Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, 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("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(1\) |
Dimension: | \(152\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70039 | −1.90947 | −0.954733 | − | 0.297463i | \(-0.903860\pi\) | ||||
−0.954733 | + | 0.297463i | \(0.903860\pi\) | |||||||
\(3\) | 3.13054 | 1.80742 | 0.903708 | − | 0.428149i | \(-0.140834\pi\) | ||||
0.903708 | + | 0.428149i | \(0.140834\pi\) | |||||||
\(4\) | 5.29213 | 2.64606 | ||||||||
\(5\) | −0.910228 | −0.407066 | −0.203533 | − | 0.979068i | \(-0.565242\pi\) | ||||
−0.203533 | + | 0.979068i | \(0.565242\pi\) | |||||||
\(6\) | −8.45368 | −3.45120 | ||||||||
\(7\) | 0.335007 | 0.126621 | 0.0633104 | − | 0.997994i | \(-0.479834\pi\) | ||||
0.0633104 | + | 0.997994i | \(0.479834\pi\) | |||||||
\(8\) | −8.89004 | −3.14310 | ||||||||
\(9\) | 6.80026 | 2.26675 | ||||||||
\(10\) | 2.45797 | 0.777280 | ||||||||
\(11\) | −2.87116 | −0.865688 | −0.432844 | − | 0.901469i | \(-0.642490\pi\) | ||||
−0.432844 | + | 0.901469i | \(0.642490\pi\) | |||||||
\(12\) | 16.5672 | 4.78254 | ||||||||
\(13\) | 1.35841 | 0.376755 | 0.188378 | − | 0.982097i | \(-0.439677\pi\) | ||||
0.188378 | + | 0.982097i | \(0.439677\pi\) | |||||||
\(14\) | −0.904652 | −0.241778 | ||||||||
\(15\) | −2.84950 | −0.735739 | ||||||||
\(16\) | 13.4224 | 3.35559 | ||||||||
\(17\) | −1.80293 | −0.437275 | −0.218637 | − | 0.975806i | \(-0.570161\pi\) | ||||
−0.218637 | + | 0.975806i | \(0.570161\pi\) | |||||||
\(18\) | −18.3634 | −4.32829 | ||||||||
\(19\) | 6.84396 | 1.57011 | 0.785057 | − | 0.619424i | \(-0.212634\pi\) | ||||
0.785057 | + | 0.619424i | \(0.212634\pi\) | |||||||
\(20\) | −4.81704 | −1.07712 | ||||||||
\(21\) | 1.04875 | 0.228857 | ||||||||
\(22\) | 7.75327 | 1.65300 | ||||||||
\(23\) | −6.94339 | −1.44780 | −0.723899 | − | 0.689906i | \(-0.757652\pi\) | ||||
−0.723899 | + | 0.689906i | \(0.757652\pi\) | |||||||
\(24\) | −27.8306 | −5.68090 | ||||||||
\(25\) | −4.17148 | −0.834297 | ||||||||
\(26\) | −3.66824 | −0.719401 | ||||||||
\(27\) | 11.8969 | 2.28955 | ||||||||
\(28\) | 1.77290 | 0.335047 | ||||||||
\(29\) | −7.95760 | −1.47769 | −0.738845 | − | 0.673876i | \(-0.764628\pi\) | ||||
−0.738845 | + | 0.673876i | \(0.764628\pi\) | |||||||
\(30\) | 7.69478 | 1.40487 | ||||||||
\(31\) | 0.990375 | 0.177877 | 0.0889383 | − | 0.996037i | \(-0.471653\pi\) | ||||
0.0889383 | + | 0.996037i | \(0.471653\pi\) | |||||||
\(32\) | −18.4656 | −3.26428 | ||||||||
\(33\) | −8.98828 | −1.56466 | ||||||||
\(34\) | 4.86862 | 0.834962 | ||||||||
\(35\) | −0.304933 | −0.0515431 | ||||||||
\(36\) | 35.9879 | 5.99798 | ||||||||
\(37\) | −9.83248 | −1.61645 | −0.808225 | − | 0.588874i | \(-0.799571\pi\) | ||||
−0.808225 | + | 0.588874i | \(0.799571\pi\) | |||||||
\(38\) | −18.4814 | −2.99808 | ||||||||
\(39\) | 4.25255 | 0.680954 | ||||||||
\(40\) | 8.09197 | 1.27945 | ||||||||
\(41\) | −5.45758 | −0.852331 | −0.426165 | − | 0.904645i | \(-0.640136\pi\) | ||||
−0.426165 | + | 0.904645i | \(0.640136\pi\) | |||||||
\(42\) | −2.83205 | −0.436994 | ||||||||
\(43\) | −12.1971 | −1.86005 | −0.930023 | − | 0.367501i | \(-0.880213\pi\) | ||||
−0.930023 | + | 0.367501i | \(0.880213\pi\) | |||||||
\(44\) | −15.1946 | −2.29067 | ||||||||
\(45\) | −6.18979 | −0.922720 | ||||||||
\(46\) | 18.7499 | 2.76452 | ||||||||
\(47\) | −11.1117 | −1.62081 | −0.810403 | − | 0.585873i | \(-0.800752\pi\) | ||||
−0.810403 | + | 0.585873i | \(0.800752\pi\) | |||||||
\(48\) | 42.0192 | 6.06495 | ||||||||
\(49\) | −6.88777 | −0.983967 | ||||||||
\(50\) | 11.2647 | 1.59306 | ||||||||
\(51\) | −5.64414 | −0.790338 | ||||||||
\(52\) | 7.18888 | 0.996918 | ||||||||
\(53\) | −10.4892 | −1.44080 | −0.720402 | − | 0.693557i | \(-0.756043\pi\) | ||||
−0.720402 | + | 0.693557i | \(0.756043\pi\) | |||||||
\(54\) | −32.1262 | −4.37183 | ||||||||
\(55\) | 2.61341 | 0.352393 | ||||||||
\(56\) | −2.97823 | −0.397983 | ||||||||
\(57\) | 21.4253 | 2.83785 | ||||||||
\(58\) | 21.4887 | 2.82160 | ||||||||
\(59\) | 8.31097 | 1.08200 | 0.540998 | − | 0.841024i | \(-0.318047\pi\) | ||||
0.540998 | + | 0.841024i | \(0.318047\pi\) | |||||||
\(60\) | −15.0799 | −1.94681 | ||||||||
\(61\) | 7.42467 | 0.950632 | 0.475316 | − | 0.879815i | \(-0.342334\pi\) | ||||
0.475316 | + | 0.879815i | \(0.342334\pi\) | |||||||
\(62\) | −2.67440 | −0.339649 | ||||||||
\(63\) | 2.27814 | 0.287018 | ||||||||
\(64\) | 23.0196 | 2.87745 | ||||||||
\(65\) | −1.23646 | −0.153364 | ||||||||
\(66\) | 24.2719 | 2.98766 | ||||||||
\(67\) | 1.37216 | 0.167636 | 0.0838182 | − | 0.996481i | \(-0.473288\pi\) | ||||
0.0838182 | + | 0.996481i | \(0.473288\pi\) | |||||||
\(68\) | −9.54134 | −1.15706 | ||||||||
\(69\) | −21.7365 | −2.61677 | ||||||||
\(70\) | 0.823440 | 0.0984199 | ||||||||
\(71\) | 2.67864 | 0.317897 | 0.158948 | − | 0.987287i | \(-0.449190\pi\) | ||||
0.158948 | + | 0.987287i | \(0.449190\pi\) | |||||||
\(72\) | −60.4546 | −7.12464 | ||||||||
\(73\) | −3.12188 | −0.365388 | −0.182694 | − | 0.983170i | \(-0.558482\pi\) | ||||
−0.182694 | + | 0.983170i | \(0.558482\pi\) | |||||||
\(74\) | 26.5516 | 3.08656 | ||||||||
\(75\) | −13.0590 | −1.50792 | ||||||||
\(76\) | 36.2191 | 4.15462 | ||||||||
\(77\) | −0.961861 | −0.109614 | ||||||||
\(78\) | −11.4836 | −1.30026 | ||||||||
\(79\) | −14.0008 | −1.57522 | −0.787609 | − | 0.616175i | \(-0.788681\pi\) | ||||
−0.787609 | + | 0.616175i | \(0.788681\pi\) | |||||||
\(80\) | −12.2174 | −1.36595 | ||||||||
\(81\) | 16.8428 | 1.87142 | ||||||||
\(82\) | 14.7376 | 1.62750 | ||||||||
\(83\) | 17.8567 | 1.96003 | 0.980016 | − | 0.198917i | \(-0.0637423\pi\) | ||||
0.980016 | + | 0.198917i | \(0.0637423\pi\) | |||||||
\(84\) | 5.55014 | 0.605569 | ||||||||
\(85\) | 1.64108 | 0.178000 | ||||||||
\(86\) | 32.9371 | 3.55170 | ||||||||
\(87\) | −24.9116 | −2.67080 | ||||||||
\(88\) | 25.5248 | 2.72095 | ||||||||
\(89\) | 2.60497 | 0.276127 | 0.138063 | − | 0.990423i | \(-0.455912\pi\) | ||||
0.138063 | + | 0.990423i | \(0.455912\pi\) | |||||||
\(90\) | 16.7149 | 1.76190 | ||||||||
\(91\) | 0.455077 | 0.0477051 | ||||||||
\(92\) | −36.7453 | −3.83096 | ||||||||
\(93\) | 3.10041 | 0.321497 | ||||||||
\(94\) | 30.0059 | 3.09488 | ||||||||
\(95\) | −6.22957 | −0.639140 | ||||||||
\(96\) | −57.8071 | −5.89992 | ||||||||
\(97\) | 10.7020 | 1.08662 | 0.543310 | − | 0.839532i | \(-0.317171\pi\) | ||||
0.543310 | + | 0.839532i | \(0.317171\pi\) | |||||||
\(98\) | 18.5997 | 1.87885 | ||||||||
\(99\) | −19.5247 | −1.96230 | ||||||||
\(100\) | −22.0760 | −2.20760 | ||||||||
\(101\) | 17.7598 | 1.76717 | 0.883584 | − | 0.468274i | \(-0.155124\pi\) | ||||
0.883584 | + | 0.468274i | \(0.155124\pi\) | |||||||
\(102\) | 15.2414 | 1.50912 | ||||||||
\(103\) | −16.6991 | −1.64541 | −0.822705 | − | 0.568468i | \(-0.807536\pi\) | ||||
−0.822705 | + | 0.568468i | \(0.807536\pi\) | |||||||
\(104\) | −12.0763 | −1.18418 | ||||||||
\(105\) | −0.954605 | −0.0931599 | ||||||||
\(106\) | 28.3250 | 2.75117 | ||||||||
\(107\) | 3.37830 | 0.326593 | 0.163296 | − | 0.986577i | \(-0.447787\pi\) | ||||
0.163296 | + | 0.986577i | \(0.447787\pi\) | |||||||
\(108\) | 62.9597 | 6.05830 | ||||||||
\(109\) | 18.3509 | 1.75770 | 0.878851 | − | 0.477097i | \(-0.158311\pi\) | ||||
0.878851 | + | 0.477097i | \(0.158311\pi\) | |||||||
\(110\) | −7.05725 | −0.672882 | ||||||||
\(111\) | −30.7809 | −2.92160 | ||||||||
\(112\) | 4.49659 | 0.424888 | ||||||||
\(113\) | 4.33945 | 0.408221 | 0.204110 | − | 0.978948i | \(-0.434570\pi\) | ||||
0.204110 | + | 0.978948i | \(0.434570\pi\) | |||||||
\(114\) | −57.8567 | −5.41878 | ||||||||
\(115\) | 6.32007 | 0.589350 | ||||||||
\(116\) | −42.1126 | −3.91006 | ||||||||
\(117\) | 9.23755 | 0.854011 | ||||||||
\(118\) | −22.4429 | −2.06604 | ||||||||
\(119\) | −0.603995 | −0.0553681 | ||||||||
\(120\) | 25.3322 | 2.31250 | ||||||||
\(121\) | −2.75642 | −0.250584 | ||||||||
\(122\) | −20.0495 | −1.81520 | ||||||||
\(123\) | −17.0852 | −1.54052 | ||||||||
\(124\) | 5.24119 | 0.470673 | ||||||||
\(125\) | 8.34814 | 0.746681 | ||||||||
\(126\) | −6.15187 | −0.548052 | ||||||||
\(127\) | −0.610893 | −0.0542080 | −0.0271040 | − | 0.999633i | \(-0.508629\pi\) | ||||
−0.0271040 | + | 0.999633i | \(0.508629\pi\) | |||||||
\(128\) | −25.2308 | −2.23011 | ||||||||
\(129\) | −38.1836 | −3.36188 | ||||||||
\(130\) | 3.33894 | 0.292844 | ||||||||
\(131\) | 1.12138 | 0.0979759 | 0.0489879 | − | 0.998799i | \(-0.484400\pi\) | ||||
0.0489879 | + | 0.998799i | \(0.484400\pi\) | |||||||
\(132\) | −47.5671 | −4.14019 | ||||||||
\(133\) | 2.29278 | 0.198809 | ||||||||
\(134\) | −3.70538 | −0.320096 | ||||||||
\(135\) | −10.8289 | −0.932000 | ||||||||
\(136\) | 16.0281 | 1.37440 | ||||||||
\(137\) | −5.91022 | −0.504944 | −0.252472 | − | 0.967604i | \(-0.581244\pi\) | ||||
−0.252472 | + | 0.967604i | \(0.581244\pi\) | |||||||
\(138\) | 58.6972 | 4.99664 | ||||||||
\(139\) | −7.92180 | −0.671918 | −0.335959 | − | 0.941877i | \(-0.609060\pi\) | ||||
−0.335959 | + | 0.941877i | \(0.609060\pi\) | |||||||
\(140\) | −1.61375 | −0.136386 | ||||||||
\(141\) | −34.7855 | −2.92947 | ||||||||
\(142\) | −7.23339 | −0.607013 | ||||||||
\(143\) | −3.90022 | −0.326152 | ||||||||
\(144\) | 91.2756 | 7.60630 | ||||||||
\(145\) | 7.24323 | 0.601518 | ||||||||
\(146\) | 8.43030 | 0.697697 | ||||||||
\(147\) | −21.5624 | −1.77844 | ||||||||
\(148\) | −52.0347 | −4.27723 | ||||||||
\(149\) | 14.3922 | 1.17906 | 0.589529 | − | 0.807748i | \(-0.299314\pi\) | ||||
0.589529 | + | 0.807748i | \(0.299314\pi\) | |||||||
\(150\) | 35.2644 | 2.87933 | ||||||||
\(151\) | −3.75370 | −0.305472 | −0.152736 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152736 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(152\) | −60.8431 | −4.93503 | ||||||||
\(153\) | −12.2604 | −0.991195 | ||||||||
\(154\) | 2.59740 | 0.209305 | ||||||||
\(155\) | −0.901467 | −0.0724076 | ||||||||
\(156\) | 22.5051 | 1.80185 | ||||||||
\(157\) | 3.81315 | 0.304322 | 0.152161 | − | 0.988356i | \(-0.451377\pi\) | ||||
0.152161 | + | 0.988356i | \(0.451377\pi\) | |||||||
\(158\) | 37.8078 | 3.00783 | ||||||||
\(159\) | −32.8369 | −2.60413 | ||||||||
\(160\) | 16.8079 | 1.32878 | ||||||||
\(161\) | −2.32609 | −0.183321 | ||||||||
\(162\) | −45.4822 | −3.57342 | ||||||||
\(163\) | 9.08991 | 0.711977 | 0.355988 | − | 0.934490i | \(-0.384144\pi\) | ||||
0.355988 | + | 0.934490i | \(0.384144\pi\) | |||||||
\(164\) | −28.8822 | −2.25532 | ||||||||
\(165\) | 8.18139 | 0.636920 | ||||||||
\(166\) | −48.2203 | −3.74262 | ||||||||
\(167\) | −23.6192 | −1.82771 | −0.913853 | − | 0.406045i | \(-0.866908\pi\) | ||||
−0.913853 | + | 0.406045i | \(0.866908\pi\) | |||||||
\(168\) | −9.32346 | −0.719320 | ||||||||
\(169\) | −11.1547 | −0.858056 | ||||||||
\(170\) | −4.43156 | −0.339885 | ||||||||
\(171\) | 46.5408 | 3.55906 | ||||||||
\(172\) | −64.5488 | −4.92180 | ||||||||
\(173\) | 23.6533 | 1.79832 | 0.899162 | − | 0.437616i | \(-0.144177\pi\) | ||||
0.899162 | + | 0.437616i | \(0.144177\pi\) | |||||||
\(174\) | 67.2710 | 5.09980 | ||||||||
\(175\) | −1.39748 | −0.105639 | ||||||||
\(176\) | −38.5378 | −2.90489 | ||||||||
\(177\) | 26.0178 | 1.95562 | ||||||||
\(178\) | −7.03445 | −0.527254 | ||||||||
\(179\) | −3.66446 | −0.273895 | −0.136947 | − | 0.990578i | \(-0.543729\pi\) | ||||
−0.136947 | + | 0.990578i | \(0.543729\pi\) | |||||||
\(180\) | −32.7572 | −2.44157 | ||||||||
\(181\) | −23.5154 | −1.74789 | −0.873944 | − | 0.486027i | \(-0.838446\pi\) | ||||
−0.873944 | + | 0.486027i | \(0.838446\pi\) | |||||||
\(182\) | −1.22889 | −0.0910913 | ||||||||
\(183\) | 23.2432 | 1.71819 | ||||||||
\(184\) | 61.7270 | 4.55058 | ||||||||
\(185\) | 8.94980 | 0.658002 | ||||||||
\(186\) | −8.37232 | −0.613888 | ||||||||
\(187\) | 5.17651 | 0.378544 | ||||||||
\(188\) | −58.8045 | −4.28876 | ||||||||
\(189\) | 3.98554 | 0.289905 | ||||||||
\(190\) | 16.8223 | 1.22042 | ||||||||
\(191\) | 22.6385 | 1.63807 | 0.819034 | − | 0.573745i | \(-0.194510\pi\) | ||||
0.819034 | + | 0.573745i | \(0.194510\pi\) | |||||||
\(192\) | 72.0637 | 5.20075 | ||||||||
\(193\) | 5.06900 | 0.364875 | 0.182437 | − | 0.983217i | \(-0.441601\pi\) | ||||
0.182437 | + | 0.983217i | \(0.441601\pi\) | |||||||
\(194\) | −28.8995 | −2.07486 | ||||||||
\(195\) | −3.87079 | −0.277193 | ||||||||
\(196\) | −36.4510 | −2.60364 | ||||||||
\(197\) | −23.1746 | −1.65112 | −0.825559 | − | 0.564316i | \(-0.809140\pi\) | ||||
−0.825559 | + | 0.564316i | \(0.809140\pi\) | |||||||
\(198\) | 52.7243 | 3.74695 | ||||||||
\(199\) | 4.50709 | 0.319499 | 0.159749 | − | 0.987158i | \(-0.448931\pi\) | ||||
0.159749 | + | 0.987158i | \(0.448931\pi\) | |||||||
\(200\) | 37.0847 | 2.62228 | ||||||||
\(201\) | 4.29561 | 0.302989 | ||||||||
\(202\) | −47.9585 | −3.37435 | ||||||||
\(203\) | −2.66586 | −0.187106 | ||||||||
\(204\) | −29.8695 | −2.09128 | ||||||||
\(205\) | 4.96764 | 0.346955 | ||||||||
\(206\) | 45.0941 | 3.14186 | ||||||||
\(207\) | −47.2169 | −3.28180 | ||||||||
\(208\) | 18.2331 | 1.26424 | ||||||||
\(209\) | −19.6501 | −1.35923 | ||||||||
\(210\) | 2.57781 | 0.177886 | ||||||||
\(211\) | 4.34279 | 0.298970 | 0.149485 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149485 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(212\) | −55.5103 | −3.81246 | ||||||||
\(213\) | 8.38559 | 0.574571 | ||||||||
\(214\) | −9.12274 | −0.623618 | ||||||||
\(215\) | 11.1022 | 0.757162 | ||||||||
\(216\) | −105.764 | −7.19630 | ||||||||
\(217\) | 0.331783 | 0.0225229 | ||||||||
\(218\) | −49.5548 | −3.35627 | ||||||||
\(219\) | −9.77316 | −0.660409 | ||||||||
\(220\) | 13.8305 | 0.932453 | ||||||||
\(221\) | −2.44912 | −0.164746 | ||||||||
\(222\) | 83.1207 | 5.57869 | ||||||||
\(223\) | −2.56579 | −0.171818 | −0.0859090 | − | 0.996303i | \(-0.527379\pi\) | ||||
−0.0859090 | + | 0.996303i | \(0.527379\pi\) | |||||||
\(224\) | −6.18610 | −0.413326 | ||||||||
\(225\) | −28.3672 | −1.89115 | ||||||||
\(226\) | −11.7182 | −0.779484 | ||||||||
\(227\) | 8.46916 | 0.562118 | 0.281059 | − | 0.959691i | \(-0.409314\pi\) | ||||
0.281059 | + | 0.959691i | \(0.409314\pi\) | |||||||
\(228\) | 113.385 | 7.50913 | ||||||||
\(229\) | 4.27224 | 0.282317 | 0.141159 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141159 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(230\) | −17.0667 | −1.12534 | ||||||||
\(231\) | −3.01114 | −0.198119 | ||||||||
\(232\) | 70.7434 | 4.64453 | ||||||||
\(233\) | −30.2017 | −1.97858 | −0.989290 | − | 0.145965i | \(-0.953371\pi\) | ||||
−0.989290 | + | 0.145965i | \(0.953371\pi\) | |||||||
\(234\) | −24.9450 | −1.63071 | ||||||||
\(235\) | 10.1142 | 0.659776 | ||||||||
\(236\) | 43.9827 | 2.86303 | ||||||||
\(237\) | −43.8302 | −2.84707 | ||||||||
\(238\) | 1.63102 | 0.105724 | ||||||||
\(239\) | 12.7096 | 0.822115 | 0.411057 | − | 0.911609i | \(-0.365160\pi\) | ||||
0.411057 | + | 0.911609i | \(0.365160\pi\) | |||||||
\(240\) | −38.2470 | −2.46884 | ||||||||
\(241\) | 9.18172 | 0.591447 | 0.295723 | − | 0.955274i | \(-0.404439\pi\) | ||||
0.295723 | + | 0.955274i | \(0.404439\pi\) | |||||||
\(242\) | 7.44343 | 0.478482 | ||||||||
\(243\) | 17.0364 | 1.09288 | ||||||||
\(244\) | 39.2923 | 2.51543 | ||||||||
\(245\) | 6.26944 | 0.400540 | ||||||||
\(246\) | 46.1367 | 2.94157 | ||||||||
\(247\) | 9.29691 | 0.591548 | ||||||||
\(248\) | −8.80447 | −0.559085 | ||||||||
\(249\) | 55.9012 | 3.54260 | ||||||||
\(250\) | −22.5433 | −1.42576 | ||||||||
\(251\) | 12.7925 | 0.807456 | 0.403728 | − | 0.914879i | \(-0.367714\pi\) | ||||
0.403728 | + | 0.914879i | \(0.367714\pi\) | |||||||
\(252\) | 12.0562 | 0.759469 | ||||||||
\(253\) | 19.9356 | 1.25334 | ||||||||
\(254\) | 1.64965 | 0.103508 | ||||||||
\(255\) | 5.13746 | 0.321720 | ||||||||
\(256\) | 22.0940 | 1.38088 | ||||||||
\(257\) | 10.8812 | 0.678749 | 0.339375 | − | 0.940651i | \(-0.389785\pi\) | ||||
0.339375 | + | 0.940651i | \(0.389785\pi\) | |||||||
\(258\) | 103.111 | 6.41939 | ||||||||
\(259\) | −3.29395 | −0.204676 | ||||||||
\(260\) | −6.54352 | −0.405812 | ||||||||
\(261\) | −54.1138 | −3.34956 | ||||||||
\(262\) | −3.02818 | −0.187082 | ||||||||
\(263\) | 12.9874 | 0.800837 | 0.400419 | − | 0.916332i | \(-0.368865\pi\) | ||||
0.400419 | + | 0.916332i | \(0.368865\pi\) | |||||||
\(264\) | 79.9062 | 4.91789 | ||||||||
\(265\) | 9.54758 | 0.586503 | ||||||||
\(266\) | −6.19141 | −0.379619 | ||||||||
\(267\) | 8.15496 | 0.499076 | ||||||||
\(268\) | 7.26166 | 0.443577 | ||||||||
\(269\) | −14.5566 | −0.887534 | −0.443767 | − | 0.896142i | \(-0.646358\pi\) | ||||
−0.443767 | + | 0.896142i | \(0.646358\pi\) | |||||||
\(270\) | 29.2422 | 1.77962 | ||||||||
\(271\) | −9.36239 | −0.568725 | −0.284362 | − | 0.958717i | \(-0.591782\pi\) | ||||
−0.284362 | + | 0.958717i | \(0.591782\pi\) | |||||||
\(272\) | −24.1996 | −1.46731 | ||||||||
\(273\) | 1.42464 | 0.0862229 | ||||||||
\(274\) | 15.9599 | 0.964174 | ||||||||
\(275\) | 11.9770 | 0.722241 | ||||||||
\(276\) | −115.033 | −6.92415 | ||||||||
\(277\) | 9.79051 | 0.588254 | 0.294127 | − | 0.955766i | \(-0.404971\pi\) | ||||
0.294127 | + | 0.955766i | \(0.404971\pi\) | |||||||
\(278\) | 21.3920 | 1.28301 | ||||||||
\(279\) | 6.73481 | 0.403203 | ||||||||
\(280\) | 2.71087 | 0.162005 | ||||||||
\(281\) | 19.6930 | 1.17478 | 0.587392 | − | 0.809303i | \(-0.300155\pi\) | ||||
0.587392 | + | 0.809303i | \(0.300155\pi\) | |||||||
\(282\) | 93.9347 | 5.59373 | ||||||||
\(283\) | 14.1195 | 0.839317 | 0.419658 | − | 0.907682i | \(-0.362150\pi\) | ||||
0.419658 | + | 0.907682i | \(0.362150\pi\) | |||||||
\(284\) | 14.1757 | 0.841174 | ||||||||
\(285\) | −19.5019 | −1.15519 | ||||||||
\(286\) | 10.5321 | 0.622777 | ||||||||
\(287\) | −1.82833 | −0.107923 | ||||||||
\(288\) | −125.571 | −7.39933 | ||||||||
\(289\) | −13.7494 | −0.808791 | ||||||||
\(290\) | −19.5596 | −1.14858 | ||||||||
\(291\) | 33.5029 | 1.96397 | ||||||||
\(292\) | −16.5214 | −0.966841 | ||||||||
\(293\) | 23.7634 | 1.38827 | 0.694137 | − | 0.719843i | \(-0.255786\pi\) | ||||
0.694137 | + | 0.719843i | \(0.255786\pi\) | |||||||
\(294\) | 58.2270 | 3.39587 | ||||||||
\(295\) | −7.56488 | −0.440444 | ||||||||
\(296\) | 87.4111 | 5.08067 | ||||||||
\(297\) | −34.1578 | −1.98204 | ||||||||
\(298\) | −38.8647 | −2.25137 | ||||||||
\(299\) | −9.43197 | −0.545465 | ||||||||
\(300\) | −69.1098 | −3.99006 | ||||||||
\(301\) | −4.08613 | −0.235521 | ||||||||
\(302\) | 10.1365 | 0.583288 | ||||||||
\(303\) | 55.5977 | 3.19401 | ||||||||
\(304\) | 91.8621 | 5.26865 | ||||||||
\(305\) | −6.75815 | −0.386970 | ||||||||
\(306\) | 33.1079 | 1.89265 | ||||||||
\(307\) | 4.23632 | 0.241780 | 0.120890 | − | 0.992666i | \(-0.461425\pi\) | ||||
0.120890 | + | 0.992666i | \(0.461425\pi\) | |||||||
\(308\) | −5.09029 | −0.290046 | ||||||||
\(309\) | −52.2771 | −2.97394 | ||||||||
\(310\) | 2.43432 | 0.138260 | ||||||||
\(311\) | −20.6468 | −1.17077 | −0.585386 | − | 0.810755i | \(-0.699057\pi\) | ||||
−0.585386 | + | 0.810755i | \(0.699057\pi\) | |||||||
\(312\) | −37.8054 | −2.14031 | ||||||||
\(313\) | 11.5386 | 0.652202 | 0.326101 | − | 0.945335i | \(-0.394265\pi\) | ||||
0.326101 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(314\) | −10.2970 | −0.581093 | ||||||||
\(315\) | −2.07363 | −0.116836 | ||||||||
\(316\) | −74.0942 | −4.16813 | ||||||||
\(317\) | 12.4923 | 0.701637 | 0.350819 | − | 0.936443i | \(-0.385903\pi\) | ||||
0.350819 | + | 0.936443i | \(0.385903\pi\) | |||||||
\(318\) | 88.6725 | 4.97251 | ||||||||
\(319\) | 22.8476 | 1.27922 | ||||||||
\(320\) | −20.9531 | −1.17131 | ||||||||
\(321\) | 10.5759 | 0.590289 | ||||||||
\(322\) | 6.28135 | 0.350046 | ||||||||
\(323\) | −12.3392 | −0.686571 | ||||||||
\(324\) | 89.1342 | 4.95190 | ||||||||
\(325\) | −5.66659 | −0.314326 | ||||||||
\(326\) | −24.5463 | −1.35950 | ||||||||
\(327\) | 57.4483 | 3.17690 | ||||||||
\(328\) | 48.5181 | 2.67896 | ||||||||
\(329\) | −3.72250 | −0.205228 | ||||||||
\(330\) | −22.0930 | −1.21618 | ||||||||
\(331\) | −19.8172 | −1.08925 | −0.544626 | − | 0.838679i | \(-0.683328\pi\) | ||||
−0.544626 | + | 0.838679i | \(0.683328\pi\) | |||||||
\(332\) | 94.5002 | 5.18637 | ||||||||
\(333\) | −66.8634 | −3.66409 | ||||||||
\(334\) | 63.7811 | 3.48994 | ||||||||
\(335\) | −1.24898 | −0.0682392 | ||||||||
\(336\) | 14.0767 | 0.767949 | ||||||||
\(337\) | −9.54812 | −0.520119 | −0.260060 | − | 0.965593i | \(-0.583742\pi\) | ||||
−0.260060 | + | 0.965593i | \(0.583742\pi\) | |||||||
\(338\) | 30.1221 | 1.63843 | ||||||||
\(339\) | 13.5848 | 0.737825 | ||||||||
\(340\) | 8.68479 | 0.470999 | ||||||||
\(341\) | −2.84353 | −0.153986 | ||||||||
\(342\) | −125.678 | −6.79591 | ||||||||
\(343\) | −4.65251 | −0.251212 | ||||||||
\(344\) | 108.433 | 5.84632 | ||||||||
\(345\) | 19.7852 | 1.06520 | ||||||||
\(346\) | −63.8731 | −3.43384 | ||||||||
\(347\) | −7.57674 | −0.406741 | −0.203370 | − | 0.979102i | \(-0.565190\pi\) | ||||
−0.203370 | + | 0.979102i | \(0.565190\pi\) | |||||||
\(348\) | −131.835 | −7.06711 | ||||||||
\(349\) | −18.8040 | −1.00656 | −0.503278 | − | 0.864125i | \(-0.667873\pi\) | ||||
−0.503278 | + | 0.864125i | \(0.667873\pi\) | |||||||
\(350\) | 3.77374 | 0.201715 | ||||||||
\(351\) | 16.1608 | 0.862601 | ||||||||
\(352\) | 53.0177 | 2.82585 | ||||||||
\(353\) | 6.75816 | 0.359701 | 0.179850 | − | 0.983694i | \(-0.442439\pi\) | ||||
0.179850 | + | 0.983694i | \(0.442439\pi\) | |||||||
\(354\) | −70.2583 | −3.73419 | ||||||||
\(355\) | −2.43818 | −0.129405 | ||||||||
\(356\) | 13.7858 | 0.730648 | ||||||||
\(357\) | −1.89083 | −0.100073 | ||||||||
\(358\) | 9.89549 | 0.522993 | ||||||||
\(359\) | −35.6097 | −1.87941 | −0.939705 | − | 0.341987i | \(-0.888900\pi\) | ||||
−0.939705 | + | 0.341987i | \(0.888900\pi\) | |||||||
\(360\) | 55.0275 | 2.90020 | ||||||||
\(361\) | 27.8398 | 1.46526 | ||||||||
\(362\) | 63.5009 | 3.33753 | ||||||||
\(363\) | −8.62909 | −0.452910 | ||||||||
\(364\) | 2.40833 | 0.126231 | ||||||||
\(365\) | 2.84162 | 0.148737 | ||||||||
\(366\) | −62.7658 | −3.28082 | ||||||||
\(367\) | −13.5997 | −0.709896 | −0.354948 | − | 0.934886i | \(-0.615501\pi\) | ||||
−0.354948 | + | 0.934886i | \(0.615501\pi\) | |||||||
\(368\) | −93.1967 | −4.85821 | ||||||||
\(369\) | −37.1130 | −1.93202 | ||||||||
\(370\) | −24.1680 | −1.25643 | ||||||||
\(371\) | −3.51396 | −0.182436 | ||||||||
\(372\) | 16.4077 | 0.850702 | ||||||||
\(373\) | 7.69833 | 0.398604 | 0.199302 | − | 0.979938i | \(-0.436132\pi\) | ||||
0.199302 | + | 0.979938i | \(0.436132\pi\) | |||||||
\(374\) | −13.9786 | −0.722817 | ||||||||
\(375\) | 26.1342 | 1.34956 | ||||||||
\(376\) | 98.7833 | 5.09436 | ||||||||
\(377\) | −10.8097 | −0.556727 | ||||||||
\(378\) | −10.7625 | −0.553564 | ||||||||
\(379\) | −1.36932 | −0.0703374 | −0.0351687 | − | 0.999381i | \(-0.511197\pi\) | ||||
−0.0351687 | + | 0.999381i | \(0.511197\pi\) | |||||||
\(380\) | −32.9677 | −1.69121 | ||||||||
\(381\) | −1.91242 | −0.0979764 | ||||||||
\(382\) | −61.1330 | −3.12784 | ||||||||
\(383\) | −25.2003 | −1.28767 | −0.643837 | − | 0.765162i | \(-0.722659\pi\) | ||||
−0.643837 | + | 0.765162i | \(0.722659\pi\) | |||||||
\(384\) | −78.9861 | −4.03074 | ||||||||
\(385\) | 0.875513 | 0.0446203 | ||||||||
\(386\) | −13.6883 | −0.696716 | ||||||||
\(387\) | −82.9437 | −4.21627 | ||||||||
\(388\) | 56.6362 | 2.87527 | ||||||||
\(389\) | −15.1749 | −0.769399 | −0.384700 | − | 0.923042i | \(-0.625695\pi\) | ||||
−0.384700 | + | 0.923042i | \(0.625695\pi\) | |||||||
\(390\) | 10.4527 | 0.529291 | ||||||||
\(391\) | 12.5185 | 0.633085 | ||||||||
\(392\) | 61.2326 | 3.09271 | ||||||||
\(393\) | 3.51054 | 0.177083 | ||||||||
\(394\) | 62.5804 | 3.15276 | ||||||||
\(395\) | 12.7440 | 0.641218 | ||||||||
\(396\) | −103.327 | −5.19238 | ||||||||
\(397\) | 3.34796 | 0.168029 | 0.0840147 | − | 0.996465i | \(-0.473226\pi\) | ||||
0.0840147 | + | 0.996465i | \(0.473226\pi\) | |||||||
\(398\) | −12.1709 | −0.610073 | ||||||||
\(399\) | 7.17763 | 0.359331 | ||||||||
\(400\) | −55.9911 | −2.79956 | ||||||||
\(401\) | −28.3491 | −1.41569 | −0.707844 | − | 0.706368i | \(-0.750332\pi\) | ||||
−0.707844 | + | 0.706368i | \(0.750332\pi\) | |||||||
\(402\) | −11.5998 | −0.578547 | ||||||||
\(403\) | 1.34534 | 0.0670159 | ||||||||
\(404\) | 93.9872 | 4.67604 | ||||||||
\(405\) | −15.3308 | −0.761793 | ||||||||
\(406\) | 7.19886 | 0.357273 | ||||||||
\(407\) | 28.2307 | 1.39934 | ||||||||
\(408\) | 50.1766 | 2.48411 | ||||||||
\(409\) | −2.86642 | −0.141735 | −0.0708677 | − | 0.997486i | \(-0.522577\pi\) | ||||
−0.0708677 | + | 0.997486i | \(0.522577\pi\) | |||||||
\(410\) | −13.4146 | −0.662500 | ||||||||
\(411\) | −18.5022 | −0.912644 | ||||||||
\(412\) | −88.3737 | −4.35386 | ||||||||
\(413\) | 2.78424 | 0.137003 | ||||||||
\(414\) | 127.504 | 6.26649 | ||||||||
\(415\) | −16.2537 | −0.797864 | ||||||||
\(416\) | −25.0838 | −1.22984 | ||||||||
\(417\) | −24.7995 | −1.21444 | ||||||||
\(418\) | 53.0631 | 2.59540 | ||||||||
\(419\) | −10.1437 | −0.495554 | −0.247777 | − | 0.968817i | \(-0.579700\pi\) | ||||
−0.247777 | + | 0.968817i | \(0.579700\pi\) | |||||||
\(420\) | −5.05189 | −0.246507 | ||||||||
\(421\) | 2.11469 | 0.103064 | 0.0515320 | − | 0.998671i | \(-0.483590\pi\) | ||||
0.0515320 | + | 0.998671i | \(0.483590\pi\) | |||||||
\(422\) | −11.7272 | −0.570873 | ||||||||
\(423\) | −75.5624 | −3.67397 | ||||||||
\(424\) | 93.2495 | 4.52860 | ||||||||
\(425\) | 7.52090 | 0.364817 | ||||||||
\(426\) | −22.6444 | −1.09713 | ||||||||
\(427\) | 2.48732 | 0.120370 | ||||||||
\(428\) | 17.8784 | 0.864185 | ||||||||
\(429\) | −12.2098 | −0.589493 | ||||||||
\(430\) | −29.9803 | −1.44578 | ||||||||
\(431\) | −18.2324 | −0.878225 | −0.439112 | − | 0.898432i | \(-0.644707\pi\) | ||||
−0.439112 | + | 0.898432i | \(0.644707\pi\) | |||||||
\(432\) | 159.684 | 7.68280 | ||||||||
\(433\) | −0.816044 | −0.0392166 | −0.0196083 | − | 0.999808i | \(-0.506242\pi\) | ||||
−0.0196083 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(434\) | −0.895945 | −0.0430067 | ||||||||
\(435\) | 22.6752 | 1.08719 | ||||||||
\(436\) | 97.1155 | 4.65099 | ||||||||
\(437\) | −47.5203 | −2.27321 | ||||||||
\(438\) | 26.3914 | 1.26103 | ||||||||
\(439\) | 23.2143 | 1.10796 | 0.553979 | − | 0.832530i | \(-0.313109\pi\) | ||||
0.553979 | + | 0.832530i | \(0.313109\pi\) | |||||||
\(440\) | −23.2334 | −1.10761 | ||||||||
\(441\) | −46.8386 | −2.23041 | ||||||||
\(442\) | 6.61359 | 0.314576 | ||||||||
\(443\) | −0.339021 | −0.0161074 | −0.00805368 | − | 0.999968i | \(-0.502564\pi\) | ||||
−0.00805368 | + | 0.999968i | \(0.502564\pi\) | |||||||
\(444\) | −162.897 | −7.73073 | ||||||||
\(445\) | −2.37112 | −0.112402 | ||||||||
\(446\) | 6.92864 | 0.328081 | ||||||||
\(447\) | 45.0554 | 2.13105 | ||||||||
\(448\) | 7.71173 | 0.364345 | ||||||||
\(449\) | 11.8952 | 0.561367 | 0.280684 | − | 0.959800i | \(-0.409439\pi\) | ||||
0.280684 | + | 0.959800i | \(0.409439\pi\) | |||||||
\(450\) | 76.6026 | 3.61108 | ||||||||
\(451\) | 15.6696 | 0.737853 | ||||||||
\(452\) | 22.9649 | 1.08018 | ||||||||
\(453\) | −11.7511 | −0.552114 | ||||||||
\(454\) | −22.8701 | −1.07334 | ||||||||
\(455\) | −0.414224 | −0.0194191 | ||||||||
\(456\) | −190.472 | −8.91965 | ||||||||
\(457\) | −23.6878 | −1.10807 | −0.554034 | − | 0.832494i | \(-0.686912\pi\) | ||||
−0.554034 | + | 0.832494i | \(0.686912\pi\) | |||||||
\(458\) | −11.5367 | −0.539076 | ||||||||
\(459\) | −21.4492 | −1.00116 | ||||||||
\(460\) | 33.4466 | 1.55946 | ||||||||
\(461\) | −33.7049 | −1.56980 | −0.784898 | − | 0.619626i | \(-0.787284\pi\) | ||||
−0.784898 | + | 0.619626i | \(0.787284\pi\) | |||||||
\(462\) | 8.13127 | 0.378301 | ||||||||
\(463\) | −15.6462 | −0.727141 | −0.363570 | − | 0.931567i | \(-0.618442\pi\) | ||||
−0.363570 | + | 0.931567i | \(0.618442\pi\) | |||||||
\(464\) | −106.810 | −4.95852 | ||||||||
\(465\) | −2.82208 | −0.130871 | ||||||||
\(466\) | 81.5565 | 3.77803 | ||||||||
\(467\) | −7.48433 | −0.346334 | −0.173167 | − | 0.984893i | \(-0.555400\pi\) | ||||
−0.173167 | + | 0.984893i | \(0.555400\pi\) | |||||||
\(468\) | 48.8863 | 2.25977 | ||||||||
\(469\) | 0.459685 | 0.0212263 | ||||||||
\(470\) | −27.3122 | −1.25982 | ||||||||
\(471\) | 11.9372 | 0.550037 | ||||||||
\(472\) | −73.8849 | −3.40083 | ||||||||
\(473\) | 35.0200 | 1.61022 | ||||||||
\(474\) | 118.359 | 5.43640 | ||||||||
\(475\) | −28.5495 | −1.30994 | ||||||||
\(476\) | −3.19642 | −0.146508 | ||||||||
\(477\) | −71.3294 | −3.26595 | ||||||||
\(478\) | −34.3209 | −1.56980 | ||||||||
\(479\) | −11.1305 | −0.508567 | −0.254284 | − | 0.967130i | \(-0.581840\pi\) | ||||
−0.254284 | + | 0.967130i | \(0.581840\pi\) | |||||||
\(480\) | 52.6177 | 2.40166 | ||||||||
\(481\) | −13.3565 | −0.609006 | ||||||||
\(482\) | −24.7943 | −1.12935 | ||||||||
\(483\) | −7.28190 | −0.331338 | ||||||||
\(484\) | −14.5873 | −0.663061 | ||||||||
\(485\) | −9.74123 | −0.442326 | ||||||||
\(486\) | −46.0049 | −2.08683 | ||||||||
\(487\) | −36.4684 | −1.65254 | −0.826271 | − | 0.563273i | \(-0.809542\pi\) | ||||
−0.826271 | + | 0.563273i | \(0.809542\pi\) | |||||||
\(488\) | −66.0056 | −2.98793 | ||||||||
\(489\) | 28.4563 | 1.28684 | ||||||||
\(490\) | −16.9300 | −0.764818 | ||||||||
\(491\) | 24.3289 | 1.09795 | 0.548974 | − | 0.835840i | \(-0.315019\pi\) | ||||
0.548974 | + | 0.835840i | \(0.315019\pi\) | |||||||
\(492\) | −90.4168 | −4.07631 | ||||||||
\(493\) | 14.3470 | 0.646156 | ||||||||
\(494\) | −25.1053 | −1.12954 | ||||||||
\(495\) | 17.7719 | 0.798787 | ||||||||
\(496\) | 13.2932 | 0.596881 | ||||||||
\(497\) | 0.897365 | 0.0402523 | ||||||||
\(498\) | −150.955 | −6.76447 | ||||||||
\(499\) | 32.9844 | 1.47659 | 0.738293 | − | 0.674480i | \(-0.235632\pi\) | ||||
0.738293 | + | 0.674480i | \(0.235632\pi\) | |||||||
\(500\) | 44.1794 | 1.97576 | ||||||||
\(501\) | −73.9407 | −3.30343 | ||||||||
\(502\) | −34.5448 | −1.54181 | ||||||||
\(503\) | 14.0983 | 0.628610 | 0.314305 | − | 0.949322i | \(-0.398229\pi\) | ||||
0.314305 | + | 0.949322i | \(0.398229\pi\) | |||||||
\(504\) | −20.2527 | −0.902129 | ||||||||
\(505\) | −16.1655 | −0.719354 | ||||||||
\(506\) | −53.8340 | −2.39321 | ||||||||
\(507\) | −34.9203 | −1.55086 | ||||||||
\(508\) | −3.23292 | −0.143438 | ||||||||
\(509\) | 25.1707 | 1.11567 | 0.557836 | − | 0.829951i | \(-0.311632\pi\) | ||||
0.557836 | + | 0.829951i | \(0.311632\pi\) | |||||||
\(510\) | −13.8732 | −0.614314 | ||||||||
\(511\) | −1.04585 | −0.0462658 | ||||||||
\(512\) | −9.20085 | −0.406624 | ||||||||
\(513\) | 81.4217 | 3.59486 | ||||||||
\(514\) | −29.3835 | −1.29605 | ||||||||
\(515\) | 15.2000 | 0.669791 | ||||||||
\(516\) | −202.072 | −8.89574 | ||||||||
\(517\) | 31.9035 | 1.40311 | ||||||||
\(518\) | 8.89497 | 0.390823 | ||||||||
\(519\) | 74.0474 | 3.25032 | ||||||||
\(520\) | 10.9922 | 0.482040 | ||||||||
\(521\) | 8.71454 | 0.381791 | 0.190895 | − | 0.981610i | \(-0.438861\pi\) | ||||
0.190895 | + | 0.981610i | \(0.438861\pi\) | |||||||
\(522\) | 146.129 | 6.39587 | ||||||||
\(523\) | 8.00491 | 0.350030 | 0.175015 | − | 0.984566i | \(-0.444003\pi\) | ||||
0.175015 | + | 0.984566i | \(0.444003\pi\) | |||||||
\(524\) | 5.93451 | 0.259250 | ||||||||
\(525\) | −4.37486 | −0.190934 | ||||||||
\(526\) | −35.0711 | −1.52917 | ||||||||
\(527\) | −1.78558 | −0.0777810 | ||||||||
\(528\) | −120.644 | −5.25035 | ||||||||
\(529\) | 25.2107 | 1.09612 | ||||||||
\(530\) | −25.7822 | −1.11991 | ||||||||
\(531\) | 56.5168 | 2.45262 | ||||||||
\(532\) | 12.1337 | 0.526062 | ||||||||
\(533\) | −7.41363 | −0.321120 | ||||||||
\(534\) | −22.0216 | −0.952968 | ||||||||
\(535\) | −3.07502 | −0.132945 | ||||||||
\(536\) | −12.1986 | −0.526899 | ||||||||
\(537\) | −11.4717 | −0.495042 | ||||||||
\(538\) | 39.3086 | 1.69472 | ||||||||
\(539\) | 19.7759 | 0.851809 | ||||||||
\(540\) | −57.3077 | −2.46613 | ||||||||
\(541\) | 21.6603 | 0.931251 | 0.465625 | − | 0.884982i | \(-0.345829\pi\) | ||||
0.465625 | + | 0.884982i | \(0.345829\pi\) | |||||||
\(542\) | 25.2821 | 1.08596 | ||||||||
\(543\) | −73.6159 | −3.15916 | ||||||||
\(544\) | 33.2921 | 1.42739 | ||||||||
\(545\) | −16.7035 | −0.715501 | ||||||||
\(546\) | −3.84708 | −0.164640 | ||||||||
\(547\) | 8.63899 | 0.369377 | 0.184688 | − | 0.982797i | \(-0.440872\pi\) | ||||
0.184688 | + | 0.982797i | \(0.440872\pi\) | |||||||
\(548\) | −31.2776 | −1.33611 | ||||||||
\(549\) | 50.4897 | 2.15485 | ||||||||
\(550\) | −32.3426 | −1.37910 | ||||||||
\(551\) | −54.4615 | −2.32014 | ||||||||
\(552\) | 193.239 | 8.22479 | ||||||||
\(553\) | −4.69039 | −0.199456 | ||||||||
\(554\) | −26.4382 | −1.12325 | ||||||||
\(555\) | 28.0177 | 1.18928 | ||||||||
\(556\) | −41.9232 | −1.77794 | ||||||||
\(557\) | 25.3346 | 1.07346 | 0.536731 | − | 0.843753i | \(-0.319659\pi\) | ||||
0.536731 | + | 0.843753i | \(0.319659\pi\) | |||||||
\(558\) | −18.1866 | −0.769902 | ||||||||
\(559\) | −16.5687 | −0.700782 | ||||||||
\(560\) | −4.09292 | −0.172958 | ||||||||
\(561\) | 16.2052 | 0.684186 | ||||||||
\(562\) | −53.1788 | −2.24321 | ||||||||
\(563\) | −28.0295 | −1.18130 | −0.590652 | − | 0.806927i | \(-0.701129\pi\) | ||||
−0.590652 | + | 0.806927i | \(0.701129\pi\) | |||||||
\(564\) | −184.090 | −7.75157 | ||||||||
\(565\) | −3.94989 | −0.166173 | ||||||||
\(566\) | −38.1282 | −1.60265 | ||||||||
\(567\) | 5.64246 | 0.236961 | ||||||||
\(568\) | −23.8132 | −0.999182 | ||||||||
\(569\) | −2.93774 | −0.123156 | −0.0615782 | − | 0.998102i | \(-0.519613\pi\) | ||||
−0.0615782 | + | 0.998102i | \(0.519613\pi\) | |||||||
\(570\) | 52.6628 | 2.20580 | ||||||||
\(571\) | 30.7347 | 1.28621 | 0.643104 | − | 0.765779i | \(-0.277646\pi\) | ||||
0.643104 | + | 0.765779i | \(0.277646\pi\) | |||||||
\(572\) | −20.6404 | −0.863020 | ||||||||
\(573\) | 70.8708 | 2.96067 | ||||||||
\(574\) | 4.93721 | 0.206075 | ||||||||
\(575\) | 28.9642 | 1.20789 | ||||||||
\(576\) | 156.539 | 6.52247 | ||||||||
\(577\) | −12.7311 | −0.530001 | −0.265001 | − | 0.964248i | \(-0.585372\pi\) | ||||
−0.265001 | + | 0.964248i | \(0.585372\pi\) | |||||||
\(578\) | 37.1289 | 1.54436 | ||||||||
\(579\) | 15.8687 | 0.659481 | ||||||||
\(580\) | 38.3321 | 1.59165 | ||||||||
\(581\) | 5.98214 | 0.248181 | ||||||||
\(582\) | −90.4710 | −3.75014 | ||||||||
\(583\) | 30.1162 | 1.24729 | ||||||||
\(584\) | 27.7536 | 1.14845 | ||||||||
\(585\) | −8.40828 | −0.347639 | ||||||||
\(586\) | −64.1706 | −2.65086 | ||||||||
\(587\) | 18.0016 | 0.743007 | 0.371503 | − | 0.928432i | \(-0.378842\pi\) | ||||
0.371503 | + | 0.928432i | \(0.378842\pi\) | |||||||
\(588\) | −114.111 | −4.70586 | ||||||||
\(589\) | 6.77809 | 0.279286 | ||||||||
\(590\) | 20.4282 | 0.841014 | ||||||||
\(591\) | −72.5488 | −2.98426 | ||||||||
\(592\) | −131.975 | −5.42414 | ||||||||
\(593\) | 32.6429 | 1.34048 | 0.670242 | − | 0.742142i | \(-0.266190\pi\) | ||||
0.670242 | + | 0.742142i | \(0.266190\pi\) | |||||||
\(594\) | 92.2396 | 3.78464 | ||||||||
\(595\) | 0.549773 | 0.0225385 | ||||||||
\(596\) | 76.1655 | 3.11986 | ||||||||
\(597\) | 14.1096 | 0.577468 | ||||||||
\(598\) | 25.4700 | 1.04155 | ||||||||
\(599\) | −5.01090 | −0.204740 | −0.102370 | − | 0.994746i | \(-0.532643\pi\) | ||||
−0.102370 | + | 0.994746i | \(0.532643\pi\) | |||||||
\(600\) | 116.095 | 4.73956 | ||||||||
\(601\) | 14.7232 | 0.600573 | 0.300286 | − | 0.953849i | \(-0.402918\pi\) | ||||
0.300286 | + | 0.953849i | \(0.402918\pi\) | |||||||
\(602\) | 11.0342 | 0.449719 | ||||||||
\(603\) | 9.33107 | 0.379991 | ||||||||
\(604\) | −19.8650 | −0.808297 | ||||||||
\(605\) | 2.50897 | 0.102004 | ||||||||
\(606\) | −150.136 | −6.09885 | ||||||||
\(607\) | 4.37686 | 0.177651 | 0.0888257 | − | 0.996047i | \(-0.471689\pi\) | ||||
0.0888257 | + | 0.996047i | \(0.471689\pi\) | |||||||
\(608\) | −126.378 | −5.12529 | ||||||||
\(609\) | −8.34556 | −0.338179 | ||||||||
\(610\) | 18.2497 | 0.738907 | ||||||||
\(611\) | −15.0942 | −0.610647 | ||||||||
\(612\) | −64.8836 | −2.62276 | ||||||||
\(613\) | −30.8178 | −1.24472 | −0.622360 | − | 0.782731i | \(-0.713826\pi\) | ||||
−0.622360 | + | 0.782731i | \(0.713826\pi\) | |||||||
\(614\) | −11.4397 | −0.461670 | ||||||||
\(615\) | 15.5514 | 0.627093 | ||||||||
\(616\) | 8.55098 | 0.344529 | ||||||||
\(617\) | −25.4753 | −1.02560 | −0.512799 | − | 0.858509i | \(-0.671391\pi\) | ||||
−0.512799 | + | 0.858509i | \(0.671391\pi\) | |||||||
\(618\) | 141.169 | 5.67864 | ||||||||
\(619\) | 1.08134 | 0.0434629 | 0.0217315 | − | 0.999764i | \(-0.493082\pi\) | ||||
0.0217315 | + | 0.999764i | \(0.493082\pi\) | |||||||
\(620\) | −4.77068 | −0.191595 | ||||||||
\(621\) | −82.6046 | −3.31481 | ||||||||
\(622\) | 55.7545 | 2.23555 | ||||||||
\(623\) | 0.872685 | 0.0349634 | ||||||||
\(624\) | 57.0793 | 2.28500 | ||||||||
\(625\) | 13.2587 | 0.530348 | ||||||||
\(626\) | −31.1589 | −1.24536 | ||||||||
\(627\) | −61.5155 | −2.45669 | ||||||||
\(628\) | 20.1797 | 0.805256 | ||||||||
\(629\) | 17.7273 | 0.706833 | ||||||||
\(630\) | 5.59961 | 0.223094 | ||||||||
\(631\) | −24.3293 | −0.968534 | −0.484267 | − | 0.874920i | \(-0.660914\pi\) | ||||
−0.484267 | + | 0.874920i | \(0.660914\pi\) | |||||||
\(632\) | 124.468 | 4.95107 | ||||||||
\(633\) | 13.5953 | 0.540363 | ||||||||
\(634\) | −33.7341 | −1.33975 | ||||||||
\(635\) | 0.556052 | 0.0220663 | ||||||||
\(636\) | −173.777 | −6.89070 | ||||||||
\(637\) | −9.35642 | −0.370715 | ||||||||
\(638\) | −61.6974 | −2.44262 | ||||||||
\(639\) | 18.2155 | 0.720593 | ||||||||
\(640\) | 22.9658 | 0.907804 | ||||||||
\(641\) | −21.8901 | −0.864608 | −0.432304 | − | 0.901728i | \(-0.642299\pi\) | ||||
−0.432304 | + | 0.901728i | \(0.642299\pi\) | |||||||
\(642\) | −28.5591 | −1.12714 | ||||||||
\(643\) | −18.8332 | −0.742708 | −0.371354 | − | 0.928491i | \(-0.621106\pi\) | ||||
−0.371354 | + | 0.928491i | \(0.621106\pi\) | |||||||
\(644\) | −12.3100 | −0.485080 | ||||||||
\(645\) | 34.7558 | 1.36851 | ||||||||
\(646\) | 33.3207 | 1.31098 | ||||||||
\(647\) | 7.15482 | 0.281285 | 0.140643 | − | 0.990060i | \(-0.455083\pi\) | ||||
0.140643 | + | 0.990060i | \(0.455083\pi\) | |||||||
\(648\) | −149.733 | −5.88207 | ||||||||
\(649\) | −23.8622 | −0.936672 | ||||||||
\(650\) | 15.3020 | 0.600194 | ||||||||
\(651\) | 1.03866 | 0.0407083 | ||||||||
\(652\) | 48.1050 | 1.88394 | ||||||||
\(653\) | 36.9824 | 1.44723 | 0.723617 | − | 0.690202i | \(-0.242478\pi\) | ||||
0.723617 | + | 0.690202i | \(0.242478\pi\) | |||||||
\(654\) | −155.133 | −6.06618 | ||||||||
\(655\) | −1.02072 | −0.0398827 | ||||||||
\(656\) | −73.2536 | −2.86007 | ||||||||
\(657\) | −21.2296 | −0.828245 | ||||||||
\(658\) | 10.0522 | 0.391876 | ||||||||
\(659\) | −15.9092 | −0.619734 | −0.309867 | − | 0.950780i | \(-0.600285\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600285\pi\) | |||||||
\(660\) | 43.2969 | 1.68533 | ||||||||
\(661\) | 31.2122 | 1.21401 | 0.607007 | − | 0.794696i | \(-0.292370\pi\) | ||||
0.607007 | + | 0.794696i | \(0.292370\pi\) | |||||||
\(662\) | 53.5143 | 2.07989 | ||||||||
\(663\) | −7.66706 | −0.297764 | ||||||||
\(664\) | −158.747 | −6.16059 | ||||||||
\(665\) | −2.08695 | −0.0809285 | ||||||||
\(666\) | 180.558 | 6.99647 | ||||||||
\(667\) | 55.2527 | 2.13939 | ||||||||
\(668\) | −124.996 | −4.83623 | ||||||||
\(669\) | −8.03230 | −0.310547 | ||||||||
\(670\) | 3.37274 | 0.130300 | ||||||||
\(671\) | −21.3174 | −0.822951 | ||||||||
\(672\) | −19.3658 | −0.747053 | ||||||||
\(673\) | 16.2384 | 0.625945 | 0.312972 | − | 0.949762i | \(-0.398675\pi\) | ||||
0.312972 | + | 0.949762i | \(0.398675\pi\) | |||||||
\(674\) | 25.7837 | 0.993150 | ||||||||
\(675\) | −49.6276 | −1.91017 | ||||||||
\(676\) | −59.0322 | −2.27047 | ||||||||
\(677\) | −28.6766 | −1.10213 | −0.551065 | − | 0.834462i | \(-0.685778\pi\) | ||||
−0.551065 | + | 0.834462i | \(0.685778\pi\) | |||||||
\(678\) | −36.6843 | −1.40885 | ||||||||
\(679\) | 3.58524 | 0.137589 | ||||||||
\(680\) | −14.5893 | −0.559472 | ||||||||
\(681\) | 26.5130 | 1.01598 | ||||||||
\(682\) | 7.67865 | 0.294031 | ||||||||
\(683\) | −22.9001 | −0.876248 | −0.438124 | − | 0.898915i | \(-0.644357\pi\) | ||||
−0.438124 | + | 0.898915i | \(0.644357\pi\) | |||||||
\(684\) | 246.300 | 9.41750 | ||||||||
\(685\) | 5.37965 | 0.205546 | ||||||||
\(686\) | 12.5636 | 0.479680 | ||||||||
\(687\) | 13.3744 | 0.510265 | ||||||||
\(688\) | −163.714 | −6.24155 | ||||||||
\(689\) | −14.2487 | −0.542830 | ||||||||
\(690\) | −53.4279 | −2.03396 | ||||||||
\(691\) | 14.9114 | 0.567258 | 0.283629 | − | 0.958934i | \(-0.408462\pi\) | ||||
0.283629 | + | 0.958934i | \(0.408462\pi\) | |||||||
\(692\) | 125.176 | 4.75848 | ||||||||
\(693\) | −6.54091 | −0.248469 | ||||||||
\(694\) | 20.4602 | 0.776658 | ||||||||
\(695\) | 7.21064 | 0.273515 | ||||||||
\(696\) | 221.465 | 8.39460 | ||||||||
\(697\) | 9.83964 | 0.372703 | ||||||||
\(698\) | 50.7782 | 1.92198 | ||||||||
\(699\) | −94.5476 | −3.57612 | ||||||||
\(700\) | −7.39563 | −0.279529 | ||||||||
\(701\) | −13.6159 | −0.514265 | −0.257133 | − | 0.966376i | \(-0.582778\pi\) | ||||
−0.257133 | + | 0.966376i | \(0.582778\pi\) | |||||||
\(702\) | −43.6406 | −1.64711 | ||||||||
\(703\) | −67.2931 | −2.53801 | ||||||||
\(704\) | −66.0930 | −2.49097 | ||||||||
\(705\) | 31.6628 | 1.19249 | ||||||||
\(706\) | −18.2497 | −0.686837 | ||||||||
\(707\) | 5.94967 | 0.223760 | ||||||||
\(708\) | 137.690 | 5.17469 | ||||||||
\(709\) | 15.4987 | 0.582065 | 0.291033 | − | 0.956713i | \(-0.406001\pi\) | ||||
0.291033 | + | 0.956713i | \(0.406001\pi\) | |||||||
\(710\) | 6.58404 | 0.247095 | ||||||||
\(711\) | −95.2094 | −3.57063 | ||||||||
\(712\) | −23.1583 | −0.867894 | ||||||||
\(713\) | −6.87656 | −0.257529 | ||||||||
\(714\) | 5.10598 | 0.191087 | ||||||||
\(715\) | 3.55009 | 0.132766 | ||||||||
\(716\) | −19.3928 | −0.724743 | ||||||||
\(717\) | 39.7878 | 1.48590 | ||||||||
\(718\) | 96.1603 | 3.58867 | ||||||||
\(719\) | −9.46399 | −0.352947 | −0.176474 | − | 0.984305i | \(-0.556469\pi\) | ||||
−0.176474 | + | 0.984305i | \(0.556469\pi\) | |||||||
\(720\) | −83.0816 | −3.09627 | ||||||||
\(721\) | −5.59432 | −0.208343 | ||||||||
\(722\) | −75.1786 | −2.79786 | ||||||||
\(723\) | 28.7437 | 1.06899 | ||||||||
\(724\) | −124.447 | −4.62502 | ||||||||
\(725\) | 33.1950 | 1.23283 | ||||||||
\(726\) | 23.3019 | 0.864816 | ||||||||
\(727\) | 5.49675 | 0.203863 | 0.101932 | − | 0.994791i | \(-0.467498\pi\) | ||||
0.101932 | + | 0.994791i | \(0.467498\pi\) | |||||||
\(728\) | −4.04566 | −0.149942 | ||||||||
\(729\) | 2.80467 | 0.103877 | ||||||||
\(730\) | −7.67350 | −0.284009 | ||||||||
\(731\) | 21.9906 | 0.813351 | ||||||||
\(732\) | 123.006 | 4.54643 | ||||||||
\(733\) | 22.8811 | 0.845132 | 0.422566 | − | 0.906332i | \(-0.361130\pi\) | ||||
0.422566 | + | 0.906332i | \(0.361130\pi\) | |||||||
\(734\) | 36.7244 | 1.35552 | ||||||||
\(735\) | 19.6267 | 0.723943 | ||||||||
\(736\) | 128.214 | 4.72602 | ||||||||
\(737\) | −3.93971 | −0.145121 | ||||||||
\(738\) | 100.220 | 3.68914 | ||||||||
\(739\) | −0.823815 | −0.0303045 | −0.0151523 | − | 0.999885i | \(-0.504823\pi\) | ||||
−0.0151523 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(740\) | 47.3635 | 1.74112 | ||||||||
\(741\) | 29.1043 | 1.06917 | ||||||||
\(742\) | 9.48909 | 0.348355 | ||||||||
\(743\) | 47.1711 | 1.73054 | 0.865270 | − | 0.501307i | \(-0.167147\pi\) | ||||
0.865270 | + | 0.501307i | \(0.167147\pi\) | |||||||
\(744\) | −27.5627 | −1.01050 | ||||||||
\(745\) | −13.1002 | −0.479955 | ||||||||
\(746\) | −20.7885 | −0.761122 | ||||||||
\(747\) | 121.431 | 4.44291 | ||||||||
\(748\) | 27.3947 | 1.00165 | ||||||||
\(749\) | 1.13176 | 0.0413534 | ||||||||
\(750\) | −70.5726 | −2.57695 | ||||||||
\(751\) | −3.46166 | −0.126318 | −0.0631589 | − | 0.998003i | \(-0.520117\pi\) | ||||
−0.0631589 | + | 0.998003i | \(0.520117\pi\) | |||||||
\(752\) | −149.145 | −5.43876 | ||||||||
\(753\) | 40.0474 | 1.45941 | ||||||||
\(754\) | 29.1904 | 1.06305 | ||||||||
\(755\) | 3.41672 | 0.124347 | ||||||||
\(756\) | 21.0920 | 0.767108 | ||||||||
\(757\) | −7.10101 | −0.258091 | −0.129045 | − | 0.991639i | \(-0.541191\pi\) | ||||
−0.129045 | + | 0.991639i | \(0.541191\pi\) | |||||||
\(758\) | 3.69771 | 0.134307 | ||||||||
\(759\) | 62.4092 | 2.26531 | ||||||||
\(760\) | 55.3811 | 2.00888 | ||||||||
\(761\) | 9.27484 | 0.336213 | 0.168106 | − | 0.985769i | \(-0.446235\pi\) | ||||
0.168106 | + | 0.985769i | \(0.446235\pi\) | |||||||
\(762\) | 5.16430 | 0.187083 | ||||||||
\(763\) | 6.14770 | 0.222562 | ||||||||
\(764\) | 119.806 | 4.33443 | ||||||||
\(765\) | 11.1598 | 0.403482 | ||||||||
\(766\) | 68.0507 | 2.45877 | ||||||||
\(767\) | 11.2897 | 0.407648 | ||||||||
\(768\) | 69.1661 | 2.49582 | ||||||||
\(769\) | −11.6503 | −0.420121 | −0.210060 | − | 0.977688i | \(-0.567366\pi\) | ||||
−0.210060 | + | 0.977688i | \(0.567366\pi\) | |||||||
\(770\) | −2.36423 | −0.0852009 | ||||||||
\(771\) | 34.0639 | 1.22678 | ||||||||
\(772\) | 26.8258 | 0.965482 | ||||||||
\(773\) | −39.6441 | −1.42590 | −0.712949 | − | 0.701216i | \(-0.752641\pi\) | ||||
−0.712949 | + | 0.701216i | \(0.752641\pi\) | |||||||
\(774\) | 223.981 | 8.05082 | ||||||||
\(775\) | −4.13133 | −0.148402 | ||||||||
\(776\) | −95.1409 | −3.41536 | ||||||||
\(777\) | −10.3118 | −0.369935 | ||||||||
\(778\) | 40.9783 | 1.46914 | ||||||||
\(779\) | −37.3515 | −1.33826 | ||||||||
\(780\) | −20.4847 | −0.733471 | ||||||||
\(781\) | −7.69082 | −0.275199 | ||||||||
\(782\) | −33.8047 | −1.20886 | ||||||||
\(783\) | −94.6705 | −3.38325 | ||||||||
\(784\) | −92.4501 | −3.30179 | ||||||||
\(785\) | −3.47084 | −0.123879 | ||||||||
\(786\) | −9.47983 | −0.338134 | ||||||||
\(787\) | 43.0250 | 1.53368 | 0.766838 | − | 0.641841i | \(-0.221829\pi\) | ||||
0.766838 | + | 0.641841i | \(0.221829\pi\) | |||||||
\(788\) | −122.643 | −4.36896 | ||||||||
\(789\) | 40.6575 | 1.44745 | ||||||||
\(790\) | −34.4137 | −1.22439 | ||||||||
\(791\) | 1.45375 | 0.0516893 | ||||||||
\(792\) | 173.575 | 6.16772 | ||||||||
\(793\) | 10.0857 | 0.358155 | ||||||||
\(794\) | −9.04082 | −0.320847 | ||||||||
\(795\) | 29.8891 | 1.06006 | ||||||||
\(796\) | 23.8521 | 0.845414 | ||||||||
\(797\) | −4.95566 | −0.175538 | −0.0877692 | − | 0.996141i | \(-0.527974\pi\) | ||||
−0.0877692 | + | 0.996141i | \(0.527974\pi\) | |||||||
\(798\) | −19.3824 | −0.686130 | ||||||||
\(799\) | 20.0336 | 0.708738 | ||||||||
\(800\) | 77.0288 | 2.72338 | ||||||||
\(801\) | 17.7145 | 0.625911 | ||||||||
\(802\) | 76.5539 | 2.70321 | ||||||||
\(803\) | 8.96342 | 0.316312 | ||||||||
\(804\) | 22.7329 | 0.801728 | ||||||||
\(805\) | 2.11727 | 0.0746240 | ||||||||
\(806\) | −3.63294 | −0.127965 | ||||||||
\(807\) | −45.5701 | −1.60414 | ||||||||
\(808\) | −157.885 | −5.55439 | ||||||||
\(809\) | 2.39932 | 0.0843556 | 0.0421778 | − | 0.999110i | \(-0.486570\pi\) | ||||
0.0421778 | + | 0.999110i | \(0.486570\pi\) | |||||||
\(810\) | 41.3992 | 1.45462 | ||||||||
\(811\) | −38.7064 | −1.35916 | −0.679582 | − | 0.733599i | \(-0.737839\pi\) | ||||
−0.679582 | + | 0.733599i | \(0.737839\pi\) | |||||||
\(812\) | −14.1080 | −0.495095 | ||||||||
\(813\) | −29.3093 | −1.02792 | ||||||||
\(814\) | −76.2339 | −2.67200 | ||||||||
\(815\) | −8.27390 | −0.289822 | ||||||||
\(816\) | −75.7577 | −2.65205 | ||||||||
\(817\) | −83.4768 | −2.92048 | ||||||||
\(818\) | 7.74047 | 0.270639 | ||||||||
\(819\) | 3.09465 | 0.108136 | ||||||||
\(820\) | 26.2894 | 0.918066 | ||||||||
\(821\) | 42.9669 | 1.49956 | 0.749778 | − | 0.661689i | \(-0.230160\pi\) | ||||
0.749778 | + | 0.661689i | \(0.230160\pi\) | |||||||
\(822\) | 49.9631 | 1.74266 | ||||||||
\(823\) | −34.8172 | −1.21365 | −0.606825 | − | 0.794835i | \(-0.707557\pi\) | ||||
−0.606825 | + | 0.794835i | \(0.707557\pi\) | |||||||
\(824\) | 148.456 | 5.17170 | ||||||||
\(825\) | 37.4945 | 1.30539 | ||||||||
\(826\) | −7.51854 | −0.261603 | ||||||||
\(827\) | −42.0406 | −1.46189 | −0.730947 | − | 0.682435i | \(-0.760921\pi\) | ||||
−0.730947 | + | 0.682435i | \(0.760921\pi\) | |||||||
\(828\) | −249.878 | −8.68385 | ||||||||
\(829\) | 3.43424 | 0.119276 | 0.0596381 | − | 0.998220i | \(-0.481005\pi\) | ||||
0.0596381 | + | 0.998220i | \(0.481005\pi\) | |||||||
\(830\) | 43.8914 | 1.52349 | ||||||||
\(831\) | 30.6495 | 1.06322 | ||||||||
\(832\) | 31.2700 | 1.08409 | ||||||||
\(833\) | 12.4182 | 0.430264 | ||||||||
\(834\) | 66.9684 | 2.31892 | ||||||||
\(835\) | 21.4988 | 0.743998 | ||||||||
\(836\) | −103.991 | −3.59660 | ||||||||
\(837\) | 11.7824 | 0.407258 | ||||||||
\(838\) | 27.3921 | 0.946244 | ||||||||
\(839\) | −4.22085 | −0.145720 | −0.0728599 | − | 0.997342i | \(-0.523213\pi\) | ||||
−0.0728599 | + | 0.997342i | \(0.523213\pi\) | |||||||
\(840\) | 8.48647 | 0.292811 | ||||||||
\(841\) | 34.3234 | 1.18357 | ||||||||
\(842\) | −5.71051 | −0.196797 | ||||||||
\(843\) | 61.6496 | 2.12332 | ||||||||
\(844\) | 22.9826 | 0.791093 | ||||||||
\(845\) | 10.1533 | 0.349286 | ||||||||
\(846\) | 204.048 | 7.01532 | ||||||||
\(847\) | −0.923422 | −0.0317292 | ||||||||
\(848\) | −140.790 | −4.83475 | ||||||||
\(849\) | 44.2016 | 1.51700 | ||||||||
\(850\) | −20.3094 | −0.696606 | ||||||||
\(851\) | 68.2707 | 2.34029 | ||||||||
\(852\) | 44.3776 | 1.52035 | ||||||||
\(853\) | −24.5056 | −0.839054 | −0.419527 | − | 0.907743i | \(-0.637804\pi\) | ||||
−0.419527 | + | 0.907743i | \(0.637804\pi\) | |||||||
\(854\) | −6.71674 | −0.229842 | ||||||||
\(855\) | −42.3627 | −1.44877 | ||||||||
\(856\) | −30.0332 | −1.02651 | ||||||||
\(857\) | −24.2650 | −0.828875 | −0.414438 | − | 0.910078i | \(-0.636022\pi\) | ||||
−0.414438 | + | 0.910078i | \(0.636022\pi\) | |||||||
\(858\) | 32.9712 | 1.12562 | ||||||||
\(859\) | 47.5984 | 1.62404 | 0.812018 | − | 0.583633i | \(-0.198369\pi\) | ||||
0.812018 | + | 0.583633i | \(0.198369\pi\) | |||||||
\(860\) | 58.7541 | 2.00350 | ||||||||
\(861\) | −5.72365 | −0.195062 | ||||||||
\(862\) | 49.2347 | 1.67694 | ||||||||
\(863\) | 2.13895 | 0.0728105 | 0.0364053 | − | 0.999337i | \(-0.488409\pi\) | ||||
0.0364053 | + | 0.999337i | \(0.488409\pi\) | |||||||
\(864\) | −219.682 | −7.47375 | ||||||||
\(865\) | −21.5299 | −0.732037 | ||||||||
\(866\) | 2.20364 | 0.0748828 | ||||||||
\(867\) | −43.0431 | −1.46182 | ||||||||
\(868\) | 1.75584 | 0.0595970 | ||||||||
\(869\) | 40.1987 | 1.36365 | ||||||||
\(870\) | −61.2320 | −2.07596 | ||||||||
\(871\) | 1.86396 | 0.0631579 | ||||||||
\(872\) | −163.141 | −5.52464 | ||||||||
\(873\) | 72.7762 | 2.46310 | ||||||||
\(874\) | 128.324 | 4.34061 | ||||||||
\(875\) | 2.79669 | 0.0945454 | ||||||||
\(876\) | −51.7208 | −1.74748 | ||||||||
\(877\) | −45.5524 | −1.53820 | −0.769098 | − | 0.639131i | \(-0.779294\pi\) | ||||
−0.769098 | + | 0.639131i | \(0.779294\pi\) | |||||||
\(878\) | −62.6878 | −2.11561 | ||||||||
\(879\) | 74.3923 | 2.50919 | ||||||||
\(880\) | 35.0782 | 1.18248 | ||||||||
\(881\) | −37.3643 | −1.25883 | −0.629417 | − | 0.777067i | \(-0.716706\pi\) | ||||
−0.629417 | + | 0.777067i | \(0.716706\pi\) | |||||||
\(882\) | 126.483 | 4.25890 | ||||||||
\(883\) | −26.1137 | −0.878795 | −0.439397 | − | 0.898293i | \(-0.644808\pi\) | ||||
−0.439397 | + | 0.898293i | \(0.644808\pi\) | |||||||
\(884\) | −12.9610 | −0.435927 | ||||||||
\(885\) | −23.6821 | −0.796067 | ||||||||
\(886\) | 0.915490 | 0.0307565 | ||||||||
\(887\) | 44.5924 | 1.49727 | 0.748633 | − | 0.662985i | \(-0.230711\pi\) | ||||
0.748633 | + | 0.662985i | \(0.230711\pi\) | |||||||
\(888\) | 273.644 | 9.18289 | ||||||||
\(889\) | −0.204654 | −0.00686387 | ||||||||
\(890\) | 6.40296 | 0.214628 | ||||||||
\(891\) | −48.3584 | −1.62007 | ||||||||
\(892\) | −13.5785 | −0.454641 | ||||||||
\(893\) | −76.0480 | −2.54485 | ||||||||
\(894\) | −121.667 | −4.06916 | ||||||||
\(895\) | 3.33550 | 0.111493 | ||||||||
\(896\) | −8.45252 | −0.282379 | ||||||||
\(897\) | −29.5271 | −0.985882 | ||||||||
\(898\) | −32.1216 | −1.07191 | ||||||||
\(899\) | −7.88101 | −0.262846 | ||||||||
\(900\) | −150.123 | −5.00409 | ||||||||
\(901\) | 18.9113 | 0.630028 | ||||||||
\(902\) | −42.3141 | −1.40891 | ||||||||
\(903\) | −12.7918 | −0.425684 | ||||||||
\(904\) | −38.5778 | −1.28308 | ||||||||
\(905\) | 21.4044 | 0.711506 | ||||||||
\(906\) | 31.7326 | 1.05424 | ||||||||
\(907\) | 20.4550 | 0.679197 | 0.339599 | − | 0.940570i | \(-0.389709\pi\) | ||||
0.339599 | + | 0.940570i | \(0.389709\pi\) | |||||||
\(908\) | 44.8198 | 1.48740 | ||||||||
\(909\) | 120.771 | 4.00573 | ||||||||
\(910\) | 1.11857 | 0.0370802 | ||||||||
\(911\) | 50.7054 | 1.67994 | 0.839972 | − | 0.542629i | \(-0.182571\pi\) | ||||
0.839972 | + | 0.542629i | \(0.182571\pi\) | |||||||
\(912\) | 287.578 | 9.52265 | ||||||||
\(913\) | −51.2696 | −1.69678 | ||||||||
\(914\) | 63.9663 | 2.11582 | ||||||||
\(915\) | −21.1566 | −0.699417 | ||||||||
\(916\) | 22.6092 | 0.747030 | ||||||||
\(917\) | 0.375672 | 0.0124058 | ||||||||
\(918\) | 57.9213 | 1.91169 | ||||||||
\(919\) | −17.3347 | −0.571818 | −0.285909 | − | 0.958257i | \(-0.592295\pi\) | ||||
−0.285909 | + | 0.958257i | \(0.592295\pi\) | |||||||
\(920\) | −56.1857 | −1.85239 | ||||||||
\(921\) | 13.2620 | 0.436997 | ||||||||
\(922\) | 91.0166 | 2.99747 | ||||||||
\(923\) | 3.63870 | 0.119769 | ||||||||
\(924\) | −15.9353 | −0.524234 | ||||||||
\(925\) | 41.0160 | 1.34860 | ||||||||
\(926\) | 42.2509 | 1.38845 | ||||||||
\(927\) | −113.558 | −3.72974 | ||||||||
\(928\) | 146.942 | 4.82359 | ||||||||
\(929\) | −16.1779 | −0.530779 | −0.265389 | − | 0.964141i | \(-0.585501\pi\) | ||||
−0.265389 | + | 0.964141i | \(0.585501\pi\) | |||||||
\(930\) | 7.62072 | 0.249893 | ||||||||
\(931\) | −47.1397 | −1.54494 | ||||||||
\(932\) | −159.831 | −5.23545 | ||||||||
\(933\) | −64.6356 | −2.11607 | ||||||||
\(934\) | 20.2106 | 0.661312 | ||||||||
\(935\) | −4.71180 | −0.154092 | ||||||||
\(936\) | −82.1222 | −2.68425 | ||||||||
\(937\) | −41.2823 | −1.34863 | −0.674317 | − | 0.738442i | \(-0.735562\pi\) | ||||
−0.674317 | + | 0.738442i | \(0.735562\pi\) | |||||||
\(938\) | −1.24133 | −0.0405309 | ||||||||
\(939\) | 36.1221 | 1.17880 | ||||||||
\(940\) | 53.5255 | 1.74581 | ||||||||
\(941\) | 25.0114 | 0.815350 | 0.407675 | − | 0.913127i | \(-0.366340\pi\) | ||||
0.407675 | + | 0.913127i | \(0.366340\pi\) | |||||||
\(942\) | −32.2351 | −1.05028 | ||||||||
\(943\) | 37.8941 | 1.23400 | ||||||||
\(944\) | 111.553 | 3.63074 | ||||||||
\(945\) | −3.62775 | −0.118011 | ||||||||
\(946\) | −94.5677 | −3.07466 | ||||||||
\(947\) | 44.7324 | 1.45361 | 0.726803 | − | 0.686846i | \(-0.241005\pi\) | ||||
0.726803 | + | 0.686846i | \(0.241005\pi\) | |||||||
\(948\) | −231.955 | −7.53354 | ||||||||
\(949\) | −4.24079 | −0.137662 | ||||||||
\(950\) | 77.0949 | 2.50129 | ||||||||
\(951\) | 39.1076 | 1.26815 | ||||||||
\(952\) | 5.36954 | 0.174028 | ||||||||
\(953\) | −25.3381 | −0.820781 | −0.410391 | − | 0.911910i | \(-0.634608\pi\) | ||||
−0.410391 | + | 0.911910i | \(0.634608\pi\) | |||||||
\(954\) | 192.618 | 6.23622 | ||||||||
\(955\) | −20.6062 | −0.666802 | ||||||||
\(956\) | 67.2608 | 2.17537 | ||||||||
\(957\) | 71.5252 | 2.31208 | ||||||||
\(958\) | 30.0568 | 0.971092 | ||||||||
\(959\) | −1.97997 | −0.0639365 | ||||||||
\(960\) | −65.5944 | −2.11705 | ||||||||
\(961\) | −30.0192 | −0.968360 | ||||||||
\(962\) | 36.0679 | 1.16288 | ||||||||
\(963\) | 22.9733 | 0.740305 | ||||||||
\(964\) | 48.5909 | 1.56501 | ||||||||
\(965\) | −4.61395 | −0.148528 | ||||||||
\(966\) | 19.6640 | 0.632679 | ||||||||
\(967\) | 53.4439 | 1.71864 | 0.859321 | − | 0.511437i | \(-0.170887\pi\) | ||||
0.859321 | + | 0.511437i | \(0.170887\pi\) | |||||||
\(968\) | 24.5047 | 0.787611 | ||||||||
\(969\) | −38.6283 | −1.24092 | ||||||||
\(970\) | 26.3052 | 0.844608 | ||||||||
\(971\) | −43.0730 | −1.38228 | −0.691140 | − | 0.722721i | \(-0.742891\pi\) | ||||
−0.691140 | + | 0.722721i | \(0.742891\pi\) | |||||||
\(972\) | 90.1587 | 2.89184 | ||||||||
\(973\) | −2.65386 | −0.0850789 | ||||||||
\(974\) | 98.4791 | 3.15547 | ||||||||
\(975\) | −17.7395 | −0.568117 | ||||||||
\(976\) | 99.6566 | 3.18993 | ||||||||
\(977\) | 6.05349 | 0.193668 | 0.0968342 | − | 0.995301i | \(-0.469128\pi\) | ||||
0.0968342 | + | 0.995301i | \(0.469128\pi\) | |||||||
\(978\) | −76.8433 | −2.45718 | ||||||||
\(979\) | −7.47930 | −0.239039 | ||||||||
\(980\) | 33.1787 | 1.05985 | ||||||||
\(981\) | 124.791 | 3.98428 | ||||||||
\(982\) | −65.6976 | −2.09649 | ||||||||
\(983\) | 27.8820 | 0.889297 | 0.444648 | − | 0.895705i | \(-0.353329\pi\) | ||||
0.444648 | + | 0.895705i | \(0.353329\pi\) | |||||||
\(984\) | 151.888 | 4.84200 | ||||||||
\(985\) | 21.0941 | 0.672115 | ||||||||
\(986\) | −38.7426 | −1.23381 | ||||||||
\(987\) | −11.6534 | −0.370932 | ||||||||
\(988\) | 49.2004 | 1.56527 | ||||||||
\(989\) | 84.6895 | 2.69297 | ||||||||
\(990\) | −47.9911 | −1.52526 | ||||||||
\(991\) | 52.9405 | 1.68171 | 0.840854 | − | 0.541261i | \(-0.182053\pi\) | ||||
0.840854 | + | 0.541261i | \(0.182053\pi\) | |||||||
\(992\) | −18.2878 | −0.580639 | ||||||||
\(993\) | −62.0385 | −1.96873 | ||||||||
\(994\) | −2.42324 | −0.0768605 | ||||||||
\(995\) | −4.10248 | −0.130057 | ||||||||
\(996\) | 295.836 | 9.37393 | ||||||||
\(997\) | 16.2377 | 0.514253 | 0.257127 | − | 0.966378i | \(-0.417224\pi\) | ||||
0.257127 | + | 0.966378i | \(0.417224\pi\) | |||||||
\(998\) | −89.0710 | −2.81949 | ||||||||
\(999\) | −116.976 | −3.70095 |
(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 | 4003.2.a.b.1.6 | ✓ | 152 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.b.1.6 | ✓ | 152 | 1.1 | even | 1 | trivial |