Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(139,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.2 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.139 |
Dual form | 690.2.d.a.139.4 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 4.00000i | − 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | − 2.23607i | − 0.707107i | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | − 2.47214i | − 0.685647i | −0.939400 | − | 0.342824i | \(-0.888617\pi\) | ||||
0.939400 | − | 0.342824i | \(-0.111383\pi\) | |||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 2.23607i | 0.577350i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 2.47214i | − 0.599581i | −0.954005 | − | 0.299791i | \(-0.903083\pi\) | ||||
0.954005 | − | 0.299791i | \(-0.0969168\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | −2.23607 | −0.500000 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −2.47214 | −0.484826 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | 0.472136 | 0.0876734 | 0.0438367 | − | 0.999039i | \(-0.486042\pi\) | ||||
0.0438367 | + | 0.999039i | \(0.486042\pi\) | |||||||
\(30\) | 2.23607 | 0.408248 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.47214 | −0.423968 | ||||||||
\(35\) | − 8.94427i | − 1.51186i | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 0.472136i | − 0.0776187i | −0.999247 | − | 0.0388093i | \(-0.987644\pi\) | ||||
0.999247 | − | 0.0388093i | \(-0.0123565\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | 2.47214 | 0.395859 | ||||||||
\(40\) | 2.23607i | 0.353553i | ||||||||
\(41\) | 10.9443 | 1.70921 | 0.854604 | − | 0.519280i | \(-0.173800\pi\) | ||||
0.854604 | + | 0.519280i | \(0.173800\pi\) | |||||||
\(42\) | − 4.00000i | − 0.617213i | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.23607 | −0.333333 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | − 4.94427i | − 0.721196i | −0.932721 | − | 0.360598i | \(-0.882573\pi\) | ||||
0.932721 | − | 0.360598i | \(-0.117427\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | − 5.00000i | − 0.707107i | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | 2.47214i | 0.342824i | ||||||||
\(53\) | − 8.94427i | − 1.22859i | −0.789076 | − | 0.614295i | \(-0.789440\pi\) | ||||
0.789076 | − | 0.614295i | \(-0.210560\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.00000 | 0.534522 | ||||||||
\(57\) | − 2.00000i | − 0.264906i | ||||||||
\(58\) | − 0.472136i | − 0.0619945i | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | − 2.23607i | − 0.288675i | ||||||||
\(61\) | −0.472136 | −0.0604508 | −0.0302254 | − | 0.999543i | \(-0.509623\pi\) | ||||
−0.0302254 | + | 0.999543i | \(0.509623\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.00000i | 0.503953i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 5.52786i | − 0.685647i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.94427i | 0.604039i | 0.953302 | + | 0.302019i | \(0.0976608\pi\) | ||||
−0.953302 | + | 0.302019i | \(0.902339\pi\) | |||||||
\(68\) | 2.47214i | 0.299791i | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | −8.94427 | −1.06904 | ||||||||
\(71\) | −7.52786 | −0.893393 | −0.446697 | − | 0.894686i | \(-0.647400\pi\) | ||||
−0.446697 | + | 0.894686i | \(0.647400\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 4.94427i | 0.578683i | 0.957226 | + | 0.289342i | \(0.0934364\pi\) | ||||
−0.957226 | + | 0.289342i | \(0.906564\pi\) | |||||||
\(74\) | −0.472136 | −0.0548847 | ||||||||
\(75\) | 5.00000i | 0.577350i | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − 2.47214i | − 0.279914i | ||||||||
\(79\) | −12.4721 | −1.40322 | −0.701612 | − | 0.712559i | \(-0.747536\pi\) | ||||
−0.701612 | + | 0.712559i | \(0.747536\pi\) | |||||||
\(80\) | 2.23607 | 0.250000 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 10.9443i | − 1.20859i | ||||||||
\(83\) | 1.52786i | 0.167705i | 0.996478 | + | 0.0838524i | \(0.0267224\pi\) | ||||
−0.996478 | + | 0.0838524i | \(0.973278\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | − 5.52786i | − 0.599581i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.472136i | 0.0506183i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.4721 | 1.74604 | 0.873021 | − | 0.487682i | \(-0.162157\pi\) | ||||
0.873021 | + | 0.487682i | \(0.162157\pi\) | |||||||
\(90\) | 2.23607i | 0.235702i | ||||||||
\(91\) | −9.88854 | −1.03660 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.94427 | −0.509963 | ||||||||
\(95\) | −4.47214 | −0.458831 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 13.4164i | 1.36223i | 0.732177 | + | 0.681115i | \(0.238505\pi\) | ||||
−0.732177 | + | 0.681115i | \(0.761495\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | 0.472136 | 0.0469793 | 0.0234896 | − | 0.999724i | \(-0.492522\pi\) | ||||
0.0234896 | + | 0.999724i | \(0.492522\pi\) | |||||||
\(102\) | − 2.47214i | − 0.244778i | ||||||||
\(103\) | 16.9443i | 1.66957i | 0.550577 | + | 0.834784i | \(0.314408\pi\) | ||||
−0.550577 | + | 0.834784i | \(0.685592\pi\) | |||||||
\(104\) | 2.47214 | 0.242413 | ||||||||
\(105\) | 8.94427 | 0.872872 | ||||||||
\(106\) | −8.94427 | −0.868744 | ||||||||
\(107\) | 2.47214i | 0.238990i | 0.992835 | + | 0.119495i | \(0.0381276\pi\) | ||||
−0.992835 | + | 0.119495i | \(0.961872\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −0.472136 | −0.0452224 | −0.0226112 | − | 0.999744i | \(-0.507198\pi\) | ||||
−0.0226112 | + | 0.999744i | \(0.507198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.472136 | 0.0448132 | ||||||||
\(112\) | − 4.00000i | − 0.377964i | ||||||||
\(113\) | 19.4164i | 1.82654i | 0.407353 | + | 0.913271i | \(0.366452\pi\) | ||||
−0.407353 | + | 0.913271i | \(0.633548\pi\) | |||||||
\(114\) | −2.00000 | −0.187317 | ||||||||
\(115\) | − 2.23607i | − 0.208514i | ||||||||
\(116\) | −0.472136 | −0.0438367 | ||||||||
\(117\) | 2.47214i | 0.228549i | ||||||||
\(118\) | − 6.00000i | − 0.552345i | ||||||||
\(119\) | −9.88854 | −0.906481 | ||||||||
\(120\) | −2.23607 | −0.204124 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0.472136i | 0.0427452i | ||||||||
\(123\) | 10.9443i | 0.986812i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | − 11.4164i | − 1.01304i | −0.862228 | − | 0.506521i | \(-0.830931\pi\) | ||||
0.862228 | − | 0.506521i | \(-0.169069\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.52786 | −0.484826 | ||||||||
\(131\) | −6.94427 | −0.606724 | −0.303362 | − | 0.952875i | \(-0.598109\pi\) | ||||
−0.303362 | + | 0.952875i | \(0.598109\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | 4.94427 | 0.427120 | ||||||||
\(135\) | − 2.23607i | − 0.192450i | ||||||||
\(136\) | 2.47214 | 0.211984 | ||||||||
\(137\) | 19.4164i | 1.65886i | 0.558614 | + | 0.829428i | \(0.311333\pi\) | ||||
−0.558614 | + | 0.829428i | \(0.688667\pi\) | |||||||
\(138\) | − 1.00000i | − 0.0851257i | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 8.94427i | 0.755929i | ||||||||
\(141\) | 4.94427 | 0.416383 | ||||||||
\(142\) | 7.52786i | 0.631724i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 1.05573 | 0.0876734 | ||||||||
\(146\) | 4.94427 | 0.409191 | ||||||||
\(147\) | − 9.00000i | − 0.742307i | ||||||||
\(148\) | 0.472136i | 0.0388093i | ||||||||
\(149\) | 13.4164 | 1.09911 | 0.549557 | − | 0.835456i | \(-0.314796\pi\) | ||||
0.549557 | + | 0.835456i | \(0.314796\pi\) | |||||||
\(150\) | 5.00000 | 0.408248 | ||||||||
\(151\) | 16.9443 | 1.37891 | 0.689453 | − | 0.724331i | \(-0.257851\pi\) | ||||
0.689453 | + | 0.724331i | \(0.257851\pi\) | |||||||
\(152\) | − 2.00000i | − 0.162221i | ||||||||
\(153\) | 2.47214i | 0.199860i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.47214 | −0.197929 | ||||||||
\(157\) | 11.5279i | 0.920024i | 0.887913 | + | 0.460012i | \(0.152155\pi\) | ||||
−0.887913 | + | 0.460012i | \(0.847845\pi\) | |||||||
\(158\) | 12.4721i | 0.992230i | ||||||||
\(159\) | 8.94427 | 0.709327 | ||||||||
\(160\) | − 2.23607i | − 0.176777i | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 4.94427i | − 0.387265i | −0.981074 | − | 0.193633i | \(-0.937973\pi\) | ||||
0.981074 | − | 0.193633i | \(-0.0620270\pi\) | |||||||
\(164\) | −10.9443 | −0.854604 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.52786 | 0.118585 | ||||||||
\(167\) | − 3.05573i | − 0.236459i | −0.992986 | − | 0.118230i | \(-0.962278\pi\) | ||||
0.992986 | − | 0.118230i | \(-0.0377219\pi\) | |||||||
\(168\) | 4.00000i | 0.308607i | ||||||||
\(169\) | 6.88854 | 0.529888 | ||||||||
\(170\) | −5.52786 | −0.423968 | ||||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 14.9443i | − 1.13619i | −0.822962 | − | 0.568096i | \(-0.807680\pi\) | ||||
0.822962 | − | 0.568096i | \(-0.192320\pi\) | |||||||
\(174\) | 0.472136 | 0.0357925 | ||||||||
\(175\) | − 20.0000i | − 1.51186i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | − 16.4721i | − 1.23464i | ||||||||
\(179\) | 18.9443 | 1.41596 | 0.707981 | − | 0.706232i | \(-0.249606\pi\) | ||||
0.707981 | + | 0.706232i | \(0.249606\pi\) | |||||||
\(180\) | 2.23607 | 0.166667 | ||||||||
\(181\) | 8.47214 | 0.629729 | 0.314864 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314864 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(182\) | 9.88854i | 0.732988i | ||||||||
\(183\) | − 0.472136i | − 0.0349013i | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | − 1.05573i | − 0.0776187i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.94427i | 0.360598i | ||||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | 4.47214i | 0.324443i | ||||||||
\(191\) | −25.8885 | −1.87323 | −0.936615 | − | 0.350361i | \(-0.886059\pi\) | ||||
−0.936615 | + | 0.350361i | \(0.886059\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | 20.0000i | 1.43963i | 0.694165 | + | 0.719816i | \(0.255774\pi\) | ||||
−0.694165 | + | 0.719816i | \(0.744226\pi\) | |||||||
\(194\) | 13.4164 | 0.963242 | ||||||||
\(195\) | 5.52786 | 0.395859 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | − 18.9443i | − 1.34972i | −0.737944 | − | 0.674862i | \(-0.764203\pi\) | ||||
0.737944 | − | 0.674862i | \(-0.235797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.4164 | −1.23462 | −0.617308 | − | 0.786721i | \(-0.711777\pi\) | ||||
−0.617308 | + | 0.786721i | \(0.711777\pi\) | |||||||
\(200\) | 5.00000i | 0.353553i | ||||||||
\(201\) | −4.94427 | −0.348742 | ||||||||
\(202\) | − 0.472136i | − 0.0332194i | ||||||||
\(203\) | − 1.88854i | − 0.132550i | ||||||||
\(204\) | −2.47214 | −0.173084 | ||||||||
\(205\) | 24.4721 | 1.70921 | ||||||||
\(206\) | 16.9443 | 1.18056 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | − 2.47214i | − 0.171412i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | − 8.94427i | − 0.617213i | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 8.94427i | 0.614295i | ||||||||
\(213\) | − 7.52786i | − 0.515801i | ||||||||
\(214\) | 2.47214 | 0.168992 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.472136i | 0.0319771i | ||||||||
\(219\) | −4.94427 | −0.334103 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.11146 | −0.411101 | ||||||||
\(222\) | − 0.472136i | − 0.0316877i | ||||||||
\(223\) | 11.4164i | 0.764499i | 0.924059 | + | 0.382250i | \(0.124851\pi\) | ||||
−0.924059 | + | 0.382250i | \(0.875149\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 19.4164 | 1.29156 | ||||||||
\(227\) | − 18.4721i | − 1.22604i | −0.790068 | − | 0.613019i | \(-0.789955\pi\) | ||||
0.790068 | − | 0.613019i | \(-0.210045\pi\) | |||||||
\(228\) | 2.00000i | 0.132453i | ||||||||
\(229\) | −25.4164 | −1.67956 | −0.839782 | − | 0.542924i | \(-0.817317\pi\) | ||||
−0.839782 | + | 0.542924i | \(0.817317\pi\) | |||||||
\(230\) | −2.23607 | −0.147442 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.472136i | 0.0309972i | ||||||||
\(233\) | 14.9443i | 0.979032i | 0.871994 | + | 0.489516i | \(0.162826\pi\) | ||||
−0.871994 | + | 0.489516i | \(0.837174\pi\) | |||||||
\(234\) | 2.47214 | 0.161609 | ||||||||
\(235\) | − 11.0557i | − 0.721196i | ||||||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | − 12.4721i | − 0.810152i | ||||||||
\(238\) | 9.88854i | 0.640979i | ||||||||
\(239\) | 12.4721 | 0.806755 | 0.403378 | − | 0.915034i | \(-0.367836\pi\) | ||||
0.403378 | + | 0.915034i | \(0.367836\pi\) | |||||||
\(240\) | 2.23607i | 0.144338i | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 11.0000i | 0.707107i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0.472136 | 0.0302254 | ||||||||
\(245\) | −20.1246 | −1.28571 | ||||||||
\(246\) | 10.9443 | 0.697781 | ||||||||
\(247\) | 4.94427i | 0.314596i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.52786 | −0.0968244 | ||||||||
\(250\) | − 11.1803i | − 0.707107i | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | − 4.00000i | − 0.251976i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −11.4164 | −0.716329 | ||||||||
\(255\) | 5.52786 | 0.346168 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.88854 | −0.117348 | ||||||||
\(260\) | 5.52786i | 0.342824i | ||||||||
\(261\) | −0.472136 | −0.0292245 | ||||||||
\(262\) | 6.94427i | 0.429019i | ||||||||
\(263\) | 20.9443i | 1.29148i | 0.763558 | + | 0.645740i | \(0.223451\pi\) | ||||
−0.763558 | + | 0.645740i | \(0.776549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 20.0000i | − 1.22859i | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 16.4721i | 1.00808i | ||||||||
\(268\) | − 4.94427i | − 0.302019i | ||||||||
\(269\) | −0.472136 | −0.0287866 | −0.0143933 | − | 0.999896i | \(-0.504582\pi\) | ||||
−0.0143933 | + | 0.999896i | \(0.504582\pi\) | |||||||
\(270\) | −2.23607 | −0.136083 | ||||||||
\(271\) | 0.944272 | 0.0573604 | 0.0286802 | − | 0.999589i | \(-0.490870\pi\) | ||||
0.0286802 | + | 0.999589i | \(0.490870\pi\) | |||||||
\(272\) | − 2.47214i | − 0.149895i | ||||||||
\(273\) | − 9.88854i | − 0.598482i | ||||||||
\(274\) | 19.4164 | 1.17299 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 27.4164i | 1.64729i | 0.567104 | + | 0.823646i | \(0.308064\pi\) | ||||
−0.567104 | + | 0.823646i | \(0.691936\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.94427 | 0.534522 | ||||||||
\(281\) | 3.52786 | 0.210455 | 0.105227 | − | 0.994448i | \(-0.466443\pi\) | ||||
0.105227 | + | 0.994448i | \(0.466443\pi\) | |||||||
\(282\) | − 4.94427i | − 0.294427i | ||||||||
\(283\) | 24.0000i | 1.42665i | 0.700832 | + | 0.713326i | \(0.252812\pi\) | ||||
−0.700832 | + | 0.713326i | \(0.747188\pi\) | |||||||
\(284\) | 7.52786 | 0.446697 | ||||||||
\(285\) | − 4.47214i | − 0.264906i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 43.7771i | − 2.58408i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 10.8885 | 0.640503 | ||||||||
\(290\) | − 1.05573i | − 0.0619945i | ||||||||
\(291\) | −13.4164 | −0.786484 | ||||||||
\(292\) | − 4.94427i | − 0.289342i | ||||||||
\(293\) | − 0.944272i | − 0.0551650i | −0.999620 | − | 0.0275825i | \(-0.991219\pi\) | ||||
0.999620 | − | 0.0275825i | \(-0.00878089\pi\) | |||||||
\(294\) | −9.00000 | −0.524891 | ||||||||
\(295\) | 13.4164 | 0.781133 | ||||||||
\(296\) | 0.472136 | 0.0274423 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 13.4164i | − 0.777192i | ||||||||
\(299\) | −2.47214 | −0.142967 | ||||||||
\(300\) | − 5.00000i | − 0.288675i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 16.9443i | − 0.975033i | ||||||||
\(303\) | 0.472136i | 0.0271235i | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | −1.05573 | −0.0604508 | ||||||||
\(306\) | 2.47214 | 0.141323 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.9443 | −0.963926 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.4721 | −1.38769 | −0.693844 | − | 0.720126i | \(-0.744084\pi\) | ||||
−0.693844 | + | 0.720126i | \(0.744084\pi\) | |||||||
\(312\) | 2.47214i | 0.139957i | ||||||||
\(313\) | − 25.4164i | − 1.43662i | −0.695723 | − | 0.718310i | \(-0.744916\pi\) | ||||
0.695723 | − | 0.718310i | \(-0.255084\pi\) | |||||||
\(314\) | 11.5279 | 0.650555 | ||||||||
\(315\) | 8.94427i | 0.503953i | ||||||||
\(316\) | 12.4721 | 0.701612 | ||||||||
\(317\) | − 18.0000i | − 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | − 8.94427i | − 0.501570i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.23607 | −0.125000 | ||||||||
\(321\) | −2.47214 | −0.137981 | ||||||||
\(322\) | 4.00000i | 0.222911i | ||||||||
\(323\) | 4.94427i | 0.275107i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | − 12.3607i | − 0.685647i | ||||||||
\(326\) | −4.94427 | −0.273838 | ||||||||
\(327\) | − 0.472136i | − 0.0261092i | ||||||||
\(328\) | 10.9443i | 0.604296i | ||||||||
\(329\) | −19.7771 | −1.09035 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | − 1.52786i | − 0.0838524i | ||||||||
\(333\) | 0.472136i | 0.0258729i | ||||||||
\(334\) | −3.05573 | −0.167202 | ||||||||
\(335\) | 11.0557i | 0.604039i | ||||||||
\(336\) | 4.00000 | 0.218218 | ||||||||
\(337\) | − 25.4164i | − 1.38452i | −0.721648 | − | 0.692260i | \(-0.756615\pi\) | ||||
0.721648 | − | 0.692260i | \(-0.243385\pi\) | |||||||
\(338\) | − 6.88854i | − 0.374687i | ||||||||
\(339\) | −19.4164 | −1.05455 | ||||||||
\(340\) | 5.52786i | 0.299791i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − 2.00000i | − 0.108148i | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.23607 | 0.120386 | ||||||||
\(346\) | −14.9443 | −0.803409 | ||||||||
\(347\) | − 8.94427i | − 0.480154i | −0.970754 | − | 0.240077i | \(-0.922827\pi\) | ||||
0.970754 | − | 0.240077i | \(-0.0771726\pi\) | |||||||
\(348\) | − 0.472136i | − 0.0253091i | ||||||||
\(349\) | 27.8885 | 1.49284 | 0.746420 | − | 0.665475i | \(-0.231771\pi\) | ||||
0.746420 | + | 0.665475i | \(0.231771\pi\) | |||||||
\(350\) | −20.0000 | −1.06904 | ||||||||
\(351\) | −2.47214 | −0.131953 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.94427i | 0.156708i | 0.996926 | + | 0.0783539i | \(0.0249664\pi\) | ||||
−0.996926 | + | 0.0783539i | \(0.975034\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | −16.8328 | −0.893393 | ||||||||
\(356\) | −16.4721 | −0.873021 | ||||||||
\(357\) | − 9.88854i | − 0.523357i | ||||||||
\(358\) | − 18.9443i | − 1.00124i | ||||||||
\(359\) | 32.9443 | 1.73873 | 0.869366 | − | 0.494169i | \(-0.164527\pi\) | ||||
0.869366 | + | 0.494169i | \(0.164527\pi\) | |||||||
\(360\) | − 2.23607i | − 0.117851i | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | − 8.47214i | − 0.445286i | ||||||||
\(363\) | − 11.0000i | − 0.577350i | ||||||||
\(364\) | 9.88854 | 0.518301 | ||||||||
\(365\) | 11.0557i | 0.578683i | ||||||||
\(366\) | −0.472136 | −0.0246789 | ||||||||
\(367\) | 12.0000i | 0.626395i | 0.949688 | + | 0.313197i | \(0.101400\pi\) | ||||
−0.949688 | + | 0.313197i | \(0.898600\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | −10.9443 | −0.569736 | ||||||||
\(370\) | −1.05573 | −0.0548847 | ||||||||
\(371\) | −35.7771 | −1.85745 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 21.4164i | − 1.10890i | −0.832217 | − | 0.554450i | \(-0.812929\pi\) | ||||
0.832217 | − | 0.554450i | \(-0.187071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.1803i | 0.577350i | ||||||||
\(376\) | 4.94427 | 0.254981 | ||||||||
\(377\) | − 1.16718i | − 0.0601130i | ||||||||
\(378\) | 4.00000i | 0.205738i | ||||||||
\(379\) | −16.8328 | −0.864644 | −0.432322 | − | 0.901719i | \(-0.642306\pi\) | ||||
−0.432322 | + | 0.901719i | \(0.642306\pi\) | |||||||
\(380\) | 4.47214 | 0.229416 | ||||||||
\(381\) | 11.4164 | 0.584880 | ||||||||
\(382\) | 25.8885i | 1.32457i | ||||||||
\(383\) | − 13.8885i | − 0.709671i | −0.934929 | − | 0.354836i | \(-0.884537\pi\) | ||||
0.934929 | − | 0.354836i | \(-0.115463\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 13.4164i | − 0.681115i | ||||||||
\(389\) | −4.47214 | −0.226746 | −0.113373 | − | 0.993552i | \(-0.536166\pi\) | ||||
−0.113373 | + | 0.993552i | \(0.536166\pi\) | |||||||
\(390\) | − 5.52786i | − 0.279914i | ||||||||
\(391\) | −2.47214 | −0.125021 | ||||||||
\(392\) | − 9.00000i | − 0.454569i | ||||||||
\(393\) | − 6.94427i | − 0.350292i | ||||||||
\(394\) | −18.9443 | −0.954399 | ||||||||
\(395\) | −27.8885 | −1.40322 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 29.3050i | − 1.47077i | −0.677648 | − | 0.735387i | \(-0.737001\pi\) | ||||
0.677648 | − | 0.735387i | \(-0.262999\pi\) | |||||||
\(398\) | 17.4164i | 0.873006i | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | 25.4164 | 1.26923 | 0.634617 | − | 0.772826i | \(-0.281158\pi\) | ||||
0.634617 | + | 0.772826i | \(0.281158\pi\) | |||||||
\(402\) | 4.94427i | 0.246598i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.472136 | −0.0234896 | ||||||||
\(405\) | 2.23607 | 0.111111 | ||||||||
\(406\) | −1.88854 | −0.0937269 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.47214i | 0.122389i | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | − 24.4721i | − 1.20859i | ||||||||
\(411\) | −19.4164 | −0.957741 | ||||||||
\(412\) | − 16.9443i | − 0.834784i | ||||||||
\(413\) | − 24.0000i | − 1.18096i | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 3.41641i | 0.167705i | ||||||||
\(416\) | −2.47214 | −0.121206 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.8885 | 1.85098 | 0.925488 | − | 0.378776i | \(-0.123655\pi\) | ||||
0.925488 | + | 0.378776i | \(0.123655\pi\) | |||||||
\(420\) | −8.94427 | −0.436436 | ||||||||
\(421\) | −37.4164 | −1.82356 | −0.911782 | − | 0.410674i | \(-0.865293\pi\) | ||||
−0.911782 | + | 0.410674i | \(0.865293\pi\) | |||||||
\(422\) | 12.0000i | 0.584151i | ||||||||
\(423\) | 4.94427i | 0.240399i | ||||||||
\(424\) | 8.94427 | 0.434372 | ||||||||
\(425\) | − 12.3607i | − 0.599581i | ||||||||
\(426\) | −7.52786 | −0.364726 | ||||||||
\(427\) | 1.88854i | 0.0913930i | ||||||||
\(428\) | − 2.47214i | − 0.119495i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | − 21.4164i | − 1.02921i | −0.857428 | − | 0.514603i | \(-0.827939\pi\) | ||||
0.857428 | − | 0.514603i | \(-0.172061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.05573i | 0.0506183i | ||||||||
\(436\) | 0.472136 | 0.0226112 | ||||||||
\(437\) | 2.00000i | 0.0956730i | ||||||||
\(438\) | 4.94427i | 0.236246i | ||||||||
\(439\) | 26.8328 | 1.28066 | 0.640330 | − | 0.768100i | \(-0.278798\pi\) | ||||
0.640330 | + | 0.768100i | \(0.278798\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 6.11146i | 0.290692i | ||||||||
\(443\) | − 8.94427i | − 0.424955i | −0.977166 | − | 0.212478i | \(-0.931847\pi\) | ||||
0.977166 | − | 0.212478i | \(-0.0681533\pi\) | |||||||
\(444\) | −0.472136 | −0.0224066 | ||||||||
\(445\) | 36.8328 | 1.74604 | ||||||||
\(446\) | 11.4164 | 0.540583 | ||||||||
\(447\) | 13.4164i | 0.634574i | ||||||||
\(448\) | 4.00000i | 0.188982i | ||||||||
\(449\) | 34.9443 | 1.64912 | 0.824561 | − | 0.565773i | \(-0.191422\pi\) | ||||
0.824561 | + | 0.565773i | \(0.191422\pi\) | |||||||
\(450\) | 5.00000i | 0.235702i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 19.4164i | − 0.913271i | ||||||||
\(453\) | 16.9443i | 0.796111i | ||||||||
\(454\) | −18.4721 | −0.866940 | ||||||||
\(455\) | −22.1115 | −1.03660 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | − 25.4164i | − 1.18893i | −0.804122 | − | 0.594465i | \(-0.797364\pi\) | ||||
0.804122 | − | 0.594465i | \(-0.202636\pi\) | |||||||
\(458\) | 25.4164i | 1.18763i | ||||||||
\(459\) | −2.47214 | −0.115389 | ||||||||
\(460\) | 2.23607i | 0.104257i | ||||||||
\(461\) | −14.3607 | −0.668844 | −0.334422 | − | 0.942424i | \(-0.608541\pi\) | ||||
−0.334422 | + | 0.942424i | \(0.608541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 15.4164i | − 0.716461i | −0.933633 | − | 0.358231i | \(-0.883380\pi\) | ||||
0.933633 | − | 0.358231i | \(-0.116620\pi\) | |||||||
\(464\) | 0.472136 | 0.0219184 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.9443 | 0.692280 | ||||||||
\(467\) | − 26.4721i | − 1.22498i | −0.790477 | − | 0.612492i | \(-0.790167\pi\) | ||||
0.790477 | − | 0.612492i | \(-0.209833\pi\) | |||||||
\(468\) | − 2.47214i | − 0.114275i | ||||||||
\(469\) | 19.7771 | 0.913221 | ||||||||
\(470\) | −11.0557 | −0.509963 | ||||||||
\(471\) | −11.5279 | −0.531176 | ||||||||
\(472\) | 6.00000i | 0.276172i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −12.4721 | −0.572864 | ||||||||
\(475\) | −10.0000 | −0.458831 | ||||||||
\(476\) | 9.88854 | 0.453241 | ||||||||
\(477\) | 8.94427i | 0.409530i | ||||||||
\(478\) | − 12.4721i | − 0.570462i | ||||||||
\(479\) | 16.9443 | 0.774204 | 0.387102 | − | 0.922037i | \(-0.373476\pi\) | ||||
0.387102 | + | 0.922037i | \(0.373476\pi\) | |||||||
\(480\) | 2.23607 | 0.102062 | ||||||||
\(481\) | −1.16718 | −0.0532190 | ||||||||
\(482\) | 2.00000i | 0.0910975i | ||||||||
\(483\) | − 4.00000i | − 0.182006i | ||||||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 30.0000i | 1.36223i | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 31.4164i | 1.42361i | 0.702375 | + | 0.711807i | \(0.252123\pi\) | ||||
−0.702375 | + | 0.711807i | \(0.747877\pi\) | |||||||
\(488\) | − 0.472136i | − 0.0213726i | ||||||||
\(489\) | 4.94427 | 0.223588 | ||||||||
\(490\) | 20.1246i | 0.909137i | ||||||||
\(491\) | 27.8885 | 1.25859 | 0.629296 | − | 0.777166i | \(-0.283343\pi\) | ||||
0.629296 | + | 0.777166i | \(0.283343\pi\) | |||||||
\(492\) | − 10.9443i | − 0.493406i | ||||||||
\(493\) | − 1.16718i | − 0.0525673i | ||||||||
\(494\) | 4.94427 | 0.222453 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.1115i | 1.35068i | ||||||||
\(498\) | 1.52786i | 0.0684652i | ||||||||
\(499\) | 24.0000 | 1.07439 | 0.537194 | − | 0.843459i | \(-0.319484\pi\) | ||||
0.537194 | + | 0.843459i | \(0.319484\pi\) | |||||||
\(500\) | −11.1803 | −0.500000 | ||||||||
\(501\) | 3.05573 | 0.136520 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 13.8885i | 0.619260i | 0.950857 | + | 0.309630i | \(0.100205\pi\) | ||||
−0.950857 | + | 0.309630i | \(0.899795\pi\) | |||||||
\(504\) | −4.00000 | −0.178174 | ||||||||
\(505\) | 1.05573 | 0.0469793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.88854i | 0.305931i | ||||||||
\(508\) | 11.4164i | 0.506521i | ||||||||
\(509\) | −1.41641 | −0.0627812 | −0.0313906 | − | 0.999507i | \(-0.509994\pi\) | ||||
−0.0313906 | + | 0.999507i | \(0.509994\pi\) | |||||||
\(510\) | − 5.52786i | − 0.244778i | ||||||||
\(511\) | 19.7771 | 0.874887 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 2.00000i | 0.0883022i | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | 37.8885i | 1.66957i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.88854i | 0.0829779i | ||||||||
\(519\) | 14.9443 | 0.655981 | ||||||||
\(520\) | 5.52786 | 0.242413 | ||||||||
\(521\) | −19.5279 | −0.855531 | −0.427766 | − | 0.903890i | \(-0.640699\pi\) | ||||
−0.427766 | + | 0.903890i | \(0.640699\pi\) | |||||||
\(522\) | 0.472136i | 0.0206648i | ||||||||
\(523\) | 4.94427i | 0.216198i | 0.994140 | + | 0.108099i | \(0.0344763\pi\) | ||||
−0.994140 | + | 0.108099i | \(0.965524\pi\) | |||||||
\(524\) | 6.94427 | 0.303362 | ||||||||
\(525\) | 20.0000 | 0.872872 | ||||||||
\(526\) | 20.9443 | 0.913214 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | −20.0000 | −0.868744 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | − 8.00000i | − 0.346844i | ||||||||
\(533\) | − 27.0557i | − 1.17191i | ||||||||
\(534\) | 16.4721 | 0.712819 | ||||||||
\(535\) | 5.52786i | 0.238990i | ||||||||
\(536\) | −4.94427 | −0.213560 | ||||||||
\(537\) | 18.9443i | 0.817506i | ||||||||
\(538\) | 0.472136i | 0.0203552i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.23607i | 0.0962250i | ||||||||
\(541\) | 40.8328 | 1.75554 | 0.877770 | − | 0.479082i | \(-0.159030\pi\) | ||||
0.877770 | + | 0.479082i | \(0.159030\pi\) | |||||||
\(542\) | − 0.944272i | − 0.0405600i | ||||||||
\(543\) | 8.47214i | 0.363574i | ||||||||
\(544\) | −2.47214 | −0.105992 | ||||||||
\(545\) | −1.05573 | −0.0452224 | ||||||||
\(546\) | −9.88854 | −0.423191 | ||||||||
\(547\) | 22.8328i | 0.976261i | 0.872771 | + | 0.488130i | \(0.162321\pi\) | ||||
−0.872771 | + | 0.488130i | \(0.837679\pi\) | |||||||
\(548\) | − 19.4164i | − 0.829428i | ||||||||
\(549\) | 0.472136 | 0.0201503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.944272 | −0.0402273 | ||||||||
\(552\) | 1.00000i | 0.0425628i | ||||||||
\(553\) | 49.8885i | 2.12148i | ||||||||
\(554\) | 27.4164 | 1.16481 | ||||||||
\(555\) | 1.05573 | 0.0448132 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.8885i | 1.26642i | 0.773981 | + | 0.633209i | \(0.218263\pi\) | ||||
−0.773981 | + | 0.633209i | \(0.781737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | − 8.94427i | − 0.377964i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 3.52786i | − 0.148814i | ||||||||
\(563\) | − 37.3050i | − 1.57222i | −0.618089 | − | 0.786108i | \(-0.712093\pi\) | ||||
0.618089 | − | 0.786108i | \(-0.287907\pi\) | |||||||
\(564\) | −4.94427 | −0.208191 | ||||||||
\(565\) | 43.4164i | 1.82654i | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | − 4.00000i | − 0.167984i | ||||||||
\(568\) | − 7.52786i | − 0.315862i | ||||||||
\(569\) | −39.3050 | −1.64775 | −0.823875 | − | 0.566772i | \(-0.808192\pi\) | ||||
−0.823875 | + | 0.566772i | \(0.808192\pi\) | |||||||
\(570\) | −4.47214 | −0.187317 | ||||||||
\(571\) | 32.8328 | 1.37401 | 0.687005 | − | 0.726652i | \(-0.258925\pi\) | ||||
0.687005 | + | 0.726652i | \(0.258925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 25.8885i | − 1.08151i | ||||||||
\(574\) | −43.7771 | −1.82722 | ||||||||
\(575\) | − 5.00000i | − 0.208514i | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 16.9443i | − 0.705399i | −0.935737 | − | 0.352700i | \(-0.885264\pi\) | ||||
0.935737 | − | 0.352700i | \(-0.114736\pi\) | |||||||
\(578\) | − 10.8885i | − 0.452904i | ||||||||
\(579\) | −20.0000 | −0.831172 | ||||||||
\(580\) | −1.05573 | −0.0438367 | ||||||||
\(581\) | 6.11146 | 0.253546 | ||||||||
\(582\) | 13.4164i | 0.556128i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −4.94427 | −0.204595 | ||||||||
\(585\) | 5.52786i | 0.228549i | ||||||||
\(586\) | −0.944272 | −0.0390075 | ||||||||
\(587\) | 29.8885i | 1.23363i | 0.787107 | + | 0.616816i | \(0.211578\pi\) | ||||
−0.787107 | + | 0.616816i | \(0.788422\pi\) | |||||||
\(588\) | 9.00000i | 0.371154i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | − 13.4164i | − 0.552345i | ||||||||
\(591\) | 18.9443 | 0.779263 | ||||||||
\(592\) | − 0.472136i | − 0.0194047i | ||||||||
\(593\) | 23.8885i | 0.980985i | 0.871445 | + | 0.490492i | \(0.163183\pi\) | ||||
−0.871445 | + | 0.490492i | \(0.836817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.1115 | −0.906481 | ||||||||
\(596\) | −13.4164 | −0.549557 | ||||||||
\(597\) | − 17.4164i | − 0.712806i | ||||||||
\(598\) | 2.47214i | 0.101093i | ||||||||
\(599\) | −26.3607 | −1.07707 | −0.538534 | − | 0.842604i | \(-0.681022\pi\) | ||||
−0.538534 | + | 0.842604i | \(0.681022\pi\) | |||||||
\(600\) | −5.00000 | −0.204124 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 4.94427i | − 0.201346i | ||||||||
\(604\) | −16.9443 | −0.689453 | ||||||||
\(605\) | −24.5967 | −1.00000 | ||||||||
\(606\) | 0.472136 | 0.0191792 | ||||||||
\(607\) | − 7.41641i | − 0.301023i | −0.988608 | − | 0.150511i | \(-0.951908\pi\) | ||||
0.988608 | − | 0.150511i | \(-0.0480920\pi\) | |||||||
\(608\) | 2.00000i | 0.0811107i | ||||||||
\(609\) | 1.88854 | 0.0765277 | ||||||||
\(610\) | 1.05573i | 0.0427452i | ||||||||
\(611\) | −12.2229 | −0.494486 | ||||||||
\(612\) | − 2.47214i | − 0.0999302i | ||||||||
\(613\) | 9.41641i | 0.380325i | 0.981753 | + | 0.190163i | \(0.0609015\pi\) | ||||
−0.981753 | + | 0.190163i | \(0.939098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.4721i | 0.986812i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 14.4721i | − 0.582626i | −0.956628 | − | 0.291313i | \(-0.905908\pi\) | ||||
0.956628 | − | 0.291313i | \(-0.0940922\pi\) | |||||||
\(618\) | 16.9443i | 0.681599i | ||||||||
\(619\) | −40.8328 | −1.64121 | −0.820605 | − | 0.571496i | \(-0.806363\pi\) | ||||
−0.820605 | + | 0.571496i | \(0.806363\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 24.4721i | 0.981243i | ||||||||
\(623\) | − 65.8885i | − 2.63977i | ||||||||
\(624\) | 2.47214 | 0.0989646 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −25.4164 | −1.01584 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 11.5279i | − 0.460012i | ||||||||
\(629\) | −1.16718 | −0.0465387 | ||||||||
\(630\) | 8.94427 | 0.356348 | ||||||||
\(631\) | −2.36068 | −0.0939772 | −0.0469886 | − | 0.998895i | \(-0.514962\pi\) | ||||
−0.0469886 | + | 0.998895i | \(0.514962\pi\) | |||||||
\(632\) | − 12.4721i | − 0.496115i | ||||||||
\(633\) | − 12.0000i | − 0.476957i | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | − 25.5279i | − 1.01304i | ||||||||
\(636\) | −8.94427 | −0.354663 | ||||||||
\(637\) | 22.2492i | 0.881546i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.52786 | 0.297798 | ||||||||
\(640\) | 2.23607i | 0.0883883i | ||||||||
\(641\) | −11.5279 | −0.455323 | −0.227662 | − | 0.973740i | \(-0.573108\pi\) | ||||
−0.227662 | + | 0.973740i | \(0.573108\pi\) | |||||||
\(642\) | 2.47214i | 0.0975674i | ||||||||
\(643\) | 12.9443i | 0.510472i | 0.966879 | + | 0.255236i | \(0.0821532\pi\) | ||||
−0.966879 | + | 0.255236i | \(0.917847\pi\) | |||||||
\(644\) | 4.00000 | 0.157622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.94427 | 0.194530 | ||||||||
\(647\) | 41.8885i | 1.64681i | 0.567455 | + | 0.823404i | \(0.307928\pi\) | ||||
−0.567455 | + | 0.823404i | \(0.692072\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.3607 | −0.484826 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.94427i | 0.193633i | ||||||||
\(653\) | 20.8328i | 0.815251i | 0.913149 | + | 0.407626i | \(0.133643\pi\) | ||||
−0.913149 | + | 0.407626i | \(0.866357\pi\) | |||||||
\(654\) | −0.472136 | −0.0184620 | ||||||||
\(655\) | −15.5279 | −0.606724 | ||||||||
\(656\) | 10.9443 | 0.427302 | ||||||||
\(657\) | − 4.94427i | − 0.192894i | ||||||||
\(658\) | 19.7771i | 0.770991i | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.2492 | −1.40993 | −0.704966 | − | 0.709241i | \(-0.749038\pi\) | ||||
−0.704966 | + | 0.709241i | \(0.749038\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 6.11146i | − 0.237349i | ||||||||
\(664\) | −1.52786 | −0.0592926 | ||||||||
\(665\) | 17.8885i | 0.693688i | ||||||||
\(666\) | 0.472136 | 0.0182949 | ||||||||
\(667\) | − 0.472136i | − 0.0182812i | ||||||||
\(668\) | 3.05573i | 0.118230i | ||||||||
\(669\) | −11.4164 | −0.441384 | ||||||||
\(670\) | 11.0557 | 0.427120 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − 4.00000i | − 0.154303i | ||||||||
\(673\) | − 38.8328i | − 1.49690i | −0.663194 | − | 0.748448i | \(-0.730800\pi\) | ||||
0.663194 | − | 0.748448i | \(-0.269200\pi\) | |||||||
\(674\) | −25.4164 | −0.979003 | ||||||||
\(675\) | − 5.00000i | − 0.192450i | ||||||||
\(676\) | −6.88854 | −0.264944 | ||||||||
\(677\) | 25.8885i | 0.994978i | 0.867470 | + | 0.497489i | \(0.165744\pi\) | ||||
−0.867470 | + | 0.497489i | \(0.834256\pi\) | |||||||
\(678\) | 19.4164i | 0.745683i | ||||||||
\(679\) | 53.6656 | 2.05950 | ||||||||
\(680\) | 5.52786 | 0.211984 | ||||||||
\(681\) | 18.4721 | 0.707854 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 12.0000i | − 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | 43.4164i | 1.65886i | ||||||||
\(686\) | 8.00000 | 0.305441 | ||||||||
\(687\) | − 25.4164i | − 0.969696i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.1115 | −0.842379 | ||||||||
\(690\) | − 2.23607i | − 0.0851257i | ||||||||
\(691\) | −39.7771 | −1.51319 | −0.756596 | − | 0.653883i | \(-0.773139\pi\) | ||||
−0.756596 | + | 0.653883i | \(0.773139\pi\) | |||||||
\(692\) | 14.9443i | 0.568096i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.94427 | −0.339520 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.472136 | −0.0178963 | ||||||||
\(697\) | − 27.0557i | − 1.02481i | ||||||||
\(698\) | − 27.8885i | − 1.05560i | ||||||||
\(699\) | −14.9443 | −0.565244 | ||||||||
\(700\) | 20.0000i | 0.755929i | ||||||||
\(701\) | 37.4164 | 1.41320 | 0.706599 | − | 0.707614i | \(-0.250228\pi\) | ||||
0.706599 | + | 0.707614i | \(0.250228\pi\) | |||||||
\(702\) | 2.47214i | 0.0933048i | ||||||||
\(703\) | 0.944272i | 0.0356139i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.0557 | 0.416383 | ||||||||
\(706\) | 2.94427 | 0.110809 | ||||||||
\(707\) | − 1.88854i | − 0.0710260i | ||||||||
\(708\) | − 6.00000i | − 0.225494i | ||||||||
\(709\) | −20.4721 | −0.768847 | −0.384424 | − | 0.923157i | \(-0.625600\pi\) | ||||
−0.384424 | + | 0.923157i | \(0.625600\pi\) | |||||||
\(710\) | 16.8328i | 0.631724i | ||||||||
\(711\) | 12.4721 | 0.467742 | ||||||||
\(712\) | 16.4721i | 0.617319i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −9.88854 | −0.370069 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.9443 | −0.707981 | ||||||||
\(717\) | 12.4721i | 0.465780i | ||||||||
\(718\) | − 32.9443i | − 1.22947i | ||||||||
\(719\) | 35.5279 | 1.32497 | 0.662483 | − | 0.749077i | \(-0.269503\pi\) | ||||
0.662483 | + | 0.749077i | \(0.269503\pi\) | |||||||
\(720\) | −2.23607 | −0.0833333 | ||||||||
\(721\) | 67.7771 | 2.52415 | ||||||||
\(722\) | 15.0000i | 0.558242i | ||||||||
\(723\) | − 2.00000i | − 0.0743808i | ||||||||
\(724\) | −8.47214 | −0.314864 | ||||||||
\(725\) | 2.36068 | 0.0876734 | ||||||||
\(726\) | −11.0000 | −0.408248 | ||||||||
\(727\) | − 0.944272i | − 0.0350211i | −0.999847 | − | 0.0175106i | \(-0.994426\pi\) | ||||
0.999847 | − | 0.0175106i | \(-0.00557407\pi\) | |||||||
\(728\) | − 9.88854i | − 0.366494i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 11.0557 | 0.409191 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.472136i | 0.0174506i | ||||||||
\(733\) | − 0.472136i | − 0.0174387i | −0.999962 | − | 0.00871937i | \(-0.997225\pi\) | ||||
0.999962 | − | 0.00871937i | \(-0.00277550\pi\) | |||||||
\(734\) | 12.0000 | 0.442928 | ||||||||
\(735\) | − 20.1246i | − 0.742307i | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 10.9443i | 0.402864i | ||||||||
\(739\) | −1.88854 | −0.0694712 | −0.0347356 | − | 0.999397i | \(-0.511059\pi\) | ||||
−0.0347356 | + | 0.999397i | \(0.511059\pi\) | |||||||
\(740\) | 1.05573i | 0.0388093i | ||||||||
\(741\) | −4.94427 | −0.181632 | ||||||||
\(742\) | 35.7771i | 1.31342i | ||||||||
\(743\) | 2.11146i | 0.0774618i | 0.999250 | + | 0.0387309i | \(0.0123315\pi\) | ||||
−0.999250 | + | 0.0387309i | \(0.987668\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.0000 | 1.09911 | ||||||||
\(746\) | −21.4164 | −0.784110 | ||||||||
\(747\) | − 1.52786i | − 0.0559016i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.88854 | 0.361320 | ||||||||
\(750\) | 11.1803 | 0.408248 | ||||||||
\(751\) | 36.4721 | 1.33089 | 0.665444 | − | 0.746448i | \(-0.268242\pi\) | ||||
0.665444 | + | 0.746448i | \(0.268242\pi\) | |||||||
\(752\) | − 4.94427i | − 0.180299i | ||||||||
\(753\) | − 12.0000i | − 0.437304i | ||||||||
\(754\) | −1.16718 | −0.0425063 | ||||||||
\(755\) | 37.8885 | 1.37891 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | − 45.4164i | − 1.65069i | −0.564631 | − | 0.825344i | \(-0.690981\pi\) | ||||
0.564631 | − | 0.825344i | \(-0.309019\pi\) | |||||||
\(758\) | 16.8328i | 0.611395i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − 4.47214i | − 0.162221i | ||||||||
\(761\) | −17.7771 | −0.644419 | −0.322209 | − | 0.946668i | \(-0.604426\pi\) | ||||
−0.322209 | + | 0.946668i | \(0.604426\pi\) | |||||||
\(762\) | − 11.4164i | − 0.413573i | ||||||||
\(763\) | 1.88854i | 0.0683699i | ||||||||
\(764\) | 25.8885 | 0.936615 | ||||||||
\(765\) | 5.52786i | 0.199860i | ||||||||
\(766\) | −13.8885 | −0.501813 | ||||||||
\(767\) | − 14.8328i | − 0.535582i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −34.9443 | −1.26012 | −0.630061 | − | 0.776545i | \(-0.716970\pi\) | ||||
−0.630061 | + | 0.776545i | \(0.716970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | − 20.0000i | − 0.719816i | ||||||||
\(773\) | − 3.05573i | − 0.109907i | −0.998489 | − | 0.0549535i | \(-0.982499\pi\) | ||||
0.998489 | − | 0.0549535i | \(-0.0175010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.4164 | −0.481621 | ||||||||
\(777\) | − 1.88854i | − 0.0677511i | ||||||||
\(778\) | 4.47214i | 0.160334i | ||||||||
\(779\) | −21.8885 | −0.784238 | ||||||||
\(780\) | −5.52786 | −0.197929 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.47214i | 0.0884034i | ||||||||
\(783\) | − 0.472136i | − 0.0168728i | ||||||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | 25.7771i | 0.920024i | ||||||||
\(786\) | −6.94427 | −0.247694 | ||||||||
\(787\) | 1.16718i | 0.0416056i | 0.999784 | + | 0.0208028i | \(0.00662222\pi\) | ||||
−0.999784 | + | 0.0208028i | \(0.993378\pi\) | |||||||
\(788\) | 18.9443i | 0.674862i | ||||||||
\(789\) | −20.9443 | −0.745636 | ||||||||
\(790\) | 27.8885i | 0.992230i | ||||||||
\(791\) | 77.6656 | 2.76147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.16718i | 0.0414479i | ||||||||
\(794\) | −29.3050 | −1.03999 | ||||||||
\(795\) | 20.0000 | 0.709327 | ||||||||
\(796\) | 17.4164 | 0.617308 | ||||||||
\(797\) | 37.8885i | 1.34208i | 0.741421 | + | 0.671041i | \(0.234152\pi\) | ||||
−0.741421 | + | 0.671041i | \(0.765848\pi\) | |||||||
\(798\) | 8.00000i | 0.283197i | ||||||||
\(799\) | −12.2229 | −0.432416 | ||||||||
\(800\) | − 5.00000i | − 0.176777i | ||||||||
\(801\) | −16.4721 | −0.582014 | ||||||||
\(802\) | − 25.4164i | − 0.897485i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.94427 | 0.174371 | ||||||||
\(805\) | −8.94427 | −0.315244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 0.472136i | − 0.0166200i | ||||||||
\(808\) | 0.472136i | 0.0166097i | ||||||||
\(809\) | 3.88854 | 0.136714 | 0.0683570 | − | 0.997661i | \(-0.478224\pi\) | ||||
0.0683570 | + | 0.997661i | \(0.478224\pi\) | |||||||
\(810\) | − 2.23607i | − 0.0785674i | ||||||||
\(811\) | −49.8885 | −1.75182 | −0.875912 | − | 0.482471i | \(-0.839739\pi\) | ||||
−0.875912 | + | 0.482471i | \(0.839739\pi\) | |||||||
\(812\) | 1.88854i | 0.0662749i | ||||||||
\(813\) | 0.944272i | 0.0331171i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 11.0557i | − 0.387265i | ||||||||
\(816\) | 2.47214 | 0.0865421 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − 18.0000i | − 0.629355i | ||||||||
\(819\) | 9.88854 | 0.345534 | ||||||||
\(820\) | −24.4721 | −0.854604 | ||||||||
\(821\) | −16.4721 | −0.574882 | −0.287441 | − | 0.957798i | \(-0.592804\pi\) | ||||
−0.287441 | + | 0.957798i | \(0.592804\pi\) | |||||||
\(822\) | 19.4164i | 0.677225i | ||||||||
\(823\) | 20.3607i | 0.709729i | 0.934918 | + | 0.354864i | \(0.115473\pi\) | ||||
−0.934918 | + | 0.354864i | \(0.884527\pi\) | |||||||
\(824\) | −16.9443 | −0.590282 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.0000 | −0.835067 | ||||||||
\(827\) | 42.4721i | 1.47690i | 0.674308 | + | 0.738450i | \(0.264442\pi\) | ||||
−0.674308 | + | 0.738450i | \(0.735558\pi\) | |||||||
\(828\) | − 1.00000i | − 0.0347524i | ||||||||
\(829\) | −30.9443 | −1.07474 | −0.537369 | − | 0.843347i | \(-0.680582\pi\) | ||||
−0.537369 | + | 0.843347i | \(0.680582\pi\) | |||||||
\(830\) | 3.41641 | 0.118585 | ||||||||
\(831\) | −27.4164 | −0.951065 | ||||||||
\(832\) | 2.47214i | 0.0857059i | ||||||||
\(833\) | 22.2492i | 0.770890i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 6.83282i | − 0.236459i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 37.8885i | − 1.30884i | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 8.94427i | 0.308607i | ||||||||
\(841\) | −28.7771 | −0.992313 | ||||||||
\(842\) | 37.4164i | 1.28945i | ||||||||
\(843\) | 3.52786i | 0.121506i | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 15.4033 | 0.529888 | ||||||||
\(846\) | 4.94427 | 0.169988 | ||||||||
\(847\) | 44.0000i | 1.51186i | ||||||||
\(848\) | − 8.94427i | − 0.307148i | ||||||||
\(849\) | −24.0000 | −0.823678 | ||||||||
\(850\) | −12.3607 | −0.423968 | ||||||||
\(851\) | −0.472136 | −0.0161846 | ||||||||
\(852\) | 7.52786i | 0.257900i | ||||||||
\(853\) | 9.52786i | 0.326228i | 0.986607 | + | 0.163114i | \(0.0521538\pi\) | ||||
−0.986607 | + | 0.163114i | \(0.947846\pi\) | |||||||
\(854\) | 1.88854 | 0.0646246 | ||||||||
\(855\) | 4.47214 | 0.152944 | ||||||||
\(856\) | −2.47214 | −0.0844959 | ||||||||
\(857\) | 23.8885i | 0.816017i | 0.912978 | + | 0.408009i | \(0.133777\pi\) | ||||
−0.912978 | + | 0.408009i | \(0.866223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.7771 | 1.35718 | 0.678588 | − | 0.734519i | \(-0.262592\pi\) | ||||
0.678588 | + | 0.734519i | \(0.262592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 43.7771 | 1.49192 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.05573i | 0.104018i | 0.998647 | + | 0.0520091i | \(0.0165625\pi\) | ||||
−0.998647 | + | 0.0520091i | \(0.983438\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | − 33.4164i | − 1.13619i | ||||||||
\(866\) | −21.4164 | −0.727759 | ||||||||
\(867\) | 10.8885i | 0.369794i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.05573 | 0.0357925 | ||||||||
\(871\) | 12.2229 | 0.414158 | ||||||||
\(872\) | − 0.472136i | − 0.0159885i | ||||||||
\(873\) | − 13.4164i | − 0.454077i | ||||||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | − 44.7214i | − 1.51186i | ||||||||
\(876\) | 4.94427 | 0.167051 | ||||||||
\(877\) | − 20.3607i | − 0.687531i | −0.939055 | − | 0.343766i | \(-0.888297\pi\) | ||||
0.939055 | − | 0.343766i | \(-0.111703\pi\) | |||||||
\(878\) | − 26.8328i | − 0.905564i | ||||||||
\(879\) | 0.944272 | 0.0318495 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.47214 | −0.150670 | −0.0753350 | − | 0.997158i | \(-0.524003\pi\) | ||||
−0.0753350 | + | 0.997158i | \(0.524003\pi\) | |||||||
\(882\) | − 9.00000i | − 0.303046i | ||||||||
\(883\) | − 19.7771i | − 0.665552i | −0.943006 | − | 0.332776i | \(-0.892015\pi\) | ||||
0.943006 | − | 0.332776i | \(-0.107985\pi\) | |||||||
\(884\) | 6.11146 | 0.205551 | ||||||||
\(885\) | 13.4164i | 0.450988i | ||||||||
\(886\) | −8.94427 | −0.300489 | ||||||||
\(887\) | − 24.0000i | − 0.805841i | −0.915235 | − | 0.402921i | \(-0.867995\pi\) | ||||
0.915235 | − | 0.402921i | \(-0.132005\pi\) | |||||||
\(888\) | 0.472136i | 0.0158438i | ||||||||
\(889\) | −45.6656 | −1.53158 | ||||||||
\(890\) | − 36.8328i | − 1.23464i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 11.4164i | − 0.382250i | ||||||||
\(893\) | 9.88854i | 0.330908i | ||||||||
\(894\) | 13.4164 | 0.448712 | ||||||||
\(895\) | 42.3607 | 1.41596 | ||||||||
\(896\) | 4.00000 | 0.133631 | ||||||||
\(897\) | − 2.47214i | − 0.0825422i | ||||||||
\(898\) | − 34.9443i | − 1.16611i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | 0.166667 | ||||||||
\(901\) | −22.1115 | −0.736639 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.4164 | −0.645780 | ||||||||
\(905\) | 18.9443 | 0.629729 | ||||||||
\(906\) | 16.9443 | 0.562936 | ||||||||
\(907\) | − 14.8328i | − 0.492516i | −0.969204 | − | 0.246258i | \(-0.920799\pi\) | ||||
0.969204 | − | 0.246258i | \(-0.0792010\pi\) | |||||||
\(908\) | 18.4721i | 0.613019i | ||||||||
\(909\) | −0.472136 | −0.0156598 | ||||||||
\(910\) | 22.1115i | 0.732988i | ||||||||
\(911\) | 24.9443 | 0.826441 | 0.413220 | − | 0.910631i | \(-0.364404\pi\) | ||||
0.413220 | + | 0.910631i | \(0.364404\pi\) | |||||||
\(912\) | − 2.00000i | − 0.0662266i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −25.4164 | −0.840700 | ||||||||
\(915\) | − 1.05573i | − 0.0349013i | ||||||||
\(916\) | 25.4164 | 0.839782 | ||||||||
\(917\) | 27.7771i | 0.917280i | ||||||||
\(918\) | 2.47214i | 0.0815926i | ||||||||
\(919\) | 9.41641 | 0.310619 | 0.155309 | − | 0.987866i | \(-0.450363\pi\) | ||||
0.155309 | + | 0.987866i | \(0.450363\pi\) | |||||||
\(920\) | 2.23607 | 0.0737210 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.3607i | 0.472944i | ||||||||
\(923\) | 18.6099i | 0.612552i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2.36068i | − 0.0776187i | ||||||||
\(926\) | −15.4164 | −0.506615 | ||||||||
\(927\) | − 16.9443i | − 0.556523i | ||||||||
\(928\) | − 0.472136i | − 0.0154986i | ||||||||
\(929\) | 10.9443 | 0.359070 | 0.179535 | − | 0.983752i | \(-0.442541\pi\) | ||||
0.179535 | + | 0.983752i | \(0.442541\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | 0.589926 | ||||||||
\(932\) | − 14.9443i | − 0.489516i | ||||||||
\(933\) | − 24.4721i | − 0.801182i | ||||||||
\(934\) | −26.4721 | −0.866195 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.47214 | −0.0808043 | ||||||||
\(937\) | − 6.58359i | − 0.215077i | −0.994201 | − | 0.107538i | \(-0.965703\pi\) | ||||
0.994201 | − | 0.107538i | \(-0.0342968\pi\) | |||||||
\(938\) | − 19.7771i | − 0.645745i | ||||||||
\(939\) | 25.4164 | 0.829433 | ||||||||
\(940\) | 11.0557i | 0.360598i | ||||||||
\(941\) | 36.4721 | 1.18896 | 0.594479 | − | 0.804111i | \(-0.297358\pi\) | ||||
0.594479 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(942\) | 11.5279i | 0.375598i | ||||||||
\(943\) | − 10.9443i | − 0.356395i | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | −8.94427 | −0.290957 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | 12.4721i | 0.405076i | ||||||||
\(949\) | 12.2229 | 0.396773 | ||||||||
\(950\) | 10.0000i | 0.324443i | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | − 9.88854i | − 0.320490i | ||||||||
\(953\) | − 12.3607i | − 0.400402i | −0.979755 | − | 0.200201i | \(-0.935841\pi\) | ||||
0.979755 | − | 0.200201i | \(-0.0641595\pi\) | |||||||
\(954\) | 8.94427 | 0.289581 | ||||||||
\(955\) | −57.8885 | −1.87323 | ||||||||
\(956\) | −12.4721 | −0.403378 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 16.9443i | − 0.547445i | ||||||||
\(959\) | 77.6656 | 2.50795 | ||||||||
\(960\) | − 2.23607i | − 0.0721688i | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 1.16718i | 0.0376315i | ||||||||
\(963\) | − 2.47214i | − 0.0796635i | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | 44.7214i | 1.43963i | ||||||||
\(966\) | −4.00000 | −0.128698 | ||||||||
\(967\) | − 55.4164i | − 1.78207i | −0.453933 | − | 0.891036i | \(-0.649979\pi\) | ||||
0.453933 | − | 0.891036i | \(-0.350021\pi\) | |||||||
\(968\) | − 11.0000i | − 0.353553i | ||||||||
\(969\) | −4.94427 | −0.158833 | ||||||||
\(970\) | 30.0000 | 0.963242 | ||||||||
\(971\) | −18.1115 | −0.581224 | −0.290612 | − | 0.956841i | \(-0.593859\pi\) | ||||
−0.290612 | + | 0.956841i | \(0.593859\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.4164 | 1.00665 | ||||||||
\(975\) | 12.3607 | 0.395859 | ||||||||
\(976\) | −0.472136 | −0.0151127 | ||||||||
\(977\) | − 1.52786i | − 0.0488807i | −0.999701 | − | 0.0244404i | \(-0.992220\pi\) | ||||
0.999701 | − | 0.0244404i | \(-0.00778038\pi\) | |||||||
\(978\) | − 4.94427i | − 0.158100i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 20.1246 | 0.642857 | ||||||||
\(981\) | 0.472136 | 0.0150741 | ||||||||
\(982\) | − 27.8885i | − 0.889959i | ||||||||
\(983\) | − 24.0000i | − 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | −10.9443 | −0.348891 | ||||||||
\(985\) | − 42.3607i | − 1.34972i | ||||||||
\(986\) | −1.16718 | −0.0371707 | ||||||||
\(987\) | − 19.7771i | − 0.629512i | ||||||||
\(988\) | − 4.94427i | − 0.157298i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.6656 | 1.70474 | 0.852372 | − | 0.522935i | \(-0.175163\pi\) | ||||
0.852372 | + | 0.522935i | \(0.175163\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 30.1115 | 0.955077 | ||||||||
\(995\) | −38.9443 | −1.23462 | ||||||||
\(996\) | 1.52786 | 0.0484122 | ||||||||
\(997\) | 7.41641i | 0.234880i | 0.993080 | + | 0.117440i | \(0.0374688\pi\) | ||||
−0.993080 | + | 0.117440i | \(0.962531\pi\) | |||||||
\(998\) | − 24.0000i | − 0.759707i | ||||||||
\(999\) | −0.472136 | −0.0149377 |
(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 | 690.2.d.a.139.2 | ✓ | 4 | |
3.2 | odd | 2 | 2070.2.d.b.829.3 | 4 | |||
5.2 | odd | 4 | 3450.2.a.bn.1.1 | 2 | |||
5.3 | odd | 4 | 3450.2.a.bc.1.2 | 2 | |||
5.4 | even | 2 | inner | 690.2.d.a.139.4 | yes | 4 | |
15.14 | odd | 2 | 2070.2.d.b.829.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.a.139.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
690.2.d.a.139.4 | yes | 4 | 5.4 | even | 2 | inner | |
2070.2.d.b.829.1 | 4 | 15.14 | odd | 2 | |||
2070.2.d.b.829.3 | 4 | 3.2 | odd | 2 | |||
3450.2.a.bc.1.2 | 2 | 5.3 | odd | 4 | |||
3450.2.a.bn.1.1 | 2 | 5.2 | odd | 4 |