Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,3,Mod(65,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("336.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bn (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: | \(9.15533688251\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-35})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} - 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(2.81174 + 1.04601i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.65 |
Dual form | 336.3.bn.d.305.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.81174 | + | 1.04601i | −0.937246 | + | 0.348669i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.12348 | + | 2.95804i | 1.02470 | + | 0.591608i | 0.915460 | − | 0.402408i | \(-0.131827\pi\) |
0.109235 | + | 0.994016i | \(0.465160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 1.00000 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.81174 | − | 5.88220i | 0.756860 | − | 0.653577i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12348 | + | 2.95804i | −0.465770 | + | 0.268913i | −0.714468 | − | 0.699669i | \(-0.753331\pi\) |
0.248697 | + | 0.968581i | \(0.419998\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.00000 | −0.461538 | −0.230769 | − | 0.973009i | \(-0.574124\pi\) | ||||
−0.230769 | + | 0.973009i | \(0.574124\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −17.5000 | − | 2.95804i | −1.16667 | − | 0.197203i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.12348 | − | 2.95804i | 0.301381 | − | 0.174002i | −0.341682 | − | 0.939816i | \(-0.610997\pi\) |
0.643063 | + | 0.765813i | \(0.277663\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.5000 | − | 19.9186i | 0.605263 | − | 1.04835i | −0.386747 | − | 0.922186i | \(-0.626401\pi\) |
0.992010 | − | 0.126161i | \(-0.0402654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −19.6822 | + | 7.32205i | −0.937246 | + | 0.348669i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.8643 | + | 20.7063i | 1.55932 | + | 0.900273i | 0.997322 | + | 0.0731333i | \(0.0232999\pi\) |
0.561996 | + | 0.827140i | \(0.310033\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | + | 8.66025i | 0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.0000 | + | 23.6643i | −0.481481 | + | 0.876456i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 47.3286i | 1.63202i | 0.578036 | + | 0.816011i | \(0.303819\pi\) | ||||
−0.578036 | + | 0.816011i | \(0.696181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.5000 | + | 33.7750i | 0.629032 | + | 1.08952i | 0.987746 | + | 0.156068i | \(0.0498820\pi\) |
−0.358714 | + | 0.933448i | \(0.616785\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.3117 | − | 13.6764i | 0.342780 | − | 0.414437i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.8643 | + | 20.7063i | 1.02470 | + | 0.591608i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −23.5000 | + | 40.7032i | −0.635135 | + | 1.10009i | 0.351351 | + | 0.936244i | \(0.385722\pi\) |
−0.986486 | + | 0.163843i | \(0.947611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.8704 | − | 6.27604i | 0.432575 | − | 0.160924i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.0000 | 0.511628 | 0.255814 | − | 0.966726i | \(-0.417657\pi\) | ||||
0.255814 | + | 0.966726i | \(0.417657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 52.2995 | − | 9.98789i | 1.16221 | − | 0.221953i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −46.1113 | − | 26.6224i | −0.981091 | − | 0.566433i | −0.0784917 | − | 0.996915i | \(-0.525010\pi\) |
−0.902599 | + | 0.430482i | \(0.858344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.3117 | + | 13.6764i | −0.221799 | + | 0.268165i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 46.1113 | − | 26.6224i | 0.870024 | − | 0.502309i | 0.00266787 | − | 0.999996i | \(-0.499151\pi\) |
0.867356 | + | 0.497688i | \(0.165817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −35.0000 | −0.636364 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.5000 | + | 68.0349i | −0.201754 | + | 1.19360i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −87.0991 | + | 50.2867i | −1.47626 | + | 0.852317i | −0.999641 | − | 0.0267957i | \(-0.991470\pi\) |
−0.476615 | + | 0.879112i | \(0.658136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 40.5000 | − | 70.1481i | 0.663934 | − | 1.14997i | −0.315639 | − | 0.948879i | \(-0.602219\pi\) |
0.979573 | − | 0.201089i | \(-0.0644479\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 47.6822 | − | 41.1754i | 0.756860 | − | 0.653577i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −30.7409 | − | 17.7482i | −0.472936 | − | 0.273050i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.5000 | + | 26.8468i | 0.231343 | + | 0.400698i | 0.958204 | − | 0.286087i | \(-0.0923546\pi\) |
−0.726860 | + | 0.686785i | \(0.759021\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −122.500 | − | 20.7063i | −1.77536 | − | 0.300091i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 94.6573i | − | 1.33320i | −0.745415 | − | 0.666601i | \(-0.767749\pi\) | ||
0.745415 | − | 0.666601i | \(-0.232251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.50000 | + | 14.7224i | 0.116438 | + | 0.201677i | 0.918354 | − | 0.395760i | \(-0.129519\pi\) |
−0.801915 | + | 0.597438i | \(0.796186\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −23.1174 | − | 19.1203i | −0.308232 | − | 0.254938i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −35.8643 | + | 20.7063i | −0.465770 | + | 0.268913i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.50000 | + | 7.79423i | −0.0569620 | + | 0.0986611i | −0.893100 | − | 0.449858i | \(-0.851475\pi\) |
0.836138 | + | 0.548519i | \(0.184808\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.7995 | − | 80.1360i | 0.145673 | − | 0.989333i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 47.3286i | 0.570225i | 0.958494 | + | 0.285112i | \(0.0920309\pi\) | ||||
−0.958494 | + | 0.285112i | \(0.907969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.0000 | 0.411765 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −49.5061 | − | 133.076i | −0.569036 | − | 1.52961i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −76.8521 | − | 44.3706i | −0.863507 | − | 0.498546i | 0.00167806 | − | 0.999999i | \(-0.499466\pi\) |
−0.865185 | + | 0.501453i | \(0.832799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −42.0000 | −0.461538 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −90.1578 | − | 74.5693i | −0.969438 | − | 0.801820i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 117.840 | − | 68.0349i | 1.24042 | − | 0.716157i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 82.0000 | 0.845361 | 0.422680 | − | 0.906279i | \(-0.361089\pi\) | ||||
0.422680 | + | 0.906279i | \(0.361089\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.5000 | + | 50.2867i | −0.176768 | + | 0.507946i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −35.8643 | + | 20.7063i | −0.355092 | + | 0.205013i | −0.666926 | − | 0.745124i | \(-0.732390\pi\) |
0.311833 | + | 0.950137i | \(0.399057\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5000 | − | 19.9186i | 0.111650 | − | 0.193384i | −0.804785 | − | 0.593566i | \(-0.797720\pi\) |
0.916436 | + | 0.400182i | \(0.131053\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −122.500 | − | 20.7063i | −1.16667 | − | 0.197203i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −46.1113 | − | 26.6224i | −0.430947 | − | 0.248807i | 0.268803 | − | 0.963195i | \(-0.413372\pi\) |
−0.699750 | + | 0.714388i | \(0.746705\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 68.5000 | + | 118.645i | 0.628440 | + | 1.08849i | 0.987865 | + | 0.155316i | \(0.0496397\pi\) |
−0.359424 | + | 0.933174i | \(0.617027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.5000 | − | 139.028i | 0.211712 | − | 1.25250i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 94.6573i | − | 0.837675i | −0.908061 | − | 0.418838i | \(-0.862438\pi\) | ||
0.908061 | − | 0.418838i | \(-0.137562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 122.500 | + | 212.176i | 1.06522 | + | 1.84501i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −40.8704 | + | 35.2932i | −0.349320 | + | 0.301651i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 35.8643 | − | 20.7063i | 0.301381 | − | 0.174002i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −43.0000 | + | 74.4782i | −0.355372 | + | 0.615522i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 88.7412i | − | 0.709930i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 78.0000 | 0.614173 | 0.307087 | − | 0.951682i | \(-0.400646\pi\) | ||||
0.307087 | + | 0.951682i | \(0.400646\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −61.8582 | + | 23.0122i | −0.479521 | + | 0.178389i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −128.087 | − | 73.9510i | −0.977762 | − | 0.564511i | −0.0761686 | − | 0.997095i | \(-0.524269\pi\) |
−0.901594 | + | 0.432584i | \(0.857602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 80.5000 | − | 139.430i | 0.605263 | − | 1.04835i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −136.605 | + | 82.7890i | −1.01189 | + | 0.613252i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 87.0991 | − | 50.2867i | 0.635760 | − | 0.367056i | −0.147220 | − | 0.989104i | \(-0.547032\pi\) |
0.782979 | + | 0.622048i | \(0.213699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −106.000 | −0.762590 | −0.381295 | − | 0.924453i | \(-0.624522\pi\) | ||||
−0.381295 | + | 0.924453i | \(0.624522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 157.500 | + | 26.6224i | 1.11702 | + | 0.188811i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30.7409 | − | 17.7482i | 0.214971 | − | 0.124114i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −140.000 | + | 242.487i | −0.965517 | + | 1.67232i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −137.775 | + | 51.2544i | −0.937246 | + | 0.348669i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 169.075 | + | 97.6153i | 1.13473 | + | 0.655136i | 0.945120 | − | 0.326723i | \(-0.105945\pi\) |
0.189609 | + | 0.981860i | \(0.439278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.5000 | − | 35.5070i | −0.135762 | − | 0.235146i | 0.790127 | − | 0.612944i | \(-0.210015\pi\) |
−0.925888 | + | 0.377798i | \(0.876681\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.5000 | − | 50.2867i | 0.114379 | − | 0.328671i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 230.727i | 1.48856i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −83.5000 | − | 144.626i | −0.531847 | − | 0.921186i | −0.999309 | − | 0.0371729i | \(-0.988165\pi\) |
0.467462 | − | 0.884013i | \(-0.345169\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −101.806 | + | 123.088i | −0.640287 | + | 0.774137i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 251.050 | + | 144.944i | 1.55932 | + | 0.900273i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 131.500 | − | 227.765i | 0.806748 | − | 1.39733i | −0.108356 | − | 0.994112i | \(-0.534559\pi\) |
0.915104 | − | 0.403217i | \(-0.132108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 98.4108 | − | 36.6103i | 0.596429 | − | 0.221880i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 189.315i | − | 1.13362i | −0.823849 | − | 0.566810i | \(-0.808177\pi\) | ||
0.823849 | − | 0.566810i | \(-0.191823\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −133.000 | −0.786982 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −38.8300 | − | 203.325i | −0.227076 | − | 1.18904i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −240.803 | − | 139.028i | −1.39193 | − | 0.803629i | −0.398398 | − | 0.917212i | \(-0.630434\pi\) |
−0.993528 | + | 0.113583i | \(0.963767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 35.0000 | + | 60.6218i | 0.200000 | + | 0.346410i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 192.300 | − | 232.499i | 1.08644 | − | 1.31355i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 76.8521 | − | 44.3706i | 0.429342 | − | 0.247880i | −0.269725 | − | 0.962938i | \(-0.586933\pi\) |
0.699066 | + | 0.715057i | \(0.253599\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.0331492 | −0.0165746 | − | 0.999863i | \(-0.505276\pi\) | ||||
−0.0165746 | + | 0.999863i | \(0.505276\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −40.5000 | + | 239.601i | −0.221311 | + | 1.30930i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −240.803 | + | 139.028i | −1.30164 | + | 0.751502i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5000 | + | 30.3109i | −0.0935829 | + | 0.162090i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −91.0000 | + | 165.650i | −0.481481 | + | 0.876456i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −46.1113 | − | 26.6224i | −0.241420 | − | 0.139384i | 0.374409 | − | 0.927264i | \(-0.377846\pi\) |
−0.615829 | + | 0.787880i | \(0.711179\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −71.5000 | − | 123.842i | −0.370466 | − | 0.641666i | 0.619171 | − | 0.785256i | \(-0.287469\pi\) |
−0.989637 | + | 0.143590i | \(0.954135\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 105.000 | + | 17.7482i | 0.538462 | + | 0.0910166i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 47.3286i | − | 0.240247i | −0.992759 | − | 0.120123i | \(-0.961671\pi\) | ||
0.992759 | − | 0.120123i | \(-0.0383290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −84.5000 | − | 146.358i | −0.424623 | − | 0.735469i | 0.571762 | − | 0.820420i | \(-0.306260\pi\) |
−0.996385 | + | 0.0849507i | \(0.972927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −71.6639 | − | 59.2730i | −0.356537 | − | 0.294891i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 331.300i | 1.63202i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 366.097 | − | 69.9153i | 1.76858 | − | 0.337755i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 136.070i | 0.651052i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 166.000 | 0.786730 | 0.393365 | − | 0.919382i | \(-0.371311\pi\) | ||||
0.393365 | + | 0.919382i | \(0.371311\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 99.0122 | + | 266.151i | 0.464846 | + | 1.24954i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 112.716 | + | 65.0769i | 0.524263 | + | 0.302683i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 136.500 | + | 236.425i | 0.629032 | + | 1.08952i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −39.2995 | − | 32.5046i | −0.179450 | − | 0.148423i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.7409 | + | 17.7482i | −0.139099 | + | 0.0803088i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 142.000 | 0.636771 | 0.318386 | − | 0.947961i | \(-0.396859\pi\) | ||||
0.318386 | + | 0.947961i | \(0.396859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 85.0000 | + | 29.5804i | 0.377778 | + | 0.131468i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 76.8521 | − | 44.3706i | 0.338556 | − | 0.195465i | −0.321077 | − | 0.947053i | \(-0.604045\pi\) |
0.659633 | + | 0.751588i | \(0.270712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 128.500 | − | 222.569i | 0.561135 | − | 0.971915i | −0.436262 | − | 0.899820i | \(-0.643698\pi\) |
0.997398 | − | 0.0720955i | \(-0.0229686\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 79.1822 | − | 95.7350i | 0.342780 | − | 0.414437i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −158.828 | − | 91.6992i | −0.681664 | − | 0.393559i | 0.118818 | − | 0.992916i | \(-0.462090\pi\) |
−0.800482 | + | 0.599357i | \(0.795423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −157.500 | − | 272.798i | −0.670213 | − | 1.16084i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.50000 | − | 26.6224i | 0.0189873 | − | 0.112331i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 283.972i | 1.18817i | 0.804404 | + | 0.594083i | \(0.202485\pi\) | ||||
−0.804404 | + | 0.594083i | \(0.797515\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.00207469 | + | 0.00359347i | 0.867061 | − | 0.498202i | \(-0.166006\pi\) |
−0.864986 | + | 0.501796i | \(0.832673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 50.6456 | + | 237.664i | 0.208418 | + | 0.978040i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 251.050 | + | 144.944i | 1.02470 | + | 0.591608i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −69.0000 | + | 119.512i | −0.279352 | + | 0.483852i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −49.5061 | − | 133.076i | −0.198820 | − | 0.534441i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 141.986i | − | 0.565681i | −0.959167 | − | 0.282840i | \(-0.908723\pi\) | ||
0.959167 | − | 0.282840i | \(-0.0912767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −245.000 | −0.968379 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −98.4108 | + | 36.6103i | −0.385925 | + | 0.143570i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 169.075 | + | 97.6153i | 0.657878 | + | 0.379826i | 0.791468 | − | 0.611211i | \(-0.209317\pi\) |
−0.133590 | + | 0.991037i | \(0.542650\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −164.500 | + | 284.922i | −0.635135 | + | 1.10009i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 278.396 | + | 322.390i | 1.06665 | + | 1.23521i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −46.1113 | + | 26.6224i | −0.175328 | + | 0.101226i | −0.585096 | − | 0.810964i | \(-0.698943\pi\) |
0.409768 | + | 0.912190i | \(0.365610\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 315.000 | 1.18868 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 262.500 | + | 44.3706i | 0.983146 | + | 0.166182i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −35.8643 | + | 20.7063i | −0.133325 | + | 0.0769750i | −0.565179 | − | 0.824968i | \(-0.691193\pi\) |
0.431854 | + | 0.901943i | \(0.357860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 43.5000 | − | 75.3442i | 0.160517 | − | 0.278023i | −0.774537 | − | 0.632528i | \(-0.782017\pi\) |
0.935054 | + | 0.354505i | \(0.115351\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 118.093 | − | 43.9323i | 0.432575 | − | 0.160924i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −51.2348 | − | 29.5804i | −0.186308 | − | 0.107565i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −155.500 | − | 269.334i | −0.561372 | − | 0.972325i | −0.997377 | − | 0.0723804i | \(-0.976940\pi\) |
0.436005 | − | 0.899944i | \(-0.356393\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 331.500 | + | 115.364i | 1.18817 | + | 0.413489i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 378.629i | 1.34743i | 0.738989 | + | 0.673717i | \(0.235303\pi\) | ||||
−0.738989 | + | 0.673717i | \(0.764697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 159.500 | + | 276.262i | 0.563604 | + | 0.976191i | 0.997178 | + | 0.0750731i | \(0.0239190\pi\) |
−0.433574 | + | 0.901118i | \(0.642748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −260.170 | + | 314.558i | −0.912877 | + | 1.10371i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −127.000 | + | 219.970i | −0.439446 | + | 0.761143i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −230.562 | + | 85.7726i | −0.792311 | + | 0.294751i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 141.986i | − | 0.484594i | −0.970202 | − | 0.242297i | \(-0.922099\pi\) | ||
0.970202 | − | 0.242297i | \(-0.0779008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −595.000 | −2.01695 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.39482 | − | 159.698i | −0.0114304 | − | 0.537704i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −215.186 | − | 124.238i | −0.719686 | − | 0.415511i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 154.000 | 0.511628 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 79.1822 | − | 95.7350i | 0.261327 | − | 0.315957i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 415.002 | − | 239.601i | 1.36066 | − | 0.785578i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −442.000 | −1.43974 | −0.719870 | − | 0.694109i | \(-0.755798\pi\) | ||||
−0.719870 | + | 0.694109i | \(0.755798\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.5000 | + | 68.0349i | −0.0372168 | + | 0.220178i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −210.062 | + | 121.280i | −0.675442 | + | 0.389967i | −0.798136 | − | 0.602478i | \(-0.794180\pi\) |
0.122693 | + | 0.992445i | \(0.460847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 128.500 | − | 222.569i | 0.410543 | − | 0.711082i | −0.584406 | − | 0.811461i | \(-0.698672\pi\) |
0.994949 | + | 0.100380i | \(0.0320058\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 366.097 | − | 69.9153i | 1.16221 | − | 0.221953i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −76.8521 | − | 44.3706i | −0.242436 | − | 0.139970i | 0.373860 | − | 0.927485i | \(-0.378034\pi\) |
−0.616296 | + | 0.787515i | \(0.711367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −140.000 | − | 242.487i | −0.438871 | − | 0.760148i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 157.500 | + | 26.6224i | 0.490654 | + | 0.0829357i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 136.070i | − | 0.421269i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −30.0000 | − | 51.9615i | −0.0923077 | − | 0.159882i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −316.708 | − | 261.948i | −0.968526 | − | 0.801066i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −322.779 | − | 186.357i | −0.981091 | − | 0.566433i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −60.5000 | + | 104.789i | −0.182779 | + | 0.316583i | −0.942826 | − | 0.333285i | \(-0.891843\pi\) |
0.760047 | + | 0.649869i | \(0.225176\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 79.3483 | + | 415.491i | 0.238283 | + | 1.24772i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 183.398i | 0.547458i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −78.0000 | −0.231454 | −0.115727 | − | 0.993281i | \(-0.536920\pi\) | ||||
−0.115727 | + | 0.993281i | \(0.536920\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 99.0122 | + | 266.151i | 0.292071 | + | 0.785107i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −199.816 | − | 115.364i | −0.585969 | − | 0.338310i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −566.376 | − | 468.448i | −1.64167 | − | 1.35782i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 568.706 | − | 328.342i | 1.63892 | − | 0.946232i | 0.657716 | − | 0.753266i | \(-0.271523\pi\) |
0.981205 | − | 0.192966i | \(-0.0618106\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −422.000 | −1.20917 | −0.604585 | − | 0.796541i | \(-0.706661\pi\) | ||||
−0.604585 | + | 0.796541i | \(0.706661\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 78.0000 | − | 141.986i | 0.222222 | − | 0.404518i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 169.075 | − | 97.6153i | 0.478965 | − | 0.276531i | −0.241020 | − | 0.970520i | \(-0.577482\pi\) |
0.719985 | + | 0.693990i | \(0.244149\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 280.000 | − | 484.974i | 0.788732 | − | 1.36612i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −79.1822 | + | 95.7350i | −0.221799 | + | 0.268165i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 117.840 | + | 68.0349i | 0.328245 | + | 0.189512i | 0.655062 | − | 0.755575i | \(-0.272643\pi\) |
−0.326817 | + | 0.945088i | \(0.605976\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −84.0000 | − | 145.492i | −0.232687 | − | 0.403026i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 43.0000 | − | 254.391i | 0.118457 | − | 0.700803i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 100.573i | 0.275543i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.5000 | − | 63.2199i | −0.0994550 | − | 0.172261i | 0.812004 | − | 0.583652i | \(-0.198377\pi\) |
−0.911459 | + | 0.411390i | \(0.865043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 322.779 | − | 186.357i | 0.870024 | − | 0.502309i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 200.500 | − | 347.276i | 0.537534 | − | 0.931035i | −0.461503 | − | 0.887139i | \(-0.652689\pi\) |
0.999036 | − | 0.0438965i | \(-0.0139772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 92.8239 | + | 249.517i | 0.247530 | + | 0.665379i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 283.972i | − | 0.753241i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −538.000 | −1.41953 | −0.709763 | − | 0.704441i | \(-0.751198\pi\) | ||||
−0.709763 | + | 0.704441i | \(0.751198\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −219.316 | + | 81.5886i | −0.575631 | + | 0.214143i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −210.062 | − | 121.280i | −0.548466 | − | 0.316657i | 0.200037 | − | 0.979788i | \(-0.435894\pi\) |
−0.748503 | + | 0.663131i | \(0.769227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −245.000 | −0.636364 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 149.858 | − | 129.408i | 0.387231 | − | 0.334388i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.8643 | + | 20.7063i | −0.0921962 | + | 0.0532295i | −0.545389 | − | 0.838183i | \(-0.683618\pi\) |
0.453193 | + | 0.891412i | \(0.350285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 245.000 | 0.626598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 437.500 | + | 73.9510i | 1.11323 | + | 0.188170i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −46.1113 | + | 26.6224i | −0.116737 | + | 0.0673984i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5000 | − | 28.5788i | 0.0415617 | − | 0.0719870i | −0.844496 | − | 0.535561i | \(-0.820100\pi\) |
0.886058 | + | 0.463574i | \(0.153433\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −80.5000 | + | 476.244i | −0.201754 | + | 1.19360i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −322.779 | − | 186.357i | −0.804935 | − | 0.464729i | 0.0402588 | − | 0.999189i | \(-0.487182\pi\) |
−0.845194 | + | 0.534460i | \(0.820515\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −117.000 | − | 202.650i | −0.290323 | − | 0.502853i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 297.500 | − | 375.671i | 0.734568 | − | 0.927583i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 278.056i | − | 0.683184i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 288.500 | + | 499.697i | 0.705379 | + | 1.22175i | 0.966555 | + | 0.256461i | \(0.0825565\pi\) |
−0.261176 | + | 0.965291i | \(0.584110\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −192.300 | + | 232.499i | −0.467882 | + | 0.565692i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −609.694 | + | 352.007i | −1.47626 | + | 0.852317i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −140.000 | + | 242.487i | −0.337349 | + | 0.584306i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 298.044 | − | 110.877i | 0.714734 | − | 0.265892i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 141.986i | − | 0.338869i | −0.985541 | − | 0.169434i | \(-0.945806\pi\) | ||
0.985541 | − | 0.169434i | \(-0.0541940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −246.000 | −0.584323 | −0.292162 | − | 0.956369i | \(-0.594374\pi\) | ||||
−0.292162 | + | 0.956369i | \(0.594374\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −470.696 | + | 89.8911i | −1.11276 | + | 0.212508i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 51.2348 | + | 29.5804i | 0.120552 | + | 0.0696009i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 283.500 | − | 491.036i | 0.663934 | − | 1.14997i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −67.8704 | + | 82.0585i | −0.158206 | + | 0.191279i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −537.965 | + | 310.594i | −1.24818 | + | 0.720636i | −0.970746 | − | 0.240109i | \(-0.922817\pi\) |
−0.277433 | + | 0.960745i | \(0.589483\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −622.000 | −1.43649 | −0.718245 | − | 0.695790i | \(-0.755054\pi\) | ||||
−0.718245 | + | 0.695790i | \(0.755054\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 140.000 | − | 828.251i | 0.321839 | − | 1.90403i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 824.880 | − | 476.244i | 1.88760 | − | 1.08980i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −124.500 | + | 215.640i | −0.283599 | + | 0.491208i | −0.972268 | − | 0.233867i | \(-0.924862\pi\) |
0.688669 | + | 0.725075i | \(0.258195\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 333.775 | − | 288.228i | 0.756860 | − | 0.653577i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −210.062 | − | 121.280i | −0.474182 | − | 0.273769i | 0.243807 | − | 0.969824i | \(-0.421604\pi\) |
−0.717989 | + | 0.696055i | \(0.754937\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −262.500 | − | 454.663i | −0.589888 | − | 1.02172i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −577.500 | − | 97.6153i | −1.29195 | − | 0.218379i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 473.286i | 1.05409i | 0.849837 | + | 0.527045i | \(0.176700\pi\) | ||||
−0.849837 | + | 0.527045i | \(0.823300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 94.7812 | + | 78.3933i | 0.209230 | + | 0.173054i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −215.186 | − | 124.238i | −0.472936 | − | 0.273050i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −303.500 | + | 525.677i | −0.664114 | + | 1.15028i | 0.315411 | + | 0.948955i | \(0.397858\pi\) |
−0.979525 | + | 0.201324i | \(0.935476\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.39482 | + | 159.698i | 0.00739612 | + | 0.347926i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 520.615i | − | 1.12932i | −0.825325 | − | 0.564658i | \(-0.809008\pi\) | ||
0.825325 | − | 0.564658i | \(-0.190992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 302.000 | 0.652268 | 0.326134 | − | 0.945324i | \(-0.394254\pi\) | ||||
0.326134 | + | 0.945324i | \(0.394254\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −241.342 | − | 648.744i | −0.519016 | − | 1.39515i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −128.087 | − | 73.9510i | −0.274276 | − | 0.158353i | 0.356553 | − | 0.934275i | \(-0.383952\pi\) |
−0.630829 | + | 0.775922i | \(0.717285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 108.500 | + | 187.928i | 0.231343 | + | 0.400698i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 386.060 | + | 319.309i | 0.819661 | + | 0.677939i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −112.716 | + | 65.0769i | −0.238301 | + | 0.137583i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 230.000 | 0.484211 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 157.500 | − | 452.580i | 0.330189 | − | 0.948805i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −128.087 | + | 73.9510i | −0.267405 | + | 0.154386i | −0.627708 | − | 0.778449i | \(-0.716007\pi\) |
0.360303 | + | 0.932835i | \(0.382673\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 141.000 | − | 244.219i | 0.293139 | − | 0.507732i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −857.500 | − | 144.944i | −1.77536 | − | 0.300091i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 420.125 | + | 242.559i | 0.866237 | + | 0.500122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 323.500 | + | 560.318i | 0.664271 | + | 1.15055i | 0.979482 | + | 0.201530i | \(0.0645913\pi\) |
−0.315211 | + | 0.949021i | \(0.602075\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −131.500 | + | 777.964i | −0.268916 | + | 1.59093i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 141.986i | − | 0.289177i | −0.989492 | − | 0.144589i | \(-0.953814\pi\) | ||
0.989492 | − | 0.144589i | \(-0.0461858\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 140.000 | + | 242.487i | 0.283976 | + | 0.491860i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −238.411 | + | 205.877i | −0.481638 | + | 0.415913i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 662.601i | − | 1.33320i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 51.5000 | − | 89.2006i | 0.103206 | − | 0.178759i | −0.809798 | − | 0.586709i | \(-0.800423\pi\) |
0.913004 | + | 0.407951i | \(0.133756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 198.024 | + | 532.303i | 0.395258 | + | 1.06248i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 283.972i | 0.564556i | 0.959333 | + | 0.282278i | \(0.0910901\pi\) | ||||
−0.959333 | + | 0.282278i | \(0.908910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −245.000 | −0.485149 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 373.961 | − | 139.119i | 0.737596 | − | 0.274396i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 169.075 | + | 97.6153i | 0.332170 | + | 0.191779i | 0.656804 | − | 0.754061i | \(-0.271908\pi\) |
−0.324634 | + | 0.945840i | \(0.605241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 59.5000 | + | 103.057i | 0.116438 | + | 0.201677i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 321.860 | + | 531.081i | 0.627407 | + | 1.03525i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 117.840 | − | 68.0349i | 0.228815 | − | 0.132107i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 315.000 | 0.609284 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 822.500 | + | 139.028i | 1.58478 | + | 0.267876i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −322.779 | + | 186.357i | −0.619537 | + | 0.357690i | −0.776689 | − | 0.629884i | \(-0.783102\pi\) |
0.157152 | + | 0.987575i | \(0.449769\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.5000 | − | 19.9186i | 0.0219885 | − | 0.0380852i | −0.854822 | − | 0.518922i | \(-0.826334\pi\) |
0.876810 | + | 0.480836i | \(0.159667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −161.822 | − | 133.842i | −0.308232 | − | 0.254938i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 199.816 | + | 115.364i | 0.379157 | + | 0.218906i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 593.000 | + | 1027.11i | 1.12098 | + | 1.94160i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −297.500 | + | 854.874i | −0.560264 | + | 1.60993i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −157.500 | − | 272.798i | −0.294393 | − | 0.509903i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −169.676 | + | 205.146i | −0.315970 | + | 0.382023i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −251.050 | + | 144.944i | −0.465770 | + | 0.268913i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 256.500 | − | 444.271i | 0.474122 | − | 0.821203i | −0.525439 | − | 0.850831i | \(-0.676099\pi\) |
0.999561 | + | 0.0296279i | \(0.00943223\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.8704 | − | 6.27604i | 0.0310689 | − | 0.0115581i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 810.503i | 1.48716i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 54.0000 | 0.0987203 | 0.0493601 | − | 0.998781i | \(-0.484282\pi\) | ||||
0.0493601 | + | 0.998781i | \(0.484282\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −136.749 | − | 716.059i | −0.249088 | − | 1.30430i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 942.719 | + | 544.279i | 1.71092 | + | 0.987803i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.5000 | + | 54.5596i | −0.0569620 | + | 0.0986611i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 531.652 | − | 642.792i | 0.957931 | − | 1.15818i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −773.645 | + | 446.664i | −1.38895 | + | 0.801910i | −0.993197 | − | 0.116447i | \(-0.962849\pi\) |
−0.395752 | + | 0.918357i | \(0.629516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −132.000 | −0.236136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.5000 | − | 103.531i | 0.0311943 | − | 0.184548i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 486.730 | − | 281.014i | 0.864530 | − | 0.499136i | −0.000996920 | − | 1.00000i | \(-0.500317\pi\) |
0.865527 | + | 0.500863i | \(0.166984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 280.000 | − | 484.974i | 0.495575 | − | 0.858361i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 82.5968 | − | 560.952i | 0.145673 | − | 0.989333i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −568.706 | − | 328.342i | −0.999483 | − | 0.577052i | −0.0913876 | − | 0.995815i | \(-0.529130\pi\) |
−0.908095 | + | 0.418764i | \(0.862464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 463.500 | + | 802.806i | 0.811734 | + | 1.40596i | 0.911650 | + | 0.410968i | \(0.134809\pi\) |
−0.0999158 | + | 0.994996i | \(0.531857\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 157.500 | + | 26.6224i | 0.274869 | + | 0.0464614i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 414.126i | 0.720218i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 176.500 | + | 305.707i | 0.305893 | + | 0.529821i | 0.977460 | − | 0.211122i | \(-0.0677118\pi\) |
−0.671567 | + | 0.740944i | \(0.734379\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 330.578 | + | 273.421i | 0.570947 | + | 0.472229i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 331.300i | 0.570225i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −157.500 | + | 272.798i | −0.270154 | + | 0.467921i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −313.797 | + | 59.9274i | −0.536406 | + | 0.102440i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 236.643i | − | 0.403140i | −0.979474 | − | 0.201570i | \(-0.935396\pi\) | ||
0.979474 | − | 0.201570i | \(-0.0646044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 897.000 | 1.52292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 49.5061 | + | 133.076i | 0.0837667 | + | 0.225170i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 660.928 | + | 381.587i | 1.11455 | + | 0.643486i | 0.940004 | − | 0.341163i | \(-0.110821\pi\) |
0.174546 | + | 0.984649i | \(0.444154\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 245.000 | 0.411765 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 390.684 | + | 323.134i | 0.654412 | + | 0.541262i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −537.965 | + | 310.594i | −0.898105 | + | 0.518521i | −0.876585 | − | 0.481247i | \(-0.840184\pi\) |
−0.0215201 | + | 0.999768i | \(0.506851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −958.000 | −1.59401 | −0.797005 | − | 0.603973i | \(-0.793584\pi\) | ||||
−0.797005 | + | 0.603973i | \(0.793584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 263.500 | + | 91.6992i | 0.436982 | + | 0.152072i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −440.619 | + | 254.391i | −0.728296 | + | 0.420482i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 403.500 | − | 698.883i | 0.664745 | − | 1.15137i | −0.314610 | − | 0.949221i | \(-0.601874\pi\) |
0.979354 | − | 0.202150i | \(-0.0647930\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −346.543 | − | 931.530i | −0.569036 | − | 1.52961i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 276.668 | + | 159.734i | 0.452811 | + | 0.261431i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −259.500 | − | 449.467i | −0.423328 | − | 0.733225i | 0.572935 | − | 0.819601i | \(-0.305805\pi\) |
−0.996263 | + | 0.0863756i | \(0.972472\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 757.258i | − | 1.22732i | −0.789569 | − | 0.613661i | \(-0.789696\pi\) | ||
0.789569 | − | 0.613661i | \(-0.210304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −344.500 | − | 596.692i | −0.556543 | − | 0.963960i | −0.997782 | − | 0.0665707i | \(-0.978794\pi\) |
0.441239 | − | 0.897390i | \(-0.354539\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −956.236 | + | 579.523i | −1.53983 | + | 0.933210i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −537.965 | − | 310.594i | −0.863507 | − | 0.498546i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 387.500 | − | 671.170i | 0.620000 | − | 1.07387i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −142.330 | − | 382.593i | −0.227002 | − | 0.610196i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 278.056i | 0.442060i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −674.000 | −1.06815 | −0.534073 | − | 0.845438i | \(-0.679339\pi\) | ||||
−0.534073 | + | 0.845438i | \(0.679339\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −466.748 | + | 173.637i | −0.737359 | + | 0.274308i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 399.631 | + | 230.727i | 0.629340 | + | 0.363350i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −294.000 | −0.461538 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −556.793 | − | 644.781i | −0.871350 | − | 1.00905i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 742.904 | − | 428.916i | 1.15898 | − | 0.669135i | 0.207918 | − | 0.978146i | \(-0.433331\pi\) |
0.951059 | + | 0.309011i | \(0.0999980\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −218.000 | −0.339036 | −0.169518 | − | 0.985527i | \(-0.554221\pi\) | ||||
−0.169518 | + | 0.985527i | \(0.554221\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −385.000 | − | 65.0769i | −0.596899 | − | 0.100894i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 445.742 | − | 257.349i | 0.688937 | − | 0.397758i | −0.114277 | − | 0.993449i | \(-0.536455\pi\) |
0.803214 | + | 0.595691i | \(0.203122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 297.500 | − | 515.285i | 0.458398 | − | 0.793968i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −631.104 | − | 521.985i | −0.969438 | − | 0.801820i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 906.855 | + | 523.573i | 1.38875 | + | 0.801796i | 0.993175 | − | 0.116636i | \(-0.0372112\pi\) |
0.395577 | + | 0.918433i | \(0.370544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −437.500 | − | 757.772i | −0.667939 | − | 1.15690i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 144.500 | + | 50.2867i | 0.219939 | + | 0.0765398i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 615.272i | 0.933645i | 0.884351 | + | 0.466823i | \(0.154601\pi\) | ||||
−0.884351 | + | 0.466823i | \(0.845399\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 260.500 | + | 451.199i | 0.394100 | + | 0.682601i | 0.992986 | − | 0.118233i | \(-0.0377231\pi\) |
−0.598886 | + | 0.800834i | \(0.704390\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 67.8704 | − | 82.0585i | 0.102369 | − | 0.123769i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 824.880 | − | 476.244i | 1.24042 | − | 0.716157i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −980.000 | + | 1697.41i | −1.46927 | + | 2.54484i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −399.267 | + | 148.533i | −0.596811 | + | 0.222022i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 479.202i | 0.714162i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 818.000 | 1.21545 | 0.607727 | − | 0.794146i | \(-0.292082\pi\) | ||||
0.607727 | + | 0.794146i | \(0.292082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −269.939 | + | 5.73829i | −0.399910 | + | 0.00850118i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 660.928 | + | 381.587i | 0.976260 | + | 0.563644i | 0.901139 | − | 0.433530i | \(-0.142732\pi\) |
0.0751214 | + | 0.997174i | \(0.476066\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 574.000 | 0.845361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −169.676 | + | 205.146i | −0.249157 | + | 0.301243i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −169.075 | + | 97.6153i | −0.247547 | + | 0.142921i | −0.618641 | − | 0.785674i | \(-0.712316\pi\) |
0.371093 | + | 0.928596i | \(0.378983\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 595.000 | 0.868613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −128.500 | + | 760.216i | −0.187045 | + | 1.10657i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −276.668 | + | 159.734i | −0.401550 | + | 0.231835i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 179.500 | − | 310.903i | 0.259768 | − | 0.449932i | −0.706411 | − | 0.707802i | \(-0.749687\pi\) |
0.966180 | + | 0.257869i | \(0.0830204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −122.500 | + | 352.007i | −0.176768 | + | 0.507946i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −543.088 | − | 313.552i | −0.781422 | − | 0.451154i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 542.500 | + | 91.6992i | 0.776109 | + | 0.131186i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 804.587i | − | 1.14777i | −0.818936 | − | 0.573885i | \(-0.805436\pi\) | ||
0.818936 | − | 0.573885i | \(-0.194564\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 540.500 | + | 936.173i | 0.768848 | + | 1.33168i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 728.197 | + | 602.290i | 1.03290 | + | 0.854312i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −251.050 | + | 144.944i | −0.355092 | + | 0.205013i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −215.500 | + | 373.257i | −0.303949 | + | 0.526455i | −0.977027 | − | 0.213116i | \(-0.931639\pi\) |
0.673078 | + | 0.739572i | \(0.264972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.1944 | + | 79.5621i | 0.0213704 | + | 0.111902i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1615.09i | 2.26520i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 210.000 | 0.293706 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −297.037 | − | 798.454i | −0.414277 | − | 1.11360i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 199.816 | + | 115.364i | 0.277908 | + | 0.160450i | 0.632476 | − | 0.774580i | \(-0.282039\pi\) |
−0.354568 | + | 0.935030i | \(0.615372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 80.5000 | − | 139.430i | 0.111650 | − | 0.193384i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.31174 | − | 1.91203i | −0.00319742 | − | 0.00264458i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −409.878 | + | 236.643i | −0.565349 | + | 0.326404i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 734.000 | 1.00963 | 0.504814 | − | 0.863228i | \(-0.331561\pi\) | ||||
0.504814 | + | 0.863228i | \(0.331561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −391.000 | − | 615.272i | −0.536351 | − | 0.843995i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 112.716 | − | 65.0769i | 0.154195 | − | 0.0890245i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −151.500 | + | 262.406i | −0.206685 | + | 0.357989i | −0.950668 | − | 0.310209i | \(-0.899601\pi\) |
0.743983 | + | 0.668198i | \(0.232934\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −857.500 | − | 144.944i | −1.16667 | − | 0.197203i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −158.828 | − | 91.6992i | −0.215506 | − | 0.124422i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 295.500 | + | 511.821i | 0.399865 | + | 0.692586i | 0.993709 | − | 0.111994i | \(-0.0357238\pi\) |
−0.593844 | + | 0.804580i | \(0.702390\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 69.0000 | − | 408.210i | 0.0931174 | − | 0.550890i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 851.915i | − | 1.14659i | −0.819349 | − | 0.573294i | \(-0.805665\pi\) | ||
0.819349 | − | 0.573294i | \(-0.194335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 577.500 | + | 1000.26i | 0.775168 | + | 1.34263i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 278.396 | + | 322.390i | 0.372686 | + | 0.431580i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −322.779 | − | 186.357i | −0.430947 | − | 0.248807i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 499.500 | − | 865.159i | 0.665113 | − | 1.15201i | −0.314141 | − | 0.949376i | \(-0.601717\pi\) |
0.979255 | − | 0.202634i | \(-0.0649501\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 148.518 | + | 399.227i | 0.197235 | + | 0.530182i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 242.559i | − | 0.321271i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1398.00 | −1.84676 | −0.923382 | − | 0.383883i | \(-0.874587\pi\) | ||||
−0.923382 | + | 0.383883i | \(0.874587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 688.876 | − | 256.272i | 0.907610 | − | 0.337644i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1142.54 | − | 659.643i | −1.50136 | − | 0.866811i | −0.999999 | − | 0.00157261i | \(-0.999499\pi\) |
−0.501361 | − | 0.865238i | \(-0.667167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 479.500 | + | 830.518i | 0.628440 | + | 1.08849i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 238.411 | − | 205.877i | 0.311648 | − | 0.269120i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 522.594 | − | 301.720i | 0.681349 | − | 0.393377i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 946.000 | 1.23017 | 0.615085 | − | 0.788461i | \(-0.289122\pi\) | ||||
0.615085 | + | 0.788461i | \(0.289122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −577.500 | − | 97.6153i | −0.749027 | − | 0.126609i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 455.989 | − | 263.266i | 0.589896 | − | 0.340576i | −0.175161 | − | 0.984540i | \(-0.556044\pi\) |
0.765056 | + | 0.643963i | \(0.222711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −195.000 | + | 337.750i | −0.251613 | + | 0.435806i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 164.500 | − | 973.195i | 0.211712 | − | 1.25250i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 280.000 | + | 484.974i | 0.358515 | + | 0.620966i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1120.00 | − | 615.272i | −1.43040 | − | 0.785788i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 987.985i | − | 1.25858i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 223.500 | + | 387.113i | 0.283990 | + | 0.491885i | 0.972364 | − | 0.233471i | \(-0.0750085\pi\) |
−0.688374 | + | 0.725356i | \(0.741675\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 101.806 | − | 123.088i | 0.129031 | − | 0.156005i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 662.601i | − | 0.837675i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −243.000 | + | 420.888i | −0.306431 | + | 0.530755i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −885.697 | + | 329.492i | −1.11408 | + | 0.414456i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1277.87i | − | 1.60335i | −0.597757 | − | 0.801677i | \(-0.703941\pi\) | ||
0.597757 | − | 0.801677i | \(-0.296059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −315.000 | −0.394243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −784.493 | + | 149.818i | −0.979392 | + | 0.187039i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −87.0991 | − | 50.2867i | −0.108467 | − | 0.0626235i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 857.500 | + | 1485.23i | 1.06522 | + | 1.84501i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 79.1822 | − | 95.7350i | 0.0981192 | − | 0.118631i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1142.54 | + | 659.643i | −1.41228 | + | 0.815381i | −0.995603 | − | 0.0936737i | \(-0.970139\pi\) |
−0.416678 | + | 0.909054i | \(0.636806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 86.0000 | 0.106042 | 0.0530210 | − | 0.998593i | \(-0.483115\pi\) | ||||
0.0530210 | + | 0.998593i | \(0.483115\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.5000 | + | 257.349i | −0.0535055 | + | 0.316543i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1347.47 | − | 777.964i | 1.65334 | − | 0.954558i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 253.000 | − | 438.209i | 0.309670 | − | 0.536363i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −286.093 | + | 247.052i | −0.349320 | + | 0.301651i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 333.026 | + | 192.273i | 0.405634 | + | 0.234193i | 0.688912 | − | 0.724845i | \(-0.258089\pi\) |
−0.283278 | + | 0.959038i | \(0.591422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −188.500 | − | 326.492i | −0.229040 | − | 0.396709i | 0.728484 | − | 0.685063i | \(-0.240225\pi\) |
−0.957524 | + | 0.288354i | \(0.906892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 175.000 | + | 29.5804i | 0.212121 | + | 0.0358550i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 141.986i | 0.171688i | 0.996309 | + | 0.0858440i | \(0.0273587\pi\) | ||||
−0.996309 | + | 0.0858440i | \(0.972641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −75.5000 | − | 130.770i | −0.0910736 | − | 0.157744i | 0.816890 | − | 0.576794i | \(-0.195697\pi\) |
−0.907963 | + | 0.419050i | \(0.862363\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 718.950 | + | 594.642i | 0.865163 | + | 0.715574i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 251.050 | − | 144.944i | 0.301381 | − | 0.174002i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 560.000 | − | 969.948i | 0.670659 | − | 1.16161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1052.76 | + | 22.3793i | −1.25778 | + | 0.0267376i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 473.286i | 0.564108i | 0.959399 | + | 0.282054i | \(0.0910157\pi\) | ||||
−0.959399 | + | 0.282054i | \(0.908984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1399.00 | −1.66350 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −396.049 | − | 1064.61i | −0.469809 | − | 1.26288i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −681.422 | − | 393.419i | −0.806417 | − | 0.465585i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −301.000 | + | 521.347i | −0.355372 | + | 0.615522i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −737.444 | − | 609.938i | −0.868603 | − | 0.718420i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1685.62 | + | 973.195i | −1.98076 | + | 1.14359i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1462.00 | −1.71395 | −0.856975 | − | 0.515357i | \(-0.827659\pi\) | ||||
−0.856975 | + | 0.515357i | \(0.827659\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 402.500 | − | 1156.59i | 0.470760 | − | 1.35274i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 169.075 | − | 97.6153i | 0.197287 | − | 0.113904i | −0.398103 | − | 0.917341i | \(-0.630331\pi\) |
0.595389 | + | 0.803437i | \(0.296998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 491.500 | − | 851.303i | 0.572177 | − | 0.991040i | −0.424165 | − | 0.905585i | \(-0.639432\pi\) |
0.996342 | − | 0.0854547i | \(-0.0272343\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −128.087 | − | 73.9510i | −0.148420 | − | 0.0856906i | 0.423951 | − | 0.905685i | \(-0.360643\pi\) |
−0.572371 | + | 0.819995i | \(0.693976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −822.500 | − | 1424.61i | −0.950867 | − | 1.64695i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 127.000 | − | 751.342i | 0.146482 | − | 0.866600i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 53.2447i | − | 0.0612713i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −93.0000 | − | 161.081i | −0.106774 | − | 0.184938i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 558.562 | − | 482.340i | 0.639820 | − | 0.552509i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 621.188i | − | 0.709930i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 176.500 | − | 305.707i | 0.201254 | − | 0.348583i | −0.747679 | − | 0.664061i | \(-0.768832\pi\) |
0.948933 | + | 0.315478i | \(0.102165\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 148.518 | + | 399.227i | 0.168963 | + | 0.454183i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −314.000 | −0.355606 | −0.177803 | − | 0.984066i | \(-0.556899\pi\) | ||||
−0.177803 | + | 0.984066i | \(0.556899\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1672.98 | − | 622.374i | 1.89038 | − | 0.703248i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −537.965 | − | 310.594i | −0.606499 | − | 0.350163i | 0.165095 | − | 0.986278i | \(-0.447207\pi\) |
−0.771594 | + | 0.636115i | \(0.780540\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 546.000 | 0.614173 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 176.591 | + | 445.478i | 0.198194 | + | 0.499975i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1060.56 | + | 612.314i | −1.18764 | + | 0.685682i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 525.000 | 0.586592 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 735.000 | + | 124.238i | 0.819398 | + | 0.138504i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1598.52 | + | 922.908i | −1.77811 | + | 1.02659i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 157.500 | − | 272.798i | 0.174806 | − | 0.302772i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −433.008 | + | 161.085i | −0.479521 | + | 0.178389i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.7409 | − | 17.7482i | −0.0339678 | − | 0.0196113i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −376.500 | − | 652.117i | −0.415105 | − | 0.718983i | 0.580335 | − | 0.814378i | \(-0.302922\pi\) |
−0.995439 | + | 0.0953956i | \(0.969588\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −122.500 | + | 352.007i | −0.134763 | + | 0.387246i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1703.83i | − | 1.87029i | −0.354270 | − | 0.935143i | \(-0.615271\pi\) | ||
0.354270 | − | 0.935143i | \(-0.384729\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −140.000 | − | 242.487i | −0.153341 | − | 0.265594i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −916.251 | + | 1107.79i | −1.00137 | + | 1.21070i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −896.608 | − | 517.657i | −0.977762 | − | 0.564511i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −284.500 | + | 492.768i | −0.309576 | + | 0.536201i | −0.978270 | − | 0.207337i | \(-0.933520\pi\) |
0.668694 | + | 0.743538i | \(0.266854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1242.79 | − | 462.335i | 1.34939 | − | 0.501993i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 567.944i | 0.615324i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −470.000 | −0.508108 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −38.8300 | − | 203.325i | −0.0418878 | − | 0.219337i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1398.71 | + | 807.545i | 1.50561 | + | 0.869263i | 0.999979 | + | 0.00651097i | \(0.00207252\pi\) |
0.505628 | + | 0.862752i | \(0.331261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 563.500 | − | 976.011i | 0.605263 | − | 1.04835i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 463.781 | − | 560.733i | 0.497086 | − | 0.601000i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −179.322 | + | 103.531i | −0.191788 | + | 0.110729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 722.000 | 0.770544 | 0.385272 | − | 0.922803i | \(-0.374108\pi\) | ||||
0.385272 | + | 0.922803i | \(0.374108\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −128.500 | + | 760.216i | −0.136848 | + | 0.809602i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 455.989 | − | 263.266i | 0.484579 | − | 0.279772i | −0.237743 | − | 0.971328i | \(-0.576408\pi\) |
0.722323 | + | 0.691556i | \(0.243074\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −956.236 | + | 579.523i | −1.01189 | + | 0.613252i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −128.087 | − | 73.9510i | −0.135255 | − | 0.0780898i | 0.430845 | − | 0.902426i | \(-0.358215\pi\) |
−0.566101 | + | 0.824336i | \(0.691549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −51.0000 | − | 88.3346i | −0.0537408 | − | 0.0930818i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 262.500 | + | 44.3706i | 0.276025 | + | 0.0466568i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 378.629i | 0.397302i | 0.980070 | + | 0.198651i | \(0.0636561\pi\) | ||||
−0.980070 | + | 0.198651i | \(0.936344\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −157.500 | − | 272.798i | −0.164921 | − | 0.285652i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 647.287 | + | 535.369i | 0.676370 | + | 0.559424i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 609.694 | − | 352.007i | 0.635760 | − | 0.367056i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −280.000 | + | 484.974i | −0.291363 | + | 0.504656i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −470.696 | + | 89.8911i | −0.488781 | + | 0.0933448i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 845.999i | − | 0.876683i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −482.000 | −0.498449 | −0.249224 | − | 0.968446i | \(-0.580176\pi\) | ||||
−0.249224 | + | 0.968446i | \(0.580176\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 142.330 | + | 382.593i | 0.146883 | + | 0.394832i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 199.816 | + | 115.364i | 0.205783 | + | 0.118809i | 0.599350 | − | 0.800487i | \(-0.295426\pi\) |
−0.393567 | + | 0.919296i | \(0.628759\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −742.000 | −0.762590 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 138.704 | + | 114.722i | 0.142261 | + | 0.117664i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 169.075 | − | 97.6153i | 0.173055 | − | 0.0999133i | −0.410971 | − | 0.911649i | \(-0.634810\pi\) |
0.584026 | + | 0.811735i | \(0.301477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 525.000 | 0.536261 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1164.50 | + | 405.251i | 1.18705 | + | 0.413100i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1275.75 | + | 736.552i | −1.29781 | + | 0.749290i | −0.980025 | − | 0.198874i | \(-0.936272\pi\) |
−0.317783 | + | 0.948163i | \(0.602938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 140.000 | − | 242.487i | 0.142132 | − | 0.246180i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1102.50 | + | 186.357i | 1.11702 | + | 0.188811i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 789.015 | + | 455.538i | 0.797791 | + | 0.460605i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −180.500 | − | 312.635i | −0.182139 | − | 0.315474i | 0.760470 | − | 0.649374i | \(-0.224969\pi\) |
−0.942609 | + | 0.333899i | \(0.891636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 60.5000 | − | 357.923i | 0.0609265 | − | 0.360446i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 999.817i | − | 1.00484i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.5000 | + | 63.2199i | 0.0366098 | + | 0.0634101i | 0.883750 | − | 0.467960i | \(-0.155011\pi\) |
−0.847140 | + | 0.531370i | \(0.821677\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −657.713 | − | 1085.25i | −0.658372 | − | 1.08634i |
(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 | 336.3.bn.d.65.1 | 4 | ||
3.2 | odd | 2 | inner | 336.3.bn.d.65.2 | 4 | ||
4.3 | odd | 2 | 84.3.p.c.65.2 | yes | 4 | ||
7.4 | even | 3 | inner | 336.3.bn.d.305.2 | 4 | ||
12.11 | even | 2 | 84.3.p.c.65.1 | yes | 4 | ||
21.11 | odd | 6 | inner | 336.3.bn.d.305.1 | 4 | ||
28.3 | even | 6 | 588.3.p.d.557.2 | 4 | |||
28.11 | odd | 6 | 84.3.p.c.53.1 | ✓ | 4 | ||
28.19 | even | 6 | 588.3.c.f.197.1 | 2 | |||
28.23 | odd | 6 | 588.3.c.e.197.2 | 2 | |||
28.27 | even | 2 | 588.3.p.d.569.1 | 4 | |||
84.11 | even | 6 | 84.3.p.c.53.2 | yes | 4 | ||
84.23 | even | 6 | 588.3.c.e.197.1 | 2 | |||
84.47 | odd | 6 | 588.3.c.f.197.2 | 2 | |||
84.59 | odd | 6 | 588.3.p.d.557.1 | 4 | |||
84.83 | odd | 2 | 588.3.p.d.569.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.3.p.c.53.1 | ✓ | 4 | 28.11 | odd | 6 | ||
84.3.p.c.53.2 | yes | 4 | 84.11 | even | 6 | ||
84.3.p.c.65.1 | yes | 4 | 12.11 | even | 2 | ||
84.3.p.c.65.2 | yes | 4 | 4.3 | odd | 2 | ||
336.3.bn.d.65.1 | 4 | 1.1 | even | 1 | trivial | ||
336.3.bn.d.65.2 | 4 | 3.2 | odd | 2 | inner | ||
336.3.bn.d.305.1 | 4 | 21.11 | odd | 6 | inner | ||
336.3.bn.d.305.2 | 4 | 7.4 | even | 3 | inner | ||
588.3.c.e.197.1 | 2 | 84.23 | even | 6 | |||
588.3.c.e.197.2 | 2 | 28.23 | odd | 6 | |||
588.3.c.f.197.1 | 2 | 28.19 | even | 6 | |||
588.3.c.f.197.2 | 2 | 84.47 | odd | 6 | |||
588.3.p.d.557.1 | 4 | 84.59 | odd | 6 | |||
588.3.p.d.557.2 | 4 | 28.3 | even | 6 | |||
588.3.p.d.569.1 | 4 | 28.27 | even | 2 | |||
588.3.p.d.569.2 | 4 | 84.83 | odd | 2 |