Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(961,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.q (of order \(3\), degree \(2\), 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: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1176) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.961 |
Dual form | 2352.2.q.bc.1537.2 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.70711 | − | 2.95680i | 0.763441 | − | 1.32232i | −0.177625 | − | 0.984098i | \(-0.556842\pi\) |
0.941067 | − | 0.338221i | \(-0.109825\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41421 | + | 4.18154i | 0.727913 | + | 1.26078i | 0.957764 | + | 0.287556i | \(0.0928428\pi\) |
−0.229851 | + | 0.973226i | \(0.573824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.41421 | −0.881546 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.12132 | − | 5.40629i | −0.757031 | − | 1.31122i | −0.944358 | − | 0.328919i | \(-0.893316\pi\) |
0.187327 | − | 0.982298i | \(-0.440018\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.585786 | + | 1.01461i | −0.134389 | + | 0.232768i | −0.925364 | − | 0.379080i | \(-0.876240\pi\) |
0.790975 | + | 0.611848i | \(0.209574\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.414214 | + | 0.717439i | −0.0863695 | + | 0.149596i | −0.905974 | − | 0.423333i | \(-0.860860\pi\) |
0.819604 | + | 0.572930i | \(0.194193\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.32843 | − | 5.76500i | −0.665685 | − | 1.15300i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.48528 | −1.57568 | −0.787839 | − | 0.615882i | \(-0.788800\pi\) | ||||
−0.787839 | + | 0.615882i | \(0.788800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.41421 | − | 9.37769i | −0.972421 | − | 1.68428i | −0.688194 | − | 0.725526i | \(-0.741596\pi\) |
−0.284227 | − | 0.958757i | \(-0.591737\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.41421 | − | 4.18154i | 0.420261 | − | 0.727913i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.82843 | − | 8.36308i | 0.793789 | − | 1.37488i | −0.129817 | − | 0.991538i | \(-0.541439\pi\) |
0.923606 | − | 0.383344i | \(-0.125228\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.707107 | + | 1.22474i | 0.113228 | + | 0.196116i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.41421 | 0.533211 | 0.266605 | − | 0.963806i | \(-0.414098\pi\) | ||||
0.266605 | + | 0.963806i | \(0.414098\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.70711 | + | 2.95680i | 0.254480 | + | 0.440773i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.585786 | + | 1.01461i | −0.0854457 | + | 0.147996i | −0.905581 | − | 0.424173i | \(-0.860565\pi\) |
0.820135 | + | 0.572170i | \(0.193898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.12132 | + | 5.40629i | −0.437072 | + | 0.757031i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.65685 | − | 8.06591i | −0.639668 | − | 1.10794i | −0.985506 | − | 0.169643i | \(-0.945738\pi\) |
0.345837 | − | 0.938294i | \(-0.387595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.4853 | 2.22287 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17157 | 0.155179 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.41421 | − | 9.37769i | −0.704871 | − | 1.22087i | −0.966738 | − | 0.255768i | \(-0.917672\pi\) |
0.261868 | − | 0.965104i | \(-0.415662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.94975 | + | 5.10911i | −0.377676 | + | 0.654155i | −0.990724 | − | 0.135891i | \(-0.956610\pi\) |
0.613047 | + | 0.790046i | \(0.289944\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.41421 | + | 4.18154i | −0.299446 | + | 0.518656i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | − | 6.92820i | −0.488678 | − | 0.846415i | 0.511237 | − | 0.859440i | \(-0.329187\pi\) |
−0.999915 | + | 0.0130248i | \(0.995854\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.828427 | 0.0997309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.82843 | −0.573029 | −0.286514 | − | 0.958076i | \(-0.592497\pi\) | ||||
−0.286514 | + | 0.958076i | \(0.592497\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.53553 | + | 2.65962i | 0.179721 | + | 0.311285i | 0.941785 | − | 0.336216i | \(-0.109147\pi\) |
−0.762064 | + | 0.647501i | \(0.775814\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.32843 | + | 5.76500i | −0.384334 | + | 0.665685i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.82843 | + | 11.8272i | −0.768258 | + | 1.33066i | 0.170249 | + | 0.985401i | \(0.445543\pi\) |
−0.938507 | + | 0.345261i | \(0.887790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.31371 | −0.802784 | −0.401392 | − | 0.915906i | \(-0.631473\pi\) | ||||
−0.401392 | + | 0.915906i | \(0.631473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.3137 | −2.31180 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.24264 | + | 7.34847i | 0.454859 | + | 0.787839i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.36396 | − | 12.7548i | 0.780578 | − | 1.35200i | −0.151027 | − | 0.988530i | \(-0.548258\pi\) |
0.931605 | − | 0.363472i | \(-0.118409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.41421 | + | 9.37769i | −0.561428 | + | 0.972421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | + | 3.46410i | 0.205196 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2426 | 1.64919 | 0.824595 | − | 0.565723i | \(-0.191403\pi\) | ||||
0.824595 | + | 0.565723i | \(0.191403\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.82843 | −0.485275 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.292893 | + | 0.507306i | 0.0291440 | + | 0.0504788i | 0.880230 | − | 0.474548i | \(-0.157389\pi\) |
−0.851086 | + | 0.525027i | \(0.824055\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.58579 | + | 4.47871i | −0.254785 | + | 0.441301i | −0.964837 | − | 0.262848i | \(-0.915338\pi\) |
0.710052 | + | 0.704149i | \(0.248671\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.24264 | + | 2.15232i | −0.120131 | + | 0.208072i | −0.919819 | − | 0.392343i | \(-0.871665\pi\) |
0.799688 | + | 0.600415i | \(0.204998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.65685 | − | 9.79796i | −0.541828 | − | 0.938474i | −0.998799 | − | 0.0489926i | \(-0.984399\pi\) |
0.456971 | − | 0.889482i | \(-0.348934\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.65685 | −0.916588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.41421 | + | 2.44949i | 0.131876 | + | 0.228416i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.707107 | − | 1.22474i | 0.0653720 | − | 0.113228i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.15685 | + | 10.6640i | −0.559714 | + | 0.969453i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.70711 | − | 2.95680i | −0.153925 | − | 0.266605i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.31371 | −0.648987 | −0.324493 | − | 0.945888i | \(-0.605194\pi\) | ||||
−0.324493 | + | 0.945888i | \(0.605194\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00000 | − | 6.92820i | −0.352180 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.65685 | + | 13.2621i | −0.668982 | + | 1.15871i | 0.309207 | + | 0.950995i | \(0.399937\pi\) |
−0.978189 | + | 0.207717i | \(0.933397\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.70711 | − | 2.95680i | 0.146924 | − | 0.254480i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.24264 | + | 10.8126i | 0.533345 | + | 0.923780i | 0.999242 | + | 0.0389412i | \(0.0123985\pi\) |
−0.465897 | + | 0.884839i | \(0.654268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.65685 | 0.819084 | 0.409542 | − | 0.912291i | \(-0.365689\pi\) | ||||
0.409542 | + | 0.912291i | \(0.365689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.17157 | 0.0986642 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.41421 | − | 5.91359i | −0.285511 | − | 0.494519i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.4853 | + | 25.0892i | −1.20294 | + | 2.08355i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.00000 | − | 8.66025i | 0.409616 | − | 0.709476i | −0.585231 | − | 0.810867i | \(-0.698996\pi\) |
0.994847 | + | 0.101391i | \(0.0323294\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.828427 | − | 1.43488i | −0.0674164 | − | 0.116769i | 0.830347 | − | 0.557247i | \(-0.188142\pi\) |
−0.897763 | + | 0.440478i | \(0.854809\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.24264 | 0.504688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −36.9706 | −2.96955 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.94975 | + | 5.10911i | 0.235415 | + | 0.407752i | 0.959393 | − | 0.282072i | \(-0.0910216\pi\) |
−0.723978 | + | 0.689823i | \(0.757688\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.65685 | + | 8.06591i | −0.369313 | + | 0.639668i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.17157 | + | 2.02922i | −0.0917647 | + | 0.158941i | −0.908254 | − | 0.418420i | \(-0.862584\pi\) |
0.816489 | + | 0.577361i | \(0.195917\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.24264 | − | 14.2767i | −0.641689 | − | 1.11144i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.82843 | 0.528400 | 0.264200 | − | 0.964468i | \(-0.414892\pi\) | ||||
0.264200 | + | 0.964468i | \(0.414892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.585786 | − | 1.01461i | −0.0447962 | − | 0.0775893i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.292893 | + | 0.507306i | −0.0222683 | + | 0.0385698i | −0.876945 | − | 0.480591i | \(-0.840422\pi\) |
0.854677 | + | 0.519161i | \(0.173755\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.41421 | + | 9.37769i | −0.406957 | + | 0.704871i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8995 | − | 18.8785i | −0.814667 | − | 1.41104i | −0.909567 | − | 0.415557i | \(-0.863587\pi\) |
0.0949006 | − | 0.995487i | \(-0.469747\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.89949 | −0.735824 | −0.367912 | − | 0.929861i | \(-0.619927\pi\) | ||||
−0.367912 | + | 0.929861i | \(0.619927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.89949 | 0.436103 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.4853 | − | 28.5533i | −1.21202 | − | 2.09928i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.0711 | − | 26.1039i | 1.10211 | − | 1.90890i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4142 | − | 18.0379i | 0.753546 | − | 1.30518i | −0.192548 | − | 0.981288i | \(-0.561675\pi\) |
0.946094 | − | 0.323892i | \(-0.104992\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.3137 | + | 17.8639i | 0.742397 | + | 1.28587i | 0.951401 | + | 0.307955i | \(0.0996445\pi\) |
−0.209004 | + | 0.977915i | \(0.567022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.82843 | 0.345771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.82843 | + | 4.89898i | 0.200502 | + | 0.347279i | 0.948690 | − | 0.316207i | \(-0.102409\pi\) |
−0.748188 | + | 0.663486i | \(0.769076\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | + | 6.92820i | −0.282138 | + | 0.488678i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.82843 | − | 10.0951i | 0.407075 | − | 0.705075i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.414214 | − | 0.717439i | −0.0287898 | − | 0.0498655i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.6569 | 1.76629 | 0.883145 | − | 0.469099i | \(-0.155421\pi\) | ||||
0.883145 | + | 0.469099i | \(0.155421\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.41421 | + | 4.18154i | 0.165419 | + | 0.286514i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.6569 | − | 23.6544i | 0.931390 | − | 1.61321i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.53553 | − | 2.65962i | 0.103762 | − | 0.179721i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.41421 | + | 7.64564i | 0.296932 | + | 0.514302i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.34315 | −0.156909 | −0.0784543 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784543 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.89949 | − | 17.1464i | −0.657053 | − | 1.13805i | −0.981375 | − | 0.192102i | \(-0.938470\pi\) |
0.324322 | − | 0.945947i | \(-0.394864\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.464466 | − | 0.804479i | 0.0306928 | − | 0.0531615i | −0.850271 | − | 0.526345i | \(-0.823562\pi\) |
0.880964 | + | 0.473184i | \(0.156895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.75736 | − | 9.97204i | 0.377177 | − | 0.653290i | −0.613473 | − | 0.789716i | \(-0.710228\pi\) |
0.990650 | + | 0.136426i | \(0.0435615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | + | 3.46410i | 0.130466 | + | 0.225973i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.6569 | 0.887108 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.82843 | 0.571063 | 0.285532 | − | 0.958369i | \(-0.407830\pi\) | ||||
0.285532 | + | 0.958369i | \(0.407830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.05025 | − | 1.81909i | −0.0676527 | − | 0.117178i | 0.830215 | − | 0.557443i | \(-0.188218\pi\) |
−0.897868 | + | 0.440265i | \(0.854884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.828427 | − | 1.43488i | 0.0527116 | − | 0.0912991i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.65685 | + | 6.33386i | 0.231744 | + | 0.401392i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.48528 | −0.535586 | −0.267793 | − | 0.963476i | \(-0.586294\pi\) | ||||
−0.267793 | + | 0.963476i | \(0.586294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.6569 | + | 18.4582i | 0.667358 | + | 1.15590i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.8787 | + | 18.8424i | −0.678593 | + | 1.17536i | 0.296811 | + | 0.954936i | \(0.404077\pi\) |
−0.975405 | + | 0.220422i | \(0.929257\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.24264 | − | 7.34847i | 0.262613 | − | 0.454859i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.58579 | + | 16.6031i | 0.591085 | + | 1.02379i | 0.994087 | + | 0.108590i | \(0.0346335\pi\) |
−0.403002 | + | 0.915199i | \(0.632033\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.7990 | −1.95340 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.7279 | −0.901334 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.02082 | − | 15.6245i | −0.550009 | − | 0.952643i | −0.998273 | − | 0.0587422i | \(-0.981291\pi\) |
0.448264 | − | 0.893901i | \(-0.352042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.41421 | − | 16.3059i | 0.571873 | − | 0.990513i | −0.424501 | − | 0.905427i | \(-0.639550\pi\) |
0.996374 | − | 0.0850852i | \(-0.0271162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.0711 | − | 27.8359i | 0.969122 | − | 1.67857i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00000 | + | 5.19615i | 0.180253 | + | 0.312207i | 0.941966 | − | 0.335707i | \(-0.108975\pi\) |
−0.761714 | + | 0.647913i | \(0.775642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.8284 | 0.648281 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.48528 | 0.267569 | 0.133785 | − | 0.991010i | \(-0.457287\pi\) | ||||
0.133785 | + | 0.991010i | \(0.457287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.58579 | + | 7.94282i | 0.272597 | + | 0.472151i | 0.969526 | − | 0.244989i | \(-0.0787842\pi\) |
−0.696929 | + | 0.717140i | \(0.745451\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | − | 3.46410i | 0.118470 | − | 0.205196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.9853 | + | 19.0271i | −0.646193 | + | 1.11924i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.12132 | − | 14.0665i | −0.476080 | − | 0.824595i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.0711 | 0.763620 | 0.381810 | − | 0.924241i | \(-0.375301\pi\) | ||||
0.381810 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.9706 | −2.15251 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.41421 | + | 4.18154i | 0.140087 | + | 0.242638i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.585786 | − | 1.01461i | 0.0338769 | − | 0.0586765i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.292893 | − | 0.507306i | 0.0168263 | − | 0.0291440i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.0711 | + | 17.4436i | 0.576668 | + | 0.998818i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.4853 | −1.62574 | −0.812870 | − | 0.582445i | \(-0.802096\pi\) | ||||
−0.812870 | + | 0.582445i | \(0.802096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.17157 | 0.294201 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.07107 | − | 1.85514i | −0.0607347 | − | 0.105196i | 0.834059 | − | 0.551675i | \(-0.186011\pi\) |
−0.894794 | + | 0.446479i | \(0.852678\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.29289 | + | 12.6317i | −0.412219 | + | 0.713984i | −0.995132 | − | 0.0985506i | \(-0.968579\pi\) |
0.582913 | + | 0.812534i | \(0.301913\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.656854 | − | 1.13770i | 0.0368926 | − | 0.0638999i | −0.846990 | − | 0.531610i | \(-0.821587\pi\) |
0.883882 | + | 0.467710i | \(0.154921\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.4853 | − | 35.4815i | −1.14696 | − | 1.98659i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.48528 | 0.138715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.31371 | 0.406946 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.70711 | + | 8.15295i | 0.261103 | + | 0.452244i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.65685 | + | 9.79796i | −0.312825 | + | 0.541828i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6569 | + | 27.1185i | −0.860579 | + | 1.49057i | 0.0107928 | + | 0.999942i | \(0.496564\pi\) |
−0.871371 | + | 0.490624i | \(0.836769\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.82843 | + | 8.36308i | 0.264596 | + | 0.458294i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −27.3137 | −1.49231 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9706 | 0.924445 | 0.462223 | − | 0.886764i | \(-0.347052\pi\) | ||||
0.462223 | + | 0.886764i | \(0.347052\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.1421 | − | 45.2795i | 1.41568 | − | 2.45202i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.41421 | − | 2.44949i | 0.0761387 | − | 0.131876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0711 | + | 20.9077i | 0.648009 | + | 1.12238i | 0.983598 | + | 0.180376i | \(0.0577314\pi\) |
−0.335589 | + | 0.942009i | \(0.608935\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.38478 | 0.341769 | 0.170885 | − | 0.985291i | \(-0.445337\pi\) | ||||
0.170885 | + | 0.985291i | \(0.445337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.41421 | −0.0754851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.94975 | + | 3.37706i | 0.103775 | + | 0.179743i | 0.913237 | − | 0.407429i | \(-0.133575\pi\) |
−0.809462 | + | 0.587172i | \(0.800241\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.24264 | + | 14.2767i | −0.437474 | + | 0.757727i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.72792 | − | 13.3852i | 0.407864 | − | 0.706441i | −0.586786 | − | 0.809742i | \(-0.699607\pi\) |
0.994650 | + | 0.103301i | \(0.0329404\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.81371 | + | 15.2658i | 0.463879 | + | 0.803463i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.3137 | 0.646302 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4853 | 0.548825 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.70711 | + | 2.95680i | −0.0888684 | + | 0.153925i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.6569 | + | 32.3146i | −0.966015 | + | 1.67319i | −0.259153 | + | 0.965836i | \(0.583443\pi\) |
−0.706862 | + | 0.707351i | \(0.749890\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.82843 | + | 4.89898i | 0.146059 | + | 0.252982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.3137 | 1.19754 | 0.598772 | − | 0.800919i | \(-0.295655\pi\) | ||||
0.598772 | + | 0.800919i | \(0.295655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.65685 | + | 6.33386i | 0.187346 | + | 0.324493i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.48528 | − | 7.76874i | 0.229187 | − | 0.396964i | −0.728380 | − | 0.685173i | \(-0.759727\pi\) |
0.957567 | + | 0.288209i | \(0.0930599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.00000 | + | 6.92820i | −0.203331 | + | 0.352180i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.07107 | − | 12.2474i | −0.358517 | − | 0.620970i | 0.629196 | − | 0.777247i | \(-0.283384\pi\) |
−0.987713 | + | 0.156276i | \(0.950051\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.17157 | 0.261538 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.3137 | 0.772474 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.3137 | + | 40.3805i | 1.17304 | + | 2.03176i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.3640 | − | 28.3432i | 0.821284 | − | 1.42251i | −0.0834430 | − | 0.996513i | \(-0.526592\pi\) |
0.904727 | − | 0.425992i | \(-0.140075\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.24264 | + | 3.88437i | −0.111992 | + | 0.193976i | −0.916573 | − | 0.399867i | \(-0.869056\pi\) |
0.804581 | + | 0.593843i | \(0.202390\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.65685 | + | 13.2621i | 0.381415 | + | 0.660630i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.41421 | −0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.6274 | 2.31124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.87868 | + | 6.71807i | 0.191788 | + | 0.332187i | 0.945843 | − | 0.324625i | \(-0.105238\pi\) |
−0.754055 | + | 0.656812i | \(0.771905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.24264 | − | 10.8126i | 0.307927 | − | 0.533345i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.4853 | + | 21.6251i | −0.612878 | + | 1.06154i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.82843 | − | 8.36308i | −0.236449 | − | 0.409542i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.17157 | 0.252648 | 0.126324 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126324 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.3137 | 1.42866 | 0.714331 | − | 0.699808i | \(-0.246731\pi\) | ||||
0.714331 | + | 0.699808i | \(0.246731\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.585786 | − | 1.01461i | −0.0284819 | − | 0.0493321i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.7782 | + | 35.9889i | −1.00789 | + | 1.74572i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.41421 | + | 5.91359i | −0.164840 | + | 0.285511i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.75736 | − | 11.7041i | −0.325491 | − | 0.563766i | 0.656121 | − | 0.754656i | \(-0.272196\pi\) |
−0.981612 | + | 0.190890i | \(0.938863\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.3848 | 0.499061 | 0.249530 | − | 0.968367i | \(-0.419724\pi\) | ||||
0.249530 | + | 0.968367i | \(0.419724\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.9706 | 1.38903 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.485281 | − | 0.840532i | −0.0232142 | − | 0.0402081i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.65685 | + | 16.7262i | −0.460897 | + | 0.798296i | −0.999006 | − | 0.0445789i | \(-0.985805\pi\) |
0.538109 | + | 0.842875i | \(0.319139\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7574 | − | 18.6323i | 0.511098 | − | 0.885247i | −0.488820 | − | 0.872385i | \(-0.662572\pi\) |
0.999917 | − | 0.0128621i | \(-0.00409425\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.1421 | − | 43.5475i | −1.19185 | − | 2.06435i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.24264 | + | 14.2767i | 0.388131 | + | 0.672262i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.828427 | + | 1.43488i | −0.0389229 | + | 0.0674164i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.3137 | − | 21.3280i | 0.576011 | − | 0.997680i | −0.419920 | − | 0.907561i | \(-0.637942\pi\) |
0.995931 | − | 0.0901192i | \(-0.0287248\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.12132 | − | 5.40629i | −0.145691 | − | 0.252344i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.75736 | −0.454446 | −0.227223 | − | 0.973843i | \(-0.572965\pi\) | ||||
−0.227223 | + | 0.973843i | \(0.572965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9706 | 0.602793 | 0.301397 | − | 0.953499i | \(-0.402547\pi\) | ||||
0.301397 | + | 0.953499i | \(0.402547\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.4853 | + | 32.0174i | 0.857234 | + | 1.48477i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.58579 | − | 4.47871i | 0.119656 | − | 0.207250i | −0.799975 | − | 0.600033i | \(-0.795154\pi\) |
0.919631 | + | 0.392783i | \(0.128488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.94975 | − | 5.10911i | 0.135917 | − | 0.235415i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.3137 | + | 33.4523i | 0.888045 | + | 1.53814i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.79899 | 0.357842 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.31371 | 0.426445 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.55635 | − | 16.5521i | −0.436641 | − | 0.756284i | 0.560787 | − | 0.827960i | \(-0.310499\pi\) |
−0.997428 | + | 0.0716760i | \(0.977165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.82843 | + | 11.8272i | −0.311349 | + | 0.539273i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.7279 | − | 48.0262i | 1.25906 | − | 2.18076i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.48528 | + | 11.2328i | 0.293876 | + | 0.509008i | 0.974723 | − | 0.223418i | \(-0.0717213\pi\) |
−0.680847 | + | 0.732426i | \(0.738388\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.34315 | 0.105961 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.14214 | 0.186932 | 0.0934660 | − | 0.995622i | \(-0.470205\pi\) | ||||
0.0934660 | + | 0.995622i | \(0.470205\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.4853 | + | 45.8739i | 1.19284 | + | 2.06605i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.24264 | + | 14.2767i | −0.370479 | + | 0.641689i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.1421 | − | 24.4949i | 0.633089 | − | 1.09654i | −0.353828 | − | 0.935311i | \(-0.615120\pi\) |
0.986917 | − | 0.161232i | \(-0.0515466\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.41421 | − | 5.91359i | −0.152536 | − | 0.264200i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.6274 | 1.36561 | 0.682805 | − | 0.730601i | \(-0.260760\pi\) | ||||
0.682805 | + | 0.730601i | \(0.260760\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.50000 | + | 9.52628i | 0.244264 | + | 0.423077i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.4645 | − | 19.8570i | 0.508154 | − | 0.880148i | −0.491802 | − | 0.870707i | \(-0.663662\pi\) |
0.999955 | − | 0.00944061i | \(-0.00300508\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.585786 | + | 1.01461i | −0.0258631 | + | 0.0447962i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.82843 | + | 15.2913i | 0.389027 | + | 0.673814i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.65685 | −0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.585786 | 0.0257132 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.63604 | + | 4.56575i | 0.115487 | + | 0.200029i | 0.917974 | − | 0.396640i | \(-0.129824\pi\) |
−0.802487 | + | 0.596669i | \(0.796490\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.828427 | − | 1.43488i | 0.0362246 | − | 0.0627428i | −0.847345 | − | 0.531043i | \(-0.821800\pi\) |
0.883569 | + | 0.468300i | \(0.155133\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.7990 | + | 58.5416i | −1.47231 | + | 2.55011i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1569 | + | 19.3242i | 0.485081 | + | 0.840184i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.8284 | 0.469914 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.82843 | −0.209142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.24264 | + | 7.34847i | 0.183425 | + | 0.317702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.8995 | + | 18.8785i | −0.470348 | + | 0.814667i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.31371 | − | 7.47156i | 0.185461 | − | 0.321228i | −0.758271 | − | 0.651940i | \(-0.773956\pi\) |
0.943732 | + | 0.330712i | \(0.107289\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.94975 | + | 8.57321i | 0.212414 | + | 0.367912i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −38.6274 | −1.65462 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.97056 | 0.212526 | 0.106263 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106263 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.94975 | − | 5.10911i | −0.125892 | − | 0.218052i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.97056 | − | 8.60927i | 0.211753 | − | 0.366767i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.4853 | + | 28.5533i | −0.699761 | + | 1.21202i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.9706 | − | 38.0541i | −0.930923 | − | 1.61241i | −0.781748 | − | 0.623594i | \(-0.785672\pi\) |
−0.149175 | − | 0.988811i | \(-0.547662\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.3137 | −0.478519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.1421 | −1.27260 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4142 | − | 23.2341i | −0.565342 | − | 0.979201i | −0.997018 | − | 0.0771719i | \(-0.975411\pi\) |
0.431676 | − | 0.902029i | \(-0.357922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2426 | − | 17.7408i | 0.430911 | − | 0.746360i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.41421 | + | 5.91359i | −0.143131 | + | 0.247911i | −0.928674 | − | 0.370897i | \(-0.879050\pi\) |
0.785543 | + | 0.618807i | \(0.212384\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.1421 | + | 34.8872i | 0.842922 | + | 1.45998i | 0.887414 | + | 0.460974i | \(0.152500\pi\) |
−0.0444914 | + | 0.999010i | \(0.514167\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.8284 | −0.870120 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.51472 | 0.229980 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.70711 | − | 8.15295i | −0.195959 | − | 0.339412i | 0.751255 | − | 0.660012i | \(-0.229449\pi\) |
−0.947215 | + | 0.320600i | \(0.896115\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.3137 | − | 17.8639i | 0.428623 | − | 0.742397i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.4853 | − | 38.9456i | 0.931245 | − | 1.61296i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.41421 | − | 4.18154i | −0.0998154 | − | 0.172885i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.8284 | −1.10733 | −0.553664 | − | 0.832740i | \(-0.686771\pi\) | ||||
−0.553664 | + | 0.832740i | \(0.686771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.6863 | 0.522730 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.00000 | − | 1.73205i | −0.0411345 | − | 0.0712470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.5355 | − | 25.1763i | 0.596903 | − | 1.03387i | −0.396372 | − | 0.918090i | \(-0.629731\pi\) |
0.993275 | − | 0.115776i | \(-0.0369356\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.82843 | − | 4.89898i | 0.115760 | − | 0.200502i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.07107 | + | 13.9795i | 0.329775 | + | 0.571187i | 0.982467 | − | 0.186436i | \(-0.0596938\pi\) |
−0.652692 | + | 0.757623i | \(0.726360\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.2426 | 0.499388 | 0.249694 | − | 0.968325i | \(-0.419670\pi\) | ||||
0.249694 | + | 0.968325i | \(0.419670\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.0208 | + | 36.4091i | 0.854618 | + | 1.48024i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7990 | + | 27.3647i | −0.641261 | + | 1.11070i | 0.343890 | + | 0.939010i | \(0.388255\pi\) |
−0.985152 | + | 0.171687i | \(0.945078\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.828427 | − | 1.43488i | 0.0335146 | − | 0.0580489i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.17157 | + | 2.02922i | 0.0473194 | + | 0.0819596i | 0.888715 | − | 0.458460i | \(-0.151599\pi\) |
−0.841396 | + | 0.540420i | \(0.818265\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.6569 | −0.470050 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4558 | 0.863780 | 0.431890 | − | 0.901926i | \(-0.357847\pi\) | ||||
0.431890 | + | 0.901926i | \(0.357847\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1421 | + | 34.8872i | 0.809581 | + | 1.40224i | 0.913155 | + | 0.407613i | \(0.133639\pi\) |
−0.103574 | + | 0.994622i | \(0.533028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.414214 | + | 0.717439i | −0.0166218 | + | 0.0287898i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.98528 | − | 12.0989i | 0.279411 | − | 0.483954i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.82843 | + | 4.89898i | 0.112956 | + | 0.195646i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −60.2843 | −2.40369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.28427 | 0.329792 | 0.164896 | − | 0.986311i | \(-0.447271\pi\) | ||||
0.164896 | + | 0.986311i | \(0.447271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.8284 | − | 22.2195i | −0.509884 | − | 0.883145i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.4853 | + | 21.6251i | −0.495463 | + | 0.858168i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.41421 | − | 4.18154i | 0.0955048 | − | 0.165419i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5858 | − | 21.7992i | −0.497109 | − | 0.861017i | 0.502886 | − | 0.864353i | \(-0.332272\pi\) |
−0.999994 | + | 0.00333540i | \(0.998938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.5147 | 0.769585 | 0.384793 | − | 0.923003i | \(-0.374273\pi\) | ||||
0.384793 | + | 0.923003i | \(0.374273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.3137 | −1.07548 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.41421 | − | 12.8418i | −0.291483 | − | 0.504863i | 0.682678 | − | 0.730720i | \(-0.260815\pi\) |
−0.974161 | + | 0.225857i | \(0.927482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.1421 | − | 45.2795i | 1.02617 | − | 1.77738i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.41421 | + | 2.44949i | −0.0553425 | + | 0.0958559i | −0.892369 | − | 0.451306i | \(-0.850958\pi\) |
0.837027 | + | 0.547162i | \(0.184292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.1421 | + | 45.2795i | 1.02146 | + | 1.76922i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.07107 | −0.119814 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.5147 | −0.993912 | −0.496956 | − | 0.867776i | \(-0.665549\pi\) | ||||
−0.496956 | + | 0.867776i | \(0.665549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.6777 | − | 20.2263i | −0.454209 | − | 0.786713i | 0.544434 | − | 0.838804i | \(-0.316745\pi\) |
−0.998642 | + | 0.0520914i | \(0.983411\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.41421 | − | 7.64564i | 0.171434 | − | 0.296932i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.51472 | − | 6.08767i | 0.136090 | − | 0.235716i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.17157 | + | 2.02922i | 0.0452956 | + | 0.0784543i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.4853 | −1.09966 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3137 | 0.590300 | 0.295150 | − | 0.955451i | \(-0.404630\pi\) | ||||
0.295150 | + | 0.955451i | \(0.404630\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.32843 | − | 5.76500i | −0.128111 | − | 0.221895i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.778175 | + | 1.34784i | −0.0299077 | + | 0.0518016i | −0.880592 | − | 0.473876i | \(-0.842855\pi\) |
0.850684 | + | 0.525677i | \(0.176188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.89949 | + | 17.1464i | −0.379349 | + | 0.657053i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.07107 | + | 10.5154i | 0.232303 | + | 0.402361i | 0.958485 | − | 0.285141i | \(-0.0920406\pi\) |
−0.726182 | + | 0.687502i | \(0.758707\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 42.6274 | 1.62871 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.928932 | −0.0354410 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.58579 | + | 11.4069i | 0.250898 | + | 0.434569i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.0000 | + | 24.2487i | −0.532585 | + | 0.922464i | 0.466691 | + | 0.884420i | \(0.345446\pi\) |
−0.999276 | + | 0.0380440i | \(0.987887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.4853 | − | 28.5533i | 0.625322 | − | 1.08309i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.6569 | − | 18.4582i | −0.403657 | − | 0.699155i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.5147 | −0.435527 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.8284 | −0.408984 | −0.204492 | − | 0.978868i | \(-0.565554\pi\) | ||||
−0.204492 | + | 0.978868i | \(0.565554\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.65685 | + | 9.79796i | 0.213352 | + | 0.369537i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.00000 | − | 3.46410i | 0.0753244 | − | 0.130466i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | − | 6.92820i | 0.150223 | − | 0.260194i | −0.781086 | − | 0.624423i | \(-0.785334\pi\) |
0.931309 | + | 0.364229i | \(0.118667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.82843 | − | 11.8272i | −0.256086 | − | 0.443554i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.97056 | 0.335950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.3137 | −0.871883 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.41421 | − | 7.64564i | −0.164852 | − | 0.285532i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.6569 | − | 23.6544i | 0.509315 | − | 0.882159i | −0.490627 | − | 0.871370i | \(-0.663232\pi\) |
0.999942 | − | 0.0107893i | \(-0.00343441\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.05025 | + | 1.81909i | −0.0390593 | + | 0.0676527i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.2426 | + | 48.9177i | 1.04891 | + | 1.81676i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4558 | −0.944105 | −0.472052 | − | 0.881570i | \(-0.656487\pi\) | ||||
−0.472052 | + | 0.881570i | \(0.656487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.9706 | − | 43.2503i | −0.923570 | − | 1.59967i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.1213 | − | 17.5306i | 0.373839 | − | 0.647509i | −0.616313 | − | 0.787501i | \(-0.711374\pi\) |
0.990153 | + | 0.139992i | \(0.0447078\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.3137 | − | 33.4523i | 0.711430 | − | 1.23223i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.1421 | − | 31.4231i | −0.667369 | − | 1.15592i | −0.978637 | − | 0.205595i | \(-0.934087\pi\) |
0.311268 | − | 0.950322i | \(-0.399246\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.65685 | −0.0608661 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.8284 | 0.617375 | 0.308688 | − | 0.951163i | \(-0.400110\pi\) | ||||
0.308688 | + | 0.951163i | \(0.400110\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.0711 | − | 29.5680i | −0.625436 | − | 1.08329i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.65685 | − | 6.33386i | 0.133797 | − | 0.231744i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.17157 | − | 15.8856i | 0.334675 | − | 0.579675i | −0.648747 | − | 0.761004i | \(-0.724707\pi\) |
0.983422 | + | 0.181329i | \(0.0580400\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.24264 | + | 7.34847i | 0.154610 | + | 0.267793i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65685 | −0.205874 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.3137 | 0.411204 | 0.205602 | − | 0.978636i | \(-0.434085\pi\) | ||||
0.205602 | + | 0.978636i | \(0.434085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.00000 | + | 3.46410i | 0.0725954 | + | 0.125739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.12132 | + | 15.7986i | −0.330648 | + | 0.572698i | −0.982639 | − | 0.185528i | \(-0.940600\pi\) |
0.651991 | + | 0.758226i | \(0.273934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.6569 | − | 18.4582i | 0.385299 | − | 0.667358i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.65685 | + | 13.2621i | 0.276473 | + | 0.478865i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.928932 | −0.0334982 | −0.0167491 | − | 0.999860i | \(-0.505332\pi\) | ||||
−0.0167491 | + | 0.999860i | \(0.505332\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7574 | 0.783572 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.292893 | − | 0.507306i | −0.0105346 | − | 0.0182465i | 0.860710 | − | 0.509096i | \(-0.170020\pi\) |
−0.871245 | + | 0.490849i | \(0.836687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.0416 | + | 62.4259i | −1.29465 | + | 2.24241i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.00000 | + | 3.46410i | −0.0716574 | + | 0.124114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6569 | − | 20.1903i | −0.417115 | − | 0.722464i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.48528 | −0.303239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1421 | 0.718904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3137 | − | 29.9882i | −0.617167 | − | 1.06896i | −0.990000 | − | 0.141066i | \(-0.954947\pi\) |
0.372833 | − | 0.927898i | \(-0.378386\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.58579 | − | 16.6031i | 0.341263 | − | 0.591085i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.17157 | − | 7.22538i | 0.148137 | − | 0.256581i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.8995 | + | 27.5387i | 0.563897 | + | 0.976698i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.786797 | 0.0278698 | 0.0139349 | − | 0.999903i | \(-0.495564\pi\) | ||||
0.0139349 | + | 0.999903i | \(0.495564\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.31371 | 0.258740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.36396 | + | 12.7548i | 0.260193 | + | 0.450667i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.41421 | + | 12.8418i | −0.261642 | + | 0.453177i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.02082 | + | 15.6245i | −0.317548 | + | 0.550009i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0000 | + | 25.9808i | 0.527372 | + | 0.913435i | 0.999491 | + | 0.0319002i | \(0.0101559\pi\) |
−0.472119 | + | 0.881535i | \(0.656511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.9706 | 0.455458 | 0.227729 | − | 0.973725i | \(-0.426870\pi\) | ||||
0.227729 | + | 0.973725i | \(0.426870\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.8284 | −0.660342 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | + | 6.92820i | 0.140114 | + | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.68629 | + | 8.11689i | −0.163953 | + | 0.283974i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00000 | + | 8.66025i | −0.174501 | + | 0.302245i | −0.939989 | − | 0.341206i | \(-0.889165\pi\) |
0.765487 | + | 0.643451i | \(0.222498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.82843 | − | 11.8272i | −0.238024 | − | 0.412270i | 0.722123 | − | 0.691764i | \(-0.243166\pi\) |
−0.960147 | + | 0.279495i | \(0.909833\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32.1421 | −1.11905 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.4558 | −1.09383 | −0.546913 | − | 0.837189i | \(-0.684197\pi\) | ||||
−0.546913 | + | 0.837189i | \(0.684197\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.3640 | + | 24.8791i | 0.498881 | + | 0.864087i | 0.999999 | − | 0.00129164i | \(-0.000411143\pi\) |
−0.501118 | + | 0.865379i | \(0.667078\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.00000 | − | 5.19615i | 0.104069 | − | 0.180253i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.6569 | − | 20.1903i | 0.403402 | − | 0.698713i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.41421 | − | 9.37769i | −0.187143 | − | 0.324140i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.8284 | 1.89289 | 0.946444 | − | 0.322869i | \(-0.104647\pi\) | ||||
0.946444 | + | 0.322869i | \(0.104647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.24264 | − | 3.88437i | −0.0772406 | − | 0.133785i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.7782 | + | 32.5248i | −0.645989 | + | 1.11889i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.58579 | − | 7.94282i | 0.157384 | − | 0.272597i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | + | 6.92820i | 0.137118 | + | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0416 | 0.412298 | 0.206149 | − | 0.978521i | \(-0.433907\pi\) | ||||
0.206149 | + | 0.978521i | \(0.433907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.84924 | + | 13.5953i | 0.268125 | + | 0.464406i | 0.968378 | − | 0.249489i | \(-0.0802626\pi\) |
−0.700253 | + | 0.713895i | \(0.746929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.5858 | − | 28.7274i | 0.565900 | − | 0.980167i | −0.431066 | − | 0.902321i | \(-0.641862\pi\) |
0.996965 | − | 0.0778465i | \(-0.0248044\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.2426 | + | 40.2574i | −0.791189 | + | 1.37038i | 0.134043 | + | 0.990976i | \(0.457204\pi\) |
−0.925231 | + | 0.379403i | \(0.876129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00000 | + | 1.73205i | 0.0340010 | + | 0.0588915i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.9706 | 0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −65.9411 | −2.23690 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.65685 | + | 9.79796i | 0.191675 | + | 0.331991i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.12132 | + | 14.0665i | −0.274865 | + | 0.476080i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.1421 | − | 31.4231i | 0.612616 | − | 1.06108i | −0.378181 | − | 0.925732i | \(-0.623450\pi\) |
0.990798 | − | 0.135351i | \(-0.0432163\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.53553 | − | 11.3199i | −0.220438 | − | 0.381810i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.9289 | 0.368205 | 0.184103 | − | 0.982907i | \(-0.441062\pi\) | ||||
0.184103 | + | 0.982907i | \(0.441062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.6569 | −0.998033 | −0.499016 | − | 0.866593i | \(-0.666305\pi\) | ||||
−0.499016 | + | 0.866593i | \(0.666305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.4853 | + | 32.0174i | 0.621376 | + | 1.07625i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.7279 | − | 25.5095i | 0.494515 | − | 0.856525i | −0.505465 | − | 0.862847i | \(-0.668679\pi\) |
0.999980 | + | 0.00632174i | \(0.00201228\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.41421 | − | 4.18154i | 0.0808792 | − | 0.140087i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.686292 | − | 1.18869i | −0.0229659 | − | 0.0397781i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −74.4264 | −2.48780 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.17157 | −0.0391177 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.9411 | + | 79.5724i | 1.53222 | + | 2.65389i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.0711 | + | 50.3526i | −0.968498 | + | 1.67749i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.8995 | + | 29.2708i | −0.561758 | + | 0.972994i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.4853 | − | 35.4815i | −0.680203 | − | 1.17815i | −0.974919 | − | 0.222561i | \(-0.928558\pi\) |
0.294716 | − | 0.955585i | \(-0.404775\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.585786 | −0.0194293 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5147 | 1.24292 | 0.621459 | − | 0.783447i | \(-0.286540\pi\) | ||||
0.621459 | + | 0.783447i | \(0.286540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.6569 | − | 30.5826i | −0.584357 | − | 1.01214i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.0711 | − | 17.4436i | 0.332939 | − | 0.576668i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.6274 | − | 35.7277i | 0.680436 | − | 1.17855i | −0.294412 | − | 0.955678i | \(-0.595124\pi\) |
0.974848 | − | 0.222871i | \(-0.0715428\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.2426 | + | 24.6690i | 0.469311 | + | 0.812870i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.82843 | 0.224760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −64.2843 | −2.11365 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.58579 | − | 4.47871i | −0.0849284 | − | 0.147100i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.56497 | − | 6.17471i | 0.116963 | − | 0.202586i | −0.801600 | − | 0.597861i | \(-0.796017\pi\) |
0.918563 | + | 0.395275i | \(0.129351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.07107 | + | 1.85514i | −0.0350652 | + | 0.0607347i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −51.4558 | − | 89.1241i | −1.68279 | − | 2.91467i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.8995 | 0.846100 | 0.423050 | − | 0.906106i | \(-0.360960\pi\) | ||||
0.423050 | + | 0.906106i | \(0.360960\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.5858 | 0.475989 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0503 | − | 20.8716i | −0.392827 | − | 0.680396i | 0.599994 | − | 0.800004i | \(-0.295170\pi\) |
−0.992821 | + | 0.119608i | \(0.961836\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.41421 | + | 2.44949i | −0.0460531 | + | 0.0797664i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.07107 | + | 7.05130i | −0.132292 | + | 0.229136i | −0.924560 | − | 0.381037i | \(-0.875567\pi\) |
0.792268 | + | 0.610174i | \(0.208900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.17157 | − | 3.76127i | −0.0704922 | − | 0.122096i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.31371 | −0.0425999 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.6274 | −1.70477 | −0.852385 | − | 0.522915i | \(-0.824844\pi\) | ||||
−0.852385 | + | 0.522915i | \(0.824844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.5563 | − | 61.5854i | −1.15058 | − | 1.99286i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.4853 | + | 35.4815i | −0.662195 | + | 1.14696i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −43.1274 | + | 74.6989i | −1.39121 | + | 2.40964i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.24264 | − | 2.15232i | −0.0400435 | − | 0.0693574i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 70.4264 | 2.26711 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.6274 | −0.341755 | −0.170877 | − | 0.985292i | \(-0.554660\pi\) | ||||
−0.170877 | + | 0.985292i | \(0.554660\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.65685 | − | 6.33386i | −0.117475 | − | 0.203473i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.6274 | + | 28.7995i | −0.533599 | + | 0.924221i | 0.465631 | + | 0.884979i | \(0.345828\pi\) |
−0.999230 | + | 0.0392417i | \(0.987506\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.70711 | − | 8.15295i | 0.150748 | − | 0.261103i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.0711 | − | 43.4244i | −0.802095 | − | 1.38927i | −0.918235 | − | 0.396036i | \(-0.870386\pi\) |
0.116141 | − | 0.993233i | \(-0.462948\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 71.1127 | 2.27277 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3137 | 0.361219 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.3137 | − | 26.5241i | −0.488431 | − | 0.845988i | 0.511480 | − | 0.859295i | \(-0.329097\pi\) |
−0.999911 | + | 0.0133071i | \(0.995764\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.41421 | − | 5.91359i | 0.108786 | − | 0.188423i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.31371 | + | 5.73951i | −0.105370 | + | 0.182506i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.343146 | + | 0.594346i | 0.0109004 | + | 0.0188800i | 0.871424 | − | 0.490530i | \(-0.163197\pi\) |
−0.860524 | + | 0.509410i | \(0.829864\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.3137 | 0.993711 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.3137 | 0.612286 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.7071 | − | 32.4017i | −0.592460 | − | 1.02617i | −0.993900 | − | 0.110285i | \(-0.964823\pi\) |
0.401440 | − | 0.915885i | \(-0.368510\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.82843 | − | 8.36308i | 0.152765 | − | 0.264596i |
(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 | 2352.2.q.bc.961.2 | 4 | ||
4.3 | odd | 2 | 1176.2.q.o.961.2 | 4 | |||
7.2 | even | 3 | 2352.2.a.bd.1.1 | 2 | |||
7.3 | odd | 6 | 2352.2.q.be.1537.1 | 4 | |||
7.4 | even | 3 | inner | 2352.2.q.bc.1537.2 | 4 | ||
7.5 | odd | 6 | 2352.2.a.bb.1.2 | 2 | |||
7.6 | odd | 2 | 2352.2.q.be.961.1 | 4 | |||
12.11 | even | 2 | 3528.2.s.bd.3313.1 | 4 | |||
21.2 | odd | 6 | 7056.2.a.cx.1.2 | 2 | |||
21.5 | even | 6 | 7056.2.a.cg.1.1 | 2 | |||
28.3 | even | 6 | 1176.2.q.k.361.1 | 4 | |||
28.11 | odd | 6 | 1176.2.q.o.361.2 | 4 | |||
28.19 | even | 6 | 1176.2.a.o.1.2 | yes | 2 | ||
28.23 | odd | 6 | 1176.2.a.j.1.1 | ✓ | 2 | ||
28.27 | even | 2 | 1176.2.q.k.961.1 | 4 | |||
56.5 | odd | 6 | 9408.2.a.du.1.1 | 2 | |||
56.19 | even | 6 | 9408.2.a.dg.1.1 | 2 | |||
56.37 | even | 6 | 9408.2.a.ds.1.2 | 2 | |||
56.51 | odd | 6 | 9408.2.a.ee.1.2 | 2 | |||
84.11 | even | 6 | 3528.2.s.bd.361.1 | 4 | |||
84.23 | even | 6 | 3528.2.a.bl.1.2 | 2 | |||
84.47 | odd | 6 | 3528.2.a.bb.1.1 | 2 | |||
84.59 | odd | 6 | 3528.2.s.bm.361.2 | 4 | |||
84.83 | odd | 2 | 3528.2.s.bm.3313.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.a.j.1.1 | ✓ | 2 | 28.23 | odd | 6 | ||
1176.2.a.o.1.2 | yes | 2 | 28.19 | even | 6 | ||
1176.2.q.k.361.1 | 4 | 28.3 | even | 6 | |||
1176.2.q.k.961.1 | 4 | 28.27 | even | 2 | |||
1176.2.q.o.361.2 | 4 | 28.11 | odd | 6 | |||
1176.2.q.o.961.2 | 4 | 4.3 | odd | 2 | |||
2352.2.a.bb.1.2 | 2 | 7.5 | odd | 6 | |||
2352.2.a.bd.1.1 | 2 | 7.2 | even | 3 | |||
2352.2.q.bc.961.2 | 4 | 1.1 | even | 1 | trivial | ||
2352.2.q.bc.1537.2 | 4 | 7.4 | even | 3 | inner | ||
2352.2.q.be.961.1 | 4 | 7.6 | odd | 2 | |||
2352.2.q.be.1537.1 | 4 | 7.3 | odd | 6 | |||
3528.2.a.bb.1.1 | 2 | 84.47 | odd | 6 | |||
3528.2.a.bl.1.2 | 2 | 84.23 | even | 6 | |||
3528.2.s.bd.361.1 | 4 | 84.11 | even | 6 | |||
3528.2.s.bd.3313.1 | 4 | 12.11 | even | 2 | |||
3528.2.s.bm.361.2 | 4 | 84.59 | odd | 6 | |||
3528.2.s.bm.3313.2 | 4 | 84.83 | odd | 2 | |||
7056.2.a.cg.1.1 | 2 | 21.5 | even | 6 | |||
7056.2.a.cx.1.2 | 2 | 21.2 | odd | 6 | |||
9408.2.a.dg.1.1 | 2 | 56.19 | even | 6 | |||
9408.2.a.ds.1.2 | 2 | 56.37 | even | 6 | |||
9408.2.a.du.1.1 | 2 | 56.5 | odd | 6 | |||
9408.2.a.ee.1.2 | 2 | 56.51 | odd | 6 |