Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,3,Mod(97,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.0218395444\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.7 | ||
Root | \(-1.60021 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.97 |
Dual form | 588.3.d.c.97.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.480662i | 0.0961323i | 0.998844 | + | 0.0480662i | \(0.0153058\pi\) | ||||
−0.998844 | + | 0.0480662i | \(0.984694\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.76316 | 0.523924 | 0.261962 | − | 0.965078i | \(-0.415631\pi\) | ||||
0.261962 | + | 0.965078i | \(0.415631\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.41991i | − 0.109224i | −0.998508 | − | 0.0546120i | \(-0.982608\pi\) | ||||
0.998508 | − | 0.0546120i | \(-0.0173922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.832530 | −0.0555020 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.0671i | 1.35689i | 0.734651 | + | 0.678445i | \(0.237346\pi\) | ||||
−0.734651 | + | 0.678445i | \(0.762654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.6739i | 0.561783i | 0.959740 | + | 0.280891i | \(0.0906300\pi\) | ||||
−0.959740 | + | 0.280891i | \(0.909370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.59980 | −0.286948 | −0.143474 | − | 0.989654i | \(-0.545827\pi\) | ||||
−0.143474 | + | 0.989654i | \(0.545827\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.7690 | 0.990759 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.20258 | −0.213882 | −0.106941 | − | 0.994265i | \(-0.534106\pi\) | ||||
−0.106941 | + | 0.994265i | \(0.534106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.9320i | 1.35265i | 0.736605 | + | 0.676323i | \(0.236428\pi\) | ||||
−0.736605 | + | 0.676323i | \(0.763572\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.98209i | 0.302488i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −60.0929 | −1.62413 | −0.812066 | − | 0.583566i | \(-0.801657\pi\) | ||||
−0.812066 | + | 0.583566i | \(0.801657\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.45936 | 0.0630605 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.8250i | 1.19085i | 0.803409 | + | 0.595427i | \(0.203017\pi\) | ||||
−0.803409 | + | 0.595427i | \(0.796983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −51.5603 | −1.19908 | −0.599539 | − | 0.800346i | \(-0.704649\pi\) | ||||
−0.599539 | + | 0.800346i | \(0.704649\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 1.44198i | − 0.0320441i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 19.2421i | − 0.409406i | −0.978824 | − | 0.204703i | \(-0.934377\pi\) | ||||
0.978824 | − | 0.204703i | \(-0.0656229\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −39.9534 | −0.783401 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 82.1345 | 1.54971 | 0.774854 | − | 0.632141i | \(-0.217824\pi\) | ||||
0.774854 | + | 0.632141i | \(0.217824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.77013i | 0.0503660i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.4877 | −0.324345 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 92.5800i | 1.56915i | 0.620032 | + | 0.784576i | \(0.287119\pi\) | ||||
−0.620032 | + | 0.784576i | \(0.712881\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.99187i | 0.0818340i | 0.999163 | + | 0.0409170i | \(0.0130279\pi\) | ||||
−0.999163 | + | 0.0409170i | \(0.986972\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.682497 | 0.0105000 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.20699 | −0.0329402 | −0.0164701 | − | 0.999864i | \(-0.505243\pi\) | ||||
−0.0164701 | + | 0.999864i | \(0.505243\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 11.4312i | − 0.165669i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −80.5899 | −1.13507 | −0.567535 | − | 0.823349i | \(-0.692103\pi\) | ||||
−0.567535 | + | 0.823349i | \(0.692103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 13.9088i | − 0.190531i | −0.995452 | − | 0.0952657i | \(-0.969630\pi\) | ||||
0.995452 | − | 0.0952657i | \(-0.0303701\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 42.9011i | 0.572015i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64.8885 | −0.821373 | −0.410687 | − | 0.911777i | \(-0.634711\pi\) | ||||
−0.410687 | + | 0.911777i | \(0.634711\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 118.005i | 1.42174i | 0.703322 | + | 0.710872i | \(0.251699\pi\) | ||||
−0.703322 | + | 0.710872i | \(0.748301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.0875 | −0.130441 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 10.7432i | − 0.123485i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 104.265i | − 1.17151i | −0.810487 | − | 0.585757i | \(-0.800797\pi\) | ||||
0.810487 | − | 0.585757i | \(-0.199203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −72.6284 | −0.780951 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.13052 | −0.0540055 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 31.7875i | − 0.327706i | −0.986485 | − | 0.163853i | \(-0.947608\pi\) | ||||
0.986485 | − | 0.163853i | \(-0.0523923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.2895 | −0.174641 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 72.5037i | 0.717859i | 0.933365 | + | 0.358929i | \(0.116858\pi\) | ||||
−0.933365 | + | 0.358929i | \(0.883142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 106.963i | 1.03847i | 0.854631 | + | 0.519236i | \(0.173783\pi\) | ||||
−0.854631 | + | 0.519236i | \(0.826217\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 196.619 | 1.83756 | 0.918782 | − | 0.394765i | \(-0.129174\pi\) | ||||
0.918782 | + | 0.394765i | \(0.129174\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 42.6922 | 0.391672 | 0.195836 | − | 0.980637i | \(-0.437258\pi\) | ||||
0.195836 | + | 0.980637i | \(0.437258\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 104.084i | − 0.937693i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 175.501 | 1.55310 | 0.776552 | − | 0.630053i | \(-0.216967\pi\) | ||||
0.776552 | + | 0.630053i | \(0.216967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.17227i | − 0.0275849i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.25973i | 0.0364080i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −87.7860 | −0.725504 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −84.5674 | −0.687540 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 23.9220i | 0.191376i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 31.0434 | 0.244436 | 0.122218 | − | 0.992503i | \(-0.460999\pi\) | ||||
0.122218 | + | 0.992503i | \(0.460999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 89.3051i | − 0.692288i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 46.5095i | − 0.355034i | −0.984118 | − | 0.177517i | \(-0.943194\pi\) | ||||
0.984118 | − | 0.177517i | \(-0.0568065\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.49759 | 0.0185007 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 45.4654 | 0.331864 | 0.165932 | − | 0.986137i | \(-0.446937\pi\) | ||||
0.165932 | + | 0.986137i | \(0.446937\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 138.075i | − 0.993343i | −0.867939 | − | 0.496672i | \(-0.834555\pi\) | ||||
0.867939 | − | 0.496672i | \(-0.165445\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.3283 | 0.236371 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 8.18318i | − 0.0572250i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 2.98134i | − 0.0205610i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 239.228 | 1.60556 | 0.802780 | − | 0.596276i | \(-0.203354\pi\) | ||||
0.802780 | + | 0.596276i | \(0.203354\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −188.146 | −1.24600 | −0.623001 | − | 0.782221i | \(-0.714087\pi\) | ||||
−0.623001 | + | 0.782221i | \(0.714087\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 69.2014i | − 0.452297i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.1551 | −0.130033 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 215.239i | − 1.37095i | −0.728097 | − | 0.685474i | \(-0.759595\pi\) | ||||
0.728097 | − | 0.685474i | \(-0.240405\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 142.261i | 0.894724i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 149.811 | 0.919083 | 0.459542 | − | 0.888156i | \(-0.348014\pi\) | ||||
0.459542 | + | 0.888156i | \(0.348014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.79801 | −0.0290788 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 137.195i | 0.821528i | 0.911742 | + | 0.410764i | \(0.134738\pi\) | ||||
−0.911742 | + | 0.410764i | \(0.865262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 166.984 | 0.988070 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 32.0216i | − 0.187261i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 251.181i | − 1.45191i | −0.687740 | − | 0.725957i | \(-0.741397\pi\) | ||||
0.687740 | − | 0.725957i | \(-0.258603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −160.353 | −0.905951 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −116.793 | −0.652477 | −0.326239 | − | 0.945287i | \(-0.605781\pi\) | ||||
−0.326239 | + | 0.945287i | \(0.605781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 117.148i | − 0.647228i | −0.946189 | − | 0.323614i | \(-0.895102\pi\) | ||||
0.946189 | − | 0.323614i | \(-0.104898\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.64618 | −0.0472469 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 28.8843i | − 0.156131i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 132.940i | 0.710907i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 341.818 | 1.78962 | 0.894812 | − | 0.446443i | \(-0.147309\pi\) | ||||
0.894812 | + | 0.446443i | \(0.147309\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −224.551 | −1.16348 | −0.581738 | − | 0.813376i | \(-0.697627\pi\) | ||||
−0.581738 | + | 0.813376i | \(0.697627\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.18212i | 0.00606215i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 257.109 | 1.30512 | 0.652560 | − | 0.757737i | \(-0.273695\pi\) | ||||
0.652560 | + | 0.757737i | \(0.273695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 245.479i | − 1.23356i | −0.787134 | − | 0.616782i | \(-0.788436\pi\) | ||||
0.787134 | − | 0.616782i | \(-0.211564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 3.82262i | − 0.0190180i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.4683 | −0.114480 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.7994 | 0.0956492 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 61.5152i | 0.294331i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −95.8210 | −0.454128 | −0.227064 | − | 0.973880i | \(-0.572913\pi\) | ||||
−0.227064 | + | 0.973880i | \(0.572913\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 139.586i | − 0.655333i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 24.7831i | − 0.115270i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.0907 | 0.110003 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.7533 | 0.148205 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 94.2091i | − 0.422462i | −0.977436 | − | 0.211231i | \(-0.932253\pi\) | ||||
0.977436 | − | 0.211231i | \(-0.0677473\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −74.3069 | −0.330253 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 224.253i | − 0.987899i | −0.869491 | − | 0.493949i | \(-0.835553\pi\) | ||||
0.869491 | − | 0.493949i | \(-0.164447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 366.724i | − 1.60142i | −0.599055 | − | 0.800708i | \(-0.704457\pi\) | ||||
0.599055 | − | 0.800708i | \(-0.295543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 69.6741 | 0.299030 | 0.149515 | − | 0.988759i | \(-0.452229\pi\) | ||||
0.149515 | + | 0.988759i | \(0.452229\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.24893 | 0.0393572 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 112.390i | − 0.474220i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −214.544 | −0.897674 | −0.448837 | − | 0.893614i | \(-0.648162\pi\) | ||||
−0.448837 | + | 0.893614i | \(0.648162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 163.395i | − 0.677989i | −0.940788 | − | 0.338994i | \(-0.889913\pi\) | ||||
0.940788 | − | 0.338994i | \(-0.110087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.1560 | 0.0613601 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −204.390 | −0.820844 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 330.546i | 1.31692i | 0.752617 | + | 0.658458i | \(0.228791\pi\) | ||||
−0.752617 | + | 0.658458i | \(0.771209\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.0357 | −0.150339 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 19.2041i | − 0.0753101i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 160.529i | − 0.624626i | −0.949979 | − | 0.312313i | \(-0.898896\pi\) | ||||
0.949979 | − | 0.312313i | \(-0.101104\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.6077 | 0.0712940 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −106.515 | −0.405002 | −0.202501 | − | 0.979282i | \(-0.564907\pi\) | ||||
−0.202501 | + | 0.979282i | \(0.564907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.4789i | 0.148977i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 180.592 | 0.676374 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 155.454i | 0.577895i | 0.957345 | + | 0.288947i | \(0.0933052\pi\) | ||||
−0.957345 | + | 0.288947i | \(0.906695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 516.080i | 1.90435i | 0.305549 | + | 0.952176i | \(0.401160\pi\) | ||||
−0.305549 | + | 0.952176i | \(0.598840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 142.748 | 0.519082 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 200.202 | 0.722750 | 0.361375 | − | 0.932421i | \(-0.382308\pi\) | ||||
0.361375 | + | 0.932421i | \(0.382308\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 125.796i | − 0.450882i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 228.093 | 0.811720 | 0.405860 | − | 0.913935i | \(-0.366972\pi\) | ||||
0.405860 | + | 0.913935i | \(0.366972\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 260.710i | 0.921236i | 0.887598 | + | 0.460618i | \(0.152372\pi\) | ||||
−0.887598 | + | 0.460618i | \(0.847628\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 8.88632i | − 0.0311801i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −243.092 | −0.841150 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 55.0576 | 0.189201 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 349.885i | − 1.19415i | −0.802186 | − | 0.597074i | \(-0.796330\pi\) | ||||
0.802186 | − | 0.597074i | \(-0.203670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −44.4996 | −0.150846 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 29.9463i | − 0.100829i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.37113i | 0.0313416i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −125.580 | −0.414456 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.39940 | −0.00786689 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 146.898i | 0.478495i | 0.970959 | + | 0.239247i | \(0.0769007\pi\) | ||||
−0.970959 | + | 0.239247i | \(0.923099\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −185.265 | −0.599562 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 80.7340i | 0.259595i | 0.991541 | + | 0.129797i | \(0.0414327\pi\) | ||||
−0.991541 | + | 0.129797i | \(0.958567\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 154.339i | − 0.493096i | −0.969131 | − | 0.246548i | \(-0.920704\pi\) | ||||
0.969131 | − | 0.246548i | \(-0.0792963\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −188.545 | −0.594780 | −0.297390 | − | 0.954756i | \(-0.596116\pi\) | ||||
−0.297390 | + | 0.954756i | \(0.596116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −35.7465 | −0.112058 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 340.555i | 1.06092i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −246.216 | −0.762277 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 35.1697i | − 0.108215i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 73.9451i | 0.226132i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 146.787 | 0.443466 | 0.221733 | − | 0.975107i | \(-0.428829\pi\) | ||||
0.221733 | + | 0.975107i | \(0.428829\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 180.279 | 0.541377 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.06082i | − 0.00316662i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 101.231 | 0.300388 | 0.150194 | − | 0.988657i | \(-0.452010\pi\) | ||||
0.150194 | + | 0.988657i | \(0.452010\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 303.976i | 0.896685i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 241.661i | 0.708684i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.49453 | 0.0159262 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 351.689 | 1.01351 | 0.506756 | − | 0.862089i | \(-0.330844\pi\) | ||||
0.506756 | + | 0.862089i | \(0.330844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 88.3780i | − 0.253232i | −0.991952 | − | 0.126616i | \(-0.959588\pi\) | ||||
0.991952 | − | 0.126616i | \(-0.0404116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.37808 | −0.0210202 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 520.542i | 1.47462i | 0.675552 | + | 0.737312i | \(0.263905\pi\) | ||||
−0.675552 | + | 0.737312i | \(0.736095\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 38.7365i | − 0.109117i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −514.265 | −1.43249 | −0.716246 | − | 0.697848i | \(-0.754141\pi\) | ||||
−0.716246 | + | 0.697848i | \(0.754141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 247.069 | 0.684400 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 152.050i | − 0.418870i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.68542 | 0.0183162 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 417.686i | 1.13811i | 0.822300 | + | 0.569054i | \(0.192690\pi\) | ||||
−0.822300 | + | 0.569054i | \(0.807310\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 146.475i | − 0.396951i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −140.314 | −0.376176 | −0.188088 | − | 0.982152i | \(-0.560229\pi\) | ||||
−0.188088 | + | 0.982152i | \(0.560229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −41.4342 | −0.110491 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.80712i | 0.0233611i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 153.298 | 0.404480 | 0.202240 | − | 0.979336i | \(-0.435178\pi\) | ||||
0.202240 | + | 0.979336i | \(0.435178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 53.7687i | 0.141125i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 121.717i | 0.317799i | 0.987295 | + | 0.158900i | \(0.0507946\pi\) | ||||
−0.987295 | + | 0.158900i | \(0.949205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 154.681 | 0.399692 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 401.271 | 1.03155 | 0.515773 | − | 0.856725i | \(-0.327505\pi\) | ||||
0.515773 | + | 0.856725i | \(0.327505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 152.238i | − 0.389356i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 80.5568 | 0.204979 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 31.1894i | − 0.0789605i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 60.2251i | 0.151700i | 0.997119 | + | 0.0758502i | \(0.0241671\pi\) | ||||
−0.997119 | + | 0.0758502i | \(0.975833\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −374.308 | −0.933436 | −0.466718 | − | 0.884406i | \(-0.654564\pi\) | ||||
−0.466718 | + | 0.884406i | \(0.654564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 59.5398 | 0.147741 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.32595i | 0.0106814i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −346.325 | −0.850921 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 614.609i | 1.50271i | 0.659897 | + | 0.751356i | \(0.270600\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 78.7484i | 0.191602i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −56.7203 | −0.136675 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 239.152 | 0.573507 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 129.067i | 0.308035i | 0.988068 | + | 0.154017i | \(0.0492212\pi\) | ||||
−0.988068 | + | 0.154017i | \(0.950779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −697.880 | −1.65767 | −0.828836 | − | 0.559492i | \(-0.810996\pi\) | ||||
−0.828836 | + | 0.559492i | \(0.810996\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 57.7263i | 0.136469i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 571.349i | 1.34435i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.1737 | 0.0330389 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −277.092 | −0.642906 | −0.321453 | − | 0.946926i | \(-0.604171\pi\) | ||||
−0.321453 | + | 0.946926i | \(0.604171\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 822.794i | 1.90022i | 0.311919 | + | 0.950109i | \(0.399028\pi\) | ||||
−0.311919 | + | 0.950109i | \(0.600972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.16384 | 0.0118709 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 70.4454i | − 0.161202i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 365.827i | − 0.833320i | −0.909062 | − | 0.416660i | \(-0.863201\pi\) | ||||
0.909062 | − | 0.416660i | \(-0.136799\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −573.392 | −1.29434 | −0.647169 | − | 0.762346i | \(-0.724047\pi\) | ||||
−0.647169 | + | 0.762346i | \(0.724047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 50.1161 | 0.112620 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 414.356i | 0.926970i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 227.961 | 0.507708 | 0.253854 | − | 0.967243i | \(-0.418302\pi\) | ||||
0.253854 | + | 0.967243i | \(0.418302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 281.386i | 0.623917i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 325.879i | − 0.719380i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −343.124 | −0.750818 | −0.375409 | − | 0.926859i | \(-0.622498\pi\) | ||||
−0.375409 | + | 0.926859i | \(0.622498\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 119.860 | 0.261134 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 611.314i | − 1.32606i | −0.748593 | − | 0.663030i | \(-0.769270\pi\) | ||||
0.748593 | − | 0.663030i | \(-0.230730\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −67.2682 | −0.145288 | −0.0726439 | − | 0.997358i | \(-0.523144\pi\) | ||||
−0.0726439 | + | 0.997358i | \(0.523144\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 34.9097i | − 0.0750746i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 93.7498i | − 0.200749i | −0.994950 | − | 0.100375i | \(-0.967996\pi\) | ||||
0.994950 | − | 0.100375i | \(-0.0320041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 372.804 | 0.791517 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −297.150 | −0.628225 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 264.381i | 0.556591i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −246.403 | −0.516569 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 353.796i | − 0.738613i | −0.929308 | − | 0.369306i | \(-0.879595\pi\) | ||||
0.929308 | − | 0.369306i | \(-0.120405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 85.3265i | 0.177394i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.2790 | 0.0315032 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 952.677 | 1.95621 | 0.978107 | − | 0.208101i | \(-0.0667281\pi\) | ||||
0.978107 | + | 0.208101i | \(0.0667281\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 259.479i | 0.530633i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −818.649 | −1.66731 | −0.833655 | − | 0.552286i | \(-0.813756\pi\) | ||||
−0.833655 | + | 0.552286i | \(0.813756\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 143.076i | − 0.290214i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 8.31039i | − 0.0167887i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.0821 | −0.0482607 | −0.0241304 | − | 0.999709i | \(-0.507682\pi\) | ||||
−0.0241304 | + | 0.999709i | \(0.507682\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −237.629 | −0.474310 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 420.445i | − 0.835874i | −0.908476 | − | 0.417937i | \(-0.862753\pi\) | ||||
0.908476 | − | 0.417937i | \(-0.137247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.8498 | −0.0690094 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 289.225i | 0.570463i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 239.869i | 0.471255i | 0.971843 | + | 0.235627i | \(0.0757145\pi\) | ||||
−0.971843 | + | 0.235627i | \(0.924285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 55.4631 | 0.108115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −51.4128 | −0.0998307 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 110.895i | − 0.214498i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 435.059 | 0.838263 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 26.8565i | − 0.0515479i | −0.999668 | − | 0.0257739i | \(-0.991795\pi\) | ||||
0.999668 | − | 0.0257739i | \(-0.00820501\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 223.737i | − 0.427796i | −0.976856 | − | 0.213898i | \(-0.931384\pi\) | ||||
0.976856 | − | 0.213898i | \(-0.0686160\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −967.252 | −1.83539 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −485.443 | −0.917661 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 277.740i | − 0.523051i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 69.3272 | 0.130070 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 94.5074i | 0.176649i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 202.292i | − 0.376708i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 986.190 | 1.82290 | 0.911451 | − | 0.411410i | \(-0.134963\pi\) | ||||
0.911451 | + | 0.411410i | \(0.134963\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 202.907 | 0.373678 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.5205i | 0.0376523i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 735.369 | 1.34437 | 0.672183 | − | 0.740385i | \(-0.265357\pi\) | ||||
0.672183 | + | 0.740385i | \(0.265357\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 14.9756i | − 0.0272780i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 66.2056i | − 0.120155i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 50.0291 | 0.0901426 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 418.568 | 0.751469 | 0.375735 | − | 0.926727i | \(-0.377390\pi\) | ||||
0.375735 | + | 0.926727i | \(0.377390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 73.2111i | 0.130968i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −230.258 | −0.410442 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 746.738i | − 1.32635i | −0.748462 | − | 0.663177i | \(-0.769208\pi\) | ||||
0.748462 | − | 0.663177i | \(-0.230792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 84.3565i | 0.149304i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −288.710 | −0.507398 | −0.253699 | − | 0.967283i | \(-0.581647\pi\) | ||||
−0.253699 | + | 0.967283i | \(0.581647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −916.207 | −1.60457 | −0.802283 | − | 0.596944i | \(-0.796382\pi\) | ||||
−0.802283 | + | 0.596944i | \(0.796382\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 592.047i | 1.03324i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −163.470 | −0.284296 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 992.068i | − 1.71936i | −0.510836 | − | 0.859678i | \(-0.670664\pi\) | ||||
0.510836 | − | 0.859678i | \(-0.329336\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 388.934i | − 0.671733i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 473.354 | 0.811929 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.04749 | −0.00349998 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 154.965i | − 0.263996i | −0.991250 | − | 0.131998i | \(-0.957861\pi\) | ||||
0.991250 | − | 0.131998i | \(-0.0421392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −447.577 | −0.759893 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 445.325i | 0.753512i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1004.17i | 1.69337i | 0.532094 | + | 0.846685i | \(0.321405\pi\) | ||||
−0.532094 | + | 0.846685i | \(0.678595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 425.182 | 0.712198 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −796.917 | −1.33041 | −0.665206 | − | 0.746660i | \(-0.731656\pi\) | ||||
−0.665206 | + | 0.746660i | \(0.731656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 467.002i | 0.777041i | 0.921440 | + | 0.388521i | \(0.127014\pi\) | ||||
−0.921440 | + | 0.388521i | \(0.872986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.62098 | 0.0109801 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 42.1953i | − 0.0697444i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 910.216i | − 1.49953i | −0.661703 | − | 0.749766i | \(-0.730166\pi\) | ||||
0.661703 | − | 0.749766i | \(-0.269834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.3221 | −0.0447170 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 775.800 | 1.26558 | 0.632790 | − | 0.774324i | \(-0.281910\pi\) | ||||
0.632790 | + | 0.774324i | \(0.281910\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 40.6483i | − 0.0660948i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 974.803 | 1.57991 | 0.789954 | − | 0.613166i | \(-0.210104\pi\) | ||||
0.789954 | + | 0.613166i | \(0.210104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 199.260i | 0.321906i | 0.986962 | + | 0.160953i | \(0.0514568\pi\) | ||||
−0.986962 | + | 0.160953i | \(0.948543\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.2935i | 0.0552231i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 607.726 | 0.972361 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −106.548 | −0.169932 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1386.17i | − 2.20377i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 751.062 | 1.19027 | 0.595136 | − | 0.803625i | \(-0.297098\pi\) | ||||
0.595136 | + | 0.803625i | \(0.297098\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 165.967i | − 0.262191i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9214i | 0.0234982i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 241.770 | 0.378356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1138.28 | −1.77578 | −0.887891 | − | 0.460053i | \(-0.847830\pi\) | ||||
−0.887891 | + | 0.460053i | \(0.847830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 647.823i | − 1.00750i | −0.863849 | − | 0.503751i | \(-0.831953\pi\) | ||||
0.863849 | − | 0.503751i | \(-0.168047\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 42.9255 | 0.0665512 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 882.943i | − 1.36467i | −0.731039 | − | 0.682336i | \(-0.760964\pi\) | ||||
0.731039 | − | 0.682336i | \(-0.239036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 533.554i | 0.822116i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 545.117 | 0.834788 | 0.417394 | − | 0.908726i | \(-0.362944\pi\) | ||||
0.417394 | + | 0.908726i | \(0.362944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.3553 | 0.0341302 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41.7264i | 0.0635104i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 698.290 | 1.05962 | 0.529810 | − | 0.848116i | \(-0.322263\pi\) | ||||
0.529810 | + | 0.848116i | \(0.322263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 571.725i | 0.864940i | 0.901648 | + | 0.432470i | \(0.142358\pi\) | ||||
−0.901648 | + | 0.432470i | \(0.857642\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.7303i | 0.0855661i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.9358 | 0.0613730 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 163.175 | 0.243909 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.7690i | 0.0428748i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 221.015 | 0.328403 | 0.164202 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164202 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 128.703i | − 0.190672i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 470.666i | 0.695222i | 0.937639 | + | 0.347611i | \(0.113007\pi\) | ||||
−0.937639 | + | 0.347611i | \(0.886993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 388.418 | 0.570364 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 215.960 | 0.316193 | 0.158097 | − | 0.987424i | \(-0.449464\pi\) | ||||
0.158097 | + | 0.987424i | \(0.449464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.8535i | 0.0319029i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 635.185 | 0.924578 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 116.624i | − 0.169265i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 80.1141i | 0.115939i | 0.998318 | + | 0.0579697i | \(0.0184627\pi\) | ||||
−0.998318 | + | 0.0579697i | \(0.981537\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 66.3672 | 0.0954924 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1126.25 | −1.61586 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 120.679i | 0.172645i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −821.973 | −1.17257 | −0.586286 | − | 0.810104i | \(-0.699411\pi\) | ||||
−0.586286 | + | 0.810104i | \(0.699411\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 641.423i | − 0.912409i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0196i | 0.0227229i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 575.456 | 0.811644 | 0.405822 | − | 0.913952i | \(-0.366985\pi\) | ||||
0.405822 | + | 0.913952i | \(0.366985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 194.665 | 0.273791 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 276.743i | − 0.388139i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.93334 | 0.00550117 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 371.601i | − 0.518272i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1213.93i | − 1.68836i | −0.536063 | − | 0.844178i | \(-0.680089\pi\) | ||||
0.536063 | − | 0.844178i | \(-0.319911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 283.009 | 0.391437 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −153.632 | −0.211906 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 379.498i | − 0.522005i | −0.965338 | − | 0.261003i | \(-0.915947\pi\) | ||||
0.965338 | − | 0.261003i | \(-0.0840532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1189.35i | − 1.62702i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1250.46i | − 1.70595i | −0.521954 | − | 0.852973i | \(-0.674797\pi\) | ||||
0.521954 | − | 0.852973i | \(-0.325203\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.7193 | −0.0172582 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 501.234 | 0.678260 | 0.339130 | − | 0.940740i | \(-0.389867\pi\) | ||||
0.339130 | + | 0.940740i | \(0.389867\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.2509i | 0.0354263i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 444.584 | 0.598363 | 0.299181 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299181 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 114.988i | 0.154346i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 354.014i | − 0.473914i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 239.335 | 0.318688 | 0.159344 | − | 0.987223i | \(-0.449062\pi\) | ||||
0.159344 | + | 0.987223i | \(0.449062\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −572.522 | −0.760322 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 90.4347i | − 0.119781i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 249.486 | 0.329572 | 0.164786 | − | 0.986329i | \(-0.447307\pi\) | ||||
0.164786 | + | 0.986329i | \(0.447307\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 65.8797i | − 0.0867981i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1375.68i | 1.80773i | 0.427821 | + | 0.903864i | \(0.359281\pi\) | ||||
−0.427821 | + | 0.903864i | \(0.640719\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33.2624 | 0.0434803 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 131.455 | 0.171389 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 528.594i | 0.687379i | 0.939083 | + | 0.343689i | \(0.111677\pi\) | ||||
−0.939083 | + | 0.343689i | \(0.888323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 278.044 | 0.360628 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 61.9934i | 0.0801984i | 0.999196 | + | 0.0400992i | \(0.0127674\pi\) | ||||
−0.999196 | + | 0.0400992i | \(0.987233\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1038.61i | 1.34015i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −521.152 | −0.669001 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −464.453 | −0.594690 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.2296i | 0.0411616i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 103.457 | 0.131792 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 163.568i | − 0.207837i | −0.994586 | − | 0.103919i | \(-0.966862\pi\) | ||||
0.994586 | − | 0.103919i | \(-0.0331381\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 184.490i | − 0.233828i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.08802 | 0.00893823 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −68.3794 | −0.0860119 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 533.394i | − 0.669253i | −0.942351 | − | 0.334626i | \(-0.891390\pi\) | ||||
0.942351 | − | 0.334626i | \(-0.108610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 443.860 | 0.555519 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 312.794i | 0.390505i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 80.1586i | − 0.0998239i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −269.254 | −0.333648 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −550.274 | −0.680191 | −0.340095 | − | 0.940391i | \(-0.610459\pi\) | ||||
−0.340095 | + | 0.940391i | \(0.610459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 415.532i | 0.512370i | 0.966628 | + | 0.256185i | \(0.0824656\pi\) | ||||
−0.966628 | + | 0.256185i | \(0.917534\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −893.876 | −1.09948 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 72.0082i | 0.0883536i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 550.348i | − 0.673621i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 869.191 | 1.05870 | 0.529349 | − | 0.848404i | \(-0.322436\pi\) | ||||
0.529349 | + | 0.848404i | \(0.322436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −421.783 | −0.512494 | −0.256247 | − | 0.966611i | \(-0.582486\pi\) | ||||
−0.256247 | + | 0.966611i | \(0.582486\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 247.246i | 0.299692i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 70.7290 | 0.0855248 | 0.0427624 | − | 0.999085i | \(-0.486384\pi\) | ||||
0.0427624 | + | 0.999085i | \(0.486384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1268.85i | − 1.53058i | −0.643685 | − | 0.765290i | \(-0.722595\pi\) | ||||
0.643685 | − | 0.765290i | \(-0.277405\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 346.759i | 0.417280i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −65.9445 | −0.0789754 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 217.885 | 0.260317 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 613.254i | 0.730935i | 0.930824 | + | 0.365467i | \(0.119091\pi\) | ||||
−0.930824 | + | 0.365467i | \(0.880909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −802.528 | −0.954254 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 395.069i | 0.468647i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 80.2627i | 0.0949855i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −451.563 | −0.531876 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 396.601 | 0.466041 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 668.244i | − 0.783404i | −0.920092 | − | 0.391702i | \(-0.871886\pi\) | ||||
0.920092 | − | 0.391702i | \(-0.128114\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.3916 | 0.0180018 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 519.712i | 0.606431i | 0.952922 | + | 0.303216i | \(0.0980602\pi\) | ||||
−0.952922 | + | 0.303216i | \(0.901940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 715.553i | − 0.833007i | −0.909134 | − | 0.416504i | \(-0.863255\pi\) | ||||
0.909134 | − | 0.416504i | \(-0.136745\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −342.716 | −0.397122 | −0.198561 | − | 0.980089i | \(-0.563627\pi\) | ||||
−0.198561 | + | 0.980089i | \(0.563627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 120.733 | 0.139576 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 421.048i | − 0.485638i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −373.963 | −0.430337 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.13374i | 0.00359786i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 95.3625i | 0.109235i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −158.550 | −0.180787 | −0.0903934 | − | 0.995906i | \(-0.528812\pi\) | ||||
−0.0903934 | + | 0.995906i | \(0.528812\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 606.019 | 0.689442 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1100.63i | 1.24930i | 0.780906 | + | 0.624648i | \(0.214758\pi\) | ||||
−0.780906 | + | 0.624648i | \(0.785242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 255.888 | 0.289794 | 0.144897 | − | 0.989447i | \(-0.453715\pi\) | ||||
0.144897 | + | 0.989447i | \(0.453715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 77.0756i | − 0.0870911i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1569.23i | − 1.76915i | −0.466400 | − | 0.884574i | \(-0.654449\pi\) | ||||
0.466400 | − | 0.884574i | \(-0.345551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.8685 | 0.0582138 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 205.388 | 0.229997 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 56.1381i | − 0.0627241i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.2313 | −0.0180951 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 260.087i | − 0.289307i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1894.61i | 2.10278i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56.3087 | 0.0622196 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 876.460 | 0.966328 | 0.483164 | − | 0.875530i | \(-0.339487\pi\) | ||||
0.483164 | + | 0.875530i | \(0.339487\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 217.511i | − 0.239286i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1778.49 | −1.95224 | −0.976118 | − | 0.217241i | \(-0.930294\pi\) | ||||
−0.976118 | + | 0.217241i | \(0.930294\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 680.080i | 0.744885i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 4.15589i | − 0.00454195i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −264.863 | −0.288208 | −0.144104 | − | 0.989563i | \(-0.546030\pi\) | ||||
−0.144104 | + | 0.989563i | \(0.546030\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −254.435 | −0.276259 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 114.431i | 0.123977i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1488.44 | −1.60912 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 320.888i | − 0.346157i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 789.390i | − 0.849720i | −0.905259 | − | 0.424860i | \(-0.860323\pi\) | ||||
0.905259 | − | 0.424860i | \(-0.139677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −139.835 | −0.149877 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −63.8989 | −0.0683411 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1446.06i | 1.54329i | 0.636053 | + | 0.771645i | \(0.280566\pi\) | ||||
−0.636053 | + | 0.771645i | \(0.719434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 267.323 | 0.284689 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1201.10i | 1.27640i | 0.769869 | + | 0.638202i | \(0.220322\pi\) | ||||
−0.769869 | + | 0.638202i | \(0.779678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 322.235i | − 0.341713i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −838.720 | −0.885660 | −0.442830 | − | 0.896606i | \(-0.646026\pi\) | ||||
−0.442830 | + | 0.896606i | \(0.646026\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.7492 | −0.0208106 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 326.570i | − 0.343396i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1377.68 | 1.44562 | 0.722812 | − | 0.691045i | \(-0.242849\pi\) | ||||
0.722812 | + | 0.691045i | \(0.242849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 164.299i | 0.172041i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 61.9147i | − 0.0646967i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −797.295 | −0.829652 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −589.858 | −0.612521 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 107.933i | − 0.111848i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 848.834 | 0.877802 | 0.438901 | − | 0.898536i | \(-0.355368\pi\) | ||||
0.438901 | + | 0.898536i | \(0.355368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 426.458i | − 0.440101i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1262.08i | 1.29977i | 0.760031 | + | 0.649887i | \(0.225184\pi\) | ||||
−0.760031 | + | 0.649887i | \(0.774816\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 60.9158 | 0.0624777 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 644.168 | 0.659332 | 0.329666 | − | 0.944098i | \(-0.393064\pi\) | ||||
0.329666 | + | 0.944098i | \(0.393064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 600.895i | − 0.613784i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −128.077 | −0.130557 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1213.77i | 1.23476i | 0.786667 | + | 0.617378i | \(0.211805\pi\) | ||||
−0.786667 | + | 0.617378i | \(0.788195\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 123.582i | 0.125464i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 340.288 | 0.344072 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1691.12 | 1.70648 | 0.853241 | − | 0.521517i | \(-0.174634\pi\) | ||||
0.853241 | + | 0.521517i | \(0.174634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 254.243i | 0.256035i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 117.992 | 0.118585 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1129.58i | 1.13297i | 0.824071 | + | 0.566487i | \(0.191698\pi\) | ||||
−0.824071 | + | 0.566487i | \(0.808302\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 312.252i | 0.312564i |
(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 | 588.3.d.c.97.7 | yes | 8 | |
3.2 | odd | 2 | 1764.3.d.h.685.4 | 8 | |||
4.3 | odd | 2 | 2352.3.f.j.97.3 | 8 | |||
7.2 | even | 3 | 588.3.m.e.325.3 | 8 | |||
7.3 | odd | 6 | 588.3.m.e.313.3 | 8 | |||
7.4 | even | 3 | 588.3.m.f.313.2 | 8 | |||
7.5 | odd | 6 | 588.3.m.f.325.2 | 8 | |||
7.6 | odd | 2 | inner | 588.3.d.c.97.2 | ✓ | 8 | |
21.2 | odd | 6 | 1764.3.z.m.325.2 | 8 | |||
21.5 | even | 6 | 1764.3.z.l.325.3 | 8 | |||
21.11 | odd | 6 | 1764.3.z.l.901.3 | 8 | |||
21.17 | even | 6 | 1764.3.z.m.901.2 | 8 | |||
21.20 | even | 2 | 1764.3.d.h.685.5 | 8 | |||
28.27 | even | 2 | 2352.3.f.j.97.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.2 | ✓ | 8 | 7.6 | odd | 2 | inner | |
588.3.d.c.97.7 | yes | 8 | 1.1 | even | 1 | trivial | |
588.3.m.e.313.3 | 8 | 7.3 | odd | 6 | |||
588.3.m.e.325.3 | 8 | 7.2 | even | 3 | |||
588.3.m.f.313.2 | 8 | 7.4 | even | 3 | |||
588.3.m.f.325.2 | 8 | 7.5 | odd | 6 | |||
1764.3.d.h.685.4 | 8 | 3.2 | odd | 2 | |||
1764.3.d.h.685.5 | 8 | 21.20 | even | 2 | |||
1764.3.z.l.325.3 | 8 | 21.5 | even | 6 | |||
1764.3.z.l.901.3 | 8 | 21.11 | odd | 6 | |||
1764.3.z.m.325.2 | 8 | 21.2 | odd | 6 | |||
1764.3.z.m.901.2 | 8 | 21.17 | even | 6 | |||
2352.3.f.j.97.3 | 8 | 4.3 | odd | 2 | |||
2352.3.f.j.97.6 | 8 | 28.27 | even | 2 |