Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2535) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.04892 | 1.44880 | 0.724402 | − | 0.689378i | \(-0.242116\pi\) | ||||
0.724402 | + | 0.689378i | \(0.242116\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.19806 | 1.09903 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.04892 | −1.15238 | −0.576191 | − | 0.817315i | \(-0.695462\pi\) | ||||
−0.576191 | + | 0.817315i | \(0.695462\pi\) | |||||||
\(8\) | 0.405813 | 0.143477 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.04892 | 0.647925 | ||||||||
\(11\) | 1.89008 | 0.569882 | 0.284941 | − | 0.958545i | \(-0.408026\pi\) | ||||
0.284941 | + | 0.958545i | \(0.408026\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −6.24698 | −1.66958 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.56465 | −0.891162 | ||||||||
\(17\) | 4.09783 | 0.993871 | 0.496935 | − | 0.867788i | \(-0.334459\pi\) | ||||
0.496935 | + | 0.867788i | \(0.334459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.58211 | −0.592376 | −0.296188 | − | 0.955130i | \(-0.595715\pi\) | ||||
−0.296188 | + | 0.955130i | \(0.595715\pi\) | |||||||
\(20\) | 2.19806 | 0.491502 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.87263 | 0.825646 | ||||||||
\(23\) | −3.02715 | −0.631204 | −0.315602 | − | 0.948892i | \(-0.602206\pi\) | ||||
−0.315602 | + | 0.948892i | \(0.602206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.70171 | −1.26650 | ||||||||
\(29\) | −3.30798 | −0.614276 | −0.307138 | − | 0.951665i | \(-0.599371\pi\) | ||||
−0.307138 | + | 0.951665i | \(0.599371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.31767 | −1.67350 | −0.836751 | − | 0.547583i | \(-0.815548\pi\) | ||||
−0.836751 | + | 0.547583i | \(0.815548\pi\) | |||||||
\(32\) | −8.11529 | −1.43459 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.39612 | 1.43992 | ||||||||
\(35\) | −3.04892 | −0.515361 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.2959 | 1.69264 | 0.846318 | − | 0.532679i | \(-0.178815\pi\) | ||||
0.846318 | + | 0.532679i | \(0.178815\pi\) | |||||||
\(38\) | −5.29052 | −0.858236 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.405813 | 0.0641647 | ||||||||
\(41\) | 0.731250 | 0.114202 | 0.0571010 | − | 0.998368i | \(-0.481814\pi\) | ||||
0.0571010 | + | 0.998368i | \(0.481814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.9390 | −1.82068 | −0.910340 | − | 0.413861i | \(-0.864180\pi\) | ||||
−0.910340 | + | 0.413861i | \(0.864180\pi\) | |||||||
\(44\) | 4.15452 | 0.626318 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.20237 | −0.914490 | ||||||||
\(47\) | −3.44504 | −0.502511 | −0.251256 | − | 0.967921i | \(-0.580843\pi\) | ||||
−0.251256 | + | 0.967921i | \(0.580843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.29590 | 0.327985 | ||||||||
\(50\) | 2.04892 | 0.289761 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.98254 | −1.23385 | −0.616923 | − | 0.787023i | \(-0.711621\pi\) | ||||
−0.616923 | + | 0.787023i | \(0.711621\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.89008 | 0.254859 | ||||||||
\(56\) | −1.23729 | −0.165340 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.77777 | −0.889965 | ||||||||
\(59\) | −1.11529 | −0.145199 | −0.0725994 | − | 0.997361i | \(-0.523129\pi\) | ||||
−0.0725994 | + | 0.997361i | \(0.523129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.75302 | 0.736599 | 0.368299 | − | 0.929707i | \(-0.379940\pi\) | ||||
0.368299 | + | 0.929707i | \(0.379940\pi\) | |||||||
\(62\) | −19.0911 | −2.42458 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.49827 | −1.18728 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5211 | −1.28536 | −0.642679 | − | 0.766136i | \(-0.722177\pi\) | ||||
−0.642679 | + | 0.766136i | \(0.722177\pi\) | |||||||
\(68\) | 9.00730 | 1.09230 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.24698 | −0.746657 | ||||||||
\(71\) | 7.41789 | 0.880342 | 0.440171 | − | 0.897914i | \(-0.354918\pi\) | ||||
0.440171 | + | 0.897914i | \(0.354918\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.2838 | 1.43771 | 0.718856 | − | 0.695159i | \(-0.244666\pi\) | ||||
0.718856 | + | 0.695159i | \(0.244666\pi\) | |||||||
\(74\) | 21.0954 | 2.45230 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.67563 | −0.651039 | ||||||||
\(77\) | −5.76271 | −0.656722 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.71917 | −0.193422 | −0.0967108 | − | 0.995313i | \(-0.530832\pi\) | ||||
−0.0967108 | + | 0.995313i | \(0.530832\pi\) | |||||||
\(80\) | −3.56465 | −0.398540 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.49827 | 0.165456 | ||||||||
\(83\) | −17.8213 | −1.95614 | −0.978072 | − | 0.208268i | \(-0.933217\pi\) | ||||
−0.978072 | + | 0.208268i | \(0.933217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.09783 | 0.444473 | ||||||||
\(86\) | −24.4620 | −2.63781 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.767021 | 0.0817647 | ||||||||
\(89\) | 1.91185 | 0.202656 | 0.101328 | − | 0.994853i | \(-0.467691\pi\) | ||||
0.101328 | + | 0.994853i | \(0.467691\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.65386 | −0.693713 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.05861 | −0.728040 | ||||||||
\(95\) | −2.58211 | −0.264918 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.59179 | 0.770830 | 0.385415 | − | 0.922743i | \(-0.374058\pi\) | ||||
0.385415 | + | 0.922743i | \(0.374058\pi\) | |||||||
\(98\) | 4.70410 | 0.475186 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.19806 | 0.219806 | ||||||||
\(101\) | −1.67696 | −0.166863 | −0.0834317 | − | 0.996513i | \(-0.526588\pi\) | ||||
−0.0834317 | + | 0.996513i | \(0.526588\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4450 | −1.02918 | −0.514590 | − | 0.857436i | \(-0.672056\pi\) | ||||
−0.514590 | + | 0.857436i | \(0.672056\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.4045 | −1.78760 | ||||||||
\(107\) | −15.0194 | −1.45198 | −0.725989 | − | 0.687706i | \(-0.758618\pi\) | ||||
−0.725989 | + | 0.687706i | \(0.758618\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.1957 | 1.35970 | 0.679849 | − | 0.733352i | \(-0.262045\pi\) | ||||
0.679849 | + | 0.733352i | \(0.262045\pi\) | |||||||
\(110\) | 3.87263 | 0.369240 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.8683 | 1.02696 | ||||||||
\(113\) | 15.8388 | 1.48999 | 0.744993 | − | 0.667072i | \(-0.232453\pi\) | ||||
0.744993 | + | 0.667072i | \(0.232453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.02715 | −0.282283 | ||||||||
\(116\) | −7.27114 | −0.675109 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.28514 | −0.210364 | ||||||||
\(119\) | −12.4940 | −1.14532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.42758 | −0.675235 | ||||||||
\(122\) | 11.7875 | 1.06719 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −20.4808 | −1.83923 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.4088 | 1.72225 | 0.861126 | − | 0.508391i | \(-0.169760\pi\) | ||||
0.861126 | + | 0.508391i | \(0.169760\pi\) | |||||||
\(128\) | −3.23059 | −0.285546 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.7168 | −1.89740 | −0.948702 | − | 0.316172i | \(-0.897602\pi\) | ||||
−0.948702 | + | 0.316172i | \(0.897602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.87263 | 0.682643 | ||||||||
\(134\) | −21.5569 | −1.86223 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.66296 | 0.142597 | ||||||||
\(137\) | −12.1806 | −1.04066 | −0.520330 | − | 0.853966i | \(-0.674191\pi\) | ||||
−0.520330 | + | 0.853966i | \(0.674191\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.46681 | −0.802965 | −0.401482 | − | 0.915867i | \(-0.631505\pi\) | ||||
−0.401482 | + | 0.915867i | \(0.631505\pi\) | |||||||
\(140\) | −6.70171 | −0.566398 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.1987 | 1.27544 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.30798 | −0.274713 | ||||||||
\(146\) | 25.1685 | 2.08296 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 22.6310 | 1.86026 | ||||||||
\(149\) | 3.59850 | 0.294800 | 0.147400 | − | 0.989077i | \(-0.452909\pi\) | ||||
0.147400 | + | 0.989077i | \(0.452909\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.52781 | −0.775362 | −0.387681 | − | 0.921794i | \(-0.626724\pi\) | ||||
−0.387681 | + | 0.921794i | \(0.626724\pi\) | |||||||
\(152\) | −1.04785 | −0.0849921 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.8073 | −0.951461 | ||||||||
\(155\) | −9.31767 | −0.748413 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4547 | −1.31323 | −0.656615 | − | 0.754226i | \(-0.728012\pi\) | ||||
−0.656615 | + | 0.754226i | \(0.728012\pi\) | |||||||
\(158\) | −3.52243 | −0.280230 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.11529 | −0.641570 | ||||||||
\(161\) | 9.22952 | 0.727388 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.42758 | 0.346795 | 0.173398 | − | 0.984852i | \(-0.444525\pi\) | ||||
0.173398 | + | 0.984852i | \(0.444525\pi\) | |||||||
\(164\) | 1.60733 | 0.125512 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −36.5144 | −2.83407 | ||||||||
\(167\) | 19.6896 | 1.52363 | 0.761815 | − | 0.647795i | \(-0.224309\pi\) | ||||
0.761815 | + | 0.647795i | \(0.224309\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.39612 | 0.643953 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −26.2427 | −2.00098 | ||||||||
\(173\) | −12.3351 | −0.937822 | −0.468911 | − | 0.883245i | \(-0.655354\pi\) | ||||
−0.468911 | + | 0.883245i | \(0.655354\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.04892 | −0.230476 | ||||||||
\(176\) | −6.73748 | −0.507857 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.91723 | 0.293609 | ||||||||
\(179\) | −7.97823 | −0.596321 | −0.298160 | − | 0.954516i | \(-0.596373\pi\) | ||||
−0.298160 | + | 0.954516i | \(0.596373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.1860 | −0.980106 | −0.490053 | − | 0.871693i | \(-0.663023\pi\) | ||||
−0.490053 | + | 0.871693i | \(0.663023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.22846 | −0.0905630 | ||||||||
\(185\) | 10.2959 | 0.756969 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.74525 | 0.566389 | ||||||||
\(188\) | −7.57242 | −0.552275 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.29052 | −0.383815 | ||||||||
\(191\) | 1.21446 | 0.0878749 | 0.0439375 | − | 0.999034i | \(-0.486010\pi\) | ||||
0.0439375 | + | 0.999034i | \(0.486010\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.32304 | 0.311180 | 0.155590 | − | 0.987822i | \(-0.450272\pi\) | ||||
0.155590 | + | 0.987822i | \(0.450272\pi\) | |||||||
\(194\) | 15.5550 | 1.11678 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.04652 | 0.360466 | ||||||||
\(197\) | −21.0519 | −1.49989 | −0.749943 | − | 0.661503i | \(-0.769919\pi\) | ||||
−0.749943 | + | 0.661503i | \(0.769919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9390 | 0.988110 | 0.494055 | − | 0.869431i | \(-0.335514\pi\) | ||||
0.494055 | + | 0.869431i | \(0.335514\pi\) | |||||||
\(200\) | 0.405813 | 0.0286953 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.43594 | −0.241752 | ||||||||
\(203\) | 10.0858 | 0.707881 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.731250 | 0.0510727 | ||||||||
\(206\) | −21.4010 | −1.49108 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.88040 | −0.337584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.58748 | −0.109287 | −0.0546434 | − | 0.998506i | \(-0.517402\pi\) | ||||
−0.0546434 | + | 0.998506i | \(0.517402\pi\) | |||||||
\(212\) | −19.7442 | −1.35604 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −30.7735 | −2.10363 | ||||||||
\(215\) | −11.9390 | −0.814233 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.4088 | 1.92851 | ||||||||
\(218\) | 29.0858 | 1.96994 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.15452 | 0.280098 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.97285 | −0.600867 | −0.300433 | − | 0.953803i | \(-0.597131\pi\) | ||||
−0.300433 | + | 0.953803i | \(0.597131\pi\) | |||||||
\(224\) | 24.7429 | 1.65320 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 32.4523 | 2.15870 | ||||||||
\(227\) | −20.5090 | −1.36123 | −0.680616 | − | 0.732640i | \(-0.738288\pi\) | ||||
−0.680616 | + | 0.732640i | \(0.738288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.46442 | −0.427181 | −0.213590 | − | 0.976923i | \(-0.568516\pi\) | ||||
−0.213590 | + | 0.976923i | \(0.568516\pi\) | |||||||
\(230\) | −6.20237 | −0.408972 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.34242 | −0.0881343 | ||||||||
\(233\) | −8.01208 | −0.524889 | −0.262444 | − | 0.964947i | \(-0.584529\pi\) | ||||
−0.262444 | + | 0.964947i | \(0.584529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.44504 | −0.224730 | ||||||||
\(236\) | −2.45148 | −0.159578 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −25.5991 | −1.65934 | ||||||||
\(239\) | −28.3099 | −1.83122 | −0.915608 | − | 0.402073i | \(-0.868290\pi\) | ||||
−0.915608 | + | 0.402073i | \(0.868290\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5187 | 1.06406 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(242\) | −15.2185 | −0.978283 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6455 | 0.809545 | ||||||||
\(245\) | 2.29590 | 0.146679 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.78123 | −0.240108 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.04892 | 0.129585 | ||||||||
\(251\) | 21.0398 | 1.32802 | 0.664011 | − | 0.747723i | \(-0.268853\pi\) | ||||
0.664011 | + | 0.747723i | \(0.268853\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.72156 | −0.359711 | ||||||||
\(254\) | 39.7670 | 2.49520 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.3773 | 0.773584 | ||||||||
\(257\) | −6.96615 | −0.434536 | −0.217268 | − | 0.976112i | \(-0.569715\pi\) | ||||
−0.217268 | + | 0.976112i | \(0.569715\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.3913 | −1.95056 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −44.4959 | −2.74896 | ||||||||
\(263\) | 16.2543 | 1.00228 | 0.501141 | − | 0.865366i | \(-0.332914\pi\) | ||||
0.501141 | + | 0.865366i | \(0.332914\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.98254 | −0.551793 | ||||||||
\(266\) | 16.1304 | 0.989016 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.1260 | −1.41265 | ||||||||
\(269\) | −16.6679 | −1.01626 | −0.508129 | − | 0.861281i | \(-0.669663\pi\) | ||||
−0.508129 | + | 0.861281i | \(0.669663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.91185 | 0.419865 | 0.209933 | − | 0.977716i | \(-0.432676\pi\) | ||||
0.209933 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(272\) | −14.6073 | −0.885700 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.9571 | −1.50771 | ||||||||
\(275\) | 1.89008 | 0.113976 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1400 | 0.669341 | 0.334670 | − | 0.942335i | \(-0.391375\pi\) | ||||
0.334670 | + | 0.942335i | \(0.391375\pi\) | |||||||
\(278\) | −19.3967 | −1.16334 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.23729 | −0.0739423 | ||||||||
\(281\) | −0.552565 | −0.0329633 | −0.0164816 | − | 0.999864i | \(-0.505247\pi\) | ||||
−0.0164816 | + | 0.999864i | \(0.505247\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.2591 | 1.02594 | 0.512972 | − | 0.858405i | \(-0.328544\pi\) | ||||
0.512972 | + | 0.858405i | \(0.328544\pi\) | |||||||
\(284\) | 16.3050 | 0.967523 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.22952 | −0.131604 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.207751 | −0.0122206 | ||||||||
\(290\) | −6.77777 | −0.398005 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 27.0006 | 1.58009 | ||||||||
\(293\) | −32.7560 | −1.91363 | −0.956813 | − | 0.290704i | \(-0.906111\pi\) | ||||
−0.956813 | + | 0.290704i | \(0.906111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.11529 | −0.0649349 | ||||||||
\(296\) | 4.17821 | 0.242854 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.37303 | 0.427108 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.4010 | 2.09812 | ||||||||
\(302\) | −19.5217 | −1.12335 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.20429 | 0.527902 | ||||||||
\(305\) | 5.75302 | 0.329417 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.07069 | −0.403545 | −0.201773 | − | 0.979432i | \(-0.564670\pi\) | ||||
−0.201773 | + | 0.979432i | \(0.564670\pi\) | |||||||
\(308\) | −12.6668 | −0.721758 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.0911 | −1.08430 | ||||||||
\(311\) | −12.9366 | −0.733568 | −0.366784 | − | 0.930306i | \(-0.619541\pi\) | ||||
−0.366784 | + | 0.930306i | \(0.619541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.6353 | 1.44899 | 0.724497 | − | 0.689278i | \(-0.242072\pi\) | ||||
0.724497 | + | 0.689278i | \(0.242072\pi\) | |||||||
\(314\) | −33.7144 | −1.90261 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.77884 | −0.212576 | ||||||||
\(317\) | 11.8998 | 0.668358 | 0.334179 | − | 0.942510i | \(-0.391541\pi\) | ||||
0.334179 | + | 0.942510i | \(0.391541\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.25236 | −0.350065 | ||||||||
\(320\) | −9.49827 | −0.530969 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.9105 | 1.05384 | ||||||||
\(323\) | −10.5810 | −0.588745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.07175 | 0.502438 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.296751 | 0.0163853 | ||||||||
\(329\) | 10.5036 | 0.579085 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.2989 | 1.88524 | 0.942618 | − | 0.333872i | \(-0.108355\pi\) | ||||
0.942618 | + | 0.333872i | \(0.108355\pi\) | |||||||
\(332\) | −39.1724 | −2.14986 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 40.3424 | 2.20744 | ||||||||
\(335\) | −10.5211 | −0.574829 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.1142 | 0.714378 | 0.357189 | − | 0.934032i | \(-0.383735\pi\) | ||||
0.357189 | + | 0.934032i | \(0.383735\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.00730 | 0.488489 | ||||||||
\(341\) | −17.6112 | −0.953698 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.3424 | 0.774418 | ||||||||
\(344\) | −4.84500 | −0.261225 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.2737 | −1.35872 | ||||||||
\(347\) | −2.91723 | −0.156605 | −0.0783026 | − | 0.996930i | \(-0.524950\pi\) | ||||
−0.0783026 | + | 0.996930i | \(0.524950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.56465 | −0.511984 | −0.255992 | − | 0.966679i | \(-0.582402\pi\) | ||||
−0.255992 | + | 0.966679i | \(0.582402\pi\) | |||||||
\(350\) | −6.24698 | −0.333915 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.3386 | −0.817549 | ||||||||
\(353\) | −18.2198 | −0.969744 | −0.484872 | − | 0.874585i | \(-0.661134\pi\) | ||||
−0.484872 | + | 0.874585i | \(0.661134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.41789 | 0.393701 | ||||||||
\(356\) | 4.20237 | 0.222725 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.3467 | −0.863952 | ||||||||
\(359\) | 15.9041 | 0.839385 | 0.419693 | − | 0.907666i | \(-0.362138\pi\) | ||||
0.419693 | + | 0.907666i | \(0.362138\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3327 | −0.649091 | ||||||||
\(362\) | −27.0170 | −1.41998 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.2838 | 0.642964 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.45712 | 0.180460 | 0.0902302 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902302 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(368\) | 10.7907 | 0.562505 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.0954 | 1.09670 | ||||||||
\(371\) | 27.3870 | 1.42186 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.2731 | −0.894365 | −0.447183 | − | 0.894443i | \(-0.647573\pi\) | ||||
−0.447183 | + | 0.894443i | \(0.647573\pi\) | |||||||
\(374\) | 15.8694 | 0.820586 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.39804 | −0.0720986 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.9028 | 0.970969 | 0.485485 | − | 0.874245i | \(-0.338643\pi\) | ||||
0.485485 | + | 0.874245i | \(0.338643\pi\) | |||||||
\(380\) | −5.67563 | −0.291154 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.48832 | 0.127313 | ||||||||
\(383\) | 9.97046 | 0.509467 | 0.254733 | − | 0.967011i | \(-0.418012\pi\) | ||||
0.254733 | + | 0.967011i | \(0.418012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.76271 | −0.293695 | ||||||||
\(386\) | 8.85756 | 0.450838 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.6872 | 0.847166 | ||||||||
\(389\) | 21.4166 | 1.08586 | 0.542932 | − | 0.839777i | \(-0.317314\pi\) | ||||
0.542932 | + | 0.839777i | \(0.317314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.4047 | −0.627335 | ||||||||
\(392\) | 0.931705 | 0.0470582 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −43.1336 | −2.17304 | ||||||||
\(395\) | −1.71917 | −0.0865008 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.4566 | 1.72933 | 0.864665 | − | 0.502349i | \(-0.167531\pi\) | ||||
0.864665 | + | 0.502349i | \(0.167531\pi\) | |||||||
\(398\) | 28.5599 | 1.43158 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.56465 | −0.178232 | ||||||||
\(401\) | −0.799545 | −0.0399274 | −0.0199637 | − | 0.999801i | \(-0.506355\pi\) | ||||
−0.0199637 | + | 0.999801i | \(0.506355\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.68605 | −0.183388 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.6649 | 1.02558 | ||||||||
\(407\) | 19.4601 | 0.964602 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.5351 | 1.65820 | 0.829102 | − | 0.559097i | \(-0.188852\pi\) | ||||
0.829102 | + | 0.559097i | \(0.188852\pi\) | |||||||
\(410\) | 1.49827 | 0.0739943 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.9589 | −1.13110 | ||||||||
\(413\) | 3.40044 | 0.167325 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.8213 | −0.874814 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.99953 | −0.489093 | ||||||||
\(419\) | 7.98361 | 0.390025 | 0.195012 | − | 0.980801i | \(-0.437525\pi\) | ||||
0.195012 | + | 0.980801i | \(0.437525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.4413 | −1.38615 | −0.693073 | − | 0.720868i | \(-0.743743\pi\) | ||||
−0.693073 | + | 0.720868i | \(0.743743\pi\) | |||||||
\(422\) | −3.25262 | −0.158335 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.64523 | −0.177028 | ||||||||
\(425\) | 4.09783 | 0.198774 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.5405 | −0.848843 | ||||||||
\(428\) | −33.0135 | −1.59577 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.4620 | −1.17966 | ||||||||
\(431\) | 6.27844 | 0.302422 | 0.151211 | − | 0.988502i | \(-0.451683\pi\) | ||||
0.151211 | + | 0.988502i | \(0.451683\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.30367 | 0.254878 | 0.127439 | − | 0.991846i | \(-0.459324\pi\) | ||||
0.127439 | + | 0.991846i | \(0.459324\pi\) | |||||||
\(434\) | 58.2073 | 2.79404 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31.2030 | 1.49435 | ||||||||
\(437\) | 7.81641 | 0.373910 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.52542 | 0.406896 | 0.203448 | − | 0.979086i | \(-0.434785\pi\) | ||||
0.203448 | + | 0.979086i | \(0.434785\pi\) | |||||||
\(440\) | 0.767021 | 0.0365663 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.1575 | 1.05273 | 0.526367 | − | 0.850257i | \(-0.323554\pi\) | ||||
0.526367 | + | 0.850257i | \(0.323554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.91185 | 0.0906306 | ||||||||
\(446\) | −18.3846 | −0.870538 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 28.9594 | 1.36821 | ||||||||
\(449\) | 21.4873 | 1.01405 | 0.507023 | − | 0.861932i | \(-0.330746\pi\) | ||||
0.507023 | + | 0.861932i | \(0.330746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.38212 | 0.0650817 | ||||||||
\(452\) | 34.8146 | 1.63754 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −42.0213 | −1.97216 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.8267 | −1.25490 | −0.627450 | − | 0.778657i | \(-0.715901\pi\) | ||||
−0.627450 | + | 0.778657i | \(0.715901\pi\) | |||||||
\(458\) | −13.2451 | −0.618901 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.65386 | −0.310238 | ||||||||
\(461\) | 13.5864 | 0.632783 | 0.316391 | − | 0.948629i | \(-0.397529\pi\) | ||||
0.316391 | + | 0.948629i | \(0.397529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0664 | 0.607246 | 0.303623 | − | 0.952792i | \(-0.401804\pi\) | ||||
0.303623 | + | 0.952792i | \(0.401804\pi\) | |||||||
\(464\) | 11.7918 | 0.547419 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.4161 | −0.760461 | ||||||||
\(467\) | −19.4470 | −0.899898 | −0.449949 | − | 0.893054i | \(-0.648558\pi\) | ||||
−0.449949 | + | 0.893054i | \(0.648558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0780 | 1.48122 | ||||||||
\(470\) | −7.05861 | −0.325589 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.452601 | −0.0208326 | ||||||||
\(473\) | −22.5657 | −1.03757 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.58211 | −0.118475 | ||||||||
\(476\) | −27.4625 | −1.25874 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −58.0046 | −2.65307 | ||||||||
\(479\) | 28.2543 | 1.29097 | 0.645485 | − | 0.763773i | \(-0.276655\pi\) | ||||
0.645485 | + | 0.763773i | \(0.276655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 33.8455 | 1.54162 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.3263 | −0.742104 | ||||||||
\(485\) | 7.59179 | 0.344726 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.38298 | −0.379869 | −0.189934 | − | 0.981797i | \(-0.560828\pi\) | ||||
−0.189934 | + | 0.981797i | \(0.560828\pi\) | |||||||
\(488\) | 2.33465 | 0.105685 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.70410 | 0.212510 | ||||||||
\(491\) | −19.5550 | −0.882503 | −0.441251 | − | 0.897384i | \(-0.645465\pi\) | ||||
−0.441251 | + | 0.897384i | \(0.645465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5555 | −0.610511 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 33.2142 | 1.49136 | ||||||||
\(497\) | −22.6165 | −1.01449 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.90217 | 0.353750 | 0.176875 | − | 0.984233i | \(-0.443401\pi\) | ||||
0.176875 | + | 0.984233i | \(0.443401\pi\) | |||||||
\(500\) | 2.19806 | 0.0983003 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 43.1089 | 1.92404 | ||||||||
\(503\) | 1.15346 | 0.0514301 | 0.0257150 | − | 0.999669i | \(-0.491814\pi\) | ||||
0.0257150 | + | 0.999669i | \(0.491814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.67696 | −0.0746236 | ||||||||
\(506\) | −11.7230 | −0.521151 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 42.6617 | 1.89281 | ||||||||
\(509\) | 15.0887 | 0.668797 | 0.334398 | − | 0.942432i | \(-0.391467\pi\) | ||||
0.334398 | + | 0.942432i | \(0.391467\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.4523 | −1.65679 | ||||||||
\(512\) | 31.8213 | 1.40632 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.2731 | −0.629558 | ||||||||
\(515\) | −10.4450 | −0.460264 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.51142 | −0.286372 | ||||||||
\(518\) | −64.3183 | −2.82598 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.0610 | −0.835078 | −0.417539 | − | 0.908659i | \(-0.637107\pi\) | ||||
−0.417539 | + | 0.908659i | \(0.637107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8984 | −0.957552 | −0.478776 | − | 0.877937i | \(-0.658919\pi\) | ||||
−0.478776 | + | 0.877937i | \(0.658919\pi\) | |||||||
\(524\) | −47.7348 | −2.08531 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 33.3037 | 1.45211 | ||||||||
\(527\) | −38.1823 | −1.66325 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.8364 | −0.601582 | ||||||||
\(530\) | −18.4045 | −0.799440 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.3045 | 0.750246 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0194 | −0.649344 | ||||||||
\(536\) | −4.26960 | −0.184419 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.1511 | −1.47236 | ||||||||
\(539\) | 4.33944 | 0.186913 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.8345 | −1.19670 | −0.598348 | − | 0.801236i | \(-0.704176\pi\) | ||||
−0.598348 | + | 0.801236i | \(0.704176\pi\) | |||||||
\(542\) | 14.1618 | 0.608302 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −33.2551 | −1.42580 | ||||||||
\(545\) | 14.1957 | 0.608076 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.0810 | 1.84201 | 0.921005 | − | 0.389552i | \(-0.127370\pi\) | ||||
0.921005 | + | 0.389552i | \(0.127370\pi\) | |||||||
\(548\) | −26.7737 | −1.14372 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.87263 | 0.165129 | ||||||||
\(551\) | 8.54155 | 0.363882 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.24160 | 0.222896 | ||||||||
\(554\) | 22.8250 | 0.969743 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.8086 | −0.882483 | ||||||||
\(557\) | 3.77346 | 0.159887 | 0.0799434 | − | 0.996799i | \(-0.474526\pi\) | ||||
0.0799434 | + | 0.996799i | \(0.474526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.8683 | 0.459270 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.13216 | −0.0477573 | ||||||||
\(563\) | −37.6708 | −1.58764 | −0.793818 | − | 0.608155i | \(-0.791910\pi\) | ||||
−0.793818 | + | 0.608155i | \(0.791910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.8388 | 0.666342 | ||||||||
\(566\) | 35.3624 | 1.48639 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.01028 | 0.126309 | ||||||||
\(569\) | 9.10513 | 0.381707 | 0.190853 | − | 0.981619i | \(-0.438874\pi\) | ||||
0.190853 | + | 0.981619i | \(0.438874\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.8334 | −0.913699 | −0.456850 | − | 0.889544i | \(-0.651022\pi\) | ||||
−0.456850 | + | 0.889544i | \(0.651022\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.56810 | −0.190669 | ||||||||
\(575\) | −3.02715 | −0.126241 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.56465 | −0.273290 | −0.136645 | − | 0.990620i | \(-0.543632\pi\) | ||||
−0.136645 | + | 0.990620i | \(0.543632\pi\) | |||||||
\(578\) | −0.425665 | −0.0177053 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.27114 | −0.301918 | ||||||||
\(581\) | 54.3357 | 2.25423 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9778 | −0.703147 | ||||||||
\(584\) | 4.98493 | 0.206278 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −67.1143 | −2.77247 | ||||||||
\(587\) | 31.8157 | 1.31317 | 0.656587 | − | 0.754251i | \(-0.272000\pi\) | ||||
0.656587 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0592 | 0.991342 | ||||||||
\(590\) | −2.28514 | −0.0940779 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −36.7012 | −1.50841 | ||||||||
\(593\) | 14.6752 | 0.602636 | 0.301318 | − | 0.953524i | \(-0.402573\pi\) | ||||
0.301318 | + | 0.953524i | \(0.402573\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.4940 | −0.512202 | ||||||||
\(596\) | 7.90972 | 0.323995 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.9705 | 0.652535 | 0.326268 | − | 0.945277i | \(-0.394209\pi\) | ||||
0.326268 | + | 0.945277i | \(0.394209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.9729 | 1.22262 | 0.611309 | − | 0.791392i | \(-0.290643\pi\) | ||||
0.611309 | + | 0.791392i | \(0.290643\pi\) | |||||||
\(602\) | 74.5827 | 3.03976 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.9427 | −0.852147 | ||||||||
\(605\) | −7.42758 | −0.301974 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.4204 | 1.76238 | 0.881190 | − | 0.472762i | \(-0.156743\pi\) | ||||
0.881190 | + | 0.472762i | \(0.156743\pi\) | |||||||
\(608\) | 20.9545 | 0.849819 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.7875 | 0.477260 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.2983 | −0.819840 | −0.409920 | − | 0.912121i | \(-0.634443\pi\) | ||||
−0.409920 | + | 0.912121i | \(0.634443\pi\) | |||||||
\(614\) | −14.4873 | −0.584658 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.33858 | −0.0942242 | ||||||||
\(617\) | 34.8039 | 1.40115 | 0.700575 | − | 0.713579i | \(-0.252927\pi\) | ||||
0.700575 | + | 0.713579i | \(0.252927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.5026 | 0.944649 | 0.472324 | − | 0.881425i | \(-0.343415\pi\) | ||||
0.472324 | + | 0.881425i | \(0.343415\pi\) | |||||||
\(620\) | −20.4808 | −0.822529 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.5060 | −1.06280 | ||||||||
\(623\) | −5.82908 | −0.233537 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 52.5247 | 2.09931 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.1685 | −1.44328 | ||||||||
\(629\) | 42.1909 | 1.68226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.80971 | 0.390518 | 0.195259 | − | 0.980752i | \(-0.437445\pi\) | ||||
0.195259 | + | 0.980752i | \(0.437445\pi\) | |||||||
\(632\) | −0.697661 | −0.0277515 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.3817 | 0.968319 | ||||||||
\(635\) | 19.4088 | 0.770215 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −12.8106 | −0.507175 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.23059 | −0.127700 | ||||||||
\(641\) | 1.23968 | 0.0489646 | 0.0244823 | − | 0.999700i | \(-0.492206\pi\) | ||||
0.0244823 | + | 0.999700i | \(0.492206\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.61596 | 0.142599 | 0.0712997 | − | 0.997455i | \(-0.477285\pi\) | ||||
0.0712997 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(644\) | 20.2871 | 0.799422 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.6797 | −0.852975 | ||||||||
\(647\) | 21.5241 | 0.846199 | 0.423100 | − | 0.906083i | \(-0.360942\pi\) | ||||
0.423100 | + | 0.906083i | \(0.360942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.10800 | −0.0827461 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.73210 | 0.381139 | ||||||||
\(653\) | −33.6069 | −1.31514 | −0.657569 | − | 0.753394i | \(-0.728415\pi\) | ||||
−0.657569 | + | 0.753394i | \(0.728415\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.7168 | −0.848545 | ||||||||
\(656\) | −2.60665 | −0.101773 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.5211 | 0.838980 | ||||||||
\(659\) | 20.0441 | 0.780809 | 0.390404 | − | 0.920644i | \(-0.372335\pi\) | ||||
0.390404 | + | 0.920644i | \(0.372335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.1847 | 0.940674 | 0.470337 | − | 0.882487i | \(-0.344132\pi\) | ||||
0.470337 | + | 0.882487i | \(0.344132\pi\) | |||||||
\(662\) | 70.2756 | 2.73134 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.23213 | −0.280661 | ||||||||
\(665\) | 7.87263 | 0.305287 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0137 | 0.387733 | ||||||||
\(668\) | 43.2790 | 1.67452 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.5569 | −0.832815 | ||||||||
\(671\) | 10.8737 | 0.419774 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.8963 | −1.69208 | −0.846039 | − | 0.533121i | \(-0.821019\pi\) | ||||
−0.846039 | + | 0.533121i | \(0.821019\pi\) | |||||||
\(674\) | 26.8700 | 1.03499 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.4698 | −0.402387 | −0.201193 | − | 0.979552i | \(-0.564482\pi\) | ||||
−0.201193 | + | 0.979552i | \(0.564482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.1468 | −0.888291 | ||||||||
\(680\) | 1.66296 | 0.0637714 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −36.0838 | −1.38172 | ||||||||
\(683\) | 2.15883 | 0.0826055 | 0.0413027 | − | 0.999147i | \(-0.486849\pi\) | ||||
0.0413027 | + | 0.999147i | \(0.486849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.1806 | −0.465397 | ||||||||
\(686\) | 29.3864 | 1.12198 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 42.5583 | 1.62252 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.86294 | 0.146953 | 0.0734765 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734765 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(692\) | −27.1134 | −1.03070 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.97716 | −0.226890 | ||||||||
\(695\) | −9.46681 | −0.359097 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.99654 | 0.113502 | ||||||||
\(698\) | −19.5972 | −0.741764 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.70171 | −0.253301 | ||||||||
\(701\) | 23.5733 | 0.890350 | 0.445175 | − | 0.895444i | \(-0.353141\pi\) | ||||
0.445175 | + | 0.895444i | \(0.353141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.5851 | −1.00268 | ||||||||
\(704\) | −17.9525 | −0.676611 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −37.3309 | −1.40497 | ||||||||
\(707\) | 5.11290 | 0.192290 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.1454 | 0.681466 | 0.340733 | − | 0.940160i | \(-0.389325\pi\) | ||||
0.340733 | + | 0.940160i | \(0.389325\pi\) | |||||||
\(710\) | 15.1987 | 0.570395 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.775856 | 0.0290764 | ||||||||
\(713\) | 28.2059 | 1.05632 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.5366 | −0.655375 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.5862 | 1.21610 | ||||||||
\(719\) | 28.7821 | 1.07339 | 0.536695 | − | 0.843776i | \(-0.319672\pi\) | ||||
0.536695 | + | 0.843776i | \(0.319672\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.8461 | 1.18601 | ||||||||
\(722\) | −25.2687 | −0.940405 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28.9836 | −1.07717 | ||||||||
\(725\) | −3.30798 | −0.122855 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.2107 | −1.04628 | −0.523139 | − | 0.852247i | \(-0.675239\pi\) | ||||
−0.523139 | + | 0.852247i | \(0.675239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 25.1685 | 0.931529 | ||||||||
\(731\) | −48.9241 | −1.80952 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.81833 | 0.0671616 | 0.0335808 | − | 0.999436i | \(-0.489309\pi\) | ||||
0.0335808 | + | 0.999436i | \(0.489309\pi\) | |||||||
\(734\) | 7.08336 | 0.261452 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24.5662 | 0.905522 | ||||||||
\(737\) | −19.8858 | −0.732502 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0707 | −0.517599 | −0.258799 | − | 0.965931i | \(-0.583327\pi\) | ||||
−0.258799 | + | 0.965931i | \(0.583327\pi\) | |||||||
\(740\) | 22.6310 | 0.831933 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 56.1138 | 2.06000 | ||||||||
\(743\) | 48.5599 | 1.78149 | 0.890744 | − | 0.454505i | \(-0.150184\pi\) | ||||
0.890744 | + | 0.454505i | \(0.150184\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.59850 | 0.131839 | ||||||||
\(746\) | −35.3911 | −1.29576 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.0245 | 0.622479 | ||||||||
\(749\) | 45.7928 | 1.67323 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0175 | −0.657466 | −0.328733 | − | 0.944423i | \(-0.606622\pi\) | ||||
−0.328733 | + | 0.944423i | \(0.606622\pi\) | |||||||
\(752\) | 12.2804 | 0.447819 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.52781 | −0.346753 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.0455 | −1.56451 | −0.782257 | − | 0.622956i | \(-0.785932\pi\) | ||||
−0.782257 | + | 0.622956i | \(0.785932\pi\) | |||||||
\(758\) | 38.7302 | 1.40674 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.04785 | −0.0380096 | ||||||||
\(761\) | 18.7730 | 0.680520 | 0.340260 | − | 0.940331i | \(-0.389485\pi\) | ||||
0.340260 | + | 0.940331i | \(0.389485\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.2814 | −1.56689 | ||||||||
\(764\) | 2.66945 | 0.0965773 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.4286 | 0.738117 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.57481 | 0.0567891 | 0.0283945 | − | 0.999597i | \(-0.490961\pi\) | ||||
0.0283945 | + | 0.999597i | \(0.490961\pi\) | |||||||
\(770\) | −11.8073 | −0.425506 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.50232 | 0.341996 | ||||||||
\(773\) | −8.51706 | −0.306337 | −0.153169 | − | 0.988200i | \(-0.548948\pi\) | ||||
−0.153169 | + | 0.988200i | \(0.548948\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.31767 | −0.334700 | ||||||||
\(776\) | 3.08085 | 0.110596 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 43.8808 | 1.57320 | ||||||||
\(779\) | −1.88816 | −0.0676505 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0204 | 0.501691 | ||||||||
\(782\) | −25.4163 | −0.908885 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.18406 | −0.292288 | ||||||||
\(785\) | −16.4547 | −0.587295 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4421 | −0.586096 | −0.293048 | − | 0.956098i | \(-0.594670\pi\) | ||||
−0.293048 | + | 0.956098i | \(0.594670\pi\) | |||||||
\(788\) | −46.2734 | −1.64842 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.52243 | −0.125323 | ||||||||
\(791\) | −48.2911 | −1.71703 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 70.5988 | 2.50546 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30.6388 | 1.08596 | ||||||||
\(797\) | −6.18359 | −0.219034 | −0.109517 | − | 0.993985i | \(-0.534930\pi\) | ||||
−0.109517 | + | 0.993985i | \(0.534930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.1172 | −0.499431 | ||||||||
\(800\) | −8.11529 | −0.286919 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.63820 | −0.0578469 | ||||||||
\(803\) | 23.2174 | 0.819326 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.22952 | 0.325298 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.680531 | −0.0239410 | ||||||||
\(809\) | −36.9517 | −1.29915 | −0.649576 | − | 0.760297i | \(-0.725053\pi\) | ||||
−0.649576 | + | 0.760297i | \(0.725053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.54958 | 0.159757 | 0.0798787 | − | 0.996805i | \(-0.474547\pi\) | ||||
0.0798787 | + | 0.996805i | \(0.474547\pi\) | |||||||
\(812\) | 22.1691 | 0.777983 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 39.8722 | 1.39752 | ||||||||
\(815\) | 4.42758 | 0.155091 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.8278 | 1.07853 | ||||||||
\(818\) | 68.7107 | 2.40241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.60733 | 0.0561305 | ||||||||
\(821\) | 46.9288 | 1.63783 | 0.818914 | − | 0.573916i | \(-0.194577\pi\) | ||||
0.818914 | + | 0.573916i | \(0.194577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.07739 | 0.107271 | 0.0536356 | − | 0.998561i | \(-0.482919\pi\) | ||||
0.0536356 | + | 0.998561i | \(0.482919\pi\) | |||||||
\(824\) | −4.23874 | −0.147663 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.96721 | 0.242420 | ||||||||
\(827\) | 55.1353 | 1.91724 | 0.958620 | − | 0.284687i | \(-0.0918898\pi\) | ||||
0.958620 | + | 0.284687i | \(0.0918898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.0853 | 1.63534 | 0.817670 | − | 0.575688i | \(-0.195266\pi\) | ||||
0.817670 | + | 0.575688i | \(0.195266\pi\) | |||||||
\(830\) | −36.5144 | −1.26743 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.40821 | 0.325975 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.6896 | 0.681388 | ||||||||
\(836\) | −10.7274 | −0.371015 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.3577 | 0.565069 | ||||||||
\(839\) | 40.2127 | 1.38829 | 0.694147 | − | 0.719833i | \(-0.255782\pi\) | ||||
0.694147 | + | 0.719833i | \(0.255782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.0573 | −0.622665 | ||||||||
\(842\) | −58.2739 | −2.00825 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.48938 | −0.120110 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.6461 | 0.778129 | ||||||||
\(848\) | 32.0196 | 1.09956 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.39612 | 0.287985 | ||||||||
\(851\) | −31.1672 | −1.06840 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.3526 | 0.628381 | 0.314190 | − | 0.949360i | \(-0.398267\pi\) | ||||
0.314190 | + | 0.949360i | \(0.398267\pi\) | |||||||
\(854\) | −35.9390 | −1.22981 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.09506 | −0.208325 | ||||||||
\(857\) | −10.1787 | −0.347697 | −0.173849 | − | 0.984772i | \(-0.555620\pi\) | ||||
−0.173849 | + | 0.984772i | \(0.555620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.1532 | 0.346423 | 0.173211 | − | 0.984885i | \(-0.444586\pi\) | ||||
0.173211 | + | 0.984885i | \(0.444586\pi\) | |||||||
\(860\) | −26.2427 | −0.894868 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.8640 | 0.438150 | ||||||||
\(863\) | −28.6088 | −0.973854 | −0.486927 | − | 0.873443i | \(-0.661882\pi\) | ||||
−0.486927 | + | 0.873443i | \(0.661882\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.3351 | −0.419407 | ||||||||
\(866\) | 10.8668 | 0.369268 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 62.4443 | 2.11950 | ||||||||
\(869\) | −3.24937 | −0.110227 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.76079 | 0.195085 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.0152 | 0.541722 | ||||||||
\(875\) | −3.04892 | −0.103072 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.0157 | −1.75644 | −0.878222 | − | 0.478253i | \(-0.841270\pi\) | ||||
−0.878222 | + | 0.478253i | \(0.841270\pi\) | |||||||
\(878\) | 17.4679 | 0.589512 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.73748 | −0.227120 | ||||||||
\(881\) | −57.2978 | −1.93041 | −0.965206 | − | 0.261490i | \(-0.915786\pi\) | ||||
−0.965206 | + | 0.261490i | \(0.915786\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.7730 | −0.732719 | −0.366360 | − | 0.930473i | \(-0.619396\pi\) | ||||
−0.366360 | + | 0.930473i | \(0.619396\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.3989 | 1.52521 | ||||||||
\(887\) | 8.35988 | 0.280697 | 0.140349 | − | 0.990102i | \(-0.455178\pi\) | ||||
0.140349 | + | 0.990102i | \(0.455178\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.1758 | −1.98469 | ||||||||
\(890\) | 3.91723 | 0.131306 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.7229 | −0.660371 | ||||||||
\(893\) | 8.89546 | 0.297675 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.97823 | −0.266683 | ||||||||
\(896\) | 9.84979 | 0.329058 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 44.0256 | 1.46915 | ||||||||
\(899\) | 30.8226 | 1.02799 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.8090 | −1.22628 | ||||||||
\(902\) | 2.83186 | 0.0942906 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.42758 | 0.213778 | ||||||||
\(905\) | −13.1860 | −0.438317 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.9168 | 0.827347 | 0.413674 | − | 0.910425i | \(-0.364245\pi\) | ||||
0.413674 | + | 0.910425i | \(0.364245\pi\) | |||||||
\(908\) | −45.0801 | −1.49604 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.4064 | −0.908015 | −0.454007 | − | 0.890998i | \(-0.650006\pi\) | ||||
−0.454007 | + | 0.890998i | \(0.650006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.6838 | −1.11477 | ||||||||
\(914\) | −54.9657 | −1.81810 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.2092 | −0.469485 | ||||||||
\(917\) | 66.2127 | 2.18653 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.7434 | 1.50894 | 0.754469 | − | 0.656336i | \(-0.227895\pi\) | ||||
0.754469 | + | 0.656336i | \(0.227895\pi\) | |||||||
\(920\) | −1.22846 | −0.0405010 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.8374 | 0.916777 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.2959 | 0.338527 | ||||||||
\(926\) | 26.7719 | 0.879780 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.8452 | 0.881237 | ||||||||
\(929\) | −15.0301 | −0.493123 | −0.246561 | − | 0.969127i | \(-0.579301\pi\) | ||||
−0.246561 | + | 0.969127i | \(0.579301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.92825 | −0.194290 | ||||||||
\(932\) | −17.6111 | −0.576869 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −39.8452 | −1.30378 | ||||||||
\(935\) | 7.74525 | 0.253297 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.1377 | −0.788543 | −0.394271 | − | 0.918994i | \(-0.629003\pi\) | ||||
−0.394271 | + | 0.918994i | \(0.629003\pi\) | |||||||
\(938\) | 65.7251 | 2.14600 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.57242 | −0.246985 | ||||||||
\(941\) | 6.97344 | 0.227328 | 0.113664 | − | 0.993519i | \(-0.463741\pi\) | ||||
0.113664 | + | 0.993519i | \(0.463741\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.21360 | −0.0720848 | ||||||||
\(944\) | 3.97563 | 0.129396 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46.2353 | −1.50324 | ||||||||
\(947\) | −11.3951 | −0.370290 | −0.185145 | − | 0.982711i | \(-0.559275\pi\) | ||||
−0.185145 | + | 0.982711i | \(0.559275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −5.29052 | −0.171647 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.07021 | −0.164327 | ||||||||
\(953\) | −30.4198 | −0.985394 | −0.492697 | − | 0.870201i | \(-0.663989\pi\) | ||||
−0.492697 | + | 0.870201i | \(0.663989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.21446 | 0.0392989 | ||||||||
\(956\) | −62.2269 | −2.01256 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 57.8907 | 1.87036 | ||||||||
\(959\) | 37.1377 | 1.19924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.8189 | 1.80061 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 36.3092 | 1.16944 | ||||||||
\(965\) | 4.32304 | 0.139164 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.3019 | 1.00660 | 0.503300 | − | 0.864112i | \(-0.332119\pi\) | ||||
0.503300 | + | 0.864112i | \(0.332119\pi\) | |||||||
\(968\) | −3.01421 | −0.0968804 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.5550 | 0.499440 | ||||||||
\(971\) | −58.7502 | −1.88538 | −0.942691 | − | 0.333667i | \(-0.891714\pi\) | ||||
−0.942691 | + | 0.333667i | \(0.891714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.8635 | 0.925322 | ||||||||
\(974\) | −17.1760 | −0.550355 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.5075 | −0.656429 | ||||||||
\(977\) | −60.2737 | −1.92832 | −0.964162 | − | 0.265312i | \(-0.914525\pi\) | ||||
−0.964162 | + | 0.265312i | \(0.914525\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.61356 | 0.115490 | ||||||||
\(980\) | 5.04652 | 0.161205 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −40.0665 | −1.27857 | ||||||||
\(983\) | 10.0030 | 0.319046 | 0.159523 | − | 0.987194i | \(-0.449004\pi\) | ||||
0.159523 | + | 0.987194i | \(0.449004\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.0519 | −0.670769 | ||||||||
\(986\) | −27.7742 | −0.884511 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.1411 | 1.14922 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7178 | −1.19815 | −0.599073 | − | 0.800694i | \(-0.704464\pi\) | ||||
−0.599073 | + | 0.800694i | \(0.704464\pi\) | |||||||
\(992\) | 75.6156 | 2.40080 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −46.3394 | −1.46980 | ||||||||
\(995\) | 13.9390 | 0.441896 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0388 | −0.539623 | −0.269811 | − | 0.962913i | \(-0.586961\pi\) | ||||
−0.269811 | + | 0.962913i | \(0.586961\pi\) | |||||||
\(998\) | 16.1909 | 0.512513 | ||||||||
\(999\) | 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 | 7605.2.a.bm.1.3 | 3 | ||
3.2 | odd | 2 | 2535.2.a.bh.1.1 | yes | 3 | ||
13.12 | even | 2 | 7605.2.a.ce.1.1 | 3 | |||
39.38 | odd | 2 | 2535.2.a.t.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2535.2.a.t.1.3 | ✓ | 3 | 39.38 | odd | 2 | ||
2535.2.a.bh.1.1 | yes | 3 | 3.2 | odd | 2 | ||
7605.2.a.bm.1.3 | 3 | 1.1 | even | 1 | trivial | ||
7605.2.a.ce.1.1 | 3 | 13.12 | even | 2 |