Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 9x^{6} + 14x^{5} + 25x^{4} - 24x^{3} - 16x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.10207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10207 | 0.779283 | 0.389642 | − | 0.920967i | \(-0.372599\pi\) | ||||
0.389642 | + | 0.920967i | \(0.372599\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.785435 | −0.392717 | ||||||||
\(5\) | 3.28432 | 1.46879 | 0.734396 | − | 0.678721i | \(-0.237466\pi\) | ||||
0.734396 | + | 0.678721i | \(0.237466\pi\) | |||||||
\(6\) | 1.10207 | 0.449919 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −3.06975 | −1.08532 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.61956 | 1.14460 | ||||||||
\(11\) | 1.40850 | 0.424678 | 0.212339 | − | 0.977196i | \(-0.431892\pi\) | ||||
0.212339 | + | 0.977196i | \(0.431892\pi\) | |||||||
\(12\) | −0.785435 | −0.226735 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.10207 | 0.294541 | ||||||||
\(15\) | 3.28432 | 0.848007 | ||||||||
\(16\) | −1.81222 | −0.453056 | ||||||||
\(17\) | 5.77983 | 1.40181 | 0.700907 | − | 0.713252i | \(-0.252779\pi\) | ||||
0.700907 | + | 0.713252i | \(0.252779\pi\) | |||||||
\(18\) | 1.10207 | 0.259761 | ||||||||
\(19\) | 6.19600 | 1.42146 | 0.710730 | − | 0.703465i | \(-0.248365\pi\) | ||||
0.710730 | + | 0.703465i | \(0.248365\pi\) | |||||||
\(20\) | −2.57962 | −0.576820 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 1.55227 | 0.330944 | ||||||||
\(23\) | 3.40145 | 0.709251 | 0.354626 | − | 0.935008i | \(-0.384608\pi\) | ||||
0.354626 | + | 0.935008i | \(0.384608\pi\) | |||||||
\(24\) | −3.06975 | −0.626611 | ||||||||
\(25\) | 5.78675 | 1.15735 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.785435 | −0.148433 | ||||||||
\(29\) | −8.57692 | −1.59269 | −0.796347 | − | 0.604840i | \(-0.793237\pi\) | ||||
−0.796347 | + | 0.604840i | \(0.793237\pi\) | |||||||
\(30\) | 3.61956 | 0.660838 | ||||||||
\(31\) | −7.64123 | −1.37240 | −0.686202 | − | 0.727411i | \(-0.740724\pi\) | ||||
−0.686202 | + | 0.727411i | \(0.740724\pi\) | |||||||
\(32\) | 4.14230 | 0.732263 | ||||||||
\(33\) | 1.40850 | 0.245188 | ||||||||
\(34\) | 6.36980 | 1.09241 | ||||||||
\(35\) | 3.28432 | 0.555151 | ||||||||
\(36\) | −0.785435 | −0.130906 | ||||||||
\(37\) | −5.59124 | −0.919195 | −0.459597 | − | 0.888127i | \(-0.652006\pi\) | ||||
−0.459597 | + | 0.888127i | \(0.652006\pi\) | |||||||
\(38\) | 6.82845 | 1.10772 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.0820 | −1.59411 | ||||||||
\(41\) | −1.15399 | −0.180223 | −0.0901116 | − | 0.995932i | \(-0.528722\pi\) | ||||
−0.0901116 | + | 0.995932i | \(0.528722\pi\) | |||||||
\(42\) | 1.10207 | 0.170054 | ||||||||
\(43\) | 0.818994 | 0.124895 | 0.0624477 | − | 0.998048i | \(-0.480109\pi\) | ||||
0.0624477 | + | 0.998048i | \(0.480109\pi\) | |||||||
\(44\) | −1.10628 | −0.166778 | ||||||||
\(45\) | 3.28432 | 0.489597 | ||||||||
\(46\) | 3.74865 | 0.552708 | ||||||||
\(47\) | −3.35146 | −0.488861 | −0.244430 | − | 0.969667i | \(-0.578601\pi\) | ||||
−0.244430 | + | 0.969667i | \(0.578601\pi\) | |||||||
\(48\) | −1.81222 | −0.261572 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.37742 | 0.901903 | ||||||||
\(51\) | 5.77983 | 0.809338 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.54281 | 0.761363 | 0.380682 | − | 0.924706i | \(-0.375689\pi\) | ||||
0.380682 | + | 0.924706i | \(0.375689\pi\) | |||||||
\(54\) | 1.10207 | 0.149973 | ||||||||
\(55\) | 4.62595 | 0.623763 | ||||||||
\(56\) | −3.06975 | −0.410213 | ||||||||
\(57\) | 6.19600 | 0.820681 | ||||||||
\(58\) | −9.45240 | −1.24116 | ||||||||
\(59\) | −4.88973 | −0.636588 | −0.318294 | − | 0.947992i | \(-0.603110\pi\) | ||||
−0.318294 | + | 0.947992i | \(0.603110\pi\) | |||||||
\(60\) | −2.57962 | −0.333027 | ||||||||
\(61\) | −2.97751 | −0.381231 | −0.190616 | − | 0.981665i | \(-0.561048\pi\) | ||||
−0.190616 | + | 0.981665i | \(0.561048\pi\) | |||||||
\(62\) | −8.42119 | −1.06949 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.18957 | 1.02370 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.55227 | 0.191071 | ||||||||
\(67\) | 0.268759 | 0.0328341 | 0.0164171 | − | 0.999865i | \(-0.494774\pi\) | ||||
0.0164171 | + | 0.999865i | \(0.494774\pi\) | |||||||
\(68\) | −4.53968 | −0.550517 | ||||||||
\(69\) | 3.40145 | 0.409486 | ||||||||
\(70\) | 3.61956 | 0.432620 | ||||||||
\(71\) | 9.28104 | 1.10146 | 0.550728 | − | 0.834684i | \(-0.314350\pi\) | ||||
0.550728 | + | 0.834684i | \(0.314350\pi\) | |||||||
\(72\) | −3.06975 | −0.361774 | ||||||||
\(73\) | 12.1448 | 1.42144 | 0.710721 | − | 0.703474i | \(-0.248369\pi\) | ||||
0.710721 | + | 0.703474i | \(0.248369\pi\) | |||||||
\(74\) | −6.16196 | −0.716313 | ||||||||
\(75\) | 5.78675 | 0.668196 | ||||||||
\(76\) | −4.86656 | −0.558232 | ||||||||
\(77\) | 1.40850 | 0.160513 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00232 | 0.675313 | 0.337657 | − | 0.941269i | \(-0.390366\pi\) | ||||
0.337657 | + | 0.941269i | \(0.390366\pi\) | |||||||
\(80\) | −5.95192 | −0.665444 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.27178 | −0.140445 | ||||||||
\(83\) | 6.02174 | 0.660972 | 0.330486 | − | 0.943811i | \(-0.392787\pi\) | ||||
0.330486 | + | 0.943811i | \(0.392787\pi\) | |||||||
\(84\) | −0.785435 | −0.0856980 | ||||||||
\(85\) | 18.9828 | 2.05897 | ||||||||
\(86\) | 0.902592 | 0.0973290 | ||||||||
\(87\) | −8.57692 | −0.919543 | ||||||||
\(88\) | −4.32374 | −0.460912 | ||||||||
\(89\) | −16.5783 | −1.75730 | −0.878650 | − | 0.477466i | \(-0.841556\pi\) | ||||
−0.878650 | + | 0.477466i | \(0.841556\pi\) | |||||||
\(90\) | 3.61956 | 0.381535 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.67162 | −0.278535 | ||||||||
\(93\) | −7.64123 | −0.792358 | ||||||||
\(94\) | −3.69355 | −0.380961 | ||||||||
\(95\) | 20.3496 | 2.08783 | ||||||||
\(96\) | 4.14230 | 0.422772 | ||||||||
\(97\) | 18.7352 | 1.90227 | 0.951134 | − | 0.308779i | \(-0.0999204\pi\) | ||||
0.951134 | + | 0.308779i | \(0.0999204\pi\) | |||||||
\(98\) | 1.10207 | 0.111326 | ||||||||
\(99\) | 1.40850 | 0.141559 | ||||||||
\(100\) | −4.54511 | −0.454511 | ||||||||
\(101\) | 15.0516 | 1.49769 | 0.748846 | − | 0.662744i | \(-0.230608\pi\) | ||||
0.748846 | + | 0.662744i | \(0.230608\pi\) | |||||||
\(102\) | 6.36980 | 0.630704 | ||||||||
\(103\) | −14.0763 | −1.38698 | −0.693488 | − | 0.720468i | \(-0.743927\pi\) | ||||
−0.693488 | + | 0.720468i | \(0.743927\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.28432 | 0.320517 | ||||||||
\(106\) | 6.10858 | 0.593318 | ||||||||
\(107\) | 7.34688 | 0.710250 | 0.355125 | − | 0.934819i | \(-0.384438\pi\) | ||||
0.355125 | + | 0.934819i | \(0.384438\pi\) | |||||||
\(108\) | −0.785435 | −0.0755785 | ||||||||
\(109\) | −4.65621 | −0.445984 | −0.222992 | − | 0.974820i | \(-0.571582\pi\) | ||||
−0.222992 | + | 0.974820i | \(0.571582\pi\) | |||||||
\(110\) | 5.09814 | 0.486089 | ||||||||
\(111\) | −5.59124 | −0.530697 | ||||||||
\(112\) | −1.81222 | −0.171239 | ||||||||
\(113\) | 7.17145 | 0.674633 | 0.337317 | − | 0.941391i | \(-0.390481\pi\) | ||||
0.337317 | + | 0.941391i | \(0.390481\pi\) | |||||||
\(114\) | 6.82845 | 0.639543 | ||||||||
\(115\) | 11.1714 | 1.04174 | ||||||||
\(116\) | 6.73661 | 0.625479 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.38884 | −0.496083 | ||||||||
\(119\) | 5.77983 | 0.529836 | ||||||||
\(120\) | −10.0820 | −0.920361 | ||||||||
\(121\) | −9.01613 | −0.819649 | ||||||||
\(122\) | −3.28143 | −0.297087 | ||||||||
\(123\) | −1.15399 | −0.104052 | ||||||||
\(124\) | 6.00169 | 0.538967 | ||||||||
\(125\) | 2.58392 | 0.231113 | ||||||||
\(126\) | 1.10207 | 0.0981805 | ||||||||
\(127\) | −11.6599 | −1.03465 | −0.517326 | − | 0.855789i | \(-0.673072\pi\) | ||||
−0.517326 | + | 0.855789i | \(0.673072\pi\) | |||||||
\(128\) | 0.740894 | 0.0654864 | ||||||||
\(129\) | 0.818994 | 0.0721084 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.68221 | 0.758568 | 0.379284 | − | 0.925280i | \(-0.376170\pi\) | ||||
0.379284 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(132\) | −1.10628 | −0.0962896 | ||||||||
\(133\) | 6.19600 | 0.537262 | ||||||||
\(134\) | 0.296192 | 0.0255871 | ||||||||
\(135\) | 3.28432 | 0.282669 | ||||||||
\(136\) | −17.7427 | −1.52142 | ||||||||
\(137\) | 12.5774 | 1.07456 | 0.537278 | − | 0.843405i | \(-0.319453\pi\) | ||||
0.537278 | + | 0.843405i | \(0.319453\pi\) | |||||||
\(138\) | 3.74865 | 0.319106 | ||||||||
\(139\) | −10.7327 | −0.910335 | −0.455167 | − | 0.890406i | \(-0.650421\pi\) | ||||
−0.455167 | + | 0.890406i | \(0.650421\pi\) | |||||||
\(140\) | −2.57962 | −0.218017 | ||||||||
\(141\) | −3.35146 | −0.282244 | ||||||||
\(142\) | 10.2284 | 0.858347 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.81222 | −0.151019 | ||||||||
\(145\) | −28.1693 | −2.33934 | ||||||||
\(146\) | 13.3845 | 1.10771 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 4.39156 | 0.360984 | ||||||||
\(149\) | 11.4702 | 0.939673 | 0.469836 | − | 0.882754i | \(-0.344313\pi\) | ||||
0.469836 | + | 0.882754i | \(0.344313\pi\) | |||||||
\(150\) | 6.37742 | 0.520714 | ||||||||
\(151\) | −9.07431 | −0.738457 | −0.369228 | − | 0.929339i | \(-0.620378\pi\) | ||||
−0.369228 | + | 0.929339i | \(0.620378\pi\) | |||||||
\(152\) | −19.0202 | −1.54274 | ||||||||
\(153\) | 5.77983 | 0.467272 | ||||||||
\(154\) | 1.55227 | 0.125085 | ||||||||
\(155\) | −25.0962 | −2.01578 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8251 | −1.34279 | −0.671393 | − | 0.741101i | \(-0.734304\pi\) | ||||
−0.671393 | + | 0.741101i | \(0.734304\pi\) | |||||||
\(158\) | 6.61499 | 0.526260 | ||||||||
\(159\) | 5.54281 | 0.439573 | ||||||||
\(160\) | 13.6046 | 1.07554 | ||||||||
\(161\) | 3.40145 | 0.268072 | ||||||||
\(162\) | 1.10207 | 0.0865870 | ||||||||
\(163\) | 20.8336 | 1.63181 | 0.815905 | − | 0.578186i | \(-0.196239\pi\) | ||||
0.815905 | + | 0.578186i | \(0.196239\pi\) | |||||||
\(164\) | 0.906385 | 0.0707768 | ||||||||
\(165\) | 4.62595 | 0.360130 | ||||||||
\(166\) | 6.63640 | 0.515084 | ||||||||
\(167\) | 6.20927 | 0.480488 | 0.240244 | − | 0.970713i | \(-0.422773\pi\) | ||||
0.240244 | + | 0.970713i | \(0.422773\pi\) | |||||||
\(168\) | −3.06975 | −0.236837 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 20.9204 | 1.60452 | ||||||||
\(171\) | 6.19600 | 0.473820 | ||||||||
\(172\) | −0.643267 | −0.0490486 | ||||||||
\(173\) | −10.5498 | −0.802086 | −0.401043 | − | 0.916059i | \(-0.631352\pi\) | ||||
−0.401043 | + | 0.916059i | \(0.631352\pi\) | |||||||
\(174\) | −9.45240 | −0.716584 | ||||||||
\(175\) | 5.78675 | 0.437437 | ||||||||
\(176\) | −2.55251 | −0.192403 | ||||||||
\(177\) | −4.88973 | −0.367534 | ||||||||
\(178\) | −18.2705 | −1.36944 | ||||||||
\(179\) | −21.0058 | −1.57005 | −0.785025 | − | 0.619465i | \(-0.787350\pi\) | ||||
−0.785025 | + | 0.619465i | \(0.787350\pi\) | |||||||
\(180\) | −2.57962 | −0.192273 | ||||||||
\(181\) | −14.6306 | −1.08748 | −0.543741 | − | 0.839253i | \(-0.682993\pi\) | ||||
−0.543741 | + | 0.839253i | \(0.682993\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.97751 | −0.220104 | ||||||||
\(184\) | −10.4416 | −0.769766 | ||||||||
\(185\) | −18.3634 | −1.35011 | ||||||||
\(186\) | −8.42119 | −0.617472 | ||||||||
\(187\) | 8.14088 | 0.595320 | ||||||||
\(188\) | 2.63235 | 0.191984 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 22.4268 | 1.62701 | ||||||||
\(191\) | −5.22863 | −0.378330 | −0.189165 | − | 0.981945i | \(-0.560578\pi\) | ||||
−0.189165 | + | 0.981945i | \(0.560578\pi\) | |||||||
\(192\) | 8.18957 | 0.591031 | ||||||||
\(193\) | 23.7024 | 1.70614 | 0.853069 | − | 0.521798i | \(-0.174739\pi\) | ||||
0.853069 | + | 0.521798i | \(0.174739\pi\) | |||||||
\(194\) | 20.6475 | 1.48241 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.785435 | −0.0561025 | ||||||||
\(197\) | −15.6200 | −1.11288 | −0.556439 | − | 0.830889i | \(-0.687833\pi\) | ||||
−0.556439 | + | 0.830889i | \(0.687833\pi\) | |||||||
\(198\) | 1.55227 | 0.110315 | ||||||||
\(199\) | −20.8348 | −1.47694 | −0.738468 | − | 0.674288i | \(-0.764450\pi\) | ||||
−0.738468 | + | 0.674288i | \(0.764450\pi\) | |||||||
\(200\) | −17.7639 | −1.25610 | ||||||||
\(201\) | 0.268759 | 0.0189568 | ||||||||
\(202\) | 16.5880 | 1.16713 | ||||||||
\(203\) | −8.57692 | −0.601982 | ||||||||
\(204\) | −4.53968 | −0.317841 | ||||||||
\(205\) | −3.79007 | −0.264710 | ||||||||
\(206\) | −15.5131 | −1.08085 | ||||||||
\(207\) | 3.40145 | 0.236417 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.72705 | 0.603663 | ||||||||
\(210\) | 3.61956 | 0.249773 | ||||||||
\(211\) | −8.96355 | −0.617076 | −0.308538 | − | 0.951212i | \(-0.599840\pi\) | ||||
−0.308538 | + | 0.951212i | \(0.599840\pi\) | |||||||
\(212\) | −4.35351 | −0.299001 | ||||||||
\(213\) | 9.28104 | 0.635926 | ||||||||
\(214\) | 8.09680 | 0.553486 | ||||||||
\(215\) | 2.68984 | 0.183445 | ||||||||
\(216\) | −3.06975 | −0.208870 | ||||||||
\(217\) | −7.64123 | −0.518720 | ||||||||
\(218\) | −5.13149 | −0.347548 | ||||||||
\(219\) | 12.1448 | 0.820670 | ||||||||
\(220\) | −3.63339 | −0.244963 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.16196 | −0.413564 | ||||||||
\(223\) | 3.42664 | 0.229465 | 0.114732 | − | 0.993396i | \(-0.463399\pi\) | ||||
0.114732 | + | 0.993396i | \(0.463399\pi\) | |||||||
\(224\) | 4.14230 | 0.276769 | ||||||||
\(225\) | 5.78675 | 0.385783 | ||||||||
\(226\) | 7.90346 | 0.525730 | ||||||||
\(227\) | 22.6121 | 1.50082 | 0.750408 | − | 0.660975i | \(-0.229857\pi\) | ||||
0.750408 | + | 0.660975i | \(0.229857\pi\) | |||||||
\(228\) | −4.86656 | −0.322296 | ||||||||
\(229\) | −14.0168 | −0.926253 | −0.463126 | − | 0.886292i | \(-0.653272\pi\) | ||||
−0.463126 | + | 0.886292i | \(0.653272\pi\) | |||||||
\(230\) | 12.3117 | 0.811813 | ||||||||
\(231\) | 1.40850 | 0.0926723 | ||||||||
\(232\) | 26.3290 | 1.72859 | ||||||||
\(233\) | 12.1663 | 0.797043 | 0.398522 | − | 0.917159i | \(-0.369523\pi\) | ||||
0.398522 | + | 0.917159i | \(0.369523\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0073 | −0.718034 | ||||||||
\(236\) | 3.84056 | 0.249999 | ||||||||
\(237\) | 6.00232 | 0.389892 | ||||||||
\(238\) | 6.36980 | 0.412893 | ||||||||
\(239\) | −9.34457 | −0.604450 | −0.302225 | − | 0.953237i | \(-0.597729\pi\) | ||||
−0.302225 | + | 0.953237i | \(0.597729\pi\) | |||||||
\(240\) | −5.95192 | −0.384194 | ||||||||
\(241\) | −21.2740 | −1.37038 | −0.685190 | − | 0.728364i | \(-0.740281\pi\) | ||||
−0.685190 | + | 0.728364i | \(0.740281\pi\) | |||||||
\(242\) | −9.93644 | −0.638739 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.33864 | 0.149716 | ||||||||
\(245\) | 3.28432 | 0.209827 | ||||||||
\(246\) | −1.27178 | −0.0810859 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 23.4567 | 1.48950 | ||||||||
\(249\) | 6.02174 | 0.381612 | ||||||||
\(250\) | 2.84767 | 0.180103 | ||||||||
\(251\) | 0.690735 | 0.0435988 | 0.0217994 | − | 0.999762i | \(-0.493060\pi\) | ||||
0.0217994 | + | 0.999762i | \(0.493060\pi\) | |||||||
\(252\) | −0.785435 | −0.0494777 | ||||||||
\(253\) | 4.79093 | 0.301203 | ||||||||
\(254\) | −12.8501 | −0.806287 | ||||||||
\(255\) | 18.9828 | 1.18875 | ||||||||
\(256\) | −15.5626 | −0.972663 | ||||||||
\(257\) | −23.3399 | −1.45590 | −0.727952 | − | 0.685629i | \(-0.759527\pi\) | ||||
−0.727952 | + | 0.685629i | \(0.759527\pi\) | |||||||
\(258\) | 0.902592 | 0.0561929 | ||||||||
\(259\) | −5.59124 | −0.347423 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.57692 | −0.530898 | ||||||||
\(262\) | 9.56843 | 0.591140 | ||||||||
\(263\) | −9.11003 | −0.561748 | −0.280874 | − | 0.959745i | \(-0.590624\pi\) | ||||
−0.280874 | + | 0.959745i | \(0.590624\pi\) | |||||||
\(264\) | −4.32374 | −0.266108 | ||||||||
\(265\) | 18.2043 | 1.11828 | ||||||||
\(266\) | 6.82845 | 0.418679 | ||||||||
\(267\) | −16.5783 | −1.01458 | ||||||||
\(268\) | −0.211092 | −0.0128945 | ||||||||
\(269\) | 4.40754 | 0.268733 | 0.134366 | − | 0.990932i | \(-0.457100\pi\) | ||||
0.134366 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(270\) | 3.61956 | 0.220279 | ||||||||
\(271\) | −13.3892 | −0.813339 | −0.406669 | − | 0.913575i | \(-0.633310\pi\) | ||||
−0.406669 | + | 0.913575i | \(0.633310\pi\) | |||||||
\(272\) | −10.4743 | −0.635100 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.8612 | 0.837383 | ||||||||
\(275\) | 8.15062 | 0.491501 | ||||||||
\(276\) | −2.67162 | −0.160812 | ||||||||
\(277\) | 8.68968 | 0.522112 | 0.261056 | − | 0.965324i | \(-0.415929\pi\) | ||||
0.261056 | + | 0.965324i | \(0.415929\pi\) | |||||||
\(278\) | −11.8282 | −0.709409 | ||||||||
\(279\) | −7.64123 | −0.457468 | ||||||||
\(280\) | −10.0820 | −0.602517 | ||||||||
\(281\) | 21.7228 | 1.29587 | 0.647936 | − | 0.761695i | \(-0.275632\pi\) | ||||
0.647936 | + | 0.761695i | \(0.275632\pi\) | |||||||
\(282\) | −3.69355 | −0.219948 | ||||||||
\(283\) | 25.3757 | 1.50843 | 0.754215 | − | 0.656628i | \(-0.228018\pi\) | ||||
0.754215 | + | 0.656628i | \(0.228018\pi\) | |||||||
\(284\) | −7.28965 | −0.432561 | ||||||||
\(285\) | 20.3496 | 1.20541 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.15399 | −0.0681179 | ||||||||
\(288\) | 4.14230 | 0.244088 | ||||||||
\(289\) | 16.4064 | 0.965085 | ||||||||
\(290\) | −31.0447 | −1.82301 | ||||||||
\(291\) | 18.7352 | 1.09827 | ||||||||
\(292\) | −9.53896 | −0.558225 | ||||||||
\(293\) | −26.5450 | −1.55077 | −0.775387 | − | 0.631486i | \(-0.782445\pi\) | ||||
−0.775387 | + | 0.631486i | \(0.782445\pi\) | |||||||
\(294\) | 1.10207 | 0.0642742 | ||||||||
\(295\) | −16.0594 | −0.935016 | ||||||||
\(296\) | 17.1637 | 0.997622 | ||||||||
\(297\) | 1.40850 | 0.0817293 | ||||||||
\(298\) | 12.6410 | 0.732271 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.54511 | −0.262412 | ||||||||
\(301\) | 0.818994 | 0.0472060 | ||||||||
\(302\) | −10.0006 | −0.575467 | ||||||||
\(303\) | 15.0516 | 0.864693 | ||||||||
\(304\) | −11.2285 | −0.644001 | ||||||||
\(305\) | −9.77909 | −0.559949 | ||||||||
\(306\) | 6.36980 | 0.364137 | ||||||||
\(307\) | −4.33093 | −0.247179 | −0.123590 | − | 0.992333i | \(-0.539441\pi\) | ||||
−0.123590 | + | 0.992333i | \(0.539441\pi\) | |||||||
\(308\) | −1.10628 | −0.0630363 | ||||||||
\(309\) | −14.0763 | −0.800771 | ||||||||
\(310\) | −27.6579 | −1.57086 | ||||||||
\(311\) | 14.9481 | 0.847629 | 0.423815 | − | 0.905749i | \(-0.360691\pi\) | ||||
0.423815 | + | 0.905749i | \(0.360691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.75971 | −0.495128 | −0.247564 | − | 0.968871i | \(-0.579630\pi\) | ||||
−0.247564 | + | 0.968871i | \(0.579630\pi\) | |||||||
\(314\) | −18.5424 | −1.04641 | ||||||||
\(315\) | 3.28432 | 0.185050 | ||||||||
\(316\) | −4.71443 | −0.265207 | ||||||||
\(317\) | −5.46319 | −0.306843 | −0.153422 | − | 0.988161i | \(-0.549029\pi\) | ||||
−0.153422 | + | 0.988161i | \(0.549029\pi\) | |||||||
\(318\) | 6.10858 | 0.342552 | ||||||||
\(319\) | −12.0806 | −0.676382 | ||||||||
\(320\) | 26.8971 | 1.50360 | ||||||||
\(321\) | 7.34688 | 0.410063 | ||||||||
\(322\) | 3.74865 | 0.208904 | ||||||||
\(323\) | 35.8118 | 1.99262 | ||||||||
\(324\) | −0.785435 | −0.0436353 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.9601 | 1.27164 | ||||||||
\(327\) | −4.65621 | −0.257489 | ||||||||
\(328\) | 3.54247 | 0.195600 | ||||||||
\(329\) | −3.35146 | −0.184772 | ||||||||
\(330\) | 5.09814 | 0.280643 | ||||||||
\(331\) | 8.61829 | 0.473704 | 0.236852 | − | 0.971546i | \(-0.423884\pi\) | ||||
0.236852 | + | 0.971546i | \(0.423884\pi\) | |||||||
\(332\) | −4.72968 | −0.259575 | ||||||||
\(333\) | −5.59124 | −0.306398 | ||||||||
\(334\) | 6.84307 | 0.374436 | ||||||||
\(335\) | 0.882689 | 0.0482265 | ||||||||
\(336\) | −1.81222 | −0.0988648 | ||||||||
\(337\) | −13.6769 | −0.745029 | −0.372515 | − | 0.928026i | \(-0.621504\pi\) | ||||
−0.372515 | + | 0.928026i | \(0.621504\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.17145 | 0.389500 | ||||||||
\(340\) | −14.9098 | −0.808595 | ||||||||
\(341\) | −10.7626 | −0.582830 | ||||||||
\(342\) | 6.82845 | 0.369240 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.51411 | −0.135552 | ||||||||
\(345\) | 11.1714 | 0.601450 | ||||||||
\(346\) | −11.6266 | −0.625053 | ||||||||
\(347\) | −3.79558 | −0.203758 | −0.101879 | − | 0.994797i | \(-0.532485\pi\) | ||||
−0.101879 | + | 0.994797i | \(0.532485\pi\) | |||||||
\(348\) | 6.73661 | 0.361120 | ||||||||
\(349\) | 11.3725 | 0.608758 | 0.304379 | − | 0.952551i | \(-0.401551\pi\) | ||||
0.304379 | + | 0.952551i | \(0.401551\pi\) | |||||||
\(350\) | 6.37742 | 0.340887 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.83442 | 0.310976 | ||||||||
\(353\) | −17.5694 | −0.935126 | −0.467563 | − | 0.883960i | \(-0.654868\pi\) | ||||
−0.467563 | + | 0.883960i | \(0.654868\pi\) | |||||||
\(354\) | −5.38884 | −0.286414 | ||||||||
\(355\) | 30.4819 | 1.61781 | ||||||||
\(356\) | 13.0212 | 0.690123 | ||||||||
\(357\) | 5.77983 | 0.305901 | ||||||||
\(358\) | −23.1500 | −1.22351 | ||||||||
\(359\) | 5.89389 | 0.311068 | 0.155534 | − | 0.987831i | \(-0.450290\pi\) | ||||
0.155534 | + | 0.987831i | \(0.450290\pi\) | |||||||
\(360\) | −10.0820 | −0.531370 | ||||||||
\(361\) | 19.3905 | 1.02055 | ||||||||
\(362\) | −16.1240 | −0.847457 | ||||||||
\(363\) | −9.01613 | −0.473224 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.8874 | 2.08780 | ||||||||
\(366\) | −3.28143 | −0.171523 | ||||||||
\(367\) | 16.1849 | 0.844846 | 0.422423 | − | 0.906399i | \(-0.361180\pi\) | ||||
0.422423 | + | 0.906399i | \(0.361180\pi\) | |||||||
\(368\) | −6.16418 | −0.321330 | ||||||||
\(369\) | −1.15399 | −0.0600744 | ||||||||
\(370\) | −20.2378 | −1.05211 | ||||||||
\(371\) | 5.54281 | 0.287768 | ||||||||
\(372\) | 6.00169 | 0.311173 | ||||||||
\(373\) | −20.2446 | −1.04823 | −0.524113 | − | 0.851649i | \(-0.675603\pi\) | ||||
−0.524113 | + | 0.851649i | \(0.675603\pi\) | |||||||
\(374\) | 8.97184 | 0.463923 | ||||||||
\(375\) | 2.58392 | 0.133433 | ||||||||
\(376\) | 10.2882 | 0.530571 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.10207 | 0.0566845 | ||||||||
\(379\) | 16.3848 | 0.841629 | 0.420815 | − | 0.907147i | \(-0.361744\pi\) | ||||
0.420815 | + | 0.907147i | \(0.361744\pi\) | |||||||
\(380\) | −15.9833 | −0.819927 | ||||||||
\(381\) | −11.6599 | −0.597356 | ||||||||
\(382\) | −5.76233 | −0.294827 | ||||||||
\(383\) | −13.2965 | −0.679417 | −0.339708 | − | 0.940531i | \(-0.610328\pi\) | ||||
−0.339708 | + | 0.940531i | \(0.610328\pi\) | |||||||
\(384\) | 0.740894 | 0.0378086 | ||||||||
\(385\) | 4.62595 | 0.235760 | ||||||||
\(386\) | 26.1218 | 1.32956 | ||||||||
\(387\) | 0.818994 | 0.0416318 | ||||||||
\(388\) | −14.7152 | −0.747054 | ||||||||
\(389\) | −30.4724 | −1.54501 | −0.772506 | − | 0.635007i | \(-0.780997\pi\) | ||||
−0.772506 | + | 0.635007i | \(0.780997\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.6598 | 0.994239 | ||||||||
\(392\) | −3.06975 | −0.155046 | ||||||||
\(393\) | 8.68221 | 0.437960 | ||||||||
\(394\) | −17.2144 | −0.867247 | ||||||||
\(395\) | 19.7135 | 0.991894 | ||||||||
\(396\) | −1.10628 | −0.0555928 | ||||||||
\(397\) | 10.7849 | 0.541279 | 0.270640 | − | 0.962681i | \(-0.412765\pi\) | ||||
0.270640 | + | 0.962681i | \(0.412765\pi\) | |||||||
\(398\) | −22.9614 | −1.15095 | ||||||||
\(399\) | 6.19600 | 0.310188 | ||||||||
\(400\) | −10.4869 | −0.524344 | ||||||||
\(401\) | −16.4052 | −0.819236 | −0.409618 | − | 0.912257i | \(-0.634338\pi\) | ||||
−0.409618 | + | 0.912257i | \(0.634338\pi\) | |||||||
\(402\) | 0.296192 | 0.0147727 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −11.8221 | −0.588170 | ||||||||
\(405\) | 3.28432 | 0.163199 | ||||||||
\(406\) | −9.45240 | −0.469115 | ||||||||
\(407\) | −7.87525 | −0.390362 | ||||||||
\(408\) | −17.7427 | −0.878392 | ||||||||
\(409\) | −23.8898 | −1.18127 | −0.590636 | − | 0.806938i | \(-0.701123\pi\) | ||||
−0.590636 | + | 0.806938i | \(0.701123\pi\) | |||||||
\(410\) | −4.17694 | −0.206284 | ||||||||
\(411\) | 12.5774 | 0.620395 | ||||||||
\(412\) | 11.0560 | 0.544689 | ||||||||
\(413\) | −4.88973 | −0.240608 | ||||||||
\(414\) | 3.74865 | 0.184236 | ||||||||
\(415\) | 19.7773 | 0.970830 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.7327 | −0.525582 | ||||||||
\(418\) | 9.61785 | 0.470425 | ||||||||
\(419\) | −28.8315 | −1.40851 | −0.704256 | − | 0.709946i | \(-0.748719\pi\) | ||||
−0.704256 | + | 0.709946i | \(0.748719\pi\) | |||||||
\(420\) | −2.57962 | −0.125872 | ||||||||
\(421\) | 13.5391 | 0.659857 | 0.329929 | − | 0.944006i | \(-0.392975\pi\) | ||||
0.329929 | + | 0.944006i | \(0.392975\pi\) | |||||||
\(422\) | −9.87848 | −0.480877 | ||||||||
\(423\) | −3.35146 | −0.162954 | ||||||||
\(424\) | −17.0150 | −0.826324 | ||||||||
\(425\) | 33.4464 | 1.62239 | ||||||||
\(426\) | 10.2284 | 0.495567 | ||||||||
\(427\) | −2.97751 | −0.144092 | ||||||||
\(428\) | −5.77050 | −0.278927 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.96440 | 0.142956 | ||||||||
\(431\) | −22.3092 | −1.07460 | −0.537299 | − | 0.843392i | \(-0.680555\pi\) | ||||
−0.537299 | + | 0.843392i | \(0.680555\pi\) | |||||||
\(432\) | −1.81222 | −0.0871906 | ||||||||
\(433\) | −10.1459 | −0.487582 | −0.243791 | − | 0.969828i | \(-0.578391\pi\) | ||||
−0.243791 | + | 0.969828i | \(0.578391\pi\) | |||||||
\(434\) | −8.42119 | −0.404230 | ||||||||
\(435\) | −28.1693 | −1.35062 | ||||||||
\(436\) | 3.65715 | 0.175146 | ||||||||
\(437\) | 21.0754 | 1.00817 | ||||||||
\(438\) | 13.3845 | 0.639535 | ||||||||
\(439\) | −35.5140 | −1.69499 | −0.847494 | − | 0.530805i | \(-0.821890\pi\) | ||||
−0.847494 | + | 0.530805i | \(0.821890\pi\) | |||||||
\(440\) | −14.2005 | −0.676984 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.6235 | −1.21741 | −0.608705 | − | 0.793396i | \(-0.708311\pi\) | ||||
−0.608705 | + | 0.793396i | \(0.708311\pi\) | |||||||
\(444\) | 4.39156 | 0.208414 | ||||||||
\(445\) | −54.4486 | −2.58111 | ||||||||
\(446\) | 3.77640 | 0.178818 | ||||||||
\(447\) | 11.4702 | 0.542520 | ||||||||
\(448\) | 8.18957 | 0.386921 | ||||||||
\(449\) | −1.37936 | −0.0650961 | −0.0325481 | − | 0.999470i | \(-0.510362\pi\) | ||||
−0.0325481 | + | 0.999470i | \(0.510362\pi\) | |||||||
\(450\) | 6.37742 | 0.300634 | ||||||||
\(451\) | −1.62539 | −0.0765368 | ||||||||
\(452\) | −5.63271 | −0.264940 | ||||||||
\(453\) | −9.07431 | −0.426348 | ||||||||
\(454\) | 24.9202 | 1.16956 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −19.0202 | −0.890702 | ||||||||
\(457\) | 12.7945 | 0.598502 | 0.299251 | − | 0.954174i | \(-0.403263\pi\) | ||||
0.299251 | + | 0.954174i | \(0.403263\pi\) | |||||||
\(458\) | −15.4475 | −0.721814 | ||||||||
\(459\) | 5.77983 | 0.269779 | ||||||||
\(460\) | −8.77444 | −0.409110 | ||||||||
\(461\) | 4.27008 | 0.198877 | 0.0994386 | − | 0.995044i | \(-0.468295\pi\) | ||||
0.0994386 | + | 0.995044i | \(0.468295\pi\) | |||||||
\(462\) | 1.55227 | 0.0722180 | ||||||||
\(463\) | 0.637577 | 0.0296307 | 0.0148154 | − | 0.999890i | \(-0.495284\pi\) | ||||
0.0148154 | + | 0.999890i | \(0.495284\pi\) | |||||||
\(464\) | 15.5433 | 0.721579 | ||||||||
\(465\) | −25.0962 | −1.16381 | ||||||||
\(466\) | 13.4082 | 0.621123 | ||||||||
\(467\) | 10.3676 | 0.479754 | 0.239877 | − | 0.970803i | \(-0.422893\pi\) | ||||
0.239877 | + | 0.970803i | \(0.422893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.268759 | 0.0124101 | ||||||||
\(470\) | −12.1308 | −0.559552 | ||||||||
\(471\) | −16.8251 | −0.775258 | ||||||||
\(472\) | 15.0103 | 0.690903 | ||||||||
\(473\) | 1.15355 | 0.0530404 | ||||||||
\(474\) | 6.61499 | 0.303837 | ||||||||
\(475\) | 35.8547 | 1.64513 | ||||||||
\(476\) | −4.53968 | −0.208076 | ||||||||
\(477\) | 5.54281 | 0.253788 | ||||||||
\(478\) | −10.2984 | −0.471038 | ||||||||
\(479\) | 25.5435 | 1.16711 | 0.583555 | − | 0.812073i | \(-0.301661\pi\) | ||||
0.583555 | + | 0.812073i | \(0.301661\pi\) | |||||||
\(480\) | 13.6046 | 0.620964 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −23.4455 | −1.06792 | ||||||||
\(483\) | 3.40145 | 0.154771 | ||||||||
\(484\) | 7.08159 | 0.321890 | ||||||||
\(485\) | 61.5322 | 2.79403 | ||||||||
\(486\) | 1.10207 | 0.0499911 | ||||||||
\(487\) | −12.8011 | −0.580074 | −0.290037 | − | 0.957015i | \(-0.593668\pi\) | ||||
−0.290037 | + | 0.957015i | \(0.593668\pi\) | |||||||
\(488\) | 9.14022 | 0.413758 | ||||||||
\(489\) | 20.8336 | 0.942126 | ||||||||
\(490\) | 3.61956 | 0.163515 | ||||||||
\(491\) | −6.83325 | −0.308380 | −0.154190 | − | 0.988041i | \(-0.549277\pi\) | ||||
−0.154190 | + | 0.988041i | \(0.549277\pi\) | |||||||
\(492\) | 0.906385 | 0.0408630 | ||||||||
\(493\) | −49.5732 | −2.23266 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.62595 | 0.207921 | ||||||||
\(496\) | 13.8476 | 0.621776 | ||||||||
\(497\) | 9.28104 | 0.416312 | ||||||||
\(498\) | 6.63640 | 0.297384 | ||||||||
\(499\) | 29.8319 | 1.33546 | 0.667729 | − | 0.744405i | \(-0.267267\pi\) | ||||
0.667729 | + | 0.744405i | \(0.267267\pi\) | |||||||
\(500\) | −2.02950 | −0.0907621 | ||||||||
\(501\) | 6.20927 | 0.277410 | ||||||||
\(502\) | 0.761241 | 0.0339758 | ||||||||
\(503\) | 19.5429 | 0.871376 | 0.435688 | − | 0.900098i | \(-0.356505\pi\) | ||||
0.435688 | + | 0.900098i | \(0.356505\pi\) | |||||||
\(504\) | −3.06975 | −0.136738 | ||||||||
\(505\) | 49.4343 | 2.19980 | ||||||||
\(506\) | 5.27996 | 0.234723 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.15811 | 0.406326 | ||||||||
\(509\) | −2.35518 | −0.104392 | −0.0521958 | − | 0.998637i | \(-0.516622\pi\) | ||||
−0.0521958 | + | 0.998637i | \(0.516622\pi\) | |||||||
\(510\) | 20.9204 | 0.926372 | ||||||||
\(511\) | 12.1448 | 0.537255 | ||||||||
\(512\) | −18.6329 | −0.823467 | ||||||||
\(513\) | 6.19600 | 0.273560 | ||||||||
\(514\) | −25.7223 | −1.13456 | ||||||||
\(515\) | −46.2309 | −2.03718 | ||||||||
\(516\) | −0.643267 | −0.0283182 | ||||||||
\(517\) | −4.72052 | −0.207608 | ||||||||
\(518\) | −6.16196 | −0.270741 | ||||||||
\(519\) | −10.5498 | −0.463085 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.5527 | 1.20711 | 0.603553 | − | 0.797323i | \(-0.293751\pi\) | ||||
0.603553 | + | 0.797323i | \(0.293751\pi\) | |||||||
\(522\) | −9.45240 | −0.413720 | ||||||||
\(523\) | 26.0767 | 1.14025 | 0.570127 | − | 0.821557i | \(-0.306894\pi\) | ||||
0.570127 | + | 0.821557i | \(0.306894\pi\) | |||||||
\(524\) | −6.81931 | −0.297903 | ||||||||
\(525\) | 5.78675 | 0.252554 | ||||||||
\(526\) | −10.0399 | −0.437761 | ||||||||
\(527\) | −44.1650 | −1.92386 | ||||||||
\(528\) | −2.55251 | −0.111084 | ||||||||
\(529\) | −11.4301 | −0.496963 | ||||||||
\(530\) | 20.0625 | 0.871460 | ||||||||
\(531\) | −4.88973 | −0.212196 | ||||||||
\(532\) | −4.86656 | −0.210992 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18.2705 | −0.790644 | ||||||||
\(535\) | 24.1295 | 1.04321 | ||||||||
\(536\) | −0.825023 | −0.0356356 | ||||||||
\(537\) | −21.0058 | −0.906468 | ||||||||
\(538\) | 4.85744 | 0.209419 | ||||||||
\(539\) | 1.40850 | 0.0606683 | ||||||||
\(540\) | −2.57962 | −0.111009 | ||||||||
\(541\) | −8.83112 | −0.379679 | −0.189840 | − | 0.981815i | \(-0.560797\pi\) | ||||
−0.189840 | + | 0.981815i | \(0.560797\pi\) | |||||||
\(542\) | −14.7559 | −0.633821 | ||||||||
\(543\) | −14.6306 | −0.627858 | ||||||||
\(544\) | 23.9418 | 1.02650 | ||||||||
\(545\) | −15.2925 | −0.655058 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.61127 | 0.410948 | 0.205474 | − | 0.978663i | \(-0.434126\pi\) | ||||
0.205474 | + | 0.978663i | \(0.434126\pi\) | |||||||
\(548\) | −9.87869 | −0.421997 | ||||||||
\(549\) | −2.97751 | −0.127077 | ||||||||
\(550\) | 8.98258 | 0.383018 | ||||||||
\(551\) | −53.1426 | −2.26395 | ||||||||
\(552\) | −10.4416 | −0.444424 | ||||||||
\(553\) | 6.00232 | 0.255244 | ||||||||
\(554\) | 9.57666 | 0.406873 | ||||||||
\(555\) | −18.3634 | −0.779484 | ||||||||
\(556\) | 8.42982 | 0.357504 | ||||||||
\(557\) | −29.2549 | −1.23957 | −0.619786 | − | 0.784771i | \(-0.712780\pi\) | ||||
−0.619786 | + | 0.784771i | \(0.712780\pi\) | |||||||
\(558\) | −8.42119 | −0.356497 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5.95192 | −0.251514 | ||||||||
\(561\) | 8.14088 | 0.343708 | ||||||||
\(562\) | 23.9401 | 1.00985 | ||||||||
\(563\) | −4.57916 | −0.192989 | −0.0964943 | − | 0.995334i | \(-0.530763\pi\) | ||||
−0.0964943 | + | 0.995334i | \(0.530763\pi\) | |||||||
\(564\) | 2.63235 | 0.110842 | ||||||||
\(565\) | 23.5533 | 0.990896 | ||||||||
\(566\) | 27.9659 | 1.17549 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −28.4905 | −1.19543 | ||||||||
\(569\) | −40.8223 | −1.71136 | −0.855681 | − | 0.517504i | \(-0.826861\pi\) | ||||
−0.855681 | + | 0.517504i | \(0.826861\pi\) | |||||||
\(570\) | 22.4268 | 0.939355 | ||||||||
\(571\) | 19.6348 | 0.821692 | 0.410846 | − | 0.911705i | \(-0.365233\pi\) | ||||
0.410846 | + | 0.911705i | \(0.365233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.22863 | −0.218429 | ||||||||
\(574\) | −1.27178 | −0.0530832 | ||||||||
\(575\) | 19.6833 | 0.820851 | ||||||||
\(576\) | 8.18957 | 0.341232 | ||||||||
\(577\) | −35.5481 | −1.47989 | −0.739944 | − | 0.672669i | \(-0.765148\pi\) | ||||
−0.739944 | + | 0.672669i | \(0.765148\pi\) | |||||||
\(578\) | 18.0811 | 0.752074 | ||||||||
\(579\) | 23.7024 | 0.985039 | ||||||||
\(580\) | 22.1252 | 0.918698 | ||||||||
\(581\) | 6.02174 | 0.249824 | ||||||||
\(582\) | 20.6475 | 0.855867 | ||||||||
\(583\) | 7.80703 | 0.323334 | ||||||||
\(584\) | −37.2816 | −1.54272 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.2545 | −1.20849 | ||||||||
\(587\) | 38.0391 | 1.57004 | 0.785020 | − | 0.619470i | \(-0.212653\pi\) | ||||
0.785020 | + | 0.619470i | \(0.212653\pi\) | |||||||
\(588\) | −0.785435 | −0.0323908 | ||||||||
\(589\) | −47.3451 | −1.95082 | ||||||||
\(590\) | −17.6987 | −0.728642 | ||||||||
\(591\) | −15.6200 | −0.642520 | ||||||||
\(592\) | 10.1326 | 0.416446 | ||||||||
\(593\) | −26.2586 | −1.07831 | −0.539155 | − | 0.842207i | \(-0.681256\pi\) | ||||
−0.539155 | + | 0.842207i | \(0.681256\pi\) | |||||||
\(594\) | 1.55227 | 0.0636903 | ||||||||
\(595\) | 18.9828 | 0.778219 | ||||||||
\(596\) | −9.00907 | −0.369026 | ||||||||
\(597\) | −20.8348 | −0.852710 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.4404 | −0.508299 | −0.254150 | − | 0.967165i | \(-0.581796\pi\) | ||||
−0.254150 | + | 0.967165i | \(0.581796\pi\) | |||||||
\(600\) | −17.7639 | −0.725207 | ||||||||
\(601\) | 19.9741 | 0.814762 | 0.407381 | − | 0.913258i | \(-0.366442\pi\) | ||||
0.407381 | + | 0.913258i | \(0.366442\pi\) | |||||||
\(602\) | 0.902592 | 0.0367869 | ||||||||
\(603\) | 0.268759 | 0.0109447 | ||||||||
\(604\) | 7.12728 | 0.290005 | ||||||||
\(605\) | −29.6119 | −1.20389 | ||||||||
\(606\) | 16.5880 | 0.673841 | ||||||||
\(607\) | 27.3862 | 1.11157 | 0.555785 | − | 0.831326i | \(-0.312418\pi\) | ||||
0.555785 | + | 0.831326i | \(0.312418\pi\) | |||||||
\(608\) | 25.6657 | 1.04088 | ||||||||
\(609\) | −8.57692 | −0.347554 | ||||||||
\(610\) | −10.7773 | −0.436359 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.53968 | −0.183506 | ||||||||
\(613\) | −2.87689 | −0.116197 | −0.0580983 | − | 0.998311i | \(-0.518504\pi\) | ||||
−0.0580983 | + | 0.998311i | \(0.518504\pi\) | |||||||
\(614\) | −4.77300 | −0.192623 | ||||||||
\(615\) | −3.79007 | −0.152831 | ||||||||
\(616\) | −4.32374 | −0.174208 | ||||||||
\(617\) | −29.9248 | −1.20473 | −0.602364 | − | 0.798222i | \(-0.705774\pi\) | ||||
−0.602364 | + | 0.798222i | \(0.705774\pi\) | |||||||
\(618\) | −15.5131 | −0.624027 | ||||||||
\(619\) | −33.5695 | −1.34927 | −0.674637 | − | 0.738150i | \(-0.735700\pi\) | ||||
−0.674637 | + | 0.738150i | \(0.735700\pi\) | |||||||
\(620\) | 19.7114 | 0.791631 | ||||||||
\(621\) | 3.40145 | 0.136495 | ||||||||
\(622\) | 16.4739 | 0.660543 | ||||||||
\(623\) | −16.5783 | −0.664197 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.4473 | −0.817892 | ||||||||
\(626\) | −9.65385 | −0.385845 | ||||||||
\(627\) | 8.72705 | 0.348525 | ||||||||
\(628\) | 13.2150 | 0.527335 | ||||||||
\(629\) | −32.3164 | −1.28854 | ||||||||
\(630\) | 3.61956 | 0.144207 | ||||||||
\(631\) | −26.4413 | −1.05261 | −0.526306 | − | 0.850295i | \(-0.676423\pi\) | ||||
−0.526306 | + | 0.850295i | \(0.676423\pi\) | |||||||
\(632\) | −18.4256 | −0.732932 | ||||||||
\(633\) | −8.96355 | −0.356269 | ||||||||
\(634\) | −6.02083 | −0.239118 | ||||||||
\(635\) | −38.2949 | −1.51969 | ||||||||
\(636\) | −4.35351 | −0.172628 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.3137 | −0.527094 | ||||||||
\(639\) | 9.28104 | 0.367152 | ||||||||
\(640\) | 2.43333 | 0.0961859 | ||||||||
\(641\) | −24.8891 | −0.983059 | −0.491530 | − | 0.870861i | \(-0.663562\pi\) | ||||
−0.491530 | + | 0.870861i | \(0.663562\pi\) | |||||||
\(642\) | 8.09680 | 0.319555 | ||||||||
\(643\) | 39.2941 | 1.54961 | 0.774804 | − | 0.632201i | \(-0.217848\pi\) | ||||
0.774804 | + | 0.632201i | \(0.217848\pi\) | |||||||
\(644\) | −2.67162 | −0.105276 | ||||||||
\(645\) | 2.68984 | 0.105912 | ||||||||
\(646\) | 39.4673 | 1.55282 | ||||||||
\(647\) | −29.1771 | −1.14707 | −0.573534 | − | 0.819182i | \(-0.694428\pi\) | ||||
−0.573534 | + | 0.819182i | \(0.694428\pi\) | |||||||
\(648\) | −3.06975 | −0.120591 | ||||||||
\(649\) | −6.88717 | −0.270345 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.64123 | −0.299483 | ||||||||
\(652\) | −16.3634 | −0.640840 | ||||||||
\(653\) | −8.06661 | −0.315671 | −0.157835 | − | 0.987465i | \(-0.550452\pi\) | ||||
−0.157835 | + | 0.987465i | \(0.550452\pi\) | |||||||
\(654\) | −5.13149 | −0.200657 | ||||||||
\(655\) | 28.5151 | 1.11418 | ||||||||
\(656\) | 2.09129 | 0.0816511 | ||||||||
\(657\) | 12.1448 | 0.473814 | ||||||||
\(658\) | −3.69355 | −0.143990 | ||||||||
\(659\) | −39.1879 | −1.52654 | −0.763271 | − | 0.646078i | \(-0.776408\pi\) | ||||
−0.763271 | + | 0.646078i | \(0.776408\pi\) | |||||||
\(660\) | −3.63339 | −0.141429 | ||||||||
\(661\) | 24.7993 | 0.964583 | 0.482291 | − | 0.876011i | \(-0.339805\pi\) | ||||
0.482291 | + | 0.876011i | \(0.339805\pi\) | |||||||
\(662\) | 9.49798 | 0.369150 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.4853 | −0.717367 | ||||||||
\(665\) | 20.3496 | 0.789125 | ||||||||
\(666\) | −6.16196 | −0.238771 | ||||||||
\(667\) | −29.1740 | −1.12962 | ||||||||
\(668\) | −4.87698 | −0.188696 | ||||||||
\(669\) | 3.42664 | 0.132481 | ||||||||
\(670\) | 0.972788 | 0.0375821 | ||||||||
\(671\) | −4.19382 | −0.161900 | ||||||||
\(672\) | 4.14230 | 0.159793 | ||||||||
\(673\) | −28.0542 | −1.08141 | −0.540706 | − | 0.841212i | \(-0.681843\pi\) | ||||
−0.540706 | + | 0.841212i | \(0.681843\pi\) | |||||||
\(674\) | −15.0730 | −0.580589 | ||||||||
\(675\) | 5.78675 | 0.222732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.7868 | −0.683602 | −0.341801 | − | 0.939772i | \(-0.611037\pi\) | ||||
−0.341801 | + | 0.939772i | \(0.611037\pi\) | |||||||
\(678\) | 7.90346 | 0.303531 | ||||||||
\(679\) | 18.7352 | 0.718990 | ||||||||
\(680\) | −58.2725 | −2.23465 | ||||||||
\(681\) | 22.6121 | 0.866497 | ||||||||
\(682\) | −11.8612 | −0.454190 | ||||||||
\(683\) | 7.53488 | 0.288314 | 0.144157 | − | 0.989555i | \(-0.453953\pi\) | ||||
0.144157 | + | 0.989555i | \(0.453953\pi\) | |||||||
\(684\) | −4.86656 | −0.186077 | ||||||||
\(685\) | 41.3080 | 1.57830 | ||||||||
\(686\) | 1.10207 | 0.0420773 | ||||||||
\(687\) | −14.0168 | −0.534772 | ||||||||
\(688\) | −1.48420 | −0.0565846 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 12.3117 | 0.468700 | ||||||||
\(691\) | 47.2784 | 1.79856 | 0.899278 | − | 0.437377i | \(-0.144093\pi\) | ||||
0.899278 | + | 0.437377i | \(0.144093\pi\) | |||||||
\(692\) | 8.28618 | 0.314993 | ||||||||
\(693\) | 1.40850 | 0.0535044 | ||||||||
\(694\) | −4.18301 | −0.158785 | ||||||||
\(695\) | −35.2496 | −1.33709 | ||||||||
\(696\) | 26.3290 | 0.997999 | ||||||||
\(697\) | −6.66987 | −0.252639 | ||||||||
\(698\) | 12.5334 | 0.474395 | ||||||||
\(699\) | 12.1663 | 0.460173 | ||||||||
\(700\) | −4.54511 | −0.171789 | ||||||||
\(701\) | −5.95873 | −0.225058 | −0.112529 | − | 0.993648i | \(-0.535895\pi\) | ||||
−0.112529 | + | 0.993648i | \(0.535895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.6434 | −1.30660 | ||||||||
\(704\) | 11.5350 | 0.434741 | ||||||||
\(705\) | −11.0073 | −0.414557 | ||||||||
\(706\) | −19.3628 | −0.728728 | ||||||||
\(707\) | 15.0516 | 0.566074 | ||||||||
\(708\) | 3.84056 | 0.144337 | ||||||||
\(709\) | 46.4175 | 1.74325 | 0.871623 | − | 0.490176i | \(-0.163068\pi\) | ||||
0.871623 | + | 0.490176i | \(0.163068\pi\) | |||||||
\(710\) | 33.5933 | 1.26073 | ||||||||
\(711\) | 6.00232 | 0.225104 | ||||||||
\(712\) | 50.8914 | 1.90724 | ||||||||
\(713\) | −25.9912 | −0.973380 | ||||||||
\(714\) | 6.36980 | 0.238384 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.4987 | 0.616586 | ||||||||
\(717\) | −9.34457 | −0.348979 | ||||||||
\(718\) | 6.49550 | 0.242410 | ||||||||
\(719\) | 14.1409 | 0.527366 | 0.263683 | − | 0.964609i | \(-0.415063\pi\) | ||||
0.263683 | + | 0.964609i | \(0.415063\pi\) | |||||||
\(720\) | −5.95192 | −0.221815 | ||||||||
\(721\) | −14.0763 | −0.524228 | ||||||||
\(722\) | 21.3697 | 0.795298 | ||||||||
\(723\) | −21.2740 | −0.791190 | ||||||||
\(724\) | 11.4914 | 0.427073 | ||||||||
\(725\) | −49.6325 | −1.84330 | ||||||||
\(726\) | −9.93644 | −0.368776 | ||||||||
\(727\) | 25.8145 | 0.957405 | 0.478703 | − | 0.877977i | \(-0.341107\pi\) | ||||
0.478703 | + | 0.877977i | \(0.341107\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 43.9589 | 1.62699 | ||||||||
\(731\) | 4.73365 | 0.175080 | ||||||||
\(732\) | 2.33864 | 0.0864386 | ||||||||
\(733\) | −35.3926 | −1.30725 | −0.653627 | − | 0.756817i | \(-0.726753\pi\) | ||||
−0.653627 | + | 0.756817i | \(0.726753\pi\) | |||||||
\(734\) | 17.8370 | 0.658375 | ||||||||
\(735\) | 3.28432 | 0.121144 | ||||||||
\(736\) | 14.0898 | 0.519358 | ||||||||
\(737\) | 0.378546 | 0.0139439 | ||||||||
\(738\) | −1.27178 | −0.0468150 | ||||||||
\(739\) | −45.9352 | −1.68975 | −0.844877 | − | 0.534961i | \(-0.820326\pi\) | ||||
−0.844877 | + | 0.534961i | \(0.820326\pi\) | |||||||
\(740\) | 14.4233 | 0.530210 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.10858 | 0.224253 | ||||||||
\(743\) | −29.8763 | −1.09605 | −0.548027 | − | 0.836461i | \(-0.684621\pi\) | ||||
−0.548027 | + | 0.836461i | \(0.684621\pi\) | |||||||
\(744\) | 23.4567 | 0.859964 | ||||||||
\(745\) | 37.6717 | 1.38018 | ||||||||
\(746\) | −22.3110 | −0.816865 | ||||||||
\(747\) | 6.02174 | 0.220324 | ||||||||
\(748\) | −6.39413 | −0.233792 | ||||||||
\(749\) | 7.34688 | 0.268449 | ||||||||
\(750\) | 2.84767 | 0.103982 | ||||||||
\(751\) | 35.8225 | 1.30718 | 0.653591 | − | 0.756848i | \(-0.273262\pi\) | ||||
0.653591 | + | 0.756848i | \(0.273262\pi\) | |||||||
\(752\) | 6.07359 | 0.221481 | ||||||||
\(753\) | 0.690735 | 0.0251718 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.8029 | −1.08464 | ||||||||
\(756\) | −0.785435 | −0.0285660 | ||||||||
\(757\) | −30.6066 | −1.11242 | −0.556208 | − | 0.831043i | \(-0.687744\pi\) | ||||
−0.556208 | + | 0.831043i | \(0.687744\pi\) | |||||||
\(758\) | 18.0572 | 0.655868 | ||||||||
\(759\) | 4.79093 | 0.173900 | ||||||||
\(760\) | −62.4684 | −2.26597 | ||||||||
\(761\) | −8.73930 | −0.316799 | −0.158400 | − | 0.987375i | \(-0.550633\pi\) | ||||
−0.158400 | + | 0.987375i | \(0.550633\pi\) | |||||||
\(762\) | −12.8501 | −0.465510 | ||||||||
\(763\) | −4.65621 | −0.168566 | ||||||||
\(764\) | 4.10675 | 0.148577 | ||||||||
\(765\) | 18.9828 | 0.686325 | ||||||||
\(766\) | −14.6537 | −0.529458 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −15.5626 | −0.561567 | ||||||||
\(769\) | 27.4420 | 0.989584 | 0.494792 | − | 0.869011i | \(-0.335244\pi\) | ||||
0.494792 | + | 0.869011i | \(0.335244\pi\) | |||||||
\(770\) | 5.09814 | 0.183724 | ||||||||
\(771\) | −23.3399 | −0.840566 | ||||||||
\(772\) | −18.6167 | −0.670030 | ||||||||
\(773\) | 13.1167 | 0.471776 | 0.235888 | − | 0.971780i | \(-0.424200\pi\) | ||||
0.235888 | + | 0.971780i | \(0.424200\pi\) | |||||||
\(774\) | 0.902592 | 0.0324430 | ||||||||
\(775\) | −44.2178 | −1.58835 | ||||||||
\(776\) | −57.5123 | −2.06457 | ||||||||
\(777\) | −5.59124 | −0.200585 | ||||||||
\(778\) | −33.5828 | −1.20400 | ||||||||
\(779\) | −7.15013 | −0.256180 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.0723 | 0.467764 | ||||||||
\(782\) | 21.6665 | 0.774794 | ||||||||
\(783\) | −8.57692 | −0.306514 | ||||||||
\(784\) | −1.81222 | −0.0647222 | ||||||||
\(785\) | −55.2589 | −1.97227 | ||||||||
\(786\) | 9.56843 | 0.341295 | ||||||||
\(787\) | 26.5973 | 0.948091 | 0.474046 | − | 0.880500i | \(-0.342793\pi\) | ||||
0.474046 | + | 0.880500i | \(0.342793\pi\) | |||||||
\(788\) | 12.2685 | 0.437046 | ||||||||
\(789\) | −9.11003 | −0.324326 | ||||||||
\(790\) | 21.7257 | 0.772967 | ||||||||
\(791\) | 7.17145 | 0.254987 | ||||||||
\(792\) | −4.32374 | −0.153637 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.8858 | 0.421810 | ||||||||
\(795\) | 18.2043 | 0.645642 | ||||||||
\(796\) | 16.3643 | 0.580019 | ||||||||
\(797\) | 5.10413 | 0.180798 | 0.0903988 | − | 0.995906i | \(-0.471186\pi\) | ||||
0.0903988 | + | 0.995906i | \(0.471186\pi\) | |||||||
\(798\) | 6.82845 | 0.241724 | ||||||||
\(799\) | −19.3709 | −0.685292 | ||||||||
\(800\) | 23.9705 | 0.847484 | ||||||||
\(801\) | −16.5783 | −0.585767 | ||||||||
\(802\) | −18.0797 | −0.638417 | ||||||||
\(803\) | 17.1059 | 0.603655 | ||||||||
\(804\) | −0.211092 | −0.00744466 | ||||||||
\(805\) | 11.1714 | 0.393742 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.40754 | 0.155153 | ||||||||
\(808\) | −46.2048 | −1.62548 | ||||||||
\(809\) | 1.42220 | 0.0500019 | 0.0250010 | − | 0.999687i | \(-0.492041\pi\) | ||||
0.0250010 | + | 0.999687i | \(0.492041\pi\) | |||||||
\(810\) | 3.61956 | 0.127178 | ||||||||
\(811\) | −4.11149 | −0.144374 | −0.0721870 | − | 0.997391i | \(-0.522998\pi\) | ||||
−0.0721870 | + | 0.997391i | \(0.522998\pi\) | |||||||
\(812\) | 6.73661 | 0.236409 | ||||||||
\(813\) | −13.3892 | −0.469581 | ||||||||
\(814\) | −8.67910 | −0.304202 | ||||||||
\(815\) | 68.4240 | 2.39679 | ||||||||
\(816\) | −10.4743 | −0.366675 | ||||||||
\(817\) | 5.07449 | 0.177534 | ||||||||
\(818\) | −26.3283 | −0.920546 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.97686 | 0.103956 | ||||||||
\(821\) | −10.9773 | −0.383110 | −0.191555 | − | 0.981482i | \(-0.561353\pi\) | ||||
−0.191555 | + | 0.981482i | \(0.561353\pi\) | |||||||
\(822\) | 13.8612 | 0.483464 | ||||||||
\(823\) | 39.3152 | 1.37044 | 0.685221 | − | 0.728335i | \(-0.259706\pi\) | ||||
0.685221 | + | 0.728335i | \(0.259706\pi\) | |||||||
\(824\) | 43.2107 | 1.50531 | ||||||||
\(825\) | 8.15062 | 0.283768 | ||||||||
\(826\) | −5.38884 | −0.187502 | ||||||||
\(827\) | −20.7986 | −0.723238 | −0.361619 | − | 0.932326i | \(-0.617776\pi\) | ||||
−0.361619 | + | 0.932326i | \(0.617776\pi\) | |||||||
\(828\) | −2.67162 | −0.0928451 | ||||||||
\(829\) | −20.8735 | −0.724968 | −0.362484 | − | 0.931990i | \(-0.618071\pi\) | ||||
−0.362484 | + | 0.931990i | \(0.618071\pi\) | |||||||
\(830\) | 21.7960 | 0.756552 | ||||||||
\(831\) | 8.68968 | 0.301442 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.77983 | 0.200259 | ||||||||
\(834\) | −11.8282 | −0.409577 | ||||||||
\(835\) | 20.3932 | 0.705736 | ||||||||
\(836\) | −6.85453 | −0.237069 | ||||||||
\(837\) | −7.64123 | −0.264119 | ||||||||
\(838\) | −31.7744 | −1.09763 | ||||||||
\(839\) | −7.27089 | −0.251019 | −0.125509 | − | 0.992092i | \(-0.540057\pi\) | ||||
−0.125509 | + | 0.992092i | \(0.540057\pi\) | |||||||
\(840\) | −10.0820 | −0.347864 | ||||||||
\(841\) | 44.5636 | 1.53668 | ||||||||
\(842\) | 14.9211 | 0.514216 | ||||||||
\(843\) | 21.7228 | 0.748172 | ||||||||
\(844\) | 7.04028 | 0.242336 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.69355 | −0.126987 | ||||||||
\(847\) | −9.01613 | −0.309798 | ||||||||
\(848\) | −10.0448 | −0.344940 | ||||||||
\(849\) | 25.3757 | 0.870892 | ||||||||
\(850\) | 36.8604 | 1.26430 | ||||||||
\(851\) | −19.0183 | −0.651940 | ||||||||
\(852\) | −7.28965 | −0.249739 | ||||||||
\(853\) | 25.1125 | 0.859835 | 0.429917 | − | 0.902868i | \(-0.358543\pi\) | ||||
0.429917 | + | 0.902868i | \(0.358543\pi\) | |||||||
\(854\) | −3.28143 | −0.112288 | ||||||||
\(855\) | 20.3496 | 0.695943 | ||||||||
\(856\) | −22.5531 | −0.770849 | ||||||||
\(857\) | −16.3023 | −0.556875 | −0.278438 | − | 0.960454i | \(-0.589817\pi\) | ||||
−0.278438 | + | 0.960454i | \(0.589817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.6024 | −0.805303 | −0.402652 | − | 0.915353i | \(-0.631911\pi\) | ||||
−0.402652 | + | 0.915353i | \(0.631911\pi\) | |||||||
\(860\) | −2.11269 | −0.0720422 | ||||||||
\(861\) | −1.15399 | −0.0393279 | ||||||||
\(862\) | −24.5864 | −0.837417 | ||||||||
\(863\) | 6.17526 | 0.210208 | 0.105104 | − | 0.994461i | \(-0.466482\pi\) | ||||
0.105104 | + | 0.994461i | \(0.466482\pi\) | |||||||
\(864\) | 4.14230 | 0.140924 | ||||||||
\(865\) | −34.6489 | −1.17810 | ||||||||
\(866\) | −11.1816 | −0.379965 | ||||||||
\(867\) | 16.4064 | 0.557192 | ||||||||
\(868\) | 6.00169 | 0.203710 | ||||||||
\(869\) | 8.45425 | 0.286791 | ||||||||
\(870\) | −31.0447 | −1.05251 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.2934 | 0.484036 | ||||||||
\(873\) | 18.7352 | 0.634089 | ||||||||
\(874\) | 23.2266 | 0.785652 | ||||||||
\(875\) | 2.58392 | 0.0873525 | ||||||||
\(876\) | −9.53896 | −0.322292 | ||||||||
\(877\) | 6.53888 | 0.220802 | 0.110401 | − | 0.993887i | \(-0.464786\pi\) | ||||
0.110401 | + | 0.993887i | \(0.464786\pi\) | |||||||
\(878\) | −39.1390 | −1.32088 | ||||||||
\(879\) | −26.5450 | −0.895340 | ||||||||
\(880\) | −8.38326 | −0.282600 | ||||||||
\(881\) | −11.7551 | −0.396039 | −0.198019 | − | 0.980198i | \(-0.563451\pi\) | ||||
−0.198019 | + | 0.980198i | \(0.563451\pi\) | |||||||
\(882\) | 1.10207 | 0.0371087 | ||||||||
\(883\) | −33.9878 | −1.14378 | −0.571890 | − | 0.820330i | \(-0.693790\pi\) | ||||
−0.571890 | + | 0.820330i | \(0.693790\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0594 | −0.539832 | ||||||||
\(886\) | −28.2390 | −0.948708 | ||||||||
\(887\) | 11.4537 | 0.384577 | 0.192289 | − | 0.981338i | \(-0.438409\pi\) | ||||
0.192289 | + | 0.981338i | \(0.438409\pi\) | |||||||
\(888\) | 17.1637 | 0.575977 | ||||||||
\(889\) | −11.6599 | −0.391061 | ||||||||
\(890\) | −60.0063 | −2.01142 | ||||||||
\(891\) | 1.40850 | 0.0471864 | ||||||||
\(892\) | −2.69140 | −0.0901147 | ||||||||
\(893\) | −20.7657 | −0.694896 | ||||||||
\(894\) | 12.6410 | 0.422777 | ||||||||
\(895\) | −68.9898 | −2.30608 | ||||||||
\(896\) | 0.740894 | 0.0247515 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.52016 | −0.0507283 | ||||||||
\(899\) | 65.5382 | 2.18582 | ||||||||
\(900\) | −4.54511 | −0.151504 | ||||||||
\(901\) | 32.0365 | 1.06729 | ||||||||
\(902\) | −1.79130 | −0.0596439 | ||||||||
\(903\) | 0.818994 | 0.0272544 | ||||||||
\(904\) | −22.0146 | −0.732194 | ||||||||
\(905\) | −48.0515 | −1.59728 | ||||||||
\(906\) | −10.0006 | −0.332246 | ||||||||
\(907\) | 31.8705 | 1.05824 | 0.529121 | − | 0.848547i | \(-0.322522\pi\) | ||||
0.529121 | + | 0.848547i | \(0.322522\pi\) | |||||||
\(908\) | −17.7603 | −0.589397 | ||||||||
\(909\) | 15.0516 | 0.499231 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.2082 | 0.636395 | 0.318197 | − | 0.948024i | \(-0.396923\pi\) | ||||
0.318197 | + | 0.948024i | \(0.396923\pi\) | |||||||
\(912\) | −11.2285 | −0.371814 | ||||||||
\(913\) | 8.48161 | 0.280700 | ||||||||
\(914\) | 14.1005 | 0.466403 | ||||||||
\(915\) | −9.77909 | −0.323287 | ||||||||
\(916\) | 11.0092 | 0.363756 | ||||||||
\(917\) | 8.68221 | 0.286712 | ||||||||
\(918\) | 6.36980 | 0.210235 | ||||||||
\(919\) | 54.3884 | 1.79411 | 0.897053 | − | 0.441922i | \(-0.145703\pi\) | ||||
0.897053 | + | 0.441922i | \(0.145703\pi\) | |||||||
\(920\) | −34.2936 | −1.13063 | ||||||||
\(921\) | −4.33093 | −0.142709 | ||||||||
\(922\) | 4.70594 | 0.154982 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.10628 | −0.0363940 | ||||||||
\(925\) | −32.3551 | −1.06383 | ||||||||
\(926\) | 0.702656 | 0.0230907 | ||||||||
\(927\) | −14.0763 | −0.462325 | ||||||||
\(928\) | −35.5282 | −1.16627 | ||||||||
\(929\) | 46.5083 | 1.52589 | 0.762944 | − | 0.646465i | \(-0.223753\pi\) | ||||
0.762944 | + | 0.646465i | \(0.223753\pi\) | |||||||
\(930\) | −27.6579 | −0.906937 | ||||||||
\(931\) | 6.19600 | 0.203066 | ||||||||
\(932\) | −9.55587 | −0.313013 | ||||||||
\(933\) | 14.9481 | 0.489379 | ||||||||
\(934\) | 11.4258 | 0.373864 | ||||||||
\(935\) | 26.7372 | 0.874401 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.6775 | 1.13286 | 0.566432 | − | 0.824108i | \(-0.308323\pi\) | ||||
0.566432 | + | 0.824108i | \(0.308323\pi\) | |||||||
\(938\) | 0.296192 | 0.00967101 | ||||||||
\(939\) | −8.75971 | −0.285862 | ||||||||
\(940\) | 8.64549 | 0.281985 | ||||||||
\(941\) | 39.8173 | 1.29801 | 0.649004 | − | 0.760785i | \(-0.275186\pi\) | ||||
0.649004 | + | 0.760785i | \(0.275186\pi\) | |||||||
\(942\) | −18.5424 | −0.604146 | ||||||||
\(943\) | −3.92524 | −0.127824 | ||||||||
\(944\) | 8.86128 | 0.288410 | ||||||||
\(945\) | 3.28432 | 0.106839 | ||||||||
\(946\) | 1.27130 | 0.0413335 | ||||||||
\(947\) | 30.3825 | 0.987300 | 0.493650 | − | 0.869661i | \(-0.335662\pi\) | ||||
0.493650 | + | 0.869661i | \(0.335662\pi\) | |||||||
\(948\) | −4.71443 | −0.153117 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 39.5145 | 1.28202 | ||||||||
\(951\) | −5.46319 | −0.177156 | ||||||||
\(952\) | −17.7427 | −0.575043 | ||||||||
\(953\) | −2.44213 | −0.0791084 | −0.0395542 | − | 0.999217i | \(-0.512594\pi\) | ||||
−0.0395542 | + | 0.999217i | \(0.512594\pi\) | |||||||
\(954\) | 6.10858 | 0.197773 | ||||||||
\(955\) | −17.1725 | −0.555688 | ||||||||
\(956\) | 7.33955 | 0.237378 | ||||||||
\(957\) | −12.0806 | −0.390510 | ||||||||
\(958\) | 28.1508 | 0.909510 | ||||||||
\(959\) | 12.5774 | 0.406144 | ||||||||
\(960\) | 26.8971 | 0.868102 | ||||||||
\(961\) | 27.3884 | 0.883495 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.34688 | 0.236750 | ||||||||
\(964\) | 16.7094 | 0.538172 | ||||||||
\(965\) | 77.8463 | 2.50596 | ||||||||
\(966\) | 3.74865 | 0.120611 | ||||||||
\(967\) | 45.3725 | 1.45908 | 0.729541 | − | 0.683938i | \(-0.239734\pi\) | ||||
0.729541 | + | 0.683938i | \(0.239734\pi\) | |||||||
\(968\) | 27.6773 | 0.889582 | ||||||||
\(969\) | 35.8118 | 1.15044 | ||||||||
\(970\) | 67.8130 | 2.17734 | ||||||||
\(971\) | 31.9137 | 1.02416 | 0.512079 | − | 0.858938i | \(-0.328875\pi\) | ||||
0.512079 | + | 0.858938i | \(0.328875\pi\) | |||||||
\(972\) | −0.785435 | −0.0251928 | ||||||||
\(973\) | −10.7327 | −0.344074 | ||||||||
\(974\) | −14.1078 | −0.452042 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.39591 | 0.172719 | ||||||||
\(977\) | −4.99280 | −0.159734 | −0.0798669 | − | 0.996806i | \(-0.525450\pi\) | ||||
−0.0798669 | + | 0.996806i | \(0.525450\pi\) | |||||||
\(978\) | 22.9601 | 0.734183 | ||||||||
\(979\) | −23.3506 | −0.746287 | ||||||||
\(980\) | −2.57962 | −0.0824029 | ||||||||
\(981\) | −4.65621 | −0.148661 | ||||||||
\(982\) | −7.53074 | −0.240316 | ||||||||
\(983\) | −18.7912 | −0.599345 | −0.299672 | − | 0.954042i | \(-0.596877\pi\) | ||||
−0.299672 | + | 0.954042i | \(0.596877\pi\) | |||||||
\(984\) | 3.54247 | 0.112930 | ||||||||
\(985\) | −51.3010 | −1.63458 | ||||||||
\(986\) | −54.6332 | −1.73988 | ||||||||
\(987\) | −3.35146 | −0.106678 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.78577 | 0.0885823 | ||||||||
\(990\) | 5.09814 | 0.162030 | ||||||||
\(991\) | 41.3604 | 1.31386 | 0.656929 | − | 0.753953i | \(-0.271855\pi\) | ||||
0.656929 | + | 0.753953i | \(0.271855\pi\) | |||||||
\(992\) | −31.6523 | −1.00496 | ||||||||
\(993\) | 8.61829 | 0.273493 | ||||||||
\(994\) | 10.2284 | 0.324425 | ||||||||
\(995\) | −68.4279 | −2.16931 | ||||||||
\(996\) | −4.72968 | −0.149866 | ||||||||
\(997\) | 12.2118 | 0.386753 | 0.193376 | − | 0.981125i | \(-0.438056\pi\) | ||||
0.193376 | + | 0.981125i | \(0.438056\pi\) | |||||||
\(998\) | 32.8769 | 1.04070 | ||||||||
\(999\) | −5.59124 | −0.176899 |
(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 | 3549.2.a.bd.1.6 | 8 | ||
13.2 | odd | 12 | 273.2.bd.a.43.6 | ✓ | 16 | ||
13.7 | odd | 12 | 273.2.bd.a.127.6 | yes | 16 | ||
13.12 | even | 2 | 3549.2.a.bb.1.3 | 8 | |||
39.2 | even | 12 | 819.2.ct.b.316.3 | 16 | |||
39.20 | even | 12 | 819.2.ct.b.127.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bd.a.43.6 | ✓ | 16 | 13.2 | odd | 12 | ||
273.2.bd.a.127.6 | yes | 16 | 13.7 | odd | 12 | ||
819.2.ct.b.127.3 | 16 | 39.20 | even | 12 | |||
819.2.ct.b.316.3 | 16 | 39.2 | even | 12 | |||
3549.2.a.bb.1.3 | 8 | 13.12 | even | 2 | |||
3549.2.a.bd.1.6 | 8 | 1.1 | even | 1 | trivial |