Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.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: | \(63.9282318582\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.10040 | −1.21267 | −0.606333 | − | 0.795211i | \(-0.707360\pi\) | ||||
−0.606333 | + | 0.795211i | \(0.707360\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.571471 | −0.255570 | −0.127785 | − | 0.991802i | \(-0.540787\pi\) | ||||
−0.127785 | + | 0.991802i | \(0.540787\pi\) | |||||||
\(6\) | −2.10040 | −0.857484 | ||||||||
\(7\) | 3.01756 | 1.14053 | 0.570265 | − | 0.821461i | \(-0.306840\pi\) | ||||
0.570265 | + | 0.821461i | \(0.306840\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.41167 | 0.470557 | ||||||||
\(10\) | −0.571471 | −0.180715 | ||||||||
\(11\) | −1.18938 | −0.358611 | −0.179305 | − | 0.983793i | \(-0.557385\pi\) | ||||
−0.179305 | + | 0.983793i | \(0.557385\pi\) | |||||||
\(12\) | −2.10040 | −0.606333 | ||||||||
\(13\) | −5.61973 | −1.55863 | −0.779316 | − | 0.626631i | \(-0.784433\pi\) | ||||
−0.779316 | + | 0.626631i | \(0.784433\pi\) | |||||||
\(14\) | 3.01756 | 0.806477 | ||||||||
\(15\) | 1.20032 | 0.309920 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.461237 | −0.111866 | −0.0559332 | − | 0.998435i | \(-0.517813\pi\) | ||||
−0.0559332 | + | 0.998435i | \(0.517813\pi\) | |||||||
\(18\) | 1.41167 | 0.332734 | ||||||||
\(19\) | 2.18243 | 0.500685 | 0.250342 | − | 0.968157i | \(-0.419457\pi\) | ||||
0.250342 | + | 0.968157i | \(0.419457\pi\) | |||||||
\(20\) | −0.571471 | −0.127785 | ||||||||
\(21\) | −6.33808 | −1.38308 | ||||||||
\(22\) | −1.18938 | −0.253576 | ||||||||
\(23\) | 0.111126 | 0.0231713 | 0.0115856 | − | 0.999933i | \(-0.496312\pi\) | ||||
0.0115856 | + | 0.999933i | \(0.496312\pi\) | |||||||
\(24\) | −2.10040 | −0.428742 | ||||||||
\(25\) | −4.67342 | −0.934684 | ||||||||
\(26\) | −5.61973 | −1.10212 | ||||||||
\(27\) | 3.33612 | 0.642037 | ||||||||
\(28\) | 3.01756 | 0.570265 | ||||||||
\(29\) | 3.20738 | 0.595595 | 0.297798 | − | 0.954629i | \(-0.403748\pi\) | ||||
0.297798 | + | 0.954629i | \(0.403748\pi\) | |||||||
\(30\) | 1.20032 | 0.219147 | ||||||||
\(31\) | 10.6915 | 1.92025 | 0.960125 | − | 0.279572i | \(-0.0901924\pi\) | ||||
0.960125 | + | 0.279572i | \(0.0901924\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.49816 | 0.434875 | ||||||||
\(34\) | −0.461237 | −0.0791015 | ||||||||
\(35\) | −1.72445 | −0.291485 | ||||||||
\(36\) | 1.41167 | 0.235278 | ||||||||
\(37\) | −2.75061 | −0.452197 | −0.226099 | − | 0.974104i | \(-0.572597\pi\) | ||||
−0.226099 | + | 0.974104i | \(0.572597\pi\) | |||||||
\(38\) | 2.18243 | 0.354038 | ||||||||
\(39\) | 11.8037 | 1.89010 | ||||||||
\(40\) | −0.571471 | −0.0903575 | ||||||||
\(41\) | −3.60037 | −0.562283 | −0.281142 | − | 0.959666i | \(-0.590713\pi\) | ||||
−0.281142 | + | 0.959666i | \(0.590713\pi\) | |||||||
\(42\) | −6.33808 | −0.977986 | ||||||||
\(43\) | 3.85351 | 0.587655 | 0.293828 | − | 0.955858i | \(-0.405071\pi\) | ||||
0.293828 | + | 0.955858i | \(0.405071\pi\) | |||||||
\(44\) | −1.18938 | −0.179305 | ||||||||
\(45\) | −0.806729 | −0.120260 | ||||||||
\(46\) | 0.111126 | 0.0163846 | ||||||||
\(47\) | −2.93386 | −0.427948 | −0.213974 | − | 0.976839i | \(-0.568641\pi\) | ||||
−0.213974 | + | 0.976839i | \(0.568641\pi\) | |||||||
\(48\) | −2.10040 | −0.303166 | ||||||||
\(49\) | 2.10567 | 0.300810 | ||||||||
\(50\) | −4.67342 | −0.660922 | ||||||||
\(51\) | 0.968781 | 0.135656 | ||||||||
\(52\) | −5.61973 | −0.779316 | ||||||||
\(53\) | −8.95066 | −1.22947 | −0.614734 | − | 0.788735i | \(-0.710736\pi\) | ||||
−0.614734 | + | 0.788735i | \(0.710736\pi\) | |||||||
\(54\) | 3.33612 | 0.453989 | ||||||||
\(55\) | 0.679695 | 0.0916500 | ||||||||
\(56\) | 3.01756 | 0.403238 | ||||||||
\(57\) | −4.58398 | −0.607163 | ||||||||
\(58\) | 3.20738 | 0.421150 | ||||||||
\(59\) | 12.8394 | 1.67154 | 0.835772 | − | 0.549076i | \(-0.185020\pi\) | ||||
0.835772 | + | 0.549076i | \(0.185020\pi\) | |||||||
\(60\) | 1.20032 | 0.154960 | ||||||||
\(61\) | −1.89738 | −0.242935 | −0.121467 | − | 0.992595i | \(-0.538760\pi\) | ||||
−0.121467 | + | 0.992595i | \(0.538760\pi\) | |||||||
\(62\) | 10.6915 | 1.35782 | ||||||||
\(63\) | 4.25980 | 0.536684 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.21151 | 0.398339 | ||||||||
\(66\) | 2.49816 | 0.307503 | ||||||||
\(67\) | 0.845266 | 0.103266 | 0.0516329 | − | 0.998666i | \(-0.483557\pi\) | ||||
0.0516329 | + | 0.998666i | \(0.483557\pi\) | |||||||
\(68\) | −0.461237 | −0.0559332 | ||||||||
\(69\) | −0.233408 | −0.0280990 | ||||||||
\(70\) | −1.72445 | −0.206111 | ||||||||
\(71\) | −9.80424 | −1.16355 | −0.581775 | − | 0.813350i | \(-0.697642\pi\) | ||||
−0.581775 | + | 0.813350i | \(0.697642\pi\) | |||||||
\(72\) | 1.41167 | 0.166367 | ||||||||
\(73\) | −7.90337 | −0.925020 | −0.462510 | − | 0.886614i | \(-0.653051\pi\) | ||||
−0.462510 | + | 0.886614i | \(0.653051\pi\) | |||||||
\(74\) | −2.75061 | −0.319752 | ||||||||
\(75\) | 9.81604 | 1.13346 | ||||||||
\(76\) | 2.18243 | 0.250342 | ||||||||
\(77\) | −3.58902 | −0.409006 | ||||||||
\(78\) | 11.8037 | 1.33650 | ||||||||
\(79\) | −1.47331 | −0.165760 | −0.0828800 | − | 0.996560i | \(-0.526412\pi\) | ||||
−0.0828800 | + | 0.996560i | \(0.526412\pi\) | |||||||
\(80\) | −0.571471 | −0.0638924 | ||||||||
\(81\) | −11.2422 | −1.24913 | ||||||||
\(82\) | −3.60037 | −0.397594 | ||||||||
\(83\) | −7.00283 | −0.768660 | −0.384330 | − | 0.923196i | \(-0.625568\pi\) | ||||
−0.384330 | + | 0.923196i | \(0.625568\pi\) | |||||||
\(84\) | −6.33808 | −0.691541 | ||||||||
\(85\) | 0.263584 | 0.0285897 | ||||||||
\(86\) | 3.85351 | 0.415535 | ||||||||
\(87\) | −6.73677 | −0.722258 | ||||||||
\(88\) | −1.18938 | −0.126788 | ||||||||
\(89\) | −16.8609 | −1.78725 | −0.893626 | − | 0.448812i | \(-0.851847\pi\) | ||||
−0.893626 | + | 0.448812i | \(0.851847\pi\) | |||||||
\(90\) | −0.806729 | −0.0850367 | ||||||||
\(91\) | −16.9579 | −1.77767 | ||||||||
\(92\) | 0.111126 | 0.0115856 | ||||||||
\(93\) | −22.4564 | −2.32862 | ||||||||
\(94\) | −2.93386 | −0.302605 | ||||||||
\(95\) | −1.24720 | −0.127960 | ||||||||
\(96\) | −2.10040 | −0.214371 | ||||||||
\(97\) | −12.0645 | −1.22496 | −0.612481 | − | 0.790485i | \(-0.709828\pi\) | ||||
−0.612481 | + | 0.790485i | \(0.709828\pi\) | |||||||
\(98\) | 2.10567 | 0.212705 | ||||||||
\(99\) | −1.67901 | −0.168747 | ||||||||
\(100\) | −4.67342 | −0.467342 | ||||||||
\(101\) | 3.12601 | 0.311050 | 0.155525 | − | 0.987832i | \(-0.450293\pi\) | ||||
0.155525 | + | 0.987832i | \(0.450293\pi\) | |||||||
\(102\) | 0.968781 | 0.0959236 | ||||||||
\(103\) | 15.3458 | 1.51207 | 0.756033 | − | 0.654533i | \(-0.227135\pi\) | ||||
0.756033 | + | 0.654533i | \(0.227135\pi\) | |||||||
\(104\) | −5.61973 | −0.551060 | ||||||||
\(105\) | 3.62203 | 0.353474 | ||||||||
\(106\) | −8.95066 | −0.869364 | ||||||||
\(107\) | 16.8821 | 1.63205 | 0.816025 | − | 0.578016i | \(-0.196173\pi\) | ||||
0.816025 | + | 0.578016i | \(0.196173\pi\) | |||||||
\(108\) | 3.33612 | 0.321019 | ||||||||
\(109\) | −4.32579 | −0.414335 | −0.207168 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207168 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(110\) | 0.679695 | 0.0648063 | ||||||||
\(111\) | 5.77737 | 0.548364 | ||||||||
\(112\) | 3.01756 | 0.285133 | ||||||||
\(113\) | 6.63395 | 0.624070 | 0.312035 | − | 0.950071i | \(-0.398989\pi\) | ||||
0.312035 | + | 0.950071i | \(0.398989\pi\) | |||||||
\(114\) | −4.58398 | −0.429329 | ||||||||
\(115\) | −0.0635051 | −0.00592188 | ||||||||
\(116\) | 3.20738 | 0.297798 | ||||||||
\(117\) | −7.93320 | −0.733425 | ||||||||
\(118\) | 12.8394 | 1.18196 | ||||||||
\(119\) | −1.39181 | −0.127587 | ||||||||
\(120\) | 1.20032 | 0.109573 | ||||||||
\(121\) | −9.58538 | −0.871398 | ||||||||
\(122\) | −1.89738 | −0.171781 | ||||||||
\(123\) | 7.56221 | 0.681862 | ||||||||
\(124\) | 10.6915 | 0.960125 | ||||||||
\(125\) | 5.52808 | 0.494447 | ||||||||
\(126\) | 4.25980 | 0.379493 | ||||||||
\(127\) | −10.1188 | −0.897902 | −0.448951 | − | 0.893556i | \(-0.648202\pi\) | ||||
−0.448951 | + | 0.893556i | \(0.648202\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.09391 | −0.712629 | ||||||||
\(130\) | 3.21151 | 0.281668 | ||||||||
\(131\) | 1.88162 | 0.164398 | 0.0821988 | − | 0.996616i | \(-0.473806\pi\) | ||||
0.0821988 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(132\) | 2.49816 | 0.217437 | ||||||||
\(133\) | 6.58562 | 0.571046 | ||||||||
\(134\) | 0.845266 | 0.0730199 | ||||||||
\(135\) | −1.90650 | −0.164085 | ||||||||
\(136\) | −0.461237 | −0.0395507 | ||||||||
\(137\) | 17.6989 | 1.51212 | 0.756060 | − | 0.654502i | \(-0.227122\pi\) | ||||
0.756060 | + | 0.654502i | \(0.227122\pi\) | |||||||
\(138\) | −0.233408 | −0.0198690 | ||||||||
\(139\) | −14.8737 | −1.26157 | −0.630784 | − | 0.775958i | \(-0.717267\pi\) | ||||
−0.630784 | + | 0.775958i | \(0.717267\pi\) | |||||||
\(140\) | −1.72445 | −0.145742 | ||||||||
\(141\) | 6.16228 | 0.518958 | ||||||||
\(142\) | −9.80424 | −0.822754 | ||||||||
\(143\) | 6.68397 | 0.558942 | ||||||||
\(144\) | 1.41167 | 0.117639 | ||||||||
\(145\) | −1.83292 | −0.152216 | ||||||||
\(146\) | −7.90337 | −0.654088 | ||||||||
\(147\) | −4.42274 | −0.364782 | ||||||||
\(148\) | −2.75061 | −0.226099 | ||||||||
\(149\) | 18.7464 | 1.53576 | 0.767882 | − | 0.640592i | \(-0.221311\pi\) | ||||
0.767882 | + | 0.640592i | \(0.221311\pi\) | |||||||
\(150\) | 9.81604 | 0.801476 | ||||||||
\(151\) | −20.4397 | −1.66336 | −0.831680 | − | 0.555256i | \(-0.812620\pi\) | ||||
−0.831680 | + | 0.555256i | \(0.812620\pi\) | |||||||
\(152\) | 2.18243 | 0.177019 | ||||||||
\(153\) | −0.651114 | −0.0526395 | ||||||||
\(154\) | −3.58902 | −0.289211 | ||||||||
\(155\) | −6.10988 | −0.490758 | ||||||||
\(156\) | 11.8037 | 0.945049 | ||||||||
\(157\) | 1.38318 | 0.110390 | 0.0551948 | − | 0.998476i | \(-0.482422\pi\) | ||||
0.0551948 | + | 0.998476i | \(0.482422\pi\) | |||||||
\(158\) | −1.47331 | −0.117210 | ||||||||
\(159\) | 18.7999 | 1.49093 | ||||||||
\(160\) | −0.571471 | −0.0451788 | ||||||||
\(161\) | 0.335328 | 0.0264276 | ||||||||
\(162\) | −11.2422 | −0.883270 | ||||||||
\(163\) | 10.4329 | 0.817165 | 0.408582 | − | 0.912721i | \(-0.366023\pi\) | ||||
0.408582 | + | 0.912721i | \(0.366023\pi\) | |||||||
\(164\) | −3.60037 | −0.281142 | ||||||||
\(165\) | −1.42763 | −0.111141 | ||||||||
\(166\) | −7.00283 | −0.543525 | ||||||||
\(167\) | 2.57038 | 0.198902 | 0.0994512 | − | 0.995042i | \(-0.468291\pi\) | ||||
0.0994512 | + | 0.995042i | \(0.468291\pi\) | |||||||
\(168\) | −6.33808 | −0.488993 | ||||||||
\(169\) | 18.5813 | 1.42933 | ||||||||
\(170\) | 0.263584 | 0.0202159 | ||||||||
\(171\) | 3.08088 | 0.235600 | ||||||||
\(172\) | 3.85351 | 0.293828 | ||||||||
\(173\) | −2.17575 | −0.165419 | −0.0827094 | − | 0.996574i | \(-0.526357\pi\) | ||||
−0.0827094 | + | 0.996574i | \(0.526357\pi\) | |||||||
\(174\) | −6.73677 | −0.510713 | ||||||||
\(175\) | −14.1023 | −1.06604 | ||||||||
\(176\) | −1.18938 | −0.0896527 | ||||||||
\(177\) | −26.9678 | −2.02702 | ||||||||
\(178\) | −16.8609 | −1.26378 | ||||||||
\(179\) | −21.0627 | −1.57430 | −0.787151 | − | 0.616761i | \(-0.788445\pi\) | ||||
−0.787151 | + | 0.616761i | \(0.788445\pi\) | |||||||
\(180\) | −0.806729 | −0.0601300 | ||||||||
\(181\) | −10.3419 | −0.768704 | −0.384352 | − | 0.923187i | \(-0.625575\pi\) | ||||
−0.384352 | + | 0.923187i | \(0.625575\pi\) | |||||||
\(182\) | −16.9579 | −1.25700 | ||||||||
\(183\) | 3.98526 | 0.294599 | ||||||||
\(184\) | 0.111126 | 0.00819229 | ||||||||
\(185\) | 1.57189 | 0.115568 | ||||||||
\(186\) | −22.4564 | −1.64658 | ||||||||
\(187\) | 0.548585 | 0.0401165 | ||||||||
\(188\) | −2.93386 | −0.213974 | ||||||||
\(189\) | 10.0670 | 0.732263 | ||||||||
\(190\) | −1.24720 | −0.0904812 | ||||||||
\(191\) | 0.655753 | 0.0474486 | 0.0237243 | − | 0.999719i | \(-0.492448\pi\) | ||||
0.0237243 | + | 0.999719i | \(0.492448\pi\) | |||||||
\(192\) | −2.10040 | −0.151583 | ||||||||
\(193\) | 2.17573 | 0.156613 | 0.0783063 | − | 0.996929i | \(-0.475049\pi\) | ||||
0.0783063 | + | 0.996929i | \(0.475049\pi\) | |||||||
\(194\) | −12.0645 | −0.866179 | ||||||||
\(195\) | −6.74545 | −0.483052 | ||||||||
\(196\) | 2.10567 | 0.150405 | ||||||||
\(197\) | 1.28802 | 0.0917673 | 0.0458837 | − | 0.998947i | \(-0.485390\pi\) | ||||
0.0458837 | + | 0.998947i | \(0.485390\pi\) | |||||||
\(198\) | −1.67901 | −0.119322 | ||||||||
\(199\) | −19.2438 | −1.36416 | −0.682079 | − | 0.731279i | \(-0.738924\pi\) | ||||
−0.682079 | + | 0.731279i | \(0.738924\pi\) | |||||||
\(200\) | −4.67342 | −0.330461 | ||||||||
\(201\) | −1.77540 | −0.125227 | ||||||||
\(202\) | 3.12601 | 0.219946 | ||||||||
\(203\) | 9.67846 | 0.679295 | ||||||||
\(204\) | 0.968781 | 0.0678282 | ||||||||
\(205\) | 2.05751 | 0.143703 | ||||||||
\(206\) | 15.3458 | 1.06919 | ||||||||
\(207\) | 0.156873 | 0.0109034 | ||||||||
\(208\) | −5.61973 | −0.389658 | ||||||||
\(209\) | −2.59574 | −0.179551 | ||||||||
\(210\) | 3.62203 | 0.249944 | ||||||||
\(211\) | −1.76956 | −0.121822 | −0.0609108 | − | 0.998143i | \(-0.519401\pi\) | ||||
−0.0609108 | + | 0.998143i | \(0.519401\pi\) | |||||||
\(212\) | −8.95066 | −0.614734 | ||||||||
\(213\) | 20.5928 | 1.41100 | ||||||||
\(214\) | 16.8821 | 1.15403 | ||||||||
\(215\) | −2.20217 | −0.150187 | ||||||||
\(216\) | 3.33612 | 0.226995 | ||||||||
\(217\) | 32.2622 | 2.19010 | ||||||||
\(218\) | −4.32579 | −0.292979 | ||||||||
\(219\) | 16.6002 | 1.12174 | ||||||||
\(220\) | 0.679695 | 0.0458250 | ||||||||
\(221\) | 2.59203 | 0.174359 | ||||||||
\(222\) | 5.77737 | 0.387752 | ||||||||
\(223\) | −12.4006 | −0.830406 | −0.415203 | − | 0.909729i | \(-0.636289\pi\) | ||||
−0.415203 | + | 0.909729i | \(0.636289\pi\) | |||||||
\(224\) | 3.01756 | 0.201619 | ||||||||
\(225\) | −6.59733 | −0.439822 | ||||||||
\(226\) | 6.63395 | 0.441284 | ||||||||
\(227\) | 3.76542 | 0.249920 | 0.124960 | − | 0.992162i | \(-0.460120\pi\) | ||||
0.124960 | + | 0.992162i | \(0.460120\pi\) | |||||||
\(228\) | −4.58398 | −0.303581 | ||||||||
\(229\) | 17.4343 | 1.15209 | 0.576044 | − | 0.817419i | \(-0.304596\pi\) | ||||
0.576044 | + | 0.817419i | \(0.304596\pi\) | |||||||
\(230\) | −0.0635051 | −0.00418740 | ||||||||
\(231\) | 7.53836 | 0.495988 | ||||||||
\(232\) | 3.20738 | 0.210575 | ||||||||
\(233\) | 5.72024 | 0.374745 | 0.187373 | − | 0.982289i | \(-0.440003\pi\) | ||||
0.187373 | + | 0.982289i | \(0.440003\pi\) | |||||||
\(234\) | −7.93320 | −0.518610 | ||||||||
\(235\) | 1.67662 | 0.109371 | ||||||||
\(236\) | 12.8394 | 0.835772 | ||||||||
\(237\) | 3.09453 | 0.201011 | ||||||||
\(238\) | −1.39181 | −0.0902176 | ||||||||
\(239\) | −0.915196 | −0.0591991 | −0.0295996 | − | 0.999562i | \(-0.509423\pi\) | ||||
−0.0295996 | + | 0.999562i | \(0.509423\pi\) | |||||||
\(240\) | 1.20032 | 0.0774801 | ||||||||
\(241\) | −8.57289 | −0.552228 | −0.276114 | − | 0.961125i | \(-0.589047\pi\) | ||||
−0.276114 | + | 0.961125i | \(0.589047\pi\) | |||||||
\(242\) | −9.58538 | −0.616172 | ||||||||
\(243\) | 13.6047 | 0.872743 | ||||||||
\(244\) | −1.89738 | −0.121467 | ||||||||
\(245\) | −1.20333 | −0.0768779 | ||||||||
\(246\) | 7.56221 | 0.482149 | ||||||||
\(247\) | −12.2647 | −0.780383 | ||||||||
\(248\) | 10.6915 | 0.678911 | ||||||||
\(249\) | 14.7087 | 0.932128 | ||||||||
\(250\) | 5.52808 | 0.349627 | ||||||||
\(251\) | −4.67991 | −0.295393 | −0.147697 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147697 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(252\) | 4.25980 | 0.268342 | ||||||||
\(253\) | −0.132170 | −0.00830947 | ||||||||
\(254\) | −10.1188 | −0.634913 | ||||||||
\(255\) | −0.553630 | −0.0346697 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.2913 | −1.57763 | −0.788813 | − | 0.614634i | \(-0.789304\pi\) | ||||
−0.788813 | + | 0.614634i | \(0.789304\pi\) | |||||||
\(258\) | −8.09391 | −0.503905 | ||||||||
\(259\) | −8.30012 | −0.515745 | ||||||||
\(260\) | 3.21151 | 0.199170 | ||||||||
\(261\) | 4.52776 | 0.280261 | ||||||||
\(262\) | 1.88162 | 0.116247 | ||||||||
\(263\) | −18.0309 | −1.11183 | −0.555917 | − | 0.831238i | \(-0.687633\pi\) | ||||
−0.555917 | + | 0.831238i | \(0.687633\pi\) | |||||||
\(264\) | 2.49816 | 0.153751 | ||||||||
\(265\) | 5.11504 | 0.314214 | ||||||||
\(266\) | 6.58562 | 0.403791 | ||||||||
\(267\) | 35.4146 | 2.16734 | ||||||||
\(268\) | 0.845266 | 0.0516329 | ||||||||
\(269\) | −7.97505 | −0.486247 | −0.243124 | − | 0.969995i | \(-0.578172\pi\) | ||||
−0.243124 | + | 0.969995i | \(0.578172\pi\) | |||||||
\(270\) | −1.90650 | −0.116026 | ||||||||
\(271\) | −29.9244 | −1.81778 | −0.908890 | − | 0.417037i | \(-0.863069\pi\) | ||||
−0.908890 | + | 0.417037i | \(0.863069\pi\) | |||||||
\(272\) | −0.461237 | −0.0279666 | ||||||||
\(273\) | 35.6183 | 2.15572 | ||||||||
\(274\) | 17.6989 | 1.06923 | ||||||||
\(275\) | 5.55846 | 0.335188 | ||||||||
\(276\) | −0.233408 | −0.0140495 | ||||||||
\(277\) | −14.1989 | −0.853129 | −0.426564 | − | 0.904457i | \(-0.640276\pi\) | ||||
−0.426564 | + | 0.904457i | \(0.640276\pi\) | |||||||
\(278\) | −14.8737 | −0.892063 | ||||||||
\(279\) | 15.0929 | 0.903586 | ||||||||
\(280\) | −1.72445 | −0.103056 | ||||||||
\(281\) | −25.5686 | −1.52529 | −0.762647 | − | 0.646815i | \(-0.776100\pi\) | ||||
−0.762647 | + | 0.646815i | \(0.776100\pi\) | |||||||
\(282\) | 6.16228 | 0.366958 | ||||||||
\(283\) | −5.66128 | −0.336528 | −0.168264 | − | 0.985742i | \(-0.553816\pi\) | ||||
−0.168264 | + | 0.985742i | \(0.553816\pi\) | |||||||
\(284\) | −9.80424 | −0.581775 | ||||||||
\(285\) | 2.61961 | 0.155172 | ||||||||
\(286\) | 6.68397 | 0.395232 | ||||||||
\(287\) | −10.8643 | −0.641301 | ||||||||
\(288\) | 1.41167 | 0.0831834 | ||||||||
\(289\) | −16.7873 | −0.987486 | ||||||||
\(290\) | −1.83292 | −0.107633 | ||||||||
\(291\) | 25.3402 | 1.48547 | ||||||||
\(292\) | −7.90337 | −0.462510 | ||||||||
\(293\) | 32.9911 | 1.92736 | 0.963680 | − | 0.267058i | \(-0.0860516\pi\) | ||||
0.963680 | + | 0.267058i | \(0.0860516\pi\) | |||||||
\(294\) | −4.42274 | −0.257939 | ||||||||
\(295\) | −7.33733 | −0.427196 | ||||||||
\(296\) | −2.75061 | −0.159876 | ||||||||
\(297\) | −3.96791 | −0.230241 | ||||||||
\(298\) | 18.7464 | 1.08595 | ||||||||
\(299\) | −0.624496 | −0.0361155 | ||||||||
\(300\) | 9.81604 | 0.566729 | ||||||||
\(301\) | 11.6282 | 0.670239 | ||||||||
\(302\) | −20.4397 | −1.17617 | ||||||||
\(303\) | −6.56587 | −0.377200 | ||||||||
\(304\) | 2.18243 | 0.125171 | ||||||||
\(305\) | 1.08430 | 0.0620868 | ||||||||
\(306\) | −0.651114 | −0.0372217 | ||||||||
\(307\) | 22.6839 | 1.29464 | 0.647319 | − | 0.762219i | \(-0.275890\pi\) | ||||
0.647319 | + | 0.762219i | \(0.275890\pi\) | |||||||
\(308\) | −3.58902 | −0.204503 | ||||||||
\(309\) | −32.2323 | −1.83363 | ||||||||
\(310\) | −6.10988 | −0.347018 | ||||||||
\(311\) | 0.327113 | 0.0185489 | 0.00927445 | − | 0.999957i | \(-0.497048\pi\) | ||||
0.00927445 | + | 0.999957i | \(0.497048\pi\) | |||||||
\(312\) | 11.8037 | 0.668251 | ||||||||
\(313\) | −2.76056 | −0.156036 | −0.0780181 | − | 0.996952i | \(-0.524859\pi\) | ||||
−0.0780181 | + | 0.996952i | \(0.524859\pi\) | |||||||
\(314\) | 1.38318 | 0.0780573 | ||||||||
\(315\) | −2.43435 | −0.137160 | ||||||||
\(316\) | −1.47331 | −0.0828800 | ||||||||
\(317\) | −21.5671 | −1.21133 | −0.605664 | − | 0.795720i | \(-0.707093\pi\) | ||||
−0.605664 | + | 0.795720i | \(0.707093\pi\) | |||||||
\(318\) | 18.7999 | 1.05425 | ||||||||
\(319\) | −3.81478 | −0.213587 | ||||||||
\(320\) | −0.571471 | −0.0319462 | ||||||||
\(321\) | −35.4590 | −1.97913 | ||||||||
\(322\) | 0.335328 | 0.0186871 | ||||||||
\(323\) | −1.00662 | −0.0560098 | ||||||||
\(324\) | −11.2422 | −0.624567 | ||||||||
\(325\) | 26.2634 | 1.45683 | ||||||||
\(326\) | 10.4329 | 0.577823 | ||||||||
\(327\) | 9.08587 | 0.502450 | ||||||||
\(328\) | −3.60037 | −0.198797 | ||||||||
\(329\) | −8.85311 | −0.488088 | ||||||||
\(330\) | −1.42763 | −0.0785884 | ||||||||
\(331\) | −0.419719 | −0.0230698 | −0.0115349 | − | 0.999933i | \(-0.503672\pi\) | ||||
−0.0115349 | + | 0.999933i | \(0.503672\pi\) | |||||||
\(332\) | −7.00283 | −0.384330 | ||||||||
\(333\) | −3.88295 | −0.212784 | ||||||||
\(334\) | 2.57038 | 0.140645 | ||||||||
\(335\) | −0.483045 | −0.0263916 | ||||||||
\(336\) | −6.33808 | −0.345770 | ||||||||
\(337\) | −24.3871 | −1.32845 | −0.664225 | − | 0.747532i | \(-0.731238\pi\) | ||||
−0.664225 | + | 0.747532i | \(0.731238\pi\) | |||||||
\(338\) | 18.5813 | 1.01069 | ||||||||
\(339\) | −13.9339 | −0.756788 | ||||||||
\(340\) | 0.263584 | 0.0142948 | ||||||||
\(341\) | −12.7162 | −0.688622 | ||||||||
\(342\) | 3.08088 | 0.166595 | ||||||||
\(343\) | −14.7689 | −0.797448 | ||||||||
\(344\) | 3.85351 | 0.207768 | ||||||||
\(345\) | 0.133386 | 0.00718126 | ||||||||
\(346\) | −2.17575 | −0.116969 | ||||||||
\(347\) | −21.5409 | −1.15638 | −0.578188 | − | 0.815904i | \(-0.696240\pi\) | ||||
−0.578188 | + | 0.815904i | \(0.696240\pi\) | |||||||
\(348\) | −6.73677 | −0.361129 | ||||||||
\(349\) | −12.6704 | −0.678234 | −0.339117 | − | 0.940744i | \(-0.610128\pi\) | ||||
−0.339117 | + | 0.940744i | \(0.610128\pi\) | |||||||
\(350\) | −14.1023 | −0.753801 | ||||||||
\(351\) | −18.7481 | −1.00070 | ||||||||
\(352\) | −1.18938 | −0.0633940 | ||||||||
\(353\) | −0.181780 | −0.00967518 | −0.00483759 | − | 0.999988i | \(-0.501540\pi\) | ||||
−0.00483759 | + | 0.999988i | \(0.501540\pi\) | |||||||
\(354\) | −26.9678 | −1.43332 | ||||||||
\(355\) | 5.60284 | 0.297368 | ||||||||
\(356\) | −16.8609 | −0.893626 | ||||||||
\(357\) | 2.92335 | 0.154720 | ||||||||
\(358\) | −21.0627 | −1.11320 | ||||||||
\(359\) | −3.44057 | −0.181587 | −0.0907933 | − | 0.995870i | \(-0.528940\pi\) | ||||
−0.0907933 | + | 0.995870i | \(0.528940\pi\) | |||||||
\(360\) | −0.806729 | −0.0425183 | ||||||||
\(361\) | −14.2370 | −0.749315 | ||||||||
\(362\) | −10.3419 | −0.543556 | ||||||||
\(363\) | 20.1331 | 1.05671 | ||||||||
\(364\) | −16.9579 | −0.888834 | ||||||||
\(365\) | 4.51655 | 0.236407 | ||||||||
\(366\) | 3.98526 | 0.208313 | ||||||||
\(367\) | 1.92925 | 0.100706 | 0.0503531 | − | 0.998731i | \(-0.483965\pi\) | ||||
0.0503531 | + | 0.998731i | \(0.483965\pi\) | |||||||
\(368\) | 0.111126 | 0.00579282 | ||||||||
\(369\) | −5.08254 | −0.264586 | ||||||||
\(370\) | 1.57189 | 0.0817188 | ||||||||
\(371\) | −27.0091 | −1.40224 | ||||||||
\(372\) | −22.4564 | −1.16431 | ||||||||
\(373\) | −19.7154 | −1.02083 | −0.510413 | − | 0.859930i | \(-0.670507\pi\) | ||||
−0.510413 | + | 0.859930i | \(0.670507\pi\) | |||||||
\(374\) | 0.548585 | 0.0283666 | ||||||||
\(375\) | −11.6112 | −0.599598 | ||||||||
\(376\) | −2.93386 | −0.151302 | ||||||||
\(377\) | −18.0246 | −0.928314 | ||||||||
\(378\) | 10.0670 | 0.517788 | ||||||||
\(379\) | 8.07357 | 0.414712 | 0.207356 | − | 0.978266i | \(-0.433514\pi\) | ||||
0.207356 | + | 0.978266i | \(0.433514\pi\) | |||||||
\(380\) | −1.24720 | −0.0639799 | ||||||||
\(381\) | 21.2536 | 1.08885 | ||||||||
\(382\) | 0.655753 | 0.0335513 | ||||||||
\(383\) | 3.38074 | 0.172748 | 0.0863740 | − | 0.996263i | \(-0.472472\pi\) | ||||
0.0863740 | + | 0.996263i | \(0.472472\pi\) | |||||||
\(384\) | −2.10040 | −0.107185 | ||||||||
\(385\) | 2.05102 | 0.104530 | ||||||||
\(386\) | 2.17573 | 0.110742 | ||||||||
\(387\) | 5.43989 | 0.276525 | ||||||||
\(388\) | −12.0645 | −0.612481 | ||||||||
\(389\) | −13.5165 | −0.685314 | −0.342657 | − | 0.939461i | \(-0.611327\pi\) | ||||
−0.342657 | + | 0.939461i | \(0.611327\pi\) | |||||||
\(390\) | −6.74545 | −0.341569 | ||||||||
\(391\) | −0.0512552 | −0.00259209 | ||||||||
\(392\) | 2.10567 | 0.106352 | ||||||||
\(393\) | −3.95214 | −0.199359 | ||||||||
\(394\) | 1.28802 | 0.0648893 | ||||||||
\(395\) | 0.841953 | 0.0423632 | ||||||||
\(396\) | −1.67901 | −0.0843733 | ||||||||
\(397\) | −16.7146 | −0.838883 | −0.419441 | − | 0.907782i | \(-0.637774\pi\) | ||||
−0.419441 | + | 0.907782i | \(0.637774\pi\) | |||||||
\(398\) | −19.2438 | −0.964605 | ||||||||
\(399\) | −13.8324 | −0.692488 | ||||||||
\(400\) | −4.67342 | −0.233671 | ||||||||
\(401\) | −12.8696 | −0.642677 | −0.321339 | − | 0.946964i | \(-0.604133\pi\) | ||||
−0.321339 | + | 0.946964i | \(0.604133\pi\) | |||||||
\(402\) | −1.77540 | −0.0885487 | ||||||||
\(403\) | −60.0833 | −2.99296 | ||||||||
\(404\) | 3.12601 | 0.155525 | ||||||||
\(405\) | 6.42459 | 0.319241 | ||||||||
\(406\) | 9.67846 | 0.480334 | ||||||||
\(407\) | 3.27151 | 0.162163 | ||||||||
\(408\) | 0.968781 | 0.0479618 | ||||||||
\(409\) | 12.6660 | 0.626295 | 0.313147 | − | 0.949705i | \(-0.398617\pi\) | ||||
0.313147 | + | 0.949705i | \(0.398617\pi\) | |||||||
\(410\) | 2.05751 | 0.101613 | ||||||||
\(411\) | −37.1747 | −1.83369 | ||||||||
\(412\) | 15.3458 | 0.756033 | ||||||||
\(413\) | 38.7436 | 1.90645 | ||||||||
\(414\) | 0.156873 | 0.00770987 | ||||||||
\(415\) | 4.00191 | 0.196446 | ||||||||
\(416\) | −5.61973 | −0.275530 | ||||||||
\(417\) | 31.2406 | 1.52986 | ||||||||
\(418\) | −2.59574 | −0.126962 | ||||||||
\(419\) | −0.334875 | −0.0163597 | −0.00817985 | − | 0.999967i | \(-0.502604\pi\) | ||||
−0.00817985 | + | 0.999967i | \(0.502604\pi\) | |||||||
\(420\) | 3.62203 | 0.176737 | ||||||||
\(421\) | 9.64771 | 0.470201 | 0.235100 | − | 0.971971i | \(-0.424458\pi\) | ||||
0.235100 | + | 0.971971i | \(0.424458\pi\) | |||||||
\(422\) | −1.76956 | −0.0861409 | ||||||||
\(423\) | −4.14165 | −0.201374 | ||||||||
\(424\) | −8.95066 | −0.434682 | ||||||||
\(425\) | 2.15555 | 0.104560 | ||||||||
\(426\) | 20.5928 | 0.997725 | ||||||||
\(427\) | −5.72546 | −0.277075 | ||||||||
\(428\) | 16.8821 | 0.816025 | ||||||||
\(429\) | −14.0390 | −0.677809 | ||||||||
\(430\) | −2.20217 | −0.106198 | ||||||||
\(431\) | 26.9205 | 1.29672 | 0.648358 | − | 0.761336i | \(-0.275456\pi\) | ||||
0.648358 | + | 0.761336i | \(0.275456\pi\) | |||||||
\(432\) | 3.33612 | 0.160509 | ||||||||
\(433\) | 15.0759 | 0.724501 | 0.362251 | − | 0.932081i | \(-0.382008\pi\) | ||||
0.362251 | + | 0.932081i | \(0.382008\pi\) | |||||||
\(434\) | 32.2622 | 1.54864 | ||||||||
\(435\) | 3.84987 | 0.184587 | ||||||||
\(436\) | −4.32579 | −0.207168 | ||||||||
\(437\) | 0.242524 | 0.0116015 | ||||||||
\(438\) | 16.6002 | 0.793189 | ||||||||
\(439\) | 8.36521 | 0.399250 | 0.199625 | − | 0.979872i | \(-0.436028\pi\) | ||||
0.199625 | + | 0.979872i | \(0.436028\pi\) | |||||||
\(440\) | 0.679695 | 0.0324032 | ||||||||
\(441\) | 2.97251 | 0.141548 | ||||||||
\(442\) | 2.59203 | 0.123290 | ||||||||
\(443\) | 3.00833 | 0.142930 | 0.0714650 | − | 0.997443i | \(-0.477233\pi\) | ||||
0.0714650 | + | 0.997443i | \(0.477233\pi\) | |||||||
\(444\) | 5.77737 | 0.274182 | ||||||||
\(445\) | 9.63552 | 0.456768 | ||||||||
\(446\) | −12.4006 | −0.587186 | ||||||||
\(447\) | −39.3748 | −1.86237 | ||||||||
\(448\) | 3.01756 | 0.142566 | ||||||||
\(449\) | −9.96365 | −0.470214 | −0.235107 | − | 0.971970i | \(-0.575544\pi\) | ||||
−0.235107 | + | 0.971970i | \(0.575544\pi\) | |||||||
\(450\) | −6.59733 | −0.311001 | ||||||||
\(451\) | 4.28220 | 0.201641 | ||||||||
\(452\) | 6.63395 | 0.312035 | ||||||||
\(453\) | 42.9315 | 2.01710 | ||||||||
\(454\) | 3.76542 | 0.176720 | ||||||||
\(455\) | 9.69093 | 0.454318 | ||||||||
\(456\) | −4.58398 | −0.214664 | ||||||||
\(457\) | 36.3378 | 1.69981 | 0.849905 | − | 0.526936i | \(-0.176659\pi\) | ||||
0.849905 | + | 0.526936i | \(0.176659\pi\) | |||||||
\(458\) | 17.4343 | 0.814649 | ||||||||
\(459\) | −1.53874 | −0.0718224 | ||||||||
\(460\) | −0.0635051 | −0.00296094 | ||||||||
\(461\) | −17.0377 | −0.793526 | −0.396763 | − | 0.917921i | \(-0.629867\pi\) | ||||
−0.396763 | + | 0.917921i | \(0.629867\pi\) | |||||||
\(462\) | 7.53836 | 0.350716 | ||||||||
\(463\) | 25.8486 | 1.20128 | 0.600642 | − | 0.799518i | \(-0.294912\pi\) | ||||
0.600642 | + | 0.799518i | \(0.294912\pi\) | |||||||
\(464\) | 3.20738 | 0.148899 | ||||||||
\(465\) | 12.8332 | 0.595125 | ||||||||
\(466\) | 5.72024 | 0.264985 | ||||||||
\(467\) | 11.2437 | 0.520297 | 0.260149 | − | 0.965569i | \(-0.416228\pi\) | ||||
0.260149 | + | 0.965569i | \(0.416228\pi\) | |||||||
\(468\) | −7.93320 | −0.366712 | ||||||||
\(469\) | 2.55064 | 0.117778 | ||||||||
\(470\) | 1.67662 | 0.0773366 | ||||||||
\(471\) | −2.90522 | −0.133866 | ||||||||
\(472\) | 12.8394 | 0.590980 | ||||||||
\(473\) | −4.58328 | −0.210739 | ||||||||
\(474\) | 3.09453 | 0.142137 | ||||||||
\(475\) | −10.1994 | −0.467982 | ||||||||
\(476\) | −1.39181 | −0.0637935 | ||||||||
\(477\) | −12.6354 | −0.578534 | ||||||||
\(478\) | −0.915196 | −0.0418601 | ||||||||
\(479\) | 20.0928 | 0.918065 | 0.459033 | − | 0.888419i | \(-0.348196\pi\) | ||||
0.459033 | + | 0.888419i | \(0.348196\pi\) | |||||||
\(480\) | 1.20032 | 0.0547867 | ||||||||
\(481\) | 15.4577 | 0.704809 | ||||||||
\(482\) | −8.57289 | −0.390484 | ||||||||
\(483\) | −0.704323 | −0.0320478 | ||||||||
\(484\) | −9.58538 | −0.435699 | ||||||||
\(485\) | 6.89450 | 0.313063 | ||||||||
\(486\) | 13.6047 | 0.617122 | ||||||||
\(487\) | −15.9412 | −0.722363 | −0.361182 | − | 0.932495i | \(-0.617627\pi\) | ||||
−0.361182 | + | 0.932495i | \(0.617627\pi\) | |||||||
\(488\) | −1.89738 | −0.0858904 | ||||||||
\(489\) | −21.9132 | −0.990947 | ||||||||
\(490\) | −1.20333 | −0.0543608 | ||||||||
\(491\) | −1.33619 | −0.0603014 | −0.0301507 | − | 0.999545i | \(-0.509599\pi\) | ||||
−0.0301507 | + | 0.999545i | \(0.509599\pi\) | |||||||
\(492\) | 7.56221 | 0.340931 | ||||||||
\(493\) | −1.47936 | −0.0666271 | ||||||||
\(494\) | −12.2647 | −0.551814 | ||||||||
\(495\) | 0.959504 | 0.0431265 | ||||||||
\(496\) | 10.6915 | 0.480062 | ||||||||
\(497\) | −29.5849 | −1.32706 | ||||||||
\(498\) | 14.7087 | 0.659114 | ||||||||
\(499\) | −22.7132 | −1.01678 | −0.508391 | − | 0.861126i | \(-0.669760\pi\) | ||||
−0.508391 | + | 0.861126i | \(0.669760\pi\) | |||||||
\(500\) | 5.52808 | 0.247223 | ||||||||
\(501\) | −5.39883 | −0.241202 | ||||||||
\(502\) | −4.67991 | −0.208875 | ||||||||
\(503\) | −25.0145 | −1.11534 | −0.557672 | − | 0.830062i | \(-0.688305\pi\) | ||||
−0.557672 | + | 0.830062i | \(0.688305\pi\) | |||||||
\(504\) | 4.25980 | 0.189747 | ||||||||
\(505\) | −1.78643 | −0.0794949 | ||||||||
\(506\) | −0.132170 | −0.00587568 | ||||||||
\(507\) | −39.0282 | −1.73330 | ||||||||
\(508\) | −10.1188 | −0.448951 | ||||||||
\(509\) | 4.74486 | 0.210312 | 0.105156 | − | 0.994456i | \(-0.466466\pi\) | ||||
0.105156 | + | 0.994456i | \(0.466466\pi\) | |||||||
\(510\) | −0.553630 | −0.0245152 | ||||||||
\(511\) | −23.8489 | −1.05501 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.28087 | 0.321458 | ||||||||
\(514\) | −25.2913 | −1.11555 | ||||||||
\(515\) | −8.76968 | −0.386438 | ||||||||
\(516\) | −8.09391 | −0.356315 | ||||||||
\(517\) | 3.48947 | 0.153467 | ||||||||
\(518\) | −8.30012 | −0.364687 | ||||||||
\(519\) | 4.56993 | 0.200598 | ||||||||
\(520\) | 3.21151 | 0.140834 | ||||||||
\(521\) | −23.5110 | −1.03003 | −0.515017 | − | 0.857180i | \(-0.672215\pi\) | ||||
−0.515017 | + | 0.857180i | \(0.672215\pi\) | |||||||
\(522\) | 4.52776 | 0.198175 | ||||||||
\(523\) | 38.5322 | 1.68489 | 0.842447 | − | 0.538780i | \(-0.181114\pi\) | ||||
0.842447 | + | 0.538780i | \(0.181114\pi\) | |||||||
\(524\) | 1.88162 | 0.0821988 | ||||||||
\(525\) | 29.6205 | 1.29274 | ||||||||
\(526\) | −18.0309 | −0.786185 | ||||||||
\(527\) | −4.93131 | −0.214811 | ||||||||
\(528\) | 2.49816 | 0.108719 | ||||||||
\(529\) | −22.9877 | −0.999463 | ||||||||
\(530\) | 5.11504 | 0.222183 | ||||||||
\(531\) | 18.1250 | 0.786556 | ||||||||
\(532\) | 6.58562 | 0.285523 | ||||||||
\(533\) | 20.2331 | 0.876393 | ||||||||
\(534\) | 35.4146 | 1.53254 | ||||||||
\(535\) | −9.64761 | −0.417103 | ||||||||
\(536\) | 0.845266 | 0.0365099 | ||||||||
\(537\) | 44.2401 | 1.90910 | ||||||||
\(538\) | −7.97505 | −0.343829 | ||||||||
\(539\) | −2.50443 | −0.107874 | ||||||||
\(540\) | −1.90650 | −0.0820426 | ||||||||
\(541\) | −21.0405 | −0.904604 | −0.452302 | − | 0.891865i | \(-0.649397\pi\) | ||||
−0.452302 | + | 0.891865i | \(0.649397\pi\) | |||||||
\(542\) | −29.9244 | −1.28536 | ||||||||
\(543\) | 21.7220 | 0.932181 | ||||||||
\(544\) | −0.461237 | −0.0197754 | ||||||||
\(545\) | 2.47206 | 0.105892 | ||||||||
\(546\) | 35.6183 | 1.52432 | ||||||||
\(547\) | −22.0336 | −0.942087 | −0.471044 | − | 0.882110i | \(-0.656123\pi\) | ||||
−0.471044 | + | 0.882110i | \(0.656123\pi\) | |||||||
\(548\) | 17.6989 | 0.756060 | ||||||||
\(549\) | −2.67848 | −0.114315 | ||||||||
\(550\) | 5.55846 | 0.237013 | ||||||||
\(551\) | 6.99989 | 0.298205 | ||||||||
\(552\) | −0.233408 | −0.00993450 | ||||||||
\(553\) | −4.44579 | −0.189054 | ||||||||
\(554\) | −14.1989 | −0.603253 | ||||||||
\(555\) | −3.30160 | −0.140145 | ||||||||
\(556\) | −14.8737 | −0.630784 | ||||||||
\(557\) | −20.2363 | −0.857440 | −0.428720 | − | 0.903437i | \(-0.641035\pi\) | ||||
−0.428720 | + | 0.903437i | \(0.641035\pi\) | |||||||
\(558\) | 15.0929 | 0.638932 | ||||||||
\(559\) | −21.6557 | −0.915939 | ||||||||
\(560\) | −1.72445 | −0.0728712 | ||||||||
\(561\) | −1.15225 | −0.0486479 | ||||||||
\(562\) | −25.5686 | −1.07855 | ||||||||
\(563\) | 13.6164 | 0.573865 | 0.286932 | − | 0.957951i | \(-0.407364\pi\) | ||||
0.286932 | + | 0.957951i | \(0.407364\pi\) | |||||||
\(564\) | 6.16228 | 0.259479 | ||||||||
\(565\) | −3.79111 | −0.159493 | ||||||||
\(566\) | −5.66128 | −0.237961 | ||||||||
\(567\) | −33.9240 | −1.42467 | ||||||||
\(568\) | −9.80424 | −0.411377 | ||||||||
\(569\) | −20.2814 | −0.850242 | −0.425121 | − | 0.905137i | \(-0.639768\pi\) | ||||
−0.425121 | + | 0.905137i | \(0.639768\pi\) | |||||||
\(570\) | 2.61961 | 0.109723 | ||||||||
\(571\) | −39.9276 | −1.67092 | −0.835459 | − | 0.549552i | \(-0.814798\pi\) | ||||
−0.835459 | + | 0.549552i | \(0.814798\pi\) | |||||||
\(572\) | 6.68397 | 0.279471 | ||||||||
\(573\) | −1.37734 | −0.0575393 | ||||||||
\(574\) | −10.8643 | −0.453469 | ||||||||
\(575\) | −0.519337 | −0.0216578 | ||||||||
\(576\) | 1.41167 | 0.0588196 | ||||||||
\(577\) | −12.3279 | −0.513216 | −0.256608 | − | 0.966516i | \(-0.582605\pi\) | ||||
−0.256608 | + | 0.966516i | \(0.582605\pi\) | |||||||
\(578\) | −16.7873 | −0.698258 | ||||||||
\(579\) | −4.56990 | −0.189919 | ||||||||
\(580\) | −1.83292 | −0.0761081 | ||||||||
\(581\) | −21.1315 | −0.876681 | ||||||||
\(582\) | 25.3402 | 1.05038 | ||||||||
\(583\) | 10.6457 | 0.440900 | ||||||||
\(584\) | −7.90337 | −0.327044 | ||||||||
\(585\) | 4.53360 | 0.187441 | ||||||||
\(586\) | 32.9911 | 1.36285 | ||||||||
\(587\) | 10.7811 | 0.444985 | 0.222493 | − | 0.974934i | \(-0.428581\pi\) | ||||
0.222493 | + | 0.974934i | \(0.428581\pi\) | |||||||
\(588\) | −4.42274 | −0.182391 | ||||||||
\(589\) | 23.3335 | 0.961440 | ||||||||
\(590\) | −7.33733 | −0.302073 | ||||||||
\(591\) | −2.70535 | −0.111283 | ||||||||
\(592\) | −2.75061 | −0.113049 | ||||||||
\(593\) | −38.5134 | −1.58156 | −0.790779 | − | 0.612102i | \(-0.790324\pi\) | ||||
−0.790779 | + | 0.612102i | \(0.790324\pi\) | |||||||
\(594\) | −3.96791 | −0.162805 | ||||||||
\(595\) | 0.795379 | 0.0326074 | ||||||||
\(596\) | 18.7464 | 0.767882 | ||||||||
\(597\) | 40.4196 | 1.65427 | ||||||||
\(598\) | −0.624496 | −0.0255375 | ||||||||
\(599\) | 6.36495 | 0.260065 | 0.130032 | − | 0.991510i | \(-0.458492\pi\) | ||||
0.130032 | + | 0.991510i | \(0.458492\pi\) | |||||||
\(600\) | 9.81604 | 0.400738 | ||||||||
\(601\) | −3.31049 | −0.135038 | −0.0675189 | − | 0.997718i | \(-0.521508\pi\) | ||||
−0.0675189 | + | 0.997718i | \(0.521508\pi\) | |||||||
\(602\) | 11.6282 | 0.473930 | ||||||||
\(603\) | 1.19324 | 0.0485924 | ||||||||
\(604\) | −20.4397 | −0.831680 | ||||||||
\(605\) | 5.47777 | 0.222703 | ||||||||
\(606\) | −6.56587 | −0.266720 | ||||||||
\(607\) | −0.296238 | −0.0120239 | −0.00601197 | − | 0.999982i | \(-0.501914\pi\) | ||||
−0.00601197 | + | 0.999982i | \(0.501914\pi\) | |||||||
\(608\) | 2.18243 | 0.0885094 | ||||||||
\(609\) | −20.3286 | −0.823757 | ||||||||
\(610\) | 1.08430 | 0.0439020 | ||||||||
\(611\) | 16.4875 | 0.667013 | ||||||||
\(612\) | −0.651114 | −0.0263197 | ||||||||
\(613\) | 41.5640 | 1.67876 | 0.839378 | − | 0.543549i | \(-0.182920\pi\) | ||||
0.839378 | + | 0.543549i | \(0.182920\pi\) | |||||||
\(614\) | 22.6839 | 0.915448 | ||||||||
\(615\) | −4.32158 | −0.174263 | ||||||||
\(616\) | −3.58902 | −0.144606 | ||||||||
\(617\) | 22.9112 | 0.922370 | 0.461185 | − | 0.887304i | \(-0.347424\pi\) | ||||
0.461185 | + | 0.887304i | \(0.347424\pi\) | |||||||
\(618\) | −32.2323 | −1.29657 | ||||||||
\(619\) | −1.82194 | −0.0732301 | −0.0366151 | − | 0.999329i | \(-0.511658\pi\) | ||||
−0.0366151 | + | 0.999329i | \(0.511658\pi\) | |||||||
\(620\) | −6.10988 | −0.245379 | ||||||||
\(621\) | 0.370729 | 0.0148768 | ||||||||
\(622\) | 0.327113 | 0.0131161 | ||||||||
\(623\) | −50.8788 | −2.03842 | ||||||||
\(624\) | 11.8037 | 0.472525 | ||||||||
\(625\) | 20.2080 | 0.808319 | ||||||||
\(626\) | −2.76056 | −0.110334 | ||||||||
\(627\) | 5.45208 | 0.217735 | ||||||||
\(628\) | 1.38318 | 0.0551948 | ||||||||
\(629\) | 1.26868 | 0.0505857 | ||||||||
\(630\) | −2.43435 | −0.0969869 | ||||||||
\(631\) | 39.0695 | 1.55533 | 0.777665 | − | 0.628678i | \(-0.216404\pi\) | ||||
0.777665 | + | 0.628678i | \(0.216404\pi\) | |||||||
\(632\) | −1.47331 | −0.0586050 | ||||||||
\(633\) | 3.71678 | 0.147729 | ||||||||
\(634\) | −21.5671 | −0.856539 | ||||||||
\(635\) | 5.78263 | 0.229477 | ||||||||
\(636\) | 18.7999 | 0.745466 | ||||||||
\(637\) | −11.8333 | −0.468852 | ||||||||
\(638\) | −3.81478 | −0.151029 | ||||||||
\(639\) | −13.8404 | −0.547516 | ||||||||
\(640\) | −0.571471 | −0.0225894 | ||||||||
\(641\) | −8.79739 | −0.347476 | −0.173738 | − | 0.984792i | \(-0.555585\pi\) | ||||
−0.173738 | + | 0.984792i | \(0.555585\pi\) | |||||||
\(642\) | −35.4590 | −1.39946 | ||||||||
\(643\) | 1.70336 | 0.0671738 | 0.0335869 | − | 0.999436i | \(-0.489307\pi\) | ||||
0.0335869 | + | 0.999436i | \(0.489307\pi\) | |||||||
\(644\) | 0.335328 | 0.0132138 | ||||||||
\(645\) | 4.62544 | 0.182126 | ||||||||
\(646\) | −1.00662 | −0.0396049 | ||||||||
\(647\) | −21.6115 | −0.849637 | −0.424819 | − | 0.905278i | \(-0.639662\pi\) | ||||
−0.424819 | + | 0.905278i | \(0.639662\pi\) | |||||||
\(648\) | −11.2422 | −0.441635 | ||||||||
\(649\) | −15.2709 | −0.599434 | ||||||||
\(650\) | 26.2634 | 1.03013 | ||||||||
\(651\) | −67.7635 | −2.65586 | ||||||||
\(652\) | 10.4329 | 0.408582 | ||||||||
\(653\) | 2.80818 | 0.109893 | 0.0549463 | − | 0.998489i | \(-0.482501\pi\) | ||||
0.0549463 | + | 0.998489i | \(0.482501\pi\) | |||||||
\(654\) | 9.08587 | 0.355286 | ||||||||
\(655\) | −1.07529 | −0.0420151 | ||||||||
\(656\) | −3.60037 | −0.140571 | ||||||||
\(657\) | −11.1570 | −0.435274 | ||||||||
\(658\) | −8.85311 | −0.345130 | ||||||||
\(659\) | 29.6050 | 1.15325 | 0.576623 | − | 0.817011i | \(-0.304370\pi\) | ||||
0.576623 | + | 0.817011i | \(0.304370\pi\) | |||||||
\(660\) | −1.42763 | −0.0555704 | ||||||||
\(661\) | −6.83459 | −0.265835 | −0.132917 | − | 0.991127i | \(-0.542434\pi\) | ||||
−0.132917 | + | 0.991127i | \(0.542434\pi\) | |||||||
\(662\) | −0.419719 | −0.0163128 | ||||||||
\(663\) | −5.44428 | −0.211439 | ||||||||
\(664\) | −7.00283 | −0.271762 | ||||||||
\(665\) | −3.76349 | −0.145942 | ||||||||
\(666\) | −3.88295 | −0.150461 | ||||||||
\(667\) | 0.356422 | 0.0138007 | ||||||||
\(668\) | 2.57038 | 0.0994512 | ||||||||
\(669\) | 26.0462 | 1.00700 | ||||||||
\(670\) | −0.483045 | −0.0186617 | ||||||||
\(671\) | 2.25670 | 0.0871190 | ||||||||
\(672\) | −6.33808 | −0.244497 | ||||||||
\(673\) | −10.2477 | −0.395020 | −0.197510 | − | 0.980301i | \(-0.563286\pi\) | ||||
−0.197510 | + | 0.980301i | \(0.563286\pi\) | |||||||
\(674\) | −24.3871 | −0.939356 | ||||||||
\(675\) | −15.5911 | −0.600102 | ||||||||
\(676\) | 18.5813 | 0.714667 | ||||||||
\(677\) | 7.34302 | 0.282215 | 0.141108 | − | 0.989994i | \(-0.454934\pi\) | ||||
0.141108 | + | 0.989994i | \(0.454934\pi\) | |||||||
\(678\) | −13.9339 | −0.535130 | ||||||||
\(679\) | −36.4053 | −1.39711 | ||||||||
\(680\) | 0.263584 | 0.0101080 | ||||||||
\(681\) | −7.90888 | −0.303069 | ||||||||
\(682\) | −12.7162 | −0.486929 | ||||||||
\(683\) | 3.12947 | 0.119746 | 0.0598730 | − | 0.998206i | \(-0.480930\pi\) | ||||
0.0598730 | + | 0.998206i | \(0.480930\pi\) | |||||||
\(684\) | 3.08088 | 0.117800 | ||||||||
\(685\) | −10.1144 | −0.386452 | ||||||||
\(686\) | −14.7689 | −0.563881 | ||||||||
\(687\) | −36.6189 | −1.39710 | ||||||||
\(688\) | 3.85351 | 0.146914 | ||||||||
\(689\) | 50.3002 | 1.91629 | ||||||||
\(690\) | 0.133386 | 0.00507792 | ||||||||
\(691\) | 29.9139 | 1.13798 | 0.568989 | − | 0.822345i | \(-0.307335\pi\) | ||||
0.568989 | + | 0.822345i | \(0.307335\pi\) | |||||||
\(692\) | −2.17575 | −0.0827094 | ||||||||
\(693\) | −5.06651 | −0.192461 | ||||||||
\(694\) | −21.5409 | −0.817681 | ||||||||
\(695\) | 8.49987 | 0.322419 | ||||||||
\(696\) | −6.73677 | −0.255357 | ||||||||
\(697\) | 1.66062 | 0.0629006 | ||||||||
\(698\) | −12.6704 | −0.479584 | ||||||||
\(699\) | −12.0148 | −0.454440 | ||||||||
\(700\) | −14.1023 | −0.533018 | ||||||||
\(701\) | −35.7472 | −1.35015 | −0.675077 | − | 0.737747i | \(-0.735890\pi\) | ||||
−0.675077 | + | 0.737747i | \(0.735890\pi\) | |||||||
\(702\) | −18.7481 | −0.707602 | ||||||||
\(703\) | −6.00302 | −0.226408 | ||||||||
\(704\) | −1.18938 | −0.0448263 | ||||||||
\(705\) | −3.52156 | −0.132630 | ||||||||
\(706\) | −0.181780 | −0.00684139 | ||||||||
\(707\) | 9.43294 | 0.354762 | ||||||||
\(708\) | −26.9678 | −1.01351 | ||||||||
\(709\) | −32.8622 | −1.23416 | −0.617082 | − | 0.786898i | \(-0.711686\pi\) | ||||
−0.617082 | + | 0.786898i | \(0.711686\pi\) | |||||||
\(710\) | 5.60284 | 0.210271 | ||||||||
\(711\) | −2.07982 | −0.0779995 | ||||||||
\(712\) | −16.8609 | −0.631889 | ||||||||
\(713\) | 1.18810 | 0.0444947 | ||||||||
\(714\) | 2.92335 | 0.109404 | ||||||||
\(715\) | −3.81970 | −0.142849 | ||||||||
\(716\) | −21.0627 | −0.787151 | ||||||||
\(717\) | 1.92228 | 0.0717887 | ||||||||
\(718\) | −3.44057 | −0.128401 | ||||||||
\(719\) | 33.5746 | 1.25212 | 0.626061 | − | 0.779774i | \(-0.284666\pi\) | ||||
0.626061 | + | 0.779774i | \(0.284666\pi\) | |||||||
\(720\) | −0.806729 | −0.0300650 | ||||||||
\(721\) | 46.3069 | 1.72456 | ||||||||
\(722\) | −14.2370 | −0.529846 | ||||||||
\(723\) | 18.0065 | 0.669668 | ||||||||
\(724\) | −10.3419 | −0.384352 | ||||||||
\(725\) | −14.9894 | −0.556694 | ||||||||
\(726\) | 20.1331 | 0.747210 | ||||||||
\(727\) | −13.6317 | −0.505573 | −0.252786 | − | 0.967522i | \(-0.581347\pi\) | ||||
−0.252786 | + | 0.967522i | \(0.581347\pi\) | |||||||
\(728\) | −16.9579 | −0.628500 | ||||||||
\(729\) | 5.15129 | 0.190789 | ||||||||
\(730\) | 4.51655 | 0.167165 | ||||||||
\(731\) | −1.77738 | −0.0657389 | ||||||||
\(732\) | 3.98526 | 0.147299 | ||||||||
\(733\) | 42.5900 | 1.57310 | 0.786549 | − | 0.617528i | \(-0.211866\pi\) | ||||
0.786549 | + | 0.617528i | \(0.211866\pi\) | |||||||
\(734\) | 1.92925 | 0.0712100 | ||||||||
\(735\) | 2.52747 | 0.0932271 | ||||||||
\(736\) | 0.111126 | 0.00409614 | ||||||||
\(737\) | −1.00534 | −0.0370322 | ||||||||
\(738\) | −5.08254 | −0.187091 | ||||||||
\(739\) | 18.8417 | 0.693105 | 0.346552 | − | 0.938031i | \(-0.387352\pi\) | ||||
0.346552 | + | 0.938031i | \(0.387352\pi\) | |||||||
\(740\) | 1.57189 | 0.0577839 | ||||||||
\(741\) | 25.7607 | 0.946343 | ||||||||
\(742\) | −27.0091 | −0.991537 | ||||||||
\(743\) | 1.11868 | 0.0410406 | 0.0205203 | − | 0.999789i | \(-0.493468\pi\) | ||||
0.0205203 | + | 0.999789i | \(0.493468\pi\) | |||||||
\(744\) | −22.4564 | −0.823291 | ||||||||
\(745\) | −10.7130 | −0.392494 | ||||||||
\(746\) | −19.7154 | −0.721832 | ||||||||
\(747\) | −9.88568 | −0.361698 | ||||||||
\(748\) | 0.548585 | 0.0200582 | ||||||||
\(749\) | 50.9426 | 1.86140 | ||||||||
\(750\) | −11.6112 | −0.423980 | ||||||||
\(751\) | −8.51148 | −0.310588 | −0.155294 | − | 0.987868i | \(-0.549633\pi\) | ||||
−0.155294 | + | 0.987868i | \(0.549633\pi\) | |||||||
\(752\) | −2.93386 | −0.106987 | ||||||||
\(753\) | 9.82967 | 0.358213 | ||||||||
\(754\) | −18.0246 | −0.656417 | ||||||||
\(755\) | 11.6807 | 0.425104 | ||||||||
\(756\) | 10.0670 | 0.366132 | ||||||||
\(757\) | 16.1593 | 0.587321 | 0.293661 | − | 0.955910i | \(-0.405126\pi\) | ||||
0.293661 | + | 0.955910i | \(0.405126\pi\) | |||||||
\(758\) | 8.07357 | 0.293245 | ||||||||
\(759\) | 0.277610 | 0.0100766 | ||||||||
\(760\) | −1.24720 | −0.0452406 | ||||||||
\(761\) | 28.7713 | 1.04296 | 0.521480 | − | 0.853264i | \(-0.325380\pi\) | ||||
0.521480 | + | 0.853264i | \(0.325380\pi\) | |||||||
\(762\) | 21.2536 | 0.769937 | ||||||||
\(763\) | −13.0533 | −0.472562 | ||||||||
\(764\) | 0.655753 | 0.0237243 | ||||||||
\(765\) | 0.372093 | 0.0134531 | ||||||||
\(766\) | 3.38074 | 0.122151 | ||||||||
\(767\) | −72.1538 | −2.60532 | ||||||||
\(768\) | −2.10040 | −0.0757916 | ||||||||
\(769\) | −19.9712 | −0.720178 | −0.360089 | − | 0.932918i | \(-0.617254\pi\) | ||||
−0.360089 | + | 0.932918i | \(0.617254\pi\) | |||||||
\(770\) | 2.05102 | 0.0739136 | ||||||||
\(771\) | 53.1217 | 1.91313 | ||||||||
\(772\) | 2.17573 | 0.0783063 | ||||||||
\(773\) | 12.3630 | 0.444665 | 0.222332 | − | 0.974971i | \(-0.428633\pi\) | ||||
0.222332 | + | 0.974971i | \(0.428633\pi\) | |||||||
\(774\) | 5.43989 | 0.195533 | ||||||||
\(775\) | −49.9659 | −1.79483 | ||||||||
\(776\) | −12.0645 | −0.433089 | ||||||||
\(777\) | 17.4336 | 0.625426 | ||||||||
\(778\) | −13.5165 | −0.484590 | ||||||||
\(779\) | −7.85757 | −0.281527 | ||||||||
\(780\) | −6.74545 | −0.241526 | ||||||||
\(781\) | 11.6609 | 0.417261 | ||||||||
\(782\) | −0.0512552 | −0.00183288 | ||||||||
\(783\) | 10.7002 | 0.382395 | ||||||||
\(784\) | 2.10567 | 0.0752024 | ||||||||
\(785\) | −0.790446 | −0.0282122 | ||||||||
\(786\) | −3.95214 | −0.140968 | ||||||||
\(787\) | −2.28758 | −0.0815436 | −0.0407718 | − | 0.999168i | \(-0.512982\pi\) | ||||
−0.0407718 | + | 0.999168i | \(0.512982\pi\) | |||||||
\(788\) | 1.28802 | 0.0458837 | ||||||||
\(789\) | 37.8721 | 1.34828 | ||||||||
\(790\) | 0.841953 | 0.0299553 | ||||||||
\(791\) | 20.0184 | 0.711771 | ||||||||
\(792\) | −1.67901 | −0.0596609 | ||||||||
\(793\) | 10.6628 | 0.378646 | ||||||||
\(794\) | −16.7146 | −0.593180 | ||||||||
\(795\) | −10.7436 | −0.381037 | ||||||||
\(796\) | −19.2438 | −0.682079 | ||||||||
\(797\) | −17.0454 | −0.603779 | −0.301890 | − | 0.953343i | \(-0.597617\pi\) | ||||
−0.301890 | + | 0.953343i | \(0.597617\pi\) | |||||||
\(798\) | −13.8324 | −0.489663 | ||||||||
\(799\) | 1.35321 | 0.0478730 | ||||||||
\(800\) | −4.67342 | −0.165230 | ||||||||
\(801\) | −23.8020 | −0.841004 | ||||||||
\(802\) | −12.8696 | −0.454442 | ||||||||
\(803\) | 9.40009 | 0.331722 | ||||||||
\(804\) | −1.77540 | −0.0626134 | ||||||||
\(805\) | −0.191630 | −0.00675408 | ||||||||
\(806\) | −60.0833 | −2.11634 | ||||||||
\(807\) | 16.7508 | 0.589655 | ||||||||
\(808\) | 3.12601 | 0.109973 | ||||||||
\(809\) | −2.04016 | −0.0717283 | −0.0358642 | − | 0.999357i | \(-0.511418\pi\) | ||||
−0.0358642 | + | 0.999357i | \(0.511418\pi\) | |||||||
\(810\) | 6.42459 | 0.225737 | ||||||||
\(811\) | 8.41659 | 0.295546 | 0.147773 | − | 0.989021i | \(-0.452789\pi\) | ||||
0.147773 | + | 0.989021i | \(0.452789\pi\) | |||||||
\(812\) | 9.67846 | 0.339647 | ||||||||
\(813\) | 62.8532 | 2.20436 | ||||||||
\(814\) | 3.27151 | 0.114666 | ||||||||
\(815\) | −5.96208 | −0.208843 | ||||||||
\(816\) | 0.968781 | 0.0339141 | ||||||||
\(817\) | 8.41004 | 0.294230 | ||||||||
\(818\) | 12.6660 | 0.442857 | ||||||||
\(819\) | −23.9389 | −0.836493 | ||||||||
\(820\) | 2.05751 | 0.0718513 | ||||||||
\(821\) | −25.0850 | −0.875472 | −0.437736 | − | 0.899104i | \(-0.644220\pi\) | ||||
−0.437736 | + | 0.899104i | \(0.644220\pi\) | |||||||
\(822\) | −37.1747 | −1.29662 | ||||||||
\(823\) | 15.3427 | 0.534813 | 0.267407 | − | 0.963584i | \(-0.413833\pi\) | ||||
0.267407 | + | 0.963584i | \(0.413833\pi\) | |||||||
\(824\) | 15.3458 | 0.534596 | ||||||||
\(825\) | −11.6750 | −0.406470 | ||||||||
\(826\) | 38.7436 | 1.34806 | ||||||||
\(827\) | −24.1699 | −0.840470 | −0.420235 | − | 0.907415i | \(-0.638052\pi\) | ||||
−0.420235 | + | 0.907415i | \(0.638052\pi\) | |||||||
\(828\) | 0.156873 | 0.00545170 | ||||||||
\(829\) | −8.91433 | −0.309607 | −0.154804 | − | 0.987945i | \(-0.549475\pi\) | ||||
−0.154804 | + | 0.987945i | \(0.549475\pi\) | |||||||
\(830\) | 4.00191 | 0.138908 | ||||||||
\(831\) | 29.8233 | 1.03456 | ||||||||
\(832\) | −5.61973 | −0.194829 | ||||||||
\(833\) | −0.971212 | −0.0336505 | ||||||||
\(834\) | 31.2406 | 1.08177 | ||||||||
\(835\) | −1.46890 | −0.0508334 | ||||||||
\(836\) | −2.59574 | −0.0897754 | ||||||||
\(837\) | 35.6682 | 1.23287 | ||||||||
\(838\) | −0.334875 | −0.0115681 | ||||||||
\(839\) | 37.9865 | 1.31144 | 0.655719 | − | 0.755005i | \(-0.272365\pi\) | ||||
0.655719 | + | 0.755005i | \(0.272365\pi\) | |||||||
\(840\) | 3.62203 | 0.124972 | ||||||||
\(841\) | −18.7127 | −0.645266 | ||||||||
\(842\) | 9.64771 | 0.332482 | ||||||||
\(843\) | 53.7042 | 1.84967 | ||||||||
\(844\) | −1.76956 | −0.0609108 | ||||||||
\(845\) | −10.6187 | −0.365294 | ||||||||
\(846\) | −4.14165 | −0.142393 | ||||||||
\(847\) | −28.9245 | −0.993856 | ||||||||
\(848\) | −8.95066 | −0.307367 | ||||||||
\(849\) | 11.8909 | 0.408096 | ||||||||
\(850\) | 2.15555 | 0.0739349 | ||||||||
\(851\) | −0.305663 | −0.0104780 | ||||||||
\(852\) | 20.5928 | 0.705498 | ||||||||
\(853\) | −50.5354 | −1.73030 | −0.865150 | − | 0.501513i | \(-0.832777\pi\) | ||||
−0.865150 | + | 0.501513i | \(0.832777\pi\) | |||||||
\(854\) | −5.72546 | −0.195921 | ||||||||
\(855\) | −1.76063 | −0.0602123 | ||||||||
\(856\) | 16.8821 | 0.577017 | ||||||||
\(857\) | 56.5372 | 1.93127 | 0.965637 | − | 0.259894i | \(-0.0836877\pi\) | ||||
0.965637 | + | 0.259894i | \(0.0836877\pi\) | |||||||
\(858\) | −14.0390 | −0.479284 | ||||||||
\(859\) | 24.4426 | 0.833969 | 0.416985 | − | 0.908914i | \(-0.363087\pi\) | ||||
0.416985 | + | 0.908914i | \(0.363087\pi\) | |||||||
\(860\) | −2.20217 | −0.0750934 | ||||||||
\(861\) | 22.8194 | 0.777684 | ||||||||
\(862\) | 26.9205 | 0.916916 | ||||||||
\(863\) | −17.3511 | −0.590639 | −0.295319 | − | 0.955399i | \(-0.595426\pi\) | ||||
−0.295319 | + | 0.955399i | \(0.595426\pi\) | |||||||
\(864\) | 3.33612 | 0.113497 | ||||||||
\(865\) | 1.24338 | 0.0422760 | ||||||||
\(866\) | 15.0759 | 0.512300 | ||||||||
\(867\) | 35.2599 | 1.19749 | ||||||||
\(868\) | 32.2622 | 1.09505 | ||||||||
\(869\) | 1.75232 | 0.0594433 | ||||||||
\(870\) | 3.84987 | 0.130523 | ||||||||
\(871\) | −4.75017 | −0.160953 | ||||||||
\(872\) | −4.32579 | −0.146490 | ||||||||
\(873\) | −17.0311 | −0.576414 | ||||||||
\(874\) | 0.242524 | 0.00820351 | ||||||||
\(875\) | 16.6813 | 0.563931 | ||||||||
\(876\) | 16.6002 | 0.560869 | ||||||||
\(877\) | −1.59693 | −0.0539245 | −0.0269622 | − | 0.999636i | \(-0.508583\pi\) | ||||
−0.0269622 | + | 0.999636i | \(0.508583\pi\) | |||||||
\(878\) | 8.36521 | 0.282312 | ||||||||
\(879\) | −69.2944 | −2.33724 | ||||||||
\(880\) | 0.679695 | 0.0229125 | ||||||||
\(881\) | 23.6990 | 0.798438 | 0.399219 | − | 0.916856i | \(-0.369281\pi\) | ||||
0.399219 | + | 0.916856i | \(0.369281\pi\) | |||||||
\(882\) | 2.97251 | 0.100090 | ||||||||
\(883\) | −34.6138 | −1.16485 | −0.582423 | − | 0.812886i | \(-0.697895\pi\) | ||||
−0.582423 | + | 0.812886i | \(0.697895\pi\) | |||||||
\(884\) | 2.59203 | 0.0871793 | ||||||||
\(885\) | 15.4113 | 0.518046 | ||||||||
\(886\) | 3.00833 | 0.101067 | ||||||||
\(887\) | −18.9605 | −0.636631 | −0.318316 | − | 0.947985i | \(-0.603117\pi\) | ||||
−0.318316 | + | 0.947985i | \(0.603117\pi\) | |||||||
\(888\) | 5.77737 | 0.193876 | ||||||||
\(889\) | −30.5342 | −1.02408 | ||||||||
\(890\) | 9.63552 | 0.322983 | ||||||||
\(891\) | 13.3712 | 0.447952 | ||||||||
\(892\) | −12.4006 | −0.415203 | ||||||||
\(893\) | −6.40296 | −0.214267 | ||||||||
\(894\) | −39.3748 | −1.31689 | ||||||||
\(895\) | 12.0367 | 0.402344 | ||||||||
\(896\) | 3.01756 | 0.100810 | ||||||||
\(897\) | 1.31169 | 0.0437960 | ||||||||
\(898\) | −9.96365 | −0.332491 | ||||||||
\(899\) | 34.2917 | 1.14369 | ||||||||
\(900\) | −6.59733 | −0.219911 | ||||||||
\(901\) | 4.12837 | 0.137536 | ||||||||
\(902\) | 4.28220 | 0.142582 | ||||||||
\(903\) | −24.4239 | −0.812775 | ||||||||
\(904\) | 6.63395 | 0.220642 | ||||||||
\(905\) | 5.91007 | 0.196457 | ||||||||
\(906\) | 42.9315 | 1.42630 | ||||||||
\(907\) | 4.62771 | 0.153661 | 0.0768304 | − | 0.997044i | \(-0.475520\pi\) | ||||
0.0768304 | + | 0.997044i | \(0.475520\pi\) | |||||||
\(908\) | 3.76542 | 0.124960 | ||||||||
\(909\) | 4.41290 | 0.146367 | ||||||||
\(910\) | 9.69093 | 0.321251 | ||||||||
\(911\) | −18.6525 | −0.617985 | −0.308993 | − | 0.951064i | \(-0.599992\pi\) | ||||
−0.308993 | + | 0.951064i | \(0.599992\pi\) | |||||||
\(912\) | −4.58398 | −0.151791 | ||||||||
\(913\) | 8.32900 | 0.275650 | ||||||||
\(914\) | 36.3378 | 1.20195 | ||||||||
\(915\) | −2.27746 | −0.0752905 | ||||||||
\(916\) | 17.4343 | 0.576044 | ||||||||
\(917\) | 5.67789 | 0.187501 | ||||||||
\(918\) | −1.53874 | −0.0507861 | ||||||||
\(919\) | 16.1258 | 0.531940 | 0.265970 | − | 0.963981i | \(-0.414308\pi\) | ||||
0.265970 | + | 0.963981i | \(0.414308\pi\) | |||||||
\(920\) | −0.0635051 | −0.00209370 | ||||||||
\(921\) | −47.6452 | −1.56996 | ||||||||
\(922\) | −17.0377 | −0.561108 | ||||||||
\(923\) | 55.0972 | 1.81355 | ||||||||
\(924\) | 7.53836 | 0.247994 | ||||||||
\(925\) | 12.8547 | 0.422661 | ||||||||
\(926\) | 25.8486 | 0.849436 | ||||||||
\(927\) | 21.6632 | 0.711513 | ||||||||
\(928\) | 3.20738 | 0.105287 | ||||||||
\(929\) | −53.3143 | −1.74918 | −0.874592 | − | 0.484859i | \(-0.838871\pi\) | ||||
−0.874592 | + | 0.484859i | \(0.838871\pi\) | |||||||
\(930\) | 12.8332 | 0.420817 | ||||||||
\(931\) | 4.59548 | 0.150611 | ||||||||
\(932\) | 5.72024 | 0.187373 | ||||||||
\(933\) | −0.687068 | −0.0224936 | ||||||||
\(934\) | 11.2437 | 0.367906 | ||||||||
\(935\) | −0.313500 | −0.0102526 | ||||||||
\(936\) | −7.93320 | −0.259305 | ||||||||
\(937\) | 42.4663 | 1.38731 | 0.693656 | − | 0.720306i | \(-0.255999\pi\) | ||||
0.693656 | + | 0.720306i | \(0.255999\pi\) | |||||||
\(938\) | 2.55064 | 0.0832814 | ||||||||
\(939\) | 5.79828 | 0.189220 | ||||||||
\(940\) | 1.67662 | 0.0546853 | ||||||||
\(941\) | 26.2983 | 0.857299 | 0.428650 | − | 0.903471i | \(-0.358990\pi\) | ||||
0.428650 | + | 0.903471i | \(0.358990\pi\) | |||||||
\(942\) | −2.90522 | −0.0946573 | ||||||||
\(943\) | −0.400093 | −0.0130288 | ||||||||
\(944\) | 12.8394 | 0.417886 | ||||||||
\(945\) | −5.75297 | −0.187144 | ||||||||
\(946\) | −4.58328 | −0.149015 | ||||||||
\(947\) | 17.9840 | 0.584400 | 0.292200 | − | 0.956357i | \(-0.405613\pi\) | ||||
0.292200 | + | 0.956357i | \(0.405613\pi\) | |||||||
\(948\) | 3.09453 | 0.100506 | ||||||||
\(949\) | 44.4148 | 1.44177 | ||||||||
\(950\) | −10.1994 | −0.330913 | ||||||||
\(951\) | 45.2995 | 1.46894 | ||||||||
\(952\) | −1.39181 | −0.0451088 | ||||||||
\(953\) | 20.9575 | 0.678879 | 0.339440 | − | 0.940628i | \(-0.389763\pi\) | ||||
0.339440 | + | 0.940628i | \(0.389763\pi\) | |||||||
\(954\) | −12.6354 | −0.409085 | ||||||||
\(955\) | −0.374744 | −0.0121264 | ||||||||
\(956\) | −0.915196 | −0.0295996 | ||||||||
\(957\) | 8.01256 | 0.259009 | ||||||||
\(958\) | 20.0928 | 0.649170 | ||||||||
\(959\) | 53.4075 | 1.72462 | ||||||||
\(960\) | 1.20032 | 0.0387401 | ||||||||
\(961\) | 83.3081 | 2.68736 | ||||||||
\(962\) | 15.4577 | 0.498375 | ||||||||
\(963\) | 23.8319 | 0.767972 | ||||||||
\(964\) | −8.57289 | −0.276114 | ||||||||
\(965\) | −1.24337 | −0.0400254 | ||||||||
\(966\) | −0.704323 | −0.0226612 | ||||||||
\(967\) | −6.51940 | −0.209650 | −0.104825 | − | 0.994491i | \(-0.533428\pi\) | ||||
−0.104825 | + | 0.994491i | \(0.533428\pi\) | |||||||
\(968\) | −9.58538 | −0.308086 | ||||||||
\(969\) | 2.11430 | 0.0679211 | ||||||||
\(970\) | 6.89450 | 0.221369 | ||||||||
\(971\) | 4.25646 | 0.136596 | 0.0682982 | − | 0.997665i | \(-0.478243\pi\) | ||||
0.0682982 | + | 0.997665i | \(0.478243\pi\) | |||||||
\(972\) | 13.6047 | 0.436371 | ||||||||
\(973\) | −44.8822 | −1.43886 | ||||||||
\(974\) | −15.9412 | −0.510788 | ||||||||
\(975\) | −55.1635 | −1.76665 | ||||||||
\(976\) | −1.89738 | −0.0607337 | ||||||||
\(977\) | −30.4906 | −0.975482 | −0.487741 | − | 0.872988i | \(-0.662179\pi\) | ||||
−0.487741 | + | 0.872988i | \(0.662179\pi\) | |||||||
\(978\) | −21.9132 | −0.700706 | ||||||||
\(979\) | 20.0540 | 0.640928 | ||||||||
\(980\) | −1.20333 | −0.0384389 | ||||||||
\(981\) | −6.10658 | −0.194968 | ||||||||
\(982\) | −1.33619 | −0.0426396 | ||||||||
\(983\) | 24.1118 | 0.769048 | 0.384524 | − | 0.923115i | \(-0.374366\pi\) | ||||
0.384524 | + | 0.923115i | \(0.374366\pi\) | |||||||
\(984\) | 7.56221 | 0.241074 | ||||||||
\(985\) | −0.736064 | −0.0234529 | ||||||||
\(986\) | −1.47936 | −0.0471125 | ||||||||
\(987\) | 18.5950 | 0.591887 | ||||||||
\(988\) | −12.2647 | −0.390192 | ||||||||
\(989\) | 0.428224 | 0.0136167 | ||||||||
\(990\) | 0.959504 | 0.0304951 | ||||||||
\(991\) | −22.7615 | −0.723043 | −0.361522 | − | 0.932364i | \(-0.617743\pi\) | ||||
−0.361522 | + | 0.932364i | \(0.617743\pi\) | |||||||
\(992\) | 10.6915 | 0.339455 | ||||||||
\(993\) | 0.881577 | 0.0279760 | ||||||||
\(994\) | −29.5849 | −0.938376 | ||||||||
\(995\) | 10.9973 | 0.348637 | ||||||||
\(996\) | 14.7087 | 0.466064 | ||||||||
\(997\) | 32.8062 | 1.03898 | 0.519491 | − | 0.854476i | \(-0.326122\pi\) | ||||
0.519491 | + | 0.854476i | \(0.326122\pi\) | |||||||
\(998\) | −22.7132 | −0.718973 | ||||||||
\(999\) | −9.17637 | −0.290328 |
(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 | 8006.2.a.a.1.15 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.a.1.15 | ✓ | 69 | 1.1 | even | 1 | trivial |