Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
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, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.e.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214i | 0.292893i | 0.989219 | + | 0.146447i | \(0.0467837\pi\) | ||||
−0.989219 | + | 0.146447i | \(0.953216\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.414214 | −0.169102 | ||||||||
\(7\) | − 4.82843i | − 1.82497i | −0.409106 | − | 0.912487i | \(-0.634159\pi\) | ||||
0.409106 | − | 0.912487i | \(-0.365841\pi\) | |||||||
\(8\) | 1.58579i | 0.560660i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.82843i | 0.527821i | ||||||||
\(13\) | − 5.65685i | − 1.56893i | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
0.620174 | − | 0.784465i | \(-0.287062\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 6.82843i | − 1.65614i | −0.560627 | − | 0.828068i | \(-0.689440\pi\) | ||||
0.560627 | − | 0.828068i | \(-0.310560\pi\) | |||||||
\(18\) | − 0.414214i | − 0.0976311i | ||||||||
\(19\) | 1.17157 | 0.268777 | 0.134389 | − | 0.990929i | \(-0.457093\pi\) | ||||
0.134389 | + | 0.990929i | \(0.457093\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.82843 | 1.05365 | ||||||||
\(22\) | − 0.414214i | − 0.0883106i | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | −1.58579 | −0.323697 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.34315 | 0.459529 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 8.82843i | − 1.66842i | ||||||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 4.41421i | 0.780330i | ||||||||
\(33\) | − 1.00000i | − 0.174078i | ||||||||
\(34\) | 2.82843 | 0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | 0.343146i | 0.0564128i | 0.999602 | + | 0.0282064i | \(0.00897957\pi\) | ||||
−0.999602 | + | 0.0282064i | \(0.991020\pi\) | |||||||
\(38\) | 0.485281i | 0.0787230i | ||||||||
\(39\) | 5.65685 | 0.905822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.828427 | −0.129379 | −0.0646893 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646893 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(42\) | 2.00000i | 0.308607i | ||||||||
\(43\) | 3.17157i | 0.483660i | 0.970319 | + | 0.241830i | \(0.0777477\pi\) | ||||
−0.970319 | + | 0.241830i | \(0.922252\pi\) | |||||||
\(44\) | −1.82843 | −0.275646 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.65685 | −0.244290 | ||||||||
\(47\) | − 4.00000i | − 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | 3.00000i | 0.433013i | ||||||||
\(49\) | −16.3137 | −2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.82843 | 0.956171 | ||||||||
\(52\) | − 10.3431i | − 1.43434i | ||||||||
\(53\) | 13.3137i | 1.82878i | 0.404836 | + | 0.914389i | \(0.367329\pi\) | ||||
−0.404836 | + | 0.914389i | \(0.632671\pi\) | |||||||
\(54\) | 0.414214 | 0.0563673 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.65685 | 1.02319 | ||||||||
\(57\) | 1.17157i | 0.155179i | ||||||||
\(58\) | − 0.343146i | − 0.0450572i | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.343146 | −0.0439353 | −0.0219677 | − | 0.999759i | \(-0.506993\pi\) | ||||
−0.0219677 | + | 0.999759i | \(0.506993\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.82843i | 0.608325i | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.414214 | 0.0509862 | ||||||||
\(67\) | 5.65685i | 0.691095i | 0.938401 | + | 0.345547i | \(0.112307\pi\) | ||||
−0.938401 | + | 0.345547i | \(0.887693\pi\) | |||||||
\(68\) | − 12.4853i | − 1.51406i | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6569 | 1.62077 | 0.810385 | − | 0.585897i | \(-0.199258\pi\) | ||||
0.810385 | + | 0.585897i | \(0.199258\pi\) | |||||||
\(72\) | − 1.58579i | − 0.186887i | ||||||||
\(73\) | 11.3137i | 1.32417i | 0.749429 | + | 0.662085i | \(0.230328\pi\) | ||||
−0.749429 | + | 0.662085i | \(0.769672\pi\) | |||||||
\(74\) | −0.142136 | −0.0165229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.14214 | 0.245720 | ||||||||
\(77\) | 4.82843i | 0.550250i | ||||||||
\(78\) | 2.34315i | 0.265309i | ||||||||
\(79\) | 8.48528 | 0.954669 | 0.477334 | − | 0.878722i | \(-0.341603\pi\) | ||||
0.477334 | + | 0.878722i | \(0.341603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 0.343146i | − 0.0378941i | ||||||||
\(83\) | 10.0000i | 1.09764i | 0.835940 | + | 0.548821i | \(0.184923\pi\) | ||||
−0.835940 | + | 0.548821i | \(0.815077\pi\) | |||||||
\(84\) | 8.82843 | 0.963260 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.31371 | −0.141661 | ||||||||
\(87\) | − 0.828427i | − 0.0888167i | ||||||||
\(88\) | − 1.58579i | − 0.169045i | ||||||||
\(89\) | 7.65685 | 0.811625 | 0.405812 | − | 0.913956i | \(-0.366989\pi\) | ||||
0.405812 | + | 0.913956i | \(0.366989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.3137 | −2.86325 | ||||||||
\(92\) | 7.31371i | 0.762507i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.65685 | 0.170891 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.41421 | −0.450524 | ||||||||
\(97\) | 0.343146i | 0.0348412i | 0.999848 | + | 0.0174206i | \(0.00554543\pi\) | ||||
−0.999848 | + | 0.0174206i | \(0.994455\pi\) | |||||||
\(98\) | − 6.75736i | − 0.682596i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.82843 | 0.480446 | 0.240223 | − | 0.970718i | \(-0.422779\pi\) | ||||
0.240223 | + | 0.970718i | \(0.422779\pi\) | |||||||
\(102\) | 2.82843i | 0.280056i | ||||||||
\(103\) | − 19.3137i | − 1.90304i | −0.307593 | − | 0.951518i | \(-0.599523\pi\) | ||||
0.307593 | − | 0.951518i | \(-0.400477\pi\) | |||||||
\(104\) | 8.97056 | 0.879636 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.51472 | −0.535637 | ||||||||
\(107\) | − 5.31371i | − 0.513696i | −0.966452 | − | 0.256848i | \(-0.917316\pi\) | ||||
0.966452 | − | 0.256848i | \(-0.0826839\pi\) | |||||||
\(108\) | − 1.82843i | − 0.175940i | ||||||||
\(109\) | 5.31371 | 0.508961 | 0.254480 | − | 0.967078i | \(-0.418096\pi\) | ||||
0.254480 | + | 0.967078i | \(0.418096\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.343146 | −0.0325700 | ||||||||
\(112\) | − 14.4853i | − 1.36873i | ||||||||
\(113\) | − 14.9706i | − 1.40831i | −0.710045 | − | 0.704156i | \(-0.751326\pi\) | ||||
0.710045 | − | 0.704156i | \(-0.248674\pi\) | |||||||
\(114\) | −0.485281 | −0.0454508 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.51472 | −0.140638 | ||||||||
\(117\) | 5.65685i | 0.522976i | ||||||||
\(118\) | 1.65685i | 0.152526i | ||||||||
\(119\) | −32.9706 | −3.02241 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 0.142136i | − 0.0128684i | ||||||||
\(123\) | − 0.828427i | − 0.0746968i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 2.48528i | 0.220533i | 0.993902 | + | 0.110267i | \(0.0351704\pi\) | ||||
−0.993902 | + | 0.110267i | \(0.964830\pi\) | |||||||
\(128\) | 10.5563i | 0.933058i | ||||||||
\(129\) | −3.17157 | −0.279241 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.3137 | −1.68745 | −0.843723 | − | 0.536778i | \(-0.819641\pi\) | ||||
−0.843723 | + | 0.536778i | \(0.819641\pi\) | |||||||
\(132\) | − 1.82843i | − 0.159144i | ||||||||
\(133\) | − 5.65685i | − 0.490511i | ||||||||
\(134\) | −2.34315 | −0.202417 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.8284 | 0.928530 | ||||||||
\(137\) | 9.31371i | 0.795724i | 0.917445 | + | 0.397862i | \(0.130248\pi\) | ||||
−0.917445 | + | 0.397862i | \(0.869752\pi\) | |||||||
\(138\) | − 1.65685i | − 0.141041i | ||||||||
\(139\) | 16.4853 | 1.39826 | 0.699132 | − | 0.714993i | \(-0.253570\pi\) | ||||
0.699132 | + | 0.714993i | \(0.253570\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | 0.336861 | ||||||||
\(142\) | 5.65685i | 0.474713i | ||||||||
\(143\) | 5.65685i | 0.473050i | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.68629 | −0.387840 | ||||||||
\(147\) | − 16.3137i | − 1.34553i | ||||||||
\(148\) | 0.627417i | 0.0515734i | ||||||||
\(149\) | −18.4853 | −1.51437 | −0.757187 | − | 0.653199i | \(-0.773427\pi\) | ||||
−0.757187 | + | 0.653199i | \(0.773427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.485281 | −0.0394916 | −0.0197458 | − | 0.999805i | \(-0.506286\pi\) | ||||
−0.0197458 | + | 0.999805i | \(0.506286\pi\) | |||||||
\(152\) | 1.85786i | 0.150693i | ||||||||
\(153\) | 6.82843i | 0.552046i | ||||||||
\(154\) | −2.00000 | −0.161165 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.3431 | 0.828114 | ||||||||
\(157\) | 18.0000i | 1.43656i | 0.695756 | + | 0.718278i | \(0.255069\pi\) | ||||
−0.695756 | + | 0.718278i | \(0.744931\pi\) | |||||||
\(158\) | 3.51472i | 0.279616i | ||||||||
\(159\) | −13.3137 | −1.05585 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.3137 | 1.52213 | ||||||||
\(162\) | 0.414214i | 0.0325437i | ||||||||
\(163\) | − 15.3137i | − 1.19946i | −0.800202 | − | 0.599731i | \(-0.795274\pi\) | ||||
0.800202 | − | 0.599731i | \(-0.204726\pi\) | |||||||
\(164\) | −1.51472 | −0.118280 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.14214 | −0.321492 | ||||||||
\(167\) | 9.31371i | 0.720716i | 0.932814 | + | 0.360358i | \(0.117346\pi\) | ||||
−0.932814 | + | 0.360358i | \(0.882654\pi\) | |||||||
\(168\) | 7.65685i | 0.590739i | ||||||||
\(169\) | −19.0000 | −1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.17157 | −0.0895924 | ||||||||
\(172\) | 5.79899i | 0.442169i | ||||||||
\(173\) | 2.82843i | 0.215041i | 0.994203 | + | 0.107521i | \(0.0342912\pi\) | ||||
−0.994203 | + | 0.107521i | \(0.965709\pi\) | |||||||
\(174\) | 0.343146 | 0.0260138 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 4.00000i | 0.300658i | ||||||||
\(178\) | 3.17157i | 0.237719i | ||||||||
\(179\) | 6.34315 | 0.474109 | 0.237054 | − | 0.971496i | \(-0.423818\pi\) | ||||
0.237054 | + | 0.971496i | \(0.423818\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | − 11.3137i | − 0.838628i | ||||||||
\(183\) | − 0.343146i | − 0.0253661i | ||||||||
\(184\) | −6.34315 | −0.467623 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.82843i | 0.499344i | ||||||||
\(188\) | − 7.31371i | − 0.533407i | ||||||||
\(189\) | −4.82843 | −0.351216 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.65685 | −0.409316 | −0.204658 | − | 0.978834i | \(-0.565608\pi\) | ||||
−0.204658 | + | 0.978834i | \(0.565608\pi\) | |||||||
\(192\) | 4.17157i | 0.301057i | ||||||||
\(193\) | − 2.34315i | − 0.168663i | −0.996438 | − | 0.0843317i | \(-0.973124\pi\) | ||||
0.996438 | − | 0.0843317i | \(-0.0268755\pi\) | |||||||
\(194\) | −0.142136 | −0.0102047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29.8284 | −2.13060 | ||||||||
\(197\) | 8.48528i | 0.604551i | 0.953221 | + | 0.302276i | \(0.0977463\pi\) | ||||
−0.953221 | + | 0.302276i | \(0.902254\pi\) | |||||||
\(198\) | 0.414214i | 0.0294369i | ||||||||
\(199\) | 10.3431 | 0.733206 | 0.366603 | − | 0.930377i | \(-0.380521\pi\) | ||||
0.366603 | + | 0.930377i | \(0.380521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.65685 | −0.399004 | ||||||||
\(202\) | 2.00000i | 0.140720i | ||||||||
\(203\) | 4.00000i | 0.280745i | ||||||||
\(204\) | 12.4853 | 0.874145 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | − 4.00000i | − 0.278019i | ||||||||
\(208\) | − 16.9706i | − 1.17670i | ||||||||
\(209\) | −1.17157 | −0.0810394 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.82843 | 0.470088 | 0.235044 | − | 0.971985i | \(-0.424477\pi\) | ||||
0.235044 | + | 0.971985i | \(0.424477\pi\) | |||||||
\(212\) | 24.3431i | 1.67189i | ||||||||
\(213\) | 13.6569i | 0.935752i | ||||||||
\(214\) | 2.20101 | 0.150458 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.58579 | 0.107899 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.20101i | 0.149071i | ||||||||
\(219\) | −11.3137 | −0.764510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.6274 | −2.59836 | ||||||||
\(222\) | − 0.142136i | − 0.00953952i | ||||||||
\(223\) | 17.6569i | 1.18239i | 0.806529 | + | 0.591195i | \(0.201344\pi\) | ||||
−0.806529 | + | 0.591195i | \(0.798656\pi\) | |||||||
\(224\) | 21.3137 | 1.42408 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.20101 | 0.412485 | ||||||||
\(227\) | − 14.0000i | − 0.929213i | −0.885517 | − | 0.464606i | \(-0.846196\pi\) | ||||
0.885517 | − | 0.464606i | \(-0.153804\pi\) | |||||||
\(228\) | 2.14214i | 0.141866i | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.82843 | −0.317687 | ||||||||
\(232\) | − 1.31371i | − 0.0862492i | ||||||||
\(233\) | 13.1716i | 0.862898i | 0.902137 | + | 0.431449i | \(0.141998\pi\) | ||||
−0.902137 | + | 0.431449i | \(0.858002\pi\) | |||||||
\(234\) | −2.34315 | −0.153176 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.31371 | 0.476082 | ||||||||
\(237\) | 8.48528i | 0.551178i | ||||||||
\(238\) | − 13.6569i | − 0.885242i | ||||||||
\(239\) | −6.34315 | −0.410304 | −0.205152 | − | 0.978730i | \(-0.565769\pi\) | ||||
−0.205152 | + | 0.978730i | \(0.565769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6569 | −1.52387 | −0.761936 | − | 0.647652i | \(-0.775751\pi\) | ||||
−0.761936 | + | 0.647652i | \(0.775751\pi\) | |||||||
\(242\) | 0.414214i | 0.0266267i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.627417 | −0.0401663 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.343146 | 0.0218782 | ||||||||
\(247\) | − 6.62742i | − 0.421692i | ||||||||
\(248\) | 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 | \(0.634244\pi\) | |||||||
\(252\) | 8.82843i | 0.556139i | ||||||||
\(253\) | − 4.00000i | − 0.251478i | ||||||||
\(254\) | −1.02944 | −0.0645926 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | − 27.6569i | − 1.72519i | −0.505898 | − | 0.862594i | \(-0.668839\pi\) | ||||
0.505898 | − | 0.862594i | \(-0.331161\pi\) | |||||||
\(258\) | − 1.31371i | − 0.0817879i | ||||||||
\(259\) | 1.65685 | 0.102952 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.828427 | 0.0512784 | ||||||||
\(262\) | − 8.00000i | − 0.494242i | ||||||||
\(263\) | − 18.0000i | − 1.10993i | −0.831875 | − | 0.554964i | \(-0.812732\pi\) | ||||
0.831875 | − | 0.554964i | \(-0.187268\pi\) | |||||||
\(264\) | 1.58579 | 0.0975984 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.34315 | 0.143667 | ||||||||
\(267\) | 7.65685i | 0.468592i | ||||||||
\(268\) | 10.3431i | 0.631808i | ||||||||
\(269\) | 24.6274 | 1.50156 | 0.750780 | − | 0.660552i | \(-0.229678\pi\) | ||||
0.750780 | + | 0.660552i | \(0.229678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.7990 | 1.68867 | 0.844334 | − | 0.535817i | \(-0.179996\pi\) | ||||
0.844334 | + | 0.535817i | \(0.179996\pi\) | |||||||
\(272\) | − 20.4853i | − 1.24210i | ||||||||
\(273\) | − 27.3137i | − 1.65310i | ||||||||
\(274\) | −3.85786 | −0.233062 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.31371 | −0.440234 | ||||||||
\(277\) | − 13.6569i | − 0.820561i | −0.911959 | − | 0.410280i | \(-0.865431\pi\) | ||||
0.911959 | − | 0.410280i | \(-0.134569\pi\) | |||||||
\(278\) | 6.82843i | 0.409542i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8284 | −1.00390 | −0.501950 | − | 0.864897i | \(-0.667384\pi\) | ||||
−0.501950 | + | 0.864897i | \(0.667384\pi\) | |||||||
\(282\) | 1.65685i | 0.0986642i | ||||||||
\(283\) | 3.17157i | 0.188530i | 0.995547 | + | 0.0942652i | \(0.0300502\pi\) | ||||
−0.995547 | + | 0.0942652i | \(0.969950\pi\) | |||||||
\(284\) | 24.9706 | 1.48173 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.34315 | −0.138553 | ||||||||
\(287\) | 4.00000i | 0.236113i | ||||||||
\(288\) | − 4.41421i | − 0.260110i | ||||||||
\(289\) | −29.6274 | −1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.343146 | −0.0201156 | ||||||||
\(292\) | 20.6863i | 1.21057i | ||||||||
\(293\) | 1.17157i | 0.0684440i | 0.999414 | + | 0.0342220i | \(0.0108953\pi\) | ||||
−0.999414 | + | 0.0342220i | \(0.989105\pi\) | |||||||
\(294\) | 6.75736 | 0.394097 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.544156 | −0.0316284 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | − 7.65685i | − 0.443550i | ||||||||
\(299\) | 22.6274 | 1.30858 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.3137 | 0.882667 | ||||||||
\(302\) | − 0.201010i | − 0.0115668i | ||||||||
\(303\) | 4.82843i | 0.277386i | ||||||||
\(304\) | 3.51472 | 0.201583 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.82843 | −0.161690 | ||||||||
\(307\) | − 8.82843i | − 0.503865i | −0.967745 | − | 0.251932i | \(-0.918934\pi\) | ||||
0.967745 | − | 0.251932i | \(-0.0810661\pi\) | |||||||
\(308\) | 8.82843i | 0.503046i | ||||||||
\(309\) | 19.3137 | 1.09872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.3137 | 1.09518 | 0.547590 | − | 0.836747i | \(-0.315545\pi\) | ||||
0.547590 | + | 0.836747i | \(0.315545\pi\) | |||||||
\(312\) | 8.97056i | 0.507858i | ||||||||
\(313\) | − 4.34315i | − 0.245489i | −0.992438 | − | 0.122745i | \(-0.960830\pi\) | ||||
0.992438 | − | 0.122745i | \(-0.0391696\pi\) | |||||||
\(314\) | −7.45584 | −0.420758 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.5147 | 0.872771 | ||||||||
\(317\) | 30.2843i | 1.70093i | 0.526028 | + | 0.850467i | \(0.323681\pi\) | ||||
−0.526028 | + | 0.850467i | \(0.676319\pi\) | |||||||
\(318\) | − 5.51472i | − 0.309250i | ||||||||
\(319\) | 0.828427 | 0.0463830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.31371 | 0.296582 | ||||||||
\(322\) | 8.00000i | 0.445823i | ||||||||
\(323\) | − 8.00000i | − 0.445132i | ||||||||
\(324\) | 1.82843 | 0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.34315 | 0.351314 | ||||||||
\(327\) | 5.31371i | 0.293849i | ||||||||
\(328\) | − 1.31371i | − 0.0725374i | ||||||||
\(329\) | −19.3137 | −1.06480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6569 | 0.970508 | 0.485254 | − | 0.874373i | \(-0.338727\pi\) | ||||
0.485254 | + | 0.874373i | \(0.338727\pi\) | |||||||
\(332\) | 18.2843i | 1.00348i | ||||||||
\(333\) | − 0.343146i | − 0.0188043i | ||||||||
\(334\) | −3.85786 | −0.211093 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.4853 | 0.790237 | ||||||||
\(337\) | − 19.3137i | − 1.05208i | −0.850458 | − | 0.526042i | \(-0.823675\pi\) | ||||
0.850458 | − | 0.526042i | \(-0.176325\pi\) | |||||||
\(338\) | − 7.87006i | − 0.428075i | ||||||||
\(339\) | 14.9706 | 0.813089 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − 0.485281i | − 0.0262410i | ||||||||
\(343\) | 44.9706i | 2.42818i | ||||||||
\(344\) | −5.02944 | −0.271169 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.17157 | −0.0629841 | ||||||||
\(347\) | − 6.68629i | − 0.358939i | −0.983764 | − | 0.179469i | \(-0.942562\pi\) | ||||
0.983764 | − | 0.179469i | \(-0.0574381\pi\) | |||||||
\(348\) | − 1.51472i | − 0.0811974i | ||||||||
\(349\) | 22.9706 | 1.22959 | 0.614793 | − | 0.788688i | \(-0.289240\pi\) | ||||
0.614793 | + | 0.788688i | \(0.289240\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | − 4.41421i | − 0.235278i | ||||||||
\(353\) | − 26.0000i | − 1.38384i | −0.721974 | − | 0.691920i | \(-0.756765\pi\) | ||||
0.721974 | − | 0.691920i | \(-0.243235\pi\) | |||||||
\(354\) | −1.65685 | −0.0880608 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | − 32.9706i | − 1.74499i | ||||||||
\(358\) | 2.62742i | 0.138863i | ||||||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6274 | −0.927759 | ||||||||
\(362\) | − 5.79899i | − 0.304788i | ||||||||
\(363\) | 1.00000i | 0.0524864i | ||||||||
\(364\) | −49.9411 | −2.61763 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.142136 | 0.00742955 | ||||||||
\(367\) | − 1.65685i | − 0.0864871i | −0.999065 | − | 0.0432435i | \(-0.986231\pi\) | ||||
0.999065 | − | 0.0432435i | \(-0.0137691\pi\) | |||||||
\(368\) | 12.0000i | 0.625543i | ||||||||
\(369\) | 0.828427 | 0.0431262 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 64.2843 | 3.33747 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.6274i | 1.79294i | 0.443105 | + | 0.896470i | \(0.353877\pi\) | ||||
−0.443105 | + | 0.896470i | \(0.646123\pi\) | |||||||
\(374\) | −2.82843 | −0.146254 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.34315 | 0.327123 | ||||||||
\(377\) | 4.68629i | 0.241356i | ||||||||
\(378\) | − 2.00000i | − 0.102869i | ||||||||
\(379\) | 0.686292 | 0.0352524 | 0.0176262 | − | 0.999845i | \(-0.494389\pi\) | ||||
0.0176262 | + | 0.999845i | \(0.494389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.48528 | −0.127325 | ||||||||
\(382\) | − 2.34315i | − 0.119886i | ||||||||
\(383\) | 8.00000i | 0.408781i | 0.978889 | + | 0.204390i | \(0.0655212\pi\) | ||||
−0.978889 | + | 0.204390i | \(0.934479\pi\) | |||||||
\(384\) | −10.5563 | −0.538701 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.970563 | 0.0494003 | ||||||||
\(387\) | − 3.17157i | − 0.161220i | ||||||||
\(388\) | 0.627417i | 0.0318523i | ||||||||
\(389\) | 12.3431 | 0.625822 | 0.312911 | − | 0.949782i | \(-0.398696\pi\) | ||||
0.312911 | + | 0.949782i | \(0.398696\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.3137 | 1.38131 | ||||||||
\(392\) | − 25.8701i | − 1.30664i | ||||||||
\(393\) | − 19.3137i | − 0.974248i | ||||||||
\(394\) | −3.51472 | −0.177069 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.82843 | 0.0918819 | ||||||||
\(397\) | 18.9706i | 0.952105i | 0.879417 | + | 0.476053i | \(0.157933\pi\) | ||||
−0.879417 | + | 0.476053i | \(0.842067\pi\) | |||||||
\(398\) | 4.28427i | 0.214751i | ||||||||
\(399\) | 5.65685 | 0.283197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.3137 | −1.46386 | −0.731928 | − | 0.681382i | \(-0.761379\pi\) | ||||
−0.731928 | + | 0.681382i | \(0.761379\pi\) | |||||||
\(402\) | − 2.34315i | − 0.116865i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.82843 | 0.439231 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.65685 | −0.0822283 | ||||||||
\(407\) | − 0.343146i | − 0.0170091i | ||||||||
\(408\) | 10.8284i | 0.536087i | ||||||||
\(409\) | 8.34315 | 0.412542 | 0.206271 | − | 0.978495i | \(-0.433867\pi\) | ||||
0.206271 | + | 0.978495i | \(0.433867\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.31371 | −0.459411 | ||||||||
\(412\) | − 35.3137i | − 1.73978i | ||||||||
\(413\) | − 19.3137i | − 0.950365i | ||||||||
\(414\) | 1.65685 | 0.0814299 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.9706 | 1.22428 | ||||||||
\(417\) | 16.4853i | 0.807288i | ||||||||
\(418\) | − 0.485281i | − 0.0237359i | ||||||||
\(419\) | 3.02944 | 0.147998 | 0.0739988 | − | 0.997258i | \(-0.476424\pi\) | ||||
0.0739988 | + | 0.997258i | \(0.476424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 2.82843i | 0.137686i | ||||||||
\(423\) | 4.00000i | 0.194487i | ||||||||
\(424\) | −21.1127 | −1.02532 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.65685 | −0.274075 | ||||||||
\(427\) | 1.65685i | 0.0801808i | ||||||||
\(428\) | − 9.71573i | − 0.469627i | ||||||||
\(429\) | −5.65685 | −0.273115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3431 | 0.498212 | 0.249106 | − | 0.968476i | \(-0.419863\pi\) | ||||
0.249106 | + | 0.968476i | \(0.419863\pi\) | |||||||
\(432\) | − 3.00000i | − 0.144338i | ||||||||
\(433\) | 4.34315i | 0.208718i | 0.994540 | + | 0.104359i | \(0.0332791\pi\) | ||||
−0.994540 | + | 0.104359i | \(0.966721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.71573 | 0.465299 | ||||||||
\(437\) | 4.68629i | 0.224176i | ||||||||
\(438\) | − 4.68629i | − 0.223920i | ||||||||
\(439\) | 3.51472 | 0.167748 | 0.0838742 | − | 0.996476i | \(-0.473271\pi\) | ||||
0.0838742 | + | 0.996476i | \(0.473271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3137 | 0.776843 | ||||||||
\(442\) | − 16.0000i | − 0.761042i | ||||||||
\(443\) | − 12.0000i | − 0.570137i | −0.958507 | − | 0.285069i | \(-0.907984\pi\) | ||||
0.958507 | − | 0.285069i | \(-0.0920164\pi\) | |||||||
\(444\) | −0.627417 | −0.0297759 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.31371 | −0.346314 | ||||||||
\(447\) | − 18.4853i | − 0.874324i | ||||||||
\(448\) | − 20.1421i | − 0.951626i | ||||||||
\(449\) | 2.97056 | 0.140190 | 0.0700948 | − | 0.997540i | \(-0.477670\pi\) | ||||
0.0700948 | + | 0.997540i | \(0.477670\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.828427 | 0.0390091 | ||||||||
\(452\) | − 27.3726i | − 1.28750i | ||||||||
\(453\) | − 0.485281i | − 0.0228005i | ||||||||
\(454\) | 5.79899 | 0.272160 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.85786 | −0.0870025 | ||||||||
\(457\) | − 0.686292i | − 0.0321034i | −0.999871 | − | 0.0160517i | \(-0.994890\pi\) | ||||
0.999871 | − | 0.0160517i | \(-0.00510963\pi\) | |||||||
\(458\) | 0.828427i | 0.0387099i | ||||||||
\(459\) | −6.82843 | −0.318724 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.1421 | −1.31071 | −0.655355 | − | 0.755321i | \(-0.727481\pi\) | ||||
−0.655355 | + | 0.755321i | \(0.727481\pi\) | |||||||
\(462\) | − 2.00000i | − 0.0930484i | ||||||||
\(463\) | 28.9706i | 1.34638i | 0.739471 | + | 0.673188i | \(0.235076\pi\) | ||||
−0.739471 | + | 0.673188i | \(0.764924\pi\) | |||||||
\(464\) | −2.48528 | −0.115376 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.45584 | −0.252737 | ||||||||
\(467\) | 22.6274i | 1.04707i | 0.852004 | + | 0.523536i | \(0.175387\pi\) | ||||
−0.852004 | + | 0.523536i | \(0.824613\pi\) | |||||||
\(468\) | 10.3431i | 0.478112i | ||||||||
\(469\) | 27.3137 | 1.26123 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0000 | −0.829396 | ||||||||
\(472\) | 6.34315i | 0.291967i | ||||||||
\(473\) | − 3.17157i | − 0.145829i | ||||||||
\(474\) | −3.51472 | −0.161436 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −60.2843 | −2.76313 | ||||||||
\(477\) | − 13.3137i | − 0.609593i | ||||||||
\(478\) | − 2.62742i | − 0.120175i | ||||||||
\(479\) | −3.02944 | −0.138419 | −0.0692093 | − | 0.997602i | \(-0.522048\pi\) | ||||
−0.0692093 | + | 0.997602i | \(0.522048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.94113 | 0.0885077 | ||||||||
\(482\) | − 9.79899i | − 0.446332i | ||||||||
\(483\) | 19.3137i | 0.878804i | ||||||||
\(484\) | 1.82843 | 0.0831103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.414214 | −0.0187891 | ||||||||
\(487\) | 20.9706i | 0.950267i | 0.879914 | + | 0.475133i | \(0.157600\pi\) | ||||
−0.879914 | + | 0.475133i | \(0.842400\pi\) | |||||||
\(488\) | − 0.544156i | − 0.0246328i | ||||||||
\(489\) | 15.3137 | 0.692510 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.6569 | 1.15788 | 0.578939 | − | 0.815371i | \(-0.303467\pi\) | ||||
0.578939 | + | 0.815371i | \(0.303467\pi\) | |||||||
\(492\) | − 1.51472i | − 0.0682888i | ||||||||
\(493\) | 5.65685i | 0.254772i | ||||||||
\(494\) | 2.74517 | 0.123511 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 65.9411i | − 2.95786i | ||||||||
\(498\) | − 4.14214i | − 0.185614i | ||||||||
\(499\) | 33.6569 | 1.50669 | 0.753344 | − | 0.657627i | \(-0.228440\pi\) | ||||
0.753344 | + | 0.657627i | \(0.228440\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.31371 | −0.416106 | ||||||||
\(502\) | − 5.37258i | − 0.239790i | ||||||||
\(503\) | 5.31371i | 0.236927i | 0.992958 | + | 0.118463i | \(0.0377968\pi\) | ||||
−0.992958 | + | 0.118463i | \(0.962203\pi\) | |||||||
\(504\) | −7.65685 | −0.341063 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.65685 | 0.0736562 | ||||||||
\(507\) | − 19.0000i | − 0.843820i | ||||||||
\(508\) | 4.54416i | 0.201614i | ||||||||
\(509\) | −41.3137 | −1.83120 | −0.915599 | − | 0.402093i | \(-0.868283\pi\) | ||||
−0.915599 | + | 0.402093i | \(0.868283\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.6274 | 2.41657 | ||||||||
\(512\) | 22.7574i | 1.00574i | ||||||||
\(513\) | − 1.17157i | − 0.0517262i | ||||||||
\(514\) | 11.4558 | 0.505296 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.79899 | −0.255286 | ||||||||
\(517\) | 4.00000i | 0.175920i | ||||||||
\(518\) | 0.686292i | 0.0301539i | ||||||||
\(519\) | −2.82843 | −0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6274 | 0.553217 | 0.276609 | − | 0.960983i | \(-0.410789\pi\) | ||||
0.276609 | + | 0.960983i | \(0.410789\pi\) | |||||||
\(522\) | 0.343146i | 0.0150191i | ||||||||
\(523\) | 26.4853i | 1.15812i | 0.815285 | + | 0.579060i | \(0.196580\pi\) | ||||
−0.815285 | + | 0.579060i | \(0.803420\pi\) | |||||||
\(524\) | −35.3137 | −1.54269 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.45584 | 0.325090 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | − 3.00000i | − 0.130558i | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | − 10.3431i | − 0.448432i | ||||||||
\(533\) | 4.68629i | 0.202986i | ||||||||
\(534\) | −3.17157 | −0.137247 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.97056 | −0.387469 | ||||||||
\(537\) | 6.34315i | 0.273727i | ||||||||
\(538\) | 10.2010i | 0.439797i | ||||||||
\(539\) | 16.3137 | 0.702681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.31371 | −0.228454 | −0.114227 | − | 0.993455i | \(-0.536439\pi\) | ||||
−0.114227 | + | 0.993455i | \(0.536439\pi\) | |||||||
\(542\) | 11.5147i | 0.494600i | ||||||||
\(543\) | − 14.0000i | − 0.600798i | ||||||||
\(544\) | 30.1421 | 1.29233 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.3137 | 0.484182 | ||||||||
\(547\) | 20.1421i | 0.861216i | 0.902539 | + | 0.430608i | \(0.141701\pi\) | ||||
−0.902539 | + | 0.430608i | \(0.858299\pi\) | |||||||
\(548\) | 17.0294i | 0.727462i | ||||||||
\(549\) | 0.343146 | 0.0146451 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.970563 | −0.0413474 | ||||||||
\(552\) | − 6.34315i | − 0.269982i | ||||||||
\(553\) | − 40.9706i | − 1.74225i | ||||||||
\(554\) | 5.65685 | 0.240337 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 30.1421 | 1.27831 | ||||||||
\(557\) | 10.8284i | 0.458815i | 0.973330 | + | 0.229408i | \(0.0736789\pi\) | ||||
−0.973330 | + | 0.229408i | \(0.926321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.9411 | 0.758829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.82843 | −0.288296 | ||||||||
\(562\) | − 6.97056i | − 0.294035i | ||||||||
\(563\) | − 20.3431i | − 0.857361i | −0.903456 | − | 0.428681i | \(-0.858979\pi\) | ||||
0.903456 | − | 0.428681i | \(-0.141021\pi\) | |||||||
\(564\) | 7.31371 | 0.307963 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.31371 | −0.0552193 | ||||||||
\(567\) | − 4.82843i | − 0.202775i | ||||||||
\(568\) | 21.6569i | 0.908701i | ||||||||
\(569\) | −15.4558 | −0.647943 | −0.323971 | − | 0.946067i | \(-0.605018\pi\) | ||||
−0.323971 | + | 0.946067i | \(0.605018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.485281 | 0.0203084 | 0.0101542 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101542 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(572\) | 10.3431i | 0.432469i | ||||||||
\(573\) | − 5.65685i | − 0.236318i | ||||||||
\(574\) | −1.65685 | −0.0691558 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.17157 | −0.173816 | ||||||||
\(577\) | 14.0000i | 0.582828i | 0.956597 | + | 0.291414i | \(0.0941257\pi\) | ||||
−0.956597 | + | 0.291414i | \(0.905874\pi\) | |||||||
\(578\) | − 12.2721i | − 0.510451i | ||||||||
\(579\) | 2.34315 | 0.0973778 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.2843 | 2.00317 | ||||||||
\(582\) | − 0.142136i | − 0.00589171i | ||||||||
\(583\) | − 13.3137i | − 0.551397i | ||||||||
\(584\) | −17.9411 | −0.742409 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.485281 | −0.0200468 | ||||||||
\(587\) | − 30.6274i | − 1.26413i | −0.774916 | − | 0.632064i | \(-0.782208\pi\) | ||||
0.774916 | − | 0.632064i | \(-0.217792\pi\) | |||||||
\(588\) | − 29.8284i | − 1.23010i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.48528 | −0.349038 | ||||||||
\(592\) | 1.02944i | 0.0423096i | ||||||||
\(593\) | 17.1716i | 0.705152i | 0.935783 | + | 0.352576i | \(0.114694\pi\) | ||||
−0.935783 | + | 0.352576i | \(0.885306\pi\) | |||||||
\(594\) | −0.414214 | −0.0169954 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.7990 | −1.38446 | ||||||||
\(597\) | 10.3431i | 0.423317i | ||||||||
\(598\) | 9.37258i | 0.383273i | ||||||||
\(599\) | −4.68629 | −0.191477 | −0.0957383 | − | 0.995407i | \(-0.530521\pi\) | ||||
−0.0957383 | + | 0.995407i | \(0.530521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.3137 | 0.706241 | 0.353120 | − | 0.935578i | \(-0.385121\pi\) | ||||
0.353120 | + | 0.935578i | \(0.385121\pi\) | |||||||
\(602\) | 6.34315i | 0.258527i | ||||||||
\(603\) | − 5.65685i | − 0.230365i | ||||||||
\(604\) | −0.887302 | −0.0361038 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.00000 | −0.0812444 | ||||||||
\(607\) | 18.4853i | 0.750294i | 0.926965 | + | 0.375147i | \(0.122408\pi\) | ||||
−0.926965 | + | 0.375147i | \(0.877592\pi\) | |||||||
\(608\) | 5.17157i | 0.209735i | ||||||||
\(609\) | −4.00000 | −0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.6274 | −0.915407 | ||||||||
\(612\) | 12.4853i | 0.504688i | ||||||||
\(613\) | − 21.9411i | − 0.886194i | −0.896474 | − | 0.443097i | \(-0.853880\pi\) | ||||
0.896474 | − | 0.443097i | \(-0.146120\pi\) | |||||||
\(614\) | 3.65685 | 0.147579 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.65685 | −0.308503 | ||||||||
\(617\) | 11.6569i | 0.469287i | 0.972081 | + | 0.234644i | \(0.0753923\pi\) | ||||
−0.972081 | + | 0.234644i | \(0.924608\pi\) | |||||||
\(618\) | 8.00000i | 0.321807i | ||||||||
\(619\) | 25.6569 | 1.03124 | 0.515618 | − | 0.856819i | \(-0.327562\pi\) | ||||
0.515618 | + | 0.856819i | \(0.327562\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 8.00000i | 0.320771i | ||||||||
\(623\) | − 36.9706i | − 1.48119i | ||||||||
\(624\) | 16.9706 | 0.679366 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.79899 | 0.0719021 | ||||||||
\(627\) | − 1.17157i | − 0.0467881i | ||||||||
\(628\) | 32.9117i | 1.31332i | ||||||||
\(629\) | 2.34315 | 0.0934273 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.3431 | 1.36718 | 0.683590 | − | 0.729867i | \(-0.260418\pi\) | ||||
0.683590 | + | 0.729867i | \(0.260418\pi\) | |||||||
\(632\) | 13.4558i | 0.535245i | ||||||||
\(633\) | 6.82843i | 0.271406i | ||||||||
\(634\) | −12.5442 | −0.498192 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.3431 | −0.965269 | ||||||||
\(637\) | 92.2843i | 3.65644i | ||||||||
\(638\) | 0.343146i | 0.0135853i | ||||||||
\(639\) | −13.6569 | −0.540257 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.9706 | −1.06527 | −0.532637 | − | 0.846344i | \(-0.678799\pi\) | ||||
−0.532637 | + | 0.846344i | \(0.678799\pi\) | |||||||
\(642\) | 2.20101i | 0.0868669i | ||||||||
\(643\) | 29.9411i | 1.18076i | 0.807124 | + | 0.590381i | \(0.201023\pi\) | ||||
−0.807124 | + | 0.590381i | \(0.798977\pi\) | |||||||
\(644\) | 35.3137 | 1.39156 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.31371 | 0.130376 | ||||||||
\(647\) | 27.3137i | 1.07381i | 0.843642 | + | 0.536906i | \(0.180407\pi\) | ||||
−0.843642 | + | 0.536906i | \(0.819593\pi\) | |||||||
\(648\) | 1.58579i | 0.0622956i | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 28.0000i | − 1.09656i | ||||||||
\(653\) | 26.9706i | 1.05544i | 0.849418 | + | 0.527720i | \(0.176953\pi\) | ||||
−0.849418 | + | 0.527720i | \(0.823047\pi\) | |||||||
\(654\) | −2.20101 | −0.0860663 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.48528 | −0.0970339 | ||||||||
\(657\) | − 11.3137i | − 0.441390i | ||||||||
\(658\) | − 8.00000i | − 0.311872i | ||||||||
\(659\) | −7.31371 | −0.284902 | −0.142451 | − | 0.989802i | \(-0.545498\pi\) | ||||
−0.142451 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.3137 | −0.517843 | −0.258922 | − | 0.965898i | \(-0.583367\pi\) | ||||
−0.258922 | + | 0.965898i | \(0.583367\pi\) | |||||||
\(662\) | 7.31371i | 0.284255i | ||||||||
\(663\) | − 38.6274i | − 1.50016i | ||||||||
\(664\) | −15.8579 | −0.615404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.142136 | 0.00550764 | ||||||||
\(667\) | − 3.31371i | − 0.128307i | ||||||||
\(668\) | 17.0294i | 0.658889i | ||||||||
\(669\) | −17.6569 | −0.682653 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.343146 | 0.0132470 | ||||||||
\(672\) | 21.3137i | 0.822194i | ||||||||
\(673\) | − 29.6569i | − 1.14319i | −0.820537 | − | 0.571594i | \(-0.806325\pi\) | ||||
0.820537 | − | 0.571594i | \(-0.193675\pi\) | |||||||
\(674\) | 8.00000 | 0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.7401 | −1.33616 | ||||||||
\(677\) | − 21.4558i | − 0.824615i | −0.911045 | − | 0.412308i | \(-0.864723\pi\) | ||||
0.911045 | − | 0.412308i | \(-0.135277\pi\) | |||||||
\(678\) | 6.20101i | 0.238148i | ||||||||
\(679\) | 1.65685 | 0.0635842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0000 | 0.536481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 24.0000i | − 0.918334i | −0.888350 | − | 0.459167i | \(-0.848148\pi\) | ||||
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(684\) | −2.14214 | −0.0819066 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.6274 | −0.711198 | ||||||||
\(687\) | 2.00000i | 0.0763048i | ||||||||
\(688\) | 9.51472i | 0.362745i | ||||||||
\(689\) | 75.3137 | 2.86922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 5.17157i | 0.196594i | ||||||||
\(693\) | − 4.82843i | − 0.183417i | ||||||||
\(694\) | 2.76955 | 0.105131 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.31371 | 0.0497960 | ||||||||
\(697\) | 5.65685i | 0.214269i | ||||||||
\(698\) | 9.51472i | 0.360137i | ||||||||
\(699\) | −13.1716 | −0.498195 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.85786 | 0.296787 | 0.148394 | − | 0.988928i | \(-0.452590\pi\) | ||||
0.148394 | + | 0.988928i | \(0.452590\pi\) | |||||||
\(702\) | − 2.34315i | − 0.0884363i | ||||||||
\(703\) | 0.402020i | 0.0151625i | ||||||||
\(704\) | −4.17157 | −0.157222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.7696 | 0.405317 | ||||||||
\(707\) | − 23.3137i | − 0.876802i | ||||||||
\(708\) | 7.31371i | 0.274866i | ||||||||
\(709\) | −29.3137 | −1.10090 | −0.550450 | − | 0.834868i | \(-0.685544\pi\) | ||||
−0.550450 | + | 0.834868i | \(0.685544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.48528 | −0.318223 | ||||||||
\(712\) | 12.1421i | 0.455046i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 13.6569 | 0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.5980 | 0.433437 | ||||||||
\(717\) | − 6.34315i | − 0.236889i | ||||||||
\(718\) | − 4.97056i | − 0.185500i | ||||||||
\(719\) | −31.5980 | −1.17841 | −0.589203 | − | 0.807985i | \(-0.700558\pi\) | ||||
−0.589203 | + | 0.807985i | \(0.700558\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −93.2548 | −3.47299 | ||||||||
\(722\) | − 7.30152i | − 0.271734i | ||||||||
\(723\) | − 23.6569i | − 0.879808i | ||||||||
\(724\) | −25.5980 | −0.951341 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.414214 | −0.0153729 | ||||||||
\(727\) | − 33.9411i | − 1.25881i | −0.777079 | − | 0.629403i | \(-0.783299\pi\) | ||||
0.777079 | − | 0.629403i | \(-0.216701\pi\) | |||||||
\(728\) | − 43.3137i | − 1.60531i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.6569 | 0.801008 | ||||||||
\(732\) | − 0.627417i | − 0.0231900i | ||||||||
\(733\) | 17.6569i | 0.652171i | 0.945340 | + | 0.326085i | \(0.105730\pi\) | ||||
−0.945340 | + | 0.326085i | \(0.894270\pi\) | |||||||
\(734\) | 0.686292 | 0.0253315 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.6569 | −0.650840 | ||||||||
\(737\) | − 5.65685i | − 0.208373i | ||||||||
\(738\) | 0.343146i | 0.0126314i | ||||||||
\(739\) | −47.1127 | −1.73307 | −0.866534 | − | 0.499118i | \(-0.833658\pi\) | ||||
−0.866534 | + | 0.499118i | \(0.833658\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.62742 | 0.243464 | ||||||||
\(742\) | 26.6274i | 0.977523i | ||||||||
\(743\) | − 47.6569i | − 1.74836i | −0.485602 | − | 0.874180i | \(-0.661399\pi\) | ||||
0.485602 | − | 0.874180i | \(-0.338601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.3431 | −0.525140 | ||||||||
\(747\) | − 10.0000i | − 0.365881i | ||||||||
\(748\) | 12.4853i | 0.456507i | ||||||||
\(749\) | −25.6569 | −0.937481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.2843 | −1.32403 | −0.662016 | − | 0.749490i | \(-0.730299\pi\) | ||||
−0.662016 | + | 0.749490i | \(0.730299\pi\) | |||||||
\(752\) | − 12.0000i | − 0.437595i | ||||||||
\(753\) | − 12.9706i | − 0.472674i | ||||||||
\(754\) | −1.94113 | −0.0706916 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.82843 | −0.321087 | ||||||||
\(757\) | 8.62742i | 0.313569i | 0.987633 | + | 0.156784i | \(0.0501128\pi\) | ||||
−0.987633 | + | 0.156784i | \(0.949887\pi\) | |||||||
\(758\) | 0.284271i | 0.0103252i | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.1716 | −0.839969 | −0.419984 | − | 0.907531i | \(-0.637964\pi\) | ||||
−0.419984 | + | 0.907531i | \(0.637964\pi\) | |||||||
\(762\) | − 1.02944i | − 0.0372926i | ||||||||
\(763\) | − 25.6569i | − 0.928840i | ||||||||
\(764\) | −10.3431 | −0.374202 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.31371 | −0.119729 | ||||||||
\(767\) | − 22.6274i | − 0.817029i | ||||||||
\(768\) | 3.97056i | 0.143275i | ||||||||
\(769\) | −33.3137 | −1.20132 | −0.600662 | − | 0.799503i | \(-0.705096\pi\) | ||||
−0.600662 | + | 0.799503i | \(0.705096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.6569 | 0.996037 | ||||||||
\(772\) | − 4.28427i | − 0.154194i | ||||||||
\(773\) | 7.65685i | 0.275398i | 0.990474 | + | 0.137699i | \(0.0439706\pi\) | ||||
−0.990474 | + | 0.137699i | \(0.956029\pi\) | |||||||
\(774\) | 1.31371 | 0.0472203 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.544156 | −0.0195341 | ||||||||
\(777\) | 1.65685i | 0.0594393i | ||||||||
\(778\) | 5.11270i | 0.183299i | ||||||||
\(779\) | −0.970563 | −0.0347740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.6569 | −0.488681 | ||||||||
\(782\) | 11.3137i | 0.404577i | ||||||||
\(783\) | 0.828427i | 0.0296056i | ||||||||
\(784\) | −48.9411 | −1.74790 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.00000 | 0.285351 | ||||||||
\(787\) | 8.14214i | 0.290236i | 0.989414 | + | 0.145118i | \(0.0463561\pi\) | ||||
−0.989414 | + | 0.145118i | \(0.953644\pi\) | |||||||
\(788\) | 15.5147i | 0.552689i | ||||||||
\(789\) | 18.0000 | 0.640817 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −72.2843 | −2.57013 | ||||||||
\(792\) | 1.58579i | 0.0563485i | ||||||||
\(793\) | 1.94113i | 0.0689314i | ||||||||
\(794\) | −7.85786 | −0.278865 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.9117 | 0.670307 | ||||||||
\(797\) | 1.02944i | 0.0364645i | 0.999834 | + | 0.0182323i | \(0.00580383\pi\) | ||||
−0.999834 | + | 0.0182323i | \(0.994196\pi\) | |||||||
\(798\) | 2.34315i | 0.0829465i | ||||||||
\(799\) | −27.3137 | −0.966290 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65685 | −0.270542 | ||||||||
\(802\) | − 12.1421i | − 0.428754i | ||||||||
\(803\) | − 11.3137i | − 0.399252i | ||||||||
\(804\) | −10.3431 | −0.364775 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.6274i | 0.866926i | ||||||||
\(808\) | 7.65685i | 0.269367i | ||||||||
\(809\) | 56.4264 | 1.98385 | 0.991923 | − | 0.126838i | \(-0.0404829\pi\) | ||||
0.991923 | + | 0.126838i | \(0.0404829\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.4853 | −0.578877 | −0.289438 | − | 0.957197i | \(-0.593468\pi\) | ||||
−0.289438 | + | 0.957197i | \(0.593468\pi\) | |||||||
\(812\) | 7.31371i | 0.256661i | ||||||||
\(813\) | 27.7990i | 0.974953i | ||||||||
\(814\) | 0.142136 | 0.00498185 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.4853 | 0.717128 | ||||||||
\(817\) | 3.71573i | 0.129997i | ||||||||
\(818\) | 3.45584i | 0.120831i | ||||||||
\(819\) | 27.3137 | 0.954418 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.17157 | −0.250290 | −0.125145 | − | 0.992138i | \(-0.539940\pi\) | ||||
−0.125145 | + | 0.992138i | \(0.539940\pi\) | |||||||
\(822\) | − 3.85786i | − 0.134558i | ||||||||
\(823\) | − 16.0000i | − 0.557725i | −0.960331 | − | 0.278862i | \(-0.910043\pi\) | ||||
0.960331 | − | 0.278862i | \(-0.0899574\pi\) | |||||||
\(824\) | 30.6274 | 1.06696 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | 0.278356 | ||||||||
\(827\) | 18.6863i | 0.649786i | 0.945751 | + | 0.324893i | \(0.105328\pi\) | ||||
−0.945751 | + | 0.324893i | \(0.894672\pi\) | |||||||
\(828\) | − 7.31371i | − 0.254169i | ||||||||
\(829\) | 38.0000 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.6569 | 0.473751 | ||||||||
\(832\) | − 23.5980i | − 0.818113i | ||||||||
\(833\) | 111.397i | 3.85968i | ||||||||
\(834\) | −6.82843 | −0.236449 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.14214 | −0.0740873 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.25483i | 0.0433475i | ||||||||
\(839\) | −22.6274 | −0.781185 | −0.390593 | − | 0.920564i | \(-0.627730\pi\) | ||||
−0.390593 | + | 0.920564i | \(0.627730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | − 2.48528i | − 0.0856485i | ||||||||
\(843\) | − 16.8284i | − 0.579602i | ||||||||
\(844\) | 12.4853 | 0.429761 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.65685 | −0.0569638 | ||||||||
\(847\) | − 4.82843i | − 0.165907i | ||||||||
\(848\) | 39.9411i | 1.37158i | ||||||||
\(849\) | −3.17157 | −0.108848 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.37258 | −0.0470515 | ||||||||
\(852\) | 24.9706i | 0.855477i | ||||||||
\(853\) | 31.3137i | 1.07216i | 0.844167 | + | 0.536080i | \(0.180096\pi\) | ||||
−0.844167 | + | 0.536080i | \(0.819904\pi\) | |||||||
\(854\) | −0.686292 | −0.0234844 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.42641 | 0.288009 | ||||||||
\(857\) | − 11.5147i | − 0.393335i | −0.980470 | − | 0.196668i | \(-0.936988\pi\) | ||||
0.980470 | − | 0.196668i | \(-0.0630120\pi\) | |||||||
\(858\) | − 2.34315i | − 0.0799937i | ||||||||
\(859\) | 19.0294 | 0.649276 | 0.324638 | − | 0.945838i | \(-0.394758\pi\) | ||||
0.324638 | + | 0.945838i | \(0.394758\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | 4.28427i | 0.145923i | ||||||||
\(863\) | 43.3137i | 1.47442i | 0.675666 | + | 0.737208i | \(0.263856\pi\) | ||||
−0.675666 | + | 0.737208i | \(0.736144\pi\) | |||||||
\(864\) | 4.41421 | 0.150175 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.79899 | −0.0611322 | ||||||||
\(867\) | − 29.6274i | − 1.00620i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.48528 | −0.287843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0000 | 1.08428 | ||||||||
\(872\) | 8.42641i | 0.285354i | ||||||||
\(873\) | − 0.343146i | − 0.0116137i | ||||||||
\(874\) | −1.94113 | −0.0656595 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.6863 | −0.698925 | ||||||||
\(877\) | − 42.6274i | − 1.43943i | −0.694272 | − | 0.719713i | \(-0.744273\pi\) | ||||
0.694272 | − | 0.719713i | \(-0.255727\pi\) | |||||||
\(878\) | 1.45584i | 0.0491324i | ||||||||
\(879\) | −1.17157 | −0.0395162 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0294 | −0.438973 | −0.219486 | − | 0.975616i | \(-0.570438\pi\) | ||||
−0.219486 | + | 0.975616i | \(0.570438\pi\) | |||||||
\(882\) | 6.75736i | 0.227532i | ||||||||
\(883\) | 50.6274i | 1.70375i | 0.523747 | + | 0.851874i | \(0.324534\pi\) | ||||
−0.523747 | + | 0.851874i | \(0.675466\pi\) | |||||||
\(884\) | −70.6274 | −2.37546 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.97056 | 0.166989 | ||||||||
\(887\) | − 4.34315i | − 0.145829i | −0.997338 | − | 0.0729143i | \(-0.976770\pi\) | ||||
0.997338 | − | 0.0729143i | \(-0.0232300\pi\) | |||||||
\(888\) | − 0.544156i | − 0.0182607i | ||||||||
\(889\) | 12.0000 | 0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 32.2843i | 1.08096i | ||||||||
\(893\) | − 4.68629i | − 0.156821i | ||||||||
\(894\) | 7.65685 | 0.256084 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50.9706 | 1.70281 | ||||||||
\(897\) | 22.6274i | 0.755507i | ||||||||
\(898\) | 1.23045i | 0.0410606i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 90.9117 | 3.02871 | ||||||||
\(902\) | 0.343146i | 0.0114255i | ||||||||
\(903\) | 15.3137i | 0.509608i | ||||||||
\(904\) | 23.7401 | 0.789584 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.201010 | 0.00667811 | ||||||||
\(907\) | 7.02944i | 0.233409i | 0.993167 | + | 0.116704i | \(0.0372330\pi\) | ||||
−0.993167 | + | 0.116704i | \(0.962767\pi\) | |||||||
\(908\) | − 25.5980i | − 0.849499i | ||||||||
\(909\) | −4.82843 | −0.160149 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0294 | −0.497947 | −0.248974 | − | 0.968510i | \(-0.580093\pi\) | ||||
−0.248974 | + | 0.968510i | \(0.580093\pi\) | |||||||
\(912\) | 3.51472i | 0.116384i | ||||||||
\(913\) | − 10.0000i | − 0.330952i | ||||||||
\(914\) | 0.284271 | 0.00940286 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.65685 | 0.120826 | ||||||||
\(917\) | 93.2548i | 3.07955i | ||||||||
\(918\) | − 2.82843i | − 0.0933520i | ||||||||
\(919\) | −28.4853 | −0.939643 | −0.469821 | − | 0.882762i | \(-0.655682\pi\) | ||||
−0.469821 | + | 0.882762i | \(0.655682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.82843 | 0.290907 | ||||||||
\(922\) | − 11.6569i | − 0.383898i | ||||||||
\(923\) | − 77.2548i | − 2.54287i | ||||||||
\(924\) | −8.82843 | −0.290434 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.0000 | −0.394344 | ||||||||
\(927\) | 19.3137i | 0.634345i | ||||||||
\(928\) | − 3.65685i | − 0.120042i | ||||||||
\(929\) | −33.5980 | −1.10231 | −0.551157 | − | 0.834402i | \(-0.685813\pi\) | ||||
−0.551157 | + | 0.834402i | \(0.685813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.1127 | −0.626393 | ||||||||
\(932\) | 24.0833i | 0.788873i | ||||||||
\(933\) | 19.3137i | 0.632302i | ||||||||
\(934\) | −9.37258 | −0.306680 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.97056 | −0.293212 | ||||||||
\(937\) | 44.9706i | 1.46912i | 0.678541 | + | 0.734562i | \(0.262612\pi\) | ||||
−0.678541 | + | 0.734562i | \(0.737388\pi\) | |||||||
\(938\) | 11.3137i | 0.369406i | ||||||||
\(939\) | 4.34315 | 0.141733 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.7696 | 1.26385 | 0.631926 | − | 0.775029i | \(-0.282265\pi\) | ||||
0.631926 | + | 0.775029i | \(0.282265\pi\) | |||||||
\(942\) | − 7.45584i | − 0.242925i | ||||||||
\(943\) | − 3.31371i | − 0.107909i | ||||||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.31371 | 0.0427123 | ||||||||
\(947\) | − 38.6274i | − 1.25522i | −0.778527 | − | 0.627611i | \(-0.784033\pi\) | ||||
0.778527 | − | 0.627611i | \(-0.215967\pi\) | |||||||
\(948\) | 15.5147i | 0.503895i | ||||||||
\(949\) | 64.0000 | 2.07753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.2843 | −0.982035 | ||||||||
\(952\) | − 52.2843i | − 1.69454i | ||||||||
\(953\) | − 27.7990i | − 0.900498i | −0.892903 | − | 0.450249i | \(-0.851335\pi\) | ||||
0.892903 | − | 0.450249i | \(-0.148665\pi\) | |||||||
\(954\) | 5.51472 | 0.178546 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.5980 | −0.375105 | ||||||||
\(957\) | 0.828427i | 0.0267792i | ||||||||
\(958\) | − 1.25483i | − 0.0405418i | ||||||||
\(959\) | 44.9706 | 1.45218 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0.804041i | 0.0259233i | ||||||||
\(963\) | 5.31371i | 0.171232i | ||||||||
\(964\) | −43.2548 | −1.39314 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.00000 | −0.257396 | ||||||||
\(967\) | − 39.4558i | − 1.26881i | −0.772999 | − | 0.634407i | \(-0.781244\pi\) | ||||
0.772999 | − | 0.634407i | \(-0.218756\pi\) | |||||||
\(968\) | 1.58579i | 0.0509691i | ||||||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.6274 | 0.341050 | 0.170525 | − | 0.985353i | \(-0.445454\pi\) | ||||
0.170525 | + | 0.985353i | \(0.445454\pi\) | |||||||
\(972\) | 1.82843i | 0.0586468i | ||||||||
\(973\) | − 79.5980i | − 2.55179i | ||||||||
\(974\) | −8.68629 | −0.278327 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.02944 | −0.0329515 | ||||||||
\(977\) | 25.3137i | 0.809857i | 0.914348 | + | 0.404929i | \(0.132704\pi\) | ||||
−0.914348 | + | 0.404929i | \(0.867296\pi\) | |||||||
\(978\) | 6.34315i | 0.202831i | ||||||||
\(979\) | −7.65685 | −0.244714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.31371 | −0.169654 | ||||||||
\(982\) | 10.6274i | 0.339135i | ||||||||
\(983\) | − 14.6274i | − 0.466542i | −0.972412 | − | 0.233271i | \(-0.925057\pi\) | ||||
0.972412 | − | 0.233271i | \(-0.0749429\pi\) | |||||||
\(984\) | 1.31371 | 0.0418795 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.34315 | −0.0746210 | ||||||||
\(987\) | − 19.3137i | − 0.614762i | ||||||||
\(988\) | − 12.1177i | − 0.385517i | ||||||||
\(989\) | −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 | ||||||||
\(993\) | 17.6569i | 0.560323i | ||||||||
\(994\) | 27.3137 | 0.866338 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.2843 | −0.579359 | ||||||||
\(997\) | − 16.6863i | − 0.528460i | −0.964460 | − | 0.264230i | \(-0.914882\pi\) | ||||
0.964460 | − | 0.264230i | \(-0.0851178\pi\) | |||||||
\(998\) | 13.9411i | 0.441299i | ||||||||
\(999\) | 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.c.e.199.3 | 4 | ||
3.2 | odd | 2 | 2475.2.c.m.199.2 | 4 | |||
5.2 | odd | 4 | 825.2.a.g.1.1 | 2 | |||
5.3 | odd | 4 | 165.2.a.a.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 825.2.c.e.199.2 | 4 | ||
15.2 | even | 4 | 2475.2.a.m.1.2 | 2 | |||
15.8 | even | 4 | 495.2.a.d.1.1 | 2 | |||
15.14 | odd | 2 | 2475.2.c.m.199.3 | 4 | |||
20.3 | even | 4 | 2640.2.a.bb.1.2 | 2 | |||
35.13 | even | 4 | 8085.2.a.ba.1.2 | 2 | |||
55.32 | even | 4 | 9075.2.a.v.1.2 | 2 | |||
55.43 | even | 4 | 1815.2.a.k.1.1 | 2 | |||
60.23 | odd | 4 | 7920.2.a.cg.1.2 | 2 | |||
165.98 | odd | 4 | 5445.2.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.a.a.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
495.2.a.d.1.1 | 2 | 15.8 | even | 4 | |||
825.2.a.g.1.1 | 2 | 5.2 | odd | 4 | |||
825.2.c.e.199.2 | 4 | 5.4 | even | 2 | inner | ||
825.2.c.e.199.3 | 4 | 1.1 | even | 1 | trivial | ||
1815.2.a.k.1.1 | 2 | 55.43 | even | 4 | |||
2475.2.a.m.1.2 | 2 | 15.2 | even | 4 | |||
2475.2.c.m.199.2 | 4 | 3.2 | odd | 2 | |||
2475.2.c.m.199.3 | 4 | 15.14 | odd | 2 | |||
2640.2.a.bb.1.2 | 2 | 20.3 | even | 4 | |||
5445.2.a.m.1.2 | 2 | 165.98 | odd | 4 | |||
7920.2.a.cg.1.2 | 2 | 60.23 | odd | 4 | |||
8085.2.a.ba.1.2 | 2 | 35.13 | even | 4 | |||
9075.2.a.v.1.2 | 2 | 55.32 | even | 4 |