Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} - 4126 x^{5} - 22759 x^{4} + 2997 x^{3} + 10504 x^{2} - 506 x - 1492 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.46518\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.46518 | 1.10246 | 0.551231 | − | 0.834353i | \(-0.314158\pi\) | ||||
0.551231 | + | 0.834353i | \(0.314158\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.952790 | −0.360121 | −0.180060 | − | 0.983656i | \(-0.557629\pi\) | ||||
−0.180060 | + | 0.983656i | \(0.557629\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.46518 | −0.779558 | ||||||||
\(11\) | 4.20399 | 1.26755 | 0.633775 | − | 0.773518i | \(-0.281505\pi\) | ||||
0.633775 | + | 0.773518i | \(0.281505\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.952790 | 0.254644 | ||||||||
\(15\) | −2.46518 | −0.636506 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.27477 | 1.76439 | 0.882196 | − | 0.470883i | \(-0.156065\pi\) | ||||
0.882196 | + | 0.470883i | \(0.156065\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.33023 | −0.993422 | −0.496711 | − | 0.867916i | \(-0.665459\pi\) | ||||
−0.496711 | + | 0.867916i | \(0.665459\pi\) | |||||||
\(20\) | 2.46518 | 0.551231 | ||||||||
\(21\) | 0.952790 | 0.207916 | ||||||||
\(22\) | −4.20399 | −0.896293 | ||||||||
\(23\) | 2.97949 | 0.621268 | 0.310634 | − | 0.950530i | \(-0.399459\pi\) | ||||
0.310634 | + | 0.950530i | \(0.399459\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.07710 | 0.215421 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.952790 | −0.180060 | ||||||||
\(29\) | 4.44123 | 0.824716 | 0.412358 | − | 0.911022i | \(-0.364705\pi\) | ||||
0.412358 | + | 0.911022i | \(0.364705\pi\) | |||||||
\(30\) | 2.46518 | 0.450078 | ||||||||
\(31\) | 2.25549 | 0.405098 | 0.202549 | − | 0.979272i | \(-0.435077\pi\) | ||||
0.202549 | + | 0.979272i | \(0.435077\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.20399 | −0.731820 | ||||||||
\(34\) | −7.27477 | −1.24761 | ||||||||
\(35\) | −2.34880 | −0.397019 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.37198 | 0.554350 | 0.277175 | − | 0.960819i | \(-0.410602\pi\) | ||||
0.277175 | + | 0.960819i | \(0.410602\pi\) | |||||||
\(38\) | 4.33023 | 0.702456 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.46518 | −0.389779 | ||||||||
\(41\) | −8.68437 | −1.35627 | −0.678135 | − | 0.734937i | \(-0.737212\pi\) | ||||
−0.678135 | + | 0.734937i | \(0.737212\pi\) | |||||||
\(42\) | −0.952790 | −0.147019 | ||||||||
\(43\) | 5.56905 | 0.849272 | 0.424636 | − | 0.905364i | \(-0.360402\pi\) | ||||
0.424636 | + | 0.905364i | \(0.360402\pi\) | |||||||
\(44\) | 4.20399 | 0.633775 | ||||||||
\(45\) | 2.46518 | 0.367487 | ||||||||
\(46\) | −2.97949 | −0.439303 | ||||||||
\(47\) | 5.13291 | 0.748711 | 0.374356 | − | 0.927285i | \(-0.377864\pi\) | ||||
0.374356 | + | 0.927285i | \(0.377864\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.09219 | −0.870313 | ||||||||
\(50\) | −1.07710 | −0.152326 | ||||||||
\(51\) | −7.27477 | −1.01867 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 8.80268 | 1.20914 | 0.604571 | − | 0.796552i | \(-0.293345\pi\) | ||||
0.604571 | + | 0.796552i | \(0.293345\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 10.3636 | 1.39742 | ||||||||
\(56\) | 0.952790 | 0.127322 | ||||||||
\(57\) | 4.33023 | 0.573553 | ||||||||
\(58\) | −4.44123 | −0.583163 | ||||||||
\(59\) | 5.12897 | 0.667736 | 0.333868 | − | 0.942620i | \(-0.391646\pi\) | ||||
0.333868 | + | 0.942620i | \(0.391646\pi\) | |||||||
\(60\) | −2.46518 | −0.318253 | ||||||||
\(61\) | −5.32855 | −0.682251 | −0.341126 | − | 0.940018i | \(-0.610808\pi\) | ||||
−0.341126 | + | 0.940018i | \(0.610808\pi\) | |||||||
\(62\) | −2.25549 | −0.286448 | ||||||||
\(63\) | −0.952790 | −0.120040 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.46518 | −0.305768 | ||||||||
\(66\) | 4.20399 | 0.517475 | ||||||||
\(67\) | 5.95796 | 0.727881 | 0.363941 | − | 0.931422i | \(-0.381431\pi\) | ||||
0.363941 | + | 0.931422i | \(0.381431\pi\) | |||||||
\(68\) | 7.27477 | 0.882196 | ||||||||
\(69\) | −2.97949 | −0.358689 | ||||||||
\(70\) | 2.34880 | 0.280735 | ||||||||
\(71\) | 12.6592 | 1.50237 | 0.751184 | − | 0.660092i | \(-0.229483\pi\) | ||||
0.751184 | + | 0.660092i | \(0.229483\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −7.23738 | −0.847072 | −0.423536 | − | 0.905879i | \(-0.639211\pi\) | ||||
−0.423536 | + | 0.905879i | \(0.639211\pi\) | |||||||
\(74\) | −3.37198 | −0.391985 | ||||||||
\(75\) | −1.07710 | −0.124373 | ||||||||
\(76\) | −4.33023 | −0.496711 | ||||||||
\(77\) | −4.00552 | −0.456471 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −9.05227 | −1.01846 | −0.509230 | − | 0.860630i | \(-0.670070\pi\) | ||||
−0.509230 | + | 0.860630i | \(0.670070\pi\) | |||||||
\(80\) | 2.46518 | 0.275615 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.68437 | 0.959028 | ||||||||
\(83\) | 7.82412 | 0.858809 | 0.429404 | − | 0.903112i | \(-0.358723\pi\) | ||||
0.429404 | + | 0.903112i | \(0.358723\pi\) | |||||||
\(84\) | 0.952790 | 0.103958 | ||||||||
\(85\) | 17.9336 | 1.94517 | ||||||||
\(86\) | −5.56905 | −0.600526 | ||||||||
\(87\) | −4.44123 | −0.476150 | ||||||||
\(88\) | −4.20399 | −0.448146 | ||||||||
\(89\) | 3.70795 | 0.393042 | 0.196521 | − | 0.980500i | \(-0.437036\pi\) | ||||
0.196521 | + | 0.980500i | \(0.437036\pi\) | |||||||
\(90\) | −2.46518 | −0.259853 | ||||||||
\(91\) | 0.952790 | 0.0998795 | ||||||||
\(92\) | 2.97949 | 0.310634 | ||||||||
\(93\) | −2.25549 | −0.233884 | ||||||||
\(94\) | −5.13291 | −0.529419 | ||||||||
\(95\) | −10.6748 | −1.09521 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −18.7132 | −1.90004 | −0.950021 | − | 0.312187i | \(-0.898939\pi\) | ||||
−0.950021 | + | 0.312187i | \(0.898939\pi\) | |||||||
\(98\) | 6.09219 | 0.615404 | ||||||||
\(99\) | 4.20399 | 0.422516 | ||||||||
\(100\) | 1.07710 | 0.107710 | ||||||||
\(101\) | −2.53136 | −0.251880 | −0.125940 | − | 0.992038i | \(-0.540195\pi\) | ||||
−0.125940 | + | 0.992038i | \(0.540195\pi\) | |||||||
\(102\) | 7.27477 | 0.720310 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 2.34880 | 0.229219 | ||||||||
\(106\) | −8.80268 | −0.854992 | ||||||||
\(107\) | 2.73402 | 0.264308 | 0.132154 | − | 0.991229i | \(-0.457811\pi\) | ||||
0.132154 | + | 0.991229i | \(0.457811\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 9.98912 | 0.956784 | 0.478392 | − | 0.878146i | \(-0.341220\pi\) | ||||
0.478392 | + | 0.878146i | \(0.341220\pi\) | |||||||
\(110\) | −10.3636 | −0.988128 | ||||||||
\(111\) | −3.37198 | −0.320054 | ||||||||
\(112\) | −0.952790 | −0.0900302 | ||||||||
\(113\) | −4.41216 | −0.415062 | −0.207531 | − | 0.978228i | \(-0.566543\pi\) | ||||
−0.207531 | + | 0.978228i | \(0.566543\pi\) | |||||||
\(114\) | −4.33023 | −0.405563 | ||||||||
\(115\) | 7.34499 | 0.684924 | ||||||||
\(116\) | 4.44123 | 0.412358 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −5.12897 | −0.472160 | ||||||||
\(119\) | −6.93133 | −0.635394 | ||||||||
\(120\) | 2.46518 | 0.225039 | ||||||||
\(121\) | 6.67349 | 0.606681 | ||||||||
\(122\) | 5.32855 | 0.482424 | ||||||||
\(123\) | 8.68437 | 0.783043 | ||||||||
\(124\) | 2.25549 | 0.202549 | ||||||||
\(125\) | −9.67064 | −0.864968 | ||||||||
\(126\) | 0.952790 | 0.0848813 | ||||||||
\(127\) | −7.68171 | −0.681642 | −0.340821 | − | 0.940128i | \(-0.610705\pi\) | ||||
−0.340821 | + | 0.940128i | \(0.610705\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.56905 | −0.490328 | ||||||||
\(130\) | 2.46518 | 0.216210 | ||||||||
\(131\) | 0.0791075 | 0.00691165 | 0.00345583 | − | 0.999994i | \(-0.498900\pi\) | ||||
0.00345583 | + | 0.999994i | \(0.498900\pi\) | |||||||
\(132\) | −4.20399 | −0.365910 | ||||||||
\(133\) | 4.12580 | 0.357752 | ||||||||
\(134\) | −5.95796 | −0.514690 | ||||||||
\(135\) | −2.46518 | −0.212169 | ||||||||
\(136\) | −7.27477 | −0.623807 | ||||||||
\(137\) | −3.99460 | −0.341281 | −0.170641 | − | 0.985333i | \(-0.554584\pi\) | ||||
−0.170641 | + | 0.985333i | \(0.554584\pi\) | |||||||
\(138\) | 2.97949 | 0.253631 | ||||||||
\(139\) | 13.0462 | 1.10657 | 0.553283 | − | 0.832994i | \(-0.313375\pi\) | ||||
0.553283 | + | 0.832994i | \(0.313375\pi\) | |||||||
\(140\) | −2.34880 | −0.198510 | ||||||||
\(141\) | −5.13291 | −0.432269 | ||||||||
\(142\) | −12.6592 | −1.06234 | ||||||||
\(143\) | −4.20399 | −0.351555 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 10.9484 | 0.909218 | ||||||||
\(146\) | 7.23738 | 0.598970 | ||||||||
\(147\) | 6.09219 | 0.502475 | ||||||||
\(148\) | 3.37198 | 0.277175 | ||||||||
\(149\) | 15.1863 | 1.24411 | 0.622056 | − | 0.782973i | \(-0.286298\pi\) | ||||
0.622056 | + | 0.782973i | \(0.286298\pi\) | |||||||
\(150\) | 1.07710 | 0.0879452 | ||||||||
\(151\) | 16.8777 | 1.37349 | 0.686744 | − | 0.726899i | \(-0.259039\pi\) | ||||
0.686744 | + | 0.726899i | \(0.259039\pi\) | |||||||
\(152\) | 4.33023 | 0.351228 | ||||||||
\(153\) | 7.27477 | 0.588131 | ||||||||
\(154\) | 4.00552 | 0.322774 | ||||||||
\(155\) | 5.56019 | 0.446605 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −2.03856 | −0.162695 | −0.0813473 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813473 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(158\) | 9.05227 | 0.720160 | ||||||||
\(159\) | −8.80268 | −0.698098 | ||||||||
\(160\) | −2.46518 | −0.194889 | ||||||||
\(161\) | −2.83883 | −0.223731 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −17.7666 | −1.39159 | −0.695795 | − | 0.718241i | \(-0.744948\pi\) | ||||
−0.695795 | + | 0.718241i | \(0.744948\pi\) | |||||||
\(164\) | −8.68437 | −0.678135 | ||||||||
\(165\) | −10.3636 | −0.806803 | ||||||||
\(166\) | −7.82412 | −0.607270 | ||||||||
\(167\) | 8.10126 | 0.626894 | 0.313447 | − | 0.949606i | \(-0.398516\pi\) | ||||
0.313447 | + | 0.949606i | \(0.398516\pi\) | |||||||
\(168\) | −0.952790 | −0.0735094 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −17.9336 | −1.37545 | ||||||||
\(171\) | −4.33023 | −0.331141 | ||||||||
\(172\) | 5.56905 | 0.424636 | ||||||||
\(173\) | −8.14139 | −0.618978 | −0.309489 | − | 0.950903i | \(-0.600158\pi\) | ||||
−0.309489 | + | 0.950903i | \(0.600158\pi\) | |||||||
\(174\) | 4.44123 | 0.336689 | ||||||||
\(175\) | −1.02625 | −0.0775776 | ||||||||
\(176\) | 4.20399 | 0.316887 | ||||||||
\(177\) | −5.12897 | −0.385517 | ||||||||
\(178\) | −3.70795 | −0.277923 | ||||||||
\(179\) | 16.2502 | 1.21459 | 0.607297 | − | 0.794475i | \(-0.292254\pi\) | ||||
0.607297 | + | 0.794475i | \(0.292254\pi\) | |||||||
\(180\) | 2.46518 | 0.183744 | ||||||||
\(181\) | 0.280385 | 0.0208409 | 0.0104204 | − | 0.999946i | \(-0.496683\pi\) | ||||
0.0104204 | + | 0.999946i | \(0.496683\pi\) | |||||||
\(182\) | −0.952790 | −0.0706255 | ||||||||
\(183\) | 5.32855 | 0.393898 | ||||||||
\(184\) | −2.97949 | −0.219651 | ||||||||
\(185\) | 8.31254 | 0.611150 | ||||||||
\(186\) | 2.25549 | 0.165381 | ||||||||
\(187\) | 30.5830 | 2.23645 | ||||||||
\(188\) | 5.13291 | 0.374356 | ||||||||
\(189\) | 0.952790 | 0.0693053 | ||||||||
\(190\) | 10.6748 | 0.774430 | ||||||||
\(191\) | −11.5986 | −0.839242 | −0.419621 | − | 0.907699i | \(-0.637837\pi\) | ||||
−0.419621 | + | 0.907699i | \(0.637837\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 6.70353 | 0.482531 | 0.241265 | − | 0.970459i | \(-0.422438\pi\) | ||||
0.241265 | + | 0.970459i | \(0.422438\pi\) | |||||||
\(194\) | 18.7132 | 1.34353 | ||||||||
\(195\) | 2.46518 | 0.176535 | ||||||||
\(196\) | −6.09219 | −0.435156 | ||||||||
\(197\) | 10.1317 | 0.721852 | 0.360926 | − | 0.932594i | \(-0.382461\pi\) | ||||
0.360926 | + | 0.932594i | \(0.382461\pi\) | |||||||
\(198\) | −4.20399 | −0.298764 | ||||||||
\(199\) | −2.03748 | −0.144433 | −0.0722166 | − | 0.997389i | \(-0.523007\pi\) | ||||
−0.0722166 | + | 0.997389i | \(0.523007\pi\) | |||||||
\(200\) | −1.07710 | −0.0761628 | ||||||||
\(201\) | −5.95796 | −0.420242 | ||||||||
\(202\) | 2.53136 | 0.178106 | ||||||||
\(203\) | −4.23156 | −0.296998 | ||||||||
\(204\) | −7.27477 | −0.509336 | ||||||||
\(205\) | −21.4085 | −1.49524 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 2.97949 | 0.207089 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −18.2042 | −1.25921 | ||||||||
\(210\) | −2.34880 | −0.162082 | ||||||||
\(211\) | 9.03933 | 0.622293 | 0.311147 | − | 0.950362i | \(-0.399287\pi\) | ||||
0.311147 | + | 0.950362i | \(0.399287\pi\) | |||||||
\(212\) | 8.80268 | 0.604571 | ||||||||
\(213\) | −12.6592 | −0.867393 | ||||||||
\(214\) | −2.73402 | −0.186894 | ||||||||
\(215\) | 13.7287 | 0.936290 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −2.14901 | −0.145884 | ||||||||
\(218\) | −9.98912 | −0.676549 | ||||||||
\(219\) | 7.23738 | 0.489057 | ||||||||
\(220\) | 10.3636 | 0.698712 | ||||||||
\(221\) | −7.27477 | −0.489354 | ||||||||
\(222\) | 3.37198 | 0.226313 | ||||||||
\(223\) | 10.3979 | 0.696294 | 0.348147 | − | 0.937440i | \(-0.386811\pi\) | ||||
0.348147 | + | 0.937440i | \(0.386811\pi\) | |||||||
\(224\) | 0.952790 | 0.0636610 | ||||||||
\(225\) | 1.07710 | 0.0718070 | ||||||||
\(226\) | 4.41216 | 0.293493 | ||||||||
\(227\) | 16.0725 | 1.06677 | 0.533386 | − | 0.845872i | \(-0.320919\pi\) | ||||
0.533386 | + | 0.845872i | \(0.320919\pi\) | |||||||
\(228\) | 4.33023 | 0.286776 | ||||||||
\(229\) | −20.0781 | −1.32680 | −0.663398 | − | 0.748267i | \(-0.730886\pi\) | ||||
−0.663398 | + | 0.748267i | \(0.730886\pi\) | |||||||
\(230\) | −7.34499 | −0.484314 | ||||||||
\(231\) | 4.00552 | 0.263544 | ||||||||
\(232\) | −4.44123 | −0.291581 | ||||||||
\(233\) | −13.2736 | −0.869585 | −0.434792 | − | 0.900531i | \(-0.643178\pi\) | ||||
−0.434792 | + | 0.900531i | \(0.643178\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 12.6535 | 0.825425 | ||||||||
\(236\) | 5.12897 | 0.333868 | ||||||||
\(237\) | 9.05227 | 0.588008 | ||||||||
\(238\) | 6.93133 | 0.449292 | ||||||||
\(239\) | −15.4499 | −0.999373 | −0.499687 | − | 0.866206i | \(-0.666551\pi\) | ||||
−0.499687 | + | 0.866206i | \(0.666551\pi\) | |||||||
\(240\) | −2.46518 | −0.159127 | ||||||||
\(241\) | 21.5308 | 1.38692 | 0.693459 | − | 0.720496i | \(-0.256086\pi\) | ||||
0.693459 | + | 0.720496i | \(0.256086\pi\) | |||||||
\(242\) | −6.67349 | −0.428988 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.32855 | −0.341126 | ||||||||
\(245\) | −15.0183 | −0.959486 | ||||||||
\(246\) | −8.68437 | −0.553695 | ||||||||
\(247\) | 4.33023 | 0.275526 | ||||||||
\(248\) | −2.25549 | −0.143224 | ||||||||
\(249\) | −7.82412 | −0.495834 | ||||||||
\(250\) | 9.67064 | 0.611625 | ||||||||
\(251\) | −7.41297 | −0.467903 | −0.233951 | − | 0.972248i | \(-0.575166\pi\) | ||||
−0.233951 | + | 0.972248i | \(0.575166\pi\) | |||||||
\(252\) | −0.952790 | −0.0600201 | ||||||||
\(253\) | 12.5258 | 0.787487 | ||||||||
\(254\) | 7.68171 | 0.481993 | ||||||||
\(255\) | −17.9336 | −1.12305 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.3253 | −1.82926 | −0.914631 | − | 0.404290i | \(-0.867519\pi\) | ||||
−0.914631 | + | 0.404290i | \(0.867519\pi\) | |||||||
\(258\) | 5.56905 | 0.346714 | ||||||||
\(259\) | −3.21279 | −0.199633 | ||||||||
\(260\) | −2.46518 | −0.152884 | ||||||||
\(261\) | 4.44123 | 0.274905 | ||||||||
\(262\) | −0.0791075 | −0.00488728 | ||||||||
\(263\) | 4.81915 | 0.297161 | 0.148581 | − | 0.988900i | \(-0.452530\pi\) | ||||
0.148581 | + | 0.988900i | \(0.452530\pi\) | |||||||
\(264\) | 4.20399 | 0.258737 | ||||||||
\(265\) | 21.7002 | 1.33303 | ||||||||
\(266\) | −4.12580 | −0.252969 | ||||||||
\(267\) | −3.70795 | −0.226923 | ||||||||
\(268\) | 5.95796 | 0.363941 | ||||||||
\(269\) | −5.25718 | −0.320536 | −0.160268 | − | 0.987074i | \(-0.551236\pi\) | ||||
−0.160268 | + | 0.987074i | \(0.551236\pi\) | |||||||
\(270\) | 2.46518 | 0.150026 | ||||||||
\(271\) | −21.4015 | −1.30005 | −0.650025 | − | 0.759913i | \(-0.725242\pi\) | ||||
−0.650025 | + | 0.759913i | \(0.725242\pi\) | |||||||
\(272\) | 7.27477 | 0.441098 | ||||||||
\(273\) | −0.952790 | −0.0576655 | ||||||||
\(274\) | 3.99460 | 0.241322 | ||||||||
\(275\) | 4.52813 | 0.273057 | ||||||||
\(276\) | −2.97949 | −0.179345 | ||||||||
\(277\) | −31.4672 | −1.89068 | −0.945341 | − | 0.326085i | \(-0.894271\pi\) | ||||
−0.945341 | + | 0.326085i | \(0.894271\pi\) | |||||||
\(278\) | −13.0462 | −0.782460 | ||||||||
\(279\) | 2.25549 | 0.135033 | ||||||||
\(280\) | 2.34880 | 0.140368 | ||||||||
\(281\) | 30.2559 | 1.80492 | 0.902458 | − | 0.430777i | \(-0.141760\pi\) | ||||
0.902458 | + | 0.430777i | \(0.141760\pi\) | |||||||
\(282\) | 5.13291 | 0.305660 | ||||||||
\(283\) | 22.6650 | 1.34729 | 0.673646 | − | 0.739054i | \(-0.264727\pi\) | ||||
0.673646 | + | 0.739054i | \(0.264727\pi\) | |||||||
\(284\) | 12.6592 | 0.751184 | ||||||||
\(285\) | 10.6748 | 0.632320 | ||||||||
\(286\) | 4.20399 | 0.248587 | ||||||||
\(287\) | 8.27438 | 0.488421 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 35.9223 | 2.11308 | ||||||||
\(290\) | −10.9484 | −0.642914 | ||||||||
\(291\) | 18.7132 | 1.09699 | ||||||||
\(292\) | −7.23738 | −0.423536 | ||||||||
\(293\) | −27.5148 | −1.60743 | −0.803717 | − | 0.595012i | \(-0.797147\pi\) | ||||
−0.803717 | + | 0.595012i | \(0.797147\pi\) | |||||||
\(294\) | −6.09219 | −0.355304 | ||||||||
\(295\) | 12.6438 | 0.736153 | ||||||||
\(296\) | −3.37198 | −0.195992 | ||||||||
\(297\) | −4.20399 | −0.243940 | ||||||||
\(298\) | −15.1863 | −0.879720 | ||||||||
\(299\) | −2.97949 | −0.172309 | ||||||||
\(300\) | −1.07710 | −0.0621867 | ||||||||
\(301\) | −5.30614 | −0.305841 | ||||||||
\(302\) | −16.8777 | −0.971202 | ||||||||
\(303\) | 2.53136 | 0.145423 | ||||||||
\(304\) | −4.33023 | −0.248356 | ||||||||
\(305\) | −13.1358 | −0.752156 | ||||||||
\(306\) | −7.27477 | −0.415871 | ||||||||
\(307\) | 4.53701 | 0.258941 | 0.129471 | − | 0.991583i | \(-0.458672\pi\) | ||||
0.129471 | + | 0.991583i | \(0.458672\pi\) | |||||||
\(308\) | −4.00552 | −0.228235 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −5.56019 | −0.315798 | ||||||||
\(311\) | −25.6533 | −1.45466 | −0.727332 | − | 0.686286i | \(-0.759240\pi\) | ||||
−0.727332 | + | 0.686286i | \(0.759240\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −0.813766 | −0.0459968 | −0.0229984 | − | 0.999736i | \(-0.507321\pi\) | ||||
−0.0229984 | + | 0.999736i | \(0.507321\pi\) | |||||||
\(314\) | 2.03856 | 0.115042 | ||||||||
\(315\) | −2.34880 | −0.132340 | ||||||||
\(316\) | −9.05227 | −0.509230 | ||||||||
\(317\) | −23.7066 | −1.33149 | −0.665747 | − | 0.746178i | \(-0.731887\pi\) | ||||
−0.665747 | + | 0.746178i | \(0.731887\pi\) | |||||||
\(318\) | 8.80268 | 0.493630 | ||||||||
\(319\) | 18.6709 | 1.04537 | ||||||||
\(320\) | 2.46518 | 0.137808 | ||||||||
\(321\) | −2.73402 | −0.152598 | ||||||||
\(322\) | 2.83883 | 0.158202 | ||||||||
\(323\) | −31.5014 | −1.75279 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −1.07710 | −0.0597470 | ||||||||
\(326\) | 17.7666 | 0.984002 | ||||||||
\(327\) | −9.98912 | −0.552400 | ||||||||
\(328\) | 8.68437 | 0.479514 | ||||||||
\(329\) | −4.89058 | −0.269627 | ||||||||
\(330\) | 10.3636 | 0.570496 | ||||||||
\(331\) | 14.7152 | 0.808818 | 0.404409 | − | 0.914578i | \(-0.367477\pi\) | ||||
0.404409 | + | 0.914578i | \(0.367477\pi\) | |||||||
\(332\) | 7.82412 | 0.429404 | ||||||||
\(333\) | 3.37198 | 0.184783 | ||||||||
\(334\) | −8.10126 | −0.443281 | ||||||||
\(335\) | 14.6874 | 0.802461 | ||||||||
\(336\) | 0.952790 | 0.0519790 | ||||||||
\(337\) | 9.99348 | 0.544380 | 0.272190 | − | 0.962244i | \(-0.412252\pi\) | ||||
0.272190 | + | 0.962244i | \(0.412252\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 4.41216 | 0.239636 | ||||||||
\(340\) | 17.9336 | 0.972587 | ||||||||
\(341\) | 9.48205 | 0.513482 | ||||||||
\(342\) | 4.33023 | 0.234152 | ||||||||
\(343\) | 12.4741 | 0.673539 | ||||||||
\(344\) | −5.56905 | −0.300263 | ||||||||
\(345\) | −7.34499 | −0.395441 | ||||||||
\(346\) | 8.14139 | 0.437684 | ||||||||
\(347\) | 16.4929 | 0.885387 | 0.442694 | − | 0.896673i | \(-0.354023\pi\) | ||||
0.442694 | + | 0.896673i | \(0.354023\pi\) | |||||||
\(348\) | −4.44123 | −0.238075 | ||||||||
\(349\) | −14.2015 | −0.760186 | −0.380093 | − | 0.924948i | \(-0.624108\pi\) | ||||
−0.380093 | + | 0.924948i | \(0.624108\pi\) | |||||||
\(350\) | 1.02625 | 0.0548556 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.20399 | −0.224073 | ||||||||
\(353\) | −19.9580 | −1.06225 | −0.531127 | − | 0.847292i | \(-0.678231\pi\) | ||||
−0.531127 | + | 0.847292i | \(0.678231\pi\) | |||||||
\(354\) | 5.12897 | 0.272602 | ||||||||
\(355\) | 31.2072 | 1.65630 | ||||||||
\(356\) | 3.70795 | 0.196521 | ||||||||
\(357\) | 6.93133 | 0.366845 | ||||||||
\(358\) | −16.2502 | −0.858847 | ||||||||
\(359\) | −0.924105 | −0.0487724 | −0.0243862 | − | 0.999703i | \(-0.507763\pi\) | ||||
−0.0243862 | + | 0.999703i | \(0.507763\pi\) | |||||||
\(360\) | −2.46518 | −0.129926 | ||||||||
\(361\) | −0.249129 | −0.0131120 | ||||||||
\(362\) | −0.280385 | −0.0147367 | ||||||||
\(363\) | −6.67349 | −0.350267 | ||||||||
\(364\) | 0.952790 | 0.0499398 | ||||||||
\(365\) | −17.8414 | −0.933864 | ||||||||
\(366\) | −5.32855 | −0.278528 | ||||||||
\(367\) | 2.52886 | 0.132005 | 0.0660026 | − | 0.997819i | \(-0.478975\pi\) | ||||
0.0660026 | + | 0.997819i | \(0.478975\pi\) | |||||||
\(368\) | 2.97949 | 0.155317 | ||||||||
\(369\) | −8.68437 | −0.452090 | ||||||||
\(370\) | −8.31254 | −0.432148 | ||||||||
\(371\) | −8.38711 | −0.435437 | ||||||||
\(372\) | −2.25549 | −0.116942 | ||||||||
\(373\) | −18.0617 | −0.935199 | −0.467600 | − | 0.883940i | \(-0.654881\pi\) | ||||
−0.467600 | + | 0.883940i | \(0.654881\pi\) | |||||||
\(374\) | −30.5830 | −1.58141 | ||||||||
\(375\) | 9.67064 | 0.499390 | ||||||||
\(376\) | −5.13291 | −0.264709 | ||||||||
\(377\) | −4.44123 | −0.228735 | ||||||||
\(378\) | −0.952790 | −0.0490062 | ||||||||
\(379\) | −17.5037 | −0.899105 | −0.449553 | − | 0.893254i | \(-0.648417\pi\) | ||||
−0.449553 | + | 0.893254i | \(0.648417\pi\) | |||||||
\(380\) | −10.6748 | −0.547605 | ||||||||
\(381\) | 7.68171 | 0.393546 | ||||||||
\(382\) | 11.5986 | 0.593434 | ||||||||
\(383\) | −13.1769 | −0.673309 | −0.336654 | − | 0.941628i | \(-0.609295\pi\) | ||||
−0.336654 | + | 0.941628i | \(0.609295\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −9.87431 | −0.503242 | ||||||||
\(386\) | −6.70353 | −0.341201 | ||||||||
\(387\) | 5.56905 | 0.283091 | ||||||||
\(388\) | −18.7132 | −0.950021 | ||||||||
\(389\) | −9.23942 | −0.468457 | −0.234229 | − | 0.972182i | \(-0.575256\pi\) | ||||
−0.234229 | + | 0.972182i | \(0.575256\pi\) | |||||||
\(390\) | −2.46518 | −0.124829 | ||||||||
\(391\) | 21.6751 | 1.09616 | ||||||||
\(392\) | 6.09219 | 0.307702 | ||||||||
\(393\) | −0.0791075 | −0.00399045 | ||||||||
\(394\) | −10.1317 | −0.510427 | ||||||||
\(395\) | −22.3155 | −1.12281 | ||||||||
\(396\) | 4.20399 | 0.211258 | ||||||||
\(397\) | 21.4383 | 1.07596 | 0.537980 | − | 0.842958i | \(-0.319188\pi\) | ||||
0.537980 | + | 0.842958i | \(0.319188\pi\) | |||||||
\(398\) | 2.03748 | 0.102130 | ||||||||
\(399\) | −4.12580 | −0.206548 | ||||||||
\(400\) | 1.07710 | 0.0538552 | ||||||||
\(401\) | 28.0184 | 1.39917 | 0.699586 | − | 0.714548i | \(-0.253368\pi\) | ||||
0.699586 | + | 0.714548i | \(0.253368\pi\) | |||||||
\(402\) | 5.95796 | 0.297156 | ||||||||
\(403\) | −2.25549 | −0.112354 | ||||||||
\(404\) | −2.53136 | −0.125940 | ||||||||
\(405\) | 2.46518 | 0.122496 | ||||||||
\(406\) | 4.23156 | 0.210009 | ||||||||
\(407\) | 14.1758 | 0.702666 | ||||||||
\(408\) | 7.27477 | 0.360155 | ||||||||
\(409\) | 23.9390 | 1.18371 | 0.591855 | − | 0.806045i | \(-0.298396\pi\) | ||||
0.591855 | + | 0.806045i | \(0.298396\pi\) | |||||||
\(410\) | 21.4085 | 1.05729 | ||||||||
\(411\) | 3.99460 | 0.197039 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −4.88684 | −0.240466 | ||||||||
\(414\) | −2.97949 | −0.146434 | ||||||||
\(415\) | 19.2879 | 0.946804 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −13.0462 | −0.638876 | ||||||||
\(418\) | 18.2042 | 0.890397 | ||||||||
\(419\) | 35.4590 | 1.73228 | 0.866142 | − | 0.499798i | \(-0.166593\pi\) | ||||
0.866142 | + | 0.499798i | \(0.166593\pi\) | |||||||
\(420\) | 2.34880 | 0.114610 | ||||||||
\(421\) | 20.3462 | 0.991615 | 0.495807 | − | 0.868433i | \(-0.334872\pi\) | ||||
0.495807 | + | 0.868433i | \(0.334872\pi\) | |||||||
\(422\) | −9.03933 | −0.440028 | ||||||||
\(423\) | 5.13291 | 0.249570 | ||||||||
\(424\) | −8.80268 | −0.427496 | ||||||||
\(425\) | 7.83569 | 0.380087 | ||||||||
\(426\) | 12.6592 | 0.613340 | ||||||||
\(427\) | 5.07699 | 0.245693 | ||||||||
\(428\) | 2.73402 | 0.132154 | ||||||||
\(429\) | 4.20399 | 0.202970 | ||||||||
\(430\) | −13.7287 | −0.662057 | ||||||||
\(431\) | 26.2796 | 1.26584 | 0.632921 | − | 0.774217i | \(-0.281856\pi\) | ||||
0.632921 | + | 0.774217i | \(0.281856\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −11.1879 | −0.537655 | −0.268828 | − | 0.963188i | \(-0.586636\pi\) | ||||
−0.268828 | + | 0.963188i | \(0.586636\pi\) | |||||||
\(434\) | 2.14901 | 0.103156 | ||||||||
\(435\) | −10.9484 | −0.524937 | ||||||||
\(436\) | 9.98912 | 0.478392 | ||||||||
\(437\) | −12.9019 | −0.617181 | ||||||||
\(438\) | −7.23738 | −0.345816 | ||||||||
\(439\) | 14.1416 | 0.674942 | 0.337471 | − | 0.941336i | \(-0.390429\pi\) | ||||
0.337471 | + | 0.941336i | \(0.390429\pi\) | |||||||
\(440\) | −10.3636 | −0.494064 | ||||||||
\(441\) | −6.09219 | −0.290104 | ||||||||
\(442\) | 7.27477 | 0.346026 | ||||||||
\(443\) | 4.08763 | 0.194209 | 0.0971047 | − | 0.995274i | \(-0.469042\pi\) | ||||
0.0971047 | + | 0.995274i | \(0.469042\pi\) | |||||||
\(444\) | −3.37198 | −0.160027 | ||||||||
\(445\) | 9.14076 | 0.433314 | ||||||||
\(446\) | −10.3979 | −0.492354 | ||||||||
\(447\) | −15.1863 | −0.718288 | ||||||||
\(448\) | −0.952790 | −0.0450151 | ||||||||
\(449\) | 27.6267 | 1.30378 | 0.651892 | − | 0.758312i | \(-0.273976\pi\) | ||||
0.651892 | + | 0.758312i | \(0.273976\pi\) | |||||||
\(450\) | −1.07710 | −0.0507752 | ||||||||
\(451\) | −36.5090 | −1.71914 | ||||||||
\(452\) | −4.41216 | −0.207531 | ||||||||
\(453\) | −16.8777 | −0.792984 | ||||||||
\(454\) | −16.0725 | −0.754321 | ||||||||
\(455\) | 2.34880 | 0.110113 | ||||||||
\(456\) | −4.33023 | −0.202781 | ||||||||
\(457\) | 17.2789 | 0.808272 | 0.404136 | − | 0.914699i | \(-0.367572\pi\) | ||||
0.404136 | + | 0.914699i | \(0.367572\pi\) | |||||||
\(458\) | 20.0781 | 0.938187 | ||||||||
\(459\) | −7.27477 | −0.339557 | ||||||||
\(460\) | 7.34499 | 0.342462 | ||||||||
\(461\) | 0.140959 | 0.00656512 | 0.00328256 | − | 0.999995i | \(-0.498955\pi\) | ||||
0.00328256 | + | 0.999995i | \(0.498955\pi\) | |||||||
\(462\) | −4.00552 | −0.186353 | ||||||||
\(463\) | −6.71840 | −0.312231 | −0.156115 | − | 0.987739i | \(-0.549897\pi\) | ||||
−0.156115 | + | 0.987739i | \(0.549897\pi\) | |||||||
\(464\) | 4.44123 | 0.206179 | ||||||||
\(465\) | −5.56019 | −0.257848 | ||||||||
\(466\) | 13.2736 | 0.614889 | ||||||||
\(467\) | −41.8427 | −1.93625 | −0.968125 | − | 0.250469i | \(-0.919415\pi\) | ||||
−0.968125 | + | 0.250469i | \(0.919415\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −5.67669 | −0.262125 | ||||||||
\(470\) | −12.6535 | −0.583664 | ||||||||
\(471\) | 2.03856 | 0.0939318 | ||||||||
\(472\) | −5.12897 | −0.236080 | ||||||||
\(473\) | 23.4122 | 1.07649 | ||||||||
\(474\) | −9.05227 | −0.415785 | ||||||||
\(475\) | −4.66411 | −0.214004 | ||||||||
\(476\) | −6.93133 | −0.317697 | ||||||||
\(477\) | 8.80268 | 0.403047 | ||||||||
\(478\) | 15.4499 | 0.706663 | ||||||||
\(479\) | −29.1826 | −1.33339 | −0.666693 | − | 0.745333i | \(-0.732291\pi\) | ||||
−0.666693 | + | 0.745333i | \(0.732291\pi\) | |||||||
\(480\) | 2.46518 | 0.112519 | ||||||||
\(481\) | −3.37198 | −0.153749 | ||||||||
\(482\) | −21.5308 | −0.980699 | ||||||||
\(483\) | 2.83883 | 0.129171 | ||||||||
\(484\) | 6.67349 | 0.303341 | ||||||||
\(485\) | −46.1315 | −2.09472 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −24.2272 | −1.09784 | −0.548919 | − | 0.835876i | \(-0.684960\pi\) | ||||
−0.548919 | + | 0.835876i | \(0.684960\pi\) | |||||||
\(488\) | 5.32855 | 0.241212 | ||||||||
\(489\) | 17.7666 | 0.803435 | ||||||||
\(490\) | 15.0183 | 0.678459 | ||||||||
\(491\) | 36.6208 | 1.65268 | 0.826338 | − | 0.563175i | \(-0.190420\pi\) | ||||
0.826338 | + | 0.563175i | \(0.190420\pi\) | |||||||
\(492\) | 8.68437 | 0.391522 | ||||||||
\(493\) | 32.3090 | 1.45512 | ||||||||
\(494\) | −4.33023 | −0.194826 | ||||||||
\(495\) | 10.3636 | 0.465808 | ||||||||
\(496\) | 2.25549 | 0.101275 | ||||||||
\(497\) | −12.0615 | −0.541034 | ||||||||
\(498\) | 7.82412 | 0.350607 | ||||||||
\(499\) | −11.6189 | −0.520132 | −0.260066 | − | 0.965591i | \(-0.583744\pi\) | ||||
−0.260066 | + | 0.965591i | \(0.583744\pi\) | |||||||
\(500\) | −9.67064 | −0.432484 | ||||||||
\(501\) | −8.10126 | −0.361937 | ||||||||
\(502\) | 7.41297 | 0.330857 | ||||||||
\(503\) | 2.00788 | 0.0895269 | 0.0447634 | − | 0.998998i | \(-0.485747\pi\) | ||||
0.0447634 | + | 0.998998i | \(0.485747\pi\) | |||||||
\(504\) | 0.952790 | 0.0424406 | ||||||||
\(505\) | −6.24026 | −0.277688 | ||||||||
\(506\) | −12.5258 | −0.556838 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −7.68171 | −0.340821 | ||||||||
\(509\) | 12.0630 | 0.534684 | 0.267342 | − | 0.963602i | \(-0.413855\pi\) | ||||
0.267342 | + | 0.963602i | \(0.413855\pi\) | |||||||
\(510\) | 17.9336 | 0.794114 | ||||||||
\(511\) | 6.89571 | 0.305048 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.33023 | 0.191184 | ||||||||
\(514\) | 29.3253 | 1.29348 | ||||||||
\(515\) | 2.46518 | 0.108629 | ||||||||
\(516\) | −5.56905 | −0.245164 | ||||||||
\(517\) | 21.5787 | 0.949029 | ||||||||
\(518\) | 3.21279 | 0.141162 | ||||||||
\(519\) | 8.14139 | 0.357367 | ||||||||
\(520\) | 2.46518 | 0.108105 | ||||||||
\(521\) | 23.0562 | 1.01011 | 0.505054 | − | 0.863088i | \(-0.331472\pi\) | ||||
0.505054 | + | 0.863088i | \(0.331472\pi\) | |||||||
\(522\) | −4.44123 | −0.194388 | ||||||||
\(523\) | 12.7046 | 0.555533 | 0.277766 | − | 0.960649i | \(-0.410406\pi\) | ||||
0.277766 | + | 0.960649i | \(0.410406\pi\) | |||||||
\(524\) | 0.0791075 | 0.00345583 | ||||||||
\(525\) | 1.02625 | 0.0447894 | ||||||||
\(526\) | −4.81915 | −0.210125 | ||||||||
\(527\) | 16.4082 | 0.714752 | ||||||||
\(528\) | −4.20399 | −0.182955 | ||||||||
\(529\) | −14.1226 | −0.614027 | ||||||||
\(530\) | −21.7002 | −0.942596 | ||||||||
\(531\) | 5.12897 | 0.222579 | ||||||||
\(532\) | 4.12580 | 0.178876 | ||||||||
\(533\) | 8.68437 | 0.376162 | ||||||||
\(534\) | 3.70795 | 0.160459 | ||||||||
\(535\) | 6.73985 | 0.291389 | ||||||||
\(536\) | −5.95796 | −0.257345 | ||||||||
\(537\) | −16.2502 | −0.701246 | ||||||||
\(538\) | 5.25718 | 0.226653 | ||||||||
\(539\) | −25.6115 | −1.10316 | ||||||||
\(540\) | −2.46518 | −0.106084 | ||||||||
\(541\) | 34.6242 | 1.48861 | 0.744306 | − | 0.667839i | \(-0.232781\pi\) | ||||
0.744306 | + | 0.667839i | \(0.232781\pi\) | |||||||
\(542\) | 21.4015 | 0.919275 | ||||||||
\(543\) | −0.280385 | −0.0120325 | ||||||||
\(544\) | −7.27477 | −0.311903 | ||||||||
\(545\) | 24.6250 | 1.05482 | ||||||||
\(546\) | 0.952790 | 0.0407757 | ||||||||
\(547\) | 20.8348 | 0.890830 | 0.445415 | − | 0.895324i | \(-0.353056\pi\) | ||||
0.445415 | + | 0.895324i | \(0.353056\pi\) | |||||||
\(548\) | −3.99460 | −0.170641 | ||||||||
\(549\) | −5.32855 | −0.227417 | ||||||||
\(550\) | −4.52813 | −0.193080 | ||||||||
\(551\) | −19.2316 | −0.819292 | ||||||||
\(552\) | 2.97949 | 0.126816 | ||||||||
\(553\) | 8.62491 | 0.366769 | ||||||||
\(554\) | 31.4672 | 1.33691 | ||||||||
\(555\) | −8.31254 | −0.352847 | ||||||||
\(556\) | 13.0462 | 0.553283 | ||||||||
\(557\) | 34.9136 | 1.47934 | 0.739669 | − | 0.672971i | \(-0.234982\pi\) | ||||
0.739669 | + | 0.672971i | \(0.234982\pi\) | |||||||
\(558\) | −2.25549 | −0.0954826 | ||||||||
\(559\) | −5.56905 | −0.235546 | ||||||||
\(560\) | −2.34880 | −0.0992548 | ||||||||
\(561\) | −30.5830 | −1.29122 | ||||||||
\(562\) | −30.2559 | −1.27627 | ||||||||
\(563\) | 7.17388 | 0.302343 | 0.151171 | − | 0.988508i | \(-0.451695\pi\) | ||||
0.151171 | + | 0.988508i | \(0.451695\pi\) | |||||||
\(564\) | −5.13291 | −0.216134 | ||||||||
\(565\) | −10.8768 | −0.457589 | ||||||||
\(566\) | −22.6650 | −0.952679 | ||||||||
\(567\) | −0.952790 | −0.0400134 | ||||||||
\(568\) | −12.6592 | −0.531168 | ||||||||
\(569\) | 9.16795 | 0.384341 | 0.192170 | − | 0.981362i | \(-0.438447\pi\) | ||||
0.192170 | + | 0.981362i | \(0.438447\pi\) | |||||||
\(570\) | −10.6748 | −0.447117 | ||||||||
\(571\) | −1.81441 | −0.0759306 | −0.0379653 | − | 0.999279i | \(-0.512088\pi\) | ||||
−0.0379653 | + | 0.999279i | \(0.512088\pi\) | |||||||
\(572\) | −4.20399 | −0.175777 | ||||||||
\(573\) | 11.5986 | 0.484537 | ||||||||
\(574\) | −8.27438 | −0.345366 | ||||||||
\(575\) | 3.20923 | 0.133834 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −12.8667 | −0.535647 | −0.267824 | − | 0.963468i | \(-0.586304\pi\) | ||||
−0.267824 | + | 0.963468i | \(0.586304\pi\) | |||||||
\(578\) | −35.9223 | −1.49417 | ||||||||
\(579\) | −6.70353 | −0.278589 | ||||||||
\(580\) | 10.9484 | 0.454609 | ||||||||
\(581\) | −7.45475 | −0.309275 | ||||||||
\(582\) | −18.7132 | −0.775689 | ||||||||
\(583\) | 37.0063 | 1.53265 | ||||||||
\(584\) | 7.23738 | 0.299485 | ||||||||
\(585\) | −2.46518 | −0.101923 | ||||||||
\(586\) | 27.5148 | 1.13663 | ||||||||
\(587\) | 8.00438 | 0.330376 | 0.165188 | − | 0.986262i | \(-0.447177\pi\) | ||||
0.165188 | + | 0.986262i | \(0.447177\pi\) | |||||||
\(588\) | 6.09219 | 0.251238 | ||||||||
\(589\) | −9.76679 | −0.402434 | ||||||||
\(590\) | −12.6438 | −0.520539 | ||||||||
\(591\) | −10.1317 | −0.416762 | ||||||||
\(592\) | 3.37198 | 0.138588 | ||||||||
\(593\) | −26.4157 | −1.08476 | −0.542381 | − | 0.840133i | \(-0.682477\pi\) | ||||
−0.542381 | + | 0.840133i | \(0.682477\pi\) | |||||||
\(594\) | 4.20399 | 0.172492 | ||||||||
\(595\) | −17.0870 | −0.700497 | ||||||||
\(596\) | 15.1863 | 0.622056 | ||||||||
\(597\) | 2.03748 | 0.0833886 | ||||||||
\(598\) | 2.97949 | 0.121841 | ||||||||
\(599\) | 37.5562 | 1.53451 | 0.767253 | − | 0.641345i | \(-0.221623\pi\) | ||||
0.767253 | + | 0.641345i | \(0.221623\pi\) | |||||||
\(600\) | 1.07710 | 0.0439726 | ||||||||
\(601\) | 2.97218 | 0.121238 | 0.0606189 | − | 0.998161i | \(-0.480693\pi\) | ||||
0.0606189 | + | 0.998161i | \(0.480693\pi\) | |||||||
\(602\) | 5.30614 | 0.216262 | ||||||||
\(603\) | 5.95796 | 0.242627 | ||||||||
\(604\) | 16.8777 | 0.686744 | ||||||||
\(605\) | 16.4513 | 0.668842 | ||||||||
\(606\) | −2.53136 | −0.102829 | ||||||||
\(607\) | −33.9595 | −1.37837 | −0.689187 | − | 0.724584i | \(-0.742032\pi\) | ||||
−0.689187 | + | 0.724584i | \(0.742032\pi\) | |||||||
\(608\) | 4.33023 | 0.175614 | ||||||||
\(609\) | 4.23156 | 0.171472 | ||||||||
\(610\) | 13.1358 | 0.531854 | ||||||||
\(611\) | −5.13291 | −0.207655 | ||||||||
\(612\) | 7.27477 | 0.294065 | ||||||||
\(613\) | −13.4030 | −0.541342 | −0.270671 | − | 0.962672i | \(-0.587246\pi\) | ||||
−0.270671 | + | 0.962672i | \(0.587246\pi\) | |||||||
\(614\) | −4.53701 | −0.183099 | ||||||||
\(615\) | 21.4085 | 0.863275 | ||||||||
\(616\) | 4.00552 | 0.161387 | ||||||||
\(617\) | 23.0444 | 0.927733 | 0.463867 | − | 0.885905i | \(-0.346462\pi\) | ||||
0.463867 | + | 0.885905i | \(0.346462\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −13.5210 | −0.543455 | −0.271727 | − | 0.962374i | \(-0.587595\pi\) | ||||
−0.271727 | + | 0.962374i | \(0.587595\pi\) | |||||||
\(620\) | 5.56019 | 0.223303 | ||||||||
\(621\) | −2.97949 | −0.119563 | ||||||||
\(622\) | 25.6533 | 1.02860 | ||||||||
\(623\) | −3.53290 | −0.141543 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −29.2254 | −1.16901 | ||||||||
\(626\) | 0.813766 | 0.0325246 | ||||||||
\(627\) | 18.2042 | 0.727006 | ||||||||
\(628\) | −2.03856 | −0.0813473 | ||||||||
\(629\) | 24.5304 | 0.978091 | ||||||||
\(630\) | 2.34880 | 0.0935783 | ||||||||
\(631\) | 21.0903 | 0.839590 | 0.419795 | − | 0.907619i | \(-0.362102\pi\) | ||||
0.419795 | + | 0.907619i | \(0.362102\pi\) | |||||||
\(632\) | 9.05227 | 0.360080 | ||||||||
\(633\) | −9.03933 | −0.359281 | ||||||||
\(634\) | 23.7066 | 0.941508 | ||||||||
\(635\) | −18.9368 | −0.751484 | ||||||||
\(636\) | −8.80268 | −0.349049 | ||||||||
\(637\) | 6.09219 | 0.241381 | ||||||||
\(638\) | −18.6709 | −0.739187 | ||||||||
\(639\) | 12.6592 | 0.500790 | ||||||||
\(640\) | −2.46518 | −0.0974447 | ||||||||
\(641\) | 36.3190 | 1.43452 | 0.717258 | − | 0.696808i | \(-0.245397\pi\) | ||||
0.717258 | + | 0.696808i | \(0.245397\pi\) | |||||||
\(642\) | 2.73402 | 0.107903 | ||||||||
\(643\) | −27.4035 | −1.08069 | −0.540344 | − | 0.841444i | \(-0.681706\pi\) | ||||
−0.540344 | + | 0.841444i | \(0.681706\pi\) | |||||||
\(644\) | −2.83883 | −0.111866 | ||||||||
\(645\) | −13.7287 | −0.540567 | ||||||||
\(646\) | 31.5014 | 1.23941 | ||||||||
\(647\) | 31.6155 | 1.24293 | 0.621467 | − | 0.783440i | \(-0.286537\pi\) | ||||
0.621467 | + | 0.783440i | \(0.286537\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 21.5621 | 0.846388 | ||||||||
\(650\) | 1.07710 | 0.0422475 | ||||||||
\(651\) | 2.14901 | 0.0842264 | ||||||||
\(652\) | −17.7666 | −0.695795 | ||||||||
\(653\) | −45.8355 | −1.79368 | −0.896841 | − | 0.442353i | \(-0.854144\pi\) | ||||
−0.896841 | + | 0.442353i | \(0.854144\pi\) | |||||||
\(654\) | 9.98912 | 0.390606 | ||||||||
\(655\) | 0.195014 | 0.00761983 | ||||||||
\(656\) | −8.68437 | −0.339068 | ||||||||
\(657\) | −7.23738 | −0.282357 | ||||||||
\(658\) | 4.89058 | 0.190655 | ||||||||
\(659\) | 11.6284 | 0.452978 | 0.226489 | − | 0.974014i | \(-0.427275\pi\) | ||||
0.226489 | + | 0.974014i | \(0.427275\pi\) | |||||||
\(660\) | −10.3636 | −0.403402 | ||||||||
\(661\) | 2.47763 | 0.0963686 | 0.0481843 | − | 0.998838i | \(-0.484657\pi\) | ||||
0.0481843 | + | 0.998838i | \(0.484657\pi\) | |||||||
\(662\) | −14.7152 | −0.571921 | ||||||||
\(663\) | 7.27477 | 0.282529 | ||||||||
\(664\) | −7.82412 | −0.303635 | ||||||||
\(665\) | 10.1708 | 0.394408 | ||||||||
\(666\) | −3.37198 | −0.130662 | ||||||||
\(667\) | 13.2326 | 0.512370 | ||||||||
\(668\) | 8.10126 | 0.313447 | ||||||||
\(669\) | −10.3979 | −0.402006 | ||||||||
\(670\) | −14.6874 | −0.567425 | ||||||||
\(671\) | −22.4012 | −0.864787 | ||||||||
\(672\) | −0.952790 | −0.0367547 | ||||||||
\(673\) | 43.6553 | 1.68279 | 0.841394 | − | 0.540423i | \(-0.181736\pi\) | ||||
0.841394 | + | 0.540423i | \(0.181736\pi\) | |||||||
\(674\) | −9.99348 | −0.384935 | ||||||||
\(675\) | −1.07710 | −0.0414578 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 16.4807 | 0.633404 | 0.316702 | − | 0.948525i | \(-0.397425\pi\) | ||||
0.316702 | + | 0.948525i | \(0.397425\pi\) | |||||||
\(678\) | −4.41216 | −0.169448 | ||||||||
\(679\) | 17.8298 | 0.684245 | ||||||||
\(680\) | −17.9336 | −0.687723 | ||||||||
\(681\) | −16.0725 | −0.615901 | ||||||||
\(682\) | −9.48205 | −0.363087 | ||||||||
\(683\) | −39.6360 | −1.51663 | −0.758315 | − | 0.651888i | \(-0.773977\pi\) | ||||
−0.758315 | + | 0.651888i | \(0.773977\pi\) | |||||||
\(684\) | −4.33023 | −0.165570 | ||||||||
\(685\) | −9.84739 | −0.376249 | ||||||||
\(686\) | −12.4741 | −0.476264 | ||||||||
\(687\) | 20.0781 | 0.766026 | ||||||||
\(688\) | 5.56905 | 0.212318 | ||||||||
\(689\) | −8.80268 | −0.335355 | ||||||||
\(690\) | 7.34499 | 0.279619 | ||||||||
\(691\) | 17.7312 | 0.674528 | 0.337264 | − | 0.941410i | \(-0.390499\pi\) | ||||
0.337264 | + | 0.941410i | \(0.390499\pi\) | |||||||
\(692\) | −8.14139 | −0.309489 | ||||||||
\(693\) | −4.00552 | −0.152157 | ||||||||
\(694\) | −16.4929 | −0.626063 | ||||||||
\(695\) | 32.1612 | 1.21995 | ||||||||
\(696\) | 4.44123 | 0.168345 | ||||||||
\(697\) | −63.1768 | −2.39299 | ||||||||
\(698\) | 14.2015 | 0.537533 | ||||||||
\(699\) | 13.2736 | 0.502055 | ||||||||
\(700\) | −1.02625 | −0.0387888 | ||||||||
\(701\) | −14.8140 | −0.559519 | −0.279759 | − | 0.960070i | \(-0.590255\pi\) | ||||
−0.279759 | + | 0.960070i | \(0.590255\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −14.6014 | −0.550704 | ||||||||
\(704\) | 4.20399 | 0.158444 | ||||||||
\(705\) | −12.6535 | −0.476560 | ||||||||
\(706\) | 19.9580 | 0.751128 | ||||||||
\(707\) | 2.41186 | 0.0907072 | ||||||||
\(708\) | −5.12897 | −0.192759 | ||||||||
\(709\) | −0.691614 | −0.0259741 | −0.0129870 | − | 0.999916i | \(-0.504134\pi\) | ||||
−0.0129870 | + | 0.999916i | \(0.504134\pi\) | |||||||
\(710\) | −31.2072 | −1.17118 | ||||||||
\(711\) | −9.05227 | −0.339487 | ||||||||
\(712\) | −3.70795 | −0.138961 | ||||||||
\(713\) | 6.72023 | 0.251674 | ||||||||
\(714\) | −6.93133 | −0.259399 | ||||||||
\(715\) | −10.3636 | −0.387576 | ||||||||
\(716\) | 16.2502 | 0.607297 | ||||||||
\(717\) | 15.4499 | 0.576988 | ||||||||
\(718\) | 0.924105 | 0.0344873 | ||||||||
\(719\) | 1.65651 | 0.0617774 | 0.0308887 | − | 0.999523i | \(-0.490166\pi\) | ||||
0.0308887 | + | 0.999523i | \(0.490166\pi\) | |||||||
\(720\) | 2.46518 | 0.0918718 | ||||||||
\(721\) | −0.952790 | −0.0354838 | ||||||||
\(722\) | 0.249129 | 0.00927161 | ||||||||
\(723\) | −21.5308 | −0.800738 | ||||||||
\(724\) | 0.280385 | 0.0104204 | ||||||||
\(725\) | 4.78368 | 0.177661 | ||||||||
\(726\) | 6.67349 | 0.247677 | ||||||||
\(727\) | 13.9570 | 0.517636 | 0.258818 | − | 0.965926i | \(-0.416667\pi\) | ||||
0.258818 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(728\) | −0.952790 | −0.0353128 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 17.8414 | 0.660341 | ||||||||
\(731\) | 40.5136 | 1.49845 | ||||||||
\(732\) | 5.32855 | 0.196949 | ||||||||
\(733\) | −30.4509 | −1.12473 | −0.562365 | − | 0.826889i | \(-0.690108\pi\) | ||||
−0.562365 | + | 0.826889i | \(0.690108\pi\) | |||||||
\(734\) | −2.52886 | −0.0933418 | ||||||||
\(735\) | 15.0183 | 0.553960 | ||||||||
\(736\) | −2.97949 | −0.109826 | ||||||||
\(737\) | 25.0472 | 0.922625 | ||||||||
\(738\) | 8.68437 | 0.319676 | ||||||||
\(739\) | 23.5770 | 0.867295 | 0.433648 | − | 0.901083i | \(-0.357226\pi\) | ||||
0.433648 | + | 0.901083i | \(0.357226\pi\) | |||||||
\(740\) | 8.31254 | 0.305575 | ||||||||
\(741\) | −4.33023 | −0.159075 | ||||||||
\(742\) | 8.38711 | 0.307900 | ||||||||
\(743\) | 0.256667 | 0.00941620 | 0.00470810 | − | 0.999989i | \(-0.498501\pi\) | ||||
0.00470810 | + | 0.999989i | \(0.498501\pi\) | |||||||
\(744\) | 2.25549 | 0.0826903 | ||||||||
\(745\) | 37.4370 | 1.37159 | ||||||||
\(746\) | 18.0617 | 0.661286 | ||||||||
\(747\) | 7.82412 | 0.286270 | ||||||||
\(748\) | 30.5830 | 1.11823 | ||||||||
\(749\) | −2.60495 | −0.0951828 | ||||||||
\(750\) | −9.67064 | −0.353122 | ||||||||
\(751\) | 22.2227 | 0.810917 | 0.405458 | − | 0.914113i | \(-0.367112\pi\) | ||||
0.405458 | + | 0.914113i | \(0.367112\pi\) | |||||||
\(752\) | 5.13291 | 0.187178 | ||||||||
\(753\) | 7.41297 | 0.270144 | ||||||||
\(754\) | 4.44123 | 0.161740 | ||||||||
\(755\) | 41.6065 | 1.51422 | ||||||||
\(756\) | 0.952790 | 0.0346526 | ||||||||
\(757\) | 4.95829 | 0.180212 | 0.0901060 | − | 0.995932i | \(-0.471279\pi\) | ||||
0.0901060 | + | 0.995932i | \(0.471279\pi\) | |||||||
\(758\) | 17.5037 | 0.635763 | ||||||||
\(759\) | −12.5258 | −0.454656 | ||||||||
\(760\) | 10.6748 | 0.387215 | ||||||||
\(761\) | 27.0921 | 0.982089 | 0.491045 | − | 0.871134i | \(-0.336615\pi\) | ||||
0.491045 | + | 0.871134i | \(0.336615\pi\) | |||||||
\(762\) | −7.68171 | −0.278279 | ||||||||
\(763\) | −9.51754 | −0.344558 | ||||||||
\(764\) | −11.5986 | −0.419621 | ||||||||
\(765\) | 17.9336 | 0.648391 | ||||||||
\(766\) | 13.1769 | 0.476101 | ||||||||
\(767\) | −5.12897 | −0.185197 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 13.1939 | 0.475784 | 0.237892 | − | 0.971292i | \(-0.423544\pi\) | ||||
0.237892 | + | 0.971292i | \(0.423544\pi\) | |||||||
\(770\) | 9.87431 | 0.355845 | ||||||||
\(771\) | 29.3253 | 1.05612 | ||||||||
\(772\) | 6.70353 | 0.241265 | ||||||||
\(773\) | 12.7483 | 0.458525 | 0.229262 | − | 0.973365i | \(-0.426369\pi\) | ||||
0.229262 | + | 0.973365i | \(0.426369\pi\) | |||||||
\(774\) | −5.56905 | −0.200175 | ||||||||
\(775\) | 2.42940 | 0.0872667 | ||||||||
\(776\) | 18.7132 | 0.671766 | ||||||||
\(777\) | 3.21279 | 0.115258 | ||||||||
\(778\) | 9.23942 | 0.331249 | ||||||||
\(779\) | 37.6053 | 1.34735 | ||||||||
\(780\) | 2.46518 | 0.0882675 | ||||||||
\(781\) | 53.2190 | 1.90433 | ||||||||
\(782\) | −21.6751 | −0.775102 | ||||||||
\(783\) | −4.44123 | −0.158717 | ||||||||
\(784\) | −6.09219 | −0.217578 | ||||||||
\(785\) | −5.02541 | −0.179364 | ||||||||
\(786\) | 0.0791075 | 0.00282167 | ||||||||
\(787\) | −13.5003 | −0.481233 | −0.240617 | − | 0.970620i | \(-0.577350\pi\) | ||||
−0.240617 | + | 0.970620i | \(0.577350\pi\) | |||||||
\(788\) | 10.1317 | 0.360926 | ||||||||
\(789\) | −4.81915 | −0.171566 | ||||||||
\(790\) | 22.3155 | 0.793949 | ||||||||
\(791\) | 4.20387 | 0.149472 | ||||||||
\(792\) | −4.20399 | −0.149382 | ||||||||
\(793\) | 5.32855 | 0.189222 | ||||||||
\(794\) | −21.4383 | −0.760818 | ||||||||
\(795\) | −21.7002 | −0.769626 | ||||||||
\(796\) | −2.03748 | −0.0722166 | ||||||||
\(797\) | 10.2484 | 0.363018 | 0.181509 | − | 0.983389i | \(-0.441902\pi\) | ||||
0.181509 | + | 0.983389i | \(0.441902\pi\) | |||||||
\(798\) | 4.12580 | 0.146052 | ||||||||
\(799\) | 37.3407 | 1.32102 | ||||||||
\(800\) | −1.07710 | −0.0380814 | ||||||||
\(801\) | 3.70795 | 0.131014 | ||||||||
\(802\) | −28.0184 | −0.989364 | ||||||||
\(803\) | −30.4259 | −1.07371 | ||||||||
\(804\) | −5.95796 | −0.210121 | ||||||||
\(805\) | −6.99823 | −0.246655 | ||||||||
\(806\) | 2.25549 | 0.0794463 | ||||||||
\(807\) | 5.25718 | 0.185061 | ||||||||
\(808\) | 2.53136 | 0.0890530 | ||||||||
\(809\) | 10.2090 | 0.358930 | 0.179465 | − | 0.983764i | \(-0.442563\pi\) | ||||
0.179465 | + | 0.983764i | \(0.442563\pi\) | |||||||
\(810\) | −2.46518 | −0.0866175 | ||||||||
\(811\) | 46.6092 | 1.63667 | 0.818336 | − | 0.574740i | \(-0.194897\pi\) | ||||
0.818336 | + | 0.574740i | \(0.194897\pi\) | |||||||
\(812\) | −4.23156 | −0.148499 | ||||||||
\(813\) | 21.4015 | 0.750585 | ||||||||
\(814\) | −14.1758 | −0.496860 | ||||||||
\(815\) | −43.7979 | −1.53417 | ||||||||
\(816\) | −7.27477 | −0.254668 | ||||||||
\(817\) | −24.1153 | −0.843686 | ||||||||
\(818\) | −23.9390 | −0.837009 | ||||||||
\(819\) | 0.952790 | 0.0332932 | ||||||||
\(820\) | −21.4085 | −0.747618 | ||||||||
\(821\) | 25.7655 | 0.899222 | 0.449611 | − | 0.893224i | \(-0.351563\pi\) | ||||
0.449611 | + | 0.893224i | \(0.351563\pi\) | |||||||
\(822\) | −3.99460 | −0.139328 | ||||||||
\(823\) | −36.5037 | −1.27244 | −0.636219 | − | 0.771508i | \(-0.719503\pi\) | ||||
−0.636219 | + | 0.771508i | \(0.719503\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −4.52813 | −0.157649 | ||||||||
\(826\) | 4.88684 | 0.170035 | ||||||||
\(827\) | −4.48815 | −0.156068 | −0.0780342 | − | 0.996951i | \(-0.524864\pi\) | ||||
−0.0780342 | + | 0.996951i | \(0.524864\pi\) | |||||||
\(828\) | 2.97949 | 0.103545 | ||||||||
\(829\) | 54.7947 | 1.90310 | 0.951550 | − | 0.307495i | \(-0.0994906\pi\) | ||||
0.951550 | + | 0.307495i | \(0.0994906\pi\) | |||||||
\(830\) | −19.2879 | −0.669491 | ||||||||
\(831\) | 31.4672 | 1.09159 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −44.3193 | −1.53557 | ||||||||
\(834\) | 13.0462 | 0.451753 | ||||||||
\(835\) | 19.9710 | 0.691126 | ||||||||
\(836\) | −18.2042 | −0.629606 | ||||||||
\(837\) | −2.25549 | −0.0779612 | ||||||||
\(838\) | −35.4590 | −1.22491 | ||||||||
\(839\) | −22.6268 | −0.781163 | −0.390581 | − | 0.920568i | \(-0.627726\pi\) | ||||
−0.390581 | + | 0.920568i | \(0.627726\pi\) | |||||||
\(840\) | −2.34880 | −0.0810412 | ||||||||
\(841\) | −9.27544 | −0.319843 | ||||||||
\(842\) | −20.3462 | −0.701177 | ||||||||
\(843\) | −30.2559 | −1.04207 | ||||||||
\(844\) | 9.03933 | 0.311147 | ||||||||
\(845\) | 2.46518 | 0.0848047 | ||||||||
\(846\) | −5.13291 | −0.176473 | ||||||||
\(847\) | −6.35844 | −0.218478 | ||||||||
\(848\) | 8.80268 | 0.302285 | ||||||||
\(849\) | −22.6650 | −0.777859 | ||||||||
\(850\) | −7.83569 | −0.268762 | ||||||||
\(851\) | 10.0468 | 0.344400 | ||||||||
\(852\) | −12.6592 | −0.433697 | ||||||||
\(853\) | 4.45209 | 0.152437 | 0.0762184 | − | 0.997091i | \(-0.475715\pi\) | ||||
0.0762184 | + | 0.997091i | \(0.475715\pi\) | |||||||
\(854\) | −5.07699 | −0.173731 | ||||||||
\(855\) | −10.6748 | −0.365070 | ||||||||
\(856\) | −2.73402 | −0.0934470 | ||||||||
\(857\) | 53.5018 | 1.82759 | 0.913793 | − | 0.406180i | \(-0.133139\pi\) | ||||
0.913793 | + | 0.406180i | \(0.133139\pi\) | |||||||
\(858\) | −4.20399 | −0.143522 | ||||||||
\(859\) | −29.9987 | −1.02354 | −0.511772 | − | 0.859122i | \(-0.671011\pi\) | ||||
−0.511772 | + | 0.859122i | \(0.671011\pi\) | |||||||
\(860\) | 13.7287 | 0.468145 | ||||||||
\(861\) | −8.27438 | −0.281990 | ||||||||
\(862\) | −26.2796 | −0.895085 | ||||||||
\(863\) | 1.75205 | 0.0596405 | 0.0298202 | − | 0.999555i | \(-0.490507\pi\) | ||||
0.0298202 | + | 0.999555i | \(0.490507\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −20.0700 | −0.682400 | ||||||||
\(866\) | 11.1879 | 0.380180 | ||||||||
\(867\) | −35.9223 | −1.21999 | ||||||||
\(868\) | −2.14901 | −0.0729422 | ||||||||
\(869\) | −38.0556 | −1.29095 | ||||||||
\(870\) | 10.9484 | 0.371187 | ||||||||
\(871\) | −5.95796 | −0.201878 | ||||||||
\(872\) | −9.98912 | −0.338274 | ||||||||
\(873\) | −18.7132 | −0.633347 | ||||||||
\(874\) | 12.9019 | 0.436413 | ||||||||
\(875\) | 9.21409 | 0.311493 | ||||||||
\(876\) | 7.23738 | 0.244529 | ||||||||
\(877\) | −5.83733 | −0.197112 | −0.0985562 | − | 0.995131i | \(-0.531422\pi\) | ||||
−0.0985562 | + | 0.995131i | \(0.531422\pi\) | |||||||
\(878\) | −14.1416 | −0.477256 | ||||||||
\(879\) | 27.5148 | 0.928053 | ||||||||
\(880\) | 10.3636 | 0.349356 | ||||||||
\(881\) | −11.7604 | −0.396218 | −0.198109 | − | 0.980180i | \(-0.563480\pi\) | ||||
−0.198109 | + | 0.980180i | \(0.563480\pi\) | |||||||
\(882\) | 6.09219 | 0.205135 | ||||||||
\(883\) | −7.36861 | −0.247973 | −0.123987 | − | 0.992284i | \(-0.539568\pi\) | ||||
−0.123987 | + | 0.992284i | \(0.539568\pi\) | |||||||
\(884\) | −7.27477 | −0.244677 | ||||||||
\(885\) | −12.6438 | −0.425018 | ||||||||
\(886\) | −4.08763 | −0.137327 | ||||||||
\(887\) | 25.0335 | 0.840543 | 0.420272 | − | 0.907398i | \(-0.361935\pi\) | ||||
0.420272 | + | 0.907398i | \(0.361935\pi\) | |||||||
\(888\) | 3.37198 | 0.113156 | ||||||||
\(889\) | 7.31906 | 0.245473 | ||||||||
\(890\) | −9.14076 | −0.306399 | ||||||||
\(891\) | 4.20399 | 0.140839 | ||||||||
\(892\) | 10.3979 | 0.348147 | ||||||||
\(893\) | −22.2267 | −0.743787 | ||||||||
\(894\) | 15.1863 | 0.507906 | ||||||||
\(895\) | 40.0595 | 1.33904 | ||||||||
\(896\) | 0.952790 | 0.0318305 | ||||||||
\(897\) | 2.97949 | 0.0994824 | ||||||||
\(898\) | −27.6267 | −0.921914 | ||||||||
\(899\) | 10.0172 | 0.334091 | ||||||||
\(900\) | 1.07710 | 0.0359035 | ||||||||
\(901\) | 64.0375 | 2.13340 | ||||||||
\(902\) | 36.5090 | 1.21562 | ||||||||
\(903\) | 5.30614 | 0.176577 | ||||||||
\(904\) | 4.41216 | 0.146746 | ||||||||
\(905\) | 0.691199 | 0.0229762 | ||||||||
\(906\) | 16.8777 | 0.560724 | ||||||||
\(907\) | 21.2088 | 0.704228 | 0.352114 | − | 0.935957i | \(-0.385463\pi\) | ||||
0.352114 | + | 0.935957i | \(0.385463\pi\) | |||||||
\(908\) | 16.0725 | 0.533386 | ||||||||
\(909\) | −2.53136 | −0.0839599 | ||||||||
\(910\) | −2.34880 | −0.0778619 | ||||||||
\(911\) | 24.4489 | 0.810029 | 0.405015 | − | 0.914310i | \(-0.367266\pi\) | ||||
0.405015 | + | 0.914310i | \(0.367266\pi\) | |||||||
\(912\) | 4.33023 | 0.143388 | ||||||||
\(913\) | 32.8925 | 1.08858 | ||||||||
\(914\) | −17.2789 | −0.571535 | ||||||||
\(915\) | 13.1358 | 0.434257 | ||||||||
\(916\) | −20.0781 | −0.663398 | ||||||||
\(917\) | −0.0753729 | −0.00248903 | ||||||||
\(918\) | 7.27477 | 0.240103 | ||||||||
\(919\) | 41.5325 | 1.37003 | 0.685016 | − | 0.728528i | \(-0.259795\pi\) | ||||
0.685016 | + | 0.728528i | \(0.259795\pi\) | |||||||
\(920\) | −7.34499 | −0.242157 | ||||||||
\(921\) | −4.53701 | −0.149500 | ||||||||
\(922\) | −0.140959 | −0.00464224 | ||||||||
\(923\) | −12.6592 | −0.416682 | ||||||||
\(924\) | 4.00552 | 0.131772 | ||||||||
\(925\) | 3.63198 | 0.119419 | ||||||||
\(926\) | 6.71840 | 0.220780 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −4.44123 | −0.145791 | ||||||||
\(929\) | −8.50079 | −0.278902 | −0.139451 | − | 0.990229i | \(-0.544534\pi\) | ||||
−0.139451 | + | 0.990229i | \(0.544534\pi\) | |||||||
\(930\) | 5.56019 | 0.182326 | ||||||||
\(931\) | 26.3806 | 0.864588 | ||||||||
\(932\) | −13.2736 | −0.434792 | ||||||||
\(933\) | 25.6533 | 0.839851 | ||||||||
\(934\) | 41.8427 | 1.36913 | ||||||||
\(935\) | 75.3926 | 2.46560 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 16.2234 | 0.529996 | 0.264998 | − | 0.964249i | \(-0.414629\pi\) | ||||
0.264998 | + | 0.964249i | \(0.414629\pi\) | |||||||
\(938\) | 5.67669 | 0.185350 | ||||||||
\(939\) | 0.813766 | 0.0265562 | ||||||||
\(940\) | 12.6535 | 0.412713 | ||||||||
\(941\) | 10.5399 | 0.343590 | 0.171795 | − | 0.985133i | \(-0.445043\pi\) | ||||
0.171795 | + | 0.985133i | \(0.445043\pi\) | |||||||
\(942\) | −2.03856 | −0.0664198 | ||||||||
\(943\) | −25.8750 | −0.842607 | ||||||||
\(944\) | 5.12897 | 0.166934 | ||||||||
\(945\) | 2.34880 | 0.0764064 | ||||||||
\(946\) | −23.4122 | −0.761197 | ||||||||
\(947\) | −29.1952 | −0.948716 | −0.474358 | − | 0.880332i | \(-0.657320\pi\) | ||||
−0.474358 | + | 0.880332i | \(0.657320\pi\) | |||||||
\(948\) | 9.05227 | 0.294004 | ||||||||
\(949\) | 7.23738 | 0.234935 | ||||||||
\(950\) | 4.66411 | 0.151324 | ||||||||
\(951\) | 23.7066 | 0.768738 | ||||||||
\(952\) | 6.93133 | 0.224646 | ||||||||
\(953\) | 8.24769 | 0.267169 | 0.133584 | − | 0.991037i | \(-0.457351\pi\) | ||||
0.133584 | + | 0.991037i | \(0.457351\pi\) | |||||||
\(954\) | −8.80268 | −0.284997 | ||||||||
\(955\) | −28.5925 | −0.925232 | ||||||||
\(956\) | −15.4499 | −0.499687 | ||||||||
\(957\) | −18.6709 | −0.603544 | ||||||||
\(958\) | 29.1826 | 0.942846 | ||||||||
\(959\) | 3.80601 | 0.122903 | ||||||||
\(960\) | −2.46518 | −0.0795633 | ||||||||
\(961\) | −25.9128 | −0.835895 | ||||||||
\(962\) | 3.37198 | 0.108717 | ||||||||
\(963\) | 2.73402 | 0.0881026 | ||||||||
\(964\) | 21.5308 | 0.693459 | ||||||||
\(965\) | 16.5254 | 0.531971 | ||||||||
\(966\) | −2.83883 | −0.0913380 | ||||||||
\(967\) | 9.20865 | 0.296130 | 0.148065 | − | 0.988978i | \(-0.452695\pi\) | ||||
0.148065 | + | 0.988978i | \(0.452695\pi\) | |||||||
\(968\) | −6.67349 | −0.214494 | ||||||||
\(969\) | 31.5014 | 1.01197 | ||||||||
\(970\) | 46.1315 | 1.48119 | ||||||||
\(971\) | −22.3311 | −0.716639 | −0.358320 | − | 0.933599i | \(-0.616650\pi\) | ||||
−0.358320 | + | 0.933599i | \(0.616650\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −12.4303 | −0.398497 | ||||||||
\(974\) | 24.2272 | 0.776289 | ||||||||
\(975\) | 1.07710 | 0.0344950 | ||||||||
\(976\) | −5.32855 | −0.170563 | ||||||||
\(977\) | 26.9515 | 0.862256 | 0.431128 | − | 0.902291i | \(-0.358116\pi\) | ||||
0.431128 | + | 0.902291i | \(0.358116\pi\) | |||||||
\(978\) | −17.7666 | −0.568114 | ||||||||
\(979\) | 15.5882 | 0.498200 | ||||||||
\(980\) | −15.0183 | −0.479743 | ||||||||
\(981\) | 9.98912 | 0.318928 | ||||||||
\(982\) | −36.6208 | −1.16862 | ||||||||
\(983\) | 4.99152 | 0.159205 | 0.0796023 | − | 0.996827i | \(-0.474635\pi\) | ||||
0.0796023 | + | 0.996827i | \(0.474635\pi\) | |||||||
\(984\) | −8.68437 | −0.276848 | ||||||||
\(985\) | 24.9764 | 0.795814 | ||||||||
\(986\) | −32.3090 | −1.02893 | ||||||||
\(987\) | 4.89058 | 0.155669 | ||||||||
\(988\) | 4.33023 | 0.137763 | ||||||||
\(989\) | 16.5930 | 0.527625 | ||||||||
\(990\) | −10.3636 | −0.329376 | ||||||||
\(991\) | −24.0329 | −0.763430 | −0.381715 | − | 0.924280i | \(-0.624666\pi\) | ||||
−0.381715 | + | 0.924280i | \(0.624666\pi\) | |||||||
\(992\) | −2.25549 | −0.0716119 | ||||||||
\(993\) | −14.7152 | −0.466971 | ||||||||
\(994\) | 12.0615 | 0.382569 | ||||||||
\(995\) | −5.02276 | −0.159232 | ||||||||
\(996\) | −7.82412 | −0.247917 | ||||||||
\(997\) | 37.8573 | 1.19895 | 0.599477 | − | 0.800392i | \(-0.295375\pi\) | ||||
0.599477 | + | 0.800392i | \(0.295375\pi\) | |||||||
\(998\) | 11.6189 | 0.367789 | ||||||||
\(999\) | −3.37198 | −0.106685 |
(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 | 8034.2.a.ba.1.11 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.ba.1.11 | ✓ | 14 | 1.1 | even | 1 | trivial |