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: | \(73\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84781 | −1.30660 | −0.653300 | − | 0.757099i | \(-0.726616\pi\) | ||||
−0.653300 | + | 0.757099i | \(0.726616\pi\) | |||||||
\(3\) | −2.80168 | −1.61755 | −0.808774 | − | 0.588120i | \(-0.799868\pi\) | ||||
−0.808774 | + | 0.588120i | \(0.799868\pi\) | |||||||
\(4\) | 1.41441 | 0.707203 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 5.17697 | 2.11349 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.08207 | 0.382568 | ||||||||
\(9\) | 4.84939 | 1.61646 | ||||||||
\(10\) | −1.84781 | −0.584329 | ||||||||
\(11\) | −1.50470 | −0.453684 | −0.226842 | − | 0.973932i | \(-0.572840\pi\) | ||||
−0.226842 | + | 0.973932i | \(0.572840\pi\) | |||||||
\(12\) | −3.96271 | −1.14394 | ||||||||
\(13\) | 2.64111 | 0.732513 | 0.366256 | − | 0.930514i | \(-0.380639\pi\) | ||||
0.366256 | + | 0.930514i | \(0.380639\pi\) | |||||||
\(14\) | −1.84781 | −0.493848 | ||||||||
\(15\) | −2.80168 | −0.723389 | ||||||||
\(16\) | −4.82827 | −1.20707 | ||||||||
\(17\) | −5.57678 | −1.35257 | −0.676284 | − | 0.736641i | \(-0.736411\pi\) | ||||
−0.676284 | + | 0.736641i | \(0.736411\pi\) | |||||||
\(18\) | −8.96075 | −2.11207 | ||||||||
\(19\) | 5.28184 | 1.21174 | 0.605868 | − | 0.795565i | \(-0.292826\pi\) | ||||
0.605868 | + | 0.795565i | \(0.292826\pi\) | |||||||
\(20\) | 1.41441 | 0.316271 | ||||||||
\(21\) | −2.80168 | −0.611376 | ||||||||
\(22\) | 2.78040 | 0.592784 | ||||||||
\(23\) | −7.51259 | −1.56648 | −0.783242 | − | 0.621717i | \(-0.786435\pi\) | ||||
−0.783242 | + | 0.621717i | \(0.786435\pi\) | |||||||
\(24\) | −3.03160 | −0.618823 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.88028 | −0.957101 | ||||||||
\(27\) | −5.18138 | −0.997157 | ||||||||
\(28\) | 1.41441 | 0.267298 | ||||||||
\(29\) | −7.57023 | −1.40576 | −0.702878 | − | 0.711310i | \(-0.748102\pi\) | ||||
−0.702878 | + | 0.711310i | \(0.748102\pi\) | |||||||
\(30\) | 5.17697 | 0.945181 | ||||||||
\(31\) | −9.14359 | −1.64224 | −0.821118 | − | 0.570758i | \(-0.806649\pi\) | ||||
−0.821118 | + | 0.570758i | \(0.806649\pi\) | |||||||
\(32\) | 6.75759 | 1.19459 | ||||||||
\(33\) | 4.21568 | 0.733856 | ||||||||
\(34\) | 10.3048 | 1.76727 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 6.85900 | 1.14317 | ||||||||
\(37\) | 0.716572 | 0.117804 | 0.0589019 | − | 0.998264i | \(-0.481240\pi\) | ||||
0.0589019 | + | 0.998264i | \(0.481240\pi\) | |||||||
\(38\) | −9.75984 | −1.58325 | ||||||||
\(39\) | −7.39954 | −1.18487 | ||||||||
\(40\) | 1.08207 | 0.171090 | ||||||||
\(41\) | −8.71600 | −1.36121 | −0.680605 | − | 0.732650i | \(-0.738283\pi\) | ||||
−0.680605 | + | 0.732650i | \(0.738283\pi\) | |||||||
\(42\) | 5.17697 | 0.798823 | ||||||||
\(43\) | −4.01864 | −0.612836 | −0.306418 | − | 0.951897i | \(-0.599131\pi\) | ||||
−0.306418 | + | 0.951897i | \(0.599131\pi\) | |||||||
\(44\) | −2.12826 | −0.320847 | ||||||||
\(45\) | 4.84939 | 0.722904 | ||||||||
\(46\) | 13.8818 | 2.04677 | ||||||||
\(47\) | −9.05205 | −1.32038 | −0.660188 | − | 0.751100i | \(-0.729524\pi\) | ||||
−0.660188 | + | 0.751100i | \(0.729524\pi\) | |||||||
\(48\) | 13.5272 | 1.95249 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.84781 | −0.261320 | ||||||||
\(51\) | 15.6243 | 2.18784 | ||||||||
\(52\) | 3.73561 | 0.518035 | ||||||||
\(53\) | −4.90340 | −0.673533 | −0.336767 | − | 0.941588i | \(-0.609333\pi\) | ||||
−0.336767 | + | 0.941588i | \(0.609333\pi\) | |||||||
\(54\) | 9.57421 | 1.30288 | ||||||||
\(55\) | −1.50470 | −0.202894 | ||||||||
\(56\) | 1.08207 | 0.144597 | ||||||||
\(57\) | −14.7980 | −1.96004 | ||||||||
\(58\) | 13.9884 | 1.83676 | ||||||||
\(59\) | −1.87071 | −0.243545 | −0.121773 | − | 0.992558i | \(-0.538858\pi\) | ||||
−0.121773 | + | 0.992558i | \(0.538858\pi\) | |||||||
\(60\) | −3.96271 | −0.511583 | ||||||||
\(61\) | 9.51937 | 1.21883 | 0.609415 | − | 0.792851i | \(-0.291404\pi\) | ||||
0.609415 | + | 0.792851i | \(0.291404\pi\) | |||||||
\(62\) | 16.8956 | 2.14575 | ||||||||
\(63\) | 4.84939 | 0.610965 | ||||||||
\(64\) | −2.83022 | −0.353778 | ||||||||
\(65\) | 2.64111 | 0.327590 | ||||||||
\(66\) | −7.78978 | −0.958856 | ||||||||
\(67\) | −1.93775 | −0.236734 | −0.118367 | − | 0.992970i | \(-0.537766\pi\) | ||||
−0.118367 | + | 0.992970i | \(0.537766\pi\) | |||||||
\(68\) | −7.88784 | −0.956541 | ||||||||
\(69\) | 21.0478 | 2.53386 | ||||||||
\(70\) | −1.84781 | −0.220856 | ||||||||
\(71\) | 8.08335 | 0.959317 | 0.479658 | − | 0.877455i | \(-0.340761\pi\) | ||||
0.479658 | + | 0.877455i | \(0.340761\pi\) | |||||||
\(72\) | 5.24736 | 0.618407 | ||||||||
\(73\) | −10.5591 | −1.23585 | −0.617926 | − | 0.786236i | \(-0.712027\pi\) | ||||
−0.617926 | + | 0.786236i | \(0.712027\pi\) | |||||||
\(74\) | −1.32409 | −0.153922 | ||||||||
\(75\) | −2.80168 | −0.323510 | ||||||||
\(76\) | 7.47066 | 0.856944 | ||||||||
\(77\) | −1.50470 | −0.171476 | ||||||||
\(78\) | 13.6730 | 1.54816 | ||||||||
\(79\) | 5.21995 | 0.587291 | 0.293645 | − | 0.955914i | \(-0.405132\pi\) | ||||
0.293645 | + | 0.955914i | \(0.405132\pi\) | |||||||
\(80\) | −4.82827 | −0.539817 | ||||||||
\(81\) | −0.0316184 | −0.00351315 | ||||||||
\(82\) | 16.1055 | 1.77856 | ||||||||
\(83\) | −3.94028 | −0.432502 | −0.216251 | − | 0.976338i | \(-0.569383\pi\) | ||||
−0.216251 | + | 0.976338i | \(0.569383\pi\) | |||||||
\(84\) | −3.96271 | −0.432367 | ||||||||
\(85\) | −5.57678 | −0.604887 | ||||||||
\(86\) | 7.42568 | 0.800732 | ||||||||
\(87\) | 21.2093 | 2.27388 | ||||||||
\(88\) | −1.62819 | −0.173565 | ||||||||
\(89\) | 9.39380 | 0.995740 | 0.497870 | − | 0.867252i | \(-0.334116\pi\) | ||||
0.497870 | + | 0.867252i | \(0.334116\pi\) | |||||||
\(90\) | −8.96075 | −0.944546 | ||||||||
\(91\) | 2.64111 | 0.276864 | ||||||||
\(92\) | −10.6259 | −1.10782 | ||||||||
\(93\) | 25.6174 | 2.65640 | ||||||||
\(94\) | 16.7265 | 1.72520 | ||||||||
\(95\) | 5.28184 | 0.541905 | ||||||||
\(96\) | −18.9326 | −1.93230 | ||||||||
\(97\) | 2.81635 | 0.285957 | 0.142978 | − | 0.989726i | \(-0.454332\pi\) | ||||
0.142978 | + | 0.989726i | \(0.454332\pi\) | |||||||
\(98\) | −1.84781 | −0.186657 | ||||||||
\(99\) | −7.29687 | −0.733363 | ||||||||
\(100\) | 1.41441 | 0.141441 | ||||||||
\(101\) | 0.859285 | 0.0855021 | 0.0427510 | − | 0.999086i | \(-0.486388\pi\) | ||||
0.0427510 | + | 0.999086i | \(0.486388\pi\) | |||||||
\(102\) | −28.8708 | −2.85864 | ||||||||
\(103\) | 1.29693 | 0.127790 | 0.0638952 | − | 0.997957i | \(-0.479648\pi\) | ||||
0.0638952 | + | 0.997957i | \(0.479648\pi\) | |||||||
\(104\) | 2.85786 | 0.280236 | ||||||||
\(105\) | −2.80168 | −0.273416 | ||||||||
\(106\) | 9.06055 | 0.880038 | ||||||||
\(107\) | −17.4788 | −1.68974 | −0.844871 | − | 0.534970i | \(-0.820323\pi\) | ||||
−0.844871 | + | 0.534970i | \(0.820323\pi\) | |||||||
\(108\) | −7.32857 | −0.705192 | ||||||||
\(109\) | 9.57399 | 0.917022 | 0.458511 | − | 0.888689i | \(-0.348383\pi\) | ||||
0.458511 | + | 0.888689i | \(0.348383\pi\) | |||||||
\(110\) | 2.78040 | 0.265101 | ||||||||
\(111\) | −2.00760 | −0.190553 | ||||||||
\(112\) | −4.82827 | −0.456228 | ||||||||
\(113\) | −2.39048 | −0.224878 | −0.112439 | − | 0.993659i | \(-0.535866\pi\) | ||||
−0.112439 | + | 0.993659i | \(0.535866\pi\) | |||||||
\(114\) | 27.3439 | 2.56099 | ||||||||
\(115\) | −7.51259 | −0.700553 | ||||||||
\(116\) | −10.7074 | −0.994155 | ||||||||
\(117\) | 12.8078 | 1.18408 | ||||||||
\(118\) | 3.45671 | 0.318216 | ||||||||
\(119\) | −5.57678 | −0.511223 | ||||||||
\(120\) | −3.03160 | −0.276746 | ||||||||
\(121\) | −8.73588 | −0.794171 | ||||||||
\(122\) | −17.5900 | −1.59252 | ||||||||
\(123\) | 24.4194 | 2.20182 | ||||||||
\(124\) | −12.9327 | −1.16140 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −8.96075 | −0.798287 | ||||||||
\(127\) | 0.245096 | 0.0217487 | 0.0108744 | − | 0.999941i | \(-0.496539\pi\) | ||||
0.0108744 | + | 0.999941i | \(0.496539\pi\) | |||||||
\(128\) | −8.28547 | −0.732339 | ||||||||
\(129\) | 11.2589 | 0.991292 | ||||||||
\(130\) | −4.88028 | −0.428029 | ||||||||
\(131\) | −5.46386 | −0.477380 | −0.238690 | − | 0.971096i | \(-0.576718\pi\) | ||||
−0.238690 | + | 0.971096i | \(0.576718\pi\) | |||||||
\(132\) | 5.96269 | 0.518985 | ||||||||
\(133\) | 5.28184 | 0.457993 | ||||||||
\(134\) | 3.58059 | 0.309316 | ||||||||
\(135\) | −5.18138 | −0.445942 | ||||||||
\(136\) | −6.03445 | −0.517450 | ||||||||
\(137\) | 3.66496 | 0.313119 | 0.156559 | − | 0.987669i | \(-0.449960\pi\) | ||||
0.156559 | + | 0.987669i | \(0.449960\pi\) | |||||||
\(138\) | −38.8924 | −3.31074 | ||||||||
\(139\) | 15.3650 | 1.30324 | 0.651622 | − | 0.758544i | \(-0.274089\pi\) | ||||
0.651622 | + | 0.758544i | \(0.274089\pi\) | |||||||
\(140\) | 1.41441 | 0.119539 | ||||||||
\(141\) | 25.3609 | 2.13577 | ||||||||
\(142\) | −14.9365 | −1.25344 | ||||||||
\(143\) | −3.97408 | −0.332329 | ||||||||
\(144\) | −23.4141 | −1.95118 | ||||||||
\(145\) | −7.57023 | −0.628673 | ||||||||
\(146\) | 19.5113 | 1.61476 | ||||||||
\(147\) | −2.80168 | −0.231078 | ||||||||
\(148\) | 1.01352 | 0.0833112 | ||||||||
\(149\) | 19.5944 | 1.60524 | 0.802618 | − | 0.596493i | \(-0.203440\pi\) | ||||
0.802618 | + | 0.596493i | \(0.203440\pi\) | |||||||
\(150\) | 5.17697 | 0.422698 | ||||||||
\(151\) | 19.5529 | 1.59119 | 0.795596 | − | 0.605828i | \(-0.207158\pi\) | ||||
0.795596 | + | 0.605828i | \(0.207158\pi\) | |||||||
\(152\) | 5.71530 | 0.463572 | ||||||||
\(153\) | −27.0440 | −2.18638 | ||||||||
\(154\) | 2.78040 | 0.224051 | ||||||||
\(155\) | −9.14359 | −0.734431 | ||||||||
\(156\) | −10.4660 | −0.837947 | ||||||||
\(157\) | 17.5114 | 1.39756 | 0.698780 | − | 0.715337i | \(-0.253727\pi\) | ||||
0.698780 | + | 0.715337i | \(0.253727\pi\) | |||||||
\(158\) | −9.64549 | −0.767354 | ||||||||
\(159\) | 13.7377 | 1.08947 | ||||||||
\(160\) | 6.75759 | 0.534235 | ||||||||
\(161\) | −7.51259 | −0.592075 | ||||||||
\(162\) | 0.0584248 | 0.00459029 | ||||||||
\(163\) | 11.1884 | 0.876347 | 0.438173 | − | 0.898890i | \(-0.355626\pi\) | ||||
0.438173 | + | 0.898890i | \(0.355626\pi\) | |||||||
\(164\) | −12.3280 | −0.962653 | ||||||||
\(165\) | 4.21568 | 0.328190 | ||||||||
\(166\) | 7.28090 | 0.565107 | ||||||||
\(167\) | −20.2741 | −1.56885 | −0.784427 | − | 0.620221i | \(-0.787043\pi\) | ||||
−0.784427 | + | 0.620221i | \(0.787043\pi\) | |||||||
\(168\) | −3.03160 | −0.233893 | ||||||||
\(169\) | −6.02453 | −0.463425 | ||||||||
\(170\) | 10.3048 | 0.790345 | ||||||||
\(171\) | 25.6137 | 1.95873 | ||||||||
\(172\) | −5.68399 | −0.433400 | ||||||||
\(173\) | 15.0656 | 1.14542 | 0.572708 | − | 0.819760i | \(-0.305893\pi\) | ||||
0.572708 | + | 0.819760i | \(0.305893\pi\) | |||||||
\(174\) | −39.1908 | −2.97105 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 7.26509 | 0.547627 | ||||||||
\(177\) | 5.24111 | 0.393946 | ||||||||
\(178\) | −17.3580 | −1.30103 | ||||||||
\(179\) | −7.73749 | −0.578327 | −0.289164 | − | 0.957280i | \(-0.593377\pi\) | ||||
−0.289164 | + | 0.957280i | \(0.593377\pi\) | |||||||
\(180\) | 6.85900 | 0.511240 | ||||||||
\(181\) | 4.73454 | 0.351916 | 0.175958 | − | 0.984398i | \(-0.443698\pi\) | ||||
0.175958 | + | 0.984398i | \(0.443698\pi\) | |||||||
\(182\) | −4.88028 | −0.361750 | ||||||||
\(183\) | −26.6702 | −1.97152 | ||||||||
\(184\) | −8.12912 | −0.599287 | ||||||||
\(185\) | 0.716572 | 0.0526834 | ||||||||
\(186\) | −47.3361 | −3.47085 | ||||||||
\(187\) | 8.39139 | 0.613639 | ||||||||
\(188\) | −12.8033 | −0.933775 | ||||||||
\(189\) | −5.18138 | −0.376890 | ||||||||
\(190\) | −9.75984 | −0.708053 | ||||||||
\(191\) | 6.16197 | 0.445865 | 0.222932 | − | 0.974834i | \(-0.428437\pi\) | ||||
0.222932 | + | 0.974834i | \(0.428437\pi\) | |||||||
\(192\) | 7.92936 | 0.572253 | ||||||||
\(193\) | −20.0392 | −1.44246 | −0.721228 | − | 0.692698i | \(-0.756422\pi\) | ||||
−0.721228 | + | 0.692698i | \(0.756422\pi\) | |||||||
\(194\) | −5.20408 | −0.373631 | ||||||||
\(195\) | −7.39954 | −0.529892 | ||||||||
\(196\) | 1.41441 | 0.101029 | ||||||||
\(197\) | 6.39547 | 0.455658 | 0.227829 | − | 0.973701i | \(-0.426837\pi\) | ||||
0.227829 | + | 0.973701i | \(0.426837\pi\) | |||||||
\(198\) | 13.4832 | 0.958212 | ||||||||
\(199\) | −10.5352 | −0.746818 | −0.373409 | − | 0.927667i | \(-0.621811\pi\) | ||||
−0.373409 | + | 0.927667i | \(0.621811\pi\) | |||||||
\(200\) | 1.08207 | 0.0765137 | ||||||||
\(201\) | 5.42894 | 0.382928 | ||||||||
\(202\) | −1.58780 | −0.111717 | ||||||||
\(203\) | −7.57023 | −0.531326 | ||||||||
\(204\) | 22.0992 | 1.54725 | ||||||||
\(205\) | −8.71600 | −0.608752 | ||||||||
\(206\) | −2.39648 | −0.166971 | ||||||||
\(207\) | −36.4314 | −2.53216 | ||||||||
\(208\) | −12.7520 | −0.884192 | ||||||||
\(209\) | −7.94758 | −0.549746 | ||||||||
\(210\) | 5.17697 | 0.357245 | ||||||||
\(211\) | −11.0595 | −0.761371 | −0.380685 | − | 0.924705i | \(-0.624312\pi\) | ||||
−0.380685 | + | 0.924705i | \(0.624312\pi\) | |||||||
\(212\) | −6.93539 | −0.476325 | ||||||||
\(213\) | −22.6469 | −1.55174 | ||||||||
\(214\) | 32.2976 | 2.20782 | ||||||||
\(215\) | −4.01864 | −0.274069 | ||||||||
\(216\) | −5.60660 | −0.381480 | ||||||||
\(217\) | −9.14359 | −0.620707 | ||||||||
\(218\) | −17.6909 | −1.19818 | ||||||||
\(219\) | 29.5833 | 1.99905 | ||||||||
\(220\) | −2.12826 | −0.143487 | ||||||||
\(221\) | −14.7289 | −0.990774 | ||||||||
\(222\) | 3.70967 | 0.248977 | ||||||||
\(223\) | −15.4637 | −1.03553 | −0.517763 | − | 0.855524i | \(-0.673235\pi\) | ||||
−0.517763 | + | 0.855524i | \(0.673235\pi\) | |||||||
\(224\) | 6.75759 | 0.451511 | ||||||||
\(225\) | 4.84939 | 0.323292 | ||||||||
\(226\) | 4.41716 | 0.293825 | ||||||||
\(227\) | −14.5606 | −0.966419 | −0.483210 | − | 0.875505i | \(-0.660529\pi\) | ||||
−0.483210 | + | 0.875505i | \(0.660529\pi\) | |||||||
\(228\) | −20.9304 | −1.38615 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 13.8818 | 0.915342 | ||||||||
\(231\) | 4.21568 | 0.277371 | ||||||||
\(232\) | −8.19149 | −0.537798 | ||||||||
\(233\) | 10.7340 | 0.703211 | 0.351605 | − | 0.936148i | \(-0.385636\pi\) | ||||
0.351605 | + | 0.936148i | \(0.385636\pi\) | |||||||
\(234\) | −23.6663 | −1.54712 | ||||||||
\(235\) | −9.05205 | −0.590491 | ||||||||
\(236\) | −2.64594 | −0.172236 | ||||||||
\(237\) | −14.6246 | −0.949971 | ||||||||
\(238\) | 10.3048 | 0.667964 | ||||||||
\(239\) | −3.18115 | −0.205772 | −0.102886 | − | 0.994693i | \(-0.532808\pi\) | ||||
−0.102886 | + | 0.994693i | \(0.532808\pi\) | |||||||
\(240\) | 13.5272 | 0.873179 | ||||||||
\(241\) | −16.8417 | −1.08487 | −0.542434 | − | 0.840098i | \(-0.682497\pi\) | ||||
−0.542434 | + | 0.840098i | \(0.682497\pi\) | |||||||
\(242\) | 16.1423 | 1.03766 | ||||||||
\(243\) | 15.6327 | 1.00284 | ||||||||
\(244\) | 13.4643 | 0.861961 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −45.1225 | −2.87690 | ||||||||
\(247\) | 13.9499 | 0.887612 | ||||||||
\(248\) | −9.89397 | −0.628268 | ||||||||
\(249\) | 11.0394 | 0.699593 | ||||||||
\(250\) | −1.84781 | −0.116866 | ||||||||
\(251\) | −6.91680 | −0.436585 | −0.218292 | − | 0.975883i | \(-0.570049\pi\) | ||||
−0.218292 | + | 0.975883i | \(0.570049\pi\) | |||||||
\(252\) | 6.85900 | 0.432076 | ||||||||
\(253\) | 11.3042 | 0.710689 | ||||||||
\(254\) | −0.452891 | −0.0284169 | ||||||||
\(255\) | 15.6243 | 0.978434 | ||||||||
\(256\) | 20.9704 | 1.31065 | ||||||||
\(257\) | 2.94231 | 0.183537 | 0.0917683 | − | 0.995780i | \(-0.470748\pi\) | ||||
0.0917683 | + | 0.995780i | \(0.470748\pi\) | |||||||
\(258\) | −20.8044 | −1.29522 | ||||||||
\(259\) | 0.716572 | 0.0445256 | ||||||||
\(260\) | 3.73561 | 0.231672 | ||||||||
\(261\) | −36.7110 | −2.27235 | ||||||||
\(262\) | 10.0962 | 0.623744 | ||||||||
\(263\) | 9.49130 | 0.585259 | 0.292629 | − | 0.956226i | \(-0.405470\pi\) | ||||
0.292629 | + | 0.956226i | \(0.405470\pi\) | |||||||
\(264\) | 4.56165 | 0.280750 | ||||||||
\(265\) | −4.90340 | −0.301213 | ||||||||
\(266\) | −9.75984 | −0.598414 | ||||||||
\(267\) | −26.3184 | −1.61066 | ||||||||
\(268\) | −2.74076 | −0.167419 | ||||||||
\(269\) | 12.2114 | 0.744542 | 0.372271 | − | 0.928124i | \(-0.378579\pi\) | ||||
0.372271 | + | 0.928124i | \(0.378579\pi\) | |||||||
\(270\) | 9.57421 | 0.582668 | ||||||||
\(271\) | 24.1656 | 1.46796 | 0.733978 | − | 0.679173i | \(-0.237662\pi\) | ||||
0.733978 | + | 0.679173i | \(0.237662\pi\) | |||||||
\(272\) | 26.9262 | 1.63264 | ||||||||
\(273\) | −7.39954 | −0.447840 | ||||||||
\(274\) | −6.77216 | −0.409121 | ||||||||
\(275\) | −1.50470 | −0.0907368 | ||||||||
\(276\) | 29.7702 | 1.79196 | ||||||||
\(277\) | −6.50345 | −0.390755 | −0.195377 | − | 0.980728i | \(-0.562593\pi\) | ||||
−0.195377 | + | 0.980728i | \(0.562593\pi\) | |||||||
\(278\) | −28.3916 | −1.70282 | ||||||||
\(279\) | −44.3408 | −2.65461 | ||||||||
\(280\) | 1.08207 | 0.0646658 | ||||||||
\(281\) | 6.85761 | 0.409091 | 0.204545 | − | 0.978857i | \(-0.434428\pi\) | ||||
0.204545 | + | 0.978857i | \(0.434428\pi\) | |||||||
\(282\) | −46.8622 | −2.79060 | ||||||||
\(283\) | −26.4464 | −1.57207 | −0.786037 | − | 0.618179i | \(-0.787871\pi\) | ||||
−0.786037 | + | 0.618179i | \(0.787871\pi\) | |||||||
\(284\) | 11.4331 | 0.678432 | ||||||||
\(285\) | −14.7980 | −0.876557 | ||||||||
\(286\) | 7.34335 | 0.434222 | ||||||||
\(287\) | −8.71600 | −0.514489 | ||||||||
\(288\) | 32.7702 | 1.93100 | ||||||||
\(289\) | 14.1005 | 0.829441 | ||||||||
\(290\) | 13.9884 | 0.821424 | ||||||||
\(291\) | −7.89049 | −0.462549 | ||||||||
\(292\) | −14.9349 | −0.873999 | ||||||||
\(293\) | 30.9524 | 1.80826 | 0.904128 | − | 0.427261i | \(-0.140522\pi\) | ||||
0.904128 | + | 0.427261i | \(0.140522\pi\) | |||||||
\(294\) | 5.17697 | 0.301927 | ||||||||
\(295\) | −1.87071 | −0.108917 | ||||||||
\(296\) | 0.775379 | 0.0450680 | ||||||||
\(297\) | 7.79642 | 0.452394 | ||||||||
\(298\) | −36.2068 | −2.09740 | ||||||||
\(299\) | −19.8416 | −1.14747 | ||||||||
\(300\) | −3.96271 | −0.228787 | ||||||||
\(301\) | −4.01864 | −0.231630 | ||||||||
\(302\) | −36.1300 | −2.07905 | ||||||||
\(303\) | −2.40744 | −0.138304 | ||||||||
\(304\) | −25.5021 | −1.46265 | ||||||||
\(305\) | 9.51937 | 0.545078 | ||||||||
\(306\) | 49.9721 | 2.85672 | ||||||||
\(307\) | 24.5961 | 1.40378 | 0.701888 | − | 0.712287i | \(-0.252341\pi\) | ||||
0.701888 | + | 0.712287i | \(0.252341\pi\) | |||||||
\(308\) | −2.12826 | −0.121269 | ||||||||
\(309\) | −3.63358 | −0.206707 | ||||||||
\(310\) | 16.8956 | 0.959607 | ||||||||
\(311\) | 17.1341 | 0.971583 | 0.485792 | − | 0.874075i | \(-0.338531\pi\) | ||||
0.485792 | + | 0.874075i | \(0.338531\pi\) | |||||||
\(312\) | −8.00679 | −0.453295 | ||||||||
\(313\) | −22.3590 | −1.26381 | −0.631903 | − | 0.775047i | \(-0.717726\pi\) | ||||
−0.631903 | + | 0.775047i | \(0.717726\pi\) | |||||||
\(314\) | −32.3577 | −1.82605 | ||||||||
\(315\) | 4.84939 | 0.273232 | ||||||||
\(316\) | 7.38314 | 0.415334 | ||||||||
\(317\) | 6.81047 | 0.382514 | 0.191257 | − | 0.981540i | \(-0.438744\pi\) | ||||
0.191257 | + | 0.981540i | \(0.438744\pi\) | |||||||
\(318\) | −25.3847 | −1.42350 | ||||||||
\(319\) | 11.3909 | 0.637769 | ||||||||
\(320\) | −2.83022 | −0.158214 | ||||||||
\(321\) | 48.9700 | 2.73324 | ||||||||
\(322\) | 13.8818 | 0.773605 | ||||||||
\(323\) | −29.4557 | −1.63896 | ||||||||
\(324\) | −0.0447213 | −0.00248451 | ||||||||
\(325\) | 2.64111 | 0.146503 | ||||||||
\(326\) | −20.6741 | −1.14503 | ||||||||
\(327\) | −26.8232 | −1.48333 | ||||||||
\(328\) | −9.43130 | −0.520756 | ||||||||
\(329\) | −9.05205 | −0.499056 | ||||||||
\(330\) | −7.78978 | −0.428813 | ||||||||
\(331\) | 13.3760 | 0.735210 | 0.367605 | − | 0.929982i | \(-0.380178\pi\) | ||||
0.367605 | + | 0.929982i | \(0.380178\pi\) | |||||||
\(332\) | −5.57316 | −0.305867 | ||||||||
\(333\) | 3.47493 | 0.190425 | ||||||||
\(334\) | 37.4626 | 2.04986 | ||||||||
\(335\) | −1.93775 | −0.105870 | ||||||||
\(336\) | 13.5272 | 0.737971 | ||||||||
\(337\) | −18.9082 | −1.02999 | −0.514996 | − | 0.857192i | \(-0.672207\pi\) | ||||
−0.514996 | + | 0.857192i | \(0.672207\pi\) | |||||||
\(338\) | 11.1322 | 0.605511 | ||||||||
\(339\) | 6.69736 | 0.363751 | ||||||||
\(340\) | −7.88784 | −0.427778 | ||||||||
\(341\) | 13.7584 | 0.745057 | ||||||||
\(342\) | −47.3292 | −2.55927 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −4.34843 | −0.234452 | ||||||||
\(345\) | 21.0478 | 1.13318 | ||||||||
\(346\) | −27.8384 | −1.49660 | ||||||||
\(347\) | −12.7372 | −0.683767 | −0.341883 | − | 0.939742i | \(-0.611065\pi\) | ||||
−0.341883 | + | 0.939742i | \(0.611065\pi\) | |||||||
\(348\) | 29.9986 | 1.60809 | ||||||||
\(349\) | 5.18065 | 0.277314 | 0.138657 | − | 0.990340i | \(-0.455721\pi\) | ||||
0.138657 | + | 0.990340i | \(0.455721\pi\) | |||||||
\(350\) | −1.84781 | −0.0987697 | ||||||||
\(351\) | −13.6846 | −0.730430 | ||||||||
\(352\) | −10.1682 | −0.541964 | ||||||||
\(353\) | 7.94750 | 0.423003 | 0.211501 | − | 0.977378i | \(-0.432165\pi\) | ||||
0.211501 | + | 0.977378i | \(0.432165\pi\) | |||||||
\(354\) | −9.68459 | −0.514730 | ||||||||
\(355\) | 8.08335 | 0.429020 | ||||||||
\(356\) | 13.2866 | 0.704191 | ||||||||
\(357\) | 15.6243 | 0.826928 | ||||||||
\(358\) | 14.2974 | 0.755642 | ||||||||
\(359\) | −28.1922 | −1.48793 | −0.743965 | − | 0.668219i | \(-0.767057\pi\) | ||||
−0.743965 | + | 0.668219i | \(0.767057\pi\) | |||||||
\(360\) | 5.24736 | 0.276560 | ||||||||
\(361\) | 8.89779 | 0.468305 | ||||||||
\(362\) | −8.74854 | −0.459813 | ||||||||
\(363\) | 24.4751 | 1.28461 | ||||||||
\(364\) | 3.73561 | 0.195799 | ||||||||
\(365\) | −10.5591 | −0.552690 | ||||||||
\(366\) | 49.2815 | 2.57598 | ||||||||
\(367\) | −17.8052 | −0.929425 | −0.464712 | − | 0.885462i | \(-0.653842\pi\) | ||||
−0.464712 | + | 0.885462i | \(0.653842\pi\) | |||||||
\(368\) | 36.2728 | 1.89085 | ||||||||
\(369\) | −42.2673 | −2.20035 | ||||||||
\(370\) | −1.32409 | −0.0688362 | ||||||||
\(371\) | −4.90340 | −0.254572 | ||||||||
\(372\) | 36.2334 | 1.87861 | ||||||||
\(373\) | −14.0957 | −0.729848 | −0.364924 | − | 0.931037i | \(-0.618905\pi\) | ||||
−0.364924 | + | 0.931037i | \(0.618905\pi\) | |||||||
\(374\) | −15.5057 | −0.801780 | ||||||||
\(375\) | −2.80168 | −0.144678 | ||||||||
\(376\) | −9.79492 | −0.505134 | ||||||||
\(377\) | −19.9938 | −1.02973 | ||||||||
\(378\) | 9.57421 | 0.492444 | ||||||||
\(379\) | −37.7772 | −1.94048 | −0.970241 | − | 0.242139i | \(-0.922151\pi\) | ||||
−0.970241 | + | 0.242139i | \(0.922151\pi\) | |||||||
\(380\) | 7.47066 | 0.383237 | ||||||||
\(381\) | −0.686679 | −0.0351796 | ||||||||
\(382\) | −11.3862 | −0.582567 | ||||||||
\(383\) | 15.7741 | 0.806018 | 0.403009 | − | 0.915196i | \(-0.367964\pi\) | ||||
0.403009 | + | 0.915196i | \(0.367964\pi\) | |||||||
\(384\) | 23.2132 | 1.18459 | ||||||||
\(385\) | −1.50470 | −0.0766866 | ||||||||
\(386\) | 37.0287 | 1.88471 | ||||||||
\(387\) | −19.4879 | −0.990627 | ||||||||
\(388\) | 3.98346 | 0.202230 | ||||||||
\(389\) | 25.8759 | 1.31196 | 0.655979 | − | 0.754779i | \(-0.272256\pi\) | ||||
0.655979 | + | 0.754779i | \(0.272256\pi\) | |||||||
\(390\) | 13.6730 | 0.692357 | ||||||||
\(391\) | 41.8961 | 2.11878 | ||||||||
\(392\) | 1.08207 | 0.0546526 | ||||||||
\(393\) | 15.3080 | 0.772185 | ||||||||
\(394\) | −11.8176 | −0.595363 | ||||||||
\(395\) | 5.21995 | 0.262644 | ||||||||
\(396\) | −10.3207 | −0.518637 | ||||||||
\(397\) | 7.76158 | 0.389543 | 0.194771 | − | 0.980849i | \(-0.437604\pi\) | ||||
0.194771 | + | 0.980849i | \(0.437604\pi\) | |||||||
\(398\) | 19.4670 | 0.975792 | ||||||||
\(399\) | −14.7980 | −0.740826 | ||||||||
\(400\) | −4.82827 | −0.241413 | ||||||||
\(401\) | −23.3281 | −1.16495 | −0.582474 | − | 0.812849i | \(-0.697915\pi\) | ||||
−0.582474 | + | 0.812849i | \(0.697915\pi\) | |||||||
\(402\) | −10.0317 | −0.500334 | ||||||||
\(403\) | −24.1492 | −1.20296 | ||||||||
\(404\) | 1.21538 | 0.0604673 | ||||||||
\(405\) | −0.0316184 | −0.00157113 | ||||||||
\(406\) | 13.9884 | 0.694230 | ||||||||
\(407\) | −1.07823 | −0.0534457 | ||||||||
\(408\) | 16.9066 | 0.837000 | ||||||||
\(409\) | −28.7450 | −1.42135 | −0.710675 | − | 0.703520i | \(-0.751610\pi\) | ||||
−0.710675 | + | 0.703520i | \(0.751610\pi\) | |||||||
\(410\) | 16.1055 | 0.795395 | ||||||||
\(411\) | −10.2680 | −0.506485 | ||||||||
\(412\) | 1.83439 | 0.0903738 | ||||||||
\(413\) | −1.87071 | −0.0920515 | ||||||||
\(414\) | 67.3184 | 3.30852 | ||||||||
\(415\) | −3.94028 | −0.193421 | ||||||||
\(416\) | 17.8476 | 0.875049 | ||||||||
\(417\) | −43.0478 | −2.10806 | ||||||||
\(418\) | 14.6856 | 0.718297 | ||||||||
\(419\) | −27.8242 | −1.35930 | −0.679651 | − | 0.733536i | \(-0.737869\pi\) | ||||
−0.679651 | + | 0.733536i | \(0.737869\pi\) | |||||||
\(420\) | −3.96271 | −0.193360 | ||||||||
\(421\) | 29.4863 | 1.43707 | 0.718536 | − | 0.695490i | \(-0.244813\pi\) | ||||
0.718536 | + | 0.695490i | \(0.244813\pi\) | |||||||
\(422\) | 20.4360 | 0.994807 | ||||||||
\(423\) | −43.8969 | −2.13434 | ||||||||
\(424\) | −5.30580 | −0.257672 | ||||||||
\(425\) | −5.57678 | −0.270514 | ||||||||
\(426\) | 41.8472 | 2.02750 | ||||||||
\(427\) | 9.51937 | 0.460675 | ||||||||
\(428\) | −24.7222 | −1.19499 | ||||||||
\(429\) | 11.1341 | 0.537559 | ||||||||
\(430\) | 7.42568 | 0.358098 | ||||||||
\(431\) | 38.0264 | 1.83167 | 0.915834 | − | 0.401558i | \(-0.131531\pi\) | ||||
0.915834 | + | 0.401558i | \(0.131531\pi\) | |||||||
\(432\) | 25.0171 | 1.20363 | ||||||||
\(433\) | 19.6289 | 0.943303 | 0.471652 | − | 0.881785i | \(-0.343658\pi\) | ||||
0.471652 | + | 0.881785i | \(0.343658\pi\) | |||||||
\(434\) | 16.8956 | 0.811016 | ||||||||
\(435\) | 21.2093 | 1.01691 | ||||||||
\(436\) | 13.5415 | 0.648521 | ||||||||
\(437\) | −39.6803 | −1.89816 | ||||||||
\(438\) | −54.6643 | −2.61196 | ||||||||
\(439\) | 21.5056 | 1.02641 | 0.513204 | − | 0.858267i | \(-0.328459\pi\) | ||||
0.513204 | + | 0.858267i | \(0.328459\pi\) | |||||||
\(440\) | −1.62819 | −0.0776207 | ||||||||
\(441\) | 4.84939 | 0.230923 | ||||||||
\(442\) | 27.2162 | 1.29454 | ||||||||
\(443\) | 3.10318 | 0.147437 | 0.0737184 | − | 0.997279i | \(-0.476513\pi\) | ||||
0.0737184 | + | 0.997279i | \(0.476513\pi\) | |||||||
\(444\) | −2.83957 | −0.134760 | ||||||||
\(445\) | 9.39380 | 0.445309 | ||||||||
\(446\) | 28.5740 | 1.35302 | ||||||||
\(447\) | −54.8972 | −2.59655 | ||||||||
\(448\) | −2.83022 | −0.133715 | ||||||||
\(449\) | 8.96756 | 0.423205 | 0.211603 | − | 0.977356i | \(-0.432132\pi\) | ||||
0.211603 | + | 0.977356i | \(0.432132\pi\) | |||||||
\(450\) | −8.96075 | −0.422414 | ||||||||
\(451\) | 13.1150 | 0.617560 | ||||||||
\(452\) | −3.38112 | −0.159034 | ||||||||
\(453\) | −54.7808 | −2.57383 | ||||||||
\(454\) | 26.9052 | 1.26272 | ||||||||
\(455\) | 2.64111 | 0.123817 | ||||||||
\(456\) | −16.0124 | −0.749850 | ||||||||
\(457\) | 12.9612 | 0.606302 | 0.303151 | − | 0.952943i | \(-0.401961\pi\) | ||||
0.303151 | + | 0.952943i | \(0.401961\pi\) | |||||||
\(458\) | −1.84781 | −0.0863425 | ||||||||
\(459\) | 28.8954 | 1.34872 | ||||||||
\(460\) | −10.6259 | −0.495433 | ||||||||
\(461\) | 33.6327 | 1.56643 | 0.783215 | − | 0.621751i | \(-0.213578\pi\) | ||||
0.783215 | + | 0.621751i | \(0.213578\pi\) | |||||||
\(462\) | −7.78978 | −0.362414 | ||||||||
\(463\) | 34.7930 | 1.61697 | 0.808483 | − | 0.588519i | \(-0.200289\pi\) | ||||
0.808483 | + | 0.588519i | \(0.200289\pi\) | |||||||
\(464\) | 36.5511 | 1.69684 | ||||||||
\(465\) | 25.6174 | 1.18798 | ||||||||
\(466\) | −19.8345 | −0.918815 | ||||||||
\(467\) | 12.1926 | 0.564204 | 0.282102 | − | 0.959384i | \(-0.408968\pi\) | ||||
0.282102 | + | 0.959384i | \(0.408968\pi\) | |||||||
\(468\) | 18.1154 | 0.837384 | ||||||||
\(469\) | −1.93775 | −0.0894769 | ||||||||
\(470\) | 16.7265 | 0.771535 | ||||||||
\(471\) | −49.0612 | −2.26062 | ||||||||
\(472\) | −2.02423 | −0.0931727 | ||||||||
\(473\) | 6.04684 | 0.278034 | ||||||||
\(474\) | 27.0235 | 1.24123 | ||||||||
\(475\) | 5.28184 | 0.242347 | ||||||||
\(476\) | −7.88784 | −0.361538 | ||||||||
\(477\) | −23.7785 | −1.08874 | ||||||||
\(478\) | 5.87817 | 0.268861 | ||||||||
\(479\) | 35.6433 | 1.62859 | 0.814293 | − | 0.580454i | \(-0.197125\pi\) | ||||
0.814293 | + | 0.580454i | \(0.197125\pi\) | |||||||
\(480\) | −18.9326 | −0.864150 | ||||||||
\(481\) | 1.89255 | 0.0862927 | ||||||||
\(482\) | 31.1203 | 1.41749 | ||||||||
\(483\) | 21.0478 | 0.957710 | ||||||||
\(484\) | −12.3561 | −0.561640 | ||||||||
\(485\) | 2.81635 | 0.127884 | ||||||||
\(486\) | −28.8863 | −1.31031 | ||||||||
\(487\) | 1.29251 | 0.0585694 | 0.0292847 | − | 0.999571i | \(-0.490677\pi\) | ||||
0.0292847 | + | 0.999571i | \(0.490677\pi\) | |||||||
\(488\) | 10.3006 | 0.466286 | ||||||||
\(489\) | −31.3464 | −1.41753 | ||||||||
\(490\) | −1.84781 | −0.0834756 | ||||||||
\(491\) | 24.3304 | 1.09802 | 0.549008 | − | 0.835817i | \(-0.315006\pi\) | ||||
0.549008 | + | 0.835817i | \(0.315006\pi\) | |||||||
\(492\) | 34.5390 | 1.55714 | ||||||||
\(493\) | 42.2175 | 1.90138 | ||||||||
\(494\) | −25.7768 | −1.15975 | ||||||||
\(495\) | −7.29687 | −0.327970 | ||||||||
\(496\) | 44.1477 | 1.98229 | ||||||||
\(497\) | 8.08335 | 0.362588 | ||||||||
\(498\) | −20.3987 | −0.914089 | ||||||||
\(499\) | −7.80369 | −0.349341 | −0.174671 | − | 0.984627i | \(-0.555886\pi\) | ||||
−0.174671 | + | 0.984627i | \(0.555886\pi\) | |||||||
\(500\) | 1.41441 | 0.0632542 | ||||||||
\(501\) | 56.8013 | 2.53770 | ||||||||
\(502\) | 12.7809 | 0.570441 | ||||||||
\(503\) | 16.0703 | 0.716541 | 0.358271 | − | 0.933618i | \(-0.383367\pi\) | ||||
0.358271 | + | 0.933618i | \(0.383367\pi\) | |||||||
\(504\) | 5.24736 | 0.233736 | ||||||||
\(505\) | 0.859285 | 0.0382377 | ||||||||
\(506\) | −20.8880 | −0.928586 | ||||||||
\(507\) | 16.8788 | 0.749612 | ||||||||
\(508\) | 0.346665 | 0.0153808 | ||||||||
\(509\) | −6.17149 | −0.273546 | −0.136773 | − | 0.990602i | \(-0.543673\pi\) | ||||
−0.136773 | + | 0.990602i | \(0.543673\pi\) | |||||||
\(510\) | −28.8708 | −1.27842 | ||||||||
\(511\) | −10.5591 | −0.467108 | ||||||||
\(512\) | −22.1785 | −0.980159 | ||||||||
\(513\) | −27.3672 | −1.20829 | ||||||||
\(514\) | −5.43684 | −0.239809 | ||||||||
\(515\) | 1.29693 | 0.0571496 | ||||||||
\(516\) | 15.9247 | 0.701045 | ||||||||
\(517\) | 13.6206 | 0.599034 | ||||||||
\(518\) | −1.32409 | −0.0581772 | ||||||||
\(519\) | −42.2089 | −1.85276 | ||||||||
\(520\) | 2.85786 | 0.125325 | ||||||||
\(521\) | 13.8626 | 0.607330 | 0.303665 | − | 0.952779i | \(-0.401790\pi\) | ||||
0.303665 | + | 0.952779i | \(0.401790\pi\) | |||||||
\(522\) | 67.8349 | 2.96905 | ||||||||
\(523\) | −13.8373 | −0.605063 | −0.302532 | − | 0.953139i | \(-0.597832\pi\) | ||||
−0.302532 | + | 0.953139i | \(0.597832\pi\) | |||||||
\(524\) | −7.72812 | −0.337605 | ||||||||
\(525\) | −2.80168 | −0.122275 | ||||||||
\(526\) | −17.5381 | −0.764699 | ||||||||
\(527\) | 50.9918 | 2.22124 | ||||||||
\(528\) | −20.3544 | −0.885813 | ||||||||
\(529\) | 33.4390 | 1.45387 | ||||||||
\(530\) | 9.06055 | 0.393565 | ||||||||
\(531\) | −9.07178 | −0.393682 | ||||||||
\(532\) | 7.47066 | 0.323894 | ||||||||
\(533\) | −23.0199 | −0.997104 | ||||||||
\(534\) | 48.6314 | 2.10449 | ||||||||
\(535\) | −17.4788 | −0.755676 | ||||||||
\(536\) | −2.09677 | −0.0905667 | ||||||||
\(537\) | 21.6779 | 0.935472 | ||||||||
\(538\) | −22.5644 | −0.972818 | ||||||||
\(539\) | −1.50470 | −0.0648120 | ||||||||
\(540\) | −7.32857 | −0.315372 | ||||||||
\(541\) | 28.5322 | 1.22669 | 0.613347 | − | 0.789814i | \(-0.289823\pi\) | ||||
0.613347 | + | 0.789814i | \(0.289823\pi\) | |||||||
\(542\) | −44.6535 | −1.91803 | ||||||||
\(543\) | −13.2647 | −0.569241 | ||||||||
\(544\) | −37.6856 | −1.61576 | ||||||||
\(545\) | 9.57399 | 0.410105 | ||||||||
\(546\) | 13.6730 | 0.585148 | ||||||||
\(547\) | −18.1568 | −0.776328 | −0.388164 | − | 0.921590i | \(-0.626891\pi\) | ||||
−0.388164 | + | 0.921590i | \(0.626891\pi\) | |||||||
\(548\) | 5.18375 | 0.221439 | ||||||||
\(549\) | 46.1631 | 1.97019 | ||||||||
\(550\) | 2.78040 | 0.118557 | ||||||||
\(551\) | −39.9847 | −1.70341 | ||||||||
\(552\) | 22.7752 | 0.969375 | ||||||||
\(553\) | 5.21995 | 0.221975 | ||||||||
\(554\) | 12.0172 | 0.510560 | ||||||||
\(555\) | −2.00760 | −0.0852180 | ||||||||
\(556\) | 21.7324 | 0.921658 | ||||||||
\(557\) | 27.7111 | 1.17416 | 0.587079 | − | 0.809529i | \(-0.300278\pi\) | ||||
0.587079 | + | 0.809529i | \(0.300278\pi\) | |||||||
\(558\) | 81.9334 | 3.46852 | ||||||||
\(559\) | −10.6137 | −0.448910 | ||||||||
\(560\) | −4.82827 | −0.204032 | ||||||||
\(561\) | −23.5099 | −0.992590 | ||||||||
\(562\) | −12.6716 | −0.534518 | ||||||||
\(563\) | 10.4878 | 0.442007 | 0.221004 | − | 0.975273i | \(-0.429067\pi\) | ||||
0.221004 | + | 0.975273i | \(0.429067\pi\) | |||||||
\(564\) | 35.8706 | 1.51043 | ||||||||
\(565\) | −2.39048 | −0.100568 | ||||||||
\(566\) | 48.8679 | 2.05407 | ||||||||
\(567\) | −0.0316184 | −0.00132785 | ||||||||
\(568\) | 8.74672 | 0.367004 | ||||||||
\(569\) | −8.73017 | −0.365988 | −0.182994 | − | 0.983114i | \(-0.558579\pi\) | ||||
−0.182994 | + | 0.983114i | \(0.558579\pi\) | |||||||
\(570\) | 27.3439 | 1.14531 | ||||||||
\(571\) | −17.4614 | −0.730736 | −0.365368 | − | 0.930863i | \(-0.619057\pi\) | ||||
−0.365368 | + | 0.930863i | \(0.619057\pi\) | |||||||
\(572\) | −5.62097 | −0.235024 | ||||||||
\(573\) | −17.2638 | −0.721207 | ||||||||
\(574\) | 16.1055 | 0.672232 | ||||||||
\(575\) | −7.51259 | −0.313297 | ||||||||
\(576\) | −13.7248 | −0.571868 | ||||||||
\(577\) | 28.6481 | 1.19264 | 0.596318 | − | 0.802749i | \(-0.296630\pi\) | ||||
0.596318 | + | 0.802749i | \(0.296630\pi\) | |||||||
\(578\) | −26.0551 | −1.08375 | ||||||||
\(579\) | 56.1434 | 2.33324 | ||||||||
\(580\) | −10.7074 | −0.444600 | ||||||||
\(581\) | −3.94028 | −0.163471 | ||||||||
\(582\) | 14.5801 | 0.604366 | ||||||||
\(583\) | 7.37814 | 0.305571 | ||||||||
\(584\) | −11.4257 | −0.472798 | ||||||||
\(585\) | 12.8078 | 0.529536 | ||||||||
\(586\) | −57.1941 | −2.36267 | ||||||||
\(587\) | −28.1539 | −1.16203 | −0.581017 | − | 0.813891i | \(-0.697345\pi\) | ||||
−0.581017 | + | 0.813891i | \(0.697345\pi\) | |||||||
\(588\) | −3.96271 | −0.163419 | ||||||||
\(589\) | −48.2949 | −1.98996 | ||||||||
\(590\) | 3.45671 | 0.142311 | ||||||||
\(591\) | −17.9180 | −0.737049 | ||||||||
\(592\) | −3.45980 | −0.142197 | ||||||||
\(593\) | −15.0159 | −0.616631 | −0.308315 | − | 0.951284i | \(-0.599765\pi\) | ||||
−0.308315 | + | 0.951284i | \(0.599765\pi\) | |||||||
\(594\) | −14.4063 | −0.591098 | ||||||||
\(595\) | −5.57678 | −0.228626 | ||||||||
\(596\) | 27.7145 | 1.13523 | ||||||||
\(597\) | 29.5161 | 1.20801 | ||||||||
\(598\) | 36.6635 | 1.49928 | ||||||||
\(599\) | −17.5227 | −0.715959 | −0.357980 | − | 0.933729i | \(-0.616534\pi\) | ||||
−0.357980 | + | 0.933729i | \(0.616534\pi\) | |||||||
\(600\) | −3.03160 | −0.123765 | ||||||||
\(601\) | −16.3683 | −0.667676 | −0.333838 | − | 0.942630i | \(-0.608344\pi\) | ||||
−0.333838 | + | 0.942630i | \(0.608344\pi\) | |||||||
\(602\) | 7.42568 | 0.302648 | ||||||||
\(603\) | −9.39688 | −0.382671 | ||||||||
\(604\) | 27.6557 | 1.12530 | ||||||||
\(605\) | −8.73588 | −0.355164 | ||||||||
\(606\) | 4.44849 | 0.180708 | ||||||||
\(607\) | −29.1914 | −1.18484 | −0.592421 | − | 0.805628i | \(-0.701828\pi\) | ||||
−0.592421 | + | 0.805628i | \(0.701828\pi\) | |||||||
\(608\) | 35.6925 | 1.44752 | ||||||||
\(609\) | 21.2093 | 0.859445 | ||||||||
\(610\) | −17.5900 | −0.712199 | ||||||||
\(611\) | −23.9075 | −0.967193 | ||||||||
\(612\) | −38.2512 | −1.54621 | ||||||||
\(613\) | 6.03784 | 0.243866 | 0.121933 | − | 0.992538i | \(-0.461091\pi\) | ||||
0.121933 | + | 0.992538i | \(0.461091\pi\) | |||||||
\(614\) | −45.4490 | −1.83417 | ||||||||
\(615\) | 24.4194 | 0.984686 | ||||||||
\(616\) | −1.62819 | −0.0656015 | ||||||||
\(617\) | 41.3215 | 1.66354 | 0.831771 | − | 0.555118i | \(-0.187327\pi\) | ||||
0.831771 | + | 0.555118i | \(0.187327\pi\) | |||||||
\(618\) | 6.71417 | 0.270083 | ||||||||
\(619\) | −39.4803 | −1.58685 | −0.793425 | − | 0.608669i | \(-0.791704\pi\) | ||||
−0.793425 | + | 0.608669i | \(0.791704\pi\) | |||||||
\(620\) | −12.9327 | −0.519392 | ||||||||
\(621\) | 38.9256 | 1.56203 | ||||||||
\(622\) | −31.6605 | −1.26947 | ||||||||
\(623\) | 9.39380 | 0.376354 | ||||||||
\(624\) | 35.7270 | 1.43022 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 41.3152 | 1.65129 | ||||||||
\(627\) | 22.2665 | 0.889240 | ||||||||
\(628\) | 24.7682 | 0.988359 | ||||||||
\(629\) | −3.99617 | −0.159338 | ||||||||
\(630\) | −8.96075 | −0.357005 | ||||||||
\(631\) | −36.8086 | −1.46533 | −0.732665 | − | 0.680590i | \(-0.761724\pi\) | ||||
−0.732665 | + | 0.680590i | \(0.761724\pi\) | |||||||
\(632\) | 5.64834 | 0.224679 | ||||||||
\(633\) | 30.9853 | 1.23155 | ||||||||
\(634\) | −12.5845 | −0.499793 | ||||||||
\(635\) | 0.245096 | 0.00972633 | ||||||||
\(636\) | 19.4307 | 0.770478 | ||||||||
\(637\) | 2.64111 | 0.104645 | ||||||||
\(638\) | −21.0483 | −0.833309 | ||||||||
\(639\) | 39.1993 | 1.55070 | ||||||||
\(640\) | −8.28547 | −0.327512 | ||||||||
\(641\) | 47.6562 | 1.88231 | 0.941154 | − | 0.337979i | \(-0.109743\pi\) | ||||
0.941154 | + | 0.337979i | \(0.109743\pi\) | |||||||
\(642\) | −90.4873 | −3.57125 | ||||||||
\(643\) | −0.999936 | −0.0394336 | −0.0197168 | − | 0.999806i | \(-0.506276\pi\) | ||||
−0.0197168 | + | 0.999806i | \(0.506276\pi\) | |||||||
\(644\) | −10.6259 | −0.418717 | ||||||||
\(645\) | 11.2589 | 0.443319 | ||||||||
\(646\) | 54.4285 | 2.14146 | ||||||||
\(647\) | −49.2219 | −1.93511 | −0.967557 | − | 0.252654i | \(-0.918696\pi\) | ||||
−0.967557 | + | 0.252654i | \(0.918696\pi\) | |||||||
\(648\) | −0.0342132 | −0.00134402 | ||||||||
\(649\) | 2.81485 | 0.110493 | ||||||||
\(650\) | −4.88028 | −0.191420 | ||||||||
\(651\) | 25.6174 | 1.00402 | ||||||||
\(652\) | 15.8250 | 0.619755 | ||||||||
\(653\) | 23.4820 | 0.918920 | 0.459460 | − | 0.888198i | \(-0.348043\pi\) | ||||
0.459460 | + | 0.888198i | \(0.348043\pi\) | |||||||
\(654\) | 49.5642 | 1.93811 | ||||||||
\(655\) | −5.46386 | −0.213491 | ||||||||
\(656\) | 42.0832 | 1.64307 | ||||||||
\(657\) | −51.2053 | −1.99771 | ||||||||
\(658\) | 16.7265 | 0.652066 | ||||||||
\(659\) | 2.00359 | 0.0780487 | 0.0390243 | − | 0.999238i | \(-0.487575\pi\) | ||||
0.0390243 | + | 0.999238i | \(0.487575\pi\) | |||||||
\(660\) | 5.96269 | 0.232097 | ||||||||
\(661\) | 41.7029 | 1.62205 | 0.811027 | − | 0.585009i | \(-0.198909\pi\) | ||||
0.811027 | + | 0.585009i | \(0.198909\pi\) | |||||||
\(662\) | −24.7163 | −0.960625 | ||||||||
\(663\) | 41.2656 | 1.60262 | ||||||||
\(664\) | −4.26365 | −0.165462 | ||||||||
\(665\) | 5.28184 | 0.204821 | ||||||||
\(666\) | −6.42102 | −0.248810 | ||||||||
\(667\) | 56.8720 | 2.20209 | ||||||||
\(668\) | −28.6758 | −1.10950 | ||||||||
\(669\) | 43.3242 | 1.67501 | ||||||||
\(670\) | 3.58059 | 0.138330 | ||||||||
\(671\) | −14.3238 | −0.552964 | ||||||||
\(672\) | −18.9326 | −0.730340 | ||||||||
\(673\) | 10.5001 | 0.404747 | 0.202374 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202374 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(674\) | 34.9387 | 1.34579 | ||||||||
\(675\) | −5.18138 | −0.199431 | ||||||||
\(676\) | −8.52113 | −0.327736 | ||||||||
\(677\) | 5.71219 | 0.219537 | 0.109769 | − | 0.993957i | \(-0.464989\pi\) | ||||
0.109769 | + | 0.993957i | \(0.464989\pi\) | |||||||
\(678\) | −12.3755 | −0.475277 | ||||||||
\(679\) | 2.81635 | 0.108081 | ||||||||
\(680\) | −6.03445 | −0.231411 | ||||||||
\(681\) | 40.7940 | 1.56323 | ||||||||
\(682\) | −25.4228 | −0.973491 | ||||||||
\(683\) | −49.9792 | −1.91240 | −0.956201 | − | 0.292710i | \(-0.905443\pi\) | ||||
−0.956201 | + | 0.292710i | \(0.905443\pi\) | |||||||
\(684\) | 36.2281 | 1.38522 | ||||||||
\(685\) | 3.66496 | 0.140031 | ||||||||
\(686\) | −1.84781 | −0.0705498 | ||||||||
\(687\) | −2.80168 | −0.106891 | ||||||||
\(688\) | 19.4031 | 0.739734 | ||||||||
\(689\) | −12.9504 | −0.493372 | ||||||||
\(690\) | −38.8924 | −1.48061 | ||||||||
\(691\) | 27.7825 | 1.05690 | 0.528448 | − | 0.848965i | \(-0.322774\pi\) | ||||
0.528448 | + | 0.848965i | \(0.322774\pi\) | |||||||
\(692\) | 21.3089 | 0.810041 | ||||||||
\(693\) | −7.29687 | −0.277185 | ||||||||
\(694\) | 23.5359 | 0.893410 | ||||||||
\(695\) | 15.3650 | 0.582828 | ||||||||
\(696\) | 22.9499 | 0.869914 | ||||||||
\(697\) | 48.6073 | 1.84113 | ||||||||
\(698\) | −9.57287 | −0.362338 | ||||||||
\(699\) | −30.0733 | −1.13748 | ||||||||
\(700\) | 1.41441 | 0.0534595 | ||||||||
\(701\) | 17.2609 | 0.651934 | 0.325967 | − | 0.945381i | \(-0.394310\pi\) | ||||
0.325967 | + | 0.945381i | \(0.394310\pi\) | |||||||
\(702\) | 25.2866 | 0.954380 | ||||||||
\(703\) | 3.78482 | 0.142747 | ||||||||
\(704\) | 4.25864 | 0.160503 | ||||||||
\(705\) | 25.3609 | 0.955147 | ||||||||
\(706\) | −14.6855 | −0.552695 | ||||||||
\(707\) | 0.859285 | 0.0323167 | ||||||||
\(708\) | 7.41306 | 0.278600 | ||||||||
\(709\) | −7.63149 | −0.286607 | −0.143303 | − | 0.989679i | \(-0.545772\pi\) | ||||
−0.143303 | + | 0.989679i | \(0.545772\pi\) | |||||||
\(710\) | −14.9365 | −0.560557 | ||||||||
\(711\) | 25.3136 | 0.949333 | ||||||||
\(712\) | 10.1647 | 0.380939 | ||||||||
\(713\) | 68.6920 | 2.57254 | ||||||||
\(714\) | −28.8708 | −1.08046 | ||||||||
\(715\) | −3.97408 | −0.148622 | ||||||||
\(716\) | −10.9440 | −0.408995 | ||||||||
\(717\) | 8.91255 | 0.332845 | ||||||||
\(718\) | 52.0939 | 1.94413 | ||||||||
\(719\) | −12.8603 | −0.479607 | −0.239804 | − | 0.970821i | \(-0.577083\pi\) | ||||
−0.239804 | + | 0.970821i | \(0.577083\pi\) | |||||||
\(720\) | −23.4141 | −0.872593 | ||||||||
\(721\) | 1.29693 | 0.0483002 | ||||||||
\(722\) | −16.4414 | −0.611887 | ||||||||
\(723\) | 47.1849 | 1.75483 | ||||||||
\(724\) | 6.69657 | 0.248876 | ||||||||
\(725\) | −7.57023 | −0.281151 | ||||||||
\(726\) | −45.2254 | −1.67847 | ||||||||
\(727\) | 39.4100 | 1.46164 | 0.730819 | − | 0.682571i | \(-0.239138\pi\) | ||||
0.730819 | + | 0.682571i | \(0.239138\pi\) | |||||||
\(728\) | 2.85786 | 0.105919 | ||||||||
\(729\) | −43.7029 | −1.61863 | ||||||||
\(730\) | 19.5113 | 0.722145 | ||||||||
\(731\) | 22.4111 | 0.828903 | ||||||||
\(732\) | −37.7225 | −1.39426 | ||||||||
\(733\) | −11.1567 | −0.412083 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(734\) | 32.9007 | 1.21439 | ||||||||
\(735\) | −2.80168 | −0.103341 | ||||||||
\(736\) | −50.7670 | −1.87130 | ||||||||
\(737\) | 2.91573 | 0.107402 | ||||||||
\(738\) | 78.1019 | 2.87497 | ||||||||
\(739\) | 22.0433 | 0.810877 | 0.405438 | − | 0.914122i | \(-0.367119\pi\) | ||||
0.405438 | + | 0.914122i | \(0.367119\pi\) | |||||||
\(740\) | 1.01352 | 0.0372579 | ||||||||
\(741\) | −39.0832 | −1.43576 | ||||||||
\(742\) | 9.06055 | 0.332623 | ||||||||
\(743\) | 41.3072 | 1.51541 | 0.757706 | − | 0.652596i | \(-0.226320\pi\) | ||||
0.757706 | + | 0.652596i | \(0.226320\pi\) | |||||||
\(744\) | 27.7197 | 1.01625 | ||||||||
\(745\) | 19.5944 | 0.717884 | ||||||||
\(746\) | 26.0462 | 0.953619 | ||||||||
\(747\) | −19.1080 | −0.699123 | ||||||||
\(748\) | 11.8688 | 0.433967 | ||||||||
\(749\) | −17.4788 | −0.638662 | ||||||||
\(750\) | 5.17697 | 0.189036 | ||||||||
\(751\) | 22.0894 | 0.806053 | 0.403026 | − | 0.915188i | \(-0.367958\pi\) | ||||
0.403026 | + | 0.915188i | \(0.367958\pi\) | |||||||
\(752\) | 43.7057 | 1.59378 | ||||||||
\(753\) | 19.3786 | 0.706197 | ||||||||
\(754\) | 36.9448 | 1.34545 | ||||||||
\(755\) | 19.5529 | 0.711602 | ||||||||
\(756\) | −7.32857 | −0.266538 | ||||||||
\(757\) | 37.8995 | 1.37748 | 0.688741 | − | 0.725008i | \(-0.258164\pi\) | ||||
0.688741 | + | 0.725008i | \(0.258164\pi\) | |||||||
\(758\) | 69.8051 | 2.53543 | ||||||||
\(759\) | −31.6707 | −1.14957 | ||||||||
\(760\) | 5.71530 | 0.207316 | ||||||||
\(761\) | −44.2860 | −1.60537 | −0.802684 | − | 0.596405i | \(-0.796595\pi\) | ||||
−0.802684 | + | 0.596405i | \(0.796595\pi\) | |||||||
\(762\) | 1.26885 | 0.0459657 | ||||||||
\(763\) | 9.57399 | 0.346602 | ||||||||
\(764\) | 8.71553 | 0.315317 | ||||||||
\(765\) | −27.0440 | −0.977777 | ||||||||
\(766\) | −29.1475 | −1.05314 | ||||||||
\(767\) | −4.94075 | −0.178400 | ||||||||
\(768\) | −58.7523 | −2.12004 | ||||||||
\(769\) | −16.8764 | −0.608580 | −0.304290 | − | 0.952579i | \(-0.598419\pi\) | ||||
−0.304290 | + | 0.952579i | \(0.598419\pi\) | |||||||
\(770\) | 2.78040 | 0.100199 | ||||||||
\(771\) | −8.24341 | −0.296879 | ||||||||
\(772\) | −28.3436 | −1.02011 | ||||||||
\(773\) | −34.0856 | −1.22597 | −0.612987 | − | 0.790093i | \(-0.710032\pi\) | ||||
−0.612987 | + | 0.790093i | \(0.710032\pi\) | |||||||
\(774\) | 36.0100 | 1.29435 | ||||||||
\(775\) | −9.14359 | −0.328447 | ||||||||
\(776\) | 3.04748 | 0.109398 | ||||||||
\(777\) | −2.00760 | −0.0720224 | ||||||||
\(778\) | −47.8137 | −1.71420 | ||||||||
\(779\) | −46.0365 | −1.64943 | ||||||||
\(780\) | −10.4660 | −0.374741 | ||||||||
\(781\) | −12.1630 | −0.435227 | ||||||||
\(782\) | −77.4160 | −2.76839 | ||||||||
\(783\) | 39.2242 | 1.40176 | ||||||||
\(784\) | −4.82827 | −0.172438 | ||||||||
\(785\) | 17.5114 | 0.625008 | ||||||||
\(786\) | −28.2862 | −1.00894 | ||||||||
\(787\) | 2.05249 | 0.0731635 | 0.0365818 | − | 0.999331i | \(-0.488353\pi\) | ||||
0.0365818 | + | 0.999331i | \(0.488353\pi\) | |||||||
\(788\) | 9.04579 | 0.322243 | ||||||||
\(789\) | −26.5916 | −0.946684 | ||||||||
\(790\) | −9.64549 | −0.343171 | ||||||||
\(791\) | −2.39048 | −0.0849959 | ||||||||
\(792\) | −7.89570 | −0.280561 | ||||||||
\(793\) | 25.1417 | 0.892809 | ||||||||
\(794\) | −14.3419 | −0.508976 | ||||||||
\(795\) | 13.7377 | 0.487227 | ||||||||
\(796\) | −14.9010 | −0.528152 | ||||||||
\(797\) | −56.2629 | −1.99293 | −0.996466 | − | 0.0839923i | \(-0.973233\pi\) | ||||
−0.996466 | + | 0.0839923i | \(0.973233\pi\) | |||||||
\(798\) | 27.3439 | 0.967963 | ||||||||
\(799\) | 50.4813 | 1.78590 | ||||||||
\(800\) | 6.75759 | 0.238917 | ||||||||
\(801\) | 45.5541 | 1.60958 | ||||||||
\(802\) | 43.1059 | 1.52212 | ||||||||
\(803\) | 15.8883 | 0.560687 | ||||||||
\(804\) | 7.67873 | 0.270808 | ||||||||
\(805\) | −7.51259 | −0.264784 | ||||||||
\(806\) | 44.6232 | 1.57179 | ||||||||
\(807\) | −34.2124 | −1.20433 | ||||||||
\(808\) | 0.929804 | 0.0327104 | ||||||||
\(809\) | −26.8246 | −0.943102 | −0.471551 | − | 0.881839i | \(-0.656306\pi\) | ||||
−0.471551 | + | 0.881839i | \(0.656306\pi\) | |||||||
\(810\) | 0.0584248 | 0.00205284 | ||||||||
\(811\) | −24.1795 | −0.849059 | −0.424529 | − | 0.905414i | \(-0.639560\pi\) | ||||
−0.424529 | + | 0.905414i | \(0.639560\pi\) | |||||||
\(812\) | −10.7074 | −0.375755 | ||||||||
\(813\) | −67.7042 | −2.37449 | ||||||||
\(814\) | 1.99236 | 0.0698321 | ||||||||
\(815\) | 11.1884 | 0.391914 | ||||||||
\(816\) | −75.4385 | −2.64087 | ||||||||
\(817\) | −21.2258 | −0.742596 | ||||||||
\(818\) | 53.1154 | 1.85714 | ||||||||
\(819\) | 12.8078 | 0.447540 | ||||||||
\(820\) | −12.3280 | −0.430511 | ||||||||
\(821\) | −7.94543 | −0.277297 | −0.138649 | − | 0.990342i | \(-0.544276\pi\) | ||||
−0.138649 | + | 0.990342i | \(0.544276\pi\) | |||||||
\(822\) | 18.9734 | 0.661773 | ||||||||
\(823\) | 0.0691044 | 0.00240883 | 0.00120441 | − | 0.999999i | \(-0.499617\pi\) | ||||
0.00120441 | + | 0.999999i | \(0.499617\pi\) | |||||||
\(824\) | 1.40337 | 0.0488886 | ||||||||
\(825\) | 4.21568 | 0.146771 | ||||||||
\(826\) | 3.45671 | 0.120274 | ||||||||
\(827\) | 48.1159 | 1.67315 | 0.836576 | − | 0.547850i | \(-0.184554\pi\) | ||||
0.836576 | + | 0.547850i | \(0.184554\pi\) | |||||||
\(828\) | −51.5289 | −1.79075 | ||||||||
\(829\) | −20.3884 | −0.708119 | −0.354060 | − | 0.935223i | \(-0.615199\pi\) | ||||
−0.354060 | + | 0.935223i | \(0.615199\pi\) | |||||||
\(830\) | 7.28090 | 0.252724 | ||||||||
\(831\) | 18.2206 | 0.632064 | ||||||||
\(832\) | −7.47494 | −0.259147 | ||||||||
\(833\) | −5.57678 | −0.193224 | ||||||||
\(834\) | 79.5442 | 2.75439 | ||||||||
\(835\) | −20.2741 | −0.701613 | ||||||||
\(836\) | −11.2411 | −0.388782 | ||||||||
\(837\) | 47.3764 | 1.63757 | ||||||||
\(838\) | 51.4139 | 1.77606 | ||||||||
\(839\) | −30.0692 | −1.03810 | −0.519052 | − | 0.854743i | \(-0.673715\pi\) | ||||
−0.519052 | + | 0.854743i | \(0.673715\pi\) | |||||||
\(840\) | −3.03160 | −0.104600 | ||||||||
\(841\) | 28.3084 | 0.976151 | ||||||||
\(842\) | −54.4850 | −1.87768 | ||||||||
\(843\) | −19.2128 | −0.661724 | ||||||||
\(844\) | −15.6427 | −0.538444 | ||||||||
\(845\) | −6.02453 | −0.207250 | ||||||||
\(846\) | 81.1131 | 2.78873 | ||||||||
\(847\) | −8.73588 | −0.300168 | ||||||||
\(848\) | 23.6749 | 0.812999 | ||||||||
\(849\) | 74.0942 | 2.54291 | ||||||||
\(850\) | 10.3048 | 0.353453 | ||||||||
\(851\) | −5.38331 | −0.184538 | ||||||||
\(852\) | −32.0319 | −1.09740 | ||||||||
\(853\) | −6.95912 | −0.238276 | −0.119138 | − | 0.992878i | \(-0.538013\pi\) | ||||
−0.119138 | + | 0.992878i | \(0.538013\pi\) | |||||||
\(854\) | −17.5900 | −0.601918 | ||||||||
\(855\) | 25.6137 | 0.875969 | ||||||||
\(856\) | −18.9133 | −0.646442 | ||||||||
\(857\) | 32.1074 | 1.09677 | 0.548384 | − | 0.836227i | \(-0.315243\pi\) | ||||
0.548384 | + | 0.836227i | \(0.315243\pi\) | |||||||
\(858\) | −20.5737 | −0.702374 | ||||||||
\(859\) | 25.0190 | 0.853638 | 0.426819 | − | 0.904337i | \(-0.359634\pi\) | ||||
0.426819 | + | 0.904337i | \(0.359634\pi\) | |||||||
\(860\) | −5.68399 | −0.193822 | ||||||||
\(861\) | 24.4194 | 0.832211 | ||||||||
\(862\) | −70.2656 | −2.39326 | ||||||||
\(863\) | −8.24030 | −0.280503 | −0.140252 | − | 0.990116i | \(-0.544791\pi\) | ||||
−0.140252 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(864\) | −35.0136 | −1.19119 | ||||||||
\(865\) | 15.0656 | 0.512245 | ||||||||
\(866\) | −36.2704 | −1.23252 | ||||||||
\(867\) | −39.5050 | −1.34166 | ||||||||
\(868\) | −12.9327 | −0.438966 | ||||||||
\(869\) | −7.85447 | −0.266445 | ||||||||
\(870\) | −39.1908 | −1.32869 | ||||||||
\(871\) | −5.11781 | −0.173410 | ||||||||
\(872\) | 10.3597 | 0.350824 | ||||||||
\(873\) | 13.6576 | 0.462238 | ||||||||
\(874\) | 73.3216 | 2.48014 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 41.8427 | 1.41374 | ||||||||
\(877\) | 53.3104 | 1.80016 | 0.900082 | − | 0.435720i | \(-0.143506\pi\) | ||||
0.900082 | + | 0.435720i | \(0.143506\pi\) | |||||||
\(878\) | −39.7383 | −1.34110 | ||||||||
\(879\) | −86.7185 | −2.92494 | ||||||||
\(880\) | 7.26509 | 0.244906 | ||||||||
\(881\) | −55.0053 | −1.85318 | −0.926588 | − | 0.376079i | \(-0.877272\pi\) | ||||
−0.926588 | + | 0.376079i | \(0.877272\pi\) | |||||||
\(882\) | −8.96075 | −0.301724 | ||||||||
\(883\) | 8.81754 | 0.296734 | 0.148367 | − | 0.988932i | \(-0.452598\pi\) | ||||
0.148367 | + | 0.988932i | \(0.452598\pi\) | |||||||
\(884\) | −20.8327 | −0.700678 | ||||||||
\(885\) | 5.24111 | 0.176178 | ||||||||
\(886\) | −5.73410 | −0.192641 | ||||||||
\(887\) | −27.2321 | −0.914364 | −0.457182 | − | 0.889373i | \(-0.651141\pi\) | ||||
−0.457182 | + | 0.889373i | \(0.651141\pi\) | |||||||
\(888\) | −2.17236 | −0.0728996 | ||||||||
\(889\) | 0.245096 | 0.00822025 | ||||||||
\(890\) | −17.3580 | −0.581840 | ||||||||
\(891\) | 0.0475762 | 0.00159386 | ||||||||
\(892\) | −21.8719 | −0.732327 | ||||||||
\(893\) | −47.8114 | −1.59995 | ||||||||
\(894\) | 101.440 | 3.39265 | ||||||||
\(895\) | −7.73749 | −0.258636 | ||||||||
\(896\) | −8.28547 | −0.276798 | ||||||||
\(897\) | 55.5897 | 1.85609 | ||||||||
\(898\) | −16.5703 | −0.552960 | ||||||||
\(899\) | 69.2191 | 2.30858 | ||||||||
\(900\) | 6.85900 | 0.228633 | ||||||||
\(901\) | 27.3452 | 0.911000 | ||||||||
\(902\) | −24.2340 | −0.806904 | ||||||||
\(903\) | 11.2589 | 0.374673 | ||||||||
\(904\) | −2.58666 | −0.0860312 | ||||||||
\(905\) | 4.73454 | 0.157382 | ||||||||
\(906\) | 101.225 | 3.36296 | ||||||||
\(907\) | −7.25001 | −0.240733 | −0.120366 | − | 0.992730i | \(-0.538407\pi\) | ||||
−0.120366 | + | 0.992730i | \(0.538407\pi\) | |||||||
\(908\) | −20.5946 | −0.683455 | ||||||||
\(909\) | 4.16700 | 0.138211 | ||||||||
\(910\) | −4.88028 | −0.161780 | ||||||||
\(911\) | 9.78287 | 0.324121 | 0.162060 | − | 0.986781i | \(-0.448186\pi\) | ||||
0.162060 | + | 0.986781i | \(0.448186\pi\) | |||||||
\(912\) | 71.4487 | 2.36590 | ||||||||
\(913\) | 5.92895 | 0.196219 | ||||||||
\(914\) | −23.9499 | −0.792194 | ||||||||
\(915\) | −26.6702 | −0.881689 | ||||||||
\(916\) | 1.41441 | 0.0467333 | ||||||||
\(917\) | −5.46386 | −0.180433 | ||||||||
\(918\) | −53.3933 | −1.76224 | ||||||||
\(919\) | 33.2592 | 1.09712 | 0.548559 | − | 0.836112i | \(-0.315176\pi\) | ||||
0.548559 | + | 0.836112i | \(0.315176\pi\) | |||||||
\(920\) | −8.12912 | −0.268009 | ||||||||
\(921\) | −68.9104 | −2.27068 | ||||||||
\(922\) | −62.1468 | −2.04670 | ||||||||
\(923\) | 21.3490 | 0.702712 | ||||||||
\(924\) | 5.96269 | 0.196158 | ||||||||
\(925\) | 0.716572 | 0.0235608 | ||||||||
\(926\) | −64.2908 | −2.11273 | ||||||||
\(927\) | 6.28932 | 0.206568 | ||||||||
\(928\) | −51.1565 | −1.67930 | ||||||||
\(929\) | −37.0764 | −1.21644 | −0.608218 | − | 0.793770i | \(-0.708115\pi\) | ||||
−0.608218 | + | 0.793770i | \(0.708115\pi\) | |||||||
\(930\) | −47.3361 | −1.55221 | ||||||||
\(931\) | 5.28184 | 0.173105 | ||||||||
\(932\) | 15.1823 | 0.497313 | ||||||||
\(933\) | −48.0041 | −1.57158 | ||||||||
\(934\) | −22.5295 | −0.737189 | ||||||||
\(935\) | 8.39139 | 0.274428 | ||||||||
\(936\) | 13.8589 | 0.452991 | ||||||||
\(937\) | −21.8967 | −0.715335 | −0.357667 | − | 0.933849i | \(-0.616428\pi\) | ||||
−0.357667 | + | 0.933849i | \(0.616428\pi\) | |||||||
\(938\) | 3.58059 | 0.116910 | ||||||||
\(939\) | 62.6427 | 2.04427 | ||||||||
\(940\) | −12.8033 | −0.417597 | ||||||||
\(941\) | 1.63707 | 0.0533671 | 0.0266835 | − | 0.999644i | \(-0.491505\pi\) | ||||
0.0266835 | + | 0.999644i | \(0.491505\pi\) | |||||||
\(942\) | 90.6558 | 2.95373 | ||||||||
\(943\) | 65.4798 | 2.13231 | ||||||||
\(944\) | 9.03227 | 0.293975 | ||||||||
\(945\) | −5.18138 | −0.168550 | ||||||||
\(946\) | −11.1734 | −0.363279 | ||||||||
\(947\) | −7.05454 | −0.229242 | −0.114621 | − | 0.993409i | \(-0.536565\pi\) | ||||
−0.114621 | + | 0.993409i | \(0.536565\pi\) | |||||||
\(948\) | −20.6852 | −0.671823 | ||||||||
\(949\) | −27.8878 | −0.905278 | ||||||||
\(950\) | −9.75984 | −0.316651 | ||||||||
\(951\) | −19.0807 | −0.618735 | ||||||||
\(952\) | −6.03445 | −0.195578 | ||||||||
\(953\) | 30.6763 | 0.993703 | 0.496851 | − | 0.867836i | \(-0.334489\pi\) | ||||
0.496851 | + | 0.867836i | \(0.334489\pi\) | |||||||
\(954\) | 43.9381 | 1.42255 | ||||||||
\(955\) | 6.16197 | 0.199397 | ||||||||
\(956\) | −4.49944 | −0.145522 | ||||||||
\(957\) | −31.9137 | −1.03162 | ||||||||
\(958\) | −65.8622 | −2.12791 | ||||||||
\(959\) | 3.66496 | 0.118348 | ||||||||
\(960\) | 7.92936 | 0.255919 | ||||||||
\(961\) | 52.6052 | 1.69694 | ||||||||
\(962\) | −3.49707 | −0.112750 | ||||||||
\(963\) | −84.7616 | −2.73140 | ||||||||
\(964\) | −23.8210 | −0.767222 | ||||||||
\(965\) | −20.0392 | −0.645086 | ||||||||
\(966\) | −38.8924 | −1.25134 | ||||||||
\(967\) | −15.0126 | −0.482773 | −0.241386 | − | 0.970429i | \(-0.577602\pi\) | ||||
−0.241386 | + | 0.970429i | \(0.577602\pi\) | |||||||
\(968\) | −9.45280 | −0.303825 | ||||||||
\(969\) | 82.5252 | 2.65109 | ||||||||
\(970\) | −5.20408 | −0.167093 | ||||||||
\(971\) | 55.0967 | 1.76814 | 0.884069 | − | 0.467357i | \(-0.154794\pi\) | ||||
0.884069 | + | 0.467357i | \(0.154794\pi\) | |||||||
\(972\) | 22.1110 | 0.709211 | ||||||||
\(973\) | 15.3650 | 0.492580 | ||||||||
\(974\) | −2.38832 | −0.0765267 | ||||||||
\(975\) | −7.39954 | −0.236975 | ||||||||
\(976\) | −45.9621 | −1.47121 | ||||||||
\(977\) | 6.87085 | 0.219818 | 0.109909 | − | 0.993942i | \(-0.464944\pi\) | ||||
0.109909 | + | 0.993942i | \(0.464944\pi\) | |||||||
\(978\) | 57.9222 | 1.85215 | ||||||||
\(979\) | −14.1348 | −0.451752 | ||||||||
\(980\) | 1.41441 | 0.0451816 | ||||||||
\(981\) | 46.4280 | 1.48233 | ||||||||
\(982\) | −44.9580 | −1.43467 | ||||||||
\(983\) | 44.7573 | 1.42754 | 0.713768 | − | 0.700382i | \(-0.246987\pi\) | ||||
0.713768 | + | 0.700382i | \(0.246987\pi\) | |||||||
\(984\) | 26.4234 | 0.842348 | ||||||||
\(985\) | 6.39547 | 0.203777 | ||||||||
\(986\) | −78.0100 | −2.48434 | ||||||||
\(987\) | 25.3609 | 0.807246 | ||||||||
\(988\) | 19.7309 | 0.627722 | ||||||||
\(989\) | 30.1904 | 0.959998 | ||||||||
\(990\) | 13.4832 | 0.428525 | ||||||||
\(991\) | −3.87009 | −0.122938 | −0.0614688 | − | 0.998109i | \(-0.519578\pi\) | ||||
−0.0614688 | + | 0.998109i | \(0.519578\pi\) | |||||||
\(992\) | −61.7886 | −1.96179 | ||||||||
\(993\) | −37.4751 | −1.18924 | ||||||||
\(994\) | −14.9365 | −0.473757 | ||||||||
\(995\) | −10.5352 | −0.333987 | ||||||||
\(996\) | 15.6142 | 0.494755 | ||||||||
\(997\) | −28.6488 | −0.907318 | −0.453659 | − | 0.891175i | \(-0.649882\pi\) | ||||
−0.453659 | + | 0.891175i | \(0.649882\pi\) | |||||||
\(998\) | 14.4198 | 0.456449 | ||||||||
\(999\) | −3.71283 | −0.117469 |
(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.o.1.16 | ✓ | 73 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.o.1.16 | ✓ | 73 | 1.1 | even | 1 | trivial |