Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,2,Mod(17,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.i (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.479102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.2 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.17 |
Dual form | 60.2.i.a.53.2 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.61803 | + | 0.618034i | 0.934172 | + | 0.356822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 1.00000i | −0.377964 | − | 0.377964i | 0.492403 | − | 0.870367i | \(-0.336119\pi\) |
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.47214i | − | 1.34840i | −0.738549 | − | 0.674200i | \(-0.764489\pi\) | ||
0.738549 | − | 0.674200i | \(-0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.61803 | − | 1.38197i | −0.934172 | − | 0.356822i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.23607 | + | 2.23607i | −0.542326 | + | 0.542326i | −0.924210 | − | 0.381884i | \(-0.875275\pi\) |
0.381884 | + | 0.924210i | \(0.375275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | − | 2.23607i | −0.218218 | − | 0.487950i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.23607 | + | 2.23607i | 0.466252 | + | 0.466252i | 0.900698 | − | 0.434446i | \(-0.143056\pi\) |
−0.434446 | + | 0.900698i | \(0.643056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.38197 | + | 4.61803i | 0.458410 | + | 0.888741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.76393 | − | 7.23607i | 0.481139 | − | 1.25964i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.23607 | + | 2.23607i | 0.377964 | + | 0.377964i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.70820 | + | 3.00000i | −1.07417 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.94427i | 1.39686i | 0.715678 | + | 0.698430i | \(0.246118\pi\) | ||||
−0.715678 | + | 0.698430i | \(0.753882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | + | 3.00000i | −0.457496 | + | 0.457496i | −0.897833 | − | 0.440337i | \(-0.854859\pi\) |
0.440337 | + | 0.897833i | \(0.354859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.00000 | − | 4.47214i | −0.745356 | − | 0.666667i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.70820 | − | 6.70820i | 0.978492 | − | 0.978492i | −0.0212814 | − | 0.999774i | \(-0.506775\pi\) |
0.999774 | + | 0.0212814i | \(0.00677460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.00000 | + | 2.23607i | −0.700140 | + | 0.313112i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.23607 | − | 2.23607i | −0.307148 | − | 0.307148i | 0.536655 | − | 0.843802i | \(-0.319688\pi\) |
−0.843802 | + | 0.536655i | \(0.819688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0000i | 1.34840i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.23607 | − | 3.23607i | 0.163721 | − | 0.428628i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.94427 | −1.16445 | −0.582223 | − | 0.813029i | \(-0.697817\pi\) | ||||
−0.582223 | + | 0.813029i | \(0.697817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.236068 | − | 4.23607i | −0.0297418 | − | 0.533694i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.70820 | − | 6.70820i | 0.832050 | − | 0.832050i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.00000i | −0.122169 | − | 0.122169i | 0.643379 | − | 0.765548i | \(-0.277532\pi\) |
−0.765548 | + | 0.643379i | \(0.777532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.23607 | + | 5.00000i | 0.269191 | + | 0.601929i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.47214i | 0.530745i | 0.964146 | + | 0.265372i | \(0.0854949\pi\) | ||||
−0.964146 | + | 0.265372i | \(0.914505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | − | 1.00000i | 0.117041 | − | 0.117041i | −0.646160 | − | 0.763202i | \(-0.723626\pi\) |
0.763202 | + | 0.646160i | \(0.223626\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.09017 | + | 3.09017i | 0.934172 | + | 0.356822i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.47214 | + | 4.47214i | −0.509647 | + | 0.509647i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.00000i | − | 0.675053i | −0.941316 | − | 0.337526i | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.70820 | − | 6.70820i | −0.736321 | − | 0.736321i | 0.235543 | − | 0.971864i | \(-0.424313\pi\) |
−0.971864 | + | 0.235543i | \(0.924313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | − | 5.00000i | 0.542326 | − | 0.542326i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.23607 | + | 2.76393i | 0.775788 | + | 0.296325i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.47214 | −0.474045 | −0.237023 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.47214 | + | 2.47214i | 0.671129 | + | 0.256349i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.47214i | 0.458831i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.00000 | + | 9.00000i | 0.913812 | + | 0.913812i | 0.996570 | − | 0.0827581i | \(-0.0263729\pi\) |
−0.0827581 | + | 0.996570i | \(0.526373\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.94427 | − | 10.0000i | 0.898933 | − | 1.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.94427i | − | 0.889988i | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||
0.895533 | − | 0.444994i | \(-0.146794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.00000 | − | 1.00000i | 0.0985329 | − | 0.0985329i | −0.656122 | − | 0.754655i | \(-0.727804\pi\) |
0.754655 | + | 0.656122i | \(0.227804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.23607 | + | 5.00000i | 0.218218 | + | 0.487950i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.23607 | + | 2.23607i | −0.216169 | + | 0.216169i | −0.806882 | − | 0.590713i | \(-0.798847\pi\) |
0.590713 | + | 0.806882i | \(0.298847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000i | 0.766261i | 0.923694 | + | 0.383131i | \(0.125154\pi\) | ||||
−0.923694 | + | 0.383131i | \(0.874846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | − | 6.70820i | −0.284747 | − | 0.636715i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.23607 | − | 2.23607i | −0.210352 | − | 0.210352i | 0.594065 | − | 0.804417i | \(-0.297522\pi\) |
−0.804417 | + | 0.594065i | \(0.797522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.00000 | − | 5.00000i | −0.466252 | − | 0.466252i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.7082 | + | 0.708204i | −1.17487 | + | 0.0654735i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.47214 | 0.409960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.52786 | + | 14.4721i | −0.498431 | + | 1.30491i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | − | 13.0000i | −1.15356 | − | 1.15356i | −0.985833 | − | 0.167731i | \(-0.946356\pi\) |
−0.167731 | − | 0.985833i | \(-0.553644\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.70820 | + | 3.00000i | −0.590624 | + | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.47214i | − | 0.390732i | −0.980730 | − | 0.195366i | \(-0.937410\pi\) | ||
0.980730 | − | 0.195366i | \(-0.0625895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | + | 2.00000i | −0.173422 | + | 0.173422i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.32624 | − | 10.3262i | −0.458410 | − | 0.888741i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.70820 | − | 6.70820i | 0.573121 | − | 0.573121i | −0.359879 | − | 0.932999i | \(-0.617182\pi\) |
0.932999 | + | 0.359879i | \(0.117182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000i | 1.18746i | 0.804663 | + | 0.593732i | \(0.202346\pi\) | ||||
−0.804663 | + | 0.593732i | \(0.797654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.0000 | − | 6.70820i | 1.26323 | − | 0.564933i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.4164 | + | 13.4164i | 1.12194 | + | 1.12194i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.0000 | −0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.09017 | − | 8.09017i | 0.254873 | − | 0.667266i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.4164 | 1.09911 | 0.549557 | − | 0.835456i | \(-0.314796\pi\) | ||||
0.549557 | + | 0.835456i | \(0.314796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.47214 | + | 0.527864i | −0.765777 | + | 0.0426753i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.94427 | −0.718421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 9.00000i | 0.718278 | + | 0.718278i | 0.968252 | − | 0.249974i | \(-0.0804222\pi\) |
−0.249974 | + | 0.968252i | \(0.580422\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.23607 | − | 5.00000i | −0.177332 | − | 0.396526i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.47214i | − | 0.352454i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0000 | − | 17.0000i | 1.33154 | − | 1.33154i | 0.427552 | − | 0.903991i | \(-0.359376\pi\) |
0.903991 | − | 0.427552i | \(-0.140624\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.18034 | + | 16.1803i | −0.481139 | + | 1.25964i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.1803 | + | 11.1803i | −0.865161 | + | 0.865161i | −0.991932 | − | 0.126771i | \(-0.959539\pi\) |
0.126771 | + | 0.991932i | \(0.459539\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | − | 4.47214i | 0.305888 | − | 0.341993i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.6525 | + | 15.6525i | 1.19004 | + | 1.19004i | 0.977057 | + | 0.212979i | \(0.0683166\pi\) |
0.212979 | + | 0.977057i | \(0.431683\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.00000 | − | 5.00000i | −0.377964 | − | 0.377964i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.4721 | − | 5.52786i | −1.08779 | − | 0.415500i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.94427 | 0.668526 | 0.334263 | − | 0.942480i | \(-0.391513\pi\) | ||||
0.334263 | + | 0.942480i | \(0.391513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.70820 | − | 3.70820i | −0.717651 | − | 0.274118i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.70820 | + | 6.70820i | 0.493197 | + | 0.493197i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0000 | + | 10.0000i | 0.731272 | + | 0.731272i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.23607 | − | 7.00000i | 0.162650 | − | 0.509175i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.47214i | 0.323592i | 0.986824 | + | 0.161796i | \(0.0517287\pi\) | ||||
−0.986824 | + | 0.161796i | \(0.948271\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.00000 | + | 3.00000i | −0.215945 | + | 0.215945i | −0.806787 | − | 0.590842i | \(-0.798796\pi\) |
0.590842 | + | 0.806787i | \(0.298796\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.0000 | − | 6.70820i | 1.07417 | − | 0.480384i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.70820 | − | 6.70820i | 0.477940 | − | 0.477940i | −0.426532 | − | 0.904472i | \(-0.640265\pi\) |
0.904472 | + | 0.426532i | \(0.140265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0000i | 1.27599i | 0.770042 | + | 0.637993i | \(0.220235\pi\) | ||||
−0.770042 | + | 0.637993i | \(0.779765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | − | 2.23607i | −0.0705346 | − | 0.157720i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.47214 | − | 4.47214i | −0.313882 | − | 0.313882i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 20.0000i | − | 1.39686i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.527864 | + | 9.47214i | 0.0366891 | + | 0.658359i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.94427 | −0.618688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.76393 | + | 7.23607i | −0.189382 | + | 0.495807i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.70820 | − | 6.70820i | 0.457496 | − | 0.457496i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | − | 4.00000i | −0.271538 | − | 0.271538i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.23607 | − | 1.00000i | 0.151099 | − | 0.0675737i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.4164i | − | 0.902485i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.00000 | + | 3.00000i | −0.200895 | + | 0.200895i | −0.800383 | − | 0.599489i | \(-0.795371\pi\) |
0.599489 | + | 0.800383i | \(0.295371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.1803 | + | 10.0000i | 0.745356 | + | 0.666667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.1803 | + | 11.1803i | −0.742065 | + | 0.742065i | −0.972975 | − | 0.230910i | \(-0.925830\pi\) |
0.230910 | + | 0.972975i | \(0.425830\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.0000i | − | 0.792982i | −0.918039 | − | 0.396491i | \(-0.870228\pi\) | ||
0.918039 | − | 0.396491i | \(-0.129772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0000 | + | 4.47214i | −0.657952 | + | 0.294245i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.1246 | − | 20.1246i | −1.31841 | − | 1.31841i | −0.915037 | − | 0.403370i | \(-0.867839\pi\) |
−0.403370 | − | 0.915037i | \(-0.632161\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.0000 | + | 15.0000i | −0.978492 | + | 0.978492i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.70820 | − | 9.70820i | 0.240874 | − | 0.630616i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0000 | −1.67481 | −0.837404 | − | 0.546585i | \(-0.815928\pi\) | ||||
−0.837404 | + | 0.546585i | \(0.815928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.90983 | + | 15.0902i | −0.250816 | + | 0.968035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.1803i | 0.714286i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | + | 6.00000i | 0.381771 | + | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.70820 | − | 15.0000i | −0.425115 | − | 0.950586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4164i | 0.846836i | 0.905934 | + | 0.423418i | \(0.139170\pi\) | ||||
−0.905934 | + | 0.423418i | \(0.860830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0000 | − | 10.0000i | 0.628695 | − | 0.628695i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.1803 | − | 5.00000i | 0.700140 | − | 0.313112i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.6525 | − | 15.6525i | 0.976375 | − | 0.976375i | −0.0233527 | − | 0.999727i | \(-0.507434\pi\) |
0.999727 | + | 0.0233527i | \(0.00743406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000i | 0.372822i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0000 | + | 8.94427i | 0.618984 | + | 0.553637i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.6525 | − | 15.6525i | −0.965173 | − | 0.965173i | 0.0342406 | − | 0.999414i | \(-0.489099\pi\) |
−0.999414 | + | 0.0342406i | \(0.989099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.00000 | + | 5.00000i | 0.307148 | + | 0.307148i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.23607 | − | 2.76393i | −0.442840 | − | 0.169150i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.3607 | −1.36335 | −0.681677 | − | 0.731653i | \(-0.738749\pi\) | ||||
−0.681677 | + | 0.731653i | \(0.738749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.70820 | + | 3.70820i | 0.587567 | + | 0.224431i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 22.3607i | − | 1.34840i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.00000 | + | 9.00000i | 0.540758 | + | 0.540758i | 0.923751 | − | 0.382993i | \(-0.125107\pi\) |
−0.382993 | + | 0.923751i | \(0.625107\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.94427 | + | 8.00000i | 0.535480 | + | 0.478947i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.8328i | 1.60071i | 0.599525 | + | 0.800356i | \(0.295356\pi\) | ||||
−0.599525 | + | 0.800356i | \(0.704644\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0000 | − | 17.0000i | 1.01055 | − | 1.01055i | 0.0106013 | − | 0.999944i | \(-0.496625\pi\) |
0.999944 | − | 0.0106013i | \(-0.00337456\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.76393 | + | 7.23607i | −0.163721 | + | 0.428628i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.94427 | − | 8.94427i | 0.527964 | − | 0.527964i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000i | 0.411765i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.00000 | + | 20.1246i | 0.527589 | + | 1.17973i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.70820 | + | 6.70820i | 0.391897 | + | 0.391897i | 0.875363 | − | 0.483466i | \(-0.160622\pi\) |
−0.483466 | + | 0.875363i | \(0.660622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.0000 | 1.16445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.6525 | − | 10.6525i | 1.19838 | − | 0.618119i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.4164 | −0.775891 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | 0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.52786 | − | 14.4721i | 0.317567 | − | 0.831402i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.4164 | 0.768221 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.0000 | − | 21.0000i | −1.19853 | − | 1.19853i | −0.974606 | − | 0.223928i | \(-0.928112\pi\) |
−0.223928 | − | 0.974606i | \(-0.571888\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.23607 | − | 1.00000i | 0.127205 | − | 0.0568880i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.47214i | 0.253592i | 0.991929 | + | 0.126796i | \(0.0404693\pi\) | ||||
−0.991929 | + | 0.126796i | \(0.959531\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.00000 | + | 3.00000i | −0.169570 | + | 0.169570i | −0.786790 | − | 0.617220i | \(-0.788259\pi\) |
0.617220 | + | 0.786790i | \(0.288259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.527864 | + | 9.47214i | 0.0297418 | + | 0.533694i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.1246 | + | 20.1246i | −1.13031 | + | 1.13031i | −0.140186 | + | 0.990125i | \(0.544770\pi\) |
−0.990125 | + | 0.140186i | \(0.955230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 20.0000i | − | 1.11979i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.00000 | + | 2.23607i | −0.279073 | + | 0.124805i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.47214 | + | 4.47214i | 0.248836 | + | 0.248836i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0000 | + | 15.0000i | −0.832050 | + | 0.832050i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.94427 | + | 12.9443i | −0.273419 | + | 0.715820i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.4164 | −0.739671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.708204 | − | 12.7082i | −0.0388093 | − | 0.696405i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.23607 | + | 2.23607i | 0.122169 | + | 0.122169i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.00000 | + | 9.00000i | 0.490261 | + | 0.490261i | 0.908388 | − | 0.418127i | \(-0.137313\pi\) |
−0.418127 | + | 0.908388i | \(0.637313\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.23607 | − | 5.00000i | −0.121447 | − | 0.271563i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 17.8885i | − | 0.968719i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.00000 | − | 11.1803i | −0.269191 | − | 0.601929i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.5967 | − | 24.5967i | 1.32042 | − | 1.32042i | 0.406990 | − | 0.913433i | \(-0.366578\pi\) |
0.913433 | − | 0.406990i | \(-0.133422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.00000i | 0.214115i | 0.994253 | + | 0.107058i | \(0.0341429\pi\) | ||||
−0.994253 | + | 0.107058i | \(0.965857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.0000 | − | 6.70820i | −1.12090 | − | 0.358057i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.70820 | + | 6.70820i | 0.357042 | + | 0.357042i | 0.862721 | − | 0.505680i | \(-0.168758\pi\) |
−0.505680 | + | 0.862721i | \(0.668758\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 10.0000i | − | 0.530745i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.23607 | + | 2.76393i | 0.382973 | + | 0.146283i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.7771 | 1.88824 | 0.944121 | − | 0.329598i | \(-0.106913\pi\) | ||||
0.944121 | + | 0.329598i | \(0.106913\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.5623 | − | 5.56231i | −0.764323 | − | 0.291945i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.23607 | + | 2.23607i | −0.117041 | + | 0.117041i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.00000 | − | 1.00000i | −0.0521996 | − | 0.0521996i | 0.680525 | − | 0.732725i | \(-0.261752\pi\) |
−0.732725 | + | 0.680525i | \(0.761752\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.8885 | + | 20.0000i | −0.931240 | + | 1.04116i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.47214i | 0.232182i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.0000 | + | 23.0000i | −1.19089 | + | 1.19089i | −0.214078 | + | 0.976816i | \(0.568675\pi\) |
−0.976816 | + | 0.214078i | \(0.931325\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0902 | − | 6.90983i | −0.934172 | − | 0.356822i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.4164 | + | 13.4164i | −0.690980 | + | 0.690980i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.00000i | − | 0.102733i | −0.998680 | − | 0.0513665i | \(-0.983642\pi\) | ||
0.998680 | − | 0.0513665i | \(-0.0163577\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.0000 | − | 29.0689i | −0.666010 | − | 1.48924i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.70820 | − | 6.70820i | −0.342773 | − | 0.342773i | 0.514636 | − | 0.857409i | \(-0.327927\pi\) |
−0.857409 | + | 0.514636i | \(0.827927\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0000 | − | 10.0000i | 0.509647 | − | 0.509647i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.7082 | + | 0.708204i | −0.645994 | + | 0.0360000i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4164 | 0.680239 | 0.340119 | − | 0.940382i | \(-0.389532\pi\) | ||||
0.340119 | + | 0.940382i | \(0.389532\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0000 | −0.505722 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.76393 | − | 7.23607i | 0.139422 | − | 0.365011i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.4164i | 0.675053i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0000 | − | 11.0000i | −0.552074 | − | 0.552074i | 0.374965 | − | 0.927039i | \(-0.377655\pi\) |
−0.927039 | + | 0.374965i | \(0.877655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.47214 | + | 2.00000i | −0.223887 | + | 0.100125i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | + | 12.0000i | −0.597763 | + | 0.597763i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.23607 | − | 20.0000i | −0.111111 | − | 0.993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.4164 | + | 13.4164i | −0.665027 | + | 0.665027i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.0000i | − | 0.593362i | −0.954977 | − | 0.296681i | \(-0.904120\pi\) | ||
0.954977 | − | 0.296681i | \(-0.0958798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.0000 | − | 6.70820i | 0.739895 | − | 0.330891i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.94427 | + | 8.94427i | 0.440119 | + | 0.440119i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0000 | + | 15.0000i | 0.736321 | + | 0.736321i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.65248 | + | 22.6525i | −0.423714 | + | 1.10930i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.8328 | 1.31087 | 0.655434 | − | 0.755252i | \(-0.272486\pi\) | ||||
0.655434 | + | 0.755252i | \(0.272486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.4164 | − | 1.58359i | 1.38165 | − | 0.0769969i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.1803 | + | 11.1803i | −0.542326 | + | 0.542326i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | + | 6.00000i | 0.290360 | + | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.4164 | + | 30.0000i | 0.647750 | + | 1.44841i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 31.3050i | − | 1.50791i | −0.656928 | − | 0.753953i | \(-0.728145\pi\) | ||
0.656928 | − | 0.753953i | \(-0.271855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | − | 17.0000i | 0.816968 | − | 0.816968i | −0.168700 | − | 0.985668i | \(-0.553957\pi\) |
0.985668 | + | 0.168700i | \(0.0539568\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.1803 | − | 6.18034i | −0.775788 | − | 0.296325i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.47214 | − | 4.47214i | 0.213931 | − | 0.213931i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.0000i | − | 1.05000i | −0.851101 | − | 0.525001i | \(-0.824065\pi\) | ||
0.851101 | − | 0.525001i | \(-0.175935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.0000 | − | 11.1803i | 0.476190 | − | 0.532397i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.1246 | + | 20.1246i | 0.956149 | + | 0.956149i | 0.999078 | − | 0.0429290i | \(-0.0136689\pi\) |
−0.0429290 | + | 0.999078i | \(0.513669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | 0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.7082 | + | 8.29180i | 1.02676 | + | 0.392188i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.47214 | 0.211053 | 0.105527 | − | 0.994416i | \(-0.466347\pi\) | ||||
0.105527 | + | 0.994416i | \(0.466347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0000 | 1.88353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.47214 | + | 2.47214i | 0.304087 | + | 0.116151i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.4164 | −0.628971 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.00000 | − | 3.00000i | −0.140334 | − | 0.140334i | 0.633450 | − | 0.773784i | \(-0.281638\pi\) |
−0.773784 | + | 0.633450i | \(0.781638\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.6525 | − | 5.00000i | −0.730595 | − | 0.233380i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.94427i | 0.416576i | 0.978068 | + | 0.208288i | \(0.0667892\pi\) | ||||
−0.978068 | + | 0.208288i | \(0.933211\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.0000 | + | 19.0000i | −0.883005 | + | 0.883005i | −0.993839 | − | 0.110834i | \(-0.964648\pi\) |
0.110834 | + | 0.993839i | \(0.464648\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.4721 | − | 5.52786i | −0.671129 | − | 0.256349i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.23607 | + | 2.23607i | −0.103473 | + | 0.103473i | −0.756948 | − | 0.653475i | \(-0.773310\pi\) |
0.653475 | + | 0.756948i | \(0.273310\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000i | 0.0923514i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.00000 | + | 20.1246i | 0.414698 | + | 0.927293i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.4164 | + | 13.4164i | 0.616887 | + | 0.616887i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 10.0000i | − | 0.458831i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.527864 | − | 9.47214i | −0.0241692 | − | 0.433699i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.7771 | −1.63470 | −0.817348 | − | 0.576144i | \(-0.804557\pi\) | ||||
−0.817348 | + | 0.576144i | \(0.804557\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.76393 | − | 7.23607i | 0.125763 | − | 0.329252i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.1246 | − | 20.1246i | −0.913812 | − | 0.913812i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.0000 | − | 21.0000i | −0.951601 | − | 0.951601i | 0.0472808 | − | 0.998882i | \(-0.484944\pi\) |
−0.998882 | + | 0.0472808i | \(0.984944\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 38.0132 | − | 17.0000i | 1.71901 | − | 0.768767i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 22.3607i | − | 1.00912i | −0.863376 | − | 0.504562i | \(-0.831654\pi\) | ||
0.863376 | − | 0.504562i | \(-0.168346\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | + | 10.0000i | −0.450377 | + | 0.450377i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.0000 | + | 22.3607i | −0.898933 | + | 1.00504i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.47214 | − | 4.47214i | 0.200603 | − | 0.200603i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.0000i | 1.70111i | 0.525883 | + | 0.850557i | \(0.323735\pi\) | ||||
−0.525883 | + | 0.850557i | \(0.676265\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.0000 | + | 11.1803i | −1.11692 | + | 0.499501i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.70820 | − | 6.70820i | −0.299104 | − | 0.299104i | 0.541559 | − | 0.840663i | \(-0.317834\pi\) |
−0.840663 | + | 0.541559i | \(0.817834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0000i | 0.889988i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.09017 | − | 8.09017i | 0.137239 | − | 0.359297i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.47214 | 0.198224 | 0.0991120 | − | 0.995076i | \(-0.468400\pi\) | ||||
0.0991120 | + | 0.995076i | \(0.468400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | −0.0884748 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.23607 | − | 4.76393i | 0.407782 | − | 0.210333i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.23607 | + | 2.23607i | −0.0985329 | + | 0.0985329i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.0000 | − | 30.0000i | −1.31940 | − | 1.31940i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.6525 | + | 35.0000i | 0.687067 | + | 1.53633i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.00000 | + | 3.00000i | −0.131181 | + | 0.131181i | −0.769649 | − | 0.638468i | \(-0.779569\pi\) |
0.638468 | + | 0.769649i | \(0.279569\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.00000 | − | 11.1803i | −0.218218 | − | 0.487950i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.94427 | + | 8.94427i | −0.389619 | + | 0.389619i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 13.0000i | − | 0.565217i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.0000 | − | 17.8885i | −0.867926 | − | 0.776297i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.8328 | − | 26.8328i | −1.16226 | − | 1.16226i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.00000 | − | 5.00000i | 0.216169 | − | 0.216169i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.4721 | + | 5.52786i | 0.624519 | + | 0.238545i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.3607 | −0.963143 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.0000 | −1.11783 | −0.558914 | − | 0.829226i | \(-0.688782\pi\) | ||||
−0.558914 | + | 0.829226i | \(0.688782\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.6525 | + | 8.65248i | 0.972111 | + | 0.371313i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 17.8885i | − | 0.766261i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.0000 | + | 27.0000i | 1.15444 | + | 1.15444i | 0.985653 | + | 0.168783i | \(0.0539839\pi\) |
0.168783 | + | 0.985653i | \(0.446016\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.4164 | − | 12.0000i | −0.572598 | − | 0.512148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.94427i | − | 0.381039i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | + | 6.00000i | −0.255146 | + | 0.255146i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.70820 | + | 15.0000i | 0.284747 | + | 0.636715i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.70820 | − | 6.70820i | 0.284236 | − | 0.284236i | −0.550560 | − | 0.834796i | \(-0.685586\pi\) |
0.834796 | + | 0.550560i | \(0.185586\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18.0000i | − | 0.761319i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0000 | + | 22.3607i | 0.422200 | + | 0.944069i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.70820 | − | 6.70820i | −0.282717 | − | 0.282717i | 0.551475 | − | 0.834192i | \(-0.314065\pi\) |
−0.834192 | + | 0.551475i | \(0.814065\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00000 | + | 5.00000i | 0.210352 | + | 0.210352i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.94427 | − | 9.94427i | 0.333628 | − | 0.417620i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.3607 | 0.937408 | 0.468704 | − | 0.883355i | \(-0.344721\pi\) | ||||
0.468704 | + | 0.883355i | \(0.344721\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.76393 | + | 7.23607i | −0.115465 | + | 0.302291i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1803 | + | 11.1803i | 0.466252 | + | 0.466252i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.0000 | − | 11.0000i | −0.457936 | − | 0.457936i | 0.440041 | − | 0.897977i | \(-0.354964\pi\) |
−0.897977 | + | 0.440041i | \(0.854964\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.70820 | + | 3.00000i | −0.278783 | + | 0.124676i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.4164i | 0.556606i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0000 | + | 10.0000i | −0.414158 | + | 0.414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.4164 | − | 1.58359i | 1.17487 | − | 0.0654735i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.70820 | − | 6.70820i | 0.276877 | − | 0.276877i | −0.554984 | − | 0.831861i | \(-0.687276\pi\) |
0.831861 | + | 0.554984i | \(0.187276\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.00000i | − | 0.329634i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0000 | − | 6.70820i | 0.617018 | − | 0.275939i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.1803 | − | 11.1803i | −0.459122 | − | 0.459122i | 0.439246 | − | 0.898367i | \(-0.355246\pi\) |
−0.898367 | + | 0.439246i | \(0.855246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.0000 | −0.409960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.1246 | + | 29.1246i | −0.455300 | + | 1.19199i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.7771 | −1.46181 | −0.730906 | − | 0.682478i | \(-0.760902\pi\) | ||||
−0.730906 | + | 0.682478i | \(0.760902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.236068 | − | 4.23607i | −0.00961343 | − | 0.172506i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.1246 | 0.818182 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.0000 | + | 27.0000i | 1.09590 | + | 1.09590i | 0.994885 | + | 0.101011i | \(0.0322077\pi\) |
0.101011 | + | 0.994885i | \(0.467792\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.47214 | − | 10.0000i | −0.181220 | − | 0.405220i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.2492i | 1.62831i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0000 | − | 21.0000i | 0.848182 | − | 0.848182i | −0.141724 | − | 0.989906i | \(-0.545265\pi\) |
0.989906 | + | 0.141724i | \(0.0452646\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.3607 | − | 32.3607i | 0.498431 | − | 1.30491i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.1246 | + | 20.1246i | −0.810186 | + | 0.810186i | −0.984662 | − | 0.174475i | \(-0.944177\pi\) |
0.174475 | + | 0.984662i | \(0.444177\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 42.0000i | − | 1.68812i | −0.536247 | − | 0.844061i | \(-0.680158\pi\) | ||
0.536247 | − | 0.844061i | \(-0.319842\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.00000 | + | 15.6525i | −0.200643 | + | 0.628112i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.47214 | + | 4.47214i | 0.179172 | + | 0.179172i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.4721 | − | 5.52786i | −0.577961 | − | 0.220762i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4164 | 0.534947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | 0.159237 | 0.0796187 | − | 0.996825i | \(-0.474630\pi\) | ||||
0.0796187 | + | 0.996825i | \(0.474630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.8885 | − | 9.88854i | −1.02898 | − | 0.393034i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 29.0689 | + | 29.0689i | 1.15356 | + | 1.15356i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 15.0000i | 0.594322 | + | 0.594322i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.94427 | + | 10.0000i | −0.353830 | + | 0.395594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 8.94427i | − | 0.353278i | −0.984276 | − | 0.176639i | \(-0.943478\pi\) | ||
0.984276 | − | 0.176639i | \(-0.0565224\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.0000 | − | 21.0000i | 0.828159 | − | 0.828159i | −0.159103 | − | 0.987262i | \(-0.550860\pi\) |
0.987262 | + | 0.159103i | \(0.0508601\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0000 | − | 6.70820i | 0.590624 | − | 0.264135i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.6525 | − | 15.6525i | 0.615362 | − | 0.615362i | −0.328976 | − | 0.944338i | \(-0.606704\pi\) |
0.944338 | + | 0.328976i | \(0.106704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0000i | 1.57014i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.00000 | − | 8.94427i | −0.156772 | − | 0.350554i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.1246 | − | 20.1246i | −0.787537 | − | 0.787537i | 0.193553 | − | 0.981090i | \(-0.437999\pi\) |
−0.981090 | + | 0.193553i | \(0.937999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.0000i | 0.390732i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.23607 | − | 0.236068i | 0.165265 | − | 0.00920989i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.94427 | 0.348419 | 0.174210 | − | 0.984709i | \(-0.444263\pi\) | ||||
0.174210 | + | 0.984709i | \(0.444263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00000 | 0.0777910 | 0.0388955 | − | 0.999243i | \(-0.487616\pi\) | ||||
0.0388955 | + | 0.999243i | \(0.487616\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.29180 | − | 21.7082i | 0.322027 | − | 0.843077i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.47214 | − | 4.47214i | 0.173422 | − | 0.173422i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000 | + | 10.0000i | 0.387202 | + | 0.387202i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.70820 | + | 3.00000i | −0.259354 | + | 0.115987i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.8328i | 1.03587i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | − | 1.00000i | 0.0385472 | − | 0.0385472i | −0.687570 | − | 0.726118i | \(-0.741323\pi\) |
0.726118 | + | 0.687570i | \(0.241323\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.9098 | + | 23.0902i | 0.458410 | + | 0.888741i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.5967 | − | 24.5967i | 0.945330 | − | 0.945330i | −0.0532513 | − | 0.998581i | \(-0.516958\pi\) |
0.998581 | + | 0.0532513i | \(0.0169584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 18.0000i | − | 0.690777i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.0000 | + | 11.1803i | −0.958002 | + | 0.428432i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.1246 | + | 20.1246i | 0.770047 | + | 0.770047i | 0.978114 | − | 0.208068i | \(-0.0667174\pi\) |
−0.208068 | + | 0.978114i | \(0.566717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0000 | + | 15.0000i | −0.573121 | + | 0.573121i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.41641 | − | 19.4164i | 0.282954 | − | 0.740782i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.4164 | 0.511124 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.0000 | −1.82601 | −0.913003 | − | 0.407953i | \(-0.866243\pi\) | ||||
−0.913003 | + | 0.407953i | \(0.866243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.9443 | + | 1.05573i | −0.719633 | + | 0.0401038i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 31.3050i | − | 1.18746i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.0000 | − | 20.0000i | −0.757554 | − | 0.757554i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.1246 | − | 45.0000i | −0.761183 | − | 1.70206i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.7771i | 1.35128i | 0.737231 | + | 0.675641i | \(0.236133\pi\) | ||||
−0.737231 | + | 0.675641i | \(0.763867\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | + | 6.00000i | −0.226294 | + | 0.226294i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.5410 | + | 15.0000i | −1.26323 | + | 0.564933i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.94427 | + | 8.94427i | −0.336384 | + | 0.336384i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.0000i | 1.05156i | 0.850620 | + | 0.525781i | \(0.176227\pi\) | ||||
−0.850620 | + | 0.525781i | \(0.823773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | − | 13.4164i | 0.450035 | − | 0.503155i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.94427 | + | 8.94427i | 0.334966 | + | 0.334966i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30.0000 | − | 30.0000i | −1.12194 | − | 1.12194i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.7771 | −1.33426 | −0.667130 | − | 0.744941i | \(-0.732478\pi\) | ||||
−0.667130 | + | 0.744941i | \(0.732478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.00000 | −0.0744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −42.0689 | − | 16.0689i | −1.56456 | − | 0.597608i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.3607 | 0.830455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.0000 | − | 21.0000i | −0.778847 | − | 0.778847i | 0.200788 | − | 0.979635i | \(-0.435650\pi\) |
−0.979635 | + | 0.200788i | \(0.935650\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 13.4164i | − | 0.496224i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00000 | − | 1.00000i | 0.0369358 | − | 0.0369358i | −0.688398 | − | 0.725333i | \(-0.741686\pi\) |
0.725333 | + | 0.688398i | \(0.241686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.90983 | + | 18.0902i | −0.254873 | + | 0.667266i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.47214 | + | 4.47214i | −0.164733 | + | 0.164733i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.0000i | 0.514998i | 0.966279 | + | 0.257499i | \(0.0828985\pi\) | ||||
−0.966279 | + | 0.257499i | \(0.917102\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | + | 13.4164i | 0.220416 | + | 0.492864i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.1803 | + | 11.1803i | 0.410167 | + | 0.410167i | 0.881797 | − | 0.471630i | \(-0.156334\pi\) |
−0.471630 | + | 0.881797i | \(0.656334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.0000 | −1.09911 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.58359 | − | 28.4164i | −0.0579406 | − | 1.03970i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.47214 | 0.163408 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | 0.437886 | 0.218943 | − | 0.975738i | \(-0.429739\pi\) | ||||
0.218943 | + | 0.975738i | \(0.429739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.29180 | + | 21.7082i | −0.302170 | + | 0.791091i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.94427 | −0.325515 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | + | 9.00000i | 0.327111 | + | 0.327111i | 0.851487 | − | 0.524376i | \(-0.175701\pi\) |
−0.524376 | + | 0.851487i | \(0.675701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.3607 | − | 10.0000i | 0.811641 | − | 0.362977i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.8885i | − | 0.648459i | −0.945978 | − | 0.324230i | \(-0.894895\pi\) | ||
0.945978 | − | 0.324230i | \(-0.105105\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | − | 8.00000i | 0.289619 | − | 0.289619i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.1803 | − | 1.18034i | 0.765777 | − | 0.0426753i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.8328 | − | 26.8328i | 0.968877 | − | 0.968877i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.00000i | 0.288487i | 0.989542 | + | 0.144244i | \(0.0460749\pi\) | ||||
−0.989542 | + | 0.144244i | \(0.953925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.0000 | − | 15.6525i | 1.26049 | − | 0.563710i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.70820 | + | 6.70820i | 0.241277 | + | 0.241277i | 0.817378 | − | 0.576101i | \(-0.195427\pi\) |
−0.576101 | + | 0.817378i | \(0.695427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.0000 | 0.718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.70820 | + | 9.70820i | −0.133031 | + | 0.348280i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.8885 | 0.640924 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0000 | 0.715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.6525 | + | 20.6525i | 0.380688 | + | 0.738059i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.1246 | − | 20.1246i | −0.718278 | − | 0.718278i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.0000 | + | 19.0000i | 0.677277 | + | 0.677277i | 0.959383 | − | 0.282106i | \(-0.0910331\pi\) |
−0.282106 | + | 0.959383i | \(0.591033\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.6525 | − | 35.0000i | −0.557243 | − | 1.24603i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.47214i | 0.159011i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | − | 18.0000i | 0.639199 | − | 0.639199i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.00000 | + | 11.1803i | 0.177332 | + | 0.396526i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.1246 | + | 20.1246i | −0.712850 | + | 0.712850i | −0.967131 | − | 0.254280i | \(-0.918161\pi\) |
0.254280 | + | 0.967131i | \(0.418161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.0000i | 1.06132i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0000 | − | 8.94427i | −0.353333 | − | 0.316030i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.47214 | − | 4.47214i | −0.157818 | − | 0.157818i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.0000i | 0.352454i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.1803 | − | 13.8197i | −1.27361 | − | 0.486475i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.47214 | −0.157232 | −0.0786160 | − | 0.996905i | \(-0.525050\pi\) | ||||
−0.0786160 | + | 0.996905i | \(0.525050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.4164 | + | 7.41641i | 0.680963 | + | 0.260105i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.0132 | + | 38.0132i | −1.33154 | + | 1.33154i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | + | 6.00000i | 0.209913 | + | 0.209913i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.4164 | + | 12.0000i | 0.468807 | + | 0.419314i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 17.8885i | − | 0.624314i | −0.950030 | − | 0.312157i | \(-0.898948\pi\) | ||
0.950030 | − | 0.312157i | \(-0.101052\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0000 | − | 17.0000i | 0.592583 | − | 0.592583i | −0.345746 | − | 0.938328i | \(-0.612374\pi\) |
0.938328 | + | 0.345746i | \(0.112374\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.8197 | − | 36.1803i | 0.481139 | − | 1.25964i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.1246 | + | 20.1246i | −0.699801 | + | 0.699801i | −0.964368 | − | 0.264566i | \(-0.914771\pi\) |
0.264566 | + | 0.964368i | \(0.414771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 16.0000i | − | 0.555703i | −0.960624 | − | 0.277851i | \(-0.910378\pi\) | ||
0.960624 | − | 0.277851i | \(-0.0896223\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.00000 | + | 20.1246i | 0.312207 | + | 0.698115i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.1803 | + | 11.1803i | 0.387376 | + | 0.387376i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.0000 | − | 25.0000i | 0.865161 | − | 0.865161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.52786 | + | 18.4721i | 0.329331 | + | 0.638490i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.7771 | 1.23516 | 0.617581 | − | 0.786507i | \(-0.288113\pi\) | ||||
0.617581 | + | 0.786507i | \(0.288113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.5836 | + | 43.4164i | −0.571169 | + | 1.49534i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.1803i | 0.384615i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000 | + | 9.00000i | 0.309244 | + | 0.309244i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38.0132 | − | 17.0000i | 1.30461 | − | 0.583438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 13.4164i | − | 0.459909i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.0000 | − | 37.0000i | 1.26686 | − | 1.26686i | 0.319152 | − | 0.947703i | \(-0.396602\pi\) |
0.947703 | − | 0.319152i | \(-0.103398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.94427 | + | 10.0000i | −0.305888 | + | 0.341993i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.70820 | − | 6.70820i | 0.229148 | − | 0.229148i | −0.583189 | − | 0.812337i | \(-0.698195\pi\) |
0.812337 | + | 0.583189i | \(0.198195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0000i | 0.477674i | 0.971060 | + | 0.238837i | \(0.0767661\pi\) | ||||
−0.971060 | + | 0.238837i | \(0.923234\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000 | − | 8.94427i | 0.681598 | − | 0.304820i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.5967 | − | 24.5967i | −0.837283 | − | 0.837283i | 0.151217 | − | 0.988501i | \(-0.451681\pi\) |
−0.988501 | + | 0.151217i | \(0.951681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.0000 | − | 35.0000i | −1.19004 | − | 1.19004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.32624 | + | 11.3262i | −0.146927 | + | 0.384659i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.8328 | −0.910241 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | 0.203302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.12461 | + | 38.1246i | 0.0719072 | + | 1.29032i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.1803 | + | 11.1803i | 0.377964 | + | 0.377964i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.00000 | + | 9.00000i | 0.303908 | + | 0.303908i | 0.842541 | − | 0.538632i | \(-0.181059\pi\) |
−0.538632 | + | 0.842541i | \(0.681059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.70820 | + | 15.0000i | 0.226262 | + | 0.505937i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 44.7214i | − | 1.50670i | −0.657619 | − | 0.753350i | \(-0.728436\pi\) | ||
0.657619 | − | 0.753350i | \(-0.271564\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.0000 | + | 23.0000i | −0.774012 | + | 0.774012i | −0.978805 | − | 0.204794i | \(-0.934348\pi\) |
0.204794 | + | 0.978805i | \(0.434348\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.3607 | + | 12.3607i | 1.08779 | + | 0.415500i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.1246 | + | 20.1246i | −0.675718 | + | 0.675718i | −0.959028 | − | 0.283310i | \(-0.908567\pi\) |
0.283310 | + | 0.959028i | \(0.408567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.0000i | 0.872012i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.0000 | − | 4.47214i | 1.34005 | − | 0.149822i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.4164 | − | 13.4164i | −0.448963 | − | 0.448963i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.7082 | − | 8.29180i | −0.724816 | − | 0.276855i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.8885 | 0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | 0.333148 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.70820 | + | 3.70820i | 0.323069 | + | 0.123401i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.3050 | −1.04061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.00000 | + | 7.00000i | 0.232431 | + | 0.232431i | 0.813707 | − | 0.581276i | \(-0.197446\pi\) |
−0.581276 | + | 0.813707i | \(0.697446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.8885 | − | 20.0000i | 0.593326 | − | 0.663358i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 49.1935i | − | 1.62985i | −0.579564 | − | 0.814927i | \(-0.696777\pi\) | ||
0.579564 | − | 0.814927i | \(-0.303223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.0000 | + | 30.0000i | −0.992855 | + | 0.992855i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.7082 | + | 8.29180i | 0.717651 | + | 0.274118i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.47214 | + | 4.47214i | −0.147683 | + | 0.147683i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.0000i | − | 0.725713i | −0.931845 | − | 0.362857i | \(-0.881802\pi\) | ||
0.931845 | − | 0.362857i | \(-0.118198\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.0000 | − | 46.9574i | −0.691974 | − | 1.54730i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.4164 | − | 13.4164i | −0.441606 | − | 0.441606i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.0000 | − | 15.0000i | −0.493197 | − | 0.493197i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.23607 | − | 0.236068i | 0.139131 | − | 0.00775349i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.47214 | 0.146726 | 0.0733630 | − | 0.997305i | \(-0.476627\pi\) | ||||
0.0733630 | + | 0.997305i | \(0.476627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.0000 | −0.327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.76393 | + | 7.23607i | −0.0904871 | + | 0.236898i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.3607 | − | 22.3607i | −0.731272 | − | 0.731272i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.0000 | − | 11.0000i | −0.359354 | − | 0.359354i | 0.504221 | − | 0.863575i | \(-0.331780\pi\) |
−0.863575 | + | 0.504221i | \(0.831780\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.70820 | + | 3.00000i | −0.218914 | + | 0.0979013i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.8328i | 0.874725i | 0.899285 | + | 0.437362i | \(0.144087\pi\) | ||||
−0.899285 | + | 0.437362i | \(0.855913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.0000 | + | 20.0000i | −0.651290 | + | 0.651290i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.00000 | + | 15.6525i | −0.162650 | + | 0.509175i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.1803 | + | 11.1803i | −0.363312 | + | 0.363312i | −0.865031 | − | 0.501719i | \(-0.832701\pi\) |
0.501719 | + | 0.865031i | \(0.332701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000i | 0.194768i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.0000 | + | 20.1246i | −1.45922 | + | 0.652585i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.5410 | + | 33.5410i | 1.08650 | + | 1.08650i | 0.995886 | + | 0.0906141i | \(0.0288830\pi\) |
0.0906141 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 10.0000i | − | 0.323592i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.3607 | − | 32.3607i | 0.399564 | − | 1.04607i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.4164 | −0.433238 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.47214 | + | 0.527864i | −0.305235 | + | 0.0170102i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.70820 | − | 6.70820i | 0.215945 | − | 0.215945i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.00000 | + | 7.00000i | 0.225105 | + | 0.225105i | 0.810644 | − | 0.585539i | \(-0.199117\pi\) |
−0.585539 | + | 0.810644i | \(0.699117\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.47214 | + | 10.0000i | 0.143666 | + | 0.321246i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 22.3607i | − | 0.717588i | −0.933417 | − | 0.358794i | \(-0.883188\pi\) | ||
0.933417 | − | 0.358794i | \(-0.116812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0000 | − | 14.0000i | 0.448819 | − | 0.448819i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −33.5410 | + | 15.0000i | −1.07417 | + | 0.480384i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.70820 | − | 6.70820i | 0.214614 | − | 0.214614i | −0.591610 | − | 0.806224i | \(-0.701507\pi\) |
0.806224 | + | 0.591610i | \(0.201507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000i | 0.639203i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0000 | + | 17.8885i | −0.510841 | + | 0.571137i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.1803 | + | 11.1803i | 0.356597 | + | 0.356597i | 0.862557 | − | 0.505960i | \(-0.168862\pi\) |
−0.505960 | + | 0.862557i | \(0.668862\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.0000 | + | 15.0000i | −0.477940 | + | 0.477940i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.7082 | − | 8.29180i | −0.690980 | − | 0.263931i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.4164 | −0.426617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.9443 | − | 4.94427i | −0.410774 | − | 0.156902i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 40.2492i | − | 1.27599i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.0000 | − | 23.0000i | −0.728417 | − | 0.728417i | 0.241887 | − | 0.970304i | \(-0.422234\pi\) |
−0.970304 | + | 0.241887i | \(0.922234\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.70820 | − | 21.0000i | 0.212238 | − | 0.664411i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))