Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1369,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.1369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1369.4 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1369 |
Dual form | 1710.2.d.g.1369.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.41421 | + | 1.73205i | 0.632456 | + | 0.774597i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.86370i | − | 1.46034i | −0.683264 | − | 0.730171i | \(-0.739440\pi\) | ||
0.683264 | − | 0.730171i | \(-0.260560\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73205 | − | 1.41421i | 0.547723 | − | 0.447214i | ||||
\(11\) | −1.03528 | −0.312148 | −0.156074 | − | 0.987745i | \(-0.549884\pi\) | ||||
−0.156074 | + | 0.987745i | \(0.549884\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.86370i | − | 1.07160i | −0.844345 | − | 0.535799i | \(-0.820010\pi\) | ||
0.844345 | − | 0.535799i | \(-0.179990\pi\) | |||||||
\(14\) | −3.86370 | −1.03262 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.535898i | 0.129974i | 0.997886 | + | 0.0649872i | \(0.0207007\pi\) | ||||
−0.997886 | + | 0.0649872i | \(0.979299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −1.41421 | − | 1.73205i | −0.316228 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.03528i | 0.220722i | ||||||||
\(23\) | − | 5.46410i | − | 1.13934i | −0.821872 | − | 0.569672i | \(-0.807070\pi\) | ||
0.821872 | − | 0.569672i | \(-0.192930\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 4.89898i | −0.200000 | + | 0.979796i | ||||
\(26\) | −3.86370 | −0.757735 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.86370i | 0.730171i | ||||||||
\(29\) | 4.62158 | 0.858206 | 0.429103 | − | 0.903256i | \(-0.358830\pi\) | ||||
0.429103 | + | 0.903256i | \(0.358830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.9282 | −1.96276 | −0.981382 | − | 0.192068i | \(-0.938481\pi\) | ||||
−0.981382 | + | 0.192068i | \(0.938481\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.535898 | 0.0919058 | ||||||||
\(35\) | 6.69213 | − | 5.46410i | 1.13118 | − | 0.923602i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.79315i | 0.294792i | 0.989078 | + | 0.147396i | \(0.0470892\pi\) | ||||
−0.989078 | + | 0.147396i | \(0.952911\pi\) | |||||||
\(38\) | − | 1.00000i | − | 0.162221i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.73205 | + | 1.41421i | −0.273861 | + | 0.223607i | ||||
\(41\) | −1.79315 | −0.280043 | −0.140022 | − | 0.990148i | \(-0.544717\pi\) | ||||
−0.140022 | + | 0.990148i | \(0.544717\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.69213i | − | 1.02054i | −0.860014 | − | 0.510270i | \(-0.829545\pi\) | ||
0.860014 | − | 0.510270i | \(-0.170455\pi\) | |||||||
\(44\) | 1.03528 | 0.156074 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.46410 | −0.805638 | ||||||||
\(47\) | 2.53590i | 0.369899i | 0.982748 | + | 0.184949i | \(0.0592121\pi\) | ||||
−0.982748 | + | 0.184949i | \(0.940788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.92820 | −1.13260 | ||||||||
\(50\) | 4.89898 | + | 1.00000i | 0.692820 | + | 0.141421i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.86370i | 0.535799i | ||||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.46410 | − | 1.79315i | −0.197419 | − | 0.241788i | ||||
\(56\) | 3.86370 | 0.516309 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 4.62158i | − | 0.606843i | ||||||
\(59\) | 6.96953 | 0.907356 | 0.453678 | − | 0.891166i | \(-0.350112\pi\) | ||||
0.453678 | + | 0.891166i | \(0.350112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 10.9282i | 1.38788i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 6.69213 | − | 5.46410i | 0.830057 | − | 0.677738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.3843i | − | 1.63515i | −0.575824 | − | 0.817574i | \(-0.695319\pi\) | ||
0.575824 | − | 0.817574i | \(-0.304681\pi\) | |||||||
\(68\) | − | 0.535898i | − | 0.0649872i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.46410 | − | 6.69213i | −0.653085 | − | 0.799863i | ||||
\(71\) | −4.14110 | −0.491459 | −0.245729 | − | 0.969338i | \(-0.579027\pi\) | ||||
−0.245729 | + | 0.969338i | \(0.579027\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.58630i | − | 0.419745i | −0.977729 | − | 0.209872i | \(-0.932695\pi\) | ||
0.977729 | − | 0.209872i | \(-0.0673049\pi\) | |||||||
\(74\) | 1.79315 | 0.208450 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 4.00000i | 0.455842i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 1.41421 | + | 1.73205i | 0.158114 | + | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.79315i | 0.198020i | ||||||||
\(83\) | − | 16.3923i | − | 1.79929i | −0.436623 | − | 0.899645i | \(-0.643826\pi\) | ||
0.436623 | − | 0.899645i | \(-0.356174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.928203 | + | 0.757875i | −0.100678 | + | 0.0822031i | ||||
\(86\) | −6.69213 | −0.721631 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.03528i | − | 0.110361i | ||||||
\(89\) | −3.86370 | −0.409552 | −0.204776 | − | 0.978809i | \(-0.565647\pi\) | ||||
−0.204776 | + | 0.978809i | \(0.565647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.9282 | −1.56490 | ||||||||
\(92\) | 5.46410i | 0.569672i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.53590 | 0.261558 | ||||||||
\(95\) | 1.41421 | + | 1.73205i | 0.145095 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.55103i | − | 0.259017i | −0.991578 | − | 0.129509i | \(-0.958660\pi\) | ||
0.991578 | − | 0.129509i | \(-0.0413400\pi\) | |||||||
\(98\) | 7.92820i | 0.800869i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | − | 4.89898i | 0.100000 | − | 0.489898i | ||||
\(101\) | 10.5558 | 1.05034 | 0.525172 | − | 0.850996i | \(-0.324001\pi\) | ||||
0.525172 | + | 0.850996i | \(0.324001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89898i | 0.482711i | 0.970437 | + | 0.241355i | \(0.0775919\pi\) | ||||
−0.970437 | + | 0.241355i | \(0.922408\pi\) | |||||||
\(104\) | 3.86370 | 0.378867 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − | 2.92820i | − | 0.283080i | −0.989933 | − | 0.141540i | \(-0.954795\pi\) | ||
0.989933 | − | 0.141540i | \(-0.0452054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.92820 | −0.855167 | −0.427583 | − | 0.903976i | \(-0.640635\pi\) | ||||
−0.427583 | + | 0.903976i | \(0.640635\pi\) | |||||||
\(110\) | −1.79315 | + | 1.46410i | −0.170970 | + | 0.139597i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 3.86370i | − | 0.365086i | ||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.46410 | − | 7.72741i | 0.882532 | − | 0.720584i | ||||
\(116\) | −4.62158 | −0.429103 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.96953i | − | 0.641597i | ||||||
\(119\) | 2.07055 | 0.189807 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.92820 | −0.902564 | ||||||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.9282 | 0.981382 | ||||||||
\(125\) | −9.89949 | + | 5.19615i | −0.885438 | + | 0.464758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.48528i | − | 0.752947i | −0.926427 | − | 0.376473i | \(-0.877137\pi\) | ||
0.926427 | − | 0.376473i | \(-0.122863\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.46410 | − | 6.69213i | −0.479233 | − | 0.586939i | ||||
\(131\) | −3.10583 | −0.271357 | −0.135679 | − | 0.990753i | \(-0.543322\pi\) | ||||
−0.135679 | + | 0.990753i | \(0.543322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.86370i | − | 0.335026i | ||||||
\(134\) | −13.3843 | −1.15622 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.535898 | −0.0459529 | ||||||||
\(137\) | 0.535898i | 0.0457849i | 0.999738 | + | 0.0228924i | \(0.00728753\pi\) | ||||
−0.999738 | + | 0.0228924i | \(0.992712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | −6.69213 | + | 5.46410i | −0.565588 | + | 0.461801i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.14110i | 0.347514i | ||||||||
\(143\) | 4.00000i | 0.334497i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.53590 | + | 8.00481i | 0.542777 | + | 0.664763i | ||||
\(146\) | −3.58630 | −0.296804 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.79315i | − | 0.147396i | ||||||
\(149\) | 20.3538 | 1.66745 | 0.833724 | − | 0.552182i | \(-0.186205\pi\) | ||||
0.833724 | + | 0.552182i | \(0.186205\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.85641 | 0.476588 | 0.238294 | − | 0.971193i | \(-0.423412\pi\) | ||||
0.238294 | + | 0.971193i | \(0.423412\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.00000 | 0.322329 | ||||||||
\(155\) | −15.4548 | − | 18.9282i | −1.24136 | − | 1.52035i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.1421i | − | 1.12867i | −0.825547 | − | 0.564333i | \(-0.809134\pi\) | ||
0.825547 | − | 0.564333i | \(-0.190866\pi\) | |||||||
\(158\) | − | 4.00000i | − | 0.318223i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.73205 | − | 1.41421i | 0.136931 | − | 0.111803i | ||||
\(161\) | −21.1117 | −1.66383 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.6627i | 1.85341i | 0.375796 | + | 0.926703i | \(0.377369\pi\) | ||||
−0.375796 | + | 0.926703i | \(0.622631\pi\) | |||||||
\(164\) | 1.79315 | 0.140022 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.3923 | −1.27229 | ||||||||
\(167\) | 10.9282i | 0.845650i | 0.906211 | + | 0.422825i | \(0.138961\pi\) | ||||
−0.906211 | + | 0.422825i | \(0.861039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.92820 | −0.148323 | ||||||||
\(170\) | 0.757875 | + | 0.928203i | 0.0581263 | + | 0.0711899i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.69213i | 0.510270i | ||||||||
\(173\) | 22.7846i | 1.73228i | 0.499800 | + | 0.866141i | \(0.333407\pi\) | ||||
−0.499800 | + | 0.866141i | \(0.666593\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.9282 | + | 3.86370i | 1.43084 | + | 0.292069i | ||||
\(176\) | −1.03528 | −0.0780369 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.86370i | 0.289597i | ||||||||
\(179\) | −16.7675 | −1.25326 | −0.626631 | − | 0.779316i | \(-0.715566\pi\) | ||||
−0.626631 | + | 0.779316i | \(0.715566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8564 | 1.47592 | 0.737958 | − | 0.674847i | \(-0.235790\pi\) | ||||
0.737958 | + | 0.674847i | \(0.235790\pi\) | |||||||
\(182\) | 14.9282i | 1.10655i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.46410 | 0.402819 | ||||||||
\(185\) | −3.10583 | + | 2.53590i | −0.228345 | + | 0.186443i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.554803i | − | 0.0405712i | ||||||
\(188\) | − | 2.53590i | − | 0.184949i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.73205 | − | 1.41421i | 0.125656 | − | 0.102598i | ||||
\(191\) | 17.2480 | 1.24802 | 0.624009 | − | 0.781417i | \(-0.285503\pi\) | ||||
0.624009 | + | 0.781417i | \(0.285503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.76268i | 0.630752i | 0.948967 | + | 0.315376i | \(0.102131\pi\) | ||||
−0.948967 | + | 0.315376i | \(0.897869\pi\) | |||||||
\(194\) | −2.55103 | −0.183153 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.92820 | 0.566300 | ||||||||
\(197\) | 23.4641i | 1.67175i | 0.548921 | + | 0.835874i | \(0.315039\pi\) | ||||
−0.548921 | + | 0.835874i | \(0.684961\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0718 | −0.926635 | −0.463318 | − | 0.886192i | \(-0.653341\pi\) | ||||
−0.463318 | + | 0.886192i | \(0.653341\pi\) | |||||||
\(200\) | −4.89898 | − | 1.00000i | −0.346410 | − | 0.0707107i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 10.5558i | − | 0.742706i | ||||||
\(203\) | − | 17.8564i | − | 1.25327i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.53590 | − | 3.10583i | −0.177115 | − | 0.216920i | ||||
\(206\) | 4.89898 | 0.341328 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.86370i | − | 0.267900i | ||||||
\(209\) | −1.03528 | −0.0716116 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8564 | −1.22929 | −0.614643 | − | 0.788806i | \(-0.710700\pi\) | ||||
−0.614643 | + | 0.788806i | \(0.710700\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.92820 | −0.200168 | ||||||||
\(215\) | 11.5911 | − | 9.46410i | 0.790507 | − | 0.645446i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 42.2233i | 2.86631i | ||||||||
\(218\) | 8.92820i | 0.604694i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.46410 | + | 1.79315i | 0.0987097 | + | 0.120894i | ||||
\(221\) | 2.07055 | 0.139280 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.5558i | − | 0.706871i | −0.935459 | − | 0.353435i | \(-0.885013\pi\) | ||
0.935459 | − | 0.353435i | \(-0.114987\pi\) | |||||||
\(224\) | −3.86370 | −0.258155 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | − | 1.85641i | − | 0.123214i | −0.998100 | − | 0.0616070i | \(-0.980377\pi\) | ||
0.998100 | − | 0.0616070i | \(-0.0196225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.85641 | 0.254839 | 0.127419 | − | 0.991849i | \(-0.459331\pi\) | ||||
0.127419 | + | 0.991849i | \(0.459331\pi\) | |||||||
\(230\) | −7.72741 | − | 9.46410i | −0.509530 | − | 0.624044i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.62158i | 0.303421i | ||||||||
\(233\) | − | 12.5359i | − | 0.821254i | −0.911803 | − | 0.410627i | \(-0.865310\pi\) | ||
0.911803 | − | 0.410627i | \(-0.134690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.39230 | + | 3.58630i | −0.286522 | + | 0.233945i | ||||
\(236\) | −6.96953 | −0.453678 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.07055i | − | 0.134214i | ||||||
\(239\) | 13.1069 | 0.847812 | 0.423906 | − | 0.905706i | \(-0.360659\pi\) | ||||
0.423906 | + | 0.905706i | \(0.360659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 9.92820i | 0.638209i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −11.2122 | − | 13.7321i | −0.716319 | − | 0.877309i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.86370i | − | 0.245842i | ||||||
\(248\) | − | 10.9282i | − | 0.693942i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.19615 | + | 9.89949i | 0.328634 | + | 0.626099i | ||||
\(251\) | 28.3586 | 1.78998 | 0.894990 | − | 0.446087i | \(-0.147183\pi\) | ||||
0.894990 | + | 0.446087i | \(0.147183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.65685i | 0.355643i | ||||||||
\(254\) | −8.48528 | −0.532414 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.7846i | 1.42126i | 0.703563 | + | 0.710632i | \(0.251591\pi\) | ||||
−0.703563 | + | 0.710632i | \(0.748409\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.92820 | 0.430498 | ||||||||
\(260\) | −6.69213 | + | 5.46410i | −0.415028 | + | 0.338869i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.10583i | 0.191879i | ||||||||
\(263\) | − | 19.3205i | − | 1.19135i | −0.803224 | − | 0.595677i | \(-0.796884\pi\) | ||
0.803224 | − | 0.595677i | \(-0.203116\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3923 | − | 8.48528i | 0.638394 | − | 0.521247i | ||||
\(266\) | −3.86370 | −0.236899 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.3843i | 0.817574i | ||||||||
\(269\) | −31.9449 | −1.94772 | −0.973858 | − | 0.227160i | \(-0.927056\pi\) | ||||
−0.973858 | + | 0.227160i | \(0.927056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9282 | 0.663841 | 0.331921 | − | 0.943307i | \(-0.392303\pi\) | ||||
0.331921 | + | 0.943307i | \(0.392303\pi\) | |||||||
\(272\) | 0.535898i | 0.0324936i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.535898 | 0.0323748 | ||||||||
\(275\) | 1.03528 | − | 5.07180i | 0.0624295 | − | 0.305841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.2832i | 1.09853i | 0.835647 | + | 0.549267i | \(0.185093\pi\) | ||||
−0.835647 | + | 0.549267i | \(0.814907\pi\) | |||||||
\(278\) | 6.92820i | 0.415526i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.46410 | + | 6.69213i | 0.326543 | + | 0.399931i | ||||
\(281\) | 31.1870 | 1.86046 | 0.930231 | − | 0.366974i | \(-0.119606\pi\) | ||||
0.930231 | + | 0.366974i | \(0.119606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.17638i | 0.307704i | 0.988094 | + | 0.153852i | \(0.0491679\pi\) | ||||
−0.988094 | + | 0.153852i | \(0.950832\pi\) | |||||||
\(284\) | 4.14110 | 0.245729 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 6.92820i | 0.408959i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7128 | 0.983107 | ||||||||
\(290\) | 8.00481 | − | 6.53590i | 0.470059 | − | 0.383801i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.58630i | 0.209872i | ||||||||
\(293\) | 19.8564i | 1.16002i | 0.814608 | + | 0.580012i | \(0.196952\pi\) | ||||
−0.814608 | + | 0.580012i | \(0.803048\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.85641 | + | 12.0716i | 0.573862 | + | 0.702835i | ||||
\(296\) | −1.79315 | −0.104225 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 20.3538i | − | 1.17906i | ||||||
\(299\) | −21.1117 | −1.22092 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.8564 | −1.49034 | ||||||||
\(302\) | − | 5.85641i | − | 0.336998i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −2.82843 | − | 3.46410i | −0.161955 | − | 0.198354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.5254i | − | 1.00023i | −0.865960 | − | 0.500113i | \(-0.833292\pi\) | ||
0.865960 | − | 0.500113i | \(-0.166708\pi\) | |||||||
\(308\) | − | 4.00000i | − | 0.227921i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.9282 | + | 15.4548i | −1.07505 | + | 0.877774i | ||||
\(311\) | 1.79315 | 0.101680 | 0.0508401 | − | 0.998707i | \(-0.483810\pi\) | ||||
0.0508401 | + | 0.998707i | \(0.483810\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.5959i | − | 1.10763i | −0.832641 | − | 0.553813i | \(-0.813172\pi\) | ||
0.832641 | − | 0.553813i | \(-0.186828\pi\) | |||||||
\(314\) | −14.1421 | −0.798087 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | 14.0000i | 0.786318i | 0.919470 | + | 0.393159i | \(0.128618\pi\) | ||||
−0.919470 | + | 0.393159i | \(0.871382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.78461 | −0.267887 | ||||||||
\(320\) | −1.41421 | − | 1.73205i | −0.0790569 | − | 0.0968246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 21.1117i | 1.17651i | ||||||||
\(323\) | 0.535898i | 0.0298182i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.9282 | + | 3.86370i | 1.04995 | + | 0.214320i | ||||
\(326\) | 23.6627 | 1.31056 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 1.79315i | − | 0.0990102i | ||||||
\(329\) | 9.79796 | 0.540179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8564 | 0.761617 | 0.380808 | − | 0.924654i | \(-0.375646\pi\) | ||||
0.380808 | + | 0.924654i | \(0.375646\pi\) | |||||||
\(332\) | 16.3923i | 0.899645i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.9282 | 0.597965 | ||||||||
\(335\) | 23.1822 | − | 18.9282i | 1.26658 | − | 1.03416i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.03528i | − | 0.0563951i | −0.999602 | − | 0.0281975i | \(-0.991023\pi\) | ||
0.999602 | − | 0.0281975i | \(-0.00897675\pi\) | |||||||
\(338\) | 1.92820i | 0.104880i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.928203 | − | 0.757875i | 0.0503389 | − | 0.0411015i | ||||
\(341\) | 11.3137 | 0.612672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.58630i | 0.193642i | ||||||||
\(344\) | 6.69213 | 0.360815 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.7846 | 1.22491 | ||||||||
\(347\) | 18.5359i | 0.995059i | 0.867447 | + | 0.497530i | \(0.165759\pi\) | ||||
−0.867447 | + | 0.497530i | \(0.834241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.14359 | −0.221801 | −0.110901 | − | 0.993831i | \(-0.535374\pi\) | ||||
−0.110901 | + | 0.993831i | \(0.535374\pi\) | |||||||
\(350\) | 3.86370 | − | 18.9282i | 0.206524 | − | 1.01176i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.03528i | 0.0551804i | ||||||||
\(353\) | − | 21.3205i | − | 1.13478i | −0.823451 | − | 0.567388i | \(-0.807954\pi\) | ||
0.823451 | − | 0.567388i | \(-0.192046\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.85641 | − | 7.17260i | −0.310826 | − | 0.380682i | ||||
\(356\) | 3.86370 | 0.204776 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.7675i | 0.886189i | ||||||||
\(359\) | 34.7733 | 1.83527 | 0.917633 | − | 0.397429i | \(-0.130097\pi\) | ||||
0.917633 | + | 0.397429i | \(0.130097\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − | 19.8564i | − | 1.04363i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.9282 | 0.782450 | ||||||||
\(365\) | 6.21166 | − | 5.07180i | 0.325133 | − | 0.265470i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.37945i | 0.280805i | 0.990094 | + | 0.140403i | \(0.0448397\pi\) | ||||
−0.990094 | + | 0.140403i | \(0.955160\pi\) | |||||||
\(368\) | − | 5.46410i | − | 0.284836i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.53590 | + | 3.10583i | 0.131835 | + | 0.161464i | ||||
\(371\) | −23.1822 | −1.20356 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 24.9754i | − | 1.29318i | −0.762840 | − | 0.646588i | \(-0.776195\pi\) | ||
0.762840 | − | 0.646588i | \(-0.223805\pi\) | |||||||
\(374\) | −0.554803 | −0.0286882 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.53590 | −0.130779 | ||||||||
\(377\) | − | 17.8564i | − | 0.919652i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.7128 | 1.83444 | 0.917222 | − | 0.398376i | \(-0.130426\pi\) | ||||
0.917222 | + | 0.398376i | \(0.130426\pi\) | |||||||
\(380\) | −1.41421 | − | 1.73205i | −0.0725476 | − | 0.0888523i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 17.2480i | − | 0.882483i | ||||||
\(383\) | 22.9282i | 1.17158i | 0.810464 | + | 0.585788i | \(0.199215\pi\) | ||||
−0.810464 | + | 0.585788i | \(0.800785\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.92820 | + | 5.65685i | −0.353094 | + | 0.288300i | ||||
\(386\) | 8.76268 | 0.446009 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.55103i | 0.129509i | ||||||||
\(389\) | −19.7990 | −1.00385 | −0.501924 | − | 0.864912i | \(-0.667374\pi\) | ||||
−0.501924 | + | 0.864912i | \(0.667374\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.92820 | 0.148086 | ||||||||
\(392\) | − | 7.92820i | − | 0.400435i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23.4641 | 1.18210 | ||||||||
\(395\) | 5.65685 | + | 6.92820i | 0.284627 | + | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 18.2832i | − | 0.917610i | −0.888537 | − | 0.458805i | \(-0.848278\pi\) | ||
0.888537 | − | 0.458805i | \(-0.151722\pi\) | |||||||
\(398\) | 13.0718i | 0.655230i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | + | 4.89898i | −0.0500000 | + | 0.244949i | ||||
\(401\) | −9.52056 | −0.475434 | −0.237717 | − | 0.971334i | \(-0.576399\pi\) | ||||
−0.237717 | + | 0.971334i | \(0.576399\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.2233i | 2.10329i | ||||||||
\(404\) | −10.5558 | −0.525172 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.8564 | −0.886199 | ||||||||
\(407\) | − | 1.85641i | − | 0.0920187i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.9282 | 1.03483 | 0.517417 | − | 0.855734i | \(-0.326894\pi\) | ||||
0.517417 | + | 0.855734i | \(0.326894\pi\) | |||||||
\(410\) | −3.10583 | + | 2.53590i | −0.153386 | + | 0.125239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 4.89898i | − | 0.241355i | ||||||
\(413\) | − | 26.9282i | − | 1.32505i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.3923 | − | 23.1822i | 1.39372 | − | 1.13797i | ||||
\(416\) | −3.86370 | −0.189434 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.03528i | 0.0506370i | ||||||||
\(419\) | 29.3195 | 1.43235 | 0.716177 | − | 0.697919i | \(-0.245890\pi\) | ||||
0.716177 | + | 0.697919i | \(0.245890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7128 | 1.44811 | 0.724057 | − | 0.689740i | \(-0.242275\pi\) | ||||
0.724057 | + | 0.689740i | \(0.242275\pi\) | |||||||
\(422\) | 17.8564i | 0.869236i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | −2.62536 | − | 0.535898i | −0.127348 | − | 0.0259949i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.72741i | 0.373955i | ||||||||
\(428\) | 2.92820i | 0.141540i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.46410 | − | 11.5911i | −0.456400 | − | 0.558973i | ||||
\(431\) | 26.2137 | 1.26267 | 0.631335 | − | 0.775510i | \(-0.282507\pi\) | ||||
0.631335 | + | 0.775510i | \(0.282507\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.8332i | − | 0.520612i | −0.965526 | − | 0.260306i | \(-0.916177\pi\) | ||
0.965526 | − | 0.260306i | \(-0.0838235\pi\) | |||||||
\(434\) | 42.2233 | 2.02678 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.92820 | 0.427583 | ||||||||
\(437\) | − | 5.46410i | − | 0.261383i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.0000 | −0.954548 | −0.477274 | − | 0.878755i | \(-0.658375\pi\) | ||||
−0.477274 | + | 0.878755i | \(0.658375\pi\) | |||||||
\(440\) | 1.79315 | − | 1.46410i | 0.0854851 | − | 0.0697983i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.07055i | − | 0.0984861i | ||||||
\(443\) | − | 16.3923i | − | 0.778822i | −0.921064 | − | 0.389411i | \(-0.872679\pi\) | ||
0.921064 | − | 0.389411i | \(-0.127321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.46410 | − | 6.69213i | −0.259023 | − | 0.317237i | ||||
\(446\) | −10.5558 | −0.499833 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.86370i | 0.182543i | ||||||||
\(449\) | −40.4302 | −1.90802 | −0.954009 | − | 0.299777i | \(-0.903088\pi\) | ||||
−0.954009 | + | 0.299777i | \(0.903088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.85641 | 0.0874148 | ||||||||
\(452\) | 6.00000i | 0.282216i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.85641 | −0.0871255 | ||||||||
\(455\) | −21.1117 | − | 25.8564i | −0.989730 | − | 1.21217i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.9411i | 1.58770i | 0.608114 | + | 0.793849i | \(0.291926\pi\) | ||||
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | − | 3.85641i | − | 0.180198i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.46410 | + | 7.72741i | −0.441266 | + | 0.360292i | ||||
\(461\) | −27.5264 | −1.28203 | −0.641016 | − | 0.767527i | \(-0.721487\pi\) | ||||
−0.641016 | + | 0.767527i | \(0.721487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8733i | 0.923591i | 0.886986 | + | 0.461796i | \(0.152795\pi\) | ||||
−0.886986 | + | 0.461796i | \(0.847205\pi\) | |||||||
\(464\) | 4.62158 | 0.214551 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.5359 | −0.580714 | ||||||||
\(467\) | 2.53590i | 0.117347i | 0.998277 | + | 0.0586737i | \(0.0186871\pi\) | ||||
−0.998277 | + | 0.0586737i | \(0.981313\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −51.7128 | −2.38788 | ||||||||
\(470\) | 3.58630 | + | 4.39230i | 0.165424 | + | 0.202602i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.96953i | 0.320799i | ||||||||
\(473\) | 6.92820i | 0.318559i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | + | 4.89898i | −0.0458831 | + | 0.224781i | ||||
\(476\) | −2.07055 | −0.0949036 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 13.1069i | − | 0.599494i | ||||||
\(479\) | 16.6932 | 0.762730 | 0.381365 | − | 0.924425i | \(-0.375454\pi\) | ||||
0.381365 | + | 0.924425i | \(0.375454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.92820 | 0.315899 | ||||||||
\(482\) | − | 10.0000i | − | 0.455488i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.92820 | 0.451282 | ||||||||
\(485\) | 4.41851 | − | 3.60770i | 0.200634 | − | 0.163817i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.38323i | 0.153309i | 0.997058 | + | 0.0766544i | \(0.0244238\pi\) | ||||
−0.997058 | + | 0.0766544i | \(0.975576\pi\) | |||||||
\(488\) | − | 2.00000i | − | 0.0905357i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.7321 | + | 11.2122i | −0.620351 | + | 0.506514i | ||||
\(491\) | −18.5606 | −0.837630 | −0.418815 | − | 0.908072i | \(-0.637554\pi\) | ||||
−0.418815 | + | 0.908072i | \(0.637554\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.47670i | 0.111545i | ||||||||
\(494\) | −3.86370 | −0.173836 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.9282 | −0.490691 | ||||||||
\(497\) | 16.0000i | 0.717698i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.8564 | −1.15749 | −0.578746 | − | 0.815508i | \(-0.696458\pi\) | ||||
−0.578746 | + | 0.815508i | \(0.696458\pi\) | |||||||
\(500\) | 9.89949 | − | 5.19615i | 0.442719 | − | 0.232379i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 28.3586i | − | 1.26571i | ||||||
\(503\) | 11.3205i | 0.504757i | 0.967629 | + | 0.252378i | \(0.0812127\pi\) | ||||
−0.967629 | + | 0.252378i | \(0.918787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.9282 | + | 18.2832i | 0.664296 | + | 0.813594i | ||||
\(506\) | 5.65685 | 0.251478 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.48528i | 0.376473i | ||||||||
\(509\) | −37.0470 | −1.64208 | −0.821039 | − | 0.570873i | \(-0.806605\pi\) | ||||
−0.821039 | + | 0.570873i | \(0.806605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8564 | −0.612971 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.7846 | 1.00499 | ||||||||
\(515\) | −8.48528 | + | 6.92820i | −0.373906 | + | 0.305293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.62536i | − | 0.115463i | ||||||
\(518\) | − | 6.92820i | − | 0.304408i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.46410 | + | 6.69213i | 0.239617 | + | 0.293469i | ||||
\(521\) | −9.52056 | −0.417103 | −0.208552 | − | 0.978011i | \(-0.566875\pi\) | ||||
−0.208552 | + | 0.978011i | \(0.566875\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.7685i | 1.17051i | 0.810851 | + | 0.585253i | \(0.199005\pi\) | ||||
−0.810851 | + | 0.585253i | \(0.800995\pi\) | |||||||
\(524\) | 3.10583 | 0.135679 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.3205 | −0.842414 | ||||||||
\(527\) | − | 5.85641i | − | 0.255109i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.85641 | −0.298105 | ||||||||
\(530\) | −8.48528 | − | 10.3923i | −0.368577 | − | 0.451413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.86370i | 0.167513i | ||||||||
\(533\) | 6.92820i | 0.300094i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.07180 | − | 4.14110i | 0.219273 | − | 0.179036i | ||||
\(536\) | 13.3843 | 0.578112 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.9449i | 1.37724i | ||||||||
\(539\) | 8.20788 | 0.353538 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.0000 | 1.11783 | 0.558914 | − | 0.829226i | \(-0.311218\pi\) | ||||
0.558914 | + | 0.829226i | \(0.311218\pi\) | |||||||
\(542\) | − | 10.9282i | − | 0.469407i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.535898 | 0.0229765 | ||||||||
\(545\) | −12.6264 | − | 15.4641i | −0.540855 | − | 0.662409i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3528i | 0.442652i | 0.975200 | + | 0.221326i | \(0.0710385\pi\) | ||||
−0.975200 | + | 0.221326i | \(0.928961\pi\) | |||||||
\(548\) | − | 0.535898i | − | 0.0228924i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.07180 | − | 1.03528i | −0.216262 | − | 0.0441443i | ||||
\(551\) | 4.62158 | 0.196886 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.4548i | − | 0.657206i | ||||||
\(554\) | 18.2832 | 0.776780 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.92820 | 0.293821 | ||||||||
\(557\) | 31.4641i | 1.33318i | 0.745426 | + | 0.666588i | \(0.232246\pi\) | ||||
−0.745426 | + | 0.666588i | \(0.767754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.8564 | −1.09361 | ||||||||
\(560\) | 6.69213 | − | 5.46410i | 0.282794 | − | 0.230900i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 31.1870i | − | 1.31555i | ||||||
\(563\) | − | 25.8564i | − | 1.08972i | −0.838528 | − | 0.544859i | \(-0.816583\pi\) | ||
0.838528 | − | 0.544859i | \(-0.183417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3923 | − | 8.48528i | 0.437208 | − | 0.356978i | ||||
\(566\) | 5.17638 | 0.217580 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 4.14110i | − | 0.173757i | ||||||
\(569\) | 44.0165 | 1.84527 | 0.922634 | − | 0.385678i | \(-0.126032\pi\) | ||||
0.922634 | + | 0.385678i | \(0.126032\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9282 | 0.624726 | 0.312363 | − | 0.949963i | \(-0.398880\pi\) | ||||
0.312363 | + | 0.949963i | \(0.398880\pi\) | |||||||
\(572\) | − | 4.00000i | − | 0.167248i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.92820 | 0.289178 | ||||||||
\(575\) | 26.7685 | + | 5.46410i | 1.11632 | + | 0.227869i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 5.65685i | − | 0.235498i | −0.993043 | − | 0.117749i | \(-0.962432\pi\) | ||
0.993043 | − | 0.117749i | \(-0.0375678\pi\) | |||||||
\(578\) | − | 16.7128i | − | 0.695161i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.53590 | − | 8.00481i | −0.271388 | − | 0.332382i | ||||
\(581\) | −63.3350 | −2.62758 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.21166i | 0.257261i | ||||||||
\(584\) | 3.58630 | 0.148402 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.8564 | 0.820261 | ||||||||
\(587\) | 24.3923i | 1.00678i | 0.864060 | + | 0.503389i | \(0.167914\pi\) | ||||
−0.864060 | + | 0.503389i | \(0.832086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.9282 | −0.450289 | ||||||||
\(590\) | 12.0716 | − | 9.85641i | 0.496979 | − | 0.405782i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.79315i | 0.0736980i | ||||||||
\(593\) | 4.53590i | 0.186267i | 0.995654 | + | 0.0931335i | \(0.0296883\pi\) | ||||
−0.995654 | + | 0.0931335i | \(0.970312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.92820 | + | 3.58630i | 0.120045 | + | 0.147024i | ||||
\(596\) | −20.3538 | −0.833724 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.1117i | 0.863320i | ||||||||
\(599\) | −20.5569 | −0.839931 | −0.419965 | − | 0.907540i | \(-0.637958\pi\) | ||||
−0.419965 | + | 0.907540i | \(0.637958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7846 | −0.766240 | −0.383120 | − | 0.923699i | \(-0.625150\pi\) | ||||
−0.383120 | + | 0.923699i | \(0.625150\pi\) | |||||||
\(602\) | 25.8564i | 1.05383i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.85641 | −0.238294 | ||||||||
\(605\) | −14.0406 | − | 17.1962i | −0.570832 | − | 0.699123i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.6066i | 1.85111i | 0.378609 | + | 0.925557i | \(0.376402\pi\) | ||||
−0.378609 | + | 0.925557i | \(0.623598\pi\) | |||||||
\(608\) | − | 1.00000i | − | 0.0405554i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.46410 | + | 2.82843i | −0.140257 | + | 0.114520i | ||||
\(611\) | 9.79796 | 0.396383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.85993i | − | 0.236680i | −0.992973 | − | 0.118340i | \(-0.962243\pi\) | ||
0.992973 | − | 0.118340i | \(-0.0377573\pi\) | |||||||
\(614\) | −17.5254 | −0.707266 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | 28.2487i | 1.13725i | 0.822597 | + | 0.568625i | \(0.192524\pi\) | ||||
−0.822597 | + | 0.568625i | \(0.807476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6410 | 1.39234 | 0.696170 | − | 0.717877i | \(-0.254886\pi\) | ||||
0.696170 | + | 0.717877i | \(0.254886\pi\) | |||||||
\(620\) | 15.4548 | + | 18.9282i | 0.620680 | + | 0.760175i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1.79315i | − | 0.0718988i | ||||||
\(623\) | 14.9282i | 0.598086i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | −19.5959 | −0.783210 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.1421i | 0.564333i | ||||||||
\(629\) | −0.960947 | −0.0383155 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.8564 | 0.870090 | 0.435045 | − | 0.900409i | \(-0.356732\pi\) | ||||
0.435045 | + | 0.900409i | \(0.356732\pi\) | |||||||
\(632\) | 4.00000i | 0.159111i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0000 | 0.556011 | ||||||||
\(635\) | 14.6969 | − | 12.0000i | 0.583230 | − | 0.476205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.6322i | 1.21369i | ||||||||
\(638\) | 4.78461i | 0.189425i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.73205 | + | 1.41421i | −0.0684653 | + | 0.0559017i | ||||
\(641\) | −17.2480 | −0.681254 | −0.340627 | − | 0.940199i | \(-0.610639\pi\) | ||||
−0.340627 | + | 0.940199i | \(0.610639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 37.0470i | − | 1.46099i | −0.682918 | − | 0.730495i | \(-0.739290\pi\) | ||
0.682918 | − | 0.730495i | \(-0.260710\pi\) | |||||||
\(644\) | 21.1117 | 0.831916 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.535898 | 0.0210846 | ||||||||
\(647\) | 13.4641i | 0.529328i | 0.964341 | + | 0.264664i | \(0.0852611\pi\) | ||||
−0.964341 | + | 0.264664i | \(0.914739\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.21539 | −0.283229 | ||||||||
\(650\) | 3.86370 | − | 18.9282i | 0.151547 | − | 0.742425i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 23.6627i | − | 0.926703i | ||||||
\(653\) | 24.2487i | 0.948925i | 0.880276 | + | 0.474463i | \(0.157358\pi\) | ||||
−0.880276 | + | 0.474463i | \(0.842642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.39230 | − | 5.37945i | −0.171622 | − | 0.210193i | ||||
\(656\) | −1.79315 | −0.0700108 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 9.79796i | − | 0.381964i | ||||||
\(659\) | 20.3538 | 0.792871 | 0.396436 | − | 0.918063i | \(-0.370247\pi\) | ||||
0.396436 | + | 0.918063i | \(0.370247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7846 | −0.419473 | −0.209736 | − | 0.977758i | \(-0.567261\pi\) | ||||
−0.209736 | + | 0.977758i | \(0.567261\pi\) | |||||||
\(662\) | − | 13.8564i | − | 0.538545i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.3923 | 0.636145 | ||||||||
\(665\) | 6.69213 | − | 5.46410i | 0.259510 | − | 0.211889i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 25.2528i | − | 0.977791i | ||||||
\(668\) | − | 10.9282i | − | 0.422825i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.9282 | − | 23.1822i | −0.731260 | − | 0.895607i | ||||
\(671\) | 2.07055 | 0.0799328 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 27.2490i | − | 1.05037i | −0.850988 | − | 0.525186i | \(-0.823996\pi\) | ||
0.850988 | − | 0.525186i | \(-0.176004\pi\) | |||||||
\(674\) | −1.03528 | −0.0398773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.92820 | 0.0741617 | ||||||||
\(677\) | 36.6410i | 1.40823i | 0.710087 | + | 0.704114i | \(0.248656\pi\) | ||||
−0.710087 | + | 0.704114i | \(0.751344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.85641 | −0.378254 | ||||||||
\(680\) | −0.757875 | − | 0.928203i | −0.0290632 | − | 0.0355950i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 11.3137i | − | 0.433224i | ||||||
\(683\) | − | 18.9282i | − | 0.724268i | −0.932126 | − | 0.362134i | \(-0.882048\pi\) | ||
0.932126 | − | 0.362134i | \(-0.117952\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.928203 | + | 0.757875i | −0.0354648 | + | 0.0289569i | ||||
\(686\) | 3.58630 | 0.136926 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 6.69213i | − | 0.255135i | ||||||
\(689\) | −23.1822 | −0.883172 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.9282 | 1.48090 | 0.740449 | − | 0.672112i | \(-0.234613\pi\) | ||||
0.740449 | + | 0.672112i | \(0.234613\pi\) | |||||||
\(692\) | − | 22.7846i | − | 0.866141i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5359 | 0.703613 | ||||||||
\(695\) | −9.79796 | − | 12.0000i | −0.371658 | − | 0.455186i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.960947i | − | 0.0363985i | ||||||
\(698\) | 4.14359i | 0.156837i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.9282 | − | 3.86370i | −0.715419 | − | 0.146034i | ||||
\(701\) | 7.52433 | 0.284190 | 0.142095 | − | 0.989853i | \(-0.454616\pi\) | ||||
0.142095 | + | 0.989853i | \(0.454616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.79315i | 0.0676300i | ||||||||
\(704\) | 1.03528 | 0.0390184 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.3205 | −0.802408 | ||||||||
\(707\) | − | 40.7846i | − | 1.53386i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.8564 | 0.445277 | 0.222638 | − | 0.974901i | \(-0.428533\pi\) | ||||
0.222638 | + | 0.974901i | \(0.428533\pi\) | |||||||
\(710\) | −7.17260 | + | 5.85641i | −0.269183 | + | 0.219787i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 3.86370i | − | 0.144798i | ||||||
\(713\) | 59.7128i | 2.23626i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.92820 | + | 5.65685i | −0.259100 | + | 0.211554i | ||||
\(716\) | 16.7675 | 0.626631 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 34.7733i | − | 1.29773i | ||||||
\(719\) | 46.6418 | 1.73945 | 0.869724 | − | 0.493539i | \(-0.164297\pi\) | ||||
0.869724 | + | 0.493539i | \(0.164297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9282 | 0.704923 | ||||||||
\(722\) | − | 1.00000i | − | 0.0372161i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.8564 | −0.737958 | ||||||||
\(725\) | −4.62158 | + | 22.6410i | −0.171641 | + | 0.840866i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.1774i | 0.562899i | 0.959576 | + | 0.281450i | \(0.0908152\pi\) | ||||
−0.959576 | + | 0.281450i | \(0.909185\pi\) | |||||||
\(728\) | − | 14.9282i | − | 0.553276i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.07180 | − | 6.21166i | −0.187716 | − | 0.229904i | ||||
\(731\) | 3.58630 | 0.132644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.8695i | − | 0.807770i | −0.914810 | − | 0.403885i | \(-0.867660\pi\) | ||
0.914810 | − | 0.403885i | \(-0.132340\pi\) | |||||||
\(734\) | 5.37945 | 0.198559 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.46410 | −0.201409 | ||||||||
\(737\) | 13.8564i | 0.510407i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.7128 | −0.872290 | −0.436145 | − | 0.899876i | \(-0.643657\pi\) | ||||
−0.436145 | + | 0.899876i | \(0.643657\pi\) | |||||||
\(740\) | 3.10583 | − | 2.53590i | 0.114173 | − | 0.0932215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 23.1822i | 0.851046i | ||||||||
\(743\) | 34.6410i | 1.27086i | 0.772160 | + | 0.635428i | \(0.219176\pi\) | ||||
−0.772160 | + | 0.635428i | \(0.780824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.7846 | + | 35.2538i | 1.05459 | + | 1.29160i | ||||
\(746\) | −24.9754 | −0.914413 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.554803i | 0.0202856i | ||||||||
\(749\) | −11.3137 | −0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.85641 | 0.213703 | 0.106852 | − | 0.994275i | \(-0.465923\pi\) | ||||
0.106852 | + | 0.994275i | \(0.465923\pi\) | |||||||
\(752\) | 2.53590i | 0.0924747i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.8564 | −0.650292 | ||||||||
\(755\) | 8.28221 | + | 10.1436i | 0.301420 | + | 0.369163i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 40.3559i | − | 1.46676i | −0.679820 | − | 0.733379i | \(-0.737942\pi\) | ||
0.679820 | − | 0.733379i | \(-0.262058\pi\) | |||||||
\(758\) | − | 35.7128i | − | 1.29715i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.73205 | + | 1.41421i | −0.0628281 | + | 0.0512989i | ||||
\(761\) | −23.1822 | −0.840355 | −0.420177 | − | 0.907442i | \(-0.638032\pi\) | ||||
−0.420177 | + | 0.907442i | \(0.638032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.4959i | 1.24884i | ||||||||
\(764\) | −17.2480 | −0.624009 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.9282 | 0.828430 | ||||||||
\(767\) | − | 26.9282i | − | 0.972321i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.8564 | −1.29302 | −0.646508 | − | 0.762908i | \(-0.723771\pi\) | ||||
−0.646508 | + | 0.762908i | \(0.723771\pi\) | |||||||
\(770\) | 5.65685 | + | 6.92820i | 0.203859 | + | 0.249675i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 8.76268i | − | 0.315376i | ||||||
\(773\) | 7.85641i | 0.282575i | 0.989969 | + | 0.141288i | \(0.0451242\pi\) | ||||
−0.989969 | + | 0.141288i | \(0.954876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9282 | − | 53.5370i | 0.392553 | − | 1.92311i | ||||
\(776\) | 2.55103 | 0.0915765 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.7990i | 0.709828i | ||||||||
\(779\) | −1.79315 | −0.0642463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.28719 | 0.153408 | ||||||||
\(782\) | − | 2.92820i | − | 0.104712i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.92820 | −0.283150 | ||||||||
\(785\) | 24.4949 | − | 20.0000i | 0.874260 | − | 0.713831i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.17260i | − | 0.255676i | −0.991795 | − | 0.127838i | \(-0.959196\pi\) | ||
0.991795 | − | 0.127838i | \(-0.0408037\pi\) | |||||||
\(788\) | − | 23.4641i | − | 0.835874i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.92820 | − | 5.65685i | 0.246494 | − | 0.201262i | ||||
\(791\) | −23.1822 | −0.824265 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.72741i | 0.274408i | ||||||||
\(794\) | −18.2832 | −0.648848 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.0718 | 0.463318 | ||||||||
\(797\) | 40.6410i | 1.43958i | 0.694193 | + | 0.719789i | \(0.255762\pi\) | ||||
−0.694193 | + | 0.719789i | \(0.744238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.35898 | −0.0480774 | ||||||||
\(800\) | 4.89898 | + | 1.00000i | 0.173205 | + | 0.0353553i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.52056i | 0.336183i | ||||||||
\(803\) | 3.71281i | 0.131022i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.8564 | − | 36.5665i | −1.05230 | − | 1.28880i | ||||
\(806\) | 42.2233 | 1.48725 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.5558i | 0.371353i | ||||||||
\(809\) | 44.8487 | 1.57680 | 0.788398 | − | 0.615166i | \(-0.210911\pi\) | ||||
0.788398 | + | 0.615166i | \(0.210911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.4974 | −1.42206 | −0.711028 | − | 0.703163i | \(-0.751770\pi\) | ||||
−0.711028 | + | 0.703163i | \(0.751770\pi\) | |||||||
\(812\) | 17.8564i | 0.626637i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.85641 | −0.0650670 | ||||||||
\(815\) | −40.9850 | + | 33.4641i | −1.43564 | + | 1.17220i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.69213i | − | 0.234128i | ||||||
\(818\) | − | 20.9282i | − | 0.731737i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.53590 | + | 3.10583i | 0.0885574 | + | 0.108460i | ||||
\(821\) | 7.93048 | 0.276776 | 0.138388 | − | 0.990378i | \(-0.455808\pi\) | ||||
0.138388 | + | 0.990378i | \(0.455808\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 47.1966i | − | 1.64517i | −0.568641 | − | 0.822586i | \(-0.692531\pi\) | ||
0.568641 | − | 0.822586i | \(-0.307469\pi\) | |||||||
\(824\) | −4.89898 | −0.170664 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −26.9282 | −0.936952 | ||||||||
\(827\) | 6.92820i | 0.240917i | 0.992718 | + | 0.120459i | \(0.0384365\pi\) | ||||
−0.992718 | + | 0.120459i | \(0.961563\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.7846 | −0.513491 | −0.256745 | − | 0.966479i | \(-0.582650\pi\) | ||||
−0.256745 | + | 0.966479i | \(0.582650\pi\) | |||||||
\(830\) | −23.1822 | − | 28.3923i | −0.804667 | − | 0.985511i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.86370i | 0.133950i | ||||||||
\(833\) | − | 4.24871i | − | 0.147209i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.9282 | + | 15.4548i | −0.655037 | + | 0.534836i | ||||
\(836\) | 1.03528 | 0.0358058 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 29.3195i | − | 1.01283i | ||||||
\(839\) | −28.2843 | −0.976481 | −0.488241 | − | 0.872709i | \(-0.662361\pi\) | ||||
−0.488241 | + | 0.872709i | \(0.662361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.64102 | −0.263483 | ||||||||
\(842\) | − | 29.7128i | − | 1.02397i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.8564 | 0.614643 | ||||||||
\(845\) | −2.72689 | − | 3.33975i | −0.0938079 | − | 0.114891i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.3596i | 1.31805i | ||||||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.535898 | + | 2.62536i | −0.0183812 | + | 0.0900489i | ||||
\(851\) | 9.79796 | 0.335870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 14.6969i | − | 0.503214i | −0.967830 | − | 0.251607i | \(-0.919041\pi\) | ||
0.967830 | − | 0.251607i | \(-0.0809590\pi\) | |||||||
\(854\) | 7.72741 | 0.264426 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.92820 | 0.100084 | ||||||||
\(857\) | 16.6410i | 0.568446i | 0.958758 | + | 0.284223i | \(0.0917357\pi\) | ||||
−0.958758 | + | 0.284223i | \(0.908264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.78461 | 0.163249 | 0.0816244 | − | 0.996663i | \(-0.473989\pi\) | ||||
0.0816244 | + | 0.996663i | \(0.473989\pi\) | |||||||
\(860\) | −11.5911 | + | 9.46410i | −0.395254 | + | 0.322723i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 26.2137i | − | 0.892843i | ||||||
\(863\) | − | 20.7846i | − | 0.707516i | −0.935337 | − | 0.353758i | \(-0.884904\pi\) | ||
0.935337 | − | 0.353758i | \(-0.115096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.4641 | + | 32.2223i | −1.34182 | + | 1.09559i | ||||
\(866\) | −10.8332 | −0.368128 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 42.2233i | − | 1.43315i | ||||||
\(869\) | −4.14110 | −0.140477 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.7128 | −1.75222 | ||||||||
\(872\) | − | 8.92820i | − | 0.302347i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.46410 | −0.184826 | ||||||||
\(875\) | 20.0764 | + | 38.2487i | 0.678706 | + | 1.29304i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 29.6713i | − | 1.00193i | −0.865468 | − | 0.500964i | \(-0.832979\pi\) | ||
0.865468 | − | 0.500964i | \(-0.167021\pi\) | |||||||
\(878\) | 20.0000i | 0.674967i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.46410 | − | 1.79315i | −0.0493549 | − | 0.0604471i | ||||
\(881\) | 38.6370 | 1.30171 | 0.650857 | − | 0.759200i | \(-0.274410\pi\) | ||||
0.650857 | + | 0.759200i | \(0.274410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 49.4703i | − | 1.66481i | −0.554170 | − | 0.832404i | \(-0.686964\pi\) | ||
0.554170 | − | 0.832404i | \(-0.313036\pi\) | |||||||
\(884\) | −2.07055 | −0.0696402 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.3923 | −0.550710 | ||||||||
\(887\) | − | 15.7128i | − | 0.527585i | −0.964580 | − | 0.263792i | \(-0.915027\pi\) | ||
0.964580 | − | 0.263792i | \(-0.0849734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.7846 | −1.09956 | ||||||||
\(890\) | −6.69213 | + | 5.46410i | −0.224321 | + | 0.183157i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.5558i | 0.353435i | ||||||||
\(893\) | 2.53590i | 0.0848606i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.7128 | − | 29.0421i | −0.792632 | − | 0.970772i | ||||
\(896\) | 3.86370 | 0.129077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.4302i | 1.34917i | ||||||||
\(899\) | −50.5055 | −1.68445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.21539 | 0.107120 | ||||||||
\(902\) | − | 1.85641i | − | 0.0618116i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 28.0812 | + | 34.3923i | 0.933451 | + | 1.14324i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 36.5665i | − | 1.21417i | −0.794637 | − | 0.607085i | \(-0.792339\pi\) | ||
0.794637 | − | 0.607085i | \(-0.207661\pi\) | |||||||
\(908\) | 1.85641i | 0.0616070i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −25.8564 | + | 21.1117i | −0.857132 | + | 0.699845i | ||||
\(911\) | −45.2548 | −1.49936 | −0.749680 | − | 0.661801i | \(-0.769792\pi\) | ||||
−0.749680 | + | 0.661801i | \(0.769792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.9706i | 0.561644i | ||||||||
\(914\) | 33.9411 | 1.12267 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.85641 | −0.127419 | ||||||||
\(917\) | 12.0000i | 0.396275i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7128 | −0.914161 | −0.457081 | − | 0.889425i | \(-0.651105\pi\) | ||||
−0.457081 | + | 0.889425i | \(0.651105\pi\) | |||||||
\(920\) | 7.72741 | + | 9.46410i | 0.254765 | + | 0.312022i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.5264i | 0.906534i | ||||||||
\(923\) | 16.0000i | 0.526646i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.78461 | − | 1.79315i | −0.288836 | − | 0.0589584i | ||||
\(926\) | 19.8733 | 0.653078 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 4.62158i | − | 0.151711i | ||||||
\(929\) | 11.3137 | 0.371191 | 0.185595 | − | 0.982626i | \(-0.440579\pi\) | ||||
0.185595 | + | 0.982626i | \(0.440579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.92820 | −0.259836 | ||||||||
\(932\) | 12.5359i | 0.410627i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.53590 | 0.0829771 | ||||||||
\(935\) | 0.960947 | − | 0.784610i | 0.0314263 | − | 0.0256595i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.5569i | − | 0.671563i | −0.941940 | − | 0.335782i | \(-0.891000\pi\) | ||
0.941940 | − | 0.335782i | \(-0.109000\pi\) | |||||||
\(938\) | 51.7128i | 1.68848i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.39230 | − | 3.58630i | 0.143261 | − | 0.116972i | ||||
\(941\) | −15.9353 | −0.519475 | −0.259738 | − | 0.965679i | \(-0.583636\pi\) | ||||
−0.259738 | + | 0.965679i | \(0.583636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.79796i | 0.319065i | ||||||||
\(944\) | 6.96953 | 0.226839 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.92820 | 0.225255 | ||||||||
\(947\) | − | 25.1769i | − | 0.818140i | −0.912503 | − | 0.409070i | \(-0.865853\pi\) | ||
0.912503 | − | 0.409070i | \(-0.134147\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.8564 | −0.449798 | ||||||||
\(950\) | 4.89898 | + | 1.00000i | 0.158944 | + | 0.0324443i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.07055i | 0.0671070i | ||||||||
\(953\) | − | 30.0000i | − | 0.971795i | −0.874016 | − | 0.485898i | \(-0.838493\pi\) | ||
0.874016 | − | 0.485898i | \(-0.161507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.3923 | + | 29.8744i | 0.789316 | + | 0.966711i | ||||
\(956\) | −13.1069 | −0.423906 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 16.6932i | − | 0.539332i | ||||||
\(959\) | 2.07055 | 0.0668616 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88.4256 | 2.85244 | ||||||||
\(962\) | − | 6.92820i | − | 0.223374i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | −15.1774 | + | 12.3923i | −0.488578 | + | 0.398922i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.2480i | − | 0.554657i | −0.960775 | − | 0.277329i | \(-0.910551\pi\) | ||
0.960775 | − | 0.277329i | \(-0.0894491\pi\) | |||||||
\(968\) | − | 9.92820i | − | 0.319105i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.60770 | − | 4.41851i | −0.115836 | − | 0.141870i | ||||
\(971\) | −54.2949 | −1.74241 | −0.871203 | − | 0.490922i | \(-0.836660\pi\) | ||||
−0.871203 | + | 0.490922i | \(0.836660\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.7685i | 0.858159i | ||||||||
\(974\) | 3.38323 | 0.108406 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | 5.71281i | 0.182769i | 0.995816 | + | 0.0913845i | \(0.0291292\pi\) | ||||
−0.995816 | + | 0.0913845i | \(0.970871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.00000 | 0.127841 | ||||||||
\(980\) | 11.2122 | + | 13.7321i | 0.358160 | + | 0.438654i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.5606i | 0.592294i | ||||||||
\(983\) | − | 7.21539i | − | 0.230135i | −0.993358 | − | 0.115068i | \(-0.963292\pi\) | ||
0.993358 | − | 0.115068i | \(-0.0367085\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.6410 | + | 33.1833i | −1.29493 | + | 1.05731i | ||||
\(986\) | 2.47670 | 0.0788741 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.86370i | 0.122921i | ||||||||
\(989\) | −36.5665 | −1.16275 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.7846 | −0.660245 | −0.330122 | − | 0.943938i | \(-0.607090\pi\) | ||||
−0.330122 | + | 0.943938i | \(0.607090\pi\) | |||||||
\(992\) | 10.9282i | 0.346971i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.0000 | 0.507489 | ||||||||
\(995\) | −18.4863 | − | 22.6410i | −0.586055 | − | 0.717768i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 18.2832i | − | 0.579036i | −0.957173 | − | 0.289518i | \(-0.906505\pi\) | ||
0.957173 | − | 0.289518i | \(-0.0934950\pi\) | |||||||
\(998\) | 25.8564i | 0.818470i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1710.2.d.g.1369.4 | yes | 8 | |
3.2 | odd | 2 | inner | 1710.2.d.g.1369.5 | yes | 8 | |
5.2 | odd | 4 | 8550.2.a.cv.1.4 | 4 | |||
5.3 | odd | 4 | 8550.2.a.cu.1.1 | 4 | |||
5.4 | even | 2 | inner | 1710.2.d.g.1369.7 | yes | 8 | |
15.2 | even | 4 | 8550.2.a.cu.1.4 | 4 | |||
15.8 | even | 4 | 8550.2.a.cv.1.1 | 4 | |||
15.14 | odd | 2 | inner | 1710.2.d.g.1369.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1710.2.d.g.1369.2 | ✓ | 8 | 15.14 | odd | 2 | inner | |
1710.2.d.g.1369.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1710.2.d.g.1369.5 | yes | 8 | 3.2 | odd | 2 | inner | |
1710.2.d.g.1369.7 | yes | 8 | 5.4 | even | 2 | inner | |
8550.2.a.cu.1.1 | 4 | 5.3 | odd | 4 | |||
8550.2.a.cu.1.4 | 4 | 15.2 | even | 4 | |||
8550.2.a.cv.1.1 | 4 | 15.8 | even | 4 | |||
8550.2.a.cv.1.4 | 4 | 5.2 | odd | 4 |