Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(2015,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("2394.2015");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2015.8 | ||
Character | \(\chi\) | \(=\) | 2394.2015 |
Dual form | 2394.2.f.b.2015.7 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.26222 | −0.564484 | −0.282242 | − | 0.959343i | \(-0.591078\pi\) | ||||
−0.282242 | + | 0.959343i | \(0.591078\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.09287 | + | 2.40949i | 0.413066 | + | 0.910701i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.26222i | − | 0.399150i | ||||||
\(11\) | − | 2.94604i | − | 0.888264i | −0.895961 | − | 0.444132i | \(-0.853512\pi\) | ||
0.895961 | − | 0.444132i | \(-0.146488\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.580865i | − | 0.161103i | −0.996750 | − | 0.0805515i | \(-0.974332\pi\) | ||
0.996750 | − | 0.0805515i | \(-0.0256682\pi\) | |||||||
\(14\) | −2.40949 | + | 1.09287i | −0.643963 | + | 0.292082i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.124939 | 0.0303021 | 0.0151510 | − | 0.999885i | \(-0.495177\pi\) | ||||
0.0151510 | + | 0.999885i | \(0.495177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 1.26222 | 0.282242 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.94604 | 0.628098 | ||||||||
\(23\) | − | 5.45717i | − | 1.13790i | −0.822372 | − | 0.568950i | \(-0.807350\pi\) | ||
0.822372 | − | 0.568950i | \(-0.192650\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.40679 | −0.681358 | ||||||||
\(26\) | 0.580865 | 0.113917 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.09287 | − | 2.40949i | −0.206533 | − | 0.455351i | ||||
\(29\) | − | 3.23794i | − | 0.601270i | −0.953739 | − | 0.300635i | \(-0.902801\pi\) | ||
0.953739 | − | 0.300635i | \(-0.0971986\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.94306i | − | 0.528589i | −0.964442 | − | 0.264294i | \(-0.914861\pi\) | ||
0.964442 | − | 0.264294i | \(-0.0851391\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.124939i | 0.0214268i | ||||||||
\(35\) | −1.37945 | − | 3.04131i | −0.233169 | − | 0.514076i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.135864 | −0.0223358 | −0.0111679 | − | 0.999938i | \(-0.503555\pi\) | ||||
−0.0111679 | + | 0.999938i | \(0.503555\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.26222i | 0.199575i | ||||||||
\(41\) | 5.43121 | 0.848213 | 0.424106 | − | 0.905612i | \(-0.360588\pi\) | ||||
0.424106 | + | 0.905612i | \(0.360588\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.47700 | −0.377739 | −0.188869 | − | 0.982002i | \(-0.560482\pi\) | ||||
−0.188869 | + | 0.982002i | \(0.560482\pi\) | |||||||
\(44\) | 2.94604i | 0.444132i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.45717 | 0.804616 | ||||||||
\(47\) | 6.95074 | 1.01387 | 0.506935 | − | 0.861984i | \(-0.330778\pi\) | ||||
0.506935 | + | 0.861984i | \(0.330778\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.61127 | + | 5.26651i | −0.658753 | + | 0.752359i | ||||
\(50\) | − | 3.40679i | − | 0.481793i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.580865i | 0.0805515i | ||||||||
\(53\) | − | 5.46970i | − | 0.751321i | −0.926757 | − | 0.375661i | \(-0.877416\pi\) | ||
0.926757 | − | 0.375661i | \(-0.122584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.71856i | 0.501411i | ||||||||
\(56\) | 2.40949 | − | 1.09287i | 0.321981 | − | 0.146041i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.23794 | 0.425162 | ||||||||
\(59\) | −6.29094 | −0.819011 | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||||
−0.409505 | + | 0.912308i | \(0.634299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.467276i | 0.0598286i | 0.999552 | + | 0.0299143i | \(0.00952343\pi\) | ||||
−0.999552 | + | 0.0299143i | \(0.990477\pi\) | |||||||
\(62\) | 2.94306 | 0.373769 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.733182i | 0.0909401i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.93507 | 0.725084 | 0.362542 | − | 0.931967i | \(-0.381909\pi\) | ||||
0.362542 | + | 0.931967i | \(0.381909\pi\) | |||||||
\(68\) | −0.124939 | −0.0151510 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.04131 | − | 1.37945i | 0.363507 | − | 0.164875i | ||||
\(71\) | − | 16.1645i | − | 1.91837i | −0.282775 | − | 0.959186i | \(-0.591255\pi\) | ||
0.282775 | − | 0.959186i | \(-0.408745\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.4154i | − | 1.33608i | −0.744127 | − | 0.668038i | \(-0.767134\pi\) | ||
0.744127 | − | 0.668038i | \(-0.232866\pi\) | |||||||
\(74\) | − | 0.135864i | − | 0.0157938i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.00000i | − | 0.114708i | ||||||
\(77\) | 7.09845 | − | 3.21964i | 0.808943 | − | 0.366912i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.468124 | 0.0526680 | 0.0263340 | − | 0.999653i | \(-0.491617\pi\) | ||||
0.0263340 | + | 0.999653i | \(0.491617\pi\) | |||||||
\(80\) | −1.26222 | −0.141121 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.43121i | 0.599777i | ||||||||
\(83\) | 9.79950 | 1.07564 | 0.537818 | − | 0.843061i | \(-0.319249\pi\) | ||||
0.537818 | + | 0.843061i | \(0.319249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.157701 | −0.0171050 | ||||||||
\(86\) | − | 2.47700i | − | 0.267102i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.94604 | −0.314049 | ||||||||
\(89\) | 9.24616 | 0.980091 | 0.490045 | − | 0.871697i | \(-0.336980\pi\) | ||||
0.490045 | + | 0.871697i | \(0.336980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.39959 | − | 0.634810i | 0.146717 | − | 0.0665462i | ||||
\(92\) | 5.45717i | 0.568950i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.95074i | 0.716915i | ||||||||
\(95\) | − | 1.26222i | − | 0.129501i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.54319i | 0.765895i | 0.923770 | + | 0.382948i | \(0.125091\pi\) | ||||
−0.923770 | + | 0.382948i | \(0.874909\pi\) | |||||||
\(98\) | −5.26651 | − | 4.61127i | −0.531998 | − | 0.465809i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.40679 | 0.340679 | ||||||||
\(101\) | 4.60873 | 0.458586 | 0.229293 | − | 0.973357i | \(-0.426359\pi\) | ||||
0.229293 | + | 0.973357i | \(0.426359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8587i | 1.16848i | 0.811582 | + | 0.584238i | \(0.198607\pi\) | ||||
−0.811582 | + | 0.584238i | \(0.801393\pi\) | |||||||
\(104\) | −0.580865 | −0.0569585 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.46970 | 0.531264 | ||||||||
\(107\) | − | 2.48007i | − | 0.239757i | −0.992789 | − | 0.119879i | \(-0.961749\pi\) | ||
0.992789 | − | 0.119879i | \(-0.0382505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.64142 | 0.636132 | 0.318066 | − | 0.948069i | \(-0.396967\pi\) | ||||
0.318066 | + | 0.948069i | \(0.396967\pi\) | |||||||
\(110\) | −3.71856 | −0.354551 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.09287 | + | 2.40949i | 0.103266 | + | 0.227675i | ||||
\(113\) | − | 5.59170i | − | 0.526023i | −0.964793 | − | 0.263012i | \(-0.915284\pi\) | ||
0.964793 | − | 0.263012i | \(-0.0847158\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.88818i | 0.642326i | ||||||||
\(116\) | 3.23794i | 0.300635i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.29094i | − | 0.579128i | ||||||
\(119\) | 0.136542 | + | 0.301038i | 0.0125168 | + | 0.0275961i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.32085 | 0.210986 | ||||||||
\(122\) | −0.467276 | −0.0423052 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.94306i | 0.264294i | ||||||||
\(125\) | 10.6113 | 0.949099 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.37751 | 0.832119 | 0.416060 | − | 0.909337i | \(-0.363411\pi\) | ||||
0.416060 | + | 0.909337i | \(0.363411\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.733182 | −0.0643043 | ||||||||
\(131\) | −14.9045 | −1.30221 | −0.651107 | − | 0.758986i | \(-0.725695\pi\) | ||||
−0.651107 | + | 0.758986i | \(0.725695\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.40949 | + | 1.09287i | −0.208929 | + | 0.0947638i | ||||
\(134\) | 5.93507i | 0.512712i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 0.124939i | − | 0.0107134i | ||||||
\(137\) | 1.93955i | 0.165707i | 0.996562 | + | 0.0828533i | \(0.0264033\pi\) | ||||
−0.996562 | + | 0.0828533i | \(0.973597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.8881i | − | 1.09316i | −0.837408 | − | 0.546579i | \(-0.815930\pi\) | ||
0.837408 | − | 0.546579i | \(-0.184070\pi\) | |||||||
\(140\) | 1.37945 | + | 3.04131i | 0.116584 | + | 0.257038i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.1645 | 1.35649 | ||||||||
\(143\) | −1.71125 | −0.143102 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.08700i | 0.339407i | ||||||||
\(146\) | 11.4154 | 0.944749 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.135864 | 0.0111679 | ||||||||
\(149\) | 4.62005i | 0.378489i | 0.981930 | + | 0.189244i | \(0.0606039\pi\) | ||||
−0.981930 | + | 0.189244i | \(0.939396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.86316 | 0.721274 | 0.360637 | − | 0.932706i | \(-0.382559\pi\) | ||||
0.360637 | + | 0.932706i | \(0.382559\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.21964 | + | 7.09845i | 0.259446 | + | 0.572009i | ||||
\(155\) | 3.71480i | 0.298380i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.9759i | − | 1.11540i | −0.830043 | − | 0.557699i | \(-0.811684\pi\) | ||
0.830043 | − | 0.557699i | \(-0.188316\pi\) | |||||||
\(158\) | 0.468124i | 0.0372419i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.26222i | − | 0.0997876i | ||||||
\(161\) | 13.1490 | − | 5.96398i | 1.03629 | − | 0.470027i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.0963 | 1.41741 | 0.708707 | − | 0.705503i | \(-0.249279\pi\) | ||||
0.708707 | + | 0.705503i | \(0.249279\pi\) | |||||||
\(164\) | −5.43121 | −0.424106 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.79950i | 0.760589i | ||||||||
\(167\) | −0.135153 | −0.0104585 | −0.00522924 | − | 0.999986i | \(-0.501665\pi\) | ||||
−0.00522924 | + | 0.999986i | \(0.501665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6626 | 0.974046 | ||||||||
\(170\) | − | 0.157701i | − | 0.0120951i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.47700 | 0.188869 | ||||||||
\(173\) | −11.2899 | −0.858353 | −0.429176 | − | 0.903221i | \(-0.641196\pi\) | ||||
−0.429176 | + | 0.903221i | \(0.641196\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.72318 | − | 8.20862i | −0.281446 | − | 0.620514i | ||||
\(176\) | − | 2.94604i | − | 0.222066i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.24616i | 0.693029i | ||||||||
\(179\) | − | 16.1068i | − | 1.20388i | −0.798543 | − | 0.601938i | \(-0.794395\pi\) | ||
0.798543 | − | 0.601938i | \(-0.205605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.83840i | − | 0.359635i | −0.983700 | − | 0.179818i | \(-0.942449\pi\) | ||
0.983700 | − | 0.179818i | \(-0.0575507\pi\) | |||||||
\(182\) | 0.634810 | + | 1.39959i | 0.0470552 | + | 0.103744i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.45717 | −0.402308 | ||||||||
\(185\) | 0.171490 | 0.0126082 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.368074i | − | 0.0269163i | ||||||
\(188\) | −6.95074 | −0.506935 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.26222 | 0.0915714 | ||||||||
\(191\) | − | 0.947510i | − | 0.0685594i | −0.999412 | − | 0.0342797i | \(-0.989086\pi\) | ||
0.999412 | − | 0.0342797i | \(-0.0109137\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.93469 | 0.715115 | 0.357557 | − | 0.933891i | \(-0.383610\pi\) | ||||
0.357557 | + | 0.933891i | \(0.383610\pi\) | |||||||
\(194\) | −7.54319 | −0.541570 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.61127 | − | 5.26651i | 0.329377 | − | 0.376180i | ||||
\(197\) | − | 22.2190i | − | 1.58304i | −0.611145 | − | 0.791519i | \(-0.709291\pi\) | ||
0.611145 | − | 0.791519i | \(-0.290709\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.47254i | − | 0.317050i | −0.987355 | − | 0.158525i | \(-0.949326\pi\) | ||
0.987355 | − | 0.158525i | \(-0.0506738\pi\) | |||||||
\(200\) | 3.40679i | 0.240896i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.60873i | 0.324269i | ||||||||
\(203\) | 7.80178 | − | 3.53864i | 0.547577 | − | 0.248364i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.85541 | −0.478802 | ||||||||
\(206\) | −11.8587 | −0.826238 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 0.580865i | − | 0.0402758i | ||||||
\(209\) | 2.94604 | 0.203782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.8585 | −0.747528 | −0.373764 | − | 0.927524i | \(-0.621933\pi\) | ||||
−0.373764 | + | 0.927524i | \(0.621933\pi\) | |||||||
\(212\) | 5.46970i | 0.375661i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.48007 | 0.169534 | ||||||||
\(215\) | 3.12653 | 0.213227 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.09127 | − | 3.21638i | 0.481387 | − | 0.218342i | ||||
\(218\) | 6.64142i | 0.449814i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 3.71856i | − | 0.250705i | ||||||
\(221\) | − | 0.0725725i | − | 0.00488176i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.40924i | 0.0943698i | 0.998886 | + | 0.0471849i | \(0.0150250\pi\) | ||||
−0.998886 | + | 0.0471849i | \(0.984975\pi\) | |||||||
\(224\) | −2.40949 | + | 1.09287i | −0.160991 | + | 0.0730204i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.59170 | 0.371955 | ||||||||
\(227\) | −13.8910 | −0.921977 | −0.460989 | − | 0.887406i | \(-0.652505\pi\) | ||||
−0.460989 | + | 0.887406i | \(0.652505\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9038i | 1.11703i | 0.829493 | + | 0.558517i | \(0.188630\pi\) | ||||
−0.829493 | + | 0.558517i | \(0.811370\pi\) | |||||||
\(230\) | −6.88818 | −0.454193 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.23794 | −0.212581 | ||||||||
\(233\) | − | 15.0715i | − | 0.987367i | −0.869642 | − | 0.493684i | \(-0.835650\pi\) | ||
0.869642 | − | 0.493684i | \(-0.164350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.77340 | −0.572313 | ||||||||
\(236\) | 6.29094 | 0.409505 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.301038 | + | 0.136542i | −0.0195134 | + | 0.00885068i | ||||
\(239\) | 24.3817i | 1.57712i | 0.614955 | + | 0.788562i | \(0.289174\pi\) | ||||
−0.614955 | + | 0.788562i | \(0.710826\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.30720i | 0.213036i | 0.994311 | + | 0.106518i | \(0.0339701\pi\) | ||||
−0.994311 | + | 0.106518i | \(0.966030\pi\) | |||||||
\(242\) | 2.32085i | 0.149190i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 0.467276i | − | 0.0299143i | ||||||
\(245\) | 5.82046 | − | 6.64752i | 0.371855 | − | 0.424694i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.580865 | 0.0369596 | ||||||||
\(248\) | −2.94306 | −0.186884 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.6113i | 0.671115i | ||||||||
\(251\) | −7.03123 | −0.443807 | −0.221904 | − | 0.975069i | \(-0.571227\pi\) | ||||
−0.221904 | + | 0.975069i | \(0.571227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.0771 | −1.01076 | ||||||||
\(254\) | 9.37751i | 0.588397i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.4173 | −0.899327 | −0.449664 | − | 0.893198i | \(-0.648456\pi\) | ||||
−0.449664 | + | 0.893198i | \(0.648456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.148481 | − | 0.327362i | −0.00922617 | − | 0.0203413i | ||||
\(260\) | − | 0.733182i | − | 0.0454700i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 14.9045i | − | 0.920805i | ||||||
\(263\) | 3.36860i | 0.207717i | 0.994592 | + | 0.103858i | \(0.0331188\pi\) | ||||
−0.994592 | + | 0.103858i | \(0.966881\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.90399i | 0.424109i | ||||||||
\(266\) | −1.09287 | − | 2.40949i | −0.0670081 | − | 0.147735i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.93507 | −0.362542 | ||||||||
\(269\) | 9.65894 | 0.588916 | 0.294458 | − | 0.955664i | \(-0.404861\pi\) | ||||
0.294458 | + | 0.955664i | \(0.404861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6946i | 1.19636i | 0.801362 | + | 0.598180i | \(0.204109\pi\) | ||||
−0.801362 | + | 0.598180i | \(0.795891\pi\) | |||||||
\(272\) | 0.124939 | 0.00757552 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.93955 | −0.117172 | ||||||||
\(275\) | 10.0365i | 0.605226i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.21766 | −0.373583 | −0.186791 | − | 0.982400i | \(-0.559809\pi\) | ||||
−0.186791 | + | 0.982400i | \(0.559809\pi\) | |||||||
\(278\) | 12.8881 | 0.772979 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.04131 | + | 1.37945i | −0.181753 | + | 0.0824377i | ||||
\(281\) | − | 13.0046i | − | 0.775791i | −0.921703 | − | 0.387896i | \(-0.873202\pi\) | ||
0.921703 | − | 0.387896i | \(-0.126798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 28.9851i | − | 1.72299i | −0.507770 | − | 0.861493i | \(-0.669530\pi\) | ||
0.507770 | − | 0.861493i | \(-0.330470\pi\) | |||||||
\(284\) | 16.1645i | 0.959186i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1.71125i | − | 0.101188i | ||||||
\(287\) | 5.93561 | + | 13.0864i | 0.350368 | + | 0.772469i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9844 | −0.999082 | ||||||||
\(290\) | −4.08700 | −0.239997 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.4154i | 0.668038i | ||||||||
\(293\) | −11.3255 | −0.661644 | −0.330822 | − | 0.943693i | \(-0.607326\pi\) | ||||
−0.330822 | + | 0.943693i | \(0.607326\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.94058 | 0.462318 | ||||||||
\(296\) | 0.135864i | 0.00789691i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.62005 | −0.267632 | ||||||||
\(299\) | −3.16988 | −0.183319 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.70704 | − | 5.96830i | −0.156031 | − | 0.344007i | ||||
\(302\) | 8.86316i | 0.510017i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | − | 0.589807i | − | 0.0337723i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2990i | 1.15852i | 0.815141 | + | 0.579262i | \(0.196659\pi\) | ||||
−0.815141 | + | 0.579262i | \(0.803341\pi\) | |||||||
\(308\) | −7.09845 | + | 3.21964i | −0.404472 | + | 0.183456i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.71480 | −0.210986 | ||||||||
\(311\) | −25.2405 | −1.43126 | −0.715630 | − | 0.698480i | \(-0.753860\pi\) | ||||
−0.715630 | + | 0.698480i | \(0.753860\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.13134i | − | 0.403087i | −0.979480 | − | 0.201544i | \(-0.935404\pi\) | ||
0.979480 | − | 0.201544i | \(-0.0645958\pi\) | |||||||
\(314\) | 13.9759 | 0.788705 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.468124 | −0.0263340 | ||||||||
\(317\) | 8.59004i | 0.482465i | 0.970467 | + | 0.241232i | \(0.0775516\pi\) | ||||
−0.970467 | + | 0.241232i | \(0.922448\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.53910 | −0.534087 | ||||||||
\(320\) | 1.26222 | 0.0705605 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.96398 | + | 13.1490i | 0.332360 | + | 0.732765i | ||||
\(323\) | 0.124939i | 0.00695177i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.97889i | 0.109769i | ||||||||
\(326\) | 18.0963i | 1.00226i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.43121i | − | 0.299889i | ||||||
\(329\) | 7.59626 | + | 16.7477i | 0.418795 | + | 0.923333i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.4273 | 1.06782 | 0.533909 | − | 0.845542i | \(-0.320722\pi\) | ||||
0.533909 | + | 0.845542i | \(0.320722\pi\) | |||||||
\(332\) | −9.79950 | −0.537818 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 0.135153i | − | 0.00739526i | ||||||
\(335\) | −7.49139 | −0.409298 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.433336 | 0.0236053 | 0.0118026 | − | 0.999930i | \(-0.496243\pi\) | ||||
0.0118026 | + | 0.999930i | \(0.496243\pi\) | |||||||
\(338\) | 12.6626i | 0.688754i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.157701 | 0.00855251 | ||||||||
\(341\) | −8.67037 | −0.469527 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.7291 | − | 5.35520i | −0.957283 | − | 0.289153i | ||||
\(344\) | 2.47700i | 0.133551i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 11.2899i | − | 0.606947i | ||||||
\(347\) | 10.9231i | 0.586380i | 0.956054 | + | 0.293190i | \(0.0947169\pi\) | ||||
−0.956054 | + | 0.293190i | \(0.905283\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8940i | 0.850789i | 0.905008 | + | 0.425394i | \(0.139865\pi\) | ||||
−0.905008 | + | 0.425394i | \(0.860135\pi\) | |||||||
\(350\) | 8.20862 | − | 3.72318i | 0.438769 | − | 0.199012i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.94604 | 0.157024 | ||||||||
\(353\) | 7.06470 | 0.376016 | 0.188008 | − | 0.982167i | \(-0.439797\pi\) | ||||
0.188008 | + | 0.982167i | \(0.439797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.4032i | 1.08289i | ||||||||
\(356\) | −9.24616 | −0.490045 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.1068 | 0.851269 | ||||||||
\(359\) | 16.2159i | 0.855841i | 0.903816 | + | 0.427921i | \(0.140754\pi\) | ||||
−0.903816 | + | 0.427921i | \(0.859246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 4.83840 | 0.254300 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.39959 | + | 0.634810i | −0.0733584 | + | 0.0332731i | ||||
\(365\) | 14.4088i | 0.754193i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 30.8759i | − | 1.61171i | −0.592113 | − | 0.805855i | \(-0.701706\pi\) | ||
0.592113 | − | 0.805855i | \(-0.298294\pi\) | |||||||
\(368\) | − | 5.45717i | − | 0.284475i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.171490i | 0.00891535i | ||||||||
\(371\) | 13.1792 | − | 5.97767i | 0.684229 | − | 0.310345i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.9801 | −1.44876 | −0.724378 | − | 0.689403i | \(-0.757873\pi\) | ||||
−0.724378 | + | 0.689403i | \(0.757873\pi\) | |||||||
\(374\) | 0.368074 | 0.0190327 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 6.95074i | − | 0.358457i | ||||||
\(377\) | −1.88081 | −0.0968664 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6929 | −1.11429 | −0.557145 | − | 0.830415i | \(-0.688103\pi\) | ||||
−0.557145 | + | 0.830415i | \(0.688103\pi\) | |||||||
\(380\) | 1.26222i | 0.0647507i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.947510 | 0.0484788 | ||||||||
\(383\) | 23.2099 | 1.18597 | 0.592985 | − | 0.805213i | \(-0.297949\pi\) | ||||
0.592985 | + | 0.805213i | \(0.297949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.95983 | + | 4.06390i | −0.456635 | + | 0.207116i | ||||
\(386\) | 9.93469i | 0.505663i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 7.54319i | − | 0.382948i | ||||||
\(389\) | − | 16.4672i | − | 0.834920i | −0.908695 | − | 0.417460i | \(-0.862920\pi\) | ||
0.908695 | − | 0.417460i | \(-0.137080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.681812i | − | 0.0344807i | ||||||
\(392\) | 5.26651 | + | 4.61127i | 0.265999 | + | 0.232904i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.2190 | 1.11938 | ||||||||
\(395\) | −0.590877 | −0.0297303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.81132i | 0.0909077i | 0.998966 | + | 0.0454539i | \(0.0144734\pi\) | ||||
−0.998966 | + | 0.0454539i | \(0.985527\pi\) | |||||||
\(398\) | 4.47254 | 0.224188 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.40679 | −0.170340 | ||||||||
\(401\) | 4.95375i | 0.247378i | 0.992321 | + | 0.123689i | \(0.0394726\pi\) | ||||
−0.992321 | + | 0.123689i | \(0.960527\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.70952 | −0.0851573 | ||||||||
\(404\) | −4.60873 | −0.229293 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.53864 | + | 7.80178i | 0.175620 | + | 0.387196i | ||||
\(407\) | 0.400259i | 0.0198401i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 30.2420i | − | 1.49537i | −0.664054 | − | 0.747685i | \(-0.731165\pi\) | ||
0.664054 | − | 0.747685i | \(-0.268835\pi\) | |||||||
\(410\) | − | 6.85541i | − | 0.338564i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 11.8587i | − | 0.584238i | ||||||
\(413\) | −6.87518 | − | 15.1580i | −0.338305 | − | 0.745874i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.3692 | −0.607179 | ||||||||
\(416\) | 0.580865 | 0.0284793 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.94604i | 0.144096i | ||||||||
\(419\) | 4.16455 | 0.203452 | 0.101726 | − | 0.994812i | \(-0.467564\pi\) | ||||
0.101726 | + | 0.994812i | \(0.467564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.1382 | −1.42011 | −0.710054 | − | 0.704147i | \(-0.751330\pi\) | ||||
−0.710054 | + | 0.704147i | \(0.751330\pi\) | |||||||
\(422\) | − | 10.8585i | − | 0.528582i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.46970 | −0.265632 | ||||||||
\(425\) | −0.425640 | −0.0206466 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.12590 | + | 0.510672i | −0.0544859 | + | 0.0247131i | ||||
\(428\) | 2.48007i | 0.119879i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.12653i | 0.150775i | ||||||||
\(431\) | 18.8415i | 0.907562i | 0.891113 | + | 0.453781i | \(0.149925\pi\) | ||||
−0.891113 | + | 0.453781i | \(0.850075\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 31.2388i | − | 1.50124i | −0.660733 | − | 0.750621i | \(-0.729754\pi\) | ||
0.660733 | − | 0.750621i | \(-0.270246\pi\) | |||||||
\(434\) | 3.21638 | + | 7.09127i | 0.154391 | + | 0.340392i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.64142 | −0.318066 | ||||||||
\(437\) | 5.45717 | 0.261052 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8375i | 1.13770i | 0.822440 | + | 0.568852i | \(0.192612\pi\) | ||||
−0.822440 | + | 0.568852i | \(0.807388\pi\) | |||||||
\(440\) | 3.71856 | 0.177275 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0725725 | 0.00345192 | ||||||||
\(443\) | 0.210570i | 0.0100045i | 0.999987 | + | 0.00500224i | \(0.00159227\pi\) | ||||
−0.999987 | + | 0.00500224i | \(0.998408\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6707 | −0.553245 | ||||||||
\(446\) | −1.40924 | −0.0667295 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.09287 | − | 2.40949i | −0.0516332 | − | 0.113838i | ||||
\(449\) | 3.49441i | 0.164911i | 0.996595 | + | 0.0824557i | \(0.0262763\pi\) | ||||
−0.996595 | + | 0.0824557i | \(0.973724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.0006i | − | 0.753437i | ||||||
\(452\) | 5.59170i | 0.263012i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 13.8910i | − | 0.651936i | ||||||
\(455\) | −1.76659 | + | 0.801272i | −0.0828192 | + | 0.0375642i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.81078 | 0.0847047 | 0.0423523 | − | 0.999103i | \(-0.486515\pi\) | ||||
0.0423523 | + | 0.999103i | \(0.486515\pi\) | |||||||
\(458\) | −16.9038 | −0.789863 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 6.88818i | − | 0.321163i | ||||||
\(461\) | −10.2919 | −0.479343 | −0.239672 | − | 0.970854i | \(-0.577040\pi\) | ||||
−0.239672 | + | 0.970854i | \(0.577040\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.465421 | −0.0216299 | −0.0108150 | − | 0.999942i | \(-0.503443\pi\) | ||||
−0.0108150 | + | 0.999942i | \(0.503443\pi\) | |||||||
\(464\) | − | 3.23794i | − | 0.150318i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.0715 | 0.698174 | ||||||||
\(467\) | 10.0215 | 0.463740 | 0.231870 | − | 0.972747i | \(-0.425516\pi\) | ||||
0.231870 | + | 0.972747i | \(0.425516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.48626 | + | 14.3005i | 0.299507 | + | 0.660335i | ||||
\(470\) | − | 8.77340i | − | 0.404687i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.29094i | 0.289564i | ||||||||
\(473\) | 7.29734i | 0.335532i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.40679i | − | 0.156314i | ||||||
\(476\) | −0.136542 | − | 0.301038i | −0.00625838 | − | 0.0137981i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.3817 | −1.11520 | ||||||||
\(479\) | −42.7360 | −1.95266 | −0.976330 | − | 0.216287i | \(-0.930605\pi\) | ||||
−0.976330 | + | 0.216287i | \(0.930605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0789184i | 0.00359837i | ||||||||
\(482\) | −3.30720 | −0.150639 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.32085 | −0.105493 | ||||||||
\(485\) | − | 9.52120i | − | 0.432335i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.59226 | 0.344038 | 0.172019 | − | 0.985094i | \(-0.444971\pi\) | ||||
0.172019 | + | 0.985094i | \(0.444971\pi\) | |||||||
\(488\) | 0.467276 | 0.0211526 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.64752 | + | 5.82046i | 0.300304 | + | 0.262942i | ||||
\(491\) | 22.2349i | 1.00345i | 0.865028 | + | 0.501724i | \(0.167301\pi\) | ||||
−0.865028 | + | 0.501724i | \(0.832699\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.404544i | − | 0.0182197i | ||||||
\(494\) | 0.580865i | 0.0261344i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.94306i | − | 0.132147i | ||||||
\(497\) | 38.9482 | − | 17.6657i | 1.74706 | − | 0.792414i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.3476 | −0.866117 | −0.433058 | − | 0.901366i | \(-0.642566\pi\) | ||||
−0.433058 | + | 0.901366i | \(0.642566\pi\) | |||||||
\(500\) | −10.6113 | −0.474550 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 7.03123i | − | 0.313819i | ||||||
\(503\) | −9.02726 | −0.402506 | −0.201253 | − | 0.979539i | \(-0.564501\pi\) | ||||
−0.201253 | + | 0.979539i | \(0.564501\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.81725 | −0.258864 | ||||||||
\(506\) | − | 16.0771i | − | 0.714712i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.37751 | −0.416060 | ||||||||
\(509\) | −3.32324 | −0.147300 | −0.0736501 | − | 0.997284i | \(-0.523465\pi\) | ||||
−0.0736501 | + | 0.997284i | \(0.523465\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.5054 | − | 12.4756i | 1.21677 | − | 0.551887i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 14.4173i | − | 0.635920i | ||||||
\(515\) | − | 14.9684i | − | 0.659586i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 20.4772i | − | 0.900585i | ||||||
\(518\) | 0.327362 | − | 0.148481i | 0.0143834 | − | 0.00652389i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.733182 | 0.0321522 | ||||||||
\(521\) | −17.4482 | −0.764419 | −0.382209 | − | 0.924076i | \(-0.624837\pi\) | ||||
−0.382209 | + | 0.924076i | \(0.624837\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 31.3099i | − | 1.36909i | −0.728972 | − | 0.684543i | \(-0.760002\pi\) | ||
0.728972 | − | 0.684543i | \(-0.239998\pi\) | |||||||
\(524\) | 14.9045 | 0.651107 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.36860 | −0.146878 | ||||||||
\(527\) | − | 0.367702i | − | 0.0160173i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.78075 | −0.294815 | ||||||||
\(530\) | −6.90399 | −0.299890 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.40949 | − | 1.09287i | 0.104465 | − | 0.0473819i | ||||
\(533\) | − | 3.15480i | − | 0.136650i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.13040i | 0.135339i | ||||||||
\(536\) | − | 5.93507i | − | 0.256356i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.65894i | 0.416427i | ||||||||
\(539\) | 15.5154 | + | 13.5850i | 0.668294 | + | 0.585147i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.85184 | −0.423564 | −0.211782 | − | 0.977317i | \(-0.567927\pi\) | ||||
−0.211782 | + | 0.977317i | \(0.567927\pi\) | |||||||
\(542\) | −19.6946 | −0.845954 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.124939i | 0.00535670i | ||||||||
\(545\) | −8.38296 | −0.359086 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0186 | 0.727663 | 0.363832 | − | 0.931465i | \(-0.381468\pi\) | ||||
0.363832 | + | 0.931465i | \(0.381468\pi\) | |||||||
\(548\) | − | 1.93955i | − | 0.0828533i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.0365 | −0.427959 | ||||||||
\(551\) | 3.23794 | 0.137941 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.511598 | + | 1.12794i | 0.0217554 | + | 0.0479648i | ||||
\(554\) | − | 6.21766i | − | 0.264163i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.8881i | 0.546579i | ||||||||
\(557\) | − | 40.5732i | − | 1.71914i | −0.511015 | − | 0.859572i | \(-0.670730\pi\) | ||
0.511015 | − | 0.859572i | \(-0.329270\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.43880i | 0.0608549i | ||||||||
\(560\) | −1.37945 | − | 3.04131i | −0.0582922 | − | 0.128519i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.0046 | 0.548567 | ||||||||
\(563\) | 8.53357 | 0.359647 | 0.179824 | − | 0.983699i | \(-0.442447\pi\) | ||||
0.179824 | + | 0.983699i | \(0.442447\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.05798i | 0.296932i | ||||||||
\(566\) | 28.9851 | 1.21834 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.1645 | −0.678247 | ||||||||
\(569\) | − | 19.3163i | − | 0.809779i | −0.914366 | − | 0.404890i | \(-0.867310\pi\) | ||
0.914366 | − | 0.404890i | \(-0.132690\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.05058 | −0.378755 | −0.189378 | − | 0.981904i | \(-0.560647\pi\) | ||||
−0.189378 | + | 0.981904i | \(0.560647\pi\) | |||||||
\(572\) | 1.71125 | 0.0715510 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.0864 | + | 5.93561i | −0.546218 | + | 0.247747i | ||||
\(575\) | 18.5914i | 0.775317i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.53186i | 0.230294i | 0.993348 | + | 0.115147i | \(0.0367340\pi\) | ||||
−0.993348 | + | 0.115147i | \(0.963266\pi\) | |||||||
\(578\) | − | 16.9844i | − | 0.706458i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 4.08700i | − | 0.169704i | ||||||
\(581\) | 10.7096 | + | 23.6118i | 0.444308 | + | 0.979582i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.1140 | −0.667372 | ||||||||
\(584\) | −11.4154 | −0.472374 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 11.3255i | − | 0.467853i | ||||||
\(587\) | −15.1982 | −0.627296 | −0.313648 | − | 0.949539i | \(-0.601551\pi\) | ||||
−0.313648 | + | 0.949539i | \(0.601551\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.94306 | 0.121267 | ||||||||
\(590\) | 7.94058i | 0.326908i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.135864 | −0.00558396 | ||||||||
\(593\) | 18.0338 | 0.740557 | 0.370279 | − | 0.928921i | \(-0.379262\pi\) | ||||
0.370279 | + | 0.928921i | \(0.379262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.172346 | − | 0.379978i | −0.00706550 | − | 0.0155776i | ||||
\(596\) | − | 4.62005i | − | 0.189244i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 3.16988i | − | 0.129626i | ||||||
\(599\) | 33.6893i | 1.37651i | 0.725471 | + | 0.688253i | \(0.241622\pi\) | ||||
−0.725471 | + | 0.688253i | \(0.758378\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.8721i | − | 0.606644i | −0.952888 | − | 0.303322i | \(-0.901904\pi\) | ||
0.952888 | − | 0.303322i | \(-0.0980957\pi\) | |||||||
\(602\) | 5.96830 | − | 2.70704i | 0.243250 | − | 0.110331i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.86316 | −0.360637 | ||||||||
\(605\) | −2.92943 | −0.119098 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.4857i | 1.72444i | 0.506533 | + | 0.862221i | \(0.330927\pi\) | ||||
−0.506533 | + | 0.862221i | \(0.669073\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.589807 | 0.0238806 | ||||||||
\(611\) | − | 4.03745i | − | 0.163338i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0605 | −0.769845 | −0.384923 | − | 0.922949i | \(-0.625772\pi\) | ||||
−0.384923 | + | 0.922949i | \(0.625772\pi\) | |||||||
\(614\) | −20.2990 | −0.819200 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.21964 | − | 7.09845i | −0.129723 | − | 0.286005i | ||||
\(617\) | − | 6.67373i | − | 0.268674i | −0.990936 | − | 0.134337i | \(-0.957110\pi\) | ||
0.990936 | − | 0.134337i | \(-0.0428905\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4.62968i | − | 0.186083i | −0.995662 | − | 0.0930414i | \(-0.970341\pi\) | ||
0.995662 | − | 0.0930414i | \(-0.0296589\pi\) | |||||||
\(620\) | − | 3.71480i | − | 0.149190i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 25.2405i | − | 1.01205i | ||||||
\(623\) | 10.1048 | + | 22.2785i | 0.404842 | + | 0.892570i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.64017 | 0.145607 | ||||||||
\(626\) | 7.13134 | 0.285026 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.9759i | 0.557699i | ||||||||
\(629\) | −0.0169746 | −0.000676822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3219 | 1.28671 | 0.643356 | − | 0.765567i | \(-0.277541\pi\) | ||||
0.643356 | + | 0.765567i | \(0.277541\pi\) | |||||||
\(632\) | − | 0.468124i | − | 0.0186210i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.59004 | −0.341154 | ||||||||
\(635\) | −11.8365 | −0.469718 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.05914 | + | 2.67853i | 0.121207 | + | 0.106127i | ||||
\(638\) | − | 9.53910i | − | 0.377656i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.26222i | 0.0498938i | ||||||||
\(641\) | − | 17.7180i | − | 0.699818i | −0.936784 | − | 0.349909i | \(-0.886212\pi\) | ||
0.936784 | − | 0.349909i | \(-0.113788\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 35.3274i | − | 1.39318i | −0.717471 | − | 0.696589i | \(-0.754700\pi\) | ||
0.717471 | − | 0.696589i | \(-0.245300\pi\) | |||||||
\(644\) | −13.1490 | + | 5.96398i | −0.518143 | + | 0.235014i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.124939 | −0.00491565 | ||||||||
\(647\) | 20.4309 | 0.803222 | 0.401611 | − | 0.915810i | \(-0.368450\pi\) | ||||
0.401611 | + | 0.915810i | \(0.368450\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.5334i | 0.727498i | ||||||||
\(650\) | −1.97889 | −0.0776183 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.0963 | −0.708707 | ||||||||
\(653\) | 16.8668i | 0.660051i | 0.943972 | + | 0.330025i | \(0.107057\pi\) | ||||
−0.943972 | + | 0.330025i | \(0.892943\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.8129 | 0.735079 | ||||||||
\(656\) | 5.43121 | 0.212053 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.7477 | + | 7.59626i | −0.652895 | + | 0.296133i | ||||
\(659\) | − | 5.01860i | − | 0.195497i | −0.995211 | − | 0.0977484i | \(-0.968836\pi\) | ||
0.995211 | − | 0.0977484i | \(-0.0311640\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.2491i | − | 0.943180i | −0.881818 | − | 0.471590i | \(-0.843680\pi\) | ||
0.881818 | − | 0.471590i | \(-0.156320\pi\) | |||||||
\(662\) | 19.4273i | 0.755062i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 9.79950i | − | 0.380295i | ||||||
\(665\) | 3.04131 | − | 1.37945i | 0.117937 | − | 0.0534926i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.6700 | −0.684185 | ||||||||
\(668\) | 0.135153 | 0.00522924 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 7.49139i | − | 0.289418i | ||||||
\(671\) | 1.37661 | 0.0531436 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.4830 | −1.21358 | −0.606791 | − | 0.794862i | \(-0.707543\pi\) | ||||
−0.606791 | + | 0.794862i | \(0.707543\pi\) | |||||||
\(674\) | 0.433336i | 0.0166915i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6626 | −0.487023 | ||||||||
\(677\) | −18.2121 | −0.699948 | −0.349974 | − | 0.936760i | \(-0.613809\pi\) | ||||
−0.349974 | + | 0.936760i | \(0.613809\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.1752 | + | 8.24372i | −0.697501 | + | 0.316365i | ||||
\(680\) | 0.157701i | 0.00604754i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 8.67037i | − | 0.332006i | ||||||
\(683\) | 5.61612i | 0.214895i | 0.994211 | + | 0.107447i | \(0.0342678\pi\) | ||||
−0.994211 | + | 0.107447i | \(0.965732\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.44814i | − | 0.0935387i | ||||||
\(686\) | 5.35520 | − | 17.7291i | 0.204462 | − | 0.676901i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.47700 | −0.0944347 | ||||||||
\(689\) | −3.17716 | −0.121040 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.0472i | 0.800674i | 0.916368 | + | 0.400337i | \(0.131107\pi\) | ||||
−0.916368 | + | 0.400337i | \(0.868893\pi\) | |||||||
\(692\) | 11.2899 | 0.429176 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.9231 | −0.414634 | ||||||||
\(695\) | 16.2677i | 0.617070i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.678568 | 0.0257026 | ||||||||
\(698\) | −15.8940 | −0.601598 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.72318 | + | 8.20862i | 0.140723 | + | 0.310257i | ||||
\(701\) | − | 27.9599i | − | 1.05603i | −0.849235 | − | 0.528016i | \(-0.822936\pi\) | ||
0.849235 | − | 0.528016i | \(-0.177064\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.135864i | − | 0.00512419i | ||||||
\(704\) | 2.94604i | 0.111033i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.06470i | 0.265884i | ||||||||
\(707\) | 5.03675 | + | 11.1047i | 0.189426 | + | 0.417635i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.62154 | 0.0608982 | 0.0304491 | − | 0.999536i | \(-0.490306\pi\) | ||||
0.0304491 | + | 0.999536i | \(0.490306\pi\) | |||||||
\(710\) | −20.4032 | −0.765719 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 9.24616i | − | 0.346514i | ||||||
\(713\) | −16.0608 | −0.601481 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.15998 | 0.0807788 | ||||||||
\(716\) | 16.1068i | 0.601938i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.2159 | −0.605171 | ||||||||
\(719\) | 8.80165 | 0.328246 | 0.164123 | − | 0.986440i | \(-0.447521\pi\) | ||||
0.164123 | + | 0.986440i | \(0.447521\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.5735 | + | 12.9601i | −1.06413 | + | 0.482658i | ||||
\(722\) | − | 1.00000i | − | 0.0372161i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.83840i | 0.179818i | ||||||||
\(725\) | 11.0310i | 0.409680i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.6658i | 0.543926i | 0.962308 | + | 0.271963i | \(0.0876728\pi\) | ||||
−0.962308 | + | 0.271963i | \(0.912327\pi\) | |||||||
\(728\) | −0.634810 | − | 1.39959i | −0.0235276 | − | 0.0518722i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.4088 | −0.533295 | ||||||||
\(731\) | −0.309473 | −0.0114463 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.9641i | 0.848200i | 0.905615 | + | 0.424100i | \(0.139409\pi\) | ||||
−0.905615 | + | 0.424100i | \(0.860591\pi\) | |||||||
\(734\) | 30.8759 | 1.13965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.45717 | 0.201154 | ||||||||
\(737\) | − | 17.4849i | − | 0.644066i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.8443 | 1.02427 | 0.512135 | − | 0.858905i | \(-0.328855\pi\) | ||||
0.512135 | + | 0.858905i | \(0.328855\pi\) | |||||||
\(740\) | −0.171490 | −0.00630411 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.97767 | + | 13.1792i | 0.219447 | + | 0.483823i | ||||
\(743\) | 31.0494i | 1.13909i | 0.821959 | + | 0.569547i | \(0.192881\pi\) | ||||
−0.821959 | + | 0.569547i | \(0.807119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5.83153i | − | 0.213651i | ||||||
\(746\) | − | 27.9801i | − | 1.02443i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.368074i | 0.0134581i | ||||||||
\(749\) | 5.97569 | − | 2.71039i | 0.218347 | − | 0.0990355i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.69902 | 0.353922 | 0.176961 | − | 0.984218i | \(-0.443373\pi\) | ||||
0.176961 | + | 0.984218i | \(0.443373\pi\) | |||||||
\(752\) | 6.95074 | 0.253468 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 1.88081i | − | 0.0684949i | ||||||
\(755\) | −11.1873 | −0.407147 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.3310 | 0.520870 | 0.260435 | − | 0.965491i | \(-0.416134\pi\) | ||||
0.260435 | + | 0.965491i | \(0.416134\pi\) | |||||||
\(758\) | − | 21.6929i | − | 0.787923i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.26222 | −0.0457857 | ||||||||
\(761\) | 35.6888 | 1.29372 | 0.646860 | − | 0.762609i | \(-0.276082\pi\) | ||||
0.646860 | + | 0.762609i | \(0.276082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.25820 | + | 16.0024i | 0.262765 | + | 0.579326i | ||||
\(764\) | 0.947510i | 0.0342797i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.2099i | 0.838608i | ||||||||
\(767\) | 3.65419i | 0.131945i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 44.8001i | − | 1.61553i | −0.589502 | − | 0.807767i | \(-0.700676\pi\) | ||
0.589502 | − | 0.807767i | \(-0.299324\pi\) | |||||||
\(770\) | −4.06390 | − | 8.95983i | −0.146453 | − | 0.322890i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.93469 | −0.357557 | ||||||||
\(773\) | −6.42581 | −0.231120 | −0.115560 | − | 0.993300i | \(-0.536866\pi\) | ||||
−0.115560 | + | 0.993300i | \(0.536866\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0264i | 0.360158i | ||||||||
\(776\) | 7.54319 | 0.270785 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.4672 | 0.590377 | ||||||||
\(779\) | 5.43121i | 0.194593i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.6212 | −1.70402 | ||||||||
\(782\) | 0.681812 | 0.0243815 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.61127 | + | 5.26651i | −0.164688 | + | 0.188090i | ||||
\(785\) | 17.6407i | 0.629624i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.06830i | − | 0.323250i | −0.986852 | − | 0.161625i | \(-0.948327\pi\) | ||
0.986852 | − | 0.161625i | \(-0.0516735\pi\) | |||||||
\(788\) | 22.2190i | 0.791519i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 0.590877i | − | 0.0210225i | ||||||
\(791\) | 13.4731 | − | 6.11100i | 0.479050 | − | 0.217282i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.271424 | 0.00963857 | ||||||||
\(794\) | −1.81132 | −0.0642815 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.47254i | 0.158525i | ||||||||
\(797\) | −36.6622 | −1.29864 | −0.649322 | − | 0.760514i | \(-0.724947\pi\) | ||||
−0.649322 | + | 0.760514i | \(0.724947\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.868417 | 0.0307224 | ||||||||
\(800\) | − | 3.40679i | − | 0.120448i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.95375 | −0.174923 | ||||||||
\(803\) | −33.6303 | −1.18679 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.5970 | + | 7.52788i | −0.584967 | + | 0.265323i | ||||
\(806\) | − | 1.70952i | − | 0.0602153i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 4.60873i | − | 0.162135i | ||||||
\(809\) | 34.6653i | 1.21877i | 0.792876 | + | 0.609383i | \(0.208583\pi\) | ||||
−0.792876 | + | 0.609383i | \(0.791417\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.5440i | 1.24812i | 0.781377 | + | 0.624060i | \(0.214518\pi\) | ||||
−0.781377 | + | 0.624060i | \(0.785482\pi\) | |||||||
\(812\) | −7.80178 | + | 3.53864i | −0.273789 | + | 0.124182i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.400259 | −0.0140291 | ||||||||
\(815\) | −22.8416 | −0.800107 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.47700i | − | 0.0866592i | ||||||
\(818\) | 30.2420 | 1.05739 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.85541 | 0.239401 | ||||||||
\(821\) | − | 43.7225i | − | 1.52593i | −0.646441 | − | 0.762964i | \(-0.723743\pi\) | ||
0.646441 | − | 0.762964i | \(-0.276257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.6982 | −0.372915 | −0.186457 | − | 0.982463i | \(-0.559701\pi\) | ||||
−0.186457 | + | 0.982463i | \(0.559701\pi\) | |||||||
\(824\) | 11.8587 | 0.413119 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.1580 | − | 6.87518i | 0.527413 | − | 0.239218i | ||||
\(827\) | − | 20.1660i | − | 0.701239i | −0.936518 | − | 0.350620i | \(-0.885971\pi\) | ||
0.936518 | − | 0.350620i | \(-0.114029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.3025i | − | 0.705134i | −0.935787 | − | 0.352567i | \(-0.885309\pi\) | ||
0.935787 | − | 0.352567i | \(-0.114691\pi\) | |||||||
\(830\) | − | 12.3692i | − | 0.429340i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.580865i | 0.0201379i | ||||||||
\(833\) | −0.576126 | + | 0.657991i | −0.0199616 | + | 0.0227980i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.170594 | 0.00590364 | ||||||||
\(836\) | −2.94604 | −0.101891 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.16455i | 0.143862i | ||||||||
\(839\) | 0.533787 | 0.0184284 | 0.00921419 | − | 0.999958i | \(-0.497067\pi\) | ||||
0.00921419 | + | 0.999958i | \(0.497067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5158 | 0.638474 | ||||||||
\(842\) | − | 29.1382i | − | 1.00417i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.8585 | 0.373764 | ||||||||
\(845\) | −15.9830 | −0.549833 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.53639 | + | 5.59206i | 0.0871513 | + | 0.192146i | ||||
\(848\) | − | 5.46970i | − | 0.187830i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 0.425640i | − | 0.0145993i | ||||||
\(851\) | 0.741431i | 0.0254159i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 54.1595i | − | 1.85439i | −0.374584 | − | 0.927193i | \(-0.622215\pi\) | ||
0.374584 | − | 0.927193i | \(-0.377785\pi\) | |||||||
\(854\) | −0.510672 | − | 1.12590i | −0.0174748 | − | 0.0385274i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.48007 | −0.0847670 | ||||||||
\(857\) | 27.5095 | 0.939707 | 0.469854 | − | 0.882744i | \(-0.344307\pi\) | ||||
0.469854 | + | 0.882744i | \(0.344307\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2347i | 0.553921i | 0.960881 | + | 0.276960i | \(0.0893271\pi\) | ||||
−0.960881 | + | 0.276960i | \(0.910673\pi\) | |||||||
\(860\) | −3.12653 | −0.106614 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.8415 | −0.641743 | ||||||||
\(863\) | 35.1989i | 1.19818i | 0.800680 | + | 0.599092i | \(0.204472\pi\) | ||||
−0.800680 | + | 0.599092i | \(0.795528\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.2503 | 0.484526 | ||||||||
\(866\) | 31.2388 | 1.06154 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.09127 | + | 3.21638i | −0.240693 | + | 0.109171i | ||||
\(869\) | − | 1.37911i | − | 0.0467831i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.44748i | − | 0.116813i | ||||||
\(872\) | − | 6.64142i | − | 0.224907i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.45717i | 0.184592i | ||||||||
\(875\) | 11.5967 | + | 25.5677i | 0.392041 | + | 0.864346i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.7067 | −0.665448 | −0.332724 | − | 0.943024i | \(-0.607968\pi\) | ||||
−0.332724 | + | 0.943024i | \(0.607968\pi\) | |||||||
\(878\) | −23.8375 | −0.804478 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.71856i | 0.125353i | ||||||||
\(881\) | 3.71631 | 0.125206 | 0.0626029 | − | 0.998039i | \(-0.480060\pi\) | ||||
0.0626029 | + | 0.998039i | \(0.480060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.15411 | −0.106144 | −0.0530722 | − | 0.998591i | \(-0.516901\pi\) | ||||
−0.0530722 | + | 0.998591i | \(0.516901\pi\) | |||||||
\(884\) | 0.0725725i | 0.00244088i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.210570 | −0.00707424 | ||||||||
\(887\) | −11.5663 | −0.388357 | −0.194178 | − | 0.980966i | \(-0.562204\pi\) | ||||
−0.194178 | + | 0.980966i | \(0.562204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.2484 | + | 22.5950i | 0.343720 | + | 0.757812i | ||||
\(890\) | − | 11.6707i | − | 0.391204i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 1.40924i | − | 0.0471849i | ||||||
\(893\) | 6.95074i | 0.232598i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.3303i | 0.679568i | ||||||||
\(896\) | 2.40949 | − | 1.09287i | 0.0804954 | − | 0.0365102i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.49441 | −0.116610 | ||||||||
\(899\) | −9.52944 | −0.317825 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.683377i | − | 0.0227666i | ||||||
\(902\) | 16.0006 | 0.532761 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.59170 | −0.185977 | ||||||||
\(905\) | 6.10714i | 0.203008i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.2545 | 0.473312 | 0.236656 | − | 0.971593i | \(-0.423949\pi\) | ||||
0.236656 | + | 0.971593i | \(0.423949\pi\) | |||||||
\(908\) | 13.8910 | 0.460989 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.801272 | − | 1.76659i | −0.0265619 | − | 0.0585620i | ||||
\(911\) | 24.0760i | 0.797675i | 0.917022 | + | 0.398837i | \(0.130586\pi\) | ||||
−0.917022 | + | 0.398837i | \(0.869414\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 28.8697i | − | 0.955449i | ||||||
\(914\) | 1.81078i | 0.0598953i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 16.9038i | − | 0.558517i | ||||||
\(917\) | −16.2887 | − | 35.9123i | −0.537900 | − | 1.18593i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.2325 | 1.65702 | 0.828508 | − | 0.559977i | \(-0.189190\pi\) | ||||
0.828508 | + | 0.559977i | \(0.189190\pi\) | |||||||
\(920\) | 6.88818 | 0.227096 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 10.2919i | − | 0.338947i | ||||||
\(923\) | −9.38939 | −0.309056 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.462859 | 0.0152187 | ||||||||
\(926\) | − | 0.465421i | − | 0.0152947i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.23794 | 0.106291 | ||||||||
\(929\) | 16.1259 | 0.529074 | 0.264537 | − | 0.964376i | \(-0.414781\pi\) | ||||
0.264537 | + | 0.964376i | \(0.414781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.26651 | − | 4.61127i | −0.172603 | − | 0.151128i | ||||
\(932\) | 15.0715i | 0.493684i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.0215i | 0.327914i | ||||||||
\(935\) | 0.464592i | 0.0151938i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.3192i | 1.90521i | 0.304218 | + | 0.952603i | \(0.401605\pi\) | ||||
−0.304218 | + | 0.952603i | \(0.598395\pi\) | |||||||
\(938\) | −14.3005 | + | 6.48626i | −0.466927 | + | 0.211784i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.77340 | 0.286157 | ||||||||
\(941\) | −41.9844 | −1.36865 | −0.684326 | − | 0.729177i | \(-0.739903\pi\) | ||||
−0.684326 | + | 0.729177i | \(0.739903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 29.6391i | − | 0.965181i | ||||||
\(944\) | −6.29094 | −0.204753 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.29734 | −0.237257 | ||||||||
\(947\) | − | 44.1729i | − | 1.43543i | −0.696339 | − | 0.717713i | \(-0.745189\pi\) | ||
0.696339 | − | 0.717713i | \(-0.254811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.63083 | −0.215246 | ||||||||
\(950\) | 3.40679 | 0.110531 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.301038 | − | 0.136542i | 0.00975671 | − | 0.00442534i | ||||
\(953\) | 22.4882i | 0.728465i | 0.931308 | + | 0.364233i | \(0.118669\pi\) | ||||
−0.931308 | + | 0.364233i | \(0.881331\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.19597i | 0.0387007i | ||||||||
\(956\) | − | 24.3817i | − | 0.788562i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 42.7360i | − | 1.38074i | ||||||
\(959\) | −4.67331 | + | 2.11967i | −0.150909 | + | 0.0684477i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.3384 | 0.720594 | ||||||||
\(962\) | −0.0789184 | −0.00254443 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 3.30720i | − | 0.106518i | ||||||
\(965\) | −12.5398 | −0.403671 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.677844 | −0.0217980 | −0.0108990 | − | 0.999941i | \(-0.503469\pi\) | ||||
−0.0108990 | + | 0.999941i | \(0.503469\pi\) | |||||||
\(968\) | − | 2.32085i | − | 0.0745950i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.52120 | 0.305707 | ||||||||
\(971\) | 44.9323 | 1.44195 | 0.720973 | − | 0.692963i | \(-0.243695\pi\) | ||||
0.720973 | + | 0.692963i | \(0.243695\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.0538 | − | 14.0851i | 0.995540 | − | 0.451546i | ||||
\(974\) | 7.59226i | 0.243272i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.467276i | 0.0149571i | ||||||||
\(977\) | − | 22.5723i | − | 0.722151i | −0.932537 | − | 0.361075i | \(-0.882410\pi\) | ||
0.932537 | − | 0.361075i | \(-0.117590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 27.2396i | − | 0.870580i | ||||||
\(980\) | −5.82046 | + | 6.64752i | −0.185928 | + | 0.212347i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.2349 | −0.709545 | ||||||||
\(983\) | −44.7270 | −1.42657 | −0.713285 | − | 0.700874i | \(-0.752793\pi\) | ||||
−0.713285 | + | 0.700874i | \(0.752793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.0453i | 0.893599i | ||||||||
\(986\) | 0.404544 | 0.0128833 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.580865 | −0.0184798 | ||||||||
\(989\) | 13.5174i | 0.429829i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.4945 | 1.34988 | 0.674941 | − | 0.737872i | \(-0.264169\pi\) | ||||
0.674941 | + | 0.737872i | \(0.264169\pi\) | |||||||
\(992\) | 2.94306 | 0.0934422 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17.6657 | + | 38.9482i | 0.560321 | + | 1.23536i | ||||
\(995\) | 5.64534i | 0.178969i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 56.9184i | − | 1.80262i | −0.433171 | − | 0.901312i | \(-0.642606\pi\) | ||
0.433171 | − | 0.901312i | \(-0.357394\pi\) | |||||||
\(998\) | − | 19.3476i | − | 0.612437i | ||||||
\(999\) | 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 | 2394.2.f.b.2015.8 | yes | 24 | |
3.2 | odd | 2 | 2394.2.f.a.2015.7 | ✓ | 24 | ||
7.6 | odd | 2 | 2394.2.f.a.2015.8 | yes | 24 | ||
21.20 | even | 2 | inner | 2394.2.f.b.2015.7 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.f.a.2015.7 | ✓ | 24 | 3.2 | odd | 2 | ||
2394.2.f.a.2015.8 | yes | 24 | 7.6 | odd | 2 | ||
2394.2.f.b.2015.7 | yes | 24 | 21.20 | even | 2 | inner | |
2394.2.f.b.2015.8 | yes | 24 | 1.1 | even | 1 | trivial |