Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.614026 | −0.434182 | −0.217091 | − | 0.976151i | \(-0.569657\pi\) | ||||
−0.217091 | + | 0.976151i | \(0.569657\pi\) | |||||||
\(3\) | −1.52615 | −0.881123 | −0.440562 | − | 0.897722i | \(-0.645221\pi\) | ||||
−0.440562 | + | 0.897722i | \(0.645221\pi\) | |||||||
\(4\) | −1.62297 | −0.811486 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.937096 | 0.382568 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.22460 | 0.786514 | ||||||||
\(9\) | −0.670866 | −0.223622 | ||||||||
\(10\) | 0.614026 | 0.194172 | ||||||||
\(11\) | −1.70380 | −0.513714 | −0.256857 | − | 0.966449i | \(-0.582687\pi\) | ||||
−0.256857 | + | 0.966449i | \(0.582687\pi\) | |||||||
\(12\) | 2.47690 | 0.715019 | ||||||||
\(13\) | −4.10542 | −1.13864 | −0.569319 | − | 0.822116i | \(-0.692793\pi\) | ||||
−0.569319 | + | 0.822116i | \(0.692793\pi\) | |||||||
\(14\) | 0.614026 | 0.164105 | ||||||||
\(15\) | 1.52615 | 0.394050 | ||||||||
\(16\) | 1.87998 | 0.469996 | ||||||||
\(17\) | −0.650974 | −0.157884 | −0.0789422 | − | 0.996879i | \(-0.525154\pi\) | ||||
−0.0789422 | + | 0.996879i | \(0.525154\pi\) | |||||||
\(18\) | 0.411929 | 0.0970927 | ||||||||
\(19\) | 6.66509 | 1.52908 | 0.764538 | − | 0.644578i | \(-0.222967\pi\) | ||||
0.764538 | + | 0.644578i | \(0.222967\pi\) | |||||||
\(20\) | 1.62297 | 0.362908 | ||||||||
\(21\) | 1.52615 | 0.333033 | ||||||||
\(22\) | 1.04618 | 0.223046 | ||||||||
\(23\) | 1.46015 | 0.304463 | 0.152231 | − | 0.988345i | \(-0.451354\pi\) | ||||
0.152231 | + | 0.988345i | \(0.451354\pi\) | |||||||
\(24\) | −3.39507 | −0.693016 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.52083 | 0.494376 | ||||||||
\(27\) | 5.60229 | 1.07816 | ||||||||
\(28\) | 1.62297 | 0.306713 | ||||||||
\(29\) | −8.37011 | −1.55429 | −0.777146 | − | 0.629321i | \(-0.783333\pi\) | ||||
−0.777146 | + | 0.629321i | \(0.783333\pi\) | |||||||
\(30\) | −0.937096 | −0.171089 | ||||||||
\(31\) | 6.49153 | 1.16591 | 0.582956 | − | 0.812503i | \(-0.301896\pi\) | ||||
0.582956 | + | 0.812503i | \(0.301896\pi\) | |||||||
\(32\) | −5.60356 | −0.990578 | ||||||||
\(33\) | 2.60025 | 0.452646 | ||||||||
\(34\) | 0.399715 | 0.0685506 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.08880 | 0.181466 | ||||||||
\(37\) | 1.26083 | 0.207279 | 0.103639 | − | 0.994615i | \(-0.466951\pi\) | ||||
0.103639 | + | 0.994615i | \(0.466951\pi\) | |||||||
\(38\) | −4.09254 | −0.663897 | ||||||||
\(39\) | 6.26549 | 1.00328 | ||||||||
\(40\) | −2.22460 | −0.351740 | ||||||||
\(41\) | −11.8525 | −1.85105 | −0.925525 | − | 0.378686i | \(-0.876376\pi\) | ||||
−0.925525 | + | 0.378686i | \(0.876376\pi\) | |||||||
\(42\) | −0.937096 | −0.144597 | ||||||||
\(43\) | −2.32014 | −0.353818 | −0.176909 | − | 0.984227i | \(-0.556610\pi\) | ||||
−0.176909 | + | 0.984227i | \(0.556610\pi\) | |||||||
\(44\) | 2.76522 | 0.416872 | ||||||||
\(45\) | 0.670866 | 0.100007 | ||||||||
\(46\) | −0.896571 | −0.132192 | ||||||||
\(47\) | −6.47208 | −0.944050 | −0.472025 | − | 0.881585i | \(-0.656477\pi\) | ||||
−0.472025 | + | 0.881585i | \(0.656477\pi\) | |||||||
\(48\) | −2.86914 | −0.414124 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.614026 | −0.0868364 | ||||||||
\(51\) | 0.993484 | 0.139116 | ||||||||
\(52\) | 6.66298 | 0.923990 | ||||||||
\(53\) | −3.55565 | −0.488406 | −0.244203 | − | 0.969724i | \(-0.578526\pi\) | ||||
−0.244203 | + | 0.969724i | \(0.578526\pi\) | |||||||
\(54\) | −3.43995 | −0.468118 | ||||||||
\(55\) | 1.70380 | 0.229740 | ||||||||
\(56\) | −2.22460 | −0.297275 | ||||||||
\(57\) | −10.1719 | −1.34730 | ||||||||
\(58\) | 5.13947 | 0.674845 | ||||||||
\(59\) | −2.36574 | −0.307993 | −0.153996 | − | 0.988071i | \(-0.549214\pi\) | ||||
−0.153996 | + | 0.988071i | \(0.549214\pi\) | |||||||
\(60\) | −2.47690 | −0.319766 | ||||||||
\(61\) | −8.50184 | −1.08855 | −0.544274 | − | 0.838907i | \(-0.683195\pi\) | ||||
−0.544274 | + | 0.838907i | \(0.683195\pi\) | |||||||
\(62\) | −3.98597 | −0.506218 | ||||||||
\(63\) | 0.670866 | 0.0845212 | ||||||||
\(64\) | −0.319237 | −0.0399047 | ||||||||
\(65\) | 4.10542 | 0.509215 | ||||||||
\(66\) | −1.59662 | −0.196531 | ||||||||
\(67\) | 10.4007 | 1.27065 | 0.635327 | − | 0.772243i | \(-0.280865\pi\) | ||||
0.635327 | + | 0.772243i | \(0.280865\pi\) | |||||||
\(68\) | 1.05651 | 0.128121 | ||||||||
\(69\) | −2.22841 | −0.268269 | ||||||||
\(70\) | −0.614026 | −0.0733901 | ||||||||
\(71\) | −6.68333 | −0.793166 | −0.396583 | − | 0.917999i | \(-0.629804\pi\) | ||||
−0.396583 | + | 0.917999i | \(0.629804\pi\) | |||||||
\(72\) | −1.49241 | −0.175882 | ||||||||
\(73\) | −8.71692 | −1.02024 | −0.510119 | − | 0.860104i | \(-0.670399\pi\) | ||||
−0.510119 | + | 0.860104i | \(0.670399\pi\) | |||||||
\(74\) | −0.774180 | −0.0899966 | ||||||||
\(75\) | −1.52615 | −0.176225 | ||||||||
\(76\) | −10.8173 | −1.24082 | ||||||||
\(77\) | 1.70380 | 0.194166 | ||||||||
\(78\) | −3.84717 | −0.435606 | ||||||||
\(79\) | 3.26503 | 0.367345 | 0.183672 | − | 0.982988i | \(-0.441201\pi\) | ||||
0.183672 | + | 0.982988i | \(0.441201\pi\) | |||||||
\(80\) | −1.87998 | −0.210188 | ||||||||
\(81\) | −6.53734 | −0.726371 | ||||||||
\(82\) | 7.27774 | 0.803692 | ||||||||
\(83\) | 14.2987 | 1.56949 | 0.784745 | − | 0.619818i | \(-0.212794\pi\) | ||||
0.784745 | + | 0.619818i | \(0.212794\pi\) | |||||||
\(84\) | −2.47690 | −0.270252 | ||||||||
\(85\) | 0.650974 | 0.0706081 | ||||||||
\(86\) | 1.42463 | 0.153622 | ||||||||
\(87\) | 12.7740 | 1.36952 | ||||||||
\(88\) | −3.79027 | −0.404044 | ||||||||
\(89\) | −11.1853 | −1.18564 | −0.592821 | − | 0.805335i | \(-0.701986\pi\) | ||||
−0.592821 | + | 0.805335i | \(0.701986\pi\) | |||||||
\(90\) | −0.411929 | −0.0434212 | ||||||||
\(91\) | 4.10542 | 0.430365 | ||||||||
\(92\) | −2.36979 | −0.247067 | ||||||||
\(93\) | −9.90705 | −1.02731 | ||||||||
\(94\) | 3.97403 | 0.409889 | ||||||||
\(95\) | −6.66509 | −0.683824 | ||||||||
\(96\) | 8.55187 | 0.872821 | ||||||||
\(97\) | −9.95302 | −1.01058 | −0.505288 | − | 0.862951i | \(-0.668614\pi\) | ||||
−0.505288 | + | 0.862951i | \(0.668614\pi\) | |||||||
\(98\) | −0.614026 | −0.0620260 | ||||||||
\(99\) | 1.14302 | 0.114878 | ||||||||
\(100\) | −1.62297 | −0.162297 | ||||||||
\(101\) | −13.4985 | −1.34315 | −0.671577 | − | 0.740935i | \(-0.734383\pi\) | ||||
−0.671577 | + | 0.740935i | \(0.734383\pi\) | |||||||
\(102\) | −0.610025 | −0.0604015 | ||||||||
\(103\) | 8.95643 | 0.882503 | 0.441251 | − | 0.897384i | \(-0.354535\pi\) | ||||
0.441251 | + | 0.897384i | \(0.354535\pi\) | |||||||
\(104\) | −9.13291 | −0.895556 | ||||||||
\(105\) | −1.52615 | −0.148937 | ||||||||
\(106\) | 2.18326 | 0.212057 | ||||||||
\(107\) | −13.7420 | −1.32849 | −0.664245 | − | 0.747515i | \(-0.731247\pi\) | ||||
−0.664245 | + | 0.747515i | \(0.731247\pi\) | |||||||
\(108\) | −9.09236 | −0.874913 | ||||||||
\(109\) | 4.23676 | 0.405808 | 0.202904 | − | 0.979199i | \(-0.434962\pi\) | ||||
0.202904 | + | 0.979199i | \(0.434962\pi\) | |||||||
\(110\) | −1.04618 | −0.0997490 | ||||||||
\(111\) | −1.92421 | −0.182638 | ||||||||
\(112\) | −1.87998 | −0.177642 | ||||||||
\(113\) | −20.3245 | −1.91197 | −0.955986 | − | 0.293411i | \(-0.905209\pi\) | ||||
−0.955986 | + | 0.293411i | \(0.905209\pi\) | |||||||
\(114\) | 6.24583 | 0.584975 | ||||||||
\(115\) | −1.46015 | −0.136160 | ||||||||
\(116\) | 13.5845 | 1.26129 | ||||||||
\(117\) | 2.75419 | 0.254625 | ||||||||
\(118\) | 1.45262 | 0.133725 | ||||||||
\(119\) | 0.650974 | 0.0596747 | ||||||||
\(120\) | 3.39507 | 0.309926 | ||||||||
\(121\) | −8.09707 | −0.736097 | ||||||||
\(122\) | 5.22035 | 0.472628 | ||||||||
\(123\) | 18.0887 | 1.63100 | ||||||||
\(124\) | −10.5356 | −0.946122 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.411929 | −0.0366976 | ||||||||
\(127\) | −5.18231 | −0.459855 | −0.229928 | − | 0.973208i | \(-0.573849\pi\) | ||||
−0.229928 | + | 0.973208i | \(0.573849\pi\) | |||||||
\(128\) | 11.4031 | 1.00790 | ||||||||
\(129\) | 3.54089 | 0.311758 | ||||||||
\(130\) | −2.52083 | −0.221092 | ||||||||
\(131\) | −21.1192 | −1.84520 | −0.922598 | − | 0.385762i | \(-0.873939\pi\) | ||||
−0.922598 | + | 0.385762i | \(0.873939\pi\) | |||||||
\(132\) | −4.22014 | −0.367316 | ||||||||
\(133\) | −6.66509 | −0.577937 | ||||||||
\(134\) | −6.38633 | −0.551695 | ||||||||
\(135\) | −5.60229 | −0.482169 | ||||||||
\(136\) | −1.44816 | −0.124178 | ||||||||
\(137\) | 13.2511 | 1.13212 | 0.566060 | − | 0.824364i | \(-0.308467\pi\) | ||||
0.566060 | + | 0.824364i | \(0.308467\pi\) | |||||||
\(138\) | 1.36830 | 0.116478 | ||||||||
\(139\) | 4.86864 | 0.412953 | 0.206476 | − | 0.978452i | \(-0.433800\pi\) | ||||
0.206476 | + | 0.978452i | \(0.433800\pi\) | |||||||
\(140\) | −1.62297 | −0.137166 | ||||||||
\(141\) | 9.87737 | 0.831824 | ||||||||
\(142\) | 4.10374 | 0.344378 | ||||||||
\(143\) | 6.99481 | 0.584935 | ||||||||
\(144\) | −1.26122 | −0.105101 | ||||||||
\(145\) | 8.37011 | 0.695100 | ||||||||
\(146\) | 5.35241 | 0.442969 | ||||||||
\(147\) | −1.52615 | −0.125875 | ||||||||
\(148\) | −2.04629 | −0.168204 | ||||||||
\(149\) | 9.15495 | 0.750003 | 0.375001 | − | 0.927024i | \(-0.377642\pi\) | ||||
0.375001 | + | 0.927024i | \(0.377642\pi\) | |||||||
\(150\) | 0.937096 | 0.0765135 | ||||||||
\(151\) | 20.6800 | 1.68291 | 0.841456 | − | 0.540326i | \(-0.181699\pi\) | ||||
0.841456 | + | 0.540326i | \(0.181699\pi\) | |||||||
\(152\) | 14.8272 | 1.20264 | ||||||||
\(153\) | 0.436717 | 0.0353064 | ||||||||
\(154\) | −1.04618 | −0.0843033 | ||||||||
\(155\) | −6.49153 | −0.521412 | ||||||||
\(156\) | −10.1687 | −0.814149 | ||||||||
\(157\) | 1.97961 | 0.157990 | 0.0789950 | − | 0.996875i | \(-0.474829\pi\) | ||||
0.0789950 | + | 0.996875i | \(0.474829\pi\) | |||||||
\(158\) | −2.00481 | −0.159494 | ||||||||
\(159\) | 5.42646 | 0.430346 | ||||||||
\(160\) | 5.60356 | 0.443000 | ||||||||
\(161\) | −1.46015 | −0.115076 | ||||||||
\(162\) | 4.01410 | 0.315377 | ||||||||
\(163\) | −22.4027 | −1.75471 | −0.877357 | − | 0.479838i | \(-0.840696\pi\) | ||||
−0.877357 | + | 0.479838i | \(0.840696\pi\) | |||||||
\(164\) | 19.2363 | 1.50210 | ||||||||
\(165\) | −2.60025 | −0.202429 | ||||||||
\(166\) | −8.77980 | −0.681444 | ||||||||
\(167\) | 19.4040 | 1.50152 | 0.750762 | − | 0.660572i | \(-0.229686\pi\) | ||||
0.750762 | + | 0.660572i | \(0.229686\pi\) | |||||||
\(168\) | 3.39507 | 0.261935 | ||||||||
\(169\) | 3.85448 | 0.296498 | ||||||||
\(170\) | −0.399715 | −0.0306567 | ||||||||
\(171\) | −4.47138 | −0.341935 | ||||||||
\(172\) | 3.76553 | 0.287119 | ||||||||
\(173\) | −23.2766 | −1.76968 | −0.884842 | − | 0.465891i | \(-0.845734\pi\) | ||||
−0.884842 | + | 0.465891i | \(0.845734\pi\) | |||||||
\(174\) | −7.84360 | −0.594622 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −3.20311 | −0.241444 | ||||||||
\(177\) | 3.61047 | 0.271379 | ||||||||
\(178\) | 6.86807 | 0.514784 | ||||||||
\(179\) | 4.71244 | 0.352224 | 0.176112 | − | 0.984370i | \(-0.443648\pi\) | ||||
0.176112 | + | 0.984370i | \(0.443648\pi\) | |||||||
\(180\) | −1.08880 | −0.0811541 | ||||||||
\(181\) | 7.10961 | 0.528453 | 0.264227 | − | 0.964461i | \(-0.414883\pi\) | ||||
0.264227 | + | 0.964461i | \(0.414883\pi\) | |||||||
\(182\) | −2.52083 | −0.186857 | ||||||||
\(183\) | 12.9751 | 0.959146 | ||||||||
\(184\) | 3.24825 | 0.239464 | ||||||||
\(185\) | −1.26083 | −0.0926978 | ||||||||
\(186\) | 6.08318 | 0.446041 | ||||||||
\(187\) | 1.10913 | 0.0811075 | ||||||||
\(188\) | 10.5040 | 0.766084 | ||||||||
\(189\) | −5.60229 | −0.407507 | ||||||||
\(190\) | 4.09254 | 0.296904 | ||||||||
\(191\) | −26.7248 | −1.93374 | −0.966869 | − | 0.255274i | \(-0.917834\pi\) | ||||
−0.966869 | + | 0.255274i | \(0.917834\pi\) | |||||||
\(192\) | 0.487204 | 0.0351609 | ||||||||
\(193\) | −8.12503 | −0.584853 | −0.292426 | − | 0.956288i | \(-0.594463\pi\) | ||||
−0.292426 | + | 0.956288i | \(0.594463\pi\) | |||||||
\(194\) | 6.11141 | 0.438774 | ||||||||
\(195\) | −6.26549 | −0.448681 | ||||||||
\(196\) | −1.62297 | −0.115927 | ||||||||
\(197\) | 15.0454 | 1.07194 | 0.535971 | − | 0.844236i | \(-0.319946\pi\) | ||||
0.535971 | + | 0.844236i | \(0.319946\pi\) | |||||||
\(198\) | −0.701844 | −0.0498779 | ||||||||
\(199\) | −6.73146 | −0.477181 | −0.238590 | − | 0.971120i | \(-0.576685\pi\) | ||||
−0.238590 | + | 0.971120i | \(0.576685\pi\) | |||||||
\(200\) | 2.22460 | 0.157303 | ||||||||
\(201\) | −15.8731 | −1.11960 | ||||||||
\(202\) | 8.28845 | 0.583173 | ||||||||
\(203\) | 8.37011 | 0.587467 | ||||||||
\(204\) | −1.61240 | −0.112890 | ||||||||
\(205\) | 11.8525 | 0.827815 | ||||||||
\(206\) | −5.49948 | −0.383167 | ||||||||
\(207\) | −0.979567 | −0.0680846 | ||||||||
\(208\) | −7.71812 | −0.535155 | ||||||||
\(209\) | −11.3560 | −0.785509 | ||||||||
\(210\) | 0.937096 | 0.0646657 | ||||||||
\(211\) | 10.7127 | 0.737490 | 0.368745 | − | 0.929531i | \(-0.379788\pi\) | ||||
0.368745 | + | 0.929531i | \(0.379788\pi\) | |||||||
\(212\) | 5.77072 | 0.396335 | ||||||||
\(213\) | 10.1998 | 0.698876 | ||||||||
\(214\) | 8.43795 | 0.576807 | ||||||||
\(215\) | 2.32014 | 0.158232 | ||||||||
\(216\) | 12.4629 | 0.847990 | ||||||||
\(217\) | −6.49153 | −0.440674 | ||||||||
\(218\) | −2.60148 | −0.176195 | ||||||||
\(219\) | 13.3033 | 0.898955 | ||||||||
\(220\) | −2.76522 | −0.186431 | ||||||||
\(221\) | 2.67252 | 0.179773 | ||||||||
\(222\) | 1.18151 | 0.0792981 | ||||||||
\(223\) | −0.791955 | −0.0530332 | −0.0265166 | − | 0.999648i | \(-0.508441\pi\) | ||||
−0.0265166 | + | 0.999648i | \(0.508441\pi\) | |||||||
\(224\) | 5.60356 | 0.374403 | ||||||||
\(225\) | −0.670866 | −0.0447244 | ||||||||
\(226\) | 12.4798 | 0.830144 | ||||||||
\(227\) | −27.2216 | −1.80676 | −0.903380 | − | 0.428841i | \(-0.858922\pi\) | ||||
−0.903380 | + | 0.428841i | \(0.858922\pi\) | |||||||
\(228\) | 16.5088 | 1.09332 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 0.896571 | 0.0591182 | ||||||||
\(231\) | −2.60025 | −0.171084 | ||||||||
\(232\) | −18.6201 | −1.22247 | ||||||||
\(233\) | −0.912968 | −0.0598105 | −0.0299053 | − | 0.999553i | \(-0.509521\pi\) | ||||
−0.0299053 | + | 0.999553i | \(0.509521\pi\) | |||||||
\(234\) | −1.69114 | −0.110553 | ||||||||
\(235\) | 6.47208 | 0.422192 | ||||||||
\(236\) | 3.83952 | 0.249932 | ||||||||
\(237\) | −4.98293 | −0.323676 | ||||||||
\(238\) | −0.399715 | −0.0259097 | ||||||||
\(239\) | 1.61620 | 0.104543 | 0.0522717 | − | 0.998633i | \(-0.483354\pi\) | ||||
0.0522717 | + | 0.998633i | \(0.483354\pi\) | |||||||
\(240\) | 2.86914 | 0.185202 | ||||||||
\(241\) | −28.1724 | −1.81474 | −0.907372 | − | 0.420328i | \(-0.861915\pi\) | ||||
−0.907372 | + | 0.420328i | \(0.861915\pi\) | |||||||
\(242\) | 4.97181 | 0.319600 | ||||||||
\(243\) | −6.82992 | −0.438139 | ||||||||
\(244\) | 13.7982 | 0.883342 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −11.1069 | −0.708152 | ||||||||
\(247\) | −27.3630 | −1.74107 | ||||||||
\(248\) | 14.4410 | 0.917007 | ||||||||
\(249\) | −21.8220 | −1.38291 | ||||||||
\(250\) | 0.614026 | 0.0388344 | ||||||||
\(251\) | 1.63256 | 0.103046 | 0.0515230 | − | 0.998672i | \(-0.483592\pi\) | ||||
0.0515230 | + | 0.998672i | \(0.483592\pi\) | |||||||
\(252\) | −1.08880 | −0.0685878 | ||||||||
\(253\) | −2.48780 | −0.156407 | ||||||||
\(254\) | 3.18207 | 0.199661 | ||||||||
\(255\) | −0.993484 | −0.0622144 | ||||||||
\(256\) | −6.36334 | −0.397709 | ||||||||
\(257\) | 17.5786 | 1.09652 | 0.548260 | − | 0.836308i | \(-0.315290\pi\) | ||||
0.548260 | + | 0.836308i | \(0.315290\pi\) | |||||||
\(258\) | −2.17420 | −0.135359 | ||||||||
\(259\) | −1.26083 | −0.0783439 | ||||||||
\(260\) | −6.66298 | −0.413221 | ||||||||
\(261\) | 5.61523 | 0.347574 | ||||||||
\(262\) | 12.9678 | 0.801151 | ||||||||
\(263\) | 23.2886 | 1.43603 | 0.718017 | − | 0.696025i | \(-0.245050\pi\) | ||||
0.718017 | + | 0.696025i | \(0.245050\pi\) | |||||||
\(264\) | 5.78452 | 0.356012 | ||||||||
\(265\) | 3.55565 | 0.218422 | ||||||||
\(266\) | 4.09254 | 0.250930 | ||||||||
\(267\) | 17.0705 | 1.04470 | ||||||||
\(268\) | −16.8801 | −1.03112 | ||||||||
\(269\) | 18.2182 | 1.11078 | 0.555391 | − | 0.831590i | \(-0.312569\pi\) | ||||
0.555391 | + | 0.831590i | \(0.312569\pi\) | |||||||
\(270\) | 3.43995 | 0.209349 | ||||||||
\(271\) | 26.1341 | 1.58753 | 0.793766 | − | 0.608223i | \(-0.208117\pi\) | ||||
0.793766 | + | 0.608223i | \(0.208117\pi\) | |||||||
\(272\) | −1.22382 | −0.0742050 | ||||||||
\(273\) | −6.26549 | −0.379205 | ||||||||
\(274\) | −8.13653 | −0.491546 | ||||||||
\(275\) | −1.70380 | −0.102743 | ||||||||
\(276\) | 3.61665 | 0.217697 | ||||||||
\(277\) | 8.61757 | 0.517779 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(278\) | −2.98947 | −0.179297 | ||||||||
\(279\) | −4.35495 | −0.260724 | ||||||||
\(280\) | 2.22460 | 0.132945 | ||||||||
\(281\) | 5.89380 | 0.351595 | 0.175797 | − | 0.984426i | \(-0.443750\pi\) | ||||
0.175797 | + | 0.984426i | \(0.443750\pi\) | |||||||
\(282\) | −6.06496 | −0.361163 | ||||||||
\(283\) | −2.92384 | −0.173804 | −0.0869022 | − | 0.996217i | \(-0.527697\pi\) | ||||
−0.0869022 | + | 0.996217i | \(0.527697\pi\) | |||||||
\(284\) | 10.8469 | 0.643643 | ||||||||
\(285\) | 10.1719 | 0.602533 | ||||||||
\(286\) | −4.29499 | −0.253968 | ||||||||
\(287\) | 11.8525 | 0.699631 | ||||||||
\(288\) | 3.75924 | 0.221515 | ||||||||
\(289\) | −16.5762 | −0.975073 | ||||||||
\(290\) | −5.13947 | −0.301800 | ||||||||
\(291\) | 15.1898 | 0.890441 | ||||||||
\(292\) | 14.1473 | 0.827909 | ||||||||
\(293\) | −1.88521 | −0.110135 | −0.0550675 | − | 0.998483i | \(-0.517537\pi\) | ||||
−0.0550675 | + | 0.998483i | \(0.517537\pi\) | |||||||
\(294\) | 0.937096 | 0.0546525 | ||||||||
\(295\) | 2.36574 | 0.137738 | ||||||||
\(296\) | 2.80483 | 0.163028 | ||||||||
\(297\) | −9.54517 | −0.553867 | ||||||||
\(298\) | −5.62138 | −0.325638 | ||||||||
\(299\) | −5.99454 | −0.346673 | ||||||||
\(300\) | 2.47690 | 0.143004 | ||||||||
\(301\) | 2.32014 | 0.133731 | ||||||||
\(302\) | −12.6980 | −0.730690 | ||||||||
\(303\) | 20.6008 | 1.18348 | ||||||||
\(304\) | 12.5303 | 0.718659 | ||||||||
\(305\) | 8.50184 | 0.486814 | ||||||||
\(306\) | −0.268155 | −0.0153294 | ||||||||
\(307\) | 9.93303 | 0.566908 | 0.283454 | − | 0.958986i | \(-0.408520\pi\) | ||||
0.283454 | + | 0.958986i | \(0.408520\pi\) | |||||||
\(308\) | −2.76522 | −0.157563 | ||||||||
\(309\) | −13.6688 | −0.777594 | ||||||||
\(310\) | 3.98597 | 0.226388 | ||||||||
\(311\) | −3.37095 | −0.191149 | −0.0955745 | − | 0.995422i | \(-0.530469\pi\) | ||||
−0.0955745 | + | 0.995422i | \(0.530469\pi\) | |||||||
\(312\) | 13.9382 | 0.789095 | ||||||||
\(313\) | −5.06918 | −0.286527 | −0.143264 | − | 0.989685i | \(-0.545760\pi\) | ||||
−0.143264 | + | 0.989685i | \(0.545760\pi\) | |||||||
\(314\) | −1.21553 | −0.0685964 | ||||||||
\(315\) | −0.670866 | −0.0377990 | ||||||||
\(316\) | −5.29905 | −0.298095 | ||||||||
\(317\) | −18.0527 | −1.01394 | −0.506971 | − | 0.861963i | \(-0.669235\pi\) | ||||
−0.506971 | + | 0.861963i | \(0.669235\pi\) | |||||||
\(318\) | −3.33199 | −0.186849 | ||||||||
\(319\) | 14.2610 | 0.798462 | ||||||||
\(320\) | 0.319237 | 0.0178459 | ||||||||
\(321\) | 20.9724 | 1.17056 | ||||||||
\(322\) | 0.896571 | 0.0499640 | ||||||||
\(323\) | −4.33880 | −0.241417 | ||||||||
\(324\) | 10.6099 | 0.589440 | ||||||||
\(325\) | −4.10542 | −0.227728 | ||||||||
\(326\) | 13.7558 | 0.761865 | ||||||||
\(327\) | −6.46593 | −0.357567 | ||||||||
\(328\) | −26.3671 | −1.45588 | ||||||||
\(329\) | 6.47208 | 0.356817 | ||||||||
\(330\) | 1.59662 | 0.0878911 | ||||||||
\(331\) | −25.2651 | −1.38869 | −0.694347 | − | 0.719640i | \(-0.744307\pi\) | ||||
−0.694347 | + | 0.719640i | \(0.744307\pi\) | |||||||
\(332\) | −23.2065 | −1.27362 | ||||||||
\(333\) | −0.845846 | −0.0463521 | ||||||||
\(334\) | −11.9145 | −0.651935 | ||||||||
\(335\) | −10.4007 | −0.568254 | ||||||||
\(336\) | 2.86914 | 0.156524 | ||||||||
\(337\) | 0.219020 | 0.0119308 | 0.00596540 | − | 0.999982i | \(-0.498101\pi\) | ||||
0.00596540 | + | 0.999982i | \(0.498101\pi\) | |||||||
\(338\) | −2.36675 | −0.128734 | ||||||||
\(339\) | 31.0183 | 1.68468 | ||||||||
\(340\) | −1.05651 | −0.0572975 | ||||||||
\(341\) | −11.0603 | −0.598946 | ||||||||
\(342\) | 2.74555 | 0.148462 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.16139 | −0.278283 | ||||||||
\(345\) | 2.22841 | 0.119974 | ||||||||
\(346\) | 14.2924 | 0.768365 | ||||||||
\(347\) | −14.1836 | −0.761417 | −0.380708 | − | 0.924695i | \(-0.624320\pi\) | ||||
−0.380708 | + | 0.924695i | \(0.624320\pi\) | |||||||
\(348\) | −20.7319 | −1.11135 | ||||||||
\(349\) | −15.8976 | −0.850977 | −0.425489 | − | 0.904964i | \(-0.639898\pi\) | ||||
−0.425489 | + | 0.904964i | \(0.639898\pi\) | |||||||
\(350\) | 0.614026 | 0.0328211 | ||||||||
\(351\) | −22.9998 | −1.22764 | ||||||||
\(352\) | 9.54733 | 0.508874 | ||||||||
\(353\) | 0.474151 | 0.0252365 | 0.0126182 | − | 0.999920i | \(-0.495983\pi\) | ||||
0.0126182 | + | 0.999920i | \(0.495983\pi\) | |||||||
\(354\) | −2.21692 | −0.117828 | ||||||||
\(355\) | 6.68333 | 0.354714 | ||||||||
\(356\) | 18.1535 | 0.962131 | ||||||||
\(357\) | −0.993484 | −0.0525808 | ||||||||
\(358\) | −2.89356 | −0.152929 | ||||||||
\(359\) | −16.5748 | −0.874783 | −0.437392 | − | 0.899271i | \(-0.644098\pi\) | ||||
−0.437392 | + | 0.899271i | \(0.644098\pi\) | |||||||
\(360\) | 1.49241 | 0.0786568 | ||||||||
\(361\) | 25.4234 | 1.33807 | ||||||||
\(362\) | −4.36549 | −0.229445 | ||||||||
\(363\) | 12.3573 | 0.648593 | ||||||||
\(364\) | −6.66298 | −0.349235 | ||||||||
\(365\) | 8.71692 | 0.456264 | ||||||||
\(366\) | −7.96704 | −0.416444 | ||||||||
\(367\) | 0.494832 | 0.0258300 | 0.0129150 | − | 0.999917i | \(-0.495889\pi\) | ||||
0.0129150 | + | 0.999917i | \(0.495889\pi\) | |||||||
\(368\) | 2.74506 | 0.143096 | ||||||||
\(369\) | 7.95144 | 0.413936 | ||||||||
\(370\) | 0.774180 | 0.0402477 | ||||||||
\(371\) | 3.55565 | 0.184600 | ||||||||
\(372\) | 16.0789 | 0.833650 | ||||||||
\(373\) | 28.1173 | 1.45586 | 0.727929 | − | 0.685653i | \(-0.240483\pi\) | ||||
0.727929 | + | 0.685653i | \(0.240483\pi\) | |||||||
\(374\) | −0.681034 | −0.0352154 | ||||||||
\(375\) | 1.52615 | 0.0788100 | ||||||||
\(376\) | −14.3978 | −0.742509 | ||||||||
\(377\) | 34.3628 | 1.76978 | ||||||||
\(378\) | 3.43995 | 0.176932 | ||||||||
\(379\) | −29.6898 | −1.52506 | −0.762531 | − | 0.646951i | \(-0.776044\pi\) | ||||
−0.762531 | + | 0.646951i | \(0.776044\pi\) | |||||||
\(380\) | 10.8173 | 0.554913 | ||||||||
\(381\) | 7.90898 | 0.405189 | ||||||||
\(382\) | 16.4097 | 0.839594 | ||||||||
\(383\) | −20.5508 | −1.05009 | −0.525047 | − | 0.851073i | \(-0.675952\pi\) | ||||
−0.525047 | + | 0.851073i | \(0.675952\pi\) | |||||||
\(384\) | −17.4029 | −0.888087 | ||||||||
\(385\) | −1.70380 | −0.0868336 | ||||||||
\(386\) | 4.98898 | 0.253932 | ||||||||
\(387\) | 1.55651 | 0.0791216 | ||||||||
\(388\) | 16.1535 | 0.820068 | ||||||||
\(389\) | −0.330569 | −0.0167605 | −0.00838025 | − | 0.999965i | \(-0.502668\pi\) | ||||
−0.00838025 | + | 0.999965i | \(0.502668\pi\) | |||||||
\(390\) | 3.84717 | 0.194809 | ||||||||
\(391\) | −0.950521 | −0.0480699 | ||||||||
\(392\) | 2.22460 | 0.112359 | ||||||||
\(393\) | 32.2311 | 1.62585 | ||||||||
\(394\) | −9.23828 | −0.465418 | ||||||||
\(395\) | −3.26503 | −0.164282 | ||||||||
\(396\) | −1.85509 | −0.0932218 | ||||||||
\(397\) | −1.94539 | −0.0976365 | −0.0488183 | − | 0.998808i | \(-0.515546\pi\) | ||||
−0.0488183 | + | 0.998808i | \(0.515546\pi\) | |||||||
\(398\) | 4.13329 | 0.207183 | ||||||||
\(399\) | 10.1719 | 0.509233 | ||||||||
\(400\) | 1.87998 | 0.0939991 | ||||||||
\(401\) | −6.31723 | −0.315467 | −0.157734 | − | 0.987482i | \(-0.550419\pi\) | ||||
−0.157734 | + | 0.987482i | \(0.550419\pi\) | |||||||
\(402\) | 9.74650 | 0.486111 | ||||||||
\(403\) | −26.6505 | −1.32755 | ||||||||
\(404\) | 21.9077 | 1.08995 | ||||||||
\(405\) | 6.53734 | 0.324843 | ||||||||
\(406\) | −5.13947 | −0.255067 | ||||||||
\(407\) | −2.14819 | −0.106482 | ||||||||
\(408\) | 2.21010 | 0.109416 | ||||||||
\(409\) | 15.5184 | 0.767337 | 0.383669 | − | 0.923471i | \(-0.374660\pi\) | ||||
0.383669 | + | 0.923471i | \(0.374660\pi\) | |||||||
\(410\) | −7.27774 | −0.359422 | ||||||||
\(411\) | −20.2232 | −0.997537 | ||||||||
\(412\) | −14.5360 | −0.716139 | ||||||||
\(413\) | 2.36574 | 0.116410 | ||||||||
\(414\) | 0.601479 | 0.0295611 | ||||||||
\(415\) | −14.2987 | −0.701898 | ||||||||
\(416\) | 23.0050 | 1.12791 | ||||||||
\(417\) | −7.43027 | −0.363862 | ||||||||
\(418\) | 6.97286 | 0.341054 | ||||||||
\(419\) | 35.1368 | 1.71655 | 0.858273 | − | 0.513193i | \(-0.171538\pi\) | ||||
0.858273 | + | 0.513193i | \(0.171538\pi\) | |||||||
\(420\) | 2.47690 | 0.120860 | ||||||||
\(421\) | −3.27712 | −0.159717 | −0.0798585 | − | 0.996806i | \(-0.525447\pi\) | ||||
−0.0798585 | + | 0.996806i | \(0.525447\pi\) | |||||||
\(422\) | −6.57785 | −0.320205 | ||||||||
\(423\) | 4.34190 | 0.211110 | ||||||||
\(424\) | −7.90990 | −0.384139 | ||||||||
\(425\) | −0.650974 | −0.0315769 | ||||||||
\(426\) | −6.26292 | −0.303440 | ||||||||
\(427\) | 8.50184 | 0.411433 | ||||||||
\(428\) | 22.3029 | 1.07805 | ||||||||
\(429\) | −10.6751 | −0.515400 | ||||||||
\(430\) | −1.42463 | −0.0687016 | ||||||||
\(431\) | −0.0630480 | −0.00303692 | −0.00151846 | − | 0.999999i | \(-0.500483\pi\) | ||||
−0.00151846 | + | 0.999999i | \(0.500483\pi\) | |||||||
\(432\) | 10.5322 | 0.506731 | ||||||||
\(433\) | 27.6159 | 1.32714 | 0.663568 | − | 0.748116i | \(-0.269041\pi\) | ||||
0.663568 | + | 0.748116i | \(0.269041\pi\) | |||||||
\(434\) | 3.98597 | 0.191333 | ||||||||
\(435\) | −12.7740 | −0.612469 | ||||||||
\(436\) | −6.87615 | −0.329308 | ||||||||
\(437\) | 9.73205 | 0.465547 | ||||||||
\(438\) | −8.16859 | −0.390310 | ||||||||
\(439\) | −9.96936 | −0.475812 | −0.237906 | − | 0.971288i | \(-0.576461\pi\) | ||||
−0.237906 | + | 0.971288i | \(0.576461\pi\) | |||||||
\(440\) | 3.79027 | 0.180694 | ||||||||
\(441\) | −0.670866 | −0.0319460 | ||||||||
\(442\) | −1.64100 | −0.0780543 | ||||||||
\(443\) | 29.9622 | 1.42355 | 0.711774 | − | 0.702408i | \(-0.247892\pi\) | ||||
0.711774 | + | 0.702408i | \(0.247892\pi\) | |||||||
\(444\) | 3.12294 | 0.148208 | ||||||||
\(445\) | 11.1853 | 0.530235 | ||||||||
\(446\) | 0.486281 | 0.0230261 | ||||||||
\(447\) | −13.9718 | −0.660845 | ||||||||
\(448\) | 0.319237 | 0.0150825 | ||||||||
\(449\) | −12.6265 | −0.595881 | −0.297941 | − | 0.954584i | \(-0.596300\pi\) | ||||
−0.297941 | + | 0.954584i | \(0.596300\pi\) | |||||||
\(450\) | 0.411929 | 0.0194185 | ||||||||
\(451\) | 20.1943 | 0.950911 | ||||||||
\(452\) | 32.9862 | 1.55154 | ||||||||
\(453\) | −31.5607 | −1.48285 | ||||||||
\(454\) | 16.7148 | 0.784462 | ||||||||
\(455\) | −4.10542 | −0.192465 | ||||||||
\(456\) | −22.6285 | −1.05967 | ||||||||
\(457\) | 30.8998 | 1.44543 | 0.722717 | − | 0.691144i | \(-0.242893\pi\) | ||||
0.722717 | + | 0.691144i | \(0.242893\pi\) | |||||||
\(458\) | −0.614026 | −0.0286915 | ||||||||
\(459\) | −3.64695 | −0.170225 | ||||||||
\(460\) | 2.36979 | 0.110492 | ||||||||
\(461\) | −11.0706 | −0.515610 | −0.257805 | − | 0.966197i | \(-0.582999\pi\) | ||||
−0.257805 | + | 0.966197i | \(0.582999\pi\) | |||||||
\(462\) | 1.59662 | 0.0742816 | ||||||||
\(463\) | −17.9537 | −0.834380 | −0.417190 | − | 0.908819i | \(-0.636985\pi\) | ||||
−0.417190 | + | 0.908819i | \(0.636985\pi\) | |||||||
\(464\) | −15.7357 | −0.730510 | ||||||||
\(465\) | 9.90705 | 0.459428 | ||||||||
\(466\) | 0.560586 | 0.0259687 | ||||||||
\(467\) | −1.37295 | −0.0635323 | −0.0317662 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317662 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(468\) | −4.46997 | −0.206624 | ||||||||
\(469\) | −10.4007 | −0.480262 | ||||||||
\(470\) | −3.97403 | −0.183308 | ||||||||
\(471\) | −3.02118 | −0.139209 | ||||||||
\(472\) | −5.26281 | −0.242241 | ||||||||
\(473\) | 3.95305 | 0.181762 | ||||||||
\(474\) | 3.05965 | 0.140534 | ||||||||
\(475\) | 6.66509 | 0.305815 | ||||||||
\(476\) | −1.05651 | −0.0484252 | ||||||||
\(477\) | 2.38537 | 0.109218 | ||||||||
\(478\) | −0.992390 | −0.0453908 | ||||||||
\(479\) | 21.0535 | 0.961959 | 0.480980 | − | 0.876732i | \(-0.340281\pi\) | ||||
0.480980 | + | 0.876732i | \(0.340281\pi\) | |||||||
\(480\) | −8.55187 | −0.390338 | ||||||||
\(481\) | −5.17622 | −0.236015 | ||||||||
\(482\) | 17.2986 | 0.787929 | ||||||||
\(483\) | 2.22841 | 0.101396 | ||||||||
\(484\) | 13.1413 | 0.597333 | ||||||||
\(485\) | 9.95302 | 0.451943 | ||||||||
\(486\) | 4.19375 | 0.190232 | ||||||||
\(487\) | 0.203246 | 0.00920995 | 0.00460497 | − | 0.999989i | \(-0.498534\pi\) | ||||
0.00460497 | + | 0.999989i | \(0.498534\pi\) | |||||||
\(488\) | −18.9132 | −0.856159 | ||||||||
\(489\) | 34.1899 | 1.54612 | ||||||||
\(490\) | 0.614026 | 0.0277389 | ||||||||
\(491\) | −1.55121 | −0.0700053 | −0.0350027 | − | 0.999387i | \(-0.511144\pi\) | ||||
−0.0350027 | + | 0.999387i | \(0.511144\pi\) | |||||||
\(492\) | −29.3575 | −1.32354 | ||||||||
\(493\) | 5.44873 | 0.245398 | ||||||||
\(494\) | 16.8016 | 0.755939 | ||||||||
\(495\) | −1.14302 | −0.0513750 | ||||||||
\(496\) | 12.2040 | 0.547974 | ||||||||
\(497\) | 6.68333 | 0.299788 | ||||||||
\(498\) | 13.3993 | 0.600436 | ||||||||
\(499\) | −15.2494 | −0.682655 | −0.341327 | − | 0.939944i | \(-0.610876\pi\) | ||||
−0.341327 | + | 0.939944i | \(0.610876\pi\) | |||||||
\(500\) | 1.62297 | 0.0725815 | ||||||||
\(501\) | −29.6134 | −1.32303 | ||||||||
\(502\) | −1.00243 | −0.0447407 | ||||||||
\(503\) | 28.6358 | 1.27681 | 0.638404 | − | 0.769701i | \(-0.279595\pi\) | ||||
0.638404 | + | 0.769701i | \(0.279595\pi\) | |||||||
\(504\) | 1.49241 | 0.0664771 | ||||||||
\(505\) | 13.4985 | 0.600677 | ||||||||
\(506\) | 1.52758 | 0.0679091 | ||||||||
\(507\) | −5.88251 | −0.261252 | ||||||||
\(508\) | 8.41074 | 0.373166 | ||||||||
\(509\) | 37.1774 | 1.64786 | 0.823930 | − | 0.566692i | \(-0.191777\pi\) | ||||
0.823930 | + | 0.566692i | \(0.191777\pi\) | |||||||
\(510\) | 0.610025 | 0.0270124 | ||||||||
\(511\) | 8.71692 | 0.385614 | ||||||||
\(512\) | −18.8990 | −0.835226 | ||||||||
\(513\) | 37.3398 | 1.64859 | ||||||||
\(514\) | −10.7937 | −0.476089 | ||||||||
\(515\) | −8.95643 | −0.394667 | ||||||||
\(516\) | −5.74676 | −0.252987 | ||||||||
\(517\) | 11.0271 | 0.484972 | ||||||||
\(518\) | 0.774180 | 0.0340155 | ||||||||
\(519\) | 35.5235 | 1.55931 | ||||||||
\(520\) | 9.13291 | 0.400505 | ||||||||
\(521\) | 4.82404 | 0.211345 | 0.105673 | − | 0.994401i | \(-0.466300\pi\) | ||||
0.105673 | + | 0.994401i | \(0.466300\pi\) | |||||||
\(522\) | −3.44789 | −0.150910 | ||||||||
\(523\) | −2.45696 | −0.107435 | −0.0537177 | − | 0.998556i | \(-0.517107\pi\) | ||||
−0.0537177 | + | 0.998556i | \(0.517107\pi\) | |||||||
\(524\) | 34.2759 | 1.49735 | ||||||||
\(525\) | 1.52615 | 0.0666066 | ||||||||
\(526\) | −14.2998 | −0.623500 | ||||||||
\(527\) | −4.22582 | −0.184080 | ||||||||
\(528\) | 4.88843 | 0.212742 | ||||||||
\(529\) | −20.8680 | −0.907302 | ||||||||
\(530\) | −2.18326 | −0.0948349 | ||||||||
\(531\) | 1.58709 | 0.0688739 | ||||||||
\(532\) | 10.8173 | 0.468987 | ||||||||
\(533\) | 48.6595 | 2.10768 | ||||||||
\(534\) | −10.4817 | −0.453588 | ||||||||
\(535\) | 13.7420 | 0.594119 | ||||||||
\(536\) | 23.1375 | 0.999387 | ||||||||
\(537\) | −7.19189 | −0.310353 | ||||||||
\(538\) | −11.1864 | −0.482281 | ||||||||
\(539\) | −1.70380 | −0.0733878 | ||||||||
\(540\) | 9.09236 | 0.391273 | ||||||||
\(541\) | −29.2787 | −1.25879 | −0.629394 | − | 0.777086i | \(-0.716697\pi\) | ||||
−0.629394 | + | 0.777086i | \(0.716697\pi\) | |||||||
\(542\) | −16.0470 | −0.689278 | ||||||||
\(543\) | −10.8503 | −0.465633 | ||||||||
\(544\) | 3.64777 | 0.156397 | ||||||||
\(545\) | −4.23676 | −0.181483 | ||||||||
\(546\) | 3.84717 | 0.164644 | ||||||||
\(547\) | 35.1000 | 1.50077 | 0.750384 | − | 0.661003i | \(-0.229869\pi\) | ||||
0.750384 | + | 0.661003i | \(0.229869\pi\) | |||||||
\(548\) | −21.5062 | −0.918700 | ||||||||
\(549\) | 5.70360 | 0.243424 | ||||||||
\(550\) | 1.04618 | 0.0446091 | ||||||||
\(551\) | −55.7876 | −2.37663 | ||||||||
\(552\) | −4.95732 | −0.210998 | ||||||||
\(553\) | −3.26503 | −0.138843 | ||||||||
\(554\) | −5.29141 | −0.224810 | ||||||||
\(555\) | 1.92421 | 0.0816782 | ||||||||
\(556\) | −7.90166 | −0.335105 | ||||||||
\(557\) | −35.8948 | −1.52091 | −0.760455 | − | 0.649391i | \(-0.775024\pi\) | ||||
−0.760455 | + | 0.649391i | \(0.775024\pi\) | |||||||
\(558\) | 2.67405 | 0.113202 | ||||||||
\(559\) | 9.52516 | 0.402871 | ||||||||
\(560\) | 1.87998 | 0.0794438 | ||||||||
\(561\) | −1.69270 | −0.0714657 | ||||||||
\(562\) | −3.61895 | −0.152656 | ||||||||
\(563\) | 38.7271 | 1.63215 | 0.816076 | − | 0.577944i | \(-0.196145\pi\) | ||||
0.816076 | + | 0.577944i | \(0.196145\pi\) | |||||||
\(564\) | −16.0307 | −0.675014 | ||||||||
\(565\) | 20.3245 | 0.855060 | ||||||||
\(566\) | 1.79532 | 0.0754627 | ||||||||
\(567\) | 6.53734 | 0.274542 | ||||||||
\(568\) | −14.8677 | −0.623836 | ||||||||
\(569\) | 36.0813 | 1.51261 | 0.756303 | − | 0.654221i | \(-0.227003\pi\) | ||||
0.756303 | + | 0.654221i | \(0.227003\pi\) | |||||||
\(570\) | −6.24583 | −0.261609 | ||||||||
\(571\) | 16.5581 | 0.692937 | 0.346468 | − | 0.938062i | \(-0.387381\pi\) | ||||
0.346468 | + | 0.938062i | \(0.387381\pi\) | |||||||
\(572\) | −11.3524 | −0.474667 | ||||||||
\(573\) | 40.7860 | 1.70386 | ||||||||
\(574\) | −7.27774 | −0.303767 | ||||||||
\(575\) | 1.46015 | 0.0608926 | ||||||||
\(576\) | 0.214166 | 0.00892356 | ||||||||
\(577\) | −1.51921 | −0.0632457 | −0.0316228 | − | 0.999500i | \(-0.510068\pi\) | ||||
−0.0316228 | + | 0.999500i | \(0.510068\pi\) | |||||||
\(578\) | 10.1782 | 0.423359 | ||||||||
\(579\) | 12.4000 | 0.515327 | ||||||||
\(580\) | −13.5845 | −0.564064 | ||||||||
\(581\) | −14.2987 | −0.593212 | ||||||||
\(582\) | −9.32693 | −0.386614 | ||||||||
\(583\) | 6.05811 | 0.250901 | ||||||||
\(584\) | −19.3916 | −0.802432 | ||||||||
\(585\) | −2.75419 | −0.113872 | ||||||||
\(586\) | 1.15757 | 0.0478186 | ||||||||
\(587\) | 40.0689 | 1.65382 | 0.826910 | − | 0.562334i | \(-0.190097\pi\) | ||||
0.826910 | + | 0.562334i | \(0.190097\pi\) | |||||||
\(588\) | 2.47690 | 0.102146 | ||||||||
\(589\) | 43.2666 | 1.78277 | ||||||||
\(590\) | −1.45262 | −0.0598036 | ||||||||
\(591\) | −22.9616 | −0.944513 | ||||||||
\(592\) | 2.37033 | 0.0974200 | ||||||||
\(593\) | 32.6835 | 1.34215 | 0.671075 | − | 0.741390i | \(-0.265833\pi\) | ||||
0.671075 | + | 0.741390i | \(0.265833\pi\) | |||||||
\(594\) | 5.86098 | 0.240479 | ||||||||
\(595\) | −0.650974 | −0.0266873 | ||||||||
\(596\) | −14.8582 | −0.608617 | ||||||||
\(597\) | 10.2732 | 0.420455 | ||||||||
\(598\) | 3.68080 | 0.150519 | ||||||||
\(599\) | −46.7229 | −1.90904 | −0.954522 | − | 0.298140i | \(-0.903634\pi\) | ||||
−0.954522 | + | 0.298140i | \(0.903634\pi\) | |||||||
\(600\) | −3.39507 | −0.138603 | ||||||||
\(601\) | −22.2308 | −0.906812 | −0.453406 | − | 0.891304i | \(-0.649791\pi\) | ||||
−0.453406 | + | 0.891304i | \(0.649791\pi\) | |||||||
\(602\) | −1.42463 | −0.0580635 | ||||||||
\(603\) | −6.97751 | −0.284146 | ||||||||
\(604\) | −33.5630 | −1.36566 | ||||||||
\(605\) | 8.09707 | 0.329193 | ||||||||
\(606\) | −12.6494 | −0.513847 | ||||||||
\(607\) | 46.3587 | 1.88164 | 0.940821 | − | 0.338904i | \(-0.110056\pi\) | ||||
0.940821 | + | 0.338904i | \(0.110056\pi\) | |||||||
\(608\) | −37.3482 | −1.51467 | ||||||||
\(609\) | −12.7740 | −0.517631 | ||||||||
\(610\) | −5.22035 | −0.211366 | ||||||||
\(611\) | 26.5706 | 1.07493 | ||||||||
\(612\) | −0.708779 | −0.0286507 | ||||||||
\(613\) | 21.5486 | 0.870341 | 0.435171 | − | 0.900348i | \(-0.356688\pi\) | ||||
0.435171 | + | 0.900348i | \(0.356688\pi\) | |||||||
\(614\) | −6.09914 | −0.246141 | ||||||||
\(615\) | −18.0887 | −0.729407 | ||||||||
\(616\) | 3.79027 | 0.152714 | ||||||||
\(617\) | 21.2545 | 0.855676 | 0.427838 | − | 0.903856i | \(-0.359275\pi\) | ||||
0.427838 | + | 0.903856i | \(0.359275\pi\) | |||||||
\(618\) | 8.39303 | 0.337617 | ||||||||
\(619\) | 23.5322 | 0.945838 | 0.472919 | − | 0.881106i | \(-0.343200\pi\) | ||||
0.472919 | + | 0.881106i | \(0.343200\pi\) | |||||||
\(620\) | 10.5356 | 0.423119 | ||||||||
\(621\) | 8.18020 | 0.328260 | ||||||||
\(622\) | 2.06985 | 0.0829934 | ||||||||
\(623\) | 11.1853 | 0.448130 | ||||||||
\(624\) | 11.7790 | 0.471538 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.11261 | 0.124405 | ||||||||
\(627\) | 17.3309 | 0.692130 | ||||||||
\(628\) | −3.21285 | −0.128207 | ||||||||
\(629\) | −0.820765 | −0.0327261 | ||||||||
\(630\) | 0.411929 | 0.0164117 | ||||||||
\(631\) | −20.2740 | −0.807097 | −0.403548 | − | 0.914958i | \(-0.632223\pi\) | ||||
−0.403548 | + | 0.914958i | \(0.632223\pi\) | |||||||
\(632\) | 7.26338 | 0.288922 | ||||||||
\(633\) | −16.3491 | −0.649820 | ||||||||
\(634\) | 11.0848 | 0.440235 | ||||||||
\(635\) | 5.18231 | 0.205654 | ||||||||
\(636\) | −8.80699 | −0.349220 | ||||||||
\(637\) | −4.10542 | −0.162663 | ||||||||
\(638\) | −8.75661 | −0.346678 | ||||||||
\(639\) | 4.48362 | 0.177369 | ||||||||
\(640\) | −11.4031 | −0.450748 | ||||||||
\(641\) | 0.259133 | 0.0102351 | 0.00511757 | − | 0.999987i | \(-0.498371\pi\) | ||||
0.00511757 | + | 0.999987i | \(0.498371\pi\) | |||||||
\(642\) | −12.8776 | −0.508238 | ||||||||
\(643\) | −13.9887 | −0.551661 | −0.275830 | − | 0.961206i | \(-0.588953\pi\) | ||||
−0.275830 | + | 0.961206i | \(0.588953\pi\) | |||||||
\(644\) | 2.36979 | 0.0933827 | ||||||||
\(645\) | −3.54089 | −0.139422 | ||||||||
\(646\) | 2.66414 | 0.104819 | ||||||||
\(647\) | 40.2024 | 1.58052 | 0.790260 | − | 0.612771i | \(-0.209945\pi\) | ||||
0.790260 | + | 0.612771i | \(0.209945\pi\) | |||||||
\(648\) | −14.5430 | −0.571301 | ||||||||
\(649\) | 4.03074 | 0.158220 | ||||||||
\(650\) | 2.52083 | 0.0988753 | ||||||||
\(651\) | 9.90705 | 0.388288 | ||||||||
\(652\) | 36.3590 | 1.42393 | ||||||||
\(653\) | −18.9775 | −0.742647 | −0.371324 | − | 0.928504i | \(-0.621096\pi\) | ||||
−0.371324 | + | 0.928504i | \(0.621096\pi\) | |||||||
\(654\) | 3.97025 | 0.155249 | ||||||||
\(655\) | 21.1192 | 0.825197 | ||||||||
\(656\) | −22.2825 | −0.869986 | ||||||||
\(657\) | 5.84789 | 0.228148 | ||||||||
\(658\) | −3.97403 | −0.154924 | ||||||||
\(659\) | −3.35032 | −0.130510 | −0.0652549 | − | 0.997869i | \(-0.520786\pi\) | ||||
−0.0652549 | + | 0.997869i | \(0.520786\pi\) | |||||||
\(660\) | 4.22014 | 0.164269 | ||||||||
\(661\) | −4.74806 | −0.184678 | −0.0923391 | − | 0.995728i | \(-0.529434\pi\) | ||||
−0.0923391 | + | 0.995728i | \(0.529434\pi\) | |||||||
\(662\) | 15.5134 | 0.602946 | ||||||||
\(663\) | −4.07867 | −0.158402 | ||||||||
\(664\) | 31.8090 | 1.23443 | ||||||||
\(665\) | 6.66509 | 0.258461 | ||||||||
\(666\) | 0.519371 | 0.0201252 | ||||||||
\(667\) | −12.2216 | −0.473224 | ||||||||
\(668\) | −31.4921 | −1.21847 | ||||||||
\(669\) | 1.20864 | 0.0467288 | ||||||||
\(670\) | 6.38633 | 0.246725 | ||||||||
\(671\) | 14.4854 | 0.559203 | ||||||||
\(672\) | −8.55187 | −0.329895 | ||||||||
\(673\) | −32.3093 | −1.24543 | −0.622716 | − | 0.782448i | \(-0.713971\pi\) | ||||
−0.622716 | + | 0.782448i | \(0.713971\pi\) | |||||||
\(674\) | −0.134484 | −0.00518013 | ||||||||
\(675\) | 5.60229 | 0.215632 | ||||||||
\(676\) | −6.25571 | −0.240604 | ||||||||
\(677\) | 37.3496 | 1.43546 | 0.717731 | − | 0.696321i | \(-0.245181\pi\) | ||||
0.717731 | + | 0.696321i | \(0.245181\pi\) | |||||||
\(678\) | −19.0460 | −0.731459 | ||||||||
\(679\) | 9.95302 | 0.381962 | ||||||||
\(680\) | 1.44816 | 0.0555343 | ||||||||
\(681\) | 41.5442 | 1.59198 | ||||||||
\(682\) | 6.79128 | 0.260052 | ||||||||
\(683\) | −18.9079 | −0.723489 | −0.361745 | − | 0.932277i | \(-0.617819\pi\) | ||||
−0.361745 | + | 0.932277i | \(0.617819\pi\) | |||||||
\(684\) | 7.25693 | 0.277476 | ||||||||
\(685\) | −13.2511 | −0.506299 | ||||||||
\(686\) | 0.614026 | 0.0234436 | ||||||||
\(687\) | −1.52615 | −0.0582263 | ||||||||
\(688\) | −4.36183 | −0.166293 | ||||||||
\(689\) | 14.5974 | 0.556118 | ||||||||
\(690\) | −1.36830 | −0.0520904 | ||||||||
\(691\) | 47.6790 | 1.81379 | 0.906897 | − | 0.421353i | \(-0.138445\pi\) | ||||
0.906897 | + | 0.421353i | \(0.138445\pi\) | |||||||
\(692\) | 37.7772 | 1.43607 | ||||||||
\(693\) | −1.14302 | −0.0434198 | ||||||||
\(694\) | 8.70911 | 0.330593 | ||||||||
\(695\) | −4.86864 | −0.184678 | ||||||||
\(696\) | 28.4171 | 1.07715 | ||||||||
\(697\) | 7.71567 | 0.292252 | ||||||||
\(698\) | 9.76152 | 0.369479 | ||||||||
\(699\) | 1.39333 | 0.0527004 | ||||||||
\(700\) | 1.62297 | 0.0613426 | ||||||||
\(701\) | −11.7448 | −0.443594 | −0.221797 | − | 0.975093i | \(-0.571192\pi\) | ||||
−0.221797 | + | 0.975093i | \(0.571192\pi\) | |||||||
\(702\) | 14.1225 | 0.533018 | ||||||||
\(703\) | 8.40352 | 0.316945 | ||||||||
\(704\) | 0.543916 | 0.0204996 | ||||||||
\(705\) | −9.87737 | −0.372003 | ||||||||
\(706\) | −0.291141 | −0.0109572 | ||||||||
\(707\) | 13.4985 | 0.507665 | ||||||||
\(708\) | −5.85969 | −0.220221 | ||||||||
\(709\) | −11.9291 | −0.448008 | −0.224004 | − | 0.974588i | \(-0.571913\pi\) | ||||
−0.224004 | + | 0.974588i | \(0.571913\pi\) | |||||||
\(710\) | −4.10374 | −0.154011 | ||||||||
\(711\) | −2.19040 | −0.0821464 | ||||||||
\(712\) | −24.8828 | −0.932524 | ||||||||
\(713\) | 9.47862 | 0.354977 | ||||||||
\(714\) | 0.610025 | 0.0228296 | ||||||||
\(715\) | −6.99481 | −0.261591 | ||||||||
\(716\) | −7.64816 | −0.285825 | ||||||||
\(717\) | −2.46657 | −0.0921156 | ||||||||
\(718\) | 10.1773 | 0.379815 | ||||||||
\(719\) | 29.9119 | 1.11553 | 0.557764 | − | 0.830000i | \(-0.311660\pi\) | ||||
0.557764 | + | 0.830000i | \(0.311660\pi\) | |||||||
\(720\) | 1.26122 | 0.0470028 | ||||||||
\(721\) | −8.95643 | −0.333555 | ||||||||
\(722\) | −15.6106 | −0.580968 | ||||||||
\(723\) | 42.9953 | 1.59901 | ||||||||
\(724\) | −11.5387 | −0.428833 | ||||||||
\(725\) | −8.37011 | −0.310858 | ||||||||
\(726\) | −7.58773 | −0.281607 | ||||||||
\(727\) | 43.6537 | 1.61903 | 0.809514 | − | 0.587101i | \(-0.199731\pi\) | ||||
0.809514 | + | 0.587101i | \(0.199731\pi\) | |||||||
\(728\) | 9.13291 | 0.338488 | ||||||||
\(729\) | 30.0355 | 1.11243 | ||||||||
\(730\) | −5.35241 | −0.198102 | ||||||||
\(731\) | 1.51035 | 0.0558624 | ||||||||
\(732\) | −21.0582 | −0.778333 | ||||||||
\(733\) | −34.8525 | −1.28731 | −0.643653 | − | 0.765318i | \(-0.722582\pi\) | ||||
−0.643653 | + | 0.765318i | \(0.722582\pi\) | |||||||
\(734\) | −0.303840 | −0.0112149 | ||||||||
\(735\) | 1.52615 | 0.0562929 | ||||||||
\(736\) | −8.18205 | −0.301594 | ||||||||
\(737\) | −17.7208 | −0.652753 | ||||||||
\(738\) | −4.88239 | −0.179723 | ||||||||
\(739\) | 21.8890 | 0.805200 | 0.402600 | − | 0.915376i | \(-0.368107\pi\) | ||||
0.402600 | + | 0.915376i | \(0.368107\pi\) | |||||||
\(740\) | 2.04629 | 0.0752230 | ||||||||
\(741\) | 41.7600 | 1.53409 | ||||||||
\(742\) | −2.18326 | −0.0801501 | ||||||||
\(743\) | 36.3758 | 1.33450 | 0.667249 | − | 0.744835i | \(-0.267472\pi\) | ||||
0.667249 | + | 0.744835i | \(0.267472\pi\) | |||||||
\(744\) | −22.0392 | −0.807996 | ||||||||
\(745\) | −9.15495 | −0.335411 | ||||||||
\(746\) | −17.2647 | −0.632107 | ||||||||
\(747\) | −9.59254 | −0.350973 | ||||||||
\(748\) | −1.80008 | −0.0658176 | ||||||||
\(749\) | 13.7420 | 0.502122 | ||||||||
\(750\) | −0.937096 | −0.0342179 | ||||||||
\(751\) | −39.5992 | −1.44500 | −0.722498 | − | 0.691373i | \(-0.757006\pi\) | ||||
−0.722498 | + | 0.691373i | \(0.757006\pi\) | |||||||
\(752\) | −12.1674 | −0.443700 | ||||||||
\(753\) | −2.49152 | −0.0907962 | ||||||||
\(754\) | −21.0997 | −0.768405 | ||||||||
\(755\) | −20.6800 | −0.752621 | ||||||||
\(756\) | 9.09236 | 0.330686 | ||||||||
\(757\) | −50.8769 | −1.84915 | −0.924577 | − | 0.380995i | \(-0.875581\pi\) | ||||
−0.924577 | + | 0.380995i | \(0.875581\pi\) | |||||||
\(758\) | 18.2303 | 0.662155 | ||||||||
\(759\) | 3.79676 | 0.137814 | ||||||||
\(760\) | −14.8272 | −0.537837 | ||||||||
\(761\) | −37.8763 | −1.37302 | −0.686508 | − | 0.727122i | \(-0.740857\pi\) | ||||
−0.686508 | + | 0.727122i | \(0.740857\pi\) | |||||||
\(762\) | −4.85632 | −0.175926 | ||||||||
\(763\) | −4.23676 | −0.153381 | ||||||||
\(764\) | 43.3736 | 1.56920 | ||||||||
\(765\) | −0.436717 | −0.0157895 | ||||||||
\(766\) | 12.6187 | 0.455932 | ||||||||
\(767\) | 9.71234 | 0.350692 | ||||||||
\(768\) | 9.71142 | 0.350431 | ||||||||
\(769\) | 47.2577 | 1.70415 | 0.852077 | − | 0.523416i | \(-0.175343\pi\) | ||||
0.852077 | + | 0.523416i | \(0.175343\pi\) | |||||||
\(770\) | 1.04618 | 0.0377016 | ||||||||
\(771\) | −26.8275 | −0.966169 | ||||||||
\(772\) | 13.1867 | 0.474600 | ||||||||
\(773\) | 6.76995 | 0.243498 | 0.121749 | − | 0.992561i | \(-0.461150\pi\) | ||||
0.121749 | + | 0.992561i | \(0.461150\pi\) | |||||||
\(774\) | −0.955734 | −0.0343532 | ||||||||
\(775\) | 6.49153 | 0.233183 | ||||||||
\(776\) | −22.1415 | −0.794832 | ||||||||
\(777\) | 1.92421 | 0.0690306 | ||||||||
\(778\) | 0.202978 | 0.00727710 | ||||||||
\(779\) | −78.9980 | −2.83040 | ||||||||
\(780\) | 10.1687 | 0.364098 | ||||||||
\(781\) | 11.3870 | 0.407461 | ||||||||
\(782\) | 0.583645 | 0.0208711 | ||||||||
\(783\) | −46.8918 | −1.67578 | ||||||||
\(784\) | 1.87998 | 0.0671422 | ||||||||
\(785\) | −1.97961 | −0.0706553 | ||||||||
\(786\) | −19.7908 | −0.705913 | ||||||||
\(787\) | 33.5533 | 1.19605 | 0.598024 | − | 0.801479i | \(-0.295953\pi\) | ||||
0.598024 | + | 0.801479i | \(0.295953\pi\) | |||||||
\(788\) | −24.4183 | −0.869867 | ||||||||
\(789\) | −35.5418 | −1.26532 | ||||||||
\(790\) | 2.00481 | 0.0713281 | ||||||||
\(791\) | 20.3245 | 0.722658 | ||||||||
\(792\) | 2.54276 | 0.0903531 | ||||||||
\(793\) | 34.9036 | 1.23946 | ||||||||
\(794\) | 1.19452 | 0.0423920 | ||||||||
\(795\) | −5.42646 | −0.192457 | ||||||||
\(796\) | 10.9250 | 0.387225 | ||||||||
\(797\) | 0.832832 | 0.0295004 | 0.0147502 | − | 0.999891i | \(-0.495305\pi\) | ||||
0.0147502 | + | 0.999891i | \(0.495305\pi\) | |||||||
\(798\) | −6.24583 | −0.221100 | ||||||||
\(799\) | 4.21316 | 0.149051 | ||||||||
\(800\) | −5.60356 | −0.198116 | ||||||||
\(801\) | 7.50385 | 0.265136 | ||||||||
\(802\) | 3.87894 | 0.136970 | ||||||||
\(803\) | 14.8519 | 0.524111 | ||||||||
\(804\) | 25.7616 | 0.908542 | ||||||||
\(805\) | 1.46015 | 0.0514636 | ||||||||
\(806\) | 16.3641 | 0.576400 | ||||||||
\(807\) | −27.8037 | −0.978735 | ||||||||
\(808\) | −30.0288 | −1.05641 | ||||||||
\(809\) | 36.6078 | 1.28706 | 0.643530 | − | 0.765421i | \(-0.277469\pi\) | ||||
0.643530 | + | 0.765421i | \(0.277469\pi\) | |||||||
\(810\) | −4.01410 | −0.141041 | ||||||||
\(811\) | −21.3984 | −0.751400 | −0.375700 | − | 0.926741i | \(-0.622598\pi\) | ||||
−0.375700 | + | 0.926741i | \(0.622598\pi\) | |||||||
\(812\) | −13.5845 | −0.476721 | ||||||||
\(813\) | −39.8845 | −1.39881 | ||||||||
\(814\) | 1.31905 | 0.0462325 | ||||||||
\(815\) | 22.4027 | 0.784732 | ||||||||
\(816\) | 1.86773 | 0.0653838 | ||||||||
\(817\) | −15.4640 | −0.541015 | ||||||||
\(818\) | −9.52872 | −0.333164 | ||||||||
\(819\) | −2.75419 | −0.0962391 | ||||||||
\(820\) | −19.2363 | −0.671760 | ||||||||
\(821\) | −39.4128 | −1.37552 | −0.687758 | − | 0.725940i | \(-0.741405\pi\) | ||||
−0.687758 | + | 0.725940i | \(0.741405\pi\) | |||||||
\(822\) | 12.4176 | 0.433113 | ||||||||
\(823\) | −4.12219 | −0.143691 | −0.0718453 | − | 0.997416i | \(-0.522889\pi\) | ||||
−0.0718453 | + | 0.997416i | \(0.522889\pi\) | |||||||
\(824\) | 19.9245 | 0.694101 | ||||||||
\(825\) | 2.60025 | 0.0905291 | ||||||||
\(826\) | −1.45262 | −0.0505432 | ||||||||
\(827\) | 45.6118 | 1.58608 | 0.793038 | − | 0.609172i | \(-0.208498\pi\) | ||||
0.793038 | + | 0.609172i | \(0.208498\pi\) | |||||||
\(828\) | 1.58981 | 0.0552497 | ||||||||
\(829\) | 52.2860 | 1.81597 | 0.907984 | − | 0.419004i | \(-0.137621\pi\) | ||||
0.907984 | + | 0.419004i | \(0.137621\pi\) | |||||||
\(830\) | 8.77980 | 0.304751 | ||||||||
\(831\) | −13.1517 | −0.456227 | ||||||||
\(832\) | 1.31060 | 0.0454370 | ||||||||
\(833\) | −0.650974 | −0.0225549 | ||||||||
\(834\) | 4.56238 | 0.157982 | ||||||||
\(835\) | −19.4040 | −0.671502 | ||||||||
\(836\) | 18.4304 | 0.637429 | ||||||||
\(837\) | 36.3674 | 1.25704 | ||||||||
\(838\) | −21.5749 | −0.745293 | ||||||||
\(839\) | −40.3138 | −1.39179 | −0.695893 | − | 0.718145i | \(-0.744991\pi\) | ||||
−0.695893 | + | 0.718145i | \(0.744991\pi\) | |||||||
\(840\) | −3.39507 | −0.117141 | ||||||||
\(841\) | 41.0588 | 1.41582 | ||||||||
\(842\) | 2.01224 | 0.0693462 | ||||||||
\(843\) | −8.99483 | −0.309798 | ||||||||
\(844\) | −17.3864 | −0.598463 | ||||||||
\(845\) | −3.85448 | −0.132598 | ||||||||
\(846\) | −2.66604 | −0.0916603 | ||||||||
\(847\) | 8.09707 | 0.278219 | ||||||||
\(848\) | −6.68457 | −0.229549 | ||||||||
\(849\) | 4.46222 | 0.153143 | ||||||||
\(850\) | 0.399715 | 0.0137101 | ||||||||
\(851\) | 1.84100 | 0.0631086 | ||||||||
\(852\) | −16.5539 | −0.567129 | ||||||||
\(853\) | −33.6098 | −1.15078 | −0.575389 | − | 0.817880i | \(-0.695149\pi\) | ||||
−0.575389 | + | 0.817880i | \(0.695149\pi\) | |||||||
\(854\) | −5.22035 | −0.178637 | ||||||||
\(855\) | 4.47138 | 0.152918 | ||||||||
\(856\) | −30.5705 | −1.04488 | ||||||||
\(857\) | −18.8306 | −0.643240 | −0.321620 | − | 0.946869i | \(-0.604227\pi\) | ||||
−0.321620 | + | 0.946869i | \(0.604227\pi\) | |||||||
\(858\) | 6.55480 | 0.223777 | ||||||||
\(859\) | −17.1295 | −0.584452 | −0.292226 | − | 0.956349i | \(-0.594396\pi\) | ||||
−0.292226 | + | 0.956349i | \(0.594396\pi\) | |||||||
\(860\) | −3.76553 | −0.128403 | ||||||||
\(861\) | −18.0887 | −0.616461 | ||||||||
\(862\) | 0.0387131 | 0.00131857 | ||||||||
\(863\) | 20.8003 | 0.708051 | 0.354026 | − | 0.935236i | \(-0.384813\pi\) | ||||
0.354026 | + | 0.935236i | \(0.384813\pi\) | |||||||
\(864\) | −31.3928 | −1.06800 | ||||||||
\(865\) | 23.2766 | 0.791427 | ||||||||
\(866\) | −16.9569 | −0.576218 | ||||||||
\(867\) | 25.2978 | 0.859159 | ||||||||
\(868\) | 10.5356 | 0.357601 | ||||||||
\(869\) | −5.56295 | −0.188710 | ||||||||
\(870\) | 7.84360 | 0.265923 | ||||||||
\(871\) | −42.6994 | −1.44682 | ||||||||
\(872\) | 9.42509 | 0.319174 | ||||||||
\(873\) | 6.67714 | 0.225987 | ||||||||
\(874\) | −5.97573 | −0.202132 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −21.5909 | −0.729490 | ||||||||
\(877\) | −26.1079 | −0.881600 | −0.440800 | − | 0.897605i | \(-0.645305\pi\) | ||||
−0.440800 | + | 0.897605i | \(0.645305\pi\) | |||||||
\(878\) | 6.12145 | 0.206589 | ||||||||
\(879\) | 2.87711 | 0.0970425 | ||||||||
\(880\) | 3.20311 | 0.107977 | ||||||||
\(881\) | −3.17163 | −0.106855 | −0.0534275 | − | 0.998572i | \(-0.517015\pi\) | ||||
−0.0534275 | + | 0.998572i | \(0.517015\pi\) | |||||||
\(882\) | 0.411929 | 0.0138704 | ||||||||
\(883\) | 0.325001 | 0.0109371 | 0.00546857 | − | 0.999985i | \(-0.498259\pi\) | ||||
0.00546857 | + | 0.999985i | \(0.498259\pi\) | |||||||
\(884\) | −4.33743 | −0.145884 | ||||||||
\(885\) | −3.61047 | −0.121365 | ||||||||
\(886\) | −18.3976 | −0.618079 | ||||||||
\(887\) | −40.4310 | −1.35754 | −0.678770 | − | 0.734350i | \(-0.737487\pi\) | ||||
−0.678770 | + | 0.734350i | \(0.737487\pi\) | |||||||
\(888\) | −4.28060 | −0.143647 | ||||||||
\(889\) | 5.18231 | 0.173809 | ||||||||
\(890\) | −6.86807 | −0.230218 | ||||||||
\(891\) | 11.1383 | 0.373147 | ||||||||
\(892\) | 1.28532 | 0.0430357 | ||||||||
\(893\) | −43.1370 | −1.44352 | ||||||||
\(894\) | 8.57907 | 0.286927 | ||||||||
\(895\) | −4.71244 | −0.157520 | ||||||||
\(896\) | −11.4031 | −0.380952 | ||||||||
\(897\) | 9.14857 | 0.305462 | ||||||||
\(898\) | 7.75300 | 0.258721 | ||||||||
\(899\) | −54.3348 | −1.81217 | ||||||||
\(900\) | 1.08880 | 0.0362932 | ||||||||
\(901\) | 2.31464 | 0.0771118 | ||||||||
\(902\) | −12.3998 | −0.412868 | ||||||||
\(903\) | −3.54089 | −0.117833 | ||||||||
\(904\) | −45.2140 | −1.50379 | ||||||||
\(905\) | −7.10961 | −0.236332 | ||||||||
\(906\) | 19.3791 | 0.643827 | ||||||||
\(907\) | −15.6741 | −0.520449 | −0.260225 | − | 0.965548i | \(-0.583797\pi\) | ||||
−0.260225 | + | 0.965548i | \(0.583797\pi\) | |||||||
\(908\) | 44.1799 | 1.46616 | ||||||||
\(909\) | 9.05571 | 0.300359 | ||||||||
\(910\) | 2.52083 | 0.0835649 | ||||||||
\(911\) | −29.4928 | −0.977139 | −0.488570 | − | 0.872525i | \(-0.662481\pi\) | ||||
−0.488570 | + | 0.872525i | \(0.662481\pi\) | |||||||
\(912\) | −19.1230 | −0.633227 | ||||||||
\(913\) | −24.3622 | −0.806270 | ||||||||
\(914\) | −18.9733 | −0.627581 | ||||||||
\(915\) | −12.9751 | −0.428943 | ||||||||
\(916\) | −1.62297 | −0.0536245 | ||||||||
\(917\) | 21.1192 | 0.697419 | ||||||||
\(918\) | 2.23932 | 0.0739086 | ||||||||
\(919\) | 38.2326 | 1.26118 | 0.630589 | − | 0.776117i | \(-0.282814\pi\) | ||||
0.630589 | + | 0.776117i | \(0.282814\pi\) | |||||||
\(920\) | −3.24825 | −0.107092 | ||||||||
\(921\) | −15.1593 | −0.499516 | ||||||||
\(922\) | 6.79765 | 0.223869 | ||||||||
\(923\) | 27.4379 | 0.903129 | ||||||||
\(924\) | 4.22014 | 0.138832 | ||||||||
\(925\) | 1.26083 | 0.0414557 | ||||||||
\(926\) | 11.0240 | 0.362273 | ||||||||
\(927\) | −6.00856 | −0.197347 | ||||||||
\(928\) | 46.9024 | 1.53965 | ||||||||
\(929\) | 13.2421 | 0.434460 | 0.217230 | − | 0.976120i | \(-0.430298\pi\) | ||||
0.217230 | + | 0.976120i | \(0.430298\pi\) | |||||||
\(930\) | −6.08318 | −0.199475 | ||||||||
\(931\) | 6.66509 | 0.218439 | ||||||||
\(932\) | 1.48172 | 0.0485354 | ||||||||
\(933\) | 5.14457 | 0.168426 | ||||||||
\(934\) | 0.843024 | 0.0275846 | ||||||||
\(935\) | −1.10913 | −0.0362724 | ||||||||
\(936\) | 6.12696 | 0.200266 | ||||||||
\(937\) | −13.6877 | −0.447158 | −0.223579 | − | 0.974686i | \(-0.571774\pi\) | ||||
−0.223579 | + | 0.974686i | \(0.571774\pi\) | |||||||
\(938\) | 6.38633 | 0.208521 | ||||||||
\(939\) | 7.73633 | 0.252466 | ||||||||
\(940\) | −10.5040 | −0.342603 | ||||||||
\(941\) | −28.2048 | −0.919449 | −0.459725 | − | 0.888062i | \(-0.652052\pi\) | ||||
−0.459725 | + | 0.888062i | \(0.652052\pi\) | |||||||
\(942\) | 1.85508 | 0.0604419 | ||||||||
\(943\) | −17.3065 | −0.563576 | ||||||||
\(944\) | −4.44754 | −0.144755 | ||||||||
\(945\) | 5.60229 | 0.182243 | ||||||||
\(946\) | −2.42728 | −0.0789176 | ||||||||
\(947\) | −38.4049 | −1.24799 | −0.623996 | − | 0.781428i | \(-0.714492\pi\) | ||||
−0.623996 | + | 0.781428i | \(0.714492\pi\) | |||||||
\(948\) | 8.08715 | 0.262658 | ||||||||
\(949\) | 35.7866 | 1.16168 | ||||||||
\(950\) | −4.09254 | −0.132779 | ||||||||
\(951\) | 27.5512 | 0.893408 | ||||||||
\(952\) | 1.44816 | 0.0469350 | ||||||||
\(953\) | 15.3032 | 0.495719 | 0.247860 | − | 0.968796i | \(-0.420273\pi\) | ||||
0.247860 | + | 0.968796i | \(0.420273\pi\) | |||||||
\(954\) | −1.46468 | −0.0474207 | ||||||||
\(955\) | 26.7248 | 0.864794 | ||||||||
\(956\) | −2.62305 | −0.0848355 | ||||||||
\(957\) | −21.7644 | −0.703543 | ||||||||
\(958\) | −12.9274 | −0.417665 | ||||||||
\(959\) | −13.2511 | −0.427901 | ||||||||
\(960\) | −0.487204 | −0.0157244 | ||||||||
\(961\) | 11.1399 | 0.359353 | ||||||||
\(962\) | 3.17833 | 0.102474 | ||||||||
\(963\) | 9.21905 | 0.297080 | ||||||||
\(964\) | 45.7230 | 1.47264 | ||||||||
\(965\) | 8.12503 | 0.261554 | ||||||||
\(966\) | −1.36830 | −0.0440244 | ||||||||
\(967\) | 17.0172 | 0.547237 | 0.273619 | − | 0.961838i | \(-0.411779\pi\) | ||||
0.273619 | + | 0.961838i | \(0.411779\pi\) | |||||||
\(968\) | −18.0127 | −0.578951 | ||||||||
\(969\) | 6.62166 | 0.212718 | ||||||||
\(970\) | −6.11141 | −0.196226 | ||||||||
\(971\) | −44.5645 | −1.43014 | −0.715071 | − | 0.699052i | \(-0.753606\pi\) | ||||
−0.715071 | + | 0.699052i | \(0.753606\pi\) | |||||||
\(972\) | 11.0848 | 0.355544 | ||||||||
\(973\) | −4.86864 | −0.156081 | ||||||||
\(974\) | −0.124798 | −0.00399879 | ||||||||
\(975\) | 6.26549 | 0.200656 | ||||||||
\(976\) | −15.9833 | −0.511613 | ||||||||
\(977\) | 42.6678 | 1.36506 | 0.682532 | − | 0.730856i | \(-0.260879\pi\) | ||||
0.682532 | + | 0.730856i | \(0.260879\pi\) | |||||||
\(978\) | −20.9935 | −0.671297 | ||||||||
\(979\) | 19.0575 | 0.609081 | ||||||||
\(980\) | 1.62297 | 0.0518439 | ||||||||
\(981\) | −2.84230 | −0.0907476 | ||||||||
\(982\) | 0.952486 | 0.0303950 | ||||||||
\(983\) | −42.8223 | −1.36582 | −0.682909 | − | 0.730503i | \(-0.739286\pi\) | ||||
−0.682909 | + | 0.730503i | \(0.739286\pi\) | |||||||
\(984\) | 40.2401 | 1.28281 | ||||||||
\(985\) | −15.0454 | −0.479387 | ||||||||
\(986\) | −3.34566 | −0.106548 | ||||||||
\(987\) | −9.87737 | −0.314400 | ||||||||
\(988\) | 44.4094 | 1.41285 | ||||||||
\(989\) | −3.38776 | −0.107725 | ||||||||
\(990\) | 0.701844 | 0.0223061 | ||||||||
\(991\) | 57.8421 | 1.83741 | 0.918707 | − | 0.394940i | \(-0.129235\pi\) | ||||
0.918707 | + | 0.394940i | \(0.129235\pi\) | |||||||
\(992\) | −36.3756 | −1.15493 | ||||||||
\(993\) | 38.5583 | 1.22361 | ||||||||
\(994\) | −4.10374 | −0.130163 | ||||||||
\(995\) | 6.73146 | 0.213402 | ||||||||
\(996\) | 35.4165 | 1.12222 | ||||||||
\(997\) | −24.1233 | −0.763991 | −0.381996 | − | 0.924164i | \(-0.624763\pi\) | ||||
−0.381996 | + | 0.924164i | \(0.624763\pi\) | |||||||
\(998\) | 9.36350 | 0.296396 | ||||||||
\(999\) | 7.06352 | 0.223480 |
(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 | 8015.2.a.l.1.25 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.25 | ✓ | 62 | 1.1 | even | 1 | trivial |