Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.3.d.b.163.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(5\) | 4.00000 | 0.800000 | 0.400000 | − | 0.916515i | \(-0.369010\pi\) | ||||
0.400000 | + | 0.916515i | \(0.369010\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410i | 0.494872i | 0.968904 | + | 0.247436i | \(0.0795879\pi\) | ||||
−0.968904 | + | 0.247436i | \(0.920412\pi\) | |||||||
\(8\) | 8.00000 | 1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.00000 | − | 6.92820i | −0.400000 | − | 0.692820i | ||||
\(11\) | 12.1244i | 1.10221i | 0.834435 | + | 0.551107i | \(0.185794\pi\) | ||||
−0.834435 | + | 0.551107i | \(0.814206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.0000 | −1.69231 | −0.846154 | − | 0.532939i | \(-0.821088\pi\) | ||||
−0.846154 | + | 0.532939i | \(0.821088\pi\) | |||||||
\(14\) | 6.00000 | − | 3.46410i | 0.428571 | − | 0.247436i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(17\) | −11.0000 | −0.647059 | −0.323529 | − | 0.946218i | \(-0.604869\pi\) | ||||
−0.323529 | + | 0.946218i | \(0.604869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.5885i | 0.820445i | 0.911985 | + | 0.410223i | \(0.134549\pi\) | ||||
−0.911985 | + | 0.410223i | \(0.865451\pi\) | |||||||
\(20\) | −8.00000 | + | 13.8564i | −0.400000 | + | 0.692820i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 21.0000 | − | 12.1244i | 0.954545 | − | 0.551107i | ||||
\(23\) | 24.2487i | 1.05429i | 0.849775 | + | 0.527146i | \(0.176738\pi\) | ||||
−0.849775 | + | 0.527146i | \(0.823262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.00000 | −0.360000 | ||||||||
\(26\) | 22.0000 | + | 38.1051i | 0.846154 | + | 1.46558i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12.0000 | − | 6.92820i | −0.428571 | − | 0.247436i | ||||
\(29\) | 34.0000 | 1.17241 | 0.586207 | − | 0.810161i | \(-0.300621\pi\) | ||||
0.586207 | + | 0.810161i | \(0.300621\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820i | 0.223490i | 0.993737 | + | 0.111745i | \(0.0356441\pi\) | ||||
−0.993737 | + | 0.111745i | \(0.964356\pi\) | |||||||
\(32\) | −16.0000 | + | 27.7128i | −0.500000 | + | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.0000 | + | 19.0526i | 0.323529 | + | 0.560369i | ||||
\(35\) | 13.8564i | 0.395897i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16.0000 | −0.432432 | −0.216216 | − | 0.976346i | \(-0.569372\pi\) | ||||
−0.216216 | + | 0.976346i | \(0.569372\pi\) | |||||||
\(38\) | 27.0000 | − | 15.5885i | 0.710526 | − | 0.410223i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 32.0000 | 0.800000 | ||||||||
\(41\) | 13.0000 | 0.317073 | 0.158537 | − | 0.987353i | \(-0.449322\pi\) | ||||
0.158537 | + | 0.987353i | \(0.449322\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.2295i | 1.16813i | 0.811708 | + | 0.584064i | \(0.198538\pi\) | ||||
−0.811708 | + | 0.584064i | \(0.801462\pi\) | |||||||
\(44\) | −42.0000 | − | 24.2487i | −0.954545 | − | 0.551107i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 42.0000 | − | 24.2487i | 0.913043 | − | 0.527146i | ||||
\(47\) | − | 3.46410i | − | 0.0737043i | −0.999321 | − | 0.0368521i | \(-0.988267\pi\) | ||
0.999321 | − | 0.0368521i | \(-0.0117331\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 37.0000 | 0.755102 | ||||||||
\(50\) | 9.00000 | + | 15.5885i | 0.180000 | + | 0.311769i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 44.0000 | − | 76.2102i | 0.846154 | − | 1.46558i | ||||
\(53\) | 52.0000 | 0.981132 | 0.490566 | − | 0.871404i | \(-0.336790\pi\) | ||||
0.490566 | + | 0.871404i | \(0.336790\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 48.4974i | 0.881771i | ||||||||
\(56\) | 27.7128i | 0.494872i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −34.0000 | − | 58.8897i | −0.586207 | − | 1.01534i | ||||
\(59\) | − | 53.6936i | − | 0.910061i | −0.890476 | − | 0.455030i | \(-0.849628\pi\) | ||
0.890476 | − | 0.455030i | \(-0.150372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −16.0000 | −0.262295 | −0.131148 | − | 0.991363i | \(-0.541866\pi\) | ||||
−0.131148 | + | 0.991363i | \(0.541866\pi\) | |||||||
\(62\) | 12.0000 | − | 6.92820i | 0.193548 | − | 0.111745i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | −88.0000 | −1.35385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 116.047i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 22.0000 | − | 38.1051i | 0.323529 | − | 0.560369i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 24.0000 | − | 13.8564i | 0.342857 | − | 0.197949i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.0000 | −0.342466 | −0.171233 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171233 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(74\) | 16.0000 | + | 27.7128i | 0.216216 | + | 0.374497i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −54.0000 | − | 31.1769i | −0.710526 | − | 0.410223i | ||||
\(77\) | −42.0000 | −0.545455 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 27.7128i | − | 0.350795i | −0.984498 | − | 0.175398i | \(-0.943879\pi\) | ||
0.984498 | − | 0.175398i | \(-0.0561211\pi\) | |||||||
\(80\) | −32.0000 | − | 55.4256i | −0.400000 | − | 0.692820i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.0000 | − | 22.5167i | −0.158537 | − | 0.274593i | ||||
\(83\) | − | 34.6410i | − | 0.417362i | −0.977984 | − | 0.208681i | \(-0.933083\pi\) | ||
0.977984 | − | 0.208681i | \(-0.0669170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44.0000 | −0.517647 | ||||||||
\(86\) | 87.0000 | − | 50.2295i | 1.01163 | − | 0.584064i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 96.9948i | 1.10221i | ||||||||
\(89\) | −2.00000 | −0.0224719 | −0.0112360 | − | 0.999937i | \(-0.503577\pi\) | ||||
−0.0112360 | + | 0.999937i | \(0.503577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 76.2102i | − | 0.837475i | ||||||
\(92\) | −84.0000 | − | 48.4974i | −0.913043 | − | 0.527146i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | + | 3.46410i | −0.0638298 | + | 0.0368521i | ||||
\(95\) | 62.3538i | 0.656356i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −43.0000 | −0.443299 | −0.221649 | − | 0.975126i | \(-0.571144\pi\) | ||||
−0.221649 | + | 0.975126i | \(0.571144\pi\) | |||||||
\(98\) | −37.0000 | − | 64.0859i | −0.377551 | − | 0.653938i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 18.0000 | − | 31.1769i | 0.180000 | − | 0.311769i | ||||
\(101\) | −20.0000 | −0.198020 | −0.0990099 | − | 0.995086i | \(-0.531568\pi\) | ||||
−0.0990099 | + | 0.995086i | \(0.531568\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 24.2487i | − | 0.235424i | −0.993048 | − | 0.117712i | \(-0.962444\pi\) | ||
0.993048 | − | 0.117712i | \(-0.0375560\pi\) | |||||||
\(104\) | −176.000 | −1.69231 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −52.0000 | − | 90.0666i | −0.490566 | − | 0.849685i | ||||
\(107\) | 15.5885i | 0.145687i | 0.997343 | + | 0.0728433i | \(0.0232073\pi\) | ||||
−0.997343 | + | 0.0728433i | \(0.976793\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −88.0000 | −0.807339 | −0.403670 | − | 0.914905i | \(-0.632266\pi\) | ||||
−0.403670 | + | 0.914905i | \(0.632266\pi\) | |||||||
\(110\) | 84.0000 | − | 48.4974i | 0.763636 | − | 0.440886i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 48.0000 | − | 27.7128i | 0.428571 | − | 0.247436i | ||||
\(113\) | −50.0000 | −0.442478 | −0.221239 | − | 0.975220i | \(-0.571010\pi\) | ||||
−0.221239 | + | 0.975220i | \(0.571010\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 96.9948i | 0.843433i | ||||||||
\(116\) | −68.0000 | + | 117.779i | −0.586207 | + | 1.01534i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −93.0000 | + | 53.6936i | −0.788136 | + | 0.455030i | ||||
\(119\) | − | 38.1051i | − | 0.320211i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26.0000 | −0.214876 | ||||||||
\(122\) | 16.0000 | + | 27.7128i | 0.131148 | + | 0.227154i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −24.0000 | − | 13.8564i | −0.193548 | − | 0.111745i | ||||
\(125\) | −136.000 | −1.08800 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 218.238i | 1.71841i | 0.511629 | + | 0.859206i | \(0.329042\pi\) | ||||
−0.511629 | + | 0.859206i | \(0.670958\pi\) | |||||||
\(128\) | −64.0000 | − | 110.851i | −0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 88.0000 | + | 152.420i | 0.676923 | + | 1.17247i | ||||
\(131\) | − | 193.990i | − | 1.48084i | −0.672146 | − | 0.740419i | \(-0.734627\pi\) | ||
0.672146 | − | 0.740419i | \(-0.265373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −54.0000 | −0.406015 | ||||||||
\(134\) | 201.000 | − | 116.047i | 1.50000 | − | 0.866025i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −88.0000 | −0.647059 | ||||||||
\(137\) | 169.000 | 1.23358 | 0.616788 | − | 0.787129i | \(-0.288433\pi\) | ||||
0.616788 | + | 0.787129i | \(0.288433\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 195.722i | − | 1.40807i | −0.710165 | − | 0.704035i | \(-0.751380\pi\) | ||
0.710165 | − | 0.704035i | \(-0.248620\pi\) | |||||||
\(140\) | −48.0000 | − | 27.7128i | −0.342857 | − | 0.197949i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 266.736i | − | 1.86529i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 136.000 | 0.937931 | ||||||||
\(146\) | 25.0000 | + | 43.3013i | 0.171233 | + | 0.296584i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32.0000 | − | 55.4256i | 0.216216 | − | 0.374497i | ||||
\(149\) | 130.000 | 0.872483 | 0.436242 | − | 0.899830i | \(-0.356309\pi\) | ||||
0.436242 | + | 0.899830i | \(0.356309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 121.244i | − | 0.802937i | −0.915873 | − | 0.401469i | \(-0.868500\pi\) | ||
0.915873 | − | 0.401469i | \(-0.131500\pi\) | |||||||
\(152\) | 124.708i | 0.820445i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 42.0000 | + | 72.7461i | 0.272727 | + | 0.472377i | ||||
\(155\) | 27.7128i | 0.178792i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.00000 | −0.0254777 | −0.0127389 | − | 0.999919i | \(-0.504055\pi\) | ||||
−0.0127389 | + | 0.999919i | \(0.504055\pi\) | |||||||
\(158\) | −48.0000 | + | 27.7128i | −0.303797 | + | 0.175398i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −64.0000 | + | 110.851i | −0.400000 | + | 0.692820i | ||||
\(161\) | −84.0000 | −0.521739 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 311.769i | − | 1.91269i | −0.292233 | − | 0.956347i | \(-0.594398\pi\) | ||
0.292233 | − | 0.956347i | \(-0.405602\pi\) | |||||||
\(164\) | −26.0000 | + | 45.0333i | −0.158537 | + | 0.274593i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −60.0000 | + | 34.6410i | −0.361446 | + | 0.208681i | ||||
\(167\) | 180.133i | 1.07864i | 0.842100 | + | 0.539321i | \(0.181319\pi\) | ||||
−0.842100 | + | 0.539321i | \(0.818681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 315.000 | 1.86391 | ||||||||
\(170\) | 44.0000 | + | 76.2102i | 0.258824 | + | 0.448296i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −174.000 | − | 100.459i | −1.01163 | − | 0.584064i | ||||
\(173\) | −2.00000 | −0.0115607 | −0.00578035 | − | 0.999983i | \(-0.501840\pi\) | ||||
−0.00578035 | + | 0.999983i | \(0.501840\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 31.1769i | − | 0.178154i | ||||||
\(176\) | 168.000 | − | 96.9948i | 0.954545 | − | 0.551107i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.00000 | + | 3.46410i | 0.0112360 | + | 0.0194612i | ||||
\(179\) | 187.061i | 1.04504i | 0.852628 | + | 0.522518i | \(0.175007\pi\) | ||||
−0.852628 | + | 0.522518i | \(0.824993\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 254.000 | 1.40331 | 0.701657 | − | 0.712514i | \(-0.252444\pi\) | ||||
0.701657 | + | 0.712514i | \(0.252444\pi\) | |||||||
\(182\) | −132.000 | + | 76.2102i | −0.725275 | + | 0.418738i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 193.990i | 1.05429i | ||||||||
\(185\) | −64.0000 | −0.345946 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 133.368i | − | 0.713197i | ||||||
\(188\) | 12.0000 | + | 6.92820i | 0.0638298 | + | 0.0368521i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 108.000 | − | 62.3538i | 0.568421 | − | 0.328178i | ||||
\(191\) | − | 3.46410i | − | 0.0181367i | −0.999959 | − | 0.00906833i | \(-0.997113\pi\) | ||
0.999959 | − | 0.00906833i | \(-0.00288658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −67.0000 | −0.347150 | −0.173575 | − | 0.984821i | \(-0.555532\pi\) | ||||
−0.173575 | + | 0.984821i | \(0.555532\pi\) | |||||||
\(194\) | 43.0000 | + | 74.4782i | 0.221649 | + | 0.383908i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −74.0000 | + | 128.172i | −0.377551 | + | 0.653938i | ||||
\(197\) | 268.000 | 1.36041 | 0.680203 | − | 0.733024i | \(-0.261892\pi\) | ||||
0.680203 | + | 0.733024i | \(0.261892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 31.1769i | − | 0.156668i | −0.996927 | − | 0.0783340i | \(-0.975040\pi\) | ||
0.996927 | − | 0.0783340i | \(-0.0249600\pi\) | |||||||
\(200\) | −72.0000 | −0.360000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.0000 | + | 34.6410i | 0.0990099 | + | 0.171490i | ||||
\(203\) | 117.779i | 0.580194i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 52.0000 | 0.253659 | ||||||||
\(206\) | −42.0000 | + | 24.2487i | −0.203883 | + | 0.117712i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 176.000 | + | 304.841i | 0.846154 | + | 1.46558i | ||||
\(209\) | −189.000 | −0.904306 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 131.636i | 0.623867i | 0.950104 | + | 0.311933i | \(0.100977\pi\) | ||||
−0.950104 | + | 0.311933i | \(0.899023\pi\) | |||||||
\(212\) | −104.000 | + | 180.133i | −0.490566 | + | 0.849685i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 27.0000 | − | 15.5885i | 0.126168 | − | 0.0728433i | ||||
\(215\) | 200.918i | 0.934502i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.0000 | −0.110599 | ||||||||
\(218\) | 88.0000 | + | 152.420i | 0.403670 | + | 0.699176i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −168.000 | − | 96.9948i | −0.763636 | − | 0.440886i | ||||
\(221\) | 242.000 | 1.09502 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 58.8897i | − | 0.264079i | −0.991244 | − | 0.132040i | \(-0.957847\pi\) | ||
0.991244 | − | 0.132040i | \(-0.0421527\pi\) | |||||||
\(224\) | −96.0000 | − | 55.4256i | −0.428571 | − | 0.247436i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 50.0000 | + | 86.6025i | 0.221239 | + | 0.383197i | ||||
\(227\) | 448.601i | 1.97622i | 0.153760 | + | 0.988108i | \(0.450862\pi\) | ||||
−0.153760 | + | 0.988108i | \(0.549138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 410.000 | 1.79039 | 0.895197 | − | 0.445672i | \(-0.147035\pi\) | ||||
0.895197 | + | 0.445672i | \(0.147035\pi\) | |||||||
\(230\) | 168.000 | − | 96.9948i | 0.730435 | − | 0.421717i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 272.000 | 1.17241 | ||||||||
\(233\) | −65.0000 | −0.278970 | −0.139485 | − | 0.990224i | \(-0.544545\pi\) | ||||
−0.139485 | + | 0.990224i | \(0.544545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 13.8564i | − | 0.0589634i | ||||||
\(236\) | 186.000 | + | 107.387i | 0.788136 | + | 0.455030i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −66.0000 | + | 38.1051i | −0.277311 | + | 0.160106i | ||||
\(239\) | − | 38.1051i | − | 0.159436i | −0.996817 | − | 0.0797178i | \(-0.974598\pi\) | ||
0.996817 | − | 0.0797178i | \(-0.0254019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −223.000 | −0.925311 | −0.462656 | − | 0.886538i | \(-0.653103\pi\) | ||||
−0.462656 | + | 0.886538i | \(0.653103\pi\) | |||||||
\(242\) | 26.0000 | + | 45.0333i | 0.107438 | + | 0.186088i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.0000 | − | 55.4256i | 0.131148 | − | 0.227154i | ||||
\(245\) | 148.000 | 0.604082 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 342.946i | − | 1.38845i | ||||||
\(248\) | 55.4256i | 0.223490i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 136.000 | + | 235.559i | 0.544000 | + | 0.942236i | ||||
\(251\) | 109.119i | 0.434738i | 0.976090 | + | 0.217369i | \(0.0697475\pi\) | ||||
−0.976090 | + | 0.217369i | \(0.930253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −294.000 | −1.16206 | ||||||||
\(254\) | 378.000 | − | 218.238i | 1.48819 | − | 0.859206i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.500000 | + | 0.866025i | ||||
\(257\) | −437.000 | −1.70039 | −0.850195 | − | 0.526469i | \(-0.823516\pi\) | ||||
−0.850195 | + | 0.526469i | \(0.823516\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 55.4256i | − | 0.213999i | ||||||
\(260\) | 176.000 | − | 304.841i | 0.676923 | − | 1.17247i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −336.000 | + | 193.990i | −1.28244 | + | 0.740419i | ||||
\(263\) | − | 315.233i | − | 1.19861i | −0.800522 | − | 0.599303i | \(-0.795445\pi\) | ||
0.800522 | − | 0.599303i | \(-0.204555\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 208.000 | 0.784906 | ||||||||
\(266\) | 54.0000 | + | 93.5307i | 0.203008 | + | 0.351619i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −402.000 | − | 232.095i | −1.50000 | − | 0.866025i | ||||
\(269\) | 304.000 | 1.13011 | 0.565056 | − | 0.825053i | \(-0.308855\pi\) | ||||
0.565056 | + | 0.825053i | \(0.308855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 311.769i | − | 1.15044i | −0.817999 | − | 0.575220i | \(-0.804917\pi\) | ||
0.817999 | − | 0.575220i | \(-0.195083\pi\) | |||||||
\(272\) | 88.0000 | + | 152.420i | 0.323529 | + | 0.560369i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −169.000 | − | 292.717i | −0.616788 | − | 1.06831i | ||||
\(275\) | − | 109.119i | − | 0.396797i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −34.0000 | −0.122744 | −0.0613718 | − | 0.998115i | \(-0.519548\pi\) | ||||
−0.0613718 | + | 0.998115i | \(0.519548\pi\) | |||||||
\(278\) | −339.000 | + | 195.722i | −1.21942 | + | 0.704035i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 110.851i | 0.395897i | ||||||||
\(281\) | −218.000 | −0.775801 | −0.387900 | − | 0.921701i | \(-0.626800\pi\) | ||||
−0.387900 | + | 0.921701i | \(0.626800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.92820i | 0.0244813i | 0.999925 | + | 0.0122406i | \(0.00389641\pi\) | ||||
−0.999925 | + | 0.0122406i | \(0.996104\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −462.000 | + | 266.736i | −1.61538 | + | 0.932643i | ||||
\(287\) | 45.0333i | 0.156911i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −168.000 | −0.581315 | ||||||||
\(290\) | −136.000 | − | 235.559i | −0.468966 | − | 0.812272i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 50.0000 | − | 86.6025i | 0.171233 | − | 0.296584i | ||||
\(293\) | 202.000 | 0.689420 | 0.344710 | − | 0.938709i | \(-0.387977\pi\) | ||||
0.344710 | + | 0.938709i | \(0.387977\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 214.774i | − | 0.728048i | ||||||
\(296\) | −128.000 | −0.432432 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −130.000 | − | 225.167i | −0.436242 | − | 0.755593i | ||||
\(299\) | − | 533.472i | − | 1.78419i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −174.000 | −0.578073 | ||||||||
\(302\) | −210.000 | + | 121.244i | −0.695364 | + | 0.401469i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 216.000 | − | 124.708i | 0.710526 | − | 0.410223i | ||||
\(305\) | −64.0000 | −0.209836 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 109.119i | 0.355437i | 0.984081 | + | 0.177719i | \(0.0568717\pi\) | ||||
−0.984081 | + | 0.177719i | \(0.943128\pi\) | |||||||
\(308\) | 84.0000 | − | 145.492i | 0.272727 | − | 0.472377i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 48.0000 | − | 27.7128i | 0.154839 | − | 0.0893962i | ||||
\(311\) | 273.664i | 0.879949i | 0.898010 | + | 0.439974i | \(0.145012\pi\) | ||||
−0.898010 | + | 0.439974i | \(0.854988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −79.0000 | −0.252396 | −0.126198 | − | 0.992005i | \(-0.540277\pi\) | ||||
−0.126198 | + | 0.992005i | \(0.540277\pi\) | |||||||
\(314\) | 4.00000 | + | 6.92820i | 0.0127389 | + | 0.0220643i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 96.0000 | + | 55.4256i | 0.303797 | + | 0.175398i | ||||
\(317\) | 502.000 | 1.58360 | 0.791798 | − | 0.610783i | \(-0.209145\pi\) | ||||
0.791798 | + | 0.610783i | \(0.209145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 412.228i | 1.29225i | ||||||||
\(320\) | 256.000 | 0.800000 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 84.0000 | + | 145.492i | 0.260870 | + | 0.451839i | ||||
\(323\) | − | 171.473i | − | 0.530876i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 198.000 | 0.609231 | ||||||||
\(326\) | −540.000 | + | 311.769i | −1.65644 | + | 0.956347i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 104.000 | 0.317073 | ||||||||
\(329\) | 12.0000 | 0.0364742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 408.764i | 1.23494i | 0.786596 | + | 0.617468i | \(0.211842\pi\) | ||||
−0.786596 | + | 0.617468i | \(0.788158\pi\) | |||||||
\(332\) | 120.000 | + | 69.2820i | 0.361446 | + | 0.208681i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 312.000 | − | 180.133i | 0.934132 | − | 0.539321i | ||||
\(335\) | 464.190i | 1.38564i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −337.000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(338\) | −315.000 | − | 545.596i | −0.931953 | − | 1.61419i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 88.0000 | − | 152.420i | 0.258824 | − | 0.448296i | ||||
\(341\) | −84.0000 | −0.246334 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 297.913i | 0.868550i | ||||||||
\(344\) | 401.836i | 1.16813i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | + | 3.46410i | 0.00578035 | + | 0.0100119i | ||||
\(347\) | − | 271.932i | − | 0.783666i | −0.920036 | − | 0.391833i | \(-0.871841\pi\) | ||
0.920036 | − | 0.391833i | \(-0.128159\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 272.000 | 0.779370 | 0.389685 | − | 0.920948i | \(-0.372584\pi\) | ||||
0.389685 | + | 0.920948i | \(0.372584\pi\) | |||||||
\(350\) | −54.0000 | + | 31.1769i | −0.154286 | + | 0.0890769i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −336.000 | − | 193.990i | −0.954545 | − | 0.551107i | ||||
\(353\) | −461.000 | −1.30595 | −0.652975 | − | 0.757380i | \(-0.726479\pi\) | ||||
−0.652975 | + | 0.757380i | \(0.726479\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.00000 | − | 6.92820i | 0.0112360 | − | 0.0194612i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 324.000 | − | 187.061i | 0.905028 | − | 0.522518i | ||||
\(359\) | − | 530.008i | − | 1.47634i | −0.674612 | − | 0.738172i | \(-0.735689\pi\) | ||
0.674612 | − | 0.738172i | \(-0.264311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 118.000 | 0.326870 | ||||||||
\(362\) | −254.000 | − | 439.941i | −0.701657 | − | 1.21531i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 264.000 | + | 152.420i | 0.725275 | + | 0.418738i | ||||
\(365\) | −100.000 | −0.273973 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 96.9948i | 0.264291i | 0.991230 | + | 0.132146i | \(0.0421866\pi\) | ||||
−0.991230 | + | 0.132146i | \(0.957813\pi\) | |||||||
\(368\) | 336.000 | − | 193.990i | 0.913043 | − | 0.527146i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 64.0000 | + | 110.851i | 0.172973 | + | 0.299598i | ||||
\(371\) | 180.133i | 0.485534i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −346.000 | −0.927614 | −0.463807 | − | 0.885936i | \(-0.653517\pi\) | ||||
−0.463807 | + | 0.885936i | \(0.653517\pi\) | |||||||
\(374\) | −231.000 | + | 133.368i | −0.617647 | + | 0.356599i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 27.7128i | − | 0.0737043i | ||||||
\(377\) | −748.000 | −1.98408 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 327.358i | 0.863740i | 0.901936 | + | 0.431870i | \(0.142146\pi\) | ||||
−0.901936 | + | 0.431870i | \(0.857854\pi\) | |||||||
\(380\) | −216.000 | − | 124.708i | −0.568421 | − | 0.328178i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.00000 | + | 3.46410i | −0.0157068 | + | 0.00906833i | ||||
\(383\) | − | 630.466i | − | 1.64613i | −0.567950 | − | 0.823063i | \(-0.692263\pi\) | ||
0.567950 | − | 0.823063i | \(-0.307737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −168.000 | −0.436364 | ||||||||
\(386\) | 67.0000 | + | 116.047i | 0.173575 | + | 0.300641i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 86.0000 | − | 148.956i | 0.221649 | − | 0.383908i | ||||
\(389\) | −146.000 | −0.375321 | −0.187661 | − | 0.982234i | \(-0.560091\pi\) | ||||
−0.187661 | + | 0.982234i | \(0.560091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 266.736i | − | 0.682189i | ||||||
\(392\) | 296.000 | 0.755102 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −268.000 | − | 464.190i | −0.680203 | − | 1.17815i | ||||
\(395\) | − | 110.851i | − | 0.280636i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 488.000 | 1.22922 | 0.614610 | − | 0.788831i | \(-0.289314\pi\) | ||||
0.614610 | + | 0.788831i | \(0.289314\pi\) | |||||||
\(398\) | −54.0000 | + | 31.1769i | −0.135678 | + | 0.0783340i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 72.0000 | + | 124.708i | 0.180000 | + | 0.311769i | ||||
\(401\) | 445.000 | 1.10973 | 0.554863 | − | 0.831942i | \(-0.312771\pi\) | ||||
0.554863 | + | 0.831942i | \(0.312771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 152.420i | − | 0.378215i | ||||||
\(404\) | 40.0000 | − | 69.2820i | 0.0990099 | − | 0.171490i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 204.000 | − | 117.779i | 0.502463 | − | 0.290097i | ||||
\(407\) | − | 193.990i | − | 0.476633i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −67.0000 | −0.163814 | −0.0819071 | − | 0.996640i | \(-0.526101\pi\) | ||||
−0.0819071 | + | 0.996640i | \(0.526101\pi\) | |||||||
\(410\) | −52.0000 | − | 90.0666i | −0.126829 | − | 0.219675i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 84.0000 | + | 48.4974i | 0.203883 | + | 0.117712i | ||||
\(413\) | 186.000 | 0.450363 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 138.564i | − | 0.333889i | ||||||
\(416\) | 352.000 | − | 609.682i | 0.846154 | − | 1.46558i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 189.000 | + | 327.358i | 0.452153 | + | 0.783152i | ||||
\(419\) | 616.610i | 1.47162i | 0.677186 | + | 0.735812i | \(0.263199\pi\) | ||||
−0.677186 | + | 0.735812i | \(0.736801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 272.000 | 0.646081 | 0.323040 | − | 0.946385i | \(-0.395295\pi\) | ||||
0.323040 | + | 0.946385i | \(0.395295\pi\) | |||||||
\(422\) | 228.000 | − | 131.636i | 0.540284 | − | 0.311933i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 416.000 | 0.981132 | ||||||||
\(425\) | 99.0000 | 0.232941 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 55.4256i | − | 0.129802i | ||||||
\(428\) | −54.0000 | − | 31.1769i | −0.126168 | − | 0.0728433i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 348.000 | − | 200.918i | 0.809302 | − | 0.467251i | ||||
\(431\) | 405.300i | 0.940371i | 0.882568 | + | 0.470185i | \(0.155813\pi\) | ||||
−0.882568 | + | 0.470185i | \(0.844187\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −439.000 | −1.01386 | −0.506928 | − | 0.861988i | \(-0.669219\pi\) | ||||
−0.506928 | + | 0.861988i | \(0.669219\pi\) | |||||||
\(434\) | 24.0000 | + | 41.5692i | 0.0552995 | + | 0.0957816i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 176.000 | − | 304.841i | 0.403670 | − | 0.699176i | ||||
\(437\) | −378.000 | −0.864989 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 845.241i | 1.92538i | 0.270611 | + | 0.962689i | \(0.412774\pi\) | ||||
−0.270611 | + | 0.962689i | \(0.587226\pi\) | |||||||
\(440\) | 387.979i | 0.881771i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −242.000 | − | 419.156i | −0.547511 | − | 0.948317i | ||||
\(443\) | − | 330.822i | − | 0.746776i | −0.927675 | − | 0.373388i | \(-0.878196\pi\) | ||
0.927675 | − | 0.373388i | \(-0.121804\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | −0.0179775 | ||||||||
\(446\) | −102.000 | + | 58.8897i | −0.228700 | + | 0.132040i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 221.703i | 0.494872i | ||||||||
\(449\) | −47.0000 | −0.104677 | −0.0523385 | − | 0.998629i | \(-0.516667\pi\) | ||||
−0.0523385 | + | 0.998629i | \(0.516667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 157.617i | 0.349483i | ||||||||
\(452\) | 100.000 | − | 173.205i | 0.221239 | − | 0.383197i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 777.000 | − | 448.601i | 1.71145 | − | 0.988108i | ||||
\(455\) | − | 304.841i | − | 0.669980i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −331.000 | −0.724289 | −0.362144 | − | 0.932122i | \(-0.617955\pi\) | ||||
−0.362144 | + | 0.932122i | \(0.617955\pi\) | |||||||
\(458\) | −410.000 | − | 710.141i | −0.895197 | − | 1.55053i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −336.000 | − | 193.990i | −0.730435 | − | 0.421717i | ||||
\(461\) | 538.000 | 1.16703 | 0.583514 | − | 0.812103i | \(-0.301677\pi\) | ||||
0.583514 | + | 0.812103i | \(0.301677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 568.113i | 1.22703i | 0.789685 | + | 0.613513i | \(0.210244\pi\) | ||||
−0.789685 | + | 0.613513i | \(0.789756\pi\) | |||||||
\(464\) | −272.000 | − | 471.118i | −0.586207 | − | 1.01534i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 65.0000 | + | 112.583i | 0.139485 | + | 0.241595i | ||||
\(467\) | − | 639.127i | − | 1.36858i | −0.729210 | − | 0.684290i | \(-0.760112\pi\) | ||
0.729210 | − | 0.684290i | \(-0.239888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −402.000 | −0.857143 | ||||||||
\(470\) | −24.0000 | + | 13.8564i | −0.0510638 | + | 0.0294817i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 429.549i | − | 0.910061i | ||||||
\(473\) | −609.000 | −1.28753 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 140.296i | − | 0.295360i | ||||||
\(476\) | 132.000 | + | 76.2102i | 0.277311 | + | 0.160106i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −66.0000 | + | 38.1051i | −0.138075 | + | 0.0797178i | ||||
\(479\) | 121.244i | 0.253118i | 0.991959 | + | 0.126559i | \(0.0403933\pi\) | ||||
−0.991959 | + | 0.126559i | \(0.959607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 352.000 | 0.731809 | ||||||||
\(482\) | 223.000 | + | 386.247i | 0.462656 | + | 0.801343i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 52.0000 | − | 90.0666i | 0.107438 | − | 0.186088i | ||||
\(485\) | −172.000 | −0.354639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 405.300i | 0.832238i | 0.909310 | + | 0.416119i | \(0.136610\pi\) | ||||
−0.909310 | + | 0.416119i | \(0.863390\pi\) | |||||||
\(488\) | −128.000 | −0.262295 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −148.000 | − | 256.344i | −0.302041 | − | 0.523150i | ||||
\(491\) | 725.729i | 1.47806i | 0.673670 | + | 0.739032i | \(0.264717\pi\) | ||||
−0.673670 | + | 0.739032i | \(0.735283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −374.000 | −0.758621 | ||||||||
\(494\) | −594.000 | + | 342.946i | −1.20243 | + | 0.694223i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 96.0000 | − | 55.4256i | 0.193548 | − | 0.111745i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 521.347i | 1.04478i | 0.852705 | + | 0.522392i | \(0.174960\pi\) | ||||
−0.852705 | + | 0.522392i | \(0.825040\pi\) | |||||||
\(500\) | 272.000 | − | 471.118i | 0.544000 | − | 0.942236i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 189.000 | − | 109.119i | 0.376494 | − | 0.217369i | ||||
\(503\) | 872.954i | 1.73549i | 0.497006 | + | 0.867747i | \(0.334433\pi\) | ||||
−0.497006 | + | 0.867747i | \(0.665567\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −80.0000 | −0.158416 | ||||||||
\(506\) | 294.000 | + | 509.223i | 0.581028 | + | 1.00637i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −756.000 | − | 436.477i | −1.48819 | − | 0.859206i | ||||
\(509\) | 760.000 | 1.49312 | 0.746562 | − | 0.665316i | \(-0.231703\pi\) | ||||
0.746562 | + | 0.665316i | \(0.231703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 86.6025i | − | 0.169477i | ||||||
\(512\) | 512.000 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 437.000 | + | 756.906i | 0.850195 | + | 1.47258i | ||||
\(515\) | − | 96.9948i | − | 0.188340i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 42.0000 | 0.0812379 | ||||||||
\(518\) | −96.0000 | + | 55.4256i | −0.185328 | + | 0.106999i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −704.000 | −1.35385 | ||||||||
\(521\) | 745.000 | 1.42994 | 0.714971 | − | 0.699154i | \(-0.246440\pi\) | ||||
0.714971 | + | 0.699154i | \(0.246440\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 561.184i | 1.07301i | 0.843897 | + | 0.536505i | \(0.180256\pi\) | ||||
−0.843897 | + | 0.536505i | \(0.819744\pi\) | |||||||
\(524\) | 672.000 | + | 387.979i | 1.28244 | + | 0.740419i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −546.000 | + | 315.233i | −1.03802 | + | 0.599303i | ||||
\(527\) | − | 76.2102i | − | 0.144611i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −59.0000 | −0.111531 | ||||||||
\(530\) | −208.000 | − | 360.267i | −0.392453 | − | 0.679748i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 108.000 | − | 187.061i | 0.203008 | − | 0.351619i | ||||
\(533\) | −286.000 | −0.536585 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 62.3538i | 0.116549i | ||||||||
\(536\) | 928.379i | 1.73205i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −304.000 | − | 526.543i | −0.565056 | − | 0.978705i | ||||
\(539\) | 448.601i | 0.832284i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −520.000 | −0.961183 | −0.480591 | − | 0.876945i | \(-0.659578\pi\) | ||||
−0.480591 | + | 0.876945i | \(0.659578\pi\) | |||||||
\(542\) | −540.000 | + | 311.769i | −0.996310 | + | 0.575220i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 176.000 | − | 304.841i | 0.323529 | − | 0.560369i | ||||
\(545\) | −352.000 | −0.645872 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 386.247i | − | 0.706119i | −0.935601 | − | 0.353060i | \(-0.885141\pi\) | ||
0.935601 | − | 0.353060i | \(-0.114859\pi\) | |||||||
\(548\) | −338.000 | + | 585.433i | −0.616788 | + | 1.06831i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −189.000 | + | 109.119i | −0.343636 | + | 0.198399i | ||||
\(551\) | 530.008i | 0.961901i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 96.0000 | 0.173599 | ||||||||
\(554\) | 34.0000 | + | 58.8897i | 0.0613718 | + | 0.106299i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 678.000 | + | 391.443i | 1.21942 | + | 0.704035i | ||||
\(557\) | 934.000 | 1.67684 | 0.838420 | − | 0.545025i | \(-0.183480\pi\) | ||||
0.838420 | + | 0.545025i | \(0.183480\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1105.05i | − | 1.97683i | ||||||
\(560\) | 192.000 | − | 110.851i | 0.342857 | − | 0.197949i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 218.000 | + | 377.587i | 0.387900 | + | 0.671863i | ||||
\(563\) | − | 708.409i | − | 1.25827i | −0.777294 | − | 0.629137i | \(-0.783408\pi\) | ||
0.777294 | − | 0.629137i | \(-0.216592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −200.000 | −0.353982 | ||||||||
\(566\) | 12.0000 | − | 6.92820i | 0.0212014 | − | 0.0122406i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −695.000 | −1.22144 | −0.610721 | − | 0.791846i | \(-0.709120\pi\) | ||||
−0.610721 | + | 0.791846i | \(0.709120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 538.668i | − | 0.943376i | −0.881765 | − | 0.471688i | \(-0.843645\pi\) | ||
0.881765 | − | 0.471688i | \(-0.156355\pi\) | |||||||
\(572\) | 924.000 | + | 533.472i | 1.61538 | + | 0.932643i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 78.0000 | − | 45.0333i | 0.135889 | − | 0.0784553i | ||||
\(575\) | − | 218.238i | − | 0.379545i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 227.000 | 0.393414 | 0.196707 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196707 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(578\) | 168.000 | + | 290.985i | 0.290657 | + | 0.503433i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −272.000 | + | 471.118i | −0.468966 | + | 0.812272i | ||||
\(581\) | 120.000 | 0.206540 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 630.466i | 1.08142i | ||||||||
\(584\) | −200.000 | −0.342466 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −202.000 | − | 349.874i | −0.344710 | − | 0.597055i | ||||
\(587\) | − | 143.760i | − | 0.244907i | −0.992474 | − | 0.122453i | \(-0.960924\pi\) | ||
0.992474 | − | 0.122453i | \(-0.0390762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −108.000 | −0.183362 | ||||||||
\(590\) | −372.000 | + | 214.774i | −0.630508 | + | 0.364024i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 128.000 | + | 221.703i | 0.216216 | + | 0.374497i | ||||
\(593\) | −506.000 | −0.853288 | −0.426644 | − | 0.904420i | \(-0.640304\pi\) | ||||
−0.426644 | + | 0.904420i | \(0.640304\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 152.420i | − | 0.256169i | ||||||
\(596\) | −260.000 | + | 450.333i | −0.436242 | + | 0.755593i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −924.000 | + | 533.472i | −1.54515 | + | 0.892093i | ||||
\(599\) | 55.4256i | 0.0925303i | 0.998929 | + | 0.0462651i | \(0.0147319\pi\) | ||||
−0.998929 | + | 0.0462651i | \(0.985268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 335.000 | 0.557404 | 0.278702 | − | 0.960378i | \(-0.410096\pi\) | ||||
0.278702 | + | 0.960378i | \(0.410096\pi\) | |||||||
\(602\) | 174.000 | + | 301.377i | 0.289037 | + | 0.500626i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 420.000 | + | 242.487i | 0.695364 | + | 0.401469i | ||||
\(605\) | −104.000 | −0.171901 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 630.466i | 1.03866i | 0.854574 | + | 0.519330i | \(0.173818\pi\) | ||||
−0.854574 | + | 0.519330i | \(0.826182\pi\) | |||||||
\(608\) | −432.000 | − | 249.415i | −0.710526 | − | 0.410223i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 64.0000 | + | 110.851i | 0.104918 | + | 0.181723i | ||||
\(611\) | 76.2102i | 0.124730i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −340.000 | −0.554649 | −0.277325 | − | 0.960776i | \(-0.589448\pi\) | ||||
−0.277325 | + | 0.960776i | \(0.589448\pi\) | |||||||
\(614\) | 189.000 | − | 109.119i | 0.307818 | − | 0.177719i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −336.000 | −0.545455 | ||||||||
\(617\) | 391.000 | 0.633712 | 0.316856 | − | 0.948474i | \(-0.397373\pi\) | ||||
0.316856 | + | 0.948474i | \(0.397373\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 12.1244i | − | 0.0195870i | −0.999952 | − | 0.00979350i | \(-0.996883\pi\) | ||
0.999952 | − | 0.00979350i | \(-0.00311742\pi\) | |||||||
\(620\) | −96.0000 | − | 55.4256i | −0.154839 | − | 0.0893962i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 474.000 | − | 273.664i | 0.762058 | − | 0.439974i | ||||
\(623\) | − | 6.92820i | − | 0.0111207i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −319.000 | −0.510400 | ||||||||
\(626\) | 79.0000 | + | 136.832i | 0.126198 | + | 0.218581i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.00000 | − | 13.8564i | 0.0127389 | − | 0.0220643i | ||||
\(629\) | 176.000 | 0.279809 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 436.477i | − | 0.691722i | −0.938286 | − | 0.345861i | \(-0.887587\pi\) | ||
0.938286 | − | 0.345861i | \(-0.112413\pi\) | |||||||
\(632\) | − | 221.703i | − | 0.350795i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −502.000 | − | 869.490i | −0.791798 | − | 1.37143i | ||||
\(635\) | 872.954i | 1.37473i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −814.000 | −1.27786 | ||||||||
\(638\) | 714.000 | − | 412.228i | 1.11912 | − | 0.646126i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −256.000 | − | 443.405i | −0.400000 | − | 0.692820i | ||||
\(641\) | 421.000 | 0.656786 | 0.328393 | − | 0.944541i | \(-0.393493\pi\) | ||||
0.328393 | + | 0.944541i | \(0.393493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 413.960i | − | 0.643795i | −0.946775 | − | 0.321897i | \(-0.895679\pi\) | ||
0.946775 | − | 0.321897i | \(-0.104321\pi\) | |||||||
\(644\) | 168.000 | − | 290.985i | 0.260870 | − | 0.451839i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −297.000 | + | 171.473i | −0.459752 | + | 0.265438i | ||||
\(647\) | 405.300i | 0.626430i | 0.949682 | + | 0.313215i | \(0.101406\pi\) | ||||
−0.949682 | + | 0.313215i | \(0.898594\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 651.000 | 1.00308 | ||||||||
\(650\) | −198.000 | − | 342.946i | −0.304615 | − | 0.527609i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1080.00 | + | 623.538i | 1.65644 | + | 0.956347i | ||||
\(653\) | 886.000 | 1.35681 | 0.678407 | − | 0.734686i | \(-0.262670\pi\) | ||||
0.678407 | + | 0.734686i | \(0.262670\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 775.959i | − | 1.18467i | ||||||
\(656\) | −104.000 | − | 180.133i | −0.158537 | − | 0.274593i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | − | 20.7846i | −0.0182371 | − | 0.0315876i | ||||
\(659\) | 838.313i | 1.27210i | 0.771649 | + | 0.636049i | \(0.219432\pi\) | ||||
−0.771649 | + | 0.636049i | \(0.780568\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 248.000 | 0.375189 | 0.187595 | − | 0.982247i | \(-0.439931\pi\) | ||||
0.187595 | + | 0.982247i | \(0.439931\pi\) | |||||||
\(662\) | 708.000 | − | 408.764i | 1.06949 | − | 0.617468i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 277.128i | − | 0.417362i | ||||||
\(665\) | −216.000 | −0.324812 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 824.456i | 1.23607i | ||||||||
\(668\) | −624.000 | − | 360.267i | −0.934132 | − | 0.539321i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 804.000 | − | 464.190i | 1.20000 | − | 0.692820i | ||||
\(671\) | − | 193.990i | − | 0.289105i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1154.00 | 1.71471 | 0.857355 | − | 0.514725i | \(-0.172106\pi\) | ||||
0.857355 | + | 0.514725i | \(0.172106\pi\) | |||||||
\(674\) | 337.000 | + | 583.701i | 0.500000 | + | 0.866025i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −630.000 | + | 1091.19i | −0.931953 | + | 1.61419i | ||||
\(677\) | 1132.00 | 1.67208 | 0.836041 | − | 0.548666i | \(-0.184864\pi\) | ||||
0.836041 | + | 0.548666i | \(0.184864\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 148.956i | − | 0.219376i | ||||||
\(680\) | −352.000 | −0.517647 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 84.0000 | + | 145.492i | 0.123167 | + | 0.213332i | ||||
\(683\) | − | 795.011i | − | 1.16400i | −0.813189 | − | 0.582000i | \(-0.802271\pi\) | ||
0.813189 | − | 0.582000i | \(-0.197729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 676.000 | 0.986861 | ||||||||
\(686\) | 516.000 | − | 297.913i | 0.752187 | − | 0.434275i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 696.000 | − | 401.836i | 1.01163 | − | 0.584064i | ||||
\(689\) | −1144.00 | −1.66038 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 900.666i | − | 1.30342i | −0.758466 | − | 0.651712i | \(-0.774051\pi\) | ||
0.758466 | − | 0.651712i | \(-0.225949\pi\) | |||||||
\(692\) | 4.00000 | − | 6.92820i | 0.00578035 | − | 0.0100119i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −471.000 | + | 271.932i | −0.678674 | + | 0.391833i | ||||
\(695\) | − | 782.887i | − | 1.12646i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −143.000 | −0.205165 | ||||||||
\(698\) | −272.000 | − | 471.118i | −0.389685 | − | 0.674954i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 108.000 | + | 62.3538i | 0.154286 | + | 0.0890769i | ||||
\(701\) | 142.000 | 0.202568 | 0.101284 | − | 0.994858i | \(-0.467705\pi\) | ||||
0.101284 | + | 0.994858i | \(0.467705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 249.415i | − | 0.354787i | ||||||
\(704\) | 775.959i | 1.10221i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 461.000 | + | 798.475i | 0.652975 | + | 1.13099i | ||||
\(707\) | − | 69.2820i | − | 0.0979944i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 740.000 | 1.04372 | 0.521862 | − | 0.853030i | \(-0.325238\pi\) | ||||
0.521862 | + | 0.853030i | \(0.325238\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.0000 | −0.0224719 | ||||||||
\(713\) | −168.000 | −0.235624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1066.94i | − | 1.49223i | ||||||
\(716\) | −648.000 | − | 374.123i | −0.905028 | − | 0.522518i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −918.000 | + | 530.008i | −1.27855 | + | 0.738172i | ||||
\(719\) | 124.708i | 0.173446i | 0.996232 | + | 0.0867230i | \(0.0276395\pi\) | ||||
−0.996232 | + | 0.0867230i | \(0.972360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 84.0000 | 0.116505 | ||||||||
\(722\) | −118.000 | − | 204.382i | −0.163435 | − | 0.283078i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −508.000 | + | 879.882i | −0.701657 | + | 1.21531i | ||||
\(725\) | −306.000 | −0.422069 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 814.064i | 1.11976i | 0.828574 | + | 0.559879i | \(0.189152\pi\) | ||||
−0.828574 | + | 0.559879i | \(0.810848\pi\) | |||||||
\(728\) | − | 609.682i | − | 0.837475i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 100.000 | + | 173.205i | 0.136986 | + | 0.237267i | ||||
\(731\) | − | 552.524i | − | 0.755847i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 914.000 | 1.24693 | 0.623465 | − | 0.781851i | \(-0.285724\pi\) | ||||
0.623465 | + | 0.781851i | \(0.285724\pi\) | |||||||
\(734\) | 168.000 | − | 96.9948i | 0.228883 | − | 0.132146i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −672.000 | − | 387.979i | −0.913043 | − | 0.527146i | ||||
\(737\) | −1407.00 | −1.90909 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 358.535i | − | 0.485162i | −0.970131 | − | 0.242581i | \(-0.922006\pi\) | ||
0.970131 | − | 0.242581i | \(-0.0779940\pi\) | |||||||
\(740\) | 128.000 | − | 221.703i | 0.172973 | − | 0.299598i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 312.000 | − | 180.133i | 0.420485 | − | 0.242767i | ||||
\(743\) | 398.372i | 0.536166i | 0.963396 | + | 0.268083i | \(0.0863902\pi\) | ||||
−0.963396 | + | 0.268083i | \(0.913610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 520.000 | 0.697987 | ||||||||
\(746\) | 346.000 | + | 599.290i | 0.463807 | + | 0.803337i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 462.000 | + | 266.736i | 0.617647 | + | 0.356599i | ||||
\(749\) | −54.0000 | −0.0720961 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1115.44i | − | 1.48527i | −0.669694 | − | 0.742637i | \(-0.733575\pi\) | ||
0.669694 | − | 0.742637i | \(-0.266425\pi\) | |||||||
\(752\) | −48.0000 | + | 27.7128i | −0.0638298 | + | 0.0368521i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 748.000 | + | 1295.57i | 0.992042 | + | 1.71827i | ||||
\(755\) | − | 484.974i | − | 0.642350i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 758.000 | 1.00132 | 0.500661 | − | 0.865644i | \(-0.333091\pi\) | ||||
0.500661 | + | 0.865644i | \(0.333091\pi\) | |||||||
\(758\) | 567.000 | − | 327.358i | 0.748021 | − | 0.431870i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 498.831i | 0.656356i | ||||||||
\(761\) | −374.000 | −0.491459 | −0.245729 | − | 0.969338i | \(-0.579027\pi\) | ||||
−0.245729 | + | 0.969338i | \(0.579027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 304.841i | − | 0.399529i | ||||||
\(764\) | 12.0000 | + | 6.92820i | 0.0157068 | + | 0.00906833i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1092.00 | + | 630.466i | −1.42559 | + | 0.823063i | ||||
\(767\) | 1181.26i | 1.54010i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.0286086 | −0.0143043 | − | 0.999898i | \(-0.504553\pi\) | ||||
−0.0143043 | + | 0.999898i | \(0.504553\pi\) | |||||||
\(770\) | 168.000 | + | 290.985i | 0.218182 | + | 0.377902i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 134.000 | − | 232.095i | 0.173575 | − | 0.300641i | ||||
\(773\) | −1334.00 | −1.72574 | −0.862872 | − | 0.505423i | \(-0.831337\pi\) | ||||
−0.862872 | + | 0.505423i | \(0.831337\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 62.3538i | − | 0.0804566i | ||||||
\(776\) | −344.000 | −0.443299 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 146.000 | + | 252.879i | 0.187661 | + | 0.325038i | ||||
\(779\) | 202.650i | 0.260141i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −462.000 | + | 266.736i | −0.590793 | + | 0.341094i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −296.000 | − | 512.687i | −0.377551 | − | 0.653938i | ||||
\(785\) | −16.0000 | −0.0203822 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 879.882i | 1.11802i | 0.829161 | + | 0.559010i | \(0.188819\pi\) | ||||
−0.829161 | + | 0.559010i | \(0.811181\pi\) | |||||||
\(788\) | −536.000 | + | 928.379i | −0.680203 | + | 1.17815i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −192.000 | + | 110.851i | −0.243038 | + | 0.140318i | ||||
\(791\) | − | 173.205i | − | 0.218970i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 352.000 | 0.443884 | ||||||||
\(794\) | −488.000 | − | 845.241i | −0.614610 | − | 1.06454i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 108.000 | + | 62.3538i | 0.135678 | + | 0.0783340i | ||||
\(797\) | 832.000 | 1.04391 | 0.521957 | − | 0.852972i | \(-0.325202\pi\) | ||||
0.521957 | + | 0.852972i | \(0.325202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.1051i | 0.0476910i | ||||||||
\(800\) | 144.000 | − | 249.415i | 0.180000 | − | 0.311769i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −445.000 | − | 770.763i | −0.554863 | − | 0.961051i | ||||
\(803\) | − | 303.109i | − | 0.377471i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −336.000 | −0.417391 | ||||||||
\(806\) | −264.000 | + | 152.420i | −0.327543 | + | 0.189107i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −160.000 | −0.198020 | ||||||||
\(809\) | 493.000 | 0.609394 | 0.304697 | − | 0.952449i | \(-0.401445\pi\) | ||||
0.304697 | + | 0.952449i | \(0.401445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 327.358i | − | 0.403647i | −0.979422 | − | 0.201823i | \(-0.935313\pi\) | ||
0.979422 | − | 0.201823i | \(-0.0646867\pi\) | |||||||
\(812\) | −408.000 | − | 235.559i | −0.502463 | − | 0.290097i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −336.000 | + | 193.990i | −0.412776 | + | 0.238317i | ||||
\(815\) | − | 1247.08i | − | 1.53016i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −783.000 | −0.958384 | ||||||||
\(818\) | 67.0000 | + | 116.047i | 0.0819071 | + | 0.141867i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −104.000 | + | 180.133i | −0.126829 | + | 0.219675i | ||||
\(821\) | −758.000 | −0.923264 | −0.461632 | − | 0.887071i | \(-0.652736\pi\) | ||||
−0.461632 | + | 0.887071i | \(0.652736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 866.025i | − | 1.05228i | −0.850398 | − | 0.526139i | \(-0.823639\pi\) | ||
0.850398 | − | 0.526139i | \(-0.176361\pi\) | |||||||
\(824\) | − | 193.990i | − | 0.235424i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −186.000 | − | 322.161i | −0.225182 | − | 0.390026i | ||||
\(827\) | 436.477i | 0.527783i | 0.964552 | + | 0.263892i | \(0.0850061\pi\) | ||||
−0.964552 | + | 0.263892i | \(0.914994\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −718.000 | −0.866104 | −0.433052 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433052 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(830\) | −240.000 | + | 138.564i | −0.289157 | + | 0.166945i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1408.00 | −1.69231 | ||||||||
\(833\) | −407.000 | −0.488595 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 720.533i | 0.862914i | ||||||||
\(836\) | 378.000 | − | 654.715i | 0.452153 | − | 0.783152i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1068.00 | − | 616.610i | 1.27446 | − | 0.735812i | ||||
\(839\) | − | 907.595i | − | 1.08176i | −0.841101 | − | 0.540879i | \(-0.818092\pi\) | ||
0.841101 | − | 0.540879i | \(-0.181908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 315.000 | 0.374554 | ||||||||
\(842\) | −272.000 | − | 471.118i | −0.323040 | − | 0.559522i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −456.000 | − | 263.272i | −0.540284 | − | 0.311933i | ||||
\(845\) | 1260.00 | 1.49112 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 90.0666i | − | 0.106336i | ||||||
\(848\) | −416.000 | − | 720.533i | −0.490566 | − | 0.849685i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −99.0000 | − | 171.473i | −0.116471 | − | 0.201733i | ||||
\(851\) | − | 387.979i | − | 0.455910i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 146.000 | 0.171161 | 0.0855803 | − | 0.996331i | \(-0.472726\pi\) | ||||
0.0855803 | + | 0.996331i | \(0.472726\pi\) | |||||||
\(854\) | −96.0000 | + | 55.4256i | −0.112412 | + | 0.0649012i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 124.708i | 0.145687i | ||||||||
\(857\) | −146.000 | −0.170362 | −0.0851809 | − | 0.996366i | \(-0.527147\pi\) | ||||
−0.0851809 | + | 0.996366i | \(0.527147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 84.8705i | 0.0988015i | 0.998779 | + | 0.0494008i | \(0.0157312\pi\) | ||||
−0.998779 | + | 0.0494008i | \(0.984269\pi\) | |||||||
\(860\) | −696.000 | − | 401.836i | −0.809302 | − | 0.467251i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 702.000 | − | 405.300i | 0.814385 | − | 0.470185i | ||||
\(863\) | − | 1184.72i | − | 1.37280i | −0.727226 | − | 0.686398i | \(-0.759191\pi\) | ||
0.727226 | − | 0.686398i | \(-0.240809\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.00000 | −0.00924855 | ||||||||
\(866\) | 439.000 | + | 760.370i | 0.506928 | + | 0.878026i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 48.0000 | − | 83.1384i | 0.0552995 | − | 0.0957816i | ||||
\(869\) | 336.000 | 0.386651 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2553.04i | − | 2.93116i | ||||||
\(872\) | −704.000 | −0.807339 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 378.000 | + | 654.715i | 0.432494 | + | 0.749102i | ||||
\(875\) | − | 471.118i | − | 0.538420i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1480.00 | −1.68757 | −0.843786 | − | 0.536680i | \(-0.819678\pi\) | ||||
−0.843786 | + | 0.536680i | \(0.819678\pi\) | |||||||
\(878\) | 1464.00 | − | 845.241i | 1.66743 | − | 0.962689i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 672.000 | − | 387.979i | 0.763636 | − | 0.440886i | ||||
\(881\) | 142.000 | 0.161180 | 0.0805902 | − | 0.996747i | \(-0.474319\pi\) | ||||
0.0805902 | + | 0.996747i | \(0.474319\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1200.31i | − | 1.35936i | −0.733511 | − | 0.679678i | \(-0.762120\pi\) | ||
0.733511 | − | 0.679678i | \(-0.237880\pi\) | |||||||
\(884\) | −484.000 | + | 838.313i | −0.547511 | + | 0.948317i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −573.000 | + | 330.822i | −0.646727 | + | 0.373388i | ||||
\(887\) | − | 630.466i | − | 0.710785i | −0.934717 | − | 0.355393i | \(-0.884347\pi\) | ||
0.934717 | − | 0.355393i | \(-0.115653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −756.000 | −0.850394 | ||||||||
\(890\) | 8.00000 | + | 13.8564i | 0.00898876 | + | 0.0155690i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 204.000 | + | 117.779i | 0.228700 | + | 0.132040i | ||||
\(893\) | 54.0000 | 0.0604703 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 748.246i | 0.836029i | ||||||||
\(896\) | 384.000 | − | 221.703i | 0.428571 | − | 0.247436i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 47.0000 | + | 81.4064i | 0.0523385 | + | 0.0906530i | ||||
\(899\) | 235.559i | 0.262023i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −572.000 | −0.634850 | ||||||||
\(902\) | 273.000 | − | 157.617i | 0.302661 | − | 0.174741i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −400.000 | −0.442478 | ||||||||
\(905\) | 1016.00 | 1.12265 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 642.591i | 0.708479i | 0.935155 | + | 0.354240i | \(0.115260\pi\) | ||||
−0.935155 | + | 0.354240i | \(0.884740\pi\) | |||||||
\(908\) | −1554.00 | − | 897.202i | −1.71145 | − | 0.988108i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −528.000 | + | 304.841i | −0.580220 | + | 0.334990i | ||||
\(911\) | 401.836i | 0.441093i | 0.975376 | + | 0.220547i | \(0.0707841\pi\) | ||||
−0.975376 | + | 0.220547i | \(0.929216\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 420.000 | 0.460022 | ||||||||
\(914\) | 331.000 | + | 573.309i | 0.362144 | + | 0.627253i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −820.000 | + | 1420.28i | −0.895197 | + | 1.55053i | ||||
\(917\) | 672.000 | 0.732824 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 779.423i | 0.848121i | 0.905634 | + | 0.424060i | \(0.139396\pi\) | ||||
−0.905634 | + | 0.424060i | \(0.860604\pi\) | |||||||
\(920\) | 775.959i | 0.843433i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −538.000 | − | 931.843i | −0.583514 | − | 1.01068i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 144.000 | 0.155676 | ||||||||
\(926\) | 984.000 | − | 568.113i | 1.06263 | − | 0.613513i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −544.000 | + | 942.236i | −0.586207 | + | 1.01534i | ||||
\(929\) | −758.000 | −0.815931 | −0.407966 | − | 0.912997i | \(-0.633762\pi\) | ||||
−0.407966 | + | 0.912997i | \(0.633762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 576.773i | 0.619520i | ||||||||
\(932\) | 130.000 | − | 225.167i | 0.139485 | − | 0.241595i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1107.00 | + | 639.127i | −1.18522 | + | 0.684290i | ||||
\(935\) | − | 533.472i | − | 0.570558i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −754.000 | −0.804696 | −0.402348 | − | 0.915487i | \(-0.631806\pi\) | ||||
−0.402348 | + | 0.915487i | \(0.631806\pi\) | |||||||
\(938\) | 402.000 | + | 696.284i | 0.428571 | + | 0.742307i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 48.0000 | + | 27.7128i | 0.0510638 | + | 0.0294817i | ||||
\(941\) | −1796.00 | −1.90861 | −0.954304 | − | 0.298838i | \(-0.903401\pi\) | ||||
−0.954304 | + | 0.298838i | \(0.903401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 315.233i | 0.334288i | ||||||||
\(944\) | −744.000 | + | 429.549i | −0.788136 | + | 0.455030i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 609.000 | + | 1054.82i | 0.643763 | + | 1.11503i | ||||
\(947\) | 105.655i | 0.111568i | 0.998443 | + | 0.0557841i | \(0.0177659\pi\) | ||||
−0.998443 | + | 0.0557841i | \(0.982234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 550.000 | 0.579557 | ||||||||
\(950\) | −243.000 | + | 140.296i | −0.255789 | + | 0.147680i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 304.841i | − | 0.320211i | ||||||
\(953\) | 1213.00 | 1.27282 | 0.636411 | − | 0.771350i | \(-0.280418\pi\) | ||||
0.636411 | + | 0.771350i | \(0.280418\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 13.8564i | − | 0.0145093i | ||||||
\(956\) | 132.000 | + | 76.2102i | 0.138075 | + | 0.0797178i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 210.000 | − | 121.244i | 0.219207 | − | 0.126559i | ||||
\(959\) | 585.433i | 0.610462i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 913.000 | 0.950052 | ||||||||
\(962\) | −352.000 | − | 609.682i | −0.365904 | − | 0.633765i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 446.000 | − | 772.495i | 0.462656 | − | 0.801343i | ||||
\(965\) | −268.000 | −0.277720 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 349.874i | 0.361814i | 0.983500 | + | 0.180907i | \(0.0579033\pi\) | ||||
−0.983500 | + | 0.180907i | \(0.942097\pi\) | |||||||
\(968\) | −208.000 | −0.214876 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 172.000 | + | 297.913i | 0.177320 | + | 0.307127i | ||||
\(971\) | 1434.14i | 1.47697i | 0.674270 | + | 0.738485i | \(0.264458\pi\) | ||||
−0.674270 | + | 0.738485i | \(0.735542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 678.000 | 0.696814 | ||||||||
\(974\) | 702.000 | − | 405.300i | 0.720739 | − | 0.416119i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 128.000 | + | 221.703i | 0.131148 | + | 0.227154i | ||||
\(977\) | 157.000 | 0.160696 | 0.0803480 | − | 0.996767i | \(-0.474397\pi\) | ||||
0.0803480 | + | 0.996767i | \(0.474397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 24.2487i | − | 0.0247689i | ||||||
\(980\) | −296.000 | + | 512.687i | −0.302041 | + | 0.523150i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1257.00 | − | 725.729i | 1.28004 | − | 0.739032i | ||||
\(983\) | − | 1406.43i | − | 1.43075i | −0.698742 | − | 0.715374i | \(-0.746256\pi\) | ||
0.698742 | − | 0.715374i | \(-0.253744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1072.00 | 1.08832 | ||||||||
\(986\) | 374.000 | + | 647.787i | 0.379310 | + | 0.656985i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1188.00 | + | 685.892i | 1.20243 | + | 0.694223i | ||||
\(989\) | −1218.00 | −1.23155 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 249.415i | − | 0.251680i | −0.992051 | − | 0.125840i | \(-0.959837\pi\) | ||
0.992051 | − | 0.125840i | \(-0.0401627\pi\) | |||||||
\(992\) | −192.000 | − | 110.851i | −0.193548 | − | 0.111745i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 124.708i | − | 0.125334i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −412.000 | −0.413240 | −0.206620 | − | 0.978421i | \(-0.566246\pi\) | ||||
−0.206620 | + | 0.978421i | \(0.566246\pi\) | |||||||
\(998\) | 903.000 | − | 521.347i | 0.904810 | − | 0.522392i | ||||
\(999\) | 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 | 324.3.d.b.163.1 | 2 | ||
3.2 | odd | 2 | 324.3.d.c.163.2 | 2 | |||
4.3 | odd | 2 | inner | 324.3.d.b.163.2 | 2 | ||
9.2 | odd | 6 | 108.3.f.b.91.1 | 2 | |||
9.4 | even | 3 | 36.3.f.b.7.1 | yes | 2 | ||
9.5 | odd | 6 | 108.3.f.a.19.1 | 2 | |||
9.7 | even | 3 | 36.3.f.a.31.1 | yes | 2 | ||
12.11 | even | 2 | 324.3.d.c.163.1 | 2 | |||
36.7 | odd | 6 | 36.3.f.b.31.1 | yes | 2 | ||
36.11 | even | 6 | 108.3.f.a.91.1 | 2 | |||
36.23 | even | 6 | 108.3.f.b.19.1 | 2 | |||
36.31 | odd | 6 | 36.3.f.a.7.1 | ✓ | 2 | ||
72.5 | odd | 6 | 1728.3.o.a.127.1 | 2 | |||
72.11 | even | 6 | 1728.3.o.a.1279.1 | 2 | |||
72.13 | even | 6 | 576.3.o.b.511.1 | 2 | |||
72.29 | odd | 6 | 1728.3.o.b.1279.1 | 2 | |||
72.43 | odd | 6 | 576.3.o.b.319.1 | 2 | |||
72.59 | even | 6 | 1728.3.o.b.127.1 | 2 | |||
72.61 | even | 6 | 576.3.o.a.319.1 | 2 | |||
72.67 | odd | 6 | 576.3.o.a.511.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.a.7.1 | ✓ | 2 | 36.31 | odd | 6 | ||
36.3.f.a.31.1 | yes | 2 | 9.7 | even | 3 | ||
36.3.f.b.7.1 | yes | 2 | 9.4 | even | 3 | ||
36.3.f.b.31.1 | yes | 2 | 36.7 | odd | 6 | ||
108.3.f.a.19.1 | 2 | 9.5 | odd | 6 | |||
108.3.f.a.91.1 | 2 | 36.11 | even | 6 | |||
108.3.f.b.19.1 | 2 | 36.23 | even | 6 | |||
108.3.f.b.91.1 | 2 | 9.2 | odd | 6 | |||
324.3.d.b.163.1 | 2 | 1.1 | even | 1 | trivial | ||
324.3.d.b.163.2 | 2 | 4.3 | odd | 2 | inner | ||
324.3.d.c.163.1 | 2 | 12.11 | even | 2 | |||
324.3.d.c.163.2 | 2 | 3.2 | odd | 2 | |||
576.3.o.a.319.1 | 2 | 72.61 | even | 6 | |||
576.3.o.a.511.1 | 2 | 72.67 | odd | 6 | |||
576.3.o.b.319.1 | 2 | 72.43 | odd | 6 | |||
576.3.o.b.511.1 | 2 | 72.13 | even | 6 | |||
1728.3.o.a.127.1 | 2 | 72.5 | odd | 6 | |||
1728.3.o.a.1279.1 | 2 | 72.11 | even | 6 | |||
1728.3.o.b.127.1 | 2 | 72.59 | even | 6 | |||
1728.3.o.b.1279.1 | 2 | 72.29 | odd | 6 |