Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.04947 | −1.44919 | −0.724597 | − | 0.689173i | \(-0.757974\pi\) | ||||
−0.724597 | + | 0.689173i | \(0.757974\pi\) | |||||||
\(3\) | −1.65528 | −0.955678 | −0.477839 | − | 0.878448i | \(-0.658580\pi\) | ||||
−0.477839 | + | 0.878448i | \(0.658580\pi\) | |||||||
\(4\) | 2.20033 | 1.10016 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.39245 | 1.38496 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.410568 | −0.145158 | ||||||||
\(9\) | −0.260041 | −0.0866802 | ||||||||
\(10\) | 2.04947 | 0.648099 | ||||||||
\(11\) | 3.07599 | 0.927445 | 0.463722 | − | 0.885981i | \(-0.346513\pi\) | ||||
0.463722 | + | 0.885981i | \(0.346513\pi\) | |||||||
\(12\) | −3.64217 | −1.05140 | ||||||||
\(13\) | −6.96455 | −1.93162 | −0.965809 | − | 0.259255i | \(-0.916523\pi\) | ||||
−0.965809 | + | 0.259255i | \(0.916523\pi\) | |||||||
\(14\) | −2.04947 | −0.547744 | ||||||||
\(15\) | 1.65528 | 0.427392 | ||||||||
\(16\) | −3.55921 | −0.889803 | ||||||||
\(17\) | 2.59404 | 0.629147 | 0.314574 | − | 0.949233i | \(-0.398138\pi\) | ||||
0.314574 | + | 0.949233i | \(0.398138\pi\) | |||||||
\(18\) | 0.532946 | 0.125616 | ||||||||
\(19\) | −5.65948 | −1.29837 | −0.649187 | − | 0.760629i | \(-0.724891\pi\) | ||||
−0.649187 | + | 0.760629i | \(0.724891\pi\) | |||||||
\(20\) | −2.20033 | −0.492009 | ||||||||
\(21\) | −1.65528 | −0.361212 | ||||||||
\(22\) | −6.30414 | −1.34405 | ||||||||
\(23\) | −2.20232 | −0.459215 | −0.229608 | − | 0.973283i | \(-0.573744\pi\) | ||||
−0.229608 | + | 0.973283i | \(0.573744\pi\) | |||||||
\(24\) | 0.679606 | 0.138724 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 14.2736 | 2.79929 | ||||||||
\(27\) | 5.39629 | 1.03852 | ||||||||
\(28\) | 2.20033 | 0.415823 | ||||||||
\(29\) | −9.39223 | −1.74409 | −0.872047 | − | 0.489423i | \(-0.837208\pi\) | ||||
−0.872047 | + | 0.489423i | \(0.837208\pi\) | |||||||
\(30\) | −3.39245 | −0.619374 | ||||||||
\(31\) | −8.85195 | −1.58986 | −0.794929 | − | 0.606702i | \(-0.792492\pi\) | ||||
−0.794929 | + | 0.606702i | \(0.792492\pi\) | |||||||
\(32\) | 8.11563 | 1.43465 | ||||||||
\(33\) | −5.09163 | −0.886338 | ||||||||
\(34\) | −5.31641 | −0.911757 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −0.572175 | −0.0953625 | ||||||||
\(37\) | −9.77015 | −1.60620 | −0.803102 | − | 0.595842i | \(-0.796818\pi\) | ||||
−0.803102 | + | 0.595842i | \(0.796818\pi\) | |||||||
\(38\) | 11.5989 | 1.88160 | ||||||||
\(39\) | 11.5283 | 1.84600 | ||||||||
\(40\) | 0.410568 | 0.0649165 | ||||||||
\(41\) | −3.61685 | −0.564857 | −0.282429 | − | 0.959288i | \(-0.591140\pi\) | ||||
−0.282429 | + | 0.959288i | \(0.591140\pi\) | |||||||
\(42\) | 3.39245 | 0.523467 | ||||||||
\(43\) | −1.57071 | −0.239531 | −0.119765 | − | 0.992802i | \(-0.538214\pi\) | ||||
−0.119765 | + | 0.992802i | \(0.538214\pi\) | |||||||
\(44\) | 6.76818 | 1.02034 | ||||||||
\(45\) | 0.260041 | 0.0387646 | ||||||||
\(46\) | 4.51359 | 0.665493 | ||||||||
\(47\) | −12.8789 | −1.87859 | −0.939293 | − | 0.343115i | \(-0.888518\pi\) | ||||
−0.939293 | + | 0.343115i | \(0.888518\pi\) | |||||||
\(48\) | 5.89150 | 0.850364 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.04947 | −0.289839 | ||||||||
\(51\) | −4.29387 | −0.601262 | ||||||||
\(52\) | −15.3243 | −2.12510 | ||||||||
\(53\) | 10.5760 | 1.45272 | 0.726360 | − | 0.687315i | \(-0.241211\pi\) | ||||
0.726360 | + | 0.687315i | \(0.241211\pi\) | |||||||
\(54\) | −11.0595 | −1.50501 | ||||||||
\(55\) | −3.07599 | −0.414766 | ||||||||
\(56\) | −0.410568 | −0.0548645 | ||||||||
\(57\) | 9.36804 | 1.24083 | ||||||||
\(58\) | 19.2491 | 2.52753 | ||||||||
\(59\) | 8.59806 | 1.11937 | 0.559686 | − | 0.828705i | \(-0.310922\pi\) | ||||
0.559686 | + | 0.828705i | \(0.310922\pi\) | |||||||
\(60\) | 3.64217 | 0.470202 | ||||||||
\(61\) | −14.7665 | −1.89066 | −0.945329 | − | 0.326118i | \(-0.894259\pi\) | ||||
−0.945329 | + | 0.326118i | \(0.894259\pi\) | |||||||
\(62\) | 18.1418 | 2.30401 | ||||||||
\(63\) | −0.260041 | −0.0327620 | ||||||||
\(64\) | −9.51433 | −1.18929 | ||||||||
\(65\) | 6.96455 | 0.863846 | ||||||||
\(66\) | 10.4351 | 1.28448 | ||||||||
\(67\) | −5.31962 | −0.649895 | −0.324947 | − | 0.945732i | \(-0.605347\pi\) | ||||
−0.324947 | + | 0.945732i | \(0.605347\pi\) | |||||||
\(68\) | 5.70774 | 0.692166 | ||||||||
\(69\) | 3.64546 | 0.438862 | ||||||||
\(70\) | 2.04947 | 0.244959 | ||||||||
\(71\) | −8.41810 | −0.999045 | −0.499522 | − | 0.866301i | \(-0.666491\pi\) | ||||
−0.499522 | + | 0.866301i | \(0.666491\pi\) | |||||||
\(72\) | 0.106764 | 0.0125823 | ||||||||
\(73\) | −6.22527 | −0.728613 | −0.364307 | − | 0.931279i | \(-0.618694\pi\) | ||||
−0.364307 | + | 0.931279i | \(0.618694\pi\) | |||||||
\(74\) | 20.0236 | 2.32770 | ||||||||
\(75\) | −1.65528 | −0.191136 | ||||||||
\(76\) | −12.4527 | −1.42843 | ||||||||
\(77\) | 3.07599 | 0.350541 | ||||||||
\(78\) | −23.6269 | −2.67522 | ||||||||
\(79\) | 12.4141 | 1.39670 | 0.698349 | − | 0.715758i | \(-0.253919\pi\) | ||||
0.698349 | + | 0.715758i | \(0.253919\pi\) | |||||||
\(80\) | 3.55921 | 0.397932 | ||||||||
\(81\) | −8.15226 | −0.905806 | ||||||||
\(82\) | 7.41263 | 0.818588 | ||||||||
\(83\) | −8.59977 | −0.943947 | −0.471974 | − | 0.881613i | \(-0.656458\pi\) | ||||
−0.471974 | + | 0.881613i | \(0.656458\pi\) | |||||||
\(84\) | −3.64217 | −0.397393 | ||||||||
\(85\) | −2.59404 | −0.281363 | ||||||||
\(86\) | 3.21912 | 0.347127 | ||||||||
\(87\) | 15.5468 | 1.66679 | ||||||||
\(88\) | −1.26290 | −0.134626 | ||||||||
\(89\) | 5.10322 | 0.540940 | 0.270470 | − | 0.962728i | \(-0.412821\pi\) | ||||
0.270470 | + | 0.962728i | \(0.412821\pi\) | |||||||
\(90\) | −0.532946 | −0.0561774 | ||||||||
\(91\) | −6.96455 | −0.730083 | ||||||||
\(92\) | −4.84583 | −0.505213 | ||||||||
\(93\) | 14.6525 | 1.51939 | ||||||||
\(94\) | 26.3950 | 2.72244 | ||||||||
\(95\) | 5.65948 | 0.580651 | ||||||||
\(96\) | −13.4337 | −1.37107 | ||||||||
\(97\) | 2.38854 | 0.242520 | 0.121260 | − | 0.992621i | \(-0.461307\pi\) | ||||
0.121260 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(98\) | −2.04947 | −0.207028 | ||||||||
\(99\) | −0.799881 | −0.0803911 | ||||||||
\(100\) | 2.20033 | 0.220033 | ||||||||
\(101\) | −16.3202 | −1.62392 | −0.811962 | − | 0.583710i | \(-0.801601\pi\) | ||||
−0.811962 | + | 0.583710i | \(0.801601\pi\) | |||||||
\(102\) | 8.80016 | 0.871346 | ||||||||
\(103\) | 9.25451 | 0.911874 | 0.455937 | − | 0.890012i | \(-0.349304\pi\) | ||||
0.455937 | + | 0.890012i | \(0.349304\pi\) | |||||||
\(104\) | 2.85942 | 0.280389 | ||||||||
\(105\) | 1.65528 | 0.161539 | ||||||||
\(106\) | −21.6751 | −2.10527 | ||||||||
\(107\) | 3.96790 | 0.383592 | 0.191796 | − | 0.981435i | \(-0.438569\pi\) | ||||
0.191796 | + | 0.981435i | \(0.438569\pi\) | |||||||
\(108\) | 11.8736 | 1.14254 | ||||||||
\(109\) | −5.33851 | −0.511337 | −0.255668 | − | 0.966765i | \(-0.582296\pi\) | ||||
−0.255668 | + | 0.966765i | \(0.582296\pi\) | |||||||
\(110\) | 6.30414 | 0.601076 | ||||||||
\(111\) | 16.1724 | 1.53501 | ||||||||
\(112\) | −3.55921 | −0.336314 | ||||||||
\(113\) | 2.55746 | 0.240586 | 0.120293 | − | 0.992738i | \(-0.461617\pi\) | ||||
0.120293 | + | 0.992738i | \(0.461617\pi\) | |||||||
\(114\) | −19.1995 | −1.79820 | ||||||||
\(115\) | 2.20232 | 0.205367 | ||||||||
\(116\) | −20.6660 | −1.91879 | ||||||||
\(117\) | 1.81107 | 0.167433 | ||||||||
\(118\) | −17.6215 | −1.62219 | ||||||||
\(119\) | 2.59404 | 0.237795 | ||||||||
\(120\) | −0.679606 | −0.0620393 | ||||||||
\(121\) | −1.53831 | −0.139846 | ||||||||
\(122\) | 30.2635 | 2.73993 | ||||||||
\(123\) | 5.98691 | 0.539821 | ||||||||
\(124\) | −19.4772 | −1.74911 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.532946 | 0.0474786 | ||||||||
\(127\) | 12.9738 | 1.15124 | 0.575619 | − | 0.817718i | \(-0.304761\pi\) | ||||
0.575619 | + | 0.817718i | \(0.304761\pi\) | |||||||
\(128\) | 3.26807 | 0.288859 | ||||||||
\(129\) | 2.59997 | 0.228914 | ||||||||
\(130\) | −14.2736 | −1.25188 | ||||||||
\(131\) | −17.0650 | −1.49097 | −0.745487 | − | 0.666520i | \(-0.767783\pi\) | ||||
−0.745487 | + | 0.666520i | \(0.767783\pi\) | |||||||
\(132\) | −11.2033 | −0.975118 | ||||||||
\(133\) | −5.65948 | −0.490739 | ||||||||
\(134\) | 10.9024 | 0.941824 | ||||||||
\(135\) | −5.39629 | −0.464438 | ||||||||
\(136\) | −1.06503 | −0.0913257 | ||||||||
\(137\) | 19.4528 | 1.66197 | 0.830984 | − | 0.556296i | \(-0.187778\pi\) | ||||
0.830984 | + | 0.556296i | \(0.187778\pi\) | |||||||
\(138\) | −7.47127 | −0.635996 | ||||||||
\(139\) | 2.63491 | 0.223490 | 0.111745 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111745 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(140\) | −2.20033 | −0.185962 | ||||||||
\(141\) | 21.3183 | 1.79532 | ||||||||
\(142\) | 17.2526 | 1.44781 | ||||||||
\(143\) | −21.4229 | −1.79147 | ||||||||
\(144\) | 0.925539 | 0.0771283 | ||||||||
\(145\) | 9.39223 | 0.779982 | ||||||||
\(146\) | 12.7585 | 1.05590 | ||||||||
\(147\) | −1.65528 | −0.136525 | ||||||||
\(148\) | −21.4976 | −1.76709 | ||||||||
\(149\) | −9.39115 | −0.769353 | −0.384677 | − | 0.923051i | \(-0.625687\pi\) | ||||
−0.384677 | + | 0.923051i | \(0.625687\pi\) | |||||||
\(150\) | 3.39245 | 0.276993 | ||||||||
\(151\) | 1.11243 | 0.0905281 | 0.0452640 | − | 0.998975i | \(-0.485587\pi\) | ||||
0.0452640 | + | 0.998975i | \(0.485587\pi\) | |||||||
\(152\) | 2.32360 | 0.188469 | ||||||||
\(153\) | −0.674556 | −0.0545346 | ||||||||
\(154\) | −6.30414 | −0.508002 | ||||||||
\(155\) | 8.85195 | 0.711006 | ||||||||
\(156\) | 25.3660 | 2.03091 | ||||||||
\(157\) | −7.75706 | −0.619080 | −0.309540 | − | 0.950886i | \(-0.600175\pi\) | ||||
−0.309540 | + | 0.950886i | \(0.600175\pi\) | |||||||
\(158\) | −25.4424 | −2.02409 | ||||||||
\(159\) | −17.5062 | −1.38833 | ||||||||
\(160\) | −8.11563 | −0.641597 | ||||||||
\(161\) | −2.20232 | −0.173567 | ||||||||
\(162\) | 16.7078 | 1.31269 | ||||||||
\(163\) | 13.7377 | 1.07602 | 0.538011 | − | 0.842938i | \(-0.319176\pi\) | ||||
0.538011 | + | 0.842938i | \(0.319176\pi\) | |||||||
\(164\) | −7.95826 | −0.621436 | ||||||||
\(165\) | 5.09163 | 0.396383 | ||||||||
\(166\) | 17.6250 | 1.36796 | ||||||||
\(167\) | 6.00009 | 0.464301 | 0.232150 | − | 0.972680i | \(-0.425424\pi\) | ||||
0.232150 | + | 0.972680i | \(0.425424\pi\) | |||||||
\(168\) | 0.679606 | 0.0524328 | ||||||||
\(169\) | 35.5049 | 2.73115 | ||||||||
\(170\) | 5.31641 | 0.407750 | ||||||||
\(171\) | 1.47170 | 0.112543 | ||||||||
\(172\) | −3.45608 | −0.263523 | ||||||||
\(173\) | 14.1260 | 1.07398 | 0.536990 | − | 0.843588i | \(-0.319561\pi\) | ||||
0.536990 | + | 0.843588i | \(0.319561\pi\) | |||||||
\(174\) | −31.8627 | −2.41550 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −10.9481 | −0.825243 | ||||||||
\(177\) | −14.2322 | −1.06976 | ||||||||
\(178\) | −10.4589 | −0.783927 | ||||||||
\(179\) | −17.6250 | −1.31736 | −0.658678 | − | 0.752425i | \(-0.728884\pi\) | ||||
−0.658678 | + | 0.752425i | \(0.728884\pi\) | |||||||
\(180\) | 0.572175 | 0.0426474 | ||||||||
\(181\) | −20.8984 | −1.55337 | −0.776685 | − | 0.629890i | \(-0.783100\pi\) | ||||
−0.776685 | + | 0.629890i | \(0.783100\pi\) | |||||||
\(182\) | 14.2736 | 1.05803 | ||||||||
\(183\) | 24.4427 | 1.80686 | ||||||||
\(184\) | 0.904203 | 0.0666587 | ||||||||
\(185\) | 9.77015 | 0.718316 | ||||||||
\(186\) | −30.0298 | −2.20189 | ||||||||
\(187\) | 7.97924 | 0.583500 | ||||||||
\(188\) | −28.3379 | −2.06675 | ||||||||
\(189\) | 5.39629 | 0.392522 | ||||||||
\(190\) | −11.5989 | −0.841476 | ||||||||
\(191\) | −16.4141 | −1.18768 | −0.593841 | − | 0.804582i | \(-0.702389\pi\) | ||||
−0.593841 | + | 0.804582i | \(0.702389\pi\) | |||||||
\(192\) | 15.7489 | 1.13658 | ||||||||
\(193\) | −21.1233 | −1.52048 | −0.760242 | − | 0.649639i | \(-0.774920\pi\) | ||||
−0.760242 | + | 0.649639i | \(0.774920\pi\) | |||||||
\(194\) | −4.89524 | −0.351458 | ||||||||
\(195\) | −11.5283 | −0.825558 | ||||||||
\(196\) | 2.20033 | 0.157166 | ||||||||
\(197\) | −22.4665 | −1.60067 | −0.800336 | − | 0.599551i | \(-0.795346\pi\) | ||||
−0.800336 | + | 0.599551i | \(0.795346\pi\) | |||||||
\(198\) | 1.63933 | 0.116502 | ||||||||
\(199\) | 11.6681 | 0.827132 | 0.413566 | − | 0.910474i | \(-0.364283\pi\) | ||||
0.413566 | + | 0.910474i | \(0.364283\pi\) | |||||||
\(200\) | −0.410568 | −0.0290316 | ||||||||
\(201\) | 8.80547 | 0.621090 | ||||||||
\(202\) | 33.4479 | 2.35338 | ||||||||
\(203\) | −9.39223 | −0.659205 | ||||||||
\(204\) | −9.44793 | −0.661487 | ||||||||
\(205\) | 3.61685 | 0.252612 | ||||||||
\(206\) | −18.9669 | −1.32148 | ||||||||
\(207\) | 0.572693 | 0.0398049 | ||||||||
\(208\) | 24.7883 | 1.71876 | ||||||||
\(209\) | −17.4085 | −1.20417 | ||||||||
\(210\) | −3.39245 | −0.234101 | ||||||||
\(211\) | −3.57294 | −0.245971 | −0.122986 | − | 0.992408i | \(-0.539247\pi\) | ||||
−0.122986 | + | 0.992408i | \(0.539247\pi\) | |||||||
\(212\) | 23.2706 | 1.59823 | ||||||||
\(213\) | 13.9343 | 0.954765 | ||||||||
\(214\) | −8.13210 | −0.555899 | ||||||||
\(215\) | 1.57071 | 0.107122 | ||||||||
\(216\) | −2.21554 | −0.150749 | ||||||||
\(217\) | −8.85195 | −0.600910 | ||||||||
\(218\) | 10.9411 | 0.741027 | ||||||||
\(219\) | 10.3046 | 0.696319 | ||||||||
\(220\) | −6.76818 | −0.456311 | ||||||||
\(221\) | −18.0663 | −1.21527 | ||||||||
\(222\) | −33.1448 | −2.22453 | ||||||||
\(223\) | 14.5832 | 0.976564 | 0.488282 | − | 0.872686i | \(-0.337624\pi\) | ||||
0.488282 | + | 0.872686i | \(0.337624\pi\) | |||||||
\(224\) | 8.11563 | 0.542249 | ||||||||
\(225\) | −0.260041 | −0.0173360 | ||||||||
\(226\) | −5.24144 | −0.348655 | ||||||||
\(227\) | −13.4862 | −0.895110 | −0.447555 | − | 0.894256i | \(-0.647705\pi\) | ||||
−0.447555 | + | 0.894256i | \(0.647705\pi\) | |||||||
\(228\) | 20.6128 | 1.36511 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | −4.51359 | −0.297617 | ||||||||
\(231\) | −5.09163 | −0.335004 | ||||||||
\(232\) | 3.85615 | 0.253169 | ||||||||
\(233\) | −5.67709 | −0.371918 | −0.185959 | − | 0.982557i | \(-0.559539\pi\) | ||||
−0.185959 | + | 0.982557i | \(0.559539\pi\) | |||||||
\(234\) | −3.71172 | −0.242643 | ||||||||
\(235\) | 12.8789 | 0.840130 | ||||||||
\(236\) | 18.9186 | 1.23149 | ||||||||
\(237\) | −20.5489 | −1.33479 | ||||||||
\(238\) | −5.31641 | −0.344612 | ||||||||
\(239\) | −13.3075 | −0.860789 | −0.430394 | − | 0.902641i | \(-0.641626\pi\) | ||||
−0.430394 | + | 0.902641i | \(0.641626\pi\) | |||||||
\(240\) | −5.89150 | −0.380295 | ||||||||
\(241\) | −14.6454 | −0.943392 | −0.471696 | − | 0.881761i | \(-0.656358\pi\) | ||||
−0.471696 | + | 0.881761i | \(0.656358\pi\) | |||||||
\(242\) | 3.15271 | 0.202664 | ||||||||
\(243\) | −2.69458 | −0.172857 | ||||||||
\(244\) | −32.4912 | −2.08003 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −12.2700 | −0.782306 | ||||||||
\(247\) | 39.4157 | 2.50796 | ||||||||
\(248\) | 3.63433 | 0.230780 | ||||||||
\(249\) | 14.2350 | 0.902109 | ||||||||
\(250\) | 2.04947 | 0.129620 | ||||||||
\(251\) | 11.1342 | 0.702784 | 0.351392 | − | 0.936229i | \(-0.385709\pi\) | ||||
0.351392 | + | 0.936229i | \(0.385709\pi\) | |||||||
\(252\) | −0.572175 | −0.0360436 | ||||||||
\(253\) | −6.77431 | −0.425897 | ||||||||
\(254\) | −26.5894 | −1.66837 | ||||||||
\(255\) | 4.29387 | 0.268893 | ||||||||
\(256\) | 12.3308 | 0.770678 | ||||||||
\(257\) | −10.7262 | −0.669080 | −0.334540 | − | 0.942382i | \(-0.608581\pi\) | ||||
−0.334540 | + | 0.942382i | \(0.608581\pi\) | |||||||
\(258\) | −5.32856 | −0.331741 | ||||||||
\(259\) | −9.77015 | −0.607088 | ||||||||
\(260\) | 15.3243 | 0.950372 | ||||||||
\(261\) | 2.44236 | 0.151178 | ||||||||
\(262\) | 34.9742 | 2.16071 | ||||||||
\(263\) | −5.68688 | −0.350668 | −0.175334 | − | 0.984509i | \(-0.556101\pi\) | ||||
−0.175334 | + | 0.984509i | \(0.556101\pi\) | |||||||
\(264\) | 2.09046 | 0.128659 | ||||||||
\(265\) | −10.5760 | −0.649676 | ||||||||
\(266\) | 11.5989 | 0.711177 | ||||||||
\(267\) | −8.44727 | −0.516964 | ||||||||
\(268\) | −11.7049 | −0.714991 | ||||||||
\(269\) | −6.08152 | −0.370797 | −0.185398 | − | 0.982663i | \(-0.559358\pi\) | ||||
−0.185398 | + | 0.982663i | \(0.559358\pi\) | |||||||
\(270\) | 11.0595 | 0.673062 | ||||||||
\(271\) | 14.6950 | 0.892658 | 0.446329 | − | 0.894869i | \(-0.352731\pi\) | ||||
0.446329 | + | 0.894869i | \(0.352731\pi\) | |||||||
\(272\) | −9.23274 | −0.559817 | ||||||||
\(273\) | 11.5283 | 0.697724 | ||||||||
\(274\) | −39.8680 | −2.40852 | ||||||||
\(275\) | 3.07599 | 0.185489 | ||||||||
\(276\) | 8.02121 | 0.482820 | ||||||||
\(277\) | −16.5986 | −0.997312 | −0.498656 | − | 0.866800i | \(-0.666173\pi\) | ||||
−0.498656 | + | 0.866800i | \(0.666173\pi\) | |||||||
\(278\) | −5.40017 | −0.323881 | ||||||||
\(279\) | 2.30187 | 0.137809 | ||||||||
\(280\) | 0.410568 | 0.0245361 | ||||||||
\(281\) | −27.8245 | −1.65987 | −0.829935 | − | 0.557861i | \(-0.811622\pi\) | ||||
−0.829935 | + | 0.557861i | \(0.811622\pi\) | |||||||
\(282\) | −43.6912 | −2.60177 | ||||||||
\(283\) | 4.12955 | 0.245476 | 0.122738 | − | 0.992439i | \(-0.460832\pi\) | ||||
0.122738 | + | 0.992439i | \(0.460832\pi\) | |||||||
\(284\) | −18.5226 | −1.09911 | ||||||||
\(285\) | −9.36804 | −0.554915 | ||||||||
\(286\) | 43.9055 | 2.59619 | ||||||||
\(287\) | −3.61685 | −0.213496 | ||||||||
\(288\) | −2.11039 | −0.124356 | ||||||||
\(289\) | −10.2709 | −0.604173 | ||||||||
\(290\) | −19.2491 | −1.13035 | ||||||||
\(291\) | −3.95371 | −0.231771 | ||||||||
\(292\) | −13.6977 | −0.801594 | ||||||||
\(293\) | 9.34494 | 0.545937 | 0.272969 | − | 0.962023i | \(-0.411994\pi\) | ||||
0.272969 | + | 0.962023i | \(0.411994\pi\) | |||||||
\(294\) | 3.39245 | 0.197852 | ||||||||
\(295\) | −8.59806 | −0.500599 | ||||||||
\(296\) | 4.01132 | 0.233153 | ||||||||
\(297\) | 16.5989 | 0.963166 | ||||||||
\(298\) | 19.2469 | 1.11494 | ||||||||
\(299\) | 15.3382 | 0.887029 | ||||||||
\(300\) | −3.64217 | −0.210281 | ||||||||
\(301\) | −1.57071 | −0.0905342 | ||||||||
\(302\) | −2.27989 | −0.131193 | ||||||||
\(303\) | 27.0146 | 1.55195 | ||||||||
\(304\) | 20.1433 | 1.15530 | ||||||||
\(305\) | 14.7665 | 0.845528 | ||||||||
\(306\) | 1.38248 | 0.0790313 | ||||||||
\(307\) | −9.64456 | −0.550444 | −0.275222 | − | 0.961381i | \(-0.588751\pi\) | ||||
−0.275222 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(308\) | 6.76818 | 0.385653 | ||||||||
\(309\) | −15.3188 | −0.871458 | ||||||||
\(310\) | −18.1418 | −1.03039 | ||||||||
\(311\) | −0.947453 | −0.0537251 | −0.0268626 | − | 0.999639i | \(-0.508552\pi\) | ||||
−0.0268626 | + | 0.999639i | \(0.508552\pi\) | |||||||
\(312\) | −4.73315 | −0.267962 | ||||||||
\(313\) | −20.7010 | −1.17009 | −0.585044 | − | 0.811002i | \(-0.698923\pi\) | ||||
−0.585044 | + | 0.811002i | \(0.698923\pi\) | |||||||
\(314\) | 15.8979 | 0.897168 | ||||||||
\(315\) | 0.260041 | 0.0146516 | ||||||||
\(316\) | 27.3151 | 1.53660 | ||||||||
\(317\) | −6.74921 | −0.379073 | −0.189537 | − | 0.981874i | \(-0.560699\pi\) | ||||
−0.189537 | + | 0.981874i | \(0.560699\pi\) | |||||||
\(318\) | 35.8784 | 2.01196 | ||||||||
\(319\) | −28.8904 | −1.61755 | ||||||||
\(320\) | 9.51433 | 0.531867 | ||||||||
\(321\) | −6.56800 | −0.366590 | ||||||||
\(322\) | 4.51359 | 0.251533 | ||||||||
\(323\) | −14.6809 | −0.816869 | ||||||||
\(324\) | −17.9376 | −0.996536 | ||||||||
\(325\) | −6.96455 | −0.386324 | ||||||||
\(326\) | −28.1551 | −1.55936 | ||||||||
\(327\) | 8.83675 | 0.488673 | ||||||||
\(328\) | 1.48496 | 0.0819934 | ||||||||
\(329\) | −12.8789 | −0.710039 | ||||||||
\(330\) | −10.4351 | −0.574435 | ||||||||
\(331\) | 6.89598 | 0.379037 | 0.189519 | − | 0.981877i | \(-0.439307\pi\) | ||||
0.189519 | + | 0.981877i | \(0.439307\pi\) | |||||||
\(332\) | −18.9223 | −1.03850 | ||||||||
\(333\) | 2.54064 | 0.139226 | ||||||||
\(334\) | −12.2970 | −0.672862 | ||||||||
\(335\) | 5.31962 | 0.290642 | ||||||||
\(336\) | 5.89150 | 0.321408 | ||||||||
\(337\) | −34.4338 | −1.87573 | −0.937865 | − | 0.346999i | \(-0.887201\pi\) | ||||
−0.937865 | + | 0.346999i | \(0.887201\pi\) | |||||||
\(338\) | −72.7663 | −3.95796 | ||||||||
\(339\) | −4.23332 | −0.229922 | ||||||||
\(340\) | −5.70774 | −0.309546 | ||||||||
\(341\) | −27.2285 | −1.47451 | ||||||||
\(342\) | −3.01620 | −0.163097 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.644884 | 0.0347698 | ||||||||
\(345\) | −3.64546 | −0.196265 | ||||||||
\(346\) | −28.9508 | −1.55641 | ||||||||
\(347\) | 18.2698 | 0.980773 | 0.490386 | − | 0.871505i | \(-0.336856\pi\) | ||||
0.490386 | + | 0.871505i | \(0.336856\pi\) | |||||||
\(348\) | 34.2081 | 1.83374 | ||||||||
\(349\) | −9.66908 | −0.517574 | −0.258787 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258787 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(350\) | −2.04947 | −0.109549 | ||||||||
\(351\) | −37.5827 | −2.00602 | ||||||||
\(352\) | 24.9636 | 1.33056 | ||||||||
\(353\) | 28.2080 | 1.50136 | 0.750680 | − | 0.660666i | \(-0.229726\pi\) | ||||
0.750680 | + | 0.660666i | \(0.229726\pi\) | |||||||
\(354\) | 29.1685 | 1.55029 | ||||||||
\(355\) | 8.41810 | 0.446786 | ||||||||
\(356\) | 11.2288 | 0.595123 | ||||||||
\(357\) | −4.29387 | −0.227256 | ||||||||
\(358\) | 36.1220 | 1.90911 | ||||||||
\(359\) | 18.4787 | 0.975266 | 0.487633 | − | 0.873049i | \(-0.337860\pi\) | ||||
0.487633 | + | 0.873049i | \(0.337860\pi\) | |||||||
\(360\) | −0.106764 | −0.00562698 | ||||||||
\(361\) | 13.0297 | 0.685776 | ||||||||
\(362\) | 42.8307 | 2.25113 | ||||||||
\(363\) | 2.54633 | 0.133648 | ||||||||
\(364\) | −15.3243 | −0.803211 | ||||||||
\(365\) | 6.22527 | 0.325846 | ||||||||
\(366\) | −50.0947 | −2.61849 | ||||||||
\(367\) | −17.6617 | −0.921935 | −0.460967 | − | 0.887417i | \(-0.652497\pi\) | ||||
−0.460967 | + | 0.887417i | \(0.652497\pi\) | |||||||
\(368\) | 7.83852 | 0.408611 | ||||||||
\(369\) | 0.940528 | 0.0489619 | ||||||||
\(370\) | −20.0236 | −1.04098 | ||||||||
\(371\) | 10.5760 | 0.549076 | ||||||||
\(372\) | 32.2403 | 1.67158 | ||||||||
\(373\) | 29.1711 | 1.51042 | 0.755212 | − | 0.655481i | \(-0.227534\pi\) | ||||
0.755212 | + | 0.655481i | \(0.227534\pi\) | |||||||
\(374\) | −16.3532 | −0.845604 | ||||||||
\(375\) | 1.65528 | 0.0854784 | ||||||||
\(376\) | 5.28769 | 0.272692 | ||||||||
\(377\) | 65.4126 | 3.36892 | ||||||||
\(378\) | −11.0595 | −0.568841 | ||||||||
\(379\) | 22.8228 | 1.17233 | 0.586164 | − | 0.810193i | \(-0.300638\pi\) | ||||
0.586164 | + | 0.810193i | \(0.300638\pi\) | |||||||
\(380\) | 12.4527 | 0.638811 | ||||||||
\(381\) | −21.4753 | −1.10021 | ||||||||
\(382\) | 33.6402 | 1.72118 | ||||||||
\(383\) | −12.1838 | −0.622564 | −0.311282 | − | 0.950318i | \(-0.600758\pi\) | ||||
−0.311282 | + | 0.950318i | \(0.600758\pi\) | |||||||
\(384\) | −5.40958 | −0.276056 | ||||||||
\(385\) | −3.07599 | −0.156767 | ||||||||
\(386\) | 43.2915 | 2.20348 | ||||||||
\(387\) | 0.408448 | 0.0207626 | ||||||||
\(388\) | 5.25558 | 0.266811 | ||||||||
\(389\) | 23.0652 | 1.16945 | 0.584727 | − | 0.811230i | \(-0.301202\pi\) | ||||
0.584727 | + | 0.811230i | \(0.301202\pi\) | |||||||
\(390\) | 23.6269 | 1.19639 | ||||||||
\(391\) | −5.71291 | −0.288914 | ||||||||
\(392\) | −0.410568 | −0.0207368 | ||||||||
\(393\) | 28.2474 | 1.42489 | ||||||||
\(394\) | 46.0445 | 2.31969 | ||||||||
\(395\) | −12.4141 | −0.624622 | ||||||||
\(396\) | −1.76000 | −0.0884434 | ||||||||
\(397\) | −20.6660 | −1.03720 | −0.518599 | − | 0.855017i | \(-0.673546\pi\) | ||||
−0.518599 | + | 0.855017i | \(0.673546\pi\) | |||||||
\(398\) | −23.9135 | −1.19868 | ||||||||
\(399\) | 9.36804 | 0.468989 | ||||||||
\(400\) | −3.55921 | −0.177961 | ||||||||
\(401\) | 11.8690 | 0.592711 | 0.296355 | − | 0.955078i | \(-0.404229\pi\) | ||||
0.296355 | + | 0.955078i | \(0.404229\pi\) | |||||||
\(402\) | −18.0466 | −0.900080 | ||||||||
\(403\) | 61.6499 | 3.07100 | ||||||||
\(404\) | −35.9099 | −1.78658 | ||||||||
\(405\) | 8.15226 | 0.405089 | ||||||||
\(406\) | 19.2491 | 0.955317 | ||||||||
\(407\) | −30.0529 | −1.48966 | ||||||||
\(408\) | 1.76293 | 0.0872779 | ||||||||
\(409\) | 11.0016 | 0.543994 | 0.271997 | − | 0.962298i | \(-0.412316\pi\) | ||||
0.271997 | + | 0.962298i | \(0.412316\pi\) | |||||||
\(410\) | −7.41263 | −0.366084 | ||||||||
\(411\) | −32.1999 | −1.58831 | ||||||||
\(412\) | 20.3630 | 1.00321 | ||||||||
\(413\) | 8.59806 | 0.423083 | ||||||||
\(414\) | −1.17372 | −0.0576850 | ||||||||
\(415\) | 8.59977 | 0.422146 | ||||||||
\(416\) | −56.5217 | −2.77120 | ||||||||
\(417\) | −4.36152 | −0.213585 | ||||||||
\(418\) | 35.6782 | 1.74508 | ||||||||
\(419\) | −31.2065 | −1.52454 | −0.762268 | − | 0.647261i | \(-0.775914\pi\) | ||||
−0.762268 | + | 0.647261i | \(0.775914\pi\) | |||||||
\(420\) | 3.64217 | 0.177719 | ||||||||
\(421\) | −14.8919 | −0.725785 | −0.362893 | − | 0.931831i | \(-0.618211\pi\) | ||||
−0.362893 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(422\) | 7.32263 | 0.356460 | ||||||||
\(423\) | 3.34905 | 0.162836 | ||||||||
\(424\) | −4.34215 | −0.210874 | ||||||||
\(425\) | 2.59404 | 0.125829 | ||||||||
\(426\) | −28.5580 | −1.38364 | ||||||||
\(427\) | −14.7665 | −0.714602 | ||||||||
\(428\) | 8.73069 | 0.422014 | ||||||||
\(429\) | 35.4609 | 1.71207 | ||||||||
\(430\) | −3.21912 | −0.155240 | ||||||||
\(431\) | −34.8670 | −1.67949 | −0.839743 | − | 0.542984i | \(-0.817294\pi\) | ||||
−0.839743 | + | 0.542984i | \(0.817294\pi\) | |||||||
\(432\) | −19.2065 | −0.924074 | ||||||||
\(433\) | −20.5393 | −0.987056 | −0.493528 | − | 0.869730i | \(-0.664293\pi\) | ||||
−0.493528 | + | 0.869730i | \(0.664293\pi\) | |||||||
\(434\) | 18.1418 | 0.870835 | ||||||||
\(435\) | −15.5468 | −0.745412 | ||||||||
\(436\) | −11.7465 | −0.562555 | ||||||||
\(437\) | 12.4640 | 0.596234 | ||||||||
\(438\) | −21.1189 | −1.00910 | ||||||||
\(439\) | −34.7253 | −1.65735 | −0.828674 | − | 0.559731i | \(-0.810904\pi\) | ||||
−0.828674 | + | 0.559731i | \(0.810904\pi\) | |||||||
\(440\) | 1.26290 | 0.0602065 | ||||||||
\(441\) | −0.260041 | −0.0123829 | ||||||||
\(442\) | 37.0264 | 1.76117 | ||||||||
\(443\) | 3.66593 | 0.174174 | 0.0870869 | − | 0.996201i | \(-0.472244\pi\) | ||||
0.0870869 | + | 0.996201i | \(0.472244\pi\) | |||||||
\(444\) | 35.5845 | 1.68877 | ||||||||
\(445\) | −5.10322 | −0.241916 | ||||||||
\(446\) | −29.8879 | −1.41523 | ||||||||
\(447\) | 15.5450 | 0.735254 | ||||||||
\(448\) | −9.51433 | −0.449510 | ||||||||
\(449\) | 17.8247 | 0.841198 | 0.420599 | − | 0.907247i | \(-0.361820\pi\) | ||||
0.420599 | + | 0.907247i | \(0.361820\pi\) | |||||||
\(450\) | 0.532946 | 0.0251233 | ||||||||
\(451\) | −11.1254 | −0.523874 | ||||||||
\(452\) | 5.62725 | 0.264684 | ||||||||
\(453\) | −1.84138 | −0.0865157 | ||||||||
\(454\) | 27.6395 | 1.29719 | ||||||||
\(455\) | 6.96455 | 0.326503 | ||||||||
\(456\) | −3.84622 | −0.180116 | ||||||||
\(457\) | 21.7161 | 1.01583 | 0.507917 | − | 0.861406i | \(-0.330416\pi\) | ||||
0.507917 | + | 0.861406i | \(0.330416\pi\) | |||||||
\(458\) | 2.04947 | 0.0957655 | ||||||||
\(459\) | 13.9982 | 0.653380 | ||||||||
\(460\) | 4.84583 | 0.225938 | ||||||||
\(461\) | −8.79549 | −0.409647 | −0.204823 | − | 0.978799i | \(-0.565662\pi\) | ||||
−0.204823 | + | 0.978799i | \(0.565662\pi\) | |||||||
\(462\) | 10.4351 | 0.485487 | ||||||||
\(463\) | 40.4584 | 1.88026 | 0.940130 | − | 0.340817i | \(-0.110704\pi\) | ||||
0.940130 | + | 0.340817i | \(0.110704\pi\) | |||||||
\(464\) | 33.4289 | 1.55190 | ||||||||
\(465\) | −14.6525 | −0.679493 | ||||||||
\(466\) | 11.6350 | 0.538982 | ||||||||
\(467\) | 8.05065 | 0.372540 | 0.186270 | − | 0.982499i | \(-0.440360\pi\) | ||||
0.186270 | + | 0.982499i | \(0.440360\pi\) | |||||||
\(468\) | 3.98494 | 0.184204 | ||||||||
\(469\) | −5.31962 | −0.245637 | ||||||||
\(470\) | −26.3950 | −1.21751 | ||||||||
\(471\) | 12.8401 | 0.591641 | ||||||||
\(472\) | −3.53009 | −0.162486 | ||||||||
\(473\) | −4.83148 | −0.222152 | ||||||||
\(474\) | 42.1143 | 1.93437 | ||||||||
\(475\) | −5.65948 | −0.259675 | ||||||||
\(476\) | 5.70774 | 0.261614 | ||||||||
\(477\) | −2.75018 | −0.125922 | ||||||||
\(478\) | 27.2733 | 1.24745 | ||||||||
\(479\) | 11.1351 | 0.508775 | 0.254387 | − | 0.967102i | \(-0.418126\pi\) | ||||
0.254387 | + | 0.967102i | \(0.418126\pi\) | |||||||
\(480\) | 13.4337 | 0.613160 | ||||||||
\(481\) | 68.0447 | 3.10257 | ||||||||
\(482\) | 30.0153 | 1.36716 | ||||||||
\(483\) | 3.64546 | 0.165874 | ||||||||
\(484\) | −3.38478 | −0.153854 | ||||||||
\(485\) | −2.38854 | −0.108458 | ||||||||
\(486\) | 5.52245 | 0.250504 | ||||||||
\(487\) | 14.4889 | 0.656554 | 0.328277 | − | 0.944582i | \(-0.393532\pi\) | ||||
0.328277 | + | 0.944582i | \(0.393532\pi\) | |||||||
\(488\) | 6.06266 | 0.274444 | ||||||||
\(489\) | −22.7398 | −1.02833 | ||||||||
\(490\) | 2.04947 | 0.0925856 | ||||||||
\(491\) | 15.2398 | 0.687762 | 0.343881 | − | 0.939013i | \(-0.388258\pi\) | ||||
0.343881 | + | 0.939013i | \(0.388258\pi\) | |||||||
\(492\) | 13.1732 | 0.593892 | ||||||||
\(493\) | −24.3638 | −1.09729 | ||||||||
\(494\) | −80.7814 | −3.63453 | ||||||||
\(495\) | 0.799881 | 0.0359520 | ||||||||
\(496\) | 31.5060 | 1.41466 | ||||||||
\(497\) | −8.41810 | −0.377603 | ||||||||
\(498\) | −29.1743 | −1.30733 | ||||||||
\(499\) | 17.2108 | 0.770463 | 0.385231 | − | 0.922820i | \(-0.374122\pi\) | ||||
0.385231 | + | 0.922820i | \(0.374122\pi\) | |||||||
\(500\) | −2.20033 | −0.0984017 | ||||||||
\(501\) | −9.93184 | −0.443722 | ||||||||
\(502\) | −22.8192 | −1.01847 | ||||||||
\(503\) | −16.4443 | −0.733213 | −0.366606 | − | 0.930376i | \(-0.619480\pi\) | ||||
−0.366606 | + | 0.930376i | \(0.619480\pi\) | |||||||
\(504\) | 0.106764 | 0.00475567 | ||||||||
\(505\) | 16.3202 | 0.726241 | ||||||||
\(506\) | 13.8837 | 0.617208 | ||||||||
\(507\) | −58.7707 | −2.61010 | ||||||||
\(508\) | 28.5466 | 1.26655 | ||||||||
\(509\) | −24.2394 | −1.07439 | −0.537197 | − | 0.843457i | \(-0.680517\pi\) | ||||
−0.537197 | + | 0.843457i | \(0.680517\pi\) | |||||||
\(510\) | −8.80016 | −0.389678 | ||||||||
\(511\) | −6.22527 | −0.275390 | ||||||||
\(512\) | −31.8078 | −1.40572 | ||||||||
\(513\) | −30.5402 | −1.34838 | ||||||||
\(514\) | 21.9829 | 0.969626 | ||||||||
\(515\) | −9.25451 | −0.407803 | ||||||||
\(516\) | 5.72078 | 0.251843 | ||||||||
\(517\) | −39.6155 | −1.74229 | ||||||||
\(518\) | 20.0236 | 0.879788 | ||||||||
\(519\) | −23.3825 | −1.02638 | ||||||||
\(520\) | −2.85942 | −0.125394 | ||||||||
\(521\) | 7.51468 | 0.329224 | 0.164612 | − | 0.986358i | \(-0.447363\pi\) | ||||
0.164612 | + | 0.986358i | \(0.447363\pi\) | |||||||
\(522\) | −5.00555 | −0.219087 | ||||||||
\(523\) | 33.1396 | 1.44909 | 0.724546 | − | 0.689226i | \(-0.242049\pi\) | ||||
0.724546 | + | 0.689226i | \(0.242049\pi\) | |||||||
\(524\) | −37.5486 | −1.64032 | ||||||||
\(525\) | −1.65528 | −0.0722424 | ||||||||
\(526\) | 11.6551 | 0.508186 | ||||||||
\(527\) | −22.9623 | −1.00026 | ||||||||
\(528\) | 18.1222 | 0.788666 | ||||||||
\(529\) | −18.1498 | −0.789121 | ||||||||
\(530\) | 21.6751 | 0.941507 | ||||||||
\(531\) | −2.23585 | −0.0970274 | ||||||||
\(532\) | −12.4527 | −0.539894 | ||||||||
\(533\) | 25.1897 | 1.09109 | ||||||||
\(534\) | 17.3124 | 0.749182 | ||||||||
\(535\) | −3.96790 | −0.171547 | ||||||||
\(536\) | 2.18407 | 0.0943373 | ||||||||
\(537\) | 29.1744 | 1.25897 | ||||||||
\(538\) | 12.4639 | 0.537356 | ||||||||
\(539\) | 3.07599 | 0.132492 | ||||||||
\(540\) | −11.8736 | −0.510959 | ||||||||
\(541\) | 39.7582 | 1.70934 | 0.854670 | − | 0.519172i | \(-0.173760\pi\) | ||||
0.854670 | + | 0.519172i | \(0.173760\pi\) | |||||||
\(542\) | −30.1170 | −1.29363 | ||||||||
\(543\) | 34.5928 | 1.48452 | ||||||||
\(544\) | 21.0523 | 0.902609 | ||||||||
\(545\) | 5.33851 | 0.228677 | ||||||||
\(546\) | −23.6269 | −1.01114 | ||||||||
\(547\) | −31.9965 | −1.36807 | −0.684036 | − | 0.729449i | \(-0.739777\pi\) | ||||
−0.684036 | + | 0.729449i | \(0.739777\pi\) | |||||||
\(548\) | 42.8026 | 1.82844 | ||||||||
\(549\) | 3.83989 | 0.163883 | ||||||||
\(550\) | −6.30414 | −0.268810 | ||||||||
\(551\) | 53.1552 | 2.26449 | ||||||||
\(552\) | −1.49671 | −0.0637042 | ||||||||
\(553\) | 12.4141 | 0.527902 | ||||||||
\(554\) | 34.0183 | 1.44530 | ||||||||
\(555\) | −16.1724 | −0.686479 | ||||||||
\(556\) | 5.79767 | 0.245876 | ||||||||
\(557\) | 19.4956 | 0.826054 | 0.413027 | − | 0.910719i | \(-0.364471\pi\) | ||||
0.413027 | + | 0.910719i | \(0.364471\pi\) | |||||||
\(558\) | −4.71761 | −0.199712 | ||||||||
\(559\) | 10.9393 | 0.462682 | ||||||||
\(560\) | 3.55921 | 0.150404 | ||||||||
\(561\) | −13.2079 | −0.557638 | ||||||||
\(562\) | 57.0254 | 2.40547 | ||||||||
\(563\) | −15.7722 | −0.664720 | −0.332360 | − | 0.943153i | \(-0.607845\pi\) | ||||
−0.332360 | + | 0.943153i | \(0.607845\pi\) | |||||||
\(564\) | 46.9072 | 1.97515 | ||||||||
\(565\) | −2.55746 | −0.107593 | ||||||||
\(566\) | −8.46339 | −0.355743 | ||||||||
\(567\) | −8.15226 | −0.342363 | ||||||||
\(568\) | 3.45621 | 0.145019 | ||||||||
\(569\) | 8.15082 | 0.341700 | 0.170850 | − | 0.985297i | \(-0.445349\pi\) | ||||
0.170850 | + | 0.985297i | \(0.445349\pi\) | |||||||
\(570\) | 19.1995 | 0.804180 | ||||||||
\(571\) | −29.1215 | −1.21869 | −0.609347 | − | 0.792903i | \(-0.708569\pi\) | ||||
−0.609347 | + | 0.792903i | \(0.708569\pi\) | |||||||
\(572\) | −47.1373 | −1.97091 | ||||||||
\(573\) | 27.1700 | 1.13504 | ||||||||
\(574\) | 7.41263 | 0.309397 | ||||||||
\(575\) | −2.20232 | −0.0918431 | ||||||||
\(576\) | 2.47411 | 0.103088 | ||||||||
\(577\) | 6.95595 | 0.289580 | 0.144790 | − | 0.989462i | \(-0.453749\pi\) | ||||
0.144790 | + | 0.989462i | \(0.453749\pi\) | |||||||
\(578\) | 21.0500 | 0.875565 | ||||||||
\(579\) | 34.9649 | 1.45309 | ||||||||
\(580\) | 20.6660 | 0.858109 | ||||||||
\(581\) | −8.59977 | −0.356778 | ||||||||
\(582\) | 8.10301 | 0.335881 | ||||||||
\(583\) | 32.5315 | 1.34732 | ||||||||
\(584\) | 2.55590 | 0.105764 | ||||||||
\(585\) | −1.81107 | −0.0748783 | ||||||||
\(586\) | −19.1522 | −0.791169 | ||||||||
\(587\) | 34.7636 | 1.43485 | 0.717423 | − | 0.696638i | \(-0.245321\pi\) | ||||
0.717423 | + | 0.696638i | \(0.245321\pi\) | |||||||
\(588\) | −3.64217 | −0.150200 | ||||||||
\(589\) | 50.0975 | 2.06423 | ||||||||
\(590\) | 17.6215 | 0.725465 | ||||||||
\(591\) | 37.1884 | 1.52973 | ||||||||
\(592\) | 34.7740 | 1.42920 | ||||||||
\(593\) | −31.5410 | −1.29523 | −0.647617 | − | 0.761966i | \(-0.724234\pi\) | ||||
−0.647617 | + | 0.761966i | \(0.724234\pi\) | |||||||
\(594\) | −34.0190 | −1.39582 | ||||||||
\(595\) | −2.59404 | −0.106345 | ||||||||
\(596\) | −20.6636 | −0.846415 | ||||||||
\(597\) | −19.3141 | −0.790472 | ||||||||
\(598\) | −31.4351 | −1.28548 | ||||||||
\(599\) | −35.1552 | −1.43640 | −0.718201 | − | 0.695836i | \(-0.755034\pi\) | ||||
−0.718201 | + | 0.695836i | \(0.755034\pi\) | |||||||
\(600\) | 0.679606 | 0.0277448 | ||||||||
\(601\) | 18.7845 | 0.766235 | 0.383118 | − | 0.923700i | \(-0.374850\pi\) | ||||
0.383118 | + | 0.923700i | \(0.374850\pi\) | |||||||
\(602\) | 3.21912 | 0.131202 | ||||||||
\(603\) | 1.38332 | 0.0563330 | ||||||||
\(604\) | 2.44771 | 0.0995958 | ||||||||
\(605\) | 1.53831 | 0.0625411 | ||||||||
\(606\) | −55.3656 | −2.24908 | ||||||||
\(607\) | 33.9488 | 1.37794 | 0.688970 | − | 0.724790i | \(-0.258063\pi\) | ||||
0.688970 | + | 0.724790i | \(0.258063\pi\) | |||||||
\(608\) | −45.9303 | −1.86272 | ||||||||
\(609\) | 15.5468 | 0.629988 | ||||||||
\(610\) | −30.2635 | −1.22533 | ||||||||
\(611\) | 89.6960 | 3.62871 | ||||||||
\(612\) | −1.48425 | −0.0599971 | ||||||||
\(613\) | 38.2603 | 1.54532 | 0.772659 | − | 0.634822i | \(-0.218926\pi\) | ||||
0.772659 | + | 0.634822i | \(0.218926\pi\) | |||||||
\(614\) | 19.7662 | 0.797701 | ||||||||
\(615\) | −5.98691 | −0.241416 | ||||||||
\(616\) | −1.26290 | −0.0508838 | ||||||||
\(617\) | −42.7562 | −1.72130 | −0.860649 | − | 0.509198i | \(-0.829942\pi\) | ||||
−0.860649 | + | 0.509198i | \(0.829942\pi\) | |||||||
\(618\) | 31.3955 | 1.26291 | ||||||||
\(619\) | −44.2766 | −1.77963 | −0.889813 | − | 0.456325i | \(-0.849166\pi\) | ||||
−0.889813 | + | 0.456325i | \(0.849166\pi\) | |||||||
\(620\) | 19.4772 | 0.782224 | ||||||||
\(621\) | −11.8844 | −0.476903 | ||||||||
\(622\) | 1.94178 | 0.0778582 | ||||||||
\(623\) | 5.10322 | 0.204456 | ||||||||
\(624\) | −41.0316 | −1.64258 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 42.4260 | 1.69568 | ||||||||
\(627\) | 28.8160 | 1.15080 | ||||||||
\(628\) | −17.0681 | −0.681090 | ||||||||
\(629\) | −25.3442 | −1.01054 | ||||||||
\(630\) | −0.532946 | −0.0212331 | ||||||||
\(631\) | −8.34822 | −0.332337 | −0.166169 | − | 0.986097i | \(-0.553140\pi\) | ||||
−0.166169 | + | 0.986097i | \(0.553140\pi\) | |||||||
\(632\) | −5.09684 | −0.202742 | ||||||||
\(633\) | 5.91422 | 0.235069 | ||||||||
\(634\) | 13.8323 | 0.549351 | ||||||||
\(635\) | −12.9738 | −0.514849 | ||||||||
\(636\) | −38.5194 | −1.52739 | ||||||||
\(637\) | −6.96455 | −0.275945 | ||||||||
\(638\) | 59.2100 | 2.34415 | ||||||||
\(639\) | 2.18905 | 0.0865974 | ||||||||
\(640\) | −3.26807 | −0.129182 | ||||||||
\(641\) | 17.3957 | 0.687090 | 0.343545 | − | 0.939136i | \(-0.388372\pi\) | ||||
0.343545 | + | 0.939136i | \(0.388372\pi\) | |||||||
\(642\) | 13.4609 | 0.531260 | ||||||||
\(643\) | −6.33390 | −0.249785 | −0.124892 | − | 0.992170i | \(-0.539859\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539859\pi\) | |||||||
\(644\) | −4.84583 | −0.190952 | ||||||||
\(645\) | −2.59997 | −0.102374 | ||||||||
\(646\) | 30.0881 | 1.18380 | ||||||||
\(647\) | −13.5351 | −0.532120 | −0.266060 | − | 0.963957i | \(-0.585722\pi\) | ||||
−0.266060 | + | 0.963957i | \(0.585722\pi\) | |||||||
\(648\) | 3.34706 | 0.131485 | ||||||||
\(649\) | 26.4475 | 1.03816 | ||||||||
\(650\) | 14.2736 | 0.559858 | ||||||||
\(651\) | 14.6525 | 0.574276 | ||||||||
\(652\) | 30.2275 | 1.18380 | ||||||||
\(653\) | −36.4724 | −1.42727 | −0.713637 | − | 0.700516i | \(-0.752953\pi\) | ||||
−0.713637 | + | 0.700516i | \(0.752953\pi\) | |||||||
\(654\) | −18.1107 | −0.708183 | ||||||||
\(655\) | 17.0650 | 0.666784 | ||||||||
\(656\) | 12.8731 | 0.502611 | ||||||||
\(657\) | 1.61882 | 0.0631563 | ||||||||
\(658\) | 26.3950 | 1.02898 | ||||||||
\(659\) | −15.1141 | −0.588760 | −0.294380 | − | 0.955688i | \(-0.595113\pi\) | ||||
−0.294380 | + | 0.955688i | \(0.595113\pi\) | |||||||
\(660\) | 11.2033 | 0.436086 | ||||||||
\(661\) | 1.28356 | 0.0499246 | 0.0249623 | − | 0.999688i | \(-0.492053\pi\) | ||||
0.0249623 | + | 0.999688i | \(0.492053\pi\) | |||||||
\(662\) | −14.1331 | −0.549299 | ||||||||
\(663\) | 29.9049 | 1.16141 | ||||||||
\(664\) | 3.53079 | 0.137021 | ||||||||
\(665\) | 5.65948 | 0.219465 | ||||||||
\(666\) | −5.20696 | −0.201766 | ||||||||
\(667\) | 20.6847 | 0.800915 | ||||||||
\(668\) | 13.2022 | 0.510807 | ||||||||
\(669\) | −24.1393 | −0.933281 | ||||||||
\(670\) | −10.9024 | −0.421197 | ||||||||
\(671\) | −45.4216 | −1.75348 | ||||||||
\(672\) | −13.4337 | −0.518215 | ||||||||
\(673\) | −43.7113 | −1.68495 | −0.842473 | − | 0.538739i | \(-0.818901\pi\) | ||||
−0.842473 | + | 0.538739i | \(0.818901\pi\) | |||||||
\(674\) | 70.5711 | 2.71830 | ||||||||
\(675\) | 5.39629 | 0.207703 | ||||||||
\(676\) | 78.1225 | 3.00471 | ||||||||
\(677\) | −6.74014 | −0.259045 | −0.129522 | − | 0.991577i | \(-0.541344\pi\) | ||||
−0.129522 | + | 0.991577i | \(0.541344\pi\) | |||||||
\(678\) | 8.67606 | 0.333202 | ||||||||
\(679\) | 2.38854 | 0.0916638 | ||||||||
\(680\) | 1.06503 | 0.0408421 | ||||||||
\(681\) | 22.3235 | 0.855437 | ||||||||
\(682\) | 55.8040 | 2.13685 | ||||||||
\(683\) | 20.4685 | 0.783204 | 0.391602 | − | 0.920135i | \(-0.371921\pi\) | ||||
0.391602 | + | 0.920135i | \(0.371921\pi\) | |||||||
\(684\) | 3.23821 | 0.123816 | ||||||||
\(685\) | −19.4528 | −0.743255 | ||||||||
\(686\) | −2.04947 | −0.0782491 | ||||||||
\(687\) | 1.65528 | 0.0631530 | ||||||||
\(688\) | 5.59049 | 0.213135 | ||||||||
\(689\) | −73.6568 | −2.80610 | ||||||||
\(690\) | 7.47127 | 0.284426 | ||||||||
\(691\) | −18.3238 | −0.697071 | −0.348535 | − | 0.937296i | \(-0.613321\pi\) | ||||
−0.348535 | + | 0.937296i | \(0.613321\pi\) | |||||||
\(692\) | 31.0819 | 1.18156 | ||||||||
\(693\) | −0.799881 | −0.0303850 | ||||||||
\(694\) | −37.4434 | −1.42133 | ||||||||
\(695\) | −2.63491 | −0.0999478 | ||||||||
\(696\) | −6.38302 | −0.241948 | ||||||||
\(697\) | −9.38226 | −0.355379 | ||||||||
\(698\) | 19.8165 | 0.750066 | ||||||||
\(699\) | 9.39718 | 0.355434 | ||||||||
\(700\) | 2.20033 | 0.0831646 | ||||||||
\(701\) | 12.0241 | 0.454145 | 0.227072 | − | 0.973878i | \(-0.427085\pi\) | ||||
0.227072 | + | 0.973878i | \(0.427085\pi\) | |||||||
\(702\) | 77.0246 | 2.90711 | ||||||||
\(703\) | 55.2940 | 2.08545 | ||||||||
\(704\) | −29.2659 | −1.10300 | ||||||||
\(705\) | −21.3183 | −0.802893 | ||||||||
\(706\) | −57.8115 | −2.17576 | ||||||||
\(707\) | −16.3202 | −0.613786 | ||||||||
\(708\) | −31.3156 | −1.17691 | ||||||||
\(709\) | 23.6644 | 0.888735 | 0.444367 | − | 0.895845i | \(-0.353428\pi\) | ||||
0.444367 | + | 0.895845i | \(0.353428\pi\) | |||||||
\(710\) | −17.2526 | −0.647480 | ||||||||
\(711\) | −3.22817 | −0.121066 | ||||||||
\(712\) | −2.09522 | −0.0785217 | ||||||||
\(713\) | 19.4948 | 0.730087 | ||||||||
\(714\) | 8.80016 | 0.329338 | ||||||||
\(715\) | 21.4229 | 0.801169 | ||||||||
\(716\) | −38.7809 | −1.44931 | ||||||||
\(717\) | 22.0276 | 0.822637 | ||||||||
\(718\) | −37.8714 | −1.41335 | ||||||||
\(719\) | −19.9337 | −0.743402 | −0.371701 | − | 0.928353i | \(-0.621225\pi\) | ||||
−0.371701 | + | 0.928353i | \(0.621225\pi\) | |||||||
\(720\) | −0.925539 | −0.0344928 | ||||||||
\(721\) | 9.25451 | 0.344656 | ||||||||
\(722\) | −26.7041 | −0.993823 | ||||||||
\(723\) | 24.2423 | 0.901579 | ||||||||
\(724\) | −45.9835 | −1.70896 | ||||||||
\(725\) | −9.39223 | −0.348819 | ||||||||
\(726\) | −5.21863 | −0.193682 | ||||||||
\(727\) | −6.91897 | −0.256610 | −0.128305 | − | 0.991735i | \(-0.540954\pi\) | ||||
−0.128305 | + | 0.991735i | \(0.540954\pi\) | |||||||
\(728\) | 2.85942 | 0.105977 | ||||||||
\(729\) | 28.9171 | 1.07100 | ||||||||
\(730\) | −12.7585 | −0.472214 | ||||||||
\(731\) | −4.07449 | −0.150700 | ||||||||
\(732\) | 53.7821 | 1.98784 | ||||||||
\(733\) | −23.9411 | −0.884284 | −0.442142 | − | 0.896945i | \(-0.645781\pi\) | ||||
−0.442142 | + | 0.896945i | \(0.645781\pi\) | |||||||
\(734\) | 36.1972 | 1.33606 | ||||||||
\(735\) | 1.65528 | 0.0610560 | ||||||||
\(736\) | −17.8732 | −0.658816 | ||||||||
\(737\) | −16.3631 | −0.602742 | ||||||||
\(738\) | −1.92758 | −0.0709554 | ||||||||
\(739\) | 14.7560 | 0.542810 | 0.271405 | − | 0.962465i | \(-0.412512\pi\) | ||||
0.271405 | + | 0.962465i | \(0.412512\pi\) | |||||||
\(740\) | 21.4976 | 0.790266 | ||||||||
\(741\) | −65.2442 | −2.39680 | ||||||||
\(742\) | −21.6751 | −0.795718 | ||||||||
\(743\) | 19.0756 | 0.699815 | 0.349908 | − | 0.936784i | \(-0.386213\pi\) | ||||
0.349908 | + | 0.936784i | \(0.386213\pi\) | |||||||
\(744\) | −6.01585 | −0.220552 | ||||||||
\(745\) | 9.39115 | 0.344065 | ||||||||
\(746\) | −59.7854 | −2.18890 | ||||||||
\(747\) | 2.23629 | 0.0818215 | ||||||||
\(748\) | 17.5569 | 0.641946 | ||||||||
\(749\) | 3.96790 | 0.144984 | ||||||||
\(750\) | −3.39245 | −0.123875 | ||||||||
\(751\) | 21.4028 | 0.780999 | 0.390499 | − | 0.920603i | \(-0.372302\pi\) | ||||
0.390499 | + | 0.920603i | \(0.372302\pi\) | |||||||
\(752\) | 45.8389 | 1.67157 | ||||||||
\(753\) | −18.4302 | −0.671635 | ||||||||
\(754\) | −134.061 | −4.88222 | ||||||||
\(755\) | −1.11243 | −0.0404854 | ||||||||
\(756\) | 11.8736 | 0.431839 | ||||||||
\(757\) | 33.8449 | 1.23011 | 0.615056 | − | 0.788483i | \(-0.289133\pi\) | ||||
0.615056 | + | 0.788483i | \(0.289133\pi\) | |||||||
\(758\) | −46.7746 | −1.69893 | ||||||||
\(759\) | 11.2134 | 0.407020 | ||||||||
\(760\) | −2.32360 | −0.0842860 | ||||||||
\(761\) | 30.4881 | 1.10519 | 0.552597 | − | 0.833449i | \(-0.313637\pi\) | ||||
0.552597 | + | 0.833449i | \(0.313637\pi\) | |||||||
\(762\) | 44.0130 | 1.59442 | ||||||||
\(763\) | −5.33851 | −0.193267 | ||||||||
\(764\) | −36.1164 | −1.30665 | ||||||||
\(765\) | 0.674556 | 0.0243886 | ||||||||
\(766\) | 24.9704 | 0.902217 | ||||||||
\(767\) | −59.8816 | −2.16220 | ||||||||
\(768\) | −20.4110 | −0.736520 | ||||||||
\(769\) | −9.51229 | −0.343022 | −0.171511 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171511 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(770\) | 6.30414 | 0.227186 | ||||||||
\(771\) | 17.7548 | 0.639424 | ||||||||
\(772\) | −46.4781 | −1.67278 | ||||||||
\(773\) | −22.7975 | −0.819970 | −0.409985 | − | 0.912092i | \(-0.634466\pi\) | ||||
−0.409985 | + | 0.912092i | \(0.634466\pi\) | |||||||
\(774\) | −0.837103 | −0.0300890 | ||||||||
\(775\) | −8.85195 | −0.317972 | ||||||||
\(776\) | −0.980659 | −0.0352036 | ||||||||
\(777\) | 16.1724 | 0.580180 | ||||||||
\(778\) | −47.2715 | −1.69477 | ||||||||
\(779\) | 20.4695 | 0.733396 | ||||||||
\(780\) | −25.3660 | −0.908250 | ||||||||
\(781\) | −25.8940 | −0.926559 | ||||||||
\(782\) | 11.7084 | 0.418693 | ||||||||
\(783\) | −50.6832 | −1.81127 | ||||||||
\(784\) | −3.55921 | −0.127115 | ||||||||
\(785\) | 7.75706 | 0.276861 | ||||||||
\(786\) | −57.8921 | −2.06494 | ||||||||
\(787\) | −1.86034 | −0.0663139 | −0.0331569 | − | 0.999450i | \(-0.510556\pi\) | ||||
−0.0331569 | + | 0.999450i | \(0.510556\pi\) | |||||||
\(788\) | −49.4337 | −1.76100 | ||||||||
\(789\) | 9.41339 | 0.335125 | ||||||||
\(790\) | 25.4424 | 0.905199 | ||||||||
\(791\) | 2.55746 | 0.0909328 | ||||||||
\(792\) | 0.328406 | 0.0116694 | ||||||||
\(793\) | 102.842 | 3.65203 | ||||||||
\(794\) | 42.3544 | 1.50310 | ||||||||
\(795\) | 17.5062 | 0.620881 | ||||||||
\(796\) | 25.6737 | 0.909981 | ||||||||
\(797\) | 50.8349 | 1.80066 | 0.900332 | − | 0.435204i | \(-0.143324\pi\) | ||||
0.900332 | + | 0.435204i | \(0.143324\pi\) | |||||||
\(798\) | −19.1995 | −0.679656 | ||||||||
\(799\) | −33.4085 | −1.18191 | ||||||||
\(800\) | 8.11563 | 0.286931 | ||||||||
\(801\) | −1.32704 | −0.0468888 | ||||||||
\(802\) | −24.3252 | −0.858953 | ||||||||
\(803\) | −19.1489 | −0.675749 | ||||||||
\(804\) | 19.3749 | 0.683301 | ||||||||
\(805\) | 2.20232 | 0.0776216 | ||||||||
\(806\) | −126.350 | −4.45047 | ||||||||
\(807\) | 10.0666 | 0.354362 | ||||||||
\(808\) | 6.70057 | 0.235725 | ||||||||
\(809\) | 16.5460 | 0.581727 | 0.290863 | − | 0.956765i | \(-0.406057\pi\) | ||||
0.290863 | + | 0.956765i | \(0.406057\pi\) | |||||||
\(810\) | −16.7078 | −0.587053 | ||||||||
\(811\) | 12.6567 | 0.444436 | 0.222218 | − | 0.974997i | \(-0.428670\pi\) | ||||
0.222218 | + | 0.974997i | \(0.428670\pi\) | |||||||
\(812\) | −20.6660 | −0.725234 | ||||||||
\(813\) | −24.3244 | −0.853093 | ||||||||
\(814\) | 61.5924 | 2.15881 | ||||||||
\(815\) | −13.7377 | −0.481212 | ||||||||
\(816\) | 15.2828 | 0.535005 | ||||||||
\(817\) | 8.88940 | 0.311001 | ||||||||
\(818\) | −22.5474 | −0.788353 | ||||||||
\(819\) | 1.81107 | 0.0632837 | ||||||||
\(820\) | 7.95826 | 0.277915 | ||||||||
\(821\) | −54.8024 | −1.91262 | −0.956308 | − | 0.292360i | \(-0.905559\pi\) | ||||
−0.956308 | + | 0.292360i | \(0.905559\pi\) | |||||||
\(822\) | 65.9928 | 2.30176 | ||||||||
\(823\) | −22.2895 | −0.776963 | −0.388481 | − | 0.921457i | \(-0.627000\pi\) | ||||
−0.388481 | + | 0.921457i | \(0.627000\pi\) | |||||||
\(824\) | −3.79961 | −0.132366 | ||||||||
\(825\) | −5.09163 | −0.177268 | ||||||||
\(826\) | −17.6215 | −0.613129 | ||||||||
\(827\) | 27.1933 | 0.945603 | 0.472802 | − | 0.881169i | \(-0.343243\pi\) | ||||
0.472802 | + | 0.881169i | \(0.343243\pi\) | |||||||
\(828\) | 1.26011 | 0.0437919 | ||||||||
\(829\) | 37.7031 | 1.30948 | 0.654741 | − | 0.755853i | \(-0.272778\pi\) | ||||
0.654741 | + | 0.755853i | \(0.272778\pi\) | |||||||
\(830\) | −17.6250 | −0.611772 | ||||||||
\(831\) | 27.4753 | 0.953109 | ||||||||
\(832\) | 66.2630 | 2.29726 | ||||||||
\(833\) | 2.59404 | 0.0898782 | ||||||||
\(834\) | 8.93881 | 0.309526 | ||||||||
\(835\) | −6.00009 | −0.207642 | ||||||||
\(836\) | −38.3044 | −1.32479 | ||||||||
\(837\) | −47.7677 | −1.65109 | ||||||||
\(838\) | 63.9568 | 2.20935 | ||||||||
\(839\) | 5.98708 | 0.206697 | 0.103349 | − | 0.994645i | \(-0.467044\pi\) | ||||
0.103349 | + | 0.994645i | \(0.467044\pi\) | |||||||
\(840\) | −0.679606 | −0.0234486 | ||||||||
\(841\) | 59.2140 | 2.04186 | ||||||||
\(842\) | 30.5205 | 1.05180 | ||||||||
\(843\) | 46.0574 | 1.58630 | ||||||||
\(844\) | −7.86163 | −0.270609 | ||||||||
\(845\) | −35.5049 | −1.22141 | ||||||||
\(846\) | −6.86377 | −0.235981 | ||||||||
\(847\) | −1.53831 | −0.0528568 | ||||||||
\(848\) | −37.6421 | −1.29263 | ||||||||
\(849\) | −6.83557 | −0.234596 | ||||||||
\(850\) | −5.31641 | −0.182351 | ||||||||
\(851\) | 21.5170 | 0.737593 | ||||||||
\(852\) | 30.6601 | 1.05040 | ||||||||
\(853\) | 11.3735 | 0.389421 | 0.194710 | − | 0.980861i | \(-0.437623\pi\) | ||||
0.194710 | + | 0.980861i | \(0.437623\pi\) | |||||||
\(854\) | 30.2635 | 1.03560 | ||||||||
\(855\) | −1.47170 | −0.0503309 | ||||||||
\(856\) | −1.62909 | −0.0556813 | ||||||||
\(857\) | 9.51534 | 0.325038 | 0.162519 | − | 0.986705i | \(-0.448038\pi\) | ||||
0.162519 | + | 0.986705i | \(0.448038\pi\) | |||||||
\(858\) | −72.6760 | −2.48112 | ||||||||
\(859\) | −22.9502 | −0.783049 | −0.391525 | − | 0.920168i | \(-0.628052\pi\) | ||||
−0.391525 | + | 0.920168i | \(0.628052\pi\) | |||||||
\(860\) | 3.45608 | 0.117851 | ||||||||
\(861\) | 5.98691 | 0.204033 | ||||||||
\(862\) | 71.4590 | 2.43390 | ||||||||
\(863\) | 27.7917 | 0.946041 | 0.473020 | − | 0.881052i | \(-0.343164\pi\) | ||||
0.473020 | + | 0.881052i | \(0.343164\pi\) | |||||||
\(864\) | 43.7943 | 1.48991 | ||||||||
\(865\) | −14.1260 | −0.480299 | ||||||||
\(866\) | 42.0947 | 1.43044 | ||||||||
\(867\) | 17.0013 | 0.577395 | ||||||||
\(868\) | −19.4772 | −0.661100 | ||||||||
\(869\) | 38.1857 | 1.29536 | ||||||||
\(870\) | 31.8627 | 1.08025 | ||||||||
\(871\) | 37.0487 | 1.25535 | ||||||||
\(872\) | 2.19182 | 0.0742245 | ||||||||
\(873\) | −0.621118 | −0.0210216 | ||||||||
\(874\) | −25.5446 | −0.864058 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 22.6735 | 0.766066 | ||||||||
\(877\) | −47.6334 | −1.60847 | −0.804233 | − | 0.594314i | \(-0.797424\pi\) | ||||
−0.804233 | + | 0.594314i | \(0.797424\pi\) | |||||||
\(878\) | 71.1685 | 2.40182 | ||||||||
\(879\) | −15.4685 | −0.521740 | ||||||||
\(880\) | 10.9481 | 0.369060 | ||||||||
\(881\) | 30.3857 | 1.02372 | 0.511861 | − | 0.859068i | \(-0.328956\pi\) | ||||
0.511861 | + | 0.859068i | \(0.328956\pi\) | |||||||
\(882\) | 0.532946 | 0.0179452 | ||||||||
\(883\) | 54.0425 | 1.81867 | 0.909337 | − | 0.416059i | \(-0.136589\pi\) | ||||
0.909337 | + | 0.416059i | \(0.136589\pi\) | |||||||
\(884\) | −39.7519 | −1.33700 | ||||||||
\(885\) | 14.2322 | 0.478411 | ||||||||
\(886\) | −7.51322 | −0.252412 | ||||||||
\(887\) | 19.3546 | 0.649865 | 0.324932 | − | 0.945737i | \(-0.394658\pi\) | ||||
0.324932 | + | 0.945737i | \(0.394658\pi\) | |||||||
\(888\) | −6.63986 | −0.222819 | ||||||||
\(889\) | 12.9738 | 0.435127 | ||||||||
\(890\) | 10.4589 | 0.350583 | ||||||||
\(891\) | −25.0762 | −0.840085 | ||||||||
\(892\) | 32.0879 | 1.07438 | ||||||||
\(893\) | 72.8882 | 2.43911 | ||||||||
\(894\) | −31.8590 | −1.06553 | ||||||||
\(895\) | 17.6250 | 0.589140 | ||||||||
\(896\) | 3.26807 | 0.109179 | ||||||||
\(897\) | −25.3890 | −0.847714 | ||||||||
\(898\) | −36.5311 | −1.21906 | ||||||||
\(899\) | 83.1396 | 2.77286 | ||||||||
\(900\) | −0.572175 | −0.0190725 | ||||||||
\(901\) | 27.4345 | 0.913975 | ||||||||
\(902\) | 22.8011 | 0.759195 | ||||||||
\(903\) | 2.59997 | 0.0865215 | ||||||||
\(904\) | −1.05001 | −0.0349229 | ||||||||
\(905\) | 20.8984 | 0.694688 | ||||||||
\(906\) | 3.77386 | 0.125378 | ||||||||
\(907\) | 6.08257 | 0.201969 | 0.100984 | − | 0.994888i | \(-0.467801\pi\) | ||||
0.100984 | + | 0.994888i | \(0.467801\pi\) | |||||||
\(908\) | −29.6741 | −0.984768 | ||||||||
\(909\) | 4.24393 | 0.140762 | ||||||||
\(910\) | −14.2736 | −0.473166 | ||||||||
\(911\) | −7.94655 | −0.263281 | −0.131640 | − | 0.991298i | \(-0.542024\pi\) | ||||
−0.131640 | + | 0.991298i | \(0.542024\pi\) | |||||||
\(912\) | −33.3428 | −1.10409 | ||||||||
\(913\) | −26.4528 | −0.875459 | ||||||||
\(914\) | −44.5064 | −1.47214 | ||||||||
\(915\) | −24.4427 | −0.808052 | ||||||||
\(916\) | −2.20033 | −0.0727009 | ||||||||
\(917\) | −17.0650 | −0.563535 | ||||||||
\(918\) | −28.6889 | −0.946874 | ||||||||
\(919\) | −33.0429 | −1.08999 | −0.544993 | − | 0.838441i | \(-0.683468\pi\) | ||||
−0.544993 | + | 0.838441i | \(0.683468\pi\) | |||||||
\(920\) | −0.904203 | −0.0298107 | ||||||||
\(921\) | 15.9645 | 0.526047 | ||||||||
\(922\) | 18.0261 | 0.593658 | ||||||||
\(923\) | 58.6283 | 1.92977 | ||||||||
\(924\) | −11.2033 | −0.368560 | ||||||||
\(925\) | −9.77015 | −0.321241 | ||||||||
\(926\) | −82.9182 | −2.72486 | ||||||||
\(927\) | −2.40655 | −0.0790414 | ||||||||
\(928\) | −76.2239 | −2.50217 | ||||||||
\(929\) | 43.6616 | 1.43249 | 0.716246 | − | 0.697848i | \(-0.245859\pi\) | ||||
0.716246 | + | 0.697848i | \(0.245859\pi\) | |||||||
\(930\) | 30.0298 | 0.984717 | ||||||||
\(931\) | −5.65948 | −0.185482 | ||||||||
\(932\) | −12.4915 | −0.409171 | ||||||||
\(933\) | 1.56830 | 0.0513439 | ||||||||
\(934\) | −16.4996 | −0.539882 | ||||||||
\(935\) | −7.97924 | −0.260949 | ||||||||
\(936\) | −0.743566 | −0.0243042 | ||||||||
\(937\) | 55.8960 | 1.82604 | 0.913021 | − | 0.407913i | \(-0.133743\pi\) | ||||
0.913021 | + | 0.407913i | \(0.133743\pi\) | |||||||
\(938\) | 10.9024 | 0.355976 | ||||||||
\(939\) | 34.2659 | 1.11823 | ||||||||
\(940\) | 28.3379 | 0.924281 | ||||||||
\(941\) | 35.6927 | 1.16355 | 0.581775 | − | 0.813350i | \(-0.302358\pi\) | ||||
0.581775 | + | 0.813350i | \(0.302358\pi\) | |||||||
\(942\) | −26.3154 | −0.857403 | ||||||||
\(943\) | 7.96546 | 0.259391 | ||||||||
\(944\) | −30.6023 | −0.996020 | ||||||||
\(945\) | −5.39629 | −0.175541 | ||||||||
\(946\) | 9.90198 | 0.321941 | ||||||||
\(947\) | 26.9384 | 0.875381 | 0.437690 | − | 0.899126i | \(-0.355797\pi\) | ||||
0.437690 | + | 0.899126i | \(0.355797\pi\) | |||||||
\(948\) | −45.2143 | −1.46849 | ||||||||
\(949\) | 43.3562 | 1.40740 | ||||||||
\(950\) | 11.5989 | 0.376319 | ||||||||
\(951\) | 11.1718 | 0.362272 | ||||||||
\(952\) | −1.06503 | −0.0345179 | ||||||||
\(953\) | −4.02006 | −0.130223 | −0.0651113 | − | 0.997878i | \(-0.520740\pi\) | ||||
−0.0651113 | + | 0.997878i | \(0.520740\pi\) | |||||||
\(954\) | 5.63641 | 0.182485 | ||||||||
\(955\) | 16.4141 | 0.531147 | ||||||||
\(956\) | −29.2808 | −0.947009 | ||||||||
\(957\) | 47.8217 | 1.54586 | ||||||||
\(958\) | −22.8210 | −0.737314 | ||||||||
\(959\) | 19.4528 | 0.628165 | ||||||||
\(960\) | −15.7489 | −0.508294 | ||||||||
\(961\) | 47.3571 | 1.52765 | ||||||||
\(962\) | −139.456 | −4.49623 | ||||||||
\(963\) | −1.03182 | −0.0332498 | ||||||||
\(964\) | −32.2247 | −1.03789 | ||||||||
\(965\) | 21.1233 | 0.679982 | ||||||||
\(966\) | −7.47127 | −0.240384 | ||||||||
\(967\) | −36.3806 | −1.16992 | −0.584961 | − | 0.811061i | \(-0.698890\pi\) | ||||
−0.584961 | + | 0.811061i | \(0.698890\pi\) | |||||||
\(968\) | 0.631580 | 0.0202997 | ||||||||
\(969\) | 24.3011 | 0.780663 | ||||||||
\(970\) | 4.89524 | 0.157177 | ||||||||
\(971\) | −51.7487 | −1.66069 | −0.830347 | − | 0.557247i | \(-0.811858\pi\) | ||||
−0.830347 | + | 0.557247i | \(0.811858\pi\) | |||||||
\(972\) | −5.92895 | −0.190171 | ||||||||
\(973\) | 2.63491 | 0.0844713 | ||||||||
\(974\) | −29.6945 | −0.951474 | ||||||||
\(975\) | 11.5283 | 0.369201 | ||||||||
\(976\) | 52.5571 | 1.68231 | ||||||||
\(977\) | 59.1147 | 1.89125 | 0.945624 | − | 0.325262i | \(-0.105452\pi\) | ||||
0.945624 | + | 0.325262i | \(0.105452\pi\) | |||||||
\(978\) | 46.6046 | 1.49025 | ||||||||
\(979\) | 15.6974 | 0.501692 | ||||||||
\(980\) | −2.20033 | −0.0702869 | ||||||||
\(981\) | 1.38823 | 0.0443228 | ||||||||
\(982\) | −31.2335 | −0.996701 | ||||||||
\(983\) | −11.6520 | −0.371642 | −0.185821 | − | 0.982584i | \(-0.559495\pi\) | ||||
−0.185821 | + | 0.982584i | \(0.559495\pi\) | |||||||
\(984\) | −2.45804 | −0.0783593 | ||||||||
\(985\) | 22.4665 | 0.715843 | ||||||||
\(986\) | 49.9330 | 1.59019 | ||||||||
\(987\) | 21.3183 | 0.678569 | ||||||||
\(988\) | 86.7276 | 2.75917 | ||||||||
\(989\) | 3.45921 | 0.109996 | ||||||||
\(990\) | −1.63933 | −0.0521014 | ||||||||
\(991\) | 12.6645 | 0.402302 | 0.201151 | − | 0.979560i | \(-0.435532\pi\) | ||||
0.201151 | + | 0.979560i | \(0.435532\pi\) | |||||||
\(992\) | −71.8392 | −2.28090 | ||||||||
\(993\) | −11.4148 | −0.362237 | ||||||||
\(994\) | 17.2526 | 0.547221 | ||||||||
\(995\) | −11.6681 | −0.369905 | ||||||||
\(996\) | 31.3218 | 0.992468 | ||||||||
\(997\) | −10.4164 | −0.329891 | −0.164946 | − | 0.986303i | \(-0.552745\pi\) | ||||
−0.164946 | + | 0.986303i | \(0.552745\pi\) | |||||||
\(998\) | −35.2731 | −1.11655 | ||||||||
\(999\) | −52.7226 | −1.66807 |
(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 | 8015.2.a.n.1.12 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.n.1.12 | ✓ | 68 | 1.1 | even | 1 | trivial |