Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,2,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1150.599");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.18279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.77580864.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 19x^{4} + 105x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.4 | ||
Root | \(-2.68740i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.2.b.j.599.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 2.68740i | − 1.55157i | −0.630997 | − | 0.775785i | \(-0.717354\pi\) | ||||
0.630997 | − | 0.775785i | \(-0.282646\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.68740 | 1.09713 | ||||||||
\(7\) | − 4.59692i | − 1.73747i | −0.495277 | − | 0.868735i | \(-0.664933\pi\) | ||||
0.495277 | − | 0.868735i | \(-0.335067\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −4.22212 | −1.40737 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.13163 | 1.54725 | 0.773623 | − | 0.633647i | \(-0.218443\pi\) | ||||
0.773623 | + | 0.633647i | \(0.218443\pi\) | |||||||
\(12\) | 2.68740i | 0.775785i | ||||||||
\(13\) | 1.22212i | 0.338954i | 0.985534 | + | 0.169477i | \(0.0542079\pi\) | ||||
−0.985534 | + | 0.169477i | \(0.945792\pi\) | |||||||
\(14\) | 4.59692 | 1.22858 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 4.68740i | − 1.13686i | −0.822731 | − | 0.568431i | \(-0.807551\pi\) | ||||
0.822731 | − | 0.568431i | \(-0.192449\pi\) | |||||||
\(18\) | − 4.22212i | − 0.995162i | ||||||||
\(19\) | 4.59692 | 1.05460 | 0.527302 | − | 0.849678i | \(-0.323204\pi\) | ||||
0.527302 | + | 0.849678i | \(0.323204\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.3537 | −2.69581 | ||||||||
\(22\) | 5.13163i | 1.09407i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | −2.68740 | −0.548563 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.22212 | −0.239677 | ||||||||
\(27\) | 3.28432i | 0.632067i | ||||||||
\(28\) | 4.59692i | 0.868735i | ||||||||
\(29\) | −3.37480 | −0.626684 | −0.313342 | − | 0.949640i | \(-0.601449\pi\) | ||||
−0.313342 | + | 0.949640i | \(0.601449\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.777884 | −0.139712 | −0.0698560 | − | 0.997557i | \(-0.522254\pi\) | ||||
−0.0698560 | + | 0.997557i | \(0.522254\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 13.7907i | − 2.40066i | ||||||||
\(34\) | 4.68740 | 0.803882 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.22212 | 0.703686 | ||||||||
\(37\) | 5.81903i | 0.956643i | 0.878185 | + | 0.478321i | \(0.158755\pi\) | ||||
−0.878185 | + | 0.478321i | \(0.841245\pi\) | |||||||
\(38\) | 4.59692i | 0.745718i | ||||||||
\(39\) | 3.28432 | 0.525911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.50643 | −1.32848 | −0.664241 | − | 0.747519i | \(-0.731245\pi\) | ||||
−0.664241 | + | 0.747519i | \(0.731245\pi\) | |||||||
\(42\) | − 12.3537i | − 1.90622i | ||||||||
\(43\) | − 8.00000i | − 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | −5.13163 | −0.773623 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | − 6.44423i | − 0.939988i | −0.882670 | − | 0.469994i | \(-0.844256\pi\) | ||||
0.882670 | − | 0.469994i | \(-0.155744\pi\) | |||||||
\(48\) | − 2.68740i | − 0.387893i | ||||||||
\(49\) | −14.1316 | −2.01880 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.5969 | −1.76392 | ||||||||
\(52\) | − 1.22212i | − 0.169477i | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | −3.28432 | −0.446939 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.59692 | −0.614289 | ||||||||
\(57\) | − 12.3537i | − 1.63629i | ||||||||
\(58\) | − 3.37480i | − 0.443133i | ||||||||
\(59\) | −9.37480 | −1.22049 | −0.610247 | − | 0.792211i | \(-0.708930\pi\) | ||||
−0.610247 | + | 0.792211i | \(0.708930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9507 | 1.40209 | 0.701044 | − | 0.713118i | \(-0.252717\pi\) | ||||
0.701044 | + | 0.713118i | \(0.252717\pi\) | |||||||
\(62\) | − 0.777884i | − 0.0987913i | ||||||||
\(63\) | 19.4087i | 2.44527i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.7907 | 1.69752 | ||||||||
\(67\) | 15.6381i | 1.91049i | 0.295810 | + | 0.955247i | \(0.404410\pi\) | ||||
−0.295810 | + | 0.955247i | \(0.595590\pi\) | |||||||
\(68\) | 4.68740i | 0.568431i | ||||||||
\(69\) | 2.68740 | 0.323525 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.31260 | 0.155777 | 0.0778885 | − | 0.996962i | \(-0.475182\pi\) | ||||
0.0778885 | + | 0.996962i | \(0.475182\pi\) | |||||||
\(72\) | 4.22212i | 0.497581i | ||||||||
\(73\) | 4.44423i | 0.520158i | 0.965587 | + | 0.260079i | \(0.0837486\pi\) | ||||
−0.965587 | + | 0.260079i | \(0.916251\pi\) | |||||||
\(74\) | −5.81903 | −0.676449 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.59692 | −0.527302 | ||||||||
\(77\) | − 23.5897i | − 2.68829i | ||||||||
\(78\) | 3.28432i | 0.371875i | ||||||||
\(79\) | 4.88847 | 0.549995 | 0.274998 | − | 0.961445i | \(-0.411323\pi\) | ||||
0.274998 | + | 0.961445i | \(0.411323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.84008 | −0.426676 | ||||||||
\(82\) | − 8.50643i | − 0.939378i | ||||||||
\(83\) | 3.81903i | 0.419193i | 0.977788 | + | 0.209597i | \(0.0672151\pi\) | ||||
−0.977788 | + | 0.209597i | \(0.932785\pi\) | |||||||
\(84\) | 12.3537 | 1.34790 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 9.06943i | 0.972345i | ||||||||
\(88\) | − 5.13163i | − 0.547034i | ||||||||
\(89\) | −8.93057 | −0.946638 | −0.473319 | − | 0.880891i | \(-0.656944\pi\) | ||||
−0.473319 | + | 0.880891i | \(0.656944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.61797 | 0.588923 | ||||||||
\(92\) | − 1.00000i | − 0.104257i | ||||||||
\(93\) | 2.09048i | 0.216773i | ||||||||
\(94\) | 6.44423 | 0.664672 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.68740 | 0.274282 | ||||||||
\(97\) | − 18.0622i | − 1.83394i | −0.398958 | − | 0.916969i | \(-0.630628\pi\) | ||||
0.398958 | − | 0.916969i | \(-0.369372\pi\) | |||||||
\(98\) | − 14.1316i | − 1.42751i | ||||||||
\(99\) | −21.6663 | −2.17755 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.37480 | 0.335805 | 0.167903 | − | 0.985804i | \(-0.446301\pi\) | ||||
0.167903 | + | 0.985804i | \(0.446301\pi\) | |||||||
\(102\) | − 12.5969i | − 1.24728i | ||||||||
\(103\) | − 13.1316i | − 1.29390i | −0.762533 | − | 0.646949i | \(-0.776045\pi\) | ||||
0.762533 | − | 0.646949i | \(-0.223955\pi\) | |||||||
\(104\) | 1.22212 | 0.119838 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 12.3054i | 1.18960i | 0.803872 | + | 0.594802i | \(0.202770\pi\) | ||||
−0.803872 | + | 0.594802i | \(0.797230\pi\) | |||||||
\(108\) | − 3.28432i | − 0.316033i | ||||||||
\(109\) | 10.5969 | 1.01500 | 0.507500 | − | 0.861652i | \(-0.330570\pi\) | ||||
0.507500 | + | 0.861652i | \(0.330570\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.6381 | 1.48430 | ||||||||
\(112\) | − 4.59692i | − 0.434368i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 12.3537 | 1.15703 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.37480 | 0.313342 | ||||||||
\(117\) | − 5.15992i | − 0.477035i | ||||||||
\(118\) | − 9.37480i | − 0.863020i | ||||||||
\(119\) | −21.5476 | −1.97526 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3337 | 1.39397 | ||||||||
\(122\) | 10.9507i | 0.991427i | ||||||||
\(123\) | 22.8602i | 2.06123i | ||||||||
\(124\) | 0.777884 | 0.0698560 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −19.4087 | −1.72907 | ||||||||
\(127\) | − 2.26326i | − 0.200832i | −0.994946 | − | 0.100416i | \(-0.967983\pi\) | ||||
0.994946 | − | 0.100416i | \(-0.0320174\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −21.4992 | −1.89290 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.93057 | 0.256045 | 0.128022 | − | 0.991771i | \(-0.459137\pi\) | ||||
0.128022 | + | 0.991771i | \(0.459137\pi\) | |||||||
\(132\) | 13.7907i | 1.20033i | ||||||||
\(133\) | − 21.1316i | − 1.83234i | ||||||||
\(134\) | −15.6381 | −1.35092 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.68740 | −0.401941 | ||||||||
\(137\) | − 19.7907i | − 1.69084i | −0.534104 | − | 0.845419i | \(-0.679351\pi\) | ||||
0.534104 | − | 0.845419i | \(-0.320649\pi\) | |||||||
\(138\) | 2.68740i | 0.228767i | ||||||||
\(139\) | −6.26326 | −0.531243 | −0.265622 | − | 0.964077i | \(-0.585577\pi\) | ||||
−0.265622 | + | 0.964077i | \(0.585577\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.3182 | −1.45846 | ||||||||
\(142\) | 1.31260i | 0.110151i | ||||||||
\(143\) | 6.27145i | 0.524445i | ||||||||
\(144\) | −4.22212 | −0.351843 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.44423 | −0.367807 | ||||||||
\(147\) | 37.9773i | 3.13232i | ||||||||
\(148\) | − 5.81903i | − 0.478321i | ||||||||
\(149\) | 19.7907 | 1.62132 | 0.810661 | − | 0.585516i | \(-0.199108\pi\) | ||||
0.810661 | + | 0.585516i | \(0.199108\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.06220 | 0.330577 | 0.165289 | − | 0.986245i | \(-0.447144\pi\) | ||||
0.165289 | + | 0.986245i | \(0.447144\pi\) | |||||||
\(152\) | − 4.59692i | − 0.372859i | ||||||||
\(153\) | 19.7907i | 1.59999i | ||||||||
\(154\) | 23.5897 | 1.90091 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.28432 | −0.262956 | ||||||||
\(157\) | 4.62520i | 0.369131i | 0.982820 | + | 0.184566i | \(0.0590878\pi\) | ||||
−0.982820 | + | 0.184566i | \(0.940912\pi\) | |||||||
\(158\) | 4.88847i | 0.388905i | ||||||||
\(159\) | 16.1244 | 1.27875 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.59692 | 0.362288 | ||||||||
\(162\) | − 3.84008i | − 0.301705i | ||||||||
\(163\) | − 12.4159i | − 0.972492i | −0.873822 | − | 0.486246i | \(-0.838366\pi\) | ||||
0.873822 | − | 0.486246i | \(-0.161634\pi\) | |||||||
\(164\) | 8.50643 | 0.664241 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.81903 | −0.296414 | ||||||||
\(167\) | 12.8885i | 0.997339i | 0.866792 | + | 0.498670i | \(0.166178\pi\) | ||||
−0.866792 | + | 0.498670i | \(0.833822\pi\) | |||||||
\(168\) | 12.3537i | 0.953112i | ||||||||
\(169\) | 11.5064 | 0.885110 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19.4087 | −1.48422 | ||||||||
\(172\) | 8.00000i | 0.609994i | ||||||||
\(173\) | 10.2432i | 0.778774i | 0.921074 | + | 0.389387i | \(0.127313\pi\) | ||||
−0.921074 | + | 0.389387i | \(0.872687\pi\) | |||||||
\(174\) | −9.06943 | −0.687552 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.13163 | 0.386811 | ||||||||
\(177\) | 25.1938i | 1.89368i | ||||||||
\(178\) | − 8.93057i | − 0.669374i | ||||||||
\(179\) | 13.1938 | 0.986153 | 0.493077 | − | 0.869986i | \(-0.335872\pi\) | ||||
0.493077 | + | 0.869986i | \(0.335872\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7907 | 1.17372 | 0.586858 | − | 0.809690i | \(-0.300364\pi\) | ||||
0.586858 | + | 0.809690i | \(0.300364\pi\) | |||||||
\(182\) | 5.61797i | 0.416431i | ||||||||
\(183\) | − 29.4288i | − 2.17544i | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.09048 | −0.153282 | ||||||||
\(187\) | − 24.0540i | − 1.75900i | ||||||||
\(188\) | 6.44423i | 0.469994i | ||||||||
\(189\) | 15.0977 | 1.09820 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.1244 | 1.16672 | 0.583360 | − | 0.812214i | \(-0.301738\pi\) | ||||
0.583360 | + | 0.812214i | \(0.301738\pi\) | |||||||
\(192\) | 2.68740i | 0.193946i | ||||||||
\(193\) | 17.9434i | 1.29160i | 0.763508 | + | 0.645798i | \(0.223475\pi\) | ||||
−0.763508 | + | 0.645798i | \(0.776525\pi\) | |||||||
\(194\) | 18.0622 | 1.29679 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.1316 | 1.00940 | ||||||||
\(197\) | 5.88123i | 0.419020i | 0.977806 | + | 0.209510i | \(0.0671869\pi\) | ||||
−0.977806 | + | 0.209510i | \(0.932813\pi\) | |||||||
\(198\) | − 21.6663i | − 1.53976i | ||||||||
\(199\) | −6.56863 | −0.465638 | −0.232819 | − | 0.972520i | \(-0.574795\pi\) | ||||
−0.232819 | + | 0.972520i | \(0.574795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 42.0257 | 2.96427 | ||||||||
\(202\) | 3.37480i | 0.237450i | ||||||||
\(203\) | 15.5137i | 1.08885i | ||||||||
\(204\) | 12.5969 | 0.881960 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.1316 | 0.914924 | ||||||||
\(207\) | − 4.22212i | − 0.293457i | ||||||||
\(208\) | 1.22212i | 0.0847385i | ||||||||
\(209\) | 23.5897 | 1.63173 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.4571 | −1.06411 | −0.532055 | − | 0.846710i | \(-0.678580\pi\) | ||||
−0.532055 | + | 0.846710i | \(0.678580\pi\) | |||||||
\(212\) | − 6.00000i | − 0.412082i | ||||||||
\(213\) | − 3.52748i | − 0.241699i | ||||||||
\(214\) | −12.3054 | −0.841177 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.28432 | 0.223469 | ||||||||
\(217\) | 3.57587i | 0.242746i | ||||||||
\(218\) | 10.5969i | 0.717714i | ||||||||
\(219\) | 11.9434 | 0.807062 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.72855 | 0.385344 | ||||||||
\(222\) | 15.6381i | 1.04956i | ||||||||
\(223\) | 10.7496i | 0.719846i | 0.932982 | + | 0.359923i | \(0.117197\pi\) | ||||
−0.932982 | + | 0.359923i | \(0.882803\pi\) | |||||||
\(224\) | 4.59692 | 0.307144 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | − 12.3054i | − 0.816736i | −0.912817 | − | 0.408368i | \(-0.866098\pi\) | ||||
0.912817 | − | 0.408368i | \(-0.133902\pi\) | |||||||
\(228\) | 12.3537i | 0.818147i | ||||||||
\(229\) | −9.63806 | −0.636901 | −0.318451 | − | 0.947939i | \(-0.603162\pi\) | ||||
−0.318451 | + | 0.947939i | \(0.603162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −63.3949 | −4.17108 | ||||||||
\(232\) | 3.37480i | 0.221566i | ||||||||
\(233\) | − 13.9434i | − 0.913464i | −0.889604 | − | 0.456732i | \(-0.849020\pi\) | ||||
0.889604 | − | 0.456732i | \(-0.150980\pi\) | |||||||
\(234\) | 5.15992 | 0.337314 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.37480 | 0.610247 | ||||||||
\(237\) | − 13.1373i | − 0.853357i | ||||||||
\(238\) | − 21.5476i | − 1.39672i | ||||||||
\(239\) | 26.3877 | 1.70688 | 0.853438 | − | 0.521194i | \(-0.174513\pi\) | ||||
0.853438 | + | 0.521194i | \(0.174513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.06943 | −0.455382 | −0.227691 | − | 0.973733i | \(-0.573118\pi\) | ||||
−0.227691 | + | 0.973733i | \(0.573118\pi\) | |||||||
\(242\) | 15.3337i | 0.985684i | ||||||||
\(243\) | 20.1728i | 1.29408i | ||||||||
\(244\) | −10.9507 | −0.701044 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −22.8602 | −1.45751 | ||||||||
\(247\) | 5.61797i | 0.357463i | ||||||||
\(248\) | 0.777884i | 0.0493957i | ||||||||
\(249\) | 10.2633 | 0.650408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9023 | −1.57182 | −0.785909 | − | 0.618342i | \(-0.787805\pi\) | ||||
−0.785909 | + | 0.618342i | \(0.787805\pi\) | |||||||
\(252\) | − 19.4087i | − 1.22263i | ||||||||
\(253\) | 5.13163i | 0.322623i | ||||||||
\(254\) | 2.26326 | 0.142010 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.444233i | 0.0277105i | 0.999904 | + | 0.0138552i | \(0.00441040\pi\) | ||||
−0.999904 | + | 0.0138552i | \(0.995590\pi\) | |||||||
\(258\) | − 21.4992i | − 1.33848i | ||||||||
\(259\) | 26.7496 | 1.66214 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.2488 | 0.881978 | ||||||||
\(262\) | 2.93057i | 0.181051i | ||||||||
\(263\) | 23.8812i | 1.47258i | 0.676666 | + | 0.736290i | \(0.263424\pi\) | ||||
−0.676666 | + | 0.736290i | \(0.736576\pi\) | |||||||
\(264\) | −13.7907 | −0.848762 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.1316 | 1.29566 | ||||||||
\(267\) | 24.0000i | 1.46878i | ||||||||
\(268\) | − 15.6381i | − 0.955247i | ||||||||
\(269\) | −16.2633 | −0.991589 | −0.495794 | − | 0.868440i | \(-0.665123\pi\) | ||||
−0.495794 | + | 0.868440i | \(0.665123\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6098 | 1.55568 | 0.777842 | − | 0.628460i | \(-0.216315\pi\) | ||||
0.777842 | + | 0.628460i | \(0.216315\pi\) | |||||||
\(272\) | − 4.68740i | − 0.284215i | ||||||||
\(273\) | − 15.0977i | − 0.913756i | ||||||||
\(274\) | 19.7907 | 1.19560 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.68740 | −0.161762 | ||||||||
\(277\) | 2.88847i | 0.173551i | 0.996228 | + | 0.0867755i | \(0.0276563\pi\) | ||||
−0.996228 | + | 0.0867755i | \(0.972344\pi\) | |||||||
\(278\) | − 6.26326i | − 0.375646i | ||||||||
\(279\) | 3.28432 | 0.196627 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.26326 | 0.254325 | 0.127163 | − | 0.991882i | \(-0.459413\pi\) | ||||
0.127163 | + | 0.991882i | \(0.459413\pi\) | |||||||
\(282\) | − 17.3182i | − 1.03129i | ||||||||
\(283\) | − 30.5686i | − 1.81712i | −0.417758 | − | 0.908558i | \(-0.637184\pi\) | ||||
0.417758 | − | 0.908558i | \(-0.362816\pi\) | |||||||
\(284\) | −1.31260 | −0.0778885 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.27145 | −0.370839 | ||||||||
\(287\) | 39.1033i | 2.30820i | ||||||||
\(288\) | − 4.22212i | − 0.248791i | ||||||||
\(289\) | −4.97171 | −0.292454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −48.5403 | −2.84549 | ||||||||
\(292\) | − 4.44423i | − 0.260079i | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | −37.9773 | −2.21488 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.81903 | 0.338224 | ||||||||
\(297\) | 16.8539i | 0.977962i | ||||||||
\(298\) | 19.7907i | 1.14645i | ||||||||
\(299\) | −1.22212 | −0.0706768 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.7753 | −2.11969 | ||||||||
\(302\) | 4.06220i | 0.233753i | ||||||||
\(303\) | − 9.06943i | − 0.521025i | ||||||||
\(304\) | 4.59692 | 0.263651 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −19.7907 | −1.13136 | ||||||||
\(307\) | − 8.54853i | − 0.487891i | −0.969789 | − | 0.243945i | \(-0.921558\pi\) | ||||
0.969789 | − | 0.243945i | \(-0.0784417\pi\) | |||||||
\(308\) | 23.5897i | 1.34415i | ||||||||
\(309\) | −35.2899 | −2.00757 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.63806 | −0.433115 | −0.216557 | − | 0.976270i | \(-0.569483\pi\) | ||||
−0.216557 | + | 0.976270i | \(0.569483\pi\) | |||||||
\(312\) | − 3.28432i | − 0.185938i | ||||||||
\(313\) | 18.2350i | 1.03070i | 0.856979 | + | 0.515351i | \(0.172338\pi\) | ||||
−0.856979 | + | 0.515351i | \(0.827662\pi\) | |||||||
\(314\) | −4.62520 | −0.261015 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.88847 | −0.274998 | ||||||||
\(317\) | − 16.8602i | − 0.946962i | −0.880804 | − | 0.473481i | \(-0.842997\pi\) | ||||
0.880804 | − | 0.473481i | \(-0.157003\pi\) | |||||||
\(318\) | 16.1244i | 0.904211i | ||||||||
\(319\) | −17.3182 | −0.969635 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.0694 | 1.84576 | ||||||||
\(322\) | 4.59692i | 0.256176i | ||||||||
\(323\) | − 21.5476i | − 1.19894i | ||||||||
\(324\) | 3.84008 | 0.213338 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.4159 | 0.687656 | ||||||||
\(327\) | − 28.4781i | − 1.57485i | ||||||||
\(328\) | 8.50643i | 0.469689i | ||||||||
\(329\) | −29.6236 | −1.63320 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.1517 | 1.05267 | 0.526337 | − | 0.850276i | \(-0.323565\pi\) | ||||
0.526337 | + | 0.850276i | \(0.323565\pi\) | |||||||
\(332\) | − 3.81903i | − 0.209597i | ||||||||
\(333\) | − 24.5686i | − 1.34635i | ||||||||
\(334\) | −12.8885 | −0.705225 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.3537 | −0.673952 | ||||||||
\(337\) | 1.70845i | 0.0930652i | 0.998917 | + | 0.0465326i | \(0.0148171\pi\) | ||||
−0.998917 | + | 0.0465326i | \(0.985183\pi\) | |||||||
\(338\) | 11.5064i | 0.625867i | ||||||||
\(339\) | 16.1244 | 0.875757 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.99181 | −0.216169 | ||||||||
\(342\) | − 19.4087i | − 1.04950i | ||||||||
\(343\) | 32.7835i | 1.77014i | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.2432 | −0.550676 | ||||||||
\(347\) | 10.6874i | 0.573730i | 0.957971 | + | 0.286865i | \(0.0926131\pi\) | ||||
−0.957971 | + | 0.286865i | \(0.907387\pi\) | |||||||
\(348\) | − 9.06943i | − 0.486173i | ||||||||
\(349\) | 12.3877 | 0.663096 | 0.331548 | − | 0.943438i | \(-0.392429\pi\) | ||||
0.331548 | + | 0.943438i | \(0.392429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.01382 | −0.214242 | ||||||||
\(352\) | 5.13163i | 0.273517i | ||||||||
\(353\) | − 5.45710i | − 0.290452i | −0.989399 | − | 0.145226i | \(-0.953609\pi\) | ||||
0.989399 | − | 0.145226i | \(-0.0463909\pi\) | |||||||
\(354\) | −25.1938 | −1.33904 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.93057 | 0.473319 | ||||||||
\(357\) | 57.9070i | 3.06476i | ||||||||
\(358\) | 13.1938i | 0.697316i | ||||||||
\(359\) | −20.1810 | −1.06511 | −0.532555 | − | 0.846395i | \(-0.678768\pi\) | ||||
−0.532555 | + | 0.846395i | \(0.678768\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.13163 | 0.112191 | ||||||||
\(362\) | 15.7907i | 0.829943i | ||||||||
\(363\) | − 41.2076i | − 2.16284i | ||||||||
\(364\) | −5.61797 | −0.294461 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 29.4288 | 1.53827 | ||||||||
\(367\) | 2.74960i | 0.143528i | 0.997422 | + | 0.0717639i | \(0.0228628\pi\) | ||||
−0.997422 | + | 0.0717639i | \(0.977137\pi\) | |||||||
\(368\) | 1.00000i | 0.0521286i | ||||||||
\(369\) | 35.9151 | 1.86967 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.5815 | 1.43196 | ||||||||
\(372\) | − 2.09048i | − 0.108387i | ||||||||
\(373\) | 12.0823i | 0.625598i | 0.949819 | + | 0.312799i | \(0.101267\pi\) | ||||
−0.949819 | + | 0.312799i | \(0.898733\pi\) | |||||||
\(374\) | 24.0540 | 1.24380 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.44423 | −0.332336 | ||||||||
\(377\) | − 4.12440i | − 0.212417i | ||||||||
\(378\) | 15.0977i | 0.776543i | ||||||||
\(379\) | −5.25603 | −0.269984 | −0.134992 | − | 0.990847i | \(-0.543101\pi\) | ||||
−0.134992 | + | 0.990847i | \(0.543101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.08230 | −0.311605 | ||||||||
\(382\) | 16.1244i | 0.824996i | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | −2.68740 | −0.137141 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.9434 | −0.913297 | ||||||||
\(387\) | 33.7769i | 1.71698i | ||||||||
\(388\) | 18.0622i | 0.916969i | ||||||||
\(389\) | −0.325463 | −0.0165017 | −0.00825083 | − | 0.999966i | \(-0.502626\pi\) | ||||
−0.00825083 | + | 0.999966i | \(0.502626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.68740 | 0.237052 | ||||||||
\(392\) | 14.1316i | 0.713755i | ||||||||
\(393\) | − 7.87560i | − 0.397272i | ||||||||
\(394\) | −5.88123 | −0.296292 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 21.6663 | 1.08878 | ||||||||
\(397\) | − 17.7568i | − 0.891190i | −0.895235 | − | 0.445595i | \(-0.852992\pi\) | ||||
0.895235 | − | 0.445595i | \(-0.147008\pi\) | |||||||
\(398\) | − 6.56863i | − 0.329256i | ||||||||
\(399\) | −56.7891 | −2.84301 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.91770 | 0.195641 | 0.0978204 | − | 0.995204i | \(-0.468813\pi\) | ||||
0.0978204 | + | 0.995204i | \(0.468813\pi\) | |||||||
\(402\) | 42.0257i | 2.09605i | ||||||||
\(403\) | − 0.950664i | − 0.0473560i | ||||||||
\(404\) | −3.37480 | −0.167903 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.5137 | −0.769930 | ||||||||
\(407\) | 29.8611i | 1.48016i | ||||||||
\(408\) | 12.5969i | 0.623640i | ||||||||
\(409\) | −9.58405 | −0.473901 | −0.236950 | − | 0.971522i | \(-0.576148\pi\) | ||||
−0.236950 | + | 0.971522i | \(0.576148\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −53.1856 | −2.62345 | ||||||||
\(412\) | 13.1316i | 0.646949i | ||||||||
\(413\) | 43.0952i | 2.12057i | ||||||||
\(414\) | 4.22212 | 0.207506 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.22212 | −0.0599192 | ||||||||
\(417\) | 16.8319i | 0.824261i | ||||||||
\(418\) | 23.5897i | 1.15381i | ||||||||
\(419\) | 20.5265 | 1.00279 | 0.501393 | − | 0.865219i | \(-0.332821\pi\) | ||||
0.501393 | + | 0.865219i | \(0.332821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.29155 | 0.111683 | 0.0558417 | − | 0.998440i | \(-0.482216\pi\) | ||||
0.0558417 | + | 0.998440i | \(0.482216\pi\) | |||||||
\(422\) | − 15.4571i | − 0.752440i | ||||||||
\(423\) | 27.2083i | 1.32291i | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.52748 | 0.170907 | ||||||||
\(427\) | − 50.3393i | − 2.43609i | ||||||||
\(428\) | − 12.3054i | − 0.594802i | ||||||||
\(429\) | 16.8539 | 0.813714 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.83189 | −0.425417 | −0.212709 | − | 0.977116i | \(-0.568229\pi\) | ||||
−0.212709 | + | 0.977116i | \(0.568229\pi\) | |||||||
\(432\) | 3.28432i | 0.158017i | ||||||||
\(433\) | − 33.3465i | − 1.60253i | −0.598309 | − | 0.801266i | \(-0.704160\pi\) | ||||
0.598309 | − | 0.801266i | \(-0.295840\pi\) | |||||||
\(434\) | −3.57587 | −0.171647 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.5969 | −0.507500 | ||||||||
\(437\) | 4.59692i | 0.219900i | ||||||||
\(438\) | 11.9434i | 0.570679i | ||||||||
\(439\) | 6.02829 | 0.287714 | 0.143857 | − | 0.989598i | \(-0.454049\pi\) | ||||
0.143857 | + | 0.989598i | \(0.454049\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 59.6654 | 2.84121 | ||||||||
\(442\) | 5.72855i | 0.272479i | ||||||||
\(443\) | 15.5275i | 0.737733i | 0.929482 | + | 0.368866i | \(0.120254\pi\) | ||||
−0.929482 | + | 0.368866i | \(0.879746\pi\) | |||||||
\(444\) | −15.6381 | −0.742150 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.7496 | −0.509008 | ||||||||
\(447\) | − 53.1856i | − 2.51559i | ||||||||
\(448\) | 4.59692i | 0.217184i | ||||||||
\(449\) | 18.3594 | 0.866433 | 0.433216 | − | 0.901290i | \(-0.357379\pi\) | ||||
0.433216 | + | 0.901290i | \(0.357379\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.6519 | −2.05549 | ||||||||
\(452\) | − 6.00000i | − 0.282216i | ||||||||
\(453\) | − 10.9168i | − 0.512914i | ||||||||
\(454\) | 12.3054 | 0.577519 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.3537 | −0.578517 | ||||||||
\(457\) | − 11.4992i | − 0.537910i | −0.963153 | − | 0.268955i | \(-0.913322\pi\) | ||||
0.963153 | − | 0.268955i | \(-0.0866782\pi\) | |||||||
\(458\) | − 9.63806i | − 0.450357i | ||||||||
\(459\) | 15.3949 | 0.718572 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.33270 | 0.0620700 | 0.0310350 | − | 0.999518i | \(-0.490120\pi\) | ||||
0.0310350 | + | 0.999518i | \(0.490120\pi\) | |||||||
\(462\) | − 63.3949i | − 2.94940i | ||||||||
\(463\) | − 35.8190i | − 1.66465i | −0.554287 | − | 0.832326i | \(-0.687009\pi\) | ||||
0.554287 | − | 0.832326i | \(-0.312991\pi\) | |||||||
\(464\) | −3.37480 | −0.156671 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.9434 | 0.645917 | ||||||||
\(467\) | − 23.7625i | − 1.09960i | −0.835298 | − | 0.549798i | \(-0.814705\pi\) | ||||
0.835298 | − | 0.549798i | \(-0.185295\pi\) | |||||||
\(468\) | 5.15992i | 0.238517i | ||||||||
\(469\) | 71.8869 | 3.31943 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.4298 | 0.572733 | ||||||||
\(472\) | 9.37480i | 0.431510i | ||||||||
\(473\) | − 41.0531i | − 1.88762i | ||||||||
\(474\) | 13.1373 | 0.603414 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.5476 | 0.987632 | ||||||||
\(477\) | − 25.3327i | − 1.15990i | ||||||||
\(478\) | 26.3877i | 1.20694i | ||||||||
\(479\) | 2.04210 | 0.0933060 | 0.0466530 | − | 0.998911i | \(-0.485145\pi\) | ||||
0.0466530 | + | 0.998911i | \(0.485145\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.11153 | −0.324258 | ||||||||
\(482\) | − 7.06943i | − 0.322004i | ||||||||
\(483\) | − 12.3537i | − 0.562115i | ||||||||
\(484\) | −15.3337 | −0.696984 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −20.1728 | −0.915056 | ||||||||
\(487\) | − 18.6252i | − 0.843988i | −0.906599 | − | 0.421994i | \(-0.861330\pi\) | ||||
0.906599 | − | 0.421994i | \(-0.138670\pi\) | |||||||
\(488\) | − 10.9507i | − 0.495713i | ||||||||
\(489\) | −33.3666 | −1.50889 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.7204 | 1.52178 | 0.760889 | − | 0.648882i | \(-0.224763\pi\) | ||||
0.760889 | + | 0.648882i | \(0.224763\pi\) | |||||||
\(492\) | − 22.8602i | − 1.03062i | ||||||||
\(493\) | 15.8190i | 0.712453i | ||||||||
\(494\) | −5.61797 | −0.252764 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.777884 | −0.0349280 | ||||||||
\(497\) | − 6.03391i | − 0.270658i | ||||||||
\(498\) | 10.2633i | 0.459908i | ||||||||
\(499\) | 16.8885 | 0.756032 | 0.378016 | − | 0.925799i | \(-0.376607\pi\) | ||||
0.378016 | + | 0.925799i | \(0.376607\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.6365 | 1.54744 | ||||||||
\(502\) | − 24.9023i | − 1.11144i | ||||||||
\(503\) | − 11.4031i | − 0.508438i | −0.967147 | − | 0.254219i | \(-0.918182\pi\) | ||||
0.967147 | − | 0.254219i | \(-0.0818185\pi\) | |||||||
\(504\) | 19.4087 | 0.864533 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.13163 | −0.228129 | ||||||||
\(507\) | − 30.9224i | − 1.37331i | ||||||||
\(508\) | 2.26326i | 0.100416i | ||||||||
\(509\) | 1.87560 | 0.0831346 | 0.0415673 | − | 0.999136i | \(-0.486765\pi\) | ||||
0.0415673 | + | 0.999136i | \(0.486765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4298 | 0.903759 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 15.0977i | 0.666581i | ||||||||
\(514\) | −0.444233 | −0.0195943 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.4992 | 0.946449 | ||||||||
\(517\) | − 33.0694i | − 1.45439i | ||||||||
\(518\) | 26.7496i | 1.17531i | ||||||||
\(519\) | 27.5275 | 1.20832 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.11153 | 0.223940 | 0.111970 | − | 0.993712i | \(-0.464284\pi\) | ||||
0.111970 | + | 0.993712i | \(0.464284\pi\) | |||||||
\(522\) | 14.2488i | 0.623653i | ||||||||
\(523\) | − 19.4571i | − 0.850799i | −0.905006 | − | 0.425400i | \(-0.860134\pi\) | ||||
0.905006 | − | 0.425400i | \(-0.139866\pi\) | |||||||
\(524\) | −2.93057 | −0.128022 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.8812 | −1.04127 | ||||||||
\(527\) | 3.64625i | 0.158833i | ||||||||
\(528\) | − 13.7907i | − 0.600165i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.5815 | 1.71769 | ||||||||
\(532\) | 21.1316i | 0.916172i | ||||||||
\(533\) | − 10.3958i | − 0.450294i | ||||||||
\(534\) | −24.0000 | −1.03858 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.6381 | 0.675461 | ||||||||
\(537\) | − 35.4571i | − 1.53009i | ||||||||
\(538\) | − 16.2633i | − 0.701159i | ||||||||
\(539\) | −72.5183 | −3.12359 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.70750 | −0.116404 | −0.0582022 | − | 0.998305i | \(-0.518537\pi\) | ||||
−0.0582022 | + | 0.998305i | \(0.518537\pi\) | |||||||
\(542\) | 25.6098i | 1.10003i | ||||||||
\(543\) | − 42.4360i | − 1.82111i | ||||||||
\(544\) | 4.68740 | 0.200971 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.0977 | 0.646123 | ||||||||
\(547\) | − 1.66635i | − 0.0712479i | −0.999365 | − | 0.0356240i | \(-0.988658\pi\) | ||||
0.999365 | − | 0.0356240i | \(-0.0113419\pi\) | |||||||
\(548\) | 19.7907i | 0.845419i | ||||||||
\(549\) | −46.2350 | −1.97326 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.5137 | −0.660904 | ||||||||
\(552\) | − 2.68740i | − 0.114383i | ||||||||
\(553\) | − 22.4719i | − 0.955601i | ||||||||
\(554\) | −2.88847 | −0.122719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.26326 | 0.265622 | ||||||||
\(557\) | − 20.9306i | − 0.886857i | −0.896310 | − | 0.443428i | \(-0.853762\pi\) | ||||
0.896310 | − | 0.443428i | \(-0.146238\pi\) | |||||||
\(558\) | 3.28432i | 0.139036i | ||||||||
\(559\) | 9.77693 | 0.413520 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −64.6427 | −2.72922 | ||||||||
\(562\) | 4.26326i | 0.179835i | ||||||||
\(563\) | 15.2761i | 0.643812i | 0.946772 | + | 0.321906i | \(0.104324\pi\) | ||||
−0.946772 | + | 0.321906i | \(0.895676\pi\) | |||||||
\(564\) | 17.3182 | 0.729229 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 30.5686 | 1.28490 | ||||||||
\(567\) | 17.6525i | 0.741337i | ||||||||
\(568\) | − 1.31260i | − 0.0550755i | ||||||||
\(569\) | −20.3877 | −0.854695 | −0.427348 | − | 0.904087i | \(-0.640552\pi\) | ||||
−0.427348 | + | 0.904087i | \(0.640552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.49357 | 0.229899 | 0.114949 | − | 0.993371i | \(-0.463329\pi\) | ||||
0.114949 | + | 0.993371i | \(0.463329\pi\) | |||||||
\(572\) | − 6.27145i | − 0.262223i | ||||||||
\(573\) | − 43.3327i | − 1.81025i | ||||||||
\(574\) | −39.1033 | −1.63214 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.22212 | 0.175922 | ||||||||
\(577\) | 17.2761i | 0.719215i | 0.933104 | + | 0.359607i | \(0.117089\pi\) | ||||
−0.933104 | + | 0.359607i | \(0.882911\pi\) | |||||||
\(578\) | − 4.97171i | − 0.206796i | ||||||||
\(579\) | 48.2212 | 2.00400 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.5558 | 0.728336 | ||||||||
\(582\) | − 48.5403i | − 2.01206i | ||||||||
\(583\) | 30.7898i | 1.27518i | ||||||||
\(584\) | 4.44423 | 0.183904 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 31.8247i | 1.31354i | 0.754089 | + | 0.656772i | \(0.228079\pi\) | ||||
−0.754089 | + | 0.656772i | \(0.771921\pi\) | |||||||
\(588\) | − 37.9773i | − 1.56616i | ||||||||
\(589\) | −3.57587 | −0.147341 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.8052 | 0.650140 | ||||||||
\(592\) | 5.81903i | 0.239161i | ||||||||
\(593\) | 12.4442i | 0.511023i | 0.966806 | + | 0.255512i | \(0.0822439\pi\) | ||||
−0.966806 | + | 0.255512i | \(0.917756\pi\) | |||||||
\(594\) | −16.8539 | −0.691524 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −19.7907 | −0.810661 | ||||||||
\(597\) | 17.6525i | 0.722470i | ||||||||
\(598\) | − 1.22212i | − 0.0499761i | ||||||||
\(599\) | −17.4370 | −0.712456 | −0.356228 | − | 0.934399i | \(-0.615937\pi\) | ||||
−0.356228 | + | 0.934399i | \(0.615937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.916751 | −0.0373951 | −0.0186975 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186975 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(602\) | − 36.7753i | − 1.49885i | ||||||||
\(603\) | − 66.0257i | − 2.68878i | ||||||||
\(604\) | −4.06220 | −0.165289 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.06943 | 0.368421 | ||||||||
\(607\) | 36.7753i | 1.49266i | 0.665574 | + | 0.746332i | \(0.268187\pi\) | ||||
−0.665574 | + | 0.746332i | \(0.731813\pi\) | |||||||
\(608\) | 4.59692i | 0.186430i | ||||||||
\(609\) | 41.6914 | 1.68942 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.87560 | 0.318613 | ||||||||
\(612\) | − 19.7907i | − 0.799994i | ||||||||
\(613\) | − 4.38766i | − 0.177216i | −0.996067 | − | 0.0886080i | \(-0.971758\pi\) | ||||
0.996067 | − | 0.0886080i | \(-0.0282418\pi\) | |||||||
\(614\) | 8.54853 | 0.344991 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −23.5897 | −0.950455 | ||||||||
\(617\) | 40.4499i | 1.62845i | 0.580549 | + | 0.814225i | \(0.302838\pi\) | ||||
−0.580549 | + | 0.814225i | \(0.697162\pi\) | |||||||
\(618\) | − 35.2899i | − 1.41957i | ||||||||
\(619\) | 39.8165 | 1.60036 | 0.800180 | − | 0.599760i | \(-0.204737\pi\) | ||||
0.800180 | + | 0.599760i | \(0.204737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.28432 | −0.131795 | ||||||||
\(622\) | − 7.63806i | − 0.306258i | ||||||||
\(623\) | 41.0531i | 1.64476i | ||||||||
\(624\) | 3.28432 | 0.131478 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.2350 | −0.728816 | ||||||||
\(627\) | − 63.3949i | − 2.53175i | ||||||||
\(628\) | − 4.62520i | − 0.184566i | ||||||||
\(629\) | 27.2761 | 1.08757 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.9013 | 1.03112 | 0.515558 | − | 0.856855i | \(-0.327585\pi\) | ||||
0.515558 | + | 0.856855i | \(0.327585\pi\) | |||||||
\(632\) | − 4.88847i | − 0.194453i | ||||||||
\(633\) | 41.5394i | 1.65104i | ||||||||
\(634\) | 16.8602 | 0.669603 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −16.1244 | −0.639374 | ||||||||
\(637\) | − 17.2705i | − 0.684282i | ||||||||
\(638\) | − 17.3182i | − 0.685635i | ||||||||
\(639\) | −5.54195 | −0.219236 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.8448 | −1.73176 | −0.865882 | − | 0.500248i | \(-0.833242\pi\) | ||||
−0.865882 | + | 0.500248i | \(0.833242\pi\) | |||||||
\(642\) | 33.0694i | 1.30515i | ||||||||
\(643\) | − 3.94343i | − 0.155514i | −0.996972 | − | 0.0777568i | \(-0.975224\pi\) | ||||
0.996972 | − | 0.0777568i | \(-0.0247758\pi\) | |||||||
\(644\) | −4.59692 | −0.181144 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.5476 | 0.847778 | ||||||||
\(647\) | 24.3456i | 0.957123i | 0.878054 | + | 0.478561i | \(0.158842\pi\) | ||||
−0.878054 | + | 0.478561i | \(0.841158\pi\) | |||||||
\(648\) | 3.84008i | 0.150853i | ||||||||
\(649\) | −48.1080 | −1.88841 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.60978 | 0.376637 | ||||||||
\(652\) | 12.4159i | 0.486246i | ||||||||
\(653\) | − 37.6921i | − 1.47500i | −0.675344 | − | 0.737502i | \(-0.736005\pi\) | ||||
0.675344 | − | 0.737502i | \(-0.263995\pi\) | |||||||
\(654\) | 28.4781 | 1.11358 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.50643 | −0.332120 | ||||||||
\(657\) | − 18.7641i | − 0.732056i | ||||||||
\(658\) | − 29.6236i | − 1.15485i | ||||||||
\(659\) | −24.6107 | −0.958698 | −0.479349 | − | 0.877624i | \(-0.659127\pi\) | ||||
−0.479349 | + | 0.877624i | \(0.659127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.3126 | 1.06234 | 0.531169 | − | 0.847266i | \(-0.321753\pi\) | ||||
0.531169 | + | 0.847266i | \(0.321753\pi\) | |||||||
\(662\) | 19.1517i | 0.744353i | ||||||||
\(663\) | − 15.3949i | − 0.597888i | ||||||||
\(664\) | 3.81903 | 0.148207 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 24.5686 | 0.952015 | ||||||||
\(667\) | − 3.37480i | − 0.130673i | ||||||||
\(668\) | − 12.8885i | − 0.498670i | ||||||||
\(669\) | 28.8885 | 1.11689 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.1948 | 2.16938 | ||||||||
\(672\) | − 12.3537i | − 0.476556i | ||||||||
\(673\) | − 22.5265i | − 0.868334i | −0.900832 | − | 0.434167i | \(-0.857043\pi\) | ||||
0.900832 | − | 0.434167i | \(-0.142957\pi\) | |||||||
\(674\) | −1.70845 | −0.0658070 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5064 | −0.442555 | ||||||||
\(677\) | − 6.00000i | − 0.230599i | −0.993331 | − | 0.115299i | \(-0.963217\pi\) | ||||
0.993331 | − | 0.115299i | \(-0.0367827\pi\) | |||||||
\(678\) | 16.1244i | 0.619254i | ||||||||
\(679\) | −83.0304 | −3.18641 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.0694 | −1.26722 | ||||||||
\(682\) | − 3.99181i | − 0.152854i | ||||||||
\(683\) | 31.9974i | 1.22435i | 0.790723 | + | 0.612174i | \(0.209705\pi\) | ||||
−0.790723 | + | 0.612174i | \(0.790295\pi\) | |||||||
\(684\) | 19.4087 | 0.742111 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −32.7835 | −1.25168 | ||||||||
\(687\) | 25.9013i | 0.988197i | ||||||||
\(688\) | − 8.00000i | − 0.304997i | ||||||||
\(689\) | −7.33270 | −0.279354 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.80617 | −0.106752 | −0.0533758 | − | 0.998574i | \(-0.516998\pi\) | ||||
−0.0533758 | + | 0.998574i | \(0.516998\pi\) | |||||||
\(692\) | − 10.2432i | − 0.389387i | ||||||||
\(693\) | 99.5984i | 3.78343i | ||||||||
\(694\) | −10.6874 | −0.405688 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9.06943 | 0.343776 | ||||||||
\(697\) | 39.8730i | 1.51030i | ||||||||
\(698\) | 12.3877i | 0.468880i | ||||||||
\(699\) | −37.4716 | −1.41730 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.37385 | 0.316276 | 0.158138 | − | 0.987417i | \(-0.449451\pi\) | ||||
0.158138 | + | 0.987417i | \(0.449451\pi\) | |||||||
\(702\) | − 4.01382i | − 0.151492i | ||||||||
\(703\) | 26.7496i | 1.00888i | ||||||||
\(704\) | −5.13163 | −0.193406 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.45710 | 0.205381 | ||||||||
\(707\) | − 15.5137i | − 0.583451i | ||||||||
\(708\) | − 25.1938i | − 0.946842i | ||||||||
\(709\) | −21.2139 | −0.796706 | −0.398353 | − | 0.917232i | \(-0.630418\pi\) | ||||
−0.398353 | + | 0.917232i | \(0.630418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.6397 | −0.774048 | ||||||||
\(712\) | 8.93057i | 0.334687i | ||||||||
\(713\) | − 0.777884i | − 0.0291320i | ||||||||
\(714\) | −57.9070 | −2.16711 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −13.1938 | −0.493077 | ||||||||
\(717\) | − 70.9142i | − 2.64834i | ||||||||
\(718\) | − 20.1810i | − 0.753147i | ||||||||
\(719\) | 28.1106 | 1.04835 | 0.524174 | − | 0.851611i | \(-0.324374\pi\) | ||||
0.524174 | + | 0.851611i | \(0.324374\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60.3650 | −2.24811 | ||||||||
\(722\) | 2.13163i | 0.0793311i | ||||||||
\(723\) | 18.9984i | 0.706558i | ||||||||
\(724\) | −15.7907 | −0.586858 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 41.2076 | 1.52936 | ||||||||
\(727\) | − 39.0330i | − 1.44765i | −0.689982 | − | 0.723826i | \(-0.742382\pi\) | ||||
0.689982 | − | 0.723826i | \(-0.257618\pi\) | |||||||
\(728\) | − 5.61797i | − 0.208216i | ||||||||
\(729\) | 42.6921 | 1.58119 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.4992 | −1.38696 | ||||||||
\(732\) | 29.4288i | 1.08772i | ||||||||
\(733\) | − 47.1373i | − 1.74105i | −0.492120 | − | 0.870527i | \(-0.663778\pi\) | ||||
0.492120 | − | 0.870527i | \(-0.336222\pi\) | |||||||
\(734\) | −2.74960 | −0.101490 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 80.2488i | 2.95600i | ||||||||
\(738\) | 35.9151i | 1.32205i | ||||||||
\(739\) | 24.5265 | 0.902223 | 0.451111 | − | 0.892468i | \(-0.351028\pi\) | ||||
0.451111 | + | 0.892468i | \(0.351028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.0977 | 0.554629 | ||||||||
\(742\) | 27.5815i | 1.01255i | ||||||||
\(743\) | 7.34651i | 0.269517i | 0.990878 | + | 0.134759i | \(0.0430259\pi\) | ||||
−0.990878 | + | 0.134759i | \(0.956974\pi\) | |||||||
\(744\) | 2.09048 | 0.0766409 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.0823 | −0.442364 | ||||||||
\(747\) | − 16.1244i | − 0.589961i | ||||||||
\(748\) | 24.0540i | 0.879502i | ||||||||
\(749\) | 56.5667 | 2.06690 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.2359 | 0.410005 | 0.205002 | − | 0.978761i | \(-0.434280\pi\) | ||||
0.205002 | + | 0.978761i | \(0.434280\pi\) | |||||||
\(752\) | − 6.44423i | − 0.234997i | ||||||||
\(753\) | 66.9224i | 2.43879i | ||||||||
\(754\) | 4.12440 | 0.150202 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −15.0977 | −0.549099 | ||||||||
\(757\) | 49.1794i | 1.78745i | 0.448611 | + | 0.893727i | \(0.351919\pi\) | ||||
−0.448611 | + | 0.893727i | \(0.648081\pi\) | |||||||
\(758\) | − 5.25603i | − 0.190908i | ||||||||
\(759\) | 13.7907 | 0.500572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.2478 | 1.56773 | 0.783867 | − | 0.620929i | \(-0.213245\pi\) | ||||
0.783867 | + | 0.620929i | \(0.213245\pi\) | |||||||
\(762\) | − 6.08230i | − 0.220338i | ||||||||
\(763\) | − 48.7131i | − 1.76353i | ||||||||
\(764\) | −16.1244 | −0.583360 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 11.4571i | − 0.413692i | ||||||||
\(768\) | − 2.68740i | − 0.0969732i | ||||||||
\(769\) | 39.6638 | 1.43031 | 0.715156 | − | 0.698964i | \(-0.246355\pi\) | ||||
0.715156 | + | 0.698964i | \(0.246355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.19383 | 0.0429948 | ||||||||
\(772\) | − 17.9434i | − 0.645798i | ||||||||
\(773\) | 2.18097i | 0.0784440i | 0.999231 | + | 0.0392220i | \(0.0124879\pi\) | ||||
−0.999231 | + | 0.0392220i | \(0.987512\pi\) | |||||||
\(774\) | −33.7769 | −1.21409 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.0622 | −0.648395 | ||||||||
\(777\) | − 71.8869i | − 2.57893i | ||||||||
\(778\) | − 0.325463i | − 0.0116684i | ||||||||
\(779\) | −39.1033 | −1.40102 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.73578 | 0.241025 | ||||||||
\(782\) | 4.68740i | 0.167621i | ||||||||
\(783\) | − 11.0839i | − 0.396106i | ||||||||
\(784\) | −14.1316 | −0.504701 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.87560 | 0.280913 | ||||||||
\(787\) | 4.76407i | 0.169821i | 0.996389 | + | 0.0849103i | \(0.0270604\pi\) | ||||
−0.996389 | + | 0.0849103i | \(0.972940\pi\) | |||||||
\(788\) | − 5.88123i | − 0.209510i | ||||||||
\(789\) | 64.1784 | 2.28481 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.5815 | 0.980685 | ||||||||
\(792\) | 21.6663i | 0.769880i | ||||||||
\(793\) | 13.3830i | 0.475244i | ||||||||
\(794\) | 17.7568 | 0.630166 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.56863 | 0.232819 | ||||||||
\(797\) | 39.7204i | 1.40697i | 0.710711 | + | 0.703484i | \(0.248373\pi\) | ||||
−0.710711 | + | 0.703484i | \(0.751627\pi\) | |||||||
\(798\) | − 56.7891i | − 2.01031i | ||||||||
\(799\) | −30.2067 | −1.06864 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.7059 | 1.33227 | ||||||||
\(802\) | 3.91770i | 0.138339i | ||||||||
\(803\) | 22.8062i | 0.804812i | ||||||||
\(804\) | −42.0257 | −1.48213 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.950664 | 0.0334857 | ||||||||
\(807\) | 43.7059i | 1.53852i | ||||||||
\(808\) | − 3.37480i | − 0.118725i | ||||||||
\(809\) | −46.8941 | −1.64871 | −0.824354 | − | 0.566074i | \(-0.808462\pi\) | ||||
−0.824354 | + | 0.566074i | \(0.808462\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.8319 | −1.29334 | −0.646671 | − | 0.762769i | \(-0.723839\pi\) | ||||
−0.646671 | + | 0.762769i | \(0.723839\pi\) | |||||||
\(812\) | − 15.5137i | − 0.544423i | ||||||||
\(813\) | − 68.8237i | − 2.41375i | ||||||||
\(814\) | −29.8611 | −1.04663 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12.5969 | −0.440980 | ||||||||
\(817\) | − 36.7753i | − 1.28661i | ||||||||
\(818\) | − 9.58405i | − 0.335099i | ||||||||
\(819\) | −23.7197 | −0.828834 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.6107 | −0.649519 | −0.324759 | − | 0.945797i | \(-0.605283\pi\) | ||||
−0.324759 | + | 0.945797i | \(0.605283\pi\) | |||||||
\(822\) | − 53.1856i | − 1.85506i | ||||||||
\(823\) | 9.31823i | 0.324813i | 0.986724 | + | 0.162407i | \(0.0519256\pi\) | ||||
−0.986724 | + | 0.162407i | \(0.948074\pi\) | |||||||
\(824\) | −13.1316 | −0.457462 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −43.0952 | −1.49947 | ||||||||
\(827\) | 53.0129i | 1.84344i | 0.387858 | + | 0.921719i | \(0.373215\pi\) | ||||
−0.387858 | + | 0.921719i | \(0.626785\pi\) | |||||||
\(828\) | 4.22212i | 0.146729i | ||||||||
\(829\) | 25.2761 | 0.877876 | 0.438938 | − | 0.898517i | \(-0.355355\pi\) | ||||
0.438938 | + | 0.898517i | \(0.355355\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.76246 | 0.269277 | ||||||||
\(832\) | − 1.22212i | − 0.0423693i | ||||||||
\(833\) | 66.2406i | 2.29510i | ||||||||
\(834\) | −16.8319 | −0.582841 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −23.5897 | −0.815866 | ||||||||
\(837\) | − 2.55481i | − 0.0883073i | ||||||||
\(838\) | 20.5265i | 0.709077i | ||||||||
\(839\) | −11.6946 | −0.403744 | −0.201872 | − | 0.979412i | \(-0.564702\pi\) | ||||
−0.201872 | + | 0.979412i | \(0.564702\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.6107 | −0.607267 | ||||||||
\(842\) | 2.29155i | 0.0789720i | ||||||||
\(843\) | − 11.4571i | − 0.394603i | ||||||||
\(844\) | 15.4571 | 0.532055 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −27.2083 | −0.935441 | ||||||||
\(847\) | − 70.4875i | − 2.42198i | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | −82.1501 | −2.81938 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.81903 | −0.199474 | ||||||||
\(852\) | 3.52748i | 0.120850i | ||||||||
\(853\) | − 38.6371i | − 1.32291i | −0.749985 | − | 0.661455i | \(-0.769939\pi\) | ||||
0.749985 | − | 0.661455i | \(-0.230061\pi\) | |||||||
\(854\) | 50.3393 | 1.72257 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.3054 | 0.420589 | ||||||||
\(857\) | 26.2488i | 0.896642i | 0.893873 | + | 0.448321i | \(0.147978\pi\) | ||||
−0.893873 | + | 0.448321i | \(0.852022\pi\) | |||||||
\(858\) | 16.8539i | 0.575383i | ||||||||
\(859\) | −37.5558 | −1.28139 | −0.640693 | − | 0.767797i | \(-0.721353\pi\) | ||||
−0.640693 | + | 0.767797i | \(0.721353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 105.086 | 3.58133 | ||||||||
\(862\) | − 8.83189i | − 0.300816i | ||||||||
\(863\) | 21.9855i | 0.748396i | 0.927349 | + | 0.374198i | \(0.122082\pi\) | ||||
−0.927349 | + | 0.374198i | \(0.877918\pi\) | |||||||
\(864\) | −3.28432 | −0.111735 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 33.3465 | 1.13316 | ||||||||
\(867\) | 13.3610i | 0.453763i | ||||||||
\(868\) | − 3.57587i | − 0.121373i | ||||||||
\(869\) | 25.0858 | 0.850978 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.1115 | −0.647570 | ||||||||
\(872\) | − 10.5969i | − 0.358857i | ||||||||
\(873\) | 76.2607i | 2.58103i | ||||||||
\(874\) | −4.59692 | −0.155493 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.9434 | −0.403531 | ||||||||
\(877\) | − 36.5064i | − 1.23273i | −0.787459 | − | 0.616367i | \(-0.788604\pi\) | ||||
0.787459 | − | 0.616367i | \(-0.211396\pi\) | |||||||
\(878\) | 6.02829i | 0.203445i | ||||||||
\(879\) | 16.1244 | 0.543862 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.4571 | −0.588145 | −0.294072 | − | 0.955783i | \(-0.595011\pi\) | ||||
−0.294072 | + | 0.955783i | \(0.595011\pi\) | |||||||
\(882\) | 59.6654i | 2.00904i | ||||||||
\(883\) | − 22.9444i | − 0.772140i | −0.922470 | − | 0.386070i | \(-0.873832\pi\) | ||||
0.922470 | − | 0.386070i | \(-0.126168\pi\) | |||||||
\(884\) | −5.72855 | −0.192672 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.5275 | −0.521656 | ||||||||
\(887\) | − 11.7223i | − 0.393595i | −0.980444 | − | 0.196798i | \(-0.936946\pi\) | ||||
0.980444 | − | 0.196798i | \(-0.0630542\pi\) | |||||||
\(888\) | − 15.6381i | − 0.524779i | ||||||||
\(889\) | −10.4040 | −0.348940 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.7059 | −0.660172 | ||||||||
\(892\) | − 10.7496i | − 0.359923i | ||||||||
\(893\) | − 29.6236i | − 0.991316i | ||||||||
\(894\) | 53.1856 | 1.77879 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.59692 | −0.153572 | ||||||||
\(897\) | 3.28432i | 0.109660i | ||||||||
\(898\) | 18.3594i | 0.612660i | ||||||||
\(899\) | 2.62520 | 0.0875554 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.1244 | 0.936960 | ||||||||
\(902\) | − 43.6519i | − 1.45345i | ||||||||
\(903\) | 98.8300i | 3.28886i | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.9168 | 0.362685 | ||||||||
\(907\) | − 1.91770i | − 0.0636763i | −0.999493 | − | 0.0318381i | \(-0.989864\pi\) | ||||
0.999493 | − | 0.0318381i | \(-0.0101361\pi\) | |||||||
\(908\) | 12.3054i | 0.408368i | ||||||||
\(909\) | −14.2488 | −0.472603 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.8319 | −1.88292 | −0.941462 | − | 0.337118i | \(-0.890548\pi\) | ||||
−0.941462 | + | 0.337118i | \(0.890548\pi\) | |||||||
\(912\) | − 12.3537i | − 0.409073i | ||||||||
\(913\) | 19.5979i | 0.648595i | ||||||||
\(914\) | 11.4992 | 0.380360 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.63806 | 0.318451 | ||||||||
\(917\) | − 13.4716i | − 0.444870i | ||||||||
\(918\) | 15.3949i | 0.508107i | ||||||||
\(919\) | 26.0257 | 0.858509 | 0.429255 | − | 0.903183i | \(-0.358776\pi\) | ||||
0.429255 | + | 0.903183i | \(0.358776\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.9733 | −0.756997 | ||||||||
\(922\) | 1.33270i | 0.0438901i | ||||||||
\(923\) | 1.60415i | 0.0528013i | ||||||||
\(924\) | 63.3949 | 2.08554 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35.8190 | 1.17709 | ||||||||
\(927\) | 55.4433i | 1.82100i | ||||||||
\(928\) | − 3.37480i | − 0.110783i | ||||||||
\(929\) | 17.1115 | 0.561411 | 0.280706 | − | 0.959794i | \(-0.409432\pi\) | ||||
0.280706 | + | 0.959794i | \(0.409432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −64.9619 | −2.12904 | ||||||||
\(932\) | 13.9434i | 0.456732i | ||||||||
\(933\) | 20.5265i | 0.672008i | ||||||||
\(934\) | 23.7625 | 0.777531 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.15992 | −0.168657 | ||||||||
\(937\) | 16.3738i | 0.534910i | 0.963570 | + | 0.267455i | \(0.0861827\pi\) | ||||
−0.963570 | + | 0.267455i | \(0.913817\pi\) | |||||||
\(938\) | 71.8869i | 2.34719i | ||||||||
\(939\) | 49.0047 | 1.59921 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.4097 | −0.534940 | −0.267470 | − | 0.963566i | \(-0.586188\pi\) | ||||
−0.267470 | + | 0.963566i | \(0.586188\pi\) | |||||||
\(942\) | 12.4298i | 0.404984i | ||||||||
\(943\) | − 8.50643i | − 0.277008i | ||||||||
\(944\) | −9.37480 | −0.305124 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 41.0531 | 1.33475 | ||||||||
\(947\) | − 21.3886i | − 0.695037i | −0.937673 | − | 0.347518i | \(-0.887024\pi\) | ||||
0.937673 | − | 0.347518i | \(-0.112976\pi\) | |||||||
\(948\) | 13.1373i | 0.426678i | ||||||||
\(949\) | −5.43137 | −0.176310 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.3100 | −1.46928 | ||||||||
\(952\) | 21.5476i | 0.698361i | ||||||||
\(953\) | 16.7276i | 0.541860i | 0.962599 | + | 0.270930i | \(0.0873312\pi\) | ||||
−0.962599 | + | 0.270930i | \(0.912669\pi\) | |||||||
\(954\) | 25.3327 | 0.820176 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −26.3877 | −0.853438 | ||||||||
\(957\) | 46.5410i | 1.50446i | ||||||||
\(958\) | 2.04210i | 0.0659773i | ||||||||
\(959\) | −90.9764 | −2.93778 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3949 | −0.980481 | ||||||||
\(962\) | − 7.11153i | − 0.229285i | ||||||||
\(963\) | − 51.9547i | − 1.67422i | ||||||||
\(964\) | 7.06943 | 0.227691 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12.3537 | 0.397475 | ||||||||
\(967\) | 45.2617i | 1.45552i | 0.685834 | + | 0.727758i | \(0.259438\pi\) | ||||
−0.685834 | + | 0.727758i | \(0.740562\pi\) | |||||||
\(968\) | − 15.3337i | − 0.492842i | ||||||||
\(969\) | −57.9070 | −1.86024 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.2560 | 1.45234 | 0.726168 | − | 0.687518i | \(-0.241300\pi\) | ||||
0.726168 | + | 0.687518i | \(0.241300\pi\) | |||||||
\(972\) | − 20.1728i | − 0.647042i | ||||||||
\(973\) | 28.7917i | 0.923019i | ||||||||
\(974\) | 18.6252 | 0.596790 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.9507 | 0.350522 | ||||||||
\(977\) | − 13.3465i | − 0.426993i | −0.976944 | − | 0.213496i | \(-0.931515\pi\) | ||||
0.976944 | − | 0.213496i | \(-0.0684852\pi\) | |||||||
\(978\) | − 33.3666i | − 1.06695i | ||||||||
\(979\) | −45.8284 | −1.46468 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.7414 | −1.42848 | ||||||||
\(982\) | 33.7204i | 1.07606i | ||||||||
\(983\) | − 5.13163i | − 0.163674i | −0.996646 | − | 0.0818368i | \(-0.973921\pi\) | ||||
0.996646 | − | 0.0818368i | \(-0.0260786\pi\) | |||||||
\(984\) | 22.8602 | 0.728756 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.8190 | −0.503781 | ||||||||
\(987\) | 79.6104i | 2.53403i | ||||||||
\(988\) | − 5.61797i | − 0.178731i | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7989 | 0.565402 | 0.282701 | − | 0.959208i | \(-0.408770\pi\) | ||||
0.282701 | + | 0.959208i | \(0.408770\pi\) | |||||||
\(992\) | − 0.777884i | − 0.0246978i | ||||||||
\(993\) | − 51.4684i | − 1.63330i | ||||||||
\(994\) | 6.03391 | 0.191384 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.2633 | −0.325204 | ||||||||
\(997\) | 40.3877i | 1.27909i | 0.768754 | + | 0.639545i | \(0.220877\pi\) | ||||
−0.768754 | + | 0.639545i | \(0.779123\pi\) | |||||||
\(998\) | 16.8885i | 0.534595i | ||||||||
\(999\) | −19.1115 | −0.604662 |
(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 | 1150.2.b.j.599.4 | 6 | ||
5.2 | odd | 4 | 1150.2.a.q.1.1 | 3 | |||
5.3 | odd | 4 | 230.2.a.d.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 1150.2.b.j.599.3 | 6 | ||
15.8 | even | 4 | 2070.2.a.z.1.1 | 3 | |||
20.3 | even | 4 | 1840.2.a.r.1.1 | 3 | |||
20.7 | even | 4 | 9200.2.a.cf.1.3 | 3 | |||
40.3 | even | 4 | 7360.2.a.ce.1.3 | 3 | |||
40.13 | odd | 4 | 7360.2.a.bz.1.1 | 3 | |||
115.68 | even | 4 | 5290.2.a.r.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.d.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
1150.2.a.q.1.1 | 3 | 5.2 | odd | 4 | |||
1150.2.b.j.599.3 | 6 | 5.4 | even | 2 | inner | ||
1150.2.b.j.599.4 | 6 | 1.1 | even | 1 | trivial | ||
1840.2.a.r.1.1 | 3 | 20.3 | even | 4 | |||
2070.2.a.z.1.1 | 3 | 15.8 | even | 4 | |||
5290.2.a.r.1.3 | 3 | 115.68 | even | 4 | |||
7360.2.a.bz.1.1 | 3 | 40.13 | odd | 4 | |||
7360.2.a.ce.1.3 | 3 | 40.3 | even | 4 | |||
9200.2.a.cf.1.3 | 3 | 20.7 | even | 4 |