Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15299 | −0.815288 | −0.407644 | − | 0.913141i | \(-0.633650\pi\) | ||||
−0.407644 | + | 0.913141i | \(0.633650\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.670610 | −0.335305 | ||||||||
\(5\) | 0.489993 | 0.219131 | 0.109566 | − | 0.993980i | \(-0.465054\pi\) | ||||
0.109566 | + | 0.993980i | \(0.465054\pi\) | |||||||
\(6\) | 1.15299 | 0.470707 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.07919 | 1.08866 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.564958 | −0.178655 | ||||||||
\(11\) | 1.66126 | 0.500888 | 0.250444 | − | 0.968131i | \(-0.419423\pi\) | ||||
0.250444 | + | 0.968131i | \(0.419423\pi\) | |||||||
\(12\) | 0.670610 | 0.193588 | ||||||||
\(13\) | −2.35343 | −0.652723 | −0.326362 | − | 0.945245i | \(-0.605823\pi\) | ||||
−0.326362 | + | 0.945245i | \(0.605823\pi\) | |||||||
\(14\) | 1.15299 | 0.308150 | ||||||||
\(15\) | −0.489993 | −0.126516 | ||||||||
\(16\) | −2.20906 | −0.552266 | ||||||||
\(17\) | 3.53643 | 0.857709 | 0.428855 | − | 0.903373i | \(-0.358917\pi\) | ||||
0.428855 | + | 0.903373i | \(0.358917\pi\) | |||||||
\(18\) | −1.15299 | −0.271763 | ||||||||
\(19\) | 4.21017 | 0.965880 | 0.482940 | − | 0.875654i | \(-0.339569\pi\) | ||||
0.482940 | + | 0.875654i | \(0.339569\pi\) | |||||||
\(20\) | −0.328594 | −0.0734758 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.91542 | −0.408368 | ||||||||
\(23\) | 7.68558 | 1.60255 | 0.801277 | − | 0.598293i | \(-0.204154\pi\) | ||||
0.801277 | + | 0.598293i | \(0.204154\pi\) | |||||||
\(24\) | −3.07919 | −0.628537 | ||||||||
\(25\) | −4.75991 | −0.951981 | ||||||||
\(26\) | 2.71348 | 0.532158 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.670610 | 0.126733 | ||||||||
\(29\) | 5.40181 | 1.00309 | 0.501545 | − | 0.865131i | \(-0.332765\pi\) | ||||
0.501545 | + | 0.865131i | \(0.332765\pi\) | |||||||
\(30\) | 0.564958 | 0.103147 | ||||||||
\(31\) | 6.30168 | 1.13182 | 0.565908 | − | 0.824469i | \(-0.308526\pi\) | ||||
0.565908 | + | 0.824469i | \(0.308526\pi\) | |||||||
\(32\) | −3.61135 | −0.638403 | ||||||||
\(33\) | −1.66126 | −0.289188 | ||||||||
\(34\) | −4.07747 | −0.699281 | ||||||||
\(35\) | −0.489993 | −0.0828239 | ||||||||
\(36\) | −0.670610 | −0.111768 | ||||||||
\(37\) | −9.09193 | −1.49470 | −0.747352 | − | 0.664428i | \(-0.768675\pi\) | ||||
−0.747352 | + | 0.664428i | \(0.768675\pi\) | |||||||
\(38\) | −4.85429 | −0.787470 | ||||||||
\(39\) | 2.35343 | 0.376850 | ||||||||
\(40\) | 1.50878 | 0.238559 | ||||||||
\(41\) | −3.34227 | −0.521975 | −0.260988 | − | 0.965342i | \(-0.584048\pi\) | ||||
−0.260988 | + | 0.965342i | \(0.584048\pi\) | |||||||
\(42\) | −1.15299 | −0.177911 | ||||||||
\(43\) | 8.34436 | 1.27250 | 0.636251 | − | 0.771482i | \(-0.280484\pi\) | ||||
0.636251 | + | 0.771482i | \(0.280484\pi\) | |||||||
\(44\) | −1.11406 | −0.167950 | ||||||||
\(45\) | 0.489993 | 0.0730438 | ||||||||
\(46\) | −8.86141 | −1.30654 | ||||||||
\(47\) | 2.83247 | 0.413158 | 0.206579 | − | 0.978430i | \(-0.433767\pi\) | ||||
0.206579 | + | 0.978430i | \(0.433767\pi\) | |||||||
\(48\) | 2.20906 | 0.318851 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.48813 | 0.776139 | ||||||||
\(51\) | −3.53643 | −0.495199 | ||||||||
\(52\) | 1.57823 | 0.218861 | ||||||||
\(53\) | 3.98738 | 0.547709 | 0.273854 | − | 0.961771i | \(-0.411701\pi\) | ||||
0.273854 | + | 0.961771i | \(0.411701\pi\) | |||||||
\(54\) | 1.15299 | 0.156902 | ||||||||
\(55\) | 0.814005 | 0.109760 | ||||||||
\(56\) | −3.07919 | −0.411474 | ||||||||
\(57\) | −4.21017 | −0.557651 | ||||||||
\(58\) | −6.22824 | −0.817808 | ||||||||
\(59\) | 12.4932 | 1.62648 | 0.813241 | − | 0.581927i | \(-0.197701\pi\) | ||||
0.813241 | + | 0.581927i | \(0.197701\pi\) | |||||||
\(60\) | 0.328594 | 0.0424213 | ||||||||
\(61\) | 11.1893 | 1.43265 | 0.716323 | − | 0.697769i | \(-0.245824\pi\) | ||||
0.716323 | + | 0.697769i | \(0.245824\pi\) | |||||||
\(62\) | −7.26579 | −0.922756 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 8.58198 | 1.07275 | ||||||||
\(65\) | −1.15316 | −0.143032 | ||||||||
\(66\) | 1.91542 | 0.235772 | ||||||||
\(67\) | 2.79602 | 0.341588 | 0.170794 | − | 0.985307i | \(-0.445367\pi\) | ||||
0.170794 | + | 0.985307i | \(0.445367\pi\) | |||||||
\(68\) | −2.37156 | −0.287594 | ||||||||
\(69\) | −7.68558 | −0.925235 | ||||||||
\(70\) | 0.564958 | 0.0675253 | ||||||||
\(71\) | 10.9437 | 1.29878 | 0.649392 | − | 0.760454i | \(-0.275024\pi\) | ||||
0.649392 | + | 0.760454i | \(0.275024\pi\) | |||||||
\(72\) | 3.07919 | 0.362886 | ||||||||
\(73\) | −10.2725 | −1.20231 | −0.601154 | − | 0.799133i | \(-0.705292\pi\) | ||||
−0.601154 | + | 0.799133i | \(0.705292\pi\) | |||||||
\(74\) | 10.4829 | 1.21861 | ||||||||
\(75\) | 4.75991 | 0.549627 | ||||||||
\(76\) | −2.82338 | −0.323864 | ||||||||
\(77\) | −1.66126 | −0.189318 | ||||||||
\(78\) | −2.71348 | −0.307241 | ||||||||
\(79\) | −16.3957 | −1.84466 | −0.922331 | − | 0.386401i | \(-0.873718\pi\) | ||||
−0.922331 | + | 0.386401i | \(0.873718\pi\) | |||||||
\(80\) | −1.08242 | −0.121019 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.85361 | 0.425560 | ||||||||
\(83\) | 13.2813 | 1.45781 | 0.728907 | − | 0.684613i | \(-0.240029\pi\) | ||||
0.728907 | + | 0.684613i | \(0.240029\pi\) | |||||||
\(84\) | −0.670610 | −0.0731695 | ||||||||
\(85\) | 1.73282 | 0.187951 | ||||||||
\(86\) | −9.62098 | −1.03746 | ||||||||
\(87\) | −5.40181 | −0.579134 | ||||||||
\(88\) | 5.11533 | 0.545296 | ||||||||
\(89\) | 2.37465 | 0.251712 | 0.125856 | − | 0.992048i | \(-0.459832\pi\) | ||||
0.125856 | + | 0.992048i | \(0.459832\pi\) | |||||||
\(90\) | −0.564958 | −0.0595518 | ||||||||
\(91\) | 2.35343 | 0.246706 | ||||||||
\(92\) | −5.15403 | −0.537344 | ||||||||
\(93\) | −6.30168 | −0.653454 | ||||||||
\(94\) | −3.26581 | −0.336843 | ||||||||
\(95\) | 2.06295 | 0.211655 | ||||||||
\(96\) | 3.61135 | 0.368582 | ||||||||
\(97\) | 0.810176 | 0.0822609 | 0.0411305 | − | 0.999154i | \(-0.486904\pi\) | ||||
0.0411305 | + | 0.999154i | \(0.486904\pi\) | |||||||
\(98\) | −1.15299 | −0.116470 | ||||||||
\(99\) | 1.66126 | 0.166963 | ||||||||
\(100\) | 3.19204 | 0.319204 | ||||||||
\(101\) | −17.1527 | −1.70676 | −0.853378 | − | 0.521292i | \(-0.825450\pi\) | ||||
−0.853378 | + | 0.521292i | \(0.825450\pi\) | |||||||
\(102\) | 4.07747 | 0.403730 | ||||||||
\(103\) | −18.2308 | −1.79633 | −0.898167 | − | 0.439655i | \(-0.855101\pi\) | ||||
−0.898167 | + | 0.439655i | \(0.855101\pi\) | |||||||
\(104\) | −7.24665 | −0.710593 | ||||||||
\(105\) | 0.489993 | 0.0478184 | ||||||||
\(106\) | −4.59742 | −0.446540 | ||||||||
\(107\) | 6.63153 | 0.641094 | 0.320547 | − | 0.947233i | \(-0.396133\pi\) | ||||
0.320547 | + | 0.947233i | \(0.396133\pi\) | |||||||
\(108\) | 0.670610 | 0.0645295 | ||||||||
\(109\) | −14.8320 | −1.42065 | −0.710324 | − | 0.703875i | \(-0.751452\pi\) | ||||
−0.710324 | + | 0.703875i | \(0.751452\pi\) | |||||||
\(110\) | −0.938541 | −0.0894863 | ||||||||
\(111\) | 9.09193 | 0.862968 | ||||||||
\(112\) | 2.20906 | 0.208737 | ||||||||
\(113\) | 10.9562 | 1.03067 | 0.515337 | − | 0.856988i | \(-0.327667\pi\) | ||||
0.515337 | + | 0.856988i | \(0.327667\pi\) | |||||||
\(114\) | 4.85429 | 0.454646 | ||||||||
\(115\) | 3.76588 | 0.351170 | ||||||||
\(116\) | −3.62250 | −0.336341 | ||||||||
\(117\) | −2.35343 | −0.217574 | ||||||||
\(118\) | −14.4046 | −1.32605 | ||||||||
\(119\) | −3.53643 | −0.324184 | ||||||||
\(120\) | −1.50878 | −0.137732 | ||||||||
\(121\) | −8.24022 | −0.749111 | ||||||||
\(122\) | −12.9012 | −1.16802 | ||||||||
\(123\) | 3.34227 | 0.301362 | ||||||||
\(124\) | −4.22597 | −0.379503 | ||||||||
\(125\) | −4.78228 | −0.427740 | ||||||||
\(126\) | 1.15299 | 0.102717 | ||||||||
\(127\) | 8.25401 | 0.732425 | 0.366213 | − | 0.930531i | \(-0.380654\pi\) | ||||
0.366213 | + | 0.930531i | \(0.380654\pi\) | |||||||
\(128\) | −2.67226 | −0.236196 | ||||||||
\(129\) | −8.34436 | −0.734680 | ||||||||
\(130\) | 1.32959 | 0.116612 | ||||||||
\(131\) | −21.0890 | −1.84255 | −0.921275 | − | 0.388911i | \(-0.872851\pi\) | ||||
−0.921275 | + | 0.388911i | \(0.872851\pi\) | |||||||
\(132\) | 1.11406 | 0.0969662 | ||||||||
\(133\) | −4.21017 | −0.365068 | ||||||||
\(134\) | −3.22379 | −0.278493 | ||||||||
\(135\) | −0.489993 | −0.0421719 | ||||||||
\(136\) | 10.8893 | 0.933753 | ||||||||
\(137\) | 18.9167 | 1.61616 | 0.808081 | − | 0.589071i | \(-0.200506\pi\) | ||||
0.808081 | + | 0.589071i | \(0.200506\pi\) | |||||||
\(138\) | 8.86141 | 0.754333 | ||||||||
\(139\) | −9.55723 | −0.810634 | −0.405317 | − | 0.914176i | \(-0.632839\pi\) | ||||
−0.405317 | + | 0.914176i | \(0.632839\pi\) | |||||||
\(140\) | 0.328594 | 0.0277713 | ||||||||
\(141\) | −2.83247 | −0.238537 | ||||||||
\(142\) | −12.6180 | −1.05888 | ||||||||
\(143\) | −3.90965 | −0.326941 | ||||||||
\(144\) | −2.20906 | −0.184089 | ||||||||
\(145\) | 2.64685 | 0.219809 | ||||||||
\(146\) | 11.8441 | 0.980227 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 6.09714 | 0.501182 | ||||||||
\(149\) | 4.15137 | 0.340093 | 0.170047 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170047 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(150\) | −5.48813 | −0.448104 | ||||||||
\(151\) | 0.748490 | 0.0609112 | 0.0304556 | − | 0.999536i | \(-0.490304\pi\) | ||||
0.0304556 | + | 0.999536i | \(0.490304\pi\) | |||||||
\(152\) | 12.9639 | 1.05151 | ||||||||
\(153\) | 3.53643 | 0.285903 | ||||||||
\(154\) | 1.91542 | 0.154349 | ||||||||
\(155\) | 3.08778 | 0.248016 | ||||||||
\(156\) | −1.57823 | −0.126360 | ||||||||
\(157\) | 18.2085 | 1.45320 | 0.726600 | − | 0.687061i | \(-0.241100\pi\) | ||||
0.726600 | + | 0.687061i | \(0.241100\pi\) | |||||||
\(158\) | 18.9041 | 1.50393 | ||||||||
\(159\) | −3.98738 | −0.316220 | ||||||||
\(160\) | −1.76954 | −0.139894 | ||||||||
\(161\) | −7.68558 | −0.605709 | ||||||||
\(162\) | −1.15299 | −0.0905876 | ||||||||
\(163\) | 19.3114 | 1.51259 | 0.756293 | − | 0.654233i | \(-0.227009\pi\) | ||||
0.756293 | + | 0.654233i | \(0.227009\pi\) | |||||||
\(164\) | 2.24136 | 0.175021 | ||||||||
\(165\) | −0.814005 | −0.0633702 | ||||||||
\(166\) | −15.3132 | −1.18854 | ||||||||
\(167\) | 6.14235 | 0.475309 | 0.237655 | − | 0.971350i | \(-0.423621\pi\) | ||||
0.237655 | + | 0.971350i | \(0.423621\pi\) | |||||||
\(168\) | 3.07919 | 0.237565 | ||||||||
\(169\) | −7.46138 | −0.573953 | ||||||||
\(170\) | −1.99793 | −0.153234 | ||||||||
\(171\) | 4.21017 | 0.321960 | ||||||||
\(172\) | −5.59581 | −0.426676 | ||||||||
\(173\) | 0.0491798 | 0.00373907 | 0.00186954 | − | 0.999998i | \(-0.499405\pi\) | ||||
0.00186954 | + | 0.999998i | \(0.499405\pi\) | |||||||
\(174\) | 6.22824 | 0.472162 | ||||||||
\(175\) | 4.75991 | 0.359815 | ||||||||
\(176\) | −3.66983 | −0.276623 | ||||||||
\(177\) | −12.4932 | −0.939050 | ||||||||
\(178\) | −2.73795 | −0.205218 | ||||||||
\(179\) | −15.3656 | −1.14848 | −0.574241 | − | 0.818687i | \(-0.694703\pi\) | ||||
−0.574241 | + | 0.818687i | \(0.694703\pi\) | |||||||
\(180\) | −0.328594 | −0.0244919 | ||||||||
\(181\) | 15.2957 | 1.13692 | 0.568460 | − | 0.822711i | \(-0.307539\pi\) | ||||
0.568460 | + | 0.822711i | \(0.307539\pi\) | |||||||
\(182\) | −2.71348 | −0.201137 | ||||||||
\(183\) | −11.1893 | −0.827138 | ||||||||
\(184\) | 23.6654 | 1.74463 | ||||||||
\(185\) | −4.45498 | −0.327537 | ||||||||
\(186\) | 7.26579 | 0.532753 | ||||||||
\(187\) | 5.87492 | 0.429617 | ||||||||
\(188\) | −1.89948 | −0.138534 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −2.37857 | −0.172559 | ||||||||
\(191\) | 11.2686 | 0.815368 | 0.407684 | − | 0.913123i | \(-0.366337\pi\) | ||||
0.407684 | + | 0.913123i | \(0.366337\pi\) | |||||||
\(192\) | −8.58198 | −0.619351 | ||||||||
\(193\) | −2.49259 | −0.179420 | −0.0897102 | − | 0.995968i | \(-0.528594\pi\) | ||||
−0.0897102 | + | 0.995968i | \(0.528594\pi\) | |||||||
\(194\) | −0.934126 | −0.0670664 | ||||||||
\(195\) | 1.15316 | 0.0825796 | ||||||||
\(196\) | −0.670610 | −0.0479007 | ||||||||
\(197\) | −18.2325 | −1.29901 | −0.649506 | − | 0.760356i | \(-0.725024\pi\) | ||||
−0.649506 | + | 0.760356i | \(0.725024\pi\) | |||||||
\(198\) | −1.91542 | −0.136123 | ||||||||
\(199\) | −7.36296 | −0.521946 | −0.260973 | − | 0.965346i | \(-0.584043\pi\) | ||||
−0.260973 | + | 0.965346i | \(0.584043\pi\) | |||||||
\(200\) | −14.6567 | −1.03638 | ||||||||
\(201\) | −2.79602 | −0.197216 | ||||||||
\(202\) | 19.7769 | 1.39150 | ||||||||
\(203\) | −5.40181 | −0.379132 | ||||||||
\(204\) | 2.37156 | 0.166043 | ||||||||
\(205\) | −1.63769 | −0.114381 | ||||||||
\(206\) | 21.0200 | 1.46453 | ||||||||
\(207\) | 7.68558 | 0.534185 | ||||||||
\(208\) | 5.19887 | 0.360477 | ||||||||
\(209\) | 6.99418 | 0.483798 | ||||||||
\(210\) | −0.564958 | −0.0389858 | ||||||||
\(211\) | −20.3317 | −1.39969 | −0.699847 | − | 0.714293i | \(-0.746749\pi\) | ||||
−0.699847 | + | 0.714293i | \(0.746749\pi\) | |||||||
\(212\) | −2.67398 | −0.183649 | ||||||||
\(213\) | −10.9437 | −0.749853 | ||||||||
\(214\) | −7.64610 | −0.522677 | ||||||||
\(215\) | 4.08867 | 0.278845 | ||||||||
\(216\) | −3.07919 | −0.209512 | ||||||||
\(217\) | −6.30168 | −0.427786 | ||||||||
\(218\) | 17.1012 | 1.15824 | ||||||||
\(219\) | 10.2725 | 0.694153 | ||||||||
\(220\) | −0.545879 | −0.0368032 | ||||||||
\(221\) | −8.32272 | −0.559847 | ||||||||
\(222\) | −10.4829 | −0.703568 | ||||||||
\(223\) | 26.3274 | 1.76302 | 0.881508 | − | 0.472169i | \(-0.156529\pi\) | ||||
0.881508 | + | 0.472169i | \(0.156529\pi\) | |||||||
\(224\) | 3.61135 | 0.241294 | ||||||||
\(225\) | −4.75991 | −0.317327 | ||||||||
\(226\) | −12.6324 | −0.840296 | ||||||||
\(227\) | −27.1964 | −1.80509 | −0.902544 | − | 0.430599i | \(-0.858302\pi\) | ||||
−0.902544 | + | 0.430599i | \(0.858302\pi\) | |||||||
\(228\) | 2.82338 | 0.186983 | ||||||||
\(229\) | −1.78613 | −0.118031 | −0.0590153 | − | 0.998257i | \(-0.518796\pi\) | ||||
−0.0590153 | + | 0.998257i | \(0.518796\pi\) | |||||||
\(230\) | −4.34203 | −0.286305 | ||||||||
\(231\) | 1.66126 | 0.109303 | ||||||||
\(232\) | 16.6332 | 1.09202 | ||||||||
\(233\) | −21.8254 | −1.42983 | −0.714915 | − | 0.699212i | \(-0.753534\pi\) | ||||
−0.714915 | + | 0.699212i | \(0.753534\pi\) | |||||||
\(234\) | 2.71348 | 0.177386 | ||||||||
\(235\) | 1.38789 | 0.0905358 | ||||||||
\(236\) | −8.37809 | −0.545367 | ||||||||
\(237\) | 16.3957 | 1.06502 | ||||||||
\(238\) | 4.07747 | 0.264303 | ||||||||
\(239\) | 19.7241 | 1.27585 | 0.637923 | − | 0.770100i | \(-0.279794\pi\) | ||||
0.637923 | + | 0.770100i | \(0.279794\pi\) | |||||||
\(240\) | 1.08242 | 0.0698702 | ||||||||
\(241\) | 20.1026 | 1.29492 | 0.647461 | − | 0.762099i | \(-0.275831\pi\) | ||||
0.647461 | + | 0.762099i | \(0.275831\pi\) | |||||||
\(242\) | 9.50091 | 0.610741 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.50367 | −0.480373 | ||||||||
\(245\) | 0.489993 | 0.0313045 | ||||||||
\(246\) | −3.85361 | −0.245697 | ||||||||
\(247\) | −9.90833 | −0.630452 | ||||||||
\(248\) | 19.4041 | 1.23216 | ||||||||
\(249\) | −13.2813 | −0.841669 | ||||||||
\(250\) | 5.51393 | 0.348732 | ||||||||
\(251\) | −12.9654 | −0.818369 | −0.409185 | − | 0.912452i | \(-0.634187\pi\) | ||||
−0.409185 | + | 0.912452i | \(0.634187\pi\) | |||||||
\(252\) | 0.670610 | 0.0422444 | ||||||||
\(253\) | 12.7677 | 0.802701 | ||||||||
\(254\) | −9.51681 | −0.597138 | ||||||||
\(255\) | −1.73282 | −0.108514 | ||||||||
\(256\) | −14.0829 | −0.880180 | ||||||||
\(257\) | 22.9838 | 1.43369 | 0.716844 | − | 0.697234i | \(-0.245586\pi\) | ||||
0.716844 | + | 0.697234i | \(0.245586\pi\) | |||||||
\(258\) | 9.62098 | 0.598976 | ||||||||
\(259\) | 9.09193 | 0.564945 | ||||||||
\(260\) | 0.773322 | 0.0479594 | ||||||||
\(261\) | 5.40181 | 0.334363 | ||||||||
\(262\) | 24.3154 | 1.50221 | ||||||||
\(263\) | −3.77883 | −0.233013 | −0.116506 | − | 0.993190i | \(-0.537170\pi\) | ||||
−0.116506 | + | 0.993190i | \(0.537170\pi\) | |||||||
\(264\) | −5.11533 | −0.314827 | ||||||||
\(265\) | 1.95379 | 0.120020 | ||||||||
\(266\) | 4.85429 | 0.297636 | ||||||||
\(267\) | −2.37465 | −0.145326 | ||||||||
\(268\) | −1.87504 | −0.114536 | ||||||||
\(269\) | −4.37680 | −0.266858 | −0.133429 | − | 0.991058i | \(-0.542599\pi\) | ||||
−0.133429 | + | 0.991058i | \(0.542599\pi\) | |||||||
\(270\) | 0.564958 | 0.0343822 | ||||||||
\(271\) | −6.23702 | −0.378872 | −0.189436 | − | 0.981893i | \(-0.560666\pi\) | ||||
−0.189436 | + | 0.981893i | \(0.560666\pi\) | |||||||
\(272\) | −7.81219 | −0.473684 | ||||||||
\(273\) | −2.35343 | −0.142436 | ||||||||
\(274\) | −21.8108 | −1.31764 | ||||||||
\(275\) | −7.90744 | −0.476836 | ||||||||
\(276\) | 5.15403 | 0.310236 | ||||||||
\(277\) | −11.7889 | −0.708326 | −0.354163 | − | 0.935184i | \(-0.615234\pi\) | ||||
−0.354163 | + | 0.935184i | \(0.615234\pi\) | |||||||
\(278\) | 11.0194 | 0.660900 | ||||||||
\(279\) | 6.30168 | 0.377272 | ||||||||
\(280\) | −1.50878 | −0.0901669 | ||||||||
\(281\) | −26.4366 | −1.57708 | −0.788538 | − | 0.614986i | \(-0.789162\pi\) | ||||
−0.788538 | + | 0.614986i | \(0.789162\pi\) | |||||||
\(282\) | 3.26581 | 0.194476 | ||||||||
\(283\) | 20.9061 | 1.24274 | 0.621370 | − | 0.783517i | \(-0.286576\pi\) | ||||
0.621370 | + | 0.783517i | \(0.286576\pi\) | |||||||
\(284\) | −7.33898 | −0.435488 | ||||||||
\(285\) | −2.06295 | −0.122199 | ||||||||
\(286\) | 4.50779 | 0.266552 | ||||||||
\(287\) | 3.34227 | 0.197288 | ||||||||
\(288\) | −3.61135 | −0.212801 | ||||||||
\(289\) | −4.49369 | −0.264334 | ||||||||
\(290\) | −3.05179 | −0.179207 | ||||||||
\(291\) | −0.810176 | −0.0474934 | ||||||||
\(292\) | 6.88885 | 0.403140 | ||||||||
\(293\) | −16.3510 | −0.955238 | −0.477619 | − | 0.878567i | \(-0.658500\pi\) | ||||
−0.477619 | + | 0.878567i | \(0.658500\pi\) | |||||||
\(294\) | 1.15299 | 0.0672439 | ||||||||
\(295\) | 6.12160 | 0.356413 | ||||||||
\(296\) | −27.9958 | −1.62722 | ||||||||
\(297\) | −1.66126 | −0.0963960 | ||||||||
\(298\) | −4.78649 | −0.277274 | ||||||||
\(299\) | −18.0874 | −1.04602 | ||||||||
\(300\) | −3.19204 | −0.184293 | ||||||||
\(301\) | −8.34436 | −0.480961 | ||||||||
\(302\) | −0.863002 | −0.0496602 | ||||||||
\(303\) | 17.1527 | 0.985396 | ||||||||
\(304\) | −9.30053 | −0.533422 | ||||||||
\(305\) | 5.48268 | 0.313938 | ||||||||
\(306\) | −4.07747 | −0.233094 | ||||||||
\(307\) | −30.0983 | −1.71780 | −0.858899 | − | 0.512145i | \(-0.828851\pi\) | ||||
−0.858899 | + | 0.512145i | \(0.828851\pi\) | |||||||
\(308\) | 1.11406 | 0.0634792 | ||||||||
\(309\) | 18.2308 | 1.03711 | ||||||||
\(310\) | −3.56018 | −0.202205 | ||||||||
\(311\) | −14.1735 | −0.803708 | −0.401854 | − | 0.915704i | \(-0.631634\pi\) | ||||
−0.401854 | + | 0.915704i | \(0.631634\pi\) | |||||||
\(312\) | 7.24665 | 0.410261 | ||||||||
\(313\) | 22.9571 | 1.29761 | 0.648806 | − | 0.760954i | \(-0.275269\pi\) | ||||
0.648806 | + | 0.760954i | \(0.275269\pi\) | |||||||
\(314\) | −20.9943 | −1.18478 | ||||||||
\(315\) | −0.489993 | −0.0276080 | ||||||||
\(316\) | 10.9951 | 0.618524 | ||||||||
\(317\) | 5.17947 | 0.290908 | 0.145454 | − | 0.989365i | \(-0.453536\pi\) | ||||
0.145454 | + | 0.989365i | \(0.453536\pi\) | |||||||
\(318\) | 4.59742 | 0.257810 | ||||||||
\(319\) | 8.97380 | 0.502436 | ||||||||
\(320\) | 4.20511 | 0.235073 | ||||||||
\(321\) | −6.63153 | −0.370136 | ||||||||
\(322\) | 8.86141 | 0.493827 | ||||||||
\(323\) | 14.8890 | 0.828444 | ||||||||
\(324\) | −0.670610 | −0.0372561 | ||||||||
\(325\) | 11.2021 | 0.621380 | ||||||||
\(326\) | −22.2659 | −1.23319 | ||||||||
\(327\) | 14.8320 | 0.820211 | ||||||||
\(328\) | −10.2915 | −0.568253 | ||||||||
\(329\) | −2.83247 | −0.156159 | ||||||||
\(330\) | 0.938541 | 0.0516650 | ||||||||
\(331\) | 22.6512 | 1.24502 | 0.622511 | − | 0.782611i | \(-0.286112\pi\) | ||||
0.622511 | + | 0.782611i | \(0.286112\pi\) | |||||||
\(332\) | −8.90658 | −0.488812 | ||||||||
\(333\) | −9.09193 | −0.498235 | ||||||||
\(334\) | −7.08208 | −0.387514 | ||||||||
\(335\) | 1.37003 | 0.0748526 | ||||||||
\(336\) | −2.20906 | −0.120514 | ||||||||
\(337\) | −12.5057 | −0.681231 | −0.340616 | − | 0.940203i | \(-0.610635\pi\) | ||||
−0.340616 | + | 0.940203i | \(0.610635\pi\) | |||||||
\(338\) | 8.60291 | 0.467937 | ||||||||
\(339\) | −10.9562 | −0.595059 | ||||||||
\(340\) | −1.16205 | −0.0630209 | ||||||||
\(341\) | 10.4687 | 0.566913 | ||||||||
\(342\) | −4.85429 | −0.262490 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 25.6939 | 1.38532 | ||||||||
\(345\) | −3.76588 | −0.202748 | ||||||||
\(346\) | −0.0567040 | −0.00304842 | ||||||||
\(347\) | −32.4067 | −1.73968 | −0.869840 | − | 0.493334i | \(-0.835778\pi\) | ||||
−0.869840 | + | 0.493334i | \(0.835778\pi\) | |||||||
\(348\) | 3.62250 | 0.194187 | ||||||||
\(349\) | 4.01916 | 0.215141 | 0.107570 | − | 0.994197i | \(-0.465693\pi\) | ||||
0.107570 | + | 0.994197i | \(0.465693\pi\) | |||||||
\(350\) | −5.48813 | −0.293353 | ||||||||
\(351\) | 2.35343 | 0.125617 | ||||||||
\(352\) | −5.99939 | −0.319768 | ||||||||
\(353\) | 25.0605 | 1.33384 | 0.666918 | − | 0.745131i | \(-0.267613\pi\) | ||||
0.666918 | + | 0.745131i | \(0.267613\pi\) | |||||||
\(354\) | 14.4046 | 0.765596 | ||||||||
\(355\) | 5.36235 | 0.284604 | ||||||||
\(356\) | −1.59246 | −0.0844004 | ||||||||
\(357\) | 3.53643 | 0.187168 | ||||||||
\(358\) | 17.7164 | 0.936343 | ||||||||
\(359\) | 20.4261 | 1.07805 | 0.539024 | − | 0.842291i | \(-0.318793\pi\) | ||||
0.539024 | + | 0.842291i | \(0.318793\pi\) | |||||||
\(360\) | 1.50878 | 0.0795198 | ||||||||
\(361\) | −1.27446 | −0.0670767 | ||||||||
\(362\) | −17.6358 | −0.926918 | ||||||||
\(363\) | 8.24022 | 0.432499 | ||||||||
\(364\) | −1.57823 | −0.0827218 | ||||||||
\(365\) | −5.03346 | −0.263463 | ||||||||
\(366\) | 12.9012 | 0.674356 | ||||||||
\(367\) | −27.7671 | −1.44943 | −0.724715 | − | 0.689049i | \(-0.758029\pi\) | ||||
−0.724715 | + | 0.689049i | \(0.758029\pi\) | |||||||
\(368\) | −16.9779 | −0.885036 | ||||||||
\(369\) | −3.34227 | −0.173992 | ||||||||
\(370\) | 5.13656 | 0.267037 | ||||||||
\(371\) | −3.98738 | −0.207014 | ||||||||
\(372\) | 4.22597 | 0.219106 | ||||||||
\(373\) | 26.3795 | 1.36588 | 0.682940 | − | 0.730474i | \(-0.260701\pi\) | ||||
0.682940 | + | 0.730474i | \(0.260701\pi\) | |||||||
\(374\) | −6.77373 | −0.350261 | ||||||||
\(375\) | 4.78228 | 0.246956 | ||||||||
\(376\) | 8.72171 | 0.449788 | ||||||||
\(377\) | −12.7128 | −0.654740 | ||||||||
\(378\) | −1.15299 | −0.0593035 | ||||||||
\(379\) | −11.6844 | −0.600185 | −0.300093 | − | 0.953910i | \(-0.597018\pi\) | ||||
−0.300093 | + | 0.953910i | \(0.597018\pi\) | |||||||
\(380\) | −1.38344 | −0.0709688 | ||||||||
\(381\) | −8.25401 | −0.422866 | ||||||||
\(382\) | −12.9926 | −0.664760 | ||||||||
\(383\) | 1.00000 | 0.0510976 | ||||||||
\(384\) | 2.67226 | 0.136368 | ||||||||
\(385\) | −0.814005 | −0.0414855 | ||||||||
\(386\) | 2.87393 | 0.146279 | ||||||||
\(387\) | 8.34436 | 0.424168 | ||||||||
\(388\) | −0.543312 | −0.0275825 | ||||||||
\(389\) | −10.7525 | −0.545174 | −0.272587 | − | 0.962131i | \(-0.587879\pi\) | ||||
−0.272587 | + | 0.962131i | \(0.587879\pi\) | |||||||
\(390\) | −1.32959 | −0.0673262 | ||||||||
\(391\) | 27.1795 | 1.37453 | ||||||||
\(392\) | 3.07919 | 0.155523 | ||||||||
\(393\) | 21.0890 | 1.06380 | ||||||||
\(394\) | 21.0219 | 1.05907 | ||||||||
\(395\) | −8.03378 | −0.404223 | ||||||||
\(396\) | −1.11406 | −0.0559834 | ||||||||
\(397\) | 16.6700 | 0.836644 | 0.418322 | − | 0.908299i | \(-0.362618\pi\) | ||||
0.418322 | + | 0.908299i | \(0.362618\pi\) | |||||||
\(398\) | 8.48943 | 0.425537 | ||||||||
\(399\) | 4.21017 | 0.210772 | ||||||||
\(400\) | 10.5149 | 0.525747 | ||||||||
\(401\) | 13.8324 | 0.690756 | 0.345378 | − | 0.938464i | \(-0.387751\pi\) | ||||
0.345378 | + | 0.938464i | \(0.387751\pi\) | |||||||
\(402\) | 3.22379 | 0.160788 | ||||||||
\(403\) | −14.8305 | −0.738762 | ||||||||
\(404\) | 11.5028 | 0.572284 | ||||||||
\(405\) | 0.489993 | 0.0243479 | ||||||||
\(406\) | 6.22824 | 0.309102 | ||||||||
\(407\) | −15.1040 | −0.748680 | ||||||||
\(408\) | −10.8893 | −0.539102 | ||||||||
\(409\) | 2.71892 | 0.134442 | 0.0672210 | − | 0.997738i | \(-0.478587\pi\) | ||||
0.0672210 | + | 0.997738i | \(0.478587\pi\) | |||||||
\(410\) | 1.88824 | 0.0932536 | ||||||||
\(411\) | −18.9167 | −0.933092 | ||||||||
\(412\) | 12.2257 | 0.602319 | ||||||||
\(413\) | −12.4932 | −0.614752 | ||||||||
\(414\) | −8.86141 | −0.435515 | ||||||||
\(415\) | 6.50775 | 0.319453 | ||||||||
\(416\) | 8.49905 | 0.416700 | ||||||||
\(417\) | 9.55723 | 0.468020 | ||||||||
\(418\) | −8.06424 | −0.394435 | ||||||||
\(419\) | 2.92821 | 0.143052 | 0.0715262 | − | 0.997439i | \(-0.477213\pi\) | ||||
0.0715262 | + | 0.997439i | \(0.477213\pi\) | |||||||
\(420\) | −0.328594 | −0.0160337 | ||||||||
\(421\) | 30.6924 | 1.49586 | 0.747929 | − | 0.663779i | \(-0.231048\pi\) | ||||
0.747929 | + | 0.663779i | \(0.231048\pi\) | |||||||
\(422\) | 23.4423 | 1.14115 | ||||||||
\(423\) | 2.83247 | 0.137719 | ||||||||
\(424\) | 12.2779 | 0.596268 | ||||||||
\(425\) | −16.8331 | −0.816523 | ||||||||
\(426\) | 12.6180 | 0.611346 | ||||||||
\(427\) | −11.1893 | −0.541489 | ||||||||
\(428\) | −4.44717 | −0.214962 | ||||||||
\(429\) | 3.90965 | 0.188760 | ||||||||
\(430\) | −4.71421 | −0.227339 | ||||||||
\(431\) | −3.45996 | −0.166660 | −0.0833301 | − | 0.996522i | \(-0.526556\pi\) | ||||
−0.0833301 | + | 0.996522i | \(0.526556\pi\) | |||||||
\(432\) | 2.20906 | 0.106284 | ||||||||
\(433\) | 0.986867 | 0.0474258 | 0.0237129 | − | 0.999719i | \(-0.492451\pi\) | ||||
0.0237129 | + | 0.999719i | \(0.492451\pi\) | |||||||
\(434\) | 7.26579 | 0.348769 | ||||||||
\(435\) | −2.64685 | −0.126907 | ||||||||
\(436\) | 9.94648 | 0.476350 | ||||||||
\(437\) | 32.3576 | 1.54787 | ||||||||
\(438\) | −11.8441 | −0.565935 | ||||||||
\(439\) | 29.5399 | 1.40986 | 0.704930 | − | 0.709277i | \(-0.250978\pi\) | ||||
0.704930 | + | 0.709277i | \(0.250978\pi\) | |||||||
\(440\) | 2.50648 | 0.119492 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 9.59603 | 0.456437 | ||||||||
\(443\) | 10.9121 | 0.518448 | 0.259224 | − | 0.965817i | \(-0.416533\pi\) | ||||
0.259224 | + | 0.965817i | \(0.416533\pi\) | |||||||
\(444\) | −6.09714 | −0.289357 | ||||||||
\(445\) | 1.16356 | 0.0551581 | ||||||||
\(446\) | −30.3553 | −1.43737 | ||||||||
\(447\) | −4.15137 | −0.196353 | ||||||||
\(448\) | −8.58198 | −0.405461 | ||||||||
\(449\) | 30.0120 | 1.41635 | 0.708176 | − | 0.706036i | \(-0.249518\pi\) | ||||
0.708176 | + | 0.706036i | \(0.249518\pi\) | |||||||
\(450\) | 5.48813 | 0.258713 | ||||||||
\(451\) | −5.55238 | −0.261451 | ||||||||
\(452\) | −7.34734 | −0.345590 | ||||||||
\(453\) | −0.748490 | −0.0351671 | ||||||||
\(454\) | 31.3572 | 1.47167 | ||||||||
\(455\) | 1.15316 | 0.0540611 | ||||||||
\(456\) | −12.9639 | −0.607091 | ||||||||
\(457\) | −22.5872 | −1.05658 | −0.528291 | − | 0.849063i | \(-0.677167\pi\) | ||||
−0.528291 | + | 0.849063i | \(0.677167\pi\) | |||||||
\(458\) | 2.05939 | 0.0962290 | ||||||||
\(459\) | −3.53643 | −0.165066 | ||||||||
\(460\) | −2.52543 | −0.117749 | ||||||||
\(461\) | 27.8924 | 1.29908 | 0.649538 | − | 0.760329i | \(-0.274962\pi\) | ||||
0.649538 | + | 0.760329i | \(0.274962\pi\) | |||||||
\(462\) | −1.91542 | −0.0891133 | ||||||||
\(463\) | 6.73171 | 0.312849 | 0.156425 | − | 0.987690i | \(-0.450003\pi\) | ||||
0.156425 | + | 0.987690i | \(0.450003\pi\) | |||||||
\(464\) | −11.9329 | −0.553972 | ||||||||
\(465\) | −3.08778 | −0.143192 | ||||||||
\(466\) | 25.1645 | 1.16572 | ||||||||
\(467\) | 9.29858 | 0.430287 | 0.215144 | − | 0.976582i | \(-0.430978\pi\) | ||||
0.215144 | + | 0.976582i | \(0.430978\pi\) | |||||||
\(468\) | 1.57823 | 0.0729537 | ||||||||
\(469\) | −2.79602 | −0.129108 | ||||||||
\(470\) | −1.60022 | −0.0738128 | ||||||||
\(471\) | −18.2085 | −0.839005 | ||||||||
\(472\) | 38.4691 | 1.77068 | ||||||||
\(473\) | 13.8621 | 0.637382 | ||||||||
\(474\) | −18.9041 | −0.868295 | ||||||||
\(475\) | −20.0400 | −0.919499 | ||||||||
\(476\) | 2.37156 | 0.108700 | ||||||||
\(477\) | 3.98738 | 0.182570 | ||||||||
\(478\) | −22.7417 | −1.04018 | ||||||||
\(479\) | 4.75609 | 0.217311 | 0.108656 | − | 0.994079i | \(-0.465345\pi\) | ||||
0.108656 | + | 0.994079i | \(0.465345\pi\) | |||||||
\(480\) | 1.76954 | 0.0807679 | ||||||||
\(481\) | 21.3972 | 0.975628 | ||||||||
\(482\) | −23.1781 | −1.05573 | ||||||||
\(483\) | 7.68558 | 0.349706 | ||||||||
\(484\) | 5.52597 | 0.251181 | ||||||||
\(485\) | 0.396980 | 0.0180259 | ||||||||
\(486\) | 1.15299 | 0.0523008 | ||||||||
\(487\) | −18.8401 | −0.853727 | −0.426863 | − | 0.904316i | \(-0.640381\pi\) | ||||
−0.426863 | + | 0.904316i | \(0.640381\pi\) | |||||||
\(488\) | 34.4541 | 1.55966 | ||||||||
\(489\) | −19.3114 | −0.873292 | ||||||||
\(490\) | −0.564958 | −0.0255222 | ||||||||
\(491\) | 6.02096 | 0.271722 | 0.135861 | − | 0.990728i | \(-0.456620\pi\) | ||||
0.135861 | + | 0.990728i | \(0.456620\pi\) | |||||||
\(492\) | −2.24136 | −0.101048 | ||||||||
\(493\) | 19.1031 | 0.860360 | ||||||||
\(494\) | 11.4242 | 0.514000 | ||||||||
\(495\) | 0.814005 | 0.0365868 | ||||||||
\(496\) | −13.9208 | −0.625063 | ||||||||
\(497\) | −10.9437 | −0.490894 | ||||||||
\(498\) | 15.3132 | 0.686203 | ||||||||
\(499\) | −8.75520 | −0.391936 | −0.195968 | − | 0.980610i | \(-0.562785\pi\) | ||||
−0.195968 | + | 0.980610i | \(0.562785\pi\) | |||||||
\(500\) | 3.20705 | 0.143423 | ||||||||
\(501\) | −6.14235 | −0.274420 | ||||||||
\(502\) | 14.9490 | 0.667207 | ||||||||
\(503\) | 4.53083 | 0.202020 | 0.101010 | − | 0.994885i | \(-0.467793\pi\) | ||||
0.101010 | + | 0.994885i | \(0.467793\pi\) | |||||||
\(504\) | −3.07919 | −0.137158 | ||||||||
\(505\) | −8.40469 | −0.374004 | ||||||||
\(506\) | −14.7211 | −0.654433 | ||||||||
\(507\) | 7.46138 | 0.331372 | ||||||||
\(508\) | −5.53522 | −0.245586 | ||||||||
\(509\) | 4.28491 | 0.189925 | 0.0949627 | − | 0.995481i | \(-0.469727\pi\) | ||||
0.0949627 | + | 0.995481i | \(0.469727\pi\) | |||||||
\(510\) | 1.99793 | 0.0884699 | ||||||||
\(511\) | 10.2725 | 0.454430 | ||||||||
\(512\) | 21.5820 | 0.953797 | ||||||||
\(513\) | −4.21017 | −0.185884 | ||||||||
\(514\) | −26.5001 | −1.16887 | ||||||||
\(515\) | −8.93295 | −0.393633 | ||||||||
\(516\) | 5.59581 | 0.246342 | ||||||||
\(517\) | 4.70546 | 0.206946 | ||||||||
\(518\) | −10.4829 | −0.460593 | ||||||||
\(519\) | −0.0491798 | −0.00215876 | ||||||||
\(520\) | −3.55081 | −0.155713 | ||||||||
\(521\) | −0.784693 | −0.0343780 | −0.0171890 | − | 0.999852i | \(-0.505472\pi\) | ||||
−0.0171890 | + | 0.999852i | \(0.505472\pi\) | |||||||
\(522\) | −6.22824 | −0.272603 | ||||||||
\(523\) | 39.3317 | 1.71986 | 0.859928 | − | 0.510415i | \(-0.170508\pi\) | ||||
0.859928 | + | 0.510415i | \(0.170508\pi\) | |||||||
\(524\) | 14.1425 | 0.617816 | ||||||||
\(525\) | −4.75991 | −0.207739 | ||||||||
\(526\) | 4.35696 | 0.189972 | ||||||||
\(527\) | 22.2854 | 0.970769 | ||||||||
\(528\) | 3.66983 | 0.159709 | ||||||||
\(529\) | 36.0681 | 1.56818 | ||||||||
\(530\) | −2.25270 | −0.0978510 | ||||||||
\(531\) | 12.4932 | 0.542161 | ||||||||
\(532\) | 2.82338 | 0.122409 | ||||||||
\(533\) | 7.86579 | 0.340705 | ||||||||
\(534\) | 2.73795 | 0.118483 | ||||||||
\(535\) | 3.24940 | 0.140484 | ||||||||
\(536\) | 8.60947 | 0.371873 | ||||||||
\(537\) | 15.3656 | 0.663076 | ||||||||
\(538\) | 5.04641 | 0.217566 | ||||||||
\(539\) | 1.66126 | 0.0715555 | ||||||||
\(540\) | 0.328594 | 0.0141404 | ||||||||
\(541\) | 25.8582 | 1.11173 | 0.555866 | − | 0.831272i | \(-0.312387\pi\) | ||||
0.555866 | + | 0.831272i | \(0.312387\pi\) | |||||||
\(542\) | 7.19123 | 0.308890 | ||||||||
\(543\) | −15.2957 | −0.656401 | ||||||||
\(544\) | −12.7713 | −0.547564 | ||||||||
\(545\) | −7.26757 | −0.311309 | ||||||||
\(546\) | 2.71348 | 0.116126 | ||||||||
\(547\) | −15.6118 | −0.667513 | −0.333757 | − | 0.942659i | \(-0.608316\pi\) | ||||
−0.333757 | + | 0.942659i | \(0.608316\pi\) | |||||||
\(548\) | −12.6857 | −0.541907 | ||||||||
\(549\) | 11.1893 | 0.477548 | ||||||||
\(550\) | 9.11721 | 0.388759 | ||||||||
\(551\) | 22.7425 | 0.968864 | ||||||||
\(552\) | −23.6654 | −1.00727 | ||||||||
\(553\) | 16.3957 | 0.697217 | ||||||||
\(554\) | 13.5925 | 0.577490 | ||||||||
\(555\) | 4.45498 | 0.189103 | ||||||||
\(556\) | 6.40917 | 0.271810 | ||||||||
\(557\) | 17.7852 | 0.753581 | 0.376791 | − | 0.926298i | \(-0.377028\pi\) | ||||
0.376791 | + | 0.926298i | \(0.377028\pi\) | |||||||
\(558\) | −7.26579 | −0.307585 | ||||||||
\(559\) | −19.6378 | −0.830592 | ||||||||
\(560\) | 1.08242 | 0.0457408 | ||||||||
\(561\) | −5.87492 | −0.248039 | ||||||||
\(562\) | 30.4812 | 1.28577 | ||||||||
\(563\) | −8.24347 | −0.347421 | −0.173710 | − | 0.984797i | \(-0.555576\pi\) | ||||
−0.173710 | + | 0.984797i | \(0.555576\pi\) | |||||||
\(564\) | 1.89948 | 0.0799825 | ||||||||
\(565\) | 5.36846 | 0.225853 | ||||||||
\(566\) | −24.1046 | −1.01319 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 33.6979 | 1.41393 | ||||||||
\(569\) | 34.4633 | 1.44478 | 0.722389 | − | 0.691487i | \(-0.243044\pi\) | ||||
0.722389 | + | 0.691487i | \(0.243044\pi\) | |||||||
\(570\) | 2.37857 | 0.0996273 | ||||||||
\(571\) | −25.0582 | −1.04865 | −0.524327 | − | 0.851517i | \(-0.675683\pi\) | ||||
−0.524327 | + | 0.851517i | \(0.675683\pi\) | |||||||
\(572\) | 2.62185 | 0.109625 | ||||||||
\(573\) | −11.2686 | −0.470753 | ||||||||
\(574\) | −3.85361 | −0.160847 | ||||||||
\(575\) | −36.5826 | −1.52560 | ||||||||
\(576\) | 8.58198 | 0.357583 | ||||||||
\(577\) | −16.2254 | −0.675470 | −0.337735 | − | 0.941241i | \(-0.609661\pi\) | ||||
−0.337735 | + | 0.941241i | \(0.609661\pi\) | |||||||
\(578\) | 5.18118 | 0.215509 | ||||||||
\(579\) | 2.49259 | 0.103588 | ||||||||
\(580\) | −1.77500 | −0.0737029 | ||||||||
\(581\) | −13.2813 | −0.551002 | ||||||||
\(582\) | 0.934126 | 0.0387208 | ||||||||
\(583\) | 6.62407 | 0.274341 | ||||||||
\(584\) | −31.6311 | −1.30890 | ||||||||
\(585\) | −1.15316 | −0.0476774 | ||||||||
\(586\) | 18.8526 | 0.778795 | ||||||||
\(587\) | 26.4202 | 1.09048 | 0.545239 | − | 0.838281i | \(-0.316439\pi\) | ||||
0.545239 | + | 0.838281i | \(0.316439\pi\) | |||||||
\(588\) | 0.670610 | 0.0276555 | ||||||||
\(589\) | 26.5312 | 1.09320 | ||||||||
\(590\) | −7.05815 | −0.290580 | ||||||||
\(591\) | 18.2325 | 0.749985 | ||||||||
\(592\) | 20.0846 | 0.825474 | ||||||||
\(593\) | 5.78924 | 0.237736 | 0.118868 | − | 0.992910i | \(-0.462074\pi\) | ||||
0.118868 | + | 0.992910i | \(0.462074\pi\) | |||||||
\(594\) | 1.91542 | 0.0785905 | ||||||||
\(595\) | −1.73282 | −0.0710388 | ||||||||
\(596\) | −2.78395 | −0.114035 | ||||||||
\(597\) | 7.36296 | 0.301346 | ||||||||
\(598\) | 20.8547 | 0.852811 | ||||||||
\(599\) | −13.3764 | −0.546543 | −0.273271 | − | 0.961937i | \(-0.588106\pi\) | ||||
−0.273271 | + | 0.961937i | \(0.588106\pi\) | |||||||
\(600\) | 14.6567 | 0.598356 | ||||||||
\(601\) | −20.4029 | −0.832253 | −0.416126 | − | 0.909307i | \(-0.636613\pi\) | ||||
−0.416126 | + | 0.909307i | \(0.636613\pi\) | |||||||
\(602\) | 9.62098 | 0.392122 | ||||||||
\(603\) | 2.79602 | 0.113863 | ||||||||
\(604\) | −0.501944 | −0.0204238 | ||||||||
\(605\) | −4.03765 | −0.164154 | ||||||||
\(606\) | −19.7769 | −0.803382 | ||||||||
\(607\) | 33.9762 | 1.37905 | 0.689525 | − | 0.724262i | \(-0.257819\pi\) | ||||
0.689525 | + | 0.724262i | \(0.257819\pi\) | |||||||
\(608\) | −15.2044 | −0.616620 | ||||||||
\(609\) | 5.40181 | 0.218892 | ||||||||
\(610\) | −6.32149 | −0.255950 | ||||||||
\(611\) | −6.66600 | −0.269678 | ||||||||
\(612\) | −2.37156 | −0.0958647 | ||||||||
\(613\) | −11.4377 | −0.461963 | −0.230981 | − | 0.972958i | \(-0.574194\pi\) | ||||
−0.230981 | + | 0.972958i | \(0.574194\pi\) | |||||||
\(614\) | 34.7030 | 1.40050 | ||||||||
\(615\) | 1.63769 | 0.0660380 | ||||||||
\(616\) | −5.11533 | −0.206103 | ||||||||
\(617\) | 24.6581 | 0.992697 | 0.496348 | − | 0.868123i | \(-0.334674\pi\) | ||||
0.496348 | + | 0.868123i | \(0.334674\pi\) | |||||||
\(618\) | −21.0200 | −0.845547 | ||||||||
\(619\) | −14.7312 | −0.592098 | −0.296049 | − | 0.955173i | \(-0.595669\pi\) | ||||
−0.296049 | + | 0.955173i | \(0.595669\pi\) | |||||||
\(620\) | −2.07069 | −0.0831611 | ||||||||
\(621\) | −7.68558 | −0.308412 | ||||||||
\(622\) | 16.3420 | 0.655254 | ||||||||
\(623\) | −2.37465 | −0.0951383 | ||||||||
\(624\) | −5.19887 | −0.208121 | ||||||||
\(625\) | 21.4563 | 0.858250 | ||||||||
\(626\) | −26.4693 | −1.05793 | ||||||||
\(627\) | −6.99418 | −0.279321 | ||||||||
\(628\) | −12.2108 | −0.487265 | ||||||||
\(629\) | −32.1529 | −1.28202 | ||||||||
\(630\) | 0.564958 | 0.0225084 | ||||||||
\(631\) | 1.66358 | 0.0662261 | 0.0331131 | − | 0.999452i | \(-0.489458\pi\) | ||||
0.0331131 | + | 0.999452i | \(0.489458\pi\) | |||||||
\(632\) | −50.4855 | −2.00821 | ||||||||
\(633\) | 20.3317 | 0.808114 | ||||||||
\(634\) | −5.97188 | −0.237174 | ||||||||
\(635\) | 4.04441 | 0.160497 | ||||||||
\(636\) | 2.67398 | 0.106030 | ||||||||
\(637\) | −2.35343 | −0.0932462 | ||||||||
\(638\) | −10.3467 | −0.409630 | ||||||||
\(639\) | 10.9437 | 0.432928 | ||||||||
\(640\) | −1.30939 | −0.0517580 | ||||||||
\(641\) | 21.0005 | 0.829470 | 0.414735 | − | 0.909942i | \(-0.363874\pi\) | ||||
0.414735 | + | 0.909942i | \(0.363874\pi\) | |||||||
\(642\) | 7.64610 | 0.301767 | ||||||||
\(643\) | −33.1526 | −1.30741 | −0.653706 | − | 0.756749i | \(-0.726787\pi\) | ||||
−0.653706 | + | 0.756749i | \(0.726787\pi\) | |||||||
\(644\) | 5.15403 | 0.203097 | ||||||||
\(645\) | −4.08867 | −0.160991 | ||||||||
\(646\) | −17.1669 | −0.675421 | ||||||||
\(647\) | −14.0292 | −0.551545 | −0.275772 | − | 0.961223i | \(-0.588934\pi\) | ||||
−0.275772 | + | 0.961223i | \(0.588934\pi\) | |||||||
\(648\) | 3.07919 | 0.120962 | ||||||||
\(649\) | 20.7545 | 0.814686 | ||||||||
\(650\) | −12.9159 | −0.506604 | ||||||||
\(651\) | 6.30168 | 0.246982 | ||||||||
\(652\) | −12.9504 | −0.507177 | ||||||||
\(653\) | −33.2643 | −1.30173 | −0.650866 | − | 0.759193i | \(-0.725594\pi\) | ||||
−0.650866 | + | 0.759193i | \(0.725594\pi\) | |||||||
\(654\) | −17.1012 | −0.668709 | ||||||||
\(655\) | −10.3334 | −0.403761 | ||||||||
\(656\) | 7.38329 | 0.288269 | ||||||||
\(657\) | −10.2725 | −0.400769 | ||||||||
\(658\) | 3.26581 | 0.127315 | ||||||||
\(659\) | 6.54041 | 0.254778 | 0.127389 | − | 0.991853i | \(-0.459340\pi\) | ||||
0.127389 | + | 0.991853i | \(0.459340\pi\) | |||||||
\(660\) | 0.545879 | 0.0212483 | ||||||||
\(661\) | 6.14150 | 0.238877 | 0.119438 | − | 0.992842i | \(-0.461891\pi\) | ||||
0.119438 | + | 0.992842i | \(0.461891\pi\) | |||||||
\(662\) | −26.1167 | −1.01505 | ||||||||
\(663\) | 8.32272 | 0.323228 | ||||||||
\(664\) | 40.8957 | 1.58706 | ||||||||
\(665\) | −2.06295 | −0.0799979 | ||||||||
\(666\) | 10.4829 | 0.406205 | ||||||||
\(667\) | 41.5160 | 1.60751 | ||||||||
\(668\) | −4.11912 | −0.159373 | ||||||||
\(669\) | −26.3274 | −1.01788 | ||||||||
\(670\) | −1.57963 | −0.0610265 | ||||||||
\(671\) | 18.5884 | 0.717595 | ||||||||
\(672\) | −3.61135 | −0.139311 | ||||||||
\(673\) | 35.9115 | 1.38429 | 0.692143 | − | 0.721761i | \(-0.256667\pi\) | ||||
0.692143 | + | 0.721761i | \(0.256667\pi\) | |||||||
\(674\) | 14.4190 | 0.555400 | ||||||||
\(675\) | 4.75991 | 0.183209 | ||||||||
\(676\) | 5.00368 | 0.192449 | ||||||||
\(677\) | 9.06359 | 0.348342 | 0.174171 | − | 0.984715i | \(-0.444275\pi\) | ||||
0.174171 | + | 0.984715i | \(0.444275\pi\) | |||||||
\(678\) | 12.6324 | 0.485145 | ||||||||
\(679\) | −0.810176 | −0.0310917 | ||||||||
\(680\) | 5.33569 | 0.204615 | ||||||||
\(681\) | 27.1964 | 1.04217 | ||||||||
\(682\) | −12.0704 | −0.462198 | ||||||||
\(683\) | 12.8911 | 0.493266 | 0.246633 | − | 0.969109i | \(-0.420676\pi\) | ||||
0.246633 | + | 0.969109i | \(0.420676\pi\) | |||||||
\(684\) | −2.82338 | −0.107955 | ||||||||
\(685\) | 9.26904 | 0.354152 | ||||||||
\(686\) | 1.15299 | 0.0440214 | ||||||||
\(687\) | 1.78613 | 0.0681450 | ||||||||
\(688\) | −18.4332 | −0.702760 | ||||||||
\(689\) | −9.38400 | −0.357502 | ||||||||
\(690\) | 4.34203 | 0.165298 | ||||||||
\(691\) | 18.4567 | 0.702126 | 0.351063 | − | 0.936352i | \(-0.385820\pi\) | ||||
0.351063 | + | 0.936352i | \(0.385820\pi\) | |||||||
\(692\) | −0.0329805 | −0.00125373 | ||||||||
\(693\) | −1.66126 | −0.0631060 | ||||||||
\(694\) | 37.3646 | 1.41834 | ||||||||
\(695\) | −4.68297 | −0.177635 | ||||||||
\(696\) | −16.6332 | −0.630480 | ||||||||
\(697\) | −11.8197 | −0.447703 | ||||||||
\(698\) | −4.63406 | −0.175402 | ||||||||
\(699\) | 21.8254 | 0.825512 | ||||||||
\(700\) | −3.19204 | −0.120648 | ||||||||
\(701\) | −31.2914 | −1.18186 | −0.590929 | − | 0.806723i | \(-0.701239\pi\) | ||||
−0.590929 | + | 0.806723i | \(0.701239\pi\) | |||||||
\(702\) | −2.71348 | −0.102414 | ||||||||
\(703\) | −38.2786 | −1.44370 | ||||||||
\(704\) | 14.2569 | 0.537327 | ||||||||
\(705\) | −1.38789 | −0.0522709 | ||||||||
\(706\) | −28.8945 | −1.08746 | ||||||||
\(707\) | 17.1527 | 0.645093 | ||||||||
\(708\) | 8.37809 | 0.314868 | ||||||||
\(709\) | 27.9348 | 1.04911 | 0.524556 | − | 0.851376i | \(-0.324231\pi\) | ||||
0.524556 | + | 0.851376i | \(0.324231\pi\) | |||||||
\(710\) | −6.18275 | −0.232035 | ||||||||
\(711\) | −16.3957 | −0.614887 | ||||||||
\(712\) | 7.31200 | 0.274029 | ||||||||
\(713\) | 48.4321 | 1.81380 | ||||||||
\(714\) | −4.07747 | −0.152596 | ||||||||
\(715\) | −1.91570 | −0.0716431 | ||||||||
\(716\) | 10.3043 | 0.385091 | ||||||||
\(717\) | −19.7241 | −0.736610 | ||||||||
\(718\) | −23.5511 | −0.878919 | ||||||||
\(719\) | −12.5904 | −0.469543 | −0.234771 | − | 0.972051i | \(-0.575434\pi\) | ||||
−0.234771 | + | 0.972051i | \(0.575434\pi\) | |||||||
\(720\) | −1.08242 | −0.0403396 | ||||||||
\(721\) | 18.2308 | 0.678950 | ||||||||
\(722\) | 1.46944 | 0.0546869 | ||||||||
\(723\) | −20.1026 | −0.747623 | ||||||||
\(724\) | −10.2574 | −0.381215 | ||||||||
\(725\) | −25.7121 | −0.954923 | ||||||||
\(726\) | −9.50091 | −0.352612 | ||||||||
\(727\) | 29.5096 | 1.09445 | 0.547226 | − | 0.836985i | \(-0.315684\pi\) | ||||
0.547226 | + | 0.836985i | \(0.315684\pi\) | |||||||
\(728\) | 7.24665 | 0.268579 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.80354 | 0.214799 | ||||||||
\(731\) | 29.5092 | 1.09144 | ||||||||
\(732\) | 7.50367 | 0.277343 | ||||||||
\(733\) | 22.8987 | 0.845782 | 0.422891 | − | 0.906181i | \(-0.361015\pi\) | ||||
0.422891 | + | 0.906181i | \(0.361015\pi\) | |||||||
\(734\) | 32.0152 | 1.18170 | ||||||||
\(735\) | −0.489993 | −0.0180737 | ||||||||
\(736\) | −27.7553 | −1.02307 | ||||||||
\(737\) | 4.64491 | 0.171097 | ||||||||
\(738\) | 3.85361 | 0.141853 | ||||||||
\(739\) | 34.1718 | 1.25703 | 0.628515 | − | 0.777798i | \(-0.283663\pi\) | ||||
0.628515 | + | 0.777798i | \(0.283663\pi\) | |||||||
\(740\) | 2.98755 | 0.109825 | ||||||||
\(741\) | 9.90833 | 0.363992 | ||||||||
\(742\) | 4.59742 | 0.168776 | ||||||||
\(743\) | 20.2979 | 0.744657 | 0.372329 | − | 0.928101i | \(-0.378559\pi\) | ||||
0.372329 | + | 0.928101i | \(0.378559\pi\) | |||||||
\(744\) | −19.4041 | −0.711388 | ||||||||
\(745\) | 2.03414 | 0.0745251 | ||||||||
\(746\) | −30.4154 | −1.11359 | ||||||||
\(747\) | 13.2813 | 0.485938 | ||||||||
\(748\) | −3.93978 | −0.144053 | ||||||||
\(749\) | −6.63153 | −0.242311 | ||||||||
\(750\) | −5.51393 | −0.201340 | ||||||||
\(751\) | −23.1211 | −0.843699 | −0.421850 | − | 0.906666i | \(-0.638619\pi\) | ||||
−0.421850 | + | 0.906666i | \(0.638619\pi\) | |||||||
\(752\) | −6.25710 | −0.228173 | ||||||||
\(753\) | 12.9654 | 0.472486 | ||||||||
\(754\) | 14.6577 | 0.533802 | ||||||||
\(755\) | 0.366754 | 0.0133476 | ||||||||
\(756\) | −0.670610 | −0.0243898 | ||||||||
\(757\) | 32.1578 | 1.16880 | 0.584398 | − | 0.811467i | \(-0.301331\pi\) | ||||
0.584398 | + | 0.811467i | \(0.301331\pi\) | |||||||
\(758\) | 13.4720 | 0.489324 | ||||||||
\(759\) | −12.7677 | −0.463440 | ||||||||
\(760\) | 6.35223 | 0.230420 | ||||||||
\(761\) | −15.4714 | −0.560838 | −0.280419 | − | 0.959878i | \(-0.590473\pi\) | ||||
−0.280419 | + | 0.959878i | \(0.590473\pi\) | |||||||
\(762\) | 9.51681 | 0.344758 | ||||||||
\(763\) | 14.8320 | 0.536954 | ||||||||
\(764\) | −7.55684 | −0.273397 | ||||||||
\(765\) | 1.73282 | 0.0626504 | ||||||||
\(766\) | −1.15299 | −0.0416593 | ||||||||
\(767\) | −29.4019 | −1.06164 | ||||||||
\(768\) | 14.0829 | 0.508172 | ||||||||
\(769\) | 12.3400 | 0.444990 | 0.222495 | − | 0.974934i | \(-0.428580\pi\) | ||||
0.222495 | + | 0.974934i | \(0.428580\pi\) | |||||||
\(770\) | 0.938541 | 0.0338227 | ||||||||
\(771\) | −22.9838 | −0.827740 | ||||||||
\(772\) | 1.67155 | 0.0601606 | ||||||||
\(773\) | 12.3636 | 0.444687 | 0.222343 | − | 0.974968i | \(-0.428629\pi\) | ||||
0.222343 | + | 0.974968i | \(0.428629\pi\) | |||||||
\(774\) | −9.62098 | −0.345819 | ||||||||
\(775\) | −29.9954 | −1.07747 | ||||||||
\(776\) | 2.49469 | 0.0895540 | ||||||||
\(777\) | −9.09193 | −0.326171 | ||||||||
\(778\) | 12.3975 | 0.444474 | ||||||||
\(779\) | −14.0715 | −0.504165 | ||||||||
\(780\) | −0.773322 | −0.0276894 | ||||||||
\(781\) | 18.1804 | 0.650546 | ||||||||
\(782\) | −31.3377 | −1.12064 | ||||||||
\(783\) | −5.40181 | −0.193045 | ||||||||
\(784\) | −2.20906 | −0.0788951 | ||||||||
\(785\) | 8.92205 | 0.318442 | ||||||||
\(786\) | −24.3154 | −0.867301 | ||||||||
\(787\) | 8.56339 | 0.305252 | 0.152626 | − | 0.988284i | \(-0.451227\pi\) | ||||
0.152626 | + | 0.988284i | \(0.451227\pi\) | |||||||
\(788\) | 12.2269 | 0.435565 | ||||||||
\(789\) | 3.77883 | 0.134530 | ||||||||
\(790\) | 9.26288 | 0.329559 | ||||||||
\(791\) | −10.9562 | −0.389558 | ||||||||
\(792\) | 5.11533 | 0.181765 | ||||||||
\(793\) | −26.3332 | −0.935121 | ||||||||
\(794\) | −19.2204 | −0.682106 | ||||||||
\(795\) | −1.95379 | −0.0692937 | ||||||||
\(796\) | 4.93767 | 0.175011 | ||||||||
\(797\) | 30.2894 | 1.07290 | 0.536452 | − | 0.843931i | \(-0.319764\pi\) | ||||
0.536452 | + | 0.843931i | \(0.319764\pi\) | |||||||
\(798\) | −4.85429 | −0.171840 | ||||||||
\(799\) | 10.0168 | 0.354369 | ||||||||
\(800\) | 17.1897 | 0.607747 | ||||||||
\(801\) | 2.37465 | 0.0839041 | ||||||||
\(802\) | −15.9486 | −0.563166 | ||||||||
\(803\) | −17.0653 | −0.602222 | ||||||||
\(804\) | 1.87504 | 0.0661275 | ||||||||
\(805\) | −3.76588 | −0.132730 | ||||||||
\(806\) | 17.0995 | 0.602304 | ||||||||
\(807\) | 4.37680 | 0.154071 | ||||||||
\(808\) | −52.8164 | −1.85807 | ||||||||
\(809\) | −8.23364 | −0.289479 | −0.144740 | − | 0.989470i | \(-0.546234\pi\) | ||||
−0.144740 | + | 0.989470i | \(0.546234\pi\) | |||||||
\(810\) | −0.564958 | −0.0198506 | ||||||||
\(811\) | 30.5891 | 1.07413 | 0.537064 | − | 0.843541i | \(-0.319533\pi\) | ||||
0.537064 | + | 0.843541i | \(0.319533\pi\) | |||||||
\(812\) | 3.62250 | 0.127125 | ||||||||
\(813\) | 6.23702 | 0.218742 | ||||||||
\(814\) | 17.4148 | 0.610390 | ||||||||
\(815\) | 9.46244 | 0.331455 | ||||||||
\(816\) | 7.81219 | 0.273481 | ||||||||
\(817\) | 35.1312 | 1.22908 | ||||||||
\(818\) | −3.13489 | −0.109609 | ||||||||
\(819\) | 2.35343 | 0.0822354 | ||||||||
\(820\) | 1.09825 | 0.0383525 | ||||||||
\(821\) | 36.0310 | 1.25749 | 0.628745 | − | 0.777611i | \(-0.283569\pi\) | ||||
0.628745 | + | 0.777611i | \(0.283569\pi\) | |||||||
\(822\) | 21.8108 | 0.760739 | ||||||||
\(823\) | −34.3488 | −1.19733 | −0.598663 | − | 0.801001i | \(-0.704301\pi\) | ||||
−0.598663 | + | 0.801001i | \(0.704301\pi\) | |||||||
\(824\) | −56.1361 | −1.95559 | ||||||||
\(825\) | 7.90744 | 0.275302 | ||||||||
\(826\) | 14.4046 | 0.501200 | ||||||||
\(827\) | 34.7799 | 1.20942 | 0.604708 | − | 0.796447i | \(-0.293290\pi\) | ||||
0.604708 | + | 0.796447i | \(0.293290\pi\) | |||||||
\(828\) | −5.15403 | −0.179115 | ||||||||
\(829\) | −0.441399 | −0.0153304 | −0.00766521 | − | 0.999971i | \(-0.502440\pi\) | ||||
−0.00766521 | + | 0.999971i | \(0.502440\pi\) | |||||||
\(830\) | −7.50338 | −0.260446 | ||||||||
\(831\) | 11.7889 | 0.408952 | ||||||||
\(832\) | −20.1971 | −0.700207 | ||||||||
\(833\) | 3.53643 | 0.122530 | ||||||||
\(834\) | −11.0194 | −0.381571 | ||||||||
\(835\) | 3.00971 | 0.104155 | ||||||||
\(836\) | −4.69037 | −0.162220 | ||||||||
\(837\) | −6.30168 | −0.217818 | ||||||||
\(838\) | −3.37620 | −0.116629 | ||||||||
\(839\) | 12.7763 | 0.441088 | 0.220544 | − | 0.975377i | \(-0.429217\pi\) | ||||
0.220544 | + | 0.975377i | \(0.429217\pi\) | |||||||
\(840\) | 1.50878 | 0.0520579 | ||||||||
\(841\) | 0.179514 | 0.00619013 | ||||||||
\(842\) | −35.3881 | −1.21956 | ||||||||
\(843\) | 26.4366 | 0.910525 | ||||||||
\(844\) | 13.6347 | 0.469324 | ||||||||
\(845\) | −3.65602 | −0.125771 | ||||||||
\(846\) | −3.26581 | −0.112281 | ||||||||
\(847\) | 8.24022 | 0.283137 | ||||||||
\(848\) | −8.80837 | −0.302481 | ||||||||
\(849\) | −20.9061 | −0.717497 | ||||||||
\(850\) | 19.4084 | 0.665702 | ||||||||
\(851\) | −69.8768 | −2.39534 | ||||||||
\(852\) | 7.33898 | 0.251429 | ||||||||
\(853\) | 8.42088 | 0.288325 | 0.144163 | − | 0.989554i | \(-0.453951\pi\) | ||||
0.144163 | + | 0.989554i | \(0.453951\pi\) | |||||||
\(854\) | 12.9012 | 0.441470 | ||||||||
\(855\) | 2.06295 | 0.0705515 | ||||||||
\(856\) | 20.4197 | 0.697933 | ||||||||
\(857\) | 0.224477 | 0.00766800 | 0.00383400 | − | 0.999993i | \(-0.498780\pi\) | ||||
0.00383400 | + | 0.999993i | \(0.498780\pi\) | |||||||
\(858\) | −4.50779 | −0.153894 | ||||||||
\(859\) | 8.15203 | 0.278144 | 0.139072 | − | 0.990282i | \(-0.455588\pi\) | ||||
0.139072 | + | 0.990282i | \(0.455588\pi\) | |||||||
\(860\) | −2.74191 | −0.0934982 | ||||||||
\(861\) | −3.34227 | −0.113904 | ||||||||
\(862\) | 3.98930 | 0.135876 | ||||||||
\(863\) | −6.14825 | −0.209289 | −0.104644 | − | 0.994510i | \(-0.533370\pi\) | ||||
−0.104644 | + | 0.994510i | \(0.533370\pi\) | |||||||
\(864\) | 3.61135 | 0.122861 | ||||||||
\(865\) | 0.0240978 | 0.000819349 0 | ||||||||
\(866\) | −1.13785 | −0.0386657 | ||||||||
\(867\) | 4.49369 | 0.152614 | ||||||||
\(868\) | 4.22597 | 0.143439 | ||||||||
\(869\) | −27.2375 | −0.923970 | ||||||||
\(870\) | 3.05179 | 0.103465 | ||||||||
\(871\) | −6.58022 | −0.222962 | ||||||||
\(872\) | −45.6706 | −1.54660 | ||||||||
\(873\) | 0.810176 | 0.0274203 | ||||||||
\(874\) | −37.3081 | −1.26196 | ||||||||
\(875\) | 4.78228 | 0.161671 | ||||||||
\(876\) | −6.88885 | −0.232753 | ||||||||
\(877\) | −22.2410 | −0.751026 | −0.375513 | − | 0.926817i | \(-0.622533\pi\) | ||||
−0.375513 | + | 0.926817i | \(0.622533\pi\) | |||||||
\(878\) | −34.0592 | −1.14944 | ||||||||
\(879\) | 16.3510 | 0.551507 | ||||||||
\(880\) | −1.79819 | −0.0606169 | ||||||||
\(881\) | 11.4881 | 0.387043 | 0.193522 | − | 0.981096i | \(-0.438009\pi\) | ||||
0.193522 | + | 0.981096i | \(0.438009\pi\) | |||||||
\(882\) | −1.15299 | −0.0388233 | ||||||||
\(883\) | 6.37351 | 0.214486 | 0.107243 | − | 0.994233i | \(-0.465798\pi\) | ||||
0.107243 | + | 0.994233i | \(0.465798\pi\) | |||||||
\(884\) | 5.58130 | 0.187719 | ||||||||
\(885\) | −6.12160 | −0.205775 | ||||||||
\(886\) | −12.5815 | −0.422684 | ||||||||
\(887\) | −18.2567 | −0.613001 | −0.306500 | − | 0.951871i | \(-0.599158\pi\) | ||||
−0.306500 | + | 0.951871i | \(0.599158\pi\) | |||||||
\(888\) | 27.9958 | 0.939477 | ||||||||
\(889\) | −8.25401 | −0.276831 | ||||||||
\(890\) | −1.34158 | −0.0449697 | ||||||||
\(891\) | 1.66126 | 0.0556543 | ||||||||
\(892\) | −17.6554 | −0.591148 | ||||||||
\(893\) | 11.9252 | 0.399061 | ||||||||
\(894\) | 4.78649 | 0.160084 | ||||||||
\(895\) | −7.52905 | −0.251668 | ||||||||
\(896\) | 2.67226 | 0.0892738 | ||||||||
\(897\) | 18.0874 | 0.603922 | ||||||||
\(898\) | −34.6036 | −1.15474 | ||||||||
\(899\) | 34.0405 | 1.13531 | ||||||||
\(900\) | 3.19204 | 0.106401 | ||||||||
\(901\) | 14.1011 | 0.469775 | ||||||||
\(902\) | 6.40185 | 0.213158 | ||||||||
\(903\) | 8.34436 | 0.277683 | ||||||||
\(904\) | 33.7363 | 1.12205 | ||||||||
\(905\) | 7.49478 | 0.249135 | ||||||||
\(906\) | 0.863002 | 0.0286713 | ||||||||
\(907\) | 8.75359 | 0.290658 | 0.145329 | − | 0.989383i | \(-0.453576\pi\) | ||||
0.145329 | + | 0.989383i | \(0.453576\pi\) | |||||||
\(908\) | 18.2382 | 0.605254 | ||||||||
\(909\) | −17.1527 | −0.568919 | ||||||||
\(910\) | −1.32959 | −0.0440754 | ||||||||
\(911\) | 27.1446 | 0.899340 | 0.449670 | − | 0.893195i | \(-0.351542\pi\) | ||||
0.449670 | + | 0.893195i | \(0.351542\pi\) | |||||||
\(912\) | 9.30053 | 0.307971 | ||||||||
\(913\) | 22.0637 | 0.730202 | ||||||||
\(914\) | 26.0428 | 0.861420 | ||||||||
\(915\) | −5.48268 | −0.181252 | ||||||||
\(916\) | 1.19779 | 0.0395762 | ||||||||
\(917\) | 21.0890 | 0.696419 | ||||||||
\(918\) | 4.07747 | 0.134577 | ||||||||
\(919\) | 52.6646 | 1.73724 | 0.868622 | − | 0.495474i | \(-0.165006\pi\) | ||||
0.868622 | + | 0.495474i | \(0.165006\pi\) | |||||||
\(920\) | 11.5959 | 0.382304 | ||||||||
\(921\) | 30.0983 | 0.991771 | ||||||||
\(922\) | −32.1597 | −1.05912 | ||||||||
\(923\) | −25.7553 | −0.847746 | ||||||||
\(924\) | −1.11406 | −0.0366498 | ||||||||
\(925\) | 43.2767 | 1.42293 | ||||||||
\(926\) | −7.76161 | −0.255062 | ||||||||
\(927\) | −18.2308 | −0.598778 | ||||||||
\(928\) | −19.5078 | −0.640376 | ||||||||
\(929\) | −0.872316 | −0.0286198 | −0.0143099 | − | 0.999898i | \(-0.504555\pi\) | ||||
−0.0143099 | + | 0.999898i | \(0.504555\pi\) | |||||||
\(930\) | 3.56018 | 0.116743 | ||||||||
\(931\) | 4.21017 | 0.137983 | ||||||||
\(932\) | 14.6363 | 0.479429 | ||||||||
\(933\) | 14.1735 | 0.464021 | ||||||||
\(934\) | −10.7212 | −0.350808 | ||||||||
\(935\) | 2.87867 | 0.0941425 | ||||||||
\(936\) | −7.24665 | −0.236864 | ||||||||
\(937\) | 52.7623 | 1.72367 | 0.861834 | − | 0.507190i | \(-0.169316\pi\) | ||||
0.861834 | + | 0.507190i | \(0.169316\pi\) | |||||||
\(938\) | 3.22379 | 0.105260 | ||||||||
\(939\) | −22.9571 | −0.749177 | ||||||||
\(940\) | −0.930731 | −0.0303571 | ||||||||
\(941\) | −46.4145 | −1.51307 | −0.756535 | − | 0.653954i | \(-0.773109\pi\) | ||||
−0.756535 | + | 0.653954i | \(0.773109\pi\) | |||||||
\(942\) | 20.9943 | 0.684031 | ||||||||
\(943\) | −25.6873 | −0.836493 | ||||||||
\(944\) | −27.5984 | −0.898250 | ||||||||
\(945\) | 0.489993 | 0.0159395 | ||||||||
\(946\) | −15.9829 | −0.519650 | ||||||||
\(947\) | −13.6636 | −0.444009 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(948\) | −10.9951 | −0.357105 | ||||||||
\(949\) | 24.1756 | 0.784774 | ||||||||
\(950\) | 23.1060 | 0.749657 | ||||||||
\(951\) | −5.17947 | −0.167956 | ||||||||
\(952\) | −10.8893 | −0.352925 | ||||||||
\(953\) | −60.3180 | −1.95389 | −0.976945 | − | 0.213490i | \(-0.931517\pi\) | ||||
−0.976945 | + | 0.213490i | \(0.931517\pi\) | |||||||
\(954\) | −4.59742 | −0.148847 | ||||||||
\(955\) | 5.52153 | 0.178673 | ||||||||
\(956\) | −13.2272 | −0.427797 | ||||||||
\(957\) | −8.97380 | −0.290082 | ||||||||
\(958\) | −5.48373 | −0.177171 | ||||||||
\(959\) | −18.9167 | −0.610852 | ||||||||
\(960\) | −4.20511 | −0.135719 | ||||||||
\(961\) | 8.71120 | 0.281006 | ||||||||
\(962\) | −24.6708 | −0.795418 | ||||||||
\(963\) | 6.63153 | 0.213698 | ||||||||
\(964\) | −13.4810 | −0.434194 | ||||||||
\(965\) | −1.22135 | −0.0393167 | ||||||||
\(966\) | −8.86141 | −0.285111 | ||||||||
\(967\) | −34.4948 | −1.10928 | −0.554638 | − | 0.832092i | \(-0.687143\pi\) | ||||
−0.554638 | + | 0.832092i | \(0.687143\pi\) | |||||||
\(968\) | −25.3732 | −0.815526 | ||||||||
\(969\) | −14.8890 | −0.478302 | ||||||||
\(970\) | −0.457715 | −0.0146963 | ||||||||
\(971\) | −6.29857 | −0.202131 | −0.101065 | − | 0.994880i | \(-0.532225\pi\) | ||||
−0.101065 | + | 0.994880i | \(0.532225\pi\) | |||||||
\(972\) | 0.670610 | 0.0215098 | ||||||||
\(973\) | 9.55723 | 0.306391 | ||||||||
\(974\) | 21.7225 | 0.696033 | ||||||||
\(975\) | −11.2021 | −0.358754 | ||||||||
\(976\) | −24.7179 | −0.791201 | ||||||||
\(977\) | −11.5571 | −0.369743 | −0.184872 | − | 0.982763i | \(-0.559187\pi\) | ||||
−0.184872 | + | 0.982763i | \(0.559187\pi\) | |||||||
\(978\) | 22.2659 | 0.711984 | ||||||||
\(979\) | 3.94491 | 0.126080 | ||||||||
\(980\) | −0.328594 | −0.0104965 | ||||||||
\(981\) | −14.8320 | −0.473549 | ||||||||
\(982\) | −6.94211 | −0.221532 | ||||||||
\(983\) | 50.0335 | 1.59582 | 0.797910 | − | 0.602777i | \(-0.205939\pi\) | ||||
0.797910 | + | 0.602777i | \(0.205939\pi\) | |||||||
\(984\) | 10.2915 | 0.328081 | ||||||||
\(985\) | −8.93379 | −0.284654 | ||||||||
\(986\) | −22.0257 | −0.701442 | ||||||||
\(987\) | 2.83247 | 0.0901584 | ||||||||
\(988\) | 6.64462 | 0.211394 | ||||||||
\(989\) | 64.1312 | 2.03925 | ||||||||
\(990\) | −0.938541 | −0.0298288 | ||||||||
\(991\) | 5.03742 | 0.160019 | 0.0800094 | − | 0.996794i | \(-0.474505\pi\) | ||||
0.0800094 | + | 0.996794i | \(0.474505\pi\) | |||||||
\(992\) | −22.7576 | −0.722554 | ||||||||
\(993\) | −22.6512 | −0.718814 | ||||||||
\(994\) | 12.6180 | 0.400220 | ||||||||
\(995\) | −3.60780 | −0.114375 | ||||||||
\(996\) | 8.90658 | 0.282216 | ||||||||
\(997\) | 21.7107 | 0.687586 | 0.343793 | − | 0.939045i | \(-0.388288\pi\) | ||||
0.343793 | + | 0.939045i | \(0.388288\pi\) | |||||||
\(998\) | 10.0947 | 0.319541 | ||||||||
\(999\) | 9.09193 | 0.287656 |
(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 | 8043.2.a.s.1.18 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.s.1.18 | ✓ | 50 | 1.1 | even | 1 | trivial |