Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.37393 | −1.37059 | −0.685295 | − | 0.728265i | \(-0.740327\pi\) | ||||
−0.685295 | + | 0.728265i | \(0.740327\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.41638 | 0.633427 | 0.316713 | − | 0.948521i | \(-0.397421\pi\) | ||||
0.316713 | + | 0.948521i | \(0.397421\pi\) | |||||||
\(6\) | 2.37393 | 0.969154 | ||||||||
\(7\) | 3.16627 | 1.19674 | 0.598369 | − | 0.801221i | \(-0.295816\pi\) | ||||
0.598369 | + | 0.801221i | \(0.295816\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.63555 | 0.878517 | ||||||||
\(10\) | −1.41638 | −0.447900 | ||||||||
\(11\) | −4.44420 | −1.33998 | −0.669989 | − | 0.742371i | \(-0.733701\pi\) | ||||
−0.669989 | + | 0.742371i | \(0.733701\pi\) | |||||||
\(12\) | −2.37393 | −0.685295 | ||||||||
\(13\) | −2.06102 | −0.571624 | −0.285812 | − | 0.958286i | \(-0.592263\pi\) | ||||
−0.285812 | + | 0.958286i | \(0.592263\pi\) | |||||||
\(14\) | −3.16627 | −0.846221 | ||||||||
\(15\) | −3.36240 | −0.868168 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.79893 | 0.678841 | 0.339420 | − | 0.940635i | \(-0.389769\pi\) | ||||
0.339420 | + | 0.940635i | \(0.389769\pi\) | |||||||
\(18\) | −2.63555 | −0.621206 | ||||||||
\(19\) | 3.09851 | 0.710847 | 0.355423 | − | 0.934705i | \(-0.384337\pi\) | ||||
0.355423 | + | 0.934705i | \(0.384337\pi\) | |||||||
\(20\) | 1.41638 | 0.316713 | ||||||||
\(21\) | −7.51651 | −1.64024 | ||||||||
\(22\) | 4.44420 | 0.947507 | ||||||||
\(23\) | 3.32085 | 0.692444 | 0.346222 | − | 0.938153i | \(-0.387464\pi\) | ||||
0.346222 | + | 0.938153i | \(0.387464\pi\) | |||||||
\(24\) | 2.37393 | 0.484577 | ||||||||
\(25\) | −2.99385 | −0.598771 | ||||||||
\(26\) | 2.06102 | 0.404199 | ||||||||
\(27\) | 0.865174 | 0.166503 | ||||||||
\(28\) | 3.16627 | 0.598369 | ||||||||
\(29\) | −2.05372 | −0.381367 | −0.190684 | − | 0.981652i | \(-0.561070\pi\) | ||||
−0.190684 | + | 0.981652i | \(0.561070\pi\) | |||||||
\(30\) | 3.36240 | 0.613888 | ||||||||
\(31\) | 2.77414 | 0.498250 | 0.249125 | − | 0.968471i | \(-0.419857\pi\) | ||||
0.249125 | + | 0.968471i | \(0.419857\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 10.5502 | 1.83656 | ||||||||
\(34\) | −2.79893 | −0.480013 | ||||||||
\(35\) | 4.48466 | 0.758045 | ||||||||
\(36\) | 2.63555 | 0.439259 | ||||||||
\(37\) | −7.57692 | −1.24564 | −0.622819 | − | 0.782366i | \(-0.714013\pi\) | ||||
−0.622819 | + | 0.782366i | \(0.714013\pi\) | |||||||
\(38\) | −3.09851 | −0.502645 | ||||||||
\(39\) | 4.89272 | 0.783462 | ||||||||
\(40\) | −1.41638 | −0.223950 | ||||||||
\(41\) | 1.40681 | 0.219706 | 0.109853 | − | 0.993948i | \(-0.464962\pi\) | ||||
0.109853 | + | 0.993948i | \(0.464962\pi\) | |||||||
\(42\) | 7.51651 | 1.15982 | ||||||||
\(43\) | −9.29805 | −1.41794 | −0.708969 | − | 0.705239i | \(-0.750840\pi\) | ||||
−0.708969 | + | 0.705239i | \(0.750840\pi\) | |||||||
\(44\) | −4.44420 | −0.669989 | ||||||||
\(45\) | 3.73296 | 0.556476 | ||||||||
\(46\) | −3.32085 | −0.489632 | ||||||||
\(47\) | −3.62831 | −0.529243 | −0.264622 | − | 0.964352i | \(-0.585247\pi\) | ||||
−0.264622 | + | 0.964352i | \(0.585247\pi\) | |||||||
\(48\) | −2.37393 | −0.342648 | ||||||||
\(49\) | 3.02526 | 0.432181 | ||||||||
\(50\) | 2.99385 | 0.423395 | ||||||||
\(51\) | −6.64448 | −0.930413 | ||||||||
\(52\) | −2.06102 | −0.285812 | ||||||||
\(53\) | 0.794159 | 0.109086 | 0.0545430 | − | 0.998511i | \(-0.482630\pi\) | ||||
0.0545430 | + | 0.998511i | \(0.482630\pi\) | |||||||
\(54\) | −0.865174 | −0.117735 | ||||||||
\(55\) | −6.29470 | −0.848777 | ||||||||
\(56\) | −3.16627 | −0.423111 | ||||||||
\(57\) | −7.35565 | −0.974280 | ||||||||
\(58\) | 2.05372 | 0.269667 | ||||||||
\(59\) | −9.14533 | −1.19062 | −0.595310 | − | 0.803496i | \(-0.702971\pi\) | ||||
−0.595310 | + | 0.803496i | \(0.702971\pi\) | |||||||
\(60\) | −3.36240 | −0.434084 | ||||||||
\(61\) | −1.82446 | −0.233598 | −0.116799 | − | 0.993156i | \(-0.537263\pi\) | ||||
−0.116799 | + | 0.993156i | \(0.537263\pi\) | |||||||
\(62\) | −2.77414 | −0.352316 | ||||||||
\(63\) | 8.34487 | 1.05135 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.91920 | −0.362082 | ||||||||
\(66\) | −10.5502 | −1.29864 | ||||||||
\(67\) | −12.9905 | −1.58704 | −0.793522 | − | 0.608541i | \(-0.791755\pi\) | ||||
−0.793522 | + | 0.608541i | \(0.791755\pi\) | |||||||
\(68\) | 2.79893 | 0.339420 | ||||||||
\(69\) | −7.88346 | −0.949057 | ||||||||
\(70\) | −4.48466 | −0.536019 | ||||||||
\(71\) | 11.9626 | 1.41970 | 0.709849 | − | 0.704354i | \(-0.248763\pi\) | ||||
0.709849 | + | 0.704354i | \(0.248763\pi\) | |||||||
\(72\) | −2.63555 | −0.310603 | ||||||||
\(73\) | 1.59346 | 0.186500 | 0.0932501 | − | 0.995643i | \(-0.470274\pi\) | ||||
0.0932501 | + | 0.995643i | \(0.470274\pi\) | |||||||
\(74\) | 7.57692 | 0.880799 | ||||||||
\(75\) | 7.10721 | 0.820669 | ||||||||
\(76\) | 3.09851 | 0.355423 | ||||||||
\(77\) | −14.0715 | −1.60360 | ||||||||
\(78\) | −4.89272 | −0.553991 | ||||||||
\(79\) | −2.45179 | −0.275848 | −0.137924 | − | 0.990443i | \(-0.544043\pi\) | ||||
−0.137924 | + | 0.990443i | \(0.544043\pi\) | |||||||
\(80\) | 1.41638 | 0.158357 | ||||||||
\(81\) | −9.96052 | −1.10672 | ||||||||
\(82\) | −1.40681 | −0.155356 | ||||||||
\(83\) | 12.3138 | 1.35162 | 0.675809 | − | 0.737077i | \(-0.263795\pi\) | ||||
0.675809 | + | 0.737077i | \(0.263795\pi\) | |||||||
\(84\) | −7.51651 | −0.820118 | ||||||||
\(85\) | 3.96437 | 0.429996 | ||||||||
\(86\) | 9.29805 | 1.00263 | ||||||||
\(87\) | 4.87540 | 0.522698 | ||||||||
\(88\) | 4.44420 | 0.473754 | ||||||||
\(89\) | 3.08210 | 0.326702 | 0.163351 | − | 0.986568i | \(-0.447770\pi\) | ||||
0.163351 | + | 0.986568i | \(0.447770\pi\) | |||||||
\(90\) | −3.73296 | −0.393488 | ||||||||
\(91\) | −6.52574 | −0.684084 | ||||||||
\(92\) | 3.32085 | 0.346222 | ||||||||
\(93\) | −6.58562 | −0.682897 | ||||||||
\(94\) | 3.62831 | 0.374231 | ||||||||
\(95\) | 4.38868 | 0.450269 | ||||||||
\(96\) | 2.37393 | 0.242288 | ||||||||
\(97\) | 14.3010 | 1.45205 | 0.726023 | − | 0.687671i | \(-0.241367\pi\) | ||||
0.726023 | + | 0.687671i | \(0.241367\pi\) | |||||||
\(98\) | −3.02526 | −0.305598 | ||||||||
\(99\) | −11.7129 | −1.17719 | ||||||||
\(100\) | −2.99385 | −0.299385 | ||||||||
\(101\) | 4.79143 | 0.476765 | 0.238382 | − | 0.971171i | \(-0.423383\pi\) | ||||
0.238382 | + | 0.971171i | \(0.423383\pi\) | |||||||
\(102\) | 6.64448 | 0.657901 | ||||||||
\(103\) | 2.36122 | 0.232658 | 0.116329 | − | 0.993211i | \(-0.462887\pi\) | ||||
0.116329 | + | 0.993211i | \(0.462887\pi\) | |||||||
\(104\) | 2.06102 | 0.202100 | ||||||||
\(105\) | −10.6463 | −1.03897 | ||||||||
\(106\) | −0.794159 | −0.0771355 | ||||||||
\(107\) | 9.64480 | 0.932398 | 0.466199 | − | 0.884680i | \(-0.345623\pi\) | ||||
0.466199 | + | 0.884680i | \(0.345623\pi\) | |||||||
\(108\) | 0.865174 | 0.0832514 | ||||||||
\(109\) | −14.6103 | −1.39941 | −0.699707 | − | 0.714430i | \(-0.746686\pi\) | ||||
−0.699707 | + | 0.714430i | \(0.746686\pi\) | |||||||
\(110\) | 6.29470 | 0.600176 | ||||||||
\(111\) | 17.9871 | 1.70726 | ||||||||
\(112\) | 3.16627 | 0.299184 | ||||||||
\(113\) | 5.83917 | 0.549303 | 0.274651 | − | 0.961544i | \(-0.411438\pi\) | ||||
0.274651 | + | 0.961544i | \(0.411438\pi\) | |||||||
\(114\) | 7.35565 | 0.688920 | ||||||||
\(115\) | 4.70359 | 0.438612 | ||||||||
\(116\) | −2.05372 | −0.190684 | ||||||||
\(117\) | −5.43192 | −0.502182 | ||||||||
\(118\) | 9.14533 | 0.841896 | ||||||||
\(119\) | 8.86218 | 0.812394 | ||||||||
\(120\) | 3.36240 | 0.306944 | ||||||||
\(121\) | 8.75093 | 0.795539 | ||||||||
\(122\) | 1.82446 | 0.165179 | ||||||||
\(123\) | −3.33966 | −0.301127 | ||||||||
\(124\) | 2.77414 | 0.249125 | ||||||||
\(125\) | −11.3224 | −1.01270 | ||||||||
\(126\) | −8.34487 | −0.743420 | ||||||||
\(127\) | −8.39481 | −0.744919 | −0.372459 | − | 0.928049i | \(-0.621485\pi\) | ||||
−0.372459 | + | 0.928049i | \(0.621485\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 22.0729 | 1.94341 | ||||||||
\(130\) | 2.91920 | 0.256030 | ||||||||
\(131\) | −6.24893 | −0.545971 | −0.272986 | − | 0.962018i | \(-0.588011\pi\) | ||||
−0.272986 | + | 0.962018i | \(0.588011\pi\) | |||||||
\(132\) | 10.5502 | 0.918280 | ||||||||
\(133\) | 9.81072 | 0.850697 | ||||||||
\(134\) | 12.9905 | 1.12221 | ||||||||
\(135\) | 1.22542 | 0.105467 | ||||||||
\(136\) | −2.79893 | −0.240007 | ||||||||
\(137\) | −1.77696 | −0.151816 | −0.0759078 | − | 0.997115i | \(-0.524185\pi\) | ||||
−0.0759078 | + | 0.997115i | \(0.524185\pi\) | |||||||
\(138\) | 7.88346 | 0.671085 | ||||||||
\(139\) | 2.82872 | 0.239928 | 0.119964 | − | 0.992778i | \(-0.461722\pi\) | ||||
0.119964 | + | 0.992778i | \(0.461722\pi\) | |||||||
\(140\) | 4.48466 | 0.379023 | ||||||||
\(141\) | 8.61336 | 0.725375 | ||||||||
\(142\) | −11.9626 | −1.00388 | ||||||||
\(143\) | 9.15959 | 0.765963 | ||||||||
\(144\) | 2.63555 | 0.219629 | ||||||||
\(145\) | −2.90886 | −0.241568 | ||||||||
\(146\) | −1.59346 | −0.131876 | ||||||||
\(147\) | −7.18177 | −0.592342 | ||||||||
\(148\) | −7.57692 | −0.622819 | ||||||||
\(149\) | −19.3924 | −1.58869 | −0.794343 | − | 0.607470i | \(-0.792185\pi\) | ||||
−0.794343 | + | 0.607470i | \(0.792185\pi\) | |||||||
\(150\) | −7.10721 | −0.580301 | ||||||||
\(151\) | 2.69389 | 0.219225 | 0.109613 | − | 0.993974i | \(-0.465039\pi\) | ||||
0.109613 | + | 0.993974i | \(0.465039\pi\) | |||||||
\(152\) | −3.09851 | −0.251322 | ||||||||
\(153\) | 7.37673 | 0.596374 | ||||||||
\(154\) | 14.0715 | 1.13392 | ||||||||
\(155\) | 3.92925 | 0.315605 | ||||||||
\(156\) | 4.89272 | 0.391731 | ||||||||
\(157\) | −5.91854 | −0.472351 | −0.236176 | − | 0.971710i | \(-0.575894\pi\) | ||||
−0.236176 | + | 0.971710i | \(0.575894\pi\) | |||||||
\(158\) | 2.45179 | 0.195054 | ||||||||
\(159\) | −1.88528 | −0.149512 | ||||||||
\(160\) | −1.41638 | −0.111975 | ||||||||
\(161\) | 10.5147 | 0.828674 | ||||||||
\(162\) | 9.96052 | 0.782572 | ||||||||
\(163\) | −15.4816 | −1.21261 | −0.606307 | − | 0.795231i | \(-0.707350\pi\) | ||||
−0.606307 | + | 0.795231i | \(0.707350\pi\) | |||||||
\(164\) | 1.40681 | 0.109853 | ||||||||
\(165\) | 14.9432 | 1.16333 | ||||||||
\(166\) | −12.3138 | −0.955738 | ||||||||
\(167\) | 23.0706 | 1.78525 | 0.892627 | − | 0.450796i | \(-0.148860\pi\) | ||||
0.892627 | + | 0.450796i | \(0.148860\pi\) | |||||||
\(168\) | 7.51651 | 0.579911 | ||||||||
\(169\) | −8.75220 | −0.673246 | ||||||||
\(170\) | −3.96437 | −0.304053 | ||||||||
\(171\) | 8.16628 | 0.624491 | ||||||||
\(172\) | −9.29805 | −0.708969 | ||||||||
\(173\) | −4.19988 | −0.319311 | −0.159656 | − | 0.987173i | \(-0.551038\pi\) | ||||
−0.159656 | + | 0.987173i | \(0.551038\pi\) | |||||||
\(174\) | −4.87540 | −0.369603 | ||||||||
\(175\) | −9.47935 | −0.716571 | ||||||||
\(176\) | −4.44420 | −0.334994 | ||||||||
\(177\) | 21.7104 | 1.63185 | ||||||||
\(178\) | −3.08210 | −0.231013 | ||||||||
\(179\) | 8.96546 | 0.670110 | 0.335055 | − | 0.942199i | \(-0.391245\pi\) | ||||
0.335055 | + | 0.942199i | \(0.391245\pi\) | |||||||
\(180\) | 3.73296 | 0.278238 | ||||||||
\(181\) | −7.69334 | −0.571841 | −0.285921 | − | 0.958253i | \(-0.592299\pi\) | ||||
−0.285921 | + | 0.958253i | \(0.592299\pi\) | |||||||
\(182\) | 6.52574 | 0.483720 | ||||||||
\(183\) | 4.33115 | 0.320168 | ||||||||
\(184\) | −3.32085 | −0.244816 | ||||||||
\(185\) | −10.7318 | −0.789020 | ||||||||
\(186\) | 6.58562 | 0.482881 | ||||||||
\(187\) | −12.4390 | −0.909631 | ||||||||
\(188\) | −3.62831 | −0.264622 | ||||||||
\(189\) | 2.73937 | 0.199260 | ||||||||
\(190\) | −4.38868 | −0.318388 | ||||||||
\(191\) | 7.44623 | 0.538790 | 0.269395 | − | 0.963030i | \(-0.413176\pi\) | ||||
0.269395 | + | 0.963030i | \(0.413176\pi\) | |||||||
\(192\) | −2.37393 | −0.171324 | ||||||||
\(193\) | −21.1416 | −1.52181 | −0.760903 | − | 0.648866i | \(-0.775244\pi\) | ||||
−0.760903 | + | 0.648866i | \(0.775244\pi\) | |||||||
\(194\) | −14.3010 | −1.02675 | ||||||||
\(195\) | 6.92997 | 0.496266 | ||||||||
\(196\) | 3.02526 | 0.216090 | ||||||||
\(197\) | 7.08373 | 0.504695 | 0.252348 | − | 0.967637i | \(-0.418797\pi\) | ||||
0.252348 | + | 0.967637i | \(0.418797\pi\) | |||||||
\(198\) | 11.7129 | 0.832402 | ||||||||
\(199\) | −5.32629 | −0.377571 | −0.188786 | − | 0.982018i | \(-0.560455\pi\) | ||||
−0.188786 | + | 0.982018i | \(0.560455\pi\) | |||||||
\(200\) | 2.99385 | 0.211697 | ||||||||
\(201\) | 30.8386 | 2.17519 | ||||||||
\(202\) | −4.79143 | −0.337124 | ||||||||
\(203\) | −6.50264 | −0.456396 | ||||||||
\(204\) | −6.64448 | −0.465206 | ||||||||
\(205\) | 1.99258 | 0.139168 | ||||||||
\(206\) | −2.36122 | −0.164514 | ||||||||
\(207\) | 8.75226 | 0.608324 | ||||||||
\(208\) | −2.06102 | −0.142906 | ||||||||
\(209\) | −13.7704 | −0.952519 | ||||||||
\(210\) | 10.6463 | 0.734662 | ||||||||
\(211\) | 25.6308 | 1.76450 | 0.882248 | − | 0.470784i | \(-0.156029\pi\) | ||||
0.882248 | + | 0.470784i | \(0.156029\pi\) | |||||||
\(212\) | 0.794159 | 0.0545430 | ||||||||
\(213\) | −28.3984 | −1.94582 | ||||||||
\(214\) | −9.64480 | −0.659305 | ||||||||
\(215\) | −13.1696 | −0.898160 | ||||||||
\(216\) | −0.865174 | −0.0588676 | ||||||||
\(217\) | 8.78367 | 0.596275 | ||||||||
\(218\) | 14.6103 | 0.989535 | ||||||||
\(219\) | −3.78276 | −0.255615 | ||||||||
\(220\) | −6.29470 | −0.424389 | ||||||||
\(221\) | −5.76866 | −0.388042 | ||||||||
\(222\) | −17.9871 | −1.20721 | ||||||||
\(223\) | −18.4835 | −1.23775 | −0.618874 | − | 0.785490i | \(-0.712411\pi\) | ||||
−0.618874 | + | 0.785490i | \(0.712411\pi\) | |||||||
\(224\) | −3.16627 | −0.211555 | ||||||||
\(225\) | −7.89046 | −0.526031 | ||||||||
\(226\) | −5.83917 | −0.388416 | ||||||||
\(227\) | 14.6988 | 0.975593 | 0.487796 | − | 0.872957i | \(-0.337801\pi\) | ||||
0.487796 | + | 0.872957i | \(0.337801\pi\) | |||||||
\(228\) | −7.35565 | −0.487140 | ||||||||
\(229\) | 11.4057 | 0.753710 | 0.376855 | − | 0.926272i | \(-0.377005\pi\) | ||||
0.376855 | + | 0.926272i | \(0.377005\pi\) | |||||||
\(230\) | −4.70359 | −0.310146 | ||||||||
\(231\) | 33.4049 | 2.19788 | ||||||||
\(232\) | 2.05372 | 0.134834 | ||||||||
\(233\) | −16.2319 | −1.06339 | −0.531694 | − | 0.846937i | \(-0.678444\pi\) | ||||
−0.531694 | + | 0.846937i | \(0.678444\pi\) | |||||||
\(234\) | 5.43192 | 0.355096 | ||||||||
\(235\) | −5.13908 | −0.335237 | ||||||||
\(236\) | −9.14533 | −0.595310 | ||||||||
\(237\) | 5.82038 | 0.378075 | ||||||||
\(238\) | −8.86218 | −0.574450 | ||||||||
\(239\) | −22.3615 | −1.44645 | −0.723223 | − | 0.690615i | \(-0.757340\pi\) | ||||
−0.723223 | + | 0.690615i | \(0.757340\pi\) | |||||||
\(240\) | −3.36240 | −0.217042 | ||||||||
\(241\) | −23.9131 | −1.54038 | −0.770188 | − | 0.637817i | \(-0.779838\pi\) | ||||
−0.770188 | + | 0.637817i | \(0.779838\pi\) | |||||||
\(242\) | −8.75093 | −0.562531 | ||||||||
\(243\) | 21.0501 | 1.35036 | ||||||||
\(244\) | −1.82446 | −0.116799 | ||||||||
\(245\) | 4.28494 | 0.273755 | ||||||||
\(246\) | 3.33966 | 0.212929 | ||||||||
\(247\) | −6.38609 | −0.406337 | ||||||||
\(248\) | −2.77414 | −0.176158 | ||||||||
\(249\) | −29.2322 | −1.85251 | ||||||||
\(250\) | 11.3224 | 0.716090 | ||||||||
\(251\) | 1.86610 | 0.117787 | 0.0588935 | − | 0.998264i | \(-0.481243\pi\) | ||||
0.0588935 | + | 0.998264i | \(0.481243\pi\) | |||||||
\(252\) | 8.34487 | 0.525677 | ||||||||
\(253\) | −14.7585 | −0.927859 | ||||||||
\(254\) | 8.39481 | 0.526737 | ||||||||
\(255\) | −9.41113 | −0.589348 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.58404 | −0.223566 | −0.111783 | − | 0.993733i | \(-0.535656\pi\) | ||||
−0.111783 | + | 0.993733i | \(0.535656\pi\) | |||||||
\(258\) | −22.0729 | −1.37420 | ||||||||
\(259\) | −23.9906 | −1.49070 | ||||||||
\(260\) | −2.91920 | −0.181041 | ||||||||
\(261\) | −5.41270 | −0.335038 | ||||||||
\(262\) | 6.24893 | 0.386060 | ||||||||
\(263\) | −18.3625 | −1.13228 | −0.566139 | − | 0.824310i | \(-0.691564\pi\) | ||||
−0.566139 | + | 0.824310i | \(0.691564\pi\) | |||||||
\(264\) | −10.5502 | −0.649322 | ||||||||
\(265\) | 1.12483 | 0.0690980 | ||||||||
\(266\) | −9.81072 | −0.601534 | ||||||||
\(267\) | −7.31670 | −0.447775 | ||||||||
\(268\) | −12.9905 | −0.793522 | ||||||||
\(269\) | 20.3637 | 1.24160 | 0.620798 | − | 0.783971i | \(-0.286809\pi\) | ||||
0.620798 | + | 0.783971i | \(0.286809\pi\) | |||||||
\(270\) | −1.22542 | −0.0745766 | ||||||||
\(271\) | 17.5673 | 1.06714 | 0.533570 | − | 0.845756i | \(-0.320850\pi\) | ||||
0.533570 | + | 0.845756i | \(0.320850\pi\) | |||||||
\(272\) | 2.79893 | 0.169710 | ||||||||
\(273\) | 15.4917 | 0.937599 | ||||||||
\(274\) | 1.77696 | 0.107350 | ||||||||
\(275\) | 13.3053 | 0.802339 | ||||||||
\(276\) | −7.88346 | −0.474529 | ||||||||
\(277\) | −20.8347 | −1.25183 | −0.625917 | − | 0.779889i | \(-0.715275\pi\) | ||||
−0.625917 | + | 0.779889i | \(0.715275\pi\) | |||||||
\(278\) | −2.82872 | −0.169655 | ||||||||
\(279\) | 7.31139 | 0.437721 | ||||||||
\(280\) | −4.48466 | −0.268009 | ||||||||
\(281\) | −8.01510 | −0.478141 | −0.239070 | − | 0.971002i | \(-0.576843\pi\) | ||||
−0.239070 | + | 0.971002i | \(0.576843\pi\) | |||||||
\(282\) | −8.61336 | −0.512918 | ||||||||
\(283\) | −2.38474 | −0.141758 | −0.0708790 | − | 0.997485i | \(-0.522580\pi\) | ||||
−0.0708790 | + | 0.997485i | \(0.522580\pi\) | |||||||
\(284\) | 11.9626 | 0.709849 | ||||||||
\(285\) | −10.4184 | −0.617135 | ||||||||
\(286\) | −9.15959 | −0.541618 | ||||||||
\(287\) | 4.45433 | 0.262931 | ||||||||
\(288\) | −2.63555 | −0.155301 | ||||||||
\(289\) | −9.16598 | −0.539175 | ||||||||
\(290\) | 2.90886 | 0.170814 | ||||||||
\(291\) | −33.9496 | −1.99016 | ||||||||
\(292\) | 1.59346 | 0.0932501 | ||||||||
\(293\) | −12.7712 | −0.746100 | −0.373050 | − | 0.927811i | \(-0.621688\pi\) | ||||
−0.373050 | + | 0.927811i | \(0.621688\pi\) | |||||||
\(294\) | 7.18177 | 0.418849 | ||||||||
\(295\) | −12.9533 | −0.754170 | ||||||||
\(296\) | 7.57692 | 0.440399 | ||||||||
\(297\) | −3.84501 | −0.223110 | ||||||||
\(298\) | 19.3924 | 1.12337 | ||||||||
\(299\) | −6.84433 | −0.395818 | ||||||||
\(300\) | 7.10721 | 0.410335 | ||||||||
\(301\) | −29.4401 | −1.69690 | ||||||||
\(302\) | −2.69389 | −0.155016 | ||||||||
\(303\) | −11.3745 | −0.653449 | ||||||||
\(304\) | 3.09851 | 0.177712 | ||||||||
\(305\) | −2.58414 | −0.147967 | ||||||||
\(306\) | −7.37673 | −0.421700 | ||||||||
\(307\) | 34.6563 | 1.97794 | 0.988971 | − | 0.148112i | \(-0.0473197\pi\) | ||||
0.988971 | + | 0.148112i | \(0.0473197\pi\) | |||||||
\(308\) | −14.0715 | −0.801801 | ||||||||
\(309\) | −5.60538 | −0.318879 | ||||||||
\(310\) | −3.92925 | −0.223166 | ||||||||
\(311\) | −3.64803 | −0.206861 | −0.103430 | − | 0.994637i | \(-0.532982\pi\) | ||||
−0.103430 | + | 0.994637i | \(0.532982\pi\) | |||||||
\(312\) | −4.89272 | −0.276996 | ||||||||
\(313\) | −26.1275 | −1.47681 | −0.738407 | − | 0.674356i | \(-0.764421\pi\) | ||||
−0.738407 | + | 0.674356i | \(0.764421\pi\) | |||||||
\(314\) | 5.91854 | 0.334003 | ||||||||
\(315\) | 11.8195 | 0.665956 | ||||||||
\(316\) | −2.45179 | −0.137924 | ||||||||
\(317\) | −30.0238 | −1.68630 | −0.843151 | − | 0.537677i | \(-0.819302\pi\) | ||||
−0.843151 | + | 0.537677i | \(0.819302\pi\) | |||||||
\(318\) | 1.88528 | 0.105721 | ||||||||
\(319\) | 9.12717 | 0.511023 | ||||||||
\(320\) | 1.41638 | 0.0791783 | ||||||||
\(321\) | −22.8961 | −1.27793 | ||||||||
\(322\) | −10.5147 | −0.585961 | ||||||||
\(323\) | 8.67252 | 0.482552 | ||||||||
\(324\) | −9.96052 | −0.553362 | ||||||||
\(325\) | 6.17039 | 0.342272 | ||||||||
\(326\) | 15.4816 | 0.857447 | ||||||||
\(327\) | 34.6839 | 1.91802 | ||||||||
\(328\) | −1.40681 | −0.0776779 | ||||||||
\(329\) | −11.4882 | −0.633365 | ||||||||
\(330\) | −14.9432 | −0.822595 | ||||||||
\(331\) | 13.8025 | 0.758656 | 0.379328 | − | 0.925262i | \(-0.376155\pi\) | ||||
0.379328 | + | 0.925262i | \(0.376155\pi\) | |||||||
\(332\) | 12.3138 | 0.675809 | ||||||||
\(333\) | −19.9694 | −1.09431 | ||||||||
\(334\) | −23.0706 | −1.26237 | ||||||||
\(335\) | −18.3996 | −1.00528 | ||||||||
\(336\) | −7.51651 | −0.410059 | ||||||||
\(337\) | −6.06005 | −0.330112 | −0.165056 | − | 0.986284i | \(-0.552780\pi\) | ||||
−0.165056 | + | 0.986284i | \(0.552780\pi\) | |||||||
\(338\) | 8.75220 | 0.476057 | ||||||||
\(339\) | −13.8618 | −0.752869 | ||||||||
\(340\) | 3.96437 | 0.214998 | ||||||||
\(341\) | −12.3288 | −0.667644 | ||||||||
\(342\) | −8.16628 | −0.441582 | ||||||||
\(343\) | −12.5851 | −0.679531 | ||||||||
\(344\) | 9.29805 | 0.501317 | ||||||||
\(345\) | −11.1660 | −0.601158 | ||||||||
\(346\) | 4.19988 | 0.225787 | ||||||||
\(347\) | −28.5321 | −1.53168 | −0.765842 | − | 0.643029i | \(-0.777677\pi\) | ||||
−0.765842 | + | 0.643029i | \(0.777677\pi\) | |||||||
\(348\) | 4.87540 | 0.261349 | ||||||||
\(349\) | −1.92898 | −0.103256 | −0.0516279 | − | 0.998666i | \(-0.516441\pi\) | ||||
−0.0516279 | + | 0.998666i | \(0.516441\pi\) | |||||||
\(350\) | 9.47935 | 0.506693 | ||||||||
\(351\) | −1.78314 | −0.0951770 | ||||||||
\(352\) | 4.44420 | 0.236877 | ||||||||
\(353\) | −14.1267 | −0.751887 | −0.375943 | − | 0.926643i | \(-0.622681\pi\) | ||||
−0.375943 | + | 0.926643i | \(0.622681\pi\) | |||||||
\(354\) | −21.7104 | −1.15389 | ||||||||
\(355\) | 16.9436 | 0.899275 | ||||||||
\(356\) | 3.08210 | 0.163351 | ||||||||
\(357\) | −21.0382 | −1.11346 | ||||||||
\(358\) | −8.96546 | −0.473839 | ||||||||
\(359\) | −18.6111 | −0.982254 | −0.491127 | − | 0.871088i | \(-0.663415\pi\) | ||||
−0.491127 | + | 0.871088i | \(0.663415\pi\) | |||||||
\(360\) | −3.73296 | −0.196744 | ||||||||
\(361\) | −9.39924 | −0.494697 | ||||||||
\(362\) | 7.69334 | 0.404353 | ||||||||
\(363\) | −20.7741 | −1.09036 | ||||||||
\(364\) | −6.52574 | −0.342042 | ||||||||
\(365\) | 2.25695 | 0.118134 | ||||||||
\(366\) | −4.33115 | −0.226393 | ||||||||
\(367\) | 15.2361 | 0.795316 | 0.397658 | − | 0.917534i | \(-0.369823\pi\) | ||||
0.397658 | + | 0.917534i | \(0.369823\pi\) | |||||||
\(368\) | 3.32085 | 0.173111 | ||||||||
\(369\) | 3.70771 | 0.193016 | ||||||||
\(370\) | 10.7318 | 0.557921 | ||||||||
\(371\) | 2.51452 | 0.130547 | ||||||||
\(372\) | −6.58562 | −0.341448 | ||||||||
\(373\) | −24.8313 | −1.28572 | −0.642859 | − | 0.765985i | \(-0.722252\pi\) | ||||
−0.642859 | + | 0.765985i | \(0.722252\pi\) | |||||||
\(374\) | 12.4390 | 0.643207 | ||||||||
\(375\) | 26.8785 | 1.38800 | ||||||||
\(376\) | 3.62831 | 0.187116 | ||||||||
\(377\) | 4.23277 | 0.217999 | ||||||||
\(378\) | −2.73937 | −0.140898 | ||||||||
\(379\) | 28.0836 | 1.44256 | 0.721279 | − | 0.692644i | \(-0.243554\pi\) | ||||
0.721279 | + | 0.692644i | \(0.243554\pi\) | |||||||
\(380\) | 4.38868 | 0.225135 | ||||||||
\(381\) | 19.9287 | 1.02098 | ||||||||
\(382\) | −7.44623 | −0.380982 | ||||||||
\(383\) | −21.3990 | −1.09344 | −0.546720 | − | 0.837316i | \(-0.684124\pi\) | ||||
−0.546720 | + | 0.837316i | \(0.684124\pi\) | |||||||
\(384\) | 2.37393 | 0.121144 | ||||||||
\(385\) | −19.9307 | −1.01576 | ||||||||
\(386\) | 21.1416 | 1.07608 | ||||||||
\(387\) | −24.5055 | −1.24568 | ||||||||
\(388\) | 14.3010 | 0.726023 | ||||||||
\(389\) | 9.28682 | 0.470861 | 0.235430 | − | 0.971891i | \(-0.424350\pi\) | ||||
0.235430 | + | 0.971891i | \(0.424350\pi\) | |||||||
\(390\) | −6.92997 | −0.350913 | ||||||||
\(391\) | 9.29482 | 0.470059 | ||||||||
\(392\) | −3.02526 | −0.152799 | ||||||||
\(393\) | 14.8345 | 0.748303 | ||||||||
\(394\) | −7.08373 | −0.356873 | ||||||||
\(395\) | −3.47268 | −0.174729 | ||||||||
\(396\) | −11.7129 | −0.588597 | ||||||||
\(397\) | −38.2160 | −1.91800 | −0.959002 | − | 0.283400i | \(-0.908538\pi\) | ||||
−0.959002 | + | 0.283400i | \(0.908538\pi\) | |||||||
\(398\) | 5.32629 | 0.266983 | ||||||||
\(399\) | −23.2900 | −1.16596 | ||||||||
\(400\) | −2.99385 | −0.149693 | ||||||||
\(401\) | 20.3989 | 1.01867 | 0.509337 | − | 0.860567i | \(-0.329891\pi\) | ||||
0.509337 | + | 0.860567i | \(0.329891\pi\) | |||||||
\(402\) | −30.8386 | −1.53809 | ||||||||
\(403\) | −5.71756 | −0.284812 | ||||||||
\(404\) | 4.79143 | 0.238382 | ||||||||
\(405\) | −14.1079 | −0.701029 | ||||||||
\(406\) | 6.50264 | 0.322721 | ||||||||
\(407\) | 33.6734 | 1.66913 | ||||||||
\(408\) | 6.64448 | 0.328951 | ||||||||
\(409\) | −17.0232 | −0.841741 | −0.420871 | − | 0.907121i | \(-0.638275\pi\) | ||||
−0.420871 | + | 0.907121i | \(0.638275\pi\) | |||||||
\(410\) | −1.99258 | −0.0984064 | ||||||||
\(411\) | 4.21837 | 0.208077 | ||||||||
\(412\) | 2.36122 | 0.116329 | ||||||||
\(413\) | −28.9566 | −1.42486 | ||||||||
\(414\) | −8.75226 | −0.430150 | ||||||||
\(415\) | 17.4411 | 0.856150 | ||||||||
\(416\) | 2.06102 | 0.101050 | ||||||||
\(417\) | −6.71518 | −0.328844 | ||||||||
\(418\) | 13.7704 | 0.673532 | ||||||||
\(419\) | 19.8428 | 0.969382 | 0.484691 | − | 0.874685i | \(-0.338932\pi\) | ||||
0.484691 | + | 0.874685i | \(0.338932\pi\) | |||||||
\(420\) | −10.6463 | −0.519485 | ||||||||
\(421\) | 4.55232 | 0.221867 | 0.110933 | − | 0.993828i | \(-0.464616\pi\) | ||||
0.110933 | + | 0.993828i | \(0.464616\pi\) | |||||||
\(422\) | −25.6308 | −1.24769 | ||||||||
\(423\) | −9.56260 | −0.464949 | ||||||||
\(424\) | −0.794159 | −0.0385677 | ||||||||
\(425\) | −8.37960 | −0.406470 | ||||||||
\(426\) | 28.3984 | 1.37591 | ||||||||
\(427\) | −5.77674 | −0.279556 | ||||||||
\(428\) | 9.64480 | 0.466199 | ||||||||
\(429\) | −21.7442 | −1.04982 | ||||||||
\(430\) | 13.1696 | 0.635095 | ||||||||
\(431\) | 8.09066 | 0.389713 | 0.194857 | − | 0.980832i | \(-0.437576\pi\) | ||||
0.194857 | + | 0.980832i | \(0.437576\pi\) | |||||||
\(432\) | 0.865174 | 0.0416257 | ||||||||
\(433\) | −6.65044 | −0.319600 | −0.159800 | − | 0.987149i | \(-0.551085\pi\) | ||||
−0.159800 | + | 0.987149i | \(0.551085\pi\) | |||||||
\(434\) | −8.78367 | −0.421630 | ||||||||
\(435\) | 6.90544 | 0.331091 | ||||||||
\(436\) | −14.6103 | −0.699707 | ||||||||
\(437\) | 10.2897 | 0.492222 | ||||||||
\(438\) | 3.78276 | 0.180747 | ||||||||
\(439\) | −10.4721 | −0.499805 | −0.249903 | − | 0.968271i | \(-0.580399\pi\) | ||||
−0.249903 | + | 0.968271i | \(0.580399\pi\) | |||||||
\(440\) | 6.29470 | 0.300088 | ||||||||
\(441\) | 7.97324 | 0.379678 | ||||||||
\(442\) | 5.76866 | 0.274387 | ||||||||
\(443\) | −19.6743 | −0.934755 | −0.467378 | − | 0.884058i | \(-0.654801\pi\) | ||||
−0.467378 | + | 0.884058i | \(0.654801\pi\) | |||||||
\(444\) | 17.9871 | 0.853630 | ||||||||
\(445\) | 4.36544 | 0.206942 | ||||||||
\(446\) | 18.4835 | 0.875220 | ||||||||
\(447\) | 46.0362 | 2.17744 | ||||||||
\(448\) | 3.16627 | 0.149592 | ||||||||
\(449\) | 39.1663 | 1.84837 | 0.924185 | − | 0.381946i | \(-0.124746\pi\) | ||||
0.924185 | + | 0.381946i | \(0.124746\pi\) | |||||||
\(450\) | 7.89046 | 0.371960 | ||||||||
\(451\) | −6.25213 | −0.294401 | ||||||||
\(452\) | 5.83917 | 0.274651 | ||||||||
\(453\) | −6.39510 | −0.300468 | ||||||||
\(454\) | −14.6988 | −0.689848 | ||||||||
\(455\) | −9.24296 | −0.433317 | ||||||||
\(456\) | 7.35565 | 0.344460 | ||||||||
\(457\) | 10.3078 | 0.482179 | 0.241090 | − | 0.970503i | \(-0.422495\pi\) | ||||
0.241090 | + | 0.970503i | \(0.422495\pi\) | |||||||
\(458\) | −11.4057 | −0.532954 | ||||||||
\(459\) | 2.42156 | 0.113029 | ||||||||
\(460\) | 4.70359 | 0.219306 | ||||||||
\(461\) | 23.9079 | 1.11350 | 0.556752 | − | 0.830679i | \(-0.312047\pi\) | ||||
0.556752 | + | 0.830679i | \(0.312047\pi\) | |||||||
\(462\) | −33.4049 | −1.55414 | ||||||||
\(463\) | −10.6920 | −0.496898 | −0.248449 | − | 0.968645i | \(-0.579921\pi\) | ||||
−0.248449 | + | 0.968645i | \(0.579921\pi\) | |||||||
\(464\) | −2.05372 | −0.0953418 | ||||||||
\(465\) | −9.32777 | −0.432565 | ||||||||
\(466\) | 16.2319 | 0.751928 | ||||||||
\(467\) | −22.5874 | −1.04522 | −0.522610 | − | 0.852572i | \(-0.675041\pi\) | ||||
−0.522610 | + | 0.852572i | \(0.675041\pi\) | |||||||
\(468\) | −5.43192 | −0.251091 | ||||||||
\(469\) | −41.1315 | −1.89928 | ||||||||
\(470\) | 5.13908 | 0.237048 | ||||||||
\(471\) | 14.0502 | 0.647400 | ||||||||
\(472\) | 9.14533 | 0.420948 | ||||||||
\(473\) | 41.3224 | 1.90001 | ||||||||
\(474\) | −5.82038 | −0.267339 | ||||||||
\(475\) | −9.27649 | −0.425634 | ||||||||
\(476\) | 8.86218 | 0.406197 | ||||||||
\(477\) | 2.09305 | 0.0958340 | ||||||||
\(478\) | 22.3615 | 1.02279 | ||||||||
\(479\) | −35.9701 | −1.64352 | −0.821758 | − | 0.569837i | \(-0.807006\pi\) | ||||
−0.821758 | + | 0.569837i | \(0.807006\pi\) | |||||||
\(480\) | 3.36240 | 0.153472 | ||||||||
\(481\) | 15.6162 | 0.712036 | ||||||||
\(482\) | 23.9131 | 1.08921 | ||||||||
\(483\) | −24.9612 | −1.13577 | ||||||||
\(484\) | 8.75093 | 0.397770 | ||||||||
\(485\) | 20.2557 | 0.919764 | ||||||||
\(486\) | −21.0501 | −0.954851 | ||||||||
\(487\) | 24.2832 | 1.10038 | 0.550189 | − | 0.835040i | \(-0.314556\pi\) | ||||
0.550189 | + | 0.835040i | \(0.314556\pi\) | |||||||
\(488\) | 1.82446 | 0.0825895 | ||||||||
\(489\) | 36.7523 | 1.66200 | ||||||||
\(490\) | −4.28494 | −0.193574 | ||||||||
\(491\) | −18.0957 | −0.816648 | −0.408324 | − | 0.912837i | \(-0.633887\pi\) | ||||
−0.408324 | + | 0.912837i | \(0.633887\pi\) | |||||||
\(492\) | −3.33966 | −0.150564 | ||||||||
\(493\) | −5.74824 | −0.258888 | ||||||||
\(494\) | 6.38609 | 0.287324 | ||||||||
\(495\) | −16.5900 | −0.745666 | ||||||||
\(496\) | 2.77414 | 0.124563 | ||||||||
\(497\) | 37.8768 | 1.69901 | ||||||||
\(498\) | 29.2322 | 1.30993 | ||||||||
\(499\) | 30.2498 | 1.35417 | 0.677084 | − | 0.735905i | \(-0.263243\pi\) | ||||
0.677084 | + | 0.735905i | \(0.263243\pi\) | |||||||
\(500\) | −11.3224 | −0.506352 | ||||||||
\(501\) | −54.7680 | −2.44685 | ||||||||
\(502\) | −1.86610 | −0.0832880 | ||||||||
\(503\) | 18.8877 | 0.842160 | 0.421080 | − | 0.907023i | \(-0.361651\pi\) | ||||
0.421080 | + | 0.907023i | \(0.361651\pi\) | |||||||
\(504\) | −8.34487 | −0.371710 | ||||||||
\(505\) | 6.78650 | 0.301995 | ||||||||
\(506\) | 14.7585 | 0.656096 | ||||||||
\(507\) | 20.7771 | 0.922744 | ||||||||
\(508\) | −8.39481 | −0.372459 | ||||||||
\(509\) | −22.7809 | −1.00974 | −0.504872 | − | 0.863194i | \(-0.668460\pi\) | ||||
−0.504872 | + | 0.863194i | \(0.668460\pi\) | |||||||
\(510\) | 9.41113 | 0.416732 | ||||||||
\(511\) | 5.04532 | 0.223192 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.68075 | 0.118358 | ||||||||
\(514\) | 3.58404 | 0.158085 | ||||||||
\(515\) | 3.34440 | 0.147372 | ||||||||
\(516\) | 22.0729 | 0.971707 | ||||||||
\(517\) | 16.1249 | 0.709174 | ||||||||
\(518\) | 23.9906 | 1.05409 | ||||||||
\(519\) | 9.97023 | 0.437645 | ||||||||
\(520\) | 2.91920 | 0.128015 | ||||||||
\(521\) | 1.81383 | 0.0794653 | 0.0397326 | − | 0.999210i | \(-0.487349\pi\) | ||||
0.0397326 | + | 0.999210i | \(0.487349\pi\) | |||||||
\(522\) | 5.41270 | 0.236907 | ||||||||
\(523\) | 7.93604 | 0.347019 | 0.173509 | − | 0.984832i | \(-0.444489\pi\) | ||||
0.173509 | + | 0.984832i | \(0.444489\pi\) | |||||||
\(524\) | −6.24893 | −0.272986 | ||||||||
\(525\) | 22.5033 | 0.982126 | ||||||||
\(526\) | 18.3625 | 0.800642 | ||||||||
\(527\) | 7.76463 | 0.338233 | ||||||||
\(528\) | 10.5502 | 0.459140 | ||||||||
\(529\) | −11.9720 | −0.520521 | ||||||||
\(530\) | −1.12483 | −0.0488597 | ||||||||
\(531\) | −24.1030 | −1.04598 | ||||||||
\(532\) | 9.81072 | 0.425349 | ||||||||
\(533\) | −2.89945 | −0.125589 | ||||||||
\(534\) | 7.31670 | 0.316624 | ||||||||
\(535\) | 13.6607 | 0.590605 | ||||||||
\(536\) | 12.9905 | 0.561105 | ||||||||
\(537\) | −21.2834 | −0.918446 | ||||||||
\(538\) | −20.3637 | −0.877941 | ||||||||
\(539\) | −13.4449 | −0.579112 | ||||||||
\(540\) | 1.22542 | 0.0527336 | ||||||||
\(541\) | −2.53307 | −0.108905 | −0.0544526 | − | 0.998516i | \(-0.517341\pi\) | ||||
−0.0544526 | + | 0.998516i | \(0.517341\pi\) | |||||||
\(542\) | −17.5673 | −0.754582 | ||||||||
\(543\) | 18.2635 | 0.783760 | ||||||||
\(544\) | −2.79893 | −0.120003 | ||||||||
\(545\) | −20.6938 | −0.886426 | ||||||||
\(546\) | −15.4917 | −0.662982 | ||||||||
\(547\) | −35.8652 | −1.53349 | −0.766743 | − | 0.641955i | \(-0.778124\pi\) | ||||
−0.766743 | + | 0.641955i | \(0.778124\pi\) | |||||||
\(548\) | −1.77696 | −0.0759078 | ||||||||
\(549\) | −4.80846 | −0.205220 | ||||||||
\(550\) | −13.3053 | −0.567340 | ||||||||
\(551\) | −6.36348 | −0.271094 | ||||||||
\(552\) | 7.88346 | 0.335542 | ||||||||
\(553\) | −7.76303 | −0.330118 | ||||||||
\(554\) | 20.8347 | 0.885181 | ||||||||
\(555\) | 25.4766 | 1.08142 | ||||||||
\(556\) | 2.82872 | 0.119964 | ||||||||
\(557\) | 26.0462 | 1.10361 | 0.551806 | − | 0.833972i | \(-0.313939\pi\) | ||||
0.551806 | + | 0.833972i | \(0.313939\pi\) | |||||||
\(558\) | −7.31139 | −0.309516 | ||||||||
\(559\) | 19.1635 | 0.810528 | ||||||||
\(560\) | 4.48466 | 0.189511 | ||||||||
\(561\) | 29.5294 | 1.24673 | ||||||||
\(562\) | 8.01510 | 0.338097 | ||||||||
\(563\) | 18.4888 | 0.779210 | 0.389605 | − | 0.920982i | \(-0.372612\pi\) | ||||
0.389605 | + | 0.920982i | \(0.372612\pi\) | |||||||
\(564\) | 8.61336 | 0.362688 | ||||||||
\(565\) | 8.27051 | 0.347943 | ||||||||
\(566\) | 2.38474 | 0.100238 | ||||||||
\(567\) | −31.5377 | −1.32446 | ||||||||
\(568\) | −11.9626 | −0.501939 | ||||||||
\(569\) | −30.1733 | −1.26493 | −0.632464 | − | 0.774589i | \(-0.717957\pi\) | ||||
−0.632464 | + | 0.774589i | \(0.717957\pi\) | |||||||
\(570\) | 10.4184 | 0.436380 | ||||||||
\(571\) | −20.6712 | −0.865063 | −0.432532 | − | 0.901619i | \(-0.642380\pi\) | ||||
−0.432532 | + | 0.901619i | \(0.642380\pi\) | |||||||
\(572\) | 9.15959 | 0.382982 | ||||||||
\(573\) | −17.6768 | −0.738461 | ||||||||
\(574\) | −4.45433 | −0.185920 | ||||||||
\(575\) | −9.94213 | −0.414615 | ||||||||
\(576\) | 2.63555 | 0.109815 | ||||||||
\(577\) | −3.45409 | −0.143795 | −0.0718977 | − | 0.997412i | \(-0.522906\pi\) | ||||
−0.0718977 | + | 0.997412i | \(0.522906\pi\) | |||||||
\(578\) | 9.16598 | 0.381254 | ||||||||
\(579\) | 50.1887 | 2.08577 | ||||||||
\(580\) | −2.90886 | −0.120784 | ||||||||
\(581\) | 38.9889 | 1.61753 | ||||||||
\(582\) | 33.9496 | 1.40725 | ||||||||
\(583\) | −3.52940 | −0.146173 | ||||||||
\(584\) | −1.59346 | −0.0659378 | ||||||||
\(585\) | −7.69370 | −0.318095 | ||||||||
\(586\) | 12.7712 | 0.527572 | ||||||||
\(587\) | −35.2812 | −1.45621 | −0.728106 | − | 0.685465i | \(-0.759599\pi\) | ||||
−0.728106 | + | 0.685465i | \(0.759599\pi\) | |||||||
\(588\) | −7.18177 | −0.296171 | ||||||||
\(589\) | 8.59570 | 0.354180 | ||||||||
\(590\) | 12.9533 | 0.533279 | ||||||||
\(591\) | −16.8163 | −0.691730 | ||||||||
\(592\) | −7.57692 | −0.311409 | ||||||||
\(593\) | 23.6069 | 0.969419 | 0.484710 | − | 0.874675i | \(-0.338925\pi\) | ||||
0.484710 | + | 0.874675i | \(0.338925\pi\) | |||||||
\(594\) | 3.84501 | 0.157763 | ||||||||
\(595\) | 12.5523 | 0.514592 | ||||||||
\(596\) | −19.3924 | −0.794343 | ||||||||
\(597\) | 12.6443 | 0.517495 | ||||||||
\(598\) | 6.84433 | 0.279885 | ||||||||
\(599\) | −18.2746 | −0.746680 | −0.373340 | − | 0.927695i | \(-0.621787\pi\) | ||||
−0.373340 | + | 0.927695i | \(0.621787\pi\) | |||||||
\(600\) | −7.10721 | −0.290150 | ||||||||
\(601\) | 33.6960 | 1.37449 | 0.687244 | − | 0.726427i | \(-0.258820\pi\) | ||||
0.687244 | + | 0.726427i | \(0.258820\pi\) | |||||||
\(602\) | 29.4401 | 1.19989 | ||||||||
\(603\) | −34.2372 | −1.39425 | ||||||||
\(604\) | 2.69389 | 0.109613 | ||||||||
\(605\) | 12.3947 | 0.503916 | ||||||||
\(606\) | 11.3745 | 0.462058 | ||||||||
\(607\) | 30.7874 | 1.24962 | 0.624811 | − | 0.780776i | \(-0.285176\pi\) | ||||
0.624811 | + | 0.780776i | \(0.285176\pi\) | |||||||
\(608\) | −3.09851 | −0.125661 | ||||||||
\(609\) | 15.4368 | 0.625532 | ||||||||
\(610\) | 2.58414 | 0.104629 | ||||||||
\(611\) | 7.47801 | 0.302528 | ||||||||
\(612\) | 7.37673 | 0.298187 | ||||||||
\(613\) | 5.25178 | 0.212117 | 0.106059 | − | 0.994360i | \(-0.466177\pi\) | ||||
0.106059 | + | 0.994360i | \(0.466177\pi\) | |||||||
\(614\) | −34.6563 | −1.39862 | ||||||||
\(615\) | −4.73025 | −0.190742 | ||||||||
\(616\) | 14.0715 | 0.566959 | ||||||||
\(617\) | −19.5456 | −0.786877 | −0.393439 | − | 0.919351i | \(-0.628715\pi\) | ||||
−0.393439 | + | 0.919351i | \(0.628715\pi\) | |||||||
\(618\) | 5.60538 | 0.225482 | ||||||||
\(619\) | −7.80734 | −0.313804 | −0.156902 | − | 0.987614i | \(-0.550151\pi\) | ||||
−0.156902 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(620\) | 3.92925 | 0.157802 | ||||||||
\(621\) | 2.87311 | 0.115294 | ||||||||
\(622\) | 3.64803 | 0.146273 | ||||||||
\(623\) | 9.75876 | 0.390977 | ||||||||
\(624\) | 4.89272 | 0.195866 | ||||||||
\(625\) | −1.06757 | −0.0427026 | ||||||||
\(626\) | 26.1275 | 1.04426 | ||||||||
\(627\) | 32.6900 | 1.30551 | ||||||||
\(628\) | −5.91854 | −0.236176 | ||||||||
\(629\) | −21.2073 | −0.845590 | ||||||||
\(630\) | −11.8195 | −0.470902 | ||||||||
\(631\) | −18.3688 | −0.731250 | −0.365625 | − | 0.930762i | \(-0.619145\pi\) | ||||
−0.365625 | + | 0.930762i | \(0.619145\pi\) | |||||||
\(632\) | 2.45179 | 0.0975270 | ||||||||
\(633\) | −60.8458 | −2.41840 | ||||||||
\(634\) | 30.0238 | 1.19240 | ||||||||
\(635\) | −11.8903 | −0.471851 | ||||||||
\(636\) | −1.88528 | −0.0747561 | ||||||||
\(637\) | −6.23513 | −0.247045 | ||||||||
\(638\) | −9.12717 | −0.361348 | ||||||||
\(639\) | 31.5280 | 1.24723 | ||||||||
\(640\) | −1.41638 | −0.0559875 | ||||||||
\(641\) | −30.0907 | −1.18851 | −0.594256 | − | 0.804276i | \(-0.702554\pi\) | ||||
−0.594256 | + | 0.804276i | \(0.702554\pi\) | |||||||
\(642\) | 22.8961 | 0.903636 | ||||||||
\(643\) | −32.7097 | −1.28994 | −0.644972 | − | 0.764206i | \(-0.723131\pi\) | ||||
−0.644972 | + | 0.764206i | \(0.723131\pi\) | |||||||
\(644\) | 10.5147 | 0.414337 | ||||||||
\(645\) | 31.2638 | 1.23101 | ||||||||
\(646\) | −8.67252 | −0.341216 | ||||||||
\(647\) | −37.2113 | −1.46293 | −0.731464 | − | 0.681880i | \(-0.761163\pi\) | ||||
−0.731464 | + | 0.681880i | \(0.761163\pi\) | |||||||
\(648\) | 9.96052 | 0.391286 | ||||||||
\(649\) | 40.6437 | 1.59540 | ||||||||
\(650\) | −6.17039 | −0.242023 | ||||||||
\(651\) | −20.8518 | −0.817248 | ||||||||
\(652\) | −15.4816 | −0.606307 | ||||||||
\(653\) | −28.6940 | −1.12288 | −0.561441 | − | 0.827517i | \(-0.689753\pi\) | ||||
−0.561441 | + | 0.827517i | \(0.689753\pi\) | |||||||
\(654\) | −34.6839 | −1.35625 | ||||||||
\(655\) | −8.85089 | −0.345833 | ||||||||
\(656\) | 1.40681 | 0.0549265 | ||||||||
\(657\) | 4.19964 | 0.163844 | ||||||||
\(658\) | 11.4882 | 0.447857 | ||||||||
\(659\) | −46.5365 | −1.81280 | −0.906402 | − | 0.422417i | \(-0.861182\pi\) | ||||
−0.906402 | + | 0.422417i | \(0.861182\pi\) | |||||||
\(660\) | 14.9432 | 0.581663 | ||||||||
\(661\) | 4.42030 | 0.171930 | 0.0859650 | − | 0.996298i | \(-0.472603\pi\) | ||||
0.0859650 | + | 0.996298i | \(0.472603\pi\) | |||||||
\(662\) | −13.8025 | −0.536451 | ||||||||
\(663\) | 13.6944 | 0.531846 | ||||||||
\(664\) | −12.3138 | −0.477869 | ||||||||
\(665\) | 13.8958 | 0.538854 | ||||||||
\(666\) | 19.9694 | 0.773797 | ||||||||
\(667\) | −6.82010 | −0.264075 | ||||||||
\(668\) | 23.0706 | 0.892627 | ||||||||
\(669\) | 43.8786 | 1.69645 | ||||||||
\(670\) | 18.3996 | 0.710838 | ||||||||
\(671\) | 8.10827 | 0.313016 | ||||||||
\(672\) | 7.51651 | 0.289956 | ||||||||
\(673\) | −4.42534 | −0.170584 | −0.0852921 | − | 0.996356i | \(-0.527182\pi\) | ||||
−0.0852921 | + | 0.996356i | \(0.527182\pi\) | |||||||
\(674\) | 6.06005 | 0.233424 | ||||||||
\(675\) | −2.59020 | −0.0996970 | ||||||||
\(676\) | −8.75220 | −0.336623 | ||||||||
\(677\) | −0.302682 | −0.0116330 | −0.00581650 | − | 0.999983i | \(-0.501851\pi\) | ||||
−0.00581650 | + | 0.999983i | \(0.501851\pi\) | |||||||
\(678\) | 13.8618 | 0.532359 | ||||||||
\(679\) | 45.2808 | 1.73772 | ||||||||
\(680\) | −3.96437 | −0.152026 | ||||||||
\(681\) | −34.8939 | −1.33714 | ||||||||
\(682\) | 12.3288 | 0.472096 | ||||||||
\(683\) | −11.5143 | −0.440582 | −0.220291 | − | 0.975434i | \(-0.570701\pi\) | ||||
−0.220291 | + | 0.975434i | \(0.570701\pi\) | |||||||
\(684\) | 8.16628 | 0.312246 | ||||||||
\(685\) | −2.51685 | −0.0961640 | ||||||||
\(686\) | 12.5851 | 0.480501 | ||||||||
\(687\) | −27.0764 | −1.03303 | ||||||||
\(688\) | −9.29805 | −0.354485 | ||||||||
\(689\) | −1.63678 | −0.0623562 | ||||||||
\(690\) | 11.1660 | 0.425083 | ||||||||
\(691\) | 4.01475 | 0.152728 | 0.0763642 | − | 0.997080i | \(-0.475669\pi\) | ||||
0.0763642 | + | 0.997080i | \(0.475669\pi\) | |||||||
\(692\) | −4.19988 | −0.159656 | ||||||||
\(693\) | −37.0863 | −1.40879 | ||||||||
\(694\) | 28.5321 | 1.08306 | ||||||||
\(695\) | 4.00655 | 0.151977 | ||||||||
\(696\) | −4.87540 | −0.184802 | ||||||||
\(697\) | 3.93756 | 0.149146 | ||||||||
\(698\) | 1.92898 | 0.0730129 | ||||||||
\(699\) | 38.5334 | 1.45747 | ||||||||
\(700\) | −9.47935 | −0.358286 | ||||||||
\(701\) | −6.99361 | −0.264145 | −0.132073 | − | 0.991240i | \(-0.542163\pi\) | ||||
−0.132073 | + | 0.991240i | \(0.542163\pi\) | |||||||
\(702\) | 1.78314 | 0.0673003 | ||||||||
\(703\) | −23.4772 | −0.885458 | ||||||||
\(704\) | −4.44420 | −0.167497 | ||||||||
\(705\) | 12.1998 | 0.459472 | ||||||||
\(706\) | 14.1267 | 0.531664 | ||||||||
\(707\) | 15.1709 | 0.570562 | ||||||||
\(708\) | 21.7104 | 0.815926 | ||||||||
\(709\) | 6.11941 | 0.229819 | 0.114910 | − | 0.993376i | \(-0.463342\pi\) | ||||
0.114910 | + | 0.993376i | \(0.463342\pi\) | |||||||
\(710\) | −16.9436 | −0.635883 | ||||||||
\(711\) | −6.46182 | −0.242337 | ||||||||
\(712\) | −3.08210 | −0.115507 | ||||||||
\(713\) | 9.21249 | 0.345010 | ||||||||
\(714\) | 21.0382 | 0.787335 | ||||||||
\(715\) | 12.9735 | 0.485181 | ||||||||
\(716\) | 8.96546 | 0.335055 | ||||||||
\(717\) | 53.0847 | 1.98248 | ||||||||
\(718\) | 18.6111 | 0.694558 | ||||||||
\(719\) | 31.1963 | 1.16343 | 0.581714 | − | 0.813394i | \(-0.302382\pi\) | ||||
0.581714 | + | 0.813394i | \(0.302382\pi\) | |||||||
\(720\) | 3.73296 | 0.139119 | ||||||||
\(721\) | 7.47627 | 0.278431 | ||||||||
\(722\) | 9.39924 | 0.349803 | ||||||||
\(723\) | 56.7680 | 2.11122 | ||||||||
\(724\) | −7.69334 | −0.285921 | ||||||||
\(725\) | 6.14855 | 0.228351 | ||||||||
\(726\) | 20.7741 | 0.771000 | ||||||||
\(727\) | −13.7522 | −0.510040 | −0.255020 | − | 0.966936i | \(-0.582082\pi\) | ||||
−0.255020 | + | 0.966936i | \(0.582082\pi\) | |||||||
\(728\) | 6.52574 | 0.241860 | ||||||||
\(729\) | −20.0899 | −0.744070 | ||||||||
\(730\) | −2.25695 | −0.0835334 | ||||||||
\(731\) | −26.0246 | −0.962555 | ||||||||
\(732\) | 4.33115 | 0.160084 | ||||||||
\(733\) | −40.8649 | −1.50938 | −0.754690 | − | 0.656081i | \(-0.772213\pi\) | ||||
−0.754690 | + | 0.656081i | \(0.772213\pi\) | |||||||
\(734\) | −15.2361 | −0.562373 | ||||||||
\(735\) | −10.1721 | −0.375205 | ||||||||
\(736\) | −3.32085 | −0.122408 | ||||||||
\(737\) | 57.7325 | 2.12660 | ||||||||
\(738\) | −3.70771 | −0.136483 | ||||||||
\(739\) | −12.5626 | −0.462124 | −0.231062 | − | 0.972939i | \(-0.574220\pi\) | ||||
−0.231062 | + | 0.972939i | \(0.574220\pi\) | |||||||
\(740\) | −10.7318 | −0.394510 | ||||||||
\(741\) | 15.1601 | 0.556922 | ||||||||
\(742\) | −2.51452 | −0.0923109 | ||||||||
\(743\) | −24.3701 | −0.894052 | −0.447026 | − | 0.894521i | \(-0.647517\pi\) | ||||
−0.447026 | + | 0.894521i | \(0.647517\pi\) | |||||||
\(744\) | 6.58562 | 0.241440 | ||||||||
\(745\) | −27.4671 | −1.00632 | ||||||||
\(746\) | 24.8313 | 0.909140 | ||||||||
\(747\) | 32.4537 | 1.18742 | ||||||||
\(748\) | −12.4390 | −0.454816 | ||||||||
\(749\) | 30.5380 | 1.11584 | ||||||||
\(750\) | −26.8785 | −0.981466 | ||||||||
\(751\) | 23.3729 | 0.852888 | 0.426444 | − | 0.904514i | \(-0.359766\pi\) | ||||
0.426444 | + | 0.904514i | \(0.359766\pi\) | |||||||
\(752\) | −3.62831 | −0.132311 | ||||||||
\(753\) | −4.42999 | −0.161438 | ||||||||
\(754\) | −4.23277 | −0.154148 | ||||||||
\(755\) | 3.81558 | 0.138863 | ||||||||
\(756\) | 2.73937 | 0.0996301 | ||||||||
\(757\) | −13.2576 | −0.481857 | −0.240929 | − | 0.970543i | \(-0.577452\pi\) | ||||
−0.240929 | + | 0.970543i | \(0.577452\pi\) | |||||||
\(758\) | −28.0836 | −1.02004 | ||||||||
\(759\) | 35.0357 | 1.27172 | ||||||||
\(760\) | −4.38868 | −0.159194 | ||||||||
\(761\) | 0.800084 | 0.0290030 | 0.0145015 | − | 0.999895i | \(-0.495384\pi\) | ||||
0.0145015 | + | 0.999895i | \(0.495384\pi\) | |||||||
\(762\) | −19.9287 | −0.721941 | ||||||||
\(763\) | −46.2602 | −1.67473 | ||||||||
\(764\) | 7.44623 | 0.269395 | ||||||||
\(765\) | 10.4483 | 0.377759 | ||||||||
\(766\) | 21.3990 | 0.773178 | ||||||||
\(767\) | 18.8487 | 0.680587 | ||||||||
\(768\) | −2.37393 | −0.0856619 | ||||||||
\(769\) | 5.26194 | 0.189750 | 0.0948751 | − | 0.995489i | \(-0.469755\pi\) | ||||
0.0948751 | + | 0.995489i | \(0.469755\pi\) | |||||||
\(770\) | 19.9307 | 0.718253 | ||||||||
\(771\) | 8.50826 | 0.306418 | ||||||||
\(772\) | −21.1416 | −0.760903 | ||||||||
\(773\) | −43.2707 | −1.55634 | −0.778170 | − | 0.628053i | \(-0.783852\pi\) | ||||
−0.778170 | + | 0.628053i | \(0.783852\pi\) | |||||||
\(774\) | 24.5055 | 0.880832 | ||||||||
\(775\) | −8.30537 | −0.298338 | ||||||||
\(776\) | −14.3010 | −0.513375 | ||||||||
\(777\) | 56.9520 | 2.04314 | ||||||||
\(778\) | −9.28682 | −0.332949 | ||||||||
\(779\) | 4.35900 | 0.156177 | ||||||||
\(780\) | 6.92997 | 0.248133 | ||||||||
\(781\) | −53.1642 | −1.90236 | ||||||||
\(782\) | −9.29482 | −0.332382 | ||||||||
\(783\) | −1.77683 | −0.0634987 | ||||||||
\(784\) | 3.02526 | 0.108045 | ||||||||
\(785\) | −8.38294 | −0.299200 | ||||||||
\(786\) | −14.8345 | −0.529130 | ||||||||
\(787\) | −52.0113 | −1.85400 | −0.927001 | − | 0.375060i | \(-0.877622\pi\) | ||||
−0.927001 | + | 0.375060i | \(0.877622\pi\) | |||||||
\(788\) | 7.08373 | 0.252348 | ||||||||
\(789\) | 43.5913 | 1.55189 | ||||||||
\(790\) | 3.47268 | 0.123552 | ||||||||
\(791\) | 18.4884 | 0.657371 | ||||||||
\(792\) | 11.7129 | 0.416201 | ||||||||
\(793\) | 3.76025 | 0.133530 | ||||||||
\(794\) | 38.2160 | 1.35623 | ||||||||
\(795\) | −2.67028 | −0.0947050 | ||||||||
\(796\) | −5.32629 | −0.188786 | ||||||||
\(797\) | 18.4528 | 0.653633 | 0.326816 | − | 0.945088i | \(-0.394024\pi\) | ||||
0.326816 | + | 0.945088i | \(0.394024\pi\) | |||||||
\(798\) | 23.2900 | 0.824456 | ||||||||
\(799\) | −10.1554 | −0.359272 | ||||||||
\(800\) | 2.99385 | 0.105849 | ||||||||
\(801\) | 8.12304 | 0.287013 | ||||||||
\(802\) | −20.3989 | −0.720312 | ||||||||
\(803\) | −7.08165 | −0.249906 | ||||||||
\(804\) | 30.8386 | 1.08759 | ||||||||
\(805\) | 14.8928 | 0.524904 | ||||||||
\(806\) | 5.71756 | 0.201392 | ||||||||
\(807\) | −48.3420 | −1.70172 | ||||||||
\(808\) | −4.79143 | −0.168562 | ||||||||
\(809\) | 4.41714 | 0.155298 | 0.0776491 | − | 0.996981i | \(-0.475259\pi\) | ||||
0.0776491 | + | 0.996981i | \(0.475259\pi\) | |||||||
\(810\) | 14.1079 | 0.495702 | ||||||||
\(811\) | −34.8498 | −1.22374 | −0.611871 | − | 0.790957i | \(-0.709583\pi\) | ||||
−0.611871 | + | 0.790957i | \(0.709583\pi\) | |||||||
\(812\) | −6.50264 | −0.228198 | ||||||||
\(813\) | −41.7037 | −1.46261 | ||||||||
\(814\) | −33.6734 | −1.18025 | ||||||||
\(815\) | −21.9279 | −0.768101 | ||||||||
\(816\) | −6.64448 | −0.232603 | ||||||||
\(817\) | −28.8101 | −1.00794 | ||||||||
\(818\) | 17.0232 | 0.595201 | ||||||||
\(819\) | −17.1989 | −0.600980 | ||||||||
\(820\) | 1.99258 | 0.0695839 | ||||||||
\(821\) | 39.2890 | 1.37120 | 0.685598 | − | 0.727980i | \(-0.259541\pi\) | ||||
0.685598 | + | 0.727980i | \(0.259541\pi\) | |||||||
\(822\) | −4.21837 | −0.147133 | ||||||||
\(823\) | 27.3813 | 0.954453 | 0.477226 | − | 0.878780i | \(-0.341642\pi\) | ||||
0.477226 | + | 0.878780i | \(0.341642\pi\) | |||||||
\(824\) | −2.36122 | −0.0822571 | ||||||||
\(825\) | −31.5859 | −1.09968 | ||||||||
\(826\) | 28.9566 | 1.00753 | ||||||||
\(827\) | 15.9293 | 0.553917 | 0.276958 | − | 0.960882i | \(-0.410674\pi\) | ||||
0.276958 | + | 0.960882i | \(0.410674\pi\) | |||||||
\(828\) | 8.75226 | 0.304162 | ||||||||
\(829\) | 30.7171 | 1.06685 | 0.533425 | − | 0.845847i | \(-0.320905\pi\) | ||||
0.533425 | + | 0.845847i | \(0.320905\pi\) | |||||||
\(830\) | −17.4411 | −0.605390 | ||||||||
\(831\) | 49.4601 | 1.71575 | ||||||||
\(832\) | −2.06102 | −0.0714530 | ||||||||
\(833\) | 8.46751 | 0.293382 | ||||||||
\(834\) | 6.71518 | 0.232528 | ||||||||
\(835\) | 32.6768 | 1.13083 | ||||||||
\(836\) | −13.7704 | −0.476259 | ||||||||
\(837\) | 2.40011 | 0.0829600 | ||||||||
\(838\) | −19.8428 | −0.685457 | ||||||||
\(839\) | 31.6241 | 1.09179 | 0.545893 | − | 0.837855i | \(-0.316191\pi\) | ||||
0.545893 | + | 0.837855i | \(0.316191\pi\) | |||||||
\(840\) | 10.6463 | 0.367331 | ||||||||
\(841\) | −24.7822 | −0.854559 | ||||||||
\(842\) | −4.55232 | −0.156883 | ||||||||
\(843\) | 19.0273 | 0.655335 | ||||||||
\(844\) | 25.6308 | 0.882248 | ||||||||
\(845\) | −12.3965 | −0.426452 | ||||||||
\(846\) | 9.56260 | 0.328769 | ||||||||
\(847\) | 27.7078 | 0.952052 | ||||||||
\(848\) | 0.794159 | 0.0272715 | ||||||||
\(849\) | 5.66120 | 0.194292 | ||||||||
\(850\) | 8.37960 | 0.287418 | ||||||||
\(851\) | −25.1618 | −0.862535 | ||||||||
\(852\) | −28.3984 | −0.972912 | ||||||||
\(853\) | 13.4862 | 0.461760 | 0.230880 | − | 0.972982i | \(-0.425839\pi\) | ||||
0.230880 | + | 0.972982i | \(0.425839\pi\) | |||||||
\(854\) | 5.77674 | 0.197676 | ||||||||
\(855\) | 11.5666 | 0.395569 | ||||||||
\(856\) | −9.64480 | −0.329652 | ||||||||
\(857\) | −7.12007 | −0.243217 | −0.121608 | − | 0.992578i | \(-0.538805\pi\) | ||||
−0.121608 | + | 0.992578i | \(0.538805\pi\) | |||||||
\(858\) | 21.7442 | 0.742336 | ||||||||
\(859\) | −2.23156 | −0.0761397 | −0.0380699 | − | 0.999275i | \(-0.512121\pi\) | ||||
−0.0380699 | + | 0.999275i | \(0.512121\pi\) | |||||||
\(860\) | −13.1696 | −0.449080 | ||||||||
\(861\) | −10.5743 | −0.360370 | ||||||||
\(862\) | −8.09066 | −0.275569 | ||||||||
\(863\) | −6.11691 | −0.208222 | −0.104111 | − | 0.994566i | \(-0.533200\pi\) | ||||
−0.104111 | + | 0.994566i | \(0.533200\pi\) | |||||||
\(864\) | −0.865174 | −0.0294338 | ||||||||
\(865\) | −5.94865 | −0.202260 | ||||||||
\(866\) | 6.65044 | 0.225991 | ||||||||
\(867\) | 21.7594 | 0.738988 | ||||||||
\(868\) | 8.78367 | 0.298137 | ||||||||
\(869\) | 10.8963 | 0.369630 | ||||||||
\(870\) | −6.90544 | −0.234116 | ||||||||
\(871\) | 26.7737 | 0.907193 | ||||||||
\(872\) | 14.6103 | 0.494767 | ||||||||
\(873\) | 37.6910 | 1.27565 | ||||||||
\(874\) | −10.2897 | −0.348053 | ||||||||
\(875\) | −35.8497 | −1.21194 | ||||||||
\(876\) | −3.78276 | −0.127808 | ||||||||
\(877\) | −25.1912 | −0.850645 | −0.425323 | − | 0.905042i | \(-0.639839\pi\) | ||||
−0.425323 | + | 0.905042i | \(0.639839\pi\) | |||||||
\(878\) | 10.4721 | 0.353416 | ||||||||
\(879\) | 30.3179 | 1.02260 | ||||||||
\(880\) | −6.29470 | −0.212194 | ||||||||
\(881\) | 43.0782 | 1.45134 | 0.725671 | − | 0.688041i | \(-0.241529\pi\) | ||||
0.725671 | + | 0.688041i | \(0.241529\pi\) | |||||||
\(882\) | −7.97324 | −0.268473 | ||||||||
\(883\) | 47.7967 | 1.60849 | 0.804244 | − | 0.594300i | \(-0.202571\pi\) | ||||
0.804244 | + | 0.594300i | \(0.202571\pi\) | |||||||
\(884\) | −5.76866 | −0.194021 | ||||||||
\(885\) | 30.7503 | 1.03366 | ||||||||
\(886\) | 19.6743 | 0.660972 | ||||||||
\(887\) | 30.3822 | 1.02014 | 0.510068 | − | 0.860134i | \(-0.329620\pi\) | ||||
0.510068 | + | 0.860134i | \(0.329620\pi\) | |||||||
\(888\) | −17.9871 | −0.603607 | ||||||||
\(889\) | −26.5802 | −0.891472 | ||||||||
\(890\) | −4.36544 | −0.146330 | ||||||||
\(891\) | 44.2666 | 1.48299 | ||||||||
\(892\) | −18.4835 | −0.618874 | ||||||||
\(893\) | −11.2423 | −0.376211 | ||||||||
\(894\) | −46.0362 | −1.53968 | ||||||||
\(895\) | 12.6985 | 0.424465 | ||||||||
\(896\) | −3.16627 | −0.105778 | ||||||||
\(897\) | 16.2480 | 0.542504 | ||||||||
\(898\) | −39.1663 | −1.30699 | ||||||||
\(899\) | −5.69732 | −0.190016 | ||||||||
\(900\) | −7.89046 | −0.263015 | ||||||||
\(901\) | 2.22280 | 0.0740521 | ||||||||
\(902\) | 6.25213 | 0.208173 | ||||||||
\(903\) | 69.8888 | 2.32576 | ||||||||
\(904\) | −5.83917 | −0.194208 | ||||||||
\(905\) | −10.8967 | −0.362219 | ||||||||
\(906\) | 6.39510 | 0.212463 | ||||||||
\(907\) | 11.0060 | 0.365450 | 0.182725 | − | 0.983164i | \(-0.441508\pi\) | ||||
0.182725 | + | 0.983164i | \(0.441508\pi\) | |||||||
\(908\) | 14.6988 | 0.487796 | ||||||||
\(909\) | 12.6281 | 0.418846 | ||||||||
\(910\) | 9.24296 | 0.306401 | ||||||||
\(911\) | 1.41592 | 0.0469115 | 0.0234558 | − | 0.999725i | \(-0.492533\pi\) | ||||
0.0234558 | + | 0.999725i | \(0.492533\pi\) | |||||||
\(912\) | −7.35565 | −0.243570 | ||||||||
\(913\) | −54.7251 | −1.81114 | ||||||||
\(914\) | −10.3078 | −0.340952 | ||||||||
\(915\) | 6.13457 | 0.202803 | ||||||||
\(916\) | 11.4057 | 0.376855 | ||||||||
\(917\) | −19.7858 | −0.653384 | ||||||||
\(918\) | −2.42156 | −0.0799235 | ||||||||
\(919\) | −16.3417 | −0.539061 | −0.269531 | − | 0.962992i | \(-0.586869\pi\) | ||||
−0.269531 | + | 0.962992i | \(0.586869\pi\) | |||||||
\(920\) | −4.70359 | −0.155073 | ||||||||
\(921\) | −82.2718 | −2.71095 | ||||||||
\(922\) | −23.9079 | −0.787366 | ||||||||
\(923\) | −24.6551 | −0.811534 | ||||||||
\(924\) | 33.4049 | 1.09894 | ||||||||
\(925\) | 22.6842 | 0.745852 | ||||||||
\(926\) | 10.6920 | 0.351360 | ||||||||
\(927\) | 6.22313 | 0.204394 | ||||||||
\(928\) | 2.05372 | 0.0674168 | ||||||||
\(929\) | 35.1659 | 1.15376 | 0.576878 | − | 0.816830i | \(-0.304271\pi\) | ||||
0.576878 | + | 0.816830i | \(0.304271\pi\) | |||||||
\(930\) | 9.32777 | 0.305870 | ||||||||
\(931\) | 9.37381 | 0.307214 | ||||||||
\(932\) | −16.2319 | −0.531694 | ||||||||
\(933\) | 8.66017 | 0.283521 | ||||||||
\(934\) | 22.5874 | 0.739082 | ||||||||
\(935\) | −17.6184 | −0.576185 | ||||||||
\(936\) | 5.43192 | 0.177548 | ||||||||
\(937\) | 14.7129 | 0.480649 | 0.240325 | − | 0.970693i | \(-0.422746\pi\) | ||||
0.240325 | + | 0.970693i | \(0.422746\pi\) | |||||||
\(938\) | 41.1315 | 1.34299 | ||||||||
\(939\) | 62.0249 | 2.02411 | ||||||||
\(940\) | −5.13908 | −0.167618 | ||||||||
\(941\) | 55.0972 | 1.79612 | 0.898059 | − | 0.439874i | \(-0.144977\pi\) | ||||
0.898059 | + | 0.439874i | \(0.144977\pi\) | |||||||
\(942\) | −14.0502 | −0.457781 | ||||||||
\(943\) | 4.67179 | 0.152134 | ||||||||
\(944\) | −9.14533 | −0.297655 | ||||||||
\(945\) | 3.88001 | 0.126217 | ||||||||
\(946\) | −41.3224 | −1.34351 | ||||||||
\(947\) | 10.8074 | 0.351192 | 0.175596 | − | 0.984462i | \(-0.443815\pi\) | ||||
0.175596 | + | 0.984462i | \(0.443815\pi\) | |||||||
\(948\) | 5.82038 | 0.189037 | ||||||||
\(949\) | −3.28415 | −0.106608 | ||||||||
\(950\) | 9.27649 | 0.300969 | ||||||||
\(951\) | 71.2743 | 2.31123 | ||||||||
\(952\) | −8.86218 | −0.287225 | ||||||||
\(953\) | −19.5550 | −0.633449 | −0.316724 | − | 0.948518i | \(-0.602583\pi\) | ||||
−0.316724 | + | 0.948518i | \(0.602583\pi\) | |||||||
\(954\) | −2.09305 | −0.0677649 | ||||||||
\(955\) | 10.5467 | 0.341284 | ||||||||
\(956\) | −22.3615 | −0.723223 | ||||||||
\(957\) | −21.6673 | −0.700403 | ||||||||
\(958\) | 35.9701 | 1.16214 | ||||||||
\(959\) | −5.62632 | −0.181683 | ||||||||
\(960\) | −3.36240 | −0.108521 | ||||||||
\(961\) | −23.3041 | −0.751747 | ||||||||
\(962\) | −15.6162 | −0.503486 | ||||||||
\(963\) | 25.4194 | 0.819127 | ||||||||
\(964\) | −23.9131 | −0.770188 | ||||||||
\(965\) | −29.9446 | −0.963952 | ||||||||
\(966\) | 24.9612 | 0.803112 | ||||||||
\(967\) | −41.7434 | −1.34238 | −0.671189 | − | 0.741287i | \(-0.734216\pi\) | ||||
−0.671189 | + | 0.741287i | \(0.734216\pi\) | |||||||
\(968\) | −8.75093 | −0.281266 | ||||||||
\(969\) | −20.5880 | −0.661381 | ||||||||
\(970\) | −20.2557 | −0.650371 | ||||||||
\(971\) | 20.1226 | 0.645765 | 0.322882 | − | 0.946439i | \(-0.395348\pi\) | ||||
0.322882 | + | 0.946439i | \(0.395348\pi\) | |||||||
\(972\) | 21.0501 | 0.675182 | ||||||||
\(973\) | 8.95648 | 0.287131 | ||||||||
\(974\) | −24.2832 | −0.778084 | ||||||||
\(975\) | −14.6481 | −0.469114 | ||||||||
\(976\) | −1.82446 | −0.0583996 | ||||||||
\(977\) | −7.04950 | −0.225534 | −0.112767 | − | 0.993621i | \(-0.535971\pi\) | ||||
−0.112767 | + | 0.993621i | \(0.535971\pi\) | |||||||
\(978\) | −36.7523 | −1.17521 | ||||||||
\(979\) | −13.6975 | −0.437773 | ||||||||
\(980\) | 4.28494 | 0.136877 | ||||||||
\(981\) | −38.5062 | −1.22941 | ||||||||
\(982\) | 18.0957 | 0.577457 | ||||||||
\(983\) | 19.8434 | 0.632906 | 0.316453 | − | 0.948608i | \(-0.397508\pi\) | ||||
0.316453 | + | 0.948608i | \(0.397508\pi\) | |||||||
\(984\) | 3.33966 | 0.106465 | ||||||||
\(985\) | 10.0333 | 0.319687 | ||||||||
\(986\) | 5.74824 | 0.183061 | ||||||||
\(987\) | 27.2722 | 0.868084 | ||||||||
\(988\) | −6.38609 | −0.203169 | ||||||||
\(989\) | −30.8774 | −0.981843 | ||||||||
\(990\) | 16.5900 | 0.527265 | ||||||||
\(991\) | 47.9333 | 1.52265 | 0.761325 | − | 0.648370i | \(-0.224549\pi\) | ||||
0.761325 | + | 0.648370i | \(0.224549\pi\) | |||||||
\(992\) | −2.77414 | −0.0880790 | ||||||||
\(993\) | −32.7663 | −1.03981 | ||||||||
\(994\) | −37.8768 | −1.20138 | ||||||||
\(995\) | −7.54408 | −0.239164 | ||||||||
\(996\) | −29.2322 | −0.926257 | ||||||||
\(997\) | −21.9692 | −0.695773 | −0.347886 | − | 0.937537i | \(-0.613101\pi\) | ||||
−0.347886 | + | 0.937537i | \(0.613101\pi\) | |||||||
\(998\) | −30.2498 | −0.957542 | ||||||||
\(999\) | −6.55535 | −0.207402 |
(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 | 4022.2.a.d.1.6 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.d.1.6 | ✓ | 37 | 1.1 | even | 1 | trivial |