Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(865,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.e (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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 919.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.919 |
Dual form | 1134.2.e.j.865.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.50000 | − | 2.59808i | −0.474342 | − | 0.821584i | ||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | −1.50000 | − | 2.59808i | −0.335410 | − | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 2.00000 | − | 3.46410i | 0.392232 | − | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | 1.50000 | + | 2.59808i | 0.278543 | + | 0.482451i | 0.971023 | − | 0.238987i | \(-0.0768152\pi\) |
−0.692480 | + | 0.721437i | \(0.743482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | − | 5.19615i | −0.514496 | − | 0.891133i | ||||
\(35\) | 7.50000 | − | 2.59808i | 1.26773 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | 2.00000 | − | 3.46410i | 0.324443 | − | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | 3.00000 | − | 5.19615i | 0.468521 | − | 0.811503i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | − | 5.19615i | −0.442326 | − | 0.766131i | ||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | − | 3.46410i | 0.277350 | − | 0.480384i | ||||
\(53\) | −4.50000 | − | 7.79423i | −0.618123 | − | 1.07062i | −0.989828 | − | 0.142269i | \(-0.954560\pi\) |
0.371706 | − | 0.928351i | \(-0.378773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.500000 | + | 2.59808i | −0.0668153 | + | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.50000 | + | 2.59808i | 0.196960 | + | 0.341144i | ||||
\(59\) | −3.00000 | −0.390567 | −0.195283 | − | 0.980747i | \(-0.562563\pi\) | ||||
−0.195283 | + | 0.980747i | \(0.562563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.0000 | −1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | −3.00000 | − | 5.19615i | −0.363803 | − | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.50000 | − | 2.59808i | 0.896421 | − | 0.310530i | ||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.50000 | + | 6.06218i | 0.409644 | + | 0.709524i | 0.994850 | − | 0.101361i | \(-0.0323196\pi\) |
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | −4.00000 | + | 6.92820i | −0.464991 | + | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.0000 | 1.91265 | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) | ||||
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | 6.00000 | + | 10.3923i | 0.658586 | + | 1.14070i | 0.980982 | + | 0.194099i | \(0.0621783\pi\) |
−0.322396 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.00000 | + | 15.5885i | −0.976187 | + | 1.69081i | ||||
\(86\) | −4.00000 | − | 6.92820i | −0.431331 | − | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | + | 6.92820i | 0.838628 | + | 0.726273i | ||||
\(92\) | −3.00000 | − | 5.19615i | −0.312772 | − | 0.541736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | −12.0000 | −1.23117 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | + | 8.66025i | 0.507673 | + | 0.879316i | 0.999961 | + | 0.00888289i | \(0.00282755\pi\) |
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(98\) | −6.50000 | − | 2.59808i | −0.656599 | − | 0.262445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | 7.50000 | − | 12.9904i | 0.746278 | − | 1.29259i | −0.203317 | − | 0.979113i | \(-0.565172\pi\) |
0.949595 | − | 0.313478i | \(-0.101494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | 2.00000 | − | 3.46410i | 0.196116 | − | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.50000 | − | 7.79423i | −0.437079 | − | 0.757042i | ||||
\(107\) | 1.50000 | − | 2.59808i | 0.145010 | − | 0.251166i | −0.784366 | − | 0.620298i | \(-0.787012\pi\) |
0.929377 | + | 0.369132i | \(0.120345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | + | 3.46410i | 0.191565 | + | 0.331801i | 0.945769 | − | 0.324840i | \(-0.105310\pi\) |
−0.754204 | + | 0.656640i | \(0.771977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.500000 | + | 2.59808i | −0.0472456 | + | 0.245495i | ||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | + | 15.5885i | −0.839254 | + | 1.45363i | ||||
\(116\) | 1.50000 | + | 2.59808i | 0.139272 | + | 0.241225i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | 15.0000 | − | 5.19615i | 1.37505 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | −10.0000 | −0.905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.00000 | 0.718421 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0000 | −1.05247 | ||||||||
\(131\) | 6.00000 | + | 10.3923i | 0.524222 | + | 0.907980i | 0.999602 | + | 0.0281993i | \(0.00897729\pi\) |
−0.475380 | + | 0.879781i | \(0.657689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | + | 6.92820i | 0.693688 | + | 0.600751i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | − | 5.19615i | −0.257248 | − | 0.445566i | ||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.00000 | + | 1.73205i | −0.0848189 | + | 0.146911i | −0.905314 | − | 0.424743i | \(-0.860365\pi\) |
0.820495 | + | 0.571654i | \(0.193698\pi\) | |||||||
\(140\) | 7.50000 | − | 2.59808i | 0.633866 | − | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.50000 | − | 7.79423i | 0.373705 | − | 0.647275i | ||||
\(146\) | 3.50000 | + | 6.06218i | 0.289662 | + | 0.501709i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | + | 6.92820i | −0.328798 | + | 0.569495i | ||||
\(149\) | 10.5000 | + | 18.1865i | 0.860194 | + | 1.48990i | 0.871742 | + | 0.489966i | \(0.162991\pi\) |
−0.0115483 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 2.00000 | − | 3.46410i | 0.162221 | − | 0.280976i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | − | 20.7846i | −0.963863 | − | 1.66946i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 17.0000 | 1.35245 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.50000 | − | 2.59808i | −0.118585 | − | 0.205396i | ||||
\(161\) | 15.0000 | − | 5.19615i | 1.18217 | − | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | + | 1.73205i | −0.0783260 | + | 0.135665i | −0.902528 | − | 0.430632i | \(-0.858291\pi\) |
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(164\) | 3.00000 | − | 5.19615i | 0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | −3.00000 | + | 5.19615i | −0.232147 | + | 0.402090i | −0.958440 | − | 0.285295i | \(-0.907908\pi\) |
0.726293 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | −9.00000 | + | 15.5885i | −0.690268 | + | 1.19558i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | −9.00000 | −0.684257 | −0.342129 | − | 0.939653i | \(-0.611148\pi\) | ||||
−0.342129 | + | 0.939653i | \(0.611148\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.00000 | − | 6.92820i | −0.604743 | − | 0.523723i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | 7.50000 | + | 12.9904i | 0.560576 | + | 0.970947i | 0.997446 | + | 0.0714220i | \(0.0227537\pi\) |
−0.436870 | + | 0.899525i | \(0.643913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 8.00000 | + | 6.92820i | 0.592999 | + | 0.513553i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 24.0000 | 1.76452 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | −18.0000 | −1.30243 | −0.651217 | − | 0.758891i | \(-0.725741\pi\) | ||||
−0.651217 | + | 0.758891i | \(0.725741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.0000 | 1.87152 | 0.935760 | − | 0.352636i | \(-0.114715\pi\) | ||||
0.935760 | + | 0.352636i | \(0.114715\pi\) | |||||||
\(194\) | 5.00000 | + | 8.66025i | 0.358979 | + | 0.621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | −15.0000 | −1.06871 | −0.534353 | − | 0.845262i | \(-0.679445\pi\) | ||||
−0.534353 | + | 0.845262i | \(0.679445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.50000 | − | 9.52628i | −0.389885 | − | 0.675300i | 0.602549 | − | 0.798082i | \(-0.294152\pi\) |
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | −2.00000 | + | 3.46410i | −0.141421 | + | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.50000 | − | 12.9904i | 0.527698 | − | 0.914000i | ||||
\(203\) | −7.50000 | + | 2.59808i | −0.526397 | + | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0000 | −1.25717 | ||||||||
\(206\) | −4.00000 | − | 6.92820i | −0.278693 | − | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | − | 3.46410i | 0.137686 | − | 0.238479i | −0.788935 | − | 0.614477i | \(-0.789367\pi\) |
0.926620 | + | 0.375999i | \(0.122700\pi\) | |||||||
\(212\) | −4.50000 | − | 7.79423i | −0.309061 | − | 0.535310i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.50000 | − | 2.59808i | 0.102538 | − | 0.177601i | ||||
\(215\) | −12.0000 | + | 20.7846i | −0.818393 | + | 1.41750i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | + | 20.7846i | −0.271538 | + | 1.41095i | ||||
\(218\) | 2.00000 | + | 3.46410i | 0.135457 | + | 0.234619i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.500000 | + | 0.866025i | 0.0334825 | + | 0.0579934i | 0.882281 | − | 0.470723i | \(-0.156007\pi\) |
−0.848799 | + | 0.528716i | \(0.822674\pi\) | |||||||
\(224\) | −0.500000 | + | 2.59808i | −0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | −1.50000 | + | 2.59808i | −0.0995585 | + | 0.172440i | −0.911502 | − | 0.411296i | \(-0.865076\pi\) |
0.811943 | + | 0.583736i | \(0.198410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | −9.00000 | + | 15.5885i | −0.593442 | + | 1.02787i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.50000 | + | 2.59808i | 0.0984798 | + | 0.170572i | ||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | − | 15.5885i | −0.587095 | − | 1.01688i | ||||
\(236\) | −3.00000 | −0.195283 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.0000 | − | 5.19615i | 0.972306 | − | 0.336817i | ||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | 5.50000 | + | 9.52628i | 0.353553 | + | 0.612372i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 3.00000 | + | 20.7846i | 0.191663 | + | 1.32788i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.00000 | − | 13.8564i | −0.509028 | − | 0.881662i | ||||
\(248\) | 8.00000 | 0.508001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.00000 | −0.189737 | ||||||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 5.00000 | 0.313728 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | − | 13.8564i | −0.994192 | − | 0.860995i | ||||
\(260\) | −12.0000 | −0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.00000 | + | 10.3923i | 0.370681 | + | 0.642039i | ||||
\(263\) | 9.00000 | − | 15.5885i | 0.554964 | − | 0.961225i | −0.442943 | − | 0.896550i | \(-0.646065\pi\) |
0.997906 | − | 0.0646755i | \(-0.0206012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.5000 | + | 23.3827i | −0.829298 | + | 1.43639i | ||||
\(266\) | 8.00000 | + | 6.92820i | 0.490511 | + | 0.424795i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.0000 | −0.610847 | ||||||||
\(269\) | −10.5000 | − | 18.1865i | −0.640196 | − | 1.10885i | −0.985389 | − | 0.170321i | \(-0.945520\pi\) |
0.345192 | − | 0.938532i | \(-0.387814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | − | 21.6506i | 0.759321 | − | 1.31518i | −0.183876 | − | 0.982949i | \(-0.558865\pi\) |
0.943197 | − | 0.332233i | \(-0.107802\pi\) | |||||||
\(272\) | −3.00000 | − | 5.19615i | −0.181902 | − | 0.315063i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | + | 10.3923i | −0.362473 | + | 0.627822i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000 | − | 24.2487i | 0.841178 | − | 1.45696i | −0.0477206 | − | 0.998861i | \(-0.515196\pi\) |
0.888899 | − | 0.458103i | \(-0.151471\pi\) | |||||||
\(278\) | −1.00000 | + | 1.73205i | −0.0599760 | + | 0.103882i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.50000 | − | 2.59808i | 0.448211 | − | 0.155265i | ||||
\(281\) | 9.00000 | + | 15.5885i | 0.536895 | + | 0.929929i | 0.999069 | + | 0.0431402i | \(0.0137362\pi\) |
−0.462174 | + | 0.886789i | \(0.652930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | + | 10.3923i | 0.708338 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 4.50000 | − | 7.79423i | 0.264249 | − | 0.457693i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.50000 | + | 6.06218i | 0.204822 | + | 0.354762i | ||||
\(293\) | 1.50000 | − | 2.59808i | 0.0876309 | − | 0.151781i | −0.818878 | − | 0.573967i | \(-0.805404\pi\) |
0.906509 | + | 0.422186i | \(0.138737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.50000 | + | 7.79423i | 0.262000 | + | 0.453798i | ||||
\(296\) | −4.00000 | + | 6.92820i | −0.232495 | + | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.5000 | + | 18.1865i | 0.608249 | + | 1.05352i | ||||
\(299\) | −24.0000 | −1.38796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | − | 6.92820i | 1.15278 | − | 0.399335i | ||||
\(302\) | −4.00000 | + | 6.92820i | −0.230174 | + | 0.398673i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 15.0000 | + | 25.9808i | 0.858898 | + | 1.48765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.0000 | − | 20.7846i | −0.681554 | − | 1.18049i | ||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | 0.282617 | 0.141308 | − | 0.989966i | \(-0.454869\pi\) | ||||
0.141308 | + | 0.989966i | \(0.454869\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.0000 | 0.956325 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.50000 | − | 2.59808i | −0.0838525 | − | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.0000 | − | 5.19615i | 0.835917 | − | 0.289570i | ||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | + | 13.8564i | 0.443760 | + | 0.768615i | ||||
\(326\) | −1.00000 | + | 1.73205i | −0.0553849 | + | 0.0959294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | − | 5.19615i | 0.165647 | − | 0.286910i | ||||
\(329\) | −3.00000 | + | 15.5885i | −0.165395 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | 0.109930 | 0.0549650 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549650 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(332\) | 6.00000 | + | 10.3923i | 0.329293 | + | 0.570352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.00000 | + | 5.19615i | −0.164153 | + | 0.284321i | ||||
\(335\) | 15.0000 | + | 25.9808i | 0.819538 | + | 1.41948i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.50000 | − | 6.06218i | 0.190657 | − | 0.330228i | −0.754811 | − | 0.655942i | \(-0.772271\pi\) |
0.945468 | + | 0.325714i | \(0.105605\pi\) | |||||||
\(338\) | −1.50000 | − | 2.59808i | −0.0815892 | − | 0.141317i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.00000 | + | 15.5885i | −0.488094 | + | 0.845403i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | −4.00000 | − | 6.92820i | −0.215666 | − | 0.373544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | −0.483843 | ||||||||
\(347\) | 33.0000 | 1.77153 | 0.885766 | − | 0.464131i | \(-0.153633\pi\) | ||||
0.885766 | + | 0.464131i | \(0.153633\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.00000 | + | 8.66025i | 0.267644 | + | 0.463573i | 0.968253 | − | 0.249973i | \(-0.0804216\pi\) |
−0.700609 | + | 0.713545i | \(0.747088\pi\) | |||||||
\(350\) | −8.00000 | − | 6.92820i | −0.427618 | − | 0.370328i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0000 | − | 25.9808i | 0.798369 | − | 1.38282i | −0.122308 | − | 0.992492i | \(-0.539030\pi\) |
0.920677 | − | 0.390324i | \(-0.127637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00000 | − | 15.5885i | −0.477670 | − | 0.827349i | ||||
\(356\) | −3.00000 | + | 5.19615i | −0.159000 | + | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.50000 | + | 12.9904i | 0.396387 | + | 0.686563i | ||||
\(359\) | −18.0000 | + | 31.1769i | −0.950004 | + | 1.64545i | −0.204595 | + | 0.978847i | \(0.565588\pi\) |
−0.745409 | + | 0.666608i | \(0.767746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | + | 6.92820i | 0.419314 | + | 0.363137i | ||||
\(365\) | 10.5000 | − | 18.1865i | 0.549595 | − | 0.951927i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.50000 | − | 16.4545i | 0.495896 | − | 0.858917i | −0.504093 | − | 0.863649i | \(-0.668173\pi\) |
0.999989 | + | 0.00473247i | \(0.00150640\pi\) | |||||||
\(368\) | −3.00000 | − | 5.19615i | −0.156386 | − | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 24.0000 | 1.24770 | ||||||||
\(371\) | 22.5000 | − | 7.79423i | 1.16814 | − | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | −12.0000 | −0.615587 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.0000 | −0.920960 | ||||||||
\(383\) | −3.00000 | − | 5.19615i | −0.153293 | − | 0.265511i | 0.779143 | − | 0.626846i | \(-0.215654\pi\) |
−0.932436 | + | 0.361335i | \(0.882321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.0000 | 1.32337 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.00000 | + | 8.66025i | 0.253837 | + | 0.439658i | ||||
\(389\) | 4.50000 | − | 7.79423i | 0.228159 | − | 0.395183i | −0.729103 | − | 0.684403i | \(-0.760063\pi\) |
0.957263 | + | 0.289220i | \(0.0933960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | + | 31.1769i | −0.910299 | + | 1.57668i | ||||
\(392\) | −6.50000 | − | 2.59808i | −0.328300 | − | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.0000 | −0.755689 | ||||||||
\(395\) | −25.5000 | − | 44.1673i | −1.28304 | − | 2.22230i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0000 | + | 27.7128i | −0.803017 | + | 1.39087i | 0.114605 | + | 0.993411i | \(0.463440\pi\) |
−0.917622 | + | 0.397455i | \(0.869893\pi\) | |||||||
\(398\) | −5.50000 | − | 9.52628i | −0.275690 | − | 0.477509i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.0000 | − | 27.7128i | 0.797017 | − | 1.38047i | ||||
\(404\) | 7.50000 | − | 12.9904i | 0.373139 | − | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.50000 | + | 2.59808i | −0.372219 | + | 0.128940i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0000 | −1.23617 | −0.618085 | − | 0.786111i | \(-0.712091\pi\) | ||||
−0.618085 | + | 0.786111i | \(0.712091\pi\) | |||||||
\(410\) | −18.0000 | −0.888957 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00000 | − | 6.92820i | −0.197066 | − | 0.341328i | ||||
\(413\) | 1.50000 | − | 7.79423i | 0.0738102 | − | 0.383529i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | − | 31.1769i | 0.883585 | − | 1.53041i | ||||
\(416\) | 2.00000 | − | 3.46410i | 0.0980581 | − | 0.169842i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | + | 10.3923i | −0.293119 | + | 0.507697i | −0.974546 | − | 0.224189i | \(-0.928027\pi\) |
0.681426 | + | 0.731887i | \(0.261360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | − | 27.7128i | −0.779792 | − | 1.35064i | −0.932061 | − | 0.362301i | \(-0.881991\pi\) |
0.152269 | − | 0.988339i | \(-0.451342\pi\) | |||||||
\(422\) | 2.00000 | − | 3.46410i | 0.0973585 | − | 0.168630i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.50000 | − | 7.79423i | −0.218539 | − | 0.378521i | ||||
\(425\) | 24.0000 | 1.16417 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.00000 | − | 25.9808i | 0.241967 | − | 1.25730i | ||||
\(428\) | 1.50000 | − | 2.59808i | 0.0725052 | − | 0.125583i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.0000 | + | 20.7846i | −0.578691 | + | 1.00232i | ||||
\(431\) | −6.00000 | − | 10.3923i | −0.289010 | − | 0.500580i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00000 | −0.336399 | −0.168199 | − | 0.985753i | \(-0.553795\pi\) | ||||
−0.168199 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(434\) | −4.00000 | + | 20.7846i | −0.192006 | + | 0.997693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | −24.0000 | −1.14808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | −39.0000 | −1.85295 | −0.926473 | − | 0.376361i | \(-0.877175\pi\) | ||||
−0.926473 | + | 0.376361i | \(0.877175\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | 0.853282 | ||||||||
\(446\) | 0.500000 | + | 0.866025i | 0.0236757 | + | 0.0410075i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | + | 2.59808i | −0.0236228 | + | 0.122748i | ||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.50000 | + | 2.59808i | −0.0703985 | + | 0.121934i | ||||
\(455\) | 6.00000 | − | 31.1769i | 0.281284 | − | 1.46160i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | −0.0467780 | −0.0233890 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233890 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(458\) | −7.00000 | − | 12.1244i | −0.327089 | − | 0.566534i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.00000 | + | 15.5885i | −0.419627 | + | 0.726816i | ||||
\(461\) | 16.5000 | + | 28.5788i | 0.768482 | + | 1.33105i | 0.938386 | + | 0.345589i | \(0.112321\pi\) |
−0.169904 | + | 0.985461i | \(0.554346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.50000 | − | 16.4545i | 0.441502 | − | 0.764705i | −0.556299 | − | 0.830982i | \(-0.687779\pi\) |
0.997801 | + | 0.0662777i | \(0.0211123\pi\) | |||||||
\(464\) | 1.50000 | + | 2.59808i | 0.0696358 | + | 0.120613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | 16.5000 | − | 28.5788i | 0.763529 | − | 1.32247i | −0.177492 | − | 0.984122i | \(-0.556798\pi\) |
0.941021 | − | 0.338349i | \(-0.109868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00000 | − | 25.9808i | 0.230879 | − | 1.19968i | ||||
\(470\) | −9.00000 | − | 15.5885i | −0.415139 | − | 0.719042i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.00000 | −0.138086 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | + | 13.8564i | 0.367065 | + | 0.635776i | ||||
\(476\) | 15.0000 | − | 5.19615i | 0.687524 | − | 0.238165i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | \(-0.648611\pi\) |
0.998392 | − | 0.0566937i | \(-0.0180558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | + | 27.7128i | 0.729537 | + | 1.26360i | ||||
\(482\) | 0.500000 | − | 0.866025i | 0.0227744 | − | 0.0394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.50000 | + | 9.52628i | 0.250000 | + | 0.433013i | ||||
\(485\) | 15.0000 | − | 25.9808i | 0.681115 | − | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.50000 | + | 11.2583i | 0.294543 | + | 0.510164i | 0.974879 | − | 0.222737i | \(-0.0714992\pi\) |
−0.680335 | + | 0.732901i | \(0.738166\pi\) | |||||||
\(488\) | −10.0000 | −0.452679 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.00000 | + | 20.7846i | 0.135526 | + | 0.938953i | ||||
\(491\) | −13.5000 | + | 23.3827i | −0.609246 | + | 1.05525i | 0.382118 | + | 0.924113i | \(0.375195\pi\) |
−0.991365 | + | 0.131132i | \(0.958139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | −8.00000 | − | 13.8564i | −0.359937 | − | 0.623429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −3.00000 | + | 15.5885i | −0.134568 | + | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.00000 | − | 1.73205i | −0.0447661 | − | 0.0775372i | 0.842774 | − | 0.538267i | \(-0.180921\pi\) |
−0.887540 | + | 0.460730i | \(0.847588\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.00000 | 0.401690 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.0000 | −2.00247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.00000 | 0.221839 | ||||||||
\(509\) | −9.00000 | − | 15.5885i | −0.398918 | − | 0.690946i | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113020i | \(0.963948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.5000 | + | 6.06218i | −0.774154 | + | 0.268175i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0000 | + | 20.7846i | −0.528783 | + | 0.915879i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −16.0000 | − | 13.8564i | −0.703000 | − | 0.608816i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.0000 | −0.526235 | ||||||||
\(521\) | 15.0000 | + | 25.9808i | 0.657162 | + | 1.13824i | 0.981347 | + | 0.192244i | \(0.0615766\pi\) |
−0.324185 | + | 0.945994i | \(0.605090\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00000 | − | 3.46410i | 0.0874539 | − | 0.151475i | −0.818980 | − | 0.573822i | \(-0.805460\pi\) |
0.906434 | + | 0.422347i | \(0.138794\pi\) | |||||||
\(524\) | 6.00000 | + | 10.3923i | 0.262111 | + | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | − | 15.5885i | 0.392419 | − | 0.679689i | ||||
\(527\) | −24.0000 | − | 41.5692i | −1.04546 | − | 1.81078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | −13.5000 | + | 23.3827i | −0.586403 | + | 1.01568i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000 | + | 6.92820i | 0.346844 | + | 0.300376i | ||||
\(533\) | −12.0000 | − | 20.7846i | −0.519778 | − | 0.900281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | −0.389104 | ||||||||
\(536\) | −10.0000 | −0.431934 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.5000 | − | 18.1865i | −0.452687 | − | 0.784077i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | 12.5000 | − | 21.6506i | 0.536921 | − | 0.929974i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.00000 | − | 5.19615i | −0.128624 | − | 0.222783i | ||||
\(545\) | 6.00000 | − | 10.3923i | 0.257012 | − | 0.445157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | + | 24.2487i | 0.598597 | + | 1.03680i | 0.993028 | + | 0.117875i | \(0.0376081\pi\) |
−0.394432 | + | 0.918925i | \(0.629059\pi\) | |||||||
\(548\) | −6.00000 | + | 10.3923i | −0.256307 | + | 0.443937i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000 | 0.511217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.50000 | + | 44.1673i | −0.361457 | + | 1.87818i | ||||
\(554\) | 14.0000 | − | 24.2487i | 0.594803 | − | 1.03023i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | + | 1.73205i | −0.0424094 | + | 0.0734553i | ||||
\(557\) | 3.00000 | + | 5.19615i | 0.127114 | + | 0.220168i | 0.922557 | − | 0.385860i | \(-0.126095\pi\) |
−0.795443 | + | 0.606028i | \(0.792762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.0000 | −1.35346 | ||||||||
\(560\) | 7.50000 | − | 2.59808i | 0.316933 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00000 | + | 15.5885i | 0.379642 | + | 0.657559i | ||||
\(563\) | 15.0000 | 0.632175 | 0.316087 | − | 0.948730i | \(-0.397631\pi\) | ||||
0.316087 | + | 0.948730i | \(0.397631\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | −0.757266 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | + | 10.3923i | 0.500870 | + | 0.433766i | ||||
\(575\) | 24.0000 | 1.00087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5000 | − | 19.9186i | −0.478751 | − | 0.829222i | 0.520952 | − | 0.853586i | \(-0.325577\pi\) |
−0.999703 | + | 0.0243645i | \(0.992244\pi\) | |||||||
\(578\) | −9.50000 | + | 16.4545i | −0.395148 | + | 0.684416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.50000 | − | 7.79423i | 0.186852 | − | 0.323638i | ||||
\(581\) | −30.0000 | + | 10.3923i | −1.24461 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.50000 | + | 6.06218i | 0.144831 | + | 0.250855i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.50000 | − | 2.59808i | 0.0619644 | − | 0.107326i | ||||
\(587\) | 7.50000 | + | 12.9904i | 0.309558 | + | 0.536170i | 0.978266 | − | 0.207355i | \(-0.0664855\pi\) |
−0.668708 | + | 0.743525i | \(0.733152\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | − | 27.7128i | 0.659269 | − | 1.14189i | ||||
\(590\) | 4.50000 | + | 7.79423i | 0.185262 | + | 0.320883i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | + | 6.92820i | −0.164399 | + | 0.284747i | ||||
\(593\) | −3.00000 | + | 5.19615i | −0.123195 | + | 0.213380i | −0.921026 | − | 0.389501i | \(-0.872647\pi\) |
0.797831 | + | 0.602881i | \(0.205981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | − | 31.1769i | −1.47586 | − | 1.27813i | ||||
\(596\) | 10.5000 | + | 18.1865i | 0.430097 | + | 0.744949i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.0000 | −0.981433 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5000 | + | 21.6506i | 0.509886 | + | 0.883148i | 0.999934 | + | 0.0114528i | \(0.00364562\pi\) |
−0.490049 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(602\) | 20.0000 | − | 6.92820i | 0.815139 | − | 0.282372i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.00000 | + | 6.92820i | −0.162758 | + | 0.281905i | ||||
\(605\) | 16.5000 | − | 28.5788i | 0.670820 | − | 1.16190i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.50000 | − | 9.52628i | −0.223238 | − | 0.386660i | 0.732551 | − | 0.680712i | \(-0.238329\pi\) |
−0.955789 | + | 0.294052i | \(0.904996\pi\) | |||||||
\(608\) | 2.00000 | − | 3.46410i | 0.0811107 | − | 0.140488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.0000 | + | 25.9808i | 0.607332 | + | 1.05193i | ||||
\(611\) | 12.0000 | − | 20.7846i | 0.485468 | − | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.00000 | + | 13.8564i | 0.323117 | + | 0.559655i | 0.981129 | − | 0.193352i | \(-0.0619359\pi\) |
−0.658012 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(614\) | 8.00000 | 0.322854 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.00000 | − | 15.5885i | 0.362326 | − | 0.627568i | −0.626017 | − | 0.779809i | \(-0.715316\pi\) |
0.988343 | + | 0.152242i | \(0.0486493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.00000 | − | 13.8564i | 0.321547 | − | 0.556936i | −0.659260 | − | 0.751915i | \(-0.729130\pi\) |
0.980807 | + | 0.194979i | \(0.0624638\pi\) | |||||||
\(620\) | −12.0000 | − | 20.7846i | −0.481932 | − | 0.834730i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | −12.0000 | − | 10.3923i | −0.480770 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 5.00000 | 0.199840 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 48.0000 | 1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 17.0000 | 0.676224 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −7.50000 | − | 12.9904i | −0.297628 | − | 0.515508i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.0000 | + | 17.3205i | −0.871672 | + | 0.686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.50000 | − | 2.59808i | −0.0592927 | − | 0.102698i | ||||
\(641\) | −12.0000 | + | 20.7846i | −0.473972 | + | 0.820943i | −0.999556 | − | 0.0297987i | \(-0.990513\pi\) |
0.525584 | + | 0.850741i | \(0.323847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.00000 | − | 13.8564i | 0.315489 | − | 0.546443i | −0.664052 | − | 0.747686i | \(-0.731165\pi\) |
0.979541 | + | 0.201243i | \(0.0644981\pi\) | |||||||
\(644\) | 15.0000 | − | 5.19615i | 0.591083 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.0000 | −0.944267 | ||||||||
\(647\) | −21.0000 | − | 36.3731i | −0.825595 | − | 1.42997i | −0.901464 | − | 0.432855i | \(-0.857506\pi\) |
0.0758684 | − | 0.997118i | \(-0.475827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 8.00000 | + | 13.8564i | 0.313786 | + | 0.543493i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | + | 1.73205i | −0.0391630 | + | 0.0678323i | ||||
\(653\) | −1.50000 | − | 2.59808i | −0.0586995 | − | 0.101671i | 0.835182 | − | 0.549973i | \(-0.185362\pi\) |
−0.893882 | + | 0.448303i | \(0.852029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.0000 | − | 31.1769i | 0.703318 | − | 1.21818i | ||||
\(656\) | 3.00000 | − | 5.19615i | 0.117130 | − | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.00000 | + | 15.5885i | −0.116952 | + | 0.607701i | ||||
\(659\) | −10.5000 | − | 18.1865i | −0.409022 | − | 0.708447i | 0.585758 | − | 0.810486i | \(-0.300797\pi\) |
−0.994780 | + | 0.102039i | \(0.967463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.0000 | 1.24466 | 0.622328 | − | 0.782757i | \(-0.286187\pi\) | ||||
0.622328 | + | 0.782757i | \(0.286187\pi\) | |||||||
\(662\) | 2.00000 | 0.0777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | + | 10.3923i | 0.232845 | + | 0.403300i | ||||
\(665\) | 6.00000 | − | 31.1769i | 0.232670 | − | 1.20899i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | −3.00000 | + | 5.19615i | −0.116073 | + | 0.201045i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.0000 | + | 25.9808i | 0.579501 | + | 1.00372i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.5000 | + | 37.2391i | 0.828764 | + | 1.43546i | 0.899008 | + | 0.437932i | \(0.144289\pi\) |
−0.0702442 | + | 0.997530i | \(0.522378\pi\) | |||||||
\(674\) | 3.50000 | − | 6.06218i | 0.134815 | − | 0.233506i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | −21.0000 | −0.807096 | −0.403548 | − | 0.914959i | \(-0.632223\pi\) | ||||
−0.403548 | + | 0.914959i | \(0.632223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.0000 | + | 8.66025i | −0.959412 | + | 0.332350i | ||||
\(680\) | −9.00000 | + | 15.5885i | −0.345134 | + | 0.597790i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.50000 | + | 7.79423i | 0.172188 | + | 0.298238i | 0.939184 | − | 0.343413i | \(-0.111583\pi\) |
−0.766997 | + | 0.641651i | \(0.778250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | 10.0000 | − | 15.5885i | 0.381802 | − | 0.595170i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | − | 6.92820i | −0.152499 | − | 0.264135i | ||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | −9.00000 | −0.342129 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.0000 | 1.25266 | ||||||||
\(695\) | 6.00000 | 0.227593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.0000 | −1.36360 | ||||||||
\(698\) | 5.00000 | + | 8.66025i | 0.189253 | + | 0.327795i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.00000 | − | 6.92820i | −0.302372 | − | 0.261861i | ||||
\(701\) | −39.0000 | −1.47301 | −0.736505 | − | 0.676432i | \(-0.763525\pi\) | ||||
−0.736505 | + | 0.676432i | \(0.763525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | + | 27.7128i | 0.603451 | + | 1.04521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | − | 25.9808i | 0.564532 | − | 0.977799i | ||||
\(707\) | 30.0000 | + | 25.9808i | 1.12827 | + | 0.977107i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00000 | 0.300446 | 0.150223 | − | 0.988652i | \(-0.452001\pi\) | ||||
0.150223 | + | 0.988652i | \(0.452001\pi\) | |||||||
\(710\) | −9.00000 | − | 15.5885i | −0.337764 | − | 0.585024i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | −24.0000 | − | 41.5692i | −0.898807 | − | 1.55678i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.50000 | + | 12.9904i | 0.280288 | + | 0.485473i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.0000 | + | 31.1769i | −0.671754 | + | 1.16351i | ||||
\(719\) | 12.0000 | − | 20.7846i | 0.447524 | − | 0.775135i | −0.550700 | − | 0.834703i | \(-0.685639\pi\) |
0.998224 | + | 0.0595683i | \(0.0189724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0000 | − | 6.92820i | 0.744839 | − | 0.258020i | ||||
\(722\) | 1.50000 | + | 2.59808i | 0.0558242 | + | 0.0966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.0000 | −0.371647 | ||||||||
\(725\) | −12.0000 | −0.445669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.5000 | − | 19.9186i | −0.426511 | − | 0.738739i | 0.570049 | − | 0.821611i | \(-0.306924\pi\) |
−0.996560 | + | 0.0828714i | \(0.973591\pi\) | |||||||
\(728\) | 8.00000 | + | 6.92820i | 0.296500 | + | 0.256776i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.5000 | − | 18.1865i | 0.388622 | − | 0.673114i | ||||
\(731\) | −24.0000 | + | 41.5692i | −0.887672 | + | 1.53749i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0000 | − | 38.1051i | −0.812589 | − | 1.40744i | −0.911047 | − | 0.412303i | \(-0.864724\pi\) |
0.0984580 | − | 0.995141i | \(-0.468609\pi\) | |||||||
\(734\) | 9.50000 | − | 16.4545i | 0.350651 | − | 0.607346i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | − | 5.19615i | −0.110581 | − | 0.191533i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.00000 | − | 12.1244i | −0.257499 | − | 0.446002i | 0.708072 | − | 0.706140i | \(-0.249565\pi\) |
−0.965571 | + | 0.260138i | \(0.916232\pi\) | |||||||
\(740\) | 24.0000 | 0.882258 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.5000 | − | 7.79423i | 0.826001 | − | 0.286135i | ||||
\(743\) | −12.0000 | + | 20.7846i | −0.440237 | + | 0.762513i | −0.997707 | − | 0.0676840i | \(-0.978439\pi\) |
0.557470 | + | 0.830197i | \(0.311772\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.5000 | − | 54.5596i | 1.15407 | − | 1.99891i | ||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000 | + | 5.19615i | 0.219235 | + | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.5000 | + | 37.2391i | 0.784546 | + | 1.35887i | 0.929270 | + | 0.369402i | \(0.120437\pi\) |
−0.144724 | + | 0.989472i | \(0.546229\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0000 | 0.437014 | ||||||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | −10.0000 | −0.363216 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.0000 | −0.435286 | ||||||||
\(761\) | −24.0000 | − | 41.5692i | −0.869999 | − | 1.50688i | −0.861996 | − | 0.506915i | \(-0.830786\pi\) |
−0.00800331 | − | 0.999968i | \(-0.502548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | + | 3.46410i | −0.362024 | + | 0.125409i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.00000 | − | 5.19615i | −0.108394 | − | 0.187745i | ||||
\(767\) | −6.00000 | + | 10.3923i | −0.216647 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.0000 | + | 22.5167i | −0.468792 | + | 0.811972i | −0.999364 | − | 0.0356685i | \(-0.988644\pi\) |
0.530572 | + | 0.847640i | \(0.321977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 26.0000 | 0.935760 | ||||||||
\(773\) | 9.00000 | + | 15.5885i | 0.323708 | + | 0.560678i | 0.981250 | − | 0.192740i | \(-0.0617373\pi\) |
−0.657542 | + | 0.753418i | \(0.728404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0000 | + | 27.7128i | −0.574737 | + | 0.995474i | ||||
\(776\) | 5.00000 | + | 8.66025i | 0.179490 | + | 0.310885i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.50000 | − | 7.79423i | 0.161333 | − | 0.279437i | ||||
\(779\) | −12.0000 | − | 20.7846i | −0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.0000 | + | 31.1769i | −0.643679 | + | 1.11488i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | −21.0000 | − | 36.3731i | −0.749522 | − | 1.29821i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0000 | −0.784215 | −0.392108 | − | 0.919919i | \(-0.628254\pi\) | ||||
−0.392108 | + | 0.919919i | \(0.628254\pi\) | |||||||
\(788\) | −15.0000 | −0.534353 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.5000 | − | 44.1673i | −0.907249 | − | 1.57140i | ||||
\(791\) | 12.0000 | + | 10.3923i | 0.426671 | + | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | + | 34.6410i | −0.710221 | + | 1.23014i | ||||
\(794\) | −16.0000 | + | 27.7128i | −0.567819 | + | 0.983491i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.50000 | − | 9.52628i | −0.194942 | − | 0.337650i | ||||
\(797\) | −9.00000 | + | 15.5885i | −0.318796 | + | 0.552171i | −0.980237 | − | 0.197826i | \(-0.936612\pi\) |
0.661441 | + | 0.749997i | \(0.269945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | − | 31.1769i | −0.636794 | − | 1.10296i | ||||
\(800\) | −2.00000 | + | 3.46410i | −0.0707107 | + | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.00000 | + | 15.5885i | 0.317801 | + | 0.550448i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | − | 31.1769i | −1.26883 | − | 1.09884i | ||||
\(806\) | 16.0000 | − | 27.7128i | 0.563576 | − | 0.976142i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.50000 | − | 12.9904i | 0.263849 | − | 0.457000i | ||||
\(809\) | −12.0000 | − | 20.7846i | −0.421898 | − | 0.730748i | 0.574228 | − | 0.818696i | \(-0.305302\pi\) |
−0.996125 | + | 0.0879478i | \(0.971969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −7.50000 | + | 2.59808i | −0.263198 | + | 0.0911746i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | 0.210171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | −25.0000 | −0.874105 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.0000 | −0.628587 | ||||||||
\(821\) | 21.0000 | 0.732905 | 0.366453 | − | 0.930437i | \(-0.380572\pi\) | ||||
0.366453 | + | 0.930437i | \(0.380572\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0000 | 0.801730 | 0.400865 | − | 0.916137i | \(-0.368710\pi\) | ||||
0.400865 | + | 0.916137i | \(0.368710\pi\) | |||||||
\(824\) | −4.00000 | − | 6.92820i | −0.139347 | − | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.50000 | − | 7.79423i | 0.0521917 | − | 0.271196i | ||||
\(827\) | 21.0000 | 0.730242 | 0.365121 | − | 0.930960i | \(-0.381028\pi\) | ||||
0.365121 | + | 0.930960i | \(0.381028\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0000 | − | 27.7128i | −0.555703 | − | 0.962506i | −0.997848 | − | 0.0655624i | \(-0.979116\pi\) |
0.442145 | − | 0.896943i | \(-0.354217\pi\) | |||||||
\(830\) | 18.0000 | − | 31.1769i | 0.624789 | − | 1.08217i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | − | 3.46410i | 0.0693375 | − | 0.120096i | ||||
\(833\) | 6.00000 | + | 41.5692i | 0.207888 | + | 1.44029i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | 0.622916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | + | 10.3923i | −0.207267 | + | 0.358996i | ||||
\(839\) | 12.0000 | + | 20.7846i | 0.414286 | + | 0.717564i | 0.995353 | − | 0.0962912i | \(-0.0306980\pi\) |
−0.581067 | + | 0.813856i | \(0.697365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | −16.0000 | − | 27.7128i | −0.551396 | − | 0.955047i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.00000 | − | 3.46410i | 0.0688428 | − | 0.119239i | ||||
\(845\) | −4.50000 | + | 7.79423i | −0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.5000 | + | 9.52628i | −0.944911 | + | 0.327327i | ||||
\(848\) | −4.50000 | − | 7.79423i | −0.154531 | − | 0.267655i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.0000 | 0.823193 | ||||||||
\(851\) | 48.0000 | 1.64542 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | − | 38.1051i | −0.753266 | − | 1.30469i | −0.946232 | − | 0.323489i | \(-0.895144\pi\) |
0.192966 | − | 0.981205i | \(-0.438189\pi\) | |||||||
\(854\) | 5.00000 | − | 25.9808i | 0.171096 | − | 0.889043i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.50000 | − | 2.59808i | 0.0512689 | − | 0.0888004i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.00000 | − | 12.1244i | −0.238837 | − | 0.413678i | 0.721544 | − | 0.692369i | \(-0.243433\pi\) |
−0.960381 | + | 0.278691i | \(0.910099\pi\) | |||||||
\(860\) | −12.0000 | + | 20.7846i | −0.409197 | + | 0.708749i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.00000 | − | 10.3923i | −0.204361 | − | 0.353963i | ||||
\(863\) | −21.0000 | + | 36.3731i | −0.714848 | + | 1.23815i | 0.248170 | + | 0.968717i | \(0.420171\pi\) |
−0.963018 | + | 0.269437i | \(0.913162\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5000 | + | 23.3827i | 0.459014 | + | 0.795035i | ||||
\(866\) | −7.00000 | −0.237870 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.00000 | + | 20.7846i | −0.135769 | + | 0.705476i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | + | 34.6410i | −0.677674 | + | 1.17377i | ||||
\(872\) | 2.00000 | + | 3.46410i | 0.0677285 | + | 0.117309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | 1.50000 | − | 7.79423i | 0.0507093 | − | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.00000 | − | 12.1244i | −0.236373 | − | 0.409410i | 0.723298 | − | 0.690536i | \(-0.242625\pi\) |
−0.959671 | + | 0.281126i | \(0.909292\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0000 | 1.07689 | 0.538443 | − | 0.842662i | \(-0.319013\pi\) | ||||
0.538443 | + | 0.842662i | \(0.319013\pi\) | |||||||
\(884\) | −24.0000 | −0.807207 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.0000 | −1.31023 | ||||||||
\(887\) | 21.0000 | + | 36.3731i | 0.705111 | + | 1.22129i | 0.966651 | + | 0.256096i | \(0.0824362\pi\) |
−0.261540 | + | 0.965193i | \(0.584230\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.50000 | + | 12.9904i | −0.0838473 | + | 0.435683i | ||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.500000 | + | 0.866025i | 0.0167412 | + | 0.0289967i | ||||
\(893\) | 12.0000 | − | 20.7846i | 0.401565 | − | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.5000 | − | 38.9711i | 0.752092 | − | 1.30266i | ||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.00000 | 0.200223 | ||||||||
\(899\) | 12.0000 | + | 20.7846i | 0.400222 | + | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.0000 | + | 46.7654i | −0.899500 | + | 1.55798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.00000 | − | 5.19615i | 0.0997785 | − | 0.172821i | ||||
\(905\) | 15.0000 | + | 25.9808i | 0.498617 | + | 0.863630i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | + | 6.92820i | −0.132818 | + | 0.230047i | −0.924762 | − | 0.380547i | \(-0.875736\pi\) |
0.791944 | + | 0.610594i | \(0.209069\pi\) | |||||||
\(908\) | −1.50000 | + | 2.59808i | −0.0497792 | + | 0.0862202i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.00000 | − | 31.1769i | 0.198898 | − | 1.03350i | ||||
\(911\) | 27.0000 | + | 46.7654i | 0.894550 | + | 1.54941i | 0.834361 | + | 0.551219i | \(0.185837\pi\) |
0.0601892 | + | 0.998187i | \(0.480830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.00000 | −0.0330771 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.00000 | − | 12.1244i | −0.231287 | − | 0.400600i | ||||
\(917\) | −30.0000 | + | 10.3923i | −0.990687 | + | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5000 | − | 32.0429i | 0.610259 | − | 1.05700i | −0.380938 | − | 0.924601i | \(-0.624399\pi\) |
0.991197 | − | 0.132398i | \(-0.0422678\pi\) | |||||||
\(920\) | −9.00000 | + | 15.5885i | −0.296721 | + | 0.513936i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.5000 | + | 28.5788i | 0.543399 | + | 0.941194i | ||||
\(923\) | 12.0000 | − | 20.7846i | 0.394985 | − | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.0000 | − | 27.7128i | −0.526077 | − | 0.911192i | ||||
\(926\) | 9.50000 | − | 16.4545i | 0.312189 | − | 0.540728i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.50000 | + | 2.59808i | 0.0492399 | + | 0.0852860i | ||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.0000 | + | 17.3205i | −0.721021 | + | 0.567657i | ||||
\(932\) | −9.00000 | + | 15.5885i | −0.294805 | + | 0.510617i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.5000 | − | 28.5788i | 0.539896 | − | 0.935128i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.00000 | −0.0326686 | −0.0163343 | − | 0.999867i | \(-0.505200\pi\) | ||||
−0.0163343 | + | 0.999867i | \(0.505200\pi\) | |||||||
\(938\) | 5.00000 | − | 25.9808i | 0.163256 | − | 0.848302i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.00000 | − | 15.5885i | −0.293548 | − | 0.508439i | ||||
\(941\) | 18.0000 | 0.586783 | 0.293392 | − | 0.955992i | \(-0.405216\pi\) | ||||
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0000 | −1.17232 | ||||||||
\(944\) | −3.00000 | −0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.0000 | 1.46230 | 0.731152 | − | 0.682215i | \(-0.238983\pi\) | ||||
0.731152 | + | 0.682215i | \(0.238983\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.0000 | 0.908918 | ||||||||
\(950\) | 8.00000 | + | 13.8564i | 0.259554 | + | 0.449561i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.0000 | − | 5.19615i | 0.486153 | − | 0.168408i | ||||
\(953\) | −48.0000 | −1.55487 | −0.777436 | − | 0.628962i | \(-0.783480\pi\) | ||||
−0.777436 | + | 0.628962i | \(0.783480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.0000 | + | 46.7654i | 0.873699 | + | 1.51329i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0000 | − | 20.7846i | 0.387702 | − | 0.671520i | ||||
\(959\) | −24.0000 | − | 20.7846i | −0.775000 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 16.0000 | + | 27.7128i | 0.515861 | + | 0.893497i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.500000 | − | 0.866025i | 0.0161039 | − | 0.0278928i | ||||
\(965\) | −39.0000 | − | 67.5500i | −1.25545 | − | 2.17451i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.5000 | − | 32.0429i | 0.594920 | − | 1.03043i | −0.398638 | − | 0.917108i | \(-0.630517\pi\) |
0.993558 | − | 0.113323i | \(-0.0361496\pi\) | |||||||
\(968\) | 5.50000 | + | 9.52628i | 0.176777 | + | 0.306186i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.0000 | − | 25.9808i | 0.481621 | − | 0.834192i | ||||
\(971\) | 1.50000 | − | 2.59808i | 0.0481373 | − | 0.0833762i | −0.840953 | − | 0.541108i | \(-0.818005\pi\) |
0.889090 | + | 0.457732i | \(0.151338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.00000 | − | 3.46410i | −0.128234 | − | 0.111054i | ||||
\(974\) | 6.50000 | + | 11.2583i | 0.208273 | + | 0.360740i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.0000 | −0.320092 | ||||||||
\(977\) | 12.0000 | 0.383914 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.00000 | + | 20.7846i | 0.0958315 | + | 0.663940i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.5000 | + | 23.3827i | −0.430802 | + | 0.746171i | ||||
\(983\) | 12.0000 | − | 20.7846i | 0.382741 | − | 0.662926i | −0.608712 | − | 0.793391i | \(-0.708314\pi\) |
0.991453 | + | 0.130465i | \(0.0416470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.5000 | + | 38.9711i | 0.716910 | + | 1.24172i | ||||
\(986\) | 9.00000 | − | 15.5885i | 0.286618 | − | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.00000 | − | 13.8564i | −0.254514 | − | 0.440831i | ||||
\(989\) | −24.0000 | + | 41.5692i | −0.763156 | + | 1.32182i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.5000 | − | 19.9186i | −0.365310 | − | 0.632735i | 0.623516 | − | 0.781810i | \(-0.285704\pi\) |
−0.988826 | + | 0.149076i | \(0.952370\pi\) | |||||||
\(992\) | 8.00000 | 0.254000 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.00000 | + | 15.5885i | −0.0951542 | + | 0.494436i | ||||
\(995\) | −16.5000 | + | 28.5788i | −0.523085 | + | 0.906010i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.0000 | + | 27.7128i | −0.506725 | + | 0.877674i | 0.493245 | + | 0.869891i | \(0.335811\pi\) |
−0.999970 | + | 0.00778294i | \(0.997523\pi\) | |||||||
\(998\) | −1.00000 | − | 1.73205i | −0.0316544 | − | 0.0548271i | ||||
\(999\) | 0 | 0 |
(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 | 1134.2.e.j.919.1 | 2 | ||
3.2 | odd | 2 | 1134.2.e.f.919.1 | 2 | |||
7.4 | even | 3 | 1134.2.h.g.109.1 | 2 | |||
9.2 | odd | 6 | 1134.2.h.k.541.1 | 2 | |||
9.4 | even | 3 | 378.2.g.a.163.1 | yes | 2 | ||
9.5 | odd | 6 | 378.2.g.f.163.1 | yes | 2 | ||
9.7 | even | 3 | 1134.2.h.g.541.1 | 2 | |||
21.11 | odd | 6 | 1134.2.h.k.109.1 | 2 | |||
63.4 | even | 3 | 378.2.g.a.109.1 | ✓ | 2 | ||
63.5 | even | 6 | 2646.2.a.m.1.1 | 1 | |||
63.11 | odd | 6 | 1134.2.e.f.865.1 | 2 | |||
63.23 | odd | 6 | 2646.2.a.b.1.1 | 1 | |||
63.25 | even | 3 | inner | 1134.2.e.j.865.1 | 2 | ||
63.32 | odd | 6 | 378.2.g.f.109.1 | yes | 2 | ||
63.40 | odd | 6 | 2646.2.a.r.1.1 | 1 | |||
63.58 | even | 3 | 2646.2.a.bc.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.a.109.1 | ✓ | 2 | 63.4 | even | 3 | ||
378.2.g.a.163.1 | yes | 2 | 9.4 | even | 3 | ||
378.2.g.f.109.1 | yes | 2 | 63.32 | odd | 6 | ||
378.2.g.f.163.1 | yes | 2 | 9.5 | odd | 6 | ||
1134.2.e.f.865.1 | 2 | 63.11 | odd | 6 | |||
1134.2.e.f.919.1 | 2 | 3.2 | odd | 2 | |||
1134.2.e.j.865.1 | 2 | 63.25 | even | 3 | inner | ||
1134.2.e.j.919.1 | 2 | 1.1 | even | 1 | trivial | ||
1134.2.h.g.109.1 | 2 | 7.4 | even | 3 | |||
1134.2.h.g.541.1 | 2 | 9.7 | even | 3 | |||
1134.2.h.k.109.1 | 2 | 21.11 | odd | 6 | |||
1134.2.h.k.541.1 | 2 | 9.2 | odd | 6 | |||
2646.2.a.b.1.1 | 1 | 63.23 | odd | 6 | |||
2646.2.a.m.1.1 | 1 | 63.5 | even | 6 | |||
2646.2.a.r.1.1 | 1 | 63.40 | odd | 6 | |||
2646.2.a.bc.1.1 | 1 | 63.58 | even | 3 |