 | + | 0.594350i | \(0.797409\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.65685 | −0.255812 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.1716 | −0.865201 | −0.432600 | − | 0.901586i | \(-0.642404\pi\) | ||||
−0.432600 | + | 0.901586i | \(0.642404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.4853 | − | 18.1610i | −0.472233 | − | 0.817932i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.41421 | − | 2.44949i | 0.0635642 | − | 0.110096i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4853 | + | 21.6251i | −0.558918 | + | 0.968074i | 0.438669 | + | 0.898649i | \(0.355450\pi\) |
−0.997587 | + | 0.0694257i | \(0.977883\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.41421 | − | 12.8418i | −0.331243 | − | 0.573729i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.3137 | 0.861156 | 0.430578 | − | 0.902553i | \(-0.358310\pi\) | ||||
0.430578 | + | 0.902553i | \(0.358310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.6274 | −1.62990 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.50000 | − | 4.33013i | −0.111029 | − | 0.192308i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.1924 | − | 31.5101i | 0.806363 | − | 1.39666i | −0.109003 | − | 0.994041i | \(-0.534766\pi\) |
0.915367 | − | 0.402621i | \(-0.131901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.41421 | − | 5.91359i | 0.150741 | − | 0.261091i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.1421 | + | 41.8154i | 1.06383 | + | 1.84261i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.71573 | −0.163418 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.5858 | −0.728035 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.12132 | − | 12.3345i | −0.311991 | − | 0.540384i | 0.666803 | − | 0.745234i | \(-0.267662\pi\) |
−0.978793 | + | 0.204851i | \(0.934329\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.48528 | + | 4.30463i | −0.108674 | + | 0.188228i | −0.915233 | − | 0.402924i | \(-0.867994\pi\) |
0.806559 | + | 0.591153i | \(0.201327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.4853 | + | 18.1610i | −0.456746 | + | 0.791107i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.156854 | − | 0.271680i | −0.00681975 | − | 0.0118122i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.48528 | −0.368230 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.4558 | −1.88228 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.8995 | + | 37.9310i | 0.946798 | + | 1.63990i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.24264 | + | 5.61642i | −0.139930 | + | 0.242366i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00000 | − | 15.5885i | 0.386940 | − | 0.670200i | −0.605096 | − | 0.796152i | \(-0.706865\pi\) |
0.992036 | + | 0.125952i | \(0.0401986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.53553 | + | 6.12372i | 0.151724 | + | 0.262794i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.3137 | −0.484626 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.02944 | 0.129529 | 0.0647647 | − | 0.997901i | \(-0.479370\pi\) | ||||
0.0647647 | + | 0.997901i | \(0.479370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.53553 | − | 9.58783i | −0.236251 | − | 0.409198i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.65685 | − | 16.7262i | 0.411396 | − | 0.712558i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.82843 | − | 4.89898i | 0.120060 | − | 0.207950i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.3137 | − | 28.2562i | −0.691234 | − | 1.19725i | −0.971434 | − | 0.237311i | \(-0.923734\pi\) |
0.280200 | − | 0.959942i | \(-0.409599\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.0000 | −2.03018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.14214 | −0.259321 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.928932 | + | 1.60896i | 0.0391498 | + | 0.0678095i | 0.884936 | − | 0.465712i | \(-0.154202\pi\) |
−0.845787 | + | 0.533521i | \(0.820868\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.0711 | − | 29.5680i | 0.718185 | − | 1.24393i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.92893 | − | 5.07306i | 0.122787 | − | 0.212674i | −0.798079 | − | 0.602553i | \(-0.794150\pi\) |
0.920866 | + | 0.389880i | \(0.127483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.8284 | − | 36.0759i | −0.871643 | − | 1.50973i | −0.860297 | − | 0.509794i | \(-0.829722\pi\) |
−0.0113458 | − | 0.999936i | \(-0.503612\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.1421 | −0.507245 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 32.1421 | 1.34042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.60660 | − | 11.4430i | −0.275036 | − | 0.476377i | 0.695108 | − | 0.718905i | \(-0.255357\pi\) |
−0.970144 | + | 0.242528i | \(0.922023\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.00000 | + | 1.73205i | −0.0415586 | + | 0.0719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.828427 | + | 1.43488i | −0.0343099 | + | 0.0594266i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.24264 | + | 12.5446i | 0.299446 | + | 0.518656i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.7990 | 1.47758 | 0.738791 | − | 0.673934i | \(-0.235397\pi\) | ||||
0.738791 | + | 0.673934i | \(0.235397\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3137 | −0.795807 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.34315 | + | 2.32640i | 0.0552496 | + | 0.0956952i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.7071 | + | 41.0619i | −0.973534 | + | 1.68621i | −0.288844 | + | 0.957376i | \(0.593271\pi\) |
−0.684690 | + | 0.728835i | \(0.740062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.82843 | + | 4.89898i | −0.115760 | + | 0.200502i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7279 | + | 20.3134i | 0.479190 | + | 0.829981i | 0.999715 | − | 0.0238650i | \(-0.00759718\pi\) |
−0.520525 | + | 0.853846i | \(0.674264\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.2426 | −0.499388 | −0.249694 | − | 0.968325i | \(-0.580330\pi\) | ||||
−0.249694 | + | 0.968325i | \(0.580330\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.3137 | −0.460730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.6066 | + | 30.4955i | 0.715810 | + | 1.23982i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.4853 | − | 21.6251i | 0.506762 | − | 0.877737i | −0.493207 | − | 0.869912i | \(-0.664176\pi\) |
0.999969 | − | 0.00782569i | \(-0.00249102\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.51472 | − | 16.4800i | 0.384924 | − | 0.666708i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.17157 | + | 8.95743i | 0.208878 | + | 0.361787i | 0.951361 | − | 0.308077i | \(-0.0996856\pi\) |
−0.742483 | + | 0.669864i | \(0.766352\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 34.9706 | 1.41015 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.48528 | −0.180571 | −0.0902853 | − | 0.995916i | \(-0.528778\pi\) | ||||
−0.0902853 | + | 0.995916i | \(0.528778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.8284 | + | 29.1477i | 0.676392 | + | 1.17154i | 0.976060 | + | 0.217501i | \(0.0697906\pi\) |
−0.299668 | + | 0.954043i | \(0.596876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.41421 | + | 4.18154i | −0.0968791 | + | 0.167799i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.98528 | − | 12.0989i | 0.279411 | − | 0.483954i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.82843 | − | 4.89898i | −0.112956 | − | 0.195646i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.2843 | −0.489806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.02944 | 0.120600 | 0.0603000 | − | 0.998180i | \(-0.480794\pi\) | ||||
0.0603000 | + | 0.998180i | \(0.480794\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.828427 | + | 1.43488i | 0.0329270 | + | 0.0570313i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.1421 | − | 59.1359i | 1.35489 | − | 2.34674i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.24264 | + | 9.08052i | −0.207396 | + | 0.359220i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.5563 | − | 30.4085i | −0.693434 | − | 1.20106i | −0.970706 | − | 0.240272i | \(-0.922764\pi\) |
0.277272 | − | 0.960792i | \(-0.410570\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.7990 | −1.25403 | −0.627015 | − | 0.779007i | \(-0.715723\pi\) | ||||
−0.627015 | + | 0.779007i | \(0.715723\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 38.6274 | 1.52095 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.100505 | − | 0.174080i | −0.00395126 | − | 0.00684379i | 0.864043 | − | 0.503418i | \(-0.167924\pi\) |
−0.867994 | + | 0.496574i | \(0.834591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.51472 | + | 6.08767i | −0.137965 | + | 0.238962i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.0711 | + | 39.9603i | −0.902841 | + | 1.56377i | −0.0790508 | + | 0.996871i | \(0.525189\pi\) |
−0.823790 | + | 0.566895i | \(0.808144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.82843 | − | 11.8272i | −0.266809 | − | 0.462126i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.75736 | 0.302643 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.5147 | −0.838094 | −0.419047 | − | 0.907964i | \(-0.637636\pi\) | ||||
−0.419047 | + | 0.907964i | \(0.637636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.46447 | − | 4.26858i | −0.0958566 | − | 0.166029i | 0.814109 | − | 0.580712i | \(-0.197226\pi\) |
−0.909966 | + | 0.414683i | \(0.863892\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.7279 | − | 27.2416i | 0.610822 | − | 1.05797i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.82843 | + | 11.8272i | −0.264398 | + | 0.457950i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.82843 | + | 11.8272i | 0.264002 | + | 0.457265i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.17157 | −0.354065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.3137 | −0.898677 | −0.449339 | − | 0.893361i | \(-0.648340\pi\) | ||||
−0.449339 | + | 0.893361i | \(0.648340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.32843 | − | 5.76500i | −0.128111 | − | 0.221895i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.8492 | + | 23.9876i | −0.532270 | + | 0.921918i | 0.467021 | + | 0.884246i | \(0.345327\pi\) |
−0.999290 | + | 0.0376716i | \(0.988006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.58579 | + | 4.47871i | −0.0990876 | + | 0.171625i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.899495 | − | 1.55797i | −0.0344182 | − | 0.0596141i | 0.848303 | − | 0.529511i | \(-0.177624\pi\) |
−0.882721 | + | 0.469897i | \(0.844291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.3137 | −1.19644 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.4142 | −0.969613 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.24264 | − | 7.34847i | −0.161632 | − | 0.279954i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.34315 | − | 7.52255i | 0.165221 | − | 0.286171i | −0.771513 | − | 0.636214i | \(-0.780500\pi\) |
0.936734 | + | 0.350043i | \(0.113833\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.7990 | + | 62.0057i | −1.35793 | + | 2.35201i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.9706 | − | 65.7669i | −1.43824 | − | 2.49110i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.8284 | −0.560863 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.14214 | −0.231985 | −0.115993 | − | 0.993250i | \(-0.537005\pi\) | ||||
−0.115993 | + | 0.993250i | \(0.537005\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.65685 | − | 9.79796i | −0.213352 | − | 0.369537i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.65685 | + | 13.2621i | −0.288374 | + | 0.499478i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.31371 | + | 5.73951i | −0.124449 | + | 0.215552i | −0.921517 | − | 0.388337i | \(-0.873050\pi\) |
0.797068 | + | 0.603889i | \(0.206383\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.82843 | + | 11.8272i | 0.256086 | + | 0.443554i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.6569 | 0.511453 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.41421 | − | 11.1097i | −0.239543 | − | 0.414901i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.31371 | + | 5.73951i | −0.123580 | + | 0.214048i | −0.921177 | − | 0.389143i | \(-0.872771\pi\) |
0.797597 | + | 0.603191i | \(0.206104\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.94975 | + | 12.0373i | −0.258464 | + | 0.447673i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.41421 | − | 16.3059i | −0.349635 | − | 0.605586i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.85786 | 0.365608 | 0.182804 | − | 0.983149i | \(-0.441483\pi\) | ||||
0.182804 | + | 0.983149i | \(0.441483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.9411 | − | 72.6442i | −1.55125 | − | 2.68684i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.02082 | − | 6.96426i | 0.148512 | − | 0.257231i | −0.782166 | − | 0.623071i | \(-0.785885\pi\) |
0.930678 | + | 0.365840i | \(0.119218\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.68629 | + | 8.11689i | −0.172622 | + | 0.298990i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.4853 | + | 28.5533i | 0.606421 | + | 1.05035i | 0.991825 | + | 0.127604i | \(0.0407286\pi\) |
−0.385404 | + | 0.922748i | \(0.625938\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.9706 | 1.06426 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.82843 | 0.177138 | 0.0885689 | − | 0.996070i | \(-0.471771\pi\) | ||||
0.0885689 | + | 0.996070i | \(0.471771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.24264 | − | 3.88437i | −0.0821640 | − | 0.142312i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.00000 | + | 3.46410i | −0.0731762 | + | 0.126745i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.1421 | − | 17.5667i | 0.370092 | − | 0.641018i | −0.619488 | − | 0.785006i | \(-0.712660\pi\) |
0.989579 | + | 0.143989i | \(0.0459929\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.07107 | − | 5.31925i | −0.111916 | − | 0.193844i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.9706 | 1.19992 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.9411 | 1.52438 | 0.762188 | − | 0.647356i | \(-0.224125\pi\) | ||||
0.762188 | + | 0.647356i | \(0.224125\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.00000 | + | 3.46410i | 0.0725954 | + | 0.125739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9497 | − | 27.6258i | 0.578178 | − | 1.00143i | −0.417510 | − | 0.908672i | \(-0.637097\pi\) |
0.995688 | − | 0.0927614i | \(-0.0295694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.6569 | + | 21.9223i | −0.457610 | + | 0.792603i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.0000 | − | 31.1769i | −0.649942 | − | 1.12573i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.8701 | 1.25745 | 0.628723 | − | 0.777629i | \(-0.283578\pi\) | ||||
0.628723 | + | 0.777629i | \(0.283578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.41421 | −0.122960 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.6777 | − | 28.8866i | −0.599854 | − | 1.03898i | −0.992842 | − | 0.119434i | \(-0.961892\pi\) |
0.392988 | − | 0.919544i | \(-0.371441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.41421 | + | 16.3059i | −0.338169 | + | 0.585725i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.9706 | − | 60.5708i | 1.25295 | − | 2.17017i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.34315 | + | 7.52255i | 0.155410 | + | 0.269178i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.82843 | 0.101080 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.828427 | 0.0295678 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.65685 | + | 13.2621i | 0.272937 | + | 0.472741i | 0.969613 | − | 0.244645i | \(-0.0786715\pi\) |
−0.696675 | + | 0.717387i | \(0.745338\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.0711 | + | 17.4436i | −0.358540 | + | 0.621009i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.4853 | − | 40.6777i | 0.833987 | − | 1.44451i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.41421 | + | 5.91359i | 0.121090 | + | 0.209733i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.4142 | −1.39612 | −0.698062 | − | 0.716038i | \(-0.745954\pi\) | ||||
−0.698062 | + | 0.716038i | \(0.745954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.2548 | 1.17647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.87868 | − | 4.98602i | −0.101713 | − | 0.176172i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.21320 | − | 5.56543i | 0.113391 | − | 0.196400i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0502525 | − | 0.0870399i | 0.00176897 | − | 0.00306395i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.31371 | + | 4.00746i | 0.0813457 | + | 0.140895i | 0.903828 | − | 0.427896i | \(-0.140745\pi\) |
−0.822483 | + | 0.568790i | \(0.807412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.6569 | −0.900934 | −0.450467 | − | 0.892793i | \(-0.648743\pi\) | ||||
−0.450467 | + | 0.892793i | \(0.648743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.14214 | −0.215414 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.65685 | + | 16.7262i | 0.338265 | + | 0.585892i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.6274 | − | 66.9046i | 1.35140 | − | 2.34070i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.34315 | − | 9.25460i | 0.186477 | − | 0.322988i | −0.757596 | − | 0.652724i | \(-0.773626\pi\) |
0.944073 | + | 0.329736i | \(0.106960\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4853 | − | 21.6251i | −0.435210 | − | 0.753805i | 0.562103 | − | 0.827067i | \(-0.309992\pi\) |
−0.997313 | + | 0.0732621i | \(0.976659\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.51472 | −0.191998 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.1421 | −1.39588 | −0.697939 | − | 0.716157i | \(-0.745900\pi\) | ||||
−0.697939 | + | 0.716157i | \(0.745900\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.1924 | − | 29.7781i | −0.597116 | − | 1.03424i | −0.993244 | − | 0.116041i | \(-0.962980\pi\) |
0.396128 | − | 0.918195i | \(-0.370354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.3137 | − | 24.7921i | 0.496537 | − | 0.860027i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.3137 | + | 43.8446i | −0.876017 | + | 1.51731i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.41421 | − | 2.44949i | −0.0488824 | − | 0.0846668i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.7990 | −0.821632 | −0.410816 | − | 0.911718i | \(-0.634756\pi\) | ||||
−0.410816 | + | 0.911718i | \(0.634756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.585786 | − | 1.01461i | −0.0201756 | − | 0.0349451i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.53553 | + | 14.7840i | −0.293631 | + | 0.508584i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0711 | + | 22.6398i | −0.448598 | + | 0.776994i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | + | 6.92820i | 0.137118 | + | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.92893 | 0.168763 | 0.0843817 | − | 0.996434i | \(-0.473108\pi\) | ||||
0.0843817 | + | 0.996434i | \(0.473108\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.3137 | −0.797312 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.60660 | + | 9.71092i | 0.191518 | + | 0.331719i | 0.945753 | − | 0.324885i | \(-0.105326\pi\) |
−0.754236 | + | 0.656604i | \(0.771992\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.27208 | − | 2.20330i | 0.0434027 | − | 0.0751757i | −0.843508 | − | 0.537117i | \(-0.819513\pi\) |
0.886911 | + | 0.461941i | \(0.152847\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.0416 | − | 46.8375i | 0.920508 | − | 1.59437i | 0.121877 | − | 0.992545i | \(-0.461109\pi\) |
0.798631 | − | 0.601821i | \(-0.205558\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.3137 | + | 49.0408i | 0.962695 | + | 1.66744i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.9706 | 1.28955 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3137 | 0.383791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | − | 41.5692i | −0.813209 | − | 1.40852i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.121320 | − | 0.210133i | 0.00410607 | − | 0.00711192i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.1421 | − | 24.4949i | 0.477546 | − | 0.827134i | −0.522123 | − | 0.852870i | \(-0.674860\pi\) |
0.999669 | + | 0.0257364i | \(0.00819306\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.878680 | + | 1.52192i | 0.0296371 | + | 0.0513330i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0416 | 1.01213 | 0.506064 | − | 0.862496i | \(-0.331100\pi\) | ||||
0.506064 | + | 0.862496i | \(0.331100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3431 | 0.348075 | 0.174037 | − | 0.984739i | \(-0.444319\pi\) | ||||
0.174037 | + | 0.984739i | \(0.444319\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.4853 | + | 25.0892i | 0.486917 | + | 0.843366i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.8995 | + | 34.4669i | −0.668160 | + | 1.15729i | 0.310259 | + | 0.950652i | \(0.399584\pi\) |
−0.978418 | + | 0.206634i | \(0.933749\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.414214 | − | 0.717439i | 0.0138767 | − | 0.0240351i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.3137 | + | 26.5241i | 0.512454 | + | 0.887596i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.1421 | 0.740130 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.4853 | −0.683984 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.00000 | − | 6.92820i | −0.133407 | − | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.41421 | − | 12.8418i | 0.247003 | − | 0.427822i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.0711 | − | 20.9077i | 0.401256 | − | 0.694996i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.8284 | + | 46.4682i | 0.890823 | + | 1.54295i | 0.838890 | + | 0.544301i | \(0.183205\pi\) |
0.0519331 | + | 0.998651i | \(0.483462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.7279 | −0.355823 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.48528 | −0.214867 | −0.107433 | − | 0.994212i | \(-0.534263\pi\) | ||||
−0.107433 | + | 0.994212i | \(0.534263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.65685 | + | 2.86976i | 0.0548339 | + | 0.0949751i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.8995 | + | 32.7349i | −0.624798 | + | 1.08218i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.6569 | − | 27.1185i | 0.516472 | − | 0.894556i | −0.483345 | − | 0.875430i | \(-0.660578\pi\) |
0.999817 | − | 0.0191258i | \(-0.00608830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.75736 | − | 9.97204i | −0.189711 | − | 0.328590i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −44.4853 | −1.46425 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0294 | −0.362646 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.07107 | + | 12.2474i | 0.232244 | + | 0.402259i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.94975 | − | 13.7694i | 0.260823 | − | 0.451758i | −0.705638 | − | 0.708572i | \(-0.749340\pi\) |
0.966461 | + | 0.256814i | \(0.0826728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.8995 | − | 20.6105i | 0.389572 | − | 0.674758i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.4853 | + | 18.1610i | 0.342905 | + | 0.593930i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.3553 | 1.67771 | 0.838853 | − | 0.544358i | \(-0.183227\pi\) | ||||
0.838853 | + | 0.544358i | \(0.183227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.7279 | 0.937500 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.36396 | + | 12.7548i | 0.240058 | + | 0.415793i | 0.960731 | − | 0.277483i | \(-0.0895001\pi\) |
−0.720672 | + | 0.693276i | \(0.756167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.7279 | + | 42.8300i | −0.805252 | + | 1.39474i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.3848 | + | 50.8959i | −0.954877 | + | 1.65390i | −0.220227 | + | 0.975449i | \(0.570680\pi\) |
−0.734650 | + | 0.678447i | \(0.762653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.4558 | + | 28.5024i | 0.534179 | + | 0.925226i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.0000 | −0.713399 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.7279 | + | 35.9018i | 0.670740 | + | 1.16176i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.17157 | − | 2.02922i | 0.0378716 | − | 0.0655955i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.5000 | − | 19.9186i | 0.370968 | − | 0.642535i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.41421 | + | 11.1097i | 0.206695 | + | 0.358006i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.82843 | 0.219815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.3137 | 1.00698 | 0.503490 | − | 0.864001i | \(-0.332049\pi\) | ||||
0.503490 | + | 0.864001i | \(0.332049\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.3137 | + | 43.8446i | 0.813193 | + | 1.40849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0000 | + | 17.3205i | −0.320915 | + | 0.555842i | −0.980677 | − | 0.195633i | \(-0.937324\pi\) |
0.659762 | + | 0.751475i | \(0.270657\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.1213 | − | 24.4588i | 0.452244 | − | 0.783310i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.89949 | + | 6.75412i | 0.124756 | + | 0.216084i | 0.921637 | − | 0.388052i | \(-0.126852\pi\) |
−0.796882 | + | 0.604136i | \(0.793519\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.76955 | −0.152436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.31371 | −0.105799 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.686292 | + | 1.18869i | 0.0218893 | + | 0.0379134i | 0.876763 | − | 0.480924i | \(-0.159699\pi\) |
−0.854873 | + | 0.518837i | \(0.826365\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.58579 | − | 7.94282i | 0.146115 | − | 0.253079i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.3137 | + | 47.3087i | −0.868525 | + | 1.50433i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.31371 | − | 16.1318i | −0.295860 | − | 0.512444i | 0.679325 | − | 0.733838i | \(-0.262273\pi\) |
−0.975185 | + | 0.221394i | \(0.928939\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.31371 | −0.232094 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.3137 | 0.612286 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.1924 | + | 47.0986i | 0.861192 | + | 1.49163i | 0.870780 | + | 0.491674i | \(0.163615\pi\) |
−0.00958804 | + | 0.999954i | \(0.503052\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.828427 | − | 1.43488i | 0.0262103 | − | 0.0453975i |
(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 | 2352.2.q.ba.961.1 | 4 | ||
4.3 | odd | 2 | 1176.2.q.n.961.1 | 4 | |||
7.2 | even | 3 | 2352.2.a.bg.1.2 | 2 | |||
7.3 | odd | 6 | 2352.2.q.bg.1537.2 | 4 | |||
7.4 | even | 3 | inner | 2352.2.q.ba.1537.1 | 4 | ||
7.5 | odd | 6 | 2352.2.a.z.1.1 | 2 | |||
7.6 | odd | 2 | 2352.2.q.bg.961.2 | 4 | |||
12.11 | even | 2 | 3528.2.s.bl.3313.2 | 4 | |||
21.2 | odd | 6 | 7056.2.a.ce.1.1 | 2 | |||
21.5 | even | 6 | 7056.2.a.cw.1.2 | 2 | |||
28.3 | even | 6 | 1176.2.q.m.361.2 | 4 | |||
28.11 | odd | 6 | 1176.2.q.n.361.1 | 4 | |||
28.19 | even | 6 | 1176.2.a.m.1.1 | yes | 2 | ||
28.23 | odd | 6 | 1176.2.a.l.1.2 | ✓ | 2 | ||
28.27 | even | 2 | 1176.2.q.m.961.2 | 4 | |||
56.5 | odd | 6 | 9408.2.a.ed.1.2 | 2 | |||
56.19 | even | 6 | 9408.2.a.dr.1.2 | 2 | |||
56.37 | even | 6 | 9408.2.a.dh.1.1 | 2 | |||
56.51 | odd | 6 | 9408.2.a.dv.1.1 | 2 | |||
84.11 | even | 6 | 3528.2.s.bl.361.2 | 4 | |||
84.23 | even | 6 | 3528.2.a.bc.1.1 | 2 | |||
84.47 | odd | 6 | 3528.2.a.bm.1.2 | 2 | |||
84.59 | odd | 6 | 3528.2.s.bc.361.1 | 4 | |||
84.83 | odd | 2 | 3528.2.s.bc.3313.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.a.l.1.2 | ✓ | 2 | 28.23 | odd | 6 | ||
1176.2.a.m.1.1 | yes | 2 | 28.19 | even | 6 | ||
1176.2.q.m.361.2 | 4 | 28.3 | even | 6 | |||
1176.2.q.m.961.2 | 4 | 28.27 | even | 2 | |||
1176.2.q.n.361.1 | 4 | 28.11 | odd | 6 | |||
1176.2.q.n.961.1 | 4 | 4.3 | odd | 2 | |||
2352.2.a.z.1.1 | 2 | 7.5 | odd | 6 | |||
2352.2.a.bg.1.2 | 2 | 7.2 | even | 3 | |||
2352.2.q.ba.961.1 | 4 | 1.1 | even | 1 | trivial | ||
2352.2.q.ba.1537.1 | 4 | 7.4 | even | 3 | inner | ||
2352.2.q.bg.961.2 | 4 | 7.6 | odd | 2 | |||
2352.2.q.bg.1537.2 | 4 | 7.3 | odd | 6 | |||
3528.2.a.bc.1.1 | 2 | 84.23 | even | 6 | |||
3528.2.a.bm.1.2 | 2 | 84.47 | odd | 6 | |||
3528.2.s.bc.361.1 | 4 | 84.59 | odd | 6 | |||
3528.2.s.bc.3313.1 | 4 | 84.83 | odd | 2 | |||
3528.2.s.bl.361.2 | 4 | 84.11 | even | 6 | |||
3528.2.s.bl.3313.2 | 4 | 12.11 | even | 2 | |||
7056.2.a.ce.1.1 | 2 | 21.2 | odd | 6 | |||
7056.2.a.cw.1.2 | 2 | 21.5 | even | 6 | |||
9408.2.a.dh.1.1 | 2 | 56.37 | even | 6 | |||
9408.2.a.dr.1.2 | 2 | 56.19 | even | 6 | |||
9408.2.a.dv.1.1 | 2 | 56.51 | odd | 6 | |||
9408.2.a.ed.1.2 | 2 | 56.5 | odd | 6 |