Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,2,Mod(1199,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2400.1199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.m (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1199.12 | ||
Character | \(\chi\) | \(=\) | 2400.1199 |
Dual form | 2400.2.m.e.1199.10 |
$q$-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 \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(1951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.730070 | + | 1.57067i | −0.421506 | + | 0.906826i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.25539 | 0.474491 | 0.237245 | − | 0.971450i | \(-0.423755\pi\) | ||||
0.237245 | + | 0.971450i | \(0.423755\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.93400 | − | 2.29339i | −0.644665 | − | 0.764465i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.02346i | 0.911609i | 0.890080 | + | 0.455804i | \(0.150648\pi\) | ||||
−0.890080 | + | 0.455804i | \(0.849352\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.65509 | −1.56844 | −0.784220 | − | 0.620483i | \(-0.786936\pi\) | ||||
−0.784220 | + | 0.620483i | \(0.786936\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.45546 | −0.595538 | −0.297769 | − | 0.954638i | \(-0.596242\pi\) | ||||
−0.297769 | + | 0.954638i | \(0.596242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.77801 | 0.407903 | 0.203951 | − | 0.978981i | \(-0.434622\pi\) | ||||
0.203951 | + | 0.978981i | \(0.434622\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.916519 | + | 1.97179i | −0.200001 | + | 0.430281i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.84074i | − | 1.84342i | −0.387878 | − | 0.921711i | \(-0.626792\pi\) | ||
0.387878 | − | 0.921711i | \(-0.373208\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.01411 | − | 1.36333i | 0.964967 | − | 0.262373i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.79561 | 0.704827 | 0.352414 | − | 0.935844i | \(-0.385361\pi\) | ||||
0.352414 | + | 0.935844i | \(0.385361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.19897i | 0.933763i | 0.884320 | + | 0.466881i | \(0.154623\pi\) | ||||
−0.884320 | + | 0.466881i | \(0.845377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.74886 | − | 2.20734i | −0.826670 | − | 0.384249i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.45436 | −1.06109 | −0.530545 | − | 0.847657i | \(-0.678013\pi\) | ||||
−0.530545 | + | 0.847657i | \(0.678013\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.12861 | − | 8.88227i | 0.661107 | − | 1.42230i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.57276i | − | 1.18267i | −0.806427 | − | 0.591333i | \(-0.798602\pi\) | ||
0.806427 | − | 0.591333i | \(-0.201398\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.37266i | 0.666824i | 0.942781 | + | 0.333412i | \(0.108200\pi\) | ||||
−0.942781 | + | 0.333412i | \(0.891800\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.83304i | − | 0.267376i | −0.991023 | − | 0.133688i | \(-0.957318\pi\) | ||
0.991023 | − | 0.133688i | \(-0.0426820\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.42401 | −0.774858 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.79266 | − | 3.85672i | 0.251023 | − | 0.540049i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 12.0528i | − | 1.65558i | −0.561035 | − | 0.827792i | \(-0.689597\pi\) | ||
0.561035 | − | 0.827792i | \(-0.310403\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.29807 | + | 2.79266i | −0.171934 | + | 0.369897i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.91093i | − | 0.639348i | −0.947528 | − | 0.319674i | \(-0.896427\pi\) | ||
0.947528 | − | 0.319674i | \(-0.103573\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.16586i | − | 1.04553i | −0.852477 | − | 0.522766i | \(-0.824900\pi\) | ||
0.852477 | − | 0.522766i | \(-0.175100\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.42791 | − | 2.87909i | −0.305888 | − | 0.362732i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.50466i | 1.03901i | 0.854467 | + | 0.519505i | \(0.173884\pi\) | ||||
−0.854467 | + | 0.519505i | \(0.826116\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.8859 | + | 6.45436i | 1.67166 | + | 0.777013i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.00770 | 0.831661 | 0.415831 | − | 0.909442i | \(-0.363491\pi\) | ||||
0.415831 | + | 0.909442i | \(0.363491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.59465i | 0.537763i | 0.963173 | + | 0.268881i | \(0.0866540\pi\) | ||||
−0.963173 | + | 0.268881i | \(0.913346\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.79561i | 0.432550i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.36659i | − | 0.828806i | −0.910093 | − | 0.414403i | \(-0.863990\pi\) | ||
0.910093 | − | 0.414403i | \(-0.136010\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.51932 | + | 8.87083i | −0.168813 | + | 0.985648i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7510 | −1.72890 | −0.864449 | − | 0.502720i | \(-0.832333\pi\) | ||||
−0.864449 | + | 0.502720i | \(0.832333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.77106 | + | 5.96165i | −0.297089 | + | 0.639156i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.65716i | 0.387658i | 0.981035 | + | 0.193829i | \(0.0620907\pi\) | ||||
−0.981035 | + | 0.193829i | \(0.937909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.09931 | −0.744210 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.16586 | − | 3.79561i | −0.846760 | − | 0.393587i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.8773i | − | 1.40903i | −0.709690 | − | 0.704514i | \(-0.751165\pi\) | ||
0.709690 | − | 0.704514i | \(-0.248835\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.93400 | − | 5.84737i | 0.696893 | − | 0.587683i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8859 | 1.38170 | 0.690848 | − | 0.723000i | \(-0.257237\pi\) | ||||
0.690848 | + | 0.723000i | \(0.257237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.36659 | −0.725852 | −0.362926 | − | 0.931818i | \(-0.618222\pi\) | ||||
−0.362926 | + | 0.931818i | \(0.618222\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.14076 | −0.786997 | −0.393499 | − | 0.919325i | \(-0.628735\pi\) | ||||
−0.393499 | + | 0.919325i | \(0.628735\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.65509i | − | 0.541659i | −0.962627 | − | 0.270830i | \(-0.912702\pi\) | ||
0.962627 | − | 0.270830i | \(-0.0872980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.71213 | − | 10.1377i | 0.447256 | − | 0.962223i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.4884 | −1.08073 | −0.540367 | − | 0.841429i | \(-0.681715\pi\) | ||||
−0.540367 | + | 0.841429i | \(0.681715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.9369 | + | 12.9693i | 1.01112 | + | 1.19902i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.08255 | −0.282577 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.85866 | 0.168969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.8943 | + | 5.52865i | 1.07247 | + | 0.498501i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.7081 | 1.92628 | 0.963142 | − | 0.268993i | \(-0.0866909\pi\) | ||||
0.963142 | + | 0.268993i | \(0.0866909\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.86799 | − | 3.19234i | −0.604693 | − | 0.281070i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12.5212i | − | 1.09398i | −0.837139 | − | 0.546990i | \(-0.815773\pi\) | ||
0.837139 | − | 0.546990i | \(-0.184227\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.23208 | 0.193546 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.4649 | 1.57757 | 0.788783 | − | 0.614672i | \(-0.210712\pi\) | ||||
0.788783 | + | 0.614672i | \(0.210712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6040 | −0.984237 | −0.492118 | − | 0.870528i | \(-0.663777\pi\) | ||||
−0.492118 | + | 0.870528i | \(0.663777\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.87909 | + | 1.33825i | 0.242463 | + | 0.112701i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 17.0980i | − | 1.42980i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.95990 | − | 8.51932i | 0.326607 | − | 0.702661i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.9233 | −0.976794 | −0.488397 | − | 0.872621i | \(-0.662418\pi\) | ||||
−0.488397 | + | 0.872621i | \(0.662418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0548i | − | 0.818247i | −0.912479 | − | 0.409124i | \(-0.865834\pi\) | ||
0.912479 | − | 0.409124i | \(-0.134166\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.74886 | + | 5.63135i | 0.383922 | + | 0.455268i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.71150 | 0.136593 | 0.0682964 | − | 0.997665i | \(-0.478244\pi\) | ||||
0.0682964 | + | 0.997665i | \(0.478244\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.9310 | + | 8.79941i | 1.50133 | + | 0.697838i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.0985i | − | 0.874687i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.9580i | − | 0.936621i | −0.883564 | − | 0.468311i | \(-0.844863\pi\) | ||
0.883564 | − | 0.468311i | \(-0.155137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.583522i | 0.0451543i | 0.999745 | + | 0.0225771i | \(0.00718713\pi\) | ||||
−0.999745 | + | 0.0225771i | \(0.992813\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.9800 | 1.46000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.43866 | − | 4.07767i | −0.262961 | − | 0.311827i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.0528i | − | 0.916360i | −0.888860 | − | 0.458180i | \(-0.848502\pi\) | ||
0.888860 | − | 0.458180i | \(-0.151498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.71344 | + | 3.58532i | 0.579778 | + | 0.269489i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.605490i | − | 0.0452565i | −0.999744 | − | 0.0226282i | \(-0.992797\pi\) | ||
0.999744 | − | 0.0226282i | \(-0.00720340\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.08790i | − | 0.526840i | −0.964681 | − | 0.263420i | \(-0.915150\pi\) | ||
0.964681 | − | 0.263420i | \(-0.0848505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8259 | + | 5.96165i | 0.948114 | + | 0.440698i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.42401i | − | 0.542897i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.29464 | − | 1.71150i | 0.457868 | − | 0.124493i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9310 | 1.36980 | 0.684899 | − | 0.728638i | \(-0.259846\pi\) | ||||
0.684899 | + | 0.728638i | \(0.259846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.27334i | − | 0.307602i | −0.988102 | − | 0.153801i | \(-0.950849\pi\) | ||
0.988102 | − | 0.153801i | \(-0.0491515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.0903i | − | 0.718901i | −0.933164 | − | 0.359450i | \(-0.882964\pi\) | ||
0.933164 | − | 0.359450i | \(-0.117036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.0199i | 1.34829i | 0.738601 | + | 0.674143i | \(0.235487\pi\) | ||||
−0.738601 | + | 0.674143i | \(0.764513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.3580 | − | 6.20900i | −0.942201 | − | 0.437949i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.76495 | 0.334434 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.2753 | + | 17.0980i | −1.40923 | + | 1.18839i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.37574i | 0.371848i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.49534 | −0.378315 | −0.189157 | − | 0.981947i | \(-0.560576\pi\) | ||||
−0.189157 | + | 0.981947i | \(0.560576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.11611 | + | 11.0068i | −0.350550 | + | 0.754172i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.52671i | 0.443062i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.21667 | − | 3.35441i | −0.487657 | − | 0.226670i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8859 | 0.934065 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.70974 | −0.516282 | −0.258141 | − | 0.966107i | \(-0.583110\pi\) | ||||
−0.258141 | + | 0.966107i | \(0.583110\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.40388 | 0.491413 | 0.245706 | − | 0.969344i | \(-0.420980\pi\) | ||||
0.245706 | + | 0.969344i | \(0.420980\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.1310i | − | 1.13205i | −0.824389 | − | 0.566024i | \(-0.808481\pi\) | ||
0.824389 | − | 0.566024i | \(-0.191519\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.96165 | − | 2.77106i | −0.392248 | − | 0.182322i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.40807 | −0.0922454 | −0.0461227 | − | 0.998936i | \(-0.514687\pi\) | ||||
−0.0461227 | + | 0.998936i | \(0.514687\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.5705 | + | 5.37812i | 0.751583 | + | 0.349347i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.50673 | −0.614939 | −0.307470 | − | 0.951558i | \(-0.599482\pi\) | ||||
−0.307470 | + | 0.951558i | \(0.599482\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.27334 | 0.146439 | 0.0732195 | − | 0.997316i | \(-0.476673\pi\) | ||||
0.0732195 | + | 0.997316i | \(0.476673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.8239 | − | 8.86267i | −0.822655 | − | 0.568540i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0548 | −0.639771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.4993 | − | 24.7396i | 0.728741 | − | 1.56781i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.49772i | 0.599491i | 0.954019 | + | 0.299745i | \(0.0969017\pi\) | ||||
−0.954019 | + | 0.299745i | \(0.903098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.7297 | 1.68048 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.3144 | −1.70382 | −0.851912 | − | 0.523686i | \(-0.824557\pi\) | ||||
−0.851912 | + | 0.523686i | \(0.824557\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.10270 | −0.503477 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.34070 | − | 8.70484i | −0.454378 | − | 0.538816i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.24952i | − | 0.0770484i | −0.999258 | − | 0.0385242i | \(-0.987734\pi\) | ||
0.999258 | − | 0.0385242i | \(-0.0122657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.74418 | − | 2.66998i | −0.351538 | − | 0.163400i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.7189 | −0.958399 | −0.479199 | − | 0.877706i | \(-0.659073\pi\) | ||||
−0.479199 | + | 0.877706i | \(0.659073\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.18299 | − | 11.1507i | 0.313689 | − | 0.674869i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.633548 | 0.0380662 | 0.0190331 | − | 0.999819i | \(-0.493941\pi\) | ||||
0.0190331 | + | 0.999819i | \(0.493941\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.9233 | − | 10.0548i | 0.713829 | − | 0.601965i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.9204i | 1.24801i | 0.781422 | + | 0.624003i | \(0.214495\pi\) | ||||
−0.781422 | + | 0.624003i | \(0.785505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.6846i | 0.872911i | 0.899726 | + | 0.436455i | \(0.143766\pi\) | ||||
−0.899726 | + | 0.436455i | \(0.856234\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.50673i | − | 0.561165i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.9707 | −0.645335 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.7967 | + | 10.1314i | 1.27774 | + | 0.593914i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.49911i | − | 0.321262i | −0.987015 | − | 0.160631i | \(-0.948647\pi\) | ||
0.987015 | − | 0.160631i | \(-0.0513528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.12197 | + | 15.1600i | 0.239181 | + | 0.879672i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 49.9952i | 2.89129i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.48937i | 0.316402i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.1377 | + | 21.8101i | −0.582393 | + | 1.25296i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.11929i | 0.349246i | 0.984635 | + | 0.174623i | \(0.0558707\pi\) | ||||
−0.984635 | + | 0.174623i | \(0.944129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.37812 | − | 11.5705i | 0.305951 | − | 0.658221i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.75819 | −0.326517 | −0.163258 | − | 0.986583i | \(-0.552200\pi\) | ||||
−0.163258 | + | 0.986583i | \(0.552200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.9800i | 1.24238i | 0.783658 | + | 0.621192i | \(0.213351\pi\) | ||||
−0.783658 | + | 0.621192i | \(0.786649\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.6815i | − | 0.993091i | −0.868011 | − | 0.496545i | \(-0.834602\pi\) | ||
0.868011 | − | 0.496545i | \(-0.165398\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4759i | 0.642527i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.94333 | − | 12.7864i | 0.331724 | − | 0.713669i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.36583 | −0.242922 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.88227 | + | 4.12861i | 0.491190 | + | 0.228313i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.30117i | − | 0.126867i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.14134 | 0.392523 | 0.196262 | − | 0.980552i | \(-0.437120\pi\) | ||||
0.196262 | + | 0.980552i | \(0.437120\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.4827 | + | 14.8024i | 0.684048 | + | 0.811166i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.90663i | 0.103861i | 0.998651 | + | 0.0519303i | \(0.0165374\pi\) | ||||
−0.998651 | + | 0.0519303i | \(0.983463\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.38731 | − | 18.0444i | 0.455536 | − | 0.980038i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.7189 | −0.851226 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5969 | −0.842154 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.530510 | 0.0284793 | 0.0142396 | − | 0.999899i | \(-0.495467\pi\) | ||||
0.0142396 | + | 0.999899i | \(0.495467\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.36659i | 0.394325i | 0.980371 | + | 0.197162i | \(0.0631726\pi\) | ||||
−0.980371 | + | 0.197162i | \(0.936827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.3553 | + | 7.70974i | −1.51349 | + | 0.411516i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2299 | 0.597708 | 0.298854 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298854 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.25048 | − | 4.84167i | 0.119108 | − | 0.256248i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.0980 | −0.902396 | −0.451198 | − | 0.892424i | \(-0.649003\pi\) | ||||
−0.451198 | + | 0.892424i | \(0.649003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8387 | −0.833615 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.35695 | + | 2.91934i | −0.0712216 | + | 0.153226i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9984 | −0.730709 | −0.365355 | − | 0.930868i | \(-0.619052\pi\) | ||||
−0.365355 | + | 0.930868i | \(0.619052\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.3673 | + | 14.6457i | −0.904107 | + | 0.762424i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 15.1309i | − | 0.785559i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.5952 | −1.11815 | −0.559077 | − | 0.829116i | \(-0.688845\pi\) | ||||
−0.559077 | + | 0.829116i | \(0.688845\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.4645 | −1.10548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7780 | 0.604996 | 0.302498 | − | 0.953150i | \(-0.402180\pi\) | ||||
0.302498 | + | 0.953150i | \(0.402180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8484 | + | 34.0963i | −0.811940 | + | 1.74680i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.8484i | 0.809818i | 0.914357 | + | 0.404909i | \(0.132697\pi\) | ||||
−0.914357 | + | 0.404909i | \(0.867303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0282 | − | 8.45670i | 0.509763 | − | 0.429878i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4770 | −0.936822 | −0.468411 | − | 0.883511i | \(-0.655173\pi\) | ||||
−0.468411 | + | 0.883511i | \(0.655173\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.7081i | 1.09783i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.6666 | + | 9.14134i | 0.992050 | + | 0.461119i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3981 | −0.923373 | −0.461687 | − | 0.887043i | \(-0.652756\pi\) | ||||
−0.461687 | + | 0.887043i | \(0.652756\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.62958 | + | 3.50586i | −0.0815809 | + | 0.175513i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 0.183464i | − | 0.00916176i | −0.999990 | − | 0.00458088i | \(-0.998542\pi\) | ||
0.999990 | − | 0.00458088i | \(-0.00145814\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 29.4006i | − | 1.46455i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 19.5145i | − | 0.967299i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.5933 | 1.51274 | 0.756371 | − | 0.654142i | \(-0.226970\pi\) | ||||
0.756371 | + | 0.654142i | \(0.226970\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.4807 | + | 29.0023i | −0.664953 | + | 1.43058i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.16511i | − | 0.303365i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.47171 | − | 18.2260i | 0.414862 | − | 0.892531i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 13.9813i | − | 0.683032i | −0.939876 | − | 0.341516i | \(-0.889060\pi\) | ||
0.939876 | − | 0.341516i | \(-0.110940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.7297i | 1.30272i | 0.758767 | + | 0.651362i | \(0.225802\pi\) | ||||
−0.758767 | + | 0.651362i | \(0.774198\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.20388 | + | 3.54509i | −0.204400 | + | 0.172368i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 10.2513i | − | 0.496095i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.8552 | + | 12.4827i | 1.29658 | + | 0.602671i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.7794 | −1.67527 | −0.837633 | − | 0.546233i | \(-0.816061\pi\) | ||||
−0.837633 | + | 0.546233i | \(0.816061\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.8667i | − | 0.954731i | −0.878705 | − | 0.477366i | \(-0.841592\pi\) | ||
0.878705 | − | 0.477366i | \(-0.158408\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 15.7189i | − | 0.751937i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.85392i | − | 0.136210i | −0.997678 | − | 0.0681051i | \(-0.978305\pi\) | ||
0.997678 | − | 0.0681051i | \(-0.0216953\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.4900 | + | 12.4394i | 0.499524 | + | 0.592352i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.6854 | 0.650212 | 0.325106 | − | 0.945678i | \(-0.394600\pi\) | ||||
0.325106 | + | 0.945678i | \(0.394600\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.70484 | − | 18.7275i | 0.411725 | − | 0.885782i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.1132i | 0.902008i | 0.892522 | + | 0.451004i | \(0.148934\pi\) | ||||
−0.892522 | + | 0.451004i | \(0.851066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.8960 | 1.07813 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.7927 | + | 7.34070i | 0.742008 | + | 0.344896i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6133i | 1.05781i | 0.848682 | + | 0.528903i | \(0.177396\pi\) | ||||
−0.848682 | + | 0.528903i | \(0.822604\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.3120 | + | 3.34760i | −0.574674 | + | 0.156253i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.2199 | −0.615711 | −0.307855 | − | 0.951433i | \(-0.599611\pi\) | ||||
−0.307855 | + | 0.951433i | \(0.599611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.5506 | 1.88455 | 0.942273 | − | 0.334845i | \(-0.108684\pi\) | ||||
0.942273 | + | 0.334845i | \(0.108684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.2492 | −0.474276 | −0.237138 | − | 0.971476i | \(-0.576209\pi\) | ||||
−0.237138 | + | 0.971476i | \(0.576209\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.6766i | 0.493001i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.24952 | + | 2.68820i | −0.0575746 | + | 0.123866i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.2206 | −0.607883 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.6419 | + | 23.3101i | −1.26564 | + | 1.06730i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.4378 | −1.43643 | −0.718215 | − | 0.695821i | \(-0.755041\pi\) | ||||
−0.718215 | + | 0.695821i | \(0.755041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.5000 | 1.66425 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.4321 | + | 8.10270i | 0.793188 | + | 0.368686i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.177431 | 0.00804018 | 0.00402009 | − | 0.999992i | \(-0.498720\pi\) | ||||
0.00402009 | + | 0.999992i | \(0.498720\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.7820 | + | 8.73016i | 0.849352 | + | 0.394791i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.75623i | − | 0.350034i | −0.984565 | − | 0.175017i | \(-0.944002\pi\) | ||
0.984565 | − | 0.175017i | \(-0.0559980\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.31999 | −0.419751 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.79736 | 0.394616 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.22067 | 0.233709 | 0.116855 | − | 0.993149i | \(-0.462719\pi\) | ||||
0.116855 | + | 0.993149i | \(0.462719\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.916519 | − | 0.426011i | −0.0409470 | − | 0.0190328i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.34171i | 0.282763i | 0.989955 | + | 0.141381i | \(0.0451544\pi\) | ||||
−0.989955 | + | 0.141381i | \(0.954846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.8567 | + | 29.8113i | −0.615399 | + | 1.32397i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.1959 | −1.51571 | −0.757854 | − | 0.652425i | \(-0.773752\pi\) | ||||
−0.757854 | + | 0.652425i | \(0.773752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.76805i | 0.255164i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.91513 | − | 2.42401i | 0.393613 | − | 0.107023i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.54212 | 0.243742 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.9310 | + | 8.79941i | 0.830978 | + | 0.386251i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.6151i | 1.42889i | 0.699689 | + | 0.714447i | \(0.253322\pi\) | ||||
−0.699689 | + | 0.714447i | \(0.746678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.6074i | 0.638736i | 0.947631 | + | 0.319368i | \(0.103471\pi\) | ||||
−0.947631 | + | 0.319368i | \(0.896529\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12.7659i | − | 0.556091i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −55.1587 | −2.39820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.2627 | + | 9.49772i | −0.488759 | + | 0.412166i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.8246i | 1.85494i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.951024 | + | 0.442050i | 0.0410397 | + | 0.0190759i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 16.3993i | − | 0.706368i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.0217i | − | 0.559846i | −0.960023 | − | 0.279923i | \(-0.909691\pi\) | ||
0.960023 | − | 0.279923i | \(-0.0903089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1327 | + | 5.17466i | 0.477752 | + | 0.222066i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.8280i | 1.61741i | 0.588214 | + | 0.808705i | \(0.299831\pi\) | ||||
−0.588214 | + | 0.808705i | \(0.700169\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.7275 | + | 15.7927i | −0.799272 | + | 0.674018i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.74863 | 0.287501 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.24791i | − | 0.393261i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 22.0135i | − | 0.932744i | −0.884589 | − | 0.466372i | \(-0.845561\pi\) | ||
0.884589 | − | 0.466372i | \(-0.154439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 24.7278i | − | 1.04587i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.6607 | + | 5.42004i | 0.492313 | + | 0.228834i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.80727 | 0.413327 | 0.206664 | − | 0.978412i | \(-0.433739\pi\) | ||||
0.206664 | + | 0.978412i | \(0.433739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.90733 | + | 11.1363i | −0.0801002 | + | 0.467681i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 22.4555i | − | 0.941384i | −0.882298 | − | 0.470692i | \(-0.844004\pi\) | ||
0.882298 | − | 0.470692i | \(-0.155996\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.92867 | −0.248107 | −0.124054 | − | 0.992276i | \(-0.539589\pi\) | ||||
−0.124054 | + | 0.992276i | \(0.539589\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8209 | + | 29.7343i | −0.577378 | + | 1.24217i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.1587i | − | 1.63020i | −0.579322 | − | 0.815098i | \(-0.696683\pi\) | ||
0.579322 | − | 0.815098i | \(-0.303317\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.71200 | + | 3.11984i | 0.278941 | + | 0.129656i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.7736 | −0.820347 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.4413 | 1.50924 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.3332 | −1.21071 | −0.605356 | − | 0.795955i | \(-0.706969\pi\) | ||||
−0.605356 | + | 0.795955i | \(0.706969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.24381i | 0.380885i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.8484 | + | 7.36659i | 0.651918 | + | 0.303021i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.6525 | −1.01236 | −0.506179 | − | 0.862428i | \(-0.668942\pi\) | ||||
−0.506179 | + | 0.862428i | \(0.668942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.8740 | − | 13.8859i | −1.22266 | − | 0.568311i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.8638 | −1.22020 | −0.610102 | − | 0.792323i | \(-0.708871\pi\) | ||||
−0.610102 | + | 0.792323i | \(0.708871\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7267 | −0.723085 | −0.361543 | − | 0.932356i | \(-0.617750\pi\) | ||||
−0.361543 | + | 0.932356i | \(0.617750\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.5046 | − | 16.4480i | 0.794287 | − | 0.669814i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.8174 | −1.04790 | −0.523949 | − | 0.851750i | \(-0.675542\pi\) | ||||
−0.523949 | + | 0.851750i | \(0.675542\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.47875 | + | 7.48416i | −0.140966 | + | 0.303274i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3660i | 0.419363i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6866 | 0.673965 | 0.336982 | − | 0.941511i | \(-0.390594\pi\) | ||||
0.336982 | + | 0.941511i | \(0.390594\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.69514 | 0.350053 | 0.175027 | − | 0.984564i | \(-0.443999\pi\) | ||||
0.175027 | + | 0.984564i | \(0.443999\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.3727 | 0.818846 | 0.409423 | − | 0.912345i | \(-0.365730\pi\) | ||||
0.409423 | + | 0.912345i | \(0.365730\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.0528 | − | 44.3285i | −0.483663 | − | 1.77884i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.59114i | 0.183940i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.44351 | − | 3.92467i | −0.337201 | − | 0.156736i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8484 | 0.631919 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.51267i | 0.179647i | 0.995958 | + | 0.0898233i | \(0.0286302\pi\) | ||||
−0.995958 | + | 0.0898233i | \(0.971370\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.01198 | − | 8.63135i | 0.159462 | − | 0.343065i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.6732 | 1.21532 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.5529 | − | 16.0714i | −0.536143 | − | 0.635776i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 25.0424i | − | 0.989114i | −0.869145 | − | 0.494557i | \(-0.835330\pi\) | ||
0.869145 | − | 0.494557i | \(-0.164670\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.7360i | 0.857184i | 0.903498 | + | 0.428592i | \(0.140990\pi\) | ||||
−0.903498 | + | 0.428592i | \(0.859010\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 21.3476i | − | 0.839259i | −0.907695 | − | 0.419629i | \(-0.862160\pi\) | ||
0.907695 | − | 0.419629i | \(-0.137840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.8480 | 0.582836 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.2513 | − | 4.76495i | −0.401780 | − | 0.186753i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9387i | 1.01506i | 0.861634 | + | 0.507530i | \(0.169441\pi\) | ||||
−0.861634 | + | 0.507530i | \(0.830559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.5373 | − | 8.88603i | 0.411101 | − | 0.346677i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.6474i | 0.804307i | 0.915572 | + | 0.402153i | \(0.131738\pi\) | ||||
−0.915572 | + | 0.402153i | \(0.868262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 9.31999i | − | 0.362506i | −0.983437 | − | 0.181253i | \(-0.941985\pi\) | ||
0.983437 | − | 0.181253i | \(-0.0580152\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.1377 | + | 21.8101i | −0.393714 | + | 0.847034i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 33.5560i | − | 1.29929i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.62865 | − | 12.1094i | 0.217616 | − | 0.468178i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.6892 | 0.953115 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 37.2520i | − | 1.43596i | −0.696063 | − | 0.717980i | \(-0.745067\pi\) | ||
0.696063 | − | 0.717980i | \(-0.254933\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.0665i | 1.42458i | 0.701885 | + | 0.712290i | \(0.252342\pi\) | ||||
−0.701885 | + | 0.712290i | \(0.747658\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17.4214i | − | 0.668571i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.40535 | + | 11.6290i | −0.207133 | + | 0.445626i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0898 | 0.998297 | 0.499149 | − | 0.866516i | \(-0.333646\pi\) | ||||
0.499149 | + | 0.866516i | \(0.333646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.9071 | + | 12.5068i | 1.02657 | + | 0.477165i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 68.1598i | 2.59668i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.8187 | −1.32457 | −0.662283 | − | 0.749254i | \(-0.730412\pi\) | ||||
−0.662283 | + | 0.749254i | \(0.730412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.70484 | − | 7.34070i | 0.330669 | − | 0.278850i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.5946i | 0.704323i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.02799 | − | 2.21160i | 0.0388820 | − | 0.0836505i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.7188 | −0.480383 | −0.240192 | − | 0.970725i | \(-0.577210\pi\) | ||||
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4759 | −0.432822 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.4321 | 0.655602 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.7263i | 1.75484i | 0.479721 | + | 0.877421i | \(0.340738\pi\) | ||||
−0.479721 | + | 0.877421i | \(0.659262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.8945 | + | 14.2470i | −0.633593 | + | 0.534303i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.9628 | 1.72132 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.94058 | − | 14.9319i | 0.259201 | − | 0.557643i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.50673 | 0.354541 | 0.177271 | − | 0.984162i | \(-0.443273\pi\) | ||||
0.177271 | + | 0.984162i | \(0.443273\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.24791 | −0.344410 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.65970 | + | 3.57067i | −0.0617249 | + | 0.132795i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.7629 | 1.17802 | 0.589011 | − | 0.808125i | \(-0.299518\pi\) | ||||
0.589011 | + | 0.808125i | \(0.299518\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.2827 | − | 13.6718i | 0.862321 | − | 0.506362i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 10.7369i | − | 0.397119i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.5852 | −0.575653 | −0.287826 | − | 0.957683i | \(-0.592933\pi\) | ||||
−0.287826 | + | 0.957683i | \(0.592933\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.7135 | −0.947171 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.17997 | 0.153763 | 0.0768813 | − | 0.997040i | \(-0.475504\pi\) | ||||
0.0768813 | + | 0.997040i | \(0.475504\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.34070 | − | 15.7927i | 0.269667 | − | 0.580161i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.1805i | 0.740351i | 0.928962 | + | 0.370176i | \(0.120702\pi\) | ||||
−0.928962 | + | 0.370176i | \(0.879298\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.4624 | + | 36.1233i | 1.11456 | + | 1.32168i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.2198 | −0.373423 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 19.0316i | − | 0.694474i | −0.937777 | − | 0.347237i | \(-0.887120\pi\) | ||
0.937777 | − | 0.347237i | \(-0.112880\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.9178 | − | 6.93400i | −0.543633 | − | 0.252689i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.22227 | −0.153461 | −0.0767305 | − | 0.997052i | \(-0.524448\pi\) | ||||
−0.0767305 | + | 0.997052i | \(0.524448\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.5145 | + | 41.9834i | −0.708332 | + | 1.52390i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 38.0795i | − | 1.38038i | −0.723628 | − | 0.690190i | \(-0.757527\pi\) | ||
0.723628 | − | 0.690190i | \(-0.242473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 7.09931i | − | 0.257012i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.7717i | 1.00278i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9600 | −0.611595 | −0.305797 | − | 0.952097i | \(-0.598923\pi\) | ||||
−0.305797 | + | 0.952097i | \(0.598923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.9414 | − | 42.9018i | 0.718172 | − | 1.54507i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 16.3849i | − | 0.589324i | −0.955602 | − | 0.294662i | \(-0.904793\pi\) | ||
0.955602 | − | 0.294662i | \(-0.0952070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.91554 | − | 12.7267i | 0.212219 | − | 0.456566i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 13.4644i | − | 0.482413i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.1875i | 0.758150i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.0316 | − | 5.17466i | 0.680135 | − | 0.184927i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.6833i | − | 0.915511i | −0.889078 | − | 0.457756i | \(-0.848653\pi\) | ||
0.889078 | − | 0.457756i | \(-0.151347\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.96257 | + | 0.912234i | 0.0698695 | + | 0.0324764i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4223 | −0.512799 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.1787i | 1.63985i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.7563i | 0.487274i | 0.969866 | + | 0.243637i | \(0.0783406\pi\) | ||||
−0.969866 | + | 0.243637i | \(0.921659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.50096i | 0.159232i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.38731 | − | 7.07293i | 0.296351 | − | 0.249910i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.8918 | −0.490229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.4759 | − | 24.6892i | 0.403971 | − | 0.869100i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.42314i | − | 0.225826i | −0.993605 | − | 0.112913i | \(-0.963982\pi\) | ||
0.993605 | − | 0.112913i | \(-0.0360181\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.8353 | 1.43392 | 0.716961 | − | 0.697114i | \(-0.245533\pi\) | ||||
0.716961 | + | 0.697114i | \(0.245533\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.77462i | 0.271999i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.7300 | + | 16.2815i | 0.479767 | + | 0.568923i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.8774 | 1.81053 | 0.905267 | − | 0.424844i | \(-0.139671\pi\) | ||||
0.905267 | + | 0.424844i | \(0.139671\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.0379 | 1.25620 | 0.628102 | − | 0.778131i | \(-0.283832\pi\) | ||||
0.628102 | + | 0.778131i | \(0.283832\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.8501 | 1.03799 | 0.518995 | − | 0.854777i | \(-0.326306\pi\) | ||||
0.518995 | + | 0.854777i | \(0.326306\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.2287i | 0.772035i | 0.922492 | + | 0.386017i | \(0.126150\pi\) | ||||
−0.922492 | + | 0.386017i | \(0.873850\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.462534 | + | 0.995094i | −0.0160451 | + | 0.0345194i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.3185 | 0.461457 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.08790 | + | 26.0682i | 0.244994 | + | 0.901050i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.17466 | 0.178649 | 0.0893246 | − | 0.996003i | \(-0.471529\pi\) | ||||
0.0893246 | + | 0.996003i | \(0.471529\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5933 | −0.503218 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.8590 | − | 15.2733i | −1.13172 | − | 0.526042i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.33334 | 0.0801745 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.0647 | − | 10.7208i | −0.791578 | − | 0.367937i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57.0613i | 1.95604i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.3283 | 1.24386 | 0.621929 | − | 0.783073i | \(-0.286349\pi\) | ||||
0.621929 | + | 0.783073i | \(0.286349\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.42274 | 0.321875 | 0.160937 | − | 0.986965i | \(-0.448548\pi\) | ||||
0.160937 | + | 0.986965i | \(0.448548\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.0480 | 0.615789 | 0.307894 | − | 0.951421i | \(-0.400376\pi\) | ||||
0.307894 | + | 0.951421i | \(0.400376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.9319 | + | 6.94058i | 0.508879 | + | 0.236534i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.3475i | − | 0.624555i | −0.949991 | − | 0.312278i | \(-0.898908\pi\) | ||
0.949991 | − | 0.312278i | \(-0.101092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.00937 | − | 17.2313i | 0.272013 | − | 0.585206i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.2726 | 0.755547 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 48.0946i | − | 1.62962i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.8262 | + | 26.8387i | −1.07715 | + | 0.908352i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.5736 | 0.559651 | 0.279826 | − | 0.960051i | \(-0.409723\pi\) | ||||
0.279826 | + | 0.960051i | \(0.409723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.63728 | + | 4.01474i | 0.291328 | + | 0.135414i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.5865i | 0.862031i | 0.902345 | + | 0.431015i | \(0.141845\pi\) | ||||
−0.902345 | + | 0.431015i | \(0.858155\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21.2127i | − | 0.713863i | −0.934131 | − | 0.356931i | \(-0.883823\pi\) | ||
0.934131 | − | 0.356931i | \(-0.116177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.2727i | 0.848574i | 0.905528 | + | 0.424287i | \(0.139475\pi\) | ||||
−0.905528 | + | 0.424287i | \(0.860525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.2520 | 0.914004 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.8206 | − | 4.59360i | −0.898525 | − | 0.153891i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3.25915i | − | 0.109063i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −78.5258 | − | 36.5000i | −2.62190 | − | 1.21870i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.7333i | 0.658142i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.5953i | 0.985962i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.62198 | − | 4.00762i | −0.286921 | − | 0.133365i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 22.7267i | − | 0.754626i | −0.926086 | − | 0.377313i | \(-0.876848\pi\) | ||
0.926086 | − | 0.377313i | \(-0.123152\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.8552 | − | 31.8458i | −0.890731 | − | 1.05626i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.92321 | 0.295639 | 0.147820 | − | 0.989014i | \(-0.452774\pi\) | ||||
0.147820 | + | 0.989014i | \(0.452774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 47.6226i | − | 1.57608i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 15.7189i | − | 0.519084i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 33.7531i | − | 1.11341i | −0.830710 | − | 0.556706i | \(-0.812065\pi\) | ||
0.830710 | − | 0.556706i | \(-0.187935\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.61137 | − | 4.46751i | −0.316705 | − | 0.147209i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.6292 | −1.30441 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.2470 | + | 16.8945i | 0.467932 | + | 0.554888i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 51.1823i | − | 1.67924i | −0.543177 | − | 0.839618i | \(-0.682779\pi\) | ||
0.543177 | − | 0.839618i | \(-0.317221\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.64393 | −0.316067 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.20388 | − | 9.04420i | 0.137629 | − | 0.296094i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.9974i | 1.86202i | 0.364990 | + | 0.931011i | \(0.381072\pi\) | ||||
−0.364990 | + | 0.931011i | \(0.618928\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.5233 | − | 16.0470i | −1.12663 | − | 0.523672i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.1960 | 1.21255 | 0.606277 | − | 0.795253i | \(-0.292662\pi\) | ||||
0.606277 | + | 0.795253i | \(0.292662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −66.9488 | −2.18015 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.5775 | −1.18861 | −0.594305 | − | 0.804240i | \(-0.702573\pi\) | ||||
−0.594305 | + | 0.804240i | \(0.702573\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 25.9831i | − | 0.843449i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.7717 | + | 12.9087i | 0.900560 | + | 0.418594i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.3524 | 0.983211 | 0.491606 | − | 0.870818i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870818i | \(0.336410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.0248 | − | 8.37821i | −0.582660 | − | 0.270829i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23.1806 | 0.748540 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.97070 | 0.128087 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.7442 | + | 18.6700i | 0.507350 | + | 0.601632i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.8174 | −0.830232 | −0.415116 | − | 0.909768i | \(-0.636259\pi\) | ||||
−0.415116 | + | 0.909768i | \(0.636259\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.18736 | − | 6.85728i | 0.102393 | − | 0.220287i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9904i | 0.737796i | 0.929470 | + | 0.368898i | \(0.120265\pi\) | ||||
−0.929470 | + | 0.368898i | \(0.879735\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.5675 | −0.467011 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.2952 | 1.16119 | 0.580593 | − | 0.814194i | \(-0.302821\pi\) | ||||
0.580593 | + | 0.814194i | \(0.302821\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.0573 | −0.353393 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.9693 | + | 10.9369i | −0.414079 | + | 0.349189i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.92523i | − | 0.220881i | −0.993883 | − | 0.110440i | \(-0.964774\pi\) | ||
0.993883 | − | 0.110440i | \(-0.0352261\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.61437 | + | 1.68001i | 0.115047 | + | 0.0534754i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 38.6575 | 1.22924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.7182i | − | 1.35699i | −0.734605 | − | 0.678495i | \(-0.762633\pi\) | ||
0.734605 | − | 0.678495i | \(-0.237367\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.21367 | + | 11.2167i | −0.165451 | + | 0.355950i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.7743 | −0.499579 | −0.249789 | − | 0.968300i | \(-0.580361\pi\) | ||||
−0.249789 | + | 0.968300i | \(0.580361\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −32.3629 | + | 8.79941i | −1.02392 | + | 0.278401i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))