Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, 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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(143\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73897 | −1.93675 | −0.968374 | − | 0.249504i | \(-0.919733\pi\) | ||||
−0.968374 | + | 0.249504i | \(0.919733\pi\) | |||||||
\(3\) | −2.10858 | −1.21739 | −0.608694 | − | 0.793405i | \(-0.708306\pi\) | ||||
−0.608694 | + | 0.793405i | \(0.708306\pi\) | |||||||
\(4\) | 5.50198 | 2.75099 | ||||||||
\(5\) | −1.32967 | −0.594646 | −0.297323 | − | 0.954777i | \(-0.596094\pi\) | ||||
−0.297323 | + | 0.954777i | \(0.596094\pi\) | |||||||
\(6\) | 5.77534 | 2.35777 | ||||||||
\(7\) | 4.16128 | 1.57282 | 0.786408 | − | 0.617707i | \(-0.211938\pi\) | ||||
0.786408 | + | 0.617707i | \(0.211938\pi\) | |||||||
\(8\) | −9.59184 | −3.39123 | ||||||||
\(9\) | 1.44610 | 0.482033 | ||||||||
\(10\) | 3.64193 | 1.15168 | ||||||||
\(11\) | 5.31866 | 1.60364 | 0.801818 | − | 0.597569i | \(-0.203866\pi\) | ||||
0.801818 | + | 0.597569i | \(0.203866\pi\) | |||||||
\(12\) | −11.6014 | −3.34902 | ||||||||
\(13\) | −6.77846 | −1.88001 | −0.940003 | − | 0.341166i | \(-0.889178\pi\) | ||||
−0.940003 | + | 0.341166i | \(0.889178\pi\) | |||||||
\(14\) | −11.3976 | −3.04615 | ||||||||
\(15\) | 2.80371 | 0.723914 | ||||||||
\(16\) | 15.2679 | 3.81696 | ||||||||
\(17\) | −6.76063 | −1.63969 | −0.819847 | − | 0.572582i | \(-0.805942\pi\) | ||||
−0.819847 | + | 0.572582i | \(0.805942\pi\) | |||||||
\(18\) | −3.96083 | −0.933576 | ||||||||
\(19\) | −3.24262 | −0.743909 | −0.371955 | − | 0.928251i | \(-0.621312\pi\) | ||||
−0.371955 | + | 0.928251i | \(0.621312\pi\) | |||||||
\(20\) | −7.31581 | −1.63587 | ||||||||
\(21\) | −8.77438 | −1.91473 | ||||||||
\(22\) | −14.5677 | −3.10584 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 20.2251 | 4.12844 | ||||||||
\(25\) | −3.23198 | −0.646396 | ||||||||
\(26\) | 18.5660 | 3.64110 | ||||||||
\(27\) | 3.27652 | 0.630567 | ||||||||
\(28\) | 22.8953 | 4.32680 | ||||||||
\(29\) | 8.05321 | 1.49544 | 0.747722 | − | 0.664012i | \(-0.231148\pi\) | ||||
0.747722 | + | 0.664012i | \(0.231148\pi\) | |||||||
\(30\) | −7.67929 | −1.40204 | ||||||||
\(31\) | −5.40902 | −0.971488 | −0.485744 | − | 0.874101i | \(-0.661451\pi\) | ||||
−0.485744 | + | 0.874101i | \(0.661451\pi\) | |||||||
\(32\) | −22.6346 | −4.00127 | ||||||||
\(33\) | −11.2148 | −1.95225 | ||||||||
\(34\) | 18.5172 | 3.17567 | ||||||||
\(35\) | −5.53312 | −0.935268 | ||||||||
\(36\) | 7.95641 | 1.32607 | ||||||||
\(37\) | −8.96409 | −1.47369 | −0.736843 | − | 0.676063i | \(-0.763685\pi\) | ||||
−0.736843 | + | 0.676063i | \(0.763685\pi\) | |||||||
\(38\) | 8.88147 | 1.44076 | ||||||||
\(39\) | 14.2929 | 2.28870 | ||||||||
\(40\) | 12.7540 | 2.01658 | ||||||||
\(41\) | 8.93996 | 1.39619 | 0.698093 | − | 0.716007i | \(-0.254032\pi\) | ||||
0.698093 | + | 0.716007i | \(0.254032\pi\) | |||||||
\(42\) | 24.0328 | 3.70834 | ||||||||
\(43\) | 1.20205 | 0.183311 | 0.0916553 | − | 0.995791i | \(-0.470784\pi\) | ||||
0.0916553 | + | 0.995791i | \(0.470784\pi\) | |||||||
\(44\) | 29.2632 | 4.41159 | ||||||||
\(45\) | −1.92283 | −0.286639 | ||||||||
\(46\) | −2.73897 | −0.403840 | ||||||||
\(47\) | 7.04061 | 1.02698 | 0.513490 | − | 0.858096i | \(-0.328353\pi\) | ||||
0.513490 | + | 0.858096i | \(0.328353\pi\) | |||||||
\(48\) | −32.1935 | −4.64673 | ||||||||
\(49\) | 10.3162 | 1.47375 | ||||||||
\(50\) | 8.85232 | 1.25191 | ||||||||
\(51\) | 14.2553 | 1.99614 | ||||||||
\(52\) | −37.2950 | −5.17188 | ||||||||
\(53\) | −3.57904 | −0.491619 | −0.245810 | − | 0.969318i | \(-0.579054\pi\) | ||||
−0.245810 | + | 0.969318i | \(0.579054\pi\) | |||||||
\(54\) | −8.97431 | −1.22125 | ||||||||
\(55\) | −7.07205 | −0.953595 | ||||||||
\(56\) | −39.9144 | −5.33378 | ||||||||
\(57\) | 6.83733 | 0.905626 | ||||||||
\(58\) | −22.0575 | −2.89630 | ||||||||
\(59\) | 9.09310 | 1.18382 | 0.591911 | − | 0.806004i | \(-0.298374\pi\) | ||||
0.591911 | + | 0.806004i | \(0.298374\pi\) | |||||||
\(60\) | 15.4260 | 1.99148 | ||||||||
\(61\) | 5.56372 | 0.712361 | 0.356181 | − | 0.934417i | \(-0.384079\pi\) | ||||
0.356181 | + | 0.934417i | \(0.384079\pi\) | |||||||
\(62\) | 14.8152 | 1.88153 | ||||||||
\(63\) | 6.01762 | 0.758149 | ||||||||
\(64\) | 31.4598 | 3.93248 | ||||||||
\(65\) | 9.01310 | 1.11794 | ||||||||
\(66\) | 30.7171 | 3.78101 | ||||||||
\(67\) | −12.4016 | −1.51509 | −0.757547 | − | 0.652780i | \(-0.773603\pi\) | ||||
−0.757547 | + | 0.652780i | \(0.773603\pi\) | |||||||
\(68\) | −37.1969 | −4.51079 | ||||||||
\(69\) | −2.10858 | −0.253843 | ||||||||
\(70\) | 15.1551 | 1.81138 | ||||||||
\(71\) | 2.85671 | 0.339029 | 0.169515 | − | 0.985528i | \(-0.445780\pi\) | ||||
0.169515 | + | 0.985528i | \(0.445780\pi\) | |||||||
\(72\) | −13.8708 | −1.63468 | ||||||||
\(73\) | 12.9418 | 1.51472 | 0.757361 | − | 0.652997i | \(-0.226489\pi\) | ||||
0.757361 | + | 0.652997i | \(0.226489\pi\) | |||||||
\(74\) | 24.5524 | 2.85416 | ||||||||
\(75\) | 6.81488 | 0.786915 | ||||||||
\(76\) | −17.8409 | −2.04649 | ||||||||
\(77\) | 22.1324 | 2.52222 | ||||||||
\(78\) | −39.1479 | −4.43263 | ||||||||
\(79\) | 4.33291 | 0.487490 | 0.243745 | − | 0.969839i | \(-0.421624\pi\) | ||||
0.243745 | + | 0.969839i | \(0.421624\pi\) | |||||||
\(80\) | −20.3012 | −2.26974 | ||||||||
\(81\) | −11.2471 | −1.24968 | ||||||||
\(82\) | −24.4863 | −2.70406 | ||||||||
\(83\) | 6.21728 | 0.682435 | 0.341218 | − | 0.939984i | \(-0.389161\pi\) | ||||
0.341218 | + | 0.939984i | \(0.389161\pi\) | |||||||
\(84\) | −48.2765 | −5.26740 | ||||||||
\(85\) | 8.98940 | 0.975037 | ||||||||
\(86\) | −3.29238 | −0.355026 | ||||||||
\(87\) | −16.9808 | −1.82053 | ||||||||
\(88\) | −51.0157 | −5.43830 | ||||||||
\(89\) | −1.41376 | −0.149858 | −0.0749291 | − | 0.997189i | \(-0.523873\pi\) | ||||
−0.0749291 | + | 0.997189i | \(0.523873\pi\) | |||||||
\(90\) | 5.26659 | 0.555147 | ||||||||
\(91\) | −28.2071 | −2.95690 | ||||||||
\(92\) | 5.50198 | 0.573621 | ||||||||
\(93\) | 11.4053 | 1.18268 | ||||||||
\(94\) | −19.2841 | −1.98900 | ||||||||
\(95\) | 4.31162 | 0.442362 | ||||||||
\(96\) | 47.7268 | 4.87109 | ||||||||
\(97\) | −0.694735 | −0.0705396 | −0.0352698 | − | 0.999378i | \(-0.511229\pi\) | ||||
−0.0352698 | + | 0.999378i | \(0.511229\pi\) | |||||||
\(98\) | −28.2559 | −2.85428 | ||||||||
\(99\) | 7.69131 | 0.773005 | ||||||||
\(100\) | −17.7823 | −1.77823 | ||||||||
\(101\) | 3.51938 | 0.350192 | 0.175096 | − | 0.984551i | \(-0.443976\pi\) | ||||
0.175096 | + | 0.984551i | \(0.443976\pi\) | |||||||
\(102\) | −39.0450 | −3.86603 | ||||||||
\(103\) | 2.21443 | 0.218194 | 0.109097 | − | 0.994031i | \(-0.465204\pi\) | ||||
0.109097 | + | 0.994031i | \(0.465204\pi\) | |||||||
\(104\) | 65.0179 | 6.37553 | ||||||||
\(105\) | 11.6670 | 1.13858 | ||||||||
\(106\) | 9.80290 | 0.952142 | ||||||||
\(107\) | −3.65970 | −0.353796 | −0.176898 | − | 0.984229i | \(-0.556606\pi\) | ||||
−0.176898 | + | 0.984229i | \(0.556606\pi\) | |||||||
\(108\) | 18.0274 | 1.73468 | ||||||||
\(109\) | −13.6009 | −1.30273 | −0.651364 | − | 0.758766i | \(-0.725803\pi\) | ||||
−0.651364 | + | 0.758766i | \(0.725803\pi\) | |||||||
\(110\) | 19.3702 | 1.84687 | ||||||||
\(111\) | 18.9015 | 1.79405 | ||||||||
\(112\) | 63.5338 | 6.00338 | ||||||||
\(113\) | −13.6744 | −1.28638 | −0.643190 | − | 0.765707i | \(-0.722389\pi\) | ||||
−0.643190 | + | 0.765707i | \(0.722389\pi\) | |||||||
\(114\) | −18.7273 | −1.75397 | ||||||||
\(115\) | −1.32967 | −0.123992 | ||||||||
\(116\) | 44.3086 | 4.11395 | ||||||||
\(117\) | −9.80232 | −0.906225 | ||||||||
\(118\) | −24.9058 | −2.29276 | ||||||||
\(119\) | −28.1329 | −2.57894 | ||||||||
\(120\) | −26.8927 | −2.45496 | ||||||||
\(121\) | 17.2881 | 1.57165 | ||||||||
\(122\) | −15.2389 | −1.37966 | ||||||||
\(123\) | −18.8506 | −1.69970 | ||||||||
\(124\) | −29.7603 | −2.67256 | ||||||||
\(125\) | 10.9458 | 0.979023 | ||||||||
\(126\) | −16.4821 | −1.46834 | ||||||||
\(127\) | 3.87782 | 0.344100 | 0.172050 | − | 0.985088i | \(-0.444961\pi\) | ||||
0.172050 | + | 0.985088i | \(0.444961\pi\) | |||||||
\(128\) | −40.8986 | −3.61496 | ||||||||
\(129\) | −2.53461 | −0.223160 | ||||||||
\(130\) | −24.6867 | −2.16516 | ||||||||
\(131\) | −4.93426 | −0.431108 | −0.215554 | − | 0.976492i | \(-0.569156\pi\) | ||||
−0.215554 | + | 0.976492i | \(0.569156\pi\) | |||||||
\(132\) | −61.7037 | −5.37061 | ||||||||
\(133\) | −13.4935 | −1.17003 | ||||||||
\(134\) | 33.9676 | 2.93436 | ||||||||
\(135\) | −4.35669 | −0.374964 | ||||||||
\(136\) | 64.8470 | 5.56058 | ||||||||
\(137\) | 5.35120 | 0.457184 | 0.228592 | − | 0.973522i | \(-0.426588\pi\) | ||||
0.228592 | + | 0.973522i | \(0.426588\pi\) | |||||||
\(138\) | 5.77534 | 0.491630 | ||||||||
\(139\) | −22.3263 | −1.89370 | −0.946848 | − | 0.321681i | \(-0.895752\pi\) | ||||
−0.946848 | + | 0.321681i | \(0.895752\pi\) | |||||||
\(140\) | −30.4431 | −2.57292 | ||||||||
\(141\) | −14.8457 | −1.25023 | ||||||||
\(142\) | −7.82446 | −0.656614 | ||||||||
\(143\) | −36.0523 | −3.01484 | ||||||||
\(144\) | 22.0788 | 1.83990 | ||||||||
\(145\) | −10.7081 | −0.889259 | ||||||||
\(146\) | −35.4472 | −2.93363 | ||||||||
\(147\) | −21.7526 | −1.79413 | ||||||||
\(148\) | −49.3203 | −4.05410 | ||||||||
\(149\) | −6.32361 | −0.518050 | −0.259025 | − | 0.965871i | \(-0.583401\pi\) | ||||
−0.259025 | + | 0.965871i | \(0.583401\pi\) | |||||||
\(150\) | −18.6658 | −1.52406 | ||||||||
\(151\) | −2.96436 | −0.241236 | −0.120618 | − | 0.992699i | \(-0.538488\pi\) | ||||
−0.120618 | + | 0.992699i | \(0.538488\pi\) | |||||||
\(152\) | 31.1028 | 2.52277 | ||||||||
\(153\) | −9.77655 | −0.790387 | ||||||||
\(154\) | −60.6202 | −4.88491 | ||||||||
\(155\) | 7.19220 | 0.577691 | ||||||||
\(156\) | 78.6393 | 6.29618 | ||||||||
\(157\) | 18.6522 | 1.48861 | 0.744303 | − | 0.667842i | \(-0.232782\pi\) | ||||
0.744303 | + | 0.667842i | \(0.232782\pi\) | |||||||
\(158\) | −11.8677 | −0.944145 | ||||||||
\(159\) | 7.54669 | 0.598491 | ||||||||
\(160\) | 30.0965 | 2.37934 | ||||||||
\(161\) | 4.16128 | 0.327955 | ||||||||
\(162\) | 30.8055 | 2.42031 | ||||||||
\(163\) | −2.00945 | −0.157392 | −0.0786962 | − | 0.996899i | \(-0.525076\pi\) | ||||
−0.0786962 | + | 0.996899i | \(0.525076\pi\) | |||||||
\(164\) | 49.1875 | 3.84090 | ||||||||
\(165\) | 14.9120 | 1.16090 | ||||||||
\(166\) | −17.0290 | −1.32170 | ||||||||
\(167\) | 21.4783 | 1.66204 | 0.831019 | − | 0.556244i | \(-0.187758\pi\) | ||||
0.831019 | + | 0.556244i | \(0.187758\pi\) | |||||||
\(168\) | 84.1625 | 6.49328 | ||||||||
\(169\) | 32.9475 | 2.53442 | ||||||||
\(170\) | −24.6217 | −1.88840 | ||||||||
\(171\) | −4.68916 | −0.358589 | ||||||||
\(172\) | 6.61365 | 0.504286 | ||||||||
\(173\) | 24.2584 | 1.84433 | 0.922164 | − | 0.386799i | \(-0.126419\pi\) | ||||
0.922164 | + | 0.386799i | \(0.126419\pi\) | |||||||
\(174\) | 46.5100 | 3.52592 | ||||||||
\(175\) | −13.4492 | −1.01666 | ||||||||
\(176\) | 81.2045 | 6.12102 | ||||||||
\(177\) | −19.1735 | −1.44117 | ||||||||
\(178\) | 3.87225 | 0.290238 | ||||||||
\(179\) | −15.2970 | −1.14335 | −0.571676 | − | 0.820479i | \(-0.693707\pi\) | ||||
−0.571676 | + | 0.820479i | \(0.693707\pi\) | |||||||
\(180\) | −10.5794 | −0.788541 | ||||||||
\(181\) | 14.5150 | 1.07889 | 0.539444 | − | 0.842021i | \(-0.318634\pi\) | ||||
0.539444 | + | 0.842021i | \(0.318634\pi\) | |||||||
\(182\) | 77.2584 | 5.72678 | ||||||||
\(183\) | −11.7315 | −0.867220 | ||||||||
\(184\) | −9.59184 | −0.707120 | ||||||||
\(185\) | 11.9193 | 0.876322 | ||||||||
\(186\) | −31.2389 | −2.29055 | ||||||||
\(187\) | −35.9575 | −2.62947 | ||||||||
\(188\) | 38.7373 | 2.82521 | ||||||||
\(189\) | 13.6345 | 0.991765 | ||||||||
\(190\) | −11.8094 | −0.856744 | ||||||||
\(191\) | −12.8433 | −0.929306 | −0.464653 | − | 0.885493i | \(-0.653821\pi\) | ||||
−0.464653 | + | 0.885493i | \(0.653821\pi\) | |||||||
\(192\) | −66.3355 | −4.78735 | ||||||||
\(193\) | −10.9023 | −0.784768 | −0.392384 | − | 0.919802i | \(-0.628349\pi\) | ||||
−0.392384 | + | 0.919802i | \(0.628349\pi\) | |||||||
\(194\) | 1.90286 | 0.136617 | ||||||||
\(195\) | −19.0048 | −1.36096 | ||||||||
\(196\) | 56.7598 | 4.05427 | ||||||||
\(197\) | −3.56179 | −0.253767 | −0.126883 | − | 0.991918i | \(-0.540497\pi\) | ||||
−0.126883 | + | 0.991918i | \(0.540497\pi\) | |||||||
\(198\) | −21.0663 | −1.49712 | ||||||||
\(199\) | 12.6910 | 0.899638 | 0.449819 | − | 0.893120i | \(-0.351488\pi\) | ||||
0.449819 | + | 0.893120i | \(0.351488\pi\) | |||||||
\(200\) | 31.0007 | 2.19208 | ||||||||
\(201\) | 26.1497 | 1.84446 | ||||||||
\(202\) | −9.63950 | −0.678233 | ||||||||
\(203\) | 33.5117 | 2.35206 | ||||||||
\(204\) | 78.4325 | 5.49138 | ||||||||
\(205\) | −11.8872 | −0.830237 | ||||||||
\(206\) | −6.06526 | −0.422586 | ||||||||
\(207\) | 1.44610 | 0.100511 | ||||||||
\(208\) | −103.493 | −7.17591 | ||||||||
\(209\) | −17.2464 | −1.19296 | ||||||||
\(210\) | −31.9557 | −2.20515 | ||||||||
\(211\) | −19.6175 | −1.35052 | −0.675261 | − | 0.737578i | \(-0.735969\pi\) | ||||
−0.675261 | + | 0.737578i | \(0.735969\pi\) | |||||||
\(212\) | −19.6918 | −1.35244 | ||||||||
\(213\) | −6.02359 | −0.412730 | ||||||||
\(214\) | 10.0238 | 0.685214 | ||||||||
\(215\) | −1.59833 | −0.109005 | ||||||||
\(216\) | −31.4279 | −2.13840 | ||||||||
\(217\) | −22.5084 | −1.52797 | ||||||||
\(218\) | 37.2524 | 2.52305 | ||||||||
\(219\) | −27.2888 | −1.84400 | ||||||||
\(220\) | −38.9103 | −2.62333 | ||||||||
\(221\) | 45.8267 | 3.08264 | ||||||||
\(222\) | −51.7707 | −3.47462 | ||||||||
\(223\) | 16.5103 | 1.10561 | 0.552806 | − | 0.833310i | \(-0.313557\pi\) | ||||
0.552806 | + | 0.833310i | \(0.313557\pi\) | |||||||
\(224\) | −94.1888 | −6.29326 | ||||||||
\(225\) | −4.67377 | −0.311584 | ||||||||
\(226\) | 37.4538 | 2.49139 | ||||||||
\(227\) | 2.31861 | 0.153892 | 0.0769459 | − | 0.997035i | \(-0.475483\pi\) | ||||
0.0769459 | + | 0.997035i | \(0.475483\pi\) | |||||||
\(228\) | 37.6189 | 2.49137 | ||||||||
\(229\) | 11.5411 | 0.762659 | 0.381330 | − | 0.924439i | \(-0.375466\pi\) | ||||
0.381330 | + | 0.924439i | \(0.375466\pi\) | |||||||
\(230\) | 3.64193 | 0.240142 | ||||||||
\(231\) | −46.6679 | −3.07052 | ||||||||
\(232\) | −77.2451 | −5.07139 | ||||||||
\(233\) | 1.30812 | 0.0856976 | 0.0428488 | − | 0.999082i | \(-0.486357\pi\) | ||||
0.0428488 | + | 0.999082i | \(0.486357\pi\) | |||||||
\(234\) | 26.8483 | 1.75513 | ||||||||
\(235\) | −9.36168 | −0.610689 | ||||||||
\(236\) | 50.0301 | 3.25668 | ||||||||
\(237\) | −9.13627 | −0.593465 | ||||||||
\(238\) | 77.0553 | 4.99475 | ||||||||
\(239\) | −19.7265 | −1.27600 | −0.638001 | − | 0.770035i | \(-0.720239\pi\) | ||||
−0.638001 | + | 0.770035i | \(0.720239\pi\) | |||||||
\(240\) | 42.8066 | 2.76316 | ||||||||
\(241\) | −4.22094 | −0.271894 | −0.135947 | − | 0.990716i | \(-0.543408\pi\) | ||||
−0.135947 | + | 0.990716i | \(0.543408\pi\) | |||||||
\(242\) | −47.3517 | −3.04388 | ||||||||
\(243\) | 13.8858 | 0.890775 | ||||||||
\(244\) | 30.6115 | 1.95970 | ||||||||
\(245\) | −13.7172 | −0.876359 | ||||||||
\(246\) | 51.6313 | 3.29189 | ||||||||
\(247\) | 21.9800 | 1.39855 | ||||||||
\(248\) | 51.8825 | 3.29454 | ||||||||
\(249\) | −13.1096 | −0.830788 | ||||||||
\(250\) | −29.9803 | −1.89612 | ||||||||
\(251\) | −3.76355 | −0.237553 | −0.118777 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118777 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(252\) | 33.1089 | 2.08566 | ||||||||
\(253\) | 5.31866 | 0.334381 | ||||||||
\(254\) | −10.6212 | −0.666436 | ||||||||
\(255\) | −18.9548 | −1.18700 | ||||||||
\(256\) | 49.1004 | 3.06878 | ||||||||
\(257\) | 6.89460 | 0.430074 | 0.215037 | − | 0.976606i | \(-0.431013\pi\) | ||||
0.215037 | + | 0.976606i | \(0.431013\pi\) | |||||||
\(258\) | 6.94224 | 0.432205 | ||||||||
\(259\) | −37.3021 | −2.31784 | ||||||||
\(260\) | 49.5899 | 3.07544 | ||||||||
\(261\) | 11.6457 | 0.720853 | ||||||||
\(262\) | 13.5148 | 0.834948 | ||||||||
\(263\) | −21.0001 | −1.29492 | −0.647460 | − | 0.762100i | \(-0.724169\pi\) | ||||
−0.647460 | + | 0.762100i | \(0.724169\pi\) | |||||||
\(264\) | 107.571 | 6.62052 | ||||||||
\(265\) | 4.75894 | 0.292339 | ||||||||
\(266\) | 36.9583 | 2.26606 | ||||||||
\(267\) | 2.98102 | 0.182436 | ||||||||
\(268\) | −68.2333 | −4.16801 | ||||||||
\(269\) | −13.9626 | −0.851314 | −0.425657 | − | 0.904885i | \(-0.639957\pi\) | ||||
−0.425657 | + | 0.904885i | \(0.639957\pi\) | |||||||
\(270\) | 11.9329 | 0.726210 | ||||||||
\(271\) | 3.96012 | 0.240560 | 0.120280 | − | 0.992740i | \(-0.461621\pi\) | ||||
0.120280 | + | 0.992740i | \(0.461621\pi\) | |||||||
\(272\) | −103.220 | −6.25866 | ||||||||
\(273\) | 59.4768 | 3.59970 | ||||||||
\(274\) | −14.6568 | −0.885450 | ||||||||
\(275\) | −17.1898 | −1.03658 | ||||||||
\(276\) | −11.6014 | −0.698320 | ||||||||
\(277\) | −15.1716 | −0.911575 | −0.455788 | − | 0.890089i | \(-0.650642\pi\) | ||||
−0.455788 | + | 0.890089i | \(0.650642\pi\) | |||||||
\(278\) | 61.1513 | 3.66761 | ||||||||
\(279\) | −7.82197 | −0.468289 | ||||||||
\(280\) | 53.0728 | 3.17171 | ||||||||
\(281\) | −26.7344 | −1.59484 | −0.797421 | − | 0.603424i | \(-0.793803\pi\) | ||||
−0.797421 | + | 0.603424i | \(0.793803\pi\) | |||||||
\(282\) | 40.6619 | 2.42138 | ||||||||
\(283\) | 21.8984 | 1.30172 | 0.650861 | − | 0.759197i | \(-0.274408\pi\) | ||||
0.650861 | + | 0.759197i | \(0.274408\pi\) | |||||||
\(284\) | 15.7176 | 0.932666 | ||||||||
\(285\) | −9.09138 | −0.538527 | ||||||||
\(286\) | 98.7463 | 5.83899 | ||||||||
\(287\) | 37.2017 | 2.19594 | ||||||||
\(288\) | −32.7318 | −1.92874 | ||||||||
\(289\) | 28.7062 | 1.68860 | ||||||||
\(290\) | 29.3292 | 1.72227 | ||||||||
\(291\) | 1.46490 | 0.0858741 | ||||||||
\(292\) | 71.2055 | 4.16699 | ||||||||
\(293\) | −14.0001 | −0.817893 | −0.408946 | − | 0.912558i | \(-0.634104\pi\) | ||||
−0.408946 | + | 0.912558i | \(0.634104\pi\) | |||||||
\(294\) | 59.5799 | 3.47477 | ||||||||
\(295\) | −12.0908 | −0.703954 | ||||||||
\(296\) | 85.9821 | 4.99761 | ||||||||
\(297\) | 17.4267 | 1.01120 | ||||||||
\(298\) | 17.3202 | 1.00333 | ||||||||
\(299\) | −6.77846 | −0.392008 | ||||||||
\(300\) | 37.4954 | 2.16480 | ||||||||
\(301\) | 5.00206 | 0.288314 | ||||||||
\(302\) | 8.11930 | 0.467213 | ||||||||
\(303\) | −7.42089 | −0.426319 | ||||||||
\(304\) | −49.5079 | −2.83947 | ||||||||
\(305\) | −7.39790 | −0.423602 | ||||||||
\(306\) | 26.7777 | 1.53078 | ||||||||
\(307\) | −21.6851 | −1.23763 | −0.618816 | − | 0.785536i | \(-0.712387\pi\) | ||||
−0.618816 | + | 0.785536i | \(0.712387\pi\) | |||||||
\(308\) | 121.772 | 6.93862 | ||||||||
\(309\) | −4.66929 | −0.265627 | ||||||||
\(310\) | −19.6993 | −1.11884 | ||||||||
\(311\) | −12.8149 | −0.726666 | −0.363333 | − | 0.931659i | \(-0.618361\pi\) | ||||
−0.363333 | + | 0.931659i | \(0.618361\pi\) | |||||||
\(312\) | −137.095 | −7.76149 | ||||||||
\(313\) | −21.7396 | −1.22880 | −0.614399 | − | 0.788996i | \(-0.710601\pi\) | ||||
−0.614399 | + | 0.788996i | \(0.710601\pi\) | |||||||
\(314\) | −51.0878 | −2.88305 | ||||||||
\(315\) | −8.00144 | −0.450830 | ||||||||
\(316\) | 23.8396 | 1.34108 | ||||||||
\(317\) | 21.8760 | 1.22868 | 0.614338 | − | 0.789043i | \(-0.289423\pi\) | ||||
0.614338 | + | 0.789043i | \(0.289423\pi\) | |||||||
\(318\) | −20.6702 | −1.15913 | ||||||||
\(319\) | 42.8323 | 2.39815 | ||||||||
\(320\) | −41.8312 | −2.33843 | ||||||||
\(321\) | 7.71675 | 0.430707 | ||||||||
\(322\) | −11.3976 | −0.635166 | ||||||||
\(323\) | 21.9222 | 1.21978 | ||||||||
\(324\) | −61.8813 | −3.43785 | ||||||||
\(325\) | 21.9079 | 1.21523 | ||||||||
\(326\) | 5.50384 | 0.304829 | ||||||||
\(327\) | 28.6785 | 1.58592 | ||||||||
\(328\) | −85.7507 | −4.73479 | ||||||||
\(329\) | 29.2980 | 1.61525 | ||||||||
\(330\) | −40.8435 | −2.24836 | ||||||||
\(331\) | −1.84728 | −0.101536 | −0.0507678 | − | 0.998710i | \(-0.516167\pi\) | ||||
−0.0507678 | + | 0.998710i | \(0.516167\pi\) | |||||||
\(332\) | 34.2074 | 1.87737 | ||||||||
\(333\) | −12.9630 | −0.710366 | ||||||||
\(334\) | −58.8284 | −3.21895 | ||||||||
\(335\) | 16.4900 | 0.900945 | ||||||||
\(336\) | −133.966 | −7.30844 | ||||||||
\(337\) | 8.69672 | 0.473741 | 0.236870 | − | 0.971541i | \(-0.423878\pi\) | ||||
0.236870 | + | 0.971541i | \(0.423878\pi\) | |||||||
\(338\) | −90.2423 | −4.90854 | ||||||||
\(339\) | 28.8335 | 1.56602 | ||||||||
\(340\) | 49.4595 | 2.68232 | ||||||||
\(341\) | −28.7687 | −1.55791 | ||||||||
\(342\) | 12.8435 | 0.694496 | ||||||||
\(343\) | 13.7998 | 0.745121 | ||||||||
\(344\) | −11.5299 | −0.621648 | ||||||||
\(345\) | 2.80371 | 0.150947 | ||||||||
\(346\) | −66.4430 | −3.57200 | ||||||||
\(347\) | 22.5800 | 1.21216 | 0.606080 | − | 0.795404i | \(-0.292741\pi\) | ||||
0.606080 | + | 0.795404i | \(0.292741\pi\) | |||||||
\(348\) | −93.4282 | −5.00828 | ||||||||
\(349\) | 1.00000 | 0.0535288 | ||||||||
\(350\) | 36.8370 | 1.96902 | ||||||||
\(351\) | −22.2098 | −1.18547 | ||||||||
\(352\) | −120.386 | −6.41657 | ||||||||
\(353\) | 26.5455 | 1.41287 | 0.706436 | − | 0.707777i | \(-0.250302\pi\) | ||||
0.706436 | + | 0.707777i | \(0.250302\pi\) | |||||||
\(354\) | 52.5158 | 2.79118 | ||||||||
\(355\) | −3.79848 | −0.201602 | ||||||||
\(356\) | −7.77848 | −0.412259 | ||||||||
\(357\) | 59.3204 | 3.13957 | ||||||||
\(358\) | 41.8981 | 2.21438 | ||||||||
\(359\) | 0.894687 | 0.0472198 | 0.0236099 | − | 0.999721i | \(-0.492484\pi\) | ||||
0.0236099 | + | 0.999721i | \(0.492484\pi\) | |||||||
\(360\) | 18.4435 | 0.972058 | ||||||||
\(361\) | −8.48539 | −0.446599 | ||||||||
\(362\) | −39.7561 | −2.08954 | ||||||||
\(363\) | −36.4533 | −1.91330 | ||||||||
\(364\) | −155.195 | −8.13442 | ||||||||
\(365\) | −17.2083 | −0.900723 | ||||||||
\(366\) | 32.1324 | 1.67959 | ||||||||
\(367\) | 9.08076 | 0.474012 | 0.237006 | − | 0.971508i | \(-0.423834\pi\) | ||||
0.237006 | + | 0.971508i | \(0.423834\pi\) | |||||||
\(368\) | 15.2679 | 0.795892 | ||||||||
\(369\) | 12.9281 | 0.673008 | ||||||||
\(370\) | −32.6466 | −1.69721 | ||||||||
\(371\) | −14.8934 | −0.773226 | ||||||||
\(372\) | 62.7519 | 3.25354 | ||||||||
\(373\) | 3.66764 | 0.189903 | 0.0949516 | − | 0.995482i | \(-0.469730\pi\) | ||||
0.0949516 | + | 0.995482i | \(0.469730\pi\) | |||||||
\(374\) | 98.4867 | 5.09263 | ||||||||
\(375\) | −23.0801 | −1.19185 | ||||||||
\(376\) | −67.5325 | −3.48272 | ||||||||
\(377\) | −54.5883 | −2.81144 | ||||||||
\(378\) | −37.3446 | −1.92080 | ||||||||
\(379\) | −12.5678 | −0.645564 | −0.322782 | − | 0.946473i | \(-0.604618\pi\) | ||||
−0.322782 | + | 0.946473i | \(0.604618\pi\) | |||||||
\(380\) | 23.7224 | 1.21694 | ||||||||
\(381\) | −8.17667 | −0.418904 | ||||||||
\(382\) | 35.1774 | 1.79983 | ||||||||
\(383\) | 11.0688 | 0.565589 | 0.282795 | − | 0.959180i | \(-0.408738\pi\) | ||||
0.282795 | + | 0.959180i | \(0.408738\pi\) | |||||||
\(384\) | 86.2378 | 4.40080 | ||||||||
\(385\) | −29.4288 | −1.49983 | ||||||||
\(386\) | 29.8612 | 1.51990 | ||||||||
\(387\) | 1.73828 | 0.0883618 | ||||||||
\(388\) | −3.82242 | −0.194054 | ||||||||
\(389\) | 0.149388 | 0.00757425 | 0.00378713 | − | 0.999993i | \(-0.498795\pi\) | ||||
0.00378713 | + | 0.999993i | \(0.498795\pi\) | |||||||
\(390\) | 52.0537 | 2.63584 | ||||||||
\(391\) | −6.76063 | −0.341900 | ||||||||
\(392\) | −98.9519 | −4.99782 | ||||||||
\(393\) | 10.4043 | 0.524826 | ||||||||
\(394\) | 9.75564 | 0.491482 | ||||||||
\(395\) | −5.76133 | −0.289884 | ||||||||
\(396\) | 42.3174 | 2.12653 | ||||||||
\(397\) | −17.5305 | −0.879829 | −0.439915 | − | 0.898040i | \(-0.644991\pi\) | ||||
−0.439915 | + | 0.898040i | \(0.644991\pi\) | |||||||
\(398\) | −34.7602 | −1.74237 | ||||||||
\(399\) | 28.4520 | 1.42438 | ||||||||
\(400\) | −49.3454 | −2.46727 | ||||||||
\(401\) | 30.8471 | 1.54043 | 0.770215 | − | 0.637784i | \(-0.220149\pi\) | ||||
0.770215 | + | 0.637784i | \(0.220149\pi\) | |||||||
\(402\) | −71.6234 | −3.57225 | ||||||||
\(403\) | 36.6648 | 1.82640 | ||||||||
\(404\) | 19.3636 | 0.963374 | ||||||||
\(405\) | 14.9549 | 0.743115 | ||||||||
\(406\) | −91.7876 | −4.55534 | ||||||||
\(407\) | −47.6769 | −2.36326 | ||||||||
\(408\) | −136.735 | −6.76938 | ||||||||
\(409\) | −0.689464 | −0.0340918 | −0.0170459 | − | 0.999855i | \(-0.505426\pi\) | ||||
−0.0170459 | + | 0.999855i | \(0.505426\pi\) | |||||||
\(410\) | 32.5587 | 1.60796 | ||||||||
\(411\) | −11.2834 | −0.556570 | ||||||||
\(412\) | 12.1837 | 0.600249 | ||||||||
\(413\) | 37.8389 | 1.86193 | ||||||||
\(414\) | −3.96083 | −0.194664 | ||||||||
\(415\) | −8.26692 | −0.405807 | ||||||||
\(416\) | 153.428 | 7.52241 | ||||||||
\(417\) | 47.0768 | 2.30536 | ||||||||
\(418\) | 47.2375 | 2.31046 | ||||||||
\(419\) | −11.2200 | −0.548131 | −0.274065 | − | 0.961711i | \(-0.588369\pi\) | ||||
−0.274065 | + | 0.961711i | \(0.588369\pi\) | |||||||
\(420\) | 64.1917 | 3.13224 | ||||||||
\(421\) | −28.8657 | −1.40683 | −0.703413 | − | 0.710781i | \(-0.748341\pi\) | ||||
−0.703413 | + | 0.710781i | \(0.748341\pi\) | |||||||
\(422\) | 53.7318 | 2.61562 | ||||||||
\(423\) | 10.1814 | 0.495038 | ||||||||
\(424\) | 34.3296 | 1.66719 | ||||||||
\(425\) | 21.8502 | 1.05989 | ||||||||
\(426\) | 16.4985 | 0.799353 | ||||||||
\(427\) | 23.1522 | 1.12041 | ||||||||
\(428\) | −20.1356 | −0.973290 | ||||||||
\(429\) | 76.0191 | 3.67023 | ||||||||
\(430\) | 4.37777 | 0.211115 | ||||||||
\(431\) | −14.2631 | −0.687031 | −0.343516 | − | 0.939147i | \(-0.611618\pi\) | ||||
−0.343516 | + | 0.939147i | \(0.611618\pi\) | |||||||
\(432\) | 50.0254 | 2.40685 | ||||||||
\(433\) | −4.43156 | −0.212967 | −0.106484 | − | 0.994314i | \(-0.533959\pi\) | ||||
−0.106484 | + | 0.994314i | \(0.533959\pi\) | |||||||
\(434\) | 61.6500 | 2.95930 | ||||||||
\(435\) | 22.5789 | 1.08257 | ||||||||
\(436\) | −74.8318 | −3.58379 | ||||||||
\(437\) | −3.24262 | −0.155116 | ||||||||
\(438\) | 74.7432 | 3.57137 | ||||||||
\(439\) | 38.7800 | 1.85087 | 0.925435 | − | 0.378906i | \(-0.123700\pi\) | ||||
0.925435 | + | 0.378906i | \(0.123700\pi\) | |||||||
\(440\) | 67.8340 | 3.23386 | ||||||||
\(441\) | 14.9183 | 0.710396 | ||||||||
\(442\) | −125.518 | −5.97029 | ||||||||
\(443\) | 9.21341 | 0.437742 | 0.218871 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218871 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(444\) | 103.996 | 4.93541 | ||||||||
\(445\) | 1.87983 | 0.0891126 | ||||||||
\(446\) | −45.2213 | −2.14129 | ||||||||
\(447\) | 13.3338 | 0.630668 | ||||||||
\(448\) | 130.913 | 6.18507 | ||||||||
\(449\) | 18.2640 | 0.861933 | 0.430966 | − | 0.902368i | \(-0.358173\pi\) | ||||
0.430966 | + | 0.902368i | \(0.358173\pi\) | |||||||
\(450\) | 12.8013 | 0.603460 | ||||||||
\(451\) | 47.5486 | 2.23898 | ||||||||
\(452\) | −75.2363 | −3.53882 | ||||||||
\(453\) | 6.25058 | 0.293678 | ||||||||
\(454\) | −6.35062 | −0.298049 | ||||||||
\(455\) | 37.5060 | 1.75831 | ||||||||
\(456\) | −65.5826 | −3.07118 | ||||||||
\(457\) | −7.84046 | −0.366761 | −0.183381 | − | 0.983042i | \(-0.558704\pi\) | ||||
−0.183381 | + | 0.983042i | \(0.558704\pi\) | |||||||
\(458\) | −31.6109 | −1.47708 | ||||||||
\(459\) | −22.1514 | −1.03394 | ||||||||
\(460\) | −7.31581 | −0.341102 | ||||||||
\(461\) | 21.0761 | 0.981610 | 0.490805 | − | 0.871269i | \(-0.336703\pi\) | ||||
0.490805 | + | 0.871269i | \(0.336703\pi\) | |||||||
\(462\) | 127.822 | 5.94683 | ||||||||
\(463\) | 24.0777 | 1.11899 | 0.559493 | − | 0.828835i | \(-0.310996\pi\) | ||||
0.559493 | + | 0.828835i | \(0.310996\pi\) | |||||||
\(464\) | 122.955 | 5.70805 | ||||||||
\(465\) | −15.1653 | −0.703274 | ||||||||
\(466\) | −3.58290 | −0.165975 | ||||||||
\(467\) | 25.5881 | 1.18408 | 0.592039 | − | 0.805909i | \(-0.298323\pi\) | ||||
0.592039 | + | 0.805909i | \(0.298323\pi\) | |||||||
\(468\) | −53.9322 | −2.49302 | ||||||||
\(469\) | −51.6065 | −2.38297 | ||||||||
\(470\) | 25.6414 | 1.18275 | ||||||||
\(471\) | −39.3296 | −1.81221 | ||||||||
\(472\) | −87.2196 | −4.01461 | ||||||||
\(473\) | 6.39328 | 0.293963 | ||||||||
\(474\) | 25.0240 | 1.14939 | ||||||||
\(475\) | 10.4801 | 0.480860 | ||||||||
\(476\) | −154.787 | −7.09464 | ||||||||
\(477\) | −5.17565 | −0.236977 | ||||||||
\(478\) | 54.0304 | 2.47129 | ||||||||
\(479\) | −21.7024 | −0.991609 | −0.495804 | − | 0.868434i | \(-0.665127\pi\) | ||||
−0.495804 | + | 0.868434i | \(0.665127\pi\) | |||||||
\(480\) | −63.4608 | −2.89657 | ||||||||
\(481\) | 60.7627 | 2.77054 | ||||||||
\(482\) | 11.5610 | 0.526591 | ||||||||
\(483\) | −8.77438 | −0.399248 | ||||||||
\(484\) | 95.1190 | 4.32359 | ||||||||
\(485\) | 0.923767 | 0.0419461 | ||||||||
\(486\) | −38.0329 | −1.72521 | ||||||||
\(487\) | −37.8849 | −1.71673 | −0.858364 | − | 0.513040i | \(-0.828519\pi\) | ||||
−0.858364 | + | 0.513040i | \(0.828519\pi\) | |||||||
\(488\) | −53.3663 | −2.41578 | ||||||||
\(489\) | 4.23709 | 0.191608 | ||||||||
\(490\) | 37.5710 | 1.69729 | ||||||||
\(491\) | −12.6115 | −0.569150 | −0.284575 | − | 0.958654i | \(-0.591852\pi\) | ||||
−0.284575 | + | 0.958654i | \(0.591852\pi\) | |||||||
\(492\) | −103.716 | −4.67586 | ||||||||
\(493\) | −54.4448 | −2.45207 | ||||||||
\(494\) | −60.2027 | −2.70865 | ||||||||
\(495\) | −10.2269 | −0.459664 | ||||||||
\(496\) | −82.5841 | −3.70814 | ||||||||
\(497\) | 11.8876 | 0.533230 | ||||||||
\(498\) | 35.9069 | 1.60903 | ||||||||
\(499\) | 21.5669 | 0.965467 | 0.482733 | − | 0.875767i | \(-0.339644\pi\) | ||||
0.482733 | + | 0.875767i | \(0.339644\pi\) | |||||||
\(500\) | 60.2236 | 2.69328 | ||||||||
\(501\) | −45.2886 | −2.02335 | ||||||||
\(502\) | 10.3083 | 0.460081 | ||||||||
\(503\) | −21.3957 | −0.953988 | −0.476994 | − | 0.878907i | \(-0.658274\pi\) | ||||
−0.476994 | + | 0.878907i | \(0.658274\pi\) | |||||||
\(504\) | −57.7201 | −2.57106 | ||||||||
\(505\) | −4.67961 | −0.208240 | ||||||||
\(506\) | −14.5677 | −0.647612 | ||||||||
\(507\) | −69.4723 | −3.08537 | ||||||||
\(508\) | 21.3357 | 0.946617 | ||||||||
\(509\) | −19.5809 | −0.867909 | −0.433954 | − | 0.900935i | \(-0.642882\pi\) | ||||
−0.433954 | + | 0.900935i | \(0.642882\pi\) | |||||||
\(510\) | 51.9169 | 2.29892 | ||||||||
\(511\) | 53.8544 | 2.38238 | ||||||||
\(512\) | −52.6877 | −2.32849 | ||||||||
\(513\) | −10.6245 | −0.469084 | ||||||||
\(514\) | −18.8841 | −0.832944 | ||||||||
\(515\) | −2.94445 | −0.129748 | ||||||||
\(516\) | −13.9454 | −0.613912 | ||||||||
\(517\) | 37.4466 | 1.64690 | ||||||||
\(518\) | 102.169 | 4.48907 | ||||||||
\(519\) | −51.1506 | −2.24526 | ||||||||
\(520\) | −86.4523 | −3.79118 | ||||||||
\(521\) | −28.8902 | −1.26570 | −0.632851 | − | 0.774274i | \(-0.718115\pi\) | ||||
−0.632851 | + | 0.774274i | \(0.718115\pi\) | |||||||
\(522\) | −31.8974 | −1.39611 | ||||||||
\(523\) | 27.2307 | 1.19072 | 0.595358 | − | 0.803461i | \(-0.297010\pi\) | ||||
0.595358 | + | 0.803461i | \(0.297010\pi\) | |||||||
\(524\) | −27.1482 | −1.18598 | ||||||||
\(525\) | 28.3586 | 1.23767 | ||||||||
\(526\) | 57.5186 | 2.50793 | ||||||||
\(527\) | 36.5684 | 1.59294 | ||||||||
\(528\) | −171.226 | −7.45165 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −13.0346 | −0.566187 | ||||||||
\(531\) | 13.1495 | 0.570641 | ||||||||
\(532\) | −74.2408 | −3.21875 | ||||||||
\(533\) | −60.5991 | −2.62484 | ||||||||
\(534\) | −8.16495 | −0.353332 | ||||||||
\(535\) | 4.86618 | 0.210383 | ||||||||
\(536\) | 118.954 | 5.13803 | ||||||||
\(537\) | 32.2549 | 1.39190 | ||||||||
\(538\) | 38.2432 | 1.64878 | ||||||||
\(539\) | 54.8686 | 2.36336 | ||||||||
\(540\) | −23.9704 | −1.03152 | ||||||||
\(541\) | −1.61460 | −0.0694169 | −0.0347084 | − | 0.999397i | \(-0.511050\pi\) | ||||
−0.0347084 | + | 0.999397i | \(0.511050\pi\) | |||||||
\(542\) | −10.8467 | −0.465905 | ||||||||
\(543\) | −30.6059 | −1.31343 | ||||||||
\(544\) | 153.024 | 6.56086 | ||||||||
\(545\) | 18.0846 | 0.774661 | ||||||||
\(546\) | −162.905 | −6.97171 | ||||||||
\(547\) | −7.37294 | −0.315244 | −0.157622 | − | 0.987500i | \(-0.550383\pi\) | ||||
−0.157622 | + | 0.987500i | \(0.550383\pi\) | |||||||
\(548\) | 29.4422 | 1.25771 | ||||||||
\(549\) | 8.04569 | 0.343382 | ||||||||
\(550\) | 47.0824 | 2.00760 | ||||||||
\(551\) | −26.1135 | −1.11247 | ||||||||
\(552\) | 20.2251 | 0.860839 | ||||||||
\(553\) | 18.0304 | 0.766732 | ||||||||
\(554\) | 41.5547 | 1.76549 | ||||||||
\(555\) | −25.1327 | −1.06682 | ||||||||
\(556\) | −122.839 | −5.20954 | ||||||||
\(557\) | −10.6786 | −0.452465 | −0.226232 | − | 0.974073i | \(-0.572641\pi\) | ||||
−0.226232 | + | 0.974073i | \(0.572641\pi\) | |||||||
\(558\) | 21.4242 | 0.906958 | ||||||||
\(559\) | −8.14803 | −0.344625 | ||||||||
\(560\) | −84.4789 | −3.56989 | ||||||||
\(561\) | 75.8192 | 3.20109 | ||||||||
\(562\) | 73.2249 | 3.08881 | ||||||||
\(563\) | −15.4854 | −0.652631 | −0.326316 | − | 0.945261i | \(-0.605807\pi\) | ||||
−0.326316 | + | 0.945261i | \(0.605807\pi\) | |||||||
\(564\) | −81.6807 | −3.43938 | ||||||||
\(565\) | 18.1824 | 0.764940 | ||||||||
\(566\) | −59.9791 | −2.52111 | ||||||||
\(567\) | −46.8023 | −1.96551 | ||||||||
\(568\) | −27.4011 | −1.14973 | ||||||||
\(569\) | 25.9639 | 1.08846 | 0.544232 | − | 0.838935i | \(-0.316821\pi\) | ||||
0.544232 | + | 0.838935i | \(0.316821\pi\) | |||||||
\(570\) | 24.9010 | 1.04299 | ||||||||
\(571\) | 15.3556 | 0.642610 | 0.321305 | − | 0.946976i | \(-0.395879\pi\) | ||||
0.321305 | + | 0.946976i | \(0.395879\pi\) | |||||||
\(572\) | −198.359 | −8.29381 | ||||||||
\(573\) | 27.0810 | 1.13133 | ||||||||
\(574\) | −101.894 | −4.25299 | ||||||||
\(575\) | −3.23198 | −0.134783 | ||||||||
\(576\) | 45.4940 | 1.89559 | ||||||||
\(577\) | 1.00501 | 0.0418391 | 0.0209195 | − | 0.999781i | \(-0.493341\pi\) | ||||
0.0209195 | + | 0.999781i | \(0.493341\pi\) | |||||||
\(578\) | −78.6255 | −3.27039 | ||||||||
\(579\) | 22.9884 | 0.955366 | ||||||||
\(580\) | −58.9158 | −2.44634 | ||||||||
\(581\) | 25.8718 | 1.07334 | ||||||||
\(582\) | −4.01233 | −0.166316 | ||||||||
\(583\) | −19.0357 | −0.788378 | ||||||||
\(584\) | −124.136 | −5.13677 | ||||||||
\(585\) | 13.0338 | 0.538883 | ||||||||
\(586\) | 38.3458 | 1.58405 | ||||||||
\(587\) | −26.0914 | −1.07691 | −0.538454 | − | 0.842655i | \(-0.680991\pi\) | ||||
−0.538454 | + | 0.842655i | \(0.680991\pi\) | |||||||
\(588\) | −119.683 | −4.93562 | ||||||||
\(589\) | 17.5394 | 0.722699 | ||||||||
\(590\) | 33.1164 | 1.36338 | ||||||||
\(591\) | 7.51030 | 0.308932 | ||||||||
\(592\) | −136.862 | −5.62501 | ||||||||
\(593\) | −39.0576 | −1.60390 | −0.801952 | − | 0.597389i | \(-0.796205\pi\) | ||||
−0.801952 | + | 0.597389i | \(0.796205\pi\) | |||||||
\(594\) | −47.7313 | −1.95844 | ||||||||
\(595\) | 37.4074 | 1.53355 | ||||||||
\(596\) | −34.7924 | −1.42515 | ||||||||
\(597\) | −26.7599 | −1.09521 | ||||||||
\(598\) | 18.5660 | 0.759221 | ||||||||
\(599\) | −5.70685 | −0.233175 | −0.116588 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116588 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(600\) | −65.3673 | −2.66861 | ||||||||
\(601\) | −47.1945 | −1.92510 | −0.962551 | − | 0.271099i | \(-0.912613\pi\) | ||||
−0.962551 | + | 0.271099i | \(0.912613\pi\) | |||||||
\(602\) | −13.7005 | −0.558391 | ||||||||
\(603\) | −17.9339 | −0.730326 | ||||||||
\(604\) | −16.3099 | −0.663638 | ||||||||
\(605\) | −22.9875 | −0.934573 | ||||||||
\(606\) | 20.3256 | 0.825673 | ||||||||
\(607\) | 40.7500 | 1.65399 | 0.826996 | − | 0.562207i | \(-0.190048\pi\) | ||||
0.826996 | + | 0.562207i | \(0.190048\pi\) | |||||||
\(608\) | 73.3955 | 2.97658 | ||||||||
\(609\) | −70.6619 | −2.86337 | ||||||||
\(610\) | 20.2627 | 0.820411 | ||||||||
\(611\) | −47.7245 | −1.93073 | ||||||||
\(612\) | −53.7904 | −2.17435 | ||||||||
\(613\) | −4.86042 | −0.196311 | −0.0981554 | − | 0.995171i | \(-0.531294\pi\) | ||||
−0.0981554 | + | 0.995171i | \(0.531294\pi\) | |||||||
\(614\) | 59.3949 | 2.39698 | ||||||||
\(615\) | 25.0650 | 1.01072 | ||||||||
\(616\) | −212.291 | −8.55344 | ||||||||
\(617\) | 15.6782 | 0.631182 | 0.315591 | − | 0.948895i | \(-0.397797\pi\) | ||||
0.315591 | + | 0.948895i | \(0.397797\pi\) | |||||||
\(618\) | 12.7891 | 0.514452 | ||||||||
\(619\) | −1.78900 | −0.0719058 | −0.0359529 | − | 0.999353i | \(-0.511447\pi\) | ||||
−0.0359529 | + | 0.999353i | \(0.511447\pi\) | |||||||
\(620\) | 39.5714 | 1.58922 | ||||||||
\(621\) | 3.27652 | 0.131482 | ||||||||
\(622\) | 35.0997 | 1.40737 | ||||||||
\(623\) | −5.88305 | −0.235699 | ||||||||
\(624\) | 218.222 | 8.73587 | ||||||||
\(625\) | 1.60562 | 0.0642247 | ||||||||
\(626\) | 59.5444 | 2.37987 | ||||||||
\(627\) | 36.3654 | 1.45229 | ||||||||
\(628\) | 102.624 | 4.09514 | ||||||||
\(629\) | 60.6029 | 2.41640 | ||||||||
\(630\) | 21.9157 | 0.873144 | ||||||||
\(631\) | 49.6501 | 1.97654 | 0.988270 | − | 0.152717i | \(-0.0488024\pi\) | ||||
0.988270 | + | 0.152717i | \(0.0488024\pi\) | |||||||
\(632\) | −41.5606 | −1.65319 | ||||||||
\(633\) | 41.3650 | 1.64411 | ||||||||
\(634\) | −59.9177 | −2.37964 | ||||||||
\(635\) | −5.15621 | −0.204618 | ||||||||
\(636\) | 41.5217 | 1.64644 | ||||||||
\(637\) | −69.9283 | −2.77066 | ||||||||
\(638\) | −117.317 | −4.64460 | ||||||||
\(639\) | 4.13108 | 0.163423 | ||||||||
\(640\) | 54.3815 | 2.14962 | ||||||||
\(641\) | −7.47091 | −0.295083 | −0.147542 | − | 0.989056i | \(-0.547136\pi\) | ||||
−0.147542 | + | 0.989056i | \(0.547136\pi\) | |||||||
\(642\) | −21.1360 | −0.834171 | ||||||||
\(643\) | −19.2332 | −0.758482 | −0.379241 | − | 0.925298i | \(-0.623815\pi\) | ||||
−0.379241 | + | 0.925298i | \(0.623815\pi\) | |||||||
\(644\) | 22.8953 | 0.902201 | ||||||||
\(645\) | 3.37019 | 0.132701 | ||||||||
\(646\) | −60.0444 | −2.36241 | ||||||||
\(647\) | −36.0011 | −1.41535 | −0.707674 | − | 0.706539i | \(-0.750256\pi\) | ||||
−0.707674 | + | 0.706539i | \(0.750256\pi\) | |||||||
\(648\) | 107.880 | 4.23794 | ||||||||
\(649\) | 48.3631 | 1.89842 | ||||||||
\(650\) | −60.0051 | −2.35359 | ||||||||
\(651\) | 47.4608 | 1.86013 | ||||||||
\(652\) | −11.0560 | −0.432985 | ||||||||
\(653\) | −19.2876 | −0.754780 | −0.377390 | − | 0.926054i | \(-0.623178\pi\) | ||||
−0.377390 | + | 0.926054i | \(0.623178\pi\) | |||||||
\(654\) | −78.5497 | −3.07153 | ||||||||
\(655\) | 6.56093 | 0.256357 | ||||||||
\(656\) | 136.494 | 5.32919 | ||||||||
\(657\) | 18.7151 | 0.730146 | ||||||||
\(658\) | −80.2464 | −3.12833 | ||||||||
\(659\) | 18.4018 | 0.716831 | 0.358415 | − | 0.933562i | \(-0.383317\pi\) | ||||
0.358415 | + | 0.933562i | \(0.383317\pi\) | |||||||
\(660\) | 82.0454 | 3.19361 | ||||||||
\(661\) | 9.08232 | 0.353261 | 0.176631 | − | 0.984277i | \(-0.443480\pi\) | ||||
0.176631 | + | 0.984277i | \(0.443480\pi\) | |||||||
\(662\) | 5.05964 | 0.196649 | ||||||||
\(663\) | −96.6291 | −3.75276 | ||||||||
\(664\) | −59.6352 | −2.31429 | ||||||||
\(665\) | 17.9418 | 0.695755 | ||||||||
\(666\) | 35.5052 | 1.37580 | ||||||||
\(667\) | 8.05321 | 0.311822 | ||||||||
\(668\) | 118.173 | 4.57225 | ||||||||
\(669\) | −34.8133 | −1.34596 | ||||||||
\(670\) | −45.1657 | −1.74490 | ||||||||
\(671\) | 29.5915 | 1.14237 | ||||||||
\(672\) | 198.604 | 7.66133 | ||||||||
\(673\) | −47.0265 | −1.81274 | −0.906369 | − | 0.422488i | \(-0.861157\pi\) | ||||
−0.906369 | + | 0.422488i | \(0.861157\pi\) | |||||||
\(674\) | −23.8201 | −0.917516 | ||||||||
\(675\) | −10.5897 | −0.407596 | ||||||||
\(676\) | 181.277 | 6.97217 | ||||||||
\(677\) | 7.50622 | 0.288488 | 0.144244 | − | 0.989542i | \(-0.453925\pi\) | ||||
0.144244 | + | 0.989542i | \(0.453925\pi\) | |||||||
\(678\) | −78.9743 | −3.03299 | ||||||||
\(679\) | −2.89099 | −0.110946 | ||||||||
\(680\) | −86.2249 | −3.30658 | ||||||||
\(681\) | −4.88897 | −0.187346 | ||||||||
\(682\) | 78.7968 | 3.01728 | ||||||||
\(683\) | 4.92760 | 0.188549 | 0.0942747 | − | 0.995546i | \(-0.469947\pi\) | ||||
0.0942747 | + | 0.995546i | \(0.469947\pi\) | |||||||
\(684\) | −25.7997 | −0.986475 | ||||||||
\(685\) | −7.11532 | −0.271863 | ||||||||
\(686\) | −37.7974 | −1.44311 | ||||||||
\(687\) | −24.3354 | −0.928452 | ||||||||
\(688\) | 18.3527 | 0.699690 | ||||||||
\(689\) | 24.2604 | 0.924247 | ||||||||
\(690\) | −7.67929 | −0.292345 | ||||||||
\(691\) | −49.7673 | −1.89324 | −0.946619 | − | 0.322356i | \(-0.895525\pi\) | ||||
−0.946619 | + | 0.322356i | \(0.895525\pi\) | |||||||
\(692\) | 133.469 | 5.07373 | ||||||||
\(693\) | 32.0057 | 1.21580 | ||||||||
\(694\) | −61.8461 | −2.34765 | ||||||||
\(695\) | 29.6866 | 1.12608 | ||||||||
\(696\) | 162.877 | 6.17385 | ||||||||
\(697\) | −60.4398 | −2.28932 | ||||||||
\(698\) | −2.73897 | −0.103672 | ||||||||
\(699\) | −2.75826 | −0.104327 | ||||||||
\(700\) | −73.9972 | −2.79683 | ||||||||
\(701\) | −4.97531 | −0.187915 | −0.0939575 | − | 0.995576i | \(-0.529952\pi\) | ||||
−0.0939575 | + | 0.995576i | \(0.529952\pi\) | |||||||
\(702\) | 60.8320 | 2.29595 | ||||||||
\(703\) | 29.0672 | 1.09629 | ||||||||
\(704\) | 167.324 | 6.30627 | ||||||||
\(705\) | 19.7398 | 0.743445 | ||||||||
\(706\) | −72.7074 | −2.73638 | ||||||||
\(707\) | 14.6451 | 0.550787 | ||||||||
\(708\) | −105.492 | −3.96464 | ||||||||
\(709\) | 31.3419 | 1.17707 | 0.588535 | − | 0.808471i | \(-0.299705\pi\) | ||||
0.588535 | + | 0.808471i | \(0.299705\pi\) | |||||||
\(710\) | 10.4039 | 0.390453 | ||||||||
\(711\) | 6.26581 | 0.234986 | ||||||||
\(712\) | 13.5606 | 0.508204 | ||||||||
\(713\) | −5.40902 | −0.202569 | ||||||||
\(714\) | −162.477 | −6.08055 | ||||||||
\(715\) | 47.9376 | 1.79276 | ||||||||
\(716\) | −84.1639 | −3.14535 | ||||||||
\(717\) | 41.5949 | 1.55339 | ||||||||
\(718\) | −2.45053 | −0.0914528 | ||||||||
\(719\) | 4.53010 | 0.168944 | 0.0844721 | − | 0.996426i | \(-0.473080\pi\) | ||||
0.0844721 | + | 0.996426i | \(0.473080\pi\) | |||||||
\(720\) | −29.3575 | −1.09409 | ||||||||
\(721\) | 9.21484 | 0.343179 | ||||||||
\(722\) | 23.2413 | 0.864950 | ||||||||
\(723\) | 8.90017 | 0.331001 | ||||||||
\(724\) | 79.8611 | 2.96801 | ||||||||
\(725\) | −26.0278 | −0.966649 | ||||||||
\(726\) | 99.8448 | 3.70559 | ||||||||
\(727\) | −41.6785 | −1.54577 | −0.772884 | − | 0.634547i | \(-0.781187\pi\) | ||||
−0.772884 | + | 0.634547i | \(0.781187\pi\) | |||||||
\(728\) | 270.558 | 10.0275 | ||||||||
\(729\) | 4.46198 | 0.165259 | ||||||||
\(730\) | 47.1331 | 1.74447 | ||||||||
\(731\) | −8.12661 | −0.300573 | ||||||||
\(732\) | −64.5467 | −2.38571 | ||||||||
\(733\) | −7.26634 | −0.268389 | −0.134194 | − | 0.990955i | \(-0.542845\pi\) | ||||
−0.134194 | + | 0.990955i | \(0.542845\pi\) | |||||||
\(734\) | −24.8720 | −0.918041 | ||||||||
\(735\) | 28.9238 | 1.06687 | ||||||||
\(736\) | −22.6346 | −0.834322 | ||||||||
\(737\) | −65.9598 | −2.42966 | ||||||||
\(738\) | −35.4096 | −1.30345 | ||||||||
\(739\) | −5.10410 | −0.187757 | −0.0938787 | − | 0.995584i | \(-0.529927\pi\) | ||||
−0.0938787 | + | 0.995584i | \(0.529927\pi\) | |||||||
\(740\) | 65.5796 | 2.41075 | ||||||||
\(741\) | −46.3465 | −1.70258 | ||||||||
\(742\) | 40.7926 | 1.49754 | ||||||||
\(743\) | 6.62458 | 0.243032 | 0.121516 | − | 0.992589i | \(-0.461224\pi\) | ||||
0.121516 | + | 0.992589i | \(0.461224\pi\) | |||||||
\(744\) | −109.398 | −4.01073 | ||||||||
\(745\) | 8.40830 | 0.308056 | ||||||||
\(746\) | −10.0456 | −0.367794 | ||||||||
\(747\) | 8.99080 | 0.328956 | ||||||||
\(748\) | −197.838 | −7.23366 | ||||||||
\(749\) | −15.2290 | −0.556456 | ||||||||
\(750\) | 63.2158 | 2.30831 | ||||||||
\(751\) | 23.5344 | 0.858782 | 0.429391 | − | 0.903119i | \(-0.358728\pi\) | ||||
0.429391 | + | 0.903119i | \(0.358728\pi\) | |||||||
\(752\) | 107.495 | 3.91994 | ||||||||
\(753\) | 7.93574 | 0.289194 | ||||||||
\(754\) | 149.516 | 5.44506 | ||||||||
\(755\) | 3.94161 | 0.143450 | ||||||||
\(756\) | 75.0169 | 2.72834 | ||||||||
\(757\) | 9.64829 | 0.350673 | 0.175337 | − | 0.984509i | \(-0.443899\pi\) | ||||
0.175337 | + | 0.984509i | \(0.443899\pi\) | |||||||
\(758\) | 34.4229 | 1.25029 | ||||||||
\(759\) | −11.2148 | −0.407072 | ||||||||
\(760\) | −41.3563 | −1.50015 | ||||||||
\(761\) | −36.5688 | −1.32562 | −0.662808 | − | 0.748789i | \(-0.730636\pi\) | ||||
−0.662808 | + | 0.748789i | \(0.730636\pi\) | |||||||
\(762\) | 22.3957 | 0.811311 | ||||||||
\(763\) | −56.5970 | −2.04895 | ||||||||
\(764\) | −70.6635 | −2.55651 | ||||||||
\(765\) | 12.9996 | 0.470000 | ||||||||
\(766\) | −30.3172 | −1.09540 | ||||||||
\(767\) | −61.6372 | −2.22559 | ||||||||
\(768\) | −103.532 | −3.73589 | ||||||||
\(769\) | 17.1423 | 0.618168 | 0.309084 | − | 0.951035i | \(-0.399978\pi\) | ||||
0.309084 | + | 0.951035i | \(0.399978\pi\) | |||||||
\(770\) | 80.6047 | 2.90479 | ||||||||
\(771\) | −14.5378 | −0.523566 | ||||||||
\(772\) | −59.9845 | −2.15889 | ||||||||
\(773\) | −22.7223 | −0.817264 | −0.408632 | − | 0.912699i | \(-0.633994\pi\) | ||||
−0.408632 | + | 0.912699i | \(0.633994\pi\) | |||||||
\(774\) | −4.76111 | −0.171134 | ||||||||
\(775\) | 17.4818 | 0.627966 | ||||||||
\(776\) | 6.66379 | 0.239216 | ||||||||
\(777\) | 78.6543 | 2.82171 | ||||||||
\(778\) | −0.409169 | −0.0146694 | ||||||||
\(779\) | −28.9889 | −1.03864 | ||||||||
\(780\) | −104.564 | −3.74400 | ||||||||
\(781\) | 15.1939 | 0.543679 | ||||||||
\(782\) | 18.5172 | 0.662174 | ||||||||
\(783\) | 26.3865 | 0.942977 | ||||||||
\(784\) | 157.507 | 5.62525 | ||||||||
\(785\) | −24.8012 | −0.885193 | ||||||||
\(786\) | −28.4970 | −1.01646 | ||||||||
\(787\) | 3.00105 | 0.106976 | 0.0534879 | − | 0.998568i | \(-0.482966\pi\) | ||||
0.0534879 | + | 0.998568i | \(0.482966\pi\) | |||||||
\(788\) | −19.5969 | −0.698110 | ||||||||
\(789\) | 44.2802 | 1.57642 | ||||||||
\(790\) | 15.7801 | 0.561432 | ||||||||
\(791\) | −56.9030 | −2.02324 | ||||||||
\(792\) | −73.7738 | −2.62144 | ||||||||
\(793\) | −37.7134 | −1.33924 | ||||||||
\(794\) | 48.0155 | 1.70401 | ||||||||
\(795\) | −10.0346 | −0.355890 | ||||||||
\(796\) | 69.8255 | 2.47490 | ||||||||
\(797\) | −15.2158 | −0.538971 | −0.269486 | − | 0.963004i | \(-0.586854\pi\) | ||||
−0.269486 | + | 0.963004i | \(0.586854\pi\) | |||||||
\(798\) | −77.9294 | −2.75867 | ||||||||
\(799\) | −47.5990 | −1.68393 | ||||||||
\(800\) | 73.1546 | 2.58640 | ||||||||
\(801\) | −2.04444 | −0.0722366 | ||||||||
\(802\) | −84.4894 | −2.98343 | ||||||||
\(803\) | 68.8329 | 2.42906 | ||||||||
\(804\) | 143.875 | 5.07409 | ||||||||
\(805\) | −5.53312 | −0.195017 | ||||||||
\(806\) | −100.424 | −3.53728 | ||||||||
\(807\) | 29.4412 | 1.03638 | ||||||||
\(808\) | −33.7574 | −1.18758 | ||||||||
\(809\) | 11.7741 | 0.413954 | 0.206977 | − | 0.978346i | \(-0.433637\pi\) | ||||
0.206977 | + | 0.978346i | \(0.433637\pi\) | |||||||
\(810\) | −40.9611 | −1.43923 | ||||||||
\(811\) | −36.0314 | −1.26523 | −0.632617 | − | 0.774465i | \(-0.718019\pi\) | ||||
−0.632617 | + | 0.774465i | \(0.718019\pi\) | |||||||
\(812\) | 184.381 | 6.47049 | ||||||||
\(813\) | −8.35022 | −0.292855 | ||||||||
\(814\) | 130.586 | 4.57703 | ||||||||
\(815\) | 2.67190 | 0.0935927 | ||||||||
\(816\) | 217.648 | 7.61921 | ||||||||
\(817\) | −3.89779 | −0.136366 | ||||||||
\(818\) | 1.88842 | 0.0660272 | ||||||||
\(819\) | −40.7902 | −1.42532 | ||||||||
\(820\) | −65.4031 | −2.28397 | ||||||||
\(821\) | −50.7652 | −1.77172 | −0.885859 | − | 0.463954i | \(-0.846430\pi\) | ||||
−0.885859 | + | 0.463954i | \(0.846430\pi\) | |||||||
\(822\) | 30.9050 | 1.07794 | ||||||||
\(823\) | −38.5229 | −1.34282 | −0.671412 | − | 0.741084i | \(-0.734312\pi\) | ||||
−0.671412 | + | 0.741084i | \(0.734312\pi\) | |||||||
\(824\) | −21.2404 | −0.739945 | ||||||||
\(825\) | 36.2460 | 1.26193 | ||||||||
\(826\) | −103.640 | −3.60609 | ||||||||
\(827\) | −0.353748 | −0.0123010 | −0.00615050 | − | 0.999981i | \(-0.501958\pi\) | ||||
−0.00615050 | + | 0.999981i | \(0.501958\pi\) | |||||||
\(828\) | 7.95641 | 0.276504 | ||||||||
\(829\) | 7.99949 | 0.277834 | 0.138917 | − | 0.990304i | \(-0.455638\pi\) | ||||
0.138917 | + | 0.990304i | \(0.455638\pi\) | |||||||
\(830\) | 22.6429 | 0.785946 | ||||||||
\(831\) | 31.9906 | 1.10974 | ||||||||
\(832\) | −213.249 | −7.39309 | ||||||||
\(833\) | −69.7444 | −2.41650 | ||||||||
\(834\) | −128.942 | −4.46491 | ||||||||
\(835\) | −28.5590 | −0.988324 | ||||||||
\(836\) | −94.8895 | −3.28182 | ||||||||
\(837\) | −17.7228 | −0.612588 | ||||||||
\(838\) | 30.7312 | 1.06159 | ||||||||
\(839\) | 22.1087 | 0.763277 | 0.381639 | − | 0.924312i | \(-0.375360\pi\) | ||||
0.381639 | + | 0.924312i | \(0.375360\pi\) | |||||||
\(840\) | −111.908 | −3.86120 | ||||||||
\(841\) | 35.8542 | 1.23635 | ||||||||
\(842\) | 79.0623 | 2.72467 | ||||||||
\(843\) | 56.3716 | 1.94154 | ||||||||
\(844\) | −107.935 | −3.71528 | ||||||||
\(845\) | −43.8092 | −1.50708 | ||||||||
\(846\) | −27.8867 | −0.958763 | ||||||||
\(847\) | 71.9407 | 2.47191 | ||||||||
\(848\) | −54.6443 | −1.87649 | ||||||||
\(849\) | −46.1744 | −1.58470 | ||||||||
\(850\) | −59.8473 | −2.05274 | ||||||||
\(851\) | −8.96409 | −0.307285 | ||||||||
\(852\) | −33.1417 | −1.13542 | ||||||||
\(853\) | −40.9231 | −1.40118 | −0.700591 | − | 0.713563i | \(-0.747080\pi\) | ||||
−0.700591 | + | 0.713563i | \(0.747080\pi\) | |||||||
\(854\) | −63.4133 | −2.16996 | ||||||||
\(855\) | 6.23502 | 0.213233 | ||||||||
\(856\) | 35.1032 | 1.19980 | ||||||||
\(857\) | 41.2493 | 1.40905 | 0.704525 | − | 0.709680i | \(-0.251160\pi\) | ||||
0.704525 | + | 0.709680i | \(0.251160\pi\) | |||||||
\(858\) | −208.214 | −7.10832 | ||||||||
\(859\) | 3.53732 | 0.120692 | 0.0603459 | − | 0.998178i | \(-0.480780\pi\) | ||||
0.0603459 | + | 0.998178i | \(0.480780\pi\) | |||||||
\(860\) | −8.79396 | −0.299872 | ||||||||
\(861\) | −78.4426 | −2.67332 | ||||||||
\(862\) | 39.0664 | 1.33061 | ||||||||
\(863\) | 4.80452 | 0.163548 | 0.0817740 | − | 0.996651i | \(-0.473941\pi\) | ||||
0.0817740 | + | 0.996651i | \(0.473941\pi\) | |||||||
\(864\) | −74.1627 | −2.52307 | ||||||||
\(865\) | −32.2556 | −1.09672 | ||||||||
\(866\) | 12.1379 | 0.412464 | ||||||||
\(867\) | −60.5292 | −2.05568 | ||||||||
\(868\) | −123.841 | −4.20344 | ||||||||
\(869\) | 23.0453 | 0.781757 | ||||||||
\(870\) | −61.8429 | −2.09667 | ||||||||
\(871\) | 84.0636 | 2.84839 | ||||||||
\(872\) | 130.457 | 4.41785 | ||||||||
\(873\) | −1.00466 | −0.0340024 | ||||||||
\(874\) | 8.88147 | 0.300420 | ||||||||
\(875\) | 45.5486 | 1.53982 | ||||||||
\(876\) | −150.142 | −5.07284 | ||||||||
\(877\) | −14.8789 | −0.502426 | −0.251213 | − | 0.967932i | \(-0.580829\pi\) | ||||
−0.251213 | + | 0.967932i | \(0.580829\pi\) | |||||||
\(878\) | −106.218 | −3.58467 | ||||||||
\(879\) | 29.5202 | 0.995693 | ||||||||
\(880\) | −107.975 | −3.63984 | ||||||||
\(881\) | −31.6261 | −1.06551 | −0.532755 | − | 0.846269i | \(-0.678843\pi\) | ||||
−0.532755 | + | 0.846269i | \(0.678843\pi\) | |||||||
\(882\) | −40.8609 | −1.37586 | ||||||||
\(883\) | −41.4051 | −1.39339 | −0.696696 | − | 0.717367i | \(-0.745347\pi\) | ||||
−0.696696 | + | 0.717367i | \(0.745347\pi\) | |||||||
\(884\) | 252.138 | 8.48031 | ||||||||
\(885\) | 25.4944 | 0.856985 | ||||||||
\(886\) | −25.2353 | −0.847796 | ||||||||
\(887\) | 13.8230 | 0.464130 | 0.232065 | − | 0.972700i | \(-0.425452\pi\) | ||||
0.232065 | + | 0.972700i | \(0.425452\pi\) | |||||||
\(888\) | −181.300 | −6.08403 | ||||||||
\(889\) | 16.1367 | 0.541207 | ||||||||
\(890\) | −5.14881 | −0.172589 | ||||||||
\(891\) | −59.8194 | −2.00403 | ||||||||
\(892\) | 90.8395 | 3.04153 | ||||||||
\(893\) | −22.8301 | −0.763979 | ||||||||
\(894\) | −36.5210 | −1.22145 | ||||||||
\(895\) | 20.3400 | 0.679890 | ||||||||
\(896\) | −170.190 | −5.68566 | ||||||||
\(897\) | 14.2929 | 0.477226 | ||||||||
\(898\) | −50.0247 | −1.66935 | ||||||||
\(899\) | −43.5599 | −1.45281 | ||||||||
\(900\) | −25.7150 | −0.857166 | ||||||||
\(901\) | 24.1966 | 0.806105 | ||||||||
\(902\) | −130.234 | −4.33633 | ||||||||
\(903\) | −10.5472 | −0.350990 | ||||||||
\(904\) | 131.163 | 4.36241 | ||||||||
\(905\) | −19.3001 | −0.641557 | ||||||||
\(906\) | −17.1202 | −0.568780 | ||||||||
\(907\) | 11.7196 | 0.389144 | 0.194572 | − | 0.980888i | \(-0.437668\pi\) | ||||
0.194572 | + | 0.980888i | \(0.437668\pi\) | |||||||
\(908\) | 12.7570 | 0.423355 | ||||||||
\(909\) | 5.08938 | 0.168804 | ||||||||
\(910\) | −102.728 | −3.40540 | ||||||||
\(911\) | −55.0134 | −1.82267 | −0.911337 | − | 0.411660i | \(-0.864949\pi\) | ||||
−0.911337 | + | 0.411660i | \(0.864949\pi\) | |||||||
\(912\) | 104.391 | 3.45674 | ||||||||
\(913\) | 33.0676 | 1.09438 | ||||||||
\(914\) | 21.4748 | 0.710324 | ||||||||
\(915\) | 15.5990 | 0.515688 | ||||||||
\(916\) | 63.4991 | 2.09807 | ||||||||
\(917\) | −20.5328 | −0.678054 | ||||||||
\(918\) | 60.6720 | 2.00247 | ||||||||
\(919\) | −8.95673 | −0.295455 | −0.147728 | − | 0.989028i | \(-0.547196\pi\) | ||||
−0.147728 | + | 0.989028i | \(0.547196\pi\) | |||||||
\(920\) | 12.7540 | 0.420486 | ||||||||
\(921\) | 45.7246 | 1.50668 | ||||||||
\(922\) | −57.7268 | −1.90113 | ||||||||
\(923\) | −19.3641 | −0.637377 | ||||||||
\(924\) | −256.766 | −8.44699 | ||||||||
\(925\) | 28.9718 | 0.952586 | ||||||||
\(926\) | −65.9482 | −2.16719 | ||||||||
\(927\) | 3.20228 | 0.105177 | ||||||||
\(928\) | −182.281 | −5.98367 | ||||||||
\(929\) | 41.2488 | 1.35333 | 0.676665 | − | 0.736291i | \(-0.263425\pi\) | ||||
0.676665 | + | 0.736291i | \(0.263425\pi\) | |||||||
\(930\) | 41.5374 | 1.36206 | ||||||||
\(931\) | −33.4517 | −1.09634 | ||||||||
\(932\) | 7.19724 | 0.235753 | ||||||||
\(933\) | 27.0212 | 0.884634 | ||||||||
\(934\) | −70.0853 | −2.29326 | ||||||||
\(935\) | 47.8115 | 1.56360 | ||||||||
\(936\) | 94.0223 | 3.07322 | ||||||||
\(937\) | −42.7270 | −1.39583 | −0.697915 | − | 0.716180i | \(-0.745889\pi\) | ||||
−0.697915 | + | 0.716180i | \(0.745889\pi\) | |||||||
\(938\) | 141.349 | 4.61520 | ||||||||
\(939\) | 45.8397 | 1.49592 | ||||||||
\(940\) | −51.5078 | −1.68000 | ||||||||
\(941\) | −28.3798 | −0.925154 | −0.462577 | − | 0.886579i | \(-0.653075\pi\) | ||||
−0.462577 | + | 0.886579i | \(0.653075\pi\) | |||||||
\(942\) | 107.723 | 3.50979 | ||||||||
\(943\) | 8.93996 | 0.291125 | ||||||||
\(944\) | 138.832 | 4.51860 | ||||||||
\(945\) | −18.1294 | −0.589749 | ||||||||
\(946\) | −17.5110 | −0.569333 | ||||||||
\(947\) | −31.7402 | −1.03142 | −0.515709 | − | 0.856764i | \(-0.672472\pi\) | ||||
−0.515709 | + | 0.856764i | \(0.672472\pi\) | |||||||
\(948\) | −50.2676 | −1.63262 | ||||||||
\(949\) | −87.7253 | −2.84769 | ||||||||
\(950\) | −28.7047 | −0.931305 | ||||||||
\(951\) | −46.1271 | −1.49578 | ||||||||
\(952\) | 269.846 | 8.74577 | ||||||||
\(953\) | −18.4466 | −0.597544 | −0.298772 | − | 0.954325i | \(-0.596577\pi\) | ||||
−0.298772 | + | 0.954325i | \(0.596577\pi\) | |||||||
\(954\) | 14.1760 | 0.458964 | ||||||||
\(955\) | 17.0773 | 0.552608 | ||||||||
\(956\) | −108.535 | −3.51027 | ||||||||
\(957\) | −90.3152 | −2.91947 | ||||||||
\(958\) | 59.4424 | 1.92050 | ||||||||
\(959\) | 22.2678 | 0.719066 | ||||||||
\(960\) | 88.2042 | 2.84678 | ||||||||
\(961\) | −1.74253 | −0.0562108 | ||||||||
\(962\) | −166.427 | −5.36584 | ||||||||
\(963\) | −5.29228 | −0.170541 | ||||||||
\(964\) | −23.2235 | −0.747979 | ||||||||
\(965\) | 14.4965 | 0.466659 | ||||||||
\(966\) | 24.0328 | 0.773243 | ||||||||
\(967\) | 2.21622 | 0.0712689 | 0.0356344 | − | 0.999365i | \(-0.488655\pi\) | ||||
0.0356344 | + | 0.999365i | \(0.488655\pi\) | |||||||
\(968\) | −165.825 | −5.32982 | ||||||||
\(969\) | −46.2247 | −1.48495 | ||||||||
\(970\) | −2.53017 | −0.0812390 | ||||||||
\(971\) | −36.3417 | −1.16626 | −0.583130 | − | 0.812379i | \(-0.698172\pi\) | ||||
−0.583130 | + | 0.812379i | \(0.698172\pi\) | |||||||
\(972\) | 76.3995 | 2.45051 | ||||||||
\(973\) | −92.9062 | −2.97844 | ||||||||
\(974\) | 103.766 | 3.32487 | ||||||||
\(975\) | −46.1944 | −1.47941 | ||||||||
\(976\) | 84.9460 | 2.71906 | ||||||||
\(977\) | 44.5489 | 1.42524 | 0.712622 | − | 0.701548i | \(-0.247507\pi\) | ||||
0.712622 | + | 0.701548i | \(0.247507\pi\) | |||||||
\(978\) | −11.6053 | −0.371096 | ||||||||
\(979\) | −7.51931 | −0.240318 | ||||||||
\(980\) | −75.4718 | −2.41086 | ||||||||
\(981\) | −19.6682 | −0.627957 | ||||||||
\(982\) | 34.5426 | 1.10230 | ||||||||
\(983\) | −5.99390 | −0.191176 | −0.0955878 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955878 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(984\) | 180.812 | 5.76408 | ||||||||
\(985\) | 4.73599 | 0.150901 | ||||||||
\(986\) | 149.123 | 4.74904 | ||||||||
\(987\) | −61.7770 | −1.96638 | ||||||||
\(988\) | 120.934 | 3.84741 | ||||||||
\(989\) | 1.20205 | 0.0382229 | ||||||||
\(990\) | 28.0112 | 0.890254 | ||||||||
\(991\) | 28.2751 | 0.898187 | 0.449094 | − | 0.893485i | \(-0.351747\pi\) | ||||
0.449094 | + | 0.893485i | \(0.351747\pi\) | |||||||
\(992\) | 122.431 | 3.88718 | ||||||||
\(993\) | 3.89513 | 0.123608 | ||||||||
\(994\) | −32.5597 | −1.03273 | ||||||||
\(995\) | −16.8748 | −0.534966 | ||||||||
\(996\) | −72.1289 | −2.28549 | ||||||||
\(997\) | −45.7222 | −1.44804 | −0.724018 | − | 0.689782i | \(-0.757707\pi\) | ||||
−0.724018 | + | 0.689782i | \(0.757707\pi\) | |||||||
\(998\) | −59.0712 | −1.86987 | ||||||||
\(999\) | −29.3710 | −0.929258 |
(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 | 8027.2.a.c.1.2 | ✓ | 143 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.c.1.2 | ✓ | 143 | 1.1 | even | 1 | trivial |