Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 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("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.13 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.d.1471.14 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.74981 | 1.41730 | 0.708648 | − | 0.705562i | \(-0.249305\pi\) | ||||
0.708648 | + | 0.705562i | \(0.249305\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.951741 | −0.286961 | −0.143480 | − | 0.989653i | \(-0.545829\pi\) | ||||
−0.143480 | + | 0.989653i | \(0.545829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.958125 | −0.265736 | −0.132868 | − | 0.991134i | \(-0.542419\pi\) | ||||
−0.132868 | + | 0.991134i | \(0.542419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.12519i | 1.72811i | 0.503396 | + | 0.864056i | \(0.332084\pi\) | ||||
−0.503396 | + | 0.864056i | \(0.667916\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.14480 | 1.86855 | 0.934273 | − | 0.356559i | \(-0.116050\pi\) | ||||
0.934273 | + | 0.356559i | \(0.116050\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.74981i | − | 0.818276i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.34339 | − | 3.43827i | −0.697145 | − | 0.716930i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.97878 | 0.738842 | 0.369421 | − | 0.929262i | \(-0.379556\pi\) | ||||
0.369421 | + | 0.929262i | \(0.379556\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 10.2840i | − | 1.84707i | −0.383518 | − | 0.923534i | \(-0.625287\pi\) | ||
0.383518 | − | 0.923534i | \(-0.374713\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.951741i | 0.165677i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.74981i | 0.633834i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.97275i | 1.31071i | 0.755320 | + | 0.655356i | \(0.227481\pi\) | ||||
−0.755320 | + | 0.655356i | \(0.772519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.958125i | 0.153423i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.05735 | 0.321305 | 0.160652 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160652 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.47788 | −0.682870 | −0.341435 | − | 0.939905i | \(-0.610913\pi\) | ||||
−0.341435 | + | 0.939905i | \(0.610913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.73241i | 0.836158i | 0.908411 | + | 0.418079i | \(0.137296\pi\) | ||||
−0.908411 | + | 0.418079i | \(0.862704\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.06110 | 1.00873 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.12519 | 0.997726 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.84488i | − | 0.802856i | −0.915891 | − | 0.401428i | \(-0.868514\pi\) | ||
0.915891 | − | 0.401428i | \(-0.131486\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.951741i | − | 0.128333i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 8.14480i | − | 1.07881i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.24677i | 0.683071i | 0.939869 | + | 0.341536i | \(0.110947\pi\) | ||||
−0.939869 | + | 0.341536i | \(0.889053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.55681i | − | 0.199329i | −0.995021 | − | 0.0996644i | \(-0.968223\pi\) | ||
0.995021 | − | 0.0996644i | \(-0.0317769\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.74981 | −0.472432 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.958125i | − | 0.118841i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.31703 | 1.01609 | 0.508044 | − | 0.861331i | \(-0.330369\pi\) | ||||
0.508044 | + | 0.861331i | \(0.330369\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.43827 | + | 3.34339i | −0.413920 | + | 0.402497i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9335i | 1.77228i | 0.463414 | + | 0.886142i | \(0.346624\pi\) | ||||
−0.463414 | + | 0.886142i | \(0.653376\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.66136 | 0.311488 | 0.155744 | − | 0.987797i | \(-0.450222\pi\) | ||||
0.155744 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.56885 | −0.406708 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4270 | 1.73567 | 0.867834 | − | 0.496854i | \(-0.165512\pi\) | ||||
0.867834 | + | 0.496854i | \(0.165512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.86616 | −0.424366 | −0.212183 | − | 0.977230i | \(-0.568057\pi\) | ||||
−0.212183 | + | 0.977230i | \(0.568057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.12519 | −0.772835 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.97878i | − | 0.426570i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.08766i | 0.327291i | 0.986519 | + | 0.163646i | \(0.0523253\pi\) | ||||
−0.986519 | + | 0.163646i | \(0.947675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.59279 | −0.376627 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.2840 | −1.06640 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.14480i | 0.835639i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.79266i | 0.588156i | 0.955781 | + | 0.294078i | \(0.0950125\pi\) | ||||
−0.955781 | + | 0.294078i | \(0.904987\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.951741 | 0.0956536 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.61688 | −0.160886 | −0.0804428 | − | 0.996759i | \(-0.525633\pi\) | ||||
−0.0804428 | + | 0.996759i | \(0.525633\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.88732 | −0.185963 | −0.0929817 | − | 0.995668i | \(-0.529640\pi\) | ||||
−0.0929817 | + | 0.995668i | \(0.529640\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.74981 | 0.365944 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4072 | 1.00611 | 0.503053 | − | 0.864255i | \(-0.332210\pi\) | ||||
0.503053 | + | 0.864255i | \(0.332210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.8316i | − | 1.42061i | −0.703895 | − | 0.710304i | \(-0.748558\pi\) | ||
0.703895 | − | 0.710304i | \(-0.251442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.97275 | 0.756740 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.06992i | − | 0.194721i | −0.995249 | − | 0.0973607i | \(-0.968960\pi\) | ||
0.995249 | − | 0.0973607i | \(-0.0310400\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.43827 | − | 3.34339i | 0.320621 | − | 0.311773i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.958125 | 0.0885787 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.7181i | 2.44925i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0942 | −0.917654 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2.05735i | − | 0.185505i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.77521i | 0.157525i | 0.996893 | + | 0.0787624i | \(0.0250968\pi\) | ||||
−0.996893 | + | 0.0787624i | \(0.974903\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.47788i | 0.394255i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.26875i | − | 0.722444i | −0.932480 | − | 0.361222i | \(-0.882360\pi\) | ||
0.932480 | − | 0.361222i | \(-0.117640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.5415 | 2.64828 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.9628i | 1.02205i | 0.859564 | + | 0.511027i | \(0.170735\pi\) | ||||
−0.859564 | + | 0.511027i | \(0.829265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6365i | 0.986993i | 0.869748 | + | 0.493497i | \(0.164282\pi\) | ||||
−0.869748 | + | 0.493497i | \(0.835718\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.73241 | 0.482756 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.911887 | 0.0762558 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.97878i | 0.330420i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 7.06110i | − | 0.582390i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.88485i | 0.809798i | 0.914361 | + | 0.404899i | \(0.132693\pi\) | ||||
−0.914361 | + | 0.404899i | \(0.867307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.5120i | 1.26235i | 0.775640 | + | 0.631175i | \(0.217427\pi\) | ||||
−0.775640 | + | 0.631175i | \(0.782573\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.12519i | − | 0.576037i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2840 | 0.826034 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.2536i | − | 1.13756i | −0.822488 | − | 0.568782i | \(-0.807415\pi\) | ||
0.822488 | − | 0.568782i | \(-0.192585\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.84488 | −0.463529 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.5371 | − | 12.8929i | −0.988061 | − | 1.01610i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.48701i | 0.429776i | 0.976639 | + | 0.214888i | \(0.0689386\pi\) | ||||
−0.976639 | + | 0.214888i | \(0.931061\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.951741 | −0.0740929 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.3069i | 1.10710i | 0.832817 | + | 0.553549i | \(0.186727\pi\) | ||||
−0.832817 | + | 0.553549i | \(0.813273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0820 | −0.929384 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.14480 | −0.622849 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.9452 | 1.66846 | 0.834231 | − | 0.551415i | \(-0.185912\pi\) | ||||
0.834231 | + | 0.551415i | \(0.185912\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.74981 | −0.283459 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.24677 | 0.394371 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 15.2193i | − | 1.13754i | −0.822496 | − | 0.568771i | \(-0.807419\pi\) | ||
0.822496 | − | 0.568771i | \(-0.192581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.5401i | − | 1.00642i | −0.864163 | − | 0.503212i | \(-0.832151\pi\) | ||
0.864163 | − | 0.503212i | \(-0.167849\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.55681 | −0.115082 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.97275 | −0.586168 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.78133i | − | 0.495900i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.74981i | 0.272759i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.2962 | 1.90273 | 0.951363 | − | 0.308072i | \(-0.0996837\pi\) | ||||
0.951363 | + | 0.308072i | \(0.0996837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.11360 | 0.584030 | 0.292015 | − | 0.956414i | \(-0.405674\pi\) | ||||
0.292015 | + | 0.956414i | \(0.405674\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.958125 | −0.0686128 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.2265 | −1.08484 | −0.542420 | − | 0.840107i | \(-0.682492\pi\) | ||||
−0.542420 | + | 0.840107i | \(0.682492\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.38626 | 0.169157 | 0.0845786 | − | 0.996417i | \(-0.473046\pi\) | ||||
0.0845786 | + | 0.996417i | \(0.473046\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.31703i | − | 0.586638i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.9197 | 1.04716 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.05735i | 0.143692i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.34339 | + | 3.43827i | 0.232382 | + | 0.238977i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.75174 | −0.536199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.5539i | − | 0.726558i | −0.931680 | − | 0.363279i | \(-0.881657\pi\) | ||
0.931680 | − | 0.363279i | \(-0.118343\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.9335 | 1.02323 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.47788i | − | 0.305389i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 38.5632i | − | 2.61784i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 2.66136i | − | 0.179838i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 6.82682i | − | 0.459222i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.0582i | 1.81195i | 0.423333 | + | 0.905974i | \(0.360860\pi\) | ||||
−0.423333 | + | 0.905974i | \(0.639140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0307 | 0.798507 | 0.399253 | − | 0.916841i | \(-0.369269\pi\) | ||||
0.399253 | + | 0.916841i | \(0.369269\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.4864i | 0.891207i | 0.895230 | + | 0.445604i | \(0.147011\pi\) | ||||
−0.895230 | + | 0.445604i | \(0.852989\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.56885i | 0.234813i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.71906 | −0.636717 | −0.318358 | − | 0.947970i | \(-0.603132\pi\) | ||||
−0.318358 | + | 0.947970i | \(0.603132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.73241 | −0.373941 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 15.4270i | − | 1.00209i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 21.9024i | − | 1.41675i | −0.705836 | − | 0.708375i | \(-0.749428\pi\) | ||
0.705836 | − | 0.708375i | \(-0.250572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.37300i | − | 0.0884430i | −0.999022 | − | 0.0442215i | \(-0.985919\pi\) | ||
0.999022 | − | 0.0442215i | \(-0.0140807\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.06110i | 0.451117i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.80374 | −0.496540 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.86616i | 0.245008i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.3289 | −1.66186 | −0.830932 | − | 0.556374i | \(-0.812192\pi\) | ||||
−0.830932 | + | 0.556374i | \(0.812192\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.18204 | + | 3.27235i | 0.200053 | + | 0.205731i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.12519i | 0.446196i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.42940 | 0.401055 | 0.200527 | − | 0.979688i | \(-0.435734\pi\) | ||||
0.200527 | + | 0.979688i | \(0.435734\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.8963i | 1.85767i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.97878 | −0.246281 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.71951 | −0.599330 | −0.299665 | − | 0.954044i | \(-0.596875\pi\) | ||||
−0.299665 | + | 0.954044i | \(0.596875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.84488 | 0.359048 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.08766 | 0.188962 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.98681 | −0.182109 | −0.0910544 | − | 0.995846i | \(-0.529024\pi\) | ||||
−0.0910544 | + | 0.995846i | \(0.529024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5815i | 1.00726i | 0.863920 | + | 0.503629i | \(0.168002\pi\) | ||||
−0.863920 | + | 0.503629i | \(0.831998\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.59279i | 0.217446i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.951741 | 0.0573922 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1673 | 1.51216 | 0.756078 | − | 0.654481i | \(-0.227113\pi\) | ||||
0.756078 | + | 0.654481i | \(0.227113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.2840i | 0.615689i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.83384i | − | 0.109398i | −0.998503 | − | 0.0546989i | \(-0.982580\pi\) | ||
0.998503 | − | 0.0546989i | \(-0.0174199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6656 | 0.812337 | 0.406169 | − | 0.913798i | \(-0.366865\pi\) | ||||
0.406169 | + | 0.913798i | \(0.366865\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.14480 | 0.482456 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.71469 | 0.455384 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −33.7683 | −1.98637 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.79266 | 0.339572 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.30871i | − | 0.134876i | −0.997723 | − | 0.0674381i | \(-0.978517\pi\) | ||
0.997723 | − | 0.0674381i | \(-0.0214825\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.24677 | −0.305479 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.951741i | − | 0.0552256i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.20339 | + | 3.29430i | 0.185257 | + | 0.190514i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.7912 | −0.967829 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.61688i | 0.0928873i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.55681 | 0.0891425 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.6583i | − | 0.665375i | −0.943037 | − | 0.332687i | \(-0.892045\pi\) | ||
0.943037 | − | 0.332687i | \(-0.107955\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.88732i | 0.107366i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.1374i | 1.48212i | 0.671440 | + | 0.741059i | \(0.265676\pi\) | ||||
−0.671440 | + | 0.741059i | \(0.734324\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.60260i | − | 0.542771i | −0.962471 | − | 0.271386i | \(-0.912518\pi\) | ||
0.962471 | − | 0.271386i | \(-0.0874819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 3.74981i | − | 0.211278i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.8211 | 1.22560 | 0.612799 | − | 0.790239i | \(-0.290044\pi\) | ||||
0.612799 | + | 0.790239i | \(0.290044\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.78677 | −0.212019 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 10.4072i | − | 0.580876i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 58.0332i | 3.22906i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.958125 | 0.0531472 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.8316 | −0.820188 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.4955i | 1.18508i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 23.3643i | − | 1.28422i | −0.766614 | − | 0.642108i | \(-0.778060\pi\) | ||
0.766614 | − | 0.642108i | \(-0.221940\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 7.97275i | − | 0.436904i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.31703i | 0.454408i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.8389i | 1.02622i | 0.858323 | + | 0.513109i | \(0.171506\pi\) | ||||
−0.858323 | + | 0.513109i | \(0.828494\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.06992 | −0.112422 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.78774i | 0.530036i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.229106 | 0.0123706 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.34339 | − | 3.43827i | −0.180002 | − | 0.185110i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.8095i | − | 0.741331i | −0.928766 | − | 0.370666i | \(-0.879130\pi\) | ||
0.928766 | − | 0.370666i | \(-0.120870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.0976 | 1.61109 | 0.805544 | − | 0.592537i | \(-0.201873\pi\) | ||||
0.805544 | + | 0.592537i | \(0.201873\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.958125i | − | 0.0511409i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.774223 | 0.0412077 | 0.0206039 | − | 0.999788i | \(-0.493441\pi\) | ||||
0.0206039 | + | 0.999788i | \(0.493441\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.9335 | −0.792589 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26.7181 | 1.41407 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.96220 | 0.314673 | 0.157336 | − | 0.987545i | \(-0.449709\pi\) | ||||
0.157336 | + | 0.987545i | \(0.449709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47.3378 | 2.49146 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.0942i | 0.529808i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.66136i | 0.139302i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.9835 | −0.625535 | −0.312768 | − | 0.949830i | \(-0.601256\pi\) | ||||
−0.312768 | + | 0.949830i | \(0.601256\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.05735 | −0.107102 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 21.9172i | − | 1.13788i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.8905i | − | 0.719221i | −0.933102 | − | 0.359611i | \(-0.882910\pi\) | ||
0.933102 | − | 0.359611i | \(-0.117090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.81217 | −0.196337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.1266 | 1.23930 | 0.619650 | − | 0.784878i | \(-0.287275\pi\) | ||||
0.619650 | + | 0.784878i | \(0.287275\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.77521 | 0.0909469 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.2488 | −0.830276 | −0.415138 | − | 0.909759i | \(-0.636267\pi\) | ||||
−0.415138 | + | 0.909759i | \(0.636267\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 3.56885i | − | 0.181886i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.47788 | 0.227623 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 10.2099i | − | 0.517662i | −0.965923 | − | 0.258831i | \(-0.916663\pi\) | ||
0.965923 | − | 0.258831i | \(-0.0833372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.4983 | − | 23.8223i | 1.23893 | − | 1.20474i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.26875 | −0.417103 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.4270i | 0.776214i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.9003 | 1.04896 | 0.524479 | − | 0.851423i | \(-0.324260\pi\) | ||||
0.524479 | + | 0.851423i | \(0.324260\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 30.5415i | − | 1.52899i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.00427i | 0.199964i | 0.994989 | + | 0.0999818i | \(0.0318785\pi\) | ||||
−0.994989 | + | 0.0999818i | \(0.968122\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.85339i | 0.490832i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.58799i | − | 0.376123i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.27963 | −0.359955 | −0.179977 | − | 0.983671i | \(-0.557602\pi\) | ||||
−0.179977 | + | 0.983671i | \(0.557602\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9628 | 0.590084 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.6744i | 0.968114i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.86616i | − | 0.189782i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.6365 | 0.569841 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.0067 | 0.977393 | 0.488697 | − | 0.872454i | \(-0.337473\pi\) | ||||
0.488697 | + | 0.872454i | \(0.337473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.66630i | − | 0.227422i | −0.993514 | − | 0.113711i | \(-0.963726\pi\) | ||
0.993514 | − | 0.113711i | \(-0.0362738\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.73241i | − | 0.278719i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 7.12519i | − | 0.345622i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.83774i | − | 0.282508i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 0.911887i | − | 0.0440263i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.6123 | 1.57088 | 0.785440 | − | 0.618937i | \(-0.212437\pi\) | ||||
0.785440 | + | 0.618937i | \(0.212437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.0237330i | − | 0.00114053i | −1.00000 | 0.000570267i | \(-0.999818\pi\) | |||
1.00000 | 0.000570267i | \(-0.000181522\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.97878 | 0.190768 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.2313 | − | 28.0041i | −1.30265 | − | 1.33962i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.75508i | 0.131493i | 0.997836 | + | 0.0657464i | \(0.0209428\pi\) | ||||
−0.997836 | + | 0.0657464i | \(0.979057\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.06110 | −0.336243 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 10.7028i | − | 0.508506i | −0.967138 | − | 0.254253i | \(-0.918170\pi\) | ||
0.967138 | − | 0.254253i | \(-0.0818296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.08766 | −0.146369 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.88485 | 0.467537 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3727 | 0.867060 | 0.433530 | − | 0.901139i | \(-0.357268\pi\) | ||||
0.433530 | + | 0.901139i | \(0.357268\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.95807 | −0.0922018 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.5120 | 0.728818 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3.59279i | − | 0.168433i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.10281i | 0.379033i | 0.981878 | + | 0.189517i | \(0.0606921\pi\) | ||||
−0.981878 | + | 0.189517i | \(0.939308\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.12519 | −0.332575 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.0210 | −0.746174 | −0.373087 | − | 0.927796i | \(-0.621701\pi\) | ||||
−0.373087 | + | 0.927796i | \(0.621701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.1086i | − | 1.02747i | −0.857948 | − | 0.513737i | \(-0.828261\pi\) | ||
0.857948 | − | 0.513737i | \(-0.171739\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 10.2840i | − | 0.476911i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.95676 | −0.0905479 | −0.0452739 | − | 0.998975i | \(-0.514416\pi\) | ||||
−0.0452739 | + | 0.998975i | \(0.514416\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.1873 | 1.44010 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.2536 | −0.656773 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.26178 | 0.195957 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.14480 | −0.373709 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.84488i | 0.267619i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00074 | 0.365563 | 0.182782 | − | 0.983154i | \(-0.441490\pi\) | ||||
0.182782 | + | 0.983154i | \(0.441490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7.63889i | − | 0.348303i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.8929 | + | 12.5371i | −0.586647 | + | 0.570457i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.79266 | −0.263031 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 33.1196i | − | 1.50079i | −0.660990 | − | 0.750395i | \(-0.729863\pi\) | ||
0.660990 | − | 0.750395i | \(-0.270137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.48701 | 0.248131 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.232141i | − | 0.0104764i | −0.999986 | − | 0.00523818i | \(-0.998333\pi\) | ||
0.999986 | − | 0.00523818i | \(-0.00166737\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.3496i | 1.27680i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.951741i | 0.0427776i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 55.9979i | 2.51185i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9.30458i | − | 0.416530i | −0.978072 | − | 0.208265i | \(-0.933218\pi\) | ||
0.978072 | − | 0.208265i | \(-0.0667817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.3069 | 0.639183 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.1845 | 1.39045 | 0.695225 | − | 0.718792i | \(-0.255305\pi\) | ||||
0.695225 | + | 0.718792i | \(0.255305\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.61688i | − | 0.0719502i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0820i | 0.536580i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.38407 | 0.105672 | 0.0528361 | − | 0.998603i | \(-0.483174\pi\) | ||||
0.0528361 | + | 0.998603i | \(0.483174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.97959 | 0.441471 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.14480i | 0.359602i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1.88732i | − | 0.0831654i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5.45577i | − | 0.239945i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 21.9452i | − | 0.963287i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.9158i | − | 1.22302i | −0.791238 | − | 0.611508i | \(-0.790563\pi\) | ||
0.791238 | − | 0.611508i | \(-0.209437\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.88398 | 0.0823809 | 0.0411904 | − | 0.999151i | \(-0.486885\pi\) | ||||
0.0411904 | + | 0.999151i | \(0.486885\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.74981i | 0.163655i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 73.2757 | 3.19194 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.643468 | + | 22.9910i | −0.0279769 | + | 0.999609i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.24677i | − | 0.227690i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.97120 | −0.0853822 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4072i | 0.449944i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.2193 | −0.656760 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.72034 | −0.289465 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5904 | −0.584299 | −0.292149 | − | 0.956373i | \(-0.594370\pi\) | ||||
−0.292149 | + | 0.956373i | \(0.594370\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5401 | −0.581060 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.8316 | 0.635315 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5944i | 0.795040i | 0.917594 | + | 0.397520i | \(0.130129\pi\) | ||||
−0.917594 | + | 0.397520i | \(0.869871\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.55681i | 0.0664429i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.4064 | 1.38056 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 57.8482 | 2.45996 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.97275i | 0.338424i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 28.2050i | − | 1.19508i | −0.801837 | − | 0.597542i | \(-0.796144\pi\) | ||
0.801837 | − | 0.597542i | \(-0.203856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.29037 | 0.181463 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.78133 | −0.286308 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.3843 | −1.40698 | −0.703491 | − | 0.710705i | \(-0.748376\pi\) | ||||
−0.703491 | + | 0.710705i | \(0.748376\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.06992 | 0.0870820 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.74981 | 0.157477 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.36287i | 0.224823i | 0.993662 | + | 0.112412i | \(0.0358575\pi\) | ||||
−0.993662 | + | 0.112412i | \(0.964142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.9916 | 0.794775 | 0.397388 | − | 0.917651i | \(-0.369917\pi\) | ||||
0.397388 | + | 0.917651i | \(0.369917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 26.2962i | − | 1.09854i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.34339 | + | 3.43827i | 0.139429 | + | 0.143386i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.4590 | −0.435414 | −0.217707 | − | 0.976014i | \(-0.569858\pi\) | ||||
−0.217707 | + | 0.976014i | \(0.569858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 8.11360i | − | 0.337190i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4974 | −0.601453 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.56281i | 0.230388i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.958125i | 0.0396136i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.1502i | 1.49208i | 0.665902 | + | 0.746040i | \(0.268047\pi\) | ||||
−0.665902 | + | 0.746040i | \(0.731953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 83.7614i | − | 3.45133i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.2265i | 0.626333i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.5082 | −1.41708 | −0.708541 | − | 0.705669i | \(-0.750646\pi\) | ||||
−0.708541 | + | 0.705669i | \(0.750646\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.7181 | −1.09534 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2.38626i | − | 0.0976629i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 21.2595i | − | 0.868641i | −0.900758 | − | 0.434320i | \(-0.856989\pi\) | ||
0.900758 | − | 0.434320i | \(-0.143011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.8456 | −0.891102 | −0.445551 | − | 0.895257i | \(-0.646992\pi\) | ||||
−0.445551 | + | 0.895257i | \(0.646992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.31703 | −0.338696 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 10.0942i | − | 0.410387i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 32.1601i | − | 1.30534i | −0.757642 | − | 0.652670i | \(-0.773649\pi\) | ||
0.757642 | − | 0.652670i | \(-0.226351\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 14.9197i | − | 0.604577i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.49237i | − | 0.222197i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.4575i | 0.907050i | 0.891243 | + | 0.453525i | \(0.149834\pi\) | ||||
−0.891243 | + | 0.453525i | \(0.850166\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.05735 | 0.0829605 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.5204i | 0.906638i | 0.891348 | + | 0.453319i | \(0.149760\pi\) | ||||
−0.891348 | + | 0.453319i | \(0.850240\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.4685 | −0.903087 | −0.451544 | − | 0.892249i | \(-0.649126\pi\) | ||||
−0.451544 | + | 0.892249i | \(0.649126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.43827 | − | 3.34339i | 0.137973 | − | 0.134166i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.5781i | 0.463868i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.75174i | 0.309575i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −56.8073 | −2.26506 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.1336 | −1.59769 | −0.798846 | − | 0.601535i | \(-0.794556\pi\) | ||||
−0.798846 | + | 0.601535i | \(0.794556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.5539 | −0.419478 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.77521 | −0.0704472 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.76541 | −0.268055 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 14.9335i | − | 0.590761i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.8547i | 0.705217i | 0.935771 | + | 0.352609i | \(0.114705\pi\) | ||||
−0.935771 | + | 0.352609i | \(0.885295\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.51422 | 0.0991513 | 0.0495757 | − | 0.998770i | \(-0.484213\pi\) | ||||
0.0495757 | + | 0.998770i | \(0.484213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.47788 | −0.176316 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.22628i | − | 0.284095i | −0.989860 | − | 0.142047i | \(-0.954631\pi\) | ||
0.989860 | − | 0.142047i | \(-0.0453685\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.99356i | − | 0.196015i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.5632 | −1.51141 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.33613 | −0.169686 | −0.0848429 | − | 0.996394i | \(-0.527039\pi\) | ||||
−0.0848429 | + | 0.996394i | \(0.527039\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.26875 | 0.323087 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.66136 | −0.103829 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.9108 | −1.24307 | −0.621534 | − | 0.783387i | \(-0.713490\pi\) | ||||
−0.621534 | + | 0.783387i | \(0.713490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 48.6433i | − | 1.89200i | −0.324162 | − | 0.946002i | \(-0.605082\pi\) | ||
0.324162 | − | 0.946002i | \(-0.394918\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.82682 | −0.265132 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.5415i | 1.18435i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.3026 | − | 13.6802i | −0.515080 | − | 0.529698i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.0582 | 1.04613 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.48168i | 0.0571995i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.2021 | −0.778733 | −0.389366 | − | 0.921083i | \(-0.627306\pi\) | ||||
−0.389366 | + | 0.921083i | \(0.627306\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 25.4292i | − | 0.977323i | −0.872473 | − | 0.488662i | \(-0.837485\pi\) | ||
0.872473 | − | 0.488662i | \(-0.162515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.7214i | 0.833591i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 12.0307i | − | 0.461018i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.95155i | 0.342522i | 0.985226 | + | 0.171261i | \(0.0547841\pi\) | ||||
−0.985226 | + | 0.171261i | \(0.945216\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.9628 | −0.457077 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.4864 | 0.514539 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.60013i | 0.213348i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.4175i | 1.68972i | 0.534987 | + | 0.844860i | \(0.320316\pi\) | ||||
−0.534987 | + | 0.844860i | \(0.679684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.56885 | 0.135569 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.6365 | −0.441397 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.6590i | 0.555250i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.71906i | 0.367609i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.5566i | − | 1.04080i | −0.853923 | − | 0.520399i | \(-0.825783\pi\) | ||
0.853923 | − | 0.520399i | \(-0.174217\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 64.9365i | 2.44913i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.73241i | 0.215895i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.06300 | −0.228022 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 16.7602i | − | 0.629444i | −0.949184 | − | 0.314722i | \(-0.898089\pi\) | ||
0.949184 | − | 0.314722i | \(-0.101911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.4270 | −0.578556 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.3593 | + | 34.3836i | −1.32422 | + | 1.28767i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.911887i | 0.0341026i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.9024 | −0.817961 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 30.6843i | − | 1.14433i | −0.820138 | − | 0.572166i | \(-0.806103\pi\) | ||
0.820138 | − | 0.572166i | \(-0.193897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.07711 | −0.263565 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.37300 | −0.0510626 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.97878 | −0.147768 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.17679 | 0.154909 | 0.0774543 | − | 0.996996i | \(-0.475321\pi\) | ||||
0.0774543 | + | 0.996996i | \(0.475321\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 31.9057i | − | 1.18008i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.01127i | 0.258967i | 0.991582 | + | 0.129484i | \(0.0413320\pi\) | ||||
−0.991582 | + | 0.129484i | \(0.958668\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.06110 | 0.260453 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.91566 | −0.291577 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.1792i | 1.77230i | 0.463397 | + | 0.886151i | \(0.346630\pi\) | ||||
−0.463397 | + | 0.886151i | \(0.653370\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.80374i | 0.286677i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.0801 | −1.87395 | −0.936973 | − | 0.349403i | \(-0.886385\pi\) | ||||
−0.936973 | + | 0.349403i | \(0.886385\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.88485 | −0.362153 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.86616 | 0.141455 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 39.0252 | 1.42595 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.2376 | 0.957423 | 0.478712 | − | 0.877972i | \(-0.341104\pi\) | ||||
0.478712 | + | 0.877972i | \(0.341104\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.3289i | 0.959478i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.5120 | −0.564540 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.6730i | 1.47828i | 0.673550 | + | 0.739142i | \(0.264769\pi\) | ||||
−0.673550 | + | 0.739142i | \(0.735231\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.27235 | − | 3.18204i | 0.118779 | − | 0.115501i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.2592 | −1.45940 | −0.729698 | − | 0.683770i | \(-0.760339\pi\) | ||||
−0.729698 | + | 0.683770i | \(0.760339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 55.6156i | − | 2.01342i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.12519 | 0.257612 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.02706i | − | 0.181517i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 23.5282i | − | 0.848448i | −0.905557 | − | 0.424224i | \(-0.860547\pi\) | ||
0.905557 | − | 0.424224i | \(-0.139453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 6.42940i | − | 0.231549i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 14.8496i | − | 0.534102i | −0.963682 | − | 0.267051i | \(-0.913951\pi\) | ||
0.963682 | − | 0.267051i | \(-0.0860492\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.2840i | 0.369413i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.8963 | 1.07252 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.7567 | 0.600372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 14.2129i | − | 0.508576i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.97878i | 0.142190i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.2536 | 0.508734 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.8210 | −1.38382 | −0.691910 | − | 0.721984i | \(-0.743230\pi\) | ||||
−0.691910 | + | 0.721984i | \(0.743230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.71951i | 0.346024i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.76180i | − | 0.275978i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.49162i | 0.0529688i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 5.84488i | − | 0.207297i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.6413i | 0.731153i | 0.930781 | + | 0.365576i | \(0.119128\pi\) | ||||
−0.930781 | + | 0.365576i | \(0.880872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.8445 | −1.44497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.08766i | − | 0.109097i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.53292 | −0.0893849 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8929 | − | 12.5371i | 0.454415 | − | 0.441874i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.98681i | 0.105141i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.9347 | 0.489919 | 0.244959 | − | 0.969533i | \(-0.421225\pi\) | ||||
0.244959 | + | 0.969533i | \(0.421225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.4224i | − | 0.611784i | −0.952066 | − | 0.305892i | \(-0.901045\pi\) | ||
0.952066 | − | 0.305892i | \(-0.0989546\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.5815 | 0.581540 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.48701 | −0.192202 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.4714 | −1.27597 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.59279 | 0.125542 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.0374 | −1.88592 | −0.942959 | − | 0.332908i | \(-0.891970\pi\) | ||||
−0.942959 | + | 0.332908i | \(0.891970\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.3346i | 0.743677i | 0.928297 | + | 0.371838i | \(0.121272\pi\) | ||||
−0.928297 | + | 0.371838i | \(0.878728\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.951741i | − | 0.0331354i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.2437 | 0.703941 | 0.351970 | − | 0.936011i | \(-0.385512\pi\) | ||||
0.351970 | + | 0.936011i | \(0.385512\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.5390 | 1.47744 | 0.738721 | − | 0.674012i | \(-0.235430\pi\) | ||||
0.738721 | + | 0.674012i | \(0.235430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 25.1673i | − | 0.873044i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 50.3116i | 1.74319i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.3069 | −0.495109 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.2840 | 0.355468 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.9418 | 1.55156 | 0.775781 | − | 0.631002i | \(-0.217356\pi\) | ||||
0.775781 | + | 0.631002i | \(0.217356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.1693 | −0.454113 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.83384 | −0.0631608 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 12.0820i | − | 0.415633i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −37.8513 | −1.30059 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 13.6656i | − | 0.469003i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.4125 | − | 26.6560i | 0.939689 | − | 0.913757i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.7311 | −0.778297 | −0.389149 | − | 0.921175i | \(-0.627231\pi\) | ||||
−0.389149 | + | 0.921175i | \(0.627231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 8.14480i | − | 0.278546i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0909 | −0.720452 | −0.360226 | − | 0.932865i | \(-0.617300\pi\) | ||||
−0.360226 | + | 0.932865i | \(0.617300\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 39.0199i | − | 1.33134i | −0.746245 | − | 0.665671i | \(-0.768145\pi\) | ||
0.746245 | − | 0.665671i | \(-0.231855\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 7.71469i | − | 0.262916i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.55995i | 0.189263i | 0.995512 | + | 0.0946314i | \(0.0301673\pi\) | ||||
−0.995512 | + | 0.0946314i | \(0.969833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.9452i | 0.746159i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.7683i | 1.14683i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.6825 | −0.498069 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.96876 | −0.270011 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.79266i | − | 0.196052i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.74981i | − | 0.126767i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.7174 | −1.37493 | −0.687465 | − | 0.726218i | \(-0.741277\pi\) | ||||
−0.687465 | + | 0.726218i | \(0.741277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.30871 | −0.0778709 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.8640i | 1.30936i | 0.755905 | + | 0.654682i | \(0.227197\pi\) | ||||
−0.755905 | + | 0.654682i | \(0.772803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 0.864710i | − | 0.0290998i | −0.999894 | − | 0.0145499i | \(-0.995368\pi\) | ||
0.999894 | − | 0.0145499i | \(-0.00463154\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.24677i | 0.176368i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 57.6788i | 1.93666i | 0.249667 | + | 0.968332i | \(0.419679\pi\) | ||||
−0.249667 | + | 0.968332i | \(0.580321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.65672i | 0.223259i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.951741 | −0.0318845 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.6893i | 1.56240i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.2193 | 0.508724 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.29430 | − | 3.20339i | 0.109993 | − | 0.106958i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 40.9180i | − | 1.36469i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.6459 | 1.38743 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.7912i | 0.558776i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.5401 | 0.450087 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.8950 | 1.19187 | 0.595936 | − | 0.803032i | \(-0.296781\pi\) | ||||
0.595936 | + | 0.803032i | \(0.296781\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.61688 | 0.0536285 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.7723 | 0.621952 | 0.310976 | − | 0.950418i | \(-0.399344\pi\) | ||||
0.310976 | + | 0.950418i | \(0.399344\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.67959 | 0.121777 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1.55681i | − | 0.0514665i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 31.0063i | − | 1.02392i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.8459 | −1.05050 | −0.525249 | − | 0.850948i | \(-0.676028\pi\) | ||||
−0.525249 | + | 0.850948i | \(0.676028\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.6583 | −0.384154 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 14.3082i | − | 0.470960i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 7.97275i | − | 0.262142i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.88732 | 0.0619878 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0575 | −0.789301 | −0.394651 | − | 0.918831i | \(-0.629134\pi\) | ||||
−0.394651 | + | 0.918831i | \(0.629134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 57.5112 | 1.88485 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.1374 | 0.855701 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.78133 | 0.221773 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.55284i | 0.148735i | 0.997231 | + | 0.0743674i | \(0.0236937\pi\) | ||||
−0.997231 | + | 0.0743674i | \(0.976306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.60260 | −0.313369 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0681i | 0.882395i | 0.897410 | + | 0.441197i | \(0.145446\pi\) | ||||
−0.897410 | + | 0.441197i | \(0.854554\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.87854 | − | 7.07374i | −0.223996 | − | 0.230353i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.74981 | −0.121981 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.71991i | 0.0883851i | 0.999023 | + | 0.0441926i | \(0.0140715\pi\) | ||||
−0.999023 | + | 0.0441926i | \(0.985928\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.54991 | −0.0827737 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.8211i | − | 0.707599i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.8434i | 1.12869i | 0.825540 | + | 0.564344i | \(0.190871\pi\) | ||||
−0.825540 | + | 0.564344i | \(0.809129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.2962i | 0.850925i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.78677i | 0.122409i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.8584i | 1.44855i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −74.7614 | −2.41166 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.4072 | −0.335369 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.11360i | 0.261186i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 60.0537i | − | 1.93120i | −0.260038 | − | 0.965598i | \(-0.583735\pi\) | ||
0.260038 | − | 0.965598i | \(-0.416265\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 58.0332 | 1.86430 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.3453 | −1.80821 | −0.904103 | − | 0.427315i | \(-0.859460\pi\) | ||||
−0.904103 | + | 0.427315i | \(0.859460\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43.6346i | 1.39886i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 0.958125i | − | 0.0306846i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.661144i | 0.0211519i | 0.999944 | + | 0.0105759i | \(0.00336649\pi\) | ||||
−0.999944 | + | 0.0105759i | \(0.996634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.93865i | − | 0.0939197i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.8316i | 0.473536i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.2675 | −1.22054 | −0.610272 | − | 0.792192i | \(-0.708940\pi\) | ||||
−0.610272 | + | 0.792192i | \(0.708940\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 15.2265i | − | 0.485155i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.4955 | 0.684208 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.9713 | + | 15.3962i | 0.476059 | + | 0.489570i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 34.3782i | − | 1.09206i | −0.837766 | − | 0.546030i | \(-0.816138\pi\) | ||
0.837766 | − | 0.546030i | \(-0.183862\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.3643 | −0.741442 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.38626i | 0.0756494i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.9533 | −1.77206 | −0.886029 | − | 0.463629i | \(-0.846547\pi\) | ||||
−0.886029 | + | 0.463629i | \(0.846547\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.97275 | −0.252247 |
(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 | 5520.2.be.d.1471.13 | yes | 32 | |
4.3 | odd | 2 | 5520.2.be.c.1471.14 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.c.1471.13 | ✓ | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.d.1471.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.13 | ✓ | 32 | 23.22 | odd | 2 | ||
5520.2.be.c.1471.14 | yes | 32 | 4.3 | odd | 2 | ||
5520.2.be.d.1471.13 | yes | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.d.1471.14 | yes | 32 | 92.91 | even | 2 | inner |