Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(24,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("575.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.b (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: | \(4.59139811622\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 23) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.24 |
Dual form | 575.2.b.d.24.4 |
$q$-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 \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.61803i | − 1.14412i | −0.820211 | − | 0.572061i | \(-0.806144\pi\) | ||||
0.820211 | − | 0.572061i | \(-0.193856\pi\) | |||||||
\(3\) | − 2.23607i | − 1.29099i | −0.763763 | − | 0.645497i | \(-0.776650\pi\) | ||||
0.763763 | − | 0.645497i | \(-0.223350\pi\) | |||||||
\(4\) | −0.618034 | −0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.61803 | −1.47706 | ||||||||
\(7\) | − 1.23607i | − 0.467190i | −0.972334 | − | 0.233595i | \(-0.924951\pi\) | ||||
0.972334 | − | 0.233595i | \(-0.0750489\pi\) | |||||||
\(8\) | − 2.23607i | − 0.790569i | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.763932 | −0.230334 | −0.115167 | − | 0.993346i | \(-0.536740\pi\) | ||||
−0.115167 | + | 0.993346i | \(0.536740\pi\) | |||||||
\(12\) | 1.38197i | 0.398939i | ||||||||
\(13\) | − 3.00000i | − 0.832050i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) | ||||
0.909353 | − | 0.416025i | \(-0.136577\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 5.23607i | 1.26993i | 0.772540 | + | 0.634967i | \(0.218986\pi\) | ||||
−0.772540 | + | 0.634967i | \(0.781014\pi\) | |||||||
\(18\) | 3.23607i | 0.762749i | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.76393 | −0.603139 | ||||||||
\(22\) | 1.23607i | 0.263531i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | −5.00000 | −1.02062 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.85410 | −0.951968 | ||||||||
\(27\) | − 2.23607i | − 0.430331i | ||||||||
\(28\) | 0.763932i | 0.144370i | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.70820 | −1.20483 | −0.602414 | − | 0.798183i | \(-0.705795\pi\) | ||||
−0.602414 | + | 0.798183i | \(0.705795\pi\) | |||||||
\(32\) | 3.38197i | 0.597853i | ||||||||
\(33\) | 1.70820i | 0.297360i | ||||||||
\(34\) | 8.47214 | 1.45296 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.23607 | 0.206011 | ||||||||
\(37\) | 3.23607i | 0.532006i | 0.963972 | + | 0.266003i | \(0.0857032\pi\) | ||||
−0.963972 | + | 0.266003i | \(0.914297\pi\) | |||||||
\(38\) | − 3.23607i | − 0.524960i | ||||||||
\(39\) | −6.70820 | −1.07417 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.47214 | 0.854604 | 0.427302 | − | 0.904109i | \(-0.359464\pi\) | ||||
0.427302 | + | 0.904109i | \(0.359464\pi\) | |||||||
\(42\) | 4.47214i | 0.690066i | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0.472136 | 0.0711772 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.61803 | −0.238566 | ||||||||
\(47\) | 2.23607i | 0.326164i | 0.986613 | + | 0.163082i | \(0.0521435\pi\) | ||||
−0.986613 | + | 0.163082i | \(0.947856\pi\) | |||||||
\(48\) | 10.8541i | 1.56665i | ||||||||
\(49\) | 5.47214 | 0.781734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.7082 | 1.63948 | ||||||||
\(52\) | 1.85410i | 0.257118i | ||||||||
\(53\) | 8.47214i | 1.16374i | 0.813283 | + | 0.581869i | \(0.197678\pi\) | ||||
−0.813283 | + | 0.581869i | \(0.802322\pi\) | |||||||
\(54\) | −3.61803 | −0.492352 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.76393 | −0.369346 | ||||||||
\(57\) | − 4.47214i | − 0.592349i | ||||||||
\(58\) | − 4.85410i | − 0.637375i | ||||||||
\(59\) | 2.47214 | 0.321845 | 0.160922 | − | 0.986967i | \(-0.448553\pi\) | ||||
0.160922 | + | 0.986967i | \(0.448553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9443 | 1.40127 | 0.700635 | − | 0.713520i | \(-0.252900\pi\) | ||||
0.700635 | + | 0.713520i | \(0.252900\pi\) | |||||||
\(62\) | 10.8541i | 1.37847i | ||||||||
\(63\) | 2.47214i | 0.311460i | ||||||||
\(64\) | −4.23607 | −0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.76393 | 0.340217 | ||||||||
\(67\) | − 7.23607i | − 0.884026i | −0.897009 | − | 0.442013i | \(-0.854264\pi\) | ||||
0.897009 | − | 0.442013i | \(-0.145736\pi\) | |||||||
\(68\) | − 3.23607i | − 0.392431i | ||||||||
\(69\) | −2.23607 | −0.269191 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.76393 | 0.921409 | 0.460705 | − | 0.887554i | \(-0.347597\pi\) | ||||
0.460705 | + | 0.887554i | \(0.347597\pi\) | |||||||
\(72\) | 4.47214i | 0.527046i | ||||||||
\(73\) | − 15.4721i | − 1.81088i | −0.424478 | − | 0.905438i | \(-0.639542\pi\) | ||||
0.424478 | − | 0.905438i | \(-0.360458\pi\) | |||||||
\(74\) | 5.23607 | 0.608681 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.23607 | −0.141787 | ||||||||
\(77\) | 0.944272i | 0.107610i | ||||||||
\(78\) | 10.8541i | 1.22899i | ||||||||
\(79\) | −6.94427 | −0.781292 | −0.390646 | − | 0.920541i | \(-0.627748\pi\) | ||||
−0.390646 | + | 0.920541i | \(0.627748\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | − 8.85410i | − 0.977772i | ||||||||
\(83\) | 13.2361i | 1.45285i | 0.687247 | + | 0.726424i | \(0.258819\pi\) | ||||
−0.687247 | + | 0.726424i | \(0.741181\pi\) | |||||||
\(84\) | 1.70820 | 0.186380 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 6.70820i | − 0.719195i | ||||||||
\(88\) | 1.70820i | 0.182095i | ||||||||
\(89\) | 1.52786 | 0.161953 | 0.0809766 | − | 0.996716i | \(-0.474196\pi\) | ||||
0.0809766 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.70820 | −0.388725 | ||||||||
\(92\) | 0.618034i | 0.0644345i | ||||||||
\(93\) | 15.0000i | 1.55543i | ||||||||
\(94\) | 3.61803 | 0.373172 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.56231 | 0.771825 | ||||||||
\(97\) | 4.29180i | 0.435766i | 0.975975 | + | 0.217883i | \(0.0699151\pi\) | ||||
−0.975975 | + | 0.217883i | \(0.930085\pi\) | |||||||
\(98\) | − 8.85410i | − 0.894399i | ||||||||
\(99\) | 1.52786 | 0.153556 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.47214 | −0.444994 | −0.222497 | − | 0.974933i | \(-0.571421\pi\) | ||||
−0.222497 | + | 0.974933i | \(0.571421\pi\) | |||||||
\(102\) | − 18.9443i | − 1.87576i | ||||||||
\(103\) | − 18.1803i | − 1.79136i | −0.444697 | − | 0.895681i | \(-0.646689\pi\) | ||||
0.444697 | − | 0.895681i | \(-0.353311\pi\) | |||||||
\(104\) | −6.70820 | −0.657794 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.7082 | 1.33146 | ||||||||
\(107\) | − 13.4164i | − 1.29701i | −0.761209 | − | 0.648507i | \(-0.775394\pi\) | ||||
0.761209 | − | 0.648507i | \(-0.224606\pi\) | |||||||
\(108\) | 1.38197i | 0.132980i | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.23607 | 0.686817 | ||||||||
\(112\) | 6.00000i | 0.566947i | ||||||||
\(113\) | − 13.2361i | − 1.24514i | −0.782562 | − | 0.622572i | \(-0.786088\pi\) | ||||
0.782562 | − | 0.622572i | \(-0.213912\pi\) | |||||||
\(114\) | −7.23607 | −0.677720 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.85410 | −0.172149 | ||||||||
\(117\) | 6.00000i | 0.554700i | ||||||||
\(118\) | − 4.00000i | − 0.368230i | ||||||||
\(119\) | 6.47214 | 0.593300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | − 17.7082i | − 1.60323i | ||||||||
\(123\) | − 12.2361i | − 1.10329i | ||||||||
\(124\) | 4.14590 | 0.372313 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | − 20.7082i | − 1.83756i | −0.394775 | − | 0.918778i | \(-0.629177\pi\) | ||||
0.394775 | − | 0.918778i | \(-0.370823\pi\) | |||||||
\(128\) | 13.6180i | 1.20368i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.29180 | 0.462346 | 0.231173 | − | 0.972913i | \(-0.425744\pi\) | ||||
0.231173 | + | 0.972913i | \(0.425744\pi\) | |||||||
\(132\) | − 1.05573i | − 0.0918893i | ||||||||
\(133\) | − 2.47214i | − 0.214361i | ||||||||
\(134\) | −11.7082 | −1.01143 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.7082 | 1.00397 | ||||||||
\(137\) | 13.8885i | 1.18658i | 0.804989 | + | 0.593289i | \(0.202171\pi\) | ||||
−0.804989 | + | 0.593289i | \(0.797829\pi\) | |||||||
\(138\) | 3.61803i | 0.307988i | ||||||||
\(139\) | −2.70820 | −0.229707 | −0.114853 | − | 0.993382i | \(-0.536640\pi\) | ||||
−0.114853 | + | 0.993382i | \(0.536640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.00000 | 0.421076 | ||||||||
\(142\) | − 12.5623i | − 1.05421i | ||||||||
\(143\) | 2.29180i | 0.191650i | ||||||||
\(144\) | 9.70820 | 0.809017 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −25.0344 | −2.07187 | ||||||||
\(147\) | − 12.2361i | − 1.00921i | ||||||||
\(148\) | − 2.00000i | − 0.164399i | ||||||||
\(149\) | 11.8885 | 0.973947 | 0.486974 | − | 0.873417i | \(-0.338101\pi\) | ||||
0.486974 | + | 0.873417i | \(0.338101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.236068 | −0.0192109 | −0.00960547 | − | 0.999954i | \(-0.503058\pi\) | ||||
−0.00960547 | + | 0.999954i | \(0.503058\pi\) | |||||||
\(152\) | − 4.47214i | − 0.362738i | ||||||||
\(153\) | − 10.4721i | − 0.846622i | ||||||||
\(154\) | 1.52786 | 0.123119 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.14590 | 0.331937 | ||||||||
\(157\) | 15.4164i | 1.23036i | 0.788385 | + | 0.615182i | \(0.210917\pi\) | ||||
−0.788385 | + | 0.615182i | \(0.789083\pi\) | |||||||
\(158\) | 11.2361i | 0.893894i | ||||||||
\(159\) | 18.9443 | 1.50238 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.23607 | −0.0974158 | ||||||||
\(162\) | 17.7984i | 1.39837i | ||||||||
\(163\) | 10.2361i | 0.801751i | 0.916133 | + | 0.400875i | \(0.131294\pi\) | ||||
−0.916133 | + | 0.400875i | \(0.868706\pi\) | |||||||
\(164\) | −3.38197 | −0.264087 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.4164 | 1.66224 | ||||||||
\(167\) | 10.4721i | 0.810358i | 0.914237 | + | 0.405179i | \(0.132791\pi\) | ||||
−0.914237 | + | 0.405179i | \(0.867209\pi\) | |||||||
\(168\) | 6.18034i | 0.476824i | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 5.05573i | − 0.384380i | −0.981358 | − | 0.192190i | \(-0.938441\pi\) | ||||
0.981358 | − | 0.192190i | \(-0.0615590\pi\) | |||||||
\(174\) | −10.8541 | −0.822847 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.70820 | 0.279516 | ||||||||
\(177\) | − 5.52786i | − 0.415500i | ||||||||
\(178\) | − 2.47214i | − 0.185294i | ||||||||
\(179\) | 12.7082 | 0.949856 | 0.474928 | − | 0.880025i | \(-0.342474\pi\) | ||||
0.474928 | + | 0.880025i | \(0.342474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6525 | −1.08911 | −0.544555 | − | 0.838725i | \(-0.683301\pi\) | ||||
−0.544555 | + | 0.838725i | \(0.683301\pi\) | |||||||
\(182\) | 6.00000i | 0.444750i | ||||||||
\(183\) | − 24.4721i | − 1.80903i | ||||||||
\(184\) | −2.23607 | −0.164845 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 24.2705 | 1.77960 | ||||||||
\(187\) | − 4.00000i | − 0.292509i | ||||||||
\(188\) | − 1.38197i | − 0.100790i | ||||||||
\(189\) | −2.76393 | −0.201046 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.81966 | −0.276381 | −0.138190 | − | 0.990406i | \(-0.544129\pi\) | ||||
−0.138190 | + | 0.990406i | \(0.544129\pi\) | |||||||
\(192\) | 9.47214i | 0.683593i | ||||||||
\(193\) | 7.94427i | 0.571841i | 0.958253 | + | 0.285921i | \(0.0922994\pi\) | ||||
−0.958253 | + | 0.285921i | \(0.907701\pi\) | |||||||
\(194\) | 6.94427 | 0.498570 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.38197 | −0.241569 | ||||||||
\(197\) | 7.47214i | 0.532368i | 0.963922 | + | 0.266184i | \(0.0857628\pi\) | ||||
−0.963922 | + | 0.266184i | \(0.914237\pi\) | |||||||
\(198\) | − 2.47214i | − 0.175687i | ||||||||
\(199\) | 25.7082 | 1.82241 | 0.911203 | − | 0.411957i | \(-0.135155\pi\) | ||||
0.911203 | + | 0.411957i | \(0.135155\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.1803 | −1.14127 | ||||||||
\(202\) | 7.23607i | 0.509128i | ||||||||
\(203\) | − 3.70820i | − 0.260265i | ||||||||
\(204\) | −7.23607 | −0.506626 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −29.4164 | −2.04954 | ||||||||
\(207\) | 2.00000i | 0.139010i | ||||||||
\(208\) | 14.5623i | 1.00971i | ||||||||
\(209\) | −1.52786 | −0.105685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.41641 | 0.235195 | 0.117598 | − | 0.993061i | \(-0.462481\pi\) | ||||
0.117598 | + | 0.993061i | \(0.462481\pi\) | |||||||
\(212\) | − 5.23607i | − 0.359615i | ||||||||
\(213\) | − 17.3607i | − 1.18953i | ||||||||
\(214\) | −21.7082 | −1.48394 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 8.29180i | 0.562884i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −34.5967 | −2.33783 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.7082 | 1.05665 | ||||||||
\(222\) | − 11.7082i | − 0.785803i | ||||||||
\(223\) | − 4.00000i | − 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 4.18034 | 0.279311 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.4164 | −1.42460 | ||||||||
\(227\) | 10.1803i | 0.675693i | 0.941201 | + | 0.337846i | \(0.109698\pi\) | ||||
−0.941201 | + | 0.337846i | \(0.890302\pi\) | |||||||
\(228\) | 2.76393i | 0.183046i | ||||||||
\(229\) | 12.0000 | 0.792982 | 0.396491 | − | 0.918039i | \(-0.370228\pi\) | ||||
0.396491 | + | 0.918039i | \(0.370228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.11146 | 0.138924 | ||||||||
\(232\) | − 6.70820i | − 0.440415i | ||||||||
\(233\) | 15.4721i | 1.01361i | 0.862060 | + | 0.506807i | \(0.169174\pi\) | ||||
−0.862060 | + | 0.506807i | \(0.830826\pi\) | |||||||
\(234\) | 9.70820 | 0.634645 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.52786 | −0.0994555 | ||||||||
\(237\) | 15.5279i | 1.00864i | ||||||||
\(238\) | − 10.4721i | − 0.678808i | ||||||||
\(239\) | −18.2361 | −1.17959 | −0.589797 | − | 0.807552i | \(-0.700792\pi\) | ||||
−0.589797 | + | 0.807552i | \(0.700792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.1246 | 1.10309 | 0.551547 | − | 0.834144i | \(-0.314038\pi\) | ||||
0.551547 | + | 0.834144i | \(0.314038\pi\) | |||||||
\(242\) | 16.8541i | 1.08342i | ||||||||
\(243\) | 17.8885i | 1.14755i | ||||||||
\(244\) | −6.76393 | −0.433016 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −19.7984 | −1.26230 | ||||||||
\(247\) | − 6.00000i | − 0.381771i | ||||||||
\(248\) | 15.0000i | 0.952501i | ||||||||
\(249\) | 29.5967 | 1.87562 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7082 | 0.991493 | 0.495747 | − | 0.868467i | \(-0.334895\pi\) | ||||
0.495747 | + | 0.868467i | \(0.334895\pi\) | |||||||
\(252\) | − 1.52786i | − 0.0962464i | ||||||||
\(253\) | 0.763932i | 0.0480280i | ||||||||
\(254\) | −33.5066 | −2.10239 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 1.47214i | 0.0918293i | 0.998945 | + | 0.0459147i | \(0.0146202\pi\) | ||||
−0.998945 | + | 0.0459147i | \(0.985380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | − 8.56231i | − 0.528981i | ||||||||
\(263\) | 14.9443i | 0.921503i | 0.887529 | + | 0.460752i | \(0.152420\pi\) | ||||
−0.887529 | + | 0.460752i | \(0.847580\pi\) | |||||||
\(264\) | 3.81966 | 0.235084 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.00000 | −0.245256 | ||||||||
\(267\) | − 3.41641i | − 0.209081i | ||||||||
\(268\) | 4.47214i | 0.273179i | ||||||||
\(269\) | −9.94427 | −0.606313 | −0.303156 | − | 0.952941i | \(-0.598040\pi\) | ||||
−0.303156 | + | 0.952941i | \(0.598040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | − 25.4164i | − 1.54110i | ||||||||
\(273\) | 8.29180i | 0.501842i | ||||||||
\(274\) | 22.4721 | 1.35759 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.38197 | 0.0831846 | ||||||||
\(277\) | 6.52786i | 0.392221i | 0.980582 | + | 0.196111i | \(0.0628312\pi\) | ||||
−0.980582 | + | 0.196111i | \(0.937169\pi\) | |||||||
\(278\) | 4.38197i | 0.262813i | ||||||||
\(279\) | 13.4164 | 0.803219 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.2361 | −0.789598 | −0.394799 | − | 0.918768i | \(-0.629186\pi\) | ||||
−0.394799 | + | 0.918768i | \(0.629186\pi\) | |||||||
\(282\) | − 8.09017i | − 0.481763i | ||||||||
\(283\) | − 14.2918i | − 0.849559i | −0.905297 | − | 0.424780i | \(-0.860352\pi\) | ||||
0.905297 | − | 0.424780i | \(-0.139648\pi\) | |||||||
\(284\) | −4.79837 | −0.284731 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.70820 | 0.219271 | ||||||||
\(287\) | − 6.76393i | − 0.399262i | ||||||||
\(288\) | − 6.76393i | − 0.398569i | ||||||||
\(289\) | −10.4164 | −0.612730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.59675 | 0.562571 | ||||||||
\(292\) | 9.56231i | 0.559592i | ||||||||
\(293\) | 10.4721i | 0.611789i | 0.952065 | + | 0.305894i | \(0.0989554\pi\) | ||||
−0.952065 | + | 0.305894i | \(0.901045\pi\) | |||||||
\(294\) | −19.7984 | −1.15466 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.23607 | 0.420588 | ||||||||
\(297\) | 1.70820i | 0.0991200i | ||||||||
\(298\) | − 19.2361i | − 1.11432i | ||||||||
\(299\) | −3.00000 | −0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.381966i | 0.0219797i | ||||||||
\(303\) | 10.0000i | 0.574485i | ||||||||
\(304\) | −9.70820 | −0.556804 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −16.9443 | −0.968640 | ||||||||
\(307\) | 18.4721i | 1.05426i | 0.849785 | + | 0.527130i | \(0.176732\pi\) | ||||
−0.849785 | + | 0.527130i | \(0.823268\pi\) | |||||||
\(308\) | − 0.583592i | − 0.0332532i | ||||||||
\(309\) | −40.6525 | −2.31264 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.18034 | −0.520569 | −0.260285 | − | 0.965532i | \(-0.583816\pi\) | ||||
−0.260285 | + | 0.965532i | \(0.583816\pi\) | |||||||
\(312\) | 15.0000i | 0.849208i | ||||||||
\(313\) | 20.3607i | 1.15085i | 0.817853 | + | 0.575427i | \(0.195164\pi\) | ||||
−0.817853 | + | 0.575427i | \(0.804836\pi\) | |||||||
\(314\) | 24.9443 | 1.40769 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.29180 | 0.241432 | ||||||||
\(317\) | − 1.41641i | − 0.0795534i | −0.999209 | − | 0.0397767i | \(-0.987335\pi\) | ||||
0.999209 | − | 0.0397767i | \(-0.0126647\pi\) | |||||||
\(318\) | − 30.6525i | − 1.71891i | ||||||||
\(319\) | −2.29180 | −0.128316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.0000 | −1.67444 | ||||||||
\(322\) | 2.00000i | 0.111456i | ||||||||
\(323\) | 10.4721i | 0.582685i | ||||||||
\(324\) | 6.79837 | 0.377687 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.5623 | 0.917301 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 12.2361i | − 0.675624i | ||||||||
\(329\) | 2.76393 | 0.152381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6525 | 0.640478 | 0.320239 | − | 0.947337i | \(-0.396237\pi\) | ||||
0.320239 | + | 0.947337i | \(0.396237\pi\) | |||||||
\(332\) | − 8.18034i | − 0.448954i | ||||||||
\(333\) | − 6.47214i | − 0.354671i | ||||||||
\(334\) | 16.9443 | 0.927149 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 13.4164 | 0.731925 | ||||||||
\(337\) | − 3.41641i | − 0.186104i | −0.995661 | − | 0.0930518i | \(-0.970338\pi\) | ||||
0.995661 | − | 0.0930518i | \(-0.0296622\pi\) | |||||||
\(338\) | − 6.47214i | − 0.352038i | ||||||||
\(339\) | −29.5967 | −1.60747 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.12461 | 0.277513 | ||||||||
\(342\) | 6.47214i | 0.349973i | ||||||||
\(343\) | − 15.4164i | − 0.832408i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.18034 | −0.439778 | ||||||||
\(347\) | 25.8885i | 1.38977i | 0.719121 | + | 0.694885i | \(0.244545\pi\) | ||||
−0.719121 | + | 0.694885i | \(0.755455\pi\) | |||||||
\(348\) | 4.14590i | 0.222243i | ||||||||
\(349\) | 2.41641 | 0.129347 | 0.0646737 | − | 0.997906i | \(-0.479399\pi\) | ||||
0.0646737 | + | 0.997906i | \(0.479399\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.70820 | −0.358057 | ||||||||
\(352\) | − 2.58359i | − 0.137706i | ||||||||
\(353\) | 35.3607i | 1.88206i | 0.338324 | + | 0.941030i | \(0.390140\pi\) | ||||
−0.338324 | + | 0.941030i | \(0.609860\pi\) | |||||||
\(354\) | −8.94427 | −0.475383 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.944272 | −0.0500463 | ||||||||
\(357\) | − 14.4721i | − 0.765947i | ||||||||
\(358\) | − 20.5623i | − 1.08675i | ||||||||
\(359\) | −15.8885 | −0.838565 | −0.419283 | − | 0.907856i | \(-0.637718\pi\) | ||||
−0.419283 | + | 0.907856i | \(0.637718\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 23.7082i | 1.24608i | ||||||||
\(363\) | 23.2918i | 1.22250i | ||||||||
\(364\) | 2.29180 | 0.120123 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −39.5967 | −2.06976 | ||||||||
\(367\) | 18.1803i | 0.949006i | 0.880254 | + | 0.474503i | \(0.157372\pi\) | ||||
−0.880254 | + | 0.474503i | \(0.842628\pi\) | |||||||
\(368\) | 4.85410i | 0.253038i | ||||||||
\(369\) | −10.9443 | −0.569736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4721 | 0.543686 | ||||||||
\(372\) | − 9.27051i | − 0.480654i | ||||||||
\(373\) | 5.70820i | 0.295560i | 0.989020 | + | 0.147780i | \(0.0472127\pi\) | ||||
−0.989020 | + | 0.147780i | \(0.952787\pi\) | |||||||
\(374\) | −6.47214 | −0.334666 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.00000 | 0.257855 | ||||||||
\(377\) | − 9.00000i | − 0.463524i | ||||||||
\(378\) | 4.47214i | 0.230022i | ||||||||
\(379\) | 20.3607 | 1.04586 | 0.522929 | − | 0.852376i | \(-0.324839\pi\) | ||||
0.522929 | + | 0.852376i | \(0.324839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −46.3050 | −2.37227 | ||||||||
\(382\) | 6.18034i | 0.316214i | ||||||||
\(383\) | − 24.9443i | − 1.27459i | −0.770619 | − | 0.637296i | \(-0.780053\pi\) | ||||
0.770619 | − | 0.637296i | \(-0.219947\pi\) | |||||||
\(384\) | 30.4508 | 1.55394 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.8541 | 0.654257 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 2.65248i | − 0.134659i | ||||||||
\(389\) | −34.4721 | −1.74781 | −0.873903 | − | 0.486100i | \(-0.838419\pi\) | ||||
−0.873903 | + | 0.486100i | \(0.838419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.23607 | 0.264799 | ||||||||
\(392\) | − 12.2361i | − 0.618015i | ||||||||
\(393\) | − 11.8328i | − 0.596887i | ||||||||
\(394\) | 12.0902 | 0.609094 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.944272 | −0.0474514 | ||||||||
\(397\) | 2.41641i | 0.121276i | 0.998160 | + | 0.0606380i | \(0.0193135\pi\) | ||||
−0.998160 | + | 0.0606380i | \(0.980686\pi\) | |||||||
\(398\) | − 41.5967i | − 2.08506i | ||||||||
\(399\) | −5.52786 | −0.276739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.18034 | 0.408507 | 0.204253 | − | 0.978918i | \(-0.434523\pi\) | ||||
0.204253 | + | 0.978918i | \(0.434523\pi\) | |||||||
\(402\) | 26.1803i | 1.30576i | ||||||||
\(403\) | 20.1246i | 1.00248i | ||||||||
\(404\) | 2.76393 | 0.137511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | − 2.47214i | − 0.122539i | ||||||||
\(408\) | − 26.1803i | − 1.29612i | ||||||||
\(409\) | 23.3607 | 1.15511 | 0.577556 | − | 0.816351i | \(-0.304007\pi\) | ||||
0.577556 | + | 0.816351i | \(0.304007\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.0557 | 1.53187 | ||||||||
\(412\) | 11.2361i | 0.553561i | ||||||||
\(413\) | − 3.05573i | − 0.150363i | ||||||||
\(414\) | 3.23607 | 0.159044 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.1459 | 0.497444 | ||||||||
\(417\) | 6.05573i | 0.296550i | ||||||||
\(418\) | 2.47214i | 0.120916i | ||||||||
\(419\) | 31.4164 | 1.53479 | 0.767396 | − | 0.641173i | \(-0.221552\pi\) | ||||
0.767396 | + | 0.641173i | \(0.221552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.7082 | −1.15547 | −0.577734 | − | 0.816225i | \(-0.696063\pi\) | ||||
−0.577734 | + | 0.816225i | \(0.696063\pi\) | |||||||
\(422\) | − 5.52786i | − 0.269092i | ||||||||
\(423\) | − 4.47214i | − 0.217443i | ||||||||
\(424\) | 18.9443 | 0.920015 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −28.0902 | −1.36097 | ||||||||
\(427\) | − 13.5279i | − 0.654659i | ||||||||
\(428\) | 8.29180i | 0.400799i | ||||||||
\(429\) | 5.12461 | 0.247419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.4721 | −1.27512 | −0.637559 | − | 0.770402i | \(-0.720056\pi\) | ||||
−0.637559 | + | 0.770402i | \(0.720056\pi\) | |||||||
\(432\) | 10.8541i | 0.522218i | ||||||||
\(433\) | − 40.1803i | − 1.93094i | −0.260507 | − | 0.965472i | \(-0.583890\pi\) | ||||
0.260507 | − | 0.965472i | \(-0.416110\pi\) | |||||||
\(434\) | 13.4164 | 0.644008 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2.00000i | − 0.0956730i | ||||||||
\(438\) | 55.9787i | 2.67477i | ||||||||
\(439\) | 5.29180 | 0.252564 | 0.126282 | − | 0.991994i | \(-0.459696\pi\) | ||||
0.126282 | + | 0.991994i | \(0.459696\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.9443 | −0.521156 | ||||||||
\(442\) | − 25.4164i | − 1.20894i | ||||||||
\(443\) | 2.12461i | 0.100943i | 0.998725 | + | 0.0504717i | \(0.0160725\pi\) | ||||
−0.998725 | + | 0.0504717i | \(0.983928\pi\) | |||||||
\(444\) | −4.47214 | −0.212238 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.47214 | −0.306465 | ||||||||
\(447\) | − 26.5836i | − 1.25736i | ||||||||
\(448\) | 5.23607i | 0.247381i | ||||||||
\(449\) | −2.94427 | −0.138949 | −0.0694744 | − | 0.997584i | \(-0.522132\pi\) | ||||
−0.0694744 | + | 0.997584i | \(0.522132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.18034 | −0.196845 | ||||||||
\(452\) | 8.18034i | 0.384771i | ||||||||
\(453\) | 0.527864i | 0.0248012i | ||||||||
\(454\) | 16.4721 | 0.773076 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.0000 | −0.468293 | ||||||||
\(457\) | 35.1246i | 1.64306i | 0.570165 | + | 0.821530i | \(0.306879\pi\) | ||||
−0.570165 | + | 0.821530i | \(0.693121\pi\) | |||||||
\(458\) | − 19.4164i | − 0.907269i | ||||||||
\(459\) | 11.7082 | 0.546492 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.47214 | 0.348012 | 0.174006 | − | 0.984745i | \(-0.444329\pi\) | ||||
0.174006 | + | 0.984745i | \(0.444329\pi\) | |||||||
\(462\) | − 3.41641i | − 0.158946i | ||||||||
\(463\) | 20.0000i | 0.929479i | 0.885448 | + | 0.464739i | \(0.153852\pi\) | ||||
−0.885448 | + | 0.464739i | \(0.846148\pi\) | |||||||
\(464\) | −14.5623 | −0.676038 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.0344 | 1.15970 | ||||||||
\(467\) | − 30.9443i | − 1.43193i | −0.698136 | − | 0.715965i | \(-0.745987\pi\) | ||||
0.698136 | − | 0.715965i | \(-0.254013\pi\) | |||||||
\(468\) | − 3.70820i | − 0.171412i | ||||||||
\(469\) | −8.94427 | −0.413008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 34.4721 | 1.58839 | ||||||||
\(472\) | − 5.52786i | − 0.254441i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 25.1246 | 1.15401 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | − 16.9443i | − 0.775825i | ||||||||
\(478\) | 29.5066i | 1.34960i | ||||||||
\(479\) | 17.5967 | 0.804016 | 0.402008 | − | 0.915636i | \(-0.368312\pi\) | ||||
0.402008 | + | 0.915636i | \(0.368312\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.70820 | 0.442656 | ||||||||
\(482\) | − 27.7082i | − 1.26207i | ||||||||
\(483\) | 2.76393i | 0.125763i | ||||||||
\(484\) | 6.43769 | 0.292622 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 28.9443 | 1.31294 | ||||||||
\(487\) | − 1.29180i | − 0.0585369i | −0.999572 | − | 0.0292684i | \(-0.990682\pi\) | ||||
0.999572 | − | 0.0292684i | \(-0.00931776\pi\) | |||||||
\(488\) | − 24.4721i | − 1.10780i | ||||||||
\(489\) | 22.8885 | 1.03506 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.6525 | 1.78949 | 0.894746 | − | 0.446576i | \(-0.147357\pi\) | ||||
0.894746 | + | 0.446576i | \(0.147357\pi\) | |||||||
\(492\) | 7.56231i | 0.340935i | ||||||||
\(493\) | 15.7082i | 0.707462i | ||||||||
\(494\) | −9.70820 | −0.436793 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.5623 | 1.46209 | ||||||||
\(497\) | − 9.59675i | − 0.430473i | ||||||||
\(498\) | − 47.8885i | − 2.14594i | ||||||||
\(499\) | −32.7082 | −1.46422 | −0.732110 | − | 0.681186i | \(-0.761464\pi\) | ||||
−0.732110 | + | 0.681186i | \(0.761464\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.4164 | 1.04617 | ||||||||
\(502\) | − 25.4164i | − 1.13439i | ||||||||
\(503\) | 9.05573i | 0.403775i | 0.979409 | + | 0.201887i | \(0.0647075\pi\) | ||||
−0.979409 | + | 0.201887i | \(0.935292\pi\) | |||||||
\(504\) | 5.52786 | 0.246231 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.23607 | 0.0549499 | ||||||||
\(507\) | − 8.94427i | − 0.397229i | ||||||||
\(508\) | 12.7984i | 0.567836i | ||||||||
\(509\) | −34.3050 | −1.52054 | −0.760270 | − | 0.649607i | \(-0.774933\pi\) | ||||
−0.760270 | + | 0.649607i | \(0.774933\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.1246 | −0.846023 | ||||||||
\(512\) | 5.29180i | 0.233867i | ||||||||
\(513\) | − 4.47214i | − 0.197450i | ||||||||
\(514\) | 2.38197 | 0.105064 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 1.70820i | − 0.0751267i | ||||||||
\(518\) | − 6.47214i | − 0.284369i | ||||||||
\(519\) | −11.3050 | −0.496232 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.58359 | 0.200811 | 0.100405 | − | 0.994947i | \(-0.467986\pi\) | ||||
0.100405 | + | 0.994947i | \(0.467986\pi\) | |||||||
\(522\) | 9.70820i | 0.424917i | ||||||||
\(523\) | − 0.875388i | − 0.0382781i | −0.999817 | − | 0.0191390i | \(-0.993907\pi\) | ||||
0.999817 | − | 0.0191390i | \(-0.00609251\pi\) | |||||||
\(524\) | −3.27051 | −0.142873 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.1803 | 1.05431 | ||||||||
\(527\) | − 35.1246i | − 1.53005i | ||||||||
\(528\) | − 8.29180i | − 0.360854i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.94427 | −0.214563 | ||||||||
\(532\) | 1.52786i | 0.0662413i | ||||||||
\(533\) | − 16.4164i | − 0.711074i | ||||||||
\(534\) | −5.52786 | −0.239214 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −16.1803 | −0.698884 | ||||||||
\(537\) | − 28.4164i | − 1.22626i | ||||||||
\(538\) | 16.0902i | 0.693696i | ||||||||
\(539\) | −4.18034 | −0.180060 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.58359 | −0.326044 | −0.163022 | − | 0.986622i | \(-0.552124\pi\) | ||||
−0.163022 | + | 0.986622i | \(0.552124\pi\) | |||||||
\(542\) | − 12.9443i | − 0.556004i | ||||||||
\(543\) | 32.7639i | 1.40603i | ||||||||
\(544\) | −17.7082 | −0.759233 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.4164 | 0.574169 | ||||||||
\(547\) | 37.5410i | 1.60514i | 0.596559 | + | 0.802569i | \(0.296534\pi\) | ||||
−0.596559 | + | 0.802569i | \(0.703466\pi\) | |||||||
\(548\) | − 8.58359i | − 0.366673i | ||||||||
\(549\) | −21.8885 | −0.934180 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | 5.00000i | 0.212814i | ||||||||
\(553\) | 8.58359i | 0.365011i | ||||||||
\(554\) | 10.5623 | 0.448749 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.67376 | 0.0709833 | ||||||||
\(557\) | 19.4164i | 0.822700i | 0.911478 | + | 0.411350i | \(0.134943\pi\) | ||||
−0.911478 | + | 0.411350i | \(0.865057\pi\) | |||||||
\(558\) | − 21.7082i | − 0.918982i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.94427 | −0.377627 | ||||||||
\(562\) | 21.4164i | 0.903397i | ||||||||
\(563\) | 15.0557i | 0.634523i | 0.948338 | + | 0.317262i | \(0.102763\pi\) | ||||
−0.948338 | + | 0.317262i | \(0.897237\pi\) | |||||||
\(564\) | −3.09017 | −0.130120 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.1246 | −0.972000 | ||||||||
\(567\) | 13.5967i | 0.571010i | ||||||||
\(568\) | − 17.3607i | − 0.728438i | ||||||||
\(569\) | −0.180340 | −0.00756024 | −0.00378012 | − | 0.999993i | \(-0.501203\pi\) | ||||
−0.00378012 | + | 0.999993i | \(0.501203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.7082 | −1.15955 | −0.579776 | − | 0.814776i | \(-0.696860\pi\) | ||||
−0.579776 | + | 0.814776i | \(0.696860\pi\) | |||||||
\(572\) | − 1.41641i | − 0.0592230i | ||||||||
\(573\) | 8.54102i | 0.356806i | ||||||||
\(574\) | −10.9443 | −0.456805 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.47214 | 0.353006 | ||||||||
\(577\) | − 12.8885i | − 0.536557i | −0.963341 | − | 0.268279i | \(-0.913545\pi\) | ||||
0.963341 | − | 0.268279i | \(-0.0864548\pi\) | |||||||
\(578\) | 16.8541i | 0.701038i | ||||||||
\(579\) | 17.7639 | 0.738244 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.3607 | 0.678755 | ||||||||
\(582\) | − 15.5279i | − 0.643651i | ||||||||
\(583\) | − 6.47214i | − 0.268048i | ||||||||
\(584\) | −34.5967 | −1.43162 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.9443 | 0.699961 | ||||||||
\(587\) | − 11.2918i | − 0.466062i | −0.972469 | − | 0.233031i | \(-0.925136\pi\) | ||||
0.972469 | − | 0.233031i | \(-0.0748644\pi\) | |||||||
\(588\) | 7.56231i | 0.311864i | ||||||||
\(589\) | −13.4164 | −0.552813 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.7082 | 0.687284 | ||||||||
\(592\) | − 15.7082i | − 0.645603i | ||||||||
\(593\) | − 14.9443i | − 0.613688i | −0.951760 | − | 0.306844i | \(-0.900727\pi\) | ||||
0.951760 | − | 0.306844i | \(-0.0992729\pi\) | |||||||
\(594\) | 2.76393 | 0.113406 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.34752 | −0.300966 | ||||||||
\(597\) | − 57.4853i | − 2.35272i | ||||||||
\(598\) | 4.85410i | 0.198499i | ||||||||
\(599\) | 1.88854 | 0.0771638 | 0.0385819 | − | 0.999255i | \(-0.487716\pi\) | ||||
0.0385819 | + | 0.999255i | \(0.487716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1115 | 0.453246 | 0.226623 | − | 0.973983i | \(-0.427232\pi\) | ||||
0.226623 | + | 0.973983i | \(0.427232\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.4721i | 0.589351i | ||||||||
\(604\) | 0.145898 | 0.00593651 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.1803 | 0.657281 | ||||||||
\(607\) | 17.5279i | 0.711434i | 0.934594 | + | 0.355717i | \(0.115763\pi\) | ||||
−0.934594 | + | 0.355717i | \(0.884237\pi\) | |||||||
\(608\) | 6.76393i | 0.274314i | ||||||||
\(609\) | −8.29180 | −0.336001 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.70820 | 0.271385 | ||||||||
\(612\) | 6.47214i | 0.261621i | ||||||||
\(613\) | 7.70820i | 0.311331i | 0.987810 | + | 0.155666i | \(0.0497523\pi\) | ||||
−0.987810 | + | 0.155666i | \(0.950248\pi\) | |||||||
\(614\) | 29.8885 | 1.20620 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.11146 | 0.0850730 | ||||||||
\(617\) | − 16.4721i | − 0.663143i | −0.943430 | − | 0.331572i | \(-0.892421\pi\) | ||||
0.943430 | − | 0.331572i | \(-0.107579\pi\) | |||||||
\(618\) | 65.7771i | 2.64594i | ||||||||
\(619\) | 7.41641 | 0.298091 | 0.149045 | − | 0.988830i | \(-0.452380\pi\) | ||||
0.149045 | + | 0.988830i | \(0.452380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.23607 | −0.0897303 | ||||||||
\(622\) | 14.8541i | 0.595595i | ||||||||
\(623\) | − 1.88854i | − 0.0756629i | ||||||||
\(624\) | 32.5623 | 1.30354 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.9443 | 1.31672 | ||||||||
\(627\) | 3.41641i | 0.136438i | ||||||||
\(628\) | − 9.52786i | − 0.380203i | ||||||||
\(629\) | −16.9443 | −0.675612 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3607 | −1.28826 | −0.644129 | − | 0.764917i | \(-0.722780\pi\) | ||||
−0.644129 | + | 0.764917i | \(0.722780\pi\) | |||||||
\(632\) | 15.5279i | 0.617665i | ||||||||
\(633\) | − 7.63932i | − 0.303636i | ||||||||
\(634\) | −2.29180 | −0.0910188 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.7082 | −0.464260 | ||||||||
\(637\) | − 16.4164i | − 0.650442i | ||||||||
\(638\) | 3.70820i | 0.146809i | ||||||||
\(639\) | −15.5279 | −0.614273 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.3050 | 1.78944 | 0.894719 | − | 0.446629i | \(-0.147376\pi\) | ||||
0.894719 | + | 0.446629i | \(0.147376\pi\) | |||||||
\(642\) | 48.5410i | 1.91576i | ||||||||
\(643\) | − 19.5967i | − 0.772820i | −0.922327 | − | 0.386410i | \(-0.873715\pi\) | ||||
0.922327 | − | 0.386410i | \(-0.126285\pi\) | |||||||
\(644\) | 0.763932 | 0.0301031 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.9443 | 0.666663 | ||||||||
\(647\) | − 6.70820i | − 0.263727i | −0.991268 | − | 0.131863i | \(-0.957904\pi\) | ||||
0.991268 | − | 0.131863i | \(-0.0420960\pi\) | |||||||
\(648\) | 24.5967i | 0.966252i | ||||||||
\(649\) | −1.88854 | −0.0741318 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.5410 | 0.726680 | ||||||||
\(652\) | − 6.32624i | − 0.247755i | ||||||||
\(653\) | − 24.3050i | − 0.951126i | −0.879682 | − | 0.475563i | \(-0.842244\pi\) | ||||
0.879682 | − | 0.475563i | \(-0.157756\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −26.5623 | −1.03708 | ||||||||
\(657\) | 30.9443i | 1.20725i | ||||||||
\(658\) | − 4.47214i | − 0.174342i | ||||||||
\(659\) | −20.6525 | −0.804506 | −0.402253 | − | 0.915528i | \(-0.631773\pi\) | ||||
−0.402253 | + | 0.915528i | \(0.631773\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.05573 | −0.196645 | −0.0983225 | − | 0.995155i | \(-0.531348\pi\) | ||||
−0.0983225 | + | 0.995155i | \(0.531348\pi\) | |||||||
\(662\) | − 18.8541i | − 0.732785i | ||||||||
\(663\) | − 35.1246i | − 1.36413i | ||||||||
\(664\) | 29.5967 | 1.14858 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.4721 | −0.405787 | ||||||||
\(667\) | − 3.00000i | − 0.116160i | ||||||||
\(668\) | − 6.47214i | − 0.250414i | ||||||||
\(669\) | −8.94427 | −0.345806 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.36068 | −0.322760 | ||||||||
\(672\) | − 9.34752i | − 0.360589i | ||||||||
\(673\) | − 3.00000i | − 0.115642i | −0.998327 | − | 0.0578208i | \(-0.981585\pi\) | ||||
0.998327 | − | 0.0578208i | \(-0.0184152\pi\) | |||||||
\(674\) | −5.52786 | −0.212925 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.47214 | −0.0950822 | ||||||||
\(677\) | 18.0000i | 0.691796i | 0.938272 | + | 0.345898i | \(0.112426\pi\) | ||||
−0.938272 | + | 0.345898i | \(0.887574\pi\) | |||||||
\(678\) | 47.8885i | 1.83915i | ||||||||
\(679\) | 5.30495 | 0.203585 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.7639 | 0.872316 | ||||||||
\(682\) | − 8.29180i | − 0.317509i | ||||||||
\(683\) | 22.5967i | 0.864641i | 0.901720 | + | 0.432320i | \(0.142305\pi\) | ||||
−0.901720 | + | 0.432320i | \(0.857695\pi\) | |||||||
\(684\) | 2.47214 | 0.0945245 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.9443 | −0.952377 | ||||||||
\(687\) | − 26.8328i | − 1.02374i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.4164 | 0.968288 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9443 | 0.948925 | 0.474462 | − | 0.880276i | \(-0.342642\pi\) | ||||
0.474462 | + | 0.880276i | \(0.342642\pi\) | |||||||
\(692\) | 3.12461i | 0.118780i | ||||||||
\(693\) | − 1.88854i | − 0.0717398i | ||||||||
\(694\) | 41.8885 | 1.59007 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −15.0000 | −0.568574 | ||||||||
\(697\) | 28.6525i | 1.08529i | ||||||||
\(698\) | − 3.90983i | − 0.147989i | ||||||||
\(699\) | 34.5967 | 1.30857 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1803 | −0.988818 | −0.494409 | − | 0.869229i | \(-0.664615\pi\) | ||||
−0.494409 | + | 0.869229i | \(0.664615\pi\) | |||||||
\(702\) | 10.8541i | 0.409662i | ||||||||
\(703\) | 6.47214i | 0.244101i | ||||||||
\(704\) | 3.23607 | 0.121964 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 57.2148 | 2.15331 | ||||||||
\(707\) | 5.52786i | 0.207897i | ||||||||
\(708\) | 3.41641i | 0.128396i | ||||||||
\(709\) | −16.0689 | −0.603480 | −0.301740 | − | 0.953390i | \(-0.597567\pi\) | ||||
−0.301740 | + | 0.953390i | \(0.597567\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.8885 | 0.520861 | ||||||||
\(712\) | − 3.41641i | − 0.128035i | ||||||||
\(713\) | 6.70820i | 0.251224i | ||||||||
\(714\) | −23.4164 | −0.876337 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.85410 | −0.293522 | ||||||||
\(717\) | 40.7771i | 1.52285i | ||||||||
\(718\) | 25.7082i | 0.959422i | ||||||||
\(719\) | 20.9443 | 0.781090 | 0.390545 | − | 0.920584i | \(-0.372287\pi\) | ||||
0.390545 | + | 0.920584i | \(0.372287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.4721 | −0.836906 | ||||||||
\(722\) | 24.2705i | 0.903255i | ||||||||
\(723\) | − 38.2918i | − 1.42409i | ||||||||
\(724\) | 9.05573 | 0.336553 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 37.6869 | 1.39869 | ||||||||
\(727\) | − 14.2918i | − 0.530053i | −0.964241 | − | 0.265027i | \(-0.914619\pi\) | ||||
0.964241 | − | 0.265027i | \(-0.0853808\pi\) | |||||||
\(728\) | 8.29180i | 0.307314i | ||||||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 15.1246i | 0.559022i | ||||||||
\(733\) | 26.7639i | 0.988548i | 0.869306 | + | 0.494274i | \(0.164566\pi\) | ||||
−0.869306 | + | 0.494274i | \(0.835434\pi\) | |||||||
\(734\) | 29.4164 | 1.08578 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.38197 | 0.124661 | ||||||||
\(737\) | 5.52786i | 0.203621i | ||||||||
\(738\) | 17.7082i | 0.651848i | ||||||||
\(739\) | −49.1803 | −1.80913 | −0.904564 | − | 0.426338i | \(-0.859803\pi\) | ||||
−0.904564 | + | 0.426338i | \(0.859803\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.4164 | −0.492864 | ||||||||
\(742\) | − 16.9443i | − 0.622044i | ||||||||
\(743\) | − 0.875388i | − 0.0321149i | −0.999871 | − | 0.0160574i | \(-0.994889\pi\) | ||||
0.999871 | − | 0.0160574i | \(-0.00511146\pi\) | |||||||
\(744\) | 33.5410 | 1.22967 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.23607 | 0.338156 | ||||||||
\(747\) | − 26.4721i | − 0.968565i | ||||||||
\(748\) | 2.47214i | 0.0903902i | ||||||||
\(749\) | −16.5836 | −0.605951 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.3607 | −1.61874 | −0.809372 | − | 0.587296i | \(-0.800192\pi\) | ||||
−0.809372 | + | 0.587296i | \(0.800192\pi\) | |||||||
\(752\) | − 10.8541i | − 0.395808i | ||||||||
\(753\) | − 35.1246i | − 1.28001i | ||||||||
\(754\) | −14.5623 | −0.530328 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.70820 | 0.0621268 | ||||||||
\(757\) | − 47.5967i | − 1.72993i | −0.501829 | − | 0.864967i | \(-0.667339\pi\) | ||||
0.501829 | − | 0.864967i | \(-0.332661\pi\) | |||||||
\(758\) | − 32.9443i | − 1.19659i | ||||||||
\(759\) | 1.70820 | 0.0620039 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.3050 | −0.591054 | −0.295527 | − | 0.955334i | \(-0.595495\pi\) | ||||
−0.295527 | + | 0.955334i | \(0.595495\pi\) | |||||||
\(762\) | 74.9230i | 2.71417i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.36068 | 0.0854064 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.3607 | −1.45829 | ||||||||
\(767\) | − 7.41641i | − 0.267791i | ||||||||
\(768\) | − 30.3262i | − 1.09430i | ||||||||
\(769\) | −17.1246 | −0.617529 | −0.308765 | − | 0.951138i | \(-0.599916\pi\) | ||||
−0.308765 | + | 0.951138i | \(0.599916\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.29180 | 0.118551 | ||||||||
\(772\) | − 4.90983i | − 0.176709i | ||||||||
\(773\) | 14.4721i | 0.520527i | 0.965538 | + | 0.260263i | \(0.0838094\pi\) | ||||
−0.965538 | + | 0.260263i | \(0.916191\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.59675 | 0.344503 | ||||||||
\(777\) | − 8.94427i | − 0.320874i | ||||||||
\(778\) | 55.7771i | 1.99971i | ||||||||
\(779\) | 10.9443 | 0.392119 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.93112 | −0.212232 | ||||||||
\(782\) | − 8.47214i | − 0.302963i | ||||||||
\(783\) | − 6.70820i | − 0.239732i | ||||||||
\(784\) | −26.5623 | −0.948654 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19.1459 | −0.682912 | ||||||||
\(787\) | 51.4164i | 1.83280i | 0.400267 | + | 0.916399i | \(0.368917\pi\) | ||||
−0.400267 | + | 0.916399i | \(0.631083\pi\) | |||||||
\(788\) | − 4.61803i | − 0.164511i | ||||||||
\(789\) | 33.4164 | 1.18966 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.3607 | −0.581719 | ||||||||
\(792\) | − 3.41641i | − 0.121397i | ||||||||
\(793\) | − 32.8328i | − 1.16593i | ||||||||
\(794\) | 3.90983 | 0.138755 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.8885 | −0.563155 | ||||||||
\(797\) | 10.3607i | 0.366994i | 0.983020 | + | 0.183497i | \(0.0587418\pi\) | ||||
−0.983020 | + | 0.183497i | \(0.941258\pi\) | |||||||
\(798\) | 8.94427i | 0.316624i | ||||||||
\(799\) | −11.7082 | −0.414206 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.05573 | −0.107969 | ||||||||
\(802\) | − 13.2361i | − 0.467382i | ||||||||
\(803\) | 11.8197i | 0.417107i | ||||||||
\(804\) | 10.0000 | 0.352673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.5623 | 1.14696 | ||||||||
\(807\) | 22.2361i | 0.782747i | ||||||||
\(808\) | 10.0000i | 0.351799i | ||||||||
\(809\) | −47.8885 | −1.68367 | −0.841836 | − | 0.539734i | \(-0.818525\pi\) | ||||
−0.841836 | + | 0.539734i | \(0.818525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.6525 | −1.95422 | −0.977111 | − | 0.212728i | \(-0.931765\pi\) | ||||
−0.977111 | + | 0.212728i | \(0.931765\pi\) | |||||||
\(812\) | 2.29180i | 0.0804263i | ||||||||
\(813\) | − 17.8885i | − 0.627379i | ||||||||
\(814\) | −4.00000 | −0.140200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −56.8328 | −1.98955 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − 37.7984i | − 1.32159i | ||||||||
\(819\) | 7.41641 | 0.259150 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0557 | −0.734850 | −0.367425 | − | 0.930053i | \(-0.619761\pi\) | ||||
−0.367425 | + | 0.930053i | \(0.619761\pi\) | |||||||
\(822\) | − 50.2492i | − 1.75264i | ||||||||
\(823\) | − 27.5410i | − 0.960020i | −0.877263 | − | 0.480010i | \(-0.840633\pi\) | ||||
0.877263 | − | 0.480010i | \(-0.159367\pi\) | |||||||
\(824\) | −40.6525 | −1.41620 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.94427 | −0.172033 | ||||||||
\(827\) | 10.4721i | 0.364152i | 0.983284 | + | 0.182076i | \(0.0582817\pi\) | ||||
−0.983284 | + | 0.182076i | \(0.941718\pi\) | |||||||
\(828\) | − 1.23607i | − 0.0429563i | ||||||||
\(829\) | 40.2492 | 1.39791 | 0.698957 | − | 0.715164i | \(-0.253648\pi\) | ||||
0.698957 | + | 0.715164i | \(0.253648\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5967 | 0.506356 | ||||||||
\(832\) | 12.7082i | 0.440578i | ||||||||
\(833\) | 28.6525i | 0.992749i | ||||||||
\(834\) | 9.79837 | 0.339290 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.944272 | 0.0326583 | ||||||||
\(837\) | 15.0000i | 0.518476i | ||||||||
\(838\) | − 50.8328i | − 1.75599i | ||||||||
\(839\) | 0.875388 | 0.0302218 | 0.0151109 | − | 0.999886i | \(-0.495190\pi\) | ||||
0.0151109 | + | 0.999886i | \(0.495190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 38.3607i | 1.32200i | ||||||||
\(843\) | 29.5967i | 1.01937i | ||||||||
\(844\) | −2.11146 | −0.0726793 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.23607 | −0.248781 | ||||||||
\(847\) | 12.8754i | 0.442404i | ||||||||
\(848\) | − 41.1246i | − 1.41222i | ||||||||
\(849\) | −31.9574 | −1.09678 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.23607 | 0.110931 | ||||||||
\(852\) | 10.7295i | 0.367586i | ||||||||
\(853\) | 37.4164i | 1.28111i | 0.767911 | + | 0.640557i | \(0.221296\pi\) | ||||
−0.767911 | + | 0.640557i | \(0.778704\pi\) | |||||||
\(854\) | −21.8885 | −0.749011 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.0000 | −1.02538 | ||||||||
\(857\) | − 7.47214i | − 0.255243i | −0.991823 | − | 0.127622i | \(-0.959266\pi\) | ||||
0.991823 | − | 0.127622i | \(-0.0407343\pi\) | |||||||
\(858\) | − 8.29180i | − 0.283077i | ||||||||
\(859\) | 3.29180 | 0.112315 | 0.0561573 | − | 0.998422i | \(-0.482115\pi\) | ||||
0.0561573 | + | 0.998422i | \(0.482115\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.1246 | −0.515445 | ||||||||
\(862\) | 42.8328i | 1.45889i | ||||||||
\(863\) | − 45.5410i | − 1.55023i | −0.631818 | − | 0.775117i | \(-0.717691\pi\) | ||||
0.631818 | − | 0.775117i | \(-0.282309\pi\) | |||||||
\(864\) | 7.56231 | 0.257275 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −65.0132 | −2.20924 | ||||||||
\(867\) | 23.2918i | 0.791031i | ||||||||
\(868\) | − 5.12461i | − 0.173941i | ||||||||
\(869\) | 5.30495 | 0.179958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.7082 | −0.735554 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 8.58359i | − 0.290511i | ||||||||
\(874\) | −3.23607 | −0.109462 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 21.3820 | 0.722430 | ||||||||
\(877\) | − 27.5279i | − 0.929550i | −0.885429 | − | 0.464775i | \(-0.846135\pi\) | ||||
0.885429 | − | 0.464775i | \(-0.153865\pi\) | |||||||
\(878\) | − 8.56231i | − 0.288964i | ||||||||
\(879\) | 23.4164 | 0.789816 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.8197 | 0.735123 | 0.367562 | − | 0.929999i | \(-0.380193\pi\) | ||||
0.367562 | + | 0.929999i | \(0.380193\pi\) | |||||||
\(882\) | 17.7082i | 0.596266i | ||||||||
\(883\) | − 4.00000i | − 0.134611i | −0.997732 | − | 0.0673054i | \(-0.978560\pi\) | ||||
0.997732 | − | 0.0673054i | \(-0.0214402\pi\) | |||||||
\(884\) | −9.70820 | −0.326522 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.43769 | 0.115492 | ||||||||
\(887\) | − 35.0689i | − 1.17750i | −0.808316 | − | 0.588749i | \(-0.799621\pi\) | ||||
0.808316 | − | 0.588749i | \(-0.200379\pi\) | |||||||
\(888\) | − 16.1803i | − 0.542977i | ||||||||
\(889\) | −25.5967 | −0.858487 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.40325 | 0.281520 | ||||||||
\(892\) | 2.47214i | 0.0827732i | ||||||||
\(893\) | 4.47214i | 0.149654i | ||||||||
\(894\) | −43.0132 | −1.43858 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.8328 | 0.562345 | ||||||||
\(897\) | 6.70820i | 0.223980i | ||||||||
\(898\) | 4.76393i | 0.158974i | ||||||||
\(899\) | −20.1246 | −0.671193 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44.3607 | −1.47787 | ||||||||
\(902\) | 6.76393i | 0.225214i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29.5967 | −0.984373 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.854102 | 0.0283756 | ||||||||
\(907\) | 40.2492i | 1.33645i | 0.743958 | + | 0.668227i | \(0.232946\pi\) | ||||
−0.743958 | + | 0.668227i | \(0.767054\pi\) | |||||||
\(908\) | − 6.29180i | − 0.208801i | ||||||||
\(909\) | 8.94427 | 0.296663 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3050 | −1.03718 | −0.518590 | − | 0.855023i | \(-0.673543\pi\) | ||||
−0.518590 | + | 0.855023i | \(0.673543\pi\) | |||||||
\(912\) | 21.7082i | 0.718830i | ||||||||
\(913\) | − 10.1115i | − 0.334640i | ||||||||
\(914\) | 56.8328 | 1.87986 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.41641 | −0.245045 | ||||||||
\(917\) | − 6.54102i | − 0.216003i | ||||||||
\(918\) | − 18.9443i | − 0.625254i | ||||||||
\(919\) | −0.875388 | −0.0288764 | −0.0144382 | − | 0.999896i | \(-0.504596\pi\) | ||||
−0.0144382 | + | 0.999896i | \(0.504596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.3050 | 1.36104 | ||||||||
\(922\) | − 12.0902i | − 0.398169i | ||||||||
\(923\) | − 23.2918i | − 0.766659i | ||||||||
\(924\) | −1.30495 | −0.0429298 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32.3607 | 1.06344 | ||||||||
\(927\) | 36.3607i | 1.19424i | ||||||||
\(928\) | 10.1459i | 0.333055i | ||||||||
\(929\) | 41.9443 | 1.37615 | 0.688073 | − | 0.725641i | \(-0.258457\pi\) | ||||
0.688073 | + | 0.725641i | \(0.258457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9443 | 0.358684 | ||||||||
\(932\) | − 9.56231i | − 0.313224i | ||||||||
\(933\) | 20.5279i | 0.672052i | ||||||||
\(934\) | −50.0689 | −1.63830 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.4164 | 0.438529 | ||||||||
\(937\) | 11.8197i | 0.386131i | 0.981186 | + | 0.193066i | \(0.0618431\pi\) | ||||
−0.981186 | + | 0.193066i | \(0.938157\pi\) | |||||||
\(938\) | 14.4721i | 0.472532i | ||||||||
\(939\) | 45.5279 | 1.48575 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.6525 | −0.803648 | −0.401824 | − | 0.915717i | \(-0.631624\pi\) | ||||
−0.401824 | + | 0.915717i | \(0.631624\pi\) | |||||||
\(942\) | − 55.7771i | − 1.81732i | ||||||||
\(943\) | − 5.47214i | − 0.178197i | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 33.1803i | − 1.07822i | −0.842237 | − | 0.539108i | \(-0.818761\pi\) | ||||
0.842237 | − | 0.539108i | \(-0.181239\pi\) | |||||||
\(948\) | − 9.59675i | − 0.311688i | ||||||||
\(949\) | −46.4164 | −1.50674 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.16718 | −0.102703 | ||||||||
\(952\) | − 14.4721i | − 0.469045i | ||||||||
\(953\) | − 11.5279i | − 0.373424i | −0.982415 | − | 0.186712i | \(-0.940217\pi\) | ||||
0.982415 | − | 0.186712i | \(-0.0597831\pi\) | |||||||
\(954\) | −27.4164 | −0.887639 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.2705 | 0.364514 | ||||||||
\(957\) | 5.12461i | 0.165655i | ||||||||
\(958\) | − 28.4721i | − 0.919893i | ||||||||
\(959\) | 17.1672 | 0.554357 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | − 15.7082i | − 0.506453i | ||||||||
\(963\) | 26.8328i | 0.864675i | ||||||||
\(964\) | −10.5836 | −0.340875 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.47214 | 0.143889 | ||||||||
\(967\) | − 39.5410i | − 1.27155i | −0.771873 | − | 0.635777i | \(-0.780680\pi\) | ||||
0.771873 | − | 0.635777i | \(-0.219320\pi\) | |||||||
\(968\) | 23.2918i | 0.748627i | ||||||||
\(969\) | 23.4164 | 0.752243 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.52786 | 0.241581 | 0.120790 | − | 0.992678i | \(-0.461457\pi\) | ||||
0.120790 | + | 0.992678i | \(0.461457\pi\) | |||||||
\(972\) | − 11.0557i | − 0.354613i | ||||||||
\(973\) | 3.34752i | 0.107317i | ||||||||
\(974\) | −2.09017 | −0.0669734 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −53.1246 | −1.70048 | ||||||||
\(977\) | − 54.6525i | − 1.74849i | −0.485487 | − | 0.874244i | \(-0.661358\pi\) | ||||
0.485487 | − | 0.874244i | \(-0.338642\pi\) | |||||||
\(978\) | − 37.0344i | − 1.18423i | ||||||||
\(979\) | −1.16718 | −0.0373034 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 64.1591i | − 2.04740i | ||||||||
\(983\) | 31.5279i | 1.00558i | 0.864408 | + | 0.502791i | \(0.167694\pi\) | ||||
−0.864408 | + | 0.502791i | \(0.832306\pi\) | |||||||
\(984\) | −27.3607 | −0.872227 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 25.4164 | 0.809423 | ||||||||
\(987\) | − 6.18034i | − 0.196722i | ||||||||
\(988\) | 3.70820i | 0.117974i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | − 22.6869i | − 0.720310i | ||||||||
\(993\) | − 26.0557i | − 0.826854i | ||||||||
\(994\) | −15.5279 | −0.492514 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.2918 | −0.579598 | ||||||||
\(997\) | − 36.8328i | − 1.16651i | −0.812290 | − | 0.583253i | \(-0.801779\pi\) | ||||
0.812290 | − | 0.583253i | \(-0.198221\pi\) | |||||||
\(998\) | 52.9230i | 1.67525i | ||||||||
\(999\) | 7.23607 | 0.228939 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))