Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [476,2,Mod(137,476)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(476, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("476.137");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 476 = 2^{2} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 476.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.80087913621\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 205.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 476.205 |
Dual form | 476.2.i.a.137.1 |
$q$-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 \(\left(\mathbb{Z}/476\mathbb{Z}\right)^\times\).
\(n\) | \(239\) | \(309\) | \(409\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | − | 3.46410i | 0.894427 | − | 1.54919i | 0.0599153 | − | 0.998203i | \(-0.480917\pi\) |
0.834512 | − | 0.550990i | \(-0.185750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00000 | −1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.500000 | + | 0.866025i | 0.121268 | + | 0.210042i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | + | 2.59808i | −0.109109 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | − | 9.52628i | −1.10000 | − | 1.90526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50000 | − | 2.59808i | 0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.0000 | + | 3.46410i | −1.69031 | + | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | − | 6.92820i | 0.657596 | − | 1.13899i | −0.323640 | − | 0.946180i | \(-0.604907\pi\) |
0.981236 | − | 0.192809i | \(-0.0617599\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.50000 | + | 4.33013i | 0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0000 | 1.52499 | 0.762493 | − | 0.646997i | \(-0.223975\pi\) | ||||
0.762493 | + | 0.646997i | \(0.223975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.00000 | − | 6.92820i | −0.596285 | − | 1.03280i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.00000 | − | 1.73205i | 0.145865 | − | 0.252646i | −0.783830 | − | 0.620975i | \(-0.786737\pi\) |
0.929695 | + | 0.368329i | \(0.120070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.500000 | − | 0.866025i | 0.0700140 | − | 0.121268i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.0000 | 1.61808 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | − | 1.73205i | −0.130189 | − | 0.225494i | 0.793560 | − | 0.608492i | \(-0.208225\pi\) |
−0.923749 | + | 0.382998i | \(0.874892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.00000 | + | 1.73205i | −0.629941 | + | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.0000 | + | 17.3205i | −1.24035 | + | 2.14834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 12.1244i | −0.855186 | − | 1.48123i | −0.876472 | − | 0.481452i | \(-0.840109\pi\) |
0.0212861 | − | 0.999773i | \(-0.493224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.00000 | 0.830747 | 0.415374 | − | 0.909651i | \(-0.363651\pi\) | ||||
0.415374 | + | 0.909651i | \(0.363651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | + | 6.92820i | 0.468165 | + | 0.810885i | 0.999338 | − | 0.0363782i | \(-0.0115821\pi\) |
−0.531174 | + | 0.847263i | \(0.678249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.50000 | + | 9.52628i | −0.635085 | + | 1.10000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.50000 | − | 7.79423i | 0.170941 | − | 0.888235i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.50000 | + | 12.9904i | −0.843816 | + | 1.46153i | 0.0428296 | + | 0.999082i | \(0.486363\pi\) |
−0.886646 | + | 0.462450i | \(0.846971\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.00000 | − | 6.92820i | −0.428845 | − | 0.742781i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.500000 | + | 0.866025i | −0.0529999 | + | 0.0917985i | −0.891308 | − | 0.453398i | \(-0.850212\pi\) |
0.838308 | + | 0.545197i | \(0.183545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0000 | + | 8.66025i | 1.04828 | + | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.0000 | + | 20.7846i | 1.23117 | + | 2.13246i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.0000 | 1.82762 | 0.913812 | − | 0.406138i | \(-0.133125\pi\) | ||||
0.913812 | + | 0.406138i | \(0.133125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.00000 | + | 6.92820i | 0.780720 | + | 0.676123i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.500000 | + | 0.866025i | −0.0483368 | + | 0.0837218i | −0.889182 | − | 0.457555i | \(-0.848725\pi\) |
0.840845 | + | 0.541276i | \(0.182059\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | + | 6.92820i | 0.383131 | + | 0.663602i | 0.991508 | − | 0.130046i | \(-0.0415126\pi\) |
−0.608377 | + | 0.793648i | \(0.708179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.00000 | −0.752577 | −0.376288 | − | 0.926503i | \(-0.622800\pi\) | ||||
−0.376288 | + | 0.926503i | \(0.622800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | − | 13.8564i | −0.746004 | − | 1.29212i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.00000 | + | 8.66025i | −0.462250 | + | 0.800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.500000 | − | 2.59808i | 0.0458349 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.00000 | + | 6.92820i | 0.360668 | + | 0.624695i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −24.0000 | −2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.00000 | − | 8.66025i | −0.440225 | − | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | − | 3.46410i | 0.174741 | − | 0.302660i | −0.765331 | − | 0.643637i | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.0000 | − | 5.19615i | 1.30066 | − | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.0000 | + | 17.3205i | −0.860663 | + | 1.49071i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.50000 | + | 6.06218i | 0.299025 | + | 0.517927i | 0.975913 | − | 0.218159i | \(-0.0700052\pi\) |
−0.676888 | + | 0.736086i | \(0.736672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.00000 | −0.0848189 | −0.0424094 | − | 0.999100i | \(-0.513503\pi\) | ||||
−0.0424094 | + | 0.999100i | \(0.513503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.50000 | − | 12.9904i | −0.627182 | − | 1.08631i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | − | 27.7128i | 1.32873 | − | 2.30142i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.50000 | − | 4.33013i | 0.453632 | − | 0.357143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.50000 | − | 9.52628i | 0.450578 | − | 0.780423i | −0.547844 | − | 0.836580i | \(-0.684551\pi\) |
0.998422 | + | 0.0561570i | \(0.0178847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.500000 | − | 0.866025i | −0.0399043 | − | 0.0691164i | 0.845383 | − | 0.534160i | \(-0.179372\pi\) |
−0.885288 | + | 0.465044i | \(0.846039\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.50000 | + | 2.59808i | −0.118958 | + | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0000 | + | 3.46410i | −0.788110 | + | 0.273009i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | + | 3.46410i | −0.156652 | + | 0.271329i | −0.933659 | − | 0.358162i | \(-0.883403\pi\) |
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00000 | − | 10.3923i | −0.467099 | − | 0.809040i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.0000 | −1.47026 | −0.735132 | − | 0.677924i | \(-0.762880\pi\) | ||||
−0.735132 | + | 0.677924i | \(0.762880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | + | 10.3923i | 0.458831 | + | 0.794719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.00000 | − | 1.73205i | 0.0760286 | − | 0.131685i | −0.825505 | − | 0.564396i | \(-0.809109\pi\) |
0.901533 | + | 0.432710i | \(0.142443\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.50000 | + | 28.5788i | −0.415761 | + | 2.16036i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00000 | + | 1.73205i | −0.0751646 | + | 0.130189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0000 | 1.33793 | 0.668965 | − | 0.743294i | \(-0.266738\pi\) | ||||
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.0000 | − | 27.7128i | −1.17634 | − | 2.03749i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.50000 | + | 2.59808i | −0.109691 | + | 0.189990i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.0000 | + | 8.66025i | 0.727393 | + | 0.629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | + | 8.66025i | 0.359908 | + | 0.623379i | 0.987945 | − | 0.154805i | \(-0.0494748\pi\) |
−0.628037 | + | 0.778183i | \(0.716141\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.0000 | 1.43223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | + | 6.06218i | 0.248108 | + | 0.429736i | 0.963001 | − | 0.269498i | \(-0.0868577\pi\) |
−0.714893 | + | 0.699234i | \(0.753524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.00000 | + | 12.1244i | −0.493742 | + | 0.855186i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0000 | − | 13.8564i | −1.12298 | − | 0.972529i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.0000 | + | 27.7128i | −1.11749 | + | 1.93555i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | − | 6.92820i | −0.278019 | − | 0.481543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.0000 | −1.24509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.50000 | − | 6.06218i | −0.239816 | − | 0.415374i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.0000 | − | 34.6410i | 1.36399 | − | 2.36250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.00000 | − | 6.92820i | 0.270295 | − | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.50000 | − | 4.33013i | −0.168168 | − | 0.291276i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.00000 | −0.401790 | −0.200895 | − | 0.979613i | \(-0.564385\pi\) | ||||
−0.200895 | + | 0.979613i | \(0.564385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.0000 | −1.46667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.5000 | − | 21.6506i | −0.829654 | − | 1.43700i | −0.898310 | − | 0.439363i | \(-0.855204\pi\) |
0.0686556 | − | 0.997640i | \(-0.478129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.50000 | + | 2.59808i | −0.493464 | + | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0000 | + | 24.2487i | −0.917170 | + | 1.58859i | −0.113478 | + | 0.993540i | \(0.536199\pi\) |
−0.803692 | + | 0.595045i | \(0.797134\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | − | 6.92820i | −0.260931 | − | 0.451946i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.0000 | 0.974355 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | + | 6.92820i | 0.257663 | + | 0.446285i | 0.965615 | − | 0.259975i | \(-0.0837143\pi\) |
−0.707953 | + | 0.706260i | \(0.750381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26.0000 | + | 10.3923i | 1.66108 | + | 0.663940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.0000 | − | 25.9808i | 0.954427 | − | 1.65312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00000 | − | 3.46410i | −0.125245 | − | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.50000 | + | 2.59808i | −0.0935674 | + | 0.162064i | −0.909010 | − | 0.416775i | \(-0.863160\pi\) |
0.815442 | + | 0.578838i | \(0.196494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.0000 | + | 6.92820i | −1.24274 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | − | 13.8564i | 0.495188 | − | 0.857690i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.00000 | − | 3.46410i | −0.123325 | − | 0.213606i | 0.797752 | − | 0.602986i | \(-0.206023\pi\) |
−0.921077 | + | 0.389380i | \(0.872689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.00000 | 0.0611990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.50000 | − | 12.9904i | 0.151307 | − | 0.786214i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5000 | − | 28.5788i | 0.994987 | − | 1.72337i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | − | 6.92820i | −0.240337 | − | 0.416275i | 0.720473 | − | 0.693482i | \(-0.243925\pi\) |
−0.960810 | + | 0.277207i | \(0.910591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.0000 | −1.13344 | −0.566722 | − | 0.823909i | \(-0.691789\pi\) | ||||
−0.566722 | + | 0.823909i | \(0.691789\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.50000 | − | 12.9904i | −0.445829 | − | 0.772198i | 0.552281 | − | 0.833658i | \(-0.313758\pi\) |
−0.998110 | + | 0.0614601i | \(0.980424\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0000 | − | 20.7846i | 0.710819 | − | 1.23117i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.0000 | + | 13.8564i | 0.944450 | + | 0.817918i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.00000 | − | 15.5885i | −0.527589 | − | 0.913812i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.0000 | −0.876309 | −0.438155 | − | 0.898900i | \(-0.644368\pi\) | ||||
−0.438155 | + | 0.898900i | \(0.644368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.50000 | − | 12.9904i | −0.435194 | − | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.0000 | + | 17.3205i | −0.578315 | + | 1.00167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.0000 | − | 17.3205i | −1.15278 | − | 0.998337i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.00000 | − | 5.19615i | 0.172345 | − | 0.298511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.0000 | − | 27.7128i | −0.916157 | − | 1.58683i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.50000 | + | 11.2583i | 0.368581 | + | 0.638401i | 0.989344 | − | 0.145597i | \(-0.0465103\pi\) |
−0.620763 | + | 0.783998i | \(0.713177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0000 | + | 25.9808i | −0.847850 | + | 1.46852i | 0.0352727 | + | 0.999378i | \(0.488770\pi\) |
−0.883123 | + | 0.469142i | \(0.844563\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00000 | + | 20.7846i | −0.225374 | + | 1.17108i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.00000 | − | 1.73205i | 0.0561656 | − | 0.0972817i | −0.836576 | − | 0.547852i | \(-0.815446\pi\) |
0.892741 | + | 0.450570i | \(0.148779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | + | 20.7846i | 0.671871 | + | 1.16371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.00000 | 0.0558146 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.5000 | + | 47.6314i | 1.52543 | + | 2.64211i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.00000 | − | 6.92820i | 0.221201 | − | 0.383131i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.00000 | + | 1.73205i | −0.275659 | + | 0.0954911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.00000 | − | 5.19615i | 0.164895 | − | 0.285606i | −0.771723 | − | 0.635959i | \(-0.780605\pi\) |
0.936618 | + | 0.350352i | \(0.113938\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.00000 | − | 13.8564i | −0.438397 | − | 0.759326i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −56.0000 | −3.05961 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.00000 | + | 6.92820i | 0.217250 | + | 0.376288i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | + | 13.8564i | −0.430706 | + | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | + | 10.3923i | 0.322097 | + | 0.557888i | 0.980921 | − | 0.194409i | \(-0.0622790\pi\) |
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.0000 | 1.33440 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5000 | + | 18.1865i | 0.558859 | + | 0.967972i | 0.997592 | + | 0.0693543i | \(0.0220939\pi\) |
−0.438733 | + | 0.898617i | \(0.644573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.0000 | − | 24.2487i | 0.743043 | − | 1.28699i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.50000 | + | 0.866025i | −0.132314 | + | 0.0458349i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.0000 | + | 19.0526i | −0.580558 | + | 1.00556i | 0.414855 | + | 0.909887i | \(0.363832\pi\) |
−0.995413 | + | 0.0956683i | \(0.969501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.0000 | 1.67496 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.50000 | + | 7.79423i | 0.234898 | + | 0.406855i | 0.959243 | − | 0.282582i | \(-0.0911910\pi\) |
−0.724345 | + | 0.689438i | \(0.757858\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.00000 | + | 13.8564i | −0.416463 | + | 0.721336i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.50000 | + | 7.79423i | −0.0778761 | + | 0.404656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5000 | + | 26.8468i | −0.802560 | + | 1.39007i | 0.115367 | + | 0.993323i | \(0.463196\pi\) |
−0.917926 | + | 0.396751i | \(0.870138\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0000 | + | 20.7846i | 0.619677 | + | 1.07331i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.0000 | −2.06010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000 | 0.0513665 | 0.0256833 | − | 0.999670i | \(-0.491824\pi\) | ||||
0.0256833 | + | 0.999670i | \(0.491824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | − | 6.92820i | −0.204926 | − | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.00000 | + | 1.73205i | −0.0510976 | + | 0.0885037i | −0.890443 | − | 0.455095i | \(-0.849605\pi\) |
0.839345 | + | 0.543599i | \(0.182939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | − | 20.7846i | −1.22315 | − | 1.05928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0000 | − | 17.3205i | 0.508329 | − | 0.880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.5000 | + | 23.3827i | 0.684477 | + | 1.18555i | 0.973601 | + | 0.228257i | \(0.0733028\pi\) |
−0.289124 | + | 0.957292i | \(0.593364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.0000 | + | 51.9615i | 1.50946 | + | 2.61447i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | + | 22.5167i | −0.652451 | + | 1.13008i | 0.330075 | + | 0.943955i | \(0.392926\pi\) |
−0.982526 | + | 0.186124i | \(0.940407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.0000 | − | 10.3923i | −0.600751 | − | 0.520266i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | − | 15.5885i | 0.449439 | − | 0.778450i | −0.548911 | − | 0.835881i | \(-0.684957\pi\) |
0.998350 | + | 0.0574304i | \(0.0182907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.00000 | −0.198762 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.50000 | − | 9.52628i | −0.271957 | − | 0.471044i | 0.697406 | − | 0.716677i | \(-0.254338\pi\) |
−0.969363 | + | 0.245633i | \(0.921004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.50000 | − | 6.06218i | 0.172642 | − | 0.299025i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.00000 | + | 5.19615i | −0.0492068 | + | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0000 | − | 41.5692i | 1.17811 | − | 2.04055i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.500000 | + | 0.866025i | 0.0244851 | + | 0.0424094i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.0000 | 1.80757 | 0.903784 | − | 0.427989i | \(-0.140778\pi\) | ||||
0.903784 | + | 0.427989i | \(0.140778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.00000 | − | 3.46410i | −0.0972433 | − | 0.168430i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.50000 | − | 9.52628i | 0.266789 | − | 0.462092i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.0000 | + | 6.92820i | −0.967868 | + | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.50000 | + | 12.9904i | −0.362103 | + | 0.627182i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.50000 | + | 12.9904i | 0.361262 | + | 0.625725i | 0.988169 | − | 0.153370i | \(-0.0490126\pi\) |
−0.626907 | + | 0.779094i | \(0.715679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −32.0000 | −1.53428 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0000 | + | 20.7846i | 0.574038 | + | 0.994263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.500000 | − | 0.866025i | 0.0238637 | − | 0.0413331i | −0.853847 | − | 0.520524i | \(-0.825737\pi\) |
0.877711 | + | 0.479191i | \(0.159070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | + | 5.19615i | 0.619048 | + | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.0000 | + | 22.5167i | −0.617649 | + | 1.06980i | 0.372265 | + | 0.928126i | \(0.378581\pi\) |
−0.989914 | + | 0.141672i | \(0.954752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 3.46410i | 0.0948091 | + | 0.164214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.0000 | −0.520282 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | − | 20.7846i | −0.565058 | − | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.00000 | + | 8.66025i | −0.234920 | + | 0.406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 50.0000 | − | 17.3205i | 2.34404 | − | 0.811998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000 | − | 22.5167i | 0.608114 | − | 1.05328i | −0.383437 | − | 0.923567i | \(-0.625260\pi\) |
0.991551 | − | 0.129718i | \(-0.0414071\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.50000 | − | 4.33013i | −0.116690 | − | 0.202113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | 0.698620 | 0.349310 | − | 0.937007i | \(-0.386416\pi\) | ||||
0.349310 | + | 0.937007i | \(0.386416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.0000 | − | 24.2487i | 0.647843 | − | 1.12210i | −0.335794 | − | 0.941935i | \(-0.609005\pi\) |
0.983637 | − | 0.180161i | \(-0.0576619\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.00000 | + | 36.3731i | −0.323230 | + | 1.67955i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.500000 | + | 0.866025i | −0.0230388 | + | 0.0399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.0000 | + | 25.9808i | 0.689701 | + | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 66.0000 | 3.02829 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.0000 | − | 27.7128i | −0.731059 | − | 1.26623i | −0.956431 | − | 0.291958i | \(-0.905693\pi\) |
0.225372 | − | 0.974273i | \(-0.427640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | + | 34.6410i | −0.911922 | + | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.00000 | + | 6.92820i | 0.364013 | + | 0.315244i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.0000 | − | 62.3538i | 1.63468 | − | 2.83134i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.50000 | + | 4.33013i | 0.113286 | + | 0.196217i | 0.917093 | − | 0.398673i | \(-0.130529\pi\) |
−0.803807 | + | 0.594890i | \(0.797196\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | −0.812329 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | + | 6.92820i | 0.180151 | + | 0.312031i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | − | 20.7846i | 0.539360 | − | 0.934199i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.0000 | − | 12.1244i | −0.627986 | − | 0.543852i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.5000 | + | 33.7750i | −0.872940 | + | 1.51198i | −0.0139987 | + | 0.999902i | \(0.504456\pi\) |
−0.858941 | + | 0.512074i | \(0.828877\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.50000 | + | 16.4545i | 0.424429 | + | 0.735132i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0000 | 0.936344 | 0.468172 | − | 0.883637i | \(-0.344913\pi\) | ||||
0.468172 | + | 0.883637i | \(0.344913\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | 1.06799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.0000 | + | 32.9090i | −0.842160 | + | 1.45866i | 0.0459045 | + | 0.998946i | \(0.485383\pi\) |
−0.888065 | + | 0.459718i | \(0.847950\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | − | 20.7846i | 0.176950 | − | 0.919457i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.0000 | − | 25.9808i | 0.662266 | − | 1.14708i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | + | 13.8564i | 0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.00000 | −0.0877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000 | + | 20.7846i | 0.525730 | + | 0.910590i | 0.999551 | + | 0.0299693i | \(0.00954094\pi\) |
−0.473821 | + | 0.880621i | \(0.657126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00000 | + | 5.19615i | −0.131181 | + | 0.227212i | −0.924132 | − | 0.382073i | \(-0.875210\pi\) |
0.792951 | + | 0.609285i | \(0.208544\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27.5000 | − | 9.52628i | 1.20020 | − | 0.415761i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.0000 | 1.73259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.00000 | + | 3.46410i | 0.0864675 | + | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.5000 | + | 12.9904i | −0.710705 | + | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.00000 | + | 12.1244i | −0.300954 | + | 0.521267i | −0.976352 | − | 0.216186i | \(-0.930638\pi\) |
0.675399 | + | 0.737453i | \(0.263972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.00000 | − | 15.5885i | −0.386227 | − | 0.668965i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 32.0000 | 1.37073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.0000 | −0.555840 | −0.277920 | − | 0.960604i | \(-0.589645\pi\) | ||||
−0.277920 | + | 0.960604i | \(0.589645\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.00000 | − | 13.8564i | −0.341432 | − | 0.591377i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.0000 | + | 41.5692i | −1.02243 | + | 1.77091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.5000 | − | 12.9904i | 1.59466 | − | 0.552407i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.0000 | + | 27.7128i | −0.679162 | + | 1.17634i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.5000 | − | 19.9186i | −0.487271 | − | 0.843978i | 0.512622 | − | 0.858614i | \(-0.328674\pi\) |
−0.999893 | + | 0.0146368i | \(0.995341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −50.0000 | −2.11477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0000 | − | 25.9808i | −0.632175 | − | 1.09496i | −0.987106 | − | 0.160066i | \(-0.948829\pi\) |
0.354932 | − | 0.934892i | \(-0.384504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0000 | + | 27.7128i | −0.673125 | + | 1.16589i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.500000 | + | 2.59808i | −0.0209980 | + | 0.109109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.5000 | + | 28.5788i | −0.691716 | + | 1.19809i | 0.279559 | + | 0.960128i | \(0.409812\pi\) |
−0.971275 | + | 0.237959i | \(0.923522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.0000 | − | 31.1769i | −0.753277 | − | 1.30471i | −0.946227 | − | 0.323505i | \(-0.895139\pi\) |
0.192950 | − | 0.981209i | \(-0.438194\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −44.0000 | −1.83493 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.50000 | − | 11.2583i | −0.270599 | − | 0.468690i | 0.698417 | − | 0.715691i | \(-0.253888\pi\) |
−0.969015 | + | 0.247001i | \(0.920555\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.00000 | − | 8.66025i | 0.207793 | − | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | − | 20.7846i | −0.995688 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.50000 | − | 7.79423i | 0.186371 | − | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20.0000 | + | 34.6410i | 0.826898 | + | 1.43223i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.00000 | −0.0825488 | −0.0412744 | − | 0.999148i | \(-0.513142\pi\) | ||||
−0.0412744 | + | 0.999148i | \(0.513142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00000 | − | 15.5885i | −0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5000 | + | 18.1865i | −0.431183 | + | 0.746831i | −0.996976 | − | 0.0777165i | \(-0.975237\pi\) |
0.565792 | + | 0.824548i | \(0.308570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.00000 | − | 6.92820i | −0.327968 | − | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.50000 | − | 6.06218i | 0.143245 | − | 0.248108i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.0000 | + | 29.4449i | 0.694601 | + | 1.20308i | 0.970315 | + | 0.241845i | \(0.0777525\pi\) |
−0.275714 | + | 0.961240i | \(0.588914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.0000 | −1.14025 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.00000 | − | 6.92820i | −0.162623 | − | 0.281672i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5000 | − | 19.9186i | 0.466771 | − | 0.808470i | −0.532509 | − | 0.846424i | \(-0.678751\pi\) |
0.999279 | + | 0.0379540i | \(0.0120840\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.00000 | + | 20.7846i | −0.162088 | + | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.00000 | + | 8.66025i | −0.202278 | + | 0.350356i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.50000 | − | 14.7224i | −0.343312 | − | 0.594633i | 0.641734 | − | 0.766927i | \(-0.278215\pi\) |
−0.985046 | + | 0.172294i | \(0.944882\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.0000 | 1.29036 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.0000 | −1.44931 | −0.724653 | − | 0.689114i | \(-0.758000\pi\) | ||||
−0.724653 | + | 0.689114i | \(0.758000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.50000 | + | 14.7224i | 0.341644 | + | 0.591744i | 0.984738 | − | 0.174042i | \(-0.0556830\pi\) |
−0.643094 | + | 0.765787i | \(0.722350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.0000 | + | 17.3205i | −0.401286 | + | 0.695048i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.50000 | − | 0.866025i | 0.100160 | − | 0.0346966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | + | 35.5070i | −0.820000 | + | 1.42028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.00000 | + | 15.5885i | 0.359425 | + | 0.622543i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.00000 | 0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.0000 | −1.19428 | −0.597141 | − | 0.802137i | \(-0.703697\pi\) | ||||
−0.597141 | + | 0.802137i | \(0.703697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.00000 | + | 3.46410i | 0.0794929 | + | 0.137686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0000 | − | 27.7128i | 0.634941 | − | 1.09975i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.00000 | − | 34.6410i | −0.198107 | − | 1.37253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.00000 | − | 12.1244i | 0.276916 | − | 0.479632i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0000 | − | 19.0526i | −0.434474 | − | 0.752531i | 0.562779 | − | 0.826608i | \(-0.309732\pi\) |
−0.997253 | + | 0.0740768i | \(0.976399\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.00000 | −0.0394362 | −0.0197181 | − | 0.999806i | \(-0.506277\pi\) | ||||
−0.0197181 | + | 0.999806i | \(0.506277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.0000 | −1.57500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.0000 | − | 24.2487i | −0.550397 | − | 0.953315i | −0.998246 | − | 0.0592060i | \(-0.981143\pi\) |
0.447849 | − | 0.894109i | \(-0.352190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.00000 | − | 5.19615i | 0.117760 | − | 0.203967i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.00000 | − | 8.66025i | 0.195665 | − | 0.338902i | −0.751453 | − | 0.659786i | \(-0.770647\pi\) |
0.947118 | + | 0.320884i | \(0.103980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | − | 13.8564i | −0.312586 | − | 0.541415i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.0000 | 0.624219 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.00000 | − | 15.5885i | −0.350059 | − | 0.606321i | 0.636200 | − | 0.771524i | \(-0.280505\pi\) |
−0.986260 | + | 0.165203i | \(0.947172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.50000 | + | 4.33013i | −0.0970920 | + | 0.168168i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | − | 62.3538i | 0.465340 | − | 2.41798i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | − | 27.7128i | 0.619522 | − | 1.07304i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.00000 | + | 5.19615i | 0.115987 | + | 0.200895i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.0000 | 1.07932 | 0.539660 | − | 0.841883i | \(-0.318553\pi\) | ||||
0.539660 | + | 0.841883i | \(0.318553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27.5000 | + | 47.6314i | 1.05848 | + | 1.83333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.00000 | − | 6.92820i | 0.153732 | − | 0.266272i | −0.778864 | − | 0.627192i | \(-0.784204\pi\) |
0.932597 | + | 0.360920i | \(0.117537\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.0000 | − | 31.1769i | −1.38155 | − | 1.19646i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.5000 | + | 21.6506i | −0.479001 | + | 0.829654i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5000 | + | 18.1865i | 0.401771 | + | 0.695888i | 0.993940 | − | 0.109926i | \(-0.0350613\pi\) |
−0.592168 | + | 0.805814i | \(0.701728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0000 | 1.06983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.50000 | + | 12.9904i | 0.285727 | + | 0.494894i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.0000 | − | 10.3923i | −0.455842 | − | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.00000 | + | 3.46410i | −0.0758643 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | − | 6.92820i | −0.151511 | − | 0.262424i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.0000 | 1.05906 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.0000 | 1.17085 | 0.585427 | − | 0.810725i | \(-0.300927\pi\) | ||||
0.585427 | + | 0.810725i | \(0.300927\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | + | 41.5692i | 0.905177 | + | 1.56781i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.00000 | + | 6.92820i | −0.150649 | + | 0.260931i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.00000 | − | 15.5885i | 0.112827 | − | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.0000 | − | 43.3013i | 0.938895 | − | 1.62621i | 0.171358 | − | 0.985209i | \(-0.445185\pi\) |
0.767537 | − | 0.641004i | \(-0.221482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.0000 | + | 25.9808i | 0.562544 | + | 0.974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −60.0000 | −2.24387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.00000 | − | 1.73205i | −0.0373457 | − | 0.0646846i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.5000 | − | 30.3109i | 0.652640 | − | 1.13041i | −0.329840 | − | 0.944037i | \(-0.606995\pi\) |
0.982480 | − | 0.186369i | \(-0.0596719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0000 | − | 3.46410i | 0.372419 | − | 0.129010i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.00000 | − | 6.92820i | 0.148762 | − | 0.257663i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −44.0000 | − | 76.2102i | −1.63412 | − | 2.83038i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0000 | 0.667583 | 0.333792 | − | 0.942647i | \(-0.391672\pi\) | ||||
0.333792 | + | 0.942647i | \(0.391672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.00000 | + | 8.66025i | 0.184932 | + | 0.320311i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.50000 | + | 2.59808i | −0.0554038 | + | 0.0959621i | −0.892397 | − | 0.451251i | \(-0.850978\pi\) |
0.836993 | + | 0.547213i | \(0.184311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.00000 | − | 27.7128i | −0.147542 | − | 1.02220i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.0000 | − | 36.3731i | 0.773545 | − | 1.33982i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0000 | − | 25.9808i | −0.551784 | − | 0.955718i | −0.998146 | − | 0.0608653i | \(-0.980614\pi\) |
0.446362 | − | 0.894852i | \(-0.352719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −30.0000 | −1.10208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.00000 | 0.0366864 | 0.0183432 | − | 0.999832i | \(-0.494161\pi\) | ||||
0.0183432 | + | 0.999832i | \(0.494161\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.0000 | − | 38.1051i | −0.806018 | − | 1.39606i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | − | 20.7846i | 0.439057 | − | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.50000 | − | 0.866025i | 0.0913480 | − | 0.0316439i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.50000 | + | 2.59808i | −0.0547358 | + | 0.0948051i | −0.892095 | − | 0.451848i | \(-0.850765\pi\) |
0.837359 | + | 0.546653i | \(0.184098\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.0000 | −1.45575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | 0.327111 | 0.163555 | − | 0.986534i | \(-0.447704\pi\) | ||||
0.163555 | + | 0.986534i | \(0.447704\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.00000 | − | 10.3923i | −0.217786 | − | 0.377217i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5000 | + | 38.9711i | −0.815624 | + | 1.41270i | 0.0932544 | + | 0.995642i | \(0.470273\pi\) |
−0.908879 | + | 0.417061i | \(0.863060\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.00000 | − | 20.7846i | 0.144810 | − | 0.752453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.00000 | − | 6.92820i | 0.144620 | − | 0.250490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.00000 | + | 8.66025i | 0.180540 | + | 0.312704i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00000 | 0.0360609 | 0.0180305 | − | 0.999837i | \(-0.494260\pi\) | ||||
0.0180305 | + | 0.999837i | \(0.494260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | 0.108042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.50000 | − | 7.79423i | −0.161854 | − | 0.280339i | 0.773680 | − | 0.633577i | \(-0.218414\pi\) |
−0.935534 | + | 0.353238i | \(0.885081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.0000 | + | 13.8564i | 0.573997 | + | 0.497096i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | − | 41.5692i | 0.859889 | − | 1.48937i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5000 | + | 18.1865i | 0.375720 | + | 0.650765i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40.0000 | −1.42948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | − | 3.46410i | −0.0712923 | − | 0.123482i | 0.828176 | − | 0.560469i | \(-0.189379\pi\) |
−0.899468 | + | 0.436987i | \(0.856046\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.00000 | + | 3.46410i | −0.0712019 | + |