Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.414214 | −0.292893 | −0.146447 | − | 0.989219i | \(-0.546784\pi\) | ||||
−0.146447 | + | 0.989219i | \(0.546784\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.414214 | −0.169102 | ||||||||
\(7\) | 4.82843 | 1.82497 | 0.912487 | − | 0.409106i | \(-0.134159\pi\) | ||||
0.912487 | + | 0.409106i | \(0.134159\pi\) | |||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.82843 | −0.527821 | ||||||||
\(13\) | −5.65685 | −1.56893 | −0.784465 | − | 0.620174i | \(-0.787062\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 6.82843 | 1.65614 | 0.828068 | − | 0.560627i | \(-0.189440\pi\) | ||||
0.828068 | + | 0.560627i | \(0.189440\pi\) | |||||||
\(18\) | −0.414214 | −0.0976311 | ||||||||
\(19\) | −1.17157 | −0.268777 | −0.134389 | − | 0.990929i | \(-0.542907\pi\) | ||||
−0.134389 | + | 0.990929i | \(0.542907\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.82843 | 1.05365 | ||||||||
\(22\) | 0.414214 | 0.0883106 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 1.58579 | 0.323697 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.34315 | 0.459529 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −8.82843 | −1.66842 | ||||||||
\(29\) | 0.828427 | 0.153835 | 0.0769175 | − | 0.997037i | \(-0.475492\pi\) | ||||
0.0769175 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | −0.343146 | −0.0564128 | −0.0282064 | − | 0.999602i | \(-0.508980\pi\) | ||||
−0.0282064 | + | 0.999602i | \(0.508980\pi\) | |||||||
\(38\) | 0.485281 | 0.0787230 | ||||||||
\(39\) | −5.65685 | −0.905822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.828427 | −0.129379 | −0.0646893 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646893 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | 3.17157 | 0.483660 | 0.241830 | − | 0.970319i | \(-0.422252\pi\) | ||||
0.241830 | + | 0.970319i | \(0.422252\pi\) | |||||||
\(44\) | 1.82843 | 0.275646 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.65685 | −0.244290 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | 16.3137 | 2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.82843 | 0.956171 | ||||||||
\(52\) | 10.3431 | 1.43434 | ||||||||
\(53\) | 13.3137 | 1.82878 | 0.914389 | − | 0.404836i | \(-0.132671\pi\) | ||||
0.914389 | + | 0.404836i | \(0.132671\pi\) | |||||||
\(54\) | −0.414214 | −0.0563673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.65685 | 1.02319 | ||||||||
\(57\) | −1.17157 | −0.155179 | ||||||||
\(58\) | −0.343146 | −0.0450572 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.343146 | −0.0439353 | −0.0219677 | − | 0.999759i | \(-0.506993\pi\) | ||||
−0.0219677 | + | 0.999759i | \(0.506993\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.82843 | 0.608325 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.414214 | 0.0509862 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | −12.4853 | −1.51406 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6569 | 1.62077 | 0.810385 | − | 0.585897i | \(-0.199258\pi\) | ||||
0.810385 | + | 0.585897i | \(0.199258\pi\) | |||||||
\(72\) | 1.58579 | 0.186887 | ||||||||
\(73\) | 11.3137 | 1.32417 | 0.662085 | − | 0.749429i | \(-0.269672\pi\) | ||||
0.662085 | + | 0.749429i | \(0.269672\pi\) | |||||||
\(74\) | 0.142136 | 0.0165229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.14214 | 0.245720 | ||||||||
\(77\) | −4.82843 | −0.550250 | ||||||||
\(78\) | 2.34315 | 0.265309 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.343146 | 0.0378941 | ||||||||
\(83\) | 10.0000 | 1.09764 | 0.548821 | − | 0.835940i | \(-0.315077\pi\) | ||||
0.548821 | + | 0.835940i | \(0.315077\pi\) | |||||||
\(84\) | −8.82843 | −0.963260 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.31371 | −0.141661 | ||||||||
\(87\) | 0.828427 | 0.0888167 | ||||||||
\(88\) | −1.58579 | −0.169045 | ||||||||
\(89\) | −7.65685 | −0.811625 | −0.405812 | − | 0.913956i | \(-0.633011\pi\) | ||||
−0.405812 | + | 0.913956i | \(0.633011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.3137 | −2.86325 | ||||||||
\(92\) | −7.31371 | −0.762507 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.65685 | −0.170891 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.41421 | −0.450524 | ||||||||
\(97\) | −0.343146 | −0.0348412 | −0.0174206 | − | 0.999848i | \(-0.505545\pi\) | ||||
−0.0174206 | + | 0.999848i | \(0.505545\pi\) | |||||||
\(98\) | −6.75736 | −0.682596 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.82843 | 0.480446 | 0.240223 | − | 0.970718i | \(-0.422779\pi\) | ||||
0.240223 | + | 0.970718i | \(0.422779\pi\) | |||||||
\(102\) | −2.82843 | −0.280056 | ||||||||
\(103\) | −19.3137 | −1.90304 | −0.951518 | − | 0.307593i | \(-0.900477\pi\) | ||||
−0.951518 | + | 0.307593i | \(0.900477\pi\) | |||||||
\(104\) | −8.97056 | −0.879636 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.51472 | −0.535637 | ||||||||
\(107\) | 5.31371 | 0.513696 | 0.256848 | − | 0.966452i | \(-0.417316\pi\) | ||||
0.256848 | + | 0.966452i | \(0.417316\pi\) | |||||||
\(108\) | −1.82843 | −0.175940 | ||||||||
\(109\) | −5.31371 | −0.508961 | −0.254480 | − | 0.967078i | \(-0.581904\pi\) | ||||
−0.254480 | + | 0.967078i | \(0.581904\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.343146 | −0.0325700 | ||||||||
\(112\) | 14.4853 | 1.36873 | ||||||||
\(113\) | −14.9706 | −1.40831 | −0.704156 | − | 0.710045i | \(-0.748674\pi\) | ||||
−0.704156 | + | 0.710045i | \(0.748674\pi\) | |||||||
\(114\) | 0.485281 | 0.0454508 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.51472 | −0.140638 | ||||||||
\(117\) | −5.65685 | −0.522976 | ||||||||
\(118\) | 1.65685 | 0.152526 | ||||||||
\(119\) | 32.9706 | 3.02241 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.142136 | 0.0128684 | ||||||||
\(123\) | −0.828427 | −0.0746968 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | −2.48528 | −0.220533 | −0.110267 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110267 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(128\) | 10.5563 | 0.933058 | ||||||||
\(129\) | 3.17157 | 0.279241 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.3137 | −1.68745 | −0.843723 | − | 0.536778i | \(-0.819641\pi\) | ||||
−0.843723 | + | 0.536778i | \(0.819641\pi\) | |||||||
\(132\) | 1.82843 | 0.159144 | ||||||||
\(133\) | −5.65685 | −0.490511 | ||||||||
\(134\) | 2.34315 | 0.202417 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.8284 | 0.928530 | ||||||||
\(137\) | −9.31371 | −0.795724 | −0.397862 | − | 0.917445i | \(-0.630248\pi\) | ||||
−0.397862 | + | 0.917445i | \(0.630248\pi\) | |||||||
\(138\) | −1.65685 | −0.141041 | ||||||||
\(139\) | −16.4853 | −1.39826 | −0.699132 | − | 0.714993i | \(-0.746430\pi\) | ||||
−0.699132 | + | 0.714993i | \(0.746430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | −5.65685 | −0.474713 | ||||||||
\(143\) | 5.65685 | 0.473050 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.68629 | −0.387840 | ||||||||
\(147\) | 16.3137 | 1.34553 | ||||||||
\(148\) | 0.627417 | 0.0515734 | ||||||||
\(149\) | 18.4853 | 1.51437 | 0.757187 | − | 0.653199i | \(-0.226573\pi\) | ||||
0.757187 | + | 0.653199i | \(0.226573\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.485281 | −0.0394916 | −0.0197458 | − | 0.999805i | \(-0.506286\pi\) | ||||
−0.0197458 | + | 0.999805i | \(0.506286\pi\) | |||||||
\(152\) | −1.85786 | −0.150693 | ||||||||
\(153\) | 6.82843 | 0.552046 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.3431 | 0.828114 | ||||||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 3.51472 | 0.279616 | ||||||||
\(159\) | 13.3137 | 1.05585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.3137 | 1.52213 | ||||||||
\(162\) | −0.414214 | −0.0325437 | ||||||||
\(163\) | −15.3137 | −1.19946 | −0.599731 | − | 0.800202i | \(-0.704726\pi\) | ||||
−0.599731 | + | 0.800202i | \(0.704726\pi\) | |||||||
\(164\) | 1.51472 | 0.118280 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.14214 | −0.321492 | ||||||||
\(167\) | −9.31371 | −0.720716 | −0.360358 | − | 0.932814i | \(-0.617346\pi\) | ||||
−0.360358 | + | 0.932814i | \(0.617346\pi\) | |||||||
\(168\) | 7.65685 | 0.590739 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.17157 | −0.0895924 | ||||||||
\(172\) | −5.79899 | −0.442169 | ||||||||
\(173\) | 2.82843 | 0.215041 | 0.107521 | − | 0.994203i | \(-0.465709\pi\) | ||||
0.107521 | + | 0.994203i | \(0.465709\pi\) | |||||||
\(174\) | −0.343146 | −0.0260138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 3.17157 | 0.237719 | ||||||||
\(179\) | −6.34315 | −0.474109 | −0.237054 | − | 0.971496i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971496i | \(0.576182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 11.3137 | 0.838628 | ||||||||
\(183\) | −0.343146 | −0.0253661 | ||||||||
\(184\) | 6.34315 | 0.467623 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.82843 | −0.499344 | ||||||||
\(188\) | −7.31371 | −0.533407 | ||||||||
\(189\) | 4.82843 | 0.351216 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.65685 | −0.409316 | −0.204658 | − | 0.978834i | \(-0.565608\pi\) | ||||
−0.204658 | + | 0.978834i | \(0.565608\pi\) | |||||||
\(192\) | −4.17157 | −0.301057 | ||||||||
\(193\) | −2.34315 | −0.168663 | −0.0843317 | − | 0.996438i | \(-0.526876\pi\) | ||||
−0.0843317 | + | 0.996438i | \(0.526876\pi\) | |||||||
\(194\) | 0.142136 | 0.0102047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.8284 | −2.13060 | ||||||||
\(197\) | −8.48528 | −0.604551 | −0.302276 | − | 0.953221i | \(-0.597746\pi\) | ||||
−0.302276 | + | 0.953221i | \(0.597746\pi\) | |||||||
\(198\) | 0.414214 | 0.0294369 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.65685 | −0.399004 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | −12.4853 | −0.874145 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | −16.9706 | −1.17670 | ||||||||
\(209\) | 1.17157 | 0.0810394 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.82843 | 0.470088 | 0.235044 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235044 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(212\) | −24.3431 | −1.67189 | ||||||||
\(213\) | 13.6569 | 0.935752 | ||||||||
\(214\) | −2.20101 | −0.150458 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.58579 | 0.107899 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.20101 | 0.149071 | ||||||||
\(219\) | 11.3137 | 0.764510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.6274 | −2.59836 | ||||||||
\(222\) | 0.142136 | 0.00953952 | ||||||||
\(223\) | 17.6569 | 1.18239 | 0.591195 | − | 0.806529i | \(-0.298656\pi\) | ||||
0.591195 | + | 0.806529i | \(0.298656\pi\) | |||||||
\(224\) | −21.3137 | −1.42408 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.20101 | 0.412485 | ||||||||
\(227\) | 14.0000 | 0.929213 | 0.464606 | − | 0.885517i | \(-0.346196\pi\) | ||||
0.464606 | + | 0.885517i | \(0.346196\pi\) | |||||||
\(228\) | 2.14214 | 0.141866 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.82843 | −0.317687 | ||||||||
\(232\) | 1.31371 | 0.0862492 | ||||||||
\(233\) | 13.1716 | 0.862898 | 0.431449 | − | 0.902137i | \(-0.358002\pi\) | ||||
0.431449 | + | 0.902137i | \(0.358002\pi\) | |||||||
\(234\) | 2.34315 | 0.153176 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.31371 | 0.476082 | ||||||||
\(237\) | −8.48528 | −0.551178 | ||||||||
\(238\) | −13.6569 | −0.885242 | ||||||||
\(239\) | 6.34315 | 0.410304 | 0.205152 | − | 0.978730i | \(-0.434231\pi\) | ||||
0.205152 | + | 0.978730i | \(0.434231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6569 | −1.52387 | −0.761936 | − | 0.647652i | \(-0.775751\pi\) | ||||
−0.761936 | + | 0.647652i | \(0.775751\pi\) | |||||||
\(242\) | −0.414214 | −0.0266267 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.627417 | 0.0401663 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.343146 | 0.0218782 | ||||||||
\(247\) | 6.62742 | 0.421692 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.0000 | 0.633724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9706 | −0.818695 | −0.409347 | − | 0.912379i | \(-0.634244\pi\) | ||||
−0.409347 | + | 0.912379i | \(0.634244\pi\) | |||||||
\(252\) | −8.82843 | −0.556139 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 1.02944 | 0.0645926 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 27.6569 | 1.72519 | 0.862594 | − | 0.505898i | \(-0.168839\pi\) | ||||
0.862594 | + | 0.505898i | \(0.168839\pi\) | |||||||
\(258\) | −1.31371 | −0.0817879 | ||||||||
\(259\) | −1.65685 | −0.102952 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.828427 | 0.0512784 | ||||||||
\(262\) | 8.00000 | 0.494242 | ||||||||
\(263\) | −18.0000 | −1.10993 | −0.554964 | − | 0.831875i | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(264\) | −1.58579 | −0.0975984 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.34315 | 0.143667 | ||||||||
\(267\) | −7.65685 | −0.468592 | ||||||||
\(268\) | 10.3431 | 0.631808 | ||||||||
\(269\) | −24.6274 | −1.50156 | −0.750780 | − | 0.660552i | \(-0.770322\pi\) | ||||
−0.750780 | + | 0.660552i | \(0.770322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.7990 | 1.68867 | 0.844334 | − | 0.535817i | \(-0.179996\pi\) | ||||
0.844334 | + | 0.535817i | \(0.179996\pi\) | |||||||
\(272\) | 20.4853 | 1.24210 | ||||||||
\(273\) | −27.3137 | −1.65310 | ||||||||
\(274\) | 3.85786 | 0.233062 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.31371 | −0.440234 | ||||||||
\(277\) | 13.6569 | 0.820561 | 0.410280 | − | 0.911959i | \(-0.365431\pi\) | ||||
0.410280 | + | 0.911959i | \(0.365431\pi\) | |||||||
\(278\) | 6.82843 | 0.409542 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8284 | −1.00390 | −0.501950 | − | 0.864897i | \(-0.667384\pi\) | ||||
−0.501950 | + | 0.864897i | \(0.667384\pi\) | |||||||
\(282\) | −1.65685 | −0.0986642 | ||||||||
\(283\) | 3.17157 | 0.188530 | 0.0942652 | − | 0.995547i | \(-0.469950\pi\) | ||||
0.0942652 | + | 0.995547i | \(0.469950\pi\) | |||||||
\(284\) | −24.9706 | −1.48173 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.34315 | −0.138553 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | −4.41421 | −0.260110 | ||||||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.343146 | −0.0201156 | ||||||||
\(292\) | −20.6863 | −1.21057 | ||||||||
\(293\) | 1.17157 | 0.0684440 | 0.0342220 | − | 0.999414i | \(-0.489105\pi\) | ||||
0.0342220 | + | 0.999414i | \(0.489105\pi\) | |||||||
\(294\) | −6.75736 | −0.394097 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.544156 | −0.0316284 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −7.65685 | −0.443550 | ||||||||
\(299\) | −22.6274 | −1.30858 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.3137 | 0.882667 | ||||||||
\(302\) | 0.201010 | 0.0115668 | ||||||||
\(303\) | 4.82843 | 0.277386 | ||||||||
\(304\) | −3.51472 | −0.201583 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.82843 | −0.161690 | ||||||||
\(307\) | 8.82843 | 0.503865 | 0.251932 | − | 0.967745i | \(-0.418934\pi\) | ||||
0.251932 | + | 0.967745i | \(0.418934\pi\) | |||||||
\(308\) | 8.82843 | 0.503046 | ||||||||
\(309\) | −19.3137 | −1.09872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3137 | 1.09518 | 0.547590 | − | 0.836747i | \(-0.315545\pi\) | ||||
0.547590 | + | 0.836747i | \(0.315545\pi\) | |||||||
\(312\) | −8.97056 | −0.507858 | ||||||||
\(313\) | −4.34315 | −0.245489 | −0.122745 | − | 0.992438i | \(-0.539170\pi\) | ||||
−0.122745 | + | 0.992438i | \(0.539170\pi\) | |||||||
\(314\) | 7.45584 | 0.420758 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.5147 | 0.872771 | ||||||||
\(317\) | −30.2843 | −1.70093 | −0.850467 | − | 0.526028i | \(-0.823681\pi\) | ||||
−0.850467 | + | 0.526028i | \(0.823681\pi\) | |||||||
\(318\) | −5.51472 | −0.309250 | ||||||||
\(319\) | −0.828427 | −0.0463830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.31371 | 0.296582 | ||||||||
\(322\) | −8.00000 | −0.445823 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | −1.82843 | −0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.34315 | 0.351314 | ||||||||
\(327\) | −5.31371 | −0.293849 | ||||||||
\(328\) | −1.31371 | −0.0725374 | ||||||||
\(329\) | 19.3137 | 1.06480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6569 | 0.970508 | 0.485254 | − | 0.874373i | \(-0.338727\pi\) | ||||
0.485254 | + | 0.874373i | \(0.338727\pi\) | |||||||
\(332\) | −18.2843 | −1.00348 | ||||||||
\(333\) | −0.343146 | −0.0188043 | ||||||||
\(334\) | 3.85786 | 0.211093 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.4853 | 0.790237 | ||||||||
\(337\) | 19.3137 | 1.05208 | 0.526042 | − | 0.850458i | \(-0.323675\pi\) | ||||
0.526042 | + | 0.850458i | \(0.323675\pi\) | |||||||
\(338\) | −7.87006 | −0.428075 | ||||||||
\(339\) | −14.9706 | −0.813089 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.485281 | 0.0262410 | ||||||||
\(343\) | 44.9706 | 2.42818 | ||||||||
\(344\) | 5.02944 | 0.271169 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.17157 | −0.0629841 | ||||||||
\(347\) | 6.68629 | 0.358939 | 0.179469 | − | 0.983764i | \(-0.442562\pi\) | ||||
0.179469 | + | 0.983764i | \(0.442562\pi\) | |||||||
\(348\) | −1.51472 | −0.0811974 | ||||||||
\(349\) | −22.9706 | −1.22959 | −0.614793 | − | 0.788688i | \(-0.710760\pi\) | ||||
−0.614793 | + | 0.788688i | \(0.710760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | 4.41421 | 0.235278 | ||||||||
\(353\) | −26.0000 | −1.38384 | −0.691920 | − | 0.721974i | \(-0.743235\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(354\) | 1.65685 | 0.0880608 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | 32.9706 | 1.74499 | ||||||||
\(358\) | 2.62742 | 0.138863 | ||||||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6274 | −0.927759 | ||||||||
\(362\) | 5.79899 | 0.304788 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 49.9411 | 2.61763 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.142136 | 0.00742955 | ||||||||
\(367\) | 1.65685 | 0.0864871 | 0.0432435 | − | 0.999065i | \(-0.486231\pi\) | ||||
0.0432435 | + | 0.999065i | \(0.486231\pi\) | |||||||
\(368\) | 12.0000 | 0.625543 | ||||||||
\(369\) | −0.828427 | −0.0431262 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 64.2843 | 3.33747 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.6274 | 1.79294 | 0.896470 | − | 0.443105i | \(-0.146123\pi\) | ||||
0.896470 | + | 0.443105i | \(0.146123\pi\) | |||||||
\(374\) | 2.82843 | 0.146254 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.34315 | 0.327123 | ||||||||
\(377\) | −4.68629 | −0.241356 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | −0.686292 | −0.0352524 | −0.0176262 | − | 0.999845i | \(-0.505611\pi\) | ||||
−0.0176262 | + | 0.999845i | \(0.505611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.48528 | −0.127325 | ||||||||
\(382\) | 2.34315 | 0.119886 | ||||||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 10.5563 | 0.538701 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.970563 | 0.0494003 | ||||||||
\(387\) | 3.17157 | 0.161220 | ||||||||
\(388\) | 0.627417 | 0.0318523 | ||||||||
\(389\) | −12.3431 | −0.625822 | −0.312911 | − | 0.949782i | \(-0.601304\pi\) | ||||
−0.312911 | + | 0.949782i | \(0.601304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.3137 | 1.38131 | ||||||||
\(392\) | 25.8701 | 1.30664 | ||||||||
\(393\) | −19.3137 | −0.974248 | ||||||||
\(394\) | 3.51472 | 0.177069 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.82843 | 0.0918819 | ||||||||
\(397\) | −18.9706 | −0.952105 | −0.476053 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476053 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(398\) | 4.28427 | 0.214751 | ||||||||
\(399\) | −5.65685 | −0.283197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.3137 | −1.46386 | −0.731928 | − | 0.681382i | \(-0.761379\pi\) | ||||
−0.731928 | + | 0.681382i | \(0.761379\pi\) | |||||||
\(402\) | 2.34315 | 0.116865 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.82843 | −0.439231 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.65685 | −0.0822283 | ||||||||
\(407\) | 0.343146 | 0.0170091 | ||||||||
\(408\) | 10.8284 | 0.536087 | ||||||||
\(409\) | −8.34315 | −0.412542 | −0.206271 | − | 0.978495i | \(-0.566133\pi\) | ||||
−0.206271 | + | 0.978495i | \(0.566133\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.31371 | −0.459411 | ||||||||
\(412\) | 35.3137 | 1.73978 | ||||||||
\(413\) | −19.3137 | −0.950365 | ||||||||
\(414\) | −1.65685 | −0.0814299 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.9706 | 1.22428 | ||||||||
\(417\) | −16.4853 | −0.807288 | ||||||||
\(418\) | −0.485281 | −0.0237359 | ||||||||
\(419\) | −3.02944 | −0.147998 | −0.0739988 | − | 0.997258i | \(-0.523576\pi\) | ||||
−0.0739988 | + | 0.997258i | \(0.523576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | −2.82843 | −0.137686 | ||||||||
\(423\) | 4.00000 | 0.194487 | ||||||||
\(424\) | 21.1127 | 1.02532 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.65685 | −0.274075 | ||||||||
\(427\) | −1.65685 | −0.0801808 | ||||||||
\(428\) | −9.71573 | −0.469627 | ||||||||
\(429\) | 5.65685 | 0.273115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3431 | 0.498212 | 0.249106 | − | 0.968476i | \(-0.419863\pi\) | ||||
0.249106 | + | 0.968476i | \(0.419863\pi\) | |||||||
\(432\) | 3.00000 | 0.144338 | ||||||||
\(433\) | 4.34315 | 0.208718 | 0.104359 | − | 0.994540i | \(-0.466721\pi\) | ||||
0.104359 | + | 0.994540i | \(0.466721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.71573 | 0.465299 | ||||||||
\(437\) | −4.68629 | −0.224176 | ||||||||
\(438\) | −4.68629 | −0.223920 | ||||||||
\(439\) | −3.51472 | −0.167748 | −0.0838742 | − | 0.996476i | \(-0.526729\pi\) | ||||
−0.0838742 | + | 0.996476i | \(0.526729\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3137 | 0.776843 | ||||||||
\(442\) | 16.0000 | 0.761042 | ||||||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | 0.627417 | 0.0297759 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.31371 | −0.346314 | ||||||||
\(447\) | 18.4853 | 0.874324 | ||||||||
\(448\) | −20.1421 | −0.951626 | ||||||||
\(449\) | −2.97056 | −0.140190 | −0.0700948 | − | 0.997540i | \(-0.522330\pi\) | ||||
−0.0700948 | + | 0.997540i | \(0.522330\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.828427 | 0.0390091 | ||||||||
\(452\) | 27.3726 | 1.28750 | ||||||||
\(453\) | −0.485281 | −0.0228005 | ||||||||
\(454\) | −5.79899 | −0.272160 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.85786 | −0.0870025 | ||||||||
\(457\) | 0.686292 | 0.0321034 | 0.0160517 | − | 0.999871i | \(-0.494890\pi\) | ||||
0.0160517 | + | 0.999871i | \(0.494890\pi\) | |||||||
\(458\) | 0.828427 | 0.0387099 | ||||||||
\(459\) | 6.82843 | 0.318724 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.1421 | −1.31071 | −0.655355 | − | 0.755321i | \(-0.727481\pi\) | ||||
−0.655355 | + | 0.755321i | \(0.727481\pi\) | |||||||
\(462\) | 2.00000 | 0.0930484 | ||||||||
\(463\) | 28.9706 | 1.34638 | 0.673188 | − | 0.739471i | \(-0.264924\pi\) | ||||
0.673188 | + | 0.739471i | \(0.264924\pi\) | |||||||
\(464\) | 2.48528 | 0.115376 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.45584 | −0.252737 | ||||||||
\(467\) | −22.6274 | −1.04707 | −0.523536 | − | 0.852004i | \(-0.675387\pi\) | ||||
−0.523536 | + | 0.852004i | \(0.675387\pi\) | |||||||
\(468\) | 10.3431 | 0.478112 | ||||||||
\(469\) | −27.3137 | −1.26123 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0000 | −0.829396 | ||||||||
\(472\) | −6.34315 | −0.291967 | ||||||||
\(473\) | −3.17157 | −0.145829 | ||||||||
\(474\) | 3.51472 | 0.161436 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −60.2843 | −2.76313 | ||||||||
\(477\) | 13.3137 | 0.609593 | ||||||||
\(478\) | −2.62742 | −0.120175 | ||||||||
\(479\) | 3.02944 | 0.138419 | 0.0692093 | − | 0.997602i | \(-0.477952\pi\) | ||||
0.0692093 | + | 0.997602i | \(0.477952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.94113 | 0.0885077 | ||||||||
\(482\) | 9.79899 | 0.446332 | ||||||||
\(483\) | 19.3137 | 0.878804 | ||||||||
\(484\) | −1.82843 | −0.0831103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.414214 | −0.0187891 | ||||||||
\(487\) | −20.9706 | −0.950267 | −0.475133 | − | 0.879914i | \(-0.657600\pi\) | ||||
−0.475133 | + | 0.879914i | \(0.657600\pi\) | |||||||
\(488\) | −0.544156 | −0.0246328 | ||||||||
\(489\) | −15.3137 | −0.692510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.6569 | 1.15788 | 0.578939 | − | 0.815371i | \(-0.303467\pi\) | ||||
0.578939 | + | 0.815371i | \(0.303467\pi\) | |||||||
\(492\) | 1.51472 | 0.0682888 | ||||||||
\(493\) | 5.65685 | 0.254772 | ||||||||
\(494\) | −2.74517 | −0.123511 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 65.9411 | 2.95786 | ||||||||
\(498\) | −4.14214 | −0.185614 | ||||||||
\(499\) | −33.6569 | −1.50669 | −0.753344 | − | 0.657627i | \(-0.771560\pi\) | ||||
−0.753344 | + | 0.657627i | \(0.771560\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.31371 | −0.416106 | ||||||||
\(502\) | 5.37258 | 0.239790 | ||||||||
\(503\) | 5.31371 | 0.236927 | 0.118463 | − | 0.992958i | \(-0.462203\pi\) | ||||
0.118463 | + | 0.992958i | \(0.462203\pi\) | |||||||
\(504\) | 7.65685 | 0.341063 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.65685 | 0.0736562 | ||||||||
\(507\) | 19.0000 | 0.843820 | ||||||||
\(508\) | 4.54416 | 0.201614 | ||||||||
\(509\) | 41.3137 | 1.83120 | 0.915599 | − | 0.402093i | \(-0.131717\pi\) | ||||
0.915599 | + | 0.402093i | \(0.131717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.6274 | 2.41657 | ||||||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | −1.17157 | −0.0517262 | ||||||||
\(514\) | −11.4558 | −0.505296 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.79899 | −0.255286 | ||||||||
\(517\) | −4.00000 | −0.175920 | ||||||||
\(518\) | 0.686292 | 0.0301539 | ||||||||
\(519\) | 2.82843 | 0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6274 | 0.553217 | 0.276609 | − | 0.960983i | \(-0.410789\pi\) | ||||
0.276609 | + | 0.960983i | \(0.410789\pi\) | |||||||
\(522\) | −0.343146 | −0.0150191 | ||||||||
\(523\) | 26.4853 | 1.15812 | 0.579060 | − | 0.815285i | \(-0.303420\pi\) | ||||
0.579060 | + | 0.815285i | \(0.303420\pi\) | |||||||
\(524\) | 35.3137 | 1.54269 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.45584 | 0.325090 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −3.00000 | −0.130558 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 10.3431 | 0.448432 | ||||||||
\(533\) | 4.68629 | 0.202986 | ||||||||
\(534\) | 3.17157 | 0.137247 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.97056 | −0.387469 | ||||||||
\(537\) | −6.34315 | −0.273727 | ||||||||
\(538\) | 10.2010 | 0.439797 | ||||||||
\(539\) | −16.3137 | −0.702681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.31371 | −0.228454 | −0.114227 | − | 0.993455i | \(-0.536439\pi\) | ||||
−0.114227 | + | 0.993455i | \(0.536439\pi\) | |||||||
\(542\) | −11.5147 | −0.494600 | ||||||||
\(543\) | −14.0000 | −0.600798 | ||||||||
\(544\) | −30.1421 | −1.29233 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.3137 | 0.484182 | ||||||||
\(547\) | −20.1421 | −0.861216 | −0.430608 | − | 0.902539i | \(-0.641701\pi\) | ||||
−0.430608 | + | 0.902539i | \(0.641701\pi\) | |||||||
\(548\) | 17.0294 | 0.727462 | ||||||||
\(549\) | −0.343146 | −0.0146451 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.970563 | −0.0413474 | ||||||||
\(552\) | 6.34315 | 0.269982 | ||||||||
\(553\) | −40.9706 | −1.74225 | ||||||||
\(554\) | −5.65685 | −0.240337 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.1421 | 1.27831 | ||||||||
\(557\) | −10.8284 | −0.458815 | −0.229408 | − | 0.973330i | \(-0.573679\pi\) | ||||
−0.229408 | + | 0.973330i | \(0.573679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.9411 | −0.758829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.82843 | −0.288296 | ||||||||
\(562\) | 6.97056 | 0.294035 | ||||||||
\(563\) | −20.3431 | −0.857361 | −0.428681 | − | 0.903456i | \(-0.641021\pi\) | ||||
−0.428681 | + | 0.903456i | \(0.641021\pi\) | |||||||
\(564\) | −7.31371 | −0.307963 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.31371 | −0.0552193 | ||||||||
\(567\) | 4.82843 | 0.202775 | ||||||||
\(568\) | 21.6569 | 0.908701 | ||||||||
\(569\) | 15.4558 | 0.647943 | 0.323971 | − | 0.946067i | \(-0.394982\pi\) | ||||
0.323971 | + | 0.946067i | \(0.394982\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.485281 | 0.0203084 | 0.0101542 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101542 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(572\) | −10.3431 | −0.432469 | ||||||||
\(573\) | −5.65685 | −0.236318 | ||||||||
\(574\) | 1.65685 | 0.0691558 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.17157 | −0.173816 | ||||||||
\(577\) | −14.0000 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(578\) | −12.2721 | −0.510451 | ||||||||
\(579\) | −2.34315 | −0.0973778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.2843 | 2.00317 | ||||||||
\(582\) | 0.142136 | 0.00589171 | ||||||||
\(583\) | −13.3137 | −0.551397 | ||||||||
\(584\) | 17.9411 | 0.742409 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.485281 | −0.0200468 | ||||||||
\(587\) | 30.6274 | 1.26413 | 0.632064 | − | 0.774916i | \(-0.282208\pi\) | ||||
0.632064 | + | 0.774916i | \(0.282208\pi\) | |||||||
\(588\) | −29.8284 | −1.23010 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.48528 | −0.349038 | ||||||||
\(592\) | −1.02944 | −0.0423096 | ||||||||
\(593\) | 17.1716 | 0.705152 | 0.352576 | − | 0.935783i | \(-0.385306\pi\) | ||||
0.352576 | + | 0.935783i | \(0.385306\pi\) | |||||||
\(594\) | 0.414214 | 0.0169954 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.7990 | −1.38446 | ||||||||
\(597\) | −10.3431 | −0.423317 | ||||||||
\(598\) | 9.37258 | 0.383273 | ||||||||
\(599\) | 4.68629 | 0.191477 | 0.0957383 | − | 0.995407i | \(-0.469479\pi\) | ||||
0.0957383 | + | 0.995407i | \(0.469479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.3137 | 0.706241 | 0.353120 | − | 0.935578i | \(-0.385121\pi\) | ||||
0.353120 | + | 0.935578i | \(0.385121\pi\) | |||||||
\(602\) | −6.34315 | −0.258527 | ||||||||
\(603\) | −5.65685 | −0.230365 | ||||||||
\(604\) | 0.887302 | 0.0361038 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.00000 | −0.0812444 | ||||||||
\(607\) | −18.4853 | −0.750294 | −0.375147 | − | 0.926965i | \(-0.622408\pi\) | ||||
−0.375147 | + | 0.926965i | \(0.622408\pi\) | |||||||
\(608\) | 5.17157 | 0.209735 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.6274 | −0.915407 | ||||||||
\(612\) | −12.4853 | −0.504688 | ||||||||
\(613\) | −21.9411 | −0.886194 | −0.443097 | − | 0.896474i | \(-0.646120\pi\) | ||||
−0.443097 | + | 0.896474i | \(0.646120\pi\) | |||||||
\(614\) | −3.65685 | −0.147579 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.65685 | −0.308503 | ||||||||
\(617\) | −11.6569 | −0.469287 | −0.234644 | − | 0.972081i | \(-0.575392\pi\) | ||||
−0.234644 | + | 0.972081i | \(0.575392\pi\) | |||||||
\(618\) | 8.00000 | 0.321807 | ||||||||
\(619\) | −25.6569 | −1.03124 | −0.515618 | − | 0.856819i | \(-0.672438\pi\) | ||||
−0.515618 | + | 0.856819i | \(0.672438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | −8.00000 | −0.320771 | ||||||||
\(623\) | −36.9706 | −1.48119 | ||||||||
\(624\) | −16.9706 | −0.679366 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.79899 | 0.0719021 | ||||||||
\(627\) | 1.17157 | 0.0467881 | ||||||||
\(628\) | 32.9117 | 1.31332 | ||||||||
\(629\) | −2.34315 | −0.0934273 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.3431 | 1.36718 | 0.683590 | − | 0.729867i | \(-0.260418\pi\) | ||||
0.683590 | + | 0.729867i | \(0.260418\pi\) | |||||||
\(632\) | −13.4558 | −0.535245 | ||||||||
\(633\) | 6.82843 | 0.271406 | ||||||||
\(634\) | 12.5442 | 0.498192 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.3431 | −0.965269 | ||||||||
\(637\) | −92.2843 | −3.65644 | ||||||||
\(638\) | 0.343146 | 0.0135853 | ||||||||
\(639\) | 13.6569 | 0.540257 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.9706 | −1.06527 | −0.532637 | − | 0.846344i | \(-0.678799\pi\) | ||||
−0.532637 | + | 0.846344i | \(0.678799\pi\) | |||||||
\(642\) | −2.20101 | −0.0868669 | ||||||||
\(643\) | 29.9411 | 1.18076 | 0.590381 | − | 0.807124i | \(-0.298977\pi\) | ||||
0.590381 | + | 0.807124i | \(0.298977\pi\) | |||||||
\(644\) | −35.3137 | −1.39156 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.31371 | 0.130376 | ||||||||
\(647\) | −27.3137 | −1.07381 | −0.536906 | − | 0.843642i | \(-0.680407\pi\) | ||||
−0.536906 | + | 0.843642i | \(0.680407\pi\) | |||||||
\(648\) | 1.58579 | 0.0622956 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28.0000 | 1.09656 | ||||||||
\(653\) | 26.9706 | 1.05544 | 0.527720 | − | 0.849418i | \(-0.323047\pi\) | ||||
0.527720 | + | 0.849418i | \(0.323047\pi\) | |||||||
\(654\) | 2.20101 | 0.0860663 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.48528 | −0.0970339 | ||||||||
\(657\) | 11.3137 | 0.441390 | ||||||||
\(658\) | −8.00000 | −0.311872 | ||||||||
\(659\) | 7.31371 | 0.284902 | 0.142451 | − | 0.989802i | \(-0.454502\pi\) | ||||
0.142451 | + | 0.989802i | \(0.454502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.3137 | −0.517843 | −0.258922 | − | 0.965898i | \(-0.583367\pi\) | ||||
−0.258922 | + | 0.965898i | \(0.583367\pi\) | |||||||
\(662\) | −7.31371 | −0.284255 | ||||||||
\(663\) | −38.6274 | −1.50016 | ||||||||
\(664\) | 15.8579 | 0.615404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.142136 | 0.00550764 | ||||||||
\(667\) | 3.31371 | 0.128307 | ||||||||
\(668\) | 17.0294 | 0.658889 | ||||||||
\(669\) | 17.6569 | 0.682653 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.343146 | 0.0132470 | ||||||||
\(672\) | −21.3137 | −0.822194 | ||||||||
\(673\) | −29.6569 | −1.14319 | −0.571594 | − | 0.820537i | \(-0.693675\pi\) | ||||
−0.571594 | + | 0.820537i | \(0.693675\pi\) | |||||||
\(674\) | −8.00000 | −0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.7401 | −1.33616 | ||||||||
\(677\) | 21.4558 | 0.824615 | 0.412308 | − | 0.911045i | \(-0.364723\pi\) | ||||
0.412308 | + | 0.911045i | \(0.364723\pi\) | |||||||
\(678\) | 6.20101 | 0.238148 | ||||||||
\(679\) | −1.65685 | −0.0635842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0000 | 0.536481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | 2.14214 | 0.0819066 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.6274 | −0.711198 | ||||||||
\(687\) | −2.00000 | −0.0763048 | ||||||||
\(688\) | 9.51472 | 0.362745 | ||||||||
\(689\) | −75.3137 | −2.86922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | −5.17157 | −0.196594 | ||||||||
\(693\) | −4.82843 | −0.183417 | ||||||||
\(694\) | −2.76955 | −0.105131 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.31371 | 0.0497960 | ||||||||
\(697\) | −5.65685 | −0.214269 | ||||||||
\(698\) | 9.51472 | 0.360137 | ||||||||
\(699\) | 13.1716 | 0.498195 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.85786 | 0.296787 | 0.148394 | − | 0.988928i | \(-0.452590\pi\) | ||||
0.148394 | + | 0.988928i | \(0.452590\pi\) | |||||||
\(702\) | 2.34315 | 0.0884363 | ||||||||
\(703\) | 0.402020 | 0.0151625 | ||||||||
\(704\) | 4.17157 | 0.157222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.7696 | 0.405317 | ||||||||
\(707\) | 23.3137 | 0.876802 | ||||||||
\(708\) | 7.31371 | 0.274866 | ||||||||
\(709\) | 29.3137 | 1.10090 | 0.550450 | − | 0.834868i | \(-0.314456\pi\) | ||||
0.550450 | + | 0.834868i | \(0.314456\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.48528 | −0.318223 | ||||||||
\(712\) | −12.1421 | −0.455046 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −13.6569 | −0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.5980 | 0.433437 | ||||||||
\(717\) | 6.34315 | 0.236889 | ||||||||
\(718\) | −4.97056 | −0.185500 | ||||||||
\(719\) | 31.5980 | 1.17841 | 0.589203 | − | 0.807985i | \(-0.299442\pi\) | ||||
0.589203 | + | 0.807985i | \(0.299442\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −93.2548 | −3.47299 | ||||||||
\(722\) | 7.30152 | 0.271734 | ||||||||
\(723\) | −23.6569 | −0.879808 | ||||||||
\(724\) | 25.5980 | 0.951341 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.414214 | −0.0153729 | ||||||||
\(727\) | 33.9411 | 1.25881 | 0.629403 | − | 0.777079i | \(-0.283299\pi\) | ||||
0.629403 | + | 0.777079i | \(0.283299\pi\) | |||||||
\(728\) | −43.3137 | −1.60531 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.6569 | 0.801008 | ||||||||
\(732\) | 0.627417 | 0.0231900 | ||||||||
\(733\) | 17.6569 | 0.652171 | 0.326085 | − | 0.945340i | \(-0.394270\pi\) | ||||
0.326085 | + | 0.945340i | \(0.394270\pi\) | |||||||
\(734\) | −0.686292 | −0.0253315 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.6569 | −0.650840 | ||||||||
\(737\) | 5.65685 | 0.208373 | ||||||||
\(738\) | 0.343146 | 0.0126314 | ||||||||
\(739\) | 47.1127 | 1.73307 | 0.866534 | − | 0.499118i | \(-0.166342\pi\) | ||||
0.866534 | + | 0.499118i | \(0.166342\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.62742 | 0.243464 | ||||||||
\(742\) | −26.6274 | −0.977523 | ||||||||
\(743\) | −47.6569 | −1.74836 | −0.874180 | − | 0.485602i | \(-0.838601\pi\) | ||||
−0.874180 | + | 0.485602i | \(0.838601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.3431 | −0.525140 | ||||||||
\(747\) | 10.0000 | 0.365881 | ||||||||
\(748\) | 12.4853 | 0.456507 | ||||||||
\(749\) | 25.6569 | 0.937481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.2843 | −1.32403 | −0.662016 | − | 0.749490i | \(-0.730299\pi\) | ||||
−0.662016 | + | 0.749490i | \(0.730299\pi\) | |||||||
\(752\) | 12.0000 | 0.437595 | ||||||||
\(753\) | −12.9706 | −0.472674 | ||||||||
\(754\) | 1.94113 | 0.0706916 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.82843 | −0.321087 | ||||||||
\(757\) | −8.62742 | −0.313569 | −0.156784 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156784 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(758\) | 0.284271 | 0.0103252 | ||||||||
\(759\) | −4.00000 | −0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.1716 | −0.839969 | −0.419984 | − | 0.907531i | \(-0.637964\pi\) | ||||
−0.419984 | + | 0.907531i | \(0.637964\pi\) | |||||||
\(762\) | 1.02944 | 0.0372926 | ||||||||
\(763\) | −25.6569 | −0.928840 | ||||||||
\(764\) | 10.3431 | 0.374202 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.31371 | −0.119729 | ||||||||
\(767\) | 22.6274 | 0.817029 | ||||||||
\(768\) | 3.97056 | 0.143275 | ||||||||
\(769\) | 33.3137 | 1.20132 | 0.600662 | − | 0.799503i | \(-0.294904\pi\) | ||||
0.600662 | + | 0.799503i | \(0.294904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.6569 | 0.996037 | ||||||||
\(772\) | 4.28427 | 0.154194 | ||||||||
\(773\) | 7.65685 | 0.275398 | 0.137699 | − | 0.990474i | \(-0.456029\pi\) | ||||
0.137699 | + | 0.990474i | \(0.456029\pi\) | |||||||
\(774\) | −1.31371 | −0.0472203 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.544156 | −0.0195341 | ||||||||
\(777\) | −1.65685 | −0.0594393 | ||||||||
\(778\) | 5.11270 | 0.183299 | ||||||||
\(779\) | 0.970563 | 0.0347740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.6569 | −0.488681 | ||||||||
\(782\) | −11.3137 | −0.404577 | ||||||||
\(783\) | 0.828427 | 0.0296056 | ||||||||
\(784\) | 48.9411 | 1.74790 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.00000 | 0.285351 | ||||||||
\(787\) | −8.14214 | −0.290236 | −0.145118 | − | 0.989414i | \(-0.546356\pi\) | ||||
−0.145118 | + | 0.989414i | \(0.546356\pi\) | |||||||
\(788\) | 15.5147 | 0.552689 | ||||||||
\(789\) | −18.0000 | −0.640817 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −72.2843 | −2.57013 | ||||||||
\(792\) | −1.58579 | −0.0563485 | ||||||||
\(793\) | 1.94113 | 0.0689314 | ||||||||
\(794\) | 7.85786 | 0.278865 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.9117 | 0.670307 | ||||||||
\(797\) | −1.02944 | −0.0364645 | −0.0182323 | − | 0.999834i | \(-0.505804\pi\) | ||||
−0.0182323 | + | 0.999834i | \(0.505804\pi\) | |||||||
\(798\) | 2.34315 | 0.0829465 | ||||||||
\(799\) | 27.3137 | 0.966290 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65685 | −0.270542 | ||||||||
\(802\) | 12.1421 | 0.428754 | ||||||||
\(803\) | −11.3137 | −0.399252 | ||||||||
\(804\) | 10.3431 | 0.364775 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.6274 | −0.866926 | ||||||||
\(808\) | 7.65685 | 0.269367 | ||||||||
\(809\) | −56.4264 | −1.98385 | −0.991923 | − | 0.126838i | \(-0.959517\pi\) | ||||
−0.991923 | + | 0.126838i | \(0.959517\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.4853 | −0.578877 | −0.289438 | − | 0.957197i | \(-0.593468\pi\) | ||||
−0.289438 | + | 0.957197i | \(0.593468\pi\) | |||||||
\(812\) | −7.31371 | −0.256661 | ||||||||
\(813\) | 27.7990 | 0.974953 | ||||||||
\(814\) | −0.142136 | −0.00498185 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.4853 | 0.717128 | ||||||||
\(817\) | −3.71573 | −0.129997 | ||||||||
\(818\) | 3.45584 | 0.120831 | ||||||||
\(819\) | −27.3137 | −0.954418 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.17157 | −0.250290 | −0.125145 | − | 0.992138i | \(-0.539940\pi\) | ||||
−0.125145 | + | 0.992138i | \(0.539940\pi\) | |||||||
\(822\) | 3.85786 | 0.134558 | ||||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | −30.6274 | −1.06696 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | −18.6863 | −0.649786 | −0.324893 | − | 0.945751i | \(-0.605328\pi\) | ||||
−0.324893 | + | 0.945751i | \(0.605328\pi\) | |||||||
\(828\) | −7.31371 | −0.254169 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.6569 | 0.473751 | ||||||||
\(832\) | 23.5980 | 0.818113 | ||||||||
\(833\) | 111.397 | 3.85968 | ||||||||
\(834\) | 6.82843 | 0.236449 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.14214 | −0.0740873 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.25483 | 0.0433475 | ||||||||
\(839\) | 22.6274 | 0.781185 | 0.390593 | − | 0.920564i | \(-0.372270\pi\) | ||||
0.390593 | + | 0.920564i | \(0.372270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | 2.48528 | 0.0856485 | ||||||||
\(843\) | −16.8284 | −0.579602 | ||||||||
\(844\) | −12.4853 | −0.429761 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.65685 | −0.0569638 | ||||||||
\(847\) | 4.82843 | 0.165907 | ||||||||
\(848\) | 39.9411 | 1.37158 | ||||||||
\(849\) | 3.17157 | 0.108848 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.37258 | −0.0470515 | ||||||||
\(852\) | −24.9706 | −0.855477 | ||||||||
\(853\) | 31.3137 | 1.07216 | 0.536080 | − | 0.844167i | \(-0.319904\pi\) | ||||
0.536080 | + | 0.844167i | \(0.319904\pi\) | |||||||
\(854\) | 0.686292 | 0.0234844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.42641 | 0.288009 | ||||||||
\(857\) | 11.5147 | 0.393335 | 0.196668 | − | 0.980470i | \(-0.436988\pi\) | ||||
0.196668 | + | 0.980470i | \(0.436988\pi\) | |||||||
\(858\) | −2.34315 | −0.0799937 | ||||||||
\(859\) | −19.0294 | −0.649276 | −0.324638 | − | 0.945838i | \(-0.605242\pi\) | ||||
−0.324638 | + | 0.945838i | \(0.605242\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | −4.28427 | −0.145923 | ||||||||
\(863\) | 43.3137 | 1.47442 | 0.737208 | − | 0.675666i | \(-0.236144\pi\) | ||||
0.737208 | + | 0.675666i | \(0.236144\pi\) | |||||||
\(864\) | −4.41421 | −0.150175 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.79899 | −0.0611322 | ||||||||
\(867\) | 29.6274 | 1.00620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.48528 | 0.287843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0000 | 1.08428 | ||||||||
\(872\) | −8.42641 | −0.285354 | ||||||||
\(873\) | −0.343146 | −0.0116137 | ||||||||
\(874\) | 1.94113 | 0.0656595 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.6863 | −0.698925 | ||||||||
\(877\) | 42.6274 | 1.43943 | 0.719713 | − | 0.694272i | \(-0.244273\pi\) | ||||
0.719713 | + | 0.694272i | \(0.244273\pi\) | |||||||
\(878\) | 1.45584 | 0.0491324 | ||||||||
\(879\) | 1.17157 | 0.0395162 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0294 | −0.438973 | −0.219486 | − | 0.975616i | \(-0.570438\pi\) | ||||
−0.219486 | + | 0.975616i | \(0.570438\pi\) | |||||||
\(882\) | −6.75736 | −0.227532 | ||||||||
\(883\) | 50.6274 | 1.70375 | 0.851874 | − | 0.523747i | \(-0.175466\pi\) | ||||
0.851874 | + | 0.523747i | \(0.175466\pi\) | |||||||
\(884\) | 70.6274 | 2.37546 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.97056 | 0.166989 | ||||||||
\(887\) | 4.34315 | 0.145829 | 0.0729143 | − | 0.997338i | \(-0.476770\pi\) | ||||
0.0729143 | + | 0.997338i | \(0.476770\pi\) | |||||||
\(888\) | −0.544156 | −0.0182607 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −32.2843 | −1.08096 | ||||||||
\(893\) | −4.68629 | −0.156821 | ||||||||
\(894\) | −7.65685 | −0.256084 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50.9706 | 1.70281 | ||||||||
\(897\) | −22.6274 | −0.755507 | ||||||||
\(898\) | 1.23045 | 0.0410606 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 90.9117 | 3.02871 | ||||||||
\(902\) | −0.343146 | −0.0114255 | ||||||||
\(903\) | 15.3137 | 0.509608 | ||||||||
\(904\) | −23.7401 | −0.789584 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.201010 | 0.00667811 | ||||||||
\(907\) | −7.02944 | −0.233409 | −0.116704 | − | 0.993167i | \(-0.537233\pi\) | ||||
−0.116704 | + | 0.993167i | \(0.537233\pi\) | |||||||
\(908\) | −25.5980 | −0.849499 | ||||||||
\(909\) | 4.82843 | 0.160149 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0294 | −0.497947 | −0.248974 | − | 0.968510i | \(-0.580093\pi\) | ||||
−0.248974 | + | 0.968510i | \(0.580093\pi\) | |||||||
\(912\) | −3.51472 | −0.116384 | ||||||||
\(913\) | −10.0000 | −0.330952 | ||||||||
\(914\) | −0.284271 | −0.00940286 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.65685 | 0.120826 | ||||||||
\(917\) | −93.2548 | −3.07955 | ||||||||
\(918\) | −2.82843 | −0.0933520 | ||||||||
\(919\) | 28.4853 | 0.939643 | 0.469821 | − | 0.882762i | \(-0.344318\pi\) | ||||
0.469821 | + | 0.882762i | \(0.344318\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.82843 | 0.290907 | ||||||||
\(922\) | 11.6569 | 0.383898 | ||||||||
\(923\) | −77.2548 | −2.54287 | ||||||||
\(924\) | 8.82843 | 0.290434 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.0000 | −0.394344 | ||||||||
\(927\) | −19.3137 | −0.634345 | ||||||||
\(928\) | −3.65685 | −0.120042 | ||||||||
\(929\) | 33.5980 | 1.10231 | 0.551157 | − | 0.834402i | \(-0.314187\pi\) | ||||
0.551157 | + | 0.834402i | \(0.314187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.1127 | −0.626393 | ||||||||
\(932\) | −24.0833 | −0.788873 | ||||||||
\(933\) | 19.3137 | 0.632302 | ||||||||
\(934\) | 9.37258 | 0.306680 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.97056 | −0.293212 | ||||||||
\(937\) | −44.9706 | −1.46912 | −0.734562 | − | 0.678541i | \(-0.762612\pi\) | ||||
−0.734562 | + | 0.678541i | \(0.762612\pi\) | |||||||
\(938\) | 11.3137 | 0.369406 | ||||||||
\(939\) | −4.34315 | −0.141733 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.7696 | 1.26385 | 0.631926 | − | 0.775029i | \(-0.282265\pi\) | ||||
0.631926 | + | 0.775029i | \(0.282265\pi\) | |||||||
\(942\) | 7.45584 | 0.242925 | ||||||||
\(943\) | −3.31371 | −0.107909 | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.31371 | 0.0427123 | ||||||||
\(947\) | 38.6274 | 1.25522 | 0.627611 | − | 0.778527i | \(-0.284033\pi\) | ||||
0.627611 | + | 0.778527i | \(0.284033\pi\) | |||||||
\(948\) | 15.5147 | 0.503895 | ||||||||
\(949\) | −64.0000 | −2.07753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.2843 | −0.982035 | ||||||||
\(952\) | 52.2843 | 1.69454 | ||||||||
\(953\) | −27.7990 | −0.900498 | −0.450249 | − | 0.892903i | \(-0.648665\pi\) | ||||
−0.450249 | + | 0.892903i | \(0.648665\pi\) | |||||||
\(954\) | −5.51472 | −0.178546 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.5980 | −0.375105 | ||||||||
\(957\) | −0.828427 | −0.0267792 | ||||||||
\(958\) | −1.25483 | −0.0405418 | ||||||||
\(959\) | −44.9706 | −1.45218 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −0.804041 | −0.0259233 | ||||||||
\(963\) | 5.31371 | 0.171232 | ||||||||
\(964\) | 43.2548 | 1.39314 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.00000 | −0.257396 | ||||||||
\(967\) | 39.4558 | 1.26881 | 0.634407 | − | 0.772999i | \(-0.281244\pi\) | ||||
0.634407 | + | 0.772999i | \(0.281244\pi\) | |||||||
\(968\) | 1.58579 | 0.0509691 | ||||||||
\(969\) | −8.00000 | −0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.6274 | 0.341050 | 0.170525 | − | 0.985353i | \(-0.445454\pi\) | ||||
0.170525 | + | 0.985353i | \(0.445454\pi\) | |||||||
\(972\) | −1.82843 | −0.0586468 | ||||||||
\(973\) | −79.5980 | −2.55179 | ||||||||
\(974\) | 8.68629 | 0.278327 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.02944 | −0.0329515 | ||||||||
\(977\) | −25.3137 | −0.809857 | −0.404929 | − | 0.914348i | \(-0.632704\pi\) | ||||
−0.404929 | + | 0.914348i | \(0.632704\pi\) | |||||||
\(978\) | 6.34315 | 0.202831 | ||||||||
\(979\) | 7.65685 | 0.244714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.31371 | −0.169654 | ||||||||
\(982\) | −10.6274 | −0.339135 | ||||||||
\(983\) | −14.6274 | −0.466542 | −0.233271 | − | 0.972412i | \(-0.574943\pi\) | ||||
−0.233271 | + | 0.972412i | \(0.574943\pi\) | |||||||
\(984\) | −1.31371 | −0.0418795 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.34315 | −0.0746210 | ||||||||
\(987\) | 19.3137 | 0.614762 | ||||||||
\(988\) | −12.1177 | −0.385517 | ||||||||
\(989\) | 12.6863 | 0.403401 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6274 | 0.464655 | 0.232328 | − | 0.972638i | \(-0.425366\pi\) | ||||
0.232328 | + | 0.972638i | \(0.425366\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6569 | 0.560323 | ||||||||
\(994\) | −27.3137 | −0.866338 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.2843 | −0.579359 | ||||||||
\(997\) | 16.6863 | 0.528460 | 0.264230 | − | 0.964460i | \(-0.414882\pi\) | ||||
0.264230 | + | 0.964460i | \(0.414882\pi\) | |||||||
\(998\) | 13.9411 | 0.441299 | ||||||||
\(999\) | −0.343146 | −0.0108567 |
(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 | 825.2.a.g.1.1 | 2 | ||
3.2 | odd | 2 | 2475.2.a.m.1.2 | 2 | |||
5.2 | odd | 4 | 825.2.c.e.199.2 | 4 | |||
5.3 | odd | 4 | 825.2.c.e.199.3 | 4 | |||
5.4 | even | 2 | 165.2.a.a.1.2 | ✓ | 2 | ||
11.10 | odd | 2 | 9075.2.a.v.1.2 | 2 | |||
15.2 | even | 4 | 2475.2.c.m.199.3 | 4 | |||
15.8 | even | 4 | 2475.2.c.m.199.2 | 4 | |||
15.14 | odd | 2 | 495.2.a.d.1.1 | 2 | |||
20.19 | odd | 2 | 2640.2.a.bb.1.2 | 2 | |||
35.34 | odd | 2 | 8085.2.a.ba.1.2 | 2 | |||
55.54 | odd | 2 | 1815.2.a.k.1.1 | 2 | |||
60.59 | even | 2 | 7920.2.a.cg.1.2 | 2 | |||
165.164 | even | 2 | 5445.2.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.a.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
495.2.a.d.1.1 | 2 | 15.14 | odd | 2 | |||
825.2.a.g.1.1 | 2 | 1.1 | even | 1 | trivial | ||
825.2.c.e.199.2 | 4 | 5.2 | odd | 4 | |||
825.2.c.e.199.3 | 4 | 5.3 | odd | 4 | |||
1815.2.a.k.1.1 | 2 | 55.54 | odd | 2 | |||
2475.2.a.m.1.2 | 2 | 3.2 | odd | 2 | |||
2475.2.c.m.199.2 | 4 | 15.8 | even | 4 | |||
2475.2.c.m.199.3 | 4 | 15.2 | even | 4 | |||
2640.2.a.bb.1.2 | 2 | 20.19 | odd | 2 | |||
5445.2.a.m.1.2 | 2 | 165.164 | even | 2 | |||
7920.2.a.cg.1.2 | 2 | 60.59 | even | 2 | |||
8085.2.a.ba.1.2 | 2 | 35.34 | odd | 2 | |||
9075.2.a.v.1.2 | 2 | 11.10 | odd | 2 |