Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(41,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 33, 53]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.ba (of order \(66\), degree \(20\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 245.1 | ||
Root | \(-0.786053 - 0.618159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.245 |
Dual form | 804.2.ba.a.233.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{61}{66}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.71442 | + | 0.246497i | 0.989821 | + | 0.142315i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.518680 | + | 0.543976i | 0.196043 | + | 0.205604i | 0.814417 | − | 0.580280i | \(-0.197057\pi\) |
−0.618374 | + | 0.785884i | \(0.712208\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.87848 | + | 0.845198i | 0.959493 | + | 0.281733i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.0950560 | − | 0.995472i | \(-0.469697\pi\) | ||||
−0.0950560 | + | 0.995472i | \(0.530303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.21014 | + | 6.27878i | −0.335631 | + | 1.74142i | 0.286109 | + | 0.958197i | \(0.407638\pi\) |
−0.621740 | + | 0.783223i | \(0.713574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.30555 | + | 3.15184i | 0.758346 | + | 0.723082i | 0.966963 | − | 0.254916i | \(-0.0820477\pi\) |
−0.208617 | + | 0.977997i | \(0.566896\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.755148 | + | 1.06046i | 0.164787 | + | 0.231411i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.27430 | − | 3.77875i | 0.654861 | − | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.72659 | + | 2.15856i | 0.909632 | + | 0.415415i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.02981 | − | 10.5316i | −0.364564 | − | 1.89154i | −0.446296 | − | 0.894886i | \(-0.647257\pi\) |
0.0817313 | − | 0.996654i | \(-0.473955\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.656310 | + | 1.13676i | 0.107897 | + | 0.186883i | 0.914918 | − | 0.403640i | \(-0.132255\pi\) |
−0.807021 | + | 0.590522i | \(0.798922\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.62238 | + | 10.4662i | −0.580045 | + | 1.67593i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.92488 | + | 9.21929i | 0.903536 | + | 1.40593i | 0.913881 | + | 0.405983i | \(0.133071\pi\) |
−0.0103449 | + | 0.999946i | \(0.503293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.306193 | − | 6.42777i | 0.0437418 | − | 0.918253i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.89019 | + | 6.21839i | 0.647722 | + | 0.823646i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.304967 | − | 3.19376i | −0.0390471 | − | 0.408919i | −0.993772 | − | 0.111430i | \(-0.964457\pi\) |
0.954725 | − | 0.297489i | \(-0.0961492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.03324 | + | 2.00421i | 0.130176 | + | 0.252507i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.979754 | − | 8.12650i | −0.119696 | − | 0.992811i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17.0103 | + | 1.62429i | −1.99090 | + | 0.190108i | −0.994850 | + | 0.101361i | \(0.967680\pi\) |
−0.996054 | + | 0.0887477i | \(0.971714\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.54498 | − | 5.67126i | 0.755750 | − | 0.654861i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.7875 | + | 5.81020i | −1.88874 | + | 0.653699i | −0.932414 | + | 0.361392i | \(0.882301\pi\) |
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.57128 | + | 4.86577i | 0.841254 | + | 0.540641i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.04318 | + | 2.59839i | −0.423841 | + | 0.272386i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.883932 | − | 18.5560i | −0.0916595 | − | 1.92417i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.63425 | − | 3.83028i | 0.673606 | − | 0.388906i | −0.123836 | − | 0.992303i | \(-0.539520\pi\) |
0.797442 | + | 0.603396i | \(0.206186\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8848 | − | 3.44700i | 1.76224 | − | 0.339643i | 0.797593 | − | 0.603196i | \(-0.206106\pi\) |
0.964645 | + | 0.263553i | \(0.0848943\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3427 | − | 8.96204i | −0.990655 | − | 0.858407i | −0.000729916 | − | 1.00000i | \(-0.500232\pi\) |
−0.989925 | + | 0.141592i | \(0.954778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.844984 | + | 2.11067i | 0.0802023 | + | 0.200336i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.814576 | − | 0.580057i | \(-0.196970\pi\) | ||||
−0.814576 | + | 0.580057i | \(0.803030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.79016 | + | 17.0505i | −0.812651 | + | 1.57632i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8012 | − | 2.08176i | −0.981929 | − | 0.189251i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.37340 | + | 2.26303i | −0.210605 | + | 0.200811i | −0.788038 | − | 0.615627i | \(-0.788903\pi\) |
0.577433 | + | 0.816438i | \(0.304054\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.88522 | + | 17.2662i | 0.694255 | + | 1.52021i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.43294i | 0.297674i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0359 | − | 9.15010i | 1.69942 | − | 0.776101i | 0.701434 | − | 0.712734i | \(-0.252543\pi\) |
0.997990 | − | 0.0633672i | \(-0.0201839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.10937 | − | 10.9444i | 0.173978 | − | 0.902682i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.49049 | − | 0.768401i | −0.121294 | − | 0.0625316i | 0.396511 | − | 0.918030i | \(-0.370221\pi\) |
−0.517806 | + | 0.855498i | \(0.673251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9069 | + | 7.16885i | −1.42913 | + | 0.572136i | −0.951836 | − | 0.306608i | \(-0.900806\pi\) |
−0.477292 | + | 0.878745i | \(0.658382\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.11104 | − | 15.7808i | 0.713632 | − | 1.23605i | −0.249853 | − | 0.968284i | \(-0.580382\pi\) |
0.963485 | − | 0.267763i | \(-0.0862844\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −25.8899 | − | 10.3647i | −1.99153 | − | 0.797288i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.85104 | + | 11.8664i | 0.523912 | + | 0.907443i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.75387 | − | 0.178819i | 0.283766 | − | 0.0135174i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.9494 | − | 13.3291i | −1.25984 | − | 0.990746i | −0.999683 | − | 0.0251785i | \(-0.991985\pi\) |
−0.260153 | − | 0.965567i | \(-0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.264409 | − | 5.55063i | 0.0195457 | − | 0.410314i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.27738 | + | 3.69075i | 0.0929159 | + | 0.268463i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.9452 | − | 20.7099i | −1.29173 | − | 1.49073i | −0.770710 | − | 0.637187i | \(-0.780098\pi\) |
−0.521018 | − | 0.853546i | \(-0.674447\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.458227 | − | 0.888835i | \(-0.651515\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.501668 | − | 2.06790i | −0.0355623 | − | 0.146590i | 0.951263 | − | 0.308382i | \(-0.0997876\pi\) |
−0.986825 | + | 0.161793i | \(0.948272\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.323444 | − | 14.1738i | 0.0228140 | − | 0.999740i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.23116 | − | 6.47306i | 0.566656 | − | 0.445624i | −0.293279 | − | 0.956027i | \(-0.594746\pi\) |
0.859935 | + | 0.510403i | \(0.170504\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.67614 | − | 6.56673i | 0.317437 | − | 0.445778i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −29.5632 | − | 1.40827i | −1.99769 | − | 0.0951619i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.24906 | + | 29.5528i | 0.284538 | + | 1.97900i | 0.167412 | + | 0.985887i | \(0.446459\pi\) |
0.117125 | + | 0.993117i | \(0.462632\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.6188 | − | 8.10961i | 0.841254 | − | 0.540641i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.3520 | − | 5.31338i | −1.01449 | − | 0.351118i | −0.231287 | − | 0.972886i | \(-0.574293\pi\) |
−0.783202 | + | 0.621768i | \(0.786415\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.371662 | − | 0.928368i | \(-0.378788\pi\) | ||||
−0.371662 | + | 0.928368i | \(0.621212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.2130 | + | 5.82308i | −1.96254 | + | 0.378250i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.53199 | − | 7.73398i | 0.227515 | − | 0.498189i | −0.761103 | − | 0.648630i | \(-0.775342\pi\) |
0.988619 | + | 0.150441i | \(0.0480694\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7810 | + | 10.2083i | 0.755750 | + | 0.654861i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.7899 | + | 16.9407i | −1.51371 | + | 1.07791i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.277957 | + | 0.946634i | −0.0172714 | + | 0.0588210i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.8919 | + | 3.29135i | 1.39058 | + | 0.199935i | 0.796582 | − | 0.604530i | \(-0.206639\pi\) |
0.593999 | + | 0.804466i | \(0.297548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.57221 | + | 3.45811i | −0.458291 | + | 0.209294i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.3119 | − | 9.19400i | −1.88135 | − | 0.552414i | −0.996199 | − | 0.0871078i | \(-0.972238\pi\) |
−0.885150 | − | 0.465306i | \(-0.845944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.05856 | − | 32.0307i | 0.183111 | − | 1.91763i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.68456 | + | 1.08188i | −0.219024 | + | 0.0643113i | −0.389404 | − | 0.921067i | \(-0.627319\pi\) |
0.170379 | + | 0.985379i | \(0.445501\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.86097 | + | 13.8478i | 0.580057 | + | 0.814576i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.3180 | − | 4.93140i | 0.722097 | − | 0.289084i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.94196 | + | 8.00486i | −0.111933 | + | 0.461392i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4344 | − | 30.1483i | 0.595524 | − | 1.72065i | −0.0932173 | − | 0.995646i | \(-0.529715\pi\) |
0.688741 | − | 0.725007i | \(-0.258164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.5117 | − | 1.50109i | 1.79264 | − | 0.0853938i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.4546 | − | 4.66627i | 1.83444 | − | 0.263753i | 0.863724 | − | 0.503966i | \(-0.168126\pi\) |
0.970720 | + | 0.240212i | \(0.0772171\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.7636 | + | 25.1314i | 1.09629 | + | 1.39404i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.5227 | − | 17.9142i | −0.858407 | − | 0.990655i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3029 | + | 29.6835i | 0.841123 | + | 1.63155i | 0.773461 | + | 0.633844i | \(0.218524\pi\) |
0.0676621 | + | 0.997708i | \(0.478446\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.928386 | + | 3.82686i | 0.0508752 | + | 0.209711i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.8201 | + | 6.50648i | −1.46098 | + | 0.354431i | −0.885981 | − | 0.463721i | \(-0.846514\pi\) |
−0.575002 | + | 0.818152i | \(0.694999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.63165 | − | 6.61286i | 0.412070 | − | 0.357061i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.945001 | − | 0.327068i | \(-0.106061\pi\) | ||||
−0.945001 | + | 0.327068i | \(0.893939\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5864 | + | 7.44612i | 0.620205 | + | 0.398582i | 0.812672 | − | 0.582722i | \(-0.198012\pi\) |
−0.192467 | + | 0.981304i | \(0.561649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.2729 | + | 27.0650i | −1.02871 | + | 1.44463i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.998867 | − | 0.0475819i | \(-0.984848\pi\) | ||||
0.998867 | + | 0.0475819i | \(0.0151515\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.0885397 | + | 1.85868i | 0.00465998 | + | 0.0978251i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.0047 | − | 6.23148i | −0.945001 | − | 0.327068i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.53090 | + | 11.3176i | −0.236511 | + | 0.590777i | −0.998377 | − | 0.0569590i | \(-0.981860\pi\) |
0.761865 | + | 0.647736i | \(0.224284\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.5668 | + | 17.6477i | 1.58269 | + | 0.913765i | 0.994465 | + | 0.105065i | \(0.0335050\pi\) |
0.588221 | + | 0.808700i | \(0.299828\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.449388 | + | 1.12252i | 0.0230835 | + | 0.0576598i | 0.939462 | − | 0.342653i | \(-0.111326\pi\) |
−0.916378 | + | 0.400313i | \(0.868901\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.62683 | + | 3.29475i | −0.237040 | + | 0.168795i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.690079 | − | 0.723734i | \(-0.257576\pi\) | ||||
−0.690079 | + | 0.723734i | \(0.742424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.26252 | + | 31.5452i | 0.470840 | + | 1.60353i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.95241 | − | 17.4133i | −0.399120 | − | 0.873951i | −0.997359 | − | 0.0726328i | \(-0.976860\pi\) |
0.598239 | − | 0.801318i | \(-0.295867\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.846208 | + | 5.88550i | −0.0423634 | + | 0.294644i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 68.5823 | 3.41633 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.8811 | + | 20.8507i | 0.983056 | + | 1.03100i | 0.999515 | + | 0.0311349i | \(0.00991216\pi\) |
−0.0164592 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.6055 | − | 10.7483i | 1.79258 | − | 0.526348i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4844 | + | 17.6248i | 0.900874 | + | 0.858981i | 0.990573 | − | 0.136988i | \(-0.0437421\pi\) |
−0.0896992 | + | 0.995969i | \(0.528591\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.57915 | − | 1.82244i | 0.0764204 | − | 0.0881939i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.86575 | + | 25.2459i | 0.233833 | + | 1.21324i | 0.889053 | + | 0.457804i | \(0.151364\pi\) |
−0.655220 | + | 0.755438i | \(0.727424\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.30065 | + | 9.18100i | 0.252986 | + | 0.438185i | 0.964347 | − | 0.264642i | \(-0.0852539\pi\) |
−0.711360 | + | 0.702827i | \(0.751921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.31411 | − | 18.2434i | 0.300672 | − | 0.868734i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) | ||||
−0.998867 | + | 0.0475819i | \(0.984848\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.36592 | − | 1.68476i | −0.111161 | − | 0.0791570i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.7494 | + | 33.9476i | 0.549613 | + | 1.58800i | 0.787240 | + | 0.616647i | \(0.211509\pi\) |
−0.237627 | + | 0.971357i | \(0.576370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.93979 | − | 30.7869i | −0.136624 | − | 1.43079i | −0.760537 | − | 0.649295i | \(-0.775064\pi\) |
0.623913 | − | 0.781494i | \(-0.285542\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.91245 | − | 4.74802i | 0.180660 | − | 0.219243i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.4671 | + | 7.87643i | −1.49600 | + | 0.362927i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.7334 | − | 2.17078i | 1.04308 | − | 0.0996020i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.93171 | + | 2.74519i | −0.361655 | + | 0.125170i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2147 | + | 1.10585i | 1.05196 | + | 0.0501109i | 0.566429 | − | 0.824110i | \(-0.308325\pi\) |
0.485528 | + | 0.874221i | \(0.338628\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.5101 | − | 24.8091i | 0.882276 | − | 1.12191i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.6252 | + | 22.3003i | −1.72910 | + | 0.998297i | −0.835381 | + | 0.549672i | \(0.814753\pi\) |
−0.893720 | + | 0.448625i | \(0.851914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.971812 | − | 0.235759i | \(-0.924242\pi\) | ||||
0.971812 | + | 0.235759i | \(0.0757576\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −41.8313 | − | 24.1513i | −1.85779 | − | 1.07260i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.70647 | − | 8.41071i | −0.429389 | − | 0.372068i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.82055 | + | 22.0327i | 0.389437 | + | 0.972767i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.9953 | + | 3.85378i | 0.874334 | + | 0.168514i | 0.606627 | − | 0.794987i | \(-0.292522\pi\) |
0.267707 | + | 0.963501i | \(0.413734\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.47978 | + | 0.618744i | 0.282801 | + | 0.0270042i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.6459 | − | 15.8718i | 0.723734 | − | 0.690079i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5721 | + | 6.19815i | −0.583509 | + | 0.266479i | −0.685222 | − | 0.728334i | \(-0.740295\pi\) |
0.101713 | + | 0.994814i | \(0.467568\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.7728 | − | 27.0297i | −1.10601 | − | 1.15995i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.79104 | + | 39.7016i | −0.162093 | + | 1.69752i | 0.439120 | + | 0.898428i | \(0.355290\pi\) |
−0.601213 | + | 0.799089i | \(0.705316\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.82152 | − | 9.45094i | 0.0777405 | − | 0.403356i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.8679 | − | 6.11835i | −0.504676 | − | 0.260179i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −65.0558 | + | 26.0444i | −2.75157 | + | 1.10156i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.28021 | + | 6.64237i | 0.0537639 | + | 0.278954i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.5196 | + | 15.0206i | 1.57015 | + | 0.628592i | 0.983444 | − | 0.181210i | \(-0.0580014\pi\) |
0.586703 | + | 0.809802i | \(0.300426\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.4565 | + | 2.16536i | −1.89238 | + | 0.0901450i | −0.961437 | − | 0.275027i | \(-0.911313\pi\) |
−0.930940 | + | 0.365172i | \(0.881010\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.6608 | − | 39.9290i | −1.06643 | − | 1.65939i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.814576 | − | 0.580057i | \(-0.803030\pi\) | ||||
0.814576 | + | 0.580057i | \(0.196970\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.4844 | − | 41.2106i | 1.09127 | − | 1.69805i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||||
0.618159 | + | 0.786053i | \(0.287879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.350339 | − | 3.66892i | −0.0143384 | − | 0.150159i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.458227 | − | 0.888835i | \(-0.651515\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.17040 | + | 21.3127i | 0.210905 | + | 0.869362i | 0.974630 | + | 0.223821i | \(0.0718530\pi\) |
−0.763725 | + | 0.645541i | \(0.776632\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.04830 | − | 24.2201i | 0.164860 | − | 0.986317i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.0899 | + | 22.2144i | −1.74897 | + | 0.901655i | −0.792469 | + | 0.609912i | \(0.791205\pi\) |
−0.956497 | + | 0.291743i | \(0.905765\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.4524 | − | 30.2393i | 1.55308 | − | 1.22135i | 0.680651 | − | 0.732608i | \(-0.261697\pi\) |
0.872426 | − | 0.488746i | \(-0.162545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.5788 | + | 28.8989i | −0.827132 | + | 1.16154i | 0.157606 | + | 0.987502i | \(0.449622\pi\) |
−0.984738 | + | 0.174042i | \(0.944317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.55787 | − | 24.7455i | −0.142315 | − | 0.989821i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.4180 | − | 15.3732i | −1.76825 | − | 0.611998i | −0.768635 | − | 0.639688i | \(-0.779064\pi\) |
−0.999617 | + | 0.0276903i | \(0.991185\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.7073 | − | 9.06859i | 0.624308 | − | 0.360444i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.9880 | + | 9.70099i | 1.58438 | + | 0.384367i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.9808 | − | 45.9416i | 0.827402 | − | 1.81176i | 0.331158 | − | 0.943575i | \(-0.392561\pi\) |
0.496245 | − | 0.868183i | \(-0.334712\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.371662 | − | 0.928368i | \(-0.621212\pi\) | ||||
0.371662 | + | 0.928368i | \(0.378788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.63556 | − | 10.1055i | 0.377647 | − | 0.396065i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
−0.458227 | + | 0.888835i | \(0.651515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −50.3366 | − | 9.70159i | −1.96382 | − | 0.378495i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.5803 | − | 46.2502i | 0.528212 | − | 1.79893i | −0.0699507 | − | 0.997550i | \(-0.522284\pi\) |
0.598163 | − | 0.801375i | \(-0.295898\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 51.7134i | 1.99935i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.3577 | − | 2.63944i | −0.707637 | − | 0.101743i | −0.220906 | − | 0.975295i | \(-0.570902\pi\) |
−0.486731 | + | 0.873552i | \(0.661811\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 23.6329 | − | 10.7928i | 0.909632 | − | 0.415415i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.690079 | − | 0.723734i | \(-0.742424\pi\) | ||||
0.690079 | + | 0.723734i | \(0.257576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.52464 | + | 1.62218i | 0.212016 | + | 0.0622535i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.189251 | − | 0.981929i | \(-0.439394\pi\) | ||||
−0.189251 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.0100 | − | 12.8936i | −0.954193 | − | 0.491921i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7399 | − | 27.7208i | −0.750942 | − | 1.05455i | −0.996369 | − | 0.0851357i | \(-0.972868\pi\) |
0.245427 | − | 0.969415i | \(-0.421072\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.189251 | − | 0.981929i | \(-0.560606\pi\) | ||||
0.189251 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.41342 | + | 5.82622i | −0.0533083 | + | 0.219740i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.6765 | + | 42.4049i | −0.551187 | + | 1.59255i | 0.233301 | + | 0.972405i | \(0.425047\pi\) |
−0.784488 | + | 0.620145i | \(0.787074\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −53.2332 | + | 2.53581i | −1.99640 | + | 0.0951002i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.1516 | + | 7.94099i | 0.415306 | + | 0.295738i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.96172 | − | 12.3887i | 0.296099 | − | 0.460740i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.0852 | + | 35.7132i | 1.04162 | + | 1.32453i | 0.944231 | + | 0.329285i | \(0.106808\pi\) |
0.0973917 | + | 0.995246i | \(0.468950\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.6812 | + | 20.4052i | 0.654861 | + | 0.755750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.5931 | + | 30.2465i | 0.575946 | + | 1.11718i | 0.979353 | + | 0.202158i | \(0.0647955\pi\) |
−0.403407 | + | 0.915020i | \(0.632174\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1286 | + | 3.18497i | −0.482945 | + | 0.117161i | −0.469837 | − | 0.882753i | \(-0.655687\pi\) |
−0.0131073 | + | 0.999914i | \(0.504172\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −44.9617 | + | 23.1794i | −1.65171 | + | 0.851515i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.6784 | − | 28.7131i | −1.63034 | − | 1.04776i | −0.948753 | − | 0.316017i | \(-0.897654\pi\) |
−0.681586 | − | 0.731738i | \(-0.738709\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.3156 | − | 36.0062i | 1.02915 | − | 1.30867i | 0.0789989 | − | 0.996875i | \(-0.474828\pi\) |
0.950150 | − | 0.311794i | \(-0.100930\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.489441 | − | 10.2746i | −0.0177190 | − | 0.371967i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.03503 | − | 15.0748i | 0.217629 | − | 0.543611i | −0.778873 | − | 0.627182i | \(-0.784208\pi\) |
0.996502 | + | 0.0835710i | \(0.0266326\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −46.4427 | − | 26.8137i | −1.66827 | − | 0.963176i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.709877 | + | 1.55441i | −0.0254667 | + | 0.0557643i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.3536 | − | 35.6009i | 0.654234 | − | 1.26904i | −0.295310 | − | 0.955402i | \(-0.595423\pi\) |
0.949544 | − | 0.313635i | \(-0.101547\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.4220 | + | 1.95006i | 0.725206 | + | 0.0692488i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3554 | − | 15.0555i | −0.504087 | − | 0.528671i | 0.421691 | − | 0.906740i | \(-0.361437\pi\) |
−0.925778 | + | 0.378069i | \(0.876588\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38.4350 | + | 11.2855i | 1.34797 | + | 0.395801i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.47272 | + | 49.1492i | −0.331409 | + | 1.71951i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.8344 | + | 4.06214i | −0.483412 | + | 0.141943i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.9275 | + | 24.7218i | 0.903776 | + | 0.861749i | 0.990921 | − | 0.134447i | \(-0.0429257\pi\) |
−0.0871445 | + | 0.996196i | \(0.527774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.3800 | − | 18.9036i | 0.568902 | − | 0.656548i | −0.396279 | − | 0.918130i | \(-0.629699\pi\) |
0.965181 | + | 0.261582i | \(0.0842442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −51.4155 | − | 23.4807i | −1.78358 | − | 0.814535i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.1391 | − | 54.1602i | 0.454155 | − | 1.87205i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | − | 25.1147i | −0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.46995 | − | 6.95537i | −0.153589 | − | 0.238989i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.58356 | + | 0.946573i | −0.225947 | + | 0.0324863i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.591100 | − | 12.4087i | 0.0202389 | − | 0.424866i | −0.965897 | − | 0.258927i | \(-0.916631\pi\) |
0.986136 | − | 0.165940i | \(-0.0530657\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.3439 | + | 32.7761i | 0.387050 | + | 1.11831i | 0.955348 | + | 0.295484i | \(0.0954809\pi\) |
−0.568298 | + | 0.822823i | \(0.692398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.4924 | + | 26.1716i | 0.458227 | + | 0.888835i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.2102 | + | 3.68251i | 1.76907 | + | 0.124777i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.3339 | − | 5.41814i | 0.755888 | − | 0.183376i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.8110 | + | 5.52029i | −1.95214 | + | 0.186407i | −0.994746 | − | 0.102376i | \(-0.967355\pi\) |
−0.957395 | + | 0.288783i | \(0.906749\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.436884 | + | 0.151207i | −0.0147023 | + | 0.00508852i | −0.334409 | − | 0.942428i | \(-0.608537\pi\) |
0.319707 | + | 0.947516i | \(0.396416\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.46207 | − | 0.117283i | −0.0825751 | − | 0.00393354i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.30250 | + | 13.2450i | −0.176456 | + | 0.440766i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −56.5398 | + | 10.8972i | −1.87737 | + | 0.361834i | −0.994230 | − | 0.107269i | \(-0.965789\pi\) |
−0.883143 | + | 0.469103i | \(0.844577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.7039 | + | 24.8599i | −0.781919 | + | 0.820053i | −0.987340 | − | 0.158621i | \(-0.949295\pi\) |
0.205421 | + | 0.978674i | \(0.434144\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.3204 | − | 49.1148i | 0.834337 | − | 1.61839i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.44450 | + | 1.24208i | 0.211894 | + | 0.0408392i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 54.3943 | + | 5.19403i | 1.78654 | + | 0.170594i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.2714 | − | 20.2823i | 0.697143 | − | 0.664725i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.3333i | 0.762265i | 0.924520 | + | 0.381133i | \(0.124466\pi\) | ||||
−0.924520 | + | 0.381133i | \(0.875534\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 56.7911 | 1.85331 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.3862 | − | 108.769i | 0.337151 | − | 3.53081i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −78.0161 | + | 31.2329i | −2.51665 | + | 1.00751i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.65987 | + | 2.87498i | −0.0533779 | + | 0.0924532i | −0.891480 | − | 0.453061i | \(-0.850332\pi\) |
0.838102 | + | 0.545514i | \(0.183665\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.3697 | + | 6.15309i | 0.492729 | + | 0.197259i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.6883 | + | 47.9575i | 0.886735 | + | 1.53587i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.1967 | − | 34.5387i | −0.708685 | − | 1.10274i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.7526 | + | 49.4079i | −1.00865 | + | 1.56949i | −0.201211 | + | 0.979548i | \(0.564488\pi\) |
−0.807442 | + | 0.589947i | \(0.799149\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.9187 | + | 54.6621i | 0.600368 | + | 1.73465i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.3494 | + | 47.7198i | 1.30955 | + | 1.51130i | 0.667033 | + | 0.745028i | \(0.267564\pi\) |
0.642516 | + | 0.766272i | \(0.277891\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.648337 | + | 6.78969i | 0.0205125 | + | 0.214816i |
(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 | 804.2.ba.a.245.1 | yes | 20 | |
3.2 | odd | 2 | CM | 804.2.ba.a.245.1 | yes | 20 | |
67.32 | odd | 66 | inner | 804.2.ba.a.233.1 | ✓ | 20 | |
201.32 | even | 66 | inner | 804.2.ba.a.233.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.ba.a.233.1 | ✓ | 20 | 67.32 | odd | 66 | inner | |
804.2.ba.a.233.1 | ✓ | 20 | 201.32 | even | 66 | inner | |
804.2.ba.a.245.1 | yes | 20 | 1.1 | even | 1 | trivial | |
804.2.ba.a.245.1 | yes | 20 | 3.2 | odd | 2 | CM |