Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,3,Mod(19,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.m (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: | \(12.0163796583\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.325 |
Dual form | 441.3.m.e.19.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | 0.963525 | − | 0.267617i | \(-0.0862360\pi\) |
−0.713525 | + | 0.700629i | \(0.752903\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.50000 | − | 2.59808i | 0.375000 | − | 0.649519i | ||||
\(5\) | −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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.00000 | 0.875000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.50000 | − | 2.59808i | −0.450000 | − | 0.259808i | ||||
\(11\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.92820i | 0.532939i | 0.963843 | + | 0.266469i | \(0.0858571\pi\) | ||||
−0.963843 | + | 0.266469i | \(0.914143\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.50000 | − | 4.33013i | −0.156250 | − | 0.270633i | ||||
\(17\) | 21.0000 | + | 12.1244i | 1.23529 | + | 0.713197i | 0.968129 | − | 0.250453i | \(-0.0805797\pi\) |
0.267165 | + | 0.963651i | \(0.413913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | − | 1.73205i | 0.157895 | − | 0.0911606i | −0.418971 | − | 0.908000i | \(-0.637609\pi\) |
0.576865 | + | 0.816839i | \(0.304276\pi\) | |||||||
\(20\) | 15.5885i | 0.779423i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.0000 | −0.500000 | ||||||||
\(23\) | 14.0000 | + | 24.2487i | 0.608696 | + | 1.05429i | 0.991456 | + | 0.130444i | \(0.0416403\pi\) |
−0.382760 | + | 0.923848i | \(0.625026\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 1.73205i | 0.0400000 | − | 0.0692820i | ||||
\(26\) | −6.00000 | + | 3.46410i | −0.230769 | + | 0.133235i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.0000 | −0.862069 | −0.431034 | − | 0.902335i | \(-0.641851\pi\) | ||||
−0.431034 | + | 0.902335i | \(0.641851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.5000 | + | 16.4545i | 0.919355 | + | 0.530790i | 0.883429 | − | 0.468565i | \(-0.155229\pi\) |
0.0359257 | + | 0.999354i | \(0.488562\pi\) | |||||||
\(32\) | 16.5000 | − | 28.5788i | 0.515625 | − | 0.893089i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 24.2487i | 0.713197i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 29.0000 | + | 50.2295i | 0.783784 | + | 1.35755i | 0.929723 | + | 0.368260i | \(0.120046\pi\) |
−0.145939 | + | 0.989294i | \(0.546620\pi\) | |||||||
\(38\) | 3.00000 | + | 1.73205i | 0.0789474 | + | 0.0455803i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −31.5000 | + | 18.1865i | −0.787500 | + | 0.454663i | ||||
\(41\) | − | 3.46410i | − | 0.0844903i | −0.999107 | − | 0.0422451i | \(-0.986549\pi\) | ||
0.999107 | − | 0.0422451i | \(-0.0134510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.0000 | 0.604651 | 0.302326 | − | 0.953205i | \(-0.402237\pi\) | ||||
0.302326 | + | 0.953205i | \(0.402237\pi\) | |||||||
\(44\) | 16.5000 | + | 28.5788i | 0.375000 | + | 0.649519i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.0000 | + | 24.2487i | −0.304348 | + | 0.527146i | ||||
\(47\) | −66.0000 | + | 38.1051i | −1.40426 | + | 0.810747i | −0.994826 | − | 0.101595i | \(-0.967606\pi\) |
−0.409429 | + | 0.912342i | \(0.634272\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.00000 | 0.0400000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 18.0000 | + | 10.3923i | 0.346154 | + | 0.199852i | ||||
\(53\) | 15.5000 | − | 26.8468i | 0.292453 | − | 0.506543i | −0.681936 | − | 0.731412i | \(-0.738862\pi\) |
0.974389 | + | 0.224868i | \(0.0721952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 57.1577i | − | 1.03923i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −12.5000 | − | 21.6506i | −0.215517 | − | 0.373287i | ||||
\(59\) | −7.50000 | − | 4.33013i | −0.127119 | − | 0.0733920i | 0.435092 | − | 0.900386i | \(-0.356716\pi\) |
−0.562211 | + | 0.826994i | \(0.690049\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | + | 6.92820i | −0.196721 | + | 0.113577i | −0.595125 | − | 0.803633i | \(-0.702898\pi\) |
0.398404 | + | 0.917210i | \(0.369564\pi\) | |||||||
\(62\) | 32.9090i | 0.530790i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | −18.0000 | − | 31.1769i | −0.276923 | − | 0.479645i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26.0000 | − | 45.0333i | 0.388060 | − | 0.672139i | −0.604129 | − | 0.796887i | \(-0.706479\pi\) |
0.992189 | + | 0.124748i | \(0.0398121\pi\) | |||||||
\(68\) | 63.0000 | − | 36.3731i | 0.926471 | − | 0.534898i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −64.0000 | −0.901408 | −0.450704 | − | 0.892673i | \(-0.648827\pi\) | ||||
−0.450704 | + | 0.892673i | \(0.648827\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | − | 3.46410i | −0.0821918 | − | 0.0474534i | 0.458341 | − | 0.888777i | \(-0.348444\pi\) |
−0.540533 | + | 0.841323i | \(0.681777\pi\) | |||||||
\(74\) | −29.0000 | + | 50.2295i | −0.391892 | + | 0.678777i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 10.3923i | − | 0.136741i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.50000 | − | 14.7224i | −0.107595 | − | 0.186360i | 0.807200 | − | 0.590277i | \(-0.200982\pi\) |
−0.914795 | + | 0.403917i | \(0.867648\pi\) | |||||||
\(80\) | 22.5000 | + | 12.9904i | 0.281250 | + | 0.162380i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | − | 1.73205i | 0.0365854 | − | 0.0211226i | ||||
\(83\) | − | 53.6936i | − | 0.646911i | −0.946243 | − | 0.323455i | \(-0.895155\pi\) | ||
0.946243 | − | 0.323455i | \(-0.104845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −126.000 | −1.48235 | ||||||||
\(86\) | 13.0000 | + | 22.5167i | 0.151163 | + | 0.261822i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −38.5000 | + | 66.6840i | −0.437500 | + | 0.757772i | ||||
\(89\) | −69.0000 | + | 39.8372i | −0.775281 | + | 0.447609i | −0.834755 | − | 0.550621i | \(-0.814391\pi\) |
0.0594743 | + | 0.998230i | \(0.481058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 84.0000 | 0.913043 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −66.0000 | − | 38.1051i | −0.702128 | − | 0.405374i | ||||
\(95\) | −9.00000 | + | 15.5885i | −0.0947368 | + | 0.164089i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 91.7987i | 0.946378i | 0.880961 | + | 0.473189i | \(0.156897\pi\) | ||||
−0.880961 | + | 0.473189i | \(0.843103\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | − | 5.19615i | −0.0300000 | − | 0.0519615i | ||||
\(101\) | −18.0000 | − | 10.3923i | −0.178218 | − | 0.102894i | 0.408237 | − | 0.912876i | \(-0.366144\pi\) |
−0.586455 | + | 0.809982i | \(0.699477\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 48.4974i | 0.466321i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 31.0000 | 0.292453 | ||||||||
\(107\) | 15.5000 | + | 26.8468i | 0.144860 | + | 0.250905i | 0.929321 | − | 0.369274i | \(-0.120394\pi\) |
−0.784461 | + | 0.620178i | \(0.787060\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 68.0000 | − | 117.779i | 0.623853 | − | 1.08055i | −0.364908 | − | 0.931043i | \(-0.618900\pi\) |
0.988761 | − | 0.149502i | \(-0.0477670\pi\) | |||||||
\(110\) | 49.5000 | − | 28.5788i | 0.450000 | − | 0.259808i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 74.0000 | 0.654867 | 0.327434 | − | 0.944874i | \(-0.393816\pi\) | ||||
0.327434 | + | 0.944874i | \(0.393816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −126.000 | − | 72.7461i | −1.09565 | − | 0.632575i | ||||
\(116\) | −37.5000 | + | 64.9519i | −0.323276 | + | 0.559930i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.66025i | − | 0.0733920i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −12.0000 | − | 6.92820i | −0.0983607 | − | 0.0567886i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 85.5000 | − | 49.3634i | 0.689516 | − | 0.398092i | ||||
\(125\) | − | 119.512i | − | 0.956092i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.00787402 | −0.00393701 | − | 0.999992i | \(-0.501253\pi\) | ||||
−0.00393701 | + | 0.999992i | \(0.501253\pi\) | |||||||
\(128\) | −59.5000 | − | 103.057i | −0.464844 | − | 0.805133i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18.0000 | − | 31.1769i | 0.138462 | − | 0.239822i | ||||
\(131\) | 157.500 | − | 90.9327i | 1.20229 | − | 0.694142i | 0.241226 | − | 0.970469i | \(-0.422450\pi\) |
0.961064 | + | 0.276326i | \(0.0891171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 52.0000 | 0.388060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 147.000 | + | 84.8705i | 1.08088 | + | 0.624048i | ||||
\(137\) | 44.0000 | − | 76.2102i | 0.321168 | − | 0.556279i | −0.659561 | − | 0.751651i | \(-0.729258\pi\) |
0.980729 | + | 0.195372i | \(0.0625913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 190.526i | − | 1.37069i | −0.728220 | − | 0.685344i | \(-0.759652\pi\) | ||
0.728220 | − | 0.685344i | \(-0.240348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −32.0000 | − | 55.4256i | −0.225352 | − | 0.390321i | ||||
\(143\) | −66.0000 | − | 38.1051i | −0.461538 | − | 0.266469i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 112.500 | − | 64.9519i | 0.775862 | − | 0.447944i | ||||
\(146\) | − | 6.92820i | − | 0.0474534i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 174.000 | 1.17568 | ||||||||
\(149\) | −115.000 | − | 199.186i | −0.771812 | − | 1.33682i | −0.936569 | − | 0.350484i | \(-0.886017\pi\) |
0.164757 | − | 0.986334i | \(-0.447316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −113.500 | + | 196.588i | −0.751656 | + | 1.30191i | 0.195364 | + | 0.980731i | \(0.437411\pi\) |
−0.947020 | + | 0.321175i | \(0.895922\pi\) | |||||||
\(152\) | 21.0000 | − | 12.1244i | 0.138158 | − | 0.0797655i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −171.000 | −1.10323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 42.0000 | + | 24.2487i | 0.267516 | + | 0.154450i | 0.627758 | − | 0.778408i | \(-0.283973\pi\) |
−0.360242 | + | 0.932859i | \(0.617306\pi\) | |||||||
\(158\) | 8.50000 | − | 14.7224i | 0.0537975 | − | 0.0931799i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 171.473i | 1.07171i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −106.000 | − | 183.597i | −0.650307 | − | 1.12636i | −0.983048 | − | 0.183346i | \(-0.941307\pi\) |
0.332742 | − | 0.943018i | \(-0.392026\pi\) | |||||||
\(164\) | −9.00000 | − | 5.19615i | −0.0548780 | − | 0.0316839i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 46.5000 | − | 26.8468i | 0.280120 | − | 0.161728i | ||||
\(167\) | − | 96.9948i | − | 0.580807i | −0.956904 | − | 0.290404i | \(-0.906210\pi\) | ||
0.956904 | − | 0.290404i | \(-0.0937896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 121.000 | 0.715976 | ||||||||
\(170\) | −63.0000 | − | 109.119i | −0.370588 | − | 0.641878i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 39.0000 | − | 67.5500i | 0.226744 | − | 0.392732i | ||||
\(173\) | 186.000 | − | 107.387i | 1.07514 | − | 0.620735i | 0.145562 | − | 0.989349i | \(-0.453501\pi\) |
0.929582 | + | 0.368614i | \(0.120168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 55.0000 | 0.312500 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −69.0000 | − | 39.8372i | −0.387640 | − | 0.223804i | ||||
\(179\) | 23.0000 | − | 39.8372i | 0.128492 | − | 0.222554i | −0.794601 | − | 0.607132i | \(-0.792320\pi\) |
0.923092 | + | 0.384578i | \(0.125653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 31.1769i | − | 0.172248i | −0.996284 | − | 0.0861241i | \(-0.972552\pi\) | ||
0.996284 | − | 0.0861241i | \(-0.0274481\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 98.0000 | + | 169.741i | 0.532609 | + | 0.922505i | ||||
\(185\) | −261.000 | − | 150.688i | −1.41081 | − | 0.814532i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −231.000 | + | 133.368i | −1.23529 | + | 0.713197i | ||||
\(188\) | 228.631i | 1.21612i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0000 | −0.0947368 | ||||||||
\(191\) | 104.000 | + | 180.133i | 0.544503 | + | 0.943106i | 0.998638 | + | 0.0521735i | \(0.0166149\pi\) |
−0.454135 | + | 0.890933i | \(0.650052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −119.500 | + | 206.980i | −0.619171 | + | 1.07244i | 0.370466 | + | 0.928846i | \(0.379198\pi\) |
−0.989637 | + | 0.143590i | \(0.954135\pi\) | |||||||
\(194\) | −79.5000 | + | 45.8993i | −0.409794 | + | 0.236595i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0000 | 0.131980 | 0.0659898 | − | 0.997820i | \(-0.478980\pi\) | ||||
0.0659898 | + | 0.997820i | \(0.478980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 210.000 | + | 121.244i | 1.05528 | + | 0.609264i | 0.924122 | − | 0.382098i | \(-0.124798\pi\) |
0.131155 | + | 0.991362i | \(0.458132\pi\) | |||||||
\(200\) | 7.00000 | − | 12.1244i | 0.0350000 | − | 0.0606218i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 20.7846i | − | 0.102894i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 15.5885i | 0.0439024 | + | 0.0760413i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 30.0000 | − | 17.3205i | 0.144231 | − | 0.0832717i | ||||
\(209\) | 38.1051i | 0.182321i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −52.0000 | −0.246445 | −0.123223 | − | 0.992379i | \(-0.539323\pi\) | ||||
−0.123223 | + | 0.992379i | \(0.539323\pi\) | |||||||
\(212\) | −46.5000 | − | 80.5404i | −0.219340 | − | 0.379907i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.5000 | + | 26.8468i | −0.0724299 | + | 0.125452i | ||||
\(215\) | −117.000 | + | 67.5500i | −0.544186 | + | 0.314186i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 136.000 | 0.623853 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −148.500 | − | 85.7365i | −0.675000 | − | 0.389711i | ||||
\(221\) | −84.0000 | + | 145.492i | −0.380090 | + | 0.658336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.5167i | − | 0.100972i | −0.998725 | − | 0.0504858i | \(-0.983923\pi\) | ||
0.998725 | − | 0.0504858i | \(-0.0160770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 37.0000 | + | 64.0859i | 0.163717 | + | 0.283566i | ||||
\(227\) | 58.5000 | + | 33.7750i | 0.257709 | + | 0.148789i | 0.623289 | − | 0.781991i | \(-0.285796\pi\) |
−0.365580 | + | 0.930780i | \(0.619129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.0000 | − | 15.5885i | 0.117904 | − | 0.0680719i | −0.439888 | − | 0.898053i | \(-0.644982\pi\) |
0.557792 | + | 0.829981i | \(0.311649\pi\) | |||||||
\(230\) | − | 145.492i | − | 0.632575i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −175.000 | −0.754310 | ||||||||
\(233\) | 131.000 | + | 226.899i | 0.562232 | + | 0.973814i | 0.997301 | + | 0.0734171i | \(0.0233904\pi\) |
−0.435070 | + | 0.900397i | \(0.643276\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 198.000 | − | 342.946i | 0.842553 | − | 1.45934i | ||||
\(236\) | −22.5000 | + | 12.9904i | −0.0953390 | + | 0.0550440i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −160.000 | −0.669456 | −0.334728 | − | 0.942315i | \(-0.608644\pi\) | ||||
−0.334728 | + | 0.942315i | \(0.608644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −409.500 | − | 236.425i | −1.69917 | − | 0.981016i | −0.946548 | − | 0.322564i | \(-0.895455\pi\) |
−0.752622 | − | 0.658452i | \(-0.771211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 41.5692i | 0.170366i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 20.7846i | 0.0485830 | + | 0.0841482i | ||||
\(248\) | 199.500 | + | 115.181i | 0.804435 | + | 0.464441i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 103.500 | − | 59.7558i | 0.414000 | − | 0.239023i | ||||
\(251\) | 67.5500i | 0.269123i | 0.990905 | + | 0.134562i | \(0.0429626\pi\) | ||||
−0.990905 | + | 0.134562i | \(0.957037\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −308.000 | −1.21739 | ||||||||
\(254\) | −0.500000 | − | 0.866025i | −0.00196850 | − | 0.00340955i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 85.5000 | − | 148.090i | 0.333984 | − | 0.578478i | ||||
\(257\) | −351.000 | + | 202.650i | −1.36576 | + | 0.788521i | −0.990383 | − | 0.138352i | \(-0.955820\pi\) |
−0.375376 | + | 0.926873i | \(0.622486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −108.000 | −0.415385 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 157.500 | + | 90.9327i | 0.601145 | + | 0.347071i | ||||
\(263\) | 53.0000 | − | 91.7987i | 0.201521 | − | 0.349044i | −0.747498 | − | 0.664264i | \(-0.768745\pi\) |
0.949019 | + | 0.315220i | \(0.102078\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 161.081i | 0.607852i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −78.0000 | − | 135.100i | −0.291045 | − | 0.504104i | ||||
\(269\) | 376.500 | + | 217.372i | 1.39963 | + | 0.808076i | 0.994353 | − | 0.106119i | \(-0.0338425\pi\) |
0.405275 | + | 0.914195i | \(0.367176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −109.500 | + | 63.2199i | −0.404059 | + | 0.233284i | −0.688234 | − | 0.725489i | \(-0.741614\pi\) |
0.284175 | + | 0.958772i | \(0.408280\pi\) | |||||||
\(272\) | − | 121.244i | − | 0.445748i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 88.0000 | 0.321168 | ||||||||
\(275\) | 11.0000 | + | 19.0526i | 0.0400000 | + | 0.0692820i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −118.000 | + | 204.382i | −0.425993 | + | 0.737841i | −0.996513 | − | 0.0834427i | \(-0.973408\pi\) |
0.570520 | + | 0.821284i | \(0.306742\pi\) | |||||||
\(278\) | 165.000 | − | 95.2628i | 0.593525 | − | 0.342672i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 116.000 | 0.412811 | 0.206406 | − | 0.978466i | \(-0.433823\pi\) | ||||
0.206406 | + | 0.978466i | \(0.433823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 321.000 | + | 185.329i | 1.13428 | + | 0.654874i | 0.945007 | − | 0.327051i | \(-0.106055\pi\) |
0.189269 | + | 0.981925i | \(0.439388\pi\) | |||||||
\(284\) | −96.0000 | + | 166.277i | −0.338028 | + | 0.585482i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 76.2102i | − | 0.266469i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 149.500 | + | 258.942i | 0.517301 | + | 0.895992i | ||||
\(290\) | 112.500 | + | 64.9519i | 0.387931 | + | 0.223972i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −18.0000 | + | 10.3923i | −0.0616438 | + | 0.0355901i | ||||
\(293\) | − | 19.0526i | − | 0.0650258i | −0.999471 | − | 0.0325129i | \(-0.989649\pi\) | ||
0.999471 | − | 0.0325129i | \(-0.0103510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.0000 | 0.152542 | ||||||||
\(296\) | 203.000 | + | 351.606i | 0.685811 | + | 1.18786i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 115.000 | − | 199.186i | 0.385906 | − | 0.668409i | ||||
\(299\) | −168.000 | + | 96.9948i | −0.561873 | + | 0.324397i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −227.000 | −0.751656 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.0000 | − | 8.66025i | −0.0493421 | − | 0.0284877i | ||||
\(305\) | 36.0000 | − | 62.3538i | 0.118033 | − | 0.204439i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 457.261i | − | 1.48945i | −0.667371 | − | 0.744725i | \(-0.732580\pi\) | ||
0.667371 | − | 0.744725i | \(-0.267420\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −85.5000 | − | 148.090i | −0.275806 | − | 0.477711i | ||||
\(311\) | 285.000 | + | 164.545i | 0.916399 | + | 0.529083i | 0.882484 | − | 0.470342i | \(-0.155869\pi\) |
0.0339143 | + | 0.999425i | \(0.489203\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −475.500 | + | 274.530i | −1.51917 | + | 0.877093i | −0.519424 | + | 0.854517i | \(0.673854\pi\) |
−0.999745 | + | 0.0225763i | \(0.992813\pi\) | |||||||
\(314\) | 48.4974i | 0.154450i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −51.0000 | −0.161392 | ||||||||
\(317\) | 93.5000 | + | 161.947i | 0.294953 | + | 0.510873i | 0.974974 | − | 0.222319i | \(-0.0713628\pi\) |
−0.680021 | + | 0.733192i | \(0.738029\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 137.500 | − | 238.157i | 0.431034 | − | 0.746574i | ||||
\(320\) | −58.5000 | + | 33.7750i | −0.182812 | + | 0.105547i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 84.0000 | 0.260062 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0000 | + | 6.92820i | 0.0369231 | + | 0.0213175i | ||||
\(326\) | 106.000 | − | 183.597i | 0.325153 | − | 0.563182i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 24.2487i | − | 0.0739290i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | + | 13.8564i | 0.0241692 | + | 0.0418623i | 0.877857 | − | 0.478923i | \(-0.158973\pi\) |
−0.853688 | + | 0.520785i | \(0.825639\pi\) | |||||||
\(332\) | −139.500 | − | 80.5404i | −0.420181 | − | 0.242591i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 84.0000 | − | 48.4974i | 0.251497 | − | 0.145202i | ||||
\(335\) | 270.200i | 0.806567i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 83.0000 | 0.246291 | 0.123145 | − | 0.992389i | \(-0.460702\pi\) | ||||
0.123145 | + | 0.992389i | \(0.460702\pi\) | |||||||
\(338\) | 60.5000 | + | 104.789i | 0.178994 | + | 0.310027i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −189.000 | + | 327.358i | −0.555882 | + | 0.962816i | ||||
\(341\) | −313.500 | + | 180.999i | −0.919355 | + | 0.530790i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 182.000 | 0.529070 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 186.000 | + | 107.387i | 0.537572 | + | 0.310367i | ||||
\(347\) | 179.000 | − | 310.037i | 0.515850 | − | 0.893479i | −0.483981 | − | 0.875079i | \(-0.660809\pi\) |
0.999831 | − | 0.0183999i | \(-0.00585720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 678.964i | 1.94546i | 0.231950 | + | 0.972728i | \(0.425489\pi\) | ||||
−0.231950 | + | 0.972728i | \(0.574511\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 181.500 | + | 314.367i | 0.515625 | + | 0.893089i | ||||
\(353\) | −558.000 | − | 322.161i | −1.58074 | − | 0.912639i | −0.994752 | − | 0.102317i | \(-0.967375\pi\) |
−0.585985 | − | 0.810322i | \(-0.699292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 288.000 | − | 166.277i | 0.811268 | − | 0.468386i | ||||
\(356\) | 239.023i | 0.671413i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 46.0000 | 0.128492 | ||||||||
\(359\) | −142.000 | − | 245.951i | −0.395543 | − | 0.685101i | 0.597627 | − | 0.801774i | \(-0.296110\pi\) |
−0.993170 | + | 0.116673i | \(0.962777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −174.500 | + | 302.243i | −0.483380 | + | 0.837238i | ||||
\(362\) | 27.0000 | − | 15.5885i | 0.0745856 | − | 0.0430620i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.0000 | 0.0986301 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −238.500 | − | 137.698i | −0.649864 | − | 0.375199i | 0.138540 | − | 0.990357i | \(-0.455759\pi\) |
−0.788404 | + | 0.615158i | \(0.789092\pi\) | |||||||
\(368\) | 70.0000 | − | 121.244i | 0.190217 | − | 0.329466i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 301.377i | − | 0.814532i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.0000 | − | 43.3013i | −0.0670241 | − | 0.116089i | 0.830566 | − | 0.556920i | \(-0.188017\pi\) |
−0.897590 | + | 0.440831i | \(0.854684\pi\) | |||||||
\(374\) | −231.000 | − | 133.368i | −0.617647 | − | 0.356599i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −462.000 | + | 266.736i | −1.22872 | + | 0.709404i | ||||
\(377\) | − | 173.205i | − | 0.459430i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 458.000 | 1.20844 | 0.604222 | − | 0.796816i | \(-0.293484\pi\) | ||||
0.604222 | + | 0.796816i | \(0.293484\pi\) | |||||||
\(380\) | 27.0000 | + | 46.7654i | 0.0710526 | + | 0.123067i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −104.000 | + | 180.133i | −0.272251 | + | 0.471553i | ||||
\(383\) | 351.000 | − | 202.650i | 0.916449 | − | 0.529112i | 0.0339486 | − | 0.999424i | \(-0.489192\pi\) |
0.882501 | + | 0.470311i | \(0.155858\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −239.000 | −0.619171 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 238.500 | + | 137.698i | 0.614691 | + | 0.354892i | ||||
\(389\) | −349.000 | + | 604.486i | −0.897172 | + | 1.55395i | −0.0660793 | + | 0.997814i | \(0.521049\pi\) |
−0.831093 | + | 0.556134i | \(0.812284\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 678.964i | 1.73648i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.0000 | + | 22.5167i | 0.0329949 | + | 0.0571489i | ||||
\(395\) | 76.5000 | + | 44.1673i | 0.193671 | + | 0.111816i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 498.000 | − | 287.520i | 1.25441 | − | 0.724233i | 0.282426 | − | 0.959289i | \(-0.408861\pi\) |
0.971982 | + | 0.235056i | \(0.0755274\pi\) | |||||||
\(398\) | 242.487i | 0.609264i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.0000 | −0.0250000 | ||||||||
\(401\) | −142.000 | − | 245.951i | −0.354115 | − | 0.613345i | 0.632851 | − | 0.774273i | \(-0.281884\pi\) |
−0.986966 | + | 0.160929i | \(0.948551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −114.000 | + | 197.454i | −0.282878 | + | 0.489960i | ||||
\(404\) | −54.0000 | + | 31.1769i | −0.133663 | + | 0.0771706i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −638.000 | −1.56757 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 181.500 | + | 104.789i | 0.443765 | + | 0.256208i | 0.705193 | − | 0.709015i | \(-0.250860\pi\) |
−0.261428 | + | 0.965223i | \(0.584193\pi\) | |||||||
\(410\) | −9.00000 | + | 15.5885i | −0.0219512 | + | 0.0380206i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 139.500 | + | 241.621i | 0.336145 | + | 0.582219i | ||||
\(416\) | 198.000 | + | 114.315i | 0.475962 | + | 0.274797i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −33.0000 | + | 19.0526i | −0.0789474 | + | 0.0455803i | ||||
\(419\) | 131.636i | 0.314167i | 0.987585 | + | 0.157083i | \(0.0502091\pi\) | ||||
−0.987585 | + | 0.157083i | \(0.949791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0000 | −0.0665083 | −0.0332542 | − | 0.999447i | \(-0.510587\pi\) | ||||
−0.0332542 | + | 0.999447i | \(0.510587\pi\) | |||||||
\(422\) | −26.0000 | − | 45.0333i | −0.0616114 | − | 0.106714i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 108.500 | − | 187.928i | 0.255896 | − | 0.443225i | ||||
\(425\) | 42.0000 | − | 24.2487i | 0.0988235 | − | 0.0570558i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 93.0000 | 0.217290 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −117.000 | − | 67.5500i | −0.272093 | − | 0.157093i | ||||
\(431\) | 59.0000 | − | 102.191i | 0.136891 | − | 0.237102i | −0.789427 | − | 0.613844i | \(-0.789622\pi\) |
0.926318 | + | 0.376742i | \(0.122956\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 561.184i | − | 1.29604i | −0.761624 | − | 0.648019i | \(-0.775598\pi\) | ||
0.761624 | − | 0.648019i | \(-0.224402\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −204.000 | − | 353.338i | −0.467890 | − | 0.810409i | ||||
\(437\) | 84.0000 | + | 48.4974i | 0.192220 | + | 0.110978i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 640.500 | − | 369.793i | 1.45900 | − | 0.842353i | 0.460036 | − | 0.887900i | \(-0.347837\pi\) |
0.998962 | + | 0.0455478i | \(0.0145033\pi\) | |||||||
\(440\) | − | 400.104i | − | 0.909327i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −168.000 | −0.380090 | ||||||||
\(443\) | −77.5000 | − | 134.234i | −0.174944 | − | 0.303011i | 0.765198 | − | 0.643795i | \(-0.222641\pi\) |
−0.940142 | + | 0.340784i | \(0.889308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 207.000 | − | 358.535i | 0.465169 | − | 0.805696i | ||||
\(446\) | 19.5000 | − | 11.2583i | 0.0437220 | − | 0.0252429i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 368.000 | 0.819599 | 0.409800 | − | 0.912176i | \(-0.365599\pi\) | ||||
0.409800 | + | 0.912176i | \(0.365599\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.0000 | + | 19.0526i | 0.0731707 | + | 0.0422451i | ||||
\(452\) | 111.000 | − | 192.258i | 0.245575 | − | 0.425349i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 67.5500i | 0.148789i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −170.500 | − | 295.315i | −0.373085 | − | 0.646203i | 0.616953 | − | 0.787000i | \(-0.288367\pi\) |
−0.990038 | + | 0.140797i | \(0.955033\pi\) | |||||||
\(458\) | 27.0000 | + | 15.5885i | 0.0589520 | + | 0.0340359i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −378.000 | + | 218.238i | −0.821739 | + | 0.474431i | ||||
\(461\) | 55.4256i | 0.120229i | 0.998191 | + | 0.0601146i | \(0.0191466\pi\) | ||||
−0.998191 | + | 0.0601146i | \(0.980853\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −178.000 | −0.384449 | −0.192225 | − | 0.981351i | \(-0.561570\pi\) | ||||
−0.192225 | + | 0.981351i | \(0.561570\pi\) | |||||||
\(464\) | 62.5000 | + | 108.253i | 0.134698 | + | 0.233304i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −131.000 | + | 226.899i | −0.281116 | + | 0.486907i | ||||
\(467\) | 570.000 | − | 329.090i | 1.22056 | − | 0.704689i | 0.255520 | − | 0.966804i | \(-0.417753\pi\) |
0.965037 | + | 0.262115i | \(0.0844200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 396.000 | 0.842553 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −52.5000 | − | 30.3109i | −0.111229 | − | 0.0642180i | ||||
\(473\) | −143.000 | + | 247.683i | −0.302326 | + | 0.523643i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.92820i | − | 0.0145857i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −80.0000 | − | 138.564i | −0.167364 | − | 0.289883i | ||||
\(479\) | 441.000 | + | 254.611i | 0.920668 | + | 0.531548i | 0.883848 | − | 0.467774i | \(-0.154944\pi\) |
0.0368199 | + | 0.999322i | \(0.488277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −348.000 | + | 200.918i | −0.723493 | + | 0.417709i | ||||
\(482\) | − | 472.850i | − | 0.981016i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −238.500 | − | 413.094i | −0.491753 | − | 0.851740i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 420.500 | − | 728.327i | 0.863450 | − | 1.49554i | −0.00512864 | − | 0.999987i | \(-0.501633\pi\) |
0.868578 | − | 0.495552i | \(-0.165034\pi\) | |||||||
\(488\) | −84.0000 | + | 48.4974i | −0.172131 | + | 0.0993800i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 959.000 | 1.95316 | 0.976578 | − | 0.215162i | \(-0.0690279\pi\) | ||||
0.976578 | + | 0.215162i | \(0.0690279\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −525.000 | − | 303.109i | −1.06491 | − | 0.614825i | ||||
\(494\) | −12.0000 | + | 20.7846i | −0.0242915 | + | 0.0420741i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 164.545i | − | 0.331744i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 59.0000 | + | 102.191i | 0.118236 | + | 0.204792i | 0.919069 | − | 0.394097i | \(-0.128943\pi\) |
−0.800832 | + | 0.598889i | \(0.795609\pi\) | |||||||
\(500\) | −310.500 | − | 179.267i | −0.621000 | − | 0.358535i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −58.5000 | + | 33.7750i | −0.116534 | + | 0.0672809i | ||||
\(503\) | − | 363.731i | − | 0.723123i | −0.932348 | − | 0.361561i | \(-0.882244\pi\) | ||
0.932348 | − | 0.361561i | \(-0.117756\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 108.000 | 0.213861 | ||||||||
\(506\) | −154.000 | − | 266.736i | −0.304348 | − | 0.527146i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.50000 | + | 2.59808i | −0.00295276 | + | 0.00511432i | ||||
\(509\) | 382.500 | − | 220.836i | 0.751473 | − | 0.433863i | −0.0747526 | − | 0.997202i | \(-0.523817\pi\) |
0.826226 | + | 0.563339i | \(0.190483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −305.000 | −0.595703 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −351.000 | − | 202.650i | −0.682879 | − | 0.394261i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 838.313i | − | 1.62149i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −126.000 | − | 218.238i | −0.242308 | − | 0.419689i | ||||
\(521\) | −843.000 | − | 486.706i | −1.61804 | − | 0.934177i | −0.987426 | − | 0.158082i | \(-0.949469\pi\) |
−0.630616 | − | 0.776095i | \(-0.717198\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 408.000 | − | 235.559i | 0.780115 | − | 0.450399i | −0.0563562 | − | 0.998411i | \(-0.517948\pi\) |
0.836471 | + | 0.548011i | \(0.184615\pi\) | |||||||
\(524\) | − | 545.596i | − | 1.04121i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 106.000 | 0.201521 | ||||||||
\(527\) | 399.000 | + | 691.088i | 0.757116 | + | 1.31136i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −127.500 | + | 220.836i | −0.241021 | + | 0.417460i | ||||
\(530\) | −139.500 | + | 80.5404i | −0.263208 | + | 0.151963i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | 0.0450281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −139.500 | − | 80.5404i | −0.260748 | − | 0.150543i | ||||
\(536\) | 182.000 | − | 315.233i | 0.339552 | − | 0.588122i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 434.745i | 0.808076i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −403.000 | − | 698.016i | −0.744917 | − | 1.29023i | −0.950234 | − | 0.311538i | \(-0.899156\pi\) |
0.205317 | − | 0.978696i | \(-0.434178\pi\) | |||||||
\(542\) | −109.500 | − | 63.2199i | −0.202030 | − | 0.116642i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 693.000 | − | 400.104i | 1.27390 | − | 0.735485i | ||||
\(545\) | 706.677i | 1.29665i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −154.000 | −0.281536 | −0.140768 | − | 0.990043i | \(-0.544957\pi\) | ||||
−0.140768 | + | 0.990043i | \(0.544957\pi\) | |||||||
\(548\) | −132.000 | − | 228.631i | −0.240876 | − | 0.417209i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −11.0000 | + | 19.0526i | −0.0200000 | + | 0.0346410i | ||||
\(551\) | −75.0000 | + | 43.3013i | −0.136116 | + | 0.0785867i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −236.000 | −0.425993 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −495.000 | − | 285.788i | −0.890288 | − | 0.514008i | ||||
\(557\) | −425.500 | + | 736.988i | −0.763914 | + | 1.32314i | 0.176905 | + | 0.984228i | \(0.443391\pi\) |
−0.940819 | + | 0.338910i | \(0.889942\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 180.133i | 0.322242i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 58.0000 | + | 100.459i | 0.103203 | + | 0.178753i | ||||
\(563\) | 370.500 | + | 213.908i | 0.658082 | + | 0.379944i | 0.791546 | − | 0.611110i | \(-0.209277\pi\) |
−0.133464 | + | 0.991054i | \(0.542610\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −333.000 | + | 192.258i | −0.589381 | + | 0.340279i | ||||
\(566\) | 370.659i | 0.654874i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −448.000 | −0.788732 | ||||||||
\(569\) | −409.000 | − | 708.409i | −0.718805 | − | 1.24501i | −0.961474 | − | 0.274897i | \(-0.911356\pi\) |
0.242669 | − | 0.970109i | \(-0.421977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −142.000 | + | 245.951i | −0.248687 | + | 0.430738i | −0.963162 | − | 0.268923i | \(-0.913332\pi\) |
0.714475 | + | 0.699661i | \(0.246666\pi\) | |||||||
\(572\) | −198.000 | + | 114.315i | −0.346154 | + | 0.199852i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 56.0000 | 0.0973913 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 655.500 | + | 378.453i | 1.13605 | + | 0.655898i | 0.945449 | − | 0.325770i | \(-0.105623\pi\) |
0.190599 | + | 0.981668i | \(0.438957\pi\) | |||||||
\(578\) | −149.500 | + | 258.942i | −0.258651 | + | 0.447996i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 389.711i | − | 0.671916i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 170.500 | + | 295.315i | 0.292453 | + | 0.506543i | ||||
\(584\) | −42.0000 | − | 24.2487i | −0.0719178 | − | 0.0415218i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.5000 | − | 9.52628i | 0.0281570 | − | 0.0162564i | ||||
\(587\) | − | 947.432i | − | 1.61402i | −0.590535 | − | 0.807012i | \(-0.701083\pi\) | ||
0.590535 | − | 0.807012i | \(-0.298917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 114.000 | 0.193548 | ||||||||
\(590\) | 22.5000 | + | 38.9711i | 0.0381356 | + | 0.0660528i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 145.000 | − | 251.147i | 0.244932 | − | 0.424235i | ||||
\(593\) | 354.000 | − | 204.382i | 0.596965 | − | 0.344658i | −0.170882 | − | 0.985292i | \(-0.554662\pi\) |
0.767847 | + | 0.640634i | \(0.221328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −690.000 | −1.15772 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −168.000 | − | 96.9948i | −0.280936 | − | 0.162199i | ||||
\(599\) | 278.000 | − | 481.510i | 0.464107 | − | 0.803857i | −0.535054 | − | 0.844818i | \(-0.679709\pi\) |
0.999161 | + | 0.0409613i | \(0.0130420\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 580.237i | 0.965453i | 0.875771 | + | 0.482726i | \(0.160353\pi\) | ||||
−0.875771 | + | 0.482726i | \(0.839647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 340.500 | + | 589.763i | 0.563742 | + | 0.976429i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −571.500 | + | 329.956i | −0.941516 | + | 0.543584i | −0.890435 | − | 0.455110i | \(-0.849600\pi\) |
−0.0510805 | + | 0.998695i | \(0.516267\pi\) | |||||||
\(608\) | − | 114.315i | − | 0.188019i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 72.0000 | 0.118033 | ||||||||
\(611\) | −264.000 | − | 457.261i | −0.432079 | − | 0.748382i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −160.000 | + | 277.128i | −0.261011 | + | 0.452085i | −0.966511 | − | 0.256625i | \(-0.917389\pi\) |
0.705500 | + | 0.708710i | \(0.250723\pi\) | |||||||
\(614\) | 396.000 | − | 228.631i | 0.644951 | − | 0.372363i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −652.000 | −1.05673 | −0.528363 | − | 0.849019i | \(-0.677194\pi\) | ||||
−0.528363 | + | 0.849019i | \(0.677194\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 558.000 | + | 322.161i | 0.901454 | + | 0.520455i | 0.877672 | − | 0.479262i | \(-0.159096\pi\) |
0.0237823 | + | 0.999717i | \(0.492429\pi\) | |||||||
\(620\) | −256.500 | + | 444.271i | −0.413710 | + | 0.716566i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 329.090i | 0.529083i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 335.500 | + | 581.103i | 0.536800 | + | 0.929765i | ||||
\(626\) | −475.500 | − | 274.530i | −0.759585 | − | 0.438546i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 126.000 | − | 72.7461i | 0.200637 | − | 0.115838i | ||||
\(629\) | 1406.43i | 2.23597i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −97.0000 | −0.153724 | −0.0768621 | − | 0.997042i | \(-0.524490\pi\) | ||||
−0.0768621 | + | 0.997042i | \(0.524490\pi\) | |||||||
\(632\) | −59.5000 | − | 103.057i | −0.0941456 | − | 0.163065i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −93.5000 | + | 161.947i | −0.147476 | + | 0.255437i | ||||
\(635\) | 4.50000 | − | 2.59808i | 0.00708661 | − | 0.00409146i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 275.000 | 0.431034 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 535.500 | + | 309.171i | 0.836719 | + | 0.483080i | ||||
\(641\) | 350.000 | − | 606.218i | 0.546022 | − | 0.945738i | −0.452520 | − | 0.891754i | \(-0.649475\pi\) |
0.998542 | − | 0.0539833i | \(-0.0171918\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 325.626i | − | 0.506416i | −0.967412 | − | 0.253208i | \(-0.918514\pi\) | ||
0.967412 | − | 0.253208i | \(-0.0814857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 42.0000 | + | 72.7461i | 0.0650155 | + | 0.112610i | ||||
\(647\) | −312.000 | − | 180.133i | −0.482226 | − | 0.278413i | 0.239118 | − | 0.970991i | \(-0.423142\pi\) |
−0.721344 | + | 0.692577i | \(0.756475\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 82.5000 | − | 47.6314i | 0.127119 | − | 0.0733920i | ||||
\(650\) | 13.8564i | 0.0213175i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −636.000 | −0.975460 | ||||||||
\(653\) | 186.500 | + | 323.027i | 0.285605 | + | 0.494682i | 0.972756 | − | 0.231833i | \(-0.0744722\pi\) |
−0.687151 | + | 0.726515i | \(0.741139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −472.500 | + | 818.394i | −0.721374 | + | 1.24946i | ||||
\(656\) | −15.0000 | + | 8.66025i | −0.0228659 | + | 0.0132016i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 818.000 | 1.24127 | 0.620637 | − | 0.784098i | \(-0.286874\pi\) | ||||
0.620637 | + | 0.784098i | \(0.286874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −327.000 | − | 188.794i | −0.494705 | − | 0.285618i | 0.231819 | − | 0.972759i | \(-0.425532\pi\) |
−0.726524 | + | 0.687141i | \(0.758866\pi\) | |||||||
\(662\) | −8.00000 | + | 13.8564i | −0.0120846 | + | 0.0209311i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 375.855i | − | 0.566047i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −350.000 | − | 606.218i | −0.524738 | − | 0.908872i | ||||
\(668\) | −252.000 | − | 145.492i | −0.377246 | − | 0.217803i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −234.000 | + | 135.100i | −0.349254 | + | 0.201642i | ||||
\(671\) | − | 152.420i | − | 0.227154i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1205.00 | 1.79049 | 0.895245 | − | 0.445574i | \(-0.147000\pi\) | ||||
0.895245 | + | 0.445574i | \(0.147000\pi\) | |||||||
\(674\) | 41.5000 | + | 71.8801i | 0.0615727 | + | 0.106647i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 181.500 | − | 314.367i | 0.268491 | − | 0.465040i | ||||
\(677\) | −466.500 | + | 269.334i | −0.689069 | + | 0.397834i | −0.803263 | − | 0.595624i | \(-0.796905\pi\) |
0.114194 | + | 0.993458i | \(0.463571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −882.000 | −1.29706 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −313.500 | − | 180.999i | −0.459677 | − | 0.265395i | ||||
\(683\) | 474.500 | − | 821.858i | 0.694729 | − | 1.20331i | −0.275543 | − | 0.961289i | \(-0.588858\pi\) |
0.970272 | − | 0.242017i | \(-0.0778091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 457.261i | 0.667535i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −65.0000 | − | 112.583i | −0.0944767 | − | 0.163639i | ||||
\(689\) | 186.000 | + | 107.387i | 0.269956 | + | 0.155859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 267.000 | − | 154.153i | 0.386397 | − | 0.223086i | −0.294201 | − | 0.955744i | \(-0.595054\pi\) |
0.680598 | + | 0.732657i | \(0.261720\pi\) | |||||||
\(692\) | − | 644.323i | − | 0.931102i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 358.000 | 0.515850 | ||||||||
\(695\) | 495.000 | + | 857.365i | 0.712230 | + | 1.23362i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.0000 | − | 72.7461i | 0.0602582 | − | 0.104370i | ||||
\(698\) | −588.000 | + | 339.482i | −0.842407 | + | 0.486364i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 413.000 | 0.589158 | 0.294579 | − | 0.955627i | \(-0.404821\pi\) | ||||
0.294579 | + | 0.955627i | \(0.404821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 174.000 | + | 100.459i | 0.247511 | + | 0.142900i | ||||
\(704\) | −71.5000 | + | 123.842i | −0.101562 | + | 0.175911i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 644.323i | − | 0.912639i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −445.000 | − | 770.763i | −0.627645 | − | 1.08711i | −0.988023 | − | 0.154306i | \(-0.950686\pi\) |
0.360379 | − | 0.932806i | \(-0.382648\pi\) | |||||||
\(710\) | 288.000 | + | 166.277i | 0.405634 | + | 0.234193i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −483.000 | + | 278.860i | −0.678371 | + | 0.391658i | ||||
\(713\) | 921.451i | 1.29236i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 396.000 | 0.553846 | ||||||||
\(716\) | −69.0000 | − | 119.512i | −0.0963687 | − | 0.166916i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 142.000 | − | 245.951i | 0.197772 | − | 0.342550i | ||||
\(719\) | 579.000 | − | 334.286i | 0.805285 | − | 0.464932i | −0.0400307 | − | 0.999198i | \(-0.512746\pi\) |
0.845316 | + | 0.534267i | \(0.179412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −349.000 | −0.483380 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −81.0000 | − | 46.7654i | −0.111878 | − | 0.0645931i | ||||
\(725\) | −25.0000 | + | 43.3013i | −0.0344828 | + | 0.0597259i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 417.424i | − | 0.574174i | −0.957905 | − | 0.287087i | \(-0.907313\pi\) | ||
0.957905 | − | 0.287087i | \(-0.0926868\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.0000 | + | 31.1769i | 0.0246575 | + | 0.0427081i | ||||
\(731\) | 546.000 | + | 315.233i | 0.746922 | + | 0.431236i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −171.000 | + | 98.7269i | −0.233288 | + | 0.134689i | −0.612088 | − | 0.790790i | \(-0.709670\pi\) |
0.378800 | + | 0.925479i | \(0.376337\pi\) | |||||||
\(734\) | − | 275.396i | − | 0.375199i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 924.000 | 1.25543 | ||||||||
\(737\) | 286.000 | + | 495.367i | 0.388060 | + | 0.672139i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 155.000 | − | 268.468i | 0.209743 | − | 0.363285i | −0.741891 | − | 0.670521i | \(-0.766071\pi\) |
0.951633 | + | 0.307236i | \(0.0994040\pi\) | |||||||
\(740\) | −783.000 | + | 452.065i | −1.05811 | + | 0.610899i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 812.000 | 1.09287 | 0.546433 | − | 0.837503i | \(-0.315985\pi\) | ||||
0.546433 | + | 0.837503i | \(0.315985\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1035.00 | + | 597.558i | 1.38926 | + | 0.802091i | ||||
\(746\) | 25.0000 | − | 43.3013i | 0.0335121 | − | 0.0580446i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 800.207i | 1.06980i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 537.500 | + | 930.977i | 0.715712 | + | 1.23965i | 0.962684 | + | 0.270628i | \(0.0872312\pi\) |
−0.246972 | + | 0.969023i | \(0.579435\pi\) | |||||||
\(752\) | 330.000 | + | 190.526i | 0.438830 | + | 0.253358i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 150.000 | − | 86.6025i | 0.198939 | − | 0.114857i | ||||
\(755\) | − | 1179.53i | − | 1.56229i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −484.000 | −0.639366 | −0.319683 | − | 0.947525i | \(-0.603576\pi\) | ||||
−0.319683 | + | 0.947525i | \(0.603576\pi\) | |||||||
\(758\) | 229.000 | + | 396.640i | 0.302111 | + | 0.523271i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −63.0000 | + | 109.119i | −0.0828947 | + | 0.143578i | ||||
\(761\) | 144.000 | − | 83.1384i | 0.189225 | − | 0.109249i | −0.402395 | − | 0.915466i | \(-0.631822\pi\) |
0.591620 | + | 0.806217i | \(0.298489\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 624.000 | 0.816754 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 351.000 | + | 202.650i | 0.458225 | + | 0.264556i | ||||
\(767\) | 30.0000 | − | 51.9615i | 0.0391134 | − | 0.0677464i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 594.093i | 0.772553i | 0.922383 | + | 0.386277i | \(0.126239\pi\) | ||||
−0.922383 | + | 0.386277i | \(0.873761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 358.500 | + | 620.940i | 0.464378 | + | 0.804327i | ||||
\(773\) | 894.000 | + | 516.151i | 1.15653 | + | 0.667725i | 0.950471 | − | 0.310814i | \(-0.100602\pi\) |
0.206062 | + | 0.978539i | \(0.433935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 57.0000 | − | 32.9090i | 0.0735484 | − | 0.0424632i | ||||
\(776\) | 642.591i | 0.828081i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −698.000 | −0.897172 | ||||||||
\(779\) | −6.00000 | − | 10.3923i | −0.00770218 | − | 0.0133406i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 352.000 | − | 609.682i | 0.450704 | − | 0.780643i | ||||
\(782\) | −588.000 | + | 339.482i | −0.751918 | + | 0.434120i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −252.000 | −0.321019 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −354.000 | − | 204.382i | −0.449809 | − | 0.259698i | 0.257940 | − | 0.966161i | \(-0.416956\pi\) |
−0.707750 | + | 0.706463i | \(0.750290\pi\) | |||||||
\(788\) | 39.0000 | − | 67.5500i | 0.0494924 | − | 0.0857233i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 88.3346i | 0.111816i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.0000 | − | 83.1384i | −0.0605296 | − | 0.104840i | ||||
\(794\) | 498.000 | + | 287.520i | 0.627204 | + | 0.362116i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 630.000 | − | 363.731i | 0.791457 | − | 0.456948i | ||||
\(797\) | 625.270i | 0.784530i | 0.919852 | + | 0.392265i | \(0.128308\pi\) | ||||
−0.919852 | + | 0.392265i | \(0.871692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1848.00 | −2.31289 | ||||||||
\(800\) | −33.0000 | − | 57.1577i | −0.0412500 | − | 0.0714471i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 142.000 | − | 245.951i | 0.177057 | − | 0.306672i | ||||
\(803\) | 66.0000 | − | 38.1051i | 0.0821918 | − | 0.0474534i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −228.000 | −0.282878 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −126.000 | − | 72.7461i | −0.155941 | − | 0.0900323i | ||||
\(809\) | −376.000 | + | 651.251i | −0.464771 | + | 0.805008i | −0.999191 | − | 0.0402116i | \(-0.987197\pi\) |
0.534420 | + | 0.845219i | \(0.320530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 270.200i | 0.333169i | 0.986027 | + | 0.166584i | \(0.0532738\pi\) | ||||
−0.986027 | + | 0.166584i | \(0.946726\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −319.000 | − | 552.524i | −0.391892 | − | 0.678777i | ||||
\(815\) | 954.000 | + | 550.792i | 1.17055 | + | 0.675819i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 78.0000 | − | 45.0333i | 0.0954712 | − | 0.0551203i | ||||
\(818\) | 209.578i | 0.256208i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 54.0000 | 0.0658537 | ||||||||
\(821\) | 441.500 | + | 764.700i | 0.537759 | + | 0.931426i | 0.999024 | + | 0.0441635i | \(0.0140622\pi\) |
−0.461265 | + | 0.887262i | \(0.652604\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 245.000 | − | 424.352i | 0.297691 | − | 0.515617i | −0.677916 | − | 0.735139i | \(-0.737117\pi\) |
0.975607 | + | 0.219523i | \(0.0704500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1279.00 | −1.54655 | −0.773277 | − | 0.634068i | \(-0.781384\pi\) | ||||
−0.773277 | + | 0.634068i | \(0.781384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1311.00 | − | 756.906i | −1.58142 | − | 0.913035i | −0.994652 | − | 0.103283i | \(-0.967065\pi\) |
−0.586771 | − | 0.809753i | \(-0.699601\pi\) | |||||||
\(830\) | −139.500 | + | 241.621i | −0.168072 | + | 0.291110i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 90.0666i | 0.108253i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 252.000 | + | 436.477i | 0.301796 | + | 0.522727i | ||||
\(836\) | 99.0000 | + | 57.1577i | 0.118421 | + | 0.0683704i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −114.000 | + | 65.8179i | −0.136038 | + | 0.0785417i | ||||
\(839\) | 523.079i | 0.623456i | 0.950171 | + | 0.311728i | \(0.100908\pi\) | ||||
−0.950171 | + | 0.311728i | \(0.899092\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −216.000 | −0.256837 | ||||||||
\(842\) | −14.0000 | − | 24.2487i | −0.0166271 | − | 0.0287989i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −78.0000 | + | 135.100i | −0.0924171 | + | 0.160071i | ||||
\(845\) | −544.500 | + | 314.367i | −0.644379 | + | 0.372032i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −155.000 | −0.182783 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 42.0000 | + | 24.2487i | 0.0494118 | + | 0.0285279i | ||||
\(851\) | −812.000 | + | 1406.43i | −0.954172 | + | 1.65267i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 387.979i | 0.454841i | 0.973797 | + | 0.227421i | \(0.0730292\pi\) | ||||
−0.973797 | + | 0.227421i | \(0.926971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 108.500 | + | 187.928i | 0.126752 | + | 0.219541i | ||||
\(857\) | −720.000 | − | 415.692i | −0.840140 | − | 0.485055i | 0.0171718 | − | 0.999853i | \(-0.494534\pi\) |
−0.857312 | + | 0.514797i | \(0.827867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −981.000 | + | 566.381i | −1.14203 | + | 0.659349i | −0.946931 | − | 0.321436i | \(-0.895835\pi\) |
−0.195094 | + | 0.980785i | \(0.562501\pi\) | |||||||
\(860\) | 405.300i | 0.471279i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 118.000 | 0.136891 | ||||||||
\(863\) | 11.0000 | + | 19.0526i | 0.0127462 | + | 0.0220771i | 0.872328 | − | 0.488921i | \(-0.162609\pi\) |
−0.859582 | + | 0.510998i | \(0.829276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −558.000 | + | 966.484i | −0.645087 | + | 1.11732i | ||||
\(866\) | 486.000 | − | 280.592i | 0.561201 | − | 0.324010i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 187.000 | 0.215190 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 312.000 | + | 180.133i | 0.358209 | + | 0.206812i | ||||
\(872\) | 476.000 | − | 824.456i | 0.545872 | − | 0.945477i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 96.9948i | 0.110978i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0000 | + | 34.6410i | 0.0228050 | + | 0.0394994i | 0.877203 | − | 0.480120i | \(-0.159407\pi\) |
−0.854398 | + | 0.519620i | \(0.826074\pi\) | |||||||
\(878\) | 640.500 | + | 369.793i | 0.729499 | + | 0.421176i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −247.500 | + | 142.894i | −0.281250 | + | 0.162380i | ||||
\(881\) | − | 20.7846i | − | 0.0235921i | −0.999930 | − | 0.0117960i | \(-0.996245\pi\) | ||
0.999930 | − | 0.0117960i | \(-0.00375488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 386.000 | 0.437146 | 0.218573 | − | 0.975821i | \(-0.429860\pi\) | ||||
0.218573 | + | 0.975821i | \(0.429860\pi\) | |||||||
\(884\) | 252.000 | + | 436.477i | 0.285068 | + | 0.493752i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 77.5000 | − | 134.234i | 0.0874718 | − | 0.151506i | ||||
\(887\) | −1494.00 | + | 862.561i | −1.68433 | + | 0.972448i | −0.725604 | + | 0.688112i | \(0.758440\pi\) |
−0.958725 | + | 0.284336i | \(0.908227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 414.000 | 0.465169 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −58.5000 | − | 33.7750i | −0.0655830 | − | 0.0378643i | ||||
\(893\) | −132.000 | + | 228.631i | −0.147816 | + | 0.256025i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 239.023i | 0.267065i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 184.000 | + | 318.697i | 0.204900 | + | 0.354897i | ||||
\(899\) | −712.500 | − | 411.362i | −0.792547 | − | 0.457577i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 651.000 | − | 375.855i | 0.722531 | − | 0.417153i | ||||
\(902\) | 38.1051i | 0.0422451i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 518.000 | 0.573009 | ||||||||
\(905\) | 81.0000 | + | 140.296i | 0.0895028 | + | 0.155023i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 296.000 | − | 512.687i | 0.326351 | − | 0.565256i | −0.655434 | − | 0.755252i | \(-0.727514\pi\) |
0.981785 | + | 0.189996i | \(0.0608477\pi\) | |||||||
\(908\) | 175.500 | − | 101.325i | 0.193282 | − | 0.111591i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 416.000 | 0.456641 | 0.228321 | − | 0.973586i | \(-0.426677\pi\) | ||||
0.228321 | + | 0.973586i | \(0.426677\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 511.500 | + | 295.315i | 0.560241 | + | 0.323455i | ||||
\(914\) | 170.500 | − | 295.315i | 0.186543 | − | 0.323101i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 93.5307i | − | 0.102108i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0000 | − | 43.3013i | −0.0272035 | − | 0.0471178i | 0.852103 | − | 0.523374i | \(-0.175327\pi\) |
−0.879307 | + | 0.476256i | \(0.841994\pi\) | |||||||
\(920\) | −882.000 | − | 509.223i | −0.958696 | − | 0.553503i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48.0000 | + | 27.7128i | −0.0520607 | + | 0.0300573i | ||||
\(923\) | − | 443.405i | − | 0.480395i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 116.000 | 0.125405 | ||||||||
\(926\) | −89.0000 | − | 154.153i | −0.0961123 | − | 0.166471i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −412.500 | + | 714.471i | −0.444504 | + | 0.769904i | ||||
\(929\) | 357.000 | − | 206.114i | 0.384284 | − | 0.221867i | −0.295396 | − | 0.955375i | \(-0.595452\pi\) |
0.679681 | + | 0.733508i | \(0.262118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 786.000 | 0.843348 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 570.000 | + | 329.090i | 0.610278 | + | 0.352344i | ||||
\(935\) | 693.000 | − | 1200.31i | 0.741176 | − | 1.28376i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1605.61i | − | 1.71357i | −0.515677 | − | 0.856783i | \(-0.672460\pi\) | ||
0.515677 | − | 0.856783i | \(-0.327540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −594.000 | − | 1028.84i | −0.631915 | − | 1.09451i | ||||
\(941\) | −1150.50 | − | 664.241i | −1.22264 | − | 0.705889i | −0.257156 | − | 0.966370i | \(-0.582786\pi\) |
−0.965479 | + | 0.260481i | \(0.916119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 84.0000 | − | 48.4974i | 0.0890774 | − | 0.0514289i | ||||
\(944\) | 43.3013i | 0.0458700i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −286.000 | −0.302326 | ||||||||
\(947\) | −685.000 | − | 1186.45i | −0.723337 | − | 1.25286i | −0.959655 | − | 0.281180i | \(-0.909274\pi\) |
0.236318 | − | 0.971676i | \(-0.424059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | − | 41.5692i | 0.0252898 | − | 0.0438032i | ||||
\(950\) | 6.00000 | − | 3.46410i | 0.00631579 | − | 0.00364642i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1150.00 | −1.20672 | −0.603358 | − | 0.797471i | \(-0.706171\pi\) | ||||
−0.603358 | + | 0.797471i | \(0.706171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −936.000 | − | 540.400i | −0.980105 | − | 0.565864i | ||||
\(956\) | −240.000 | + | 415.692i | −0.251046 | + | 0.434824i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 509.223i | 0.531548i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.0000 | + | 105.655i | 0.0634755 | + | 0.109943i | ||||
\(962\) | −348.000 | − | 200.918i | −0.361746 | − | 0.208854i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1228.50 | + | 709.275i | −1.27438 | + | 0.735762i | ||||
\(965\) | − | 1241.88i | − | 1.28692i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.00000 | 0.00517063 | 0.00258532 | − | 0.999997i | \(-0.499177\pi\) | ||||
0.00258532 | + | 0.999997i | \(0.499177\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 238.500 | − | 413.094i | 0.245876 | − | 0.425870i | ||||
\(971\) | 385.500 | − | 222.569i | 0.397013 | − | 0.229216i | −0.288181 | − | 0.957576i | \(-0.593051\pi\) |
0.685195 | + | 0.728360i | \(0.259717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 841.000 | 0.863450 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 60.0000 | + | 34.6410i | 0.0614754 | + | 0.0354928i | ||||
\(977\) | 479.000 | − | 829.652i | 0.490276 | − | 0.849184i | −0.509661 | − | 0.860375i | \(-0.670229\pi\) |
0.999937 | + | 0.0111917i | \(0.00356252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 876.418i | − | 0.895217i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 479.500 | + | 830.518i | 0.488289 | + | 0.845742i | ||||
\(983\) | 243.000 | + | 140.296i | 0.247202 | + | 0.142722i | 0.618483 | − | 0.785798i | \(-0.287748\pi\) |
−0.371280 | + | 0.928521i | \(0.621081\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −117.000 | + | 67.5500i | −0.118782 | + | 0.0685787i | ||||
\(986\) | − | 606.218i | − | 0.614825i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 72.0000 | 0.0728745 | ||||||||
\(989\) | 364.000 | + | 630.466i | 0.368049 | + | 0.637479i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −461.500 | + | 799.341i | −0.465691 | + | 0.806601i | −0.999232 | − | 0.0391732i | \(-0.987528\pi\) |
0.533541 | + | 0.845774i | \(0.320861\pi\) | |||||||
\(992\) | 940.500 | − | 542.998i | 0.948085 | − | 0.547377i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1260.00 | −1.26633 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.0000 | − | 10.3923i | −0.0180542 | − | 0.0104236i | 0.490946 | − | 0.871190i | \(-0.336651\pi\) |
−0.509000 | + | 0.860767i | \(0.669985\pi\) | |||||||
\(998\) | −59.0000 | + | 102.191i | −0.0591182 | + | 0.102396i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.3.m.e.325.1 | 2 | ||
3.2 | odd | 2 | 147.3.f.c.31.1 | 2 | |||
7.2 | even | 3 | 63.3.m.c.19.1 | 2 | |||
7.3 | odd | 6 | 441.3.d.b.244.2 | 2 | |||
7.4 | even | 3 | 441.3.d.b.244.1 | 2 | |||
7.5 | odd | 6 | inner | 441.3.m.e.19.1 | 2 | ||
7.6 | odd | 2 | 63.3.m.c.10.1 | 2 | |||
21.2 | odd | 6 | 21.3.f.b.19.1 | yes | 2 | ||
21.5 | even | 6 | 147.3.f.c.19.1 | 2 | |||
21.11 | odd | 6 | 147.3.d.b.97.2 | 2 | |||
21.17 | even | 6 | 147.3.d.b.97.1 | 2 | |||
21.20 | even | 2 | 21.3.f.b.10.1 | ✓ | 2 | ||
28.23 | odd | 6 | 1008.3.cg.g.145.1 | 2 | |||
28.27 | even | 2 | 1008.3.cg.g.577.1 | 2 | |||
84.11 | even | 6 | 2352.3.f.d.97.1 | 2 | |||
84.23 | even | 6 | 336.3.bh.a.145.1 | 2 | |||
84.59 | odd | 6 | 2352.3.f.d.97.2 | 2 | |||
84.83 | odd | 2 | 336.3.bh.a.241.1 | 2 | |||
105.2 | even | 12 | 525.3.s.c.124.1 | 4 | |||
105.23 | even | 12 | 525.3.s.c.124.2 | 4 | |||
105.44 | odd | 6 | 525.3.o.g.376.1 | 2 | |||
105.62 | odd | 4 | 525.3.s.c.199.2 | 4 | |||
105.83 | odd | 4 | 525.3.s.c.199.1 | 4 | |||
105.104 | even | 2 | 525.3.o.g.451.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.f.b.10.1 | ✓ | 2 | 21.20 | even | 2 | ||
21.3.f.b.19.1 | yes | 2 | 21.2 | odd | 6 | ||
63.3.m.c.10.1 | 2 | 7.6 | odd | 2 | |||
63.3.m.c.19.1 | 2 | 7.2 | even | 3 | |||
147.3.d.b.97.1 | 2 | 21.17 | even | 6 | |||
147.3.d.b.97.2 | 2 | 21.11 | odd | 6 | |||
147.3.f.c.19.1 | 2 | 21.5 | even | 6 | |||
147.3.f.c.31.1 | 2 | 3.2 | odd | 2 | |||
336.3.bh.a.145.1 | 2 | 84.23 | even | 6 | |||
336.3.bh.a.241.1 | 2 | 84.83 | odd | 2 | |||
441.3.d.b.244.1 | 2 | 7.4 | even | 3 | |||
441.3.d.b.244.2 | 2 | 7.3 | odd | 6 | |||
441.3.m.e.19.1 | 2 | 7.5 | odd | 6 | inner | ||
441.3.m.e.325.1 | 2 | 1.1 | even | 1 | trivial | ||
525.3.o.g.376.1 | 2 | 105.44 | odd | 6 | |||
525.3.o.g.451.1 | 2 | 105.104 | even | 2 | |||
525.3.s.c.124.1 | 4 | 105.2 | even | 12 | |||
525.3.s.c.124.2 | 4 | 105.23 | even | 12 | |||
525.3.s.c.199.1 | 4 | 105.83 | odd | 4 | |||
525.3.s.c.199.2 | 4 | 105.62 | odd | 4 | |||
1008.3.cg.g.145.1 | 2 | 28.23 | odd | 6 | |||
1008.3.cg.g.577.1 | 2 | 28.27 | even | 2 | |||
2352.3.f.d.97.1 | 2 | 84.11 | even | 6 | |||
2352.3.f.d.97.2 | 2 | 84.59 | odd | 6 |