Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6047,2,Mod(1,6047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6047, 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("6047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.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: | \(48.2855381023\) |
Analytic rank: | \(0\) |
Dimension: | \(287\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65477 | −1.87721 | −0.938604 | − | 0.344996i | \(-0.887880\pi\) | ||||
−0.938604 | + | 0.344996i | \(0.887880\pi\) | |||||||
\(3\) | 2.03227 | 1.17333 | 0.586665 | − | 0.809830i | \(-0.300441\pi\) | ||||
0.586665 | + | 0.809830i | \(0.300441\pi\) | |||||||
\(4\) | 5.04782 | 2.52391 | ||||||||
\(5\) | −0.522833 | −0.233818 | −0.116909 | − | 0.993143i | \(-0.537299\pi\) | ||||
−0.116909 | + | 0.993143i | \(0.537299\pi\) | |||||||
\(6\) | −5.39521 | −2.20258 | ||||||||
\(7\) | 4.81464 | 1.81976 | 0.909882 | − | 0.414867i | \(-0.136172\pi\) | ||||
0.909882 | + | 0.414867i | \(0.136172\pi\) | |||||||
\(8\) | −8.09128 | −2.86070 | ||||||||
\(9\) | 1.13010 | 0.376701 | ||||||||
\(10\) | 1.38800 | 0.438925 | ||||||||
\(11\) | 3.60821 | 1.08792 | 0.543958 | − | 0.839112i | \(-0.316925\pi\) | ||||
0.543958 | + | 0.839112i | \(0.316925\pi\) | |||||||
\(12\) | 10.2585 | 2.96138 | ||||||||
\(13\) | 4.41348 | 1.22408 | 0.612039 | − | 0.790828i | \(-0.290350\pi\) | ||||
0.612039 | + | 0.790828i | \(0.290350\pi\) | |||||||
\(14\) | −12.7818 | −3.41608 | ||||||||
\(15\) | −1.06253 | −0.274345 | ||||||||
\(16\) | 11.3849 | 2.84622 | ||||||||
\(17\) | −2.41333 | −0.585318 | −0.292659 | − | 0.956217i | \(-0.594540\pi\) | ||||
−0.292659 | + | 0.956217i | \(0.594540\pi\) | |||||||
\(18\) | −3.00017 | −0.707147 | ||||||||
\(19\) | 2.25640 | 0.517654 | 0.258827 | − | 0.965924i | \(-0.416664\pi\) | ||||
0.258827 | + | 0.965924i | \(0.416664\pi\) | |||||||
\(20\) | −2.63917 | −0.590135 | ||||||||
\(21\) | 9.78463 | 2.13518 | ||||||||
\(22\) | −9.57898 | −2.04225 | ||||||||
\(23\) | −1.20092 | −0.250410 | −0.125205 | − | 0.992131i | \(-0.539959\pi\) | ||||
−0.125205 | + | 0.992131i | \(0.539959\pi\) | |||||||
\(24\) | −16.4436 | −3.35654 | ||||||||
\(25\) | −4.72665 | −0.945329 | ||||||||
\(26\) | −11.7168 | −2.29785 | ||||||||
\(27\) | −3.80012 | −0.731334 | ||||||||
\(28\) | 24.3035 | 4.59292 | ||||||||
\(29\) | −1.24365 | −0.230940 | −0.115470 | − | 0.993311i | \(-0.536837\pi\) | ||||
−0.115470 | + | 0.993311i | \(0.536837\pi\) | |||||||
\(30\) | 2.82079 | 0.515003 | ||||||||
\(31\) | −1.42425 | −0.255803 | −0.127901 | − | 0.991787i | \(-0.540824\pi\) | ||||
−0.127901 | + | 0.991787i | \(0.540824\pi\) | |||||||
\(32\) | −14.0417 | −2.48224 | ||||||||
\(33\) | 7.33285 | 1.27648 | ||||||||
\(34\) | 6.40683 | 1.09876 | ||||||||
\(35\) | −2.51725 | −0.425493 | ||||||||
\(36\) | 5.70457 | 0.950761 | ||||||||
\(37\) | −8.07978 | −1.32831 | −0.664154 | − | 0.747596i | \(-0.731208\pi\) | ||||
−0.664154 | + | 0.747596i | \(0.731208\pi\) | |||||||
\(38\) | −5.99023 | −0.971744 | ||||||||
\(39\) | 8.96936 | 1.43625 | ||||||||
\(40\) | 4.23038 | 0.668882 | ||||||||
\(41\) | −1.38721 | −0.216645 | −0.108323 | − | 0.994116i | \(-0.534548\pi\) | ||||
−0.108323 | + | 0.994116i | \(0.534548\pi\) | |||||||
\(42\) | −25.9760 | −4.00818 | ||||||||
\(43\) | 6.93078 | 1.05693 | 0.528467 | − | 0.848954i | \(-0.322767\pi\) | ||||
0.528467 | + | 0.848954i | \(0.322767\pi\) | |||||||
\(44\) | 18.2136 | 2.74581 | ||||||||
\(45\) | −0.590855 | −0.0880795 | ||||||||
\(46\) | 3.18818 | 0.470071 | ||||||||
\(47\) | −3.62546 | −0.528827 | −0.264414 | − | 0.964409i | \(-0.585178\pi\) | ||||
−0.264414 | + | 0.964409i | \(0.585178\pi\) | |||||||
\(48\) | 23.1371 | 3.33955 | ||||||||
\(49\) | 16.1808 | 2.31154 | ||||||||
\(50\) | 12.5482 | 1.77458 | ||||||||
\(51\) | −4.90452 | −0.686770 | ||||||||
\(52\) | 22.2784 | 3.08946 | ||||||||
\(53\) | 9.49752 | 1.30458 | 0.652292 | − | 0.757967i | \(-0.273807\pi\) | ||||
0.652292 | + | 0.757967i | \(0.273807\pi\) | |||||||
\(54\) | 10.0885 | 1.37287 | ||||||||
\(55\) | −1.88649 | −0.254374 | ||||||||
\(56\) | −38.9566 | −5.20580 | ||||||||
\(57\) | 4.58561 | 0.607378 | ||||||||
\(58\) | 3.30161 | 0.433523 | ||||||||
\(59\) | 2.47468 | 0.322175 | 0.161088 | − | 0.986940i | \(-0.448500\pi\) | ||||
0.161088 | + | 0.986940i | \(0.448500\pi\) | |||||||
\(60\) | −5.36349 | −0.692423 | ||||||||
\(61\) | −0.360298 | −0.0461314 | −0.0230657 | − | 0.999734i | \(-0.507343\pi\) | ||||
−0.0230657 | + | 0.999734i | \(0.507343\pi\) | |||||||
\(62\) | 3.78106 | 0.480195 | ||||||||
\(63\) | 5.44105 | 0.685508 | ||||||||
\(64\) | 14.5078 | 1.81347 | ||||||||
\(65\) | −2.30751 | −0.286211 | ||||||||
\(66\) | −19.4670 | −2.39623 | ||||||||
\(67\) | 4.70398 | 0.574682 | 0.287341 | − | 0.957828i | \(-0.407229\pi\) | ||||
0.287341 | + | 0.957828i | \(0.407229\pi\) | |||||||
\(68\) | −12.1820 | −1.47729 | ||||||||
\(69\) | −2.44060 | −0.293813 | ||||||||
\(70\) | 6.68273 | 0.798739 | ||||||||
\(71\) | −5.24469 | −0.622430 | −0.311215 | − | 0.950339i | \(-0.600736\pi\) | ||||
−0.311215 | + | 0.950339i | \(0.600736\pi\) | |||||||
\(72\) | −9.14399 | −1.07763 | ||||||||
\(73\) | 10.8620 | 1.27130 | 0.635651 | − | 0.771976i | \(-0.280732\pi\) | ||||
0.635651 | + | 0.771976i | \(0.280732\pi\) | |||||||
\(74\) | 21.4500 | 2.49351 | ||||||||
\(75\) | −9.60580 | −1.10918 | ||||||||
\(76\) | 11.3899 | 1.30651 | ||||||||
\(77\) | 17.3722 | 1.97975 | ||||||||
\(78\) | −23.8116 | −2.69613 | ||||||||
\(79\) | 14.8876 | 1.67499 | 0.837495 | − | 0.546446i | \(-0.184019\pi\) | ||||
0.837495 | + | 0.546446i | \(0.184019\pi\) | |||||||
\(80\) | −5.95238 | −0.665496 | ||||||||
\(81\) | −11.1132 | −1.23480 | ||||||||
\(82\) | 3.68272 | 0.406688 | ||||||||
\(83\) | 10.4213 | 1.14389 | 0.571945 | − | 0.820292i | \(-0.306189\pi\) | ||||
0.571945 | + | 0.820292i | \(0.306189\pi\) | |||||||
\(84\) | 49.3911 | 5.38901 | ||||||||
\(85\) | 1.26177 | 0.136858 | ||||||||
\(86\) | −18.3996 | −1.98408 | ||||||||
\(87\) | −2.52743 | −0.270969 | ||||||||
\(88\) | −29.1950 | −3.11220 | ||||||||
\(89\) | 11.1368 | 1.18049 | 0.590247 | − | 0.807223i | \(-0.299030\pi\) | ||||
0.590247 | + | 0.807223i | \(0.299030\pi\) | |||||||
\(90\) | 1.56859 | 0.165344 | ||||||||
\(91\) | 21.2493 | 2.22753 | ||||||||
\(92\) | −6.06205 | −0.632012 | ||||||||
\(93\) | −2.89445 | −0.300141 | ||||||||
\(94\) | 9.62477 | 0.992719 | ||||||||
\(95\) | −1.17972 | −0.121037 | ||||||||
\(96\) | −28.5364 | −2.91249 | ||||||||
\(97\) | −10.2611 | −1.04185 | −0.520927 | − | 0.853601i | \(-0.674414\pi\) | ||||
−0.520927 | + | 0.853601i | \(0.674414\pi\) | |||||||
\(98\) | −42.9563 | −4.33924 | ||||||||
\(99\) | 4.07766 | 0.409820 | ||||||||
\(100\) | −23.8593 | −2.38593 | ||||||||
\(101\) | −4.84754 | −0.482348 | −0.241174 | − | 0.970482i | \(-0.577532\pi\) | ||||
−0.241174 | + | 0.970482i | \(0.577532\pi\) | |||||||
\(102\) | 13.0204 | 1.28921 | ||||||||
\(103\) | 5.34844 | 0.526997 | 0.263499 | − | 0.964660i | \(-0.415124\pi\) | ||||
0.263499 | + | 0.964660i | \(0.415124\pi\) | |||||||
\(104\) | −35.7107 | −3.50172 | ||||||||
\(105\) | −5.11572 | −0.499244 | ||||||||
\(106\) | −25.2138 | −2.44898 | ||||||||
\(107\) | −8.84373 | −0.854956 | −0.427478 | − | 0.904026i | \(-0.640598\pi\) | ||||
−0.427478 | + | 0.904026i | \(0.640598\pi\) | |||||||
\(108\) | −19.1824 | −1.84582 | ||||||||
\(109\) | −3.69398 | −0.353819 | −0.176909 | − | 0.984227i | \(-0.556610\pi\) | ||||
−0.176909 | + | 0.984227i | \(0.556610\pi\) | |||||||
\(110\) | 5.00821 | 0.477514 | ||||||||
\(111\) | −16.4203 | −1.55854 | ||||||||
\(112\) | 54.8140 | 5.17944 | ||||||||
\(113\) | 8.84350 | 0.831927 | 0.415963 | − | 0.909381i | \(-0.363444\pi\) | ||||
0.415963 | + | 0.909381i | \(0.363444\pi\) | |||||||
\(114\) | −12.1737 | −1.14018 | ||||||||
\(115\) | 0.627882 | 0.0585503 | ||||||||
\(116\) | −6.27773 | −0.582873 | ||||||||
\(117\) | 4.98769 | 0.461112 | ||||||||
\(118\) | −6.56970 | −0.604790 | ||||||||
\(119\) | −11.6193 | −1.06514 | ||||||||
\(120\) | 8.59726 | 0.784819 | ||||||||
\(121\) | 2.01919 | 0.183563 | ||||||||
\(122\) | 0.956509 | 0.0865983 | ||||||||
\(123\) | −2.81917 | −0.254196 | ||||||||
\(124\) | −7.18936 | −0.645624 | ||||||||
\(125\) | 5.08541 | 0.454853 | ||||||||
\(126\) | −14.4448 | −1.28684 | ||||||||
\(127\) | 14.6220 | 1.29749 | 0.648745 | − | 0.761006i | \(-0.275294\pi\) | ||||
0.648745 | + | 0.761006i | \(0.275294\pi\) | |||||||
\(128\) | −10.4314 | −0.922017 | ||||||||
\(129\) | 14.0852 | 1.24013 | ||||||||
\(130\) | 6.12591 | 0.537278 | ||||||||
\(131\) | 3.34402 | 0.292168 | 0.146084 | − | 0.989272i | \(-0.453333\pi\) | ||||
0.146084 | + | 0.989272i | \(0.453333\pi\) | |||||||
\(132\) | 37.0149 | 3.22173 | ||||||||
\(133\) | 10.8638 | 0.942008 | ||||||||
\(134\) | −12.4880 | −1.07880 | ||||||||
\(135\) | 1.98683 | 0.170999 | ||||||||
\(136\) | 19.5269 | 1.67442 | ||||||||
\(137\) | 13.0448 | 1.11449 | 0.557247 | − | 0.830347i | \(-0.311858\pi\) | ||||
0.557247 | + | 0.830347i | \(0.311858\pi\) | |||||||
\(138\) | 6.47923 | 0.551548 | ||||||||
\(139\) | 21.5263 | 1.82583 | 0.912917 | − | 0.408144i | \(-0.133824\pi\) | ||||
0.912917 | + | 0.408144i | \(0.133824\pi\) | |||||||
\(140\) | −12.7066 | −1.07391 | ||||||||
\(141\) | −7.36789 | −0.620489 | ||||||||
\(142\) | 13.9235 | 1.16843 | ||||||||
\(143\) | 15.9248 | 1.33169 | ||||||||
\(144\) | 12.8661 | 1.07217 | ||||||||
\(145\) | 0.650221 | 0.0539980 | ||||||||
\(146\) | −28.8362 | −2.38650 | ||||||||
\(147\) | 32.8836 | 2.71220 | ||||||||
\(148\) | −40.7853 | −3.35253 | ||||||||
\(149\) | −12.2235 | −1.00139 | −0.500694 | − | 0.865624i | \(-0.666922\pi\) | ||||
−0.500694 | + | 0.865624i | \(0.666922\pi\) | |||||||
\(150\) | 25.5012 | 2.08217 | ||||||||
\(151\) | 2.05134 | 0.166935 | 0.0834676 | − | 0.996510i | \(-0.473400\pi\) | ||||
0.0834676 | + | 0.996510i | \(0.473400\pi\) | |||||||
\(152\) | −18.2572 | −1.48085 | ||||||||
\(153\) | −2.72731 | −0.220490 | ||||||||
\(154\) | −46.1194 | −3.71641 | ||||||||
\(155\) | 0.744644 | 0.0598113 | ||||||||
\(156\) | 45.2757 | 3.62496 | ||||||||
\(157\) | 1.72793 | 0.137904 | 0.0689520 | − | 0.997620i | \(-0.478034\pi\) | ||||
0.0689520 | + | 0.997620i | \(0.478034\pi\) | |||||||
\(158\) | −39.5233 | −3.14430 | ||||||||
\(159\) | 19.3015 | 1.53071 | ||||||||
\(160\) | 7.34145 | 0.580392 | ||||||||
\(161\) | −5.78202 | −0.455687 | ||||||||
\(162\) | 29.5030 | 2.31797 | ||||||||
\(163\) | −15.1929 | −1.19000 | −0.594999 | − | 0.803727i | \(-0.702847\pi\) | ||||
−0.594999 | + | 0.803727i | \(0.702847\pi\) | |||||||
\(164\) | −7.00237 | −0.546793 | ||||||||
\(165\) | −3.83385 | −0.298465 | ||||||||
\(166\) | −27.6663 | −2.14732 | ||||||||
\(167\) | −19.1259 | −1.48001 | −0.740004 | − | 0.672603i | \(-0.765176\pi\) | ||||
−0.740004 | + | 0.672603i | \(0.765176\pi\) | |||||||
\(168\) | −79.1702 | −6.10811 | ||||||||
\(169\) | 6.47877 | 0.498367 | ||||||||
\(170\) | −3.34970 | −0.256910 | ||||||||
\(171\) | 2.54997 | 0.195001 | ||||||||
\(172\) | 34.9853 | 2.66761 | ||||||||
\(173\) | 18.1718 | 1.38158 | 0.690789 | − | 0.723056i | \(-0.257263\pi\) | ||||
0.690789 | + | 0.723056i | \(0.257263\pi\) | |||||||
\(174\) | 6.70975 | 0.508665 | ||||||||
\(175\) | −22.7571 | −1.72028 | ||||||||
\(176\) | 41.0790 | 3.09645 | ||||||||
\(177\) | 5.02920 | 0.378018 | ||||||||
\(178\) | −29.5656 | −2.21603 | ||||||||
\(179\) | −16.0253 | −1.19778 | −0.598892 | − | 0.800829i | \(-0.704392\pi\) | ||||
−0.598892 | + | 0.800829i | \(0.704392\pi\) | |||||||
\(180\) | −2.98253 | −0.222305 | ||||||||
\(181\) | 12.5306 | 0.931391 | 0.465695 | − | 0.884945i | \(-0.345804\pi\) | ||||
0.465695 | + | 0.884945i | \(0.345804\pi\) | |||||||
\(182\) | −56.4121 | −4.18154 | ||||||||
\(183\) | −0.732221 | −0.0541274 | ||||||||
\(184\) | 9.71700 | 0.716347 | ||||||||
\(185\) | 4.22437 | 0.310582 | ||||||||
\(186\) | 7.68412 | 0.563427 | ||||||||
\(187\) | −8.70779 | −0.636777 | ||||||||
\(188\) | −18.3007 | −1.33471 | ||||||||
\(189\) | −18.2962 | −1.33086 | ||||||||
\(190\) | 3.13189 | 0.227211 | ||||||||
\(191\) | −5.05883 | −0.366044 | −0.183022 | − | 0.983109i | \(-0.558588\pi\) | ||||
−0.183022 | + | 0.983109i | \(0.558588\pi\) | |||||||
\(192\) | 29.4836 | 2.12780 | ||||||||
\(193\) | −9.52018 | −0.685278 | −0.342639 | − | 0.939467i | \(-0.611321\pi\) | ||||
−0.342639 | + | 0.939467i | \(0.611321\pi\) | |||||||
\(194\) | 27.2408 | 1.95578 | ||||||||
\(195\) | −4.68947 | −0.335820 | ||||||||
\(196\) | 81.6777 | 5.83412 | ||||||||
\(197\) | 11.7235 | 0.835264 | 0.417632 | − | 0.908616i | \(-0.362860\pi\) | ||||
0.417632 | + | 0.908616i | \(0.362860\pi\) | |||||||
\(198\) | −10.8253 | −0.769317 | ||||||||
\(199\) | 1.94989 | 0.138224 | 0.0691119 | − | 0.997609i | \(-0.477983\pi\) | ||||
0.0691119 | + | 0.997609i | \(0.477983\pi\) | |||||||
\(200\) | 38.2446 | 2.70430 | ||||||||
\(201\) | 9.55973 | 0.674292 | ||||||||
\(202\) | 12.8691 | 0.905467 | ||||||||
\(203\) | −5.98774 | −0.420257 | ||||||||
\(204\) | −24.7571 | −1.73335 | ||||||||
\(205\) | 0.725277 | 0.0506555 | ||||||||
\(206\) | −14.1989 | −0.989284 | ||||||||
\(207\) | −1.35717 | −0.0943297 | ||||||||
\(208\) | 50.2468 | 3.48399 | ||||||||
\(209\) | 8.14157 | 0.563164 | ||||||||
\(210\) | 13.5811 | 0.937184 | ||||||||
\(211\) | 11.4882 | 0.790883 | 0.395442 | − | 0.918491i | \(-0.370592\pi\) | ||||
0.395442 | + | 0.918491i | \(0.370592\pi\) | |||||||
\(212\) | 47.9418 | 3.29266 | ||||||||
\(213\) | −10.6586 | −0.730316 | ||||||||
\(214\) | 23.4781 | 1.60493 | ||||||||
\(215\) | −3.62364 | −0.247130 | ||||||||
\(216\) | 30.7479 | 2.09213 | ||||||||
\(217\) | −6.85725 | −0.465501 | ||||||||
\(218\) | 9.80667 | 0.664192 | ||||||||
\(219\) | 22.0745 | 1.49166 | ||||||||
\(220\) | −9.52267 | −0.642018 | ||||||||
\(221\) | −10.6512 | −0.716474 | ||||||||
\(222\) | 43.5921 | 2.92571 | ||||||||
\(223\) | 15.6030 | 1.04486 | 0.522428 | − | 0.852684i | \(-0.325027\pi\) | ||||
0.522428 | + | 0.852684i | \(0.325027\pi\) | |||||||
\(224\) | −67.6057 | −4.51709 | ||||||||
\(225\) | −5.34160 | −0.356107 | ||||||||
\(226\) | −23.4775 | −1.56170 | ||||||||
\(227\) | 6.56721 | 0.435881 | 0.217940 | − | 0.975962i | \(-0.430066\pi\) | ||||
0.217940 | + | 0.975962i | \(0.430066\pi\) | |||||||
\(228\) | 23.1473 | 1.53297 | ||||||||
\(229\) | 1.86678 | 0.123360 | 0.0616802 | − | 0.998096i | \(-0.480354\pi\) | ||||
0.0616802 | + | 0.998096i | \(0.480354\pi\) | |||||||
\(230\) | −1.66688 | −0.109911 | ||||||||
\(231\) | 35.3050 | 2.32290 | ||||||||
\(232\) | 10.0627 | 0.660650 | ||||||||
\(233\) | −21.8503 | −1.43146 | −0.715732 | − | 0.698375i | \(-0.753907\pi\) | ||||
−0.715732 | + | 0.698375i | \(0.753907\pi\) | |||||||
\(234\) | −13.2412 | −0.865603 | ||||||||
\(235\) | 1.89551 | 0.123649 | ||||||||
\(236\) | 12.4917 | 0.813142 | ||||||||
\(237\) | 30.2556 | 1.96531 | ||||||||
\(238\) | 30.8466 | 1.99949 | ||||||||
\(239\) | 13.4085 | 0.867321 | 0.433661 | − | 0.901076i | \(-0.357222\pi\) | ||||
0.433661 | + | 0.901076i | \(0.357222\pi\) | |||||||
\(240\) | −12.0968 | −0.780846 | ||||||||
\(241\) | 5.48297 | 0.353189 | 0.176595 | − | 0.984284i | \(-0.443492\pi\) | ||||
0.176595 | + | 0.984284i | \(0.443492\pi\) | |||||||
\(242\) | −5.36050 | −0.344586 | ||||||||
\(243\) | −11.1846 | −0.717490 | ||||||||
\(244\) | −1.81872 | −0.116432 | ||||||||
\(245\) | −8.45984 | −0.540479 | ||||||||
\(246\) | 7.48426 | 0.477179 | ||||||||
\(247\) | 9.95857 | 0.633649 | ||||||||
\(248\) | 11.5240 | 0.731775 | ||||||||
\(249\) | 21.1789 | 1.34216 | ||||||||
\(250\) | −13.5006 | −0.853853 | ||||||||
\(251\) | 4.52226 | 0.285443 | 0.142721 | − | 0.989763i | \(-0.454415\pi\) | ||||
0.142721 | + | 0.989763i | \(0.454415\pi\) | |||||||
\(252\) | 27.4654 | 1.73016 | ||||||||
\(253\) | −4.33318 | −0.272425 | ||||||||
\(254\) | −38.8180 | −2.43566 | ||||||||
\(255\) | 2.56424 | 0.160579 | ||||||||
\(256\) | −1.32241 | −0.0826507 | ||||||||
\(257\) | 14.3919 | 0.897742 | 0.448871 | − | 0.893597i | \(-0.351826\pi\) | ||||
0.448871 | + | 0.893597i | \(0.351826\pi\) | |||||||
\(258\) | −37.3930 | −2.32798 | ||||||||
\(259\) | −38.9012 | −2.41721 | ||||||||
\(260\) | −11.6479 | −0.722372 | ||||||||
\(261\) | −1.40546 | −0.0869955 | ||||||||
\(262\) | −8.87761 | −0.548461 | ||||||||
\(263\) | −2.92231 | −0.180197 | −0.0900987 | − | 0.995933i | \(-0.528718\pi\) | ||||
−0.0900987 | + | 0.995933i | \(0.528718\pi\) | |||||||
\(264\) | −59.3321 | −3.65164 | ||||||||
\(265\) | −4.96561 | −0.305035 | ||||||||
\(266\) | −28.8408 | −1.76834 | ||||||||
\(267\) | 22.6328 | 1.38511 | ||||||||
\(268\) | 23.7448 | 1.45045 | ||||||||
\(269\) | 14.6405 | 0.892645 | 0.446323 | − | 0.894872i | \(-0.352733\pi\) | ||||
0.446323 | + | 0.894872i | \(0.352733\pi\) | |||||||
\(270\) | −5.27458 | −0.321001 | ||||||||
\(271\) | 4.83669 | 0.293808 | 0.146904 | − | 0.989151i | \(-0.453069\pi\) | ||||
0.146904 | + | 0.989151i | \(0.453069\pi\) | |||||||
\(272\) | −27.4754 | −1.66594 | ||||||||
\(273\) | 43.1842 | 2.61363 | ||||||||
\(274\) | −34.6310 | −2.09214 | ||||||||
\(275\) | −17.0547 | −1.02844 | ||||||||
\(276\) | −12.3197 | −0.741558 | ||||||||
\(277\) | −25.9166 | −1.55718 | −0.778590 | − | 0.627534i | \(-0.784065\pi\) | ||||
−0.778590 | + | 0.627534i | \(0.784065\pi\) | |||||||
\(278\) | −57.1474 | −3.42747 | ||||||||
\(279\) | −1.60955 | −0.0963613 | ||||||||
\(280\) | 20.3678 | 1.21721 | ||||||||
\(281\) | 21.7773 | 1.29912 | 0.649561 | − | 0.760309i | \(-0.274953\pi\) | ||||
0.649561 | + | 0.760309i | \(0.274953\pi\) | |||||||
\(282\) | 19.5601 | 1.16479 | ||||||||
\(283\) | 17.3429 | 1.03093 | 0.515464 | − | 0.856911i | \(-0.327620\pi\) | ||||
0.515464 | + | 0.856911i | \(0.327620\pi\) | |||||||
\(284\) | −26.4743 | −1.57096 | ||||||||
\(285\) | −2.39750 | −0.142016 | ||||||||
\(286\) | −42.2766 | −2.49987 | ||||||||
\(287\) | −6.67890 | −0.394243 | ||||||||
\(288\) | −15.8686 | −0.935064 | ||||||||
\(289\) | −11.1759 | −0.657403 | ||||||||
\(290\) | −1.72619 | −0.101365 | ||||||||
\(291\) | −20.8532 | −1.22244 | ||||||||
\(292\) | 54.8295 | 3.20865 | ||||||||
\(293\) | 1.49021 | 0.0870589 | 0.0435295 | − | 0.999052i | \(-0.486140\pi\) | ||||
0.0435295 | + | 0.999052i | \(0.486140\pi\) | |||||||
\(294\) | −87.2986 | −5.09136 | ||||||||
\(295\) | −1.29384 | −0.0753303 | ||||||||
\(296\) | 65.3757 | 3.79989 | ||||||||
\(297\) | −13.7117 | −0.795631 | ||||||||
\(298\) | 32.4506 | 1.87981 | ||||||||
\(299\) | −5.30025 | −0.306521 | ||||||||
\(300\) | −48.4884 | −2.79948 | ||||||||
\(301\) | 33.3692 | 1.92337 | ||||||||
\(302\) | −5.44583 | −0.313372 | ||||||||
\(303\) | −9.85148 | −0.565953 | ||||||||
\(304\) | 25.6888 | 1.47335 | ||||||||
\(305\) | 0.188376 | 0.0107864 | ||||||||
\(306\) | 7.24039 | 0.413906 | ||||||||
\(307\) | 21.4206 | 1.22254 | 0.611270 | − | 0.791422i | \(-0.290659\pi\) | ||||
0.611270 | + | 0.791422i | \(0.290659\pi\) | |||||||
\(308\) | 87.6920 | 4.99672 | ||||||||
\(309\) | 10.8694 | 0.618341 | ||||||||
\(310\) | −1.97686 | −0.112278 | ||||||||
\(311\) | −23.7181 | −1.34493 | −0.672466 | − | 0.740128i | \(-0.734765\pi\) | ||||
−0.672466 | + | 0.740128i | \(0.734765\pi\) | |||||||
\(312\) | −72.5735 | −4.10867 | ||||||||
\(313\) | −9.15550 | −0.517499 | −0.258750 | − | 0.965944i | \(-0.583310\pi\) | ||||
−0.258750 | + | 0.965944i | \(0.583310\pi\) | |||||||
\(314\) | −4.58727 | −0.258874 | ||||||||
\(315\) | −2.84476 | −0.160284 | ||||||||
\(316\) | 75.1501 | 4.22752 | ||||||||
\(317\) | −23.6848 | −1.33027 | −0.665137 | − | 0.746721i | \(-0.731627\pi\) | ||||
−0.665137 | + | 0.746721i | \(0.731627\pi\) | |||||||
\(318\) | −51.2411 | −2.87346 | ||||||||
\(319\) | −4.48736 | −0.251244 | ||||||||
\(320\) | −7.58512 | −0.424021 | ||||||||
\(321\) | −17.9728 | −1.00314 | ||||||||
\(322\) | 15.3499 | 0.855419 | ||||||||
\(323\) | −5.44543 | −0.302992 | ||||||||
\(324\) | −56.0973 | −3.11652 | ||||||||
\(325\) | −20.8609 | −1.15716 | ||||||||
\(326\) | 40.3336 | 2.23387 | ||||||||
\(327\) | −7.50714 | −0.415146 | ||||||||
\(328\) | 11.2243 | 0.619757 | ||||||||
\(329\) | −17.4553 | −0.962341 | ||||||||
\(330\) | 10.1780 | 0.560281 | ||||||||
\(331\) | −18.8800 | −1.03774 | −0.518868 | − | 0.854854i | \(-0.673647\pi\) | ||||
−0.518868 | + | 0.854854i | \(0.673647\pi\) | |||||||
\(332\) | 52.6051 | 2.88708 | ||||||||
\(333\) | −9.13099 | −0.500375 | ||||||||
\(334\) | 50.7749 | 2.77828 | ||||||||
\(335\) | −2.45939 | −0.134371 | ||||||||
\(336\) | 111.397 | 6.07719 | ||||||||
\(337\) | −32.3827 | −1.76400 | −0.881999 | − | 0.471251i | \(-0.843803\pi\) | ||||
−0.881999 | + | 0.471251i | \(0.843803\pi\) | |||||||
\(338\) | −17.1997 | −0.935538 | ||||||||
\(339\) | 17.9723 | 0.976124 | ||||||||
\(340\) | 6.36917 | 0.345417 | ||||||||
\(341\) | −5.13900 | −0.278292 | ||||||||
\(342\) | −6.76959 | −0.366057 | ||||||||
\(343\) | 44.2022 | 2.38669 | ||||||||
\(344\) | −56.0788 | −3.02357 | ||||||||
\(345\) | 1.27602 | 0.0686987 | ||||||||
\(346\) | −48.2421 | −2.59351 | ||||||||
\(347\) | 13.0596 | 0.701075 | 0.350537 | − | 0.936549i | \(-0.385999\pi\) | ||||
0.350537 | + | 0.936549i | \(0.385999\pi\) | |||||||
\(348\) | −12.7580 | −0.683902 | ||||||||
\(349\) | 6.31506 | 0.338037 | 0.169019 | − | 0.985613i | \(-0.445940\pi\) | ||||
0.169019 | + | 0.985613i | \(0.445940\pi\) | |||||||
\(350\) | 60.4150 | 3.22932 | ||||||||
\(351\) | −16.7718 | −0.895210 | ||||||||
\(352\) | −50.6654 | −2.70047 | ||||||||
\(353\) | −35.1580 | −1.87127 | −0.935637 | − | 0.352965i | \(-0.885174\pi\) | ||||
−0.935637 | + | 0.352965i | \(0.885174\pi\) | |||||||
\(354\) | −13.3514 | −0.709618 | ||||||||
\(355\) | 2.74210 | 0.145535 | ||||||||
\(356\) | 56.2163 | 2.97946 | ||||||||
\(357\) | −23.6135 | −1.24976 | ||||||||
\(358\) | 42.5435 | 2.24849 | ||||||||
\(359\) | −3.15282 | −0.166400 | −0.0831998 | − | 0.996533i | \(-0.526514\pi\) | ||||
−0.0831998 | + | 0.996533i | \(0.526514\pi\) | |||||||
\(360\) | 4.78077 | 0.251969 | ||||||||
\(361\) | −13.9087 | −0.732034 | ||||||||
\(362\) | −33.2659 | −1.74841 | ||||||||
\(363\) | 4.10353 | 0.215380 | ||||||||
\(364\) | 107.263 | 5.62209 | ||||||||
\(365\) | −5.67901 | −0.297253 | ||||||||
\(366\) | 1.94388 | 0.101608 | ||||||||
\(367\) | −4.52578 | −0.236244 | −0.118122 | − | 0.992999i | \(-0.537687\pi\) | ||||
−0.118122 | + | 0.992999i | \(0.537687\pi\) | |||||||
\(368\) | −13.6723 | −0.712720 | ||||||||
\(369\) | −1.56769 | −0.0816106 | ||||||||
\(370\) | −11.2147 | −0.583027 | ||||||||
\(371\) | 45.7272 | 2.37404 | ||||||||
\(372\) | −14.6107 | −0.757529 | ||||||||
\(373\) | −28.8487 | −1.49373 | −0.746866 | − | 0.664975i | \(-0.768442\pi\) | ||||
−0.746866 | + | 0.664975i | \(0.768442\pi\) | |||||||
\(374\) | 23.1172 | 1.19536 | ||||||||
\(375\) | 10.3349 | 0.533692 | ||||||||
\(376\) | 29.3346 | 1.51282 | ||||||||
\(377\) | −5.48883 | −0.282689 | ||||||||
\(378\) | 48.5724 | 2.49829 | ||||||||
\(379\) | −0.655969 | −0.0336949 | −0.0168474 | − | 0.999858i | \(-0.505363\pi\) | ||||
−0.0168474 | + | 0.999858i | \(0.505363\pi\) | |||||||
\(380\) | −5.95502 | −0.305486 | ||||||||
\(381\) | 29.7157 | 1.52238 | ||||||||
\(382\) | 13.4300 | 0.687141 | ||||||||
\(383\) | −13.9227 | −0.711415 | −0.355707 | − | 0.934597i | \(-0.615760\pi\) | ||||
−0.355707 | + | 0.934597i | \(0.615760\pi\) | |||||||
\(384\) | −21.1994 | −1.08183 | ||||||||
\(385\) | −9.08278 | −0.462901 | ||||||||
\(386\) | 25.2739 | 1.28641 | ||||||||
\(387\) | 7.83250 | 0.398148 | ||||||||
\(388\) | −51.7961 | −2.62955 | ||||||||
\(389\) | 12.2774 | 0.622491 | 0.311246 | − | 0.950330i | \(-0.399254\pi\) | ||||
0.311246 | + | 0.950330i | \(0.399254\pi\) | |||||||
\(390\) | 12.4495 | 0.630404 | ||||||||
\(391\) | 2.89822 | 0.146569 | ||||||||
\(392\) | −130.923 | −6.61262 | ||||||||
\(393\) | 6.79593 | 0.342810 | ||||||||
\(394\) | −31.1232 | −1.56796 | ||||||||
\(395\) | −7.78374 | −0.391642 | ||||||||
\(396\) | 20.5833 | 1.03435 | ||||||||
\(397\) | −22.7736 | −1.14297 | −0.571486 | − | 0.820612i | \(-0.693633\pi\) | ||||
−0.571486 | + | 0.820612i | \(0.693633\pi\) | |||||||
\(398\) | −5.17651 | −0.259475 | ||||||||
\(399\) | 22.0781 | 1.10529 | ||||||||
\(400\) | −53.8122 | −2.69061 | ||||||||
\(401\) | −38.3309 | −1.91416 | −0.957078 | − | 0.289830i | \(-0.906401\pi\) | ||||
−0.957078 | + | 0.289830i | \(0.906401\pi\) | |||||||
\(402\) | −25.3789 | −1.26579 | ||||||||
\(403\) | −6.28589 | −0.313123 | ||||||||
\(404\) | −24.4695 | −1.21740 | ||||||||
\(405\) | 5.81033 | 0.288718 | ||||||||
\(406\) | 15.8961 | 0.788909 | ||||||||
\(407\) | −29.1536 | −1.44509 | ||||||||
\(408\) | 39.6838 | 1.96464 | ||||||||
\(409\) | 4.26725 | 0.211002 | 0.105501 | − | 0.994419i | \(-0.466355\pi\) | ||||
0.105501 | + | 0.994419i | \(0.466355\pi\) | |||||||
\(410\) | −1.92545 | −0.0950910 | ||||||||
\(411\) | 26.5105 | 1.30767 | ||||||||
\(412\) | 26.9980 | 1.33009 | ||||||||
\(413\) | 11.9147 | 0.586283 | ||||||||
\(414\) | 3.60297 | 0.177077 | ||||||||
\(415\) | −5.44862 | −0.267462 | ||||||||
\(416\) | −61.9726 | −3.03846 | ||||||||
\(417\) | 43.7471 | 2.14231 | ||||||||
\(418\) | −21.6140 | −1.05718 | ||||||||
\(419\) | −4.44115 | −0.216965 | −0.108482 | − | 0.994098i | \(-0.534599\pi\) | ||||
−0.108482 | + | 0.994098i | \(0.534599\pi\) | |||||||
\(420\) | −25.8233 | −1.26005 | ||||||||
\(421\) | 9.01192 | 0.439214 | 0.219607 | − | 0.975588i | \(-0.429523\pi\) | ||||
0.219607 | + | 0.975588i | \(0.429523\pi\) | |||||||
\(422\) | −30.4987 | −1.48465 | ||||||||
\(423\) | −4.09715 | −0.199210 | ||||||||
\(424\) | −76.8471 | −3.73202 | ||||||||
\(425\) | 11.4069 | 0.553318 | ||||||||
\(426\) | 28.2962 | 1.37095 | ||||||||
\(427\) | −1.73471 | −0.0839483 | ||||||||
\(428\) | −44.6416 | −2.15783 | ||||||||
\(429\) | 32.3633 | 1.56252 | ||||||||
\(430\) | 9.61993 | 0.463914 | ||||||||
\(431\) | 5.67668 | 0.273436 | 0.136718 | − | 0.990610i | \(-0.456345\pi\) | ||||
0.136718 | + | 0.990610i | \(0.456345\pi\) | |||||||
\(432\) | −43.2639 | −2.08154 | ||||||||
\(433\) | −9.64897 | −0.463700 | −0.231850 | − | 0.972752i | \(-0.574478\pi\) | ||||
−0.231850 | + | 0.972752i | \(0.574478\pi\) | |||||||
\(434\) | 18.2045 | 0.873842 | ||||||||
\(435\) | 1.32142 | 0.0633574 | ||||||||
\(436\) | −18.6465 | −0.893007 | ||||||||
\(437\) | −2.70976 | −0.129626 | ||||||||
\(438\) | −58.6028 | −2.80015 | ||||||||
\(439\) | 8.83641 | 0.421739 | 0.210869 | − | 0.977514i | \(-0.432371\pi\) | ||||
0.210869 | + | 0.977514i | \(0.432371\pi\) | |||||||
\(440\) | 15.2641 | 0.727688 | ||||||||
\(441\) | 18.2860 | 0.870760 | ||||||||
\(442\) | 28.2764 | 1.34497 | ||||||||
\(443\) | 34.6655 | 1.64701 | 0.823504 | − | 0.567310i | \(-0.192016\pi\) | ||||
0.823504 | + | 0.567310i | \(0.192016\pi\) | |||||||
\(444\) | −82.8865 | −3.93362 | ||||||||
\(445\) | −5.82266 | −0.276020 | ||||||||
\(446\) | −41.4225 | −1.96141 | ||||||||
\(447\) | −24.8414 | −1.17496 | ||||||||
\(448\) | 69.8496 | 3.30008 | ||||||||
\(449\) | 11.9749 | 0.565130 | 0.282565 | − | 0.959248i | \(-0.408815\pi\) | ||||
0.282565 | + | 0.959248i | \(0.408815\pi\) | |||||||
\(450\) | 14.1807 | 0.668487 | ||||||||
\(451\) | −5.00533 | −0.235692 | ||||||||
\(452\) | 44.6404 | 2.09971 | ||||||||
\(453\) | 4.16886 | 0.195870 | ||||||||
\(454\) | −17.4344 | −0.818239 | ||||||||
\(455\) | −11.1098 | −0.520837 | ||||||||
\(456\) | −37.1034 | −1.73753 | ||||||||
\(457\) | −21.8291 | −1.02112 | −0.510560 | − | 0.859842i | \(-0.670562\pi\) | ||||
−0.510560 | + | 0.859842i | \(0.670562\pi\) | |||||||
\(458\) | −4.95588 | −0.231573 | ||||||||
\(459\) | 9.17094 | 0.428063 | ||||||||
\(460\) | 3.16944 | 0.147776 | ||||||||
\(461\) | 11.8226 | 0.550634 | 0.275317 | − | 0.961354i | \(-0.411217\pi\) | ||||
0.275317 | + | 0.961354i | \(0.411217\pi\) | |||||||
\(462\) | −93.7268 | −4.36057 | ||||||||
\(463\) | 9.71467 | 0.451479 | 0.225740 | − | 0.974188i | \(-0.427520\pi\) | ||||
0.225740 | + | 0.974188i | \(0.427520\pi\) | |||||||
\(464\) | −14.1588 | −0.657306 | ||||||||
\(465\) | 1.51332 | 0.0701783 | ||||||||
\(466\) | 58.0077 | 2.68715 | ||||||||
\(467\) | −17.4011 | −0.805228 | −0.402614 | − | 0.915370i | \(-0.631898\pi\) | ||||
−0.402614 | + | 0.915370i | \(0.631898\pi\) | |||||||
\(468\) | 25.1770 | 1.16381 | ||||||||
\(469\) | 22.6480 | 1.04579 | ||||||||
\(470\) | −5.03214 | −0.232115 | ||||||||
\(471\) | 3.51162 | 0.161807 | ||||||||
\(472\) | −20.0233 | −0.921647 | ||||||||
\(473\) | 25.0077 | 1.14986 | ||||||||
\(474\) | −80.3218 | −3.68930 | ||||||||
\(475\) | −10.6652 | −0.489353 | ||||||||
\(476\) | −58.6522 | −2.68832 | ||||||||
\(477\) | 10.7332 | 0.491439 | ||||||||
\(478\) | −35.5964 | −1.62814 | ||||||||
\(479\) | −24.6594 | −1.12672 | −0.563358 | − | 0.826213i | \(-0.690491\pi\) | ||||
−0.563358 | + | 0.826213i | \(0.690491\pi\) | |||||||
\(480\) | 14.9198 | 0.680991 | ||||||||
\(481\) | −35.6599 | −1.62595 | ||||||||
\(482\) | −14.5561 | −0.663010 | ||||||||
\(483\) | −11.7506 | −0.534670 | ||||||||
\(484\) | 10.1925 | 0.463296 | ||||||||
\(485\) | 5.36483 | 0.243604 | ||||||||
\(486\) | 29.6925 | 1.34688 | ||||||||
\(487\) | 16.7779 | 0.760280 | 0.380140 | − | 0.924929i | \(-0.375876\pi\) | ||||
0.380140 | + | 0.924929i | \(0.375876\pi\) | |||||||
\(488\) | 2.91527 | 0.131968 | ||||||||
\(489\) | −30.8759 | −1.39626 | ||||||||
\(490\) | 22.4590 | 1.01459 | ||||||||
\(491\) | 13.8578 | 0.625396 | 0.312698 | − | 0.949853i | \(-0.398767\pi\) | ||||
0.312698 | + | 0.949853i | \(0.398767\pi\) | |||||||
\(492\) | −14.2307 | −0.641569 | ||||||||
\(493\) | 3.00134 | 0.135173 | ||||||||
\(494\) | −26.4377 | −1.18949 | ||||||||
\(495\) | −2.13193 | −0.0958232 | ||||||||
\(496\) | −16.2149 | −0.728070 | ||||||||
\(497\) | −25.2513 | −1.13268 | ||||||||
\(498\) | −56.2253 | −2.51952 | ||||||||
\(499\) | −29.3963 | −1.31596 | −0.657979 | − | 0.753036i | \(-0.728589\pi\) | ||||
−0.657979 | + | 0.753036i | \(0.728589\pi\) | |||||||
\(500\) | 25.6702 | 1.14801 | ||||||||
\(501\) | −38.8689 | −1.73654 | ||||||||
\(502\) | −12.0056 | −0.535835 | ||||||||
\(503\) | 2.86864 | 0.127906 | 0.0639532 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639532 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(504\) | −44.0250 | −1.96103 | ||||||||
\(505\) | 2.53445 | 0.112782 | ||||||||
\(506\) | 11.5036 | 0.511398 | ||||||||
\(507\) | 13.1666 | 0.584748 | ||||||||
\(508\) | 73.8091 | 3.27475 | ||||||||
\(509\) | −5.52853 | −0.245048 | −0.122524 | − | 0.992466i | \(-0.539099\pi\) | ||||
−0.122524 | + | 0.992466i | \(0.539099\pi\) | |||||||
\(510\) | −6.80748 | −0.301440 | ||||||||
\(511\) | 52.2967 | 2.31347 | ||||||||
\(512\) | 24.3736 | 1.07717 | ||||||||
\(513\) | −8.57461 | −0.378578 | ||||||||
\(514\) | −38.2072 | −1.68525 | ||||||||
\(515\) | −2.79634 | −0.123221 | ||||||||
\(516\) | 71.0995 | 3.12998 | ||||||||
\(517\) | −13.0814 | −0.575320 | ||||||||
\(518\) | 103.274 | 4.53760 | ||||||||
\(519\) | 36.9300 | 1.62105 | ||||||||
\(520\) | 18.6707 | 0.818764 | ||||||||
\(521\) | 32.4592 | 1.42206 | 0.711031 | − | 0.703161i | \(-0.248229\pi\) | ||||
0.711031 | + | 0.703161i | \(0.248229\pi\) | |||||||
\(522\) | 3.73117 | 0.163309 | ||||||||
\(523\) | −39.8265 | −1.74149 | −0.870745 | − | 0.491735i | \(-0.836363\pi\) | ||||
−0.870745 | + | 0.491735i | \(0.836363\pi\) | |||||||
\(524\) | 16.8800 | 0.737407 | ||||||||
\(525\) | −46.2485 | −2.01845 | ||||||||
\(526\) | 7.75807 | 0.338268 | ||||||||
\(527\) | 3.43718 | 0.149726 | ||||||||
\(528\) | 83.4834 | 3.63315 | ||||||||
\(529\) | −21.5578 | −0.937295 | ||||||||
\(530\) | 13.1826 | 0.572615 | ||||||||
\(531\) | 2.79664 | 0.121364 | ||||||||
\(532\) | 54.8383 | 2.37754 | ||||||||
\(533\) | −6.12240 | −0.265191 | ||||||||
\(534\) | −60.0851 | −2.60014 | ||||||||
\(535\) | 4.62379 | 0.199904 | ||||||||
\(536\) | −38.0612 | −1.64399 | ||||||||
\(537\) | −32.5676 | −1.40540 | ||||||||
\(538\) | −38.8671 | −1.67568 | ||||||||
\(539\) | 58.3837 | 2.51476 | ||||||||
\(540\) | 10.0292 | 0.431586 | ||||||||
\(541\) | −12.9623 | −0.557294 | −0.278647 | − | 0.960394i | \(-0.589886\pi\) | ||||
−0.278647 | + | 0.960394i | \(0.589886\pi\) | |||||||
\(542\) | −12.8403 | −0.551539 | ||||||||
\(543\) | 25.4655 | 1.09283 | ||||||||
\(544\) | 33.8872 | 1.45290 | ||||||||
\(545\) | 1.93133 | 0.0827292 | ||||||||
\(546\) | −114.644 | −4.90633 | ||||||||
\(547\) | 7.27574 | 0.311088 | 0.155544 | − | 0.987829i | \(-0.450287\pi\) | ||||
0.155544 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(548\) | 65.8479 | 2.81288 | ||||||||
\(549\) | −0.407174 | −0.0173778 | ||||||||
\(550\) | 45.2765 | 1.93060 | ||||||||
\(551\) | −2.80618 | −0.119547 | ||||||||
\(552\) | 19.7475 | 0.840511 | ||||||||
\(553\) | 71.6786 | 3.04808 | ||||||||
\(554\) | 68.8028 | 2.92315 | ||||||||
\(555\) | 8.58505 | 0.364415 | ||||||||
\(556\) | 108.661 | 4.60825 | ||||||||
\(557\) | 9.87120 | 0.418256 | 0.209128 | − | 0.977888i | \(-0.432937\pi\) | ||||
0.209128 | + | 0.977888i | \(0.432937\pi\) | |||||||
\(558\) | 4.27299 | 0.180890 | ||||||||
\(559\) | 30.5888 | 1.29377 | ||||||||
\(560\) | −28.6586 | −1.21105 | ||||||||
\(561\) | −17.6965 | −0.747149 | ||||||||
\(562\) | −57.8137 | −2.43872 | ||||||||
\(563\) | 22.7966 | 0.960763 | 0.480382 | − | 0.877060i | \(-0.340498\pi\) | ||||
0.480382 | + | 0.877060i | \(0.340498\pi\) | |||||||
\(564\) | −37.1918 | −1.56606 | ||||||||
\(565\) | −4.62367 | −0.194519 | ||||||||
\(566\) | −46.0415 | −1.93527 | ||||||||
\(567\) | −53.5060 | −2.24704 | ||||||||
\(568\) | 42.4363 | 1.78059 | ||||||||
\(569\) | −36.3099 | −1.52219 | −0.761094 | − | 0.648641i | \(-0.775338\pi\) | ||||
−0.761094 | + | 0.648641i | \(0.775338\pi\) | |||||||
\(570\) | 6.36483 | 0.266593 | ||||||||
\(571\) | −43.1428 | −1.80547 | −0.902734 | − | 0.430198i | \(-0.858444\pi\) | ||||
−0.902734 | + | 0.430198i | \(0.858444\pi\) | |||||||
\(572\) | 80.3853 | 3.36108 | ||||||||
\(573\) | −10.2809 | −0.429490 | ||||||||
\(574\) | 17.7310 | 0.740076 | ||||||||
\(575\) | 5.67634 | 0.236720 | ||||||||
\(576\) | 16.3953 | 0.683136 | ||||||||
\(577\) | 35.5300 | 1.47913 | 0.739567 | − | 0.673083i | \(-0.235030\pi\) | ||||
0.739567 | + | 0.673083i | \(0.235030\pi\) | |||||||
\(578\) | 29.6694 | 1.23408 | ||||||||
\(579\) | −19.3475 | −0.804057 | ||||||||
\(580\) | 3.28220 | 0.136286 | ||||||||
\(581\) | 50.1750 | 2.08161 | ||||||||
\(582\) | 55.3606 | 2.29477 | ||||||||
\(583\) | 34.2691 | 1.41928 | ||||||||
\(584\) | −87.8876 | −3.63681 | ||||||||
\(585\) | −2.60773 | −0.107816 | ||||||||
\(586\) | −3.95617 | −0.163428 | ||||||||
\(587\) | −1.37204 | −0.0566300 | −0.0283150 | − | 0.999599i | \(-0.509014\pi\) | ||||
−0.0283150 | + | 0.999599i | \(0.509014\pi\) | |||||||
\(588\) | 165.991 | 6.84534 | ||||||||
\(589\) | −3.21368 | −0.132417 | ||||||||
\(590\) | 3.43486 | 0.141411 | ||||||||
\(591\) | 23.8252 | 0.980039 | ||||||||
\(592\) | −91.9872 | −3.78065 | ||||||||
\(593\) | 9.07464 | 0.372651 | 0.186326 | − | 0.982488i | \(-0.440342\pi\) | ||||
0.186326 | + | 0.982488i | \(0.440342\pi\) | |||||||
\(594\) | 36.4013 | 1.49357 | ||||||||
\(595\) | 6.07495 | 0.249049 | ||||||||
\(596\) | −61.7021 | −2.52741 | ||||||||
\(597\) | 3.96269 | 0.162182 | ||||||||
\(598\) | 14.0710 | 0.575404 | ||||||||
\(599\) | 13.8286 | 0.565022 | 0.282511 | − | 0.959264i | \(-0.408833\pi\) | ||||
0.282511 | + | 0.959264i | \(0.408833\pi\) | |||||||
\(600\) | 77.7232 | 3.17304 | ||||||||
\(601\) | −21.5366 | −0.878498 | −0.439249 | − | 0.898365i | \(-0.644755\pi\) | ||||
−0.439249 | + | 0.898365i | \(0.644755\pi\) | |||||||
\(602\) | −88.5877 | −3.61056 | ||||||||
\(603\) | 5.31599 | 0.216484 | ||||||||
\(604\) | 10.3548 | 0.421330 | ||||||||
\(605\) | −1.05570 | −0.0429203 | ||||||||
\(606\) | 26.1535 | 1.06241 | ||||||||
\(607\) | −12.7145 | −0.516066 | −0.258033 | − | 0.966136i | \(-0.583074\pi\) | ||||
−0.258033 | + | 0.966136i | \(0.583074\pi\) | |||||||
\(608\) | −31.6837 | −1.28494 | ||||||||
\(609\) | −12.1687 | −0.493099 | ||||||||
\(610\) | −0.500094 | −0.0202482 | ||||||||
\(611\) | −16.0009 | −0.647326 | ||||||||
\(612\) | −13.7670 | −0.556497 | ||||||||
\(613\) | −20.2443 | −0.817659 | −0.408830 | − | 0.912611i | \(-0.634063\pi\) | ||||
−0.408830 | + | 0.912611i | \(0.634063\pi\) | |||||||
\(614\) | −56.8670 | −2.29496 | ||||||||
\(615\) | 1.47395 | 0.0594356 | ||||||||
\(616\) | −140.564 | −5.66347 | ||||||||
\(617\) | −27.4499 | −1.10509 | −0.552546 | − | 0.833482i | \(-0.686344\pi\) | ||||
−0.552546 | + | 0.833482i | \(0.686344\pi\) | |||||||
\(618\) | −28.8559 | −1.16076 | ||||||||
\(619\) | 26.1234 | 1.04999 | 0.524995 | − | 0.851105i | \(-0.324067\pi\) | ||||
0.524995 | + | 0.851105i | \(0.324067\pi\) | |||||||
\(620\) | 3.75883 | 0.150958 | ||||||||
\(621\) | 4.56366 | 0.183133 | ||||||||
\(622\) | 62.9663 | 2.52472 | ||||||||
\(623\) | 53.6195 | 2.14822 | ||||||||
\(624\) | 102.115 | 4.08787 | ||||||||
\(625\) | 20.9744 | 0.838977 | ||||||||
\(626\) | 24.3058 | 0.971454 | ||||||||
\(627\) | 16.5458 | 0.660777 | ||||||||
\(628\) | 8.72229 | 0.348057 | ||||||||
\(629\) | 19.4991 | 0.777482 | ||||||||
\(630\) | 7.55219 | 0.300886 | ||||||||
\(631\) | 27.9930 | 1.11438 | 0.557192 | − | 0.830384i | \(-0.311879\pi\) | ||||
0.557192 | + | 0.830384i | \(0.311879\pi\) | |||||||
\(632\) | −120.460 | −4.79164 | ||||||||
\(633\) | 23.3472 | 0.927966 | ||||||||
\(634\) | 62.8779 | 2.49720 | ||||||||
\(635\) | −7.64484 | −0.303376 | ||||||||
\(636\) | 97.4305 | 3.86337 | ||||||||
\(637\) | 71.4135 | 2.82951 | ||||||||
\(638\) | 11.9129 | 0.471637 | ||||||||
\(639\) | −5.92705 | −0.234470 | ||||||||
\(640\) | 5.45389 | 0.215584 | ||||||||
\(641\) | −24.8962 | −0.983342 | −0.491671 | − | 0.870781i | \(-0.663614\pi\) | ||||
−0.491671 | + | 0.870781i | \(0.663614\pi\) | |||||||
\(642\) | 47.7138 | 1.88311 | ||||||||
\(643\) | 7.39794 | 0.291746 | 0.145873 | − | 0.989303i | \(-0.453401\pi\) | ||||
0.145873 | + | 0.989303i | \(0.453401\pi\) | |||||||
\(644\) | −29.1866 | −1.15011 | ||||||||
\(645\) | −7.36419 | −0.289965 | ||||||||
\(646\) | 14.4564 | 0.568779 | ||||||||
\(647\) | −44.9537 | −1.76731 | −0.883657 | − | 0.468136i | \(-0.844926\pi\) | ||||
−0.883657 | + | 0.468136i | \(0.844926\pi\) | |||||||
\(648\) | 89.9198 | 3.53238 | ||||||||
\(649\) | 8.92916 | 0.350500 | ||||||||
\(650\) | 55.3811 | 2.17222 | ||||||||
\(651\) | −13.9358 | −0.546186 | ||||||||
\(652\) | −76.6909 | −3.00345 | ||||||||
\(653\) | −33.4300 | −1.30822 | −0.654108 | − | 0.756401i | \(-0.726956\pi\) | ||||
−0.654108 | + | 0.756401i | \(0.726956\pi\) | |||||||
\(654\) | 19.9298 | 0.779316 | ||||||||
\(655\) | −1.74836 | −0.0683141 | ||||||||
\(656\) | −15.7932 | −0.616619 | ||||||||
\(657\) | 12.2752 | 0.478901 | ||||||||
\(658\) | 46.3398 | 1.80651 | ||||||||
\(659\) | 6.93984 | 0.270338 | 0.135169 | − | 0.990823i | \(-0.456842\pi\) | ||||
0.135169 | + | 0.990823i | \(0.456842\pi\) | |||||||
\(660\) | −19.3526 | −0.753299 | ||||||||
\(661\) | −34.1413 | −1.32794 | −0.663972 | − | 0.747758i | \(-0.731130\pi\) | ||||
−0.663972 | + | 0.747758i | \(0.731130\pi\) | |||||||
\(662\) | 50.1220 | 1.94805 | ||||||||
\(663\) | −21.6460 | −0.840660 | ||||||||
\(664\) | −84.3220 | −3.27233 | ||||||||
\(665\) | −5.67993 | −0.220258 | ||||||||
\(666\) | 24.2407 | 0.939309 | ||||||||
\(667\) | 1.49353 | 0.0578297 | ||||||||
\(668\) | −96.5442 | −3.73541 | ||||||||
\(669\) | 31.7095 | 1.22596 | ||||||||
\(670\) | 6.52913 | 0.252242 | ||||||||
\(671\) | −1.30003 | −0.0501872 | ||||||||
\(672\) | −137.393 | −5.30004 | ||||||||
\(673\) | 15.7571 | 0.607393 | 0.303697 | − | 0.952769i | \(-0.401779\pi\) | ||||
0.303697 | + | 0.952769i | \(0.401779\pi\) | |||||||
\(674\) | 85.9688 | 3.31139 | ||||||||
\(675\) | 17.9618 | 0.691352 | ||||||||
\(676\) | 32.7037 | 1.25783 | ||||||||
\(677\) | 41.4036 | 1.59127 | 0.795634 | − | 0.605778i | \(-0.207138\pi\) | ||||
0.795634 | + | 0.605778i | \(0.207138\pi\) | |||||||
\(678\) | −47.7125 | −1.83239 | ||||||||
\(679\) | −49.4034 | −1.89593 | ||||||||
\(680\) | −10.2093 | −0.391509 | ||||||||
\(681\) | 13.3463 | 0.511432 | ||||||||
\(682\) | 13.6429 | 0.522412 | ||||||||
\(683\) | 49.4339 | 1.89154 | 0.945769 | − | 0.324841i | \(-0.105311\pi\) | ||||
0.945769 | + | 0.324841i | \(0.105311\pi\) | |||||||
\(684\) | 12.8718 | 0.492165 | ||||||||
\(685\) | −6.82025 | −0.260588 | ||||||||
\(686\) | −117.347 | −4.48032 | ||||||||
\(687\) | 3.79379 | 0.144742 | ||||||||
\(688\) | 78.9060 | 3.00826 | ||||||||
\(689\) | 41.9171 | 1.59691 | ||||||||
\(690\) | −3.38755 | −0.128962 | ||||||||
\(691\) | 2.17090 | 0.0825849 | 0.0412925 | − | 0.999147i | \(-0.486852\pi\) | ||||
0.0412925 | + | 0.999147i | \(0.486852\pi\) | |||||||
\(692\) | 91.7281 | 3.48698 | ||||||||
\(693\) | 19.6325 | 0.745775 | ||||||||
\(694\) | −34.6702 | −1.31606 | ||||||||
\(695\) | −11.2546 | −0.426913 | ||||||||
\(696\) | 20.4501 | 0.775160 | ||||||||
\(697\) | 3.34778 | 0.126806 | ||||||||
\(698\) | −16.7651 | −0.634567 | ||||||||
\(699\) | −44.4057 | −1.67958 | ||||||||
\(700\) | −114.874 | −4.34182 | ||||||||
\(701\) | 14.8442 | 0.560658 | 0.280329 | − | 0.959904i | \(-0.409556\pi\) | ||||
0.280329 | + | 0.959904i | \(0.409556\pi\) | |||||||
\(702\) | 44.5252 | 1.68050 | ||||||||
\(703\) | −18.2312 | −0.687603 | ||||||||
\(704\) | 52.3470 | 1.97290 | ||||||||
\(705\) | 3.85218 | 0.145081 | ||||||||
\(706\) | 93.3366 | 3.51277 | ||||||||
\(707\) | −23.3392 | −0.877759 | ||||||||
\(708\) | 25.3865 | 0.954083 | ||||||||
\(709\) | −22.4308 | −0.842408 | −0.421204 | − | 0.906966i | \(-0.638392\pi\) | ||||
−0.421204 | + | 0.906966i | \(0.638392\pi\) | |||||||
\(710\) | −7.27964 | −0.273200 | ||||||||
\(711\) | 16.8246 | 0.630971 | ||||||||
\(712\) | −90.1105 | −3.37704 | ||||||||
\(713\) | 1.71041 | 0.0640555 | ||||||||
\(714\) | 62.6885 | 2.34606 | ||||||||
\(715\) | −8.32598 | −0.311374 | ||||||||
\(716\) | −80.8927 | −3.02310 | ||||||||
\(717\) | 27.2496 | 1.01765 | ||||||||
\(718\) | 8.37003 | 0.312367 | ||||||||
\(719\) | −3.79952 | −0.141698 | −0.0708491 | − | 0.997487i | \(-0.522571\pi\) | ||||
−0.0708491 | + | 0.997487i | \(0.522571\pi\) | |||||||
\(720\) | −6.72681 | −0.250693 | ||||||||
\(721\) | 25.7508 | 0.959010 | ||||||||
\(722\) | 36.9243 | 1.37418 | ||||||||
\(723\) | 11.1429 | 0.414407 | ||||||||
\(724\) | 63.2521 | 2.35075 | ||||||||
\(725\) | 5.87830 | 0.218315 | ||||||||
\(726\) | −10.8940 | −0.404313 | ||||||||
\(727\) | 44.2672 | 1.64178 | 0.820890 | − | 0.571086i | \(-0.193478\pi\) | ||||
0.820890 | + | 0.571086i | \(0.193478\pi\) | |||||||
\(728\) | −171.934 | −6.37230 | ||||||||
\(729\) | 10.6095 | 0.392946 | ||||||||
\(730\) | 15.0765 | 0.558006 | ||||||||
\(731\) | −16.7262 | −0.618642 | ||||||||
\(732\) | −3.69612 | −0.136613 | ||||||||
\(733\) | 21.0691 | 0.778207 | 0.389103 | − | 0.921194i | \(-0.372785\pi\) | ||||
0.389103 | + | 0.921194i | \(0.372785\pi\) | |||||||
\(734\) | 12.0149 | 0.443479 | ||||||||
\(735\) | −17.1926 | −0.634160 | ||||||||
\(736\) | 16.8630 | 0.621578 | ||||||||
\(737\) | 16.9729 | 0.625207 | ||||||||
\(738\) | 4.16186 | 0.153200 | ||||||||
\(739\) | 37.7493 | 1.38863 | 0.694315 | − | 0.719671i | \(-0.255708\pi\) | ||||
0.694315 | + | 0.719671i | \(0.255708\pi\) | |||||||
\(740\) | 21.3239 | 0.783881 | ||||||||
\(741\) | 20.2385 | 0.743479 | ||||||||
\(742\) | −121.395 | −4.45656 | ||||||||
\(743\) | 31.1083 | 1.14125 | 0.570626 | − | 0.821210i | \(-0.306700\pi\) | ||||
0.570626 | + | 0.821210i | \(0.306700\pi\) | |||||||
\(744\) | 23.4198 | 0.858613 | ||||||||
\(745\) | 6.39084 | 0.234142 | ||||||||
\(746\) | 76.5869 | 2.80404 | ||||||||
\(747\) | 11.7772 | 0.430905 | ||||||||
\(748\) | −43.9554 | −1.60717 | ||||||||
\(749\) | −42.5794 | −1.55582 | ||||||||
\(750\) | −27.4368 | −1.00185 | ||||||||
\(751\) | 13.2161 | 0.482261 | 0.241130 | − | 0.970493i | \(-0.422482\pi\) | ||||
0.241130 | + | 0.970493i | \(0.422482\pi\) | |||||||
\(752\) | −41.2753 | −1.50516 | ||||||||
\(753\) | 9.19044 | 0.334918 | ||||||||
\(754\) | 14.5716 | 0.530666 | ||||||||
\(755\) | −1.07250 | −0.0390324 | ||||||||
\(756\) | −92.3562 | −3.35896 | ||||||||
\(757\) | 45.8183 | 1.66529 | 0.832647 | − | 0.553805i | \(-0.186825\pi\) | ||||
0.832647 | + | 0.553805i | \(0.186825\pi\) | |||||||
\(758\) | 1.74145 | 0.0632523 | ||||||||
\(759\) | −8.80618 | −0.319644 | ||||||||
\(760\) | 9.54544 | 0.346250 | ||||||||
\(761\) | −18.9676 | −0.687574 | −0.343787 | − | 0.939048i | \(-0.611710\pi\) | ||||
−0.343787 | + | 0.939048i | \(0.611710\pi\) | |||||||
\(762\) | −78.8885 | −2.85783 | ||||||||
\(763\) | −17.7852 | −0.643867 | ||||||||
\(764\) | −25.5361 | −0.923863 | ||||||||
\(765\) | 1.42593 | 0.0515545 | ||||||||
\(766\) | 36.9615 | 1.33547 | ||||||||
\(767\) | 10.9219 | 0.394368 | ||||||||
\(768\) | −2.68749 | −0.0969765 | ||||||||
\(769\) | −51.1167 | −1.84331 | −0.921657 | − | 0.388006i | \(-0.873164\pi\) | ||||
−0.921657 | + | 0.388006i | \(0.873164\pi\) | |||||||
\(770\) | 24.1127 | 0.868962 | ||||||||
\(771\) | 29.2482 | 1.05335 | ||||||||
\(772\) | −48.0562 | −1.72958 | ||||||||
\(773\) | 10.8544 | 0.390406 | 0.195203 | − | 0.980763i | \(-0.437464\pi\) | ||||
0.195203 | + | 0.980763i | \(0.437464\pi\) | |||||||
\(774\) | −20.7935 | −0.747408 | ||||||||
\(775\) | 6.73193 | 0.241818 | ||||||||
\(776\) | 83.0253 | 2.98043 | ||||||||
\(777\) | −79.0577 | −2.83618 | ||||||||
\(778\) | −32.5938 | −1.16855 | ||||||||
\(779\) | −3.13009 | −0.112147 | ||||||||
\(780\) | −23.6716 | −0.847580 | ||||||||
\(781\) | −18.9240 | −0.677152 | ||||||||
\(782\) | −7.69412 | −0.275141 | ||||||||
\(783\) | 4.72603 | 0.168895 | ||||||||
\(784\) | 184.216 | 6.57914 | ||||||||
\(785\) | −0.903419 | −0.0322444 | ||||||||
\(786\) | −18.0417 | −0.643525 | ||||||||
\(787\) | 52.0046 | 1.85376 | 0.926882 | − | 0.375353i | \(-0.122479\pi\) | ||||
0.926882 | + | 0.375353i | \(0.122479\pi\) | |||||||
\(788\) | 59.1781 | 2.10813 | ||||||||
\(789\) | −5.93891 | −0.211431 | ||||||||
\(790\) | 20.6641 | 0.735194 | ||||||||
\(791\) | 42.5783 | 1.51391 | ||||||||
\(792\) | −32.9934 | −1.17237 | ||||||||
\(793\) | −1.59017 | −0.0564685 | ||||||||
\(794\) | 60.4587 | 2.14560 | ||||||||
\(795\) | −10.0914 | −0.357907 | ||||||||
\(796\) | 9.84269 | 0.348865 | ||||||||
\(797\) | −30.4897 | −1.08000 | −0.540000 | − | 0.841665i | \(-0.681576\pi\) | ||||
−0.540000 | + | 0.841665i | \(0.681576\pi\) | |||||||
\(798\) | −58.6122 | −2.07485 | ||||||||
\(799\) | 8.74941 | 0.309532 | ||||||||
\(800\) | 66.3701 | 2.34654 | ||||||||
\(801\) | 12.5857 | 0.444694 | ||||||||
\(802\) | 101.760 | 3.59327 | ||||||||
\(803\) | 39.1924 | 1.38307 | ||||||||
\(804\) | 48.2558 | 1.70185 | ||||||||
\(805\) | 3.02303 | 0.106548 | ||||||||
\(806\) | 16.6876 | 0.587796 | ||||||||
\(807\) | 29.7533 | 1.04737 | ||||||||
\(808\) | 39.2228 | 1.37985 | ||||||||
\(809\) | 10.8070 | 0.379953 | 0.189976 | − | 0.981789i | \(-0.439159\pi\) | ||||
0.189976 | + | 0.981789i | \(0.439159\pi\) | |||||||
\(810\) | −15.4251 | −0.541983 | ||||||||
\(811\) | −27.6590 | −0.971240 | −0.485620 | − | 0.874170i | \(-0.661406\pi\) | ||||
−0.485620 | + | 0.874170i | \(0.661406\pi\) | |||||||
\(812\) | −30.2250 | −1.06069 | ||||||||
\(813\) | 9.82944 | 0.344733 | ||||||||
\(814\) | 77.3961 | 2.71273 | ||||||||
\(815\) | 7.94333 | 0.278243 | ||||||||
\(816\) | −55.8373 | −1.95470 | ||||||||
\(817\) | 15.6386 | 0.547126 | ||||||||
\(818\) | −11.3286 | −0.396095 | ||||||||
\(819\) | 24.0139 | 0.839115 | ||||||||
\(820\) | 3.66107 | 0.127850 | ||||||||
\(821\) | 35.7352 | 1.24717 | 0.623583 | − | 0.781757i | \(-0.285676\pi\) | ||||
0.623583 | + | 0.781757i | \(0.285676\pi\) | |||||||
\(822\) | −70.3794 | −2.45476 | ||||||||
\(823\) | −32.3160 | −1.12646 | −0.563232 | − | 0.826299i | \(-0.690442\pi\) | ||||
−0.563232 | + | 0.826299i | \(0.690442\pi\) | |||||||
\(824\) | −43.2757 | −1.50758 | ||||||||
\(825\) | −34.6598 | −1.20670 | ||||||||
\(826\) | −31.6308 | −1.10058 | ||||||||
\(827\) | −19.6875 | −0.684603 | −0.342301 | − | 0.939590i | \(-0.611206\pi\) | ||||
−0.342301 | + | 0.939590i | \(0.611206\pi\) | |||||||
\(828\) | −6.85075 | −0.238080 | ||||||||
\(829\) | −40.7168 | −1.41415 | −0.707076 | − | 0.707138i | \(-0.749986\pi\) | ||||
−0.707076 | + | 0.707138i | \(0.749986\pi\) | |||||||
\(830\) | 14.4648 | 0.502082 | ||||||||
\(831\) | −52.6695 | −1.82708 | ||||||||
\(832\) | 64.0296 | 2.21983 | ||||||||
\(833\) | −39.0495 | −1.35298 | ||||||||
\(834\) | −116.139 | −4.02155 | ||||||||
\(835\) | 9.99965 | 0.346052 | ||||||||
\(836\) | 41.0972 | 1.42138 | ||||||||
\(837\) | 5.41233 | 0.187077 | ||||||||
\(838\) | 11.7903 | 0.407288 | ||||||||
\(839\) | 13.6771 | 0.472184 | 0.236092 | − | 0.971731i | \(-0.424133\pi\) | ||||
0.236092 | + | 0.971731i | \(0.424133\pi\) | |||||||
\(840\) | 41.3927 | 1.42819 | ||||||||
\(841\) | −27.4533 | −0.946667 | ||||||||
\(842\) | −23.9246 | −0.824496 | ||||||||
\(843\) | 44.2572 | 1.52430 | ||||||||
\(844\) | 57.9906 | 1.99612 | ||||||||
\(845\) | −3.38731 | −0.116527 | ||||||||
\(846\) | 10.8770 | 0.373959 | ||||||||
\(847\) | 9.72169 | 0.334041 | ||||||||
\(848\) | 108.128 | 3.71313 | ||||||||
\(849\) | 35.2454 | 1.20962 | ||||||||
\(850\) | −30.2828 | −1.03869 | ||||||||
\(851\) | 9.70319 | 0.332621 | ||||||||
\(852\) | −53.8028 | −1.84325 | ||||||||
\(853\) | −40.0027 | −1.36967 | −0.684833 | − | 0.728700i | \(-0.740125\pi\) | ||||
−0.684833 | + | 0.728700i | \(0.740125\pi\) | |||||||
\(854\) | 4.60525 | 0.157588 | ||||||||
\(855\) | −1.33321 | −0.0455947 | ||||||||
\(856\) | 71.5571 | 2.44577 | ||||||||
\(857\) | −31.5976 | −1.07935 | −0.539677 | − | 0.841872i | \(-0.681454\pi\) | ||||
−0.539677 | + | 0.841872i | \(0.681454\pi\) | |||||||
\(858\) | −85.9173 | −2.93317 | ||||||||
\(859\) | 8.52813 | 0.290976 | 0.145488 | − | 0.989360i | \(-0.453525\pi\) | ||||
0.145488 | + | 0.989360i | \(0.453525\pi\) | |||||||
\(860\) | −18.2915 | −0.623734 | ||||||||
\(861\) | −13.5733 | −0.462577 | ||||||||
\(862\) | −15.0703 | −0.513297 | ||||||||
\(863\) | 30.5439 | 1.03972 | 0.519862 | − | 0.854250i | \(-0.325983\pi\) | ||||
0.519862 | + | 0.854250i | \(0.325983\pi\) | |||||||
\(864\) | 53.3601 | 1.81535 | ||||||||
\(865\) | −9.50082 | −0.323038 | ||||||||
\(866\) | 25.6158 | 0.870462 | ||||||||
\(867\) | −22.7123 | −0.771351 | ||||||||
\(868\) | −34.6142 | −1.17488 | ||||||||
\(869\) | 53.7177 | 1.82225 | ||||||||
\(870\) | −3.50808 | −0.118935 | ||||||||
\(871\) | 20.7609 | 0.703456 | ||||||||
\(872\) | 29.8890 | 1.01217 | ||||||||
\(873\) | −11.5961 | −0.392468 | ||||||||
\(874\) | 7.19381 | 0.243334 | ||||||||
\(875\) | 24.4844 | 0.827724 | ||||||||
\(876\) | 111.428 | 3.76481 | ||||||||
\(877\) | −39.3688 | −1.32939 | −0.664695 | − | 0.747115i | \(-0.731439\pi\) | ||||
−0.664695 | + | 0.747115i | \(0.731439\pi\) | |||||||
\(878\) | −23.4587 | −0.791691 | ||||||||
\(879\) | 3.02850 | 0.102149 | ||||||||
\(880\) | −21.4774 | −0.724004 | ||||||||
\(881\) | 54.5669 | 1.83840 | 0.919202 | − | 0.393786i | \(-0.128835\pi\) | ||||
0.919202 | + | 0.393786i | \(0.128835\pi\) | |||||||
\(882\) | −48.5451 | −1.63460 | ||||||||
\(883\) | 6.96298 | 0.234323 | 0.117161 | − | 0.993113i | \(-0.462620\pi\) | ||||
0.117161 | + | 0.993113i | \(0.462620\pi\) | |||||||
\(884\) | −53.7651 | −1.80832 | ||||||||
\(885\) | −2.62943 | −0.0883873 | ||||||||
\(886\) | −92.0291 | −3.09178 | ||||||||
\(887\) | −3.55517 | −0.119371 | −0.0596855 | − | 0.998217i | \(-0.519010\pi\) | ||||
−0.0596855 | + | 0.998217i | \(0.519010\pi\) | |||||||
\(888\) | 132.861 | 4.45852 | ||||||||
\(889\) | 70.3995 | 2.36112 | ||||||||
\(890\) | 15.4578 | 0.518148 | ||||||||
\(891\) | −40.0987 | −1.34336 | ||||||||
\(892\) | 78.7612 | 2.63712 | ||||||||
\(893\) | −8.18049 | −0.273750 | ||||||||
\(894\) | 65.9483 | 2.20564 | ||||||||
\(895\) | 8.37853 | 0.280063 | ||||||||
\(896\) | −50.2236 | −1.67785 | ||||||||
\(897\) | −10.7715 | −0.359650 | ||||||||
\(898\) | −31.7906 | −1.06087 | ||||||||
\(899\) | 1.77127 | 0.0590752 | ||||||||
\(900\) | −26.9635 | −0.898782 | ||||||||
\(901\) | −22.9206 | −0.763596 | ||||||||
\(902\) | 13.2880 | 0.442443 | ||||||||
\(903\) | 67.8151 | 2.25675 | ||||||||
\(904\) | −71.5552 | −2.37989 | ||||||||
\(905\) | −6.55140 | −0.217776 | ||||||||
\(906\) | −11.0674 | −0.367689 | ||||||||
\(907\) | −8.90405 | −0.295654 | −0.147827 | − | 0.989013i | \(-0.547228\pi\) | ||||
−0.147827 | + | 0.989013i | \(0.547228\pi\) | |||||||
\(908\) | 33.1501 | 1.10012 | ||||||||
\(909\) | −5.47822 | −0.181701 | ||||||||
\(910\) | 29.4941 | 0.977719 | ||||||||
\(911\) | −6.64310 | −0.220096 | −0.110048 | − | 0.993926i | \(-0.535100\pi\) | ||||
−0.110048 | + | 0.993926i | \(0.535100\pi\) | |||||||
\(912\) | 52.2065 | 1.72873 | ||||||||
\(913\) | 37.6024 | 1.24446 | ||||||||
\(914\) | 57.9512 | 1.91686 | ||||||||
\(915\) | 0.382829 | 0.0126559 | ||||||||
\(916\) | 9.42317 | 0.311350 | ||||||||
\(917\) | 16.1003 | 0.531677 | ||||||||
\(918\) | −24.3468 | −0.803563 | ||||||||
\(919\) | 5.72843 | 0.188963 | 0.0944817 | − | 0.995527i | \(-0.469881\pi\) | ||||
0.0944817 | + | 0.995527i | \(0.469881\pi\) | |||||||
\(920\) | −5.08037 | −0.167495 | ||||||||
\(921\) | 43.5324 | 1.43444 | ||||||||
\(922\) | −31.3864 | −1.03365 | ||||||||
\(923\) | −23.1473 | −0.761903 | ||||||||
\(924\) | 178.213 | 5.86279 | ||||||||
\(925\) | 38.1903 | 1.25569 | ||||||||
\(926\) | −25.7903 | −0.847520 | ||||||||
\(927\) | 6.04429 | 0.198521 | ||||||||
\(928\) | 17.4630 | 0.573250 | ||||||||
\(929\) | 8.36149 | 0.274332 | 0.137166 | − | 0.990548i | \(-0.456201\pi\) | ||||
0.137166 | + | 0.990548i | \(0.456201\pi\) | |||||||
\(930\) | −4.01751 | −0.131739 | ||||||||
\(931\) | 36.5103 | 1.19658 | ||||||||
\(932\) | −110.297 | −3.61289 | ||||||||
\(933\) | −48.2016 | −1.57805 | ||||||||
\(934\) | 46.1960 | 1.51158 | ||||||||
\(935\) | 4.55272 | 0.148890 | ||||||||
\(936\) | −40.3568 | −1.31910 | ||||||||
\(937\) | −30.9702 | −1.01175 | −0.505876 | − | 0.862606i | \(-0.668831\pi\) | ||||
−0.505876 | + | 0.862606i | \(0.668831\pi\) | |||||||
\(938\) | −60.1252 | −1.96316 | ||||||||
\(939\) | −18.6064 | −0.607197 | ||||||||
\(940\) | 9.56818 | 0.312080 | ||||||||
\(941\) | −13.1099 | −0.427371 | −0.213685 | − | 0.976903i | \(-0.568547\pi\) | ||||
−0.213685 | + | 0.976903i | \(0.568547\pi\) | |||||||
\(942\) | −9.32255 | −0.303745 | ||||||||
\(943\) | 1.66593 | 0.0542501 | ||||||||
\(944\) | 28.1738 | 0.916981 | ||||||||
\(945\) | 9.56587 | 0.311178 | ||||||||
\(946\) | −66.3898 | −2.15852 | ||||||||
\(947\) | 50.7977 | 1.65070 | 0.825352 | − | 0.564618i | \(-0.190977\pi\) | ||||
0.825352 | + | 0.564618i | \(0.190977\pi\) | |||||||
\(948\) | 152.725 | 4.96028 | ||||||||
\(949\) | 47.9392 | 1.55617 | ||||||||
\(950\) | 28.3137 | 0.918618 | ||||||||
\(951\) | −48.1339 | −1.56085 | ||||||||
\(952\) | 94.0150 | 3.04704 | ||||||||
\(953\) | −7.94039 | −0.257214 | −0.128607 | − | 0.991696i | \(-0.541051\pi\) | ||||
−0.128607 | + | 0.991696i | \(0.541051\pi\) | |||||||
\(954\) | −28.4942 | −0.922533 | ||||||||
\(955\) | 2.64492 | 0.0855876 | ||||||||
\(956\) | 67.6835 | 2.18904 | ||||||||
\(957\) | −9.11950 | −0.294792 | ||||||||
\(958\) | 65.4651 | 2.11508 | ||||||||
\(959\) | 62.8061 | 2.02811 | ||||||||
\(960\) | −15.4150 | −0.497517 | ||||||||
\(961\) | −28.9715 | −0.934565 | ||||||||
\(962\) | 94.6690 | 3.05225 | ||||||||
\(963\) | −9.99434 | −0.322063 | ||||||||
\(964\) | 27.6771 | 0.891419 | ||||||||
\(965\) | 4.97746 | 0.160230 | ||||||||
\(966\) | 31.1952 | 1.00369 | ||||||||
\(967\) | 23.2056 | 0.746240 | 0.373120 | − | 0.927783i | \(-0.378288\pi\) | ||||
0.373120 | + | 0.927783i | \(0.378288\pi\) | |||||||
\(968\) | −16.3378 | −0.525118 | ||||||||
\(969\) | −11.0666 | −0.355509 | ||||||||
\(970\) | −14.2424 | −0.457296 | ||||||||
\(971\) | −3.65287 | −0.117226 | −0.0586130 | − | 0.998281i | \(-0.518668\pi\) | ||||
−0.0586130 | + | 0.998281i | \(0.518668\pi\) | |||||||
\(972\) | −56.4576 | −1.81088 | ||||||||
\(973\) | 103.641 | 3.32259 | ||||||||
\(974\) | −44.5416 | −1.42720 | ||||||||
\(975\) | −42.3950 | −1.35773 | ||||||||
\(976\) | −4.10194 | −0.131300 | ||||||||
\(977\) | 32.1244 | 1.02775 | 0.513875 | − | 0.857865i | \(-0.328210\pi\) | ||||
0.513875 | + | 0.857865i | \(0.328210\pi\) | |||||||
\(978\) | 81.9686 | 2.62107 | ||||||||
\(979\) | 40.1838 | 1.28428 | ||||||||
\(980\) | −42.7038 | −1.36412 | ||||||||
\(981\) | −4.17458 | −0.133284 | ||||||||
\(982\) | −36.7894 | −1.17400 | ||||||||
\(983\) | −3.35423 | −0.106983 | −0.0534917 | − | 0.998568i | \(-0.517035\pi\) | ||||
−0.0534917 | + | 0.998568i | \(0.517035\pi\) | |||||||
\(984\) | 22.8107 | 0.727179 | ||||||||
\(985\) | −6.12942 | −0.195300 | ||||||||
\(986\) | −7.96787 | −0.253749 | ||||||||
\(987\) | −35.4738 | −1.12914 | ||||||||
\(988\) | 50.2691 | 1.59927 | ||||||||
\(989\) | −8.32333 | −0.264667 | ||||||||
\(990\) | 5.65979 | 0.179880 | ||||||||
\(991\) | −15.1526 | −0.481337 | −0.240668 | − | 0.970607i | \(-0.577367\pi\) | ||||
−0.240668 | + | 0.970607i | \(0.577367\pi\) | |||||||
\(992\) | 19.9989 | 0.634964 | ||||||||
\(993\) | −38.3691 | −1.21761 | ||||||||
\(994\) | 67.0365 | 2.12627 | ||||||||
\(995\) | −1.01946 | −0.0323192 | ||||||||
\(996\) | 106.908 | 3.38749 | ||||||||
\(997\) | 13.8661 | 0.439142 | 0.219571 | − | 0.975596i | \(-0.429534\pi\) | ||||
0.219571 | + | 0.975596i | \(0.429534\pi\) | |||||||
\(998\) | 78.0405 | 2.47033 | ||||||||
\(999\) | 30.7042 | 0.971437 |
(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 | 6047.2.a.b.1.10 | ✓ | 287 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.b.1.10 | ✓ | 287 | 1.1 | even | 1 | trivial |