Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(545,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.545");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.e (of order \(2\), degree \(1\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.10070523904.11 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 545.7 | ||
Root | \(1.68014 - 0.420861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.545 |
Dual form | 546.2.e.h.545.8 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.68014 | − | 0.420861i | 0.970030 | − | 0.242984i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 0.841723i | − | 0.376430i | −0.982128 | − | 0.188215i | \(-0.939730\pi\) | ||
0.982128 | − | 0.188215i | \(-0.0602702\pi\) | |||||||
\(6\) | 1.68014 | − | 0.420861i | 0.685915 | − | 0.171816i | ||||
\(7\) | 0.595188 | − | 2.57794i | 0.224960 | − | 0.974368i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.64575 | − | 1.41421i | 0.881917 | − | 0.471405i | ||||
\(10\) | − | 0.841723i | − | 0.266176i | ||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 1.68014 | − | 0.420861i | 0.485015 | − | 0.121492i | ||||
\(13\) | −2.27533 | + | 2.79694i | −0.631063 | + | 0.775732i | ||||
\(14\) | 0.595188 | − | 2.57794i | 0.159071 | − | 0.688982i | ||||
\(15\) | −0.354249 | − | 1.41421i | −0.0914666 | − | 0.365148i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.33981 | −1.05256 | −0.526280 | − | 0.850311i | \(-0.676414\pi\) | ||||
−0.526280 | + | 0.850311i | \(0.676414\pi\) | |||||||
\(18\) | 2.64575 | − | 1.41421i | 0.623610 | − | 0.333333i | ||||
\(19\) | −4.55066 | −1.04399 | −0.521996 | − | 0.852948i | \(-0.674813\pi\) | ||||
−0.521996 | + | 0.852948i | \(0.674813\pi\) | |||||||
\(20\) | − | 0.841723i | − | 0.188215i | ||||||
\(21\) | −0.0849536 | − | 4.58179i | −0.0185384 | − | 0.999828i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.98430i | 1.66484i | 0.554144 | + | 0.832421i | \(0.313046\pi\) | ||||
−0.554144 | + | 0.832421i | \(0.686954\pi\) | |||||||
\(24\) | 1.68014 | − | 0.420861i | 0.342957 | − | 0.0859080i | ||||
\(25\) | 4.29150 | 0.858301 | ||||||||
\(26\) | −2.27533 | + | 2.79694i | −0.446229 | + | 0.548525i | ||||
\(27\) | 3.85005 | − | 3.48957i | 0.740942 | − | 0.671569i | ||||
\(28\) | 0.595188 | − | 2.57794i | 0.112480 | − | 0.487184i | ||||
\(29\) | − | 2.32744i | − | 0.432195i | −0.976372 | − | 0.216098i | \(-0.930667\pi\) | ||
0.976372 | − | 0.216098i | \(-0.0693330\pi\) | |||||||
\(30\) | −0.354249 | − | 1.41421i | −0.0646767 | − | 0.258199i | ||||
\(31\) | 5.53019 | 0.993252 | 0.496626 | − | 0.867965i | \(-0.334572\pi\) | ||||
0.496626 | + | 0.867965i | \(0.334572\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.33981 | −0.744272 | ||||||||
\(35\) | −2.16991 | − | 0.500983i | −0.366781 | − | 0.0846816i | ||||
\(36\) | 2.64575 | − | 1.41421i | 0.440959 | − | 0.235702i | ||||
\(37\) | − | 5.15587i | − | 0.847620i | −0.905751 | − | 0.423810i | \(-0.860692\pi\) | ||
0.905751 | − | 0.423810i | \(-0.139308\pi\) | |||||||
\(38\) | −4.55066 | −0.738214 | ||||||||
\(39\) | −2.64575 | + | 5.65685i | −0.423659 | + | 0.905822i | ||||
\(40\) | − | 0.841723i | − | 0.133088i | ||||||
\(41\) | 10.8896i | 1.70067i | 0.526244 | + | 0.850334i | \(0.323600\pi\) | ||||
−0.526244 | + | 0.850334i | \(0.676400\pi\) | |||||||
\(42\) | −0.0849536 | − | 4.58179i | −0.0131086 | − | 0.706985i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.19038 | − | 2.22699i | −0.177451 | − | 0.331980i | ||||
\(46\) | 7.98430i | 1.17722i | ||||||||
\(47\) | 7.82087i | 1.14079i | 0.821370 | + | 0.570396i | \(0.193210\pi\) | ||||
−0.821370 | + | 0.570396i | \(0.806790\pi\) | |||||||
\(48\) | 1.68014 | − | 0.420861i | 0.242508 | − | 0.0607461i | ||||
\(49\) | −6.29150 | − | 3.06871i | −0.898786 | − | 0.438387i | ||||
\(50\) | 4.29150 | 0.606910 | ||||||||
\(51\) | −7.29150 | + | 1.82646i | −1.02101 | + | 0.255756i | ||||
\(52\) | −2.27533 | + | 2.79694i | −0.315531 | + | 0.387866i | ||||
\(53\) | 7.98430i | 1.09673i | 0.836240 | + | 0.548364i | \(0.184749\pi\) | ||||
−0.836240 | + | 0.548364i | \(0.815251\pi\) | |||||||
\(54\) | 3.85005 | − | 3.48957i | 0.523925 | − | 0.474871i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.595188 | − | 2.57794i | 0.0795353 | − | 0.344491i | ||||
\(57\) | −7.64575 | + | 1.91520i | −1.01270 | + | 0.253674i | ||||
\(58\) | − | 2.32744i | − | 0.305608i | ||||||
\(59\) | − | 3.91044i | − | 0.509095i | −0.967060 | − | 0.254548i | \(-0.918073\pi\) | ||
0.967060 | − | 0.254548i | \(-0.0819266\pi\) | |||||||
\(60\) | −0.354249 | − | 1.41421i | −0.0457333 | − | 0.182574i | ||||
\(61\) | − | 5.59388i | − | 0.716223i | −0.933679 | − | 0.358112i | \(-0.883421\pi\) | ||
0.933679 | − | 0.358112i | \(-0.116579\pi\) | |||||||
\(62\) | 5.53019 | 0.702335 | ||||||||
\(63\) | −2.07103 | − | 7.66230i | −0.260926 | − | 0.965359i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.35425 | + | 1.91520i | 0.292009 | + | 0.237551i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.82646i | − | 0.223138i | −0.993757 | − | 0.111569i | \(-0.964412\pi\) | ||
0.993757 | − | 0.111569i | \(-0.0355876\pi\) | |||||||
\(68\) | −4.33981 | −0.526280 | ||||||||
\(69\) | 3.36028 | + | 13.4148i | 0.404531 | + | 1.61495i | ||||
\(70\) | −2.16991 | − | 0.500983i | −0.259354 | − | 0.0598790i | ||||
\(71\) | −14.5830 | −1.73068 | −0.865342 | − | 0.501182i | \(-0.832899\pi\) | ||||
−0.865342 | + | 0.501182i | \(0.832899\pi\) | |||||||
\(72\) | 2.64575 | − | 1.41421i | 0.311805 | − | 0.166667i | ||||
\(73\) | −3.14944 | −0.368614 | −0.184307 | − | 0.982869i | \(-0.559004\pi\) | ||||
−0.184307 | + | 0.982869i | \(0.559004\pi\) | |||||||
\(74\) | − | 5.15587i | − | 0.599358i | ||||||
\(75\) | 7.21033 | − | 1.80613i | 0.832577 | − | 0.208554i | ||||
\(76\) | −4.55066 | −0.521996 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.64575 | + | 5.65685i | −0.299572 | + | 0.640513i | ||||
\(79\) | −11.2915 | −1.27039 | −0.635197 | − | 0.772350i | \(-0.719081\pi\) | ||||
−0.635197 | + | 0.772350i | \(0.719081\pi\) | |||||||
\(80\) | − | 0.841723i | − | 0.0941075i | ||||||
\(81\) | 5.00000 | − | 7.48331i | 0.555556 | − | 0.831479i | ||||
\(82\) | 10.8896i | 1.20255i | ||||||||
\(83\) | 7.27733i | 0.798790i | 0.916779 | + | 0.399395i | \(0.130780\pi\) | ||||
−0.916779 | + | 0.399395i | \(0.869220\pi\) | |||||||
\(84\) | −0.0849536 | − | 4.58179i | −0.00926920 | − | 0.499914i | ||||
\(85\) | 3.65292i | 0.396215i | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | −0.979531 | − | 3.91044i | −0.105017 | − | 0.419243i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 12.5730i | − | 1.33274i | −0.745622 | − | 0.666369i | \(-0.767848\pi\) | ||
0.745622 | − | 0.666369i | \(-0.232152\pi\) | |||||||
\(90\) | −1.19038 | − | 2.22699i | −0.125477 | − | 0.234745i | ||||
\(91\) | 5.85608 | + | 7.53036i | 0.613884 | + | 0.789396i | ||||
\(92\) | 7.98430i | 0.832421i | ||||||||
\(93\) | 9.29150 | − | 2.32744i | 0.963484 | − | 0.241345i | ||||
\(94\) | 7.82087i | 0.806661i | ||||||||
\(95\) | 3.83039i | 0.392990i | ||||||||
\(96\) | 1.68014 | − | 0.420861i | 0.171479 | − | 0.0429540i | ||||
\(97\) | 9.87000 | 1.00215 | 0.501074 | − | 0.865405i | \(-0.332939\pi\) | ||||
0.501074 | + | 0.865405i | \(0.332939\pi\) | |||||||
\(98\) | −6.29150 | − | 3.06871i | −0.635538 | − | 0.309987i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.29150 | 0.429150 | ||||||||
\(101\) | −5.74103 | −0.571254 | −0.285627 | − | 0.958341i | \(-0.592202\pi\) | ||||
−0.285627 | + | 0.958341i | \(0.592202\pi\) | |||||||
\(102\) | −7.29150 | + | 1.82646i | −0.721966 | + | 0.180847i | ||||
\(103\) | − | 9.20614i | − | 0.907108i | −0.891229 | − | 0.453554i | \(-0.850156\pi\) | ||
0.891229 | − | 0.453554i | \(-0.149844\pi\) | |||||||
\(104\) | −2.27533 | + | 2.79694i | −0.223114 | + | 0.274263i | ||||
\(105\) | −3.85660 | + | 0.0715074i | −0.376365 | + | 0.00697841i | ||||
\(106\) | 7.98430i | 0.775504i | ||||||||
\(107\) | − | 5.65685i | − | 0.546869i | −0.961891 | − | 0.273434i | \(-0.911840\pi\) | ||
0.961891 | − | 0.273434i | \(-0.0881596\pi\) | |||||||
\(108\) | 3.85005 | − | 3.48957i | 0.370471 | − | 0.335784i | ||||
\(109\) | 15.4676i | 1.48153i | 0.671765 | + | 0.740764i | \(0.265536\pi\) | ||||
−0.671765 | + | 0.740764i | \(0.734464\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.16991 | − | 8.66259i | −0.205958 | − | 0.822217i | ||||
\(112\) | 0.595188 | − | 2.57794i | 0.0562400 | − | 0.243592i | ||||
\(113\) | − | 14.1421i | − | 1.33038i | −0.746674 | − | 0.665190i | \(-0.768350\pi\) | ||
0.746674 | − | 0.665190i | \(-0.231650\pi\) | |||||||
\(114\) | −7.64575 | + | 1.91520i | −0.716090 | + | 0.179375i | ||||
\(115\) | 6.72057 | 0.626696 | ||||||||
\(116\) | − | 2.32744i | − | 0.216098i | ||||||
\(117\) | −2.06448 | + | 10.6178i | −0.190862 | + | 0.981617i | ||||
\(118\) | − | 3.91044i | − | 0.359985i | ||||||
\(119\) | −2.58301 | + | 11.1878i | −0.236784 | + | 1.02558i | ||||
\(120\) | −0.354249 | − | 1.41421i | −0.0323383 | − | 0.129099i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 5.59388i | − | 0.506446i | ||||||
\(123\) | 4.58301 | + | 18.2960i | 0.413236 | + | 1.64970i | ||||
\(124\) | 5.53019 | 0.496626 | ||||||||
\(125\) | − | 7.82087i | − | 0.699520i | ||||||
\(126\) | −2.07103 | − | 7.66230i | −0.184502 | − | 0.682612i | ||||
\(127\) | −6.58301 | −0.584147 | −0.292074 | − | 0.956396i | \(-0.594345\pi\) | ||||
−0.292074 | + | 0.956396i | \(0.594345\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 13.4411 | − | 3.36689i | 1.18343 | − | 0.296438i | ||||
\(130\) | 2.35425 | + | 1.91520i | 0.206481 | + | 0.167974i | ||||
\(131\) | −1.40122 | −0.122425 | −0.0612126 | − | 0.998125i | \(-0.519497\pi\) | ||||
−0.0612126 | + | 0.998125i | \(0.519497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.70850 | + | 11.7313i | −0.234857 | + | 1.01723i | ||||
\(134\) | − | 1.82646i | − | 0.157782i | ||||||
\(135\) | −2.93725 | − | 3.24067i | −0.252799 | − | 0.278913i | ||||
\(136\) | −4.33981 | −0.372136 | ||||||||
\(137\) | 1.29150 | 0.110341 | 0.0551703 | − | 0.998477i | \(-0.482430\pi\) | ||||
0.0551703 | + | 0.998477i | \(0.482430\pi\) | |||||||
\(138\) | 3.36028 | + | 13.4148i | 0.286046 | + | 1.14194i | ||||
\(139\) | − | 8.66259i | − | 0.734752i | −0.930073 | − | 0.367376i | \(-0.880256\pi\) | ||
0.930073 | − | 0.367376i | \(-0.119744\pi\) | |||||||
\(140\) | −2.16991 | − | 0.500983i | −0.183391 | − | 0.0423408i | ||||
\(141\) | 3.29150 | + | 13.1402i | 0.277195 | + | 1.10660i | ||||
\(142\) | −14.5830 | −1.22378 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.64575 | − | 1.41421i | 0.220479 | − | 0.117851i | ||||
\(145\) | −1.95906 | −0.162691 | ||||||||
\(146\) | −3.14944 | −0.260649 | ||||||||
\(147\) | −11.8621 | − | 2.50802i | −0.978371 | − | 0.206858i | ||||
\(148\) | − | 5.15587i | − | 0.423810i | ||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 7.21033 | − | 1.80613i | 0.588721 | − | 0.147470i | ||||
\(151\) | 13.6412i | 1.11010i | 0.831817 | + | 0.555051i | \(0.187301\pi\) | ||||
−0.831817 | + | 0.555051i | \(0.812699\pi\) | |||||||
\(152\) | −4.55066 | −0.369107 | ||||||||
\(153\) | −11.4821 | + | 6.13742i | −0.928270 | + | 0.496181i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4.65489i | − | 0.373890i | ||||||
\(156\) | −2.64575 | + | 5.65685i | −0.211830 | + | 0.452911i | ||||
\(157\) | − | 17.8687i | − | 1.42608i | −0.701123 | − | 0.713040i | \(-0.747318\pi\) | ||
0.701123 | − | 0.713040i | \(-0.252682\pi\) | |||||||
\(158\) | −11.2915 | −0.898304 | ||||||||
\(159\) | 3.36028 | + | 13.4148i | 0.266488 | + | 1.06386i | ||||
\(160\) | − | 0.841723i | − | 0.0665440i | ||||||
\(161\) | 20.5830 | + | 4.75216i | 1.62217 | + | 0.374523i | ||||
\(162\) | 5.00000 | − | 7.48331i | 0.392837 | − | 0.587945i | ||||
\(163\) | − | 8.48528i | − | 0.664619i | −0.943170 | − | 0.332309i | \(-0.892172\pi\) | ||
0.943170 | − | 0.332309i | \(-0.107828\pi\) | |||||||
\(164\) | 10.8896i | 0.850334i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.27733i | 0.564830i | ||||||||
\(167\) | 1.68345i | 0.130269i | 0.997876 | + | 0.0651345i | \(0.0207476\pi\) | ||||
−0.997876 | + | 0.0651345i | \(0.979252\pi\) | |||||||
\(168\) | −0.0849536 | − | 4.58179i | −0.00655431 | − | 0.353493i | ||||
\(169\) | −2.64575 | − | 12.7279i | −0.203519 | − | 0.979071i | ||||
\(170\) | 3.65292i | 0.280166i | ||||||||
\(171\) | −12.0399 | + | 6.43560i | −0.920715 | + | 0.492143i | ||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | −14.4207 | −1.09638 | −0.548191 | − | 0.836353i | \(-0.684683\pi\) | ||||
−0.548191 | + | 0.836353i | \(0.684683\pi\) | |||||||
\(174\) | −0.979531 | − | 3.91044i | −0.0742581 | − | 0.296449i | ||||
\(175\) | 2.55425 | − | 11.0632i | 0.193083 | − | 0.836301i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.64575 | − | 6.57008i | −0.123702 | − | 0.493838i | ||||
\(178\) | − | 12.5730i | − | 0.942388i | ||||||
\(179\) | 11.3137i | 0.845626i | 0.906217 | + | 0.422813i | \(0.138957\pi\) | ||||
−0.906217 | + | 0.422813i | \(0.861043\pi\) | |||||||
\(180\) | −1.19038 | − | 2.22699i | −0.0887254 | − | 0.165990i | ||||
\(181\) | − | 10.6442i | − | 0.791178i | −0.918428 | − | 0.395589i | \(-0.870540\pi\) | ||
0.918428 | − | 0.395589i | \(-0.129460\pi\) | |||||||
\(182\) | 5.85608 | + | 7.53036i | 0.434082 | + | 0.558187i | ||||
\(183\) | −2.35425 | − | 9.39851i | −0.174031 | − | 0.694758i | ||||
\(184\) | 7.98430i | 0.588610i | ||||||||
\(185\) | −4.33981 | −0.319070 | ||||||||
\(186\) | 9.29150 | − | 2.32744i | 0.681286 | − | 0.170656i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.82087i | 0.570396i | ||||||||
\(189\) | −6.70439 | − | 12.0021i | −0.487673 | − | 0.873026i | ||||
\(190\) | 3.83039i | 0.277886i | ||||||||
\(191\) | − | 0.500983i | − | 0.0362499i | −0.999836 | − | 0.0181249i | \(-0.994230\pi\) | ||
0.999836 | − | 0.0181249i | \(-0.00576966\pi\) | |||||||
\(192\) | 1.68014 | − | 0.420861i | 0.121254 | − | 0.0303731i | ||||
\(193\) | 8.48528i | 0.610784i | 0.952227 | + | 0.305392i | \(0.0987875\pi\) | ||||
−0.952227 | + | 0.305392i | \(0.901213\pi\) | |||||||
\(194\) | 9.87000 | 0.708625 | ||||||||
\(195\) | 4.76150 | + | 2.22699i | 0.340978 | + | 0.159478i | ||||
\(196\) | −6.29150 | − | 3.06871i | −0.449393 | − | 0.219194i | ||||
\(197\) | 8.58301 | 0.611514 | 0.305757 | − | 0.952110i | \(-0.401091\pi\) | ||||
0.305757 | + | 0.952110i | \(0.401091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4442i | 1.80369i | 0.432056 | + | 0.901847i | \(0.357788\pi\) | ||||
−0.432056 | + | 0.901847i | \(0.642212\pi\) | |||||||
\(200\) | 4.29150 | 0.303455 | ||||||||
\(201\) | −0.768687 | − | 3.06871i | −0.0542190 | − | 0.216450i | ||||
\(202\) | −5.74103 | −0.403938 | ||||||||
\(203\) | −6.00000 | − | 1.38527i | −0.421117 | − | 0.0972266i | ||||
\(204\) | −7.29150 | + | 1.82646i | −0.510507 | + | 0.127878i | ||||
\(205\) | 9.16601 | 0.640182 | ||||||||
\(206\) | − | 9.20614i | − | 0.641422i | ||||||
\(207\) | 11.2915 | + | 21.1245i | 0.784814 | + | 1.46825i | ||||
\(208\) | −2.27533 | + | 2.79694i | −0.157766 | + | 0.193933i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.85660 | + | 0.0715074i | −0.266130 | + | 0.00493448i | ||||
\(211\) | 10.5830 | 0.728564 | 0.364282 | − | 0.931289i | \(-0.381314\pi\) | ||||
0.364282 | + | 0.931289i | \(0.381314\pi\) | |||||||
\(212\) | 7.98430i | 0.548364i | ||||||||
\(213\) | −24.5015 | + | 6.13742i | −1.67882 | + | 0.420529i | ||||
\(214\) | − | 5.65685i | − | 0.386695i | ||||||
\(215\) | − | 6.73378i | − | 0.459240i | ||||||
\(216\) | 3.85005 | − | 3.48957i | 0.261963 | − | 0.237435i | ||||
\(217\) | 3.29150 | − | 14.2565i | 0.223442 | − | 0.967793i | ||||
\(218\) | 15.4676i | 1.04760i | ||||||||
\(219\) | −5.29150 | + | 1.32548i | −0.357567 | + | 0.0895675i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.87451 | − | 12.1382i | 0.664231 | − | 0.816504i | ||||
\(222\) | −2.16991 | − | 8.66259i | −0.145635 | − | 0.581395i | ||||
\(223\) | −14.6315 | −0.979798 | −0.489899 | − | 0.871779i | \(-0.662966\pi\) | ||||
−0.489899 | + | 0.871779i | \(0.662966\pi\) | |||||||
\(224\) | 0.595188 | − | 2.57794i | 0.0397677 | − | 0.172246i | ||||
\(225\) | 11.3542 | − | 6.06910i | 0.756950 | − | 0.404607i | ||||
\(226\) | − | 14.1421i | − | 0.940721i | ||||||
\(227\) | − | 8.96077i | − | 0.594747i | −0.954761 | − | 0.297374i | \(-0.903889\pi\) | ||
0.954761 | − | 0.297374i | \(-0.0961107\pi\) | |||||||
\(228\) | −7.64575 | + | 1.91520i | −0.506352 | + | 0.126837i | ||||
\(229\) | 24.2907 | 1.60517 | 0.802586 | − | 0.596536i | \(-0.203457\pi\) | ||||
0.802586 | + | 0.596536i | \(0.203457\pi\) | |||||||
\(230\) | 6.72057 | 0.443141 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2.32744i | − | 0.152804i | ||||||
\(233\) | − | 22.6274i | − | 1.48237i | −0.671300 | − | 0.741186i | \(-0.734264\pi\) | ||
0.671300 | − | 0.741186i | \(-0.265736\pi\) | |||||||
\(234\) | −2.06448 | + | 10.6178i | −0.134960 | + | 0.694108i | ||||
\(235\) | 6.58301 | 0.429428 | ||||||||
\(236\) | − | 3.91044i | − | 0.254548i | ||||||
\(237\) | −18.9713 | + | 4.75216i | −1.23232 | + | 0.308686i | ||||
\(238\) | −2.58301 | + | 11.1878i | −0.167431 | + | 0.725195i | ||||
\(239\) | −21.8745 | −1.41494 | −0.707472 | − | 0.706741i | \(-0.750165\pi\) | ||||
−0.707472 | + | 0.706741i | \(0.750165\pi\) | |||||||
\(240\) | −0.354249 | − | 1.41421i | −0.0228667 | − | 0.0912871i | ||||
\(241\) | 25.6919 | 1.65496 | 0.827480 | − | 0.561495i | \(-0.189774\pi\) | ||||
0.827480 | + | 0.561495i | \(0.189774\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | 5.25127 | − | 14.6773i | 0.336869 | − | 0.941551i | ||||
\(244\) | − | 5.59388i | − | 0.358112i | ||||||
\(245\) | −2.58301 | + | 5.29570i | −0.165022 | + | 0.338330i | ||||
\(246\) | 4.58301 | + | 18.2960i | 0.292202 | + | 1.16651i | ||||
\(247\) | 10.3542 | − | 12.7279i | 0.658825 | − | 0.809858i | ||||
\(248\) | 5.53019 | 0.351167 | ||||||||
\(249\) | 3.06275 | + | 12.2269i | 0.194094 | + | 0.774851i | ||||
\(250\) | − | 7.82087i | − | 0.494635i | ||||||
\(251\) | 5.74103 | 0.362371 | 0.181185 | − | 0.983449i | \(-0.442007\pi\) | ||||
0.181185 | + | 0.983449i | \(0.442007\pi\) | |||||||
\(252\) | −2.07103 | − | 7.66230i | −0.130463 | − | 0.482679i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.58301 | −0.413054 | ||||||||
\(255\) | 1.53737 | + | 6.13742i | 0.0962741 | + | 0.384340i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.8219 | 0.986942 | 0.493471 | − | 0.869762i | \(-0.335728\pi\) | ||||
0.493471 | + | 0.869762i | \(0.335728\pi\) | |||||||
\(258\) | 13.4411 | − | 3.36689i | 0.836808 | − | 0.209614i | ||||
\(259\) | −13.2915 | − | 3.06871i | −0.825894 | − | 0.190681i | ||||
\(260\) | 2.35425 | + | 1.91520i | 0.146004 | + | 0.118775i | ||||
\(261\) | −3.29150 | − | 6.15784i | −0.203739 | − | 0.381161i | ||||
\(262\) | −1.40122 | −0.0865677 | ||||||||
\(263\) | 16.4696i | 1.01556i | 0.861487 | + | 0.507779i | \(0.169533\pi\) | ||||
−0.861487 | + | 0.507779i | \(0.830467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.72057 | 0.412841 | ||||||||
\(266\) | −2.70850 | + | 11.7313i | −0.166069 | + | 0.719292i | ||||
\(267\) | −5.29150 | − | 21.1245i | −0.323835 | − | 1.29280i | ||||
\(268\) | − | 1.82646i | − | 0.111569i | ||||||
\(269\) | 23.1003 | 1.40845 | 0.704225 | − | 0.709977i | \(-0.251295\pi\) | ||||
0.704225 | + | 0.709977i | \(0.251295\pi\) | |||||||
\(270\) | −2.93725 | − | 3.24067i | −0.178756 | − | 0.197221i | ||||
\(271\) | −23.3111 | −1.41605 | −0.708025 | − | 0.706187i | \(-0.750414\pi\) | ||||
−0.708025 | + | 0.706187i | \(0.750414\pi\) | |||||||
\(272\) | −4.33981 | −0.263140 | ||||||||
\(273\) | 13.0083 | + | 10.1875i | 0.787297 | + | 0.616574i | ||||
\(274\) | 1.29150 | 0.0780225 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.36028 | + | 13.4148i | 0.202265 | + | 0.807473i | ||||
\(277\) | 31.1660 | 1.87258 | 0.936292 | − | 0.351222i | \(-0.114234\pi\) | ||||
0.936292 | + | 0.351222i | \(0.114234\pi\) | |||||||
\(278\) | − | 8.66259i | − | 0.519548i | ||||||
\(279\) | 14.6315 | − | 7.82087i | 0.875965 | − | 0.468223i | ||||
\(280\) | −2.16991 | − | 0.500983i | −0.129677 | − | 0.0299395i | ||||
\(281\) | 13.2915 | 0.792905 | 0.396452 | − | 0.918055i | \(-0.370241\pi\) | ||||
0.396452 | + | 0.918055i | \(0.370241\pi\) | |||||||
\(282\) | 3.29150 | + | 13.1402i | 0.196006 | + | 0.782486i | ||||
\(283\) | 14.8000i | 0.879770i | 0.898054 | + | 0.439885i | \(0.144981\pi\) | ||||
−0.898054 | + | 0.439885i | \(0.855019\pi\) | |||||||
\(284\) | −14.5830 | −0.865342 | ||||||||
\(285\) | 1.61206 | + | 6.43560i | 0.0954905 | + | 0.381212i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.0726 | + | 6.48135i | 1.65708 | + | 0.382582i | ||||
\(288\) | 2.64575 | − | 1.41421i | 0.155902 | − | 0.0833333i | ||||
\(289\) | 1.83399 | 0.107882 | ||||||||
\(290\) | −1.95906 | −0.115040 | ||||||||
\(291\) | 16.5830 | − | 4.15390i | 0.972113 | − | 0.243506i | ||||
\(292\) | −3.14944 | −0.184307 | ||||||||
\(293\) | − | 13.1166i | − | 0.766278i | −0.923691 | − | 0.383139i | \(-0.874843\pi\) | ||
0.923691 | − | 0.383139i | \(-0.125157\pi\) | |||||||
\(294\) | −11.8621 | − | 2.50802i | −0.691813 | − | 0.146271i | ||||
\(295\) | −3.29150 | −0.191639 | ||||||||
\(296\) | − | 5.15587i | − | 0.299679i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | −22.3316 | − | 18.1669i | −1.29147 | − | 1.05062i | ||||
\(300\) | 7.21033 | − | 1.80613i | 0.416289 | − | 0.104277i | ||||
\(301\) | 4.76150 | − | 20.6235i | 0.274449 | − | 1.18872i | ||||
\(302\) | 13.6412i | 0.784960i | ||||||||
\(303\) | −9.64575 | + | 2.41618i | −0.554134 | + | 0.138806i | ||||
\(304\) | −4.55066 | −0.260998 | ||||||||
\(305\) | −4.70850 | −0.269608 | ||||||||
\(306\) | −11.4821 | + | 6.13742i | −0.656386 | + | 0.350853i | ||||
\(307\) | −8.89047 | −0.507406 | −0.253703 | − | 0.967282i | \(-0.581649\pi\) | ||||
−0.253703 | + | 0.967282i | \(0.581649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.87451 | − | 15.4676i | −0.220413 | − | 0.879922i | ||||
\(310\) | − | 4.65489i | − | 0.264380i | ||||||
\(311\) | −7.14226 | −0.405000 | −0.202500 | − | 0.979282i | \(-0.564907\pi\) | ||||
−0.202500 | + | 0.979282i | \(0.564907\pi\) | |||||||
\(312\) | −2.64575 | + | 5.65685i | −0.149786 | + | 0.320256i | ||||
\(313\) | − | 33.5633i | − | 1.89711i | −0.316614 | − | 0.948555i | \(-0.602546\pi\) | ||
0.316614 | − | 0.948555i | \(-0.397454\pi\) | |||||||
\(314\) | − | 17.8687i | − | 1.00839i | ||||||
\(315\) | −6.44953 | + | 1.74324i | −0.363390 | + | 0.0982202i | ||||
\(316\) | −11.2915 | −0.635197 | ||||||||
\(317\) | −6.00000 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(318\) | 3.36028 | + | 13.4148i | 0.188435 | + | 0.752262i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 0.841723i | − | 0.0470537i | ||||||
\(321\) | −2.38075 | − | 9.50432i | −0.132881 | − | 0.530479i | ||||
\(322\) | 20.5830 | + | 4.75216i | 1.14705 | + | 0.264827i | ||||
\(323\) | 19.7490 | 1.09886 | ||||||||
\(324\) | 5.00000 | − | 7.48331i | 0.277778 | − | 0.415740i | ||||
\(325\) | −9.76458 | + | 12.0031i | −0.541642 | + | 0.665811i | ||||
\(326\) | − | 8.48528i | − | 0.469956i | ||||||
\(327\) | 6.50972 | + | 25.9878i | 0.359988 | + | 1.43713i | ||||
\(328\) | 10.8896i | 0.601277i | ||||||||
\(329\) | 20.1617 | + | 4.65489i | 1.11155 | + | 0.256632i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8.48528i | − | 0.466393i | −0.972430 | − | 0.233197i | \(-0.925081\pi\) | ||
0.972430 | − | 0.233197i | \(-0.0749186\pi\) | |||||||
\(332\) | 7.27733i | 0.399395i | ||||||||
\(333\) | −7.29150 | − | 13.6412i | −0.399572 | − | 0.747531i | ||||
\(334\) | 1.68345i | 0.0921141i | ||||||||
\(335\) | −1.53737 | −0.0839957 | ||||||||
\(336\) | −0.0849536 | − | 4.58179i | −0.00463460 | − | 0.249957i | ||||
\(337\) | 11.8745 | 0.646846 | 0.323423 | − | 0.946255i | \(-0.395166\pi\) | ||||
0.323423 | + | 0.946255i | \(0.395166\pi\) | |||||||
\(338\) | −2.64575 | − | 12.7279i | −0.143910 | − | 0.692308i | ||||
\(339\) | −5.95188 | − | 23.7608i | −0.323262 | − | 1.29051i | ||||
\(340\) | 3.65292i | 0.198107i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −12.0399 | + | 6.43560i | −0.651044 | + | 0.347998i | ||||
\(343\) | −11.6556 | + | 14.3926i | −0.629342 | + | 0.777129i | ||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 11.2915 | − | 2.82843i | 0.607914 | − | 0.152277i | ||||
\(346\) | −14.4207 | −0.775260 | ||||||||
\(347\) | − | 2.00393i | − | 0.107577i | −0.998552 | − | 0.0537884i | \(-0.982870\pi\) | ||
0.998552 | − | 0.0537884i | \(-0.0171296\pi\) | |||||||
\(348\) | −0.979531 | − | 3.91044i | −0.0525084 | − | 0.209621i | ||||
\(349\) | 15.6110 | 0.835640 | 0.417820 | − | 0.908530i | \(-0.362794\pi\) | ||||
0.417820 | + | 0.908530i | \(0.362794\pi\) | |||||||
\(350\) | 2.55425 | − | 11.0632i | 0.136530 | − | 0.591354i | ||||
\(351\) | 1.00000 | + | 18.7083i | 0.0533761 | + | 0.998574i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.83925i | 0.310792i | 0.987852 | + | 0.155396i | \(0.0496653\pi\) | ||||
−0.987852 | + | 0.155396i | \(0.950335\pi\) | |||||||
\(354\) | −1.64575 | − | 6.57008i | −0.0874707 | − | 0.349196i | ||||
\(355\) | 12.2748i | 0.651481i | ||||||||
\(356\) | − | 12.5730i | − | 0.666369i | ||||||
\(357\) | 0.368683 | + | 19.8841i | 0.0195128 | + | 1.05238i | ||||
\(358\) | 11.3137i | 0.597948i | ||||||||
\(359\) | −16.7085 | −0.881841 | −0.440920 | − | 0.897546i | \(-0.645348\pi\) | ||||
−0.440920 | + | 0.897546i | \(0.645348\pi\) | |||||||
\(360\) | −1.19038 | − | 2.22699i | −0.0627383 | − | 0.117373i | ||||
\(361\) | 1.70850 | 0.0899209 | ||||||||
\(362\) | − | 10.6442i | − | 0.559448i | ||||||
\(363\) | −18.4816 | + | 4.62948i | −0.970030 | + | 0.242984i | ||||
\(364\) | 5.85608 | + | 7.53036i | 0.306942 | + | 0.394698i | ||||
\(365\) | 2.65095i | 0.138757i | ||||||||
\(366\) | −2.35425 | − | 9.39851i | −0.123059 | − | 0.491268i | ||||
\(367\) | 8.11905i | 0.423811i | 0.977290 | + | 0.211905i | \(0.0679669\pi\) | ||||
−0.977290 | + | 0.211905i | \(0.932033\pi\) | |||||||
\(368\) | 7.98430i | 0.416210i | ||||||||
\(369\) | 15.4002 | + | 28.8111i | 0.801702 | + | 1.49985i | ||||
\(370\) | −4.33981 | −0.225616 | ||||||||
\(371\) | 20.5830 | + | 4.75216i | 1.06862 | + | 0.246720i | ||||
\(372\) | 9.29150 | − | 2.32744i | 0.481742 | − | 0.120672i | ||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.29150 | − | 13.1402i | −0.169972 | − | 0.678555i | ||||
\(376\) | 7.82087i | 0.403331i | ||||||||
\(377\) | 6.50972 | + | 5.29570i | 0.335268 | + | 0.272743i | ||||
\(378\) | −6.70439 | − | 12.0021i | −0.344837 | − | 0.617323i | ||||
\(379\) | 15.1441i | 0.777900i | 0.921259 | + | 0.388950i | \(0.127162\pi\) | ||||
−0.921259 | + | 0.388950i | \(0.872838\pi\) | |||||||
\(380\) | 3.83039i | 0.196495i | ||||||||
\(381\) | −11.0604 | + | 2.77053i | −0.566640 | + | 0.141939i | ||||
\(382\) | − | 0.500983i | − | 0.0256325i | ||||||
\(383\) | − | 39.1044i | − | 1.99814i | −0.0431294 | − | 0.999069i | \(-0.513733\pi\) | ||
0.0431294 | − | 0.999069i | \(-0.486267\pi\) | |||||||
\(384\) | 1.68014 | − | 0.420861i | 0.0857394 | − | 0.0214770i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 21.1660 | − | 11.3137i | 1.07593 | − | 0.575108i | ||||
\(388\) | 9.87000 | 0.501074 | ||||||||
\(389\) | − | 12.6392i | − | 0.640832i | −0.947277 | − | 0.320416i | \(-0.896177\pi\) | ||
0.947277 | − | 0.320416i | \(-0.103823\pi\) | |||||||
\(390\) | 4.76150 | + | 2.22699i | 0.241108 | + | 0.112768i | ||||
\(391\) | − | 34.6504i | − | 1.75234i | ||||||
\(392\) | −6.29150 | − | 3.06871i | −0.317769 | − | 0.154993i | ||||
\(393\) | −2.35425 | + | 0.589720i | −0.118756 | + | 0.0297474i | ||||
\(394\) | 8.58301 | 0.432406 | ||||||||
\(395\) | 9.50432i | 0.478214i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0327 | −0.804660 | −0.402330 | − | 0.915495i | \(-0.631799\pi\) | ||||
−0.402330 | + | 0.915495i | \(0.631799\pi\) | |||||||
\(398\) | 25.4442i | 1.27540i | ||||||||
\(399\) | 0.386595 | + | 20.8502i | 0.0193540 | + | 1.04381i | ||||
\(400\) | 4.29150 | 0.214575 | ||||||||
\(401\) | 6.00000 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | −0.768687 | − | 3.06871i | −0.0383386 | − | 0.153053i | ||||
\(403\) | −12.5830 | + | 15.4676i | −0.626804 | + | 0.770497i | ||||
\(404\) | −5.74103 | −0.285627 | ||||||||
\(405\) | −6.29888 | − | 4.20861i | −0.312994 | − | 0.209128i | ||||
\(406\) | −6.00000 | − | 1.38527i | −0.297775 | − | 0.0687496i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.29150 | + | 1.82646i | −0.360983 | + | 0.0904233i | ||||
\(409\) | 1.19038 | 0.0588603 | 0.0294301 | − | 0.999567i | \(-0.490631\pi\) | ||||
0.0294301 | + | 0.999567i | \(0.490631\pi\) | |||||||
\(410\) | 9.16601 | 0.452677 | ||||||||
\(411\) | 2.16991 | − | 0.543544i | 0.107034 | − | 0.0268110i | ||||
\(412\) | − | 9.20614i | − | 0.453554i | ||||||
\(413\) | −10.0808 | − | 2.32744i | −0.496046 | − | 0.114526i | ||||
\(414\) | 11.2915 | + | 21.1245i | 0.554947 | + | 1.03821i | ||||
\(415\) | 6.12549 | 0.300689 | ||||||||
\(416\) | −2.27533 | + | 2.79694i | −0.111557 | + | 0.137131i | ||||
\(417\) | −3.64575 | − | 14.5544i | −0.178533 | − | 0.712731i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.9027 | 1.26543 | 0.632716 | − | 0.774384i | \(-0.281940\pi\) | ||||
0.632716 | + | 0.774384i | \(0.281940\pi\) | |||||||
\(420\) | −3.85660 | + | 0.0715074i | −0.188183 | + | 0.00348920i | ||||
\(421\) | − | 11.8147i | − | 0.575813i | −0.957659 | − | 0.287906i | \(-0.907041\pi\) | ||
0.957659 | − | 0.287906i | \(-0.0929592\pi\) | |||||||
\(422\) | 10.5830 | 0.515173 | ||||||||
\(423\) | 11.0604 | + | 20.6921i | 0.537774 | + | 1.00608i | ||||
\(424\) | 7.98430i | 0.387752i | ||||||||
\(425\) | −18.6243 | −0.903412 | ||||||||
\(426\) | −24.5015 | + | 6.13742i | −1.18710 | + | 0.297359i | ||||
\(427\) | −14.4207 | − | 3.32941i | −0.697865 | − | 0.161121i | ||||
\(428\) | − | 5.65685i | − | 0.273434i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 6.73378i | − | 0.324732i | ||||||
\(431\) | 7.29150 | 0.351219 | 0.175610 | − | 0.984460i | \(-0.443810\pi\) | ||||
0.175610 | + | 0.984460i | \(0.443810\pi\) | |||||||
\(432\) | 3.85005 | − | 3.48957i | 0.185236 | − | 0.167892i | ||||
\(433\) | 17.3252i | 0.832595i | 0.909228 | + | 0.416298i | \(0.136673\pi\) | ||||
−0.909228 | + | 0.416298i | \(0.863327\pi\) | |||||||
\(434\) | 3.29150 | − | 14.2565i | 0.157997 | − | 0.684333i | ||||
\(435\) | −3.29150 | + | 0.824494i | −0.157815 | + | 0.0395315i | ||||
\(436\) | 15.4676i | 0.740764i | ||||||||
\(437\) | − | 36.3338i | − | 1.73808i | ||||||
\(438\) | −5.29150 | + | 1.32548i | −0.252838 | + | 0.0633338i | ||||
\(439\) | 8.11905i | 0.387501i | 0.981051 | + | 0.193751i | \(0.0620652\pi\) | ||||
−0.981051 | + | 0.193751i | \(0.937935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.9856 | + | 0.778479i | −0.999313 | + | 0.0370704i | ||||
\(442\) | 9.87451 | − | 12.1382i | 0.469682 | − | 0.577355i | ||||
\(443\) | − | 5.65685i | − | 0.268765i | −0.990930 | − | 0.134383i | \(-0.957095\pi\) | ||
0.990930 | − | 0.134383i | \(-0.0429051\pi\) | |||||||
\(444\) | −2.16991 | − | 8.66259i | −0.102979 | − | 0.411108i | ||||
\(445\) | −10.5830 | −0.501683 | ||||||||
\(446\) | −14.6315 | −0.692822 | ||||||||
\(447\) | 10.0808 | − | 2.52517i | 0.476808 | − | 0.119436i | ||||
\(448\) | 0.595188 | − | 2.57794i | 0.0281200 | − | 0.121796i | ||||
\(449\) | −30.4575 | −1.43738 | −0.718689 | − | 0.695331i | \(-0.755258\pi\) | ||||
−0.718689 | + | 0.695331i | \(0.755258\pi\) | |||||||
\(450\) | 11.3542 | − | 6.06910i | 0.535244 | − | 0.286100i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 14.1421i | − | 0.665190i | ||||||
\(453\) | 5.74103 | + | 22.9191i | 0.269737 | + | 1.07683i | ||||
\(454\) | − | 8.96077i | − | 0.420550i | ||||||
\(455\) | 6.33847 | − | 4.92920i | 0.297152 | − | 0.231084i | ||||
\(456\) | −7.64575 | + | 1.91520i | −0.358045 | + | 0.0896873i | ||||
\(457\) | − | 12.1382i | − | 0.567801i | −0.958854 | − | 0.283901i | \(-0.908371\pi\) | ||
0.958854 | − | 0.283901i | \(-0.0916286\pi\) | |||||||
\(458\) | 24.2907 | 1.13503 | ||||||||
\(459\) | −16.7085 | + | 15.1441i | −0.779886 | + | 0.706866i | ||||
\(460\) | 6.72057 | 0.313348 | ||||||||
\(461\) | 15.3964i | 0.717081i | 0.933514 | + | 0.358540i | \(0.116725\pi\) | ||||
−0.933514 | + | 0.358540i | \(0.883275\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7794i | 1.19807i | 0.800724 | + | 0.599034i | \(0.204449\pi\) | ||||
−0.800724 | + | 0.599034i | \(0.795551\pi\) | |||||||
\(464\) | − | 2.32744i | − | 0.108049i | ||||||
\(465\) | −1.95906 | − | 7.82087i | −0.0908494 | − | 0.362684i | ||||
\(466\) | − | 22.6274i | − | 1.04819i | ||||||
\(467\) | 7.27841 | 0.336805 | 0.168402 | − | 0.985718i | \(-0.446139\pi\) | ||||
0.168402 | + | 0.985718i | \(0.446139\pi\) | |||||||
\(468\) | −2.06448 | + | 10.6178i | −0.0954309 | + | 0.490808i | ||||
\(469\) | −4.70850 | − | 1.08709i | −0.217418 | − | 0.0501970i | ||||
\(470\) | 6.58301 | 0.303651 | ||||||||
\(471\) | −7.52026 | − | 30.0220i | −0.346515 | − | 1.38334i | ||||
\(472\) | − | 3.91044i | − | 0.179992i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −18.9713 | + | 4.75216i | −0.871382 | + | 0.218274i | ||||
\(475\) | −19.5292 | −0.896060 | ||||||||
\(476\) | −2.58301 | + | 11.1878i | −0.118392 | + | 0.512790i | ||||
\(477\) | 11.2915 | + | 21.1245i | 0.517002 | + | 0.967223i | ||||
\(478\) | −21.8745 | −1.00052 | ||||||||
\(479\) | 17.9215i | 0.818856i | 0.912342 | + | 0.409428i | \(0.134272\pi\) | ||||
−0.912342 | + | 0.409428i | \(0.865728\pi\) | |||||||
\(480\) | −0.354249 | − | 1.41421i | −0.0161692 | − | 0.0645497i | ||||
\(481\) | 14.4207 | + | 11.7313i | 0.657526 | + | 0.534901i | ||||
\(482\) | 25.6919 | 1.17023 | ||||||||
\(483\) | 36.5824 | − | 0.678295i | 1.66456 | − | 0.0308635i | ||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | − | 8.30781i | − | 0.377238i | ||||||
\(486\) | 5.25127 | − | 14.6773i | 0.238202 | − | 0.665777i | ||||
\(487\) | − | 17.2941i | − | 0.783669i | −0.920036 | − | 0.391835i | \(-0.871841\pi\) | ||
0.920036 | − | 0.391835i | \(-0.128159\pi\) | |||||||
\(488\) | − | 5.59388i | − | 0.253223i | ||||||
\(489\) | −3.57113 | − | 14.2565i | −0.161492 | − | 0.644700i | ||||
\(490\) | −2.58301 | + | 5.29570i | −0.116688 | + | 0.239235i | ||||
\(491\) | − | 26.2803i | − | 1.18602i | −0.805197 | − | 0.593008i | \(-0.797940\pi\) | ||
0.805197 | − | 0.593008i | \(-0.202060\pi\) | |||||||
\(492\) | 4.58301 | + | 18.2960i | 0.206618 | + | 0.824849i | ||||
\(493\) | 10.1007i | 0.454911i | ||||||||
\(494\) | 10.3542 | − | 12.7279i | 0.465860 | − | 0.572656i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.53019 | 0.248313 | ||||||||
\(497\) | −8.67963 | + | 37.5940i | −0.389335 | + | 1.68632i | ||||
\(498\) | 3.06275 | + | 12.2269i | 0.137245 | + | 0.547902i | ||||
\(499\) | 18.7970i | 0.841470i | 0.907184 | + | 0.420735i | \(0.138228\pi\) | ||||
−0.907184 | + | 0.420735i | \(0.861772\pi\) | |||||||
\(500\) | − | 7.82087i | − | 0.349760i | ||||||
\(501\) | 0.708497 | + | 2.82843i | 0.0316533 | + | 0.126365i | ||||
\(502\) | 5.74103 | 0.256235 | ||||||||
\(503\) | 8.67963 | 0.387006 | 0.193503 | − | 0.981100i | \(-0.438015\pi\) | ||||
0.193503 | + | 0.981100i | \(0.438015\pi\) | |||||||
\(504\) | −2.07103 | − | 7.66230i | −0.0922511 | − | 0.341306i | ||||
\(505\) | 4.83236i | 0.215037i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.80193 | − | 20.2712i | −0.435319 | − | 0.900276i | ||||
\(508\) | −6.58301 | −0.292074 | ||||||||
\(509\) | 15.3964i | 0.682432i | 0.939985 | + | 0.341216i | \(0.110839\pi\) | ||||
−0.939985 | + | 0.341216i | \(0.889161\pi\) | |||||||
\(510\) | 1.53737 | + | 6.13742i | 0.0680760 | + | 0.271770i | ||||
\(511\) | −1.87451 | + | 8.11905i | −0.0829233 | + | 0.359166i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −17.5203 | + | 15.8799i | −0.773538 | + | 0.701113i | ||||
\(514\) | 15.8219 | 0.697873 | ||||||||
\(515\) | −7.74902 | −0.341462 | ||||||||
\(516\) | 13.4411 | − | 3.36689i | 0.591713 | − | 0.148219i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.2915 | − | 3.06871i | −0.583995 | − | 0.134831i | ||||
\(519\) | −24.2288 | + | 6.06910i | −1.06352 | + | 0.266404i | ||||
\(520\) | 2.35425 | + | 1.91520i | 0.103241 | + | 0.0839869i | ||||
\(521\) | 2.80244 | 0.122777 | 0.0613886 | − | 0.998114i | \(-0.480447\pi\) | ||||
0.0613886 | + | 0.998114i | \(0.480447\pi\) | |||||||
\(522\) | −3.29150 | − | 6.15784i | −0.144065 | − | 0.269521i | ||||
\(523\) | 32.1252i | 1.40474i | 0.711813 | + | 0.702369i | \(0.247874\pi\) | ||||
−0.711813 | + | 0.702369i | \(0.752126\pi\) | |||||||
\(524\) | −1.40122 | −0.0612126 | ||||||||
\(525\) | −0.364579 | − | 19.6628i | −0.0159115 | − | 0.858153i | ||||
\(526\) | 16.4696i | 0.718108i | ||||||||
\(527\) | −24.0000 | −1.04546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −40.7490 | −1.77170 | ||||||||
\(530\) | 6.72057 | 0.291923 | ||||||||
\(531\) | −5.53019 | − | 10.3460i | −0.239990 | − | 0.448980i | ||||
\(532\) | −2.70850 | + | 11.7313i | −0.117428 | + | 0.508617i | ||||
\(533\) | −30.4575 | − | 24.7774i | −1.31926 | − | 1.07323i | ||||
\(534\) | −5.29150 | − | 21.1245i | −0.228986 | − | 0.914145i | ||||
\(535\) | −4.76150 | −0.205858 | ||||||||
\(536\) | − | 1.82646i | − | 0.0788911i | ||||||
\(537\) | 4.76150 | + | 19.0086i | 0.205474 | + | 0.820283i | ||||
\(538\) | 23.1003 | 0.995924 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.93725 | − | 3.24067i | −0.126399 | − | 0.139456i | ||||
\(541\) | 29.4323i | 1.26539i | 0.774400 | + | 0.632696i | \(0.218052\pi\) | ||||
−0.774400 | + | 0.632696i | \(0.781948\pi\) | |||||||
\(542\) | −23.3111 | −1.00130 | ||||||||
\(543\) | −4.47974 | − | 17.8838i | −0.192244 | − | 0.767467i | ||||
\(544\) | −4.33981 | −0.186068 | ||||||||
\(545\) | 13.0194 | 0.557692 | ||||||||
\(546\) | 13.0083 | + | 10.1875i | 0.556703 | + | 0.435983i | ||||
\(547\) | −6.58301 | −0.281469 | −0.140734 | − | 0.990047i | \(-0.544946\pi\) | ||||
−0.140734 | + | 0.990047i | \(0.544946\pi\) | |||||||
\(548\) | 1.29150 | 0.0551703 | ||||||||
\(549\) | −7.91094 | − | 14.8000i | −0.337631 | − | 0.631649i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.5914i | 0.451209i | ||||||||
\(552\) | 3.36028 | + | 13.4148i | 0.143023 | + | 0.570970i | ||||
\(553\) | −6.72057 | + | 29.1088i | −0.285788 | + | 1.23783i | ||||
\(554\) | 31.1660 | 1.32412 | ||||||||
\(555\) | −7.29150 | + | 1.82646i | −0.309507 | + | 0.0775289i | ||||
\(556\) | − | 8.66259i | − | 0.367376i | ||||||
\(557\) | −23.1660 | −0.981575 | −0.490788 | − | 0.871279i | \(-0.663291\pi\) | ||||
−0.490788 | + | 0.871279i | \(0.663291\pi\) | |||||||
\(558\) | 14.6315 | − | 7.82087i | 0.619401 | − | 0.331084i | ||||
\(559\) | −18.2026 | + | 22.3755i | −0.769889 | + | 0.946384i | ||||
\(560\) | −2.16991 | − | 0.500983i | −0.0916953 | − | 0.0211704i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.2915 | 0.560668 | ||||||||
\(563\) | 7.27841 | 0.306748 | 0.153374 | − | 0.988168i | \(-0.450986\pi\) | ||||
0.153374 | + | 0.988168i | \(0.450986\pi\) | |||||||
\(564\) | 3.29150 | + | 13.1402i | 0.138597 | + | 0.553301i | ||||
\(565\) | −11.9038 | −0.500795 | ||||||||
\(566\) | 14.8000i | 0.622091i | ||||||||
\(567\) | −16.3156 | − | 17.3437i | −0.685189 | − | 0.728365i | ||||
\(568\) | −14.5830 | −0.611889 | ||||||||
\(569\) | 30.1107i | 1.26231i | 0.775658 | + | 0.631154i | \(0.217418\pi\) | ||||
−0.775658 | + | 0.631154i | \(0.782582\pi\) | |||||||
\(570\) | 1.61206 | + | 6.43560i | 0.0675220 | + | 0.269558i | ||||
\(571\) | −1.41699 | −0.0592994 | −0.0296497 | − | 0.999560i | \(-0.509439\pi\) | ||||
−0.0296497 | + | 0.999560i | \(0.509439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.210845 | − | 0.841723i | −0.00880816 | − | 0.0351635i | ||||
\(574\) | 28.0726 | + | 6.48135i | 1.17173 | + | 0.270526i | ||||
\(575\) | 34.2646i | 1.42893i | ||||||||
\(576\) | 2.64575 | − | 1.41421i | 0.110240 | − | 0.0589256i | ||||
\(577\) | 5.53019 | 0.230225 | 0.115112 | − | 0.993352i | \(-0.463277\pi\) | ||||
0.115112 | + | 0.993352i | \(0.463277\pi\) | |||||||
\(578\) | 1.83399 | 0.0762839 | ||||||||
\(579\) | 3.57113 | + | 14.2565i | 0.148411 | + | 0.592479i | ||||
\(580\) | −1.95906 | −0.0813457 | ||||||||
\(581\) | 18.7605 | + | 4.33138i | 0.778316 | + | 0.179696i | ||||
\(582\) | 16.5830 | − | 4.15390i | 0.687388 | − | 0.172185i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3.14944 | −0.130325 | ||||||||
\(585\) | 8.93725 | + | 1.73772i | 0.369510 | + | 0.0718461i | ||||
\(586\) | − | 13.1166i | − | 0.541841i | ||||||
\(587\) | 8.36441i | 0.345236i | 0.984989 | + | 0.172618i | \(0.0552227\pi\) | ||||
−0.984989 | + | 0.172618i | \(0.944777\pi\) | |||||||
\(588\) | −11.8621 | − | 2.50802i | −0.489185 | − | 0.103429i | ||||
\(589\) | −25.1660 | −1.03695 | ||||||||
\(590\) | −3.29150 | −0.135509 | ||||||||
\(591\) | 14.4207 | − | 3.61226i | 0.593187 | − | 0.148588i | ||||
\(592\) | − | 5.15587i | − | 0.211905i | ||||||
\(593\) | − | 41.0860i | − | 1.68720i | −0.536973 | − | 0.843599i | \(-0.680432\pi\) | ||
0.536973 | − | 0.843599i | \(-0.319568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.41699 | + | 2.17417i | 0.386059 | + | 0.0891325i | ||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 10.7085 | + | 42.7499i | 0.438270 | + | 1.74964i | ||||
\(598\) | −22.3316 | − | 18.1669i | −0.913207 | − | 0.742900i | ||||
\(599\) | 23.7754i | 0.971437i | 0.874115 | + | 0.485719i | \(0.161442\pi\) | ||||
−0.874115 | + | 0.485719i | \(0.838558\pi\) | |||||||
\(600\) | 7.21033 | − | 1.80613i | 0.294361 | − | 0.0737349i | ||||
\(601\) | 22.3755i | 0.912717i | 0.889796 | + | 0.456358i | \(0.150846\pi\) | ||||
−0.889796 | + | 0.456358i | \(0.849154\pi\) | |||||||
\(602\) | 4.76150 | − | 20.6235i | 0.194064 | − | 0.840550i | ||||
\(603\) | −2.58301 | − | 4.83236i | −0.105188 | − | 0.196789i | ||||
\(604\) | 13.6412i | 0.555051i | ||||||||
\(605\) | 9.25895i | 0.376430i | ||||||||
\(606\) | −9.64575 | + | 2.41618i | −0.391832 | + | 0.0981506i | ||||
\(607\) | − | 26.5313i | − | 1.07687i | −0.842666 | − | 0.538437i | \(-0.819015\pi\) | ||
0.842666 | − | 0.538437i | \(-0.180985\pi\) | |||||||
\(608\) | −4.55066 | −0.184554 | ||||||||
\(609\) | −10.6639 | + | 0.197725i | −0.432121 | + | 0.00801221i | ||||
\(610\) | −4.70850 | −0.190641 | ||||||||
\(611\) | −21.8745 | − | 17.7951i | −0.884948 | − | 0.719911i | ||||
\(612\) | −11.4821 | + | 6.13742i | −0.464135 | + | 0.248091i | ||||
\(613\) | − | 32.4382i | − | 1.31017i | −0.755557 | − | 0.655083i | \(-0.772634\pi\) | ||
0.755557 | − | 0.655083i | \(-0.227366\pi\) | |||||||
\(614\) | −8.89047 | −0.358790 | ||||||||
\(615\) | 15.4002 | − | 3.85762i | 0.620996 | − | 0.155554i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.1660 | 0.449527 | 0.224763 | − | 0.974413i | \(-0.427839\pi\) | ||||
0.224763 | + | 0.974413i | \(0.427839\pi\) | |||||||
\(618\) | −3.87451 | − | 15.4676i | −0.155856 | − | 0.622199i | ||||
\(619\) | −26.2497 | −1.05507 | −0.527533 | − | 0.849535i | \(-0.676883\pi\) | ||||
−0.527533 | + | 0.849535i | \(0.676883\pi\) | |||||||
\(620\) | − | 4.65489i | − | 0.186945i | ||||||
\(621\) | 27.8618 | + | 30.7399i | 1.11806 | + | 1.23355i | ||||
\(622\) | −7.14226 | −0.286378 | ||||||||
\(623\) | −32.4125 | − | 7.48331i | −1.29858 | − | 0.299813i | ||||
\(624\) | −2.64575 | + | 5.65685i | −0.105915 | + | 0.226455i | ||||
\(625\) | 14.8745 | 0.594980 | ||||||||
\(626\) | − | 33.5633i | − | 1.34146i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 17.8687i | − | 0.713040i | ||||||
\(629\) | 22.3755i | 0.892171i | ||||||||
\(630\) | −6.44953 | + | 1.74324i | −0.256956 | + | 0.0694521i | ||||
\(631\) | − | 19.1205i | − | 0.761176i | −0.924745 | − | 0.380588i | \(-0.875722\pi\) | ||
0.924745 | − | 0.380588i | \(-0.124278\pi\) | |||||||
\(632\) | −11.2915 | −0.449152 | ||||||||
\(633\) | 17.7809 | − | 4.45398i | 0.706729 | − | 0.177030i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 5.54107i | 0.219890i | ||||||||
\(636\) | 3.36028 | + | 13.4148i | 0.133244 | + | 0.531929i | ||||
\(637\) | 22.8982 | − | 10.6146i | 0.907262 | − | 0.420567i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.5830 | + | 20.6235i | −1.52632 | + | 0.815852i | ||||
\(640\) | − | 0.841723i | − | 0.0332720i | ||||||
\(641\) | 13.1402i | 0.519005i | 0.965742 | + | 0.259503i | \(0.0835587\pi\) | ||||
−0.965742 | + | 0.259503i | \(0.916441\pi\) | |||||||
\(642\) | −2.38075 | − | 9.50432i | −0.0939608 | − | 0.375105i | ||||
\(643\) | −4.55066 | −0.179460 | −0.0897302 | − | 0.995966i | \(-0.528600\pi\) | ||||
−0.0897302 | + | 0.995966i | \(0.528600\pi\) | |||||||
\(644\) | 20.5830 | + | 4.75216i | 0.811084 | + | 0.187261i | ||||
\(645\) | −2.83399 | − | 11.3137i | −0.111588 | − | 0.445477i | ||||
\(646\) | 19.7490 | 0.777015 | ||||||||
\(647\) | 2.80244 | 0.110175 | 0.0550877 | − | 0.998482i | \(-0.482456\pi\) | ||||
0.0550877 | + | 0.998482i | \(0.482456\pi\) | |||||||
\(648\) | 5.00000 | − | 7.48331i | 0.196419 | − | 0.293972i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −9.76458 | + | 12.0031i | −0.382998 | + | 0.470799i | ||||
\(651\) | −0.469810 | − | 25.3382i | −0.0184133 | − | 0.993081i | ||||
\(652\) | − | 8.48528i | − | 0.332309i | ||||||
\(653\) | 32.2607i | 1.26246i | 0.775596 | + | 0.631229i | \(0.217449\pi\) | ||||
−0.775596 | + | 0.631229i | \(0.782551\pi\) | |||||||
\(654\) | 6.50972 | + | 25.9878i | 0.254550 | + | 1.01620i | ||||
\(655\) | 1.17944i | 0.0460845i | ||||||||
\(656\) | 10.8896i | 0.425167i | ||||||||
\(657\) | −8.33263 | + | 4.45398i | −0.325087 | + | 0.173766i | ||||
\(658\) | 20.1617 | + | 4.65489i | 0.785985 | + | 0.181466i | ||||
\(659\) | 1.00197i | 0.0390311i | 0.999810 | + | 0.0195155i | \(0.00621238\pi\) | ||||
−0.999810 | + | 0.0195155i | \(0.993788\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.4329 | 1.22260 | 0.611300 | − | 0.791399i | \(-0.290647\pi\) | ||||
0.611300 | + | 0.791399i | \(0.290647\pi\) | |||||||
\(662\) | − | 8.48528i | − | 0.329790i | ||||||
\(663\) | 11.4821 | − | 24.5497i | 0.445927 | − | 0.953431i | ||||
\(664\) | 7.27733i | 0.282415i | ||||||||
\(665\) | 9.87451 | + | 2.27980i | 0.382917 | + | 0.0884070i | ||||
\(666\) | −7.29150 | − | 13.6412i | −0.282540 | − | 0.528584i | ||||
\(667\) | 18.5830 | 0.719537 | ||||||||
\(668\) | 1.68345i | 0.0651345i | ||||||||
\(669\) | −24.5830 | + | 6.15784i | −0.950434 | + | 0.238076i | ||||
\(670\) | −1.53737 | −0.0593939 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.0849536 | − | 4.58179i | −0.00327716 | − | 0.176746i | ||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 11.8745 | 0.457389 | ||||||||
\(675\) | 16.5225 | − | 14.9755i | 0.635951 | − | 0.576408i | ||||
\(676\) | −2.64575 | − | 12.7279i | −0.101760 | − | 0.489535i | ||||
\(677\) | −43.2620 | −1.66269 | −0.831347 | − | 0.555754i | \(-0.812430\pi\) | ||||
−0.831347 | + | 0.555754i | \(0.812430\pi\) | |||||||
\(678\) | −5.95188 | − | 23.7608i | −0.228581 | − | 0.912528i | ||||
\(679\) | 5.87451 | − | 25.4442i | 0.225443 | − | 0.976460i | ||||
\(680\) | 3.65292i | 0.140083i | ||||||||
\(681\) | −3.77124 | − | 15.0554i | −0.144514 | − | 0.576923i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.5830 | 1.93550 | 0.967752 | − | 0.251903i | \(-0.0810564\pi\) | ||||
0.967752 | + | 0.251903i | \(0.0810564\pi\) | |||||||
\(684\) | −12.0399 | + | 6.43560i | −0.460358 | + | 0.246071i | ||||
\(685\) | − | 1.08709i | − | 0.0415355i | ||||||
\(686\) | −11.6556 | + | 14.3926i | −0.445012 | + | 0.549513i | ||||
\(687\) | 40.8118 | − | 10.2230i | 1.55707 | − | 0.390032i | ||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | −22.3316 | − | 18.1669i | −0.850766 | − | 0.692104i | ||||
\(690\) | 11.2915 | − | 2.82843i | 0.429860 | − | 0.107676i | ||||
\(691\) | 15.6110 | 0.593872 | 0.296936 | − | 0.954897i | \(-0.404035\pi\) | ||||
0.296936 | + | 0.954897i | \(0.404035\pi\) | |||||||
\(692\) | −14.4207 | −0.548191 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 2.00393i | − | 0.0760683i | ||||||
\(695\) | −7.29150 | −0.276582 | ||||||||
\(696\) | −0.979531 | − | 3.91044i | −0.0371290 | − | 0.148225i | ||||
\(697\) | − | 47.2588i | − | 1.79005i | ||||||
\(698\) | 15.6110 | 0.590887 | ||||||||
\(699\) | −9.52301 | − | 38.0173i | −0.360193 | − | 1.43794i | ||||
\(700\) | 2.55425 | − | 11.0632i | 0.0965416 | − | 0.418150i | ||||
\(701\) | − | 8.98626i | − | 0.339407i | −0.985495 | − | 0.169703i | \(-0.945719\pi\) | ||
0.985495 | − | 0.169703i | \(-0.0542809\pi\) | |||||||
\(702\) | 1.00000 | + | 18.7083i | 0.0377426 | + | 0.706099i | ||||
\(703\) | 23.4626i | 0.884909i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.0604 | − | 2.77053i | 0.416558 | − | 0.104344i | ||||
\(706\) | 5.83925i | 0.219763i | ||||||||
\(707\) | −3.41699 | + | 14.8000i | −0.128509 | + | 0.556612i | ||||
\(708\) | −1.64575 | − | 6.57008i | −0.0618511 | − | 0.246919i | ||||
\(709\) | 28.7853i | 1.08105i | 0.841327 | + | 0.540526i | \(0.181775\pi\) | ||||
−0.841327 | + | 0.540526i | \(0.818225\pi\) | |||||||
\(710\) | 12.2748i | 0.460667i | ||||||||
\(711\) | −29.8745 | + | 15.9686i | −1.12038 | + | 0.598869i | ||||
\(712\) | − | 12.5730i | − | 0.471194i | ||||||
\(713\) | 44.1547i | 1.65361i | ||||||||
\(714\) | 0.368683 | + | 19.8841i | 0.0137976 | + | 0.744144i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.3137i | 0.422813i | ||||||||
\(717\) | −36.7523 | + | 9.20614i | −1.37254 | + | 0.343809i | ||||
\(718\) | −16.7085 | −0.623556 | ||||||||
\(719\) | −27.3040 | −1.01827 | −0.509133 | − | 0.860688i | \(-0.670034\pi\) | ||||
−0.509133 | + | 0.860688i | \(0.670034\pi\) | |||||||
\(720\) | −1.19038 | − | 2.22699i | −0.0443627 | − | 0.0829950i | ||||
\(721\) | −23.7328 | − | 5.47938i | −0.883857 | − | 0.204063i | ||||
\(722\) | 1.70850 | 0.0635837 | ||||||||
\(723\) | 43.1660 | − | 10.8127i | 1.60536 | − | 0.402130i | ||||
\(724\) | − | 10.6442i | − | 0.395589i | ||||||
\(725\) | − | 9.98823i | − | 0.370954i | ||||||
\(726\) | −18.4816 | + | 4.62948i | −0.685915 | + | 0.171816i | ||||
\(727\) | − | 13.1694i | − | 0.488426i | −0.969722 | − | 0.244213i | \(-0.921470\pi\) | ||
0.969722 | − | 0.244213i | \(-0.0785295\pi\) | |||||||
\(728\) | 5.85608 | + | 7.53036i | 0.217041 | + | 0.279094i | ||||
\(729\) | 2.64575 | − | 26.8701i | 0.0979908 | − | 0.995187i | ||||
\(730\) | 2.65095i | 0.0981162i | ||||||||
\(731\) | −34.7185 | −1.28411 | ||||||||
\(732\) | −2.35425 | − | 9.39851i | −0.0870155 | − | 0.347379i | ||||
\(733\) | −10.4278 | −0.385161 | −0.192581 | − | 0.981281i | \(-0.561686\pi\) | ||||
−0.192581 | + | 0.981281i | \(0.561686\pi\) | |||||||
\(734\) | 8.11905i | 0.299680i | ||||||||
\(735\) | −2.11106 | + | 9.98462i | −0.0778675 | + | 0.368288i | ||||
\(736\) | 7.98430i | 0.294305i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 15.4002 | + | 28.8111i | 0.566889 | + | 1.06055i | ||||
\(739\) | − | 18.7970i | − | 0.691460i | −0.938334 | − | 0.345730i | \(-0.887631\pi\) | ||
0.938334 | − | 0.345730i | \(-0.112369\pi\) | |||||||
\(740\) | −4.33981 | −0.159535 | ||||||||
\(741\) | 12.0399 | − | 25.7424i | 0.442297 | − | 0.945671i | ||||
\(742\) | 20.5830 | + | 4.75216i | 0.755626 | + | 0.174457i | ||||
\(743\) | −7.29150 | −0.267499 | −0.133750 | − | 0.991015i | \(-0.542702\pi\) | ||||
−0.133750 | + | 0.991015i | \(0.542702\pi\) | |||||||
\(744\) | 9.29150 | − | 2.32744i | 0.340643 | − | 0.0853282i | ||||
\(745\) | − | 5.05034i | − | 0.185030i | ||||||
\(746\) | −22.0000 | −0.805477 | ||||||||
\(747\) | 10.2917 | + | 19.2540i | 0.376553 | + | 0.704467i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.5830 | − | 3.36689i | −0.532851 | − | 0.123024i | ||||
\(750\) | −3.29150 | − | 13.1402i | −0.120189 | − | 0.479811i | ||||
\(751\) | 13.1660 | 0.480435 | 0.240217 | − | 0.970719i | \(-0.422781\pi\) | ||||
0.240217 | + | 0.970719i | \(0.422781\pi\) | |||||||
\(752\) | 7.82087i | 0.285198i | ||||||||
\(753\) | 9.64575 | − | 2.41618i | 0.351511 | − | 0.0880505i | ||||
\(754\) | 6.50972 | + | 5.29570i | 0.237070 | + | 0.192858i | ||||
\(755\) | 11.4821 | 0.417875 | ||||||||
\(756\) | −6.70439 | − | 12.0021i | −0.243836 | − | 0.436513i | ||||
\(757\) | 4.58301 | 0.166572 | 0.0832861 | − | 0.996526i | \(-0.473458\pi\) | ||||
0.0832861 | + | 0.996526i | \(0.473458\pi\) | |||||||
\(758\) | 15.1441i | 0.550059i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.83039i | 0.138943i | ||||||||
\(761\) | − | 11.4859i | − | 0.416365i | −0.978090 | − | 0.208183i | \(-0.933245\pi\) | ||
0.978090 | − | 0.208183i | \(-0.0667548\pi\) | |||||||
\(762\) | −11.0604 | + | 2.77053i | −0.400675 | + | 0.100366i | ||||
\(763\) | 39.8745 | + | 9.20614i | 1.44355 | + | 0.333285i | ||||
\(764\) | − | 0.500983i | − | 0.0181249i | ||||||
\(765\) | 5.16601 | + | 9.66472i | 0.186778 | + | 0.349429i | ||||
\(766\) | − | 39.1044i | − | 1.41290i | ||||||
\(767\) | 10.9373 | + | 8.89753i | 0.394921 | + | 0.321271i | ||||
\(768\) | 1.68014 | − | 0.420861i | 0.0606269 | − | 0.0151865i | ||||
\(769\) | −21.7738 | −0.785182 | −0.392591 | − | 0.919713i | \(-0.628421\pi\) | ||||
−0.392591 | + | 0.919713i | \(0.628421\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.5830 | − | 6.65882i | 0.957364 | − | 0.239812i | ||||
\(772\) | 8.48528i | 0.305392i | ||||||||
\(773\) | 10.3460i | 0.372121i | 0.982538 | + | 0.186061i | \(0.0595721\pi\) | ||||
−0.982538 | + | 0.186061i | \(0.940428\pi\) | |||||||
\(774\) | 21.1660 | − | 11.3137i | 0.760797 | − | 0.406663i | ||||
\(775\) | 23.7328 | 0.852508 | ||||||||
\(776\) | 9.87000 | 0.354313 | ||||||||
\(777\) | −23.6231 | + | 0.438010i | −0.847474 | + | 0.0157135i | ||||
\(778\) | − | 12.6392i | − | 0.453137i | ||||||
\(779\) | − | 49.5548i | − | 1.77548i | ||||||
\(780\) | 4.76150 | + | 2.22699i | 0.170489 | + | 0.0797390i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 34.6504i | − | 1.23909i | ||||||
\(783\) | −8.12179 | − | 8.96077i | −0.290249 | − | 0.320232i | ||||
\(784\) | −6.29150 | − | 3.06871i | −0.224697 | − | 0.109597i | ||||
\(785\) | −15.0405 | −0.536819 | ||||||||
\(786\) | −2.35425 | + | 0.589720i | −0.0839733 | + | 0.0210346i | ||||
\(787\) | 54.3971 | 1.93905 | 0.969523 | − | 0.245001i | \(-0.0787881\pi\) | ||||
0.969523 | + | 0.245001i | \(0.0787881\pi\) | |||||||
\(788\) | 8.58301 | 0.305757 | ||||||||
\(789\) | 6.93141 | + | 27.6712i | 0.246765 | + | 0.985122i | ||||
\(790\) | 9.50432i | 0.338148i | ||||||||
\(791\) | −36.4575 | − | 8.41723i | −1.29628 | − | 0.299282i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.6458 | + | 12.7279i | 0.555597 | + | 0.451982i | ||||
\(794\) | −16.0327 | −0.568980 | ||||||||
\(795\) | 11.2915 | − | 2.82843i | 0.400468 | − | 0.100314i | ||||
\(796\) | 25.4442i | 0.901847i | ||||||||
\(797\) | 8.54348 | 0.302625 | 0.151313 | − | 0.988486i | \(-0.451650\pi\) | ||||
0.151313 | + | 0.988486i | \(0.451650\pi\) | |||||||
\(798\) | 0.386595 | + | 20.8502i | 0.0136853 | + | 0.738088i | ||||
\(799\) | − | 33.9411i | − | 1.20075i | ||||||
\(800\) | 4.29150 | 0.151728 | ||||||||
\(801\) | −17.7809 | − | 33.2651i | −0.628259 | − | 1.17536i | ||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.768687 | − | 3.06871i | −0.0271095 | − | 0.108225i | ||||
\(805\) | 4.00000 | − | 17.3252i | 0.140981 | − | 0.610633i | ||||
\(806\) | −12.5830 | + | 15.4676i | −0.443217 | + | 0.544823i | ||||
\(807\) | 38.8118 | − | 9.72202i | 1.36624 | − | 0.342231i | ||||
\(808\) | −5.74103 | −0.201969 | ||||||||
\(809\) | − | 0.177473i | − | 0.00623961i | −0.999995 | − | 0.00311980i | \(-0.999007\pi\) | ||
0.999995 | − | 0.00311980i | \(-0.000993066\pi\) | |||||||
\(810\) | −6.29888 | − | 4.20861i | −0.221320 | − | 0.147876i | ||||
\(811\) | −6.08803 | −0.213780 | −0.106890 | − | 0.994271i | \(-0.534089\pi\) | ||||
−0.106890 | + | 0.994271i | \(0.534089\pi\) | |||||||
\(812\) | −6.00000 | − | 1.38527i | −0.210559 | − | 0.0486133i | ||||
\(813\) | −39.1660 | + | 9.81076i | −1.37361 | + | 0.344078i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.14226 | −0.250182 | ||||||||
\(816\) | −7.29150 | + | 1.82646i | −0.255254 | + | 0.0639389i | ||||
\(817\) | −36.4053 | −1.27366 | ||||||||
\(818\) | 1.19038 | 0.0416205 | ||||||||
\(819\) | 26.1433 | + | 11.6417i | 0.913520 | + | 0.406794i | ||||
\(820\) | 9.16601 | 0.320091 | ||||||||
\(821\) | 42.0000 | 1.46581 | 0.732905 | − | 0.680331i | \(-0.238164\pi\) | ||||
0.732905 | + | 0.680331i | \(0.238164\pi\) | |||||||
\(822\) | 2.16991 | − | 0.543544i | 0.0756842 | − | 0.0189583i | ||||
\(823\) | −25.8745 | −0.901929 | −0.450964 | − | 0.892542i | \(-0.648920\pi\) | ||||
−0.450964 | + | 0.892542i | \(0.648920\pi\) | |||||||
\(824\) | − | 9.20614i | − | 0.320711i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.0808 | − | 2.32744i | −0.350758 | − | 0.0809821i | ||||
\(827\) | 43.7490 | 1.52130 | 0.760651 | − | 0.649161i | \(-0.224880\pi\) | ||||
0.760651 | + | 0.649161i | \(0.224880\pi\) | |||||||
\(828\) | 11.2915 | + | 21.1245i | 0.392407 | + | 0.734126i | ||||
\(829\) | − | 30.1436i | − | 1.04693i | −0.852047 | − | 0.523465i | \(-0.824639\pi\) | ||
0.852047 | − | 0.523465i | \(-0.175361\pi\) | |||||||
\(830\) | 6.12549 | 0.212619 | ||||||||
\(831\) | 52.3633 | − | 13.1166i | 1.81646 | − | 0.455009i | ||||
\(832\) | −2.27533 | + | 2.79694i | −0.0788829 | + | 0.0969665i | ||||
\(833\) | 27.3040 | + | 13.3176i | 0.946026 | + | 0.461429i | ||||
\(834\) | −3.64575 | − | 14.5544i | −0.126242 | − | 0.503977i | ||||
\(835\) | 1.41699 | 0.0490371 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.2915 | − | 19.2980i | 0.735942 | − | 0.667037i | ||||
\(838\) | 25.9027 | 0.894795 | ||||||||
\(839\) | 48.6087i | 1.67816i | 0.544010 | + | 0.839079i | \(0.316905\pi\) | ||||
−0.544010 | + | 0.839079i | \(0.683095\pi\) | |||||||
\(840\) | −3.85660 | + | 0.0715074i | −0.133065 | + | 0.00246724i | ||||
\(841\) | 23.5830 | 0.813207 | ||||||||
\(842\) | − | 11.8147i | − | 0.407161i | ||||||
\(843\) | 22.3316 | − | 5.59388i | 0.769141 | − | 0.192663i | ||||
\(844\) | 10.5830 | 0.364282 | ||||||||
\(845\) | −10.7134 | + | 2.22699i | −0.368552 | + | 0.0766108i | ||||
\(846\) | 11.0604 | + | 20.6921i | 0.380264 | + | 0.711408i | ||||
\(847\) | −6.54707 | + | 28.3573i | −0.224960 | + | 0.974368i | ||||
\(848\) | 7.98430i | 0.274182i | ||||||||
\(849\) | 6.22876 | + | 24.8661i | 0.213770 | + | 0.853403i | ||||
\(850\) | −18.6243 | −0.638809 | ||||||||
\(851\) | 41.1660 | 1.41115 | ||||||||
\(852\) | −24.5015 | + | 6.13742i | −0.839408 | + | 0.210265i | ||||
\(853\) | 35.7727 | 1.22484 | 0.612418 | − | 0.790534i | \(-0.290197\pi\) | ||||
0.612418 | + | 0.790534i | \(0.290197\pi\) | |||||||
\(854\) | −14.4207 | − | 3.32941i | −0.493465 | − | 0.113930i | ||||
\(855\) | 5.41699 | + | 10.1343i | 0.185257 | + | 0.346585i | ||||
\(856\) | − | 5.65685i | − | 0.193347i | ||||||
\(857\) | 20.1617 | 0.688711 | 0.344355 | − | 0.938839i | \(-0.388098\pi\) | ||||
0.344355 | + | 0.938839i | \(0.388098\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2123i | 1.13319i | 0.823997 | + | 0.566594i | \(0.191739\pi\) | ||||
−0.823997 | + | 0.566594i | \(0.808261\pi\) | |||||||
\(860\) | − | 6.73378i | − | 0.229620i | ||||||
\(861\) | 49.8938 | − | 0.925109i | 1.70037 | − | 0.0315276i | ||||
\(862\) | 7.29150 | 0.248350 | ||||||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 3.85005 | − | 3.48957i | 0.130981 | − | 0.118718i | ||||
\(865\) | 12.1382i | 0.412711i | ||||||||
\(866\) | 17.3252i | 0.588734i | ||||||||
\(867\) | 3.08136 | − | 0.771855i | 0.104649 | − | 0.0262136i | ||||
\(868\) | 3.29150 | − | 14.2565i | 0.111721 | − | 0.483896i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.29150 | + | 0.824494i | −0.111592 | + | 0.0279530i | ||||
\(871\) | 5.10850 | + | 4.15580i | 0.173095 | + | 0.140814i | ||||
\(872\) | 15.4676i | 0.523799i | ||||||||
\(873\) | 26.1136 | − | 13.9583i | 0.883811 | − | 0.472417i | ||||
\(874\) | − | 36.3338i | − | 1.22901i | ||||||
\(875\) | −20.1617 | − | 4.65489i | −0.681590 | − | 0.157364i | ||||
\(876\) | −5.29150 | + | 1.32548i | −0.178783 | + | 0.0447837i | ||||
\(877\) | − | 36.0911i | − | 1.21871i | −0.792898 | − | 0.609355i | \(-0.791428\pi\) | ||
0.792898 | − | 0.609355i | \(-0.208572\pi\) | |||||||
\(878\) | 8.11905i | 0.274005i | ||||||||
\(879\) | −5.52026 | − | 22.0377i | −0.186194 | − | 0.743313i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.5015 | −0.825477 | −0.412738 | − | 0.910850i | \(-0.635428\pi\) | ||||
−0.412738 | + | 0.910850i | \(0.635428\pi\) | |||||||
\(882\) | −20.9856 | + | 0.778479i | −0.706621 | + | 0.0262127i | ||||
\(883\) | −6.58301 | −0.221536 | −0.110768 | − | 0.993846i | \(-0.535331\pi\) | ||||
−0.110768 | + | 0.993846i | \(0.535331\pi\) | |||||||
\(884\) | 9.87451 | − | 12.1382i | 0.332116 | − | 0.408252i | ||||
\(885\) | −5.53019 | + | 1.38527i | −0.185895 | + | 0.0465652i | ||||
\(886\) | − | 5.65685i | − | 0.190046i | ||||||
\(887\) | 44.6632 | 1.49964 | 0.749822 | − | 0.661640i | \(-0.230139\pi\) | ||||
0.749822 | + | 0.661640i | \(0.230139\pi\) | |||||||
\(888\) | −2.16991 | − | 8.66259i | −0.0728173 | − | 0.290698i | ||||
\(889\) | −3.91813 | + | 16.9706i | −0.131410 | + | 0.569174i | ||||
\(890\) | −10.5830 | −0.354743 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.6315 | −0.489899 | ||||||||
\(893\) | − | 35.5901i | − | 1.19098i | ||||||
\(894\) | 10.0808 | − | 2.52517i | 0.337154 | − | 0.0844543i | ||||
\(895\) | 9.52301 | 0.318319 | ||||||||
\(896\) | 0.595188 | − | 2.57794i | 0.0198838 | − | 0.0861228i | ||||
\(897\) | −45.1660 | − | 21.1245i | −1.50805 | − | 0.705325i | ||||
\(898\) | −30.4575 | −1.01638 | ||||||||
\(899\) | − | 12.8712i | − | 0.429279i | ||||||
\(900\) | 11.3542 | − | 6.06910i | 0.378475 | − | 0.202303i | ||||
\(901\) | − | 34.6504i | − | 1.15437i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.679629 | − | 36.6543i | −0.0226166 | − | 1.21978i | ||||
\(904\) | − | 14.1421i | − | 0.470360i | ||||||
\(905\) | −8.95948 | −0.297823 | ||||||||
\(906\) | 5.74103 | + | 22.9191i | 0.190733 | + | 0.761435i | ||||
\(907\) | −4.00000 | −0.132818 | −0.0664089 | − | 0.997792i | \(-0.521154\pi\) | ||||
−0.0664089 | + | 0.997792i | \(0.521154\pi\) | |||||||
\(908\) | − | 8.96077i | − | 0.297374i | ||||||
\(909\) | −15.1894 | + | 8.11905i | −0.503799 | + | 0.269292i | ||||
\(910\) | 6.33847 | − | 4.92920i | 0.210118 | − | 0.163401i | ||||
\(911\) | 21.3019i | 0.705765i | 0.935668 | + | 0.352882i | \(0.114798\pi\) | ||||
−0.935668 | + | 0.352882i | \(0.885202\pi\) | |||||||
\(912\) | −7.64575 | + | 1.91520i | −0.253176 | + | 0.0634185i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 12.1382i | − | 0.401496i | ||||||
\(915\) | −7.91094 | + | 1.98162i | −0.261528 | + | 0.0655105i | ||||
\(916\) | 24.2907 | 0.802586 | ||||||||
\(917\) | −0.833990 | + | 3.61226i | −0.0275408 | + | 0.119287i | ||||
\(918\) | −16.7085 | + | 15.1441i | −0.551463 | + | 0.499830i | ||||
\(919\) | −1.87451 | −0.0618343 | −0.0309172 | − | 0.999522i | \(-0.509843\pi\) | ||||
−0.0309172 | + | 0.999522i | \(0.509843\pi\) | |||||||
\(920\) | 6.72057 | 0.221571 | ||||||||
\(921\) | −14.9373 | + | 3.74166i | −0.492199 | + | 0.123292i | ||||
\(922\) | 15.3964i | 0.507053i | ||||||||
\(923\) | 33.1811 | − | 40.7878i | 1.09217 | − | 1.34255i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 22.1264i | − | 0.727513i | ||||||
\(926\) | 25.7794i | 0.847162i | ||||||||
\(927\) | −13.0194 | − | 24.3571i | −0.427615 | − | 0.799994i | ||||
\(928\) | − | 2.32744i | − | 0.0764021i | ||||||
\(929\) | 35.4393i | 1.16273i | 0.813645 | + | 0.581363i | \(0.197480\pi\) | ||||
−0.813645 | + | 0.581363i | \(0.802520\pi\) | |||||||
\(930\) | −1.95906 | − | 7.82087i | −0.0642402 | − | 0.256456i | ||||
\(931\) | 28.6305 | + | 13.9647i | 0.938326 | + | 0.457673i | ||||
\(932\) | − | 22.6274i | − | 0.741186i | ||||||
\(933\) | −12.0000 | + | 3.00590i | −0.392862 | + | 0.0984087i | ||||
\(934\) | 7.27841 | 0.238157 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.06448 | + | 10.6178i | −0.0674798 | + | 0.347054i | ||||
\(937\) | 40.7878i | 1.33248i | 0.745738 | + | 0.666240i | \(0.232097\pi\) | ||||
−0.745738 | + | 0.666240i | \(0.767903\pi\) | |||||||
\(938\) | −4.70850 | − | 1.08709i | −0.153738 | − | 0.0354947i | ||||
\(939\) | −14.1255 | − | 56.3911i | −0.460968 | − | 1.84025i | ||||
\(940\) | 6.58301 | 0.214714 | ||||||||
\(941\) | − | 10.9424i | − | 0.356712i | −0.983966 | − | 0.178356i | \(-0.942922\pi\) | ||
0.983966 | − | 0.178356i | \(-0.0570779\pi\) | |||||||
\(942\) | −7.52026 | − | 30.0220i | −0.245023 | − | 0.978169i | ||||
\(943\) | −86.9457 | −2.83134 | ||||||||
\(944\) | − | 3.91044i | − | 0.127274i | ||||||
\(945\) | −10.1025 | + | 5.64324i | −0.328633 | + | 0.183575i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.0000 | 1.16984 | 0.584921 | − | 0.811090i | \(-0.301125\pi\) | ||||
0.584921 | + | 0.811090i | \(0.301125\pi\) | |||||||
\(948\) | −18.9713 | + | 4.75216i | −0.616160 | + | 0.154343i | ||||
\(949\) | 7.16601 | − | 8.80879i | 0.232619 | − | 0.285945i | ||||
\(950\) | −19.5292 | −0.633610 | ||||||||
\(951\) | −10.0808 | + | 2.52517i | −0.326894 | + | 0.0818842i | ||||
\(952\) | −2.58301 | + | 11.1878i | −0.0837157 | + | 0.362597i | ||||
\(953\) | − | 19.6215i | − | 0.635603i | −0.948157 | − | 0.317802i | \(-0.897055\pi\) | ||
0.948157 | − | 0.317802i | \(-0.102945\pi\) | |||||||
\(954\) | 11.2915 | + | 21.1245i | 0.365576 | + | 0.683930i | ||||
\(955\) | −0.421689 | −0.0136455 | ||||||||
\(956\) | −21.8745 | −0.707472 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.9215i | 0.579019i | ||||||||
\(959\) | 0.768687 | − | 3.32941i | 0.0248222 | − | 0.107512i | ||||
\(960\) | −0.354249 | − | 1.41421i | −0.0114333 | − | 0.0456435i | ||||
\(961\) | −0.416995 | −0.0134514 | ||||||||
\(962\) | 14.4207 | + | 11.7313i | 0.464941 | + | 0.378232i | ||||
\(963\) | −8.00000 | − | 14.9666i | −0.257796 | − | 0.482293i | ||||
\(964\) | 25.6919 | 0.827480 | ||||||||
\(965\) | 7.14226 | 0.229917 | ||||||||
\(966\) | 36.5824 | − | 0.678295i | 1.17702 | − | 0.0218238i | ||||
\(967\) | − | 23.9529i | − | 0.770273i | −0.922860 | − | 0.385137i | \(-0.874154\pi\) | ||
0.922860 | − | 0.385137i | \(-0.125846\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 33.1811 | − | 8.31160i | 1.06593 | − | 0.267007i | ||||
\(970\) | − | 8.30781i | − | 0.266748i | ||||||
\(971\) | −36.1197 | −1.15914 | −0.579569 | − | 0.814923i | \(-0.696779\pi\) | ||||
−0.579569 | + | 0.814923i | \(0.696779\pi\) | |||||||
\(972\) | 5.25127 | − | 14.6773i | 0.168435 | − | 0.470776i | ||||
\(973\) | −22.3316 | − | 5.15587i | −0.715918 | − | 0.165290i | ||||
\(974\) | − | 17.2941i | − | 0.554138i | ||||||
\(975\) | −11.3542 | + | 24.2764i | −0.363627 | + | 0.777467i | ||||
\(976\) | − | 5.59388i | − | 0.179056i | ||||||
\(977\) | −54.4575 | −1.74225 | −0.871125 | − | 0.491061i | \(-0.836609\pi\) | ||||
−0.871125 | + | 0.491061i | \(0.836609\pi\) | |||||||
\(978\) | −3.57113 | − | 14.2565i | −0.114192 | − | 0.455872i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.58301 | + | 5.29570i | −0.0825111 | + | 0.169165i | ||||
\(981\) | 21.8745 | + | 40.9235i | 0.698399 | + | 1.30659i | ||||
\(982\) | − | 26.2803i | − | 0.838639i | ||||||
\(983\) | 3.85762i | 0.123039i | 0.998106 | + | 0.0615195i | \(0.0195946\pi\) | ||||
−0.998106 | + | 0.0615195i | \(0.980405\pi\) | |||||||
\(984\) | 4.58301 | + | 18.2960i | 0.146101 | + | 0.583256i | ||||
\(985\) | − | 7.22451i | − | 0.230192i | ||||||
\(986\) | 10.1007i | 0.321671i | ||||||||
\(987\) | 35.8336 | − | 0.664411i | 1.14060 | − | 0.0211484i | ||||
\(988\) | 10.3542 | − | 12.7279i | 0.329413 | − | 0.404929i | ||||
\(989\) | 63.8744i | 2.03109i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.2915 | −0.358686 | −0.179343 | − | 0.983787i | \(-0.557397\pi\) | ||||
−0.179343 | + | 0.983787i | \(0.557397\pi\) | |||||||
\(992\) | 5.53019 | 0.175584 | ||||||||
\(993\) | −3.57113 | − | 14.2565i | −0.113326 | − | 0.452416i | ||||
\(994\) | −8.67963 | + | 37.5940i | −0.275301 | + | 1.19241i | ||||
\(995\) | 21.4170 | 0.678964 | ||||||||
\(996\) | 3.06275 | + | 12.2269i | 0.0970468 | + | 0.387425i | ||||
\(997\) | 12.8184i | 0.405963i | 0.979183 | + | 0.202981i | \(0.0650631\pi\) | ||||
−0.979183 | + | 0.202981i | \(0.934937\pi\) | |||||||
\(998\) | 18.7970i | 0.595009i | ||||||||
\(999\) | −17.9918 | − | 19.8504i | −0.569235 | − | 0.628037i |
(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 | 546.2.e.h.545.7 | yes | 8 | |
3.2 | odd | 2 | 546.2.e.f.545.1 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 546.2.e.h.545.2 | yes | 8 | |
13.12 | even | 2 | 546.2.e.f.545.7 | yes | 8 | ||
21.20 | even | 2 | 546.2.e.f.545.8 | yes | 8 | ||
39.38 | odd | 2 | inner | 546.2.e.h.545.1 | yes | 8 | |
91.90 | odd | 2 | 546.2.e.f.545.2 | yes | 8 | ||
273.272 | even | 2 | inner | 546.2.e.h.545.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.e.f.545.1 | ✓ | 8 | 3.2 | odd | 2 | ||
546.2.e.f.545.2 | yes | 8 | 91.90 | odd | 2 | ||
546.2.e.f.545.7 | yes | 8 | 13.12 | even | 2 | ||
546.2.e.f.545.8 | yes | 8 | 21.20 | even | 2 | ||
546.2.e.h.545.1 | yes | 8 | 39.38 | odd | 2 | inner | |
546.2.e.h.545.2 | yes | 8 | 7.6 | odd | 2 | inner | |
546.2.e.h.545.7 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.e.h.545.8 | yes | 8 | 273.272 | even | 2 | inner |