Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1351,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.b (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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.2 | ||
Root | \(2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1351 |
Dual form | 1950.2.b.k.1351.3 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | 4.60555i | 1.74073i | 0.492403 | + | 0.870367i | \(0.336119\pi\) | ||||
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.60555 | −1.00000 | ||||||||
\(14\) | 4.60555 | 1.23089 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.60555 | −1.11701 | −0.558505 | − | 0.829501i | \(-0.688625\pi\) | ||||
−0.558505 | + | 0.829501i | \(0.688625\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 4.60555i | − 1.05659i | −0.849062 | − | 0.528293i | \(-0.822832\pi\) | ||||
0.849062 | − | 0.528293i | \(-0.177168\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.60555i | 1.00501i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.39445 | 0.290763 | 0.145381 | − | 0.989376i | \(-0.453559\pi\) | ||||
0.145381 | + | 0.989376i | \(0.453559\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.60555i | 0.707107i | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 4.60555i | − 0.870367i | ||||||||
\(29\) | 4.60555 | 0.855229 | 0.427615 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427615 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000i | 1.07763i | 0.842424 | + | 0.538816i | \(0.181128\pi\) | ||||
−0.842424 | + | 0.538816i | \(0.818872\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.60555i | 0.789846i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 9.21110i | 1.51430i | 0.653243 | + | 0.757148i | \(0.273408\pi\) | ||||
−0.653243 | + | 0.757148i | \(0.726592\pi\) | |||||||
\(38\) | −4.60555 | −0.747119 | ||||||||
\(39\) | −3.60555 | −0.577350 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.21110i | 0.501490i | 0.968053 | + | 0.250745i | \(0.0806756\pi\) | ||||
−0.968053 | + | 0.250745i | \(0.919324\pi\) | |||||||
\(42\) | 4.60555 | 0.710652 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 1.39445i | − 0.205600i | ||||||||
\(47\) | 9.21110i | 1.34358i | 0.740743 | + | 0.671789i | \(0.234474\pi\) | ||||
−0.740743 | + | 0.671789i | \(0.765526\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −14.2111 | −2.03016 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60555 | −0.644906 | ||||||||
\(52\) | 3.60555 | 0.500000 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.60555 | −0.615443 | ||||||||
\(57\) | − 4.60555i | − 0.610020i | ||||||||
\(58\) | − 4.60555i | − 0.604739i | ||||||||
\(59\) | − 9.21110i | − 1.19918i | −0.800306 | − | 0.599592i | \(-0.795330\pi\) | ||||
0.800306 | − | 0.599592i | \(-0.204670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2111 | −1.43543 | −0.717717 | − | 0.696335i | \(-0.754813\pi\) | ||||
−0.717717 | + | 0.696335i | \(0.754813\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 4.60555i | 0.580245i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.21110i | 0.392299i | 0.980574 | + | 0.196149i | \(0.0628437\pi\) | ||||
−0.980574 | + | 0.196149i | \(0.937156\pi\) | |||||||
\(68\) | 4.60555 | 0.558505 | ||||||||
\(69\) | 1.39445 | 0.167872 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.21110i | 1.09316i | 0.837408 | + | 0.546578i | \(0.184070\pi\) | ||||
−0.837408 | + | 0.546578i | \(0.815930\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 1.39445i | 0.163208i | 0.996665 | + | 0.0816039i | \(0.0260043\pi\) | ||||
−0.996665 | + | 0.0816039i | \(0.973996\pi\) | |||||||
\(74\) | 9.21110 | 1.07077 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.60555i | 0.528293i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.60555i | 0.408248i | ||||||||
\(79\) | −14.4222 | −1.62262 | −0.811312 | − | 0.584613i | \(-0.801246\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.21110 | 0.354607 | ||||||||
\(83\) | − 2.78890i | − 0.306121i | −0.988217 | − | 0.153061i | \(-0.951087\pi\) | ||||
0.988217 | − | 0.153061i | \(-0.0489130\pi\) | |||||||
\(84\) | − 4.60555i | − 0.502507i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000i | 0.862662i | ||||||||
\(87\) | 4.60555 | 0.493767 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.2111i | 1.61237i | 0.591661 | + | 0.806187i | \(0.298472\pi\) | ||||
−0.591661 | + | 0.806187i | \(0.701528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 16.6056i | − 1.74073i | ||||||||
\(92\) | −1.39445 | −0.145381 | ||||||||
\(93\) | 6.00000i | 0.622171i | ||||||||
\(94\) | 9.21110 | 0.950053 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | − 1.39445i | − 0.141585i | −0.997491 | − | 0.0707924i | \(-0.977447\pi\) | ||||
0.997491 | − | 0.0707924i | \(-0.0225528\pi\) | |||||||
\(98\) | 14.2111i | 1.43554i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.39445 | −0.735775 | −0.367888 | − | 0.929870i | \(-0.619919\pi\) | ||||
−0.367888 | + | 0.929870i | \(0.619919\pi\) | |||||||
\(102\) | 4.60555i | 0.456018i | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | − 3.60555i | − 0.353553i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000i | 0.582772i | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.39445i | 0.133564i | 0.997768 | + | 0.0667820i | \(0.0212732\pi\) | ||||
−0.997768 | + | 0.0667820i | \(0.978727\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.21110i | 0.874279i | ||||||||
\(112\) | 4.60555i | 0.435184i | ||||||||
\(113\) | 13.8167 | 1.29976 | 0.649881 | − | 0.760036i | \(-0.274819\pi\) | ||||
0.649881 | + | 0.760036i | \(0.274819\pi\) | |||||||
\(114\) | −4.60555 | −0.431349 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.60555 | −0.427615 | ||||||||
\(117\) | −3.60555 | −0.333333 | ||||||||
\(118\) | −9.21110 | −0.847951 | ||||||||
\(119\) | − 21.2111i | − 1.94442i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 11.2111i | 1.01501i | ||||||||
\(123\) | 3.21110i | 0.289535i | ||||||||
\(124\) | − 6.00000i | − 0.538816i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.60555 | 0.410295 | ||||||||
\(127\) | −1.21110 | −0.107468 | −0.0537340 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537340 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.6056 | 1.97506 | 0.987528 | − | 0.157443i | \(-0.0503250\pi\) | ||||
0.987528 | + | 0.157443i | \(0.0503250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.2111 | 1.83924 | ||||||||
\(134\) | 3.21110 | 0.277397 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 4.60555i | − 0.394923i | ||||||||
\(137\) | − 3.21110i | − 0.274343i | −0.990547 | − | 0.137172i | \(-0.956199\pi\) | ||||
0.990547 | − | 0.137172i | \(-0.0438011\pi\) | |||||||
\(138\) | − 1.39445i | − 0.118703i | ||||||||
\(139\) | 17.2111 | 1.45983 | 0.729913 | − | 0.683540i | \(-0.239560\pi\) | ||||
0.729913 | + | 0.683540i | \(0.239560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.21110i | 0.775715i | ||||||||
\(142\) | 9.21110 | 0.772979 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.39445 | 0.115405 | ||||||||
\(147\) | −14.2111 | −1.17211 | ||||||||
\(148\) | − 9.21110i | − 0.757148i | ||||||||
\(149\) | 15.2111i | 1.24614i | 0.782165 | + | 0.623071i | \(0.214115\pi\) | ||||
−0.782165 | + | 0.623071i | \(0.785885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.00000i | 0.488273i | 0.969741 | + | 0.244137i | \(0.0785045\pi\) | ||||
−0.969741 | + | 0.244137i | \(0.921495\pi\) | |||||||
\(152\) | 4.60555 | 0.373560 | ||||||||
\(153\) | −4.60555 | −0.372337 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.60555 | 0.288675 | ||||||||
\(157\) | −20.4222 | −1.62987 | −0.814935 | − | 0.579553i | \(-0.803227\pi\) | ||||
−0.814935 | + | 0.579553i | \(0.803227\pi\) | |||||||
\(158\) | 14.4222i | 1.14737i | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.42221i | 0.506141i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 24.4222i | − 1.91289i | −0.291905 | − | 0.956447i | \(-0.594289\pi\) | ||||
0.291905 | − | 0.956447i | \(-0.405711\pi\) | |||||||
\(164\) | − 3.21110i | − 0.250745i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.78890 | −0.216460 | ||||||||
\(167\) | − 9.21110i | − 0.712777i | −0.934338 | − | 0.356388i | \(-0.884008\pi\) | ||||
0.934338 | − | 0.356388i | \(-0.115992\pi\) | |||||||
\(168\) | −4.60555 | −0.355326 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 4.60555i | − 0.352195i | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 12.4222 | 0.944443 | 0.472221 | − | 0.881480i | \(-0.343452\pi\) | ||||
0.472221 | + | 0.881480i | \(0.343452\pi\) | |||||||
\(174\) | − 4.60555i | − 0.349146i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 9.21110i | − 0.692349i | ||||||||
\(178\) | 15.2111 | 1.14012 | ||||||||
\(179\) | −19.8167 | −1.48117 | −0.740583 | − | 0.671965i | \(-0.765451\pi\) | ||||
−0.740583 | + | 0.671965i | \(0.765451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.42221 | 0.626018 | 0.313009 | − | 0.949750i | \(-0.398663\pi\) | ||||
0.313009 | + | 0.949750i | \(0.398663\pi\) | |||||||
\(182\) | −16.6056 | −1.23089 | ||||||||
\(183\) | −11.2111 | −0.828749 | ||||||||
\(184\) | 1.39445i | 0.102800i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 9.21110i | − 0.671789i | ||||||||
\(189\) | 4.60555i | 0.335005i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − 7.81665i | − 0.562655i | −0.959612 | − | 0.281328i | \(-0.909225\pi\) | ||||
0.959612 | − | 0.281328i | \(-0.0907747\pi\) | |||||||
\(194\) | −1.39445 | −0.100116 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.2111 | 1.01508 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.4222 | 1.58947 | 0.794734 | − | 0.606958i | \(-0.207610\pi\) | ||||
0.794734 | + | 0.606958i | \(0.207610\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.21110i | 0.226494i | ||||||||
\(202\) | 7.39445i | 0.520272i | ||||||||
\(203\) | 21.2111i | 1.48873i | ||||||||
\(204\) | 4.60555 | 0.322453 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − 4.00000i | − 0.278693i | ||||||||
\(207\) | 1.39445 | 0.0969209 | ||||||||
\(208\) | −3.60555 | −0.250000 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2111 | −1.18486 | −0.592431 | − | 0.805622i | \(-0.701832\pi\) | ||||
−0.592431 | + | 0.805622i | \(0.701832\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 9.21110i | 0.631134i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −27.6333 | −1.87587 | ||||||||
\(218\) | 1.39445 | 0.0944440 | ||||||||
\(219\) | 1.39445i | 0.0942281i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.6056 | 1.11701 | ||||||||
\(222\) | 9.21110 | 0.618209 | ||||||||
\(223\) | − 1.81665i | − 0.121652i | −0.998148 | − | 0.0608261i | \(-0.980627\pi\) | ||||
0.998148 | − | 0.0608261i | \(-0.0193735\pi\) | |||||||
\(224\) | 4.60555 | 0.307721 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 13.8167i | − 0.919070i | ||||||||
\(227\) | − 24.0000i | − 1.59294i | −0.604681 | − | 0.796468i | \(-0.706699\pi\) | ||||
0.604681 | − | 0.796468i | \(-0.293301\pi\) | |||||||
\(228\) | 4.60555i | 0.305010i | ||||||||
\(229\) | − 19.8167i | − 1.30952i | −0.755836 | − | 0.654761i | \(-0.772769\pi\) | ||||
0.755836 | − | 0.654761i | \(-0.227231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.60555i | 0.302369i | ||||||||
\(233\) | 1.81665 | 0.119013 | 0.0595065 | − | 0.998228i | \(-0.481047\pi\) | ||||
0.0595065 | + | 0.998228i | \(0.481047\pi\) | |||||||
\(234\) | 3.60555i | 0.235702i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.21110i | 0.599592i | ||||||||
\(237\) | −14.4222 | −0.936823 | ||||||||
\(238\) | −21.2111 | −1.37491 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 6.42221i | − 0.413691i | −0.978374 | − | 0.206845i | \(-0.933680\pi\) | ||||
0.978374 | − | 0.206845i | \(-0.0663197\pi\) | |||||||
\(242\) | − 11.0000i | − 0.707107i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.2111 | 0.717717 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.21110 | 0.204732 | ||||||||
\(247\) | 16.6056i | 1.05659i | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | − 2.78890i | − 0.176739i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3944 | −0.845450 | −0.422725 | − | 0.906258i | \(-0.638926\pi\) | ||||
−0.422725 | + | 0.906258i | \(0.638926\pi\) | |||||||
\(252\) | − 4.60555i | − 0.290122i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.21110i | 0.0759913i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.6056 | 1.78437 | 0.892183 | − | 0.451675i | \(-0.149173\pi\) | ||||
0.892183 | + | 0.451675i | \(0.149173\pi\) | |||||||
\(258\) | 8.00000i | 0.498058i | ||||||||
\(259\) | −42.4222 | −2.63599 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.60555 | 0.285076 | ||||||||
\(262\) | − 22.6056i | − 1.39658i | ||||||||
\(263\) | 7.81665 | 0.481996 | 0.240998 | − | 0.970526i | \(-0.422525\pi\) | ||||
0.240998 | + | 0.970526i | \(0.422525\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − 21.2111i | − 1.30054i | ||||||||
\(267\) | 15.2111i | 0.930904i | ||||||||
\(268\) | − 3.21110i | − 0.196149i | ||||||||
\(269\) | 25.8167 | 1.57407 | 0.787035 | − | 0.616909i | \(-0.211615\pi\) | ||||
0.787035 | + | 0.616909i | \(0.211615\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 0.422205i | − 0.0256471i | −0.999918 | − | 0.0128236i | \(-0.995918\pi\) | ||||
0.999918 | − | 0.0128236i | \(-0.00408198\pi\) | |||||||
\(272\) | −4.60555 | −0.279253 | ||||||||
\(273\) | − 16.6056i | − 1.00501i | ||||||||
\(274\) | −3.21110 | −0.193990 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.39445 | −0.0839359 | ||||||||
\(277\) | 16.4222 | 0.986715 | 0.493357 | − | 0.869827i | \(-0.335770\pi\) | ||||
0.493357 | + | 0.869827i | \(0.335770\pi\) | |||||||
\(278\) | − 17.2111i | − 1.03225i | ||||||||
\(279\) | 6.00000i | 0.359211i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2111i | 1.62328i | 0.584159 | + | 0.811639i | \(0.301424\pi\) | ||||
−0.584159 | + | 0.811639i | \(0.698576\pi\) | |||||||
\(282\) | 9.21110 | 0.548513 | ||||||||
\(283\) | −10.4222 | −0.619536 | −0.309768 | − | 0.950812i | \(-0.600251\pi\) | ||||
−0.309768 | + | 0.950812i | \(0.600251\pi\) | |||||||
\(284\) | − 9.21110i | − 0.546578i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.7889 | −0.872961 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | 4.21110 | 0.247712 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.39445i | − 0.0817440i | ||||||||
\(292\) | − 1.39445i | − 0.0816039i | ||||||||
\(293\) | − 18.0000i | − 1.05157i | −0.850617 | − | 0.525786i | \(-0.823771\pi\) | ||||
0.850617 | − | 0.525786i | \(-0.176229\pi\) | |||||||
\(294\) | 14.2111i | 0.828808i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.21110 | −0.535384 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2111 | 0.881156 | ||||||||
\(299\) | −5.02776 | −0.290763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 36.8444i | − 2.12368i | ||||||||
\(302\) | 6.00000 | 0.345261 | ||||||||
\(303\) | −7.39445 | −0.424800 | ||||||||
\(304\) | − 4.60555i | − 0.264146i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.60555i | 0.263282i | ||||||||
\(307\) | 8.78890i | 0.501609i | 0.968038 | + | 0.250804i | \(0.0806951\pi\) | ||||
−0.968038 | + | 0.250804i | \(0.919305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | − 3.60555i | − 0.204124i | ||||||||
\(313\) | −3.57779 | −0.202229 | −0.101114 | − | 0.994875i | \(-0.532241\pi\) | ||||
−0.101114 | + | 0.994875i | \(0.532241\pi\) | |||||||
\(314\) | 20.4222i | 1.15249i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.4222 | 0.811312 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 6.00000i | 0.336463i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.42221 | 0.357895 | ||||||||
\(323\) | 21.2111i | 1.18022i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −24.4222 | −1.35262 | ||||||||
\(327\) | 1.39445i | 0.0771132i | ||||||||
\(328\) | −3.21110 | −0.177303 | ||||||||
\(329\) | −42.4222 | −2.33881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 16.6056i | − 0.912724i | −0.889794 | − | 0.456362i | \(-0.849152\pi\) | ||||
0.889794 | − | 0.456362i | \(-0.150848\pi\) | |||||||
\(332\) | 2.78890i | 0.153061i | ||||||||
\(333\) | 9.21110i | 0.504765i | ||||||||
\(334\) | −9.21110 | −0.504009 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.60555i | 0.251253i | ||||||||
\(337\) | −13.6333 | −0.742654 | −0.371327 | − | 0.928502i | \(-0.621097\pi\) | ||||
−0.371327 | + | 0.928502i | \(0.621097\pi\) | |||||||
\(338\) | − 13.0000i | − 0.707107i | ||||||||
\(339\) | 13.8167 | 0.750418 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.60555 | −0.249040 | ||||||||
\(343\) | − 33.2111i | − 1.79323i | ||||||||
\(344\) | − 8.00000i | − 0.431331i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 12.4222i | − 0.667822i | ||||||||
\(347\) | 27.6333 | 1.48343 | 0.741717 | − | 0.670713i | \(-0.234012\pi\) | ||||
0.741717 | + | 0.670713i | \(0.234012\pi\) | |||||||
\(348\) | −4.60555 | −0.246883 | ||||||||
\(349\) | − 7.81665i | − 0.418416i | −0.977871 | − | 0.209208i | \(-0.932911\pi\) | ||||
0.977871 | − | 0.209208i | \(-0.0670886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.60555 | −0.192450 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.78890i | 0.467786i | 0.972262 | + | 0.233893i | \(0.0751465\pi\) | ||||
−0.972262 | + | 0.233893i | \(0.924853\pi\) | |||||||
\(354\) | −9.21110 | −0.489565 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − 15.2111i | − 0.806187i | ||||||||
\(357\) | − 21.2111i | − 1.12261i | ||||||||
\(358\) | 19.8167i | 1.04734i | ||||||||
\(359\) | 15.6333i | 0.825094i | 0.910936 | + | 0.412547i | \(0.135361\pi\) | ||||
−0.910936 | + | 0.412547i | \(0.864639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.21110 | −0.116374 | ||||||||
\(362\) | − 8.42221i | − 0.442661i | ||||||||
\(363\) | 11.0000 | 0.577350 | ||||||||
\(364\) | 16.6056i | 0.870367i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.2111i | 0.586014i | ||||||||
\(367\) | 19.6333 | 1.02485 | 0.512425 | − | 0.858732i | \(-0.328747\pi\) | ||||
0.512425 | + | 0.858732i | \(0.328747\pi\) | |||||||
\(368\) | 1.39445 | 0.0726907 | ||||||||
\(369\) | 3.21110i | 0.167163i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 27.6333i | − 1.43465i | ||||||||
\(372\) | − 6.00000i | − 0.311086i | ||||||||
\(373\) | 20.4222 | 1.05742 | 0.528711 | − | 0.848802i | \(-0.322676\pi\) | ||||
0.528711 | + | 0.848802i | \(0.322676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.21110 | −0.475026 | ||||||||
\(377\) | −16.6056 | −0.855229 | ||||||||
\(378\) | 4.60555 | 0.236884 | ||||||||
\(379\) | 35.0278i | 1.79925i | 0.436658 | + | 0.899627i | \(0.356162\pi\) | ||||
−0.436658 | + | 0.899627i | \(0.643838\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.21110 | −0.0620467 | ||||||||
\(382\) | 12.0000i | 0.613973i | ||||||||
\(383\) | 27.6333i | 1.41200i | 0.708214 | + | 0.705998i | \(0.249501\pi\) | ||||
−0.708214 | + | 0.705998i | \(0.750499\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.81665 | −0.397857 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | 1.39445i | 0.0707924i | ||||||||
\(389\) | 4.60555 | 0.233511 | 0.116755 | − | 0.993161i | \(-0.462751\pi\) | ||||
0.116755 | + | 0.993161i | \(0.462751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.42221 | −0.324785 | ||||||||
\(392\) | − 14.2111i | − 0.717769i | ||||||||
\(393\) | 22.6056 | 1.14030 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.63331i | 0.182350i | 0.995835 | + | 0.0911752i | \(0.0290623\pi\) | ||||
−0.995835 | + | 0.0911752i | \(0.970938\pi\) | |||||||
\(398\) | − 22.4222i | − 1.12392i | ||||||||
\(399\) | 21.2111 | 1.06188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.78890i | 0.438897i | 0.975624 | + | 0.219448i | \(0.0704257\pi\) | ||||
−0.975624 | + | 0.219448i | \(0.929574\pi\) | |||||||
\(402\) | 3.21110 | 0.160155 | ||||||||
\(403\) | − 21.6333i | − 1.07763i | ||||||||
\(404\) | 7.39445 | 0.367888 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.2111 | 1.05269 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − 4.60555i | − 0.228009i | ||||||||
\(409\) | − 14.7889i | − 0.731264i | −0.930760 | − | 0.365632i | \(-0.880853\pi\) | ||||
0.930760 | − | 0.365632i | \(-0.119147\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 3.21110i | − 0.158392i | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 42.4222 | 2.08746 | ||||||||
\(414\) | − 1.39445i | − 0.0685334i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.60555i | 0.176777i | ||||||||
\(417\) | 17.2111 | 0.842831 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.18335 | 0.204370 | 0.102185 | − | 0.994765i | \(-0.467417\pi\) | ||||
0.102185 | + | 0.994765i | \(0.467417\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 19.8167i | − 0.965805i | −0.875674 | − | 0.482902i | \(-0.839583\pi\) | ||||
0.875674 | − | 0.482902i | \(-0.160417\pi\) | |||||||
\(422\) | 17.2111i | 0.837823i | ||||||||
\(423\) | 9.21110i | 0.447859i | ||||||||
\(424\) | − 6.00000i | − 0.291386i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.21110 | 0.446279 | ||||||||
\(427\) | − 51.6333i | − 2.49871i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000i | 0.578020i | 0.957326 | + | 0.289010i | \(0.0933260\pi\) | ||||
−0.957326 | + | 0.289010i | \(0.906674\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −19.2111 | −0.923227 | −0.461613 | − | 0.887081i | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887081i | \(0.652729\pi\) | |||||||
\(434\) | 27.6333i | 1.32644i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 1.39445i | − 0.0667820i | ||||||||
\(437\) | − 6.42221i | − 0.307216i | ||||||||
\(438\) | 1.39445 | 0.0666293 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.2111 | −0.676719 | ||||||||
\(442\) | − 16.6056i | − 0.789846i | ||||||||
\(443\) | −15.6333 | −0.742761 | −0.371380 | − | 0.928481i | \(-0.621115\pi\) | ||||
−0.371380 | + | 0.928481i | \(0.621115\pi\) | |||||||
\(444\) | − 9.21110i | − 0.437140i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.81665 | −0.0860211 | ||||||||
\(447\) | 15.2111i | 0.719460i | ||||||||
\(448\) | − 4.60555i | − 0.217592i | ||||||||
\(449\) | 33.6333i | 1.58725i | 0.608405 | + | 0.793627i | \(0.291810\pi\) | ||||
−0.608405 | + | 0.793627i | \(0.708190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −13.8167 | −0.649881 | ||||||||
\(453\) | 6.00000i | 0.281905i | ||||||||
\(454\) | −24.0000 | −1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.60555 | 0.215675 | ||||||||
\(457\) | − 38.2389i | − 1.78874i | −0.447330 | − | 0.894369i | \(-0.647625\pi\) | ||||
0.447330 | − | 0.894369i | \(-0.352375\pi\) | |||||||
\(458\) | −19.8167 | −0.925971 | ||||||||
\(459\) | −4.60555 | −0.214969 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 33.6333i | − 1.56646i | −0.621733 | − | 0.783230i | \(-0.713571\pi\) | ||||
0.621733 | − | 0.783230i | \(-0.286429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.3944i | 1.45902i | 0.683968 | + | 0.729512i | \(0.260253\pi\) | ||||
−0.683968 | + | 0.729512i | \(0.739747\pi\) | |||||||
\(464\) | 4.60555 | 0.213807 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − 1.81665i | − 0.0841549i | ||||||||
\(467\) | 30.4222 | 1.40777 | 0.703886 | − | 0.710313i | \(-0.251447\pi\) | ||||
0.703886 | + | 0.710313i | \(0.251447\pi\) | |||||||
\(468\) | 3.60555 | 0.166667 | ||||||||
\(469\) | −14.7889 | −0.682888 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.4222 | −0.941006 | ||||||||
\(472\) | 9.21110 | 0.423975 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 14.4222i | 0.662434i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.2111i | 0.972209i | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.57779i | 0.254856i | 0.991848 | + | 0.127428i | \(0.0406722\pi\) | ||||
−0.991848 | + | 0.127428i | \(0.959328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 33.2111i | − 1.51430i | ||||||||
\(482\) | −6.42221 | −0.292523 | ||||||||
\(483\) | 6.42221i | 0.292220i | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | 0.972244i | 0.0440566i | 0.999757 | + | 0.0220283i | \(0.00701239\pi\) | ||||
−0.999757 | + | 0.0220283i | \(0.992988\pi\) | |||||||
\(488\) | − 11.2111i | − 0.507503i | ||||||||
\(489\) | − 24.4222i | − 1.10441i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.81665 | 0.352761 | 0.176380 | − | 0.984322i | \(-0.443561\pi\) | ||||
0.176380 | + | 0.984322i | \(0.443561\pi\) | |||||||
\(492\) | − 3.21110i | − 0.144768i | ||||||||
\(493\) | −21.2111 | −0.955300 | ||||||||
\(494\) | 16.6056 | 0.747119 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000i | 0.269408i | ||||||||
\(497\) | −42.4222 | −1.90290 | ||||||||
\(498\) | −2.78890 | −0.124973 | ||||||||
\(499\) | 23.0278i | 1.03086i | 0.856930 | + | 0.515432i | \(0.172369\pi\) | ||||
−0.856930 | + | 0.515432i | \(0.827631\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 9.21110i | − 0.411522i | ||||||||
\(502\) | 13.3944i | 0.597824i | ||||||||
\(503\) | −23.4500 | −1.04558 | −0.522791 | − | 0.852461i | \(-0.675109\pi\) | ||||
−0.522791 | + | 0.852461i | \(0.675109\pi\) | |||||||
\(504\) | −4.60555 | −0.205148 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.0000 | 0.577350 | ||||||||
\(508\) | 1.21110 | 0.0537340 | ||||||||
\(509\) | − 33.6333i | − 1.49077i | −0.666634 | − | 0.745385i | \(-0.732266\pi\) | ||||
0.666634 | − | 0.745385i | \(-0.267734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.42221 | −0.284102 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 4.60555i | − 0.203340i | ||||||||
\(514\) | − 28.6056i | − 1.26174i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 42.4222i | 1.86392i | ||||||||
\(519\) | 12.4222 | 0.545274 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.6333 | 0.947772 | 0.473886 | − | 0.880586i | \(-0.342851\pi\) | ||||
0.473886 | + | 0.880586i | \(0.342851\pi\) | |||||||
\(522\) | − 4.60555i | − 0.201580i | ||||||||
\(523\) | −32.8444 | −1.43619 | −0.718093 | − | 0.695947i | \(-0.754985\pi\) | ||||
−0.718093 | + | 0.695947i | \(0.754985\pi\) | |||||||
\(524\) | −22.6056 | −0.987528 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − 7.81665i | − 0.340822i | ||||||||
\(527\) | − 27.6333i | − 1.20373i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0555 | −0.915457 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 9.21110i | − 0.399728i | ||||||||
\(532\) | −21.2111 | −0.919618 | ||||||||
\(533\) | − 11.5778i | − 0.501490i | ||||||||
\(534\) | 15.2111 | 0.658249 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.21110 | −0.138699 | ||||||||
\(537\) | −19.8167 | −0.855152 | ||||||||
\(538\) | − 25.8167i | − 1.11303i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.97224i | 0.299760i | 0.988704 | + | 0.149880i | \(0.0478888\pi\) | ||||
−0.988704 | + | 0.149880i | \(0.952111\pi\) | |||||||
\(542\) | −0.422205 | −0.0181353 | ||||||||
\(543\) | 8.42221 | 0.361431 | ||||||||
\(544\) | 4.60555i | 0.197461i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.6056 | −0.710652 | ||||||||
\(547\) | −14.4222 | −0.616649 | −0.308324 | − | 0.951281i | \(-0.599768\pi\) | ||||
−0.308324 | + | 0.951281i | \(0.599768\pi\) | |||||||
\(548\) | 3.21110i | 0.137172i | ||||||||
\(549\) | −11.2111 | −0.478478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 21.2111i | − 0.903623i | ||||||||
\(552\) | 1.39445i | 0.0593517i | ||||||||
\(553\) | − 66.4222i | − 2.82456i | ||||||||
\(554\) | − 16.4222i | − 0.697713i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2111 | −0.729913 | ||||||||
\(557\) | − 11.5778i | − 0.490567i | −0.969451 | − | 0.245283i | \(-0.921119\pi\) | ||||
0.969451 | − | 0.245283i | \(-0.0788810\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | 28.8444 | 1.21999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.2111 | 1.14783 | ||||||||
\(563\) | −34.0555 | −1.43527 | −0.717634 | − | 0.696420i | \(-0.754775\pi\) | ||||
−0.717634 | + | 0.696420i | \(0.754775\pi\) | |||||||
\(564\) | − 9.21110i | − 0.387857i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.4222i | 0.438078i | ||||||||
\(567\) | 4.60555i | 0.193415i | ||||||||
\(568\) | −9.21110 | −0.386489 | ||||||||
\(569\) | 33.6333 | 1.40998 | 0.704991 | − | 0.709216i | \(-0.250951\pi\) | ||||
0.704991 | + | 0.709216i | \(0.250951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.0555 | −1.25778 | −0.628892 | − | 0.777493i | \(-0.716491\pi\) | ||||
−0.628892 | + | 0.777493i | \(0.716491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | −0.501307 | ||||||||
\(574\) | 14.7889i | 0.617277i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 37.3944i | 1.55675i | 0.627799 | + | 0.778376i | \(0.283956\pi\) | ||||
−0.627799 | + | 0.778376i | \(0.716044\pi\) | |||||||
\(578\) | − 4.21110i | − 0.175159i | ||||||||
\(579\) | − 7.81665i | − 0.324849i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8444 | 0.532876 | ||||||||
\(582\) | −1.39445 | −0.0578018 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.39445 | −0.0577027 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 6.42221i | 0.265073i | 0.991178 | + | 0.132536i | \(0.0423121\pi\) | ||||
−0.991178 | + | 0.132536i | \(0.957688\pi\) | |||||||
\(588\) | 14.2111 | 0.586056 | ||||||||
\(589\) | 27.6333 | 1.13861 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000i | 0.246807i | ||||||||
\(592\) | 9.21110i | 0.378574i | ||||||||
\(593\) | 24.4222i | 1.00290i | 0.865187 | + | 0.501450i | \(0.167200\pi\) | ||||
−0.865187 | + | 0.501450i | \(0.832800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 15.2111i | − 0.623071i | ||||||||
\(597\) | 22.4222 | 0.917680 | ||||||||
\(598\) | 5.02776i | 0.205600i | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.63331 | 0.0666240 | 0.0333120 | − | 0.999445i | \(-0.489394\pi\) | ||||
0.0333120 | + | 0.999445i | \(0.489394\pi\) | |||||||
\(602\) | −36.8444 | −1.50167 | ||||||||
\(603\) | 3.21110i | 0.130766i | ||||||||
\(604\) | − 6.00000i | − 0.244137i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.39445i | 0.300379i | ||||||||
\(607\) | −17.2111 | −0.698577 | −0.349289 | − | 0.937015i | \(-0.613577\pi\) | ||||
−0.349289 | + | 0.937015i | \(0.613577\pi\) | |||||||
\(608\) | −4.60555 | −0.186780 | ||||||||
\(609\) | 21.2111i | 0.859517i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 33.2111i | − 1.34358i | ||||||||
\(612\) | 4.60555 | 0.186168 | ||||||||
\(613\) | 33.2111i | 1.34138i | 0.741736 | + | 0.670692i | \(0.234003\pi\) | ||||
−0.741736 | + | 0.670692i | \(0.765997\pi\) | |||||||
\(614\) | 8.78890 | 0.354691 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.4222i | − 0.500099i | −0.968233 | − | 0.250050i | \(-0.919553\pi\) | ||||
0.968233 | − | 0.250050i | \(-0.0804469\pi\) | |||||||
\(618\) | − 4.00000i | − 0.160904i | ||||||||
\(619\) | 25.8167i | 1.03766i | 0.854878 | + | 0.518829i | \(0.173632\pi\) | ||||
−0.854878 | + | 0.518829i | \(0.826368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.39445 | 0.0559573 | ||||||||
\(622\) | − 12.0000i | − 0.481156i | ||||||||
\(623\) | −70.0555 | −2.80671 | ||||||||
\(624\) | −3.60555 | −0.144338 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.57779i | 0.142997i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.4222 | 0.814935 | ||||||||
\(629\) | − 42.4222i | − 1.69148i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.21110i | 0.127832i | 0.997955 | + | 0.0639160i | \(0.0203590\pi\) | ||||
−0.997955 | + | 0.0639160i | \(0.979641\pi\) | |||||||
\(632\) | − 14.4222i | − 0.573685i | ||||||||
\(633\) | −17.2111 | −0.684080 | ||||||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 51.2389 | 2.03016 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.21110i | 0.364386i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.422205 | 0.0166761 | 0.00833805 | − | 0.999965i | \(-0.497346\pi\) | ||||
0.00833805 | + | 0.999965i | \(0.497346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 9.63331i | − 0.379901i | −0.981794 | − | 0.189950i | \(-0.939167\pi\) | ||||
0.981794 | − | 0.189950i | \(-0.0608327\pi\) | |||||||
\(644\) | − 6.42221i | − 0.253070i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.2111 | 0.834540 | ||||||||
\(647\) | 34.6056 | 1.36048 | 0.680242 | − | 0.732987i | \(-0.261875\pi\) | ||||
0.680242 | + | 0.732987i | \(0.261875\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.6333 | −1.08303 | ||||||||
\(652\) | 24.4222i | 0.956447i | ||||||||
\(653\) | −39.2111 | −1.53445 | −0.767225 | − | 0.641379i | \(-0.778363\pi\) | ||||
−0.767225 | + | 0.641379i | \(0.778363\pi\) | |||||||
\(654\) | 1.39445 | 0.0545273 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.21110i | 0.125372i | ||||||||
\(657\) | 1.39445i | 0.0544026i | ||||||||
\(658\) | 42.4222i | 1.65379i | ||||||||
\(659\) | −26.2389 | −1.02212 | −0.511060 | − | 0.859545i | \(-0.670747\pi\) | ||||
−0.511060 | + | 0.859545i | \(0.670747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.2389i | 1.95407i | 0.213090 | + | 0.977033i | \(0.431647\pi\) | ||||
−0.213090 | + | 0.977033i | \(0.568353\pi\) | |||||||
\(662\) | −16.6056 | −0.645393 | ||||||||
\(663\) | 16.6056 | 0.644906 | ||||||||
\(664\) | 2.78890 | 0.108230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.21110 | 0.356923 | ||||||||
\(667\) | 6.42221 | 0.248669 | ||||||||
\(668\) | 9.21110i | 0.356388i | ||||||||
\(669\) | − 1.81665i | − 0.0702359i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 4.60555 | 0.177663 | ||||||||
\(673\) | 37.6333 | 1.45066 | 0.725329 | − | 0.688403i | \(-0.241688\pi\) | ||||
0.725329 | + | 0.688403i | \(0.241688\pi\) | |||||||
\(674\) | 13.6333i | 0.525135i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 28.0555 | 1.07826 | 0.539130 | − | 0.842222i | \(-0.318753\pi\) | ||||
0.539130 | + | 0.842222i | \(0.318753\pi\) | |||||||
\(678\) | − 13.8167i | − 0.530625i | ||||||||
\(679\) | 6.42221 | 0.246462 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − 24.0000i | − 0.919682i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 9.21110i | − 0.352453i | −0.984350 | − | 0.176227i | \(-0.943611\pi\) | ||||
0.984350 | − | 0.176227i | \(-0.0563891\pi\) | |||||||
\(684\) | 4.60555i | 0.176098i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −33.2111 | −1.26801 | ||||||||
\(687\) | − 19.8167i | − 0.756053i | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | 21.6333 | 0.824163 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2389i | 0.769922i | 0.922933 | + | 0.384961i | \(0.125785\pi\) | ||||
−0.922933 | + | 0.384961i | \(0.874215\pi\) | |||||||
\(692\) | −12.4222 | −0.472221 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − 27.6333i | − 1.04895i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.60555i | 0.174573i | ||||||||
\(697\) | − 14.7889i | − 0.560169i | ||||||||
\(698\) | −7.81665 | −0.295865 | ||||||||
\(699\) | 1.81665 | 0.0687122 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.0278 | 1.77621 | 0.888107 | − | 0.459637i | \(-0.152020\pi\) | ||||
0.888107 | + | 0.459637i | \(0.152020\pi\) | |||||||
\(702\) | 3.60555i | 0.136083i | ||||||||
\(703\) | 42.4222 | 1.59998 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.78890 | 0.330775 | ||||||||
\(707\) | − 34.0555i | − 1.28079i | ||||||||
\(708\) | 9.21110i | 0.346174i | ||||||||
\(709\) | − 1.39445i | − 0.0523696i | −0.999657 | − | 0.0261848i | \(-0.991664\pi\) | ||||
0.999657 | − | 0.0261848i | \(-0.00833584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.4222 | −0.540875 | ||||||||
\(712\) | −15.2111 | −0.570060 | ||||||||
\(713\) | 8.36669i | 0.313335i | ||||||||
\(714\) | −21.2111 | −0.793806 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.8167 | 0.740583 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.6333 | 0.583430 | ||||||||
\(719\) | −51.6333 | −1.92560 | −0.962799 | − | 0.270220i | \(-0.912904\pi\) | ||||
−0.962799 | + | 0.270220i | \(0.912904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.4222i | 0.686079i | ||||||||
\(722\) | 2.21110i | 0.0822887i | ||||||||
\(723\) | − 6.42221i | − 0.238844i | ||||||||
\(724\) | −8.42221 | −0.313009 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − 11.0000i | − 0.408248i | ||||||||
\(727\) | 14.4222 | 0.534890 | 0.267445 | − | 0.963573i | \(-0.413821\pi\) | ||||
0.267445 | + | 0.963573i | \(0.413821\pi\) | |||||||
\(728\) | 16.6056 | 0.615443 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.8444 | 1.36274 | ||||||||
\(732\) | 11.2111 | 0.414374 | ||||||||
\(733\) | 34.0555i | 1.25787i | 0.777458 | + | 0.628935i | \(0.216509\pi\) | ||||
−0.777458 | + | 0.628935i | \(0.783491\pi\) | |||||||
\(734\) | − 19.6333i | − 0.724679i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 1.39445i | − 0.0514001i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 3.21110 | 0.118202 | ||||||||
\(739\) | 20.2389i | 0.744498i | 0.928133 | + | 0.372249i | \(0.121413\pi\) | ||||
−0.928133 | + | 0.372249i | \(0.878587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.6056i | 0.610020i | ||||||||
\(742\) | −27.6333 | −1.01445 | ||||||||
\(743\) | − 36.8444i | − 1.35169i | −0.737044 | − | 0.675845i | \(-0.763779\pi\) | ||||
0.737044 | − | 0.675845i | \(-0.236221\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − 20.4222i | − 0.747710i | ||||||||
\(747\) | − 2.78890i | − 0.102040i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4222 | −0.380312 | −0.190156 | − | 0.981754i | \(-0.560899\pi\) | ||||
−0.190156 | + | 0.981754i | \(0.560899\pi\) | |||||||
\(752\) | 9.21110i | 0.335894i | ||||||||
\(753\) | −13.3944 | −0.488121 | ||||||||
\(754\) | 16.6056i | 0.604739i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − 4.60555i | − 0.167502i | ||||||||
\(757\) | −12.7889 | −0.464820 | −0.232410 | − | 0.972618i | \(-0.574661\pi\) | ||||
−0.232410 | + | 0.972618i | \(0.574661\pi\) | |||||||
\(758\) | 35.0278 | 1.27227 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.6333i | 1.21921i | 0.792707 | + | 0.609603i | \(0.208671\pi\) | ||||
−0.792707 | + | 0.609603i | \(0.791329\pi\) | |||||||
\(762\) | 1.21110i | 0.0438736i | ||||||||
\(763\) | −6.42221 | −0.232499 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.6333 | 0.998432 | ||||||||
\(767\) | 33.2111i | 1.19918i | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | − 12.8444i | − 0.463181i | −0.972813 | − | 0.231591i | \(-0.925607\pi\) | ||||
0.972813 | − | 0.231591i | \(-0.0743930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.6056 | 1.03020 | ||||||||
\(772\) | 7.81665i | 0.281328i | ||||||||
\(773\) | − 30.0000i | − 1.07903i | −0.841978 | − | 0.539513i | \(-0.818609\pi\) | ||||
0.841978 | − | 0.539513i | \(-0.181391\pi\) | |||||||
\(774\) | 8.00000i | 0.287554i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.39445 | 0.0500578 | ||||||||
\(777\) | −42.4222 | −1.52189 | ||||||||
\(778\) | − 4.60555i | − 0.165117i | ||||||||
\(779\) | 14.7889 | 0.529867 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.42221i | 0.229658i | ||||||||
\(783\) | 4.60555 | 0.164589 | ||||||||
\(784\) | −14.2111 | −0.507539 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − 22.6056i | − 0.806313i | ||||||||
\(787\) | − 49.2666i | − 1.75617i | −0.478509 | − | 0.878083i | \(-0.658823\pi\) | ||||
0.478509 | − | 0.878083i | \(-0.341177\pi\) | |||||||
\(788\) | − 6.00000i | − 0.213741i | ||||||||
\(789\) | 7.81665 | 0.278280 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 63.6333i | 2.26254i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.4222 | 1.43543 | ||||||||
\(794\) | 3.63331 | 0.128941 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.4222 | −0.794734 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | − 21.2111i | − 0.750865i | ||||||||
\(799\) | − 42.4222i | − 1.50079i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.2111i | 0.537458i | ||||||||
\(802\) | 8.78890 | 0.310347 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − 3.21110i | − 0.113247i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.6333 | −0.762001 | ||||||||
\(807\) | 25.8167 | 0.908789 | ||||||||
\(808\) | − 7.39445i | − 0.260136i | ||||||||
\(809\) | −6.84441 | −0.240637 | −0.120318 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120318 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.2389i | 1.13206i | 0.824385 | + | 0.566030i | \(0.191521\pi\) | ||||
−0.824385 | + | 0.566030i | \(0.808479\pi\) | |||||||
\(812\) | − 21.2111i | − 0.744364i | ||||||||
\(813\) | − 0.422205i | − 0.0148074i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.60555 | −0.161227 | ||||||||
\(817\) | 36.8444i | 1.28902i | ||||||||
\(818\) | −14.7889 | −0.517082 | ||||||||
\(819\) | − 16.6056i | − 0.580245i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 3.21110i | − 0.112068i | −0.998429 | − | 0.0560341i | \(-0.982154\pi\) | ||||
0.998429 | − | 0.0560341i | \(-0.0178456\pi\) | |||||||
\(822\) | −3.21110 | −0.112000 | ||||||||
\(823\) | 4.00000 | 0.139431 | 0.0697156 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697156 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(824\) | 4.00000i | 0.139347i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − 42.4222i | − 1.47606i | ||||||||
\(827\) | 27.6333i | 0.960904i | 0.877021 | + | 0.480452i | \(0.159527\pi\) | ||||
−0.877021 | + | 0.480452i | \(0.840473\pi\) | |||||||
\(828\) | −1.39445 | −0.0484604 | ||||||||
\(829\) | 46.8444 | 1.62697 | 0.813487 | − | 0.581583i | \(-0.197567\pi\) | ||||
0.813487 | + | 0.581583i | \(0.197567\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.4222 | 0.569680 | ||||||||
\(832\) | 3.60555 | 0.125000 | ||||||||
\(833\) | 65.4500 | 2.26771 | ||||||||
\(834\) | − 17.2111i | − 0.595972i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.00000i | 0.207390i | ||||||||
\(838\) | − 4.18335i | − 0.144511i | ||||||||
\(839\) | − 18.4222i | − 0.636005i | −0.948090 | − | 0.318003i | \(-0.896988\pi\) | ||||
0.948090 | − | 0.318003i | \(-0.103012\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | −19.8167 | −0.682927 | ||||||||
\(843\) | 27.2111i | 0.937200i | ||||||||
\(844\) | 17.2111 | 0.592431 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.21110 | 0.316684 | ||||||||
\(847\) | 50.6611i | 1.74073i | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | −10.4222 | −0.357689 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.8444i | 0.440301i | ||||||||
\(852\) | − 9.21110i | − 0.315567i | ||||||||
\(853\) | 14.7889i | 0.506362i | 0.967419 | + | 0.253181i | \(0.0814769\pi\) | ||||
−0.967419 | + | 0.253181i | \(0.918523\pi\) | |||||||
\(854\) | −51.6333 | −1.76686 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.0278 | 0.786613 | 0.393307 | − | 0.919407i | \(-0.371331\pi\) | ||||
0.393307 | + | 0.919407i | \(0.371331\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.2111 | 0.860192 | 0.430096 | − | 0.902783i | \(-0.358480\pi\) | ||||
0.430096 | + | 0.902783i | \(0.358480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.7889 | −0.504004 | ||||||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | − 51.6333i | − 1.75762i | −0.477173 | − | 0.878809i | \(-0.658339\pi\) | ||||
0.477173 | − | 0.878809i | \(-0.341661\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.2111i | 0.652820i | ||||||||
\(867\) | 4.21110 | 0.143017 | ||||||||
\(868\) | 27.6333 | 0.937936 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 11.5778i | − 0.392299i | ||||||||
\(872\) | −1.39445 | −0.0472220 | ||||||||
\(873\) | − 1.39445i | − 0.0471949i | ||||||||
\(874\) | −6.42221 | −0.217234 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − 1.39445i | − 0.0471141i | ||||||||
\(877\) | 24.8444i | 0.838936i | 0.907770 | + | 0.419468i | \(0.137783\pi\) | ||||
−0.907770 | + | 0.419468i | \(0.862217\pi\) | |||||||
\(878\) | − 8.00000i | − 0.269987i | ||||||||
\(879\) | − 18.0000i | − 0.607125i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.2111 | 1.32106 | 0.660528 | − | 0.750802i | \(-0.270333\pi\) | ||||
0.660528 | + | 0.750802i | \(0.270333\pi\) | |||||||
\(882\) | 14.2111i | 0.478513i | ||||||||
\(883\) | −9.57779 | −0.322318 | −0.161159 | − | 0.986928i | \(-0.551523\pi\) | ||||
−0.161159 | + | 0.986928i | \(0.551523\pi\) | |||||||
\(884\) | −16.6056 | −0.558505 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.6333i | 0.525211i | ||||||||
\(887\) | −6.97224 | −0.234105 | −0.117053 | − | 0.993126i | \(-0.537345\pi\) | ||||
−0.117053 | + | 0.993126i | \(0.537345\pi\) | |||||||
\(888\) | −9.21110 | −0.309104 | ||||||||
\(889\) | − 5.57779i | − 0.187073i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.81665i | 0.0608261i | ||||||||
\(893\) | 42.4222 | 1.41960 | ||||||||
\(894\) | 15.2111 | 0.508735 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.60555 | −0.153861 | ||||||||
\(897\) | −5.02776 | −0.167872 | ||||||||
\(898\) | 33.6333 | 1.12236 | ||||||||
\(899\) | 27.6333i | 0.921622i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.6333 | 0.920599 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 36.8444i | − 1.22611i | ||||||||
\(904\) | 13.8167i | 0.459535i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.00000 | 0.199337 | ||||||||
\(907\) | −21.5778 | −0.716479 | −0.358239 | − | 0.933630i | \(-0.616623\pi\) | ||||
−0.358239 | + | 0.933630i | \(0.616623\pi\) | |||||||
\(908\) | 24.0000i | 0.796468i | ||||||||
\(909\) | −7.39445 | −0.245258 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.6333 | −0.915532 | −0.457766 | − | 0.889073i | \(-0.651350\pi\) | ||||
−0.457766 | + | 0.889073i | \(0.651350\pi\) | |||||||
\(912\) | − 4.60555i | − 0.152505i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −38.2389 | −1.26483 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.8167i | 0.654761i | ||||||||
\(917\) | 104.111i | 3.43805i | ||||||||
\(918\) | 4.60555i | 0.152006i | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.78890i | 0.289604i | ||||||||
\(922\) | −33.6333 | −1.10765 | ||||||||
\(923\) | − 33.2111i | − 1.09316i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.3944 | 1.03169 | ||||||||
\(927\) | 4.00000 | 0.131377 | ||||||||
\(928\) | − 4.60555i | − 0.151185i | ||||||||
\(929\) | 39.2111i | 1.28647i | 0.765667 | + | 0.643237i | \(0.222409\pi\) | ||||
−0.765667 | + | 0.643237i | \(0.777591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 65.4500i | 2.14504i | ||||||||
\(932\) | −1.81665 | −0.0595065 | ||||||||
\(933\) | 12.0000 | 0.392862 | ||||||||
\(934\) | − 30.4222i | − 0.995445i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − 3.60555i | − 0.117851i | ||||||||
\(937\) | 10.3667 | 0.338665 | 0.169333 | − | 0.985559i | \(-0.445839\pi\) | ||||
0.169333 | + | 0.985559i | \(0.445839\pi\) | |||||||
\(938\) | 14.7889i | 0.482875i | ||||||||
\(939\) | −3.57779 | −0.116757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 54.0000i | − 1.76035i | −0.474650 | − | 0.880175i | \(-0.657425\pi\) | ||||
0.474650 | − | 0.880175i | \(-0.342575\pi\) | |||||||
\(942\) | 20.4222i | 0.665391i | ||||||||
\(943\) | 4.47772i | 0.145815i | ||||||||
\(944\) | − 9.21110i | − 0.299796i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.6333i | 0.508014i | 0.967202 | + | 0.254007i | \(0.0817487\pi\) | ||||
−0.967202 | + | 0.254007i | \(0.918251\pi\) | |||||||
\(948\) | 14.4222 | 0.468411 | ||||||||
\(949\) | − 5.02776i | − 0.163208i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000i | 0.583690i | ||||||||
\(952\) | 21.2111 | 0.687456 | ||||||||
\(953\) | 20.2389 | 0.655601 | 0.327800 | − | 0.944747i | \(-0.393693\pi\) | ||||
0.327800 | + | 0.944747i | \(0.393693\pi\) | |||||||
\(954\) | 6.00000i | 0.194257i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.57779 | 0.180210 | ||||||||
\(959\) | 14.7889 | 0.477558 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.00000 | −0.161290 | ||||||||
\(962\) | −33.2111 | −1.07077 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.42221i | 0.206845i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.42221 | 0.206631 | ||||||||
\(967\) | 8.23886i | 0.264944i | 0.991187 | + | 0.132472i | \(0.0422914\pi\) | ||||
−0.991187 | + | 0.132472i | \(0.957709\pi\) | |||||||
\(968\) | 11.0000i | 0.353553i | ||||||||
\(969\) | 21.2111i | 0.681399i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.0278 | −1.70174 | −0.850871 | − | 0.525375i | \(-0.823925\pi\) | ||||
−0.850871 | + | 0.525375i | \(0.823925\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 79.2666i | 2.54117i | ||||||||
\(974\) | 0.972244 | 0.0311527 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.2111 | −0.358859 | ||||||||
\(977\) | − 18.8444i | − 0.602886i | −0.953484 | − | 0.301443i | \(-0.902532\pi\) | ||||
0.953484 | − | 0.301443i | \(-0.0974683\pi\) | |||||||
\(978\) | −24.4222 | −0.780936 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.39445i | 0.0445213i | ||||||||
\(982\) | − 7.81665i | − 0.249439i | ||||||||
\(983\) | 42.4222i | 1.35306i | 0.736416 | + | 0.676529i | \(0.236517\pi\) | ||||
−0.736416 | + | 0.676529i | \(0.763483\pi\) | |||||||
\(984\) | −3.21110 | −0.102366 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.2111i | 0.675499i | ||||||||
\(987\) | −42.4222 | −1.35031 | ||||||||
\(988\) | − 16.6056i | − 0.528293i | ||||||||
\(989\) | −11.1556 | −0.354727 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.4222 | −0.712265 | −0.356132 | − | 0.934436i | \(-0.615905\pi\) | ||||
−0.356132 | + | 0.934436i | \(0.615905\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | − 16.6056i | − 0.526961i | ||||||||
\(994\) | 42.4222i | 1.34555i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.78890i | 0.0883696i | ||||||||
\(997\) | 16.4222 | 0.520096 | 0.260048 | − | 0.965596i | \(-0.416262\pi\) | ||||
0.260048 | + | 0.965596i | \(0.416262\pi\) | |||||||
\(998\) | 23.0278 | 0.728931 | ||||||||
\(999\) | 9.21110i | 0.291426i |
(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 | 1950.2.b.k.1351.2 | 4 | ||
5.2 | odd | 4 | 1950.2.f.n.649.1 | 4 | |||
5.3 | odd | 4 | 1950.2.f.m.649.4 | 4 | |||
5.4 | even | 2 | 390.2.b.c.181.3 | yes | 4 | ||
13.12 | even | 2 | inner | 1950.2.b.k.1351.3 | 4 | ||
15.14 | odd | 2 | 1170.2.b.d.181.1 | 4 | |||
20.19 | odd | 2 | 3120.2.g.q.961.4 | 4 | |||
65.12 | odd | 4 | 1950.2.f.m.649.2 | 4 | |||
65.34 | odd | 4 | 5070.2.a.z.1.1 | 2 | |||
65.38 | odd | 4 | 1950.2.f.n.649.3 | 4 | |||
65.44 | odd | 4 | 5070.2.a.bf.1.2 | 2 | |||
65.64 | even | 2 | 390.2.b.c.181.2 | ✓ | 4 | ||
195.194 | odd | 2 | 1170.2.b.d.181.4 | 4 | |||
260.259 | odd | 2 | 3120.2.g.q.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.c.181.2 | ✓ | 4 | 65.64 | even | 2 | ||
390.2.b.c.181.3 | yes | 4 | 5.4 | even | 2 | ||
1170.2.b.d.181.1 | 4 | 15.14 | odd | 2 | |||
1170.2.b.d.181.4 | 4 | 195.194 | odd | 2 | |||
1950.2.b.k.1351.2 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.b.k.1351.3 | 4 | 13.12 | even | 2 | inner | ||
1950.2.f.m.649.2 | 4 | 65.12 | odd | 4 | |||
1950.2.f.m.649.4 | 4 | 5.3 | odd | 4 | |||
1950.2.f.n.649.1 | 4 | 5.2 | odd | 4 | |||
1950.2.f.n.649.3 | 4 | 65.38 | odd | 4 | |||
3120.2.g.q.961.1 | 4 | 260.259 | odd | 2 | |||
3120.2.g.q.961.4 | 4 | 20.19 | odd | 2 | |||
5070.2.a.z.1.1 | 2 | 65.34 | odd | 4 | |||
5070.2.a.bf.1.2 | 2 | 65.44 | odd | 4 |