Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,2,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("230.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(1.83655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.68740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-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 | ||||||||
\(3\) | 2.68740 | 1.55157 | 0.775785 | − | 0.630997i | \(-0.217354\pi\) | ||||
0.775785 | + | 0.630997i | \(0.217354\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.68740 | 1.09713 | ||||||||
\(7\) | −4.59692 | −1.73747 | −0.868735 | − | 0.495277i | \(-0.835067\pi\) | ||||
−0.868735 | + | 0.495277i | \(0.835067\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.22212 | 1.40737 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 5.13163 | 1.54725 | 0.773623 | − | 0.633647i | \(-0.218443\pi\) | ||||
0.773623 | + | 0.633647i | \(0.218443\pi\) | |||||||
\(12\) | 2.68740 | 0.775785 | ||||||||
\(13\) | −1.22212 | −0.338954 | −0.169477 | − | 0.985534i | \(-0.554208\pi\) | ||||
−0.169477 | + | 0.985534i | \(0.554208\pi\) | |||||||
\(14\) | −4.59692 | −1.22858 | ||||||||
\(15\) | −2.68740 | −0.693884 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.68740 | −1.13686 | −0.568431 | − | 0.822731i | \(-0.692449\pi\) | ||||
−0.568431 | + | 0.822731i | \(0.692449\pi\) | |||||||
\(18\) | 4.22212 | 0.995162 | ||||||||
\(19\) | −4.59692 | −1.05460 | −0.527302 | − | 0.849678i | \(-0.676796\pi\) | ||||
−0.527302 | + | 0.849678i | \(0.676796\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −12.3537 | −2.69581 | ||||||||
\(22\) | 5.13163 | 1.09407 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 2.68740 | 0.548563 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.22212 | −0.239677 | ||||||||
\(27\) | 3.28432 | 0.632067 | ||||||||
\(28\) | −4.59692 | −0.868735 | ||||||||
\(29\) | 3.37480 | 0.626684 | 0.313342 | − | 0.949640i | \(-0.398551\pi\) | ||||
0.313342 | + | 0.949640i | \(0.398551\pi\) | |||||||
\(30\) | −2.68740 | −0.490650 | ||||||||
\(31\) | −0.777884 | −0.139712 | −0.0698560 | − | 0.997557i | \(-0.522254\pi\) | ||||
−0.0698560 | + | 0.997557i | \(0.522254\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 13.7907 | 2.40066 | ||||||||
\(34\) | −4.68740 | −0.803882 | ||||||||
\(35\) | 4.59692 | 0.777021 | ||||||||
\(36\) | 4.22212 | 0.703686 | ||||||||
\(37\) | 5.81903 | 0.956643 | 0.478321 | − | 0.878185i | \(-0.341245\pi\) | ||||
0.478321 | + | 0.878185i | \(0.341245\pi\) | |||||||
\(38\) | −4.59692 | −0.745718 | ||||||||
\(39\) | −3.28432 | −0.525911 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.50643 | −1.32848 | −0.664241 | − | 0.747519i | \(-0.731245\pi\) | ||||
−0.664241 | + | 0.747519i | \(0.731245\pi\) | |||||||
\(42\) | −12.3537 | −1.90622 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 5.13163 | 0.773623 | ||||||||
\(45\) | −4.22212 | −0.629396 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −6.44423 | −0.939988 | −0.469994 | − | 0.882670i | \(-0.655744\pi\) | ||||
−0.469994 | + | 0.882670i | \(0.655744\pi\) | |||||||
\(48\) | 2.68740 | 0.387893 | ||||||||
\(49\) | 14.1316 | 2.01880 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −12.5969 | −1.76392 | ||||||||
\(52\) | −1.22212 | −0.169477 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 3.28432 | 0.446939 | ||||||||
\(55\) | −5.13163 | −0.691949 | ||||||||
\(56\) | −4.59692 | −0.614289 | ||||||||
\(57\) | −12.3537 | −1.63629 | ||||||||
\(58\) | 3.37480 | 0.443133 | ||||||||
\(59\) | 9.37480 | 1.22049 | 0.610247 | − | 0.792211i | \(-0.291070\pi\) | ||||
0.610247 | + | 0.792211i | \(0.291070\pi\) | |||||||
\(60\) | −2.68740 | −0.346942 | ||||||||
\(61\) | 10.9507 | 1.40209 | 0.701044 | − | 0.713118i | \(-0.252717\pi\) | ||||
0.701044 | + | 0.713118i | \(0.252717\pi\) | |||||||
\(62\) | −0.777884 | −0.0987913 | ||||||||
\(63\) | −19.4087 | −2.44527 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.22212 | 0.151585 | ||||||||
\(66\) | 13.7907 | 1.69752 | ||||||||
\(67\) | 15.6381 | 1.91049 | 0.955247 | − | 0.295810i | \(-0.0955895\pi\) | ||||
0.955247 | + | 0.295810i | \(0.0955895\pi\) | |||||||
\(68\) | −4.68740 | −0.568431 | ||||||||
\(69\) | −2.68740 | −0.323525 | ||||||||
\(70\) | 4.59692 | 0.549436 | ||||||||
\(71\) | 1.31260 | 0.155777 | 0.0778885 | − | 0.996962i | \(-0.475182\pi\) | ||||
0.0778885 | + | 0.996962i | \(0.475182\pi\) | |||||||
\(72\) | 4.22212 | 0.497581 | ||||||||
\(73\) | −4.44423 | −0.520158 | −0.260079 | − | 0.965587i | \(-0.583749\pi\) | ||||
−0.260079 | + | 0.965587i | \(0.583749\pi\) | |||||||
\(74\) | 5.81903 | 0.676449 | ||||||||
\(75\) | 2.68740 | 0.310314 | ||||||||
\(76\) | −4.59692 | −0.527302 | ||||||||
\(77\) | −23.5897 | −2.68829 | ||||||||
\(78\) | −3.28432 | −0.371875 | ||||||||
\(79\) | −4.88847 | −0.549995 | −0.274998 | − | 0.961445i | \(-0.588677\pi\) | ||||
−0.274998 | + | 0.961445i | \(0.588677\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −3.84008 | −0.426676 | ||||||||
\(82\) | −8.50643 | −0.939378 | ||||||||
\(83\) | −3.81903 | −0.419193 | −0.209597 | − | 0.977788i | \(-0.567215\pi\) | ||||
−0.209597 | + | 0.977788i | \(0.567215\pi\) | |||||||
\(84\) | −12.3537 | −1.34790 | ||||||||
\(85\) | 4.68740 | 0.508420 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 9.06943 | 0.972345 | ||||||||
\(88\) | 5.13163 | 0.547034 | ||||||||
\(89\) | 8.93057 | 0.946638 | 0.473319 | − | 0.880891i | \(-0.343056\pi\) | ||||
0.473319 | + | 0.880891i | \(0.343056\pi\) | |||||||
\(90\) | −4.22212 | −0.445050 | ||||||||
\(91\) | 5.61797 | 0.588923 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −2.09048 | −0.216773 | ||||||||
\(94\) | −6.44423 | −0.664672 | ||||||||
\(95\) | 4.59692 | 0.471634 | ||||||||
\(96\) | 2.68740 | 0.274282 | ||||||||
\(97\) | −18.0622 | −1.83394 | −0.916969 | − | 0.398958i | \(-0.869372\pi\) | ||||
−0.916969 | + | 0.398958i | \(0.869372\pi\) | |||||||
\(98\) | 14.1316 | 1.42751 | ||||||||
\(99\) | 21.6663 | 2.17755 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.37480 | 0.335805 | 0.167903 | − | 0.985804i | \(-0.446301\pi\) | ||||
0.167903 | + | 0.985804i | \(0.446301\pi\) | |||||||
\(102\) | −12.5969 | −1.24728 | ||||||||
\(103\) | 13.1316 | 1.29390 | 0.646949 | − | 0.762533i | \(-0.276045\pi\) | ||||
0.646949 | + | 0.762533i | \(0.276045\pi\) | |||||||
\(104\) | −1.22212 | −0.119838 | ||||||||
\(105\) | 12.3537 | 1.20560 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 12.3054 | 1.18960 | 0.594802 | − | 0.803872i | \(-0.297230\pi\) | ||||
0.594802 | + | 0.803872i | \(0.297230\pi\) | |||||||
\(108\) | 3.28432 | 0.316033 | ||||||||
\(109\) | −10.5969 | −1.01500 | −0.507500 | − | 0.861652i | \(-0.669430\pi\) | ||||
−0.507500 | + | 0.861652i | \(0.669430\pi\) | |||||||
\(110\) | −5.13163 | −0.489282 | ||||||||
\(111\) | 15.6381 | 1.48430 | ||||||||
\(112\) | −4.59692 | −0.434368 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | −12.3537 | −1.15703 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 3.37480 | 0.313342 | ||||||||
\(117\) | −5.15992 | −0.477035 | ||||||||
\(118\) | 9.37480 | 0.863020 | ||||||||
\(119\) | 21.5476 | 1.97526 | ||||||||
\(120\) | −2.68740 | −0.245325 | ||||||||
\(121\) | 15.3337 | 1.39397 | ||||||||
\(122\) | 10.9507 | 0.991427 | ||||||||
\(123\) | −22.8602 | −2.06123 | ||||||||
\(124\) | −0.777884 | −0.0698560 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −19.4087 | −1.72907 | ||||||||
\(127\) | −2.26326 | −0.200832 | −0.100416 | − | 0.994946i | \(-0.532017\pi\) | ||||
−0.100416 | + | 0.994946i | \(0.532017\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 21.4992 | 1.89290 | ||||||||
\(130\) | 1.22212 | 0.107187 | ||||||||
\(131\) | 2.93057 | 0.256045 | 0.128022 | − | 0.991771i | \(-0.459137\pi\) | ||||
0.128022 | + | 0.991771i | \(0.459137\pi\) | |||||||
\(132\) | 13.7907 | 1.20033 | ||||||||
\(133\) | 21.1316 | 1.83234 | ||||||||
\(134\) | 15.6381 | 1.35092 | ||||||||
\(135\) | −3.28432 | −0.282669 | ||||||||
\(136\) | −4.68740 | −0.401941 | ||||||||
\(137\) | −19.7907 | −1.69084 | −0.845419 | − | 0.534104i | \(-0.820649\pi\) | ||||
−0.845419 | + | 0.534104i | \(0.820649\pi\) | |||||||
\(138\) | −2.68740 | −0.228767 | ||||||||
\(139\) | 6.26326 | 0.531243 | 0.265622 | − | 0.964077i | \(-0.414423\pi\) | ||||
0.265622 | + | 0.964077i | \(0.414423\pi\) | |||||||
\(140\) | 4.59692 | 0.388510 | ||||||||
\(141\) | −17.3182 | −1.45846 | ||||||||
\(142\) | 1.31260 | 0.110151 | ||||||||
\(143\) | −6.27145 | −0.524445 | ||||||||
\(144\) | 4.22212 | 0.351843 | ||||||||
\(145\) | −3.37480 | −0.280262 | ||||||||
\(146\) | −4.44423 | −0.367807 | ||||||||
\(147\) | 37.9773 | 3.13232 | ||||||||
\(148\) | 5.81903 | 0.478321 | ||||||||
\(149\) | −19.7907 | −1.62132 | −0.810661 | − | 0.585516i | \(-0.800892\pi\) | ||||
−0.810661 | + | 0.585516i | \(0.800892\pi\) | |||||||
\(150\) | 2.68740 | 0.219425 | ||||||||
\(151\) | 4.06220 | 0.330577 | 0.165289 | − | 0.986245i | \(-0.447144\pi\) | ||||
0.165289 | + | 0.986245i | \(0.447144\pi\) | |||||||
\(152\) | −4.59692 | −0.372859 | ||||||||
\(153\) | −19.7907 | −1.59999 | ||||||||
\(154\) | −23.5897 | −1.90091 | ||||||||
\(155\) | 0.777884 | 0.0624811 | ||||||||
\(156\) | −3.28432 | −0.262956 | ||||||||
\(157\) | 4.62520 | 0.369131 | 0.184566 | − | 0.982820i | \(-0.440912\pi\) | ||||
0.184566 | + | 0.982820i | \(0.440912\pi\) | |||||||
\(158\) | −4.88847 | −0.388905 | ||||||||
\(159\) | −16.1244 | −1.27875 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 4.59692 | 0.362288 | ||||||||
\(162\) | −3.84008 | −0.301705 | ||||||||
\(163\) | 12.4159 | 0.972492 | 0.486246 | − | 0.873822i | \(-0.338366\pi\) | ||||
0.486246 | + | 0.873822i | \(0.338366\pi\) | |||||||
\(164\) | −8.50643 | −0.664241 | ||||||||
\(165\) | −13.7907 | −1.07361 | ||||||||
\(166\) | −3.81903 | −0.296414 | ||||||||
\(167\) | 12.8885 | 0.997339 | 0.498670 | − | 0.866792i | \(-0.333822\pi\) | ||||
0.498670 | + | 0.866792i | \(0.333822\pi\) | |||||||
\(168\) | −12.3537 | −0.953112 | ||||||||
\(169\) | −11.5064 | −0.885110 | ||||||||
\(170\) | 4.68740 | 0.359507 | ||||||||
\(171\) | −19.4087 | −1.48422 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | −10.2432 | −0.778774 | −0.389387 | − | 0.921074i | \(-0.627313\pi\) | ||||
−0.389387 | + | 0.921074i | \(0.627313\pi\) | |||||||
\(174\) | 9.06943 | 0.687552 | ||||||||
\(175\) | −4.59692 | −0.347494 | ||||||||
\(176\) | 5.13163 | 0.386811 | ||||||||
\(177\) | 25.1938 | 1.89368 | ||||||||
\(178\) | 8.93057 | 0.669374 | ||||||||
\(179\) | −13.1938 | −0.986153 | −0.493077 | − | 0.869986i | \(-0.664128\pi\) | ||||
−0.493077 | + | 0.869986i | \(0.664128\pi\) | |||||||
\(180\) | −4.22212 | −0.314698 | ||||||||
\(181\) | 15.7907 | 1.17372 | 0.586858 | − | 0.809690i | \(-0.300364\pi\) | ||||
0.586858 | + | 0.809690i | \(0.300364\pi\) | |||||||
\(182\) | 5.61797 | 0.416431 | ||||||||
\(183\) | 29.4288 | 2.17544 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −5.81903 | −0.427824 | ||||||||
\(186\) | −2.09048 | −0.153282 | ||||||||
\(187\) | −24.0540 | −1.75900 | ||||||||
\(188\) | −6.44423 | −0.469994 | ||||||||
\(189\) | −15.0977 | −1.09820 | ||||||||
\(190\) | 4.59692 | 0.333495 | ||||||||
\(191\) | 16.1244 | 1.16672 | 0.583360 | − | 0.812214i | \(-0.301738\pi\) | ||||
0.583360 | + | 0.812214i | \(0.301738\pi\) | |||||||
\(192\) | 2.68740 | 0.193946 | ||||||||
\(193\) | −17.9434 | −1.29160 | −0.645798 | − | 0.763508i | \(-0.723475\pi\) | ||||
−0.645798 | + | 0.763508i | \(0.723475\pi\) | |||||||
\(194\) | −18.0622 | −1.29679 | ||||||||
\(195\) | 3.28432 | 0.235195 | ||||||||
\(196\) | 14.1316 | 1.00940 | ||||||||
\(197\) | 5.88123 | 0.419020 | 0.209510 | − | 0.977806i | \(-0.432813\pi\) | ||||
0.209510 | + | 0.977806i | \(0.432813\pi\) | |||||||
\(198\) | 21.6663 | 1.53976 | ||||||||
\(199\) | 6.56863 | 0.465638 | 0.232819 | − | 0.972520i | \(-0.425205\pi\) | ||||
0.232819 | + | 0.972520i | \(0.425205\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 42.0257 | 2.96427 | ||||||||
\(202\) | 3.37480 | 0.237450 | ||||||||
\(203\) | −15.5137 | −1.08885 | ||||||||
\(204\) | −12.5969 | −0.881960 | ||||||||
\(205\) | 8.50643 | 0.594115 | ||||||||
\(206\) | 13.1316 | 0.914924 | ||||||||
\(207\) | −4.22212 | −0.293457 | ||||||||
\(208\) | −1.22212 | −0.0847385 | ||||||||
\(209\) | −23.5897 | −1.63173 | ||||||||
\(210\) | 12.3537 | 0.852490 | ||||||||
\(211\) | −15.4571 | −1.06411 | −0.532055 | − | 0.846710i | \(-0.678580\pi\) | ||||
−0.532055 | + | 0.846710i | \(0.678580\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 3.52748 | 0.241699 | ||||||||
\(214\) | 12.3054 | 0.841177 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 3.28432 | 0.223469 | ||||||||
\(217\) | 3.57587 | 0.242746 | ||||||||
\(218\) | −10.5969 | −0.717714 | ||||||||
\(219\) | −11.9434 | −0.807062 | ||||||||
\(220\) | −5.13163 | −0.345975 | ||||||||
\(221\) | 5.72855 | 0.385344 | ||||||||
\(222\) | 15.6381 | 1.04956 | ||||||||
\(223\) | −10.7496 | −0.719846 | −0.359923 | − | 0.932982i | \(-0.617197\pi\) | ||||
−0.359923 | + | 0.932982i | \(0.617197\pi\) | |||||||
\(224\) | −4.59692 | −0.307144 | ||||||||
\(225\) | 4.22212 | 0.281474 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | −12.3054 | −0.816736 | −0.408368 | − | 0.912817i | \(-0.633902\pi\) | ||||
−0.408368 | + | 0.912817i | \(0.633902\pi\) | |||||||
\(228\) | −12.3537 | −0.818147 | ||||||||
\(229\) | 9.63806 | 0.636901 | 0.318451 | − | 0.947939i | \(-0.396838\pi\) | ||||
0.318451 | + | 0.947939i | \(0.396838\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | −63.3949 | −4.17108 | ||||||||
\(232\) | 3.37480 | 0.221566 | ||||||||
\(233\) | 13.9434 | 0.913464 | 0.456732 | − | 0.889604i | \(-0.349020\pi\) | ||||
0.456732 | + | 0.889604i | \(0.349020\pi\) | |||||||
\(234\) | −5.15992 | −0.337314 | ||||||||
\(235\) | 6.44423 | 0.420375 | ||||||||
\(236\) | 9.37480 | 0.610247 | ||||||||
\(237\) | −13.1373 | −0.853357 | ||||||||
\(238\) | 21.5476 | 1.39672 | ||||||||
\(239\) | −26.3877 | −1.70688 | −0.853438 | − | 0.521194i | \(-0.825487\pi\) | ||||
−0.853438 | + | 0.521194i | \(0.825487\pi\) | |||||||
\(240\) | −2.68740 | −0.173471 | ||||||||
\(241\) | −7.06943 | −0.455382 | −0.227691 | − | 0.973733i | \(-0.573118\pi\) | ||||
−0.227691 | + | 0.973733i | \(0.573118\pi\) | |||||||
\(242\) | 15.3337 | 0.985684 | ||||||||
\(243\) | −20.1728 | −1.29408 | ||||||||
\(244\) | 10.9507 | 0.701044 | ||||||||
\(245\) | −14.1316 | −0.902837 | ||||||||
\(246\) | −22.8602 | −1.45751 | ||||||||
\(247\) | 5.61797 | 0.357463 | ||||||||
\(248\) | −0.777884 | −0.0493957 | ||||||||
\(249\) | −10.2633 | −0.650408 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −24.9023 | −1.57182 | −0.785909 | − | 0.618342i | \(-0.787805\pi\) | ||||
−0.785909 | + | 0.618342i | \(0.787805\pi\) | |||||||
\(252\) | −19.4087 | −1.22263 | ||||||||
\(253\) | −5.13163 | −0.322623 | ||||||||
\(254\) | −2.26326 | −0.142010 | ||||||||
\(255\) | 12.5969 | 0.788849 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.444233 | 0.0277105 | 0.0138552 | − | 0.999904i | \(-0.495590\pi\) | ||||
0.0138552 | + | 0.999904i | \(0.495590\pi\) | |||||||
\(258\) | 21.4992 | 1.33848 | ||||||||
\(259\) | −26.7496 | −1.66214 | ||||||||
\(260\) | 1.22212 | 0.0757924 | ||||||||
\(261\) | 14.2488 | 0.881978 | ||||||||
\(262\) | 2.93057 | 0.181051 | ||||||||
\(263\) | −23.8812 | −1.47258 | −0.736290 | − | 0.676666i | \(-0.763424\pi\) | ||||
−0.736290 | + | 0.676666i | \(0.763424\pi\) | |||||||
\(264\) | 13.7907 | 0.848762 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 21.1316 | 1.29566 | ||||||||
\(267\) | 24.0000 | 1.46878 | ||||||||
\(268\) | 15.6381 | 0.955247 | ||||||||
\(269\) | 16.2633 | 0.991589 | 0.495794 | − | 0.868440i | \(-0.334877\pi\) | ||||
0.495794 | + | 0.868440i | \(0.334877\pi\) | |||||||
\(270\) | −3.28432 | −0.199877 | ||||||||
\(271\) | 25.6098 | 1.55568 | 0.777842 | − | 0.628460i | \(-0.216315\pi\) | ||||
0.777842 | + | 0.628460i | \(0.216315\pi\) | |||||||
\(272\) | −4.68740 | −0.284215 | ||||||||
\(273\) | 15.0977 | 0.913756 | ||||||||
\(274\) | −19.7907 | −1.19560 | ||||||||
\(275\) | 5.13163 | 0.309449 | ||||||||
\(276\) | −2.68740 | −0.161762 | ||||||||
\(277\) | 2.88847 | 0.173551 | 0.0867755 | − | 0.996228i | \(-0.472344\pi\) | ||||
0.0867755 | + | 0.996228i | \(0.472344\pi\) | |||||||
\(278\) | 6.26326 | 0.375646 | ||||||||
\(279\) | −3.28432 | −0.196627 | ||||||||
\(280\) | 4.59692 | 0.274718 | ||||||||
\(281\) | 4.26326 | 0.254325 | 0.127163 | − | 0.991882i | \(-0.459413\pi\) | ||||
0.127163 | + | 0.991882i | \(0.459413\pi\) | |||||||
\(282\) | −17.3182 | −1.03129 | ||||||||
\(283\) | 30.5686 | 1.81712 | 0.908558 | − | 0.417758i | \(-0.137184\pi\) | ||||
0.908558 | + | 0.417758i | \(0.137184\pi\) | |||||||
\(284\) | 1.31260 | 0.0778885 | ||||||||
\(285\) | 12.3537 | 0.731773 | ||||||||
\(286\) | −6.27145 | −0.370839 | ||||||||
\(287\) | 39.1033 | 2.30820 | ||||||||
\(288\) | 4.22212 | 0.248791 | ||||||||
\(289\) | 4.97171 | 0.292454 | ||||||||
\(290\) | −3.37480 | −0.198175 | ||||||||
\(291\) | −48.5403 | −2.84549 | ||||||||
\(292\) | −4.44423 | −0.260079 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 37.9773 | 2.21488 | ||||||||
\(295\) | −9.37480 | −0.545822 | ||||||||
\(296\) | 5.81903 | 0.338224 | ||||||||
\(297\) | 16.8539 | 0.977962 | ||||||||
\(298\) | −19.7907 | −1.14645 | ||||||||
\(299\) | 1.22212 | 0.0706768 | ||||||||
\(300\) | 2.68740 | 0.155157 | ||||||||
\(301\) | −36.7753 | −2.11969 | ||||||||
\(302\) | 4.06220 | 0.233753 | ||||||||
\(303\) | 9.06943 | 0.521025 | ||||||||
\(304\) | −4.59692 | −0.263651 | ||||||||
\(305\) | −10.9507 | −0.627033 | ||||||||
\(306\) | −19.7907 | −1.13136 | ||||||||
\(307\) | −8.54853 | −0.487891 | −0.243945 | − | 0.969789i | \(-0.578442\pi\) | ||||
−0.243945 | + | 0.969789i | \(0.578442\pi\) | |||||||
\(308\) | −23.5897 | −1.34415 | ||||||||
\(309\) | 35.2899 | 2.00757 | ||||||||
\(310\) | 0.777884 | 0.0441808 | ||||||||
\(311\) | −7.63806 | −0.433115 | −0.216557 | − | 0.976270i | \(-0.569483\pi\) | ||||
−0.216557 | + | 0.976270i | \(0.569483\pi\) | |||||||
\(312\) | −3.28432 | −0.185938 | ||||||||
\(313\) | −18.2350 | −1.03070 | −0.515351 | − | 0.856979i | \(-0.672338\pi\) | ||||
−0.515351 | + | 0.856979i | \(0.672338\pi\) | |||||||
\(314\) | 4.62520 | 0.261015 | ||||||||
\(315\) | 19.4087 | 1.09356 | ||||||||
\(316\) | −4.88847 | −0.274998 | ||||||||
\(317\) | −16.8602 | −0.946962 | −0.473481 | − | 0.880804i | \(-0.657003\pi\) | ||||
−0.473481 | + | 0.880804i | \(0.657003\pi\) | |||||||
\(318\) | −16.1244 | −0.904211 | ||||||||
\(319\) | 17.3182 | 0.969635 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 33.0694 | 1.84576 | ||||||||
\(322\) | 4.59692 | 0.256176 | ||||||||
\(323\) | 21.5476 | 1.19894 | ||||||||
\(324\) | −3.84008 | −0.213338 | ||||||||
\(325\) | −1.22212 | −0.0677908 | ||||||||
\(326\) | 12.4159 | 0.687656 | ||||||||
\(327\) | −28.4781 | −1.57485 | ||||||||
\(328\) | −8.50643 | −0.469689 | ||||||||
\(329\) | 29.6236 | 1.63320 | ||||||||
\(330\) | −13.7907 | −0.759156 | ||||||||
\(331\) | 19.1517 | 1.05267 | 0.526337 | − | 0.850276i | \(-0.323565\pi\) | ||||
0.526337 | + | 0.850276i | \(0.323565\pi\) | |||||||
\(332\) | −3.81903 | −0.209597 | ||||||||
\(333\) | 24.5686 | 1.34635 | ||||||||
\(334\) | 12.8885 | 0.705225 | ||||||||
\(335\) | −15.6381 | −0.854399 | ||||||||
\(336\) | −12.3537 | −0.673952 | ||||||||
\(337\) | 1.70845 | 0.0930652 | 0.0465326 | − | 0.998917i | \(-0.485183\pi\) | ||||
0.0465326 | + | 0.998917i | \(0.485183\pi\) | |||||||
\(338\) | −11.5064 | −0.625867 | ||||||||
\(339\) | −16.1244 | −0.875757 | ||||||||
\(340\) | 4.68740 | 0.254210 | ||||||||
\(341\) | −3.99181 | −0.216169 | ||||||||
\(342\) | −19.4087 | −1.04950 | ||||||||
\(343\) | −32.7835 | −1.77014 | ||||||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 2.68740 | 0.144685 | ||||||||
\(346\) | −10.2432 | −0.550676 | ||||||||
\(347\) | 10.6874 | 0.573730 | 0.286865 | − | 0.957971i | \(-0.407387\pi\) | ||||
0.286865 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(348\) | 9.06943 | 0.486173 | ||||||||
\(349\) | −12.3877 | −0.663096 | −0.331548 | − | 0.943438i | \(-0.607571\pi\) | ||||
−0.331548 | + | 0.943438i | \(0.607571\pi\) | |||||||
\(350\) | −4.59692 | −0.245715 | ||||||||
\(351\) | −4.01382 | −0.214242 | ||||||||
\(352\) | 5.13163 | 0.273517 | ||||||||
\(353\) | 5.45710 | 0.290452 | 0.145226 | − | 0.989399i | \(-0.453609\pi\) | ||||
0.145226 | + | 0.989399i | \(0.453609\pi\) | |||||||
\(354\) | 25.1938 | 1.33904 | ||||||||
\(355\) | −1.31260 | −0.0696656 | ||||||||
\(356\) | 8.93057 | 0.473319 | ||||||||
\(357\) | 57.9070 | 3.06476 | ||||||||
\(358\) | −13.1938 | −0.697316 | ||||||||
\(359\) | 20.1810 | 1.06511 | 0.532555 | − | 0.846395i | \(-0.321232\pi\) | ||||
0.532555 | + | 0.846395i | \(0.321232\pi\) | |||||||
\(360\) | −4.22212 | −0.222525 | ||||||||
\(361\) | 2.13163 | 0.112191 | ||||||||
\(362\) | 15.7907 | 0.829943 | ||||||||
\(363\) | 41.2076 | 2.16284 | ||||||||
\(364\) | 5.61797 | 0.294461 | ||||||||
\(365\) | 4.44423 | 0.232622 | ||||||||
\(366\) | 29.4288 | 1.53827 | ||||||||
\(367\) | 2.74960 | 0.143528 | 0.0717639 | − | 0.997422i | \(-0.477137\pi\) | ||||
0.0717639 | + | 0.997422i | \(0.477137\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −35.9151 | −1.86967 | ||||||||
\(370\) | −5.81903 | −0.302517 | ||||||||
\(371\) | 27.5815 | 1.43196 | ||||||||
\(372\) | −2.09048 | −0.108387 | ||||||||
\(373\) | −12.0823 | −0.625598 | −0.312799 | − | 0.949819i | \(-0.601267\pi\) | ||||
−0.312799 | + | 0.949819i | \(0.601267\pi\) | |||||||
\(374\) | −24.0540 | −1.24380 | ||||||||
\(375\) | −2.68740 | −0.138777 | ||||||||
\(376\) | −6.44423 | −0.332336 | ||||||||
\(377\) | −4.12440 | −0.212417 | ||||||||
\(378\) | −15.0977 | −0.776543 | ||||||||
\(379\) | 5.25603 | 0.269984 | 0.134992 | − | 0.990847i | \(-0.456899\pi\) | ||||
0.134992 | + | 0.990847i | \(0.456899\pi\) | |||||||
\(380\) | 4.59692 | 0.235817 | ||||||||
\(381\) | −6.08230 | −0.311605 | ||||||||
\(382\) | 16.1244 | 0.824996 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 2.68740 | 0.137141 | ||||||||
\(385\) | 23.5897 | 1.20224 | ||||||||
\(386\) | −17.9434 | −0.913297 | ||||||||
\(387\) | 33.7769 | 1.71698 | ||||||||
\(388\) | −18.0622 | −0.916969 | ||||||||
\(389\) | 0.325463 | 0.0165017 | 0.00825083 | − | 0.999966i | \(-0.497374\pi\) | ||||
0.00825083 | + | 0.999966i | \(0.497374\pi\) | |||||||
\(390\) | 3.28432 | 0.166308 | ||||||||
\(391\) | 4.68740 | 0.237052 | ||||||||
\(392\) | 14.1316 | 0.713755 | ||||||||
\(393\) | 7.87560 | 0.397272 | ||||||||
\(394\) | 5.88123 | 0.296292 | ||||||||
\(395\) | 4.88847 | 0.245965 | ||||||||
\(396\) | 21.6663 | 1.08878 | ||||||||
\(397\) | −17.7568 | −0.891190 | −0.445595 | − | 0.895235i | \(-0.647008\pi\) | ||||
−0.445595 | + | 0.895235i | \(0.647008\pi\) | |||||||
\(398\) | 6.56863 | 0.329256 | ||||||||
\(399\) | 56.7891 | 2.84301 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 3.91770 | 0.195641 | 0.0978204 | − | 0.995204i | \(-0.468813\pi\) | ||||
0.0978204 | + | 0.995204i | \(0.468813\pi\) | |||||||
\(402\) | 42.0257 | 2.09605 | ||||||||
\(403\) | 0.950664 | 0.0473560 | ||||||||
\(404\) | 3.37480 | 0.167903 | ||||||||
\(405\) | 3.84008 | 0.190815 | ||||||||
\(406\) | −15.5137 | −0.769930 | ||||||||
\(407\) | 29.8611 | 1.48016 | ||||||||
\(408\) | −12.5969 | −0.623640 | ||||||||
\(409\) | 9.58405 | 0.473901 | 0.236950 | − | 0.971522i | \(-0.423852\pi\) | ||||
0.236950 | + | 0.971522i | \(0.423852\pi\) | |||||||
\(410\) | 8.50643 | 0.420103 | ||||||||
\(411\) | −53.1856 | −2.62345 | ||||||||
\(412\) | 13.1316 | 0.646949 | ||||||||
\(413\) | −43.0952 | −2.12057 | ||||||||
\(414\) | −4.22212 | −0.207506 | ||||||||
\(415\) | 3.81903 | 0.187469 | ||||||||
\(416\) | −1.22212 | −0.0599192 | ||||||||
\(417\) | 16.8319 | 0.824261 | ||||||||
\(418\) | −23.5897 | −1.15381 | ||||||||
\(419\) | −20.5265 | −1.00279 | −0.501393 | − | 0.865219i | \(-0.667179\pi\) | ||||
−0.501393 | + | 0.865219i | \(0.667179\pi\) | |||||||
\(420\) | 12.3537 | 0.602801 | ||||||||
\(421\) | 2.29155 | 0.111683 | 0.0558417 | − | 0.998440i | \(-0.482216\pi\) | ||||
0.0558417 | + | 0.998440i | \(0.482216\pi\) | |||||||
\(422\) | −15.4571 | −0.752440 | ||||||||
\(423\) | −27.2083 | −1.32291 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −4.68740 | −0.227372 | ||||||||
\(426\) | 3.52748 | 0.170907 | ||||||||
\(427\) | −50.3393 | −2.43609 | ||||||||
\(428\) | 12.3054 | 0.594802 | ||||||||
\(429\) | −16.8539 | −0.813714 | ||||||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | −8.83189 | −0.425417 | −0.212709 | − | 0.977116i | \(-0.568229\pi\) | ||||
−0.212709 | + | 0.977116i | \(0.568229\pi\) | |||||||
\(432\) | 3.28432 | 0.158017 | ||||||||
\(433\) | 33.3465 | 1.60253 | 0.801266 | − | 0.598309i | \(-0.204160\pi\) | ||||
0.801266 | + | 0.598309i | \(0.204160\pi\) | |||||||
\(434\) | 3.57587 | 0.171647 | ||||||||
\(435\) | −9.06943 | −0.434846 | ||||||||
\(436\) | −10.5969 | −0.507500 | ||||||||
\(437\) | 4.59692 | 0.219900 | ||||||||
\(438\) | −11.9434 | −0.570679 | ||||||||
\(439\) | −6.02829 | −0.287714 | −0.143857 | − | 0.989598i | \(-0.545951\pi\) | ||||
−0.143857 | + | 0.989598i | \(0.545951\pi\) | |||||||
\(440\) | −5.13163 | −0.244641 | ||||||||
\(441\) | 59.6654 | 2.84121 | ||||||||
\(442\) | 5.72855 | 0.272479 | ||||||||
\(443\) | −15.5275 | −0.737733 | −0.368866 | − | 0.929482i | \(-0.620254\pi\) | ||||
−0.368866 | + | 0.929482i | \(0.620254\pi\) | |||||||
\(444\) | 15.6381 | 0.742150 | ||||||||
\(445\) | −8.93057 | −0.423349 | ||||||||
\(446\) | −10.7496 | −0.509008 | ||||||||
\(447\) | −53.1856 | −2.51559 | ||||||||
\(448\) | −4.59692 | −0.217184 | ||||||||
\(449\) | −18.3594 | −0.866433 | −0.433216 | − | 0.901290i | \(-0.642621\pi\) | ||||
−0.433216 | + | 0.901290i | \(0.642621\pi\) | |||||||
\(450\) | 4.22212 | 0.199032 | ||||||||
\(451\) | −43.6519 | −2.05549 | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 10.9168 | 0.512914 | ||||||||
\(454\) | −12.3054 | −0.577519 | ||||||||
\(455\) | −5.61797 | −0.263374 | ||||||||
\(456\) | −12.3537 | −0.578517 | ||||||||
\(457\) | −11.4992 | −0.537910 | −0.268955 | − | 0.963153i | \(-0.586678\pi\) | ||||
−0.268955 | + | 0.963153i | \(0.586678\pi\) | |||||||
\(458\) | 9.63806 | 0.450357 | ||||||||
\(459\) | −15.3949 | −0.718572 | ||||||||
\(460\) | 1.00000 | 0.0466252 | ||||||||
\(461\) | 1.33270 | 0.0620700 | 0.0310350 | − | 0.999518i | \(-0.490120\pi\) | ||||
0.0310350 | + | 0.999518i | \(0.490120\pi\) | |||||||
\(462\) | −63.3949 | −2.94940 | ||||||||
\(463\) | 35.8190 | 1.66465 | 0.832326 | − | 0.554287i | \(-0.187009\pi\) | ||||
0.832326 | + | 0.554287i | \(0.187009\pi\) | |||||||
\(464\) | 3.37480 | 0.156671 | ||||||||
\(465\) | 2.09048 | 0.0969439 | ||||||||
\(466\) | 13.9434 | 0.645917 | ||||||||
\(467\) | −23.7625 | −1.09960 | −0.549798 | − | 0.835298i | \(-0.685295\pi\) | ||||
−0.549798 | + | 0.835298i | \(0.685295\pi\) | |||||||
\(468\) | −5.15992 | −0.238517 | ||||||||
\(469\) | −71.8869 | −3.31943 | ||||||||
\(470\) | 6.44423 | 0.297250 | ||||||||
\(471\) | 12.4298 | 0.572733 | ||||||||
\(472\) | 9.37480 | 0.431510 | ||||||||
\(473\) | 41.0531 | 1.88762 | ||||||||
\(474\) | −13.1373 | −0.603414 | ||||||||
\(475\) | −4.59692 | −0.210921 | ||||||||
\(476\) | 21.5476 | 0.987632 | ||||||||
\(477\) | −25.3327 | −1.15990 | ||||||||
\(478\) | −26.3877 | −1.20694 | ||||||||
\(479\) | −2.04210 | −0.0933060 | −0.0466530 | − | 0.998911i | \(-0.514855\pi\) | ||||
−0.0466530 | + | 0.998911i | \(0.514855\pi\) | |||||||
\(480\) | −2.68740 | −0.122662 | ||||||||
\(481\) | −7.11153 | −0.324258 | ||||||||
\(482\) | −7.06943 | −0.322004 | ||||||||
\(483\) | 12.3537 | 0.562115 | ||||||||
\(484\) | 15.3337 | 0.696984 | ||||||||
\(485\) | 18.0622 | 0.820162 | ||||||||
\(486\) | −20.1728 | −0.915056 | ||||||||
\(487\) | −18.6252 | −0.843988 | −0.421994 | − | 0.906599i | \(-0.638670\pi\) | ||||
−0.421994 | + | 0.906599i | \(0.638670\pi\) | |||||||
\(488\) | 10.9507 | 0.495713 | ||||||||
\(489\) | 33.3666 | 1.50889 | ||||||||
\(490\) | −14.1316 | −0.638402 | ||||||||
\(491\) | 33.7204 | 1.52178 | 0.760889 | − | 0.648882i | \(-0.224763\pi\) | ||||
0.760889 | + | 0.648882i | \(0.224763\pi\) | |||||||
\(492\) | −22.8602 | −1.03062 | ||||||||
\(493\) | −15.8190 | −0.712453 | ||||||||
\(494\) | 5.61797 | 0.252764 | ||||||||
\(495\) | −21.6663 | −0.973830 | ||||||||
\(496\) | −0.777884 | −0.0349280 | ||||||||
\(497\) | −6.03391 | −0.270658 | ||||||||
\(498\) | −10.2633 | −0.459908 | ||||||||
\(499\) | −16.8885 | −0.756032 | −0.378016 | − | 0.925799i | \(-0.623393\pi\) | ||||
−0.378016 | + | 0.925799i | \(0.623393\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 34.6365 | 1.54744 | ||||||||
\(502\) | −24.9023 | −1.11144 | ||||||||
\(503\) | 11.4031 | 0.508438 | 0.254219 | − | 0.967147i | \(-0.418182\pi\) | ||||
0.254219 | + | 0.967147i | \(0.418182\pi\) | |||||||
\(504\) | −19.4087 | −0.864533 | ||||||||
\(505\) | −3.37480 | −0.150177 | ||||||||
\(506\) | −5.13163 | −0.228129 | ||||||||
\(507\) | −30.9224 | −1.37331 | ||||||||
\(508\) | −2.26326 | −0.100416 | ||||||||
\(509\) | −1.87560 | −0.0831346 | −0.0415673 | − | 0.999136i | \(-0.513235\pi\) | ||||
−0.0415673 | + | 0.999136i | \(0.513235\pi\) | |||||||
\(510\) | 12.5969 | 0.557801 | ||||||||
\(511\) | 20.4298 | 0.903759 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −15.0977 | −0.666581 | ||||||||
\(514\) | 0.444233 | 0.0195943 | ||||||||
\(515\) | −13.1316 | −0.578649 | ||||||||
\(516\) | 21.4992 | 0.946449 | ||||||||
\(517\) | −33.0694 | −1.45439 | ||||||||
\(518\) | −26.7496 | −1.17531 | ||||||||
\(519\) | −27.5275 | −1.20832 | ||||||||
\(520\) | 1.22212 | 0.0535933 | ||||||||
\(521\) | 5.11153 | 0.223940 | 0.111970 | − | 0.993712i | \(-0.464284\pi\) | ||||
0.111970 | + | 0.993712i | \(0.464284\pi\) | |||||||
\(522\) | 14.2488 | 0.623653 | ||||||||
\(523\) | 19.4571 | 0.850799 | 0.425400 | − | 0.905006i | \(-0.360134\pi\) | ||||
0.425400 | + | 0.905006i | \(0.360134\pi\) | |||||||
\(524\) | 2.93057 | 0.128022 | ||||||||
\(525\) | −12.3537 | −0.539162 | ||||||||
\(526\) | −23.8812 | −1.04127 | ||||||||
\(527\) | 3.64625 | 0.158833 | ||||||||
\(528\) | 13.7907 | 0.600165 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.00000 | 0.260623 | ||||||||
\(531\) | 39.5815 | 1.71769 | ||||||||
\(532\) | 21.1316 | 0.916172 | ||||||||
\(533\) | 10.3958 | 0.450294 | ||||||||
\(534\) | 24.0000 | 1.03858 | ||||||||
\(535\) | −12.3054 | −0.532007 | ||||||||
\(536\) | 15.6381 | 0.675461 | ||||||||
\(537\) | −35.4571 | −1.53009 | ||||||||
\(538\) | 16.2633 | 0.701159 | ||||||||
\(539\) | 72.5183 | 3.12359 | ||||||||
\(540\) | −3.28432 | −0.141334 | ||||||||
\(541\) | −2.70750 | −0.116404 | −0.0582022 | − | 0.998305i | \(-0.518537\pi\) | ||||
−0.0582022 | + | 0.998305i | \(0.518537\pi\) | |||||||
\(542\) | 25.6098 | 1.10003 | ||||||||
\(543\) | 42.4360 | 1.82111 | ||||||||
\(544\) | −4.68740 | −0.200971 | ||||||||
\(545\) | 10.5969 | 0.453922 | ||||||||
\(546\) | 15.0977 | 0.646123 | ||||||||
\(547\) | −1.66635 | −0.0712479 | −0.0356240 | − | 0.999365i | \(-0.511342\pi\) | ||||
−0.0356240 | + | 0.999365i | \(0.511342\pi\) | |||||||
\(548\) | −19.7907 | −0.845419 | ||||||||
\(549\) | 46.2350 | 1.97326 | ||||||||
\(550\) | 5.13163 | 0.218814 | ||||||||
\(551\) | −15.5137 | −0.660904 | ||||||||
\(552\) | −2.68740 | −0.114383 | ||||||||
\(553\) | 22.4719 | 0.955601 | ||||||||
\(554\) | 2.88847 | 0.122719 | ||||||||
\(555\) | −15.6381 | −0.663799 | ||||||||
\(556\) | 6.26326 | 0.265622 | ||||||||
\(557\) | −20.9306 | −0.886857 | −0.443428 | − | 0.896310i | \(-0.646238\pi\) | ||||
−0.443428 | + | 0.896310i | \(0.646238\pi\) | |||||||
\(558\) | −3.28432 | −0.139036 | ||||||||
\(559\) | −9.77693 | −0.413520 | ||||||||
\(560\) | 4.59692 | 0.194255 | ||||||||
\(561\) | −64.6427 | −2.72922 | ||||||||
\(562\) | 4.26326 | 0.179835 | ||||||||
\(563\) | −15.2761 | −0.643812 | −0.321906 | − | 0.946772i | \(-0.604324\pi\) | ||||
−0.321906 | + | 0.946772i | \(0.604324\pi\) | |||||||
\(564\) | −17.3182 | −0.729229 | ||||||||
\(565\) | 6.00000 | 0.252422 | ||||||||
\(566\) | 30.5686 | 1.28490 | ||||||||
\(567\) | 17.6525 | 0.741337 | ||||||||
\(568\) | 1.31260 | 0.0550755 | ||||||||
\(569\) | 20.3877 | 0.854695 | 0.427348 | − | 0.904087i | \(-0.359448\pi\) | ||||
0.427348 | + | 0.904087i | \(0.359448\pi\) | |||||||
\(570\) | 12.3537 | 0.517442 | ||||||||
\(571\) | 5.49357 | 0.229899 | 0.114949 | − | 0.993371i | \(-0.463329\pi\) | ||||
0.114949 | + | 0.993371i | \(0.463329\pi\) | |||||||
\(572\) | −6.27145 | −0.262223 | ||||||||
\(573\) | 43.3327 | 1.81025 | ||||||||
\(574\) | 39.1033 | 1.63214 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 4.22212 | 0.175922 | ||||||||
\(577\) | 17.2761 | 0.719215 | 0.359607 | − | 0.933104i | \(-0.382911\pi\) | ||||
0.359607 | + | 0.933104i | \(0.382911\pi\) | |||||||
\(578\) | 4.97171 | 0.206796 | ||||||||
\(579\) | −48.2212 | −2.00400 | ||||||||
\(580\) | −3.37480 | −0.140131 | ||||||||
\(581\) | 17.5558 | 0.728336 | ||||||||
\(582\) | −48.5403 | −2.01206 | ||||||||
\(583\) | −30.7898 | −1.27518 | ||||||||
\(584\) | −4.44423 | −0.183904 | ||||||||
\(585\) | 5.15992 | 0.213336 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 31.8247 | 1.31354 | 0.656772 | − | 0.754089i | \(-0.271921\pi\) | ||||
0.656772 | + | 0.754089i | \(0.271921\pi\) | |||||||
\(588\) | 37.9773 | 1.56616 | ||||||||
\(589\) | 3.57587 | 0.147341 | ||||||||
\(590\) | −9.37480 | −0.385954 | ||||||||
\(591\) | 15.8052 | 0.650140 | ||||||||
\(592\) | 5.81903 | 0.239161 | ||||||||
\(593\) | −12.4442 | −0.511023 | −0.255512 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255512 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(594\) | 16.8539 | 0.691524 | ||||||||
\(595\) | −21.5476 | −0.883365 | ||||||||
\(596\) | −19.7907 | −0.810661 | ||||||||
\(597\) | 17.6525 | 0.722470 | ||||||||
\(598\) | 1.22212 | 0.0499761 | ||||||||
\(599\) | 17.4370 | 0.712456 | 0.356228 | − | 0.934399i | \(-0.384063\pi\) | ||||
0.356228 | + | 0.934399i | \(0.384063\pi\) | |||||||
\(600\) | 2.68740 | 0.109713 | ||||||||
\(601\) | −0.916751 | −0.0373951 | −0.0186975 | − | 0.999825i | \(-0.505952\pi\) | ||||
−0.0186975 | + | 0.999825i | \(0.505952\pi\) | |||||||
\(602\) | −36.7753 | −1.49885 | ||||||||
\(603\) | 66.0257 | 2.68878 | ||||||||
\(604\) | 4.06220 | 0.165289 | ||||||||
\(605\) | −15.3337 | −0.623402 | ||||||||
\(606\) | 9.06943 | 0.368421 | ||||||||
\(607\) | 36.7753 | 1.49266 | 0.746332 | − | 0.665574i | \(-0.231813\pi\) | ||||
0.746332 | + | 0.665574i | \(0.231813\pi\) | |||||||
\(608\) | −4.59692 | −0.186430 | ||||||||
\(609\) | −41.6914 | −1.68942 | ||||||||
\(610\) | −10.9507 | −0.443379 | ||||||||
\(611\) | 7.87560 | 0.318613 | ||||||||
\(612\) | −19.7907 | −0.799994 | ||||||||
\(613\) | 4.38766 | 0.177216 | 0.0886080 | − | 0.996067i | \(-0.471758\pi\) | ||||
0.0886080 | + | 0.996067i | \(0.471758\pi\) | |||||||
\(614\) | −8.54853 | −0.344991 | ||||||||
\(615\) | 22.8602 | 0.921811 | ||||||||
\(616\) | −23.5897 | −0.950455 | ||||||||
\(617\) | 40.4499 | 1.62845 | 0.814225 | − | 0.580549i | \(-0.197162\pi\) | ||||
0.814225 | + | 0.580549i | \(0.197162\pi\) | |||||||
\(618\) | 35.2899 | 1.41957 | ||||||||
\(619\) | −39.8165 | −1.60036 | −0.800180 | − | 0.599760i | \(-0.795263\pi\) | ||||
−0.800180 | + | 0.599760i | \(0.795263\pi\) | |||||||
\(620\) | 0.777884 | 0.0312406 | ||||||||
\(621\) | −3.28432 | −0.131795 | ||||||||
\(622\) | −7.63806 | −0.306258 | ||||||||
\(623\) | −41.0531 | −1.64476 | ||||||||
\(624\) | −3.28432 | −0.131478 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.2350 | −0.728816 | ||||||||
\(627\) | −63.3949 | −2.53175 | ||||||||
\(628\) | 4.62520 | 0.184566 | ||||||||
\(629\) | −27.2761 | −1.08757 | ||||||||
\(630\) | 19.4087 | 0.773262 | ||||||||
\(631\) | 25.9013 | 1.03112 | 0.515558 | − | 0.856855i | \(-0.327585\pi\) | ||||
0.515558 | + | 0.856855i | \(0.327585\pi\) | |||||||
\(632\) | −4.88847 | −0.194453 | ||||||||
\(633\) | −41.5394 | −1.65104 | ||||||||
\(634\) | −16.8602 | −0.669603 | ||||||||
\(635\) | 2.26326 | 0.0898149 | ||||||||
\(636\) | −16.1244 | −0.639374 | ||||||||
\(637\) | −17.2705 | −0.684282 | ||||||||
\(638\) | 17.3182 | 0.685635 | ||||||||
\(639\) | 5.54195 | 0.219236 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −43.8448 | −1.73176 | −0.865882 | − | 0.500248i | \(-0.833242\pi\) | ||||
−0.865882 | + | 0.500248i | \(0.833242\pi\) | |||||||
\(642\) | 33.0694 | 1.30515 | ||||||||
\(643\) | 3.94343 | 0.155514 | 0.0777568 | − | 0.996972i | \(-0.475224\pi\) | ||||
0.0777568 | + | 0.996972i | \(0.475224\pi\) | |||||||
\(644\) | 4.59692 | 0.181144 | ||||||||
\(645\) | −21.4992 | −0.846530 | ||||||||
\(646\) | 21.5476 | 0.847778 | ||||||||
\(647\) | 24.3456 | 0.957123 | 0.478561 | − | 0.878054i | \(-0.341158\pi\) | ||||
0.478561 | + | 0.878054i | \(0.341158\pi\) | |||||||
\(648\) | −3.84008 | −0.150853 | ||||||||
\(649\) | 48.1080 | 1.88841 | ||||||||
\(650\) | −1.22212 | −0.0479353 | ||||||||
\(651\) | 9.60978 | 0.376637 | ||||||||
\(652\) | 12.4159 | 0.486246 | ||||||||
\(653\) | 37.6921 | 1.47500 | 0.737502 | − | 0.675344i | \(-0.236005\pi\) | ||||
0.737502 | + | 0.675344i | \(0.236005\pi\) | |||||||
\(654\) | −28.4781 | −1.11358 | ||||||||
\(655\) | −2.93057 | −0.114507 | ||||||||
\(656\) | −8.50643 | −0.332120 | ||||||||
\(657\) | −18.7641 | −0.732056 | ||||||||
\(658\) | 29.6236 | 1.15485 | ||||||||
\(659\) | 24.6107 | 0.958698 | 0.479349 | − | 0.877624i | \(-0.340873\pi\) | ||||
0.479349 | + | 0.877624i | \(0.340873\pi\) | |||||||
\(660\) | −13.7907 | −0.536804 | ||||||||
\(661\) | 27.3126 | 1.06234 | 0.531169 | − | 0.847266i | \(-0.321753\pi\) | ||||
0.531169 | + | 0.847266i | \(0.321753\pi\) | |||||||
\(662\) | 19.1517 | 0.744353 | ||||||||
\(663\) | 15.3949 | 0.597888 | ||||||||
\(664\) | −3.81903 | −0.148207 | ||||||||
\(665\) | −21.1316 | −0.819450 | ||||||||
\(666\) | 24.5686 | 0.952015 | ||||||||
\(667\) | −3.37480 | −0.130673 | ||||||||
\(668\) | 12.8885 | 0.498670 | ||||||||
\(669\) | −28.8885 | −1.11689 | ||||||||
\(670\) | −15.6381 | −0.604151 | ||||||||
\(671\) | 56.1948 | 2.16938 | ||||||||
\(672\) | −12.3537 | −0.476556 | ||||||||
\(673\) | 22.5265 | 0.868334 | 0.434167 | − | 0.900832i | \(-0.357043\pi\) | ||||
0.434167 | + | 0.900832i | \(0.357043\pi\) | |||||||
\(674\) | 1.70845 | 0.0658070 | ||||||||
\(675\) | 3.28432 | 0.126413 | ||||||||
\(676\) | −11.5064 | −0.442555 | ||||||||
\(677\) | −6.00000 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(678\) | −16.1244 | −0.619254 | ||||||||
\(679\) | 83.0304 | 3.18641 | ||||||||
\(680\) | 4.68740 | 0.179754 | ||||||||
\(681\) | −33.0694 | −1.26722 | ||||||||
\(682\) | −3.99181 | −0.152854 | ||||||||
\(683\) | −31.9974 | −1.22435 | −0.612174 | − | 0.790723i | \(-0.709705\pi\) | ||||
−0.612174 | + | 0.790723i | \(0.709705\pi\) | |||||||
\(684\) | −19.4087 | −0.742111 | ||||||||
\(685\) | 19.7907 | 0.756166 | ||||||||
\(686\) | −32.7835 | −1.25168 | ||||||||
\(687\) | 25.9013 | 0.988197 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | 7.33270 | 0.279354 | ||||||||
\(690\) | 2.68740 | 0.102308 | ||||||||
\(691\) | −2.80617 | −0.106752 | −0.0533758 | − | 0.998574i | \(-0.516998\pi\) | ||||
−0.0533758 | + | 0.998574i | \(0.516998\pi\) | |||||||
\(692\) | −10.2432 | −0.389387 | ||||||||
\(693\) | −99.5984 | −3.78343 | ||||||||
\(694\) | 10.6874 | 0.405688 | ||||||||
\(695\) | −6.26326 | −0.237579 | ||||||||
\(696\) | 9.06943 | 0.343776 | ||||||||
\(697\) | 39.8730 | 1.51030 | ||||||||
\(698\) | −12.3877 | −0.468880 | ||||||||
\(699\) | 37.4716 | 1.41730 | ||||||||
\(700\) | −4.59692 | −0.173747 | ||||||||
\(701\) | 8.37385 | 0.316276 | 0.158138 | − | 0.987417i | \(-0.449451\pi\) | ||||
0.158138 | + | 0.987417i | \(0.449451\pi\) | |||||||
\(702\) | −4.01382 | −0.151492 | ||||||||
\(703\) | −26.7496 | −1.00888 | ||||||||
\(704\) | 5.13163 | 0.193406 | ||||||||
\(705\) | 17.3182 | 0.652242 | ||||||||
\(706\) | 5.45710 | 0.205381 | ||||||||
\(707\) | −15.5137 | −0.583451 | ||||||||
\(708\) | 25.1938 | 0.946842 | ||||||||
\(709\) | 21.2139 | 0.796706 | 0.398353 | − | 0.917232i | \(-0.369582\pi\) | ||||
0.398353 | + | 0.917232i | \(0.369582\pi\) | |||||||
\(710\) | −1.31260 | −0.0492610 | ||||||||
\(711\) | −20.6397 | −0.774048 | ||||||||
\(712\) | 8.93057 | 0.334687 | ||||||||
\(713\) | 0.777884 | 0.0291320 | ||||||||
\(714\) | 57.9070 | 2.16711 | ||||||||
\(715\) | 6.27145 | 0.234539 | ||||||||
\(716\) | −13.1938 | −0.493077 | ||||||||
\(717\) | −70.9142 | −2.64834 | ||||||||
\(718\) | 20.1810 | 0.753147 | ||||||||
\(719\) | −28.1106 | −1.04835 | −0.524174 | − | 0.851611i | \(-0.675626\pi\) | ||||
−0.524174 | + | 0.851611i | \(0.675626\pi\) | |||||||
\(720\) | −4.22212 | −0.157349 | ||||||||
\(721\) | −60.3650 | −2.24811 | ||||||||
\(722\) | 2.13163 | 0.0793311 | ||||||||
\(723\) | −18.9984 | −0.706558 | ||||||||
\(724\) | 15.7907 | 0.586858 | ||||||||
\(725\) | 3.37480 | 0.125337 | ||||||||
\(726\) | 41.2076 | 1.52936 | ||||||||
\(727\) | −39.0330 | −1.44765 | −0.723826 | − | 0.689982i | \(-0.757618\pi\) | ||||
−0.723826 | + | 0.689982i | \(0.757618\pi\) | |||||||
\(728\) | 5.61797 | 0.208216 | ||||||||
\(729\) | −42.6921 | −1.58119 | ||||||||
\(730\) | 4.44423 | 0.164488 | ||||||||
\(731\) | −37.4992 | −1.38696 | ||||||||
\(732\) | 29.4288 | 1.08772 | ||||||||
\(733\) | 47.1373 | 1.74105 | 0.870527 | − | 0.492120i | \(-0.163778\pi\) | ||||
0.870527 | + | 0.492120i | \(0.163778\pi\) | |||||||
\(734\) | 2.74960 | 0.101490 | ||||||||
\(735\) | −37.9773 | −1.40082 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 80.2488 | 2.95600 | ||||||||
\(738\) | −35.9151 | −1.32205 | ||||||||
\(739\) | −24.5265 | −0.902223 | −0.451111 | − | 0.892468i | \(-0.648972\pi\) | ||||
−0.451111 | + | 0.892468i | \(0.648972\pi\) | |||||||
\(740\) | −5.81903 | −0.213912 | ||||||||
\(741\) | 15.0977 | 0.554629 | ||||||||
\(742\) | 27.5815 | 1.01255 | ||||||||
\(743\) | −7.34651 | −0.269517 | −0.134759 | − | 0.990878i | \(-0.543026\pi\) | ||||
−0.134759 | + | 0.990878i | \(0.543026\pi\) | |||||||
\(744\) | −2.09048 | −0.0766409 | ||||||||
\(745\) | 19.7907 | 0.725077 | ||||||||
\(746\) | −12.0823 | −0.442364 | ||||||||
\(747\) | −16.1244 | −0.589961 | ||||||||
\(748\) | −24.0540 | −0.879502 | ||||||||
\(749\) | −56.5667 | −2.06690 | ||||||||
\(750\) | −2.68740 | −0.0981300 | ||||||||
\(751\) | 11.2359 | 0.410005 | 0.205002 | − | 0.978761i | \(-0.434280\pi\) | ||||
0.205002 | + | 0.978761i | \(0.434280\pi\) | |||||||
\(752\) | −6.44423 | −0.234997 | ||||||||
\(753\) | −66.9224 | −2.43879 | ||||||||
\(754\) | −4.12440 | −0.150202 | ||||||||
\(755\) | −4.06220 | −0.147839 | ||||||||
\(756\) | −15.0977 | −0.549099 | ||||||||
\(757\) | 49.1794 | 1.78745 | 0.893727 | − | 0.448611i | \(-0.148081\pi\) | ||||
0.893727 | + | 0.448611i | \(0.148081\pi\) | |||||||
\(758\) | 5.25603 | 0.190908 | ||||||||
\(759\) | −13.7907 | −0.500572 | ||||||||
\(760\) | 4.59692 | 0.166748 | ||||||||
\(761\) | 43.2478 | 1.56773 | 0.783867 | − | 0.620929i | \(-0.213245\pi\) | ||||
0.783867 | + | 0.620929i | \(0.213245\pi\) | |||||||
\(762\) | −6.08230 | −0.220338 | ||||||||
\(763\) | 48.7131 | 1.76353 | ||||||||
\(764\) | 16.1244 | 0.583360 | ||||||||
\(765\) | 19.7907 | 0.715536 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.4571 | −0.413692 | ||||||||
\(768\) | 2.68740 | 0.0969732 | ||||||||
\(769\) | −39.6638 | −1.43031 | −0.715156 | − | 0.698964i | \(-0.753645\pi\) | ||||
−0.715156 | + | 0.698964i | \(0.753645\pi\) | |||||||
\(770\) | 23.5897 | 0.850113 | ||||||||
\(771\) | 1.19383 | 0.0429948 | ||||||||
\(772\) | −17.9434 | −0.645798 | ||||||||
\(773\) | −2.18097 | −0.0784440 | −0.0392220 | − | 0.999231i | \(-0.512488\pi\) | ||||
−0.0392220 | + | 0.999231i | \(0.512488\pi\) | |||||||
\(774\) | 33.7769 | 1.21409 | ||||||||
\(775\) | −0.777884 | −0.0279424 | ||||||||
\(776\) | −18.0622 | −0.648395 | ||||||||
\(777\) | −71.8869 | −2.57893 | ||||||||
\(778\) | 0.325463 | 0.0116684 | ||||||||
\(779\) | 39.1033 | 1.40102 | ||||||||
\(780\) | 3.28432 | 0.117597 | ||||||||
\(781\) | 6.73578 | 0.241025 | ||||||||
\(782\) | 4.68740 | 0.167621 | ||||||||
\(783\) | 11.0839 | 0.396106 | ||||||||
\(784\) | 14.1316 | 0.504701 | ||||||||
\(785\) | −4.62520 | −0.165080 | ||||||||
\(786\) | 7.87560 | 0.280913 | ||||||||
\(787\) | 4.76407 | 0.169821 | 0.0849103 | − | 0.996389i | \(-0.472940\pi\) | ||||
0.0849103 | + | 0.996389i | \(0.472940\pi\) | |||||||
\(788\) | 5.88123 | 0.209510 | ||||||||
\(789\) | −64.1784 | −2.28481 | ||||||||
\(790\) | 4.88847 | 0.173924 | ||||||||
\(791\) | 27.5815 | 0.980685 | ||||||||
\(792\) | 21.6663 | 0.769880 | ||||||||
\(793\) | −13.3830 | −0.475244 | ||||||||
\(794\) | −17.7568 | −0.630166 | ||||||||
\(795\) | 16.1244 | 0.571873 | ||||||||
\(796\) | 6.56863 | 0.232819 | ||||||||
\(797\) | 39.7204 | 1.40697 | 0.703484 | − | 0.710711i | \(-0.251627\pi\) | ||||
0.703484 | + | 0.710711i | \(0.251627\pi\) | |||||||
\(798\) | 56.7891 | 2.01031 | ||||||||
\(799\) | 30.2067 | 1.06864 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 37.7059 | 1.33227 | ||||||||
\(802\) | 3.91770 | 0.138339 | ||||||||
\(803\) | −22.8062 | −0.804812 | ||||||||
\(804\) | 42.0257 | 1.48213 | ||||||||
\(805\) | −4.59692 | −0.162020 | ||||||||
\(806\) | 0.950664 | 0.0334857 | ||||||||
\(807\) | 43.7059 | 1.53852 | ||||||||
\(808\) | 3.37480 | 0.118725 | ||||||||
\(809\) | 46.8941 | 1.64871 | 0.824354 | − | 0.566074i | \(-0.191538\pi\) | ||||
0.824354 | + | 0.566074i | \(0.191538\pi\) | |||||||
\(810\) | 3.84008 | 0.134927 | ||||||||
\(811\) | −36.8319 | −1.29334 | −0.646671 | − | 0.762769i | \(-0.723839\pi\) | ||||
−0.646671 | + | 0.762769i | \(0.723839\pi\) | |||||||
\(812\) | −15.5137 | −0.544423 | ||||||||
\(813\) | 68.8237 | 2.41375 | ||||||||
\(814\) | 29.8611 | 1.04663 | ||||||||
\(815\) | −12.4159 | −0.434912 | ||||||||
\(816\) | −12.5969 | −0.440980 | ||||||||
\(817\) | −36.7753 | −1.28661 | ||||||||
\(818\) | 9.58405 | 0.335099 | ||||||||
\(819\) | 23.7197 | 0.828834 | ||||||||
\(820\) | 8.50643 | 0.297057 | ||||||||
\(821\) | −18.6107 | −0.649519 | −0.324759 | − | 0.945797i | \(-0.605283\pi\) | ||||
−0.324759 | + | 0.945797i | \(0.605283\pi\) | |||||||
\(822\) | −53.1856 | −1.85506 | ||||||||
\(823\) | −9.31823 | −0.324813 | −0.162407 | − | 0.986724i | \(-0.551926\pi\) | ||||
−0.162407 | + | 0.986724i | \(0.551926\pi\) | |||||||
\(824\) | 13.1316 | 0.457462 | ||||||||
\(825\) | 13.7907 | 0.480132 | ||||||||
\(826\) | −43.0952 | −1.49947 | ||||||||
\(827\) | 53.0129 | 1.84344 | 0.921719 | − | 0.387858i | \(-0.126785\pi\) | ||||
0.921719 | + | 0.387858i | \(0.126785\pi\) | |||||||
\(828\) | −4.22212 | −0.146729 | ||||||||
\(829\) | −25.2761 | −0.877876 | −0.438938 | − | 0.898517i | \(-0.644645\pi\) | ||||
−0.438938 | + | 0.898517i | \(0.644645\pi\) | |||||||
\(830\) | 3.81903 | 0.132561 | ||||||||
\(831\) | 7.76246 | 0.269277 | ||||||||
\(832\) | −1.22212 | −0.0423693 | ||||||||
\(833\) | −66.2406 | −2.29510 | ||||||||
\(834\) | 16.8319 | 0.582841 | ||||||||
\(835\) | −12.8885 | −0.446024 | ||||||||
\(836\) | −23.5897 | −0.815866 | ||||||||
\(837\) | −2.55481 | −0.0883073 | ||||||||
\(838\) | −20.5265 | −0.709077 | ||||||||
\(839\) | 11.6946 | 0.403744 | 0.201872 | − | 0.979412i | \(-0.435298\pi\) | ||||
0.201872 | + | 0.979412i | \(0.435298\pi\) | |||||||
\(840\) | 12.3537 | 0.426245 | ||||||||
\(841\) | −17.6107 | −0.607267 | ||||||||
\(842\) | 2.29155 | 0.0789720 | ||||||||
\(843\) | 11.4571 | 0.394603 | ||||||||
\(844\) | −15.4571 | −0.532055 | ||||||||
\(845\) | 11.5064 | 0.395833 | ||||||||
\(846\) | −27.2083 | −0.935441 | ||||||||
\(847\) | −70.4875 | −2.42198 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 82.1501 | 2.81938 | ||||||||
\(850\) | −4.68740 | −0.160776 | ||||||||
\(851\) | −5.81903 | −0.199474 | ||||||||
\(852\) | 3.52748 | 0.120850 | ||||||||
\(853\) | 38.6371 | 1.32291 | 0.661455 | − | 0.749985i | \(-0.269939\pi\) | ||||
0.661455 | + | 0.749985i | \(0.269939\pi\) | |||||||
\(854\) | −50.3393 | −1.72257 | ||||||||
\(855\) | 19.4087 | 0.663764 | ||||||||
\(856\) | 12.3054 | 0.420589 | ||||||||
\(857\) | 26.2488 | 0.896642 | 0.448321 | − | 0.893873i | \(-0.352022\pi\) | ||||
0.448321 | + | 0.893873i | \(0.352022\pi\) | |||||||
\(858\) | −16.8539 | −0.575383 | ||||||||
\(859\) | 37.5558 | 1.28139 | 0.640693 | − | 0.767797i | \(-0.278647\pi\) | ||||
0.640693 | + | 0.767797i | \(0.278647\pi\) | |||||||
\(860\) | −8.00000 | −0.272798 | ||||||||
\(861\) | 105.086 | 3.58133 | ||||||||
\(862\) | −8.83189 | −0.300816 | ||||||||
\(863\) | −21.9855 | −0.748396 | −0.374198 | − | 0.927349i | \(-0.622082\pi\) | ||||
−0.374198 | + | 0.927349i | \(0.622082\pi\) | |||||||
\(864\) | 3.28432 | 0.111735 | ||||||||
\(865\) | 10.2432 | 0.348278 | ||||||||
\(866\) | 33.3465 | 1.13316 | ||||||||
\(867\) | 13.3610 | 0.453763 | ||||||||
\(868\) | 3.57587 | 0.121373 | ||||||||
\(869\) | −25.0858 | −0.850978 | ||||||||
\(870\) | −9.06943 | −0.307483 | ||||||||
\(871\) | −19.1115 | −0.647570 | ||||||||
\(872\) | −10.5969 | −0.358857 | ||||||||
\(873\) | −76.2607 | −2.58103 | ||||||||
\(874\) | 4.59692 | 0.155493 | ||||||||
\(875\) | 4.59692 | 0.155404 | ||||||||
\(876\) | −11.9434 | −0.403531 | ||||||||
\(877\) | −36.5064 | −1.23273 | −0.616367 | − | 0.787459i | \(-0.711396\pi\) | ||||
−0.616367 | + | 0.787459i | \(0.711396\pi\) | |||||||
\(878\) | −6.02829 | −0.203445 | ||||||||
\(879\) | −16.1244 | −0.543862 | ||||||||
\(880\) | −5.13163 | −0.172987 | ||||||||
\(881\) | −17.4571 | −0.588145 | −0.294072 | − | 0.955783i | \(-0.595011\pi\) | ||||
−0.294072 | + | 0.955783i | \(0.595011\pi\) | |||||||
\(882\) | 59.6654 | 2.00904 | ||||||||
\(883\) | 22.9444 | 0.772140 | 0.386070 | − | 0.922470i | \(-0.373832\pi\) | ||||
0.386070 | + | 0.922470i | \(0.373832\pi\) | |||||||
\(884\) | 5.72855 | 0.192672 | ||||||||
\(885\) | −25.1938 | −0.846881 | ||||||||
\(886\) | −15.5275 | −0.521656 | ||||||||
\(887\) | −11.7223 | −0.393595 | −0.196798 | − | 0.980444i | \(-0.563054\pi\) | ||||
−0.196798 | + | 0.980444i | \(0.563054\pi\) | |||||||
\(888\) | 15.6381 | 0.524779 | ||||||||
\(889\) | 10.4040 | 0.348940 | ||||||||
\(890\) | −8.93057 | −0.299353 | ||||||||
\(891\) | −19.7059 | −0.660172 | ||||||||
\(892\) | −10.7496 | −0.359923 | ||||||||
\(893\) | 29.6236 | 0.991316 | ||||||||
\(894\) | −53.1856 | −1.77879 | ||||||||
\(895\) | 13.1938 | 0.441021 | ||||||||
\(896\) | −4.59692 | −0.153572 | ||||||||
\(897\) | 3.28432 | 0.109660 | ||||||||
\(898\) | −18.3594 | −0.612660 | ||||||||
\(899\) | −2.62520 | −0.0875554 | ||||||||
\(900\) | 4.22212 | 0.140737 | ||||||||
\(901\) | 28.1244 | 0.936960 | ||||||||
\(902\) | −43.6519 | −1.45345 | ||||||||
\(903\) | −98.8300 | −3.28886 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | −15.7907 | −0.524902 | ||||||||
\(906\) | 10.9168 | 0.362685 | ||||||||
\(907\) | −1.91770 | −0.0636763 | −0.0318381 | − | 0.999493i | \(-0.510136\pi\) | ||||
−0.0318381 | + | 0.999493i | \(0.510136\pi\) | |||||||
\(908\) | −12.3054 | −0.408368 | ||||||||
\(909\) | 14.2488 | 0.472603 | ||||||||
\(910\) | −5.61797 | −0.186234 | ||||||||
\(911\) | −56.8319 | −1.88292 | −0.941462 | − | 0.337118i | \(-0.890548\pi\) | ||||
−0.941462 | + | 0.337118i | \(0.890548\pi\) | |||||||
\(912\) | −12.3537 | −0.409073 | ||||||||
\(913\) | −19.5979 | −0.648595 | ||||||||
\(914\) | −11.4992 | −0.380360 | ||||||||
\(915\) | −29.4288 | −0.972886 | ||||||||
\(916\) | 9.63806 | 0.318451 | ||||||||
\(917\) | −13.4716 | −0.444870 | ||||||||
\(918\) | −15.3949 | −0.508107 | ||||||||
\(919\) | −26.0257 | −0.858509 | −0.429255 | − | 0.903183i | \(-0.641224\pi\) | ||||
−0.429255 | + | 0.903183i | \(0.641224\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | −22.9733 | −0.756997 | ||||||||
\(922\) | 1.33270 | 0.0438901 | ||||||||
\(923\) | −1.60415 | −0.0528013 | ||||||||
\(924\) | −63.3949 | −2.08554 | ||||||||
\(925\) | 5.81903 | 0.191329 | ||||||||
\(926\) | 35.8190 | 1.17709 | ||||||||
\(927\) | 55.4433 | 1.82100 | ||||||||
\(928\) | 3.37480 | 0.110783 | ||||||||
\(929\) | −17.1115 | −0.561411 | −0.280706 | − | 0.959794i | \(-0.590568\pi\) | ||||
−0.280706 | + | 0.959794i | \(0.590568\pi\) | |||||||
\(930\) | 2.09048 | 0.0685497 | ||||||||
\(931\) | −64.9619 | −2.12904 | ||||||||
\(932\) | 13.9434 | 0.456732 | ||||||||
\(933\) | −20.5265 | −0.672008 | ||||||||
\(934\) | −23.7625 | −0.777531 | ||||||||
\(935\) | 24.0540 | 0.786650 | ||||||||
\(936\) | −5.15992 | −0.168657 | ||||||||
\(937\) | 16.3738 | 0.534910 | 0.267455 | − | 0.963570i | \(-0.413817\pi\) | ||||
0.267455 | + | 0.963570i | \(0.413817\pi\) | |||||||
\(938\) | −71.8869 | −2.34719 | ||||||||
\(939\) | −49.0047 | −1.59921 | ||||||||
\(940\) | 6.44423 | 0.210188 | ||||||||
\(941\) | −16.4097 | −0.534940 | −0.267470 | − | 0.963566i | \(-0.586188\pi\) | ||||
−0.267470 | + | 0.963566i | \(0.586188\pi\) | |||||||
\(942\) | 12.4298 | 0.404984 | ||||||||
\(943\) | 8.50643 | 0.277008 | ||||||||
\(944\) | 9.37480 | 0.305124 | ||||||||
\(945\) | 15.0977 | 0.491129 | ||||||||
\(946\) | 41.0531 | 1.33475 | ||||||||
\(947\) | −21.3886 | −0.695037 | −0.347518 | − | 0.937673i | \(-0.612976\pi\) | ||||
−0.347518 | + | 0.937673i | \(0.612976\pi\) | |||||||
\(948\) | −13.1373 | −0.426678 | ||||||||
\(949\) | 5.43137 | 0.176310 | ||||||||
\(950\) | −4.59692 | −0.149144 | ||||||||
\(951\) | −45.3100 | −1.46928 | ||||||||
\(952\) | 21.5476 | 0.698361 | ||||||||
\(953\) | −16.7276 | −0.541860 | −0.270930 | − | 0.962599i | \(-0.587331\pi\) | ||||
−0.270930 | + | 0.962599i | \(0.587331\pi\) | |||||||
\(954\) | −25.3327 | −0.820176 | ||||||||
\(955\) | −16.1244 | −0.521773 | ||||||||
\(956\) | −26.3877 | −0.853438 | ||||||||
\(957\) | 46.5410 | 1.50446 | ||||||||
\(958\) | −2.04210 | −0.0659773 | ||||||||
\(959\) | 90.9764 | 2.93778 | ||||||||
\(960\) | −2.68740 | −0.0867354 | ||||||||
\(961\) | −30.3949 | −0.980481 | ||||||||
\(962\) | −7.11153 | −0.229285 | ||||||||
\(963\) | 51.9547 | 1.67422 | ||||||||
\(964\) | −7.06943 | −0.227691 | ||||||||
\(965\) | 17.9434 | 0.577619 | ||||||||
\(966\) | 12.3537 | 0.397475 | ||||||||
\(967\) | 45.2617 | 1.45552 | 0.727758 | − | 0.685834i | \(-0.240562\pi\) | ||||
0.727758 | + | 0.685834i | \(0.240562\pi\) | |||||||
\(968\) | 15.3337 | 0.492842 | ||||||||
\(969\) | 57.9070 | 1.86024 | ||||||||
\(970\) | 18.0622 | 0.579942 | ||||||||
\(971\) | 45.2560 | 1.45234 | 0.726168 | − | 0.687518i | \(-0.241300\pi\) | ||||
0.726168 | + | 0.687518i | \(0.241300\pi\) | |||||||
\(972\) | −20.1728 | −0.647042 | ||||||||
\(973\) | −28.7917 | −0.923019 | ||||||||
\(974\) | −18.6252 | −0.596790 | ||||||||
\(975\) | −3.28432 | −0.105182 | ||||||||
\(976\) | 10.9507 | 0.350522 | ||||||||
\(977\) | −13.3465 | −0.426993 | −0.213496 | − | 0.976944i | \(-0.568485\pi\) | ||||
−0.213496 | + | 0.976944i | \(0.568485\pi\) | |||||||
\(978\) | 33.3666 | 1.06695 | ||||||||
\(979\) | 45.8284 | 1.46468 | ||||||||
\(980\) | −14.1316 | −0.451418 | ||||||||
\(981\) | −44.7414 | −1.42848 | ||||||||
\(982\) | 33.7204 | 1.07606 | ||||||||
\(983\) | 5.13163 | 0.163674 | 0.0818368 | − | 0.996646i | \(-0.473921\pi\) | ||||
0.0818368 | + | 0.996646i | \(0.473921\pi\) | |||||||
\(984\) | −22.8602 | −0.728756 | ||||||||
\(985\) | −5.88123 | −0.187392 | ||||||||
\(986\) | −15.8190 | −0.503781 | ||||||||
\(987\) | 79.6104 | 2.53403 | ||||||||
\(988\) | 5.61797 | 0.178731 | ||||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | −21.6663 | −0.688602 | ||||||||
\(991\) | 17.7989 | 0.565402 | 0.282701 | − | 0.959208i | \(-0.408770\pi\) | ||||
0.282701 | + | 0.959208i | \(0.408770\pi\) | |||||||
\(992\) | −0.777884 | −0.0246978 | ||||||||
\(993\) | 51.4684 | 1.63330 | ||||||||
\(994\) | −6.03391 | −0.191384 | ||||||||
\(995\) | −6.56863 | −0.208240 | ||||||||
\(996\) | −10.2633 | −0.325204 | ||||||||
\(997\) | 40.3877 | 1.27909 | 0.639545 | − | 0.768754i | \(-0.279123\pi\) | ||||
0.639545 | + | 0.768754i | \(0.279123\pi\) | |||||||
\(998\) | −16.8885 | −0.534595 | ||||||||
\(999\) | 19.1115 | 0.604662 |
(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 | 230.2.a.d.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 2070.2.a.z.1.1 | 3 | |||
4.3 | odd | 2 | 1840.2.a.r.1.1 | 3 | |||
5.2 | odd | 4 | 1150.2.b.j.599.4 | 6 | |||
5.3 | odd | 4 | 1150.2.b.j.599.3 | 6 | |||
5.4 | even | 2 | 1150.2.a.q.1.1 | 3 | |||
8.3 | odd | 2 | 7360.2.a.ce.1.3 | 3 | |||
8.5 | even | 2 | 7360.2.a.bz.1.1 | 3 | |||
20.19 | odd | 2 | 9200.2.a.cf.1.3 | 3 | |||
23.22 | odd | 2 | 5290.2.a.r.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.d.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1150.2.a.q.1.1 | 3 | 5.4 | even | 2 | |||
1150.2.b.j.599.3 | 6 | 5.3 | odd | 4 | |||
1150.2.b.j.599.4 | 6 | 5.2 | odd | 4 | |||
1840.2.a.r.1.1 | 3 | 4.3 | odd | 2 | |||
2070.2.a.z.1.1 | 3 | 3.2 | odd | 2 | |||
5290.2.a.r.1.3 | 3 | 23.22 | odd | 2 | |||
7360.2.a.bz.1.1 | 3 | 8.5 | even | 2 | |||
7360.2.a.ce.1.3 | 3 | 8.3 | odd | 2 | |||
9200.2.a.cf.1.3 | 3 | 20.19 | odd | 2 |