Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4007,2,Mod(1,4007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4007, 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("4007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4007.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: | \(31.9960560899\) |
Analytic rank: | \(0\) |
Dimension: | \(195\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42566 | −1.71520 | −0.857599 | − | 0.514318i | \(-0.828045\pi\) | ||||
−0.857599 | + | 0.514318i | \(0.828045\pi\) | |||||||
\(3\) | 0.883893 | 0.510316 | 0.255158 | − | 0.966899i | \(-0.417873\pi\) | ||||
0.255158 | + | 0.966899i | \(0.417873\pi\) | |||||||
\(4\) | 3.88381 | 1.94191 | ||||||||
\(5\) | −3.90163 | −1.74486 | −0.872430 | − | 0.488739i | \(-0.837457\pi\) | ||||
−0.872430 | + | 0.488739i | \(0.837457\pi\) | |||||||
\(6\) | −2.14402 | −0.875293 | ||||||||
\(7\) | 3.11093 | 1.17582 | 0.587910 | − | 0.808926i | \(-0.299951\pi\) | ||||
0.587910 | + | 0.808926i | \(0.299951\pi\) | |||||||
\(8\) | −4.56949 | −1.61556 | ||||||||
\(9\) | −2.21873 | −0.739578 | ||||||||
\(10\) | 9.46401 | 2.99278 | ||||||||
\(11\) | −4.04677 | −1.22015 | −0.610074 | − | 0.792345i | \(-0.708860\pi\) | ||||
−0.610074 | + | 0.792345i | \(0.708860\pi\) | |||||||
\(12\) | 3.43288 | 0.990986 | ||||||||
\(13\) | −0.946888 | −0.262619 | −0.131310 | − | 0.991341i | \(-0.541918\pi\) | ||||
−0.131310 | + | 0.991341i | \(0.541918\pi\) | |||||||
\(14\) | −7.54604 | −2.01676 | ||||||||
\(15\) | −3.44862 | −0.890430 | ||||||||
\(16\) | 3.31639 | 0.829096 | ||||||||
\(17\) | 5.88549 | 1.42744 | 0.713720 | − | 0.700431i | \(-0.247009\pi\) | ||||
0.713720 | + | 0.700431i | \(0.247009\pi\) | |||||||
\(18\) | 5.38189 | 1.26852 | ||||||||
\(19\) | 2.85900 | 0.655899 | 0.327950 | − | 0.944695i | \(-0.393642\pi\) | ||||
0.327950 | + | 0.944695i | \(0.393642\pi\) | |||||||
\(20\) | −15.1532 | −3.38836 | ||||||||
\(21\) | 2.74973 | 0.600039 | ||||||||
\(22\) | 9.81608 | 2.09280 | ||||||||
\(23\) | 2.29889 | 0.479351 | 0.239676 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239676 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(24\) | −4.03894 | −0.824445 | ||||||||
\(25\) | 10.2227 | 2.04454 | ||||||||
\(26\) | 2.29683 | 0.450445 | ||||||||
\(27\) | −4.61280 | −0.887734 | ||||||||
\(28\) | 12.0823 | 2.28333 | ||||||||
\(29\) | 0.00945516 | 0.00175578 | 0.000877890 | − | 1.00000i | \(-0.499721\pi\) | ||||
0.000877890 | 1.00000i | \(0.499721\pi\) | ||||||||
\(30\) | 8.36517 | 1.52726 | ||||||||
\(31\) | 5.58748 | 1.00354 | 0.501771 | − | 0.865001i | \(-0.332682\pi\) | ||||
0.501771 | + | 0.865001i | \(0.332682\pi\) | |||||||
\(32\) | 1.09456 | 0.193493 | ||||||||
\(33\) | −3.57691 | −0.622660 | ||||||||
\(34\) | −14.2762 | −2.44834 | ||||||||
\(35\) | −12.1377 | −2.05164 | ||||||||
\(36\) | −8.61715 | −1.43619 | ||||||||
\(37\) | −6.12901 | −1.00760 | −0.503801 | − | 0.863820i | \(-0.668066\pi\) | ||||
−0.503801 | + | 0.863820i | \(0.668066\pi\) | |||||||
\(38\) | −6.93495 | −1.12500 | ||||||||
\(39\) | −0.836948 | −0.134019 | ||||||||
\(40\) | 17.8284 | 2.81892 | ||||||||
\(41\) | −12.3441 | −1.92783 | −0.963916 | − | 0.266207i | \(-0.914230\pi\) | ||||
−0.963916 | + | 0.266207i | \(0.914230\pi\) | |||||||
\(42\) | −6.66989 | −1.02919 | ||||||||
\(43\) | −3.12777 | −0.476980 | −0.238490 | − | 0.971145i | \(-0.576652\pi\) | ||||
−0.238490 | + | 0.971145i | \(0.576652\pi\) | |||||||
\(44\) | −15.7169 | −2.36941 | ||||||||
\(45\) | 8.65667 | 1.29046 | ||||||||
\(46\) | −5.57632 | −0.822183 | ||||||||
\(47\) | −6.03246 | −0.879924 | −0.439962 | − | 0.898016i | \(-0.645008\pi\) | ||||
−0.439962 | + | 0.898016i | \(0.645008\pi\) | |||||||
\(48\) | 2.93133 | 0.423101 | ||||||||
\(49\) | 2.67786 | 0.382552 | ||||||||
\(50\) | −24.7967 | −3.50679 | ||||||||
\(51\) | 5.20214 | 0.728445 | ||||||||
\(52\) | −3.67754 | −0.509983 | ||||||||
\(53\) | −12.3487 | −1.69623 | −0.848113 | − | 0.529815i | \(-0.822261\pi\) | ||||
−0.848113 | + | 0.529815i | \(0.822261\pi\) | |||||||
\(54\) | 11.1891 | 1.52264 | ||||||||
\(55\) | 15.7890 | 2.12899 | ||||||||
\(56\) | −14.2153 | −1.89960 | ||||||||
\(57\) | 2.52705 | 0.334716 | ||||||||
\(58\) | −0.0229350 | −0.00301151 | ||||||||
\(59\) | 14.1608 | 1.84358 | 0.921789 | − | 0.387692i | \(-0.126728\pi\) | ||||
0.921789 | + | 0.387692i | \(0.126728\pi\) | |||||||
\(60\) | −13.3938 | −1.72913 | ||||||||
\(61\) | 15.1240 | 1.93643 | 0.968214 | − | 0.250122i | \(-0.0804709\pi\) | ||||
0.968214 | + | 0.250122i | \(0.0804709\pi\) | |||||||
\(62\) | −13.5533 | −1.72127 | ||||||||
\(63\) | −6.90232 | −0.869610 | ||||||||
\(64\) | −9.28780 | −1.16098 | ||||||||
\(65\) | 3.69440 | 0.458234 | ||||||||
\(66\) | 8.67636 | 1.06799 | ||||||||
\(67\) | −9.98172 | −1.21946 | −0.609731 | − | 0.792609i | \(-0.708722\pi\) | ||||
−0.609731 | + | 0.792609i | \(0.708722\pi\) | |||||||
\(68\) | 22.8581 | 2.77196 | ||||||||
\(69\) | 2.03197 | 0.244621 | ||||||||
\(70\) | 29.4418 | 3.51897 | ||||||||
\(71\) | −6.92927 | −0.822353 | −0.411176 | − | 0.911556i | \(-0.634882\pi\) | ||||
−0.411176 | + | 0.911556i | \(0.634882\pi\) | |||||||
\(72\) | 10.1385 | 1.19483 | ||||||||
\(73\) | 1.49674 | 0.175180 | 0.0875901 | − | 0.996157i | \(-0.472083\pi\) | ||||
0.0875901 | + | 0.996157i | \(0.472083\pi\) | |||||||
\(74\) | 14.8669 | 1.72824 | ||||||||
\(75\) | 9.03576 | 1.04336 | ||||||||
\(76\) | 11.1038 | 1.27370 | ||||||||
\(77\) | −12.5892 | −1.43467 | ||||||||
\(78\) | 2.03015 | 0.229869 | ||||||||
\(79\) | −7.63328 | −0.858811 | −0.429406 | − | 0.903112i | \(-0.641277\pi\) | ||||
−0.429406 | + | 0.903112i | \(0.641277\pi\) | |||||||
\(80\) | −12.9393 | −1.44666 | ||||||||
\(81\) | 2.57898 | 0.286553 | ||||||||
\(82\) | 29.9427 | 3.30662 | ||||||||
\(83\) | −4.79115 | −0.525897 | −0.262949 | − | 0.964810i | \(-0.584695\pi\) | ||||
−0.262949 | + | 0.964810i | \(0.584695\pi\) | |||||||
\(84\) | 10.6794 | 1.16522 | ||||||||
\(85\) | −22.9630 | −2.49068 | ||||||||
\(86\) | 7.58689 | 0.818115 | ||||||||
\(87\) | 0.00835735 | 0.000896002 0 | ||||||||
\(88\) | 18.4917 | 1.97122 | ||||||||
\(89\) | −2.65473 | −0.281401 | −0.140700 | − | 0.990052i | \(-0.544935\pi\) | ||||
−0.140700 | + | 0.990052i | \(0.544935\pi\) | |||||||
\(90\) | −20.9981 | −2.21340 | ||||||||
\(91\) | −2.94570 | −0.308793 | ||||||||
\(92\) | 8.92846 | 0.930856 | ||||||||
\(93\) | 4.93874 | 0.512123 | ||||||||
\(94\) | 14.6327 | 1.50925 | ||||||||
\(95\) | −11.1547 | −1.14445 | ||||||||
\(96\) | 0.967476 | 0.0987426 | ||||||||
\(97\) | 3.16063 | 0.320913 | 0.160457 | − | 0.987043i | \(-0.448703\pi\) | ||||
0.160457 | + | 0.987043i | \(0.448703\pi\) | |||||||
\(98\) | −6.49558 | −0.656153 | ||||||||
\(99\) | 8.97870 | 0.902394 | ||||||||
\(100\) | 39.7030 | 3.97030 | ||||||||
\(101\) | 18.4609 | 1.83693 | 0.918464 | − | 0.395504i | \(-0.129430\pi\) | ||||
0.918464 | + | 0.395504i | \(0.129430\pi\) | |||||||
\(102\) | −12.6186 | −1.24943 | ||||||||
\(103\) | 1.25958 | 0.124110 | 0.0620549 | − | 0.998073i | \(-0.480235\pi\) | ||||
0.0620549 | + | 0.998073i | \(0.480235\pi\) | |||||||
\(104\) | 4.32679 | 0.424277 | ||||||||
\(105\) | −10.7284 | −1.04699 | ||||||||
\(106\) | 29.9538 | 2.90937 | ||||||||
\(107\) | 7.23269 | 0.699211 | 0.349605 | − | 0.936897i | \(-0.386316\pi\) | ||||
0.349605 | + | 0.936897i | \(0.386316\pi\) | |||||||
\(108\) | −17.9153 | −1.72390 | ||||||||
\(109\) | −14.8454 | −1.42193 | −0.710965 | − | 0.703228i | \(-0.751741\pi\) | ||||
−0.710965 | + | 0.703228i | \(0.751741\pi\) | |||||||
\(110\) | −38.2987 | −3.65164 | ||||||||
\(111\) | −5.41739 | −0.514196 | ||||||||
\(112\) | 10.3170 | 0.974868 | ||||||||
\(113\) | 15.6805 | 1.47509 | 0.737547 | − | 0.675295i | \(-0.235984\pi\) | ||||
0.737547 | + | 0.675295i | \(0.235984\pi\) | |||||||
\(114\) | −6.12975 | −0.574104 | ||||||||
\(115\) | −8.96941 | −0.836401 | ||||||||
\(116\) | 0.0367221 | 0.00340956 | ||||||||
\(117\) | 2.10089 | 0.194227 | ||||||||
\(118\) | −34.3492 | −3.16210 | ||||||||
\(119\) | 18.3093 | 1.67841 | ||||||||
\(120\) | 15.7584 | 1.43854 | ||||||||
\(121\) | 5.37635 | 0.488759 | ||||||||
\(122\) | −36.6856 | −3.32136 | ||||||||
\(123\) | −10.9109 | −0.983803 | ||||||||
\(124\) | 21.7007 | 1.94878 | ||||||||
\(125\) | −20.3770 | −1.82257 | ||||||||
\(126\) | 16.7427 | 1.49155 | ||||||||
\(127\) | 5.38145 | 0.477526 | 0.238763 | − | 0.971078i | \(-0.423258\pi\) | ||||
0.238763 | + | 0.971078i | \(0.423258\pi\) | |||||||
\(128\) | 20.3399 | 1.79781 | ||||||||
\(129\) | −2.76461 | −0.243410 | ||||||||
\(130\) | −8.96136 | −0.785963 | ||||||||
\(131\) | −8.21114 | −0.717411 | −0.358706 | − | 0.933451i | \(-0.616782\pi\) | ||||
−0.358706 | + | 0.933451i | \(0.616782\pi\) | |||||||
\(132\) | −13.8921 | −1.20915 | ||||||||
\(133\) | 8.89413 | 0.771219 | ||||||||
\(134\) | 24.2122 | 2.09162 | ||||||||
\(135\) | 17.9974 | 1.54897 | ||||||||
\(136\) | −26.8937 | −2.30611 | ||||||||
\(137\) | 5.81231 | 0.496579 | 0.248290 | − | 0.968686i | \(-0.420132\pi\) | ||||
0.248290 | + | 0.968686i | \(0.420132\pi\) | |||||||
\(138\) | −4.92887 | −0.419573 | ||||||||
\(139\) | −9.42614 | −0.799515 | −0.399757 | − | 0.916621i | \(-0.630906\pi\) | ||||
−0.399757 | + | 0.916621i | \(0.630906\pi\) | |||||||
\(140\) | −47.1405 | −3.98410 | ||||||||
\(141\) | −5.33205 | −0.449039 | ||||||||
\(142\) | 16.8080 | 1.41050 | ||||||||
\(143\) | 3.83184 | 0.320434 | ||||||||
\(144\) | −7.35817 | −0.613181 | ||||||||
\(145\) | −0.0368905 | −0.00306359 | ||||||||
\(146\) | −3.63058 | −0.300469 | ||||||||
\(147\) | 2.36694 | 0.195222 | ||||||||
\(148\) | −23.8039 | −1.95667 | ||||||||
\(149\) | 9.85339 | 0.807221 | 0.403611 | − | 0.914931i | \(-0.367755\pi\) | ||||
0.403611 | + | 0.914931i | \(0.367755\pi\) | |||||||
\(150\) | −21.9177 | −1.78957 | ||||||||
\(151\) | 0.429968 | 0.0349903 | 0.0174951 | − | 0.999847i | \(-0.494431\pi\) | ||||
0.0174951 | + | 0.999847i | \(0.494431\pi\) | |||||||
\(152\) | −13.0642 | −1.05964 | ||||||||
\(153\) | −13.0583 | −1.05570 | ||||||||
\(154\) | 30.5371 | 2.46075 | ||||||||
\(155\) | −21.8003 | −1.75104 | ||||||||
\(156\) | −3.25055 | −0.260252 | ||||||||
\(157\) | 15.0776 | 1.20333 | 0.601663 | − | 0.798750i | \(-0.294505\pi\) | ||||
0.601663 | + | 0.798750i | \(0.294505\pi\) | |||||||
\(158\) | 18.5157 | 1.47303 | ||||||||
\(159\) | −10.9149 | −0.865611 | ||||||||
\(160\) | −4.27057 | −0.337619 | ||||||||
\(161\) | 7.15167 | 0.563631 | ||||||||
\(162\) | −6.25571 | −0.491495 | ||||||||
\(163\) | −4.01817 | −0.314727 | −0.157364 | − | 0.987541i | \(-0.550299\pi\) | ||||
−0.157364 | + | 0.987541i | \(0.550299\pi\) | |||||||
\(164\) | −47.9424 | −3.74367 | ||||||||
\(165\) | 13.9558 | 1.08646 | ||||||||
\(166\) | 11.6217 | 0.902018 | ||||||||
\(167\) | 11.2395 | 0.869741 | 0.434871 | − | 0.900493i | \(-0.356794\pi\) | ||||
0.434871 | + | 0.900493i | \(0.356794\pi\) | |||||||
\(168\) | −12.5648 | −0.969399 | ||||||||
\(169\) | −12.1034 | −0.931031 | ||||||||
\(170\) | 55.7003 | 4.27202 | ||||||||
\(171\) | −6.34335 | −0.485088 | ||||||||
\(172\) | −12.1477 | −0.926250 | ||||||||
\(173\) | −2.34529 | −0.178309 | −0.0891546 | − | 0.996018i | \(-0.528417\pi\) | ||||
−0.0891546 | + | 0.996018i | \(0.528417\pi\) | |||||||
\(174\) | −0.0202721 | −0.00153682 | ||||||||
\(175\) | 31.8020 | 2.40401 | ||||||||
\(176\) | −13.4206 | −1.01162 | ||||||||
\(177\) | 12.5166 | 0.940807 | ||||||||
\(178\) | 6.43947 | 0.482658 | ||||||||
\(179\) | 4.26830 | 0.319028 | 0.159514 | − | 0.987196i | \(-0.449007\pi\) | ||||
0.159514 | + | 0.987196i | \(0.449007\pi\) | |||||||
\(180\) | 33.6209 | 2.50595 | ||||||||
\(181\) | 15.5371 | 1.15486 | 0.577432 | − | 0.816439i | \(-0.304055\pi\) | ||||
0.577432 | + | 0.816439i | \(0.304055\pi\) | |||||||
\(182\) | 7.14526 | 0.529642 | ||||||||
\(183\) | 13.3680 | 0.988190 | ||||||||
\(184\) | −10.5047 | −0.774420 | ||||||||
\(185\) | 23.9131 | 1.75813 | ||||||||
\(186\) | −11.9797 | −0.878393 | ||||||||
\(187\) | −23.8172 | −1.74169 | ||||||||
\(188\) | −23.4289 | −1.70873 | ||||||||
\(189\) | −14.3501 | −1.04382 | ||||||||
\(190\) | 27.0576 | 1.96296 | ||||||||
\(191\) | 21.4607 | 1.55284 | 0.776421 | − | 0.630214i | \(-0.217033\pi\) | ||||
0.776421 | + | 0.630214i | \(0.217033\pi\) | |||||||
\(192\) | −8.20942 | −0.592464 | ||||||||
\(193\) | 23.2972 | 1.67697 | 0.838486 | − | 0.544924i | \(-0.183441\pi\) | ||||
0.838486 | + | 0.544924i | \(0.183441\pi\) | |||||||
\(194\) | −7.66661 | −0.550430 | ||||||||
\(195\) | 3.26546 | 0.233844 | ||||||||
\(196\) | 10.4003 | 0.742880 | ||||||||
\(197\) | −23.3973 | −1.66699 | −0.833494 | − | 0.552528i | \(-0.813663\pi\) | ||||
−0.833494 | + | 0.552528i | \(0.813663\pi\) | |||||||
\(198\) | −21.7793 | −1.54778 | ||||||||
\(199\) | 4.65562 | 0.330028 | 0.165014 | − | 0.986291i | \(-0.447233\pi\) | ||||
0.165014 | + | 0.986291i | \(0.447233\pi\) | |||||||
\(200\) | −46.7125 | −3.30307 | ||||||||
\(201\) | −8.82277 | −0.622310 | ||||||||
\(202\) | −44.7798 | −3.15070 | ||||||||
\(203\) | 0.0294143 | 0.00206448 | ||||||||
\(204\) | 20.2041 | 1.41457 | ||||||||
\(205\) | 48.1623 | 3.36380 | ||||||||
\(206\) | −3.05530 | −0.212873 | ||||||||
\(207\) | −5.10062 | −0.354518 | ||||||||
\(208\) | −3.14024 | −0.217737 | ||||||||
\(209\) | −11.5697 | −0.800293 | ||||||||
\(210\) | 26.0234 | 1.79579 | ||||||||
\(211\) | 9.97191 | 0.686495 | 0.343247 | − | 0.939245i | \(-0.388473\pi\) | ||||
0.343247 | + | 0.939245i | \(0.388473\pi\) | |||||||
\(212\) | −47.9601 | −3.29391 | ||||||||
\(213\) | −6.12473 | −0.419660 | ||||||||
\(214\) | −17.5440 | −1.19929 | ||||||||
\(215\) | 12.2034 | 0.832263 | ||||||||
\(216\) | 21.0781 | 1.43419 | ||||||||
\(217\) | 17.3822 | 1.17998 | ||||||||
\(218\) | 36.0098 | 2.43889 | ||||||||
\(219\) | 1.32296 | 0.0893972 | ||||||||
\(220\) | 61.3215 | 4.13429 | ||||||||
\(221\) | −5.57290 | −0.374873 | ||||||||
\(222\) | 13.1407 | 0.881948 | ||||||||
\(223\) | −1.17397 | −0.0786148 | −0.0393074 | − | 0.999227i | \(-0.512515\pi\) | ||||
−0.0393074 | + | 0.999227i | \(0.512515\pi\) | |||||||
\(224\) | 3.40510 | 0.227513 | ||||||||
\(225\) | −22.6814 | −1.51209 | ||||||||
\(226\) | −38.0355 | −2.53008 | ||||||||
\(227\) | 13.0429 | 0.865690 | 0.432845 | − | 0.901468i | \(-0.357510\pi\) | ||||
0.432845 | + | 0.901468i | \(0.357510\pi\) | |||||||
\(228\) | 9.81459 | 0.649987 | ||||||||
\(229\) | 6.64751 | 0.439280 | 0.219640 | − | 0.975581i | \(-0.429512\pi\) | ||||
0.219640 | + | 0.975581i | \(0.429512\pi\) | |||||||
\(230\) | 21.7567 | 1.43459 | ||||||||
\(231\) | −11.1275 | −0.732136 | ||||||||
\(232\) | −0.0432053 | −0.00283656 | ||||||||
\(233\) | −10.9099 | −0.714732 | −0.357366 | − | 0.933964i | \(-0.616325\pi\) | ||||
−0.357366 | + | 0.933964i | \(0.616325\pi\) | |||||||
\(234\) | −5.09604 | −0.333139 | ||||||||
\(235\) | 23.5364 | 1.53535 | ||||||||
\(236\) | 54.9979 | 3.58006 | ||||||||
\(237\) | −6.74701 | −0.438265 | ||||||||
\(238\) | −44.4121 | −2.87881 | ||||||||
\(239\) | 6.51719 | 0.421562 | 0.210781 | − | 0.977533i | \(-0.432399\pi\) | ||||
0.210781 | + | 0.977533i | \(0.432399\pi\) | |||||||
\(240\) | −11.4370 | −0.738252 | ||||||||
\(241\) | −5.96773 | −0.384415 | −0.192208 | − | 0.981354i | \(-0.561565\pi\) | ||||
−0.192208 | + | 0.981354i | \(0.561565\pi\) | |||||||
\(242\) | −13.0412 | −0.838319 | ||||||||
\(243\) | 16.1179 | 1.03397 | ||||||||
\(244\) | 58.7388 | 3.76036 | ||||||||
\(245\) | −10.4480 | −0.667500 | ||||||||
\(246\) | 26.4661 | 1.68742 | ||||||||
\(247\) | −2.70715 | −0.172252 | ||||||||
\(248\) | −25.5319 | −1.62128 | ||||||||
\(249\) | −4.23486 | −0.268374 | ||||||||
\(250\) | 49.4276 | 3.12608 | ||||||||
\(251\) | 11.7067 | 0.738919 | 0.369460 | − | 0.929247i | \(-0.379543\pi\) | ||||
0.369460 | + | 0.929247i | \(0.379543\pi\) | |||||||
\(252\) | −26.8073 | −1.68870 | ||||||||
\(253\) | −9.30307 | −0.584879 | ||||||||
\(254\) | −13.0536 | −0.819053 | ||||||||
\(255\) | −20.2968 | −1.27104 | ||||||||
\(256\) | −30.7620 | −1.92263 | ||||||||
\(257\) | −13.0168 | −0.811964 | −0.405982 | − | 0.913881i | \(-0.633070\pi\) | ||||
−0.405982 | + | 0.913881i | \(0.633070\pi\) | |||||||
\(258\) | 6.70600 | 0.417497 | ||||||||
\(259\) | −19.0669 | −1.18476 | ||||||||
\(260\) | 14.3484 | 0.889848 | ||||||||
\(261\) | −0.0209785 | −0.00129854 | ||||||||
\(262\) | 19.9174 | 1.23050 | ||||||||
\(263\) | −7.23593 | −0.446186 | −0.223093 | − | 0.974797i | \(-0.571615\pi\) | ||||
−0.223093 | + | 0.974797i | \(0.571615\pi\) | |||||||
\(264\) | 16.3447 | 1.00594 | ||||||||
\(265\) | 48.1801 | 2.95968 | ||||||||
\(266\) | −21.5741 | −1.32279 | ||||||||
\(267\) | −2.34650 | −0.143603 | ||||||||
\(268\) | −38.7671 | −2.36808 | ||||||||
\(269\) | 16.6165 | 1.01313 | 0.506564 | − | 0.862202i | \(-0.330915\pi\) | ||||
0.506564 | + | 0.862202i | \(0.330915\pi\) | |||||||
\(270\) | −43.6556 | −2.65680 | ||||||||
\(271\) | 28.9520 | 1.75871 | 0.879355 | − | 0.476167i | \(-0.157974\pi\) | ||||
0.879355 | + | 0.476167i | \(0.157974\pi\) | |||||||
\(272\) | 19.5185 | 1.18349 | ||||||||
\(273\) | −2.60368 | −0.157582 | ||||||||
\(274\) | −14.0987 | −0.851732 | ||||||||
\(275\) | −41.3689 | −2.49464 | ||||||||
\(276\) | 7.89180 | 0.475031 | ||||||||
\(277\) | −19.6366 | −1.17985 | −0.589925 | − | 0.807458i | \(-0.700843\pi\) | ||||
−0.589925 | + | 0.807458i | \(0.700843\pi\) | |||||||
\(278\) | 22.8646 | 1.37133 | ||||||||
\(279\) | −12.3971 | −0.742197 | ||||||||
\(280\) | 55.4630 | 3.31455 | ||||||||
\(281\) | 8.17625 | 0.487754 | 0.243877 | − | 0.969806i | \(-0.421581\pi\) | ||||
0.243877 | + | 0.969806i | \(0.421581\pi\) | |||||||
\(282\) | 12.9337 | 0.770192 | ||||||||
\(283\) | 8.62086 | 0.512457 | 0.256228 | − | 0.966616i | \(-0.417520\pi\) | ||||
0.256228 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(284\) | −26.9120 | −1.59693 | ||||||||
\(285\) | −9.85960 | −0.584032 | ||||||||
\(286\) | −9.29473 | −0.549609 | ||||||||
\(287\) | −38.4017 | −2.26678 | ||||||||
\(288\) | −2.42854 | −0.143103 | ||||||||
\(289\) | 17.6389 | 1.03759 | ||||||||
\(290\) | 0.0894838 | 0.00525467 | ||||||||
\(291\) | 2.79366 | 0.163767 | ||||||||
\(292\) | 5.81306 | 0.340184 | ||||||||
\(293\) | 12.9161 | 0.754564 | 0.377282 | − | 0.926098i | \(-0.376859\pi\) | ||||
0.377282 | + | 0.926098i | \(0.376859\pi\) | |||||||
\(294\) | −5.74140 | −0.334845 | ||||||||
\(295\) | −55.2501 | −3.21679 | ||||||||
\(296\) | 28.0064 | 1.62784 | ||||||||
\(297\) | 18.6669 | 1.08317 | ||||||||
\(298\) | −23.9009 | −1.38454 | ||||||||
\(299\) | −2.17679 | −0.125887 | ||||||||
\(300\) | 35.0932 | 2.02611 | ||||||||
\(301\) | −9.73025 | −0.560842 | ||||||||
\(302\) | −1.04295 | −0.0600153 | ||||||||
\(303\) | 16.3175 | 0.937414 | ||||||||
\(304\) | 9.48154 | 0.543804 | ||||||||
\(305\) | −59.0082 | −3.37880 | ||||||||
\(306\) | 31.6750 | 1.81074 | ||||||||
\(307\) | 24.3540 | 1.38996 | 0.694978 | − | 0.719031i | \(-0.255414\pi\) | ||||
0.694978 | + | 0.719031i | \(0.255414\pi\) | |||||||
\(308\) | −48.8941 | −2.78600 | ||||||||
\(309\) | 1.11333 | 0.0633352 | ||||||||
\(310\) | 52.8800 | 3.00338 | ||||||||
\(311\) | −18.8675 | −1.06988 | −0.534940 | − | 0.844890i | \(-0.679666\pi\) | ||||
−0.534940 | + | 0.844890i | \(0.679666\pi\) | |||||||
\(312\) | 3.82442 | 0.216515 | ||||||||
\(313\) | 9.09787 | 0.514242 | 0.257121 | − | 0.966379i | \(-0.417226\pi\) | ||||
0.257121 | + | 0.966379i | \(0.417226\pi\) | |||||||
\(314\) | −36.5732 | −2.06394 | ||||||||
\(315\) | 26.9303 | 1.51735 | ||||||||
\(316\) | −29.6463 | −1.66773 | ||||||||
\(317\) | −20.8411 | −1.17056 | −0.585278 | − | 0.810833i | \(-0.699014\pi\) | ||||
−0.585278 | + | 0.810833i | \(0.699014\pi\) | |||||||
\(318\) | 26.4759 | 1.48470 | ||||||||
\(319\) | −0.0382629 | −0.00214231 | ||||||||
\(320\) | 36.2375 | 2.02574 | ||||||||
\(321\) | 6.39293 | 0.356818 | ||||||||
\(322\) | −17.3475 | −0.966739 | ||||||||
\(323\) | 16.8266 | 0.936257 | ||||||||
\(324\) | 10.0163 | 0.556459 | ||||||||
\(325\) | −9.67974 | −0.536935 | ||||||||
\(326\) | 9.74670 | 0.539820 | ||||||||
\(327\) | −13.1217 | −0.725633 | ||||||||
\(328\) | 56.4064 | 3.11452 | ||||||||
\(329\) | −18.7665 | −1.03463 | ||||||||
\(330\) | −33.8519 | −1.86349 | ||||||||
\(331\) | −10.1695 | −0.558968 | −0.279484 | − | 0.960150i | \(-0.590163\pi\) | ||||
−0.279484 | + | 0.960150i | \(0.590163\pi\) | |||||||
\(332\) | −18.6079 | −1.02124 | ||||||||
\(333\) | 13.5986 | 0.745201 | ||||||||
\(334\) | −27.2633 | −1.49178 | ||||||||
\(335\) | 38.9449 | 2.12779 | ||||||||
\(336\) | 9.11915 | 0.497490 | ||||||||
\(337\) | −7.75213 | −0.422285 | −0.211143 | − | 0.977455i | \(-0.567718\pi\) | ||||
−0.211143 | + | 0.977455i | \(0.567718\pi\) | |||||||
\(338\) | 29.3587 | 1.59690 | ||||||||
\(339\) | 13.8599 | 0.752764 | ||||||||
\(340\) | −89.1839 | −4.83668 | ||||||||
\(341\) | −22.6113 | −1.22447 | ||||||||
\(342\) | 15.3868 | 0.832023 | ||||||||
\(343\) | −13.4459 | −0.726008 | ||||||||
\(344\) | 14.2923 | 0.770589 | ||||||||
\(345\) | −7.92799 | −0.426829 | ||||||||
\(346\) | 5.68887 | 0.305836 | ||||||||
\(347\) | 3.41398 | 0.183272 | 0.0916360 | − | 0.995793i | \(-0.470790\pi\) | ||||
0.0916360 | + | 0.995793i | \(0.470790\pi\) | |||||||
\(348\) | 0.0324584 | 0.00173995 | ||||||||
\(349\) | −20.0888 | −1.07533 | −0.537664 | − | 0.843159i | \(-0.680693\pi\) | ||||
−0.537664 | + | 0.843159i | \(0.680693\pi\) | |||||||
\(350\) | −77.1408 | −4.12335 | ||||||||
\(351\) | 4.36781 | 0.233136 | ||||||||
\(352\) | −4.42944 | −0.236090 | ||||||||
\(353\) | 6.75227 | 0.359387 | 0.179694 | − | 0.983723i | \(-0.442489\pi\) | ||||
0.179694 | + | 0.983723i | \(0.442489\pi\) | |||||||
\(354\) | −30.3610 | −1.61367 | ||||||||
\(355\) | 27.0354 | 1.43489 | ||||||||
\(356\) | −10.3105 | −0.546454 | ||||||||
\(357\) | 16.1835 | 0.856520 | ||||||||
\(358\) | −10.3534 | −0.547196 | ||||||||
\(359\) | 20.6256 | 1.08858 | 0.544288 | − | 0.838899i | \(-0.316800\pi\) | ||||
0.544288 | + | 0.838899i | \(0.316800\pi\) | |||||||
\(360\) | −39.5565 | −2.08481 | ||||||||
\(361\) | −10.8261 | −0.569796 | ||||||||
\(362\) | −37.6877 | −1.98082 | ||||||||
\(363\) | 4.75212 | 0.249422 | ||||||||
\(364\) | −11.4405 | −0.599647 | ||||||||
\(365\) | −5.83972 | −0.305665 | ||||||||
\(366\) | −32.4262 | −1.69494 | ||||||||
\(367\) | 17.6641 | 0.922061 | 0.461030 | − | 0.887384i | \(-0.347480\pi\) | ||||
0.461030 | + | 0.887384i | \(0.347480\pi\) | |||||||
\(368\) | 7.62400 | 0.397428 | ||||||||
\(369\) | 27.3884 | 1.42578 | ||||||||
\(370\) | −58.0050 | −3.01554 | ||||||||
\(371\) | −38.4159 | −1.99446 | ||||||||
\(372\) | 19.1811 | 0.994496 | ||||||||
\(373\) | −30.1479 | −1.56100 | −0.780500 | − | 0.625156i | \(-0.785035\pi\) | ||||
−0.780500 | + | 0.625156i | \(0.785035\pi\) | |||||||
\(374\) | 57.7724 | 2.98734 | ||||||||
\(375\) | −18.0111 | −0.930088 | ||||||||
\(376\) | 27.5652 | 1.42157 | ||||||||
\(377\) | −0.00895298 | −0.000461102 0 | ||||||||
\(378\) | 34.8084 | 1.79035 | ||||||||
\(379\) | 29.1566 | 1.49767 | 0.748837 | − | 0.662754i | \(-0.230612\pi\) | ||||
0.748837 | + | 0.662754i | \(0.230612\pi\) | |||||||
\(380\) | −43.3229 | −2.22242 | ||||||||
\(381\) | 4.75663 | 0.243689 | ||||||||
\(382\) | −52.0563 | −2.66343 | ||||||||
\(383\) | 4.99716 | 0.255343 | 0.127672 | − | 0.991817i | \(-0.459250\pi\) | ||||
0.127672 | + | 0.991817i | \(0.459250\pi\) | |||||||
\(384\) | 17.9783 | 0.917451 | ||||||||
\(385\) | 49.1184 | 2.50330 | ||||||||
\(386\) | −56.5111 | −2.87634 | ||||||||
\(387\) | 6.93968 | 0.352764 | ||||||||
\(388\) | 12.2753 | 0.623184 | ||||||||
\(389\) | 14.2149 | 0.720726 | 0.360363 | − | 0.932812i | \(-0.382653\pi\) | ||||
0.360363 | + | 0.932812i | \(0.382653\pi\) | |||||||
\(390\) | −7.92088 | −0.401089 | ||||||||
\(391\) | 13.5301 | 0.684245 | ||||||||
\(392\) | −12.2365 | −0.618035 | ||||||||
\(393\) | −7.25777 | −0.366106 | ||||||||
\(394\) | 56.7538 | 2.85922 | ||||||||
\(395\) | 29.7822 | 1.49851 | ||||||||
\(396\) | 34.8716 | 1.75236 | ||||||||
\(397\) | −4.74227 | −0.238007 | −0.119004 | − | 0.992894i | \(-0.537970\pi\) | ||||
−0.119004 | + | 0.992894i | \(0.537970\pi\) | |||||||
\(398\) | −11.2929 | −0.566064 | ||||||||
\(399\) | 7.86146 | 0.393565 | ||||||||
\(400\) | 33.9024 | 1.69512 | ||||||||
\(401\) | 31.9566 | 1.59584 | 0.797918 | − | 0.602767i | \(-0.205935\pi\) | ||||
0.797918 | + | 0.602767i | \(0.205935\pi\) | |||||||
\(402\) | 21.4010 | 1.06739 | ||||||||
\(403\) | −5.29072 | −0.263550 | ||||||||
\(404\) | 71.6987 | 3.56715 | ||||||||
\(405\) | −10.0622 | −0.499995 | ||||||||
\(406\) | −0.0713491 | −0.00354099 | ||||||||
\(407\) | 24.8027 | 1.22942 | ||||||||
\(408\) | −23.7711 | −1.17685 | ||||||||
\(409\) | 17.6517 | 0.872820 | 0.436410 | − | 0.899748i | \(-0.356250\pi\) | ||||
0.436410 | + | 0.899748i | \(0.356250\pi\) | |||||||
\(410\) | −116.825 | −5.76958 | ||||||||
\(411\) | 5.13746 | 0.253412 | ||||||||
\(412\) | 4.89196 | 0.241010 | ||||||||
\(413\) | 44.0532 | 2.16772 | ||||||||
\(414\) | 12.3724 | 0.608068 | ||||||||
\(415\) | 18.6933 | 0.917617 | ||||||||
\(416\) | −1.03643 | −0.0508151 | ||||||||
\(417\) | −8.33170 | −0.408005 | ||||||||
\(418\) | 28.0641 | 1.37266 | ||||||||
\(419\) | 19.2842 | 0.942097 | 0.471048 | − | 0.882107i | \(-0.343876\pi\) | ||||
0.471048 | + | 0.882107i | \(0.343876\pi\) | |||||||
\(420\) | −41.6671 | −2.03315 | ||||||||
\(421\) | 17.9521 | 0.874933 | 0.437466 | − | 0.899235i | \(-0.355876\pi\) | ||||
0.437466 | + | 0.899235i | \(0.355876\pi\) | |||||||
\(422\) | −24.1884 | −1.17748 | ||||||||
\(423\) | 13.3844 | 0.650772 | ||||||||
\(424\) | 56.4273 | 2.74035 | ||||||||
\(425\) | 60.1655 | 2.91846 | ||||||||
\(426\) | 14.8565 | 0.719800 | ||||||||
\(427\) | 47.0496 | 2.27689 | ||||||||
\(428\) | 28.0904 | 1.35780 | ||||||||
\(429\) | 3.38693 | 0.163523 | ||||||||
\(430\) | −29.6012 | −1.42750 | ||||||||
\(431\) | −15.6238 | −0.752574 | −0.376287 | − | 0.926503i | \(-0.622799\pi\) | ||||
−0.376287 | + | 0.926503i | \(0.622799\pi\) | |||||||
\(432\) | −15.2978 | −0.736017 | ||||||||
\(433\) | 29.3853 | 1.41217 | 0.706085 | − | 0.708128i | \(-0.250460\pi\) | ||||
0.706085 | + | 0.708128i | \(0.250460\pi\) | |||||||
\(434\) | −42.1634 | −2.02391 | ||||||||
\(435\) | −0.0326073 | −0.00156340 | ||||||||
\(436\) | −57.6567 | −2.76125 | ||||||||
\(437\) | 6.57252 | 0.314406 | ||||||||
\(438\) | −3.20904 | −0.153334 | ||||||||
\(439\) | 22.5148 | 1.07457 | 0.537285 | − | 0.843401i | \(-0.319450\pi\) | ||||
0.537285 | + | 0.843401i | \(0.319450\pi\) | |||||||
\(440\) | −72.1476 | −3.43950 | ||||||||
\(441\) | −5.94146 | −0.282927 | ||||||||
\(442\) | 13.5179 | 0.642983 | ||||||||
\(443\) | −8.73009 | −0.414779 | −0.207389 | − | 0.978258i | \(-0.566497\pi\) | ||||
−0.207389 | + | 0.978258i | \(0.566497\pi\) | |||||||
\(444\) | −21.0401 | −0.998520 | ||||||||
\(445\) | 10.3578 | 0.491005 | ||||||||
\(446\) | 2.84765 | 0.134840 | ||||||||
\(447\) | 8.70934 | 0.411938 | ||||||||
\(448\) | −28.8937 | −1.36510 | ||||||||
\(449\) | 28.6173 | 1.35053 | 0.675267 | − | 0.737574i | \(-0.264029\pi\) | ||||
0.675267 | + | 0.737574i | \(0.264029\pi\) | |||||||
\(450\) | 55.0174 | 2.59354 | ||||||||
\(451\) | 49.9539 | 2.35224 | ||||||||
\(452\) | 60.9000 | 2.86450 | ||||||||
\(453\) | 0.380045 | 0.0178561 | ||||||||
\(454\) | −31.6377 | −1.48483 | ||||||||
\(455\) | 11.4930 | 0.538801 | ||||||||
\(456\) | −11.5473 | −0.540753 | ||||||||
\(457\) | −12.1756 | −0.569549 | −0.284775 | − | 0.958594i | \(-0.591919\pi\) | ||||
−0.284775 | + | 0.958594i | \(0.591919\pi\) | |||||||
\(458\) | −16.1246 | −0.753452 | ||||||||
\(459\) | −27.1486 | −1.26719 | ||||||||
\(460\) | −34.8355 | −1.62421 | ||||||||
\(461\) | −32.9683 | −1.53549 | −0.767743 | − | 0.640758i | \(-0.778620\pi\) | ||||
−0.767743 | + | 0.640758i | \(0.778620\pi\) | |||||||
\(462\) | 26.9915 | 1.25576 | ||||||||
\(463\) | 26.7143 | 1.24152 | 0.620760 | − | 0.784001i | \(-0.286824\pi\) | ||||
0.620760 | + | 0.784001i | \(0.286824\pi\) | |||||||
\(464\) | 0.0313570 | 0.00145571 | ||||||||
\(465\) | −19.2691 | −0.893584 | ||||||||
\(466\) | 26.4637 | 1.22591 | ||||||||
\(467\) | 30.0414 | 1.39015 | 0.695075 | − | 0.718937i | \(-0.255371\pi\) | ||||
0.695075 | + | 0.718937i | \(0.255371\pi\) | |||||||
\(468\) | 8.15947 | 0.377172 | ||||||||
\(469\) | −31.0524 | −1.43387 | ||||||||
\(470\) | −57.0912 | −2.63342 | ||||||||
\(471\) | 13.3270 | 0.614076 | ||||||||
\(472\) | −64.7076 | −2.97841 | ||||||||
\(473\) | 12.6573 | 0.581986 | ||||||||
\(474\) | 16.3659 | 0.751712 | ||||||||
\(475\) | 29.2266 | 1.34101 | ||||||||
\(476\) | 71.1100 | 3.25932 | ||||||||
\(477\) | 27.3985 | 1.25449 | ||||||||
\(478\) | −15.8085 | −0.723062 | ||||||||
\(479\) | −42.4129 | −1.93790 | −0.968948 | − | 0.247263i | \(-0.920469\pi\) | ||||
−0.968948 | + | 0.247263i | \(0.920469\pi\) | |||||||
\(480\) | −3.77473 | −0.172292 | ||||||||
\(481\) | 5.80348 | 0.264616 | ||||||||
\(482\) | 14.4757 | 0.659349 | ||||||||
\(483\) | 6.32131 | 0.287630 | ||||||||
\(484\) | 20.8807 | 0.949125 | ||||||||
\(485\) | −12.3316 | −0.559949 | ||||||||
\(486\) | −39.0966 | −1.77346 | ||||||||
\(487\) | 37.5946 | 1.70357 | 0.851787 | − | 0.523888i | \(-0.175519\pi\) | ||||
0.851787 | + | 0.523888i | \(0.175519\pi\) | |||||||
\(488\) | −69.1089 | −3.12841 | ||||||||
\(489\) | −3.55163 | −0.160610 | ||||||||
\(490\) | 25.3433 | 1.14489 | ||||||||
\(491\) | 28.8246 | 1.30084 | 0.650418 | − | 0.759576i | \(-0.274594\pi\) | ||||
0.650418 | + | 0.759576i | \(0.274594\pi\) | |||||||
\(492\) | −42.3759 | −1.91045 | ||||||||
\(493\) | 0.0556482 | 0.00250627 | ||||||||
\(494\) | 6.56662 | 0.295446 | ||||||||
\(495\) | −35.0315 | −1.57455 | ||||||||
\(496\) | 18.5302 | 0.832033 | ||||||||
\(497\) | −21.5564 | −0.966939 | ||||||||
\(498\) | 10.2723 | 0.460314 | ||||||||
\(499\) | 7.11177 | 0.318367 | 0.159183 | − | 0.987249i | \(-0.449114\pi\) | ||||
0.159183 | + | 0.987249i | \(0.449114\pi\) | |||||||
\(500\) | −79.1404 | −3.53927 | ||||||||
\(501\) | 9.93454 | 0.443843 | ||||||||
\(502\) | −28.3964 | −1.26739 | ||||||||
\(503\) | 37.3522 | 1.66545 | 0.832726 | − | 0.553685i | \(-0.186779\pi\) | ||||
0.832726 | + | 0.553685i | \(0.186779\pi\) | |||||||
\(504\) | 31.5400 | 1.40491 | ||||||||
\(505\) | −72.0276 | −3.20518 | ||||||||
\(506\) | 22.5661 | 1.00318 | ||||||||
\(507\) | −10.6981 | −0.475120 | ||||||||
\(508\) | 20.9006 | 0.927312 | ||||||||
\(509\) | 6.92505 | 0.306947 | 0.153474 | − | 0.988153i | \(-0.450954\pi\) | ||||
0.153474 | + | 0.988153i | \(0.450954\pi\) | |||||||
\(510\) | 49.2331 | 2.18008 | ||||||||
\(511\) | 4.65625 | 0.205980 | ||||||||
\(512\) | 33.9384 | 1.49988 | ||||||||
\(513\) | −13.1880 | −0.582264 | ||||||||
\(514\) | 31.5742 | 1.39268 | ||||||||
\(515\) | −4.91440 | −0.216554 | ||||||||
\(516\) | −10.7372 | −0.472680 | ||||||||
\(517\) | 24.4120 | 1.07364 | ||||||||
\(518\) | 46.2498 | 2.03210 | ||||||||
\(519\) | −2.07299 | −0.0909940 | ||||||||
\(520\) | −16.8815 | −0.740304 | ||||||||
\(521\) | 14.0097 | 0.613776 | 0.306888 | − | 0.951746i | \(-0.400712\pi\) | ||||
0.306888 | + | 0.951746i | \(0.400712\pi\) | |||||||
\(522\) | 0.0508866 | 0.00222725 | ||||||||
\(523\) | −28.1650 | −1.23157 | −0.615784 | − | 0.787915i | \(-0.711161\pi\) | ||||
−0.615784 | + | 0.787915i | \(0.711161\pi\) | |||||||
\(524\) | −31.8906 | −1.39315 | ||||||||
\(525\) | 28.1096 | 1.22680 | ||||||||
\(526\) | 17.5519 | 0.765298 | ||||||||
\(527\) | 32.8851 | 1.43250 | ||||||||
\(528\) | −11.8624 | −0.516245 | ||||||||
\(529\) | −17.7151 | −0.770222 | ||||||||
\(530\) | −116.868 | −5.07644 | ||||||||
\(531\) | −31.4190 | −1.36347 | ||||||||
\(532\) | 34.5432 | 1.49764 | ||||||||
\(533\) | 11.6885 | 0.506286 | ||||||||
\(534\) | 5.69180 | 0.246308 | ||||||||
\(535\) | −28.2193 | −1.22003 | ||||||||
\(536\) | 45.6114 | 1.97011 | ||||||||
\(537\) | 3.77272 | 0.162805 | ||||||||
\(538\) | −40.3060 | −1.73772 | ||||||||
\(539\) | −10.8367 | −0.466770 | ||||||||
\(540\) | 69.8987 | 3.00796 | ||||||||
\(541\) | −4.72267 | −0.203043 | −0.101522 | − | 0.994833i | \(-0.532371\pi\) | ||||
−0.101522 | + | 0.994833i | \(0.532371\pi\) | |||||||
\(542\) | −70.2277 | −3.01654 | ||||||||
\(543\) | 13.7331 | 0.589345 | ||||||||
\(544\) | 6.44203 | 0.276200 | ||||||||
\(545\) | 57.9211 | 2.48107 | ||||||||
\(546\) | 6.31564 | 0.270284 | ||||||||
\(547\) | −1.66563 | −0.0712173 | −0.0356086 | − | 0.999366i | \(-0.511337\pi\) | ||||
−0.0356086 | + | 0.999366i | \(0.511337\pi\) | |||||||
\(548\) | 22.5739 | 0.964311 | ||||||||
\(549\) | −33.5561 | −1.43214 | ||||||||
\(550\) | 100.347 | 4.27880 | ||||||||
\(551\) | 0.0270323 | 0.00115161 | ||||||||
\(552\) | −9.28507 | −0.395199 | ||||||||
\(553\) | −23.7466 | −1.00981 | ||||||||
\(554\) | 47.6317 | 2.02368 | ||||||||
\(555\) | 21.1366 | 0.897200 | ||||||||
\(556\) | −36.6094 | −1.55258 | ||||||||
\(557\) | 14.6966 | 0.622713 | 0.311356 | − | 0.950293i | \(-0.399217\pi\) | ||||
0.311356 | + | 0.950293i | \(0.399217\pi\) | |||||||
\(558\) | 30.0712 | 1.27302 | ||||||||
\(559\) | 2.96164 | 0.125264 | ||||||||
\(560\) | −40.2532 | −1.70101 | ||||||||
\(561\) | −21.0519 | −0.888811 | ||||||||
\(562\) | −19.8328 | −0.836595 | ||||||||
\(563\) | 27.5442 | 1.16085 | 0.580426 | − | 0.814313i | \(-0.302886\pi\) | ||||
0.580426 | + | 0.814313i | \(0.302886\pi\) | |||||||
\(564\) | −20.7087 | −0.871993 | ||||||||
\(565\) | −61.1793 | −2.57383 | ||||||||
\(566\) | −20.9113 | −0.878965 | ||||||||
\(567\) | 8.02300 | 0.336935 | ||||||||
\(568\) | 31.6632 | 1.32856 | ||||||||
\(569\) | −31.1795 | −1.30711 | −0.653556 | − | 0.756878i | \(-0.726724\pi\) | ||||
−0.653556 | + | 0.756878i | \(0.726724\pi\) | |||||||
\(570\) | 23.9160 | 1.00173 | ||||||||
\(571\) | −30.6349 | −1.28203 | −0.641015 | − | 0.767529i | \(-0.721486\pi\) | ||||
−0.641015 | + | 0.767529i | \(0.721486\pi\) | |||||||
\(572\) | 14.8821 | 0.622254 | ||||||||
\(573\) | 18.9690 | 0.792440 | ||||||||
\(574\) | 93.1495 | 3.88798 | ||||||||
\(575\) | 23.5008 | 0.980052 | ||||||||
\(576\) | 20.6072 | 0.858632 | ||||||||
\(577\) | 11.1179 | 0.462846 | 0.231423 | − | 0.972853i | \(-0.425662\pi\) | ||||
0.231423 | + | 0.972853i | \(0.425662\pi\) | |||||||
\(578\) | −42.7860 | −1.77966 | ||||||||
\(579\) | 20.5923 | 0.855785 | ||||||||
\(580\) | −0.143276 | −0.00594921 | ||||||||
\(581\) | −14.9049 | −0.618360 | ||||||||
\(582\) | −6.77646 | −0.280893 | ||||||||
\(583\) | 49.9724 | 2.06965 | ||||||||
\(584\) | −6.83934 | −0.283014 | ||||||||
\(585\) | −8.19689 | −0.338900 | ||||||||
\(586\) | −31.3299 | −1.29423 | ||||||||
\(587\) | −10.6454 | −0.439384 | −0.219692 | − | 0.975569i | \(-0.570505\pi\) | ||||
−0.219692 | + | 0.975569i | \(0.570505\pi\) | |||||||
\(588\) | 9.19277 | 0.379104 | ||||||||
\(589\) | 15.9746 | 0.658222 | ||||||||
\(590\) | 134.018 | 5.51743 | ||||||||
\(591\) | −20.6807 | −0.850691 | ||||||||
\(592\) | −20.3262 | −0.835400 | ||||||||
\(593\) | 35.5784 | 1.46103 | 0.730515 | − | 0.682896i | \(-0.239280\pi\) | ||||
0.730515 | + | 0.682896i | \(0.239280\pi\) | |||||||
\(594\) | −45.2796 | −1.85785 | ||||||||
\(595\) | −71.4361 | −2.92859 | ||||||||
\(596\) | 38.2687 | 1.56755 | ||||||||
\(597\) | 4.11507 | 0.168419 | ||||||||
\(598\) | 5.28015 | 0.215921 | ||||||||
\(599\) | −26.9808 | −1.10240 | −0.551202 | − | 0.834372i | \(-0.685831\pi\) | ||||
−0.551202 | + | 0.834372i | \(0.685831\pi\) | |||||||
\(600\) | −41.2888 | −1.68561 | ||||||||
\(601\) | −4.45306 | −0.181644 | −0.0908221 | − | 0.995867i | \(-0.528949\pi\) | ||||
−0.0908221 | + | 0.995867i | \(0.528949\pi\) | |||||||
\(602\) | 23.6022 | 0.961956 | ||||||||
\(603\) | 22.1468 | 0.901886 | ||||||||
\(604\) | 1.66991 | 0.0679478 | ||||||||
\(605\) | −20.9765 | −0.852816 | ||||||||
\(606\) | −39.5806 | −1.60785 | ||||||||
\(607\) | 47.5453 | 1.92980 | 0.964902 | − | 0.262611i | \(-0.0845836\pi\) | ||||
0.964902 | + | 0.262611i | \(0.0845836\pi\) | |||||||
\(608\) | 3.12935 | 0.126912 | ||||||||
\(609\) | 0.0259991 | 0.00105354 | ||||||||
\(610\) | 143.134 | 5.79531 | ||||||||
\(611\) | 5.71206 | 0.231085 | ||||||||
\(612\) | −50.7161 | −2.05008 | ||||||||
\(613\) | −9.04020 | −0.365130 | −0.182565 | − | 0.983194i | \(-0.558440\pi\) | ||||
−0.182565 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(614\) | −59.0744 | −2.38405 | ||||||||
\(615\) | 42.5703 | 1.71660 | ||||||||
\(616\) | 57.5262 | 2.31780 | ||||||||
\(617\) | −30.5482 | −1.22982 | −0.614911 | − | 0.788596i | \(-0.710808\pi\) | ||||
−0.614911 | + | 0.788596i | \(0.710808\pi\) | |||||||
\(618\) | −2.70056 | −0.108632 | ||||||||
\(619\) | −21.5445 | −0.865948 | −0.432974 | − | 0.901406i | \(-0.642536\pi\) | ||||
−0.432974 | + | 0.901406i | \(0.642536\pi\) | |||||||
\(620\) | −84.6682 | −3.40036 | ||||||||
\(621\) | −10.6043 | −0.425537 | ||||||||
\(622\) | 45.7662 | 1.83506 | ||||||||
\(623\) | −8.25867 | −0.330877 | ||||||||
\(624\) | −2.77564 | −0.111115 | ||||||||
\(625\) | 28.3899 | 1.13560 | ||||||||
\(626\) | −22.0683 | −0.882028 | ||||||||
\(627\) | −10.2264 | −0.408402 | ||||||||
\(628\) | 58.5587 | 2.33675 | ||||||||
\(629\) | −36.0722 | −1.43829 | ||||||||
\(630\) | −65.3236 | −2.60255 | ||||||||
\(631\) | −5.38228 | −0.214265 | −0.107133 | − | 0.994245i | \(-0.534167\pi\) | ||||
−0.107133 | + | 0.994245i | \(0.534167\pi\) | |||||||
\(632\) | 34.8802 | 1.38746 | ||||||||
\(633\) | 8.81410 | 0.350329 | ||||||||
\(634\) | 50.5535 | 2.00774 | ||||||||
\(635\) | −20.9964 | −0.833217 | ||||||||
\(636\) | −42.3916 | −1.68094 | ||||||||
\(637\) | −2.53564 | −0.100466 | ||||||||
\(638\) | 0.0928126 | 0.00367449 | ||||||||
\(639\) | 15.3742 | 0.608194 | ||||||||
\(640\) | −79.3587 | −3.13693 | ||||||||
\(641\) | 37.0044 | 1.46158 | 0.730792 | − | 0.682600i | \(-0.239151\pi\) | ||||
0.730792 | + | 0.682600i | \(0.239151\pi\) | |||||||
\(642\) | −15.5070 | −0.612014 | ||||||||
\(643\) | 34.8339 | 1.37371 | 0.686857 | − | 0.726793i | \(-0.258990\pi\) | ||||
0.686857 | + | 0.726793i | \(0.258990\pi\) | |||||||
\(644\) | 27.7758 | 1.09452 | ||||||||
\(645\) | 10.7865 | 0.424717 | ||||||||
\(646\) | −40.8156 | −1.60587 | ||||||||
\(647\) | −3.33463 | −0.131098 | −0.0655488 | − | 0.997849i | \(-0.520880\pi\) | ||||
−0.0655488 | + | 0.997849i | \(0.520880\pi\) | |||||||
\(648\) | −11.7846 | −0.462943 | ||||||||
\(649\) | −57.3055 | −2.24944 | ||||||||
\(650\) | 23.4797 | 0.920951 | ||||||||
\(651\) | 15.3640 | 0.602165 | ||||||||
\(652\) | −15.6058 | −0.611171 | ||||||||
\(653\) | 27.7472 | 1.08583 | 0.542916 | − | 0.839787i | \(-0.317320\pi\) | ||||
0.542916 | + | 0.839787i | \(0.317320\pi\) | |||||||
\(654\) | 31.8288 | 1.24461 | ||||||||
\(655\) | 32.0368 | 1.25178 | ||||||||
\(656\) | −40.9379 | −1.59836 | ||||||||
\(657\) | −3.32087 | −0.129559 | ||||||||
\(658\) | 45.5212 | 1.77460 | ||||||||
\(659\) | −32.9934 | −1.28524 | −0.642620 | − | 0.766185i | \(-0.722153\pi\) | ||||
−0.642620 | + | 0.766185i | \(0.722153\pi\) | |||||||
\(660\) | 54.2016 | 2.10980 | ||||||||
\(661\) | 22.5514 | 0.877149 | 0.438575 | − | 0.898695i | \(-0.355484\pi\) | ||||
0.438575 | + | 0.898695i | \(0.355484\pi\) | |||||||
\(662\) | 24.6678 | 0.958741 | ||||||||
\(663\) | −4.92584 | −0.191304 | ||||||||
\(664\) | 21.8931 | 0.849617 | ||||||||
\(665\) | −34.7016 | −1.34567 | ||||||||
\(666\) | −32.9856 | −1.27817 | ||||||||
\(667\) | 0.0217364 | 0.000841636 0 | ||||||||
\(668\) | 43.6523 | 1.68896 | ||||||||
\(669\) | −1.03766 | −0.0401184 | ||||||||
\(670\) | −94.4671 | −3.64958 | ||||||||
\(671\) | −61.2033 | −2.36273 | ||||||||
\(672\) | 3.00975 | 0.116104 | ||||||||
\(673\) | 2.18819 | 0.0843485 | 0.0421743 | − | 0.999110i | \(-0.486572\pi\) | ||||
0.0421743 | + | 0.999110i | \(0.486572\pi\) | |||||||
\(674\) | 18.8040 | 0.724303 | ||||||||
\(675\) | −47.1552 | −1.81501 | ||||||||
\(676\) | −47.0074 | −1.80798 | ||||||||
\(677\) | 19.0576 | 0.732445 | 0.366222 | − | 0.930527i | \(-0.380651\pi\) | ||||
0.366222 | + | 0.930527i | \(0.380651\pi\) | |||||||
\(678\) | −33.6193 | −1.29114 | ||||||||
\(679\) | 9.83249 | 0.377336 | ||||||||
\(680\) | 104.929 | 4.02384 | ||||||||
\(681\) | 11.5286 | 0.441775 | ||||||||
\(682\) | 54.8472 | 2.10021 | ||||||||
\(683\) | 28.2352 | 1.08039 | 0.540194 | − | 0.841540i | \(-0.318351\pi\) | ||||
0.540194 | + | 0.841540i | \(0.318351\pi\) | |||||||
\(684\) | −24.6364 | −0.941997 | ||||||||
\(685\) | −22.6775 | −0.866462 | ||||||||
\(686\) | 32.6150 | 1.24525 | ||||||||
\(687\) | 5.87569 | 0.224171 | ||||||||
\(688\) | −10.3729 | −0.395462 | ||||||||
\(689\) | 11.6928 | 0.445462 | ||||||||
\(690\) | 19.2306 | 0.732096 | ||||||||
\(691\) | −20.9880 | −0.798419 | −0.399210 | − | 0.916860i | \(-0.630715\pi\) | ||||
−0.399210 | + | 0.916860i | \(0.630715\pi\) | |||||||
\(692\) | −9.10867 | −0.346260 | ||||||||
\(693\) | 27.9321 | 1.06105 | ||||||||
\(694\) | −8.28114 | −0.314348 | ||||||||
\(695\) | 36.7773 | 1.39504 | ||||||||
\(696\) | −0.0381888 | −0.00144754 | ||||||||
\(697\) | −72.6513 | −2.75186 | ||||||||
\(698\) | 48.7285 | 1.84440 | ||||||||
\(699\) | −9.64320 | −0.364739 | ||||||||
\(700\) | 123.513 | 4.66836 | ||||||||
\(701\) | −30.2574 | −1.14281 | −0.571403 | − | 0.820670i | \(-0.693601\pi\) | ||||
−0.571403 | + | 0.820670i | \(0.693601\pi\) | |||||||
\(702\) | −10.5948 | −0.399875 | ||||||||
\(703\) | −17.5228 | −0.660886 | ||||||||
\(704\) | 37.5856 | 1.41656 | ||||||||
\(705\) | 20.8037 | 0.783511 | ||||||||
\(706\) | −16.3787 | −0.616420 | ||||||||
\(707\) | 57.4305 | 2.15990 | ||||||||
\(708\) | 48.6122 | 1.82696 | ||||||||
\(709\) | −29.4684 | −1.10671 | −0.553354 | − | 0.832946i | \(-0.686652\pi\) | ||||
−0.553354 | + | 0.832946i | \(0.686652\pi\) | |||||||
\(710\) | −65.5787 | −2.46112 | ||||||||
\(711\) | 16.9362 | 0.635158 | ||||||||
\(712\) | 12.1308 | 0.454619 | ||||||||
\(713\) | 12.8450 | 0.481049 | ||||||||
\(714\) | −39.2556 | −1.46910 | ||||||||
\(715\) | −14.9504 | −0.559113 | ||||||||
\(716\) | 16.5773 | 0.619522 | ||||||||
\(717\) | 5.76050 | 0.215130 | ||||||||
\(718\) | −50.0306 | −1.86712 | ||||||||
\(719\) | 39.2031 | 1.46203 | 0.731014 | − | 0.682362i | \(-0.239047\pi\) | ||||
0.731014 | + | 0.682362i | \(0.239047\pi\) | |||||||
\(720\) | 28.7088 | 1.06992 | ||||||||
\(721\) | 3.91845 | 0.145931 | ||||||||
\(722\) | 26.2605 | 0.977314 | ||||||||
\(723\) | −5.27484 | −0.196173 | ||||||||
\(724\) | 60.3432 | 2.24264 | ||||||||
\(725\) | 0.0966572 | 0.00358976 | ||||||||
\(726\) | −11.5270 | −0.427808 | ||||||||
\(727\) | 26.0858 | 0.967470 | 0.483735 | − | 0.875215i | \(-0.339280\pi\) | ||||
0.483735 | + | 0.875215i | \(0.339280\pi\) | |||||||
\(728\) | 13.4603 | 0.498873 | ||||||||
\(729\) | 6.50961 | 0.241097 | ||||||||
\(730\) | 14.1652 | 0.524276 | ||||||||
\(731\) | −18.4084 | −0.680860 | ||||||||
\(732\) | 51.9188 | 1.91897 | ||||||||
\(733\) | 4.19431 | 0.154921 | 0.0774603 | − | 0.996995i | \(-0.475319\pi\) | ||||
0.0774603 | + | 0.996995i | \(0.475319\pi\) | |||||||
\(734\) | −42.8472 | −1.58152 | ||||||||
\(735\) | −9.23493 | −0.340636 | ||||||||
\(736\) | 2.51628 | 0.0927512 | ||||||||
\(737\) | 40.3937 | 1.48792 | ||||||||
\(738\) | −66.4348 | −2.44550 | ||||||||
\(739\) | −30.8014 | −1.13305 | −0.566525 | − | 0.824045i | \(-0.691712\pi\) | ||||
−0.566525 | + | 0.824045i | \(0.691712\pi\) | |||||||
\(740\) | 92.8740 | 3.41412 | ||||||||
\(741\) | −2.39283 | −0.0879029 | ||||||||
\(742\) | 93.1839 | 3.42089 | ||||||||
\(743\) | 17.8003 | 0.653031 | 0.326516 | − | 0.945192i | \(-0.394125\pi\) | ||||
0.326516 | + | 0.945192i | \(0.394125\pi\) | |||||||
\(744\) | −22.5675 | −0.827365 | ||||||||
\(745\) | −38.4442 | −1.40849 | ||||||||
\(746\) | 73.1285 | 2.67743 | ||||||||
\(747\) | 10.6303 | 0.388942 | ||||||||
\(748\) | −92.5016 | −3.38219 | ||||||||
\(749\) | 22.5004 | 0.822146 | ||||||||
\(750\) | 43.6887 | 1.59529 | ||||||||
\(751\) | −38.3122 | −1.39803 | −0.699016 | − | 0.715106i | \(-0.746378\pi\) | ||||
−0.699016 | + | 0.715106i | \(0.746378\pi\) | |||||||
\(752\) | −20.0060 | −0.729542 | ||||||||
\(753\) | 10.3475 | 0.377082 | ||||||||
\(754\) | 0.0217169 | 0.000790881 0 | ||||||||
\(755\) | −1.67757 | −0.0610531 | ||||||||
\(756\) | −55.7331 | −2.02699 | ||||||||
\(757\) | −47.6636 | −1.73236 | −0.866182 | − | 0.499728i | \(-0.833433\pi\) | ||||
−0.866182 | + | 0.499728i | \(0.833433\pi\) | |||||||
\(758\) | −70.7240 | −2.56881 | ||||||||
\(759\) | −8.22292 | −0.298473 | ||||||||
\(760\) | 50.9715 | 1.84893 | ||||||||
\(761\) | 28.8267 | 1.04497 | 0.522484 | − | 0.852649i | \(-0.325005\pi\) | ||||
0.522484 | + | 0.852649i | \(0.325005\pi\) | |||||||
\(762\) | −11.5379 | −0.417976 | ||||||||
\(763\) | −46.1829 | −1.67193 | ||||||||
\(764\) | 83.3494 | 3.01548 | ||||||||
\(765\) | 50.9487 | 1.84205 | ||||||||
\(766\) | −12.1214 | −0.437964 | ||||||||
\(767\) | −13.4087 | −0.484159 | ||||||||
\(768\) | −27.1904 | −0.981147 | ||||||||
\(769\) | −9.54578 | −0.344230 | −0.172115 | − | 0.985077i | \(-0.555060\pi\) | ||||
−0.172115 | + | 0.985077i | \(0.555060\pi\) | |||||||
\(770\) | −119.144 | −4.29366 | ||||||||
\(771\) | −11.5054 | −0.414358 | ||||||||
\(772\) | 90.4821 | 3.25652 | ||||||||
\(773\) | −33.0754 | −1.18964 | −0.594821 | − | 0.803858i | \(-0.702777\pi\) | ||||
−0.594821 | + | 0.803858i | \(0.702777\pi\) | |||||||
\(774\) | −16.8333 | −0.605060 | ||||||||
\(775\) | 57.1191 | 2.05178 | ||||||||
\(776\) | −14.4425 | −0.518454 | ||||||||
\(777\) | −16.8531 | −0.604601 | ||||||||
\(778\) | −34.4806 | −1.23619 | ||||||||
\(779\) | −35.2919 | −1.26446 | ||||||||
\(780\) | 12.6824 | 0.454104 | ||||||||
\(781\) | 28.0412 | 1.00339 | ||||||||
\(782\) | −32.8193 | −1.17362 | ||||||||
\(783\) | −0.0436148 | −0.00155867 | ||||||||
\(784\) | 8.88082 | 0.317172 | ||||||||
\(785\) | −58.8273 | −2.09964 | ||||||||
\(786\) | 17.6049 | 0.627945 | ||||||||
\(787\) | 19.9927 | 0.712662 | 0.356331 | − | 0.934360i | \(-0.384028\pi\) | ||||
0.356331 | + | 0.934360i | \(0.384028\pi\) | |||||||
\(788\) | −90.8708 | −3.23714 | ||||||||
\(789\) | −6.39579 | −0.227696 | ||||||||
\(790\) | −72.2415 | −2.57024 | ||||||||
\(791\) | 48.7808 | 1.73445 | ||||||||
\(792\) | −41.0281 | −1.45787 | ||||||||
\(793\) | −14.3207 | −0.508544 | ||||||||
\(794\) | 11.5031 | 0.408230 | ||||||||
\(795\) | 42.5860 | 1.51037 | ||||||||
\(796\) | 18.0816 | 0.640884 | ||||||||
\(797\) | −26.8830 | −0.952244 | −0.476122 | − | 0.879379i | \(-0.657958\pi\) | ||||
−0.476122 | + | 0.879379i | \(0.657958\pi\) | |||||||
\(798\) | −19.0692 | −0.675043 | ||||||||
\(799\) | −35.5039 | −1.25604 | ||||||||
\(800\) | 11.1894 | 0.395604 | ||||||||
\(801\) | 5.89014 | 0.208118 | ||||||||
\(802\) | −77.5157 | −2.73717 | ||||||||
\(803\) | −6.05696 | −0.213746 | ||||||||
\(804\) | −34.2660 | −1.20847 | ||||||||
\(805\) | −27.9032 | −0.983457 | ||||||||
\(806\) | 12.8335 | 0.452040 | ||||||||
\(807\) | 14.6872 | 0.517015 | ||||||||
\(808\) | −84.3569 | −2.96767 | ||||||||
\(809\) | −10.5239 | −0.370001 | −0.185001 | − | 0.982738i | \(-0.559229\pi\) | ||||
−0.185001 | + | 0.982738i | \(0.559229\pi\) | |||||||
\(810\) | 24.4075 | 0.857591 | ||||||||
\(811\) | −26.3575 | −0.925535 | −0.462768 | − | 0.886480i | \(-0.653144\pi\) | ||||
−0.462768 | + | 0.886480i | \(0.653144\pi\) | |||||||
\(812\) | 0.114240 | 0.00400903 | ||||||||
\(813\) | 25.5905 | 0.897497 | ||||||||
\(814\) | −60.1628 | −2.10871 | ||||||||
\(815\) | 15.6774 | 0.549155 | ||||||||
\(816\) | 17.2523 | 0.603951 | ||||||||
\(817\) | −8.94228 | −0.312851 | ||||||||
\(818\) | −42.8170 | −1.49706 | ||||||||
\(819\) | 6.53572 | 0.228376 | ||||||||
\(820\) | 187.053 | 6.53218 | ||||||||
\(821\) | 17.3354 | 0.605008 | 0.302504 | − | 0.953148i | \(-0.402177\pi\) | ||||
0.302504 | + | 0.953148i | \(0.402177\pi\) | |||||||
\(822\) | −12.4617 | −0.434653 | ||||||||
\(823\) | 49.6355 | 1.73019 | 0.865093 | − | 0.501612i | \(-0.167260\pi\) | ||||
0.865093 | + | 0.501612i | \(0.167260\pi\) | |||||||
\(824\) | −5.75562 | −0.200507 | ||||||||
\(825\) | −36.5657 | −1.27305 | ||||||||
\(826\) | −106.858 | −3.71806 | ||||||||
\(827\) | 21.3746 | 0.743269 | 0.371635 | − | 0.928379i | \(-0.378797\pi\) | ||||
0.371635 | + | 0.928379i | \(0.378797\pi\) | |||||||
\(828\) | −19.8099 | −0.688440 | ||||||||
\(829\) | 3.63824 | 0.126361 | 0.0631806 | − | 0.998002i | \(-0.479876\pi\) | ||||
0.0631806 | + | 0.998002i | \(0.479876\pi\) | |||||||
\(830\) | −45.3435 | −1.57390 | ||||||||
\(831\) | −17.3567 | −0.602096 | ||||||||
\(832\) | 8.79451 | 0.304895 | ||||||||
\(833\) | 15.7605 | 0.546070 | ||||||||
\(834\) | 20.2099 | 0.699810 | ||||||||
\(835\) | −43.8525 | −1.51758 | ||||||||
\(836\) | −44.9346 | −1.55410 | ||||||||
\(837\) | −25.7740 | −0.890878 | ||||||||
\(838\) | −46.7770 | −1.61588 | ||||||||
\(839\) | 54.8337 | 1.89307 | 0.946535 | − | 0.322602i | \(-0.104557\pi\) | ||||
0.946535 | + | 0.322602i | \(0.104557\pi\) | |||||||
\(840\) | 49.0233 | 1.69147 | ||||||||
\(841\) | −28.9999 | −0.999997 | ||||||||
\(842\) | −43.5457 | −1.50068 | ||||||||
\(843\) | 7.22693 | 0.248909 | ||||||||
\(844\) | 38.7291 | 1.33311 | ||||||||
\(845\) | 47.2230 | 1.62452 | ||||||||
\(846\) | −32.4660 | −1.11620 | ||||||||
\(847\) | 16.7254 | 0.574693 | ||||||||
\(848\) | −40.9531 | −1.40634 | ||||||||
\(849\) | 7.61992 | 0.261515 | ||||||||
\(850\) | −145.941 | −5.00573 | ||||||||
\(851\) | −14.0899 | −0.482996 | ||||||||
\(852\) | −23.7873 | −0.814940 | ||||||||
\(853\) | −42.2586 | −1.44691 | −0.723453 | − | 0.690374i | \(-0.757446\pi\) | ||||
−0.723453 | + | 0.690374i | \(0.757446\pi\) | |||||||
\(854\) | −114.126 | −3.90532 | ||||||||
\(855\) | 24.7494 | 0.846412 | ||||||||
\(856\) | −33.0497 | −1.12962 | ||||||||
\(857\) | 51.7846 | 1.76893 | 0.884464 | − | 0.466609i | \(-0.154524\pi\) | ||||
0.884464 | + | 0.466609i | \(0.154524\pi\) | |||||||
\(858\) | −8.21554 | −0.280474 | ||||||||
\(859\) | 46.6205 | 1.59067 | 0.795336 | − | 0.606169i | \(-0.207295\pi\) | ||||
0.795336 | + | 0.606169i | \(0.207295\pi\) | |||||||
\(860\) | 47.3956 | 1.61618 | ||||||||
\(861\) | −33.9430 | −1.15678 | ||||||||
\(862\) | 37.8981 | 1.29081 | ||||||||
\(863\) | −54.4874 | −1.85477 | −0.927387 | − | 0.374104i | \(-0.877950\pi\) | ||||
−0.927387 | + | 0.374104i | \(0.877950\pi\) | |||||||
\(864\) | −5.04900 | −0.171770 | ||||||||
\(865\) | 9.15045 | 0.311125 | ||||||||
\(866\) | −71.2788 | −2.42215 | ||||||||
\(867\) | 15.5909 | 0.529496 | ||||||||
\(868\) | 67.5094 | 2.29142 | ||||||||
\(869\) | 30.8901 | 1.04788 | ||||||||
\(870\) | 0.0790941 | 0.00268154 | ||||||||
\(871\) | 9.45157 | 0.320254 | ||||||||
\(872\) | 67.8358 | 2.29721 | ||||||||
\(873\) | −7.01259 | −0.237340 | ||||||||
\(874\) | −15.9427 | −0.539269 | ||||||||
\(875\) | −63.3913 | −2.14302 | ||||||||
\(876\) | 5.13812 | 0.173601 | ||||||||
\(877\) | −8.69795 | −0.293709 | −0.146854 | − | 0.989158i | \(-0.546915\pi\) | ||||
−0.146854 | + | 0.989158i | \(0.546915\pi\) | |||||||
\(878\) | −54.6131 | −1.84310 | ||||||||
\(879\) | 11.4164 | 0.385066 | ||||||||
\(880\) | 52.3624 | 1.76513 | ||||||||
\(881\) | −53.1014 | −1.78903 | −0.894515 | − | 0.447038i | \(-0.852479\pi\) | ||||
−0.894515 | + | 0.447038i | \(0.852479\pi\) | |||||||
\(882\) | 14.4120 | 0.485276 | ||||||||
\(883\) | −25.8248 | −0.869074 | −0.434537 | − | 0.900654i | \(-0.643088\pi\) | ||||
−0.434537 | + | 0.900654i | \(0.643088\pi\) | |||||||
\(884\) | −21.6441 | −0.727970 | ||||||||
\(885\) | −48.8352 | −1.64158 | ||||||||
\(886\) | 21.1762 | 0.711428 | ||||||||
\(887\) | 39.5207 | 1.32698 | 0.663488 | − | 0.748187i | \(-0.269075\pi\) | ||||
0.663488 | + | 0.748187i | \(0.269075\pi\) | |||||||
\(888\) | 24.7547 | 0.830713 | ||||||||
\(889\) | 16.7413 | 0.561485 | ||||||||
\(890\) | −25.1244 | −0.842172 | ||||||||
\(891\) | −10.4365 | −0.349637 | ||||||||
\(892\) | −4.55948 | −0.152663 | ||||||||
\(893\) | −17.2468 | −0.577142 | ||||||||
\(894\) | −21.1259 | −0.706555 | ||||||||
\(895\) | −16.6533 | −0.556659 | ||||||||
\(896\) | 63.2759 | 2.11390 | ||||||||
\(897\) | −1.92405 | −0.0642421 | ||||||||
\(898\) | −69.4157 | −2.31643 | ||||||||
\(899\) | 0.0528306 | 0.00176200 | ||||||||
\(900\) | −88.0904 | −2.93635 | ||||||||
\(901\) | −72.6782 | −2.42126 | ||||||||
\(902\) | −121.171 | −4.03456 | ||||||||
\(903\) | −8.60050 | −0.286207 | ||||||||
\(904\) | −71.6517 | −2.38310 | ||||||||
\(905\) | −60.6200 | −2.01508 | ||||||||
\(906\) | −0.921860 | −0.0306267 | ||||||||
\(907\) | −2.91718 | −0.0968633 | −0.0484317 | − | 0.998826i | \(-0.515422\pi\) | ||||
−0.0484317 | + | 0.998826i | \(0.515422\pi\) | |||||||
\(908\) | 50.6563 | 1.68109 | ||||||||
\(909\) | −40.9598 | −1.35855 | ||||||||
\(910\) | −27.8781 | −0.924151 | ||||||||
\(911\) | −30.6229 | −1.01458 | −0.507290 | − | 0.861775i | \(-0.669353\pi\) | ||||
−0.507290 | + | 0.861775i | \(0.669353\pi\) | |||||||
\(912\) | 8.38067 | 0.277512 | ||||||||
\(913\) | 19.3887 | 0.641672 | ||||||||
\(914\) | 29.5338 | 0.976890 | ||||||||
\(915\) | −52.1569 | −1.72425 | ||||||||
\(916\) | 25.8177 | 0.853040 | ||||||||
\(917\) | −25.5443 | −0.843546 | ||||||||
\(918\) | 65.8532 | 2.17348 | ||||||||
\(919\) | −24.0520 | −0.793403 | −0.396702 | − | 0.917948i | \(-0.629845\pi\) | ||||
−0.396702 | + | 0.917948i | \(0.629845\pi\) | |||||||
\(920\) | 40.9856 | 1.35125 | ||||||||
\(921\) | 21.5263 | 0.709316 | ||||||||
\(922\) | 79.9697 | 2.63366 | ||||||||
\(923\) | 6.56124 | 0.215966 | ||||||||
\(924\) | −43.2172 | −1.42174 | ||||||||
\(925\) | −62.6549 | −2.06008 | ||||||||
\(926\) | −64.7998 | −2.12945 | ||||||||
\(927\) | −2.79466 | −0.0917888 | ||||||||
\(928\) | 0.0103493 | 0.000339731 0 | ||||||||
\(929\) | −23.2196 | −0.761810 | −0.380905 | − | 0.924614i | \(-0.624388\pi\) | ||||
−0.380905 | + | 0.924614i | \(0.624388\pi\) | |||||||
\(930\) | 46.7403 | 1.53267 | ||||||||
\(931\) | 7.65600 | 0.250915 | ||||||||
\(932\) | −42.3721 | −1.38794 | ||||||||
\(933\) | −16.6769 | −0.545977 | ||||||||
\(934\) | −72.8701 | −2.38438 | ||||||||
\(935\) | 92.9259 | 3.03900 | ||||||||
\(936\) | −9.60000 | −0.313786 | ||||||||
\(937\) | 45.5877 | 1.48928 | 0.744642 | − | 0.667464i | \(-0.232620\pi\) | ||||
0.744642 | + | 0.667464i | \(0.232620\pi\) | |||||||
\(938\) | 75.3225 | 2.45937 | ||||||||
\(939\) | 8.04155 | 0.262426 | ||||||||
\(940\) | 91.4110 | 2.98150 | ||||||||
\(941\) | −44.0343 | −1.43548 | −0.717738 | − | 0.696313i | \(-0.754822\pi\) | ||||
−0.717738 | + | 0.696313i | \(0.754822\pi\) | |||||||
\(942\) | −32.3268 | −1.05326 | ||||||||
\(943\) | −28.3778 | −0.924109 | ||||||||
\(944\) | 46.9626 | 1.52850 | ||||||||
\(945\) | 55.9887 | 1.82131 | ||||||||
\(946\) | −30.7024 | −0.998221 | ||||||||
\(947\) | −30.4291 | −0.988814 | −0.494407 | − | 0.869230i | \(-0.664615\pi\) | ||||
−0.494407 | + | 0.869230i | \(0.664615\pi\) | |||||||
\(948\) | −26.2041 | −0.851070 | ||||||||
\(949\) | −1.41725 | −0.0460057 | ||||||||
\(950\) | −70.8938 | −2.30010 | ||||||||
\(951\) | −18.4213 | −0.597353 | ||||||||
\(952\) | −83.6642 | −2.71157 | ||||||||
\(953\) | −29.9776 | −0.971070 | −0.485535 | − | 0.874217i | \(-0.661375\pi\) | ||||
−0.485535 | + | 0.874217i | \(0.661375\pi\) | |||||||
\(954\) | −66.4594 | −2.15170 | ||||||||
\(955\) | −83.7317 | −2.70949 | ||||||||
\(956\) | 25.3115 | 0.818634 | ||||||||
\(957\) | −0.0338203 | −0.00109325 | ||||||||
\(958\) | 102.879 | 3.32388 | ||||||||
\(959\) | 18.0817 | 0.583888 | ||||||||
\(960\) | 32.0301 | 1.03377 | ||||||||
\(961\) | 0.219966 | 0.00709569 | ||||||||
\(962\) | −14.0773 | −0.453869 | ||||||||
\(963\) | −16.0474 | −0.517121 | ||||||||
\(964\) | −23.1776 | −0.746499 | ||||||||
\(965\) | −90.8971 | −2.92608 | ||||||||
\(966\) | −15.3333 | −0.493342 | ||||||||
\(967\) | −5.76588 | −0.185418 | −0.0927091 | − | 0.995693i | \(-0.529553\pi\) | ||||
−0.0927091 | + | 0.995693i | \(0.529553\pi\) | |||||||
\(968\) | −24.5672 | −0.789619 | ||||||||
\(969\) | 14.8729 | 0.477787 | ||||||||
\(970\) | 29.9122 | 0.960424 | ||||||||
\(971\) | 36.9145 | 1.18464 | 0.592321 | − | 0.805702i | \(-0.298212\pi\) | ||||
0.592321 | + | 0.805702i | \(0.298212\pi\) | |||||||
\(972\) | 62.5991 | 2.00787 | ||||||||
\(973\) | −29.3240 | −0.940085 | ||||||||
\(974\) | −91.1916 | −2.92197 | ||||||||
\(975\) | −8.55586 | −0.274007 | ||||||||
\(976\) | 50.1570 | 1.60549 | ||||||||
\(977\) | 44.8482 | 1.43482 | 0.717411 | − | 0.696650i | \(-0.245327\pi\) | ||||
0.717411 | + | 0.696650i | \(0.245327\pi\) | |||||||
\(978\) | 8.61504 | 0.275479 | ||||||||
\(979\) | 10.7431 | 0.343350 | ||||||||
\(980\) | −40.5782 | −1.29622 | ||||||||
\(981\) | 32.9379 | 1.05163 | ||||||||
\(982\) | −69.9186 | −2.23119 | ||||||||
\(983\) | 25.3840 | 0.809623 | 0.404811 | − | 0.914400i | \(-0.367337\pi\) | ||||
0.404811 | + | 0.914400i | \(0.367337\pi\) | |||||||
\(984\) | 49.8573 | 1.58939 | ||||||||
\(985\) | 91.2875 | 2.90866 | ||||||||
\(986\) | −0.134984 | −0.00429875 | ||||||||
\(987\) | −16.5876 | −0.527989 | ||||||||
\(988\) | −10.5141 | −0.334497 | ||||||||
\(989\) | −7.19038 | −0.228641 | ||||||||
\(990\) | 84.9745 | 2.70067 | ||||||||
\(991\) | 53.6456 | 1.70411 | 0.852054 | − | 0.523454i | \(-0.175357\pi\) | ||||
0.852054 | + | 0.523454i | \(0.175357\pi\) | |||||||
\(992\) | 6.11585 | 0.194178 | ||||||||
\(993\) | −8.98877 | −0.285250 | ||||||||
\(994\) | 52.2886 | 1.65849 | ||||||||
\(995\) | −18.1645 | −0.575853 | ||||||||
\(996\) | −16.4474 | −0.521157 | ||||||||
\(997\) | −17.1353 | −0.542681 | −0.271340 | − | 0.962483i | \(-0.587467\pi\) | ||||
−0.271340 | + | 0.962483i | \(0.587467\pi\) | |||||||
\(998\) | −17.2507 | −0.546062 | ||||||||
\(999\) | 28.2719 | 0.894483 |
(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 | 4007.2.a.b.1.18 | ✓ | 195 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4007.2.a.b.1.18 | ✓ | 195 | 1.1 | even | 1 | trivial |