Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.626356 | −0.442900 | −0.221450 | − | 0.975172i | \(-0.571079\pi\) | ||||
−0.221450 | + | 0.975172i | \(0.571079\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.60768 | −0.803839 | ||||||||
\(5\) | −1.73582 | −0.776284 | −0.388142 | − | 0.921600i | \(-0.626883\pi\) | ||||
−0.388142 | + | 0.921600i | \(0.626883\pi\) | |||||||
\(6\) | −0.626356 | −0.255709 | ||||||||
\(7\) | −3.52892 | −1.33381 | −0.666904 | − | 0.745144i | \(-0.732381\pi\) | ||||
−0.666904 | + | 0.745144i | \(0.732381\pi\) | |||||||
\(8\) | 2.25969 | 0.798921 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.08724 | 0.343816 | ||||||||
\(11\) | −5.10748 | −1.53996 | −0.769981 | − | 0.638067i | \(-0.779734\pi\) | ||||
−0.769981 | + | 0.638067i | \(0.779734\pi\) | |||||||
\(12\) | −1.60768 | −0.464097 | ||||||||
\(13\) | −6.25342 | −1.73439 | −0.867193 | − | 0.497972i | \(-0.834078\pi\) | ||||
−0.867193 | + | 0.497972i | \(0.834078\pi\) | |||||||
\(14\) | 2.21036 | 0.590744 | ||||||||
\(15\) | −1.73582 | −0.448188 | ||||||||
\(16\) | 1.79999 | 0.449997 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.626356 | −0.147633 | ||||||||
\(19\) | −1.32233 | −0.303363 | −0.151682 | − | 0.988429i | \(-0.548469\pi\) | ||||
−0.151682 | + | 0.988429i | \(0.548469\pi\) | |||||||
\(20\) | 2.79065 | 0.624007 | ||||||||
\(21\) | −3.52892 | −0.770075 | ||||||||
\(22\) | 3.19910 | 0.682050 | ||||||||
\(23\) | −4.67299 | −0.974386 | −0.487193 | − | 0.873294i | \(-0.661979\pi\) | ||||
−0.487193 | + | 0.873294i | \(0.661979\pi\) | |||||||
\(24\) | 2.25969 | 0.461257 | ||||||||
\(25\) | −1.98692 | −0.397383 | ||||||||
\(26\) | 3.91686 | 0.768160 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.67338 | 1.07217 | ||||||||
\(29\) | −1.94307 | −0.360819 | −0.180410 | − | 0.983592i | \(-0.557742\pi\) | ||||
−0.180410 | + | 0.983592i | \(0.557742\pi\) | |||||||
\(30\) | 1.08724 | 0.198502 | ||||||||
\(31\) | −2.74559 | −0.493122 | −0.246561 | − | 0.969127i | \(-0.579301\pi\) | ||||
−0.246561 | + | 0.969127i | \(0.579301\pi\) | |||||||
\(32\) | −5.64681 | −0.998225 | ||||||||
\(33\) | −5.10748 | −0.889098 | ||||||||
\(34\) | −0.626356 | −0.107419 | ||||||||
\(35\) | 6.12559 | 1.03541 | ||||||||
\(36\) | −1.60768 | −0.267946 | ||||||||
\(37\) | 2.56583 | 0.421820 | 0.210910 | − | 0.977505i | \(-0.432357\pi\) | ||||
0.210910 | + | 0.977505i | \(0.432357\pi\) | |||||||
\(38\) | 0.828249 | 0.134360 | ||||||||
\(39\) | −6.25342 | −1.00135 | ||||||||
\(40\) | −3.92242 | −0.620189 | ||||||||
\(41\) | −5.78701 | −0.903780 | −0.451890 | − | 0.892074i | \(-0.649250\pi\) | ||||
−0.451890 | + | 0.892074i | \(0.649250\pi\) | |||||||
\(42\) | 2.21036 | 0.341066 | ||||||||
\(43\) | 2.16341 | 0.329917 | 0.164959 | − | 0.986301i | \(-0.447251\pi\) | ||||
0.164959 | + | 0.986301i | \(0.447251\pi\) | |||||||
\(44\) | 8.21118 | 1.23788 | ||||||||
\(45\) | −1.73582 | −0.258761 | ||||||||
\(46\) | 2.92695 | 0.431556 | ||||||||
\(47\) | −12.8066 | −1.86803 | −0.934017 | − | 0.357228i | \(-0.883722\pi\) | ||||
−0.934017 | + | 0.357228i | \(0.883722\pi\) | |||||||
\(48\) | 1.79999 | 0.259806 | ||||||||
\(49\) | 5.45331 | 0.779044 | ||||||||
\(50\) | 1.24452 | 0.176001 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 10.0535 | 1.39417 | ||||||||
\(53\) | −4.09434 | −0.562401 | −0.281201 | − | 0.959649i | \(-0.590733\pi\) | ||||
−0.281201 | + | 0.959649i | \(0.590733\pi\) | |||||||
\(54\) | −0.626356 | −0.0852362 | ||||||||
\(55\) | 8.86568 | 1.19545 | ||||||||
\(56\) | −7.97428 | −1.06561 | ||||||||
\(57\) | −1.32233 | −0.175147 | ||||||||
\(58\) | 1.21705 | 0.159807 | ||||||||
\(59\) | −5.16861 | −0.672896 | −0.336448 | − | 0.941702i | \(-0.609226\pi\) | ||||
−0.336448 | + | 0.941702i | \(0.609226\pi\) | |||||||
\(60\) | 2.79065 | 0.360271 | ||||||||
\(61\) | −9.98052 | −1.27788 | −0.638938 | − | 0.769259i | \(-0.720626\pi\) | ||||
−0.638938 | + | 0.769259i | \(0.720626\pi\) | |||||||
\(62\) | 1.71971 | 0.218404 | ||||||||
\(63\) | −3.52892 | −0.444603 | ||||||||
\(64\) | −0.0630639 | −0.00788298 | ||||||||
\(65\) | 10.8548 | 1.34638 | ||||||||
\(66\) | 3.19910 | 0.393782 | ||||||||
\(67\) | −2.06118 | −0.251813 | −0.125907 | − | 0.992042i | \(-0.540184\pi\) | ||||
−0.125907 | + | 0.992042i | \(0.540184\pi\) | |||||||
\(68\) | −1.60768 | −0.194960 | ||||||||
\(69\) | −4.67299 | −0.562562 | ||||||||
\(70\) | −3.83680 | −0.458585 | ||||||||
\(71\) | 7.20147 | 0.854657 | 0.427329 | − | 0.904096i | \(-0.359455\pi\) | ||||
0.427329 | + | 0.904096i | \(0.359455\pi\) | |||||||
\(72\) | 2.25969 | 0.266307 | ||||||||
\(73\) | 10.0866 | 1.18055 | 0.590276 | − | 0.807202i | \(-0.299019\pi\) | ||||
0.590276 | + | 0.807202i | \(0.299019\pi\) | |||||||
\(74\) | −1.60712 | −0.186824 | ||||||||
\(75\) | −1.98692 | −0.229429 | ||||||||
\(76\) | 2.12588 | 0.243855 | ||||||||
\(77\) | 18.0239 | 2.05401 | ||||||||
\(78\) | 3.91686 | 0.443498 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −3.12446 | −0.349325 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.62473 | 0.400284 | ||||||||
\(83\) | 16.6953 | 1.83255 | 0.916274 | − | 0.400551i | \(-0.131181\pi\) | ||||
0.916274 | + | 0.400551i | \(0.131181\pi\) | |||||||
\(84\) | 5.67338 | 0.619016 | ||||||||
\(85\) | −1.73582 | −0.188276 | ||||||||
\(86\) | −1.35506 | −0.146120 | ||||||||
\(87\) | −1.94307 | −0.208319 | ||||||||
\(88\) | −11.5413 | −1.23031 | ||||||||
\(89\) | −14.4469 | −1.53136 | −0.765682 | − | 0.643219i | \(-0.777598\pi\) | ||||
−0.765682 | + | 0.643219i | \(0.777598\pi\) | |||||||
\(90\) | 1.08724 | 0.114605 | ||||||||
\(91\) | 22.0679 | 2.31334 | ||||||||
\(92\) | 7.51267 | 0.783250 | ||||||||
\(93\) | −2.74559 | −0.284704 | ||||||||
\(94\) | 8.02149 | 0.827353 | ||||||||
\(95\) | 2.29533 | 0.235496 | ||||||||
\(96\) | −5.64681 | −0.576325 | ||||||||
\(97\) | −4.30641 | −0.437250 | −0.218625 | − | 0.975809i | \(-0.570157\pi\) | ||||
−0.218625 | + | 0.975809i | \(0.570157\pi\) | |||||||
\(98\) | −3.41571 | −0.345039 | ||||||||
\(99\) | −5.10748 | −0.513321 | ||||||||
\(100\) | 3.19432 | 0.319432 | ||||||||
\(101\) | 10.3955 | 1.03439 | 0.517194 | − | 0.855868i | \(-0.326977\pi\) | ||||
0.517194 | + | 0.855868i | \(0.326977\pi\) | |||||||
\(102\) | −0.626356 | −0.0620184 | ||||||||
\(103\) | −3.10646 | −0.306089 | −0.153044 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153044 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(104\) | −14.1308 | −1.38564 | ||||||||
\(105\) | 6.12559 | 0.597796 | ||||||||
\(106\) | 2.56452 | 0.249088 | ||||||||
\(107\) | 10.2602 | 0.991889 | 0.495944 | − | 0.868354i | \(-0.334822\pi\) | ||||
0.495944 | + | 0.868354i | \(0.334822\pi\) | |||||||
\(108\) | −1.60768 | −0.154699 | ||||||||
\(109\) | −2.89139 | −0.276945 | −0.138473 | − | 0.990366i | \(-0.544219\pi\) | ||||
−0.138473 | + | 0.990366i | \(0.544219\pi\) | |||||||
\(110\) | −5.55307 | −0.529464 | ||||||||
\(111\) | 2.56583 | 0.243538 | ||||||||
\(112\) | −6.35202 | −0.600210 | ||||||||
\(113\) | 1.87221 | 0.176123 | 0.0880614 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880614 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(114\) | 0.828249 | 0.0775726 | ||||||||
\(115\) | 8.11149 | 0.756400 | ||||||||
\(116\) | 3.12383 | 0.290041 | ||||||||
\(117\) | −6.25342 | −0.578129 | ||||||||
\(118\) | 3.23739 | 0.298026 | ||||||||
\(119\) | −3.52892 | −0.323496 | ||||||||
\(120\) | −3.92242 | −0.358067 | ||||||||
\(121\) | 15.0863 | 1.37148 | ||||||||
\(122\) | 6.25136 | 0.565971 | ||||||||
\(123\) | −5.78701 | −0.521797 | ||||||||
\(124\) | 4.41402 | 0.396391 | ||||||||
\(125\) | 12.1281 | 1.08477 | ||||||||
\(126\) | 2.21036 | 0.196915 | ||||||||
\(127\) | −16.9024 | −1.49984 | −0.749921 | − | 0.661528i | \(-0.769908\pi\) | ||||
−0.749921 | + | 0.661528i | \(0.769908\pi\) | |||||||
\(128\) | 11.3331 | 1.00172 | ||||||||
\(129\) | 2.16341 | 0.190478 | ||||||||
\(130\) | −6.79899 | −0.596310 | ||||||||
\(131\) | −2.88794 | −0.252321 | −0.126160 | − | 0.992010i | \(-0.540265\pi\) | ||||
−0.126160 | + | 0.992010i | \(0.540265\pi\) | |||||||
\(132\) | 8.21118 | 0.714692 | ||||||||
\(133\) | 4.66640 | 0.404628 | ||||||||
\(134\) | 1.29103 | 0.111528 | ||||||||
\(135\) | −1.73582 | −0.149396 | ||||||||
\(136\) | 2.25969 | 0.193767 | ||||||||
\(137\) | 4.43192 | 0.378645 | 0.189322 | − | 0.981915i | \(-0.439371\pi\) | ||||
0.189322 | + | 0.981915i | \(0.439371\pi\) | |||||||
\(138\) | 2.92695 | 0.249159 | ||||||||
\(139\) | 2.19056 | 0.185801 | 0.0929005 | − | 0.995675i | \(-0.470386\pi\) | ||||
0.0929005 | + | 0.995675i | \(0.470386\pi\) | |||||||
\(140\) | −9.84798 | −0.832306 | ||||||||
\(141\) | −12.8066 | −1.07851 | ||||||||
\(142\) | −4.51068 | −0.378528 | ||||||||
\(143\) | 31.9392 | 2.67089 | ||||||||
\(144\) | 1.79999 | 0.149999 | ||||||||
\(145\) | 3.37283 | 0.280098 | ||||||||
\(146\) | −6.31782 | −0.522866 | ||||||||
\(147\) | 5.45331 | 0.449782 | ||||||||
\(148\) | −4.12503 | −0.339076 | ||||||||
\(149\) | −9.39545 | −0.769705 | −0.384853 | − | 0.922978i | \(-0.625748\pi\) | ||||
−0.384853 | + | 0.922978i | \(0.625748\pi\) | |||||||
\(150\) | 1.24452 | 0.101614 | ||||||||
\(151\) | −14.3366 | −1.16669 | −0.583347 | − | 0.812223i | \(-0.698257\pi\) | ||||
−0.583347 | + | 0.812223i | \(0.698257\pi\) | |||||||
\(152\) | −2.98806 | −0.242363 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −11.2894 | −0.909724 | ||||||||
\(155\) | 4.76585 | 0.382802 | ||||||||
\(156\) | 10.0535 | 0.804923 | ||||||||
\(157\) | −15.6020 | −1.24517 | −0.622586 | − | 0.782551i | \(-0.713918\pi\) | ||||
−0.622586 | + | 0.782551i | \(0.713918\pi\) | |||||||
\(158\) | −0.626356 | −0.0498302 | ||||||||
\(159\) | −4.09434 | −0.324703 | ||||||||
\(160\) | 9.80187 | 0.774906 | ||||||||
\(161\) | 16.4906 | 1.29964 | ||||||||
\(162\) | −0.626356 | −0.0492111 | ||||||||
\(163\) | −3.58037 | −0.280436 | −0.140218 | − | 0.990121i | \(-0.544780\pi\) | ||||
−0.140218 | + | 0.990121i | \(0.544780\pi\) | |||||||
\(164\) | 9.30366 | 0.726494 | ||||||||
\(165\) | 8.86568 | 0.690192 | ||||||||
\(166\) | −10.4572 | −0.811636 | ||||||||
\(167\) | 11.7391 | 0.908397 | 0.454198 | − | 0.890901i | \(-0.349926\pi\) | ||||
0.454198 | + | 0.890901i | \(0.349926\pi\) | |||||||
\(168\) | −7.97428 | −0.615229 | ||||||||
\(169\) | 26.1053 | 2.00810 | ||||||||
\(170\) | 1.08724 | 0.0833877 | ||||||||
\(171\) | −1.32233 | −0.101121 | ||||||||
\(172\) | −3.47807 | −0.265200 | ||||||||
\(173\) | −6.72410 | −0.511224 | −0.255612 | − | 0.966779i | \(-0.582277\pi\) | ||||
−0.255612 | + | 0.966779i | \(0.582277\pi\) | |||||||
\(174\) | 1.21705 | 0.0922646 | ||||||||
\(175\) | 7.01168 | 0.530033 | ||||||||
\(176\) | −9.19340 | −0.692979 | ||||||||
\(177\) | −5.16861 | −0.388497 | ||||||||
\(178\) | 9.04887 | 0.678242 | ||||||||
\(179\) | 23.0226 | 1.72079 | 0.860394 | − | 0.509629i | \(-0.170217\pi\) | ||||
0.860394 | + | 0.509629i | \(0.170217\pi\) | |||||||
\(180\) | 2.79065 | 0.208002 | ||||||||
\(181\) | 0.0754824 | 0.00561057 | 0.00280528 | − | 0.999996i | \(-0.499107\pi\) | ||||
0.00280528 | + | 0.999996i | \(0.499107\pi\) | |||||||
\(182\) | −13.8223 | −1.02458 | ||||||||
\(183\) | −9.98052 | −0.737782 | ||||||||
\(184\) | −10.5595 | −0.778458 | ||||||||
\(185\) | −4.45383 | −0.327452 | ||||||||
\(186\) | 1.71971 | 0.126095 | ||||||||
\(187\) | −5.10748 | −0.373496 | ||||||||
\(188\) | 20.5889 | 1.50160 | ||||||||
\(189\) | −3.52892 | −0.256692 | ||||||||
\(190\) | −1.43769 | −0.104301 | ||||||||
\(191\) | −16.2498 | −1.17579 | −0.587897 | − | 0.808936i | \(-0.700044\pi\) | ||||
−0.587897 | + | 0.808936i | \(0.700044\pi\) | |||||||
\(192\) | −0.0630639 | −0.00455124 | ||||||||
\(193\) | −16.3940 | −1.18007 | −0.590035 | − | 0.807378i | \(-0.700886\pi\) | ||||
−0.590035 | + | 0.807378i | \(0.700886\pi\) | |||||||
\(194\) | 2.69735 | 0.193658 | ||||||||
\(195\) | 10.8548 | 0.777331 | ||||||||
\(196\) | −8.76717 | −0.626227 | ||||||||
\(197\) | −22.5649 | −1.60769 | −0.803843 | − | 0.594842i | \(-0.797215\pi\) | ||||
−0.803843 | + | 0.594842i | \(0.797215\pi\) | |||||||
\(198\) | 3.19910 | 0.227350 | ||||||||
\(199\) | 16.8334 | 1.19329 | 0.596643 | − | 0.802506i | \(-0.296501\pi\) | ||||
0.596643 | + | 0.802506i | \(0.296501\pi\) | |||||||
\(200\) | −4.48982 | −0.317478 | ||||||||
\(201\) | −2.06118 | −0.145385 | ||||||||
\(202\) | −6.51126 | −0.458131 | ||||||||
\(203\) | 6.85695 | 0.481264 | ||||||||
\(204\) | −1.60768 | −0.112560 | ||||||||
\(205\) | 10.0452 | 0.701590 | ||||||||
\(206\) | 1.94575 | 0.135567 | ||||||||
\(207\) | −4.67299 | −0.324795 | ||||||||
\(208\) | −11.2561 | −0.780469 | ||||||||
\(209\) | 6.75377 | 0.467168 | ||||||||
\(210\) | −3.83680 | −0.264764 | ||||||||
\(211\) | −0.565736 | −0.0389469 | −0.0194734 | − | 0.999810i | \(-0.506199\pi\) | ||||
−0.0194734 | + | 0.999810i | \(0.506199\pi\) | |||||||
\(212\) | 6.58239 | 0.452080 | ||||||||
\(213\) | 7.20147 | 0.493437 | ||||||||
\(214\) | −6.42652 | −0.439308 | ||||||||
\(215\) | −3.75530 | −0.256109 | ||||||||
\(216\) | 2.25969 | 0.153752 | ||||||||
\(217\) | 9.68897 | 0.657730 | ||||||||
\(218\) | 1.81104 | 0.122659 | ||||||||
\(219\) | 10.0866 | 0.681592 | ||||||||
\(220\) | −14.2532 | −0.960948 | ||||||||
\(221\) | −6.25342 | −0.420651 | ||||||||
\(222\) | −1.60712 | −0.107863 | ||||||||
\(223\) | 3.71956 | 0.249080 | 0.124540 | − | 0.992215i | \(-0.460254\pi\) | ||||
0.124540 | + | 0.992215i | \(0.460254\pi\) | |||||||
\(224\) | 19.9272 | 1.33144 | ||||||||
\(225\) | −1.98692 | −0.132461 | ||||||||
\(226\) | −1.17267 | −0.0780048 | ||||||||
\(227\) | −12.1820 | −0.808550 | −0.404275 | − | 0.914638i | \(-0.632476\pi\) | ||||
−0.404275 | + | 0.914638i | \(0.632476\pi\) | |||||||
\(228\) | 2.12588 | 0.140790 | ||||||||
\(229\) | 8.01590 | 0.529705 | 0.264853 | − | 0.964289i | \(-0.414677\pi\) | ||||
0.264853 | + | 0.964289i | \(0.414677\pi\) | |||||||
\(230\) | −5.08068 | −0.335010 | ||||||||
\(231\) | 18.0239 | 1.18589 | ||||||||
\(232\) | −4.39074 | −0.288266 | ||||||||
\(233\) | 6.77495 | 0.443842 | 0.221921 | − | 0.975065i | \(-0.428767\pi\) | ||||
0.221921 | + | 0.975065i | \(0.428767\pi\) | |||||||
\(234\) | 3.91686 | 0.256053 | ||||||||
\(235\) | 22.2300 | 1.45013 | ||||||||
\(236\) | 8.30947 | 0.540900 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 2.21036 | 0.143276 | ||||||||
\(239\) | 19.1256 | 1.23713 | 0.618566 | − | 0.785733i | \(-0.287714\pi\) | ||||
0.618566 | + | 0.785733i | \(0.287714\pi\) | |||||||
\(240\) | −3.12446 | −0.201683 | ||||||||
\(241\) | 11.5938 | 0.746822 | 0.373411 | − | 0.927666i | \(-0.378188\pi\) | ||||
0.373411 | + | 0.927666i | \(0.378188\pi\) | |||||||
\(242\) | −9.44941 | −0.607431 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 16.0455 | 1.02721 | ||||||||
\(245\) | −9.46599 | −0.604760 | ||||||||
\(246\) | 3.62473 | 0.231104 | ||||||||
\(247\) | 8.26908 | 0.526149 | ||||||||
\(248\) | −6.20417 | −0.393965 | ||||||||
\(249\) | 16.6953 | 1.05802 | ||||||||
\(250\) | −7.59647 | −0.480443 | ||||||||
\(251\) | 4.85890 | 0.306691 | 0.153346 | − | 0.988173i | \(-0.450995\pi\) | ||||
0.153346 | + | 0.988173i | \(0.450995\pi\) | |||||||
\(252\) | 5.67338 | 0.357389 | ||||||||
\(253\) | 23.8672 | 1.50052 | ||||||||
\(254\) | 10.5869 | 0.664280 | ||||||||
\(255\) | −1.73582 | −0.108701 | ||||||||
\(256\) | −6.97244 | −0.435777 | ||||||||
\(257\) | 21.2911 | 1.32810 | 0.664051 | − | 0.747687i | \(-0.268836\pi\) | ||||
0.664051 | + | 0.747687i | \(0.268836\pi\) | |||||||
\(258\) | −1.35506 | −0.0843626 | ||||||||
\(259\) | −9.05463 | −0.562627 | ||||||||
\(260\) | −17.4511 | −1.08227 | ||||||||
\(261\) | −1.94307 | −0.120273 | ||||||||
\(262\) | 1.80888 | 0.111753 | ||||||||
\(263\) | 15.1049 | 0.931405 | 0.465703 | − | 0.884941i | \(-0.345802\pi\) | ||||
0.465703 | + | 0.884941i | \(0.345802\pi\) | |||||||
\(264\) | −11.5413 | −0.710319 | ||||||||
\(265\) | 7.10706 | 0.436583 | ||||||||
\(266\) | −2.92283 | −0.179210 | ||||||||
\(267\) | −14.4469 | −0.884134 | ||||||||
\(268\) | 3.31372 | 0.202417 | ||||||||
\(269\) | −8.22219 | −0.501316 | −0.250658 | − | 0.968076i | \(-0.580647\pi\) | ||||
−0.250658 | + | 0.968076i | \(0.580647\pi\) | |||||||
\(270\) | 1.08724 | 0.0661675 | ||||||||
\(271\) | −9.72698 | −0.590872 | −0.295436 | − | 0.955362i | \(-0.595465\pi\) | ||||
−0.295436 | + | 0.955362i | \(0.595465\pi\) | |||||||
\(272\) | 1.79999 | 0.109140 | ||||||||
\(273\) | 22.0679 | 1.33561 | ||||||||
\(274\) | −2.77596 | −0.167702 | ||||||||
\(275\) | 10.1481 | 0.611956 | ||||||||
\(276\) | 7.51267 | 0.452210 | ||||||||
\(277\) | 7.03106 | 0.422455 | 0.211228 | − | 0.977437i | \(-0.432254\pi\) | ||||
0.211228 | + | 0.977437i | \(0.432254\pi\) | |||||||
\(278\) | −1.37207 | −0.0822913 | ||||||||
\(279\) | −2.74559 | −0.164374 | ||||||||
\(280\) | 13.8419 | 0.827214 | ||||||||
\(281\) | −18.2953 | −1.09141 | −0.545703 | − | 0.837979i | \(-0.683737\pi\) | ||||
−0.545703 | + | 0.837979i | \(0.683737\pi\) | |||||||
\(282\) | 8.02149 | 0.477673 | ||||||||
\(283\) | −24.7438 | −1.47086 | −0.735432 | − | 0.677598i | \(-0.763021\pi\) | ||||
−0.735432 | + | 0.677598i | \(0.763021\pi\) | |||||||
\(284\) | −11.5777 | −0.687007 | ||||||||
\(285\) | 2.29533 | 0.135964 | ||||||||
\(286\) | −20.0053 | −1.18294 | ||||||||
\(287\) | 20.4219 | 1.20547 | ||||||||
\(288\) | −5.64681 | −0.332742 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −2.11259 | −0.124056 | ||||||||
\(291\) | −4.30641 | −0.252446 | ||||||||
\(292\) | −16.2161 | −0.948973 | ||||||||
\(293\) | −5.77026 | −0.337102 | −0.168551 | − | 0.985693i | \(-0.553909\pi\) | ||||
−0.168551 | + | 0.985693i | \(0.553909\pi\) | |||||||
\(294\) | −3.41571 | −0.199208 | ||||||||
\(295\) | 8.97180 | 0.522358 | ||||||||
\(296\) | 5.79799 | 0.337001 | ||||||||
\(297\) | −5.10748 | −0.296366 | ||||||||
\(298\) | 5.88489 | 0.340903 | ||||||||
\(299\) | 29.2222 | 1.68996 | ||||||||
\(300\) | 3.19432 | 0.184424 | ||||||||
\(301\) | −7.63451 | −0.440046 | ||||||||
\(302\) | 8.97979 | 0.516729 | ||||||||
\(303\) | 10.3955 | 0.597204 | ||||||||
\(304\) | −2.38018 | −0.136513 | ||||||||
\(305\) | 17.3244 | 0.991994 | ||||||||
\(306\) | −0.626356 | −0.0358064 | ||||||||
\(307\) | −26.8692 | −1.53351 | −0.766753 | − | 0.641942i | \(-0.778129\pi\) | ||||
−0.766753 | + | 0.641942i | \(0.778129\pi\) | |||||||
\(308\) | −28.9766 | −1.65110 | ||||||||
\(309\) | −3.10646 | −0.176720 | ||||||||
\(310\) | −2.98512 | −0.169543 | ||||||||
\(311\) | 6.33580 | 0.359270 | 0.179635 | − | 0.983733i | \(-0.442508\pi\) | ||||
0.179635 | + | 0.983733i | \(0.442508\pi\) | |||||||
\(312\) | −14.1308 | −0.799998 | ||||||||
\(313\) | −8.48733 | −0.479733 | −0.239866 | − | 0.970806i | \(-0.577104\pi\) | ||||
−0.239866 | + | 0.970806i | \(0.577104\pi\) | |||||||
\(314\) | 9.77238 | 0.551487 | ||||||||
\(315\) | 6.12559 | 0.345138 | ||||||||
\(316\) | −1.60768 | −0.0904390 | ||||||||
\(317\) | −16.2865 | −0.914742 | −0.457371 | − | 0.889276i | \(-0.651209\pi\) | ||||
−0.457371 | + | 0.889276i | \(0.651209\pi\) | |||||||
\(318\) | 2.56452 | 0.143811 | ||||||||
\(319\) | 9.92419 | 0.555648 | ||||||||
\(320\) | 0.109468 | 0.00611943 | ||||||||
\(321\) | 10.2602 | 0.572667 | ||||||||
\(322\) | −10.3290 | −0.575613 | ||||||||
\(323\) | −1.32233 | −0.0735764 | ||||||||
\(324\) | −1.60768 | −0.0893155 | ||||||||
\(325\) | 12.4250 | 0.689217 | ||||||||
\(326\) | 2.24259 | 0.124205 | ||||||||
\(327\) | −2.89139 | −0.159894 | ||||||||
\(328\) | −13.0769 | −0.722049 | ||||||||
\(329\) | 45.1935 | 2.49160 | ||||||||
\(330\) | −5.55307 | −0.305686 | ||||||||
\(331\) | −1.73976 | −0.0956260 | −0.0478130 | − | 0.998856i | \(-0.515225\pi\) | ||||
−0.0478130 | + | 0.998856i | \(0.515225\pi\) | |||||||
\(332\) | −26.8407 | −1.47307 | ||||||||
\(333\) | 2.56583 | 0.140607 | ||||||||
\(334\) | −7.35283 | −0.402329 | ||||||||
\(335\) | 3.57785 | 0.195479 | ||||||||
\(336\) | −6.35202 | −0.346531 | ||||||||
\(337\) | −25.4157 | −1.38448 | −0.692242 | − | 0.721666i | \(-0.743377\pi\) | ||||
−0.692242 | + | 0.721666i | \(0.743377\pi\) | |||||||
\(338\) | −16.3512 | −0.889387 | ||||||||
\(339\) | 1.87221 | 0.101685 | ||||||||
\(340\) | 2.79065 | 0.151344 | ||||||||
\(341\) | 14.0230 | 0.759389 | ||||||||
\(342\) | 0.828249 | 0.0447866 | ||||||||
\(343\) | 5.45815 | 0.294712 | ||||||||
\(344\) | 4.88864 | 0.263578 | ||||||||
\(345\) | 8.11149 | 0.436708 | ||||||||
\(346\) | 4.21168 | 0.226421 | ||||||||
\(347\) | 8.73270 | 0.468796 | 0.234398 | − | 0.972141i | \(-0.424688\pi\) | ||||
0.234398 | + | 0.972141i | \(0.424688\pi\) | |||||||
\(348\) | 3.12383 | 0.167455 | ||||||||
\(349\) | −15.1012 | −0.808349 | −0.404175 | − | 0.914682i | \(-0.632441\pi\) | ||||
−0.404175 | + | 0.914682i | \(0.632441\pi\) | |||||||
\(350\) | −4.39181 | −0.234752 | ||||||||
\(351\) | −6.25342 | −0.333783 | ||||||||
\(352\) | 28.8410 | 1.53723 | ||||||||
\(353\) | 17.8898 | 0.952177 | 0.476088 | − | 0.879397i | \(-0.342054\pi\) | ||||
0.476088 | + | 0.879397i | \(0.342054\pi\) | |||||||
\(354\) | 3.23739 | 0.172065 | ||||||||
\(355\) | −12.5005 | −0.663457 | ||||||||
\(356\) | 23.2259 | 1.23097 | ||||||||
\(357\) | −3.52892 | −0.186771 | ||||||||
\(358\) | −14.4203 | −0.762138 | ||||||||
\(359\) | −14.9200 | −0.787446 | −0.393723 | − | 0.919229i | \(-0.628813\pi\) | ||||
−0.393723 | + | 0.919229i | \(0.628813\pi\) | |||||||
\(360\) | −3.92242 | −0.206730 | ||||||||
\(361\) | −17.2514 | −0.907971 | ||||||||
\(362\) | −0.0472788 | −0.00248492 | ||||||||
\(363\) | 15.0863 | 0.791827 | ||||||||
\(364\) | −35.4780 | −1.85955 | ||||||||
\(365\) | −17.5086 | −0.916443 | ||||||||
\(366\) | 6.25136 | 0.326764 | ||||||||
\(367\) | 21.7045 | 1.13297 | 0.566483 | − | 0.824073i | \(-0.308304\pi\) | ||||
0.566483 | + | 0.824073i | \(0.308304\pi\) | |||||||
\(368\) | −8.41133 | −0.438471 | ||||||||
\(369\) | −5.78701 | −0.301260 | ||||||||
\(370\) | 2.78968 | 0.145029 | ||||||||
\(371\) | 14.4486 | 0.750136 | ||||||||
\(372\) | 4.41402 | 0.228856 | ||||||||
\(373\) | −31.6257 | −1.63752 | −0.818758 | − | 0.574138i | \(-0.805337\pi\) | ||||
−0.818758 | + | 0.574138i | \(0.805337\pi\) | |||||||
\(374\) | 3.19910 | 0.165421 | ||||||||
\(375\) | 12.1281 | 0.626290 | ||||||||
\(376\) | −28.9389 | −1.49241 | ||||||||
\(377\) | 12.1508 | 0.625800 | ||||||||
\(378\) | 2.21036 | 0.113689 | ||||||||
\(379\) | −0.419298 | −0.0215379 | −0.0107689 | − | 0.999942i | \(-0.503428\pi\) | ||||
−0.0107689 | + | 0.999942i | \(0.503428\pi\) | |||||||
\(380\) | −3.69015 | −0.189301 | ||||||||
\(381\) | −16.9024 | −0.865934 | ||||||||
\(382\) | 10.1781 | 0.520759 | ||||||||
\(383\) | 36.8028 | 1.88053 | 0.940267 | − | 0.340437i | \(-0.110575\pi\) | ||||
0.940267 | + | 0.340437i | \(0.110575\pi\) | |||||||
\(384\) | 11.3331 | 0.578341 | ||||||||
\(385\) | −31.2863 | −1.59450 | ||||||||
\(386\) | 10.2685 | 0.522653 | ||||||||
\(387\) | 2.16341 | 0.109972 | ||||||||
\(388\) | 6.92333 | 0.351479 | ||||||||
\(389\) | −21.3161 | −1.08077 | −0.540385 | − | 0.841418i | \(-0.681721\pi\) | ||||
−0.540385 | + | 0.841418i | \(0.681721\pi\) | |||||||
\(390\) | −6.79899 | −0.344280 | ||||||||
\(391\) | −4.67299 | −0.236323 | ||||||||
\(392\) | 12.3228 | 0.622395 | ||||||||
\(393\) | −2.88794 | −0.145677 | ||||||||
\(394\) | 14.1337 | 0.712045 | ||||||||
\(395\) | −1.73582 | −0.0873388 | ||||||||
\(396\) | 8.21118 | 0.412627 | ||||||||
\(397\) | 37.9639 | 1.90535 | 0.952677 | − | 0.303986i | \(-0.0983175\pi\) | ||||
0.952677 | + | 0.303986i | \(0.0983175\pi\) | |||||||
\(398\) | −10.5437 | −0.528507 | ||||||||
\(399\) | 4.66640 | 0.233612 | ||||||||
\(400\) | −3.57643 | −0.178821 | ||||||||
\(401\) | −5.80297 | −0.289787 | −0.144893 | − | 0.989447i | \(-0.546284\pi\) | ||||
−0.144893 | + | 0.989447i | \(0.546284\pi\) | |||||||
\(402\) | 1.29103 | 0.0643908 | ||||||||
\(403\) | 17.1693 | 0.855264 | ||||||||
\(404\) | −16.7126 | −0.831481 | ||||||||
\(405\) | −1.73582 | −0.0862538 | ||||||||
\(406\) | −4.29489 | −0.213152 | ||||||||
\(407\) | −13.1049 | −0.649587 | ||||||||
\(408\) | 2.25969 | 0.111871 | ||||||||
\(409\) | −18.1294 | −0.896441 | −0.448220 | − | 0.893923i | \(-0.647942\pi\) | ||||
−0.448220 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(410\) | −6.29189 | −0.310734 | ||||||||
\(411\) | 4.43192 | 0.218611 | ||||||||
\(412\) | 4.99419 | 0.246046 | ||||||||
\(413\) | 18.2396 | 0.897514 | ||||||||
\(414\) | 2.92695 | 0.143852 | ||||||||
\(415\) | −28.9801 | −1.42258 | ||||||||
\(416\) | 35.3119 | 1.73131 | ||||||||
\(417\) | 2.19056 | 0.107272 | ||||||||
\(418\) | −4.23026 | −0.206909 | ||||||||
\(419\) | −14.0537 | −0.686567 | −0.343283 | − | 0.939232i | \(-0.611539\pi\) | ||||
−0.343283 | + | 0.939232i | \(0.611539\pi\) | |||||||
\(420\) | −9.84798 | −0.480532 | ||||||||
\(421\) | −9.92808 | −0.483865 | −0.241932 | − | 0.970293i | \(-0.577781\pi\) | ||||
−0.241932 | + | 0.970293i | \(0.577781\pi\) | |||||||
\(422\) | 0.354352 | 0.0172496 | ||||||||
\(423\) | −12.8066 | −0.622678 | ||||||||
\(424\) | −9.25195 | −0.449314 | ||||||||
\(425\) | −1.98692 | −0.0963796 | ||||||||
\(426\) | −4.51068 | −0.218543 | ||||||||
\(427\) | 35.2205 | 1.70444 | ||||||||
\(428\) | −16.4951 | −0.797319 | ||||||||
\(429\) | 31.9392 | 1.54204 | ||||||||
\(430\) | 2.35215 | 0.113431 | ||||||||
\(431\) | −23.4739 | −1.13070 | −0.565349 | − | 0.824852i | \(-0.691258\pi\) | ||||
−0.565349 | + | 0.824852i | \(0.691258\pi\) | |||||||
\(432\) | 1.79999 | 0.0866020 | ||||||||
\(433\) | −25.4109 | −1.22117 | −0.610584 | − | 0.791951i | \(-0.709065\pi\) | ||||
−0.610584 | + | 0.791951i | \(0.709065\pi\) | |||||||
\(434\) | −6.06874 | −0.291309 | ||||||||
\(435\) | 3.37283 | 0.161715 | ||||||||
\(436\) | 4.64843 | 0.222619 | ||||||||
\(437\) | 6.17924 | 0.295593 | ||||||||
\(438\) | −6.31782 | −0.301877 | ||||||||
\(439\) | 26.5277 | 1.26610 | 0.633048 | − | 0.774113i | \(-0.281804\pi\) | ||||
0.633048 | + | 0.774113i | \(0.281804\pi\) | |||||||
\(440\) | 20.0337 | 0.955068 | ||||||||
\(441\) | 5.45331 | 0.259681 | ||||||||
\(442\) | 3.91686 | 0.186306 | ||||||||
\(443\) | −34.5811 | −1.64300 | −0.821498 | − | 0.570211i | \(-0.806861\pi\) | ||||
−0.821498 | + | 0.570211i | \(0.806861\pi\) | |||||||
\(444\) | −4.12503 | −0.195765 | ||||||||
\(445\) | 25.0772 | 1.18877 | ||||||||
\(446\) | −2.32977 | −0.110318 | ||||||||
\(447\) | −9.39545 | −0.444390 | ||||||||
\(448\) | 0.222548 | 0.0105144 | ||||||||
\(449\) | 25.5656 | 1.20652 | 0.603258 | − | 0.797546i | \(-0.293869\pi\) | ||||
0.603258 | + | 0.797546i | \(0.293869\pi\) | |||||||
\(450\) | 1.24452 | 0.0586671 | ||||||||
\(451\) | 29.5570 | 1.39179 | ||||||||
\(452\) | −3.00991 | −0.141574 | ||||||||
\(453\) | −14.3366 | −0.673591 | ||||||||
\(454\) | 7.63028 | 0.358107 | ||||||||
\(455\) | −38.3059 | −1.79581 | ||||||||
\(456\) | −2.98806 | −0.139929 | ||||||||
\(457\) | −29.1740 | −1.36470 | −0.682352 | − | 0.731024i | \(-0.739043\pi\) | ||||
−0.682352 | + | 0.731024i | \(0.739043\pi\) | |||||||
\(458\) | −5.02080 | −0.234607 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −13.0407 | −0.608024 | ||||||||
\(461\) | −4.00888 | −0.186712 | −0.0933560 | − | 0.995633i | \(-0.529759\pi\) | ||||
−0.0933560 | + | 0.995633i | \(0.529759\pi\) | |||||||
\(462\) | −11.2894 | −0.525229 | ||||||||
\(463\) | −27.5624 | −1.28093 | −0.640466 | − | 0.767987i | \(-0.721259\pi\) | ||||
−0.640466 | + | 0.767987i | \(0.721259\pi\) | |||||||
\(464\) | −3.49750 | −0.162368 | ||||||||
\(465\) | 4.76585 | 0.221011 | ||||||||
\(466\) | −4.24353 | −0.196578 | ||||||||
\(467\) | 1.76806 | 0.0818161 | 0.0409080 | − | 0.999163i | \(-0.486975\pi\) | ||||
0.0409080 | + | 0.999163i | \(0.486975\pi\) | |||||||
\(468\) | 10.0535 | 0.464723 | ||||||||
\(469\) | 7.27375 | 0.335871 | ||||||||
\(470\) | −13.9239 | −0.642261 | ||||||||
\(471\) | −15.6020 | −0.718901 | ||||||||
\(472\) | −11.6795 | −0.537591 | ||||||||
\(473\) | −11.0496 | −0.508060 | ||||||||
\(474\) | −0.626356 | −0.0287695 | ||||||||
\(475\) | 2.62736 | 0.120552 | ||||||||
\(476\) | 5.67338 | 0.260039 | ||||||||
\(477\) | −4.09434 | −0.187467 | ||||||||
\(478\) | −11.9794 | −0.547926 | ||||||||
\(479\) | 9.74005 | 0.445034 | 0.222517 | − | 0.974929i | \(-0.428573\pi\) | ||||
0.222517 | + | 0.974929i | \(0.428573\pi\) | |||||||
\(480\) | 9.80187 | 0.447392 | ||||||||
\(481\) | −16.0452 | −0.731599 | ||||||||
\(482\) | −7.26184 | −0.330768 | ||||||||
\(483\) | 16.4906 | 0.750350 | ||||||||
\(484\) | −24.2540 | −1.10245 | ||||||||
\(485\) | 7.47517 | 0.339430 | ||||||||
\(486\) | −0.626356 | −0.0284121 | ||||||||
\(487\) | −6.53289 | −0.296034 | −0.148017 | − | 0.988985i | \(-0.547289\pi\) | ||||
−0.148017 | + | 0.988985i | \(0.547289\pi\) | |||||||
\(488\) | −22.5529 | −1.02092 | ||||||||
\(489\) | −3.58037 | −0.161910 | ||||||||
\(490\) | 5.92907 | 0.267848 | ||||||||
\(491\) | 32.2958 | 1.45749 | 0.728745 | − | 0.684785i | \(-0.240104\pi\) | ||||
0.728745 | + | 0.684785i | \(0.240104\pi\) | |||||||
\(492\) | 9.30366 | 0.419441 | ||||||||
\(493\) | −1.94307 | −0.0875115 | ||||||||
\(494\) | −5.17939 | −0.233032 | ||||||||
\(495\) | 8.86568 | 0.398483 | ||||||||
\(496\) | −4.94202 | −0.221903 | ||||||||
\(497\) | −25.4134 | −1.13995 | ||||||||
\(498\) | −10.4572 | −0.468598 | ||||||||
\(499\) | −20.5314 | −0.919110 | −0.459555 | − | 0.888149i | \(-0.651991\pi\) | ||||
−0.459555 | + | 0.888149i | \(0.651991\pi\) | |||||||
\(500\) | −19.4980 | −0.871978 | ||||||||
\(501\) | 11.7391 | 0.524463 | ||||||||
\(502\) | −3.04340 | −0.135834 | ||||||||
\(503\) | −26.7932 | −1.19465 | −0.597324 | − | 0.802000i | \(-0.703769\pi\) | ||||
−0.597324 | + | 0.802000i | \(0.703769\pi\) | |||||||
\(504\) | −7.97428 | −0.355202 | ||||||||
\(505\) | −18.0447 | −0.802978 | ||||||||
\(506\) | −14.9494 | −0.664580 | ||||||||
\(507\) | 26.1053 | 1.15938 | ||||||||
\(508\) | 27.1736 | 1.20563 | ||||||||
\(509\) | −2.37616 | −0.105322 | −0.0526608 | − | 0.998612i | \(-0.516770\pi\) | ||||
−0.0526608 | + | 0.998612i | \(0.516770\pi\) | |||||||
\(510\) | 1.08724 | 0.0481439 | ||||||||
\(511\) | −35.5950 | −1.57463 | ||||||||
\(512\) | −18.2990 | −0.808710 | ||||||||
\(513\) | −1.32233 | −0.0583823 | ||||||||
\(514\) | −13.3358 | −0.588217 | ||||||||
\(515\) | 5.39227 | 0.237612 | ||||||||
\(516\) | −3.47807 | −0.153113 | ||||||||
\(517\) | 65.4094 | 2.87670 | ||||||||
\(518\) | 5.67142 | 0.249188 | ||||||||
\(519\) | −6.72410 | −0.295155 | ||||||||
\(520\) | 24.5286 | 1.07565 | ||||||||
\(521\) | 24.3131 | 1.06518 | 0.532588 | − | 0.846375i | \(-0.321220\pi\) | ||||
0.532588 | + | 0.846375i | \(0.321220\pi\) | |||||||
\(522\) | 1.21705 | 0.0532690 | ||||||||
\(523\) | −29.6613 | −1.29700 | −0.648499 | − | 0.761215i | \(-0.724603\pi\) | ||||
−0.648499 | + | 0.761215i | \(0.724603\pi\) | |||||||
\(524\) | 4.64288 | 0.202825 | ||||||||
\(525\) | 7.01168 | 0.306015 | ||||||||
\(526\) | −9.46101 | −0.412520 | ||||||||
\(527\) | −2.74559 | −0.119600 | ||||||||
\(528\) | −9.19340 | −0.400091 | ||||||||
\(529\) | −1.16314 | −0.0505713 | ||||||||
\(530\) | −4.45155 | −0.193363 | ||||||||
\(531\) | −5.16861 | −0.224299 | ||||||||
\(532\) | −7.50208 | −0.325256 | ||||||||
\(533\) | 36.1886 | 1.56750 | ||||||||
\(534\) | 9.04887 | 0.391583 | ||||||||
\(535\) | −17.8099 | −0.769987 | ||||||||
\(536\) | −4.65763 | −0.201179 | ||||||||
\(537\) | 23.0226 | 0.993498 | ||||||||
\(538\) | 5.15002 | 0.222033 | ||||||||
\(539\) | −27.8527 | −1.19970 | ||||||||
\(540\) | 2.79065 | 0.120090 | ||||||||
\(541\) | 7.81470 | 0.335980 | 0.167990 | − | 0.985789i | \(-0.446272\pi\) | ||||
0.167990 | + | 0.985789i | \(0.446272\pi\) | |||||||
\(542\) | 6.09255 | 0.261697 | ||||||||
\(543\) | 0.0754824 | 0.00323926 | ||||||||
\(544\) | −5.64681 | −0.242105 | ||||||||
\(545\) | 5.01895 | 0.214988 | ||||||||
\(546\) | −13.8223 | −0.591541 | ||||||||
\(547\) | 41.5044 | 1.77460 | 0.887301 | − | 0.461191i | \(-0.152578\pi\) | ||||
0.887301 | + | 0.461191i | \(0.152578\pi\) | |||||||
\(548\) | −7.12511 | −0.304370 | ||||||||
\(549\) | −9.98052 | −0.425958 | ||||||||
\(550\) | −6.35634 | −0.271035 | ||||||||
\(551\) | 2.56938 | 0.109459 | ||||||||
\(552\) | −10.5595 | −0.449443 | ||||||||
\(553\) | −3.52892 | −0.150065 | ||||||||
\(554\) | −4.40394 | −0.187106 | ||||||||
\(555\) | −4.45383 | −0.189055 | ||||||||
\(556\) | −3.52172 | −0.149354 | ||||||||
\(557\) | 20.4459 | 0.866322 | 0.433161 | − | 0.901316i | \(-0.357398\pi\) | ||||
0.433161 | + | 0.901316i | \(0.357398\pi\) | |||||||
\(558\) | 1.71971 | 0.0728013 | ||||||||
\(559\) | −13.5287 | −0.572204 | ||||||||
\(560\) | 11.0260 | 0.465933 | ||||||||
\(561\) | −5.10748 | −0.215638 | ||||||||
\(562\) | 11.4594 | 0.483384 | ||||||||
\(563\) | 9.16137 | 0.386106 | 0.193053 | − | 0.981188i | \(-0.438161\pi\) | ||||
0.193053 | + | 0.981188i | \(0.438161\pi\) | |||||||
\(564\) | 20.5889 | 0.866949 | ||||||||
\(565\) | −3.24983 | −0.136721 | ||||||||
\(566\) | 15.4984 | 0.651446 | ||||||||
\(567\) | −3.52892 | −0.148201 | ||||||||
\(568\) | 16.2731 | 0.682804 | ||||||||
\(569\) | 16.4516 | 0.689689 | 0.344844 | − | 0.938660i | \(-0.387932\pi\) | ||||
0.344844 | + | 0.938660i | \(0.387932\pi\) | |||||||
\(570\) | −1.43769 | −0.0602184 | ||||||||
\(571\) | 35.0552 | 1.46702 | 0.733508 | − | 0.679681i | \(-0.237882\pi\) | ||||
0.733508 | + | 0.679681i | \(0.237882\pi\) | |||||||
\(572\) | −51.3480 | −2.14697 | ||||||||
\(573\) | −16.2498 | −0.678844 | ||||||||
\(574\) | −12.7914 | −0.533902 | ||||||||
\(575\) | 9.28485 | 0.387205 | ||||||||
\(576\) | −0.0630639 | −0.00262766 | ||||||||
\(577\) | −37.8797 | −1.57695 | −0.788476 | − | 0.615066i | \(-0.789129\pi\) | ||||
−0.788476 | + | 0.615066i | \(0.789129\pi\) | |||||||
\(578\) | −0.626356 | −0.0260530 | ||||||||
\(579\) | −16.3940 | −0.681313 | ||||||||
\(580\) | −5.42242 | −0.225154 | ||||||||
\(581\) | −58.9165 | −2.44427 | ||||||||
\(582\) | 2.69735 | 0.111809 | ||||||||
\(583\) | 20.9118 | 0.866077 | ||||||||
\(584\) | 22.7927 | 0.943167 | ||||||||
\(585\) | 10.8548 | 0.448792 | ||||||||
\(586\) | 3.61423 | 0.149303 | ||||||||
\(587\) | 9.23673 | 0.381241 | 0.190620 | − | 0.981664i | \(-0.438950\pi\) | ||||
0.190620 | + | 0.981664i | \(0.438950\pi\) | |||||||
\(588\) | −8.76717 | −0.361552 | ||||||||
\(589\) | 3.63057 | 0.149595 | ||||||||
\(590\) | −5.61953 | −0.231353 | ||||||||
\(591\) | −22.5649 | −0.928198 | ||||||||
\(592\) | 4.61847 | 0.189818 | ||||||||
\(593\) | −25.1196 | −1.03154 | −0.515770 | − | 0.856727i | \(-0.672494\pi\) | ||||
−0.515770 | + | 0.856727i | \(0.672494\pi\) | |||||||
\(594\) | 3.19910 | 0.131261 | ||||||||
\(595\) | 6.12559 | 0.251125 | ||||||||
\(596\) | 15.1049 | 0.618719 | ||||||||
\(597\) | 16.8334 | 0.688944 | ||||||||
\(598\) | −18.3035 | −0.748485 | ||||||||
\(599\) | −25.5580 | −1.04427 | −0.522136 | − | 0.852862i | \(-0.674865\pi\) | ||||
−0.522136 | + | 0.852862i | \(0.674865\pi\) | |||||||
\(600\) | −4.48982 | −0.183296 | ||||||||
\(601\) | −39.8088 | −1.62384 | −0.811918 | − | 0.583771i | \(-0.801577\pi\) | ||||
−0.811918 | + | 0.583771i | \(0.801577\pi\) | |||||||
\(602\) | 4.78192 | 0.194897 | ||||||||
\(603\) | −2.06118 | −0.0839378 | ||||||||
\(604\) | 23.0486 | 0.937834 | ||||||||
\(605\) | −26.1872 | −1.06466 | ||||||||
\(606\) | −6.51126 | −0.264502 | ||||||||
\(607\) | 19.8694 | 0.806474 | 0.403237 | − | 0.915096i | \(-0.367885\pi\) | ||||
0.403237 | + | 0.915096i | \(0.367885\pi\) | |||||||
\(608\) | 7.46695 | 0.302825 | ||||||||
\(609\) | 6.85695 | 0.277858 | ||||||||
\(610\) | −10.8513 | −0.439354 | ||||||||
\(611\) | 80.0851 | 3.23989 | ||||||||
\(612\) | −1.60768 | −0.0649866 | ||||||||
\(613\) | −16.6254 | −0.671494 | −0.335747 | − | 0.941952i | \(-0.608989\pi\) | ||||
−0.335747 | + | 0.941952i | \(0.608989\pi\) | |||||||
\(614\) | 16.8297 | 0.679191 | ||||||||
\(615\) | 10.0452 | 0.405063 | ||||||||
\(616\) | 40.7284 | 1.64100 | ||||||||
\(617\) | 18.9369 | 0.762371 | 0.381186 | − | 0.924499i | \(-0.375516\pi\) | ||||
0.381186 | + | 0.924499i | \(0.375516\pi\) | |||||||
\(618\) | 1.94575 | 0.0782695 | ||||||||
\(619\) | −25.1054 | −1.00907 | −0.504535 | − | 0.863391i | \(-0.668336\pi\) | ||||
−0.504535 | + | 0.863391i | \(0.668336\pi\) | |||||||
\(620\) | −7.66196 | −0.307712 | ||||||||
\(621\) | −4.67299 | −0.187521 | ||||||||
\(622\) | −3.96846 | −0.159121 | ||||||||
\(623\) | 50.9819 | 2.04255 | ||||||||
\(624\) | −11.2561 | −0.450604 | ||||||||
\(625\) | −11.1176 | −0.444703 | ||||||||
\(626\) | 5.31609 | 0.212474 | ||||||||
\(627\) | 6.75377 | 0.269720 | ||||||||
\(628\) | 25.0830 | 1.00092 | ||||||||
\(629\) | 2.56583 | 0.102306 | ||||||||
\(630\) | −3.83680 | −0.152862 | ||||||||
\(631\) | −37.8868 | −1.50825 | −0.754125 | − | 0.656731i | \(-0.771939\pi\) | ||||
−0.754125 | + | 0.656731i | \(0.771939\pi\) | |||||||
\(632\) | 2.25969 | 0.0898856 | ||||||||
\(633\) | −0.565736 | −0.0224860 | ||||||||
\(634\) | 10.2012 | 0.405140 | ||||||||
\(635\) | 29.3395 | 1.16430 | ||||||||
\(636\) | 6.58239 | 0.261009 | ||||||||
\(637\) | −34.1018 | −1.35116 | ||||||||
\(638\) | −6.21607 | −0.246097 | ||||||||
\(639\) | 7.20147 | 0.284886 | ||||||||
\(640\) | −19.6723 | −0.777616 | ||||||||
\(641\) | 27.7198 | 1.09487 | 0.547434 | − | 0.836849i | \(-0.315605\pi\) | ||||
0.547434 | + | 0.836849i | \(0.315605\pi\) | |||||||
\(642\) | −6.42652 | −0.253634 | ||||||||
\(643\) | −25.7562 | −1.01572 | −0.507862 | − | 0.861438i | \(-0.669564\pi\) | ||||
−0.507862 | + | 0.861438i | \(0.669564\pi\) | |||||||
\(644\) | −26.5116 | −1.04471 | ||||||||
\(645\) | −3.75530 | −0.147865 | ||||||||
\(646\) | 0.828249 | 0.0325870 | ||||||||
\(647\) | −0.609702 | −0.0239698 | −0.0119849 | − | 0.999928i | \(-0.503815\pi\) | ||||
−0.0119849 | + | 0.999928i | \(0.503815\pi\) | |||||||
\(648\) | 2.25969 | 0.0887690 | ||||||||
\(649\) | 26.3986 | 1.03623 | ||||||||
\(650\) | −7.78249 | −0.305254 | ||||||||
\(651\) | 9.68897 | 0.379741 | ||||||||
\(652\) | 5.75609 | 0.225426 | ||||||||
\(653\) | −9.53439 | −0.373109 | −0.186555 | − | 0.982445i | \(-0.559732\pi\) | ||||
−0.186555 | + | 0.982445i | \(0.559732\pi\) | |||||||
\(654\) | 1.81104 | 0.0708173 | ||||||||
\(655\) | 5.01296 | 0.195873 | ||||||||
\(656\) | −10.4166 | −0.406698 | ||||||||
\(657\) | 10.0866 | 0.393517 | ||||||||
\(658\) | −28.3072 | −1.10353 | ||||||||
\(659\) | 32.3470 | 1.26006 | 0.630030 | − | 0.776571i | \(-0.283043\pi\) | ||||
0.630030 | + | 0.776571i | \(0.283043\pi\) | |||||||
\(660\) | −14.2532 | −0.554804 | ||||||||
\(661\) | −0.160299 | −0.00623489 | −0.00311745 | − | 0.999995i | \(-0.500992\pi\) | ||||
−0.00311745 | + | 0.999995i | \(0.500992\pi\) | |||||||
\(662\) | 1.08971 | 0.0423528 | ||||||||
\(663\) | −6.25342 | −0.242863 | ||||||||
\(664\) | 37.7262 | 1.46406 | ||||||||
\(665\) | −8.10005 | −0.314107 | ||||||||
\(666\) | −1.60712 | −0.0622748 | ||||||||
\(667\) | 9.07995 | 0.351577 | ||||||||
\(668\) | −18.8727 | −0.730205 | ||||||||
\(669\) | 3.71956 | 0.143807 | ||||||||
\(670\) | −2.24100 | −0.0865775 | ||||||||
\(671\) | 50.9753 | 1.96788 | ||||||||
\(672\) | 19.9272 | 0.768707 | ||||||||
\(673\) | −15.1200 | −0.582835 | −0.291417 | − | 0.956596i | \(-0.594127\pi\) | ||||
−0.291417 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(674\) | 15.9193 | 0.613188 | ||||||||
\(675\) | −1.98692 | −0.0764765 | ||||||||
\(676\) | −41.9689 | −1.61419 | ||||||||
\(677\) | 2.69920 | 0.103739 | 0.0518694 | − | 0.998654i | \(-0.483482\pi\) | ||||
0.0518694 | + | 0.998654i | \(0.483482\pi\) | |||||||
\(678\) | −1.17267 | −0.0450361 | ||||||||
\(679\) | 15.1970 | 0.583207 | ||||||||
\(680\) | −3.92242 | −0.150418 | ||||||||
\(681\) | −12.1820 | −0.466816 | ||||||||
\(682\) | −8.78340 | −0.336334 | ||||||||
\(683\) | 20.0421 | 0.766890 | 0.383445 | − | 0.923564i | \(-0.374738\pi\) | ||||
0.383445 | + | 0.923564i | \(0.374738\pi\) | |||||||
\(684\) | 2.12588 | 0.0812851 | ||||||||
\(685\) | −7.69304 | −0.293936 | ||||||||
\(686\) | −3.41874 | −0.130528 | ||||||||
\(687\) | 8.01590 | 0.305826 | ||||||||
\(688\) | 3.89411 | 0.148462 | ||||||||
\(689\) | 25.6037 | 0.975421 | ||||||||
\(690\) | −5.08068 | −0.193418 | ||||||||
\(691\) | 25.6849 | 0.977099 | 0.488550 | − | 0.872536i | \(-0.337526\pi\) | ||||
0.488550 | + | 0.872536i | \(0.337526\pi\) | |||||||
\(692\) | 10.8102 | 0.410942 | ||||||||
\(693\) | 18.0239 | 0.684672 | ||||||||
\(694\) | −5.46978 | −0.207630 | ||||||||
\(695\) | −3.80243 | −0.144234 | ||||||||
\(696\) | −4.39074 | −0.166430 | ||||||||
\(697\) | −5.78701 | −0.219199 | ||||||||
\(698\) | 9.45873 | 0.358018 | ||||||||
\(699\) | 6.77495 | 0.256252 | ||||||||
\(700\) | −11.2725 | −0.426062 | ||||||||
\(701\) | 48.5394 | 1.83331 | 0.916654 | − | 0.399682i | \(-0.130879\pi\) | ||||
0.916654 | + | 0.399682i | \(0.130879\pi\) | |||||||
\(702\) | 3.91686 | 0.147833 | ||||||||
\(703\) | −3.39288 | −0.127965 | ||||||||
\(704\) | 0.322097 | 0.0121395 | ||||||||
\(705\) | 22.2300 | 0.837230 | ||||||||
\(706\) | −11.2054 | −0.421719 | ||||||||
\(707\) | −36.6848 | −1.37967 | ||||||||
\(708\) | 8.30947 | 0.312289 | ||||||||
\(709\) | −8.73886 | −0.328195 | −0.164097 | − | 0.986444i | \(-0.552471\pi\) | ||||
−0.164097 | + | 0.986444i | \(0.552471\pi\) | |||||||
\(710\) | 7.82975 | 0.293845 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −32.6454 | −1.22344 | ||||||||
\(713\) | 12.8301 | 0.480491 | ||||||||
\(714\) | 2.21036 | 0.0827207 | ||||||||
\(715\) | −55.4408 | −2.07337 | ||||||||
\(716\) | −37.0129 | −1.38324 | ||||||||
\(717\) | 19.1256 | 0.714259 | ||||||||
\(718\) | 9.34521 | 0.348760 | ||||||||
\(719\) | −30.7778 | −1.14782 | −0.573910 | − | 0.818919i | \(-0.694574\pi\) | ||||
−0.573910 | + | 0.818919i | \(0.694574\pi\) | |||||||
\(720\) | −3.12446 | −0.116442 | ||||||||
\(721\) | 10.9625 | 0.408263 | ||||||||
\(722\) | 10.8055 | 0.402140 | ||||||||
\(723\) | 11.5938 | 0.431178 | ||||||||
\(724\) | −0.121351 | −0.00450999 | ||||||||
\(725\) | 3.86072 | 0.143384 | ||||||||
\(726\) | −9.44941 | −0.350700 | ||||||||
\(727\) | 53.6437 | 1.98954 | 0.994768 | − | 0.102163i | \(-0.0325763\pi\) | ||||
0.994768 | + | 0.102163i | \(0.0325763\pi\) | |||||||
\(728\) | 49.8665 | 1.84818 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.9666 | 0.405893 | ||||||||
\(731\) | 2.16341 | 0.0800166 | ||||||||
\(732\) | 16.0455 | 0.593058 | ||||||||
\(733\) | −36.9991 | −1.36659 | −0.683297 | − | 0.730141i | \(-0.739454\pi\) | ||||
−0.683297 | + | 0.730141i | \(0.739454\pi\) | |||||||
\(734\) | −13.5947 | −0.501791 | ||||||||
\(735\) | −9.46599 | −0.349158 | ||||||||
\(736\) | 26.3875 | 0.972657 | ||||||||
\(737\) | 10.5274 | 0.387783 | ||||||||
\(738\) | 3.62473 | 0.133428 | ||||||||
\(739\) | −31.6269 | −1.16341 | −0.581707 | − | 0.813399i | \(-0.697615\pi\) | ||||
−0.581707 | + | 0.813399i | \(0.697615\pi\) | |||||||
\(740\) | 7.16033 | 0.263219 | ||||||||
\(741\) | 8.26908 | 0.303772 | ||||||||
\(742\) | −9.04998 | −0.332235 | ||||||||
\(743\) | 0.954026 | 0.0349998 | 0.0174999 | − | 0.999847i | \(-0.494429\pi\) | ||||
0.0174999 | + | 0.999847i | \(0.494429\pi\) | |||||||
\(744\) | −6.20417 | −0.227456 | ||||||||
\(745\) | 16.3088 | 0.597510 | ||||||||
\(746\) | 19.8089 | 0.725257 | ||||||||
\(747\) | 16.6953 | 0.610850 | ||||||||
\(748\) | 8.21118 | 0.300231 | ||||||||
\(749\) | −36.2074 | −1.32299 | ||||||||
\(750\) | −7.59647 | −0.277384 | ||||||||
\(751\) | 18.0772 | 0.659647 | 0.329823 | − | 0.944043i | \(-0.393011\pi\) | ||||
0.329823 | + | 0.944043i | \(0.393011\pi\) | |||||||
\(752\) | −23.0517 | −0.840610 | ||||||||
\(753\) | 4.85890 | 0.177068 | ||||||||
\(754\) | −7.61074 | −0.277167 | ||||||||
\(755\) | 24.8858 | 0.905685 | ||||||||
\(756\) | 5.67338 | 0.206339 | ||||||||
\(757\) | −13.5096 | −0.491016 | −0.245508 | − | 0.969395i | \(-0.578955\pi\) | ||||
−0.245508 | + | 0.969395i | \(0.578955\pi\) | |||||||
\(758\) | 0.262630 | 0.00953914 | ||||||||
\(759\) | 23.8672 | 0.866325 | ||||||||
\(760\) | 5.18674 | 0.188143 | ||||||||
\(761\) | −37.8935 | −1.37364 | −0.686819 | − | 0.726829i | \(-0.740993\pi\) | ||||
−0.686819 | + | 0.726829i | \(0.740993\pi\) | |||||||
\(762\) | 10.5869 | 0.383522 | ||||||||
\(763\) | 10.2035 | 0.369392 | ||||||||
\(764\) | 26.1244 | 0.945149 | ||||||||
\(765\) | −1.73582 | −0.0627588 | ||||||||
\(766\) | −23.0516 | −0.832889 | ||||||||
\(767\) | 32.3215 | 1.16706 | ||||||||
\(768\) | −6.97244 | −0.251596 | ||||||||
\(769\) | 39.1108 | 1.41037 | 0.705185 | − | 0.709023i | \(-0.250864\pi\) | ||||
0.705185 | + | 0.709023i | \(0.250864\pi\) | |||||||
\(770\) | 19.5964 | 0.706204 | ||||||||
\(771\) | 21.2911 | 0.766780 | ||||||||
\(772\) | 26.3564 | 0.948586 | ||||||||
\(773\) | −31.4211 | −1.13014 | −0.565070 | − | 0.825043i | \(-0.691151\pi\) | ||||
−0.565070 | + | 0.825043i | \(0.691151\pi\) | |||||||
\(774\) | −1.35506 | −0.0487068 | ||||||||
\(775\) | 5.45525 | 0.195958 | ||||||||
\(776\) | −9.73115 | −0.349328 | ||||||||
\(777\) | −9.05463 | −0.324833 | ||||||||
\(778\) | 13.3515 | 0.478673 | ||||||||
\(779\) | 7.65234 | 0.274174 | ||||||||
\(780\) | −17.4511 | −0.624849 | ||||||||
\(781\) | −36.7813 | −1.31614 | ||||||||
\(782\) | 2.92695 | 0.104668 | ||||||||
\(783\) | −1.94307 | −0.0694397 | ||||||||
\(784\) | 9.81590 | 0.350568 | ||||||||
\(785\) | 27.0823 | 0.966607 | ||||||||
\(786\) | 1.80888 | 0.0645206 | ||||||||
\(787\) | 37.7518 | 1.34571 | 0.672854 | − | 0.739776i | \(-0.265068\pi\) | ||||
0.672854 | + | 0.739776i | \(0.265068\pi\) | |||||||
\(788\) | 36.2772 | 1.29232 | ||||||||
\(789\) | 15.1049 | 0.537747 | ||||||||
\(790\) | 1.08724 | 0.0386824 | ||||||||
\(791\) | −6.60689 | −0.234914 | ||||||||
\(792\) | −11.5413 | −0.410103 | ||||||||
\(793\) | 62.4124 | 2.21633 | ||||||||
\(794\) | −23.7789 | −0.843881 | ||||||||
\(795\) | 7.10706 | 0.252061 | ||||||||
\(796\) | −27.0627 | −0.959211 | ||||||||
\(797\) | −34.8148 | −1.23320 | −0.616601 | − | 0.787276i | \(-0.711491\pi\) | ||||
−0.616601 | + | 0.787276i | \(0.711491\pi\) | |||||||
\(798\) | −2.92283 | −0.103467 | ||||||||
\(799\) | −12.8066 | −0.453065 | ||||||||
\(800\) | 11.2197 | 0.396678 | ||||||||
\(801\) | −14.4469 | −0.510455 | ||||||||
\(802\) | 3.63472 | 0.128347 | ||||||||
\(803\) | −51.5173 | −1.81800 | ||||||||
\(804\) | 3.31372 | 0.116866 | ||||||||
\(805\) | −28.6248 | −1.00889 | ||||||||
\(806\) | −10.7541 | −0.378797 | ||||||||
\(807\) | −8.22219 | −0.289435 | ||||||||
\(808\) | 23.4905 | 0.826394 | ||||||||
\(809\) | 42.9762 | 1.51096 | 0.755481 | − | 0.655171i | \(-0.227403\pi\) | ||||
0.755481 | + | 0.655171i | \(0.227403\pi\) | |||||||
\(810\) | 1.08724 | 0.0382018 | ||||||||
\(811\) | −29.2375 | −1.02667 | −0.513334 | − | 0.858189i | \(-0.671590\pi\) | ||||
−0.513334 | + | 0.858189i | \(0.671590\pi\) | |||||||
\(812\) | −11.0238 | −0.386859 | ||||||||
\(813\) | −9.72698 | −0.341140 | ||||||||
\(814\) | 8.20835 | 0.287702 | ||||||||
\(815\) | 6.21490 | 0.217698 | ||||||||
\(816\) | 1.79999 | 0.0630122 | ||||||||
\(817\) | −2.86074 | −0.100085 | ||||||||
\(818\) | 11.3554 | 0.397034 | ||||||||
\(819\) | 22.0679 | 0.771113 | ||||||||
\(820\) | −16.1495 | −0.563965 | ||||||||
\(821\) | 8.94659 | 0.312238 | 0.156119 | − | 0.987738i | \(-0.450102\pi\) | ||||
0.156119 | + | 0.987738i | \(0.450102\pi\) | |||||||
\(822\) | −2.77596 | −0.0968227 | ||||||||
\(823\) | −22.4428 | −0.782308 | −0.391154 | − | 0.920325i | \(-0.627924\pi\) | ||||
−0.391154 | + | 0.920325i | \(0.627924\pi\) | |||||||
\(824\) | −7.01964 | −0.244541 | ||||||||
\(825\) | 10.1481 | 0.353313 | ||||||||
\(826\) | −11.4245 | −0.397509 | ||||||||
\(827\) | −16.2648 | −0.565582 | −0.282791 | − | 0.959182i | \(-0.591260\pi\) | ||||
−0.282791 | + | 0.959182i | \(0.591260\pi\) | |||||||
\(828\) | 7.51267 | 0.261083 | ||||||||
\(829\) | 17.9406 | 0.623104 | 0.311552 | − | 0.950229i | \(-0.399151\pi\) | ||||
0.311552 | + | 0.950229i | \(0.399151\pi\) | |||||||
\(830\) | 18.1519 | 0.630060 | ||||||||
\(831\) | 7.03106 | 0.243905 | ||||||||
\(832\) | 0.394365 | 0.0136721 | ||||||||
\(833\) | 5.45331 | 0.188946 | ||||||||
\(834\) | −1.37207 | −0.0475109 | ||||||||
\(835\) | −20.3770 | −0.705174 | ||||||||
\(836\) | −10.8579 | −0.375528 | ||||||||
\(837\) | −2.74559 | −0.0949013 | ||||||||
\(838\) | 8.80260 | 0.304081 | ||||||||
\(839\) | −21.0534 | −0.726844 | −0.363422 | − | 0.931625i | \(-0.618392\pi\) | ||||
−0.363422 | + | 0.931625i | \(0.618392\pi\) | |||||||
\(840\) | 13.8419 | 0.477592 | ||||||||
\(841\) | −25.2245 | −0.869810 | ||||||||
\(842\) | 6.21851 | 0.214304 | ||||||||
\(843\) | −18.2953 | −0.630124 | ||||||||
\(844\) | 0.909522 | 0.0313070 | ||||||||
\(845\) | −45.3141 | −1.55885 | ||||||||
\(846\) | 8.02149 | 0.275784 | ||||||||
\(847\) | −53.2385 | −1.82930 | ||||||||
\(848\) | −7.36977 | −0.253079 | ||||||||
\(849\) | −24.7438 | −0.849204 | ||||||||
\(850\) | 1.24452 | 0.0426866 | ||||||||
\(851\) | −11.9901 | −0.411016 | ||||||||
\(852\) | −11.5777 | −0.396644 | ||||||||
\(853\) | −27.1058 | −0.928086 | −0.464043 | − | 0.885813i | \(-0.653602\pi\) | ||||
−0.464043 | + | 0.885813i | \(0.653602\pi\) | |||||||
\(854\) | −22.0606 | −0.754897 | ||||||||
\(855\) | 2.29533 | 0.0784987 | ||||||||
\(856\) | 23.1848 | 0.792441 | ||||||||
\(857\) | −20.2780 | −0.692683 | −0.346341 | − | 0.938109i | \(-0.612576\pi\) | ||||
−0.346341 | + | 0.938109i | \(0.612576\pi\) | |||||||
\(858\) | −20.0053 | −0.682970 | ||||||||
\(859\) | 46.5813 | 1.58933 | 0.794666 | − | 0.607047i | \(-0.207646\pi\) | ||||
0.794666 | + | 0.607047i | \(0.207646\pi\) | |||||||
\(860\) | 6.03731 | 0.205871 | ||||||||
\(861\) | 20.4219 | 0.695978 | ||||||||
\(862\) | 14.7030 | 0.500786 | ||||||||
\(863\) | 13.4056 | 0.456331 | 0.228166 | − | 0.973622i | \(-0.426727\pi\) | ||||
0.228166 | + | 0.973622i | \(0.426727\pi\) | |||||||
\(864\) | −5.64681 | −0.192108 | ||||||||
\(865\) | 11.6718 | 0.396855 | ||||||||
\(866\) | 15.9162 | 0.540856 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −15.5767 | −0.528709 | ||||||||
\(869\) | −5.10748 | −0.173259 | ||||||||
\(870\) | −2.11259 | −0.0716235 | ||||||||
\(871\) | 12.8894 | 0.436742 | ||||||||
\(872\) | −6.53365 | −0.221257 | ||||||||
\(873\) | −4.30641 | −0.145750 | ||||||||
\(874\) | −3.87040 | −0.130918 | ||||||||
\(875\) | −42.7990 | −1.44687 | ||||||||
\(876\) | −16.2161 | −0.547890 | ||||||||
\(877\) | 51.3560 | 1.73417 | 0.867084 | − | 0.498162i | \(-0.165991\pi\) | ||||
0.867084 | + | 0.498162i | \(0.165991\pi\) | |||||||
\(878\) | −16.6157 | −0.560754 | ||||||||
\(879\) | −5.77026 | −0.194626 | ||||||||
\(880\) | 15.9581 | 0.537948 | ||||||||
\(881\) | −26.8889 | −0.905911 | −0.452955 | − | 0.891533i | \(-0.649630\pi\) | ||||
−0.452955 | + | 0.891533i | \(0.649630\pi\) | |||||||
\(882\) | −3.41571 | −0.115013 | ||||||||
\(883\) | −18.6065 | −0.626160 | −0.313080 | − | 0.949727i | \(-0.601361\pi\) | ||||
−0.313080 | + | 0.949727i | \(0.601361\pi\) | |||||||
\(884\) | 10.0535 | 0.338135 | ||||||||
\(885\) | 8.97180 | 0.301584 | ||||||||
\(886\) | 21.6601 | 0.727684 | ||||||||
\(887\) | −27.9580 | −0.938738 | −0.469369 | − | 0.883002i | \(-0.655519\pi\) | ||||
−0.469369 | + | 0.883002i | \(0.655519\pi\) | |||||||
\(888\) | 5.79799 | 0.194568 | ||||||||
\(889\) | 59.6472 | 2.00050 | ||||||||
\(890\) | −15.7072 | −0.526508 | ||||||||
\(891\) | −5.10748 | −0.171107 | ||||||||
\(892\) | −5.97986 | −0.200220 | ||||||||
\(893\) | 16.9346 | 0.566693 | ||||||||
\(894\) | 5.88489 | 0.196820 | ||||||||
\(895\) | −39.9631 | −1.33582 | ||||||||
\(896\) | −39.9937 | −1.33610 | ||||||||
\(897\) | 29.2222 | 0.975700 | ||||||||
\(898\) | −16.0132 | −0.534367 | ||||||||
\(899\) | 5.33487 | 0.177928 | ||||||||
\(900\) | 3.19432 | 0.106477 | ||||||||
\(901\) | −4.09434 | −0.136402 | ||||||||
\(902\) | −18.5132 | −0.616423 | ||||||||
\(903\) | −7.63451 | −0.254061 | ||||||||
\(904\) | 4.23062 | 0.140708 | ||||||||
\(905\) | −0.131024 | −0.00435539 | ||||||||
\(906\) | 8.97979 | 0.298334 | ||||||||
\(907\) | −21.6435 | −0.718660 | −0.359330 | − | 0.933211i | \(-0.616995\pi\) | ||||
−0.359330 | + | 0.933211i | \(0.616995\pi\) | |||||||
\(908\) | 19.5848 | 0.649944 | ||||||||
\(909\) | 10.3955 | 0.344796 | ||||||||
\(910\) | 23.9931 | 0.795364 | ||||||||
\(911\) | −40.7545 | −1.35026 | −0.675128 | − | 0.737700i | \(-0.735912\pi\) | ||||
−0.675128 | + | 0.737700i | \(0.735912\pi\) | |||||||
\(912\) | −2.38018 | −0.0788156 | ||||||||
\(913\) | −85.2709 | −2.82206 | ||||||||
\(914\) | 18.2733 | 0.604428 | ||||||||
\(915\) | 17.3244 | 0.572728 | ||||||||
\(916\) | −12.8870 | −0.425798 | ||||||||
\(917\) | 10.1913 | 0.336547 | ||||||||
\(918\) | −0.626356 | −0.0206728 | ||||||||
\(919\) | −39.4323 | −1.30075 | −0.650376 | − | 0.759612i | \(-0.725389\pi\) | ||||
−0.650376 | + | 0.759612i | \(0.725389\pi\) | |||||||
\(920\) | 18.3294 | 0.604304 | ||||||||
\(921\) | −26.8692 | −0.885371 | ||||||||
\(922\) | 2.51098 | 0.0826948 | ||||||||
\(923\) | −45.0338 | −1.48231 | ||||||||
\(924\) | −28.9766 | −0.953262 | ||||||||
\(925\) | −5.09810 | −0.167624 | ||||||||
\(926\) | 17.2638 | 0.567325 | ||||||||
\(927\) | −3.10646 | −0.102030 | ||||||||
\(928\) | 10.9722 | 0.360179 | ||||||||
\(929\) | −13.9715 | −0.458389 | −0.229195 | − | 0.973381i | \(-0.573609\pi\) | ||||
−0.229195 | + | 0.973381i | \(0.573609\pi\) | |||||||
\(930\) | −2.98512 | −0.0978859 | ||||||||
\(931\) | −7.21108 | −0.236333 | ||||||||
\(932\) | −10.8919 | −0.356778 | ||||||||
\(933\) | 6.33580 | 0.207425 | ||||||||
\(934\) | −1.10743 | −0.0362364 | ||||||||
\(935\) | 8.86568 | 0.289939 | ||||||||
\(936\) | −14.1308 | −0.461879 | ||||||||
\(937\) | 30.7648 | 1.00504 | 0.502521 | − | 0.864565i | \(-0.332406\pi\) | ||||
0.502521 | + | 0.864565i | \(0.332406\pi\) | |||||||
\(938\) | −4.55596 | −0.148757 | ||||||||
\(939\) | −8.48733 | −0.276974 | ||||||||
\(940\) | −35.7387 | −1.16567 | ||||||||
\(941\) | 14.9333 | 0.486810 | 0.243405 | − | 0.969925i | \(-0.421736\pi\) | ||||
0.243405 | + | 0.969925i | \(0.421736\pi\) | |||||||
\(942\) | 9.77238 | 0.318401 | ||||||||
\(943\) | 27.0427 | 0.880631 | ||||||||
\(944\) | −9.30344 | −0.302801 | ||||||||
\(945\) | 6.12559 | 0.199265 | ||||||||
\(946\) | 6.92096 | 0.225020 | ||||||||
\(947\) | −31.9890 | −1.03950 | −0.519751 | − | 0.854318i | \(-0.673975\pi\) | ||||
−0.519751 | + | 0.854318i | \(0.673975\pi\) | |||||||
\(948\) | −1.60768 | −0.0522150 | ||||||||
\(949\) | −63.0760 | −2.04753 | ||||||||
\(950\) | −1.64566 | −0.0533923 | ||||||||
\(951\) | −16.2865 | −0.528127 | ||||||||
\(952\) | −7.97428 | −0.258448 | ||||||||
\(953\) | −10.5114 | −0.340499 | −0.170250 | − | 0.985401i | \(-0.554457\pi\) | ||||
−0.170250 | + | 0.985401i | \(0.554457\pi\) | |||||||
\(954\) | 2.56452 | 0.0830292 | ||||||||
\(955\) | 28.2068 | 0.912749 | ||||||||
\(956\) | −30.7478 | −0.994455 | ||||||||
\(957\) | 9.92419 | 0.320804 | ||||||||
\(958\) | −6.10073 | −0.197106 | ||||||||
\(959\) | −15.6399 | −0.505039 | ||||||||
\(960\) | 0.109468 | 0.00353306 | ||||||||
\(961\) | −23.4618 | −0.756831 | ||||||||
\(962\) | 10.0500 | 0.324026 | ||||||||
\(963\) | 10.2602 | 0.330630 | ||||||||
\(964\) | −18.6391 | −0.600325 | ||||||||
\(965\) | 28.4572 | 0.916069 | ||||||||
\(966\) | −10.3290 | −0.332330 | ||||||||
\(967\) | 2.41004 | 0.0775016 | 0.0387508 | − | 0.999249i | \(-0.487662\pi\) | ||||
0.0387508 | + | 0.999249i | \(0.487662\pi\) | |||||||
\(968\) | 34.0904 | 1.09571 | ||||||||
\(969\) | −1.32233 | −0.0424794 | ||||||||
\(970\) | −4.68211 | −0.150334 | ||||||||
\(971\) | −54.5068 | −1.74921 | −0.874603 | − | 0.484839i | \(-0.838878\pi\) | ||||
−0.874603 | + | 0.484839i | \(0.838878\pi\) | |||||||
\(972\) | −1.60768 | −0.0515663 | ||||||||
\(973\) | −7.73033 | −0.247823 | ||||||||
\(974\) | 4.09191 | 0.131113 | ||||||||
\(975\) | 12.4250 | 0.397919 | ||||||||
\(976\) | −17.9648 | −0.575040 | ||||||||
\(977\) | −55.2952 | −1.76905 | −0.884526 | − | 0.466492i | \(-0.845518\pi\) | ||||
−0.884526 | + | 0.466492i | \(0.845518\pi\) | |||||||
\(978\) | 2.24259 | 0.0717100 | ||||||||
\(979\) | 73.7870 | 2.35824 | ||||||||
\(980\) | 15.2183 | 0.486130 | ||||||||
\(981\) | −2.89139 | −0.0923151 | ||||||||
\(982\) | −20.2287 | −0.645523 | ||||||||
\(983\) | −15.3859 | −0.490734 | −0.245367 | − | 0.969430i | \(-0.578908\pi\) | ||||
−0.245367 | + | 0.969430i | \(0.578908\pi\) | |||||||
\(984\) | −13.0769 | −0.416875 | ||||||||
\(985\) | 39.1688 | 1.24802 | ||||||||
\(986\) | 1.21705 | 0.0387589 | ||||||||
\(987\) | 45.1935 | 1.43853 | ||||||||
\(988\) | −13.2940 | −0.422939 | ||||||||
\(989\) | −10.1096 | −0.321467 | ||||||||
\(990\) | −5.55307 | −0.176488 | ||||||||
\(991\) | −18.3831 | −0.583958 | −0.291979 | − | 0.956425i | \(-0.594314\pi\) | ||||
−0.291979 | + | 0.956425i | \(0.594314\pi\) | |||||||
\(992\) | 15.5038 | 0.492246 | ||||||||
\(993\) | −1.73976 | −0.0552097 | ||||||||
\(994\) | 15.9179 | 0.504884 | ||||||||
\(995\) | −29.2198 | −0.926329 | ||||||||
\(996\) | −26.8407 | −0.850480 | ||||||||
\(997\) | −32.4101 | −1.02644 | −0.513220 | − | 0.858257i | \(-0.671547\pi\) | ||||
−0.513220 | + | 0.858257i | \(0.671547\pi\) | |||||||
\(998\) | 12.8599 | 0.407074 | ||||||||
\(999\) | 2.56583 | 0.0811794 |
(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 | 4029.2.a.k.1.13 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.13 | ✓ | 31 | 1.1 | even | 1 | trivial |