Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.539189 | −0.311301 | −0.155650 | − | 0.987812i | \(-0.549747\pi\) | ||||
−0.155650 | + | 0.987812i | \(0.549747\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.70928 | −0.903092 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.539189 | 0.149544 | 0.0747720 | − | 0.997201i | \(-0.476177\pi\) | ||||
0.0747720 | + | 0.997201i | \(0.476177\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.539189 | −0.139218 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.46081 | 0.354299 | 0.177149 | − | 0.984184i | \(-0.443312\pi\) | ||||
0.177149 | + | 0.984184i | \(0.443312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41855 | 0.325438 | 0.162719 | − | 0.986672i | \(-0.447974\pi\) | ||||
0.162719 | + | 0.986672i | \(0.447974\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.539189 | 0.117661 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.70928 | 0.356409 | 0.178204 | − | 0.983994i | \(-0.442971\pi\) | ||||
0.178204 | + | 0.983994i | \(0.442971\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.07838 | 0.592434 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.68035 | −1.24051 | −0.620255 | − | 0.784401i | \(-0.712971\pi\) | ||||
−0.620255 | + | 0.784401i | \(0.712971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.248464 | 0.0446255 | 0.0223127 | − | 0.999751i | \(-0.492897\pi\) | ||||
0.0223127 | + | 0.999751i | \(0.492897\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.539189 | 0.0938607 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.04945 | 0.336927 | 0.168464 | − | 0.985708i | \(-0.446119\pi\) | ||||
0.168464 | + | 0.985708i | \(0.446119\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.290725 | −0.0465532 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.32684 | 1.14426 | 0.572130 | − | 0.820163i | \(-0.306117\pi\) | ||||
0.572130 | + | 0.820163i | \(0.306117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.97107 | 1.06308 | 0.531539 | − | 0.847034i | \(-0.321614\pi\) | ||||
0.531539 | + | 0.847034i | \(0.321614\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.70928 | −0.403875 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.2195 | −1.63654 | −0.818269 | − | 0.574836i | \(-0.805066\pi\) | ||||
−0.818269 | + | 0.574836i | \(0.805066\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.787653 | −0.110293 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.89269 | −0.534702 | −0.267351 | − | 0.963599i | \(-0.586148\pi\) | ||||
−0.267351 | + | 0.963599i | \(0.586148\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.764867 | −0.101309 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.829914 | −0.108046 | −0.0540228 | − | 0.998540i | \(-0.517204\pi\) | ||||
−0.0540228 | + | 0.998540i | \(0.517204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.35350 | 0.429372 | 0.214686 | − | 0.976683i | \(-0.431127\pi\) | ||||
0.214686 | + | 0.976683i | \(0.431127\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.70928 | 0.341337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.539189 | 0.0668781 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.630898 | −0.0770764 | −0.0385382 | − | 0.999257i | \(-0.512270\pi\) | ||||
−0.0385382 | + | 0.999257i | \(0.512270\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.921622 | −0.110950 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8371 | 1.28613 | 0.643064 | − | 0.765813i | \(-0.277663\pi\) | ||||
0.643064 | + | 0.765813i | \(0.277663\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.46081 | −1.10730 | −0.553652 | − | 0.832748i | \(-0.686766\pi\) | ||||
−0.553652 | + | 0.832748i | \(0.686766\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.539189 | −0.0622602 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.63090 | −0.295999 | −0.148000 | − | 0.988987i | \(-0.547283\pi\) | ||||
−0.148000 | + | 0.988987i | \(0.547283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.46800 | 0.718667 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.02052 | −0.990131 | −0.495065 | − | 0.868856i | \(-0.664856\pi\) | ||||
−0.495065 | + | 0.868856i | \(0.664856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.46081 | 0.158447 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.60197 | 0.386172 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.764867 | 0.0810757 | 0.0405379 | − | 0.999178i | \(-0.487093\pi\) | ||||
0.0405379 | + | 0.999178i | \(0.487093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.539189 | −0.0565224 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.133969 | −0.0138920 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.41855 | 0.145540 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.2351 | −1.14075 | −0.570377 | − | 0.821383i | \(-0.693203\pi\) | ||||
−0.570377 | + | 0.821383i | \(0.693203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.70928 | 0.272292 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.4257 | −1.13690 | −0.568452 | − | 0.822717i | \(-0.692457\pi\) | ||||
−0.568452 | + | 0.822717i | \(0.692457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.90602 | −0.483405 | −0.241702 | − | 0.970350i | \(-0.577706\pi\) | ||||
−0.241702 | + | 0.970350i | \(0.577706\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.539189 | 0.0526194 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.0989 | −1.55634 | −0.778170 | − | 0.628054i | \(-0.783852\pi\) | ||||
−0.778170 | + | 0.628054i | \(0.783852\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.4391 | 1.57458 | 0.787289 | − | 0.616585i | \(-0.211484\pi\) | ||||
0.787289 | + | 0.616585i | \(0.211484\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.10504 | −0.104886 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.23513 | −0.492480 | −0.246240 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246240 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70928 | 0.159391 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.46081 | −0.135052 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.46081 | −0.133912 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.95055 | −0.356209 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.17727 | −0.814351 | −0.407176 | − | 0.913350i | \(-0.633486\pi\) | ||||
−0.407176 | + | 0.913350i | \(0.633486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.75872 | −0.330937 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.9939 | −1.83424 | −0.917121 | − | 0.398609i | \(-0.869493\pi\) | ||||
−0.917121 | + | 0.398609i | \(0.869493\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.41855 | −0.123004 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.07838 | 0.264945 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.20620 | 0.701103 | 0.350552 | − | 0.936543i | \(-0.385994\pi\) | ||||
0.350552 | + | 0.936543i | \(0.385994\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.9155 | −1.34993 | −0.674967 | − | 0.737848i | \(-0.735842\pi\) | ||||
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.04945 | 0.509455 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.539189 | −0.0450892 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.68035 | −0.554773 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.539189 | −0.0444715 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.02052 | 0.411297 | 0.205648 | − | 0.978626i | \(-0.434070\pi\) | ||||
0.205648 | + | 0.978626i | \(0.434070\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9711 | −1.05557 | −0.527785 | − | 0.849378i | \(-0.676977\pi\) | ||||
−0.527785 | + | 0.849378i | \(0.676977\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.95774 | −0.319964 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.248464 | 0.0199571 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.313511 | 0.0250209 | 0.0125105 | − | 0.999922i | \(-0.496018\pi\) | ||||
0.0125105 | + | 0.999922i | \(0.496018\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.09890 | 0.166453 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.70928 | −0.134710 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.9916 | 1.72251 | 0.861257 | − | 0.508169i | \(-0.169678\pi\) | ||||
0.861257 | + | 0.508169i | \(0.169678\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.539189 | 0.0419758 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.1978 | 1.40819 | 0.704094 | − | 0.710107i | \(-0.251353\pi\) | ||||
0.704094 | + | 0.710107i | \(0.251353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7093 | −0.977637 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.84324 | −0.293900 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.64423 | 0.733237 | 0.366619 | − | 0.930371i | \(-0.380515\pi\) | ||||
0.366619 | + | 0.930371i | \(0.380515\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.447480 | 0.0336347 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.6225 | −1.39191 | −0.695955 | − | 0.718085i | \(-0.745019\pi\) | ||||
−0.695955 | + | 0.718085i | \(0.745019\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.10504 | −0.528113 | −0.264057 | − | 0.964507i | \(-0.585061\pi\) | ||||
−0.264057 | + | 0.964507i | \(0.585061\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.80817 | −0.133664 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.04945 | 0.150678 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.46081 | −0.106825 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.07838 | −0.223919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.0722 | −1.01823 | −0.509116 | − | 0.860698i | \(-0.670027\pi\) | ||||
−0.509116 | + | 0.860698i | \(0.670027\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.15449 | −0.658954 | −0.329477 | − | 0.944164i | \(-0.606872\pi\) | ||||
−0.329477 | + | 0.944164i | \(0.606872\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.290725 | −0.0208192 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.3051 | −1.44668 | −0.723339 | − | 0.690493i | \(-0.757394\pi\) | ||||
−0.723339 | + | 0.690493i | \(0.757394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8443 | −1.05228 | −0.526142 | − | 0.850397i | \(-0.676362\pi\) | ||||
−0.526142 | + | 0.850397i | \(0.676362\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.340173 | 0.0239940 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.68035 | 0.468868 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.32684 | 0.511729 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.63090 | −0.321870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.41855 | −0.0981232 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.18342 | −0.287998 | −0.143999 | − | 0.989578i | \(-0.545996\pi\) | ||||
−0.143999 | + | 0.989578i | \(0.545996\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.84324 | −0.400373 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.97107 | 0.475423 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.248464 | −0.0168669 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.10116 | 0.344705 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.787653 | 0.0529833 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.8154 | 1.46086 | 0.730432 | − | 0.682985i | \(-0.239319\pi\) | ||||
0.730432 | + | 0.682985i | \(0.239319\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.70928 | −0.180618 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.8371 | 0.984773 | 0.492387 | − | 0.870377i | \(-0.336125\pi\) | ||||
0.492387 | + | 0.870377i | \(0.336125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.8638 | −1.24655 | −0.623276 | − | 0.782002i | \(-0.714199\pi\) | ||||
−0.623276 | + | 0.782002i | \(0.714199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.539189 | −0.0354760 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.18568 | −0.0776768 | −0.0388384 | − | 0.999246i | \(-0.512366\pi\) | ||||
−0.0388384 | + | 0.999246i | \(0.512366\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2195 | −0.731882 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.41855 | 0.0921448 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.17727 | 0.0761516 | 0.0380758 | − | 0.999275i | \(-0.487877\pi\) | ||||
0.0380758 | + | 0.999275i | \(0.487877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.2690 | 1.88538 | 0.942690 | − | 0.333669i | \(-0.108287\pi\) | ||||
0.942690 | + | 0.333669i | \(0.108287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.7226 | −0.816156 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.764867 | 0.0486673 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.86376 | 0.308228 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.0072 | −0.884126 | −0.442063 | − | 0.896984i | \(-0.645753\pi\) | ||||
−0.442063 | + | 0.896984i | \(0.645753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.70928 | −0.107461 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.787653 | −0.0493248 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.4124 | −0.774265 | −0.387132 | − | 0.922024i | \(-0.626534\pi\) | ||||
−0.387132 | + | 0.922024i | \(0.626534\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.04945 | −0.127347 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0989 | 1.12029 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.8638 | −0.793214 | −0.396607 | − | 0.917989i | \(-0.629812\pi\) | ||||
−0.396607 | + | 0.917989i | \(0.629812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.89269 | −0.239126 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.412408 | −0.0252389 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5236 | −0.641635 | −0.320817 | − | 0.947141i | \(-0.603958\pi\) | ||||
−0.320817 | + | 0.947141i | \(0.603958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.2351 | −0.682486 | −0.341243 | − | 0.939975i | \(-0.610848\pi\) | ||||
−0.341243 | + | 0.939975i | \(0.610848\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.290725 | 0.0175955 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.1217 | −1.68967 | −0.844834 | − | 0.535028i | \(-0.820301\pi\) | ||||
−0.844834 | + | 0.535028i | \(0.820301\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.673158 | −0.0403009 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.47187 | 0.326425 | 0.163212 | − | 0.986591i | \(-0.447814\pi\) | ||||
0.163212 | + | 0.986591i | \(0.447814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7382 | 0.638320 | 0.319160 | − | 0.947701i | \(-0.396599\pi\) | ||||
0.319160 | + | 0.947701i | \(0.396599\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.764867 | −0.0453068 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.32684 | −0.432490 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8660 | −0.874472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.05786 | 0.355118 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0300 | 1.40385 | 0.701923 | − | 0.712253i | \(-0.252325\pi\) | ||||
0.701923 | + | 0.712253i | \(0.252325\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.829914 | −0.0483194 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.07838 | −0.178626 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.921622 | 0.0532988 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.97107 | −0.401806 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.16063 | 0.353919 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.35350 | 0.192021 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.9421 | 1.36645 | 0.683225 | − | 0.730208i | \(-0.260577\pi\) | ||||
0.683225 | + | 0.730208i | \(0.260577\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.64527 | 0.150484 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.32684 | −0.415467 | −0.207734 | − | 0.978185i | \(-0.566609\pi\) | ||||
−0.207734 | + | 0.978185i | \(0.566609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.5814 | −0.824192 | −0.412096 | − | 0.911140i | \(-0.635203\pi\) | ||||
−0.412096 | + | 0.911140i | \(0.635203\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.70928 | 0.152650 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.8843 | 1.22914 | 0.614572 | − | 0.788861i | \(-0.289329\pi\) | ||||
0.614572 | + | 0.788861i | \(0.289329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.68035 | 0.374028 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.68035 | 0.484490 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.07223 | 0.115302 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.539189 | 0.0299088 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.86376 | −0.490167 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.2195 | 0.618553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.3751 | 1.39474 | 0.697370 | − | 0.716711i | \(-0.254353\pi\) | ||||
0.697370 | + | 0.716711i | \(0.254353\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.55252 | −0.304276 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.630898 | −0.0344696 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.9854 | 0.707362 | 0.353681 | − | 0.935366i | \(-0.384930\pi\) | ||||
0.353681 | + | 0.935366i | \(0.384930\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.82273 | 0.153309 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.248464 | −0.0134551 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.921622 | −0.0496185 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0183 | 1.28937 | 0.644684 | − | 0.764449i | \(-0.276989\pi\) | ||||
0.644684 | + | 0.764449i | \(0.276989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4791 | −1.36386 | −0.681931 | − | 0.731416i | \(-0.738860\pi\) | ||||
−0.681931 | + | 0.731416i | \(0.738860\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.65983 | 0.0885950 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.4124 | 0.767095 | 0.383548 | − | 0.923521i | \(-0.374702\pi\) | ||||
0.383548 | + | 0.923521i | \(0.374702\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8371 | 0.575174 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.787653 | 0.0416870 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3691 | −0.916706 | −0.458353 | − | 0.888770i | \(-0.651560\pi\) | ||||
−0.458353 | + | 0.888770i | \(0.651560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.9877 | −0.894090 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.539189 | −0.0283001 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.46081 | −0.495201 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.0772 | 1.72661 | 0.863307 | − | 0.504680i | \(-0.168389\pi\) | ||||
0.863307 | + | 0.504680i | \(0.168389\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.8504 | −1.03337 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.89269 | 0.202099 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0905 | −1.04025 | −0.520123 | − | 0.854091i | \(-0.674114\pi\) | ||||
−0.520123 | + | 0.854091i | \(0.674114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.539189 | −0.0278436 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.60197 | −0.185511 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.8904 | 0.764870 | 0.382435 | − | 0.923982i | \(-0.375086\pi\) | ||||
0.382435 | + | 0.923982i | \(0.375086\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.94828 | 0.253508 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.1929 | −0.571929 | −0.285965 | − | 0.958240i | \(-0.592314\pi\) | ||||
−0.285965 | + | 0.958240i | \(0.592314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.8865 | −0.960057 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.2413 | −1.02627 | −0.513137 | − | 0.858307i | \(-0.671517\pi\) | ||||
−0.513137 | + | 0.858307i | \(0.671517\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.49693 | 0.126275 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.3197 | 0.571001 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.63090 | −0.132375 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.57531 | −0.480571 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.764867 | 0.0382912 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.8843 | −1.09285 | −0.546424 | − | 0.837508i | \(-0.684011\pi\) | ||||
−0.546424 | + | 0.837508i | \(0.684011\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.133969 | 0.00667348 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.46800 | 0.321397 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.04945 | −0.101587 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.3002 | −0.954332 | −0.477166 | − | 0.878813i | \(-0.658336\pi\) | ||||
−0.477166 | + | 0.878813i | \(0.658336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.42469 | −0.218254 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.829914 | 0.0408374 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.02052 | −0.442800 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.58145 | 0.420235 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.2895 | 1.57745 | 0.788723 | − | 0.614749i | \(-0.210743\pi\) | ||||
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.6309 | −1.00549 | −0.502744 | − | 0.864435i | \(-0.667676\pi\) | ||||
−0.502744 | + | 0.864435i | \(0.667676\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.3968 | 1.47794 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.46081 | 0.0708597 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.35350 | −0.162287 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.290725 | 0.0140363 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.1012 | −0.631061 | −0.315530 | − | 0.948915i | \(-0.602182\pi\) | ||||
−0.315530 | + | 0.948915i | \(0.602182\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.11942 | −0.438251 | −0.219126 | − | 0.975697i | \(-0.570320\pi\) | ||||
−0.219126 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.60197 | 0.172701 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.42469 | 0.115989 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.1773 | −1.01074 | −0.505368 | − | 0.862904i | \(-0.668643\pi\) | ||||
−0.505368 | + | 0.862904i | \(0.668643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.70928 | −0.129013 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.0183 | −0.761050 | −0.380525 | − | 0.924771i | \(-0.624257\pi\) | ||||
−0.380525 | + | 0.924771i | \(0.624257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.764867 | 0.0362582 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.70701 | −0.128037 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.79380 | −0.462198 | −0.231099 | − | 0.972930i | \(-0.574232\pi\) | ||||
−0.231099 | + | 0.972930i | \(0.574232\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.32684 | −0.345008 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.99386 | 0.328600 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.539189 | −0.0252776 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.1422 | −1.08255 | −0.541273 | − | 0.840847i | \(-0.682058\pi\) | ||||
−0.541273 | + | 0.840847i | \(0.682058\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.49693 | 0.209899 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.0544 | 1.16690 | 0.583449 | − | 0.812150i | \(-0.301703\pi\) | ||||
0.583449 | + | 0.812150i | \(0.301703\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.8865 | 1.06363 | 0.531814 | − | 0.846861i | \(-0.321511\pi\) | ||||
0.531814 | + | 0.846861i | \(0.321511\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.133969 | −0.00621267 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.70209 | 0.263861 | 0.131931 | − | 0.991259i | \(-0.457882\pi\) | ||||
0.131931 | + | 0.991259i | \(0.457882\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.630898 | 0.0291321 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.169042 | −0.00778903 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.97107 | −0.320530 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.41855 | 0.0650876 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.5464 | 0.482885 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.3545 | −1.47832 | −0.739159 | − | 0.673531i | \(-0.764777\pi\) | ||||
−0.739159 | + | 0.673531i | \(0.764777\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.10504 | 0.0503855 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.921622 | 0.0419353 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.2351 | −0.510161 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.0060 | −1.72221 | −0.861107 | − | 0.508423i | \(-0.830229\pi\) | ||||
−0.861107 | + | 0.508423i | \(0.830229\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.8576 | −0.536220 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.3174 | 0.826652 | 0.413326 | − | 0.910583i | \(-0.364367\pi\) | ||||
0.413326 | + | 0.910583i | \(0.364367\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.75872 | −0.439511 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.70928 | 0.121773 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.8371 | −0.486110 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.88882 | −0.442684 | −0.221342 | − | 0.975196i | \(-0.571044\pi\) | ||||
−0.221342 | + | 0.975196i | \(0.571044\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.81205 | −0.438370 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.1834 | −1.16746 | −0.583730 | − | 0.811948i | \(-0.698408\pi\) | ||||
−0.583730 | + | 0.811948i | \(0.698408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4257 | −0.508439 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.85270 | 0.304339 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.5958 | 1.00154 | 0.500771 | − | 0.865580i | \(-0.333050\pi\) | ||||
0.500771 | + | 0.865580i | \(0.333050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.46081 | 0.418522 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.36683 | 0.192800 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.90602 | −0.216185 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.2195 | 0.493435 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.20006 | −0.228257 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.9770 | −1.26951 | −0.634753 | − | 0.772715i | \(-0.718898\pi\) | ||||
−0.634753 | + | 0.772715i | \(0.718898\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.41855 | −0.236937 | −0.118468 | − | 0.992958i | \(-0.537798\pi\) | ||||
−0.118468 | + | 0.992958i | \(0.537798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.539189 | 0.0235321 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.362959 | 0.0158108 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0784 | −0.872973 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.24846 | 0.0975750 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.95055 | 0.171117 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.0989 | −0.696016 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.0410 | 0.433303 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.5031 | 0.752516 | 0.376258 | − | 0.926515i | \(-0.377211\pi\) | ||||
0.376258 | + | 0.926515i | \(0.377211\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.83096 | 0.164402 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.4391 | 0.704172 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.711543 | 0.0304234 | 0.0152117 | − | 0.999884i | \(-0.495158\pi\) | ||||
0.0152117 | + | 0.999884i | \(0.495158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.08557 | −0.387762 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.47641 | −0.403709 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.63090 | 0.111877 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.10504 | −0.0469063 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0700 | −0.892763 | −0.446382 | − | 0.894843i | \(-0.647288\pi\) | ||||
−0.446382 | + | 0.894843i | \(0.647288\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.75872 | 0.158977 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.787653 | 0.0332547 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.9672 | 0.799372 | 0.399686 | − | 0.916652i | \(-0.369119\pi\) | ||||
0.399686 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.23513 | −0.220244 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.46800 | −0.271630 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.1194 | 0.549995 | 0.274997 | − | 0.961445i | \(-0.411323\pi\) | ||||
0.274997 | + | 0.961445i | \(0.411323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.97334 | −0.249976 | −0.124988 | − | 0.992158i | \(-0.539889\pi\) | ||||
−0.124988 | + | 0.992158i | \(0.539889\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.58759 | 0.316976 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.70928 | 0.0712817 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.02052 | 0.125746 | 0.0628729 | − | 0.998022i | \(-0.479974\pi\) | ||||
0.0628729 | + | 0.998022i | \(0.479974\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.93600 | 0.205133 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.02052 | 0.374234 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.89269 | 0.161219 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.46081 | −0.0603971 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.3558 | −0.509977 | −0.254989 | − | 0.966944i | \(-0.582072\pi\) | ||||
−0.254989 | + | 0.966944i | \(0.582072\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.352459 | 0.0145228 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.9483 | 0.450352 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.2544 | 1.48879 | 0.744395 | − | 0.667739i | \(-0.232738\pi\) | ||||
0.744395 | + | 0.667739i | \(0.232738\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.46081 | −0.0598874 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.00388 | 0.327577 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.73206 | 0.152488 | 0.0762440 | − | 0.997089i | \(-0.475707\pi\) | ||||
0.0762440 | + | 0.997089i | \(0.475707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.75154 | 0.397773 | 0.198887 | − | 0.980022i | \(-0.436267\pi\) | ||||
0.198887 | + | 0.980022i | \(0.436267\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.70928 | 0.0696071 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.6270 | −0.918402 | −0.459201 | − | 0.888332i | \(-0.651864\pi\) | ||||
−0.459201 | + | 0.888332i | \(0.651864\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.60197 | −0.145959 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.04945 | −0.244734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.3195 | 1.46693 | 0.733465 | − | 0.679727i | \(-0.237902\pi\) | ||||
0.733465 | + | 0.679727i | \(0.237902\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.95055 | −0.159302 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.6248 | −1.75627 | −0.878133 | − | 0.478416i | \(-0.841211\pi\) | ||||
−0.878133 | + | 0.478416i | \(0.841211\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.5246 | 1.26708 | 0.633541 | − | 0.773709i | \(-0.281601\pi\) | ||||
0.633541 | + | 0.773709i | \(0.281601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.26180 | 0.211149 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.764867 | −0.0306437 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.764867 | 0.0305458 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.99386 | 0.119373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.04718 | 0.360163 | 0.180081 | − | 0.983652i | \(-0.442364\pi\) | ||||
0.180081 | + | 0.983652i | \(0.442364\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.25565 | 0.0896541 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.17727 | −0.364189 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.539189 | 0.0213634 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.3607 | −1.16149 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.0265 | 1.46246 | 0.731229 | − | 0.682132i | \(-0.238947\pi\) | ||||
0.731229 | + | 0.682132i | \(0.238947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.4341 | 0.924153 | 0.462076 | − | 0.886840i | \(-0.347105\pi\) | ||||
0.462076 | + | 0.886840i | \(0.347105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.75872 | −0.148000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.0833 | −1.57584 | −0.787919 | − | 0.615779i | \(-0.788841\pi\) | ||||
−0.787919 | + | 0.615779i | \(0.788841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.829914 | 0.0325770 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.133969 | 0.00525066 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.2351 | 1.30059 | 0.650296 | − | 0.759681i | \(-0.274645\pi\) | ||||
0.650296 | + | 0.759681i | \(0.274645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9939 | −0.820298 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.6319 | 0.999997 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.0228 | −1.09161 | −0.545806 | − | 0.837911i | \(-0.683777\pi\) | ||||
−0.545806 | + | 0.837911i | \(0.683777\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.863763 | 0.0335965 | 0.0167983 | − | 0.999859i | \(-0.494653\pi\) | ||||
0.0167983 | + | 0.999859i | \(0.494653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.424694 | −0.0164937 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.41855 | −0.0550090 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.4186 | −0.442128 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.7626 | −0.454768 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.35350 | −0.129461 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.6309 | 1.02655 | 0.513273 | − | 0.858225i | \(-0.328433\pi\) | ||||
0.513273 | + | 0.858225i | \(0.328433\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.07838 | 0.118487 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.8794 | −1.03306 | −0.516529 | − | 0.856270i | \(-0.672776\pi\) | ||||
−0.516529 | + | 0.856270i | \(0.672776\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.2351 | 0.431165 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.00000 | −0.306561 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.46186 | −0.323784 | −0.161892 | − | 0.986808i | \(-0.551760\pi\) | ||||
−0.161892 | + | 0.986808i | \(0.551760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.20620 | 0.313543 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.1711 | 0.388053 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.09890 | −0.0799616 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.4836 | −1.27378 | −0.636888 | − | 0.770956i | \(-0.719779\pi\) | ||||
−0.636888 | + | 0.770956i | \(0.719779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.70928 | −0.102917 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.9155 | −0.603709 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.7031 | 0.405410 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.639308 | 0.0241809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.0677 | −1.28672 | −0.643360 | − | 0.765564i | \(-0.722460\pi\) | ||||
−0.643360 | + | 0.765564i | \(0.722460\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.90725 | 0.109649 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.04945 | 0.227835 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4257 | 0.429709 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.523590 | −0.0196639 | −0.00983193 | − | 0.999952i | \(-0.503130\pi\) | ||||
−0.00983193 | + | 0.999952i | \(0.503130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.12783 | 0.267314 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.424694 | 0.0159049 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.539189 | −0.0201645 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.634773 | −0.0237060 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.0856 | −1.68141 | −0.840704 | − | 0.541495i | \(-0.817858\pi\) | ||||
−0.840704 | + | 0.541495i | \(0.817858\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.90602 | 0.182710 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.7815 | −0.586921 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.68035 | −0.248102 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.33072 | 0.197705 | 0.0988527 | − | 0.995102i | \(-0.468483\pi\) | ||||
0.0988527 | + | 0.995102i | \(0.468483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.5441 | −0.464597 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1834 | 0.376647 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.2979 | 0.749721 | 0.374860 | − | 0.927081i | \(-0.377691\pi\) | ||||
0.374860 | + | 0.927081i | \(0.377691\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.539189 | −0.0198883 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.630898 | 0.0232394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.4641 | 1.01028 | 0.505142 | − | 0.863036i | \(-0.331440\pi\) | ||||
0.505142 | + | 0.863036i | \(0.331440\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.412408 | −0.0151502 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.9483 | −0.621772 | −0.310886 | − | 0.950447i | \(-0.600626\pi\) | ||||
−0.310886 | + | 0.950447i | \(0.600626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.02052 | 0.183938 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.4391 | 0.894179 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.0989 | 0.588241 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9216 | −0.690460 | −0.345230 | − | 0.938518i | \(-0.612199\pi\) | ||||
−0.345230 | + | 0.938518i | \(0.612199\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.55252 | 0.275229 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.9711 | −0.472066 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4436 | −0.524962 | −0.262481 | − | 0.964937i | \(-0.584541\pi\) | ||||
−0.262481 | + | 0.964937i | \(0.584541\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.921622 | 0.0334528 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.4934 | −1.35914 | −0.679568 | − | 0.733612i | \(-0.737833\pi\) | ||||
−0.679568 | + | 0.733612i | \(0.737833\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4391 | −0.595134 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.95774 | −0.143092 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.447480 | −0.0161576 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.63582 | −0.0589891 | −0.0294946 | − | 0.999565i | \(-0.509390\pi\) | ||||
−0.0294946 | + | 0.999565i | \(0.509390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.69263 | 0.241029 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.1194 | −1.40703 | −0.703514 | − | 0.710682i | \(-0.748387\pi\) | ||||
−0.703514 | + | 0.710682i | \(0.748387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.248464 | 0.00892510 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.10504 | 0.0396431 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3935 | 0.372386 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.8371 | −0.387782 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.5646 | −0.734920 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.313511 | 0.0111897 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.8515 | 1.38491 | 0.692453 | − | 0.721463i | \(-0.256530\pi\) | ||||
0.692453 | + | 0.721463i | \(0.256530\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.93600 | 0.246928 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.23513 | 0.186140 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.80817 | 0.0642101 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.09890 | 0.0744402 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.3484 | −0.827043 | −0.413521 | − | 0.910494i | \(-0.635701\pi\) | ||||
−0.413521 | + | 0.910494i | \(0.635701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.3896 | −0.579823 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.07223 | −0.0732188 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.46081 | 0.333865 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.70928 | −0.0602440 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.67420 | 0.199741 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.7259 | −1.50216 | −0.751082 | − | 0.660209i | \(-0.770468\pi\) | ||||
−0.751082 | + | 0.660209i | \(0.770468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.95652 | −0.279391 | −0.139696 | − | 0.990195i | \(-0.544612\pi\) | ||||
−0.139696 | + | 0.990195i | \(0.544612\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.05786 | 0.212458 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.9916 | 0.770332 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.88882 | 0.345966 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.46081 | 0.0510449 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.9565 | −0.836088 | −0.418044 | − | 0.908427i | \(-0.637284\pi\) | ||||
−0.418044 | + | 0.908427i | \(0.637284\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.50904 | 0.0526017 | 0.0263009 | − | 0.999654i | \(-0.491627\pi\) | ||||
0.0263009 | + | 0.999654i | \(0.491627\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.539189 | 0.0187721 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.4368 | 1.23226 | 0.616129 | − | 0.787645i | \(-0.288700\pi\) | ||||
0.616129 | + | 0.787645i | \(0.288700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.3423 | 1.74846 | 0.874230 | − | 0.485513i | \(-0.161367\pi\) | ||||
0.874230 | + | 0.485513i | \(0.161367\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.1629 | 0.525995 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.46081 | 0.0506141 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.1978 | 0.629761 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.764867 | 0.0264377 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.4585 | −0.706307 | −0.353154 | − | 0.935565i | \(-0.614891\pi\) | ||||
−0.353154 | + | 0.935565i | \(0.614891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6270 | 0.538863 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.95037 | −0.101616 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7093 | −0.437212 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.78992 | −0.198710 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.50307 | 0.120084 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.7903 | 0.985761 | 0.492881 | − | 0.870097i | \(-0.335944\pi\) | ||||
0.492881 | + | 0.870097i | \(0.335944\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.84324 | −0.131436 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.4219 | 1.82486 | 0.912428 | − | 0.409237i | \(-0.134205\pi\) | ||||
0.912428 | + | 0.409237i | \(0.134205\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.3162 | −0.966135 | −0.483068 | − | 0.875583i | \(-0.660477\pi\) | ||||
−0.483068 | + | 0.875583i | \(0.660477\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.95055 | 0.134634 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.67438 | 0.0910370 | 0.0455185 | − | 0.998963i | \(-0.485506\pi\) | ||||
0.0455185 | + | 0.998963i | \(0.485506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.64423 | 0.327914 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.01560 | 0.272224 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.63090 | 0.0892471 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.340173 | −0.0115263 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.4391 | 1.03021 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.1278 | 0.510830 | 0.255415 | − | 0.966831i | \(-0.417788\pi\) | ||||
0.255415 | + | 0.966831i | \(0.417788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.9567 | −0.437018 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.0989 | 1.35097 | 0.675483 | − | 0.737375i | \(-0.263935\pi\) | ||||
0.675483 | + | 0.737375i | \(0.263935\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.2702 | 0.513883 | 0.256942 | − | 0.966427i | \(-0.417285\pi\) | ||||
0.256942 | + | 0.966427i | \(0.417285\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.447480 | 0.0150419 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.6430 | 0.861008 | 0.430504 | − | 0.902589i | \(-0.358336\pi\) | ||||
0.430504 | + | 0.902589i | \(0.358336\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.17727 | 0.307796 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.46800 | −0.216686 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.9155 | −0.532591 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.6225 | −0.622481 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.496928 | −0.0165920 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.65983 | −0.0553583 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.68649 | −0.189444 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.75872 | 0.125082 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.10504 | −0.236180 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3424 | 0.443028 | 0.221514 | − | 0.975157i | \(-0.428900\pi\) | ||||
0.221514 | + | 0.975157i | \(0.428900\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.9555 | 1.02673 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.6742 | −0.585572 | −0.292786 | − | 0.956178i | \(-0.594582\pi\) | ||||
−0.292786 | + | 0.956178i | \(0.594582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.02052 | 0.298536 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.80817 | −0.0597763 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.9939 | 0.693278 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.81658 | −0.257845 | −0.128923 | − | 0.991655i | \(-0.541152\pi\) | ||||
−0.128923 | + | 0.991655i | \(0.541152\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.9093 | −0.425377 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.84324 | 0.192333 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.04945 | 0.0673854 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.2918 | 0.436559 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.1461 | 0.956252 | 0.478126 | − | 0.878291i | \(-0.341316\pi\) | ||||
0.478126 | + | 0.878291i | \(0.341316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.41855 | 0.0464911 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.95055 | 0.129335 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.46081 | −0.0477736 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.62985 | −0.118582 | −0.0592911 | − | 0.998241i | \(-0.518884\pi\) | ||||
−0.0592911 | + | 0.998241i | \(0.518884\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.86216 | 0.256572 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.8648 | 1.69074 | 0.845372 | − | 0.534178i | \(-0.179379\pi\) | ||||
0.845372 | + | 0.534178i | \(0.179379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.5236 | 0.407824 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.07838 | −0.100140 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.6514 | 0.638585 | 0.319293 | − | 0.947656i | \(-0.396555\pi\) | ||||
0.319293 | + | 0.947656i | \(0.396555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.10116 | −0.165591 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.7998 | −0.382633 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.2267 | 0.622815 | 0.311407 | − | 0.950277i | \(-0.399200\pi\) | ||||
0.311407 | + | 0.950277i | \(0.399200\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.0722 | −0.455367 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.60197 | −0.116435 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.20620 | −0.264992 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9383 | −0.998009 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 43.6163 | 1.40552 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.15449 | −0.294693 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.7565 | −0.474536 | −0.237268 | − | 0.971444i | \(-0.576252\pi\) | ||||
−0.237268 | + | 0.971444i | \(0.576252\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.11733 | −0.0358937 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.7331 | 1.69229 | 0.846143 | − | 0.532956i | \(-0.178919\pi\) | ||||
0.846143 | + | 0.532956i | \(0.178919\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.9155 | 0.510227 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.290725 | −0.00931064 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.1727 | −1.18926 | −0.594631 | − | 0.803999i | \(-0.702702\pi\) | ||||
−0.594631 | + | 0.803999i | \(0.702702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.764867 | −0.0244452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.5380 | −1.42199 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.0566 | −0.958658 | −0.479329 | − | 0.877635i | \(-0.659120\pi\) | ||||
−0.479329 | + | 0.877635i | \(0.659120\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.3051 | −0.646974 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.04945 | −0.192556 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.9155 | 0.378890 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.82273 | 0.216731 | 0.108366 | − | 0.994111i | \(-0.465438\pi\) | ||||
0.108366 | + | 0.994111i | \(0.465438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.6820 | −0.434184 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.8443 | −0.470596 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.7308 | 1.89169 | 0.945847 | − | 0.324612i | \(-0.105234\pi\) | ||||
0.945847 | + | 0.324612i | \(0.105234\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.30898 | 0.199607 |
(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 | 6160.2.a.bj.1.2 | 3 | ||
4.3 | odd | 2 | 385.2.a.g.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 3465.2.a.ba.1.1 | 3 | |||
20.3 | even | 4 | 1925.2.b.o.1849.1 | 6 | |||
20.7 | even | 4 | 1925.2.b.o.1849.6 | 6 | |||
20.19 | odd | 2 | 1925.2.a.u.1.1 | 3 | |||
28.27 | even | 2 | 2695.2.a.i.1.3 | 3 | |||
44.43 | even | 2 | 4235.2.a.o.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.a.g.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
1925.2.a.u.1.1 | 3 | 20.19 | odd | 2 | |||
1925.2.b.o.1849.1 | 6 | 20.3 | even | 4 | |||
1925.2.b.o.1849.6 | 6 | 20.7 | even | 4 | |||
2695.2.a.i.1.3 | 3 | 28.27 | even | 2 | |||
3465.2.a.ba.1.1 | 3 | 12.11 | even | 2 | |||
4235.2.a.o.1.1 | 3 | 44.43 | even | 2 | |||
6160.2.a.bj.1.2 | 3 | 1.1 | even | 1 | trivial |