Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.27011 | −1.31065 | −0.655323 | − | 0.755349i | \(-0.727468\pi\) | ||||
−0.655323 | + | 0.755349i | \(0.727468\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.81074 | −0.809786 | −0.404893 | − | 0.914364i | \(-0.632691\pi\) | ||||
−0.404893 | + | 0.914364i | \(0.632691\pi\) | |||||||
\(6\) | −2.27011 | −0.926767 | ||||||||
\(7\) | 2.75406 | 1.04094 | 0.520469 | − | 0.853880i | \(-0.325757\pi\) | ||||
0.520469 | + | 0.853880i | \(0.325757\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.15338 | 0.717795 | ||||||||
\(10\) | −1.81074 | −0.572605 | ||||||||
\(11\) | −3.69732 | −1.11478 | −0.557392 | − | 0.830249i | \(-0.688198\pi\) | ||||
−0.557392 | + | 0.830249i | \(0.688198\pi\) | |||||||
\(12\) | −2.27011 | −0.655323 | ||||||||
\(13\) | 4.65829 | 1.29198 | 0.645989 | − | 0.763347i | \(-0.276445\pi\) | ||||
0.645989 | + | 0.763347i | \(0.276445\pi\) | |||||||
\(14\) | 2.75406 | 0.736055 | ||||||||
\(15\) | 4.11056 | 1.06134 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00896 | 0.972317 | 0.486158 | − | 0.873871i | \(-0.338398\pi\) | ||||
0.486158 | + | 0.873871i | \(0.338398\pi\) | |||||||
\(18\) | 2.15338 | 0.507557 | ||||||||
\(19\) | 6.43083 | 1.47533 | 0.737667 | − | 0.675165i | \(-0.235927\pi\) | ||||
0.737667 | + | 0.675165i | \(0.235927\pi\) | |||||||
\(20\) | −1.81074 | −0.404893 | ||||||||
\(21\) | −6.25202 | −1.36430 | ||||||||
\(22\) | −3.69732 | −0.788272 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.27011 | −0.463384 | ||||||||
\(25\) | −1.72124 | −0.344247 | ||||||||
\(26\) | 4.65829 | 0.913566 | ||||||||
\(27\) | 1.92191 | 0.369872 | ||||||||
\(28\) | 2.75406 | 0.520469 | ||||||||
\(29\) | −0.101640 | −0.0188742 | −0.00943708 | − | 0.999955i | \(-0.503004\pi\) | ||||
−0.00943708 | + | 0.999955i | \(0.503004\pi\) | |||||||
\(30\) | 4.11056 | 0.750483 | ||||||||
\(31\) | 2.69271 | 0.483625 | 0.241812 | − | 0.970323i | \(-0.422258\pi\) | ||||
0.241812 | + | 0.970323i | \(0.422258\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.39332 | 1.46109 | ||||||||
\(34\) | 4.00896 | 0.687532 | ||||||||
\(35\) | −4.98688 | −0.842937 | ||||||||
\(36\) | 2.15338 | 0.358897 | ||||||||
\(37\) | −1.93485 | −0.318087 | −0.159043 | − | 0.987272i | \(-0.550841\pi\) | ||||
−0.159043 | + | 0.987272i | \(0.550841\pi\) | |||||||
\(38\) | 6.43083 | 1.04322 | ||||||||
\(39\) | −10.5748 | −1.69333 | ||||||||
\(40\) | −1.81074 | −0.286302 | ||||||||
\(41\) | −10.3411 | −1.61501 | −0.807506 | − | 0.589860i | \(-0.799183\pi\) | ||||
−0.807506 | + | 0.589860i | \(0.799183\pi\) | |||||||
\(42\) | −6.25202 | −0.964707 | ||||||||
\(43\) | 1.32687 | 0.202346 | 0.101173 | − | 0.994869i | \(-0.467740\pi\) | ||||
0.101173 | + | 0.994869i | \(0.467740\pi\) | |||||||
\(44\) | −3.69732 | −0.557392 | ||||||||
\(45\) | −3.89921 | −0.581260 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −7.72731 | −1.12714 | −0.563572 | − | 0.826067i | \(-0.690573\pi\) | ||||
−0.563572 | + | 0.826067i | \(0.690573\pi\) | |||||||
\(48\) | −2.27011 | −0.327662 | ||||||||
\(49\) | 0.584869 | 0.0835527 | ||||||||
\(50\) | −1.72124 | −0.243420 | ||||||||
\(51\) | −9.10078 | −1.27436 | ||||||||
\(52\) | 4.65829 | 0.645989 | ||||||||
\(53\) | −5.32055 | −0.730833 | −0.365417 | − | 0.930844i | \(-0.619073\pi\) | ||||
−0.365417 | + | 0.930844i | \(0.619073\pi\) | |||||||
\(54\) | 1.92191 | 0.261539 | ||||||||
\(55\) | 6.69487 | 0.902736 | ||||||||
\(56\) | 2.75406 | 0.368027 | ||||||||
\(57\) | −14.5987 | −1.93364 | ||||||||
\(58\) | −0.101640 | −0.0133460 | ||||||||
\(59\) | −2.92210 | −0.380425 | −0.190213 | − | 0.981743i | \(-0.560918\pi\) | ||||
−0.190213 | + | 0.981743i | \(0.560918\pi\) | |||||||
\(60\) | 4.11056 | 0.530671 | ||||||||
\(61\) | 12.7177 | 1.62833 | 0.814165 | − | 0.580633i | \(-0.197195\pi\) | ||||
0.814165 | + | 0.580633i | \(0.197195\pi\) | |||||||
\(62\) | 2.69271 | 0.341975 | ||||||||
\(63\) | 5.93056 | 0.747180 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.43493 | −1.04622 | ||||||||
\(66\) | 8.39332 | 1.03315 | ||||||||
\(67\) | 4.34132 | 0.530377 | 0.265188 | − | 0.964197i | \(-0.414566\pi\) | ||||
0.265188 | + | 0.964197i | \(0.414566\pi\) | |||||||
\(68\) | 4.00896 | 0.486158 | ||||||||
\(69\) | −2.27011 | −0.273289 | ||||||||
\(70\) | −4.98688 | −0.596046 | ||||||||
\(71\) | −7.06119 | −0.838009 | −0.419005 | − | 0.907984i | \(-0.637621\pi\) | ||||
−0.419005 | + | 0.907984i | \(0.637621\pi\) | |||||||
\(72\) | 2.15338 | 0.253779 | ||||||||
\(73\) | 8.48812 | 0.993459 | 0.496730 | − | 0.867905i | \(-0.334534\pi\) | ||||
0.496730 | + | 0.867905i | \(0.334534\pi\) | |||||||
\(74\) | −1.93485 | −0.224921 | ||||||||
\(75\) | 3.90739 | 0.451187 | ||||||||
\(76\) | 6.43083 | 0.737667 | ||||||||
\(77\) | −10.1827 | −1.16042 | ||||||||
\(78\) | −10.5748 | −1.19736 | ||||||||
\(79\) | 15.8125 | 1.77904 | 0.889522 | − | 0.456893i | \(-0.151038\pi\) | ||||
0.889522 | + | 0.456893i | \(0.151038\pi\) | |||||||
\(80\) | −1.81074 | −0.202446 | ||||||||
\(81\) | −10.8231 | −1.20257 | ||||||||
\(82\) | −10.3411 | −1.14199 | ||||||||
\(83\) | 1.11213 | 0.122072 | 0.0610361 | − | 0.998136i | \(-0.480560\pi\) | ||||
0.0610361 | + | 0.998136i | \(0.480560\pi\) | |||||||
\(84\) | −6.25202 | −0.682151 | ||||||||
\(85\) | −7.25917 | −0.787368 | ||||||||
\(86\) | 1.32687 | 0.143080 | ||||||||
\(87\) | 0.230735 | 0.0247373 | ||||||||
\(88\) | −3.69732 | −0.394136 | ||||||||
\(89\) | −2.13754 | −0.226578 | −0.113289 | − | 0.993562i | \(-0.536139\pi\) | ||||
−0.113289 | + | 0.993562i | \(0.536139\pi\) | |||||||
\(90\) | −3.89921 | −0.411013 | ||||||||
\(91\) | 12.8292 | 1.34487 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −6.11274 | −0.633861 | ||||||||
\(94\) | −7.72731 | −0.797012 | ||||||||
\(95\) | −11.6445 | −1.19470 | ||||||||
\(96\) | −2.27011 | −0.231692 | ||||||||
\(97\) | 13.2507 | 1.34541 | 0.672704 | − | 0.739911i | \(-0.265133\pi\) | ||||
0.672704 | + | 0.739911i | \(0.265133\pi\) | |||||||
\(98\) | 0.584869 | 0.0590807 | ||||||||
\(99\) | −7.96175 | −0.800186 | ||||||||
\(100\) | −1.72124 | −0.172124 | ||||||||
\(101\) | 4.26314 | 0.424198 | 0.212099 | − | 0.977248i | \(-0.431970\pi\) | ||||
0.212099 | + | 0.977248i | \(0.431970\pi\) | |||||||
\(102\) | −9.10078 | −0.901111 | ||||||||
\(103\) | −6.87758 | −0.677668 | −0.338834 | − | 0.940846i | \(-0.610032\pi\) | ||||
−0.338834 | + | 0.940846i | \(0.610032\pi\) | |||||||
\(104\) | 4.65829 | 0.456783 | ||||||||
\(105\) | 11.3208 | 1.10479 | ||||||||
\(106\) | −5.32055 | −0.516777 | ||||||||
\(107\) | −12.5985 | −1.21795 | −0.608973 | − | 0.793191i | \(-0.708418\pi\) | ||||
−0.608973 | + | 0.793191i | \(0.708418\pi\) | |||||||
\(108\) | 1.92191 | 0.184936 | ||||||||
\(109\) | −14.3119 | −1.37083 | −0.685417 | − | 0.728150i | \(-0.740380\pi\) | ||||
−0.685417 | + | 0.728150i | \(0.740380\pi\) | |||||||
\(110\) | 6.69487 | 0.638331 | ||||||||
\(111\) | 4.39231 | 0.416899 | ||||||||
\(112\) | 2.75406 | 0.260235 | ||||||||
\(113\) | 19.2766 | 1.81339 | 0.906694 | − | 0.421789i | \(-0.138598\pi\) | ||||
0.906694 | + | 0.421789i | \(0.138598\pi\) | |||||||
\(114\) | −14.5987 | −1.36729 | ||||||||
\(115\) | −1.81074 | −0.168852 | ||||||||
\(116\) | −0.101640 | −0.00943708 | ||||||||
\(117\) | 10.0311 | 0.927374 | ||||||||
\(118\) | −2.92210 | −0.269001 | ||||||||
\(119\) | 11.0409 | 1.01212 | ||||||||
\(120\) | 4.11056 | 0.375241 | ||||||||
\(121\) | 2.67019 | 0.242745 | ||||||||
\(122\) | 12.7177 | 1.15140 | ||||||||
\(123\) | 23.4754 | 2.11671 | ||||||||
\(124\) | 2.69271 | 0.241812 | ||||||||
\(125\) | 12.1704 | 1.08855 | ||||||||
\(126\) | 5.93056 | 0.528336 | ||||||||
\(127\) | 10.9371 | 0.970514 | 0.485257 | − | 0.874371i | \(-0.338726\pi\) | ||||
0.485257 | + | 0.874371i | \(0.338726\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.01214 | −0.265204 | ||||||||
\(130\) | −8.43493 | −0.739792 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 8.39332 | 0.730544 | ||||||||
\(133\) | 17.7109 | 1.53573 | ||||||||
\(134\) | 4.34132 | 0.375033 | ||||||||
\(135\) | −3.48007 | −0.299517 | ||||||||
\(136\) | 4.00896 | 0.343766 | ||||||||
\(137\) | 13.8943 | 1.18707 | 0.593537 | − | 0.804807i | \(-0.297731\pi\) | ||||
0.593537 | + | 0.804807i | \(0.297731\pi\) | |||||||
\(138\) | −2.27011 | −0.193244 | ||||||||
\(139\) | −11.9258 | −1.01153 | −0.505766 | − | 0.862670i | \(-0.668790\pi\) | ||||
−0.505766 | + | 0.862670i | \(0.668790\pi\) | |||||||
\(140\) | −4.98688 | −0.421468 | ||||||||
\(141\) | 17.5418 | 1.47729 | ||||||||
\(142\) | −7.06119 | −0.592562 | ||||||||
\(143\) | −17.2232 | −1.44028 | ||||||||
\(144\) | 2.15338 | 0.179449 | ||||||||
\(145\) | 0.184044 | 0.0152840 | ||||||||
\(146\) | 8.48812 | 0.702482 | ||||||||
\(147\) | −1.32771 | −0.109508 | ||||||||
\(148\) | −1.93485 | −0.159043 | ||||||||
\(149\) | −11.3134 | −0.926829 | −0.463414 | − | 0.886142i | \(-0.653376\pi\) | ||||
−0.463414 | + | 0.886142i | \(0.653376\pi\) | |||||||
\(150\) | 3.90739 | 0.319037 | ||||||||
\(151\) | 24.0616 | 1.95811 | 0.979054 | − | 0.203599i | \(-0.0652640\pi\) | ||||
0.979054 | + | 0.203599i | \(0.0652640\pi\) | |||||||
\(152\) | 6.43083 | 0.521609 | ||||||||
\(153\) | 8.63284 | 0.697924 | ||||||||
\(154\) | −10.1827 | −0.820542 | ||||||||
\(155\) | −4.87579 | −0.391633 | ||||||||
\(156\) | −10.5748 | −0.846663 | ||||||||
\(157\) | 21.9569 | 1.75235 | 0.876175 | − | 0.481993i | \(-0.160087\pi\) | ||||
0.876175 | + | 0.481993i | \(0.160087\pi\) | |||||||
\(158\) | 15.8125 | 1.25797 | ||||||||
\(159\) | 12.0782 | 0.957864 | ||||||||
\(160\) | −1.81074 | −0.143151 | ||||||||
\(161\) | 2.75406 | 0.217051 | ||||||||
\(162\) | −10.8231 | −0.850342 | ||||||||
\(163\) | −12.3485 | −0.967206 | −0.483603 | − | 0.875287i | \(-0.660672\pi\) | ||||
−0.483603 | + | 0.875287i | \(0.660672\pi\) | |||||||
\(164\) | −10.3411 | −0.807506 | ||||||||
\(165\) | −15.1981 | −1.18317 | ||||||||
\(166\) | 1.11213 | 0.0863181 | ||||||||
\(167\) | 15.6335 | 1.20976 | 0.604878 | − | 0.796318i | \(-0.293222\pi\) | ||||
0.604878 | + | 0.796318i | \(0.293222\pi\) | |||||||
\(168\) | −6.25202 | −0.482354 | ||||||||
\(169\) | 8.69966 | 0.669205 | ||||||||
\(170\) | −7.25917 | −0.556753 | ||||||||
\(171\) | 13.8480 | 1.05899 | ||||||||
\(172\) | 1.32687 | 0.101173 | ||||||||
\(173\) | −10.9627 | −0.833476 | −0.416738 | − | 0.909027i | \(-0.636827\pi\) | ||||
−0.416738 | + | 0.909027i | \(0.636827\pi\) | |||||||
\(174\) | 0.230735 | 0.0174919 | ||||||||
\(175\) | −4.74040 | −0.358340 | ||||||||
\(176\) | −3.69732 | −0.278696 | ||||||||
\(177\) | 6.63348 | 0.498603 | ||||||||
\(178\) | −2.13754 | −0.160215 | ||||||||
\(179\) | −7.23995 | −0.541139 | −0.270570 | − | 0.962700i | \(-0.587212\pi\) | ||||
−0.270570 | + | 0.962700i | \(0.587212\pi\) | |||||||
\(180\) | −3.89921 | −0.290630 | ||||||||
\(181\) | 7.36721 | 0.547600 | 0.273800 | − | 0.961787i | \(-0.411719\pi\) | ||||
0.273800 | + | 0.961787i | \(0.411719\pi\) | |||||||
\(182\) | 12.8292 | 0.950966 | ||||||||
\(183\) | −28.8705 | −2.13417 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 3.50350 | 0.257582 | ||||||||
\(186\) | −6.11274 | −0.448208 | ||||||||
\(187\) | −14.8224 | −1.08392 | ||||||||
\(188\) | −7.72731 | −0.563572 | ||||||||
\(189\) | 5.29306 | 0.385014 | ||||||||
\(190\) | −11.6445 | −0.844784 | ||||||||
\(191\) | 10.7749 | 0.779642 | 0.389821 | − | 0.920891i | \(-0.372537\pi\) | ||||
0.389821 | + | 0.920891i | \(0.372537\pi\) | |||||||
\(192\) | −2.27011 | −0.163831 | ||||||||
\(193\) | 17.7801 | 1.27984 | 0.639922 | − | 0.768440i | \(-0.278967\pi\) | ||||
0.639922 | + | 0.768440i | \(0.278967\pi\) | |||||||
\(194\) | 13.2507 | 0.951347 | ||||||||
\(195\) | 19.1482 | 1.37123 | ||||||||
\(196\) | 0.584869 | 0.0417764 | ||||||||
\(197\) | 7.90253 | 0.563032 | 0.281516 | − | 0.959557i | \(-0.409163\pi\) | ||||
0.281516 | + | 0.959557i | \(0.409163\pi\) | |||||||
\(198\) | −7.96175 | −0.565817 | ||||||||
\(199\) | −21.6123 | −1.53206 | −0.766028 | − | 0.642807i | \(-0.777770\pi\) | ||||
−0.766028 | + | 0.642807i | \(0.777770\pi\) | |||||||
\(200\) | −1.72124 | −0.121710 | ||||||||
\(201\) | −9.85526 | −0.695136 | ||||||||
\(202\) | 4.26314 | 0.299953 | ||||||||
\(203\) | −0.279924 | −0.0196468 | ||||||||
\(204\) | −9.10078 | −0.637182 | ||||||||
\(205\) | 18.7250 | 1.30781 | ||||||||
\(206\) | −6.87758 | −0.479184 | ||||||||
\(207\) | 2.15338 | 0.149671 | ||||||||
\(208\) | 4.65829 | 0.322994 | ||||||||
\(209\) | −23.7769 | −1.64468 | ||||||||
\(210\) | 11.3208 | 0.781206 | ||||||||
\(211\) | −22.9211 | −1.57795 | −0.788977 | − | 0.614423i | \(-0.789389\pi\) | ||||
−0.788977 | + | 0.614423i | \(0.789389\pi\) | |||||||
\(212\) | −5.32055 | −0.365417 | ||||||||
\(213\) | 16.0297 | 1.09833 | ||||||||
\(214\) | −12.5985 | −0.861218 | ||||||||
\(215\) | −2.40261 | −0.163857 | ||||||||
\(216\) | 1.92191 | 0.130769 | ||||||||
\(217\) | 7.41590 | 0.503424 | ||||||||
\(218\) | −14.3119 | −0.969327 | ||||||||
\(219\) | −19.2689 | −1.30207 | ||||||||
\(220\) | 6.69487 | 0.451368 | ||||||||
\(221\) | 18.6749 | 1.25621 | ||||||||
\(222\) | 4.39231 | 0.294792 | ||||||||
\(223\) | −25.4911 | −1.70701 | −0.853505 | − | 0.521084i | \(-0.825528\pi\) | ||||
−0.853505 | + | 0.521084i | \(0.825528\pi\) | |||||||
\(224\) | 2.75406 | 0.184014 | ||||||||
\(225\) | −3.70648 | −0.247099 | ||||||||
\(226\) | 19.2766 | 1.28226 | ||||||||
\(227\) | 12.9585 | 0.860086 | 0.430043 | − | 0.902809i | \(-0.358498\pi\) | ||||
0.430043 | + | 0.902809i | \(0.358498\pi\) | |||||||
\(228\) | −14.5987 | −0.966821 | ||||||||
\(229\) | −21.0076 | −1.38822 | −0.694110 | − | 0.719869i | \(-0.744202\pi\) | ||||
−0.694110 | + | 0.719869i | \(0.744202\pi\) | |||||||
\(230\) | −1.81074 | −0.119396 | ||||||||
\(231\) | 23.1157 | 1.52090 | ||||||||
\(232\) | −0.101640 | −0.00667302 | ||||||||
\(233\) | 16.4743 | 1.07927 | 0.539635 | − | 0.841899i | \(-0.318562\pi\) | ||||
0.539635 | + | 0.841899i | \(0.318562\pi\) | |||||||
\(234\) | 10.0311 | 0.655752 | ||||||||
\(235\) | 13.9921 | 0.912745 | ||||||||
\(236\) | −2.92210 | −0.190213 | ||||||||
\(237\) | −35.8960 | −2.33170 | ||||||||
\(238\) | 11.0409 | 0.715678 | ||||||||
\(239\) | 17.6869 | 1.14407 | 0.572035 | − | 0.820229i | \(-0.306154\pi\) | ||||
0.572035 | + | 0.820229i | \(0.306154\pi\) | |||||||
\(240\) | 4.11056 | 0.265336 | ||||||||
\(241\) | 17.7352 | 1.14243 | 0.571213 | − | 0.820802i | \(-0.306473\pi\) | ||||
0.571213 | + | 0.820802i | \(0.306473\pi\) | |||||||
\(242\) | 2.67019 | 0.171646 | ||||||||
\(243\) | 18.8038 | 1.20627 | ||||||||
\(244\) | 12.7177 | 0.814165 | ||||||||
\(245\) | −1.05904 | −0.0676598 | ||||||||
\(246\) | 23.4754 | 1.49674 | ||||||||
\(247\) | 29.9567 | 1.90610 | ||||||||
\(248\) | 2.69271 | 0.170987 | ||||||||
\(249\) | −2.52465 | −0.159993 | ||||||||
\(250\) | 12.1704 | 0.769723 | ||||||||
\(251\) | 5.27663 | 0.333058 | 0.166529 | − | 0.986037i | \(-0.446744\pi\) | ||||
0.166529 | + | 0.986037i | \(0.446744\pi\) | |||||||
\(252\) | 5.93056 | 0.373590 | ||||||||
\(253\) | −3.69732 | −0.232449 | ||||||||
\(254\) | 10.9371 | 0.686257 | ||||||||
\(255\) | 16.4791 | 1.03196 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.2124 | 0.761786 | 0.380893 | − | 0.924619i | \(-0.375617\pi\) | ||||
0.380893 | + | 0.924619i | \(0.375617\pi\) | |||||||
\(258\) | −3.01214 | −0.187528 | ||||||||
\(259\) | −5.32869 | −0.331109 | ||||||||
\(260\) | −8.43493 | −0.523112 | ||||||||
\(261\) | −0.218871 | −0.0135478 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 29.5732 | 1.82356 | 0.911781 | − | 0.410676i | \(-0.134707\pi\) | ||||
0.911781 | + | 0.410676i | \(0.134707\pi\) | |||||||
\(264\) | 8.39332 | 0.516573 | ||||||||
\(265\) | 9.63410 | 0.591818 | ||||||||
\(266\) | 17.7109 | 1.08593 | ||||||||
\(267\) | 4.85244 | 0.296964 | ||||||||
\(268\) | 4.34132 | 0.265188 | ||||||||
\(269\) | 21.9667 | 1.33933 | 0.669666 | − | 0.742662i | \(-0.266437\pi\) | ||||
0.669666 | + | 0.742662i | \(0.266437\pi\) | |||||||
\(270\) | −3.48007 | −0.211790 | ||||||||
\(271\) | −12.9223 | −0.784973 | −0.392487 | − | 0.919758i | \(-0.628385\pi\) | ||||
−0.392487 | + | 0.919758i | \(0.628385\pi\) | |||||||
\(272\) | 4.00896 | 0.243079 | ||||||||
\(273\) | −29.1237 | −1.76265 | ||||||||
\(274\) | 13.8943 | 0.839388 | ||||||||
\(275\) | 6.36397 | 0.383762 | ||||||||
\(276\) | −2.27011 | −0.136644 | ||||||||
\(277\) | −18.2265 | −1.09513 | −0.547563 | − | 0.836764i | \(-0.684444\pi\) | ||||
−0.547563 | + | 0.836764i | \(0.684444\pi\) | |||||||
\(278\) | −11.9258 | −0.715262 | ||||||||
\(279\) | 5.79844 | 0.347143 | ||||||||
\(280\) | −4.98688 | −0.298023 | ||||||||
\(281\) | 3.48382 | 0.207827 | 0.103914 | − | 0.994586i | \(-0.466863\pi\) | ||||
0.103914 | + | 0.994586i | \(0.466863\pi\) | |||||||
\(282\) | 17.5418 | 1.04460 | ||||||||
\(283\) | 7.53303 | 0.447792 | 0.223896 | − | 0.974613i | \(-0.428122\pi\) | ||||
0.223896 | + | 0.974613i | \(0.428122\pi\) | |||||||
\(284\) | −7.06119 | −0.419005 | ||||||||
\(285\) | 26.4343 | 1.56584 | ||||||||
\(286\) | −17.2232 | −1.01843 | ||||||||
\(287\) | −28.4801 | −1.68113 | ||||||||
\(288\) | 2.15338 | 0.126889 | ||||||||
\(289\) | −0.928206 | −0.0546003 | ||||||||
\(290\) | 0.184044 | 0.0108074 | ||||||||
\(291\) | −30.0806 | −1.76336 | ||||||||
\(292\) | 8.48812 | 0.496730 | ||||||||
\(293\) | 17.4488 | 1.01937 | 0.509686 | − | 0.860361i | \(-0.329762\pi\) | ||||
0.509686 | + | 0.860361i | \(0.329762\pi\) | |||||||
\(294\) | −1.32771 | −0.0774339 | ||||||||
\(295\) | 5.29115 | 0.308063 | ||||||||
\(296\) | −1.93485 | −0.112461 | ||||||||
\(297\) | −7.10592 | −0.412327 | ||||||||
\(298\) | −11.3134 | −0.655367 | ||||||||
\(299\) | 4.65829 | 0.269396 | ||||||||
\(300\) | 3.90739 | 0.225593 | ||||||||
\(301\) | 3.65429 | 0.210630 | ||||||||
\(302\) | 24.0616 | 1.38459 | ||||||||
\(303\) | −9.67777 | −0.555973 | ||||||||
\(304\) | 6.43083 | 0.368834 | ||||||||
\(305\) | −23.0283 | −1.31860 | ||||||||
\(306\) | 8.63284 | 0.493506 | ||||||||
\(307\) | 18.3659 | 1.04820 | 0.524099 | − | 0.851657i | \(-0.324402\pi\) | ||||
0.524099 | + | 0.851657i | \(0.324402\pi\) | |||||||
\(308\) | −10.1827 | −0.580211 | ||||||||
\(309\) | 15.6128 | 0.888183 | ||||||||
\(310\) | −4.87579 | −0.276926 | ||||||||
\(311\) | 28.2526 | 1.60206 | 0.801028 | − | 0.598627i | \(-0.204287\pi\) | ||||
0.801028 | + | 0.598627i | \(0.204287\pi\) | |||||||
\(312\) | −10.5748 | −0.598681 | ||||||||
\(313\) | −8.91799 | −0.504074 | −0.252037 | − | 0.967718i | \(-0.581101\pi\) | ||||
−0.252037 | + | 0.967718i | \(0.581101\pi\) | |||||||
\(314\) | 21.9569 | 1.23910 | ||||||||
\(315\) | −10.7387 | −0.605055 | ||||||||
\(316\) | 15.8125 | 0.889522 | ||||||||
\(317\) | −32.5822 | −1.83000 | −0.914998 | − | 0.403458i | \(-0.867808\pi\) | ||||
−0.914998 | + | 0.403458i | \(0.867808\pi\) | |||||||
\(318\) | 12.0782 | 0.677312 | ||||||||
\(319\) | 0.375797 | 0.0210406 | ||||||||
\(320\) | −1.81074 | −0.101223 | ||||||||
\(321\) | 28.6000 | 1.59630 | ||||||||
\(322\) | 2.75406 | 0.153478 | ||||||||
\(323\) | 25.7810 | 1.43449 | ||||||||
\(324\) | −10.8231 | −0.601283 | ||||||||
\(325\) | −8.01802 | −0.444760 | ||||||||
\(326\) | −12.3485 | −0.683918 | ||||||||
\(327\) | 32.4896 | 1.79668 | ||||||||
\(328\) | −10.3411 | −0.570993 | ||||||||
\(329\) | −21.2815 | −1.17329 | ||||||||
\(330\) | −15.1981 | −0.836626 | ||||||||
\(331\) | 24.3121 | 1.33632 | 0.668158 | − | 0.744019i | \(-0.267083\pi\) | ||||
0.668158 | + | 0.744019i | \(0.267083\pi\) | |||||||
\(332\) | 1.11213 | 0.0610361 | ||||||||
\(333\) | −4.16647 | −0.228321 | ||||||||
\(334\) | 15.6335 | 0.855426 | ||||||||
\(335\) | −7.86098 | −0.429491 | ||||||||
\(336\) | −6.25202 | −0.341076 | ||||||||
\(337\) | 22.6806 | 1.23549 | 0.617746 | − | 0.786377i | \(-0.288046\pi\) | ||||
0.617746 | + | 0.786377i | \(0.288046\pi\) | |||||||
\(338\) | 8.69966 | 0.473199 | ||||||||
\(339\) | −43.7599 | −2.37671 | ||||||||
\(340\) | −7.25917 | −0.393684 | ||||||||
\(341\) | −9.95582 | −0.539138 | ||||||||
\(342\) | 13.8480 | 0.748817 | ||||||||
\(343\) | −17.6677 | −0.953965 | ||||||||
\(344\) | 1.32687 | 0.0715402 | ||||||||
\(345\) | 4.11056 | 0.221305 | ||||||||
\(346\) | −10.9627 | −0.589357 | ||||||||
\(347\) | 24.6481 | 1.32318 | 0.661589 | − | 0.749867i | \(-0.269882\pi\) | ||||
0.661589 | + | 0.749867i | \(0.269882\pi\) | |||||||
\(348\) | 0.230735 | 0.0123687 | ||||||||
\(349\) | 26.4989 | 1.41846 | 0.709228 | − | 0.704979i | \(-0.249044\pi\) | ||||
0.709228 | + | 0.704979i | \(0.249044\pi\) | |||||||
\(350\) | −4.74040 | −0.253385 | ||||||||
\(351\) | 8.95281 | 0.477866 | ||||||||
\(352\) | −3.69732 | −0.197068 | ||||||||
\(353\) | 10.3969 | 0.553369 | 0.276684 | − | 0.960961i | \(-0.410764\pi\) | ||||
0.276684 | + | 0.960961i | \(0.410764\pi\) | |||||||
\(354\) | 6.63348 | 0.352565 | ||||||||
\(355\) | 12.7859 | 0.678608 | ||||||||
\(356\) | −2.13754 | −0.113289 | ||||||||
\(357\) | −25.0641 | −1.32653 | ||||||||
\(358\) | −7.23995 | −0.382643 | ||||||||
\(359\) | −12.5720 | −0.663525 | −0.331763 | − | 0.943363i | \(-0.607643\pi\) | ||||
−0.331763 | + | 0.943363i | \(0.607643\pi\) | |||||||
\(360\) | −3.89921 | −0.205506 | ||||||||
\(361\) | 22.3556 | 1.17661 | ||||||||
\(362\) | 7.36721 | 0.387212 | ||||||||
\(363\) | −6.06162 | −0.318153 | ||||||||
\(364\) | 12.8292 | 0.672434 | ||||||||
\(365\) | −15.3697 | −0.804489 | ||||||||
\(366\) | −28.8705 | −1.50908 | ||||||||
\(367\) | −17.1556 | −0.895516 | −0.447758 | − | 0.894155i | \(-0.647777\pi\) | ||||
−0.447758 | + | 0.894155i | \(0.647777\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −22.2684 | −1.15925 | ||||||||
\(370\) | 3.50350 | 0.182138 | ||||||||
\(371\) | −14.6531 | −0.760753 | ||||||||
\(372\) | −6.11274 | −0.316931 | ||||||||
\(373\) | 18.4286 | 0.954195 | 0.477097 | − | 0.878850i | \(-0.341689\pi\) | ||||
0.477097 | + | 0.878850i | \(0.341689\pi\) | |||||||
\(374\) | −14.8224 | −0.766450 | ||||||||
\(375\) | −27.6281 | −1.42671 | ||||||||
\(376\) | −7.72731 | −0.398506 | ||||||||
\(377\) | −0.473471 | −0.0243850 | ||||||||
\(378\) | 5.29306 | 0.272246 | ||||||||
\(379\) | −23.4999 | −1.20711 | −0.603554 | − | 0.797322i | \(-0.706249\pi\) | ||||
−0.603554 | + | 0.797322i | \(0.706249\pi\) | |||||||
\(380\) | −11.6445 | −0.597352 | ||||||||
\(381\) | −24.8285 | −1.27200 | ||||||||
\(382\) | 10.7749 | 0.551290 | ||||||||
\(383\) | −0.0335359 | −0.00171360 | −0.000856801 | − | 1.00000i | \(-0.500273\pi\) | ||||
−0.000856801 | 1.00000i | \(0.500273\pi\) | ||||||||
\(384\) | −2.27011 | −0.115846 | ||||||||
\(385\) | 18.4381 | 0.939693 | ||||||||
\(386\) | 17.7801 | 0.904986 | ||||||||
\(387\) | 2.85726 | 0.145243 | ||||||||
\(388\) | 13.2507 | 0.672704 | ||||||||
\(389\) | −13.5552 | −0.687277 | −0.343639 | − | 0.939102i | \(-0.611660\pi\) | ||||
−0.343639 | + | 0.939102i | \(0.611660\pi\) | |||||||
\(390\) | 19.1482 | 0.969606 | ||||||||
\(391\) | 4.00896 | 0.202742 | ||||||||
\(392\) | 0.584869 | 0.0295403 | ||||||||
\(393\) | −2.27011 | −0.114512 | ||||||||
\(394\) | 7.90253 | 0.398124 | ||||||||
\(395\) | −28.6322 | −1.44064 | ||||||||
\(396\) | −7.96175 | −0.400093 | ||||||||
\(397\) | 9.69121 | 0.486388 | 0.243194 | − | 0.969978i | \(-0.421805\pi\) | ||||
0.243194 | + | 0.969978i | \(0.421805\pi\) | |||||||
\(398\) | −21.6123 | −1.08333 | ||||||||
\(399\) | −40.2057 | −2.01280 | ||||||||
\(400\) | −1.72124 | −0.0860618 | ||||||||
\(401\) | −13.6563 | −0.681961 | −0.340980 | − | 0.940070i | \(-0.610759\pi\) | ||||
−0.340980 | + | 0.940070i | \(0.610759\pi\) | |||||||
\(402\) | −9.85526 | −0.491535 | ||||||||
\(403\) | 12.5434 | 0.624832 | ||||||||
\(404\) | 4.26314 | 0.212099 | ||||||||
\(405\) | 19.5978 | 0.973820 | ||||||||
\(406\) | −0.279924 | −0.0138924 | ||||||||
\(407\) | 7.15375 | 0.354598 | ||||||||
\(408\) | −9.10078 | −0.450556 | ||||||||
\(409\) | 14.9273 | 0.738109 | 0.369055 | − | 0.929408i | \(-0.379682\pi\) | ||||
0.369055 | + | 0.929408i | \(0.379682\pi\) | |||||||
\(410\) | 18.7250 | 0.924763 | ||||||||
\(411\) | −31.5416 | −1.55583 | ||||||||
\(412\) | −6.87758 | −0.338834 | ||||||||
\(413\) | −8.04765 | −0.395999 | ||||||||
\(414\) | 2.15338 | 0.105833 | ||||||||
\(415\) | −2.01377 | −0.0988523 | ||||||||
\(416\) | 4.65829 | 0.228391 | ||||||||
\(417\) | 27.0728 | 1.32576 | ||||||||
\(418\) | −23.7769 | −1.16296 | ||||||||
\(419\) | −37.9670 | −1.85481 | −0.927404 | − | 0.374062i | \(-0.877965\pi\) | ||||
−0.927404 | + | 0.374062i | \(0.877965\pi\) | |||||||
\(420\) | 11.3208 | 0.552396 | ||||||||
\(421\) | 15.6129 | 0.760926 | 0.380463 | − | 0.924796i | \(-0.375765\pi\) | ||||
0.380463 | + | 0.924796i | \(0.375765\pi\) | |||||||
\(422\) | −22.9211 | −1.11578 | ||||||||
\(423\) | −16.6399 | −0.809058 | ||||||||
\(424\) | −5.32055 | −0.258389 | ||||||||
\(425\) | −6.90038 | −0.334717 | ||||||||
\(426\) | 16.0297 | 0.776639 | ||||||||
\(427\) | 35.0253 | 1.69499 | ||||||||
\(428\) | −12.5985 | −0.608973 | ||||||||
\(429\) | 39.0985 | 1.88769 | ||||||||
\(430\) | −2.40261 | −0.115864 | ||||||||
\(431\) | −4.74475 | −0.228547 | −0.114273 | − | 0.993449i | \(-0.536454\pi\) | ||||
−0.114273 | + | 0.993449i | \(0.536454\pi\) | |||||||
\(432\) | 1.92191 | 0.0924679 | ||||||||
\(433\) | −3.48483 | −0.167470 | −0.0837352 | − | 0.996488i | \(-0.526685\pi\) | ||||
−0.0837352 | + | 0.996488i | \(0.526685\pi\) | |||||||
\(434\) | 7.41590 | 0.355974 | ||||||||
\(435\) | −0.417799 | −0.0200319 | ||||||||
\(436\) | −14.3119 | −0.685417 | ||||||||
\(437\) | 6.43083 | 0.307628 | ||||||||
\(438\) | −19.2689 | −0.920706 | ||||||||
\(439\) | −12.8079 | −0.611289 | −0.305644 | − | 0.952146i | \(-0.598872\pi\) | ||||
−0.305644 | + | 0.952146i | \(0.598872\pi\) | |||||||
\(440\) | 6.69487 | 0.319166 | ||||||||
\(441\) | 1.25945 | 0.0599737 | ||||||||
\(442\) | 18.6749 | 0.888275 | ||||||||
\(443\) | 13.8069 | 0.655986 | 0.327993 | − | 0.944680i | \(-0.393628\pi\) | ||||
0.327993 | + | 0.944680i | \(0.393628\pi\) | |||||||
\(444\) | 4.39231 | 0.208450 | ||||||||
\(445\) | 3.87051 | 0.183480 | ||||||||
\(446\) | −25.4911 | −1.20704 | ||||||||
\(447\) | 25.6826 | 1.21475 | ||||||||
\(448\) | 2.75406 | 0.130117 | ||||||||
\(449\) | 23.4179 | 1.10516 | 0.552580 | − | 0.833460i | \(-0.313643\pi\) | ||||
0.552580 | + | 0.833460i | \(0.313643\pi\) | |||||||
\(450\) | −3.70648 | −0.174725 | ||||||||
\(451\) | 38.2344 | 1.80039 | ||||||||
\(452\) | 19.2766 | 0.906694 | ||||||||
\(453\) | −54.6225 | −2.56639 | ||||||||
\(454\) | 12.9585 | 0.608172 | ||||||||
\(455\) | −23.2303 | −1.08906 | ||||||||
\(456\) | −14.5987 | −0.683646 | ||||||||
\(457\) | −22.7518 | −1.06428 | −0.532142 | − | 0.846655i | \(-0.678613\pi\) | ||||
−0.532142 | + | 0.846655i | \(0.678613\pi\) | |||||||
\(458\) | −21.0076 | −0.981620 | ||||||||
\(459\) | 7.70487 | 0.359632 | ||||||||
\(460\) | −1.81074 | −0.0844260 | ||||||||
\(461\) | −23.3017 | −1.08527 | −0.542634 | − | 0.839969i | \(-0.682573\pi\) | ||||
−0.542634 | + | 0.839969i | \(0.682573\pi\) | |||||||
\(462\) | 23.1157 | 1.07544 | ||||||||
\(463\) | 30.1375 | 1.40061 | 0.700304 | − | 0.713845i | \(-0.253048\pi\) | ||||
0.700304 | + | 0.713845i | \(0.253048\pi\) | |||||||
\(464\) | −0.101640 | −0.00471854 | ||||||||
\(465\) | 11.0686 | 0.513292 | ||||||||
\(466\) | 16.4743 | 0.763159 | ||||||||
\(467\) | −18.2579 | −0.844877 | −0.422439 | − | 0.906392i | \(-0.638826\pi\) | ||||
−0.422439 | + | 0.906392i | \(0.638826\pi\) | |||||||
\(468\) | 10.0311 | 0.463687 | ||||||||
\(469\) | 11.9563 | 0.552089 | ||||||||
\(470\) | 13.9921 | 0.645408 | ||||||||
\(471\) | −49.8445 | −2.29671 | ||||||||
\(472\) | −2.92210 | −0.134501 | ||||||||
\(473\) | −4.90587 | −0.225572 | ||||||||
\(474\) | −35.8960 | −1.64876 | ||||||||
\(475\) | −11.0690 | −0.507880 | ||||||||
\(476\) | 11.0409 | 0.506061 | ||||||||
\(477\) | −11.4572 | −0.524588 | ||||||||
\(478\) | 17.6869 | 0.808979 | ||||||||
\(479\) | 11.4631 | 0.523763 | 0.261881 | − | 0.965100i | \(-0.415657\pi\) | ||||
0.261881 | + | 0.965100i | \(0.415657\pi\) | |||||||
\(480\) | 4.11056 | 0.187621 | ||||||||
\(481\) | −9.01308 | −0.410961 | ||||||||
\(482\) | 17.7352 | 0.807817 | ||||||||
\(483\) | −6.25202 | −0.284477 | ||||||||
\(484\) | 2.67019 | 0.121372 | ||||||||
\(485\) | −23.9936 | −1.08949 | ||||||||
\(486\) | 18.8038 | 0.852959 | ||||||||
\(487\) | 19.3792 | 0.878156 | 0.439078 | − | 0.898449i | \(-0.355305\pi\) | ||||
0.439078 | + | 0.898449i | \(0.355305\pi\) | |||||||
\(488\) | 12.7177 | 0.575702 | ||||||||
\(489\) | 28.0323 | 1.26767 | ||||||||
\(490\) | −1.05904 | −0.0478427 | ||||||||
\(491\) | 8.63766 | 0.389812 | 0.194906 | − | 0.980822i | \(-0.437560\pi\) | ||||
0.194906 | + | 0.980822i | \(0.437560\pi\) | |||||||
\(492\) | 23.4754 | 1.05835 | ||||||||
\(493\) | −0.407473 | −0.0183517 | ||||||||
\(494\) | 29.9567 | 1.34781 | ||||||||
\(495\) | 14.4166 | 0.647979 | ||||||||
\(496\) | 2.69271 | 0.120906 | ||||||||
\(497\) | −19.4470 | −0.872316 | ||||||||
\(498\) | −2.52465 | −0.113132 | ||||||||
\(499\) | −12.5381 | −0.561281 | −0.280640 | − | 0.959813i | \(-0.590547\pi\) | ||||
−0.280640 | + | 0.959813i | \(0.590547\pi\) | |||||||
\(500\) | 12.1704 | 0.544276 | ||||||||
\(501\) | −35.4897 | −1.58556 | ||||||||
\(502\) | 5.27663 | 0.235508 | ||||||||
\(503\) | 36.7462 | 1.63843 | 0.819216 | − | 0.573485i | \(-0.194409\pi\) | ||||
0.819216 | + | 0.573485i | \(0.194409\pi\) | |||||||
\(504\) | 5.93056 | 0.264168 | ||||||||
\(505\) | −7.71941 | −0.343509 | ||||||||
\(506\) | −3.69732 | −0.164366 | ||||||||
\(507\) | −19.7492 | −0.877091 | ||||||||
\(508\) | 10.9371 | 0.485257 | ||||||||
\(509\) | −6.54858 | −0.290261 | −0.145130 | − | 0.989413i | \(-0.546360\pi\) | ||||
−0.145130 | + | 0.989413i | \(0.546360\pi\) | |||||||
\(510\) | 16.4791 | 0.729707 | ||||||||
\(511\) | 23.3768 | 1.03413 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 12.3595 | 0.545684 | ||||||||
\(514\) | 12.2124 | 0.538664 | ||||||||
\(515\) | 12.4535 | 0.548766 | ||||||||
\(516\) | −3.01214 | −0.132602 | ||||||||
\(517\) | 28.5704 | 1.25652 | ||||||||
\(518\) | −5.32869 | −0.234129 | ||||||||
\(519\) | 24.8864 | 1.09239 | ||||||||
\(520\) | −8.43493 | −0.369896 | ||||||||
\(521\) | −14.0049 | −0.613564 | −0.306782 | − | 0.951780i | \(-0.599252\pi\) | ||||
−0.306782 | + | 0.951780i | \(0.599252\pi\) | |||||||
\(522\) | −0.218871 | −0.00957972 | ||||||||
\(523\) | −29.6434 | −1.29621 | −0.648107 | − | 0.761549i | \(-0.724439\pi\) | ||||
−0.648107 | + | 0.761549i | \(0.724439\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 10.7612 | 0.469658 | ||||||||
\(526\) | 29.5732 | 1.28945 | ||||||||
\(527\) | 10.7950 | 0.470237 | ||||||||
\(528\) | 8.39332 | 0.365272 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 9.63410 | 0.418479 | ||||||||
\(531\) | −6.29240 | −0.273067 | ||||||||
\(532\) | 17.7109 | 0.767866 | ||||||||
\(533\) | −48.1719 | −2.08656 | ||||||||
\(534\) | 4.85244 | 0.209985 | ||||||||
\(535\) | 22.8126 | 0.986275 | ||||||||
\(536\) | 4.34132 | 0.187516 | ||||||||
\(537\) | 16.4355 | 0.709242 | ||||||||
\(538\) | 21.9667 | 0.947051 | ||||||||
\(539\) | −2.16245 | −0.0931433 | ||||||||
\(540\) | −3.48007 | −0.149758 | ||||||||
\(541\) | 36.3124 | 1.56119 | 0.780596 | − | 0.625035i | \(-0.214915\pi\) | ||||
0.780596 | + | 0.625035i | \(0.214915\pi\) | |||||||
\(542\) | −12.9223 | −0.555060 | ||||||||
\(543\) | −16.7244 | −0.717711 | ||||||||
\(544\) | 4.00896 | 0.171883 | ||||||||
\(545\) | 25.9151 | 1.11008 | ||||||||
\(546\) | −29.1237 | −1.24638 | ||||||||
\(547\) | 14.2823 | 0.610667 | 0.305333 | − | 0.952246i | \(-0.401232\pi\) | ||||
0.305333 | + | 0.952246i | \(0.401232\pi\) | |||||||
\(548\) | 13.8943 | 0.593537 | ||||||||
\(549\) | 27.3860 | 1.16881 | ||||||||
\(550\) | 6.36397 | 0.271360 | ||||||||
\(551\) | −0.653633 | −0.0278457 | ||||||||
\(552\) | −2.27011 | −0.0966221 | ||||||||
\(553\) | 43.5486 | 1.85187 | ||||||||
\(554\) | −18.2265 | −0.774371 | ||||||||
\(555\) | −7.95331 | −0.337599 | ||||||||
\(556\) | −11.9258 | −0.505766 | ||||||||
\(557\) | 20.4947 | 0.868390 | 0.434195 | − | 0.900819i | \(-0.357033\pi\) | ||||
0.434195 | + | 0.900819i | \(0.357033\pi\) | |||||||
\(558\) | 5.79844 | 0.245467 | ||||||||
\(559\) | 6.18095 | 0.261427 | ||||||||
\(560\) | −4.98688 | −0.210734 | ||||||||
\(561\) | 33.6485 | 1.42064 | ||||||||
\(562\) | 3.48382 | 0.146956 | ||||||||
\(563\) | 39.8683 | 1.68025 | 0.840124 | − | 0.542395i | \(-0.182482\pi\) | ||||
0.840124 | + | 0.542395i | \(0.182482\pi\) | |||||||
\(564\) | 17.5418 | 0.738644 | ||||||||
\(565\) | −34.9048 | −1.46846 | ||||||||
\(566\) | 7.53303 | 0.316637 | ||||||||
\(567\) | −29.8075 | −1.25180 | ||||||||
\(568\) | −7.06119 | −0.296281 | ||||||||
\(569\) | 34.0073 | 1.42566 | 0.712831 | − | 0.701336i | \(-0.247413\pi\) | ||||
0.712831 | + | 0.701336i | \(0.247413\pi\) | |||||||
\(570\) | 26.4343 | 1.10721 | ||||||||
\(571\) | −34.0898 | −1.42661 | −0.713307 | − | 0.700852i | \(-0.752803\pi\) | ||||
−0.713307 | + | 0.700852i | \(0.752803\pi\) | |||||||
\(572\) | −17.2232 | −0.720138 | ||||||||
\(573\) | −24.4601 | −1.02183 | ||||||||
\(574\) | −28.4801 | −1.18874 | ||||||||
\(575\) | −1.72124 | −0.0717805 | ||||||||
\(576\) | 2.15338 | 0.0897243 | ||||||||
\(577\) | 14.6652 | 0.610519 | 0.305259 | − | 0.952269i | \(-0.401257\pi\) | ||||
0.305259 | + | 0.952269i | \(0.401257\pi\) | |||||||
\(578\) | −0.928206 | −0.0386083 | ||||||||
\(579\) | −40.3628 | −1.67742 | ||||||||
\(580\) | 0.184044 | 0.00764201 | ||||||||
\(581\) | 3.06288 | 0.127070 | ||||||||
\(582\) | −30.0806 | −1.24688 | ||||||||
\(583\) | 19.6718 | 0.814722 | ||||||||
\(584\) | 8.48812 | 0.351241 | ||||||||
\(585\) | −18.1636 | −0.750974 | ||||||||
\(586\) | 17.4488 | 0.720805 | ||||||||
\(587\) | −28.6183 | −1.18120 | −0.590601 | − | 0.806964i | \(-0.701109\pi\) | ||||
−0.590601 | + | 0.806964i | \(0.701109\pi\) | |||||||
\(588\) | −1.32771 | −0.0547540 | ||||||||
\(589\) | 17.3164 | 0.713508 | ||||||||
\(590\) | 5.29115 | 0.217833 | ||||||||
\(591\) | −17.9396 | −0.737936 | ||||||||
\(592\) | −1.93485 | −0.0795217 | ||||||||
\(593\) | 16.6164 | 0.682354 | 0.341177 | − | 0.939999i | \(-0.389174\pi\) | ||||
0.341177 | + | 0.939999i | \(0.389174\pi\) | |||||||
\(594\) | −7.10592 | −0.291559 | ||||||||
\(595\) | −19.9922 | −0.819602 | ||||||||
\(596\) | −11.3134 | −0.463414 | ||||||||
\(597\) | 49.0622 | 2.00798 | ||||||||
\(598\) | 4.65829 | 0.190492 | ||||||||
\(599\) | −3.64354 | −0.148871 | −0.0744356 | − | 0.997226i | \(-0.523716\pi\) | ||||
−0.0744356 | + | 0.997226i | \(0.523716\pi\) | |||||||
\(600\) | 3.90739 | 0.159519 | ||||||||
\(601\) | 7.47458 | 0.304894 | 0.152447 | − | 0.988312i | \(-0.451285\pi\) | ||||
0.152447 | + | 0.988312i | \(0.451285\pi\) | |||||||
\(602\) | 3.65429 | 0.148938 | ||||||||
\(603\) | 9.34852 | 0.380701 | ||||||||
\(604\) | 24.0616 | 0.979054 | ||||||||
\(605\) | −4.83501 | −0.196571 | ||||||||
\(606\) | −9.67777 | −0.393133 | ||||||||
\(607\) | −21.8790 | −0.888041 | −0.444020 | − | 0.896017i | \(-0.646448\pi\) | ||||
−0.444020 | + | 0.896017i | \(0.646448\pi\) | |||||||
\(608\) | 6.43083 | 0.260805 | ||||||||
\(609\) | 0.635458 | 0.0257501 | ||||||||
\(610\) | −23.0283 | −0.932390 | ||||||||
\(611\) | −35.9961 | −1.45624 | ||||||||
\(612\) | 8.63284 | 0.348962 | ||||||||
\(613\) | −40.9160 | −1.65258 | −0.826291 | − | 0.563243i | \(-0.809554\pi\) | ||||
−0.826291 | + | 0.563243i | \(0.809554\pi\) | |||||||
\(614\) | 18.3659 | 0.741188 | ||||||||
\(615\) | −42.5078 | −1.71408 | ||||||||
\(616\) | −10.1827 | −0.410271 | ||||||||
\(617\) | 0.932093 | 0.0375247 | 0.0187623 | − | 0.999824i | \(-0.494027\pi\) | ||||
0.0187623 | + | 0.999824i | \(0.494027\pi\) | |||||||
\(618\) | 15.6128 | 0.628040 | ||||||||
\(619\) | −43.7154 | −1.75707 | −0.878534 | − | 0.477679i | \(-0.841478\pi\) | ||||
−0.878534 | + | 0.477679i | \(0.841478\pi\) | |||||||
\(620\) | −4.87579 | −0.195816 | ||||||||
\(621\) | 1.92191 | 0.0771236 | ||||||||
\(622\) | 28.2526 | 1.13282 | ||||||||
\(623\) | −5.88691 | −0.235854 | ||||||||
\(624\) | −10.5748 | −0.423331 | ||||||||
\(625\) | −13.4312 | −0.537246 | ||||||||
\(626\) | −8.91799 | −0.356434 | ||||||||
\(627\) | 53.9760 | 2.15559 | ||||||||
\(628\) | 21.9569 | 0.876175 | ||||||||
\(629\) | −7.75673 | −0.309281 | ||||||||
\(630\) | −10.7387 | −0.427839 | ||||||||
\(631\) | −12.4796 | −0.496806 | −0.248403 | − | 0.968657i | \(-0.579906\pi\) | ||||
−0.248403 | + | 0.968657i | \(0.579906\pi\) | |||||||
\(632\) | 15.8125 | 0.628987 | ||||||||
\(633\) | 52.0333 | 2.06814 | ||||||||
\(634\) | −32.5822 | −1.29400 | ||||||||
\(635\) | −19.8043 | −0.785908 | ||||||||
\(636\) | 12.0782 | 0.478932 | ||||||||
\(637\) | 2.72449 | 0.107948 | ||||||||
\(638\) | 0.375797 | 0.0148780 | ||||||||
\(639\) | −15.2055 | −0.601518 | ||||||||
\(640\) | −1.81074 | −0.0715756 | ||||||||
\(641\) | 19.4722 | 0.769107 | 0.384553 | − | 0.923103i | \(-0.374355\pi\) | ||||
0.384553 | + | 0.923103i | \(0.374355\pi\) | |||||||
\(642\) | 28.6000 | 1.12875 | ||||||||
\(643\) | 11.4979 | 0.453433 | 0.226716 | − | 0.973961i | \(-0.427201\pi\) | ||||
0.226716 | + | 0.973961i | \(0.427201\pi\) | |||||||
\(644\) | 2.75406 | 0.108525 | ||||||||
\(645\) | 5.45419 | 0.214759 | ||||||||
\(646\) | 25.7810 | 1.01434 | ||||||||
\(647\) | 16.8266 | 0.661523 | 0.330761 | − | 0.943714i | \(-0.392694\pi\) | ||||
0.330761 | + | 0.943714i | \(0.392694\pi\) | |||||||
\(648\) | −10.8231 | −0.425171 | ||||||||
\(649\) | 10.8039 | 0.424092 | ||||||||
\(650\) | −8.01802 | −0.314493 | ||||||||
\(651\) | −16.8349 | −0.659811 | ||||||||
\(652\) | −12.3485 | −0.483603 | ||||||||
\(653\) | 8.87311 | 0.347232 | 0.173616 | − | 0.984813i | \(-0.444455\pi\) | ||||
0.173616 | + | 0.984813i | \(0.444455\pi\) | |||||||
\(654\) | 32.4896 | 1.27044 | ||||||||
\(655\) | −1.81074 | −0.0707513 | ||||||||
\(656\) | −10.3411 | −0.403753 | ||||||||
\(657\) | 18.2782 | 0.713100 | ||||||||
\(658\) | −21.2815 | −0.829640 | ||||||||
\(659\) | −8.54643 | −0.332922 | −0.166461 | − | 0.986048i | \(-0.553234\pi\) | ||||
−0.166461 | + | 0.986048i | \(0.553234\pi\) | |||||||
\(660\) | −15.1981 | −0.591584 | ||||||||
\(661\) | 31.6866 | 1.23247 | 0.616233 | − | 0.787564i | \(-0.288658\pi\) | ||||
0.616233 | + | 0.787564i | \(0.288658\pi\) | |||||||
\(662\) | 24.3121 | 0.944918 | ||||||||
\(663\) | −42.3940 | −1.64645 | ||||||||
\(664\) | 1.11213 | 0.0431590 | ||||||||
\(665\) | −32.0698 | −1.24361 | ||||||||
\(666\) | −4.16647 | −0.161447 | ||||||||
\(667\) | −0.101640 | −0.00393553 | ||||||||
\(668\) | 15.6335 | 0.604878 | ||||||||
\(669\) | 57.8675 | 2.23729 | ||||||||
\(670\) | −7.86098 | −0.303696 | ||||||||
\(671\) | −47.0213 | −1.81524 | ||||||||
\(672\) | −6.25202 | −0.241177 | ||||||||
\(673\) | −13.7173 | −0.528764 | −0.264382 | − | 0.964418i | \(-0.585168\pi\) | ||||
−0.264382 | + | 0.964418i | \(0.585168\pi\) | |||||||
\(674\) | 22.6806 | 0.873625 | ||||||||
\(675\) | −3.30806 | −0.127327 | ||||||||
\(676\) | 8.69966 | 0.334602 | ||||||||
\(677\) | 6.22810 | 0.239365 | 0.119683 | − | 0.992812i | \(-0.461812\pi\) | ||||
0.119683 | + | 0.992812i | \(0.461812\pi\) | |||||||
\(678\) | −43.7599 | −1.68059 | ||||||||
\(679\) | 36.4934 | 1.40049 | ||||||||
\(680\) | −7.25917 | −0.278377 | ||||||||
\(681\) | −29.4172 | −1.12727 | ||||||||
\(682\) | −9.95582 | −0.381228 | ||||||||
\(683\) | 8.25264 | 0.315779 | 0.157889 | − | 0.987457i | \(-0.449531\pi\) | ||||
0.157889 | + | 0.987457i | \(0.449531\pi\) | |||||||
\(684\) | 13.8480 | 0.529493 | ||||||||
\(685\) | −25.1590 | −0.961275 | ||||||||
\(686\) | −17.6677 | −0.674555 | ||||||||
\(687\) | 47.6894 | 1.81947 | ||||||||
\(688\) | 1.32687 | 0.0505865 | ||||||||
\(689\) | −24.7846 | −0.944220 | ||||||||
\(690\) | 4.11056 | 0.156486 | ||||||||
\(691\) | −37.9457 | −1.44352 | −0.721761 | − | 0.692142i | \(-0.756667\pi\) | ||||
−0.721761 | + | 0.692142i | \(0.756667\pi\) | |||||||
\(692\) | −10.9627 | −0.416738 | ||||||||
\(693\) | −21.9272 | −0.832945 | ||||||||
\(694\) | 24.6481 | 0.935628 | ||||||||
\(695\) | 21.5945 | 0.819125 | ||||||||
\(696\) | 0.230735 | 0.00874597 | ||||||||
\(697\) | −41.4572 | −1.57030 | ||||||||
\(698\) | 26.4989 | 1.00300 | ||||||||
\(699\) | −37.3985 | −1.41454 | ||||||||
\(700\) | −4.74040 | −0.179170 | ||||||||
\(701\) | 47.6696 | 1.80045 | 0.900227 | − | 0.435421i | \(-0.143400\pi\) | ||||
0.900227 | + | 0.435421i | \(0.143400\pi\) | |||||||
\(702\) | 8.95281 | 0.337902 | ||||||||
\(703\) | −12.4427 | −0.469284 | ||||||||
\(704\) | −3.69732 | −0.139348 | ||||||||
\(705\) | −31.7636 | −1.19629 | ||||||||
\(706\) | 10.3969 | 0.391291 | ||||||||
\(707\) | 11.7409 | 0.441564 | ||||||||
\(708\) | 6.63348 | 0.249301 | ||||||||
\(709\) | −16.6544 | −0.625467 | −0.312734 | − | 0.949841i | \(-0.601245\pi\) | ||||
−0.312734 | + | 0.949841i | \(0.601245\pi\) | |||||||
\(710\) | 12.7859 | 0.479848 | ||||||||
\(711\) | 34.0503 | 1.27699 | ||||||||
\(712\) | −2.13754 | −0.0801076 | ||||||||
\(713\) | 2.69271 | 0.100843 | ||||||||
\(714\) | −25.0641 | −0.938001 | ||||||||
\(715\) | 31.1867 | 1.16631 | ||||||||
\(716\) | −7.23995 | −0.270570 | ||||||||
\(717\) | −40.1511 | −1.49947 | ||||||||
\(718\) | −12.5720 | −0.469183 | ||||||||
\(719\) | −45.3495 | −1.69125 | −0.845625 | − | 0.533778i | \(-0.820772\pi\) | ||||
−0.845625 | + | 0.533778i | \(0.820772\pi\) | |||||||
\(720\) | −3.89921 | −0.145315 | ||||||||
\(721\) | −18.9413 | −0.705411 | ||||||||
\(722\) | 22.3556 | 0.831990 | ||||||||
\(723\) | −40.2608 | −1.49732 | ||||||||
\(724\) | 7.36721 | 0.273800 | ||||||||
\(725\) | 0.174947 | 0.00649738 | ||||||||
\(726\) | −6.06162 | −0.224968 | ||||||||
\(727\) | 34.3081 | 1.27242 | 0.636209 | − | 0.771516i | \(-0.280501\pi\) | ||||
0.636209 | + | 0.771516i | \(0.280501\pi\) | |||||||
\(728\) | 12.8292 | 0.475483 | ||||||||
\(729\) | −10.2174 | −0.378424 | ||||||||
\(730\) | −15.3697 | −0.568860 | ||||||||
\(731\) | 5.31938 | 0.196744 | ||||||||
\(732\) | −28.8705 | −1.06708 | ||||||||
\(733\) | −45.7316 | −1.68914 | −0.844568 | − | 0.535449i | \(-0.820142\pi\) | ||||
−0.844568 | + | 0.535449i | \(0.820142\pi\) | |||||||
\(734\) | −17.1556 | −0.633225 | ||||||||
\(735\) | 2.40414 | 0.0886781 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −16.0513 | −0.591256 | ||||||||
\(738\) | −22.2684 | −0.819711 | ||||||||
\(739\) | 47.3456 | 1.74163 | 0.870817 | − | 0.491607i | \(-0.163590\pi\) | ||||
0.870817 | + | 0.491607i | \(0.163590\pi\) | |||||||
\(740\) | 3.50350 | 0.128791 | ||||||||
\(741\) | −68.0049 | −2.49822 | ||||||||
\(742\) | −14.6531 | −0.537933 | ||||||||
\(743\) | −0.480359 | −0.0176227 | −0.00881133 | − | 0.999961i | \(-0.502805\pi\) | ||||
−0.00881133 | + | 0.999961i | \(0.502805\pi\) | |||||||
\(744\) | −6.11274 | −0.224104 | ||||||||
\(745\) | 20.4856 | 0.750533 | ||||||||
\(746\) | 18.4286 | 0.674718 | ||||||||
\(747\) | 2.39484 | 0.0876227 | ||||||||
\(748\) | −14.8224 | −0.541962 | ||||||||
\(749\) | −34.6972 | −1.26781 | ||||||||
\(750\) | −27.6281 | −1.00883 | ||||||||
\(751\) | −46.8718 | −1.71038 | −0.855188 | − | 0.518318i | \(-0.826559\pi\) | ||||
−0.855188 | + | 0.518318i | \(0.826559\pi\) | |||||||
\(752\) | −7.72731 | −0.281786 | ||||||||
\(753\) | −11.9785 | −0.436521 | ||||||||
\(754\) | −0.473471 | −0.0172428 | ||||||||
\(755\) | −43.5693 | −1.58565 | ||||||||
\(756\) | 5.29306 | 0.192507 | ||||||||
\(757\) | 17.6363 | 0.641003 | 0.320502 | − | 0.947248i | \(-0.396149\pi\) | ||||
0.320502 | + | 0.947248i | \(0.396149\pi\) | |||||||
\(758\) | −23.4999 | −0.853554 | ||||||||
\(759\) | 8.39332 | 0.304658 | ||||||||
\(760\) | −11.6445 | −0.422392 | ||||||||
\(761\) | 15.2743 | 0.553694 | 0.276847 | − | 0.960914i | \(-0.410711\pi\) | ||||
0.276847 | + | 0.960914i | \(0.410711\pi\) | |||||||
\(762\) | −24.8285 | −0.899441 | ||||||||
\(763\) | −39.4160 | −1.42695 | ||||||||
\(764\) | 10.7749 | 0.389821 | ||||||||
\(765\) | −15.6318 | −0.565168 | ||||||||
\(766\) | −0.0335359 | −0.00121170 | ||||||||
\(767\) | −13.6120 | −0.491500 | ||||||||
\(768\) | −2.27011 | −0.0819154 | ||||||||
\(769\) | −4.83977 | −0.174527 | −0.0872634 | − | 0.996185i | \(-0.527812\pi\) | ||||
−0.0872634 | + | 0.996185i | \(0.527812\pi\) | |||||||
\(770\) | 18.4381 | 0.664463 | ||||||||
\(771\) | −27.7233 | −0.998432 | ||||||||
\(772\) | 17.7801 | 0.639922 | ||||||||
\(773\) | −35.7120 | −1.28447 | −0.642236 | − | 0.766507i | \(-0.721993\pi\) | ||||
−0.642236 | + | 0.766507i | \(0.721993\pi\) | |||||||
\(774\) | 2.85726 | 0.102702 | ||||||||
\(775\) | −4.63479 | −0.166487 | ||||||||
\(776\) | 13.2507 | 0.475674 | ||||||||
\(777\) | 12.0967 | 0.433967 | ||||||||
\(778\) | −13.5552 | −0.485979 | ||||||||
\(779\) | −66.5020 | −2.38268 | ||||||||
\(780\) | 19.1482 | 0.685615 | ||||||||
\(781\) | 26.1075 | 0.934200 | ||||||||
\(782\) | 4.00896 | 0.143360 | ||||||||
\(783\) | −0.195344 | −0.00698102 | ||||||||
\(784\) | 0.584869 | 0.0208882 | ||||||||
\(785\) | −39.7581 | −1.41903 | ||||||||
\(786\) | −2.27011 | −0.0809720 | ||||||||
\(787\) | −20.9918 | −0.748276 | −0.374138 | − | 0.927373i | \(-0.622061\pi\) | ||||
−0.374138 | + | 0.927373i | \(0.622061\pi\) | |||||||
\(788\) | 7.90253 | 0.281516 | ||||||||
\(789\) | −67.1344 | −2.39005 | ||||||||
\(790\) | −28.6322 | −1.01869 | ||||||||
\(791\) | 53.0889 | 1.88762 | ||||||||
\(792\) | −7.96175 | −0.282909 | ||||||||
\(793\) | 59.2426 | 2.10377 | ||||||||
\(794\) | 9.69121 | 0.343928 | ||||||||
\(795\) | −21.8704 | −0.775665 | ||||||||
\(796\) | −21.6123 | −0.766028 | ||||||||
\(797\) | −14.1563 | −0.501443 | −0.250721 | − | 0.968059i | \(-0.580668\pi\) | ||||
−0.250721 | + | 0.968059i | \(0.580668\pi\) | |||||||
\(798\) | −40.2057 | −1.42327 | ||||||||
\(799\) | −30.9785 | −1.09594 | ||||||||
\(800\) | −1.72124 | −0.0608549 | ||||||||
\(801\) | −4.60294 | −0.162637 | ||||||||
\(802\) | −13.6563 | −0.482219 | ||||||||
\(803\) | −31.3833 | −1.10749 | ||||||||
\(804\) | −9.85526 | −0.347568 | ||||||||
\(805\) | −4.98688 | −0.175764 | ||||||||
\(806\) | 12.5434 | 0.441823 | ||||||||
\(807\) | −49.8667 | −1.75539 | ||||||||
\(808\) | 4.26314 | 0.149977 | ||||||||
\(809\) | 38.0797 | 1.33881 | 0.669405 | − | 0.742898i | \(-0.266549\pi\) | ||||
0.669405 | + | 0.742898i | \(0.266549\pi\) | |||||||
\(810\) | 19.5978 | 0.688595 | ||||||||
\(811\) | −28.9634 | −1.01704 | −0.508520 | − | 0.861050i | \(-0.669807\pi\) | ||||
−0.508520 | + | 0.861050i | \(0.669807\pi\) | |||||||
\(812\) | −0.279924 | −0.00982342 | ||||||||
\(813\) | 29.3350 | 1.02882 | ||||||||
\(814\) | 7.15375 | 0.250739 | ||||||||
\(815\) | 22.3598 | 0.783229 | ||||||||
\(816\) | −9.10078 | −0.318591 | ||||||||
\(817\) | 8.53289 | 0.298528 | ||||||||
\(818\) | 14.9273 | 0.521922 | ||||||||
\(819\) | 27.6262 | 0.965339 | ||||||||
\(820\) | 18.7250 | 0.653906 | ||||||||
\(821\) | 44.6184 | 1.55719 | 0.778596 | − | 0.627525i | \(-0.215932\pi\) | ||||
0.778596 | + | 0.627525i | \(0.215932\pi\) | |||||||
\(822\) | −31.5416 | −1.10014 | ||||||||
\(823\) | −11.2686 | −0.392799 | −0.196400 | − | 0.980524i | \(-0.562925\pi\) | ||||
−0.196400 | + | 0.980524i | \(0.562925\pi\) | |||||||
\(824\) | −6.87758 | −0.239592 | ||||||||
\(825\) | −14.4469 | −0.502976 | ||||||||
\(826\) | −8.04765 | −0.280014 | ||||||||
\(827\) | −15.8935 | −0.552670 | −0.276335 | − | 0.961061i | \(-0.589120\pi\) | ||||
−0.276335 | + | 0.961061i | \(0.589120\pi\) | |||||||
\(828\) | 2.15338 | 0.0748353 | ||||||||
\(829\) | −4.08082 | −0.141733 | −0.0708664 | − | 0.997486i | \(-0.522576\pi\) | ||||
−0.0708664 | + | 0.997486i | \(0.522576\pi\) | |||||||
\(830\) | −2.01377 | −0.0698991 | ||||||||
\(831\) | 41.3762 | 1.43532 | ||||||||
\(832\) | 4.65829 | 0.161497 | ||||||||
\(833\) | 2.34472 | 0.0812397 | ||||||||
\(834\) | 27.0728 | 0.937455 | ||||||||
\(835\) | −28.3081 | −0.979643 | ||||||||
\(836\) | −23.7769 | −0.822340 | ||||||||
\(837\) | 5.17514 | 0.178879 | ||||||||
\(838\) | −37.9670 | −1.31155 | ||||||||
\(839\) | −36.8015 | −1.27053 | −0.635264 | − | 0.772295i | \(-0.719109\pi\) | ||||
−0.635264 | + | 0.772295i | \(0.719109\pi\) | |||||||
\(840\) | 11.3208 | 0.390603 | ||||||||
\(841\) | −28.9897 | −0.999644 | ||||||||
\(842\) | 15.6129 | 0.538056 | ||||||||
\(843\) | −7.90865 | −0.272388 | ||||||||
\(844\) | −22.9211 | −0.788977 | ||||||||
\(845\) | −15.7528 | −0.541912 | ||||||||
\(846\) | −16.6399 | −0.572090 | ||||||||
\(847\) | 7.35388 | 0.252682 | ||||||||
\(848\) | −5.32055 | −0.182708 | ||||||||
\(849\) | −17.1008 | −0.586897 | ||||||||
\(850\) | −6.90038 | −0.236681 | ||||||||
\(851\) | −1.93485 | −0.0663257 | ||||||||
\(852\) | 16.0297 | 0.549167 | ||||||||
\(853\) | −13.2963 | −0.455256 | −0.227628 | − | 0.973748i | \(-0.573097\pi\) | ||||
−0.227628 | + | 0.973748i | \(0.573097\pi\) | |||||||
\(854\) | 35.0253 | 1.19854 | ||||||||
\(855\) | −25.0752 | −0.857552 | ||||||||
\(856\) | −12.5985 | −0.430609 | ||||||||
\(857\) | 8.53081 | 0.291407 | 0.145703 | − | 0.989328i | \(-0.453455\pi\) | ||||
0.145703 | + | 0.989328i | \(0.453455\pi\) | |||||||
\(858\) | 39.0985 | 1.33480 | ||||||||
\(859\) | −8.07792 | −0.275615 | −0.137808 | − | 0.990459i | \(-0.544006\pi\) | ||||
−0.137808 | + | 0.990459i | \(0.544006\pi\) | |||||||
\(860\) | −2.40261 | −0.0819285 | ||||||||
\(861\) | 64.6529 | 2.20336 | ||||||||
\(862\) | −4.74475 | −0.161607 | ||||||||
\(863\) | −22.2800 | −0.758420 | −0.379210 | − | 0.925311i | \(-0.623804\pi\) | ||||
−0.379210 | + | 0.925311i | \(0.623804\pi\) | |||||||
\(864\) | 1.92191 | 0.0653847 | ||||||||
\(865\) | 19.8505 | 0.674937 | ||||||||
\(866\) | −3.48483 | −0.118419 | ||||||||
\(867\) | 2.10713 | 0.0715617 | ||||||||
\(868\) | 7.41590 | 0.251712 | ||||||||
\(869\) | −58.4639 | −1.98325 | ||||||||
\(870\) | −0.417799 | −0.0141647 | ||||||||
\(871\) | 20.2231 | 0.685234 | ||||||||
\(872\) | −14.3119 | −0.484663 | ||||||||
\(873\) | 28.5339 | 0.965727 | ||||||||
\(874\) | 6.43083 | 0.217526 | ||||||||
\(875\) | 33.5180 | 1.13312 | ||||||||
\(876\) | −19.2689 | −0.651037 | ||||||||
\(877\) | −14.1688 | −0.478445 | −0.239222 | − | 0.970965i | \(-0.576893\pi\) | ||||
−0.239222 | + | 0.970965i | \(0.576893\pi\) | |||||||
\(878\) | −12.8079 | −0.432246 | ||||||||
\(879\) | −39.6107 | −1.33604 | ||||||||
\(880\) | 6.69487 | 0.225684 | ||||||||
\(881\) | 34.4160 | 1.15950 | 0.579752 | − | 0.814793i | \(-0.303149\pi\) | ||||
0.579752 | + | 0.814793i | \(0.303149\pi\) | |||||||
\(882\) | 1.25945 | 0.0424078 | ||||||||
\(883\) | 2.77337 | 0.0933315 | 0.0466657 | − | 0.998911i | \(-0.485140\pi\) | ||||
0.0466657 | + | 0.998911i | \(0.485140\pi\) | |||||||
\(884\) | 18.6749 | 0.628105 | ||||||||
\(885\) | −12.0115 | −0.403761 | ||||||||
\(886\) | 13.8069 | 0.463852 | ||||||||
\(887\) | −5.21881 | −0.175230 | −0.0876152 | − | 0.996154i | \(-0.527925\pi\) | ||||
−0.0876152 | + | 0.996154i | \(0.527925\pi\) | |||||||
\(888\) | 4.39231 | 0.147396 | ||||||||
\(889\) | 30.1216 | 1.01025 | ||||||||
\(890\) | 3.87051 | 0.129740 | ||||||||
\(891\) | 40.0165 | 1.34060 | ||||||||
\(892\) | −25.4911 | −0.853505 | ||||||||
\(893\) | −49.6931 | −1.66291 | ||||||||
\(894\) | 25.6826 | 0.858955 | ||||||||
\(895\) | 13.1096 | 0.438207 | ||||||||
\(896\) | 2.75406 | 0.0920068 | ||||||||
\(897\) | −10.5748 | −0.353083 | ||||||||
\(898\) | 23.4179 | 0.781466 | ||||||||
\(899\) | −0.273688 | −0.00912801 | ||||||||
\(900\) | −3.70648 | −0.123549 | ||||||||
\(901\) | −21.3299 | −0.710601 | ||||||||
\(902\) | 38.2344 | 1.27307 | ||||||||
\(903\) | −8.29563 | −0.276061 | ||||||||
\(904\) | 19.2766 | 0.641129 | ||||||||
\(905\) | −13.3401 | −0.443439 | ||||||||
\(906\) | −54.6225 | −1.81471 | ||||||||
\(907\) | −4.98783 | −0.165618 | −0.0828091 | − | 0.996565i | \(-0.526389\pi\) | ||||
−0.0828091 | + | 0.996565i | \(0.526389\pi\) | |||||||
\(908\) | 12.9585 | 0.430043 | ||||||||
\(909\) | 9.18017 | 0.304487 | ||||||||
\(910\) | −23.2303 | −0.770078 | ||||||||
\(911\) | 10.7217 | 0.355225 | 0.177612 | − | 0.984101i | \(-0.443163\pi\) | ||||
0.177612 | + | 0.984101i | \(0.443163\pi\) | |||||||
\(912\) | −14.5987 | −0.483410 | ||||||||
\(913\) | −4.11190 | −0.136084 | ||||||||
\(914\) | −22.7518 | −0.752563 | ||||||||
\(915\) | 52.2768 | 1.72822 | ||||||||
\(916\) | −21.0076 | −0.694110 | ||||||||
\(917\) | 2.75406 | 0.0909472 | ||||||||
\(918\) | 7.70487 | 0.254298 | ||||||||
\(919\) | 30.5345 | 1.00724 | 0.503620 | − | 0.863926i | \(-0.332001\pi\) | ||||
0.503620 | + | 0.863926i | \(0.332001\pi\) | |||||||
\(920\) | −1.81074 | −0.0596982 | ||||||||
\(921\) | −41.6926 | −1.37382 | ||||||||
\(922\) | −23.3017 | −0.767401 | ||||||||
\(923\) | −32.8931 | −1.08269 | ||||||||
\(924\) | 23.1157 | 0.760452 | ||||||||
\(925\) | 3.33033 | 0.109501 | ||||||||
\(926\) | 30.1375 | 0.990379 | ||||||||
\(927\) | −14.8101 | −0.486426 | ||||||||
\(928\) | −0.101640 | −0.00333651 | ||||||||
\(929\) | 15.0845 | 0.494905 | 0.247453 | − | 0.968900i | \(-0.420407\pi\) | ||||
0.247453 | + | 0.968900i | \(0.420407\pi\) | |||||||
\(930\) | 11.0686 | 0.362952 | ||||||||
\(931\) | 3.76119 | 0.123268 | ||||||||
\(932\) | 16.4743 | 0.539635 | ||||||||
\(933\) | −64.1363 | −2.09973 | ||||||||
\(934\) | −18.2579 | −0.597418 | ||||||||
\(935\) | 26.8395 | 0.877746 | ||||||||
\(936\) | 10.0311 | 0.327876 | ||||||||
\(937\) | −31.2724 | −1.02162 | −0.510812 | − | 0.859693i | \(-0.670655\pi\) | ||||
−0.510812 | + | 0.859693i | \(0.670655\pi\) | |||||||
\(938\) | 11.9563 | 0.390386 | ||||||||
\(939\) | 20.2448 | 0.660663 | ||||||||
\(940\) | 13.9921 | 0.456373 | ||||||||
\(941\) | 4.54397 | 0.148129 | 0.0740646 | − | 0.997253i | \(-0.476403\pi\) | ||||
0.0740646 | + | 0.997253i | \(0.476403\pi\) | |||||||
\(942\) | −49.8445 | −1.62402 | ||||||||
\(943\) | −10.3411 | −0.336753 | ||||||||
\(944\) | −2.92210 | −0.0951063 | ||||||||
\(945\) | −9.58434 | −0.311778 | ||||||||
\(946\) | −4.90587 | −0.159504 | ||||||||
\(947\) | 41.8729 | 1.36069 | 0.680344 | − | 0.732893i | \(-0.261831\pi\) | ||||
0.680344 | + | 0.732893i | \(0.261831\pi\) | |||||||
\(948\) | −35.8960 | −1.16585 | ||||||||
\(949\) | 39.5401 | 1.28353 | ||||||||
\(950\) | −11.0690 | −0.359125 | ||||||||
\(951\) | 73.9650 | 2.39848 | ||||||||
\(952\) | 11.0409 | 0.357839 | ||||||||
\(953\) | −7.67464 | −0.248606 | −0.124303 | − | 0.992244i | \(-0.539669\pi\) | ||||
−0.124303 | + | 0.992244i | \(0.539669\pi\) | |||||||
\(954\) | −11.4572 | −0.370940 | ||||||||
\(955\) | −19.5104 | −0.631343 | ||||||||
\(956\) | 17.6869 | 0.572035 | ||||||||
\(957\) | −0.853100 | −0.0275768 | ||||||||
\(958\) | 11.4631 | 0.370356 | ||||||||
\(959\) | 38.2659 | 1.23567 | ||||||||
\(960\) | 4.11056 | 0.132668 | ||||||||
\(961\) | −23.7493 | −0.766107 | ||||||||
\(962\) | −9.01308 | −0.290593 | ||||||||
\(963\) | −27.1295 | −0.874235 | ||||||||
\(964\) | 17.7352 | 0.571213 | ||||||||
\(965\) | −32.1951 | −1.03640 | ||||||||
\(966\) | −6.25202 | −0.201155 | ||||||||
\(967\) | 41.8258 | 1.34503 | 0.672514 | − | 0.740085i | \(-0.265215\pi\) | ||||
0.672514 | + | 0.740085i | \(0.265215\pi\) | |||||||
\(968\) | 2.67019 | 0.0858232 | ||||||||
\(969\) | −58.5256 | −1.88011 | ||||||||
\(970\) | −23.9936 | −0.770387 | ||||||||
\(971\) | −53.8138 | −1.72697 | −0.863484 | − | 0.504377i | \(-0.831722\pi\) | ||||
−0.863484 | + | 0.504377i | \(0.831722\pi\) | |||||||
\(972\) | 18.8038 | 0.603133 | ||||||||
\(973\) | −32.8444 | −1.05294 | ||||||||
\(974\) | 19.3792 | 0.620950 | ||||||||
\(975\) | 18.2018 | 0.582923 | ||||||||
\(976\) | 12.7177 | 0.407083 | ||||||||
\(977\) | −9.80855 | −0.313803 | −0.156902 | − | 0.987614i | \(-0.550151\pi\) | ||||
−0.156902 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(978\) | 28.0323 | 0.896375 | ||||||||
\(979\) | 7.90316 | 0.252586 | ||||||||
\(980\) | −1.05904 | −0.0338299 | ||||||||
\(981\) | −30.8191 | −0.983978 | ||||||||
\(982\) | 8.63766 | 0.275639 | ||||||||
\(983\) | −54.4333 | −1.73615 | −0.868077 | − | 0.496430i | \(-0.834644\pi\) | ||||
−0.868077 | + | 0.496430i | \(0.834644\pi\) | |||||||
\(984\) | 23.4754 | 0.748370 | ||||||||
\(985\) | −14.3094 | −0.455935 | ||||||||
\(986\) | −0.407473 | −0.0129766 | ||||||||
\(987\) | 48.3113 | 1.53777 | ||||||||
\(988\) | 29.9567 | 0.953049 | ||||||||
\(989\) | 1.32687 | 0.0421921 | ||||||||
\(990\) | 14.4166 | 0.458191 | ||||||||
\(991\) | 37.2744 | 1.18406 | 0.592030 | − | 0.805916i | \(-0.298327\pi\) | ||||
0.592030 | + | 0.805916i | \(0.298327\pi\) | |||||||
\(992\) | 2.69271 | 0.0854936 | ||||||||
\(993\) | −55.1911 | −1.75144 | ||||||||
\(994\) | −19.4470 | −0.616820 | ||||||||
\(995\) | 39.1342 | 1.24064 | ||||||||
\(996\) | −2.52465 | −0.0799967 | ||||||||
\(997\) | −61.2371 | −1.93940 | −0.969700 | − | 0.244300i | \(-0.921442\pi\) | ||||
−0.969700 | + | 0.244300i | \(0.921442\pi\) | |||||||
\(998\) | −12.5381 | −0.396885 | ||||||||
\(999\) | −3.71860 | −0.117651 |
(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 | 6026.2.a.m.1.9 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.m.1.9 | ✓ | 41 | 1.1 | even | 1 | trivial |