Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.a (trivial) |
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: | yes |
Analytic conductor: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 690) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.00000 | 1.51186 | 0.755929 | − | 0.654654i | \(-0.227186\pi\) | ||||
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.47214 | −0.685647 | −0.342824 | − | 0.939400i | \(-0.611383\pi\) | ||||
−0.342824 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(14\) | 4.00000 | 1.06904 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.47214 | 0.599581 | 0.299791 | − | 0.954005i | \(-0.403083\pi\) | ||||
0.299791 | + | 0.954005i | \(0.403083\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.47214 | −0.484826 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | −0.472136 | −0.0876734 | −0.0438367 | − | 0.999039i | \(-0.513958\pi\) | ||||
−0.0438367 | + | 0.999039i | \(0.513958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.47214 | 0.423968 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.472136 | 0.0776187 | 0.0388093 | − | 0.999247i | \(-0.487644\pi\) | ||||
0.0388093 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | −2.47214 | −0.395859 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9443 | 1.70921 | 0.854604 | − | 0.519280i | \(-0.173800\pi\) | ||||
0.854604 | + | 0.519280i | \(0.173800\pi\) | |||||||
\(42\) | 4.00000 | 0.617213 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 4.94427 | 0.721196 | 0.360598 | − | 0.932721i | \(-0.382573\pi\) | ||||
0.360598 | + | 0.932721i | \(0.382573\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.47214 | 0.346168 | ||||||||
\(52\) | −2.47214 | −0.342824 | ||||||||
\(53\) | −8.94427 | −1.22859 | −0.614295 | − | 0.789076i | \(-0.710560\pi\) | ||||
−0.614295 | + | 0.789076i | \(0.710560\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.00000 | 0.534522 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −0.472136 | −0.0619945 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.472136 | −0.0604508 | −0.0302254 | − | 0.999543i | \(-0.509623\pi\) | ||||
−0.0302254 | + | 0.999543i | \(0.509623\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.00000 | 0.503953 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.94427 | −0.604039 | −0.302019 | − | 0.953302i | \(-0.597661\pi\) | ||||
−0.302019 | + | 0.953302i | \(0.597661\pi\) | |||||||
\(68\) | 2.47214 | 0.299791 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.52786 | −0.893393 | −0.446697 | − | 0.894686i | \(-0.647400\pi\) | ||||
−0.446697 | + | 0.894686i | \(0.647400\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 4.94427 | 0.578683 | 0.289342 | − | 0.957226i | \(-0.406564\pi\) | ||||
0.289342 | + | 0.957226i | \(0.406564\pi\) | |||||||
\(74\) | 0.472136 | 0.0548847 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.47214 | −0.279914 | ||||||||
\(79\) | 12.4721 | 1.40322 | 0.701612 | − | 0.712559i | \(-0.252464\pi\) | ||||
0.701612 | + | 0.712559i | \(0.252464\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.9443 | 1.20859 | ||||||||
\(83\) | 1.52786 | 0.167705 | 0.0838524 | − | 0.996478i | \(-0.473278\pi\) | ||||
0.0838524 | + | 0.996478i | \(0.473278\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.472136 | −0.0506183 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.4721 | −1.74604 | −0.873021 | − | 0.487682i | \(-0.837843\pi\) | ||||
−0.873021 | + | 0.487682i | \(0.837843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.88854 | −1.03660 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.94427 | 0.509963 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −13.4164 | −1.36223 | −0.681115 | − | 0.732177i | \(-0.738505\pi\) | ||||
−0.681115 | + | 0.732177i | \(0.738505\pi\) | |||||||
\(98\) | 9.00000 | 0.909137 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.472136 | 0.0469793 | 0.0234896 | − | 0.999724i | \(-0.492522\pi\) | ||||
0.0234896 | + | 0.999724i | \(0.492522\pi\) | |||||||
\(102\) | 2.47214 | 0.244778 | ||||||||
\(103\) | 16.9443 | 1.66957 | 0.834784 | − | 0.550577i | \(-0.185592\pi\) | ||||
0.834784 | + | 0.550577i | \(0.185592\pi\) | |||||||
\(104\) | −2.47214 | −0.242413 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.94427 | −0.868744 | ||||||||
\(107\) | −2.47214 | −0.238990 | −0.119495 | − | 0.992835i | \(-0.538128\pi\) | ||||
−0.119495 | + | 0.992835i | \(0.538128\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 0.472136 | 0.0452224 | 0.0226112 | − | 0.999744i | \(-0.492802\pi\) | ||||
0.0226112 | + | 0.999744i | \(0.492802\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.472136 | 0.0448132 | ||||||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 19.4164 | 1.82654 | 0.913271 | − | 0.407353i | \(-0.133548\pi\) | ||||
0.913271 | + | 0.407353i | \(0.133548\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.472136 | −0.0438367 | ||||||||
\(117\) | −2.47214 | −0.228549 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 9.88854 | 0.906481 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | −0.472136 | −0.0427452 | ||||||||
\(123\) | 10.9443 | 0.986812 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | 11.4164 | 1.01304 | 0.506521 | − | 0.862228i | \(-0.330931\pi\) | ||||
0.506521 | + | 0.862228i | \(0.330931\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.94427 | −0.606724 | −0.303362 | − | 0.952875i | \(-0.598109\pi\) | ||||
−0.303362 | + | 0.952875i | \(0.598109\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | 0.693688 | ||||||||
\(134\) | −4.94427 | −0.427120 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.47214 | 0.211984 | ||||||||
\(137\) | −19.4164 | −1.65886 | −0.829428 | − | 0.558614i | \(-0.811333\pi\) | ||||
−0.829428 | + | 0.558614i | \(0.811333\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.94427 | 0.416383 | ||||||||
\(142\) | −7.52786 | −0.631724 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.94427 | 0.409191 | ||||||||
\(147\) | 9.00000 | 0.742307 | ||||||||
\(148\) | 0.472136 | 0.0388093 | ||||||||
\(149\) | −13.4164 | −1.09911 | −0.549557 | − | 0.835456i | \(-0.685204\pi\) | ||||
−0.549557 | + | 0.835456i | \(0.685204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9443 | 1.37891 | 0.689453 | − | 0.724331i | \(-0.257851\pi\) | ||||
0.689453 | + | 0.724331i | \(0.257851\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | 2.47214 | 0.199860 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.47214 | −0.197929 | ||||||||
\(157\) | −11.5279 | −0.920024 | −0.460012 | − | 0.887913i | \(-0.652155\pi\) | ||||
−0.460012 | + | 0.887913i | \(0.652155\pi\) | |||||||
\(158\) | 12.4721 | 0.992230 | ||||||||
\(159\) | −8.94427 | −0.709327 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −4.94427 | −0.387265 | −0.193633 | − | 0.981074i | \(-0.562027\pi\) | ||||
−0.193633 | + | 0.981074i | \(0.562027\pi\) | |||||||
\(164\) | 10.9443 | 0.854604 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.52786 | 0.118585 | ||||||||
\(167\) | 3.05573 | 0.236459 | 0.118230 | − | 0.992986i | \(-0.462278\pi\) | ||||
0.118230 | + | 0.992986i | \(0.462278\pi\) | |||||||
\(168\) | 4.00000 | 0.308607 | ||||||||
\(169\) | −6.88854 | −0.529888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.9443 | −1.13619 | −0.568096 | − | 0.822962i | \(-0.692320\pi\) | ||||
−0.568096 | + | 0.822962i | \(0.692320\pi\) | |||||||
\(174\) | −0.472136 | −0.0357925 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | −16.4721 | −1.23464 | ||||||||
\(179\) | −18.9443 | −1.41596 | −0.707981 | − | 0.706232i | \(-0.750394\pi\) | ||||
−0.707981 | + | 0.706232i | \(0.750394\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.47214 | 0.629729 | 0.314864 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314864 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(182\) | −9.88854 | −0.732988 | ||||||||
\(183\) | −0.472136 | −0.0349013 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.94427 | 0.360598 | ||||||||
\(189\) | 4.00000 | 0.290957 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.8885 | −1.87323 | −0.936615 | − | 0.350361i | \(-0.886059\pi\) | ||||
−0.936615 | + | 0.350361i | \(0.886059\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 20.0000 | 1.43963 | 0.719816 | − | 0.694165i | \(-0.244226\pi\) | ||||
0.719816 | + | 0.694165i | \(0.244226\pi\) | |||||||
\(194\) | −13.4164 | −0.963242 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | 18.9443 | 1.34972 | 0.674862 | − | 0.737944i | \(-0.264203\pi\) | ||||
0.674862 | + | 0.737944i | \(0.264203\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.4164 | 1.23462 | 0.617308 | − | 0.786721i | \(-0.288223\pi\) | ||||
0.617308 | + | 0.786721i | \(0.288223\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.94427 | −0.348742 | ||||||||
\(202\) | 0.472136 | 0.0332194 | ||||||||
\(203\) | −1.88854 | −0.132550 | ||||||||
\(204\) | 2.47214 | 0.173084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.9443 | 1.18056 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −2.47214 | −0.171412 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | −8.94427 | −0.614295 | ||||||||
\(213\) | −7.52786 | −0.515801 | ||||||||
\(214\) | −2.47214 | −0.168992 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.472136 | 0.0319771 | ||||||||
\(219\) | 4.94427 | 0.334103 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.11146 | −0.411101 | ||||||||
\(222\) | 0.472136 | 0.0316877 | ||||||||
\(223\) | 11.4164 | 0.764499 | 0.382250 | − | 0.924059i | \(-0.375149\pi\) | ||||
0.382250 | + | 0.924059i | \(0.375149\pi\) | |||||||
\(224\) | 4.00000 | 0.267261 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.4164 | 1.29156 | ||||||||
\(227\) | 18.4721 | 1.22604 | 0.613019 | − | 0.790068i | \(-0.289955\pi\) | ||||
0.613019 | + | 0.790068i | \(0.289955\pi\) | |||||||
\(228\) | 2.00000 | 0.132453 | ||||||||
\(229\) | 25.4164 | 1.67956 | 0.839782 | − | 0.542924i | \(-0.182683\pi\) | ||||
0.839782 | + | 0.542924i | \(0.182683\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.472136 | −0.0309972 | ||||||||
\(233\) | 14.9443 | 0.979032 | 0.489516 | − | 0.871994i | \(-0.337174\pi\) | ||||
0.489516 | + | 0.871994i | \(0.337174\pi\) | |||||||
\(234\) | −2.47214 | −0.161609 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | 12.4721 | 0.810152 | ||||||||
\(238\) | 9.88854 | 0.640979 | ||||||||
\(239\) | −12.4721 | −0.806755 | −0.403378 | − | 0.915034i | \(-0.632164\pi\) | ||||
−0.403378 | + | 0.915034i | \(0.632164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.472136 | −0.0302254 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.9443 | 0.697781 | ||||||||
\(247\) | −4.94427 | −0.314596 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.52786 | 0.0968244 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 4.00000 | 0.251976 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 11.4164 | 0.716329 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.0000 | −1.12281 | −0.561405 | − | 0.827541i | \(-0.689739\pi\) | ||||
−0.561405 | + | 0.827541i | \(0.689739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.88854 | 0.117348 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.472136 | −0.0292245 | ||||||||
\(262\) | −6.94427 | −0.429019 | ||||||||
\(263\) | 20.9443 | 1.29148 | 0.645740 | − | 0.763558i | \(-0.276549\pi\) | ||||
0.645740 | + | 0.763558i | \(0.276549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | −16.4721 | −1.00808 | ||||||||
\(268\) | −4.94427 | −0.302019 | ||||||||
\(269\) | 0.472136 | 0.0287866 | 0.0143933 | − | 0.999896i | \(-0.495418\pi\) | ||||
0.0143933 | + | 0.999896i | \(0.495418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.944272 | 0.0573604 | 0.0286802 | − | 0.999589i | \(-0.490870\pi\) | ||||
0.0286802 | + | 0.999589i | \(0.490870\pi\) | |||||||
\(272\) | 2.47214 | 0.149895 | ||||||||
\(273\) | −9.88854 | −0.598482 | ||||||||
\(274\) | −19.4164 | −1.17299 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −27.4164 | −1.64729 | −0.823646 | − | 0.567104i | \(-0.808064\pi\) | ||||
−0.823646 | + | 0.567104i | \(0.808064\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.52786 | 0.210455 | 0.105227 | − | 0.994448i | \(-0.466443\pi\) | ||||
0.105227 | + | 0.994448i | \(0.466443\pi\) | |||||||
\(282\) | 4.94427 | 0.294427 | ||||||||
\(283\) | 24.0000 | 1.42665 | 0.713326 | − | 0.700832i | \(-0.247188\pi\) | ||||
0.713326 | + | 0.700832i | \(0.247188\pi\) | |||||||
\(284\) | −7.52786 | −0.446697 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 43.7771 | 2.58408 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.4164 | −0.786484 | ||||||||
\(292\) | 4.94427 | 0.289342 | ||||||||
\(293\) | −0.944272 | −0.0551650 | −0.0275825 | − | 0.999620i | \(-0.508781\pi\) | ||||
−0.0275825 | + | 0.999620i | \(0.508781\pi\) | |||||||
\(294\) | 9.00000 | 0.524891 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.472136 | 0.0274423 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.4164 | −0.777192 | ||||||||
\(299\) | 2.47214 | 0.142967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 16.9443 | 0.975033 | ||||||||
\(303\) | 0.472136 | 0.0271235 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.47214 | 0.141323 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 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 | \(0.744084\pi\) | |||||||
\(312\) | −2.47214 | −0.139957 | ||||||||
\(313\) | −25.4164 | −1.43662 | −0.718310 | − | 0.695723i | \(-0.755084\pi\) | ||||
−0.718310 | + | 0.695723i | \(0.755084\pi\) | |||||||
\(314\) | −11.5279 | −0.650555 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.4721 | 0.701612 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | −8.94427 | −0.501570 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.47214 | −0.137981 | ||||||||
\(322\) | −4.00000 | −0.222911 | ||||||||
\(323\) | 4.94427 | 0.275107 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.94427 | −0.273838 | ||||||||
\(327\) | 0.472136 | 0.0261092 | ||||||||
\(328\) | 10.9443 | 0.604296 | ||||||||
\(329\) | 19.7771 | 1.09035 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 1.52786 | 0.0838524 | ||||||||
\(333\) | 0.472136 | 0.0258729 | ||||||||
\(334\) | 3.05573 | 0.167202 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.00000 | 0.218218 | ||||||||
\(337\) | 25.4164 | 1.38452 | 0.692260 | − | 0.721648i | \(-0.256615\pi\) | ||||
0.692260 | + | 0.721648i | \(0.256615\pi\) | |||||||
\(338\) | −6.88854 | −0.374687 | ||||||||
\(339\) | 19.4164 | 1.05455 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.00000 | 0.108148 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.9443 | −0.803409 | ||||||||
\(347\) | 8.94427 | 0.480154 | 0.240077 | − | 0.970754i | \(-0.422827\pi\) | ||||
0.240077 | + | 0.970754i | \(0.422827\pi\) | |||||||
\(348\) | −0.472136 | −0.0253091 | ||||||||
\(349\) | −27.8885 | −1.49284 | −0.746420 | − | 0.665475i | \(-0.768229\pi\) | ||||
−0.746420 | + | 0.665475i | \(0.768229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.47214 | −0.131953 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.94427 | 0.156708 | 0.0783539 | − | 0.996926i | \(-0.475034\pi\) | ||||
0.0783539 | + | 0.996926i | \(0.475034\pi\) | |||||||
\(354\) | −6.00000 | −0.318896 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16.4721 | −0.873021 | ||||||||
\(357\) | 9.88854 | 0.523357 | ||||||||
\(358\) | −18.9443 | −1.00124 | ||||||||
\(359\) | −32.9443 | −1.73873 | −0.869366 | − | 0.494169i | \(-0.835473\pi\) | ||||
−0.869366 | + | 0.494169i | \(0.835473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 8.47214 | 0.445286 | ||||||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | −9.88854 | −0.518301 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.472136 | −0.0246789 | ||||||||
\(367\) | −12.0000 | −0.626395 | −0.313197 | − | 0.949688i | \(-0.601400\pi\) | ||||
−0.313197 | + | 0.949688i | \(0.601400\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 10.9443 | 0.569736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.7771 | −1.85745 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.4164 | −1.10890 | −0.554450 | − | 0.832217i | \(-0.687071\pi\) | ||||
−0.554450 | + | 0.832217i | \(0.687071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.94427 | 0.254981 | ||||||||
\(377\) | 1.16718 | 0.0601130 | ||||||||
\(378\) | 4.00000 | 0.205738 | ||||||||
\(379\) | 16.8328 | 0.864644 | 0.432322 | − | 0.901719i | \(-0.357694\pi\) | ||||
0.432322 | + | 0.901719i | \(0.357694\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.4164 | 0.584880 | ||||||||
\(382\) | −25.8885 | −1.32457 | ||||||||
\(383\) | −13.8885 | −0.709671 | −0.354836 | − | 0.934929i | \(-0.615463\pi\) | ||||
−0.354836 | + | 0.934929i | \(0.615463\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.4164 | −0.681115 | ||||||||
\(389\) | 4.47214 | 0.226746 | 0.113373 | − | 0.993552i | \(-0.463834\pi\) | ||||
0.113373 | + | 0.993552i | \(0.463834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.47214 | −0.125021 | ||||||||
\(392\) | 9.00000 | 0.454569 | ||||||||
\(393\) | −6.94427 | −0.350292 | ||||||||
\(394\) | 18.9443 | 0.954399 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.3050 | 1.47077 | 0.735387 | − | 0.677648i | \(-0.237001\pi\) | ||||
0.735387 | + | 0.677648i | \(0.237001\pi\) | |||||||
\(398\) | 17.4164 | 0.873006 | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.4164 | 1.26923 | 0.634617 | − | 0.772826i | \(-0.281158\pi\) | ||||
0.634617 | + | 0.772826i | \(0.281158\pi\) | |||||||
\(402\) | −4.94427 | −0.246598 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.472136 | 0.0234896 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.88854 | −0.0937269 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.47214 | 0.122389 | ||||||||
\(409\) | −18.0000 | −0.890043 | −0.445021 | − | 0.895520i | \(-0.646804\pi\) | ||||
−0.445021 | + | 0.895520i | \(0.646804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.4164 | −0.957741 | ||||||||
\(412\) | 16.9443 | 0.834784 | ||||||||
\(413\) | −24.0000 | −1.18096 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.47214 | −0.121206 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.8885 | −1.85098 | −0.925488 | − | 0.378776i | \(-0.876345\pi\) | ||||
−0.925488 | + | 0.378776i | \(0.876345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.4164 | −1.82356 | −0.911782 | − | 0.410674i | \(-0.865293\pi\) | ||||
−0.911782 | + | 0.410674i | \(0.865293\pi\) | |||||||
\(422\) | −12.0000 | −0.584151 | ||||||||
\(423\) | 4.94427 | 0.240399 | ||||||||
\(424\) | −8.94427 | −0.434372 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.52786 | −0.364726 | ||||||||
\(427\) | −1.88854 | −0.0913930 | ||||||||
\(428\) | −2.47214 | −0.119495 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −21.4164 | −1.02921 | −0.514603 | − | 0.857428i | \(-0.672061\pi\) | ||||
−0.514603 | + | 0.857428i | \(0.672061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.472136 | 0.0226112 | ||||||||
\(437\) | −2.00000 | −0.0956730 | ||||||||
\(438\) | 4.94427 | 0.236246 | ||||||||
\(439\) | −26.8328 | −1.28066 | −0.640330 | − | 0.768100i | \(-0.721202\pi\) | ||||
−0.640330 | + | 0.768100i | \(0.721202\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | −6.11146 | −0.290692 | ||||||||
\(443\) | −8.94427 | −0.424955 | −0.212478 | − | 0.977166i | \(-0.568153\pi\) | ||||
−0.212478 | + | 0.977166i | \(0.568153\pi\) | |||||||
\(444\) | 0.472136 | 0.0224066 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.4164 | 0.540583 | ||||||||
\(447\) | −13.4164 | −0.634574 | ||||||||
\(448\) | 4.00000 | 0.188982 | ||||||||
\(449\) | −34.9443 | −1.64912 | −0.824561 | − | 0.565773i | \(-0.808578\pi\) | ||||
−0.824561 | + | 0.565773i | \(0.808578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 19.4164 | 0.913271 | ||||||||
\(453\) | 16.9443 | 0.796111 | ||||||||
\(454\) | 18.4721 | 0.866940 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 25.4164 | 1.18893 | 0.594465 | − | 0.804122i | \(-0.297364\pi\) | ||||
0.594465 | + | 0.804122i | \(0.297364\pi\) | |||||||
\(458\) | 25.4164 | 1.18763 | ||||||||
\(459\) | 2.47214 | 0.115389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.3607 | −0.668844 | −0.334422 | − | 0.942424i | \(-0.608541\pi\) | ||||
−0.334422 | + | 0.942424i | \(0.608541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.4164 | −0.716461 | −0.358231 | − | 0.933633i | \(-0.616620\pi\) | ||||
−0.358231 | + | 0.933633i | \(0.616620\pi\) | |||||||
\(464\) | −0.472136 | −0.0219184 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.9443 | 0.692280 | ||||||||
\(467\) | 26.4721 | 1.22498 | 0.612492 | − | 0.790477i | \(-0.290167\pi\) | ||||
0.612492 | + | 0.790477i | \(0.290167\pi\) | |||||||
\(468\) | −2.47214 | −0.114275 | ||||||||
\(469\) | −19.7771 | −0.913221 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5279 | −0.531176 | ||||||||
\(472\) | −6.00000 | −0.276172 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12.4721 | 0.572864 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.88854 | 0.453241 | ||||||||
\(477\) | −8.94427 | −0.409530 | ||||||||
\(478\) | −12.4721 | −0.570462 | ||||||||
\(479\) | −16.9443 | −0.774204 | −0.387102 | − | 0.922037i | \(-0.626524\pi\) | ||||
−0.387102 | + | 0.922037i | \(0.626524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.16718 | −0.0532190 | ||||||||
\(482\) | −2.00000 | −0.0910975 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −31.4164 | −1.42361 | −0.711807 | − | 0.702375i | \(-0.752123\pi\) | ||||
−0.711807 | + | 0.702375i | \(0.752123\pi\) | |||||||
\(488\) | −0.472136 | −0.0213726 | ||||||||
\(489\) | −4.94427 | −0.223588 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.8885 | 1.25859 | 0.629296 | − | 0.777166i | \(-0.283343\pi\) | ||||
0.629296 | + | 0.777166i | \(0.283343\pi\) | |||||||
\(492\) | 10.9443 | 0.493406 | ||||||||
\(493\) | −1.16718 | −0.0525673 | ||||||||
\(494\) | −4.94427 | −0.222453 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.1115 | −1.35068 | ||||||||
\(498\) | 1.52786 | 0.0684652 | ||||||||
\(499\) | −24.0000 | −1.07439 | −0.537194 | − | 0.843459i | \(-0.680516\pi\) | ||||
−0.537194 | + | 0.843459i | \(0.680516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.05573 | 0.136520 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 13.8885 | 0.619260 | 0.309630 | − | 0.950857i | \(-0.399795\pi\) | ||||
0.309630 | + | 0.950857i | \(0.399795\pi\) | |||||||
\(504\) | 4.00000 | 0.178174 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.88854 | −0.305931 | ||||||||
\(508\) | 11.4164 | 0.506521 | ||||||||
\(509\) | 1.41641 | 0.0627812 | 0.0313906 | − | 0.999507i | \(-0.490006\pi\) | ||||
0.0313906 | + | 0.999507i | \(0.490006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.7771 | 0.874887 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.00000 | 0.0883022 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.88854 | 0.0829779 | ||||||||
\(519\) | −14.9443 | −0.655981 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.5279 | −0.855531 | −0.427766 | − | 0.903890i | \(-0.640699\pi\) | ||||
−0.427766 | + | 0.903890i | \(0.640699\pi\) | |||||||
\(522\) | −0.472136 | −0.0206648 | ||||||||
\(523\) | 4.94427 | 0.216198 | 0.108099 | − | 0.994140i | \(-0.465524\pi\) | ||||
0.108099 | + | 0.994140i | \(0.465524\pi\) | |||||||
\(524\) | −6.94427 | −0.303362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.9443 | 0.913214 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 8.00000 | 0.346844 | ||||||||
\(533\) | −27.0557 | −1.17191 | ||||||||
\(534\) | −16.4721 | −0.712819 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.94427 | −0.213560 | ||||||||
\(537\) | −18.9443 | −0.817506 | ||||||||
\(538\) | 0.472136 | 0.0203552 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.8328 | 1.75554 | 0.877770 | − | 0.479082i | \(-0.159030\pi\) | ||||
0.877770 | + | 0.479082i | \(0.159030\pi\) | |||||||
\(542\) | 0.944272 | 0.0405600 | ||||||||
\(543\) | 8.47214 | 0.363574 | ||||||||
\(544\) | 2.47214 | 0.105992 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.88854 | −0.423191 | ||||||||
\(547\) | −22.8328 | −0.976261 | −0.488130 | − | 0.872771i | \(-0.662321\pi\) | ||||
−0.488130 | + | 0.872771i | \(0.662321\pi\) | |||||||
\(548\) | −19.4164 | −0.829428 | ||||||||
\(549\) | −0.472136 | −0.0201503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.944272 | −0.0402273 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 49.8885 | 2.12148 | ||||||||
\(554\) | −27.4164 | −1.16481 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.8885 | −1.26642 | −0.633209 | − | 0.773981i | \(-0.718263\pi\) | ||||
−0.633209 | + | 0.773981i | \(0.718263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.52786 | 0.148814 | ||||||||
\(563\) | −37.3050 | −1.57222 | −0.786108 | − | 0.618089i | \(-0.787907\pi\) | ||||
−0.786108 | + | 0.618089i | \(0.787907\pi\) | |||||||
\(564\) | 4.94427 | 0.208191 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | 4.00000 | 0.167984 | ||||||||
\(568\) | −7.52786 | −0.315862 | ||||||||
\(569\) | 39.3050 | 1.64775 | 0.823875 | − | 0.566772i | \(-0.191808\pi\) | ||||
0.823875 | + | 0.566772i | \(0.191808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.8328 | 1.37401 | 0.687005 | − | 0.726652i | \(-0.258925\pi\) | ||||
0.687005 | + | 0.726652i | \(0.258925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.8885 | −1.08151 | ||||||||
\(574\) | 43.7771 | 1.82722 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 16.9443 | 0.705399 | 0.352700 | − | 0.935737i | \(-0.385264\pi\) | ||||
0.352700 | + | 0.935737i | \(0.385264\pi\) | |||||||
\(578\) | −10.8885 | −0.452904 | ||||||||
\(579\) | 20.0000 | 0.831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.11146 | 0.253546 | ||||||||
\(582\) | −13.4164 | −0.556128 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.94427 | 0.204595 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.944272 | −0.0390075 | ||||||||
\(587\) | −29.8885 | −1.23363 | −0.616816 | − | 0.787107i | \(-0.711578\pi\) | ||||
−0.616816 | + | 0.787107i | \(0.711578\pi\) | |||||||
\(588\) | 9.00000 | 0.371154 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.9443 | 0.779263 | ||||||||
\(592\) | 0.472136 | 0.0194047 | ||||||||
\(593\) | 23.8885 | 0.980985 | 0.490492 | − | 0.871445i | \(-0.336817\pi\) | ||||
0.490492 | + | 0.871445i | \(0.336817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.4164 | −0.549557 | ||||||||
\(597\) | 17.4164 | 0.712806 | ||||||||
\(598\) | 2.47214 | 0.101093 | ||||||||
\(599\) | 26.3607 | 1.07707 | 0.538534 | − | 0.842604i | \(-0.318978\pi\) | ||||
0.538534 | + | 0.842604i | \(0.318978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.94427 | −0.201346 | ||||||||
\(604\) | 16.9443 | 0.689453 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.472136 | 0.0191792 | ||||||||
\(607\) | 7.41641 | 0.301023 | 0.150511 | − | 0.988608i | \(-0.451908\pi\) | ||||
0.150511 | + | 0.988608i | \(0.451908\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | −1.88854 | −0.0765277 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2229 | −0.494486 | ||||||||
\(612\) | 2.47214 | 0.0999302 | ||||||||
\(613\) | 9.41641 | 0.380325 | 0.190163 | − | 0.981753i | \(-0.439098\pi\) | ||||
0.190163 | + | 0.981753i | \(0.439098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.4721 | 0.582626 | 0.291313 | − | 0.956628i | \(-0.405908\pi\) | ||||
0.291313 | + | 0.956628i | \(0.405908\pi\) | |||||||
\(618\) | 16.9443 | 0.681599 | ||||||||
\(619\) | 40.8328 | 1.64121 | 0.820605 | − | 0.571496i | \(-0.193637\pi\) | ||||
0.820605 | + | 0.571496i | \(0.193637\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −24.4721 | −0.981243 | ||||||||
\(623\) | −65.8885 | −2.63977 | ||||||||
\(624\) | −2.47214 | −0.0989646 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.4164 | −1.01584 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.5279 | −0.460012 | ||||||||
\(629\) | 1.16718 | 0.0465387 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.36068 | −0.0939772 | −0.0469886 | − | 0.998895i | \(-0.514962\pi\) | ||||
−0.0469886 | + | 0.998895i | \(0.514962\pi\) | |||||||
\(632\) | 12.4721 | 0.496115 | ||||||||
\(633\) | −12.0000 | −0.476957 | ||||||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.94427 | −0.354663 | ||||||||
\(637\) | −22.2492 | −0.881546 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.52786 | −0.297798 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.5279 | −0.455323 | −0.227662 | − | 0.973740i | \(-0.573108\pi\) | ||||
−0.227662 | + | 0.973740i | \(0.573108\pi\) | |||||||
\(642\) | −2.47214 | −0.0975674 | ||||||||
\(643\) | 12.9443 | 0.510472 | 0.255236 | − | 0.966879i | \(-0.417847\pi\) | ||||
0.255236 | + | 0.966879i | \(0.417847\pi\) | |||||||
\(644\) | −4.00000 | −0.157622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.94427 | 0.194530 | ||||||||
\(647\) | −41.8885 | −1.64681 | −0.823404 | − | 0.567455i | \(-0.807928\pi\) | ||||
−0.823404 | + | 0.567455i | \(0.807928\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.94427 | −0.193633 | ||||||||
\(653\) | 20.8328 | 0.815251 | 0.407626 | − | 0.913149i | \(-0.366357\pi\) | ||||
0.407626 | + | 0.913149i | \(0.366357\pi\) | |||||||
\(654\) | 0.472136 | 0.0184620 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.9443 | 0.427302 | ||||||||
\(657\) | 4.94427 | 0.192894 | ||||||||
\(658\) | 19.7771 | 0.770991 | ||||||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.2492 | −1.40993 | −0.704966 | − | 0.709241i | \(-0.749038\pi\) | ||||
−0.704966 | + | 0.709241i | \(0.749038\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.11146 | −0.237349 | ||||||||
\(664\) | 1.52786 | 0.0592926 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.472136 | 0.0182949 | ||||||||
\(667\) | 0.472136 | 0.0182812 | ||||||||
\(668\) | 3.05573 | 0.118230 | ||||||||
\(669\) | 11.4164 | 0.441384 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.00000 | 0.154303 | ||||||||
\(673\) | −38.8328 | −1.49690 | −0.748448 | − | 0.663194i | \(-0.769200\pi\) | ||||
−0.748448 | + | 0.663194i | \(0.769200\pi\) | |||||||
\(674\) | 25.4164 | 0.979003 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.88854 | −0.264944 | ||||||||
\(677\) | −25.8885 | −0.994978 | −0.497489 | − | 0.867470i | \(-0.665744\pi\) | ||||
−0.497489 | + | 0.867470i | \(0.665744\pi\) | |||||||
\(678\) | 19.4164 | 0.745683 | ||||||||
\(679\) | −53.6656 | −2.05950 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.4721 | 0.707854 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 2.00000 | 0.0764719 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.00000 | 0.305441 | ||||||||
\(687\) | 25.4164 | 0.969696 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.1115 | 0.842379 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.7771 | −1.51319 | −0.756596 | − | 0.653883i | \(-0.773139\pi\) | ||||
−0.756596 | + | 0.653883i | \(0.773139\pi\) | |||||||
\(692\) | −14.9443 | −0.568096 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.94427 | 0.339520 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.472136 | −0.0178963 | ||||||||
\(697\) | 27.0557 | 1.02481 | ||||||||
\(698\) | −27.8885 | −1.05560 | ||||||||
\(699\) | 14.9443 | 0.565244 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.4164 | 1.41320 | 0.706599 | − | 0.707614i | \(-0.250228\pi\) | ||||
0.706599 | + | 0.707614i | \(0.250228\pi\) | |||||||
\(702\) | −2.47214 | −0.0933048 | ||||||||
\(703\) | 0.944272 | 0.0356139 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.94427 | 0.110809 | ||||||||
\(707\) | 1.88854 | 0.0710260 | ||||||||
\(708\) | −6.00000 | −0.225494 | ||||||||
\(709\) | 20.4721 | 0.768847 | 0.384424 | − | 0.923157i | \(-0.374400\pi\) | ||||
0.384424 | + | 0.923157i | \(0.374400\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.4721 | 0.467742 | ||||||||
\(712\) | −16.4721 | −0.617319 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 9.88854 | 0.370069 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.9443 | −0.707981 | ||||||||
\(717\) | −12.4721 | −0.465780 | ||||||||
\(718\) | −32.9443 | −1.22947 | ||||||||
\(719\) | −35.5279 | −1.32497 | −0.662483 | − | 0.749077i | \(-0.730497\pi\) | ||||
−0.662483 | + | 0.749077i | \(0.730497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 67.7771 | 2.52415 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | −2.00000 | −0.0743808 | ||||||||
\(724\) | 8.47214 | 0.314864 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.0000 | −0.408248 | ||||||||
\(727\) | 0.944272 | 0.0350211 | 0.0175106 | − | 0.999847i | \(-0.494426\pi\) | ||||
0.0175106 | + | 0.999847i | \(0.494426\pi\) | |||||||
\(728\) | −9.88854 | −0.366494 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.472136 | −0.0174506 | ||||||||
\(733\) | −0.472136 | −0.0174387 | −0.00871937 | − | 0.999962i | \(-0.502775\pi\) | ||||
−0.00871937 | + | 0.999962i | \(0.502775\pi\) | |||||||
\(734\) | −12.0000 | −0.442928 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 10.9443 | 0.402864 | ||||||||
\(739\) | 1.88854 | 0.0694712 | 0.0347356 | − | 0.999397i | \(-0.488941\pi\) | ||||
0.0347356 | + | 0.999397i | \(0.488941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.94427 | −0.181632 | ||||||||
\(742\) | −35.7771 | −1.31342 | ||||||||
\(743\) | 2.11146 | 0.0774618 | 0.0387309 | − | 0.999250i | \(-0.487668\pi\) | ||||
0.0387309 | + | 0.999250i | \(0.487668\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −21.4164 | −0.784110 | ||||||||
\(747\) | 1.52786 | 0.0559016 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.88854 | −0.361320 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.4721 | 1.33089 | 0.665444 | − | 0.746448i | \(-0.268242\pi\) | ||||
0.665444 | + | 0.746448i | \(0.268242\pi\) | |||||||
\(752\) | 4.94427 | 0.180299 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 1.16718 | 0.0425063 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | 45.4164 | 1.65069 | 0.825344 | − | 0.564631i | \(-0.190981\pi\) | ||||
0.825344 | + | 0.564631i | \(0.190981\pi\) | |||||||
\(758\) | 16.8328 | 0.611395 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.7771 | −0.644419 | −0.322209 | − | 0.946668i | \(-0.604426\pi\) | ||||
−0.322209 | + | 0.946668i | \(0.604426\pi\) | |||||||
\(762\) | 11.4164 | 0.413573 | ||||||||
\(763\) | 1.88854 | 0.0683699 | ||||||||
\(764\) | −25.8885 | −0.936615 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.8885 | −0.501813 | ||||||||
\(767\) | 14.8328 | 0.535582 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 34.9443 | 1.26012 | 0.630061 | − | 0.776545i | \(-0.283030\pi\) | ||||
0.630061 | + | 0.776545i | \(0.283030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 20.0000 | 0.719816 | ||||||||
\(773\) | −3.05573 | −0.109907 | −0.0549535 | − | 0.998489i | \(-0.517501\pi\) | ||||
−0.0549535 | + | 0.998489i | \(0.517501\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.4164 | −0.481621 | ||||||||
\(777\) | 1.88854 | 0.0677511 | ||||||||
\(778\) | 4.47214 | 0.160334 | ||||||||
\(779\) | 21.8885 | 0.784238 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.47214 | −0.0884034 | ||||||||
\(783\) | −0.472136 | −0.0168728 | ||||||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.94427 | −0.247694 | ||||||||
\(787\) | −1.16718 | −0.0416056 | −0.0208028 | − | 0.999784i | \(-0.506622\pi\) | ||||
−0.0208028 | + | 0.999784i | \(0.506622\pi\) | |||||||
\(788\) | 18.9443 | 0.674862 | ||||||||
\(789\) | 20.9443 | 0.745636 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 77.6656 | 2.76147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.16718 | 0.0414479 | ||||||||
\(794\) | 29.3050 | 1.03999 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.4164 | 0.617308 | ||||||||
\(797\) | −37.8885 | −1.34208 | −0.671041 | − | 0.741421i | \(-0.734152\pi\) | ||||
−0.671041 | + | 0.741421i | \(0.734152\pi\) | |||||||
\(798\) | 8.00000 | 0.283197 | ||||||||
\(799\) | 12.2229 | 0.432416 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.4721 | −0.582014 | ||||||||
\(802\) | 25.4164 | 0.897485 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.94427 | −0.174371 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.472136 | 0.0166200 | ||||||||
\(808\) | 0.472136 | 0.0166097 | ||||||||
\(809\) | −3.88854 | −0.136714 | −0.0683570 | − | 0.997661i | \(-0.521776\pi\) | ||||
−0.0683570 | + | 0.997661i | \(0.521776\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.8885 | −1.75182 | −0.875912 | − | 0.482471i | \(-0.839739\pi\) | ||||
−0.875912 | + | 0.482471i | \(0.839739\pi\) | |||||||
\(812\) | −1.88854 | −0.0662749 | ||||||||
\(813\) | 0.944272 | 0.0331171 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.47214 | 0.0865421 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −18.0000 | −0.629355 | ||||||||
\(819\) | −9.88854 | −0.345534 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.4721 | −0.574882 | −0.287441 | − | 0.957798i | \(-0.592804\pi\) | ||||
−0.287441 | + | 0.957798i | \(0.592804\pi\) | |||||||
\(822\) | −19.4164 | −0.677225 | ||||||||
\(823\) | 20.3607 | 0.709729 | 0.354864 | − | 0.934918i | \(-0.384527\pi\) | ||||
0.354864 | + | 0.934918i | \(0.384527\pi\) | |||||||
\(824\) | 16.9443 | 0.590282 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.0000 | −0.835067 | ||||||||
\(827\) | −42.4721 | −1.47690 | −0.738450 | − | 0.674308i | \(-0.764442\pi\) | ||||
−0.738450 | + | 0.674308i | \(0.764442\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 30.9443 | 1.07474 | 0.537369 | − | 0.843347i | \(-0.319418\pi\) | ||||
0.537369 | + | 0.843347i | \(0.319418\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.4164 | −0.951065 | ||||||||
\(832\) | −2.47214 | −0.0857059 | ||||||||
\(833\) | 22.2492 | 0.770890 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −37.8885 | −1.30884 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7771 | −0.992313 | ||||||||
\(842\) | −37.4164 | −1.28945 | ||||||||
\(843\) | 3.52786 | 0.121506 | ||||||||
\(844\) | −12.0000 | −0.413057 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.94427 | 0.169988 | ||||||||
\(847\) | −44.0000 | −1.51186 | ||||||||
\(848\) | −8.94427 | −0.307148 | ||||||||
\(849\) | 24.0000 | 0.823678 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.472136 | −0.0161846 | ||||||||
\(852\) | −7.52786 | −0.257900 | ||||||||
\(853\) | 9.52786 | 0.326228 | 0.163114 | − | 0.986607i | \(-0.447846\pi\) | ||||
0.163114 | + | 0.986607i | \(0.447846\pi\) | |||||||
\(854\) | −1.88854 | −0.0646246 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.47214 | −0.0844959 | ||||||||
\(857\) | −23.8885 | −0.816017 | −0.408009 | − | 0.912978i | \(-0.633777\pi\) | ||||
−0.408009 | + | 0.912978i | \(0.633777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.7771 | −1.35718 | −0.678588 | − | 0.734519i | \(-0.737408\pi\) | ||||
−0.678588 | + | 0.734519i | \(0.737408\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 43.7771 | 1.49192 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.05573 | 0.104018 | 0.0520091 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520091 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.4164 | −0.727759 | ||||||||
\(867\) | −10.8885 | −0.369794 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.2229 | 0.414158 | ||||||||
\(872\) | 0.472136 | 0.0159885 | ||||||||
\(873\) | −13.4164 | −0.454077 | ||||||||
\(874\) | −2.00000 | −0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.94427 | 0.167051 | ||||||||
\(877\) | 20.3607 | 0.687531 | 0.343766 | − | 0.939055i | \(-0.388297\pi\) | ||||
0.343766 | + | 0.939055i | \(0.388297\pi\) | |||||||
\(878\) | −26.8328 | −0.905564 | ||||||||
\(879\) | −0.944272 | −0.0318495 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.47214 | −0.150670 | −0.0753350 | − | 0.997158i | \(-0.524003\pi\) | ||||
−0.0753350 | + | 0.997158i | \(0.524003\pi\) | |||||||
\(882\) | 9.00000 | 0.303046 | ||||||||
\(883\) | −19.7771 | −0.665552 | −0.332776 | − | 0.943006i | \(-0.607985\pi\) | ||||
−0.332776 | + | 0.943006i | \(0.607985\pi\) | |||||||
\(884\) | −6.11146 | −0.205551 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.94427 | −0.300489 | ||||||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | 0.472136 | 0.0158438 | ||||||||
\(889\) | 45.6656 | 1.53158 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.4164 | 0.382250 | ||||||||
\(893\) | 9.88854 | 0.330908 | ||||||||
\(894\) | −13.4164 | −0.448712 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.00000 | 0.133631 | ||||||||
\(897\) | 2.47214 | 0.0825422 | ||||||||
\(898\) | −34.9443 | −1.16611 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.1115 | −0.736639 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.4164 | 0.645780 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 16.9443 | 0.562936 | ||||||||
\(907\) | 14.8328 | 0.492516 | 0.246258 | − | 0.969204i | \(-0.420799\pi\) | ||||
0.246258 | + | 0.969204i | \(0.420799\pi\) | |||||||
\(908\) | 18.4721 | 0.613019 | ||||||||
\(909\) | 0.472136 | 0.0156598 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9443 | 0.826441 | 0.413220 | − | 0.910631i | \(-0.364404\pi\) | ||||
0.413220 | + | 0.910631i | \(0.364404\pi\) | |||||||
\(912\) | 2.00000 | 0.0662266 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 25.4164 | 0.840700 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.4164 | 0.839782 | ||||||||
\(917\) | −27.7771 | −0.917280 | ||||||||
\(918\) | 2.47214 | 0.0815926 | ||||||||
\(919\) | −9.41641 | −0.310619 | −0.155309 | − | 0.987866i | \(-0.549637\pi\) | ||||
−0.155309 | + | 0.987866i | \(0.549637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.3607 | −0.472944 | ||||||||
\(923\) | 18.6099 | 0.612552 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.4164 | −0.506615 | ||||||||
\(927\) | 16.9443 | 0.556523 | ||||||||
\(928\) | −0.472136 | −0.0154986 | ||||||||
\(929\) | −10.9443 | −0.359070 | −0.179535 | − | 0.983752i | \(-0.557459\pi\) | ||||
−0.179535 | + | 0.983752i | \(0.557459\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | 0.589926 | ||||||||
\(932\) | 14.9443 | 0.489516 | ||||||||
\(933\) | −24.4721 | −0.801182 | ||||||||
\(934\) | 26.4721 | 0.866195 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.47214 | −0.0808043 | ||||||||
\(937\) | 6.58359 | 0.215077 | 0.107538 | − | 0.994201i | \(-0.465703\pi\) | ||||
0.107538 | + | 0.994201i | \(0.465703\pi\) | |||||||
\(938\) | −19.7771 | −0.645745 | ||||||||
\(939\) | −25.4164 | −0.829433 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.4721 | 1.18896 | 0.594479 | − | 0.804111i | \(-0.297358\pi\) | ||||
0.594479 | + | 0.804111i | \(0.297358\pi\) | |||||||
\(942\) | −11.5279 | −0.375598 | ||||||||
\(943\) | −10.9443 | −0.356395 | ||||||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 12.4721 | 0.405076 | ||||||||
\(949\) | −12.2229 | −0.396773 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 9.88854 | 0.320490 | ||||||||
\(953\) | −12.3607 | −0.400402 | −0.200201 | − | 0.979755i | \(-0.564159\pi\) | ||||
−0.200201 | + | 0.979755i | \(0.564159\pi\) | |||||||
\(954\) | −8.94427 | −0.289581 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.4721 | −0.403378 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.9443 | −0.547445 | ||||||||
\(959\) | −77.6656 | −2.50795 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −1.16718 | −0.0376315 | ||||||||
\(963\) | −2.47214 | −0.0796635 | ||||||||
\(964\) | −2.00000 | −0.0644157 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.00000 | −0.128698 | ||||||||
\(967\) | 55.4164 | 1.78207 | 0.891036 | − | 0.453933i | \(-0.149979\pi\) | ||||
0.891036 | + | 0.453933i | \(0.149979\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 4.94427 | 0.158833 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.1115 | −0.581224 | −0.290612 | − | 0.956841i | \(-0.593859\pi\) | ||||
−0.290612 | + | 0.956841i | \(0.593859\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −31.4164 | −1.00665 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.472136 | −0.0151127 | ||||||||
\(977\) | 1.52786 | 0.0488807 | 0.0244404 | − | 0.999701i | \(-0.492220\pi\) | ||||
0.0244404 | + | 0.999701i | \(0.492220\pi\) | |||||||
\(978\) | −4.94427 | −0.158100 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.472136 | 0.0150741 | ||||||||
\(982\) | 27.8885 | 0.889959 | ||||||||
\(983\) | −24.0000 | −0.765481 | −0.382741 | − | 0.923856i | \(-0.625020\pi\) | ||||
−0.382741 | + | 0.923856i | \(0.625020\pi\) | |||||||
\(984\) | 10.9443 | 0.348891 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.16718 | −0.0371707 | ||||||||
\(987\) | 19.7771 | 0.629512 | ||||||||
\(988\) | −4.94427 | −0.157298 | ||||||||
\(989\) | 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 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.52786 | 0.0484122 | ||||||||
\(997\) | −7.41641 | −0.234880 | −0.117440 | − | 0.993080i | \(-0.537469\pi\) | ||||
−0.117440 | + | 0.993080i | \(0.537469\pi\) | |||||||
\(998\) | −24.0000 | −0.759707 | ||||||||
\(999\) | 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 | 3450.2.a.bn.1.1 | 2 | ||
5.2 | odd | 4 | 690.2.d.a.139.4 | yes | 4 | ||
5.3 | odd | 4 | 690.2.d.a.139.2 | ✓ | 4 | ||
5.4 | even | 2 | 3450.2.a.bc.1.2 | 2 | |||
15.2 | even | 4 | 2070.2.d.b.829.1 | 4 | |||
15.8 | even | 4 | 2070.2.d.b.829.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.a.139.2 | ✓ | 4 | 5.3 | odd | 4 | ||
690.2.d.a.139.4 | yes | 4 | 5.2 | odd | 4 | ||
2070.2.d.b.829.1 | 4 | 15.2 | even | 4 | |||
2070.2.d.b.829.3 | 4 | 15.8 | even | 4 | |||
3450.2.a.bc.1.2 | 2 | 5.4 | even | 2 | |||
3450.2.a.bn.1.1 | 2 | 1.1 | even | 1 | trivial |