Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(353,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.m (of order \(6\), degree \(2\), 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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.19 | ||
Character | \(\chi\) | \(=\) | 684.353 |
Dual form | 684.3.m.a.653.19 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.358884 | − | 2.97846i | −0.119628 | − | 0.992819i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.408400i | 0.0816799i | 0.999166 | + | 0.0408400i | \(0.0130034\pi\) | ||||
−0.999166 | + | 0.0408400i | \(0.986997\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.674294 | + | 1.16791i | −0.0963277 | + | 0.166844i | −0.910162 | − | 0.414253i | \(-0.864043\pi\) |
0.813834 | + | 0.581097i | \(0.197376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.74240 | + | 2.13784i | −0.971378 | + | 0.237538i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.2588 | + | 9.38701i | 1.47807 | + | 0.853365i | 0.999693 | − | 0.0247891i | \(-0.00789141\pi\) |
0.478378 | + | 0.878154i | \(0.341225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.16100 | − | 5.47501i | 0.243154 | − | 0.421155i | −0.718457 | − | 0.695571i | \(-0.755151\pi\) |
0.961611 | + | 0.274416i | \(0.0884847\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.21640 | − | 0.146568i | 0.0810934 | − | 0.00977120i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.03860 | + | 0.599639i | 0.0610944 | + | 0.0352729i | 0.530236 | − | 0.847850i | \(-0.322103\pi\) |
−0.469142 | + | 0.883123i | \(0.655437\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34979 | − | 18.4954i | −0.228936 | − | 0.973441i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.72057 | + | 1.58921i | 0.177170 | + | 0.0756767i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 15.2278 | + | 8.79180i | 0.662080 | + | 0.382252i | 0.793069 | − | 0.609132i | \(-0.208482\pi\) |
−0.130989 | + | 0.991384i | \(0.541815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.8332 | 0.993328 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.50497 | + | 25.2716i | 0.352036 | + | 0.935986i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 18.6058i | − | 0.641581i | −0.947150 | − | 0.320790i | \(-0.896052\pi\) | ||
0.947150 | − | 0.320790i | \(-0.103948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.2202 | + | 28.0943i | 0.523234 | + | 0.906267i | 0.999634 | + | 0.0270391i | \(0.00860787\pi\) |
−0.476401 | + | 0.879228i | \(0.658059\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 22.1238 | − | 51.7949i | 0.670418 | − | 1.56954i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.476974 | − | 0.275381i | −0.0136278 | − | 0.00786804i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.2245 | 0.492555 | 0.246278 | − | 0.969199i | \(-0.420793\pi\) | ||||
0.246278 | + | 0.969199i | \(0.420793\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −17.4415 | − | 7.45001i | −0.447218 | − | 0.191026i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 38.8063i | − | 0.946495i | −0.880929 | − | 0.473248i | \(-0.843082\pi\) | ||
0.880929 | − | 0.473248i | \(-0.156918\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33.5545 | − | 58.1180i | −0.780337 | − | 1.35158i | −0.931746 | − | 0.363111i | \(-0.881714\pi\) |
0.151409 | − | 0.988471i | \(-0.451619\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.873093 | − | 3.57039i | −0.0194021 | − | 0.0793421i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 72.1364i | − | 1.53482i | −0.641158 | − | 0.767409i | \(-0.721546\pi\) | ||
0.641158 | − | 0.767409i | \(-0.278454\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.5907 | + | 40.8602i | 0.481442 | + | 0.833882i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.41326 | − | 3.30864i | 0.0277110 | − | 0.0648753i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.40004 | − | 3.11771i | 0.101887 | − | 0.0588248i | −0.448190 | − | 0.893938i | \(-0.647931\pi\) |
0.550078 | + | 0.835113i | \(0.314598\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.83365 | + | 6.64008i | −0.0697028 | + | 0.120729i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −53.5266 | + | 19.5934i | −0.939064 | + | 0.343743i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 46.7552i | − | 0.792461i | −0.918151 | − | 0.396230i | \(-0.870318\pi\) | ||
0.918151 | − | 0.396230i | \(-0.129682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16.6456 | 0.272878 | 0.136439 | − | 0.990648i | \(-0.456434\pi\) | ||||
0.136439 | + | 0.990648i | \(0.456434\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.39814 | − | 11.6519i | 0.0539388 | − | 0.184951i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.23599 | + | 1.29095i | 0.0343999 | + | 0.0198608i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −27.5634 | + | 47.7412i | −0.411394 | + | 0.712556i | −0.995042 | − | 0.0994509i | \(-0.968291\pi\) |
0.583648 | + | 0.812007i | \(0.301625\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.7210 | − | 48.5107i | 0.300304 | − | 0.703054i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48.7622 | + | 28.1528i | 0.686791 | + | 0.396519i | 0.802409 | − | 0.596775i | \(-0.203551\pi\) |
−0.115618 | + | 0.993294i | \(0.536885\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −27.9801 | + | 48.4629i | −0.383289 | + | 0.663875i | −0.991530 | − | 0.129877i | \(-0.958542\pi\) |
0.608242 | + | 0.793752i | \(0.291875\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.91224 | − | 73.9646i | −0.118830 | − | 0.986195i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.9264 | + | 12.6592i | −0.284758 | + | 0.164405i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −39.1200 | − | 67.7578i | −0.495189 | − | 0.857693i | 0.504795 | − | 0.863239i | \(-0.331568\pi\) |
−0.999985 | + | 0.00554598i | \(0.998235\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 71.8593 | − | 37.3797i | 0.887152 | − | 0.461478i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −57.7054 | − | 33.3162i | −0.695246 | − | 0.401400i | 0.110329 | − | 0.993895i | \(-0.464810\pi\) |
−0.805574 | + | 0.592495i | \(0.798143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.244892 | + | 0.424166i | −0.00288108 | + | 0.00499018i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −55.4167 | + | 6.67734i | −0.636973 | + | 0.0767510i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 130.049 | − | 75.0837i | 1.46122 | − | 0.843637i | 0.462154 | − | 0.886800i | \(-0.347077\pi\) |
0.999068 | + | 0.0431625i | \(0.0137433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.26289 | + | 7.38353i | 0.0468449 | + | 0.0811377i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 77.8564 | − | 58.3939i | 0.837166 | − | 0.627891i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.55351 | − | 1.77645i | 0.0795106 | − | 0.0186995i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 37.2866 | + | 64.5822i | 0.384398 | + | 0.665796i | 0.991685 | − | 0.128686i | \(-0.0410758\pi\) |
−0.607288 | + | 0.794482i | \(0.707742\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −162.209 | − | 47.3064i | −1.63847 | − | 0.477842i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 9.68089i | − | 0.0958504i | −0.998851 | − | 0.0479252i | \(-0.984739\pi\) | ||
0.998851 | − | 0.0479252i | \(-0.0152609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −61.7097 | − | 106.884i | −0.599123 | − | 1.03771i | −0.992951 | − | 0.118527i | \(-0.962183\pi\) |
0.393828 | − | 0.919184i | \(-0.371151\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.649033 | + | 1.51948i | −0.00618126 | + | 0.0144712i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 4.24390i | − | 0.0396626i | −0.999803 | − | 0.0198313i | \(-0.993687\pi\) | ||
0.999803 | − | 0.0198313i | \(-0.00631292\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 55.1273 | − | 95.4833i | 0.505755 | − | 0.875993i | −0.494223 | − | 0.869335i | \(-0.664547\pi\) |
0.999978 | − | 0.00665808i | \(-0.00211935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.54050 | − | 54.2810i | −0.0589234 | − | 0.489018i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 182.752 | − | 105.512i | 1.61727 | − | 0.933732i | 0.629649 | − | 0.776880i | \(-0.283199\pi\) |
0.987622 | − | 0.156852i | \(-0.0501346\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.59057 | + | 6.21905i | −0.0312223 | + | 0.0540787i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.9300 | + | 54.6225i | −0.136154 | + | 0.466859i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.40065 | + | 0.808665i | −0.0117702 | + | 0.00679551i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 115.732 | + | 200.454i | 0.956463 | + | 1.65664i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −115.583 | + | 13.9270i | −0.939698 | + | 0.113227i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.3519i | 0.162815i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 101.232 | + | 175.338i | 0.797099 | + | 1.38062i | 0.921498 | + | 0.388383i | \(0.126966\pi\) |
−0.124399 | + | 0.992232i | \(0.539700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −161.060 | + | 120.798i | −1.24853 | + | 0.936420i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 11.2194i | − | 0.0856439i | −0.999083 | − | 0.0428220i | \(-0.986365\pi\) | ||
0.999083 | − | 0.0428220i | \(-0.0136348\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.5340 | + | 7.39116i | 0.184466 | + | 0.0555726i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.3209 | + | 3.88183i | −0.0764513 | + | 0.0287543i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 28.5762i | 0.208585i | 0.994547 | + | 0.104293i | \(0.0332579\pi\) | ||||
−0.994547 | + | 0.104293i | \(0.966742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.42714 | + | 9.40008i | −0.0390442 | + | 0.0676265i | −0.884887 | − | 0.465806i | \(-0.845765\pi\) |
0.845843 | + | 0.533432i | \(0.179098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −214.855 | + | 25.8886i | −1.52380 | + | 0.183607i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 102.788 | − | 59.3447i | 0.718797 | − | 0.414998i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.59862 | 0.0524043 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 113.234 | − | 84.9278i | 0.770300 | − | 0.577740i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 213.661i | 1.43397i | 0.697090 | + | 0.716984i | \(0.254478\pi\) | ||||
−0.697090 | + | 0.716984i | \(0.745522\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −39.8969 | + | 69.1035i | −0.264218 | + | 0.457639i | −0.967358 | − | 0.253412i | \(-0.918447\pi\) |
0.703140 | + | 0.711051i | \(0.251781\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.3618 | − | 3.02191i | −0.0677244 | − | 0.0197511i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4737 | + | 6.62434i | −0.0740239 | + | 0.0427377i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −161.183 | −1.02665 | −0.513323 | − | 0.858196i | \(-0.671586\pi\) | ||||
−0.513323 | + | 0.858196i | \(0.671586\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.2240 | − | 14.9649i | −0.0705909 | − | 0.0941187i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.5361 | + | 11.8565i | −0.127553 | + | 0.0736429i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 92.2041 | 0.565670 | 0.282835 | − | 0.959169i | \(-0.408725\pi\) | ||||
0.282835 | + | 0.959169i | \(0.408725\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.1530 | + | 9.03535i | 0.128200 | + | 0.0547597i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 215.048 | + | 124.158i | 1.28771 | + | 0.743462i | 0.978246 | − | 0.207448i | \(-0.0665156\pi\) |
0.309468 | + | 0.950910i | \(0.399849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 64.5162 | + | 111.745i | 0.381752 | + | 0.661215i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 77.5678 | + | 152.395i | 0.453613 | + | 0.891199i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 91.7749 | − | 52.9863i | 0.530491 | − | 0.306279i | −0.210725 | − | 0.977545i | \(-0.567583\pi\) |
0.741216 | + | 0.671266i | \(0.234249\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.7449 | + | 29.0030i | −0.0956850 | + | 0.165731i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −139.258 | + | 16.7797i | −0.786770 | + | 0.0948005i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 15.0274i | − | 0.0839519i | −0.999119 | − | 0.0419759i | \(-0.986635\pi\) | ||
0.999119 | − | 0.0419759i | \(-0.0133653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 122.841 | + | 212.766i | 0.678678 | + | 1.17551i | 0.975379 | + | 0.220535i | \(0.0707802\pi\) |
−0.296701 | + | 0.954970i | \(0.595886\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.97383 | − | 49.5781i | −0.0326439 | − | 0.270919i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.44290i | 0.0402319i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.2576 | + | 19.4988i | 0.0602012 | + | 0.104272i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −35.9242 | − | 5.93954i | −0.190075 | − | 0.0314261i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −170.032 | − | 98.1680i | −0.890220 | − | 0.513969i | −0.0162053 | − | 0.999869i | \(-0.505159\pi\) |
−0.874014 | + | 0.485900i | \(0.838492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −244.586 | −1.26729 | −0.633643 | − | 0.773625i | \(-0.718441\pi\) | ||||
−0.633643 | + | 0.773625i | \(0.718441\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.04258 | − | 7.12311i | 0.0156030 | − | 0.0365288i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 63.2665i | 0.321150i | 0.987024 | + | 0.160575i | \(0.0513348\pi\) | ||||
−0.987024 | + | 0.160575i | \(0.948665\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 78.9137 | + | 136.683i | 0.396551 | + | 0.686847i | 0.993298 | − | 0.115583i | \(-0.0368736\pi\) |
−0.596747 | + | 0.802430i | \(0.703540\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 152.087 | + | 64.9629i | 0.756653 | + | 0.323198i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.7300 | + | 12.5458i | 0.107044 | + | 0.0618020i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.8485 | 0.0773097 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −151.923 | − | 44.3068i | −0.733930 | − | 0.214042i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 102.894 | − | 341.544i | 0.492317 | − | 1.63418i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −255.404 | −1.21045 | −0.605223 | − | 0.796056i | \(-0.706916\pi\) | ||||
−0.605223 | + | 0.796056i | \(0.706916\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 66.3521 | − | 155.340i | 0.311512 | − | 0.729294i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.7354 | − | 13.7036i | 0.110397 | − | 0.0637378i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −43.7488 | −0.201608 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 154.386 | + | 65.9449i | 0.704960 | + | 0.301118i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.56606 | − | 3.79091i | 0.0297107 | − | 0.0171535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 45.1583 | + | 78.2165i | 0.202504 | + | 0.350746i | 0.949334 | − | 0.314268i | \(-0.101759\pi\) |
−0.746831 | + | 0.665014i | \(0.768426\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −217.102 | + | 53.0894i | −0.964898 | + | 0.235953i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −380.442 | − | 219.649i | −1.67596 | − | 0.967615i | −0.964195 | − | 0.265195i | \(-0.914564\pi\) |
−0.711763 | − | 0.702420i | \(-0.752103\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 187.314 | + | 324.438i | 0.817967 | + | 1.41676i | 0.907178 | + | 0.420747i | \(0.138232\pi\) |
−0.0892114 | + | 0.996013i | \(0.528435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 45.5739 | + | 60.7636i | 0.197290 | + | 0.263046i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3281 | + | 11.7364i | 0.0872451 | + | 0.0503710i | 0.542988 | − | 0.839741i | \(-0.317293\pi\) |
−0.455743 | + | 0.890112i | \(0.650626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.4605 | 0.125364 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −187.774 | + | 140.834i | −0.792295 | + | 0.594237i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −98.5086 | + | 56.8740i | −0.412170 | + | 0.237966i | −0.691722 | − | 0.722164i | \(-0.743148\pi\) |
0.279552 | + | 0.960131i | \(0.409814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −150.618 | −0.624973 | −0.312486 | − | 0.949922i | \(-0.601162\pi\) | ||||
−0.312486 | + | 0.949922i | \(0.601162\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −137.123 | − | 200.615i | −0.564292 | − | 0.825575i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.6873 | + | 9.63441i | −0.0681114 | + | 0.0393241i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −115.012 | − | 34.6488i | −0.465636 | − | 0.140278i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −78.5214 | + | 183.830i | −0.315347 | + | 0.738272i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 291.490 | − | 168.292i | 1.16131 | − | 0.670485i | 0.209695 | − | 0.977767i | \(-0.432753\pi\) |
0.951619 | + | 0.307282i | \(0.0994195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 165.057 | + | 285.888i | 0.652401 | + | 1.12999i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.35125 | + | 0.577174i | 0.00529901 | + | 0.00226343i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −285.715 | − | 164.958i | −1.11173 | − | 0.641859i | −0.172455 | − | 0.985017i | \(-0.555170\pi\) |
−0.939278 | + | 0.343158i | \(0.888503\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2887 | + | 21.2846i | −0.0474467 | + | 0.0821801i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 39.7763 | + | 162.660i | 0.152400 | + | 0.623217i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −415.338 | + | 239.796i | −1.57923 | + | 0.911770i | −0.584265 | + | 0.811563i | \(0.698617\pi\) |
−0.994967 | + | 0.100207i | \(0.968049\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.27327 | + | 2.20537i | 0.00480480 | + | 0.00832216i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −270.306 | − | 360.398i | −1.01238 | − | 1.34981i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 76.7941 | + | 44.3371i | 0.285480 | + | 0.164822i | 0.635902 | − | 0.771770i | \(-0.280628\pi\) |
−0.350422 | + | 0.936592i | \(0.613962\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −245.103 | + | 424.531i | −0.904439 | + | 1.56654i | −0.0827714 | + | 0.996569i | \(0.526377\pi\) |
−0.821668 | + | 0.569966i | \(0.806956\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.4617 | − | 15.3467i | 0.0749511 | − | 0.0562148i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 403.758 | + | 233.110i | 1.46821 | + | 0.847671i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −48.2162 | + | 83.5130i | −0.174066 | + | 0.301491i | −0.939838 | − | 0.341622i | \(-0.889024\pi\) |
0.765772 | + | 0.643112i | \(0.222357\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −201.865 | − | 210.935i | −0.723531 | − | 0.756041i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 489.608i | 1.74238i | 0.490947 | + | 0.871189i | \(0.336651\pi\) | ||||
−0.490947 | + | 0.871189i | \(0.663349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −154.090 | −0.544486 | −0.272243 | − | 0.962229i | \(-0.587765\pi\) | ||||
−0.272243 | + | 0.962229i | \(0.587765\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.00192 | − | 21.8603i | −0.0280769 | − | 0.0767027i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 45.3223 | + | 26.1669i | 0.157918 | + | 0.0911737i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −143.781 | − | 249.036i | −0.497512 | − | 0.861715i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 178.974 | − | 134.234i | 0.615030 | − | 0.461285i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 407.976 | − | 235.545i | 1.39241 | − | 0.803907i | 0.398827 | − | 0.917026i | \(-0.369417\pi\) |
0.993581 | + | 0.113119i | \(0.0360840\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.0948 | 0.0647281 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −82.6858 | + | 500.109i | −0.278404 | + | 1.68387i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 96.2705 | − | 55.5818i | 0.321975 | − | 0.185892i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 90.5023 | 0.300672 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.8341 | + | 3.47432i | −0.0951621 | + | 0.0114664i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.79804i | 0.0222887i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.2167 | − | 38.4804i | 0.0723670 | − | 0.125343i | −0.827571 | − | 0.561361i | \(-0.810278\pi\) |
0.899938 | + | 0.436017i | \(0.143611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −296.204 | + | 222.159i | −0.958587 | + | 0.718960i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 198.767 | − | 114.758i | 0.639122 | − | 0.368997i | −0.145155 | − | 0.989409i | \(-0.546368\pi\) |
0.784276 | + | 0.620412i | \(0.213035\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.3554 | 0.0873975 | 0.0436988 | − | 0.999045i | \(-0.486086\pi\) | ||||
0.0436988 | + | 0.999045i | \(0.486086\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.75863 | + | 1.38780i | 0.0151067 | + | 0.00440571i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 476.138i | − | 1.50201i | −0.660294 | − | 0.751007i | \(-0.729568\pi\) | ||
0.660294 | − | 0.751007i | \(-0.270432\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 174.653 | − | 302.508i | 0.547502 | − | 0.948302i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6403 | + | 1.52307i | −0.0393778 | + | 0.00474476i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.57284 | − | 21.8177i | 0.0203493 | − | 0.0675470i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 78.4978 | − | 135.962i | 0.241532 | − | 0.418345i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −304.177 | − | 129.927i | −0.930205 | − | 0.397330i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 84.2490 | + | 48.6412i | 0.256076 | + | 0.147845i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 243.510 | − | 421.772i | 0.735680 | − | 1.27424i | −0.218744 | − | 0.975782i | \(-0.570196\pi\) |
0.954424 | − | 0.298453i | \(-0.0964706\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −159.326 | + | 38.9612i | −0.478457 | + | 0.117000i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.4975 | − | 11.2569i | −0.0582015 | − | 0.0336026i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 228.628 | 0.678420 | 0.339210 | − | 0.940711i | \(-0.389840\pi\) | ||||
0.339210 | + | 0.940711i | \(0.389840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −379.849 | − | 506.451i | −1.12050 | − | 1.49396i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 609.039i | 1.78604i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −129.709 | −0.378160 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.8118 | + | 8.46244i | 0.0574254 | + | 0.0245288i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 146.453i | − | 0.422056i | −0.977480 | − | 0.211028i | \(-0.932319\pi\) | ||
0.977480 | − | 0.211028i | \(-0.0676811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 204.639 | − | 354.445i | 0.586358 | − | 1.01560i | −0.408347 | − | 0.912827i | \(-0.633895\pi\) |
0.994705 | − | 0.102775i | \(-0.0327720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 168.408 | + | 27.8438i | 0.479794 | + | 0.0793270i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −297.654 | − | 171.851i | −0.843213 | − | 0.486829i | 0.0151420 | − | 0.999885i | \(-0.495180\pi\) |
−0.858355 | + | 0.513056i | \(0.828513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.4976 | + | 19.9144i | −0.0323876 | + | 0.0560970i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.91124 | + | 3.88156i | 0.00815475 | + | 0.0108727i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 221.301 | + | 127.768i | 0.616438 | + | 0.355900i | 0.775481 | − | 0.631371i | \(-0.217508\pi\) |
−0.159043 | + | 0.987272i | \(0.550841\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −323.159 | + | 160.902i | −0.895176 | + | 0.445712i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 555.508 | − | 416.642i | 1.53033 | − | 1.14777i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.7922 | − | 11.4270i | −0.0542253 | − | 0.0313070i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −435.247 | −1.18596 | −0.592980 | − | 0.805217i | \(-0.702049\pi\) | ||||
−0.592980 | + | 0.805217i | \(0.702049\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 82.9617 | + | 339.260i | 0.224828 | + | 0.919405i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.40902i | 0.0226658i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 240.282 | + | 416.180i | 0.644187 | + | 1.11577i | 0.984489 | + | 0.175449i | \(0.0561376\pi\) |
−0.340301 | + | 0.940316i | \(0.610529\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 60.6171 | − | 7.30396i | 0.161646 | − | 0.0194772i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −101.867 | − | 58.8131i | −0.270205 | − | 0.156003i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −48.0148 | −0.126688 | −0.0633440 | − | 0.997992i | \(-0.520177\pi\) | ||||
−0.0633440 | + | 0.997992i | \(0.520177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 485.907 | − | 364.440i | 1.27535 | − | 0.956535i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.54731i | 0.00926191i | 0.999989 | + | 0.00463096i | \(0.00147408\pi\) | ||||
−0.999989 | + | 0.00463096i | \(0.998526\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.17002 | − | 8.95473i | −0.0134286 | − | 0.0232590i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 417.594 | + | 436.357i | 1.07905 | + | 1.12754i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 380.289i | 0.977608i | 0.872394 | + | 0.488804i | \(0.162567\pi\) | ||||
−0.872394 | + | 0.488804i | \(0.837433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.5438 | + | 18.2624i | 0.0269663 | + | 0.0467069i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.4164 | + | 4.02645i | −0.0850289 | + | 0.0102454i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.6722 | − | 15.9766i | 0.0700563 | − | 0.0404470i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 269.312 | − | 466.462i | 0.678368 | − | 1.17497i | −0.297105 | − | 0.954845i | \(-0.596021\pi\) |
0.975472 | − | 0.220122i | \(-0.0706456\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.2094 | − | 75.7260i | 0.0331062 | − | 0.189790i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 182.689i | − | 0.455583i | −0.973710 | − | 0.227791i | \(-0.926850\pi\) | ||
0.973710 | − | 0.227791i | \(-0.0731505\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 205.089 | 0.508905 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.2659 | + | 29.3473i | 0.0376935 | + | 0.0724625i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 296.309 | + | 171.074i | 0.728032 | + | 0.420329i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −72.2717 | + | 125.178i | −0.176703 | + | 0.306059i | −0.940749 | − | 0.339103i | \(-0.889877\pi\) |
0.764046 | + | 0.645162i | \(0.223210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 85.1130 | − | 10.2555i | 0.207088 | − | 0.0249527i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 54.6059 | + | 31.5267i | 0.132218 | + | 0.0763359i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.6063 | − | 23.5669i | 0.0327863 | − | 0.0567876i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.9454 | + | 12.7910i | 0.0718116 | + | 0.0306738i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −177.986 | + | 102.760i | −0.424787 | + | 0.245251i | −0.697123 | − | 0.716951i | \(-0.745537\pi\) |
0.272336 | + | 0.962202i | \(0.412204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 365.466 | + | 633.006i | 0.868091 | + | 1.50358i | 0.863945 | + | 0.503587i | \(0.167987\pi\) |
0.00414664 | + | 0.999991i | \(0.498680\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 154.216 | + | 630.646i | 0.364577 | + | 1.49089i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.7919 | + | 14.8909i | 0.0606868 | + | 0.0350375i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.2240 | + | 19.4405i | −0.0262857 | + | 0.0455282i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −213.645 | − | 284.852i | −0.498006 | − | 0.663990i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −283.508 | + | 163.683i | −0.657791 | + | 0.379776i | −0.791435 | − | 0.611253i | \(-0.790666\pi\) |
0.133644 | + | 0.991029i | \(0.457332\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.1647 | − | 33.1942i | −0.0442603 | − | 0.0766610i | 0.843047 | − | 0.537841i | \(-0.180760\pi\) |
−0.887307 | + | 0.461179i | \(0.847426\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.72702 | − | 22.6321i | −0.00626902 | − | 0.0520279i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 96.3699 | − | 319.887i | 0.220526 | − | 0.732008i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −259.325 | − | 449.164i | −0.590717 | − | 1.02315i | −0.994136 | − | 0.108137i | \(-0.965511\pi\) |
0.403419 | − | 0.915016i | \(-0.367822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −293.592 | − | 306.783i | −0.665741 | − | 0.695654i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 351.874i | − | 0.794298i | −0.917754 | − | 0.397149i | \(-0.870000\pi\) | ||
0.917754 | − | 0.397149i | \(-0.130000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.6642 | + | 53.1119i | 0.0689082 | + | 0.119353i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 636.381 | − | 76.6796i | 1.42367 | − | 0.171543i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 135.369i | 0.301490i | 0.988573 | + | 0.150745i | \(0.0481673\pi\) | ||||
−0.988573 | + | 0.150745i | \(0.951833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 364.275 | − | 630.943i | 0.807706 | − | 1.39899i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 220.140 | + | 94.0311i | 0.485961 | + | 0.207574i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.01543 | + | 1.74096i | −0.00662732 | + | 0.00382629i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −211.591 | + | 366.486i | −0.463000 | + | 0.801940i | −0.999109 | − | 0.0422092i | \(-0.986560\pi\) |
0.536109 | + | 0.844149i | \(0.319894\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.28194 | + | 31.9468i | −0.0115075 | + | 0.0696008i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8711 | − | 6.85378i | 0.0257507 | − | 0.0148672i | −0.487069 | − | 0.873363i | \(-0.661934\pi\) |
0.512820 | + | 0.858496i | \(0.328601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 284.747 | + | 493.196i | 0.615004 | + | 1.06522i | 0.990384 | + | 0.138348i | \(0.0441791\pi\) |
−0.375379 | + | 0.926871i | \(0.622488\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23.8480 | + | 31.7965i | 0.0512861 | + | 0.0683797i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 253.177i | 0.542135i | 0.962560 | + | 0.271067i | \(0.0873766\pi\) | ||||
−0.962560 | + | 0.271067i | \(0.912623\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.1717 | − | 64.3832i | −0.0792573 | − | 0.137278i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 57.8461 | + | 480.078i | 0.122816 | + | 1.01927i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1259.90i | − | 2.66365i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −108.019 | − | 459.300i | −0.227409 | − | 0.966947i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.5441 | + | 38.8007i | −0.0849982 | + | 0.0813432i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 804.989i | − | 1.68056i | −0.542151 | − | 0.840281i | \(-0.682390\pi\) | ||
0.542151 | − | 0.840281i | \(-0.317610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 57.6078 | − | 99.7796i | 0.119767 | − | 0.207442i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 42.6842 | + | 56.9107i | 0.0883731 | + | 0.117828i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.3754 | + | 15.2278i | −0.0543822 | + | 0.0313976i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 61.4828 | 0.126248 | 0.0631240 | − | 0.998006i | \(-0.479894\pi\) | ||||
0.0631240 | + | 0.998006i | \(0.479894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.0906 | − | 274.626i | −0.0676699 | − | 0.561607i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9649i | 0.0630650i | 0.999503 | + | 0.0315325i | \(0.0100388\pi\) | ||||
−0.999503 | + | 0.0315325i | \(0.989961\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.1568 | − | 19.3241i | 0.0226304 | − | 0.0391970i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.3199 | − | 66.2460i | 0.0390301 | − | 0.133830i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −65.7600 | + | 37.9666i | −0.132314 | + | 0.0763915i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −399.854 | −0.801311 | −0.400656 | − | 0.916229i | \(-0.631218\pi\) | ||||
−0.400656 | + | 0.916229i | \(0.631218\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 292.622 | − | 685.070i | 0.584077 | − | 1.36741i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −687.500 | + | 396.928i | −1.36680 | + | 0.789122i | −0.990518 | − | 0.137384i | \(-0.956131\pi\) |
−0.376281 | + | 0.926506i | \(0.622797\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.95367 | 0.00782905 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 309.675 | − | 232.262i | 0.610798 | − | 0.458111i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 50.5625 | + | 29.1923i | 0.0993370 | + | 0.0573523i | 0.548846 | − | 0.835924i | \(-0.315068\pi\) |
−0.449508 | + | 0.893276i | \(0.648401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.7336 | − | 65.3565i | −0.0738426 | − | 0.127899i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 426.064 | − | 285.724i | 0.830534 | − | 0.556968i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 43.6515 | − | 25.2022i | 0.0847602 | − | 0.0489363i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 677.146 | − | 1172.85i | 1.30976 | − | 2.26857i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −190.754 | − | 254.332i | −0.367541 | − | 0.490042i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 288.228i | − | 0.553221i | −0.960982 | − | 0.276611i | \(-0.910789\pi\) | ||
0.960982 | − | 0.276611i | \(-0.0892112\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −250.728 | − | 434.274i | −0.479404 | − | 0.830352i | 0.520317 | − | 0.853973i | \(-0.325814\pi\) |
−0.999721 | + | 0.0236209i | \(0.992481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 92.3936 | + | 39.4652i | 0.175988 | + | 0.0751718i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 38.9051i | 0.0738238i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −109.908 | − | 190.367i | −0.207766 | − | 0.359862i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 99.9551 | + | 408.753i | 0.188239 | + | 0.769779i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −212.465 | − | 122.667i | −0.398621 | − | 0.230144i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.73321 | 0.00323964 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −44.7584 | + | 5.39309i | −0.0833490 | + | 0.0100430i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 885.783i | 1.64338i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.5607 | + | 75.4493i | 0.0805188 | + | 0.139463i | 0.903473 | − | 0.428645i | \(-0.141009\pi\) |
−0.822954 | + | 0.568108i | \(0.807676\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 589.630 | − | 442.234i | 1.08587 | − | 0.814428i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.9953 | + | 22.5140i | 0.0715511 | + | 0.0413100i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −99.5526 | −0.181997 | −0.0909987 | − | 0.995851i | \(-0.529006\pi\) | ||||
−0.0909987 | + | 0.995851i | \(0.529006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −145.522 | + | 35.5856i | −0.265068 | + | 0.0648189i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −344.122 | + | 80.9315i | −0.624541 | + | 0.146881i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 105.513 | 0.190802 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.1683 | − | 2.67114i | 0.0399430 | − | 0.00481286i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −371.103 | + | 214.256i | −0.666252 | + | 0.384661i | −0.794655 | − | 0.607061i | \(-0.792348\pi\) |
0.128403 | + | 0.991722i | \(0.459015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −424.263 | −0.758967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 54.0361 | − | 40.5282i | 0.0963210 | − | 0.0722427i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.3925 | − | 19.8565i | 0.0610880 | − | 0.0352692i | −0.469145 | − | 0.883121i | \(-0.655438\pi\) |
0.530233 | + | 0.847852i | \(0.322104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.0909 | + | 74.6357i | 0.0762672 | + | 0.132099i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.79806 | + | 109.130i | −0.00846219 | + | 0.192469i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −174.227 | − | 100.590i | −0.306199 | − | 0.176784i | 0.339025 | − | 0.940777i | \(-0.389903\pi\) |
−0.645224 | + | 0.763993i | \(0.723236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −409.604 | − | 709.455i | −0.717345 | − | 1.24248i | −0.962048 | − | 0.272880i | \(-0.912024\pi\) |
0.244703 | − | 0.969598i | \(-0.421310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −231.367 | + | 541.664i | −0.403782 | + | 0.945312i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 378.156 | + | 218.329i | 0.657663 | + | 0.379702i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −193.192 | −0.334821 | −0.167411 | − | 0.985887i | \(-0.553541\pi\) | ||||
−0.167411 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 87.7781 | + | 728.490i | 0.151603 | + | 1.25819i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 77.8208 | − | 44.9298i | 0.133943 | − | 0.0773319i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 117.064 | 0.200796 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.3078 | − | 6.50582i | −0.0381330 | − | 0.0111211i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −246.428 | + | 142.275i | −0.419809 | + | 0.242377i | −0.694996 | − | 0.719014i | \(-0.744594\pi\) |
0.275186 | + | 0.961391i | \(0.411260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 449.060 | − | 422.204i | 0.762411 | − | 0.716815i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 188.436 | − | 22.7053i | 0.318843 | − | 0.0384185i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −639.315 | + | 369.109i | −1.07810 | + | 0.622443i | −0.930384 | − | 0.366587i | \(-0.880526\pi\) |
−0.147719 | + | 0.989029i | \(0.547193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.330259 | − | 0.572025i | −0.000555056 | − | 0.000961386i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 378.782 | − | 284.094i | 0.634476 | − | 0.475870i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 740.966 | + | 427.797i | 1.23700 | + | 0.714185i | 0.968481 | − | 0.249088i | \(-0.0801310\pi\) |
0.268523 | + | 0.963273i | \(0.413464\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −78.0380 | + | 135.166i | −0.129847 | + | 0.224901i | −0.923617 | − | 0.383316i | \(-0.874782\pi\) |
0.793770 | + | 0.608218i | \(0.208115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 138.907 | − | 476.299i | 0.230360 | − | 0.789883i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −81.8652 | + | 47.2649i | −0.135314 | + | 0.0781238i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −382.625 | − | 662.726i | −0.630354 | − | 1.09181i | −0.987479 | − | 0.157749i | \(-0.949576\pi\) |
0.357125 | − | 0.934057i | \(-0.383757\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.5686 | − | 69.2242i | 0.0485527 | − | 0.113669i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −394.948 | − | 228.023i | −0.646396 | − | 0.373197i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −280.740 | + | 486.256i | −0.457978 | + | 0.793241i | −0.998854 | − | 0.0478616i | \(-0.984759\pi\) |
0.540876 | + | 0.841102i | \(0.318093\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.68777 | − | 47.2040i | −0.00924840 | − | 0.0767545i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −422.747 | − | 244.073i | −0.685165 | − | 0.395580i | 0.116633 | − | 0.993175i | \(-0.462790\pi\) |
−0.801798 | + | 0.597595i | \(0.796123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −469.611 | + | 813.389i | −0.758660 | + | 1.31404i | 0.184874 | + | 0.982762i | \(0.440812\pi\) |
−0.943534 | + | 0.331276i | \(0.892521\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −77.4429 | + | 468.398i | −0.124707 | + | 0.754265i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 202.514i | 0.325062i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 612.519 | 0.980030 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1054.20 | − | 183.891i | −1.68134 | − | 0.293287i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.9281 | + | 10.9281i | 0.0300924 | + | 0.0173738i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −390.095 | − | 675.665i | −0.618217 | − | 1.07078i | −0.989811 | − | 0.142388i | \(-0.954522\pi\) |
0.371594 | − | 0.928395i | \(-0.378811\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 91.6604 | + | 760.710i | 0.144803 | + | 1.20175i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −71.6081 | + | 41.3429i | −0.112769 | + | 0.0651070i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 298.280 | 0.468258 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −486.485 | − | 141.878i | −0.761322 | − | 0.222031i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −123.462 | + | 71.2809i | −0.192609 | + | 0.111203i | −0.593203 | − | 0.805053i | \(-0.702137\pi\) |
0.400594 | + | 0.916255i | \(0.368804\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −316.855 | −0.492776 | −0.246388 | − | 0.969171i | \(-0.579244\pi\) | ||||
−0.246388 | + | 0.969171i | \(0.579244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −49.3339 | − | 65.7768i | −0.0764867 | − | 0.101980i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 713.825i | 1.10328i | 0.834081 | + | 0.551642i | \(0.185998\pi\) | ||||
−0.834081 | + | 0.551642i | \(0.814002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 438.891 | − | 760.182i | 0.676258 | − | 1.17131i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.7008 | + | 130.304i | 0.0241179 | + | 0.200160i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 473.652 | − | 273.463i | 0.725348 | − | 0.418780i | −0.0913700 | − | 0.995817i | \(-0.529125\pi\) |
0.816718 | + | 0.577037i | \(0.195791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.58198 | 0.00699539 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 141.007 | − | 483.499i | 0.214623 | − | 0.735920i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 954.820i | 1.44889i | 0.689331 | + | 0.724446i | \(0.257904\pi\) | ||||
−0.689331 | + | 0.724446i | \(0.742096\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 133.808 | − | 231.761i | 0.202432 | − | 0.350623i | −0.746879 | − | 0.664959i | \(-0.768449\pi\) |
0.949311 | + | 0.314337i | \(0.101782\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.6475 | − | 18.1962i | −0.0205845 | − | 0.0274453i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.01855 | + | 10.0197i | −0.00453917 | + | 0.0150672i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 163.579 | − | 283.327i | 0.245246 | − | 0.424778i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 216.758 | − | 162.573i | 0.324003 | − | 0.243008i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 270.637 | + | 156.252i | 0.403333 | + | 0.232865i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 96.0817 | − | 166.418i | 0.142766 | − | 0.247278i | −0.785771 | − | 0.618517i | \(-0.787734\pi\) |
0.928537 | + | 0.371239i | \(0.121067\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 236.039 | + | 627.576i | 0.349687 | + | 0.929742i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −302.982 | − | 174.926i | −0.447536 | − | 0.258385i | 0.259253 | − | 0.965809i | \(-0.416524\pi\) |
−0.706789 | + | 0.707425i | \(0.749857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −100.568 | −0.148113 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −517.679 | + | 1211.96i | −0.760175 | + | 1.77968i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 221.137i | 0.323773i | 0.986809 | + | 0.161886i | \(0.0517578\pi\) | ||||
−0.986809 | + | 0.161886i | \(0.948242\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.6705 | −0.0170372 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 899.100 | − | 674.343i | 1.30873 | − | 0.981577i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 39.4204i | − | 0.0572139i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −64.4573 | + | 111.643i | −0.0932811 | + | 0.161568i | −0.908890 | − | 0.417036i | \(-0.863069\pi\) |
0.815609 | + | 0.578604i | \(0.196402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 164.626 | − | 157.547i | 0.237556 | − | 0.227341i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.83899 | − | 2.21644i | −0.00552372 | − | 0.00318912i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.2698 | − | 40.3044i | 0.0333856 | − | 0.0578255i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.6611 | − | 64.7584i | 0.0395723 | − | 0.0926444i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −286.317 | − | 165.305i | −0.408441 | − | 0.235813i | 0.281679 | − | 0.959509i | \(-0.409109\pi\) |
−0.690120 | + | 0.723695i | \(0.742442\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −79.2729 | − | 337.070i | −0.112764 | − | 0.479474i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.5729 | − | 87.7468i | −0.0149970 | − | 0.124464i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3064 | + | 6.52777i | 0.0159921 | + | 0.00923305i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 454.924 | 0.641642 | 0.320821 | − | 0.947140i | \(-0.396041\pi\) | ||||
0.320821 | + | 0.947140i | \(0.396041\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 486.858 | + | 508.733i | 0.684751 | + | 0.715518i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 570.421i | 0.800029i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.2363 | + | 41.9786i | 0.0338970 | + | 0.0587113i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 204.750 | + | 272.993i | 0.285565 | + | 0.380743i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 104.799 | + | 60.5055i | 0.145756 | + | 0.0841523i | 0.571104 | − | 0.820877i | \(-0.306515\pi\) |
−0.425348 | + | 0.905030i | \(0.639848\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 166.442 | 0.230849 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 54.0546 | + | 448.611i | 0.0747643 | + | 0.620485i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 462.043i | − | 0.637300i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −234.018 | − | 405.331i | −0.321895 | − | 0.557539i | 0.658984 | − | 0.752157i | \(-0.270987\pi\) |
−0.980879 | + | 0.194618i | \(0.937653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −548.311 | + | 480.412i | −0.752141 | + | 0.659002i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 80.4822i | − | 0.110099i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −618.776 | − | 1071.75i | −0.844170 | − | 1.46215i | −0.886340 | − | 0.463035i | \(-0.846761\pi\) |
0.0421703 | − | 0.999110i | \(-0.486573\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 34.6845 | + | 46.2447i | 0.0471898 | + | 0.0629180i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −896.295 | + | 517.476i | −1.21614 | + | 0.702139i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 202.246 | − | 350.300i | 0.273675 | − | 0.474020i | −0.696125 | − | 0.717921i | \(-0.745094\pi\) |
0.969800 | + | 0.243901i | \(0.0784273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −61.9238 | + | 354.994i | −0.0835679 | + | 0.479074i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 43.4991i | − | 0.0585452i | −0.999571 | − | 0.0292726i | \(-0.990681\pi\) | ||
0.999571 | − | 0.0292726i | \(-0.00931908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −87.2591 | −0.117126 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 575.709 | + | 167.899i | 0.770694 | + | 0.224764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.95650 | + | 2.86164i | 0.00661749 | + | 0.00382061i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −422.721 | + | 732.175i | −0.562878 | + | 0.974933i | 0.434366 | + | 0.900737i | \(0.356973\pi\) |
−0.997244 | + | 0.0741967i | \(0.976361\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −605.860 | − | 807.792i | −0.804596 | − | 1.07277i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.2218 | − | 16.2939i | −0.0373799 | − | 0.0215813i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −301.336 | + | 521.930i | −0.398067 | + | 0.689472i | −0.993487 | − | 0.113942i | \(-0.963652\pi\) |
0.595421 | + | 0.803414i | \(0.296985\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 792.268 | − | 594.217i | 1.04383 | − | 0.782895i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −737.213 | + | 425.630i | −0.968743 | + | 0.559304i | −0.898853 | − | 0.438251i | \(-0.855598\pi\) |
−0.0698901 | + | 0.997555i | \(0.522265\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 74.3440 | + | 128.768i | 0.0974364 | + | 0.168765i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.23415 | − | 4.23177i | 0.00161327 | − | 0.00553172i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −255.985 | − | 147.793i | −0.333749 | − | 0.192690i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 257.280 | − | 445.622i | 0.334564 | − | 0.579483i | −0.648837 | − | 0.760928i | \(-0.724744\pi\) |
0.983401 | + | 0.181445i | \(0.0580775\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −388.781 | + | 910.191i | −0.504255 | + | 1.18053i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1074.64 | − | 620.446i | 1.39023 | − | 0.802647i | 0.396886 | − | 0.917868i | \(-0.370091\pi\) |
0.993340 | + | 0.115221i | \(0.0367576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 402.801 | + | 697.671i | 0.519743 | + | 0.900221i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 67.8056 | + | 28.9626i | 0.0872659 | + | 0.0372749i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −717.738 | + | 168.799i | −0.921358 | + | 0.216687i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 528.542 | + | 915.462i | 0.676751 | + | 1.17217i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 470.200 | − | 176.848i | 0.600511 | − | 0.225860i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 65.8272i | − | 0.0838563i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 440.525 | + | 763.012i | 0.559752 | + | 0.969519i | 0.997517 | + | 0.0704296i | \(0.0224370\pi\) |
−0.437765 | + | 0.899090i | \(0.644230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 863.279 | + | 1151.01i | 1.09414 | + | 1.45882i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 284.584i | 0.359777i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.6167 | − | 91.1347i | 0.0663514 | − | 0.114924i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.11165 | − | 4.58386i | 0.00768761 | − | 0.00576586i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 211.398 | − | 122.050i | 0.265242 | − | 0.153137i | −0.361482 | − | 0.932379i | \(-0.617729\pi\) |
0.626723 | + | 0.779242i | \(0.284396\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.2558 | − | 74.9212i | 0.0541374 | − | 0.0937688i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −976.422 | + | 934.436i | −1.21900 | + | 1.16659i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −909.844 | + | 525.299i | −1.13306 | + | 0.654170i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.84220 | − | 8.38693i | −0.00601515 | − | 0.0104185i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 104.496 | − | 244.640i | 0.129487 | − | 0.303147i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 964.150i | 1.19178i | 0.803066 | + | 0.595890i | \(0.203201\pi\) | ||||
−0.803066 | + | 0.595890i | \(0.796799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 583.549 | + | 1010.74i | 0.719543 | + | 1.24628i | 0.961181 | + | 0.275918i | \(0.0889818\pi\) |
−0.241639 | + | 0.970366i | \(0.577685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1352.41 | + | 577.671i | 1.66348 | + | 0.710543i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.6561i | 0.0462038i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −928.961 | + | 873.404i | −1.13704 | + | 1.06904i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −53.0527 | − | 55.4365i | −0.0647774 | − | 0.0676880i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 217.047i | − | 0.264369i | −0.991225 | − | 0.132184i | \(-0.957801\pi\) | ||
0.991225 | − | 0.132184i | \(-0.0421991\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8366 | − | 20.5015i | 0.0143822 | − | 0.0249107i | −0.858745 | − | 0.512404i | \(-0.828755\pi\) |
0.873127 | + | 0.487493i | \(0.162089\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 549.405 | − | 1286.23i | 0.665945 | − | 1.55907i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −837.637 | + | 483.610i | −1.01286 | + | 0.584777i | −0.912029 | − | 0.410127i | \(-0.865484\pi\) |
−0.100834 | + | 0.994903i | \(0.532151\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1211.41 | −1.46129 | −0.730643 | − | 0.682760i | \(-0.760780\pi\) | ||||
−0.730643 | + | 0.682760i | \(0.760780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 266.044 | + | 113.638i | 0.320149 | + | 0.136749i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 56.5835i | 0.0679273i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50.7062 | + | 87.8256i | −0.0607259 | + | 0.105180i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −555.816 | + | 676.948i | −0.664057 | + | 0.808779i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −632.585 | + | 365.223i | −0.753975 | + | 0.435307i | −0.827128 | − | 0.562013i | \(-0.810027\pi\) |
0.0731537 | + | 0.997321i | \(0.476694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 494.823 | 0.588374 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1458.28 | − | 175.713i | 1.72987 | − | 0.208437i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −45.6367 | + | 26.3484i | −0.0540080 | + | 0.0311815i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −312.149 | −0.368535 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 55.3003 | + | 458.949i | 0.0651358 | + | 0.540576i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 277.521 | + | 160.227i | 0.326111 | + | 0.188280i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −580.803 | − | 1005.98i | −0.680894 | − | 1.17934i | −0.974708 | − | 0.223481i | \(-0.928258\pi\) |
0.293814 | − | 0.955863i | \(-0.405075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −62.2381 | + | 31.6787i | −0.0727931 | + | 0.0370511i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 492.247 | − | 284.199i | 0.574384 | − | 0.331621i | −0.184514 | − | 0.982830i | \(-0.559071\pi\) |
0.758898 | + | 0.651209i | \(0.225738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −785.882 | + | 1361.19i | −0.914880 | + | 1.58462i | −0.107802 | + | 0.994172i | \(0.534381\pi\) |
−0.807078 | + | 0.590445i | \(0.798952\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 61.6714 | − | 144.381i | 0.0716276 | − | 0.167690i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1302.81i | 1.50963i | 0.655935 | + | 0.754817i | \(0.272275\pi\) | ||||
−0.655935 | + | 0.754817i | \(0.727725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.6396 | + | 37.4808i | 0.0250169 | + | 0.0433305i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −690.142 | + | 517.620i | −0.796011 | + | 0.597024i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1468.88i | − | 1.69031i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 174.256 | + | 301.820i | 0.200064 | + | 0.346521i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −464.041 | − | 484.891i | −0.531547 | − | 0.555431i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.7692 | − | 13.7231i | −0.0271648 | − | 0.0156836i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −649.548 | −0.740647 | −0.370324 | − | 0.928903i | \(-0.620753\pi\) | ||||
−0.370324 | + | 0.928903i | \(0.620753\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −847.976 | − | 1130.60i | −0.964706 | − | 1.28624i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 94.7789i | 0.107581i | 0.998552 | + | 0.0537905i | \(0.0171303\pi\) | ||||
−0.998552 | + | 0.0537905i | \(0.982870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −301.040 | − | 521.416i | −0.340929 | − | 0.590506i | 0.643677 | − | 0.765297i | \(-0.277408\pi\) |
−0.984605 | + | 0.174792i | \(0.944075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.85282 | − | 56.8730i | −0.00774329 | − | 0.0642633i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 579.211 | + | 334.408i | 0.653000 | + | 0.377010i | 0.789605 | − | 0.613616i | \(-0.210286\pi\) |
−0.136605 | + | 0.990626i | \(0.543619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −273.039 | −0.307131 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1519.23 | + | 66.7950i | 1.70508 | + | 0.0749663i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1334.19 | + | 313.778i | −1.49406 | + | 0.351375i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.13718 | 0.00685718 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −200.098 | − | 266.790i | −0.223074 | − | 0.297425i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 522.718 | − | 301.791i | 0.581444 | − | 0.335697i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.47800 | 0.00829967 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.4798 | − | 269.557i | −0.0359688 | − | 0.298513i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −86.8937 | + | 50.1681i | −0.0960152 | + | 0.0554344i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −326.741 | − | 565.932i | −0.360244 | − | 0.623960i | 0.627757 | − | 0.778409i | \(-0.283973\pi\) |
−0.988001 | + | 0.154449i | \(0.950640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.6962 | + | 84.6343i | 0.0227681 | + | 0.0931070i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 424.165 | + | 244.892i | 0.465604 | + | 0.268816i | 0.714398 | − | 0.699740i | \(-0.246701\pi\) |
−0.248794 | + | 0.968556i | \(0.580034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −625.480 | − | 1083.36i | −0.685082 | − | 1.18660i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.2477 | − | 2.43971i | 0.0221286 | − | 0.00266635i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1032 | + | 7.56514i | 0.0142892 | + | 0.00824988i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1708.16 | −1.85871 | −0.929357 | − | 0.369183i | \(-0.879637\pi\) | ||||
−0.929357 | + | 0.369183i | \(0.879637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −122.585 | − | 52.3614i | −0.133100 | − | 0.0568528i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 308.274 | − | 177.982i | 0.333992 | − | 0.192830i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 452.574 | 0.489269 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 767.992 | + | 802.500i | 0.828471 | + | 0.865696i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 235.424 | − | 135.922i | 0.253416 | − | 0.146310i | −0.367911 | − | 0.929861i | \(-0.619927\pi\) |
0.621328 | + | 0.783551i | \(0.286594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 653.111 | − | 614.052i | 0.701516 | − | 0.659561i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −413.136 | − | 550.833i | −0.442804 | − | 0.590390i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.96330 | + | 4.59761i | −0.00851689 | + | 0.00491723i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.2537 | + | 55.8650i | 0.0344223 | + | 0.0596212i | 0.882723 | − | 0.469893i | \(-0.155708\pi\) |
−0.848301 | + | 0.529514i | \(0.822374\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.81742 | − | 81.4769i | −0.0104552 | − | 0.0867699i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 130.105 | + | 75.1159i | 0.138262 | + | 0.0798256i | 0.567535 | − | 0.823349i | \(-0.307897\pi\) |
−0.429273 | + | 0.903175i | \(0.641230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 341.177 | − | 590.937i | 0.361800 | − | 0.626656i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.42571 | − | 14.6714i | 0.00256689 | − | 0.0155253i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −271.801 | + | 156.924i | −0.287013 | + | 0.165707i | −0.636594 | − | 0.771199i | \(-0.719657\pi\) |
0.349581 | + | 0.936906i | \(0.386324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 176.890 | + | 306.382i | 0.186396 | + | 0.322848i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1418.16 | + | 170.878i | −1.49123 | + | 0.179683i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −268.594 | − | 155.073i | −0.281841 | − | 0.162721i | 0.352416 | − | 0.935844i | \(-0.385360\pi\) |
−0.634256 | + | 0.773123i | \(0.718694\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.0918 | − | 69.4410i | 0.0419809 | − | 0.0727131i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −963.688 | − | 411.632i | −1.00699 | − | 0.430127i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.3745 | − | 19.2688i | −0.0348013 | − | 0.0200926i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.6928 | + | 79.1422i | −0.0475471 | + | 0.0823540i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.07278 | + | 37.1019i | 0.00942137 | + | 0.0385274i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 99.8889i | − | 0.103512i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1841.93 | 1.90479 | 0.952394 | − | 0.304871i | \(-0.0986133\pi\) | ||||
0.952394 | + | 0.304871i | \(0.0986133\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −67.3419 | − | 11.7469i | −0.0694963 | − | 0.0121227i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.2443 | − | 34.7821i | −0.0620436 | − | 0.0358209i | 0.468657 | − | 0.883380i | \(-0.344738\pi\) |
−0.530701 | + | 0.847559i | \(0.678071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.31897 | − | 12.6768i | −0.00752207 | − | 0.0130286i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −433.129 | − | 185.008i | −0.444235 | − | 0.189751i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 181.310 | − | 104.679i | 0.185578 | − | 0.107143i | −0.404333 | − | 0.914612i | \(-0.632496\pi\) |
0.589911 | + | 0.807468i | \(0.299163\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2819.25 | 2.87972 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −277.817 | + | 952.607i | −0.283198 | + | 0.971057i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 933.627 | − | 539.030i | 0.949773 | − | 0.548352i | 0.0567625 | − | 0.998388i | \(-0.481922\pi\) |
0.893010 | + | 0.450036i | \(0.148589\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.8380 | −0.0262315 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 114.640 | − | 268.388i | 0.116150 | − | 0.271923i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1180.02i | − | 1.19314i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −168.849 | + | 292.455i | −0.170382 | + | 0.295111i | −0.938554 | − | 0.345134i | \(-0.887834\pi\) |
0.768171 | + | 0.640244i | \(0.221167\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1343.62 | − | 573.917i | −1.35309 | − | 0.577963i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −55.8211 | + | 32.2283i | −0.0561016 | + | 0.0323903i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −405.821 | −0.407042 | −0.203521 | − | 0.979071i | \(-0.565238\pi\) | ||||
−0.203521 | + | 0.979071i | \(0.565238\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 173.224 | + | 460.564i | 0.173397 | + | 0.461025i |
(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 | 684.3.m.a.353.19 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.m.a.1493.18 | 80 | |||
9.4 | even | 3 | 2052.3.be.a.125.23 | 80 | |||
9.5 | odd | 6 | 684.3.be.a.581.35 | yes | 80 | ||
19.7 | even | 3 | 684.3.be.a.425.35 | yes | 80 | ||
57.26 | odd | 6 | 2052.3.be.a.197.23 | 80 | |||
171.121 | even | 3 | 2052.3.m.a.881.23 | 80 | |||
171.140 | odd | 6 | inner | 684.3.m.a.653.19 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.19 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.m.a.653.19 | yes | 80 | 171.140 | odd | 6 | inner | |
684.3.be.a.425.35 | yes | 80 | 19.7 | even | 3 | ||
684.3.be.a.581.35 | yes | 80 | 9.5 | odd | 6 | ||
2052.3.m.a.881.23 | 80 | 171.121 | even | 3 | |||
2052.3.m.a.1493.18 | 80 | 3.2 | odd | 2 | |||
2052.3.be.a.125.23 | 80 | 9.4 | even | 3 | |||
2052.3.be.a.197.23 | 80 | 57.26 | odd | 6 |