Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61803 | −1.85123 | −0.925615 | − | 0.378467i | \(-0.876451\pi\) | ||||
−0.925615 | + | 0.378467i | \(0.876451\pi\) | |||||||
\(3\) | −0.381966 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.236068 | 0.0892253 | 0.0446127 | − | 0.999004i | \(-0.485795\pi\) | ||||
0.0446127 | + | 0.999004i | \(0.485795\pi\) | |||||||
\(8\) | −7.47214 | −2.64180 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 8.47214 | 2.67912 | ||||||||
\(11\) | −1.38197 | −0.416678 | −0.208339 | − | 0.978057i | \(-0.566806\pi\) | ||||
−0.208339 | + | 0.978057i | \(0.566806\pi\) | |||||||
\(12\) | −1.85410 | −0.535233 | ||||||||
\(13\) | 3.61803 | 1.00346 | 0.501731 | − | 0.865024i | \(-0.332697\pi\) | ||||
0.501731 | + | 0.865024i | \(0.332697\pi\) | |||||||
\(14\) | −0.618034 | −0.165177 | ||||||||
\(15\) | 1.23607 | 0.319151 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | −5.09017 | −1.23455 | −0.617274 | − | 0.786748i | \(-0.711763\pi\) | ||||
−0.617274 | + | 0.786748i | \(0.711763\pi\) | |||||||
\(18\) | 7.47214 | 1.76120 | ||||||||
\(19\) | 3.23607 | 0.742405 | 0.371202 | − | 0.928552i | \(-0.378946\pi\) | ||||
0.371202 | + | 0.928552i | \(0.378946\pi\) | |||||||
\(20\) | −15.7082 | −3.51246 | ||||||||
\(21\) | −0.0901699 | −0.0196767 | ||||||||
\(22\) | 3.61803 | 0.771367 | ||||||||
\(23\) | 6.61803 | 1.37996 | 0.689978 | − | 0.723831i | \(-0.257620\pi\) | ||||
0.689978 | + | 0.723831i | \(0.257620\pi\) | |||||||
\(24\) | 2.85410 | 0.582591 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | −9.47214 | −1.85764 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 1.14590 | 0.216554 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −3.23607 | −0.590822 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −10.8541 | −1.91875 | ||||||||
\(33\) | 0.527864 | 0.0918893 | ||||||||
\(34\) | 13.3262 | 2.28543 | ||||||||
\(35\) | −0.763932 | −0.129128 | ||||||||
\(36\) | −13.8541 | −2.30902 | ||||||||
\(37\) | 1.85410 | 0.304812 | 0.152406 | − | 0.988318i | \(-0.451298\pi\) | ||||
0.152406 | + | 0.988318i | \(0.451298\pi\) | |||||||
\(38\) | −8.47214 | −1.37436 | ||||||||
\(39\) | −1.38197 | −0.221292 | ||||||||
\(40\) | 24.1803 | 3.82325 | ||||||||
\(41\) | 0.527864 | 0.0824385 | 0.0412193 | − | 0.999150i | \(-0.486876\pi\) | ||||
0.0412193 | + | 0.999150i | \(0.486876\pi\) | |||||||
\(42\) | 0.236068 | 0.0364261 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −6.70820 | −1.01130 | ||||||||
\(45\) | 9.23607 | 1.37683 | ||||||||
\(46\) | −17.3262 | −2.55461 | ||||||||
\(47\) | 7.85410 | 1.14564 | 0.572819 | − | 0.819682i | \(-0.305850\pi\) | ||||
0.572819 | + | 0.819682i | \(0.305850\pi\) | |||||||
\(48\) | −3.76393 | −0.543277 | ||||||||
\(49\) | −6.94427 | −0.992039 | ||||||||
\(50\) | −14.3262 | −2.02604 | ||||||||
\(51\) | 1.94427 | 0.272253 | ||||||||
\(52\) | 17.5623 | 2.43545 | ||||||||
\(53\) | −3.61803 | −0.496975 | −0.248488 | − | 0.968635i | \(-0.579934\pi\) | ||||
−0.248488 | + | 0.968635i | \(0.579934\pi\) | |||||||
\(54\) | −5.85410 | −0.796642 | ||||||||
\(55\) | 4.47214 | 0.603023 | ||||||||
\(56\) | −1.76393 | −0.235715 | ||||||||
\(57\) | −1.23607 | −0.163721 | ||||||||
\(58\) | −7.85410 | −1.03129 | ||||||||
\(59\) | −6.09017 | −0.792873 | −0.396436 | − | 0.918062i | \(-0.629753\pi\) | ||||
−0.396436 | + | 0.918062i | \(0.629753\pi\) | |||||||
\(60\) | 6.00000 | 0.774597 | ||||||||
\(61\) | −3.85410 | −0.493467 | −0.246734 | − | 0.969083i | \(-0.579357\pi\) | ||||
−0.246734 | + | 0.969083i | \(0.579357\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.673762 | −0.0848860 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | −11.7082 | −1.45222 | ||||||||
\(66\) | −1.38197 | −0.170108 | ||||||||
\(67\) | 2.85410 | 0.348684 | 0.174342 | − | 0.984685i | \(-0.444220\pi\) | ||||
0.174342 | + | 0.984685i | \(0.444220\pi\) | |||||||
\(68\) | −24.7082 | −2.99631 | ||||||||
\(69\) | −2.52786 | −0.304319 | ||||||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | 13.7984 | 1.63757 | 0.818783 | − | 0.574103i | \(-0.194649\pi\) | ||||
0.818783 | + | 0.574103i | \(0.194649\pi\) | |||||||
\(72\) | 21.3262 | 2.51332 | ||||||||
\(73\) | −4.85410 | −0.568130 | −0.284065 | − | 0.958805i | \(-0.591683\pi\) | ||||
−0.284065 | + | 0.958805i | \(0.591683\pi\) | |||||||
\(74\) | −4.85410 | −0.564278 | ||||||||
\(75\) | −2.09017 | −0.241352 | ||||||||
\(76\) | 15.7082 | 1.80185 | ||||||||
\(77\) | −0.326238 | −0.0371783 | ||||||||
\(78\) | 3.61803 | 0.409662 | ||||||||
\(79\) | −3.61803 | −0.407061 | −0.203530 | − | 0.979069i | \(-0.565242\pi\) | ||||
−0.203530 | + | 0.979069i | \(0.565242\pi\) | |||||||
\(80\) | −31.8885 | −3.56525 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | −1.38197 | −0.152613 | ||||||||
\(83\) | −13.0344 | −1.43072 | −0.715358 | − | 0.698758i | \(-0.753736\pi\) | ||||
−0.715358 | + | 0.698758i | \(0.753736\pi\) | |||||||
\(84\) | −0.437694 | −0.0477563 | ||||||||
\(85\) | 16.4721 | 1.78665 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.14590 | −0.122853 | ||||||||
\(88\) | 10.3262 | 1.10078 | ||||||||
\(89\) | 4.85410 | 0.514534 | 0.257267 | − | 0.966340i | \(-0.417178\pi\) | ||||
0.257267 | + | 0.966340i | \(0.417178\pi\) | |||||||
\(90\) | −24.1803 | −2.54883 | ||||||||
\(91\) | 0.854102 | 0.0895342 | ||||||||
\(92\) | 32.1246 | 3.34922 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.5623 | −2.12084 | ||||||||
\(95\) | −10.4721 | −1.07442 | ||||||||
\(96\) | 4.14590 | 0.423139 | ||||||||
\(97\) | −4.76393 | −0.483704 | −0.241852 | − | 0.970313i | \(-0.577755\pi\) | ||||
−0.241852 | + | 0.970313i | \(0.577755\pi\) | |||||||
\(98\) | 18.1803 | 1.83649 | ||||||||
\(99\) | 3.94427 | 0.396414 | ||||||||
\(100\) | 26.5623 | 2.65623 | ||||||||
\(101\) | 8.23607 | 0.819519 | 0.409760 | − | 0.912194i | \(-0.365613\pi\) | ||||
0.409760 | + | 0.912194i | \(0.365613\pi\) | |||||||
\(102\) | −5.09017 | −0.504002 | ||||||||
\(103\) | 10.4164 | 1.02636 | 0.513180 | − | 0.858281i | \(-0.328467\pi\) | ||||
0.513180 | + | 0.858281i | \(0.328467\pi\) | |||||||
\(104\) | −27.0344 | −2.65095 | ||||||||
\(105\) | 0.291796 | 0.0284764 | ||||||||
\(106\) | 9.47214 | 0.920015 | ||||||||
\(107\) | 16.4721 | 1.59242 | 0.796211 | − | 0.605019i | \(-0.206835\pi\) | ||||
0.796211 | + | 0.605019i | \(0.206835\pi\) | |||||||
\(108\) | 10.8541 | 1.04444 | ||||||||
\(109\) | −7.14590 | −0.684453 | −0.342226 | − | 0.939618i | \(-0.611181\pi\) | ||||
−0.342226 | + | 0.939618i | \(0.611181\pi\) | |||||||
\(110\) | −11.7082 | −1.11633 | ||||||||
\(111\) | −0.708204 | −0.0672197 | ||||||||
\(112\) | 2.32624 | 0.219809 | ||||||||
\(113\) | −13.3820 | −1.25887 | −0.629435 | − | 0.777053i | \(-0.716714\pi\) | ||||
−0.629435 | + | 0.777053i | \(0.716714\pi\) | |||||||
\(114\) | 3.23607 | 0.303086 | ||||||||
\(115\) | −21.4164 | −1.99709 | ||||||||
\(116\) | 14.5623 | 1.35208 | ||||||||
\(117\) | −10.3262 | −0.954661 | ||||||||
\(118\) | 15.9443 | 1.46779 | ||||||||
\(119\) | −1.20163 | −0.110153 | ||||||||
\(120\) | −9.23607 | −0.843134 | ||||||||
\(121\) | −9.09017 | −0.826379 | ||||||||
\(122\) | 10.0902 | 0.913521 | ||||||||
\(123\) | −0.201626 | −0.0181800 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 1.76393 | 0.157144 | ||||||||
\(127\) | 16.6525 | 1.47767 | 0.738834 | − | 0.673887i | \(-0.235377\pi\) | ||||
0.738834 | + | 0.673887i | \(0.235377\pi\) | |||||||
\(128\) | −1.09017 | −0.0963583 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 30.6525 | 2.68840 | ||||||||
\(131\) | −7.94427 | −0.694094 | −0.347047 | − | 0.937848i | \(-0.612816\pi\) | ||||
−0.347047 | + | 0.937848i | \(0.612816\pi\) | |||||||
\(132\) | 2.56231 | 0.223020 | ||||||||
\(133\) | 0.763932 | 0.0662413 | ||||||||
\(134\) | −7.47214 | −0.645494 | ||||||||
\(135\) | −7.23607 | −0.622782 | ||||||||
\(136\) | 38.0344 | 3.26143 | ||||||||
\(137\) | −9.70820 | −0.829428 | −0.414714 | − | 0.909952i | \(-0.636118\pi\) | ||||
−0.414714 | + | 0.909952i | \(0.636118\pi\) | |||||||
\(138\) | 6.61803 | 0.563364 | ||||||||
\(139\) | −18.7082 | −1.58681 | −0.793405 | − | 0.608695i | \(-0.791693\pi\) | ||||
−0.793405 | + | 0.608695i | \(0.791693\pi\) | |||||||
\(140\) | −3.70820 | −0.313400 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | −36.1246 | −3.03151 | ||||||||
\(143\) | −5.00000 | −0.418121 | ||||||||
\(144\) | −28.1246 | −2.34372 | ||||||||
\(145\) | −9.70820 | −0.806222 | ||||||||
\(146\) | 12.7082 | 1.05174 | ||||||||
\(147\) | 2.65248 | 0.218773 | ||||||||
\(148\) | 9.00000 | 0.739795 | ||||||||
\(149\) | 9.00000 | 0.737309 | 0.368654 | − | 0.929567i | \(-0.379819\pi\) | ||||
0.368654 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(150\) | 5.47214 | 0.446798 | ||||||||
\(151\) | −2.14590 | −0.174631 | −0.0873154 | − | 0.996181i | \(-0.527829\pi\) | ||||
−0.0873154 | + | 0.996181i | \(0.527829\pi\) | |||||||
\(152\) | −24.1803 | −1.96128 | ||||||||
\(153\) | 14.5279 | 1.17451 | ||||||||
\(154\) | 0.854102 | 0.0688255 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.70820 | −0.537086 | ||||||||
\(157\) | −11.8541 | −0.946060 | −0.473030 | − | 0.881046i | \(-0.656840\pi\) | ||||
−0.473030 | + | 0.881046i | \(0.656840\pi\) | |||||||
\(158\) | 9.47214 | 0.753563 | ||||||||
\(159\) | 1.38197 | 0.109597 | ||||||||
\(160\) | 35.1246 | 2.77684 | ||||||||
\(161\) | 1.56231 | 0.123127 | ||||||||
\(162\) | −20.1803 | −1.58552 | ||||||||
\(163\) | 14.0000 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(164\) | 2.56231 | 0.200082 | ||||||||
\(165\) | −1.70820 | −0.132983 | ||||||||
\(166\) | 34.1246 | 2.64858 | ||||||||
\(167\) | 9.76393 | 0.755556 | 0.377778 | − | 0.925896i | \(-0.376688\pi\) | ||||
0.377778 | + | 0.925896i | \(0.376688\pi\) | |||||||
\(168\) | 0.673762 | 0.0519819 | ||||||||
\(169\) | 0.0901699 | 0.00693615 | ||||||||
\(170\) | −43.1246 | −3.30751 | ||||||||
\(171\) | −9.23607 | −0.706300 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.23607 | −0.626177 | −0.313088 | − | 0.949724i | \(-0.601364\pi\) | ||||
−0.313088 | + | 0.949724i | \(0.601364\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 1.29180 | 0.0976506 | ||||||||
\(176\) | −13.6180 | −1.02650 | ||||||||
\(177\) | 2.32624 | 0.174851 | ||||||||
\(178\) | −12.7082 | −0.952520 | ||||||||
\(179\) | −21.6525 | −1.61838 | −0.809191 | − | 0.587546i | \(-0.800094\pi\) | ||||
−0.809191 | + | 0.587546i | \(0.800094\pi\) | |||||||
\(180\) | 44.8328 | 3.34164 | ||||||||
\(181\) | −21.6180 | −1.60686 | −0.803428 | − | 0.595402i | \(-0.796993\pi\) | ||||
−0.803428 | + | 0.595402i | \(0.796993\pi\) | |||||||
\(182\) | −2.23607 | −0.165748 | ||||||||
\(183\) | 1.47214 | 0.108823 | ||||||||
\(184\) | −49.4508 | −3.64557 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.03444 | 0.514409 | ||||||||
\(188\) | 38.1246 | 2.78052 | ||||||||
\(189\) | 0.527864 | 0.0383965 | ||||||||
\(190\) | 27.4164 | 1.98900 | ||||||||
\(191\) | −23.4721 | −1.69838 | −0.849192 | − | 0.528084i | \(-0.822911\pi\) | ||||
−0.849192 | + | 0.528084i | \(0.822911\pi\) | |||||||
\(192\) | −3.32624 | −0.240051 | ||||||||
\(193\) | −10.7082 | −0.770793 | −0.385397 | − | 0.922751i | \(-0.625935\pi\) | ||||
−0.385397 | + | 0.922751i | \(0.625935\pi\) | |||||||
\(194\) | 12.4721 | 0.895447 | ||||||||
\(195\) | 4.47214 | 0.320256 | ||||||||
\(196\) | −33.7082 | −2.40773 | ||||||||
\(197\) | 14.9443 | 1.06474 | 0.532368 | − | 0.846513i | \(-0.321302\pi\) | ||||
0.532368 | + | 0.846513i | \(0.321302\pi\) | |||||||
\(198\) | −10.3262 | −0.733854 | ||||||||
\(199\) | −15.9443 | −1.13026 | −0.565130 | − | 0.825002i | \(-0.691174\pi\) | ||||
−0.565130 | + | 0.825002i | \(0.691174\pi\) | |||||||
\(200\) | −40.8885 | −2.89126 | ||||||||
\(201\) | −1.09017 | −0.0768947 | ||||||||
\(202\) | −21.5623 | −1.51712 | ||||||||
\(203\) | 0.708204 | 0.0497062 | ||||||||
\(204\) | 9.43769 | 0.660771 | ||||||||
\(205\) | −1.70820 | −0.119306 | ||||||||
\(206\) | −27.2705 | −1.90003 | ||||||||
\(207\) | −18.8885 | −1.31284 | ||||||||
\(208\) | 35.6525 | 2.47205 | ||||||||
\(209\) | −4.47214 | −0.309344 | ||||||||
\(210\) | −0.763932 | −0.0527163 | ||||||||
\(211\) | −4.76393 | −0.327963 | −0.163981 | − | 0.986463i | \(-0.552434\pi\) | ||||
−0.163981 | + | 0.986463i | \(0.552434\pi\) | |||||||
\(212\) | −17.5623 | −1.20618 | ||||||||
\(213\) | −5.27051 | −0.361129 | ||||||||
\(214\) | −43.1246 | −2.94794 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −16.7082 | −1.13685 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.7082 | 1.26708 | ||||||||
\(219\) | 1.85410 | 0.125289 | ||||||||
\(220\) | 21.7082 | 1.46357 | ||||||||
\(221\) | −18.4164 | −1.23882 | ||||||||
\(222\) | 1.85410 | 0.124439 | ||||||||
\(223\) | 7.23607 | 0.484563 | 0.242281 | − | 0.970206i | \(-0.422104\pi\) | ||||
0.242281 | + | 0.970206i | \(0.422104\pi\) | |||||||
\(224\) | −2.56231 | −0.171201 | ||||||||
\(225\) | −15.6180 | −1.04120 | ||||||||
\(226\) | 35.0344 | 2.33046 | ||||||||
\(227\) | 7.47214 | 0.495943 | 0.247972 | − | 0.968767i | \(-0.420236\pi\) | ||||
0.247972 | + | 0.968767i | \(0.420236\pi\) | |||||||
\(228\) | −6.00000 | −0.397360 | ||||||||
\(229\) | −15.7082 | −1.03803 | −0.519014 | − | 0.854766i | \(-0.673701\pi\) | ||||
−0.519014 | + | 0.854766i | \(0.673701\pi\) | |||||||
\(230\) | 56.0689 | 3.69707 | ||||||||
\(231\) | 0.124612 | 0.00819885 | ||||||||
\(232\) | −22.4164 | −1.47171 | ||||||||
\(233\) | −11.0344 | −0.722890 | −0.361445 | − | 0.932393i | \(-0.617717\pi\) | ||||
−0.361445 | + | 0.932393i | \(0.617717\pi\) | |||||||
\(234\) | 27.0344 | 1.76730 | ||||||||
\(235\) | −25.4164 | −1.65798 | ||||||||
\(236\) | −29.5623 | −1.92434 | ||||||||
\(237\) | 1.38197 | 0.0897683 | ||||||||
\(238\) | 3.14590 | 0.203918 | ||||||||
\(239\) | −21.7082 | −1.40419 | −0.702093 | − | 0.712085i | \(-0.747751\pi\) | ||||
−0.702093 | + | 0.712085i | \(0.747751\pi\) | |||||||
\(240\) | 12.1803 | 0.786238 | ||||||||
\(241\) | −29.2705 | −1.88548 | −0.942740 | − | 0.333530i | \(-0.891760\pi\) | ||||
−0.942740 | + | 0.333530i | \(0.891760\pi\) | |||||||
\(242\) | 23.7984 | 1.52982 | ||||||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | −18.7082 | −1.19767 | ||||||||
\(245\) | 22.4721 | 1.43569 | ||||||||
\(246\) | 0.527864 | 0.0336554 | ||||||||
\(247\) | 11.7082 | 0.744975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.97871 | 0.315513 | ||||||||
\(250\) | 4.00000 | 0.252982 | ||||||||
\(251\) | −6.81966 | −0.430453 | −0.215227 | − | 0.976564i | \(-0.569049\pi\) | ||||
−0.215227 | + | 0.976564i | \(0.569049\pi\) | |||||||
\(252\) | −3.27051 | −0.206023 | ||||||||
\(253\) | −9.14590 | −0.574998 | ||||||||
\(254\) | −43.5967 | −2.73550 | ||||||||
\(255\) | −6.29180 | −0.394008 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | 23.5623 | 1.46978 | 0.734888 | − | 0.678188i | \(-0.237235\pi\) | ||||
0.734888 | + | 0.678188i | \(0.237235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.437694 | 0.0271970 | ||||||||
\(260\) | −56.8328 | −3.52462 | ||||||||
\(261\) | −8.56231 | −0.529993 | ||||||||
\(262\) | 20.7984 | 1.28493 | ||||||||
\(263\) | −10.5066 | −0.647863 | −0.323932 | − | 0.946080i | \(-0.605005\pi\) | ||||
−0.323932 | + | 0.946080i | \(0.605005\pi\) | |||||||
\(264\) | −3.94427 | −0.242753 | ||||||||
\(265\) | 11.7082 | 0.719229 | ||||||||
\(266\) | −2.00000 | −0.122628 | ||||||||
\(267\) | −1.85410 | −0.113469 | ||||||||
\(268\) | 13.8541 | 0.846274 | ||||||||
\(269\) | −8.56231 | −0.522053 | −0.261027 | − | 0.965332i | \(-0.584061\pi\) | ||||
−0.261027 | + | 0.965332i | \(0.584061\pi\) | |||||||
\(270\) | 18.9443 | 1.15291 | ||||||||
\(271\) | 7.14590 | 0.434082 | 0.217041 | − | 0.976162i | \(-0.430359\pi\) | ||||
0.217041 | + | 0.976162i | \(0.430359\pi\) | |||||||
\(272\) | −50.1591 | −3.04134 | ||||||||
\(273\) | −0.326238 | −0.0197448 | ||||||||
\(274\) | 25.4164 | 1.53546 | ||||||||
\(275\) | −7.56231 | −0.456024 | ||||||||
\(276\) | −12.2705 | −0.738598 | ||||||||
\(277\) | −3.52786 | −0.211969 | −0.105984 | − | 0.994368i | \(-0.533799\pi\) | ||||
−0.105984 | + | 0.994368i | \(0.533799\pi\) | |||||||
\(278\) | 48.9787 | 2.93755 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.70820 | 0.341130 | ||||||||
\(281\) | −1.47214 | −0.0878203 | −0.0439101 | − | 0.999035i | \(-0.513982\pi\) | ||||
−0.0439101 | + | 0.999035i | \(0.513982\pi\) | |||||||
\(282\) | 7.85410 | 0.467705 | ||||||||
\(283\) | 15.2361 | 0.905690 | 0.452845 | − | 0.891589i | \(-0.350409\pi\) | ||||
0.452845 | + | 0.891589i | \(0.350409\pi\) | |||||||
\(284\) | 66.9787 | 3.97446 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 13.0902 | 0.774038 | ||||||||
\(287\) | 0.124612 | 0.00735560 | ||||||||
\(288\) | 30.9787 | 1.82544 | ||||||||
\(289\) | 8.90983 | 0.524108 | ||||||||
\(290\) | 25.4164 | 1.49250 | ||||||||
\(291\) | 1.81966 | 0.106670 | ||||||||
\(292\) | −23.5623 | −1.37888 | ||||||||
\(293\) | −0.909830 | −0.0531528 | −0.0265764 | − | 0.999647i | \(-0.508461\pi\) | ||||
−0.0265764 | + | 0.999647i | \(0.508461\pi\) | |||||||
\(294\) | −6.94427 | −0.404998 | ||||||||
\(295\) | 19.7082 | 1.14746 | ||||||||
\(296\) | −13.8541 | −0.805253 | ||||||||
\(297\) | −3.09017 | −0.179310 | ||||||||
\(298\) | −23.5623 | −1.36493 | ||||||||
\(299\) | 23.9443 | 1.38473 | ||||||||
\(300\) | −10.1459 | −0.585774 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.61803 | 0.323282 | ||||||||
\(303\) | −3.14590 | −0.180727 | ||||||||
\(304\) | 31.8885 | 1.82893 | ||||||||
\(305\) | 12.4721 | 0.714152 | ||||||||
\(306\) | −38.0344 | −2.17428 | ||||||||
\(307\) | 28.2148 | 1.61030 | 0.805151 | − | 0.593069i | \(-0.202084\pi\) | ||||
0.805151 | + | 0.593069i | \(0.202084\pi\) | |||||||
\(308\) | −1.58359 | −0.0902335 | ||||||||
\(309\) | −3.97871 | −0.226341 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8328 | 1.35143 | 0.675717 | − | 0.737161i | \(-0.263834\pi\) | ||||
0.675717 | + | 0.737161i | \(0.263834\pi\) | |||||||
\(312\) | 10.3262 | 0.584608 | ||||||||
\(313\) | −27.1246 | −1.53317 | −0.766587 | − | 0.642141i | \(-0.778047\pi\) | ||||
−0.766587 | + | 0.642141i | \(0.778047\pi\) | |||||||
\(314\) | 31.0344 | 1.75137 | ||||||||
\(315\) | 2.18034 | 0.122848 | ||||||||
\(316\) | −17.5623 | −0.987957 | ||||||||
\(317\) | −29.3050 | −1.64593 | −0.822965 | − | 0.568092i | \(-0.807682\pi\) | ||||
−0.822965 | + | 0.568092i | \(0.807682\pi\) | |||||||
\(318\) | −3.61803 | −0.202889 | ||||||||
\(319\) | −4.14590 | −0.232126 | ||||||||
\(320\) | −28.1803 | −1.57533 | ||||||||
\(321\) | −6.29180 | −0.351174 | ||||||||
\(322\) | −4.09017 | −0.227936 | ||||||||
\(323\) | −16.4721 | −0.916534 | ||||||||
\(324\) | 37.4164 | 2.07869 | ||||||||
\(325\) | 19.7984 | 1.09822 | ||||||||
\(326\) | −36.6525 | −2.02999 | ||||||||
\(327\) | 2.72949 | 0.150941 | ||||||||
\(328\) | −3.94427 | −0.217786 | ||||||||
\(329\) | 1.85410 | 0.102220 | ||||||||
\(330\) | 4.47214 | 0.246183 | ||||||||
\(331\) | 3.47214 | 0.190846 | 0.0954229 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954229 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(332\) | −63.2705 | −3.47242 | ||||||||
\(333\) | −5.29180 | −0.289989 | ||||||||
\(334\) | −25.5623 | −1.39871 | ||||||||
\(335\) | −9.23607 | −0.504620 | ||||||||
\(336\) | −0.888544 | −0.0484740 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | −0.236068 | −0.0128404 | ||||||||
\(339\) | 5.11146 | 0.277616 | ||||||||
\(340\) | 79.9574 | 4.33630 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 24.1803 | 1.30752 | ||||||||
\(343\) | −3.29180 | −0.177740 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.18034 | 0.440415 | ||||||||
\(346\) | 21.5623 | 1.15920 | ||||||||
\(347\) | −1.09017 | −0.0585234 | −0.0292617 | − | 0.999572i | \(-0.509316\pi\) | ||||
−0.0292617 | + | 0.999572i | \(0.509316\pi\) | |||||||
\(348\) | −5.56231 | −0.298171 | ||||||||
\(349\) | 7.29180 | 0.390321 | 0.195160 | − | 0.980771i | \(-0.437477\pi\) | ||||
0.195160 | + | 0.980771i | \(0.437477\pi\) | |||||||
\(350\) | −3.38197 | −0.180774 | ||||||||
\(351\) | 8.09017 | 0.431821 | ||||||||
\(352\) | 15.0000 | 0.799503 | ||||||||
\(353\) | −12.7639 | −0.679356 | −0.339678 | − | 0.940542i | \(-0.610318\pi\) | ||||
−0.339678 | + | 0.940542i | \(0.610318\pi\) | |||||||
\(354\) | −6.09017 | −0.323689 | ||||||||
\(355\) | −44.6525 | −2.36991 | ||||||||
\(356\) | 23.5623 | 1.24880 | ||||||||
\(357\) | 0.458980 | 0.0242918 | ||||||||
\(358\) | 56.6869 | 2.99600 | ||||||||
\(359\) | −36.6525 | −1.93444 | −0.967222 | − | 0.253933i | \(-0.918276\pi\) | ||||
−0.967222 | + | 0.253933i | \(0.918276\pi\) | |||||||
\(360\) | −69.0132 | −3.63731 | ||||||||
\(361\) | −8.52786 | −0.448835 | ||||||||
\(362\) | 56.5967 | 2.97466 | ||||||||
\(363\) | 3.47214 | 0.182240 | ||||||||
\(364\) | 4.14590 | 0.217304 | ||||||||
\(365\) | 15.7082 | 0.822205 | ||||||||
\(366\) | −3.85410 | −0.201457 | ||||||||
\(367\) | −3.18034 | −0.166012 | −0.0830062 | − | 0.996549i | \(-0.526452\pi\) | ||||
−0.0830062 | + | 0.996549i | \(0.526452\pi\) | |||||||
\(368\) | 65.2148 | 3.39956 | ||||||||
\(369\) | −1.50658 | −0.0784293 | ||||||||
\(370\) | 15.7082 | 0.816631 | ||||||||
\(371\) | −0.854102 | −0.0443428 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | −18.4164 | −0.952290 | ||||||||
\(375\) | 0.583592 | 0.0301366 | ||||||||
\(376\) | −58.6869 | −3.02655 | ||||||||
\(377\) | 10.8541 | 0.559015 | ||||||||
\(378\) | −1.38197 | −0.0710807 | ||||||||
\(379\) | 17.3607 | 0.891758 | 0.445879 | − | 0.895093i | \(-0.352891\pi\) | ||||
0.445879 | + | 0.895093i | \(0.352891\pi\) | |||||||
\(380\) | −50.8328 | −2.60767 | ||||||||
\(381\) | −6.36068 | −0.325867 | ||||||||
\(382\) | 61.4508 | 3.14410 | ||||||||
\(383\) | −2.12461 | −0.108563 | −0.0542813 | − | 0.998526i | \(-0.517287\pi\) | ||||
−0.0542813 | + | 0.998526i | \(0.517287\pi\) | |||||||
\(384\) | 0.416408 | 0.0212497 | ||||||||
\(385\) | 1.05573 | 0.0538049 | ||||||||
\(386\) | 28.0344 | 1.42692 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23.1246 | −1.17397 | ||||||||
\(389\) | 23.0689 | 1.16964 | 0.584819 | − | 0.811164i | \(-0.301165\pi\) | ||||
0.584819 | + | 0.811164i | \(0.301165\pi\) | |||||||
\(390\) | −11.7082 | −0.592868 | ||||||||
\(391\) | −33.6869 | −1.70362 | ||||||||
\(392\) | 51.8885 | 2.62077 | ||||||||
\(393\) | 3.03444 | 0.153067 | ||||||||
\(394\) | −39.1246 | −1.97107 | ||||||||
\(395\) | 11.7082 | 0.589104 | ||||||||
\(396\) | 19.1459 | 0.962118 | ||||||||
\(397\) | 5.58359 | 0.280232 | 0.140116 | − | 0.990135i | \(-0.455252\pi\) | ||||
0.140116 | + | 0.990135i | \(0.455252\pi\) | |||||||
\(398\) | 41.7426 | 2.09237 | ||||||||
\(399\) | −0.291796 | −0.0146081 | ||||||||
\(400\) | 53.9230 | 2.69615 | ||||||||
\(401\) | 1.41641 | 0.0707320 | 0.0353660 | − | 0.999374i | \(-0.488740\pi\) | ||||
0.0353660 | + | 0.999374i | \(0.488740\pi\) | |||||||
\(402\) | 2.85410 | 0.142350 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 39.9787 | 1.98902 | ||||||||
\(405\) | −24.9443 | −1.23949 | ||||||||
\(406\) | −1.85410 | −0.0920175 | ||||||||
\(407\) | −2.56231 | −0.127009 | ||||||||
\(408\) | −14.5279 | −0.719236 | ||||||||
\(409\) | 20.0902 | 0.993395 | 0.496697 | − | 0.867924i | \(-0.334546\pi\) | ||||
0.496697 | + | 0.867924i | \(0.334546\pi\) | |||||||
\(410\) | 4.47214 | 0.220863 | ||||||||
\(411\) | 3.70820 | 0.182912 | ||||||||
\(412\) | 50.5623 | 2.49103 | ||||||||
\(413\) | −1.43769 | −0.0707443 | ||||||||
\(414\) | 49.4508 | 2.43038 | ||||||||
\(415\) | 42.1803 | 2.07055 | ||||||||
\(416\) | −39.2705 | −1.92540 | ||||||||
\(417\) | 7.14590 | 0.349936 | ||||||||
\(418\) | 11.7082 | 0.572667 | ||||||||
\(419\) | −5.76393 | −0.281587 | −0.140793 | − | 0.990039i | \(-0.544965\pi\) | ||||
−0.140793 | + | 0.990039i | \(0.544965\pi\) | |||||||
\(420\) | 1.41641 | 0.0691136 | ||||||||
\(421\) | 23.6525 | 1.15275 | 0.576376 | − | 0.817185i | \(-0.304467\pi\) | ||||
0.576376 | + | 0.817185i | \(0.304467\pi\) | |||||||
\(422\) | 12.4721 | 0.607134 | ||||||||
\(423\) | −22.4164 | −1.08992 | ||||||||
\(424\) | 27.0344 | 1.31291 | ||||||||
\(425\) | −27.8541 | −1.35112 | ||||||||
\(426\) | 13.7984 | 0.668533 | ||||||||
\(427\) | −0.909830 | −0.0440298 | ||||||||
\(428\) | 79.9574 | 3.86489 | ||||||||
\(429\) | 1.90983 | 0.0922075 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.201626 | −0.00971199 | −0.00485599 | − | 0.999988i | \(-0.501546\pi\) | ||||
−0.00485599 | + | 0.999988i | \(0.501546\pi\) | |||||||
\(432\) | 22.0344 | 1.06013 | ||||||||
\(433\) | −21.2918 | −1.02322 | −0.511609 | − | 0.859218i | \(-0.670950\pi\) | ||||
−0.511609 | + | 0.859218i | \(0.670950\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.70820 | 0.177795 | ||||||||
\(436\) | −34.6869 | −1.66120 | ||||||||
\(437\) | 21.4164 | 1.02449 | ||||||||
\(438\) | −4.85410 | −0.231938 | ||||||||
\(439\) | 7.85410 | 0.374856 | 0.187428 | − | 0.982278i | \(-0.439985\pi\) | ||||
0.187428 | + | 0.982278i | \(0.439985\pi\) | |||||||
\(440\) | −33.4164 | −1.59306 | ||||||||
\(441\) | 19.8197 | 0.943793 | ||||||||
\(442\) | 48.2148 | 2.29334 | ||||||||
\(443\) | −6.47214 | −0.307500 | −0.153750 | − | 0.988110i | \(-0.549135\pi\) | ||||
−0.153750 | + | 0.988110i | \(0.549135\pi\) | |||||||
\(444\) | −3.43769 | −0.163146 | ||||||||
\(445\) | −15.7082 | −0.744640 | ||||||||
\(446\) | −18.9443 | −0.897037 | ||||||||
\(447\) | −3.43769 | −0.162597 | ||||||||
\(448\) | 2.05573 | 0.0971240 | ||||||||
\(449\) | 20.8328 | 0.983161 | 0.491581 | − | 0.870832i | \(-0.336419\pi\) | ||||
0.491581 | + | 0.870832i | \(0.336419\pi\) | |||||||
\(450\) | 40.8885 | 1.92750 | ||||||||
\(451\) | −0.729490 | −0.0343504 | ||||||||
\(452\) | −64.9574 | −3.05534 | ||||||||
\(453\) | 0.819660 | 0.0385110 | ||||||||
\(454\) | −19.5623 | −0.918105 | ||||||||
\(455\) | −2.76393 | −0.129575 | ||||||||
\(456\) | 9.23607 | 0.432519 | ||||||||
\(457\) | −2.29180 | −0.107206 | −0.0536028 | − | 0.998562i | \(-0.517070\pi\) | ||||
−0.0536028 | + | 0.998562i | \(0.517070\pi\) | |||||||
\(458\) | 41.1246 | 1.92163 | ||||||||
\(459\) | −11.3820 | −0.531265 | ||||||||
\(460\) | −103.957 | −4.84704 | ||||||||
\(461\) | 17.5967 | 0.819562 | 0.409781 | − | 0.912184i | \(-0.365605\pi\) | ||||
0.409781 | + | 0.912184i | \(0.365605\pi\) | |||||||
\(462\) | −0.326238 | −0.0151780 | ||||||||
\(463\) | 23.8328 | 1.10760 | 0.553802 | − | 0.832648i | \(-0.313176\pi\) | ||||
0.553802 | + | 0.832648i | \(0.313176\pi\) | |||||||
\(464\) | 29.5623 | 1.37240 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.8885 | 1.33824 | ||||||||
\(467\) | −32.9443 | −1.52448 | −0.762240 | − | 0.647295i | \(-0.775900\pi\) | ||||
−0.762240 | + | 0.647295i | \(0.775900\pi\) | |||||||
\(468\) | −50.1246 | −2.31701 | ||||||||
\(469\) | 0.673762 | 0.0311114 | ||||||||
\(470\) | 66.5410 | 3.06931 | ||||||||
\(471\) | 4.52786 | 0.208633 | ||||||||
\(472\) | 45.5066 | 2.09461 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3.61803 | −0.166182 | ||||||||
\(475\) | 17.7082 | 0.812508 | ||||||||
\(476\) | −5.83282 | −0.267347 | ||||||||
\(477\) | 10.3262 | 0.472806 | ||||||||
\(478\) | 56.8328 | 2.59947 | ||||||||
\(479\) | −36.1803 | −1.65312 | −0.826561 | − | 0.562847i | \(-0.809706\pi\) | ||||
−0.826561 | + | 0.562847i | \(0.809706\pi\) | |||||||
\(480\) | −13.4164 | −0.612372 | ||||||||
\(481\) | 6.70820 | 0.305868 | ||||||||
\(482\) | 76.6312 | 3.49046 | ||||||||
\(483\) | −0.596748 | −0.0271530 | ||||||||
\(484\) | −44.1246 | −2.00566 | ||||||||
\(485\) | 15.4164 | 0.700023 | ||||||||
\(486\) | 25.2705 | 1.14629 | ||||||||
\(487\) | −14.3262 | −0.649184 | −0.324592 | − | 0.945854i | \(-0.605227\pi\) | ||||
−0.324592 | + | 0.945854i | \(0.605227\pi\) | |||||||
\(488\) | 28.7984 | 1.30364 | ||||||||
\(489\) | −5.34752 | −0.241823 | ||||||||
\(490\) | −58.8328 | −2.65780 | ||||||||
\(491\) | −9.65248 | −0.435610 | −0.217805 | − | 0.975992i | \(-0.569890\pi\) | ||||
−0.217805 | + | 0.975992i | \(0.569890\pi\) | |||||||
\(492\) | −0.978714 | −0.0441238 | ||||||||
\(493\) | −15.2705 | −0.687749 | ||||||||
\(494\) | −30.6525 | −1.37912 | ||||||||
\(495\) | −12.7639 | −0.573696 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.25735 | 0.146112 | ||||||||
\(498\) | −13.0344 | −0.584087 | ||||||||
\(499\) | 7.14590 | 0.319894 | 0.159947 | − | 0.987126i | \(-0.448868\pi\) | ||||
0.159947 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(500\) | −7.41641 | −0.331672 | ||||||||
\(501\) | −3.72949 | −0.166621 | ||||||||
\(502\) | 17.8541 | 0.796868 | ||||||||
\(503\) | −4.52786 | −0.201887 | −0.100944 | − | 0.994892i | \(-0.532186\pi\) | ||||
−0.100944 | + | 0.994892i | \(0.532186\pi\) | |||||||
\(504\) | 5.03444 | 0.224252 | ||||||||
\(505\) | −26.6525 | −1.18602 | ||||||||
\(506\) | 23.9443 | 1.06445 | ||||||||
\(507\) | −0.0344419 | −0.00152962 | ||||||||
\(508\) | 80.8328 | 3.58638 | ||||||||
\(509\) | 5.29180 | 0.234555 | 0.117277 | − | 0.993099i | \(-0.462583\pi\) | ||||
0.117277 | + | 0.993099i | \(0.462583\pi\) | |||||||
\(510\) | 16.4721 | 0.729398 | ||||||||
\(511\) | −1.14590 | −0.0506915 | ||||||||
\(512\) | 40.3050 | 1.78124 | ||||||||
\(513\) | 7.23607 | 0.319480 | ||||||||
\(514\) | −61.6869 | −2.72089 | ||||||||
\(515\) | −33.7082 | −1.48536 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.8541 | −0.477363 | ||||||||
\(518\) | −1.14590 | −0.0503479 | ||||||||
\(519\) | 3.14590 | 0.138090 | ||||||||
\(520\) | 87.4853 | 3.83648 | ||||||||
\(521\) | 7.03444 | 0.308184 | 0.154092 | − | 0.988056i | \(-0.450755\pi\) | ||||
0.154092 | + | 0.988056i | \(0.450755\pi\) | |||||||
\(522\) | 22.4164 | 0.981140 | ||||||||
\(523\) | −17.8328 | −0.779775 | −0.389887 | − | 0.920863i | \(-0.627486\pi\) | ||||
−0.389887 | + | 0.920863i | \(0.627486\pi\) | |||||||
\(524\) | −38.5623 | −1.68460 | ||||||||
\(525\) | −0.493422 | −0.0215347 | ||||||||
\(526\) | 27.5066 | 1.19934 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 5.20163 | 0.226372 | ||||||||
\(529\) | 20.7984 | 0.904277 | ||||||||
\(530\) | −30.6525 | −1.33146 | ||||||||
\(531\) | 17.3820 | 0.754313 | ||||||||
\(532\) | 3.70820 | 0.160771 | ||||||||
\(533\) | 1.90983 | 0.0827239 | ||||||||
\(534\) | 4.85410 | 0.210058 | ||||||||
\(535\) | −53.3050 | −2.30457 | ||||||||
\(536\) | −21.3262 | −0.921153 | ||||||||
\(537\) | 8.27051 | 0.356899 | ||||||||
\(538\) | 22.4164 | 0.966440 | ||||||||
\(539\) | 9.59675 | 0.413361 | ||||||||
\(540\) | −35.1246 | −1.51152 | ||||||||
\(541\) | −20.0557 | −0.862263 | −0.431132 | − | 0.902289i | \(-0.641886\pi\) | ||||
−0.431132 | + | 0.902289i | \(0.641886\pi\) | |||||||
\(542\) | −18.7082 | −0.803586 | ||||||||
\(543\) | 8.25735 | 0.354357 | ||||||||
\(544\) | 55.2492 | 2.36879 | ||||||||
\(545\) | 23.1246 | 0.990550 | ||||||||
\(546\) | 0.854102 | 0.0365522 | ||||||||
\(547\) | 21.0000 | 0.897895 | 0.448948 | − | 0.893558i | \(-0.351799\pi\) | ||||
0.448948 | + | 0.893558i | \(0.351799\pi\) | |||||||
\(548\) | −47.1246 | −2.01306 | ||||||||
\(549\) | 11.0000 | 0.469469 | ||||||||
\(550\) | 19.7984 | 0.844205 | ||||||||
\(551\) | 9.70820 | 0.413583 | ||||||||
\(552\) | 18.8885 | 0.803950 | ||||||||
\(553\) | −0.854102 | −0.0363201 | ||||||||
\(554\) | 9.23607 | 0.392403 | ||||||||
\(555\) | 2.29180 | 0.0972813 | ||||||||
\(556\) | −90.8115 | −3.85127 | ||||||||
\(557\) | −18.4377 | −0.781230 | −0.390615 | − | 0.920554i | \(-0.627738\pi\) | ||||
−0.390615 | + | 0.920554i | \(0.627738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.52786 | −0.318110 | ||||||||
\(561\) | −2.68692 | −0.113442 | ||||||||
\(562\) | 3.85410 | 0.162575 | ||||||||
\(563\) | 14.3262 | 0.603779 | 0.301889 | − | 0.953343i | \(-0.402383\pi\) | ||||
0.301889 | + | 0.953343i | \(0.402383\pi\) | |||||||
\(564\) | −14.5623 | −0.613184 | ||||||||
\(565\) | 43.3050 | 1.82185 | ||||||||
\(566\) | −39.8885 | −1.67664 | ||||||||
\(567\) | 1.81966 | 0.0764185 | ||||||||
\(568\) | −103.103 | −4.32612 | ||||||||
\(569\) | −8.05573 | −0.337714 | −0.168857 | − | 0.985641i | \(-0.554008\pi\) | ||||
−0.168857 | + | 0.985641i | \(0.554008\pi\) | |||||||
\(570\) | −10.4721 | −0.438630 | ||||||||
\(571\) | −20.8197 | −0.871276 | −0.435638 | − | 0.900122i | \(-0.643477\pi\) | ||||
−0.435638 | + | 0.900122i | \(0.643477\pi\) | |||||||
\(572\) | −24.2705 | −1.01480 | ||||||||
\(573\) | 8.96556 | 0.374542 | ||||||||
\(574\) | −0.326238 | −0.0136169 | ||||||||
\(575\) | 36.2148 | 1.51026 | ||||||||
\(576\) | −24.8541 | −1.03559 | ||||||||
\(577\) | 23.2148 | 0.966444 | 0.483222 | − | 0.875498i | \(-0.339466\pi\) | ||||
0.483222 | + | 0.875498i | \(0.339466\pi\) | |||||||
\(578\) | −23.3262 | −0.970244 | ||||||||
\(579\) | 4.09017 | 0.169982 | ||||||||
\(580\) | −47.1246 | −1.95674 | ||||||||
\(581\) | −3.07701 | −0.127656 | ||||||||
\(582\) | −4.76393 | −0.197471 | ||||||||
\(583\) | 5.00000 | 0.207079 | ||||||||
\(584\) | 36.2705 | 1.50088 | ||||||||
\(585\) | 33.4164 | 1.38160 | ||||||||
\(586\) | 2.38197 | 0.0983981 | ||||||||
\(587\) | −26.7426 | −1.10379 | −0.551894 | − | 0.833915i | \(-0.686095\pi\) | ||||
−0.551894 | + | 0.833915i | \(0.686095\pi\) | |||||||
\(588\) | 12.8754 | 0.530972 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −51.5967 | −2.12420 | ||||||||
\(591\) | −5.70820 | −0.234804 | ||||||||
\(592\) | 18.2705 | 0.750913 | ||||||||
\(593\) | −21.5279 | −0.884043 | −0.442022 | − | 0.897004i | \(-0.645739\pi\) | ||||
−0.442022 | + | 0.897004i | \(0.645739\pi\) | |||||||
\(594\) | 8.09017 | 0.331944 | ||||||||
\(595\) | 3.88854 | 0.159415 | ||||||||
\(596\) | 43.6869 | 1.78949 | ||||||||
\(597\) | 6.09017 | 0.249254 | ||||||||
\(598\) | −62.6869 | −2.56346 | ||||||||
\(599\) | 31.7639 | 1.29784 | 0.648920 | − | 0.760857i | \(-0.275221\pi\) | ||||
0.648920 | + | 0.760857i | \(0.275221\pi\) | |||||||
\(600\) | 15.6180 | 0.637604 | ||||||||
\(601\) | 2.58359 | 0.105387 | 0.0526935 | − | 0.998611i | \(-0.483219\pi\) | ||||
0.0526935 | + | 0.998611i | \(0.483219\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.14590 | −0.331727 | ||||||||
\(604\) | −10.4164 | −0.423838 | ||||||||
\(605\) | 29.4164 | 1.19595 | ||||||||
\(606\) | 8.23607 | 0.334567 | ||||||||
\(607\) | −17.1459 | −0.695931 | −0.347965 | − | 0.937507i | \(-0.613127\pi\) | ||||
−0.347965 | + | 0.937507i | \(0.613127\pi\) | |||||||
\(608\) | −35.1246 | −1.42449 | ||||||||
\(609\) | −0.270510 | −0.0109616 | ||||||||
\(610\) | −32.6525 | −1.32206 | ||||||||
\(611\) | 28.4164 | 1.14960 | ||||||||
\(612\) | 70.5197 | 2.85059 | ||||||||
\(613\) | 29.7984 | 1.20354 | 0.601772 | − | 0.798668i | \(-0.294461\pi\) | ||||
0.601772 | + | 0.798668i | \(0.294461\pi\) | |||||||
\(614\) | −73.8673 | −2.98104 | ||||||||
\(615\) | 0.652476 | 0.0263104 | ||||||||
\(616\) | 2.43769 | 0.0982175 | ||||||||
\(617\) | −3.70820 | −0.149287 | −0.0746433 | − | 0.997210i | \(-0.523782\pi\) | ||||
−0.0746433 | + | 0.997210i | \(0.523782\pi\) | |||||||
\(618\) | 10.4164 | 0.419009 | ||||||||
\(619\) | 3.27051 | 0.131453 | 0.0657264 | − | 0.997838i | \(-0.479064\pi\) | ||||
0.0657264 | + | 0.997838i | \(0.479064\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.7984 | 0.593838 | ||||||||
\(622\) | −62.3951 | −2.50182 | ||||||||
\(623\) | 1.14590 | 0.0459094 | ||||||||
\(624\) | −13.6180 | −0.545158 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 71.0132 | 2.83826 | ||||||||
\(627\) | 1.70820 | 0.0682191 | ||||||||
\(628\) | −57.5410 | −2.29614 | ||||||||
\(629\) | −9.43769 | −0.376306 | ||||||||
\(630\) | −5.70820 | −0.227420 | ||||||||
\(631\) | −15.9098 | −0.633360 | −0.316680 | − | 0.948532i | \(-0.602568\pi\) | ||||
−0.316680 | + | 0.948532i | \(0.602568\pi\) | |||||||
\(632\) | 27.0344 | 1.07537 | ||||||||
\(633\) | 1.81966 | 0.0723250 | ||||||||
\(634\) | 76.7214 | 3.04699 | ||||||||
\(635\) | −53.8885 | −2.13850 | ||||||||
\(636\) | 6.70820 | 0.265998 | ||||||||
\(637\) | −25.1246 | −0.995473 | ||||||||
\(638\) | 10.8541 | 0.429718 | ||||||||
\(639\) | −39.3820 | −1.55793 | ||||||||
\(640\) | 3.52786 | 0.139451 | ||||||||
\(641\) | 33.1803 | 1.31054 | 0.655272 | − | 0.755393i | \(-0.272554\pi\) | ||||
0.655272 | + | 0.755393i | \(0.272554\pi\) | |||||||
\(642\) | 16.4721 | 0.650103 | ||||||||
\(643\) | 29.5623 | 1.16582 | 0.582912 | − | 0.812535i | \(-0.301913\pi\) | ||||
0.582912 | + | 0.812535i | \(0.301913\pi\) | |||||||
\(644\) | 7.58359 | 0.298835 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 43.1246 | 1.69672 | ||||||||
\(647\) | −37.3262 | −1.46745 | −0.733723 | − | 0.679449i | \(-0.762219\pi\) | ||||
−0.733723 | + | 0.679449i | \(0.762219\pi\) | |||||||
\(648\) | −57.5967 | −2.26261 | ||||||||
\(649\) | 8.41641 | 0.330373 | ||||||||
\(650\) | −51.8328 | −2.03305 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 67.9574 | 2.66142 | ||||||||
\(653\) | 2.88854 | 0.113037 | 0.0565187 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565187 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(654\) | −7.14590 | −0.279427 | ||||||||
\(655\) | 25.7082 | 1.00450 | ||||||||
\(656\) | 5.20163 | 0.203089 | ||||||||
\(657\) | 13.8541 | 0.540500 | ||||||||
\(658\) | −4.85410 | −0.189233 | ||||||||
\(659\) | 15.3607 | 0.598367 | 0.299184 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299184 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(660\) | −8.29180 | −0.322758 | ||||||||
\(661\) | 30.3951 | 1.18223 | 0.591117 | − | 0.806586i | \(-0.298687\pi\) | ||||
0.591117 | + | 0.806586i | \(0.298687\pi\) | |||||||
\(662\) | −9.09017 | −0.353299 | ||||||||
\(663\) | 7.03444 | 0.273195 | ||||||||
\(664\) | 97.3951 | 3.77966 | ||||||||
\(665\) | −2.47214 | −0.0958653 | ||||||||
\(666\) | 13.8541 | 0.536836 | ||||||||
\(667\) | 19.8541 | 0.768754 | ||||||||
\(668\) | 47.3951 | 1.83377 | ||||||||
\(669\) | −2.76393 | −0.106860 | ||||||||
\(670\) | 24.1803 | 0.934168 | ||||||||
\(671\) | 5.32624 | 0.205617 | ||||||||
\(672\) | 0.978714 | 0.0377547 | ||||||||
\(673\) | −39.8328 | −1.53544 | −0.767721 | − | 0.640784i | \(-0.778609\pi\) | ||||
−0.767721 | + | 0.640784i | \(0.778609\pi\) | |||||||
\(674\) | −73.3050 | −2.82360 | ||||||||
\(675\) | 12.2361 | 0.470966 | ||||||||
\(676\) | 0.437694 | 0.0168344 | ||||||||
\(677\) | −36.2361 | −1.39267 | −0.696333 | − | 0.717719i | \(-0.745186\pi\) | ||||
−0.696333 | + | 0.717719i | \(0.745186\pi\) | |||||||
\(678\) | −13.3820 | −0.513931 | ||||||||
\(679\) | −1.12461 | −0.0431586 | ||||||||
\(680\) | −123.082 | −4.71998 | ||||||||
\(681\) | −2.85410 | −0.109369 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.1246 | 1.11442 | 0.557211 | − | 0.830371i | \(-0.311871\pi\) | ||||
0.557211 | + | 0.830371i | \(0.311871\pi\) | |||||||
\(684\) | −44.8328 | −1.71423 | ||||||||
\(685\) | 31.4164 | 1.20036 | ||||||||
\(686\) | 8.61803 | 0.329038 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.0902 | −0.498696 | ||||||||
\(690\) | −21.4164 | −0.815309 | ||||||||
\(691\) | 49.2705 | 1.87434 | 0.937169 | − | 0.348875i | \(-0.113436\pi\) | ||||
0.937169 | + | 0.348875i | \(0.113436\pi\) | |||||||
\(692\) | −39.9787 | −1.51976 | ||||||||
\(693\) | 0.931116 | 0.0353702 | ||||||||
\(694\) | 2.85410 | 0.108340 | ||||||||
\(695\) | 60.5410 | 2.29645 | ||||||||
\(696\) | 8.56231 | 0.324553 | ||||||||
\(697\) | −2.68692 | −0.101774 | ||||||||
\(698\) | −19.0902 | −0.722574 | ||||||||
\(699\) | 4.21478 | 0.159418 | ||||||||
\(700\) | 6.27051 | 0.237003 | ||||||||
\(701\) | 23.5066 | 0.887831 | 0.443916 | − | 0.896069i | \(-0.353589\pi\) | ||||
0.443916 | + | 0.896069i | \(0.353589\pi\) | |||||||
\(702\) | −21.1803 | −0.799400 | ||||||||
\(703\) | 6.00000 | 0.226294 | ||||||||
\(704\) | −12.0344 | −0.453565 | ||||||||
\(705\) | 9.70820 | 0.365632 | ||||||||
\(706\) | 33.4164 | 1.25764 | ||||||||
\(707\) | 1.94427 | 0.0731219 | ||||||||
\(708\) | 11.2918 | 0.424372 | ||||||||
\(709\) | −6.88854 | −0.258705 | −0.129352 | − | 0.991599i | \(-0.541290\pi\) | ||||
−0.129352 | + | 0.991599i | \(0.541290\pi\) | |||||||
\(710\) | 116.902 | 4.38724 | ||||||||
\(711\) | 10.3262 | 0.387264 | ||||||||
\(712\) | −36.2705 | −1.35929 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −1.20163 | −0.0449697 | ||||||||
\(715\) | 16.1803 | 0.605110 | ||||||||
\(716\) | −105.103 | −3.92790 | ||||||||
\(717\) | 8.29180 | 0.309663 | ||||||||
\(718\) | 95.9574 | 3.58110 | ||||||||
\(719\) | 13.7984 | 0.514593 | 0.257296 | − | 0.966333i | \(-0.417168\pi\) | ||||
0.257296 | + | 0.966333i | \(0.417168\pi\) | |||||||
\(720\) | 91.0132 | 3.39186 | ||||||||
\(721\) | 2.45898 | 0.0915772 | ||||||||
\(722\) | 22.3262 | 0.830897 | ||||||||
\(723\) | 11.1803 | 0.415801 | ||||||||
\(724\) | −104.936 | −3.89992 | ||||||||
\(725\) | 16.4164 | 0.609690 | ||||||||
\(726\) | −9.09017 | −0.337368 | ||||||||
\(727\) | 28.9787 | 1.07476 | 0.537381 | − | 0.843340i | \(-0.319414\pi\) | ||||
0.537381 | + | 0.843340i | \(0.319414\pi\) | |||||||
\(728\) | −6.38197 | −0.236531 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | −41.1246 | −1.52209 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 7.14590 | 0.264120 | ||||||||
\(733\) | −42.5410 | −1.57129 | −0.785644 | − | 0.618679i | \(-0.787668\pi\) | ||||
−0.785644 | + | 0.618679i | \(0.787668\pi\) | |||||||
\(734\) | 8.32624 | 0.307327 | ||||||||
\(735\) | −8.58359 | −0.316611 | ||||||||
\(736\) | −71.8328 | −2.64779 | ||||||||
\(737\) | −3.94427 | −0.145289 | ||||||||
\(738\) | 3.94427 | 0.145191 | ||||||||
\(739\) | −17.5410 | −0.645257 | −0.322628 | − | 0.946526i | \(-0.604566\pi\) | ||||
−0.322628 | + | 0.946526i | \(0.604566\pi\) | |||||||
\(740\) | −29.1246 | −1.07064 | ||||||||
\(741\) | −4.47214 | −0.164288 | ||||||||
\(742\) | 2.23607 | 0.0820886 | ||||||||
\(743\) | −11.3607 | −0.416783 | −0.208391 | − | 0.978045i | \(-0.566823\pi\) | ||||
−0.208391 | + | 0.978045i | \(0.566823\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.1246 | −1.06704 | ||||||||
\(746\) | −15.7082 | −0.575118 | ||||||||
\(747\) | 37.2016 | 1.36114 | ||||||||
\(748\) | 34.1459 | 1.24850 | ||||||||
\(749\) | 3.88854 | 0.142084 | ||||||||
\(750\) | −1.52786 | −0.0557897 | ||||||||
\(751\) | 8.97871 | 0.327638 | 0.163819 | − | 0.986490i | \(-0.447619\pi\) | ||||
0.163819 | + | 0.986490i | \(0.447619\pi\) | |||||||
\(752\) | 77.3951 | 2.82231 | ||||||||
\(753\) | 2.60488 | 0.0949270 | ||||||||
\(754\) | −28.4164 | −1.03486 | ||||||||
\(755\) | 6.94427 | 0.252728 | ||||||||
\(756\) | 2.56231 | 0.0931902 | ||||||||
\(757\) | 15.9787 | 0.580756 | 0.290378 | − | 0.956912i | \(-0.406219\pi\) | ||||
0.290378 | + | 0.956912i | \(0.406219\pi\) | |||||||
\(758\) | −45.4508 | −1.65085 | ||||||||
\(759\) | 3.49342 | 0.126803 | ||||||||
\(760\) | 78.2492 | 2.83840 | ||||||||
\(761\) | −10.0902 | −0.365768 | −0.182884 | − | 0.983134i | \(-0.558543\pi\) | ||||
−0.182884 | + | 0.983134i | \(0.558543\pi\) | |||||||
\(762\) | 16.6525 | 0.603256 | ||||||||
\(763\) | −1.68692 | −0.0610705 | ||||||||
\(764\) | −113.936 | −4.12206 | ||||||||
\(765\) | −47.0132 | −1.69976 | ||||||||
\(766\) | 5.56231 | 0.200974 | ||||||||
\(767\) | −22.0344 | −0.795618 | ||||||||
\(768\) | 5.56231 | 0.200712 | ||||||||
\(769\) | −15.8885 | −0.572956 | −0.286478 | − | 0.958087i | \(-0.592484\pi\) | ||||
−0.286478 | + | 0.958087i | \(0.592484\pi\) | |||||||
\(770\) | −2.76393 | −0.0996052 | ||||||||
\(771\) | −9.00000 | −0.324127 | ||||||||
\(772\) | −51.9787 | −1.87075 | ||||||||
\(773\) | −33.5967 | −1.20839 | −0.604196 | − | 0.796836i | \(-0.706505\pi\) | ||||
−0.604196 | + | 0.796836i | \(0.706505\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 35.5967 | 1.27785 | ||||||||
\(777\) | −0.167184 | −0.00599770 | ||||||||
\(778\) | −60.3951 | −2.16527 | ||||||||
\(779\) | 1.70820 | 0.0612028 | ||||||||
\(780\) | 21.7082 | 0.777278 | ||||||||
\(781\) | −19.0689 | −0.682338 | ||||||||
\(782\) | 88.1935 | 3.15379 | ||||||||
\(783\) | 6.70820 | 0.239732 | ||||||||
\(784\) | −68.4296 | −2.44391 | ||||||||
\(785\) | 38.3607 | 1.36915 | ||||||||
\(786\) | −7.94427 | −0.283363 | ||||||||
\(787\) | −45.4508 | −1.62015 | −0.810074 | − | 0.586328i | \(-0.800573\pi\) | ||||
−0.810074 | + | 0.586328i | \(0.800573\pi\) | |||||||
\(788\) | 72.5410 | 2.58417 | ||||||||
\(789\) | 4.01316 | 0.142872 | ||||||||
\(790\) | −30.6525 | −1.09057 | ||||||||
\(791\) | −3.15905 | −0.112323 | ||||||||
\(792\) | −29.4721 | −1.04725 | ||||||||
\(793\) | −13.9443 | −0.495176 | ||||||||
\(794\) | −14.6180 | −0.518775 | ||||||||
\(795\) | −4.47214 | −0.158610 | ||||||||
\(796\) | −77.3951 | −2.74320 | ||||||||
\(797\) | −3.76393 | −0.133325 | −0.0666627 | − | 0.997776i | \(-0.521235\pi\) | ||||
−0.0666627 | + | 0.997776i | \(0.521235\pi\) | |||||||
\(798\) | 0.763932 | 0.0270429 | ||||||||
\(799\) | −39.9787 | −1.41435 | ||||||||
\(800\) | −59.3951 | −2.09993 | ||||||||
\(801\) | −13.8541 | −0.489511 | ||||||||
\(802\) | −3.70820 | −0.130941 | ||||||||
\(803\) | 6.70820 | 0.236727 | ||||||||
\(804\) | −5.29180 | −0.186627 | ||||||||
\(805\) | −5.05573 | −0.178191 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.27051 | 0.115127 | ||||||||
\(808\) | −61.5410 | −2.16501 | ||||||||
\(809\) | −37.7426 | −1.32696 | −0.663480 | − | 0.748194i | \(-0.730921\pi\) | ||||
−0.663480 | + | 0.748194i | \(0.730921\pi\) | |||||||
\(810\) | 65.3050 | 2.29458 | ||||||||
\(811\) | −26.3951 | −0.926858 | −0.463429 | − | 0.886134i | \(-0.653381\pi\) | ||||
−0.463429 | + | 0.886134i | \(0.653381\pi\) | |||||||
\(812\) | 3.43769 | 0.120639 | ||||||||
\(813\) | −2.72949 | −0.0957274 | ||||||||
\(814\) | 6.70820 | 0.235122 | ||||||||
\(815\) | −45.3050 | −1.58696 | ||||||||
\(816\) | 19.1591 | 0.670701 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −52.5967 | −1.83900 | ||||||||
\(819\) | −2.43769 | −0.0851799 | ||||||||
\(820\) | −8.29180 | −0.289562 | ||||||||
\(821\) | −15.3262 | −0.534889 | −0.267445 | − | 0.963573i | \(-0.586179\pi\) | ||||
−0.267445 | + | 0.963573i | \(0.586179\pi\) | |||||||
\(822\) | −9.70820 | −0.338612 | ||||||||
\(823\) | −24.0132 | −0.837046 | −0.418523 | − | 0.908206i | \(-0.637452\pi\) | ||||
−0.418523 | + | 0.908206i | \(0.637452\pi\) | |||||||
\(824\) | −77.8328 | −2.71143 | ||||||||
\(825\) | 2.88854 | 0.100566 | ||||||||
\(826\) | 3.76393 | 0.130964 | ||||||||
\(827\) | −13.1803 | −0.458325 | −0.229163 | − | 0.973388i | \(-0.573599\pi\) | ||||
−0.229163 | + | 0.973388i | \(0.573599\pi\) | |||||||
\(828\) | −91.6869 | −3.18634 | ||||||||
\(829\) | −41.1591 | −1.42951 | −0.714757 | − | 0.699373i | \(-0.753462\pi\) | ||||
−0.714757 | + | 0.699373i | \(0.753462\pi\) | |||||||
\(830\) | −110.430 | −3.83307 | ||||||||
\(831\) | 1.34752 | 0.0467451 | ||||||||
\(832\) | 31.5066 | 1.09229 | ||||||||
\(833\) | 35.3475 | 1.22472 | ||||||||
\(834\) | −18.7082 | −0.647812 | ||||||||
\(835\) | −31.5967 | −1.09345 | ||||||||
\(836\) | −21.7082 | −0.750794 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.0902 | 0.521281 | ||||||||
\(839\) | −9.88854 | −0.341390 | −0.170695 | − | 0.985324i | \(-0.554601\pi\) | ||||
−0.170695 | + | 0.985324i | \(0.554601\pi\) | |||||||
\(840\) | −2.18034 | −0.0752289 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −61.9230 | −2.13401 | ||||||||
\(843\) | 0.562306 | 0.0193668 | ||||||||
\(844\) | −23.1246 | −0.795982 | ||||||||
\(845\) | −0.291796 | −0.0100381 | ||||||||
\(846\) | 58.6869 | 2.01770 | ||||||||
\(847\) | −2.14590 | −0.0737339 | ||||||||
\(848\) | −35.6525 | −1.22431 | ||||||||
\(849\) | −5.81966 | −0.199730 | ||||||||
\(850\) | 72.9230 | 2.50124 | ||||||||
\(851\) | 12.2705 | 0.420628 | ||||||||
\(852\) | −25.5836 | −0.876479 | ||||||||
\(853\) | 53.7426 | 1.84011 | 0.920057 | − | 0.391786i | \(-0.128142\pi\) | ||||
0.920057 | + | 0.391786i | \(0.128142\pi\) | |||||||
\(854\) | 2.38197 | 0.0815092 | ||||||||
\(855\) | 29.8885 | 1.02217 | ||||||||
\(856\) | −123.082 | −4.20686 | ||||||||
\(857\) | −13.8197 | −0.472071 | −0.236035 | − | 0.971744i | \(-0.575848\pi\) | ||||
−0.236035 | + | 0.971744i | \(0.575848\pi\) | |||||||
\(858\) | −5.00000 | −0.170697 | ||||||||
\(859\) | −22.5836 | −0.770542 | −0.385271 | − | 0.922803i | \(-0.625892\pi\) | ||||
−0.385271 | + | 0.922803i | \(0.625892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0475975 | −0.00162212 | ||||||||
\(862\) | 0.527864 | 0.0179791 | ||||||||
\(863\) | −28.5066 | −0.970375 | −0.485188 | − | 0.874410i | \(-0.661249\pi\) | ||||
−0.485188 | + | 0.874410i | \(0.661249\pi\) | |||||||
\(864\) | −24.2705 | −0.825700 | ||||||||
\(865\) | 26.6525 | 0.906211 | ||||||||
\(866\) | 55.7426 | 1.89421 | ||||||||
\(867\) | −3.40325 | −0.115581 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.00000 | 0.169613 | ||||||||
\(870\) | −9.70820 | −0.329139 | ||||||||
\(871\) | 10.3262 | 0.349891 | ||||||||
\(872\) | 53.3951 | 1.80819 | ||||||||
\(873\) | 13.5967 | 0.460180 | ||||||||
\(874\) | −56.0689 | −1.89656 | ||||||||
\(875\) | −0.360680 | −0.0121932 | ||||||||
\(876\) | 9.00000 | 0.304082 | ||||||||
\(877\) | 23.6525 | 0.798687 | 0.399344 | − | 0.916801i | \(-0.369238\pi\) | ||||
0.399344 | + | 0.916801i | \(0.369238\pi\) | |||||||
\(878\) | −20.5623 | −0.693944 | ||||||||
\(879\) | 0.347524 | 0.0117217 | ||||||||
\(880\) | 44.0689 | 1.48556 | ||||||||
\(881\) | 38.2361 | 1.28821 | 0.644103 | − | 0.764939i | \(-0.277231\pi\) | ||||
0.644103 | + | 0.764939i | \(0.277231\pi\) | |||||||
\(882\) | −51.8885 | −1.74718 | ||||||||
\(883\) | −27.1246 | −0.912816 | −0.456408 | − | 0.889771i | \(-0.650864\pi\) | ||||
−0.456408 | + | 0.889771i | \(0.650864\pi\) | |||||||
\(884\) | −89.3951 | −3.00668 | ||||||||
\(885\) | −7.52786 | −0.253046 | ||||||||
\(886\) | 16.9443 | 0.569254 | ||||||||
\(887\) | 40.9574 | 1.37522 | 0.687608 | − | 0.726082i | \(-0.258661\pi\) | ||||
0.687608 | + | 0.726082i | \(0.258661\pi\) | |||||||
\(888\) | 5.29180 | 0.177581 | ||||||||
\(889\) | 3.93112 | 0.131845 | ||||||||
\(890\) | 41.1246 | 1.37850 | ||||||||
\(891\) | −10.6525 | −0.356871 | ||||||||
\(892\) | 35.1246 | 1.17606 | ||||||||
\(893\) | 25.4164 | 0.850528 | ||||||||
\(894\) | 9.00000 | 0.301005 | ||||||||
\(895\) | 70.0689 | 2.34214 | ||||||||
\(896\) | −0.257354 | −0.00859760 | ||||||||
\(897\) | −9.14590 | −0.305373 | ||||||||
\(898\) | −54.5410 | −1.82006 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −75.8115 | −2.52705 | ||||||||
\(901\) | 18.4164 | 0.613540 | ||||||||
\(902\) | 1.90983 | 0.0635904 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 99.9919 | 3.32568 | ||||||||
\(905\) | 69.9574 | 2.32546 | ||||||||
\(906\) | −2.14590 | −0.0712927 | ||||||||
\(907\) | −8.29180 | −0.275325 | −0.137662 | − | 0.990479i | \(-0.543959\pi\) | ||||
−0.137662 | + | 0.990479i | \(0.543959\pi\) | |||||||
\(908\) | 36.2705 | 1.20368 | ||||||||
\(909\) | −23.5066 | −0.779664 | ||||||||
\(910\) | 7.23607 | 0.239873 | ||||||||
\(911\) | 3.97871 | 0.131821 | 0.0659103 | − | 0.997826i | \(-0.479005\pi\) | ||||
0.0659103 | + | 0.997826i | \(0.479005\pi\) | |||||||
\(912\) | −12.1803 | −0.403331 | ||||||||
\(913\) | 18.0132 | 0.596148 | ||||||||
\(914\) | 6.00000 | 0.198462 | ||||||||
\(915\) | −4.76393 | −0.157491 | ||||||||
\(916\) | −76.2492 | −2.51935 | ||||||||
\(917\) | −1.87539 | −0.0619308 | ||||||||
\(918\) | 29.7984 | 0.983493 | ||||||||
\(919\) | −44.3951 | −1.46446 | −0.732230 | − | 0.681057i | \(-0.761520\pi\) | ||||
−0.732230 | + | 0.681057i | \(0.761520\pi\) | |||||||
\(920\) | 160.026 | 5.27591 | ||||||||
\(921\) | −10.7771 | −0.355117 | ||||||||
\(922\) | −46.0689 | −1.51720 | ||||||||
\(923\) | 49.9230 | 1.64324 | ||||||||
\(924\) | 0.604878 | 0.0198990 | ||||||||
\(925\) | 10.1459 | 0.333595 | ||||||||
\(926\) | −62.3951 | −2.05043 | ||||||||
\(927\) | −29.7295 | −0.976445 | ||||||||
\(928\) | −32.5623 | −1.06891 | ||||||||
\(929\) | 30.7639 | 1.00933 | 0.504666 | − | 0.863315i | \(-0.331616\pi\) | ||||
0.504666 | + | 0.863315i | \(0.331616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.4721 | −0.736495 | ||||||||
\(932\) | −53.5623 | −1.75449 | ||||||||
\(933\) | −9.10333 | −0.298029 | ||||||||
\(934\) | 86.2492 | 2.82216 | ||||||||
\(935\) | −22.7639 | −0.744460 | ||||||||
\(936\) | 77.1591 | 2.52202 | ||||||||
\(937\) | −39.6738 | −1.29609 | −0.648043 | − | 0.761604i | \(-0.724412\pi\) | ||||
−0.648043 | + | 0.761604i | \(0.724412\pi\) | |||||||
\(938\) | −1.76393 | −0.0575944 | ||||||||
\(939\) | 10.3607 | 0.338108 | ||||||||
\(940\) | −123.374 | −4.02401 | ||||||||
\(941\) | −21.7639 | −0.709484 | −0.354742 | − | 0.934964i | \(-0.615431\pi\) | ||||
−0.354742 | + | 0.934964i | \(0.615431\pi\) | |||||||
\(942\) | −11.8541 | −0.386228 | ||||||||
\(943\) | 3.49342 | 0.113761 | ||||||||
\(944\) | −60.0132 | −1.95326 | ||||||||
\(945\) | −1.70820 | −0.0555679 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.3607 | −0.629138 | −0.314569 | − | 0.949235i | \(-0.601860\pi\) | ||||
−0.314569 | + | 0.949235i | \(0.601860\pi\) | |||||||
\(948\) | 6.70820 | 0.217872 | ||||||||
\(949\) | −17.5623 | −0.570097 | ||||||||
\(950\) | −46.3607 | −1.50414 | ||||||||
\(951\) | 11.1935 | 0.362974 | ||||||||
\(952\) | 8.97871 | 0.291002 | ||||||||
\(953\) | −3.11146 | −0.100790 | −0.0503950 | − | 0.998729i | \(-0.516048\pi\) | ||||
−0.0503950 | + | 0.998729i | \(0.516048\pi\) | |||||||
\(954\) | −27.0344 | −0.875272 | ||||||||
\(955\) | 75.9574 | 2.45792 | ||||||||
\(956\) | −105.374 | −3.40803 | ||||||||
\(957\) | 1.58359 | 0.0511903 | ||||||||
\(958\) | 94.7214 | 3.06031 | ||||||||
\(959\) | −2.29180 | −0.0740060 | ||||||||
\(960\) | 10.7639 | 0.347404 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −17.5623 | −0.566231 | ||||||||
\(963\) | −47.0132 | −1.51498 | ||||||||
\(964\) | −142.082 | −4.57615 | ||||||||
\(965\) | 34.6525 | 1.11550 | ||||||||
\(966\) | 1.56231 | 0.0502664 | ||||||||
\(967\) | −49.1033 | −1.57906 | −0.789528 | − | 0.613714i | \(-0.789675\pi\) | ||||
−0.789528 | + | 0.613714i | \(0.789675\pi\) | |||||||
\(968\) | 67.9230 | 2.18313 | ||||||||
\(969\) | 6.29180 | 0.202122 | ||||||||
\(970\) | −40.3607 | −1.29590 | ||||||||
\(971\) | 27.3607 | 0.878046 | 0.439023 | − | 0.898476i | \(-0.355325\pi\) | ||||
0.439023 | + | 0.898476i | \(0.355325\pi\) | |||||||
\(972\) | −46.8541 | −1.50285 | ||||||||
\(973\) | −4.41641 | −0.141584 | ||||||||
\(974\) | 37.5066 | 1.20179 | ||||||||
\(975\) | −7.56231 | −0.242188 | ||||||||
\(976\) | −37.9787 | −1.21567 | ||||||||
\(977\) | 36.7639 | 1.17618 | 0.588091 | − | 0.808795i | \(-0.299880\pi\) | ||||
0.588091 | + | 0.808795i | \(0.299880\pi\) | |||||||
\(978\) | 14.0000 | 0.447671 | ||||||||
\(979\) | −6.70820 | −0.214395 | ||||||||
\(980\) | 109.082 | 3.48450 | ||||||||
\(981\) | 20.3951 | 0.651166 | ||||||||
\(982\) | 25.2705 | 0.806414 | ||||||||
\(983\) | −1.52786 | −0.0487313 | −0.0243656 | − | 0.999703i | \(-0.507757\pi\) | ||||
−0.0243656 | + | 0.999703i | \(0.507757\pi\) | |||||||
\(984\) | 1.50658 | 0.0480279 | ||||||||
\(985\) | −48.3607 | −1.54090 | ||||||||
\(986\) | 39.9787 | 1.27318 | ||||||||
\(987\) | −0.708204 | −0.0225424 | ||||||||
\(988\) | 56.8328 | 1.80809 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 33.4164 | 1.06204 | ||||||||
\(991\) | −33.1803 | −1.05401 | −0.527004 | − | 0.849863i | \(-0.676685\pi\) | ||||
−0.527004 | + | 0.849863i | \(0.676685\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.32624 | −0.0420869 | ||||||||
\(994\) | −8.52786 | −0.270487 | ||||||||
\(995\) | 51.5967 | 1.63573 | ||||||||
\(996\) | 24.1672 | 0.765767 | ||||||||
\(997\) | 36.4508 | 1.15441 | 0.577205 | − | 0.816599i | \(-0.304143\pi\) | ||||
0.577205 | + | 0.816599i | \(0.304143\pi\) | |||||||
\(998\) | −18.7082 | −0.592198 | ||||||||
\(999\) | 4.14590 | 0.131170 |
(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 | 1849.2.a.e.1.1 | 2 | ||
43.6 | even | 3 | 43.2.c.b.36.1 | yes | 4 | ||
43.36 | even | 3 | 43.2.c.b.6.1 | ✓ | 4 | ||
43.42 | odd | 2 | 1849.2.a.h.1.2 | 2 | |||
129.92 | odd | 6 | 387.2.h.d.208.2 | 4 | |||
129.122 | odd | 6 | 387.2.h.d.307.2 | 4 | |||
172.79 | odd | 6 | 688.2.i.e.49.2 | 4 | |||
172.135 | odd | 6 | 688.2.i.e.337.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.c.b.6.1 | ✓ | 4 | 43.36 | even | 3 | ||
43.2.c.b.36.1 | yes | 4 | 43.6 | even | 3 | ||
387.2.h.d.208.2 | 4 | 129.92 | odd | 6 | |||
387.2.h.d.307.2 | 4 | 129.122 | odd | 6 | |||
688.2.i.e.49.2 | 4 | 172.79 | odd | 6 | |||
688.2.i.e.337.2 | 4 | 172.135 | odd | 6 | |||
1849.2.a.e.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1849.2.a.h.1.2 | 2 | 43.42 | odd | 2 |