Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(799,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, 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("950.799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.63107136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 13x^{4} + 42x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.6 | ||
Root | \(2.77339i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.799 |
Dual form | 950.2.b.h.799.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.77339i | 1.02387i | 0.859025 | + | 0.511933i | \(0.171070\pi\) | ||||
−0.859025 | + | 0.511933i | \(0.828930\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.77339 | −0.723982 | ||||||||
\(7\) | − 2.69168i | − 1.01736i | −0.860956 | − | 0.508679i | \(-0.830134\pi\) | ||||
0.860956 | − | 0.508679i | \(-0.169866\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −0.144903 | −0.0483010 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.54677 | 1.67242 | 0.836208 | − | 0.548413i | \(-0.184768\pi\) | ||||
0.836208 | + | 0.548413i | \(0.184768\pi\) | |||||||
\(12\) | − 1.77339i | − 0.511933i | ||||||||
\(13\) | 2.91829i | 0.809388i | 0.914452 | + | 0.404694i | \(0.132622\pi\) | ||||
−0.914452 | + | 0.404694i | \(0.867378\pi\) | |||||||
\(14\) | 2.69168 | 0.719381 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.91829i | 1.19286i | 0.802665 | + | 0.596430i | \(0.203415\pi\) | ||||
−0.802665 | + | 0.596430i | \(0.796585\pi\) | |||||||
\(18\) | − 0.144903i | − 0.0341539i | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.77339 | 1.04164 | ||||||||
\(22\) | 5.54677i | 1.18258i | ||||||||
\(23\) | − 3.60997i | − 0.752730i | −0.926471 | − | 0.376365i | \(-0.877174\pi\) | ||||
0.926471 | − | 0.376365i | \(-0.122826\pi\) | |||||||
\(24\) | 1.77339 | 0.361991 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.91829 | −0.572324 | ||||||||
\(27\) | 5.06319i | 0.974412i | ||||||||
\(28\) | 2.69168i | 0.508679i | ||||||||
\(29\) | −1.08171 | −0.200868 | −0.100434 | − | 0.994944i | \(-0.532023\pi\) | ||||
−0.100434 | + | 0.994944i | \(0.532023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.54677 | 1.35544 | 0.677720 | − | 0.735320i | \(-0.262968\pi\) | ||||
0.677720 | + | 0.735320i | \(0.262968\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 9.83658i | 1.71233i | ||||||||
\(34\) | −4.91829 | −0.843480 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.144903 | 0.0241505 | ||||||||
\(37\) | 4.54677i | 0.747485i | 0.927532 | + | 0.373743i | \(0.121926\pi\) | ||||
−0.927532 | + | 0.373743i | \(0.878074\pi\) | |||||||
\(38\) | − 1.00000i | − 0.162221i | ||||||||
\(39\) | −5.17526 | −0.828705 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 4.77339i | 0.736550i | ||||||||
\(43\) | 9.54677i | 1.45587i | 0.685646 | + | 0.727935i | \(0.259520\pi\) | ||||
−0.685646 | + | 0.727935i | \(0.740480\pi\) | |||||||
\(44\) | −5.54677 | −0.836208 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.60997 | 0.532261 | ||||||||
\(47\) | − 0.836581i | − 0.122028i | −0.998137 | − | 0.0610139i | \(-0.980567\pi\) | ||||
0.998137 | − | 0.0610139i | \(-0.0194334\pi\) | |||||||
\(48\) | 1.77339i | 0.255966i | ||||||||
\(49\) | −0.245129 | −0.0350184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.72203 | −1.22133 | ||||||||
\(52\) | − 2.91829i | − 0.404694i | ||||||||
\(53\) | − 9.78523i | − 1.34410i | −0.740504 | − | 0.672052i | \(-0.765413\pi\) | ||||
0.740504 | − | 0.672052i | \(-0.234587\pi\) | |||||||
\(54\) | −5.06319 | −0.689013 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.69168 | −0.359691 | ||||||||
\(57\) | − 1.77339i | − 0.234891i | ||||||||
\(58\) | − 1.08171i | − 0.142035i | ||||||||
\(59\) | −12.9933 | −1.69159 | −0.845793 | − | 0.533511i | \(-0.820872\pi\) | ||||
−0.845793 | + | 0.533511i | \(0.820872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.38336 | −0.945342 | −0.472671 | − | 0.881239i | \(-0.656710\pi\) | ||||
−0.472671 | + | 0.881239i | \(0.656710\pi\) | |||||||
\(62\) | 7.54677i | 0.958441i | ||||||||
\(63\) | 0.390032i | 0.0491394i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.83658 | −1.21080 | ||||||||
\(67\) | 2.85510i | 0.348806i | 0.984674 | + | 0.174403i | \(0.0557995\pi\) | ||||
−0.984674 | + | 0.174403i | \(0.944201\pi\) | |||||||
\(68\) | − 4.91829i | − 0.596430i | ||||||||
\(69\) | 6.40187 | 0.770695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4769 | 1.71809 | 0.859046 | − | 0.511898i | \(-0.171057\pi\) | ||||
0.859046 | + | 0.511898i | \(0.171057\pi\) | |||||||
\(72\) | 0.144903i | 0.0170770i | ||||||||
\(73\) | − 5.15674i | − 0.603551i | −0.953379 | − | 0.301776i | \(-0.902421\pi\) | ||||
0.953379 | − | 0.301776i | \(-0.0975793\pi\) | |||||||
\(74\) | −4.54677 | −0.528552 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | − 14.9301i | − 1.70145i | ||||||||
\(78\) | − 5.17526i | − 0.585983i | ||||||||
\(79\) | 3.09355 | 0.348052 | 0.174026 | − | 0.984741i | \(-0.444322\pi\) | ||||
0.174026 | + | 0.984741i | \(0.444322\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.41371 | −1.04597 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.71019i | − 0.187718i | −0.995585 | − | 0.0938591i | \(-0.970080\pi\) | ||||
0.995585 | − | 0.0938591i | \(-0.0299203\pi\) | |||||||
\(84\) | −4.77339 | −0.520819 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.54677 | −1.02946 | ||||||||
\(87\) | − 1.91829i | − 0.205662i | ||||||||
\(88\) | − 5.54677i | − 0.591288i | ||||||||
\(89\) | 5.09355 | 0.539915 | 0.269958 | − | 0.962872i | \(-0.412990\pi\) | ||||
0.269958 | + | 0.962872i | \(0.412990\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.85510 | 0.823438 | ||||||||
\(92\) | 3.60997i | 0.376365i | ||||||||
\(93\) | 13.3834i | 1.38779i | ||||||||
\(94\) | 0.836581 | 0.0862867 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.77339 | −0.180996 | ||||||||
\(97\) | − 17.2570i | − 1.75218i | −0.482148 | − | 0.876090i | \(-0.660143\pi\) | ||||
0.482148 | − | 0.876090i | \(-0.339857\pi\) | |||||||
\(98\) | − 0.245129i | − 0.0247618i | ||||||||
\(99\) | −0.803744 | −0.0807793 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.38336 | −0.933679 | −0.466839 | − | 0.884342i | \(-0.654607\pi\) | ||||
−0.466839 | + | 0.884342i | \(0.654607\pi\) | |||||||
\(102\) | − 8.72203i | − 0.863610i | ||||||||
\(103\) | 12.9301i | 1.27404i | 0.770846 | + | 0.637022i | \(0.219834\pi\) | ||||
−0.770846 | + | 0.637022i | \(0.780166\pi\) | |||||||
\(104\) | 2.91829 | 0.286162 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.78523 | 0.950425 | ||||||||
\(107\) | 18.9420i | 1.83119i | 0.402102 | + | 0.915595i | \(0.368280\pi\) | ||||
−0.402102 | + | 0.915595i | \(0.631720\pi\) | |||||||
\(108\) | − 5.06319i | − 0.487206i | ||||||||
\(109\) | 2.69168 | 0.257816 | 0.128908 | − | 0.991657i | \(-0.458853\pi\) | ||||
0.128908 | + | 0.991657i | \(0.458853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.06319 | −0.765324 | ||||||||
\(112\) | − 2.69168i | − 0.254340i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 1.77339 | 0.166093 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.08171 | 0.100434 | ||||||||
\(117\) | − 0.422869i | − 0.0390942i | ||||||||
\(118\) | − 12.9933i | − 1.19613i | ||||||||
\(119\) | 13.2385 | 1.21357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.7667 | 1.79697 | ||||||||
\(122\) | − 7.38336i | − 0.668458i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.54677 | −0.677720 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.390032 | −0.0347468 | ||||||||
\(127\) | − 1.87361i | − 0.166256i | −0.996539 | − | 0.0831282i | \(-0.973509\pi\) | ||||
0.996539 | − | 0.0831282i | \(-0.0264911\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −16.9301 | −1.49061 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.5468 | −1.00885 | −0.504423 | − | 0.863457i | \(-0.668295\pi\) | ||||
−0.504423 | + | 0.863457i | \(0.668295\pi\) | |||||||
\(132\) | − 9.83658i | − 0.856164i | ||||||||
\(133\) | 2.69168i | 0.233398i | ||||||||
\(134\) | −2.85510 | −0.246643 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.91829 | 0.421740 | ||||||||
\(137\) | 4.23845i | 0.362115i | 0.983472 | + | 0.181058i | \(0.0579521\pi\) | ||||
−0.983472 | + | 0.181058i | \(0.942048\pi\) | |||||||
\(138\) | 6.40187i | 0.544964i | ||||||||
\(139\) | −9.21994 | −0.782025 | −0.391012 | − | 0.920385i | \(-0.627875\pi\) | ||||
−0.391012 | + | 0.920385i | \(0.627875\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.48358 | 0.124940 | ||||||||
\(142\) | 14.4769i | 1.21487i | ||||||||
\(143\) | 16.1871i | 1.35363i | ||||||||
\(144\) | −0.144903 | −0.0120752 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.15674 | 0.426775 | ||||||||
\(147\) | − 0.434709i | − 0.0358542i | ||||||||
\(148\) | − 4.54677i | − 0.373743i | ||||||||
\(149\) | 7.25697 | 0.594514 | 0.297257 | − | 0.954797i | \(-0.403928\pi\) | ||||
0.297257 | + | 0.954797i | \(0.403928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | − 0.712675i | − 0.0576163i | ||||||||
\(154\) | 14.9301 | 1.20310 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.17526 | 0.414352 | ||||||||
\(157\) | − 9.54677i | − 0.761916i | −0.924592 | − | 0.380958i | \(-0.875594\pi\) | ||||
0.924592 | − | 0.380958i | \(-0.124406\pi\) | |||||||
\(158\) | 3.09355i | 0.246110i | ||||||||
\(159\) | 17.3530 | 1.37618 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.71687 | −0.765797 | ||||||||
\(162\) | − 9.41371i | − 0.739611i | ||||||||
\(163\) | − 15.7102i | − 1.23052i | −0.788325 | − | 0.615259i | \(-0.789052\pi\) | ||||
0.788325 | − | 0.615259i | \(-0.210948\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.71019 | 0.132737 | ||||||||
\(167\) | 6.45323i | 0.499366i | 0.968328 | + | 0.249683i | \(0.0803263\pi\) | ||||
−0.968328 | + | 0.249683i | \(0.919674\pi\) | |||||||
\(168\) | − 4.77339i | − 0.368275i | ||||||||
\(169\) | 4.48358 | 0.344891 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.144903 | 0.0110810 | ||||||||
\(172\) | − 9.54677i | − 0.727935i | ||||||||
\(173\) | 0.873614i | 0.0664196i | 0.999448 | + | 0.0332098i | \(0.0105730\pi\) | ||||
−0.999448 | + | 0.0332098i | \(0.989427\pi\) | |||||||
\(174\) | 1.91829 | 0.145425 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.54677 | 0.418104 | ||||||||
\(177\) | − 23.0422i | − 1.73196i | ||||||||
\(178\) | 5.09355i | 0.381778i | ||||||||
\(179\) | 12.3834 | 0.925575 | 0.462788 | − | 0.886469i | \(-0.346849\pi\) | ||||
0.462788 | + | 0.886469i | \(0.346849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6403 | −1.31119 | −0.655597 | − | 0.755111i | \(-0.727583\pi\) | ||||
−0.655597 | + | 0.755111i | \(0.727583\pi\) | |||||||
\(182\) | 7.85510i | 0.582259i | ||||||||
\(183\) | − 13.0935i | − 0.967903i | ||||||||
\(184\) | −3.60997 | −0.266130 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.3834 | −0.981315 | ||||||||
\(187\) | 27.2806i | 1.99496i | ||||||||
\(188\) | 0.836581i | 0.0610139i | ||||||||
\(189\) | 13.6285 | 0.991326 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1567 | −1.09670 | −0.548352 | − | 0.836248i | \(-0.684744\pi\) | ||||
−0.548352 | + | 0.836248i | \(0.684744\pi\) | |||||||
\(192\) | − 1.77339i | − 0.127983i | ||||||||
\(193\) | − 23.3834i | − 1.68317i | −0.540124 | − | 0.841585i | \(-0.681623\pi\) | ||||
0.540124 | − | 0.841585i | \(-0.318377\pi\) | |||||||
\(194\) | 17.2570 | 1.23898 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.245129 | 0.0175092 | ||||||||
\(197\) | − 23.0935i | − 1.64535i | −0.568514 | − | 0.822674i | \(-0.692481\pi\) | ||||
0.568514 | − | 0.822674i | \(-0.307519\pi\) | |||||||
\(198\) | − 0.803744i | − 0.0571196i | ||||||||
\(199\) | 25.7852 | 1.82787 | 0.913933 | − | 0.405865i | \(-0.133030\pi\) | ||||
0.913933 | + | 0.405865i | \(0.133030\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.06319 | −0.357130 | ||||||||
\(202\) | − 9.38336i | − 0.660211i | ||||||||
\(203\) | 2.91161i | 0.204355i | ||||||||
\(204\) | 8.72203 | 0.610665 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.9301 | −0.900885 | ||||||||
\(207\) | 0.523095i | 0.0363576i | ||||||||
\(208\) | 2.91829i | 0.202347i | ||||||||
\(209\) | −5.54677 | −0.383678 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.2266 | 0.979400 | 0.489700 | − | 0.871891i | \(-0.337106\pi\) | ||||
0.489700 | + | 0.871891i | \(0.337106\pi\) | |||||||
\(212\) | 9.78523i | 0.672052i | ||||||||
\(213\) | 25.6732i | 1.75910i | ||||||||
\(214\) | −18.9420 | −1.29485 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.06319 | 0.344507 | ||||||||
\(217\) | − 20.3135i | − 1.37897i | ||||||||
\(218\) | 2.69168i | 0.182303i | ||||||||
\(219\) | 9.14490 | 0.617955 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.3530 | −0.965487 | ||||||||
\(222\) | − 8.06319i | − 0.541166i | ||||||||
\(223\) | 4.45323i | 0.298210i | 0.988821 | + | 0.149105i | \(0.0476392\pi\) | ||||
−0.988821 | + | 0.149105i | \(0.952361\pi\) | |||||||
\(224\) | 2.69168 | 0.179845 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 5.94865i | 0.394826i | 0.980320 | + | 0.197413i | \(0.0632539\pi\) | ||||
−0.980320 | + | 0.197413i | \(0.936746\pi\) | |||||||
\(228\) | 1.77339i | 0.117445i | ||||||||
\(229\) | −1.09355 | −0.0722638 | −0.0361319 | − | 0.999347i | \(-0.511504\pi\) | ||||
−0.0361319 | + | 0.999347i | \(0.511504\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26.4769 | 1.74205 | ||||||||
\(232\) | 1.08171i | 0.0710177i | ||||||||
\(233\) | − 14.0935i | − 0.923299i | −0.887062 | − | 0.461650i | \(-0.847258\pi\) | ||||
0.887062 | − | 0.461650i | \(-0.152742\pi\) | |||||||
\(234\) | 0.422869 | 0.0276438 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.9933 | 0.845793 | ||||||||
\(237\) | 5.48606i | 0.356358i | ||||||||
\(238\) | 13.2385i | 0.858121i | ||||||||
\(239\) | −15.6100 | −1.00972 | −0.504862 | − | 0.863200i | \(-0.668457\pi\) | ||||
−0.504862 | + | 0.863200i | \(0.668457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.21994 | −0.336246 | −0.168123 | − | 0.985766i | \(-0.553771\pi\) | ||||
−0.168123 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(242\) | 19.7667i | 1.27065i | ||||||||
\(243\) | − 1.50458i | − 0.0965188i | ||||||||
\(244\) | 7.38336 | 0.472671 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.91829i | − 0.185686i | ||||||||
\(248\) | − 7.54677i | − 0.479221i | ||||||||
\(249\) | 3.03284 | 0.192198 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.6403 | −1.80776 | −0.903881 | − | 0.427785i | \(-0.859294\pi\) | ||||
−0.903881 | + | 0.427785i | \(0.859294\pi\) | |||||||
\(252\) | − 0.390032i | − 0.0245697i | ||||||||
\(253\) | − 20.0237i | − 1.25888i | ||||||||
\(254\) | 1.87361 | 0.117561 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.45323i | 0.402541i | 0.979536 | + | 0.201271i | \(0.0645070\pi\) | ||||
−0.979536 | + | 0.201271i | \(0.935493\pi\) | |||||||
\(258\) | − 16.9301i | − 1.05402i | ||||||||
\(259\) | 12.2385 | 0.760460 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.156743 | 0.00970214 | ||||||||
\(262\) | − 11.5468i | − 0.713362i | ||||||||
\(263\) | − 22.1871i | − 1.36812i | −0.729428 | − | 0.684058i | \(-0.760214\pi\) | ||||
0.729428 | − | 0.684058i | \(-0.239786\pi\) | |||||||
\(264\) | 9.83658 | 0.605400 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.69168 | −0.165037 | ||||||||
\(267\) | 9.03284i | 0.552801i | ||||||||
\(268\) | − 2.85510i | − 0.174403i | ||||||||
\(269\) | 20.4070 | 1.24424 | 0.622119 | − | 0.782922i | \(-0.286272\pi\) | ||||
0.622119 | + | 0.782922i | \(0.286272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.9368 | 0.968092 | 0.484046 | − | 0.875043i | \(-0.339167\pi\) | ||||
0.484046 | + | 0.875043i | \(0.339167\pi\) | |||||||
\(272\) | 4.91829i | 0.298215i | ||||||||
\(273\) | 13.9301i | 0.843090i | ||||||||
\(274\) | −4.23845 | −0.256054 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.40187 | −0.385347 | ||||||||
\(277\) | 4.02368i | 0.241759i | 0.992667 | + | 0.120880i | \(0.0385715\pi\) | ||||
−0.992667 | + | 0.120880i | \(0.961428\pi\) | |||||||
\(278\) | − 9.21994i | − 0.552975i | ||||||||
\(279\) | −1.09355 | −0.0654691 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.67316 | 0.0998124 | 0.0499062 | − | 0.998754i | \(-0.484108\pi\) | ||||
0.0499062 | + | 0.998754i | \(0.484108\pi\) | |||||||
\(282\) | 1.48358i | 0.0883460i | ||||||||
\(283\) | − 16.8931i | − 1.00419i | −0.864812 | − | 0.502095i | \(-0.832563\pi\) | ||||
0.864812 | − | 0.502095i | \(-0.167437\pi\) | |||||||
\(284\) | −14.4769 | −0.859046 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.1871 | −0.957163 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − 0.144903i | − 0.00853849i | ||||||||
\(289\) | −7.18958 | −0.422916 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.6033 | 1.79400 | ||||||||
\(292\) | 5.15674i | 0.301776i | ||||||||
\(293\) | 1.08171i | 0.0631942i | 0.999501 | + | 0.0315971i | \(0.0100593\pi\) | ||||
−0.999501 | + | 0.0315971i | \(0.989941\pi\) | |||||||
\(294\) | 0.434709 | 0.0253527 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.54677 | 0.264276 | ||||||||
\(297\) | 28.0844i | 1.62962i | ||||||||
\(298\) | 7.25697i | 0.420385i | ||||||||
\(299\) | 10.5349 | 0.609251 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.6968 | 1.48114 | ||||||||
\(302\) | 20.0000i | 1.15087i | ||||||||
\(303\) | − 16.6403i | − 0.955962i | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.712675 | 0.0407409 | ||||||||
\(307\) | 2.38336i | 0.136025i | 0.997684 | + | 0.0680126i | \(0.0216658\pi\) | ||||
−0.997684 | + | 0.0680126i | \(0.978334\pi\) | |||||||
\(308\) | 14.9301i | 0.850723i | ||||||||
\(309\) | −22.9301 | −1.30445 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.4584 | −1.67043 | −0.835216 | − | 0.549922i | \(-0.814657\pi\) | ||||
−0.835216 | + | 0.549922i | \(0.814657\pi\) | |||||||
\(312\) | 5.17526i | 0.292991i | ||||||||
\(313\) | − 32.0355i | − 1.81075i | −0.424608 | − | 0.905377i | \(-0.639588\pi\) | ||||
0.424608 | − | 0.905377i | \(-0.360412\pi\) | |||||||
\(314\) | 9.54677 | 0.538756 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.09355 | −0.174026 | ||||||||
\(317\) | − 26.6665i | − 1.49774i | −0.662717 | − | 0.748870i | \(-0.730597\pi\) | ||||
0.662717 | − | 0.748870i | \(-0.269403\pi\) | |||||||
\(318\) | 17.3530i | 0.973108i | ||||||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.5915 | −1.87489 | ||||||||
\(322\) | − 9.71687i | − 0.541500i | ||||||||
\(323\) | − 4.91829i | − 0.273661i | ||||||||
\(324\) | 9.41371 | 0.522984 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.7102 | 0.870107 | ||||||||
\(327\) | 4.77339i | 0.263969i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.25181 | −0.124146 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8721 | −1.09227 | −0.546135 | − | 0.837697i | \(-0.683901\pi\) | ||||
−0.546135 | + | 0.837697i | \(0.683901\pi\) | |||||||
\(332\) | 1.71019i | 0.0938591i | ||||||||
\(333\) | − 0.658841i | − 0.0361043i | ||||||||
\(334\) | −6.45323 | −0.353105 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.77339 | 0.260410 | ||||||||
\(337\) | 27.5705i | 1.50186i | 0.660383 | + | 0.750929i | \(0.270394\pi\) | ||||
−0.660383 | + | 0.750929i | \(0.729606\pi\) | |||||||
\(338\) | 4.48358i | 0.243875i | ||||||||
\(339\) | −10.6403 | −0.577903 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.8603 | 2.26686 | ||||||||
\(342\) | 0.144903i | 0.00783545i | ||||||||
\(343\) | − 18.1819i | − 0.981732i | ||||||||
\(344\) | 9.54677 | 0.514728 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.873614 | −0.0469658 | ||||||||
\(347\) | − 27.2806i | − 1.46450i | −0.681035 | − | 0.732251i | \(-0.738470\pi\) | ||||
0.681035 | − | 0.732251i | \(-0.261530\pi\) | |||||||
\(348\) | 1.91829i | 0.102831i | ||||||||
\(349\) | −30.9538 | −1.65692 | −0.828460 | − | 0.560049i | \(-0.810782\pi\) | ||||
−0.828460 | + | 0.560049i | \(0.810782\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.7759 | −0.788677 | ||||||||
\(352\) | 5.54677i | 0.295644i | ||||||||
\(353\) | − 11.1819i | − 0.595154i | −0.954698 | − | 0.297577i | \(-0.903821\pi\) | ||||
0.954698 | − | 0.297577i | \(-0.0961786\pi\) | |||||||
\(354\) | 23.0422 | 1.22468 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.09355 | −0.269958 | ||||||||
\(357\) | 23.4769i | 1.24253i | ||||||||
\(358\) | 12.3834i | 0.654481i | ||||||||
\(359\) | −20.3387 | −1.07343 | −0.536717 | − | 0.843762i | \(-0.680336\pi\) | ||||
−0.536717 | + | 0.843762i | \(0.680336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 17.6403i | − 0.927155i | ||||||||
\(363\) | 35.0540i | 1.83986i | ||||||||
\(364\) | −7.85510 | −0.411719 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.0935 | 0.684411 | ||||||||
\(367\) | − 32.9538i | − 1.72017i | −0.510147 | − | 0.860087i | \(-0.670409\pi\) | ||||
0.510147 | − | 0.860087i | \(-0.329591\pi\) | |||||||
\(368\) | − 3.60997i | − 0.188183i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.3387 | −1.36744 | ||||||||
\(372\) | − 13.3834i | − 0.693895i | ||||||||
\(373\) | 10.0869i | 0.522278i | 0.965301 | + | 0.261139i | \(0.0840982\pi\) | ||||
−0.965301 | + | 0.261139i | \(0.915902\pi\) | |||||||
\(374\) | −27.2806 | −1.41065 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.836581 | −0.0431434 | ||||||||
\(377\) | − 3.15674i | − 0.162581i | ||||||||
\(378\) | 13.6285i | 0.700974i | ||||||||
\(379\) | 18.4256 | 0.946457 | 0.473229 | − | 0.880940i | \(-0.343088\pi\) | ||||
0.473229 | + | 0.880940i | \(0.343088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.32264 | 0.170224 | ||||||||
\(382\) | − 15.1567i | − 0.775486i | ||||||||
\(383\) | − 28.1871i | − 1.44029i | −0.693822 | − | 0.720147i | \(-0.744074\pi\) | ||||
0.693822 | − | 0.720147i | \(-0.255926\pi\) | |||||||
\(384\) | 1.77339 | 0.0904978 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.3834 | 1.19018 | ||||||||
\(387\) | − 1.38336i | − 0.0703199i | ||||||||
\(388\) | 17.2570i | 0.876090i | ||||||||
\(389\) | −20.0237 | −1.01524 | −0.507620 | − | 0.861581i | \(-0.669475\pi\) | ||||
−0.507620 | + | 0.861581i | \(0.669475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.7549 | 0.897902 | ||||||||
\(392\) | 0.245129i | 0.0123809i | ||||||||
\(393\) | − 20.4769i | − 1.03292i | ||||||||
\(394\) | 23.0935 | 1.16344 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.803744 | 0.0403896 | ||||||||
\(397\) | − 8.32684i | − 0.417912i | −0.977925 | − | 0.208956i | \(-0.932993\pi\) | ||||
0.977925 | − | 0.208956i | \(-0.0670066\pi\) | |||||||
\(398\) | 25.7852i | 1.29250i | ||||||||
\(399\) | −4.77339 | −0.238968 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.1501 | −1.10612 | −0.553061 | − | 0.833141i | \(-0.686540\pi\) | ||||
−0.553061 | + | 0.833141i | \(0.686540\pi\) | |||||||
\(402\) | − 5.06319i | − 0.252529i | ||||||||
\(403\) | 22.0237i | 1.09708i | ||||||||
\(404\) | 9.38336 | 0.466839 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.91161 | −0.144501 | ||||||||
\(407\) | 25.2199i | 1.25011i | ||||||||
\(408\) | 8.72203i | 0.431805i | ||||||||
\(409\) | −34.0237 | −1.68236 | −0.841181 | − | 0.540753i | \(-0.818139\pi\) | ||||
−0.841181 | + | 0.540753i | \(0.818139\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.51642 | −0.370758 | ||||||||
\(412\) | − 12.9301i | − 0.637022i | ||||||||
\(413\) | 34.9738i | 1.72095i | ||||||||
\(414\) | −0.523095 | −0.0257087 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.91829 | −0.143081 | ||||||||
\(417\) | − 16.3505i | − 0.800688i | ||||||||
\(418\) | − 5.54677i | − 0.271302i | ||||||||
\(419\) | −37.5334 | −1.83363 | −0.916814 | − | 0.399315i | \(-0.869248\pi\) | ||||
−0.916814 | + | 0.399315i | \(0.869248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.8341 | 1.64897 | 0.824487 | − | 0.565882i | \(-0.191464\pi\) | ||||
0.824487 | + | 0.565882i | \(0.191464\pi\) | |||||||
\(422\) | 14.2266i | 0.692541i | ||||||||
\(423\) | 0.121223i | 0.00589406i | ||||||||
\(424\) | −9.78523 | −0.475213 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −25.6732 | −1.24387 | ||||||||
\(427\) | 19.8736i | 0.961752i | ||||||||
\(428\) | − 18.9420i | − 0.915595i | ||||||||
\(429\) | −28.7060 | −1.38594 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.8037 | 1.19475 | 0.597377 | − | 0.801960i | \(-0.296210\pi\) | ||||
0.597377 | + | 0.801960i | \(0.296210\pi\) | |||||||
\(432\) | 5.06319i | 0.243603i | ||||||||
\(433\) | − 1.68651i | − 0.0810487i | −0.999179 | − | 0.0405244i | \(-0.987097\pi\) | ||||
0.999179 | − | 0.0405244i | \(-0.0129028\pi\) | |||||||
\(434\) | 20.3135 | 0.975079 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.69168 | −0.128908 | ||||||||
\(437\) | 3.60997i | 0.172688i | ||||||||
\(438\) | 9.14490i | 0.436960i | ||||||||
\(439\) | −0.326839 | −0.0155992 | −0.00779958 | − | 0.999970i | \(-0.502483\pi\) | ||||
−0.00779958 | + | 0.999970i | \(0.502483\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0355199 | 0.00169142 | ||||||||
\(442\) | − 14.3530i | − 0.682703i | ||||||||
\(443\) | − 0.490258i | − 0.0232929i | −0.999932 | − | 0.0116464i | \(-0.996293\pi\) | ||||
0.999932 | − | 0.0116464i | \(-0.00370726\pi\) | |||||||
\(444\) | 8.06319 | 0.382662 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.45323 | −0.210866 | ||||||||
\(447\) | 12.8694i | 0.608703i | ||||||||
\(448\) | 2.69168i | 0.127170i | ||||||||
\(449\) | −23.5468 | −1.11124 | −0.555621 | − | 0.831436i | \(-0.687519\pi\) | ||||
−0.555621 | + | 0.831436i | \(0.687519\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 6.00000i | − 0.282216i | ||||||||
\(453\) | 35.4677i | 1.66642i | ||||||||
\(454\) | −5.94865 | −0.279184 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.77339 | −0.0830465 | ||||||||
\(457\) | − 8.01184i | − 0.374778i | −0.982286 | − | 0.187389i | \(-0.939997\pi\) | ||||
0.982286 | − | 0.187389i | \(-0.0600025\pi\) | |||||||
\(458\) | − 1.09355i | − 0.0510982i | ||||||||
\(459\) | −24.9023 | −1.16234 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.83658 | 0.178687 | 0.0893437 | − | 0.996001i | \(-0.471523\pi\) | ||||
0.0893437 | + | 0.996001i | \(0.471523\pi\) | |||||||
\(462\) | 26.4769i | 1.23182i | ||||||||
\(463\) | 6.58381i | 0.305975i | 0.988228 | + | 0.152988i | \(0.0488895\pi\) | ||||
−0.988228 | + | 0.152988i | \(0.951110\pi\) | |||||||
\(464\) | −1.08171 | −0.0502171 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0935 | 0.652871 | ||||||||
\(467\) | 22.6033i | 1.04596i | 0.852346 | + | 0.522978i | \(0.175179\pi\) | ||||
−0.852346 | + | 0.522978i | \(0.824821\pi\) | |||||||
\(468\) | 0.422869i | 0.0195471i | ||||||||
\(469\) | 7.68500 | 0.354860 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.9301 | 0.780099 | ||||||||
\(472\) | 12.9933i | 0.598066i | ||||||||
\(473\) | 52.9538i | 2.43482i | ||||||||
\(474\) | −5.48606 | −0.251983 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.2385 | −0.606783 | ||||||||
\(477\) | 1.41791i | 0.0649215i | ||||||||
\(478\) | − 15.6100i | − 0.713983i | ||||||||
\(479\) | 35.7904 | 1.63530 | 0.817652 | − | 0.575712i | \(-0.195275\pi\) | ||||
0.817652 | + | 0.575712i | \(0.195275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.2688 | −0.605006 | ||||||||
\(482\) | − 5.21994i | − 0.237762i | ||||||||
\(483\) | − 17.2318i | − 0.784073i | ||||||||
\(484\) | −19.7667 | −0.898487 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.50458 | 0.0682491 | ||||||||
\(487\) | − 21.4070i | − 0.970045i | −0.874502 | − | 0.485023i | \(-0.838811\pi\) | ||||
0.874502 | − | 0.485023i | \(-0.161189\pi\) | |||||||
\(488\) | 7.38336i | 0.334229i | ||||||||
\(489\) | 27.8603 | 1.25988 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.32684 | −0.195267 | −0.0976337 | − | 0.995222i | \(-0.531127\pi\) | ||||
−0.0976337 | + | 0.995222i | \(0.531127\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.32016i | − 0.239608i | ||||||||
\(494\) | 2.91829 | 0.131300 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.54677 | 0.338860 | ||||||||
\(497\) | − 38.9672i | − 1.74792i | ||||||||
\(498\) | 3.03284i | 0.135905i | ||||||||
\(499\) | 37.6968 | 1.68754 | 0.843771 | − | 0.536703i | \(-0.180330\pi\) | ||||
0.843771 | + | 0.536703i | \(0.180330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.4441 | −0.511283 | ||||||||
\(502\) | − 28.6403i | − 1.27828i | ||||||||
\(503\) | 16.9183i | 0.754349i | 0.926142 | + | 0.377175i | \(0.123104\pi\) | ||||
−0.926142 | + | 0.377175i | \(0.876896\pi\) | |||||||
\(504\) | 0.390032 | 0.0173734 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.0237 | 0.890161 | ||||||||
\(507\) | 7.95113i | 0.353122i | ||||||||
\(508\) | 1.87361i | 0.0831282i | ||||||||
\(509\) | 6.79955 | 0.301385 | 0.150692 | − | 0.988581i | \(-0.451850\pi\) | ||||
0.150692 | + | 0.988581i | \(0.451850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8803 | −0.614028 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 5.06319i | − 0.223545i | ||||||||
\(514\) | −6.45323 | −0.284640 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16.9301 | 0.745307 | ||||||||
\(517\) | − 4.64032i | − 0.204081i | ||||||||
\(518\) | 12.2385i | 0.537727i | ||||||||
\(519\) | −1.54926 | −0.0680048 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.35968 | −0.0595685 | −0.0297842 | − | 0.999556i | \(-0.509482\pi\) | ||||
−0.0297842 | + | 0.999556i | \(0.509482\pi\) | |||||||
\(522\) | 0.156743i | 0.00686045i | ||||||||
\(523\) | 21.9486i | 0.959747i | 0.877338 | + | 0.479874i | \(0.159318\pi\) | ||||
−0.877338 | + | 0.479874i | \(0.840682\pi\) | |||||||
\(524\) | 11.5468 | 0.504423 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.1871 | 0.967404 | ||||||||
\(527\) | 37.1172i | 1.61685i | ||||||||
\(528\) | 9.83658i | 0.428082i | ||||||||
\(529\) | 9.96813 | 0.433397 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.88277 | 0.0817053 | ||||||||
\(532\) | − 2.69168i | − 0.116699i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.03284 | −0.390889 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.85510 | 0.123321 | ||||||||
\(537\) | 21.9605i | 0.947665i | ||||||||
\(538\) | 20.4070i | 0.879810i | ||||||||
\(539\) | −1.35968 | −0.0585654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.8973 | −1.71532 | −0.857659 | − | 0.514218i | \(-0.828082\pi\) | ||||
−0.857659 | + | 0.514218i | \(0.828082\pi\) | |||||||
\(542\) | 15.9368i | 0.684544i | ||||||||
\(543\) | − 31.2831i | − 1.34249i | ||||||||
\(544\) | −4.91829 | −0.210870 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.9301 | −0.596155 | ||||||||
\(547\) | − 7.34632i | − 0.314106i | −0.987590 | − | 0.157053i | \(-0.949801\pi\) | ||||
0.987590 | − | 0.157053i | \(-0.0501994\pi\) | |||||||
\(548\) | − 4.23845i | − 0.181058i | ||||||||
\(549\) | 1.06987 | 0.0456609 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.08171 | 0.0460824 | ||||||||
\(552\) | − 6.40187i | − 0.272482i | ||||||||
\(553\) | − 8.32684i | − 0.354093i | ||||||||
\(554\) | −4.02368 | −0.170950 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.21994 | 0.391012 | ||||||||
\(557\) | − 26.9672i | − 1.14264i | −0.820729 | − | 0.571318i | \(-0.806432\pi\) | ||||
0.820729 | − | 0.571318i | \(-0.193568\pi\) | |||||||
\(558\) | − 1.09355i | − 0.0462936i | ||||||||
\(559\) | −27.8603 | −1.17836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.3792 | −2.04257 | ||||||||
\(562\) | 1.67316i | 0.0705780i | ||||||||
\(563\) | 44.8973i | 1.89220i | 0.323881 | + | 0.946098i | \(0.395012\pi\) | ||||
−0.323881 | + | 0.946098i | \(0.604988\pi\) | |||||||
\(564\) | −1.48358 | −0.0624701 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.8931 | 0.710070 | ||||||||
\(567\) | 25.3387i | 1.06412i | ||||||||
\(568\) | − 14.4769i | − 0.607437i | ||||||||
\(569\) | −31.1172 | −1.30450 | −0.652251 | − | 0.758003i | \(-0.726175\pi\) | ||||
−0.652251 | + | 0.758003i | \(0.726175\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.2570 | 1.39176 | 0.695880 | − | 0.718158i | \(-0.255014\pi\) | ||||
0.695880 | + | 0.718158i | \(0.255014\pi\) | |||||||
\(572\) | − 16.1871i | − 0.676817i | ||||||||
\(573\) | − 26.8788i | − 1.12288i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.144903 | 0.00603762 | ||||||||
\(577\) | 23.4702i | 0.977078i | 0.872542 | + | 0.488539i | \(0.162470\pi\) | ||||
−0.872542 | + | 0.488539i | \(0.837530\pi\) | |||||||
\(578\) | − 7.18958i | − 0.299047i | ||||||||
\(579\) | 41.4677 | 1.72334 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.60329 | −0.190977 | ||||||||
\(582\) | 30.6033i | 1.26855i | ||||||||
\(583\) | − 54.2765i | − 2.24790i | ||||||||
\(584\) | −5.15674 | −0.213388 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.08171 | −0.0446850 | ||||||||
\(587\) | − 10.1501i | − 0.418938i | −0.977815 | − | 0.209469i | \(-0.932826\pi\) | ||||
0.977815 | − | 0.209469i | \(-0.0671735\pi\) | |||||||
\(588\) | 0.434709i | 0.0179271i | ||||||||
\(589\) | −7.54677 | −0.310959 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.9538 | 1.68461 | ||||||||
\(592\) | 4.54677i | 0.186871i | ||||||||
\(593\) | 16.6732i | 0.684685i | 0.939575 | + | 0.342342i | \(0.111220\pi\) | ||||
−0.939575 | + | 0.342342i | \(0.888780\pi\) | |||||||
\(594\) | −28.0844 | −1.15232 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.25697 | −0.297257 | ||||||||
\(597\) | 45.7272i | 1.87149i | ||||||||
\(598\) | 10.5349i | 0.430806i | ||||||||
\(599\) | −18.2765 | −0.746756 | −0.373378 | − | 0.927679i | \(-0.621800\pi\) | ||||
−0.373378 | + | 0.927679i | \(0.621800\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.96297 | 0.324816 | 0.162408 | − | 0.986724i | \(-0.448074\pi\) | ||||
0.162408 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(602\) | 25.6968i | 1.04733i | ||||||||
\(603\) | − 0.413712i | − 0.0168477i | ||||||||
\(604\) | −20.0000 | −0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.6403 | 0.675967 | ||||||||
\(607\) | − 6.93013i | − 0.281285i | −0.990060 | − | 0.140643i | \(-0.955083\pi\) | ||||
0.990060 | − | 0.140643i | \(-0.0449169\pi\) | |||||||
\(608\) | − 1.00000i | − 0.0405554i | ||||||||
\(609\) | −5.16342 | −0.209232 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.44139 | 0.0987679 | ||||||||
\(612\) | 0.712675i | 0.0288082i | ||||||||
\(613\) | 34.2765i | 1.38441i | 0.721700 | + | 0.692206i | \(0.243361\pi\) | ||||
−0.721700 | + | 0.692206i | \(0.756639\pi\) | |||||||
\(614\) | −2.38336 | −0.0961844 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.9301 | −0.601552 | ||||||||
\(617\) | 35.5139i | 1.42974i | 0.699259 | + | 0.714869i | \(0.253514\pi\) | ||||
−0.699259 | + | 0.714869i | \(0.746486\pi\) | |||||||
\(618\) | − 22.9301i | − 0.922385i | ||||||||
\(619\) | 29.5334 | 1.18705 | 0.593524 | − | 0.804816i | \(-0.297736\pi\) | ||||
0.593524 | + | 0.804816i | \(0.297736\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.2780 | 0.733470 | ||||||||
\(622\) | − 29.4584i | − 1.18117i | ||||||||
\(623\) | − 13.7102i | − 0.549287i | ||||||||
\(624\) | −5.17526 | −0.207176 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.0355 | 1.28040 | ||||||||
\(627\) | − 9.83658i | − 0.392835i | ||||||||
\(628\) | 9.54677i | 0.380958i | ||||||||
\(629\) | −22.3624 | −0.891646 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.1634 | −0.603646 | −0.301823 | − | 0.953364i | \(-0.597595\pi\) | ||||
−0.301823 | + | 0.953364i | \(0.597595\pi\) | |||||||
\(632\) | − 3.09355i | − 0.123055i | ||||||||
\(633\) | 25.2293i | 1.00277i | ||||||||
\(634\) | 26.6665 | 1.05906 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −17.3530 | −0.688091 | ||||||||
\(637\) | − 0.715358i | − 0.0283435i | ||||||||
\(638\) | − 6.00000i | − 0.237542i | ||||||||
\(639\) | −2.09775 | −0.0829855 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.0802 | −0.990608 | −0.495304 | − | 0.868720i | \(-0.664943\pi\) | ||||
−0.495304 | + | 0.868720i | \(0.664943\pi\) | |||||||
\(642\) | − 33.5915i | − 1.32575i | ||||||||
\(643\) | − 19.1306i | − 0.754437i | −0.926124 | − | 0.377218i | \(-0.876881\pi\) | ||||
0.926124 | − | 0.377218i | \(-0.123119\pi\) | |||||||
\(644\) | 9.71687 | 0.382898 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.91829 | 0.193508 | ||||||||
\(647\) | 12.4019i | 0.487568i | 0.969830 | + | 0.243784i | \(0.0783888\pi\) | ||||
−0.969830 | + | 0.243784i | \(0.921611\pi\) | |||||||
\(648\) | 9.41371i | 0.369806i | ||||||||
\(649\) | −72.0710 | −2.82904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.0237 | 1.41188 | ||||||||
\(652\) | 15.7102i | 0.615259i | ||||||||
\(653\) | 10.7801i | 0.421856i | 0.977502 | + | 0.210928i | \(0.0676486\pi\) | ||||
−0.977502 | + | 0.210928i | \(0.932351\pi\) | |||||||
\(654\) | −4.77339 | −0.186654 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.747227i | 0.0291521i | ||||||||
\(658\) | − 2.25181i | − 0.0877845i | ||||||||
\(659\) | −8.56529 | −0.333656 | −0.166828 | − | 0.985986i | \(-0.553353\pi\) | ||||
−0.166828 | + | 0.985986i | \(0.553353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.2883 | −1.02250 | −0.511248 | − | 0.859433i | \(-0.670817\pi\) | ||||
−0.511248 | + | 0.859433i | \(0.670817\pi\) | |||||||
\(662\) | − 19.8721i | − 0.772351i | ||||||||
\(663\) | − 25.4534i | − 0.988529i | ||||||||
\(664\) | −1.71019 | −0.0663684 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.658841 | 0.0255296 | ||||||||
\(667\) | 3.90494i | 0.151200i | ||||||||
\(668\) | − 6.45323i | − 0.249683i | ||||||||
\(669\) | −7.89729 | −0.305327 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.9538 | −1.58100 | ||||||||
\(672\) | 4.77339i | 0.184137i | ||||||||
\(673\) | 12.9301i | 0.498420i | 0.968449 | + | 0.249210i | \(0.0801709\pi\) | ||||
−0.968449 | + | 0.249210i | \(0.919829\pi\) | |||||||
\(674\) | −27.5705 | −1.06197 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.48358 | −0.172445 | ||||||||
\(677\) | − 15.9250i | − 0.612046i | −0.952024 | − | 0.306023i | \(-0.901002\pi\) | ||||
0.952024 | − | 0.306023i | \(-0.0989985\pi\) | |||||||
\(678\) | − 10.6403i | − 0.408639i | ||||||||
\(679\) | −46.4502 | −1.78260 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5493 | −0.404248 | ||||||||
\(682\) | 41.8603i | 1.60291i | ||||||||
\(683\) | − 13.2898i | − 0.508520i | −0.967136 | − | 0.254260i | \(-0.918168\pi\) | ||||
0.967136 | − | 0.254260i | \(-0.0818319\pi\) | |||||||
\(684\) | −0.144903 | −0.00554050 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.1819 | 0.694190 | ||||||||
\(687\) | − 1.93929i | − 0.0739884i | ||||||||
\(688\) | 9.54677i | 0.363967i | ||||||||
\(689\) | 28.5561 | 1.08790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.2570 | 1.03690 | 0.518452 | − | 0.855107i | \(-0.326508\pi\) | ||||
0.518452 | + | 0.855107i | \(0.326508\pi\) | |||||||
\(692\) | − 0.873614i | − 0.0332098i | ||||||||
\(693\) | 2.16342i | 0.0821815i | ||||||||
\(694\) | 27.2806 | 1.03556 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.91829 | −0.0727126 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − 30.9538i | − 1.17162i | ||||||||
\(699\) | 24.9933 | 0.945334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.4441 | −1.56532 | −0.782660 | − | 0.622449i | \(-0.786138\pi\) | ||||
−0.782660 | + | 0.622449i | \(0.786138\pi\) | |||||||
\(702\) | − 14.7759i | − 0.557679i | ||||||||
\(703\) | − 4.54677i | − 0.171485i | ||||||||
\(704\) | −5.54677 | −0.209052 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.1819 | 0.420838 | ||||||||
\(707\) | 25.2570i | 0.949886i | ||||||||
\(708\) | 23.0422i | 0.865979i | ||||||||
\(709\) | 36.7904 | 1.38169 | 0.690846 | − | 0.723002i | \(-0.257238\pi\) | ||||
0.690846 | + | 0.723002i | \(0.257238\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.448264 | −0.0168112 | ||||||||
\(712\) | − 5.09355i | − 0.190889i | ||||||||
\(713\) | − 27.2436i | − 1.02028i | ||||||||
\(714\) | −23.4769 | −0.878601 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.3834 | −0.462788 | ||||||||
\(717\) | − 27.6825i | − 1.03382i | ||||||||
\(718\) | − 20.3387i | − 0.759033i | ||||||||
\(719\) | 4.13726 | 0.154294 | 0.0771469 | − | 0.997020i | \(-0.475419\pi\) | ||||
0.0771469 | + | 0.997020i | \(0.475419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.8037 | 1.29616 | ||||||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | − 9.25697i | − 0.344270i | ||||||||
\(724\) | 17.6403 | 0.655597 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −35.0540 | −1.30098 | ||||||||
\(727\) | − 40.4374i | − 1.49974i | −0.661585 | − | 0.749870i | \(-0.730116\pi\) | ||||
0.661585 | − | 0.749870i | \(-0.269884\pi\) | |||||||
\(728\) | − 7.85510i | − 0.291129i | ||||||||
\(729\) | −25.5729 | −0.947146 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.9538 | −1.73665 | ||||||||
\(732\) | 13.0935i | 0.483952i | ||||||||
\(733\) | − 28.1264i | − 1.03887i | −0.854509 | − | 0.519436i | \(-0.826142\pi\) | ||||
0.854509 | − | 0.519436i | \(-0.173858\pi\) | |||||||
\(734\) | 32.9538 | 1.21635 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.60997 | 0.133065 | ||||||||
\(737\) | 15.8366i | 0.583348i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.1501 | 1.40337 | 0.701686 | − | 0.712486i | \(-0.252431\pi\) | ||||
0.701686 | + | 0.712486i | \(0.252431\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.17526 | 0.190118 | ||||||||
\(742\) | − 26.3387i | − 0.966923i | ||||||||
\(743\) | 17.8232i | 0.653871i | 0.945047 | + | 0.326935i | \(0.106016\pi\) | ||||
−0.945047 | + | 0.326935i | \(0.893984\pi\) | |||||||
\(744\) | 13.3834 | 0.490658 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.0869 | −0.369307 | ||||||||
\(747\) | 0.247812i | 0.00906697i | ||||||||
\(748\) | − 27.2806i | − 0.997479i | ||||||||
\(749\) | 50.9857 | 1.86298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.6968 | 0.864710 | 0.432355 | − | 0.901703i | \(-0.357683\pi\) | ||||
0.432355 | + | 0.901703i | \(0.357683\pi\) | |||||||
\(752\) | − 0.836581i | − 0.0305070i | ||||||||
\(753\) | − 50.7904i | − 1.85090i | ||||||||
\(754\) | 3.15674 | 0.114962 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.6285 | −0.495663 | ||||||||
\(757\) | − 6.51394i | − 0.236753i | −0.992969 | − | 0.118377i | \(-0.962231\pi\) | ||||
0.992969 | − | 0.118377i | \(-0.0377690\pi\) | |||||||
\(758\) | 18.4256i | 0.669246i | ||||||||
\(759\) | 35.5097 | 1.28892 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.7786 | 1.26072 | 0.630361 | − | 0.776302i | \(-0.282907\pi\) | ||||
0.630361 | + | 0.776302i | \(0.282907\pi\) | |||||||
\(762\) | 3.32264i | 0.120367i | ||||||||
\(763\) | − 7.24513i | − 0.262291i | ||||||||
\(764\) | 15.1567 | 0.548352 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.1871 | 1.01844 | ||||||||
\(767\) | − 37.9183i | − 1.36915i | ||||||||
\(768\) | 1.77339i | 0.0639916i | ||||||||
\(769\) | 27.6850 | 0.998347 | 0.499173 | − | 0.866502i | \(-0.333637\pi\) | ||||
0.499173 | + | 0.866502i | \(0.333637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.4441 | −0.412148 | ||||||||
\(772\) | 23.3834i | 0.841585i | ||||||||
\(773\) | 19.9738i | 0.718409i | 0.933259 | + | 0.359205i | \(0.116952\pi\) | ||||
−0.933259 | + | 0.359205i | \(0.883048\pi\) | |||||||
\(774\) | 1.38336 | 0.0497237 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.2570 | −0.619489 | ||||||||
\(777\) | 21.7035i | 0.778609i | ||||||||
\(778\) | − 20.0237i | − 0.717884i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.3001 | 2.87336 | ||||||||
\(782\) | 17.7549i | 0.634913i | ||||||||
\(783\) | − 5.47691i | − 0.195729i | ||||||||
\(784\) | −0.245129 | −0.00875461 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20.4769 | 0.730387 | ||||||||
\(787\) | 42.0118i | 1.49756i | 0.662818 | + | 0.748780i | \(0.269360\pi\) | ||||
−0.662818 | + | 0.748780i | \(0.730640\pi\) | |||||||
\(788\) | 23.0935i | 0.822674i | ||||||||
\(789\) | 39.3463 | 1.40077 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.1501 | 0.574230 | ||||||||
\(792\) | 0.803744i | 0.0285598i | ||||||||
\(793\) | − 21.5468i | − 0.765148i | ||||||||
\(794\) | 8.32684 | 0.295508 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.7852 | −0.913933 | ||||||||
\(797\) | − 45.1054i | − 1.59771i | −0.601520 | − | 0.798857i | \(-0.705438\pi\) | ||||
0.601520 | − | 0.798857i | \(-0.294562\pi\) | |||||||
\(798\) | − 4.77339i | − 0.168976i | ||||||||
\(799\) | 4.11455 | 0.145562 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.738070 | −0.0260784 | ||||||||
\(802\) | − 22.1501i | − 0.782146i | ||||||||
\(803\) | − 28.6033i | − 1.00939i | ||||||||
\(804\) | 5.06319 | 0.178565 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −22.0237 | −0.775751 | ||||||||
\(807\) | 36.1896i | 1.27393i | ||||||||
\(808\) | 9.38336i | 0.330105i | ||||||||
\(809\) | −6.85510 | −0.241012 | −0.120506 | − | 0.992713i | \(-0.538452\pi\) | ||||
−0.120506 | + | 0.992713i | \(0.538452\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.1819 | −0.533110 | −0.266555 | − | 0.963820i | \(-0.585885\pi\) | ||||
−0.266555 | + | 0.963820i | \(0.585885\pi\) | |||||||
\(812\) | − 2.91161i | − 0.102178i | ||||||||
\(813\) | 28.2621i | 0.991196i | ||||||||
\(814\) | −25.2199 | −0.883958 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.72203 | −0.305332 | ||||||||
\(817\) | − 9.54677i | − 0.333999i | ||||||||
\(818\) | − 34.0237i | − 1.18961i | ||||||||
\(819\) | −1.13823 | −0.0397729 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.5006 | 0.785276 | 0.392638 | − | 0.919693i | \(-0.371563\pi\) | ||||
0.392638 | + | 0.919693i | \(0.371563\pi\) | |||||||
\(822\) | − 7.51642i | − 0.262165i | ||||||||
\(823\) | 16.1896i | 0.564333i | 0.959365 | + | 0.282167i | \(0.0910531\pi\) | ||||
−0.959365 | + | 0.282167i | \(0.908947\pi\) | |||||||
\(824\) | 12.9301 | 0.450442 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −34.9738 | −1.21690 | ||||||||
\(827\) | − 25.0817i | − 0.872177i | −0.899904 | − | 0.436088i | \(-0.856364\pi\) | ||||
0.899904 | − | 0.436088i | \(-0.143636\pi\) | |||||||
\(828\) | − 0.523095i | − 0.0181788i | ||||||||
\(829\) | −21.3068 | −0.740016 | −0.370008 | − | 0.929029i | \(-0.620645\pi\) | ||||
−0.370008 | + | 0.929029i | \(0.620645\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.13554 | −0.247529 | ||||||||
\(832\) | − 2.91829i | − 0.101174i | ||||||||
\(833\) | − 1.20562i | − 0.0417721i | ||||||||
\(834\) | 16.3505 | 0.566172 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.54677 | 0.191839 | ||||||||
\(837\) | 38.2108i | 1.32076i | ||||||||
\(838\) | − 37.5334i | − 1.29657i | ||||||||
\(839\) | 11.4727 | 0.396082 | 0.198041 | − | 0.980194i | \(-0.436542\pi\) | ||||
0.198041 | + | 0.980194i | \(0.436542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8299 | −0.959652 | ||||||||
\(842\) | 33.8341i | 1.16600i | ||||||||
\(843\) | 2.96716i | 0.102195i | ||||||||
\(844\) | −14.2266 | −0.489700 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.121223 | −0.00416773 | ||||||||
\(847\) | − 53.2056i | − 1.82817i | ||||||||
\(848\) | − 9.78523i | − 0.336026i | ||||||||
\(849\) | 29.9580 | 1.02816 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.4137 | 0.562655 | ||||||||
\(852\) | − 25.6732i | − 0.879548i | ||||||||
\(853\) | 38.9908i | 1.33502i | 0.744600 | + | 0.667511i | \(0.232640\pi\) | ||||
−0.744600 | + | 0.667511i | \(0.767360\pi\) | |||||||
\(854\) | −19.8736 | −0.680061 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9420 | 0.647423 | ||||||||
\(857\) | − 29.8973i | − 1.02127i | −0.859797 | − | 0.510636i | \(-0.829410\pi\) | ||||
0.859797 | − | 0.510636i | \(-0.170590\pi\) | |||||||
\(858\) | − 28.7060i | − 0.980007i | ||||||||
\(859\) | 6.47691 | 0.220989 | 0.110495 | − | 0.993877i | \(-0.464757\pi\) | ||||
0.110495 | + | 0.993877i | \(0.464757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.8037i | 0.844819i | ||||||||
\(863\) | 5.09355i | 0.173386i | 0.996235 | + | 0.0866932i | \(0.0276300\pi\) | ||||
−0.996235 | + | 0.0866932i | \(0.972370\pi\) | |||||||
\(864\) | −5.06319 | −0.172253 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.68651 | 0.0573101 | ||||||||
\(867\) | − 12.7499i | − 0.433010i | ||||||||
\(868\) | 20.3135i | 0.689485i | ||||||||
\(869\) | 17.1592 | 0.582087 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.33200 | −0.282319 | ||||||||
\(872\) | − 2.69168i | − 0.0911517i | ||||||||
\(873\) | 2.50059i | 0.0846320i | ||||||||
\(874\) | −3.60997 | −0.122109 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.14490 | −0.308978 | ||||||||
\(877\) | − 29.8341i | − 1.00743i | −0.863871 | − | 0.503713i | \(-0.831967\pi\) | ||||
0.863871 | − | 0.503713i | \(-0.168033\pi\) | |||||||
\(878\) | − 0.326839i | − 0.0110303i | ||||||||
\(879\) | −1.91829 | −0.0647023 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.5796 | −0.390127 | −0.195064 | − | 0.980791i | \(-0.562491\pi\) | ||||
−0.195064 | + | 0.980791i | \(0.562491\pi\) | |||||||
\(882\) | 0.0355199i | 0.00119602i | ||||||||
\(883\) | 48.0237i | 1.61613i | 0.589096 | + | 0.808063i | \(0.299484\pi\) | ||||
−0.589096 | + | 0.808063i | \(0.700516\pi\) | |||||||
\(884\) | 14.3530 | 0.482744 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.490258 | 0.0164705 | ||||||||
\(887\) | 9.38336i | 0.315062i | 0.987514 | + | 0.157531i | \(0.0503535\pi\) | ||||
−0.987514 | + | 0.157531i | \(0.949647\pi\) | |||||||
\(888\) | 8.06319i | 0.270583i | ||||||||
\(889\) | −5.04316 | −0.169142 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −52.2157 | −1.74929 | ||||||||
\(892\) | − 4.45323i | − 0.149105i | ||||||||
\(893\) | 0.836581i | 0.0279951i | ||||||||
\(894\) | −12.8694 | −0.430418 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.69168 | −0.0899226 | ||||||||
\(897\) | 18.6825i | 0.623791i | ||||||||
\(898\) | − 23.5468i | − 0.785766i | ||||||||
\(899\) | −8.16342 | −0.272265 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.1266 | 1.60333 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 45.5705i | 1.51649i | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −35.4677 | −1.17834 | ||||||||
\(907\) | − 19.4347i | − 0.645319i | −0.946515 | − | 0.322659i | \(-0.895423\pi\) | ||||
0.946515 | − | 0.322659i | \(-0.104577\pi\) | |||||||
\(908\) | − 5.94865i | − 0.197413i | ||||||||
\(909\) | 1.35968 | 0.0450976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.9866 | −0.662187 | −0.331094 | − | 0.943598i | \(-0.607418\pi\) | ||||
−0.331094 | + | 0.943598i | \(0.607418\pi\) | |||||||
\(912\) | − 1.77339i | − 0.0587227i | ||||||||
\(913\) | − 9.48606i | − 0.313943i | ||||||||
\(914\) | 8.01184 | 0.265008 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.09355 | 0.0361319 | ||||||||
\(917\) | 31.0802i | 1.02636i | ||||||||
\(918\) | − 24.9023i | − 0.821897i | ||||||||
\(919\) | −6.15158 | −0.202922 | −0.101461 | − | 0.994840i | \(-0.532352\pi\) | ||||
−0.101461 | + | 0.994840i | \(0.532352\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.22661 | −0.139272 | ||||||||
\(922\) | 3.83658i | 0.126351i | ||||||||
\(923\) | 42.2478i | 1.39060i | ||||||||
\(924\) | −26.4769 | −0.871026 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.58381 | −0.216357 | ||||||||
\(927\) | − 1.87361i | − 0.0615375i | ||||||||
\(928\) | − 1.08171i | − 0.0355089i | ||||||||
\(929\) | 7.17010 | 0.235243 | 0.117622 | − | 0.993058i | \(-0.462473\pi\) | ||||
0.117622 | + | 0.993058i | \(0.462473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.245129 | 0.00803378 | ||||||||
\(932\) | 14.0935i | 0.461650i | ||||||||
\(933\) | − 52.2411i | − 1.71030i | ||||||||
\(934\) | −22.6033 | −0.739602 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.422869 | −0.0138219 | ||||||||
\(937\) | − 24.2646i | − 0.792690i | −0.918102 | − | 0.396345i | \(-0.870278\pi\) | ||||
0.918102 | − | 0.396345i | \(-0.129722\pi\) | |||||||
\(938\) | 7.68500i | 0.250924i | ||||||||
\(939\) | 56.8114 | 1.85397 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.44806 | −0.242800 | −0.121400 | − | 0.992604i | \(-0.538738\pi\) | ||||
−0.121400 | + | 0.992604i | \(0.538738\pi\) | |||||||
\(942\) | 16.9301i | 0.551613i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −12.9933 | −0.422897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −52.9538 | −1.72168 | ||||||||
\(947\) | − 52.9538i | − 1.72077i | −0.509647 | − | 0.860384i | \(-0.670224\pi\) | ||||
0.509647 | − | 0.860384i | \(-0.329776\pi\) | |||||||
\(948\) | − 5.48606i | − 0.178179i | ||||||||
\(949\) | 15.0489 | 0.488507 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.2900 | 1.53348 | ||||||||
\(952\) | − 13.2385i | − 0.429061i | ||||||||
\(953\) | 12.8694i | 0.416881i | 0.978035 | + | 0.208441i | \(0.0668388\pi\) | ||||
−0.978035 | + | 0.208441i | \(0.933161\pi\) | |||||||
\(954\) | −1.41791 | −0.0459065 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.6100 | 0.504862 | ||||||||
\(957\) | − 10.6403i | − 0.343953i | ||||||||
\(958\) | 35.7904i | 1.15634i | ||||||||
\(959\) | 11.4085 | 0.368401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.9538 | 0.837220 | ||||||||
\(962\) | − 13.2688i | − 0.427804i | ||||||||
\(963\) | − 2.74475i | − 0.0884482i | ||||||||
\(964\) | 5.21994 | 0.168123 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 17.2318 | 0.554423 | ||||||||
\(967\) | 25.8603i | 0.831610i | 0.909454 | + | 0.415805i | \(0.136500\pi\) | ||||
−0.909454 | + | 0.415805i | \(0.863500\pi\) | |||||||
\(968\) | − 19.7667i | − 0.635326i | ||||||||
\(969\) | 8.72203 | 0.280192 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.0935 | 1.12621 | 0.563103 | − | 0.826387i | \(-0.309608\pi\) | ||||
0.563103 | + | 0.826387i | \(0.309608\pi\) | |||||||
\(972\) | 1.50458i | 0.0482594i | ||||||||
\(973\) | 24.8171i | 0.795600i | ||||||||
\(974\) | 21.4070 | 0.685926 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.38336 | −0.236335 | ||||||||
\(977\) | − 42.1737i | − 1.34926i | −0.738157 | − | 0.674629i | \(-0.764304\pi\) | ||||
0.738157 | − | 0.674629i | \(-0.235696\pi\) | |||||||
\(978\) | 27.8603i | 0.890873i | ||||||||
\(979\) | 28.2528 | 0.902963 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.390032 | −0.0124528 | ||||||||
\(982\) | − 4.32684i | − 0.138075i | ||||||||
\(983\) | 42.6270i | 1.35959i | 0.733403 | + | 0.679795i | \(0.237931\pi\) | ||||
−0.733403 | + | 0.679795i | \(0.762069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.32016 | 0.169428 | ||||||||
\(987\) | − 3.99332i | − 0.127109i | ||||||||
\(988\) | 2.91829i | 0.0928432i | ||||||||
\(989\) | 34.4636 | 1.09588 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.1737 | −1.08556 | −0.542782 | − | 0.839873i | \(-0.682629\pi\) | ||||
−0.542782 | + | 0.839873i | \(0.682629\pi\) | |||||||
\(992\) | 7.54677i | 0.239610i | ||||||||
\(993\) | − 35.2409i | − 1.11834i | ||||||||
\(994\) | 38.9672 | 1.23596 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.03284 | −0.0960991 | ||||||||
\(997\) | 29.3834i | 0.930580i | 0.885158 | + | 0.465290i | \(0.154050\pi\) | ||||
−0.885158 | + | 0.465290i | \(0.845950\pi\) | |||||||
\(998\) | 37.6968i | 1.19327i | ||||||||
\(999\) | −23.0212 | −0.728359 |
(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 | 950.2.b.h.799.6 | 6 | ||
5.2 | odd | 4 | 950.2.a.j.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 950.2.a.l.1.1 | yes | 3 | ||
5.4 | even | 2 | inner | 950.2.b.h.799.1 | 6 | ||
15.2 | even | 4 | 8550.2.a.cp.1.3 | 3 | |||
15.8 | even | 4 | 8550.2.a.ci.1.1 | 3 | |||
20.3 | even | 4 | 7600.2.a.bk.1.3 | 3 | |||
20.7 | even | 4 | 7600.2.a.bz.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.j.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
950.2.a.l.1.1 | yes | 3 | 5.3 | odd | 4 | ||
950.2.b.h.799.1 | 6 | 5.4 | even | 2 | inner | ||
950.2.b.h.799.6 | 6 | 1.1 | even | 1 | trivial | ||
7600.2.a.bk.1.3 | 3 | 20.3 | even | 4 | |||
7600.2.a.bz.1.1 | 3 | 20.7 | even | 4 | |||
8550.2.a.ci.1.1 | 3 | 15.8 | even | 4 | |||
8550.2.a.cp.1.3 | 3 | 15.2 | even | 4 |