Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, 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("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.40164 | −1.69821 | −0.849107 | − | 0.528220i | \(-0.822860\pi\) | ||||
−0.849107 | + | 0.528220i | \(0.822860\pi\) | |||||||
\(3\) | −1.91938 | −1.10815 | −0.554077 | − | 0.832465i | \(-0.686929\pi\) | ||||
−0.554077 | + | 0.832465i | \(0.686929\pi\) | |||||||
\(4\) | 3.76787 | 1.88393 | ||||||||
\(5\) | −2.41584 | −1.08040 | −0.540198 | − | 0.841538i | \(-0.681651\pi\) | ||||
−0.540198 | + | 0.841538i | \(0.681651\pi\) | |||||||
\(6\) | 4.60966 | 1.88188 | ||||||||
\(7\) | −1.95333 | −0.738288 | −0.369144 | − | 0.929372i | \(-0.620349\pi\) | ||||
−0.369144 | + | 0.929372i | \(0.620349\pi\) | |||||||
\(8\) | −4.24578 | −1.50111 | ||||||||
\(9\) | 0.684021 | 0.228007 | ||||||||
\(10\) | 5.80197 | 1.83474 | ||||||||
\(11\) | −0.661784 | −0.199535 | −0.0997677 | − | 0.995011i | \(-0.531810\pi\) | ||||
−0.0997677 | + | 0.995011i | \(0.531810\pi\) | |||||||
\(12\) | −7.23197 | −2.08769 | ||||||||
\(13\) | 3.28103 | 0.909993 | 0.454996 | − | 0.890493i | \(-0.349641\pi\) | ||||
0.454996 | + | 0.890493i | \(0.349641\pi\) | |||||||
\(14\) | 4.69118 | 1.25377 | ||||||||
\(15\) | 4.63691 | 1.19725 | ||||||||
\(16\) | 2.66109 | 0.665274 | ||||||||
\(17\) | −6.82644 | −1.65565 | −0.827827 | − | 0.560984i | \(-0.810423\pi\) | ||||
−0.827827 | + | 0.560984i | \(0.810423\pi\) | |||||||
\(18\) | −1.64277 | −0.387205 | ||||||||
\(19\) | 3.26699 | 0.749498 | 0.374749 | − | 0.927126i | \(-0.377729\pi\) | ||||
0.374749 | + | 0.927126i | \(0.377729\pi\) | |||||||
\(20\) | −9.10256 | −2.03539 | ||||||||
\(21\) | 3.74918 | 0.818137 | ||||||||
\(22\) | 1.58937 | 0.338854 | ||||||||
\(23\) | −6.36815 | −1.32785 | −0.663925 | − | 0.747799i | \(-0.731111\pi\) | ||||
−0.663925 | + | 0.747799i | \(0.731111\pi\) | |||||||
\(24\) | 8.14927 | 1.66346 | ||||||||
\(25\) | 0.836275 | 0.167255 | ||||||||
\(26\) | −7.87984 | −1.54536 | ||||||||
\(27\) | 4.44525 | 0.855488 | ||||||||
\(28\) | −7.35988 | −1.39089 | ||||||||
\(29\) | −1.41430 | −0.262629 | −0.131315 | − | 0.991341i | \(-0.541920\pi\) | ||||
−0.131315 | + | 0.991341i | \(0.541920\pi\) | |||||||
\(30\) | −11.1362 | −2.03318 | ||||||||
\(31\) | −3.18044 | −0.571224 | −0.285612 | − | 0.958345i | \(-0.592197\pi\) | ||||
−0.285612 | + | 0.958345i | \(0.592197\pi\) | |||||||
\(32\) | 2.10057 | 0.371333 | ||||||||
\(33\) | 1.27022 | 0.221116 | ||||||||
\(34\) | 16.3946 | 2.81166 | ||||||||
\(35\) | 4.71892 | 0.797643 | ||||||||
\(36\) | 2.57730 | 0.429550 | ||||||||
\(37\) | 5.91293 | 0.972080 | 0.486040 | − | 0.873937i | \(-0.338441\pi\) | ||||
0.486040 | + | 0.873937i | \(0.338441\pi\) | |||||||
\(38\) | −7.84612 | −1.27281 | ||||||||
\(39\) | −6.29753 | −1.00841 | ||||||||
\(40\) | 10.2571 | 1.62179 | ||||||||
\(41\) | 0.877003 | 0.136965 | 0.0684824 | − | 0.997652i | \(-0.478184\pi\) | ||||
0.0684824 | + | 0.997652i | \(0.478184\pi\) | |||||||
\(42\) | −9.00417 | −1.38937 | ||||||||
\(43\) | 4.37063 | 0.666515 | 0.333258 | − | 0.942836i | \(-0.391852\pi\) | ||||
0.333258 | + | 0.942836i | \(0.391852\pi\) | |||||||
\(44\) | −2.49351 | −0.375912 | ||||||||
\(45\) | −1.65248 | −0.246338 | ||||||||
\(46\) | 15.2940 | 2.25498 | ||||||||
\(47\) | −10.3864 | −1.51501 | −0.757505 | − | 0.652829i | \(-0.773582\pi\) | ||||
−0.757505 | + | 0.652829i | \(0.773582\pi\) | |||||||
\(48\) | −5.10765 | −0.737226 | ||||||||
\(49\) | −3.18452 | −0.454931 | ||||||||
\(50\) | −2.00843 | −0.284035 | ||||||||
\(51\) | 13.1025 | 1.83472 | ||||||||
\(52\) | 12.3625 | 1.71437 | ||||||||
\(53\) | −6.93570 | −0.952691 | −0.476346 | − | 0.879258i | \(-0.658039\pi\) | ||||
−0.476346 | + | 0.879258i | \(0.658039\pi\) | |||||||
\(54\) | −10.6759 | −1.45280 | ||||||||
\(55\) | 1.59876 | 0.215577 | ||||||||
\(56\) | 8.29340 | 1.10825 | ||||||||
\(57\) | −6.27059 | −0.830560 | ||||||||
\(58\) | 3.39664 | 0.446001 | ||||||||
\(59\) | −7.14427 | −0.930104 | −0.465052 | − | 0.885283i | \(-0.653964\pi\) | ||||
−0.465052 | + | 0.885283i | \(0.653964\pi\) | |||||||
\(60\) | 17.4713 | 2.25553 | ||||||||
\(61\) | 2.14088 | 0.274112 | 0.137056 | − | 0.990563i | \(-0.456236\pi\) | ||||
0.137056 | + | 0.990563i | \(0.456236\pi\) | |||||||
\(62\) | 7.63827 | 0.970062 | ||||||||
\(63\) | −1.33612 | −0.168335 | ||||||||
\(64\) | −10.3670 | −1.29588 | ||||||||
\(65\) | −7.92643 | −0.983152 | ||||||||
\(66\) | −3.05060 | −0.375503 | ||||||||
\(67\) | −11.2787 | −1.37791 | −0.688956 | − | 0.724803i | \(-0.741931\pi\) | ||||
−0.688956 | + | 0.724803i | \(0.741931\pi\) | |||||||
\(68\) | −25.7211 | −3.11914 | ||||||||
\(69\) | 12.2229 | 1.47146 | ||||||||
\(70\) | −11.3331 | −1.35457 | ||||||||
\(71\) | 7.19157 | 0.853482 | 0.426741 | − | 0.904374i | \(-0.359662\pi\) | ||||
0.426741 | + | 0.904374i | \(0.359662\pi\) | |||||||
\(72\) | −2.90420 | −0.342263 | ||||||||
\(73\) | −9.65095 | −1.12956 | −0.564779 | − | 0.825242i | \(-0.691039\pi\) | ||||
−0.564779 | + | 0.825242i | \(0.691039\pi\) | |||||||
\(74\) | −14.2007 | −1.65080 | ||||||||
\(75\) | −1.60513 | −0.185344 | ||||||||
\(76\) | 12.3096 | 1.41201 | ||||||||
\(77\) | 1.29268 | 0.147315 | ||||||||
\(78\) | 15.1244 | 1.71250 | ||||||||
\(79\) | −0.353871 | −0.0398136 | −0.0199068 | − | 0.999802i | \(-0.506337\pi\) | ||||
−0.0199068 | + | 0.999802i | \(0.506337\pi\) | |||||||
\(80\) | −6.42877 | −0.718759 | ||||||||
\(81\) | −10.5842 | −1.17602 | ||||||||
\(82\) | −2.10624 | −0.232596 | ||||||||
\(83\) | 0.410926 | 0.0451050 | 0.0225525 | − | 0.999746i | \(-0.492821\pi\) | ||||
0.0225525 | + | 0.999746i | \(0.492821\pi\) | |||||||
\(84\) | 14.1264 | 1.54132 | ||||||||
\(85\) | 16.4916 | 1.78876 | ||||||||
\(86\) | −10.4967 | −1.13189 | ||||||||
\(87\) | 2.71458 | 0.291034 | ||||||||
\(88\) | 2.80979 | 0.299525 | ||||||||
\(89\) | 1.94551 | 0.206223 | 0.103112 | − | 0.994670i | \(-0.467120\pi\) | ||||
0.103112 | + | 0.994670i | \(0.467120\pi\) | |||||||
\(90\) | 3.96867 | 0.418334 | ||||||||
\(91\) | −6.40891 | −0.671837 | ||||||||
\(92\) | −23.9943 | −2.50158 | ||||||||
\(93\) | 6.10448 | 0.633005 | ||||||||
\(94\) | 24.9444 | 2.57281 | ||||||||
\(95\) | −7.89251 | −0.809755 | ||||||||
\(96\) | −4.03180 | −0.411494 | ||||||||
\(97\) | −12.5183 | −1.27104 | −0.635519 | − | 0.772085i | \(-0.719214\pi\) | ||||
−0.635519 | + | 0.772085i | \(0.719214\pi\) | |||||||
\(98\) | 7.64806 | 0.772570 | ||||||||
\(99\) | −0.452674 | −0.0454954 | ||||||||
\(100\) | 3.15097 | 0.315097 | ||||||||
\(101\) | 3.68698 | 0.366868 | 0.183434 | − | 0.983032i | \(-0.441279\pi\) | ||||
0.183434 | + | 0.983032i | \(0.441279\pi\) | |||||||
\(102\) | −31.4675 | −3.11575 | ||||||||
\(103\) | −9.34932 | −0.921216 | −0.460608 | − | 0.887604i | \(-0.652369\pi\) | ||||
−0.460608 | + | 0.887604i | \(0.652369\pi\) | |||||||
\(104\) | −13.9305 | −1.36600 | ||||||||
\(105\) | −9.05740 | −0.883912 | ||||||||
\(106\) | 16.6570 | 1.61787 | ||||||||
\(107\) | 1.71192 | 0.165498 | 0.0827489 | − | 0.996570i | \(-0.473630\pi\) | ||||
0.0827489 | + | 0.996570i | \(0.473630\pi\) | |||||||
\(108\) | 16.7491 | 1.61168 | ||||||||
\(109\) | −7.64974 | −0.732712 | −0.366356 | − | 0.930475i | \(-0.619395\pi\) | ||||
−0.366356 | + | 0.930475i | \(0.619395\pi\) | |||||||
\(110\) | −3.83965 | −0.366096 | ||||||||
\(111\) | −11.3492 | −1.07722 | ||||||||
\(112\) | −5.19799 | −0.491164 | ||||||||
\(113\) | −15.0525 | −1.41602 | −0.708011 | − | 0.706201i | \(-0.750407\pi\) | ||||
−0.708011 | + | 0.706201i | \(0.750407\pi\) | |||||||
\(114\) | 15.0597 | 1.41047 | ||||||||
\(115\) | 15.3844 | 1.43460 | ||||||||
\(116\) | −5.32890 | −0.494776 | ||||||||
\(117\) | 2.24429 | 0.207485 | ||||||||
\(118\) | 17.1580 | 1.57952 | ||||||||
\(119\) | 13.3343 | 1.22235 | ||||||||
\(120\) | −19.6873 | −1.79720 | ||||||||
\(121\) | −10.5620 | −0.960186 | ||||||||
\(122\) | −5.14162 | −0.465501 | ||||||||
\(123\) | −1.68330 | −0.151778 | ||||||||
\(124\) | −11.9835 | −1.07615 | ||||||||
\(125\) | 10.0589 | 0.899694 | ||||||||
\(126\) | 3.20887 | 0.285869 | ||||||||
\(127\) | −11.8598 | −1.05239 | −0.526193 | − | 0.850365i | \(-0.676381\pi\) | ||||
−0.526193 | + | 0.850365i | \(0.676381\pi\) | |||||||
\(128\) | 20.6967 | 1.82934 | ||||||||
\(129\) | −8.38890 | −0.738602 | ||||||||
\(130\) | 19.0364 | 1.66960 | ||||||||
\(131\) | −6.50084 | −0.567981 | −0.283991 | − | 0.958827i | \(-0.591658\pi\) | ||||
−0.283991 | + | 0.958827i | \(0.591658\pi\) | |||||||
\(132\) | 4.78600 | 0.416568 | ||||||||
\(133\) | −6.38149 | −0.553346 | ||||||||
\(134\) | 27.0873 | 2.33999 | ||||||||
\(135\) | −10.7390 | −0.924265 | ||||||||
\(136\) | 28.9835 | 2.48532 | ||||||||
\(137\) | −1.46698 | −0.125333 | −0.0626663 | − | 0.998035i | \(-0.519960\pi\) | ||||
−0.0626663 | + | 0.998035i | \(0.519960\pi\) | |||||||
\(138\) | −29.3550 | −2.49886 | ||||||||
\(139\) | 15.2297 | 1.29177 | 0.645885 | − | 0.763435i | \(-0.276489\pi\) | ||||
0.645885 | + | 0.763435i | \(0.276489\pi\) | |||||||
\(140\) | 17.7803 | 1.50271 | ||||||||
\(141\) | 19.9354 | 1.67887 | ||||||||
\(142\) | −17.2715 | −1.44940 | ||||||||
\(143\) | −2.17133 | −0.181576 | ||||||||
\(144\) | 1.82024 | 0.151687 | ||||||||
\(145\) | 3.41673 | 0.283744 | ||||||||
\(146\) | 23.1781 | 1.91823 | ||||||||
\(147\) | 6.11230 | 0.504134 | ||||||||
\(148\) | 22.2791 | 1.83133 | ||||||||
\(149\) | 5.26037 | 0.430946 | 0.215473 | − | 0.976510i | \(-0.430871\pi\) | ||||
0.215473 | + | 0.976510i | \(0.430871\pi\) | |||||||
\(150\) | 3.85494 | 0.314755 | ||||||||
\(151\) | −2.08132 | −0.169376 | −0.0846879 | − | 0.996408i | \(-0.526989\pi\) | ||||
−0.0846879 | + | 0.996408i | \(0.526989\pi\) | |||||||
\(152\) | −13.8709 | −1.12508 | ||||||||
\(153\) | −4.66942 | −0.377500 | ||||||||
\(154\) | −3.10455 | −0.250172 | ||||||||
\(155\) | 7.68343 | 0.617148 | ||||||||
\(156\) | −23.7283 | −1.89978 | ||||||||
\(157\) | −0.112095 | −0.00894618 | −0.00447309 | − | 0.999990i | \(-0.501424\pi\) | ||||
−0.00447309 | + | 0.999990i | \(0.501424\pi\) | |||||||
\(158\) | 0.849871 | 0.0676121 | ||||||||
\(159\) | 13.3122 | 1.05573 | ||||||||
\(160\) | −5.07465 | −0.401186 | ||||||||
\(161\) | 12.4391 | 0.980336 | ||||||||
\(162\) | 25.4194 | 1.99713 | ||||||||
\(163\) | −12.9707 | −1.01594 | −0.507970 | − | 0.861375i | \(-0.669604\pi\) | ||||
−0.507970 | + | 0.861375i | \(0.669604\pi\) | |||||||
\(164\) | 3.30443 | 0.258033 | ||||||||
\(165\) | −3.06863 | −0.238893 | ||||||||
\(166\) | −0.986897 | −0.0765981 | ||||||||
\(167\) | −20.1266 | −1.55745 | −0.778723 | − | 0.627367i | \(-0.784132\pi\) | ||||
−0.778723 | + | 0.627367i | \(0.784132\pi\) | |||||||
\(168\) | −15.9182 | −1.22811 | ||||||||
\(169\) | −2.23487 | −0.171913 | ||||||||
\(170\) | −39.6068 | −3.03770 | ||||||||
\(171\) | 2.23469 | 0.170891 | ||||||||
\(172\) | 16.4680 | 1.25567 | ||||||||
\(173\) | −8.09988 | −0.615822 | −0.307911 | − | 0.951415i | \(-0.599630\pi\) | ||||
−0.307911 | + | 0.951415i | \(0.599630\pi\) | |||||||
\(174\) | −6.51945 | −0.494238 | ||||||||
\(175\) | −1.63352 | −0.123482 | ||||||||
\(176\) | −1.76107 | −0.132746 | ||||||||
\(177\) | 13.7126 | 1.03070 | ||||||||
\(178\) | −4.67240 | −0.350211 | ||||||||
\(179\) | −3.91190 | −0.292389 | −0.146194 | − | 0.989256i | \(-0.546703\pi\) | ||||
−0.146194 | + | 0.989256i | \(0.546703\pi\) | |||||||
\(180\) | −6.22634 | −0.464084 | ||||||||
\(181\) | −19.4450 | −1.44533 | −0.722666 | − | 0.691197i | \(-0.757084\pi\) | ||||
−0.722666 | + | 0.691197i | \(0.757084\pi\) | |||||||
\(182\) | 15.3919 | 1.14092 | ||||||||
\(183\) | −4.10916 | −0.303758 | ||||||||
\(184\) | 27.0378 | 1.99325 | ||||||||
\(185\) | −14.2847 | −1.05023 | ||||||||
\(186\) | −14.6607 | −1.07498 | ||||||||
\(187\) | 4.51763 | 0.330361 | ||||||||
\(188\) | −39.1346 | −2.85418 | ||||||||
\(189\) | −8.68302 | −0.631596 | ||||||||
\(190\) | 18.9550 | 1.37514 | ||||||||
\(191\) | −6.89866 | −0.499169 | −0.249585 | − | 0.968353i | \(-0.580294\pi\) | ||||
−0.249585 | + | 0.968353i | \(0.580294\pi\) | |||||||
\(192\) | 19.8982 | 1.43603 | ||||||||
\(193\) | −5.56850 | −0.400829 | −0.200415 | − | 0.979711i | \(-0.564229\pi\) | ||||
−0.200415 | + | 0.979711i | \(0.564229\pi\) | |||||||
\(194\) | 30.0644 | 2.15850 | ||||||||
\(195\) | 15.2138 | 1.08948 | ||||||||
\(196\) | −11.9988 | −0.857060 | ||||||||
\(197\) | −11.2946 | −0.804707 | −0.402354 | − | 0.915484i | \(-0.631808\pi\) | ||||
−0.402354 | + | 0.915484i | \(0.631808\pi\) | |||||||
\(198\) | 1.08716 | 0.0772610 | ||||||||
\(199\) | −23.3799 | −1.65736 | −0.828679 | − | 0.559724i | \(-0.810907\pi\) | ||||
−0.828679 | + | 0.559724i | \(0.810907\pi\) | |||||||
\(200\) | −3.55064 | −0.251068 | ||||||||
\(201\) | 21.6481 | 1.52694 | ||||||||
\(202\) | −8.85478 | −0.623020 | ||||||||
\(203\) | 2.76259 | 0.193896 | ||||||||
\(204\) | 49.3686 | 3.45649 | ||||||||
\(205\) | −2.11870 | −0.147976 | ||||||||
\(206\) | 22.4537 | 1.56442 | ||||||||
\(207\) | −4.35594 | −0.302759 | ||||||||
\(208\) | 8.73112 | 0.605394 | ||||||||
\(209\) | −2.16204 | −0.149551 | ||||||||
\(210\) | 21.7526 | 1.50107 | ||||||||
\(211\) | 17.2283 | 1.18605 | 0.593023 | − | 0.805185i | \(-0.297934\pi\) | ||||
0.593023 | + | 0.805185i | \(0.297934\pi\) | |||||||
\(212\) | −26.1328 | −1.79481 | ||||||||
\(213\) | −13.8034 | −0.945790 | ||||||||
\(214\) | −4.11142 | −0.281051 | ||||||||
\(215\) | −10.5587 | −0.720100 | ||||||||
\(216\) | −18.8735 | −1.28418 | ||||||||
\(217\) | 6.21244 | 0.421728 | ||||||||
\(218\) | 18.3719 | 1.24430 | ||||||||
\(219\) | 18.5238 | 1.25173 | ||||||||
\(220\) | 6.02393 | 0.406133 | ||||||||
\(221\) | −22.3977 | −1.50663 | ||||||||
\(222\) | 27.2566 | 1.82934 | ||||||||
\(223\) | −10.6011 | −0.709903 | −0.354951 | − | 0.934885i | \(-0.615503\pi\) | ||||
−0.354951 | + | 0.934885i | \(0.615503\pi\) | |||||||
\(224\) | −4.10311 | −0.274150 | ||||||||
\(225\) | 0.572029 | 0.0381353 | ||||||||
\(226\) | 36.1507 | 2.40471 | ||||||||
\(227\) | 9.03942 | 0.599968 | 0.299984 | − | 0.953944i | \(-0.403019\pi\) | ||||
0.299984 | + | 0.953944i | \(0.403019\pi\) | |||||||
\(228\) | −23.6268 | −1.56472 | ||||||||
\(229\) | 0.468543 | 0.0309622 | 0.0154811 | − | 0.999880i | \(-0.495072\pi\) | ||||
0.0154811 | + | 0.999880i | \(0.495072\pi\) | |||||||
\(230\) | −36.9478 | −2.43627 | ||||||||
\(231\) | −2.48114 | −0.163247 | ||||||||
\(232\) | 6.00482 | 0.394236 | ||||||||
\(233\) | −8.82531 | −0.578165 | −0.289082 | − | 0.957304i | \(-0.593350\pi\) | ||||
−0.289082 | + | 0.957304i | \(0.593350\pi\) | |||||||
\(234\) | −5.38997 | −0.352353 | ||||||||
\(235\) | 25.0918 | 1.63681 | ||||||||
\(236\) | −26.9187 | −1.75226 | ||||||||
\(237\) | 0.679213 | 0.0441197 | ||||||||
\(238\) | −32.0241 | −2.07581 | ||||||||
\(239\) | −16.2907 | −1.05376 | −0.526878 | − | 0.849941i | \(-0.676638\pi\) | ||||
−0.526878 | + | 0.849941i | \(0.676638\pi\) | |||||||
\(240\) | 12.3393 | 0.796496 | ||||||||
\(241\) | 2.78334 | 0.179291 | 0.0896454 | − | 0.995974i | \(-0.471427\pi\) | ||||
0.0896454 | + | 0.995974i | \(0.471427\pi\) | |||||||
\(242\) | 25.3662 | 1.63060 | ||||||||
\(243\) | 6.97933 | 0.447724 | ||||||||
\(244\) | 8.06656 | 0.516408 | ||||||||
\(245\) | 7.69327 | 0.491505 | ||||||||
\(246\) | 4.04268 | 0.257752 | ||||||||
\(247\) | 10.7191 | 0.682038 | ||||||||
\(248\) | 13.5035 | 0.857470 | ||||||||
\(249\) | −0.788724 | −0.0499834 | ||||||||
\(250\) | −24.1578 | −1.52787 | ||||||||
\(251\) | 1.46310 | 0.0923501 | 0.0461750 | − | 0.998933i | \(-0.485297\pi\) | ||||
0.0461750 | + | 0.998933i | \(0.485297\pi\) | |||||||
\(252\) | −5.03431 | −0.317132 | ||||||||
\(253\) | 4.21434 | 0.264953 | ||||||||
\(254\) | 28.4829 | 1.78718 | ||||||||
\(255\) | −31.6536 | −1.98222 | ||||||||
\(256\) | −28.9719 | −1.81074 | ||||||||
\(257\) | −9.95063 | −0.620703 | −0.310352 | − | 0.950622i | \(-0.600447\pi\) | ||||
−0.310352 | + | 0.950622i | \(0.600447\pi\) | |||||||
\(258\) | 20.1471 | 1.25430 | ||||||||
\(259\) | −11.5499 | −0.717675 | ||||||||
\(260\) | −29.8657 | −1.85219 | ||||||||
\(261\) | −0.967412 | −0.0598813 | ||||||||
\(262\) | 15.6127 | 0.964554 | ||||||||
\(263\) | −14.9582 | −0.922359 | −0.461180 | − | 0.887307i | \(-0.652574\pi\) | ||||
−0.461180 | + | 0.887307i | \(0.652574\pi\) | |||||||
\(264\) | −5.39305 | −0.331920 | ||||||||
\(265\) | 16.7555 | 1.02928 | ||||||||
\(266\) | 15.3260 | 0.939700 | ||||||||
\(267\) | −3.73416 | −0.228527 | ||||||||
\(268\) | −42.4966 | −2.59590 | ||||||||
\(269\) | −5.04541 | −0.307624 | −0.153812 | − | 0.988100i | \(-0.549155\pi\) | ||||
−0.153812 | + | 0.988100i | \(0.549155\pi\) | |||||||
\(270\) | 25.7912 | 1.56960 | ||||||||
\(271\) | 28.3487 | 1.72206 | 0.861030 | − | 0.508555i | \(-0.169820\pi\) | ||||
0.861030 | + | 0.508555i | \(0.169820\pi\) | |||||||
\(272\) | −18.1658 | −1.10146 | ||||||||
\(273\) | 12.3011 | 0.744499 | ||||||||
\(274\) | 3.52316 | 0.212842 | ||||||||
\(275\) | −0.553433 | −0.0333733 | ||||||||
\(276\) | 46.0543 | 2.77214 | ||||||||
\(277\) | 23.1036 | 1.38816 | 0.694080 | − | 0.719898i | \(-0.255811\pi\) | ||||
0.694080 | + | 0.719898i | \(0.255811\pi\) | |||||||
\(278\) | −36.5763 | −2.19370 | ||||||||
\(279\) | −2.17549 | −0.130243 | ||||||||
\(280\) | −20.0355 | −1.19735 | ||||||||
\(281\) | 6.86479 | 0.409519 | 0.204760 | − | 0.978812i | \(-0.434359\pi\) | ||||
0.204760 | + | 0.978812i | \(0.434359\pi\) | |||||||
\(282\) | −47.8777 | −2.85108 | ||||||||
\(283\) | 1.80221 | 0.107130 | 0.0535651 | − | 0.998564i | \(-0.482942\pi\) | ||||
0.0535651 | + | 0.998564i | \(0.482942\pi\) | |||||||
\(284\) | 27.0969 | 1.60790 | ||||||||
\(285\) | 15.1487 | 0.897333 | ||||||||
\(286\) | 5.21475 | 0.308355 | ||||||||
\(287\) | −1.71307 | −0.101119 | ||||||||
\(288\) | 1.43684 | 0.0846664 | ||||||||
\(289\) | 29.6002 | 1.74119 | ||||||||
\(290\) | −8.20574 | −0.481858 | ||||||||
\(291\) | 24.0273 | 1.40851 | ||||||||
\(292\) | −36.3635 | −2.12801 | ||||||||
\(293\) | 7.23580 | 0.422720 | 0.211360 | − | 0.977408i | \(-0.432211\pi\) | ||||
0.211360 | + | 0.977408i | \(0.432211\pi\) | |||||||
\(294\) | −14.6795 | −0.856127 | ||||||||
\(295\) | 17.2594 | 1.00488 | ||||||||
\(296\) | −25.1050 | −1.45920 | ||||||||
\(297\) | −2.94179 | −0.170700 | ||||||||
\(298\) | −12.6335 | −0.731839 | ||||||||
\(299\) | −20.8941 | −1.20833 | ||||||||
\(300\) | −6.04791 | −0.349177 | ||||||||
\(301\) | −8.53727 | −0.492080 | ||||||||
\(302\) | 4.99859 | 0.287637 | ||||||||
\(303\) | −7.07671 | −0.406546 | ||||||||
\(304\) | 8.69376 | 0.498621 | ||||||||
\(305\) | −5.17202 | −0.296149 | ||||||||
\(306\) | 11.2143 | 0.641077 | ||||||||
\(307\) | 24.1293 | 1.37713 | 0.688565 | − | 0.725174i | \(-0.258241\pi\) | ||||
0.688565 | + | 0.725174i | \(0.258241\pi\) | |||||||
\(308\) | 4.87065 | 0.277531 | ||||||||
\(309\) | 17.9449 | 1.02085 | ||||||||
\(310\) | −18.4528 | −1.04805 | ||||||||
\(311\) | 2.09617 | 0.118863 | 0.0594314 | − | 0.998232i | \(-0.481071\pi\) | ||||
0.0594314 | + | 0.998232i | \(0.481071\pi\) | |||||||
\(312\) | 26.7380 | 1.51374 | ||||||||
\(313\) | 9.93427 | 0.561518 | 0.280759 | − | 0.959778i | \(-0.409414\pi\) | ||||
0.280759 | + | 0.959778i | \(0.409414\pi\) | |||||||
\(314\) | 0.269212 | 0.0151925 | ||||||||
\(315\) | 3.22784 | 0.181868 | ||||||||
\(316\) | −1.33334 | −0.0750062 | ||||||||
\(317\) | 5.38850 | 0.302648 | 0.151324 | − | 0.988484i | \(-0.451646\pi\) | ||||
0.151324 | + | 0.988484i | \(0.451646\pi\) | |||||||
\(318\) | −31.9712 | −1.79286 | ||||||||
\(319\) | 0.935963 | 0.0524038 | ||||||||
\(320\) | 25.0450 | 1.40006 | ||||||||
\(321\) | −3.28583 | −0.183397 | ||||||||
\(322\) | −29.8742 | −1.66482 | ||||||||
\(323\) | −22.3019 | −1.24091 | ||||||||
\(324\) | −39.8798 | −2.21554 | ||||||||
\(325\) | 2.74384 | 0.152201 | ||||||||
\(326\) | 31.1508 | 1.72529 | ||||||||
\(327\) | 14.6828 | 0.811958 | ||||||||
\(328\) | −3.72356 | −0.205599 | ||||||||
\(329\) | 20.2880 | 1.11851 | ||||||||
\(330\) | 7.36975 | 0.405691 | ||||||||
\(331\) | 16.5480 | 0.909559 | 0.454779 | − | 0.890604i | \(-0.349718\pi\) | ||||
0.454779 | + | 0.890604i | \(0.349718\pi\) | |||||||
\(332\) | 1.54832 | 0.0849749 | ||||||||
\(333\) | 4.04457 | 0.221641 | ||||||||
\(334\) | 48.3369 | 2.64488 | ||||||||
\(335\) | 27.2475 | 1.48869 | ||||||||
\(336\) | 9.97691 | 0.544285 | ||||||||
\(337\) | 15.5503 | 0.847079 | 0.423539 | − | 0.905878i | \(-0.360788\pi\) | ||||
0.423539 | + | 0.905878i | \(0.360788\pi\) | |||||||
\(338\) | 5.36736 | 0.291946 | ||||||||
\(339\) | 28.8915 | 1.56917 | ||||||||
\(340\) | 62.1380 | 3.36991 | ||||||||
\(341\) | 2.10477 | 0.113979 | ||||||||
\(342\) | −5.36691 | −0.290209 | ||||||||
\(343\) | 19.8937 | 1.07416 | ||||||||
\(344\) | −18.5567 | −1.00051 | ||||||||
\(345\) | −29.5285 | −1.58976 | ||||||||
\(346\) | 19.4530 | 1.04580 | ||||||||
\(347\) | 0.237153 | 0.0127310 | 0.00636551 | − | 0.999980i | \(-0.497974\pi\) | ||||
0.00636551 | + | 0.999980i | \(0.497974\pi\) | |||||||
\(348\) | 10.2282 | 0.548289 | ||||||||
\(349\) | −12.1902 | −0.652525 | −0.326263 | − | 0.945279i | \(-0.605789\pi\) | ||||
−0.326263 | + | 0.945279i | \(0.605789\pi\) | |||||||
\(350\) | 3.92312 | 0.209700 | ||||||||
\(351\) | 14.5850 | 0.778488 | ||||||||
\(352\) | −1.39013 | −0.0740940 | ||||||||
\(353\) | −14.5713 | −0.775551 | −0.387775 | − | 0.921754i | \(-0.626756\pi\) | ||||
−0.387775 | + | 0.921754i | \(0.626756\pi\) | |||||||
\(354\) | −32.9326 | −1.75035 | ||||||||
\(355\) | −17.3737 | −0.922098 | ||||||||
\(356\) | 7.33041 | 0.388511 | ||||||||
\(357\) | −25.5935 | −1.35455 | ||||||||
\(358\) | 9.39497 | 0.496539 | ||||||||
\(359\) | 19.9049 | 1.05054 | 0.525270 | − | 0.850936i | \(-0.323964\pi\) | ||||
0.525270 | + | 0.850936i | \(0.323964\pi\) | |||||||
\(360\) | 7.01608 | 0.369780 | ||||||||
\(361\) | −8.32680 | −0.438252 | ||||||||
\(362\) | 46.6998 | 2.45449 | ||||||||
\(363\) | 20.2726 | 1.06403 | ||||||||
\(364\) | −24.1479 | −1.26570 | ||||||||
\(365\) | 23.3151 | 1.22037 | ||||||||
\(366\) | 9.86873 | 0.515847 | ||||||||
\(367\) | 10.6854 | 0.557775 | 0.278887 | − | 0.960324i | \(-0.410034\pi\) | ||||
0.278887 | + | 0.960324i | \(0.410034\pi\) | |||||||
\(368\) | −16.9462 | −0.883384 | ||||||||
\(369\) | 0.599888 | 0.0312289 | ||||||||
\(370\) | 34.3067 | 1.78352 | ||||||||
\(371\) | 13.5477 | 0.703360 | ||||||||
\(372\) | 23.0009 | 1.19254 | ||||||||
\(373\) | −11.8408 | −0.613092 | −0.306546 | − | 0.951856i | \(-0.599173\pi\) | ||||
−0.306546 | + | 0.951856i | \(0.599173\pi\) | |||||||
\(374\) | −10.8497 | −0.561025 | ||||||||
\(375\) | −19.3068 | −0.997000 | ||||||||
\(376\) | 44.0983 | 2.27420 | ||||||||
\(377\) | −4.64036 | −0.238991 | ||||||||
\(378\) | 20.8535 | 1.07259 | ||||||||
\(379\) | −1.89434 | −0.0973059 | −0.0486530 | − | 0.998816i | \(-0.515493\pi\) | ||||
−0.0486530 | + | 0.998816i | \(0.515493\pi\) | |||||||
\(380\) | −29.7379 | −1.52552 | ||||||||
\(381\) | 22.7635 | 1.16621 | ||||||||
\(382\) | 16.5681 | 0.847697 | ||||||||
\(383\) | 12.8909 | 0.658696 | 0.329348 | − | 0.944209i | \(-0.393171\pi\) | ||||
0.329348 | + | 0.944209i | \(0.393171\pi\) | |||||||
\(384\) | −39.7248 | −2.02720 | ||||||||
\(385\) | −3.12291 | −0.159158 | ||||||||
\(386\) | 13.3735 | 0.680694 | ||||||||
\(387\) | 2.98960 | 0.151970 | ||||||||
\(388\) | −47.1672 | −2.39455 | ||||||||
\(389\) | −14.7884 | −0.749800 | −0.374900 | − | 0.927065i | \(-0.622323\pi\) | ||||
−0.374900 | + | 0.927065i | \(0.622323\pi\) | |||||||
\(390\) | −36.5381 | −1.85018 | ||||||||
\(391\) | 43.4718 | 2.19846 | ||||||||
\(392\) | 13.5208 | 0.682901 | ||||||||
\(393\) | 12.4776 | 0.629411 | ||||||||
\(394\) | 27.1256 | 1.36657 | ||||||||
\(395\) | 0.854896 | 0.0430145 | ||||||||
\(396\) | −1.70562 | −0.0857104 | ||||||||
\(397\) | −3.24499 | −0.162861 | −0.0814306 | − | 0.996679i | \(-0.525949\pi\) | ||||
−0.0814306 | + | 0.996679i | \(0.525949\pi\) | |||||||
\(398\) | 56.1501 | 2.81455 | ||||||||
\(399\) | 12.2485 | 0.613193 | ||||||||
\(400\) | 2.22541 | 0.111270 | ||||||||
\(401\) | 24.0365 | 1.20032 | 0.600162 | − | 0.799878i | \(-0.295103\pi\) | ||||
0.600162 | + | 0.799878i | \(0.295103\pi\) | |||||||
\(402\) | −51.9909 | −2.59307 | ||||||||
\(403\) | −10.4351 | −0.519810 | ||||||||
\(404\) | 13.8920 | 0.691155 | ||||||||
\(405\) | 25.5697 | 1.27057 | ||||||||
\(406\) | −6.63475 | −0.329277 | ||||||||
\(407\) | −3.91308 | −0.193964 | ||||||||
\(408\) | −55.6304 | −2.75412 | ||||||||
\(409\) | −0.423743 | −0.0209527 | −0.0104764 | − | 0.999945i | \(-0.503335\pi\) | ||||
−0.0104764 | + | 0.999945i | \(0.503335\pi\) | |||||||
\(410\) | 5.08834 | 0.251295 | ||||||||
\(411\) | 2.81569 | 0.138888 | ||||||||
\(412\) | −35.2270 | −1.73551 | ||||||||
\(413\) | 13.9551 | 0.686685 | ||||||||
\(414\) | 10.4614 | 0.514150 | ||||||||
\(415\) | −0.992732 | −0.0487313 | ||||||||
\(416\) | 6.89204 | 0.337910 | ||||||||
\(417\) | −29.2317 | −1.43148 | ||||||||
\(418\) | 5.19244 | 0.253970 | ||||||||
\(419\) | −10.3485 | −0.505556 | −0.252778 | − | 0.967524i | \(-0.581344\pi\) | ||||
−0.252778 | + | 0.967524i | \(0.581344\pi\) | |||||||
\(420\) | −34.1271 | −1.66523 | ||||||||
\(421\) | −19.2110 | −0.936288 | −0.468144 | − | 0.883652i | \(-0.655077\pi\) | ||||
−0.468144 | + | 0.883652i | \(0.655077\pi\) | |||||||
\(422\) | −41.3762 | −2.01416 | ||||||||
\(423\) | −7.10451 | −0.345433 | ||||||||
\(424\) | 29.4474 | 1.43009 | ||||||||
\(425\) | −5.70877 | −0.276916 | ||||||||
\(426\) | 33.1507 | 1.60616 | ||||||||
\(427\) | −4.18184 | −0.202373 | ||||||||
\(428\) | 6.45030 | 0.311787 | ||||||||
\(429\) | 4.16761 | 0.201214 | ||||||||
\(430\) | 25.3583 | 1.22288 | ||||||||
\(431\) | −5.96194 | −0.287177 | −0.143588 | − | 0.989637i | \(-0.545864\pi\) | ||||
−0.143588 | + | 0.989637i | \(0.545864\pi\) | |||||||
\(432\) | 11.8292 | 0.569134 | ||||||||
\(433\) | −12.7289 | −0.611713 | −0.305857 | − | 0.952078i | \(-0.598943\pi\) | ||||
−0.305857 | + | 0.952078i | \(0.598943\pi\) | |||||||
\(434\) | −14.9200 | −0.716185 | ||||||||
\(435\) | −6.55800 | −0.314432 | ||||||||
\(436\) | −28.8232 | −1.38038 | ||||||||
\(437\) | −20.8047 | −0.995222 | ||||||||
\(438\) | −44.4876 | −2.12570 | ||||||||
\(439\) | 35.8163 | 1.70942 | 0.854709 | − | 0.519108i | \(-0.173736\pi\) | ||||
0.854709 | + | 0.519108i | \(0.173736\pi\) | |||||||
\(440\) | −6.78800 | −0.323605 | ||||||||
\(441\) | −2.17827 | −0.103727 | ||||||||
\(442\) | 53.7912 | 2.55859 | ||||||||
\(443\) | 4.99409 | 0.237276 | 0.118638 | − | 0.992938i | \(-0.462147\pi\) | ||||
0.118638 | + | 0.992938i | \(0.462147\pi\) | |||||||
\(444\) | −42.7622 | −2.02940 | ||||||||
\(445\) | −4.70003 | −0.222803 | ||||||||
\(446\) | 25.4600 | 1.20557 | ||||||||
\(447\) | −10.0966 | −0.477555 | ||||||||
\(448\) | 20.2502 | 0.956730 | ||||||||
\(449\) | 16.8464 | 0.795031 | 0.397515 | − | 0.917595i | \(-0.369873\pi\) | ||||
0.397515 | + | 0.917595i | \(0.369873\pi\) | |||||||
\(450\) | −1.37381 | −0.0647619 | ||||||||
\(451\) | −0.580386 | −0.0273293 | ||||||||
\(452\) | −56.7159 | −2.66769 | ||||||||
\(453\) | 3.99485 | 0.187695 | ||||||||
\(454\) | −21.7094 | −1.01887 | ||||||||
\(455\) | 15.4829 | 0.725849 | ||||||||
\(456\) | 26.6236 | 1.24676 | ||||||||
\(457\) | 34.6162 | 1.61928 | 0.809639 | − | 0.586928i | \(-0.199663\pi\) | ||||
0.809639 | + | 0.586928i | \(0.199663\pi\) | |||||||
\(458\) | −1.12527 | −0.0525804 | ||||||||
\(459\) | −30.3452 | −1.41639 | ||||||||
\(460\) | 57.9665 | 2.70270 | ||||||||
\(461\) | 17.6626 | 0.822630 | 0.411315 | − | 0.911493i | \(-0.365070\pi\) | ||||
0.411315 | + | 0.911493i | \(0.365070\pi\) | |||||||
\(462\) | 5.95881 | 0.277229 | ||||||||
\(463\) | 19.9329 | 0.926361 | 0.463181 | − | 0.886264i | \(-0.346708\pi\) | ||||
0.463181 | + | 0.886264i | \(0.346708\pi\) | |||||||
\(464\) | −3.76359 | −0.174720 | ||||||||
\(465\) | −14.7474 | −0.683896 | ||||||||
\(466\) | 21.1952 | 0.981848 | ||||||||
\(467\) | 4.76380 | 0.220442 | 0.110221 | − | 0.993907i | \(-0.464844\pi\) | ||||
0.110221 | + | 0.993907i | \(0.464844\pi\) | |||||||
\(468\) | 8.45618 | 0.390887 | ||||||||
\(469\) | 22.0310 | 1.01730 | ||||||||
\(470\) | −60.2615 | −2.77966 | ||||||||
\(471\) | 0.215153 | 0.00991375 | ||||||||
\(472\) | 30.3330 | 1.39619 | ||||||||
\(473\) | −2.89241 | −0.132993 | ||||||||
\(474\) | −1.63123 | −0.0749247 | ||||||||
\(475\) | 2.73210 | 0.125357 | ||||||||
\(476\) | 50.2417 | 2.30283 | ||||||||
\(477\) | −4.74416 | −0.217220 | ||||||||
\(478\) | 39.1243 | 1.78951 | ||||||||
\(479\) | 26.7735 | 1.22331 | 0.611657 | − | 0.791123i | \(-0.290503\pi\) | ||||
0.611657 | + | 0.791123i | \(0.290503\pi\) | |||||||
\(480\) | 9.74018 | 0.444576 | ||||||||
\(481\) | 19.4005 | 0.884586 | ||||||||
\(482\) | −6.68458 | −0.304474 | ||||||||
\(483\) | −23.8753 | −1.08636 | ||||||||
\(484\) | −39.7964 | −1.80893 | ||||||||
\(485\) | 30.2421 | 1.37323 | ||||||||
\(486\) | −16.7618 | −0.760332 | ||||||||
\(487\) | −22.1954 | −1.00577 | −0.502884 | − | 0.864354i | \(-0.667728\pi\) | ||||
−0.502884 | + | 0.864354i | \(0.667728\pi\) | |||||||
\(488\) | −9.08971 | −0.411472 | ||||||||
\(489\) | 24.8956 | 1.12582 | ||||||||
\(490\) | −18.4765 | −0.834682 | ||||||||
\(491\) | 22.1242 | 0.998452 | 0.499226 | − | 0.866472i | \(-0.333618\pi\) | ||||
0.499226 | + | 0.866472i | \(0.333618\pi\) | |||||||
\(492\) | −6.34246 | −0.285940 | ||||||||
\(493\) | 9.65464 | 0.434823 | ||||||||
\(494\) | −25.7433 | −1.15825 | ||||||||
\(495\) | 1.09359 | 0.0491531 | ||||||||
\(496\) | −8.46346 | −0.380020 | ||||||||
\(497\) | −14.0475 | −0.630116 | ||||||||
\(498\) | 1.89423 | 0.0848825 | ||||||||
\(499\) | −40.8792 | −1.83000 | −0.915001 | − | 0.403450i | \(-0.867811\pi\) | ||||
−0.915001 | + | 0.403450i | \(0.867811\pi\) | |||||||
\(500\) | 37.9006 | 1.69496 | ||||||||
\(501\) | 38.6307 | 1.72589 | ||||||||
\(502\) | −3.51384 | −0.156830 | ||||||||
\(503\) | −21.5219 | −0.959613 | −0.479807 | − | 0.877374i | \(-0.659293\pi\) | ||||
−0.479807 | + | 0.877374i | \(0.659293\pi\) | |||||||
\(504\) | 5.67285 | 0.252689 | ||||||||
\(505\) | −8.90714 | −0.396362 | ||||||||
\(506\) | −10.1213 | −0.449948 | ||||||||
\(507\) | 4.28957 | 0.190507 | ||||||||
\(508\) | −44.6862 | −1.98263 | ||||||||
\(509\) | −13.5703 | −0.601494 | −0.300747 | − | 0.953704i | \(-0.597236\pi\) | ||||
−0.300747 | + | 0.953704i | \(0.597236\pi\) | |||||||
\(510\) | 76.0205 | 3.36624 | ||||||||
\(511\) | 18.8515 | 0.833939 | ||||||||
\(512\) | 28.1867 | 1.24569 | ||||||||
\(513\) | 14.5226 | 0.641187 | ||||||||
\(514\) | 23.8978 | 1.05409 | ||||||||
\(515\) | 22.5864 | 0.995278 | ||||||||
\(516\) | −31.6083 | −1.39148 | ||||||||
\(517\) | 6.87355 | 0.302298 | ||||||||
\(518\) | 27.7387 | 1.21877 | ||||||||
\(519\) | 15.5467 | 0.682426 | ||||||||
\(520\) | 33.6539 | 1.47582 | ||||||||
\(521\) | 17.3415 | 0.759744 | 0.379872 | − | 0.925039i | \(-0.375968\pi\) | ||||
0.379872 | + | 0.925039i | \(0.375968\pi\) | |||||||
\(522\) | 2.32337 | 0.101691 | ||||||||
\(523\) | 13.1524 | 0.575115 | 0.287558 | − | 0.957763i | \(-0.407157\pi\) | ||||
0.287558 | + | 0.957763i | \(0.407157\pi\) | |||||||
\(524\) | −24.4943 | −1.07004 | ||||||||
\(525\) | 3.13534 | 0.136838 | ||||||||
\(526\) | 35.9241 | 1.56636 | ||||||||
\(527\) | 21.7111 | 0.945750 | ||||||||
\(528\) | 3.38016 | 0.147103 | ||||||||
\(529\) | 17.5533 | 0.763188 | ||||||||
\(530\) | −40.2407 | −1.74794 | ||||||||
\(531\) | −4.88683 | −0.212070 | ||||||||
\(532\) | −24.0446 | −1.04247 | ||||||||
\(533\) | 2.87747 | 0.124637 | ||||||||
\(534\) | 8.96811 | 0.388088 | ||||||||
\(535\) | −4.13573 | −0.178803 | ||||||||
\(536\) | 47.8869 | 2.06840 | ||||||||
\(537\) | 7.50842 | 0.324012 | ||||||||
\(538\) | 12.1172 | 0.522411 | ||||||||
\(539\) | 2.10746 | 0.0907748 | ||||||||
\(540\) | −40.4631 | −1.74126 | ||||||||
\(541\) | 34.9176 | 1.50122 | 0.750612 | − | 0.660743i | \(-0.229759\pi\) | ||||
0.750612 | + | 0.660743i | \(0.229759\pi\) | |||||||
\(542\) | −68.0833 | −2.92443 | ||||||||
\(543\) | 37.3223 | 1.60165 | ||||||||
\(544\) | −14.3394 | −0.614798 | ||||||||
\(545\) | 18.4805 | 0.791619 | ||||||||
\(546\) | −29.5429 | −1.26432 | ||||||||
\(547\) | 37.3153 | 1.59549 | 0.797744 | − | 0.602996i | \(-0.206027\pi\) | ||||
0.797744 | + | 0.602996i | \(0.206027\pi\) | |||||||
\(548\) | −5.52739 | −0.236118 | ||||||||
\(549\) | 1.46441 | 0.0624994 | ||||||||
\(550\) | 1.32915 | 0.0566750 | ||||||||
\(551\) | −4.62051 | −0.196840 | ||||||||
\(552\) | −51.8958 | −2.20883 | ||||||||
\(553\) | 0.691226 | 0.0293939 | ||||||||
\(554\) | −55.4865 | −2.35739 | ||||||||
\(555\) | 27.4177 | 1.16382 | ||||||||
\(556\) | 57.3837 | 2.43361 | ||||||||
\(557\) | −39.1178 | −1.65748 | −0.828738 | − | 0.559637i | \(-0.810941\pi\) | ||||
−0.828738 | + | 0.559637i | \(0.810941\pi\) | |||||||
\(558\) | 5.22474 | 0.221181 | ||||||||
\(559\) | 14.3402 | 0.606524 | ||||||||
\(560\) | 12.5575 | 0.530651 | ||||||||
\(561\) | −8.67104 | −0.366092 | ||||||||
\(562\) | −16.4868 | −0.695452 | ||||||||
\(563\) | −41.5306 | −1.75031 | −0.875153 | − | 0.483846i | \(-0.839240\pi\) | ||||
−0.875153 | + | 0.483846i | \(0.839240\pi\) | |||||||
\(564\) | 75.1141 | 3.16287 | ||||||||
\(565\) | 36.3645 | 1.52986 | ||||||||
\(566\) | −4.32825 | −0.181930 | ||||||||
\(567\) | 20.6744 | 0.868241 | ||||||||
\(568\) | −30.5338 | −1.28117 | ||||||||
\(569\) | −9.13224 | −0.382844 | −0.191422 | − | 0.981508i | \(-0.561310\pi\) | ||||
−0.191422 | + | 0.981508i | \(0.561310\pi\) | |||||||
\(570\) | −36.3818 | −1.52387 | ||||||||
\(571\) | −7.11507 | −0.297756 | −0.148878 | − | 0.988856i | \(-0.547566\pi\) | ||||
−0.148878 | + | 0.988856i | \(0.547566\pi\) | |||||||
\(572\) | −8.18128 | −0.342077 | ||||||||
\(573\) | 13.2411 | 0.553157 | ||||||||
\(574\) | 4.11418 | 0.171723 | ||||||||
\(575\) | −5.32552 | −0.222090 | ||||||||
\(576\) | −7.09125 | −0.295469 | ||||||||
\(577\) | −44.1924 | −1.83975 | −0.919877 | − | 0.392207i | \(-0.871712\pi\) | ||||
−0.919877 | + | 0.392207i | \(0.871712\pi\) | |||||||
\(578\) | −71.0890 | −2.95691 | ||||||||
\(579\) | 10.6881 | 0.444181 | ||||||||
\(580\) | 12.8738 | 0.534554 | ||||||||
\(581\) | −0.802674 | −0.0333005 | ||||||||
\(582\) | −57.7050 | −2.39195 | ||||||||
\(583\) | 4.58993 | 0.190096 | ||||||||
\(584\) | 40.9758 | 1.69559 | ||||||||
\(585\) | −5.42184 | −0.224165 | ||||||||
\(586\) | −17.3778 | −0.717869 | ||||||||
\(587\) | 30.8270 | 1.27237 | 0.636183 | − | 0.771538i | \(-0.280512\pi\) | ||||
0.636183 | + | 0.771538i | \(0.280512\pi\) | |||||||
\(588\) | 23.0303 | 0.949755 | ||||||||
\(589\) | −10.3905 | −0.428132 | ||||||||
\(590\) | −41.4508 | −1.70650 | ||||||||
\(591\) | 21.6786 | 0.891740 | ||||||||
\(592\) | 15.7349 | 0.646699 | ||||||||
\(593\) | −26.1364 | −1.07329 | −0.536646 | − | 0.843807i | \(-0.680309\pi\) | ||||
−0.536646 | + | 0.843807i | \(0.680309\pi\) | |||||||
\(594\) | 7.06512 | 0.289885 | ||||||||
\(595\) | −32.2134 | −1.32062 | ||||||||
\(596\) | 19.8204 | 0.811874 | ||||||||
\(597\) | 44.8749 | 1.83661 | ||||||||
\(598\) | 50.1800 | 2.05201 | ||||||||
\(599\) | −42.9686 | −1.75565 | −0.877824 | − | 0.478983i | \(-0.841005\pi\) | ||||
−0.877824 | + | 0.478983i | \(0.841005\pi\) | |||||||
\(600\) | 6.81503 | 0.278222 | ||||||||
\(601\) | −12.3714 | −0.504638 | −0.252319 | − | 0.967644i | \(-0.581193\pi\) | ||||
−0.252319 | + | 0.967644i | \(0.581193\pi\) | |||||||
\(602\) | 20.5034 | 0.835658 | ||||||||
\(603\) | −7.71486 | −0.314173 | ||||||||
\(604\) | −7.84216 | −0.319093 | ||||||||
\(605\) | 25.5162 | 1.03738 | ||||||||
\(606\) | 16.9957 | 0.690403 | ||||||||
\(607\) | −17.9270 | −0.727635 | −0.363817 | − | 0.931470i | \(-0.618527\pi\) | ||||
−0.363817 | + | 0.931470i | \(0.618527\pi\) | |||||||
\(608\) | 6.86255 | 0.278313 | ||||||||
\(609\) | −5.30247 | −0.214867 | ||||||||
\(610\) | 12.4213 | 0.502925 | ||||||||
\(611\) | −34.0780 | −1.37865 | ||||||||
\(612\) | −17.5938 | −0.711186 | ||||||||
\(613\) | −9.50776 | −0.384015 | −0.192007 | − | 0.981393i | \(-0.561500\pi\) | ||||
−0.192007 | + | 0.981393i | \(0.561500\pi\) | |||||||
\(614\) | −57.9498 | −2.33866 | ||||||||
\(615\) | 4.06658 | 0.163981 | ||||||||
\(616\) | −5.48844 | −0.221135 | ||||||||
\(617\) | −38.4300 | −1.54713 | −0.773566 | − | 0.633715i | \(-0.781529\pi\) | ||||
−0.773566 | + | 0.633715i | \(0.781529\pi\) | |||||||
\(618\) | −43.0972 | −1.73362 | ||||||||
\(619\) | 15.3425 | 0.616669 | 0.308334 | − | 0.951278i | \(-0.400228\pi\) | ||||
0.308334 | + | 0.951278i | \(0.400228\pi\) | |||||||
\(620\) | 28.9502 | 1.16267 | ||||||||
\(621\) | −28.3080 | −1.13596 | ||||||||
\(622\) | −5.03424 | −0.201855 | ||||||||
\(623\) | −3.80021 | −0.152252 | ||||||||
\(624\) | −16.7583 | −0.670870 | ||||||||
\(625\) | −28.4820 | −1.13928 | ||||||||
\(626\) | −23.8585 | −0.953578 | ||||||||
\(627\) | 4.14978 | 0.165726 | ||||||||
\(628\) | −0.422360 | −0.0168540 | ||||||||
\(629\) | −40.3642 | −1.60943 | ||||||||
\(630\) | −7.75210 | −0.308851 | ||||||||
\(631\) | 2.60971 | 0.103891 | 0.0519455 | − | 0.998650i | \(-0.483458\pi\) | ||||
0.0519455 | + | 0.998650i | \(0.483458\pi\) | |||||||
\(632\) | 1.50246 | 0.0597646 | ||||||||
\(633\) | −33.0677 | −1.31432 | ||||||||
\(634\) | −12.9412 | −0.513962 | ||||||||
\(635\) | 28.6514 | 1.13699 | ||||||||
\(636\) | 50.1588 | 1.98892 | ||||||||
\(637\) | −10.4485 | −0.413984 | ||||||||
\(638\) | −2.24784 | −0.0889930 | ||||||||
\(639\) | 4.91918 | 0.194600 | ||||||||
\(640\) | −49.9998 | −1.97642 | ||||||||
\(641\) | 25.5763 | 1.01020 | 0.505101 | − | 0.863060i | \(-0.331455\pi\) | ||||
0.505101 | + | 0.863060i | \(0.331455\pi\) | |||||||
\(642\) | 7.89138 | 0.311448 | ||||||||
\(643\) | 28.9415 | 1.14134 | 0.570671 | − | 0.821179i | \(-0.306683\pi\) | ||||
0.570671 | + | 0.821179i | \(0.306683\pi\) | |||||||
\(644\) | 46.8688 | 1.84689 | ||||||||
\(645\) | 20.2662 | 0.797982 | ||||||||
\(646\) | 53.5610 | 2.10733 | ||||||||
\(647\) | 47.9062 | 1.88339 | 0.941694 | − | 0.336470i | \(-0.109233\pi\) | ||||
0.941694 | + | 0.336470i | \(0.109233\pi\) | |||||||
\(648\) | 44.9381 | 1.76534 | ||||||||
\(649\) | 4.72796 | 0.185589 | ||||||||
\(650\) | −6.58971 | −0.258470 | ||||||||
\(651\) | −11.9240 | −0.467340 | ||||||||
\(652\) | −48.8717 | −1.91396 | ||||||||
\(653\) | 23.3821 | 0.915013 | 0.457507 | − | 0.889206i | \(-0.348743\pi\) | ||||
0.457507 | + | 0.889206i | \(0.348743\pi\) | |||||||
\(654\) | −35.2627 | −1.37888 | ||||||||
\(655\) | 15.7050 | 0.613644 | ||||||||
\(656\) | 2.33379 | 0.0911191 | ||||||||
\(657\) | −6.60145 | −0.257547 | ||||||||
\(658\) | −48.7245 | −1.89948 | ||||||||
\(659\) | 6.71032 | 0.261397 | 0.130699 | − | 0.991422i | \(-0.458278\pi\) | ||||
0.130699 | + | 0.991422i | \(0.458278\pi\) | |||||||
\(660\) | −11.5622 | −0.450058 | ||||||||
\(661\) | 9.78504 | 0.380594 | 0.190297 | − | 0.981727i | \(-0.439055\pi\) | ||||
0.190297 | + | 0.981727i | \(0.439055\pi\) | |||||||
\(662\) | −39.7422 | −1.54463 | ||||||||
\(663\) | 42.9897 | 1.66958 | ||||||||
\(664\) | −1.74470 | −0.0677076 | ||||||||
\(665\) | 15.4167 | 0.597832 | ||||||||
\(666\) | −9.71359 | −0.376394 | ||||||||
\(667\) | 9.00649 | 0.348733 | ||||||||
\(668\) | −75.8346 | −2.93413 | ||||||||
\(669\) | 20.3476 | 0.786682 | ||||||||
\(670\) | −65.4387 | −2.52812 | ||||||||
\(671\) | −1.41680 | −0.0546950 | ||||||||
\(672\) | 7.87542 | 0.303801 | ||||||||
\(673\) | −45.2457 | −1.74409 | −0.872047 | − | 0.489421i | \(-0.837208\pi\) | ||||
−0.872047 | + | 0.489421i | \(0.837208\pi\) | |||||||
\(674\) | −37.3462 | −1.43852 | ||||||||
\(675\) | 3.71745 | 0.143085 | ||||||||
\(676\) | −8.42071 | −0.323874 | ||||||||
\(677\) | −0.600190 | −0.0230672 | −0.0115336 | − | 0.999933i | \(-0.503671\pi\) | ||||
−0.0115336 | + | 0.999933i | \(0.503671\pi\) | |||||||
\(678\) | −69.3870 | −2.66479 | ||||||||
\(679\) | 24.4523 | 0.938393 | ||||||||
\(680\) | −70.0196 | −2.68513 | ||||||||
\(681\) | −17.3501 | −0.664857 | ||||||||
\(682\) | −5.05489 | −0.193562 | ||||||||
\(683\) | −16.1530 | −0.618079 | −0.309039 | − | 0.951049i | \(-0.600007\pi\) | ||||
−0.309039 | + | 0.951049i | \(0.600007\pi\) | |||||||
\(684\) | 8.42000 | 0.321947 | ||||||||
\(685\) | 3.54399 | 0.135409 | ||||||||
\(686\) | −47.7774 | −1.82415 | ||||||||
\(687\) | −0.899312 | −0.0343109 | ||||||||
\(688\) | 11.6307 | 0.443415 | ||||||||
\(689\) | −22.7562 | −0.866942 | ||||||||
\(690\) | 70.9169 | 2.69976 | ||||||||
\(691\) | −45.3242 | −1.72421 | −0.862106 | − | 0.506727i | \(-0.830855\pi\) | ||||
−0.862106 | + | 0.506727i | \(0.830855\pi\) | |||||||
\(692\) | −30.5193 | −1.16017 | ||||||||
\(693\) | 0.884220 | 0.0335887 | ||||||||
\(694\) | −0.569555 | −0.0216200 | ||||||||
\(695\) | −36.7926 | −1.39562 | ||||||||
\(696\) | −11.5255 | −0.436874 | ||||||||
\(697\) | −5.98680 | −0.226766 | ||||||||
\(698\) | 29.2764 | 1.10813 | ||||||||
\(699\) | 16.9391 | 0.640696 | ||||||||
\(700\) | −6.15488 | −0.232633 | ||||||||
\(701\) | 25.1855 | 0.951243 | 0.475621 | − | 0.879650i | \(-0.342223\pi\) | ||||
0.475621 | + | 0.879650i | \(0.342223\pi\) | |||||||
\(702\) | −35.0278 | −1.32204 | ||||||||
\(703\) | 19.3175 | 0.728572 | ||||||||
\(704\) | 6.86072 | 0.258573 | ||||||||
\(705\) | −48.1608 | −1.81384 | ||||||||
\(706\) | 34.9949 | 1.31705 | ||||||||
\(707\) | −7.20187 | −0.270854 | ||||||||
\(708\) | 51.6671 | 1.94177 | ||||||||
\(709\) | −31.2398 | −1.17323 | −0.586617 | − | 0.809864i | \(-0.699541\pi\) | ||||
−0.586617 | + | 0.809864i | \(0.699541\pi\) | |||||||
\(710\) | 41.7253 | 1.56592 | ||||||||
\(711\) | −0.242055 | −0.00907778 | ||||||||
\(712\) | −8.26019 | −0.309564 | ||||||||
\(713\) | 20.2535 | 0.758501 | ||||||||
\(714\) | 61.4664 | 2.30032 | ||||||||
\(715\) | 5.24558 | 0.196174 | ||||||||
\(716\) | −14.7395 | −0.550842 | ||||||||
\(717\) | 31.2680 | 1.16773 | ||||||||
\(718\) | −47.8043 | −1.78404 | ||||||||
\(719\) | 35.8470 | 1.33687 | 0.668434 | − | 0.743771i | \(-0.266965\pi\) | ||||
0.668434 | + | 0.743771i | \(0.266965\pi\) | |||||||
\(720\) | −4.39741 | −0.163882 | ||||||||
\(721\) | 18.2623 | 0.680123 | ||||||||
\(722\) | 19.9980 | 0.744247 | ||||||||
\(723\) | −5.34229 | −0.198682 | ||||||||
\(724\) | −73.2660 | −2.72291 | ||||||||
\(725\) | −1.18275 | −0.0439261 | ||||||||
\(726\) | −48.6874 | −1.80696 | ||||||||
\(727\) | 29.3426 | 1.08826 | 0.544129 | − | 0.839002i | \(-0.316860\pi\) | ||||
0.544129 | + | 0.839002i | \(0.316860\pi\) | |||||||
\(728\) | 27.2108 | 1.00850 | ||||||||
\(729\) | 18.3566 | 0.679872 | ||||||||
\(730\) | −55.9945 | −2.07245 | ||||||||
\(731\) | −29.8358 | −1.10352 | ||||||||
\(732\) | −15.4828 | −0.572260 | ||||||||
\(733\) | 5.96577 | 0.220351 | 0.110175 | − | 0.993912i | \(-0.464859\pi\) | ||||
0.110175 | + | 0.993912i | \(0.464859\pi\) | |||||||
\(734\) | −25.6625 | −0.947221 | ||||||||
\(735\) | −14.7663 | −0.544664 | ||||||||
\(736\) | −13.3768 | −0.493074 | ||||||||
\(737\) | 7.46406 | 0.274942 | ||||||||
\(738\) | −1.44071 | −0.0530334 | ||||||||
\(739\) | 14.3069 | 0.526287 | 0.263144 | − | 0.964757i | \(-0.415241\pi\) | ||||
0.263144 | + | 0.964757i | \(0.415241\pi\) | |||||||
\(740\) | −53.8228 | −1.97857 | ||||||||
\(741\) | −20.5740 | −0.755803 | ||||||||
\(742\) | −32.5366 | −1.19446 | ||||||||
\(743\) | 3.57676 | 0.131219 | 0.0656093 | − | 0.997845i | \(-0.479101\pi\) | ||||
0.0656093 | + | 0.997845i | \(0.479101\pi\) | |||||||
\(744\) | −25.9183 | −0.950210 | ||||||||
\(745\) | −12.7082 | −0.465592 | ||||||||
\(746\) | 28.4373 | 1.04116 | ||||||||
\(747\) | 0.281082 | 0.0102843 | ||||||||
\(748\) | 17.0218 | 0.622379 | ||||||||
\(749\) | −3.34394 | −0.122185 | ||||||||
\(750\) | 46.3680 | 1.69312 | ||||||||
\(751\) | 17.9465 | 0.654878 | 0.327439 | − | 0.944872i | \(-0.393814\pi\) | ||||
0.327439 | + | 0.944872i | \(0.393814\pi\) | |||||||
\(752\) | −27.6392 | −1.00790 | ||||||||
\(753\) | −2.80825 | −0.102338 | ||||||||
\(754\) | 11.1445 | 0.405858 | ||||||||
\(755\) | 5.02814 | 0.182993 | ||||||||
\(756\) | −32.7165 | −1.18989 | ||||||||
\(757\) | 17.9786 | 0.653442 | 0.326721 | − | 0.945121i | \(-0.394056\pi\) | ||||
0.326721 | + | 0.945121i | \(0.394056\pi\) | |||||||
\(758\) | 4.54953 | 0.165246 | ||||||||
\(759\) | −8.08892 | −0.293609 | ||||||||
\(760\) | 33.5099 | 1.21553 | ||||||||
\(761\) | 2.63730 | 0.0956020 | 0.0478010 | − | 0.998857i | \(-0.484779\pi\) | ||||
0.0478010 | + | 0.998857i | \(0.484779\pi\) | |||||||
\(762\) | −54.6696 | −1.98047 | ||||||||
\(763\) | 14.9424 | 0.540952 | ||||||||
\(764\) | −25.9932 | −0.940402 | ||||||||
\(765\) | 11.2806 | 0.407850 | ||||||||
\(766\) | −30.9594 | −1.11861 | ||||||||
\(767\) | −23.4405 | −0.846388 | ||||||||
\(768\) | 55.6081 | 2.00658 | ||||||||
\(769\) | −44.4599 | −1.60326 | −0.801632 | − | 0.597817i | \(-0.796035\pi\) | ||||
−0.801632 | + | 0.597817i | \(0.796035\pi\) | |||||||
\(770\) | 7.50009 | 0.270285 | ||||||||
\(771\) | 19.0990 | 0.687835 | ||||||||
\(772\) | −20.9814 | −0.755136 | ||||||||
\(773\) | 27.6340 | 0.993927 | 0.496964 | − | 0.867771i | \(-0.334448\pi\) | ||||
0.496964 | + | 0.867771i | \(0.334448\pi\) | |||||||
\(774\) | −7.17994 | −0.258078 | ||||||||
\(775\) | −2.65972 | −0.0955401 | ||||||||
\(776\) | 53.1499 | 1.90797 | ||||||||
\(777\) | 22.1686 | 0.795295 | ||||||||
\(778\) | 35.5163 | 1.27332 | ||||||||
\(779\) | 2.86516 | 0.102655 | ||||||||
\(780\) | 57.3237 | 2.05252 | ||||||||
\(781\) | −4.75926 | −0.170300 | ||||||||
\(782\) | −104.403 | −3.73346 | ||||||||
\(783\) | −6.28692 | −0.224676 | ||||||||
\(784\) | −8.47430 | −0.302653 | ||||||||
\(785\) | 0.270804 | 0.00966541 | ||||||||
\(786\) | −29.9667 | −1.06888 | ||||||||
\(787\) | 33.5212 | 1.19490 | 0.597451 | − | 0.801905i | \(-0.296180\pi\) | ||||
0.597451 | + | 0.801905i | \(0.296180\pi\) | |||||||
\(788\) | −42.5566 | −1.51602 | ||||||||
\(789\) | 28.7104 | 1.02212 | ||||||||
\(790\) | −2.05315 | −0.0730478 | ||||||||
\(791\) | 29.4025 | 1.04543 | ||||||||
\(792\) | 1.92195 | 0.0682937 | ||||||||
\(793\) | 7.02428 | 0.249440 | ||||||||
\(794\) | 7.79328 | 0.276573 | ||||||||
\(795\) | −32.1602 | −1.14061 | ||||||||
\(796\) | −88.0924 | −3.12235 | ||||||||
\(797\) | 13.9337 | 0.493556 | 0.246778 | − | 0.969072i | \(-0.420628\pi\) | ||||
0.246778 | + | 0.969072i | \(0.420628\pi\) | |||||||
\(798\) | −29.4165 | −1.04133 | ||||||||
\(799\) | 70.9020 | 2.50833 | ||||||||
\(800\) | 1.75666 | 0.0621072 | ||||||||
\(801\) | 1.33077 | 0.0470203 | ||||||||
\(802\) | −57.7269 | −2.03841 | ||||||||
\(803\) | 6.38684 | 0.225387 | ||||||||
\(804\) | 81.5672 | 2.87665 | ||||||||
\(805\) | −30.0508 | −1.05915 | ||||||||
\(806\) | 25.0614 | 0.882749 | ||||||||
\(807\) | 9.68405 | 0.340895 | ||||||||
\(808\) | −15.6541 | −0.550709 | ||||||||
\(809\) | 36.6018 | 1.28685 | 0.643425 | − | 0.765509i | \(-0.277513\pi\) | ||||
0.643425 | + | 0.765509i | \(0.277513\pi\) | |||||||
\(810\) | −61.4091 | −2.15770 | ||||||||
\(811\) | −41.5592 | −1.45934 | −0.729671 | − | 0.683798i | \(-0.760327\pi\) | ||||
−0.729671 | + | 0.683798i | \(0.760327\pi\) | |||||||
\(812\) | 10.4091 | 0.365287 | ||||||||
\(813\) | −54.4119 | −1.90831 | ||||||||
\(814\) | 9.39781 | 0.329393 | ||||||||
\(815\) | 31.3350 | 1.09762 | ||||||||
\(816\) | 34.8671 | 1.22059 | ||||||||
\(817\) | 14.2788 | 0.499552 | ||||||||
\(818\) | 1.01768 | 0.0355822 | ||||||||
\(819\) | −4.38383 | −0.153183 | ||||||||
\(820\) | −7.98297 | −0.278777 | ||||||||
\(821\) | −10.9706 | −0.382876 | −0.191438 | − | 0.981505i | \(-0.561315\pi\) | ||||
−0.191438 | + | 0.981505i | \(0.561315\pi\) | |||||||
\(822\) | −6.76228 | −0.235861 | ||||||||
\(823\) | −28.1758 | −0.982146 | −0.491073 | − | 0.871118i | \(-0.663395\pi\) | ||||
−0.491073 | + | 0.871118i | \(0.663395\pi\) | |||||||
\(824\) | 39.6952 | 1.38285 | ||||||||
\(825\) | 1.06225 | 0.0369828 | ||||||||
\(826\) | −33.5151 | −1.16614 | ||||||||
\(827\) | −53.1178 | −1.84709 | −0.923544 | − | 0.383493i | \(-0.874721\pi\) | ||||
−0.923544 | + | 0.383493i | \(0.874721\pi\) | |||||||
\(828\) | −16.4126 | −0.570378 | ||||||||
\(829\) | −42.9561 | −1.49193 | −0.745964 | − | 0.665986i | \(-0.768011\pi\) | ||||
−0.745964 | + | 0.665986i | \(0.768011\pi\) | |||||||
\(830\) | 2.38418 | 0.0827562 | ||||||||
\(831\) | −44.3446 | −1.53830 | ||||||||
\(832\) | −34.0144 | −1.17924 | ||||||||
\(833\) | 21.7389 | 0.753208 | ||||||||
\(834\) | 70.2039 | 2.43096 | ||||||||
\(835\) | 48.6227 | 1.68266 | ||||||||
\(836\) | −8.14628 | −0.281745 | ||||||||
\(837\) | −14.1378 | −0.488675 | ||||||||
\(838\) | 24.8533 | 0.858542 | ||||||||
\(839\) | 33.6731 | 1.16252 | 0.581262 | − | 0.813717i | \(-0.302559\pi\) | ||||
0.581262 | + | 0.813717i | \(0.302559\pi\) | |||||||
\(840\) | 38.4558 | 1.32685 | ||||||||
\(841\) | −26.9997 | −0.931026 | ||||||||
\(842\) | 46.1379 | 1.59002 | ||||||||
\(843\) | −13.1762 | −0.453811 | ||||||||
\(844\) | 64.9141 | 2.23443 | ||||||||
\(845\) | 5.39910 | 0.185735 | ||||||||
\(846\) | 17.0625 | 0.586619 | ||||||||
\(847\) | 20.6311 | 0.708894 | ||||||||
\(848\) | −18.4565 | −0.633800 | ||||||||
\(849\) | −3.45912 | −0.118717 | ||||||||
\(850\) | 13.7104 | 0.470263 | ||||||||
\(851\) | −37.6544 | −1.29078 | ||||||||
\(852\) | −52.0092 | −1.78181 | ||||||||
\(853\) | 17.2295 | 0.589928 | 0.294964 | − | 0.955508i | \(-0.404692\pi\) | ||||
0.294964 | + | 0.955508i | \(0.404692\pi\) | |||||||
\(854\) | 10.0433 | 0.343674 | ||||||||
\(855\) | −5.39864 | −0.184630 | ||||||||
\(856\) | −7.26845 | −0.248430 | ||||||||
\(857\) | 22.5237 | 0.769394 | 0.384697 | − | 0.923043i | \(-0.374306\pi\) | ||||
0.384697 | + | 0.923043i | \(0.374306\pi\) | |||||||
\(858\) | −10.0091 | −0.341705 | ||||||||
\(859\) | −35.6082 | −1.21494 | −0.607468 | − | 0.794344i | \(-0.707815\pi\) | ||||
−0.607468 | + | 0.794344i | \(0.707815\pi\) | |||||||
\(860\) | −39.7839 | −1.35662 | ||||||||
\(861\) | 3.28804 | 0.112056 | ||||||||
\(862\) | 14.3184 | 0.487688 | ||||||||
\(863\) | −53.5774 | −1.82379 | −0.911897 | − | 0.410418i | \(-0.865383\pi\) | ||||
−0.911897 | + | 0.410418i | \(0.865383\pi\) | |||||||
\(864\) | 9.33757 | 0.317670 | ||||||||
\(865\) | 19.5680 | 0.665332 | ||||||||
\(866\) | 30.5703 | 1.03882 | ||||||||
\(867\) | −56.8141 | −1.92951 | ||||||||
\(868\) | 23.4077 | 0.794508 | ||||||||
\(869\) | 0.234186 | 0.00794423 | ||||||||
\(870\) | 15.7499 | 0.533973 | ||||||||
\(871\) | −37.0057 | −1.25389 | ||||||||
\(872\) | 32.4791 | 1.09988 | ||||||||
\(873\) | −8.56276 | −0.289806 | ||||||||
\(874\) | 49.9653 | 1.69010 | ||||||||
\(875\) | −19.6483 | −0.664233 | ||||||||
\(876\) | 69.7954 | 2.35817 | ||||||||
\(877\) | 0.600351 | 0.0202724 | 0.0101362 | − | 0.999949i | \(-0.496773\pi\) | ||||
0.0101362 | + | 0.999949i | \(0.496773\pi\) | |||||||
\(878\) | −86.0177 | −2.90296 | ||||||||
\(879\) | −13.8883 | −0.468439 | ||||||||
\(880\) | 4.25446 | 0.143418 | ||||||||
\(881\) | −19.2905 | −0.649915 | −0.324958 | − | 0.945729i | \(-0.605350\pi\) | ||||
−0.324958 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(882\) | 5.23143 | 0.176151 | ||||||||
\(883\) | 9.00751 | 0.303127 | 0.151563 | − | 0.988448i | \(-0.451569\pi\) | ||||
0.151563 | + | 0.988448i | \(0.451569\pi\) | |||||||
\(884\) | −84.3916 | −2.83840 | ||||||||
\(885\) | −33.1273 | −1.11356 | ||||||||
\(886\) | −11.9940 | −0.402946 | ||||||||
\(887\) | −2.58077 | −0.0866539 | −0.0433269 | − | 0.999061i | \(-0.513796\pi\) | ||||
−0.0433269 | + | 0.999061i | \(0.513796\pi\) | |||||||
\(888\) | 48.1861 | 1.61702 | ||||||||
\(889\) | 23.1661 | 0.776965 | ||||||||
\(890\) | 11.2878 | 0.378367 | ||||||||
\(891\) | 7.00444 | 0.234658 | ||||||||
\(892\) | −39.9436 | −1.33741 | ||||||||
\(893\) | −33.9322 | −1.13550 | ||||||||
\(894\) | 24.2485 | 0.810991 | ||||||||
\(895\) | 9.45051 | 0.315896 | ||||||||
\(896\) | −40.4273 | −1.35058 | ||||||||
\(897\) | 40.1036 | 1.33902 | ||||||||
\(898\) | −40.4590 | −1.35013 | ||||||||
\(899\) | 4.49811 | 0.150020 | ||||||||
\(900\) | 2.15533 | 0.0718443 | ||||||||
\(901\) | 47.3461 | 1.57733 | ||||||||
\(902\) | 1.39388 | 0.0464111 | ||||||||
\(903\) | 16.3863 | 0.545301 | ||||||||
\(904\) | 63.9097 | 2.12561 | ||||||||
\(905\) | 46.9759 | 1.56153 | ||||||||
\(906\) | −9.59419 | −0.318746 | ||||||||
\(907\) | 6.34947 | 0.210831 | 0.105415 | − | 0.994428i | \(-0.466383\pi\) | ||||
0.105415 | + | 0.994428i | \(0.466383\pi\) | |||||||
\(908\) | 34.0594 | 1.13030 | ||||||||
\(909\) | 2.52197 | 0.0836484 | ||||||||
\(910\) | −37.1843 | −1.23265 | ||||||||
\(911\) | 52.1970 | 1.72936 | 0.864682 | − | 0.502319i | \(-0.167520\pi\) | ||||
0.864682 | + | 0.502319i | \(0.167520\pi\) | |||||||
\(912\) | −16.6866 | −0.552550 | ||||||||
\(913\) | −0.271945 | −0.00900005 | ||||||||
\(914\) | −83.1356 | −2.74988 | ||||||||
\(915\) | 9.92708 | 0.328179 | ||||||||
\(916\) | 1.76541 | 0.0583307 | ||||||||
\(917\) | 12.6983 | 0.419334 | ||||||||
\(918\) | 72.8782 | 2.40534 | ||||||||
\(919\) | 24.2446 | 0.799755 | 0.399877 | − | 0.916569i | \(-0.369053\pi\) | ||||
0.399877 | + | 0.916569i | \(0.369053\pi\) | |||||||
\(920\) | −65.3189 | −2.15350 | ||||||||
\(921\) | −46.3133 | −1.52607 | ||||||||
\(922\) | −42.4192 | −1.39700 | ||||||||
\(923\) | 23.5957 | 0.776662 | ||||||||
\(924\) | −9.34863 | −0.307547 | ||||||||
\(925\) | 4.94484 | 0.162585 | ||||||||
\(926\) | −47.8717 | −1.57316 | ||||||||
\(927\) | −6.39513 | −0.210044 | ||||||||
\(928\) | −2.97085 | −0.0975228 | ||||||||
\(929\) | 9.67059 | 0.317282 | 0.158641 | − | 0.987336i | \(-0.449289\pi\) | ||||
0.158641 | + | 0.987336i | \(0.449289\pi\) | |||||||
\(930\) | 35.4180 | 1.16140 | ||||||||
\(931\) | −10.4038 | −0.340970 | ||||||||
\(932\) | −33.2526 | −1.08922 | ||||||||
\(933\) | −4.02334 | −0.131718 | ||||||||
\(934\) | −11.4409 | −0.374359 | ||||||||
\(935\) | −10.9139 | −0.356921 | ||||||||
\(936\) | −9.52876 | −0.311457 | ||||||||
\(937\) | −34.0517 | −1.11242 | −0.556210 | − | 0.831042i | \(-0.687745\pi\) | ||||
−0.556210 | + | 0.831042i | \(0.687745\pi\) | |||||||
\(938\) | −52.9104 | −1.72759 | ||||||||
\(939\) | −19.0676 | −0.622249 | ||||||||
\(940\) | 94.5428 | 3.08364 | ||||||||
\(941\) | 5.38602 | 0.175579 | 0.0877896 | − | 0.996139i | \(-0.472020\pi\) | ||||
0.0877896 | + | 0.996139i | \(0.472020\pi\) | |||||||
\(942\) | −0.516721 | −0.0168357 | ||||||||
\(943\) | −5.58488 | −0.181869 | ||||||||
\(944\) | −19.0116 | −0.618774 | ||||||||
\(945\) | 20.9768 | 0.682374 | ||||||||
\(946\) | 6.94653 | 0.225851 | ||||||||
\(947\) | 51.0898 | 1.66020 | 0.830098 | − | 0.557617i | \(-0.188284\pi\) | ||||
0.830098 | + | 0.557617i | \(0.188284\pi\) | |||||||
\(948\) | 2.55919 | 0.0831185 | ||||||||
\(949\) | −31.6650 | −1.02789 | ||||||||
\(950\) | −6.56151 | −0.212884 | ||||||||
\(951\) | −10.3426 | −0.335381 | ||||||||
\(952\) | −56.6143 | −1.83488 | ||||||||
\(953\) | 1.43687 | 0.0465448 | 0.0232724 | − | 0.999729i | \(-0.492591\pi\) | ||||
0.0232724 | + | 0.999729i | \(0.492591\pi\) | |||||||
\(954\) | 11.3938 | 0.368886 | ||||||||
\(955\) | 16.6660 | 0.539301 | ||||||||
\(956\) | −61.3811 | −1.98521 | ||||||||
\(957\) | −1.79647 | −0.0580716 | ||||||||
\(958\) | −64.3004 | −2.07745 | ||||||||
\(959\) | 2.86549 | 0.0925315 | ||||||||
\(960\) | −48.0709 | −1.55148 | ||||||||
\(961\) | −20.8848 | −0.673703 | ||||||||
\(962\) | −46.5929 | −1.50222 | ||||||||
\(963\) | 1.17099 | 0.0377346 | ||||||||
\(964\) | 10.4873 | 0.337772 | ||||||||
\(965\) | 13.4526 | 0.433054 | ||||||||
\(966\) | 57.3399 | 1.84488 | ||||||||
\(967\) | −22.1536 | −0.712411 | −0.356205 | − | 0.934408i | \(-0.615930\pi\) | ||||
−0.356205 | + | 0.934408i | \(0.615930\pi\) | |||||||
\(968\) | 44.8441 | 1.44134 | ||||||||
\(969\) | 42.8058 | 1.37512 | ||||||||
\(970\) | −72.6307 | −2.33203 | ||||||||
\(971\) | 0.788995 | 0.0253201 | 0.0126600 | − | 0.999920i | \(-0.495970\pi\) | ||||
0.0126600 | + | 0.999920i | \(0.495970\pi\) | |||||||
\(972\) | 26.2972 | 0.843482 | ||||||||
\(973\) | −29.7487 | −0.953698 | ||||||||
\(974\) | 53.3052 | 1.70801 | ||||||||
\(975\) | −5.26647 | −0.168662 | ||||||||
\(976\) | 5.69709 | 0.182359 | ||||||||
\(977\) | −42.9843 | −1.37519 | −0.687594 | − | 0.726095i | \(-0.741333\pi\) | ||||
−0.687594 | + | 0.726095i | \(0.741333\pi\) | |||||||
\(978\) | −59.7903 | −1.91188 | ||||||||
\(979\) | −1.28750 | −0.0411488 | ||||||||
\(980\) | 28.9872 | 0.925964 | ||||||||
\(981\) | −5.23258 | −0.167063 | ||||||||
\(982\) | −53.1344 | −1.69559 | ||||||||
\(983\) | 32.5447 | 1.03801 | 0.519007 | − | 0.854770i | \(-0.326302\pi\) | ||||
0.519007 | + | 0.854770i | \(0.326302\pi\) | |||||||
\(984\) | 7.14693 | 0.227836 | ||||||||
\(985\) | 27.2859 | 0.869402 | ||||||||
\(986\) | −23.1870 | −0.738423 | ||||||||
\(987\) | −38.9404 | −1.23949 | ||||||||
\(988\) | 40.3880 | 1.28491 | ||||||||
\(989\) | −27.8328 | −0.885033 | ||||||||
\(990\) | −2.62640 | −0.0834725 | ||||||||
\(991\) | −28.1564 | −0.894418 | −0.447209 | − | 0.894430i | \(-0.647582\pi\) | ||||
−0.447209 | + | 0.894430i | \(0.647582\pi\) | |||||||
\(992\) | −6.68075 | −0.212114 | ||||||||
\(993\) | −31.7619 | −1.00793 | ||||||||
\(994\) | 33.7370 | 1.07007 | ||||||||
\(995\) | 56.4821 | 1.79060 | ||||||||
\(996\) | −2.97181 | −0.0941654 | ||||||||
\(997\) | −1.49681 | −0.0474044 | −0.0237022 | − | 0.999719i | \(-0.507545\pi\) | ||||
−0.0237022 | + | 0.999719i | \(0.507545\pi\) | |||||||
\(998\) | 98.1770 | 3.10774 | ||||||||
\(999\) | 26.2844 | 0.831603 |
(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 | 4001.2.a.b.1.18 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.18 | ✓ | 184 | 1.1 | even | 1 | trivial |