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: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30662 | −1.63103 | −0.815513 | − | 0.578739i | \(-0.803545\pi\) | ||||
−0.815513 | + | 0.578739i | \(0.803545\pi\) | |||||||
\(3\) | 1.34001 | 0.773655 | 0.386828 | − | 0.922152i | \(-0.373571\pi\) | ||||
0.386828 | + | 0.922152i | \(0.373571\pi\) | |||||||
\(4\) | 3.32049 | 1.66025 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.09089 | −1.26185 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.04587 | −1.07688 | ||||||||
\(9\) | −1.20437 | −0.401457 | ||||||||
\(10\) | −2.30662 | −0.729417 | ||||||||
\(11\) | 2.13364 | 0.643317 | 0.321658 | − | 0.946856i | \(-0.395760\pi\) | ||||
0.321658 | + | 0.946856i | \(0.395760\pi\) | |||||||
\(12\) | 4.44949 | 1.28446 | ||||||||
\(13\) | −5.11222 | −1.41788 | −0.708938 | − | 0.705271i | \(-0.750825\pi\) | ||||
−0.708938 | + | 0.705271i | \(0.750825\pi\) | |||||||
\(14\) | 2.30662 | 0.616470 | ||||||||
\(15\) | 1.34001 | 0.345989 | ||||||||
\(16\) | 0.384674 | 0.0961685 | ||||||||
\(17\) | 6.69278 | 1.62324 | 0.811619 | − | 0.584187i | \(-0.198587\pi\) | ||||
0.811619 | + | 0.584187i | \(0.198587\pi\) | |||||||
\(18\) | 2.77803 | 0.654787 | ||||||||
\(19\) | 1.81879 | 0.417259 | 0.208629 | − | 0.977995i | \(-0.433100\pi\) | ||||
0.208629 | + | 0.977995i | \(0.433100\pi\) | |||||||
\(20\) | 3.32049 | 0.742484 | ||||||||
\(21\) | −1.34001 | −0.292414 | ||||||||
\(22\) | −4.92149 | −1.04927 | ||||||||
\(23\) | −3.98265 | −0.830441 | −0.415220 | − | 0.909721i | \(-0.636296\pi\) | ||||
−0.415220 | + | 0.909721i | \(0.636296\pi\) | |||||||
\(24\) | −4.08149 | −0.833131 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 11.7919 | 2.31259 | ||||||||
\(27\) | −5.63390 | −1.08425 | ||||||||
\(28\) | −3.32049 | −0.627514 | ||||||||
\(29\) | −1.75406 | −0.325721 | −0.162860 | − | 0.986649i | \(-0.552072\pi\) | ||||
−0.162860 | + | 0.986649i | \(0.552072\pi\) | |||||||
\(30\) | −3.09089 | −0.564317 | ||||||||
\(31\) | −2.92661 | −0.525635 | −0.262818 | − | 0.964846i | \(-0.584652\pi\) | ||||
−0.262818 | + | 0.964846i | \(0.584652\pi\) | |||||||
\(32\) | 5.20444 | 0.920023 | ||||||||
\(33\) | 2.85910 | 0.497705 | ||||||||
\(34\) | −15.4377 | −2.64754 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −3.99910 | −0.666517 | ||||||||
\(37\) | −9.15383 | −1.50488 | −0.752441 | − | 0.658660i | \(-0.771124\pi\) | ||||
−0.752441 | + | 0.658660i | \(0.771124\pi\) | |||||||
\(38\) | −4.19525 | −0.680560 | ||||||||
\(39\) | −6.85043 | −1.09695 | ||||||||
\(40\) | −3.04587 | −0.481594 | ||||||||
\(41\) | 7.82062 | 1.22138 | 0.610688 | − | 0.791871i | \(-0.290893\pi\) | ||||
0.610688 | + | 0.791871i | \(0.290893\pi\) | |||||||
\(42\) | 3.09089 | 0.476935 | ||||||||
\(43\) | 2.14000 | 0.326347 | 0.163174 | − | 0.986597i | \(-0.447827\pi\) | ||||
0.163174 | + | 0.986597i | \(0.447827\pi\) | |||||||
\(44\) | 7.08473 | 1.06806 | ||||||||
\(45\) | −1.20437 | −0.179537 | ||||||||
\(46\) | 9.18646 | 1.35447 | ||||||||
\(47\) | 8.57240 | 1.25041 | 0.625207 | − | 0.780459i | \(-0.285015\pi\) | ||||
0.625207 | + | 0.780459i | \(0.285015\pi\) | |||||||
\(48\) | 0.515467 | 0.0744013 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.30662 | −0.326205 | ||||||||
\(51\) | 8.96840 | 1.25583 | ||||||||
\(52\) | −16.9751 | −2.35402 | ||||||||
\(53\) | 1.87390 | 0.257400 | 0.128700 | − | 0.991684i | \(-0.458920\pi\) | ||||
0.128700 | + | 0.991684i | \(0.458920\pi\) | |||||||
\(54\) | 12.9953 | 1.76843 | ||||||||
\(55\) | 2.13364 | 0.287700 | ||||||||
\(56\) | 3.04587 | 0.407021 | ||||||||
\(57\) | 2.43720 | 0.322815 | ||||||||
\(58\) | 4.04595 | 0.531259 | ||||||||
\(59\) | −2.65256 | −0.345334 | −0.172667 | − | 0.984980i | \(-0.555238\pi\) | ||||
−0.172667 | + | 0.984980i | \(0.555238\pi\) | |||||||
\(60\) | 4.44949 | 0.574427 | ||||||||
\(61\) | 9.50037 | 1.21640 | 0.608199 | − | 0.793785i | \(-0.291892\pi\) | ||||
0.608199 | + | 0.793785i | \(0.291892\pi\) | |||||||
\(62\) | 6.75058 | 0.857324 | ||||||||
\(63\) | 1.20437 | 0.151737 | ||||||||
\(64\) | −12.7740 | −1.59675 | ||||||||
\(65\) | −5.11222 | −0.634093 | ||||||||
\(66\) | −6.59485 | −0.811770 | ||||||||
\(67\) | −6.97130 | −0.851680 | −0.425840 | − | 0.904798i | \(-0.640021\pi\) | ||||
−0.425840 | + | 0.904798i | \(0.640021\pi\) | |||||||
\(68\) | 22.2233 | 2.69497 | ||||||||
\(69\) | −5.33680 | −0.642475 | ||||||||
\(70\) | 2.30662 | 0.275694 | ||||||||
\(71\) | 0.142255 | 0.0168825 | 0.00844125 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844125 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(72\) | 3.66836 | 0.432320 | ||||||||
\(73\) | 10.1640 | 1.18960 | 0.594802 | − | 0.803872i | \(-0.297230\pi\) | ||||
0.594802 | + | 0.803872i | \(0.297230\pi\) | |||||||
\(74\) | 21.1144 | 2.45450 | ||||||||
\(75\) | 1.34001 | 0.154731 | ||||||||
\(76\) | 6.03927 | 0.692752 | ||||||||
\(77\) | −2.13364 | −0.243151 | ||||||||
\(78\) | 15.8013 | 1.78915 | ||||||||
\(79\) | 4.48655 | 0.504777 | 0.252388 | − | 0.967626i | \(-0.418784\pi\) | ||||
0.252388 | + | 0.967626i | \(0.418784\pi\) | |||||||
\(80\) | 0.384674 | 0.0430079 | ||||||||
\(81\) | −3.93637 | −0.437375 | ||||||||
\(82\) | −18.0392 | −1.99210 | ||||||||
\(83\) | −15.2528 | −1.67421 | −0.837106 | − | 0.547041i | \(-0.815754\pi\) | ||||
−0.837106 | + | 0.547041i | \(0.815754\pi\) | |||||||
\(84\) | −4.44949 | −0.485479 | ||||||||
\(85\) | 6.69278 | 0.725934 | ||||||||
\(86\) | −4.93617 | −0.532281 | ||||||||
\(87\) | −2.35046 | −0.251996 | ||||||||
\(88\) | −6.49878 | −0.692773 | ||||||||
\(89\) | 11.1872 | 1.18584 | 0.592922 | − | 0.805260i | \(-0.297974\pi\) | ||||
0.592922 | + | 0.805260i | \(0.297974\pi\) | |||||||
\(90\) | 2.77803 | 0.292830 | ||||||||
\(91\) | 5.11222 | 0.535907 | ||||||||
\(92\) | −13.2244 | −1.37874 | ||||||||
\(93\) | −3.92169 | −0.406660 | ||||||||
\(94\) | −19.7733 | −2.03946 | ||||||||
\(95\) | 1.81879 | 0.186604 | ||||||||
\(96\) | 6.97400 | 0.711781 | ||||||||
\(97\) | −2.15068 | −0.218368 | −0.109184 | − | 0.994022i | \(-0.534824\pi\) | ||||
−0.109184 | + | 0.994022i | \(0.534824\pi\) | |||||||
\(98\) | −2.30662 | −0.233004 | ||||||||
\(99\) | −2.56970 | −0.258264 | ||||||||
\(100\) | 3.32049 | 0.332049 | ||||||||
\(101\) | −7.98830 | −0.794866 | −0.397433 | − | 0.917631i | \(-0.630099\pi\) | ||||
−0.397433 | + | 0.917631i | \(0.630099\pi\) | |||||||
\(102\) | −20.6867 | −2.04829 | ||||||||
\(103\) | −10.2062 | −1.00564 | −0.502821 | − | 0.864391i | \(-0.667705\pi\) | ||||
−0.502821 | + | 0.864391i | \(0.667705\pi\) | |||||||
\(104\) | 15.5712 | 1.52688 | ||||||||
\(105\) | −1.34001 | −0.130772 | ||||||||
\(106\) | −4.32238 | −0.419827 | ||||||||
\(107\) | 18.0542 | 1.74536 | 0.872681 | − | 0.488290i | \(-0.162379\pi\) | ||||
0.872681 | + | 0.488290i | \(0.162379\pi\) | |||||||
\(108\) | −18.7073 | −1.80011 | ||||||||
\(109\) | 1.81976 | 0.174302 | 0.0871509 | − | 0.996195i | \(-0.472224\pi\) | ||||
0.0871509 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(110\) | −4.92149 | −0.469246 | ||||||||
\(111\) | −12.2662 | −1.16426 | ||||||||
\(112\) | −0.384674 | −0.0363483 | ||||||||
\(113\) | 5.19513 | 0.488716 | 0.244358 | − | 0.969685i | \(-0.421423\pi\) | ||||
0.244358 | + | 0.969685i | \(0.421423\pi\) | |||||||
\(114\) | −5.62168 | −0.526519 | ||||||||
\(115\) | −3.98265 | −0.371384 | ||||||||
\(116\) | −5.82434 | −0.540776 | ||||||||
\(117\) | 6.15702 | 0.569216 | ||||||||
\(118\) | 6.11844 | 0.563248 | ||||||||
\(119\) | −6.69278 | −0.613526 | ||||||||
\(120\) | −4.08149 | −0.372588 | ||||||||
\(121\) | −6.44758 | −0.586144 | ||||||||
\(122\) | −21.9137 | −1.98398 | ||||||||
\(123\) | 10.4797 | 0.944924 | ||||||||
\(124\) | −9.71779 | −0.872683 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.77803 | −0.247486 | ||||||||
\(127\) | −2.89657 | −0.257029 | −0.128514 | − | 0.991708i | \(-0.541021\pi\) | ||||
−0.128514 | + | 0.991708i | \(0.541021\pi\) | |||||||
\(128\) | 19.0559 | 1.68432 | ||||||||
\(129\) | 2.86763 | 0.252480 | ||||||||
\(130\) | 11.7919 | 1.03422 | ||||||||
\(131\) | −5.92357 | −0.517545 | −0.258773 | − | 0.965938i | \(-0.583318\pi\) | ||||
−0.258773 | + | 0.965938i | \(0.583318\pi\) | |||||||
\(132\) | 9.49361 | 0.826313 | ||||||||
\(133\) | −1.81879 | −0.157709 | ||||||||
\(134\) | 16.0801 | 1.38911 | ||||||||
\(135\) | −5.63390 | −0.484889 | ||||||||
\(136\) | −20.3853 | −1.74803 | ||||||||
\(137\) | 12.8189 | 1.09519 | 0.547597 | − | 0.836742i | \(-0.315543\pi\) | ||||
0.547597 | + | 0.836742i | \(0.315543\pi\) | |||||||
\(138\) | 12.3100 | 1.04789 | ||||||||
\(139\) | 7.58899 | 0.643689 | 0.321845 | − | 0.946792i | \(-0.395697\pi\) | ||||
0.321845 | + | 0.946792i | \(0.395697\pi\) | |||||||
\(140\) | −3.32049 | −0.280633 | ||||||||
\(141\) | 11.4871 | 0.967389 | ||||||||
\(142\) | −0.328127 | −0.0275358 | ||||||||
\(143\) | −10.9076 | −0.912143 | ||||||||
\(144\) | −0.463291 | −0.0386075 | ||||||||
\(145\) | −1.75406 | −0.145667 | ||||||||
\(146\) | −23.4444 | −1.94028 | ||||||||
\(147\) | 1.34001 | 0.110522 | ||||||||
\(148\) | −30.3952 | −2.49847 | ||||||||
\(149\) | 12.7889 | 1.04771 | 0.523856 | − | 0.851807i | \(-0.324493\pi\) | ||||
0.523856 | + | 0.851807i | \(0.324493\pi\) | |||||||
\(150\) | −3.09089 | −0.252370 | ||||||||
\(151\) | −18.3320 | −1.49184 | −0.745919 | − | 0.666037i | \(-0.767989\pi\) | ||||
−0.745919 | + | 0.666037i | \(0.767989\pi\) | |||||||
\(152\) | −5.53979 | −0.449336 | ||||||||
\(153\) | −8.06059 | −0.651660 | ||||||||
\(154\) | 4.92149 | 0.396585 | ||||||||
\(155\) | −2.92661 | −0.235071 | ||||||||
\(156\) | −22.7468 | −1.82120 | ||||||||
\(157\) | 4.70588 | 0.375570 | 0.187785 | − | 0.982210i | \(-0.439869\pi\) | ||||
0.187785 | + | 0.982210i | \(0.439869\pi\) | |||||||
\(158\) | −10.3488 | −0.823304 | ||||||||
\(159\) | 2.51105 | 0.199139 | ||||||||
\(160\) | 5.20444 | 0.411447 | ||||||||
\(161\) | 3.98265 | 0.313877 | ||||||||
\(162\) | 9.07971 | 0.713370 | ||||||||
\(163\) | 7.97144 | 0.624371 | 0.312186 | − | 0.950021i | \(-0.398939\pi\) | ||||
0.312186 | + | 0.950021i | \(0.398939\pi\) | |||||||
\(164\) | 25.9683 | 2.02778 | ||||||||
\(165\) | 2.85910 | 0.222581 | ||||||||
\(166\) | 35.1824 | 2.73068 | ||||||||
\(167\) | −4.51016 | −0.349006 | −0.174503 | − | 0.984657i | \(-0.555832\pi\) | ||||
−0.174503 | + | 0.984657i | \(0.555832\pi\) | |||||||
\(168\) | 4.08149 | 0.314894 | ||||||||
\(169\) | 13.1348 | 1.01037 | ||||||||
\(170\) | −15.4377 | −1.18402 | ||||||||
\(171\) | −2.19050 | −0.167512 | ||||||||
\(172\) | 7.10586 | 0.541817 | ||||||||
\(173\) | 2.43568 | 0.185182 | 0.0925908 | − | 0.995704i | \(-0.470485\pi\) | ||||
0.0925908 | + | 0.995704i | \(0.470485\pi\) | |||||||
\(174\) | 5.42161 | 0.411011 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0.820756 | 0.0618668 | ||||||||
\(177\) | −3.55446 | −0.267169 | ||||||||
\(178\) | −25.8047 | −1.93414 | ||||||||
\(179\) | 21.0843 | 1.57592 | 0.787959 | − | 0.615728i | \(-0.211138\pi\) | ||||
0.787959 | + | 0.615728i | \(0.211138\pi\) | |||||||
\(180\) | −3.99910 | −0.298076 | ||||||||
\(181\) | 16.3844 | 1.21785 | 0.608923 | − | 0.793229i | \(-0.291602\pi\) | ||||
0.608923 | + | 0.793229i | \(0.291602\pi\) | |||||||
\(182\) | −11.7919 | −0.874077 | ||||||||
\(183\) | 12.7306 | 0.941073 | ||||||||
\(184\) | 12.1306 | 0.894282 | ||||||||
\(185\) | −9.15383 | −0.673003 | ||||||||
\(186\) | 9.04585 | 0.663274 | ||||||||
\(187\) | 14.2800 | 1.04426 | ||||||||
\(188\) | 28.4646 | 2.07599 | ||||||||
\(189\) | 5.63390 | 0.409806 | ||||||||
\(190\) | −4.19525 | −0.304356 | ||||||||
\(191\) | 19.3468 | 1.39989 | 0.699944 | − | 0.714198i | \(-0.253208\pi\) | ||||
0.699944 | + | 0.714198i | \(0.253208\pi\) | |||||||
\(192\) | −17.1173 | −1.23533 | ||||||||
\(193\) | 8.93297 | 0.643009 | 0.321505 | − | 0.946908i | \(-0.395811\pi\) | ||||
0.321505 | + | 0.946908i | \(0.395811\pi\) | |||||||
\(194\) | 4.96080 | 0.356165 | ||||||||
\(195\) | −6.85043 | −0.490570 | ||||||||
\(196\) | 3.32049 | 0.237178 | ||||||||
\(197\) | −14.8284 | −1.05648 | −0.528241 | − | 0.849095i | \(-0.677148\pi\) | ||||
−0.528241 | + | 0.849095i | \(0.677148\pi\) | |||||||
\(198\) | 5.92731 | 0.421235 | ||||||||
\(199\) | 0.193330 | 0.0137048 | 0.00685241 | − | 0.999977i | \(-0.497819\pi\) | ||||
0.00685241 | + | 0.999977i | \(0.497819\pi\) | |||||||
\(200\) | −3.04587 | −0.215375 | ||||||||
\(201\) | −9.34162 | −0.658907 | ||||||||
\(202\) | 18.4260 | 1.29645 | ||||||||
\(203\) | 1.75406 | 0.123111 | ||||||||
\(204\) | 29.7795 | 2.08498 | ||||||||
\(205\) | 7.82062 | 0.546216 | ||||||||
\(206\) | 23.5417 | 1.64023 | ||||||||
\(207\) | 4.79660 | 0.333386 | ||||||||
\(208\) | −1.96654 | −0.136355 | ||||||||
\(209\) | 3.88064 | 0.268429 | ||||||||
\(210\) | 3.09089 | 0.213292 | ||||||||
\(211\) | 11.5861 | 0.797623 | 0.398811 | − | 0.917033i | \(-0.369423\pi\) | ||||
0.398811 | + | 0.917033i | \(0.369423\pi\) | |||||||
\(212\) | 6.22228 | 0.427348 | ||||||||
\(213\) | 0.190623 | 0.0130612 | ||||||||
\(214\) | −41.6441 | −2.84673 | ||||||||
\(215\) | 2.14000 | 0.145947 | ||||||||
\(216\) | 17.1601 | 1.16760 | ||||||||
\(217\) | 2.92661 | 0.198671 | ||||||||
\(218\) | −4.19750 | −0.284291 | ||||||||
\(219\) | 13.6199 | 0.920344 | ||||||||
\(220\) | 7.08473 | 0.477652 | ||||||||
\(221\) | −34.2150 | −2.30155 | ||||||||
\(222\) | 28.2935 | 1.89894 | ||||||||
\(223\) | 8.31512 | 0.556822 | 0.278411 | − | 0.960462i | \(-0.410192\pi\) | ||||
0.278411 | + | 0.960462i | \(0.410192\pi\) | |||||||
\(224\) | −5.20444 | −0.347736 | ||||||||
\(225\) | −1.20437 | −0.0802914 | ||||||||
\(226\) | −11.9832 | −0.797109 | ||||||||
\(227\) | 5.24230 | 0.347943 | 0.173972 | − | 0.984751i | \(-0.444340\pi\) | ||||
0.173972 | + | 0.984751i | \(0.444340\pi\) | |||||||
\(228\) | 8.09269 | 0.535951 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | 9.18646 | 0.605738 | ||||||||
\(231\) | −2.85910 | −0.188115 | ||||||||
\(232\) | 5.34263 | 0.350761 | ||||||||
\(233\) | −20.0824 | −1.31564 | −0.657820 | − | 0.753175i | \(-0.728521\pi\) | ||||
−0.657820 | + | 0.753175i | \(0.728521\pi\) | |||||||
\(234\) | −14.2019 | −0.928407 | ||||||||
\(235\) | 8.57240 | 0.559202 | ||||||||
\(236\) | −8.80780 | −0.573339 | ||||||||
\(237\) | 6.01203 | 0.390523 | ||||||||
\(238\) | 15.4377 | 1.00068 | ||||||||
\(239\) | 21.6093 | 1.39779 | 0.698894 | − | 0.715225i | \(-0.253676\pi\) | ||||
0.698894 | + | 0.715225i | \(0.253676\pi\) | |||||||
\(240\) | 0.515467 | 0.0332733 | ||||||||
\(241\) | 12.5819 | 0.810473 | 0.405237 | − | 0.914212i | \(-0.367189\pi\) | ||||
0.405237 | + | 0.914212i | \(0.367189\pi\) | |||||||
\(242\) | 14.8721 | 0.956016 | ||||||||
\(243\) | 11.6269 | 0.745868 | ||||||||
\(244\) | 31.5459 | 2.01952 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −24.1727 | −1.54120 | ||||||||
\(247\) | −9.29805 | −0.591621 | ||||||||
\(248\) | 8.91407 | 0.566044 | ||||||||
\(249\) | −20.4389 | −1.29526 | ||||||||
\(250\) | −2.30662 | −0.145883 | ||||||||
\(251\) | −21.7549 | −1.37316 | −0.686578 | − | 0.727056i | \(-0.740888\pi\) | ||||
−0.686578 | + | 0.727056i | \(0.740888\pi\) | |||||||
\(252\) | 3.99910 | 0.251920 | ||||||||
\(253\) | −8.49755 | −0.534236 | ||||||||
\(254\) | 6.68128 | 0.419221 | ||||||||
\(255\) | 8.96840 | 0.561623 | ||||||||
\(256\) | −18.4066 | −1.15041 | ||||||||
\(257\) | −10.6124 | −0.661984 | −0.330992 | − | 0.943634i | \(-0.607383\pi\) | ||||
−0.330992 | + | 0.943634i | \(0.607383\pi\) | |||||||
\(258\) | −6.61452 | −0.411802 | ||||||||
\(259\) | 9.15383 | 0.568792 | ||||||||
\(260\) | −16.9751 | −1.05275 | ||||||||
\(261\) | 2.11254 | 0.130763 | ||||||||
\(262\) | 13.6634 | 0.844129 | ||||||||
\(263\) | 19.9740 | 1.23165 | 0.615824 | − | 0.787883i | \(-0.288823\pi\) | ||||
0.615824 | + | 0.787883i | \(0.288823\pi\) | |||||||
\(264\) | −8.70844 | −0.535967 | ||||||||
\(265\) | 1.87390 | 0.115113 | ||||||||
\(266\) | 4.19525 | 0.257227 | ||||||||
\(267\) | 14.9910 | 0.917435 | ||||||||
\(268\) | −23.1481 | −1.41400 | ||||||||
\(269\) | 18.1961 | 1.10943 | 0.554717 | − | 0.832039i | \(-0.312827\pi\) | ||||
0.554717 | + | 0.832039i | \(0.312827\pi\) | |||||||
\(270\) | 12.9953 | 0.790867 | ||||||||
\(271\) | 17.6524 | 1.07231 | 0.536155 | − | 0.844120i | \(-0.319876\pi\) | ||||
0.536155 | + | 0.844120i | \(0.319876\pi\) | |||||||
\(272\) | 2.57454 | 0.156104 | ||||||||
\(273\) | 6.85043 | 0.414607 | ||||||||
\(274\) | −29.5684 | −1.78629 | ||||||||
\(275\) | 2.13364 | 0.128663 | ||||||||
\(276\) | −17.7208 | −1.06667 | ||||||||
\(277\) | 21.8701 | 1.31405 | 0.657023 | − | 0.753870i | \(-0.271815\pi\) | ||||
0.657023 | + | 0.753870i | \(0.271815\pi\) | |||||||
\(278\) | −17.5049 | −1.04987 | ||||||||
\(279\) | 3.52473 | 0.211020 | ||||||||
\(280\) | 3.04587 | 0.182025 | ||||||||
\(281\) | 11.8771 | 0.708530 | 0.354265 | − | 0.935145i | \(-0.384731\pi\) | ||||
0.354265 | + | 0.935145i | \(0.384731\pi\) | |||||||
\(282\) | −26.4964 | −1.57784 | ||||||||
\(283\) | −23.7270 | −1.41042 | −0.705212 | − | 0.708997i | \(-0.749148\pi\) | ||||
−0.705212 | + | 0.708997i | \(0.749148\pi\) | |||||||
\(284\) | 0.472355 | 0.0280291 | ||||||||
\(285\) | 2.43720 | 0.144367 | ||||||||
\(286\) | 25.1598 | 1.48773 | ||||||||
\(287\) | −7.82062 | −0.461637 | ||||||||
\(288\) | −6.26808 | −0.369350 | ||||||||
\(289\) | 27.7933 | 1.63490 | ||||||||
\(290\) | 4.04595 | 0.237586 | ||||||||
\(291\) | −2.88193 | −0.168942 | ||||||||
\(292\) | 33.7494 | 1.97504 | ||||||||
\(293\) | −31.7416 | −1.85437 | −0.927183 | − | 0.374609i | \(-0.877777\pi\) | ||||
−0.927183 | + | 0.374609i | \(0.877777\pi\) | |||||||
\(294\) | −3.09089 | −0.180265 | ||||||||
\(295\) | −2.65256 | −0.154438 | ||||||||
\(296\) | 27.8814 | 1.62057 | ||||||||
\(297\) | −12.0207 | −0.697513 | ||||||||
\(298\) | −29.4992 | −1.70884 | ||||||||
\(299\) | 20.3602 | 1.17746 | ||||||||
\(300\) | 4.44949 | 0.256892 | ||||||||
\(301\) | −2.14000 | −0.123348 | ||||||||
\(302\) | 42.2849 | 2.43322 | ||||||||
\(303\) | −10.7044 | −0.614952 | ||||||||
\(304\) | 0.699641 | 0.0401272 | ||||||||
\(305\) | 9.50037 | 0.543990 | ||||||||
\(306\) | 18.5927 | 1.06287 | ||||||||
\(307\) | 4.21455 | 0.240537 | 0.120269 | − | 0.992741i | \(-0.461624\pi\) | ||||
0.120269 | + | 0.992741i | \(0.461624\pi\) | |||||||
\(308\) | −7.08473 | −0.403690 | ||||||||
\(309\) | −13.6764 | −0.778021 | ||||||||
\(310\) | 6.75058 | 0.383407 | ||||||||
\(311\) | −12.3433 | −0.699925 | −0.349962 | − | 0.936764i | \(-0.613806\pi\) | ||||
−0.349962 | + | 0.936764i | \(0.613806\pi\) | |||||||
\(312\) | 20.8655 | 1.18128 | ||||||||
\(313\) | −4.35993 | −0.246438 | −0.123219 | − | 0.992380i | \(-0.539322\pi\) | ||||
−0.123219 | + | 0.992380i | \(0.539322\pi\) | |||||||
\(314\) | −10.8547 | −0.612565 | ||||||||
\(315\) | 1.20437 | 0.0678587 | ||||||||
\(316\) | 14.8976 | 0.838053 | ||||||||
\(317\) | 11.3273 | 0.636204 | 0.318102 | − | 0.948056i | \(-0.396954\pi\) | ||||
0.318102 | + | 0.948056i | \(0.396954\pi\) | |||||||
\(318\) | −5.79203 | −0.324801 | ||||||||
\(319\) | −3.74253 | −0.209541 | ||||||||
\(320\) | −12.7740 | −0.714088 | ||||||||
\(321\) | 24.1928 | 1.35031 | ||||||||
\(322\) | −9.18646 | −0.511942 | ||||||||
\(323\) | 12.1728 | 0.677310 | ||||||||
\(324\) | −13.0707 | −0.726149 | ||||||||
\(325\) | −5.11222 | −0.283575 | ||||||||
\(326\) | −18.3871 | −1.01837 | ||||||||
\(327\) | 2.43850 | 0.134850 | ||||||||
\(328\) | −23.8206 | −1.31527 | ||||||||
\(329\) | −8.57240 | −0.472612 | ||||||||
\(330\) | −6.59485 | −0.363035 | ||||||||
\(331\) | 31.0058 | 1.70423 | 0.852117 | − | 0.523351i | \(-0.175318\pi\) | ||||
0.852117 | + | 0.523351i | \(0.175318\pi\) | |||||||
\(332\) | −50.6468 | −2.77960 | ||||||||
\(333\) | 11.0246 | 0.604145 | ||||||||
\(334\) | 10.4032 | 0.569238 | ||||||||
\(335\) | −6.97130 | −0.380883 | ||||||||
\(336\) | −0.515467 | −0.0281210 | ||||||||
\(337\) | 21.4857 | 1.17040 | 0.585200 | − | 0.810889i | \(-0.301016\pi\) | ||||
0.585200 | + | 0.810889i | \(0.301016\pi\) | |||||||
\(338\) | −30.2970 | −1.64794 | ||||||||
\(339\) | 6.96152 | 0.378098 | ||||||||
\(340\) | 22.2233 | 1.20523 | ||||||||
\(341\) | −6.24433 | −0.338150 | ||||||||
\(342\) | 5.05264 | 0.273216 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.51816 | −0.351436 | ||||||||
\(345\) | −5.33680 | −0.287324 | ||||||||
\(346\) | −5.61819 | −0.302036 | ||||||||
\(347\) | −30.3497 | −1.62926 | −0.814629 | − | 0.579982i | \(-0.803059\pi\) | ||||
−0.814629 | + | 0.579982i | \(0.803059\pi\) | |||||||
\(348\) | −7.80467 | −0.418374 | ||||||||
\(349\) | −10.6029 | −0.567558 | −0.283779 | − | 0.958890i | \(-0.591588\pi\) | ||||
−0.283779 | + | 0.958890i | \(0.591588\pi\) | |||||||
\(350\) | 2.30662 | 0.123294 | ||||||||
\(351\) | 28.8018 | 1.53732 | ||||||||
\(352\) | 11.1044 | 0.591866 | ||||||||
\(353\) | 8.89537 | 0.473453 | 0.236726 | − | 0.971576i | \(-0.423925\pi\) | ||||
0.236726 | + | 0.971576i | \(0.423925\pi\) | |||||||
\(354\) | 8.19878 | 0.435760 | ||||||||
\(355\) | 0.142255 | 0.00755009 | ||||||||
\(356\) | 37.1471 | 1.96879 | ||||||||
\(357\) | −8.96840 | −0.474658 | ||||||||
\(358\) | −48.6335 | −2.57036 | ||||||||
\(359\) | 22.6885 | 1.19745 | 0.598725 | − | 0.800954i | \(-0.295674\pi\) | ||||
0.598725 | + | 0.800954i | \(0.295674\pi\) | |||||||
\(360\) | 3.66836 | 0.193339 | ||||||||
\(361\) | −15.6920 | −0.825895 | ||||||||
\(362\) | −37.7927 | −1.98634 | ||||||||
\(363\) | −8.63983 | −0.453473 | ||||||||
\(364\) | 16.9751 | 0.889736 | ||||||||
\(365\) | 10.1640 | 0.532007 | ||||||||
\(366\) | −29.3646 | −1.53491 | ||||||||
\(367\) | 4.27002 | 0.222893 | 0.111447 | − | 0.993770i | \(-0.464452\pi\) | ||||
0.111447 | + | 0.993770i | \(0.464452\pi\) | |||||||
\(368\) | −1.53202 | −0.0798622 | ||||||||
\(369\) | −9.41894 | −0.490330 | ||||||||
\(370\) | 21.1144 | 1.09769 | ||||||||
\(371\) | −1.87390 | −0.0972882 | ||||||||
\(372\) | −13.0219 | −0.675156 | ||||||||
\(373\) | −0.378616 | −0.0196040 | −0.00980199 | − | 0.999952i | \(-0.503120\pi\) | ||||
−0.00980199 | + | 0.999952i | \(0.503120\pi\) | |||||||
\(374\) | −32.9385 | −1.70321 | ||||||||
\(375\) | 1.34001 | 0.0691978 | ||||||||
\(376\) | −26.1104 | −1.34654 | ||||||||
\(377\) | 8.96714 | 0.461831 | ||||||||
\(378\) | −12.9953 | −0.668404 | ||||||||
\(379\) | −6.03309 | −0.309899 | −0.154950 | − | 0.987922i | \(-0.549522\pi\) | ||||
−0.154950 | + | 0.987922i | \(0.549522\pi\) | |||||||
\(380\) | 6.03927 | 0.309808 | ||||||||
\(381\) | −3.88143 | −0.198852 | ||||||||
\(382\) | −44.6257 | −2.28325 | ||||||||
\(383\) | −24.4874 | −1.25125 | −0.625624 | − | 0.780124i | \(-0.715156\pi\) | ||||
−0.625624 | + | 0.780124i | \(0.715156\pi\) | |||||||
\(384\) | 25.5351 | 1.30308 | ||||||||
\(385\) | −2.13364 | −0.108740 | ||||||||
\(386\) | −20.6050 | −1.04876 | ||||||||
\(387\) | −2.57736 | −0.131014 | ||||||||
\(388\) | −7.14131 | −0.362545 | ||||||||
\(389\) | 9.71828 | 0.492736 | 0.246368 | − | 0.969176i | \(-0.420763\pi\) | ||||
0.246368 | + | 0.969176i | \(0.420763\pi\) | |||||||
\(390\) | 15.8013 | 0.800132 | ||||||||
\(391\) | −26.6550 | −1.34800 | ||||||||
\(392\) | −3.04587 | −0.153840 | ||||||||
\(393\) | −7.93765 | −0.400402 | ||||||||
\(394\) | 34.2035 | 1.72315 | ||||||||
\(395\) | 4.48655 | 0.225743 | ||||||||
\(396\) | −8.53265 | −0.428782 | ||||||||
\(397\) | −5.00564 | −0.251226 | −0.125613 | − | 0.992079i | \(-0.540090\pi\) | ||||
−0.125613 | + | 0.992079i | \(0.540090\pi\) | |||||||
\(398\) | −0.445939 | −0.0223529 | ||||||||
\(399\) | −2.43720 | −0.122012 | ||||||||
\(400\) | 0.384674 | 0.0192337 | ||||||||
\(401\) | −3.46530 | −0.173049 | −0.0865243 | − | 0.996250i | \(-0.527576\pi\) | ||||
−0.0865243 | + | 0.996250i | \(0.527576\pi\) | |||||||
\(402\) | 21.5476 | 1.07469 | ||||||||
\(403\) | 14.9615 | 0.745285 | ||||||||
\(404\) | −26.5251 | −1.31967 | ||||||||
\(405\) | −3.93637 | −0.195600 | ||||||||
\(406\) | −4.04595 | −0.200797 | ||||||||
\(407\) | −19.5310 | −0.968115 | ||||||||
\(408\) | −27.3165 | −1.35237 | ||||||||
\(409\) | 25.1305 | 1.24262 | 0.621312 | − | 0.783563i | \(-0.286600\pi\) | ||||
0.621312 | + | 0.783563i | \(0.286600\pi\) | |||||||
\(410\) | −18.0392 | −0.890892 | ||||||||
\(411\) | 17.1775 | 0.847303 | ||||||||
\(412\) | −33.8894 | −1.66961 | ||||||||
\(413\) | 2.65256 | 0.130524 | ||||||||
\(414\) | −11.0639 | −0.543762 | ||||||||
\(415\) | −15.2528 | −0.748730 | ||||||||
\(416\) | −26.6062 | −1.30448 | ||||||||
\(417\) | 10.1693 | 0.497994 | ||||||||
\(418\) | −8.95116 | −0.437815 | ||||||||
\(419\) | −10.0820 | −0.492537 | −0.246268 | − | 0.969202i | \(-0.579204\pi\) | ||||
−0.246268 | + | 0.969202i | \(0.579204\pi\) | |||||||
\(420\) | −4.44949 | −0.217113 | ||||||||
\(421\) | −32.3274 | −1.57554 | −0.787770 | − | 0.615969i | \(-0.788764\pi\) | ||||
−0.787770 | + | 0.615969i | \(0.788764\pi\) | |||||||
\(422\) | −26.7248 | −1.30094 | ||||||||
\(423\) | −10.3244 | −0.501988 | ||||||||
\(424\) | −5.70766 | −0.277188 | ||||||||
\(425\) | 6.69278 | 0.324647 | ||||||||
\(426\) | −0.439694 | −0.0213032 | ||||||||
\(427\) | −9.50037 | −0.459755 | ||||||||
\(428\) | 59.9487 | 2.89773 | ||||||||
\(429\) | −14.6164 | −0.705684 | ||||||||
\(430\) | −4.93617 | −0.238043 | ||||||||
\(431\) | 2.37000 | 0.114159 | 0.0570794 | − | 0.998370i | \(-0.481821\pi\) | ||||
0.0570794 | + | 0.998370i | \(0.481821\pi\) | |||||||
\(432\) | −2.16722 | −0.104270 | ||||||||
\(433\) | 37.6774 | 1.81066 | 0.905329 | − | 0.424710i | \(-0.139624\pi\) | ||||
0.905329 | + | 0.424710i | \(0.139624\pi\) | |||||||
\(434\) | −6.75058 | −0.324038 | ||||||||
\(435\) | −2.35046 | −0.112696 | ||||||||
\(436\) | 6.04251 | 0.289384 | ||||||||
\(437\) | −7.24361 | −0.346509 | ||||||||
\(438\) | −31.4158 | −1.50111 | ||||||||
\(439\) | 10.0246 | 0.478448 | 0.239224 | − | 0.970964i | \(-0.423107\pi\) | ||||
0.239224 | + | 0.970964i | \(0.423107\pi\) | |||||||
\(440\) | −6.49878 | −0.309817 | ||||||||
\(441\) | −1.20437 | −0.0573510 | ||||||||
\(442\) | 78.9209 | 3.75389 | ||||||||
\(443\) | −1.84452 | −0.0876360 | −0.0438180 | − | 0.999040i | \(-0.513952\pi\) | ||||
−0.0438180 | + | 0.999040i | \(0.513952\pi\) | |||||||
\(444\) | −40.7299 | −1.93296 | ||||||||
\(445\) | 11.1872 | 0.530326 | ||||||||
\(446\) | −19.1798 | −0.908190 | ||||||||
\(447\) | 17.1373 | 0.810568 | ||||||||
\(448\) | 12.7740 | 0.603515 | ||||||||
\(449\) | 6.87189 | 0.324304 | 0.162152 | − | 0.986766i | \(-0.448156\pi\) | ||||
0.162152 | + | 0.986766i | \(0.448156\pi\) | |||||||
\(450\) | 2.77803 | 0.130957 | ||||||||
\(451\) | 16.6864 | 0.785732 | ||||||||
\(452\) | 17.2504 | 0.811389 | ||||||||
\(453\) | −24.5651 | −1.15417 | ||||||||
\(454\) | −12.0920 | −0.567505 | ||||||||
\(455\) | 5.11222 | 0.239665 | ||||||||
\(456\) | −7.42338 | −0.347631 | ||||||||
\(457\) | −3.39644 | −0.158879 | −0.0794395 | − | 0.996840i | \(-0.525313\pi\) | ||||
−0.0794395 | + | 0.996840i | \(0.525313\pi\) | |||||||
\(458\) | 2.30662 | 0.107781 | ||||||||
\(459\) | −37.7065 | −1.75999 | ||||||||
\(460\) | −13.2244 | −0.616589 | ||||||||
\(461\) | −1.36813 | −0.0637203 | −0.0318601 | − | 0.999492i | \(-0.510143\pi\) | ||||
−0.0318601 | + | 0.999492i | \(0.510143\pi\) | |||||||
\(462\) | 6.59485 | 0.306820 | ||||||||
\(463\) | 11.7058 | 0.544016 | 0.272008 | − | 0.962295i | \(-0.412312\pi\) | ||||
0.272008 | + | 0.962295i | \(0.412312\pi\) | |||||||
\(464\) | −0.674741 | −0.0313241 | ||||||||
\(465\) | −3.92169 | −0.181864 | ||||||||
\(466\) | 46.3224 | 2.14584 | ||||||||
\(467\) | 20.3654 | 0.942396 | 0.471198 | − | 0.882027i | \(-0.343822\pi\) | ||||
0.471198 | + | 0.882027i | \(0.343822\pi\) | |||||||
\(468\) | 20.4443 | 0.945039 | ||||||||
\(469\) | 6.97130 | 0.321905 | ||||||||
\(470\) | −19.7733 | −0.912073 | ||||||||
\(471\) | 6.30593 | 0.290562 | ||||||||
\(472\) | 8.07934 | 0.371882 | ||||||||
\(473\) | 4.56599 | 0.209945 | ||||||||
\(474\) | −13.8675 | −0.636953 | ||||||||
\(475\) | 1.81879 | 0.0834518 | ||||||||
\(476\) | −22.2233 | −1.01860 | ||||||||
\(477\) | −2.25688 | −0.103335 | ||||||||
\(478\) | −49.8444 | −2.27983 | ||||||||
\(479\) | 6.59641 | 0.301398 | 0.150699 | − | 0.988580i | \(-0.451848\pi\) | ||||
0.150699 | + | 0.988580i | \(0.451848\pi\) | |||||||
\(480\) | 6.97400 | 0.318318 | ||||||||
\(481\) | 46.7964 | 2.13373 | ||||||||
\(482\) | −29.0217 | −1.32190 | ||||||||
\(483\) | 5.33680 | 0.242833 | ||||||||
\(484\) | −21.4091 | −0.973142 | ||||||||
\(485\) | −2.15068 | −0.0976573 | ||||||||
\(486\) | −26.8189 | −1.21653 | ||||||||
\(487\) | 32.0801 | 1.45369 | 0.726843 | − | 0.686803i | \(-0.240987\pi\) | ||||
0.726843 | + | 0.686803i | \(0.240987\pi\) | |||||||
\(488\) | −28.9369 | −1.30991 | ||||||||
\(489\) | 10.6818 | 0.483048 | ||||||||
\(490\) | −2.30662 | −0.104202 | ||||||||
\(491\) | −12.4351 | −0.561187 | −0.280594 | − | 0.959827i | \(-0.590531\pi\) | ||||
−0.280594 | + | 0.959827i | \(0.590531\pi\) | |||||||
\(492\) | 34.7978 | 1.56881 | ||||||||
\(493\) | −11.7395 | −0.528722 | ||||||||
\(494\) | 21.4471 | 0.964949 | ||||||||
\(495\) | −2.56970 | −0.115499 | ||||||||
\(496\) | −1.12579 | −0.0505495 | ||||||||
\(497\) | −0.142255 | −0.00638099 | ||||||||
\(498\) | 47.1448 | 2.11261 | ||||||||
\(499\) | −8.41527 | −0.376719 | −0.188360 | − | 0.982100i | \(-0.560317\pi\) | ||||
−0.188360 | + | 0.982100i | \(0.560317\pi\) | |||||||
\(500\) | 3.32049 | 0.148497 | ||||||||
\(501\) | −6.04366 | −0.270011 | ||||||||
\(502\) | 50.1802 | 2.23965 | ||||||||
\(503\) | −15.1360 | −0.674882 | −0.337441 | − | 0.941347i | \(-0.609561\pi\) | ||||
−0.337441 | + | 0.941347i | \(0.609561\pi\) | |||||||
\(504\) | −3.66836 | −0.163402 | ||||||||
\(505\) | −7.98830 | −0.355475 | ||||||||
\(506\) | 19.6006 | 0.871353 | ||||||||
\(507\) | 17.6008 | 0.781679 | ||||||||
\(508\) | −9.61803 | −0.426731 | ||||||||
\(509\) | 41.8204 | 1.85366 | 0.926828 | − | 0.375486i | \(-0.122524\pi\) | ||||
0.926828 | + | 0.375486i | \(0.122524\pi\) | |||||||
\(510\) | −20.6867 | −0.916021 | ||||||||
\(511\) | −10.1640 | −0.449628 | ||||||||
\(512\) | 4.34534 | 0.192039 | ||||||||
\(513\) | −10.2469 | −0.452411 | ||||||||
\(514\) | 24.4788 | 1.07971 | ||||||||
\(515\) | −10.2062 | −0.449737 | ||||||||
\(516\) | 9.52192 | 0.419179 | ||||||||
\(517\) | 18.2904 | 0.804412 | ||||||||
\(518\) | −21.1144 | −0.927714 | ||||||||
\(519\) | 3.26384 | 0.143267 | ||||||||
\(520\) | 15.5712 | 0.682840 | ||||||||
\(521\) | 8.61494 | 0.377427 | 0.188714 | − | 0.982032i | \(-0.439568\pi\) | ||||
0.188714 | + | 0.982032i | \(0.439568\pi\) | |||||||
\(522\) | −4.87282 | −0.213278 | ||||||||
\(523\) | 24.9923 | 1.09284 | 0.546418 | − | 0.837512i | \(-0.315991\pi\) | ||||
0.546418 | + | 0.837512i | \(0.315991\pi\) | |||||||
\(524\) | −19.6692 | −0.859252 | ||||||||
\(525\) | −1.34001 | −0.0584829 | ||||||||
\(526\) | −46.0724 | −2.00885 | ||||||||
\(527\) | −19.5872 | −0.853230 | ||||||||
\(528\) | 1.09982 | 0.0478636 | ||||||||
\(529\) | −7.13847 | −0.310368 | ||||||||
\(530\) | −4.32238 | −0.187752 | ||||||||
\(531\) | 3.19467 | 0.138637 | ||||||||
\(532\) | −6.03927 | −0.261836 | ||||||||
\(533\) | −39.9808 | −1.73176 | ||||||||
\(534\) | −34.5785 | −1.49636 | ||||||||
\(535\) | 18.0542 | 0.780550 | ||||||||
\(536\) | 21.2337 | 0.917154 | ||||||||
\(537\) | 28.2532 | 1.21922 | ||||||||
\(538\) | −41.9714 | −1.80952 | ||||||||
\(539\) | 2.13364 | 0.0919024 | ||||||||
\(540\) | −18.7073 | −0.805035 | ||||||||
\(541\) | −15.3379 | −0.659428 | −0.329714 | − | 0.944081i | \(-0.606952\pi\) | ||||
−0.329714 | + | 0.944081i | \(0.606952\pi\) | |||||||
\(542\) | −40.7175 | −1.74897 | ||||||||
\(543\) | 21.9553 | 0.942194 | ||||||||
\(544\) | 34.8322 | 1.49342 | ||||||||
\(545\) | 1.81976 | 0.0779501 | ||||||||
\(546\) | −15.8013 | −0.676235 | ||||||||
\(547\) | 7.37892 | 0.315500 | 0.157750 | − | 0.987479i | \(-0.449576\pi\) | ||||
0.157750 | + | 0.987479i | \(0.449576\pi\) | |||||||
\(548\) | 42.5651 | 1.81829 | ||||||||
\(549\) | −11.4420 | −0.488332 | ||||||||
\(550\) | −4.92149 | −0.209853 | ||||||||
\(551\) | −3.19026 | −0.135910 | ||||||||
\(552\) | 16.2552 | 0.691866 | ||||||||
\(553\) | −4.48655 | −0.190788 | ||||||||
\(554\) | −50.4460 | −2.14324 | ||||||||
\(555\) | −12.2662 | −0.520673 | ||||||||
\(556\) | 25.1992 | 1.06868 | ||||||||
\(557\) | −30.1600 | −1.27792 | −0.638959 | − | 0.769241i | \(-0.720635\pi\) | ||||
−0.638959 | + | 0.769241i | \(0.720635\pi\) | |||||||
\(558\) | −8.13021 | −0.344179 | ||||||||
\(559\) | −10.9402 | −0.462720 | ||||||||
\(560\) | −0.384674 | −0.0162554 | ||||||||
\(561\) | 19.1353 | 0.807894 | ||||||||
\(562\) | −27.3960 | −1.15563 | ||||||||
\(563\) | −34.7175 | −1.46317 | −0.731584 | − | 0.681752i | \(-0.761219\pi\) | ||||
−0.731584 | + | 0.681752i | \(0.761219\pi\) | |||||||
\(564\) | 38.1428 | 1.60610 | ||||||||
\(565\) | 5.19513 | 0.218561 | ||||||||
\(566\) | 54.7292 | 2.30044 | ||||||||
\(567\) | 3.93637 | 0.165312 | ||||||||
\(568\) | −0.433288 | −0.0181804 | ||||||||
\(569\) | 23.4408 | 0.982687 | 0.491344 | − | 0.870966i | \(-0.336506\pi\) | ||||
0.491344 | + | 0.870966i | \(0.336506\pi\) | |||||||
\(570\) | −5.62168 | −0.235466 | ||||||||
\(571\) | −20.8255 | −0.871520 | −0.435760 | − | 0.900063i | \(-0.643520\pi\) | ||||
−0.435760 | + | 0.900063i | \(0.643520\pi\) | |||||||
\(572\) | −36.2187 | −1.51438 | ||||||||
\(573\) | 25.9249 | 1.08303 | ||||||||
\(574\) | 18.0392 | 0.752942 | ||||||||
\(575\) | −3.98265 | −0.166088 | ||||||||
\(576\) | 15.3846 | 0.641027 | ||||||||
\(577\) | 1.69444 | 0.0705406 | 0.0352703 | − | 0.999378i | \(-0.488771\pi\) | ||||
0.0352703 | + | 0.999378i | \(0.488771\pi\) | |||||||
\(578\) | −64.1085 | −2.66656 | ||||||||
\(579\) | 11.9703 | 0.497468 | ||||||||
\(580\) | −5.82434 | −0.241842 | ||||||||
\(581\) | 15.2528 | 0.632793 | ||||||||
\(582\) | 6.64752 | 0.275549 | ||||||||
\(583\) | 3.99823 | 0.165590 | ||||||||
\(584\) | −30.9582 | −1.28106 | ||||||||
\(585\) | 6.15702 | 0.254561 | ||||||||
\(586\) | 73.2158 | 3.02452 | ||||||||
\(587\) | −31.8268 | −1.31363 | −0.656816 | − | 0.754051i | \(-0.728097\pi\) | ||||
−0.656816 | + | 0.754051i | \(0.728097\pi\) | |||||||
\(588\) | 4.44949 | 0.183494 | ||||||||
\(589\) | −5.32289 | −0.219326 | ||||||||
\(590\) | 6.11844 | 0.251892 | ||||||||
\(591\) | −19.8703 | −0.817353 | ||||||||
\(592\) | −3.52124 | −0.144722 | ||||||||
\(593\) | −25.8737 | −1.06251 | −0.531253 | − | 0.847213i | \(-0.678279\pi\) | ||||
−0.531253 | + | 0.847213i | \(0.678279\pi\) | |||||||
\(594\) | 27.7272 | 1.13766 | ||||||||
\(595\) | −6.69278 | −0.274377 | ||||||||
\(596\) | 42.4656 | 1.73946 | ||||||||
\(597\) | 0.259065 | 0.0106028 | ||||||||
\(598\) | −46.9633 | −1.92047 | ||||||||
\(599\) | −2.32211 | −0.0948790 | −0.0474395 | − | 0.998874i | \(-0.515106\pi\) | ||||
−0.0474395 | + | 0.998874i | \(0.515106\pi\) | |||||||
\(600\) | −4.08149 | −0.166626 | ||||||||
\(601\) | 41.7928 | 1.70476 | 0.852382 | − | 0.522919i | \(-0.175157\pi\) | ||||
0.852382 | + | 0.522919i | \(0.175157\pi\) | |||||||
\(602\) | 4.93617 | 0.201183 | ||||||||
\(603\) | 8.39604 | 0.341913 | ||||||||
\(604\) | −60.8712 | −2.47682 | ||||||||
\(605\) | −6.44758 | −0.262131 | ||||||||
\(606\) | 24.6910 | 1.00300 | ||||||||
\(607\) | 7.93106 | 0.321912 | 0.160956 | − | 0.986962i | \(-0.448542\pi\) | ||||
0.160956 | + | 0.986962i | \(0.448542\pi\) | |||||||
\(608\) | 9.46577 | 0.383888 | ||||||||
\(609\) | 2.35046 | 0.0952454 | ||||||||
\(610\) | −21.9137 | −0.887261 | ||||||||
\(611\) | −43.8240 | −1.77293 | ||||||||
\(612\) | −26.7651 | −1.08192 | ||||||||
\(613\) | 1.54597 | 0.0624411 | 0.0312206 | − | 0.999513i | \(-0.490061\pi\) | ||||
0.0312206 | + | 0.999513i | \(0.490061\pi\) | |||||||
\(614\) | −9.72136 | −0.392322 | ||||||||
\(615\) | 10.4797 | 0.422583 | ||||||||
\(616\) | 6.49878 | 0.261843 | ||||||||
\(617\) | 44.2377 | 1.78094 | 0.890471 | − | 0.455040i | \(-0.150375\pi\) | ||||
0.890471 | + | 0.455040i | \(0.150375\pi\) | |||||||
\(618\) | 31.5461 | 1.26897 | ||||||||
\(619\) | −16.0738 | −0.646059 | −0.323029 | − | 0.946389i | \(-0.604701\pi\) | ||||
−0.323029 | + | 0.946389i | \(0.604701\pi\) | |||||||
\(620\) | −9.71779 | −0.390276 | ||||||||
\(621\) | 22.4379 | 0.900401 | ||||||||
\(622\) | 28.4713 | 1.14160 | ||||||||
\(623\) | −11.1872 | −0.448207 | ||||||||
\(624\) | −2.63518 | −0.105492 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.0567 | 0.401946 | ||||||||
\(627\) | 5.20010 | 0.207672 | ||||||||
\(628\) | 15.6258 | 0.623539 | ||||||||
\(629\) | −61.2646 | −2.44278 | ||||||||
\(630\) | −2.77803 | −0.110679 | ||||||||
\(631\) | 15.6480 | 0.622938 | 0.311469 | − | 0.950256i | \(-0.399179\pi\) | ||||
0.311469 | + | 0.950256i | \(0.399179\pi\) | |||||||
\(632\) | −13.6654 | −0.543582 | ||||||||
\(633\) | 15.5255 | 0.617085 | ||||||||
\(634\) | −26.1278 | −1.03767 | ||||||||
\(635\) | −2.89657 | −0.114947 | ||||||||
\(636\) | 8.33792 | 0.330620 | ||||||||
\(637\) | −5.11222 | −0.202554 | ||||||||
\(638\) | 8.63259 | 0.341768 | ||||||||
\(639\) | −0.171327 | −0.00677761 | ||||||||
\(640\) | 19.0559 | 0.753250 | ||||||||
\(641\) | 28.5834 | 1.12898 | 0.564488 | − | 0.825442i | \(-0.309074\pi\) | ||||
0.564488 | + | 0.825442i | \(0.309074\pi\) | |||||||
\(642\) | −55.8035 | −2.20239 | ||||||||
\(643\) | −19.9142 | −0.785338 | −0.392669 | − | 0.919680i | \(-0.628448\pi\) | ||||
−0.392669 | + | 0.919680i | \(0.628448\pi\) | |||||||
\(644\) | 13.2244 | 0.521113 | ||||||||
\(645\) | 2.86763 | 0.112913 | ||||||||
\(646\) | −28.0779 | −1.10471 | ||||||||
\(647\) | 32.5545 | 1.27985 | 0.639924 | − | 0.768438i | \(-0.278966\pi\) | ||||
0.639924 | + | 0.768438i | \(0.278966\pi\) | |||||||
\(648\) | 11.9897 | 0.470999 | ||||||||
\(649\) | −5.65960 | −0.222159 | ||||||||
\(650\) | 11.7919 | 0.462518 | ||||||||
\(651\) | 3.92169 | 0.153703 | ||||||||
\(652\) | 26.4691 | 1.03661 | ||||||||
\(653\) | −13.3877 | −0.523901 | −0.261951 | − | 0.965081i | \(-0.584366\pi\) | ||||
−0.261951 | + | 0.965081i | \(0.584366\pi\) | |||||||
\(654\) | −5.62470 | −0.219943 | ||||||||
\(655\) | −5.92357 | −0.231453 | ||||||||
\(656\) | 3.00839 | 0.117458 | ||||||||
\(657\) | −12.2412 | −0.477575 | ||||||||
\(658\) | 19.7733 | 0.770842 | ||||||||
\(659\) | 25.6259 | 0.998244 | 0.499122 | − | 0.866532i | \(-0.333656\pi\) | ||||
0.499122 | + | 0.866532i | \(0.333656\pi\) | |||||||
\(660\) | 9.49361 | 0.369538 | ||||||||
\(661\) | −3.24804 | −0.126334 | −0.0631671 | − | 0.998003i | \(-0.520120\pi\) | ||||
−0.0631671 | + | 0.998003i | \(0.520120\pi\) | |||||||
\(662\) | −71.5186 | −2.77965 | ||||||||
\(663\) | −45.8484 | −1.78061 | ||||||||
\(664\) | 46.4580 | 1.80292 | ||||||||
\(665\) | −1.81879 | −0.0705296 | ||||||||
\(666\) | −25.4296 | −0.985377 | ||||||||
\(667\) | 6.98581 | 0.270492 | ||||||||
\(668\) | −14.9759 | −0.579436 | ||||||||
\(669\) | 11.1423 | 0.430788 | ||||||||
\(670\) | 16.0801 | 0.621230 | ||||||||
\(671\) | 20.2704 | 0.782529 | ||||||||
\(672\) | −6.97400 | −0.269028 | ||||||||
\(673\) | −22.3938 | −0.863218 | −0.431609 | − | 0.902061i | \(-0.642054\pi\) | ||||
−0.431609 | + | 0.902061i | \(0.642054\pi\) | |||||||
\(674\) | −49.5593 | −1.90895 | ||||||||
\(675\) | −5.63390 | −0.216849 | ||||||||
\(676\) | 43.6141 | 1.67746 | ||||||||
\(677\) | −40.6462 | −1.56216 | −0.781081 | − | 0.624430i | \(-0.785331\pi\) | ||||
−0.781081 | + | 0.624430i | \(0.785331\pi\) | |||||||
\(678\) | −16.0576 | −0.616688 | ||||||||
\(679\) | 2.15068 | 0.0825355 | ||||||||
\(680\) | −20.3853 | −0.781741 | ||||||||
\(681\) | 7.02473 | 0.269188 | ||||||||
\(682\) | 14.4033 | 0.551531 | ||||||||
\(683\) | −25.6084 | −0.979878 | −0.489939 | − | 0.871757i | \(-0.662981\pi\) | ||||
−0.489939 | + | 0.871757i | \(0.662981\pi\) | |||||||
\(684\) | −7.27353 | −0.278110 | ||||||||
\(685\) | 12.8189 | 0.489786 | ||||||||
\(686\) | 2.30662 | 0.0880671 | ||||||||
\(687\) | −1.34001 | −0.0511246 | ||||||||
\(688\) | 0.823203 | 0.0313843 | ||||||||
\(689\) | −9.57981 | −0.364962 | ||||||||
\(690\) | 12.3100 | 0.468632 | ||||||||
\(691\) | 20.6425 | 0.785278 | 0.392639 | − | 0.919693i | \(-0.371562\pi\) | ||||
0.392639 | + | 0.919693i | \(0.371562\pi\) | |||||||
\(692\) | 8.08767 | 0.307447 | ||||||||
\(693\) | 2.56970 | 0.0976146 | ||||||||
\(694\) | 70.0052 | 2.65736 | ||||||||
\(695\) | 7.58899 | 0.287867 | ||||||||
\(696\) | 7.15918 | 0.271368 | ||||||||
\(697\) | 52.3417 | 1.98258 | ||||||||
\(698\) | 24.4567 | 0.925701 | ||||||||
\(699\) | −26.9106 | −1.01785 | ||||||||
\(700\) | −3.32049 | −0.125503 | ||||||||
\(701\) | −30.3761 | −1.14729 | −0.573644 | − | 0.819104i | \(-0.694471\pi\) | ||||
−0.573644 | + | 0.819104i | \(0.694471\pi\) | |||||||
\(702\) | −66.4347 | −2.50742 | ||||||||
\(703\) | −16.6489 | −0.627925 | ||||||||
\(704\) | −27.2551 | −1.02722 | ||||||||
\(705\) | 11.4871 | 0.432630 | ||||||||
\(706\) | −20.5182 | −0.772214 | ||||||||
\(707\) | 7.98830 | 0.300431 | ||||||||
\(708\) | −11.8025 | −0.443567 | ||||||||
\(709\) | −29.0714 | −1.09180 | −0.545900 | − | 0.837850i | \(-0.683812\pi\) | ||||
−0.545900 | + | 0.837850i | \(0.683812\pi\) | |||||||
\(710\) | −0.328127 | −0.0123144 | ||||||||
\(711\) | −5.40348 | −0.202646 | ||||||||
\(712\) | −34.0748 | −1.27701 | ||||||||
\(713\) | 11.6557 | 0.436509 | ||||||||
\(714\) | 20.6867 | 0.774179 | ||||||||
\(715\) | −10.9076 | −0.407923 | ||||||||
\(716\) | 70.0104 | 2.61641 | ||||||||
\(717\) | 28.9567 | 1.08141 | ||||||||
\(718\) | −52.3336 | −1.95307 | ||||||||
\(719\) | −11.2470 | −0.419442 | −0.209721 | − | 0.977761i | \(-0.567255\pi\) | ||||
−0.209721 | + | 0.977761i | \(0.567255\pi\) | |||||||
\(720\) | −0.463291 | −0.0172658 | ||||||||
\(721\) | 10.2062 | 0.380097 | ||||||||
\(722\) | 36.1955 | 1.34706 | ||||||||
\(723\) | 16.8599 | 0.627027 | ||||||||
\(724\) | 54.4044 | 2.02192 | ||||||||
\(725\) | −1.75406 | −0.0651441 | ||||||||
\(726\) | 19.9288 | 0.739627 | ||||||||
\(727\) | −3.02930 | −0.112350 | −0.0561752 | − | 0.998421i | \(-0.517891\pi\) | ||||
−0.0561752 | + | 0.998421i | \(0.517891\pi\) | |||||||
\(728\) | −15.5712 | −0.577105 | ||||||||
\(729\) | 27.3893 | 1.01442 | ||||||||
\(730\) | −23.4444 | −0.867718 | ||||||||
\(731\) | 14.3226 | 0.529739 | ||||||||
\(732\) | 42.2718 | 1.56241 | ||||||||
\(733\) | −40.3539 | −1.49050 | −0.745252 | − | 0.666783i | \(-0.767671\pi\) | ||||
−0.745252 | + | 0.666783i | \(0.767671\pi\) | |||||||
\(734\) | −9.84931 | −0.363545 | ||||||||
\(735\) | 1.34001 | 0.0494270 | ||||||||
\(736\) | −20.7275 | −0.764025 | ||||||||
\(737\) | −14.8742 | −0.547900 | ||||||||
\(738\) | 21.7259 | 0.799741 | ||||||||
\(739\) | 34.9877 | 1.28704 | 0.643521 | − | 0.765429i | \(-0.277473\pi\) | ||||
0.643521 | + | 0.765429i | \(0.277473\pi\) | |||||||
\(740\) | −30.3952 | −1.11735 | ||||||||
\(741\) | −12.4595 | −0.457711 | ||||||||
\(742\) | 4.32238 | 0.158680 | ||||||||
\(743\) | −8.40431 | −0.308324 | −0.154162 | − | 0.988046i | \(-0.549268\pi\) | ||||
−0.154162 | + | 0.988046i | \(0.549268\pi\) | |||||||
\(744\) | 11.9449 | 0.437923 | ||||||||
\(745\) | 12.7889 | 0.468551 | ||||||||
\(746\) | 0.873322 | 0.0319746 | ||||||||
\(747\) | 18.3700 | 0.672125 | ||||||||
\(748\) | 47.4165 | 1.73372 | ||||||||
\(749\) | −18.0542 | −0.659685 | ||||||||
\(750\) | −3.09089 | −0.112863 | ||||||||
\(751\) | 15.7806 | 0.575842 | 0.287921 | − | 0.957654i | \(-0.407036\pi\) | ||||
0.287921 | + | 0.957654i | \(0.407036\pi\) | |||||||
\(752\) | 3.29758 | 0.120250 | ||||||||
\(753\) | −29.1518 | −1.06235 | ||||||||
\(754\) | −20.6838 | −0.753259 | ||||||||
\(755\) | −18.3320 | −0.667170 | ||||||||
\(756\) | 18.7073 | 0.680379 | ||||||||
\(757\) | −23.4198 | −0.851206 | −0.425603 | − | 0.904910i | \(-0.639938\pi\) | ||||
−0.425603 | + | 0.904910i | \(0.639938\pi\) | |||||||
\(758\) | 13.9160 | 0.505454 | ||||||||
\(759\) | −11.3868 | −0.413315 | ||||||||
\(760\) | −5.53979 | −0.200949 | ||||||||
\(761\) | −27.1790 | −0.985237 | −0.492619 | − | 0.870245i | \(-0.663960\pi\) | ||||
−0.492619 | + | 0.870245i | \(0.663960\pi\) | |||||||
\(762\) | 8.95299 | 0.324333 | ||||||||
\(763\) | −1.81976 | −0.0658799 | ||||||||
\(764\) | 64.2409 | 2.32416 | ||||||||
\(765\) | −8.06059 | −0.291431 | ||||||||
\(766\) | 56.4831 | 2.04082 | ||||||||
\(767\) | 13.5605 | 0.489640 | ||||||||
\(768\) | −24.6651 | −0.890025 | ||||||||
\(769\) | −11.4436 | −0.412667 | −0.206334 | − | 0.978482i | \(-0.566153\pi\) | ||||
−0.206334 | + | 0.978482i | \(0.566153\pi\) | |||||||
\(770\) | 4.92149 | 0.177358 | ||||||||
\(771\) | −14.2207 | −0.512148 | ||||||||
\(772\) | 29.6618 | 1.06755 | ||||||||
\(773\) | −18.6610 | −0.671188 | −0.335594 | − | 0.942007i | \(-0.608937\pi\) | ||||
−0.335594 | + | 0.942007i | \(0.608937\pi\) | |||||||
\(774\) | 5.94498 | 0.213688 | ||||||||
\(775\) | −2.92661 | −0.105127 | ||||||||
\(776\) | 6.55069 | 0.235156 | ||||||||
\(777\) | 12.2662 | 0.440049 | ||||||||
\(778\) | −22.4164 | −0.803665 | ||||||||
\(779\) | 14.2241 | 0.509630 | ||||||||
\(780\) | −22.7468 | −0.814466 | ||||||||
\(781\) | 0.303520 | 0.0108608 | ||||||||
\(782\) | 61.4830 | 2.19863 | ||||||||
\(783\) | 9.88220 | 0.353161 | ||||||||
\(784\) | 0.384674 | 0.0137384 | ||||||||
\(785\) | 4.70588 | 0.167960 | ||||||||
\(786\) | 18.3091 | 0.653065 | ||||||||
\(787\) | 37.2693 | 1.32851 | 0.664254 | − | 0.747507i | \(-0.268749\pi\) | ||||
0.664254 | + | 0.747507i | \(0.268749\pi\) | |||||||
\(788\) | −49.2377 | −1.75402 | ||||||||
\(789\) | 26.7654 | 0.952872 | ||||||||
\(790\) | −10.3488 | −0.368193 | ||||||||
\(791\) | −5.19513 | −0.184717 | ||||||||
\(792\) | 7.82695 | 0.278119 | ||||||||
\(793\) | −48.5680 | −1.72470 | ||||||||
\(794\) | 11.5461 | 0.409756 | ||||||||
\(795\) | 2.51105 | 0.0890578 | ||||||||
\(796\) | 0.641951 | 0.0227533 | ||||||||
\(797\) | 36.4354 | 1.29061 | 0.645304 | − | 0.763926i | \(-0.276731\pi\) | ||||
0.645304 | + | 0.763926i | \(0.276731\pi\) | |||||||
\(798\) | 5.62168 | 0.199005 | ||||||||
\(799\) | 57.3732 | 2.02972 | ||||||||
\(800\) | 5.20444 | 0.184005 | ||||||||
\(801\) | −13.4736 | −0.476066 | ||||||||
\(802\) | 7.99312 | 0.282247 | ||||||||
\(803\) | 21.6863 | 0.765292 | ||||||||
\(804\) | −31.0188 | −1.09395 | ||||||||
\(805\) | 3.98265 | 0.140370 | ||||||||
\(806\) | −34.5105 | −1.21558 | ||||||||
\(807\) | 24.3829 | 0.858320 | ||||||||
\(808\) | 24.3313 | 0.855972 | ||||||||
\(809\) | 2.43358 | 0.0855602 | 0.0427801 | − | 0.999085i | \(-0.486379\pi\) | ||||
0.0427801 | + | 0.999085i | \(0.486379\pi\) | |||||||
\(810\) | 9.07971 | 0.319029 | ||||||||
\(811\) | 39.3768 | 1.38271 | 0.691353 | − | 0.722517i | \(-0.257015\pi\) | ||||
0.691353 | + | 0.722517i | \(0.257015\pi\) | |||||||
\(812\) | 5.82434 | 0.204394 | ||||||||
\(813\) | 23.6545 | 0.829598 | ||||||||
\(814\) | 45.0505 | 1.57902 | ||||||||
\(815\) | 7.97144 | 0.279227 | ||||||||
\(816\) | 3.44991 | 0.120771 | ||||||||
\(817\) | 3.89221 | 0.136171 | ||||||||
\(818\) | −57.9665 | −2.02675 | ||||||||
\(819\) | −6.15702 | −0.215144 | ||||||||
\(820\) | 25.9683 | 0.906852 | ||||||||
\(821\) | −16.2534 | −0.567249 | −0.283625 | − | 0.958935i | \(-0.591537\pi\) | ||||
−0.283625 | + | 0.958935i | \(0.591537\pi\) | |||||||
\(822\) | −39.6219 | −1.38197 | ||||||||
\(823\) | 20.1585 | 0.702680 | 0.351340 | − | 0.936248i | \(-0.385726\pi\) | ||||
0.351340 | + | 0.936248i | \(0.385726\pi\) | |||||||
\(824\) | 31.0866 | 1.08295 | ||||||||
\(825\) | 2.85910 | 0.0995411 | ||||||||
\(826\) | −6.11844 | −0.212888 | ||||||||
\(827\) | 41.8891 | 1.45663 | 0.728314 | − | 0.685244i | \(-0.240304\pi\) | ||||
0.728314 | + | 0.685244i | \(0.240304\pi\) | |||||||
\(828\) | 15.9270 | 0.553503 | ||||||||
\(829\) | −11.9814 | −0.416132 | −0.208066 | − | 0.978115i | \(-0.566717\pi\) | ||||
−0.208066 | + | 0.978115i | \(0.566717\pi\) | |||||||
\(830\) | 35.1824 | 1.22120 | ||||||||
\(831\) | 29.3062 | 1.01662 | ||||||||
\(832\) | 65.3035 | 2.26399 | ||||||||
\(833\) | 6.69278 | 0.231891 | ||||||||
\(834\) | −23.4567 | −0.812241 | ||||||||
\(835\) | −4.51016 | −0.156080 | ||||||||
\(836\) | 12.8856 | 0.445659 | ||||||||
\(837\) | 16.4882 | 0.569917 | ||||||||
\(838\) | 23.2553 | 0.803340 | ||||||||
\(839\) | 27.0619 | 0.934282 | 0.467141 | − | 0.884183i | \(-0.345284\pi\) | ||||
0.467141 | + | 0.884183i | \(0.345284\pi\) | |||||||
\(840\) | 4.08149 | 0.140825 | ||||||||
\(841\) | −25.9233 | −0.893906 | ||||||||
\(842\) | 74.5669 | 2.56975 | ||||||||
\(843\) | 15.9155 | 0.548158 | ||||||||
\(844\) | 38.4717 | 1.32425 | ||||||||
\(845\) | 13.1348 | 0.451852 | ||||||||
\(846\) | 23.8144 | 0.818755 | ||||||||
\(847\) | 6.44758 | 0.221542 | ||||||||
\(848\) | 0.720842 | 0.0247538 | ||||||||
\(849\) | −31.7944 | −1.09118 | ||||||||
\(850\) | −15.4377 | −0.529508 | ||||||||
\(851\) | 36.4566 | 1.24971 | ||||||||
\(852\) | 0.632960 | 0.0216849 | ||||||||
\(853\) | 55.5730 | 1.90278 | 0.951391 | − | 0.307984i | \(-0.0996545\pi\) | ||||
0.951391 | + | 0.307984i | \(0.0996545\pi\) | |||||||
\(854\) | 21.9137 | 0.749872 | ||||||||
\(855\) | −2.19050 | −0.0749134 | ||||||||
\(856\) | −54.9906 | −1.87954 | ||||||||
\(857\) | 2.79983 | 0.0956402 | 0.0478201 | − | 0.998856i | \(-0.484773\pi\) | ||||
0.0478201 | + | 0.998856i | \(0.484773\pi\) | |||||||
\(858\) | 33.7144 | 1.15099 | ||||||||
\(859\) | 14.7394 | 0.502902 | 0.251451 | − | 0.967870i | \(-0.419092\pi\) | ||||
0.251451 | + | 0.967870i | \(0.419092\pi\) | |||||||
\(860\) | 7.10586 | 0.242308 | ||||||||
\(861\) | −10.4797 | −0.357148 | ||||||||
\(862\) | −5.46668 | −0.186196 | ||||||||
\(863\) | 13.7773 | 0.468984 | 0.234492 | − | 0.972118i | \(-0.424657\pi\) | ||||
0.234492 | + | 0.972118i | \(0.424657\pi\) | |||||||
\(864\) | −29.3213 | −0.997531 | ||||||||
\(865\) | 2.43568 | 0.0828157 | ||||||||
\(866\) | −86.9073 | −2.95323 | ||||||||
\(867\) | 37.2433 | 1.26485 | ||||||||
\(868\) | 9.71779 | 0.329843 | ||||||||
\(869\) | 9.57269 | 0.324731 | ||||||||
\(870\) | 5.42161 | 0.183810 | ||||||||
\(871\) | 35.6389 | 1.20758 | ||||||||
\(872\) | −5.54276 | −0.187701 | ||||||||
\(873\) | 2.59022 | 0.0876656 | ||||||||
\(874\) | 16.7082 | 0.565165 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 45.2246 | 1.52800 | ||||||||
\(877\) | 34.1222 | 1.15223 | 0.576113 | − | 0.817370i | \(-0.304569\pi\) | ||||
0.576113 | + | 0.817370i | \(0.304569\pi\) | |||||||
\(878\) | −23.1229 | −0.780361 | ||||||||
\(879\) | −42.5341 | −1.43464 | ||||||||
\(880\) | 0.820756 | 0.0276677 | ||||||||
\(881\) | 52.7646 | 1.77768 | 0.888842 | − | 0.458215i | \(-0.151511\pi\) | ||||
0.888842 | + | 0.458215i | \(0.151511\pi\) | |||||||
\(882\) | 2.77803 | 0.0935410 | ||||||||
\(883\) | 1.67074 | 0.0562250 | 0.0281125 | − | 0.999605i | \(-0.491050\pi\) | ||||
0.0281125 | + | 0.999605i | \(0.491050\pi\) | |||||||
\(884\) | −113.611 | −3.82113 | ||||||||
\(885\) | −3.55446 | −0.119482 | ||||||||
\(886\) | 4.25461 | 0.142937 | ||||||||
\(887\) | −8.15940 | −0.273966 | −0.136983 | − | 0.990573i | \(-0.543741\pi\) | ||||
−0.136983 | + | 0.990573i | \(0.543741\pi\) | |||||||
\(888\) | 37.3613 | 1.25376 | ||||||||
\(889\) | 2.89657 | 0.0971478 | ||||||||
\(890\) | −25.8047 | −0.864975 | ||||||||
\(891\) | −8.39880 | −0.281370 | ||||||||
\(892\) | 27.6103 | 0.924460 | ||||||||
\(893\) | 15.5914 | 0.521746 | ||||||||
\(894\) | −39.5293 | −1.32206 | ||||||||
\(895\) | 21.0843 | 0.704772 | ||||||||
\(896\) | −19.0559 | −0.636612 | ||||||||
\(897\) | 27.2829 | 0.910950 | ||||||||
\(898\) | −15.8508 | −0.528949 | ||||||||
\(899\) | 5.13345 | 0.171210 | ||||||||
\(900\) | −3.99910 | −0.133303 | ||||||||
\(901\) | 12.5416 | 0.417822 | ||||||||
\(902\) | −38.4891 | −1.28155 | ||||||||
\(903\) | −2.86763 | −0.0954286 | ||||||||
\(904\) | −15.8237 | −0.526287 | ||||||||
\(905\) | 16.3844 | 0.544638 | ||||||||
\(906\) | 56.6623 | 1.88248 | ||||||||
\(907\) | 43.3624 | 1.43982 | 0.719912 | − | 0.694065i | \(-0.244182\pi\) | ||||
0.719912 | + | 0.694065i | \(0.244182\pi\) | |||||||
\(908\) | 17.4070 | 0.577671 | ||||||||
\(909\) | 9.62088 | 0.319105 | ||||||||
\(910\) | −11.7919 | −0.390899 | ||||||||
\(911\) | 49.1852 | 1.62958 | 0.814789 | − | 0.579758i | \(-0.196853\pi\) | ||||
0.814789 | + | 0.579758i | \(0.196853\pi\) | |||||||
\(912\) | 0.937526 | 0.0310446 | ||||||||
\(913\) | −32.5440 | −1.07705 | ||||||||
\(914\) | 7.83430 | 0.259136 | ||||||||
\(915\) | 12.7306 | 0.420861 | ||||||||
\(916\) | −3.32049 | −0.109712 | ||||||||
\(917\) | 5.92357 | 0.195614 | ||||||||
\(918\) | 86.9744 | 2.87058 | ||||||||
\(919\) | −39.9475 | −1.31775 | −0.658873 | − | 0.752254i | \(-0.728967\pi\) | ||||
−0.658873 | + | 0.752254i | \(0.728967\pi\) | |||||||
\(920\) | 12.1306 | 0.399935 | ||||||||
\(921\) | 5.64754 | 0.186093 | ||||||||
\(922\) | 3.15576 | 0.103929 | ||||||||
\(923\) | −0.727237 | −0.0239373 | ||||||||
\(924\) | −9.49361 | −0.312317 | ||||||||
\(925\) | −9.15383 | −0.300976 | ||||||||
\(926\) | −27.0009 | −0.887304 | ||||||||
\(927\) | 12.2920 | 0.403722 | ||||||||
\(928\) | −9.12889 | −0.299671 | ||||||||
\(929\) | 31.4181 | 1.03080 | 0.515398 | − | 0.856951i | \(-0.327644\pi\) | ||||
0.515398 | + | 0.856951i | \(0.327644\pi\) | |||||||
\(930\) | 9.04585 | 0.296625 | ||||||||
\(931\) | 1.81879 | 0.0596084 | ||||||||
\(932\) | −66.6833 | −2.18429 | ||||||||
\(933\) | −16.5402 | −0.541501 | ||||||||
\(934\) | −46.9751 | −1.53707 | ||||||||
\(935\) | 14.2800 | 0.467005 | ||||||||
\(936\) | −18.7535 | −0.612976 | ||||||||
\(937\) | 1.23159 | 0.0402342 | 0.0201171 | − | 0.999798i | \(-0.493596\pi\) | ||||
0.0201171 | + | 0.999798i | \(0.493596\pi\) | |||||||
\(938\) | −16.0801 | −0.525035 | ||||||||
\(939\) | −5.84235 | −0.190658 | ||||||||
\(940\) | 28.4646 | 0.928412 | ||||||||
\(941\) | 21.6748 | 0.706579 | 0.353289 | − | 0.935514i | \(-0.385063\pi\) | ||||
0.353289 | + | 0.935514i | \(0.385063\pi\) | |||||||
\(942\) | −14.5454 | −0.473914 | ||||||||
\(943\) | −31.1468 | −1.01428 | ||||||||
\(944\) | −1.02037 | −0.0332102 | ||||||||
\(945\) | 5.63390 | 0.183271 | ||||||||
\(946\) | −10.5320 | −0.342425 | ||||||||
\(947\) | −6.97102 | −0.226528 | −0.113264 | − | 0.993565i | \(-0.536131\pi\) | ||||
−0.113264 | + | 0.993565i | \(0.536131\pi\) | |||||||
\(948\) | 19.9629 | 0.648364 | ||||||||
\(949\) | −51.9606 | −1.68671 | ||||||||
\(950\) | −4.19525 | −0.136112 | ||||||||
\(951\) | 15.1787 | 0.492203 | ||||||||
\(952\) | 20.3853 | 0.660692 | ||||||||
\(953\) | −32.6424 | −1.05739 | −0.528696 | − | 0.848811i | \(-0.677319\pi\) | ||||
−0.528696 | + | 0.848811i | \(0.677319\pi\) | |||||||
\(954\) | 5.20575 | 0.168542 | ||||||||
\(955\) | 19.3468 | 0.626049 | ||||||||
\(956\) | 71.7534 | 2.32067 | ||||||||
\(957\) | −5.01503 | −0.162113 | ||||||||
\(958\) | −15.2154 | −0.491587 | ||||||||
\(959\) | −12.8189 | −0.413944 | ||||||||
\(960\) | −17.1173 | −0.552458 | ||||||||
\(961\) | −22.4349 | −0.723708 | ||||||||
\(962\) | −107.942 | −3.48018 | ||||||||
\(963\) | −21.7439 | −0.700688 | ||||||||
\(964\) | 41.7782 | 1.34558 | ||||||||
\(965\) | 8.93297 | 0.287563 | ||||||||
\(966\) | −12.3100 | −0.396066 | ||||||||
\(967\) | −25.2873 | −0.813183 | −0.406592 | − | 0.913610i | \(-0.633283\pi\) | ||||
−0.406592 | + | 0.913610i | \(0.633283\pi\) | |||||||
\(968\) | 19.6385 | 0.631205 | ||||||||
\(969\) | 16.3116 | 0.524005 | ||||||||
\(970\) | 4.96080 | 0.159282 | ||||||||
\(971\) | 9.07379 | 0.291192 | 0.145596 | − | 0.989344i | \(-0.453490\pi\) | ||||
0.145596 | + | 0.989344i | \(0.453490\pi\) | |||||||
\(972\) | 38.6071 | 1.23832 | ||||||||
\(973\) | −7.58899 | −0.243292 | ||||||||
\(974\) | −73.9965 | −2.37100 | ||||||||
\(975\) | −6.85043 | −0.219389 | ||||||||
\(976\) | 3.65455 | 0.116979 | ||||||||
\(977\) | 52.2123 | 1.67042 | 0.835210 | − | 0.549932i | \(-0.185346\pi\) | ||||
0.835210 | + | 0.549932i | \(0.185346\pi\) | |||||||
\(978\) | −24.6389 | −0.787864 | ||||||||
\(979\) | 23.8695 | 0.762873 | ||||||||
\(980\) | 3.32049 | 0.106069 | ||||||||
\(981\) | −2.19167 | −0.0699747 | ||||||||
\(982\) | 28.6830 | 0.915311 | ||||||||
\(983\) | −54.7691 | −1.74686 | −0.873432 | − | 0.486946i | \(-0.838111\pi\) | ||||
−0.873432 | + | 0.486946i | \(0.838111\pi\) | |||||||
\(984\) | −31.9198 | −1.01757 | ||||||||
\(985\) | −14.8284 | −0.472473 | ||||||||
\(986\) | 27.0786 | 0.862359 | ||||||||
\(987\) | −11.4871 | −0.365639 | ||||||||
\(988\) | −30.8741 | −0.982236 | ||||||||
\(989\) | −8.52289 | −0.271012 | ||||||||
\(990\) | 5.92731 | 0.188382 | ||||||||
\(991\) | 10.5226 | 0.334261 | 0.167130 | − | 0.985935i | \(-0.446550\pi\) | ||||
0.167130 | + | 0.985935i | \(0.446550\pi\) | |||||||
\(992\) | −15.2314 | −0.483596 | ||||||||
\(993\) | 41.5481 | 1.31849 | ||||||||
\(994\) | 0.328127 | 0.0104076 | ||||||||
\(995\) | 0.193330 | 0.00612898 | ||||||||
\(996\) | −67.8672 | −2.15045 | ||||||||
\(997\) | −28.9360 | −0.916412 | −0.458206 | − | 0.888846i | \(-0.651508\pi\) | ||||
−0.458206 | + | 0.888846i | \(0.651508\pi\) | |||||||
\(998\) | 19.4108 | 0.614438 | ||||||||
\(999\) | 51.5718 | 1.63166 |
(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.m.1.8 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.m.1.8 | ✓ | 67 | 1.1 | even | 1 | trivial |