Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(1049,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.1049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.1049 |
Dual form | 1050.2.d.f.1049.3 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.61803 | + | 0.618034i | 0.934172 | + | 0.356822i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.61803 | + | 0.618034i | 0.660560 | + | 0.252311i | ||||
\(7\) | −2.61803 | + | 0.381966i | −0.989524 | + | 0.144370i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214i | 1.34840i | 0.738549 | + | 0.674200i | \(0.235511\pi\) | ||||
−0.738549 | + | 0.674200i | \(0.764489\pi\) | |||||||
\(12\) | 1.61803 | + | 0.618034i | 0.467086 | + | 0.178411i | ||||
\(13\) | 3.23607 | 0.897524 | 0.448762 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448762 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(14\) | −2.61803 | + | 0.381966i | −0.699699 | + | 0.102085i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.763932i | − | 0.185281i | −0.995700 | − | 0.0926404i | \(-0.970469\pi\) | ||
0.995700 | − | 0.0926404i | \(-0.0295307\pi\) | |||||||
\(18\) | 2.23607 | + | 2.00000i | 0.527046 | + | 0.471405i | ||||
\(19\) | 0.472136i | 0.108315i | 0.998532 | + | 0.0541577i | \(0.0172474\pi\) | ||||
−0.998532 | + | 0.0541577i | \(0.982753\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.47214 | − | 1.00000i | −0.975900 | − | 0.218218i | ||||
\(22\) | 4.47214i | 0.953463i | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 1.61803 | + | 0.618034i | 0.330280 | + | 0.126156i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.23607 | 0.634645 | ||||||||
\(27\) | 2.38197 | + | 4.61803i | 0.458410 | + | 0.888741i | ||||
\(28\) | −2.61803 | + | 0.381966i | −0.494762 | + | 0.0721848i | ||||
\(29\) | 5.70820i | 1.05999i | 0.848002 | + | 0.529993i | \(0.177806\pi\) | ||||
−0.848002 | + | 0.529993i | \(0.822194\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.23607i | − | 1.29964i | −0.760090 | − | 0.649818i | \(-0.774845\pi\) | ||
0.760090 | − | 0.649818i | \(-0.225155\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.76393 | + | 7.23607i | −0.481139 | + | 1.25964i | ||||
\(34\) | − | 0.763932i | − | 0.131013i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.23607 | + | 2.00000i | 0.372678 | + | 0.333333i | ||||
\(37\) | 5.23607i | 0.860804i | 0.902637 | + | 0.430402i | \(0.141628\pi\) | ||||
−0.902637 | + | 0.430402i | \(0.858372\pi\) | |||||||
\(38\) | 0.472136i | 0.0765906i | ||||||||
\(39\) | 5.23607 | + | 2.00000i | 0.838442 | + | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.47214 | −1.01078 | −0.505389 | − | 0.862892i | \(-0.668651\pi\) | ||||
−0.505389 | + | 0.862892i | \(0.668651\pi\) | |||||||
\(42\) | −4.47214 | − | 1.00000i | −0.690066 | − | 0.154303i | ||||
\(43\) | − | 12.9443i | − | 1.97398i | −0.160773 | − | 0.986991i | \(-0.551399\pi\) | ||
0.160773 | − | 0.986991i | \(-0.448601\pi\) | |||||||
\(44\) | 4.47214i | 0.674200i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | − | 2.47214i | − | 0.360598i | −0.983612 | − | 0.180299i | \(-0.942293\pi\) | ||
0.983612 | − | 0.180299i | \(-0.0577065\pi\) | |||||||
\(48\) | 1.61803 | + | 0.618034i | 0.233543 | + | 0.0892055i | ||||
\(49\) | 6.70820 | − | 2.00000i | 0.958315 | − | 0.285714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.472136 | − | 1.23607i | 0.0661123 | − | 0.173084i | ||||
\(52\) | 3.23607 | 0.448762 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 2.38197 | + | 4.61803i | 0.324145 | + | 0.628435i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.61803 | + | 0.381966i | −0.349850 | + | 0.0510424i | ||||
\(57\) | −0.291796 | + | 0.763932i | −0.0386493 | + | 0.101185i | ||||
\(58\) | 5.70820i | 0.749524i | ||||||||
\(59\) | −4.47214 | −0.582223 | −0.291111 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291111 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.76393i | 0.353885i | 0.984221 | + | 0.176943i | \(0.0566207\pi\) | ||||
−0.984221 | + | 0.176943i | \(0.943379\pi\) | |||||||
\(62\) | − | 7.23607i | − | 0.918982i | ||||||
\(63\) | −6.61803 | − | 4.38197i | −0.833794 | − | 0.552076i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.76393 | + | 7.23607i | −0.340217 | + | 0.890698i | ||||
\(67\) | − | 12.0000i | − | 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | − | 0.763932i | − | 0.0926404i | ||||||
\(69\) | 6.47214 | + | 2.47214i | 0.779154 | + | 0.297610i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.76393i | 0.328018i | 0.986459 | + | 0.164009i | \(0.0524427\pi\) | ||||
−0.986459 | + | 0.164009i | \(0.947557\pi\) | |||||||
\(72\) | 2.23607 | + | 2.00000i | 0.263523 | + | 0.235702i | ||||
\(73\) | −6.76393 | −0.791658 | −0.395829 | − | 0.918324i | \(-0.629543\pi\) | ||||
−0.395829 | + | 0.918324i | \(0.629543\pi\) | |||||||
\(74\) | 5.23607i | 0.608681i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.472136i | 0.0541577i | ||||||||
\(77\) | −1.70820 | − | 11.7082i | −0.194668 | − | 1.33427i | ||||
\(78\) | 5.23607 | + | 2.00000i | 0.592868 | + | 0.226455i | ||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | −6.47214 | −0.714728 | ||||||||
\(83\) | − | 16.6525i | − | 1.82785i | −0.405887 | − | 0.913923i | \(-0.633037\pi\) | ||
0.405887 | − | 0.913923i | \(-0.366963\pi\) | |||||||
\(84\) | −4.47214 | − | 1.00000i | −0.487950 | − | 0.109109i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 12.9443i | − | 1.39582i | ||||||
\(87\) | −3.52786 | + | 9.23607i | −0.378227 | + | 0.990210i | ||||
\(88\) | 4.47214i | 0.476731i | ||||||||
\(89\) | −14.4721 | −1.53404 | −0.767022 | − | 0.641621i | \(-0.778262\pi\) | ||||
−0.767022 | + | 0.641621i | \(0.778262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.47214 | + | 1.23607i | −0.888121 | + | 0.129575i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 4.47214 | − | 11.7082i | 0.463739 | − | 1.21408i | ||||
\(94\) | − | 2.47214i | − | 0.254981i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.61803 | + | 0.618034i | 0.165140 | + | 0.0630778i | ||||
\(97\) | −5.23607 | −0.531642 | −0.265821 | − | 0.964022i | \(-0.585643\pi\) | ||||
−0.265821 | + | 0.964022i | \(0.585643\pi\) | |||||||
\(98\) | 6.70820 | − | 2.00000i | 0.677631 | − | 0.202031i | ||||
\(99\) | −8.94427 | + | 10.0000i | −0.898933 | + | 1.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.52786 | 0.351036 | 0.175518 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175518 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(102\) | 0.472136 | − | 1.23607i | 0.0467484 | − | 0.122389i | ||||
\(103\) | 16.6525 | 1.64082 | 0.820409 | − | 0.571778i | \(-0.193746\pi\) | ||||
0.820409 | + | 0.571778i | \(0.193746\pi\) | |||||||
\(104\) | 3.23607 | 0.317323 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.47214 | 0.822887 | ||||||||
\(107\) | −15.4164 | −1.49036 | −0.745180 | − | 0.666863i | \(-0.767637\pi\) | ||||
−0.745180 | + | 0.666863i | \(0.767637\pi\) | |||||||
\(108\) | 2.38197 | + | 4.61803i | 0.229205 | + | 0.444371i | ||||
\(109\) | 4.47214 | 0.428353 | 0.214176 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214176 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.23607 | + | 8.47214i | −0.307154 | + | 0.804140i | ||||
\(112\) | −2.61803 | + | 0.381966i | −0.247381 | + | 0.0360924i | ||||
\(113\) | −14.9443 | −1.40584 | −0.702919 | − | 0.711269i | \(-0.748121\pi\) | ||||
−0.702919 | + | 0.711269i | \(0.748121\pi\) | |||||||
\(114\) | −0.291796 | + | 0.763932i | −0.0273292 | + | 0.0715488i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.70820i | 0.529993i | ||||||||
\(117\) | 7.23607 | + | 6.47214i | 0.668975 | + | 0.598349i | ||||
\(118\) | −4.47214 | −0.411693 | ||||||||
\(119\) | 0.291796 | + | 2.00000i | 0.0267489 | + | 0.183340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 2.76393i | 0.250235i | ||||||||
\(123\) | −10.4721 | − | 4.00000i | −0.944241 | − | 0.360668i | ||||
\(124\) | − | 7.23607i | − | 0.649818i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.61803 | − | 4.38197i | −0.589581 | − | 0.390377i | ||||
\(127\) | − | 13.7082i | − | 1.21641i | −0.793781 | − | 0.608203i | \(-0.791891\pi\) | ||
0.793781 | − | 0.608203i | \(-0.208109\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.00000 | − | 20.9443i | 0.704361 | − | 1.84404i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.4164 | 1.87116 | 0.935580 | − | 0.353114i | \(-0.114877\pi\) | ||||
0.935580 | + | 0.353114i | \(0.114877\pi\) | |||||||
\(132\) | −2.76393 | + | 7.23607i | −0.240569 | + | 0.629819i | ||||
\(133\) | −0.180340 | − | 1.23607i | −0.0156375 | − | 0.107181i | ||||
\(134\) | − | 12.0000i | − | 1.03664i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 0.763932i | − | 0.0655066i | ||||||
\(137\) | 12.4721 | 1.06557 | 0.532783 | − | 0.846252i | \(-0.321146\pi\) | ||||
0.532783 | + | 0.846252i | \(0.321146\pi\) | |||||||
\(138\) | 6.47214 | + | 2.47214i | 0.550945 | + | 0.210442i | ||||
\(139\) | 20.4721i | 1.73642i | 0.496194 | + | 0.868212i | \(0.334731\pi\) | ||||
−0.496194 | + | 0.868212i | \(0.665269\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.52786 | − | 4.00000i | 0.128669 | − | 0.336861i | ||||
\(142\) | 2.76393i | 0.231944i | ||||||||
\(143\) | 14.4721i | 1.21022i | ||||||||
\(144\) | 2.23607 | + | 2.00000i | 0.186339 | + | 0.166667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.76393 | −0.559787 | ||||||||
\(147\) | 12.0902 | + | 0.909830i | 0.997180 | + | 0.0750415i | ||||
\(148\) | 5.23607i | 0.430402i | ||||||||
\(149\) | − | 17.7082i | − | 1.45071i | −0.688374 | − | 0.725356i | \(-0.741675\pi\) | ||
0.688374 | − | 0.725356i | \(-0.258325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.05573 | 0.248672 | 0.124336 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124336 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(152\) | 0.472136i | 0.0382953i | ||||||||
\(153\) | 1.52786 | − | 1.70820i | 0.123520 | − | 0.138100i | ||||
\(154\) | −1.70820 | − | 11.7082i | −0.137651 | − | 0.943474i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.23607 | + | 2.00000i | 0.419221 | + | 0.160128i | ||||
\(157\) | 4.76393 | 0.380203 | 0.190102 | − | 0.981764i | \(-0.439118\pi\) | ||||
0.190102 | + | 0.981764i | \(0.439118\pi\) | |||||||
\(158\) | −8.94427 | −0.711568 | ||||||||
\(159\) | 13.7082 | + | 5.23607i | 1.08713 | + | 0.415247i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.4721 | + | 1.52786i | −0.825320 | + | 0.120413i | ||||
\(162\) | 1.00000 | + | 8.94427i | 0.0785674 | + | 0.702728i | ||||
\(163\) | 1.52786i | 0.119672i | 0.998208 | + | 0.0598358i | \(0.0190577\pi\) | ||||
−0.998208 | + | 0.0598358i | \(0.980942\pi\) | |||||||
\(164\) | −6.47214 | −0.505389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 16.6525i | − | 1.29248i | ||||||
\(167\) | − | 16.9443i | − | 1.31119i | −0.755114 | − | 0.655594i | \(-0.772418\pi\) | ||
0.755114 | − | 0.655594i | \(-0.227582\pi\) | |||||||
\(168\) | −4.47214 | − | 1.00000i | −0.345033 | − | 0.0771517i | ||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.944272 | + | 1.05573i | −0.0722103 | + | 0.0807335i | ||||
\(172\) | − | 12.9443i | − | 0.986991i | ||||||
\(173\) | 17.4164i | 1.32414i | 0.749440 | + | 0.662072i | \(0.230323\pi\) | ||||
−0.749440 | + | 0.662072i | \(0.769677\pi\) | |||||||
\(174\) | −3.52786 | + | 9.23607i | −0.267447 | + | 0.700185i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.47214i | 0.337100i | ||||||||
\(177\) | −7.23607 | − | 2.76393i | −0.543896 | − | 0.207750i | ||||
\(178\) | −14.4721 | −1.08473 | ||||||||
\(179\) | 2.94427i | 0.220065i | 0.993928 | + | 0.110033i | \(0.0350955\pi\) | ||||
−0.993928 | + | 0.110033i | \(0.964904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.18034i | 0.459381i | 0.973264 | + | 0.229691i | \(0.0737714\pi\) | ||||
−0.973264 | + | 0.229691i | \(0.926229\pi\) | |||||||
\(182\) | −8.47214 | + | 1.23607i | −0.627996 | + | 0.0916235i | ||||
\(183\) | −1.70820 | + | 4.47214i | −0.126274 | + | 0.330590i | ||||
\(184\) | 4.00000 | 0.294884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.47214 | − | 11.7082i | 0.327913 | − | 0.858487i | ||||
\(187\) | 3.41641 | 0.249832 | ||||||||
\(188\) | − | 2.47214i | − | 0.180299i | ||||||
\(189\) | −8.00000 | − | 11.1803i | −0.581914 | − | 0.813250i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.76393i | − | 0.199991i | −0.994988 | − | 0.0999956i | \(-0.968117\pi\) | ||
0.994988 | − | 0.0999956i | \(-0.0318829\pi\) | |||||||
\(192\) | 1.61803 | + | 0.618034i | 0.116772 | + | 0.0446028i | ||||
\(193\) | 6.00000i | 0.431889i | 0.976406 | + | 0.215945i | \(0.0692831\pi\) | ||||
−0.976406 | + | 0.215945i | \(0.930717\pi\) | |||||||
\(194\) | −5.23607 | −0.375928 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.70820 | − | 2.00000i | 0.479157 | − | 0.142857i | ||||
\(197\) | 12.4721 | 0.888603 | 0.444301 | − | 0.895877i | \(-0.353452\pi\) | ||||
0.444301 | + | 0.895877i | \(0.353452\pi\) | |||||||
\(198\) | −8.94427 | + | 10.0000i | −0.635642 | + | 0.710669i | ||||
\(199\) | − | 0.180340i | − | 0.0127840i | −0.999980 | − | 0.00639198i | \(-0.997965\pi\) | ||
0.999980 | − | 0.00639198i | \(-0.00203464\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.41641 | − | 19.4164i | 0.523113 | − | 1.36953i | ||||
\(202\) | 3.52786 | 0.248220 | ||||||||
\(203\) | −2.18034 | − | 14.9443i | −0.153030 | − | 1.04888i | ||||
\(204\) | 0.472136 | − | 1.23607i | 0.0330561 | − | 0.0865421i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.6525 | 1.16023 | ||||||||
\(207\) | 8.94427 | + | 8.00000i | 0.621670 | + | 0.556038i | ||||
\(208\) | 3.23607 | 0.224381 | ||||||||
\(209\) | −2.11146 | −0.146052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 8.47214 | 0.581869 | ||||||||
\(213\) | −1.70820 | + | 4.47214i | −0.117044 | + | 0.306426i | ||||
\(214\) | −15.4164 | −1.05384 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.38197 | + | 4.61803i | 0.162072 | + | 0.314217i | ||||
\(217\) | 2.76393 | + | 18.9443i | 0.187628 | + | 1.28602i | ||||
\(218\) | 4.47214 | 0.302891 | ||||||||
\(219\) | −10.9443 | − | 4.18034i | −0.739545 | − | 0.282481i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.47214i | − | 0.166294i | ||||||
\(222\) | −3.23607 | + | 8.47214i | −0.217191 | + | 0.568613i | ||||
\(223\) | 4.29180 | 0.287400 | 0.143700 | − | 0.989621i | \(-0.454100\pi\) | ||||
0.143700 | + | 0.989621i | \(0.454100\pi\) | |||||||
\(224\) | −2.61803 | + | 0.381966i | −0.174925 | + | 0.0255212i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.9443 | −0.994078 | ||||||||
\(227\) | − | 5.23607i | − | 0.347530i | −0.984787 | − | 0.173765i | \(-0.944407\pi\) | ||
0.984787 | − | 0.173765i | \(-0.0555933\pi\) | |||||||
\(228\) | −0.291796 | + | 0.763932i | −0.0193247 | + | 0.0505926i | ||||
\(229\) | 13.2361i | 0.874664i | 0.899300 | + | 0.437332i | \(0.144077\pi\) | ||||
−0.899300 | + | 0.437332i | \(0.855923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.47214 | − | 20.0000i | 0.294245 | − | 1.31590i | ||||
\(232\) | 5.70820i | 0.374762i | ||||||||
\(233\) | −20.4721 | −1.34117 | −0.670587 | − | 0.741831i | \(-0.733958\pi\) | ||||
−0.670587 | + | 0.741831i | \(0.733958\pi\) | |||||||
\(234\) | 7.23607 | + | 6.47214i | 0.473037 | + | 0.423097i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.47214 | −0.291111 | ||||||||
\(237\) | −14.4721 | − | 5.52786i | −0.940066 | − | 0.359073i | ||||
\(238\) | 0.291796 | + | 2.00000i | 0.0189143 | + | 0.129641i | ||||
\(239\) | − | 22.1803i | − | 1.43473i | −0.696699 | − | 0.717363i | \(-0.745349\pi\) | ||
0.696699 | − | 0.717363i | \(-0.254651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.8885i | − | 1.15230i | −0.817343 | − | 0.576151i | \(-0.804554\pi\) | ||
0.817343 | − | 0.576151i | \(-0.195446\pi\) | |||||||
\(242\) | −9.00000 | −0.578542 | ||||||||
\(243\) | −3.90983 | + | 15.0902i | −0.250816 | + | 0.968035i | ||||
\(244\) | 2.76393i | 0.176943i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.4721 | − | 4.00000i | −0.667679 | − | 0.255031i | ||||
\(247\) | 1.52786i | 0.0972157i | ||||||||
\(248\) | − | 7.23607i | − | 0.459491i | ||||||
\(249\) | 10.2918 | − | 26.9443i | 0.652216 | − | 1.70752i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.52786 | 0.222677 | 0.111338 | − | 0.993783i | \(-0.464486\pi\) | ||||
0.111338 | + | 0.993783i | \(0.464486\pi\) | |||||||
\(252\) | −6.61803 | − | 4.38197i | −0.416897 | − | 0.276038i | ||||
\(253\) | 17.8885i | 1.12464i | ||||||||
\(254\) | − | 13.7082i | − | 0.860129i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.18034i | 0.510276i | 0.966905 | + | 0.255138i | \(0.0821208\pi\) | ||||
−0.966905 | + | 0.255138i | \(0.917879\pi\) | |||||||
\(258\) | 8.00000 | − | 20.9443i | 0.498058 | − | 1.30393i | ||||
\(259\) | −2.00000 | − | 13.7082i | −0.124274 | − | 0.851786i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.4164 | + | 12.7639i | −0.706658 | + | 0.790068i | ||||
\(262\) | 21.4164 | 1.32311 | ||||||||
\(263\) | −4.94427 | −0.304877 | −0.152438 | − | 0.988313i | \(-0.548713\pi\) | ||||
−0.152438 | + | 0.988313i | \(0.548713\pi\) | |||||||
\(264\) | −2.76393 | + | 7.23607i | −0.170108 | + | 0.445349i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.180340 | − | 1.23607i | −0.0110573 | − | 0.0757882i | ||||
\(267\) | −23.4164 | − | 8.94427i | −1.43306 | − | 0.547381i | ||||
\(268\) | − | 12.0000i | − | 0.733017i | ||||||
\(269\) | −4.47214 | −0.272671 | −0.136335 | − | 0.990663i | \(-0.543533\pi\) | ||||
−0.136335 | + | 0.990663i | \(0.543533\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.2918i | 1.11115i | 0.831467 | + | 0.555574i | \(0.187501\pi\) | ||||
−0.831467 | + | 0.555574i | \(0.812499\pi\) | |||||||
\(272\) | − | 0.763932i | − | 0.0463202i | ||||||
\(273\) | −14.4721 | − | 3.23607i | −0.875894 | − | 0.195856i | ||||
\(274\) | 12.4721 | 0.753469 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.47214 | + | 2.47214i | 0.389577 | + | 0.148805i | ||||
\(277\) | 23.1246i | 1.38942i | 0.719288 | + | 0.694712i | \(0.244468\pi\) | ||||
−0.719288 | + | 0.694712i | \(0.755532\pi\) | |||||||
\(278\) | 20.4721i | 1.22784i | ||||||||
\(279\) | 14.4721 | − | 16.1803i | 0.866424 | − | 0.968692i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.0000i | − | 1.19310i | −0.802576 | − | 0.596550i | \(-0.796538\pi\) | ||
0.802576 | − | 0.596550i | \(-0.203462\pi\) | |||||||
\(282\) | 1.52786 | − | 4.00000i | 0.0909830 | − | 0.238197i | ||||
\(283\) | 8.76393 | 0.520962 | 0.260481 | − | 0.965479i | \(-0.416119\pi\) | ||||
0.260481 | + | 0.965479i | \(0.416119\pi\) | |||||||
\(284\) | 2.76393i | 0.164009i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.4721i | 0.855755i | ||||||||
\(287\) | 16.9443 | − | 2.47214i | 1.00019 | − | 0.145926i | ||||
\(288\) | 2.23607 | + | 2.00000i | 0.131762 | + | 0.117851i | ||||
\(289\) | 16.4164 | 0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.47214 | − | 3.23607i | −0.496645 | − | 0.189702i | ||||
\(292\) | −6.76393 | −0.395829 | ||||||||
\(293\) | − | 29.4164i | − | 1.71852i | −0.511535 | − | 0.859262i | \(-0.670923\pi\) | ||
0.511535 | − | 0.859262i | \(-0.329077\pi\) | |||||||
\(294\) | 12.0902 | + | 0.909830i | 0.705113 | + | 0.0530624i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.23607i | 0.304340i | ||||||||
\(297\) | −20.6525 | + | 10.6525i | −1.19838 | + | 0.618119i | ||||
\(298\) | − | 17.7082i | − | 1.02581i | ||||||
\(299\) | 12.9443 | 0.748587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.94427 | + | 33.8885i | 0.284983 | + | 1.95330i | ||||
\(302\) | 3.05573 | 0.175837 | ||||||||
\(303\) | 5.70820 | + | 2.18034i | 0.327928 | + | 0.125257i | ||||
\(304\) | 0.472136i | 0.0270789i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.52786 | − | 1.70820i | 0.0873422 | − | 0.0976515i | ||||
\(307\) | −4.18034 | −0.238585 | −0.119292 | − | 0.992859i | \(-0.538063\pi\) | ||||
−0.119292 | + | 0.992859i | \(0.538063\pi\) | |||||||
\(308\) | −1.70820 | − | 11.7082i | −0.0973340 | − | 0.667137i | ||||
\(309\) | 26.9443 | + | 10.2918i | 1.53281 | + | 0.585480i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.4721 | −1.50110 | −0.750549 | − | 0.660815i | \(-0.770211\pi\) | ||||
−0.750549 | + | 0.660815i | \(0.770211\pi\) | |||||||
\(312\) | 5.23607 | + | 2.00000i | 0.296434 | + | 0.113228i | ||||
\(313\) | 7.70820 | 0.435693 | 0.217847 | − | 0.975983i | \(-0.430097\pi\) | ||||
0.217847 | + | 0.975983i | \(0.430097\pi\) | |||||||
\(314\) | 4.76393 | 0.268844 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.94427 | −0.503155 | ||||||||
\(317\) | 6.94427 | 0.390029 | 0.195015 | − | 0.980800i | \(-0.437525\pi\) | ||||
0.195015 | + | 0.980800i | \(0.437525\pi\) | |||||||
\(318\) | 13.7082 | + | 5.23607i | 0.768718 | + | 0.293624i | ||||
\(319\) | −25.5279 | −1.42929 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.9443 | − | 9.52786i | −1.39225 | − | 0.531794i | ||||
\(322\) | −10.4721 | + | 1.52786i | −0.583589 | + | 0.0851445i | ||||
\(323\) | 0.360680 | 0.0200688 | ||||||||
\(324\) | 1.00000 | + | 8.94427i | 0.0555556 | + | 0.496904i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.52786i | 0.0846206i | ||||||||
\(327\) | 7.23607 | + | 2.76393i | 0.400155 | + | 0.152846i | ||||
\(328\) | −6.47214 | −0.357364 | ||||||||
\(329\) | 0.944272 | + | 6.47214i | 0.0520594 | + | 0.356820i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.9443 | 1.15120 | 0.575601 | − | 0.817731i | \(-0.304768\pi\) | ||||
0.575601 | + | 0.817731i | \(0.304768\pi\) | |||||||
\(332\) | − | 16.6525i | − | 0.913923i | ||||||
\(333\) | −10.4721 | + | 11.7082i | −0.573870 | + | 0.641606i | ||||
\(334\) | − | 16.9443i | − | 0.927149i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.47214 | − | 1.00000i | −0.243975 | − | 0.0545545i | ||||
\(337\) | − | 5.41641i | − | 0.295051i | −0.989058 | − | 0.147525i | \(-0.952869\pi\) | ||
0.989058 | − | 0.147525i | \(-0.0471308\pi\) | |||||||
\(338\) | −2.52786 | −0.137498 | ||||||||
\(339\) | −24.1803 | − | 9.23607i | −1.31330 | − | 0.501634i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.3607 | 1.75243 | ||||||||
\(342\) | −0.944272 | + | 1.05573i | −0.0510604 | + | 0.0570872i | ||||
\(343\) | −16.7984 | + | 7.79837i | −0.907027 | + | 0.421073i | ||||
\(344\) | − | 12.9443i | − | 0.697908i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.4164i | 0.936312i | ||||||||
\(347\) | −6.47214 | −0.347442 | −0.173721 | − | 0.984795i | \(-0.555579\pi\) | ||||
−0.173721 | + | 0.984795i | \(0.555579\pi\) | |||||||
\(348\) | −3.52786 | + | 9.23607i | −0.189113 | + | 0.495105i | ||||
\(349\) | 2.18034i | 0.116711i | 0.998296 | + | 0.0583555i | \(0.0185857\pi\) | ||||
−0.998296 | + | 0.0583555i | \(0.981414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.70820 | + | 14.9443i | 0.411433 | + | 0.797666i | ||||
\(352\) | 4.47214i | 0.238366i | ||||||||
\(353\) | − | 14.2918i | − | 0.760676i | −0.924848 | − | 0.380338i | \(-0.875808\pi\) | ||
0.924848 | − | 0.380338i | \(-0.124192\pi\) | |||||||
\(354\) | −7.23607 | − | 2.76393i | −0.384593 | − | 0.146901i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.4721 | −0.767022 | ||||||||
\(357\) | −0.763932 | + | 3.41641i | −0.0404316 | + | 0.180815i | ||||
\(358\) | 2.94427i | 0.155610i | ||||||||
\(359\) | 10.1803i | 0.537298i | 0.963238 | + | 0.268649i | \(0.0865771\pi\) | ||||
−0.963238 | + | 0.268649i | \(0.913423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7771 | 0.988268 | ||||||||
\(362\) | 6.18034i | 0.324831i | ||||||||
\(363\) | −14.5623 | − | 5.56231i | −0.764323 | − | 0.291945i | ||||
\(364\) | −8.47214 | + | 1.23607i | −0.444061 | + | 0.0647876i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.70820 | + | 4.47214i | −0.0892892 | + | 0.233762i | ||||
\(367\) | −14.1803 | −0.740208 | −0.370104 | − | 0.928990i | \(-0.620678\pi\) | ||||
−0.370104 | + | 0.928990i | \(0.620678\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | −14.4721 | − | 12.9443i | −0.753389 | − | 0.673852i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.1803 | + | 3.23607i | −1.15155 | + | 0.168008i | ||||
\(372\) | 4.47214 | − | 11.7082i | 0.231869 | − | 0.607042i | ||||
\(373\) | 9.81966i | 0.508443i | 0.967146 | + | 0.254221i | \(0.0818192\pi\) | ||||
−0.967146 | + | 0.254221i | \(0.918181\pi\) | |||||||
\(374\) | 3.41641 | 0.176658 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 2.47214i | − | 0.127491i | ||||||
\(377\) | 18.4721i | 0.951363i | ||||||||
\(378\) | −8.00000 | − | 11.1803i | −0.411476 | − | 0.575055i | ||||
\(379\) | −17.8885 | −0.918873 | −0.459436 | − | 0.888211i | \(-0.651949\pi\) | ||||
−0.459436 | + | 0.888211i | \(0.651949\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.47214 | − | 22.1803i | 0.434041 | − | 1.13633i | ||||
\(382\) | − | 2.76393i | − | 0.141415i | ||||||
\(383\) | 21.8885i | 1.11845i | 0.829015 | + | 0.559226i | \(0.188902\pi\) | ||||
−0.829015 | + | 0.559226i | \(0.811098\pi\) | |||||||
\(384\) | 1.61803 | + | 0.618034i | 0.0825700 | + | 0.0315389i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000i | 0.305392i | ||||||||
\(387\) | 25.8885 | − | 28.9443i | 1.31599 | − | 1.47132i | ||||
\(388\) | −5.23607 | −0.265821 | ||||||||
\(389\) | 7.81966i | 0.396473i | 0.980154 | + | 0.198236i | \(0.0635213\pi\) | ||||
−0.980154 | + | 0.198236i | \(0.936479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.05573i | − | 0.154535i | ||||||
\(392\) | 6.70820 | − | 2.00000i | 0.338815 | − | 0.101015i | ||||
\(393\) | 34.6525 | + | 13.2361i | 1.74799 | + | 0.667671i | ||||
\(394\) | 12.4721 | 0.628337 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −8.94427 | + | 10.0000i | −0.449467 | + | 0.502519i | ||||
\(397\) | 17.1246 | 0.859460 | 0.429730 | − | 0.902958i | \(-0.358609\pi\) | ||||
0.429730 | + | 0.902958i | \(0.358609\pi\) | |||||||
\(398\) | − | 0.180340i | − | 0.00903962i | ||||||
\(399\) | 0.472136 | − | 2.11146i | 0.0236364 | − | 0.105705i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.52786i | − | 0.276048i | −0.990429 | − | 0.138024i | \(-0.955925\pi\) | ||
0.990429 | − | 0.138024i | \(-0.0440752\pi\) | |||||||
\(402\) | 7.41641 | − | 19.4164i | 0.369897 | − | 0.968402i | ||||
\(403\) | − | 23.4164i | − | 1.16645i | ||||||
\(404\) | 3.52786 | 0.175518 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.18034 | − | 14.9443i | −0.108208 | − | 0.741672i | ||||
\(407\) | −23.4164 | −1.16071 | ||||||||
\(408\) | 0.472136 | − | 1.23607i | 0.0233742 | − | 0.0611945i | ||||
\(409\) | 19.4164i | 0.960080i | 0.877247 | + | 0.480040i | \(0.159378\pi\) | ||||
−0.877247 | + | 0.480040i | \(0.840622\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.1803 | + | 7.70820i | 0.995423 | + | 0.380218i | ||||
\(412\) | 16.6525 | 0.820409 | ||||||||
\(413\) | 11.7082 | − | 1.70820i | 0.576123 | − | 0.0840552i | ||||
\(414\) | 8.94427 | + | 8.00000i | 0.439587 | + | 0.393179i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.23607 | 0.158661 | ||||||||
\(417\) | −12.6525 | + | 33.1246i | −0.619594 | + | 1.62212i | ||||
\(418\) | −2.11146 | −0.103275 | ||||||||
\(419\) | −16.8328 | −0.822337 | −0.411168 | − | 0.911559i | \(-0.634879\pi\) | ||||
−0.411168 | + | 0.911559i | \(0.634879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4721 | −0.607855 | −0.303927 | − | 0.952695i | \(-0.598298\pi\) | ||||
−0.303927 | + | 0.952695i | \(0.598298\pi\) | |||||||
\(422\) | −8.00000 | −0.389434 | ||||||||
\(423\) | 4.94427 | − | 5.52786i | 0.240399 | − | 0.268774i | ||||
\(424\) | 8.47214 | 0.411443 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.70820 | + | 4.47214i | −0.0827628 | + | 0.216676i | ||||
\(427\) | −1.05573 | − | 7.23607i | −0.0510903 | − | 0.350178i | ||||
\(428\) | −15.4164 | −0.745180 | ||||||||
\(429\) | −8.94427 | + | 23.4164i | −0.431834 | + | 1.13055i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 9.59675i | − | 0.462259i | −0.972923 | − | 0.231130i | \(-0.925758\pi\) | ||
0.972923 | − | 0.231130i | \(-0.0742421\pi\) | |||||||
\(432\) | 2.38197 | + | 4.61803i | 0.114602 | + | 0.222185i | ||||
\(433\) | −4.65248 | −0.223584 | −0.111792 | − | 0.993732i | \(-0.535659\pi\) | ||||
−0.111792 | + | 0.993732i | \(0.535659\pi\) | |||||||
\(434\) | 2.76393 | + | 18.9443i | 0.132673 | + | 0.909354i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.47214 | 0.214176 | ||||||||
\(437\) | 1.88854i | 0.0903413i | ||||||||
\(438\) | −10.9443 | − | 4.18034i | −0.522938 | − | 0.199744i | ||||
\(439\) | 12.1803i | 0.581336i | 0.956824 | + | 0.290668i | \(0.0938775\pi\) | ||||
−0.956824 | + | 0.290668i | \(0.906123\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.0000 | + | 8.94427i | 0.904762 | + | 0.425918i | ||||
\(442\) | − | 2.47214i | − | 0.117588i | ||||||
\(443\) | 9.52786 | 0.452682 | 0.226341 | − | 0.974048i | \(-0.427324\pi\) | ||||
0.226341 | + | 0.974048i | \(0.427324\pi\) | |||||||
\(444\) | −3.23607 | + | 8.47214i | −0.153577 | + | 0.402070i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.29180 | 0.203222 | ||||||||
\(447\) | 10.9443 | − | 28.6525i | 0.517646 | − | 1.35522i | ||||
\(448\) | −2.61803 | + | 0.381966i | −0.123690 | + | 0.0180462i | ||||
\(449\) | − | 1.52786i | − | 0.0721044i | −0.999350 | − | 0.0360522i | \(-0.988522\pi\) | ||
0.999350 | − | 0.0360522i | \(-0.0114783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 28.9443i | − | 1.36293i | ||||||
\(452\) | −14.9443 | −0.702919 | ||||||||
\(453\) | 4.94427 | + | 1.88854i | 0.232302 | + | 0.0887315i | ||||
\(454\) | − | 5.23607i | − | 0.245741i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.291796 | + | 0.763932i | −0.0136646 | + | 0.0357744i | ||||
\(457\) | 9.05573i | 0.423609i | 0.977312 | + | 0.211805i | \(0.0679340\pi\) | ||||
−0.977312 | + | 0.211805i | \(0.932066\pi\) | |||||||
\(458\) | 13.2361i | 0.618481i | ||||||||
\(459\) | 3.52786 | − | 1.81966i | 0.164667 | − | 0.0849345i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.9443 | −0.509726 | −0.254863 | − | 0.966977i | \(-0.582030\pi\) | ||||
−0.254863 | + | 0.966977i | \(0.582030\pi\) | |||||||
\(462\) | 4.47214 | − | 20.0000i | 0.208063 | − | 0.930484i | ||||
\(463\) | − | 0.180340i | − | 0.00838111i | −0.999991 | − | 0.00419055i | \(-0.998666\pi\) | ||
0.999991 | − | 0.00419055i | \(-0.00133390\pi\) | |||||||
\(464\) | 5.70820i | 0.264997i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.4721 | −0.948353 | ||||||||
\(467\) | 20.2918i | 0.938992i | 0.882935 | + | 0.469496i | \(0.155564\pi\) | ||||
−0.882935 | + | 0.469496i | \(0.844436\pi\) | |||||||
\(468\) | 7.23607 | + | 6.47214i | 0.334487 | + | 0.299175i | ||||
\(469\) | 4.58359 | + | 31.4164i | 0.211651 | + | 1.45067i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.70820 | + | 2.94427i | 0.355175 | + | 0.135665i | ||||
\(472\) | −4.47214 | −0.205847 | ||||||||
\(473\) | 57.8885 | 2.66172 | ||||||||
\(474\) | −14.4721 | − | 5.52786i | −0.664727 | − | 0.253903i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.291796 | + | 2.00000i | 0.0133745 | + | 0.0916698i | ||||
\(477\) | 18.9443 | + | 16.9443i | 0.867399 | + | 0.775825i | ||||
\(478\) | − | 22.1803i | − | 1.01451i | ||||||
\(479\) | 2.11146 | 0.0964749 | 0.0482374 | − | 0.998836i | \(-0.484640\pi\) | ||||
0.0482374 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.9443i | 0.772592i | ||||||||
\(482\) | − | 17.8885i | − | 0.814801i | ||||||
\(483\) | −17.8885 | − | 4.00000i | −0.813957 | − | 0.182006i | ||||
\(484\) | −9.00000 | −0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.90983 | + | 15.0902i | −0.177353 | + | 0.684504i | ||||
\(487\) | − | 31.5967i | − | 1.43179i | −0.698210 | − | 0.715893i | \(-0.746020\pi\) | ||
0.698210 | − | 0.715893i | \(-0.253980\pi\) | |||||||
\(488\) | 2.76393i | 0.125117i | ||||||||
\(489\) | −0.944272 | + | 2.47214i | −0.0427015 | + | 0.111794i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4164i | 0.605474i | 0.953074 | + | 0.302737i | \(0.0979004\pi\) | ||||
−0.953074 | + | 0.302737i | \(0.902100\pi\) | |||||||
\(492\) | −10.4721 | − | 4.00000i | −0.472120 | − | 0.180334i | ||||
\(493\) | 4.36068 | 0.196395 | ||||||||
\(494\) | 1.52786i | 0.0687419i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 7.23607i | − | 0.324909i | ||||||
\(497\) | −1.05573 | − | 7.23607i | −0.0473559 | − | 0.324582i | ||||
\(498\) | 10.2918 | − | 26.9443i | 0.461186 | − | 1.20740i | ||||
\(499\) | 17.8885 | 0.800801 | 0.400401 | − | 0.916340i | \(-0.368871\pi\) | ||||
0.400401 | + | 0.916340i | \(0.368871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4721 | − | 27.4164i | 0.467861 | − | 1.22487i | ||||
\(502\) | 3.52786 | 0.157456 | ||||||||
\(503\) | 16.3607i | 0.729487i | 0.931108 | + | 0.364743i | \(0.118843\pi\) | ||||
−0.931108 | + | 0.364743i | \(0.881157\pi\) | |||||||
\(504\) | −6.61803 | − | 4.38197i | −0.294791 | − | 0.195188i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.8885i | 0.795243i | ||||||||
\(507\) | −4.09017 | − | 1.56231i | −0.181651 | − | 0.0693844i | ||||
\(508\) | − | 13.7082i | − | 0.608203i | ||||||
\(509\) | 24.4721 | 1.08471 | 0.542354 | − | 0.840150i | \(-0.317533\pi\) | ||||
0.542354 | + | 0.840150i | \(0.317533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7082 | − | 2.58359i | 0.783365 | − | 0.114291i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.18034 | + | 1.12461i | −0.0962644 | + | 0.0496528i | ||||
\(514\) | 8.18034i | 0.360819i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.00000 | − | 20.9443i | 0.352180 | − | 0.922020i | ||||
\(517\) | 11.0557 | 0.486230 | ||||||||
\(518\) | −2.00000 | − | 13.7082i | −0.0878750 | − | 0.602304i | ||||
\(519\) | −10.7639 | + | 28.1803i | −0.472484 | + | 1.23698i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.0557 | 0.834847 | 0.417423 | − | 0.908712i | \(-0.362933\pi\) | ||||
0.417423 | + | 0.908712i | \(0.362933\pi\) | |||||||
\(522\) | −11.4164 | + | 12.7639i | −0.499683 | + | 0.558662i | ||||
\(523\) | 24.5410 | 1.07310 | 0.536552 | − | 0.843867i | \(-0.319727\pi\) | ||||
0.536552 | + | 0.843867i | \(0.319727\pi\) | |||||||
\(524\) | 21.4164 | 0.935580 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.94427 | −0.215580 | ||||||||
\(527\) | −5.52786 | −0.240798 | ||||||||
\(528\) | −2.76393 | + | 7.23607i | −0.120285 | + | 0.314909i | ||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0000 | − | 8.94427i | −0.433963 | − | 0.388148i | ||||
\(532\) | −0.180340 | − | 1.23607i | −0.00781873 | − | 0.0535903i | ||||
\(533\) | −20.9443 | −0.907197 | ||||||||
\(534\) | −23.4164 | − | 8.94427i | −1.01333 | − | 0.387056i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 12.0000i | − | 0.518321i | ||||||
\(537\) | −1.81966 | + | 4.76393i | −0.0785241 | + | 0.205579i | ||||
\(538\) | −4.47214 | −0.192807 | ||||||||
\(539\) | 8.94427 | + | 30.0000i | 0.385257 | + | 1.29219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0557 | 0.561310 | 0.280655 | − | 0.959809i | \(-0.409448\pi\) | ||||
0.280655 | + | 0.959809i | \(0.409448\pi\) | |||||||
\(542\) | 18.2918i | 0.785700i | ||||||||
\(543\) | −3.81966 | + | 10.0000i | −0.163917 | + | 0.429141i | ||||
\(544\) | − | 0.763932i | − | 0.0327533i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.4721 | − | 3.23607i | −0.619350 | − | 0.138491i | ||||
\(547\) | − | 8.58359i | − | 0.367008i | −0.983019 | − | 0.183504i | \(-0.941256\pi\) | ||
0.983019 | − | 0.183504i | \(-0.0587440\pi\) | |||||||
\(548\) | 12.4721 | 0.532783 | ||||||||
\(549\) | −5.52786 | + | 6.18034i | −0.235923 | + | 0.263770i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.69505 | −0.114813 | ||||||||
\(552\) | 6.47214 | + | 2.47214i | 0.275472 | + | 0.105221i | ||||
\(553\) | 23.4164 | − | 3.41641i | 0.995767 | − | 0.145280i | ||||
\(554\) | 23.1246i | 0.982471i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.4721i | 0.868212i | ||||||||
\(557\) | −16.4721 | −0.697947 | −0.348973 | − | 0.937133i | \(-0.613470\pi\) | ||||
−0.348973 | + | 0.937133i | \(0.613470\pi\) | |||||||
\(558\) | 14.4721 | − | 16.1803i | 0.612654 | − | 0.684968i | ||||
\(559\) | − | 41.8885i | − | 1.77170i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.52786 | + | 2.11146i | 0.233387 | + | 0.0891457i | ||||
\(562\) | − | 20.0000i | − | 0.843649i | ||||||
\(563\) | 17.8197i | 0.751009i | 0.926821 | + | 0.375505i | \(0.122531\pi\) | ||||
−0.926821 | + | 0.375505i | \(0.877469\pi\) | |||||||
\(564\) | 1.52786 | − | 4.00000i | 0.0643347 | − | 0.168430i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.76393 | 0.368376 | ||||||||
\(567\) | −6.03444 | − | 23.0344i | −0.253423 | − | 0.967356i | ||||
\(568\) | 2.76393i | 0.115972i | ||||||||
\(569\) | 18.4721i | 0.774392i | 0.921997 | + | 0.387196i | \(0.126556\pi\) | ||||
−0.921997 | + | 0.387196i | \(0.873444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.8328 | −1.45771 | −0.728854 | − | 0.684669i | \(-0.759947\pi\) | ||||
−0.728854 | + | 0.684669i | \(0.759947\pi\) | |||||||
\(572\) | 14.4721i | 0.605110i | ||||||||
\(573\) | 1.70820 | − | 4.47214i | 0.0713612 | − | 0.186826i | ||||
\(574\) | 16.9443 | − | 2.47214i | 0.707240 | − | 0.103185i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.23607 | + | 2.00000i | 0.0931695 | + | 0.0833333i | ||||
\(577\) | −14.1803 | −0.590335 | −0.295168 | − | 0.955445i | \(-0.595375\pi\) | ||||
−0.295168 | + | 0.955445i | \(0.595375\pi\) | |||||||
\(578\) | 16.4164 | 0.682833 | ||||||||
\(579\) | −3.70820 | + | 9.70820i | −0.154108 | + | 0.403459i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.36068 | + | 43.5967i | 0.263885 | + | 1.80870i | ||||
\(582\) | −8.47214 | − | 3.23607i | −0.351181 | − | 0.134139i | ||||
\(583\) | 37.8885i | 1.56918i | ||||||||
\(584\) | −6.76393 | −0.279893 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 29.4164i | − | 1.21518i | ||||||
\(587\) | 23.7082i | 0.978542i | 0.872132 | + | 0.489271i | \(0.162737\pi\) | ||||
−0.872132 | + | 0.489271i | \(0.837263\pi\) | |||||||
\(588\) | 12.0902 | + | 0.909830i | 0.498590 | + | 0.0375208i | ||||
\(589\) | 3.41641 | 0.140771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.1803 | + | 7.70820i | 0.830108 | + | 0.317073i | ||||
\(592\) | 5.23607i | 0.215201i | ||||||||
\(593\) | 47.0132i | 1.93060i | 0.261145 | + | 0.965299i | \(0.415900\pi\) | ||||
−0.261145 | + | 0.965299i | \(0.584100\pi\) | |||||||
\(594\) | −20.6525 | + | 10.6525i | −0.847381 | + | 0.437076i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 17.7082i | − | 0.725356i | ||||||
\(597\) | 0.111456 | − | 0.291796i | 0.00456160 | − | 0.0119424i | ||||
\(598\) | 12.9443 | 0.529331 | ||||||||
\(599\) | 41.2361i | 1.68486i | 0.538806 | + | 0.842430i | \(0.318876\pi\) | ||||
−0.538806 | + | 0.842430i | \(0.681124\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.4721i | 0.590331i | 0.955446 | + | 0.295165i | \(0.0953747\pi\) | ||||
−0.955446 | + | 0.295165i | \(0.904625\pi\) | |||||||
\(602\) | 4.94427 | + | 33.8885i | 0.201513 | + | 1.38119i | ||||
\(603\) | 24.0000 | − | 26.8328i | 0.977356 | − | 1.09272i | ||||
\(604\) | 3.05573 | 0.124336 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.70820 | + | 2.18034i | 0.231880 | + | 0.0885703i | ||||
\(607\) | 14.7639 | 0.599250 | 0.299625 | − | 0.954057i | \(-0.403139\pi\) | ||||
0.299625 | + | 0.954057i | \(0.403139\pi\) | |||||||
\(608\) | 0.472136i | 0.0191476i | ||||||||
\(609\) | 5.70820 | − | 25.5279i | 0.231308 | − | 1.03444i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 8.00000i | − | 0.323645i | ||||||
\(612\) | 1.52786 | − | 1.70820i | 0.0617602 | − | 0.0690501i | ||||
\(613\) | 20.0689i | 0.810575i | 0.914189 | + | 0.405287i | \(0.132829\pi\) | ||||
−0.914189 | + | 0.405287i | \(0.867171\pi\) | |||||||
\(614\) | −4.18034 | −0.168705 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.70820 | − | 11.7082i | −0.0688255 | − | 0.471737i | ||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 26.9443 | + | 10.2918i | 1.08386 | + | 0.413997i | ||||
\(619\) | − | 14.0000i | − | 0.562708i | −0.959604 | − | 0.281354i | \(-0.909217\pi\) | ||
0.959604 | − | 0.281354i | \(-0.0907834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.52786 | + | 18.4721i | 0.382340 | + | 0.741261i | ||||
\(622\) | −26.4721 | −1.06144 | ||||||||
\(623\) | 37.8885 | − | 5.52786i | 1.51797 | − | 0.221469i | ||||
\(624\) | 5.23607 | + | 2.00000i | 0.209610 | + | 0.0800641i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.70820 | 0.308082 | ||||||||
\(627\) | −3.41641 | − | 1.30495i | −0.136438 | − | 0.0521148i | ||||
\(628\) | 4.76393 | 0.190102 | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8885 | 1.18984 | 0.594922 | − | 0.803783i | \(-0.297183\pi\) | ||||
0.594922 | + | 0.803783i | \(0.297183\pi\) | |||||||
\(632\) | −8.94427 | −0.355784 | ||||||||
\(633\) | −12.9443 | − | 4.94427i | −0.514489 | − | 0.196517i | ||||
\(634\) | 6.94427 | 0.275792 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.7082 | + | 5.23607i | 0.543566 | + | 0.207624i | ||||
\(637\) | 21.7082 | − | 6.47214i | 0.860110 | − | 0.256435i | ||||
\(638\) | −25.5279 | −1.01066 | ||||||||
\(639\) | −5.52786 | + | 6.18034i | −0.218679 | + | 0.244490i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.41641i | 0.134940i | 0.997721 | + | 0.0674700i | \(0.0214927\pi\) | ||||
−0.997721 | + | 0.0674700i | \(0.978507\pi\) | |||||||
\(642\) | −24.9443 | − | 9.52786i | −0.984472 | − | 0.376035i | ||||
\(643\) | −25.7082 | −1.01383 | −0.506916 | − | 0.861995i | \(-0.669215\pi\) | ||||
−0.506916 | + | 0.861995i | \(0.669215\pi\) | |||||||
\(644\) | −10.4721 | + | 1.52786i | −0.412660 | + | 0.0602063i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.360680 | 0.0141908 | ||||||||
\(647\) | 18.8328i | 0.740394i | 0.928953 | + | 0.370197i | \(0.120710\pi\) | ||||
−0.928953 | + | 0.370197i | \(0.879290\pi\) | |||||||
\(648\) | 1.00000 | + | 8.94427i | 0.0392837 | + | 0.351364i | ||||
\(649\) | − | 20.0000i | − | 0.785069i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.23607 | + | 32.3607i | −0.283604 | + | 1.26832i | ||||
\(652\) | 1.52786i | 0.0598358i | ||||||||
\(653\) | 11.8885 | 0.465235 | 0.232617 | − | 0.972568i | \(-0.425271\pi\) | ||||
0.232617 | + | 0.972568i | \(0.425271\pi\) | |||||||
\(654\) | 7.23607 | + | 2.76393i | 0.282953 | + | 0.108078i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.47214 | −0.252694 | ||||||||
\(657\) | −15.1246 | − | 13.5279i | −0.590067 | − | 0.527772i | ||||
\(658\) | 0.944272 | + | 6.47214i | 0.0368116 | + | 0.252310i | ||||
\(659\) | − | 40.4721i | − | 1.57657i | −0.615310 | − | 0.788285i | \(-0.710969\pi\) | ||
0.615310 | − | 0.788285i | \(-0.289031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.7082i | 1.23331i | 0.787235 | + | 0.616653i | \(0.211512\pi\) | ||||
−0.787235 | + | 0.616653i | \(0.788488\pi\) | |||||||
\(662\) | 20.9443 | 0.814022 | ||||||||
\(663\) | 1.52786 | − | 4.00000i | 0.0593373 | − | 0.155347i | ||||
\(664\) | − | 16.6525i | − | 0.646241i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.4721 | + | 11.7082i | −0.405787 | + | 0.453684i | ||||
\(667\) | 22.8328i | 0.884090i | ||||||||
\(668\) | − | 16.9443i | − | 0.655594i | ||||||
\(669\) | 6.94427 | + | 2.65248i | 0.268481 | + | 0.102551i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.3607 | −0.477179 | ||||||||
\(672\) | −4.47214 | − | 1.00000i | −0.172516 | − | 0.0385758i | ||||
\(673\) | − | 28.4721i | − | 1.09752i | −0.835980 | − | 0.548760i | \(-0.815100\pi\) | ||
0.835980 | − | 0.548760i | \(-0.184900\pi\) | |||||||
\(674\) | − | 5.41641i | − | 0.208632i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.52786 | −0.0972255 | ||||||||
\(677\) | − | 18.0000i | − | 0.691796i | −0.938272 | − | 0.345898i | \(-0.887574\pi\) | ||
0.938272 | − | 0.345898i | \(-0.112426\pi\) | |||||||
\(678\) | −24.1803 | − | 9.23607i | −0.928640 | − | 0.354709i | ||||
\(679\) | 13.7082 | − | 2.00000i | 0.526073 | − | 0.0767530i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.23607 | − | 8.47214i | 0.124006 | − | 0.324653i | ||||
\(682\) | 32.3607 | 1.23915 | ||||||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | −0.944272 | + | 1.05573i | −0.0361051 | + | 0.0403668i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.7984 | + | 7.79837i | −0.641365 | + | 0.297743i | ||||
\(687\) | −8.18034 | + | 21.4164i | −0.312099 | + | 0.817087i | ||||
\(688\) | − | 12.9443i | − | 0.493496i | ||||||
\(689\) | 27.4164 | 1.04448 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 38.9443i | − | 1.48151i | −0.671775 | − | 0.740755i | \(-0.734468\pi\) | ||
0.671775 | − | 0.740755i | \(-0.265532\pi\) | |||||||
\(692\) | 17.4164i | 0.662072i | ||||||||
\(693\) | 19.5967 | − | 29.5967i | 0.744419 | − | 1.12429i | ||||
\(694\) | −6.47214 | −0.245679 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.52786 | + | 9.23607i | −0.133723 | + | 0.350092i | ||||
\(697\) | 4.94427i | 0.187278i | ||||||||
\(698\) | 2.18034i | 0.0825271i | ||||||||
\(699\) | −33.1246 | − | 12.6525i | −1.25289 | − | 0.478561i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.0689i | − | 0.531374i | −0.964059 | − | 0.265687i | \(-0.914401\pi\) | ||
0.964059 | − | 0.265687i | \(-0.0855988\pi\) | |||||||
\(702\) | 7.70820 | + | 14.9443i | 0.290927 | + | 0.564035i | ||||
\(703\) | −2.47214 | −0.0932384 | ||||||||
\(704\) | 4.47214i | 0.168550i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 14.2918i | − | 0.537879i | ||||||
\(707\) | −9.23607 | + | 1.34752i | −0.347358 | + | 0.0506789i | ||||
\(708\) | −7.23607 | − | 2.76393i | −0.271948 | − | 0.103875i | ||||
\(709\) | 24.4721 | 0.919070 | 0.459535 | − | 0.888160i | \(-0.348016\pi\) | ||||
0.459535 | + | 0.888160i | \(0.348016\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.0000 | − | 17.8885i | −0.750059 | − | 0.670873i | ||||
\(712\) | −14.4721 | −0.542366 | ||||||||
\(713\) | − | 28.9443i | − | 1.08397i | ||||||
\(714\) | −0.763932 | + | 3.41641i | −0.0285894 | + | 0.127856i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.94427i | 0.110033i | ||||||||
\(717\) | 13.7082 | − | 35.8885i | 0.511942 | − | 1.34028i | ||||
\(718\) | 10.1803i | 0.379927i | ||||||||
\(719\) | −25.5279 | −0.952029 | −0.476014 | − | 0.879438i | \(-0.657919\pi\) | ||||
−0.476014 | + | 0.879438i | \(0.657919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.5967 | + | 6.36068i | −1.62363 | + | 0.236884i | ||||
\(722\) | 18.7771 | 0.698811 | ||||||||
\(723\) | 11.0557 | − | 28.9443i | 0.411167 | − | 1.07645i | ||||
\(724\) | 6.18034i | 0.229691i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.5623 | − | 5.56231i | −0.540458 | − | 0.206437i | ||||
\(727\) | −39.7082 | −1.47270 | −0.736348 | − | 0.676603i | \(-0.763451\pi\) | ||||
−0.736348 | + | 0.676603i | \(0.763451\pi\) | |||||||
\(728\) | −8.47214 | + | 1.23607i | −0.313998 | + | 0.0458117i | ||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.88854 | −0.365741 | ||||||||
\(732\) | −1.70820 | + | 4.47214i | −0.0631370 | + | 0.165295i | ||||
\(733\) | −38.0689 | −1.40611 | −0.703053 | − | 0.711137i | \(-0.748180\pi\) | ||||
−0.703053 | + | 0.711137i | \(0.748180\pi\) | |||||||
\(734\) | −14.1803 | −0.523406 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 53.6656 | 1.97680 | ||||||||
\(738\) | −14.4721 | − | 12.9443i | −0.532727 | − | 0.476485i | ||||
\(739\) | 8.94427 | 0.329020 | 0.164510 | − | 0.986375i | \(-0.447396\pi\) | ||||
0.164510 | + | 0.986375i | \(0.447396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.944272 | + | 2.47214i | −0.0346887 | + | 0.0908162i | ||||
\(742\) | −22.1803 | + | 3.23607i | −0.814266 | + | 0.118800i | ||||
\(743\) | −1.52786 | −0.0560519 | −0.0280259 | − | 0.999607i | \(-0.508922\pi\) | ||||
−0.0280259 | + | 0.999607i | \(0.508922\pi\) | |||||||
\(744\) | 4.47214 | − | 11.7082i | 0.163956 | − | 0.429244i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.81966i | 0.359523i | ||||||||
\(747\) | 33.3050 | − | 37.2361i | 1.21856 | − | 1.36240i | ||||
\(748\) | 3.41641 | 0.124916 | ||||||||
\(749\) | 40.3607 | − | 5.88854i | 1.47475 | − | 0.215163i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.4164 | 1.29236 | 0.646182 | − | 0.763184i | \(-0.276365\pi\) | ||||
0.646182 | + | 0.763184i | \(0.276365\pi\) | |||||||
\(752\) | − | 2.47214i | − | 0.0901495i | ||||||
\(753\) | 5.70820 | + | 2.18034i | 0.208019 | + | 0.0794560i | ||||
\(754\) | 18.4721i | 0.672716i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.00000 | − | 11.1803i | −0.290957 | − | 0.406625i | ||||
\(757\) | 28.6525i | 1.04139i | 0.853742 | + | 0.520696i | \(0.174327\pi\) | ||||
−0.853742 | + | 0.520696i | \(0.825673\pi\) | |||||||
\(758\) | −17.8885 | −0.649741 | ||||||||
\(759\) | −11.0557 | + | 28.9443i | −0.401298 | + | 1.05061i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8885 | −1.08346 | −0.541729 | − | 0.840553i | \(-0.682230\pi\) | ||||
−0.541729 | + | 0.840553i | \(0.682230\pi\) | |||||||
\(762\) | 8.47214 | − | 22.1803i | 0.306913 | − | 0.803509i | ||||
\(763\) | −11.7082 | + | 1.70820i | −0.423865 | + | 0.0618411i | ||||
\(764\) | − | 2.76393i | − | 0.0999956i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.8885i | 0.790865i | ||||||||
\(767\) | −14.4721 | −0.522559 | ||||||||
\(768\) | 1.61803 | + | 0.618034i | 0.0583858 | + | 0.0223014i | ||||
\(769\) | 36.0000i | 1.29819i | 0.760706 | + | 0.649097i | \(0.224853\pi\) | ||||
−0.760706 | + | 0.649097i | \(0.775147\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.05573 | + | 13.2361i | −0.182078 | + | 0.476685i | ||||
\(772\) | 6.00000i | 0.215945i | ||||||||
\(773\) | 37.4164i | 1.34577i | 0.739745 | + | 0.672887i | \(0.234946\pi\) | ||||
−0.739745 | + | 0.672887i | \(0.765054\pi\) | |||||||
\(774\) | 25.8885 | − | 28.9443i | 0.930544 | − | 1.04038i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.23607 | −0.187964 | ||||||||
\(777\) | 5.23607 | − | 23.4164i | 0.187843 | − | 0.840059i | ||||
\(778\) | 7.81966i | 0.280348i | ||||||||
\(779\) | − | 3.05573i | − | 0.109483i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3607 | −0.442300 | ||||||||
\(782\) | − | 3.05573i | − | 0.109273i | ||||||
\(783\) | −26.3607 | + | 13.5967i | −0.942054 | + | 0.485908i | ||||
\(784\) | 6.70820 | − | 2.00000i | 0.239579 | − | 0.0714286i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34.6525 | + | 13.2361i | 1.23601 | + | 0.472115i | ||||
\(787\) | −49.7082 | −1.77191 | −0.885953 | − | 0.463775i | \(-0.846495\pi\) | ||||
−0.885953 | + | 0.463775i | \(0.846495\pi\) | |||||||
\(788\) | 12.4721 | 0.444301 | ||||||||
\(789\) | −8.00000 | − | 3.05573i | −0.284808 | − | 0.108787i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.1246 | − | 5.70820i | 1.39111 | − | 0.202960i | ||||
\(792\) | −8.94427 | + | 10.0000i | −0.317821 | + | 0.355335i | ||||
\(793\) | 8.94427i | 0.317620i | ||||||||
\(794\) | 17.1246 | 0.607730 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 0.180340i | − | 0.00639198i | ||||||
\(797\) | 5.41641i | 0.191859i | 0.995388 | + | 0.0959295i | \(0.0305823\pi\) | ||||
−0.995388 | + | 0.0959295i | \(0.969418\pi\) | |||||||
\(798\) | 0.472136 | − | 2.11146i | 0.0167134 | − | 0.0747447i | ||||
\(799\) | −1.88854 | −0.0668119 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.3607 | − | 28.9443i | −1.14341 | − | 1.02270i | ||||
\(802\) | − | 5.52786i | − | 0.195196i | ||||||
\(803\) | − | 30.2492i | − | 1.06747i | ||||||
\(804\) | 7.41641 | − | 19.4164i | 0.261557 | − | 0.684764i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 23.4164i | − | 0.824808i | ||||||
\(807\) | −7.23607 | − | 2.76393i | −0.254722 | − | 0.0972950i | ||||
\(808\) | 3.52786 | 0.124110 | ||||||||
\(809\) | − | 8.36068i | − | 0.293946i | −0.989141 | − | 0.146973i | \(-0.953047\pi\) | ||
0.989141 | − | 0.146973i | \(-0.0469530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.8328i | − | 0.591080i | −0.955330 | − | 0.295540i | \(-0.904500\pi\) | ||
0.955330 | − | 0.295540i | \(-0.0954996\pi\) | |||||||
\(812\) | −2.18034 | − | 14.9443i | −0.0765149 | − | 0.524441i | ||||
\(813\) | −11.3050 | + | 29.5967i | −0.396482 | + | 1.03800i | ||||
\(814\) | −23.4164 | −0.820745 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.472136 | − | 1.23607i | 0.0165281 | − | 0.0432710i | ||||
\(817\) | 6.11146 | 0.213813 | ||||||||
\(818\) | 19.4164i | 0.678879i | ||||||||
\(819\) | −21.4164 | − | 14.1803i | −0.748350 | − | 0.495501i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.2918i | 0.638388i | 0.947689 | + | 0.319194i | \(0.103412\pi\) | ||||
−0.947689 | + | 0.319194i | \(0.896588\pi\) | |||||||
\(822\) | 20.1803 | + | 7.70820i | 0.703870 | + | 0.268854i | ||||
\(823\) | − | 0.180340i | − | 0.00628625i | −0.999995 | − | 0.00314313i | \(-0.999000\pi\) | ||
0.999995 | − | 0.00314313i | \(-0.00100049\pi\) | |||||||
\(824\) | 16.6525 | 0.580116 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7082 | − | 1.70820i | 0.407381 | − | 0.0594360i | ||||
\(827\) | 14.8328 | 0.515788 | 0.257894 | − | 0.966173i | \(-0.416972\pi\) | ||||
0.257894 | + | 0.966173i | \(0.416972\pi\) | |||||||
\(828\) | 8.94427 | + | 8.00000i | 0.310835 | + | 0.278019i | ||||
\(829\) | − | 30.1803i | − | 1.04821i | −0.851655 | − | 0.524103i | \(-0.824401\pi\) | ||
0.851655 | − | 0.524103i | \(-0.175599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2918 | + | 37.4164i | −0.495777 | + | 1.29796i | ||||
\(832\) | 3.23607 | 0.112190 | ||||||||
\(833\) | −1.52786 | − | 5.12461i | −0.0529374 | − | 0.177557i | ||||
\(834\) | −12.6525 | + | 33.1246i | −0.438119 | + | 1.14701i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.11146 | −0.0730262 | ||||||||
\(837\) | 33.4164 | − | 17.2361i | 1.15504 | − | 0.595766i | ||||
\(838\) | −16.8328 | −0.581480 | ||||||||
\(839\) | 14.4721 | 0.499634 | 0.249817 | − | 0.968293i | \(-0.419630\pi\) | ||||
0.249817 | + | 0.968293i | \(0.419630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.58359 | −0.123572 | ||||||||
\(842\) | −12.4721 | −0.429818 | ||||||||
\(843\) | 12.3607 | − | 32.3607i | 0.425724 | − | 1.11456i | ||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.94427 | − | 5.52786i | 0.169988 | − | 0.190052i | ||||
\(847\) | 23.5623 | − | 3.43769i | 0.809610 | − | 0.118121i | ||||
\(848\) | 8.47214 | 0.290934 | ||||||||
\(849\) | 14.1803 | + | 5.41641i | 0.486668 | + | 0.185891i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.9443i | 0.717960i | ||||||||
\(852\) | −1.70820 | + | 4.47214i | −0.0585221 | + | 0.153213i | ||||
\(853\) | −5.70820 | −0.195445 | −0.0977226 | − | 0.995214i | \(-0.531156\pi\) | ||||
−0.0977226 | + | 0.995214i | \(0.531156\pi\) | |||||||
\(854\) | −1.05573 | − | 7.23607i | −0.0361263 | − | 0.247613i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.4164 | −0.526922 | ||||||||
\(857\) | 42.6525i | 1.45698i | 0.685056 | + | 0.728490i | \(0.259778\pi\) | ||||
−0.685056 | + | 0.728490i | \(0.740222\pi\) | |||||||
\(858\) | −8.94427 | + | 23.4164i | −0.305352 | + | 0.799423i | ||||
\(859\) | 34.9443i | 1.19228i | 0.802879 | + | 0.596142i | \(0.203300\pi\) | ||||
−0.802879 | + | 0.596142i | \(0.796700\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.9443 | + | 6.47214i | 0.986418 | + | 0.220570i | ||||
\(862\) | − | 9.59675i | − | 0.326867i | ||||||
\(863\) | −21.5279 | −0.732817 | −0.366409 | − | 0.930454i | \(-0.619413\pi\) | ||||
−0.366409 | + | 0.930454i | \(0.619413\pi\) | |||||||
\(864\) | 2.38197 | + | 4.61803i | 0.0810361 | + | 0.157109i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.65248 | −0.158098 | ||||||||
\(867\) | 26.5623 | + | 10.1459i | 0.902103 | + | 0.344573i | ||||
\(868\) | 2.76393 | + | 18.9443i | 0.0938140 | + | 0.643010i | ||||
\(869\) | − | 40.0000i | − | 1.35691i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 38.8328i | − | 1.31580i | ||||||
\(872\) | 4.47214 | 0.151446 | ||||||||
\(873\) | −11.7082 | − | 10.4721i | −0.396263 | − | 0.354428i | ||||
\(874\) | 1.88854i | 0.0638809i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.9443 | − | 4.18034i | −0.369773 | − | 0.141241i | ||||
\(877\) | 7.34752i | 0.248108i | 0.992275 | + | 0.124054i | \(0.0395896\pi\) | ||||
−0.992275 | + | 0.124054i | \(0.960410\pi\) | |||||||
\(878\) | 12.1803i | 0.411067i | ||||||||
\(879\) | 18.1803 | − | 47.5967i | 0.613208 | − | 1.60540i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.4164 | 0.384629 | 0.192314 | − | 0.981333i | \(-0.438401\pi\) | ||||
0.192314 | + | 0.981333i | \(0.438401\pi\) | |||||||
\(882\) | 19.0000 | + | 8.94427i | 0.639763 | + | 0.301169i | ||||
\(883\) | − | 21.8885i | − | 0.736608i | −0.929705 | − | 0.368304i | \(-0.879939\pi\) | ||
0.929705 | − | 0.368304i | \(-0.120061\pi\) | |||||||
\(884\) | − | 2.47214i | − | 0.0831469i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.52786 | 0.320095 | ||||||||
\(887\) | 26.4721i | 0.888847i | 0.895817 | + | 0.444424i | \(0.146592\pi\) | ||||
−0.895817 | + | 0.444424i | \(0.853408\pi\) | |||||||
\(888\) | −3.23607 | + | 8.47214i | −0.108595 | + | 0.284306i | ||||
\(889\) | 5.23607 | + | 35.8885i | 0.175612 | + | 1.20366i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.0000 | + | 4.47214i | −1.34005 | + | 0.149822i | ||||
\(892\) | 4.29180 | 0.143700 | ||||||||
\(893\) | 1.16718 | 0.0390583 | ||||||||
\(894\) | 10.9443 | − | 28.6525i | 0.366031 | − | 0.958282i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.61803 | + | 0.381966i | −0.0874624 | + | 0.0127606i | ||||
\(897\) | 20.9443 | + | 8.00000i | 0.699309 | + | 0.267112i | ||||
\(898\) | − | 1.52786i | − | 0.0509855i | ||||||
\(899\) | 41.3050 | 1.37760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.47214i | − | 0.215618i | ||||||
\(902\) | − | 28.9443i | − | 0.963739i | ||||||
\(903\) | −12.9443 | + | 57.8885i | −0.430758 | + | 1.92641i | ||||
\(904\) | −14.9443 | −0.497039 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.94427 | + | 1.88854i | 0.164262 | + | 0.0627427i | ||||
\(907\) | − | 26.4721i | − | 0.878993i | −0.898244 | − | 0.439496i | \(-0.855157\pi\) | ||
0.898244 | − | 0.439496i | \(-0.144843\pi\) | |||||||
\(908\) | − | 5.23607i | − | 0.173765i | ||||||
\(909\) | 7.88854 | + | 7.05573i | 0.261646 | + | 0.234024i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19.3475i | − | 0.641012i | −0.947246 | − | 0.320506i | \(-0.896147\pi\) | ||
0.947246 | − | 0.320506i | \(-0.103853\pi\) | |||||||
\(912\) | −0.291796 | + | 0.763932i | −0.00966233 | + | 0.0252963i | ||||
\(913\) | 74.4721 | 2.46467 | ||||||||
\(914\) | 9.05573i | 0.299537i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.2361i | 0.437332i | ||||||||
\(917\) | −56.0689 | + | 8.18034i | −1.85156 | + | 0.270139i | ||||
\(918\) | 3.52786 | − | 1.81966i | 0.116437 | − | 0.0600577i | ||||
\(919\) | −44.7214 | −1.47522 | −0.737611 | − | 0.675226i | \(-0.764046\pi\) | ||||
−0.737611 | + | 0.675226i | \(0.764046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.76393 | − | 2.58359i | −0.222879 | − | 0.0851323i | ||||
\(922\) | −10.9443 | −0.360430 | ||||||||
\(923\) | 8.94427i | 0.294404i | ||||||||
\(924\) | 4.47214 | − | 20.0000i | 0.147122 | − | 0.657952i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 0.180340i | − | 0.00592634i | ||||||
\(927\) | 37.2361 | + | 33.3050i | 1.22299 | + | 1.09388i | ||||
\(928\) | 5.70820i | 0.187381i | ||||||||
\(929\) | 2.11146 | 0.0692746 | 0.0346373 | − | 0.999400i | \(-0.488972\pi\) | ||||
0.0346373 | + | 0.999400i | \(0.488972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.944272 | + | 3.16718i | 0.0309473 | + | 0.103800i | ||||
\(932\) | −20.4721 | −0.670587 | ||||||||
\(933\) | −42.8328 | − | 16.3607i | −1.40228 | − | 0.535625i | ||||
\(934\) | 20.2918i | 0.663968i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.23607 | + | 6.47214i | 0.236518 | + | 0.211548i | ||||
\(937\) | 16.0689 | 0.524948 | 0.262474 | − | 0.964939i | \(-0.415462\pi\) | ||||
0.262474 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(938\) | 4.58359 | + | 31.4164i | 0.149660 | + | 1.02578i | ||||
\(939\) | 12.4721 | + | 4.76393i | 0.407013 | + | 0.155465i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.0000 | −0.717180 | −0.358590 | − | 0.933495i | \(-0.616742\pi\) | ||||
−0.358590 | + | 0.933495i | \(0.616742\pi\) | |||||||
\(942\) | 7.70820 | + | 2.94427i | 0.251147 | + | 0.0959296i | ||||
\(943\) | −25.8885 | −0.843047 | ||||||||
\(944\) | −4.47214 | −0.145556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57.8885 | 1.88212 | ||||||||
\(947\) | 15.6393 | 0.508210 | 0.254105 | − | 0.967177i | \(-0.418219\pi\) | ||||
0.254105 | + | 0.967177i | \(0.418219\pi\) | |||||||
\(948\) | −14.4721 | − | 5.52786i | −0.470033 | − | 0.179537i | ||||
\(949\) | −21.8885 | −0.710532 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.2361 | + | 4.29180i | 0.364354 | + | 0.139171i | ||||
\(952\) | 0.291796 | + | 2.00000i | 0.00945716 | + | 0.0648204i | ||||
\(953\) | −49.4164 | −1.60075 | −0.800377 | − | 0.599497i | \(-0.795367\pi\) | ||||
−0.800377 | + | 0.599497i | \(0.795367\pi\) | |||||||
\(954\) | 18.9443 | + | 16.9443i | 0.613343 | + | 0.548591i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 22.1803i | − | 0.717363i | ||||||
\(957\) | −41.3050 | − | 15.7771i | −1.33520 | − | 0.510001i | ||||
\(958\) | 2.11146 | 0.0682181 | ||||||||
\(959\) | −32.6525 | + | 4.76393i | −1.05440 | + | 0.153835i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3607 | −0.689054 | ||||||||
\(962\) | 16.9443i | 0.546305i | ||||||||
\(963\) | −34.4721 | − | 30.8328i | −1.11085 | − | 0.993574i | ||||
\(964\) | − | 17.8885i | − | 0.576151i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.8885 | − | 4.00000i | −0.575554 | − | 0.128698i | ||||
\(967\) | 45.4853i | 1.46271i | 0.681998 | + | 0.731354i | \(0.261111\pi\) | ||||
−0.681998 | + | 0.731354i | \(0.738889\pi\) | |||||||
\(968\) | −9.00000 | −0.289271 | ||||||||
\(969\) | 0.583592 | + | 0.222912i | 0.0187477 | + | 0.00716098i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.0000 | 1.86131 | 0.930654 | − | 0.365900i | \(-0.119239\pi\) | ||||
0.930654 | + | 0.365900i | \(0.119239\pi\) | |||||||
\(972\) | −3.90983 | + | 15.0902i | −0.125408 | + | 0.484017i | ||||
\(973\) | −7.81966 | − | 53.5967i | −0.250687 | − | 1.71823i | ||||
\(974\) | − | 31.5967i | − | 1.01243i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.76393i | 0.0884713i | ||||||||
\(977\) | −25.4164 | −0.813143 | −0.406571 | − | 0.913619i | \(-0.633276\pi\) | ||||
−0.406571 | + | 0.913619i | \(0.633276\pi\) | |||||||
\(978\) | −0.944272 | + | 2.47214i | −0.0301945 | + | 0.0790502i | ||||
\(979\) | − | 64.7214i | − | 2.06850i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | + | 8.94427i | 0.319275 | + | 0.285569i | ||||
\(982\) | 13.4164i | 0.428135i | ||||||||
\(983\) | − | 39.4164i | − | 1.25719i | −0.777734 | − | 0.628594i | \(-0.783631\pi\) | ||
0.777734 | − | 0.628594i | \(-0.216369\pi\) | |||||||
\(984\) | −10.4721 | − | 4.00000i | −0.333840 | − | 0.127515i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.36068 | 0.138872 | ||||||||
\(987\) | −2.47214 | + | 11.0557i | −0.0786890 | + | 0.351908i | ||||
\(988\) | 1.52786i | 0.0486078i | ||||||||
\(989\) | − | 51.7771i | − | 1.64642i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4721 | 0.840915 | 0.420458 | − | 0.907312i | \(-0.361870\pi\) | ||||
0.420458 | + | 0.907312i | \(0.361870\pi\) | |||||||
\(992\) | − | 7.23607i | − | 0.229745i | ||||||
\(993\) | 33.8885 | + | 12.9443i | 1.07542 | + | 0.410774i | ||||
\(994\) | −1.05573 | − | 7.23607i | −0.0334857 | − | 0.229514i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10.2918 | − | 26.9443i | 0.326108 | − | 0.853762i | ||||
\(997\) | −20.7639 | −0.657600 | −0.328800 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328800 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(998\) | 17.8885 | 0.566252 | ||||||||
\(999\) | −24.1803 | + | 12.4721i | −0.765032 | + | 0.394601i |
(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 | 1050.2.d.f.1049.4 | 4 | ||
3.2 | odd | 2 | 1050.2.d.c.1049.3 | 4 | |||
5.2 | odd | 4 | 1050.2.b.a.251.4 | 4 | |||
5.3 | odd | 4 | 210.2.b.b.41.1 | yes | 4 | ||
5.4 | even | 2 | 1050.2.d.a.1049.1 | 4 | |||
7.6 | odd | 2 | 1050.2.d.d.1049.1 | 4 | |||
15.2 | even | 4 | 1050.2.b.c.251.1 | 4 | |||
15.8 | even | 4 | 210.2.b.a.41.4 | yes | 4 | ||
15.14 | odd | 2 | 1050.2.d.d.1049.2 | 4 | |||
20.3 | even | 4 | 1680.2.f.e.881.3 | 4 | |||
21.20 | even | 2 | 1050.2.d.a.1049.2 | 4 | |||
35.13 | even | 4 | 210.2.b.a.41.2 | ✓ | 4 | ||
35.27 | even | 4 | 1050.2.b.c.251.3 | 4 | |||
35.34 | odd | 2 | 1050.2.d.c.1049.4 | 4 | |||
60.23 | odd | 4 | 1680.2.f.i.881.1 | 4 | |||
105.62 | odd | 4 | 1050.2.b.a.251.2 | 4 | |||
105.83 | odd | 4 | 210.2.b.b.41.3 | yes | 4 | ||
105.104 | even | 2 | inner | 1050.2.d.f.1049.3 | 4 | ||
140.83 | odd | 4 | 1680.2.f.i.881.2 | 4 | |||
420.83 | even | 4 | 1680.2.f.e.881.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.b.a.41.2 | ✓ | 4 | 35.13 | even | 4 | ||
210.2.b.a.41.4 | yes | 4 | 15.8 | even | 4 | ||
210.2.b.b.41.1 | yes | 4 | 5.3 | odd | 4 | ||
210.2.b.b.41.3 | yes | 4 | 105.83 | odd | 4 | ||
1050.2.b.a.251.2 | 4 | 105.62 | odd | 4 | |||
1050.2.b.a.251.4 | 4 | 5.2 | odd | 4 | |||
1050.2.b.c.251.1 | 4 | 15.2 | even | 4 | |||
1050.2.b.c.251.3 | 4 | 35.27 | even | 4 | |||
1050.2.d.a.1049.1 | 4 | 5.4 | even | 2 | |||
1050.2.d.a.1049.2 | 4 | 21.20 | even | 2 | |||
1050.2.d.c.1049.3 | 4 | 3.2 | odd | 2 | |||
1050.2.d.c.1049.4 | 4 | 35.34 | odd | 2 | |||
1050.2.d.d.1049.1 | 4 | 7.6 | odd | 2 | |||
1050.2.d.d.1049.2 | 4 | 15.14 | odd | 2 | |||
1050.2.d.f.1049.3 | 4 | 105.104 | even | 2 | inner | ||
1050.2.d.f.1049.4 | 4 | 1.1 | even | 1 | trivial | ||
1680.2.f.e.881.3 | 4 | 20.3 | even | 4 | |||
1680.2.f.e.881.4 | 4 | 420.83 | even | 4 | |||
1680.2.f.i.881.1 | 4 | 60.23 | odd | 4 | |||
1680.2.f.i.881.2 | 4 | 140.83 | odd | 4 |