Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(239,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.j (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.36594701583\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.4 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.239 |
Dual form | 672.2.j.c.239.3 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.61803 | + | 0.618034i | 0.934172 | + | 0.356822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.23607 | 1.44721 | 0.723607 | − | 0.690212i | \(-0.242483\pi\) | ||||
0.723607 | + | 0.690212i | \(0.242483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214i | 1.34840i | 0.738549 | + | 0.674200i | \(0.235511\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.23607i | − | 0.342824i | −0.985199 | − | 0.171412i | \(-0.945167\pi\) | ||
0.985199 | − | 0.171412i | \(-0.0548329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.23607 | + | 2.00000i | 1.35195 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.23607 | −1.66007 | −0.830034 | − | 0.557713i | \(-0.811679\pi\) | ||||
−0.830034 | + | 0.557713i | \(0.811679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.618034 | − | 1.61803i | 0.134866 | − | 0.353084i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.472136 | 0.0984472 | 0.0492236 | − | 0.998788i | \(-0.484325\pi\) | ||||
0.0492236 | + | 0.998788i | \(0.484325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.38197 | + | 4.61803i | 0.458410 | + | 0.888741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.94427i | − | 1.60644i | −0.595683 | − | 0.803219i | \(-0.703119\pi\) | ||
0.595683 | − | 0.803219i | \(-0.296881\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.76393 | + | 7.23607i | −0.481139 | + | 1.25964i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.23607i | − | 0.546995i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.47214i | − | 1.06401i | −0.846740 | − | 0.532006i | \(-0.821438\pi\) | ||
0.846740 | − | 0.532006i | \(-0.178562\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.763932 | − | 2.00000i | 0.122327 | − | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.47214i | 0.698430i | 0.937043 | + | 0.349215i | \(0.113552\pi\) | ||||
−0.937043 | + | 0.349215i | \(0.886448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.472136 | 0.0720001 | 0.0360000 | − | 0.999352i | \(-0.488538\pi\) | ||||
0.0360000 | + | 0.999352i | \(0.488538\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.23607 | + | 6.47214i | 1.07869 | + | 0.964809i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.47214 | −0.360598 | −0.180299 | − | 0.983612i | \(-0.557707\pi\) | ||||
−0.180299 | + | 0.983612i | \(0.557707\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.23607 | − | 3.23607i | 0.173084 | − | 0.453140i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4721 | −1.43846 | −0.719229 | − | 0.694773i | \(-0.755505\pi\) | ||||
−0.719229 | + | 0.694773i | \(0.755505\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4721i | 1.95142i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.7082 | − | 4.47214i | −1.55079 | − | 0.592349i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.23607i | − | 0.160922i | −0.996758 | − | 0.0804612i | \(-0.974361\pi\) | ||
0.996758 | − | 0.0804612i | \(-0.0256393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7082i | 1.49908i | 0.661958 | + | 0.749541i | \(0.269726\pi\) | ||||
−0.661958 | + | 0.749541i | \(0.730274\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | − | 2.23607i | 0.251976 | − | 0.281718i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.00000i | − | 0.496139i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9443 | 1.33706 | 0.668528 | − | 0.743687i | \(-0.266925\pi\) | ||||
0.668528 | + | 0.743687i | \(0.266925\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.763932 | + | 0.291796i | 0.0919666 | + | 0.0351281i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.94427 | 0.824133 | 0.412067 | − | 0.911154i | \(-0.364807\pi\) | ||||
0.412067 | + | 0.911154i | \(0.364807\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.472136 | −0.0552593 | −0.0276297 | − | 0.999618i | \(-0.508796\pi\) | ||||
−0.0276297 | + | 0.999618i | \(0.508796\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.85410 | + | 3.38197i | 1.02238 | + | 0.390516i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.47214 | 0.509647 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94427i | 0.556274i | 0.960541 | + | 0.278137i | \(0.0897169\pi\) | ||||
−0.960541 | + | 0.278137i | \(0.910283\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.2361i | − | 1.45285i | −0.687247 | − | 0.726424i | \(-0.741181\pi\) | ||
0.687247 | − | 0.726424i | \(-0.258819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.47214i | − | 0.702002i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.00000i | − | 0.635999i | −0.948091 | − | 0.317999i | \(-0.896989\pi\) | ||
0.948091 | − | 0.317999i | \(-0.103011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23607 | −0.129575 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.52786 | − | 14.4721i | 0.573213 | − | 1.50069i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −23.4164 | −2.40247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.52786 | 0.358200 | 0.179100 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179100 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.94427 | + | 10.0000i | −0.898933 | + | 1.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.29180 | −0.626057 | −0.313029 | − | 0.949744i | \(-0.601344\pi\) | ||||
−0.313029 | + | 0.949744i | \(0.601344\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.52786i | − | 0.150545i | −0.997163 | − | 0.0752725i | \(-0.976017\pi\) | ||
0.997163 | − | 0.0752725i | \(-0.0239827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | − | 5.23607i | 0.195180 | − | 0.510988i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.00000i | 0.193347i | 0.995316 | + | 0.0966736i | \(0.0308203\pi\) | ||||
−0.995316 | + | 0.0966736i | \(0.969180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.41641i | 0.710363i | 0.934797 | + | 0.355182i | \(0.115581\pi\) | ||||
−0.934797 | + | 0.355182i | \(0.884419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | − | 10.4721i | 0.379663 | − | 0.993971i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.9443i | − | 1.21769i | −0.793287 | − | 0.608847i | \(-0.791632\pi\) | ||
0.793287 | − | 0.608847i | \(-0.208368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.52786 | 0.142474 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.47214 | − | 2.76393i | 0.228549 | − | 0.255526i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.76393 | + | 7.23607i | −0.249215 | + | 0.652454i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.9443i | − | 1.50356i | −0.659413 | − | 0.751780i | \(-0.729195\pi\) | ||
0.659413 | − | 0.751780i | \(-0.270805\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.763932 | + | 0.291796i | 0.0672605 | + | 0.0256912i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.76393i | − | 0.241486i | −0.992684 | − | 0.120743i | \(-0.961472\pi\) | ||
0.992684 | − | 0.120743i | \(-0.0385277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.23607i | 0.627447i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.70820 | + | 14.9443i | 0.663417 | + | 1.28620i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.9443i | 1.44765i | 0.689985 | + | 0.723823i | \(0.257617\pi\) | ||||
−0.689985 | + | 0.723823i | \(0.742383\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6525 | −0.903531 | −0.451766 | − | 0.892137i | \(-0.649206\pi\) | ||||
−0.451766 | + | 0.892137i | \(0.649206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | − | 1.52786i | −0.336861 | − | 0.128669i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.52786 | 0.462263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.61803 | − | 0.618034i | −0.133453 | − | 0.0509746i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.4164 | −1.91835 | −0.959173 | − | 0.282819i | \(-0.908731\pi\) | ||||
−0.959173 | + | 0.282819i | \(0.908731\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.94427i | 0.727875i | 0.931423 | + | 0.363937i | \(0.118568\pi\) | ||||
−0.931423 | + | 0.363937i | \(0.881432\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | − | 4.47214i | 0.323381 | − | 0.361551i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 28.9443i | − | 2.32486i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.70820i | − | 0.295947i | −0.988991 | − | 0.147973i | \(-0.952725\pi\) | ||
0.988991 | − | 0.147973i | \(-0.0472750\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.9443 | − | 6.47214i | −1.34377 | − | 0.513274i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.472136i | − | 0.0372095i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.47214 | −0.663589 | −0.331794 | − | 0.943352i | \(-0.607654\pi\) | ||||
−0.331794 | + | 0.943352i | \(0.607654\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.94427 | + | 23.4164i | −0.696311 | + | 1.82296i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.944272 | 0.0730700 | 0.0365350 | − | 0.999332i | \(-0.488368\pi\) | ||||
0.0365350 | + | 0.999332i | \(0.488368\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4721 | 0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.1803 | − | 14.4721i | −1.23734 | − | 1.10671i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.7082 | −1.34633 | −0.673165 | − | 0.739492i | \(-0.735066\pi\) | ||||
−0.673165 | + | 0.739492i | \(0.735066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.47214i | − | 0.413655i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.763932 | − | 2.00000i | 0.0574206 | − | 0.150329i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.9443i | 1.11699i | 0.829509 | + | 0.558494i | \(0.188620\pi\) | ||||
−0.829509 | + | 0.558494i | \(0.811380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.2361i | − | 1.28115i | −0.767897 | − | 0.640573i | \(-0.778697\pi\) | ||
0.767897 | − | 0.640573i | \(-0.221303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.23607 | + | 18.9443i | −0.534906 | + | 1.40040i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 20.9443i | − | 1.53985i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.94427 | 0.654070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.61803 | − | 2.38197i | 0.335913 | − | 0.173263i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.00000 | −0.144715 | −0.0723575 | − | 0.997379i | \(-0.523052\pi\) | ||||
−0.0723575 | + | 0.997379i | \(0.523052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5279 | −0.829794 | −0.414897 | − | 0.909868i | \(-0.636182\pi\) | ||||
−0.414897 | + | 0.909868i | \(0.636182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.47214 | − | 6.47214i | 0.177033 | − | 0.463479i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4721 | 1.60107 | 0.800537 | − | 0.599284i | \(-0.204548\pi\) | ||||
0.800537 | + | 0.599284i | \(0.204548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.4721i | 0.742350i | 0.928563 | + | 0.371175i | \(0.121045\pi\) | ||||
−0.928563 | + | 0.371175i | \(0.878955\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.7082 | + | 6.76393i | 1.24904 | + | 0.477091i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.4721i | 1.01078i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.05573 | + | 0.944272i | 0.0733782 | + | 0.0656314i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 32.3607i | − | 2.23844i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.05573 | 0.623422 | 0.311711 | − | 0.950177i | \(-0.399098\pi\) | ||||
0.311711 | + | 0.950177i | \(0.399098\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.2361 | + | 4.29180i | 0.769883 | + | 0.294069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.52786 | 0.104199 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.94427 | −0.607177 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.763932 | − | 0.291796i | −0.0516217 | − | 0.0197178i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47214 | −0.166294 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.583592i | 0.0390802i | 0.999809 | + | 0.0195401i | \(0.00622021\pi\) | ||||
−0.999809 | + | 0.0195401i | \(0.993780\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2361 | + | 10.9443i | 0.815738 | + | 0.729618i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.291796i | 0.0193672i | 0.999953 | + | 0.00968359i | \(0.00308243\pi\) | ||||
−0.999953 | + | 0.00968359i | \(0.996918\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.29180i | − | 0.283610i | −0.989895 | − | 0.141805i | \(-0.954709\pi\) | ||
0.989895 | − | 0.141805i | \(-0.0452906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.23607 | + | 2.76393i | 0.476098 | + | 0.181853i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0000i | 1.04819i | 0.851658 | + | 0.524097i | \(0.175597\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.05573 | + | 8.00000i | −0.198491 | + | 0.519656i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.4164 | −0.867835 | −0.433918 | − | 0.900953i | \(-0.642869\pi\) | ||||
−0.433918 | + | 0.900953i | \(0.642869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.52786 | −0.227250 | −0.113625 | − | 0.993524i | \(-0.536246\pi\) | ||||
−0.113625 | + | 0.993524i | \(0.536246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.90983 | + | 15.0902i | −0.250816 | + | 0.968035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.23607 | −0.206745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94427i | 0.569110i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.18034 | − | 21.4164i | 0.518408 | − | 1.35721i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.29180i | 0.523374i | 0.965153 | + | 0.261687i | \(0.0842787\pi\) | ||||
−0.965153 | + | 0.261687i | \(0.915721\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.11146i | 0.132746i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.00000 | − | 10.4721i | 0.250490 | − | 0.655791i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.41641i | 0.0883531i | 0.999024 | + | 0.0441765i | \(0.0140664\pi\) | ||||
−0.999024 | + | 0.0441765i | \(0.985934\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.47214 | −0.402159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.0000 | −0.863277 | −0.431638 | − | 0.902047i | \(-0.642064\pi\) | ||||
−0.431638 | + | 0.902047i | \(0.642064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.8885 | −2.08176 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.70820 | − | 9.70820i | 0.226938 | − | 0.594132i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.1803 | 0.986533 | 0.493266 | − | 0.869878i | \(-0.335803\pi\) | ||||
0.493266 | + | 0.869878i | \(0.335803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.4721i | − | 0.879120i | −0.898213 | − | 0.439560i | \(-0.855134\pi\) | ||
0.898213 | − | 0.439560i | \(-0.144866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | − | 0.763932i | −0.121046 | − | 0.0462353i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.4721i | 1.47573i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.0000i | − | 0.721010i | −0.932757 | − | 0.360505i | \(-0.882604\pi\) | ||
0.932757 | − | 0.360505i | \(-0.117396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.8885 | − | 20.0000i | 1.07096 | − | 1.19737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.8885i | 1.06714i | 0.845756 | + | 0.533571i | \(0.179150\pi\) | ||||
−0.845756 | + | 0.533571i | \(0.820850\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.23607 | 0.192364 | 0.0961821 | − | 0.995364i | \(-0.469337\pi\) | ||||
0.0961821 | + | 0.995364i | \(0.469337\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −37.8885 | − | 14.4721i | −2.24432 | − | 0.857255i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.47214 | 0.263982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.70820 | + | 2.18034i | 0.334621 | + | 0.127814i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.1246 | 1.70148 | 0.850739 | − | 0.525588i | \(-0.176155\pi\) | ||||
0.850739 | + | 0.525588i | \(0.176155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.00000i | − | 0.232889i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −20.6525 | + | 10.6525i | −1.19838 | + | 0.618119i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 0.583592i | − | 0.0337500i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 0.472136i | − | 0.0272135i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1803 | − | 3.88854i | −0.584845 | − | 0.223391i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.8885i | 2.16949i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1246 | 0.977353 | 0.488677 | − | 0.872465i | \(-0.337480\pi\) | ||||
0.488677 | + | 0.872465i | \(0.337480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.944272 | − | 2.47214i | 0.0537178 | − | 0.140635i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.3607 | 1.15455 | 0.577274 | − | 0.816550i | \(-0.304116\pi\) | ||||
0.577274 | + | 0.816550i | \(0.304116\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.94427 | 0.166420 | 0.0832100 | − | 0.996532i | \(-0.473483\pi\) | ||||
0.0832100 | + | 0.996532i | \(0.473483\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.47214 | − | 7.23607i | 0.364664 | − | 0.407706i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.47214 | 0.138849 | 0.0694245 | − | 0.997587i | \(-0.477884\pi\) | ||||
0.0694245 | + | 0.997587i | \(0.477884\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.23607 | + | 3.23607i | −0.0689906 | + | 0.180620i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.4721i | 0.805251i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.76393i | − | 0.375195i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.58359 | + | 12.0000i | −0.253473 | + | 0.663602i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.47214i | 0.136293i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.3607 | 1.66877 | 0.834387 | − | 0.551179i | \(-0.185822\pi\) | ||||
0.834387 | + | 0.551179i | \(0.185822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.9443 | − | 14.4721i | 0.709342 | − | 0.793068i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 35.4164 | 1.93501 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.4721 | −0.897294 | −0.448647 | − | 0.893709i | \(-0.648094\pi\) | ||||
−0.448647 | + | 0.893709i | \(0.648094\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.00000 | − | 20.9443i | 0.434500 | − | 1.13754i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.0000 | 2.16612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.47214 | + | 0.944272i | 0.133095 | + | 0.0508379i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.52786i | 0.404117i | 0.979373 | + | 0.202058i | \(0.0647631\pi\) | ||||
−0.979373 | + | 0.202058i | \(0.935237\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.1803i | − | 1.18729i | −0.804728 | − | 0.593643i | \(-0.797689\pi\) | ||
0.804728 | − | 0.593643i | \(-0.202311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.70820 | − | 2.94427i | 0.304681 | − | 0.157154i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.4721i | 1.08962i | 0.838559 | + | 0.544811i | \(0.183399\pi\) | ||||
−0.838559 | + | 0.544811i | \(0.816601\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.4721 | 1.19270 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.23607 | − | 1.23607i | −0.171271 | − | 0.0654197i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.4164 | −0.708091 | −0.354045 | − | 0.935228i | \(-0.615194\pi\) | ||||
−0.354045 | + | 0.935228i | \(0.615194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.3607 | 1.75583 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.5623 | − | 5.56231i | −0.764323 | − | 0.291945i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.52786 | −0.0799721 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.47214i | − | 0.129044i | −0.997916 | − | 0.0645222i | \(-0.979448\pi\) | ||
0.997916 | − | 0.0645222i | \(-0.0205523\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.94427 | + | 10.0000i | −0.465620 | + | 0.520579i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4721i | 0.543686i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.8885i | 1.75468i | 0.479867 | + | 0.877341i | \(0.340685\pi\) | ||||
−0.479867 | + | 0.877341i | \(0.659315\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.47214 | + | 0.944272i | 0.127661 | + | 0.0487620i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.47214 | −0.229718 | −0.114859 | − | 0.993382i | \(-0.536642\pi\) | ||||
−0.114859 | + | 0.993382i | \(0.536642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4721 | − | 27.4164i | 0.536504 | − | 1.40459i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.4721 | 1.55705 | 0.778527 | − | 0.627611i | \(-0.215967\pi\) | ||||
0.778527 | + | 0.627611i | \(0.215967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4721 | 0.737568 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.05573 | + | 0.944272i | 0.0536657 | + | 0.0480000i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.9443 | −1.46753 | −0.733766 | − | 0.679402i | \(-0.762239\pi\) | ||||
−0.733766 | + | 0.679402i | \(0.762239\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.944272i | − | 0.0477539i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.70820 | − | 4.47214i | 0.0861675 | − | 0.225589i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.0000i | 0.805047i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.7639i | 1.54400i | 0.635624 | + | 0.771999i | \(0.280743\pi\) | ||||
−0.635624 | + | 0.771999i | \(0.719257\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.47214 | + | 11.7082i | −0.223887 | + | 0.586143i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8885i | 0.893311i | 0.894706 | + | 0.446656i | \(0.147385\pi\) | ||||
−0.894706 | + | 0.446656i | \(0.852615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0557 | −0.550725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.23607 | + | 28.9443i | 0.160802 | + | 1.43825i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.9443 | 1.43471 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4721 | + | 27.4164i | −0.516552 | + | 1.35235i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.23607 | −0.0608229 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 42.8328i | − | 2.10258i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.2361 | − | 6.58359i | −0.844054 | − | 0.322400i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 35.7082i | − | 1.74446i | −0.489096 | − | 0.872230i | \(-0.662673\pi\) | ||
0.489096 | − | 0.872230i | \(-0.337327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.94427i | 0.435917i | 0.975958 | + | 0.217959i | \(0.0699398\pi\) | ||||
−0.975958 | + | 0.217959i | \(0.930060\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.52786 | − | 4.94427i | −0.268774 | − | 0.240399i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 10.9443i | − | 0.530875i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.7082 | 0.566600 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.94427 | + | 3.41641i | 0.431834 | + | 0.164946i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4721 | 0.600762 | 0.300381 | − | 0.953819i | \(-0.402886\pi\) | ||||
0.300381 | + | 0.953819i | \(0.402886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3607 | 1.26681 | 0.633407 | − | 0.773819i | \(-0.281656\pi\) | ||||
0.633407 | + | 0.773819i | \(0.281656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.41641 | −0.163429 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.8885i | 1.61741i | 0.588213 | + | 0.808706i | \(0.299832\pi\) | ||||
−0.588213 | + | 0.808706i | \(0.700168\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.23607 | − | 2.00000i | −0.106479 | − | 0.0952381i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.94427i | 0.139887i | 0.997551 | + | 0.0699433i | \(0.0222818\pi\) | ||||
−0.997551 | + | 0.0699433i | \(0.977718\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 19.4164i | − | 0.920426i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.8885 | − | 14.4721i | −1.79207 | − | 0.684509i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13.8885i | − | 0.655441i | −0.944775 | − | 0.327720i | \(-0.893720\pi\) | ||
0.944775 | − | 0.327720i | \(-0.106280\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.0000 | −0.941763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.52786 | + | 14.4721i | −0.259722 | + | 0.679960i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.4164 | 1.00182 | 0.500909 | − | 0.865500i | \(-0.332999\pi\) | ||||
0.500909 | + | 0.865500i | \(0.332999\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.23607 | − | 4.76393i | 0.431103 | − | 0.222361i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.18034 | 0.380996 | 0.190498 | − | 0.981688i | \(-0.438990\pi\) | ||||
0.190498 | + | 0.981688i | \(0.438990\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9443i | 0.601571i | 0.953692 | + | 0.300786i | \(0.0972489\pi\) | ||||
−0.953692 | + | 0.300786i | \(0.902751\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.8885 | − | 46.8328i | 0.829561 | − | 2.17182i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.291796i | 0.0135027i | 0.999977 | + | 0.00675136i | \(0.00214904\pi\) | ||||
−0.999977 | + | 0.00675136i | \(0.997851\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10.9443i | − | 0.505360i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.29180 | − | 6.00000i | 0.105600 | − | 0.276465i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.11146i | 0.0970849i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.5967 | −1.81682 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.4164 | − | 20.9443i | −1.07216 | − | 0.958972i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.4721 | −1.57507 | −0.787536 | − | 0.616269i | \(-0.788644\pi\) | ||||
−0.787536 | + | 0.616269i | \(0.788644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.291796 | − | 0.763932i | 0.0132772 | − | 0.0347601i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.4164 | 0.518392 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.8885i | 1.35438i | 0.735809 | + | 0.677190i | \(0.236802\pi\) | ||||
−0.735809 | + | 0.677190i | \(0.763198\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.7082 | − | 5.23607i | −0.619906 | − | 0.236783i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.8885i | 1.25859i | 0.777166 | + | 0.629296i | \(0.216657\pi\) | ||||
−0.777166 | + | 0.629296i | \(0.783343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.9443 | + | 32.3607i | −1.30095 | + | 1.45450i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.94427i | − | 0.311493i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.8885 | −1.24846 | −0.624231 | − | 0.781240i | \(-0.714588\pi\) | ||||
−0.624231 | + | 0.781240i | \(0.714588\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.52786 | + | 0.583592i | 0.0682599 | + | 0.0260730i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.5836 | 0.561075 | 0.280537 | − | 0.959843i | \(-0.409487\pi\) | ||||
0.280537 | + | 0.959843i | \(0.409487\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.3607 | −0.906038 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.5623 | + | 7.09017i | 0.824381 | + | 0.314886i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.12461 | −0.227144 | −0.113572 | − | 0.993530i | \(-0.536229\pi\) | ||||
−0.113572 | + | 0.993530i | \(0.536229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.472136i | 0.0208861i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.2361 | − | 33.4164i | −0.760991 | − | 1.47537i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4.94427i | − | 0.217871i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.0557i | − | 0.486230i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.6525 | − | 10.9443i | −1.25770 | − | 0.480400i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.58359i | 0.288432i | 0.989546 | + | 0.144216i | \(0.0460661\pi\) | ||||
−0.989546 | + | 0.144216i | \(0.953934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.7082 | −1.12414 | −0.562071 | − | 0.827089i | \(-0.689995\pi\) | ||||
−0.562071 | + | 0.827089i | \(0.689995\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.38197 | − | 8.85410i | 0.147601 | − | 0.386425i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.8885 | −0.779237 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7771 | −0.990308 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.47214 | − | 2.76393i | 0.107282 | − | 0.119944i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.52786 | 0.239438 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.47214i | 0.279815i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.23607 | + | 24.1803i | −0.398566 | + | 1.04346i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 4.47214i | − | 0.192629i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 8.94427i | − | 0.384544i | −0.981342 | − | 0.192272i | \(-0.938414\pi\) | ||
0.981342 | − | 0.192272i | \(-0.0615856\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.6525 | − | 27.8885i | 0.457141 | − | 1.19681i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.0000i | 1.02805i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.4721 | −1.38841 | −0.694204 | − | 0.719778i | \(-0.744244\pi\) | ||||
−0.694204 | + | 0.719778i | \(0.744244\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.4164 | + | 26.1803i | −0.999388 | + | 1.11735i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.94427 | 0.210252 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.9443 | − | 33.8885i | 0.549454 | − | 1.43849i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.47214 | 0.104748 | 0.0523739 | − | 0.998628i | \(-0.483321\pi\) | ||||
0.0523739 | + | 0.998628i | \(0.483321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.583592i | − | 0.0246833i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4721 | + | 5.52786i | 0.611014 | + | 0.233387i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 9.81966i | − | 0.413849i | −0.978357 | − | 0.206925i | \(-0.933654\pi\) | ||
0.978357 | − | 0.206925i | \(-0.0663455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 41.8885i | − | 1.76226i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.94427 | − | 1.00000i | 0.375624 | − | 0.0419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 13.8885i | − | 0.582238i | −0.956687 | − | 0.291119i | \(-0.905972\pi\) | ||
0.956687 | − | 0.291119i | \(-0.0940276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.5279 | 0.984610 | 0.492305 | − | 0.870423i | \(-0.336154\pi\) | ||||
0.492305 | + | 0.870423i | \(0.336154\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.23607 | − | 1.23607i | −0.135189 | − | 0.0516375i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.58359 | 0.107743 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.05573 | 0.376995 | 0.188497 | − | 0.982074i | \(-0.439638\pi\) | ||||
0.188497 | + | 0.982074i | \(0.439638\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.6525 | − | 7.12461i | −0.775170 | − | 0.296089i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.2361 | −0.549125 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 46.8328i | − | 1.93962i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.00000 | − | 8.94427i | 0.330759 | − | 0.369800i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.7082i | 0.978542i | 0.872132 | + | 0.489271i | \(0.162737\pi\) | ||||
−0.872132 | + | 0.489271i | \(0.837263\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 64.7214i | 2.66680i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.3607 | + | 13.8885i | 1.49568 | + | 0.571298i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.41641i | 0.386686i | 0.981131 | + | 0.193343i | \(0.0619329\pi\) | ||||
−0.981131 | + | 0.193343i | \(0.938067\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.47214 | −0.265332 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.47214 | + | 16.9443i | −0.264887 | + | 0.693483i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.05573 | −0.0431359 | −0.0215679 | − | 0.999767i | \(-0.506866\pi\) | ||||
−0.0215679 | + | 0.999767i | \(0.506866\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.52786 | 0.307068 | 0.153534 | − | 0.988143i | \(-0.450935\pi\) | ||||
0.153534 | + | 0.988143i | \(0.450935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.4721 | + | 21.8885i | 0.996582 | + | 0.891370i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −29.1246 | −1.18408 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.47214i | − | 0.100341i | −0.998741 | − | 0.0501705i | \(-0.984024\pi\) | ||
0.998741 | − | 0.0501705i | \(-0.0159765\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.05573i | 0.123622i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 0.583592i | − | 0.0235711i | −0.999931 | − | 0.0117855i | \(-0.996248\pi\) | ||
0.999931 | − | 0.0117855i | \(-0.00375154\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.94427 | + | 23.4164i | −0.360668 | + | 0.944241i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 32.0000i | − | 1.28827i | −0.764911 | − | 0.644136i | \(-0.777217\pi\) | ||
0.764911 | − | 0.644136i | \(-0.222783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.12461 | −0.205976 | −0.102988 | − | 0.994683i | \(-0.532840\pi\) | ||||
−0.102988 | + | 0.994683i | \(0.532840\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.12461 | + | 2.18034i | 0.0451291 | + | 0.0874940i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0000 | − | 52.3607i | 0.798723 | − | 2.09108i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.9443 | −0.516122 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.6525 | + | 5.59675i | 0.582384 | + | 0.222451i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 54.8328i | − | 2.17597i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.23607i | 0.0489748i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.5279 | + | 13.8885i | 0.614273 | + | 0.549422i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 40.0000i | − | 1.57991i | −0.613168 | − | 0.789953i | \(-0.710105\pi\) | ||
0.613168 | − | 0.789953i | \(-0.289895\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.1803 | 1.26907 | 0.634534 | − | 0.772895i | \(-0.281192\pi\) | ||||
0.634534 | + | 0.772895i | \(0.281192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.47214 | + | 0.944272i | 0.0973403 | + | 0.0371807i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.52786 | 0.216988 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.4721 | − | 5.52786i | −0.567208 | − | 0.216654i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.8328 | 0.423921 | 0.211960 | − | 0.977278i | \(-0.432015\pi\) | ||||
0.211960 | + | 0.977278i | \(0.432015\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 8.94427i | − | 0.349482i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.05573 | − | 0.944272i | −0.0411879 | − | 0.0368396i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 46.3607i | − | 1.80596i | −0.429687 | − | 0.902978i | \(-0.641376\pi\) | ||
0.429687 | − | 0.902978i | \(-0.358624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 35.1246i | − | 1.36619i | −0.730330 | − | 0.683095i | \(-0.760634\pi\) | ||
0.730330 | − | 0.683095i | \(-0.239366\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.00000 | − | 1.52786i | −0.155347 | − | 0.0593373i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.4164i | 0.908049i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.360680 | + | 0.944272i | −0.0139447 | + | 0.0365077i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.3607 | −2.02136 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.9443 | 0.884437 | 0.442218 | − | 0.896907i | \(-0.354192\pi\) | ||||
0.442218 | + | 0.896907i | \(0.354192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.0344 | + | 25.2705i | 0.501696 | + | 0.972662i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.1803 | 0.929326 | 0.464663 | − | 0.885488i | \(-0.346175\pi\) | ||||
0.464663 | + | 0.885488i | \(0.346175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.52786i | − | 0.135387i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.180340 | + | 0.472136i | −0.00691064 | + | 0.0180923i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.9443i | 1.64322i | 0.570052 | + | 0.821608i | \(0.306923\pi\) | ||||
−0.570052 | + | 0.821608i | \(0.693077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 54.8328i | 2.09505i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.65248 | − | 6.94427i | 0.101198 | − | 0.264940i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9443i | 0.493137i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.65248 | −0.100905 | −0.0504525 | − | 0.998726i | \(-0.516066\pi\) | ||||
−0.0504525 | + | 0.998726i | \(0.516066\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.0000 | + | 8.94427i | 0.379869 | + | 0.339765i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.4721 | −1.30760 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.94427 | 0.338788 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.88854 | + | 25.8885i | −0.374019 | + | 0.979195i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.88854 | −0.222407 | −0.111204 | − | 0.993798i | \(-0.535471\pi\) | ||||
−0.111204 | + | 0.993798i | \(0.535471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.8328i | 1.76633i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.9443 | − | 4.94427i | −0.487509 | − | 0.186212i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.29180i | 0.236627i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 10.4721i | − | 0.393289i | −0.980475 | − | 0.196645i | \(-0.936995\pi\) | ||
0.980475 | − | 0.196645i | \(-0.0630045\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.88854 | + | 11.0557i | −0.370849 | + | 0.414622i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.22291i | − | 0.158149i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.8885 | 0.668994 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.7082 | − | 8.29180i | −0.810708 | − | 0.309663i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.3607 | 1.20685 | 0.603425 | − | 0.797420i | \(-0.293802\pi\) | ||||
0.603425 | + | 0.797420i | \(0.293802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.52786 | −0.0569006 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.70820 | − | 2.18034i | −0.212290 | − | 0.0810877i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 11.4164i | − | 0.423411i | −0.977333 | − | 0.211706i | \(-0.932098\pi\) | ||
0.977333 | − | 0.211706i | \(-0.0679018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 0.944272i | − | 0.0349252i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 42.5410i | − | 1.57129i | −0.618679 | − | 0.785644i | \(-0.712332\pi\) | ||
0.618679 | − | 0.785644i | \(-0.287668\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.23607 | − | 2.00000i | −0.193135 | − | 0.0737711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.9443i | 1.80289i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.47214 | −0.164510 | −0.0822551 | − | 0.996611i | \(-0.526212\pi\) | ||||
−0.0822551 | + | 0.996611i | \(0.526212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.52786 | + | 14.4721i | −0.203071 | + | 0.531647i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.3050 | 1.73545 | 0.867725 | − | 0.497044i | \(-0.165581\pi\) | ||||
0.867725 | + | 0.497044i | \(0.165581\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −75.7771 | −2.77626 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.4721 | − | 29.5967i | 0.968565 | − | 1.08289i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.00000 | 0.0730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.8328i | 0.979143i | 0.871963 | + | 0.489572i | \(0.162847\pi\) | ||||
−0.871963 | + | 0.489572i | \(0.837153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.12461 | + | 13.4164i | −0.186751 | + | 0.488921i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.9443i | 1.05339i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.58359i | − | 0.311976i | −0.987759 | − | 0.155988i | \(-0.950144\pi\) | ||
0.987759 | − | 0.155988i | \(-0.0498561\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.30495 | + | 3.41641i | −0.0473667 | + | 0.124008i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 51.3050i | − | 1.85980i | −0.367809 | − | 0.929902i | \(-0.619892\pi\) | ||
0.367809 | − | 0.929902i | \(-0.380108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.41641 | 0.268492 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.9443 | − | 14.4721i | 0.468001 | − | 0.523241i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.52786 | −0.0551680 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.3607 | 0.806347 | 0.403173 | − | 0.915124i | \(-0.367907\pi\) | ||||
0.403173 | + | 0.915124i | \(0.367907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.875388 | + | 2.29180i | −0.0315263 | + | 0.0825370i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.65248 | −0.239273 | −0.119636 | − | 0.992818i | \(-0.538173\pi\) | ||||
−0.119636 | + | 0.992818i | \(0.538173\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 48.9443i | − | 1.75813i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.4721 | − | 4.00000i | −0.375686 | − | 0.143499i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 32.3607i | − | 1.15944i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.0557i | 1.11126i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 12.0000i | − | 0.428298i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.1246 | 0.610426 | 0.305213 | − | 0.952284i | \(-0.401272\pi\) | ||||
0.305213 | + | 0.952284i | \(0.401272\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.6525 | − | 8.65248i | −0.806449 | − | 0.308036i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.9443 | −0.460245 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.4721 | 0.513921 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −54.8328 | − | 20.9443i | −1.94472 | − | 0.742817i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.0689 | −0.923407 | −0.461704 | − | 0.887034i | \(-0.652762\pi\) | ||||
−0.461704 | + | 0.887034i | \(0.652762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.94427i | 0.174916i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0000 | − | 13.4164i | 0.423999 | − | 0.474045i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.11146i | − | 0.0745117i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.52786i | − | 0.0538501i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.1803 | + | 10.0000i | 0.921592 | + | 0.352017i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 40.7214i | − | 1.43169i | −0.698261 | − | 0.715843i | \(-0.746042\pi\) | ||
0.698261 | − | 0.715843i | \(-0.253958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.0689 | 1.47724 | 0.738619 | − | 0.674123i | \(-0.235478\pi\) | ||||
0.738619 | + | 0.674123i | \(0.235478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.94427 | − | 23.4164i | 0.313689 | − | 0.821249i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.4164 | −0.960355 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.41641 | −0.119525 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.76393 | − | 2.47214i | −0.0965796 | − | 0.0863834i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.5279 | −0.472126 | −0.236063 | − | 0.971738i | \(-0.575857\pi\) | ||||
−0.236063 | + | 0.971738i | \(0.575857\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 22.8328i | − | 0.795902i | −0.917407 | − | 0.397951i | \(-0.869721\pi\) | ||
0.917407 | − | 0.397951i | \(-0.130279\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.1246 | + | 39.5967i | −0.526571 | + | 1.37858i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.00000i | 0.0695468i | 0.999395 | + | 0.0347734i | \(0.0110710\pi\) | ||||
−0.999395 | + | 0.0347734i | \(0.988929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.6525i | 0.856216i | 0.903728 | + | 0.428108i | \(0.140820\pi\) | ||||
−0.903728 | + | 0.428108i | \(0.859180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.41641 | − | 19.4164i | 0.257272 | − | 0.673548i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.05573 | 0.105748 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.3050 | − | 21.3050i | 1.42771 | − | 0.736407i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −55.7771 | −1.92564 | −0.962819 | − | 0.270146i | \(-0.912928\pi\) | ||||
−0.962819 | + | 0.270146i | \(0.912928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.0557 | + | 28.9443i | −0.380780 | + | 0.996894i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.1246 | 1.27713 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000i | 0.309244i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.23607 | + | 2.00000i | 0.179701 | + | 0.0686398i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.05573i | − | 0.104749i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.1246i | − | 0.654814i | −0.944883 | − | 0.327407i | \(-0.893825\pi\) | ||
0.944883 | − | 0.327407i | \(-0.106175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −52.3607 | − | 46.8328i | −1.79070 | − | 1.60165i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.3050i | 1.34263i | 0.741171 | + | 0.671316i | \(0.234271\pi\) | ||||
−0.741171 | + | 0.671316i | \(0.765729\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0689 | 0.480024 | 0.240012 | − | 0.970770i | \(-0.422849\pi\) | ||||
0.240012 | + | 0.970770i | \(0.422849\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.23607 | + | 2.76393i | 0.246605 | + | 0.0941946i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 50.7214 | 1.72658 | 0.863288 | − | 0.504712i | \(-0.168401\pi\) | ||||
0.863288 | + | 0.504712i | \(0.168401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.3050 | −1.94843 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.0344 | + | 8.03444i | 0.714367 | + | 0.272864i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.1115 | −0.750080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 13.5279i | − | 0.458374i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.88854 | + | 7.05573i | 0.266987 | + | 0.238800i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.52786i | − | 0.0516512i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.4164i | 1.06086i | 0.847730 | + | 0.530428i | \(0.177969\pi\) | ||||
−0.847730 | + | 0.530428i | \(0.822031\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47.1246 | + | 18.0000i | 1.58947 | + | 0.607125i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.4164i | 0.452010i | 0.974126 | + | 0.226005i | \(0.0725666\pi\) | ||||
−0.974126 | + | 0.226005i | \(0.927433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.94427 | −0.0990826 | −0.0495413 | − | 0.998772i | \(-0.515776\pi\) | ||||
−0.0495413 | + | 0.998772i | \(0.515776\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.47214 | − | 6.47214i | 0.0830999 | − | 0.217558i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.88854 | −0.197718 | −0.0988590 | − | 0.995101i | \(-0.531519\pi\) | ||||
−0.0988590 | + | 0.995101i | \(0.531519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.9443 | −0.568293 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.0000 | + | 4.47214i | −1.34005 | + | 0.149822i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.8885 | 0.598617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.3607i | 1.61652i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.360680 | − | 0.944272i | 0.0120427 | − | 0.0315283i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.9443i | 0.697755i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.291796 | − | 0.763932i | 0.00971037 | − | 0.0254221i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 55.7771i | − | 1.85409i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.7214 | −1.41854 | −0.709270 | − | 0.704937i | \(-0.750975\pi\) | ||||
−0.709270 | + | 0.704937i | \(0.750975\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.0689 | − | 12.5836i | −0.466635 | − | 0.417371i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.3607 | −1.80105 | −0.900525 | − | 0.434805i | \(-0.856817\pi\) | ||||
−0.900525 | + | 0.434805i | \(0.856817\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.1935 | 1.95902 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.4164 | + | 61.3050i | −0.774123 | + | 2.02668i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.76393 | −0.0912731 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.0557i | 0.892486i | 0.894912 | + | 0.446243i | \(0.147238\pi\) | ||||
−0.894912 | + | 0.446243i | \(0.852762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.7082 | + | 10.5836i | 0.913016 | + | 0.348741i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 8.58359i | − | 0.282532i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 35.4164i | − | 1.16448i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.05573 | − | 3.41641i | 0.100363 | − | 0.112210i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 54.9443i | − | 1.80266i | −0.433130 | − | 0.901332i | \(-0.642591\pi\) | ||
0.433130 | − | 0.901332i | \(-0.357409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.23607 | 0.237153 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.9443 | + | 12.5836i | 1.07855 | + | 0.411968i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.9443 | 0.946579 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.4164 | 0.699644 | 0.349822 | − | 0.936816i | \(-0.386242\pi\) | ||||
0.349822 | + | 0.936816i | \(0.386242\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.76393 | + | 1.81966i | 0.155465 | + | 0.0593824i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0689 | 0.849821 | 0.424911 | − | 0.905235i | \(-0.360306\pi\) | ||||
0.424911 | + | 0.905235i | \(0.360306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.11146i | 0.0687585i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.9443 | − | 7.70820i | 0.486137 | − | 0.250748i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.4721i | 0.535272i | 0.963520 | + | 0.267636i | \(0.0862425\pi\) | ||||
−0.963520 | + | 0.267636i | \(0.913757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.583592i | 0.0189442i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00000 | + | 1.52786i | 0.129709 | + | 0.0495444i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.8885i | 1.09776i | 0.835902 | + | 0.548879i | \(0.184945\pi\) | ||||
−0.835902 | + | 0.548879i | \(0.815055\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.47214 | −0.209433 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9443 | 0.547159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −49.0000 | −1.58065 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | + | 4.47214i | −0.128898 | + | 0.144113i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37.3050 | −1.20089 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.944272i | 0.0303657i | 0.999885 | + | 0.0151829i | \(0.00483304\pi\) | ||||
−0.999885 | + | 0.0151829i | \(0.995167\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.94427 | + | 23.4164i | −0.287331 | + | 0.752243i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 28.2918i | − | 0.907927i | −0.891020 | − | 0.453963i | \(-0.850010\pi\) | ||
0.891020 | − | 0.453963i | \(-0.149990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.6525i | 0.341503i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.18034 | − | 10.9443i | 0.133878 | − | 0.350497i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8885i | 0.828248i | 0.910220 | + | 0.414124i | \(0.135912\pi\) | ||||
−0.910220 | + | 0.414124i | \(0.864088\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.8328 | 0.857581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.8328 | + | 16.5836i | −0.473575 | + | 0.529473i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.9443 | −1.68866 | −0.844330 | − | 0.535824i | \(-0.820001\pi\) | ||||
−0.844330 | + | 0.535824i | \(0.820001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.7214 | 2.31710 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.52786 | + | 4.00000i | −0.0486324 | + | 0.127321i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.222912 | 0.00708820 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000i | 1.27064i | 0.772248 | + | 0.635321i | \(0.219132\pi\) | ||||
−0.772248 | + | 0.635321i | \(0.780868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.1246 | + | 18.7639i | 1.55892 | + | 0.595455i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.8885i | 1.07434i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.1246i | 1.36577i | 0.730526 | + | 0.682885i | \(0.239275\pi\) | ||||
−0.730526 | + | 0.682885i | \(0.760725\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.8885 | − | 15.4164i | 0.945632 | − | 0.487754i |
(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 | 672.2.j.c.239.4 | 4 | ||
3.2 | odd | 2 | 672.2.j.b.239.3 | 4 | |||
4.3 | odd | 2 | 168.2.j.a.155.1 | ✓ | 4 | ||
8.3 | odd | 2 | 672.2.j.b.239.4 | 4 | |||
8.5 | even | 2 | 168.2.j.c.155.1 | yes | 4 | ||
12.11 | even | 2 | 168.2.j.c.155.3 | yes | 4 | ||
24.5 | odd | 2 | 168.2.j.a.155.3 | yes | 4 | ||
24.11 | even | 2 | inner | 672.2.j.c.239.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.j.a.155.1 | ✓ | 4 | 4.3 | odd | 2 | ||
168.2.j.a.155.3 | yes | 4 | 24.5 | odd | 2 | ||
168.2.j.c.155.1 | yes | 4 | 8.5 | even | 2 | ||
168.2.j.c.155.3 | yes | 4 | 12.11 | even | 2 | ||
672.2.j.b.239.3 | 4 | 3.2 | odd | 2 | |||
672.2.j.b.239.4 | 4 | 8.3 | odd | 2 | |||
672.2.j.c.239.3 | 4 | 24.11 | even | 2 | inner | ||
672.2.j.c.239.4 | 4 | 1.1 | even | 1 | trivial |