Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30278 | −0.921201 | −0.460601 | − | 0.887607i | \(-0.652366\pi\) | ||||
−0.460601 | + | 0.887607i | \(0.652366\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | −0.302776 | −0.151388 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.30278 | −0.531856 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | −1.30278 | −0.411974 | ||||||||
\(11\) | 5.60555 | 1.69014 | 0.845069 | − | 0.534658i | \(-0.179559\pi\) | ||||
0.845069 | + | 0.534658i | \(0.179559\pi\) | |||||||
\(12\) | −0.302776 | −0.0874038 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.30278 | −0.348181 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −3.30278 | −0.825694 | ||||||||
\(17\) | 0.394449 | 0.0956679 | 0.0478339 | − | 0.998855i | \(-0.484768\pi\) | ||||
0.0478339 | + | 0.998855i | \(0.484768\pi\) | |||||||
\(18\) | 2.60555 | 0.614134 | ||||||||
\(19\) | −1.60555 | −0.368339 | −0.184169 | − | 0.982895i | \(-0.558959\pi\) | ||||
−0.184169 | + | 0.982895i | \(0.558959\pi\) | |||||||
\(20\) | −0.302776 | −0.0677027 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −7.30278 | −1.55696 | ||||||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | −0.302776 | −0.0572192 | ||||||||
\(29\) | 8.21110 | 1.52476 | 0.762382 | − | 0.647128i | \(-0.224030\pi\) | ||||
0.762382 | + | 0.647128i | \(0.224030\pi\) | |||||||
\(30\) | −1.30278 | −0.237853 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −1.69722 | −0.300030 | ||||||||
\(33\) | 5.60555 | 0.975801 | ||||||||
\(34\) | −0.513878 | −0.0881294 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.605551 | 0.100925 | ||||||||
\(37\) | 3.60555 | 0.592749 | 0.296374 | − | 0.955072i | \(-0.404222\pi\) | ||||
0.296374 | + | 0.955072i | \(0.404222\pi\) | |||||||
\(38\) | 2.09167 | 0.339314 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | −1.30278 | −0.201023 | ||||||||
\(43\) | 4.21110 | 0.642187 | 0.321094 | − | 0.947047i | \(-0.395950\pi\) | ||||
0.321094 | + | 0.947047i | \(0.395950\pi\) | |||||||
\(44\) | −1.69722 | −0.255866 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 3.90833 | 0.576251 | ||||||||
\(47\) | 5.21110 | 0.760117 | 0.380059 | − | 0.924962i | \(-0.375904\pi\) | ||||
0.380059 | + | 0.924962i | \(0.375904\pi\) | |||||||
\(48\) | −3.30278 | −0.476715 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −1.30278 | −0.184240 | ||||||||
\(51\) | 0.394449 | 0.0552339 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2111 | 1.53996 | 0.769982 | − | 0.638066i | \(-0.220265\pi\) | ||||
0.769982 | + | 0.638066i | \(0.220265\pi\) | |||||||
\(54\) | 6.51388 | 0.886427 | ||||||||
\(55\) | 5.60555 | 0.755852 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | −1.60555 | −0.212660 | ||||||||
\(58\) | −10.6972 | −1.40461 | ||||||||
\(59\) | −10.8167 | −1.40821 | −0.704104 | − | 0.710097i | \(-0.748651\pi\) | ||||
−0.704104 | + | 0.710097i | \(0.748651\pi\) | |||||||
\(60\) | −0.302776 | −0.0390882 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | −5.21110 | −0.661811 | ||||||||
\(63\) | −2.00000 | −0.251976 | ||||||||
\(64\) | 8.81665 | 1.10208 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.30278 | −0.898910 | ||||||||
\(67\) | 7.00000 | 0.855186 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(68\) | −0.119429 | −0.0144829 | ||||||||
\(69\) | −3.00000 | −0.361158 | ||||||||
\(70\) | −1.30278 | −0.155711 | ||||||||
\(71\) | 16.8167 | 1.99577 | 0.997885 | − | 0.0650069i | \(-0.0207069\pi\) | ||||
0.997885 | + | 0.0650069i | \(0.0207069\pi\) | |||||||
\(72\) | −6.00000 | −0.707107 | ||||||||
\(73\) | 15.2111 | 1.78032 | 0.890162 | − | 0.455643i | \(-0.150591\pi\) | ||||
0.890162 | + | 0.455643i | \(0.150591\pi\) | |||||||
\(74\) | −4.69722 | −0.546041 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.486122 | 0.0557620 | ||||||||
\(77\) | 5.60555 | 0.638812 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.21110 | −1.03633 | −0.518165 | − | 0.855281i | \(-0.673385\pi\) | ||||
−0.518165 | + | 0.855281i | \(0.673385\pi\) | |||||||
\(80\) | −3.30278 | −0.369262 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.90833 | 0.431603 | ||||||||
\(83\) | −5.21110 | −0.571993 | −0.285996 | − | 0.958231i | \(-0.592325\pi\) | ||||
−0.285996 | + | 0.958231i | \(0.592325\pi\) | |||||||
\(84\) | −0.302776 | −0.0330355 | ||||||||
\(85\) | 0.394449 | 0.0427840 | ||||||||
\(86\) | −5.48612 | −0.591584 | ||||||||
\(87\) | 8.21110 | 0.880323 | ||||||||
\(88\) | 16.8167 | 1.79266 | ||||||||
\(89\) | −8.21110 | −0.870375 | −0.435188 | − | 0.900340i | \(-0.643318\pi\) | ||||
−0.435188 | + | 0.900340i | \(0.643318\pi\) | |||||||
\(90\) | 2.60555 | 0.274649 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.908327 | 0.0946996 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | −6.78890 | −0.700221 | ||||||||
\(95\) | −1.60555 | −0.164726 | ||||||||
\(96\) | −1.69722 | −0.173222 | ||||||||
\(97\) | 15.6056 | 1.58450 | 0.792252 | − | 0.610194i | \(-0.208909\pi\) | ||||
0.792252 | + | 0.610194i | \(0.208909\pi\) | |||||||
\(98\) | 7.81665 | 0.789601 | ||||||||
\(99\) | −11.2111 | −1.12676 | ||||||||
\(100\) | −0.302776 | −0.0302776 | ||||||||
\(101\) | −9.00000 | −0.895533 | −0.447767 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | −0.513878 | −0.0508815 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | −14.6056 | −1.41862 | ||||||||
\(107\) | −8.21110 | −0.793797 | −0.396899 | − | 0.917862i | \(-0.629914\pi\) | ||||
−0.396899 | + | 0.917862i | \(0.629914\pi\) | |||||||
\(108\) | 1.51388 | 0.145673 | ||||||||
\(109\) | 4.78890 | 0.458693 | 0.229347 | − | 0.973345i | \(-0.426341\pi\) | ||||
0.229347 | + | 0.973345i | \(0.426341\pi\) | |||||||
\(110\) | −7.30278 | −0.696292 | ||||||||
\(111\) | 3.60555 | 0.342224 | ||||||||
\(112\) | −3.30278 | −0.312083 | ||||||||
\(113\) | 5.60555 | 0.527326 | 0.263663 | − | 0.964615i | \(-0.415069\pi\) | ||||
0.263663 | + | 0.964615i | \(0.415069\pi\) | |||||||
\(114\) | 2.09167 | 0.195903 | ||||||||
\(115\) | −3.00000 | −0.279751 | ||||||||
\(116\) | −2.48612 | −0.230831 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.0917 | 1.29724 | ||||||||
\(119\) | 0.394449 | 0.0361591 | ||||||||
\(120\) | 3.00000 | 0.273861 | ||||||||
\(121\) | 20.4222 | 1.85656 | ||||||||
\(122\) | 1.30278 | 0.117948 | ||||||||
\(123\) | −3.00000 | −0.270501 | ||||||||
\(124\) | −1.21110 | −0.108760 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.60555 | 0.232121 | ||||||||
\(127\) | 10.2111 | 0.906089 | 0.453044 | − | 0.891488i | \(-0.350338\pi\) | ||||
0.453044 | + | 0.891488i | \(0.350338\pi\) | |||||||
\(128\) | −8.09167 | −0.715210 | ||||||||
\(129\) | 4.21110 | 0.370767 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.78890 | −0.593149 | −0.296574 | − | 0.955010i | \(-0.595844\pi\) | ||||
−0.296574 | + | 0.955010i | \(0.595844\pi\) | |||||||
\(132\) | −1.69722 | −0.147724 | ||||||||
\(133\) | −1.60555 | −0.139219 | ||||||||
\(134\) | −9.11943 | −0.787799 | ||||||||
\(135\) | −5.00000 | −0.430331 | ||||||||
\(136\) | 1.18335 | 0.101471 | ||||||||
\(137\) | −5.60555 | −0.478915 | −0.239457 | − | 0.970907i | \(-0.576970\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576970\pi\) | |||||||
\(138\) | 3.90833 | 0.332699 | ||||||||
\(139\) | 13.6056 | 1.15401 | 0.577004 | − | 0.816741i | \(-0.304222\pi\) | ||||
0.577004 | + | 0.816741i | \(0.304222\pi\) | |||||||
\(140\) | −0.302776 | −0.0255892 | ||||||||
\(141\) | 5.21110 | 0.438854 | ||||||||
\(142\) | −21.9083 | −1.83851 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.60555 | 0.550463 | ||||||||
\(145\) | 8.21110 | 0.681895 | ||||||||
\(146\) | −19.8167 | −1.64004 | ||||||||
\(147\) | −6.00000 | −0.494872 | ||||||||
\(148\) | −1.09167 | −0.0897350 | ||||||||
\(149\) | −3.00000 | −0.245770 | −0.122885 | − | 0.992421i | \(-0.539215\pi\) | ||||
−0.122885 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(150\) | −1.30278 | −0.106371 | ||||||||
\(151\) | −13.2111 | −1.07510 | −0.537552 | − | 0.843231i | \(-0.680651\pi\) | ||||
−0.537552 | + | 0.843231i | \(0.680651\pi\) | |||||||
\(152\) | −4.81665 | −0.390682 | ||||||||
\(153\) | −0.788897 | −0.0637786 | ||||||||
\(154\) | −7.30278 | −0.588474 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.21110 | −0.256274 | −0.128137 | − | 0.991756i | \(-0.540900\pi\) | ||||
−0.128137 | + | 0.991756i | \(0.540900\pi\) | |||||||
\(158\) | 12.0000 | 0.954669 | ||||||||
\(159\) | 11.2111 | 0.889098 | ||||||||
\(160\) | −1.69722 | −0.134177 | ||||||||
\(161\) | −3.00000 | −0.236433 | ||||||||
\(162\) | −1.30278 | −0.102356 | ||||||||
\(163\) | 18.2111 | 1.42640 | 0.713202 | − | 0.700959i | \(-0.247244\pi\) | ||||
0.713202 | + | 0.700959i | \(0.247244\pi\) | |||||||
\(164\) | 0.908327 | 0.0709284 | ||||||||
\(165\) | 5.60555 | 0.436392 | ||||||||
\(166\) | 6.78890 | 0.526921 | ||||||||
\(167\) | −9.00000 | −0.696441 | −0.348220 | − | 0.937413i | \(-0.613214\pi\) | ||||
−0.348220 | + | 0.937413i | \(0.613214\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.513878 | −0.0394127 | ||||||||
\(171\) | 3.21110 | 0.245559 | ||||||||
\(172\) | −1.27502 | −0.0972193 | ||||||||
\(173\) | −16.8167 | −1.27855 | −0.639273 | − | 0.768980i | \(-0.720765\pi\) | ||||
−0.639273 | + | 0.768980i | \(0.720765\pi\) | |||||||
\(174\) | −10.6972 | −0.810954 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −18.5139 | −1.39554 | ||||||||
\(177\) | −10.8167 | −0.813029 | ||||||||
\(178\) | 10.6972 | 0.801791 | ||||||||
\(179\) | 1.18335 | 0.0884474 | 0.0442237 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442237 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(180\) | 0.605551 | 0.0451351 | ||||||||
\(181\) | −25.6333 | −1.90531 | −0.952654 | − | 0.304055i | \(-0.901659\pi\) | ||||
−0.952654 | + | 0.304055i | \(0.901659\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −9.00000 | −0.663489 | ||||||||
\(185\) | 3.60555 | 0.265085 | ||||||||
\(186\) | −5.21110 | −0.382097 | ||||||||
\(187\) | 2.21110 | 0.161692 | ||||||||
\(188\) | −1.57779 | −0.115073 | ||||||||
\(189\) | −5.00000 | −0.363696 | ||||||||
\(190\) | 2.09167 | 0.151746 | ||||||||
\(191\) | −4.81665 | −0.348521 | −0.174260 | − | 0.984700i | \(-0.555753\pi\) | ||||
−0.174260 | + | 0.984700i | \(0.555753\pi\) | |||||||
\(192\) | 8.81665 | 0.636287 | ||||||||
\(193\) | −8.39445 | −0.604246 | −0.302123 | − | 0.953269i | \(-0.597695\pi\) | ||||
−0.302123 | + | 0.953269i | \(0.597695\pi\) | |||||||
\(194\) | −20.3305 | −1.45965 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.81665 | 0.129761 | ||||||||
\(197\) | −22.8167 | −1.62562 | −0.812810 | − | 0.582529i | \(-0.802063\pi\) | ||||
−0.812810 | + | 0.582529i | \(0.802063\pi\) | |||||||
\(198\) | 14.6056 | 1.03797 | ||||||||
\(199\) | −8.81665 | −0.624996 | −0.312498 | − | 0.949918i | \(-0.601166\pi\) | ||||
−0.312498 | + | 0.949918i | \(0.601166\pi\) | |||||||
\(200\) | 3.00000 | 0.212132 | ||||||||
\(201\) | 7.00000 | 0.493742 | ||||||||
\(202\) | 11.7250 | 0.824967 | ||||||||
\(203\) | 8.21110 | 0.576306 | ||||||||
\(204\) | −0.119429 | −0.00836174 | ||||||||
\(205\) | −3.00000 | −0.209529 | ||||||||
\(206\) | 5.21110 | 0.363075 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | −1.30278 | −0.0899001 | ||||||||
\(211\) | −16.3944 | −1.12864 | −0.564320 | − | 0.825556i | \(-0.690862\pi\) | ||||
−0.564320 | + | 0.825556i | \(0.690862\pi\) | |||||||
\(212\) | −3.39445 | −0.233132 | ||||||||
\(213\) | 16.8167 | 1.15226 | ||||||||
\(214\) | 10.6972 | 0.731247 | ||||||||
\(215\) | 4.21110 | 0.287195 | ||||||||
\(216\) | −15.0000 | −1.02062 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | −6.23886 | −0.422549 | ||||||||
\(219\) | 15.2111 | 1.02787 | ||||||||
\(220\) | −1.69722 | −0.114427 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.69722 | −0.315257 | ||||||||
\(223\) | −10.2111 | −0.683786 | −0.341893 | − | 0.939739i | \(-0.611068\pi\) | ||||
−0.341893 | + | 0.939739i | \(0.611068\pi\) | |||||||
\(224\) | −1.69722 | −0.113401 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | −7.30278 | −0.485773 | ||||||||
\(227\) | −1.42221 | −0.0943951 | −0.0471975 | − | 0.998886i | \(-0.515029\pi\) | ||||
−0.0471975 | + | 0.998886i | \(0.515029\pi\) | |||||||
\(228\) | 0.486122 | 0.0321942 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 3.90833 | 0.257707 | ||||||||
\(231\) | 5.60555 | 0.368818 | ||||||||
\(232\) | 24.6333 | 1.61726 | ||||||||
\(233\) | 0.788897 | 0.0516824 | 0.0258412 | − | 0.999666i | \(-0.491774\pi\) | ||||
0.0258412 | + | 0.999666i | \(0.491774\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.21110 | 0.339935 | ||||||||
\(236\) | 3.27502 | 0.213186 | ||||||||
\(237\) | −9.21110 | −0.598325 | ||||||||
\(238\) | −0.513878 | −0.0333098 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −3.30278 | −0.213193 | ||||||||
\(241\) | −16.2111 | −1.04425 | −0.522124 | − | 0.852869i | \(-0.674860\pi\) | ||||
−0.522124 | + | 0.852869i | \(0.674860\pi\) | |||||||
\(242\) | −26.6056 | −1.71027 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0.302776 | 0.0193832 | ||||||||
\(245\) | −6.00000 | −0.383326 | ||||||||
\(246\) | 3.90833 | 0.249186 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 12.0000 | 0.762001 | ||||||||
\(249\) | −5.21110 | −0.330240 | ||||||||
\(250\) | −1.30278 | −0.0823948 | ||||||||
\(251\) | −28.8167 | −1.81889 | −0.909446 | − | 0.415823i | \(-0.863494\pi\) | ||||
−0.909446 | + | 0.415823i | \(0.863494\pi\) | |||||||
\(252\) | 0.605551 | 0.0381461 | ||||||||
\(253\) | −16.8167 | −1.05725 | ||||||||
\(254\) | −13.3028 | −0.834690 | ||||||||
\(255\) | 0.394449 | 0.0247013 | ||||||||
\(256\) | −7.09167 | −0.443230 | ||||||||
\(257\) | −23.6056 | −1.47247 | −0.736237 | − | 0.676724i | \(-0.763399\pi\) | ||||
−0.736237 | + | 0.676724i | \(0.763399\pi\) | |||||||
\(258\) | −5.48612 | −0.341551 | ||||||||
\(259\) | 3.60555 | 0.224038 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.4222 | −1.01651 | ||||||||
\(262\) | 8.84441 | 0.546409 | ||||||||
\(263\) | 26.2111 | 1.61625 | 0.808123 | − | 0.589014i | \(-0.200484\pi\) | ||||
0.808123 | + | 0.589014i | \(0.200484\pi\) | |||||||
\(264\) | 16.8167 | 1.03499 | ||||||||
\(265\) | 11.2111 | 0.688693 | ||||||||
\(266\) | 2.09167 | 0.128249 | ||||||||
\(267\) | −8.21110 | −0.502511 | ||||||||
\(268\) | −2.11943 | −0.129465 | ||||||||
\(269\) | −9.00000 | −0.548740 | −0.274370 | − | 0.961624i | \(-0.588469\pi\) | ||||
−0.274370 | + | 0.961624i | \(0.588469\pi\) | |||||||
\(270\) | 6.51388 | 0.396422 | ||||||||
\(271\) | −0.816654 | −0.0496082 | −0.0248041 | − | 0.999692i | \(-0.507896\pi\) | ||||
−0.0248041 | + | 0.999692i | \(0.507896\pi\) | |||||||
\(272\) | −1.30278 | −0.0789924 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.30278 | 0.441177 | ||||||||
\(275\) | 5.60555 | 0.338027 | ||||||||
\(276\) | 0.908327 | 0.0546749 | ||||||||
\(277\) | 20.3944 | 1.22538 | 0.612692 | − | 0.790322i | \(-0.290087\pi\) | ||||
0.612692 | + | 0.790322i | \(0.290087\pi\) | |||||||
\(278\) | −17.7250 | −1.06307 | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | −6.78890 | −0.404273 | ||||||||
\(283\) | 5.00000 | 0.297219 | 0.148610 | − | 0.988896i | \(-0.452520\pi\) | ||||
0.148610 | + | 0.988896i | \(0.452520\pi\) | |||||||
\(284\) | −5.09167 | −0.302135 | ||||||||
\(285\) | −1.60555 | −0.0951046 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.00000 | −0.177084 | ||||||||
\(288\) | 3.39445 | 0.200020 | ||||||||
\(289\) | −16.8444 | −0.990848 | ||||||||
\(290\) | −10.6972 | −0.628163 | ||||||||
\(291\) | 15.6056 | 0.914814 | ||||||||
\(292\) | −4.60555 | −0.269520 | ||||||||
\(293\) | −17.6056 | −1.02853 | −0.514264 | − | 0.857632i | \(-0.671935\pi\) | ||||
−0.514264 | + | 0.857632i | \(0.671935\pi\) | |||||||
\(294\) | 7.81665 | 0.455877 | ||||||||
\(295\) | −10.8167 | −0.629770 | ||||||||
\(296\) | 10.8167 | 0.628705 | ||||||||
\(297\) | −28.0278 | −1.62634 | ||||||||
\(298\) | 3.90833 | 0.226403 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.302776 | −0.0174808 | ||||||||
\(301\) | 4.21110 | 0.242724 | ||||||||
\(302\) | 17.2111 | 0.990388 | ||||||||
\(303\) | −9.00000 | −0.517036 | ||||||||
\(304\) | 5.30278 | 0.304135 | ||||||||
\(305\) | −1.00000 | −0.0572598 | ||||||||
\(306\) | 1.02776 | 0.0587529 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | −1.69722 | −0.0967083 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | −5.21110 | −0.295971 | ||||||||
\(311\) | 5.21110 | 0.295495 | 0.147747 | − | 0.989025i | \(-0.452798\pi\) | ||||
0.147747 | + | 0.989025i | \(0.452798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 4.18335 | 0.236080 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 2.78890 | 0.156888 | ||||||||
\(317\) | −6.00000 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(318\) | −14.6056 | −0.819039 | ||||||||
\(319\) | 46.0278 | 2.57706 | ||||||||
\(320\) | 8.81665 | 0.492866 | ||||||||
\(321\) | −8.21110 | −0.458299 | ||||||||
\(322\) | 3.90833 | 0.217803 | ||||||||
\(323\) | −0.633308 | −0.0352382 | ||||||||
\(324\) | −0.302776 | −0.0168209 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.7250 | −1.31401 | ||||||||
\(327\) | 4.78890 | 0.264827 | ||||||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 5.21110 | 0.287297 | ||||||||
\(330\) | −7.30278 | −0.402005 | ||||||||
\(331\) | 26.0278 | 1.43061 | 0.715307 | − | 0.698810i | \(-0.246287\pi\) | ||||
0.715307 | + | 0.698810i | \(0.246287\pi\) | |||||||
\(332\) | 1.57779 | 0.0865927 | ||||||||
\(333\) | −7.21110 | −0.395166 | ||||||||
\(334\) | 11.7250 | 0.641562 | ||||||||
\(335\) | 7.00000 | 0.382451 | ||||||||
\(336\) | −3.30278 | −0.180181 | ||||||||
\(337\) | 17.6333 | 0.960547 | 0.480274 | − | 0.877119i | \(-0.340537\pi\) | ||||
0.480274 | + | 0.877119i | \(0.340537\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.60555 | 0.304452 | ||||||||
\(340\) | −0.119429 | −0.00647697 | ||||||||
\(341\) | 22.4222 | 1.21423 | ||||||||
\(342\) | −4.18335 | −0.226209 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 12.6333 | 0.681142 | ||||||||
\(345\) | −3.00000 | −0.161515 | ||||||||
\(346\) | 21.9083 | 1.17780 | ||||||||
\(347\) | 20.2111 | 1.08499 | 0.542494 | − | 0.840059i | \(-0.317480\pi\) | ||||
0.542494 | + | 0.840059i | \(0.317480\pi\) | |||||||
\(348\) | −2.48612 | −0.133270 | ||||||||
\(349\) | 18.2111 | 0.974818 | 0.487409 | − | 0.873174i | \(-0.337942\pi\) | ||||
0.487409 | + | 0.873174i | \(0.337942\pi\) | |||||||
\(350\) | −1.30278 | −0.0696363 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.51388 | −0.507091 | ||||||||
\(353\) | 4.81665 | 0.256365 | 0.128182 | − | 0.991751i | \(-0.459086\pi\) | ||||
0.128182 | + | 0.991751i | \(0.459086\pi\) | |||||||
\(354\) | 14.0917 | 0.748964 | ||||||||
\(355\) | 16.8167 | 0.892535 | ||||||||
\(356\) | 2.48612 | 0.131764 | ||||||||
\(357\) | 0.394449 | 0.0208764 | ||||||||
\(358\) | −1.54163 | −0.0814779 | ||||||||
\(359\) | 10.4222 | 0.550063 | 0.275031 | − | 0.961435i | \(-0.411312\pi\) | ||||
0.275031 | + | 0.961435i | \(0.411312\pi\) | |||||||
\(360\) | −6.00000 | −0.316228 | ||||||||
\(361\) | −16.4222 | −0.864327 | ||||||||
\(362\) | 33.3944 | 1.75517 | ||||||||
\(363\) | 20.4222 | 1.07189 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.2111 | 0.796185 | ||||||||
\(366\) | 1.30278 | 0.0680972 | ||||||||
\(367\) | −17.4222 | −0.909432 | −0.454716 | − | 0.890637i | \(-0.650259\pi\) | ||||
−0.454716 | + | 0.890637i | \(0.650259\pi\) | |||||||
\(368\) | 9.90833 | 0.516507 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | −4.69722 | −0.244197 | ||||||||
\(371\) | 11.2111 | 0.582051 | ||||||||
\(372\) | −1.21110 | −0.0627927 | ||||||||
\(373\) | −27.6056 | −1.42936 | −0.714681 | − | 0.699451i | \(-0.753428\pi\) | ||||
−0.714681 | + | 0.699451i | \(0.753428\pi\) | |||||||
\(374\) | −2.88057 | −0.148951 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 15.6333 | 0.806226 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.51388 | 0.335038 | ||||||||
\(379\) | −2.39445 | −0.122995 | −0.0614973 | − | 0.998107i | \(-0.519588\pi\) | ||||
−0.0614973 | + | 0.998107i | \(0.519588\pi\) | |||||||
\(380\) | 0.486122 | 0.0249375 | ||||||||
\(381\) | 10.2111 | 0.523131 | ||||||||
\(382\) | 6.27502 | 0.321058 | ||||||||
\(383\) | −18.6333 | −0.952118 | −0.476059 | − | 0.879413i | \(-0.657935\pi\) | ||||
−0.476059 | + | 0.879413i | \(0.657935\pi\) | |||||||
\(384\) | −8.09167 | −0.412926 | ||||||||
\(385\) | 5.60555 | 0.285685 | ||||||||
\(386\) | 10.9361 | 0.556632 | ||||||||
\(387\) | −8.42221 | −0.428125 | ||||||||
\(388\) | −4.72498 | −0.239875 | ||||||||
\(389\) | −0.788897 | −0.0399987 | −0.0199993 | − | 0.999800i | \(-0.506366\pi\) | ||||
−0.0199993 | + | 0.999800i | \(0.506366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.18335 | −0.0598444 | ||||||||
\(392\) | −18.0000 | −0.909137 | ||||||||
\(393\) | −6.78890 | −0.342455 | ||||||||
\(394\) | 29.7250 | 1.49752 | ||||||||
\(395\) | −9.21110 | −0.463461 | ||||||||
\(396\) | 3.39445 | 0.170577 | ||||||||
\(397\) | 14.0278 | 0.704033 | 0.352016 | − | 0.935994i | \(-0.385496\pi\) | ||||
0.352016 | + | 0.935994i | \(0.385496\pi\) | |||||||
\(398\) | 11.4861 | 0.575747 | ||||||||
\(399\) | −1.60555 | −0.0803781 | ||||||||
\(400\) | −3.30278 | −0.165139 | ||||||||
\(401\) | 2.21110 | 0.110417 | 0.0552086 | − | 0.998475i | \(-0.482418\pi\) | ||||
0.0552086 | + | 0.998475i | \(0.482418\pi\) | |||||||
\(402\) | −9.11943 | −0.454836 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.72498 | 0.135573 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −10.6972 | −0.530894 | ||||||||
\(407\) | 20.2111 | 1.00183 | ||||||||
\(408\) | 1.18335 | 0.0585844 | ||||||||
\(409\) | 6.21110 | 0.307119 | 0.153560 | − | 0.988139i | \(-0.450926\pi\) | ||||
0.153560 | + | 0.988139i | \(0.450926\pi\) | |||||||
\(410\) | 3.90833 | 0.193019 | ||||||||
\(411\) | −5.60555 | −0.276501 | ||||||||
\(412\) | 1.21110 | 0.0596667 | ||||||||
\(413\) | −10.8167 | −0.532253 | ||||||||
\(414\) | −7.81665 | −0.384168 | ||||||||
\(415\) | −5.21110 | −0.255803 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6056 | 0.666267 | ||||||||
\(418\) | 11.7250 | 0.573488 | ||||||||
\(419\) | −33.2389 | −1.62382 | −0.811912 | − | 0.583779i | \(-0.801573\pi\) | ||||
−0.811912 | + | 0.583779i | \(0.801573\pi\) | |||||||
\(420\) | −0.302776 | −0.0147739 | ||||||||
\(421\) | −3.57779 | −0.174371 | −0.0871855 | − | 0.996192i | \(-0.527787\pi\) | ||||
−0.0871855 | + | 0.996192i | \(0.527787\pi\) | |||||||
\(422\) | 21.3583 | 1.03971 | ||||||||
\(423\) | −10.4222 | −0.506745 | ||||||||
\(424\) | 33.6333 | 1.63338 | ||||||||
\(425\) | 0.394449 | 0.0191336 | ||||||||
\(426\) | −21.9083 | −1.06146 | ||||||||
\(427\) | −1.00000 | −0.0483934 | ||||||||
\(428\) | 2.48612 | 0.120171 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.48612 | −0.264564 | ||||||||
\(431\) | 21.2389 | 1.02304 | 0.511520 | − | 0.859271i | \(-0.329083\pi\) | ||||
0.511520 | + | 0.859271i | \(0.329083\pi\) | |||||||
\(432\) | 16.5139 | 0.794524 | ||||||||
\(433\) | −3.60555 | −0.173272 | −0.0866359 | − | 0.996240i | \(-0.527612\pi\) | ||||
−0.0866359 | + | 0.996240i | \(0.527612\pi\) | |||||||
\(434\) | −5.21110 | −0.250141 | ||||||||
\(435\) | 8.21110 | 0.393692 | ||||||||
\(436\) | −1.44996 | −0.0694406 | ||||||||
\(437\) | 4.81665 | 0.230412 | ||||||||
\(438\) | −19.8167 | −0.946876 | ||||||||
\(439\) | 23.2389 | 1.10913 | 0.554565 | − | 0.832140i | \(-0.312885\pi\) | ||||
0.554565 | + | 0.832140i | \(0.312885\pi\) | |||||||
\(440\) | 16.8167 | 0.801703 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.4222 | −1.06531 | −0.532656 | − | 0.846332i | \(-0.678806\pi\) | ||||
−0.532656 | + | 0.846332i | \(0.678806\pi\) | |||||||
\(444\) | −1.09167 | −0.0518085 | ||||||||
\(445\) | −8.21110 | −0.389244 | ||||||||
\(446\) | 13.3028 | 0.629905 | ||||||||
\(447\) | −3.00000 | −0.141895 | ||||||||
\(448\) | 8.81665 | 0.416548 | ||||||||
\(449\) | 12.6333 | 0.596203 | 0.298101 | − | 0.954534i | \(-0.403647\pi\) | ||||
0.298101 | + | 0.954534i | \(0.403647\pi\) | |||||||
\(450\) | 2.60555 | 0.122827 | ||||||||
\(451\) | −16.8167 | −0.791865 | ||||||||
\(452\) | −1.69722 | −0.0798307 | ||||||||
\(453\) | −13.2111 | −0.620712 | ||||||||
\(454\) | 1.85281 | 0.0869569 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.81665 | −0.225560 | ||||||||
\(457\) | 5.18335 | 0.242467 | 0.121233 | − | 0.992624i | \(-0.461315\pi\) | ||||
0.121233 | + | 0.992624i | \(0.461315\pi\) | |||||||
\(458\) | 18.2389 | 0.852246 | ||||||||
\(459\) | −1.97224 | −0.0920564 | ||||||||
\(460\) | 0.908327 | 0.0423510 | ||||||||
\(461\) | −21.7889 | −1.01481 | −0.507405 | − | 0.861708i | \(-0.669395\pi\) | ||||
−0.507405 | + | 0.861708i | \(0.669395\pi\) | |||||||
\(462\) | −7.30278 | −0.339756 | ||||||||
\(463\) | 5.57779 | 0.259222 | 0.129611 | − | 0.991565i | \(-0.458627\pi\) | ||||
0.129611 | + | 0.991565i | \(0.458627\pi\) | |||||||
\(464\) | −27.1194 | −1.25899 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | −1.02776 | −0.0476099 | ||||||||
\(467\) | 17.2111 | 0.796435 | 0.398217 | − | 0.917291i | \(-0.369629\pi\) | ||||
0.398217 | + | 0.917291i | \(0.369629\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.00000 | 0.323230 | ||||||||
\(470\) | −6.78890 | −0.313148 | ||||||||
\(471\) | −3.21110 | −0.147960 | ||||||||
\(472\) | −32.4500 | −1.49363 | ||||||||
\(473\) | 23.6056 | 1.08538 | ||||||||
\(474\) | 12.0000 | 0.551178 | ||||||||
\(475\) | −1.60555 | −0.0736677 | ||||||||
\(476\) | −0.119429 | −0.00547404 | ||||||||
\(477\) | −22.4222 | −1.02664 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.18335 | 0.328215 | 0.164108 | − | 0.986442i | \(-0.447526\pi\) | ||||
0.164108 | + | 0.986442i | \(0.447526\pi\) | |||||||
\(480\) | −1.69722 | −0.0774673 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 21.1194 | 0.961964 | ||||||||
\(483\) | −3.00000 | −0.136505 | ||||||||
\(484\) | −6.18335 | −0.281061 | ||||||||
\(485\) | 15.6056 | 0.708612 | ||||||||
\(486\) | −20.8444 | −0.945522 | ||||||||
\(487\) | 1.00000 | 0.0453143 | 0.0226572 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226572 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(488\) | −3.00000 | −0.135804 | ||||||||
\(489\) | 18.2111 | 0.823535 | ||||||||
\(490\) | 7.81665 | 0.353120 | ||||||||
\(491\) | 4.81665 | 0.217373 | 0.108686 | − | 0.994076i | \(-0.465336\pi\) | ||||
0.108686 | + | 0.994076i | \(0.465336\pi\) | |||||||
\(492\) | 0.908327 | 0.0409505 | ||||||||
\(493\) | 3.23886 | 0.145871 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.2111 | −0.503902 | ||||||||
\(496\) | −13.2111 | −0.593196 | ||||||||
\(497\) | 16.8167 | 0.754330 | ||||||||
\(498\) | 6.78890 | 0.304218 | ||||||||
\(499\) | 26.4222 | 1.18282 | 0.591410 | − | 0.806371i | \(-0.298571\pi\) | ||||
0.591410 | + | 0.806371i | \(0.298571\pi\) | |||||||
\(500\) | −0.302776 | −0.0135405 | ||||||||
\(501\) | −9.00000 | −0.402090 | ||||||||
\(502\) | 37.5416 | 1.67557 | ||||||||
\(503\) | 3.00000 | 0.133763 | 0.0668817 | − | 0.997761i | \(-0.478695\pi\) | ||||
0.0668817 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(504\) | −6.00000 | −0.267261 | ||||||||
\(505\) | −9.00000 | −0.400495 | ||||||||
\(506\) | 21.9083 | 0.973944 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.09167 | −0.137171 | ||||||||
\(509\) | −3.00000 | −0.132973 | −0.0664863 | − | 0.997787i | \(-0.521179\pi\) | ||||
−0.0664863 | + | 0.997787i | \(0.521179\pi\) | |||||||
\(510\) | −0.513878 | −0.0227549 | ||||||||
\(511\) | 15.2111 | 0.672900 | ||||||||
\(512\) | 25.4222 | 1.12351 | ||||||||
\(513\) | 8.02776 | 0.354434 | ||||||||
\(514\) | 30.7527 | 1.35645 | ||||||||
\(515\) | −4.00000 | −0.176261 | ||||||||
\(516\) | −1.27502 | −0.0561296 | ||||||||
\(517\) | 29.2111 | 1.28470 | ||||||||
\(518\) | −4.69722 | −0.206384 | ||||||||
\(519\) | −16.8167 | −0.738169 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 21.3944 | 0.936410 | ||||||||
\(523\) | 27.4222 | 1.19909 | 0.599545 | − | 0.800341i | \(-0.295348\pi\) | ||||
0.599545 | + | 0.800341i | \(0.295348\pi\) | |||||||
\(524\) | 2.05551 | 0.0897955 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | −34.1472 | −1.48889 | ||||||||
\(527\) | 1.57779 | 0.0687298 | ||||||||
\(528\) | −18.5139 | −0.805713 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | −14.6056 | −0.634425 | ||||||||
\(531\) | 21.6333 | 0.938806 | ||||||||
\(532\) | 0.486122 | 0.0210761 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10.6972 | 0.462914 | ||||||||
\(535\) | −8.21110 | −0.354997 | ||||||||
\(536\) | 21.0000 | 0.907062 | ||||||||
\(537\) | 1.18335 | 0.0510652 | ||||||||
\(538\) | 11.7250 | 0.505500 | ||||||||
\(539\) | −33.6333 | −1.44869 | ||||||||
\(540\) | 1.51388 | 0.0651469 | ||||||||
\(541\) | −17.6333 | −0.758115 | −0.379058 | − | 0.925373i | \(-0.623752\pi\) | ||||
−0.379058 | + | 0.925373i | \(0.623752\pi\) | |||||||
\(542\) | 1.06392 | 0.0456991 | ||||||||
\(543\) | −25.6333 | −1.10003 | ||||||||
\(544\) | −0.669468 | −0.0287032 | ||||||||
\(545\) | 4.78890 | 0.205134 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.8444 | −1.06227 | −0.531135 | − | 0.847287i | \(-0.678234\pi\) | ||||
−0.531135 | + | 0.847287i | \(0.678234\pi\) | |||||||
\(548\) | 1.69722 | 0.0725018 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | −7.30278 | −0.311391 | ||||||||
\(551\) | −13.1833 | −0.561629 | ||||||||
\(552\) | −9.00000 | −0.383065 | ||||||||
\(553\) | −9.21110 | −0.391696 | ||||||||
\(554\) | −26.5694 | −1.12883 | ||||||||
\(555\) | 3.60555 | 0.153047 | ||||||||
\(556\) | −4.11943 | −0.174703 | ||||||||
\(557\) | −5.60555 | −0.237515 | −0.118757 | − | 0.992923i | \(-0.537891\pi\) | ||||
−0.118757 | + | 0.992923i | \(0.537891\pi\) | |||||||
\(558\) | 10.4222 | 0.441207 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.30278 | −0.139568 | ||||||||
\(561\) | 2.21110 | 0.0933528 | ||||||||
\(562\) | −7.81665 | −0.329726 | ||||||||
\(563\) | −19.4222 | −0.818548 | −0.409274 | − | 0.912411i | \(-0.634218\pi\) | ||||
−0.409274 | + | 0.912411i | \(0.634218\pi\) | |||||||
\(564\) | −1.57779 | −0.0664372 | ||||||||
\(565\) | 5.60555 | 0.235827 | ||||||||
\(566\) | −6.51388 | −0.273799 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 50.4500 | 2.11683 | ||||||||
\(569\) | 1.42221 | 0.0596219 | 0.0298110 | − | 0.999556i | \(-0.490509\pi\) | ||||
0.0298110 | + | 0.999556i | \(0.490509\pi\) | |||||||
\(570\) | 2.09167 | 0.0876105 | ||||||||
\(571\) | −36.8444 | −1.54189 | −0.770945 | − | 0.636901i | \(-0.780216\pi\) | ||||
−0.770945 | + | 0.636901i | \(0.780216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.81665 | −0.201219 | ||||||||
\(574\) | 3.90833 | 0.163130 | ||||||||
\(575\) | −3.00000 | −0.125109 | ||||||||
\(576\) | −17.6333 | −0.734721 | ||||||||
\(577\) | −29.6333 | −1.23365 | −0.616825 | − | 0.787100i | \(-0.711582\pi\) | ||||
−0.616825 | + | 0.787100i | \(0.711582\pi\) | |||||||
\(578\) | 21.9445 | 0.912770 | ||||||||
\(579\) | −8.39445 | −0.348861 | ||||||||
\(580\) | −2.48612 | −0.103231 | ||||||||
\(581\) | −5.21110 | −0.216193 | ||||||||
\(582\) | −20.3305 | −0.842728 | ||||||||
\(583\) | 62.8444 | 2.60275 | ||||||||
\(584\) | 45.6333 | 1.88832 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.9361 | 0.947481 | ||||||||
\(587\) | 4.57779 | 0.188946 | 0.0944729 | − | 0.995527i | \(-0.469883\pi\) | ||||
0.0944729 | + | 0.995527i | \(0.469883\pi\) | |||||||
\(588\) | 1.81665 | 0.0749175 | ||||||||
\(589\) | −6.42221 | −0.264622 | ||||||||
\(590\) | 14.0917 | 0.580145 | ||||||||
\(591\) | −22.8167 | −0.938552 | ||||||||
\(592\) | −11.9083 | −0.489429 | ||||||||
\(593\) | −35.2111 | −1.44595 | −0.722973 | − | 0.690876i | \(-0.757225\pi\) | ||||
−0.722973 | + | 0.690876i | \(0.757225\pi\) | |||||||
\(594\) | 36.5139 | 1.49818 | ||||||||
\(595\) | 0.394449 | 0.0161708 | ||||||||
\(596\) | 0.908327 | 0.0372065 | ||||||||
\(597\) | −8.81665 | −0.360842 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.78890 | −0.277387 | −0.138693 | − | 0.990335i | \(-0.544290\pi\) | ||||
−0.138693 | + | 0.990335i | \(0.544290\pi\) | |||||||
\(600\) | 3.00000 | 0.122474 | ||||||||
\(601\) | 28.2111 | 1.15075 | 0.575377 | − | 0.817888i | \(-0.304855\pi\) | ||||
0.575377 | + | 0.817888i | \(0.304855\pi\) | |||||||
\(602\) | −5.48612 | −0.223598 | ||||||||
\(603\) | −14.0000 | −0.570124 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | 20.4222 | 0.830281 | ||||||||
\(606\) | 11.7250 | 0.476295 | ||||||||
\(607\) | −19.7889 | −0.803207 | −0.401603 | − | 0.915814i | \(-0.631547\pi\) | ||||
−0.401603 | + | 0.915814i | \(0.631547\pi\) | |||||||
\(608\) | 2.72498 | 0.110513 | ||||||||
\(609\) | 8.21110 | 0.332731 | ||||||||
\(610\) | 1.30278 | 0.0527478 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.238859 | 0.00965530 | ||||||||
\(613\) | −1.60555 | −0.0648476 | −0.0324238 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324238 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(614\) | −20.8444 | −0.841212 | ||||||||
\(615\) | −3.00000 | −0.120972 | ||||||||
\(616\) | 16.8167 | 0.677562 | ||||||||
\(617\) | −26.4500 | −1.06484 | −0.532418 | − | 0.846482i | \(-0.678716\pi\) | ||||
−0.532418 | + | 0.846482i | \(0.678716\pi\) | |||||||
\(618\) | 5.21110 | 0.209621 | ||||||||
\(619\) | 14.4222 | 0.579677 | 0.289839 | − | 0.957076i | \(-0.406398\pi\) | ||||
0.289839 | + | 0.957076i | \(0.406398\pi\) | |||||||
\(620\) | −1.21110 | −0.0486390 | ||||||||
\(621\) | 15.0000 | 0.601929 | ||||||||
\(622\) | −6.78890 | −0.272210 | ||||||||
\(623\) | −8.21110 | −0.328971 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.2389 | −0.728971 | ||||||||
\(627\) | −9.00000 | −0.359425 | ||||||||
\(628\) | 0.972244 | 0.0387967 | ||||||||
\(629\) | 1.42221 | 0.0567070 | ||||||||
\(630\) | 2.60555 | 0.103808 | ||||||||
\(631\) | −0.0277564 | −0.00110496 | −0.000552482 | − | 1.00000i | \(-0.500176\pi\) | ||||
−0.000552482 | 1.00000i | \(0.500176\pi\) | ||||||||
\(632\) | −27.6333 | −1.09919 | ||||||||
\(633\) | −16.3944 | −0.651621 | ||||||||
\(634\) | 7.81665 | 0.310439 | ||||||||
\(635\) | 10.2111 | 0.405215 | ||||||||
\(636\) | −3.39445 | −0.134599 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −59.9638 | −2.37399 | ||||||||
\(639\) | −33.6333 | −1.33051 | ||||||||
\(640\) | −8.09167 | −0.319851 | ||||||||
\(641\) | −19.4222 | −0.767131 | −0.383565 | − | 0.923514i | \(-0.625304\pi\) | ||||
−0.383565 | + | 0.923514i | \(0.625304\pi\) | |||||||
\(642\) | 10.6972 | 0.422186 | ||||||||
\(643\) | 40.6333 | 1.60242 | 0.801211 | − | 0.598382i | \(-0.204190\pi\) | ||||
0.801211 | + | 0.598382i | \(0.204190\pi\) | |||||||
\(644\) | 0.908327 | 0.0357931 | ||||||||
\(645\) | 4.21110 | 0.165812 | ||||||||
\(646\) | 0.825058 | 0.0324615 | ||||||||
\(647\) | 10.5778 | 0.415856 | 0.207928 | − | 0.978144i | \(-0.433328\pi\) | ||||
0.207928 | + | 0.978144i | \(0.433328\pi\) | |||||||
\(648\) | 3.00000 | 0.117851 | ||||||||
\(649\) | −60.6333 | −2.38007 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | −5.51388 | −0.215940 | ||||||||
\(653\) | −28.8167 | −1.12768 | −0.563841 | − | 0.825883i | \(-0.690677\pi\) | ||||
−0.563841 | + | 0.825883i | \(0.690677\pi\) | |||||||
\(654\) | −6.23886 | −0.243959 | ||||||||
\(655\) | −6.78890 | −0.265264 | ||||||||
\(656\) | 9.90833 | 0.386855 | ||||||||
\(657\) | −30.4222 | −1.18688 | ||||||||
\(658\) | −6.78890 | −0.264659 | ||||||||
\(659\) | −13.1833 | −0.513550 | −0.256775 | − | 0.966471i | \(-0.582660\pi\) | ||||
−0.256775 | + | 0.966471i | \(0.582660\pi\) | |||||||
\(660\) | −1.69722 | −0.0660644 | ||||||||
\(661\) | −38.6333 | −1.50266 | −0.751331 | − | 0.659926i | \(-0.770588\pi\) | ||||
−0.751331 | + | 0.659926i | \(0.770588\pi\) | |||||||
\(662\) | −33.9083 | −1.31788 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.6333 | −0.606690 | ||||||||
\(665\) | −1.60555 | −0.0622606 | ||||||||
\(666\) | 9.39445 | 0.364027 | ||||||||
\(667\) | −24.6333 | −0.953805 | ||||||||
\(668\) | 2.72498 | 0.105433 | ||||||||
\(669\) | −10.2111 | −0.394784 | ||||||||
\(670\) | −9.11943 | −0.352314 | ||||||||
\(671\) | −5.60555 | −0.216400 | ||||||||
\(672\) | −1.69722 | −0.0654719 | ||||||||
\(673\) | −10.3944 | −0.400677 | −0.200338 | − | 0.979727i | \(-0.564204\pi\) | ||||
−0.200338 | + | 0.979727i | \(0.564204\pi\) | |||||||
\(674\) | −22.9722 | −0.884858 | ||||||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.6333 | 1.29263 | 0.646317 | − | 0.763069i | \(-0.276309\pi\) | ||||
0.646317 | + | 0.763069i | \(0.276309\pi\) | |||||||
\(678\) | −7.30278 | −0.280461 | ||||||||
\(679\) | 15.6056 | 0.598886 | ||||||||
\(680\) | 1.18335 | 0.0453793 | ||||||||
\(681\) | −1.42221 | −0.0544990 | ||||||||
\(682\) | −29.2111 | −1.11855 | ||||||||
\(683\) | −21.7889 | −0.833729 | −0.416864 | − | 0.908969i | \(-0.636871\pi\) | ||||
−0.416864 | + | 0.908969i | \(0.636871\pi\) | |||||||
\(684\) | −0.972244 | −0.0371747 | ||||||||
\(685\) | −5.60555 | −0.214177 | ||||||||
\(686\) | 16.9361 | 0.646623 | ||||||||
\(687\) | −14.0000 | −0.534133 | ||||||||
\(688\) | −13.9083 | −0.530250 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.90833 | 0.148787 | ||||||||
\(691\) | −6.02776 | −0.229307 | −0.114653 | − | 0.993406i | \(-0.536576\pi\) | ||||
−0.114653 | + | 0.993406i | \(0.536576\pi\) | |||||||
\(692\) | 5.09167 | 0.193556 | ||||||||
\(693\) | −11.2111 | −0.425875 | ||||||||
\(694\) | −26.3305 | −0.999493 | ||||||||
\(695\) | 13.6056 | 0.516088 | ||||||||
\(696\) | 24.6333 | 0.933723 | ||||||||
\(697\) | −1.18335 | −0.0448224 | ||||||||
\(698\) | −23.7250 | −0.898004 | ||||||||
\(699\) | 0.788897 | 0.0298388 | ||||||||
\(700\) | −0.302776 | −0.0114438 | ||||||||
\(701\) | −7.57779 | −0.286209 | −0.143105 | − | 0.989708i | \(-0.545709\pi\) | ||||
−0.143105 | + | 0.989708i | \(0.545709\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.78890 | −0.218332 | ||||||||
\(704\) | 49.4222 | 1.86267 | ||||||||
\(705\) | 5.21110 | 0.196261 | ||||||||
\(706\) | −6.27502 | −0.236163 | ||||||||
\(707\) | −9.00000 | −0.338480 | ||||||||
\(708\) | 3.27502 | 0.123083 | ||||||||
\(709\) | −43.8444 | −1.64661 | −0.823306 | − | 0.567598i | \(-0.807873\pi\) | ||||
−0.823306 | + | 0.567598i | \(0.807873\pi\) | |||||||
\(710\) | −21.9083 | −0.822205 | ||||||||
\(711\) | 18.4222 | 0.690887 | ||||||||
\(712\) | −24.6333 | −0.923172 | ||||||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | −0.513878 | −0.0192314 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.358288 | −0.0133899 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.5778 | −0.506719 | ||||||||
\(719\) | −18.3944 | −0.685997 | −0.342999 | − | 0.939336i | \(-0.611443\pi\) | ||||
−0.342999 | + | 0.939336i | \(0.611443\pi\) | |||||||
\(720\) | 6.60555 | 0.246174 | ||||||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | 21.3944 | 0.796219 | ||||||||
\(723\) | −16.2111 | −0.602897 | ||||||||
\(724\) | 7.76114 | 0.288441 | ||||||||
\(725\) | 8.21110 | 0.304953 | ||||||||
\(726\) | −26.6056 | −0.987425 | ||||||||
\(727\) | 42.4222 | 1.57335 | 0.786676 | − | 0.617366i | \(-0.211800\pi\) | ||||
0.786676 | + | 0.617366i | \(0.211800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −19.8167 | −0.733447 | ||||||||
\(731\) | 1.66106 | 0.0614367 | ||||||||
\(732\) | 0.302776 | 0.0111909 | ||||||||
\(733\) | −10.8444 | −0.400547 | −0.200274 | − | 0.979740i | \(-0.564183\pi\) | ||||
−0.200274 | + | 0.979740i | \(0.564183\pi\) | |||||||
\(734\) | 22.6972 | 0.837770 | ||||||||
\(735\) | −6.00000 | −0.221313 | ||||||||
\(736\) | 5.09167 | 0.187682 | ||||||||
\(737\) | 39.2389 | 1.44538 | ||||||||
\(738\) | −7.81665 | −0.287735 | ||||||||
\(739\) | 28.3944 | 1.04451 | 0.522253 | − | 0.852790i | \(-0.325092\pi\) | ||||
0.522253 | + | 0.852790i | \(0.325092\pi\) | |||||||
\(740\) | −1.09167 | −0.0401307 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.6056 | −0.536187 | ||||||||
\(743\) | 6.63331 | 0.243352 | 0.121676 | − | 0.992570i | \(-0.461173\pi\) | ||||
0.121676 | + | 0.992570i | \(0.461173\pi\) | |||||||
\(744\) | 12.0000 | 0.439941 | ||||||||
\(745\) | −3.00000 | −0.109911 | ||||||||
\(746\) | 35.9638 | 1.31673 | ||||||||
\(747\) | 10.4222 | 0.381329 | ||||||||
\(748\) | −0.669468 | −0.0244782 | ||||||||
\(749\) | −8.21110 | −0.300027 | ||||||||
\(750\) | −1.30278 | −0.0475706 | ||||||||
\(751\) | −18.4500 | −0.673249 | −0.336624 | − | 0.941639i | \(-0.609285\pi\) | ||||
−0.336624 | + | 0.941639i | \(0.609285\pi\) | |||||||
\(752\) | −17.2111 | −0.627624 | ||||||||
\(753\) | −28.8167 | −1.05014 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.2111 | −0.480801 | ||||||||
\(756\) | 1.51388 | 0.0550592 | ||||||||
\(757\) | −20.8167 | −0.756594 | −0.378297 | − | 0.925684i | \(-0.623490\pi\) | ||||
−0.378297 | + | 0.925684i | \(0.623490\pi\) | |||||||
\(758\) | 3.11943 | 0.113303 | ||||||||
\(759\) | −16.8167 | −0.610406 | ||||||||
\(760\) | −4.81665 | −0.174718 | ||||||||
\(761\) | 24.6333 | 0.892957 | 0.446478 | − | 0.894794i | \(-0.352678\pi\) | ||||
0.446478 | + | 0.894794i | \(0.352678\pi\) | |||||||
\(762\) | −13.3028 | −0.481909 | ||||||||
\(763\) | 4.78890 | 0.173370 | ||||||||
\(764\) | 1.45837 | 0.0527618 | ||||||||
\(765\) | −0.788897 | −0.0285226 | ||||||||
\(766\) | 24.2750 | 0.877092 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −7.09167 | −0.255899 | ||||||||
\(769\) | −11.0000 | −0.396670 | −0.198335 | − | 0.980134i | \(-0.563553\pi\) | ||||
−0.198335 | + | 0.980134i | \(0.563553\pi\) | |||||||
\(770\) | −7.30278 | −0.263174 | ||||||||
\(771\) | −23.6056 | −0.850133 | ||||||||
\(772\) | 2.54163 | 0.0914754 | ||||||||
\(773\) | −29.6056 | −1.06484 | −0.532419 | − | 0.846481i | \(-0.678717\pi\) | ||||
−0.532419 | + | 0.846481i | \(0.678717\pi\) | |||||||
\(774\) | 10.9722 | 0.394389 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 46.8167 | 1.68062 | ||||||||
\(777\) | 3.60555 | 0.129348 | ||||||||
\(778\) | 1.02776 | 0.0368469 | ||||||||
\(779\) | 4.81665 | 0.172575 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 94.2666 | 3.37312 | ||||||||
\(782\) | 1.54163 | 0.0551287 | ||||||||
\(783\) | −41.0555 | −1.46720 | ||||||||
\(784\) | 19.8167 | 0.707738 | ||||||||
\(785\) | −3.21110 | −0.114609 | ||||||||
\(786\) | 8.84441 | 0.315470 | ||||||||
\(787\) | 28.6333 | 1.02067 | 0.510334 | − | 0.859977i | \(-0.329522\pi\) | ||||
0.510334 | + | 0.859977i | \(0.329522\pi\) | |||||||
\(788\) | 6.90833 | 0.246099 | ||||||||
\(789\) | 26.2111 | 0.933140 | ||||||||
\(790\) | 12.0000 | 0.426941 | ||||||||
\(791\) | 5.60555 | 0.199310 | ||||||||
\(792\) | −33.6333 | −1.19511 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −18.2750 | −0.648556 | ||||||||
\(795\) | 11.2111 | 0.397617 | ||||||||
\(796\) | 2.66947 | 0.0946168 | ||||||||
\(797\) | 50.4500 | 1.78703 | 0.893515 | − | 0.449034i | \(-0.148232\pi\) | ||||
0.893515 | + | 0.449034i | \(0.148232\pi\) | |||||||
\(798\) | 2.09167 | 0.0740444 | ||||||||
\(799\) | 2.05551 | 0.0727188 | ||||||||
\(800\) | −1.69722 | −0.0600059 | ||||||||
\(801\) | 16.4222 | 0.580250 | ||||||||
\(802\) | −2.88057 | −0.101716 | ||||||||
\(803\) | 85.2666 | 3.00899 | ||||||||
\(804\) | −2.11943 | −0.0747465 | ||||||||
\(805\) | −3.00000 | −0.105736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.00000 | −0.316815 | ||||||||
\(808\) | −27.0000 | −0.949857 | ||||||||
\(809\) | 17.0555 | 0.599640 | 0.299820 | − | 0.953996i | \(-0.403073\pi\) | ||||
0.299820 | + | 0.953996i | \(0.403073\pi\) | |||||||
\(810\) | −1.30278 | −0.0457749 | ||||||||
\(811\) | 17.5778 | 0.617240 | 0.308620 | − | 0.951185i | \(-0.400133\pi\) | ||||
0.308620 | + | 0.951185i | \(0.400133\pi\) | |||||||
\(812\) | −2.48612 | −0.0872458 | ||||||||
\(813\) | −0.816654 | −0.0286413 | ||||||||
\(814\) | −26.3305 | −0.922885 | ||||||||
\(815\) | 18.2111 | 0.637907 | ||||||||
\(816\) | −1.30278 | −0.0456063 | ||||||||
\(817\) | −6.76114 | −0.236542 | ||||||||
\(818\) | −8.09167 | −0.282919 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.908327 | 0.0317202 | ||||||||
\(821\) | 7.42221 | 0.259037 | 0.129518 | − | 0.991577i | \(-0.458657\pi\) | ||||
0.129518 | + | 0.991577i | \(0.458657\pi\) | |||||||
\(822\) | 7.30278 | 0.254714 | ||||||||
\(823\) | 26.6333 | 0.928379 | 0.464189 | − | 0.885736i | \(-0.346346\pi\) | ||||
0.464189 | + | 0.885736i | \(0.346346\pi\) | |||||||
\(824\) | −12.0000 | −0.418040 | ||||||||
\(825\) | 5.60555 | 0.195160 | ||||||||
\(826\) | 14.0917 | 0.490312 | ||||||||
\(827\) | 13.5778 | 0.472146 | 0.236073 | − | 0.971735i | \(-0.424140\pi\) | ||||
0.236073 | + | 0.971735i | \(0.424140\pi\) | |||||||
\(828\) | −1.81665 | −0.0631331 | ||||||||
\(829\) | 0.577795 | 0.0200676 | 0.0100338 | − | 0.999950i | \(-0.496806\pi\) | ||||
0.0100338 | + | 0.999950i | \(0.496806\pi\) | |||||||
\(830\) | 6.78890 | 0.235646 | ||||||||
\(831\) | 20.3944 | 0.707476 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.36669 | −0.0820010 | ||||||||
\(834\) | −17.7250 | −0.613766 | ||||||||
\(835\) | −9.00000 | −0.311458 | ||||||||
\(836\) | 2.72498 | 0.0942454 | ||||||||
\(837\) | −20.0000 | −0.691301 | ||||||||
\(838\) | 43.3028 | 1.49587 | ||||||||
\(839\) | −16.0278 | −0.553340 | −0.276670 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276670 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(840\) | 3.00000 | 0.103510 | ||||||||
\(841\) | 38.4222 | 1.32490 | ||||||||
\(842\) | 4.66106 | 0.160631 | ||||||||
\(843\) | 6.00000 | 0.206651 | ||||||||
\(844\) | 4.96384 | 0.170862 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.5778 | 0.466814 | ||||||||
\(847\) | 20.4222 | 0.701715 | ||||||||
\(848\) | −37.0278 | −1.27154 | ||||||||
\(849\) | 5.00000 | 0.171600 | ||||||||
\(850\) | −0.513878 | −0.0176259 | ||||||||
\(851\) | −10.8167 | −0.370790 | ||||||||
\(852\) | −5.09167 | −0.174438 | ||||||||
\(853\) | −32.7889 | −1.12267 | −0.561335 | − | 0.827589i | \(-0.689712\pi\) | ||||
−0.561335 | + | 0.827589i | \(0.689712\pi\) | |||||||
\(854\) | 1.30278 | 0.0445801 | ||||||||
\(855\) | 3.21110 | 0.109817 | ||||||||
\(856\) | −24.6333 | −0.841949 | ||||||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.2111 | 0.860192 | 0.430096 | − | 0.902783i | \(-0.358480\pi\) | ||||
0.430096 | + | 0.902783i | \(0.358480\pi\) | |||||||
\(860\) | −1.27502 | −0.0434778 | ||||||||
\(861\) | −3.00000 | −0.102240 | ||||||||
\(862\) | −27.6695 | −0.942426 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | 8.48612 | 0.288704 | ||||||||
\(865\) | −16.8167 | −0.571783 | ||||||||
\(866\) | 4.69722 | 0.159618 | ||||||||
\(867\) | −16.8444 | −0.572066 | ||||||||
\(868\) | −1.21110 | −0.0411075 | ||||||||
\(869\) | −51.6333 | −1.75154 | ||||||||
\(870\) | −10.6972 | −0.362670 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.3667 | 0.486518 | ||||||||
\(873\) | −31.2111 | −1.05634 | ||||||||
\(874\) | −6.27502 | −0.212256 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −4.60555 | −0.155607 | ||||||||
\(877\) | 38.0278 | 1.28411 | 0.642053 | − | 0.766660i | \(-0.278083\pi\) | ||||
0.642053 | + | 0.766660i | \(0.278083\pi\) | |||||||
\(878\) | −30.2750 | −1.02173 | ||||||||
\(879\) | −17.6056 | −0.593821 | ||||||||
\(880\) | −18.5139 | −0.624103 | ||||||||
\(881\) | 35.8444 | 1.20763 | 0.603814 | − | 0.797125i | \(-0.293647\pi\) | ||||
0.603814 | + | 0.797125i | \(0.293647\pi\) | |||||||
\(882\) | −15.6333 | −0.526401 | ||||||||
\(883\) | −31.6333 | −1.06455 | −0.532273 | − | 0.846573i | \(-0.678662\pi\) | ||||
−0.532273 | + | 0.846573i | \(0.678662\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.8167 | −0.363598 | ||||||||
\(886\) | 29.2111 | 0.981366 | ||||||||
\(887\) | 35.0555 | 1.17705 | 0.588524 | − | 0.808479i | \(-0.299709\pi\) | ||||
0.588524 | + | 0.808479i | \(0.299709\pi\) | |||||||
\(888\) | 10.8167 | 0.362983 | ||||||||
\(889\) | 10.2111 | 0.342469 | ||||||||
\(890\) | 10.6972 | 0.358572 | ||||||||
\(891\) | 5.60555 | 0.187793 | ||||||||
\(892\) | 3.09167 | 0.103517 | ||||||||
\(893\) | −8.36669 | −0.279981 | ||||||||
\(894\) | 3.90833 | 0.130714 | ||||||||
\(895\) | 1.18335 | 0.0395549 | ||||||||
\(896\) | −8.09167 | −0.270324 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.4584 | −0.549223 | ||||||||
\(899\) | 32.8444 | 1.09542 | ||||||||
\(900\) | 0.605551 | 0.0201850 | ||||||||
\(901\) | 4.42221 | 0.147325 | ||||||||
\(902\) | 21.9083 | 0.729467 | ||||||||
\(903\) | 4.21110 | 0.140137 | ||||||||
\(904\) | 16.8167 | 0.559314 | ||||||||
\(905\) | −25.6333 | −0.852080 | ||||||||
\(906\) | 17.2111 | 0.571801 | ||||||||
\(907\) | 48.2666 | 1.60267 | 0.801333 | − | 0.598218i | \(-0.204124\pi\) | ||||
0.801333 | + | 0.598218i | \(0.204124\pi\) | |||||||
\(908\) | 0.430609 | 0.0142903 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | 5.30278 | 0.175592 | ||||||||
\(913\) | −29.2111 | −0.966746 | ||||||||
\(914\) | −6.75274 | −0.223361 | ||||||||
\(915\) | −1.00000 | −0.0330590 | ||||||||
\(916\) | 4.23886 | 0.140056 | ||||||||
\(917\) | −6.78890 | −0.224189 | ||||||||
\(918\) | 2.56939 | 0.0848025 | ||||||||
\(919\) | −17.1833 | −0.566826 | −0.283413 | − | 0.958998i | \(-0.591467\pi\) | ||||
−0.283413 | + | 0.958998i | \(0.591467\pi\) | |||||||
\(920\) | −9.00000 | −0.296721 | ||||||||
\(921\) | 16.0000 | 0.527218 | ||||||||
\(922\) | 28.3860 | 0.934845 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.69722 | −0.0558346 | ||||||||
\(925\) | 3.60555 | 0.118550 | ||||||||
\(926\) | −7.26662 | −0.238796 | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | −13.9361 | −0.457474 | ||||||||
\(929\) | −13.4222 | −0.440368 | −0.220184 | − | 0.975458i | \(-0.570666\pi\) | ||||
−0.220184 | + | 0.975458i | \(0.570666\pi\) | |||||||
\(930\) | −5.21110 | −0.170879 | ||||||||
\(931\) | 9.63331 | 0.315719 | ||||||||
\(932\) | −0.238859 | −0.00782408 | ||||||||
\(933\) | 5.21110 | 0.170604 | ||||||||
\(934\) | −22.4222 | −0.733677 | ||||||||
\(935\) | 2.21110 | 0.0723108 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.4777 | −1.51836 | −0.759180 | − | 0.650880i | \(-0.774400\pi\) | ||||
−0.759180 | + | 0.650880i | \(0.774400\pi\) | |||||||
\(938\) | −9.11943 | −0.297760 | ||||||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | −1.57779 | −0.0514620 | ||||||||
\(941\) | −33.6333 | −1.09641 | −0.548207 | − | 0.836343i | \(-0.684689\pi\) | ||||
−0.548207 | + | 0.836343i | \(0.684689\pi\) | |||||||
\(942\) | 4.18335 | 0.136301 | ||||||||
\(943\) | 9.00000 | 0.293080 | ||||||||
\(944\) | 35.7250 | 1.16275 | ||||||||
\(945\) | −5.00000 | −0.162650 | ||||||||
\(946\) | −30.7527 | −0.999858 | ||||||||
\(947\) | −24.6333 | −0.800475 | −0.400237 | − | 0.916411i | \(-0.631072\pi\) | ||||
−0.400237 | + | 0.916411i | \(0.631072\pi\) | |||||||
\(948\) | 2.78890 | 0.0905792 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.09167 | 0.0678628 | ||||||||
\(951\) | −6.00000 | −0.194563 | ||||||||
\(952\) | 1.18335 | 0.0383525 | ||||||||
\(953\) | 50.4500 | 1.63423 | 0.817117 | − | 0.576471i | \(-0.195571\pi\) | ||||
0.817117 | + | 0.576471i | \(0.195571\pi\) | |||||||
\(954\) | 29.2111 | 0.945744 | ||||||||
\(955\) | −4.81665 | −0.155863 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 46.0278 | 1.48787 | ||||||||
\(958\) | −9.35829 | −0.302353 | ||||||||
\(959\) | −5.60555 | −0.181013 | ||||||||
\(960\) | 8.81665 | 0.284556 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.4222 | 0.529198 | ||||||||
\(964\) | 4.90833 | 0.158087 | ||||||||
\(965\) | −8.39445 | −0.270227 | ||||||||
\(966\) | 3.90833 | 0.125748 | ||||||||
\(967\) | −56.4777 | −1.81620 | −0.908100 | − | 0.418752i | \(-0.862468\pi\) | ||||
−0.908100 | + | 0.418752i | \(0.862468\pi\) | |||||||
\(968\) | 61.2666 | 1.96918 | ||||||||
\(969\) | −0.633308 | −0.0203448 | ||||||||
\(970\) | −20.3305 | −0.652774 | ||||||||
\(971\) | −7.97224 | −0.255841 | −0.127921 | − | 0.991784i | \(-0.540830\pi\) | ||||
−0.127921 | + | 0.991784i | \(0.540830\pi\) | |||||||
\(972\) | −4.84441 | −0.155385 | ||||||||
\(973\) | 13.6056 | 0.436174 | ||||||||
\(974\) | −1.30278 | −0.0417436 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.30278 | 0.105719 | ||||||||
\(977\) | −7.18335 | −0.229816 | −0.114908 | − | 0.993376i | \(-0.536657\pi\) | ||||
−0.114908 | + | 0.993376i | \(0.536657\pi\) | |||||||
\(978\) | −23.7250 | −0.758641 | ||||||||
\(979\) | −46.0278 | −1.47105 | ||||||||
\(980\) | 1.81665 | 0.0580309 | ||||||||
\(981\) | −9.57779 | −0.305795 | ||||||||
\(982\) | −6.27502 | −0.200244 | ||||||||
\(983\) | 10.4222 | 0.332417 | 0.166208 | − | 0.986091i | \(-0.446848\pi\) | ||||
0.166208 | + | 0.986091i | \(0.446848\pi\) | |||||||
\(984\) | −9.00000 | −0.286910 | ||||||||
\(985\) | −22.8167 | −0.726999 | ||||||||
\(986\) | −4.21951 | −0.134376 | ||||||||
\(987\) | 5.21110 | 0.165871 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.6333 | −0.401716 | ||||||||
\(990\) | 14.6056 | 0.464195 | ||||||||
\(991\) | 3.97224 | 0.126182 | 0.0630912 | − | 0.998008i | \(-0.479904\pi\) | ||||
0.0630912 | + | 0.998008i | \(0.479904\pi\) | |||||||
\(992\) | −6.78890 | −0.215548 | ||||||||
\(993\) | 26.0278 | 0.825966 | ||||||||
\(994\) | −21.9083 | −0.694890 | ||||||||
\(995\) | −8.81665 | −0.279507 | ||||||||
\(996\) | 1.57779 | 0.0499943 | ||||||||
\(997\) | 46.4500 | 1.47109 | 0.735543 | − | 0.677479i | \(-0.236927\pi\) | ||||
0.735543 | + | 0.677479i | \(0.236927\pi\) | |||||||
\(998\) | −34.4222 | −1.08962 | ||||||||
\(999\) | −18.0278 | −0.570373 |
(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 | 845.2.a.f.1.1 | 2 | ||
3.2 | odd | 2 | 7605.2.a.bb.1.2 | 2 | |||
5.4 | even | 2 | 4225.2.a.t.1.2 | 2 | |||
13.2 | odd | 12 | 845.2.m.d.316.2 | 8 | |||
13.3 | even | 3 | 845.2.e.d.191.2 | 4 | |||
13.4 | even | 6 | 65.2.e.b.16.1 | ✓ | 4 | ||
13.5 | odd | 4 | 845.2.c.d.506.3 | 4 | |||
13.6 | odd | 12 | 845.2.m.d.361.3 | 8 | |||
13.7 | odd | 12 | 845.2.m.d.361.2 | 8 | |||
13.8 | odd | 4 | 845.2.c.d.506.2 | 4 | |||
13.9 | even | 3 | 845.2.e.d.146.2 | 4 | |||
13.10 | even | 6 | 65.2.e.b.61.1 | yes | 4 | ||
13.11 | odd | 12 | 845.2.m.d.316.3 | 8 | |||
13.12 | even | 2 | 845.2.a.c.1.2 | 2 | |||
39.17 | odd | 6 | 585.2.j.d.406.2 | 4 | |||
39.23 | odd | 6 | 585.2.j.d.451.2 | 4 | |||
39.38 | odd | 2 | 7605.2.a.bg.1.1 | 2 | |||
52.23 | odd | 6 | 1040.2.q.o.321.1 | 4 | |||
52.43 | odd | 6 | 1040.2.q.o.81.1 | 4 | |||
65.4 | even | 6 | 325.2.e.a.276.2 | 4 | |||
65.17 | odd | 12 | 325.2.o.b.224.3 | 8 | |||
65.23 | odd | 12 | 325.2.o.b.74.3 | 8 | |||
65.43 | odd | 12 | 325.2.o.b.224.2 | 8 | |||
65.49 | even | 6 | 325.2.e.a.126.2 | 4 | |||
65.62 | odd | 12 | 325.2.o.b.74.2 | 8 | |||
65.64 | even | 2 | 4225.2.a.x.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.e.b.16.1 | ✓ | 4 | 13.4 | even | 6 | ||
65.2.e.b.61.1 | yes | 4 | 13.10 | even | 6 | ||
325.2.e.a.126.2 | 4 | 65.49 | even | 6 | |||
325.2.e.a.276.2 | 4 | 65.4 | even | 6 | |||
325.2.o.b.74.2 | 8 | 65.62 | odd | 12 | |||
325.2.o.b.74.3 | 8 | 65.23 | odd | 12 | |||
325.2.o.b.224.2 | 8 | 65.43 | odd | 12 | |||
325.2.o.b.224.3 | 8 | 65.17 | odd | 12 | |||
585.2.j.d.406.2 | 4 | 39.17 | odd | 6 | |||
585.2.j.d.451.2 | 4 | 39.23 | odd | 6 | |||
845.2.a.c.1.2 | 2 | 13.12 | even | 2 | |||
845.2.a.f.1.1 | 2 | 1.1 | even | 1 | trivial | ||
845.2.c.d.506.2 | 4 | 13.8 | odd | 4 | |||
845.2.c.d.506.3 | 4 | 13.5 | odd | 4 | |||
845.2.e.d.146.2 | 4 | 13.9 | even | 3 | |||
845.2.e.d.191.2 | 4 | 13.3 | even | 3 | |||
845.2.m.d.316.2 | 8 | 13.2 | odd | 12 | |||
845.2.m.d.316.3 | 8 | 13.11 | odd | 12 | |||
845.2.m.d.361.2 | 8 | 13.7 | odd | 12 | |||
845.2.m.d.361.3 | 8 | 13.6 | odd | 12 | |||
1040.2.q.o.81.1 | 4 | 52.43 | odd | 6 | |||
1040.2.q.o.321.1 | 4 | 52.23 | odd | 6 | |||
4225.2.a.t.1.2 | 2 | 5.4 | even | 2 | |||
4225.2.a.x.1.1 | 2 | 65.64 | even | 2 | |||
7605.2.a.bb.1.2 | 2 | 3.2 | odd | 2 | |||
7605.2.a.bg.1.1 | 2 | 39.38 | odd | 2 |