Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6043,2,Mod(1,6043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6043, 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("6043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6043 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6043.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: | \(48.2535979415\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43851 | −1.72428 | −0.862142 | − | 0.506667i | \(-0.830877\pi\) | ||||
−0.862142 | + | 0.506667i | \(0.830877\pi\) | |||||||
\(3\) | 1.58144 | 0.913043 | 0.456521 | − | 0.889712i | \(-0.349095\pi\) | ||||
0.456521 | + | 0.889712i | \(0.349095\pi\) | |||||||
\(4\) | 3.94631 | 1.97315 | ||||||||
\(5\) | 0.896601 | 0.400972 | 0.200486 | − | 0.979697i | \(-0.435748\pi\) | ||||
0.200486 | + | 0.979697i | \(0.435748\pi\) | |||||||
\(6\) | −3.85634 | −1.57434 | ||||||||
\(7\) | −4.81539 | −1.82004 | −0.910022 | − | 0.414559i | \(-0.863936\pi\) | ||||
−0.910022 | + | 0.414559i | \(0.863936\pi\) | |||||||
\(8\) | −4.74608 | −1.67799 | ||||||||
\(9\) | −0.499059 | −0.166353 | ||||||||
\(10\) | −2.18637 | −0.691390 | ||||||||
\(11\) | 1.11181 | 0.335224 | 0.167612 | − | 0.985853i | \(-0.446394\pi\) | ||||
0.167612 | + | 0.985853i | \(0.446394\pi\) | |||||||
\(12\) | 6.24084 | 1.80157 | ||||||||
\(13\) | 0.578731 | 0.160511 | 0.0802556 | − | 0.996774i | \(-0.474426\pi\) | ||||
0.0802556 | + | 0.996774i | \(0.474426\pi\) | |||||||
\(14\) | 11.7423 | 3.13827 | ||||||||
\(15\) | 1.41792 | 0.366105 | ||||||||
\(16\) | 3.68073 | 0.920182 | ||||||||
\(17\) | −1.16637 | −0.282886 | −0.141443 | − | 0.989946i | \(-0.545174\pi\) | ||||
−0.141443 | + | 0.989946i | \(0.545174\pi\) | |||||||
\(18\) | 1.21696 | 0.286840 | ||||||||
\(19\) | 1.62999 | 0.373945 | 0.186973 | − | 0.982365i | \(-0.440132\pi\) | ||||
0.186973 | + | 0.982365i | \(0.440132\pi\) | |||||||
\(20\) | 3.53827 | 0.791180 | ||||||||
\(21\) | −7.61523 | −1.66178 | ||||||||
\(22\) | −2.71116 | −0.578021 | ||||||||
\(23\) | −1.28716 | −0.268392 | −0.134196 | − | 0.990955i | \(-0.542845\pi\) | ||||
−0.134196 | + | 0.990955i | \(0.542845\pi\) | |||||||
\(24\) | −7.50563 | −1.53208 | ||||||||
\(25\) | −4.19611 | −0.839221 | ||||||||
\(26\) | −1.41124 | −0.276767 | ||||||||
\(27\) | −5.53354 | −1.06493 | ||||||||
\(28\) | −19.0030 | −3.59123 | ||||||||
\(29\) | 3.02920 | 0.562509 | 0.281254 | − | 0.959633i | \(-0.409249\pi\) | ||||
0.281254 | + | 0.959633i | \(0.409249\pi\) | |||||||
\(30\) | −3.45760 | −0.631269 | ||||||||
\(31\) | −3.86085 | −0.693429 | −0.346714 | − | 0.937971i | \(-0.612703\pi\) | ||||
−0.346714 | + | 0.937971i | \(0.612703\pi\) | |||||||
\(32\) | 0.516685 | 0.0913379 | ||||||||
\(33\) | 1.75826 | 0.306073 | ||||||||
\(34\) | 2.84419 | 0.487775 | ||||||||
\(35\) | −4.31748 | −0.729788 | ||||||||
\(36\) | −1.96944 | −0.328240 | ||||||||
\(37\) | 8.11384 | 1.33391 | 0.666953 | − | 0.745099i | \(-0.267598\pi\) | ||||
0.666953 | + | 0.745099i | \(0.267598\pi\) | |||||||
\(38\) | −3.97474 | −0.644787 | ||||||||
\(39\) | 0.915227 | 0.146554 | ||||||||
\(40\) | −4.25534 | −0.672829 | ||||||||
\(41\) | −3.93263 | −0.614174 | −0.307087 | − | 0.951681i | \(-0.599354\pi\) | ||||
−0.307087 | + | 0.951681i | \(0.599354\pi\) | |||||||
\(42\) | 18.5698 | 2.86538 | ||||||||
\(43\) | 2.76513 | 0.421679 | 0.210839 | − | 0.977521i | \(-0.432380\pi\) | ||||
0.210839 | + | 0.977521i | \(0.432380\pi\) | |||||||
\(44\) | 4.38755 | 0.661448 | ||||||||
\(45\) | −0.447457 | −0.0667029 | ||||||||
\(46\) | 3.13875 | 0.462784 | ||||||||
\(47\) | −5.64736 | −0.823752 | −0.411876 | − | 0.911240i | \(-0.635126\pi\) | ||||
−0.411876 | + | 0.911240i | \(0.635126\pi\) | |||||||
\(48\) | 5.82084 | 0.840166 | ||||||||
\(49\) | 16.1879 | 2.31256 | ||||||||
\(50\) | 10.2322 | 1.44706 | ||||||||
\(51\) | −1.84454 | −0.258287 | ||||||||
\(52\) | 2.28385 | 0.316713 | ||||||||
\(53\) | −2.41261 | −0.331398 | −0.165699 | − | 0.986176i | \(-0.552988\pi\) | ||||
−0.165699 | + | 0.986176i | \(0.552988\pi\) | |||||||
\(54\) | 13.4936 | 1.83624 | ||||||||
\(55\) | 0.996851 | 0.134415 | ||||||||
\(56\) | 22.8542 | 3.05402 | ||||||||
\(57\) | 2.57772 | 0.341428 | ||||||||
\(58\) | −7.38673 | −0.969925 | ||||||||
\(59\) | −1.11978 | −0.145783 | −0.0728917 | − | 0.997340i | \(-0.523223\pi\) | ||||
−0.0728917 | + | 0.997340i | \(0.523223\pi\) | |||||||
\(60\) | 5.59554 | 0.722381 | ||||||||
\(61\) | 7.72304 | 0.988834 | 0.494417 | − | 0.869225i | \(-0.335382\pi\) | ||||
0.494417 | + | 0.869225i | \(0.335382\pi\) | |||||||
\(62\) | 9.41470 | 1.19567 | ||||||||
\(63\) | 2.40316 | 0.302770 | ||||||||
\(64\) | −8.62140 | −1.07767 | ||||||||
\(65\) | 0.518891 | 0.0643605 | ||||||||
\(66\) | −4.28752 | −0.527757 | ||||||||
\(67\) | 14.5128 | 1.77302 | 0.886512 | − | 0.462706i | \(-0.153121\pi\) | ||||
0.886512 | + | 0.462706i | \(0.153121\pi\) | |||||||
\(68\) | −4.60285 | −0.558177 | ||||||||
\(69\) | −2.03556 | −0.245053 | ||||||||
\(70\) | 10.5282 | 1.25836 | ||||||||
\(71\) | −8.74928 | −1.03835 | −0.519174 | − | 0.854668i | \(-0.673760\pi\) | ||||
−0.519174 | + | 0.854668i | \(0.673760\pi\) | |||||||
\(72\) | 2.36857 | 0.279139 | ||||||||
\(73\) | 3.29600 | 0.385768 | 0.192884 | − | 0.981222i | \(-0.438216\pi\) | ||||
0.192884 | + | 0.981222i | \(0.438216\pi\) | |||||||
\(74\) | −19.7856 | −2.30003 | ||||||||
\(75\) | −6.63587 | −0.766245 | ||||||||
\(76\) | 6.43244 | 0.737851 | ||||||||
\(77\) | −5.35380 | −0.610122 | ||||||||
\(78\) | −2.23179 | −0.252700 | ||||||||
\(79\) | −11.0627 | −1.24465 | −0.622326 | − | 0.782758i | \(-0.713812\pi\) | ||||
−0.622326 | + | 0.782758i | \(0.713812\pi\) | |||||||
\(80\) | 3.30015 | 0.368968 | ||||||||
\(81\) | −7.25376 | −0.805974 | ||||||||
\(82\) | 9.58974 | 1.05901 | ||||||||
\(83\) | −7.76197 | −0.851986 | −0.425993 | − | 0.904726i | \(-0.640075\pi\) | ||||
−0.425993 | + | 0.904726i | \(0.640075\pi\) | |||||||
\(84\) | −30.0520 | −3.27895 | ||||||||
\(85\) | −1.04577 | −0.113429 | ||||||||
\(86\) | −6.74279 | −0.727094 | ||||||||
\(87\) | 4.79049 | 0.513595 | ||||||||
\(88\) | −5.27675 | −0.562503 | ||||||||
\(89\) | −11.9317 | −1.26475 | −0.632377 | − | 0.774661i | \(-0.717921\pi\) | ||||
−0.632377 | + | 0.774661i | \(0.717921\pi\) | |||||||
\(90\) | 1.09113 | 0.115015 | ||||||||
\(91\) | −2.78681 | −0.292138 | ||||||||
\(92\) | −5.07954 | −0.529578 | ||||||||
\(93\) | −6.10569 | −0.633130 | ||||||||
\(94\) | 13.7711 | 1.42038 | ||||||||
\(95\) | 1.46145 | 0.149942 | ||||||||
\(96\) | 0.817105 | 0.0833954 | ||||||||
\(97\) | 8.15339 | 0.827851 | 0.413925 | − | 0.910311i | \(-0.364157\pi\) | ||||
0.413925 | + | 0.910311i | \(0.364157\pi\) | |||||||
\(98\) | −39.4744 | −3.98751 | ||||||||
\(99\) | −0.554859 | −0.0557654 | ||||||||
\(100\) | −16.5591 | −1.65591 | ||||||||
\(101\) | 16.1139 | 1.60339 | 0.801695 | − | 0.597733i | \(-0.203932\pi\) | ||||
0.801695 | + | 0.597733i | \(0.203932\pi\) | |||||||
\(102\) | 4.49791 | 0.445360 | ||||||||
\(103\) | −8.78031 | −0.865149 | −0.432575 | − | 0.901598i | \(-0.642395\pi\) | ||||
−0.432575 | + | 0.901598i | \(0.642395\pi\) | |||||||
\(104\) | −2.74671 | −0.269337 | ||||||||
\(105\) | −6.82782 | −0.666327 | ||||||||
\(106\) | 5.88316 | 0.571423 | ||||||||
\(107\) | 13.4372 | 1.29902 | 0.649511 | − | 0.760352i | \(-0.274974\pi\) | ||||
0.649511 | + | 0.760352i | \(0.274974\pi\) | |||||||
\(108\) | −21.8370 | −2.10127 | ||||||||
\(109\) | −6.82296 | −0.653521 | −0.326760 | − | 0.945107i | \(-0.605957\pi\) | ||||
−0.326760 | + | 0.945107i | \(0.605957\pi\) | |||||||
\(110\) | −2.43083 | −0.231770 | ||||||||
\(111\) | 12.8315 | 1.21791 | ||||||||
\(112\) | −17.7241 | −1.67477 | ||||||||
\(113\) | 11.2354 | 1.05694 | 0.528469 | − | 0.848953i | \(-0.322766\pi\) | ||||
0.528469 | + | 0.848953i | \(0.322766\pi\) | |||||||
\(114\) | −6.28579 | −0.588718 | ||||||||
\(115\) | −1.15407 | −0.107618 | ||||||||
\(116\) | 11.9542 | 1.10992 | ||||||||
\(117\) | −0.288821 | −0.0267015 | ||||||||
\(118\) | 2.73060 | 0.251372 | ||||||||
\(119\) | 5.61651 | 0.514865 | ||||||||
\(120\) | −6.72956 | −0.614322 | ||||||||
\(121\) | −9.76388 | −0.887625 | ||||||||
\(122\) | −18.8327 | −1.70503 | ||||||||
\(123\) | −6.21921 | −0.560767 | ||||||||
\(124\) | −15.2361 | −1.36824 | ||||||||
\(125\) | −8.24524 | −0.737477 | ||||||||
\(126\) | −5.86012 | −0.522061 | ||||||||
\(127\) | 2.22804 | 0.197706 | 0.0988531 | − | 0.995102i | \(-0.468483\pi\) | ||||
0.0988531 | + | 0.995102i | \(0.468483\pi\) | |||||||
\(128\) | 19.9900 | 1.76688 | ||||||||
\(129\) | 4.37288 | 0.385011 | ||||||||
\(130\) | −1.26532 | −0.110976 | ||||||||
\(131\) | −11.7145 | −1.02350 | −0.511752 | − | 0.859133i | \(-0.671003\pi\) | ||||
−0.511752 | + | 0.859133i | \(0.671003\pi\) | |||||||
\(132\) | 6.93863 | 0.603930 | ||||||||
\(133\) | −7.84902 | −0.680597 | ||||||||
\(134\) | −35.3896 | −3.05720 | ||||||||
\(135\) | −4.96138 | −0.427008 | ||||||||
\(136\) | 5.53568 | 0.474680 | ||||||||
\(137\) | 15.3150 | 1.30845 | 0.654226 | − | 0.756299i | \(-0.272995\pi\) | ||||
0.654226 | + | 0.756299i | \(0.272995\pi\) | |||||||
\(138\) | 4.96374 | 0.422541 | ||||||||
\(139\) | −3.19049 | −0.270614 | −0.135307 | − | 0.990804i | \(-0.543202\pi\) | ||||
−0.135307 | + | 0.990804i | \(0.543202\pi\) | |||||||
\(140\) | −17.0381 | −1.43998 | ||||||||
\(141\) | −8.93093 | −0.752120 | ||||||||
\(142\) | 21.3352 | 1.79041 | ||||||||
\(143\) | 0.643440 | 0.0538071 | ||||||||
\(144\) | −1.83690 | −0.153075 | ||||||||
\(145\) | 2.71599 | 0.225551 | ||||||||
\(146\) | −8.03733 | −0.665174 | ||||||||
\(147\) | 25.6002 | 2.11147 | ||||||||
\(148\) | 32.0197 | 2.63200 | ||||||||
\(149\) | 19.1616 | 1.56978 | 0.784889 | − | 0.619636i | \(-0.212720\pi\) | ||||
0.784889 | + | 0.619636i | \(0.212720\pi\) | |||||||
\(150\) | 16.1816 | 1.32122 | ||||||||
\(151\) | −6.83338 | −0.556092 | −0.278046 | − | 0.960568i | \(-0.589687\pi\) | ||||
−0.278046 | + | 0.960568i | \(0.589687\pi\) | |||||||
\(152\) | −7.73606 | −0.627477 | ||||||||
\(153\) | 0.582086 | 0.0470589 | ||||||||
\(154\) | 13.0553 | 1.05202 | ||||||||
\(155\) | −3.46164 | −0.278046 | ||||||||
\(156\) | 3.61177 | 0.289173 | ||||||||
\(157\) | −9.27884 | −0.740532 | −0.370266 | − | 0.928926i | \(-0.620734\pi\) | ||||
−0.370266 | + | 0.928926i | \(0.620734\pi\) | |||||||
\(158\) | 26.9765 | 2.14613 | ||||||||
\(159\) | −3.81539 | −0.302580 | ||||||||
\(160\) | 0.463261 | 0.0366240 | ||||||||
\(161\) | 6.19818 | 0.488485 | ||||||||
\(162\) | 17.6883 | 1.38973 | ||||||||
\(163\) | −2.98770 | −0.234014 | −0.117007 | − | 0.993131i | \(-0.537330\pi\) | ||||
−0.117007 | + | 0.993131i | \(0.537330\pi\) | |||||||
\(164\) | −15.5194 | −1.21186 | ||||||||
\(165\) | 1.57646 | 0.122727 | ||||||||
\(166\) | 18.9276 | 1.46907 | ||||||||
\(167\) | 19.6671 | 1.52188 | 0.760941 | − | 0.648821i | \(-0.224737\pi\) | ||||
0.760941 | + | 0.648821i | \(0.224737\pi\) | |||||||
\(168\) | 36.1425 | 2.78845 | ||||||||
\(169\) | −12.6651 | −0.974236 | ||||||||
\(170\) | 2.55011 | 0.195584 | ||||||||
\(171\) | −0.813460 | −0.0622068 | ||||||||
\(172\) | 10.9121 | 0.832037 | ||||||||
\(173\) | 24.2816 | 1.84610 | 0.923050 | − | 0.384681i | \(-0.125689\pi\) | ||||
0.923050 | + | 0.384681i | \(0.125689\pi\) | |||||||
\(174\) | −11.6816 | −0.885583 | ||||||||
\(175\) | 20.2059 | 1.52742 | ||||||||
\(176\) | 4.09228 | 0.308467 | ||||||||
\(177\) | −1.77087 | −0.133107 | ||||||||
\(178\) | 29.0954 | 2.18080 | ||||||||
\(179\) | 2.75883 | 0.206204 | 0.103102 | − | 0.994671i | \(-0.467123\pi\) | ||||
0.103102 | + | 0.994671i | \(0.467123\pi\) | |||||||
\(180\) | −1.76580 | −0.131615 | ||||||||
\(181\) | 15.3589 | 1.14162 | 0.570808 | − | 0.821084i | \(-0.306630\pi\) | ||||
0.570808 | + | 0.821084i | \(0.306630\pi\) | |||||||
\(182\) | 6.79566 | 0.503728 | ||||||||
\(183\) | 12.2135 | 0.902848 | ||||||||
\(184\) | 6.10898 | 0.450360 | ||||||||
\(185\) | 7.27488 | 0.534860 | ||||||||
\(186\) | 14.8887 | 1.09170 | ||||||||
\(187\) | −1.29678 | −0.0948300 | ||||||||
\(188\) | −22.2862 | −1.62539 | ||||||||
\(189\) | 26.6461 | 1.93822 | ||||||||
\(190\) | −3.56375 | −0.258542 | ||||||||
\(191\) | 15.1762 | 1.09811 | 0.549054 | − | 0.835787i | \(-0.314988\pi\) | ||||
0.549054 | + | 0.835787i | \(0.314988\pi\) | |||||||
\(192\) | −13.6342 | −0.983963 | ||||||||
\(193\) | 5.12372 | 0.368813 | 0.184407 | − | 0.982850i | \(-0.440964\pi\) | ||||
0.184407 | + | 0.982850i | \(0.440964\pi\) | |||||||
\(194\) | −19.8821 | −1.42745 | ||||||||
\(195\) | 0.820594 | 0.0587639 | ||||||||
\(196\) | 63.8826 | 4.56304 | ||||||||
\(197\) | 11.0526 | 0.787467 | 0.393733 | − | 0.919225i | \(-0.371183\pi\) | ||||
0.393733 | + | 0.919225i | \(0.371183\pi\) | |||||||
\(198\) | 1.35303 | 0.0961554 | ||||||||
\(199\) | −4.36134 | −0.309167 | −0.154584 | − | 0.987980i | \(-0.549404\pi\) | ||||
−0.154584 | + | 0.987980i | \(0.549404\pi\) | |||||||
\(200\) | 19.9151 | 1.40821 | ||||||||
\(201\) | 22.9511 | 1.61885 | ||||||||
\(202\) | −39.2938 | −2.76470 | ||||||||
\(203\) | −14.5868 | −1.02379 | ||||||||
\(204\) | −7.27911 | −0.509640 | ||||||||
\(205\) | −3.52600 | −0.246267 | ||||||||
\(206\) | 21.4108 | 1.49176 | ||||||||
\(207\) | 0.642369 | 0.0446478 | ||||||||
\(208\) | 2.13015 | 0.147700 | ||||||||
\(209\) | 1.81224 | 0.125355 | ||||||||
\(210\) | 16.6497 | 1.14894 | ||||||||
\(211\) | 5.67880 | 0.390945 | 0.195472 | − | 0.980709i | \(-0.437376\pi\) | ||||
0.195472 | + | 0.980709i | \(0.437376\pi\) | |||||||
\(212\) | −9.52091 | −0.653899 | ||||||||
\(213\) | −13.8364 | −0.948057 | ||||||||
\(214\) | −32.7667 | −2.23988 | ||||||||
\(215\) | 2.47922 | 0.169082 | ||||||||
\(216\) | 26.2626 | 1.78695 | ||||||||
\(217\) | 18.5915 | 1.26207 | ||||||||
\(218\) | 16.6378 | 1.12686 | ||||||||
\(219\) | 5.21242 | 0.352223 | ||||||||
\(220\) | 3.93388 | 0.265222 | ||||||||
\(221\) | −0.675013 | −0.0454063 | ||||||||
\(222\) | −31.2897 | −2.10003 | ||||||||
\(223\) | 20.0040 | 1.33957 | 0.669783 | − | 0.742557i | \(-0.266387\pi\) | ||||
0.669783 | + | 0.742557i | \(0.266387\pi\) | |||||||
\(224\) | −2.48804 | −0.166239 | ||||||||
\(225\) | 2.09410 | 0.139607 | ||||||||
\(226\) | −27.3976 | −1.82246 | ||||||||
\(227\) | 2.99520 | 0.198798 | 0.0993992 | − | 0.995048i | \(-0.468308\pi\) | ||||
0.0993992 | + | 0.995048i | \(0.468308\pi\) | |||||||
\(228\) | 10.1725 | 0.673690 | ||||||||
\(229\) | 28.5826 | 1.88879 | 0.944396 | − | 0.328809i | \(-0.106647\pi\) | ||||
0.944396 | + | 0.328809i | \(0.106647\pi\) | |||||||
\(230\) | 2.81421 | 0.185563 | ||||||||
\(231\) | −8.46669 | −0.557067 | ||||||||
\(232\) | −14.3768 | −0.943886 | ||||||||
\(233\) | −2.94172 | −0.192719 | −0.0963593 | − | 0.995347i | \(-0.530720\pi\) | ||||
−0.0963593 | + | 0.995347i | \(0.530720\pi\) | |||||||
\(234\) | 0.704291 | 0.0460409 | ||||||||
\(235\) | −5.06343 | −0.330302 | ||||||||
\(236\) | −4.41901 | −0.287653 | ||||||||
\(237\) | −17.4950 | −1.13642 | ||||||||
\(238\) | −13.6959 | −0.887773 | ||||||||
\(239\) | −13.0690 | −0.845363 | −0.422682 | − | 0.906278i | \(-0.638911\pi\) | ||||
−0.422682 | + | 0.906278i | \(0.638911\pi\) | |||||||
\(240\) | 5.21897 | 0.336883 | ||||||||
\(241\) | −13.7823 | −0.887799 | −0.443899 | − | 0.896077i | \(-0.646405\pi\) | ||||
−0.443899 | + | 0.896077i | \(0.646405\pi\) | |||||||
\(242\) | 23.8093 | 1.53052 | ||||||||
\(243\) | 5.12925 | 0.329041 | ||||||||
\(244\) | 30.4775 | 1.95112 | ||||||||
\(245\) | 14.5141 | 0.927274 | ||||||||
\(246\) | 15.1656 | 0.966921 | ||||||||
\(247\) | 0.943325 | 0.0600223 | ||||||||
\(248\) | 18.3239 | 1.16357 | ||||||||
\(249\) | −12.2751 | −0.777900 | ||||||||
\(250\) | 20.1061 | 1.27162 | ||||||||
\(251\) | 10.5204 | 0.664043 | 0.332021 | − | 0.943272i | \(-0.392269\pi\) | ||||
0.332021 | + | 0.943272i | \(0.392269\pi\) | |||||||
\(252\) | 9.48361 | 0.597411 | ||||||||
\(253\) | −1.43108 | −0.0899713 | ||||||||
\(254\) | −5.43308 | −0.340902 | ||||||||
\(255\) | −1.65381 | −0.103566 | ||||||||
\(256\) | −31.5028 | −1.96893 | ||||||||
\(257\) | −6.25664 | −0.390279 | −0.195139 | − | 0.980776i | \(-0.562516\pi\) | ||||
−0.195139 | + | 0.980776i | \(0.562516\pi\) | |||||||
\(258\) | −10.6633 | −0.663868 | ||||||||
\(259\) | −39.0713 | −2.42777 | ||||||||
\(260\) | 2.04770 | 0.126993 | ||||||||
\(261\) | −1.51175 | −0.0935750 | ||||||||
\(262\) | 28.5659 | 1.76481 | ||||||||
\(263\) | −1.72239 | −0.106207 | −0.0531035 | − | 0.998589i | \(-0.516911\pi\) | ||||
−0.0531035 | + | 0.998589i | \(0.516911\pi\) | |||||||
\(264\) | −8.34484 | −0.513589 | ||||||||
\(265\) | −2.16315 | −0.132881 | ||||||||
\(266\) | 19.1399 | 1.17354 | ||||||||
\(267\) | −18.8692 | −1.15478 | ||||||||
\(268\) | 57.2721 | 3.49845 | ||||||||
\(269\) | −17.5496 | −1.07002 | −0.535008 | − | 0.844847i | \(-0.679692\pi\) | ||||
−0.535008 | + | 0.844847i | \(0.679692\pi\) | |||||||
\(270\) | 12.0983 | 0.736282 | ||||||||
\(271\) | −6.51776 | −0.395926 | −0.197963 | − | 0.980210i | \(-0.563433\pi\) | ||||
−0.197963 | + | 0.980210i | \(0.563433\pi\) | |||||||
\(272\) | −4.29308 | −0.260306 | ||||||||
\(273\) | −4.40717 | −0.266734 | ||||||||
\(274\) | −37.3458 | −2.25614 | ||||||||
\(275\) | −4.66528 | −0.281327 | ||||||||
\(276\) | −8.03297 | −0.483528 | ||||||||
\(277\) | 30.9632 | 1.86040 | 0.930198 | − | 0.367059i | \(-0.119635\pi\) | ||||
0.930198 | + | 0.367059i | \(0.119635\pi\) | |||||||
\(278\) | 7.78003 | 0.466615 | ||||||||
\(279\) | 1.92679 | 0.115354 | ||||||||
\(280\) | 20.4911 | 1.22458 | ||||||||
\(281\) | 22.1759 | 1.32290 | 0.661452 | − | 0.749987i | \(-0.269940\pi\) | ||||
0.661452 | + | 0.749987i | \(0.269940\pi\) | |||||||
\(282\) | 21.7781 | 1.29687 | ||||||||
\(283\) | 6.67333 | 0.396688 | 0.198344 | − | 0.980132i | \(-0.436444\pi\) | ||||
0.198344 | + | 0.980132i | \(0.436444\pi\) | |||||||
\(284\) | −34.5274 | −2.04882 | ||||||||
\(285\) | 2.31119 | 0.136903 | ||||||||
\(286\) | −1.56903 | −0.0927788 | ||||||||
\(287\) | 18.9371 | 1.11782 | ||||||||
\(288\) | −0.257856 | −0.0151943 | ||||||||
\(289\) | −15.6396 | −0.919976 | ||||||||
\(290\) | −6.62295 | −0.388913 | ||||||||
\(291\) | 12.8941 | 0.755863 | ||||||||
\(292\) | 13.0070 | 0.761180 | ||||||||
\(293\) | 0.872822 | 0.0509908 | 0.0254954 | − | 0.999675i | \(-0.491884\pi\) | ||||
0.0254954 | + | 0.999675i | \(0.491884\pi\) | |||||||
\(294\) | −62.4262 | −3.64077 | ||||||||
\(295\) | −1.00400 | −0.0584551 | ||||||||
\(296\) | −38.5089 | −2.23829 | ||||||||
\(297\) | −6.15225 | −0.356990 | ||||||||
\(298\) | −46.7256 | −2.70674 | ||||||||
\(299\) | −0.744921 | −0.0430799 | ||||||||
\(300\) | −26.1872 | −1.51192 | ||||||||
\(301\) | −13.3152 | −0.767474 | ||||||||
\(302\) | 16.6632 | 0.958861 | ||||||||
\(303\) | 25.4831 | 1.46396 | ||||||||
\(304\) | 5.99955 | 0.344098 | ||||||||
\(305\) | 6.92449 | 0.396495 | ||||||||
\(306\) | −1.41942 | −0.0811428 | ||||||||
\(307\) | 15.9290 | 0.909114 | 0.454557 | − | 0.890718i | \(-0.349798\pi\) | ||||
0.454557 | + | 0.890718i | \(0.349798\pi\) | |||||||
\(308\) | −21.1277 | −1.20386 | ||||||||
\(309\) | −13.8855 | −0.789918 | ||||||||
\(310\) | 8.44123 | 0.479430 | ||||||||
\(311\) | 7.62252 | 0.432234 | 0.216117 | − | 0.976368i | \(-0.430661\pi\) | ||||
0.216117 | + | 0.976368i | \(0.430661\pi\) | |||||||
\(312\) | −4.34374 | −0.245916 | ||||||||
\(313\) | −14.0046 | −0.791586 | −0.395793 | − | 0.918340i | \(-0.629530\pi\) | ||||
−0.395793 | + | 0.918340i | \(0.629530\pi\) | |||||||
\(314\) | 22.6265 | 1.27689 | ||||||||
\(315\) | 2.15468 | 0.121402 | ||||||||
\(316\) | −43.6569 | −2.45589 | ||||||||
\(317\) | 1.69959 | 0.0954583 | 0.0477292 | − | 0.998860i | \(-0.484802\pi\) | ||||
0.0477292 | + | 0.998860i | \(0.484802\pi\) | |||||||
\(318\) | 9.30385 | 0.521734 | ||||||||
\(319\) | 3.36790 | 0.188566 | ||||||||
\(320\) | −7.72996 | −0.432118 | ||||||||
\(321\) | 21.2501 | 1.18606 | ||||||||
\(322\) | −15.1143 | −0.842287 | ||||||||
\(323\) | −1.90117 | −0.105784 | ||||||||
\(324\) | −28.6256 | −1.59031 | ||||||||
\(325\) | −2.42842 | −0.134704 | ||||||||
\(326\) | 7.28551 | 0.403507 | ||||||||
\(327\) | −10.7901 | −0.596692 | ||||||||
\(328\) | 18.6646 | 1.03058 | ||||||||
\(329\) | 27.1942 | 1.49926 | ||||||||
\(330\) | −3.84420 | −0.211616 | ||||||||
\(331\) | 18.6325 | 1.02413 | 0.512066 | − | 0.858946i | \(-0.328880\pi\) | ||||
0.512066 | + | 0.858946i | \(0.328880\pi\) | |||||||
\(332\) | −30.6311 | −1.68110 | ||||||||
\(333\) | −4.04928 | −0.221899 | ||||||||
\(334\) | −47.9582 | −2.62416 | ||||||||
\(335\) | 13.0122 | 0.710934 | ||||||||
\(336\) | −28.0296 | −1.52914 | ||||||||
\(337\) | −7.95857 | −0.433531 | −0.216765 | − | 0.976224i | \(-0.569551\pi\) | ||||
−0.216765 | + | 0.976224i | \(0.569551\pi\) | |||||||
\(338\) | 30.8838 | 1.67986 | ||||||||
\(339\) | 17.7681 | 0.965030 | ||||||||
\(340\) | −4.12692 | −0.223814 | ||||||||
\(341\) | −4.29253 | −0.232454 | ||||||||
\(342\) | 1.98363 | 0.107262 | ||||||||
\(343\) | −44.2435 | −2.38892 | ||||||||
\(344\) | −13.1235 | −0.707574 | ||||||||
\(345\) | −1.82509 | −0.0982596 | ||||||||
\(346\) | −59.2109 | −3.18320 | ||||||||
\(347\) | 2.69492 | 0.144671 | 0.0723354 | − | 0.997380i | \(-0.476955\pi\) | ||||
0.0723354 | + | 0.997380i | \(0.476955\pi\) | |||||||
\(348\) | 18.9048 | 1.01340 | ||||||||
\(349\) | −11.1102 | −0.594718 | −0.297359 | − | 0.954766i | \(-0.596106\pi\) | ||||
−0.297359 | + | 0.954766i | \(0.596106\pi\) | |||||||
\(350\) | −49.2721 | −2.63371 | ||||||||
\(351\) | −3.20243 | −0.170933 | ||||||||
\(352\) | 0.574456 | 0.0306186 | ||||||||
\(353\) | 10.4402 | 0.555675 | 0.277837 | − | 0.960628i | \(-0.410382\pi\) | ||||
0.277837 | + | 0.960628i | \(0.410382\pi\) | |||||||
\(354\) | 4.31827 | 0.229513 | ||||||||
\(355\) | −7.84462 | −0.416349 | ||||||||
\(356\) | −47.0860 | −2.49556 | ||||||||
\(357\) | 8.88215 | 0.470093 | ||||||||
\(358\) | −6.72741 | −0.355555 | ||||||||
\(359\) | 32.7921 | 1.73070 | 0.865352 | − | 0.501165i | \(-0.167095\pi\) | ||||
0.865352 | + | 0.501165i | \(0.167095\pi\) | |||||||
\(360\) | 2.12367 | 0.111927 | ||||||||
\(361\) | −16.3431 | −0.860165 | ||||||||
\(362\) | −37.4527 | −1.96847 | ||||||||
\(363\) | −15.4410 | −0.810440 | ||||||||
\(364\) | −10.9976 | −0.576432 | ||||||||
\(365\) | 2.95520 | 0.154682 | ||||||||
\(366\) | −29.7827 | −1.55677 | ||||||||
\(367\) | −24.1027 | −1.25815 | −0.629074 | − | 0.777345i | \(-0.716566\pi\) | ||||
−0.629074 | + | 0.777345i | \(0.716566\pi\) | |||||||
\(368\) | −4.73769 | −0.246969 | ||||||||
\(369\) | 1.96261 | 0.102170 | ||||||||
\(370\) | −17.7398 | −0.922250 | ||||||||
\(371\) | 11.6177 | 0.603159 | ||||||||
\(372\) | −24.0949 | −1.24926 | ||||||||
\(373\) | 17.1020 | 0.885510 | 0.442755 | − | 0.896643i | \(-0.354001\pi\) | ||||
0.442755 | + | 0.896643i | \(0.354001\pi\) | |||||||
\(374\) | 3.16221 | 0.163514 | ||||||||
\(375\) | −13.0393 | −0.673348 | ||||||||
\(376\) | 26.8028 | 1.38225 | ||||||||
\(377\) | 1.75309 | 0.0902890 | ||||||||
\(378\) | −64.9767 | −3.34204 | ||||||||
\(379\) | 19.5608 | 1.00477 | 0.502386 | − | 0.864643i | \(-0.332455\pi\) | ||||
0.502386 | + | 0.864643i | \(0.332455\pi\) | |||||||
\(380\) | 5.76733 | 0.295858 | ||||||||
\(381\) | 3.52350 | 0.180514 | ||||||||
\(382\) | −37.0071 | −1.89345 | ||||||||
\(383\) | 30.0414 | 1.53505 | 0.767523 | − | 0.641022i | \(-0.221489\pi\) | ||||
0.767523 | + | 0.641022i | \(0.221489\pi\) | |||||||
\(384\) | 31.6128 | 1.61324 | ||||||||
\(385\) | −4.80022 | −0.244642 | ||||||||
\(386\) | −12.4942 | −0.635939 | ||||||||
\(387\) | −1.37996 | −0.0701475 | ||||||||
\(388\) | 32.1758 | 1.63348 | ||||||||
\(389\) | 5.41311 | 0.274456 | 0.137228 | − | 0.990540i | \(-0.456181\pi\) | ||||
0.137228 | + | 0.990540i | \(0.456181\pi\) | |||||||
\(390\) | −2.00102 | −0.101326 | ||||||||
\(391\) | 1.50130 | 0.0759242 | ||||||||
\(392\) | −76.8293 | −3.88047 | ||||||||
\(393\) | −18.5258 | −0.934502 | ||||||||
\(394\) | −26.9519 | −1.35782 | ||||||||
\(395\) | −9.91885 | −0.499071 | ||||||||
\(396\) | −2.18964 | −0.110034 | ||||||||
\(397\) | −8.35115 | −0.419132 | −0.209566 | − | 0.977794i | \(-0.567205\pi\) | ||||
−0.209566 | + | 0.977794i | \(0.567205\pi\) | |||||||
\(398\) | 10.6351 | 0.533092 | ||||||||
\(399\) | −12.4127 | −0.621414 | ||||||||
\(400\) | −15.4447 | −0.772237 | ||||||||
\(401\) | −2.66623 | −0.133145 | −0.0665725 | − | 0.997782i | \(-0.521206\pi\) | ||||
−0.0665725 | + | 0.997782i | \(0.521206\pi\) | |||||||
\(402\) | −55.9664 | −2.79135 | ||||||||
\(403\) | −2.23439 | −0.111303 | ||||||||
\(404\) | 63.5903 | 3.16373 | ||||||||
\(405\) | −6.50374 | −0.323173 | ||||||||
\(406\) | 35.5699 | 1.76531 | ||||||||
\(407\) | 9.02105 | 0.447157 | ||||||||
\(408\) | 8.75432 | 0.433403 | ||||||||
\(409\) | −19.9202 | −0.984991 | −0.492495 | − | 0.870315i | \(-0.663915\pi\) | ||||
−0.492495 | + | 0.870315i | \(0.663915\pi\) | |||||||
\(410\) | 8.59818 | 0.424634 | ||||||||
\(411\) | 24.2198 | 1.19467 | ||||||||
\(412\) | −34.6498 | −1.70707 | ||||||||
\(413\) | 5.39219 | 0.265332 | ||||||||
\(414\) | −1.56642 | −0.0769854 | ||||||||
\(415\) | −6.95939 | −0.341623 | ||||||||
\(416\) | 0.299022 | 0.0146608 | ||||||||
\(417\) | −5.04556 | −0.247082 | ||||||||
\(418\) | −4.41915 | −0.216148 | ||||||||
\(419\) | 34.0205 | 1.66201 | 0.831004 | − | 0.556266i | \(-0.187767\pi\) | ||||
0.831004 | + | 0.556266i | \(0.187767\pi\) | |||||||
\(420\) | −26.9447 | −1.31477 | ||||||||
\(421\) | −12.0876 | −0.589112 | −0.294556 | − | 0.955634i | \(-0.595172\pi\) | ||||
−0.294556 | + | 0.955634i | \(0.595172\pi\) | |||||||
\(422\) | −13.8478 | −0.674100 | ||||||||
\(423\) | 2.81836 | 0.137033 | ||||||||
\(424\) | 11.4504 | 0.556083 | ||||||||
\(425\) | 4.89420 | 0.237404 | ||||||||
\(426\) | 33.7402 | 1.63472 | ||||||||
\(427\) | −37.1894 | −1.79972 | ||||||||
\(428\) | 53.0273 | 2.56317 | ||||||||
\(429\) | 1.01756 | 0.0491282 | ||||||||
\(430\) | −6.04560 | −0.291545 | ||||||||
\(431\) | 15.9542 | 0.768488 | 0.384244 | − | 0.923232i | \(-0.374462\pi\) | ||||
0.384244 | + | 0.923232i | \(0.374462\pi\) | |||||||
\(432\) | −20.3675 | −0.979930 | ||||||||
\(433\) | −7.50972 | −0.360894 | −0.180447 | − | 0.983585i | \(-0.557754\pi\) | ||||
−0.180447 | + | 0.983585i | \(0.557754\pi\) | |||||||
\(434\) | −45.3354 | −2.17617 | ||||||||
\(435\) | 4.29516 | 0.205937 | ||||||||
\(436\) | −26.9255 | −1.28950 | ||||||||
\(437\) | −2.09806 | −0.100364 | ||||||||
\(438\) | −12.7105 | −0.607332 | ||||||||
\(439\) | −19.3047 | −0.921361 | −0.460680 | − | 0.887566i | \(-0.652395\pi\) | ||||
−0.460680 | + | 0.887566i | \(0.652395\pi\) | |||||||
\(440\) | −4.73114 | −0.225548 | ||||||||
\(441\) | −8.07873 | −0.384702 | ||||||||
\(442\) | 1.64602 | 0.0782934 | ||||||||
\(443\) | 14.2949 | 0.679172 | 0.339586 | − | 0.940575i | \(-0.389713\pi\) | ||||
0.339586 | + | 0.940575i | \(0.389713\pi\) | |||||||
\(444\) | 50.6371 | 2.40313 | ||||||||
\(445\) | −10.6980 | −0.507132 | ||||||||
\(446\) | −48.7798 | −2.30979 | ||||||||
\(447\) | 30.3028 | 1.43328 | ||||||||
\(448\) | 41.5154 | 1.96142 | ||||||||
\(449\) | −29.7460 | −1.40380 | −0.701901 | − | 0.712275i | \(-0.747665\pi\) | ||||
−0.701901 | + | 0.712275i | \(0.747665\pi\) | |||||||
\(450\) | −5.10648 | −0.240722 | ||||||||
\(451\) | −4.37234 | −0.205886 | ||||||||
\(452\) | 44.3384 | 2.08550 | ||||||||
\(453\) | −10.8066 | −0.507736 | ||||||||
\(454\) | −7.30381 | −0.342785 | ||||||||
\(455\) | −2.49866 | −0.117139 | ||||||||
\(456\) | −12.2341 | −0.572914 | ||||||||
\(457\) | 21.0017 | 0.982419 | 0.491209 | − | 0.871042i | \(-0.336555\pi\) | ||||
0.491209 | + | 0.871042i | \(0.336555\pi\) | |||||||
\(458\) | −69.6989 | −3.25681 | ||||||||
\(459\) | 6.45414 | 0.301253 | ||||||||
\(460\) | −4.55432 | −0.212346 | ||||||||
\(461\) | 2.51435 | 0.117105 | 0.0585524 | − | 0.998284i | \(-0.481352\pi\) | ||||
0.0585524 | + | 0.998284i | \(0.481352\pi\) | |||||||
\(462\) | 20.6461 | 0.960542 | ||||||||
\(463\) | 7.67175 | 0.356536 | 0.178268 | − | 0.983982i | \(-0.442951\pi\) | ||||
0.178268 | + | 0.983982i | \(0.442951\pi\) | |||||||
\(464\) | 11.1497 | 0.517611 | ||||||||
\(465\) | −5.47437 | −0.253868 | ||||||||
\(466\) | 7.17341 | 0.332302 | ||||||||
\(467\) | −4.54158 | −0.210159 | −0.105080 | − | 0.994464i | \(-0.533510\pi\) | ||||
−0.105080 | + | 0.994464i | \(0.533510\pi\) | |||||||
\(468\) | −1.13978 | −0.0526862 | ||||||||
\(469\) | −69.8849 | −3.22698 | ||||||||
\(470\) | 12.3472 | 0.569534 | ||||||||
\(471\) | −14.6739 | −0.676138 | ||||||||
\(472\) | 5.31459 | 0.244624 | ||||||||
\(473\) | 3.07431 | 0.141357 | ||||||||
\(474\) | 42.6616 | 1.95951 | ||||||||
\(475\) | −6.83960 | −0.313823 | ||||||||
\(476\) | 22.1645 | 1.01591 | ||||||||
\(477\) | 1.20403 | 0.0551289 | ||||||||
\(478\) | 31.8688 | 1.45765 | ||||||||
\(479\) | 7.01939 | 0.320724 | 0.160362 | − | 0.987058i | \(-0.448734\pi\) | ||||
0.160362 | + | 0.987058i | \(0.448734\pi\) | |||||||
\(480\) | 0.732618 | 0.0334393 | ||||||||
\(481\) | 4.69573 | 0.214107 | ||||||||
\(482\) | 33.6083 | 1.53082 | ||||||||
\(483\) | 9.80203 | 0.446008 | ||||||||
\(484\) | −38.5313 | −1.75142 | ||||||||
\(485\) | 7.31034 | 0.331945 | ||||||||
\(486\) | −12.5077 | −0.567361 | ||||||||
\(487\) | −1.25980 | −0.0570872 | −0.0285436 | − | 0.999593i | \(-0.509087\pi\) | ||||
−0.0285436 | + | 0.999593i | \(0.509087\pi\) | |||||||
\(488\) | −36.6542 | −1.65926 | ||||||||
\(489\) | −4.72485 | −0.213665 | ||||||||
\(490\) | −35.3928 | −1.59888 | ||||||||
\(491\) | 6.14749 | 0.277432 | 0.138716 | − | 0.990332i | \(-0.455702\pi\) | ||||
0.138716 | + | 0.990332i | \(0.455702\pi\) | |||||||
\(492\) | −24.5429 | −1.10648 | ||||||||
\(493\) | −3.53316 | −0.159126 | ||||||||
\(494\) | −2.30030 | −0.103496 | ||||||||
\(495\) | −0.497487 | −0.0223604 | ||||||||
\(496\) | −14.2107 | −0.638081 | ||||||||
\(497\) | 42.1312 | 1.88984 | ||||||||
\(498\) | 29.9328 | 1.34132 | ||||||||
\(499\) | −34.7842 | −1.55716 | −0.778578 | − | 0.627548i | \(-0.784059\pi\) | ||||
−0.778578 | + | 0.627548i | \(0.784059\pi\) | |||||||
\(500\) | −32.5383 | −1.45516 | ||||||||
\(501\) | 31.1022 | 1.38954 | ||||||||
\(502\) | −25.6541 | −1.14500 | ||||||||
\(503\) | 30.2069 | 1.34686 | 0.673430 | − | 0.739251i | \(-0.264820\pi\) | ||||
0.673430 | + | 0.739251i | \(0.264820\pi\) | |||||||
\(504\) | −11.4056 | −0.508045 | ||||||||
\(505\) | 14.4477 | 0.642915 | ||||||||
\(506\) | 3.48970 | 0.155136 | ||||||||
\(507\) | −20.0290 | −0.889519 | ||||||||
\(508\) | 8.79252 | 0.390105 | ||||||||
\(509\) | 32.4177 | 1.43689 | 0.718445 | − | 0.695584i | \(-0.244854\pi\) | ||||
0.718445 | + | 0.695584i | \(0.244854\pi\) | |||||||
\(510\) | 4.03283 | 0.178577 | ||||||||
\(511\) | −15.8715 | −0.702115 | ||||||||
\(512\) | 36.8399 | 1.62811 | ||||||||
\(513\) | −9.01960 | −0.398225 | ||||||||
\(514\) | 15.2569 | 0.672951 | ||||||||
\(515\) | −7.87244 | −0.346901 | ||||||||
\(516\) | 17.2567 | 0.759686 | ||||||||
\(517\) | −6.27879 | −0.276141 | ||||||||
\(518\) | 95.2755 | 4.18616 | ||||||||
\(519\) | 38.3999 | 1.68557 | ||||||||
\(520\) | −2.46270 | −0.107997 | ||||||||
\(521\) | −7.30325 | −0.319961 | −0.159981 | − | 0.987120i | \(-0.551143\pi\) | ||||
−0.159981 | + | 0.987120i | \(0.551143\pi\) | |||||||
\(522\) | 3.68641 | 0.161350 | ||||||||
\(523\) | −30.3284 | −1.32617 | −0.663083 | − | 0.748546i | \(-0.730753\pi\) | ||||
−0.663083 | + | 0.748546i | \(0.730753\pi\) | |||||||
\(524\) | −46.2292 | −2.01953 | ||||||||
\(525\) | 31.9543 | 1.39460 | ||||||||
\(526\) | 4.20005 | 0.183131 | ||||||||
\(527\) | 4.50317 | 0.196161 | ||||||||
\(528\) | 6.47167 | 0.281643 | ||||||||
\(529\) | −21.3432 | −0.927966 | ||||||||
\(530\) | 5.27485 | 0.229125 | ||||||||
\(531\) | 0.558838 | 0.0242515 | ||||||||
\(532\) | −30.9747 | −1.34292 | ||||||||
\(533\) | −2.27594 | −0.0985817 | ||||||||
\(534\) | 46.0126 | 1.99116 | ||||||||
\(535\) | 12.0478 | 0.520872 | ||||||||
\(536\) | −68.8791 | −2.97512 | ||||||||
\(537\) | 4.36291 | 0.188273 | ||||||||
\(538\) | 42.7947 | 1.84501 | ||||||||
\(539\) | 17.9979 | 0.775226 | ||||||||
\(540\) | −19.5791 | −0.842552 | ||||||||
\(541\) | −2.08832 | −0.0897839 | −0.0448920 | − | 0.998992i | \(-0.514294\pi\) | ||||
−0.0448920 | + | 0.998992i | \(0.514294\pi\) | |||||||
\(542\) | 15.8936 | 0.682688 | ||||||||
\(543\) | 24.2891 | 1.04234 | ||||||||
\(544\) | −0.602645 | −0.0258382 | ||||||||
\(545\) | −6.11747 | −0.262044 | ||||||||
\(546\) | 10.7469 | 0.459925 | ||||||||
\(547\) | 0.518080 | 0.0221515 | 0.0110758 | − | 0.999939i | \(-0.496474\pi\) | ||||
0.0110758 | + | 0.999939i | \(0.496474\pi\) | |||||||
\(548\) | 60.4378 | 2.58178 | ||||||||
\(549\) | −3.85425 | −0.164495 | ||||||||
\(550\) | 11.3763 | 0.485087 | ||||||||
\(551\) | 4.93757 | 0.210347 | ||||||||
\(552\) | 9.66096 | 0.411198 | ||||||||
\(553\) | 53.2712 | 2.26532 | ||||||||
\(554\) | −75.5038 | −3.20785 | ||||||||
\(555\) | 11.5048 | 0.488350 | ||||||||
\(556\) | −12.5907 | −0.533963 | ||||||||
\(557\) | 27.7223 | 1.17463 | 0.587316 | − | 0.809358i | \(-0.300185\pi\) | ||||
0.587316 | + | 0.809358i | \(0.300185\pi\) | |||||||
\(558\) | −4.69849 | −0.198903 | ||||||||
\(559\) | 1.60027 | 0.0676842 | ||||||||
\(560\) | −15.8915 | −0.671538 | ||||||||
\(561\) | −2.05078 | −0.0865838 | ||||||||
\(562\) | −54.0761 | −2.28106 | ||||||||
\(563\) | −45.6536 | −1.92407 | −0.962035 | − | 0.272928i | \(-0.912008\pi\) | ||||
−0.962035 | + | 0.272928i | \(0.912008\pi\) | |||||||
\(564\) | −35.2442 | −1.48405 | ||||||||
\(565\) | 10.0737 | 0.423803 | ||||||||
\(566\) | −16.2729 | −0.684003 | ||||||||
\(567\) | 34.9297 | 1.46691 | ||||||||
\(568\) | 41.5248 | 1.74234 | ||||||||
\(569\) | 42.5241 | 1.78270 | 0.891351 | − | 0.453313i | \(-0.149758\pi\) | ||||
0.891351 | + | 0.453313i | \(0.149758\pi\) | |||||||
\(570\) | −5.63585 | −0.236060 | ||||||||
\(571\) | 25.1272 | 1.05154 | 0.525771 | − | 0.850626i | \(-0.323777\pi\) | ||||
0.525771 | + | 0.850626i | \(0.323777\pi\) | |||||||
\(572\) | 2.53921 | 0.106170 | ||||||||
\(573\) | 24.0001 | 1.00262 | ||||||||
\(574\) | −46.1783 | −1.92745 | ||||||||
\(575\) | 5.40107 | 0.225240 | ||||||||
\(576\) | 4.30258 | 0.179274 | ||||||||
\(577\) | −12.0819 | −0.502974 | −0.251487 | − | 0.967861i | \(-0.580920\pi\) | ||||
−0.251487 | + | 0.967861i | \(0.580920\pi\) | |||||||
\(578\) | 38.1372 | 1.58630 | ||||||||
\(579\) | 8.10284 | 0.336742 | ||||||||
\(580\) | 10.7181 | 0.445046 | ||||||||
\(581\) | 37.3769 | 1.55065 | ||||||||
\(582\) | −31.4422 | −1.30332 | ||||||||
\(583\) | −2.68237 | −0.111092 | ||||||||
\(584\) | −15.6431 | −0.647316 | ||||||||
\(585\) | −0.258957 | −0.0107066 | ||||||||
\(586\) | −2.12838 | −0.0879226 | ||||||||
\(587\) | −13.2011 | −0.544868 | −0.272434 | − | 0.962174i | \(-0.587829\pi\) | ||||
−0.272434 | + | 0.962174i | \(0.587829\pi\) | |||||||
\(588\) | 101.026 | 4.16625 | ||||||||
\(589\) | −6.29314 | −0.259304 | ||||||||
\(590\) | 2.44826 | 0.100793 | ||||||||
\(591\) | 17.4790 | 0.718991 | ||||||||
\(592\) | 29.8648 | 1.22744 | ||||||||
\(593\) | 7.63273 | 0.313439 | 0.156719 | − | 0.987643i | \(-0.449908\pi\) | ||||
0.156719 | + | 0.987643i | \(0.449908\pi\) | |||||||
\(594\) | 15.0023 | 0.615551 | ||||||||
\(595\) | 5.03577 | 0.206446 | ||||||||
\(596\) | 75.6175 | 3.09741 | ||||||||
\(597\) | −6.89718 | −0.282283 | ||||||||
\(598\) | 1.81649 | 0.0742819 | ||||||||
\(599\) | −21.1836 | −0.865537 | −0.432768 | − | 0.901505i | \(-0.642463\pi\) | ||||
−0.432768 | + | 0.901505i | \(0.642463\pi\) | |||||||
\(600\) | 31.4944 | 1.28575 | ||||||||
\(601\) | 40.3995 | 1.64793 | 0.823965 | − | 0.566640i | \(-0.191757\pi\) | ||||
0.823965 | + | 0.566640i | \(0.191757\pi\) | |||||||
\(602\) | 32.4691 | 1.32334 | ||||||||
\(603\) | −7.24275 | −0.294948 | ||||||||
\(604\) | −26.9666 | −1.09726 | ||||||||
\(605\) | −8.75431 | −0.355913 | ||||||||
\(606\) | −62.1406 | −2.52429 | ||||||||
\(607\) | 38.7043 | 1.57096 | 0.785480 | − | 0.618887i | \(-0.212416\pi\) | ||||
0.785480 | + | 0.618887i | \(0.212416\pi\) | |||||||
\(608\) | 0.842191 | 0.0341554 | ||||||||
\(609\) | −23.0681 | −0.934765 | ||||||||
\(610\) | −16.8854 | −0.683670 | ||||||||
\(611\) | −3.26830 | −0.132221 | ||||||||
\(612\) | 2.29709 | 0.0928544 | ||||||||
\(613\) | 13.2930 | 0.536899 | 0.268449 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268449 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(614\) | −38.8428 | −1.56757 | ||||||||
\(615\) | −5.57615 | −0.224852 | ||||||||
\(616\) | 25.4096 | 1.02378 | ||||||||
\(617\) | −23.1606 | −0.932411 | −0.466205 | − | 0.884677i | \(-0.654379\pi\) | ||||
−0.466205 | + | 0.884677i | \(0.654379\pi\) | |||||||
\(618\) | 33.8599 | 1.36204 | ||||||||
\(619\) | 5.79996 | 0.233120 | 0.116560 | − | 0.993184i | \(-0.462813\pi\) | ||||
0.116560 | + | 0.993184i | \(0.462813\pi\) | |||||||
\(620\) | −13.6607 | −0.548627 | ||||||||
\(621\) | 7.12256 | 0.285819 | ||||||||
\(622\) | −18.5876 | −0.745293 | ||||||||
\(623\) | 57.4556 | 2.30191 | ||||||||
\(624\) | 3.36870 | 0.134856 | ||||||||
\(625\) | 13.5878 | 0.543513 | ||||||||
\(626\) | 34.1502 | 1.36492 | ||||||||
\(627\) | 2.86594 | 0.114455 | ||||||||
\(628\) | −36.6172 | −1.46118 | ||||||||
\(629\) | −9.46372 | −0.377343 | ||||||||
\(630\) | −5.25419 | −0.209332 | ||||||||
\(631\) | 23.8440 | 0.949213 | 0.474607 | − | 0.880198i | \(-0.342590\pi\) | ||||
0.474607 | + | 0.880198i | \(0.342590\pi\) | |||||||
\(632\) | 52.5046 | 2.08852 | ||||||||
\(633\) | 8.98066 | 0.356949 | ||||||||
\(634\) | −4.14445 | −0.164597 | ||||||||
\(635\) | 1.99766 | 0.0792747 | ||||||||
\(636\) | −15.0567 | −0.597037 | ||||||||
\(637\) | 9.36847 | 0.371192 | ||||||||
\(638\) | −8.21265 | −0.325142 | ||||||||
\(639\) | 4.36640 | 0.172732 | ||||||||
\(640\) | 17.9230 | 0.708470 | ||||||||
\(641\) | −13.4636 | −0.531781 | −0.265891 | − | 0.964003i | \(-0.585666\pi\) | ||||
−0.265891 | + | 0.964003i | \(0.585666\pi\) | |||||||
\(642\) | −51.8184 | −2.04511 | ||||||||
\(643\) | −3.35562 | −0.132333 | −0.0661664 | − | 0.997809i | \(-0.521077\pi\) | ||||
−0.0661664 | + | 0.997809i | \(0.521077\pi\) | |||||||
\(644\) | 24.4599 | 0.963856 | ||||||||
\(645\) | 3.92073 | 0.154379 | ||||||||
\(646\) | 4.63600 | 0.182401 | ||||||||
\(647\) | 12.1359 | 0.477111 | 0.238555 | − | 0.971129i | \(-0.423326\pi\) | ||||
0.238555 | + | 0.971129i | \(0.423326\pi\) | |||||||
\(648\) | 34.4270 | 1.35242 | ||||||||
\(649\) | −1.24499 | −0.0488701 | ||||||||
\(650\) | 5.92171 | 0.232269 | ||||||||
\(651\) | 29.4012 | 1.15233 | ||||||||
\(652\) | −11.7904 | −0.461746 | ||||||||
\(653\) | −39.6742 | −1.55257 | −0.776286 | − | 0.630381i | \(-0.782899\pi\) | ||||
−0.776286 | + | 0.630381i | \(0.782899\pi\) | |||||||
\(654\) | 26.3117 | 1.02887 | ||||||||
\(655\) | −10.5033 | −0.410397 | ||||||||
\(656\) | −14.4749 | −0.565152 | ||||||||
\(657\) | −1.64490 | −0.0641736 | ||||||||
\(658\) | −66.3132 | −2.58516 | ||||||||
\(659\) | −6.92579 | −0.269791 | −0.134895 | − | 0.990860i | \(-0.543070\pi\) | ||||
−0.134895 | + | 0.990860i | \(0.543070\pi\) | |||||||
\(660\) | 6.22118 | 0.242159 | ||||||||
\(661\) | 11.5447 | 0.449037 | 0.224519 | − | 0.974470i | \(-0.427919\pi\) | ||||
0.224519 | + | 0.974470i | \(0.427919\pi\) | |||||||
\(662\) | −45.4354 | −1.76590 | ||||||||
\(663\) | −1.06749 | −0.0414579 | ||||||||
\(664\) | 36.8389 | 1.42963 | ||||||||
\(665\) | −7.03745 | −0.272900 | ||||||||
\(666\) | 9.87419 | 0.382617 | ||||||||
\(667\) | −3.89908 | −0.150973 | ||||||||
\(668\) | 77.6123 | 3.00291 | ||||||||
\(669\) | 31.6350 | 1.22308 | ||||||||
\(670\) | −31.7304 | −1.22585 | ||||||||
\(671\) | 8.58656 | 0.331481 | ||||||||
\(672\) | −3.93468 | −0.151783 | ||||||||
\(673\) | −1.60379 | −0.0618214 | −0.0309107 | − | 0.999522i | \(-0.509841\pi\) | ||||
−0.0309107 | + | 0.999522i | \(0.509841\pi\) | |||||||
\(674\) | 19.4070 | 0.747530 | ||||||||
\(675\) | 23.2193 | 0.893712 | ||||||||
\(676\) | −49.9803 | −1.92232 | ||||||||
\(677\) | 8.12062 | 0.312101 | 0.156050 | − | 0.987749i | \(-0.450124\pi\) | ||||
0.156050 | + | 0.987749i | \(0.450124\pi\) | |||||||
\(678\) | −43.3276 | −1.66399 | ||||||||
\(679\) | −39.2617 | −1.50673 | ||||||||
\(680\) | 4.96330 | 0.190334 | ||||||||
\(681\) | 4.73672 | 0.181512 | ||||||||
\(682\) | 10.4674 | 0.400816 | ||||||||
\(683\) | −43.3503 | −1.65875 | −0.829377 | − | 0.558690i | \(-0.811304\pi\) | ||||
−0.829377 | + | 0.558690i | \(0.811304\pi\) | |||||||
\(684\) | −3.21016 | −0.122744 | ||||||||
\(685\) | 13.7315 | 0.524653 | ||||||||
\(686\) | 107.888 | 4.11918 | ||||||||
\(687\) | 45.2016 | 1.72455 | ||||||||
\(688\) | 10.1777 | 0.388021 | ||||||||
\(689\) | −1.39625 | −0.0531930 | ||||||||
\(690\) | 4.45049 | 0.169427 | ||||||||
\(691\) | 18.7520 | 0.713358 | 0.356679 | − | 0.934227i | \(-0.383909\pi\) | ||||
0.356679 | + | 0.934227i | \(0.383909\pi\) | |||||||
\(692\) | 95.8228 | 3.64264 | ||||||||
\(693\) | 2.67186 | 0.101496 | ||||||||
\(694\) | −6.57158 | −0.249454 | ||||||||
\(695\) | −2.86060 | −0.108509 | ||||||||
\(696\) | −22.7361 | −0.861809 | ||||||||
\(697\) | 4.58689 | 0.173741 | ||||||||
\(698\) | 27.0924 | 1.02546 | ||||||||
\(699\) | −4.65215 | −0.175960 | ||||||||
\(700\) | 79.7386 | 3.01383 | ||||||||
\(701\) | −11.5565 | −0.436484 | −0.218242 | − | 0.975895i | \(-0.570032\pi\) | ||||
−0.218242 | + | 0.975895i | \(0.570032\pi\) | |||||||
\(702\) | 7.80915 | 0.294737 | ||||||||
\(703\) | 13.2255 | 0.498808 | ||||||||
\(704\) | −9.58536 | −0.361262 | ||||||||
\(705\) | −8.00749 | −0.301579 | ||||||||
\(706\) | −25.4584 | −0.958141 | ||||||||
\(707\) | −77.5945 | −2.91824 | ||||||||
\(708\) | −6.98839 | −0.262640 | ||||||||
\(709\) | −13.2332 | −0.496982 | −0.248491 | − | 0.968634i | \(-0.579935\pi\) | ||||
−0.248491 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(710\) | 19.1291 | 0.717904 | ||||||||
\(711\) | 5.52094 | 0.207052 | ||||||||
\(712\) | 56.6287 | 2.12225 | ||||||||
\(713\) | 4.96954 | 0.186111 | ||||||||
\(714\) | −21.6592 | −0.810574 | ||||||||
\(715\) | 0.576909 | 0.0215752 | ||||||||
\(716\) | 10.8872 | 0.406873 | ||||||||
\(717\) | −20.6678 | −0.771853 | ||||||||
\(718\) | −79.9638 | −2.98422 | ||||||||
\(719\) | −36.7782 | −1.37160 | −0.685798 | − | 0.727792i | \(-0.740547\pi\) | ||||
−0.685798 | + | 0.727792i | \(0.740547\pi\) | |||||||
\(720\) | −1.64697 | −0.0613788 | ||||||||
\(721\) | 42.2806 | 1.57461 | ||||||||
\(722\) | 39.8528 | 1.48317 | ||||||||
\(723\) | −21.7959 | −0.810598 | ||||||||
\(724\) | 60.6108 | 2.25258 | ||||||||
\(725\) | −12.7109 | −0.472069 | ||||||||
\(726\) | 37.6528 | 1.39743 | ||||||||
\(727\) | 31.0644 | 1.15212 | 0.576058 | − | 0.817409i | \(-0.304590\pi\) | ||||
0.576058 | + | 0.817409i | \(0.304590\pi\) | |||||||
\(728\) | 13.2264 | 0.490205 | ||||||||
\(729\) | 29.8729 | 1.10640 | ||||||||
\(730\) | −7.20628 | −0.266716 | ||||||||
\(731\) | −3.22516 | −0.119287 | ||||||||
\(732\) | 48.1982 | 1.78146 | ||||||||
\(733\) | 24.1664 | 0.892605 | 0.446303 | − | 0.894882i | \(-0.352740\pi\) | ||||
0.446303 | + | 0.894882i | \(0.352740\pi\) | |||||||
\(734\) | 58.7745 | 2.16940 | ||||||||
\(735\) | 22.9532 | 0.846641 | ||||||||
\(736\) | −0.665058 | −0.0245143 | ||||||||
\(737\) | 16.1355 | 0.594360 | ||||||||
\(738\) | −4.78584 | −0.176169 | ||||||||
\(739\) | 5.18206 | 0.190625 | 0.0953127 | − | 0.995447i | \(-0.469615\pi\) | ||||
0.0953127 | + | 0.995447i | \(0.469615\pi\) | |||||||
\(740\) | 28.7089 | 1.05536 | ||||||||
\(741\) | 1.49181 | 0.0548030 | ||||||||
\(742\) | −28.3297 | −1.04002 | ||||||||
\(743\) | −40.4383 | −1.48354 | −0.741768 | − | 0.670657i | \(-0.766012\pi\) | ||||
−0.741768 | + | 0.670657i | \(0.766012\pi\) | |||||||
\(744\) | 28.9781 | 1.06239 | ||||||||
\(745\) | 17.1803 | 0.629438 | ||||||||
\(746\) | −41.7034 | −1.52687 | ||||||||
\(747\) | 3.87368 | 0.141730 | ||||||||
\(748\) | −5.11749 | −0.187114 | ||||||||
\(749\) | −64.7053 | −2.36428 | ||||||||
\(750\) | 31.7965 | 1.16104 | ||||||||
\(751\) | −2.81925 | −0.102876 | −0.0514379 | − | 0.998676i | \(-0.516380\pi\) | ||||
−0.0514379 | + | 0.998676i | \(0.516380\pi\) | |||||||
\(752\) | −20.7864 | −0.758002 | ||||||||
\(753\) | 16.6374 | 0.606299 | ||||||||
\(754\) | −4.27493 | −0.155684 | ||||||||
\(755\) | −6.12682 | −0.222978 | ||||||||
\(756\) | 105.154 | 3.82441 | ||||||||
\(757\) | 25.7620 | 0.936337 | 0.468168 | − | 0.883639i | \(-0.344914\pi\) | ||||
0.468168 | + | 0.883639i | \(0.344914\pi\) | |||||||
\(758\) | −47.6992 | −1.73251 | ||||||||
\(759\) | −2.26316 | −0.0821476 | ||||||||
\(760\) | −6.93616 | −0.251601 | ||||||||
\(761\) | 5.05305 | 0.183173 | 0.0915864 | − | 0.995797i | \(-0.470806\pi\) | ||||
0.0915864 | + | 0.995797i | \(0.470806\pi\) | |||||||
\(762\) | −8.59207 | −0.311258 | ||||||||
\(763\) | 32.8552 | 1.18944 | ||||||||
\(764\) | 59.8898 | 2.16674 | ||||||||
\(765\) | 0.521899 | 0.0188693 | ||||||||
\(766\) | −73.2562 | −2.64685 | ||||||||
\(767\) | −0.648054 | −0.0233999 | ||||||||
\(768\) | −49.8197 | −1.79771 | ||||||||
\(769\) | 26.0837 | 0.940602 | 0.470301 | − | 0.882506i | \(-0.344145\pi\) | ||||
0.470301 | + | 0.882506i | \(0.344145\pi\) | |||||||
\(770\) | 11.7054 | 0.421832 | ||||||||
\(771\) | −9.89448 | −0.356341 | ||||||||
\(772\) | 20.2198 | 0.727726 | ||||||||
\(773\) | 27.6929 | 0.996043 | 0.498021 | − | 0.867165i | \(-0.334060\pi\) | ||||
0.498021 | + | 0.867165i | \(0.334060\pi\) | |||||||
\(774\) | 3.36505 | 0.120954 | ||||||||
\(775\) | 16.2005 | 0.581940 | ||||||||
\(776\) | −38.6966 | −1.38913 | ||||||||
\(777\) | −61.7887 | −2.21666 | ||||||||
\(778\) | −13.1999 | −0.473239 | ||||||||
\(779\) | −6.41014 | −0.229667 | ||||||||
\(780\) | 3.23831 | 0.115950 | ||||||||
\(781\) | −9.72755 | −0.348079 | ||||||||
\(782\) | −3.66094 | −0.130915 | ||||||||
\(783\) | −16.7622 | −0.599033 | ||||||||
\(784\) | 59.5834 | 2.12798 | ||||||||
\(785\) | −8.31943 | −0.296933 | ||||||||
\(786\) | 45.1752 | 1.61135 | ||||||||
\(787\) | 2.28851 | 0.0815765 | 0.0407883 | − | 0.999168i | \(-0.487013\pi\) | ||||
0.0407883 | + | 0.999168i | \(0.487013\pi\) | |||||||
\(788\) | 43.6171 | 1.55379 | ||||||||
\(789\) | −2.72385 | −0.0969716 | ||||||||
\(790\) | 24.1872 | 0.860541 | ||||||||
\(791\) | −54.1028 | −1.92367 | ||||||||
\(792\) | 2.63341 | 0.0935740 | ||||||||
\(793\) | 4.46956 | 0.158719 | ||||||||
\(794\) | 20.3643 | 0.722703 | ||||||||
\(795\) | −3.42089 | −0.121326 | ||||||||
\(796\) | −17.2112 | −0.610034 | ||||||||
\(797\) | 42.7969 | 1.51594 | 0.757972 | − | 0.652287i | \(-0.226190\pi\) | ||||
0.757972 | + | 0.652287i | \(0.226190\pi\) | |||||||
\(798\) | 30.2685 | 1.07149 | ||||||||
\(799\) | 6.58689 | 0.233028 | ||||||||
\(800\) | −2.16807 | −0.0766527 | ||||||||
\(801\) | 5.95460 | 0.210396 | ||||||||
\(802\) | 6.50161 | 0.229580 | ||||||||
\(803\) | 3.66453 | 0.129319 | ||||||||
\(804\) | 90.5722 | 3.19423 | ||||||||
\(805\) | 5.55730 | 0.195869 | ||||||||
\(806\) | 5.44858 | 0.191918 | ||||||||
\(807\) | −27.7536 | −0.976971 | ||||||||
\(808\) | −76.4777 | −2.69048 | ||||||||
\(809\) | 45.6299 | 1.60426 | 0.802131 | − | 0.597148i | \(-0.203700\pi\) | ||||
0.802131 | + | 0.597148i | \(0.203700\pi\) | |||||||
\(810\) | 15.8594 | 0.557242 | ||||||||
\(811\) | −10.0620 | −0.353323 | −0.176661 | − | 0.984272i | \(-0.556530\pi\) | ||||
−0.176661 | + | 0.984272i | \(0.556530\pi\) | |||||||
\(812\) | −57.5639 | −2.02010 | ||||||||
\(813\) | −10.3074 | −0.361497 | ||||||||
\(814\) | −21.9979 | −0.771025 | ||||||||
\(815\) | −2.67877 | −0.0938333 | ||||||||
\(816\) | −6.78924 | −0.237671 | ||||||||
\(817\) | 4.50714 | 0.157685 | ||||||||
\(818\) | 48.5755 | 1.69840 | ||||||||
\(819\) | 1.39078 | 0.0485979 | ||||||||
\(820\) | −13.9147 | −0.485922 | ||||||||
\(821\) | 7.69354 | 0.268506 | 0.134253 | − | 0.990947i | \(-0.457136\pi\) | ||||
0.134253 | + | 0.990947i | \(0.457136\pi\) | |||||||
\(822\) | −59.0600 | −2.05995 | ||||||||
\(823\) | −49.1667 | −1.71384 | −0.856921 | − | 0.515448i | \(-0.827626\pi\) | ||||
−0.856921 | + | 0.515448i | \(0.827626\pi\) | |||||||
\(824\) | 41.6721 | 1.45171 | ||||||||
\(825\) | −7.37784 | −0.256863 | ||||||||
\(826\) | −13.1489 | −0.457508 | ||||||||
\(827\) | 1.86119 | 0.0647198 | 0.0323599 | − | 0.999476i | \(-0.489698\pi\) | ||||
0.0323599 | + | 0.999476i | \(0.489698\pi\) | |||||||
\(828\) | 2.53499 | 0.0880969 | ||||||||
\(829\) | −21.1085 | −0.733128 | −0.366564 | − | 0.930393i | \(-0.619466\pi\) | ||||
−0.366564 | + | 0.930393i | \(0.619466\pi\) | |||||||
\(830\) | 16.9705 | 0.589055 | ||||||||
\(831\) | 48.9663 | 1.69862 | ||||||||
\(832\) | −4.98947 | −0.172979 | ||||||||
\(833\) | −18.8811 | −0.654191 | ||||||||
\(834\) | 12.3036 | 0.426040 | ||||||||
\(835\) | 17.6335 | 0.610233 | ||||||||
\(836\) | 7.15165 | 0.247345 | ||||||||
\(837\) | 21.3642 | 0.738453 | ||||||||
\(838\) | −82.9591 | −2.86577 | ||||||||
\(839\) | 22.0072 | 0.759774 | 0.379887 | − | 0.925033i | \(-0.375963\pi\) | ||||
0.379887 | + | 0.925033i | \(0.375963\pi\) | |||||||
\(840\) | 32.4054 | 1.11809 | ||||||||
\(841\) | −19.8239 | −0.683584 | ||||||||
\(842\) | 29.4756 | 1.01580 | ||||||||
\(843\) | 35.0698 | 1.20787 | ||||||||
\(844\) | 22.4103 | 0.771394 | ||||||||
\(845\) | −11.3555 | −0.390642 | ||||||||
\(846\) | −6.87259 | −0.236285 | ||||||||
\(847\) | 47.0168 | 1.61552 | ||||||||
\(848\) | −8.88017 | −0.304946 | ||||||||
\(849\) | 10.5534 | 0.362193 | ||||||||
\(850\) | −11.9345 | −0.409351 | ||||||||
\(851\) | −10.4438 | −0.358010 | ||||||||
\(852\) | −54.6028 | −1.87066 | ||||||||
\(853\) | 20.7488 | 0.710425 | 0.355213 | − | 0.934786i | \(-0.384408\pi\) | ||||
0.355213 | + | 0.934786i | \(0.384408\pi\) | |||||||
\(854\) | 90.6866 | 3.10323 | ||||||||
\(855\) | −0.729349 | −0.0249432 | ||||||||
\(856\) | −63.7740 | −2.17975 | ||||||||
\(857\) | −18.5597 | −0.633987 | −0.316993 | − | 0.948428i | \(-0.602673\pi\) | ||||
−0.316993 | + | 0.948428i | \(0.602673\pi\) | |||||||
\(858\) | −2.48132 | −0.0847110 | ||||||||
\(859\) | 48.8721 | 1.66749 | 0.833747 | − | 0.552147i | \(-0.186191\pi\) | ||||
0.833747 | + | 0.552147i | \(0.186191\pi\) | |||||||
\(860\) | 9.78378 | 0.333624 | ||||||||
\(861\) | 29.9479 | 1.02062 | ||||||||
\(862\) | −38.9044 | −1.32509 | ||||||||
\(863\) | −17.4500 | −0.594004 | −0.297002 | − | 0.954877i | \(-0.595987\pi\) | ||||
−0.297002 | + | 0.954877i | \(0.595987\pi\) | |||||||
\(864\) | −2.85910 | −0.0972685 | ||||||||
\(865\) | 21.7710 | 0.740235 | ||||||||
\(866\) | 18.3125 | 0.622284 | ||||||||
\(867\) | −24.7330 | −0.839977 | ||||||||
\(868\) | 73.3677 | 2.49026 | ||||||||
\(869\) | −12.2996 | −0.417237 | ||||||||
\(870\) | −10.4738 | −0.355094 | ||||||||
\(871\) | 8.39903 | 0.284590 | ||||||||
\(872\) | 32.3823 | 1.09660 | ||||||||
\(873\) | −4.06902 | −0.137715 | ||||||||
\(874\) | 5.11613 | 0.173056 | ||||||||
\(875\) | 39.7040 | 1.34224 | ||||||||
\(876\) | 20.5698 | 0.694990 | ||||||||
\(877\) | 9.18644 | 0.310204 | 0.155102 | − | 0.987898i | \(-0.450429\pi\) | ||||
0.155102 | + | 0.987898i | \(0.450429\pi\) | |||||||
\(878\) | 47.0745 | 1.58869 | ||||||||
\(879\) | 1.38031 | 0.0465568 | ||||||||
\(880\) | 3.66914 | 0.123687 | ||||||||
\(881\) | 45.1446 | 1.52096 | 0.760479 | − | 0.649362i | \(-0.224964\pi\) | ||||
0.760479 | + | 0.649362i | \(0.224964\pi\) | |||||||
\(882\) | 19.7000 | 0.663335 | ||||||||
\(883\) | −42.7531 | −1.43875 | −0.719377 | − | 0.694619i | \(-0.755573\pi\) | ||||
−0.719377 | + | 0.694619i | \(0.755573\pi\) | |||||||
\(884\) | −2.66381 | −0.0895936 | ||||||||
\(885\) | −1.58776 | −0.0533720 | ||||||||
\(886\) | −34.8582 | −1.17109 | ||||||||
\(887\) | −21.2224 | −0.712577 | −0.356289 | − | 0.934376i | \(-0.615958\pi\) | ||||
−0.356289 | + | 0.934376i | \(0.615958\pi\) | |||||||
\(888\) | −60.8994 | −2.04365 | ||||||||
\(889\) | −10.7289 | −0.359834 | ||||||||
\(890\) | 26.0870 | 0.874439 | ||||||||
\(891\) | −8.06481 | −0.270181 | ||||||||
\(892\) | 78.9419 | 2.64317 | ||||||||
\(893\) | −9.20513 | −0.308038 | ||||||||
\(894\) | −73.8936 | −2.47137 | ||||||||
\(895\) | 2.47357 | 0.0826822 | ||||||||
\(896\) | −96.2593 | −3.21580 | ||||||||
\(897\) | −1.17804 | −0.0393338 | ||||||||
\(898\) | 72.5358 | 2.42055 | ||||||||
\(899\) | −11.6953 | −0.390060 | ||||||||
\(900\) | 8.26397 | 0.275466 | ||||||||
\(901\) | 2.81399 | 0.0937476 | ||||||||
\(902\) | 10.6620 | 0.355005 | ||||||||
\(903\) | −21.0571 | −0.700737 | ||||||||
\(904\) | −53.3242 | −1.77354 | ||||||||
\(905\) | 13.7708 | 0.457756 | ||||||||
\(906\) | 26.3518 | 0.875481 | ||||||||
\(907\) | −11.1931 | −0.371660 | −0.185830 | − | 0.982582i | \(-0.559497\pi\) | ||||
−0.185830 | + | 0.982582i | \(0.559497\pi\) | |||||||
\(908\) | 11.8200 | 0.392260 | ||||||||
\(909\) | −8.04176 | −0.266728 | ||||||||
\(910\) | 6.09300 | 0.201981 | ||||||||
\(911\) | −41.9453 | −1.38971 | −0.694855 | − | 0.719150i | \(-0.744532\pi\) | ||||
−0.694855 | + | 0.719150i | \(0.744532\pi\) | |||||||
\(912\) | 9.48790 | 0.314176 | ||||||||
\(913\) | −8.62984 | −0.285606 | ||||||||
\(914\) | −51.2128 | −1.69397 | ||||||||
\(915\) | 10.9506 | 0.362017 | ||||||||
\(916\) | 112.796 | 3.72688 | ||||||||
\(917\) | 56.4100 | 1.86282 | ||||||||
\(918\) | −15.7385 | −0.519446 | ||||||||
\(919\) | −35.4702 | −1.17005 | −0.585027 | − | 0.811014i | \(-0.698916\pi\) | ||||
−0.585027 | + | 0.811014i | \(0.698916\pi\) | |||||||
\(920\) | 5.47732 | 0.180582 | ||||||||
\(921\) | 25.1906 | 0.830060 | ||||||||
\(922\) | −6.13125 | −0.201922 | ||||||||
\(923\) | −5.06348 | −0.166667 | ||||||||
\(924\) | −33.4122 | −1.09918 | ||||||||
\(925\) | −34.0465 | −1.11944 | ||||||||
\(926\) | −18.7076 | −0.614770 | ||||||||
\(927\) | 4.38189 | 0.143920 | ||||||||
\(928\) | 1.56514 | 0.0513784 | ||||||||
\(929\) | −24.6247 | −0.807911 | −0.403956 | − | 0.914779i | \(-0.632365\pi\) | ||||
−0.403956 | + | 0.914779i | \(0.632365\pi\) | |||||||
\(930\) | 13.3493 | 0.437740 | ||||||||
\(931\) | 26.3862 | 0.864771 | ||||||||
\(932\) | −11.6089 | −0.380264 | ||||||||
\(933\) | 12.0545 | 0.394648 | ||||||||
\(934\) | 11.0747 | 0.362374 | ||||||||
\(935\) | −1.16270 | −0.0380242 | ||||||||
\(936\) | 1.37077 | 0.0448049 | ||||||||
\(937\) | −40.7076 | −1.32986 | −0.664930 | − | 0.746905i | \(-0.731539\pi\) | ||||
−0.664930 | + | 0.746905i | \(0.731539\pi\) | |||||||
\(938\) | 170.415 | 5.56423 | ||||||||
\(939\) | −22.1474 | −0.722752 | ||||||||
\(940\) | −19.9818 | −0.651736 | ||||||||
\(941\) | 22.7954 | 0.743109 | 0.371554 | − | 0.928411i | \(-0.378825\pi\) | ||||
0.371554 | + | 0.928411i | \(0.378825\pi\) | |||||||
\(942\) | 35.7824 | 1.16585 | ||||||||
\(943\) | 5.06193 | 0.164839 | ||||||||
\(944\) | −4.12162 | −0.134147 | ||||||||
\(945\) | 23.8910 | 0.777173 | ||||||||
\(946\) | −7.49671 | −0.243739 | ||||||||
\(947\) | 27.0133 | 0.877813 | 0.438906 | − | 0.898533i | \(-0.355366\pi\) | ||||
0.438906 | + | 0.898533i | \(0.355366\pi\) | |||||||
\(948\) | −69.0406 | −2.24233 | ||||||||
\(949\) | 1.90750 | 0.0619201 | ||||||||
\(950\) | 16.6784 | 0.541119 | ||||||||
\(951\) | 2.68779 | 0.0871575 | ||||||||
\(952\) | −26.6564 | −0.863939 | ||||||||
\(953\) | 18.2096 | 0.589867 | 0.294933 | − | 0.955518i | \(-0.404703\pi\) | ||||
0.294933 | + | 0.955518i | \(0.404703\pi\) | |||||||
\(954\) | −2.93604 | −0.0950579 | ||||||||
\(955\) | 13.6070 | 0.440311 | ||||||||
\(956\) | −51.5743 | −1.66803 | ||||||||
\(957\) | 5.32612 | 0.172169 | ||||||||
\(958\) | −17.1168 | −0.553019 | ||||||||
\(959\) | −73.7478 | −2.38144 | ||||||||
\(960\) | −12.2244 | −0.394542 | ||||||||
\(961\) | −16.0939 | −0.519157 | ||||||||
\(962\) | −11.4506 | −0.369181 | ||||||||
\(963\) | −6.70595 | −0.216096 | ||||||||
\(964\) | −54.3894 | −1.75176 | ||||||||
\(965\) | 4.59393 | 0.147884 | ||||||||
\(966\) | −23.9023 | −0.769044 | ||||||||
\(967\) | 44.9168 | 1.44443 | 0.722213 | − | 0.691671i | \(-0.243125\pi\) | ||||
0.722213 | + | 0.691671i | \(0.243125\pi\) | |||||||
\(968\) | 46.3402 | 1.48943 | ||||||||
\(969\) | −3.00657 | −0.0965850 | ||||||||
\(970\) | −17.8263 | −0.572368 | ||||||||
\(971\) | 44.7003 | 1.43450 | 0.717251 | − | 0.696815i | \(-0.245400\pi\) | ||||
0.717251 | + | 0.696815i | \(0.245400\pi\) | |||||||
\(972\) | 20.2416 | 0.649249 | ||||||||
\(973\) | 15.3634 | 0.492529 | ||||||||
\(974\) | 3.07204 | 0.0984345 | ||||||||
\(975\) | −3.84039 | −0.122991 | ||||||||
\(976\) | 28.4264 | 0.909908 | ||||||||
\(977\) | 56.6433 | 1.81218 | 0.906089 | − | 0.423086i | \(-0.139053\pi\) | ||||
0.906089 | + | 0.423086i | \(0.139053\pi\) | |||||||
\(978\) | 11.5216 | 0.368419 | ||||||||
\(979\) | −13.2658 | −0.423976 | ||||||||
\(980\) | 57.2772 | 1.82965 | ||||||||
\(981\) | 3.40506 | 0.108715 | ||||||||
\(982\) | −14.9907 | −0.478372 | ||||||||
\(983\) | 5.71416 | 0.182253 | 0.0911267 | − | 0.995839i | \(-0.470953\pi\) | ||||
0.0911267 | + | 0.995839i | \(0.470953\pi\) | |||||||
\(984\) | 29.5169 | 0.940963 | ||||||||
\(985\) | 9.90980 | 0.315752 | ||||||||
\(986\) | 8.61564 | 0.274378 | ||||||||
\(987\) | 43.0059 | 1.36889 | ||||||||
\(988\) | 3.72265 | 0.118433 | ||||||||
\(989\) | −3.55917 | −0.113175 | ||||||||
\(990\) | 1.21313 | 0.0385557 | ||||||||
\(991\) | −59.4451 | −1.88833 | −0.944167 | − | 0.329467i | \(-0.893131\pi\) | ||||
−0.944167 | + | 0.329467i | \(0.893131\pi\) | |||||||
\(992\) | −1.99484 | −0.0633363 | ||||||||
\(993\) | 29.4661 | 0.935077 | ||||||||
\(994\) | −102.737 | −3.25862 | ||||||||
\(995\) | −3.91038 | −0.123967 | ||||||||
\(996\) | −48.4411 | −1.53492 | ||||||||
\(997\) | −31.3308 | −0.992255 | −0.496128 | − | 0.868250i | \(-0.665245\pi\) | ||||
−0.496128 | + | 0.868250i | \(0.665245\pi\) | |||||||
\(998\) | 84.8215 | 2.68498 | ||||||||
\(999\) | −44.8982 | −1.42052 |
(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 | 6043.2.a.c.1.19 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6043.2.a.c.1.19 | ✓ | 259 | 1.1 | even | 1 | trivial |