Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 373.2 | ||
Root | \(0.228425 - 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.373 |
Dual form | 784.2.x.i.557.2 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.228425 | − | 1.39564i | 0.161521 | − | 0.986869i | ||||
\(3\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(4\) | −1.89564 | − | 0.637600i | −0.947822 | − | 0.318800i | ||||
\(5\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.32288 | + | 2.50000i | −0.467707 | + | 0.883883i | ||||
\(9\) | −2.59808 | − | 1.50000i | −0.866025 | − | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70046 | + | 6.34621i | −0.512709 | + | 1.91346i | −0.123371 | + | 0.992361i | \(0.539370\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.18693 | + | 2.41733i | 0.796733 | + | 0.604332i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | −2.68693 | + | 3.28335i | −0.633316 | + | 0.773893i | ||||
\(19\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.46863 | + | 3.82288i | 1.80552 | + | 0.815040i | ||||
\(23\) | 4.58258 | + | 2.64575i | 0.955533 | + | 0.551677i | 0.894795 | − | 0.446476i | \(-0.147321\pi\) |
0.0607377 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.33013 | + | 2.50000i | −0.866025 | + | 0.500000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.29150 | + | 6.29150i | −1.16830 | + | 1.16830i | −0.185695 | + | 0.982607i | \(0.559454\pi\) |
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | 4.10170 | − | 3.89564i | 0.725085 | − | 0.688659i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.96863 | + | 4.50000i | 0.661438 | + | 0.750000i | ||||
\(37\) | 3.13025 | − | 0.838748i | 0.514610 | − | 0.137889i | 0.00783774 | − | 0.999969i | \(-0.497505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.35425 | − | 3.35425i | −0.511518 | − | 0.511518i | 0.403473 | − | 0.914991i | \(-0.367803\pi\) |
−0.914991 | + | 0.403473i | \(0.867803\pi\) | |||||||
\(44\) | 7.26982 | − | 10.9459i | 1.09597 | − | 1.65016i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.73930 | − | 5.79129i | 0.698772 | − | 0.853879i | ||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.50000 | + | 6.61438i | 0.353553 | + | 0.935414i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.76695 | + | 14.0585i | −0.517431 | + | 1.93108i | −0.231367 | + | 0.972867i | \(0.574320\pi\) |
−0.286064 | + | 0.958211i | \(0.592347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.34356 | + | 10.2178i | 0.964257 | + | 1.34167i | ||||
\(59\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.50000 | − | 6.61438i | −0.562500 | − | 0.826797i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.11044 | + | 2.17319i | 0.990848 | + | 0.265497i | 0.717607 | − | 0.696449i | \(-0.245238\pi\) |
0.273241 | + | 0.961946i | \(0.411904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 16.0000i | − | 1.89885i | −0.313993 | − | 0.949425i | \(-0.601667\pi\) | ||
0.313993 | − | 0.949425i | \(-0.398333\pi\) | |||||||
\(72\) | 7.18693 | − | 4.51088i | 0.846988 | − | 0.531612i | ||||
\(73\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(74\) | −0.455566 | − | 4.56031i | −0.0529585 | − | 0.530125i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.93725 | + | 13.7477i | −0.893011 | + | 1.54674i | −0.0567635 | + | 0.998388i | \(0.518078\pi\) |
−0.836247 | + | 0.548352i | \(0.815255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.44753 | + | 3.91514i | −0.587422 | + | 0.422181i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.6160 | − | 12.6464i | −1.45147 | − | 1.34811i | ||||
\(89\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.00000 | − | 7.93725i | −0.729800 | − | 0.827516i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.9373 | − | 13.9373i | 1.40075 | − | 1.40075i | ||||
\(100\) | 9.80238 | − | 1.97822i | 0.980238 | − | 0.197822i | ||||
\(101\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.7601 | + | 8.46863i | 1.82214 | + | 0.822546i | ||||
\(107\) | 17.2744 | − | 4.62867i | 1.66998 | − | 0.447470i | 0.704875 | − | 0.709331i | \(-0.251003\pi\) |
0.965106 | + | 0.261861i | \(0.0843362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.5226 | − | 5.23105i | −1.86992 | − | 0.501044i | −0.999969 | − | 0.00790932i | \(-0.997482\pi\) |
−0.869953 | − | 0.493135i | \(-0.835851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −21.1660 | −1.99113 | −0.995565 | − | 0.0940721i | \(-0.970012\pi\) | ||||
−0.995565 | + | 0.0940721i | \(0.970012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.9379 | − | 7.91498i | 1.47980 | − | 0.734888i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27.8566 | − | 16.0830i | −2.53242 | − | 1.46209i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | −10.2592 | + | 4.76951i | −0.906796 | + | 0.421569i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.88562 | − | 10.8229i | 0.422053 | − | 0.934954i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3303 | − | 10.5830i | 1.56606 | − | 0.904167i | 0.569442 | − | 0.822031i | \(-0.307159\pi\) |
0.996621 | − | 0.0821359i | \(-0.0261741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −22.3303 | − | 3.65480i | −1.87392 | − | 0.306704i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.65390 | − | 11.0608i | −0.387825 | − | 0.921733i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.46863 | − | 0.405881i | −0.531718 | − | 0.0333632i | ||||
\(149\) | −7.79795 | + | 2.08946i | −0.638833 | + | 0.171175i | −0.563675 | − | 0.825997i | \(-0.690613\pi\) |
−0.0751583 | + | 0.997172i | \(0.523946\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.58258 | + | 2.64575i | −0.372925 | + | 0.215308i | −0.674735 | − | 0.738060i | \(-0.735742\pi\) |
0.301811 | + | 0.953368i | \(0.402409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(158\) | 17.3739 | + | 14.2179i | 1.38219 | + | 1.13112i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.9059 | − | 4.50000i | 0.935414 | − | 0.353553i | ||||
\(163\) | 0.755017 | + | 2.81776i | 0.0591375 | + | 0.220704i | 0.989170 | − | 0.146772i | \(-0.0468885\pi\) |
−0.930033 | + | 0.367477i | \(0.880222\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.21979 | + | 8.49713i | 0.321756 | + | 0.647900i | ||||
\(173\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.7601 | + | 16.1144i | −1.56485 | + | 1.21467i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.8029 | + | 5.57411i | 1.55488 | + | 0.416629i | 0.931038 | − | 0.364922i | \(-0.118904\pi\) |
0.623841 | + | 0.781551i | \(0.285571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.6766 | + | 7.95644i | −0.934528 | + | 0.586556i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.2288 | + | 22.9129i | −0.957199 | + | 1.65792i | −0.227946 | + | 0.973674i | \(0.573201\pi\) |
−0.729253 | + | 0.684244i | \(0.760132\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5830 | − | 18.3303i | −0.761781 | − | 1.31944i | −0.941932 | − | 0.335805i | \(-0.890992\pi\) |
0.180150 | − | 0.983639i | \(-0.442342\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.2915 | + | 18.2915i | 1.30322 | + | 1.30322i | 0.926212 | + | 0.377004i | \(0.123046\pi\) |
0.377004 | + | 0.926212i | \(0.376954\pi\) | |||||||
\(198\) | −16.2678 | − | 22.6351i | −1.15610 | − | 1.60860i | ||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | −0.521780 | − | 14.1325i | −0.0368954 | − | 0.999319i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.93725 | − | 13.7477i | −0.551677 | − | 0.955533i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.22876 | − | 7.22876i | 0.497648 | − | 0.497648i | −0.413057 | − | 0.910705i | \(-0.635539\pi\) |
0.910705 | + | 0.413057i | \(0.135539\pi\) | |||||||
\(212\) | 16.1045 | − | 24.2480i | 1.10606 | − | 1.66536i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.51406 | − | 25.1662i | −0.171858 | − | 1.72033i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.7601 | + | 26.0516i | −0.796496 | + | 1.76444i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 1.00000 | ||||||||
\(226\) | −4.83485 | + | 29.5402i | −0.321609 | + | 1.96499i | ||||
\(227\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.40588 | − | 24.0516i | −0.486220 | − | 1.57907i | ||||
\(233\) | −18.3303 | − | 10.5830i | −1.20086 | − | 0.693316i | −0.240112 | − | 0.970745i | \(-0.577184\pi\) |
−0.960746 | + | 0.277429i | \(0.910518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(242\) | −28.8093 | + | 35.2041i | −1.85193 | + | 2.26301i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.5830 | + | 24.5830i | −1.54552 | + | 1.54552i | ||||
\(254\) | −3.65480 | + | 22.3303i | −0.229323 | + | 1.40113i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.31307 | + | 15.4077i | 0.269567 | + | 0.962982i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.7831 | − | 6.90855i | 1.59593 | − | 0.427628i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.7128 | − | 16.0000i | 1.70885 | − | 0.986602i | 0.772851 | − | 0.634588i | \(-0.218830\pi\) |
0.935995 | − | 0.352014i | \(-0.114503\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.9889 | − | 9.29081i | −0.854507 | − | 0.567526i | ||||
\(269\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.5830 | − | 28.0000i | −0.639343 | − | 1.69154i | ||||
\(275\) | −8.50231 | − | 31.7311i | −0.512709 | − | 1.91346i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.98035 | + | 14.8549i | −0.239156 | + | 0.892542i | 0.737075 | + | 0.675810i | \(0.236206\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.1660i | − | 1.26266i | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||
0.775515 | − | 0.631329i | \(-0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(284\) | −10.2016 | + | 30.3303i | −0.605354 | + | 1.79977i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −16.5000 | + | 3.96863i | −0.972272 | + | 0.233854i | ||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.04406 | + | 8.93519i | −0.118809 | + | 0.519347i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.13489 | + | 11.3604i | 0.0657422 | + | 0.658093i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.64575 | + | 7.00000i | 0.152246 | + | 0.402805i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.8118 | − | 21.0000i | 1.33952 | − | 1.18134i | ||||
\(317\) | 8.15926 | + | 30.4508i | 0.458269 | + | 1.71029i | 0.678294 | + | 0.734791i | \(0.262720\pi\) |
−0.220024 | + | 0.975494i | \(0.570614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.2288 | − | 50.6257i | −1.63650 | − | 2.83449i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.56080 | − | 17.6443i | −0.197822 | − | 0.980238i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.10506 | − | 0.410088i | 0.227358 | − | 0.0227126i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.2026 | − | 7.55687i | 1.55016 | − | 0.415363i | 0.620625 | − | 0.784107i | \(-0.286879\pi\) |
0.929531 | + | 0.368744i | \(0.120212\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.39075 | − | 2.51624i | −0.514610 | − | 0.137889i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.1660 | 1.15299 | 0.576493 | − | 0.817102i | \(-0.304421\pi\) | ||||
0.576493 | + | 0.817102i | \(0.304421\pi\) | |||||||
\(338\) | 18.1434 | + | 2.96953i | 0.986869 | + | 0.161521i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.8229 | − | 3.94837i | 0.691363 | − | 0.212882i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.04683 | + | 22.5671i | −0.324611 | + | 1.21147i | 0.590091 | + | 0.807337i | \(0.299092\pi\) |
−0.914702 | + | 0.404128i | \(0.867575\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 17.7478 | + | 32.6547i | 0.945961 | + | 1.74050i | ||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.5314 | − | 27.7601i | 0.662304 | − | 1.46717i | ||||
\(359\) | 32.0780 | + | 18.5203i | 1.69301 | + | 0.977462i | 0.952063 | + | 0.305903i | \(0.0989582\pi\) |
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4545 | − | 9.50000i | 0.866025 | − | 0.500000i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(368\) | 8.20871 | + | 19.5094i | 0.427909 | + | 1.01700i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.7113 | − | 9.83675i | 1.90084 | − | 0.509328i | 0.904227 | − | 0.427051i | \(-0.140448\pi\) |
0.996610 | − | 0.0822766i | \(-0.0262191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.5203 | + | 24.5203i | 1.25952 | + | 1.25952i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) |
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.9564 | + | 23.6965i | 1.48154 | + | 1.21242i | ||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.0000 | + | 10.5830i | −1.42516 | + | 0.538661i | ||||
\(387\) | 3.68322 | + | 13.7460i | 0.187229 | + | 0.698747i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.01766 | − | 18.7262i | 0.254405 | − | 0.949454i | −0.714015 | − | 0.700130i | \(-0.753125\pi\) |
0.968420 | − | 0.249323i | \(-0.0802082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 29.7067 | − | 21.3502i | 1.49660 | − | 1.07561i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −35.3065 | + | 17.5337i | −1.77422 | + | 0.881100i | ||||
\(397\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.8431 | − | 2.50000i | −0.992157 | − | 0.125000i | ||||
\(401\) | −10.5830 | + | 18.3303i | −0.528490 | + | 0.915372i | 0.470958 | + | 0.882156i | \(0.343908\pi\) |
−0.999448 | + | 0.0332161i | \(0.989425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.2915i | 1.05538i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −21.0000 | + | 7.93725i | −1.03209 | + | 0.390095i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.87451 | + | 2.87451i | 0.140095 | + | 0.140095i | 0.773676 | − | 0.633581i | \(-0.218416\pi\) |
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | −8.43754 | − | 11.7400i | −0.410733 | − | 0.571494i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30.1629 | − | 28.0150i | −1.46484 | − | 1.36053i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −35.6974 | − | 2.23987i | −1.72550 | − | 0.108268i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | + | 27.7128i | 0.770693 | + | 1.33488i | 0.937184 | + | 0.348836i | \(0.113423\pi\) |
−0.166491 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.6725 | + | 22.3638i | 1.61262 | + | 1.07103i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.6389 | − | 3.11863i | 0.552980 | − | 0.148171i | 0.0285009 | − | 0.999594i | \(-0.490927\pi\) |
0.524479 | + | 0.851423i | \(0.324260\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 3.42638 | − | 20.9347i | 0.161521 | − | 0.986869i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 40.1232 | + | 13.4955i | 1.88724 | + | 0.634773i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.19615 | + | 3.00000i | 0.243066 | + | 0.140334i | 0.616585 | − | 0.787288i | \(-0.288516\pi\) |
−0.373519 | + | 0.927622i | \(0.621849\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.8745 | −0.737751 | −0.368875 | − | 0.929479i | \(-0.620257\pi\) | ||||
−0.368875 | + | 0.929479i | \(0.620257\pi\) | |||||||
\(464\) | −35.2592 | + | 4.84198i | −1.63687 | + | 0.224783i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.9572 | + | 23.1652i | −0.878176 | + | 1.07310i | ||||
\(467\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.9906 | − | 15.5830i | 1.24103 | − | 0.716507i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.8745 | − | 30.8745i | 1.41365 | − | 1.41365i | ||||
\(478\) | 3.65480 | − | 22.3303i | 0.167167 | − | 1.02136i | ||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 42.5516 | + | 48.2490i | 1.93417 | + | 2.19314i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.0780 | + | 18.5203i | −1.45359 | + | 0.839233i | −0.998683 | − | 0.0513038i | \(-0.983662\pi\) |
−0.454911 | + | 0.890537i | \(0.650329\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3542 | + | 19.3542i | 0.873445 | + | 0.873445i | 0.992846 | − | 0.119401i | \(-0.0380974\pi\) |
−0.119401 | + | 0.992846i | \(0.538097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.4305 | − | 42.6593i | −0.511700 | − | 1.90969i | −0.401735 | − | 0.915756i | \(-0.631593\pi\) |
−0.109965 | − | 0.993935i | \(-0.535074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 28.6937 | + | 39.9245i | 1.27559 | + | 1.77486i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.3303 | + | 10.2016i | 1.34569 | + | 0.452623i | ||||
\(509\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.4889 | − | 2.50000i | 0.993878 | − | 0.110485i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | −3.75238 | − | 37.5621i | −0.164237 | − | 1.64405i | ||||
\(523\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0000 | − | 42.3320i | −0.697633 | − | 1.84576i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.50000 | + | 4.33013i | 0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −16.1621 | + | 17.4012i | −0.698095 | + | 0.751619i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.411959 | − | 1.53745i | −0.0177115 | − | 0.0661002i | 0.956504 | − | 0.291718i | \(-0.0942267\pi\) |
−0.974216 | + | 0.225617i | \(0.927560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.9373 | + | 29.9373i | −1.28002 | + | 1.28002i | −0.339372 | + | 0.940652i | \(0.610215\pi\) |
−0.940652 | + | 0.339372i | \(0.889785\pi\) | |||||||
\(548\) | −41.4955 | + | 8.37420i | −1.77260 | + | 0.357728i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −46.2274 | + | 4.61803i | −1.97114 | + | 0.196913i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19.8229 | + | 8.94837i | 0.842193 | + | 0.380180i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.1903 | − | 6.48176i | −1.02497 | − | 0.274641i | −0.293101 | − | 0.956082i | \(-0.594687\pi\) |
−0.731873 | + | 0.681441i | \(0.761354\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.5402 | − | 4.83485i | −1.24608 | − | 0.203946i | ||||
\(563\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 40.0000 | + | 21.1660i | 1.67836 | + | 0.888106i | ||||
\(569\) | 19.0526 | + | 11.0000i | 0.798725 | + | 0.461144i | 0.843025 | − | 0.537874i | \(-0.180772\pi\) |
−0.0443003 | + | 0.999018i | \(0.514106\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.44776 | − | 35.2595i | 0.395376 | − | 1.47557i | −0.425762 | − | 0.904835i | \(-0.639994\pi\) |
0.821138 | − | 0.570730i | \(-0.193340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.4575 | −1.10335 | ||||||||
\(576\) | 1.76978 | + | 23.9347i | 0.0737406 | + | 0.997277i | ||||
\(577\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(578\) | −18.6057 | − | 15.2259i | −0.773893 | − | 0.633316i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −82.8124 | − | 47.8118i | −3.42974 | − | 1.98016i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.0034 | + | 4.89380i | 0.493338 | + | 0.201134i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.1144 | + | 1.01111i | 0.660071 | + | 0.0414168i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.7128 | + | 16.0000i | −1.13231 | + | 0.653742i | −0.944516 | − | 0.328465i | \(-0.893469\pi\) |
−0.187799 | + | 0.982208i | \(0.560135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.8118 | − | 17.8118i | −0.725351 | − | 0.725351i | ||||
\(604\) | 10.3739 | − | 2.09355i | 0.422107 | − | 0.0851854i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.7650 | + | 47.6395i | −0.515572 | + | 1.92414i | −0.171564 | + | 0.985173i | \(0.554882\pi\) |
−0.344008 | + | 0.938967i | \(0.611785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 26.0000i | − | 1.04672i | −0.852111 | − | 0.523360i | \(-0.824678\pi\) | ||
0.852111 | − | 0.523360i | \(-0.175322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5000 | − | 21.6506i | 0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000i | 0.636950i | 0.947931 | + | 0.318475i | \(0.103171\pi\) | ||||
−0.947931 | + | 0.318475i | \(0.896829\pi\) | |||||||
\(632\) | −23.8693 | − | 38.0297i | −0.949470 | − | 1.51274i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 44.3622 | − | 4.43170i | 1.76185 | − | 0.176005i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −77.3320 | + | 29.2288i | −3.06160 | + | 1.15718i | ||||
\(639\) | −24.0000 | + | 41.5692i | −0.949425 | + | 1.64445i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5830 | + | 18.3303i | 0.418004 | + | 0.724003i | 0.995739 | − | 0.0922210i | \(-0.0293966\pi\) |
−0.577735 | + | 0.816224i | \(0.696063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(648\) | −25.4385 | + | 0.939205i | −0.999319 | + | 0.0368954i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.365363 | − | 5.82288i | 0.0143087 | − | 0.228041i | ||||
\(653\) | 11.0875 | + | 41.3790i | 0.433886 | + | 1.61928i | 0.743719 | + | 0.668493i | \(0.233060\pi\) |
−0.309833 | + | 0.950791i | \(0.600273\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.77124 | − | 8.77124i | 0.341679 | − | 0.341679i | −0.515319 | − | 0.856998i | \(-0.672327\pi\) |
0.856998 | + | 0.515319i | \(0.172327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(662\) | −4.10451 | − | 41.0870i | −0.159526 | − | 1.59689i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.65687 | + | 12.5314i | −0.219199 | + | 0.485581i | ||||
\(667\) | −45.4770 | + | 12.1855i | −1.76088 | + | 0.471826i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0000 | −1.15642 | −0.578208 | − | 0.815890i | \(-0.696248\pi\) | ||||
−0.578208 | + | 0.815890i | \(0.696248\pi\) | |||||||
\(674\) | 4.83485 | − | 29.5402i | 0.186231 | − | 1.13785i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.28880 | − | 24.6434i | 0.318800 | − | 0.947822i | ||||
\(677\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.4851 | + | 39.1308i | −0.401200 | + | 1.49730i | 0.409757 | + | 0.912194i | \(0.365613\pi\) |
−0.810958 | + | 0.585105i | \(0.801053\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.58145 | − | 18.7981i | −0.0984168 | − | 0.716670i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.1144 | + | 13.5941i | 1.14313 | + | 0.516026i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.4575 | − | 27.4575i | 1.03706 | − | 1.03706i | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) |
0.999286 | − | 0.0377695i | \(-0.0120253\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 49.6283 | − | 17.3105i | 1.87044 | − | 0.652412i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.0436 | + | 8.58605i | −1.20342 | + | 0.322456i | −0.804178 | − | 0.594389i | \(-0.797394\pi\) |
−0.399244 | + | 0.916845i | \(0.630727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.2432 | − | 23.8118i | 1.54674 | − | 0.893011i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −35.8808 | − | 23.8304i | −1.34093 | − | 0.890586i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.1751 | − | 40.5390i | 1.23808 | − | 1.51290i | ||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.50000 | − | 25.1346i | −0.353553 | − | 0.935414i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.5142 | − | 42.9718i | 0.427628 | − | 1.59593i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.1033 | − | 7.00000i | 1.07276 | − | 0.258023i | ||||
\(737\) | −27.5830 | + | 47.7752i | −1.01603 | + | 1.75982i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.6742 | − | 6.61142i | −0.907654 | − | 0.243205i | −0.225354 | − | 0.974277i | \(-0.572354\pi\) |
−0.682300 | + | 0.731072i | \(0.739020\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.0405i | 1.35888i | 0.733729 | + | 0.679442i | \(0.237778\pi\) | ||||
−0.733729 | + | 0.679442i | \(0.762222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.34283 | − | 53.4828i | −0.195615 | − | 1.95814i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | − | 41.5692i | 0.875772 | − | 1.51688i | 0.0198348 | − | 0.999803i | \(-0.493686\pi\) |
0.855938 | − | 0.517079i | \(-0.172981\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.7085 | − | 21.7085i | −0.789009 | − | 0.789009i | 0.192323 | − | 0.981332i | \(-0.438398\pi\) |
−0.981332 | + | 0.192323i | \(0.938398\pi\) | |||||||
\(758\) | 39.8226 | − | 28.6205i | 1.44642 | − | 1.03954i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 39.6863 | − | 35.0000i | 1.43580 | − | 1.26626i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.37420 | + | 41.4955i | 0.301394 | + | 1.49345i | ||||
\(773\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(774\) | 20.0258 | − | 2.00054i | 0.719813 | − | 0.0719079i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.9889 | − | 11.2804i | −0.895895 | − | 0.404422i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 101.539 | + | 27.2074i | 3.63337 | + | 0.973558i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(788\) | −23.0115 | − | 46.3368i | −0.819751 | − | 1.65068i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 16.4059 | + | 53.2804i | 0.582958 | + | 1.89324i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −8.02178 | + | 27.1229i | −0.283613 | + | 0.958939i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.1652 | + | 18.9572i | 0.817990 | + | 0.669402i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.9090 | + | 19.0000i | −1.15702 | + | 0.668004i | −0.950587 | − | 0.310457i | \(-0.899518\pi\) |
−0.206430 | + | 0.978461i | \(0.566185\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.7154 | + | 4.86351i | 1.04152 | + | 0.170466i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.1154 | + | 5.65784i | −0.736931 | + | 0.197460i | −0.607714 | − | 0.794156i | \(-0.707913\pi\) |
−0.129217 | + | 0.991616i | \(0.541246\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.7128 | + | 16.0000i | −0.966008 | + | 0.557725i | −0.898017 | − | 0.439961i | \(-0.854992\pi\) |
−0.0679910 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.5203 | − | 40.5203i | −1.40903 | − | 1.40903i | −0.765015 | − | 0.644013i | \(-0.777268\pi\) |
−0.644013 | − | 0.765015i | \(-0.722732\pi\) | |||||||
\(828\) | 6.28065 | + | 31.1216i | 0.218268 | + | 1.08155i | ||||
\(829\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 50.1660i | − | 1.72986i | ||||||
\(842\) | 4.66840 | − | 3.35518i | 0.160884 | − | 0.115627i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.3122 | + | 9.09409i | −0.630332 | + | 0.313032i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −45.9889 | + | 35.6974i | −1.57926 | + | 1.22585i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.5637 | + | 4.43824i | 0.567797 | + | 0.152141i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.2802 | + | 49.3092i | −0.385551 | + | 1.68535i | ||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42.3320 | − | 16.0000i | 1.44183 | − | 0.544962i | ||||
\(863\) | 29.1033 | − | 50.4083i | 0.990687 | − | 1.71592i | 0.377424 | − | 0.926041i | \(-0.376810\pi\) |
0.613263 | − | 0.789879i | \(-0.289857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −73.7490 | − | 73.7490i | −2.50176 | − | 2.50176i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 38.9035 | − | 41.8864i | 1.31744 | − | 1.41845i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.34016 | − | 12.4657i | −0.112789 | − | 0.420935i | 0.886323 | − | 0.463068i | \(-0.153251\pi\) |
−0.999112 | + | 0.0421327i | \(0.986585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.1033 | + | 35.1033i | −1.18132 | + | 1.18132i | −0.201916 | + | 0.979403i | \(0.564717\pi\) |
−0.979403 | + | 0.201916i | \(0.935283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.69388 | − | 16.9561i | −0.0569071 | − | 0.569652i | ||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −57.1159 | + | 15.3042i | −1.91346 | + | 0.512709i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.456850 | + | 2.79129i | −0.0152453 | + | 0.0931465i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −28.4347 | − | 9.56400i | −0.947822 | − | 0.318800i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.0000 | − | 52.9150i | 0.931266 | − | 1.75993i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0123 | + | 37.3666i | −0.332455 | + | 1.24074i | 0.574148 | + | 0.818752i | \(0.305333\pi\) |
−0.906602 | + | 0.421986i | \(0.861333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 5.37386 | − | 6.56670i | 0.177752 | − | 0.217207i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.5692 | + | 24.0000i | 1.37124 | + | 0.791687i | 0.991084 | − | 0.133235i | \(-0.0425364\pi\) |
0.380158 | + | 0.924922i | \(0.375870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.4575 | + | 11.4575i | −0.376721 | + | 0.376721i | ||||
\(926\) | −3.62614 | + | 22.1552i | −0.119162 | + | 0.728064i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.29641 | + | 50.3153i | −0.0425569 | + | 1.65168i | ||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 28.0000 | + | 31.7490i | 0.917170 | + | 1.03997i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.5830 | − | 41.2288i | −0.506647 | − | 1.34046i | ||||
\(947\) | 6.99228 | + | 26.0955i | 0.227219 | + | 0.847991i | 0.981504 | + | 0.191444i | \(0.0613171\pi\) |
−0.754285 | + | 0.656547i | \(0.772016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.1660i | 0.685634i | 0.939402 | + | 0.342817i | \(0.111381\pi\) | ||||
−0.939402 | + | 0.342817i | \(0.888619\pi\) | |||||||
\(954\) | −36.0373 | − | 50.1423i | −1.16675 | − | 1.62342i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −30.3303 | − | 10.2016i | −0.980952 | − | 0.329943i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −51.8233 | − | 13.8860i | −1.66998 | − | 0.447470i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 47.6235i | − | 1.53147i | −0.643157 | − | 0.765735i | \(-0.722376\pi\) | ||
0.643157 | − | 0.765735i | \(-0.277624\pi\) | |||||||
\(968\) | 77.0583 | − | 48.3656i | 2.47675 | − | 1.55453i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18.5203 | + | 49.0000i | 0.593427 | + | 1.57006i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.0000 | − | 39.8372i | −0.735835 | − | 1.27450i | −0.954356 | − | 0.298672i | \(-0.903456\pi\) |
0.218521 | − | 0.975832i | \(-0.429877\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.8745 | + | 42.8745i | 1.36888 | + | 1.36888i | ||||
\(982\) | 31.4326 | − | 22.5906i | 1.00306 | − | 0.720896i | ||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.49659 | − | 24.2456i | −0.206580 | − | 0.770965i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.1033 | + | 50.4083i | 0.924496 | + | 1.60127i | 0.792370 | + | 0.610040i | \(0.208847\pi\) |
0.132125 | + | 0.991233i | \(0.457820\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(998\) | −62.1482 | + | 6.20848i | −1.96727 | + | 0.196526i | ||||
\(999\) | 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 | 784.2.x.i.373.2 | 8 | ||
7.2 | even | 3 | 784.2.m.f.197.1 | ✓ | 4 | ||
7.3 | odd | 6 | inner | 784.2.x.i.165.2 | 8 | ||
7.4 | even | 3 | inner | 784.2.x.i.165.2 | 8 | ||
7.5 | odd | 6 | 784.2.m.f.197.1 | ✓ | 4 | ||
7.6 | odd | 2 | CM | 784.2.x.i.373.2 | 8 | ||
16.13 | even | 4 | inner | 784.2.x.i.765.2 | 8 | ||
112.13 | odd | 4 | inner | 784.2.x.i.765.2 | 8 | ||
112.45 | odd | 12 | inner | 784.2.x.i.557.2 | 8 | ||
112.61 | odd | 12 | 784.2.m.f.589.1 | yes | 4 | ||
112.93 | even | 12 | 784.2.m.f.589.1 | yes | 4 | ||
112.109 | even | 12 | inner | 784.2.x.i.557.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.m.f.197.1 | ✓ | 4 | 7.2 | even | 3 | ||
784.2.m.f.197.1 | ✓ | 4 | 7.5 | odd | 6 | ||
784.2.m.f.589.1 | yes | 4 | 112.61 | odd | 12 | ||
784.2.m.f.589.1 | yes | 4 | 112.93 | even | 12 | ||
784.2.x.i.165.2 | 8 | 7.3 | odd | 6 | inner | ||
784.2.x.i.165.2 | 8 | 7.4 | even | 3 | inner | ||
784.2.x.i.373.2 | 8 | 1.1 | even | 1 | trivial | ||
784.2.x.i.373.2 | 8 | 7.6 | odd | 2 | CM | ||
784.2.x.i.557.2 | 8 | 112.45 | odd | 12 | inner | ||
784.2.x.i.557.2 | 8 | 112.109 | even | 12 | inner | ||
784.2.x.i.765.2 | 8 | 16.13 | even | 4 | inner | ||
784.2.x.i.765.2 | 8 | 112.13 | odd | 4 | inner |