Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66751 | −1.88622 | −0.943108 | − | 0.332485i | \(-0.892113\pi\) | ||||
−0.943108 | + | 0.332485i | \(0.892113\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.11563 | 2.55781 | ||||||||
\(5\) | −0.759881 | −0.339829 | −0.169915 | − | 0.985459i | \(-0.554349\pi\) | ||||
−0.169915 | + | 0.985459i | \(0.554349\pi\) | |||||||
\(6\) | 2.66751 | 1.08901 | ||||||||
\(7\) | −3.14723 | −1.18954 | −0.594771 | − | 0.803895i | \(-0.702757\pi\) | ||||
−0.594771 | + | 0.803895i | \(0.702757\pi\) | |||||||
\(8\) | −8.31098 | −2.93838 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.02699 | 0.640992 | ||||||||
\(11\) | 2.82913 | 0.853016 | 0.426508 | − | 0.904484i | \(-0.359744\pi\) | ||||
0.426508 | + | 0.904484i | \(0.359744\pi\) | |||||||
\(12\) | −5.11563 | −1.47675 | ||||||||
\(13\) | −3.24759 | −0.900718 | −0.450359 | − | 0.892848i | \(-0.648704\pi\) | ||||
−0.450359 | + | 0.892848i | \(0.648704\pi\) | |||||||
\(14\) | 8.39529 | 2.24374 | ||||||||
\(15\) | 0.759881 | 0.196201 | ||||||||
\(16\) | 11.9384 | 2.98460 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.66751 | −0.628739 | ||||||||
\(19\) | 6.68456 | 1.53354 | 0.766772 | − | 0.641920i | \(-0.221862\pi\) | ||||
0.766772 | + | 0.641920i | \(0.221862\pi\) | |||||||
\(20\) | −3.88727 | −0.869220 | ||||||||
\(21\) | 3.14723 | 0.686783 | ||||||||
\(22\) | −7.54675 | −1.60897 | ||||||||
\(23\) | 3.37760 | 0.704278 | 0.352139 | − | 0.935948i | \(-0.385454\pi\) | ||||
0.352139 | + | 0.935948i | \(0.385454\pi\) | |||||||
\(24\) | 8.31098 | 1.69647 | ||||||||
\(25\) | −4.42258 | −0.884516 | ||||||||
\(26\) | 8.66298 | 1.69895 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −16.1001 | −3.04263 | ||||||||
\(29\) | 3.85637 | 0.716109 | 0.358055 | − | 0.933701i | \(-0.383440\pi\) | ||||
0.358055 | + | 0.933701i | \(0.383440\pi\) | |||||||
\(30\) | −2.02699 | −0.370077 | ||||||||
\(31\) | 2.88443 | 0.518058 | 0.259029 | − | 0.965870i | \(-0.416597\pi\) | ||||
0.259029 | + | 0.965870i | \(0.416597\pi\) | |||||||
\(32\) | −15.2239 | −2.69123 | ||||||||
\(33\) | −2.82913 | −0.492489 | ||||||||
\(34\) | 2.66751 | 0.457475 | ||||||||
\(35\) | 2.39153 | 0.404242 | ||||||||
\(36\) | 5.11563 | 0.852605 | ||||||||
\(37\) | −4.84157 | −0.795949 | −0.397974 | − | 0.917397i | \(-0.630287\pi\) | ||||
−0.397974 | + | 0.917397i | \(0.630287\pi\) | |||||||
\(38\) | −17.8312 | −2.89260 | ||||||||
\(39\) | 3.24759 | 0.520030 | ||||||||
\(40\) | 6.31536 | 0.998546 | ||||||||
\(41\) | −2.20878 | −0.344954 | −0.172477 | − | 0.985014i | \(-0.555177\pi\) | ||||
−0.172477 | + | 0.985014i | \(0.555177\pi\) | |||||||
\(42\) | −8.39529 | −1.29542 | ||||||||
\(43\) | −7.84352 | −1.19612 | −0.598062 | − | 0.801450i | \(-0.704063\pi\) | ||||
−0.598062 | + | 0.801450i | \(0.704063\pi\) | |||||||
\(44\) | 14.4728 | 2.18186 | ||||||||
\(45\) | −0.759881 | −0.113276 | ||||||||
\(46\) | −9.00979 | −1.32842 | ||||||||
\(47\) | −8.89782 | −1.29788 | −0.648940 | − | 0.760840i | \(-0.724787\pi\) | ||||
−0.648940 | + | 0.760840i | \(0.724787\pi\) | |||||||
\(48\) | −11.9384 | −1.72316 | ||||||||
\(49\) | 2.90509 | 0.415013 | ||||||||
\(50\) | 11.7973 | 1.66839 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −16.6134 | −2.30387 | ||||||||
\(53\) | 6.46681 | 0.888284 | 0.444142 | − | 0.895956i | \(-0.353508\pi\) | ||||
0.444142 | + | 0.895956i | \(0.353508\pi\) | |||||||
\(54\) | 2.66751 | 0.363003 | ||||||||
\(55\) | −2.14981 | −0.289880 | ||||||||
\(56\) | 26.1566 | 3.49532 | ||||||||
\(57\) | −6.68456 | −0.885392 | ||||||||
\(58\) | −10.2869 | −1.35074 | ||||||||
\(59\) | −2.68202 | −0.349169 | −0.174585 | − | 0.984642i | \(-0.555858\pi\) | ||||
−0.174585 | + | 0.984642i | \(0.555858\pi\) | |||||||
\(60\) | 3.88727 | 0.501844 | ||||||||
\(61\) | 0.513119 | 0.0656981 | 0.0328491 | − | 0.999460i | \(-0.489542\pi\) | ||||
0.0328491 | + | 0.999460i | \(0.489542\pi\) | |||||||
\(62\) | −7.69425 | −0.977170 | ||||||||
\(63\) | −3.14723 | −0.396514 | ||||||||
\(64\) | 16.7331 | 2.09164 | ||||||||
\(65\) | 2.46778 | 0.306090 | ||||||||
\(66\) | 7.54675 | 0.928941 | ||||||||
\(67\) | 0.811036 | 0.0990839 | 0.0495419 | − | 0.998772i | \(-0.484224\pi\) | ||||
0.0495419 | + | 0.998772i | \(0.484224\pi\) | |||||||
\(68\) | −5.11563 | −0.620361 | ||||||||
\(69\) | −3.37760 | −0.406615 | ||||||||
\(70\) | −6.37943 | −0.762487 | ||||||||
\(71\) | −2.81349 | −0.333900 | −0.166950 | − | 0.985965i | \(-0.553392\pi\) | ||||
−0.166950 | + | 0.985965i | \(0.553392\pi\) | |||||||
\(72\) | −8.31098 | −0.979458 | ||||||||
\(73\) | 9.87519 | 1.15580 | 0.577902 | − | 0.816106i | \(-0.303872\pi\) | ||||
0.577902 | + | 0.816106i | \(0.303872\pi\) | |||||||
\(74\) | 12.9149 | 1.50133 | ||||||||
\(75\) | 4.42258 | 0.510676 | ||||||||
\(76\) | 34.1957 | 3.92252 | ||||||||
\(77\) | −8.90395 | −1.01470 | ||||||||
\(78\) | −8.66298 | −0.980889 | ||||||||
\(79\) | −11.0802 | −1.24662 | −0.623310 | − | 0.781975i | \(-0.714213\pi\) | ||||
−0.623310 | + | 0.781975i | \(0.714213\pi\) | |||||||
\(80\) | −9.07177 | −1.01425 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.89195 | 0.650657 | ||||||||
\(83\) | −2.15464 | −0.236503 | −0.118251 | − | 0.992984i | \(-0.537729\pi\) | ||||
−0.118251 | + | 0.992984i | \(0.537729\pi\) | |||||||
\(84\) | 16.1001 | 1.75666 | ||||||||
\(85\) | 0.759881 | 0.0824207 | ||||||||
\(86\) | 20.9227 | 2.25615 | ||||||||
\(87\) | −3.85637 | −0.413446 | ||||||||
\(88\) | −23.5129 | −2.50648 | ||||||||
\(89\) | 1.54344 | 0.163604 | 0.0818019 | − | 0.996649i | \(-0.473933\pi\) | ||||
0.0818019 | + | 0.996649i | \(0.473933\pi\) | |||||||
\(90\) | 2.02699 | 0.213664 | ||||||||
\(91\) | 10.2209 | 1.07144 | ||||||||
\(92\) | 17.2785 | 1.80141 | ||||||||
\(93\) | −2.88443 | −0.299101 | ||||||||
\(94\) | 23.7350 | 2.44808 | ||||||||
\(95\) | −5.07947 | −0.521143 | ||||||||
\(96\) | 15.2239 | 1.55378 | ||||||||
\(97\) | −1.93782 | −0.196756 | −0.0983778 | − | 0.995149i | \(-0.531365\pi\) | ||||
−0.0983778 | + | 0.995149i | \(0.531365\pi\) | |||||||
\(98\) | −7.74936 | −0.782804 | ||||||||
\(99\) | 2.82913 | 0.284339 | ||||||||
\(100\) | −22.6243 | −2.26243 | ||||||||
\(101\) | 12.3656 | 1.23042 | 0.615212 | − | 0.788361i | \(-0.289070\pi\) | ||||
0.615212 | + | 0.788361i | \(0.289070\pi\) | |||||||
\(102\) | −2.66751 | −0.264123 | ||||||||
\(103\) | 2.43192 | 0.239624 | 0.119812 | − | 0.992797i | \(-0.461771\pi\) | ||||
0.119812 | + | 0.992797i | \(0.461771\pi\) | |||||||
\(104\) | 26.9906 | 2.64665 | ||||||||
\(105\) | −2.39153 | −0.233389 | ||||||||
\(106\) | −17.2503 | −1.67550 | ||||||||
\(107\) | 15.3997 | 1.48874 | 0.744370 | − | 0.667767i | \(-0.232750\pi\) | ||||
0.744370 | + | 0.667767i | \(0.232750\pi\) | |||||||
\(108\) | −5.11563 | −0.492252 | ||||||||
\(109\) | −6.96117 | −0.666759 | −0.333380 | − | 0.942793i | \(-0.608189\pi\) | ||||
−0.333380 | + | 0.942793i | \(0.608189\pi\) | |||||||
\(110\) | 5.73464 | 0.546776 | ||||||||
\(111\) | 4.84157 | 0.459541 | ||||||||
\(112\) | −37.5729 | −3.55031 | ||||||||
\(113\) | 13.1260 | 1.23479 | 0.617393 | − | 0.786655i | \(-0.288189\pi\) | ||||
0.617393 | + | 0.786655i | \(0.288189\pi\) | |||||||
\(114\) | 17.8312 | 1.67004 | ||||||||
\(115\) | −2.56657 | −0.239334 | ||||||||
\(116\) | 19.7277 | 1.83167 | ||||||||
\(117\) | −3.24759 | −0.300239 | ||||||||
\(118\) | 7.15432 | 0.658609 | ||||||||
\(119\) | 3.14723 | 0.288507 | ||||||||
\(120\) | −6.31536 | −0.576511 | ||||||||
\(121\) | −2.99600 | −0.272364 | ||||||||
\(122\) | −1.36875 | −0.123921 | ||||||||
\(123\) | 2.20878 | 0.199159 | ||||||||
\(124\) | 14.7557 | 1.32510 | ||||||||
\(125\) | 7.16004 | 0.640414 | ||||||||
\(126\) | 8.39529 | 0.747912 | ||||||||
\(127\) | −2.80815 | −0.249183 | −0.124591 | − | 0.992208i | \(-0.539762\pi\) | ||||
−0.124591 | + | 0.992208i | \(0.539762\pi\) | |||||||
\(128\) | −14.1880 | −1.25405 | ||||||||
\(129\) | 7.84352 | 0.690583 | ||||||||
\(130\) | −6.58284 | −0.577353 | ||||||||
\(131\) | −7.57495 | −0.661826 | −0.330913 | − | 0.943661i | \(-0.607357\pi\) | ||||
−0.330913 | + | 0.943661i | \(0.607357\pi\) | |||||||
\(132\) | −14.4728 | −1.25970 | ||||||||
\(133\) | −21.0379 | −1.82422 | ||||||||
\(134\) | −2.16345 | −0.186894 | ||||||||
\(135\) | 0.759881 | 0.0654002 | ||||||||
\(136\) | 8.31098 | 0.712661 | ||||||||
\(137\) | 14.2870 | 1.22062 | 0.610311 | − | 0.792162i | \(-0.291045\pi\) | ||||
0.610311 | + | 0.792162i | \(0.291045\pi\) | |||||||
\(138\) | 9.00979 | 0.766964 | ||||||||
\(139\) | −9.78869 | −0.830266 | −0.415133 | − | 0.909761i | \(-0.636265\pi\) | ||||
−0.415133 | + | 0.909761i | \(0.636265\pi\) | |||||||
\(140\) | 12.2342 | 1.03397 | ||||||||
\(141\) | 8.89782 | 0.749331 | ||||||||
\(142\) | 7.50503 | 0.629808 | ||||||||
\(143\) | −9.18785 | −0.768327 | ||||||||
\(144\) | 11.9384 | 0.994866 | ||||||||
\(145\) | −2.93038 | −0.243355 | ||||||||
\(146\) | −26.3422 | −2.18010 | ||||||||
\(147\) | −2.90509 | −0.239608 | ||||||||
\(148\) | −24.7677 | −2.03589 | ||||||||
\(149\) | 19.6890 | 1.61299 | 0.806495 | − | 0.591241i | \(-0.201362\pi\) | ||||
0.806495 | + | 0.591241i | \(0.201362\pi\) | |||||||
\(150\) | −11.7973 | −0.963245 | ||||||||
\(151\) | 17.7580 | 1.44513 | 0.722564 | − | 0.691304i | \(-0.242964\pi\) | ||||
0.722564 | + | 0.691304i | \(0.242964\pi\) | |||||||
\(152\) | −55.5553 | −4.50613 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 23.7514 | 1.91394 | ||||||||
\(155\) | −2.19182 | −0.176051 | ||||||||
\(156\) | 16.6134 | 1.33014 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 29.5566 | 2.35140 | ||||||||
\(159\) | −6.46681 | −0.512851 | ||||||||
\(160\) | 11.5683 | 0.914557 | ||||||||
\(161\) | −10.6301 | −0.837769 | ||||||||
\(162\) | −2.66751 | −0.209580 | ||||||||
\(163\) | −5.38266 | −0.421602 | −0.210801 | − | 0.977529i | \(-0.567607\pi\) | ||||
−0.210801 | + | 0.977529i | \(0.567607\pi\) | |||||||
\(164\) | −11.2993 | −0.882327 | ||||||||
\(165\) | 2.14981 | 0.167362 | ||||||||
\(166\) | 5.74754 | 0.446096 | ||||||||
\(167\) | 7.00409 | 0.541993 | 0.270997 | − | 0.962580i | \(-0.412647\pi\) | ||||
0.270997 | + | 0.962580i | \(0.412647\pi\) | |||||||
\(168\) | −26.1566 | −2.01803 | ||||||||
\(169\) | −2.45319 | −0.188707 | ||||||||
\(170\) | −2.02699 | −0.155463 | ||||||||
\(171\) | 6.68456 | 0.511181 | ||||||||
\(172\) | −40.1245 | −3.05947 | ||||||||
\(173\) | 15.4732 | 1.17640 | 0.588202 | − | 0.808714i | \(-0.299836\pi\) | ||||
0.588202 | + | 0.808714i | \(0.299836\pi\) | |||||||
\(174\) | 10.2869 | 0.779848 | ||||||||
\(175\) | 13.9189 | 1.05217 | ||||||||
\(176\) | 33.7753 | 2.54591 | ||||||||
\(177\) | 2.68202 | 0.201593 | ||||||||
\(178\) | −4.11714 | −0.308592 | ||||||||
\(179\) | −4.49026 | −0.335618 | −0.167809 | − | 0.985820i | \(-0.553669\pi\) | ||||
−0.167809 | + | 0.985820i | \(0.553669\pi\) | |||||||
\(180\) | −3.88727 | −0.289740 | ||||||||
\(181\) | −12.5814 | −0.935165 | −0.467583 | − | 0.883949i | \(-0.654875\pi\) | ||||
−0.467583 | + | 0.883949i | \(0.654875\pi\) | |||||||
\(182\) | −27.2644 | −2.02097 | ||||||||
\(183\) | −0.513119 | −0.0379308 | ||||||||
\(184\) | −28.0711 | −2.06943 | ||||||||
\(185\) | 3.67902 | 0.270487 | ||||||||
\(186\) | 7.69425 | 0.564169 | ||||||||
\(187\) | −2.82913 | −0.206887 | ||||||||
\(188\) | −45.5179 | −3.31974 | ||||||||
\(189\) | 3.14723 | 0.228928 | ||||||||
\(190\) | 13.5496 | 0.982989 | ||||||||
\(191\) | 10.5539 | 0.763653 | 0.381826 | − | 0.924234i | \(-0.375295\pi\) | ||||
0.381826 | + | 0.924234i | \(0.375295\pi\) | |||||||
\(192\) | −16.7331 | −1.20761 | ||||||||
\(193\) | −6.12973 | −0.441228 | −0.220614 | − | 0.975361i | \(-0.570806\pi\) | ||||
−0.220614 | + | 0.975361i | \(0.570806\pi\) | |||||||
\(194\) | 5.16915 | 0.371124 | ||||||||
\(195\) | −2.46778 | −0.176721 | ||||||||
\(196\) | 14.8613 | 1.06152 | ||||||||
\(197\) | −0.641410 | −0.0456985 | −0.0228493 | − | 0.999739i | \(-0.507274\pi\) | ||||
−0.0228493 | + | 0.999739i | \(0.507274\pi\) | |||||||
\(198\) | −7.54675 | −0.536324 | ||||||||
\(199\) | 0.0117886 | 0.000835670 0 | 0.000417835 | − | 1.00000i | \(-0.499867\pi\) | ||||
0.000417835 | 1.00000i | \(0.499867\pi\) | ||||||||
\(200\) | 36.7560 | 2.59904 | ||||||||
\(201\) | −0.811036 | −0.0572061 | ||||||||
\(202\) | −32.9854 | −2.32085 | ||||||||
\(203\) | −12.1369 | −0.851843 | ||||||||
\(204\) | 5.11563 | 0.358166 | ||||||||
\(205\) | 1.67841 | 0.117225 | ||||||||
\(206\) | −6.48718 | −0.451983 | ||||||||
\(207\) | 3.37760 | 0.234759 | ||||||||
\(208\) | −38.7710 | −2.68828 | ||||||||
\(209\) | 18.9115 | 1.30814 | ||||||||
\(210\) | 6.37943 | 0.440222 | ||||||||
\(211\) | −15.8802 | −1.09324 | −0.546618 | − | 0.837382i | \(-0.684085\pi\) | ||||
−0.546618 | + | 0.837382i | \(0.684085\pi\) | |||||||
\(212\) | 33.0818 | 2.27207 | ||||||||
\(213\) | 2.81349 | 0.192777 | ||||||||
\(214\) | −41.0788 | −2.80809 | ||||||||
\(215\) | 5.96014 | 0.406478 | ||||||||
\(216\) | 8.31098 | 0.565491 | ||||||||
\(217\) | −9.07797 | −0.616253 | ||||||||
\(218\) | 18.5690 | 1.25765 | ||||||||
\(219\) | −9.87519 | −0.667303 | ||||||||
\(220\) | −10.9976 | −0.741459 | ||||||||
\(221\) | 3.24759 | 0.218456 | ||||||||
\(222\) | −12.9149 | −0.866794 | ||||||||
\(223\) | 5.26595 | 0.352634 | 0.176317 | − | 0.984333i | \(-0.443582\pi\) | ||||
0.176317 | + | 0.984333i | \(0.443582\pi\) | |||||||
\(224\) | 47.9131 | 3.20133 | ||||||||
\(225\) | −4.42258 | −0.294839 | ||||||||
\(226\) | −35.0137 | −2.32908 | ||||||||
\(227\) | 1.83842 | 0.122021 | 0.0610103 | − | 0.998137i | \(-0.480568\pi\) | ||||
0.0610103 | + | 0.998137i | \(0.480568\pi\) | |||||||
\(228\) | −34.1957 | −2.26467 | ||||||||
\(229\) | 6.83685 | 0.451792 | 0.225896 | − | 0.974151i | \(-0.427469\pi\) | ||||
0.225896 | + | 0.974151i | \(0.427469\pi\) | |||||||
\(230\) | 6.84637 | 0.451436 | ||||||||
\(231\) | 8.90395 | 0.585837 | ||||||||
\(232\) | −32.0502 | −2.10420 | ||||||||
\(233\) | 8.06025 | 0.528044 | 0.264022 | − | 0.964517i | \(-0.414951\pi\) | ||||
0.264022 | + | 0.964517i | \(0.414951\pi\) | |||||||
\(234\) | 8.66298 | 0.566317 | ||||||||
\(235\) | 6.76129 | 0.441058 | ||||||||
\(236\) | −13.7202 | −0.893110 | ||||||||
\(237\) | 11.0802 | 0.719737 | ||||||||
\(238\) | −8.39529 | −0.544186 | ||||||||
\(239\) | −12.4804 | −0.807292 | −0.403646 | − | 0.914915i | \(-0.632257\pi\) | ||||
−0.403646 | + | 0.914915i | \(0.632257\pi\) | |||||||
\(240\) | 9.07177 | 0.585580 | ||||||||
\(241\) | −0.772995 | −0.0497930 | −0.0248965 | − | 0.999690i | \(-0.507926\pi\) | ||||
−0.0248965 | + | 0.999690i | \(0.507926\pi\) | |||||||
\(242\) | 7.99188 | 0.513738 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.62492 | 0.168044 | ||||||||
\(245\) | −2.20752 | −0.141033 | ||||||||
\(246\) | −5.89195 | −0.375657 | ||||||||
\(247\) | −21.7087 | −1.38129 | ||||||||
\(248\) | −23.9724 | −1.52225 | ||||||||
\(249\) | 2.15464 | 0.136545 | ||||||||
\(250\) | −19.0995 | −1.20796 | ||||||||
\(251\) | 5.60340 | 0.353684 | 0.176842 | − | 0.984239i | \(-0.443412\pi\) | ||||
0.176842 | + | 0.984239i | \(0.443412\pi\) | |||||||
\(252\) | −16.1001 | −1.01421 | ||||||||
\(253\) | 9.55567 | 0.600760 | ||||||||
\(254\) | 7.49077 | 0.470013 | ||||||||
\(255\) | −0.759881 | −0.0475856 | ||||||||
\(256\) | 4.38052 | 0.273782 | ||||||||
\(257\) | −12.4898 | −0.779093 | −0.389546 | − | 0.921007i | \(-0.627368\pi\) | ||||
−0.389546 | + | 0.921007i | \(0.627368\pi\) | |||||||
\(258\) | −20.9227 | −1.30259 | ||||||||
\(259\) | 15.2375 | 0.946815 | ||||||||
\(260\) | 12.6242 | 0.782922 | ||||||||
\(261\) | 3.85637 | 0.238703 | ||||||||
\(262\) | 20.2063 | 1.24835 | ||||||||
\(263\) | −24.6807 | −1.52188 | −0.760939 | − | 0.648824i | \(-0.775261\pi\) | ||||
−0.760939 | + | 0.648824i | \(0.775261\pi\) | |||||||
\(264\) | 23.5129 | 1.44712 | ||||||||
\(265\) | −4.91401 | −0.301865 | ||||||||
\(266\) | 56.1188 | 3.44087 | ||||||||
\(267\) | −1.54344 | −0.0944567 | ||||||||
\(268\) | 4.14896 | 0.253438 | ||||||||
\(269\) | −22.8330 | −1.39215 | −0.696077 | − | 0.717967i | \(-0.745073\pi\) | ||||
−0.696077 | + | 0.717967i | \(0.745073\pi\) | |||||||
\(270\) | −2.02699 | −0.123359 | ||||||||
\(271\) | 32.3091 | 1.96264 | 0.981318 | − | 0.192393i | \(-0.0616249\pi\) | ||||
0.981318 | + | 0.192393i | \(0.0616249\pi\) | |||||||
\(272\) | −11.9384 | −0.723872 | ||||||||
\(273\) | −10.2209 | −0.618598 | ||||||||
\(274\) | −38.1108 | −2.30236 | ||||||||
\(275\) | −12.5121 | −0.754506 | ||||||||
\(276\) | −17.2785 | −1.04005 | ||||||||
\(277\) | −6.19453 | −0.372193 | −0.186096 | − | 0.982531i | \(-0.559584\pi\) | ||||
−0.186096 | + | 0.982531i | \(0.559584\pi\) | |||||||
\(278\) | 26.1115 | 1.56606 | ||||||||
\(279\) | 2.88443 | 0.172686 | ||||||||
\(280\) | −19.8759 | −1.18781 | ||||||||
\(281\) | −9.37561 | −0.559302 | −0.279651 | − | 0.960102i | \(-0.590219\pi\) | ||||
−0.279651 | + | 0.960102i | \(0.590219\pi\) | |||||||
\(282\) | −23.7350 | −1.41340 | ||||||||
\(283\) | −4.59361 | −0.273062 | −0.136531 | − | 0.990636i | \(-0.543595\pi\) | ||||
−0.136531 | + | 0.990636i | \(0.543595\pi\) | |||||||
\(284\) | −14.3928 | −0.854055 | ||||||||
\(285\) | 5.07947 | 0.300882 | ||||||||
\(286\) | 24.5087 | 1.44923 | ||||||||
\(287\) | 6.95155 | 0.410337 | ||||||||
\(288\) | −15.2239 | −0.897075 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 7.81683 | 0.459020 | ||||||||
\(291\) | 1.93782 | 0.113597 | ||||||||
\(292\) | 50.5178 | 2.95633 | ||||||||
\(293\) | 12.3861 | 0.723605 | 0.361802 | − | 0.932255i | \(-0.382162\pi\) | ||||
0.361802 | + | 0.932255i | \(0.382162\pi\) | |||||||
\(294\) | 7.74936 | 0.451952 | ||||||||
\(295\) | 2.03802 | 0.118658 | ||||||||
\(296\) | 40.2382 | 2.33880 | ||||||||
\(297\) | −2.82913 | −0.164163 | ||||||||
\(298\) | −52.5208 | −3.04245 | ||||||||
\(299\) | −10.9690 | −0.634356 | ||||||||
\(300\) | 22.6243 | 1.30621 | ||||||||
\(301\) | 24.6854 | 1.42284 | ||||||||
\(302\) | −47.3698 | −2.72582 | ||||||||
\(303\) | −12.3656 | −0.710386 | ||||||||
\(304\) | 79.8029 | 4.57701 | ||||||||
\(305\) | −0.389909 | −0.0223261 | ||||||||
\(306\) | 2.66751 | 0.152492 | ||||||||
\(307\) | −5.33559 | −0.304518 | −0.152259 | − | 0.988341i | \(-0.548655\pi\) | ||||
−0.152259 | + | 0.988341i | \(0.548655\pi\) | |||||||
\(308\) | −45.5493 | −2.59541 | ||||||||
\(309\) | −2.43192 | −0.138347 | ||||||||
\(310\) | 5.84671 | 0.332071 | ||||||||
\(311\) | 12.3195 | 0.698576 | 0.349288 | − | 0.937015i | \(-0.386424\pi\) | ||||
0.349288 | + | 0.937015i | \(0.386424\pi\) | |||||||
\(312\) | −26.9906 | −1.52804 | ||||||||
\(313\) | 22.9268 | 1.29590 | 0.647948 | − | 0.761684i | \(-0.275627\pi\) | ||||
0.647948 | + | 0.761684i | \(0.275627\pi\) | |||||||
\(314\) | 2.66751 | 0.150536 | ||||||||
\(315\) | 2.39153 | 0.134747 | ||||||||
\(316\) | −56.6822 | −3.18862 | ||||||||
\(317\) | −9.94107 | −0.558346 | −0.279173 | − | 0.960241i | \(-0.590060\pi\) | ||||
−0.279173 | + | 0.960241i | \(0.590060\pi\) | |||||||
\(318\) | 17.2503 | 0.967349 | ||||||||
\(319\) | 10.9102 | 0.610852 | ||||||||
\(320\) | −12.7152 | −0.710799 | ||||||||
\(321\) | −15.3997 | −0.859525 | ||||||||
\(322\) | 28.3559 | 1.58021 | ||||||||
\(323\) | −6.68456 | −0.371939 | ||||||||
\(324\) | 5.11563 | 0.284202 | ||||||||
\(325\) | 14.3627 | 0.796700 | ||||||||
\(326\) | 14.3583 | 0.795233 | ||||||||
\(327\) | 6.96117 | 0.384954 | ||||||||
\(328\) | 18.3571 | 1.01360 | ||||||||
\(329\) | 28.0035 | 1.54388 | ||||||||
\(330\) | −5.73464 | −0.315681 | ||||||||
\(331\) | −6.48028 | −0.356188 | −0.178094 | − | 0.984013i | \(-0.556993\pi\) | ||||
−0.178094 | + | 0.984013i | \(0.556993\pi\) | |||||||
\(332\) | −11.0224 | −0.604930 | ||||||||
\(333\) | −4.84157 | −0.265316 | ||||||||
\(334\) | −18.6835 | −1.02232 | ||||||||
\(335\) | −0.616291 | −0.0336716 | ||||||||
\(336\) | 37.5729 | 2.04977 | ||||||||
\(337\) | 28.1226 | 1.53194 | 0.765968 | − | 0.642878i | \(-0.222260\pi\) | ||||
0.765968 | + | 0.642878i | \(0.222260\pi\) | |||||||
\(338\) | 6.54392 | 0.355942 | ||||||||
\(339\) | −13.1260 | −0.712904 | ||||||||
\(340\) | 3.88727 | 0.210817 | ||||||||
\(341\) | 8.16043 | 0.441912 | ||||||||
\(342\) | −17.8312 | −0.964198 | ||||||||
\(343\) | 12.8877 | 0.695868 | ||||||||
\(344\) | 65.1873 | 3.51466 | ||||||||
\(345\) | 2.56657 | 0.138180 | ||||||||
\(346\) | −41.2749 | −2.21895 | ||||||||
\(347\) | 8.85764 | 0.475503 | 0.237751 | − | 0.971326i | \(-0.423590\pi\) | ||||
0.237751 | + | 0.971326i | \(0.423590\pi\) | |||||||
\(348\) | −19.7277 | −1.05752 | ||||||||
\(349\) | −35.0088 | −1.87398 | −0.936988 | − | 0.349361i | \(-0.886399\pi\) | ||||
−0.936988 | + | 0.349361i | \(0.886399\pi\) | |||||||
\(350\) | −37.1289 | −1.98462 | ||||||||
\(351\) | 3.24759 | 0.173343 | ||||||||
\(352\) | −43.0704 | −2.29566 | ||||||||
\(353\) | −14.7136 | −0.783127 | −0.391564 | − | 0.920151i | \(-0.628066\pi\) | ||||
−0.391564 | + | 0.920151i | \(0.628066\pi\) | |||||||
\(354\) | −7.15432 | −0.380248 | ||||||||
\(355\) | 2.13792 | 0.113469 | ||||||||
\(356\) | 7.89564 | 0.418468 | ||||||||
\(357\) | −3.14723 | −0.166569 | ||||||||
\(358\) | 11.9778 | 0.633048 | ||||||||
\(359\) | 24.9632 | 1.31751 | 0.658754 | − | 0.752358i | \(-0.271084\pi\) | ||||
0.658754 | + | 0.752358i | \(0.271084\pi\) | |||||||
\(360\) | 6.31536 | 0.332849 | ||||||||
\(361\) | 25.6833 | 1.35176 | ||||||||
\(362\) | 33.5610 | 1.76392 | ||||||||
\(363\) | 2.99600 | 0.157249 | ||||||||
\(364\) | 52.2864 | 2.74055 | ||||||||
\(365\) | −7.50397 | −0.392776 | ||||||||
\(366\) | 1.36875 | 0.0715458 | ||||||||
\(367\) | −4.99446 | −0.260709 | −0.130354 | − | 0.991467i | \(-0.541612\pi\) | ||||
−0.130354 | + | 0.991467i | \(0.541612\pi\) | |||||||
\(368\) | 40.3231 | 2.10199 | ||||||||
\(369\) | −2.20878 | −0.114985 | ||||||||
\(370\) | −9.81382 | −0.510196 | ||||||||
\(371\) | −20.3526 | −1.05665 | ||||||||
\(372\) | −14.7557 | −0.765045 | ||||||||
\(373\) | 34.4089 | 1.78162 | 0.890812 | − | 0.454372i | \(-0.150136\pi\) | ||||
0.890812 | + | 0.454372i | \(0.150136\pi\) | |||||||
\(374\) | 7.54675 | 0.390233 | ||||||||
\(375\) | −7.16004 | −0.369743 | ||||||||
\(376\) | 73.9496 | 3.81366 | ||||||||
\(377\) | −12.5239 | −0.645012 | ||||||||
\(378\) | −8.39529 | −0.431807 | ||||||||
\(379\) | −24.9110 | −1.27959 | −0.639796 | − | 0.768545i | \(-0.720981\pi\) | ||||
−0.639796 | + | 0.768545i | \(0.720981\pi\) | |||||||
\(380\) | −25.9847 | −1.33299 | ||||||||
\(381\) | 2.80815 | 0.143866 | ||||||||
\(382\) | −28.1527 | −1.44041 | ||||||||
\(383\) | −21.9404 | −1.12110 | −0.560551 | − | 0.828120i | \(-0.689411\pi\) | ||||
−0.560551 | + | 0.828120i | \(0.689411\pi\) | |||||||
\(384\) | 14.1880 | 0.724029 | ||||||||
\(385\) | 6.76594 | 0.344824 | ||||||||
\(386\) | 16.3511 | 0.832251 | ||||||||
\(387\) | −7.84352 | −0.398708 | ||||||||
\(388\) | −9.91315 | −0.503264 | ||||||||
\(389\) | −29.5598 | −1.49874 | −0.749370 | − | 0.662152i | \(-0.769643\pi\) | ||||
−0.749370 | + | 0.662152i | \(0.769643\pi\) | |||||||
\(390\) | 6.58284 | 0.333335 | ||||||||
\(391\) | −3.37760 | −0.170812 | ||||||||
\(392\) | −24.1441 | −1.21946 | ||||||||
\(393\) | 7.57495 | 0.382105 | ||||||||
\(394\) | 1.71097 | 0.0861974 | ||||||||
\(395\) | 8.41964 | 0.423638 | ||||||||
\(396\) | 14.4728 | 0.727285 | ||||||||
\(397\) | 13.6910 | 0.687132 | 0.343566 | − | 0.939128i | \(-0.388365\pi\) | ||||
0.343566 | + | 0.939128i | \(0.388365\pi\) | |||||||
\(398\) | −0.0314462 | −0.00157626 | ||||||||
\(399\) | 21.0379 | 1.05321 | ||||||||
\(400\) | −52.7985 | −2.63993 | ||||||||
\(401\) | −12.4462 | −0.621535 | −0.310767 | − | 0.950486i | \(-0.600586\pi\) | ||||
−0.310767 | + | 0.950486i | \(0.600586\pi\) | |||||||
\(402\) | 2.16345 | 0.107903 | ||||||||
\(403\) | −9.36742 | −0.466624 | ||||||||
\(404\) | 63.2579 | 3.14720 | ||||||||
\(405\) | −0.759881 | −0.0377588 | ||||||||
\(406\) | 32.3753 | 1.60676 | ||||||||
\(407\) | −13.6974 | −0.678957 | ||||||||
\(408\) | −8.31098 | −0.411455 | ||||||||
\(409\) | −6.29135 | −0.311087 | −0.155544 | − | 0.987829i | \(-0.549713\pi\) | ||||
−0.155544 | + | 0.987829i | \(0.549713\pi\) | |||||||
\(410\) | −4.47718 | −0.221112 | ||||||||
\(411\) | −14.2870 | −0.704726 | ||||||||
\(412\) | 12.4408 | 0.612914 | ||||||||
\(413\) | 8.44094 | 0.415352 | ||||||||
\(414\) | −9.00979 | −0.442807 | ||||||||
\(415\) | 1.63727 | 0.0803706 | ||||||||
\(416\) | 49.4408 | 2.42404 | ||||||||
\(417\) | 9.78869 | 0.479354 | ||||||||
\(418\) | −50.4467 | −2.46743 | ||||||||
\(419\) | 17.2067 | 0.840602 | 0.420301 | − | 0.907385i | \(-0.361925\pi\) | ||||
0.420301 | + | 0.907385i | \(0.361925\pi\) | |||||||
\(420\) | −12.2342 | −0.596966 | ||||||||
\(421\) | −0.690778 | −0.0336664 | −0.0168332 | − | 0.999858i | \(-0.505358\pi\) | ||||
−0.0168332 | + | 0.999858i | \(0.505358\pi\) | |||||||
\(422\) | 42.3606 | 2.06208 | ||||||||
\(423\) | −8.89782 | −0.432627 | ||||||||
\(424\) | −53.7455 | −2.61011 | ||||||||
\(425\) | 4.42258 | 0.214527 | ||||||||
\(426\) | −7.50503 | −0.363620 | ||||||||
\(427\) | −1.61491 | −0.0781507 | ||||||||
\(428\) | 78.7789 | 3.80792 | ||||||||
\(429\) | 9.18785 | 0.443594 | ||||||||
\(430\) | −15.8988 | −0.766706 | ||||||||
\(431\) | 38.5781 | 1.85824 | 0.929120 | − | 0.369778i | \(-0.120566\pi\) | ||||
0.929120 | + | 0.369778i | \(0.120566\pi\) | |||||||
\(432\) | −11.9384 | −0.574386 | ||||||||
\(433\) | 13.0955 | 0.629328 | 0.314664 | − | 0.949203i | \(-0.398108\pi\) | ||||
0.314664 | + | 0.949203i | \(0.398108\pi\) | |||||||
\(434\) | 24.2156 | 1.16239 | ||||||||
\(435\) | 2.93038 | 0.140501 | ||||||||
\(436\) | −35.6108 | −1.70545 | ||||||||
\(437\) | 22.5778 | 1.08004 | ||||||||
\(438\) | 26.3422 | 1.25868 | ||||||||
\(439\) | 13.1677 | 0.628459 | 0.314230 | − | 0.949347i | \(-0.398254\pi\) | ||||
0.314230 | + | 0.949347i | \(0.398254\pi\) | |||||||
\(440\) | 17.8670 | 0.851776 | ||||||||
\(441\) | 2.90509 | 0.138338 | ||||||||
\(442\) | −8.66298 | −0.412056 | ||||||||
\(443\) | −4.89848 | −0.232734 | −0.116367 | − | 0.993206i | \(-0.537125\pi\) | ||||
−0.116367 | + | 0.993206i | \(0.537125\pi\) | |||||||
\(444\) | 24.7677 | 1.17542 | ||||||||
\(445\) | −1.17283 | −0.0555974 | ||||||||
\(446\) | −14.0470 | −0.665145 | ||||||||
\(447\) | −19.6890 | −0.931260 | ||||||||
\(448\) | −52.6630 | −2.48809 | ||||||||
\(449\) | −23.1431 | −1.09219 | −0.546095 | − | 0.837723i | \(-0.683886\pi\) | ||||
−0.546095 | + | 0.837723i | \(0.683886\pi\) | |||||||
\(450\) | 11.7973 | 0.556130 | ||||||||
\(451\) | −6.24893 | −0.294251 | ||||||||
\(452\) | 67.1475 | 3.15835 | ||||||||
\(453\) | −17.7580 | −0.834345 | ||||||||
\(454\) | −4.90402 | −0.230157 | ||||||||
\(455\) | −7.76668 | −0.364108 | ||||||||
\(456\) | 55.5553 | 2.60161 | ||||||||
\(457\) | −25.7840 | −1.20612 | −0.603062 | − | 0.797694i | \(-0.706053\pi\) | ||||
−0.603062 | + | 0.797694i | \(0.706053\pi\) | |||||||
\(458\) | −18.2374 | −0.852177 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −13.1296 | −0.612172 | ||||||||
\(461\) | 13.4365 | 0.625799 | 0.312899 | − | 0.949786i | \(-0.398700\pi\) | ||||
0.312899 | + | 0.949786i | \(0.398700\pi\) | |||||||
\(462\) | −23.7514 | −1.10502 | ||||||||
\(463\) | 0.619263 | 0.0287796 | 0.0143898 | − | 0.999896i | \(-0.495419\pi\) | ||||
0.0143898 | + | 0.999896i | \(0.495419\pi\) | |||||||
\(464\) | 46.0388 | 2.13730 | ||||||||
\(465\) | 2.19182 | 0.101643 | ||||||||
\(466\) | −21.5008 | −0.996006 | ||||||||
\(467\) | 24.8542 | 1.15011 | 0.575057 | − | 0.818113i | \(-0.304980\pi\) | ||||
0.575057 | + | 0.818113i | \(0.304980\pi\) | |||||||
\(468\) | −16.6134 | −0.767956 | ||||||||
\(469\) | −2.55252 | −0.117865 | ||||||||
\(470\) | −18.0358 | −0.831930 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 22.2902 | 1.02599 | ||||||||
\(473\) | −22.1903 | −1.02031 | ||||||||
\(474\) | −29.5566 | −1.35758 | ||||||||
\(475\) | −29.5630 | −1.35644 | ||||||||
\(476\) | 16.1001 | 0.737946 | ||||||||
\(477\) | 6.46681 | 0.296095 | ||||||||
\(478\) | 33.2917 | 1.52273 | ||||||||
\(479\) | 9.89026 | 0.451897 | 0.225949 | − | 0.974139i | \(-0.427452\pi\) | ||||
0.225949 | + | 0.974139i | \(0.427452\pi\) | |||||||
\(480\) | −11.5683 | −0.528020 | ||||||||
\(481\) | 15.7234 | 0.716925 | ||||||||
\(482\) | 2.06197 | 0.0939203 | ||||||||
\(483\) | 10.6301 | 0.483686 | ||||||||
\(484\) | −15.3264 | −0.696657 | ||||||||
\(485\) | 1.47251 | 0.0668633 | ||||||||
\(486\) | 2.66751 | 0.121001 | ||||||||
\(487\) | 24.4457 | 1.10774 | 0.553869 | − | 0.832604i | \(-0.313151\pi\) | ||||
0.553869 | + | 0.832604i | \(0.313151\pi\) | |||||||
\(488\) | −4.26452 | −0.193046 | ||||||||
\(489\) | 5.38266 | 0.243412 | ||||||||
\(490\) | 5.88860 | 0.266020 | ||||||||
\(491\) | −8.26575 | −0.373028 | −0.186514 | − | 0.982452i | \(-0.559719\pi\) | ||||
−0.186514 | + | 0.982452i | \(0.559719\pi\) | |||||||
\(492\) | 11.2993 | 0.509412 | ||||||||
\(493\) | −3.85637 | −0.173682 | ||||||||
\(494\) | 57.9082 | 2.60541 | ||||||||
\(495\) | −2.14981 | −0.0966266 | ||||||||
\(496\) | 34.4354 | 1.54620 | ||||||||
\(497\) | 8.85473 | 0.397189 | ||||||||
\(498\) | −5.74754 | −0.257553 | ||||||||
\(499\) | −7.59437 | −0.339971 | −0.169985 | − | 0.985447i | \(-0.554372\pi\) | ||||
−0.169985 | + | 0.985447i | \(0.554372\pi\) | |||||||
\(500\) | 36.6281 | 1.63806 | ||||||||
\(501\) | −7.00409 | −0.312920 | ||||||||
\(502\) | −14.9472 | −0.667124 | ||||||||
\(503\) | −1.76162 | −0.0785466 | −0.0392733 | − | 0.999229i | \(-0.512504\pi\) | ||||
−0.0392733 | + | 0.999229i | \(0.512504\pi\) | |||||||
\(504\) | 26.1566 | 1.16511 | ||||||||
\(505\) | −9.39640 | −0.418134 | ||||||||
\(506\) | −25.4899 | −1.13316 | ||||||||
\(507\) | 2.45319 | 0.108950 | ||||||||
\(508\) | −14.3654 | −0.637363 | ||||||||
\(509\) | −8.11323 | −0.359613 | −0.179806 | − | 0.983702i | \(-0.557547\pi\) | ||||
−0.179806 | + | 0.983702i | \(0.557547\pi\) | |||||||
\(510\) | 2.02699 | 0.0897568 | ||||||||
\(511\) | −31.0795 | −1.37488 | ||||||||
\(512\) | 16.6909 | 0.737642 | ||||||||
\(513\) | −6.68456 | −0.295131 | ||||||||
\(514\) | 33.3167 | 1.46954 | ||||||||
\(515\) | −1.84797 | −0.0814313 | ||||||||
\(516\) | 40.1245 | 1.76638 | ||||||||
\(517\) | −25.1731 | −1.10711 | ||||||||
\(518\) | −40.6464 | −1.78590 | ||||||||
\(519\) | −15.4732 | −0.679198 | ||||||||
\(520\) | −20.5097 | −0.899408 | ||||||||
\(521\) | −4.52635 | −0.198303 | −0.0991515 | − | 0.995072i | \(-0.531613\pi\) | ||||
−0.0991515 | + | 0.995072i | \(0.531613\pi\) | |||||||
\(522\) | −10.2869 | −0.450246 | ||||||||
\(523\) | −10.0719 | −0.440412 | −0.220206 | − | 0.975453i | \(-0.570673\pi\) | ||||
−0.220206 | + | 0.975453i | \(0.570673\pi\) | |||||||
\(524\) | −38.7506 | −1.69283 | ||||||||
\(525\) | −13.9189 | −0.607471 | ||||||||
\(526\) | 65.8361 | 2.87059 | ||||||||
\(527\) | −2.88443 | −0.125648 | ||||||||
\(528\) | −33.7753 | −1.46988 | ||||||||
\(529\) | −11.5918 | −0.503993 | ||||||||
\(530\) | 13.1082 | 0.569383 | ||||||||
\(531\) | −2.68202 | −0.116390 | ||||||||
\(532\) | −107.622 | −4.66600 | ||||||||
\(533\) | 7.17320 | 0.310706 | ||||||||
\(534\) | 4.11714 | 0.178166 | ||||||||
\(535\) | −11.7019 | −0.505918 | ||||||||
\(536\) | −6.74051 | −0.291146 | ||||||||
\(537\) | 4.49026 | 0.193769 | ||||||||
\(538\) | 60.9074 | 2.62590 | ||||||||
\(539\) | 8.21888 | 0.354012 | ||||||||
\(540\) | 3.88727 | 0.167281 | ||||||||
\(541\) | 9.80129 | 0.421390 | 0.210695 | − | 0.977552i | \(-0.432427\pi\) | ||||
0.210695 | + | 0.977552i | \(0.432427\pi\) | |||||||
\(542\) | −86.1849 | −3.70196 | ||||||||
\(543\) | 12.5814 | 0.539918 | ||||||||
\(544\) | 15.2239 | 0.652718 | ||||||||
\(545\) | 5.28966 | 0.226584 | ||||||||
\(546\) | 27.2644 | 1.16681 | ||||||||
\(547\) | 29.0640 | 1.24269 | 0.621344 | − | 0.783538i | \(-0.286587\pi\) | ||||
0.621344 | + | 0.783538i | \(0.286587\pi\) | |||||||
\(548\) | 73.0870 | 3.12212 | ||||||||
\(549\) | 0.513119 | 0.0218994 | ||||||||
\(550\) | 33.3761 | 1.42316 | ||||||||
\(551\) | 25.7781 | 1.09818 | ||||||||
\(552\) | 28.0711 | 1.19479 | ||||||||
\(553\) | 34.8720 | 1.48291 | ||||||||
\(554\) | 16.5240 | 0.702037 | ||||||||
\(555\) | −3.67902 | −0.156166 | ||||||||
\(556\) | −50.0753 | −2.12367 | ||||||||
\(557\) | −9.33729 | −0.395634 | −0.197817 | − | 0.980239i | \(-0.563385\pi\) | ||||
−0.197817 | + | 0.980239i | \(0.563385\pi\) | |||||||
\(558\) | −7.69425 | −0.325723 | ||||||||
\(559\) | 25.4725 | 1.07737 | ||||||||
\(560\) | 28.5510 | 1.20650 | ||||||||
\(561\) | 2.82913 | 0.119446 | ||||||||
\(562\) | 25.0096 | 1.05497 | ||||||||
\(563\) | −15.9171 | −0.670826 | −0.335413 | − | 0.942071i | \(-0.608876\pi\) | ||||
−0.335413 | + | 0.942071i | \(0.608876\pi\) | |||||||
\(564\) | 45.5179 | 1.91665 | ||||||||
\(565\) | −9.97417 | −0.419617 | ||||||||
\(566\) | 12.2535 | 0.515053 | ||||||||
\(567\) | −3.14723 | −0.132171 | ||||||||
\(568\) | 23.3829 | 0.981124 | ||||||||
\(569\) | −12.6052 | −0.528437 | −0.264218 | − | 0.964463i | \(-0.585114\pi\) | ||||
−0.264218 | + | 0.964463i | \(0.585114\pi\) | |||||||
\(570\) | −13.5496 | −0.567529 | ||||||||
\(571\) | −26.5004 | −1.10901 | −0.554504 | − | 0.832181i | \(-0.687092\pi\) | ||||
−0.554504 | + | 0.832181i | \(0.687092\pi\) | |||||||
\(572\) | −47.0016 | −1.96524 | ||||||||
\(573\) | −10.5539 | −0.440895 | ||||||||
\(574\) | −18.5434 | −0.773985 | ||||||||
\(575\) | −14.9377 | −0.622945 | ||||||||
\(576\) | 16.7331 | 0.697212 | ||||||||
\(577\) | 13.4575 | 0.560244 | 0.280122 | − | 0.959964i | \(-0.409625\pi\) | ||||
0.280122 | + | 0.959964i | \(0.409625\pi\) | |||||||
\(578\) | −2.66751 | −0.110954 | ||||||||
\(579\) | 6.12973 | 0.254743 | ||||||||
\(580\) | −14.9907 | −0.622456 | ||||||||
\(581\) | 6.78117 | 0.281330 | ||||||||
\(582\) | −5.16915 | −0.214268 | ||||||||
\(583\) | 18.2955 | 0.757721 | ||||||||
\(584\) | −82.0725 | −3.39618 | ||||||||
\(585\) | 2.46778 | 0.102030 | ||||||||
\(586\) | −33.0401 | −1.36488 | ||||||||
\(587\) | −1.73388 | −0.0715648 | −0.0357824 | − | 0.999360i | \(-0.511392\pi\) | ||||
−0.0357824 | + | 0.999360i | \(0.511392\pi\) | |||||||
\(588\) | −14.8613 | −0.612872 | ||||||||
\(589\) | 19.2811 | 0.794465 | ||||||||
\(590\) | −5.43644 | −0.223815 | ||||||||
\(591\) | 0.641410 | 0.0263841 | ||||||||
\(592\) | −57.8005 | −2.37559 | ||||||||
\(593\) | −31.5011 | −1.29360 | −0.646798 | − | 0.762661i | \(-0.723892\pi\) | ||||
−0.646798 | + | 0.762661i | \(0.723892\pi\) | |||||||
\(594\) | 7.54675 | 0.309647 | ||||||||
\(595\) | −2.39153 | −0.0980430 | ||||||||
\(596\) | 100.722 | 4.12573 | ||||||||
\(597\) | −0.0117886 | −0.000482474 0 | ||||||||
\(598\) | 29.2601 | 1.19653 | ||||||||
\(599\) | 10.1964 | 0.416612 | 0.208306 | − | 0.978064i | \(-0.433205\pi\) | ||||
0.208306 | + | 0.978064i | \(0.433205\pi\) | |||||||
\(600\) | −36.7560 | −1.50056 | ||||||||
\(601\) | −37.4615 | −1.52809 | −0.764043 | − | 0.645165i | \(-0.776788\pi\) | ||||
−0.764043 | + | 0.645165i | \(0.776788\pi\) | |||||||
\(602\) | −65.8486 | −2.68379 | ||||||||
\(603\) | 0.811036 | 0.0330280 | ||||||||
\(604\) | 90.8435 | 3.69637 | ||||||||
\(605\) | 2.27661 | 0.0925573 | ||||||||
\(606\) | 32.9854 | 1.33994 | ||||||||
\(607\) | 34.0661 | 1.38270 | 0.691351 | − | 0.722519i | \(-0.257016\pi\) | ||||
0.691351 | + | 0.722519i | \(0.257016\pi\) | |||||||
\(608\) | −101.765 | −4.12711 | ||||||||
\(609\) | 12.1369 | 0.491812 | ||||||||
\(610\) | 1.04009 | 0.0421120 | ||||||||
\(611\) | 28.8964 | 1.16902 | ||||||||
\(612\) | −5.11563 | −0.206787 | ||||||||
\(613\) | 13.1212 | 0.529962 | 0.264981 | − | 0.964254i | \(-0.414634\pi\) | ||||
0.264981 | + | 0.964254i | \(0.414634\pi\) | |||||||
\(614\) | 14.2328 | 0.574387 | ||||||||
\(615\) | −1.67841 | −0.0676801 | ||||||||
\(616\) | 74.0005 | 2.98157 | ||||||||
\(617\) | 24.5517 | 0.988415 | 0.494208 | − | 0.869344i | \(-0.335458\pi\) | ||||
0.494208 | + | 0.869344i | \(0.335458\pi\) | |||||||
\(618\) | 6.48718 | 0.260952 | ||||||||
\(619\) | −45.6370 | −1.83431 | −0.917154 | − | 0.398534i | \(-0.869519\pi\) | ||||
−0.917154 | + | 0.398534i | \(0.869519\pi\) | |||||||
\(620\) | −11.2125 | −0.450307 | ||||||||
\(621\) | −3.37760 | −0.135538 | ||||||||
\(622\) | −32.8625 | −1.31767 | ||||||||
\(623\) | −4.85755 | −0.194614 | ||||||||
\(624\) | 38.7710 | 1.55208 | ||||||||
\(625\) | 16.6721 | 0.666885 | ||||||||
\(626\) | −61.1574 | −2.44434 | ||||||||
\(627\) | −18.9115 | −0.755253 | ||||||||
\(628\) | −5.11563 | −0.204136 | ||||||||
\(629\) | 4.84157 | 0.193046 | ||||||||
\(630\) | −6.37943 | −0.254162 | ||||||||
\(631\) | −35.7625 | −1.42368 | −0.711841 | − | 0.702340i | \(-0.752139\pi\) | ||||
−0.711841 | + | 0.702340i | \(0.752139\pi\) | |||||||
\(632\) | 92.0874 | 3.66304 | ||||||||
\(633\) | 15.8802 | 0.631180 | ||||||||
\(634\) | 26.5179 | 1.05316 | ||||||||
\(635\) | 2.13386 | 0.0846796 | ||||||||
\(636\) | −33.0818 | −1.31178 | ||||||||
\(637\) | −9.43452 | −0.373809 | ||||||||
\(638\) | −29.1030 | −1.15220 | ||||||||
\(639\) | −2.81349 | −0.111300 | ||||||||
\(640\) | 10.7812 | 0.426165 | ||||||||
\(641\) | −44.2584 | −1.74810 | −0.874051 | − | 0.485834i | \(-0.838516\pi\) | ||||
−0.874051 | + | 0.485834i | \(0.838516\pi\) | |||||||
\(642\) | 41.0788 | 1.62125 | ||||||||
\(643\) | −1.36480 | −0.0538225 | −0.0269112 | − | 0.999638i | \(-0.508567\pi\) | ||||
−0.0269112 | + | 0.999638i | \(0.508567\pi\) | |||||||
\(644\) | −54.3796 | −2.14286 | ||||||||
\(645\) | −5.96014 | −0.234680 | ||||||||
\(646\) | 17.8312 | 0.701557 | ||||||||
\(647\) | −14.8379 | −0.583340 | −0.291670 | − | 0.956519i | \(-0.594211\pi\) | ||||
−0.291670 | + | 0.956519i | \(0.594211\pi\) | |||||||
\(648\) | −8.31098 | −0.326486 | ||||||||
\(649\) | −7.58779 | −0.297847 | ||||||||
\(650\) | −38.3127 | −1.50275 | ||||||||
\(651\) | 9.07797 | 0.355794 | ||||||||
\(652\) | −27.5357 | −1.07838 | ||||||||
\(653\) | −29.1855 | −1.14212 | −0.571059 | − | 0.820909i | \(-0.693467\pi\) | ||||
−0.571059 | + | 0.820909i | \(0.693467\pi\) | |||||||
\(654\) | −18.5690 | −0.726106 | ||||||||
\(655\) | 5.75606 | 0.224908 | ||||||||
\(656\) | −26.3693 | −1.02955 | ||||||||
\(657\) | 9.87519 | 0.385268 | ||||||||
\(658\) | −74.6998 | −2.91210 | ||||||||
\(659\) | −33.3257 | −1.29819 | −0.649093 | − | 0.760709i | \(-0.724851\pi\) | ||||
−0.649093 | + | 0.760709i | \(0.724851\pi\) | |||||||
\(660\) | 10.9976 | 0.428081 | ||||||||
\(661\) | 32.2325 | 1.25370 | 0.626849 | − | 0.779141i | \(-0.284344\pi\) | ||||
0.626849 | + | 0.779141i | \(0.284344\pi\) | |||||||
\(662\) | 17.2862 | 0.671848 | ||||||||
\(663\) | −3.24759 | −0.126126 | ||||||||
\(664\) | 17.9072 | 0.694934 | ||||||||
\(665\) | 15.9863 | 0.619922 | ||||||||
\(666\) | 12.9149 | 0.500444 | ||||||||
\(667\) | 13.0253 | 0.504340 | ||||||||
\(668\) | 35.8303 | 1.38632 | ||||||||
\(669\) | −5.26595 | −0.203594 | ||||||||
\(670\) | 1.64397 | 0.0635119 | ||||||||
\(671\) | 1.45168 | 0.0560415 | ||||||||
\(672\) | −47.9131 | −1.84829 | ||||||||
\(673\) | −19.6485 | −0.757394 | −0.378697 | − | 0.925521i | \(-0.623628\pi\) | ||||
−0.378697 | + | 0.925521i | \(0.623628\pi\) | |||||||
\(674\) | −75.0175 | −2.88956 | ||||||||
\(675\) | 4.42258 | 0.170225 | ||||||||
\(676\) | −12.5496 | −0.482677 | ||||||||
\(677\) | −18.9303 | −0.727549 | −0.363775 | − | 0.931487i | \(-0.618512\pi\) | ||||
−0.363775 | + | 0.931487i | \(0.618512\pi\) | |||||||
\(678\) | 35.0137 | 1.34469 | ||||||||
\(679\) | 6.09877 | 0.234049 | ||||||||
\(680\) | −6.31536 | −0.242183 | ||||||||
\(681\) | −1.83842 | −0.0704486 | ||||||||
\(682\) | −21.7680 | −0.833542 | ||||||||
\(683\) | 14.8209 | 0.567107 | 0.283554 | − | 0.958956i | \(-0.408487\pi\) | ||||
0.283554 | + | 0.958956i | \(0.408487\pi\) | |||||||
\(684\) | 34.1957 | 1.30751 | ||||||||
\(685\) | −10.8564 | −0.414803 | ||||||||
\(686\) | −34.3780 | −1.31256 | ||||||||
\(687\) | −6.83685 | −0.260842 | ||||||||
\(688\) | −93.6390 | −3.56995 | ||||||||
\(689\) | −21.0015 | −0.800094 | ||||||||
\(690\) | −6.84637 | −0.260637 | ||||||||
\(691\) | −22.7929 | −0.867083 | −0.433542 | − | 0.901134i | \(-0.642736\pi\) | ||||
−0.433542 | + | 0.901134i | \(0.642736\pi\) | |||||||
\(692\) | 79.1551 | 3.00902 | ||||||||
\(693\) | −8.90395 | −0.338233 | ||||||||
\(694\) | −23.6279 | −0.896902 | ||||||||
\(695\) | 7.43825 | 0.282149 | ||||||||
\(696\) | 32.0502 | 1.21486 | ||||||||
\(697\) | 2.20878 | 0.0836635 | ||||||||
\(698\) | 93.3864 | 3.53473 | ||||||||
\(699\) | −8.06025 | −0.304867 | ||||||||
\(700\) | 71.2039 | 2.69126 | ||||||||
\(701\) | 1.59758 | 0.0603396 | 0.0301698 | − | 0.999545i | \(-0.490395\pi\) | ||||
0.0301698 | + | 0.999545i | \(0.490395\pi\) | |||||||
\(702\) | −8.66298 | −0.326963 | ||||||||
\(703\) | −32.3637 | −1.22062 | ||||||||
\(704\) | 47.3402 | 1.78420 | ||||||||
\(705\) | −6.76129 | −0.254645 | ||||||||
\(706\) | 39.2488 | 1.47715 | ||||||||
\(707\) | −38.9175 | −1.46364 | ||||||||
\(708\) | 13.7202 | 0.515637 | ||||||||
\(709\) | −46.1682 | −1.73388 | −0.866941 | − | 0.498411i | \(-0.833917\pi\) | ||||
−0.866941 | + | 0.498411i | \(0.833917\pi\) | |||||||
\(710\) | −5.70293 | −0.214027 | ||||||||
\(711\) | −11.0802 | −0.415540 | ||||||||
\(712\) | −12.8275 | −0.480730 | ||||||||
\(713\) | 9.74243 | 0.364857 | ||||||||
\(714\) | 8.39529 | 0.314186 | ||||||||
\(715\) | 6.98168 | 0.261100 | ||||||||
\(716\) | −22.9705 | −0.858448 | ||||||||
\(717\) | 12.4804 | 0.466090 | ||||||||
\(718\) | −66.5897 | −2.48511 | ||||||||
\(719\) | 10.1788 | 0.379605 | 0.189803 | − | 0.981822i | \(-0.439215\pi\) | ||||
0.189803 | + | 0.981822i | \(0.439215\pi\) | |||||||
\(720\) | −9.07177 | −0.338085 | ||||||||
\(721\) | −7.65382 | −0.285043 | ||||||||
\(722\) | −68.5107 | −2.54970 | ||||||||
\(723\) | 0.772995 | 0.0287480 | ||||||||
\(724\) | −64.3616 | −2.39198 | ||||||||
\(725\) | −17.0551 | −0.633410 | ||||||||
\(726\) | −7.99188 | −0.296607 | ||||||||
\(727\) | 19.1832 | 0.711466 | 0.355733 | − | 0.934588i | \(-0.384231\pi\) | ||||
0.355733 | + | 0.934588i | \(0.384231\pi\) | |||||||
\(728\) | −84.9458 | −3.14830 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 20.0169 | 0.740861 | ||||||||
\(731\) | 7.84352 | 0.290103 | ||||||||
\(732\) | −2.62492 | −0.0970200 | ||||||||
\(733\) | 52.3403 | 1.93323 | 0.966617 | − | 0.256225i | \(-0.0824789\pi\) | ||||
0.966617 | + | 0.256225i | \(0.0824789\pi\) | |||||||
\(734\) | 13.3228 | 0.491754 | ||||||||
\(735\) | 2.20752 | 0.0814257 | ||||||||
\(736\) | −51.4201 | −1.89537 | ||||||||
\(737\) | 2.29453 | 0.0845201 | ||||||||
\(738\) | 5.89195 | 0.216886 | ||||||||
\(739\) | −1.11122 | −0.0408767 | −0.0204384 | − | 0.999791i | \(-0.506506\pi\) | ||||
−0.0204384 | + | 0.999791i | \(0.506506\pi\) | |||||||
\(740\) | 18.8205 | 0.691855 | ||||||||
\(741\) | 21.7087 | 0.797488 | ||||||||
\(742\) | 54.2907 | 1.99308 | ||||||||
\(743\) | −36.5068 | −1.33930 | −0.669652 | − | 0.742675i | \(-0.733557\pi\) | ||||
−0.669652 | + | 0.742675i | \(0.733557\pi\) | |||||||
\(744\) | 23.9724 | 0.878871 | ||||||||
\(745\) | −14.9613 | −0.548141 | ||||||||
\(746\) | −91.7861 | −3.36053 | ||||||||
\(747\) | −2.15464 | −0.0788343 | ||||||||
\(748\) | −14.4728 | −0.529178 | ||||||||
\(749\) | −48.4663 | −1.77092 | ||||||||
\(750\) | 19.0995 | 0.697416 | ||||||||
\(751\) | 0.573211 | 0.0209168 | 0.0104584 | − | 0.999945i | \(-0.496671\pi\) | ||||
0.0104584 | + | 0.999945i | \(0.496671\pi\) | |||||||
\(752\) | −106.226 | −3.87365 | ||||||||
\(753\) | −5.60340 | −0.204199 | ||||||||
\(754\) | 33.4076 | 1.21663 | ||||||||
\(755\) | −13.4940 | −0.491097 | ||||||||
\(756\) | 16.1001 | 0.585554 | ||||||||
\(757\) | −37.0281 | −1.34581 | −0.672905 | − | 0.739729i | \(-0.734954\pi\) | ||||
−0.672905 | + | 0.739729i | \(0.734954\pi\) | |||||||
\(758\) | 66.4505 | 2.41359 | ||||||||
\(759\) | −9.55567 | −0.346849 | ||||||||
\(760\) | 42.2154 | 1.53131 | ||||||||
\(761\) | −32.2101 | −1.16762 | −0.583808 | − | 0.811892i | \(-0.698438\pi\) | ||||
−0.583808 | + | 0.811892i | \(0.698438\pi\) | |||||||
\(762\) | −7.49077 | −0.271362 | ||||||||
\(763\) | 21.9084 | 0.793139 | ||||||||
\(764\) | 53.9898 | 1.95328 | ||||||||
\(765\) | 0.759881 | 0.0274736 | ||||||||
\(766\) | 58.5263 | 2.11464 | ||||||||
\(767\) | 8.71008 | 0.314503 | ||||||||
\(768\) | −4.38052 | −0.158068 | ||||||||
\(769\) | −32.9179 | −1.18705 | −0.593525 | − | 0.804815i | \(-0.702264\pi\) | ||||
−0.593525 | + | 0.804815i | \(0.702264\pi\) | |||||||
\(770\) | −18.0482 | −0.650414 | ||||||||
\(771\) | 12.4898 | 0.449809 | ||||||||
\(772\) | −31.3574 | −1.12858 | ||||||||
\(773\) | 20.2927 | 0.729876 | 0.364938 | − | 0.931032i | \(-0.381090\pi\) | ||||
0.364938 | + | 0.931032i | \(0.381090\pi\) | |||||||
\(774\) | 20.9227 | 0.752050 | ||||||||
\(775\) | −12.7566 | −0.458231 | ||||||||
\(776\) | 16.1052 | 0.578142 | ||||||||
\(777\) | −15.2375 | −0.546644 | ||||||||
\(778\) | 78.8511 | 2.82695 | ||||||||
\(779\) | −14.7647 | −0.529001 | ||||||||
\(780\) | −12.6242 | −0.452020 | ||||||||
\(781\) | −7.95975 | −0.284822 | ||||||||
\(782\) | 9.00979 | 0.322189 | ||||||||
\(783\) | −3.85637 | −0.137815 | ||||||||
\(784\) | 34.6821 | 1.23865 | ||||||||
\(785\) | 0.759881 | 0.0271213 | ||||||||
\(786\) | −20.2063 | −0.720734 | ||||||||
\(787\) | −21.3572 | −0.761300 | −0.380650 | − | 0.924719i | \(-0.624300\pi\) | ||||
−0.380650 | + | 0.924719i | \(0.624300\pi\) | |||||||
\(788\) | −3.28121 | −0.116888 | ||||||||
\(789\) | 24.6807 | 0.878656 | ||||||||
\(790\) | −22.4595 | −0.799073 | ||||||||
\(791\) | −41.3105 | −1.46883 | ||||||||
\(792\) | −23.5129 | −0.835494 | ||||||||
\(793\) | −1.66640 | −0.0591755 | ||||||||
\(794\) | −36.5210 | −1.29608 | ||||||||
\(795\) | 4.91401 | 0.174282 | ||||||||
\(796\) | 0.0603060 | 0.00213749 | ||||||||
\(797\) | −30.8470 | −1.09266 | −0.546329 | − | 0.837571i | \(-0.683975\pi\) | ||||
−0.546329 | + | 0.837571i | \(0.683975\pi\) | |||||||
\(798\) | −56.1188 | −1.98659 | ||||||||
\(799\) | 8.89782 | 0.314782 | ||||||||
\(800\) | 67.3288 | 2.38043 | ||||||||
\(801\) | 1.54344 | 0.0545346 | ||||||||
\(802\) | 33.2005 | 1.17235 | ||||||||
\(803\) | 27.9382 | 0.985919 | ||||||||
\(804\) | −4.14896 | −0.146323 | ||||||||
\(805\) | 8.07761 | 0.284698 | ||||||||
\(806\) | 24.9877 | 0.880155 | ||||||||
\(807\) | 22.8330 | 0.803760 | ||||||||
\(808\) | −102.770 | −3.61545 | ||||||||
\(809\) | −22.5476 | −0.792731 | −0.396365 | − | 0.918093i | \(-0.629729\pi\) | ||||
−0.396365 | + | 0.918093i | \(0.629729\pi\) | |||||||
\(810\) | 2.02699 | 0.0712213 | ||||||||
\(811\) | 10.1874 | 0.357728 | 0.178864 | − | 0.983874i | \(-0.442758\pi\) | ||||
0.178864 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(812\) | −62.0878 | −2.17886 | ||||||||
\(813\) | −32.3091 | −1.13313 | ||||||||
\(814\) | 36.5381 | 1.28066 | ||||||||
\(815\) | 4.09018 | 0.143273 | ||||||||
\(816\) | 11.9384 | 0.417927 | ||||||||
\(817\) | −52.4304 | −1.83431 | ||||||||
\(818\) | 16.7823 | 0.586778 | ||||||||
\(819\) | 10.2209 | 0.357148 | ||||||||
\(820\) | 8.58613 | 0.299841 | ||||||||
\(821\) | 16.8083 | 0.586613 | 0.293306 | − | 0.956018i | \(-0.405244\pi\) | ||||
0.293306 | + | 0.956018i | \(0.405244\pi\) | |||||||
\(822\) | 38.1108 | 1.32927 | ||||||||
\(823\) | −31.5932 | −1.10127 | −0.550634 | − | 0.834746i | \(-0.685614\pi\) | ||||
−0.550634 | + | 0.834746i | \(0.685614\pi\) | |||||||
\(824\) | −20.2116 | −0.704105 | ||||||||
\(825\) | 12.5121 | 0.435614 | ||||||||
\(826\) | −22.5163 | −0.783443 | ||||||||
\(827\) | 16.1401 | 0.561246 | 0.280623 | − | 0.959818i | \(-0.409459\pi\) | ||||
0.280623 | + | 0.959818i | \(0.409459\pi\) | |||||||
\(828\) | 17.2785 | 0.600471 | ||||||||
\(829\) | 9.65887 | 0.335467 | 0.167733 | − | 0.985832i | \(-0.446355\pi\) | ||||
0.167733 | + | 0.985832i | \(0.446355\pi\) | |||||||
\(830\) | −4.36745 | −0.151596 | ||||||||
\(831\) | 6.19453 | 0.214886 | ||||||||
\(832\) | −54.3422 | −1.88398 | ||||||||
\(833\) | −2.90509 | −0.100655 | ||||||||
\(834\) | −26.1115 | −0.904166 | ||||||||
\(835\) | −5.32228 | −0.184185 | ||||||||
\(836\) | 96.7443 | 3.34597 | ||||||||
\(837\) | −2.88443 | −0.0997004 | ||||||||
\(838\) | −45.8991 | −1.58556 | ||||||||
\(839\) | 3.22548 | 0.111356 | 0.0556779 | − | 0.998449i | \(-0.482268\pi\) | ||||
0.0556779 | + | 0.998449i | \(0.482268\pi\) | |||||||
\(840\) | 19.8759 | 0.685784 | ||||||||
\(841\) | −14.1284 | −0.487188 | ||||||||
\(842\) | 1.84266 | 0.0635022 | ||||||||
\(843\) | 9.37561 | 0.322913 | ||||||||
\(844\) | −81.2370 | −2.79629 | ||||||||
\(845\) | 1.86413 | 0.0641281 | ||||||||
\(846\) | 23.7350 | 0.816028 | ||||||||
\(847\) | 9.42913 | 0.323989 | ||||||||
\(848\) | 77.2033 | 2.65117 | ||||||||
\(849\) | 4.59361 | 0.157652 | ||||||||
\(850\) | −11.7973 | −0.404644 | ||||||||
\(851\) | −16.3529 | −0.560569 | ||||||||
\(852\) | 14.3928 | 0.493089 | ||||||||
\(853\) | −3.62450 | −0.124100 | −0.0620502 | − | 0.998073i | \(-0.519764\pi\) | ||||
−0.0620502 | + | 0.998073i | \(0.519764\pi\) | |||||||
\(854\) | 4.30778 | 0.147409 | ||||||||
\(855\) | −5.07947 | −0.173714 | ||||||||
\(856\) | −127.986 | −4.37448 | ||||||||
\(857\) | −1.86891 | −0.0638408 | −0.0319204 | − | 0.999490i | \(-0.510162\pi\) | ||||
−0.0319204 | + | 0.999490i | \(0.510162\pi\) | |||||||
\(858\) | −24.5087 | −0.836714 | ||||||||
\(859\) | −3.90668 | −0.133294 | −0.0666471 | − | 0.997777i | \(-0.521230\pi\) | ||||
−0.0666471 | + | 0.997777i | \(0.521230\pi\) | |||||||
\(860\) | 30.4899 | 1.03970 | ||||||||
\(861\) | −6.95155 | −0.236908 | ||||||||
\(862\) | −102.908 | −3.50504 | ||||||||
\(863\) | −17.9763 | −0.611921 | −0.305961 | − | 0.952044i | \(-0.598978\pi\) | ||||
−0.305961 | + | 0.952044i | \(0.598978\pi\) | |||||||
\(864\) | 15.2239 | 0.517927 | ||||||||
\(865\) | −11.7578 | −0.399777 | ||||||||
\(866\) | −34.9323 | −1.18705 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −46.4395 | −1.57626 | ||||||||
\(869\) | −31.3474 | −1.06339 | ||||||||
\(870\) | −7.81683 | −0.265015 | ||||||||
\(871\) | −2.63391 | −0.0892466 | ||||||||
\(872\) | 57.8542 | 1.95919 | ||||||||
\(873\) | −1.93782 | −0.0655852 | ||||||||
\(874\) | −60.2265 | −2.03719 | ||||||||
\(875\) | −22.5343 | −0.761800 | ||||||||
\(876\) | −50.5178 | −1.70684 | ||||||||
\(877\) | −2.79679 | −0.0944408 | −0.0472204 | − | 0.998884i | \(-0.515036\pi\) | ||||
−0.0472204 | + | 0.998884i | \(0.515036\pi\) | |||||||
\(878\) | −35.1250 | −1.18541 | ||||||||
\(879\) | −12.3861 | −0.417773 | ||||||||
\(880\) | −25.6652 | −0.865175 | ||||||||
\(881\) | 37.1342 | 1.25108 | 0.625542 | − | 0.780190i | \(-0.284878\pi\) | ||||
0.625542 | + | 0.780190i | \(0.284878\pi\) | |||||||
\(882\) | −7.74936 | −0.260935 | ||||||||
\(883\) | −7.30786 | −0.245929 | −0.122965 | − | 0.992411i | \(-0.539240\pi\) | ||||
−0.122965 | + | 0.992411i | \(0.539240\pi\) | |||||||
\(884\) | 16.6134 | 0.558770 | ||||||||
\(885\) | −2.03802 | −0.0685072 | ||||||||
\(886\) | 13.0668 | 0.438987 | ||||||||
\(887\) | −58.8423 | −1.97573 | −0.987866 | − | 0.155309i | \(-0.950363\pi\) | ||||
−0.987866 | + | 0.155309i | \(0.950363\pi\) | |||||||
\(888\) | −40.2382 | −1.35030 | ||||||||
\(889\) | 8.83790 | 0.296414 | ||||||||
\(890\) | 3.12853 | 0.104869 | ||||||||
\(891\) | 2.82913 | 0.0947795 | ||||||||
\(892\) | 26.9387 | 0.901973 | ||||||||
\(893\) | −59.4780 | −1.99036 | ||||||||
\(894\) | 52.5208 | 1.75656 | ||||||||
\(895\) | 3.41206 | 0.114053 | ||||||||
\(896\) | 44.6530 | 1.49175 | ||||||||
\(897\) | 10.9690 | 0.366245 | ||||||||
\(898\) | 61.7345 | 2.06011 | ||||||||
\(899\) | 11.1234 | 0.370986 | ||||||||
\(900\) | −22.6243 | −0.754143 | ||||||||
\(901\) | −6.46681 | −0.215441 | ||||||||
\(902\) | 16.6691 | 0.555021 | ||||||||
\(903\) | −24.6854 | −0.821478 | ||||||||
\(904\) | −109.090 | −3.62827 | ||||||||
\(905\) | 9.56034 | 0.317797 | ||||||||
\(906\) | 47.3698 | 1.57376 | ||||||||
\(907\) | 1.07045 | 0.0355438 | 0.0177719 | − | 0.999842i | \(-0.494343\pi\) | ||||
0.0177719 | + | 0.999842i | \(0.494343\pi\) | |||||||
\(908\) | 9.40470 | 0.312106 | ||||||||
\(909\) | 12.3656 | 0.410142 | ||||||||
\(910\) | 20.7177 | 0.686786 | ||||||||
\(911\) | −14.1314 | −0.468193 | −0.234097 | − | 0.972213i | \(-0.575213\pi\) | ||||
−0.234097 | + | 0.972213i | \(0.575213\pi\) | |||||||
\(912\) | −79.8029 | −2.64254 | ||||||||
\(913\) | −6.09577 | −0.201741 | ||||||||
\(914\) | 68.7791 | 2.27501 | ||||||||
\(915\) | 0.389909 | 0.0128900 | ||||||||
\(916\) | 34.9748 | 1.15560 | ||||||||
\(917\) | 23.8401 | 0.787271 | ||||||||
\(918\) | −2.66751 | −0.0880411 | ||||||||
\(919\) | 44.3813 | 1.46401 | 0.732003 | − | 0.681302i | \(-0.238586\pi\) | ||||
0.732003 | + | 0.681302i | \(0.238586\pi\) | |||||||
\(920\) | 21.3307 | 0.703254 | ||||||||
\(921\) | 5.33559 | 0.175814 | ||||||||
\(922\) | −35.8420 | −1.18039 | ||||||||
\(923\) | 9.13706 | 0.300750 | ||||||||
\(924\) | 45.5493 | 1.49846 | ||||||||
\(925\) | 21.4122 | 0.704029 | ||||||||
\(926\) | −1.65189 | −0.0542845 | ||||||||
\(927\) | 2.43192 | 0.0798747 | ||||||||
\(928\) | −58.7088 | −1.92721 | ||||||||
\(929\) | 0.674930 | 0.0221437 | 0.0110719 | − | 0.999939i | \(-0.496476\pi\) | ||||
0.0110719 | + | 0.999939i | \(0.496476\pi\) | |||||||
\(930\) | −5.84671 | −0.191721 | ||||||||
\(931\) | 19.4192 | 0.636440 | ||||||||
\(932\) | 41.2332 | 1.35064 | ||||||||
\(933\) | −12.3195 | −0.403323 | ||||||||
\(934\) | −66.2989 | −2.16936 | ||||||||
\(935\) | 2.14981 | 0.0703062 | ||||||||
\(936\) | 26.9906 | 0.882216 | ||||||||
\(937\) | −12.7371 | −0.416103 | −0.208052 | − | 0.978118i | \(-0.566712\pi\) | ||||
−0.208052 | + | 0.978118i | \(0.566712\pi\) | |||||||
\(938\) | 6.80889 | 0.222318 | ||||||||
\(939\) | −22.9268 | −0.748186 | ||||||||
\(940\) | 34.5882 | 1.12814 | ||||||||
\(941\) | −48.5758 | −1.58352 | −0.791762 | − | 0.610829i | \(-0.790836\pi\) | ||||
−0.791762 | + | 0.610829i | \(0.790836\pi\) | |||||||
\(942\) | −2.66751 | −0.0869123 | ||||||||
\(943\) | −7.46037 | −0.242943 | ||||||||
\(944\) | −32.0190 | −1.04213 | ||||||||
\(945\) | −2.39153 | −0.0777963 | ||||||||
\(946\) | 59.1931 | 1.92453 | ||||||||
\(947\) | −3.47933 | −0.113063 | −0.0565315 | − | 0.998401i | \(-0.518004\pi\) | ||||
−0.0565315 | + | 0.998401i | \(0.518004\pi\) | |||||||
\(948\) | 56.6822 | 1.84095 | ||||||||
\(949\) | −32.0705 | −1.04105 | ||||||||
\(950\) | 78.8597 | 2.55855 | ||||||||
\(951\) | 9.94107 | 0.322361 | ||||||||
\(952\) | −26.1566 | −0.847741 | ||||||||
\(953\) | −44.1556 | −1.43034 | −0.715171 | − | 0.698950i | \(-0.753651\pi\) | ||||
−0.715171 | + | 0.698950i | \(0.753651\pi\) | |||||||
\(954\) | −17.2503 | −0.558499 | ||||||||
\(955\) | −8.01971 | −0.259512 | ||||||||
\(956\) | −63.8453 | −2.06490 | ||||||||
\(957\) | −10.9102 | −0.352676 | ||||||||
\(958\) | −26.3824 | −0.852376 | ||||||||
\(959\) | −44.9646 | −1.45198 | ||||||||
\(960\) | 12.7152 | 0.410380 | ||||||||
\(961\) | −22.6801 | −0.731616 | ||||||||
\(962\) | −41.9424 | −1.35228 | ||||||||
\(963\) | 15.3997 | 0.496247 | ||||||||
\(964\) | −3.95435 | −0.127361 | ||||||||
\(965\) | 4.65787 | 0.149942 | ||||||||
\(966\) | −28.3559 | −0.912337 | ||||||||
\(967\) | 26.8292 | 0.862768 | 0.431384 | − | 0.902169i | \(-0.358026\pi\) | ||||
0.431384 | + | 0.902169i | \(0.358026\pi\) | |||||||
\(968\) | 24.8997 | 0.800308 | ||||||||
\(969\) | 6.68456 | 0.214739 | ||||||||
\(970\) | −3.92794 | −0.126119 | ||||||||
\(971\) | −4.26089 | −0.136738 | −0.0683692 | − | 0.997660i | \(-0.521780\pi\) | ||||
−0.0683692 | + | 0.997660i | \(0.521780\pi\) | |||||||
\(972\) | −5.11563 | −0.164084 | ||||||||
\(973\) | 30.8073 | 0.987637 | ||||||||
\(974\) | −65.2091 | −2.08943 | ||||||||
\(975\) | −14.3627 | −0.459975 | ||||||||
\(976\) | 6.12582 | 0.196083 | ||||||||
\(977\) | −40.5153 | −1.29620 | −0.648100 | − | 0.761555i | \(-0.724436\pi\) | ||||
−0.648100 | + | 0.761555i | \(0.724436\pi\) | |||||||
\(978\) | −14.3583 | −0.459128 | ||||||||
\(979\) | 4.36659 | 0.139557 | ||||||||
\(980\) | −11.2929 | −0.360737 | ||||||||
\(981\) | −6.96117 | −0.222253 | ||||||||
\(982\) | 22.0490 | 0.703612 | ||||||||
\(983\) | 22.5853 | 0.720358 | 0.360179 | − | 0.932883i | \(-0.382716\pi\) | ||||
0.360179 | + | 0.932883i | \(0.382716\pi\) | |||||||
\(984\) | −18.3571 | −0.585204 | ||||||||
\(985\) | 0.487395 | 0.0155297 | ||||||||
\(986\) | 10.2869 | 0.327602 | ||||||||
\(987\) | −28.0035 | −0.891362 | ||||||||
\(988\) | −111.054 | −3.53308 | ||||||||
\(989\) | −26.4922 | −0.842404 | ||||||||
\(990\) | 5.73464 | 0.182259 | ||||||||
\(991\) | −49.4913 | −1.57214 | −0.786072 | − | 0.618135i | \(-0.787889\pi\) | ||||
−0.786072 | + | 0.618135i | \(0.787889\pi\) | |||||||
\(992\) | −43.9121 | −1.39421 | ||||||||
\(993\) | 6.48028 | 0.205645 | ||||||||
\(994\) | −23.6201 | −0.749184 | ||||||||
\(995\) | −0.00895792 | −0.000283985 0 | ||||||||
\(996\) | 11.0224 | 0.349257 | ||||||||
\(997\) | −45.5599 | −1.44290 | −0.721448 | − | 0.692468i | \(-0.756523\pi\) | ||||
−0.721448 | + | 0.692468i | \(0.756523\pi\) | |||||||
\(998\) | 20.2581 | 0.641259 | ||||||||
\(999\) | 4.84157 | 0.153180 |
(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 | 8007.2.a.f.1.2 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.2 | ✓ | 48 | 1.1 | even | 1 | trivial |