Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(881,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.5 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.881 |
Dual form | 4410.2.b.b.881.4 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.00000i | − 0.316228i | ||||||||
\(11\) | − 3.98174i | − 1.20054i | −0.799798 | − | 0.600270i | \(-0.795060\pi\) | ||||
0.799798 | − | 0.600270i | \(-0.204940\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0681483i | 0.0189010i | 0.999955 | + | 0.00945048i | \(0.00300822\pi\) | ||||
−0.999955 | + | 0.00945048i | \(0.996992\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.32780 | −1.77725 | −0.888627 | − | 0.458631i | \(-0.848340\pi\) | ||||
−0.888627 | + | 0.458631i | \(0.848340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.03528i | − 0.466924i | −0.972366 | − | 0.233462i | \(-0.924994\pi\) | ||||
0.972366 | − | 0.233462i | \(-0.0750055\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.98174 | 0.848910 | ||||||||
\(23\) | 3.73205i | 0.778186i | 0.921198 | + | 0.389093i | \(0.127212\pi\) | ||||
−0.921198 | + | 0.389093i | \(0.872788\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.0681483 | −0.0133650 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.898979i | 0.166936i | 0.996510 | + | 0.0834681i | \(0.0265997\pi\) | ||||
−0.996510 | + | 0.0834681i | \(0.973400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.82843i | 0.867211i | 0.901103 | + | 0.433606i | \(0.142759\pi\) | ||||
−0.901103 | + | 0.433606i | \(0.857241\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 7.32780i | − 1.25671i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.06815 | −0.668799 | −0.334400 | − | 0.942431i | \(-0.608534\pi\) | ||||
−0.334400 | + | 0.942431i | \(0.608534\pi\) | |||||||
\(38\) | 2.03528 | 0.330165 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 1.68921 | 0.263810 | 0.131905 | − | 0.991262i | \(-0.457891\pi\) | ||||
0.131905 | + | 0.991262i | \(0.457891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.964724 | −0.147119 | −0.0735595 | − | 0.997291i | \(-0.523436\pi\) | ||||
−0.0735595 | + | 0.997291i | \(0.523436\pi\) | |||||||
\(44\) | 3.98174i | 0.600270i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.73205 | −0.550261 | ||||||||
\(47\) | 1.66150 | 0.242354 | 0.121177 | − | 0.992631i | \(-0.461333\pi\) | ||||
0.121177 | + | 0.992631i | \(0.461333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 0.0681483i | − 0.00945048i | ||||||||
\(53\) | − 13.2268i | − 1.81684i | −0.418060 | − | 0.908419i | \(-0.637290\pi\) | ||||
0.418060 | − | 0.908419i | \(-0.362710\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.98174i | 0.536898i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.898979 | −0.118042 | ||||||||
\(59\) | 10.6422 | 1.38550 | 0.692751 | − | 0.721177i | \(-0.256399\pi\) | ||||
0.692751 | + | 0.721177i | \(0.256399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.52056i | 0.962909i | 0.876471 | + | 0.481454i | \(0.159891\pi\) | ||||
−0.876471 | + | 0.481454i | \(0.840109\pi\) | |||||||
\(62\) | −4.82843 | −0.613211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 0.0681483i | − 0.00845276i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6629 | 1.30268 | 0.651341 | − | 0.758785i | \(-0.274207\pi\) | ||||
0.651341 | + | 0.758785i | \(0.274207\pi\) | |||||||
\(68\) | 7.32780 | 0.888627 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.93426i | 1.17898i | 0.807776 | + | 0.589490i | \(0.200671\pi\) | ||||
−0.807776 | + | 0.589490i | \(0.799329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6569i | 1.36433i | 0.731198 | + | 0.682166i | \(0.238962\pi\) | ||||
−0.731198 | + | 0.682166i | \(0.761038\pi\) | |||||||
\(74\) | − 4.06815i | − 0.472913i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.03528i | 0.233462i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.5498 | 1.97450 | 0.987252 | − | 0.159163i | \(-0.0508795\pi\) | ||||
0.987252 | + | 0.159163i | \(0.0508795\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.68921i | 0.186542i | ||||||||
\(83\) | −14.3490 | −1.57501 | −0.787503 | − | 0.616311i | \(-0.788626\pi\) | ||||
−0.787503 | + | 0.616311i | \(0.788626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.32780 | 0.794812 | ||||||||
\(86\) | − 0.964724i | − 0.104029i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.98174 | −0.424455 | ||||||||
\(89\) | 1.82791 | 0.193758 | 0.0968791 | − | 0.995296i | \(-0.469114\pi\) | ||||
0.0968791 | + | 0.995296i | \(0.469114\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 3.73205i | − 0.389093i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.66150i | 0.171370i | ||||||||
\(95\) | 2.03528i | 0.208815i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1502i | 1.74134i | 0.491870 | + | 0.870668i | \(0.336313\pi\) | ||||
−0.491870 | + | 0.870668i | \(0.663687\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 6.73545 | 0.670202 | 0.335101 | − | 0.942182i | \(-0.391229\pi\) | ||||
0.335101 | + | 0.942182i | \(0.391229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.520042i | 0.0512413i | 0.999672 | + | 0.0256206i | \(0.00815619\pi\) | ||||
−0.999672 | + | 0.0256206i | \(0.991844\pi\) | |||||||
\(104\) | 0.0681483 | 0.00668250 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.2268 | 1.28470 | ||||||||
\(107\) | 6.12701i | 0.592320i | 0.955138 | + | 0.296160i | \(0.0957062\pi\) | ||||
−0.955138 | + | 0.296160i | \(0.904294\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5546 | 1.29829 | 0.649147 | − | 0.760663i | \(-0.275126\pi\) | ||||
0.649147 | + | 0.760663i | \(0.275126\pi\) | |||||||
\(110\) | −3.98174 | −0.379644 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6982i | 1.10047i | 0.835009 | + | 0.550236i | \(0.185462\pi\) | ||||
−0.835009 | + | 0.550236i | \(0.814538\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.73205i | − 0.348016i | ||||||||
\(116\) | − 0.898979i | − 0.0834681i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.6422i | 0.979698i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.85425 | −0.441296 | ||||||||
\(122\) | −7.52056 | −0.680879 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 4.82843i | − 0.433606i | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7530 | 0.954173 | 0.477086 | − | 0.878856i | \(-0.341693\pi\) | ||||
0.477086 | + | 0.878856i | \(0.341693\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0681483 | 0.00597701 | ||||||||
\(131\) | −3.70915 | −0.324070 | −0.162035 | − | 0.986785i | \(-0.551806\pi\) | ||||
−0.162035 | + | 0.986785i | \(0.551806\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.6629i | 0.921135i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.32780i | 0.628354i | ||||||||
\(137\) | − 13.5206i | − 1.15514i | −0.816341 | − | 0.577570i | \(-0.804001\pi\) | ||||
0.816341 | − | 0.577570i | \(-0.195999\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.06251i | 0.768672i | 0.923193 | + | 0.384336i | \(0.125570\pi\) | ||||
−0.923193 | + | 0.384336i | \(0.874430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.93426 | −0.833664 | ||||||||
\(143\) | 0.271349 | 0.0226913 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 0.898979i | − 0.0746562i | ||||||||
\(146\) | −11.6569 | −0.964728 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.06815 | 0.334400 | ||||||||
\(149\) | − 15.2865i | − 1.25232i | −0.779696 | − | 0.626158i | \(-0.784626\pi\) | ||||
0.779696 | − | 0.626158i | \(-0.215374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.87883 | −0.803928 | −0.401964 | − | 0.915656i | \(-0.631672\pi\) | ||||
−0.401964 | + | 0.915656i | \(0.631672\pi\) | |||||||
\(152\) | −2.03528 | −0.165083 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.82843i | − 0.387829i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 14.2884i | − 1.14034i | −0.821528 | − | 0.570168i | \(-0.806878\pi\) | ||||
0.821528 | − | 0.570168i | \(-0.193122\pi\) | |||||||
\(158\) | 17.5498i | 1.39619i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1.00000i | − 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.97758 | 0.781504 | 0.390752 | − | 0.920496i | \(-0.372215\pi\) | ||||
0.390752 | + | 0.920496i | \(0.372215\pi\) | |||||||
\(164\) | −1.68921 | −0.131905 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 14.3490i | − 1.11370i | ||||||||
\(167\) | −13.7778 | −1.06616 | −0.533079 | − | 0.846065i | \(-0.678965\pi\) | ||||
−0.533079 | + | 0.846065i | \(0.678965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9954 | 0.999643 | ||||||||
\(170\) | 7.32780i | 0.562017i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.964724 | 0.0735595 | ||||||||
\(173\) | 8.27276 | 0.628966 | 0.314483 | − | 0.949263i | \(-0.398169\pi\) | ||||
0.314483 | + | 0.949263i | \(0.398169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 3.98174i | − 0.300135i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.82791i | 0.137008i | ||||||||
\(179\) | 11.5182i | 0.860907i | 0.902613 | + | 0.430454i | \(0.141646\pi\) | ||||
−0.902613 | + | 0.430454i | \(0.858354\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5924i | 1.23330i | 0.787237 | + | 0.616650i | \(0.211511\pi\) | ||||
−0.787237 | + | 0.616650i | \(0.788489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.73205 | 0.275130 | ||||||||
\(185\) | 4.06815 | 0.299096 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.1774i | 2.13366i | ||||||||
\(188\) | −1.66150 | −0.121177 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.03528 | −0.147654 | ||||||||
\(191\) | 18.4336i | 1.33381i | 0.745142 | + | 0.666905i | \(0.232382\pi\) | ||||
−0.745142 | + | 0.666905i | \(0.767618\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.35827 | −0.457679 | −0.228839 | − | 0.973464i | \(-0.573493\pi\) | ||||
−0.228839 | + | 0.973464i | \(0.573493\pi\) | |||||||
\(194\) | −17.1502 | −1.23131 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 12.8389i | − 0.914734i | −0.889278 | − | 0.457367i | \(-0.848792\pi\) | ||||
0.889278 | − | 0.457367i | \(-0.151208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.62962i | 0.682626i | 0.939950 | + | 0.341313i | \(0.110872\pi\) | ||||
−0.939950 | + | 0.341313i | \(0.889128\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.73545i | 0.473905i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.68921 | −0.117980 | ||||||||
\(206\) | −0.520042 | −0.0362331 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0681483i | 0.00472524i | ||||||||
\(209\) | −8.10394 | −0.560561 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5619 | −1.00248 | −0.501241 | − | 0.865308i | \(-0.667123\pi\) | ||||
−0.501241 | + | 0.865308i | \(0.667123\pi\) | |||||||
\(212\) | 13.2268i | 0.908419i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.12701 | −0.418834 | ||||||||
\(215\) | 0.964724 | 0.0657936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.5546i | 0.918033i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 3.98174i | − 0.268449i | ||||||||
\(221\) | − 0.499378i | − 0.0335918i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 23.6609i | − 1.58445i | −0.610227 | − | 0.792227i | \(-0.708922\pi\) | ||||
0.610227 | − | 0.792227i | \(-0.291078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.6982 | −0.778152 | ||||||||
\(227\) | 8.64048 | 0.573489 | 0.286744 | − | 0.958007i | \(-0.407427\pi\) | ||||
0.286744 | + | 0.958007i | \(0.407427\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 14.0754i | − 0.930126i | −0.885278 | − | 0.465063i | \(-0.846032\pi\) | ||||
0.885278 | − | 0.465063i | \(-0.153968\pi\) | |||||||
\(230\) | 3.73205 | 0.246084 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.898979 | 0.0590209 | ||||||||
\(233\) | 20.1976i | 1.32319i | 0.749863 | + | 0.661593i | \(0.230119\pi\) | ||||
−0.749863 | + | 0.661593i | \(0.769881\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.66150 | −0.108384 | ||||||||
\(236\) | −10.6422 | −0.692751 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.5040i | 1.52035i | 0.649721 | + | 0.760173i | \(0.274886\pi\) | ||||
−0.649721 | + | 0.760173i | \(0.725114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8685i | 0.957765i | 0.877879 | + | 0.478883i | \(0.158958\pi\) | ||||
−0.877879 | + | 0.478883i | \(0.841042\pi\) | |||||||
\(242\) | − 4.85425i | − 0.312043i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 7.52056i | − 0.481454i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.138701 | 0.00882531 | ||||||||
\(248\) | 4.82843 | 0.306605 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.00000i | − 0.0632456i | ||||||||
\(251\) | −4.31736 | −0.272509 | −0.136255 | − | 0.990674i | \(-0.543507\pi\) | ||||
−0.136255 | + | 0.990674i | \(0.543507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.8601 | 0.934244 | ||||||||
\(254\) | 10.7530i | 0.674702i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.83324 | −0.301489 | −0.150744 | − | 0.988573i | \(-0.548167\pi\) | ||||
−0.150744 | + | 0.988573i | \(0.548167\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.0681483i | 0.00422638i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 3.70915i | − 0.229152i | ||||||||
\(263\) | − 6.66490i | − 0.410975i | −0.978660 | − | 0.205488i | \(-0.934122\pi\) | ||||
0.978660 | − | 0.205488i | \(-0.0658780\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.2268i | 0.812515i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.6629 | −0.651341 | ||||||||
\(269\) | −31.7400 | −1.93522 | −0.967612 | − | 0.252441i | \(-0.918767\pi\) | ||||
−0.967612 | + | 0.252441i | \(0.918767\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.4641i | 1.06087i | 0.847726 | + | 0.530434i | \(0.177971\pi\) | ||||
−0.847726 | + | 0.530434i | \(0.822029\pi\) | |||||||
\(272\) | −7.32780 | −0.444313 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.5206 | 0.816807 | ||||||||
\(275\) | − 3.98174i | − 0.240108i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.5047 | −1.41226 | −0.706130 | − | 0.708082i | \(-0.749561\pi\) | ||||
−0.706130 | + | 0.708082i | \(0.749561\pi\) | |||||||
\(278\) | −9.06251 | −0.543533 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4159i | 0.919635i | 0.888013 | + | 0.459817i | \(0.152085\pi\) | ||||
−0.888013 | + | 0.459817i | \(0.847915\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.7108i | 1.64724i | 0.567144 | + | 0.823619i | \(0.308048\pi\) | ||||
−0.567144 | + | 0.823619i | \(0.691952\pi\) | |||||||
\(284\) | − 9.93426i | − 0.589490i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.271349i | 0.0160452i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.6967 | 2.15863 | ||||||||
\(290\) | 0.898979 | 0.0527899 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 11.6569i | − 0.682166i | ||||||||
\(293\) | 2.84377 | 0.166135 | 0.0830673 | − | 0.996544i | \(-0.473528\pi\) | ||||
0.0830673 | + | 0.996544i | \(0.473528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6422 | −0.619615 | ||||||||
\(296\) | 4.06815i | 0.236456i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2865 | 0.885522 | ||||||||
\(299\) | −0.254333 | −0.0147085 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 9.87883i | − 0.568463i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 2.03528i | − 0.116731i | ||||||||
\(305\) | − 7.52056i | − 0.430626i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.52180i | − 0.143927i | −0.997407 | − | 0.0719634i | \(-0.977074\pi\) | ||||
0.997407 | − | 0.0719634i | \(-0.0229265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.82843 | 0.274236 | ||||||||
\(311\) | −10.9939 | −0.623410 | −0.311705 | − | 0.950179i | \(-0.600900\pi\) | ||||
−0.311705 | + | 0.950179i | \(0.600900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.9461i | 1.41004i | 0.709188 | + | 0.705020i | \(0.249062\pi\) | ||||
−0.709188 | + | 0.705020i | \(0.750938\pi\) | |||||||
\(314\) | 14.2884 | 0.806339 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.5498 | −0.987252 | ||||||||
\(317\) | 15.0693i | 0.846377i | 0.906042 | + | 0.423188i | \(0.139089\pi\) | ||||
−0.906042 | + | 0.423188i | \(0.860911\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.57950 | 0.200414 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.9141i | 0.829843i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0681483i | 0.00378019i | ||||||||
\(326\) | 9.97758i | 0.552607i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 1.68921i | − 0.0932711i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.1808 | 1.65889 | 0.829444 | − | 0.558590i | \(-0.188658\pi\) | ||||
0.829444 | + | 0.558590i | \(0.188658\pi\) | |||||||
\(332\) | 14.3490 | 0.787503 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 13.7778i | − 0.753888i | ||||||||
\(335\) | −10.6629 | −0.582577 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.5911 | −1.17614 | −0.588071 | − | 0.808809i | \(-0.700113\pi\) | ||||
−0.588071 | + | 0.808809i | \(0.700113\pi\) | |||||||
\(338\) | 12.9954i | 0.706854i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.32780 | −0.397406 | ||||||||
\(341\) | 19.2255 | 1.04112 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.964724i | 0.0520144i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.27276i | 0.444746i | ||||||||
\(347\) | − 23.1842i | − 1.24459i | −0.782781 | − | 0.622297i | \(-0.786200\pi\) | ||||
0.782781 | − | 0.622297i | \(-0.213800\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.7287i | 0.574292i | 0.957887 | + | 0.287146i | \(0.0927064\pi\) | ||||
−0.957887 | + | 0.287146i | \(0.907294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.98174 | 0.212227 | ||||||||
\(353\) | −8.74756 | −0.465585 | −0.232793 | − | 0.972526i | \(-0.574786\pi\) | ||||
−0.232793 | + | 0.972526i | \(0.574786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 9.93426i | − 0.527256i | ||||||||
\(356\) | −1.82791 | −0.0968791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.5182 | −0.608753 | ||||||||
\(359\) | − 25.7566i | − 1.35938i | −0.733498 | − | 0.679691i | \(-0.762114\pi\) | ||||
0.733498 | − | 0.679691i | \(-0.237886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.8577 | 0.781982 | ||||||||
\(362\) | −16.5924 | −0.872075 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 11.6569i | − 0.610148i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 19.9377i | − 1.04074i | −0.853941 | − | 0.520369i | \(-0.825794\pi\) | ||||
0.853941 | − | 0.520369i | \(-0.174206\pi\) | |||||||
\(368\) | 3.73205i | 0.194547i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.06815i | 0.211493i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.03152 | 0.0534103 | 0.0267052 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267052 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(374\) | −29.1774 | −1.50873 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 1.66150i | − 0.0856852i | ||||||||
\(377\) | −0.0612640 | −0.00315525 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.09497 | 0.261711 | 0.130855 | − | 0.991401i | \(-0.458228\pi\) | ||||
0.130855 | + | 0.991401i | \(0.458228\pi\) | |||||||
\(380\) | − 2.03528i | − 0.104407i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.4336 | −0.943147 | ||||||||
\(383\) | 8.46750 | 0.432669 | 0.216335 | − | 0.976319i | \(-0.430590\pi\) | ||||
0.216335 | + | 0.976319i | \(0.430590\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 6.35827i | − 0.323628i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 17.1502i | − 0.870668i | ||||||||
\(389\) | − 5.74150i | − 0.291106i | −0.989350 | − | 0.145553i | \(-0.953504\pi\) | ||||
0.989350 | − | 0.145553i | \(-0.0464961\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 27.3477i | − 1.38303i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.8389 | 0.646815 | ||||||||
\(395\) | −17.5498 | −0.883025 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.8758i | 0.846973i | 0.905902 | + | 0.423487i | \(0.139194\pi\) | ||||
−0.905902 | + | 0.423487i | \(0.860806\pi\) | |||||||
\(398\) | −9.62962 | −0.482689 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − 1.88876i | − 0.0943203i | −0.998887 | − | 0.0471602i | \(-0.984983\pi\) | ||||
0.998887 | − | 0.0471602i | \(-0.0150171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.329049 | −0.0163911 | ||||||||
\(404\) | −6.73545 | −0.335101 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.1983i | 0.802920i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 32.9802i | − 1.63076i | −0.578923 | − | 0.815382i | \(-0.696527\pi\) | ||||
0.578923 | − | 0.815382i | \(-0.303473\pi\) | |||||||
\(410\) | − 1.68921i | − 0.0834242i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 0.520042i | − 0.0256206i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.3490 | 0.704364 | ||||||||
\(416\) | −0.0681483 | −0.00334125 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 8.10394i | − 0.396377i | ||||||||
\(419\) | 0.300470 | 0.0146789 | 0.00733945 | − | 0.999973i | \(-0.497664\pi\) | ||||
0.00733945 | + | 0.999973i | \(0.497664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.8625 | 1.40667 | 0.703335 | − | 0.710858i | \(-0.251693\pi\) | ||||
0.703335 | + | 0.710858i | \(0.251693\pi\) | |||||||
\(422\) | − 14.5619i | − 0.708862i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.2268 | −0.642349 | ||||||||
\(425\) | −7.32780 | −0.355451 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 6.12701i | − 0.296160i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.964724i | 0.0465231i | ||||||||
\(431\) | 33.5897i | 1.61796i | 0.587839 | + | 0.808978i | \(0.299979\pi\) | ||||
−0.587839 | + | 0.808978i | \(0.700021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2207i | 0.539234i | 0.962968 | + | 0.269617i | \(0.0868971\pi\) | ||||
−0.962968 | + | 0.269617i | \(0.913103\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.5546 | −0.649147 | ||||||||
\(437\) | 7.59575 | 0.363354 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 16.8673i | − 0.805031i | −0.915413 | − | 0.402515i | \(-0.868136\pi\) | ||||
0.915413 | − | 0.402515i | \(-0.131864\pi\) | |||||||
\(440\) | 3.98174 | 0.189822 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.499378 | 0.0237530 | ||||||||
\(443\) | − 2.05646i | − 0.0977052i | −0.998806 | − | 0.0488526i | \(-0.984444\pi\) | ||||
0.998806 | − | 0.0488526i | \(-0.0155565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.82791 | −0.0866513 | ||||||||
\(446\) | 23.6609 | 1.12038 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.5892i | 0.594122i | 0.954858 | + | 0.297061i | \(0.0960065\pi\) | ||||
−0.954858 | + | 0.297061i | \(0.903994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 6.72600i | − 0.316715i | ||||||||
\(452\) | − 11.6982i | − 0.550236i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.64048i | 0.405518i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.9529 | 1.63503 | 0.817515 | − | 0.575907i | \(-0.195351\pi\) | ||||
0.817515 | + | 0.575907i | \(0.195351\pi\) | |||||||
\(458\) | 14.0754 | 0.657698 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.73205i | 0.174008i | ||||||||
\(461\) | 23.3750 | 1.08868 | 0.544341 | − | 0.838864i | \(-0.316780\pi\) | ||||
0.544341 | + | 0.838864i | \(0.316780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.35693 | −0.295431 | −0.147716 | − | 0.989030i | \(-0.547192\pi\) | ||||
−0.147716 | + | 0.989030i | \(0.547192\pi\) | |||||||
\(464\) | 0.898979i | 0.0417341i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.1976 | −0.935634 | ||||||||
\(467\) | −7.79315 | −0.360624 | −0.180312 | − | 0.983609i | \(-0.557711\pi\) | ||||
−0.180312 | + | 0.983609i | \(0.557711\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 1.66150i | − 0.0766392i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 10.6422i | − 0.489849i | ||||||||
\(473\) | 3.84128i | 0.176622i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.03528i | − 0.0933849i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.5040 | −1.07505 | ||||||||
\(479\) | −27.5040 | −1.25669 | −0.628344 | − | 0.777935i | \(-0.716267\pi\) | ||||
−0.628344 | + | 0.777935i | \(0.716267\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 0.277238i | − 0.0126409i | ||||||||
\(482\) | −14.8685 | −0.677242 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.85425 | 0.220648 | ||||||||
\(485\) | − 17.1502i | − 0.778750i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.4468 | 1.60625 | 0.803124 | − | 0.595812i | \(-0.203170\pi\) | ||||
0.803124 | + | 0.595812i | \(0.203170\pi\) | |||||||
\(488\) | 7.52056 | 0.340440 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.64349i | 0.0741695i | 0.999312 | + | 0.0370848i | \(0.0118072\pi\) | ||||
−0.999312 | + | 0.0370848i | \(0.988193\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6.58755i | − 0.296688i | ||||||||
\(494\) | 0.138701i | 0.00624044i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.82843i | 0.216803i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.7330 | −1.55486 | −0.777430 | − | 0.628969i | \(-0.783477\pi\) | ||||
−0.777430 | + | 0.628969i | \(0.783477\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 4.31736i | − 0.192693i | ||||||||
\(503\) | 28.9613 | 1.29132 | 0.645660 | − | 0.763625i | \(-0.276582\pi\) | ||||
0.645660 | + | 0.763625i | \(0.276582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.73545 | −0.299724 | ||||||||
\(506\) | 14.8601i | 0.660610i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.7530 | −0.477086 | ||||||||
\(509\) | 21.4621 | 0.951291 | 0.475646 | − | 0.879637i | \(-0.342214\pi\) | ||||
0.475646 | + | 0.879637i | \(0.342214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 4.83324i | − 0.213185i | ||||||||
\(515\) | − 0.520042i | − 0.0229158i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.61565i | − 0.290956i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0681483 | −0.00298850 | ||||||||
\(521\) | 40.2436 | 1.76310 | 0.881552 | − | 0.472087i | \(-0.156499\pi\) | ||||
0.881552 | + | 0.472087i | \(0.156499\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.6889i | 1.29820i | 0.760701 | + | 0.649102i | \(0.224855\pi\) | ||||
−0.760701 | + | 0.649102i | \(0.775145\pi\) | |||||||
\(524\) | 3.70915 | 0.162035 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.66490 | 0.290603 | ||||||||
\(527\) | − 35.3818i | − 1.54125i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.07180 | 0.394426 | ||||||||
\(530\) | −13.2268 | −0.574535 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.115117i | 0.00498627i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 6.12701i | − 0.264894i | ||||||||
\(536\) | − 10.6629i | − 0.460567i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 31.7400i | − 1.36841i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2583 | −0.741992 | −0.370996 | − | 0.928635i | \(-0.620984\pi\) | ||||
−0.370996 | + | 0.928635i | \(0.620984\pi\) | |||||||
\(542\) | −17.4641 | −0.750147 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 7.32780i | − 0.314177i | ||||||||
\(545\) | −13.5546 | −0.580615 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.9703 | −0.768354 | −0.384177 | − | 0.923260i | \(-0.625515\pi\) | ||||
−0.384177 | + | 0.923260i | \(0.625515\pi\) | |||||||
\(548\) | 13.5206i | 0.577570i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.98174 | 0.169782 | ||||||||
\(551\) | 1.82967 | 0.0779466 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 23.5047i | − 0.998619i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 9.06251i | − 0.384336i | ||||||||
\(557\) | 45.2546i | 1.91750i | 0.284256 | + | 0.958748i | \(0.408253\pi\) | ||||
−0.284256 | + | 0.958748i | \(0.591747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 0.0657443i | − 0.00278069i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.4159 | −0.650280 | ||||||||
\(563\) | 15.8667 | 0.668703 | 0.334351 | − | 0.942448i | \(-0.391483\pi\) | ||||
0.334351 | + | 0.942448i | \(0.391483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 11.6982i | − 0.492146i | ||||||||
\(566\) | −27.7108 | −1.16477 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.93426 | 0.416832 | ||||||||
\(569\) | − 0.0605496i | − 0.00253837i | −0.999999 | − | 0.00126918i | \(-0.999596\pi\) | ||||
0.999999 | − | 0.00126918i | \(-0.000403994\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.5649 | −0.567674 | −0.283837 | − | 0.958873i | \(-0.591607\pi\) | ||||
−0.283837 | + | 0.958873i | \(0.591607\pi\) | |||||||
\(572\) | −0.271349 | −0.0113457 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.73205i | 0.155637i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.6768i | 1.81829i | 0.416481 | + | 0.909144i | \(0.363263\pi\) | ||||
−0.416481 | + | 0.909144i | \(0.636737\pi\) | |||||||
\(578\) | 36.6967i | 1.52638i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.898979i | 0.0373281i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52.6656 | −2.18119 | ||||||||
\(584\) | 11.6569 | 0.482364 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.84377i | 0.117475i | ||||||||
\(587\) | −45.4100 | −1.87427 | −0.937135 | − | 0.348967i | \(-0.886532\pi\) | ||||
−0.937135 | + | 0.348967i | \(0.886532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.82718 | 0.404922 | ||||||||
\(590\) | − 10.6422i | − 0.438134i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.06815 | −0.167200 | ||||||||
\(593\) | 25.7012 | 1.05542 | 0.527711 | − | 0.849424i | \(-0.323050\pi\) | ||||
0.527711 | + | 0.849424i | \(0.323050\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.2865i | 0.626158i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 0.254333i | − 0.0104005i | ||||||||
\(599\) | − 26.5982i | − 1.08677i | −0.839483 | − | 0.543386i | \(-0.817142\pi\) | ||||
0.839483 | − | 0.543386i | \(-0.182858\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.9681i | 0.528979i | 0.964389 | + | 0.264489i | \(0.0852034\pi\) | ||||
−0.964389 | + | 0.264489i | \(0.914797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.87883 | 0.401964 | ||||||||
\(605\) | 4.85425 | 0.197353 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 16.3115i | − 0.662064i | −0.943620 | − | 0.331032i | \(-0.892603\pi\) | ||||
0.943620 | − | 0.331032i | \(-0.107397\pi\) | |||||||
\(608\) | 2.03528 | 0.0825413 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.52056 | 0.304498 | ||||||||
\(611\) | 0.113228i | 0.00458073i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.3879 | −0.581122 | −0.290561 | − | 0.956856i | \(-0.593842\pi\) | ||||
−0.290561 | + | 0.956856i | \(0.593842\pi\) | |||||||
\(614\) | 2.52180 | 0.101772 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 8.65760i | − 0.348542i | −0.984698 | − | 0.174271i | \(-0.944243\pi\) | ||||
0.984698 | − | 0.174271i | \(-0.0557569\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 44.8553i | − 1.80289i | −0.432896 | − | 0.901444i | \(-0.642508\pi\) | ||||
0.432896 | − | 0.901444i | \(-0.357492\pi\) | |||||||
\(620\) | 4.82843i | 0.193914i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 10.9939i | − 0.440817i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.9461 | −0.997049 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.2884i | 0.570168i | ||||||||
\(629\) | 29.8106 | 1.18863 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.1878 | −1.52023 | −0.760116 | − | 0.649788i | \(-0.774858\pi\) | ||||
−0.760116 | + | 0.649788i | \(0.774858\pi\) | |||||||
\(632\) | − 17.5498i | − 0.698093i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.0693 | −0.598479 | ||||||||
\(635\) | −10.7530 | −0.426719 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.57950i | 0.141714i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | − 8.55094i | − 0.337742i | −0.985638 | − | 0.168871i | \(-0.945988\pi\) | ||||
0.985638 | − | 0.168871i | \(-0.0540121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.75058i | 0.108472i | 0.998528 | + | 0.0542361i | \(0.0172724\pi\) | ||||
−0.998528 | + | 0.0542361i | \(0.982728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.9141 | −0.586788 | ||||||||
\(647\) | 27.7626 | 1.09146 | 0.545731 | − | 0.837961i | \(-0.316252\pi\) | ||||
0.545731 | + | 0.837961i | \(0.316252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 42.3746i | − 1.66335i | ||||||||
\(650\) | −0.0681483 | −0.00267300 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.97758 | −0.390752 | ||||||||
\(653\) | − 14.1199i | − 0.552553i | −0.961078 | − | 0.276277i | \(-0.910899\pi\) | ||||
0.961078 | − | 0.276277i | \(-0.0891006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.70915 | 0.144928 | ||||||||
\(656\) | 1.68921 | 0.0659526 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 9.92570i | − 0.386650i | −0.981135 | − | 0.193325i | \(-0.938073\pi\) | ||||
0.981135 | − | 0.193325i | \(-0.0619272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 18.3631i | − 0.714241i | −0.934058 | − | 0.357121i | \(-0.883759\pi\) | ||||
0.934058 | − | 0.357121i | \(-0.116241\pi\) | |||||||
\(662\) | 30.1808i | 1.17301i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.3490i | 0.556849i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.35504 | −0.129908 | ||||||||
\(668\) | 13.7778 | 0.533079 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 10.6629i | − 0.411944i | ||||||||
\(671\) | 29.9449 | 1.15601 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.6050 | −1.25683 | −0.628415 | − | 0.777878i | \(-0.716296\pi\) | ||||
−0.628415 | + | 0.777878i | \(0.716296\pi\) | |||||||
\(674\) | − 21.5911i | − 0.831658i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9954 | −0.499821 | ||||||||
\(677\) | −18.3385 | −0.704804 | −0.352402 | − | 0.935849i | \(-0.614635\pi\) | ||||
−0.352402 | + | 0.935849i | \(0.614635\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 7.32780i | − 0.281008i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.2255i | 0.736184i | ||||||||
\(683\) | − 24.4770i | − 0.936587i | −0.883573 | − | 0.468294i | \(-0.844869\pi\) | ||||
0.883573 | − | 0.468294i | \(-0.155131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.5206i | 0.516594i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.964724 | −0.0367798 | ||||||||
\(689\) | 0.901383 | 0.0343400 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 18.3734i | − 0.698957i | −0.936944 | − | 0.349479i | \(-0.886359\pi\) | ||||
0.936944 | − | 0.349479i | \(-0.113641\pi\) | |||||||
\(692\) | −8.27276 | −0.314483 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.1842 | 0.880061 | ||||||||
\(695\) | − 9.06251i | − 0.343761i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.3782 | −0.468858 | ||||||||
\(698\) | −10.7287 | −0.406085 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 14.2399i | − 0.537834i | −0.963163 | − | 0.268917i | \(-0.913334\pi\) | ||||
0.963163 | − | 0.268917i | \(-0.0866658\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.27981i | 0.312279i | ||||||||
\(704\) | 3.98174i | 0.150067i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 8.74756i | − 0.329219i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.5171 | 1.40898 | 0.704492 | − | 0.709712i | \(-0.251175\pi\) | ||||
0.704492 | + | 0.709712i | \(0.251175\pi\) | |||||||
\(710\) | 9.93426 | 0.372826 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 1.82791i | − 0.0685039i | ||||||||
\(713\) | −18.0199 | −0.674852 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.271349 | −0.0101479 | ||||||||
\(716\) | − 11.5182i | − 0.430454i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.7566 | 0.961229 | ||||||||
\(719\) | −5.31467 | −0.198204 | −0.0991019 | − | 0.995077i | \(-0.531597\pi\) | ||||
−0.0991019 | + | 0.995077i | \(0.531597\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.8577i | 0.552945i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 16.5924i | − 0.616650i | ||||||||
\(725\) | 0.898979i | 0.0333873i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 2.93413i | − 0.108821i | −0.998519 | − | 0.0544104i | \(-0.982672\pi\) | ||||
0.998519 | − | 0.0544104i | \(-0.0173279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.6569 | 0.431440 | ||||||||
\(731\) | 7.06931 | 0.261468 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.6482i | 0.504108i | 0.967713 | + | 0.252054i | \(0.0811061\pi\) | ||||
−0.967713 | + | 0.252054i | \(0.918894\pi\) | |||||||
\(734\) | 19.9377 | 0.735914 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.73205 | −0.137565 | ||||||||
\(737\) | − 42.4569i | − 1.56392i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3300 | 1.15249 | 0.576246 | − | 0.817277i | \(-0.304517\pi\) | ||||
0.576246 | + | 0.817277i | \(0.304517\pi\) | |||||||
\(740\) | −4.06815 | −0.149548 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 4.72061i | − 0.173182i | −0.996244 | − | 0.0865911i | \(-0.972403\pi\) | ||||
0.996244 | − | 0.0865911i | \(-0.0275974\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.2865i | 0.560053i | ||||||||
\(746\) | 1.03152i | 0.0377668i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 29.1774i | − 1.06683i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.6788 | −0.937032 | −0.468516 | − | 0.883455i | \(-0.655211\pi\) | ||||
−0.468516 | + | 0.883455i | \(0.655211\pi\) | |||||||
\(752\) | 1.66150 | 0.0605886 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 0.0612640i | − 0.00223110i | ||||||||
\(755\) | 9.87883 | 0.359527 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.8781 | −1.37670 | −0.688352 | − | 0.725377i | \(-0.741665\pi\) | ||||
−0.688352 | + | 0.725377i | \(0.741665\pi\) | |||||||
\(758\) | 5.09497i | 0.185058i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.03528 | 0.0738272 | ||||||||
\(761\) | −20.7066 | −0.750615 | −0.375308 | − | 0.926900i | \(-0.622463\pi\) | ||||
−0.375308 | + | 0.926900i | \(0.622463\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 18.4336i | − 0.666905i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.46750i | 0.305943i | ||||||||
\(767\) | 0.725251i | 0.0261873i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 3.34563i | − 0.120647i | −0.998179 | − | 0.0603233i | \(-0.980787\pi\) | ||||
0.998179 | − | 0.0603233i | \(-0.0192132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.35827 | 0.228839 | ||||||||
\(773\) | −28.7264 | −1.03322 | −0.516609 | − | 0.856221i | \(-0.672806\pi\) | ||||
−0.516609 | + | 0.856221i | \(0.672806\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.82843i | 0.173442i | ||||||||
\(776\) | 17.1502 | 0.615656 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.74150 | 0.205843 | ||||||||
\(779\) | − 3.43801i | − 0.123180i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.5556 | 1.41541 | ||||||||
\(782\) | 27.3477 | 0.977953 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.2884i | 0.509974i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.49030i | 0.195708i | 0.995201 | + | 0.0978541i | \(0.0311978\pi\) | ||||
−0.995201 | + | 0.0978541i | \(0.968802\pi\) | |||||||
\(788\) | 12.8389i | 0.457367i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 17.5498i | − 0.624393i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.512514 | −0.0181999 | ||||||||
\(794\) | −16.8758 | −0.598901 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 9.62962i | − 0.341313i | ||||||||
\(797\) | 50.8854 | 1.80245 | 0.901227 | − | 0.433347i | \(-0.142668\pi\) | ||||
0.901227 | + | 0.433347i | \(0.142668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.1751 | −0.430725 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.88876 | 0.0666945 | ||||||||
\(803\) | 46.4146 | 1.63793 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 0.329049i | − 0.0115903i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 6.73545i | − 0.236952i | ||||||||
\(809\) | 2.08433i | 0.0732812i | 0.999329 | + | 0.0366406i | \(0.0116657\pi\) | ||||
−0.999329 | + | 0.0366406i | \(0.988334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 27.0199i | − 0.948797i | −0.880310 | − | 0.474398i | \(-0.842666\pi\) | ||||
0.880310 | − | 0.474398i | \(-0.157334\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.1983 | −0.567750 | ||||||||
\(815\) | −9.97758 | −0.349499 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.96348i | 0.0686934i | ||||||||
\(818\) | 32.9802 | 1.15312 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.68921 | 0.0589898 | ||||||||
\(821\) | − 9.30787i | − 0.324847i | −0.986721 | − | 0.162423i | \(-0.948069\pi\) | ||||
0.986721 | − | 0.162423i | \(-0.0519311\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.5186 | −1.41239 | −0.706195 | − | 0.708018i | \(-0.749590\pi\) | ||||
−0.706195 | + | 0.708018i | \(0.749590\pi\) | |||||||
\(824\) | 0.520042 | 0.0181165 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 14.0131i | − 0.487284i | −0.969865 | − | 0.243642i | \(-0.921658\pi\) | ||||
0.969865 | − | 0.243642i | \(-0.0783423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 21.7707i | − 0.756129i | −0.925779 | − | 0.378064i | \(-0.876590\pi\) | ||||
0.925779 | − | 0.378064i | \(-0.123410\pi\) | |||||||
\(830\) | 14.3490i | 0.498061i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 0.0681483i | − 0.00236262i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.7778 | 0.476801 | ||||||||
\(836\) | 8.10394 | 0.280281 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.300470i | 0.0103796i | ||||||||
\(839\) | 53.7026 | 1.85402 | 0.927009 | − | 0.375039i | \(-0.122371\pi\) | ||||
0.927009 | + | 0.375039i | \(0.122371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1918 | 0.972132 | ||||||||
\(842\) | 28.8625i | 0.994666i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.5619 | 0.501241 | ||||||||
\(845\) | −12.9954 | −0.447054 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 13.2268i | − 0.454210i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 7.32780i | − 0.251342i | ||||||||
\(851\) | − 15.1825i | − 0.520451i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.95355i | 0.272324i | 0.990687 | + | 0.136162i | \(0.0434768\pi\) | ||||
−0.990687 | + | 0.136162i | \(0.956523\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.12701 | 0.209417 | ||||||||
\(857\) | 2.29303 | 0.0783283 | 0.0391641 | − | 0.999233i | \(-0.487530\pi\) | ||||
0.0391641 | + | 0.999233i | \(0.487530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 44.0003i | − 1.50127i | −0.660716 | − | 0.750636i | \(-0.729747\pi\) | ||||
0.660716 | − | 0.750636i | \(-0.270253\pi\) | |||||||
\(860\) | −0.964724 | −0.0328968 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.5897 | −1.14407 | ||||||||
\(863\) | 33.1352i | 1.12794i | 0.825797 | + | 0.563968i | \(0.190726\pi\) | ||||
−0.825797 | + | 0.563968i | \(0.809274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.27276 | −0.281282 | ||||||||
\(866\) | −11.2207 | −0.381296 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 69.8787i | − 2.37047i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.726659i | 0.0246219i | ||||||||
\(872\) | − 13.5546i | − 0.459016i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.59575i | 0.256930i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.68871 | −0.192094 | −0.0960471 | − | 0.995377i | \(-0.530620\pi\) | ||||
−0.0960471 | + | 0.995377i | \(0.530620\pi\) | |||||||
\(878\) | 16.8673 | 0.569243 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.98174i | 0.134224i | ||||||||
\(881\) | −22.4073 | −0.754923 | −0.377461 | − | 0.926025i | \(-0.623203\pi\) | ||||
−0.377461 | + | 0.926025i | \(0.623203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.7564 | −0.631204 | −0.315602 | − | 0.948892i | \(-0.602206\pi\) | ||||
−0.315602 | + | 0.948892i | \(0.602206\pi\) | |||||||
\(884\) | 0.499378i | 0.0167959i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.05646 | 0.0690880 | ||||||||
\(887\) | 1.47090 | 0.0493880 | 0.0246940 | − | 0.999695i | \(-0.492139\pi\) | ||||
0.0246940 | + | 0.999695i | \(0.492139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 1.82791i | − 0.0612717i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.6609i | 0.792227i | ||||||||
\(893\) | − 3.38161i | − 0.113161i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 11.5182i | − 0.385009i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.5892 | −0.420108 | ||||||||
\(899\) | −4.34066 | −0.144769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 96.9233i | 3.22898i | ||||||||
\(902\) | 6.72600 | 0.223951 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.6982 | 0.389076 | ||||||||
\(905\) | − 16.5924i | − 0.551549i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.8459 | 0.625767 | 0.312883 | − | 0.949792i | \(-0.398705\pi\) | ||||
0.312883 | + | 0.949792i | \(0.398705\pi\) | |||||||
\(908\) | −8.64048 | −0.286744 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 5.45859i | − 0.180851i | −0.995903 | − | 0.0904256i | \(-0.971177\pi\) | ||||
0.995903 | − | 0.0904256i | \(-0.0288227\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.1339i | 1.89086i | ||||||||
\(914\) | 34.9529i | 1.15614i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0754i | 0.465063i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.9611 | 0.988324 | 0.494162 | − | 0.869370i | \(-0.335475\pi\) | ||||
0.494162 | + | 0.869370i | \(0.335475\pi\) | |||||||
\(920\) | −3.73205 | −0.123042 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.3750i | 0.769814i | ||||||||
\(923\) | −0.677003 | −0.0222838 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.06815 | −0.133760 | ||||||||
\(926\) | − 6.35693i | − 0.208902i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.898979 | −0.0295104 | ||||||||
\(929\) | −46.7863 | −1.53501 | −0.767504 | − | 0.641044i | \(-0.778502\pi\) | ||||
−0.767504 | + | 0.641044i | \(0.778502\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 20.1976i | − 0.661593i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 7.79315i | − 0.255000i | ||||||||
\(935\) | − 29.1774i | − 0.954203i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 19.1632i | − 0.626036i | −0.949747 | − | 0.313018i | \(-0.898660\pi\) | ||||
0.949747 | − | 0.313018i | \(-0.101340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.66150 | 0.0541921 | ||||||||
\(941\) | 50.4949 | 1.64609 | 0.823043 | − | 0.567979i | \(-0.192274\pi\) | ||||
0.823043 | + | 0.567979i | \(0.192274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.30422i | 0.205294i | ||||||||
\(944\) | 10.6422 | 0.346375 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.84128 | −0.124891 | ||||||||
\(947\) | 36.0618i | 1.17185i | 0.810365 | + | 0.585925i | \(0.199269\pi\) | ||||
−0.810365 | + | 0.585925i | \(0.800731\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.794395 | −0.0257872 | ||||||||
\(950\) | 2.03528 | 0.0660331 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 29.7944i | − 0.965137i | −0.875858 | − | 0.482568i | \(-0.839704\pi\) | ||||
0.875858 | − | 0.482568i | \(-0.160296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 18.4336i | − 0.596498i | ||||||||
\(956\) | − 23.5040i | − 0.760173i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 27.5040i | − 0.888613i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.68629 | 0.247945 | ||||||||
\(962\) | 0.277238 | 0.00893850 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 14.8685i | − 0.478883i | ||||||||
\(965\) | 6.35827 | 0.204680 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.5198 | −0.370453 | −0.185226 | − | 0.982696i | \(-0.559302\pi\) | ||||
−0.185226 | + | 0.982696i | \(0.559302\pi\) | |||||||
\(968\) | 4.85425i | 0.156022i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.1502 | 0.550659 | ||||||||
\(971\) | 42.4693 | 1.36291 | 0.681453 | − | 0.731862i | \(-0.261348\pi\) | ||||
0.681453 | + | 0.731862i | \(0.261348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 35.4468i | 1.13579i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.52056i | 0.240727i | ||||||||
\(977\) | 18.1610i | 0.581023i | 0.956871 | + | 0.290512i | \(0.0938255\pi\) | ||||
−0.956871 | + | 0.290512i | \(0.906175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 7.27827i | − 0.232614i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.64349 | −0.0524458 | ||||||||
\(983\) | −12.3998 | −0.395491 | −0.197746 | − | 0.980253i | \(-0.563362\pi\) | ||||
−0.197746 | + | 0.980253i | \(0.563362\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.8389i | 0.409082i | ||||||||
\(986\) | 6.58755 | 0.209790 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.138701 | −0.00441266 | ||||||||
\(989\) | − 3.60040i | − 0.114486i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.7201 | 0.689962 | 0.344981 | − | 0.938610i | \(-0.387885\pi\) | ||||
0.344981 | + | 0.938610i | \(0.387885\pi\) | |||||||
\(992\) | −4.82843 | −0.153303 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 9.62962i | − 0.305280i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4763i | 1.34524i | 0.739989 | + | 0.672619i | \(0.234831\pi\) | ||||
−0.739989 | + | 0.672619i | \(0.765169\pi\) | |||||||
\(998\) | − 34.7330i | − 1.09945i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4410.2.b.b.881.5 | 8 | ||
3.2 | odd | 2 | 4410.2.b.e.881.4 | 8 | |||
7.2 | even | 3 | 630.2.be.b.521.3 | yes | 8 | ||
7.3 | odd | 6 | 630.2.be.a.341.1 | ✓ | 8 | ||
7.6 | odd | 2 | 4410.2.b.e.881.5 | 8 | |||
21.2 | odd | 6 | 630.2.be.a.521.1 | yes | 8 | ||
21.17 | even | 6 | 630.2.be.b.341.3 | yes | 8 | ||
21.20 | even | 2 | inner | 4410.2.b.b.881.4 | 8 | ||
35.2 | odd | 12 | 3150.2.bp.f.899.4 | 8 | |||
35.3 | even | 12 | 3150.2.bp.a.1349.4 | 8 | |||
35.9 | even | 6 | 3150.2.bf.c.1151.2 | 8 | |||
35.17 | even | 12 | 3150.2.bp.d.1349.1 | 8 | |||
35.23 | odd | 12 | 3150.2.bp.c.899.1 | 8 | |||
35.24 | odd | 6 | 3150.2.bf.b.1601.4 | 8 | |||
105.2 | even | 12 | 3150.2.bp.a.899.4 | 8 | |||
105.17 | odd | 12 | 3150.2.bp.c.1349.1 | 8 | |||
105.23 | even | 12 | 3150.2.bp.d.899.1 | 8 | |||
105.38 | odd | 12 | 3150.2.bp.f.1349.4 | 8 | |||
105.44 | odd | 6 | 3150.2.bf.b.1151.4 | 8 | |||
105.59 | even | 6 | 3150.2.bf.c.1601.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.1 | ✓ | 8 | 7.3 | odd | 6 | ||
630.2.be.a.521.1 | yes | 8 | 21.2 | odd | 6 | ||
630.2.be.b.341.3 | yes | 8 | 21.17 | even | 6 | ||
630.2.be.b.521.3 | yes | 8 | 7.2 | even | 3 | ||
3150.2.bf.b.1151.4 | 8 | 105.44 | odd | 6 | |||
3150.2.bf.b.1601.4 | 8 | 35.24 | odd | 6 | |||
3150.2.bf.c.1151.2 | 8 | 35.9 | even | 6 | |||
3150.2.bf.c.1601.2 | 8 | 105.59 | even | 6 | |||
3150.2.bp.a.899.4 | 8 | 105.2 | even | 12 | |||
3150.2.bp.a.1349.4 | 8 | 35.3 | even | 12 | |||
3150.2.bp.c.899.1 | 8 | 35.23 | odd | 12 | |||
3150.2.bp.c.1349.1 | 8 | 105.17 | odd | 12 | |||
3150.2.bp.d.899.1 | 8 | 105.23 | even | 12 | |||
3150.2.bp.d.1349.1 | 8 | 35.17 | even | 12 | |||
3150.2.bp.f.899.4 | 8 | 35.2 | odd | 12 | |||
3150.2.bp.f.1349.4 | 8 | 105.38 | odd | 12 | |||
4410.2.b.b.881.4 | 8 | 21.20 | even | 2 | inner | ||
4410.2.b.b.881.5 | 8 | 1.1 | even | 1 | trivial | ||
4410.2.b.e.881.4 | 8 | 3.2 | odd | 2 | |||
4410.2.b.e.881.5 | 8 | 7.6 | odd | 2 |