Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("384.383");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (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: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.2 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.2.c.d.383.1 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.618034 | + | 1.61803i | −0.356822 | + | 0.934172i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.23607i | − | 1.44721i | −0.690212 | − | 0.723607i | \(-0.742483\pi\) | ||
0.690212 | − | 0.723607i | \(-0.257517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.23607i | − | 0.467190i | −0.972334 | − | 0.233595i | \(-0.924951\pi\) | ||
0.972334 | − | 0.233595i | \(-0.0750489\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | − | 2.00000i | −0.745356 | − | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.23607 | −1.57873 | −0.789367 | − | 0.613922i | \(-0.789591\pi\) | ||||
−0.789367 | + | 0.613922i | \(0.789591\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47214 | −1.24035 | −0.620174 | − | 0.784465i | \(-0.712938\pi\) | ||||
−0.620174 | + | 0.784465i | \(0.712938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.23607 | + | 2.00000i | 1.35195 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.47214i | − | 0.599581i | −0.954005 | − | 0.299791i | \(-0.903083\pi\) | ||
0.954005 | − | 0.299791i | \(-0.0969168\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.763932i | − | 0.175258i | −0.996153 | − | 0.0876290i | \(-0.972071\pi\) | ||
0.996153 | − | 0.0876290i | \(-0.0279290\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 0.763932i | 0.436436 | + | 0.166704i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47214 | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.47214 | −1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.61803 | − | 2.38197i | 0.888741 | − | 0.458410i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.76393i | − | 0.884640i | −0.896857 | − | 0.442320i | \(-0.854156\pi\) | ||
0.896857 | − | 0.442320i | \(-0.145844\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.23607i | − | 0.940426i | −0.882553 | − | 0.470213i | \(-0.844177\pi\) | ||
0.882553 | − | 0.470213i | \(-0.155823\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.23607 | − | 8.47214i | 0.563327 | − | 1.47481i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00000 | −0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.47214 | 1.39281 | 0.696405 | − | 0.717649i | \(-0.254782\pi\) | ||||
0.696405 | + | 0.717649i | \(0.254782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.76393 | − | 7.23607i | 0.442583 | − | 1.15870i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.47214i | 1.01078i | 0.862892 | + | 0.505389i | \(0.168651\pi\) | ||||
−0.862892 | + | 0.505389i | \(0.831349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.23607i | 1.10349i | 0.834013 | + | 0.551745i | \(0.186038\pi\) | ||||
−0.834013 | + | 0.551745i | \(0.813962\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.47214 | + | 7.23607i | −0.964809 | + | 1.07869i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.47214 | 0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | + | 1.52786i | 0.560112 | + | 0.213944i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.23607i | − | 0.444508i | −0.974989 | − | 0.222254i | \(-0.928659\pi\) | ||
0.974989 | − | 0.222254i | \(-0.0713414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.9443i | 2.28477i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.23607 | + | 0.472136i | 0.163721 | + | 0.0625359i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.23607 | 0.160922 | 0.0804612 | − | 0.996758i | \(-0.474361\pi\) | ||||
0.0804612 | + | 0.996758i | \(0.474361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.472136 | 0.0604508 | 0.0302254 | − | 0.999543i | \(-0.490377\pi\) | ||||
0.0302254 | + | 0.999543i | \(0.490377\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.47214 | + | 2.76393i | −0.311460 | + | 0.348223i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4721i | 1.79505i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.70820i | − | 1.18605i | −0.805186 | − | 0.593023i | \(-0.797934\pi\) | ||
0.805186 | − | 0.593023i | \(-0.202066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.52786 | + | 4.00000i | −0.183933 | + | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.4164 | −1.82959 | −0.914796 | − | 0.403917i | \(-0.867648\pi\) | ||||
−0.914796 | + | 0.403917i | \(0.867648\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.38197 | − | 8.85410i | 0.390516 | − | 1.02238i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.47214i | 0.737568i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.291796i | − | 0.0328296i | −0.999865 | − | 0.0164148i | \(-0.994775\pi\) | ||
0.999865 | − | 0.0164148i | \(-0.00522523\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.76393 | −0.303381 | −0.151690 | − | 0.988428i | \(-0.548472\pi\) | ||||
−0.151690 | + | 0.988428i | \(0.548472\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.70820 | + | 2.94427i | 0.826406 | + | 0.315659i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.00000i | 0.423999i | 0.977270 | + | 0.212000i | \(0.0679975\pi\) | ||||
−0.977270 | + | 0.212000i | \(0.932002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.52786i | 0.579478i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.47214 | + | 3.23607i | 0.878520 | + | 0.335565i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.47214 | −0.253636 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.472136 | 0.0479381 | 0.0239691 | − | 0.999713i | \(-0.492370\pi\) | ||||
0.0239691 | + | 0.999713i | \(0.492370\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.7082 | + | 10.4721i | 1.17672 | + | 1.05249i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.70820i | 0.169973i | 0.996382 | + | 0.0849863i | \(0.0270847\pi\) | ||||
−0.996382 | + | 0.0849863i | \(0.972915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.1803i | − | 1.39723i | −0.715498 | − | 0.698615i | \(-0.753800\pi\) | ||
0.715498 | − | 0.698615i | \(-0.246200\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.47214 | − | 6.47214i | 0.241256 | − | 0.631616i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1803 | 1.37087 | 0.685433 | − | 0.728136i | \(-0.259613\pi\) | ||||
0.685433 | + | 0.728136i | \(0.259613\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.47214 | 0.811483 | 0.405742 | − | 0.913988i | \(-0.367013\pi\) | ||||
0.405742 | + | 0.913988i | \(0.367013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.23607 | + | 13.7082i | −0.496986 | + | 1.30113i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.00000i | − | 0.752577i | −0.926503 | − | 0.376288i | \(-0.877200\pi\) | ||
0.926503 | − | 0.376288i | \(-0.122800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.00000i | − | 0.746004i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.0000 | + | 8.94427i | 0.924500 | + | 0.826898i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.05573 | −0.280118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.4721 | − | 4.00000i | −0.944241 | − | 0.360668i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.52786i | 0.136656i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.2361i | − | 1.17451i | −0.809402 | − | 0.587256i | \(-0.800208\pi\) | ||
0.809402 | − | 0.587256i | \(-0.199792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.7082 | − | 4.47214i | −1.03085 | − | 0.393750i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.76393 | 0.590967 | 0.295484 | − | 0.955348i | \(-0.404519\pi\) | ||||
0.295484 | + | 0.955348i | \(0.404519\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.944272 | −0.0818788 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.70820 | − | 14.9443i | −0.663417 | − | 1.28620i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.52786i | 0.130534i | 0.997868 | + | 0.0652671i | \(0.0207899\pi\) | ||||
−0.997868 | + | 0.0652671i | \(0.979210\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.70820i | − | 0.823439i | −0.911311 | − | 0.411720i | \(-0.864928\pi\) | ||
0.911311 | − | 0.411720i | \(-0.135072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.94427 | − | 12.9443i | 0.416383 | − | 1.09010i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.4164 | 1.95818 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.4164 | −1.28026 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.38197 | + | 8.85410i | −0.278940 | + | 0.730274i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.70820i | 0.795327i | 0.917531 | + | 0.397664i | \(0.130179\pi\) | ||||
−0.917531 | + | 0.397664i | \(0.869821\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.7082i | 1.60383i | 0.597438 | + | 0.801915i | \(0.296186\pi\) | ||||
−0.597438 | + | 0.801915i | \(0.703814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.94427 | + | 5.52786i | −0.399721 | + | 0.446901i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.9443 | −1.36100 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.47214 | −0.356915 | −0.178458 | − | 0.983948i | \(-0.557111\pi\) | ||||
−0.178458 | + | 0.983948i | \(0.557111\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.23607 | + | 2.00000i | 0.415247 | + | 0.158610i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.05573i | − | 0.240825i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.18034i | 0.327429i | 0.986508 | + | 0.163715i | \(0.0523477\pi\) | ||||
−0.986508 | + | 0.163715i | \(0.947652\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −27.4164 | − | 10.4721i | −2.13436 | − | 0.815255i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.5279 | 1.04682 | 0.523409 | − | 0.852082i | \(-0.324660\pi\) | ||||
0.523409 | + | 0.852082i | \(0.324660\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.52786 | + | 1.70820i | −0.116839 | + | 0.130630i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22.6525i | − | 1.72224i | −0.508405 | − | 0.861118i | \(-0.669765\pi\) | ||
0.508405 | − | 0.861118i | \(-0.330235\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.76393i | 0.511305i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.763932 | + | 2.00000i | −0.0574206 | + | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.18034 | −0.461940 | −0.230970 | − | 0.972961i | \(-0.574190\pi\) | ||||
−0.230970 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4721 | −1.52168 | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||||
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.291796 | + | 0.763932i | −0.0215702 | + | 0.0564715i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 27.4164i | − | 2.01569i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9443i | 0.946579i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.94427 | − | 5.70820i | −0.214164 | − | 0.415211i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9443 | −0.936615 | −0.468307 | − | 0.883566i | \(-0.655136\pi\) | ||||
−0.468307 | + | 0.883566i | \(0.655136\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8885 | −0.855756 | −0.427878 | − | 0.903836i | \(-0.640739\pi\) | ||||
−0.427878 | + | 0.903836i | \(0.640739\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −23.4164 | − | 8.94427i | −1.67688 | − | 0.640513i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.76393i | 0.339416i | 0.985494 | + | 0.169708i | \(0.0542825\pi\) | ||||
−0.985494 | + | 0.169708i | \(0.945718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.18034i | − | 0.438113i | −0.975712 | − | 0.219056i | \(-0.929702\pi\) | ||
0.975712 | − | 0.219056i | \(-0.0702979\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.7082 | + | 6.00000i | 1.10797 | + | 0.423207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.88854 | −0.413295 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.9443 | 1.46281 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.52786 | − | 4.94427i | −0.384213 | − | 0.343651i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000i | 0.276686i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2361i | 0.773523i | 0.922180 | + | 0.386761i | \(0.126406\pi\) | ||||
−0.922180 | + | 0.386761i | \(0.873594\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.52786 | − | 24.9443i | 0.652838 | − | 1.70915i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.4164 | 1.59699 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.47214 | −0.439357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.23607 | − | 3.23607i | 0.0835257 | − | 0.218673i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.0557i | 0.743689i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.1803i | − | 0.681726i | −0.940113 | − | 0.340863i | \(-0.889281\pi\) | ||
0.940113 | − | 0.340863i | \(-0.110719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2361 | + | 10.9443i | 0.815738 | + | 0.729618i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.18034 | 0.144714 | 0.0723571 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723571 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5279 | 0.761783 | 0.380891 | − | 0.924620i | \(-0.375617\pi\) | ||||
0.380891 | + | 0.924620i | \(0.375617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4721 | − | 4.00000i | −0.689016 | − | 0.263181i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 24.9443i | − | 1.63415i | −0.576529 | − | 0.817077i | \(-0.695593\pi\) | ||
0.576529 | − | 0.817077i | \(-0.304407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.8885i | 1.68878i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.472136 | + | 0.180340i | 0.0306685 | + | 0.0117143i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.0902 | − | 3.90983i | −0.968035 | − | 0.250816i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 17.7082i | − | 1.13134i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.41641i | 0.217381i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.70820 | − | 4.47214i | 0.108253 | − | 0.283410i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.7082 | 1.49645 | 0.748224 | − | 0.663446i | \(-0.230907\pi\) | ||||
0.748224 | + | 0.663446i | \(0.230907\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.9443 | −0.813799 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.94427 | − | 12.9443i | 0.309622 | − | 0.810602i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 20.9443i | − | 1.30647i | −0.757156 | − | 0.653234i | \(-0.773412\pi\) | ||
0.757156 | − | 0.653234i | \(-0.226588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 10.4721i | − | 0.650707i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.52786 | + | 10.6525i | −0.589760 | + | 0.659372i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.4721 | 0.645740 | 0.322870 | − | 0.946443i | \(-0.395352\pi\) | ||||
0.322870 | + | 0.946443i | \(0.395352\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4721 | −0.643298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.47214 | − | 2.47214i | −0.396088 | − | 0.151292i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.1803i | 0.986533i | 0.869878 | + | 0.493266i | \(0.164197\pi\) | ||||
−0.869878 | + | 0.493266i | \(0.835803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 0.291796i | − | 0.0177253i | −0.999961 | − | 0.00886267i | \(-0.997179\pi\) | ||
0.999961 | − | 0.00886267i | \(-0.00282111\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.94427 | − | 3.41641i | −0.541332 | − | 0.206770i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.6525 | 1.72781 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.52786 | −0.452306 | −0.226153 | − | 0.974092i | \(-0.572615\pi\) | ||||
−0.226153 | + | 0.974092i | \(0.572615\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.4721 | + | 11.7082i | −0.626950 | + | 0.700952i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.9443i | 1.48805i | 0.668151 | + | 0.744025i | \(0.267086\pi\) | ||||
−0.668151 | + | 0.744025i | \(0.732914\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.7639i | − | 1.23429i | −0.786850 | − | 0.617144i | \(-0.788290\pi\) | ||
0.786850 | − | 0.617144i | \(-0.211710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.52786 | − | 4.00000i | 0.0905029 | − | 0.236940i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.00000 | 0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8885 | 0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.291796 | + | 0.763932i | −0.0171054 | + | 0.0447825i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.7639i | 1.21304i | 0.795068 | + | 0.606521i | \(0.207435\pi\) | ||||
−0.795068 | + | 0.606521i | \(0.792565\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.00000i | − | 0.232889i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.1803 | + | 12.4721i | −1.40309 | + | 0.723707i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.0557 | −0.639369 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.94427 | 0.515539 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.76393 | − | 1.05573i | −0.158784 | − | 0.0606500i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.52786i | − | 0.0874852i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 27.5967i | − | 1.57503i | −0.616296 | − | 0.787515i | \(-0.711367\pi\) | ||
0.616296 | − | 0.787515i | \(-0.288633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.9443 | + | 8.76393i | 1.30525 | + | 0.498563i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.52786 | 0.313456 | 0.156728 | − | 0.987642i | \(-0.449905\pi\) | ||||
0.156728 | + | 0.987642i | \(0.449905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.472136 | −0.0266867 | −0.0133434 | − | 0.999911i | \(-0.504247\pi\) | ||||
−0.0133434 | + | 0.999911i | \(0.504247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.94427 | + | 8.00000i | 0.503953 | + | 0.450749i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.1246i | 0.737152i | 0.929598 | + | 0.368576i | \(0.120155\pi\) | ||||
−0.929598 | + | 0.368576i | \(0.879845\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9443i | 1.39661i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.76393 | + | 22.9443i | −0.489155 | + | 1.28062i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.88854 | −0.105081 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.4721 | 1.35747 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.23607 | + | 13.7082i | −0.289555 | + | 0.758065i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.88854i | 0.545173i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 32.5410i | − | 1.78862i | −0.447452 | − | 0.894308i | \(-0.647668\pi\) | ||
0.447452 | − | 0.894308i | \(-0.352332\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.9443 | − | 16.9443i | −1.03814 | − | 0.928540i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31.4164 | −1.71646 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3607 | 1.21806 | 0.609032 | − | 0.793146i | \(-0.291558\pi\) | ||||
0.609032 | + | 0.793146i | \(0.291558\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.9443 | + | 4.94427i | 0.703036 | + | 0.268536i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.4164i | 1.48468i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.4164i | − | 0.832408i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.9443 | + | 4.94427i | 0.696896 | + | 0.266191i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.7082 | 1.27272 | 0.636362 | − | 0.771391i | \(-0.280439\pi\) | ||||
0.636362 | + | 0.771391i | \(0.280439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.4721 | −1.52408 | −0.762039 | − | 0.647531i | \(-0.775802\pi\) | ||||
−0.762039 | + | 0.647531i | \(0.775802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.6525 | + | 10.6525i | −1.10235 | + | 0.568587i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.88854i | − | 0.526314i | −0.964753 | − | 0.263157i | \(-0.915236\pi\) | ||
0.964753 | − | 0.263157i | \(-0.0847637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.8885i | 2.64781i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.88854 | − | 4.94427i | 0.0999523 | − | 0.261679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.4164 | −1.65809 | −0.829047 | − | 0.559178i | \(-0.811117\pi\) | ||||
−0.829047 | + | 0.559178i | \(0.811117\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4164 | 0.969285 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.1459 | + | 26.5623i | −0.532522 | + | 1.39416i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.47214i | 0.338767i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5.23607i | − | 0.273321i | −0.990618 | − | 0.136660i | \(-0.956363\pi\) | ||
0.990618 | − | 0.136660i | \(-0.0436369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.9443 | − | 14.4721i | 0.673852 | − | 0.753389i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | −0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.58359 | −0.133773 | −0.0668867 | − | 0.997761i | \(-0.521307\pi\) | ||||
−0.0668867 | + | 0.997761i | \(0.521307\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.47214 | − | 0.944272i | −0.127661 | − | 0.0487620i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.3050i | 1.09726i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.6525i | − | 0.547181i | −0.961846 | − | 0.273590i | \(-0.911789\pi\) | ||
0.961846 | − | 0.273590i | \(-0.0882113\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.4164 | + | 8.18034i | 1.09720 | + | 0.419092i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.9443 | 1.47898 | 0.739492 | − | 0.673166i | \(-0.235066\pi\) | ||||
0.739492 | + | 0.673166i | \(0.235066\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.9443 | 1.06742 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.4721 | − | 16.1803i | 0.735660 | − | 0.822493i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 32.1803i | − | 1.63161i | −0.578328 | − | 0.815804i | \(-0.696295\pi\) | ||
0.578328 | − | 0.815804i | \(-0.303705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.11146i | − | 0.309070i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.18034 | + | 10.9443i | −0.210870 | + | 0.552065i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.944272 | −0.0475115 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.4164 | −0.874104 | −0.437052 | − | 0.899436i | \(-0.643978\pi\) | ||||
−0.437052 | + | 0.899436i | \(0.643978\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.583592 | − | 1.52786i | 0.0292161 | − | 0.0764889i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.3607i | 1.41626i | 0.706080 | + | 0.708132i | \(0.250462\pi\) | ||||
−0.706080 | + | 0.708132i | \(0.749538\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.4164i | 1.16645i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 28.9443 | − | 3.23607i | 1.43825 | − | 0.160802i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.3607 | −2.19888 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.8885 | −1.57679 | −0.788394 | − | 0.615171i | \(-0.789087\pi\) | ||||
−0.788394 | + | 0.615171i | \(0.789087\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.47214 | − | 0.944272i | −0.121941 | − | 0.0465775i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.52786i | − | 0.0751813i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.94427i | 0.439057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.7082 | + | 6.00000i | 0.769234 | + | 0.293821i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1803 | 0.497342 | 0.248671 | − | 0.968588i | \(-0.420006\pi\) | ||||
0.248671 | + | 0.968588i | \(0.420006\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4164 | 1.04377 | 0.521886 | − | 0.853015i | \(-0.325229\pi\) | ||||
0.521886 | + | 0.853015i | \(0.325229\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.8885 | + | 16.0000i | 0.869771 | + | 0.777947i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.5279i | 0.656198i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 0.583592i | − | 0.0282420i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.4721 | + | 37.8885i | −0.698721 | + | 1.82928i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000 | 0.385346 | 0.192673 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192673 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.4721 | 0.791600 | 0.395800 | − | 0.918337i | \(-0.370467\pi\) | ||||
0.395800 | + | 0.918337i | \(0.370467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.52786 | − | 24.9443i | 0.456826 | − | 1.19599i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.88854i | − | 0.0903413i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.1803i | − | 1.05861i | −0.848432 | − | 0.529305i | \(-0.822453\pi\) | ||
0.848432 | − | 0.529305i | \(-0.177547\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.2361 | − | 10.9443i | −0.582670 | − | 0.521156i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.2918 | −0.774047 | −0.387023 | − | 0.922070i | \(-0.626497\pi\) | ||||
−0.387023 | + | 0.922070i | \(0.626497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.9443 | 0.613617 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.7082 | − | 6.00000i | −0.742973 | − | 0.283790i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.583592i | 0.0275414i | 0.999905 | + | 0.0137707i | \(0.00438349\pi\) | ||||
−0.999905 | + | 0.0137707i | \(0.995617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 33.8885i | − | 1.59575i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.8885 | − | 12.1803i | −1.49825 | − | 0.572282i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.8885 | 0.838628 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.88854 | − | 11.4164i | −0.274854 | − | 0.532872i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.18034i | 0.380996i | 0.981688 | + | 0.190498i | \(0.0610103\pi\) | ||||
−0.981688 | + | 0.190498i | \(0.938990\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.7639i | 1.61562i | 0.589445 | + | 0.807808i | \(0.299346\pi\) | ||||
−0.589445 | + | 0.807808i | \(0.700654\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.4721 | − | 27.4164i | 0.485634 | − | 1.27141i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.7639 | −0.498095 | −0.249048 | − | 0.968491i | \(-0.580118\pi\) | ||||
−0.249048 | + | 0.968491i | \(0.580118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0000 | −0.554109 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.76393 | − | 7.23607i | 0.127355 | − | 0.333420i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 37.8885i | − | 1.74212i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.18034i | 0.191807i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.47214 | + | 7.23607i | −0.296339 | + | 0.331317i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.11146 | −0.279240 | −0.139620 | − | 0.990205i | \(-0.544588\pi\) | ||||
−0.139620 | + | 0.990205i | \(0.544588\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.8885 | −1.72757 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.94427 | + | 1.88854i | 0.224972 | + | 0.0859317i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.52786i | − | 0.0693767i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.6525i | 1.47962i | 0.672813 | + | 0.739812i | \(0.265086\pi\) | ||||
−0.672813 | + | 0.739812i | \(0.734914\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.76393 | − | 2.58359i | −0.305876 | − | 0.116834i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.0689 | 1.44725 | 0.723624 | − | 0.690194i | \(-0.242475\pi\) | ||||
0.723624 | + | 0.690194i | \(0.242475\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.7771 | −0.530413 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 33.8885 | − | 37.8885i | 1.52318 | − | 1.70296i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.0557i | 0.854766i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.2361i | 1.21925i | 0.792688 | + | 0.609627i | \(0.208681\pi\) | ||||
−0.792688 | + | 0.609627i | \(0.791319\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.36068 | + | 21.8885i | −0.373528 | + | 0.977908i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.5279 | 0.959880 | 0.479940 | − | 0.877301i | \(-0.340658\pi\) | ||||
0.479940 | + | 0.877301i | \(0.340658\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.52786 | 0.245987 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.32624 | + | 11.3262i | −0.192135 | + | 0.503016i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 25.7082i | − | 1.13950i | −0.821819 | − | 0.569748i | \(-0.807041\pi\) | ||
0.821819 | − | 0.569748i | \(-0.192959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.47214i | 0.109361i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.81966 | − | 3.52786i | −0.0803400 | − | 0.155759i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.8885 | −2.02209 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.8885 | 1.84226 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.6525 | + | 14.0000i | 1.60887 | + | 0.614532i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 24.3607i | − | 1.06726i | −0.845718 | − | 0.533630i | \(-0.820827\pi\) | ||
0.845718 | − | 0.533630i | \(-0.179173\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 11.8197i | − | 0.516838i | −0.966033 | − | 0.258419i | \(-0.916799\pi\) | ||
0.966033 | − | 0.258419i | \(-0.0832015\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.9443 | − | 4.18034i | −0.477647 | − | 0.182445i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.9443 | −0.563861 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.76393 | − | 2.47214i | −0.119944 | − | 0.107282i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 28.9443i | − | 1.25372i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 45.8885i | − | 1.98393i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.81966 | − | 10.0000i | 0.164831 | − | 0.431532i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.6525 | −1.23415 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3607 | 1.13333 | 0.566667 | − | 0.823947i | \(-0.308233\pi\) | ||||
0.566667 | + | 0.823947i | \(0.308233\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6525 | − | 33.1246i | 0.542970 | − | 1.42151i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 27.4164i | − | 1.17439i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.23607i | 0.309392i | 0.987962 | + | 0.154696i | \(0.0494398\pi\) | ||||
−0.987962 | + | 0.154696i | \(0.950560\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.05573 | − | 0.944272i | −0.0450574 | − | 0.0403005i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.63932 | −0.155040 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.360680 | −0.0153377 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 44.3607 | + | 16.9443i | 1.88301 | + | 0.719244i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14.6525i | − | 0.620845i | −0.950599 | − | 0.310423i | \(-0.899529\pi\) | ||
0.950599 | − | 0.310423i | \(-0.100471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 32.3607i | − | 1.36871i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.9443 | − | 8.00000i | −0.884268 | − | 0.337760i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.5410 | −1.28715 | −0.643575 | − | 0.765383i | \(-0.722550\pi\) | ||||
−0.643575 | + | 0.765383i | \(0.722550\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.8885 | −1.08914 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.0557 | − | 1.23607i | 0.464297 | − | 0.0519100i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.4721i | 1.94821i | 0.226089 | + | 0.974107i | \(0.427406\pi\) | ||||
−0.226089 | + | 0.974107i | \(0.572594\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.12461i | 0.214458i | 0.994234 | + | 0.107229i | \(0.0341979\pi\) | ||||
−0.994234 | + | 0.107229i | \(0.965802\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | − | 20.9443i | 0.334205 | − | 0.874960i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5279 | −0.564151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.4721 | 1.18531 | 0.592655 | − | 0.805456i | \(-0.298080\pi\) | ||||
0.592655 | + | 0.805456i | \(0.298080\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.34752 | − | 19.2361i | 0.305353 | − | 0.799424i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.41641i | 0.141736i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.9443i | 0.701760i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.9443 | − | 32.3607i | 1.19670 | − | 1.33795i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.5967 | −0.891393 | −0.445697 | − | 0.895184i | \(-0.647044\pi\) | ||||
−0.445697 | + | 0.895184i | \(0.647044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.70820 | − | 2.94427i | −0.317073 | − | 0.121111i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.9443i | − | 1.18860i | −0.804244 | − | 0.594299i | \(-0.797429\pi\) | ||
0.804244 | − | 0.594299i | \(-0.202571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.88854i | 0.405391i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.0000 | + | 3.81966i | 0.409273 | + | 0.156328i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.41641 | −0.303026 | −0.151513 | − | 0.988455i | \(-0.548415\pi\) | ||||
−0.151513 | + | 0.988455i | \(0.548415\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.7771 | 1.37780 | 0.688898 | − | 0.724858i | \(-0.258095\pi\) | ||||
0.688898 | + | 0.724858i | \(0.258095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.4164 | + | 21.7082i | −0.790697 | + | 0.884026i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 53.1246i | − | 2.15982i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7639i | 1.41102i | 0.708698 | + | 0.705512i | \(0.249283\pi\) | ||||
−0.708698 | + | 0.705512i | \(0.750717\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.63932 | − | 9.52786i | 0.147473 | − | 0.386089i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.7771 | 1.44739 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.3050 | −0.779720 | −0.389860 | − | 0.920874i | \(-0.627477\pi\) | ||||
−0.389860 | + | 0.920874i | \(0.627477\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.9443 | + | 33.8885i | −0.521963 | + | 1.36652i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.8885i | 0.881200i | 0.897704 | + | 0.440600i | \(0.145234\pi\) | ||||
−0.897704 | + | 0.440600i | \(0.854766\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.1246i | 1.17062i | 0.810811 | + | 0.585308i | \(0.199027\pi\) | ||||
−0.810811 | + | 0.585308i | \(0.800973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.4164 | − | 5.88854i | 0.458125 | − | 0.236299i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.94427 | 0.198088 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.47214 | − | 2.47214i | −0.258472 | − | 0.0987276i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 20.9443i | − | 0.835103i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.1246i | − | 0.761339i | −0.924711 | − | 0.380669i | \(-0.875694\pi\) | ||
0.924711 | − | 0.380669i | \(-0.124306\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.1803 | − | 6.94427i | −0.722604 | − | 0.276010i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.8328 | −1.69977 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.4721 | −0.969621 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.4721 | + | 30.8328i | 1.36370 | + | 1.21973i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.3050i | 0.999485i | 0.866174 | + | 0.499743i | \(0.166572\pi\) | ||||
−0.866174 | + | 0.499743i | \(0.833428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.3475i | 0.526375i | 0.964745 | + | 0.263187i | \(0.0847738\pi\) | ||||
−0.964745 | + | 0.263187i | \(0.915226\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.4721 | + | 37.8885i | −0.569840 | + | 1.49186i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.3050 | 1.30935 | 0.654676 | − | 0.755909i | \(-0.272805\pi\) | ||||
0.654676 | + | 0.755909i | \(0.272805\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.47214 | −0.254054 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | − | 10.4721i | 0.156772 | − | 0.410435i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.2918i | 0.559281i | 0.960105 | + | 0.279641i | \(0.0902153\pi\) | ||||
−0.960105 | + | 0.279641i | \(0.909785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 21.8885i | − | 0.855256i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.47214 | + | 4.00000i | 0.174475 | + | 0.156055i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.2918 | −1.10209 | −0.551046 | − | 0.834475i | \(-0.685771\pi\) | ||||
−0.551046 | + | 0.834475i | \(0.685771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −51.3050 | −1.99553 | −0.997766 | − | 0.0668107i | \(-0.978718\pi\) | ||||
−0.997766 | + | 0.0668107i | \(0.978718\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.8885 | − | 6.83282i | −0.694733 | − | 0.265365i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.05573i | 0.118496i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.7771i | − | 0.456011i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.4721 | + | 6.29180i | 0.636850 | + | 0.243255i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.47214 | −0.0954358 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.4164 | −0.979731 | −0.489865 | − | 0.871798i | \(-0.662954\pi\) | ||||
−0.489865 | + | 0.871798i | \(0.662954\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.2705 | + | 13.0344i | −0.972662 | + | 0.501696i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 14.2918i | − | 0.549278i | −0.961547 | − | 0.274639i | \(-0.911442\pi\) | ||
0.961547 | − | 0.274639i | \(-0.0885584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 0.583592i | − | 0.0223962i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.34752 | + | 3.52786i | −0.0516372 | + | 0.135188i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.2361 | −0.506464 | −0.253232 | − | 0.967406i | \(-0.581494\pi\) | ||||
−0.253232 | + | 0.967406i | \(0.581494\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.94427 | 0.188911 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.12461 | + | 18.6525i | −0.271821 | + | 0.711636i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.4721i | 0.551344i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.7082i | − | 1.13015i | −0.825038 | − | 0.565077i | \(-0.808847\pi\) | ||
0.825038 | − | 0.565077i | \(-0.191153\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.9443 | − | 14.4721i | 0.491712 | − | 0.549751i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.4164 | −1.19169 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000 | 0.606043 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 40.3607 | + | 15.4164i | 1.52658 | + | 0.583102i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.2918i | 0.539794i | 0.962889 | + | 0.269897i | \(0.0869896\pi\) | ||||
−0.962889 | + | 0.269897i | \(0.913010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.47214i | − | 0.244101i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −41.8885 | − | 16.0000i | −1.57761 | − | 0.602595i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.11146 | 0.0794095 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.52786 | −0.282715 | −0.141357 | − | 0.989959i | \(-0.545147\pi\) | ||||
−0.141357 | + | 0.989959i | \(0.545147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.583592 | + | 0.652476i | −0.0218864 | + | 0.0244698i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.9443i | − | 0.484767i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 75.7771i | − | 2.83390i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.94427 | + | 12.9443i | −0.184647 | + | 0.483413i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.8328 | −1.14987 | −0.574935 | − | 0.818199i | \(-0.694973\pi\) | ||||
−0.574935 | + | 0.818199i | \(0.694973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.5279 | −0.652772 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.23607 | − | 3.23607i | 0.0459699 | − | 0.120351i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.0689i | 0.968174i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 14.1803i | − | 0.525920i | −0.964807 | − | 0.262960i | \(-0.915301\pi\) | ||
0.964807 | − | 0.262960i | \(-0.0846987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.6525 | − | 22.0000i | 0.579721 | − | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.8885 | 0.661632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4164 | 1.08652 | 0.543260 | − | 0.839565i | \(-0.317190\pi\) | ||||
0.543260 | + | 0.839565i | \(0.317190\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.6525 | + | 10.9443i | 1.05686 | + | 0.403686i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 50.8328i | 1.87245i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.1246i | 0.482797i | 0.970426 | + | 0.241398i | \(0.0776060\pi\) | ||||
−0.970426 | + | 0.241398i | \(0.922394\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.52786 | − | 2.11146i | −0.203071 | − | 0.0775663i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.41641 | 0.272082 | 0.136041 | − | 0.990703i | \(-0.456562\pi\) | ||||
0.136041 | + | 0.990703i | \(0.456562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.4164 | 1.15101 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.18034 | + | 5.52786i | 0.226127 | + | 0.202254i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 17.5279i | − | 0.640454i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.5967i | 0.642114i | 0.947060 | + | 0.321057i | \(0.104038\pi\) | ||||
−0.947060 | + | 0.321057i | \(0.895962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.6525 | + | 38.3607i | −0.533966 | + | 1.39794i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.7771 | 2.32109 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.41641 | 0.196863 | 0.0984313 | − | 0.995144i | \(-0.468618\pi\) | ||||
0.0984313 | + | 0.995144i | \(0.468618\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | − | 20.9443i | 0.290382 | − | 0.760229i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 42.2492i | − | 1.53153i | −0.643119 | − | 0.765767i | \(-0.722360\pi\) | ||
0.643119 | − | 0.765767i | \(-0.277640\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 10.4721i | − | 0.379117i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.8885 | + | 16.0000i | 0.646762 | + | 0.578481i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.52786 | −0.199600 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.7771 | 1.79501 | 0.897504 | − | 0.441007i | \(-0.145378\pi\) | ||||
0.897504 | + | 0.441007i | \(0.145378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.8885 | + | 12.9443i | 1.22047 | + | 0.466177i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.81966i | 0.281254i | 0.990063 | + | 0.140627i | \(0.0449118\pi\) | ||||
−0.990063 | + | 0.140627i | \(0.955088\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.6525i | 1.02923i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.9443 | + | 6.47214i | 0.607872 | + | 0.232187i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.94427 | 0.177147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.7214 | 2.88844 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.3475 | − | 22.0000i | −0.405527 | − | 0.786216i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.4721i | 0.516533i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.1803i | 1.00452i | 0.864716 | + | 0.502260i | \(0.167498\pi\) | ||||
−0.864716 | + | 0.502260i | \(0.832502\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.47214 | + | 16.9443i | −0.230414 | + | 0.603232i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.88854 | −0.351596 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.11146 | −0.0749800 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.47214 | − | 16.9443i | 0.229543 | − | 0.600951i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.0689i | 1.77353i | 0.462220 | + | 0.886765i | \(0.347053\pi\) | ||||
−0.462220 | + | 0.886765i | \(0.652947\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.7771i | 0.699663i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.00000 | − | 8.94427i | 0.282666 | − | 0.316030i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.4721 | 0.369554 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.88854 | −0.348525 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.1803 | − | 10.0000i | −0.921592 | − | 0.352017i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.41641i | − | 0.120115i | −0.998195 | − | 0.0600573i | \(-0.980872\pi\) | ||
0.998195 | − | 0.0600573i | \(-0.0191283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.1803i | 1.83230i | 0.400836 | + | 0.916150i | \(0.368720\pi\) | ||||
−0.400836 | + | 0.916150i | \(0.631280\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.472136 | + | 0.180340i | 0.0165585 | + | 0.00632480i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5279 | 0.473860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.52786 | 0.193395 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.0557 | − | 12.3607i | 0.386318 | − | 0.431917i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.4296i | 1.76000i | 0.474970 | + | 0.880002i | \(0.342459\pi\) | ||||
−0.474970 | + | 0.880002i | \(0.657541\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 51.1246i | − | 1.78209i | −0.453913 | − | 0.891046i | \(-0.649972\pi\) | ||
0.453913 | − | 0.891046i | \(-0.350028\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.7082 | + | 46.3607i | −0.616521 | + | 1.61407i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.1246 | 0.665028 | 0.332514 | − | 0.943098i | \(-0.392103\pi\) | ||||
0.332514 | + | 0.943098i | \(0.392103\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.47214 | −0.155324 | −0.0776619 | − | 0.996980i | \(-0.524745\pi\) | ||||
−0.0776619 | + | 0.996980i | \(0.524745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.65248 | − | 12.1803i | 0.161393 | − | 0.422531i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 13.5279i | − | 0.468713i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 43.7771i | − | 1.51497i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.4721 | − | 24.1803i | −0.431100 | − | 0.835795i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.4164 | −1.08461 | −0.542307 | − | 0.840180i | \(-0.682449\pi\) | ||||
−0.542307 | + | 0.840180i | \(0.682449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.30495 | 0.217412 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −40.3607 | − | 15.4164i | −1.39010 | − | 0.530969i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 22.6525i | − | 0.779269i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.2918i | − | 0.697234i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.5967 | + | 12.8328i | 1.15304 | + | 0.440421i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.9443 | 0.717960 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.3050 | 1.34578 | 0.672888 | − | 0.739744i | \(-0.265054\pi\) | ||||
0.672888 | + | 0.739744i | \(0.265054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.52786 | + | 4.94427i | 0.189049 | + | 0.169091i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.63932i | − | 0.260954i | −0.991451 | − | 0.130477i | \(-0.958349\pi\) | ||
0.991451 | − | 0.130477i | \(-0.0416509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 16.7639i | − | 0.571978i | −0.958233 | − | 0.285989i | \(-0.907678\pi\) | ||
0.958233 | − | 0.285989i | \(-0.0923221\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.94427 | + | 12.9443i | −0.168500 | + | 0.441140i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.8328 | −0.777238 | −0.388619 | − | 0.921399i | \(-0.627048\pi\) | ||||
−0.388619 | + | 0.921399i | \(0.627048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −73.3050 | −2.49244 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.72949 | + | 17.6180i | −0.228545 | + | 0.598340i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.52786i | 0.0518292i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.4164i | 1.47111i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.05573 | − | 0.944272i | −0.0357310 | − | 0.0319588i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.88854 | 0.0638444 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.5836 | −0.627523 | −0.313762 | − | 0.949502i | \(-0.601589\pi\) | ||||
−0.313762 | + | 0.949502i | \(0.601589\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33.5967 | − | 12.8328i | −1.13319 | − | 0.432840i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 24.0000i | − | 0.808581i | −0.914631 | − | 0.404290i | \(-0.867519\pi\) | ||
0.914631 | − | 0.404290i | \(-0.132481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 0.763932i | − | 0.0257084i | −0.999917 | − | 0.0128542i | \(-0.995908\pi\) | ||
0.999917 | − | 0.0128542i | \(-0.00409173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.47214 | + | 2.47214i | 0.217558 | + | 0.0830999i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.3607 | −0.683645 | −0.341822 | − | 0.939765i | \(-0.611044\pi\) | ||||
−0.341822 | + | 0.939765i | \(0.611044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.3607 | −0.548720 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.23607 | − | 46.8328i | −0.175415 | − | 1.56896i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.11146i | 0.204512i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000i | 0.668526i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.83282 | − | 17.8885i | 0.228141 | − | 0.597281i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.9443 | −0.831938 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.00000 | −0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.52786 | + | 14.4721i | −0.183956 | + | 0.481603i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 66.2492i | 2.20220i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.2361i | 1.30281i | 0.758729 | + | 0.651406i | \(0.225821\pi\) | ||||
−0.758729 | + | 0.651406i | \(0.774179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.41641 | − | 3.81966i | 0.113315 | − | 0.126690i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.8885 | 1.12278 | 0.561389 | − | 0.827552i | \(-0.310267\pi\) | ||||
0.561389 | + | 0.827552i | \(0.310267\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4721 | 0.478958 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.47214 | + | 0.944272i | 0.0817263 | + | 0.0312167i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 8.36068i | − | 0.276094i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.5410i | 1.93109i | 0.260236 | + | 0.965545i | \(0.416200\pi\) | ||||
−0.260236 | + | 0.965545i | \(0.583800\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.6525 | + | 17.0557i | 1.47135 | + | 0.562005i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 68.9443 | 2.26933 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.3607 | −1.52433 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.3607 | + | 31.7082i | −0.931487 | + | 1.04143i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.4164i | 1.55568i | 0.628461 | + | 0.777841i | \(0.283685\pi\) | ||||
−0.628461 | + | 0.777841i | \(0.716315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.18034i | − | 0.137005i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.41641 | + | 8.94427i | −0.111848 | + | 0.292822i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.8885 | 1.36990 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.3607 | −0.469143 | −0.234571 | − | 0.972099i | \(-0.575369\pi\) | ||||
−0.234571 | + | 0.972099i | \(0.575369\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.291796 | − | 0.763932i | 0.00952240 | − | 0.0249300i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.70820i | − | 0.0556859i | −0.999612 | − | 0.0278429i | \(-0.991136\pi\) | ||
0.999612 | − | 0.0278429i | \(-0.00886382\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000i | 0.521032i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.4721 | + | 9.52786i | −0.600899 | + | 0.309941i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.0689 | −0.782134 | −0.391067 | − | 0.920362i | \(-0.627894\pi\) | ||||
−0.391067 | + | 0.920362i | \(0.627894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.94427 | 0.290343 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.2361 | − | 8.11146i | −0.688627 | − | 0.263032i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.3607i | 0.789120i | 0.918870 | + | 0.394560i | \(0.129103\pi\) | ||||
−0.918870 | + | 0.394560i | \(0.870897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.8885i | 1.35548i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −40.3607 | − | 15.4164i | −1.30468 | − | 0.498342i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.88854 | 0.0609843 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.58359 | 0.115600 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −31.7082 | − | 28.3607i | −1.02178 | − | 0.913910i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 38.4721i | 1.23846i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.23607i | − | 0.297012i | −0.988912 | − | 0.148506i | \(-0.952554\pi\) | ||
0.988912 | − | 0.148506i | \(-0.0474464\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.16718 | − | 3.05573i | 0.0374954 | − | 0.0981641i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0132 | −0.545978 | −0.272989 | − | 0.962017i | \(-0.588012\pi\) | ||||
−0.272989 | + | 0.962017i | \(0.588012\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | −0.384702 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.1246 | + | 39.5967i | −0.484375 | + | 1.26811i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 60.3607i | − | 1.93111i | −0.260200 | − | 0.965555i | \(-0.583789\pi\) | ||
0.260200 | − | 0.965555i | \(-0.416211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 20.9443i | − | 0.669382i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.9443 | − | 16.9443i | −0.604844 | − | 0.540989i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.5279 | 0.686632 | 0.343316 | − | 0.939220i | \(-0.388450\pi\) | ||||
0.343316 | + | 0.939220i | \(0.388450\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.4164 | 0.491208 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.0000 | − | 6.11146i | −0.509286 | − | 0.194530i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.8885i | 0.568823i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 50.1803i | − | 1.59403i | −0.603959 | − | 0.797016i | \(-0.706411\pi\) | ||
0.603959 | − | 0.797016i | \(-0.293589\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 52.6525 | + | 20.1115i | 1.67088 | + | 0.638218i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.0000 | −0.634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.3607 | 0.581489 | 0.290744 | − | 0.956801i | \(-0.406097\pi\) | ||||
0.290744 | + | 0.956801i | \(0.406097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.1246 | − | 20.1803i | 1.23785 | − | 0.638478i |
(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 | 384.2.c.d.383.2 | yes | 4 | |
3.2 | odd | 2 | 384.2.c.a.383.4 | yes | 4 | ||
4.3 | odd | 2 | 384.2.c.a.383.3 | ✓ | 4 | ||
8.3 | odd | 2 | 384.2.c.c.383.2 | yes | 4 | ||
8.5 | even | 2 | 384.2.c.b.383.3 | yes | 4 | ||
12.11 | even | 2 | inner | 384.2.c.d.383.1 | yes | 4 | |
16.3 | odd | 4 | 768.2.f.e.383.4 | 4 | |||
16.5 | even | 4 | 768.2.f.f.383.4 | 4 | |||
16.11 | odd | 4 | 768.2.f.c.383.1 | 4 | |||
16.13 | even | 4 | 768.2.f.b.383.1 | 4 | |||
24.5 | odd | 2 | 384.2.c.c.383.1 | yes | 4 | ||
24.11 | even | 2 | 384.2.c.b.383.4 | yes | 4 | ||
48.5 | odd | 4 | 768.2.f.e.383.3 | 4 | |||
48.11 | even | 4 | 768.2.f.b.383.2 | 4 | |||
48.29 | odd | 4 | 768.2.f.c.383.2 | 4 | |||
48.35 | even | 4 | 768.2.f.f.383.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.2.c.a.383.3 | ✓ | 4 | 4.3 | odd | 2 | ||
384.2.c.a.383.4 | yes | 4 | 3.2 | odd | 2 | ||
384.2.c.b.383.3 | yes | 4 | 8.5 | even | 2 | ||
384.2.c.b.383.4 | yes | 4 | 24.11 | even | 2 | ||
384.2.c.c.383.1 | yes | 4 | 24.5 | odd | 2 | ||
384.2.c.c.383.2 | yes | 4 | 8.3 | odd | 2 | ||
384.2.c.d.383.1 | yes | 4 | 12.11 | even | 2 | inner | |
384.2.c.d.383.2 | yes | 4 | 1.1 | even | 1 | trivial | |
768.2.f.b.383.1 | 4 | 16.13 | even | 4 | |||
768.2.f.b.383.2 | 4 | 48.11 | even | 4 | |||
768.2.f.c.383.1 | 4 | 16.11 | odd | 4 | |||
768.2.f.c.383.2 | 4 | 48.29 | odd | 4 | |||
768.2.f.e.383.3 | 4 | 48.5 | odd | 4 | |||
768.2.f.e.383.4 | 4 | 16.3 | odd | 4 | |||
768.2.f.f.383.3 | 4 | 48.35 | even | 4 | |||
768.2.f.f.383.4 | 4 | 16.5 | even | 4 |