Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(26,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.bk (of order \(6\), 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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.26 |
Dual form | 1575.2.bk.c.1151.1 |
$q$-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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 2.59808i | 0.188982 | + | 0.981981i | ||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.22474 | + | 0.707107i | −0.369274 | + | 0.213201i | −0.673141 | − | 0.739514i | \(-0.735055\pi\) |
0.303867 | + | 0.952714i | \(0.401722\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.19615i | − | 1.44115i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||
0.693375 | − | 0.720577i | \(-0.256123\pi\) | |||||||
\(14\) | 1.22474 | − | 3.53553i | 0.327327 | − | 0.944911i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 2.44949 | + | 4.24264i | 0.594089 | + | 1.02899i | 0.993675 | + | 0.112296i | \(0.0358205\pi\) |
−0.399586 | + | 0.916696i | \(0.630846\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | + | 0.866025i | 0.344124 | + | 0.198680i | 0.662094 | − | 0.749421i | \(-0.269668\pi\) |
−0.317970 | + | 0.948101i | \(0.603001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −4.89898 | − | 2.82843i | −1.02151 | − | 0.589768i | −0.106967 | − | 0.994263i | \(-0.534114\pi\) |
−0.914540 | + | 0.404495i | \(0.867447\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.67423 | + | 6.36396i | −0.720577 | + | 1.24808i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843i | 0.525226i | 0.964901 | + | 0.262613i | \(0.0845842\pi\) | ||||
−0.964901 | + | 0.262613i | \(0.915416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | − | 0.866025i | 0.269408 | − | 0.155543i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.92820i | − | 1.18818i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.500000 | + | 0.866025i | −0.0821995 | + | 0.142374i | −0.904194 | − | 0.427121i | \(-0.859528\pi\) |
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | −1.22474 | − | 2.12132i | −0.198680 | − | 0.344124i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.34847 | −1.14764 | −0.573819 | − | 0.818982i | \(-0.694539\pi\) | ||||
−0.573819 | + | 0.818982i | \(0.694539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | + | 6.92820i | 0.589768 | + | 1.02151i | ||||
\(47\) | −6.12372 | + | 10.6066i | −0.893237 | + | 1.54713i | −0.0572655 | + | 0.998359i | \(0.518238\pi\) |
−0.835971 | + | 0.548773i | \(0.815095\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.44949 | + | 1.41421i | −0.336463 | + | 0.194257i | −0.658707 | − | 0.752400i | \(-0.728896\pi\) |
0.322244 | + | 0.946657i | \(0.395563\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.34847 | + | 1.41421i | −0.981981 | + | 0.188982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | − | 3.46410i | 0.262613 | − | 0.454859i | ||||
\(59\) | −2.44949 | − | 4.24264i | −0.318896 | − | 0.552345i | 0.661362 | − | 0.750067i | \(-0.269979\pi\) |
−0.980258 | + | 0.197722i | \(0.936646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 1.73205i | −0.384111 | − | 0.221766i | 0.295495 | − | 0.955344i | \(-0.404516\pi\) |
−0.679605 | + | 0.733578i | \(0.737849\pi\) | |||||||
\(62\) | −2.44949 | −0.311086 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.50000 | + | 9.52628i | 0.671932 | + | 1.16382i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) |
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.07107i | 0.839181i | 0.907713 | + | 0.419591i | \(0.137826\pi\) | ||||
−0.907713 | + | 0.419591i | \(0.862174\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.50000 | + | 0.866025i | −0.175562 | + | 0.101361i | −0.585206 | − | 0.810885i | \(-0.698986\pi\) |
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 1.22474 | − | 0.707107i | 0.142374 | − | 0.0821995i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.44949 | − | 2.82843i | −0.279145 | − | 0.322329i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.50000 | + | 4.33013i | −0.281272 | + | 0.487177i | −0.971698 | − | 0.236225i | \(-0.924090\pi\) |
0.690426 | + | 0.723403i | \(0.257423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.00000 | + | 5.19615i | 0.993884 | + | 0.573819i | ||||
\(83\) | −7.34847 | −0.806599 | −0.403300 | − | 0.915068i | \(-0.632137\pi\) | ||||
−0.403300 | + | 0.915068i | \(0.632137\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.22474 | − | 0.707107i | −0.132068 | − | 0.0762493i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | − | 3.46410i | −0.213201 | − | 0.369274i | ||||
\(89\) | 2.44949 | − | 4.24264i | 0.259645 | − | 0.449719i | −0.706502 | − | 0.707712i | \(-0.749728\pi\) |
0.966147 | + | 0.257993i | \(0.0830610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5000 | − | 2.59808i | 1.41518 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 15.0000 | − | 8.66025i | 1.54713 | − | 0.893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.3923i | − | 1.05518i | −0.849500 | − | 0.527589i | \(-0.823096\pi\) | ||
0.849500 | − | 0.527589i | \(-0.176904\pi\) | |||||||
\(98\) | 9.79796 | + | 1.41421i | 0.989743 | + | 0.142857i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.57321 | + | 14.8492i | 0.853067 | + | 1.47755i | 0.878427 | + | 0.477876i | \(0.158593\pi\) |
−0.0253604 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.50000 | + | 4.33013i | 0.738997 | + | 0.426660i | 0.821705 | − | 0.569914i | \(-0.193023\pi\) |
−0.0827075 | + | 0.996574i | \(0.526357\pi\) | |||||||
\(104\) | 14.6969 | 1.44115 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | 0.388514 | ||||||||
\(107\) | 2.44949 | + | 1.41421i | 0.236801 | + | 0.136717i | 0.613706 | − | 0.789535i | \(-0.289678\pi\) |
−0.376905 | + | 0.926252i | \(0.623012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | + | 0.866025i | 0.0478913 | + | 0.0829502i | 0.888977 | − | 0.457951i | \(-0.151417\pi\) |
−0.841086 | + | 0.540901i | \(0.818083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.0000 | + | 3.46410i | 0.944911 | + | 0.327327i | ||||
\(113\) | 1.41421i | 0.133038i | 0.997785 | + | 0.0665190i | \(0.0211893\pi\) | ||||
−0.997785 | + | 0.0665190i | \(0.978811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.92820i | 0.637793i | ||||||||
\(119\) | −9.79796 | + | 8.48528i | −0.898177 | + | 0.777844i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.50000 | + | 7.79423i | −0.409091 | + | 0.708566i | ||||
\(122\) | 2.44949 | + | 4.24264i | 0.221766 | + | 0.384111i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.0000 | −0.976092 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.22474 | + | 2.12132i | −0.107006 | + | 0.185341i | −0.914556 | − | 0.404459i | \(-0.867460\pi\) |
0.807550 | + | 0.589799i | \(0.200793\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50000 | + | 4.33013i | −0.130066 | + | 0.375470i | ||||
\(134\) | − | 15.5563i | − | 1.34386i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0000 | + | 6.92820i | −1.02899 | + | 0.594089i | ||||
\(137\) | −9.79796 | + | 5.65685i | −0.837096 | + | 0.483298i | −0.856276 | − | 0.516518i | \(-0.827228\pi\) |
0.0191800 | + | 0.999816i | \(0.493894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.19615i | 0.440732i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) | ||||
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.00000 | − | 8.66025i | 0.419591 | − | 0.726752i | ||||
\(143\) | 3.67423 | + | 6.36396i | 0.307255 | + | 0.532181i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.44949 | 0.202721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.89898 | + | 2.82843i | 0.401340 | + | 0.231714i | 0.687062 | − | 0.726599i | \(-0.258900\pi\) |
−0.285722 | + | 0.958313i | \(0.592233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0000 | + | 19.0526i | 0.895167 | + | 1.55048i | 0.833597 | + | 0.552372i | \(0.186277\pi\) |
0.0615699 | + | 0.998103i | \(0.480389\pi\) | |||||||
\(152\) | −2.44949 | + | 4.24264i | −0.198680 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | + | 5.19615i | 0.0805823 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.0000 | + | 8.66025i | −1.19713 | + | 0.691164i | −0.959914 | − | 0.280293i | \(-0.909568\pi\) |
−0.237216 | + | 0.971457i | \(0.576235\pi\) | |||||||
\(158\) | 6.12372 | − | 3.53553i | 0.487177 | − | 0.281272i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.89898 | − | 14.1421i | 0.386094 | − | 1.11456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.00000 | + | 8.66025i | −0.391630 | + | 0.678323i | −0.992665 | − | 0.120900i | \(-0.961422\pi\) |
0.601035 | + | 0.799223i | \(0.294755\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.00000 | + | 5.19615i | 0.698535 | + | 0.403300i | ||||
\(167\) | 7.34847 | 0.568642 | 0.284321 | − | 0.958729i | \(-0.408232\pi\) | ||||
0.284321 | + | 0.958729i | \(0.408232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.0000 | −1.07692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.89898 | − | 8.48528i | 0.372463 | − | 0.645124i | −0.617481 | − | 0.786586i | \(-0.711847\pi\) |
0.989944 | + | 0.141462i | \(0.0451802\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.65685i | 0.426401i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.00000 | + | 3.46410i | −0.449719 | + | 0.259645i | ||||
\(179\) | −8.57321 | + | 4.94975i | −0.640792 | + | 0.369961i | −0.784920 | − | 0.619598i | \(-0.787296\pi\) |
0.144127 | + | 0.989559i | \(0.453962\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.5885i | − | 1.15868i | −0.815086 | − | 0.579340i | \(-0.803310\pi\) | ||
0.815086 | − | 0.579340i | \(-0.196690\pi\) | |||||||
\(182\) | −18.3712 | − | 6.36396i | −1.36176 | − | 0.471728i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | − | 13.8564i | 0.589768 | − | 1.02151i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | − | 3.46410i | −0.438763 | − | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.22474 | + | 0.707107i | 0.0886194 | + | 0.0511645i | 0.543655 | − | 0.839309i | \(-0.317040\pi\) |
−0.455035 | + | 0.890473i | \(0.650373\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | −7.34847 | + | 12.7279i | −0.527589 | + | 0.913812i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.7990i | − | 1.41062i | −0.708899 | − | 0.705310i | \(-0.750808\pi\) | ||
0.708899 | − | 0.705310i | \(-0.249192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0000 | + | 6.92820i | −0.850657 | + | 0.491127i | −0.860873 | − | 0.508821i | \(-0.830082\pi\) |
0.0102152 | + | 0.999948i | \(0.496748\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 24.2487i | − | 1.70613i | ||||||
\(203\) | −7.34847 | + | 1.41421i | −0.515761 | + | 0.0992583i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.12372 | − | 10.6066i | −0.426660 | − | 0.738997i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.0000 | − | 10.3923i | −1.24808 | − | 0.720577i | ||||
\(209\) | −2.44949 | −0.169435 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0000 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.00000 | − | 3.46410i | −0.136717 | − | 0.236801i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.00000 | + | 3.46410i | 0.203653 | + | 0.235159i | ||||
\(218\) | − | 1.41421i | − | 0.0957826i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.0454 | − | 12.7279i | 1.48293 | − | 0.856173i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7846i | 1.39184i | 0.718119 | + | 0.695920i | \(0.245003\pi\) | ||||
−0.718119 | + | 0.695920i | \(0.754997\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.00000 | − | 1.73205i | 0.0665190 | − | 0.115214i | ||||
\(227\) | 13.4722 | + | 23.3345i | 0.894181 | + | 1.54877i | 0.834815 | + | 0.550530i | \(0.185575\pi\) |
0.0593658 | + | 0.998236i | \(0.481092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5000 | + | 11.2583i | 1.28860 | + | 0.743971i | 0.978404 | − | 0.206702i | \(-0.0662732\pi\) |
0.310192 | + | 0.950674i | \(0.399607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.00000 | −0.525226 | ||||||||
\(233\) | −8.57321 | − | 4.94975i | −0.561650 | − | 0.324269i | 0.192158 | − | 0.981364i | \(-0.438452\pi\) |
−0.753807 | + | 0.657095i | \(0.771785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.0000 | − | 3.46410i | 1.16677 | − | 0.224544i | ||||
\(239\) | − | 26.8701i | − | 1.73808i | −0.494742 | − | 0.869040i | \(-0.664738\pi\) | ||
0.494742 | − | 0.869040i | \(-0.335262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.0000 | + | 6.92820i | −0.772988 | + | 0.446285i | −0.833939 | − | 0.551856i | \(-0.813920\pi\) |
0.0609515 | + | 0.998141i | \(0.480586\pi\) | |||||||
\(242\) | 11.0227 | − | 6.36396i | 0.708566 | − | 0.409091i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.50000 | − | 7.79423i | 0.286328 | − | 0.495935i | ||||
\(248\) | 2.44949 | + | 4.24264i | 0.155543 | + | 0.269408i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 13.4722 | + | 7.77817i | 0.845321 | + | 0.488046i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.22474 | − | 2.12132i | 0.0763975 | − | 0.132324i | −0.825296 | − | 0.564701i | \(-0.808992\pi\) |
0.901693 | + | 0.432377i | \(0.142325\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | − | 0.866025i | −0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.00000 | − | 1.73205i | 0.185341 | − | 0.107006i | ||||
\(263\) | 12.2474 | − | 7.07107i | 0.755210 | − | 0.436021i | −0.0723633 | − | 0.997378i | \(-0.523054\pi\) |
0.827573 | + | 0.561358i | \(0.189721\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.89898 | − | 4.24264i | 0.300376 | − | 0.260133i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.57321 | + | 14.8492i | 0.522718 | + | 0.905374i | 0.999651 | + | 0.0264343i | \(0.00841529\pi\) |
−0.476932 | + | 0.878940i | \(0.658251\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | − | 6.92820i | −0.728948 | − | 0.420858i | 0.0890891 | − | 0.996024i | \(-0.471604\pi\) |
−0.818037 | + | 0.575165i | \(0.804938\pi\) | |||||||
\(272\) | 19.5959 | 1.18818 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.0000 | 0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.5000 | + | 19.9186i | 0.690968 | + | 1.19679i | 0.971521 | + | 0.236953i | \(0.0761488\pi\) |
−0.280553 | + | 0.959839i | \(0.590518\pi\) | |||||||
\(278\) | 3.67423 | − | 6.36396i | 0.220366 | − | 0.381685i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.6274i | − | 1.34984i | −0.737892 | − | 0.674919i | \(-0.764178\pi\) | ||
0.737892 | − | 0.674919i | \(-0.235822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.50000 | + | 0.866025i | −0.0891657 | + | 0.0514799i | −0.543920 | − | 0.839137i | \(-0.683060\pi\) |
0.454754 | + | 0.890617i | \(0.349727\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 10.3923i | − | 0.614510i | ||||||
\(287\) | −3.67423 | − | 19.0919i | −0.216883 | − | 1.12696i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50000 | + | 6.06218i | −0.205882 | + | 0.356599i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6969 | −0.858604 | −0.429302 | − | 0.903161i | \(-0.641240\pi\) | ||||
−0.429302 | + | 0.903161i | \(0.641240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.44949 | − | 1.41421i | −0.142374 | − | 0.0821995i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.00000 | − | 6.92820i | −0.231714 | − | 0.401340i | ||||
\(299\) | −14.6969 | + | 25.4558i | −0.849946 | + | 1.47215i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | + | 2.59808i | 0.0288195 | + | 0.149751i | ||||
\(302\) | − | 31.1127i | − | 1.79033i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.00000 | − | 3.46410i | 0.344124 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.5885i | − | 0.889680i | −0.895610 | − | 0.444840i | \(-0.853260\pi\) | ||
0.895610 | − | 0.444840i | \(-0.146740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.57321 | + | 14.8492i | 0.486142 | + | 0.842023i | 0.999873 | − | 0.0159282i | \(-0.00507031\pi\) |
−0.513731 | + | 0.857951i | \(0.671737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5000 | − | 6.06218i | −0.593495 | − | 0.342655i | 0.172983 | − | 0.984925i | \(-0.444659\pi\) |
−0.766478 | + | 0.642270i | \(0.777993\pi\) | |||||||
\(314\) | 24.4949 | 1.38233 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2474 | − | 7.07107i | −0.687885 | − | 0.397151i | 0.114934 | − | 0.993373i | \(-0.463334\pi\) |
−0.802819 | + | 0.596222i | \(0.796668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | − | 3.46410i | −0.111979 | − | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.0000 | + | 13.8564i | −0.891645 | + | 0.772187i | ||||
\(323\) | 8.48528i | 0.472134i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.2474 | − | 7.07107i | 0.678323 | − | 0.391630i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 20.7846i | − | 1.14764i | ||||||
\(329\) | −30.6186 | − | 10.6066i | −1.68806 | − | 0.584761i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5000 | − | 26.8468i | 0.851957 | − | 1.47563i | −0.0274825 | − | 0.999622i | \(-0.508749\pi\) |
0.879440 | − | 0.476011i | \(-0.157918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.00000 | − | 5.19615i | −0.492458 | − | 0.284321i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0000 | −1.25289 | −0.626445 | − | 0.779466i | \(-0.715491\pi\) | ||||
−0.626445 | + | 0.779466i | \(0.715491\pi\) | |||||||
\(338\) | 17.1464 | + | 9.89949i | 0.932643 | + | 0.538462i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.22474 | + | 2.12132i | −0.0663237 | + | 0.114876i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 2.82843i | 0.152499i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | + | 6.92820i | −0.645124 | + | 0.372463i | ||||
\(347\) | 26.9444 | − | 15.5563i | 1.44645 | − | 0.835109i | 0.448183 | − | 0.893942i | \(-0.352071\pi\) |
0.998268 | + | 0.0588334i | \(0.0187381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3923i | 0.556287i | 0.960539 | + | 0.278144i | \(0.0897191\pi\) | ||||
−0.960539 | + | 0.278144i | \(0.910281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.57321 | − | 14.8492i | −0.456306 | − | 0.790345i | 0.542456 | − | 0.840084i | \(-0.317494\pi\) |
−0.998762 | + | 0.0497387i | \(0.984161\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.0000 | 0.739923 | ||||||||
\(359\) | −24.4949 | − | 14.1421i | −1.29279 | − | 0.746393i | −0.313643 | − | 0.949541i | \(-0.601550\pi\) |
−0.979148 | + | 0.203148i | \(0.934883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | ||||
\(362\) | −11.0227 | + | 19.0919i | −0.579340 | + | 1.00345i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | + | 0.866025i | −0.0782994 | + | 0.0452062i | −0.538639 | − | 0.842537i | \(-0.681061\pi\) |
0.460339 | + | 0.887743i | \(0.347728\pi\) | |||||||
\(368\) | −19.5959 | + | 11.3137i | −1.02151 | + | 0.589768i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.89898 | − | 5.65685i | −0.254342 | − | 0.293689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.5000 | − | 25.1147i | 0.750782 | − | 1.30039i | −0.196663 | − | 0.980471i | \(-0.563010\pi\) |
0.947444 | − | 0.319921i | \(-0.103656\pi\) | |||||||
\(374\) | 4.89898 | + | 8.48528i | 0.253320 | + | 0.438763i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −30.0000 | − | 17.3205i | −1.54713 | − | 0.893237i | ||||
\(377\) | 14.6969 | 0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.00000 | −0.359566 | −0.179783 | − | 0.983706i | \(-0.557540\pi\) | ||||
−0.179783 | + | 0.983706i | \(0.557540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.00000 | − | 1.73205i | −0.0511645 | − | 0.0886194i | ||||
\(383\) | −9.79796 | + | 16.9706i | −0.500652 | + | 0.867155i | 0.499347 | + | 0.866402i | \(0.333573\pi\) |
−1.00000 | 0.000753393i | \(0.999760\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 15.5563i | − | 0.791797i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.2702 | + | 13.4350i | −1.17984 | + | 0.681183i | −0.955978 | − | 0.293437i | \(-0.905201\pi\) |
−0.223865 | + | 0.974620i | \(0.571868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 27.7128i | − | 1.40150i | ||||||
\(392\) | −7.34847 | − | 18.3848i | −0.371154 | − | 0.928571i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.0000 | + | 24.2487i | −0.705310 | + | 1.22163i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.50000 | − | 0.866025i | −0.0752828 | − | 0.0434646i | 0.461886 | − | 0.886939i | \(-0.347173\pi\) |
−0.537169 | + | 0.843475i | \(0.680506\pi\) | |||||||
\(398\) | 19.5959 | 0.982255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.1464 | − | 9.89949i | −0.856252 | − | 0.494357i | 0.00650355 | − | 0.999979i | \(-0.497930\pi\) |
−0.862755 | + | 0.505622i | \(0.831263\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.50000 | − | 7.79423i | −0.224161 | − | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.0000 | + | 3.46410i | 0.496292 | + | 0.171920i | ||||
\(407\) | − | 1.41421i | − | 0.0701000i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5000 | − | 16.4545i | 1.40923 | − | 0.813622i | 0.413920 | − | 0.910313i | \(-0.364159\pi\) |
0.995314 | + | 0.0966915i | \(0.0308260\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.79796 | − | 8.48528i | 0.482126 | − | 0.417533i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.00000 | + | 1.73205i | 0.146735 | + | 0.0847174i | ||||
\(419\) | 36.7423 | 1.79498 | 0.897491 | − | 0.441034i | \(-0.145388\pi\) | ||||
0.897491 | + | 0.441034i | \(0.145388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 26.9444 | + | 15.5563i | 1.31163 | + | 0.757271i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.00000 | − | 6.92820i | −0.194257 | − | 0.336463i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.00000 | − | 8.66025i | 0.145180 | − | 0.419099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4722 | − | 7.77817i | 0.648933 | − | 0.374661i | −0.139114 | − | 0.990276i | \(-0.544426\pi\) |
0.788047 | + | 0.615615i | \(0.211092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5885i | 0.749133i | 0.927200 | + | 0.374567i | \(0.122209\pi\) | ||||
−0.927200 | + | 0.374567i | \(0.877791\pi\) | |||||||
\(434\) | −1.22474 | − | 6.36396i | −0.0587896 | − | 0.305480i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.89898 | − | 8.48528i | −0.234350 | − | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.0000 | + | 13.8564i | 1.14546 | + | 0.661330i | 0.947776 | − | 0.318936i | \(-0.103326\pi\) |
0.197681 | + | 0.980266i | \(0.436659\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.0000 | −1.71235 | ||||||||
\(443\) | −34.2929 | − | 19.7990i | −1.62930 | − | 0.940678i | −0.984301 | − | 0.176497i | \(-0.943523\pi\) |
−0.645002 | − | 0.764181i | \(-0.723143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.6969 | − | 25.4558i | 0.695920 | − | 1.20537i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.00000 | − | 20.7846i | −0.188982 | − | 0.981981i | ||||
\(449\) | 7.07107i | 0.333704i | 0.985982 | + | 0.166852i | \(0.0533603\pi\) | ||||
−0.985982 | + | 0.166852i | \(0.946640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 5.19615i | 0.423793 | − | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 38.1051i | − | 1.78836i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.50000 | − | 4.33013i | 0.116945 | − | 0.202555i | −0.801611 | − | 0.597847i | \(-0.796023\pi\) |
0.918556 | + | 0.395292i | \(0.129357\pi\) | |||||||
\(458\) | −15.9217 | − | 27.5772i | −0.743971 | − | 1.28860i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.6969 | −0.684505 | −0.342252 | − | 0.939608i | \(-0.611190\pi\) | ||||
−0.342252 | + | 0.939608i | \(0.611190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0000 | 0.604161 | 0.302081 | − | 0.953282i | \(-0.402319\pi\) | ||||
0.302081 | + | 0.953282i | \(0.402319\pi\) | |||||||
\(464\) | 9.79796 | + | 5.65685i | 0.454859 | + | 0.262613i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.00000 | + | 12.1244i | 0.324269 | + | 0.561650i | ||||
\(467\) | −13.4722 | + | 23.3345i | −0.623419 | + | 1.07979i | 0.365426 | + | 0.930841i | \(0.380923\pi\) |
−0.988844 | + | 0.148952i | \(0.952410\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.0000 | + | 19.0526i | −1.01587 | + | 0.879765i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0000 | − | 6.92820i | 0.552345 | − | 0.318896i | ||||
\(473\) | −1.22474 | + | 0.707107i | −0.0563138 | + | 0.0325128i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19.0000 | + | 32.9090i | −0.869040 | + | 1.50522i | ||||
\(479\) | −2.44949 | − | 4.24264i | −0.111920 | − | 0.193851i | 0.804624 | − | 0.593784i | \(-0.202367\pi\) |
−0.916544 | + | 0.399933i | \(0.869033\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | + | 2.59808i | 0.205182 | + | 0.118462i | ||||
\(482\) | 19.5959 | 0.892570 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.50000 | + | 14.7224i | 0.385172 | + | 0.667137i | 0.991793 | − | 0.127854i | \(-0.0408089\pi\) |
−0.606621 | + | 0.794991i | \(0.707476\pi\) | |||||||
\(488\) | 4.89898 | − | 8.48528i | 0.221766 | − | 0.384111i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3137i | 0.510581i | 0.966864 | + | 0.255290i | \(0.0821710\pi\) | ||||
−0.966864 | + | 0.255290i | \(0.917829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | + | 6.92820i | −0.540453 | + | 0.312031i | ||||
\(494\) | −11.0227 | + | 6.36396i | −0.495935 | + | 0.286328i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.92820i | − | 0.311086i | ||||||
\(497\) | −18.3712 | + | 3.53553i | −0.824060 | + | 0.158590i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5000 | − | 21.6506i | 0.559577 | − | 0.969216i | −0.437955 | − | 0.898997i | \(-0.644297\pi\) |
0.997532 | − | 0.0702185i | \(-0.0223697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.0454 | −0.982956 | −0.491478 | − | 0.870890i | \(-0.663543\pi\) | ||||
−0.491478 | + | 0.870890i | \(0.663543\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.79796 | − | 5.65685i | −0.435572 | − | 0.251478i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.22474 | + | 2.12132i | −0.0542859 | + | 0.0940259i | −0.891891 | − | 0.452250i | \(-0.850622\pi\) |
0.837605 | + | 0.546276i | \(0.183955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | − | 3.46410i | −0.132712 | − | 0.153243i | ||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.00000 | + | 1.73205i | −0.132324 | + | 0.0763975i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 17.3205i | − | 0.761755i | ||||||
\(518\) | 2.44949 | + | 2.82843i | 0.107624 | + | 0.124274i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.44949 | − | 4.24264i | −0.107314 | − | 0.185873i | 0.807367 | − | 0.590049i | \(-0.200892\pi\) |
−0.914681 | + | 0.404176i | \(0.867558\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.50000 | − | 0.866025i | −0.0655904 | − | 0.0378686i | 0.466846 | − | 0.884339i | \(-0.345390\pi\) |
−0.532437 | + | 0.846470i | \(0.678724\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.0000 | −0.872041 | ||||||||
\(527\) | 7.34847 | + | 4.24264i | 0.320104 | + | 0.184812i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.50000 | + | 7.79423i | 0.195652 | + | 0.338880i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.1838i | 1.65392i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −26.9444 | + | 15.5563i | −1.16382 | + | 0.671932i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 24.2487i | − | 1.04544i | ||||||
\(539\) | 6.12372 | − | 7.77817i | 0.263767 | − | 0.335030i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.50000 | + | 14.7224i | −0.365444 | + | 0.632967i | −0.988847 | − | 0.148933i | \(-0.952416\pi\) |
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | 9.79796 | + | 16.9706i | 0.420858 | + | 0.728948i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0000 | 0.427569 | 0.213785 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213785 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.44949 | + | 4.24264i | −0.104352 | + | 0.180743i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.5000 | − | 4.33013i | −0.531554 | − | 0.184136i | ||||
\(554\) | − | 32.5269i | − | 1.38194i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.4722 | + | 7.77817i | −0.570835 | + | 0.329572i | −0.757483 | − | 0.652855i | \(-0.773571\pi\) |
0.186648 | + | 0.982427i | \(0.440238\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.19615i | − | 0.219774i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.0000 | + | 27.7128i | −0.674919 | + | 1.16899i | ||||
\(563\) | 13.4722 | + | 23.3345i | 0.567785 | + | 0.983433i | 0.996785 | + | 0.0801281i | \(0.0255329\pi\) |
−0.428999 | + | 0.903305i | \(0.641134\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.44949 | 0.102960 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.0000 | −0.839181 | ||||||||
\(569\) | 1.22474 | + | 0.707107i | 0.0513440 | + | 0.0296435i | 0.525452 | − | 0.850823i | \(-0.323896\pi\) |
−0.474108 | + | 0.880467i | \(0.657229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.50000 | − | 9.52628i | −0.230168 | − | 0.398662i | 0.727690 | − | 0.685907i | \(-0.240594\pi\) |
−0.957857 | + | 0.287244i | \(0.907261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.00000 | + | 25.9808i | −0.375653 | + | 1.08442i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.50000 | + | 0.866025i | −0.0624458 | + | 0.0360531i | −0.530898 | − | 0.847436i | \(-0.678145\pi\) |
0.468452 | + | 0.883489i | \(0.344812\pi\) | |||||||
\(578\) | 8.57321 | − | 4.94975i | 0.356599 | − | 0.205882i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.67423 | − | 19.0919i | −0.152433 | − | 0.792065i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | − | 3.46410i | 0.0828315 | − | 0.143468i | ||||
\(584\) | −2.44949 | − | 4.24264i | −0.101361 | − | 0.175562i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.0000 | + | 10.3923i | 0.743573 | + | 0.429302i | ||||
\(587\) | 14.6969 | 0.606608 | 0.303304 | − | 0.952894i | \(-0.401910\pi\) | ||||
0.303304 | + | 0.952894i | \(0.401910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000 | + | 3.46410i | 0.0821995 | + | 0.142374i | ||||
\(593\) | 8.57321 | − | 14.8492i | 0.352060 | − | 0.609785i | −0.634550 | − | 0.772881i | \(-0.718815\pi\) |
0.986610 | + | 0.163096i | \(0.0521481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 36.0000 | − | 20.7846i | 1.47215 | − | 0.849946i | ||||
\(599\) | −4.89898 | + | 2.82843i | −0.200167 | + | 0.115566i | −0.596733 | − | 0.802440i | \(-0.703535\pi\) |
0.396566 | + | 0.918006i | \(0.370202\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9808i | 1.05978i | 0.848067 | + | 0.529889i | \(0.177766\pi\) | ||||
−0.848067 | + | 0.529889i | \(0.822234\pi\) | |||||||
\(602\) | 1.22474 | − | 3.53553i | 0.0499169 | − | 0.144098i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.5000 | + | 19.9186i | 1.40031 | + | 0.808470i | 0.994424 | − | 0.105453i | \(-0.0336291\pi\) |
0.405887 | + | 0.913923i | \(0.366962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 55.1135 | + | 31.8198i | 2.22965 | + | 1.28729i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.00000 | + | 6.92820i | 0.161558 | + | 0.279827i | 0.935428 | − | 0.353518i | \(-0.115015\pi\) |
−0.773869 | + | 0.633345i | \(0.781681\pi\) | |||||||
\(614\) | −11.0227 | + | 19.0919i | −0.444840 | + | 0.770486i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.00000 | − | 6.92820i | 0.322329 | − | 0.279145i | ||||
\(617\) | − | 24.0416i | − | 0.967880i | −0.875101 | − | 0.483940i | \(-0.839205\pi\) | ||
0.875101 | − | 0.483940i | \(-0.160795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5000 | + | 14.7224i | −1.02493 | + | 0.591744i | −0.915529 | − | 0.402253i | \(-0.868227\pi\) |
−0.109403 | + | 0.993997i | \(0.534894\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 24.2487i | − | 0.972285i | ||||||
\(623\) | 12.2474 | + | 4.24264i | 0.490684 | + | 0.169978i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.57321 | + | 14.8492i | 0.342655 | + | 0.593495i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.89898 | −0.195335 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0000 | 1.51276 | 0.756378 | − | 0.654135i | \(-0.226967\pi\) | ||||
0.756378 | + | 0.654135i | \(0.226967\pi\) | |||||||
\(632\) | −12.2474 | − | 7.07107i | −0.487177 | − | 0.281272i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0000 | + | 17.3205i | 0.397151 | + | 0.687885i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.5000 | + | 33.7750i | 0.534889 | + | 1.33821i | ||||
\(638\) | 5.65685i | 0.223957i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.2474 | + | 7.07107i | −0.483745 | + | 0.279290i | −0.721976 | − | 0.691918i | \(-0.756766\pi\) |
0.238231 | + | 0.971209i | \(0.423433\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.9808i | 1.02458i | 0.858812 | + | 0.512291i | \(0.171203\pi\) | ||||
−0.858812 | + | 0.512291i | \(0.828797\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | − | 10.3923i | 0.236067 | − | 0.408880i | ||||
\(647\) | −8.57321 | − | 14.8492i | −0.337048 | − | 0.583784i | 0.646828 | − | 0.762636i | \(-0.276095\pi\) |
−0.983876 | + | 0.178852i | \(0.942762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | + | 3.46410i | 0.235521 | + | 0.135978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.12372 | + | 3.53553i | 0.239640 | + | 0.138356i | 0.615011 | − | 0.788518i | \(-0.289151\pi\) |
−0.375371 | + | 0.926875i | \(0.622485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −14.6969 | + | 25.4558i | −0.573819 | + | 0.993884i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30.0000 | + | 34.6410i | 1.16952 | + | 1.35045i | ||||
\(659\) | − | 22.6274i | − | 0.881439i | −0.897645 | − | 0.440720i | \(-0.854723\pi\) | ||
0.897645 | − | 0.440720i | \(-0.145277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.5000 | + | 14.7224i | −0.991835 | + | 0.572636i | −0.905822 | − | 0.423658i | \(-0.860746\pi\) |
−0.0860127 | + | 0.996294i | \(0.527413\pi\) | |||||||
\(662\) | −37.9671 | + | 21.9203i | −1.47563 | + | 0.851957i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 20.7846i | − | 0.806599i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | − | 13.8564i | 0.309761 | − | 0.536522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.89898 | 0.189123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.0000 | −1.34915 | −0.674575 | − | 0.738206i | \(-0.735673\pi\) | ||||
−0.674575 | + | 0.738206i | \(0.735673\pi\) | |||||||
\(674\) | 28.1691 | + | 16.2635i | 1.08503 | + | 0.626445i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.89898 | − | 8.48528i | 0.188283 | − | 0.326116i | −0.756395 | − | 0.654115i | \(-0.773041\pi\) |
0.944678 | + | 0.327999i | \(0.106374\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.0000 | − | 5.19615i | 1.03616 | − | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.00000 | − | 1.73205i | 0.114876 | − | 0.0663237i | ||||
\(683\) | 41.6413 | − | 24.0416i | 1.59336 | − | 0.919927i | 0.600636 | − | 0.799522i | \(-0.294914\pi\) |
0.992725 | − | 0.120405i | \(-0.0384193\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.22474 | + | 26.1630i | 0.0467610 | + | 0.998906i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | 7.34847 | + | 12.7279i | 0.279954 | + | 0.484895i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.5000 | + | 21.6506i | 1.42657 | + | 0.823629i | 0.996848 | − | 0.0793336i | \(-0.0252792\pi\) |
0.429719 | + | 0.902963i | \(0.358613\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −44.0000 | −1.67022 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | − | 31.1769i | −0.681799 | − | 1.18091i | ||||
\(698\) | 7.34847 | − | 12.7279i | 0.278144 | − | 0.481759i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.65685i | − | 0.213656i | −0.994277 | − | 0.106828i | \(-0.965931\pi\) | ||
0.994277 | − | 0.106828i | \(-0.0340695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.50000 | + | 0.866025i | −0.0565736 | + | 0.0326628i | ||||
\(704\) | 9.79796 | − | 5.65685i | 0.369274 | − | 0.213201i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.2487i | 0.912612i | ||||||||
\(707\) | −34.2929 | + | 29.6985i | −1.28972 | + | 1.11693i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.0000 | − | 34.6410i | 0.751116 | − | 1.30097i | −0.196167 | − | 0.980571i | \(-0.562849\pi\) |
0.947282 | − | 0.320400i | \(-0.103817\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.0000 | + | 6.92820i | 0.449719 | + | 0.259645i | ||||
\(713\) | −9.79796 | −0.366936 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.0000 | + | 34.6410i | 0.746393 | + | 1.29279i | ||||
\(719\) | 13.4722 | − | 23.3345i | 0.502428 | − | 0.870231i | −0.497568 | − | 0.867425i | \(-0.665774\pi\) |
0.999996 | − | 0.00280593i | \(-0.000893157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.50000 | + | 21.6506i | −0.279315 | + | 0.806312i | ||||
\(722\) | 22.6274i | 0.842105i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.9808i | − | 0.963573i | −0.876289 | − | 0.481787i | \(-0.839988\pi\) | ||
0.876289 | − | 0.481787i | \(-0.160012\pi\) | |||||||
\(728\) | 7.34847 | + | 38.1838i | 0.272352 | + | 1.41518i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.44949 | + | 4.24264i | 0.0905977 | + | 0.156920i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.5000 | + | 19.9186i | 1.27429 | + | 0.735710i | 0.975792 | − | 0.218702i | \(-0.0701821\pi\) |
0.298495 | + | 0.954411i | \(0.403515\pi\) | |||||||
\(734\) | 2.44949 | 0.0904123 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.4722 | − | 7.77817i | −0.496255 | − | 0.286513i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.500000 | + | 0.866025i | 0.0183928 | + | 0.0318573i | 0.875075 | − | 0.483987i | \(-0.160812\pi\) |
−0.856683 | + | 0.515844i | \(0.827478\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.00000 | + | 10.3923i | 0.0734223 | + | 0.381514i | ||||
\(743\) | − | 24.0416i | − | 0.882002i | −0.897507 | − | 0.441001i | \(-0.854624\pi\) | ||
0.897507 | − | 0.441001i | \(-0.145376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −35.5176 | + | 20.5061i | −1.30039 | + | 0.750782i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.44949 | + | 7.07107i | −0.0895024 | + | 0.258371i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.5000 | + | 25.1147i | −0.529113 | + | 0.916450i | 0.470311 | + | 0.882501i | \(0.344142\pi\) |
−0.999424 | + | 0.0339490i | \(0.989192\pi\) | |||||||
\(752\) | 24.4949 | + | 42.4264i | 0.893237 | + | 1.54713i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.0000 | − | 10.3923i | −0.655521 | − | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 8.57321 | + | 4.94975i | 0.311393 | + | 0.179783i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2474 | + | 21.2132i | −0.443970 | + | 0.768978i | −0.997980 | − | 0.0635319i | \(-0.979764\pi\) |
0.554010 | + | 0.832510i | \(0.313097\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | + | 1.73205i | −0.0724049 | + | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | − | 13.8564i | 0.867155 | − | 0.500652i | ||||
\(767\) | −22.0454 | + | 12.7279i | −0.796014 | + | 0.459579i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.9808i | − | 0.936890i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) | ||
0.883493 | − | 0.468445i | \(-0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.4722 | + | 23.3345i | 0.484561 | + | 0.839284i | 0.999843 | − | 0.0177365i | \(-0.00564599\pi\) |
−0.515282 | + | 0.857021i | \(0.672313\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.3939 | 1.05518 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.0000 | 1.36237 | ||||||||
\(779\) | −11.0227 | − | 6.36396i | −0.394929 | − | 0.228013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.00000 | − | 8.66025i | −0.178914 | − | 0.309888i | ||||
\(782\) | −19.5959 | + | 33.9411i | −0.700749 | + | 1.21373i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.00000 | + | 27.7128i | −0.142857 | + | 0.989743i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.0000 | − | 22.5167i | 1.39020 | − | 0.802632i | 0.396863 | − | 0.917878i | \(-0.370099\pi\) |
0.993337 | + | 0.115246i | \(0.0367655\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.67423 | + | 0.707107i | −0.130641 | + | 0.0251418i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.00000 | + | 15.5885i | −0.319599 | + | 0.553562i | ||||
\(794\) | 1.22474 | + | 2.12132i | 0.0434646 | + | 0.0752828i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.3939 | 1.04118 | 0.520592 | − | 0.853805i | \(-0.325711\pi\) | ||||
0.520592 | + | 0.853805i | \(0.325711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.0000 | −2.12265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.0000 | + | 24.2487i | 0.494357 | + | 0.856252i | ||||
\(803\) | 1.22474 | − | 2.12132i | 0.0432203 | − | 0.0748598i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.7279i | 0.448322i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −42.0000 | + | 24.2487i | −1.47755 | + | 0.853067i | ||||
\(809\) | 35.5176 | − | 20.5061i | 1.24873 | − | 0.720956i | 0.277876 | − | 0.960617i | \(-0.410370\pi\) |
0.970857 | + | 0.239661i | \(0.0770363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.00000 | + | 1.73205i | −0.0350500 | + | 0.0607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.50000 | + | 0.866025i | 0.0524784 | + | 0.0302984i | ||||
\(818\) | −46.5403 | −1.62724 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.8207 | − | 12.0208i | −0.726646 | − | 0.419529i | 0.0905478 | − | 0.995892i | \(-0.471138\pi\) |
−0.817194 | + | 0.576363i | \(0.804472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.0000 | − | 29.4449i | −0.592583 | − | 1.02638i | −0.993883 | − | 0.110437i | \(-0.964775\pi\) |
0.401300 | − | 0.915947i | \(-0.368558\pi\) | |||||||
\(824\) | −12.2474 | + | 21.2132i | −0.426660 | + | 0.738997i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | + | 3.46410i | −0.626300 | + | 0.120532i | ||||
\(827\) | − | 7.07107i | − | 0.245885i | −0.992414 | − | 0.122943i | \(-0.960767\pi\) | ||
0.992414 | − | 0.122943i | \(-0.0392331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.50000 | − | 0.866025i | 0.0520972 | − | 0.0300783i | −0.473725 | − | 0.880673i | \(-0.657091\pi\) |
0.525822 | + | 0.850594i | \(0.323758\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.5692i | 1.44115i | ||||||||
\(833\) | −26.9444 | − | 21.2132i | −0.933568 | − | 0.734994i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −45.0000 | − | 25.9808i | −1.55450 | − | 0.897491i | ||||
\(839\) | −14.6969 | −0.507395 | −0.253697 | − | 0.967284i | \(-0.581647\pi\) | ||||
−0.253697 | + | 0.967284i | \(0.581647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 1.22474 | + | 0.707107i | 0.0422075 | + | 0.0243685i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.5000 | − | 7.79423i | −0.773109 | − | 0.267813i | ||||
\(848\) | 11.3137i | 0.388514i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89898 | − | 2.82843i | 0.167935 | − | 0.0969572i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.3731i | 1.24539i | 0.782465 | + | 0.622695i | \(0.213962\pi\) | ||||
−0.782465 | + | 0.622695i | \(0.786038\pi\) | |||||||
\(854\) | −9.79796 | + | 8.48528i | −0.335279 | + | 0.290360i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | + | 6.92820i | −0.136717 | + | 0.236801i | ||||
\(857\) | −19.5959 | − | 33.9411i | −0.669384 | − | 1.15941i | −0.978077 | − | 0.208245i | \(-0.933225\pi\) |
0.308693 | − | 0.951162i | \(-0.400108\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.0000 | + | 19.0526i | 1.12595 | + | 0.650065i | 0.942912 | − | 0.333042i | \(-0.108075\pi\) |
0.183033 | + | 0.983107i | \(0.441408\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.0000 | −0.749323 | ||||||||
\(863\) | 35.5176 | + | 20.5061i | 1.20903 | + | 0.698036i | 0.962548 | − | 0.271111i | \(-0.0873910\pi\) |
0.246485 | + | 0.969147i | \(0.420724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.0227 | − | 19.0919i | 0.374567 | − | 0.648769i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 7.07107i | − | 0.239870i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.5000 | − | 28.5788i | 1.67724 | − | 0.968357i | ||||
\(872\) | −2.44949 | + | 1.41421i | −0.0829502 | + | 0.0478913i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.8564i | 0.468700i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0000 | − | 17.3205i | 0.337676 | − | 0.584872i | −0.646319 | − | 0.763067i | \(-0.723693\pi\) |
0.983995 | + | 0.178195i | \(0.0570259\pi\) | |||||||
\(878\) | −19.5959 | − | 33.9411i | −0.661330 | − | 1.14546i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0000 | −0.370179 | −0.185090 | − | 0.982722i | \(-0.559258\pi\) | ||||
−0.185090 | + | 0.982722i | \(0.559258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.0000 | + | 48.4974i | 0.940678 | + | 1.62930i | ||||
\(887\) | −20.8207 | + | 36.0624i | −0.699089 | + | 1.21086i | 0.269693 | + | 0.962946i | \(0.413078\pi\) |
−0.968783 | + | 0.247912i | \(0.920256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.50000 | − | 28.5788i | −0.184464 | − | 0.958503i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.3712 | + | 10.6066i | −0.614768 | + | 0.354936i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.79796 | + | 28.2843i | −0.327327 | + | 0.944911i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.00000 | − | 8.66025i | 0.166852 | − | 0.288996i | ||||
\(899\) | 2.44949 | + | 4.24264i | 0.0816951 | + | 0.141500i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | − | 6.92820i | −0.399778 | − | 0.230812i | ||||
\(902\) | −14.6969 | −0.489355 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.00000 | −0.133038 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.50000 | + | 4.33013i | 0.0830111 | + | 0.143780i | 0.904542 | − | 0.426385i | \(-0.140213\pi\) |
−0.821531 | + | 0.570164i | \(0.806880\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.7401i | 1.78049i | 0.455483 | + | 0.890245i | \(0.349467\pi\) | ||||
−0.455483 | + | 0.890245i | \(0.650533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00000 | − | 5.19615i | 0.297857 | − | 0.171968i | ||||
\(914\) | −6.12372 | + | 3.53553i | −0.202555 | + | 0.116945i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.12372 | − | 2.12132i | −0.202223 | − | 0.0700522i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.50000 | + | 14.7224i | −0.280389 | + | 0.485648i | −0.971481 | − | 0.237119i | \(-0.923797\pi\) |
0.691091 | + | 0.722767i | \(0.257130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.0000 | + | 10.3923i | 0.592798 | + | 0.342252i | ||||
\(923\) | 36.7423 | 1.20939 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.9217 | − | 9.19239i | −0.523219 | − | 0.302081i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.1691 | − | 48.7904i | 0.924199 | − | 1.60076i | 0.131355 | − | 0.991335i | \(-0.458067\pi\) |
0.792844 | − | 0.609425i | \(-0.208600\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.0000 | − | 1.73205i | −0.393284 | − | 0.0567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 33.0000 | − | 19.0526i | 1.07979 | − | 0.623419i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.7654i | 1.52776i | 0.645359 | + | 0.763879i | \(0.276708\pi\) | ||||
−0.645359 | + | 0.763879i | \(0.723292\pi\) | |||||||
\(938\) | 40.4166 | − | 7.77817i | 1.31965 | − | 0.253966i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.4949 | − | 42.4264i | −0.798511 | − | 1.38306i | −0.920586 | − | 0.390540i | \(-0.872288\pi\) |
0.122075 | − | 0.992521i | \(-0.461045\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0000 | + | 20.7846i | 1.17232 | + | 0.676840i | ||||
\(944\) | −19.5959 | −0.637793 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | 42.8661 | + | 24.7487i | 1.39296 | + | 0.804226i | 0.993642 | − | 0.112586i | \(-0.0359135\pi\) |
0.399318 | + | 0.916812i | \(0.369247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.50000 | + | 7.79423i | 0.146076 | + | 0.253011i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −24.0000 | − | 27.7128i | −0.777844 | − | 0.898177i | ||||
\(953\) | 5.65685i | 0.183243i | 0.995794 | + | 0.0916217i | \(0.0292051\pi\) | ||||
−0.995794 | + | 0.0916217i | \(0.970795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.92820i | 0.223840i | ||||||||
\(959\) | −19.5959 | − | 22.6274i | −0.632785 | − | 0.730677i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | + | 24.2487i | −0.451613 | + | 0.782216i | ||||
\(962\) | −3.67423 | − | 6.36396i | −0.118462 | − | 0.205182i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0000 | 0.418052 | 0.209026 | − | 0.977910i | \(-0.432971\pi\) | ||||
0.209026 | + | 0.977910i | \(0.432971\pi\) | |||||||
\(968\) | −22.0454 | − | 12.7279i | −0.708566 | − | 0.409091i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.5959 | + | 33.9411i | −0.628863 | + | 1.08922i | 0.358917 | + | 0.933369i | \(0.383146\pi\) |
−0.987780 | + | 0.155853i | \(0.950187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.5000 | + | 2.59808i | −0.432790 | + | 0.0832905i | ||||
\(974\) | − | 24.0416i | − | 0.770344i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0000 | + | 6.92820i | −0.384111 | + | 0.221766i | ||||
\(977\) | −6.12372 | + | 3.53553i | −0.195915 | + | 0.113112i | −0.594749 | − | 0.803912i | \(-0.702748\pi\) |
0.398833 | + | 0.917023i | \(0.369415\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.92820i | 0.221426i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.00000 | − | 13.8564i | 0.255290 | − | 0.442176i | ||||
\(983\) | 2.44949 | + | 4.24264i | 0.0781266 | + | 0.135319i | 0.902442 | − | 0.430812i | \(-0.141773\pi\) |
−0.824315 | + | 0.566131i | \(0.808439\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.5959 | 0.624061 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.89898 | − | 2.82843i | −0.155778 | − | 0.0899388i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5000 | − | 30.3109i | −0.555906 | − | 0.962857i | −0.997832 | − | 0.0658059i | \(-0.979038\pi\) |
0.441927 | − | 0.897051i | \(-0.354295\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.0000 | + | 8.66025i | 0.792952 | + | 0.274687i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.5000 | − | 14.7224i | 0.807593 | − | 0.466264i | −0.0385262 | − | 0.999258i | \(-0.512266\pi\) |
0.846119 | + | 0.532993i | \(0.178933\pi\) | |||||||
\(998\) | −30.6186 | + | 17.6777i | −0.969216 | + | 0.559577i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))