Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(229,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("380.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.c (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: | \(3.03431527681\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.1 | ||
Root | \(-2.28825i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.229 |
Dual form | 380.2.c.a.229.4 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.28825i | − 1.32112i | −0.750774 | − | 0.660560i | \(-0.770319\pi\) | ||||
0.750774 | − | 0.660560i | \(-0.229681\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.82843i | − 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | −0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.23607 | −1.57873 | −0.789367 | − | 0.613922i | \(-0.789591\pi\) | ||||
−0.789367 | + | 0.613922i | \(0.789591\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.03631i | 1.11947i | 0.828671 | + | 0.559735i | \(0.189097\pi\) | ||||
−0.828671 | + | 0.559735i | \(0.810903\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.11667i | 1.32112i | ||||||||
\(16\) | 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 | ||||||||
\(21\) | −6.47214 | −1.41234 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − 1.74806i | − 0.336415i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.9814i | 2.08570i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.32456i | 1.06904i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.86474i | − 1.12856i | −0.825585 | − | 0.564278i | \(-0.809155\pi\) | ||||
0.825585 | − | 0.564278i | \(-0.190845\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.23607 | 1.47895 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48528i | 1.29399i | 0.762493 | + | 0.646997i | \(0.223975\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.00000 | 0.745356 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | − 2.28825i | − 0.303086i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.4721 | 1.36336 | 0.681678 | − | 0.731652i | \(-0.261251\pi\) | ||||
0.681678 | + | 0.731652i | \(0.261251\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70820 | 0.218713 | 0.109357 | − | 0.994003i | \(-0.465121\pi\) | ||||
0.109357 | + | 0.994003i | \(0.465121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.32456i | 0.796819i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 9.02546i | − 1.11947i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.62054i | − 0.197981i | −0.995088 | − | 0.0989905i | \(-0.968439\pi\) | ||||
0.995088 | − | 0.0989905i | \(-0.0315613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.9443 | −2.03985 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.52786 | −0.181324 | −0.0906621 | − | 0.995882i | \(-0.528898\pi\) | ||||
−0.0906621 | + | 0.995882i | \(0.528898\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 13.7295i | − 1.60691i | −0.595363 | − | 0.803457i | \(-0.702992\pi\) | ||||
0.595363 | − | 0.803457i | \(-0.297008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 11.4412i | − 1.32112i | ||||||||
\(76\) | 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 | ||||||||
\(81\) | −10.7082 | −1.18980 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 10.2333i | 1.09713i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.9443 | 1.58409 | 0.792045 | − | 0.610463i | \(-0.209017\pi\) | ||||
0.792045 | + | 0.610463i | \(0.209017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.4164 | 1.19676 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.15298i | 0.949120i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.23607 | −0.229416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 4.44897i | − 0.451725i | −0.974159 | − | 0.225862i | \(-0.927480\pi\) | ||||
0.974159 | − | 0.225862i | \(-0.0725199\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.7082 | 1.17672 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.763932 | 0.0760141 | 0.0380070 | − | 0.999277i | \(-0.487899\pi\) | ||||
0.0380070 | + | 0.999277i | \(0.487899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 15.3500i | − 1.51248i | −0.654293 | − | 0.756241i | \(-0.727034\pi\) | ||||
0.654293 | − | 0.756241i | \(-0.272966\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.4721 | 1.41234 | ||||||||
\(106\) | 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 | ||||||||
\(111\) | −15.7082 | −1.49096 | ||||||||
\(112\) | 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 | ||||||||
\(117\) | − 9.02546i | − 0.834404i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.05573 | 0.280118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.7295i | 1.23794i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.1058i | 0.896747i | 0.893846 | + | 0.448374i | \(0.147997\pi\) | ||||
−0.893846 | + | 0.448374i | \(0.852003\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.4164 | 1.70952 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | 3.90879i | 0.336415i | ||||||||
\(136\) | 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 | ||||||||
\(141\) | −19.4164 | −1.63516 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 21.1344i | − 1.76735i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.28825i | 0.188731i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.6525 | −1.52807 | −0.764035 | − | 0.645175i | \(-0.776785\pi\) | ||||
−0.764035 | + | 0.645175i | \(0.776785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 2.41577i | − 0.195303i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.94427 | 0.718421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.3863i | 1.54720i | 0.633676 | + | 0.773599i | \(0.281545\pi\) | ||||
−0.633676 | + | 0.773599i | \(0.718455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.7082 | −1.24574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.9443 | −1.65064 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.48528i | − 0.664619i | −0.943170 | − | 0.332309i | \(-0.892172\pi\) | ||||
0.943170 | − | 0.332309i | \(-0.107828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 26.7912i | − 2.08570i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | −2.23607 | −0.170996 | ||||||||
\(172\) | 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 | ||||||||
\(177\) | − 23.9628i | − 1.80116i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5279 | 1.01112 | 0.505560 | − | 0.862791i | \(-0.331286\pi\) | ||||
0.505560 | + | 0.862791i | \(0.331286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 3.90879i | − 0.288946i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.3500i | 1.12856i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.65685i | − 0.413670i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.94427 | −0.359643 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.9443 | −1.51547 | −0.757737 | − | 0.652560i | \(-0.773695\pi\) | ||||
−0.757737 | + | 0.652560i | \(0.773695\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.44897i | 0.320244i | 0.987097 | + | 0.160122i | \(0.0511888\pi\) | ||||
−0.987097 | + | 0.160122i | \(0.948811\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.6525 | −1.47895 | ||||||||
\(196\) | 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 | ||||||||
\(201\) | −3.70820 | −0.261557 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.6491i | 0.887794i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.4164 | 0.937043 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.5579i | 1.15085i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 3.49613i | 0.239551i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 18.9737i | − 1.29399i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3137i | 0.768025i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −31.4164 | −2.12292 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.36068 | −0.293331 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 28.6668i | − 1.91967i | −0.280560 | − | 0.959836i | \(-0.590520\pi\) | ||||
0.280560 | − | 0.959836i | \(-0.409480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.1803 | −0.745356 | ||||||||
\(226\) | 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 | ||||||||
\(231\) | 33.8885 | 2.22970 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | − 26.1235i | − 1.69691i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.88854 | −0.380898 | −0.190449 | − | 0.981697i | \(-0.560994\pi\) | ||||
−0.190449 | + | 0.981697i | \(0.560994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.8328 | 1.59962 | 0.799811 | − | 0.600252i | \(-0.204933\pi\) | ||||
0.799811 | + | 0.600252i | \(0.204933\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.2588i | 1.23545i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.23607 | 0.142857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.03631i | 0.256824i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.8885 | 1.88655 | 0.943274 | − | 0.332015i | \(-0.107728\pi\) | ||||
0.943274 | + | 0.332015i | \(0.107728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 38.7727i | 2.43762i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.52786 | −0.346168 | ||||||||
\(256\) | 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 | ||||||||
\(261\) | 10.0000 | 0.618984 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | − 34.1962i | − 2.09277i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.94427 | 0.179515 | 0.0897577 | − | 0.995964i | \(-0.471391\pi\) | ||||
0.0897577 | + | 0.995964i | \(0.471391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.1246 | −1.16174 | −0.580869 | − | 0.813997i | \(-0.697287\pi\) | ||||
−0.580869 | + | 0.813997i | \(0.697287\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 26.1235i | − 1.58107i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −26.1803 | −1.57873 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.24109i | 0.194738i | 0.995248 | + | 0.0973691i | \(0.0310427\pi\) | ||||
−0.995248 | + | 0.0973691i | \(0.968957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.94427 | 0.535480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.41641 | 0.0844958 | 0.0422479 | − | 0.999107i | \(-0.486548\pi\) | ||||
0.0422479 | + | 0.999107i | \(0.486548\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.5579i | 0.984265i | 0.870520 | + | 0.492133i | \(0.163782\pi\) | ||||
−0.870520 | + | 0.492133i | \(0.836218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.11667i | 0.303086i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9706i | 1.00174i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8328 | 0.931342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.1803 | −0.596782 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 9.15298i | 0.531110i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.8885 | 1.72850 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | 1.38334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 1.74806i | − 0.100424i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.81966 | −0.218713 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4.03631i | − 0.230364i | −0.993344 | − | 0.115182i | \(-0.963255\pi\) | ||||
0.993344 | − | 0.115182i | \(-0.0367452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −35.1246 | −1.99817 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.70820 | 0.210273 | 0.105136 | − | 0.994458i | \(-0.466472\pi\) | ||||
0.105136 | + | 0.994458i | \(0.466472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.4589i | 1.55207i | 0.630689 | + | 0.776036i | \(0.282772\pi\) | ||||
−0.630689 | + | 0.776036i | \(0.717228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 14.1421i | − 0.796819i | ||||||||
\(316\) | 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 | ||||||||
\(321\) | 37.5967 | 2.09845 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.08036i | 0.0601130i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.1815i | 1.11947i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.57649i | 0.253081i | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 15.3500i | 0.841176i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.62365i | 0.197981i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 7.27740i | − 0.396425i | −0.980159 | − | 0.198213i | \(-0.936486\pi\) | ||||
0.980159 | − | 0.198213i | \(-0.0635136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.7082 | 1.50490 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.9443 | 1.13420 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 16.9706i | − 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 37.8885 | 2.03985 | ||||||||
\(346\) | 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 | ||||||||
\(351\) | 7.05573 | 0.376607 | ||||||||
\(352\) | 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 | ||||||||
\(357\) | − 6.99226i | − 0.370069i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.1246 | 0.587135 | 0.293567 | − | 0.955938i | \(-0.405158\pi\) | ||||
0.293567 | + | 0.955938i | \(0.405158\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 37.5648i | − 1.97164i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.7000i | 1.60691i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 8.48528i | − 0.442928i | −0.975169 | − | 0.221464i | \(-0.928916\pi\) | ||||
0.975169 | − | 0.221464i | \(-0.0710835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.4164 | 0.698430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.4164 | −1.00805 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 34.3237i | − 1.77721i | −0.458670 | − | 0.888606i | \(-0.651674\pi\) | ||||
0.458670 | − | 0.888606i | \(-0.348326\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.5834i | 1.32112i | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 23.1246 | 1.18471 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | − 18.9737i | − 0.964486i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.94427 | −0.149281 | −0.0746403 | − | 0.997211i | \(-0.523781\pi\) | ||||
−0.0746403 | + | 0.997211i | \(0.523781\pi\) | |||||||
\(390\) | 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 | \(-0.720059\pi\) | ||||
0.637566 | − | 0.770395i | \(-0.279941\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.47214 | −0.324012 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.47214 | 0.223328 | 0.111664 | − | 0.993746i | \(-0.464382\pi\) | ||||
0.111664 | + | 0.993746i | \(0.464382\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 16.1452i | − 0.804252i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 23.9443 | 1.18980 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 2.47214 | 0.121941 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 29.6197i | − 1.45749i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.7264i | 0.575625i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.9442i | 1.76020i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.05573 | 0.149282 | 0.0746410 | − | 0.997210i | \(-0.476219\pi\) | ||||
0.0746410 | + | 0.997210i | \(0.476219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.9737i | 0.922531i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.40182i | 0.262027i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.83153i | − 0.233814i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −48.3607 | −2.33488 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.4721 | 0.504425 | 0.252213 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252213 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 37.9774i | − 1.82508i | −0.408989 | − | 0.912540i | \(-0.634118\pi\) | ||||
0.408989 | − | 0.912540i | \(-0.365882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 22.8825i | − 1.09713i | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 2.23607 | 0.106479 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 42.6814i | 2.01876i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.52786 | 0.355262 | 0.177631 | − | 0.984097i | \(-0.443157\pi\) | ||||
0.177631 | + | 0.984097i | \(0.443157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.4164 | 1.47934 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.3060i | 0.860089i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.5279 | −1.19676 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.9473i | 1.77510i | 0.460710 | + | 0.887551i | \(0.347595\pi\) | ||||
−0.460710 | + | 0.887551i | \(0.652405\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.88854 | 0.0881497 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8885 | −0.553705 | −0.276852 | − | 0.960912i | \(-0.589291\pi\) | ||||
−0.276852 | + | 0.960912i | \(0.589291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.5285i | 1.55820i | 0.626900 | + | 0.779100i | \(0.284324\pi\) | ||||
−0.626900 | + | 0.779100i | \(0.715676\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 20.4667i | − 0.949120i | ||||||||
\(466\) | 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 | ||||||||
\(471\) | 44.3607 | 2.04403 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 44.4295i | − 2.04287i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00000 | 0.229416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.3500i | 0.702829i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.76393 | −0.309052 | −0.154526 | − | 0.987989i | \(-0.549385\pi\) | ||||
−0.154526 | + | 0.987989i | \(0.549385\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7082 | 1.26339 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 47.9256i | 2.18069i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.94820i | 0.451725i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 17.7658i | − 0.805044i | −0.915410 | − | 0.402522i | \(-0.868134\pi\) | ||||
0.915410 | − | 0.402522i | \(-0.131866\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.4164 | −0.878040 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.8885 | −1.34885 | −0.674426 | − | 0.738343i | \(-0.735609\pi\) | ||||
−0.674426 | + | 0.738343i | \(0.735609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.83153i | − 0.217601i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26.1803 | −1.17672 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 10.7639 | 0.480897 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 7.53244i | 0.334527i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.4164 | 1.65845 | 0.829227 | − | 0.558913i | \(-0.188781\pi\) | ||||
0.829227 | + | 0.558913i | \(0.188781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38.8328 | −1.71786 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 1.74806i | − 0.0771789i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.3237i | 1.51248i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.4295i | 1.95401i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.1803 | −1.32477 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.8885 | 1.57231 | 0.786153 | − | 0.618032i | \(-0.212070\pi\) | ||||
0.786153 | + | 0.618032i | \(0.212070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.62365i | 0.158451i | 0.996857 | + | 0.0792255i | \(0.0252447\pi\) | ||||
−0.996857 | + | 0.0792255i | \(0.974755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −32.3607 | −1.41234 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 4.32145i | − 0.188245i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31.8328 | −1.38404 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.4164 | −1.01619 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 24.2179i | − 1.04899i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 36.7394i | − 1.58838i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 30.9551i | − 1.33581i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − 13.7295i | − 0.589188i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.47214 | 0.191565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.20788i | − 0.0516453i | −0.999667 | − | 0.0258227i | \(-0.991779\pi\) | ||||
0.999667 | − | 0.0258227i | \(-0.00822052\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.81966 | −0.163019 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.47214 | −0.190519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 32.2905i | − 1.37313i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 35.1246 | 1.49096 | ||||||||
\(556\) | 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 | ||||||||
\(561\) | −12.9443 | −0.546508 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 30.2874i | 1.27195i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.0557 | 0.882702 | 0.441351 | − | 0.897335i | \(-0.354499\pi\) | ||||
0.441351 | + | 0.897335i | \(0.354499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.1246 | −0.632945 | −0.316473 | − | 0.948602i | \(-0.602499\pi\) | ||||
−0.316473 | + | 0.948602i | \(0.602499\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 47.9256i | 2.00212i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 37.0246i | − 1.54403i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.65685i | 0.235498i | 0.993043 | + | 0.117749i | \(0.0375678\pi\) | ||||
−0.993043 | + | 0.117749i | \(0.962432\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.1803 | 0.423080 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.8328 | −0.615369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.9442i | 1.48866i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20.1815i | 0.834404i | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 28.9443 | 1.19061 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | − 36.6119i | − 1.49843i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0000 | 1.47092 | 0.735460 | − | 0.677568i | \(-0.236966\pi\) | ||||
0.735460 | + | 0.677568i | \(0.236966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.8328 | −1.50244 | −0.751221 | − | 0.660051i | \(-0.770535\pi\) | ||||
−0.751221 | + | 0.660051i | \(0.770535\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.62365i | 0.147566i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.7082 | −1.49240 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 12.9343i | − 0.524985i | −0.964934 | − | 0.262493i | \(-0.915455\pi\) | ||||
0.964934 | − | 0.262493i | \(-0.0845445\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.9443 | 1.17288 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.2492 | 1.38558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20.2117i | − 0.816341i | −0.912906 | − | 0.408170i | \(-0.866167\pi\) | ||||
0.912906 | − | 0.408170i | \(-0.133833\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 30.7000i | − 1.23794i | ||||||||
\(616\) | 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 | ||||||||
\(621\) | −12.9443 | −0.519436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 42.2688i | − 1.69346i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.9814i | 0.478491i | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 26.1235i | 1.03832i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 22.5973i | − 0.896747i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.03631i | − 0.159924i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.41641 | 0.135151 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −47.8885 | −1.89148 | −0.945742 | − | 0.324919i | \(-0.894663\pi\) | ||||
−0.945742 | + | 0.324919i | \(0.894663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 11.7264i | − 0.462443i | −0.972901 | − | 0.231221i | \(-0.925728\pi\) | ||||
0.972901 | − | 0.231221i | \(-0.0742722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −43.4164 | −1.70952 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 25.8885 | 1.01465 | ||||||||
\(652\) | 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 | ||||||||
\(657\) | 30.7000i | 1.19772i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.0557 | 1.05394 | 0.526971 | − | 0.849883i | \(-0.323328\pi\) | ||||
0.526971 | + | 0.849883i | \(0.323328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.0000 | −1.01128 | −0.505641 | − | 0.862744i | \(-0.668744\pi\) | ||||
−0.505641 | + | 0.862744i | \(0.668744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.97831i | 0.387525i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.32456i | 0.245256i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.1158i | 1.28225i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −65.5967 | −2.53612 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.94427 | −0.345290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.8090i | 1.65016i | 0.565013 | + | 0.825082i | \(0.308871\pi\) | ||||
−0.565013 | + | 0.825082i | \(0.691129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 8.74032i | − 0.336415i | ||||||||
\(676\) | 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 | ||||||||
\(681\) | −35.1246 | −1.34598 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | − 13.0618i | − 0.498338i | ||||||||
\(688\) | 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 | ||||||||
\(693\) | − 33.1158i | − 1.25797i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.1246 | 1.33235 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 6.48218i | − 0.245530i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.9443 | 1.09477 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.1246 | 1.55326 | 0.776628 | − | 0.629960i | \(-0.216929\pi\) | ||||
0.776628 | + | 0.629960i | \(0.216929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 6.86474i | − 0.258908i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 43.4164 | 1.63516 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | −25.5279 | −0.957370 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.6197i | 1.10927i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 47.2579i | 1.76735i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.4744i | 0.503212i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.5967 | 0.805423 | 0.402711 | − | 0.915327i | \(-0.368068\pi\) | ||||
0.402711 | + | 0.915327i | \(0.368068\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.4164 | −1.61691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 56.8236i | − 2.11329i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.3607 | −0.830455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.48528i | − 0.314702i | −0.987543 | − | 0.157351i | \(-0.949705\pi\) | ||||
0.987543 | − | 0.157351i | \(-0.0502953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.9443 | 0.442380 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.16718 | −0.339061 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 33.9411i | − 1.25364i | −0.779162 | − | 0.626822i | \(-0.784355\pi\) | ||||
0.779162 | − | 0.626822i | \(-0.215645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 5.11667i | − 0.188731i | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 9.23607 | 0.339295 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 11.7264i | 0.429045i | ||||||||
\(748\) | 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 | ||||||||
\(753\) | − 68.3923i | − 2.49236i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.8885 | 0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.825324i | 0.0299969i | 0.999888 | + | 0.0149985i | \(0.00477434\pi\) | ||||
−0.999888 | + | 0.0149985i | \(0.995226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 88.7214 | 3.22038 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.5410 | 0.889611 | 0.444806 | − | 0.895627i | \(-0.353273\pi\) | ||||
0.444806 | + | 0.895627i | \(0.353273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.65685i | 0.204792i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.40182i | 0.195303i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | −10.7639 | −0.387654 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | 44.4295i | 1.59390i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | −0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.81758i | 0.279378i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 43.3491i | − 1.54720i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.62365i | 0.129169i | 0.997912 | + | 0.0645845i | \(0.0205722\pi\) | ||||
−0.997912 | + | 0.0645845i | \(0.979428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.8885 | 0.779253 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.2492 | 1.21776 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.89484i | 0.244843i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.1246 | 1.24574 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | −33.4164 | −1.18071 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 71.8885i | 2.53689i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 46.8328 | 1.65064 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 6.73722i | − 0.237161i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4721 | 0.579129 | 0.289565 | − | 0.957158i | \(-0.406489\pi\) | ||||
0.289565 | + | 0.957158i | \(0.406489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.7618i | 1.53479i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.9737i | 0.664619i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.48528i | 0.296862i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.5279 | −0.892016 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0557 | 0.734850 | 0.367425 | − | 0.930053i | \(-0.380239\pi\) | ||||
0.367425 | + | 0.930053i | \(0.380239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00310i | 0.0698238i | 0.999390 | + | 0.0349119i | \(0.0111151\pi\) | ||||
−0.999390 | + | 0.0349119i | \(0.988885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 59.9070i | 2.08570i | ||||||||
\(826\) | 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 | ||||||||
\(831\) | 7.41641 | 0.257272 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.08036i | − 0.0374324i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 10.5185i | − 0.364007i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.99226i | 0.241688i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.3050 | 0.459338 | 0.229669 | − | 0.973269i | \(-0.426236\pi\) | ||||
0.229669 | + | 0.973269i | \(0.426236\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 3.24109i | − 0.111629i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.36068 | 0.253215 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 46.4326i | − 1.59544i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.8885 | 1.30033 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.8328 | −1.74253 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.4884i | 0.359115i | 0.983747 | + | 0.179558i | \(0.0574667\pi\) | ||||
−0.983747 | + | 0.179558i | \(0.942533\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.00000 | 0.170996 | ||||||||
\(856\) | 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 | ||||||||
\(861\) | 38.8328 | 1.32342 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | − 36.2294i | − 1.23041i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59.7771 | −2.02780 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.54102 | 0.221634 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.94820i | 0.336696i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.6228i | 1.06904i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 4.44897i | − 0.150231i | −0.997175 | − | 0.0751155i | \(-0.976067\pi\) | ||||
0.997175 | − | 0.0751155i | \(-0.0239326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.7082 | −0.529825 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.6525 | −1.03271 | −0.516354 | − | 0.856375i | \(-0.672711\pi\) | ||||
−0.516354 | + | 0.856375i | \(0.672711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 14.9675i | − 0.503695i | −0.967767 | − | 0.251848i | \(-0.918962\pi\) | ||||
0.967767 | − | 0.251848i | \(-0.0810382\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 53.5825i | 1.80116i | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 56.0689 | 1.87838 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.48528i | − 0.283949i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.2492 | −1.01112 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 68.3923i | − 2.28355i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.8885 | 0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.41641 | 0.247076 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 54.9179i | − 1.82755i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.4164 | −0.445976 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 8.86784i | − 0.294452i | −0.989103 | − | 0.147226i | \(-0.952966\pi\) | ||||
0.989103 | − | 0.147226i | \(-0.0470344\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.70820 | −0.0566575 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.5279 | −1.24335 | −0.621677 | − | 0.783274i | \(-0.713548\pi\) | ||||
−0.621677 | + | 0.783274i | \(0.713548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.4589i | 0.908759i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.74032i | 0.288946i | ||||||||
\(916\) | 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 | ||||||||
\(921\) | −9.23607 | −0.304339 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 6.16693i | − 0.202987i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 34.3237i | − 1.12856i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.3237i | 1.12734i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.4721 | −0.540433 | −0.270217 | − | 0.962800i | \(-0.587095\pi\) | ||||
−0.270217 | + | 0.962800i | \(0.587095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 8.48528i | − 0.277796i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.6491i | 0.413670i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 51.6768i | − 1.68821i | −0.536180 | − | 0.844104i | \(-0.680133\pi\) | ||||
0.536180 | − | 0.844104i | \(-0.319867\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.8328 | 2.05047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0557 | −0.686397 | −0.343199 | − | 0.939263i | \(-0.611510\pi\) | ||||
−0.343199 | + | 0.939263i | \(0.611510\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.4295i | 1.44682i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.0557 | 0.359643 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | −30.1803 | −0.978665 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | − 53.5825i | − 1.73208i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.05573 | 0.0986746 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 36.7394i | − 1.18391i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 9.94820i | − 0.320244i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 16.5579i | − 0.532466i | −0.963909 | − | 0.266233i | \(-0.914221\pi\) | ||||
0.963909 | − | 0.266233i | \(-0.0857791\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.47214 | 0.0794164 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.36068 | 0.139941 | 0.0699704 | − | 0.997549i | \(-0.477710\pi\) | ||||
0.0699704 | + | 0.997549i | \(0.477710\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.4295i | 1.42434i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 46.1803 | 1.47895 | ||||||||
\(976\) | 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 | ||||||||
\(981\) | 4.47214 | 0.142784 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 54.9179i | 1.74806i | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 44.4295i | 1.40993i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35.7771 | −1.13421 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.7000i | 0.972280i | 0.873881 | + | 0.486140i | \(0.161595\pi\) | ||||
−0.873881 | + | 0.486140i | \(0.838405\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.0000 | −0.379663 |
(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 | 380.2.c.a.229.1 | ✓ | 4 | |
3.2 | odd | 2 | 3420.2.f.a.1369.3 | 4 | |||
4.3 | odd | 2 | 1520.2.d.f.609.4 | 4 | |||
5.2 | odd | 4 | 1900.2.a.j.1.1 | 4 | |||
5.3 | odd | 4 | 1900.2.a.j.1.4 | 4 | |||
5.4 | even | 2 | inner | 380.2.c.a.229.4 | yes | 4 | |
15.14 | odd | 2 | 3420.2.f.a.1369.4 | 4 | |||
20.3 | even | 4 | 7600.2.a.ce.1.1 | 4 | |||
20.7 | even | 4 | 7600.2.a.ce.1.4 | 4 | |||
20.19 | odd | 2 | 1520.2.d.f.609.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.a.229.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
380.2.c.a.229.4 | yes | 4 | 5.4 | even | 2 | inner | |
1520.2.d.f.609.1 | 4 | 20.19 | odd | 2 | |||
1520.2.d.f.609.4 | 4 | 4.3 | odd | 2 | |||
1900.2.a.j.1.1 | 4 | 5.2 | odd | 4 | |||
1900.2.a.j.1.4 | 4 | 5.3 | odd | 4 | |||
3420.2.f.a.1369.3 | 4 | 3.2 | odd | 2 | |||
3420.2.f.a.1369.4 | 4 | 15.14 | odd | 2 | |||
7600.2.a.ce.1.1 | 4 | 20.3 | even | 4 | |||
7600.2.a.ce.1.4 | 4 | 20.7 | even | 4 |