Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.636672 | 0.240639 | 0.120320 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120320 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.50466 | −1.05670 | −0.528348 | − | 0.849028i | \(-0.677188\pi\) | ||||
−0.528348 | + | 0.849028i | \(0.677188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.141336 | −0.0391996 | −0.0195998 | − | 0.999808i | \(-0.506239\pi\) | ||||
−0.0195998 | + | 0.999808i | \(0.506239\pi\) | |||||||
\(14\) | −0.636672 | −0.170158 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.14134 | −0.519350 | −0.259675 | − | 0.965696i | \(-0.583615\pi\) | ||||
−0.259675 | + | 0.965696i | \(0.583615\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.50466 | 0.747197 | ||||||||
\(23\) | −4.91934 | −1.02575 | −0.512877 | − | 0.858462i | \(-0.671420\pi\) | ||||
−0.512877 | + | 0.858462i | \(0.671420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.141336 | 0.0277183 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.636672 | 0.120320 | ||||||||
\(29\) | −7.15066 | −1.32785 | −0.663923 | − | 0.747801i | \(-0.731110\pi\) | ||||
−0.663923 | + | 0.747801i | \(0.731110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.78734 | −1.39865 | −0.699323 | − | 0.714805i | \(-0.746515\pi\) | ||||
−0.699323 | + | 0.714805i | \(0.746515\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.14134 | 0.367236 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.27334 | 0.538134 | 0.269067 | − | 0.963121i | \(-0.413285\pi\) | ||||
0.269067 | + | 0.963121i | \(0.413285\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.23132 | 0.660821 | 0.330411 | − | 0.943837i | \(-0.392813\pi\) | ||||
0.330411 | + | 0.943837i | \(0.392813\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.49534 | 0.380535 | 0.190268 | − | 0.981732i | \(-0.439064\pi\) | ||||
0.190268 | + | 0.981732i | \(0.439064\pi\) | |||||||
\(44\) | −3.50466 | −0.528348 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.91934 | 0.725318 | ||||||||
\(47\) | 10.2827 | 1.49988 | 0.749941 | − | 0.661505i | \(-0.230082\pi\) | ||||
0.749941 | + | 0.661505i | \(0.230082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.59465 | −0.942093 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.141336 | −0.0195998 | ||||||||
\(53\) | −8.14134 | −1.11830 | −0.559149 | − | 0.829067i | \(-0.688872\pi\) | ||||
−0.559149 | + | 0.829067i | \(0.688872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.636672 | −0.0850788 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.15066 | 0.938928 | ||||||||
\(59\) | 5.64600 | 0.735047 | 0.367523 | − | 0.930014i | \(-0.380206\pi\) | ||||
0.367523 | + | 0.930014i | \(0.380206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.49534 | −0.831643 | −0.415821 | − | 0.909446i | \(-0.636506\pi\) | ||||
−0.415821 | + | 0.909446i | \(0.636506\pi\) | |||||||
\(62\) | 7.78734 | 0.988993 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.37266 | 1.02288 | 0.511441 | − | 0.859318i | \(-0.329112\pi\) | ||||
0.511441 | + | 0.859318i | \(0.329112\pi\) | |||||||
\(68\) | −2.14134 | −0.259675 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.95798 | 1.06312 | 0.531558 | − | 0.847022i | \(-0.321607\pi\) | ||||
0.531558 | + | 0.847022i | \(0.321607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.69735 | −0.432742 | −0.216371 | − | 0.976311i | \(-0.569422\pi\) | ||||
−0.216371 | + | 0.976311i | \(0.569422\pi\) | |||||||
\(74\) | −3.27334 | −0.380518 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −2.23132 | −0.254283 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.17997 | −0.470283 | −0.235142 | − | 0.971961i | \(-0.575555\pi\) | ||||
−0.235142 | + | 0.971961i | \(0.575555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.23132 | −0.467271 | ||||||||
\(83\) | 9.00933 | 0.988902 | 0.494451 | − | 0.869205i | \(-0.335369\pi\) | ||||
0.494451 | + | 0.869205i | \(0.335369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.49534 | −0.269079 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.50466 | 0.373598 | ||||||||
\(89\) | 6.77801 | 0.718467 | 0.359234 | − | 0.933248i | \(-0.383038\pi\) | ||||
0.359234 | + | 0.933248i | \(0.383038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0899847 | −0.00943296 | ||||||||
\(92\) | −4.91934 | −0.512877 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.2827 | −1.06058 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5653 | 1.47889 | 0.739443 | − | 0.673219i | \(-0.235089\pi\) | ||||
0.739443 | + | 0.673219i | \(0.235089\pi\) | |||||||
\(98\) | 6.59465 | 0.666160 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.6167 | 1.65342 | 0.826712 | − | 0.562626i | \(-0.190209\pi\) | ||||
0.826712 | + | 0.562626i | \(0.190209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.06068 | 0.892775 | 0.446388 | − | 0.894840i | \(-0.352710\pi\) | ||||
0.446388 | + | 0.894840i | \(0.352710\pi\) | |||||||
\(104\) | 0.141336 | 0.0138591 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.14134 | 0.790756 | ||||||||
\(107\) | −0.0899847 | −0.00869915 | −0.00434958 | − | 0.999991i | \(-0.501385\pi\) | ||||
−0.00434958 | + | 0.999991i | \(0.501385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5946 | −1.30213 | −0.651066 | − | 0.759021i | \(-0.725678\pi\) | ||||
−0.651066 | + | 0.759021i | \(0.725678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.636672 | 0.0601598 | ||||||||
\(113\) | −11.5233 | −1.08402 | −0.542011 | − | 0.840371i | \(-0.682337\pi\) | ||||
−0.542011 | + | 0.840371i | \(0.682337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.15066 | −0.663923 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.64600 | −0.519756 | ||||||||
\(119\) | −1.36333 | −0.124976 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.28267 | 0.116607 | ||||||||
\(122\) | 6.49534 | 0.588060 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.78734 | −0.699323 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.29200 | −0.292118 | −0.146059 | − | 0.989276i | \(-0.546659\pi\) | ||||
−0.146059 | + | 0.989276i | \(0.546659\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0187 | −1.57430 | −0.787149 | − | 0.616763i | \(-0.788444\pi\) | ||||
−0.787149 | + | 0.616763i | \(0.788444\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.636672 | 0.0552064 | ||||||||
\(134\) | −8.37266 | −0.723287 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.14134 | 0.183618 | ||||||||
\(137\) | 14.4240 | 1.23233 | 0.616163 | − | 0.787619i | \(-0.288686\pi\) | ||||
0.616163 | + | 0.787619i | \(0.288686\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4720 | 1.31232 | 0.656158 | − | 0.754624i | \(-0.272181\pi\) | ||||
0.656158 | + | 0.754624i | \(0.272181\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.95798 | −0.751737 | ||||||||
\(143\) | 0.495336 | 0.0414220 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.69735 | 0.305995 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.27334 | 0.269067 | ||||||||
\(149\) | 17.1893 | 1.40820 | 0.704101 | − | 0.710100i | \(-0.251350\pi\) | ||||
0.704101 | + | 0.710100i | \(0.251350\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.29200 | 0.267899 | 0.133950 | − | 0.990988i | \(-0.457234\pi\) | ||||
0.133950 | + | 0.990988i | \(0.457234\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.23132 | 0.179805 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.1893 | 1.21224 | 0.606119 | − | 0.795374i | \(-0.292726\pi\) | ||||
0.606119 | + | 0.795374i | \(0.292726\pi\) | |||||||
\(158\) | 4.17997 | 0.332541 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.13201 | −0.246837 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0700 | −1.10205 | −0.551024 | − | 0.834489i | \(-0.685763\pi\) | ||||
−0.551024 | + | 0.834489i | \(0.685763\pi\) | |||||||
\(164\) | 4.23132 | 0.330411 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.00933 | −0.699260 | ||||||||
\(167\) | 14.7967 | 1.14500 | 0.572500 | − | 0.819905i | \(-0.305974\pi\) | ||||
0.572500 | + | 0.819905i | \(0.305974\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9800 | −0.998463 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.49534 | 0.190268 | ||||||||
\(173\) | 17.2920 | 1.31469 | 0.657343 | − | 0.753591i | \(-0.271680\pi\) | ||||
0.657343 | + | 0.753591i | \(0.271680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.50466 | −0.264174 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.77801 | −0.508033 | ||||||||
\(179\) | −17.7360 | −1.32565 | −0.662825 | − | 0.748774i | \(-0.730643\pi\) | ||||
−0.662825 | + | 0.748774i | \(0.730643\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.17997 | 0.459354 | 0.229677 | − | 0.973267i | \(-0.426233\pi\) | ||||
0.229677 | + | 0.973267i | \(0.426233\pi\) | |||||||
\(182\) | 0.0899847 | 0.00667011 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.91934 | 0.362659 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.50466 | 0.548795 | ||||||||
\(188\) | 10.2827 | 0.749941 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6367 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0187 | 1.44097 | 0.720487 | − | 0.693468i | \(-0.243918\pi\) | ||||
0.720487 | + | 0.693468i | \(0.243918\pi\) | |||||||
\(194\) | −14.5653 | −1.04573 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.59465 | −0.471046 | ||||||||
\(197\) | 9.94865 | 0.708812 | 0.354406 | − | 0.935092i | \(-0.384683\pi\) | ||||
0.354406 | + | 0.935092i | \(0.384683\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.74870 | 0.691067 | 0.345534 | − | 0.938406i | \(-0.387698\pi\) | ||||
0.345534 | + | 0.938406i | \(0.387698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −16.6167 | −1.16915 | ||||||||
\(203\) | −4.55263 | −0.319532 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.06068 | −0.631287 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.141336 | −0.00979990 | ||||||||
\(209\) | −3.50466 | −0.242423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.7580 | −1.42904 | −0.714521 | − | 0.699614i | \(-0.753355\pi\) | ||||
−0.714521 | + | 0.699614i | \(0.753355\pi\) | |||||||
\(212\) | −8.14134 | −0.559149 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.0899847 | 0.00615123 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.95798 | −0.336569 | ||||||||
\(218\) | 13.5946 | 0.920746 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.302648 | 0.0203583 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7267 | −0.718310 | −0.359155 | − | 0.933278i | \(-0.616935\pi\) | ||||
−0.359155 | + | 0.933278i | \(0.616935\pi\) | |||||||
\(224\) | −0.636672 | −0.0425394 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.5233 | 0.766520 | ||||||||
\(227\) | −12.5526 | −0.833147 | −0.416574 | − | 0.909102i | \(-0.636769\pi\) | ||||
−0.416574 | + | 0.909102i | \(0.636769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4720 | 1.68324 | 0.841618 | − | 0.540074i | \(-0.181604\pi\) | ||||
0.841618 | + | 0.540074i | \(0.181604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.15066 | 0.469464 | ||||||||
\(233\) | 3.11203 | 0.203876 | 0.101938 | − | 0.994791i | \(-0.467496\pi\) | ||||
0.101938 | + | 0.994791i | \(0.467496\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.64600 | 0.367523 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.36333 | 0.0883714 | ||||||||
\(239\) | 1.54330 | 0.0998276 | 0.0499138 | − | 0.998754i | \(-0.484105\pi\) | ||||
0.0499138 | + | 0.998754i | \(0.484105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2827 | 0.662365 | 0.331183 | − | 0.943567i | \(-0.392552\pi\) | ||||
0.331183 | + | 0.943567i | \(0.392552\pi\) | |||||||
\(242\) | −1.28267 | −0.0824533 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.49534 | −0.415821 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.141336 | −0.00899300 | ||||||||
\(248\) | 7.78734 | 0.494496 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.51399 | 0.158682 | 0.0793409 | − | 0.996848i | \(-0.474718\pi\) | ||||
0.0793409 | + | 0.996848i | \(0.474718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.2406 | 1.08391 | ||||||||
\(254\) | 3.29200 | 0.206559 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.7967 | 1.54677 | 0.773387 | − | 0.633934i | \(-0.218561\pi\) | ||||
0.773387 | + | 0.633934i | \(0.218561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.08405 | 0.129496 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.0187 | 1.11320 | ||||||||
\(263\) | 22.5653 | 1.39144 | 0.695719 | − | 0.718314i | \(-0.255086\pi\) | ||||
0.695719 | + | 0.718314i | \(0.255086\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.636672 | −0.0390369 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.37266 | 0.511441 | ||||||||
\(269\) | 26.5653 | 1.61972 | 0.809859 | − | 0.586625i | \(-0.199544\pi\) | ||||
0.809859 | + | 0.586625i | \(0.199544\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.9380 | −1.51488 | −0.757438 | − | 0.652907i | \(-0.773549\pi\) | ||||
−0.757438 | + | 0.652907i | \(0.773549\pi\) | |||||||
\(272\) | −2.14134 | −0.129838 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.4240 | −0.871386 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.5467 | 1.11436 | 0.557181 | − | 0.830391i | \(-0.311883\pi\) | ||||
0.557181 | + | 0.830391i | \(0.311883\pi\) | |||||||
\(278\) | −15.4720 | −0.927947 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.7967 | −1.47925 | −0.739623 | − | 0.673022i | \(-0.764996\pi\) | ||||
−0.739623 | + | 0.673022i | \(0.764996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5747 | 0.806931 | 0.403465 | − | 0.914995i | \(-0.367806\pi\) | ||||
0.403465 | + | 0.914995i | \(0.367806\pi\) | |||||||
\(284\) | 8.95798 | 0.531558 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.495336 | −0.0292898 | ||||||||
\(287\) | 2.69396 | 0.159020 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.4147 | −0.730275 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.69735 | −0.216371 | ||||||||
\(293\) | 15.6133 | 0.912139 | 0.456070 | − | 0.889944i | \(-0.349257\pi\) | ||||
0.456070 | + | 0.889944i | \(0.349257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.27334 | −0.190259 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.1893 | −0.995749 | ||||||||
\(299\) | 0.695281 | 0.0402091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.58871 | 0.0915717 | ||||||||
\(302\) | −3.29200 | −0.189433 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.0187 | 1.94155 | 0.970774 | − | 0.239997i | \(-0.0771464\pi\) | ||||
0.970774 | + | 0.239997i | \(0.0771464\pi\) | |||||||
\(308\) | −2.23132 | −0.127141 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.93800 | −0.506828 | −0.253414 | − | 0.967358i | \(-0.581553\pi\) | ||||
−0.253414 | + | 0.967358i | \(0.581553\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.4240 | −1.04139 | −0.520693 | − | 0.853744i | \(-0.674326\pi\) | ||||
−0.520693 | + | 0.853744i | \(0.674326\pi\) | |||||||
\(314\) | −15.1893 | −0.857182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.17997 | −0.235142 | ||||||||
\(317\) | −33.5547 | −1.88462 | −0.942310 | − | 0.334742i | \(-0.891351\pi\) | ||||
−0.942310 | + | 0.334742i | \(0.891351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.0607 | 1.40313 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.13201 | 0.174540 | ||||||||
\(323\) | −2.14134 | −0.119147 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.0700 | 0.779266 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.23132 | −0.233636 | ||||||||
\(329\) | 6.54669 | 0.360931 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.25130 | 0.123742 | 0.0618712 | − | 0.998084i | \(-0.480293\pi\) | ||||
0.0618712 | + | 0.998084i | \(0.480293\pi\) | |||||||
\(332\) | 9.00933 | 0.494451 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.7967 | −0.809638 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.3620 | −1.16366 | −0.581831 | − | 0.813309i | \(-0.697664\pi\) | ||||
−0.581831 | + | 0.813309i | \(0.697664\pi\) | |||||||
\(338\) | 12.9800 | 0.706020 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.2920 | 1.47794 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.65533 | −0.467344 | ||||||||
\(344\) | −2.49534 | −0.134539 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.2920 | −0.929624 | ||||||||
\(347\) | −11.5560 | −0.620359 | −0.310180 | − | 0.950678i | \(-0.600389\pi\) | ||||
−0.310180 | + | 0.950678i | \(0.600389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1120 | −0.915986 | −0.457993 | − | 0.888956i | \(-0.651432\pi\) | ||||
−0.457993 | + | 0.888956i | \(0.651432\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.50466 | 0.186799 | ||||||||
\(353\) | −11.6974 | −0.622587 | −0.311294 | − | 0.950314i | \(-0.600762\pi\) | ||||
−0.311294 | + | 0.950314i | \(0.600762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.77801 | 0.359234 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.7360 | 0.937376 | ||||||||
\(359\) | 4.47536 | 0.236200 | 0.118100 | − | 0.993002i | \(-0.462320\pi\) | ||||
0.118100 | + | 0.993002i | \(0.462320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −6.17997 | −0.324812 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0899847 | −0.00471648 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.7453 | 0.978497 | 0.489249 | − | 0.872144i | \(-0.337271\pi\) | ||||
0.489249 | + | 0.872144i | \(0.337271\pi\) | |||||||
\(368\) | −4.91934 | −0.256439 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.18336 | −0.269107 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.69735 | 0.0878855 | 0.0439428 | − | 0.999034i | \(-0.486008\pi\) | ||||
0.0439428 | + | 0.999034i | \(0.486008\pi\) | |||||||
\(374\) | −7.50466 | −0.388057 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.2827 | −0.530288 | ||||||||
\(377\) | 1.01065 | 0.0520510 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.63667 | 0.135437 | 0.0677184 | − | 0.997704i | \(-0.478428\pi\) | ||||
0.0677184 | + | 0.997704i | \(0.478428\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.6367 | 0.748877 | ||||||||
\(383\) | −12.4953 | −0.638482 | −0.319241 | − | 0.947674i | \(-0.603428\pi\) | ||||
−0.319241 | + | 0.947674i | \(0.603428\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.0187 | −1.01892 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.5653 | 0.739443 | ||||||||
\(389\) | 4.51399 | 0.228869 | 0.114434 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114434 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.5340 | 0.532726 | ||||||||
\(392\) | 6.59465 | 0.333080 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.94865 | −0.501206 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.6774 | −1.79060 | −0.895298 | − | 0.445468i | \(-0.853037\pi\) | ||||
−0.895298 | + | 0.445468i | \(0.853037\pi\) | |||||||
\(398\) | −9.74870 | −0.488658 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.3434 | −0.766210 | −0.383105 | − | 0.923705i | \(-0.625145\pi\) | ||||
−0.383105 | + | 0.923705i | \(0.625145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.10063 | 0.0548264 | ||||||||
\(404\) | 16.6167 | 0.826712 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.55263 | 0.225943 | ||||||||
\(407\) | −11.4720 | −0.568644 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.3620 | 1.45186 | 0.725929 | − | 0.687770i | \(-0.241410\pi\) | ||||
0.725929 | + | 0.687770i | \(0.241410\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.06068 | 0.446388 | ||||||||
\(413\) | 3.59465 | 0.176881 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.141336 | 0.00692957 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.50466 | 0.171419 | ||||||||
\(419\) | −25.1379 | −1.22807 | −0.614035 | − | 0.789279i | \(-0.710454\pi\) | ||||
−0.614035 | + | 0.789279i | \(0.710454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5454 | 0.708898 | 0.354449 | − | 0.935075i | \(-0.384668\pi\) | ||||
0.354449 | + | 0.935075i | \(0.384668\pi\) | |||||||
\(422\) | 20.7580 | 1.01049 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.14134 | 0.395378 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.13540 | −0.200126 | ||||||||
\(428\) | −0.0899847 | −0.00434958 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.4020 | −0.934560 | −0.467280 | − | 0.884109i | \(-0.654766\pi\) | ||||
−0.467280 | + | 0.884109i | \(0.654766\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.50466 | 0.264537 | 0.132269 | − | 0.991214i | \(-0.457774\pi\) | ||||
0.132269 | + | 0.991214i | \(0.457774\pi\) | |||||||
\(434\) | 4.95798 | 0.237991 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.5946 | −0.651066 | ||||||||
\(437\) | −4.91934 | −0.235324 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2500 | 0.584660 | 0.292330 | − | 0.956318i | \(-0.405570\pi\) | ||||
0.292330 | + | 0.956318i | \(0.405570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.302648 | −0.0143955 | ||||||||
\(443\) | −31.6006 | −1.50139 | −0.750695 | − | 0.660649i | \(-0.770281\pi\) | ||||
−0.750695 | + | 0.660649i | \(0.770281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.7267 | 0.507922 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.636672 | 0.0300799 | ||||||||
\(449\) | 36.0187 | 1.69983 | 0.849913 | − | 0.526923i | \(-0.176655\pi\) | ||||
0.849913 | + | 0.526923i | \(0.176655\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.8294 | −0.698287 | ||||||||
\(452\) | −11.5233 | −0.542011 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.5526 | 0.589124 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.1413 | 1.03573 | 0.517864 | − | 0.855463i | \(-0.326727\pi\) | ||||
0.517864 | + | 0.855463i | \(0.326727\pi\) | |||||||
\(458\) | −25.4720 | −1.19023 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.31537 | 0.107837 | 0.0539187 | − | 0.998545i | \(-0.482829\pi\) | ||||
0.0539187 | + | 0.998545i | \(0.482829\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8387 | 0.736086 | 0.368043 | − | 0.929809i | \(-0.380028\pi\) | ||||
0.368043 | + | 0.929809i | \(0.380028\pi\) | |||||||
\(464\) | −7.15066 | −0.331961 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.11203 | −0.144162 | ||||||||
\(467\) | −23.1379 | −1.07070 | −0.535348 | − | 0.844631i | \(-0.679820\pi\) | ||||
−0.535348 | + | 0.844631i | \(0.679820\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.33063 | 0.246146 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.64600 | −0.259878 | ||||||||
\(473\) | −8.74531 | −0.402110 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.36333 | −0.0624880 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.54330 | −0.0705888 | ||||||||
\(479\) | 10.1214 | 0.462457 | 0.231228 | − | 0.972900i | \(-0.425726\pi\) | ||||
0.231228 | + | 0.972900i | \(0.425726\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.462642 | −0.0210946 | ||||||||
\(482\) | −10.2827 | −0.468363 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.28267 | 0.0583033 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.3854 | 0.923750 | 0.461875 | − | 0.886945i | \(-0.347177\pi\) | ||||
0.461875 | + | 0.886945i | \(0.347177\pi\) | |||||||
\(488\) | 6.49534 | 0.294030 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.78734 | 0.351438 | 0.175719 | − | 0.984440i | \(-0.443775\pi\) | ||||
0.175719 | + | 0.984440i | \(0.443775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.3120 | 0.689617 | ||||||||
\(494\) | 0.141336 | 0.00635901 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.78734 | −0.349662 | ||||||||
\(497\) | 5.70329 | 0.255828 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.31537 | 0.193182 | 0.0965912 | − | 0.995324i | \(-0.469206\pi\) | ||||
0.0965912 | + | 0.995324i | \(0.469206\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.51399 | −0.112205 | ||||||||
\(503\) | −18.5526 | −0.827221 | −0.413610 | − | 0.910454i | \(-0.635732\pi\) | ||||
−0.413610 | + | 0.910454i | \(0.635732\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −17.2406 | −0.766440 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.29200 | −0.146059 | ||||||||
\(509\) | 7.73599 | 0.342892 | 0.171446 | − | 0.985194i | \(-0.445156\pi\) | ||||
0.171446 | + | 0.985194i | \(0.445156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.35400 | −0.104135 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.7967 | −1.09373 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.0373 | −1.58492 | ||||||||
\(518\) | −2.08405 | −0.0915677 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.2080 | −0.666273 | −0.333136 | − | 0.942879i | \(-0.608107\pi\) | ||||
−0.333136 | + | 0.942879i | \(0.608107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.2113 | −0.796327 | −0.398163 | − | 0.917315i | \(-0.630352\pi\) | ||||
−0.398163 | + | 0.917315i | \(0.630352\pi\) | |||||||
\(524\) | −18.0187 | −0.787149 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.5653 | −0.983896 | ||||||||
\(527\) | 16.6753 | 0.726388 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.19995 | 0.0521715 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.636672 | 0.0276032 | ||||||||
\(533\) | −0.598038 | −0.0259039 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.37266 | −0.361644 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.5653 | −1.14531 | ||||||||
\(539\) | 23.1120 | 0.995506 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.5140 | 0.709992 | 0.354996 | − | 0.934868i | \(-0.384482\pi\) | ||||
0.354996 | + | 0.934868i | \(0.384482\pi\) | |||||||
\(542\) | 24.9380 | 1.07118 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.14134 | 0.0918090 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2827 | 0.696197 | 0.348098 | − | 0.937458i | \(-0.386828\pi\) | ||||
0.348098 | + | 0.937458i | \(0.386828\pi\) | |||||||
\(548\) | 14.4240 | 0.616163 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.15066 | −0.304629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.66127 | −0.113169 | ||||||||
\(554\) | −18.5467 | −0.787973 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.4720 | 0.656158 | ||||||||
\(557\) | −37.4533 | −1.58695 | −0.793474 | − | 0.608604i | \(-0.791730\pi\) | ||||
−0.793474 | + | 0.608604i | \(0.791730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.352681 | −0.0149168 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.7967 | 1.04598 | ||||||||
\(563\) | 29.1307 | 1.22771 | 0.613856 | − | 0.789418i | \(-0.289618\pi\) | ||||
0.613856 | + | 0.789418i | \(0.289618\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.5747 | −0.570586 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.95798 | −0.375868 | ||||||||
\(569\) | −14.8480 | −0.622461 | −0.311231 | − | 0.950334i | \(-0.600741\pi\) | ||||
−0.311231 | + | 0.950334i | \(0.600741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.9087 | 1.75382 | 0.876912 | − | 0.480651i | \(-0.159599\pi\) | ||||
0.876912 | + | 0.480651i | \(0.159599\pi\) | |||||||
\(572\) | 0.495336 | 0.0207110 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.69396 | −0.112444 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.4427 | 0.684517 | 0.342259 | − | 0.939606i | \(-0.388808\pi\) | ||||
0.342259 | + | 0.939606i | \(0.388808\pi\) | |||||||
\(578\) | 12.4147 | 0.516383 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.73599 | 0.237969 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.5327 | 1.18170 | ||||||||
\(584\) | 3.69735 | 0.152998 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.6133 | −0.644980 | ||||||||
\(587\) | 42.5327 | 1.75551 | 0.877755 | − | 0.479109i | \(-0.159040\pi\) | ||||
0.877755 | + | 0.479109i | \(0.159040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.78734 | −0.320872 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.27334 | 0.134534 | ||||||||
\(593\) | −3.92273 | −0.161087 | −0.0805437 | − | 0.996751i | \(-0.525666\pi\) | ||||
−0.0805437 | + | 0.996751i | \(0.525666\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.1893 | 0.704101 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.695281 | −0.0284322 | ||||||||
\(599\) | 10.7594 | 0.439615 | 0.219808 | − | 0.975543i | \(-0.429457\pi\) | ||||
0.219808 | + | 0.975543i | \(0.429457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.2220 | 1.02883 | 0.514413 | − | 0.857542i | \(-0.328010\pi\) | ||||
0.514413 | + | 0.857542i | \(0.328010\pi\) | |||||||
\(602\) | −1.58871 | −0.0647510 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.29200 | 0.133950 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.2920 | 1.59481 | 0.797407 | − | 0.603442i | \(-0.206205\pi\) | ||||
0.797407 | + | 0.603442i | \(0.206205\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.45331 | −0.0587947 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.80599 | 0.396060 | 0.198030 | − | 0.980196i | \(-0.436546\pi\) | ||||
0.198030 | + | 0.980196i | \(0.436546\pi\) | |||||||
\(614\) | −34.0187 | −1.37288 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.23132 | 0.0899025 | ||||||||
\(617\) | 35.0093 | 1.40942 | 0.704711 | − | 0.709494i | \(-0.251077\pi\) | ||||
0.704711 | + | 0.709494i | \(0.251077\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.4206 | 0.539420 | 0.269710 | − | 0.962942i | \(-0.413072\pi\) | ||||
0.269710 | + | 0.962942i | \(0.413072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.93800 | 0.358381 | ||||||||
\(623\) | 4.31537 | 0.172891 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.4240 | 0.736371 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.1893 | 0.606119 | ||||||||
\(629\) | −7.00933 | −0.279480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.5254 | 1.61329 | 0.806645 | − | 0.591036i | \(-0.201281\pi\) | ||||
0.806645 | + | 0.591036i | \(0.201281\pi\) | |||||||
\(632\) | 4.17997 | 0.166270 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 33.5547 | 1.33263 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.932062 | 0.0369296 | ||||||||
\(638\) | −25.0607 | −0.992162 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.0700 | 1.02970 | 0.514852 | − | 0.857279i | \(-0.327847\pi\) | ||||
0.514852 | + | 0.857279i | \(0.327847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.1400 | 1.18861 | 0.594303 | − | 0.804241i | \(-0.297428\pi\) | ||||
0.594303 | + | 0.804241i | \(0.297428\pi\) | |||||||
\(644\) | −3.13201 | −0.123418 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.14134 | 0.0842497 | ||||||||
\(647\) | 20.1086 | 0.790552 | 0.395276 | − | 0.918562i | \(-0.370649\pi\) | ||||
0.395276 | + | 0.918562i | \(0.370649\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.7873 | −0.776721 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.0700 | −0.551024 | ||||||||
\(653\) | 28.0373 | 1.09718 | 0.548592 | − | 0.836090i | \(-0.315164\pi\) | ||||
0.548592 | + | 0.836090i | \(0.315164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.23132 | 0.165205 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.54669 | −0.255216 | ||||||||
\(659\) | −4.90069 | −0.190904 | −0.0954518 | − | 0.995434i | \(-0.530430\pi\) | ||||
−0.0954518 | + | 0.995434i | \(0.530430\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.03863 | −0.312667 | −0.156333 | − | 0.987704i | \(-0.549967\pi\) | ||||
−0.156333 | + | 0.987704i | \(0.549967\pi\) | |||||||
\(662\) | −2.25130 | −0.0874991 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.00933 | −0.349630 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.1766 | 1.36204 | ||||||||
\(668\) | 14.7967 | 0.572500 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.7640 | 0.878793 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.82936 | −0.186158 | −0.0930791 | − | 0.995659i | \(-0.529671\pi\) | ||||
−0.0930791 | + | 0.995659i | \(0.529671\pi\) | |||||||
\(674\) | 21.3620 | 0.822834 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9800 | −0.499232 | ||||||||
\(677\) | −12.8094 | −0.492305 | −0.246152 | − | 0.969231i | \(-0.579166\pi\) | ||||
−0.246152 | + | 0.969231i | \(0.579166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.27334 | 0.355878 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.2920 | −1.04506 | ||||||||
\(683\) | −37.1307 | −1.42077 | −0.710383 | − | 0.703815i | \(-0.751478\pi\) | ||||
−0.710383 | + | 0.703815i | \(0.751478\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.65533 | 0.330462 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.49534 | 0.0951338 | ||||||||
\(689\) | 1.15066 | 0.0438368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.1986 | −0.692308 | −0.346154 | − | 0.938178i | \(-0.612513\pi\) | ||||
−0.346154 | + | 0.938178i | \(0.612513\pi\) | |||||||
\(692\) | 17.2920 | 0.657343 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.5560 | 0.438660 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.06068 | −0.343198 | ||||||||
\(698\) | 17.1120 | 0.647700 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.2827 | 0.992683 | 0.496341 | − | 0.868127i | \(-0.334676\pi\) | ||||
0.496341 | + | 0.868127i | \(0.334676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.27334 | 0.123456 | ||||||||
\(704\) | −3.50466 | −0.132087 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.6974 | 0.440236 | ||||||||
\(707\) | 10.5794 | 0.397879 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9253 | −0.560531 | −0.280265 | − | 0.959923i | \(-0.590422\pi\) | ||||
−0.280265 | + | 0.959923i | \(0.590422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.77801 | −0.254017 | ||||||||
\(713\) | 38.3086 | 1.43467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.7360 | −0.662825 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.47536 | −0.167019 | ||||||||
\(719\) | −32.3327 | −1.20581 | −0.602903 | − | 0.797814i | \(-0.705989\pi\) | ||||
−0.602903 | + | 0.797814i | \(0.705989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.76868 | 0.214837 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.17997 | 0.229677 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0246 | −1.55861 | −0.779303 | − | 0.626647i | \(-0.784427\pi\) | ||||
−0.779303 | + | 0.626647i | \(0.784427\pi\) | |||||||
\(728\) | 0.0899847 | 0.00333506 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.34335 | −0.197631 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.5840 | 0.981903 | 0.490951 | − | 0.871187i | \(-0.336649\pi\) | ||||
0.490951 | + | 0.871187i | \(0.336649\pi\) | |||||||
\(734\) | −18.7453 | −0.691902 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.91934 | 0.181329 | ||||||||
\(737\) | −29.3434 | −1.08088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.14728 | 0.299702 | 0.149851 | − | 0.988709i | \(-0.452121\pi\) | ||||
0.149851 | + | 0.988709i | \(0.452121\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.18336 | 0.190287 | ||||||||
\(743\) | −35.8247 | −1.31428 | −0.657139 | − | 0.753769i | \(-0.728234\pi\) | ||||
−0.657139 | + | 0.753769i | \(0.728234\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.69735 | −0.0621445 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.50466 | 0.274398 | ||||||||
\(749\) | −0.0572907 | −0.00209336 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.8994 | −0.543686 | −0.271843 | − | 0.962342i | \(-0.587633\pi\) | ||||
−0.271843 | + | 0.962342i | \(0.587633\pi\) | |||||||
\(752\) | 10.2827 | 0.374970 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.01065 | −0.0368056 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.7920 | −1.73703 | −0.868514 | − | 0.495664i | \(-0.834925\pi\) | ||||
−0.868514 | + | 0.495664i | \(0.834925\pi\) | |||||||
\(758\) | −2.63667 | −0.0957682 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.9053 | 1.41032 | 0.705158 | − | 0.709050i | \(-0.250876\pi\) | ||||
0.705158 | + | 0.709050i | \(0.250876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.65533 | −0.313344 | ||||||||
\(764\) | −14.6367 | −0.529536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.4953 | 0.451475 | ||||||||
\(767\) | −0.797984 | −0.0288135 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.74663 | 0.315412 | 0.157706 | − | 0.987486i | \(-0.449590\pi\) | ||||
0.157706 | + | 0.987486i | \(0.449590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.0187 | 0.720487 | ||||||||
\(773\) | 23.4707 | 0.844181 | 0.422090 | − | 0.906554i | \(-0.361297\pi\) | ||||
0.422090 | + | 0.906554i | \(0.361297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.5653 | −0.522865 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.51399 | −0.161834 | ||||||||
\(779\) | 4.23132 | 0.151603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.3947 | −1.12339 | ||||||||
\(782\) | −10.5340 | −0.376694 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.59465 | −0.235523 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.26063 | 0.0449364 | 0.0224682 | − | 0.999748i | \(-0.492848\pi\) | ||||
0.0224682 | + | 0.999748i | \(0.492848\pi\) | |||||||
\(788\) | 9.94865 | 0.354406 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.33657 | −0.260859 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.918026 | 0.0326000 | ||||||||
\(794\) | 35.6774 | 1.26614 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.74870 | 0.345534 | ||||||||
\(797\) | 38.6481 | 1.36898 | 0.684492 | − | 0.729020i | \(-0.260024\pi\) | ||||
0.684492 | + | 0.729020i | \(0.260024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.0187 | −0.778964 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.3434 | 0.541793 | ||||||||
\(803\) | 12.9580 | 0.457277 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.10063 | −0.0387681 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.6167 | −0.584573 | ||||||||
\(809\) | −51.6506 | −1.81594 | −0.907970 | − | 0.419036i | \(-0.862368\pi\) | ||||
−0.907970 | + | 0.419036i | \(0.862368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.19269 | 0.287684 | 0.143842 | − | 0.989601i | \(-0.454054\pi\) | ||||
0.143842 | + | 0.989601i | \(0.454054\pi\) | |||||||
\(812\) | −4.55263 | −0.159766 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.4720 | 0.402092 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.49534 | 0.0873007 | ||||||||
\(818\) | −29.3620 | −1.02662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.9600 | 1.74362 | 0.871809 | − | 0.489846i | \(-0.162947\pi\) | ||||
0.871809 | + | 0.489846i | \(0.162947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.8421 | −0.587078 | −0.293539 | − | 0.955947i | \(-0.594833\pi\) | ||||
−0.293539 | + | 0.955947i | \(0.594833\pi\) | |||||||
\(824\) | −9.06068 | −0.315644 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.59465 | −0.125074 | ||||||||
\(827\) | 41.7487 | 1.45174 | 0.725872 | − | 0.687829i | \(-0.241436\pi\) | ||||
0.725872 | + | 0.687829i | \(0.241436\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.98002 | −0.207695 | −0.103847 | − | 0.994593i | \(-0.533115\pi\) | ||||
−0.103847 | + | 0.994593i | \(0.533115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.141336 | −0.00489995 | ||||||||
\(833\) | 14.1214 | 0.489276 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.50466 | −0.121211 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.1379 | 0.868376 | ||||||||
\(839\) | −32.0373 | −1.10605 | −0.553025 | − | 0.833164i | \(-0.686527\pi\) | ||||
−0.553025 | + | 0.833164i | \(0.686527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.1320 | 0.763173 | ||||||||
\(842\) | −14.5454 | −0.501267 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.7580 | −0.714521 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.816641 | 0.0280601 | ||||||||
\(848\) | −8.14134 | −0.279575 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.1027 | −0.551994 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.8480 | −1.39861 | −0.699305 | − | 0.714824i | \(-0.746507\pi\) | ||||
−0.699305 | + | 0.714824i | \(0.746507\pi\) | |||||||
\(854\) | 4.13540 | 0.141510 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0899847 | 0.00307561 | ||||||||
\(857\) | −28.8667 | −0.986067 | −0.493033 | − | 0.870010i | \(-0.664112\pi\) | ||||
−0.493033 | + | 0.870010i | \(0.664112\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5047 | −0.392534 | −0.196267 | − | 0.980550i | \(-0.562882\pi\) | ||||
−0.196267 | + | 0.980550i | \(0.562882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.4020 | 0.660833 | ||||||||
\(863\) | 31.6074 | 1.07593 | 0.537964 | − | 0.842968i | \(-0.319194\pi\) | ||||
0.537964 | + | 0.842968i | \(0.319194\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.50466 | −0.187056 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.95798 | −0.168285 | ||||||||
\(869\) | 14.6494 | 0.496947 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.18336 | −0.0400966 | ||||||||
\(872\) | 13.5946 | 0.460373 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.91934 | 0.166399 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0641 | 0.407375 | 0.203687 | − | 0.979036i | \(-0.434707\pi\) | ||||
0.203687 | + | 0.979036i | \(0.434707\pi\) | |||||||
\(878\) | −12.2500 | −0.413417 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.8480 | 0.769769 | 0.384885 | − | 0.922965i | \(-0.374241\pi\) | ||||
0.384885 | + | 0.922965i | \(0.374241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.1773 | −1.15016 | −0.575079 | − | 0.818098i | \(-0.695029\pi\) | ||||
−0.575079 | + | 0.818098i | \(0.695029\pi\) | |||||||
\(884\) | 0.302648 | 0.0101792 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.6006 | 1.06164 | ||||||||
\(887\) | −26.6167 | −0.893701 | −0.446851 | − | 0.894609i | \(-0.647454\pi\) | ||||
−0.446851 | + | 0.894609i | \(0.647454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.09592 | −0.0702950 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.7267 | −0.359155 | ||||||||
\(893\) | 10.2827 | 0.344097 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.636672 | −0.0212697 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.0187 | −1.20196 | ||||||||
\(899\) | 55.6846 | 1.85719 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.4333 | 0.580789 | ||||||||
\(902\) | 14.8294 | 0.493764 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.5233 | 0.383260 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.1434 | 0.436420 | 0.218210 | − | 0.975902i | \(-0.429978\pi\) | ||||
0.218210 | + | 0.975902i | \(0.429978\pi\) | |||||||
\(908\) | −12.5526 | −0.416574 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.9253 | 1.09086 | 0.545432 | − | 0.838155i | \(-0.316366\pi\) | ||||
0.545432 | + | 0.838155i | \(0.316366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.5747 | −1.04497 | ||||||||
\(914\) | −22.1413 | −0.732370 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.4720 | 0.841618 | ||||||||
\(917\) | −11.4720 | −0.378838 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.1273 | −0.795886 | −0.397943 | − | 0.917410i | \(-0.630276\pi\) | ||||
−0.397943 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.31537 | −0.0762525 | ||||||||
\(923\) | −1.26609 | −0.0416737 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.8387 | −0.520492 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.15066 | 0.234732 | ||||||||
\(929\) | 15.9359 | 0.522841 | 0.261420 | − | 0.965225i | \(-0.415809\pi\) | ||||
0.261420 | + | 0.965225i | \(0.415809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.59465 | −0.216131 | ||||||||
\(932\) | 3.11203 | 0.101938 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.1379 | 0.757097 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.5547 | 0.769498 | 0.384749 | − | 0.923021i | \(-0.374288\pi\) | ||||
0.384749 | + | 0.923021i | \(0.374288\pi\) | |||||||
\(938\) | −5.33063 | −0.174051 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.6974 | 0.837710 | 0.418855 | − | 0.908053i | \(-0.362432\pi\) | ||||
0.418855 | + | 0.908053i | \(0.362432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.8153 | −0.677840 | ||||||||
\(944\) | 5.64600 | 0.183762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.74531 | 0.284335 | ||||||||
\(947\) | 16.3013 | 0.529722 | 0.264861 | − | 0.964287i | \(-0.414674\pi\) | ||||
0.264861 | + | 0.964287i | \(0.414674\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.522569 | 0.0169633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.36333 | 0.0441857 | ||||||||
\(953\) | −10.2754 | −0.332853 | −0.166427 | − | 0.986054i | \(-0.553223\pi\) | ||||
−0.166427 | + | 0.986054i | \(0.553223\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.54330 | 0.0499138 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.1214 | −0.327006 | ||||||||
\(959\) | 9.18336 | 0.296546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6426 | 0.956213 | ||||||||
\(962\) | 0.462642 | 0.0149162 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.2827 | 0.331183 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.2920 | −1.71376 | −0.856878 | − | 0.515520i | \(-0.827599\pi\) | ||||
−0.856878 | + | 0.515520i | \(0.827599\pi\) | |||||||
\(968\) | −1.28267 | −0.0412266 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.54669 | −0.0817271 | −0.0408635 | − | 0.999165i | \(-0.513011\pi\) | ||||
−0.0408635 | + | 0.999165i | \(0.513011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.85057 | 0.315795 | ||||||||
\(974\) | −20.3854 | −0.653190 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.49534 | −0.207911 | ||||||||
\(977\) | 49.2966 | 1.57714 | 0.788569 | − | 0.614946i | \(-0.210822\pi\) | ||||
0.788569 | + | 0.614946i | \(0.210822\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.7546 | −0.759202 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.78734 | −0.248504 | ||||||||
\(983\) | 36.7453 | 1.17199 | 0.585997 | − | 0.810313i | \(-0.300703\pi\) | ||||
0.585997 | + | 0.810313i | \(0.300703\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.3120 | −0.487633 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.141336 | −0.00449650 | ||||||||
\(989\) | −12.2754 | −0.390335 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.5674 | −1.12984 | −0.564918 | − | 0.825147i | \(-0.691092\pi\) | ||||
−0.564918 | + | 0.825147i | \(0.691092\pi\) | |||||||
\(992\) | 7.78734 | 0.247248 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.70329 | −0.180897 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.4299 | −1.53379 | −0.766896 | − | 0.641771i | \(-0.778200\pi\) | ||||
−0.766896 | + | 0.641771i | \(0.778200\pi\) | |||||||
\(998\) | −4.31537 | −0.136601 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8550.2.a.ck.1.2 | 3 | ||
3.2 | odd | 2 | 950.2.a.n.1.2 | 3 | |||
5.2 | odd | 4 | 1710.2.d.d.1369.2 | 6 | |||
5.3 | odd | 4 | 1710.2.d.d.1369.5 | 6 | |||
5.4 | even | 2 | 8550.2.a.cl.1.2 | 3 | |||
12.11 | even | 2 | 7600.2.a.bi.1.2 | 3 | |||
15.2 | even | 4 | 190.2.b.b.39.5 | yes | 6 | ||
15.8 | even | 4 | 190.2.b.b.39.2 | ✓ | 6 | ||
15.14 | odd | 2 | 950.2.a.i.1.2 | 3 | |||
60.23 | odd | 4 | 1520.2.d.j.609.3 | 6 | |||
60.47 | odd | 4 | 1520.2.d.j.609.4 | 6 | |||
60.59 | even | 2 | 7600.2.a.cd.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.b.39.2 | ✓ | 6 | 15.8 | even | 4 | ||
190.2.b.b.39.5 | yes | 6 | 15.2 | even | 4 | ||
950.2.a.i.1.2 | 3 | 15.14 | odd | 2 | |||
950.2.a.n.1.2 | 3 | 3.2 | odd | 2 | |||
1520.2.d.j.609.3 | 6 | 60.23 | odd | 4 | |||
1520.2.d.j.609.4 | 6 | 60.47 | odd | 4 | |||
1710.2.d.d.1369.2 | 6 | 5.2 | odd | 4 | |||
1710.2.d.d.1369.5 | 6 | 5.3 | odd | 4 | |||
7600.2.a.bi.1.2 | 3 | 12.11 | even | 2 | |||
7600.2.a.cd.1.2 | 3 | 60.59 | even | 2 | |||
8550.2.a.ck.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8550.2.a.cl.1.2 | 3 | 5.4 | even | 2 |