Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Root | \(0.500000 - 2.05195i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.289 |
Dual form | 3024.2.t.g.1873.3 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.460505 | 0.205944 | 0.102972 | − | 0.994684i | \(-0.467165\pi\) | ||||
0.102972 | + | 0.994684i | \(0.467165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.25729 | + | 1.38008i | −0.853177 | + | 0.521621i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.64766 | −1.09981 | −0.549906 | − | 0.835227i | \(-0.685336\pi\) | ||||
−0.549906 | + | 0.835227i | \(0.685336\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.730252 | + | 1.26483i | 0.202536 | + | 0.350802i | 0.949345 | − | 0.314236i | \(-0.101748\pi\) |
−0.746809 | + | 0.665038i | \(0.768415\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.86693 | + | 3.23361i | 0.452796 | + | 0.784266i | 0.998558 | − | 0.0536743i | \(-0.0170933\pi\) |
−0.545763 | + | 0.837940i | \(0.683760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.02704 | − | 3.51094i | 0.465035 | − | 0.805465i | −0.534168 | − | 0.845378i | \(-0.679375\pi\) |
0.999203 | + | 0.0399136i | \(0.0127083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.13307 | 0.236262 | 0.118131 | − | 0.992998i | \(-0.462310\pi\) | ||||
0.118131 | + | 0.992998i | \(0.462310\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.78794 | −0.957587 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.48755 | − | 7.77266i | 0.833317 | − | 1.44335i | −0.0620772 | − | 0.998071i | \(-0.519772\pi\) |
0.895394 | − | 0.445275i | \(-0.146894\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.257295 | + | 0.445647i | −0.0462115 | + | 0.0800406i | −0.888206 | − | 0.459446i | \(-0.848048\pi\) |
0.841994 | + | 0.539486i | \(0.181381\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.03950 | + | 0.635534i | −0.175707 | + | 0.107425i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.55408 | + | 7.88791i | −0.748687 | + | 1.29676i | 0.199765 | + | 0.979844i | \(0.435982\pi\) |
−0.948452 | + | 0.316920i | \(0.897351\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.472958 | + | 0.819187i | 0.0738636 | + | 0.127936i | 0.900592 | − | 0.434666i | \(-0.143134\pi\) |
−0.826728 | + | 0.562602i | \(0.809800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.66372 | + | 8.07779i | −0.711210 | + | 1.23185i | 0.253193 | + | 0.967416i | \(0.418519\pi\) |
−0.964403 | + | 0.264436i | \(0.914814\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.16372 | − | 2.01561i | −0.169745 | − | 0.294007i | 0.768585 | − | 0.639748i | \(-0.220961\pi\) |
−0.938330 | + | 0.345740i | \(0.887628\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.19076 | − | 6.23049i | 0.455822 | − | 0.890071i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.21780 | − | 10.7695i | −0.854080 | − | 1.47931i | −0.877495 | − | 0.479585i | \(-0.840787\pi\) |
0.0234151 | − | 0.999726i | \(-0.492546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.67977 | −0.226500 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.44805 | − | 11.1684i | 0.839465 | − | 1.45400i | −0.0508779 | − | 0.998705i | \(-0.516202\pi\) |
0.890343 | − | 0.455291i | \(-0.150465\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.04163 | − | 10.4644i | −0.773552 | − | 1.33983i | −0.935605 | − | 0.353049i | \(-0.885145\pi\) |
0.162053 | − | 0.986782i | \(-0.448188\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.336285 | + | 0.582462i | 0.0417110 | + | 0.0722456i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.16012 | + | 2.00938i | −0.141731 | + | 0.245485i | −0.928148 | − | 0.372210i | \(-0.878600\pi\) |
0.786418 | + | 0.617695i | \(0.211933\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.67977 | 0.199352 | 0.0996758 | − | 0.995020i | \(-0.468219\pi\) | ||||
0.0996758 | + | 0.995020i | \(0.468219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.62062 | − | 11.4673i | −0.774885 | − | 1.34214i | −0.934859 | − | 0.355019i | \(-0.884474\pi\) |
0.159974 | − | 0.987121i | \(-0.448859\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.23385 | − | 5.03407i | 0.938334 | − | 0.573685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.50360 | − | 4.33636i | −0.281677 | − | 0.487879i | 0.690121 | − | 0.723694i | \(-0.257557\pi\) |
−0.971798 | + | 0.235815i | \(0.924224\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.32383 | − | 5.75705i | 0.364838 | − | 0.631918i | −0.623912 | − | 0.781494i | \(-0.714458\pi\) |
0.988750 | + | 0.149577i | \(0.0477911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.859728 | + | 1.48909i | 0.0932506 | + | 0.161515i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.36333 | − | 2.36135i | 0.144512 | − | 0.250303i | −0.784679 | − | 0.619903i | \(-0.787172\pi\) |
0.929191 | + | 0.369600i | \(0.120505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.39397 | − | 1.84730i | −0.355784 | − | 0.193649i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.933463 | − | 1.61680i | 0.0957713 | − | 0.165881i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.59358 | + | 9.68836i | −0.567942 | + | 0.983704i | 0.428827 | + | 0.903386i | \(0.358927\pi\) |
−0.996769 | + | 0.0803178i | \(0.974406\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.7558 | −1.36876 | −0.684378 | − | 0.729127i | \(-0.739926\pi\) | ||||
−0.684378 | + | 0.729127i | \(0.739926\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.1623 | −1.09985 | −0.549925 | − | 0.835214i | \(-0.685344\pi\) | ||||
−0.549925 | + | 0.835214i | \(0.685344\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.89037 | + | 6.73832i | −0.376096 | + | 0.651418i | −0.990490 | − | 0.137581i | \(-0.956067\pi\) |
0.614394 | + | 0.788999i | \(0.289400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.75729 | − | 6.50783i | −0.359884 | − | 0.623337i | 0.628058 | − | 0.778167i | \(-0.283850\pi\) |
−0.987941 | + | 0.154830i | \(0.950517\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.03064 | − | 5.24922i | −0.285099 | − | 0.493805i | 0.687534 | − | 0.726152i | \(-0.258693\pi\) |
−0.972633 | + | 0.232346i | \(0.925360\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.521786 | 0.0486568 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.67684 | − | 4.72270i | −0.795405 | − | 0.432929i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.30545 | 0.209586 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.50739 | −0.403153 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.80992 | −0.781754 | −0.390877 | − | 0.920443i | \(-0.627828\pi\) | ||||
−0.390877 | + | 0.920443i | \(0.627828\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.1373 | 1.84678 | 0.923389 | − | 0.383865i | \(-0.125407\pi\) | ||||
0.923389 | + | 0.383865i | \(0.125407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.269748 | + | 10.7227i | 0.0233901 | + | 0.929777i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.40642 | 0.376466 | 0.188233 | − | 0.982124i | \(-0.439724\pi\) | ||||
0.188233 | + | 0.982124i | \(0.439724\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.01245 | + | 1.75362i | 0.0858751 | + | 0.148740i | 0.905764 | − | 0.423783i | \(-0.139298\pi\) |
−0.819889 | + | 0.572523i | \(0.805965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.66372 | − | 4.61369i | −0.222751 | − | 0.385816i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.06654 | − | 3.57935i | 0.171617 | − | 0.297249i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.16225 | 0.750601 | 0.375300 | − | 0.926903i | \(-0.377540\pi\) | ||||
0.375300 | + | 0.926903i | \(0.377540\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.103896 | 0.00845496 | 0.00422748 | − | 0.999991i | \(-0.498654\pi\) | ||||
0.00422748 | + | 0.999991i | \(0.498654\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.118485 | + | 0.205223i | −0.00951698 | + | 0.0164839i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4911 | + | 18.1712i | −0.837285 | + | 1.45022i | 0.0548721 | + | 0.998493i | \(0.482525\pi\) |
−0.892157 | + | 0.451726i | \(0.850808\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.55768 | + | 1.56373i | −0.201574 | + | 0.123239i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5182 | − | 19.9501i | 0.902174 | − | 1.56261i | 0.0775078 | − | 0.996992i | \(-0.475304\pi\) |
0.824666 | − | 0.565620i | \(-0.191363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.31498 | − | 9.20581i | −0.411285 | − | 0.712367i | 0.583745 | − | 0.811937i | \(-0.301587\pi\) |
−0.995031 | + | 0.0995698i | \(0.968253\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.43346 | − | 9.41103i | 0.417959 | − | 0.723926i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.46936 | + | 2.54500i | 0.111713 | + | 0.193493i | 0.916461 | − | 0.400124i | \(-0.131033\pi\) |
−0.804748 | + | 0.593617i | \(0.797699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.8078 | − | 6.60773i | 0.816991 | − | 0.499498i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.58113 | − | 7.93474i | −0.342409 | − | 0.593071i | 0.642470 | − | 0.766311i | \(-0.277910\pi\) |
−0.984880 | + | 0.173240i | \(0.944576\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.4284 | 1.66709 | 0.833545 | − | 0.552452i | \(-0.186308\pi\) | ||||
0.833545 | + | 0.552452i | \(0.186308\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.09718 | + | 3.63242i | −0.154188 | + | 0.267061i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.80992 | − | 11.7951i | −0.497990 | − | 0.862545i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.24484 | − | 2.15613i | −0.0900736 | − | 0.156012i | 0.817468 | − | 0.575974i | \(-0.195377\pi\) |
−0.907542 | + | 0.419962i | \(0.862044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.24484 | + | 3.88818i | −0.161587 | + | 0.279877i | −0.935438 | − | 0.353491i | \(-0.884995\pi\) |
0.773851 | + | 0.633368i | \(0.218328\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.7339 | −0.907249 | −0.453625 | − | 0.891193i | \(-0.649869\pi\) | ||||
−0.453625 | + | 0.891193i | \(0.649869\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.47296 | + | 2.55124i | 0.104415 | + | 0.180852i | 0.913499 | − | 0.406841i | \(-0.133370\pi\) |
−0.809084 | + | 0.587693i | \(0.800036\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.597178 | + | 23.7384i | 0.0419137 | + | 1.66611i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.217799 | + | 0.377240i | 0.0152118 | + | 0.0263476i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.39397 | + | 12.8067i | −0.511451 | + | 0.885860i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.608168 | + | 1.05338i | 0.0418680 | + | 0.0725176i | 0.886200 | − | 0.463303i | \(-0.153336\pi\) |
−0.844332 | + | 0.535820i | \(0.820002\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.14766 | + | 3.71986i | −0.146469 | + | 0.253693i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0342393 | − | 1.36104i | −0.00232432 | − | 0.0923937i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.72665 | + | 4.72270i | −0.183415 | + | 0.317683i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.445916 | − | 0.772349i | 0.0298607 | − | 0.0517203i | −0.850709 | − | 0.525637i | \(-0.823827\pi\) |
0.880570 | + | 0.473917i | \(0.157160\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.6519 | −0.972483 | −0.486242 | − | 0.873824i | \(-0.661632\pi\) | ||||
−0.486242 | + | 0.873824i | \(0.661632\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.57587 | −0.632791 | −0.316396 | − | 0.948627i | \(-0.602473\pi\) | ||||
−0.316396 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.21420 | + | 12.4954i | −0.472618 | + | 0.818598i | −0.999509 | − | 0.0313345i | \(-0.990024\pi\) |
0.526891 | + | 0.849933i | \(0.323358\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.535897 | − | 0.928200i | −0.0349580 | − | 0.0605491i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.15486 | − | 15.8567i | −0.592179 | − | 1.02568i | −0.993938 | − | 0.109938i | \(-0.964935\pi\) |
0.401760 | − | 0.915745i | \(-0.368399\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0933847 | 0.00601544 | 0.00300772 | − | 0.999995i | \(-0.499043\pi\) | ||||
0.00300772 | + | 0.999995i | \(0.499043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.46936 | − | 2.86917i | 0.0938739 | − | 0.183305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.92101 | 0.376745 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.2733 | −1.15340 | −0.576702 | − | 0.816955i | \(-0.695661\pi\) | ||||
−0.576702 | + | 0.816955i | \(0.695661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.13307 | −0.259844 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.0512 | 1.31314 | 0.656568 | − | 0.754267i | \(-0.272008\pi\) | ||||
0.656568 | + | 0.754267i | \(0.272008\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.606032 | − | 24.0903i | −0.0376570 | − | 1.49690i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.16518 | −0.318499 | −0.159249 | − | 0.987238i | \(-0.550907\pi\) | ||||
−0.159249 | + | 0.987238i | \(0.550907\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.86333 | − | 4.95943i | −0.175893 | − | 0.304655i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.42840 | − | 14.5984i | −0.513889 | − | 0.890081i | −0.999870 | − | 0.0161123i | \(-0.994871\pi\) |
0.485981 | − | 0.873969i | \(-0.338462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5562 | + | 21.7480i | −0.762736 | + | 1.32110i | 0.178699 | + | 0.983904i | \(0.442811\pi\) |
−0.941435 | + | 0.337194i | \(0.890522\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.4648 | 1.05317 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.38151 | 0.203176 | 0.101588 | − | 0.994827i | \(-0.467608\pi\) | ||||
0.101588 | + | 0.994827i | \(0.467608\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1388 | − | 17.5609i | 0.604831 | − | 1.04760i | −0.387248 | − | 0.921976i | \(-0.626574\pi\) |
0.992078 | − | 0.125622i | \(-0.0400925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.67471 | − | 15.0250i | 0.515658 | − | 0.893145i | −0.484177 | − | 0.874970i | \(-0.660881\pi\) |
0.999835 | − | 0.0181754i | \(-0.00578571\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.19815 | − | 1.19643i | −0.129753 | − | 0.0706228i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.52918 | − | 2.64861i | 0.0899517 | − | 0.155801i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.93560 | + | 8.54871i | 0.288341 | + | 0.499421i | 0.973414 | − | 0.229054i | \(-0.0735631\pi\) |
−0.685073 | + | 0.728474i | \(0.740230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.96936 | − | 5.14308i | 0.172883 | − | 0.299442i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.827430 | + | 1.43315i | 0.0478515 | + | 0.0828813i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.620621 | − | 24.6703i | −0.0357720 | − | 1.42197i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.78220 | − | 4.81891i | −0.159308 | − | 0.275930i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.78794 | −0.444481 | −0.222240 | − | 0.974992i | \(-0.571337\pi\) | ||||
−0.222240 | + | 0.974992i | \(0.571337\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.70535 | + | 13.3461i | −0.436930 | + | 0.756785i | −0.997451 | − | 0.0713552i | \(-0.977268\pi\) |
0.560521 | + | 0.828140i | \(0.310601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.24844 | − | 7.35851i | −0.240136 | − | 0.415928i | 0.720617 | − | 0.693334i | \(-0.243859\pi\) |
−0.960753 | + | 0.277406i | \(0.910525\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.05262 | − | 12.2155i | −0.396115 | − | 0.686091i | 0.597128 | − | 0.802146i | \(-0.296308\pi\) |
−0.993243 | + | 0.116055i | \(0.962975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.3691 | + | 28.3520i | −0.916491 | + | 1.58741i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.1373 | 0.842264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.49640 | − | 6.05594i | −0.193945 | − | 0.335923i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.40856 | + | 2.94381i | 0.298183 | + | 0.162298i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.7719 | + | 23.8536i | 0.756971 | + | 1.31111i | 0.944388 | + | 0.328832i | \(0.106655\pi\) |
−0.187417 | + | 0.982280i | \(0.560012\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.534239 | + | 0.925330i | −0.0291886 | + | 0.0505562i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.748440 | + | 1.29634i | 0.0407701 | + | 0.0706159i | 0.885690 | − | 0.464276i | \(-0.153686\pi\) |
−0.844920 | + | 0.534892i | \(0.820352\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.938524 | − | 1.62557i | 0.0508239 | − | 0.0880296i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.39610 | + | 18.4676i | 0.0753825 | + | 0.997155i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.14406 | − | 15.8380i | 0.490879 | − | 0.850228i | −0.509066 | − | 0.860728i | \(-0.670009\pi\) |
0.999945 | + | 0.0105001i | \(0.00334233\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.90136 | + | 6.75735i | −0.208835 | + | 0.361713i | −0.951348 | − | 0.308119i | \(-0.900300\pi\) |
0.742513 | + | 0.669832i | \(0.233634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.9253 | −1.43309 | −0.716544 | − | 0.697542i | \(-0.754277\pi\) | ||||
−0.716544 | + | 0.697542i | \(0.754277\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.773541 | 0.0410553 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.13161 | + | 5.42411i | −0.165280 | + | 0.286274i | −0.936755 | − | 0.349987i | \(-0.886186\pi\) |
0.771475 | + | 0.636260i | \(0.219519\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.28220 | + | 2.22084i | 0.0674842 | + | 0.116886i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.04883 | − | 5.28073i | −0.159583 | − | 0.276406i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.2733 | −1.52806 | −0.764028 | − | 0.645183i | \(-0.776781\pi\) | ||||
−0.764028 | + | 0.645183i | \(0.776781\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.8982 | + | 15.7290i | 1.50032 | + | 0.816608i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8597 | 0.924742 | 0.462371 | − | 0.886687i | \(-0.346999\pi\) | ||||
0.462371 | + | 0.886687i | \(0.346999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.1082 | 0.675105 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4255 | 1.15192 | 0.575960 | − | 0.817478i | \(-0.304629\pi\) | ||||
0.575960 | + | 0.817478i | \(0.304629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.1403 | −0.722534 | −0.361267 | − | 0.932462i | \(-0.617656\pi\) | ||||
−0.361267 | + | 0.932462i | \(0.617656\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.79173 | − | 2.31821i | 0.193244 | − | 0.118147i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.1301 | 1.17275 | 0.586373 | − | 0.810041i | \(-0.300555\pi\) | ||||
0.586373 | + | 0.810041i | \(0.300555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.11537 | + | 3.66392i | 0.106979 | + | 0.185292i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.15292 | − | 1.99691i | −0.0580097 | − | 0.100476i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.13307 | + | 8.89075i | −0.257622 | + | 0.446214i | −0.965604 | − | 0.260016i | \(-0.916272\pi\) |
0.707983 | + | 0.706230i | \(0.249605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.0335 | −1.69955 | −0.849775 | − | 0.527146i | \(-0.823262\pi\) | ||||
−0.849775 | + | 0.527146i | \(0.823262\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.751560 | −0.0374379 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.6118 | − | 28.7724i | 0.823415 | − | 1.42620i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.74484 | − | 3.02215i | 0.0862769 | − | 0.149436i | −0.819658 | − | 0.572854i | \(-0.805836\pi\) |
0.905935 | + | 0.423418i | \(0.139170\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.858071 | + | 34.1091i | 0.0422229 | + | 1.67840i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.53064 | − | 2.65115i | 0.0751362 | − | 0.130140i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4897 | + | 25.0969i | 0.707867 | + | 1.22606i | 0.965647 | + | 0.259858i | \(0.0836759\pi\) |
−0.257779 | + | 0.966204i | \(0.582991\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.06128 | + | 1.83819i | −0.0517237 | + | 0.0895881i | −0.890728 | − | 0.454537i | \(-0.849805\pi\) |
0.839004 | + | 0.544125i | \(0.183138\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.93872 | − | 15.4823i | −0.433592 | − | 0.751003i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.0795 | + | 15.2833i | 1.35886 | + | 0.739612i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.9356 | + | 18.9410i | 0.526749 | + | 0.912356i | 0.999514 | + | 0.0311679i | \(0.00992265\pi\) |
−0.472765 | + | 0.881189i | \(0.656744\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0512 | −0.627199 | −0.313599 | − | 0.949555i | \(-0.601535\pi\) | ||||
−0.313599 | + | 0.949555i | \(0.601535\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.29679 | − | 3.97816i | 0.109870 | − | 0.190301i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.43200 | + | 4.21235i | 0.116073 | + | 0.201044i | 0.918208 | − | 0.396098i | \(-0.129636\pi\) |
−0.802135 | + | 0.597143i | \(0.796303\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.76975 | + | 9.99350i | 0.274129 | + | 0.474805i | 0.969915 | − | 0.243444i | \(-0.0782771\pi\) |
−0.695786 | + | 0.718249i | \(0.744944\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.627819 | − | 1.08741i | 0.0297615 | − | 0.0515484i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.4251 | 1.24708 | 0.623538 | − | 0.781793i | \(-0.285694\pi\) | ||||
0.623538 | + | 0.781793i | \(0.285694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.72519 | − | 2.98812i | −0.0812361 | − | 0.140705i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.56294 | − | 0.850689i | −0.0732717 | − | 0.0398809i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.86906 | + | 3.23731i | 0.0874310 | + | 0.151435i | 0.906425 | − | 0.422368i | \(-0.138801\pi\) |
−0.818994 | + | 0.573803i | \(0.805468\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.90496 | − | 13.6918i | 0.368171 | − | 0.637690i | −0.621109 | − | 0.783724i | \(-0.713318\pi\) |
0.989280 | + | 0.146034i | \(0.0466509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.1965 | − | 33.2493i | −0.892137 | − | 1.54523i | −0.837309 | − | 0.546730i | \(-0.815872\pi\) |
−0.0548278 | − | 0.998496i | \(-0.517461\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.15652 | − | 5.46725i | 0.146066 | − | 0.252994i | −0.783704 | − | 0.621134i | \(-0.786672\pi\) |
0.929770 | + | 0.368140i | \(0.120005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.154382 | − | 6.13682i | −0.00712869 | − | 0.283372i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.0117 | − | 29.4651i | 0.782197 | − | 1.35481i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.70535 | + | 16.8102i | −0.445312 | + | 0.771303i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.4136 | −0.932722 | −0.466361 | − | 0.884594i | \(-0.654435\pi\) | ||||
−0.466361 | + | 0.884594i | \(0.654435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3025 | −0.606543 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.57587 | + | 4.46154i | −0.116964 | + | 0.202588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.18190 | − | 10.7074i | −0.280129 | − | 0.485197i | 0.691287 | − | 0.722580i | \(-0.257044\pi\) |
−0.971416 | + | 0.237383i | \(0.923710\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.207004 | + | 0.358541i | 0.00934194 | + | 0.0161807i | 0.870659 | − | 0.491888i | \(-0.163693\pi\) |
−0.861317 | + | 0.508069i | \(0.830360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.5117 | 1.50929 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.79173 | + | 2.31821i | −0.170082 | + | 0.103986i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.923935 | 0.0413610 | 0.0206805 | − | 0.999786i | \(-0.493417\pi\) | ||||
0.0206805 | + | 0.999786i | \(0.493417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.8142 | −1.06182 | −0.530911 | − | 0.847428i | \(-0.678150\pi\) | ||||
−0.530911 | + | 0.847428i | \(0.678150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.33463 | −0.281887 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.6342 | 1.35784 | 0.678919 | − | 0.734213i | \(-0.262449\pi\) | ||||
0.678919 | + | 0.734213i | \(0.262449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.7704 | + | 16.7480i | 1.36120 | + | 0.740887i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.14027 | −0.226507 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.24484 | + | 7.35228i | 0.186688 | + | 0.323353i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.4518 | + | 23.2993i | 0.589336 | + | 1.02076i | 0.994320 | + | 0.106436i | \(0.0339439\pi\) |
−0.404984 | + | 0.914324i | \(0.632723\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.85301 | − | 13.6018i | 0.343388 | − | 0.594766i | −0.641671 | − | 0.766980i | \(-0.721759\pi\) |
0.985060 | + | 0.172214i | \(0.0550920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.92140 | −0.0836975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7161 | −0.944180 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.690757 | + | 1.19643i | −0.0299200 | + | 0.0518230i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.79153 | + | 3.10303i | −0.0774548 | + | 0.134156i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.6388 | + | 22.7267i | −0.501319 | + | 0.978910i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.05934 | + | 3.56688i | −0.0885379 | + | 0.153352i | −0.906893 | − | 0.421360i | \(-0.861553\pi\) |
0.818355 | + | 0.574713i | \(0.194886\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.73025 | − | 2.99689i | −0.0741159 | − | 0.128372i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.8602 | − | 20.5425i | 0.507106 | − | 0.878333i | −0.492860 | − | 0.870108i | \(-0.664049\pi\) |
0.999966 | − | 0.00822465i | \(-0.00261802\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.1929 | − | 31.5110i | −0.775043 | − | 1.34241i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6359 | + | 6.33327i | 0.494808 | + | 0.269318i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.0313 | + | 36.4273i | 0.891125 | + | 1.54347i | 0.838528 | + | 0.544859i | \(0.183417\pi\) |
0.0525975 | + | 0.998616i | \(0.483250\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.6228 | −0.576181 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.91216 | + | 10.2402i | −0.249168 | + | 0.431571i | −0.963295 | − | 0.268445i | \(-0.913490\pi\) |
0.714127 | + | 0.700016i | \(0.246824\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.39562 | − | 2.41729i | −0.0587144 | − | 0.101696i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.10078 | + | 12.2989i | 0.297680 | + | 0.515597i | 0.975605 | − | 0.219534i | \(-0.0704538\pi\) |
−0.677925 | + | 0.735131i | \(0.737120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.97869 | − | 10.3554i | 0.250200 | − | 0.433360i | −0.713380 | − | 0.700777i | \(-0.752837\pi\) |
0.963581 | + | 0.267417i | \(0.0861701\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.42509 | −0.226242 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.3135 | + | 36.9161i | 0.887293 | + | 1.53684i | 0.843062 | + | 0.537816i | \(0.180750\pi\) |
0.0442307 | + | 0.999021i | \(0.485916\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.442317 | + | 17.5825i | 0.0183504 | + | 0.729445i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.6804 | + | 39.2837i | 0.939328 | + | 1.62696i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.5328 | − | 35.5638i | 0.847478 | − | 1.46788i | −0.0359730 | − | 0.999353i | \(-0.511453\pi\) |
0.883451 | − | 0.468523i | \(-0.155214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.04309 | + | 1.80669i | 0.0429799 | + | 0.0744434i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.1008 | + | 27.8874i | −0.661180 | + | 1.14520i | 0.319126 | + | 0.947712i | \(0.396611\pi\) |
−0.980306 | + | 0.197485i | \(0.936723\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.99573 | − | 2.17483i | −0.163809 | − | 0.0891592i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.53590 | + | 16.5167i | −0.389626 | + | 0.674852i | −0.992399 | − | 0.123060i | \(-0.960729\pi\) |
0.602773 | + | 0.797913i | \(0.294062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.27188 | − | 7.39912i | 0.174254 | − | 0.301816i | −0.765649 | − | 0.643259i | \(-0.777582\pi\) |
0.939903 | + | 0.341442i | \(0.110915\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.06167 | 0.0431631 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.0115 | −1.54284 | −0.771419 | − | 0.636328i | \(-0.780453\pi\) | ||||
−0.771419 | + | 0.636328i | \(0.780453\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.69961 | − | 2.94381i | 0.0687589 | − | 0.119094i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.3296 | + | 19.6234i | 0.457597 | + | 0.792581i | 0.998833 | − | 0.0482894i | \(-0.0153770\pi\) |
−0.541237 | + | 0.840870i | \(0.682044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.1388 | + | 17.5609i | 0.408173 | + | 0.706977i | 0.994685 | − | 0.102964i | \(-0.0328327\pi\) |
−0.586512 | + | 0.809941i | \(0.699499\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.06128 | −0.0828499 | −0.0414249 | − | 0.999142i | \(-0.513190\pi\) | ||||
−0.0414249 | + | 0.999142i | \(0.513190\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.181424 | + | 7.21177i | 0.00726860 | + | 0.288933i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.8640 | 0.874560 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.0085 | −1.35601 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.63715 | −0.0651740 | −0.0325870 | − | 0.999469i | \(-0.510375\pi\) | ||||
−0.0325870 | + | 0.999469i | \(0.510375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.05701 | −0.160998 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.2106 | − | 0.514055i | 0.404559 | − | 0.0203676i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9325 | −0.866281 | −0.433140 | − | 0.901326i | \(-0.642595\pi\) | ||||
−0.433140 | + | 0.901326i | \(0.642595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.1819 | + | 24.5638i | 0.559280 | + | 0.968701i | 0.997557 | + | 0.0698609i | \(0.0222555\pi\) |
−0.438277 | + | 0.898840i | \(0.644411\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.3904 | + | 30.1210i | 0.683686 | + | 1.18418i | 0.973848 | + | 0.227201i | \(0.0729575\pi\) |
−0.290162 | + | 0.956978i | \(0.593709\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.5203 | + | 40.7384i | −0.923253 | + | 1.59912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.19863 | 0.125172 | 0.0625860 | − | 0.998040i | \(-0.480065\pi\) | ||||
0.0625860 | + | 0.998040i | \(0.480065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.73385 | 0.380333 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.30418 | − | 9.18711i | 0.206622 | − | 0.357879i | −0.744027 | − | 0.668150i | \(-0.767086\pi\) |
0.950648 | + | 0.310271i | \(0.100420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.06507 | + | 8.77297i | −0.197009 | + | 0.341229i | −0.947557 | − | 0.319586i | \(-0.896456\pi\) |
0.750549 | + | 0.660815i | \(0.229789\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.124220 | + | 4.93786i | 0.00481705 | + | 0.191482i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.08472 | − | 8.80700i | 0.196881 | − | 0.341008i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.0378 | + | 38.1707i | 0.850761 | + | 1.47356i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.60817 | − | 2.78543i | 0.0619903 | − | 0.107370i | −0.833365 | − | 0.552724i | \(-0.813589\pi\) |
0.895355 | + | 0.445353i | \(0.146922\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6819 | − | 25.4298i | −0.564271 | − | 0.977347i | −0.997117 | − | 0.0758786i | \(-0.975824\pi\) |
0.432846 | − | 0.901468i | \(-0.357509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.744363 | − | 29.5891i | −0.0285660 | − | 1.13552i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6278 | + | 21.8720i | 0.483190 | + | 0.836910i | 0.999814 | − | 0.0193029i | \(-0.00614468\pi\) |
−0.516624 | + | 0.856213i | \(0.672811\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.02918 | 0.0775309 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.08113 | − | 15.7290i | 0.345963 | − | 0.599226i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.68190 | − | 13.3054i | −0.292233 | − | 0.506163i | 0.682104 | − | 0.731255i | \(-0.261065\pi\) |
−0.974338 | + | 0.225092i | \(0.927732\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.466240 | + | 0.807551i | 0.0176855 | + | 0.0306321i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.76595 | + | 3.05872i | −0.0668903 | + | 0.115857i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3700 | 0.504980 | 0.252490 | − | 0.967600i | \(-0.418751\pi\) | ||||
0.252490 | + | 0.967600i | \(0.418751\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.4626 | + | 31.9782i | 0.696332 | + | 1.20608i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.0510 | − | 18.9842i | 1.16779 | − | 0.713972i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.562939 | + | 0.975038i | 0.0211416 | + | 0.0366183i | 0.876403 | − | 0.481579i | \(-0.159937\pi\) |
−0.855261 | + | 0.518197i | \(0.826603\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.291534 | + | 0.504951i | −0.0109180 | + | 0.0189106i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.22665 | − | 2.12463i | −0.0458743 | − | 0.0794565i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.13667 | − | 15.8252i | 0.340740 | − | 0.590180i | −0.643830 | − | 0.765169i | \(-0.722656\pi\) |
0.984570 | + | 0.174989i | \(0.0559889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.1965 | − | 15.4048i | 0.938366 | − | 0.573705i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.4861 | + | 37.2150i | −0.797973 | + | 1.38213i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.8478 | − | 25.7171i | 0.550673 | − | 0.953793i | −0.447553 | − | 0.894257i | \(-0.647705\pi\) |
0.998226 | − | 0.0595359i | \(-0.0189621\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.8272 | −1.28813 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.2278 | 0.710195 | 0.355098 | − | 0.934829i | \(-0.384448\pi\) | ||||
0.355098 | + | 0.934829i | \(0.384448\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.23171 | − | 7.32955i | 0.155877 | − | 0.269987i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.1336 | + | 26.2121i | 0.556697 | + | 0.964227i | 0.997769 | + | 0.0667556i | \(0.0212648\pi\) |
−0.441073 | + | 0.897471i | \(0.645402\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.8815 | − | 20.5794i | −0.435890 | − | 0.754984i | 0.561477 | − | 0.827492i | \(-0.310233\pi\) |
−0.997368 | + | 0.0725076i | \(0.976900\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.21926 | 0.154582 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.517709 | − | 20.5794i | −0.0189167 | − | 0.751954i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6683 | −0.462273 | −0.231136 | − | 0.972921i | \(-0.574244\pi\) | ||||
−0.231136 | + | 0.972921i | \(0.574244\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.0478448 | 0.00174125 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.0799 | −1.05693 | −0.528464 | − | 0.848955i | \(-0.677232\pi\) | ||||
−0.528464 | + | 0.848955i | \(0.677232\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.2029 | −1.05860 | −0.529302 | − | 0.848433i | \(-0.677546\pi\) | ||||
−0.529302 | + | 0.848433i | \(0.677546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.4626 | + | 9.50471i | 0.632190 | + | 0.344094i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.8348 | 0.680086 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.5869 | + | 21.8011i | 0.453894 | + | 0.786167i | 0.998624 | − | 0.0524443i | \(-0.0167012\pi\) |
−0.544730 | + | 0.838611i | \(0.683368\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.752039 | + | 1.30257i | 0.0270490 | + | 0.0468502i | 0.879233 | − | 0.476392i | \(-0.158056\pi\) |
−0.852184 | + | 0.523242i | \(0.824722\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.23191 | − | 2.13373i | 0.0442515 | − | 0.0766458i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.83482 | 0.137397 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.12722 | −0.219249 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.83122 | + | 8.36792i | −0.172434 | + | 0.298664i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.47656 | + | 12.9498i | −0.266510 | + | 0.461610i | −0.967958 | − | 0.251111i | \(-0.919204\pi\) |
0.701448 | + | 0.712721i | \(0.252537\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0854 | + | 7.66652i | 0.500819 | + | 0.272590i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.82383 | − | 15.2833i | 0.313343 | − | 0.542727i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.56294 | + | 7.90324i | 0.161628 | + | 0.279947i | 0.935453 | − | 0.353452i | \(-0.114992\pi\) |
−0.773825 | + | 0.633400i | \(0.781659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.34514 | − | 7.52600i | 0.153720 | − | 0.266251i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.1498 | + | 41.8287i | 0.852228 | + | 1.47610i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.17783 | + | 0.720107i | −0.0415129 | + | 0.0253804i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.7755 | − | 30.7880i | −0.624953 | − | 1.08245i | −0.988550 | − | 0.150894i | \(-0.951785\pi\) |
0.363597 | − | 0.931556i | \(-0.381548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.5070 | 0.474295 | 0.237148 | − | 0.971474i | \(-0.423788\pi\) | ||||
0.237148 | + | 0.971474i | \(0.423788\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.30418 | − | 9.18711i | 0.185797 | − | 0.321810i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.9071 | + | 32.7480i | 0.661475 | + | 1.14571i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.8114 | + | 18.7259i | 0.377320 | + | 0.653537i | 0.990671 | − | 0.136273i | \(-0.0435125\pi\) |
−0.613352 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.753501 | + | 1.30510i | −0.0262654 | + | 0.0454930i | −0.878859 | − | 0.477081i | \(-0.841695\pi\) |
0.852594 | + | 0.522574i | \(0.175028\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.3786 | 0.812953 | 0.406477 | − | 0.913661i | \(-0.366757\pi\) | ||||
0.406477 | + | 0.913661i | \(0.366757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0095 | − | 19.0691i | −0.382377 | − | 0.662296i | 0.609025 | − | 0.793151i | \(-0.291561\pi\) |
−0.991401 | + | 0.130855i | \(0.958228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.1039 | − | 1.31421i | 0.904446 | − | 0.0455345i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.44757 | − | 4.23932i | −0.0847018 | − | 0.146708i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.06507 | + | 1.84476i | −0.0367705 | + | 0.0636883i | −0.883825 | − | 0.467818i | \(-0.845040\pi\) |
0.847055 | + | 0.531506i | \(0.178374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.7762 | − | 44.6456i | −0.888833 | − | 1.53950i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.50214 | − | 4.33383i | 0.0860761 | − | 0.149088i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.20408 | + | 3.18171i | −0.178814 | + | 0.109325i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.16012 | + | 8.93758i | −0.176887 | + | 0.306376i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.50146 | + | 6.06471i | −0.119888 | + | 0.207652i | −0.919723 | − | 0.392568i | \(-0.871587\pi\) |
0.799835 | + | 0.600220i | \(0.204920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.9282 | −0.373300 | −0.186650 | − | 0.982426i | \(-0.559763\pi\) | ||||
−0.186650 | + | 0.982426i | \(0.559763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.9076 | 0.474520 | 0.237260 | − | 0.971446i | \(-0.423751\pi\) | ||||
0.237260 | + | 0.971446i | \(0.423751\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.4231 | + | 31.9098i | −0.627131 | + | 1.08622i | 0.360993 | + | 0.932568i | \(0.382438\pi\) |
−0.988125 | + | 0.153655i | \(0.950896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.676647 | + | 1.17199i | 0.0230067 | + | 0.0398488i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.13229 | + | 15.8176i | 0.309792 | + | 0.536575i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.38871 | −0.114822 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.1745 | − | 6.22056i | 0.343961 | − | 0.210293i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3595 | −0.349817 | −0.174908 | − | 0.984585i | \(-0.555963\pi\) | ||||
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.34806 | −0.314944 | −0.157472 | − | 0.987523i | \(-0.550334\pi\) | ||||
−0.157472 | + | 0.987523i | \(0.550334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.29494 | −0.0772308 | −0.0386154 | − | 0.999254i | \(-0.512295\pi\) | ||||
−0.0386154 | + | 0.999254i | \(0.512295\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.6726 | −0.929154 | −0.464577 | − | 0.885533i | \(-0.653794\pi\) | ||||
−0.464577 | + | 0.885533i | \(0.653794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.8866 | − | 12.1584i | 0.666974 | − | 0.407779i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.43560 | −0.315750 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.10963 | − | 3.65399i | −0.0705172 | − | 0.122139i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.30924 | + | 3.99973i | 0.0770176 | + | 0.133398i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.2163 | − | 40.2119i | 0.773448 | − | 1.33965i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.3284 | 0.343327 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.93152 | 0.0973396 | 0.0486698 | − | 0.998815i | \(-0.484502\pi\) | ||||
0.0486698 | + | 0.998815i | \(0.484502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.3171 | − | 26.5300i | 0.507479 | − | 0.878979i | −0.492484 | − | 0.870322i | \(-0.663911\pi\) |
0.999963 | − | 0.00865719i | \(-0.00275570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.1242 | + | 20.9998i | −0.401253 | + | 0.694991i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.7132 | + | 29.1712i | −1.57563 | + | 0.963319i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.1857 | + | 22.8383i | −0.434956 | + | 0.753366i | −0.997292 | − | 0.0735429i | \(-0.976569\pi\) |
0.562336 | + | 0.826909i | \(0.309903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.22665 | + | 2.12463i | 0.0403758 | + | 0.0699329i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.8047 | − | 37.7668i | 0.716933 | − | 1.24176i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.93706 | + | 15.4794i | 0.293215 | + | 0.507864i | 0.974568 | − | 0.224091i | \(-0.0719413\pi\) |
−0.681353 | + | 0.731955i | \(0.738608\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.4071 | − | 23.8320i | −0.504947 | − | 0.781063i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.13600 | − | 5.43171i | −0.102558 | − | 0.177636i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.9134 | 0.519869 | 0.259934 | − | 0.965626i | \(-0.416299\pi\) | ||||
0.259934 | + | 0.965626i | \(0.416299\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.14027 | + | 14.0994i | −0.265365 | + | 0.459626i | −0.967659 | − | 0.252261i | \(-0.918826\pi\) |
0.702294 | + | 0.711887i | \(0.252159\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.535897 | + | 0.928200i | 0.0174512 | + | 0.0302264i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.2951 | + | 24.7599i | 0.464529 | + | 0.804589i | 0.999180 | − | 0.0404846i | \(-0.0128902\pi\) |
−0.534651 | + | 0.845073i | \(0.679557\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.66945 | − | 16.7480i | 0.313884 | − | 0.543662i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.3537 | 0.950859 | 0.475430 | − | 0.879754i | \(-0.342293\pi\) | ||||
0.475430 | + | 0.879754i | \(0.342293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.573256 | − | 0.992908i | −0.0185501 | − | 0.0321297i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.94659 | + | 6.08121i | −0.321192 | + | 0.196373i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3676 | + | 26.6175i | 0.495729 | + | 0.858628i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.03376 | + | 1.79053i | −0.0332779 | + | 0.0576391i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.69815 | + | 8.13743i | 0.151082 | + | 0.261682i | 0.931626 | − | 0.363419i | \(-0.118391\pi\) |
−0.780543 | + | 0.625102i | \(0.785057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.77335 | − | 13.4638i | 0.249459 | − | 0.432075i | −0.713917 | − | 0.700230i | \(-0.753081\pi\) |
0.963376 | + | 0.268155i | \(0.0864140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.70554 | − | 2.56117i | −0.150853 | − | 0.0821074i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.79893 | + | 8.31198i | −0.153531 | + | 0.265924i | −0.932523 | − | 0.361110i | \(-0.882398\pi\) |
0.778992 | + | 0.627034i | \(0.215731\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.97296 | + | 8.61342i | −0.158936 | + | 0.275286i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.8535 | −1.49439 | −0.747197 | − | 0.664603i | \(-0.768601\pi\) | ||||
−0.747197 | + | 0.664603i | \(0.768601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.86400 | −0.186843 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.28434 | + | 9.15274i | −0.168032 | + | 0.291040i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.8260 | − | 18.7511i | −0.343898 | − | 0.595649i | 0.641255 | − | 0.767328i | \(-0.278414\pi\) |
−0.985153 | + | 0.171679i | \(0.945081\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.678304 | + | 1.17486i | 0.0215037 | + | 0.0372455i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.2379 | −1.81274 | −0.906372 | − | 0.422481i | \(-0.861159\pi\) | ||||
−0.906372 | + | 0.422481i | \(0.861159\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))