Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.54663 | −1.09363 | −0.546815 | − | 0.837253i | \(-0.684160\pi\) | ||||
−0.546815 | + | 0.837253i | \(0.684160\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.392054 | 0.196027 | ||||||||
\(5\) | 3.59105 | 1.60596 | 0.802982 | − | 0.596003i | \(-0.203245\pi\) | ||||
0.802982 | + | 0.596003i | \(0.203245\pi\) | |||||||
\(6\) | 1.54663 | 0.631408 | ||||||||
\(7\) | −3.93711 | −1.48809 | −0.744043 | − | 0.668131i | \(-0.767094\pi\) | ||||
−0.744043 | + | 0.668131i | \(0.767094\pi\) | |||||||
\(8\) | 2.48689 | 0.879249 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.55401 | −1.75633 | ||||||||
\(11\) | 3.85540 | 1.16245 | 0.581224 | − | 0.813744i | \(-0.302574\pi\) | ||||
0.581224 | + | 0.813744i | \(0.302574\pi\) | |||||||
\(12\) | −0.392054 | −0.113176 | ||||||||
\(13\) | −1.41847 | −0.393414 | −0.196707 | − | 0.980462i | \(-0.563025\pi\) | ||||
−0.196707 | + | 0.980462i | \(0.563025\pi\) | |||||||
\(14\) | 6.08924 | 1.62742 | ||||||||
\(15\) | −3.59105 | −0.927204 | ||||||||
\(16\) | −4.63040 | −1.15760 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.54663 | −0.364543 | ||||||||
\(19\) | −0.145814 | −0.0334521 | −0.0167261 | − | 0.999860i | \(-0.505324\pi\) | ||||
−0.0167261 | + | 0.999860i | \(0.505324\pi\) | |||||||
\(20\) | 1.40789 | 0.314813 | ||||||||
\(21\) | 3.93711 | 0.859147 | ||||||||
\(22\) | −5.96287 | −1.27129 | ||||||||
\(23\) | −0.400691 | −0.0835498 | −0.0417749 | − | 0.999127i | \(-0.513301\pi\) | ||||
−0.0417749 | + | 0.999127i | \(0.513301\pi\) | |||||||
\(24\) | −2.48689 | −0.507635 | ||||||||
\(25\) | 7.89562 | 1.57912 | ||||||||
\(26\) | 2.19385 | 0.430249 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.54356 | −0.291705 | ||||||||
\(29\) | −4.77127 | −0.886003 | −0.443002 | − | 0.896521i | \(-0.646086\pi\) | ||||
−0.443002 | + | 0.896521i | \(0.646086\pi\) | |||||||
\(30\) | 5.55401 | 1.01402 | ||||||||
\(31\) | 9.59732 | 1.72373 | 0.861865 | − | 0.507138i | \(-0.169297\pi\) | ||||
0.861865 | + | 0.507138i | \(0.169297\pi\) | |||||||
\(32\) | 2.18772 | 0.386738 | ||||||||
\(33\) | −3.85540 | −0.671140 | ||||||||
\(34\) | 1.54663 | 0.265244 | ||||||||
\(35\) | −14.1383 | −2.38981 | ||||||||
\(36\) | 0.392054 | 0.0653424 | ||||||||
\(37\) | −8.11194 | −1.33360 | −0.666798 | − | 0.745239i | \(-0.732335\pi\) | ||||
−0.666798 | + | 0.745239i | \(0.732335\pi\) | |||||||
\(38\) | 0.225520 | 0.0365842 | ||||||||
\(39\) | 1.41847 | 0.227137 | ||||||||
\(40\) | 8.93055 | 1.41204 | ||||||||
\(41\) | 2.99059 | 0.467052 | 0.233526 | − | 0.972351i | \(-0.424974\pi\) | ||||
0.233526 | + | 0.972351i | \(0.424974\pi\) | |||||||
\(42\) | −6.08924 | −0.939589 | ||||||||
\(43\) | 3.02827 | 0.461807 | 0.230904 | − | 0.972977i | \(-0.425832\pi\) | ||||
0.230904 | + | 0.972977i | \(0.425832\pi\) | |||||||
\(44\) | 1.51153 | 0.227871 | ||||||||
\(45\) | 3.59105 | 0.535322 | ||||||||
\(46\) | 0.619719 | 0.0913725 | ||||||||
\(47\) | −8.05420 | −1.17483 | −0.587413 | − | 0.809287i | \(-0.699854\pi\) | ||||
−0.587413 | + | 0.809287i | \(0.699854\pi\) | |||||||
\(48\) | 4.63040 | 0.668341 | ||||||||
\(49\) | 8.50081 | 1.21440 | ||||||||
\(50\) | −12.2116 | −1.72698 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −0.556118 | −0.0771197 | ||||||||
\(53\) | 4.69749 | 0.645250 | 0.322625 | − | 0.946527i | \(-0.395435\pi\) | ||||
0.322625 | + | 0.946527i | \(0.395435\pi\) | |||||||
\(54\) | 1.54663 | 0.210469 | ||||||||
\(55\) | 13.8449 | 1.86685 | ||||||||
\(56\) | −9.79116 | −1.30840 | ||||||||
\(57\) | 0.145814 | 0.0193136 | ||||||||
\(58\) | 7.37938 | 0.968960 | ||||||||
\(59\) | −8.98276 | −1.16946 | −0.584728 | − | 0.811230i | \(-0.698799\pi\) | ||||
−0.584728 | + | 0.811230i | \(0.698799\pi\) | |||||||
\(60\) | −1.40789 | −0.181757 | ||||||||
\(61\) | −11.7945 | −1.51014 | −0.755068 | − | 0.655647i | \(-0.772396\pi\) | ||||
−0.755068 | + | 0.655647i | \(0.772396\pi\) | |||||||
\(62\) | −14.8435 | −1.88512 | ||||||||
\(63\) | −3.93711 | −0.496029 | ||||||||
\(64\) | 5.87722 | 0.734652 | ||||||||
\(65\) | −5.09380 | −0.631808 | ||||||||
\(66\) | 5.96287 | 0.733979 | ||||||||
\(67\) | −5.49370 | −0.671162 | −0.335581 | − | 0.942011i | \(-0.608933\pi\) | ||||
−0.335581 | + | 0.942011i | \(0.608933\pi\) | |||||||
\(68\) | −0.392054 | −0.0475436 | ||||||||
\(69\) | 0.400691 | 0.0482375 | ||||||||
\(70\) | 21.8667 | 2.61357 | ||||||||
\(71\) | 12.1394 | 1.44068 | 0.720341 | − | 0.693620i | \(-0.243985\pi\) | ||||
0.720341 | + | 0.693620i | \(0.243985\pi\) | |||||||
\(72\) | 2.48689 | 0.293083 | ||||||||
\(73\) | 6.38728 | 0.747575 | 0.373787 | − | 0.927514i | \(-0.378059\pi\) | ||||
0.373787 | + | 0.927514i | \(0.378059\pi\) | |||||||
\(74\) | 12.5461 | 1.45846 | ||||||||
\(75\) | −7.89562 | −0.911707 | ||||||||
\(76\) | −0.0571672 | −0.00655752 | ||||||||
\(77\) | −15.1791 | −1.72982 | ||||||||
\(78\) | −2.19385 | −0.248404 | ||||||||
\(79\) | 8.76482 | 0.986119 | 0.493059 | − | 0.869996i | \(-0.335879\pi\) | ||||
0.493059 | + | 0.869996i | \(0.335879\pi\) | |||||||
\(80\) | −16.6280 | −1.85907 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.62533 | −0.510783 | ||||||||
\(83\) | −6.68788 | −0.734091 | −0.367045 | − | 0.930203i | \(-0.619631\pi\) | ||||
−0.367045 | + | 0.930203i | \(0.619631\pi\) | |||||||
\(84\) | 1.54356 | 0.168416 | ||||||||
\(85\) | −3.59105 | −0.389504 | ||||||||
\(86\) | −4.68361 | −0.505046 | ||||||||
\(87\) | 4.77127 | 0.511534 | ||||||||
\(88\) | 9.58798 | 1.02208 | ||||||||
\(89\) | −7.17883 | −0.760954 | −0.380477 | − | 0.924790i | \(-0.624240\pi\) | ||||
−0.380477 | + | 0.924790i | \(0.624240\pi\) | |||||||
\(90\) | −5.55401 | −0.585444 | ||||||||
\(91\) | 5.58468 | 0.585433 | ||||||||
\(92\) | −0.157092 | −0.0163780 | ||||||||
\(93\) | −9.59732 | −0.995196 | ||||||||
\(94\) | 12.4568 | 1.28483 | ||||||||
\(95\) | −0.523626 | −0.0537229 | ||||||||
\(96\) | −2.18772 | −0.223283 | ||||||||
\(97\) | −11.2410 | −1.14135 | −0.570675 | − | 0.821176i | \(-0.693318\pi\) | ||||
−0.570675 | + | 0.821176i | \(0.693318\pi\) | |||||||
\(98\) | −13.1476 | −1.32811 | ||||||||
\(99\) | 3.85540 | 0.387483 | ||||||||
\(100\) | 3.09551 | 0.309551 | ||||||||
\(101\) | 1.25851 | 0.125227 | 0.0626135 | − | 0.998038i | \(-0.480056\pi\) | ||||
0.0626135 | + | 0.998038i | \(0.480056\pi\) | |||||||
\(102\) | −1.54663 | −0.153139 | ||||||||
\(103\) | −10.7296 | −1.05722 | −0.528610 | − | 0.848865i | \(-0.677287\pi\) | ||||
−0.528610 | + | 0.848865i | \(0.677287\pi\) | |||||||
\(104\) | −3.52759 | −0.345908 | ||||||||
\(105\) | 14.1383 | 1.37976 | ||||||||
\(106\) | −7.26527 | −0.705665 | ||||||||
\(107\) | −12.5171 | −1.21007 | −0.605035 | − | 0.796199i | \(-0.706841\pi\) | ||||
−0.605035 | + | 0.796199i | \(0.706841\pi\) | |||||||
\(108\) | −0.392054 | −0.0377254 | ||||||||
\(109\) | 4.19169 | 0.401491 | 0.200745 | − | 0.979643i | \(-0.435664\pi\) | ||||
0.200745 | + | 0.979643i | \(0.435664\pi\) | |||||||
\(110\) | −21.4130 | −2.04164 | ||||||||
\(111\) | 8.11194 | 0.769952 | ||||||||
\(112\) | 18.2304 | 1.72261 | ||||||||
\(113\) | 3.05047 | 0.286964 | 0.143482 | − | 0.989653i | \(-0.454170\pi\) | ||||
0.143482 | + | 0.989653i | \(0.454170\pi\) | |||||||
\(114\) | −0.225520 | −0.0211219 | ||||||||
\(115\) | −1.43890 | −0.134178 | ||||||||
\(116\) | −1.87060 | −0.173681 | ||||||||
\(117\) | −1.41847 | −0.131138 | ||||||||
\(118\) | 13.8930 | 1.27895 | ||||||||
\(119\) | 3.93711 | 0.360914 | ||||||||
\(120\) | −8.93055 | −0.815243 | ||||||||
\(121\) | 3.86415 | 0.351286 | ||||||||
\(122\) | 18.2417 | 1.65153 | ||||||||
\(123\) | −2.99059 | −0.269653 | ||||||||
\(124\) | 3.76267 | 0.337898 | ||||||||
\(125\) | 10.3983 | 0.930052 | ||||||||
\(126\) | 6.08924 | 0.542472 | ||||||||
\(127\) | 8.27405 | 0.734203 | 0.367102 | − | 0.930181i | \(-0.380350\pi\) | ||||
0.367102 | + | 0.930181i | \(0.380350\pi\) | |||||||
\(128\) | −13.4653 | −1.19018 | ||||||||
\(129\) | −3.02827 | −0.266625 | ||||||||
\(130\) | 7.87821 | 0.690965 | ||||||||
\(131\) | 3.42735 | 0.299449 | 0.149724 | − | 0.988728i | \(-0.452161\pi\) | ||||
0.149724 | + | 0.988728i | \(0.452161\pi\) | |||||||
\(132\) | −1.51153 | −0.131562 | ||||||||
\(133\) | 0.574087 | 0.0497796 | ||||||||
\(134\) | 8.49670 | 0.734003 | ||||||||
\(135\) | −3.59105 | −0.309068 | ||||||||
\(136\) | −2.48689 | −0.213249 | ||||||||
\(137\) | −22.2343 | −1.89960 | −0.949802 | − | 0.312852i | \(-0.898716\pi\) | ||||
−0.949802 | + | 0.312852i | \(0.898716\pi\) | |||||||
\(138\) | −0.619719 | −0.0527540 | ||||||||
\(139\) | 8.46971 | 0.718392 | 0.359196 | − | 0.933262i | \(-0.383051\pi\) | ||||
0.359196 | + | 0.933262i | \(0.383051\pi\) | |||||||
\(140\) | −5.54299 | −0.468469 | ||||||||
\(141\) | 8.05420 | 0.678286 | ||||||||
\(142\) | −18.7751 | −1.57557 | ||||||||
\(143\) | −5.46879 | −0.457323 | ||||||||
\(144\) | −4.63040 | −0.385867 | ||||||||
\(145\) | −17.1339 | −1.42289 | ||||||||
\(146\) | −9.87874 | −0.817570 | ||||||||
\(147\) | −8.50081 | −0.701135 | ||||||||
\(148\) | −3.18032 | −0.261421 | ||||||||
\(149\) | 3.96393 | 0.324738 | 0.162369 | − | 0.986730i | \(-0.448087\pi\) | ||||
0.162369 | + | 0.986730i | \(0.448087\pi\) | |||||||
\(150\) | 12.2116 | 0.997071 | ||||||||
\(151\) | −9.32731 | −0.759046 | −0.379523 | − | 0.925182i | \(-0.623912\pi\) | ||||
−0.379523 | + | 0.925182i | \(0.623912\pi\) | |||||||
\(152\) | −0.362625 | −0.0294127 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 23.4765 | 1.89179 | ||||||||
\(155\) | 34.4644 | 2.76825 | ||||||||
\(156\) | 0.556118 | 0.0445251 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −13.5559 | −1.07845 | ||||||||
\(159\) | −4.69749 | −0.372535 | ||||||||
\(160\) | 7.85620 | 0.621087 | ||||||||
\(161\) | 1.57756 | 0.124329 | ||||||||
\(162\) | −1.54663 | −0.121514 | ||||||||
\(163\) | 13.7238 | 1.07493 | 0.537465 | − | 0.843286i | \(-0.319382\pi\) | ||||
0.537465 | + | 0.843286i | \(0.319382\pi\) | |||||||
\(164\) | 1.17247 | 0.0915549 | ||||||||
\(165\) | −13.8449 | −1.07783 | ||||||||
\(166\) | 10.3437 | 0.802824 | ||||||||
\(167\) | 5.47079 | 0.423342 | 0.211671 | − | 0.977341i | \(-0.432109\pi\) | ||||
0.211671 | + | 0.977341i | \(0.432109\pi\) | |||||||
\(168\) | 9.79116 | 0.755404 | ||||||||
\(169\) | −10.9879 | −0.845226 | ||||||||
\(170\) | 5.55401 | 0.425973 | ||||||||
\(171\) | −0.145814 | −0.0111507 | ||||||||
\(172\) | 1.18725 | 0.0905268 | ||||||||
\(173\) | −9.34451 | −0.710450 | −0.355225 | − | 0.934781i | \(-0.615596\pi\) | ||||
−0.355225 | + | 0.934781i | \(0.615596\pi\) | |||||||
\(174\) | −7.37938 | −0.559429 | ||||||||
\(175\) | −31.0859 | −2.34987 | ||||||||
\(176\) | −17.8521 | −1.34565 | ||||||||
\(177\) | 8.98276 | 0.675185 | ||||||||
\(178\) | 11.1030 | 0.832202 | ||||||||
\(179\) | 3.01972 | 0.225704 | 0.112852 | − | 0.993612i | \(-0.464001\pi\) | ||||
0.112852 | + | 0.993612i | \(0.464001\pi\) | |||||||
\(180\) | 1.40789 | 0.104938 | ||||||||
\(181\) | 1.97516 | 0.146813 | 0.0734063 | − | 0.997302i | \(-0.476613\pi\) | ||||
0.0734063 | + | 0.997302i | \(0.476613\pi\) | |||||||
\(182\) | −8.63741 | −0.640248 | ||||||||
\(183\) | 11.7945 | 0.871877 | ||||||||
\(184\) | −0.996474 | −0.0734610 | ||||||||
\(185\) | −29.1304 | −2.14171 | ||||||||
\(186\) | 14.8435 | 1.08838 | ||||||||
\(187\) | −3.85540 | −0.281935 | ||||||||
\(188\) | −3.15768 | −0.230298 | ||||||||
\(189\) | 3.93711 | 0.286382 | ||||||||
\(190\) | 0.809854 | 0.0587530 | ||||||||
\(191\) | −18.7075 | −1.35363 | −0.676815 | − | 0.736153i | \(-0.736640\pi\) | ||||
−0.676815 | + | 0.736153i | \(0.736640\pi\) | |||||||
\(192\) | −5.87722 | −0.424152 | ||||||||
\(193\) | −5.35036 | −0.385127 | −0.192564 | − | 0.981284i | \(-0.561680\pi\) | ||||
−0.192564 | + | 0.981284i | \(0.561680\pi\) | |||||||
\(194\) | 17.3856 | 1.24821 | ||||||||
\(195\) | 5.09380 | 0.364775 | ||||||||
\(196\) | 3.33278 | 0.238056 | ||||||||
\(197\) | −4.07175 | −0.290100 | −0.145050 | − | 0.989424i | \(-0.546334\pi\) | ||||
−0.145050 | + | 0.989424i | \(0.546334\pi\) | |||||||
\(198\) | −5.96287 | −0.423763 | ||||||||
\(199\) | 2.43646 | 0.172716 | 0.0863581 | − | 0.996264i | \(-0.472477\pi\) | ||||
0.0863581 | + | 0.996264i | \(0.472477\pi\) | |||||||
\(200\) | 19.6355 | 1.38844 | ||||||||
\(201\) | 5.49370 | 0.387495 | ||||||||
\(202\) | −1.94645 | −0.136952 | ||||||||
\(203\) | 18.7850 | 1.31845 | ||||||||
\(204\) | 0.392054 | 0.0274493 | ||||||||
\(205\) | 10.7394 | 0.750070 | ||||||||
\(206\) | 16.5947 | 1.15621 | ||||||||
\(207\) | −0.400691 | −0.0278499 | ||||||||
\(208\) | 6.56810 | 0.455416 | ||||||||
\(209\) | −0.562174 | −0.0388864 | ||||||||
\(210\) | −21.8667 | −1.50895 | ||||||||
\(211\) | −6.39005 | −0.439909 | −0.219955 | − | 0.975510i | \(-0.570591\pi\) | ||||
−0.219955 | + | 0.975510i | \(0.570591\pi\) | |||||||
\(212\) | 1.84167 | 0.126486 | ||||||||
\(213\) | −12.1394 | −0.831778 | ||||||||
\(214\) | 19.3592 | 1.32337 | ||||||||
\(215\) | 10.8747 | 0.741646 | ||||||||
\(216\) | −2.48689 | −0.169212 | ||||||||
\(217\) | −37.7857 | −2.56506 | ||||||||
\(218\) | −6.48297 | −0.439082 | ||||||||
\(219\) | −6.38728 | −0.431612 | ||||||||
\(220\) | 5.42797 | 0.365953 | ||||||||
\(221\) | 1.41847 | 0.0954168 | ||||||||
\(222\) | −12.5461 | −0.842042 | ||||||||
\(223\) | 15.7994 | 1.05801 | 0.529004 | − | 0.848619i | \(-0.322566\pi\) | ||||
0.529004 | + | 0.848619i | \(0.322566\pi\) | |||||||
\(224\) | −8.61329 | −0.575499 | ||||||||
\(225\) | 7.89562 | 0.526374 | ||||||||
\(226\) | −4.71793 | −0.313832 | ||||||||
\(227\) | 22.3025 | 1.48027 | 0.740133 | − | 0.672460i | \(-0.234762\pi\) | ||||
0.740133 | + | 0.672460i | \(0.234762\pi\) | |||||||
\(228\) | 0.0571672 | 0.00378599 | ||||||||
\(229\) | 8.60868 | 0.568878 | 0.284439 | − | 0.958694i | \(-0.408193\pi\) | ||||
0.284439 | + | 0.958694i | \(0.408193\pi\) | |||||||
\(230\) | 2.22544 | 0.146741 | ||||||||
\(231\) | 15.1791 | 0.998714 | ||||||||
\(232\) | −11.8656 | −0.779018 | ||||||||
\(233\) | 16.5862 | 1.08660 | 0.543299 | − | 0.839539i | \(-0.317175\pi\) | ||||
0.543299 | + | 0.839539i | \(0.317175\pi\) | |||||||
\(234\) | 2.19385 | 0.143416 | ||||||||
\(235\) | −28.9230 | −1.88673 | ||||||||
\(236\) | −3.52173 | −0.229245 | ||||||||
\(237\) | −8.76482 | −0.569336 | ||||||||
\(238\) | −6.08924 | −0.394706 | ||||||||
\(239\) | −20.8882 | −1.35115 | −0.675574 | − | 0.737292i | \(-0.736104\pi\) | ||||
−0.675574 | + | 0.737292i | \(0.736104\pi\) | |||||||
\(240\) | 16.6280 | 1.07333 | ||||||||
\(241\) | −14.4173 | −0.928699 | −0.464349 | − | 0.885652i | \(-0.653712\pi\) | ||||
−0.464349 | + | 0.885652i | \(0.653712\pi\) | |||||||
\(242\) | −5.97639 | −0.384177 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.62410 | −0.296027 | ||||||||
\(245\) | 30.5268 | 1.95029 | ||||||||
\(246\) | 4.62533 | 0.294900 | ||||||||
\(247\) | 0.206834 | 0.0131605 | ||||||||
\(248\) | 23.8675 | 1.51559 | ||||||||
\(249\) | 6.68788 | 0.423827 | ||||||||
\(250\) | −16.0823 | −1.01713 | ||||||||
\(251\) | 23.9164 | 1.50959 | 0.754794 | − | 0.655962i | \(-0.227737\pi\) | ||||
0.754794 | + | 0.655962i | \(0.227737\pi\) | |||||||
\(252\) | −1.54356 | −0.0972351 | ||||||||
\(253\) | −1.54482 | −0.0971223 | ||||||||
\(254\) | −12.7969 | −0.802947 | ||||||||
\(255\) | 3.59105 | 0.224880 | ||||||||
\(256\) | 9.07136 | 0.566960 | ||||||||
\(257\) | 4.37343 | 0.272807 | 0.136404 | − | 0.990653i | \(-0.456446\pi\) | ||||
0.136404 | + | 0.990653i | \(0.456446\pi\) | |||||||
\(258\) | 4.68361 | 0.291589 | ||||||||
\(259\) | 31.9376 | 1.98451 | ||||||||
\(260\) | −1.99705 | −0.123852 | ||||||||
\(261\) | −4.77127 | −0.295334 | ||||||||
\(262\) | −5.30083 | −0.327486 | ||||||||
\(263\) | −5.15870 | −0.318099 | −0.159050 | − | 0.987271i | \(-0.550843\pi\) | ||||
−0.159050 | + | 0.987271i | \(0.550843\pi\) | |||||||
\(264\) | −9.58798 | −0.590099 | ||||||||
\(265\) | 16.8689 | 1.03625 | ||||||||
\(266\) | −0.887898 | −0.0544405 | ||||||||
\(267\) | 7.17883 | 0.439337 | ||||||||
\(268\) | −2.15383 | −0.131566 | ||||||||
\(269\) | −23.3617 | −1.42439 | −0.712193 | − | 0.701984i | \(-0.752298\pi\) | ||||
−0.712193 | + | 0.701984i | \(0.752298\pi\) | |||||||
\(270\) | 5.55401 | 0.338006 | ||||||||
\(271\) | 11.8120 | 0.717528 | 0.358764 | − | 0.933428i | \(-0.383198\pi\) | ||||
0.358764 | + | 0.933428i | \(0.383198\pi\) | |||||||
\(272\) | 4.63040 | 0.280759 | ||||||||
\(273\) | −5.58468 | −0.338000 | ||||||||
\(274\) | 34.3882 | 2.07746 | ||||||||
\(275\) | 30.4408 | 1.83565 | ||||||||
\(276\) | 0.157092 | 0.00945585 | ||||||||
\(277\) | 12.8652 | 0.772992 | 0.386496 | − | 0.922291i | \(-0.373685\pi\) | ||||
0.386496 | + | 0.922291i | \(0.373685\pi\) | |||||||
\(278\) | −13.0995 | −0.785655 | ||||||||
\(279\) | 9.59732 | 0.574577 | ||||||||
\(280\) | −35.1605 | −2.10124 | ||||||||
\(281\) | 22.4357 | 1.33840 | 0.669201 | − | 0.743082i | \(-0.266637\pi\) | ||||
0.669201 | + | 0.743082i | \(0.266637\pi\) | |||||||
\(282\) | −12.4568 | −0.741794 | ||||||||
\(283\) | 1.03185 | 0.0613370 | 0.0306685 | − | 0.999530i | \(-0.490236\pi\) | ||||
0.0306685 | + | 0.999530i | \(0.490236\pi\) | |||||||
\(284\) | 4.75930 | 0.282413 | ||||||||
\(285\) | 0.523626 | 0.0310169 | ||||||||
\(286\) | 8.45817 | 0.500142 | ||||||||
\(287\) | −11.7743 | −0.695014 | ||||||||
\(288\) | 2.18772 | 0.128913 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 26.4997 | 1.55612 | ||||||||
\(291\) | 11.2410 | 0.658958 | ||||||||
\(292\) | 2.50416 | 0.146545 | ||||||||
\(293\) | 14.6591 | 0.856394 | 0.428197 | − | 0.903685i | \(-0.359149\pi\) | ||||
0.428197 | + | 0.903685i | \(0.359149\pi\) | |||||||
\(294\) | 13.1476 | 0.766783 | ||||||||
\(295\) | −32.2575 | −1.87810 | ||||||||
\(296\) | −20.1735 | −1.17256 | ||||||||
\(297\) | −3.85540 | −0.223713 | ||||||||
\(298\) | −6.13072 | −0.355143 | ||||||||
\(299\) | 0.568369 | 0.0328696 | ||||||||
\(300\) | −3.09551 | −0.178719 | ||||||||
\(301\) | −11.9226 | −0.687209 | ||||||||
\(302\) | 14.4259 | 0.830115 | ||||||||
\(303\) | −1.25851 | −0.0722998 | ||||||||
\(304\) | 0.675179 | 0.0387242 | ||||||||
\(305\) | −42.3547 | −2.42522 | ||||||||
\(306\) | 1.54663 | 0.0884148 | ||||||||
\(307\) | 20.9980 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(308\) | −5.95105 | −0.339092 | ||||||||
\(309\) | 10.7296 | 0.610386 | ||||||||
\(310\) | −53.3036 | −3.02744 | ||||||||
\(311\) | 5.09870 | 0.289121 | 0.144560 | − | 0.989496i | \(-0.453823\pi\) | ||||
0.144560 | + | 0.989496i | \(0.453823\pi\) | |||||||
\(312\) | 3.52759 | 0.199710 | ||||||||
\(313\) | −26.1297 | −1.47694 | −0.738468 | − | 0.674289i | \(-0.764450\pi\) | ||||
−0.738468 | + | 0.674289i | \(0.764450\pi\) | |||||||
\(314\) | 1.54663 | 0.0872812 | ||||||||
\(315\) | −14.1383 | −0.796605 | ||||||||
\(316\) | 3.43628 | 0.193306 | ||||||||
\(317\) | −19.6132 | −1.10159 | −0.550794 | − | 0.834641i | \(-0.685675\pi\) | ||||
−0.550794 | + | 0.834641i | \(0.685675\pi\) | |||||||
\(318\) | 7.26527 | 0.407416 | ||||||||
\(319\) | −18.3952 | −1.02993 | ||||||||
\(320\) | 21.1054 | 1.17983 | ||||||||
\(321\) | 12.5171 | 0.698635 | ||||||||
\(322\) | −2.43990 | −0.135970 | ||||||||
\(323\) | 0.145814 | 0.00811333 | ||||||||
\(324\) | 0.392054 | 0.0217808 | ||||||||
\(325\) | −11.1997 | −0.621248 | ||||||||
\(326\) | −21.2256 | −1.17558 | ||||||||
\(327\) | −4.19169 | −0.231801 | ||||||||
\(328\) | 7.43728 | 0.410655 | ||||||||
\(329\) | 31.7103 | 1.74824 | ||||||||
\(330\) | 21.4130 | 1.17874 | ||||||||
\(331\) | −18.1817 | −0.999357 | −0.499679 | − | 0.866211i | \(-0.666549\pi\) | ||||
−0.499679 | + | 0.866211i | \(0.666549\pi\) | |||||||
\(332\) | −2.62201 | −0.143902 | ||||||||
\(333\) | −8.11194 | −0.444532 | ||||||||
\(334\) | −8.46127 | −0.462980 | ||||||||
\(335\) | −19.7281 | −1.07786 | ||||||||
\(336\) | −18.2304 | −0.994549 | ||||||||
\(337\) | −32.1581 | −1.75176 | −0.875882 | − | 0.482525i | \(-0.839720\pi\) | ||||
−0.875882 | + | 0.482525i | \(0.839720\pi\) | |||||||
\(338\) | 16.9942 | 0.924364 | ||||||||
\(339\) | −3.05047 | −0.165679 | ||||||||
\(340\) | −1.40789 | −0.0763533 | ||||||||
\(341\) | 37.0016 | 2.00375 | ||||||||
\(342\) | 0.225520 | 0.0121947 | ||||||||
\(343\) | −5.90886 | −0.319049 | ||||||||
\(344\) | 7.53099 | 0.406044 | ||||||||
\(345\) | 1.43890 | 0.0774677 | ||||||||
\(346\) | 14.4525 | 0.776970 | ||||||||
\(347\) | −4.85588 | −0.260677 | −0.130339 | − | 0.991470i | \(-0.541606\pi\) | ||||
−0.130339 | + | 0.991470i | \(0.541606\pi\) | |||||||
\(348\) | 1.87060 | 0.100275 | ||||||||
\(349\) | −1.73178 | −0.0927002 | −0.0463501 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463501 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(350\) | 48.0783 | 2.56989 | ||||||||
\(351\) | 1.41847 | 0.0757125 | ||||||||
\(352\) | 8.43454 | 0.449563 | ||||||||
\(353\) | −11.0390 | −0.587545 | −0.293773 | − | 0.955875i | \(-0.594911\pi\) | ||||
−0.293773 | + | 0.955875i | \(0.594911\pi\) | |||||||
\(354\) | −13.8930 | −0.738403 | ||||||||
\(355\) | 43.5931 | 2.31368 | ||||||||
\(356\) | −2.81449 | −0.149168 | ||||||||
\(357\) | −3.93711 | −0.208374 | ||||||||
\(358\) | −4.67037 | −0.246837 | ||||||||
\(359\) | 31.7766 | 1.67710 | 0.838552 | − | 0.544821i | \(-0.183403\pi\) | ||||
0.838552 | + | 0.544821i | \(0.183403\pi\) | |||||||
\(360\) | 8.93055 | 0.470681 | ||||||||
\(361\) | −18.9787 | −0.998881 | ||||||||
\(362\) | −3.05484 | −0.160559 | ||||||||
\(363\) | −3.86415 | −0.202815 | ||||||||
\(364\) | 2.18950 | 0.114761 | ||||||||
\(365\) | 22.9370 | 1.20058 | ||||||||
\(366\) | −18.2417 | −0.953511 | ||||||||
\(367\) | −2.61589 | −0.136548 | −0.0682742 | − | 0.997667i | \(-0.521749\pi\) | ||||
−0.0682742 | + | 0.997667i | \(0.521749\pi\) | |||||||
\(368\) | 1.85536 | 0.0967172 | ||||||||
\(369\) | 2.99059 | 0.155684 | ||||||||
\(370\) | 45.0538 | 2.34224 | ||||||||
\(371\) | −18.4945 | −0.960188 | ||||||||
\(372\) | −3.76267 | −0.195085 | ||||||||
\(373\) | 12.3696 | 0.640472 | 0.320236 | − | 0.947338i | \(-0.396238\pi\) | ||||
0.320236 | + | 0.947338i | \(0.396238\pi\) | |||||||
\(374\) | 5.96287 | 0.308333 | ||||||||
\(375\) | −10.3983 | −0.536966 | ||||||||
\(376\) | −20.0299 | −1.03296 | ||||||||
\(377\) | 6.76792 | 0.348566 | ||||||||
\(378\) | −6.08924 | −0.313196 | ||||||||
\(379\) | −9.19981 | −0.472563 | −0.236281 | − | 0.971685i | \(-0.575929\pi\) | ||||
−0.236281 | + | 0.971685i | \(0.575929\pi\) | |||||||
\(380\) | −0.205290 | −0.0105312 | ||||||||
\(381\) | −8.27405 | −0.423893 | ||||||||
\(382\) | 28.9336 | 1.48037 | ||||||||
\(383\) | −34.5042 | −1.76308 | −0.881542 | − | 0.472105i | \(-0.843494\pi\) | ||||
−0.881542 | + | 0.472105i | \(0.843494\pi\) | |||||||
\(384\) | 13.4653 | 0.687148 | ||||||||
\(385\) | −54.5090 | −2.77804 | ||||||||
\(386\) | 8.27501 | 0.421187 | ||||||||
\(387\) | 3.02827 | 0.153936 | ||||||||
\(388\) | −4.40708 | −0.223735 | ||||||||
\(389\) | −13.3264 | −0.675678 | −0.337839 | − | 0.941204i | \(-0.609696\pi\) | ||||
−0.337839 | + | 0.941204i | \(0.609696\pi\) | |||||||
\(390\) | −7.87821 | −0.398929 | ||||||||
\(391\) | 0.400691 | 0.0202638 | ||||||||
\(392\) | 21.1406 | 1.06776 | ||||||||
\(393\) | −3.42735 | −0.172887 | ||||||||
\(394\) | 6.29748 | 0.317262 | ||||||||
\(395\) | 31.4749 | 1.58367 | ||||||||
\(396\) | 1.51153 | 0.0759571 | ||||||||
\(397\) | −4.13738 | −0.207649 | −0.103825 | − | 0.994596i | \(-0.533108\pi\) | ||||
−0.103825 | + | 0.994596i | \(0.533108\pi\) | |||||||
\(398\) | −3.76830 | −0.188888 | ||||||||
\(399\) | −0.574087 | −0.0287403 | ||||||||
\(400\) | −36.5599 | −1.82799 | ||||||||
\(401\) | 20.6376 | 1.03059 | 0.515295 | − | 0.857013i | \(-0.327682\pi\) | ||||
0.515295 | + | 0.857013i | \(0.327682\pi\) | |||||||
\(402\) | −8.49670 | −0.423777 | ||||||||
\(403\) | −13.6135 | −0.678139 | ||||||||
\(404\) | 0.493406 | 0.0245479 | ||||||||
\(405\) | 3.59105 | 0.178441 | ||||||||
\(406\) | −29.0534 | −1.44190 | ||||||||
\(407\) | −31.2748 | −1.55024 | ||||||||
\(408\) | 2.48689 | 0.123119 | ||||||||
\(409\) | 27.3417 | 1.35196 | 0.675981 | − | 0.736919i | \(-0.263720\pi\) | ||||
0.675981 | + | 0.736919i | \(0.263720\pi\) | |||||||
\(410\) | −16.6098 | −0.820299 | ||||||||
\(411\) | 22.2343 | 1.09674 | ||||||||
\(412\) | −4.20659 | −0.207244 | ||||||||
\(413\) | 35.3661 | 1.74025 | ||||||||
\(414\) | 0.619719 | 0.0304575 | ||||||||
\(415\) | −24.0165 | −1.17892 | ||||||||
\(416\) | −3.10322 | −0.152148 | ||||||||
\(417\) | −8.46971 | −0.414764 | ||||||||
\(418\) | 0.869473 | 0.0425273 | ||||||||
\(419\) | −27.5130 | −1.34410 | −0.672049 | − | 0.740506i | \(-0.734586\pi\) | ||||
−0.672049 | + | 0.740506i | \(0.734586\pi\) | |||||||
\(420\) | 5.54299 | 0.270470 | ||||||||
\(421\) | −25.6647 | −1.25082 | −0.625410 | − | 0.780297i | \(-0.715068\pi\) | ||||
−0.625410 | + | 0.780297i | \(0.715068\pi\) | |||||||
\(422\) | 9.88303 | 0.481098 | ||||||||
\(423\) | −8.05420 | −0.391609 | ||||||||
\(424\) | 11.6822 | 0.567335 | ||||||||
\(425\) | −7.89562 | −0.382994 | ||||||||
\(426\) | 18.7751 | 0.909657 | ||||||||
\(427\) | 46.4363 | 2.24721 | ||||||||
\(428\) | −4.90737 | −0.237207 | ||||||||
\(429\) | 5.46879 | 0.264035 | ||||||||
\(430\) | −16.8191 | −0.811087 | ||||||||
\(431\) | 10.4757 | 0.504595 | 0.252298 | − | 0.967650i | \(-0.418814\pi\) | ||||
0.252298 | + | 0.967650i | \(0.418814\pi\) | |||||||
\(432\) | 4.63040 | 0.222780 | ||||||||
\(433\) | −26.0663 | −1.25267 | −0.626334 | − | 0.779555i | \(-0.715445\pi\) | ||||
−0.626334 | + | 0.779555i | \(0.715445\pi\) | |||||||
\(434\) | 58.4403 | 2.80523 | ||||||||
\(435\) | 17.1339 | 0.821506 | ||||||||
\(436\) | 1.64337 | 0.0787031 | ||||||||
\(437\) | 0.0584265 | 0.00279492 | ||||||||
\(438\) | 9.87874 | 0.472024 | ||||||||
\(439\) | −5.14461 | −0.245539 | −0.122769 | − | 0.992435i | \(-0.539178\pi\) | ||||
−0.122769 | + | 0.992435i | \(0.539178\pi\) | |||||||
\(440\) | 34.4309 | 1.64143 | ||||||||
\(441\) | 8.50081 | 0.404801 | ||||||||
\(442\) | −2.19385 | −0.104351 | ||||||||
\(443\) | 30.7733 | 1.46208 | 0.731041 | − | 0.682334i | \(-0.239035\pi\) | ||||
0.731041 | + | 0.682334i | \(0.239035\pi\) | |||||||
\(444\) | 3.18032 | 0.150931 | ||||||||
\(445\) | −25.7795 | −1.22207 | ||||||||
\(446\) | −24.4358 | −1.15707 | ||||||||
\(447\) | −3.96393 | −0.187487 | ||||||||
\(448\) | −23.1392 | −1.09323 | ||||||||
\(449\) | 20.7647 | 0.979948 | 0.489974 | − | 0.871737i | \(-0.337006\pi\) | ||||
0.489974 | + | 0.871737i | \(0.337006\pi\) | |||||||
\(450\) | −12.2116 | −0.575659 | ||||||||
\(451\) | 11.5299 | 0.542924 | ||||||||
\(452\) | 1.19595 | 0.0562527 | ||||||||
\(453\) | 9.32731 | 0.438235 | ||||||||
\(454\) | −34.4936 | −1.61886 | ||||||||
\(455\) | 20.0548 | 0.940186 | ||||||||
\(456\) | 0.362625 | 0.0169815 | ||||||||
\(457\) | −11.0585 | −0.517293 | −0.258647 | − | 0.965972i | \(-0.583277\pi\) | ||||
−0.258647 | + | 0.965972i | \(0.583277\pi\) | |||||||
\(458\) | −13.3144 | −0.622142 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −0.564126 | −0.0263025 | ||||||||
\(461\) | −24.8112 | −1.15557 | −0.577787 | − | 0.816188i | \(-0.696083\pi\) | ||||
−0.577787 | + | 0.816188i | \(0.696083\pi\) | |||||||
\(462\) | −23.4765 | −1.09222 | ||||||||
\(463\) | 4.78200 | 0.222239 | 0.111119 | − | 0.993807i | \(-0.464556\pi\) | ||||
0.111119 | + | 0.993807i | \(0.464556\pi\) | |||||||
\(464\) | 22.0929 | 1.02564 | ||||||||
\(465\) | −34.4644 | −1.59825 | ||||||||
\(466\) | −25.6527 | −1.18834 | ||||||||
\(467\) | −15.7466 | −0.728667 | −0.364333 | − | 0.931269i | \(-0.618703\pi\) | ||||
−0.364333 | + | 0.931269i | \(0.618703\pi\) | |||||||
\(468\) | −0.556118 | −0.0257066 | ||||||||
\(469\) | 21.6293 | 0.998747 | ||||||||
\(470\) | 44.7331 | 2.06338 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −22.3391 | −1.02824 | ||||||||
\(473\) | 11.6752 | 0.536827 | ||||||||
\(474\) | 13.5559 | 0.622643 | ||||||||
\(475\) | −1.15129 | −0.0528250 | ||||||||
\(476\) | 1.54356 | 0.0707489 | ||||||||
\(477\) | 4.69749 | 0.215083 | ||||||||
\(478\) | 32.3063 | 1.47766 | ||||||||
\(479\) | 10.3222 | 0.471635 | 0.235817 | − | 0.971797i | \(-0.424223\pi\) | ||||
0.235817 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(480\) | −7.85620 | −0.358585 | ||||||||
\(481\) | 11.5066 | 0.524654 | ||||||||
\(482\) | 22.2982 | 1.01565 | ||||||||
\(483\) | −1.57756 | −0.0717815 | ||||||||
\(484\) | 1.51495 | 0.0688616 | ||||||||
\(485\) | −40.3669 | −1.83297 | ||||||||
\(486\) | 1.54663 | 0.0701564 | ||||||||
\(487\) | 25.0533 | 1.13527 | 0.567636 | − | 0.823280i | \(-0.307858\pi\) | ||||
0.567636 | + | 0.823280i | \(0.307858\pi\) | |||||||
\(488\) | −29.3317 | −1.32779 | ||||||||
\(489\) | −13.7238 | −0.620611 | ||||||||
\(490\) | −47.2136 | −2.13289 | ||||||||
\(491\) | −41.1123 | −1.85537 | −0.927685 | − | 0.373363i | \(-0.878204\pi\) | ||||
−0.927685 | + | 0.373363i | \(0.878204\pi\) | |||||||
\(492\) | −1.17247 | −0.0528593 | ||||||||
\(493\) | 4.77127 | 0.214887 | ||||||||
\(494\) | −0.319895 | −0.0143927 | ||||||||
\(495\) | 13.8449 | 0.622284 | ||||||||
\(496\) | −44.4394 | −1.99539 | ||||||||
\(497\) | −47.7941 | −2.14386 | ||||||||
\(498\) | −10.3437 | −0.463510 | ||||||||
\(499\) | 33.2480 | 1.48838 | 0.744192 | − | 0.667966i | \(-0.232835\pi\) | ||||
0.744192 | + | 0.667966i | \(0.232835\pi\) | |||||||
\(500\) | 4.07670 | 0.182315 | ||||||||
\(501\) | −5.47079 | −0.244417 | ||||||||
\(502\) | −36.9897 | −1.65093 | ||||||||
\(503\) | 11.1986 | 0.499323 | 0.249661 | − | 0.968333i | \(-0.419681\pi\) | ||||
0.249661 | + | 0.968333i | \(0.419681\pi\) | |||||||
\(504\) | −9.79116 | −0.436133 | ||||||||
\(505\) | 4.51939 | 0.201110 | ||||||||
\(506\) | 2.38927 | 0.106216 | ||||||||
\(507\) | 10.9879 | 0.487991 | ||||||||
\(508\) | 3.24388 | 0.143924 | ||||||||
\(509\) | −8.34251 | −0.369775 | −0.184888 | − | 0.982760i | \(-0.559192\pi\) | ||||
−0.184888 | + | 0.982760i | \(0.559192\pi\) | |||||||
\(510\) | −5.55401 | −0.245936 | ||||||||
\(511\) | −25.1474 | −1.11246 | ||||||||
\(512\) | 12.9006 | 0.570131 | ||||||||
\(513\) | 0.145814 | 0.00643786 | ||||||||
\(514\) | −6.76406 | −0.298350 | ||||||||
\(515\) | −38.5305 | −1.69786 | ||||||||
\(516\) | −1.18725 | −0.0522657 | ||||||||
\(517\) | −31.0522 | −1.36567 | ||||||||
\(518\) | −49.3955 | −2.17032 | ||||||||
\(519\) | 9.34451 | 0.410179 | ||||||||
\(520\) | −12.6677 | −0.555517 | ||||||||
\(521\) | 25.9794 | 1.13818 | 0.569090 | − | 0.822275i | \(-0.307296\pi\) | ||||
0.569090 | + | 0.822275i | \(0.307296\pi\) | |||||||
\(522\) | 7.37938 | 0.322987 | ||||||||
\(523\) | 3.60811 | 0.157772 | 0.0788859 | − | 0.996884i | \(-0.474864\pi\) | ||||
0.0788859 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(524\) | 1.34371 | 0.0587001 | ||||||||
\(525\) | 31.0859 | 1.35670 | ||||||||
\(526\) | 7.97859 | 0.347883 | ||||||||
\(527\) | −9.59732 | −0.418066 | ||||||||
\(528\) | 17.8521 | 0.776912 | ||||||||
\(529\) | −22.8394 | −0.993019 | ||||||||
\(530\) | −26.0899 | −1.13327 | ||||||||
\(531\) | −8.98276 | −0.389819 | ||||||||
\(532\) | 0.225073 | 0.00975816 | ||||||||
\(533\) | −4.24208 | −0.183745 | ||||||||
\(534\) | −11.1030 | −0.480472 | ||||||||
\(535\) | −44.9494 | −1.94333 | ||||||||
\(536\) | −13.6622 | −0.590118 | ||||||||
\(537\) | −3.01972 | −0.130310 | ||||||||
\(538\) | 36.1318 | 1.55775 | ||||||||
\(539\) | 32.7741 | 1.41168 | ||||||||
\(540\) | −1.40789 | −0.0605857 | ||||||||
\(541\) | −21.7946 | −0.937025 | −0.468513 | − | 0.883457i | \(-0.655210\pi\) | ||||
−0.468513 | + | 0.883457i | \(0.655210\pi\) | |||||||
\(542\) | −18.2688 | −0.784710 | ||||||||
\(543\) | −1.97516 | −0.0847623 | ||||||||
\(544\) | −2.18772 | −0.0937977 | ||||||||
\(545\) | 15.0525 | 0.644780 | ||||||||
\(546\) | 8.63741 | 0.369647 | ||||||||
\(547\) | −28.8135 | −1.23198 | −0.615989 | − | 0.787755i | \(-0.711243\pi\) | ||||
−0.615989 | + | 0.787755i | \(0.711243\pi\) | |||||||
\(548\) | −8.71705 | −0.372374 | ||||||||
\(549\) | −11.7945 | −0.503378 | ||||||||
\(550\) | −47.0806 | −2.00752 | ||||||||
\(551\) | 0.695720 | 0.0296387 | ||||||||
\(552\) | 0.996474 | 0.0424128 | ||||||||
\(553\) | −34.5080 | −1.46743 | ||||||||
\(554\) | −19.8976 | −0.845368 | ||||||||
\(555\) | 29.1304 | 1.23652 | ||||||||
\(556\) | 3.32059 | 0.140824 | ||||||||
\(557\) | 11.8907 | 0.503826 | 0.251913 | − | 0.967750i | \(-0.418940\pi\) | ||||
0.251913 | + | 0.967750i | \(0.418940\pi\) | |||||||
\(558\) | −14.8435 | −0.628374 | ||||||||
\(559\) | −4.29552 | −0.181681 | ||||||||
\(560\) | 65.4662 | 2.76645 | ||||||||
\(561\) | 3.85540 | 0.162775 | ||||||||
\(562\) | −34.6997 | −1.46372 | ||||||||
\(563\) | 13.3514 | 0.562696 | 0.281348 | − | 0.959606i | \(-0.409218\pi\) | ||||
0.281348 | + | 0.959606i | \(0.409218\pi\) | |||||||
\(564\) | 3.15768 | 0.132962 | ||||||||
\(565\) | 10.9544 | 0.460854 | ||||||||
\(566\) | −1.59588 | −0.0670800 | ||||||||
\(567\) | −3.93711 | −0.165343 | ||||||||
\(568\) | 30.1894 | 1.26672 | ||||||||
\(569\) | −4.47621 | −0.187653 | −0.0938263 | − | 0.995589i | \(-0.529910\pi\) | ||||
−0.0938263 | + | 0.995589i | \(0.529910\pi\) | |||||||
\(570\) | −0.809854 | −0.0339211 | ||||||||
\(571\) | 35.2715 | 1.47607 | 0.738033 | − | 0.674764i | \(-0.235755\pi\) | ||||
0.738033 | + | 0.674764i | \(0.235755\pi\) | |||||||
\(572\) | −2.14406 | −0.0896477 | ||||||||
\(573\) | 18.7075 | 0.781519 | ||||||||
\(574\) | 18.2104 | 0.760089 | ||||||||
\(575\) | −3.16370 | −0.131935 | ||||||||
\(576\) | 5.87722 | 0.244884 | ||||||||
\(577\) | 19.2534 | 0.801530 | 0.400765 | − | 0.916181i | \(-0.368744\pi\) | ||||
0.400765 | + | 0.916181i | \(0.368744\pi\) | |||||||
\(578\) | −1.54663 | −0.0643312 | ||||||||
\(579\) | 5.35036 | 0.222353 | ||||||||
\(580\) | −6.71741 | −0.278925 | ||||||||
\(581\) | 26.3309 | 1.09239 | ||||||||
\(582\) | −17.3856 | −0.720657 | ||||||||
\(583\) | 18.1107 | 0.750070 | ||||||||
\(584\) | 15.8845 | 0.657304 | ||||||||
\(585\) | −5.09380 | −0.210603 | ||||||||
\(586\) | −22.6722 | −0.936579 | ||||||||
\(587\) | −4.00735 | −0.165401 | −0.0827005 | − | 0.996574i | \(-0.526354\pi\) | ||||
−0.0827005 | + | 0.996574i | \(0.526354\pi\) | |||||||
\(588\) | −3.33278 | −0.137442 | ||||||||
\(589\) | −1.39943 | −0.0576624 | ||||||||
\(590\) | 49.8903 | 2.05395 | ||||||||
\(591\) | 4.07175 | 0.167489 | ||||||||
\(592\) | 37.5616 | 1.54377 | ||||||||
\(593\) | −35.0361 | −1.43876 | −0.719381 | − | 0.694616i | \(-0.755574\pi\) | ||||
−0.719381 | + | 0.694616i | \(0.755574\pi\) | |||||||
\(594\) | 5.96287 | 0.244660 | ||||||||
\(595\) | 14.1383 | 0.579615 | ||||||||
\(596\) | 1.55407 | 0.0636574 | ||||||||
\(597\) | −2.43646 | −0.0997178 | ||||||||
\(598\) | −0.879054 | −0.0359472 | ||||||||
\(599\) | −23.8079 | −0.972765 | −0.486382 | − | 0.873746i | \(-0.661684\pi\) | ||||
−0.486382 | + | 0.873746i | \(0.661684\pi\) | |||||||
\(600\) | −19.6355 | −0.801618 | ||||||||
\(601\) | 18.5378 | 0.756171 | 0.378086 | − | 0.925771i | \(-0.376583\pi\) | ||||
0.378086 | + | 0.925771i | \(0.376583\pi\) | |||||||
\(602\) | 18.4399 | 0.751553 | ||||||||
\(603\) | −5.49370 | −0.223721 | ||||||||
\(604\) | −3.65681 | −0.148794 | ||||||||
\(605\) | 13.8763 | 0.564153 | ||||||||
\(606\) | 1.94645 | 0.0790692 | ||||||||
\(607\) | −14.2576 | −0.578698 | −0.289349 | − | 0.957224i | \(-0.593439\pi\) | ||||
−0.289349 | + | 0.957224i | \(0.593439\pi\) | |||||||
\(608\) | −0.319001 | −0.0129372 | ||||||||
\(609\) | −18.7850 | −0.761207 | ||||||||
\(610\) | 65.5069 | 2.65230 | ||||||||
\(611\) | 11.4247 | 0.462193 | ||||||||
\(612\) | −0.392054 | −0.0158479 | ||||||||
\(613\) | −28.1775 | −1.13808 | −0.569039 | − | 0.822310i | \(-0.692685\pi\) | ||||
−0.569039 | + | 0.822310i | \(0.692685\pi\) | |||||||
\(614\) | −32.4760 | −1.31062 | ||||||||
\(615\) | −10.7394 | −0.433053 | ||||||||
\(616\) | −37.7489 | −1.52095 | ||||||||
\(617\) | −25.3219 | −1.01942 | −0.509711 | − | 0.860346i | \(-0.670248\pi\) | ||||
−0.509711 | + | 0.860346i | \(0.670248\pi\) | |||||||
\(618\) | −16.5947 | −0.667537 | ||||||||
\(619\) | −33.7829 | −1.35785 | −0.678925 | − | 0.734208i | \(-0.737554\pi\) | ||||
−0.678925 | + | 0.734208i | \(0.737554\pi\) | |||||||
\(620\) | 13.5119 | 0.542652 | ||||||||
\(621\) | 0.400691 | 0.0160792 | ||||||||
\(622\) | −7.88579 | −0.316191 | ||||||||
\(623\) | 28.2638 | 1.13237 | ||||||||
\(624\) | −6.56810 | −0.262934 | ||||||||
\(625\) | −2.13732 | −0.0854928 | ||||||||
\(626\) | 40.4128 | 1.61522 | ||||||||
\(627\) | 0.562174 | 0.0224510 | ||||||||
\(628\) | −0.392054 | −0.0156447 | ||||||||
\(629\) | 8.11194 | 0.323444 | ||||||||
\(630\) | 21.8667 | 0.871191 | ||||||||
\(631\) | 13.9029 | 0.553464 | 0.276732 | − | 0.960947i | \(-0.410749\pi\) | ||||
0.276732 | + | 0.960947i | \(0.410749\pi\) | |||||||
\(632\) | 21.7971 | 0.867044 | ||||||||
\(633\) | 6.39005 | 0.253982 | ||||||||
\(634\) | 30.3343 | 1.20473 | ||||||||
\(635\) | 29.7125 | 1.17911 | ||||||||
\(636\) | −1.84167 | −0.0730270 | ||||||||
\(637\) | −12.0582 | −0.477762 | ||||||||
\(638\) | 28.4505 | 1.12637 | ||||||||
\(639\) | 12.1394 | 0.480227 | ||||||||
\(640\) | −48.3545 | −1.91138 | ||||||||
\(641\) | −38.0252 | −1.50191 | −0.750953 | − | 0.660355i | \(-0.770406\pi\) | ||||
−0.750953 | + | 0.660355i | \(0.770406\pi\) | |||||||
\(642\) | −19.3592 | −0.764048 | ||||||||
\(643\) | −38.6521 | −1.52429 | −0.762146 | − | 0.647406i | \(-0.775854\pi\) | ||||
−0.762146 | + | 0.647406i | \(0.775854\pi\) | |||||||
\(644\) | 0.618490 | 0.0243719 | ||||||||
\(645\) | −10.8747 | −0.428190 | ||||||||
\(646\) | −0.225520 | −0.00887298 | ||||||||
\(647\) | 19.4338 | 0.764021 | 0.382011 | − | 0.924158i | \(-0.375232\pi\) | ||||
0.382011 | + | 0.924158i | \(0.375232\pi\) | |||||||
\(648\) | 2.48689 | 0.0976943 | ||||||||
\(649\) | −34.6322 | −1.35943 | ||||||||
\(650\) | 17.3218 | 0.679416 | ||||||||
\(651\) | 37.7857 | 1.48094 | ||||||||
\(652\) | 5.38047 | 0.210715 | ||||||||
\(653\) | 45.7883 | 1.79183 | 0.895917 | − | 0.444222i | \(-0.146520\pi\) | ||||
0.895917 | + | 0.444222i | \(0.146520\pi\) | |||||||
\(654\) | 6.48297 | 0.253504 | ||||||||
\(655\) | 12.3078 | 0.480904 | ||||||||
\(656\) | −13.8477 | −0.540660 | ||||||||
\(657\) | 6.38728 | 0.249192 | ||||||||
\(658\) | −49.0439 | −1.91193 | ||||||||
\(659\) | −3.29596 | −0.128392 | −0.0641961 | − | 0.997937i | \(-0.520448\pi\) | ||||
−0.0641961 | + | 0.997937i | \(0.520448\pi\) | |||||||
\(660\) | −5.42797 | −0.211283 | ||||||||
\(661\) | 16.2719 | 0.632902 | 0.316451 | − | 0.948609i | \(-0.397509\pi\) | ||||
0.316451 | + | 0.948609i | \(0.397509\pi\) | |||||||
\(662\) | 28.1203 | 1.09293 | ||||||||
\(663\) | −1.41847 | −0.0550889 | ||||||||
\(664\) | −16.6320 | −0.645448 | ||||||||
\(665\) | 2.06157 | 0.0799444 | ||||||||
\(666\) | 12.5461 | 0.486153 | ||||||||
\(667\) | 1.91180 | 0.0740254 | ||||||||
\(668\) | 2.14485 | 0.0829866 | ||||||||
\(669\) | −15.7994 | −0.610841 | ||||||||
\(670\) | 30.5120 | 1.17878 | ||||||||
\(671\) | −45.4727 | −1.75545 | ||||||||
\(672\) | 8.61329 | 0.332265 | ||||||||
\(673\) | −10.3424 | −0.398672 | −0.199336 | − | 0.979931i | \(-0.563878\pi\) | ||||
−0.199336 | + | 0.979931i | \(0.563878\pi\) | |||||||
\(674\) | 49.7366 | 1.91578 | ||||||||
\(675\) | −7.89562 | −0.303902 | ||||||||
\(676\) | −4.30787 | −0.165687 | ||||||||
\(677\) | 24.6411 | 0.947036 | 0.473518 | − | 0.880784i | \(-0.342984\pi\) | ||||
0.473518 | + | 0.880784i | \(0.342984\pi\) | |||||||
\(678\) | 4.71793 | 0.181191 | ||||||||
\(679\) | 44.2570 | 1.69843 | ||||||||
\(680\) | −8.93055 | −0.342471 | ||||||||
\(681\) | −22.3025 | −0.854632 | ||||||||
\(682\) | −57.2276 | −2.19136 | ||||||||
\(683\) | −1.94550 | −0.0744423 | −0.0372212 | − | 0.999307i | \(-0.511851\pi\) | ||||
−0.0372212 | + | 0.999307i | \(0.511851\pi\) | |||||||
\(684\) | −0.0571672 | −0.00218584 | ||||||||
\(685\) | −79.8444 | −3.05070 | ||||||||
\(686\) | 9.13880 | 0.348921 | ||||||||
\(687\) | −8.60868 | −0.328442 | ||||||||
\(688\) | −14.0221 | −0.534588 | ||||||||
\(689\) | −6.66326 | −0.253850 | ||||||||
\(690\) | −2.22544 | −0.0847210 | ||||||||
\(691\) | 10.8166 | 0.411484 | 0.205742 | − | 0.978606i | \(-0.434039\pi\) | ||||
0.205742 | + | 0.978606i | \(0.434039\pi\) | |||||||
\(692\) | −3.66356 | −0.139268 | ||||||||
\(693\) | −15.1791 | −0.576608 | ||||||||
\(694\) | 7.51023 | 0.285085 | ||||||||
\(695\) | 30.4151 | 1.15371 | ||||||||
\(696\) | 11.8656 | 0.449766 | ||||||||
\(697\) | −2.99059 | −0.113277 | ||||||||
\(698\) | 2.67842 | 0.101380 | ||||||||
\(699\) | −16.5862 | −0.627348 | ||||||||
\(700\) | −12.1874 | −0.460639 | ||||||||
\(701\) | −7.31867 | −0.276422 | −0.138211 | − | 0.990403i | \(-0.544135\pi\) | ||||
−0.138211 | + | 0.990403i | \(0.544135\pi\) | |||||||
\(702\) | −2.19385 | −0.0828014 | ||||||||
\(703\) | 1.18284 | 0.0446116 | ||||||||
\(704\) | 22.6591 | 0.853995 | ||||||||
\(705\) | 28.9230 | 1.08930 | ||||||||
\(706\) | 17.0732 | 0.642557 | ||||||||
\(707\) | −4.95491 | −0.186348 | ||||||||
\(708\) | 3.52173 | 0.132355 | ||||||||
\(709\) | 30.5669 | 1.14797 | 0.573983 | − | 0.818867i | \(-0.305398\pi\) | ||||
0.573983 | + | 0.818867i | \(0.305398\pi\) | |||||||
\(710\) | −67.4223 | −2.53031 | ||||||||
\(711\) | 8.76482 | 0.328706 | ||||||||
\(712\) | −17.8530 | −0.669068 | ||||||||
\(713\) | −3.84556 | −0.144017 | ||||||||
\(714\) | 6.08924 | 0.227884 | ||||||||
\(715\) | −19.6387 | −0.734445 | ||||||||
\(716\) | 1.18389 | 0.0442441 | ||||||||
\(717\) | 20.8882 | 0.780086 | ||||||||
\(718\) | −49.1465 | −1.83413 | ||||||||
\(719\) | −39.3686 | −1.46820 | −0.734100 | − | 0.679041i | \(-0.762396\pi\) | ||||
−0.734100 | + | 0.679041i | \(0.762396\pi\) | |||||||
\(720\) | −16.6280 | −0.619689 | ||||||||
\(721\) | 42.2436 | 1.57324 | ||||||||
\(722\) | 29.3530 | 1.09241 | ||||||||
\(723\) | 14.4173 | 0.536185 | ||||||||
\(724\) | 0.774370 | 0.0287792 | ||||||||
\(725\) | −37.6722 | −1.39911 | ||||||||
\(726\) | 5.97639 | 0.221805 | ||||||||
\(727\) | −2.95851 | −0.109725 | −0.0548626 | − | 0.998494i | \(-0.517472\pi\) | ||||
−0.0548626 | + | 0.998494i | \(0.517472\pi\) | |||||||
\(728\) | 13.8885 | 0.514742 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −35.4750 | −1.31299 | ||||||||
\(731\) | −3.02827 | −0.112005 | ||||||||
\(732\) | 4.62410 | 0.170912 | ||||||||
\(733\) | −0.125750 | −0.00464466 | −0.00232233 | − | 0.999997i | \(-0.500739\pi\) | ||||
−0.00232233 | + | 0.999997i | \(0.500739\pi\) | |||||||
\(734\) | 4.04581 | 0.149333 | ||||||||
\(735\) | −30.5268 | −1.12600 | ||||||||
\(736\) | −0.876599 | −0.0323119 | ||||||||
\(737\) | −21.1804 | −0.780191 | ||||||||
\(738\) | −4.62533 | −0.170261 | ||||||||
\(739\) | −33.9560 | −1.24909 | −0.624546 | − | 0.780988i | \(-0.714716\pi\) | ||||
−0.624546 | + | 0.780988i | \(0.714716\pi\) | |||||||
\(740\) | −11.4207 | −0.419833 | ||||||||
\(741\) | −0.206834 | −0.00759823 | ||||||||
\(742\) | 28.6041 | 1.05009 | ||||||||
\(743\) | −49.6319 | −1.82082 | −0.910409 | − | 0.413709i | \(-0.864233\pi\) | ||||
−0.910409 | + | 0.413709i | \(0.864233\pi\) | |||||||
\(744\) | −23.8675 | −0.875025 | ||||||||
\(745\) | 14.2347 | 0.521517 | ||||||||
\(746\) | −19.1311 | −0.700440 | ||||||||
\(747\) | −6.68788 | −0.244697 | ||||||||
\(748\) | −1.51153 | −0.0552669 | ||||||||
\(749\) | 49.2810 | 1.80069 | ||||||||
\(750\) | 16.0823 | 0.587242 | ||||||||
\(751\) | 9.54133 | 0.348168 | 0.174084 | − | 0.984731i | \(-0.444304\pi\) | ||||
0.174084 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(752\) | 37.2942 | 1.35998 | ||||||||
\(753\) | −23.9164 | −0.871561 | ||||||||
\(754\) | −10.4674 | −0.381202 | ||||||||
\(755\) | −33.4948 | −1.21900 | ||||||||
\(756\) | 1.54356 | 0.0561387 | ||||||||
\(757\) | −23.4545 | −0.852467 | −0.426233 | − | 0.904613i | \(-0.640160\pi\) | ||||
−0.426233 | + | 0.904613i | \(0.640160\pi\) | |||||||
\(758\) | 14.2287 | 0.516809 | ||||||||
\(759\) | 1.54482 | 0.0560736 | ||||||||
\(760\) | −1.30220 | −0.0472358 | ||||||||
\(761\) | −35.8791 | −1.30061 | −0.650307 | − | 0.759671i | \(-0.725360\pi\) | ||||
−0.650307 | + | 0.759671i | \(0.725360\pi\) | |||||||
\(762\) | 12.7969 | 0.463582 | ||||||||
\(763\) | −16.5031 | −0.597453 | ||||||||
\(764\) | −7.33437 | −0.265348 | ||||||||
\(765\) | −3.59105 | −0.129835 | ||||||||
\(766\) | 53.3652 | 1.92816 | ||||||||
\(767\) | 12.7418 | 0.460080 | ||||||||
\(768\) | −9.07136 | −0.327334 | ||||||||
\(769\) | 3.71044 | 0.133802 | 0.0669009 | − | 0.997760i | \(-0.478689\pi\) | ||||
0.0669009 | + | 0.997760i | \(0.478689\pi\) | |||||||
\(770\) | 84.3051 | 3.03814 | ||||||||
\(771\) | −4.37343 | −0.157505 | ||||||||
\(772\) | −2.09763 | −0.0754954 | ||||||||
\(773\) | −28.0966 | −1.01056 | −0.505282 | − | 0.862954i | \(-0.668612\pi\) | ||||
−0.505282 | + | 0.862954i | \(0.668612\pi\) | |||||||
\(774\) | −4.68361 | −0.168349 | ||||||||
\(775\) | 75.7768 | 2.72198 | ||||||||
\(776\) | −27.9551 | −1.00353 | ||||||||
\(777\) | −31.9376 | −1.14575 | ||||||||
\(778\) | 20.6110 | 0.738942 | ||||||||
\(779\) | −0.436072 | −0.0156239 | ||||||||
\(780\) | 1.99705 | 0.0715057 | ||||||||
\(781\) | 46.8023 | 1.67472 | ||||||||
\(782\) | −0.619719 | −0.0221611 | ||||||||
\(783\) | 4.77127 | 0.170511 | ||||||||
\(784\) | −39.3622 | −1.40579 | ||||||||
\(785\) | −3.59105 | −0.128170 | ||||||||
\(786\) | 5.30083 | 0.189074 | ||||||||
\(787\) | 29.7364 | 1.05999 | 0.529995 | − | 0.848001i | \(-0.322194\pi\) | ||||
0.529995 | + | 0.848001i | \(0.322194\pi\) | |||||||
\(788\) | −1.59635 | −0.0568675 | ||||||||
\(789\) | 5.15870 | 0.183655 | ||||||||
\(790\) | −48.6799 | −1.73195 | ||||||||
\(791\) | −12.0100 | −0.427027 | ||||||||
\(792\) | 9.58798 | 0.340694 | ||||||||
\(793\) | 16.7302 | 0.594108 | ||||||||
\(794\) | 6.39898 | 0.227091 | ||||||||
\(795\) | −16.8689 | −0.598279 | ||||||||
\(796\) | 0.955225 | 0.0338571 | ||||||||
\(797\) | −47.7145 | −1.69013 | −0.845067 | − | 0.534661i | \(-0.820439\pi\) | ||||
−0.845067 | + | 0.534661i | \(0.820439\pi\) | |||||||
\(798\) | 0.887898 | 0.0314313 | ||||||||
\(799\) | 8.05420 | 0.284937 | ||||||||
\(800\) | 17.2734 | 0.610707 | ||||||||
\(801\) | −7.17883 | −0.253651 | ||||||||
\(802\) | −31.9186 | −1.12709 | ||||||||
\(803\) | 24.6256 | 0.869017 | ||||||||
\(804\) | 2.15383 | 0.0759596 | ||||||||
\(805\) | 5.66510 | 0.199668 | ||||||||
\(806\) | 21.0551 | 0.741633 | ||||||||
\(807\) | 23.3617 | 0.822370 | ||||||||
\(808\) | 3.12979 | 0.110106 | ||||||||
\(809\) | −49.6772 | −1.74656 | −0.873278 | − | 0.487222i | \(-0.838010\pi\) | ||||
−0.873278 | + | 0.487222i | \(0.838010\pi\) | |||||||
\(810\) | −5.55401 | −0.195148 | ||||||||
\(811\) | −29.3652 | −1.03115 | −0.515576 | − | 0.856844i | \(-0.672422\pi\) | ||||
−0.515576 | + | 0.856844i | \(0.672422\pi\) | |||||||
\(812\) | 7.36475 | 0.258452 | ||||||||
\(813\) | −11.8120 | −0.414265 | ||||||||
\(814\) | 48.3705 | 1.69538 | ||||||||
\(815\) | 49.2828 | 1.72630 | ||||||||
\(816\) | −4.63040 | −0.162096 | ||||||||
\(817\) | −0.441566 | −0.0154484 | ||||||||
\(818\) | −42.2875 | −1.47855 | ||||||||
\(819\) | 5.58468 | 0.195144 | ||||||||
\(820\) | 4.21041 | 0.147034 | ||||||||
\(821\) | −15.7994 | −0.551402 | −0.275701 | − | 0.961244i | \(-0.588910\pi\) | ||||
−0.275701 | + | 0.961244i | \(0.588910\pi\) | |||||||
\(822\) | −34.3882 | −1.19942 | ||||||||
\(823\) | −55.5050 | −1.93478 | −0.967392 | − | 0.253285i | \(-0.918489\pi\) | ||||
−0.967392 | + | 0.253285i | \(0.918489\pi\) | |||||||
\(824\) | −26.6834 | −0.929560 | ||||||||
\(825\) | −30.4408 | −1.05981 | ||||||||
\(826\) | −54.6981 | −1.90319 | ||||||||
\(827\) | 22.2330 | 0.773115 | 0.386558 | − | 0.922265i | \(-0.373664\pi\) | ||||
0.386558 | + | 0.922265i | \(0.373664\pi\) | |||||||
\(828\) | −0.157092 | −0.00545934 | ||||||||
\(829\) | 0.296851 | 0.0103101 | 0.00515504 | − | 0.999987i | \(-0.498359\pi\) | ||||
0.00515504 | + | 0.999987i | \(0.498359\pi\) | |||||||
\(830\) | 37.1446 | 1.28931 | ||||||||
\(831\) | −12.8652 | −0.446287 | ||||||||
\(832\) | −8.33667 | −0.289022 | ||||||||
\(833\) | −8.50081 | −0.294536 | ||||||||
\(834\) | 13.0995 | 0.453598 | ||||||||
\(835\) | 19.6459 | 0.679873 | ||||||||
\(836\) | −0.220403 | −0.00762278 | ||||||||
\(837\) | −9.59732 | −0.331732 | ||||||||
\(838\) | 42.5524 | 1.46995 | ||||||||
\(839\) | −46.9989 | −1.62258 | −0.811291 | − | 0.584643i | \(-0.801235\pi\) | ||||
−0.811291 | + | 0.584643i | \(0.801235\pi\) | |||||||
\(840\) | 35.1605 | 1.21315 | ||||||||
\(841\) | −6.23494 | −0.214998 | ||||||||
\(842\) | 39.6937 | 1.36793 | ||||||||
\(843\) | −22.4357 | −0.772727 | ||||||||
\(844\) | −2.50525 | −0.0862342 | ||||||||
\(845\) | −39.4582 | −1.35740 | ||||||||
\(846\) | 12.4568 | 0.428275 | ||||||||
\(847\) | −15.2136 | −0.522744 | ||||||||
\(848\) | −21.7513 | −0.746942 | ||||||||
\(849\) | −1.03185 | −0.0354130 | ||||||||
\(850\) | 12.2116 | 0.418853 | ||||||||
\(851\) | 3.25038 | 0.111422 | ||||||||
\(852\) | −4.75930 | −0.163051 | ||||||||
\(853\) | 50.4261 | 1.72656 | 0.863278 | − | 0.504729i | \(-0.168407\pi\) | ||||
0.863278 | + | 0.504729i | \(0.168407\pi\) | |||||||
\(854\) | −71.8197 | −2.45762 | ||||||||
\(855\) | −0.523626 | −0.0179076 | ||||||||
\(856\) | −31.1286 | −1.06395 | ||||||||
\(857\) | −44.8707 | −1.53275 | −0.766376 | − | 0.642392i | \(-0.777942\pi\) | ||||
−0.766376 | + | 0.642392i | \(0.777942\pi\) | |||||||
\(858\) | −8.45817 | −0.288757 | ||||||||
\(859\) | −42.3143 | −1.44374 | −0.721872 | − | 0.692027i | \(-0.756718\pi\) | ||||
−0.721872 | + | 0.692027i | \(0.756718\pi\) | |||||||
\(860\) | 4.26346 | 0.145383 | ||||||||
\(861\) | 11.7743 | 0.401267 | ||||||||
\(862\) | −16.2020 | −0.551841 | ||||||||
\(863\) | −55.3235 | −1.88323 | −0.941617 | − | 0.336686i | \(-0.890694\pi\) | ||||
−0.941617 | + | 0.336686i | \(0.890694\pi\) | |||||||
\(864\) | −2.18772 | −0.0744277 | ||||||||
\(865\) | −33.5566 | −1.14096 | ||||||||
\(866\) | 40.3149 | 1.36995 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −14.8140 | −0.502821 | ||||||||
\(869\) | 33.7919 | 1.14631 | ||||||||
\(870\) | −26.4997 | −0.898424 | ||||||||
\(871\) | 7.79266 | 0.264044 | ||||||||
\(872\) | 10.4243 | 0.353010 | ||||||||
\(873\) | −11.2410 | −0.380450 | ||||||||
\(874\) | −0.0903639 | −0.00305660 | ||||||||
\(875\) | −40.9392 | −1.38400 | ||||||||
\(876\) | −2.50416 | −0.0846077 | ||||||||
\(877\) | −32.4277 | −1.09500 | −0.547502 | − | 0.836804i | \(-0.684421\pi\) | ||||
−0.547502 | + | 0.836804i | \(0.684421\pi\) | |||||||
\(878\) | 7.95679 | 0.268529 | ||||||||
\(879\) | −14.6591 | −0.494440 | ||||||||
\(880\) | −64.1076 | −2.16107 | ||||||||
\(881\) | 11.8303 | 0.398572 | 0.199286 | − | 0.979941i | \(-0.436138\pi\) | ||||
0.199286 | + | 0.979941i | \(0.436138\pi\) | |||||||
\(882\) | −13.1476 | −0.442702 | ||||||||
\(883\) | −32.2787 | −1.08626 | −0.543132 | − | 0.839647i | \(-0.682762\pi\) | ||||
−0.543132 | + | 0.839647i | \(0.682762\pi\) | |||||||
\(884\) | 0.556118 | 0.0187043 | ||||||||
\(885\) | 32.2575 | 1.08432 | ||||||||
\(886\) | −47.5947 | −1.59898 | ||||||||
\(887\) | −45.7989 | −1.53778 | −0.768889 | − | 0.639383i | \(-0.779190\pi\) | ||||
−0.768889 | + | 0.639383i | \(0.779190\pi\) | |||||||
\(888\) | 20.1735 | 0.676979 | ||||||||
\(889\) | −32.5758 | −1.09256 | ||||||||
\(890\) | 39.8713 | 1.33649 | ||||||||
\(891\) | 3.85540 | 0.129161 | ||||||||
\(892\) | 6.19423 | 0.207398 | ||||||||
\(893\) | 1.17442 | 0.0393004 | ||||||||
\(894\) | 6.13072 | 0.205042 | ||||||||
\(895\) | 10.8439 | 0.362473 | ||||||||
\(896\) | 53.0143 | 1.77108 | ||||||||
\(897\) | −0.568369 | −0.0189773 | ||||||||
\(898\) | −32.1153 | −1.07170 | ||||||||
\(899\) | −45.7914 | −1.52723 | ||||||||
\(900\) | 3.09551 | 0.103184 | ||||||||
\(901\) | −4.69749 | −0.156496 | ||||||||
\(902\) | −17.8325 | −0.593758 | ||||||||
\(903\) | 11.9226 | 0.396761 | ||||||||
\(904\) | 7.58618 | 0.252313 | ||||||||
\(905\) | 7.09290 | 0.235776 | ||||||||
\(906\) | −14.4259 | −0.479267 | ||||||||
\(907\) | −48.8416 | −1.62176 | −0.810879 | − | 0.585214i | \(-0.801010\pi\) | ||||
−0.810879 | + | 0.585214i | \(0.801010\pi\) | |||||||
\(908\) | 8.74377 | 0.290172 | ||||||||
\(909\) | 1.25851 | 0.0417423 | ||||||||
\(910\) | −31.0174 | −1.02822 | ||||||||
\(911\) | 14.8665 | 0.492550 | 0.246275 | − | 0.969200i | \(-0.420793\pi\) | ||||
0.246275 | + | 0.969200i | \(0.420793\pi\) | |||||||
\(912\) | −0.675179 | −0.0223574 | ||||||||
\(913\) | −25.7845 | −0.853342 | ||||||||
\(914\) | 17.1033 | 0.565728 | ||||||||
\(915\) | 42.3547 | 1.40020 | ||||||||
\(916\) | 3.37507 | 0.111515 | ||||||||
\(917\) | −13.4938 | −0.445606 | ||||||||
\(918\) | −1.54663 | −0.0510463 | ||||||||
\(919\) | −22.9265 | −0.756275 | −0.378137 | − | 0.925749i | \(-0.623435\pi\) | ||||
−0.378137 | + | 0.925749i | \(0.623435\pi\) | |||||||
\(920\) | −3.57839 | −0.117976 | ||||||||
\(921\) | −20.9980 | −0.691906 | ||||||||
\(922\) | 38.3737 | 1.26377 | ||||||||
\(923\) | −17.2194 | −0.566784 | ||||||||
\(924\) | 5.95105 | 0.195775 | ||||||||
\(925\) | −64.0488 | −2.10591 | ||||||||
\(926\) | −7.39598 | −0.243047 | ||||||||
\(927\) | −10.7296 | −0.352407 | ||||||||
\(928\) | −10.4382 | −0.342651 | ||||||||
\(929\) | −35.1905 | −1.15456 | −0.577281 | − | 0.816546i | \(-0.695886\pi\) | ||||
−0.577281 | + | 0.816546i | \(0.695886\pi\) | |||||||
\(930\) | 53.3036 | 1.74789 | ||||||||
\(931\) | −1.23954 | −0.0406243 | ||||||||
\(932\) | 6.50269 | 0.213003 | ||||||||
\(933\) | −5.09870 | −0.166924 | ||||||||
\(934\) | 24.3542 | 0.796892 | ||||||||
\(935\) | −13.8449 | −0.452778 | ||||||||
\(936\) | −3.52759 | −0.115303 | ||||||||
\(937\) | 29.5193 | 0.964355 | 0.482177 | − | 0.876074i | \(-0.339846\pi\) | ||||
0.482177 | + | 0.876074i | \(0.339846\pi\) | |||||||
\(938\) | −33.4524 | −1.09226 | ||||||||
\(939\) | 26.1297 | 0.852709 | ||||||||
\(940\) | −11.3394 | −0.369850 | ||||||||
\(941\) | −33.4722 | −1.09116 | −0.545581 | − | 0.838058i | \(-0.683691\pi\) | ||||
−0.545581 | + | 0.838058i | \(0.683691\pi\) | |||||||
\(942\) | −1.54663 | −0.0503918 | ||||||||
\(943\) | −1.19830 | −0.0390221 | ||||||||
\(944\) | 41.5938 | 1.35376 | ||||||||
\(945\) | 14.1383 | 0.459920 | ||||||||
\(946\) | −18.0572 | −0.587090 | ||||||||
\(947\) | 7.38623 | 0.240020 | 0.120010 | − | 0.992773i | \(-0.461707\pi\) | ||||
0.120010 | + | 0.992773i | \(0.461707\pi\) | |||||||
\(948\) | −3.43628 | −0.111605 | ||||||||
\(949\) | −9.06018 | −0.294106 | ||||||||
\(950\) | 1.78062 | 0.0577710 | ||||||||
\(951\) | 19.6132 | 0.636002 | ||||||||
\(952\) | 9.79116 | 0.317333 | ||||||||
\(953\) | −41.9183 | −1.35787 | −0.678934 | − | 0.734199i | \(-0.737558\pi\) | ||||
−0.678934 | + | 0.734199i | \(0.737558\pi\) | |||||||
\(954\) | −7.26527 | −0.235222 | ||||||||
\(955\) | −67.1797 | −2.17388 | ||||||||
\(956\) | −8.18932 | −0.264862 | ||||||||
\(957\) | 18.3952 | 0.594632 | ||||||||
\(958\) | −15.9646 | −0.515794 | ||||||||
\(959\) | 87.5388 | 2.82678 | ||||||||
\(960\) | −21.1054 | −0.681173 | ||||||||
\(961\) | 61.1086 | 1.97124 | ||||||||
\(962\) | −17.7964 | −0.573778 | ||||||||
\(963\) | −12.5171 | −0.403357 | ||||||||
\(964\) | −5.65236 | −0.182050 | ||||||||
\(965\) | −19.2134 | −0.618501 | ||||||||
\(966\) | 2.43990 | 0.0785025 | ||||||||
\(967\) | 24.8001 | 0.797519 | 0.398759 | − | 0.917056i | \(-0.369441\pi\) | ||||
0.398759 | + | 0.917056i | \(0.369441\pi\) | |||||||
\(968\) | 9.60971 | 0.308868 | ||||||||
\(969\) | −0.145814 | −0.00468423 | ||||||||
\(970\) | 62.4325 | 2.00459 | ||||||||
\(971\) | 47.0133 | 1.50873 | 0.754365 | − | 0.656455i | \(-0.227945\pi\) | ||||
0.754365 | + | 0.656455i | \(0.227945\pi\) | |||||||
\(972\) | −0.392054 | −0.0125751 | ||||||||
\(973\) | −33.3462 | −1.06903 | ||||||||
\(974\) | −38.7481 | −1.24157 | ||||||||
\(975\) | 11.1997 | 0.358678 | ||||||||
\(976\) | 54.6134 | 1.74813 | ||||||||
\(977\) | 3.12781 | 0.100067 | 0.0500337 | − | 0.998748i | \(-0.484067\pi\) | ||||
0.0500337 | + | 0.998748i | \(0.484067\pi\) | |||||||
\(978\) | 21.2256 | 0.678719 | ||||||||
\(979\) | −27.6773 | −0.884570 | ||||||||
\(980\) | 11.9682 | 0.382309 | ||||||||
\(981\) | 4.19169 | 0.133830 | ||||||||
\(982\) | 63.5853 | 2.02909 | ||||||||
\(983\) | 14.5096 | 0.462785 | 0.231393 | − | 0.972860i | \(-0.425672\pi\) | ||||
0.231393 | + | 0.972860i | \(0.425672\pi\) | |||||||
\(984\) | −7.43728 | −0.237092 | ||||||||
\(985\) | −14.6219 | −0.465891 | ||||||||
\(986\) | −7.37938 | −0.235007 | ||||||||
\(987\) | −31.7103 | −1.00935 | ||||||||
\(988\) | 0.0810900 | 0.00257982 | ||||||||
\(989\) | −1.21340 | −0.0385839 | ||||||||
\(990\) | −21.4130 | −0.680548 | ||||||||
\(991\) | −24.3752 | −0.774303 | −0.387152 | − | 0.922016i | \(-0.626541\pi\) | ||||
−0.387152 | + | 0.922016i | \(0.626541\pi\) | |||||||
\(992\) | 20.9962 | 0.666631 | ||||||||
\(993\) | 18.1817 | 0.576979 | ||||||||
\(994\) | 73.9196 | 2.34459 | ||||||||
\(995\) | 8.74945 | 0.277376 | ||||||||
\(996\) | 2.62201 | 0.0830817 | ||||||||
\(997\) | 17.2128 | 0.545136 | 0.272568 | − | 0.962137i | \(-0.412127\pi\) | ||||
0.272568 | + | 0.962137i | \(0.412127\pi\) | |||||||
\(998\) | −51.4222 | −1.62774 | ||||||||
\(999\) | 8.11194 | 0.256651 |
(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 | 8007.2.a.f.1.12 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.12 | ✓ | 48 | 1.1 | even | 1 | trivial |