Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1369,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.1369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.f (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: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1369.4 | ||
Root | \(2.28825i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.1369 |
Dual form | 3420.2.f.a.1369.3 |
$q$-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 \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843i | 1.06904i | 0.845154 | + | 0.534522i | \(0.179509\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23607 | 1.57873 | 0.789367 | − | 0.613922i | \(-0.210409\pi\) | ||||
0.789367 | + | 0.613922i | \(0.210409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.03631i | − 1.11947i | −0.828671 | − | 0.559735i | \(-0.810903\pi\) | ||||
0.828671 | − | 0.559735i | \(-0.189097\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.08036i | 0.262027i | 0.991381 | + | 0.131013i | \(0.0418230\pi\) | ||||
−0.991381 | + | 0.131013i | \(0.958177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 7.40492i | − 1.54403i | −0.635603 | − | 0.772016i | \(-0.719248\pi\) | ||||
0.635603 | − | 0.772016i | \(-0.280752\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.32456i | 1.06904i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.86474i | 1.12856i | 0.825585 | + | 0.564278i | \(0.190845\pi\) | ||||
−0.825585 | + | 0.564278i | \(0.809155\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.48528i | − 1.29399i | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
0.762493 | − | 0.646997i | \(-0.223975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 8.48528i | − 1.23771i | −0.785507 | − | 0.618853i | \(-0.787598\pi\) | ||||
0.785507 | − | 0.618853i | \(-0.212402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 6.86474i | − 0.942944i | −0.881881 | − | 0.471472i | \(-0.843723\pi\) | ||||
0.881881 | − | 0.471472i | \(-0.156277\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.7082 | 1.57873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4721 | −1.36336 | −0.681678 | − | 0.731652i | \(-0.738749\pi\) | ||||
−0.681678 | + | 0.731652i | \(0.738749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70820 | 0.218713 | 0.109357 | − | 0.994003i | \(-0.465121\pi\) | ||||
0.109357 | + | 0.994003i | \(0.465121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 9.02546i | − 1.11947i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.62054i | 0.197981i | 0.995088 | + | 0.0989905i | \(0.0315613\pi\) | ||||
−0.995088 | + | 0.0989905i | \(0.968439\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.52786 | 0.181324 | 0.0906621 | − | 0.995882i | \(-0.471102\pi\) | ||||
0.0906621 | + | 0.995882i | \(0.471102\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7295i | 1.60691i | 0.595363 | + | 0.803457i | \(0.297008\pi\) | ||||
−0.595363 | + | 0.803457i | \(0.702992\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.8098i | 1.68774i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4164 | 1.28445 | 0.642223 | − | 0.766518i | \(-0.278012\pi\) | ||||
0.642223 | + | 0.766518i | \(0.278012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.24419i | − 0.575625i | −0.957687 | − | 0.287812i | \(-0.907072\pi\) | ||||
0.957687 | − | 0.287812i | \(-0.0929280\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.41577i | 0.262027i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.9443 | −1.58409 | −0.792045 | − | 0.610463i | \(-0.790983\pi\) | ||||
−0.792045 | + | 0.610463i | \(0.790983\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.4164 | 1.19676 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.23607 | 0.229416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.44897i | 0.451725i | 0.974159 | + | 0.225862i | \(0.0725199\pi\) | ||||
−0.974159 | + | 0.225862i | \(0.927480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.763932 | −0.0760141 | −0.0380070 | − | 0.999277i | \(-0.512101\pi\) | ||||
−0.0380070 | + | 0.999277i | \(0.512101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3500i | 1.51248i | 0.654293 | + | 0.756241i | \(0.272966\pi\) | ||||
−0.654293 | + | 0.756241i | \(0.727034\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4304i | 1.58838i | 0.607666 | + | 0.794192i | \(0.292106\pi\) | ||||
−0.607666 | + | 0.794192i | \(0.707894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1089i | 1.13911i | 0.821952 | + | 0.569556i | \(0.192885\pi\) | ||||
−0.821952 | + | 0.569556i | \(0.807115\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 16.5579i | − 1.54403i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.05573 | −0.280118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 10.1058i | − 0.896747i | −0.893846 | − | 0.448374i | \(-0.852003\pi\) | ||||
0.893846 | − | 0.448374i | \(-0.147997\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82843i | 0.245256i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.08036i | 0.0923016i | 0.998934 | + | 0.0461508i | \(0.0146955\pi\) | ||||
−0.998934 | + | 0.0461508i | \(0.985305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7082 | −1.33235 | −0.666176 | − | 0.745794i | \(-0.732070\pi\) | ||||
−0.666176 | + | 0.745794i | \(0.732070\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 21.1344i | − 1.76735i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.6525 | 1.52807 | 0.764035 | − | 0.645175i | \(-0.223215\pi\) | ||||
0.764035 | + | 0.645175i | \(0.223215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.94427 | −0.718421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 19.3863i | − 1.54720i | −0.633676 | − | 0.773599i | \(-0.718455\pi\) | ||||
0.633676 | − | 0.773599i | \(-0.281545\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.9443 | 1.65064 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48528i | 0.664619i | 0.943170 | + | 0.332309i | \(0.107828\pi\) | ||||
−0.943170 | + | 0.332309i | \(0.892172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.70401i | 0.364007i | 0.983298 | + | 0.182004i | \(0.0582583\pi\) | ||||
−0.983298 | + | 0.182004i | \(0.941742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.29180 | −0.253215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 13.1893i | − 1.00276i | −0.865226 | − | 0.501382i | \(-0.832825\pi\) | ||||
0.865226 | − | 0.501382i | \(-0.167175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.1421i | 1.06904i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.5279 | −1.01112 | −0.505560 | − | 0.862791i | \(-0.668714\pi\) | ||||
−0.505560 | + | 0.862791i | \(0.668714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.3500i | 1.12856i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.65685i | 0.413670i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.9443 | 1.51547 | 0.757737 | − | 0.652560i | \(-0.226305\pi\) | ||||
0.757737 | + | 0.652560i | \(0.226305\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4.44897i | − 0.320244i | −0.987097 | − | 0.160122i | \(-0.948811\pi\) | ||||
0.987097 | − | 0.160122i | \(-0.0511888\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6491i | 0.901212i | 0.892723 | + | 0.450606i | \(0.148792\pi\) | ||||
−0.892723 | + | 0.450606i | \(0.851208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.6491i | 0.887794i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.4164 | 0.937043 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.23607 | 0.362186 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4164 | −0.785938 | −0.392969 | − | 0.919552i | \(-0.628552\pi\) | ||||
−0.392969 | + | 0.919552i | \(0.628552\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 18.9737i | − 1.29399i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 11.3137i | − 0.768025i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.36068 | 0.293331 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.6668i | 1.91967i | 0.280560 | + | 0.959836i | \(0.409480\pi\) | ||||
−0.280560 | + | 0.959836i | \(0.590520\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 15.3500i | − 1.01882i | −0.860525 | − | 0.509408i | \(-0.829864\pi\) | ||||
0.860525 | − | 0.509408i | \(-0.170136\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.70820 | 0.377209 | 0.188604 | − | 0.982053i | \(-0.439604\pi\) | ||||
0.188604 | + | 0.982053i | \(0.439604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.6491i | 0.828671i | 0.910124 | + | 0.414335i | \(0.135986\pi\) | ||||
−0.910124 | + | 0.414335i | \(0.864014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 18.9737i | − 1.23771i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.88854 | 0.380898 | 0.190449 | − | 0.981697i | \(-0.439006\pi\) | ||||
0.190449 | + | 0.981697i | \(0.439006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.8328 | 1.59962 | 0.799811 | − | 0.600252i | \(-0.204933\pi\) | ||||
0.799811 | + | 0.600252i | \(0.204933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.23607 | −0.142857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.03631i | − 0.256824i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.8885 | −1.88655 | −0.943274 | − | 0.332015i | \(-0.892272\pi\) | ||||
−0.943274 | + | 0.332015i | \(0.892272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 38.7727i | − 2.43762i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 4.70401i | − 0.293428i | −0.989179 | − | 0.146714i | \(-0.953130\pi\) | ||||
0.989179 | − | 0.146714i | \(-0.0468697\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.4164 | −1.20648 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.56564i | 0.589843i | 0.955522 | + | 0.294921i | \(0.0952935\pi\) | ||||
−0.955522 | + | 0.294921i | \(0.904707\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 15.3500i | − 0.942944i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.94427 | −0.179515 | −0.0897577 | − | 0.995964i | \(-0.528609\pi\) | ||||
−0.0897577 | + | 0.995964i | \(0.528609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.1246 | −1.16174 | −0.580869 | − | 0.813997i | \(-0.697287\pi\) | ||||
−0.580869 | + | 0.813997i | \(0.697287\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.1803 | 1.57873 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.24109i | − 0.194738i | −0.995248 | − | 0.0973691i | \(-0.968957\pi\) | ||||
0.995248 | − | 0.0973691i | \(-0.0310427\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.41641 | −0.0844958 | −0.0422479 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422479 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 16.5579i | − 0.984265i | −0.870520 | − | 0.492133i | \(-0.836218\pi\) | ||||
0.870520 | − | 0.492133i | \(-0.163782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9706i | 1.00174i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8328 | 0.931342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 6.86474i | − 0.401042i | −0.979689 | − | 0.200521i | \(-0.935736\pi\) | ||||
0.979689 | − | 0.200521i | \(-0.0642635\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.4164 | −1.36336 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.8885 | −1.72850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | 1.38334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.81966 | 0.218713 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.03631i | 0.230364i | 0.993344 | + | 0.115182i | \(0.0367452\pi\) | ||||
−0.993344 | + | 0.115182i | \(0.963255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.70820 | −0.210273 | −0.105136 | − | 0.994458i | \(-0.533528\pi\) | ||||
−0.105136 | + | 0.994458i | \(0.533528\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 27.4589i | − 1.55207i | −0.630689 | − | 0.776036i | \(-0.717228\pi\) | ||||
0.630689 | − | 0.776036i | \(-0.282772\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 13.1893i | − 0.740784i | −0.928875 | − | 0.370392i | \(-0.879223\pi\) | ||||
0.928875 | − | 0.370392i | \(-0.120777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.4164 | 1.31107 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.08036i | 0.0601130i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 20.1815i | − 1.11947i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.0000 | 1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4164 | −1.06722 | −0.533611 | − | 0.845730i | \(-0.679165\pi\) | ||||
−0.533611 | + | 0.845730i | \(0.679165\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.62365i | 0.197981i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.27740i | 0.396425i | 0.980159 | + | 0.198213i | \(0.0635136\pi\) | ||||
−0.980159 | + | 0.198213i | \(0.936486\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.9443 | −1.13420 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 34.8639i | − 1.87159i | −0.352544 | − | 0.935795i | \(-0.614683\pi\) | ||||
0.352544 | − | 0.935795i | \(-0.385317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.41641 | 0.0758186 | 0.0379093 | − | 0.999281i | \(-0.487930\pi\) | ||||
0.0379093 | + | 0.999281i | \(0.487930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8902i | 0.845750i | 0.906188 | + | 0.422875i | \(0.138979\pi\) | ||||
−0.906188 | + | 0.422875i | \(0.861021\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.41641 | 0.181324 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1246 | −0.587135 | −0.293567 | − | 0.955938i | \(-0.594842\pi\) | ||||
−0.293567 | + | 0.955938i | \(0.594842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.7000i | 1.60691i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.48528i | 0.442928i | 0.975169 | + | 0.221464i | \(0.0710835\pi\) | ||||
−0.975169 | + | 0.221464i | \(0.928916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.4164 | 1.00805 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.3237i | 1.77721i | 0.458670 | + | 0.888606i | \(0.348326\pi\) | ||||
−0.458670 | + | 0.888606i | \(0.651674\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 18.0509i | − 0.929670i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.6777i | 1.20987i | 0.796274 | + | 0.604936i | \(0.206801\pi\) | ||||
−0.796274 | + | 0.604936i | \(0.793199\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 33.1158i | 1.68774i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.94427 | 0.149281 | 0.0746403 | − | 0.997211i | \(-0.476219\pi\) | ||||
0.0746403 | + | 0.997211i | \(0.476219\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.5279 | 1.28445 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.7000i | 1.54079i | 0.637566 | + | 0.770395i | \(0.279941\pi\) | ||||
−0.637566 | + | 0.770395i | \(0.720059\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.47214 | −0.223328 | −0.111664 | − | 0.993746i | \(-0.535618\pi\) | ||||
−0.111664 | + | 0.993746i | \(0.535618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.1452i | 0.804252i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.9442i | 1.78169i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.41641 | 0.465611 | 0.232806 | − | 0.972523i | \(-0.425209\pi\) | ||||
0.232806 | + | 0.972523i | \(0.425209\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 29.6197i | − 1.45749i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 11.7264i | − 0.575625i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.05573 | −0.149282 | −0.0746410 | − | 0.997210i | \(-0.523781\pi\) | ||||
−0.0746410 | + | 0.997210i | \(0.523781\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.40182i | 0.262027i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.83153i | 0.233814i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4721 | −0.504425 | −0.252213 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252213 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.9774i | 1.82508i | 0.408989 | + | 0.912540i | \(0.365882\pi\) | ||||
−0.408989 | + | 0.912540i | \(0.634118\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.40492i | − 0.354225i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.8328 | −1.66248 | −0.831240 | − | 0.555914i | \(-0.812368\pi\) | ||||
−0.831240 | + | 0.555914i | \(0.812368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.24419i | 0.249159i | 0.992210 | + | 0.124580i | \(0.0397582\pi\) | ||||
−0.992210 | + | 0.124580i | \(0.960242\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.4164 | −1.58409 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.52786 | −0.355262 | −0.177631 | − | 0.984097i | \(-0.556843\pi\) | ||||
−0.177631 | + | 0.984097i | \(0.556843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.4164 | 1.47934 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.5279 | 1.19676 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 37.9473i | − 1.77510i | −0.460710 | − | 0.887551i | \(-0.652405\pi\) | ||||
0.460710 | − | 0.887551i | \(-0.347595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8885 | 0.553705 | 0.276852 | − | 0.960912i | \(-0.410709\pi\) | ||||
0.276852 | + | 0.960912i | \(0.410709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 33.5285i | − 1.55820i | −0.626900 | − | 0.779100i | \(-0.715676\pi\) | ||||
0.626900 | − | 0.779100i | \(-0.284324\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 11.7264i | − 0.542632i | −0.962490 | − | 0.271316i | \(-0.912541\pi\) | ||||
0.962490 | − | 0.271316i | \(-0.0874588\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.58359 | −0.211651 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 44.4295i | − 2.04287i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00000 | 0.229416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.76393 | 0.309052 | 0.154526 | − | 0.987989i | \(-0.450615\pi\) | ||||
0.154526 | + | 0.987989i | \(0.450615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7082 | 1.26339 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.94820i | 0.451725i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7658i | 0.805044i | 0.915410 | + | 0.402522i | \(0.131866\pi\) | ||||
−0.915410 | + | 0.402522i | \(0.868134\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.8885 | 1.34885 | 0.674426 | − | 0.738343i | \(-0.264391\pi\) | ||||
0.674426 | + | 0.738343i | \(0.264391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.83153i | 0.217601i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.32145i | 0.193844i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.1246 | −1.03520 | −0.517600 | − | 0.855623i | \(-0.673174\pi\) | ||||
−0.517600 | + | 0.855623i | \(0.673174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.1853i | 1.74719i | 0.486656 | + | 0.873593i | \(0.338216\pi\) | ||||
−0.486656 | + | 0.873593i | \(0.661784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.70820 | −0.0760141 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.4164 | −1.65845 | −0.829227 | − | 0.558913i | \(-0.811219\pi\) | ||||
−0.829227 | + | 0.558913i | \(0.811219\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38.8328 | −1.71786 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.3237i | 1.51248i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 44.4295i | − 1.95401i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.8885 | −1.57231 | −0.786153 | − | 0.618032i | \(-0.787930\pi\) | ||||
−0.786153 | + | 0.618032i | \(0.787930\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 3.62365i | − 0.158451i | −0.996857 | − | 0.0792255i | \(-0.974755\pi\) | ||||
0.996857 | − | 0.0792255i | \(-0.0252447\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 4.32145i | − 0.188245i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31.8328 | −1.38404 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 24.2179i | − 1.04899i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.7394i | 1.58838i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.23607 | −0.225533 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.70820 | −0.0734414 | −0.0367207 | − | 0.999326i | \(-0.511691\pi\) | ||||
−0.0367207 | + | 0.999326i | \(0.511691\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.47214 | −0.191565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.20788i | 0.0516453i | 0.999667 | + | 0.0258227i | \(0.00822052\pi\) | ||||
−0.999667 | + | 0.0258227i | \(0.991779\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.47214 | 0.190519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.2905i | 1.37313i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.5687i | 0.490184i | 0.969500 | + | 0.245092i | \(0.0788181\pi\) | ||||
−0.969500 | + | 0.245092i | \(0.921182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.2492 | −1.44859 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 17.3531i | − 0.731347i | −0.930743 | − | 0.365673i | \(-0.880839\pi\) | ||||
0.930743 | − | 0.365673i | \(-0.119161\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.0764i | 1.13911i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.0557 | −0.882702 | −0.441351 | − | 0.897335i | \(-0.645501\pi\) | ||||
−0.441351 | + | 0.897335i | \(0.645501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.1246 | −0.632945 | −0.316473 | − | 0.948602i | \(-0.602499\pi\) | ||||
−0.316473 | + | 0.948602i | \(0.602499\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 37.0246i | − 1.54403i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 5.65685i | − 0.235498i | −0.993043 | − | 0.117749i | \(-0.962432\pi\) | ||||
0.993043 | − | 0.117749i | \(-0.0375678\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.8328 | 0.615369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 35.9442i | − 1.48866i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 37.0246i | − 1.52817i | −0.645117 | − | 0.764084i | \(-0.723191\pi\) | ||||
0.645117 | − | 0.764084i | \(-0.276809\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 14.8098i | − 0.608167i | −0.952645 | − | 0.304084i | \(-0.901650\pi\) | ||||
0.952645 | − | 0.304084i | \(-0.0983502\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.83282 | −0.280118 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.0000 | −1.47092 | −0.735460 | − | 0.677568i | \(-0.763034\pi\) | ||||
−0.735460 | + | 0.677568i | \(0.763034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.8328 | −1.50244 | −0.751221 | − | 0.660051i | \(-0.770535\pi\) | ||||
−0.751221 | + | 0.660051i | \(0.770535\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.7082 | 1.49240 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9343i | 0.524985i | 0.964934 | + | 0.262493i | \(0.0845445\pi\) | ||||
−0.964934 | + | 0.262493i | \(0.915455\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.2492 | −1.38558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.2117i | 0.816341i | 0.912906 | + | 0.408170i | \(0.133833\pi\) | ||||
−0.912906 | + | 0.408170i | \(0.866167\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.5393i | 1.14895i | 0.818522 | + | 0.574475i | \(0.194794\pi\) | ||||
−0.818522 | + | 0.574475i | \(0.805206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.875388 | −0.0351848 | −0.0175924 | − | 0.999845i | \(-0.505600\pi\) | ||||
−0.0175924 | + | 0.999845i | \(0.505600\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 42.2688i | − 1.69346i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.41641 | −0.295712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.7082 | 0.466096 | 0.233048 | − | 0.972465i | \(-0.425130\pi\) | ||||
0.233048 | + | 0.972465i | \(0.425130\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 22.5973i | − 0.896747i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.03631i | 0.159924i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.8885 | 1.89148 | 0.945742 | − | 0.324919i | \(-0.105337\pi\) | ||||
0.945742 | + | 0.324919i | \(0.105337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7264i | 0.462443i | 0.972901 | + | 0.231221i | \(0.0742722\pi\) | ||||
−0.972901 | + | 0.231221i | \(0.925728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 34.8639i | − 1.37064i | −0.728242 | − | 0.685320i | \(-0.759662\pi\) | ||||
0.728242 | − | 0.685320i | \(-0.240338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −54.8328 | −2.15238 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.24109i | − 0.126834i | −0.997987 | − | 0.0634168i | \(-0.979800\pi\) | ||||
0.997987 | − | 0.0634168i | \(-0.0201998\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.0557 | −1.05394 | −0.526971 | − | 0.849883i | \(-0.676672\pi\) | ||||
−0.526971 | + | 0.849883i | \(0.676672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.0000 | −1.01128 | −0.505641 | − | 0.862744i | \(-0.668744\pi\) | ||||
−0.505641 | + | 0.862744i | \(0.668744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.32456i | 0.245256i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 33.1158i | − 1.28225i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.94427 | 0.345290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 42.8090i | − 1.65016i | −0.565013 | − | 0.825082i | \(-0.691129\pi\) | ||||
0.565013 | − | 0.825082i | \(-0.308871\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0022i | 1.15308i | 0.817069 | + | 0.576540i | \(0.195597\pi\) | ||||
−0.817069 | + | 0.576540i | \(0.804403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.5836 | −0.482914 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.1058i | 0.386689i | 0.981131 | + | 0.193344i | \(0.0619334\pi\) | ||||
−0.981131 | + | 0.193344i | \(0.938067\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.41577i | 0.0923016i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.7082 | −1.05560 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1246 | −0.575367 | −0.287684 | − | 0.957725i | \(-0.592885\pi\) | ||||
−0.287684 | + | 0.957725i | \(0.592885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.1246 | −1.33235 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.48218i | 0.245530i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.1246 | −1.55326 | −0.776628 | − | 0.629960i | \(-0.783071\pi\) | ||||
−0.776628 | + | 0.629960i | \(0.783071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.86474i | 0.258908i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.16073i | − 0.0812625i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.58359 | −0.247252 | −0.123626 | − | 0.992329i | \(-0.539452\pi\) | ||||
−0.123626 | + | 0.992329i | \(0.539452\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.6197i | 1.10927i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 47.2579i | − 1.76735i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.5967 | −0.805423 | −0.402711 | − | 0.915327i | \(-0.631932\pi\) | ||||
−0.402711 | + | 0.915327i | \(0.631932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.4164 | −1.61691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.3607 | 0.830455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.48528i | 0.314702i | 0.987543 | + | 0.157351i | \(0.0502953\pi\) | ||||
−0.987543 | + | 0.157351i | \(0.949705\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.16718 | 0.339061 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.9411i | 1.25364i | 0.779162 | + | 0.626822i | \(0.215645\pi\) | ||||
−0.779162 | + | 0.626822i | \(0.784355\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.48528i | 0.312559i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.8328 | −1.28135 | −0.640673 | − | 0.767814i | \(-0.721345\pi\) | ||||
−0.640673 | + | 0.767814i | \(0.721345\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.86474i | 0.251843i | 0.992040 | + | 0.125921i | \(0.0401887\pi\) | ||||
−0.992040 | + | 0.125921i | \(0.959811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.7082 | 1.52807 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.4721 | −1.69805 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.4164 | 1.73025 | 0.865125 | − | 0.501557i | \(-0.167239\pi\) | ||||
0.865125 | + | 0.501557i | \(0.167239\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.8885 | −0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 0.825324i | − 0.0299969i | −0.999888 | − | 0.0149985i | \(-0.995226\pi\) | ||||
0.999888 | − | 0.0149985i | \(-0.00477434\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.5410 | −0.889611 | −0.444806 | − | 0.895627i | \(-0.646727\pi\) | ||||
−0.444806 | + | 0.895627i | \(0.646727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 5.65685i | − 0.204792i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.2688i | 1.52624i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.5410 | −1.02922 | −0.514608 | − | 0.857426i | \(-0.672062\pi\) | ||||
−0.514608 | + | 0.857426i | \(0.672062\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.3500i | 0.552102i | 0.961143 | + | 0.276051i | \(0.0890258\pi\) | ||||
−0.961143 | + | 0.276051i | \(0.910974\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.0000 | −0.718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 43.3491i | − 1.54720i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.62365i | − 0.129169i | −0.997912 | − | 0.0645845i | \(-0.979428\pi\) | ||||
0.997912 | − | 0.0645845i | \(-0.0205722\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.2492 | −1.21776 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 6.89484i | − 0.244843i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 14.1120i | − 0.499874i | −0.968262 | − | 0.249937i | \(-0.919590\pi\) | ||||
0.968262 | − | 0.249937i | \(-0.0804099\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.16718 | 0.324312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 71.8885i | 2.53689i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 46.8328 | 1.65064 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4721 | −0.579129 | −0.289565 | − | 0.957158i | \(-0.593511\pi\) | ||||
−0.289565 | + | 0.957158i | \(0.593511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.9737i | 0.664619i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 8.48528i | − 0.296862i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0557 | −0.734850 | −0.367425 | − | 0.930053i | \(-0.619761\pi\) | ||||
−0.367425 | + | 0.930053i | \(0.619761\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 2.00310i | − 0.0698238i | −0.999390 | − | 0.0349119i | \(-0.988885\pi\) | ||||
0.999390 | − | 0.0349119i | \(-0.0111151\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 20.5942i | − 0.716131i | −0.933696 | − | 0.358065i | \(-0.883436\pi\) | ||||
0.933696 | − | 0.358065i | \(-0.116564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.08036i | − 0.0374324i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5185i | 0.364007i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.3050 | −0.459338 | −0.229669 | − | 0.973269i | \(-0.573764\pi\) | ||||
−0.229669 | + | 0.973269i | \(0.573764\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.36068 | −0.253215 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.4326i | 1.59544i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.8328 | 1.74253 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 10.4884i | − 0.359115i | −0.983747 | − | 0.179558i | \(-0.942533\pi\) | ||||
0.983747 | − | 0.179558i | \(-0.0574667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 40.8059i | − 1.39390i | −0.717119 | − | 0.696951i | \(-0.754540\pi\) | ||||
0.717119 | − | 0.696951i | \(-0.245460\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0000 | −1.36478 | −0.682391 | − | 0.730987i | \(-0.739060\pi\) | ||||
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 20.5942i | − 0.701035i | −0.936556 | − | 0.350518i | \(-0.886006\pi\) | ||||
0.936556 | − | 0.350518i | \(-0.113994\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 29.4922i | − 1.00276i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 59.7771 | 2.02780 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.54102 | 0.221634 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.6228i | 1.06904i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.44897i | 0.150231i | 0.997175 | + | 0.0751155i | \(0.0239326\pi\) | ||||
−0.997175 | + | 0.0751155i | \(0.976067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.6525 | 1.03271 | 0.516354 | − | 0.856375i | \(-0.327289\pi\) | ||||
0.516354 | + | 0.856375i | \(0.327289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.9675i | 0.503695i | 0.967767 | + | 0.251848i | \(0.0810382\pi\) | ||||
−0.967767 | + | 0.251848i | \(0.918962\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 36.3268i | − 1.21973i | −0.792504 | − | 0.609867i | \(-0.791223\pi\) | ||||
0.792504 | − | 0.609867i | \(-0.208777\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.5836 | 0.958663 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.48528i | − 0.283949i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.2492 | −1.01112 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.8885 | −0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.41641 | 0.247076 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.4164 | 0.445976 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.86784i | 0.294452i | 0.989103 | + | 0.147226i | \(0.0470344\pi\) | ||||
−0.989103 | + | 0.147226i | \(0.952966\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5279 | 1.24335 | 0.621677 | − | 0.783274i | \(-0.286452\pi\) | ||||
0.621677 | + | 0.783274i | \(0.286452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 27.4589i | − 0.908759i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8328 | 0.885133 | 0.442566 | − | 0.896736i | \(-0.354068\pi\) | ||||
0.442566 | + | 0.896736i | \(0.354068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 6.16693i | − 0.202987i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.3237i | 1.12856i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.4721 | 0.540433 | 0.270217 | − | 0.962800i | \(-0.412905\pi\) | ||||
0.270217 | + | 0.962800i | \(0.412905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.6491i | 0.413670i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.6768i | 1.68821i | 0.536180 | + | 0.844104i | \(0.319867\pi\) | ||||
−0.536180 | + | 0.844104i | \(0.680133\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0557 | 0.686397 | 0.343199 | − | 0.939263i | \(-0.388490\pi\) | ||||
0.343199 | + | 0.939263i | \(0.388490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 44.4295i | − 1.44682i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.6969i | 0.932525i | 0.884646 | + | 0.466263i | \(0.154400\pi\) | ||||
−0.884646 | + | 0.466263i | \(0.845600\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.4164 | 1.79889 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 27.0764i | − 0.877090i | −0.898709 | − | 0.438545i | \(-0.855494\pi\) | ||||
0.898709 | − | 0.438545i | \(-0.144506\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.8328 | 1.51547 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.05573 | −0.0986746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 9.94820i | − 0.320244i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5579i | 0.532466i | 0.963909 | + | 0.266233i | \(0.0857791\pi\) | ||||
−0.963909 | + | 0.266233i | \(0.914221\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.36068 | −0.139941 | −0.0699704 | − | 0.997549i | \(-0.522290\pi\) | ||||
−0.0699704 | + | 0.997549i | \(0.522290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 44.4295i | − 1.42434i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 47.1304i | − 1.50784i | −0.656969 | − | 0.753918i | \(-0.728162\pi\) | ||||
0.656969 | − | 0.753918i | \(-0.271838\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −78.2492 | −2.50086 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 33.4009i | − 1.06532i | −0.846328 | − | 0.532662i | \(-0.821192\pi\) | ||||
0.846328 | − | 0.532662i | \(-0.178808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.2843i | 0.901212i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −62.8328 | −1.99797 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.8328 | −0.471180 | −0.235590 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.7771 | 1.13421 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 30.7000i | − 0.972280i | −0.873881 | − | 0.486140i | \(-0.838405\pi\) | ||||
0.873881 | − | 0.486140i | \(-0.161595\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3420.2.f.a.1369.4 | 4 | ||
3.2 | odd | 2 | 380.2.c.a.229.4 | yes | 4 | ||
5.4 | even | 2 | inner | 3420.2.f.a.1369.3 | 4 | ||
12.11 | even | 2 | 1520.2.d.f.609.1 | 4 | |||
15.2 | even | 4 | 1900.2.a.j.1.4 | 4 | |||
15.8 | even | 4 | 1900.2.a.j.1.1 | 4 | |||
15.14 | odd | 2 | 380.2.c.a.229.1 | ✓ | 4 | ||
60.23 | odd | 4 | 7600.2.a.ce.1.4 | 4 | |||
60.47 | odd | 4 | 7600.2.a.ce.1.1 | 4 | |||
60.59 | even | 2 | 1520.2.d.f.609.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.a.229.1 | ✓ | 4 | 15.14 | odd | 2 | ||
380.2.c.a.229.4 | yes | 4 | 3.2 | odd | 2 | ||
1520.2.d.f.609.1 | 4 | 12.11 | even | 2 | |||
1520.2.d.f.609.4 | 4 | 60.59 | even | 2 | |||
1900.2.a.j.1.1 | 4 | 15.8 | even | 4 | |||
1900.2.a.j.1.4 | 4 | 15.2 | even | 4 | |||
3420.2.f.a.1369.3 | 4 | 5.4 | even | 2 | inner | ||
3420.2.f.a.1369.4 | 4 | 1.1 | even | 1 | trivial | ||
7600.2.a.ce.1.1 | 4 | 60.47 | odd | 4 | |||
7600.2.a.ce.1.4 | 4 | 60.23 | odd | 4 |