Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(79,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.79");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.10355792167\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 207.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.207 |
Dual form | 224.3.o.a.79.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | −0.770579 | − | 0.637344i | \(-0.780033\pi\) |
0.937246 | + | 0.348669i | \(0.113366\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.50000 | + | 2.59808i | −0.900000 | + | 0.519615i | −0.877200 | − | 0.480125i | \(-0.840591\pi\) |
−0.0227998 | + | 0.999740i | \(0.507258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.00000 | + | 6.92820i | 0.444444 | + | 0.769800i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.50000 | − | 14.7224i | 0.772727 | − | 1.33840i | −0.163336 | − | 0.986571i | \(-0.552225\pi\) |
0.936063 | − | 0.351832i | \(-0.114441\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 13.8564i | − | 1.06588i | −0.846154 | − | 0.532939i | \(-0.821088\pi\) | ||
0.846154 | − | 0.532939i | \(-0.178912\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.19615i | 0.346410i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.5000 | − | 21.6506i | 0.735294 | − | 1.27357i | −0.219300 | − | 0.975657i | \(-0.570377\pi\) |
0.954594 | − | 0.297909i | \(-0.0962893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.184211 | − | 0.319062i | 0.759100 | − | 0.650974i | \(-0.225639\pi\) |
−0.943310 | + | 0.331912i | \(0.892306\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.50000 | − | 4.33013i | −0.261905 | − | 0.206197i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50000 | + | 2.59808i | −0.195652 | + | 0.112960i | −0.594626 | − | 0.804003i | \(-0.702700\pi\) |
0.398974 | + | 0.916962i | \(0.369366\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 1.73205i | 0.0400000 | − | 0.0692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.0000 | 0.629630 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.8564i | 0.477807i | 0.971043 | + | 0.238904i | \(0.0767880\pi\) | ||||
−0.971043 | + | 0.238904i | \(0.923212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.5000 | − | 16.4545i | −0.919355 | − | 0.530790i | −0.0359257 | − | 0.999354i | \(-0.511438\pi\) |
−0.883429 | + | 0.468565i | \(0.844771\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.50000 | − | 14.7224i | −0.257576 | − | 0.446134i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.5000 | + | 33.7750i | 0.385714 | + | 0.965000i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.50000 | − | 4.33013i | 0.202703 | − | 0.117030i | −0.395213 | − | 0.918590i | \(-0.629329\pi\) |
0.597916 | + | 0.801559i | \(0.295996\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.0000 | − | 6.92820i | −0.307692 | − | 0.177646i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 26.0000 | 0.634146 | 0.317073 | − | 0.948401i | \(-0.397300\pi\) | ||||
0.317073 | + | 0.948401i | \(0.397300\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14.0000 | −0.325581 | −0.162791 | − | 0.986661i | \(-0.552050\pi\) | ||||
−0.162791 | + | 0.986661i | \(0.552050\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −36.0000 | − | 20.7846i | −0.800000 | − | 0.461880i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 43.5000 | − | 25.1147i | 0.925532 | − | 0.534356i | 0.0401362 | − | 0.999194i | \(-0.487221\pi\) |
0.885396 | + | 0.464838i | \(0.153887\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −47.0000 | − | 13.8564i | −0.959184 | − | 0.282784i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.5000 | − | 21.6506i | −0.245098 | − | 0.424522i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 79.5000 | + | 45.8993i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 88.3346i | 1.60608i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.00000 | −0.122807 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −27.5000 | + | 47.6314i | −0.466102 | + | 0.807312i | −0.999250 | − | 0.0387097i | \(-0.987675\pi\) |
0.533149 | + | 0.846021i | \(0.321009\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19.5000 | − | 11.2583i | 0.319672 | − | 0.184563i | −0.331574 | − | 0.943429i | \(-0.607580\pi\) |
0.651246 | + | 0.758866i | \(0.274246\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 52.0000 | − | 20.7846i | 0.825397 | − | 0.329914i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 36.0000 | + | 62.3538i | 0.553846 | + | 0.959290i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.50000 | − | 14.7224i | 0.126866 | − | 0.219738i | −0.795595 | − | 0.605829i | \(-0.792842\pi\) |
0.922461 | + | 0.386091i | \(0.126175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.19615i | 0.0753066i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −59.5000 | + | 103.057i | −0.815068 | + | 1.41174i | 0.0942102 | + | 0.995552i | \(0.469967\pi\) |
−0.909279 | + | 0.416188i | \(0.863366\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | − | 1.73205i | −0.0133333 | − | 0.0230940i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −93.5000 | − | 73.6122i | −1.21429 | − | 0.956002i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64.5000 | + | 37.2391i | −0.816456 | + | 0.471381i | −0.849193 | − | 0.528083i | \(-0.822911\pi\) |
0.0327370 | + | 0.999464i | \(0.489578\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −27.5000 | + | 47.6314i | −0.339506 | + | 0.588042i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −110.000 | −1.32530 | −0.662651 | − | 0.748929i | \(-0.730569\pi\) | ||||
−0.662651 | + | 0.748929i | \(0.730569\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 129.904i | 1.52828i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0000 | + | 6.92820i | 0.137931 | + | 0.0796345i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −35.5000 | − | 61.4878i | −0.398876 | − | 0.690874i | 0.594711 | − | 0.803939i | \(-0.297266\pi\) |
−0.993588 | + | 0.113065i | \(0.963933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −96.0000 | − | 13.8564i | −1.05495 | − | 0.152268i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28.5000 | + | 16.4545i | −0.306452 | + | 0.176930i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 31.5000 | + | 18.1865i | 0.331579 | + | 0.191437i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −22.0000 | −0.226804 | −0.113402 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113402 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 136.000 | 1.37374 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 67.5000 | + | 38.9711i | 0.668317 | + | 0.385853i | 0.795439 | − | 0.606034i | \(-0.207241\pi\) |
−0.127122 | + | 0.991887i | \(0.540574\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 139.500 | − | 80.5404i | 1.35437 | − | 0.781945i | 0.365511 | − | 0.930807i | \(-0.380894\pi\) |
0.988858 | + | 0.148862i | \(0.0475610\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 36.0000 | + | 5.19615i | 0.342857 | + | 0.0494872i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 32.5000 | + | 56.2917i | 0.303738 | + | 0.526090i | 0.976980 | − | 0.213333i | \(-0.0684318\pi\) |
−0.673241 | + | 0.739423i | \(0.735098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.50000 | + | 4.33013i | 0.0688073 | + | 0.0397259i | 0.534009 | − | 0.845479i | \(-0.320685\pi\) |
−0.465202 | + | 0.885205i | \(0.654018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8.66025i | − | 0.0780203i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 122.000 | 1.07965 | 0.539823 | − | 0.841779i | \(-0.318491\pi\) | ||||
0.539823 | + | 0.841779i | \(0.318491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.5000 | − | 23.3827i | 0.117391 | − | 0.203328i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 96.0000 | − | 55.4256i | 0.820513 | − | 0.473723i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −137.500 | − | 108.253i | −1.15546 | − | 0.909691i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −84.0000 | − | 145.492i | −0.694215 | − | 1.20242i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.0000 | − | 22.5167i | 0.105691 | − | 0.183062i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 119.512i | − | 0.956092i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 166.277i | 1.30927i | 0.755947 | + | 0.654633i | \(0.227177\pi\) | ||||
−0.755947 | + | 0.654633i | \(0.772823\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.00000 | + | 12.1244i | −0.0542636 | + | 0.0939873i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.50000 | + | 14.7224i | 0.0648855 | + | 0.112385i | 0.896643 | − | 0.442754i | \(-0.145998\pi\) |
−0.831758 | + | 0.555139i | \(0.812665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −45.5000 | + | 18.1865i | −0.342105 | + | 0.136741i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −76.5000 | + | 44.1673i | −0.566667 | + | 0.327165i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 72.5000 | − | 125.574i | 0.529197 | − | 0.916596i | −0.470223 | − | 0.882548i | \(-0.655827\pi\) |
0.999420 | − | 0.0340486i | \(-0.0108401\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 82.0000 | 0.589928 | 0.294964 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294964 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 50.2295i | − | 0.356237i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −204.000 | − | 117.779i | −1.42657 | − | 0.823633i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36.0000 | − | 62.3538i | −0.248276 | − | 0.430026i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −35.5000 | + | 33.7750i | −0.241497 | + | 0.229762i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.50000 | + | 2.59808i | −0.0302013 | + | 0.0174368i | −0.515025 | − | 0.857175i | \(-0.672217\pi\) |
0.484823 | + | 0.874612i | \(0.338884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 31.5000 | + | 18.1865i | 0.208609 | + | 0.120441i | 0.600665 | − | 0.799501i | \(-0.294903\pi\) |
−0.392056 | + | 0.919942i | \(0.628236\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 200.000 | 1.30719 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 171.000 | 1.10323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −268.500 | − | 155.019i | −1.71019 | − | 0.987379i | −0.934282 | − | 0.356534i | \(-0.883958\pi\) |
−0.775909 | − | 0.630845i | \(-0.782708\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 79.5000 | − | 45.8993i | 0.500000 | − | 0.288675i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5000 | + | 33.7750i | 0.0838509 | + | 0.209783i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.50000 | + | 14.7224i | 0.0521472 | + | 0.0903217i | 0.890921 | − | 0.454159i | \(-0.150060\pi\) |
−0.838773 | + | 0.544481i | \(0.816727\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 76.5000 | + | 44.1673i | 0.463636 | + | 0.267681i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.8564i | 0.0829725i | 0.999139 | + | 0.0414862i | \(0.0132093\pi\) | ||||
−0.999139 | + | 0.0414862i | \(0.986791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −0.136095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 28.0000 | − | 48.4974i | 0.163743 | − | 0.283611i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 91.5000 | − | 52.8275i | 0.528902 | − | 0.305362i | −0.211667 | − | 0.977342i | \(-0.567889\pi\) |
0.740569 | + | 0.671980i | \(0.234556\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.0000 | − | 8.66025i | −0.0628571 | − | 0.0494872i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.5000 | + | 47.6314i | 0.155367 | + | 0.269104i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 44.5000 | − | 77.0763i | 0.248603 | − | 0.430594i | −0.714535 | − | 0.699600i | \(-0.753362\pi\) |
0.963139 | + | 0.269006i | \(0.0866951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 249.415i | 1.37799i | 0.724768 | + | 0.688993i | \(0.241947\pi\) | ||||
−0.724768 | + | 0.688993i | \(0.758053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 22.5167i | − | 0.123042i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.5000 | + | 38.9711i | −0.121622 | + | 0.210655i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −212.500 | − | 368.061i | −1.13636 | − | 1.96824i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.0000 | − | 117.779i | 0.0899471 | − | 0.623172i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 187.500 | − | 108.253i | 0.981675 | − | 0.566771i | 0.0788999 | − | 0.996883i | \(-0.474859\pi\) |
0.902776 | + | 0.430112i | \(0.141526\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 36.5000 | − | 63.2199i | 0.189119 | − | 0.327564i | −0.755838 | − | 0.654759i | \(-0.772770\pi\) |
0.944957 | + | 0.327195i | \(0.106103\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 72.0000 | 0.369231 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 207.846i | 1.05506i | 0.849538 | + | 0.527528i | \(0.176881\pi\) | ||||
−0.849538 | + | 0.527528i | \(0.823119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 55.5000 | + | 32.0429i | 0.278894 | + | 0.161020i | 0.632923 | − | 0.774215i | \(-0.281855\pi\) |
−0.354028 | + | 0.935235i | \(0.615188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.50000 | − | 14.7224i | −0.0422886 | − | 0.0732459i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 96.0000 | + | 13.8564i | 0.472906 | + | 0.0682582i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −117.000 | + | 67.5500i | −0.570732 | + | 0.329512i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −36.0000 | − | 20.7846i | −0.173913 | − | 0.100409i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −119.000 | −0.569378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −302.000 | −1.43128 | −0.715640 | − | 0.698470i | \(-0.753865\pi\) | ||||
−0.715640 | + | 0.698470i | \(0.753865\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 63.0000 | − | 36.3731i | 0.293023 | − | 0.169177i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −142.500 | + | 180.999i | −0.656682 | + | 0.834098i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 59.5000 | + | 103.057i | 0.271689 | + | 0.470580i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −300.000 | − | 173.205i | −1.35747 | − | 0.783733i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 138.564i | − | 0.621364i | −0.950514 | − | 0.310682i | \(-0.899443\pi\) | ||
0.950514 | − | 0.310682i | \(-0.100557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.0000 | 0.0711111 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.5000 | + | 47.6314i | −0.121145 | + | 0.209830i | −0.920220 | − | 0.391402i | \(-0.871990\pi\) |
0.799074 | + | 0.601232i | \(0.205323\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 283.500 | − | 163.679i | 1.23799 | − | 0.714755i | 0.269308 | − | 0.963054i | \(-0.413205\pi\) |
0.968683 | + | 0.248300i | \(0.0798717\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −110.500 | + | 44.1673i | −0.478355 | + | 0.191200i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 192.500 | + | 333.420i | 0.826180 | + | 1.43099i | 0.901014 | + | 0.433790i | \(0.142824\pi\) |
−0.0748337 | + | 0.997196i | \(0.523843\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −130.500 | + | 226.033i | −0.555319 | + | 0.961841i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 74.4782i | 0.314254i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 429.549i | 1.79727i | 0.438693 | + | 0.898637i | \(0.355442\pi\) | ||||
−0.438693 | + | 0.898637i | \(0.644558\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 72.5000 | − | 125.574i | 0.300830 | − | 0.521053i | −0.675494 | − | 0.737365i | \(-0.736070\pi\) |
0.976324 | + | 0.216313i | \(0.0694030\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 104.000 | + | 180.133i | 0.427984 | + | 0.741289i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 247.500 | − | 59.7558i | 1.01020 | − | 0.243901i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −84.0000 | + | 48.4974i | −0.340081 | + | 0.196346i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −55.0000 | + | 95.2628i | −0.220884 | + | 0.382582i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 58.0000 | 0.231076 | 0.115538 | − | 0.993303i | \(-0.463141\pi\) | ||||
0.115538 | + | 0.993303i | \(0.463141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 88.3346i | 0.349149i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 112.500 | + | 64.9519i | 0.441176 | + | 0.254713i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −59.5000 | − | 103.057i | −0.231518 | − | 0.401000i | 0.726737 | − | 0.686915i | \(-0.241036\pi\) |
−0.958255 | + | 0.285915i | \(0.907702\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.5000 | − | 56.2917i | −0.0868726 | − | 0.217342i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −96.0000 | + | 55.4256i | −0.367816 | + | 0.212359i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 283.500 | + | 163.679i | 1.07795 | + | 0.622353i | 0.930342 | − | 0.366694i | \(-0.119510\pi\) |
0.147605 | + | 0.989046i | \(0.452844\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −477.000 | −1.80000 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −71.0000 | −0.265918 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 115.500 | + | 66.6840i | 0.429368 | + | 0.247896i | 0.699077 | − | 0.715046i | \(-0.253594\pi\) |
−0.269709 | + | 0.962942i | \(0.586928\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −376.500 | + | 217.372i | −1.38930 | + | 0.802112i | −0.993236 | − | 0.116111i | \(-0.962957\pi\) |
−0.396063 | + | 0.918223i | \(0.629624\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −60.0000 | + | 76.2102i | −0.219780 | + | 0.279158i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.0000 | − | 29.4449i | −0.0618182 | − | 0.107072i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 175.500 | + | 101.325i | 0.633574 | + | 0.365794i | 0.782135 | − | 0.623109i | \(-0.214131\pi\) |
−0.148561 | + | 0.988903i | \(0.547464\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 263.272i | − | 0.943626i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 74.0000 | 0.263345 | 0.131673 | − | 0.991293i | \(-0.457965\pi\) | ||||
0.131673 | + | 0.991293i | \(0.457965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −231.500 | + | 400.970i | −0.818021 | + | 1.41685i | 0.0891169 | + | 0.996021i | \(0.471596\pi\) |
−0.907138 | + | 0.420833i | \(0.861738\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 31.5000 | − | 18.1865i | 0.110526 | − | 0.0638124i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.0000 | − | 180.133i | 0.0905923 | − | 0.627642i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −168.000 | − | 290.985i | −0.581315 | − | 1.00687i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0000 | + | 19.0526i | −0.0378007 | + | 0.0654727i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 110.851i | 0.378332i | 0.981945 | + | 0.189166i | \(0.0605784\pi\) | ||||
−0.981945 | + | 0.189166i | \(0.939422\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 285.788i | − | 0.968774i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 144.500 | − | 250.281i | 0.486532 | − | 0.842698i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.0000 | + | 62.3538i | 0.120401 | + | 0.208541i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0000 | + | 96.9948i | −0.0465116 | + | 0.322242i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 67.5000 | − | 38.9711i | 0.222772 | − | 0.128618i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −58.5000 | + | 101.325i | −0.191803 | + | 0.332213i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 274.000 | 0.892508 | 0.446254 | − | 0.894906i | \(-0.352758\pi\) | ||||
0.446254 | + | 0.894906i | \(0.352758\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 161.081i | − | 0.521297i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 43.5000 | + | 25.1147i | 0.139871 | + | 0.0807548i | 0.568303 | − | 0.822820i | \(-0.307600\pi\) |
−0.428431 | + | 0.903574i | \(0.640934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 204.500 | + | 354.204i | 0.653355 | + | 1.13164i | 0.982304 | + | 0.187296i | \(0.0599723\pi\) |
−0.328949 | + | 0.944348i | \(0.606694\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −180.000 | + | 228.631i | −0.571429 | + | 0.725812i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 163.500 | − | 94.3968i | 0.515773 | − | 0.297782i | −0.219431 | − | 0.975628i | \(-0.570420\pi\) |
0.735203 | + | 0.677847i | \(0.237087\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 204.000 | + | 117.779i | 0.639498 | + | 0.369215i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 65.0000 | 0.202492 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −175.000 | −0.541796 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0000 | − | 13.8564i | −0.0738462 | − | 0.0426351i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.50000 | − | 4.33013i | 0.0229358 | − | 0.0132420i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −130.500 | − | 326.492i | −0.396657 | − | 0.992376i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −147.500 | − | 255.477i | −0.445619 | − | 0.771835i | 0.552476 | − | 0.833529i | \(-0.313683\pi\) |
−0.998095 | + | 0.0616936i | \(0.980350\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 60.0000 | + | 34.6410i | 0.180180 | + | 0.104027i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 88.3346i | 0.263685i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0000 | 0.0771513 | 0.0385757 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385757 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 61.0000 | − | 105.655i | 0.179941 | − | 0.311667i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −484.500 | + | 279.726i | −1.42082 | + | 0.820311i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −143.000 | + | 311.769i | −0.416910 | + | 0.908948i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.5000 | − | 23.3827i | −0.0391304 | − | 0.0677759i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 188.500 | − | 326.492i | 0.543228 | − | 0.940898i | −0.455488 | − | 0.890242i | \(-0.650535\pi\) |
0.998716 | − | 0.0506562i | \(-0.0161313\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 96.9948i | 0.277922i | 0.990298 | + | 0.138961i | \(0.0443763\pi\) | ||||
−0.990298 | + | 0.138961i | \(0.955624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 235.559i | − | 0.671108i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −251.500 | + | 435.611i | −0.712465 | + | 1.23402i | 0.251465 | + | 0.967866i | \(0.419088\pi\) |
−0.963929 | + | 0.266158i | \(0.914246\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −162.500 | + | 64.9519i | −0.455182 | + | 0.181938i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −160.500 | + | 92.6647i | −0.447075 | + | 0.258119i | −0.706594 | − | 0.707619i | \(-0.749769\pi\) |
0.259519 | + | 0.965738i | \(0.416436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 156.000 | − | 270.200i | 0.432133 | − | 0.748476i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −168.000 | −0.462810 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 618.342i | − | 1.69409i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −256.500 | − | 148.090i | −0.698910 | − | 0.403516i | 0.108031 | − | 0.994147i | \(-0.465545\pi\) |
−0.806941 | + | 0.590632i | \(0.798879\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 104.000 | + | 180.133i | 0.281843 | + | 0.488166i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 397.500 | − | 504.893i | 1.07143 | − | 1.36090i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 103.500 | − | 59.7558i | 0.277480 | − | 0.160203i | −0.354802 | − | 0.934941i | \(-0.615452\pi\) |
0.632282 | + | 0.774738i | \(0.282118\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −103.500 | − | 59.7558i | −0.276000 | − | 0.159349i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 192.000 | 0.509284 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 634.000 | 1.67282 | 0.836412 | − | 0.548102i | \(-0.184649\pi\) | ||||
0.836412 | + | 0.548102i | \(0.184649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 144.000 | + | 83.1384i | 0.377953 | + | 0.218211i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 211.500 | − | 122.110i | 0.552219 | − | 0.318824i | −0.197797 | − | 0.980243i | \(-0.563379\pi\) |
0.750017 | + | 0.661419i | \(0.230045\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 612.000 | + | 88.3346i | 1.58961 | + | 0.229440i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −56.0000 | − | 96.9948i | −0.144703 | − | 0.250633i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −508.500 | − | 293.583i | −1.30720 | − | 0.754711i | −0.325570 | − | 0.945518i | \(-0.605556\pi\) |
−0.981628 | + | 0.190807i | \(0.938890\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 129.904i | 0.332235i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0000 | 0.0432570 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 193.500 | − | 335.152i | 0.489873 | − | 0.848486i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −208.500 | + | 120.378i | −0.525189 | + | 0.303218i | −0.739055 | − | 0.673645i | \(-0.764728\pi\) |
0.213866 | + | 0.976863i | \(0.431394\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.00000 | + | 48.4974i | −0.0175439 | + | 0.121547i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −59.5000 | − | 103.057i | −0.148379 | − | 0.257000i | 0.782249 | − | 0.622965i | \(-0.214072\pi\) |
−0.930629 | + | 0.365965i | \(0.880739\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −228.000 | + | 394.908i | −0.565757 | + | 0.979920i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 285.788i | − | 0.705650i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 147.224i | − | 0.361731i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 72.5000 | − | 125.574i | 0.177262 | − | 0.307026i | −0.763680 | − | 0.645595i | \(-0.776609\pi\) |
0.940942 | + | 0.338569i | \(0.109943\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −72.5000 | − | 125.574i | −0.176399 | − | 0.305532i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 302.500 | + | 238.157i | 0.732446 | + | 0.576651i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 495.000 | − | 285.788i | 1.19277 | − | 0.688647i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 41.0000 | − | 71.0141i | 0.0983213 | − | 0.170298i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −302.000 | −0.720764 | −0.360382 | − | 0.932805i | \(-0.617354\pi\) | ||||
−0.360382 | + | 0.932805i | \(0.617354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 401.836i | − | 0.954479i | −0.878773 | − | 0.477240i | \(-0.841637\pi\) | ||
0.878773 | − | 0.477240i | \(-0.158363\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 348.000 | + | 200.918i | 0.822695 | + | 0.474983i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.0000 | − | 43.3013i | −0.0588235 | − | 0.101885i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −58.5000 | − | 146.358i | −0.137002 | − | 0.342759i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −204.000 | + | 117.779i | −0.475524 | + | 0.274544i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −700.500 | − | 404.434i | −1.62529 | − | 0.938362i | −0.985473 | − | 0.169835i | \(-0.945677\pi\) |
−0.639817 | − | 0.768527i | \(-0.720990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 410.000 | 0.946882 | 0.473441 | − | 0.880825i | \(-0.343012\pi\) | ||||
0.473441 | + | 0.880825i | \(0.343012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −72.0000 | −0.165517 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.5000 | + | 18.1865i | 0.0720824 | + | 0.0416168i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −424.500 | + | 245.085i | −0.966970 | + | 0.558281i | −0.898311 | − | 0.439360i | \(-0.855205\pi\) |
−0.0686591 | + | 0.997640i | \(0.521872\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −92.0000 | − | 381.051i | −0.208617 | − | 0.864062i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 200.500 | + | 347.276i | 0.452596 | + | 0.783919i | 0.998546 | − | 0.0538983i | \(-0.0171647\pi\) |
−0.545950 | + | 0.837817i | \(0.683831\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 319.500 | + | 184.463i | 0.717978 | + | 0.414525i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.19615i | 0.0116245i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −310.000 | −0.690423 | −0.345212 | − | 0.938525i | \(-0.612193\pi\) | ||||
−0.345212 | + | 0.938525i | \(0.612193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 221.000 | − | 382.783i | 0.490022 | − | 0.848743i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 31.5000 | − | 18.1865i | 0.0695364 | − | 0.0401469i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 468.000 | − | 187.061i | 1.02857 | − | 0.411124i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −83.5000 | − | 144.626i | −0.182713 | − | 0.316469i | 0.760090 | − | 0.649818i | \(-0.225155\pi\) |
−0.942804 | + | 0.333349i | \(0.891821\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 212.500 | − | 368.061i | 0.462963 | − | 0.801875i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8564i | 0.0300573i | 0.999887 | + | 0.0150286i | \(0.00478394\pi\) | ||||
−0.999887 | + | 0.0150286i | \(0.995216\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 609.682i | − | 1.31681i | −0.752665 | − | 0.658404i | \(-0.771232\pi\) | ||
0.752665 | − | 0.658404i | \(-0.228768\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 85.5000 | − | 148.090i | 0.183871 | − | 0.318474i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 392.500 | + | 679.830i | 0.840471 | + | 1.45574i | 0.889497 | + | 0.456941i | \(0.151055\pi\) |
−0.0490258 | + | 0.998798i | \(0.515612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −93.5000 | − | 73.6122i | −0.199360 | − | 0.156956i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −268.500 | + | 155.019i | −0.570064 | + | 0.329126i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −119.000 | + | 206.114i | −0.251586 | + | 0.435759i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0000 | −0.0294737 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 734.390i | 1.53960i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 535.500 | + | 309.171i | 1.11795 | + | 0.645451i | 0.940878 | − | 0.338746i | \(-0.110003\pi\) |
0.177076 | + | 0.984197i | \(0.443336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −60.0000 | − | 103.923i | −0.124740 | − | 0.216056i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 36.0000 | + | 5.19615i | 0.0745342 | + | 0.0107581i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 99.0000 | − | 57.1577i | 0.204124 | − | 0.117851i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −340.500 | − | 196.588i | −0.699179 | − | 0.403671i | 0.107863 | − | 0.994166i | \(-0.465599\pi\) |
−0.807041 | + | 0.590495i | \(0.798933\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.0000 | 0.0347648 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −422.000 | −0.859470 | −0.429735 | − | 0.902955i | \(-0.641393\pi\) | ||||
−0.429735 | + | 0.902955i | \(0.641393\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 300.000 | + | 173.205i | 0.608519 | + | 0.351329i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −612.000 | + | 353.338i | −1.23636 | + | 0.713815i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.5000 | + | 56.2917i | 0.0651303 | + | 0.112809i | 0.896752 | − | 0.442534i | \(-0.145920\pi\) |
−0.831622 | + | 0.555343i | \(0.812587\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | + | 6.92820i | 0.0239521 | + | 0.0138287i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 249.415i | 0.495855i | 0.968779 | + | 0.247928i | \(0.0797496\pi\) | ||||
−0.968779 | + | 0.247928i | \(0.920250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −405.000 | −0.801980 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.5000 | + | 19.9186i | −0.0226824 | + | 0.0392871i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −472.500 | + | 272.798i | −0.928291 | + | 0.535949i | −0.886271 | − | 0.463168i | \(-0.846713\pi\) |
−0.0420202 | + | 0.999117i | \(0.513379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 654.500 | + | 515.285i | 1.28082 | + | 1.00839i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −59.5000 | − | 103.057i | −0.115984 | − | 0.200891i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −418.500 | + | 724.863i | −0.812621 | + | 1.40750i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 853.901i | − | 1.65165i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 105.655i | − | 0.203574i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5000 | − | 21.6506i | 0.0239923 | − | 0.0415559i | −0.853780 | − | 0.520634i | \(-0.825696\pi\) |
0.877772 | + | 0.479078i | \(0.159029\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 296.500 | + | 513.553i | 0.566922 | + | 0.981937i | 0.996868 | + | 0.0790826i | \(0.0251991\pi\) |
−0.429946 | + | 0.902854i | \(0.641468\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.0000 | + | 5.19615i | −0.0247619 | + | 0.00989743i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −712.500 | + | 411.362i | −1.35199 | + | 0.780573i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −251.000 | + | 434.745i | −0.474480 | + | 0.821824i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −440.000 | −0.828625 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 360.267i | − | 0.675922i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −292.500 | − | 168.875i | −0.546729 | − | 0.315654i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −44.5000 | − | 77.0763i | −0.0828678 | − | 0.143531i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −603.500 | + | 574.175i | −1.11967 | + | 1.06526i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 655.500 | − | 378.453i | 1.21165 | − | 0.699544i | 0.248528 | − | 0.968625i | \(-0.420053\pi\) |
0.963117 | + | 0.269081i | \(0.0867200\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 216.000 | + | 124.708i | 0.397790 | + | 0.229664i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −45.0000 | −0.0825688 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −662.000 | −1.21024 | −0.605119 | − | 0.796135i | \(-0.706874\pi\) | ||||
−0.605119 | + | 0.796135i | \(0.706874\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 156.000 | + | 90.0666i | 0.284153 | + | 0.164056i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 84.0000 | − | 48.4974i | 0.152450 | − | 0.0880171i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 193.500 | + | 484.108i | 0.349910 | + | 0.875422i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.5000 | + | 38.9711i | 0.0405405 | + | 0.0702183i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 511.500 | + | 295.315i | 0.918312 | + | 0.530188i | 0.883096 | − | 0.469192i | \(-0.155455\pi\) |
0.0352161 | + | 0.999380i | \(0.488788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 193.990i | 0.347030i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −425.000 | −0.757576 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 368.500 | − | 638.261i | 0.654529 | − | 1.13368i | −0.327482 | − | 0.944857i | \(-0.606200\pi\) |
0.982012 | − | 0.188821i | \(-0.0604665\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −549.000 | + | 316.965i | −0.971681 | + | 0.561001i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 302.500 | + | 238.157i | 0.533510 | + | 0.420030i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 60.5000 | + | 104.789i | 0.106327 | + | 0.184164i | 0.914280 | − | 0.405084i | \(-0.132758\pi\) |
−0.807953 | + | 0.589247i | \(0.799424\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 368.500 | − | 638.261i | 0.645359 | − | 1.11779i | −0.338859 | − | 0.940837i | \(-0.610041\pi\) |
0.984218 | − | 0.176958i | \(-0.0566255\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 216.506i | − | 0.377847i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.3923i | 0.0180736i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.5000 | + | 40.7032i | −0.0407279 | + | 0.0705428i | −0.885671 | − | 0.464314i | \(-0.846301\pi\) |
0.844943 | + | 0.534857i | \(0.179634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.5000 | − | 63.2199i | −0.0630397 | − | 0.109188i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −110.000 | + | 762.102i | −0.189329 | + | 1.31171i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1351.50 | − | 780.289i | 2.31818 | − | 1.33840i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −288.000 | + | 498.831i | −0.492308 | + | 0.852702i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −446.000 | −0.759796 | −0.379898 | − | 0.925028i | \(-0.624041\pi\) | ||||
−0.379898 | + | 0.925028i | \(0.624041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 230.363i | 0.391108i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 180.000 | + | 103.923i | 0.304569 | + | 0.175843i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −107.500 | − | 186.195i | −0.181282 | − | 0.313989i | 0.761036 | − | 0.648710i | \(-0.224691\pi\) |
−0.942317 | + | 0.334721i | \(0.891358\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 900.000 | + | 129.904i | 1.51261 | + | 0.218326i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 55.5000 | − | 32.0429i | 0.0929648 | − | 0.0536733i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −244.500 | − | 141.162i | −0.408180 | − | 0.235663i | 0.281827 | − | 0.959465i | \(-0.409059\pi\) |
−0.690008 | + | 0.723802i | \(0.742393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 266.000 | 0.442596 | 0.221298 | − | 0.975206i | \(-0.428971\pi\) | ||||
0.221298 | + | 0.975206i | \(0.428971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 136.000 | 0.225539 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 756.000 | + | 436.477i | 1.24959 | + | 0.721449i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 571.500 | − | 329.956i | 0.941516 | − | 0.543584i | 0.0510805 | − | 0.998695i | \(-0.483733\pi\) |
0.890435 | + | 0.455110i | \(0.150400\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 60.0000 | − | 76.2102i | 0.0985222 | − | 0.125140i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −348.000 | − | 602.754i | −0.569558 | − | 0.986504i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −604.500 | − | 349.008i | −0.986134 | − | 0.569345i | −0.0820174 | − | 0.996631i | \(-0.526136\pi\) |
−0.904116 | + | 0.427286i | \(0.859470\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 135.100i | 0.219675i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −118.000 | −0.191248 | −0.0956240 | − | 0.995418i | \(-0.530485\pi\) | ||||
−0.0956240 | + | 0.995418i | \(0.530485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −459.500 | + | 795.877i | −0.742326 | + | 1.28575i | 0.209107 | + | 0.977893i | \(0.432944\pi\) |
−0.951434 | + | 0.307854i | \(0.900389\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −76.5000 | + | 44.1673i | −0.123188 | + | 0.0711229i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −461.500 | + | 184.463i | −0.740770 | + | 0.296089i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 335.500 | + | 581.103i | 0.536800 | + | 0.929765i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −59.5000 | + | 103.057i | −0.0948963 | + | 0.164365i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 216.506i | − | 0.344207i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 166.277i | 0.263513i | 0.991282 | + | 0.131757i | \(0.0420617\pi\) | ||||
−0.991282 | + | 0.131757i | \(0.957938\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −151.000 | + | 261.540i | −0.238547 | + | 0.413175i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −432.000 | − | 748.246i | −0.680315 | − | 1.17834i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −192.000 | + | 651.251i | −0.301413 | + | 1.02237i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.500000 | − | 0.866025i | 0.000780031 | − | 0.00135105i | −0.865635 | − | 0.500675i | \(-0.833085\pi\) |
0.866415 | + | 0.499324i | \(0.166418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 514.000 | 0.799378 | 0.399689 | − | 0.916651i | \(-0.369118\pi\) | ||||
0.399689 | + | 0.916651i | \(0.369118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 72.7461i | − | 0.112785i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −52.5000 | − | 30.3109i | −0.0811437 | − | 0.0468484i | 0.458879 | − | 0.888499i | \(-0.348251\pi\) |
−0.540023 | + | 0.841650i | \(0.681584\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 467.500 | + | 809.734i | 0.720339 | + | 1.24766i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 85.5000 | + | 213.908i | 0.131336 | + | 0.328584i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 283.500 | − | 163.679i | 0.434150 | − | 0.250657i | −0.266963 | − | 0.963707i | \(-0.586020\pi\) |
0.701113 | + | 0.713050i | \(0.252687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −76.5000 | − | 44.1673i | −0.116794 | − | 0.0674310i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −952.000 | −1.44901 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −542.000 | −0.822458 | −0.411229 | − | 0.911532i | \(-0.634900\pi\) | ||||
−0.411229 | + | 0.911532i | \(0.634900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1024.50 | − | 591.495i | −1.54992 | − | 0.894849i | −0.998146 | − | 0.0608582i | \(-0.980616\pi\) |
−0.551778 | − | 0.833991i | \(-0.686050\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −300.000 | + | 173.205i | −0.452489 | + | 0.261244i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 157.500 | − | 200.052i | 0.236842 | − | 0.300830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.0000 | − | 62.3538i | −0.0539730 | − | 0.0934840i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −120.000 | − | 69.2820i | −0.179372 | − | 0.103561i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 382.783i | − | 0.570467i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 218.000 | 0.323923 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.0000 | − | 29.4449i | 0.0251852 | − | 0.0436220i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −556.500 | + | 321.295i | −0.822009 | + | 0.474587i | −0.851109 | − | 0.524989i | \(-0.824069\pi\) |
0.0290999 | + | 0.999577i | \(0.490736\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.0000 | + | 152.420i | −0.0324006 | + | 0.224478i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.5000 | + | 47.6314i | 0.0403818 | + | 0.0699433i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −183.500 | + | 317.831i | −0.268668 | + | 0.465346i | −0.968518 | − | 0.248943i | \(-0.919917\pi\) |
0.699850 | + | 0.714289i | \(0.253250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 753.442i | 1.09992i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 327.358i | − | 0.476503i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 636.000 | − | 1101.58i | 0.923077 | − | 1.59882i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 248.500 | + | 430.415i | 0.359624 | + | 0.622887i | 0.987898 | − | 0.155105i | \(-0.0495717\pi\) |
−0.628274 | + | 0.777992i | \(0.716238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 136.000 | − | 942.236i | 0.196248 | − | 1.35965i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −369.000 | + | 213.042i | −0.530935 | + | 0.306536i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 325.000 | − | 562.917i | 0.466284 | − | 0.807628i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 385.000 | 0.550787 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 332.554i | − | 0.474399i | −0.971461 | − | 0.237200i | \(-0.923770\pi\) | ||
0.971461 | − | 0.237200i | \(-0.0762295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −52.5000 | − | 30.3109i | −0.0746799 | − | 0.0431165i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 130.500 | + | 226.033i | 0.185106 | + | 0.320614i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 337.500 | − | 428.683i | 0.477369 | − | 0.606340i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 343.500 | − | 198.320i | 0.484485 | − | 0.279718i | −0.237799 | − | 0.971314i | \(-0.576426\pi\) |
0.722284 | + | 0.691597i | \(0.243092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −516.000 | − | 297.913i | −0.725738 | − | 0.419005i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 171.000 | 0.239832 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1224.00 | 1.71189 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 372.000 | + | 214.774i | 0.518828 | + | 0.299546i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 55.5000 | − | 32.0429i | 0.0771905 | − | 0.0445660i | −0.460908 | − | 0.887448i | \(-0.652476\pi\) |
0.538098 | + | 0.842882i | \(0.319143\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −418.500 | − | 1047.02i | −0.580444 | − | 1.45218i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −72.5000 | − | 125.574i | −0.100277 | − | 0.173684i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.0000 | + | 13.8564i | 0.0331034 | + | 0.0191123i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 55.4256i | − | 0.0762388i | −0.999273 | − | 0.0381194i | \(-0.987863\pi\) | ||
0.999273 | − | 0.0381194i | \(-0.0121367\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −287.000 | −0.393690 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −175.000 | + | 303.109i | −0.239398 | + | 0.414650i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 715.500 | − | 413.094i | 0.976126 | − | 0.563566i | 0.0750273 | − | 0.997181i | \(-0.476096\pi\) |
0.901098 | + | 0.433615i | \(0.142762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 72.0000 | − | 244.219i | 0.0979592 | − | 0.332271i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −144.500 | − | 250.281i | −0.196065 | − | 0.339595i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 356.500 | − | 617.476i | 0.482409 | − | 0.835556i | −0.517387 | − | 0.855751i | \(-0.673095\pi\) |
0.999796 | + | 0.0201950i | \(0.00642870\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 96.9948i | 0.130897i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 637.395i | 0.857866i | 0.903336 | + | 0.428933i | \(0.141110\pi\) | ||||
−0.903336 | + | 0.428933i | \(0.858890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5000 | − | 23.3827i | 0.0181208 | − | 0.0313862i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −440.000 | − | 762.102i | −0.589023 | − | 1.02022i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 422.500 | − | 168.875i | 0.564085 | − | 0.225467i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1012.50 | + | 584.567i | −1.34820 | + | 0.778385i | −0.987995 | − | 0.154487i | \(-0.950627\pi\) |
−0.360208 | + | 0.932872i | \(0.617294\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.0000 | − | 50.2295i | 0.0385126 | − | 0.0667058i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −189.000 | −0.250331 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1039.23i | − | 1.37283i | −0.727211 | − | 0.686414i | \(-0.759184\pi\) | ||
0.727211 | − | 0.686414i | \(-0.240816\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 76.5000 | + | 44.1673i | 0.100791 | + | 0.0581914i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −431.500 | − | 747.380i | −0.567017 | − | 0.982102i | −0.996859 | − | 0.0791982i | \(-0.974764\pi\) |
0.429842 | − | 0.902904i | \(-0.358569\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.5000 | − | 47.6314i | 0.0491481 | − | 0.0624265i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −900.000 | + | 519.615i | −1.17647 | + | 0.679236i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 660.000 | + | 381.051i | 0.860495 | + | 0.496807i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 410.000 | 0.533160 | 0.266580 | − | 0.963813i | \(-0.414106\pi\) | ||||
0.266580 | + | 0.963813i | \(0.414106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −119.000 | −0.154345 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 691.500 | + | 399.238i | 0.894567 | + | 0.516478i | 0.875433 | − | 0.483339i | \(-0.160576\pi\) |
0.0191332 | + | 0.999817i | \(0.493909\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −57.0000 | + | 32.9090i | −0.0735484 | + | 0.0424632i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −60.0000 | − | 8.66025i | −0.0772201 | − | 0.0111458i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −91.0000 | − | 157.617i | −0.116816 | − | 0.202332i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 235.559i | 0.300842i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1611.00 | 2.05223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5000 | + | 26.8468i | −0.0196950 | + | 0.0341128i | −0.875705 | − | 0.482847i | \(-0.839603\pi\) |
0.856010 | + | 0.516959i | \(0.172936\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 283.500 | − | 163.679i | 0.359316 | − | 0.207451i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 122.000 | − | 845.241i | 0.154235 | − | 1.06857i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −156.000 | − | 270.200i | −0.196721 | − | 0.340731i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −238.500 | + | 413.094i | −0.300000 | + | 0.519615i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 595.825i | − | 0.747585i | −0.927512 | − | 0.373793i | \(-0.878057\pi\) | ||
0.927512 | − | 0.373793i | \(-0.121943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1255.74i | − | 1.57164i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 284.000 | − | 491.902i | 0.354557 | − | 0.614110i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1011.50 | + | 1751.97i | 1.25965 | + | 2.18178i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −148.500 | − | 116.913i | −0.184472 | − | 0.145234i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 115.500 | − | 66.6840i | 0.143123 | − | 0.0826319i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 156.500 | − | 271.066i | 0.193449 | − | 0.335063i | −0.752942 | − | 0.658087i | \(-0.771366\pi\) |
0.946391 | + | 0.323024i | \(0.104699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1138.00 | 1.40321 | 0.701603 | − | 0.712568i | \(-0.252468\pi\) | ||||
0.701603 | + | 0.712568i | \(0.252468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 434.745i | 0.534741i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −76.5000 | − | 44.1673i | −0.0938650 | − | 0.0541930i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.0000 | + | 84.8705i | 0.0599755 | + | 0.103881i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −288.000 | − | 720.533i | −0.351648 | − | 0.879772i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1060.50 | + | 612.280i | −1.29172 | + | 0.745773i | −0.978959 | − | 0.204059i | \(-0.934587\pi\) |
−0.312759 | + | 0.949833i | \(0.601253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −100.500 | − | 58.0237i | −0.122114 | − | 0.0705027i | 0.437699 | − | 0.899122i | \(-0.355794\pi\) |
−0.559813 | + | 0.828619i | \(0.689127\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34.0000 | −0.0412121 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 754.000 | 0.911729 | 0.455865 | − | 0.890049i | \(-0.349330\pi\) | ||||
0.455865 | + | 0.890049i | \(0.349330\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −784.500 | − | 452.931i | −0.946321 | − | 0.546359i | −0.0543848 | − | 0.998520i | \(-0.517320\pi\) |
−0.891936 | + | 0.452161i | \(0.850653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 175.500 | − | 101.325i | 0.211191 | − | 0.121931i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −887.500 | + | 844.375i | −1.06543 | + | 1.01366i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.0000 | − | 62.3538i | −0.0431138 | − | 0.0746752i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −484.500 | − | 279.726i | −0.578853 | − | 0.334201i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1053.09i | − | 1.25517i | −0.778548 | − | 0.627585i | \(-0.784044\pi\) | ||
0.778548 | − | 0.627585i | \(-0.215956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 649.000 | 0.771700 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.0000 | − | 64.0859i | 0.0438909 | − | 0.0760212i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 103.500 | − | 59.7558i | 0.122485 | − | 0.0707169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1092.00 | + | 436.477i | −1.28926 | + | 0.515321i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 231.500 | + | 400.970i | 0.272674 | + | 0.472285i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.5000 | + | 38.9711i | −0.0264395 | + | 0.0457945i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 845.241i | 0.990904i | 0.868635 | + | 0.495452i | \(0.164997\pi\) | ||||
−0.868635 | + | 0.495452i | \(0.835003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 290.985i | 0.340333i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −443.500 | + | 768.165i | −0.517503 | + | 0.896341i | 0.482290 | + | 0.876011i | \(0.339805\pi\) |
−0.999793 | + | 0.0203300i | \(0.993528\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −831.500 | − | 1440.20i | −0.967986 | − | 1.67660i | −0.701369 | − | 0.712798i | \(-0.747427\pi\) |
−0.266617 | − | 0.963803i | \(-0.585906\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −143.000 | − | 112.583i | −0.166086 | − | 0.130759i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 487.500 | − | 281.458i | 0.564890 | − | 0.326139i | −0.190216 | − | 0.981742i | \(-0.560919\pi\) |
0.755106 | + | 0.655603i | \(0.227585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −274.500 | + | 475.448i | −0.317341 | + | 0.549651i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −336.000 | −0.387543 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1266.13i | 1.45700i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −204.000 | − | 117.779i | −0.234214 | − | 0.135223i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −88.0000 | − | 152.420i | −0.100802 | − | 0.174594i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −828.000 | − | 119.512i | −0.946286 | − | 0.136585i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 103.500 | − | 59.7558i | 0.118016 | − | 0.0681365i | −0.439830 | − | 0.898081i | \(-0.644961\pi\) |
0.557846 | + | 0.829944i | \(0.311628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 96.0000 | + | 55.4256i | 0.109215 | + | 0.0630553i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −574.000 | −0.651532 | −0.325766 | − | 0.945450i | \(-0.605622\pi\) | ||||
−0.325766 | + | 0.945450i | \(0.605622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1166.00 | −1.32050 | −0.660249 | − | 0.751047i | \(-0.729549\pi\) | ||||
−0.660249 | + | 0.751047i | \(0.729549\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −247.500 | − | 142.894i | −0.279661 | − | 0.161462i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −472.500 | + | 272.798i | −0.532694 | + | 0.307551i | −0.742113 | − | 0.670275i | \(-0.766176\pi\) |
0.209419 | + | 0.977826i | \(0.432843\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1152.00 | + | 166.277i | 1.29584 | + | 0.187038i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 467.500 | + | 809.734i | 0.524691 | + | 0.908792i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −304.500 | − | 175.803i | −0.340985 | − | 0.196868i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 462.458i | 0.516712i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 72.0000 | 0.0802676 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 228.000 | − | 394.908i | 0.253615 | − | 0.439274i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1987.50 | − | 1147.48i | 2.20588 | − | 1.27357i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 77.0000 | + | 60.6218i | 0.0852713 | + | 0.0671338i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −648.000 | − | 1122.37i | −0.716022 | − | 1.24019i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 260.500 | − | 451.199i | 0.287211 | − | 0.497463i | −0.685932 | − | 0.727665i | \(-0.740605\pi\) |
0.973143 | + | 0.230202i | \(0.0739387\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 623.538i | 0.685961i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1191.65i | 1.30807i | 0.756465 | + | 0.654035i | \(0.226925\pi\) | ||||
−0.756465 | + | 0.654035i | \(0.773075\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −935.000 | + | 1619.47i | −1.02410 | + | 1.77379i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 58.5000 | + | 101.325i | 0.0639344 | + | 0.110738i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 110.500 | − | 44.1673i | 0.120502 | − | 0.0481650i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1207.50 | − | 697.150i | 1.31393 | − | 0.758597i | 0.331184 | − | 0.943566i | \(-0.392552\pi\) |
0.982744 | + | 0.184969i | \(0.0592186\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 137.000 | − | 237.291i | 0.148751 | − | 0.257645i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 17.3205i | − | 0.0187249i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1116.00 | + | 644.323i | 1.20388 | + | 0.695062i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 480.500 | + | 832.250i | 0.517223 | + | 0.895856i | 0.999800 | + | 0.0200027i | \(0.00636749\pi\) |
−0.482577 | + | 0.875853i | \(0.660299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 80.5000 | + | 333.420i | 0.0864662 | + | 0.358131i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 43.5000 | − | 25.1147i | 0.0466238 | − | 0.0269183i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1912.50 | + | 1104.18i | 2.04545 | + | 1.18094i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −142.000 | −0.151547 | −0.0757737 | − | 0.997125i | \(-0.524143\pi\) | ||||
−0.0757737 | + | 0.997125i | \(0.524143\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 409.000 | 0.435570 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1060.50 | − | 612.280i | −1.12699 | − | 0.650669i | −0.183816 | − | 0.982961i | \(-0.558845\pi\) |
−0.943177 | + | 0.332291i | \(0.892178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −117.000 | + | 67.5500i | −0.124072 | + | 0.0716331i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 229.500 | + | 574.175i | 0.242857 | + | 0.607592i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −87.5000 | − | 151.554i | −0.0923970 | − | 0.160036i | 0.816122 | − | 0.577879i | \(-0.196120\pi\) |
−0.908519 | + | 0.417843i | \(0.862786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1428.00 | + | 824.456i | 1.50474 | + | 0.868763i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 188.794i | − | 0.198521i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −454.000 | −0.476390 | −0.238195 | − | 0.971217i | \(-0.576556\pi\) | ||||
−0.238195 | + | 0.971217i | \(0.576556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −562.500 | + | 974.279i | −0.589005 | + | 1.02019i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 204.000 | − | 117.779i | 0.213166 | − | 0.123072i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −797.500 | − | 627.868i | −0.831595 | − | 0.654712i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.0000 | + | 105.655i | 0.0634755 | + | 0.109943i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −260.000 | + | 450.333i | −0.269990 | + | 0.467636i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 379.319i | 0.393077i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 720.533i | 0.745122i | 0.928008 | + | 0.372561i | \(0.121520\pi\) | ||||
−0.928008 | + | 0.372561i | \(0.878480\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −87.5000 | + | 151.554i | −0.0902993 | + | 0.156403i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −819.500 | − | 1419.42i | −0.843975 | − | 1.46181i | −0.886508 | − | 0.462713i | \(-0.846876\pi\) |
0.0425329 | − | 0.999095i | \(-0.486457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 82.0000 | − | 568.113i | 0.0842754 | − | 0.583877i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24.0000 | + | 13.8564i | −0.0246154 | + | 0.0142117i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 396.500 | − | 686.758i | 0.405834 | − | 0.702925i | −0.588584 | − | 0.808436i | \(-0.700314\pi\) |
0.994418 | + | 0.105511i | \(0.0336477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1207.00 | −1.23289 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 69.2820i | 0.0706239i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1336.50 | − | 771.629i | −1.35961 | − | 0.784973i | −0.370042 | − | 0.929015i | \(-0.620657\pi\) |
−0.989572 | + | 0.144042i | \(0.953990\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −540.000 | − | 935.307i | −0.548223 | − | 0.949551i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −348.000 | − | 50.2295i | −0.352584 | − | 0.0508911i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.0000 | − | 36.3731i | 0.0637007 | − | 0.0367776i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 775.500 | + | 447.735i | 0.782543 | + | 0.451801i | 0.837331 | − | 0.546697i | \(-0.184115\pi\) |
−0.0547878 | + | 0.998498i | \(0.517448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −295.000 | −0.297080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −333.000 | −0.334673 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −688.500 | − | 397.506i | −0.690572 | − | 0.398702i | 0.113254 | − | 0.993566i | \(-0.463872\pi\) |
−0.803826 | + | 0.594864i | \(0.797206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 127.500 | − | 73.6122i | 0.127628 | − | 0.0736858i |
(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 | 224.3.o.a.207.1 | 2 | ||
4.3 | odd | 2 | 56.3.k.a.11.1 | ✓ | 2 | ||
7.2 | even | 3 | 224.3.o.b.79.1 | 2 | |||
7.3 | odd | 6 | 1568.3.g.f.687.2 | 2 | |||
7.4 | even | 3 | 1568.3.g.c.687.1 | 2 | |||
8.3 | odd | 2 | 224.3.o.b.207.1 | 2 | |||
8.5 | even | 2 | 56.3.k.b.11.1 | yes | 2 | ||
28.3 | even | 6 | 392.3.g.d.99.1 | 2 | |||
28.11 | odd | 6 | 392.3.g.e.99.1 | 2 | |||
28.19 | even | 6 | 392.3.k.c.275.1 | 2 | |||
28.23 | odd | 6 | 56.3.k.b.51.1 | yes | 2 | ||
28.27 | even | 2 | 392.3.k.a.67.1 | 2 | |||
56.3 | even | 6 | 1568.3.g.f.687.1 | 2 | |||
56.5 | odd | 6 | 392.3.k.a.275.1 | 2 | |||
56.11 | odd | 6 | 1568.3.g.c.687.2 | 2 | |||
56.13 | odd | 2 | 392.3.k.c.67.1 | 2 | |||
56.37 | even | 6 | 56.3.k.a.51.1 | yes | 2 | ||
56.45 | odd | 6 | 392.3.g.d.99.2 | 2 | |||
56.51 | odd | 6 | inner | 224.3.o.a.79.1 | 2 | ||
56.53 | even | 6 | 392.3.g.e.99.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.k.a.11.1 | ✓ | 2 | 4.3 | odd | 2 | ||
56.3.k.a.51.1 | yes | 2 | 56.37 | even | 6 | ||
56.3.k.b.11.1 | yes | 2 | 8.5 | even | 2 | ||
56.3.k.b.51.1 | yes | 2 | 28.23 | odd | 6 | ||
224.3.o.a.79.1 | 2 | 56.51 | odd | 6 | inner | ||
224.3.o.a.207.1 | 2 | 1.1 | even | 1 | trivial | ||
224.3.o.b.79.1 | 2 | 7.2 | even | 3 | |||
224.3.o.b.207.1 | 2 | 8.3 | odd | 2 | |||
392.3.g.d.99.1 | 2 | 28.3 | even | 6 | |||
392.3.g.d.99.2 | 2 | 56.45 | odd | 6 | |||
392.3.g.e.99.1 | 2 | 28.11 | odd | 6 | |||
392.3.g.e.99.2 | 2 | 56.53 | even | 6 | |||
392.3.k.a.67.1 | 2 | 28.27 | even | 2 | |||
392.3.k.a.275.1 | 2 | 56.5 | odd | 6 | |||
392.3.k.c.67.1 | 2 | 56.13 | odd | 2 | |||
392.3.k.c.275.1 | 2 | 28.19 | even | 6 | |||
1568.3.g.c.687.1 | 2 | 7.4 | even | 3 | |||
1568.3.g.c.687.2 | 2 | 56.11 | odd | 6 | |||
1568.3.g.f.687.1 | 2 | 56.3 | even | 6 | |||
1568.3.g.f.687.2 | 2 | 7.3 | odd | 6 |