Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(139,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.d (of order \(2\), degree \(1\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.139 |
Dual form | 690.2.d.a.139.3 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 4.00000i | − 1.51186i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
0.654654 | − | 0.755929i | \(-0.272814\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.23607i | 0.707107i | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | 6.47214i | 1.79505i | 0.440966 | + | 0.897524i | \(0.354636\pi\) | ||||
−0.440966 | + | 0.897524i | \(0.645364\pi\) | |||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | − 2.23607i | − 0.577350i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.47214i | 1.56972i | 0.619671 | + | 0.784862i | \(0.287266\pi\) | ||||
−0.619671 | + | 0.784862i | \(0.712734\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 2.23607 | 0.500000 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 6.47214 | 1.26929 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 4.00000i | 0.755929i | ||||||||
\(29\) | −8.47214 | −1.57324 | −0.786618 | − | 0.617440i | \(-0.788170\pi\) | ||||
−0.786618 | + | 0.617440i | \(0.788170\pi\) | |||||||
\(30\) | −2.23607 | −0.408248 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.47214 | 1.10996 | ||||||||
\(35\) | 8.94427i | 1.51186i | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.47214i | 1.39281i | 0.717649 | + | 0.696405i | \(0.245218\pi\) | ||||
−0.717649 | + | 0.696405i | \(0.754782\pi\) | |||||||
\(38\) | 2.00000i | 0.324443i | ||||||||
\(39\) | −6.47214 | −1.03637 | ||||||||
\(40\) | − 2.23607i | − 0.353553i | ||||||||
\(41\) | −6.94427 | −1.08451 | −0.542257 | − | 0.840213i | \(-0.682430\pi\) | ||||
−0.542257 | + | 0.840213i | \(0.682430\pi\) | |||||||
\(42\) | − 4.00000i | − 0.617213i | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.23607 | 0.333333 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 12.9443i | 1.88812i | 0.329779 | + | 0.944058i | \(0.393026\pi\) | ||||
−0.329779 | + | 0.944058i | \(0.606974\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | − 5.00000i | − 0.707107i | ||||||||
\(51\) | −6.47214 | −0.906280 | ||||||||
\(52\) | − 6.47214i | − 0.897524i | ||||||||
\(53\) | 8.94427i | 1.22859i | 0.789076 | + | 0.614295i | \(0.210560\pi\) | ||||
−0.789076 | + | 0.614295i | \(0.789440\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.00000 | 0.534522 | ||||||||
\(57\) | − 2.00000i | − 0.264906i | ||||||||
\(58\) | 8.47214i | 1.11245i | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 2.23607i | 0.288675i | ||||||||
\(61\) | 8.47214 | 1.08475 | 0.542373 | − | 0.840138i | \(-0.317526\pi\) | ||||
0.542373 | + | 0.840138i | \(0.317526\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.00000i | 0.503953i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 14.4721i | − 1.79505i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 12.9443i | − 1.58139i | −0.612207 | − | 0.790697i | \(-0.709718\pi\) | ||||
0.612207 | − | 0.790697i | \(-0.290282\pi\) | |||||||
\(68\) | − 6.47214i | − 0.784862i | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 8.94427 | 1.06904 | ||||||||
\(71\) | −16.4721 | −1.95488 | −0.977441 | − | 0.211207i | \(-0.932261\pi\) | ||||
−0.977441 | + | 0.211207i | \(0.932261\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 12.9443i | − 1.51501i | −0.652828 | − | 0.757506i | \(-0.726418\pi\) | ||||
0.652828 | − | 0.757506i | \(-0.273582\pi\) | |||||||
\(74\) | 8.47214 | 0.984866 | ||||||||
\(75\) | 5.00000i | 0.577350i | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.47214i | 0.732825i | ||||||||
\(79\) | −3.52786 | −0.396916 | −0.198458 | − | 0.980109i | \(-0.563593\pi\) | ||||
−0.198458 | + | 0.980109i | \(0.563593\pi\) | |||||||
\(80\) | −2.23607 | −0.250000 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.94427i | 0.766867i | ||||||||
\(83\) | 10.4721i | 1.14947i | 0.818341 | + | 0.574733i | \(0.194894\pi\) | ||||
−0.818341 | + | 0.574733i | \(0.805106\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | − 14.4721i | − 1.56972i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 8.47214i | − 0.908308i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.52786 | 0.797952 | 0.398976 | − | 0.916961i | \(-0.369366\pi\) | ||||
0.398976 | + | 0.916961i | \(0.369366\pi\) | |||||||
\(90\) | − 2.23607i | − 0.235702i | ||||||||
\(91\) | 25.8885 | 2.71386 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.9443 | 1.33510 | ||||||||
\(95\) | 4.47214 | 0.458831 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − 13.4164i | − 1.36223i | −0.732177 | − | 0.681115i | \(-0.761495\pi\) | ||||
0.732177 | − | 0.681115i | \(-0.238505\pi\) | |||||||
\(98\) | 9.00000i | 0.909137i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | −8.47214 | −0.843009 | −0.421505 | − | 0.906826i | \(-0.638498\pi\) | ||||
−0.421505 | + | 0.906826i | \(0.638498\pi\) | |||||||
\(102\) | 6.47214i | 0.640837i | ||||||||
\(103\) | − 0.944272i | − 0.0930419i | −0.998917 | − | 0.0465209i | \(-0.985187\pi\) | ||||
0.998917 | − | 0.0465209i | \(-0.0148134\pi\) | |||||||
\(104\) | −6.47214 | −0.634645 | ||||||||
\(105\) | −8.94427 | −0.872872 | ||||||||
\(106\) | 8.94427 | 0.868744 | ||||||||
\(107\) | − 6.47214i | − 0.625685i | −0.949805 | − | 0.312842i | \(-0.898719\pi\) | ||||
0.949805 | − | 0.312842i | \(-0.101281\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 8.47214 | 0.811483 | 0.405742 | − | 0.913988i | \(-0.367013\pi\) | ||||
0.405742 | + | 0.913988i | \(0.367013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.47214 | −0.804140 | ||||||||
\(112\) | − 4.00000i | − 0.377964i | ||||||||
\(113\) | − 7.41641i | − 0.697677i | −0.937183 | − | 0.348838i | \(-0.886576\pi\) | ||||
0.937183 | − | 0.348838i | \(-0.113424\pi\) | |||||||
\(114\) | −2.00000 | −0.187317 | ||||||||
\(115\) | 2.23607i | 0.208514i | ||||||||
\(116\) | 8.47214 | 0.786618 | ||||||||
\(117\) | − 6.47214i | − 0.598349i | ||||||||
\(118\) | − 6.00000i | − 0.552345i | ||||||||
\(119\) | 25.8885 | 2.37320 | ||||||||
\(120\) | 2.23607 | 0.204124 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − 8.47214i | − 0.767031i | ||||||||
\(123\) | − 6.94427i | − 0.626144i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | 15.4164i | 1.36798i | 0.729489 | + | 0.683992i | \(0.239758\pi\) | ||||
−0.729489 | + | 0.683992i | \(0.760242\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.4721 | −1.26929 | ||||||||
\(131\) | 10.9443 | 0.956205 | 0.478103 | − | 0.878304i | \(-0.341325\pi\) | ||||
0.478103 | + | 0.878304i | \(0.341325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | −12.9443 | −1.11821 | ||||||||
\(135\) | 2.23607i | 0.192450i | ||||||||
\(136\) | −6.47214 | −0.554981 | ||||||||
\(137\) | − 7.41641i | − 0.633626i | −0.948488 | − | 0.316813i | \(-0.897387\pi\) | ||||
0.948488 | − | 0.316813i | \(-0.102613\pi\) | |||||||
\(138\) | − 1.00000i | − 0.0851257i | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | − 8.94427i | − 0.755929i | ||||||||
\(141\) | −12.9443 | −1.09010 | ||||||||
\(142\) | 16.4721i | 1.38231i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 18.9443 | 1.57324 | ||||||||
\(146\) | −12.9443 | −1.07128 | ||||||||
\(147\) | − 9.00000i | − 0.742307i | ||||||||
\(148\) | − 8.47214i | − 0.696405i | ||||||||
\(149\) | −13.4164 | −1.09911 | −0.549557 | − | 0.835456i | \(-0.685204\pi\) | ||||
−0.549557 | + | 0.835456i | \(0.685204\pi\) | |||||||
\(150\) | 5.00000 | 0.408248 | ||||||||
\(151\) | −0.944272 | −0.0768438 | −0.0384219 | − | 0.999262i | \(-0.512233\pi\) | ||||
−0.0384219 | + | 0.999262i | \(0.512233\pi\) | |||||||
\(152\) | − 2.00000i | − 0.162221i | ||||||||
\(153\) | − 6.47214i | − 0.523241i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.47214 | 0.518186 | ||||||||
\(157\) | 20.4721i | 1.63385i | 0.576741 | + | 0.816927i | \(0.304324\pi\) | ||||
−0.576741 | + | 0.816927i | \(0.695676\pi\) | |||||||
\(158\) | 3.52786i | 0.280662i | ||||||||
\(159\) | −8.94427 | −0.709327 | ||||||||
\(160\) | 2.23607i | 0.176777i | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 12.9443i | 1.01387i | 0.861983 | + | 0.506937i | \(0.169222\pi\) | ||||
−0.861983 | + | 0.506937i | \(0.830778\pi\) | |||||||
\(164\) | 6.94427 | 0.542257 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.4721 | 0.812795 | ||||||||
\(167\) | − 20.9443i | − 1.62072i | −0.585935 | − | 0.810358i | \(-0.699273\pi\) | ||||
0.585935 | − | 0.810358i | \(-0.300727\pi\) | |||||||
\(168\) | 4.00000i | 0.308607i | ||||||||
\(169\) | −28.8885 | −2.22220 | ||||||||
\(170\) | −14.4721 | −1.10996 | ||||||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.94427i | 0.223849i | 0.993717 | + | 0.111924i | \(0.0357015\pi\) | ||||
−0.993717 | + | 0.111924i | \(0.964299\pi\) | |||||||
\(174\) | −8.47214 | −0.642271 | ||||||||
\(175\) | − 20.0000i | − 1.51186i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | − 7.52786i | − 0.564237i | ||||||||
\(179\) | 1.05573 | 0.0789088 | 0.0394544 | − | 0.999221i | \(-0.487438\pi\) | ||||
0.0394544 | + | 0.999221i | \(0.487438\pi\) | |||||||
\(180\) | −2.23607 | −0.166667 | ||||||||
\(181\) | −0.472136 | −0.0350936 | −0.0175468 | − | 0.999846i | \(-0.505586\pi\) | ||||
−0.0175468 | + | 0.999846i | \(0.505586\pi\) | |||||||
\(182\) | − 25.8885i | − 1.91899i | ||||||||
\(183\) | 8.47214i | 0.626278i | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | − 18.9443i | − 1.39281i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 12.9443i | − 0.944058i | ||||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | − 4.47214i | − 0.324443i | ||||||||
\(191\) | 9.88854 | 0.715510 | 0.357755 | − | 0.933816i | \(-0.383542\pi\) | ||||
0.357755 | + | 0.933816i | \(0.383542\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | 20.0000i | 1.43963i | 0.694165 | + | 0.719816i | \(0.255774\pi\) | ||||
−0.694165 | + | 0.719816i | \(0.744226\pi\) | |||||||
\(194\) | −13.4164 | −0.963242 | ||||||||
\(195\) | 14.4721 | 1.03637 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | − 1.05573i | − 0.0752175i | −0.999293 | − | 0.0376088i | \(-0.988026\pi\) | ||||
0.999293 | − | 0.0376088i | \(-0.0119741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.41641 | 0.667511 | 0.333756 | − | 0.942660i | \(-0.391684\pi\) | ||||
0.333756 | + | 0.942660i | \(0.391684\pi\) | |||||||
\(200\) | 5.00000i | 0.353553i | ||||||||
\(201\) | 12.9443 | 0.913019 | ||||||||
\(202\) | 8.47214i | 0.596097i | ||||||||
\(203\) | 33.8885i | 2.37851i | ||||||||
\(204\) | 6.47214 | 0.453140 | ||||||||
\(205\) | 15.5279 | 1.08451 | ||||||||
\(206\) | −0.944272 | −0.0657905 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 6.47214i | 0.448762i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 8.94427i | 0.617213i | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | − 8.94427i | − 0.614295i | ||||||||
\(213\) | − 16.4721i | − 1.12865i | ||||||||
\(214\) | −6.47214 | −0.442426 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 8.47214i | − 0.573805i | ||||||||
\(219\) | 12.9443 | 0.874693 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −41.8885 | −2.81773 | ||||||||
\(222\) | 8.47214i | 0.568613i | ||||||||
\(223\) | − 15.4164i | − 1.03236i | −0.856480 | − | 0.516180i | \(-0.827354\pi\) | ||||
0.856480 | − | 0.516180i | \(-0.172646\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | −7.41641 | −0.493332 | ||||||||
\(227\) | − 9.52786i | − 0.632387i | −0.948695 | − | 0.316193i | \(-0.897595\pi\) | ||||
0.948695 | − | 0.316193i | \(-0.102405\pi\) | |||||||
\(228\) | 2.00000i | 0.132453i | ||||||||
\(229\) | 1.41641 | 0.0935989 | 0.0467994 | − | 0.998904i | \(-0.485098\pi\) | ||||
0.0467994 | + | 0.998904i | \(0.485098\pi\) | |||||||
\(230\) | 2.23607 | 0.147442 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 8.47214i | − 0.556223i | ||||||||
\(233\) | − 2.94427i | − 0.192886i | −0.995339 | − | 0.0964428i | \(-0.969254\pi\) | ||||
0.995339 | − | 0.0964428i | \(-0.0307465\pi\) | |||||||
\(234\) | −6.47214 | −0.423097 | ||||||||
\(235\) | − 28.9443i | − 1.88812i | ||||||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | − 3.52786i | − 0.229159i | ||||||||
\(238\) | − 25.8885i | − 1.67811i | ||||||||
\(239\) | 3.52786 | 0.228199 | 0.114099 | − | 0.993469i | \(-0.463602\pi\) | ||||
0.114099 | + | 0.993469i | \(0.463602\pi\) | |||||||
\(240\) | − 2.23607i | − 0.144338i | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 11.0000i | 0.707107i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −8.47214 | −0.542373 | ||||||||
\(245\) | 20.1246 | 1.28571 | ||||||||
\(246\) | −6.94427 | −0.442751 | ||||||||
\(247\) | − 12.9443i | − 0.823624i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.4721 | −0.663645 | ||||||||
\(250\) | 11.1803i | 0.707107i | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | − 4.00000i | − 0.251976i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 15.4164 | 0.967311 | ||||||||
\(255\) | 14.4721 | 0.906280 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.8885 | 2.10573 | ||||||||
\(260\) | 14.4721i | 0.897524i | ||||||||
\(261\) | 8.47214 | 0.524412 | ||||||||
\(262\) | − 10.9443i | − 0.676139i | ||||||||
\(263\) | 3.05573i | 0.188424i | 0.995552 | + | 0.0942121i | \(0.0300332\pi\) | ||||
−0.995552 | + | 0.0942121i | \(0.969967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 20.0000i | − 1.22859i | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 7.52786i | 0.460698i | ||||||||
\(268\) | 12.9443i | 0.790697i | ||||||||
\(269\) | 8.47214 | 0.516555 | 0.258278 | − | 0.966071i | \(-0.416845\pi\) | ||||
0.258278 | + | 0.966071i | \(0.416845\pi\) | |||||||
\(270\) | 2.23607 | 0.136083 | ||||||||
\(271\) | −16.9443 | −1.02929 | −0.514646 | − | 0.857403i | \(-0.672076\pi\) | ||||
−0.514646 | + | 0.857403i | \(0.672076\pi\) | |||||||
\(272\) | 6.47214i | 0.392431i | ||||||||
\(273\) | 25.8885i | 1.56685i | ||||||||
\(274\) | −7.41641 | −0.448042 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 0.583592i | 0.0350647i | 0.999846 | + | 0.0175323i | \(0.00558100\pi\) | ||||
−0.999846 | + | 0.0175323i | \(0.994419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.94427 | −0.534522 | ||||||||
\(281\) | 12.4721 | 0.744025 | 0.372013 | − | 0.928228i | \(-0.378668\pi\) | ||||
0.372013 | + | 0.928228i | \(0.378668\pi\) | |||||||
\(282\) | 12.9443i | 0.770820i | ||||||||
\(283\) | 24.0000i | 1.42665i | 0.700832 | + | 0.713326i | \(0.252812\pi\) | ||||
−0.700832 | + | 0.713326i | \(0.747188\pi\) | |||||||
\(284\) | 16.4721 | 0.977441 | ||||||||
\(285\) | 4.47214i | 0.264906i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.7771i | 1.63963i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −24.8885 | −1.46403 | ||||||||
\(290\) | − 18.9443i | − 1.11245i | ||||||||
\(291\) | 13.4164 | 0.786484 | ||||||||
\(292\) | 12.9443i | 0.757506i | ||||||||
\(293\) | 16.9443i | 0.989895i | 0.868923 | + | 0.494947i | \(0.164813\pi\) | ||||
−0.868923 | + | 0.494947i | \(0.835187\pi\) | |||||||
\(294\) | −9.00000 | −0.524891 | ||||||||
\(295\) | −13.4164 | −0.781133 | ||||||||
\(296\) | −8.47214 | −0.492433 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.4164i | 0.777192i | ||||||||
\(299\) | 6.47214 | 0.374293 | ||||||||
\(300\) | − 5.00000i | − 0.288675i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.944272i | 0.0543367i | ||||||||
\(303\) | − 8.47214i | − 0.486711i | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | −18.9443 | −1.08475 | ||||||||
\(306\) | −6.47214 | −0.369987 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.944272 | 0.0537178 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.5279 | −0.880504 | −0.440252 | − | 0.897874i | \(-0.645111\pi\) | ||||
−0.440252 | + | 0.897874i | \(0.645111\pi\) | |||||||
\(312\) | − 6.47214i | − 0.366413i | ||||||||
\(313\) | 1.41641i | 0.0800601i | 0.999198 | + | 0.0400301i | \(0.0127454\pi\) | ||||
−0.999198 | + | 0.0400301i | \(0.987255\pi\) | |||||||
\(314\) | 20.4721 | 1.15531 | ||||||||
\(315\) | − 8.94427i | − 0.503953i | ||||||||
\(316\) | 3.52786 | 0.198458 | ||||||||
\(317\) | − 18.0000i | − 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 8.94427i | 0.501570i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.23607 | 0.125000 | ||||||||
\(321\) | 6.47214 | 0.361239 | ||||||||
\(322\) | 4.00000i | 0.222911i | ||||||||
\(323\) | − 12.9443i | − 0.720239i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 32.3607i | 1.79505i | ||||||||
\(326\) | 12.9443 | 0.716917 | ||||||||
\(327\) | 8.47214i | 0.468510i | ||||||||
\(328\) | − 6.94427i | − 0.383433i | ||||||||
\(329\) | 51.7771 | 2.85456 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | − 10.4721i | − 0.574733i | ||||||||
\(333\) | − 8.47214i | − 0.464270i | ||||||||
\(334\) | −20.9443 | −1.14602 | ||||||||
\(335\) | 28.9443i | 1.58139i | ||||||||
\(336\) | 4.00000 | 0.218218 | ||||||||
\(337\) | 1.41641i | 0.0771567i | 0.999256 | + | 0.0385783i | \(0.0122829\pi\) | ||||
−0.999256 | + | 0.0385783i | \(0.987717\pi\) | |||||||
\(338\) | 28.8885i | 1.57133i | ||||||||
\(339\) | 7.41641 | 0.402804 | ||||||||
\(340\) | 14.4721i | 0.784862i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − 2.00000i | − 0.108148i | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.23607 | −0.120386 | ||||||||
\(346\) | 2.94427 | 0.158285 | ||||||||
\(347\) | 8.94427i | 0.480154i | 0.970754 | + | 0.240077i | \(0.0771726\pi\) | ||||
−0.970754 | + | 0.240077i | \(0.922827\pi\) | |||||||
\(348\) | 8.47214i | 0.454154i | ||||||||
\(349\) | −7.88854 | −0.422264 | −0.211132 | − | 0.977458i | \(-0.567715\pi\) | ||||
−0.211132 | + | 0.977458i | \(0.567715\pi\) | |||||||
\(350\) | −20.0000 | −1.06904 | ||||||||
\(351\) | 6.47214 | 0.345457 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 14.9443i | − 0.795403i | −0.917515 | − | 0.397702i | \(-0.869808\pi\) | ||||
0.917515 | − | 0.397702i | \(-0.130192\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | 36.8328 | 1.95488 | ||||||||
\(356\) | −7.52786 | −0.398976 | ||||||||
\(357\) | 25.8885i | 1.37017i | ||||||||
\(358\) | − 1.05573i | − 0.0557970i | ||||||||
\(359\) | 15.0557 | 0.794611 | 0.397305 | − | 0.917686i | \(-0.369945\pi\) | ||||
0.397305 | + | 0.917686i | \(0.369945\pi\) | |||||||
\(360\) | 2.23607i | 0.117851i | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0.472136i | 0.0248149i | ||||||||
\(363\) | − 11.0000i | − 0.577350i | ||||||||
\(364\) | −25.8885 | −1.35693 | ||||||||
\(365\) | 28.9443i | 1.51501i | ||||||||
\(366\) | 8.47214 | 0.442846 | ||||||||
\(367\) | 12.0000i | 0.626395i | 0.949688 | + | 0.313197i | \(0.101400\pi\) | ||||
−0.949688 | + | 0.313197i | \(0.898600\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | 6.94427 | 0.361504 | ||||||||
\(370\) | −18.9443 | −0.984866 | ||||||||
\(371\) | 35.7771 | 1.85745 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.41641i | 0.280451i | 0.990120 | + | 0.140225i | \(0.0447827\pi\) | ||||
−0.990120 | + | 0.140225i | \(0.955217\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 11.1803i | − 0.577350i | ||||||||
\(376\) | −12.9443 | −0.667550 | ||||||||
\(377\) | − 54.8328i | − 2.82403i | ||||||||
\(378\) | 4.00000i | 0.205738i | ||||||||
\(379\) | 36.8328 | 1.89197 | 0.945987 | − | 0.324204i | \(-0.105096\pi\) | ||||
0.945987 | + | 0.324204i | \(0.105096\pi\) | |||||||
\(380\) | −4.47214 | −0.229416 | ||||||||
\(381\) | −15.4164 | −0.789807 | ||||||||
\(382\) | − 9.88854i | − 0.505942i | ||||||||
\(383\) | 21.8885i | 1.11845i | 0.829015 | + | 0.559226i | \(0.188902\pi\) | ||||
−0.829015 | + | 0.559226i | \(0.811098\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.4164i | 0.681115i | ||||||||
\(389\) | 4.47214 | 0.226746 | 0.113373 | − | 0.993552i | \(-0.463834\pi\) | ||||
0.113373 | + | 0.993552i | \(0.463834\pi\) | |||||||
\(390\) | − 14.4721i | − 0.732825i | ||||||||
\(391\) | 6.47214 | 0.327310 | ||||||||
\(392\) | − 9.00000i | − 0.454569i | ||||||||
\(393\) | 10.9443i | 0.552065i | ||||||||
\(394\) | −1.05573 | −0.0531868 | ||||||||
\(395\) | 7.88854 | 0.396916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.3050i | 1.67153i | 0.549089 | + | 0.835764i | \(0.314975\pi\) | ||||
−0.549089 | + | 0.835764i | \(0.685025\pi\) | |||||||
\(398\) | − 9.41641i | − 0.472002i | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | −1.41641 | −0.0707320 | −0.0353660 | − | 0.999374i | \(-0.511260\pi\) | ||||
−0.0353660 | + | 0.999374i | \(0.511260\pi\) | |||||||
\(402\) | − 12.9443i | − 0.645602i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.47214 | 0.421505 | ||||||||
\(405\) | −2.23607 | −0.111111 | ||||||||
\(406\) | 33.8885 | 1.68186 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − 6.47214i | − 0.320418i | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | − 15.5279i | − 0.766867i | ||||||||
\(411\) | 7.41641 | 0.365824 | ||||||||
\(412\) | 0.944272i | 0.0465209i | ||||||||
\(413\) | − 24.0000i | − 1.18096i | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | − 23.4164i | − 1.14947i | ||||||||
\(416\) | 6.47214 | 0.317323 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.11146 | 0.103151 | 0.0515757 | − | 0.998669i | \(-0.483576\pi\) | ||||
0.0515757 | + | 0.998669i | \(0.483576\pi\) | |||||||
\(420\) | 8.94427 | 0.436436 | ||||||||
\(421\) | −10.5836 | −0.515813 | −0.257906 | − | 0.966170i | \(-0.583033\pi\) | ||||
−0.257906 | + | 0.966170i | \(0.583033\pi\) | |||||||
\(422\) | 12.0000i | 0.584151i | ||||||||
\(423\) | − 12.9443i | − 0.629372i | ||||||||
\(424\) | −8.94427 | −0.434372 | ||||||||
\(425\) | 32.3607i | 1.56972i | ||||||||
\(426\) | −16.4721 | −0.798078 | ||||||||
\(427\) | − 33.8885i | − 1.63998i | ||||||||
\(428\) | 6.47214i | 0.312842i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | 5.41641i | 0.260296i | 0.991495 | + | 0.130148i | \(0.0415452\pi\) | ||||
−0.991495 | + | 0.130148i | \(0.958455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.9443i | 0.908308i | ||||||||
\(436\) | −8.47214 | −0.405742 | ||||||||
\(437\) | 2.00000i | 0.0956730i | ||||||||
\(438\) | − 12.9443i | − 0.618501i | ||||||||
\(439\) | −26.8328 | −1.28066 | −0.640330 | − | 0.768100i | \(-0.721202\pi\) | ||||
−0.640330 | + | 0.768100i | \(0.721202\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 41.8885i | 1.99243i | ||||||||
\(443\) | 8.94427i | 0.424955i | 0.977166 | + | 0.212478i | \(0.0681533\pi\) | ||||
−0.977166 | + | 0.212478i | \(0.931847\pi\) | |||||||
\(444\) | 8.47214 | 0.402070 | ||||||||
\(445\) | −16.8328 | −0.797952 | ||||||||
\(446\) | −15.4164 | −0.729988 | ||||||||
\(447\) | − 13.4164i | − 0.634574i | ||||||||
\(448\) | 4.00000i | 0.188982i | ||||||||
\(449\) | 17.0557 | 0.804910 | 0.402455 | − | 0.915440i | \(-0.368157\pi\) | ||||
0.402455 | + | 0.915440i | \(0.368157\pi\) | |||||||
\(450\) | 5.00000i | 0.235702i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.41641i | 0.348838i | ||||||||
\(453\) | − 0.944272i | − 0.0443658i | ||||||||
\(454\) | −9.52786 | −0.447165 | ||||||||
\(455\) | −57.8885 | −2.71386 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 1.41641i | 0.0662568i | 0.999451 | + | 0.0331284i | \(0.0105470\pi\) | ||||
−0.999451 | + | 0.0331284i | \(0.989453\pi\) | |||||||
\(458\) | − 1.41641i | − 0.0661844i | ||||||||
\(459\) | 6.47214 | 0.302093 | ||||||||
\(460\) | − 2.23607i | − 0.104257i | ||||||||
\(461\) | 30.3607 | 1.41404 | 0.707019 | − | 0.707195i | \(-0.250040\pi\) | ||||
0.707019 | + | 0.707195i | \(0.250040\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4164i | 0.530565i | 0.964171 | + | 0.265283i | \(0.0854653\pi\) | ||||
−0.964171 | + | 0.265283i | \(0.914535\pi\) | |||||||
\(464\) | −8.47214 | −0.393309 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.94427 | −0.136391 | ||||||||
\(467\) | − 17.5279i | − 0.811093i | −0.914074 | − | 0.405546i | \(-0.867081\pi\) | ||||
0.914074 | − | 0.405546i | \(-0.132919\pi\) | |||||||
\(468\) | 6.47214i | 0.299175i | ||||||||
\(469\) | −51.7771 | −2.39084 | ||||||||
\(470\) | −28.9443 | −1.33510 | ||||||||
\(471\) | −20.4721 | −0.943306 | ||||||||
\(472\) | 6.00000i | 0.276172i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3.52786 | −0.162040 | ||||||||
\(475\) | −10.0000 | −0.458831 | ||||||||
\(476\) | −25.8885 | −1.18660 | ||||||||
\(477\) | − 8.94427i | − 0.409530i | ||||||||
\(478\) | − 3.52786i | − 0.161361i | ||||||||
\(479\) | −0.944272 | −0.0431449 | −0.0215724 | − | 0.999767i | \(-0.506867\pi\) | ||||
−0.0215724 | + | 0.999767i | \(0.506867\pi\) | |||||||
\(480\) | −2.23607 | −0.102062 | ||||||||
\(481\) | −54.8328 | −2.50016 | ||||||||
\(482\) | 2.00000i | 0.0910975i | ||||||||
\(483\) | − 4.00000i | − 0.182006i | ||||||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 30.0000i | 1.36223i | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 4.58359i | 0.207702i | 0.994593 | + | 0.103851i | \(0.0331166\pi\) | ||||
−0.994593 | + | 0.103851i | \(0.966883\pi\) | |||||||
\(488\) | 8.47214i | 0.383516i | ||||||||
\(489\) | −12.9443 | −0.585360 | ||||||||
\(490\) | − 20.1246i | − 0.909137i | ||||||||
\(491\) | −7.88854 | −0.356005 | −0.178002 | − | 0.984030i | \(-0.556964\pi\) | ||||
−0.178002 | + | 0.984030i | \(0.556964\pi\) | |||||||
\(492\) | 6.94427i | 0.313072i | ||||||||
\(493\) | − 54.8328i | − 2.46955i | ||||||||
\(494\) | −12.9443 | −0.582390 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 65.8885i | 2.95551i | ||||||||
\(498\) | 10.4721i | 0.469268i | ||||||||
\(499\) | 24.0000 | 1.07439 | 0.537194 | − | 0.843459i | \(-0.319484\pi\) | ||||
0.537194 | + | 0.843459i | \(0.319484\pi\) | |||||||
\(500\) | 11.1803 | 0.500000 | ||||||||
\(501\) | 20.9443 | 0.935721 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | − 21.8885i | − 0.975962i | −0.872854 | − | 0.487981i | \(-0.837734\pi\) | ||||
0.872854 | − | 0.487981i | \(-0.162266\pi\) | |||||||
\(504\) | −4.00000 | −0.178174 | ||||||||
\(505\) | 18.9443 | 0.843009 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 28.8885i | − 1.28299i | ||||||||
\(508\) | − 15.4164i | − 0.683992i | ||||||||
\(509\) | 25.4164 | 1.12656 | 0.563281 | − | 0.826265i | \(-0.309539\pi\) | ||||
0.563281 | + | 0.826265i | \(0.309539\pi\) | |||||||
\(510\) | − 14.4721i | − 0.640837i | ||||||||
\(511\) | −51.7771 | −2.29048 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 2.00000i | 0.0883022i | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | 2.11146i | 0.0930419i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 33.8885i | − 1.48898i | ||||||||
\(519\) | −2.94427 | −0.129239 | ||||||||
\(520\) | 14.4721 | 0.634645 | ||||||||
\(521\) | −28.4721 | −1.24739 | −0.623693 | − | 0.781669i | \(-0.714369\pi\) | ||||
−0.623693 | + | 0.781669i | \(0.714369\pi\) | |||||||
\(522\) | − 8.47214i | − 0.370815i | ||||||||
\(523\) | − 12.9443i | − 0.566013i | −0.959118 | − | 0.283007i | \(-0.908668\pi\) | ||||
0.959118 | − | 0.283007i | \(-0.0913319\pi\) | |||||||
\(524\) | −10.9443 | −0.478103 | ||||||||
\(525\) | 20.0000 | 0.872872 | ||||||||
\(526\) | 3.05573 | 0.133236 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | −20.0000 | −0.868744 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | − 8.00000i | − 0.346844i | ||||||||
\(533\) | − 44.9443i | − 1.94675i | ||||||||
\(534\) | 7.52786 | 0.325763 | ||||||||
\(535\) | 14.4721i | 0.625685i | ||||||||
\(536\) | 12.9443 | 0.559107 | ||||||||
\(537\) | 1.05573i | 0.0455580i | ||||||||
\(538\) | − 8.47214i | − 0.365260i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − 2.23607i | − 0.0962250i | ||||||||
\(541\) | −12.8328 | −0.551726 | −0.275863 | − | 0.961197i | \(-0.588964\pi\) | ||||
−0.275863 | + | 0.961197i | \(0.588964\pi\) | |||||||
\(542\) | 16.9443i | 0.727819i | ||||||||
\(543\) | − 0.472136i | − 0.0202613i | ||||||||
\(544\) | 6.47214 | 0.277491 | ||||||||
\(545\) | −18.9443 | −0.811483 | ||||||||
\(546\) | 25.8885 | 1.10793 | ||||||||
\(547\) | − 30.8328i | − 1.31832i | −0.752004 | − | 0.659158i | \(-0.770913\pi\) | ||||
0.752004 | − | 0.659158i | \(-0.229087\pi\) | |||||||
\(548\) | 7.41641i | 0.316813i | ||||||||
\(549\) | −8.47214 | −0.361582 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9443 | 0.721850 | ||||||||
\(552\) | 1.00000i | 0.0425628i | ||||||||
\(553\) | 14.1115i | 0.600080i | ||||||||
\(554\) | 0.583592 | 0.0247945 | ||||||||
\(555\) | 18.9443 | 0.804140 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.88854i | − 0.249506i | −0.992188 | − | 0.124753i | \(-0.960186\pi\) | ||||
0.992188 | − | 0.124753i | \(-0.0398138\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.94427i | 0.377964i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 12.4721i | − 0.526105i | ||||||||
\(563\) | 25.3050i | 1.06648i | 0.845965 | + | 0.533238i | \(0.179025\pi\) | ||||
−0.845965 | + | 0.533238i | \(0.820975\pi\) | |||||||
\(564\) | 12.9443 | 0.545052 | ||||||||
\(565\) | 16.5836i | 0.697677i | ||||||||
\(566\) | 24.0000 | 1.00880 | ||||||||
\(567\) | − 4.00000i | − 0.167984i | ||||||||
\(568\) | − 16.4721i | − 0.691155i | ||||||||
\(569\) | 23.3050 | 0.976994 | 0.488497 | − | 0.872565i | \(-0.337545\pi\) | ||||
0.488497 | + | 0.872565i | \(0.337545\pi\) | |||||||
\(570\) | 4.47214 | 0.187317 | ||||||||
\(571\) | −20.8328 | −0.871826 | −0.435913 | − | 0.899989i | \(-0.643575\pi\) | ||||
−0.435913 | + | 0.899989i | \(0.643575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.88854i | 0.413100i | ||||||||
\(574\) | 27.7771 | 1.15939 | ||||||||
\(575\) | − 5.00000i | − 0.208514i | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 0.944272i | 0.0393106i | 0.999807 | + | 0.0196553i | \(0.00625687\pi\) | ||||
−0.999807 | + | 0.0196553i | \(0.993743\pi\) | |||||||
\(578\) | 24.8885i | 1.03523i | ||||||||
\(579\) | −20.0000 | −0.831172 | ||||||||
\(580\) | −18.9443 | −0.786618 | ||||||||
\(581\) | 41.8885 | 1.73783 | ||||||||
\(582\) | − 13.4164i | − 0.556128i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.9443 | 0.535638 | ||||||||
\(585\) | 14.4721i | 0.598349i | ||||||||
\(586\) | 16.9443 | 0.699961 | ||||||||
\(587\) | − 5.88854i | − 0.243046i | −0.992589 | − | 0.121523i | \(-0.961222\pi\) | ||||
0.992589 | − | 0.121523i | \(-0.0387779\pi\) | |||||||
\(588\) | 9.00000i | 0.371154i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 13.4164i | 0.552345i | ||||||||
\(591\) | 1.05573 | 0.0434269 | ||||||||
\(592\) | 8.47214i | 0.348203i | ||||||||
\(593\) | − 11.8885i | − 0.488204i | −0.969750 | − | 0.244102i | \(-0.921507\pi\) | ||||
0.969750 | − | 0.244102i | \(-0.0784932\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −57.8885 | −2.37320 | ||||||||
\(596\) | 13.4164 | 0.549557 | ||||||||
\(597\) | 9.41641i | 0.385388i | ||||||||
\(598\) | − 6.47214i | − 0.264665i | ||||||||
\(599\) | 18.3607 | 0.750197 | 0.375099 | − | 0.926985i | \(-0.377609\pi\) | ||||
0.375099 | + | 0.926985i | \(0.377609\pi\) | |||||||
\(600\) | −5.00000 | −0.204124 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.9443i | 0.527132i | ||||||||
\(604\) | 0.944272 | 0.0384219 | ||||||||
\(605\) | 24.5967 | 1.00000 | ||||||||
\(606\) | −8.47214 | −0.344157 | ||||||||
\(607\) | 19.4164i | 0.788088i | 0.919092 | + | 0.394044i | \(0.128924\pi\) | ||||
−0.919092 | + | 0.394044i | \(0.871076\pi\) | |||||||
\(608\) | 2.00000i | 0.0811107i | ||||||||
\(609\) | −33.8885 | −1.37323 | ||||||||
\(610\) | 18.9443i | 0.767031i | ||||||||
\(611\) | −83.7771 | −3.38926 | ||||||||
\(612\) | 6.47214i | 0.261621i | ||||||||
\(613\) | − 17.4164i | − 0.703442i | −0.936105 | − | 0.351721i | \(-0.885597\pi\) | ||||
0.936105 | − | 0.351721i | \(-0.114403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.5279i | 0.626144i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 5.52786i | − 0.222543i | −0.993790 | − | 0.111272i | \(-0.964508\pi\) | ||||
0.993790 | − | 0.111272i | \(-0.0354924\pi\) | |||||||
\(618\) | − 0.944272i | − 0.0379842i | ||||||||
\(619\) | 12.8328 | 0.515794 | 0.257897 | − | 0.966172i | \(-0.416970\pi\) | ||||
0.257897 | + | 0.966172i | \(0.416970\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 15.5279i | 0.622611i | ||||||||
\(623\) | − 30.1115i | − 1.20639i | ||||||||
\(624\) | −6.47214 | −0.259093 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 1.41641 | 0.0566110 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 20.4721i | − 0.816927i | ||||||||
\(629\) | −54.8328 | −2.18633 | ||||||||
\(630\) | −8.94427 | −0.356348 | ||||||||
\(631\) | 42.3607 | 1.68635 | 0.843176 | − | 0.537638i | \(-0.180683\pi\) | ||||
0.843176 | + | 0.537638i | \(0.180683\pi\) | |||||||
\(632\) | − 3.52786i | − 0.140331i | ||||||||
\(633\) | − 12.0000i | − 0.476957i | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | − 34.4721i | − 1.36798i | ||||||||
\(636\) | 8.94427 | 0.354663 | ||||||||
\(637\) | − 58.2492i | − 2.30792i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.4721 | 0.651628 | ||||||||
\(640\) | − 2.23607i | − 0.0883883i | ||||||||
\(641\) | −20.4721 | −0.808601 | −0.404300 | − | 0.914626i | \(-0.632485\pi\) | ||||
−0.404300 | + | 0.914626i | \(0.632485\pi\) | |||||||
\(642\) | − 6.47214i | − 0.255435i | ||||||||
\(643\) | − 4.94427i | − 0.194983i | −0.995236 | − | 0.0974915i | \(-0.968918\pi\) | ||||
0.995236 | − | 0.0974915i | \(-0.0310819\pi\) | |||||||
\(644\) | 4.00000 | 0.157622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.9443 | −0.509286 | ||||||||
\(647\) | 6.11146i | 0.240266i | 0.992758 | + | 0.120133i | \(0.0383321\pi\) | ||||
−0.992758 | + | 0.120133i | \(0.961668\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 32.3607 | 1.26929 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 12.9443i | − 0.506937i | ||||||||
\(653\) | − 32.8328i | − 1.28485i | −0.766350 | − | 0.642424i | \(-0.777929\pi\) | ||||
0.766350 | − | 0.642424i | \(-0.222071\pi\) | |||||||
\(654\) | 8.47214 | 0.331287 | ||||||||
\(655\) | −24.4721 | −0.956205 | ||||||||
\(656\) | −6.94427 | −0.271128 | ||||||||
\(657\) | 12.9443i | 0.505004i | ||||||||
\(658\) | − 51.7771i | − 2.01848i | ||||||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.2492 | 1.72110 | 0.860548 | − | 0.509370i | \(-0.170121\pi\) | ||||
0.860548 | + | 0.509370i | \(0.170121\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 41.8885i | − 1.62682i | ||||||||
\(664\) | −10.4721 | −0.406398 | ||||||||
\(665\) | − 17.8885i | − 0.693688i | ||||||||
\(666\) | −8.47214 | −0.328289 | ||||||||
\(667\) | 8.47214i | 0.328042i | ||||||||
\(668\) | 20.9443i | 0.810358i | ||||||||
\(669\) | 15.4164 | 0.596033 | ||||||||
\(670\) | 28.9443 | 1.11821 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − 4.00000i | − 0.154303i | ||||||||
\(673\) | 14.8328i | 0.571763i | 0.958265 | + | 0.285882i | \(0.0922864\pi\) | ||||
−0.958265 | + | 0.285882i | \(0.907714\pi\) | |||||||
\(674\) | 1.41641 | 0.0545580 | ||||||||
\(675\) | − 5.00000i | − 0.192450i | ||||||||
\(676\) | 28.8885 | 1.11110 | ||||||||
\(677\) | − 9.88854i | − 0.380048i | −0.981779 | − | 0.190024i | \(-0.939143\pi\) | ||||
0.981779 | − | 0.190024i | \(-0.0608565\pi\) | |||||||
\(678\) | − 7.41641i | − 0.284825i | ||||||||
\(679\) | −53.6656 | −2.05950 | ||||||||
\(680\) | 14.4721 | 0.554981 | ||||||||
\(681\) | 9.52786 | 0.365109 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 12.0000i | − 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | 16.5836i | 0.633626i | ||||||||
\(686\) | 8.00000 | 0.305441 | ||||||||
\(687\) | 1.41641i | 0.0540393i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.8885 | −2.20538 | ||||||||
\(690\) | 2.23607i | 0.0851257i | ||||||||
\(691\) | 31.7771 | 1.20886 | 0.604429 | − | 0.796659i | \(-0.293401\pi\) | ||||
0.604429 | + | 0.796659i | \(0.293401\pi\) | |||||||
\(692\) | − 2.94427i | − 0.111924i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.94427 | 0.339520 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.47214 | 0.321135 | ||||||||
\(697\) | − 44.9443i | − 1.70239i | ||||||||
\(698\) | 7.88854i | 0.298586i | ||||||||
\(699\) | 2.94427 | 0.111363 | ||||||||
\(700\) | 20.0000i | 0.755929i | ||||||||
\(701\) | 10.5836 | 0.399737 | 0.199868 | − | 0.979823i | \(-0.435949\pi\) | ||||
0.199868 | + | 0.979823i | \(0.435949\pi\) | |||||||
\(702\) | − 6.47214i | − 0.244275i | ||||||||
\(703\) | − 16.9443i | − 0.639065i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 28.9443 | 1.09010 | ||||||||
\(706\) | −14.9443 | −0.562435 | ||||||||
\(707\) | 33.8885i | 1.27451i | ||||||||
\(708\) | − 6.00000i | − 0.225494i | ||||||||
\(709\) | −11.5279 | −0.432938 | −0.216469 | − | 0.976289i | \(-0.569454\pi\) | ||||
−0.216469 | + | 0.976289i | \(0.569454\pi\) | |||||||
\(710\) | − 36.8328i | − 1.38231i | ||||||||
\(711\) | 3.52786 | 0.132305 | ||||||||
\(712\) | 7.52786i | 0.282119i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 25.8885 | 0.968854 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.05573 | −0.0394544 | ||||||||
\(717\) | 3.52786i | 0.131750i | ||||||||
\(718\) | − 15.0557i | − 0.561875i | ||||||||
\(719\) | 44.4721 | 1.65853 | 0.829265 | − | 0.558855i | \(-0.188759\pi\) | ||||
0.829265 | + | 0.558855i | \(0.188759\pi\) | |||||||
\(720\) | 2.23607 | 0.0833333 | ||||||||
\(721\) | −3.77709 | −0.140666 | ||||||||
\(722\) | 15.0000i | 0.558242i | ||||||||
\(723\) | − 2.00000i | − 0.0743808i | ||||||||
\(724\) | 0.472136 | 0.0175468 | ||||||||
\(725\) | −42.3607 | −1.57324 | ||||||||
\(726\) | −11.0000 | −0.408248 | ||||||||
\(727\) | 16.9443i | 0.628428i | 0.949352 | + | 0.314214i | \(0.101741\pi\) | ||||
−0.949352 | + | 0.314214i | \(0.898259\pi\) | |||||||
\(728\) | 25.8885i | 0.959493i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 28.9443 | 1.07128 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − 8.47214i | − 0.313139i | ||||||||
\(733\) | 8.47214i | 0.312925i | 0.987684 | + | 0.156463i | \(0.0500091\pi\) | ||||
−0.987684 | + | 0.156463i | \(0.949991\pi\) | |||||||
\(734\) | 12.0000 | 0.442928 | ||||||||
\(735\) | 20.1246i | 0.742307i | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − 6.94427i | − 0.255622i | ||||||||
\(739\) | 33.8885 | 1.24661 | 0.623305 | − | 0.781979i | \(-0.285789\pi\) | ||||
0.623305 | + | 0.781979i | \(0.285789\pi\) | |||||||
\(740\) | 18.9443i | 0.696405i | ||||||||
\(741\) | 12.9443 | 0.475520 | ||||||||
\(742\) | − 35.7771i | − 1.31342i | ||||||||
\(743\) | 37.8885i | 1.39000i | 0.719012 | + | 0.694998i | \(0.244595\pi\) | ||||
−0.719012 | + | 0.694998i | \(0.755405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.0000 | 1.09911 | ||||||||
\(746\) | 5.41641 | 0.198309 | ||||||||
\(747\) | − 10.4721i | − 0.383155i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.8885 | −0.945947 | ||||||||
\(750\) | −11.1803 | −0.408248 | ||||||||
\(751\) | 27.5279 | 1.00451 | 0.502253 | − | 0.864721i | \(-0.332505\pi\) | ||||
0.502253 | + | 0.864721i | \(0.332505\pi\) | |||||||
\(752\) | 12.9443i | 0.472029i | ||||||||
\(753\) | − 12.0000i | − 0.437304i | ||||||||
\(754\) | −54.8328 | −1.99689 | ||||||||
\(755\) | 2.11146 | 0.0768438 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | − 18.5836i | − 0.675432i | −0.941248 | − | 0.337716i | \(-0.890346\pi\) | ||||
0.941248 | − | 0.337716i | \(-0.109654\pi\) | |||||||
\(758\) | − 36.8328i | − 1.33783i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.47214i | 0.162221i | ||||||||
\(761\) | 53.7771 | 1.94942 | 0.974709 | − | 0.223478i | \(-0.0717411\pi\) | ||||
0.974709 | + | 0.223478i | \(0.0717411\pi\) | |||||||
\(762\) | 15.4164i | 0.558478i | ||||||||
\(763\) | − 33.8885i | − 1.22685i | ||||||||
\(764\) | −9.88854 | −0.357755 | ||||||||
\(765\) | 14.4721i | 0.523241i | ||||||||
\(766\) | 21.8885 | 0.790865 | ||||||||
\(767\) | 38.8328i | 1.40217i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −17.0557 | −0.615045 | −0.307523 | − | 0.951541i | \(-0.599500\pi\) | ||||
−0.307523 | + | 0.951541i | \(0.599500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | − 20.0000i | − 0.719816i | ||||||||
\(773\) | − 20.9443i | − 0.753313i | −0.926353 | − | 0.376657i | \(-0.877074\pi\) | ||||
0.926353 | − | 0.376657i | \(-0.122926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.4164 | 0.481621 | ||||||||
\(777\) | 33.8885i | 1.21574i | ||||||||
\(778\) | − 4.47214i | − 0.160334i | ||||||||
\(779\) | 13.8885 | 0.497609 | ||||||||
\(780\) | −14.4721 | −0.518186 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 6.47214i | − 0.231443i | ||||||||
\(783\) | 8.47214i | 0.302769i | ||||||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | − 45.7771i | − 1.63385i | ||||||||
\(786\) | 10.9443 | 0.390369 | ||||||||
\(787\) | 54.8328i | 1.95458i | 0.211909 | + | 0.977289i | \(0.432032\pi\) | ||||
−0.211909 | + | 0.977289i | \(0.567968\pi\) | |||||||
\(788\) | 1.05573i | 0.0376088i | ||||||||
\(789\) | −3.05573 | −0.108787 | ||||||||
\(790\) | − 7.88854i | − 0.280662i | ||||||||
\(791\) | −29.6656 | −1.05479 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.8328i | 1.94717i | ||||||||
\(794\) | 33.3050 | 1.18195 | ||||||||
\(795\) | 20.0000 | 0.709327 | ||||||||
\(796\) | −9.41641 | −0.333756 | ||||||||
\(797\) | 2.11146i | 0.0747916i | 0.999301 | + | 0.0373958i | \(0.0119062\pi\) | ||||
−0.999301 | + | 0.0373958i | \(0.988094\pi\) | |||||||
\(798\) | 8.00000i | 0.283197i | ||||||||
\(799\) | −83.7771 | −2.96382 | ||||||||
\(800\) | − 5.00000i | − 0.176777i | ||||||||
\(801\) | −7.52786 | −0.265984 | ||||||||
\(802\) | 1.41641i | 0.0500151i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −12.9443 | −0.456509 | ||||||||
\(805\) | 8.94427 | 0.315244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.47214i | 0.298233i | ||||||||
\(808\) | − 8.47214i | − 0.298049i | ||||||||
\(809\) | −31.8885 | −1.12114 | −0.560571 | − | 0.828107i | \(-0.689418\pi\) | ||||
−0.560571 | + | 0.828107i | \(0.689418\pi\) | |||||||
\(810\) | 2.23607i | 0.0785674i | ||||||||
\(811\) | −14.1115 | −0.495520 | −0.247760 | − | 0.968821i | \(-0.579694\pi\) | ||||
−0.247760 | + | 0.968821i | \(0.579694\pi\) | |||||||
\(812\) | − 33.8885i | − 1.18925i | ||||||||
\(813\) | − 16.9443i | − 0.594262i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 28.9443i | − 1.01387i | ||||||||
\(816\) | −6.47214 | −0.226570 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − 18.0000i | − 0.629355i | ||||||||
\(819\) | −25.8885 | −0.904619 | ||||||||
\(820\) | −15.5279 | −0.542257 | ||||||||
\(821\) | −7.52786 | −0.262724 | −0.131362 | − | 0.991334i | \(-0.541935\pi\) | ||||
−0.131362 | + | 0.991334i | \(0.541935\pi\) | |||||||
\(822\) | − 7.41641i | − 0.258677i | ||||||||
\(823\) | − 24.3607i | − 0.849160i | −0.905390 | − | 0.424580i | \(-0.860422\pi\) | ||||
0.905390 | − | 0.424580i | \(-0.139578\pi\) | |||||||
\(824\) | 0.944272 | 0.0328953 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.0000 | −0.835067 | ||||||||
\(827\) | 33.5279i | 1.16588i | 0.812516 | + | 0.582939i | \(0.198097\pi\) | ||||
−0.812516 | + | 0.582939i | \(0.801903\pi\) | |||||||
\(828\) | − 1.00000i | − 0.0347524i | ||||||||
\(829\) | −13.0557 | −0.453444 | −0.226722 | − | 0.973959i | \(-0.572801\pi\) | ||||
−0.226722 | + | 0.973959i | \(0.572801\pi\) | |||||||
\(830\) | −23.4164 | −0.812795 | ||||||||
\(831\) | −0.583592 | −0.0202446 | ||||||||
\(832\) | − 6.47214i | − 0.224381i | ||||||||
\(833\) | − 58.2492i | − 2.01822i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.8328i | 1.62072i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 2.11146i | − 0.0729390i | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | − 8.94427i | − 0.308607i | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 10.5836i | 0.364735i | ||||||||
\(843\) | 12.4721i | 0.429563i | ||||||||
\(844\) | 12.0000 | 0.413057 | ||||||||
\(845\) | 64.5967 | 2.22220 | ||||||||
\(846\) | −12.9443 | −0.445033 | ||||||||
\(847\) | 44.0000i | 1.51186i | ||||||||
\(848\) | 8.94427i | 0.307148i | ||||||||
\(849\) | −24.0000 | −0.823678 | ||||||||
\(850\) | 32.3607 | 1.10996 | ||||||||
\(851\) | 8.47214 | 0.290421 | ||||||||
\(852\) | 16.4721i | 0.564326i | ||||||||
\(853\) | 18.4721i | 0.632474i | 0.948680 | + | 0.316237i | \(0.102419\pi\) | ||||
−0.948680 | + | 0.316237i | \(0.897581\pi\) | |||||||
\(854\) | −33.8885 | −1.15964 | ||||||||
\(855\) | −4.47214 | −0.152944 | ||||||||
\(856\) | 6.47214 | 0.221213 | ||||||||
\(857\) | − 11.8885i | − 0.406105i | −0.979168 | − | 0.203052i | \(-0.934914\pi\) | ||||
0.979168 | − | 0.203052i | \(-0.0650862\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.7771 | −1.08422 | −0.542110 | − | 0.840307i | \(-0.682374\pi\) | ||||
−0.542110 | + | 0.840307i | \(0.682374\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.7771 | −0.946641 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.9443i | 0.712951i | 0.934305 | + | 0.356476i | \(0.116022\pi\) | ||||
−0.934305 | + | 0.356476i | \(0.883978\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | − 6.58359i | − 0.223849i | ||||||||
\(866\) | 5.41641 | 0.184057 | ||||||||
\(867\) | − 24.8885i | − 0.845259i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 18.9443 | 0.642271 | ||||||||
\(871\) | 83.7771 | 2.83868 | ||||||||
\(872\) | 8.47214i | 0.286903i | ||||||||
\(873\) | 13.4164i | 0.454077i | ||||||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 44.7214i | 1.51186i | ||||||||
\(876\) | −12.9443 | −0.437346 | ||||||||
\(877\) | 24.3607i | 0.822602i | 0.911500 | + | 0.411301i | \(0.134925\pi\) | ||||
−0.911500 | + | 0.411301i | \(0.865075\pi\) | |||||||
\(878\) | 26.8328i | 0.905564i | ||||||||
\(879\) | −16.9443 | −0.571516 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.47214 | 0.150670 | 0.0753350 | − | 0.997158i | \(-0.475997\pi\) | ||||
0.0753350 | + | 0.997158i | \(0.475997\pi\) | |||||||
\(882\) | − 9.00000i | − 0.303046i | ||||||||
\(883\) | 51.7771i | 1.74244i | 0.490895 | + | 0.871219i | \(0.336670\pi\) | ||||
−0.490895 | + | 0.871219i | \(0.663330\pi\) | |||||||
\(884\) | 41.8885 | 1.40886 | ||||||||
\(885\) | − 13.4164i | − 0.450988i | ||||||||
\(886\) | 8.94427 | 0.300489 | ||||||||
\(887\) | − 24.0000i | − 0.805841i | −0.915235 | − | 0.402921i | \(-0.867995\pi\) | ||||
0.915235 | − | 0.402921i | \(-0.132005\pi\) | |||||||
\(888\) | − 8.47214i | − 0.284306i | ||||||||
\(889\) | 61.6656 | 2.06820 | ||||||||
\(890\) | 16.8328i | 0.564237i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.4164i | 0.516180i | ||||||||
\(893\) | − 25.8885i | − 0.866327i | ||||||||
\(894\) | −13.4164 | −0.448712 | ||||||||
\(895\) | −2.36068 | −0.0789088 | ||||||||
\(896\) | 4.00000 | 0.133631 | ||||||||
\(897\) | 6.47214i | 0.216098i | ||||||||
\(898\) | − 17.0557i | − 0.569157i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | 0.166667 | ||||||||
\(901\) | −57.8885 | −1.92855 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.41641 | 0.246666 | ||||||||
\(905\) | 1.05573 | 0.0350936 | ||||||||
\(906\) | −0.944272 | −0.0313713 | ||||||||
\(907\) | 38.8328i | 1.28942i | 0.764426 | + | 0.644711i | \(0.223022\pi\) | ||||
−0.764426 | + | 0.644711i | \(0.776978\pi\) | |||||||
\(908\) | 9.52786i | 0.316193i | ||||||||
\(909\) | 8.47214 | 0.281003 | ||||||||
\(910\) | 57.8885i | 1.91899i | ||||||||
\(911\) | 7.05573 | 0.233767 | 0.116883 | − | 0.993146i | \(-0.462710\pi\) | ||||
0.116883 | + | 0.993146i | \(0.462710\pi\) | |||||||
\(912\) | − 2.00000i | − 0.0662266i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.41641 | 0.0468506 | ||||||||
\(915\) | − 18.9443i | − 0.626278i | ||||||||
\(916\) | −1.41641 | −0.0467994 | ||||||||
\(917\) | − 43.7771i | − 1.44565i | ||||||||
\(918\) | − 6.47214i | − 0.213612i | ||||||||
\(919\) | −17.4164 | −0.574514 | −0.287257 | − | 0.957854i | \(-0.592743\pi\) | ||||
−0.287257 | + | 0.957854i | \(0.592743\pi\) | |||||||
\(920\) | −2.23607 | −0.0737210 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 30.3607i | − 0.999876i | ||||||||
\(923\) | − 106.610i | − 3.50911i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.3607i | 1.39281i | ||||||||
\(926\) | 11.4164 | 0.375166 | ||||||||
\(927\) | 0.944272i | 0.0310140i | ||||||||
\(928\) | 8.47214i | 0.278111i | ||||||||
\(929\) | −6.94427 | −0.227834 | −0.113917 | − | 0.993490i | \(-0.536340\pi\) | ||||
−0.113917 | + | 0.993490i | \(0.536340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | 0.589926 | ||||||||
\(932\) | 2.94427i | 0.0964428i | ||||||||
\(933\) | − 15.5279i | − 0.508359i | ||||||||
\(934\) | −17.5279 | −0.573529 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.47214 | 0.211548 | ||||||||
\(937\) | − 33.4164i | − 1.09167i | −0.837894 | − | 0.545833i | \(-0.816213\pi\) | ||||
0.837894 | − | 0.545833i | \(-0.183787\pi\) | |||||||
\(938\) | 51.7771i | 1.69058i | ||||||||
\(939\) | −1.41641 | −0.0462227 | ||||||||
\(940\) | 28.9443i | 0.944058i | ||||||||
\(941\) | 27.5279 | 0.897383 | 0.448691 | − | 0.893687i | \(-0.351890\pi\) | ||||
0.448691 | + | 0.893687i | \(0.351890\pi\) | |||||||
\(942\) | 20.4721i | 0.667018i | ||||||||
\(943\) | 6.94427i | 0.226137i | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 8.94427 | 0.290957 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000i | 0.389948i | 0.980808 | + | 0.194974i | \(0.0624622\pi\) | ||||
−0.980808 | + | 0.194974i | \(0.937538\pi\) | |||||||
\(948\) | 3.52786i | 0.114580i | ||||||||
\(949\) | 83.7771 | 2.71952 | ||||||||
\(950\) | 10.0000i | 0.324443i | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 25.8885i | 0.839053i | ||||||||
\(953\) | 32.3607i | 1.04827i | 0.851637 | + | 0.524133i | \(0.175610\pi\) | ||||
−0.851637 | + | 0.524133i | \(0.824390\pi\) | |||||||
\(954\) | −8.94427 | −0.289581 | ||||||||
\(955\) | −22.1115 | −0.715510 | ||||||||
\(956\) | −3.52786 | −0.114099 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.944272i | 0.0305080i | ||||||||
\(959\) | −29.6656 | −0.957953 | ||||||||
\(960\) | 2.23607i | 0.0721688i | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 54.8328i | 1.76788i | ||||||||
\(963\) | 6.47214i | 0.208562i | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | − 44.7214i | − 1.43963i | ||||||||
\(966\) | −4.00000 | −0.128698 | ||||||||
\(967\) | − 28.5836i | − 0.919186i | −0.888130 | − | 0.459593i | \(-0.847995\pi\) | ||||
0.888130 | − | 0.459593i | \(-0.152005\pi\) | |||||||
\(968\) | − 11.0000i | − 0.353553i | ||||||||
\(969\) | 12.9443 | 0.415830 | ||||||||
\(970\) | 30.0000 | 0.963242 | ||||||||
\(971\) | −53.8885 | −1.72937 | −0.864683 | − | 0.502318i | \(-0.832481\pi\) | ||||
−0.864683 | + | 0.502318i | \(0.832481\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.58359 | 0.146868 | ||||||||
\(975\) | −32.3607 | −1.03637 | ||||||||
\(976\) | 8.47214 | 0.271186 | ||||||||
\(977\) | − 10.4721i | − 0.335033i | −0.985869 | − | 0.167517i | \(-0.946425\pi\) | ||||
0.985869 | − | 0.167517i | \(-0.0535748\pi\) | |||||||
\(978\) | 12.9443i | 0.413912i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −20.1246 | −0.642857 | ||||||||
\(981\) | −8.47214 | −0.270494 | ||||||||
\(982\) | 7.88854i | 0.251734i | ||||||||
\(983\) | − 24.0000i | − 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | 6.94427 | 0.221375 | ||||||||
\(985\) | 2.36068i | 0.0752175i | ||||||||
\(986\) | −54.8328 | −1.74623 | ||||||||
\(987\) | 51.7771i | 1.64808i | ||||||||
\(988\) | 12.9443i | 0.411812i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.6656 | −1.70474 | −0.852372 | − | 0.522935i | \(-0.824837\pi\) | ||||
−0.852372 | + | 0.522935i | \(0.824837\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 65.8885 | 2.08986 | ||||||||
\(995\) | −21.0557 | −0.667511 | ||||||||
\(996\) | 10.4721 | 0.331822 | ||||||||
\(997\) | − 19.4164i | − 0.614924i | −0.951560 | − | 0.307462i | \(-0.900520\pi\) | ||||
0.951560 | − | 0.307462i | \(-0.0994797\pi\) | |||||||
\(998\) | − 24.0000i | − 0.759707i | ||||||||
\(999\) | 8.47214 | 0.268047 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 690.2.d.a.139.1 | ✓ | 4 | |
3.2 | odd | 2 | 2070.2.d.b.829.4 | 4 | |||
5.2 | odd | 4 | 3450.2.a.bn.1.2 | 2 | |||
5.3 | odd | 4 | 3450.2.a.bc.1.1 | 2 | |||
5.4 | even | 2 | inner | 690.2.d.a.139.3 | yes | 4 | |
15.14 | odd | 2 | 2070.2.d.b.829.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.a.139.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
690.2.d.a.139.3 | yes | 4 | 5.4 | even | 2 | inner | |
2070.2.d.b.829.2 | 4 | 15.14 | odd | 2 | |||
2070.2.d.b.829.4 | 4 | 3.2 | odd | 2 | |||
3450.2.a.bc.1.1 | 2 | 5.3 | odd | 4 | |||
3450.2.a.bn.1.2 | 2 | 5.2 | odd | 4 |