Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(1\) |
Dimension: | \(142\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15511 | −1.52389 | −0.761946 | − | 0.647641i | \(-0.775756\pi\) | ||||
−0.761946 | + | 0.647641i | \(0.775756\pi\) | |||||||
\(3\) | 1.98414 | 1.14555 | 0.572773 | − | 0.819714i | \(-0.305868\pi\) | ||||
0.572773 | + | 0.819714i | \(0.305868\pi\) | |||||||
\(4\) | 2.64449 | 1.32225 | ||||||||
\(5\) | −3.20612 | −1.43382 | −0.716910 | − | 0.697166i | \(-0.754444\pi\) | ||||
−0.716910 | + | 0.697166i | \(0.754444\pi\) | |||||||
\(6\) | −4.27605 | −1.74569 | ||||||||
\(7\) | 1.44494 | 0.546136 | 0.273068 | − | 0.961995i | \(-0.411962\pi\) | ||||
0.273068 | + | 0.961995i | \(0.411962\pi\) | |||||||
\(8\) | −1.38895 | −0.491069 | ||||||||
\(9\) | 0.936828 | 0.312276 | ||||||||
\(10\) | 6.90953 | 2.18499 | ||||||||
\(11\) | −1.78531 | −0.538293 | −0.269146 | − | 0.963099i | \(-0.586742\pi\) | ||||
−0.269146 | + | 0.963099i | \(0.586742\pi\) | |||||||
\(12\) | 5.24706 | 1.51469 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −3.11400 | −0.832252 | ||||||||
\(15\) | −6.36140 | −1.64251 | ||||||||
\(16\) | −2.29564 | −0.573911 | ||||||||
\(17\) | −1.06140 | −0.257427 | −0.128714 | − | 0.991682i | \(-0.541085\pi\) | ||||
−0.128714 | + | 0.991682i | \(0.541085\pi\) | |||||||
\(18\) | −2.01897 | −0.475875 | ||||||||
\(19\) | 0.795328 | 0.182461 | 0.0912303 | − | 0.995830i | \(-0.470920\pi\) | ||||
0.0912303 | + | 0.995830i | \(0.470920\pi\) | |||||||
\(20\) | −8.47856 | −1.89586 | ||||||||
\(21\) | 2.86697 | 0.625624 | ||||||||
\(22\) | 3.84755 | 0.820300 | ||||||||
\(23\) | 2.00280 | 0.417614 | 0.208807 | − | 0.977957i | \(-0.433042\pi\) | ||||
0.208807 | + | 0.977957i | \(0.433042\pi\) | |||||||
\(24\) | −2.75588 | −0.562542 | ||||||||
\(25\) | 5.27920 | 1.05584 | ||||||||
\(26\) | −2.15511 | −0.422652 | ||||||||
\(27\) | −4.09363 | −0.787819 | ||||||||
\(28\) | 3.82113 | 0.722126 | ||||||||
\(29\) | −6.27710 | −1.16563 | −0.582814 | − | 0.812605i | \(-0.698049\pi\) | ||||
−0.582814 | + | 0.812605i | \(0.698049\pi\) | |||||||
\(30\) | 13.7095 | 2.50300 | ||||||||
\(31\) | 10.4068 | 1.86912 | 0.934561 | − | 0.355803i | \(-0.115792\pi\) | ||||
0.934561 | + | 0.355803i | \(0.115792\pi\) | |||||||
\(32\) | 7.72526 | 1.36565 | ||||||||
\(33\) | −3.54232 | −0.616639 | ||||||||
\(34\) | 2.28743 | 0.392291 | ||||||||
\(35\) | −4.63265 | −0.783060 | ||||||||
\(36\) | 2.47744 | 0.412906 | ||||||||
\(37\) | −3.52102 | −0.578852 | −0.289426 | − | 0.957200i | \(-0.593464\pi\) | ||||
−0.289426 | + | 0.957200i | \(0.593464\pi\) | |||||||
\(38\) | −1.71402 | −0.278050 | ||||||||
\(39\) | 1.98414 | 0.317717 | ||||||||
\(40\) | 4.45315 | 0.704104 | ||||||||
\(41\) | −7.24903 | −1.13211 | −0.566054 | − | 0.824368i | \(-0.691531\pi\) | ||||
−0.566054 | + | 0.824368i | \(0.691531\pi\) | |||||||
\(42\) | −6.17863 | −0.953383 | ||||||||
\(43\) | 10.4078 | 1.58717 | 0.793587 | − | 0.608457i | \(-0.208211\pi\) | ||||
0.793587 | + | 0.608457i | \(0.208211\pi\) | |||||||
\(44\) | −4.72125 | −0.711756 | ||||||||
\(45\) | −3.00358 | −0.447748 | ||||||||
\(46\) | −4.31626 | −0.636398 | ||||||||
\(47\) | 6.99850 | 1.02084 | 0.510418 | − | 0.859926i | \(-0.329491\pi\) | ||||
0.510418 | + | 0.859926i | \(0.329491\pi\) | |||||||
\(48\) | −4.55489 | −0.657441 | ||||||||
\(49\) | −4.91215 | −0.701736 | ||||||||
\(50\) | −11.3773 | −1.60899 | ||||||||
\(51\) | −2.10597 | −0.294895 | ||||||||
\(52\) | 2.64449 | 0.366725 | ||||||||
\(53\) | −6.32045 | −0.868181 | −0.434091 | − | 0.900869i | \(-0.642930\pi\) | ||||
−0.434091 | + | 0.900869i | \(0.642930\pi\) | |||||||
\(54\) | 8.82222 | 1.20055 | ||||||||
\(55\) | 5.72393 | 0.771815 | ||||||||
\(56\) | −2.00695 | −0.268190 | ||||||||
\(57\) | 1.57804 | 0.209017 | ||||||||
\(58\) | 13.5278 | 1.77629 | ||||||||
\(59\) | 1.77323 | 0.230855 | 0.115428 | − | 0.993316i | \(-0.463176\pi\) | ||||
0.115428 | + | 0.993316i | \(0.463176\pi\) | |||||||
\(60\) | −16.8227 | −2.17180 | ||||||||
\(61\) | 12.1182 | 1.55157 | 0.775787 | − | 0.630995i | \(-0.217353\pi\) | ||||
0.775787 | + | 0.630995i | \(0.217353\pi\) | |||||||
\(62\) | −22.4279 | −2.84834 | ||||||||
\(63\) | 1.35366 | 0.170545 | ||||||||
\(64\) | −12.0575 | −1.50719 | ||||||||
\(65\) | −3.20612 | −0.397670 | ||||||||
\(66\) | 7.63409 | 0.939691 | ||||||||
\(67\) | −4.99222 | −0.609897 | −0.304949 | − | 0.952369i | \(-0.598639\pi\) | ||||
−0.304949 | + | 0.952369i | \(0.598639\pi\) | |||||||
\(68\) | −2.80686 | −0.340382 | ||||||||
\(69\) | 3.97385 | 0.478396 | ||||||||
\(70\) | 9.98386 | 1.19330 | ||||||||
\(71\) | 7.36867 | 0.874500 | 0.437250 | − | 0.899340i | \(-0.355953\pi\) | ||||
0.437250 | + | 0.899340i | \(0.355953\pi\) | |||||||
\(72\) | −1.30121 | −0.153349 | ||||||||
\(73\) | 15.3578 | 1.79749 | 0.898747 | − | 0.438467i | \(-0.144478\pi\) | ||||
0.898747 | + | 0.438467i | \(0.144478\pi\) | |||||||
\(74\) | 7.58817 | 0.882107 | ||||||||
\(75\) | 10.4747 | 1.20951 | ||||||||
\(76\) | 2.10324 | 0.241258 | ||||||||
\(77\) | −2.57967 | −0.293981 | ||||||||
\(78\) | −4.27605 | −0.484167 | ||||||||
\(79\) | −12.0223 | −1.35262 | −0.676308 | − | 0.736619i | \(-0.736421\pi\) | ||||
−0.676308 | + | 0.736619i | \(0.736421\pi\) | |||||||
\(80\) | 7.36011 | 0.822885 | ||||||||
\(81\) | −10.9328 | −1.21476 | ||||||||
\(82\) | 15.6224 | 1.72521 | ||||||||
\(83\) | 6.29160 | 0.690592 | 0.345296 | − | 0.938494i | \(-0.387778\pi\) | ||||
0.345296 | + | 0.938494i | \(0.387778\pi\) | |||||||
\(84\) | 7.58168 | 0.827229 | ||||||||
\(85\) | 3.40297 | 0.369104 | ||||||||
\(86\) | −22.4299 | −2.41868 | ||||||||
\(87\) | −12.4547 | −1.33528 | ||||||||
\(88\) | 2.47972 | 0.264339 | ||||||||
\(89\) | −12.7667 | −1.35327 | −0.676634 | − | 0.736320i | \(-0.736562\pi\) | ||||
−0.676634 | + | 0.736320i | \(0.736562\pi\) | |||||||
\(90\) | 6.47305 | 0.682319 | ||||||||
\(91\) | 1.44494 | 0.151471 | ||||||||
\(92\) | 5.29640 | 0.552188 | ||||||||
\(93\) | 20.6487 | 2.14117 | ||||||||
\(94\) | −15.0825 | −1.55564 | ||||||||
\(95\) | −2.54992 | −0.261616 | ||||||||
\(96\) | 15.3280 | 1.56441 | ||||||||
\(97\) | 16.0625 | 1.63090 | 0.815452 | − | 0.578824i | \(-0.196488\pi\) | ||||
0.815452 | + | 0.578824i | \(0.196488\pi\) | |||||||
\(98\) | 10.5862 | 1.06937 | ||||||||
\(99\) | −1.67253 | −0.168096 | ||||||||
\(100\) | 13.9608 | 1.39608 | ||||||||
\(101\) | −12.0055 | −1.19459 | −0.597294 | − | 0.802022i | \(-0.703757\pi\) | ||||
−0.597294 | + | 0.802022i | \(0.703757\pi\) | |||||||
\(102\) | 4.53859 | 0.449387 | ||||||||
\(103\) | −16.5723 | −1.63292 | −0.816458 | − | 0.577405i | \(-0.804066\pi\) | ||||
−0.816458 | + | 0.577405i | \(0.804066\pi\) | |||||||
\(104\) | −1.38895 | −0.136198 | ||||||||
\(105\) | −9.19184 | −0.897032 | ||||||||
\(106\) | 13.6213 | 1.32301 | ||||||||
\(107\) | −11.4089 | −1.10294 | −0.551469 | − | 0.834196i | \(-0.685932\pi\) | ||||
−0.551469 | + | 0.834196i | \(0.685932\pi\) | |||||||
\(108\) | −10.8256 | −1.04169 | ||||||||
\(109\) | −8.54034 | −0.818016 | −0.409008 | − | 0.912531i | \(-0.634125\pi\) | ||||
−0.409008 | + | 0.912531i | \(0.634125\pi\) | |||||||
\(110\) | −12.3357 | −1.17616 | ||||||||
\(111\) | −6.98621 | −0.663101 | ||||||||
\(112\) | −3.31707 | −0.313433 | ||||||||
\(113\) | 14.4287 | 1.35734 | 0.678668 | − | 0.734445i | \(-0.262558\pi\) | ||||
0.678668 | + | 0.734445i | \(0.262558\pi\) | |||||||
\(114\) | −3.40086 | −0.318519 | ||||||||
\(115\) | −6.42123 | −0.598783 | ||||||||
\(116\) | −16.5998 | −1.54125 | ||||||||
\(117\) | 0.936828 | 0.0866098 | ||||||||
\(118\) | −3.82151 | −0.351798 | ||||||||
\(119\) | −1.53366 | −0.140590 | ||||||||
\(120\) | 8.83568 | 0.806584 | ||||||||
\(121\) | −7.81265 | −0.710241 | ||||||||
\(122\) | −26.1160 | −2.36443 | ||||||||
\(123\) | −14.3831 | −1.29688 | ||||||||
\(124\) | 27.5208 | 2.47144 | ||||||||
\(125\) | −0.895150 | −0.0800647 | ||||||||
\(126\) | −2.91728 | −0.259892 | ||||||||
\(127\) | −0.533754 | −0.0473630 | −0.0236815 | − | 0.999720i | \(-0.507539\pi\) | ||||
−0.0236815 | + | 0.999720i | \(0.507539\pi\) | |||||||
\(128\) | 10.5347 | 0.931143 | ||||||||
\(129\) | 20.6506 | 1.81818 | ||||||||
\(130\) | 6.90953 | 0.606006 | ||||||||
\(131\) | 6.07953 | 0.531171 | 0.265585 | − | 0.964087i | \(-0.414435\pi\) | ||||
0.265585 | + | 0.964087i | \(0.414435\pi\) | |||||||
\(132\) | −9.36765 | −0.815349 | ||||||||
\(133\) | 1.14920 | 0.0996483 | ||||||||
\(134\) | 10.7588 | 0.929418 | ||||||||
\(135\) | 13.1247 | 1.12959 | ||||||||
\(136\) | 1.47423 | 0.126414 | ||||||||
\(137\) | −4.98174 | −0.425619 | −0.212810 | − | 0.977094i | \(-0.568261\pi\) | ||||
−0.212810 | + | 0.977094i | \(0.568261\pi\) | |||||||
\(138\) | −8.56408 | −0.729023 | ||||||||
\(139\) | 2.29173 | 0.194382 | 0.0971912 | − | 0.995266i | \(-0.469014\pi\) | ||||
0.0971912 | + | 0.995266i | \(0.469014\pi\) | |||||||
\(140\) | −12.2510 | −1.03540 | ||||||||
\(141\) | 13.8860 | 1.16942 | ||||||||
\(142\) | −15.8803 | −1.33264 | ||||||||
\(143\) | −1.78531 | −0.149296 | ||||||||
\(144\) | −2.15062 | −0.179219 | ||||||||
\(145\) | 20.1251 | 1.67130 | ||||||||
\(146\) | −33.0977 | −2.73919 | ||||||||
\(147\) | −9.74642 | −0.803871 | ||||||||
\(148\) | −9.31131 | −0.765385 | ||||||||
\(149\) | −3.79949 | −0.311266 | −0.155633 | − | 0.987815i | \(-0.549742\pi\) | ||||
−0.155633 | + | 0.987815i | \(0.549742\pi\) | |||||||
\(150\) | −22.5741 | −1.84317 | ||||||||
\(151\) | −14.9673 | −1.21802 | −0.609012 | − | 0.793161i | \(-0.708434\pi\) | ||||
−0.609012 | + | 0.793161i | \(0.708434\pi\) | |||||||
\(152\) | −1.10467 | −0.0896007 | ||||||||
\(153\) | −0.994349 | −0.0803883 | ||||||||
\(154\) | 5.55947 | 0.447995 | ||||||||
\(155\) | −33.3655 | −2.67999 | ||||||||
\(156\) | 5.24706 | 0.420101 | ||||||||
\(157\) | 4.00970 | 0.320009 | 0.160004 | − | 0.987116i | \(-0.448849\pi\) | ||||
0.160004 | + | 0.987116i | \(0.448849\pi\) | |||||||
\(158\) | 25.9094 | 2.06124 | ||||||||
\(159\) | −12.5407 | −0.994542 | ||||||||
\(160\) | −24.7681 | −1.95809 | ||||||||
\(161\) | 2.89393 | 0.228074 | ||||||||
\(162\) | 23.5615 | 1.85116 | ||||||||
\(163\) | 2.41945 | 0.189506 | 0.0947530 | − | 0.995501i | \(-0.469794\pi\) | ||||
0.0947530 | + | 0.995501i | \(0.469794\pi\) | |||||||
\(164\) | −19.1700 | −1.49693 | ||||||||
\(165\) | 11.3571 | 0.884150 | ||||||||
\(166\) | −13.5591 | −1.05239 | ||||||||
\(167\) | 18.1432 | 1.40396 | 0.701982 | − | 0.712195i | \(-0.252299\pi\) | ||||
0.701982 | + | 0.712195i | \(0.252299\pi\) | |||||||
\(168\) | −3.98208 | −0.307224 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −7.33377 | −0.562475 | ||||||||
\(171\) | 0.745086 | 0.0569781 | ||||||||
\(172\) | 27.5233 | 2.09864 | ||||||||
\(173\) | −12.9664 | −0.985821 | −0.492910 | − | 0.870080i | \(-0.664067\pi\) | ||||
−0.492910 | + | 0.870080i | \(0.664067\pi\) | |||||||
\(174\) | 26.8412 | 2.03482 | ||||||||
\(175\) | 7.62812 | 0.576632 | ||||||||
\(176\) | 4.09845 | 0.308932 | ||||||||
\(177\) | 3.51835 | 0.264455 | ||||||||
\(178\) | 27.5136 | 2.06223 | ||||||||
\(179\) | 3.30127 | 0.246748 | 0.123374 | − | 0.992360i | \(-0.460628\pi\) | ||||
0.123374 | + | 0.992360i | \(0.460628\pi\) | |||||||
\(180\) | −7.94296 | −0.592033 | ||||||||
\(181\) | 6.96513 | 0.517714 | 0.258857 | − | 0.965916i | \(-0.416654\pi\) | ||||
0.258857 | + | 0.965916i | \(0.416654\pi\) | |||||||
\(182\) | −3.11400 | −0.230825 | ||||||||
\(183\) | 24.0442 | 1.77740 | ||||||||
\(184\) | −2.78180 | −0.205077 | ||||||||
\(185\) | 11.2888 | 0.829969 | ||||||||
\(186\) | −44.5001 | −3.26291 | ||||||||
\(187\) | 1.89493 | 0.138571 | ||||||||
\(188\) | 18.5075 | 1.34980 | ||||||||
\(189\) | −5.91505 | −0.430256 | ||||||||
\(190\) | 5.49534 | 0.398674 | ||||||||
\(191\) | −11.0142 | −0.796956 | −0.398478 | − | 0.917178i | \(-0.630462\pi\) | ||||
−0.398478 | + | 0.917178i | \(0.630462\pi\) | |||||||
\(192\) | −23.9238 | −1.72655 | ||||||||
\(193\) | −25.6542 | −1.84663 | −0.923315 | − | 0.384042i | \(-0.874532\pi\) | ||||
−0.923315 | + | 0.384042i | \(0.874532\pi\) | |||||||
\(194\) | −34.6165 | −2.48532 | ||||||||
\(195\) | −6.36140 | −0.455550 | ||||||||
\(196\) | −12.9901 | −0.927868 | ||||||||
\(197\) | 8.47097 | 0.603532 | 0.301766 | − | 0.953382i | \(-0.402424\pi\) | ||||
0.301766 | + | 0.953382i | \(0.402424\pi\) | |||||||
\(198\) | 3.60449 | 0.256160 | ||||||||
\(199\) | −16.1683 | −1.14614 | −0.573070 | − | 0.819506i | \(-0.694248\pi\) | ||||
−0.573070 | + | 0.819506i | \(0.694248\pi\) | |||||||
\(200\) | −7.33256 | −0.518490 | ||||||||
\(201\) | −9.90529 | −0.698666 | ||||||||
\(202\) | 25.8731 | 1.82042 | ||||||||
\(203\) | −9.07003 | −0.636591 | ||||||||
\(204\) | −5.56922 | −0.389923 | ||||||||
\(205\) | 23.2412 | 1.62324 | ||||||||
\(206\) | 35.7151 | 2.48839 | ||||||||
\(207\) | 1.87628 | 0.130411 | ||||||||
\(208\) | −2.29564 | −0.159174 | ||||||||
\(209\) | −1.41991 | −0.0982172 | ||||||||
\(210\) | 19.8094 | 1.36698 | ||||||||
\(211\) | 13.8361 | 0.952516 | 0.476258 | − | 0.879305i | \(-0.341993\pi\) | ||||
0.476258 | + | 0.879305i | \(0.341993\pi\) | |||||||
\(212\) | −16.7144 | −1.14795 | ||||||||
\(213\) | 14.6205 | 1.00178 | ||||||||
\(214\) | 24.5874 | 1.68076 | ||||||||
\(215\) | −33.3686 | −2.27572 | ||||||||
\(216\) | 5.68586 | 0.386873 | ||||||||
\(217\) | 15.0372 | 1.02079 | ||||||||
\(218\) | 18.4054 | 1.24657 | ||||||||
\(219\) | 30.4721 | 2.05911 | ||||||||
\(220\) | 15.1369 | 1.02053 | ||||||||
\(221\) | −1.06140 | −0.0713974 | ||||||||
\(222\) | 15.0560 | 1.01049 | ||||||||
\(223\) | −4.24439 | −0.284225 | −0.142113 | − | 0.989851i | \(-0.545389\pi\) | ||||
−0.142113 | + | 0.989851i | \(0.545389\pi\) | |||||||
\(224\) | 11.1625 | 0.745828 | ||||||||
\(225\) | 4.94571 | 0.329714 | ||||||||
\(226\) | −31.0954 | −2.06843 | ||||||||
\(227\) | 9.14520 | 0.606988 | 0.303494 | − | 0.952833i | \(-0.401847\pi\) | ||||
0.303494 | + | 0.952833i | \(0.401847\pi\) | |||||||
\(228\) | 4.17313 | 0.276372 | ||||||||
\(229\) | −3.28239 | −0.216906 | −0.108453 | − | 0.994102i | \(-0.534590\pi\) | ||||
−0.108453 | + | 0.994102i | \(0.534590\pi\) | |||||||
\(230\) | 13.8384 | 0.912480 | ||||||||
\(231\) | −5.11844 | −0.336769 | ||||||||
\(232\) | 8.71859 | 0.572404 | ||||||||
\(233\) | −0.470381 | −0.0308157 | −0.0154078 | − | 0.999881i | \(-0.504905\pi\) | ||||
−0.0154078 | + | 0.999881i | \(0.504905\pi\) | |||||||
\(234\) | −2.01897 | −0.131984 | ||||||||
\(235\) | −22.4380 | −1.46370 | ||||||||
\(236\) | 4.68930 | 0.305247 | ||||||||
\(237\) | −23.8540 | −1.54948 | ||||||||
\(238\) | 3.30520 | 0.214244 | ||||||||
\(239\) | 22.9218 | 1.48269 | 0.741345 | − | 0.671124i | \(-0.234188\pi\) | ||||
0.741345 | + | 0.671124i | \(0.234188\pi\) | |||||||
\(240\) | 14.6035 | 0.942653 | ||||||||
\(241\) | 4.50551 | 0.290225 | 0.145113 | − | 0.989415i | \(-0.453646\pi\) | ||||
0.145113 | + | 0.989415i | \(0.453646\pi\) | |||||||
\(242\) | 16.8371 | 1.08233 | ||||||||
\(243\) | −9.41144 | −0.603744 | ||||||||
\(244\) | 32.0464 | 2.05156 | ||||||||
\(245\) | 15.7489 | 1.00616 | ||||||||
\(246\) | 30.9972 | 1.97631 | ||||||||
\(247\) | 0.795328 | 0.0506055 | ||||||||
\(248\) | −14.4546 | −0.917867 | ||||||||
\(249\) | 12.4834 | 0.791105 | ||||||||
\(250\) | 1.92915 | 0.122010 | ||||||||
\(251\) | 30.3983 | 1.91873 | 0.959363 | − | 0.282176i | \(-0.0910561\pi\) | ||||
0.959363 | + | 0.282176i | \(0.0910561\pi\) | |||||||
\(252\) | 3.57974 | 0.225503 | ||||||||
\(253\) | −3.57564 | −0.224798 | ||||||||
\(254\) | 1.15030 | 0.0721761 | ||||||||
\(255\) | 6.75199 | 0.422826 | ||||||||
\(256\) | 1.41160 | 0.0882253 | ||||||||
\(257\) | −28.1035 | −1.75305 | −0.876523 | − | 0.481360i | \(-0.840143\pi\) | ||||
−0.876523 | + | 0.481360i | \(0.840143\pi\) | |||||||
\(258\) | −44.5042 | −2.77071 | ||||||||
\(259\) | −5.08766 | −0.316132 | ||||||||
\(260\) | −8.47856 | −0.525818 | ||||||||
\(261\) | −5.88057 | −0.363998 | ||||||||
\(262\) | −13.1020 | −0.809447 | ||||||||
\(263\) | −21.3141 | −1.31428 | −0.657142 | − | 0.753767i | \(-0.728235\pi\) | ||||
−0.657142 | + | 0.753767i | \(0.728235\pi\) | |||||||
\(264\) | 4.92012 | 0.302812 | ||||||||
\(265\) | 20.2641 | 1.24482 | ||||||||
\(266\) | −2.47665 | −0.151853 | ||||||||
\(267\) | −25.3310 | −1.55023 | ||||||||
\(268\) | −13.2019 | −0.806435 | ||||||||
\(269\) | −14.2474 | −0.868676 | −0.434338 | − | 0.900750i | \(-0.643018\pi\) | ||||
−0.434338 | + | 0.900750i | \(0.643018\pi\) | |||||||
\(270\) | −28.2851 | −1.72138 | ||||||||
\(271\) | −7.52736 | −0.457254 | −0.228627 | − | 0.973514i | \(-0.573424\pi\) | ||||
−0.228627 | + | 0.973514i | \(0.573424\pi\) | |||||||
\(272\) | 2.43659 | 0.147740 | ||||||||
\(273\) | 2.86697 | 0.173517 | ||||||||
\(274\) | 10.7362 | 0.648597 | ||||||||
\(275\) | −9.42503 | −0.568351 | ||||||||
\(276\) | 10.5088 | 0.632557 | ||||||||
\(277\) | 16.2655 | 0.977299 | 0.488649 | − | 0.872480i | \(-0.337490\pi\) | ||||
0.488649 | + | 0.872480i | \(0.337490\pi\) | |||||||
\(278\) | −4.93894 | −0.296218 | ||||||||
\(279\) | 9.74942 | 0.583682 | ||||||||
\(280\) | 6.43452 | 0.384536 | ||||||||
\(281\) | −15.4849 | −0.923751 | −0.461875 | − | 0.886945i | \(-0.652823\pi\) | ||||
−0.461875 | + | 0.886945i | \(0.652823\pi\) | |||||||
\(282\) | −29.9259 | −1.78206 | ||||||||
\(283\) | −24.8749 | −1.47866 | −0.739330 | − | 0.673344i | \(-0.764857\pi\) | ||||
−0.739330 | + | 0.673344i | \(0.764857\pi\) | |||||||
\(284\) | 19.4864 | 1.15630 | ||||||||
\(285\) | −5.05940 | −0.299693 | ||||||||
\(286\) | 3.84755 | 0.227510 | ||||||||
\(287\) | −10.4744 | −0.618285 | ||||||||
\(288\) | 7.23725 | 0.426459 | ||||||||
\(289\) | −15.8734 | −0.933731 | ||||||||
\(290\) | −43.3719 | −2.54688 | ||||||||
\(291\) | 31.8704 | 1.86828 | ||||||||
\(292\) | 40.6136 | 2.37673 | ||||||||
\(293\) | 1.79886 | 0.105090 | 0.0525451 | − | 0.998619i | \(-0.483267\pi\) | ||||
0.0525451 | + | 0.998619i | \(0.483267\pi\) | |||||||
\(294\) | 21.0046 | 1.22501 | ||||||||
\(295\) | −5.68519 | −0.331005 | ||||||||
\(296\) | 4.89052 | 0.284256 | ||||||||
\(297\) | 7.30842 | 0.424077 | ||||||||
\(298\) | 8.18831 | 0.474336 | ||||||||
\(299\) | 2.00280 | 0.115825 | ||||||||
\(300\) | 27.7003 | 1.59928 | ||||||||
\(301\) | 15.0386 | 0.866813 | ||||||||
\(302\) | 32.2562 | 1.85614 | ||||||||
\(303\) | −23.8206 | −1.36846 | ||||||||
\(304\) | −1.82579 | −0.104716 | ||||||||
\(305\) | −38.8523 | −2.22468 | ||||||||
\(306\) | 2.14293 | 0.122503 | ||||||||
\(307\) | −21.8289 | −1.24584 | −0.622920 | − | 0.782286i | \(-0.714054\pi\) | ||||
−0.622920 | + | 0.782286i | \(0.714054\pi\) | |||||||
\(308\) | −6.82192 | −0.388715 | ||||||||
\(309\) | −32.8818 | −1.87058 | ||||||||
\(310\) | 71.9064 | 4.08401 | ||||||||
\(311\) | −9.37801 | −0.531778 | −0.265889 | − | 0.964004i | \(-0.585666\pi\) | ||||
−0.265889 | + | 0.964004i | \(0.585666\pi\) | |||||||
\(312\) | −2.75588 | −0.156021 | ||||||||
\(313\) | 27.7292 | 1.56735 | 0.783674 | − | 0.621172i | \(-0.213343\pi\) | ||||
0.783674 | + | 0.621172i | \(0.213343\pi\) | |||||||
\(314\) | −8.64134 | −0.487659 | ||||||||
\(315\) | −4.34000 | −0.244531 | ||||||||
\(316\) | −31.7929 | −1.78849 | ||||||||
\(317\) | −5.37862 | −0.302094 | −0.151047 | − | 0.988527i | \(-0.548264\pi\) | ||||
−0.151047 | + | 0.988527i | \(0.548264\pi\) | |||||||
\(318\) | 27.0266 | 1.51557 | ||||||||
\(319\) | 11.2066 | 0.627449 | ||||||||
\(320\) | 38.6578 | 2.16104 | ||||||||
\(321\) | −22.6369 | −1.26347 | ||||||||
\(322\) | −6.23673 | −0.347560 | ||||||||
\(323\) | −0.844160 | −0.0469703 | ||||||||
\(324\) | −28.9118 | −1.60621 | ||||||||
\(325\) | 5.27920 | 0.292837 | ||||||||
\(326\) | −5.21418 | −0.288787 | ||||||||
\(327\) | −16.9453 | −0.937075 | ||||||||
\(328\) | 10.0686 | 0.555943 | ||||||||
\(329\) | 10.1124 | 0.557515 | ||||||||
\(330\) | −24.4758 | −1.34735 | ||||||||
\(331\) | −5.26321 | −0.289292 | −0.144646 | − | 0.989483i | \(-0.546204\pi\) | ||||
−0.144646 | + | 0.989483i | \(0.546204\pi\) | |||||||
\(332\) | 16.6381 | 0.913133 | ||||||||
\(333\) | −3.29859 | −0.180762 | ||||||||
\(334\) | −39.1006 | −2.13949 | ||||||||
\(335\) | 16.0057 | 0.874483 | ||||||||
\(336\) | −6.58154 | −0.359052 | ||||||||
\(337\) | 25.8015 | 1.40550 | 0.702749 | − | 0.711438i | \(-0.251956\pi\) | ||||
0.702749 | + | 0.711438i | \(0.251956\pi\) | |||||||
\(338\) | −2.15511 | −0.117222 | ||||||||
\(339\) | 28.6286 | 1.55489 | ||||||||
\(340\) | 8.99913 | 0.488047 | ||||||||
\(341\) | −18.5795 | −1.00613 | ||||||||
\(342\) | −1.60574 | −0.0868285 | ||||||||
\(343\) | −17.2123 | −0.929379 | ||||||||
\(344\) | −14.4559 | −0.779412 | ||||||||
\(345\) | −12.7406 | −0.685933 | ||||||||
\(346\) | 27.9441 | 1.50228 | ||||||||
\(347\) | −5.79355 | −0.311014 | −0.155507 | − | 0.987835i | \(-0.549701\pi\) | ||||
−0.155507 | + | 0.987835i | \(0.549701\pi\) | |||||||
\(348\) | −32.9363 | −1.76557 | ||||||||
\(349\) | −5.69565 | −0.304881 | −0.152440 | − | 0.988313i | \(-0.548713\pi\) | ||||
−0.152440 | + | 0.988313i | \(0.548713\pi\) | |||||||
\(350\) | −16.4394 | −0.878725 | ||||||||
\(351\) | −4.09363 | −0.218502 | ||||||||
\(352\) | −13.7920 | −0.735118 | ||||||||
\(353\) | 11.2156 | 0.596949 | 0.298474 | − | 0.954418i | \(-0.403522\pi\) | ||||
0.298474 | + | 0.954418i | \(0.403522\pi\) | |||||||
\(354\) | −7.58242 | −0.403001 | ||||||||
\(355\) | −23.6248 | −1.25388 | ||||||||
\(356\) | −33.7614 | −1.78935 | ||||||||
\(357\) | −3.04300 | −0.161052 | ||||||||
\(358\) | −7.11459 | −0.376018 | ||||||||
\(359\) | −29.7593 | −1.57064 | −0.785319 | − | 0.619091i | \(-0.787501\pi\) | ||||
−0.785319 | + | 0.619091i | \(0.787501\pi\) | |||||||
\(360\) | 4.17183 | 0.219875 | ||||||||
\(361\) | −18.3675 | −0.966708 | ||||||||
\(362\) | −15.0106 | −0.788941 | ||||||||
\(363\) | −15.5014 | −0.813614 | ||||||||
\(364\) | 3.82113 | 0.200282 | ||||||||
\(365\) | −49.2389 | −2.57728 | ||||||||
\(366\) | −51.8179 | −2.70856 | ||||||||
\(367\) | −12.3699 | −0.645702 | −0.322851 | − | 0.946450i | \(-0.604641\pi\) | ||||
−0.322851 | + | 0.946450i | \(0.604641\pi\) | |||||||
\(368\) | −4.59772 | −0.239673 | ||||||||
\(369\) | −6.79110 | −0.353530 | ||||||||
\(370\) | −24.3286 | −1.26478 | ||||||||
\(371\) | −9.13267 | −0.474145 | ||||||||
\(372\) | 54.6052 | 2.83115 | ||||||||
\(373\) | −3.68423 | −0.190762 | −0.0953811 | − | 0.995441i | \(-0.530407\pi\) | ||||
−0.0953811 | + | 0.995441i | \(0.530407\pi\) | |||||||
\(374\) | −4.08378 | −0.211167 | ||||||||
\(375\) | −1.77611 | −0.0917178 | ||||||||
\(376\) | −9.72058 | −0.501301 | ||||||||
\(377\) | −6.27710 | −0.323287 | ||||||||
\(378\) | 12.7476 | 0.655664 | ||||||||
\(379\) | −30.5241 | −1.56792 | −0.783959 | − | 0.620812i | \(-0.786803\pi\) | ||||
−0.783959 | + | 0.620812i | \(0.786803\pi\) | |||||||
\(380\) | −6.74323 | −0.345920 | ||||||||
\(381\) | −1.05905 | −0.0542565 | ||||||||
\(382\) | 23.7367 | 1.21448 | ||||||||
\(383\) | −0.249694 | −0.0127588 | −0.00637939 | − | 0.999980i | \(-0.502031\pi\) | ||||
−0.00637939 | + | 0.999980i | \(0.502031\pi\) | |||||||
\(384\) | 20.9023 | 1.06667 | ||||||||
\(385\) | 8.27073 | 0.421516 | ||||||||
\(386\) | 55.2876 | 2.81407 | ||||||||
\(387\) | 9.75032 | 0.495637 | ||||||||
\(388\) | 42.4773 | 2.15646 | ||||||||
\(389\) | −26.7589 | −1.35673 | −0.678364 | − | 0.734726i | \(-0.737311\pi\) | ||||
−0.678364 | + | 0.734726i | \(0.737311\pi\) | |||||||
\(390\) | 13.7095 | 0.694208 | ||||||||
\(391\) | −2.12577 | −0.107505 | ||||||||
\(392\) | 6.82274 | 0.344600 | ||||||||
\(393\) | 12.0627 | 0.608481 | ||||||||
\(394\) | −18.2559 | −0.919717 | ||||||||
\(395\) | 38.5449 | 1.93941 | ||||||||
\(396\) | −4.42300 | −0.222264 | ||||||||
\(397\) | 8.45450 | 0.424319 | 0.212160 | − | 0.977235i | \(-0.431950\pi\) | ||||
0.212160 | + | 0.977235i | \(0.431950\pi\) | |||||||
\(398\) | 34.8444 | 1.74659 | ||||||||
\(399\) | 2.28018 | 0.114152 | ||||||||
\(400\) | −12.1192 | −0.605958 | ||||||||
\(401\) | −1.61347 | −0.0805728 | −0.0402864 | − | 0.999188i | \(-0.512827\pi\) | ||||
−0.0402864 | + | 0.999188i | \(0.512827\pi\) | |||||||
\(402\) | 21.3470 | 1.06469 | ||||||||
\(403\) | 10.4068 | 0.518401 | ||||||||
\(404\) | −31.7484 | −1.57954 | ||||||||
\(405\) | 35.0520 | 1.74175 | ||||||||
\(406\) | 19.5469 | 0.970097 | ||||||||
\(407\) | 6.28612 | 0.311592 | ||||||||
\(408\) | 2.92509 | 0.144813 | ||||||||
\(409\) | −30.1802 | −1.49231 | −0.746157 | − | 0.665771i | \(-0.768103\pi\) | ||||
−0.746157 | + | 0.665771i | \(0.768103\pi\) | |||||||
\(410\) | −50.0874 | −2.47364 | ||||||||
\(411\) | −9.88450 | −0.487566 | ||||||||
\(412\) | −43.8253 | −2.15912 | ||||||||
\(413\) | 2.56221 | 0.126078 | ||||||||
\(414\) | −4.04360 | −0.198732 | ||||||||
\(415\) | −20.1716 | −0.990185 | ||||||||
\(416\) | 7.72526 | 0.378762 | ||||||||
\(417\) | 4.54713 | 0.222674 | ||||||||
\(418\) | 3.06006 | 0.149672 | ||||||||
\(419\) | −1.08788 | −0.0531464 | −0.0265732 | − | 0.999647i | \(-0.508460\pi\) | ||||
−0.0265732 | + | 0.999647i | \(0.508460\pi\) | |||||||
\(420\) | −24.3078 | −1.18610 | ||||||||
\(421\) | 32.5833 | 1.58801 | 0.794007 | − | 0.607908i | \(-0.207991\pi\) | ||||
0.794007 | + | 0.607908i | \(0.207991\pi\) | |||||||
\(422\) | −29.8183 | −1.45153 | ||||||||
\(423\) | 6.55640 | 0.318783 | ||||||||
\(424\) | 8.77881 | 0.426337 | ||||||||
\(425\) | −5.60334 | −0.271802 | ||||||||
\(426\) | −31.5088 | −1.52660 | ||||||||
\(427\) | 17.5100 | 0.847370 | ||||||||
\(428\) | −30.1707 | −1.45836 | ||||||||
\(429\) | −3.54232 | −0.171025 | ||||||||
\(430\) | 71.9130 | 3.46795 | ||||||||
\(431\) | −16.0729 | −0.774205 | −0.387103 | − | 0.922037i | \(-0.626524\pi\) | ||||
−0.387103 | + | 0.922037i | \(0.626524\pi\) | |||||||
\(432\) | 9.39751 | 0.452138 | ||||||||
\(433\) | −2.24522 | −0.107898 | −0.0539491 | − | 0.998544i | \(-0.517181\pi\) | ||||
−0.0539491 | + | 0.998544i | \(0.517181\pi\) | |||||||
\(434\) | −32.4069 | −1.55558 | ||||||||
\(435\) | 39.9312 | 1.91455 | ||||||||
\(436\) | −22.5849 | −1.08162 | ||||||||
\(437\) | 1.59289 | 0.0761981 | ||||||||
\(438\) | −65.6707 | −3.13787 | ||||||||
\(439\) | 13.3023 | 0.634885 | 0.317443 | − | 0.948278i | \(-0.397176\pi\) | ||||
0.317443 | + | 0.948278i | \(0.397176\pi\) | |||||||
\(440\) | −7.95027 | −0.379014 | ||||||||
\(441\) | −4.60184 | −0.219135 | ||||||||
\(442\) | 2.28743 | 0.108802 | ||||||||
\(443\) | −13.9235 | −0.661523 | −0.330762 | − | 0.943714i | \(-0.607306\pi\) | ||||
−0.330762 | + | 0.943714i | \(0.607306\pi\) | |||||||
\(444\) | −18.4750 | −0.876783 | ||||||||
\(445\) | 40.9316 | 1.94034 | ||||||||
\(446\) | 9.14711 | 0.433128 | ||||||||
\(447\) | −7.53873 | −0.356570 | ||||||||
\(448\) | −17.4224 | −0.823129 | ||||||||
\(449\) | −10.9141 | −0.515068 | −0.257534 | − | 0.966269i | \(-0.582910\pi\) | ||||
−0.257534 | + | 0.966269i | \(0.582910\pi\) | |||||||
\(450\) | −10.6585 | −0.502448 | ||||||||
\(451\) | 12.9418 | 0.609405 | ||||||||
\(452\) | 38.1565 | 1.79473 | ||||||||
\(453\) | −29.6973 | −1.39530 | ||||||||
\(454\) | −19.7089 | −0.924984 | ||||||||
\(455\) | −4.63265 | −0.217182 | ||||||||
\(456\) | −2.19183 | −0.102642 | ||||||||
\(457\) | −28.6280 | −1.33916 | −0.669580 | − | 0.742740i | \(-0.733526\pi\) | ||||
−0.669580 | + | 0.742740i | \(0.733526\pi\) | |||||||
\(458\) | 7.07390 | 0.330542 | ||||||||
\(459\) | 4.34497 | 0.202806 | ||||||||
\(460\) | −16.9809 | −0.791738 | ||||||||
\(461\) | −14.8945 | −0.693705 | −0.346853 | − | 0.937920i | \(-0.612750\pi\) | ||||
−0.346853 | + | 0.937920i | \(0.612750\pi\) | |||||||
\(462\) | 11.0308 | 0.513199 | ||||||||
\(463\) | 10.5295 | 0.489347 | 0.244673 | − | 0.969606i | \(-0.421319\pi\) | ||||
0.244673 | + | 0.969606i | \(0.421319\pi\) | |||||||
\(464\) | 14.4100 | 0.668967 | ||||||||
\(465\) | −66.2021 | −3.07005 | ||||||||
\(466\) | 1.01372 | 0.0469597 | ||||||||
\(467\) | 18.9886 | 0.878686 | 0.439343 | − | 0.898319i | \(-0.355211\pi\) | ||||
0.439343 | + | 0.898319i | \(0.355211\pi\) | |||||||
\(468\) | 2.47744 | 0.114520 | ||||||||
\(469\) | −7.21346 | −0.333087 | ||||||||
\(470\) | 48.3564 | 2.23051 | ||||||||
\(471\) | 7.95582 | 0.366585 | ||||||||
\(472\) | −2.46293 | −0.113366 | ||||||||
\(473\) | −18.5812 | −0.854364 | ||||||||
\(474\) | 51.4079 | 2.36124 | ||||||||
\(475\) | 4.19869 | 0.192649 | ||||||||
\(476\) | −4.05574 | −0.185895 | ||||||||
\(477\) | −5.92118 | −0.271112 | ||||||||
\(478\) | −49.3991 | −2.25946 | ||||||||
\(479\) | −13.3420 | −0.609610 | −0.304805 | − | 0.952415i | \(-0.598591\pi\) | ||||
−0.304805 | + | 0.952415i | \(0.598591\pi\) | |||||||
\(480\) | −49.1435 | −2.24308 | ||||||||
\(481\) | −3.52102 | −0.160545 | ||||||||
\(482\) | −9.70986 | −0.442272 | ||||||||
\(483\) | 5.74198 | 0.261269 | ||||||||
\(484\) | −20.6605 | −0.939114 | ||||||||
\(485\) | −51.4984 | −2.33842 | ||||||||
\(486\) | 20.2827 | 0.920041 | ||||||||
\(487\) | −2.21402 | −0.100327 | −0.0501634 | − | 0.998741i | \(-0.515974\pi\) | ||||
−0.0501634 | + | 0.998741i | \(0.515974\pi\) | |||||||
\(488\) | −16.8316 | −0.761929 | ||||||||
\(489\) | 4.80054 | 0.217088 | ||||||||
\(490\) | −33.9407 | −1.53328 | ||||||||
\(491\) | 0.0656429 | 0.00296242 | 0.00148121 | − | 0.999999i | \(-0.499529\pi\) | ||||
0.00148121 | + | 0.999999i | \(0.499529\pi\) | |||||||
\(492\) | −38.0360 | −1.71480 | ||||||||
\(493\) | 6.66251 | 0.300064 | ||||||||
\(494\) | −1.71402 | −0.0771173 | ||||||||
\(495\) | 5.36234 | 0.241019 | ||||||||
\(496\) | −23.8904 | −1.07271 | ||||||||
\(497\) | 10.6473 | 0.477596 | ||||||||
\(498\) | −26.9032 | −1.20556 | ||||||||
\(499\) | −34.9872 | −1.56624 | −0.783121 | − | 0.621869i | \(-0.786374\pi\) | ||||
−0.783121 | + | 0.621869i | \(0.786374\pi\) | |||||||
\(500\) | −2.36722 | −0.105865 | ||||||||
\(501\) | 35.9987 | 1.60831 | ||||||||
\(502\) | −65.5117 | −2.92393 | ||||||||
\(503\) | 24.7479 | 1.10345 | 0.551727 | − | 0.834025i | \(-0.313969\pi\) | ||||
0.551727 | + | 0.834025i | \(0.313969\pi\) | |||||||
\(504\) | −1.88017 | −0.0837494 | ||||||||
\(505\) | 38.4909 | 1.71282 | ||||||||
\(506\) | 7.70588 | 0.342568 | ||||||||
\(507\) | 1.98414 | 0.0881189 | ||||||||
\(508\) | −1.41151 | −0.0626256 | ||||||||
\(509\) | 25.9601 | 1.15066 | 0.575330 | − | 0.817921i | \(-0.304874\pi\) | ||||
0.575330 | + | 0.817921i | \(0.304874\pi\) | |||||||
\(510\) | −14.5513 | −0.644341 | ||||||||
\(511\) | 22.1911 | 0.981676 | ||||||||
\(512\) | −24.1115 | −1.06559 | ||||||||
\(513\) | −3.25578 | −0.143746 | ||||||||
\(514\) | 60.5660 | 2.67145 | ||||||||
\(515\) | 53.1327 | 2.34131 | ||||||||
\(516\) | 54.6103 | 2.40408 | ||||||||
\(517\) | −12.4945 | −0.549509 | ||||||||
\(518\) | 10.9645 | 0.481750 | ||||||||
\(519\) | −25.7273 | −1.12930 | ||||||||
\(520\) | 4.45315 | 0.195283 | ||||||||
\(521\) | 1.54924 | 0.0678734 | 0.0339367 | − | 0.999424i | \(-0.489196\pi\) | ||||
0.0339367 | + | 0.999424i | \(0.489196\pi\) | |||||||
\(522\) | 12.6733 | 0.554694 | ||||||||
\(523\) | 31.4091 | 1.37342 | 0.686711 | − | 0.726930i | \(-0.259054\pi\) | ||||
0.686711 | + | 0.726930i | \(0.259054\pi\) | |||||||
\(524\) | 16.0773 | 0.702339 | ||||||||
\(525\) | 15.1353 | 0.660559 | ||||||||
\(526\) | 45.9342 | 2.00283 | ||||||||
\(527\) | −11.0458 | −0.481163 | ||||||||
\(528\) | 8.13191 | 0.353896 | ||||||||
\(529\) | −18.9888 | −0.825599 | ||||||||
\(530\) | −43.6714 | −1.89696 | ||||||||
\(531\) | 1.66121 | 0.0720905 | ||||||||
\(532\) | 3.03905 | 0.131760 | ||||||||
\(533\) | −7.24903 | −0.313990 | ||||||||
\(534\) | 54.5910 | 2.36238 | ||||||||
\(535\) | 36.5782 | 1.58141 | ||||||||
\(536\) | 6.93396 | 0.299501 | ||||||||
\(537\) | 6.55019 | 0.282662 | ||||||||
\(538\) | 30.7046 | 1.32377 | ||||||||
\(539\) | 8.76973 | 0.377739 | ||||||||
\(540\) | 34.7081 | 1.49360 | ||||||||
\(541\) | 15.5046 | 0.666593 | 0.333297 | − | 0.942822i | \(-0.391839\pi\) | ||||
0.333297 | + | 0.942822i | \(0.391839\pi\) | |||||||
\(542\) | 16.2223 | 0.696806 | ||||||||
\(543\) | 13.8198 | 0.593066 | ||||||||
\(544\) | −8.19959 | −0.351554 | ||||||||
\(545\) | 27.3813 | 1.17289 | ||||||||
\(546\) | −6.17863 | −0.264421 | ||||||||
\(547\) | 1.07613 | 0.0460121 | 0.0230060 | − | 0.999735i | \(-0.492676\pi\) | ||||
0.0230060 | + | 0.999735i | \(0.492676\pi\) | |||||||
\(548\) | −13.1742 | −0.562773 | ||||||||
\(549\) | 11.3527 | 0.484519 | ||||||||
\(550\) | 20.3120 | 0.866105 | ||||||||
\(551\) | −4.99235 | −0.212681 | ||||||||
\(552\) | −5.51949 | −0.234925 | ||||||||
\(553\) | −17.3715 | −0.738711 | ||||||||
\(554\) | −35.0539 | −1.48930 | ||||||||
\(555\) | 22.3986 | 0.950768 | ||||||||
\(556\) | 6.06048 | 0.257021 | ||||||||
\(557\) | −23.9714 | −1.01570 | −0.507851 | − | 0.861445i | \(-0.669560\pi\) | ||||
−0.507851 | + | 0.861445i | \(0.669560\pi\) | |||||||
\(558\) | −21.0111 | −0.889469 | ||||||||
\(559\) | 10.4078 | 0.440203 | ||||||||
\(560\) | 10.6349 | 0.449407 | ||||||||
\(561\) | 3.75982 | 0.158740 | ||||||||
\(562\) | 33.3716 | 1.40770 | ||||||||
\(563\) | −35.5533 | −1.49839 | −0.749197 | − | 0.662347i | \(-0.769560\pi\) | ||||
−0.749197 | + | 0.662347i | \(0.769560\pi\) | |||||||
\(564\) | 36.7215 | 1.54625 | ||||||||
\(565\) | −46.2600 | −1.94617 | ||||||||
\(566\) | 53.6081 | 2.25332 | ||||||||
\(567\) | −15.7973 | −0.663424 | ||||||||
\(568\) | −10.2347 | −0.429439 | ||||||||
\(569\) | −5.73879 | −0.240583 | −0.120291 | − | 0.992739i | \(-0.538383\pi\) | ||||
−0.120291 | + | 0.992739i | \(0.538383\pi\) | |||||||
\(570\) | 10.9036 | 0.456700 | ||||||||
\(571\) | 47.5790 | 1.99112 | 0.995559 | − | 0.0941359i | \(-0.0300088\pi\) | ||||
0.995559 | + | 0.0941359i | \(0.0300088\pi\) | |||||||
\(572\) | −4.72125 | −0.197405 | ||||||||
\(573\) | −21.8537 | −0.912950 | ||||||||
\(574\) | 22.5735 | 0.942199 | ||||||||
\(575\) | 10.5732 | 0.440933 | ||||||||
\(576\) | −11.2958 | −0.470659 | ||||||||
\(577\) | 17.6140 | 0.733282 | 0.366641 | − | 0.930362i | \(-0.380508\pi\) | ||||
0.366641 | + | 0.930362i | \(0.380508\pi\) | |||||||
\(578\) | 34.2090 | 1.42291 | ||||||||
\(579\) | −50.9017 | −2.11540 | ||||||||
\(580\) | 53.2208 | 2.20987 | ||||||||
\(581\) | 9.09097 | 0.377157 | ||||||||
\(582\) | −68.6842 | −2.84705 | ||||||||
\(583\) | 11.2840 | 0.467336 | ||||||||
\(584\) | −21.3312 | −0.882693 | ||||||||
\(585\) | −3.00358 | −0.124183 | ||||||||
\(586\) | −3.87673 | −0.160146 | ||||||||
\(587\) | −18.9106 | −0.780523 | −0.390262 | − | 0.920704i | \(-0.627615\pi\) | ||||
−0.390262 | + | 0.920704i | \(0.627615\pi\) | |||||||
\(588\) | −25.7743 | −1.06292 | ||||||||
\(589\) | 8.27684 | 0.341041 | ||||||||
\(590\) | 12.2522 | 0.504415 | ||||||||
\(591\) | 16.8076 | 0.691373 | ||||||||
\(592\) | 8.08300 | 0.332209 | ||||||||
\(593\) | 24.1298 | 0.990890 | 0.495445 | − | 0.868639i | \(-0.335005\pi\) | ||||
0.495445 | + | 0.868639i | \(0.335005\pi\) | |||||||
\(594\) | −15.7504 | −0.646248 | ||||||||
\(595\) | 4.91709 | 0.201581 | ||||||||
\(596\) | −10.0477 | −0.411571 | ||||||||
\(597\) | −32.0802 | −1.31296 | ||||||||
\(598\) | −4.31626 | −0.176505 | ||||||||
\(599\) | −8.71567 | −0.356113 | −0.178056 | − | 0.984020i | \(-0.556981\pi\) | ||||
−0.178056 | + | 0.984020i | \(0.556981\pi\) | |||||||
\(600\) | −14.5488 | −0.593954 | ||||||||
\(601\) | −23.9910 | −0.978612 | −0.489306 | − | 0.872112i | \(-0.662750\pi\) | ||||
−0.489306 | + | 0.872112i | \(0.662750\pi\) | |||||||
\(602\) | −32.4099 | −1.32093 | ||||||||
\(603\) | −4.67686 | −0.190456 | ||||||||
\(604\) | −39.5810 | −1.61053 | ||||||||
\(605\) | 25.0483 | 1.01836 | ||||||||
\(606\) | 51.3359 | 2.08538 | ||||||||
\(607\) | 25.4497 | 1.03297 | 0.516486 | − | 0.856296i | \(-0.327240\pi\) | ||||
0.516486 | + | 0.856296i | \(0.327240\pi\) | |||||||
\(608\) | 6.14412 | 0.249177 | ||||||||
\(609\) | −17.9963 | −0.729245 | ||||||||
\(610\) | 83.7309 | 3.39017 | ||||||||
\(611\) | 6.99850 | 0.283129 | ||||||||
\(612\) | −2.62955 | −0.106293 | ||||||||
\(613\) | 24.9852 | 1.00914 | 0.504571 | − | 0.863370i | \(-0.331651\pi\) | ||||
0.504571 | + | 0.863370i | \(0.331651\pi\) | |||||||
\(614\) | 47.0436 | 1.89853 | ||||||||
\(615\) | 46.1140 | 1.85950 | ||||||||
\(616\) | 3.58304 | 0.144365 | ||||||||
\(617\) | 26.7234 | 1.07585 | 0.537923 | − | 0.842994i | \(-0.319209\pi\) | ||||
0.537923 | + | 0.842994i | \(0.319209\pi\) | |||||||
\(618\) | 70.8639 | 2.85056 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −88.2349 | −3.54360 | ||||||||
\(621\) | −8.19874 | −0.329004 | ||||||||
\(622\) | 20.2106 | 0.810373 | ||||||||
\(623\) | −18.4471 | −0.739068 | ||||||||
\(624\) | −4.55489 | −0.182341 | ||||||||
\(625\) | −23.5260 | −0.941042 | ||||||||
\(626\) | −59.7595 | −2.38847 | ||||||||
\(627\) | −2.81731 | −0.112512 | ||||||||
\(628\) | 10.6036 | 0.423131 | ||||||||
\(629\) | 3.73720 | 0.149012 | ||||||||
\(630\) | 9.35316 | 0.372639 | ||||||||
\(631\) | −11.4253 | −0.454835 | −0.227417 | − | 0.973797i | \(-0.573028\pi\) | ||||
−0.227417 | + | 0.973797i | \(0.573028\pi\) | |||||||
\(632\) | 16.6984 | 0.664227 | ||||||||
\(633\) | 27.4528 | 1.09115 | ||||||||
\(634\) | 11.5915 | 0.460358 | ||||||||
\(635\) | 1.71128 | 0.0679101 | ||||||||
\(636\) | −33.1638 | −1.31503 | ||||||||
\(637\) | −4.91215 | −0.194626 | ||||||||
\(638\) | −24.1514 | −0.956165 | ||||||||
\(639\) | 6.90318 | 0.273085 | ||||||||
\(640\) | −33.7755 | −1.33509 | ||||||||
\(641\) | −46.9163 | −1.85308 | −0.926542 | − | 0.376191i | \(-0.877234\pi\) | ||||
−0.926542 | + | 0.376191i | \(0.877234\pi\) | |||||||
\(642\) | 48.7849 | 1.92539 | ||||||||
\(643\) | −2.14213 | −0.0844774 | −0.0422387 | − | 0.999108i | \(-0.513449\pi\) | ||||
−0.0422387 | + | 0.999108i | \(0.513449\pi\) | |||||||
\(644\) | 7.65298 | 0.301570 | ||||||||
\(645\) | −66.2082 | −2.60695 | ||||||||
\(646\) | 1.81926 | 0.0715777 | ||||||||
\(647\) | 37.3190 | 1.46716 | 0.733581 | − | 0.679602i | \(-0.237847\pi\) | ||||
0.733581 | + | 0.679602i | \(0.237847\pi\) | |||||||
\(648\) | 15.1852 | 0.596530 | ||||||||
\(649\) | −3.16578 | −0.124268 | ||||||||
\(650\) | −11.3773 | −0.446252 | ||||||||
\(651\) | 29.8361 | 1.16937 | ||||||||
\(652\) | 6.39822 | 0.250574 | ||||||||
\(653\) | −0.221600 | −0.00867188 | −0.00433594 | − | 0.999991i | \(-0.501380\pi\) | ||||
−0.00433594 | + | 0.999991i | \(0.501380\pi\) | |||||||
\(654\) | 36.5189 | 1.42800 | ||||||||
\(655\) | −19.4917 | −0.761604 | ||||||||
\(656\) | 16.6412 | 0.649729 | ||||||||
\(657\) | 14.3876 | 0.561315 | ||||||||
\(658\) | −21.7933 | −0.849593 | ||||||||
\(659\) | −43.6436 | −1.70011 | −0.850056 | − | 0.526692i | \(-0.823432\pi\) | ||||
−0.850056 | + | 0.526692i | \(0.823432\pi\) | |||||||
\(660\) | 30.0338 | 1.16906 | ||||||||
\(661\) | −3.92641 | −0.152720 | −0.0763598 | − | 0.997080i | \(-0.524330\pi\) | ||||
−0.0763598 | + | 0.997080i | \(0.524330\pi\) | |||||||
\(662\) | 11.3428 | 0.440850 | ||||||||
\(663\) | −2.10597 | −0.0817890 | ||||||||
\(664\) | −8.73872 | −0.339128 | ||||||||
\(665\) | −3.68447 | −0.142878 | ||||||||
\(666\) | 7.10882 | 0.275461 | ||||||||
\(667\) | −12.5718 | −0.486782 | ||||||||
\(668\) | 47.9796 | 1.85639 | ||||||||
\(669\) | −8.42147 | −0.325593 | ||||||||
\(670\) | −34.4940 | −1.33262 | ||||||||
\(671\) | −21.6348 | −0.835200 | ||||||||
\(672\) | 22.1481 | 0.854381 | ||||||||
\(673\) | −30.4414 | −1.17343 | −0.586715 | − | 0.809794i | \(-0.699579\pi\) | ||||
−0.586715 | + | 0.809794i | \(0.699579\pi\) | |||||||
\(674\) | −55.6050 | −2.14183 | ||||||||
\(675\) | −21.6111 | −0.831811 | ||||||||
\(676\) | 2.64449 | 0.101711 | ||||||||
\(677\) | −7.03644 | −0.270432 | −0.135216 | − | 0.990816i | \(-0.543173\pi\) | ||||
−0.135216 | + | 0.990816i | \(0.543173\pi\) | |||||||
\(678\) | −61.6977 | −2.36948 | ||||||||
\(679\) | 23.2094 | 0.890695 | ||||||||
\(680\) | −4.72656 | −0.181255 | ||||||||
\(681\) | 18.1454 | 0.695333 | ||||||||
\(682\) | 40.0408 | 1.53324 | ||||||||
\(683\) | −4.09008 | −0.156502 | −0.0782512 | − | 0.996934i | \(-0.524934\pi\) | ||||
−0.0782512 | + | 0.996934i | \(0.524934\pi\) | |||||||
\(684\) | 1.97037 | 0.0753391 | ||||||||
\(685\) | 15.9721 | 0.610261 | ||||||||
\(686\) | 37.0944 | 1.41627 | ||||||||
\(687\) | −6.51273 | −0.248476 | ||||||||
\(688\) | −23.8926 | −0.910897 | ||||||||
\(689\) | −6.32045 | −0.240790 | ||||||||
\(690\) | 27.4575 | 1.04529 | ||||||||
\(691\) | 25.0542 | 0.953107 | 0.476554 | − | 0.879145i | \(-0.341886\pi\) | ||||
0.476554 | + | 0.879145i | \(0.341886\pi\) | |||||||
\(692\) | −34.2897 | −1.30350 | ||||||||
\(693\) | −2.41671 | −0.0918032 | ||||||||
\(694\) | 12.4857 | 0.473952 | ||||||||
\(695\) | −7.34757 | −0.278709 | ||||||||
\(696\) | 17.2989 | 0.655715 | ||||||||
\(697\) | 7.69411 | 0.291435 | ||||||||
\(698\) | 12.2747 | 0.464606 | ||||||||
\(699\) | −0.933303 | −0.0353008 | ||||||||
\(700\) | 20.1725 | 0.762450 | ||||||||
\(701\) | −10.3232 | −0.389903 | −0.194951 | − | 0.980813i | \(-0.562455\pi\) | ||||
−0.194951 | + | 0.980813i | \(0.562455\pi\) | |||||||
\(702\) | 8.82222 | 0.332973 | ||||||||
\(703\) | −2.80036 | −0.105618 | ||||||||
\(704\) | 21.5264 | 0.811308 | ||||||||
\(705\) | −44.5203 | −1.67673 | ||||||||
\(706\) | −24.1709 | −0.909685 | ||||||||
\(707\) | −17.3472 | −0.652407 | ||||||||
\(708\) | 9.30424 | 0.349675 | ||||||||
\(709\) | 4.04652 | 0.151970 | 0.0759851 | − | 0.997109i | \(-0.475790\pi\) | ||||
0.0759851 | + | 0.997109i | \(0.475790\pi\) | |||||||
\(710\) | 50.9141 | 1.91077 | ||||||||
\(711\) | −11.2628 | −0.422389 | ||||||||
\(712\) | 17.7323 | 0.664547 | ||||||||
\(713\) | 20.8428 | 0.780571 | ||||||||
\(714\) | 6.55799 | 0.245427 | ||||||||
\(715\) | 5.72393 | 0.214063 | ||||||||
\(716\) | 8.73018 | 0.326262 | ||||||||
\(717\) | 45.4802 | 1.69849 | ||||||||
\(718\) | 64.1346 | 2.39348 | ||||||||
\(719\) | −35.8604 | −1.33737 | −0.668684 | − | 0.743546i | \(-0.733142\pi\) | ||||
−0.668684 | + | 0.743546i | \(0.733142\pi\) | |||||||
\(720\) | 6.89516 | 0.256967 | ||||||||
\(721\) | −23.9460 | −0.891794 | ||||||||
\(722\) | 39.5839 | 1.47316 | ||||||||
\(723\) | 8.93958 | 0.332466 | ||||||||
\(724\) | 18.4192 | 0.684546 | ||||||||
\(725\) | −33.1381 | −1.23072 | ||||||||
\(726\) | 33.4073 | 1.23986 | ||||||||
\(727\) | 35.7101 | 1.32441 | 0.662206 | − | 0.749322i | \(-0.269620\pi\) | ||||
0.662206 | + | 0.749322i | \(0.269620\pi\) | |||||||
\(728\) | −2.00695 | −0.0743826 | ||||||||
\(729\) | 14.1249 | 0.523143 | ||||||||
\(730\) | 106.115 | 3.92750 | ||||||||
\(731\) | −11.0468 | −0.408582 | ||||||||
\(732\) | 63.5847 | 2.35016 | ||||||||
\(733\) | −29.2357 | −1.07985 | −0.539923 | − | 0.841715i | \(-0.681546\pi\) | ||||
−0.539923 | + | 0.841715i | \(0.681546\pi\) | |||||||
\(734\) | 26.6584 | 0.983980 | ||||||||
\(735\) | 31.2482 | 1.15261 | ||||||||
\(736\) | 15.4722 | 0.570313 | ||||||||
\(737\) | 8.91269 | 0.328303 | ||||||||
\(738\) | 14.6355 | 0.538742 | ||||||||
\(739\) | 15.1785 | 0.558348 | 0.279174 | − | 0.960240i | \(-0.409939\pi\) | ||||
0.279174 | + | 0.960240i | \(0.409939\pi\) | |||||||
\(740\) | 29.8532 | 1.09742 | ||||||||
\(741\) | 1.57804 | 0.0579709 | ||||||||
\(742\) | 19.6819 | 0.722545 | ||||||||
\(743\) | −19.6363 | −0.720385 | −0.360193 | − | 0.932878i | \(-0.617289\pi\) | ||||
−0.360193 | + | 0.932878i | \(0.617289\pi\) | |||||||
\(744\) | −28.6800 | −1.05146 | ||||||||
\(745\) | 12.1816 | 0.446300 | ||||||||
\(746\) | 7.93992 | 0.290701 | ||||||||
\(747\) | 5.89415 | 0.215656 | ||||||||
\(748\) | 5.01113 | 0.183225 | ||||||||
\(749\) | −16.4851 | −0.602354 | ||||||||
\(750\) | 3.82770 | 0.139768 | ||||||||
\(751\) | −25.8769 | −0.944262 | −0.472131 | − | 0.881529i | \(-0.656515\pi\) | ||||
−0.472131 | + | 0.881529i | \(0.656515\pi\) | |||||||
\(752\) | −16.0661 | −0.585869 | ||||||||
\(753\) | 60.3147 | 2.19799 | ||||||||
\(754\) | 13.5278 | 0.492655 | ||||||||
\(755\) | 47.9870 | 1.74643 | ||||||||
\(756\) | −15.6423 | −0.568905 | ||||||||
\(757\) | 22.7535 | 0.826991 | 0.413496 | − | 0.910506i | \(-0.364308\pi\) | ||||
0.413496 | + | 0.910506i | \(0.364308\pi\) | |||||||
\(758\) | 65.7828 | 2.38934 | ||||||||
\(759\) | −7.09458 | −0.257517 | ||||||||
\(760\) | 3.54171 | 0.128471 | ||||||||
\(761\) | −18.2672 | −0.662186 | −0.331093 | − | 0.943598i | \(-0.607417\pi\) | ||||
−0.331093 | + | 0.943598i | \(0.607417\pi\) | |||||||
\(762\) | 2.28236 | 0.0826811 | ||||||||
\(763\) | −12.3403 | −0.446748 | ||||||||
\(764\) | −29.1268 | −1.05377 | ||||||||
\(765\) | 3.18800 | 0.115262 | ||||||||
\(766\) | 0.538118 | 0.0194430 | ||||||||
\(767\) | 1.77323 | 0.0640277 | ||||||||
\(768\) | 2.80083 | 0.101066 | ||||||||
\(769\) | −37.9425 | −1.36824 | −0.684122 | − | 0.729368i | \(-0.739814\pi\) | ||||
−0.684122 | + | 0.729368i | \(0.739814\pi\) | |||||||
\(770\) | −17.8243 | −0.642344 | ||||||||
\(771\) | −55.7613 | −2.00820 | ||||||||
\(772\) | −67.8424 | −2.44170 | ||||||||
\(773\) | 38.3058 | 1.37776 | 0.688882 | − | 0.724873i | \(-0.258102\pi\) | ||||
0.688882 | + | 0.724873i | \(0.258102\pi\) | |||||||
\(774\) | −21.0130 | −0.755297 | ||||||||
\(775\) | 54.9398 | 1.97349 | ||||||||
\(776\) | −22.3101 | −0.800886 | ||||||||
\(777\) | −10.0946 | −0.362143 | ||||||||
\(778\) | 57.6683 | 2.06751 | ||||||||
\(779\) | −5.76535 | −0.206565 | ||||||||
\(780\) | −16.8227 | −0.602349 | ||||||||
\(781\) | −13.1554 | −0.470737 | ||||||||
\(782\) | 4.58127 | 0.163826 | ||||||||
\(783\) | 25.6961 | 0.918305 | ||||||||
\(784\) | 11.2765 | 0.402734 | ||||||||
\(785\) | −12.8556 | −0.458835 | ||||||||
\(786\) | −25.9964 | −0.927259 | ||||||||
\(787\) | −1.44271 | −0.0514271 | −0.0257135 | − | 0.999669i | \(-0.508186\pi\) | ||||
−0.0257135 | + | 0.999669i | \(0.508186\pi\) | |||||||
\(788\) | 22.4014 | 0.798017 | ||||||||
\(789\) | −42.2903 | −1.50557 | ||||||||
\(790\) | −83.0686 | −2.95545 | ||||||||
\(791\) | 20.8486 | 0.741289 | ||||||||
\(792\) | 2.32307 | 0.0825467 | ||||||||
\(793\) | 12.1182 | 0.430329 | ||||||||
\(794\) | −18.2204 | −0.646617 | ||||||||
\(795\) | 40.2070 | 1.42599 | ||||||||
\(796\) | −42.7569 | −1.51548 | ||||||||
\(797\) | −4.73650 | −0.167775 | −0.0838877 | − | 0.996475i | \(-0.526734\pi\) | ||||
−0.0838877 | + | 0.996475i | \(0.526734\pi\) | |||||||
\(798\) | −4.91403 | −0.173955 | ||||||||
\(799\) | −7.42820 | −0.262791 | ||||||||
\(800\) | 40.7832 | 1.44190 | ||||||||
\(801\) | −11.9602 | −0.422593 | ||||||||
\(802\) | 3.47720 | 0.122784 | ||||||||
\(803\) | −27.4185 | −0.967578 | ||||||||
\(804\) | −26.1945 | −0.923808 | ||||||||
\(805\) | −9.27829 | −0.327017 | ||||||||
\(806\) | −22.4279 | −0.789987 | ||||||||
\(807\) | −28.2688 | −0.995109 | ||||||||
\(808\) | 16.6750 | 0.586625 | ||||||||
\(809\) | −53.6218 | −1.88524 | −0.942622 | − | 0.333863i | \(-0.891648\pi\) | ||||
−0.942622 | + | 0.333863i | \(0.891648\pi\) | |||||||
\(810\) | −75.5408 | −2.65423 | ||||||||
\(811\) | −34.1003 | −1.19742 | −0.598711 | − | 0.800965i | \(-0.704320\pi\) | ||||
−0.598711 | + | 0.800965i | \(0.704320\pi\) | |||||||
\(812\) | −23.9856 | −0.841731 | ||||||||
\(813\) | −14.9354 | −0.523806 | ||||||||
\(814\) | −13.5473 | −0.474832 | ||||||||
\(815\) | −7.75704 | −0.271717 | ||||||||
\(816\) | 4.83455 | 0.169243 | ||||||||
\(817\) | 8.27761 | 0.289597 | ||||||||
\(818\) | 65.0415 | 2.27412 | ||||||||
\(819\) | 1.35366 | 0.0473007 | ||||||||
\(820\) | 61.4613 | 2.14632 | ||||||||
\(821\) | −1.52946 | −0.0533784 | −0.0266892 | − | 0.999644i | \(-0.508496\pi\) | ||||
−0.0266892 | + | 0.999644i | \(0.508496\pi\) | |||||||
\(822\) | 21.3022 | 0.742998 | ||||||||
\(823\) | −51.7188 | −1.80281 | −0.901403 | − | 0.432982i | \(-0.857461\pi\) | ||||
−0.901403 | + | 0.432982i | \(0.857461\pi\) | |||||||
\(824\) | 23.0181 | 0.801874 | ||||||||
\(825\) | −18.7006 | −0.651072 | ||||||||
\(826\) | −5.52184 | −0.192130 | ||||||||
\(827\) | 4.07925 | 0.141849 | 0.0709247 | − | 0.997482i | \(-0.477405\pi\) | ||||
0.0709247 | + | 0.997482i | \(0.477405\pi\) | |||||||
\(828\) | 4.96182 | 0.172435 | ||||||||
\(829\) | 8.70954 | 0.302495 | 0.151247 | − | 0.988496i | \(-0.451671\pi\) | ||||
0.151247 | + | 0.988496i | \(0.451671\pi\) | |||||||
\(830\) | 43.4720 | 1.50894 | ||||||||
\(831\) | 32.2731 | 1.11954 | ||||||||
\(832\) | −12.0575 | −0.418018 | ||||||||
\(833\) | 5.21375 | 0.180646 | ||||||||
\(834\) | −9.79956 | −0.339331 | ||||||||
\(835\) | −58.1693 | −2.01303 | ||||||||
\(836\) | −3.75494 | −0.129867 | ||||||||
\(837\) | −42.6017 | −1.47253 | ||||||||
\(838\) | 2.34450 | 0.0809894 | ||||||||
\(839\) | −18.8791 | −0.651779 | −0.325890 | − | 0.945408i | \(-0.605664\pi\) | ||||
−0.325890 | + | 0.945408i | \(0.605664\pi\) | |||||||
\(840\) | 12.7670 | 0.440504 | ||||||||
\(841\) | 10.4020 | 0.358690 | ||||||||
\(842\) | −70.2206 | −2.41996 | ||||||||
\(843\) | −30.7242 | −1.05820 | ||||||||
\(844\) | 36.5895 | 1.25946 | ||||||||
\(845\) | −3.20612 | −0.110294 | ||||||||
\(846\) | −14.1297 | −0.485791 | ||||||||
\(847\) | −11.2888 | −0.387888 | ||||||||
\(848\) | 14.5095 | 0.498259 | ||||||||
\(849\) | −49.3554 | −1.69387 | ||||||||
\(850\) | 12.0758 | 0.414197 | ||||||||
\(851\) | −7.05191 | −0.241736 | ||||||||
\(852\) | 38.6638 | 1.32460 | ||||||||
\(853\) | 46.2514 | 1.58362 | 0.791809 | − | 0.610769i | \(-0.209140\pi\) | ||||
0.791809 | + | 0.610769i | \(0.209140\pi\) | |||||||
\(854\) | −37.7360 | −1.29130 | ||||||||
\(855\) | −2.38883 | −0.0816964 | ||||||||
\(856\) | 15.8464 | 0.541618 | ||||||||
\(857\) | −25.9528 | −0.886532 | −0.443266 | − | 0.896390i | \(-0.646180\pi\) | ||||
−0.443266 | + | 0.896390i | \(0.646180\pi\) | |||||||
\(858\) | 7.63409 | 0.260623 | ||||||||
\(859\) | −44.9547 | −1.53383 | −0.766916 | − | 0.641747i | \(-0.778210\pi\) | ||||
−0.766916 | + | 0.641747i | \(0.778210\pi\) | |||||||
\(860\) | −88.2431 | −3.00907 | ||||||||
\(861\) | −20.7827 | −0.708274 | ||||||||
\(862\) | 34.6389 | 1.17981 | ||||||||
\(863\) | −14.1731 | −0.482459 | −0.241230 | − | 0.970468i | \(-0.577551\pi\) | ||||
−0.241230 | + | 0.970468i | \(0.577551\pi\) | |||||||
\(864\) | −31.6244 | −1.07588 | ||||||||
\(865\) | 41.5720 | 1.41349 | ||||||||
\(866\) | 4.83869 | 0.164425 | ||||||||
\(867\) | −31.4952 | −1.06963 | ||||||||
\(868\) | 39.7659 | 1.34974 | ||||||||
\(869\) | 21.4636 | 0.728103 | ||||||||
\(870\) | −86.0560 | −2.91757 | ||||||||
\(871\) | −4.99222 | −0.169155 | ||||||||
\(872\) | 11.8621 | 0.401702 | ||||||||
\(873\) | 15.0479 | 0.509293 | ||||||||
\(874\) | −3.43284 | −0.116118 | ||||||||
\(875\) | −1.29344 | −0.0437262 | ||||||||
\(876\) | 80.5832 | 2.72265 | ||||||||
\(877\) | 37.3884 | 1.26252 | 0.631258 | − | 0.775573i | \(-0.282539\pi\) | ||||
0.631258 | + | 0.775573i | \(0.282539\pi\) | |||||||
\(878\) | −28.6679 | −0.967496 | ||||||||
\(879\) | 3.56919 | 0.120386 | ||||||||
\(880\) | −13.1401 | −0.442953 | ||||||||
\(881\) | 32.6995 | 1.10167 | 0.550837 | − | 0.834613i | \(-0.314309\pi\) | ||||
0.550837 | + | 0.834613i | \(0.314309\pi\) | |||||||
\(882\) | 9.91747 | 0.333939 | ||||||||
\(883\) | −3.81884 | −0.128514 | −0.0642570 | − | 0.997933i | \(-0.520468\pi\) | ||||
−0.0642570 | + | 0.997933i | \(0.520468\pi\) | |||||||
\(884\) | −2.80686 | −0.0944050 | ||||||||
\(885\) | −11.2802 | −0.379181 | ||||||||
\(886\) | 30.0065 | 1.00809 | ||||||||
\(887\) | 10.6807 | 0.358622 | 0.179311 | − | 0.983792i | \(-0.442613\pi\) | ||||
0.179311 | + | 0.983792i | \(0.442613\pi\) | |||||||
\(888\) | 9.70350 | 0.325628 | ||||||||
\(889\) | −0.771242 | −0.0258666 | ||||||||
\(890\) | −88.2119 | −2.95687 | ||||||||
\(891\) | 19.5186 | 0.653896 | ||||||||
\(892\) | −11.2242 | −0.375816 | ||||||||
\(893\) | 5.56610 | 0.186262 | ||||||||
\(894\) | 16.2468 | 0.543374 | ||||||||
\(895\) | −10.5843 | −0.353793 | ||||||||
\(896\) | 15.2220 | 0.508531 | ||||||||
\(897\) | 3.97385 | 0.132683 | ||||||||
\(898\) | 23.5211 | 0.784908 | ||||||||
\(899\) | −65.3248 | −2.17870 | ||||||||
\(900\) | 13.0789 | 0.435963 | ||||||||
\(901\) | 6.70852 | 0.223493 | ||||||||
\(902\) | −27.8910 | −0.928668 | ||||||||
\(903\) | 29.8388 | 0.992974 | ||||||||
\(904\) | −20.0407 | −0.666545 | ||||||||
\(905\) | −22.3310 | −0.742309 | ||||||||
\(906\) | 64.0010 | 2.12629 | ||||||||
\(907\) | 44.5948 | 1.48075 | 0.740374 | − | 0.672195i | \(-0.234649\pi\) | ||||
0.740374 | + | 0.672195i | \(0.234649\pi\) | |||||||
\(908\) | 24.1844 | 0.802588 | ||||||||
\(909\) | −11.2471 | −0.373041 | ||||||||
\(910\) | 9.98386 | 0.330962 | ||||||||
\(911\) | −4.95396 | −0.164132 | −0.0820660 | − | 0.996627i | \(-0.526152\pi\) | ||||
−0.0820660 | + | 0.996627i | \(0.526152\pi\) | |||||||
\(912\) | −3.62263 | −0.119957 | ||||||||
\(913\) | −11.2325 | −0.371741 | ||||||||
\(914\) | 61.6964 | 2.04074 | ||||||||
\(915\) | −77.0886 | −2.54847 | ||||||||
\(916\) | −8.68025 | −0.286803 | ||||||||
\(917\) | 8.78455 | 0.290091 | ||||||||
\(918\) | −9.36389 | −0.309054 | ||||||||
\(919\) | −30.8533 | −1.01776 | −0.508878 | − | 0.860838i | \(-0.669940\pi\) | ||||
−0.508878 | + | 0.860838i | \(0.669940\pi\) | |||||||
\(920\) | 8.91878 | 0.294043 | ||||||||
\(921\) | −43.3116 | −1.42717 | ||||||||
\(922\) | 32.0992 | 1.05713 | ||||||||
\(923\) | 7.36867 | 0.242543 | ||||||||
\(924\) | −13.5357 | −0.445291 | ||||||||
\(925\) | −18.5882 | −0.611175 | ||||||||
\(926\) | −22.6922 | −0.745712 | ||||||||
\(927\) | −15.5254 | −0.509921 | ||||||||
\(928\) | −48.4923 | −1.59184 | ||||||||
\(929\) | −54.5545 | −1.78988 | −0.894938 | − | 0.446190i | \(-0.852780\pi\) | ||||
−0.894938 | + | 0.446190i | \(0.852780\pi\) | |||||||
\(930\) | 142.673 | 4.67842 | ||||||||
\(931\) | −3.90677 | −0.128039 | ||||||||
\(932\) | −1.24392 | −0.0407459 | ||||||||
\(933\) | −18.6073 | −0.609177 | ||||||||
\(934\) | −40.9224 | −1.33902 | ||||||||
\(935\) | −6.07538 | −0.198686 | ||||||||
\(936\) | −1.30121 | −0.0425314 | ||||||||
\(937\) | 41.4863 | 1.35530 | 0.677649 | − | 0.735385i | \(-0.262999\pi\) | ||||
0.677649 | + | 0.735385i | \(0.262999\pi\) | |||||||
\(938\) | 15.5458 | 0.507588 | ||||||||
\(939\) | 55.0188 | 1.79547 | ||||||||
\(940\) | −59.3372 | −1.93537 | ||||||||
\(941\) | 28.4939 | 0.928873 | 0.464437 | − | 0.885606i | \(-0.346257\pi\) | ||||
0.464437 | + | 0.885606i | \(0.346257\pi\) | |||||||
\(942\) | −17.1457 | −0.558636 | ||||||||
\(943\) | −14.5184 | −0.472784 | ||||||||
\(944\) | −4.07071 | −0.132490 | ||||||||
\(945\) | 18.9643 | 0.616910 | ||||||||
\(946\) | 40.0445 | 1.30196 | ||||||||
\(947\) | −53.0786 | −1.72482 | −0.862411 | − | 0.506208i | \(-0.831047\pi\) | ||||
−0.862411 | + | 0.506208i | \(0.831047\pi\) | |||||||
\(948\) | −63.0817 | −2.04880 | ||||||||
\(949\) | 15.3578 | 0.498535 | ||||||||
\(950\) | −9.04864 | −0.293577 | ||||||||
\(951\) | −10.6720 | −0.346062 | ||||||||
\(952\) | 2.13018 | 0.0690394 | ||||||||
\(953\) | −24.5554 | −0.795426 | −0.397713 | − | 0.917510i | \(-0.630196\pi\) | ||||
−0.397713 | + | 0.917510i | \(0.630196\pi\) | |||||||
\(954\) | 12.7608 | 0.413146 | ||||||||
\(955\) | 35.3127 | 1.14269 | ||||||||
\(956\) | 60.6166 | 1.96048 | ||||||||
\(957\) | 22.2355 | 0.718772 | ||||||||
\(958\) | 28.7534 | 0.928979 | ||||||||
\(959\) | −7.19832 | −0.232446 | ||||||||
\(960\) | 76.7026 | 2.47557 | ||||||||
\(961\) | 77.3022 | 2.49362 | ||||||||
\(962\) | 7.58817 | 0.244653 | ||||||||
\(963\) | −10.6882 | −0.344421 | ||||||||
\(964\) | 11.9148 | 0.383749 | ||||||||
\(965\) | 82.2505 | 2.64774 | ||||||||
\(966\) | −12.3746 | −0.398146 | ||||||||
\(967\) | −53.4093 | −1.71753 | −0.858763 | − | 0.512373i | \(-0.828767\pi\) | ||||
−0.858763 | + | 0.512373i | \(0.828767\pi\) | |||||||
\(968\) | 10.8514 | 0.348777 | ||||||||
\(969\) | −1.67493 | −0.0538067 | ||||||||
\(970\) | 110.985 | 3.56350 | ||||||||
\(971\) | 43.7089 | 1.40269 | 0.701343 | − | 0.712824i | \(-0.252584\pi\) | ||||
0.701343 | + | 0.712824i | \(0.252584\pi\) | |||||||
\(972\) | −24.8885 | −0.798298 | ||||||||
\(973\) | 3.31142 | 0.106159 | ||||||||
\(974\) | 4.77145 | 0.152887 | ||||||||
\(975\) | 10.4747 | 0.335459 | ||||||||
\(976\) | −27.8190 | −0.890465 | ||||||||
\(977\) | 10.5564 | 0.337728 | 0.168864 | − | 0.985639i | \(-0.445990\pi\) | ||||
0.168864 | + | 0.985639i | \(0.445990\pi\) | |||||||
\(978\) | −10.3457 | −0.330818 | ||||||||
\(979\) | 22.7926 | 0.728454 | ||||||||
\(980\) | 41.6480 | 1.33040 | ||||||||
\(981\) | −8.00083 | −0.255447 | ||||||||
\(982\) | −0.141468 | −0.00451441 | ||||||||
\(983\) | −8.85818 | −0.282532 | −0.141266 | − | 0.989972i | \(-0.545117\pi\) | ||||
−0.141266 | + | 0.989972i | \(0.545117\pi\) | |||||||
\(984\) | 19.9775 | 0.636858 | ||||||||
\(985\) | −27.1589 | −0.865356 | ||||||||
\(986\) | −14.3584 | −0.457266 | ||||||||
\(987\) | 20.0645 | 0.638659 | ||||||||
\(988\) | 2.10324 | 0.0669129 | ||||||||
\(989\) | 20.8448 | 0.662826 | ||||||||
\(990\) | −11.5564 | −0.367287 | ||||||||
\(991\) | −6.95532 | −0.220943 | −0.110471 | − | 0.993879i | \(-0.535236\pi\) | ||||
−0.110471 | + | 0.993879i | \(0.535236\pi\) | |||||||
\(992\) | 80.3955 | 2.55256 | ||||||||
\(993\) | −10.4430 | −0.331397 | ||||||||
\(994\) | −22.9460 | −0.727804 | ||||||||
\(995\) | 51.8375 | 1.64336 | ||||||||
\(996\) | 33.0123 | 1.04604 | ||||||||
\(997\) | −28.0571 | −0.888578 | −0.444289 | − | 0.895883i | \(-0.646544\pi\) | ||||
−0.444289 | + | 0.895883i | \(0.646544\pi\) | |||||||
\(998\) | 75.4012 | 2.38678 | ||||||||
\(999\) | 14.4137 | 0.456031 |
(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 | 8047.2.a.b.1.20 | ✓ | 142 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.b.1.20 | ✓ | 142 | 1.1 | even | 1 | trivial |