Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.801938 | −0.567056 | −0.283528 | − | 0.958964i | \(-0.591505\pi\) | ||||
−0.283528 | + | 0.958964i | \(0.591505\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.35690 | −0.678448 | ||||||||
\(5\) | 3.04892 | 1.36352 | 0.681759 | − | 0.731577i | \(-0.261215\pi\) | ||||
0.681759 | + | 0.731577i | \(0.261215\pi\) | |||||||
\(6\) | −0.801938 | −0.327390 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.69202 | 0.951773 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.44504 | −0.773190 | ||||||||
\(11\) | −2.15883 | −0.650913 | −0.325456 | − | 0.945557i | \(-0.605518\pi\) | ||||
−0.325456 | + | 0.945557i | \(0.605518\pi\) | |||||||
\(12\) | −1.35690 | −0.391702 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.801938 | 0.214327 | ||||||||
\(15\) | 3.04892 | 0.787227 | ||||||||
\(16\) | 0.554958 | 0.138740 | ||||||||
\(17\) | 0.801938 | 0.194498 | 0.0972492 | − | 0.995260i | \(-0.468996\pi\) | ||||
0.0972492 | + | 0.995260i | \(0.468996\pi\) | |||||||
\(18\) | −0.801938 | −0.189019 | ||||||||
\(19\) | 1.39612 | 0.320293 | 0.160146 | − | 0.987093i | \(-0.448803\pi\) | ||||
0.160146 | + | 0.987093i | \(0.448803\pi\) | |||||||
\(20\) | −4.13706 | −0.925075 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.73125 | 0.369104 | ||||||||
\(23\) | 3.02715 | 0.631204 | 0.315602 | − | 0.948892i | \(-0.397794\pi\) | ||||
0.315602 | + | 0.948892i | \(0.397794\pi\) | |||||||
\(24\) | 2.69202 | 0.549507 | ||||||||
\(25\) | 4.29590 | 0.859179 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.35690 | 0.256429 | ||||||||
\(29\) | 2.47219 | 0.459074 | 0.229537 | − | 0.973300i | \(-0.426279\pi\) | ||||
0.229537 | + | 0.973300i | \(0.426279\pi\) | |||||||
\(30\) | −2.44504 | −0.446402 | ||||||||
\(31\) | 6.26875 | 1.12590 | 0.562950 | − | 0.826491i | \(-0.309666\pi\) | ||||
0.562950 | + | 0.826491i | \(0.309666\pi\) | |||||||
\(32\) | −5.82908 | −1.03045 | ||||||||
\(33\) | −2.15883 | −0.375805 | ||||||||
\(34\) | −0.643104 | −0.110291 | ||||||||
\(35\) | −3.04892 | −0.515361 | ||||||||
\(36\) | −1.35690 | −0.226149 | ||||||||
\(37\) | −10.7506 | −1.76739 | −0.883696 | − | 0.468061i | \(-0.844953\pi\) | ||||
−0.883696 | + | 0.468061i | \(0.844953\pi\) | |||||||
\(38\) | −1.11960 | −0.181624 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.20775 | 1.29776 | ||||||||
\(41\) | 5.20775 | 0.813314 | 0.406657 | − | 0.913581i | \(-0.366694\pi\) | ||||
0.406657 | + | 0.913581i | \(0.366694\pi\) | |||||||
\(42\) | 0.801938 | 0.123742 | ||||||||
\(43\) | −8.63102 | −1.31622 | −0.658109 | − | 0.752922i | \(-0.728644\pi\) | ||||
−0.658109 | + | 0.752922i | \(0.728644\pi\) | |||||||
\(44\) | 2.92931 | 0.441610 | ||||||||
\(45\) | 3.04892 | 0.454506 | ||||||||
\(46\) | −2.42758 | −0.357928 | ||||||||
\(47\) | 9.15883 | 1.33595 | 0.667977 | − | 0.744182i | \(-0.267161\pi\) | ||||
0.667977 | + | 0.744182i | \(0.267161\pi\) | |||||||
\(48\) | 0.554958 | 0.0801013 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.44504 | −0.487202 | ||||||||
\(51\) | 0.801938 | 0.112294 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.21983 | 0.167557 | 0.0837784 | − | 0.996484i | \(-0.473301\pi\) | ||||
0.0837784 | + | 0.996484i | \(0.473301\pi\) | |||||||
\(54\) | −0.801938 | −0.109130 | ||||||||
\(55\) | −6.58211 | −0.887531 | ||||||||
\(56\) | −2.69202 | −0.359737 | ||||||||
\(57\) | 1.39612 | 0.184921 | ||||||||
\(58\) | −1.98254 | −0.260320 | ||||||||
\(59\) | 8.63102 | 1.12366 | 0.561832 | − | 0.827252i | \(-0.310097\pi\) | ||||
0.561832 | + | 0.827252i | \(0.310097\pi\) | |||||||
\(60\) | −4.13706 | −0.534093 | ||||||||
\(61\) | −10.0858 | −1.29135 | −0.645674 | − | 0.763613i | \(-0.723424\pi\) | ||||
−0.645674 | + | 0.763613i | \(0.723424\pi\) | |||||||
\(62\) | −5.02715 | −0.638448 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 3.56465 | 0.445581 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.73125 | 0.213102 | ||||||||
\(67\) | 12.7899 | 1.56253 | 0.781265 | − | 0.624200i | \(-0.214575\pi\) | ||||
0.781265 | + | 0.624200i | \(0.214575\pi\) | |||||||
\(68\) | −1.08815 | −0.131957 | ||||||||
\(69\) | 3.02715 | 0.364426 | ||||||||
\(70\) | 2.44504 | 0.292238 | ||||||||
\(71\) | 14.1250 | 1.67633 | 0.838163 | − | 0.545419i | \(-0.183629\pi\) | ||||
0.838163 | + | 0.545419i | \(0.183629\pi\) | |||||||
\(72\) | 2.69202 | 0.317258 | ||||||||
\(73\) | 10.1250 | 1.18504 | 0.592520 | − | 0.805556i | \(-0.298133\pi\) | ||||
0.592520 | + | 0.805556i | \(0.298133\pi\) | |||||||
\(74\) | 8.62133 | 1.00221 | ||||||||
\(75\) | 4.29590 | 0.496047 | ||||||||
\(76\) | −1.89440 | −0.217302 | ||||||||
\(77\) | 2.15883 | 0.246022 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.33513 | 0.150213 | 0.0751067 | − | 0.997176i | \(-0.476070\pi\) | ||||
0.0751067 | + | 0.997176i | \(0.476070\pi\) | |||||||
\(80\) | 1.69202 | 0.189174 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.17629 | −0.461194 | ||||||||
\(83\) | −8.92692 | −0.979857 | −0.489928 | − | 0.871763i | \(-0.662977\pi\) | ||||
−0.489928 | + | 0.871763i | \(0.662977\pi\) | |||||||
\(84\) | 1.35690 | 0.148049 | ||||||||
\(85\) | 2.44504 | 0.265202 | ||||||||
\(86\) | 6.92154 | 0.746369 | ||||||||
\(87\) | 2.47219 | 0.265046 | ||||||||
\(88\) | −5.81163 | −0.619521 | ||||||||
\(89\) | 2.50604 | 0.265640 | 0.132820 | − | 0.991140i | \(-0.457597\pi\) | ||||
0.132820 | + | 0.991140i | \(0.457597\pi\) | |||||||
\(90\) | −2.44504 | −0.257730 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.10752 | −0.428239 | ||||||||
\(93\) | 6.26875 | 0.650039 | ||||||||
\(94\) | −7.34481 | −0.757560 | ||||||||
\(95\) | 4.25667 | 0.436725 | ||||||||
\(96\) | −5.82908 | −0.594928 | ||||||||
\(97\) | −2.32304 | −0.235869 | −0.117935 | − | 0.993021i | \(-0.537627\pi\) | ||||
−0.117935 | + | 0.993021i | \(0.537627\pi\) | |||||||
\(98\) | −0.801938 | −0.0810079 | ||||||||
\(99\) | −2.15883 | −0.216971 | ||||||||
\(100\) | −5.82908 | −0.582908 | ||||||||
\(101\) | 14.7724 | 1.46991 | 0.734954 | − | 0.678117i | \(-0.237204\pi\) | ||||
0.734954 | + | 0.678117i | \(0.237204\pi\) | |||||||
\(102\) | −0.643104 | −0.0636768 | ||||||||
\(103\) | −10.1642 | −1.00151 | −0.500755 | − | 0.865589i | \(-0.666944\pi\) | ||||
−0.500755 | + | 0.865589i | \(0.666944\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.04892 | −0.297544 | ||||||||
\(106\) | −0.978230 | −0.0950141 | ||||||||
\(107\) | −17.2784 | −1.67037 | −0.835185 | − | 0.549969i | \(-0.814639\pi\) | ||||
−0.835185 | + | 0.549969i | \(0.814639\pi\) | |||||||
\(108\) | −1.35690 | −0.130567 | ||||||||
\(109\) | 14.2959 | 1.36930 | 0.684649 | − | 0.728873i | \(-0.259955\pi\) | ||||
0.684649 | + | 0.728873i | \(0.259955\pi\) | |||||||
\(110\) | 5.27844 | 0.503279 | ||||||||
\(111\) | −10.7506 | −1.02040 | ||||||||
\(112\) | −0.554958 | −0.0524386 | ||||||||
\(113\) | 16.2687 | 1.53044 | 0.765218 | − | 0.643772i | \(-0.222631\pi\) | ||||
0.765218 | + | 0.643772i | \(0.222631\pi\) | |||||||
\(114\) | −1.11960 | −0.104861 | ||||||||
\(115\) | 9.22952 | 0.860657 | ||||||||
\(116\) | −3.35450 | −0.311458 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.92154 | −0.637180 | ||||||||
\(119\) | −0.801938 | −0.0735135 | ||||||||
\(120\) | 8.20775 | 0.749262 | ||||||||
\(121\) | −6.33944 | −0.576312 | ||||||||
\(122\) | 8.08815 | 0.732266 | ||||||||
\(123\) | 5.20775 | 0.469567 | ||||||||
\(124\) | −8.50604 | −0.763865 | ||||||||
\(125\) | −2.14675 | −0.192011 | ||||||||
\(126\) | 0.801938 | 0.0714423 | ||||||||
\(127\) | −4.51142 | −0.400324 | −0.200162 | − | 0.979763i | \(-0.564147\pi\) | ||||
−0.200162 | + | 0.979763i | \(0.564147\pi\) | |||||||
\(128\) | 8.79954 | 0.777777 | ||||||||
\(129\) | −8.63102 | −0.759919 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.04892 | 0.0916443 | 0.0458222 | − | 0.998950i | \(-0.485409\pi\) | ||||
0.0458222 | + | 0.998950i | \(0.485409\pi\) | |||||||
\(132\) | 2.92931 | 0.254964 | ||||||||
\(133\) | −1.39612 | −0.121059 | ||||||||
\(134\) | −10.2567 | −0.886041 | ||||||||
\(135\) | 3.04892 | 0.262409 | ||||||||
\(136\) | 2.15883 | 0.185118 | ||||||||
\(137\) | −12.3599 | −1.05598 | −0.527988 | − | 0.849252i | \(-0.677053\pi\) | ||||
−0.527988 | + | 0.849252i | \(0.677053\pi\) | |||||||
\(138\) | −2.42758 | −0.206650 | ||||||||
\(139\) | 13.6015 | 1.15366 | 0.576831 | − | 0.816863i | \(-0.304289\pi\) | ||||
0.576831 | + | 0.816863i | \(0.304289\pi\) | |||||||
\(140\) | 4.13706 | 0.349646 | ||||||||
\(141\) | 9.15883 | 0.771313 | ||||||||
\(142\) | −11.3274 | −0.950571 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.554958 | 0.0462465 | ||||||||
\(145\) | 7.53750 | 0.625955 | ||||||||
\(146\) | −8.11960 | −0.671983 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 14.5875 | 1.19908 | ||||||||
\(149\) | −8.33513 | −0.682840 | −0.341420 | − | 0.939911i | \(-0.610908\pi\) | ||||
−0.341420 | + | 0.939911i | \(0.610908\pi\) | |||||||
\(150\) | −3.44504 | −0.281286 | ||||||||
\(151\) | −11.4819 | −0.934382 | −0.467191 | − | 0.884156i | \(-0.654734\pi\) | ||||
−0.467191 | + | 0.884156i | \(0.654734\pi\) | |||||||
\(152\) | 3.75840 | 0.304846 | ||||||||
\(153\) | 0.801938 | 0.0648328 | ||||||||
\(154\) | −1.73125 | −0.139508 | ||||||||
\(155\) | 19.1129 | 1.53519 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.99330 | −0.238891 | −0.119445 | − | 0.992841i | \(-0.538112\pi\) | ||||
−0.119445 | + | 0.992841i | \(0.538112\pi\) | |||||||
\(158\) | −1.07069 | −0.0851793 | ||||||||
\(159\) | 1.21983 | 0.0967390 | ||||||||
\(160\) | −17.7724 | −1.40503 | ||||||||
\(161\) | −3.02715 | −0.238573 | ||||||||
\(162\) | −0.801938 | −0.0630062 | ||||||||
\(163\) | 15.6353 | 1.22465 | 0.612327 | − | 0.790605i | \(-0.290234\pi\) | ||||
0.612327 | + | 0.790605i | \(0.290234\pi\) | |||||||
\(164\) | −7.06638 | −0.551791 | ||||||||
\(165\) | −6.58211 | −0.512416 | ||||||||
\(166\) | 7.15883 | 0.555633 | ||||||||
\(167\) | 6.70171 | 0.518594 | 0.259297 | − | 0.965798i | \(-0.416509\pi\) | ||||
0.259297 | + | 0.965798i | \(0.416509\pi\) | |||||||
\(168\) | −2.69202 | −0.207694 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.96077 | −0.150384 | ||||||||
\(171\) | 1.39612 | 0.106764 | ||||||||
\(172\) | 11.7114 | 0.892986 | ||||||||
\(173\) | −7.05131 | −0.536101 | −0.268051 | − | 0.963405i | \(-0.586379\pi\) | ||||
−0.268051 | + | 0.963405i | \(0.586379\pi\) | |||||||
\(174\) | −1.98254 | −0.150296 | ||||||||
\(175\) | −4.29590 | −0.324739 | ||||||||
\(176\) | −1.19806 | −0.0903073 | ||||||||
\(177\) | 8.63102 | 0.648747 | ||||||||
\(178\) | −2.00969 | −0.150633 | ||||||||
\(179\) | 6.46144 | 0.482950 | 0.241475 | − | 0.970407i | \(-0.422369\pi\) | ||||
0.241475 | + | 0.970407i | \(0.422369\pi\) | |||||||
\(180\) | −4.13706 | −0.308358 | ||||||||
\(181\) | −0.576728 | −0.0428679 | −0.0214339 | − | 0.999770i | \(-0.506823\pi\) | ||||
−0.0214339 | + | 0.999770i | \(0.506823\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0858 | −0.745560 | ||||||||
\(184\) | 8.14914 | 0.600763 | ||||||||
\(185\) | −32.7778 | −2.40987 | ||||||||
\(186\) | −5.02715 | −0.368608 | ||||||||
\(187\) | −1.73125 | −0.126602 | ||||||||
\(188\) | −12.4276 | −0.906375 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −3.41358 | −0.247647 | ||||||||
\(191\) | −9.12498 | −0.660261 | −0.330130 | − | 0.943935i | \(-0.607093\pi\) | ||||
−0.330130 | + | 0.943935i | \(0.607093\pi\) | |||||||
\(192\) | 3.56465 | 0.257256 | ||||||||
\(193\) | −7.26636 | −0.523044 | −0.261522 | − | 0.965198i | \(-0.584224\pi\) | ||||
−0.261522 | + | 0.965198i | \(0.584224\pi\) | |||||||
\(194\) | 1.86294 | 0.133751 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.35690 | −0.0969211 | ||||||||
\(197\) | −5.65519 | −0.402915 | −0.201458 | − | 0.979497i | \(-0.564568\pi\) | ||||
−0.201458 | + | 0.979497i | \(0.564568\pi\) | |||||||
\(198\) | 1.73125 | 0.123035 | ||||||||
\(199\) | 17.2892 | 1.22560 | 0.612799 | − | 0.790239i | \(-0.290043\pi\) | ||||
0.612799 | + | 0.790239i | \(0.290043\pi\) | |||||||
\(200\) | 11.5646 | 0.817744 | ||||||||
\(201\) | 12.7899 | 0.902127 | ||||||||
\(202\) | −11.8465 | −0.833520 | ||||||||
\(203\) | −2.47219 | −0.173514 | ||||||||
\(204\) | −1.08815 | −0.0761855 | ||||||||
\(205\) | 15.8780 | 1.10897 | ||||||||
\(206\) | 8.15106 | 0.567912 | ||||||||
\(207\) | 3.02715 | 0.210401 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.01400 | −0.208483 | ||||||||
\(210\) | 2.44504 | 0.168724 | ||||||||
\(211\) | 9.16852 | 0.631187 | 0.315594 | − | 0.948894i | \(-0.397796\pi\) | ||||
0.315594 | + | 0.948894i | \(0.397796\pi\) | |||||||
\(212\) | −1.65519 | −0.113679 | ||||||||
\(213\) | 14.1250 | 0.967828 | ||||||||
\(214\) | 13.8562 | 0.947193 | ||||||||
\(215\) | −26.3153 | −1.79469 | ||||||||
\(216\) | 2.69202 | 0.183169 | ||||||||
\(217\) | −6.26875 | −0.425550 | ||||||||
\(218\) | −11.4644 | −0.776468 | ||||||||
\(219\) | 10.1250 | 0.684183 | ||||||||
\(220\) | 8.93123 | 0.602143 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 8.62133 | 0.578626 | ||||||||
\(223\) | 19.0978 | 1.27889 | 0.639443 | − | 0.768839i | \(-0.279165\pi\) | ||||
0.639443 | + | 0.768839i | \(0.279165\pi\) | |||||||
\(224\) | 5.82908 | 0.389472 | ||||||||
\(225\) | 4.29590 | 0.286393 | ||||||||
\(226\) | −13.0465 | −0.867842 | ||||||||
\(227\) | 27.9463 | 1.85486 | 0.927430 | − | 0.373996i | \(-0.122013\pi\) | ||||
0.927430 | + | 0.373996i | \(0.122013\pi\) | |||||||
\(228\) | −1.89440 | −0.125459 | ||||||||
\(229\) | 19.8388 | 1.31098 | 0.655492 | − | 0.755203i | \(-0.272461\pi\) | ||||
0.655492 | + | 0.755203i | \(0.272461\pi\) | |||||||
\(230\) | −7.40150 | −0.488041 | ||||||||
\(231\) | 2.15883 | 0.142041 | ||||||||
\(232\) | 6.65519 | 0.436934 | ||||||||
\(233\) | −5.71379 | −0.374323 | −0.187161 | − | 0.982329i | \(-0.559929\pi\) | ||||
−0.187161 | + | 0.982329i | \(0.559929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.9245 | 1.82160 | ||||||||
\(236\) | −11.7114 | −0.762347 | ||||||||
\(237\) | 1.33513 | 0.0867257 | ||||||||
\(238\) | 0.643104 | 0.0416862 | ||||||||
\(239\) | −11.3840 | −0.736373 | −0.368186 | − | 0.929752i | \(-0.620021\pi\) | ||||
−0.368186 | + | 0.929752i | \(0.620021\pi\) | |||||||
\(240\) | 1.69202 | 0.109220 | ||||||||
\(241\) | 26.4403 | 1.70317 | 0.851583 | − | 0.524219i | \(-0.175643\pi\) | ||||
0.851583 | + | 0.524219i | \(0.175643\pi\) | |||||||
\(242\) | 5.08383 | 0.326801 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 13.6853 | 0.876113 | ||||||||
\(245\) | 3.04892 | 0.194788 | ||||||||
\(246\) | −4.17629 | −0.266271 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 16.8756 | 1.07160 | ||||||||
\(249\) | −8.92692 | −0.565721 | ||||||||
\(250\) | 1.72156 | 0.108881 | ||||||||
\(251\) | −22.5972 | −1.42632 | −0.713160 | − | 0.701001i | \(-0.752737\pi\) | ||||
−0.713160 | + | 0.701001i | \(0.752737\pi\) | |||||||
\(252\) | 1.35690 | 0.0854764 | ||||||||
\(253\) | −6.53511 | −0.410859 | ||||||||
\(254\) | 3.61788 | 0.227006 | ||||||||
\(255\) | 2.44504 | 0.153114 | ||||||||
\(256\) | −14.1860 | −0.886624 | ||||||||
\(257\) | 11.0392 | 0.688608 | 0.344304 | − | 0.938858i | \(-0.388115\pi\) | ||||
0.344304 | + | 0.938858i | \(0.388115\pi\) | |||||||
\(258\) | 6.92154 | 0.430916 | ||||||||
\(259\) | 10.7506 | 0.668011 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.47219 | 0.153025 | ||||||||
\(262\) | −0.841166 | −0.0519674 | ||||||||
\(263\) | −14.2470 | −0.878506 | −0.439253 | − | 0.898363i | \(-0.644757\pi\) | ||||
−0.439253 | + | 0.898363i | \(0.644757\pi\) | |||||||
\(264\) | −5.81163 | −0.357681 | ||||||||
\(265\) | 3.71917 | 0.228467 | ||||||||
\(266\) | 1.11960 | 0.0686474 | ||||||||
\(267\) | 2.50604 | 0.153367 | ||||||||
\(268\) | −17.3545 | −1.06009 | ||||||||
\(269\) | 20.3666 | 1.24177 | 0.620886 | − | 0.783901i | \(-0.286773\pi\) | ||||
0.620886 | + | 0.783901i | \(0.286773\pi\) | |||||||
\(270\) | −2.44504 | −0.148801 | ||||||||
\(271\) | 16.9976 | 1.03253 | 0.516266 | − | 0.856429i | \(-0.327322\pi\) | ||||
0.516266 | + | 0.856429i | \(0.327322\pi\) | |||||||
\(272\) | 0.445042 | 0.0269846 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.91185 | 0.598797 | ||||||||
\(275\) | −9.27413 | −0.559251 | ||||||||
\(276\) | −4.10752 | −0.247244 | ||||||||
\(277\) | −15.2620 | −0.917007 | −0.458504 | − | 0.888692i | \(-0.651614\pi\) | ||||
−0.458504 | + | 0.888692i | \(0.651614\pi\) | |||||||
\(278\) | −10.9075 | −0.654191 | ||||||||
\(279\) | 6.26875 | 0.375300 | ||||||||
\(280\) | −8.20775 | −0.490507 | ||||||||
\(281\) | −9.80492 | −0.584913 | −0.292456 | − | 0.956279i | \(-0.594473\pi\) | ||||
−0.292456 | + | 0.956279i | \(0.594473\pi\) | |||||||
\(282\) | −7.34481 | −0.437377 | ||||||||
\(283\) | 4.69202 | 0.278912 | 0.139456 | − | 0.990228i | \(-0.455465\pi\) | ||||
0.139456 | + | 0.990228i | \(0.455465\pi\) | |||||||
\(284\) | −19.1661 | −1.13730 | ||||||||
\(285\) | 4.25667 | 0.252143 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.20775 | −0.307404 | ||||||||
\(288\) | −5.82908 | −0.343482 | ||||||||
\(289\) | −16.3569 | −0.962170 | ||||||||
\(290\) | −6.04461 | −0.354951 | ||||||||
\(291\) | −2.32304 | −0.136179 | ||||||||
\(292\) | −13.7385 | −0.803988 | ||||||||
\(293\) | 21.0441 | 1.22941 | 0.614706 | − | 0.788757i | \(-0.289275\pi\) | ||||
0.614706 | + | 0.788757i | \(0.289275\pi\) | |||||||
\(294\) | −0.801938 | −0.0467700 | ||||||||
\(295\) | 26.3153 | 1.53213 | ||||||||
\(296\) | −28.9409 | −1.68216 | ||||||||
\(297\) | −2.15883 | −0.125268 | ||||||||
\(298\) | 6.68425 | 0.387208 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.82908 | −0.336542 | ||||||||
\(301\) | 8.63102 | 0.497484 | ||||||||
\(302\) | 9.20775 | 0.529847 | ||||||||
\(303\) | 14.7724 | 0.848652 | ||||||||
\(304\) | 0.774791 | 0.0444373 | ||||||||
\(305\) | −30.7506 | −1.76078 | ||||||||
\(306\) | −0.643104 | −0.0367638 | ||||||||
\(307\) | 12.8140 | 0.731335 | 0.365667 | − | 0.930746i | \(-0.380841\pi\) | ||||
0.365667 | + | 0.930746i | \(0.380841\pi\) | |||||||
\(308\) | −2.92931 | −0.166913 | ||||||||
\(309\) | −10.1642 | −0.578222 | ||||||||
\(310\) | −15.3274 | −0.870535 | ||||||||
\(311\) | 9.16315 | 0.519594 | 0.259797 | − | 0.965663i | \(-0.416344\pi\) | ||||
0.259797 | + | 0.965663i | \(0.416344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0683 | 0.625617 | 0.312809 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312809 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(314\) | 2.40044 | 0.135464 | ||||||||
\(315\) | −3.04892 | −0.171787 | ||||||||
\(316\) | −1.81163 | −0.101912 | ||||||||
\(317\) | 15.9420 | 0.895391 | 0.447696 | − | 0.894186i | \(-0.352245\pi\) | ||||
0.447696 | + | 0.894186i | \(0.352245\pi\) | |||||||
\(318\) | −0.978230 | −0.0548564 | ||||||||
\(319\) | −5.33704 | −0.298817 | ||||||||
\(320\) | 10.8683 | 0.607557 | ||||||||
\(321\) | −17.2784 | −0.964388 | ||||||||
\(322\) | 2.42758 | 0.135284 | ||||||||
\(323\) | 1.11960 | 0.0622965 | ||||||||
\(324\) | −1.35690 | −0.0753831 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.5386 | −0.694447 | ||||||||
\(327\) | 14.2959 | 0.790565 | ||||||||
\(328\) | 14.0194 | 0.774091 | ||||||||
\(329\) | −9.15883 | −0.504943 | ||||||||
\(330\) | 5.27844 | 0.290568 | ||||||||
\(331\) | −5.32736 | −0.292818 | −0.146409 | − | 0.989224i | \(-0.546772\pi\) | ||||
−0.146409 | + | 0.989224i | \(0.546772\pi\) | |||||||
\(332\) | 12.1129 | 0.664782 | ||||||||
\(333\) | −10.7506 | −0.589131 | ||||||||
\(334\) | −5.37435 | −0.294072 | ||||||||
\(335\) | 38.9952 | 2.13054 | ||||||||
\(336\) | −0.554958 | −0.0302754 | ||||||||
\(337\) | −29.5937 | −1.61207 | −0.806036 | − | 0.591866i | \(-0.798391\pi\) | ||||
−0.806036 | + | 0.591866i | \(0.798391\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.2687 | 0.883597 | ||||||||
\(340\) | −3.31767 | −0.179926 | ||||||||
\(341\) | −13.5332 | −0.732863 | ||||||||
\(342\) | −1.11960 | −0.0605413 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −23.2349 | −1.25274 | ||||||||
\(345\) | 9.22952 | 0.496901 | ||||||||
\(346\) | 5.65471 | 0.303999 | ||||||||
\(347\) | 20.2717 | 1.08824 | 0.544122 | − | 0.839006i | \(-0.316863\pi\) | ||||
0.544122 | + | 0.839006i | \(0.316863\pi\) | |||||||
\(348\) | −3.35450 | −0.179820 | ||||||||
\(349\) | −12.0325 | −0.644086 | −0.322043 | − | 0.946725i | \(-0.604370\pi\) | ||||
−0.322043 | + | 0.946725i | \(0.604370\pi\) | |||||||
\(350\) | 3.44504 | 0.184145 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.5840 | 0.670731 | ||||||||
\(353\) | −34.6843 | −1.84606 | −0.923028 | − | 0.384732i | \(-0.874294\pi\) | ||||
−0.923028 | + | 0.384732i | \(0.874294\pi\) | |||||||
\(354\) | −6.92154 | −0.367876 | ||||||||
\(355\) | 43.0659 | 2.28570 | ||||||||
\(356\) | −3.40044 | −0.180223 | ||||||||
\(357\) | −0.801938 | −0.0424430 | ||||||||
\(358\) | −5.18167 | −0.273860 | ||||||||
\(359\) | 29.5991 | 1.56218 | 0.781090 | − | 0.624418i | \(-0.214664\pi\) | ||||
0.781090 | + | 0.624418i | \(0.214664\pi\) | |||||||
\(360\) | 8.20775 | 0.432586 | ||||||||
\(361\) | −17.0508 | −0.897412 | ||||||||
\(362\) | 0.462500 | 0.0243085 | ||||||||
\(363\) | −6.33944 | −0.332734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.8702 | 1.61582 | ||||||||
\(366\) | 8.08815 | 0.422774 | ||||||||
\(367\) | 33.7362 | 1.76101 | 0.880506 | − | 0.474034i | \(-0.157203\pi\) | ||||
0.880506 | + | 0.474034i | \(0.157203\pi\) | |||||||
\(368\) | 1.67994 | 0.0875729 | ||||||||
\(369\) | 5.20775 | 0.271105 | ||||||||
\(370\) | 26.2857 | 1.36653 | ||||||||
\(371\) | −1.21983 | −0.0633305 | ||||||||
\(372\) | −8.50604 | −0.441018 | ||||||||
\(373\) | 24.5827 | 1.27284 | 0.636422 | − | 0.771341i | \(-0.280414\pi\) | ||||
0.636422 | + | 0.771341i | \(0.280414\pi\) | |||||||
\(374\) | 1.38835 | 0.0717901 | ||||||||
\(375\) | −2.14675 | −0.110858 | ||||||||
\(376\) | 24.6558 | 1.27152 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.801938 | 0.0412472 | ||||||||
\(379\) | 1.93230 | 0.0992554 | 0.0496277 | − | 0.998768i | \(-0.484197\pi\) | ||||
0.0496277 | + | 0.998768i | \(0.484197\pi\) | |||||||
\(380\) | −5.77586 | −0.296295 | ||||||||
\(381\) | −4.51142 | −0.231127 | ||||||||
\(382\) | 7.31767 | 0.374404 | ||||||||
\(383\) | −18.9638 | −0.969003 | −0.484501 | − | 0.874791i | \(-0.660999\pi\) | ||||
−0.484501 | + | 0.874791i | \(0.660999\pi\) | |||||||
\(384\) | 8.79954 | 0.449050 | ||||||||
\(385\) | 6.58211 | 0.335455 | ||||||||
\(386\) | 5.82717 | 0.296595 | ||||||||
\(387\) | −8.63102 | −0.438740 | ||||||||
\(388\) | 3.15213 | 0.160025 | ||||||||
\(389\) | 17.4711 | 0.885821 | 0.442911 | − | 0.896566i | \(-0.353946\pi\) | ||||
0.442911 | + | 0.896566i | \(0.353946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.42758 | 0.122768 | ||||||||
\(392\) | 2.69202 | 0.135968 | ||||||||
\(393\) | 1.04892 | 0.0529109 | ||||||||
\(394\) | 4.53511 | 0.228475 | ||||||||
\(395\) | 4.07069 | 0.204819 | ||||||||
\(396\) | 2.92931 | 0.147203 | ||||||||
\(397\) | 27.2204 | 1.36615 | 0.683077 | − | 0.730346i | \(-0.260641\pi\) | ||||
0.683077 | + | 0.730346i | \(0.260641\pi\) | |||||||
\(398\) | −13.8649 | −0.694982 | ||||||||
\(399\) | −1.39612 | −0.0698936 | ||||||||
\(400\) | 2.38404 | 0.119202 | ||||||||
\(401\) | −21.3274 | −1.06504 | −0.532519 | − | 0.846418i | \(-0.678754\pi\) | ||||
−0.532519 | + | 0.846418i | \(0.678754\pi\) | |||||||
\(402\) | −10.2567 | −0.511556 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −20.0446 | −0.997256 | ||||||||
\(405\) | 3.04892 | 0.151502 | ||||||||
\(406\) | 1.98254 | 0.0983919 | ||||||||
\(407\) | 23.2088 | 1.15042 | ||||||||
\(408\) | 2.15883 | 0.106878 | ||||||||
\(409\) | −27.2597 | −1.34790 | −0.673952 | − | 0.738776i | \(-0.735404\pi\) | ||||
−0.673952 | + | 0.738776i | \(0.735404\pi\) | |||||||
\(410\) | −12.7332 | −0.628846 | ||||||||
\(411\) | −12.3599 | −0.609668 | ||||||||
\(412\) | 13.7918 | 0.679472 | ||||||||
\(413\) | −8.63102 | −0.424705 | ||||||||
\(414\) | −2.42758 | −0.119309 | ||||||||
\(415\) | −27.2174 | −1.33605 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6015 | 0.666067 | ||||||||
\(418\) | 2.41704 | 0.118221 | ||||||||
\(419\) | 27.2989 | 1.33364 | 0.666819 | − | 0.745220i | \(-0.267655\pi\) | ||||
0.666819 | + | 0.745220i | \(0.267655\pi\) | |||||||
\(420\) | 4.13706 | 0.201868 | ||||||||
\(421\) | −0.817003 | −0.0398183 | −0.0199092 | − | 0.999802i | \(-0.506338\pi\) | ||||
−0.0199092 | + | 0.999802i | \(0.506338\pi\) | |||||||
\(422\) | −7.35258 | −0.357918 | ||||||||
\(423\) | 9.15883 | 0.445318 | ||||||||
\(424\) | 3.28382 | 0.159476 | ||||||||
\(425\) | 3.44504 | 0.167109 | ||||||||
\(426\) | −11.3274 | −0.548812 | ||||||||
\(427\) | 10.0858 | 0.488084 | ||||||||
\(428\) | 23.4450 | 1.13326 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.1032 | 1.01769 | ||||||||
\(431\) | −28.5623 | −1.37580 | −0.687898 | − | 0.725808i | \(-0.741466\pi\) | ||||
−0.687898 | + | 0.725808i | \(0.741466\pi\) | |||||||
\(432\) | 0.554958 | 0.0267004 | ||||||||
\(433\) | −12.5013 | −0.600772 | −0.300386 | − | 0.953818i | \(-0.597115\pi\) | ||||
−0.300386 | + | 0.953818i | \(0.597115\pi\) | |||||||
\(434\) | 5.02715 | 0.241311 | ||||||||
\(435\) | 7.53750 | 0.361395 | ||||||||
\(436\) | −19.3980 | −0.928998 | ||||||||
\(437\) | 4.22627 | 0.202170 | ||||||||
\(438\) | −8.11960 | −0.387970 | ||||||||
\(439\) | 4.28514 | 0.204519 | 0.102259 | − | 0.994758i | \(-0.467393\pi\) | ||||
0.102259 | + | 0.994758i | \(0.467393\pi\) | |||||||
\(440\) | −17.7192 | −0.844728 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.5724 | −0.834891 | −0.417445 | − | 0.908702i | \(-0.637074\pi\) | ||||
−0.417445 | + | 0.908702i | \(0.637074\pi\) | |||||||
\(444\) | 14.5875 | 0.692291 | ||||||||
\(445\) | 7.64071 | 0.362204 | ||||||||
\(446\) | −15.3153 | −0.725199 | ||||||||
\(447\) | −8.33513 | −0.394238 | ||||||||
\(448\) | −3.56465 | −0.168414 | ||||||||
\(449\) | 22.5550 | 1.06443 | 0.532217 | − | 0.846608i | \(-0.321359\pi\) | ||||
0.532217 | + | 0.846608i | \(0.321359\pi\) | |||||||
\(450\) | −3.44504 | −0.162401 | ||||||||
\(451\) | −11.2427 | −0.529397 | ||||||||
\(452\) | −22.0750 | −1.03832 | ||||||||
\(453\) | −11.4819 | −0.539466 | ||||||||
\(454\) | −22.4112 | −1.05181 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.75840 | 0.176003 | ||||||||
\(457\) | 23.7496 | 1.11096 | 0.555479 | − | 0.831531i | \(-0.312535\pi\) | ||||
0.555479 | + | 0.831531i | \(0.312535\pi\) | |||||||
\(458\) | −15.9095 | −0.743400 | ||||||||
\(459\) | 0.801938 | 0.0374312 | ||||||||
\(460\) | −12.5235 | −0.583911 | ||||||||
\(461\) | −13.4657 | −0.627162 | −0.313581 | − | 0.949561i | \(-0.601529\pi\) | ||||
−0.313581 | + | 0.949561i | \(0.601529\pi\) | |||||||
\(462\) | −1.73125 | −0.0805450 | ||||||||
\(463\) | −25.2556 | −1.17373 | −0.586864 | − | 0.809686i | \(-0.699638\pi\) | ||||
−0.586864 | + | 0.809686i | \(0.699638\pi\) | |||||||
\(464\) | 1.37196 | 0.0636917 | ||||||||
\(465\) | 19.1129 | 0.886340 | ||||||||
\(466\) | 4.58211 | 0.212262 | ||||||||
\(467\) | −33.9734 | −1.57210 | −0.786052 | − | 0.618161i | \(-0.787878\pi\) | ||||
−0.786052 | + | 0.618161i | \(0.787878\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7899 | −0.590581 | ||||||||
\(470\) | −22.3937 | −1.03295 | ||||||||
\(471\) | −2.99330 | −0.137924 | ||||||||
\(472\) | 23.2349 | 1.06947 | ||||||||
\(473\) | 18.6329 | 0.856744 | ||||||||
\(474\) | −1.07069 | −0.0491783 | ||||||||
\(475\) | 5.99761 | 0.275189 | ||||||||
\(476\) | 1.08815 | 0.0498751 | ||||||||
\(477\) | 1.21983 | 0.0558523 | ||||||||
\(478\) | 9.12929 | 0.417564 | ||||||||
\(479\) | 0.325437 | 0.0148696 | 0.00743480 | − | 0.999972i | \(-0.497633\pi\) | ||||
0.00743480 | + | 0.999972i | \(0.497633\pi\) | |||||||
\(480\) | −17.7724 | −0.811195 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −21.2034 | −0.965790 | ||||||||
\(483\) | −3.02715 | −0.137740 | ||||||||
\(484\) | 8.60196 | 0.390998 | ||||||||
\(485\) | −7.08277 | −0.321612 | ||||||||
\(486\) | −0.801938 | −0.0363766 | ||||||||
\(487\) | −10.3696 | −0.469890 | −0.234945 | − | 0.972009i | \(-0.575491\pi\) | ||||
−0.234945 | + | 0.972009i | \(0.575491\pi\) | |||||||
\(488\) | −27.1511 | −1.22907 | ||||||||
\(489\) | 15.6353 | 0.707054 | ||||||||
\(490\) | −2.44504 | −0.110456 | ||||||||
\(491\) | −15.6692 | −0.707140 | −0.353570 | − | 0.935408i | \(-0.615032\pi\) | ||||
−0.353570 | + | 0.935408i | \(0.615032\pi\) | |||||||
\(492\) | −7.06638 | −0.318577 | ||||||||
\(493\) | 1.98254 | 0.0892892 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.58211 | −0.295844 | ||||||||
\(496\) | 3.47889 | 0.156207 | ||||||||
\(497\) | −14.1250 | −0.633592 | ||||||||
\(498\) | 7.15883 | 0.320795 | ||||||||
\(499\) | −21.5700 | −0.965607 | −0.482803 | − | 0.875729i | \(-0.660381\pi\) | ||||
−0.482803 | + | 0.875729i | \(0.660381\pi\) | |||||||
\(500\) | 2.91292 | 0.130270 | ||||||||
\(501\) | 6.70171 | 0.299410 | ||||||||
\(502\) | 18.1215 | 0.808803 | ||||||||
\(503\) | −9.46980 | −0.422237 | −0.211119 | − | 0.977460i | \(-0.567711\pi\) | ||||
−0.211119 | + | 0.977460i | \(0.567711\pi\) | |||||||
\(504\) | −2.69202 | −0.119912 | ||||||||
\(505\) | 45.0398 | 2.00425 | ||||||||
\(506\) | 5.24075 | 0.232980 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.12152 | 0.271599 | ||||||||
\(509\) | 5.43834 | 0.241050 | 0.120525 | − | 0.992710i | \(-0.461542\pi\) | ||||
0.120525 | + | 0.992710i | \(0.461542\pi\) | |||||||
\(510\) | −1.96077 | −0.0868244 | ||||||||
\(511\) | −10.1250 | −0.447903 | ||||||||
\(512\) | −6.22282 | −0.275012 | ||||||||
\(513\) | 1.39612 | 0.0616404 | ||||||||
\(514\) | −8.85277 | −0.390479 | ||||||||
\(515\) | −30.9898 | −1.36558 | ||||||||
\(516\) | 11.7114 | 0.515566 | ||||||||
\(517\) | −19.7724 | −0.869589 | ||||||||
\(518\) | −8.62133 | −0.378800 | ||||||||
\(519\) | −7.05131 | −0.309518 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.5424 | −1.64476 | −0.822381 | − | 0.568937i | \(-0.807355\pi\) | ||||
−0.822381 | + | 0.568937i | \(0.807355\pi\) | |||||||
\(522\) | −1.98254 | −0.0867735 | ||||||||
\(523\) | 31.8485 | 1.39264 | 0.696318 | − | 0.717733i | \(-0.254820\pi\) | ||||
0.696318 | + | 0.717733i | \(0.254820\pi\) | |||||||
\(524\) | −1.42327 | −0.0621759 | ||||||||
\(525\) | −4.29590 | −0.187488 | ||||||||
\(526\) | 11.4252 | 0.498162 | ||||||||
\(527\) | 5.02715 | 0.218986 | ||||||||
\(528\) | −1.19806 | −0.0521390 | ||||||||
\(529\) | −13.8364 | −0.601582 | ||||||||
\(530\) | −2.98254 | −0.129553 | ||||||||
\(531\) | 8.63102 | 0.374554 | ||||||||
\(532\) | 1.89440 | 0.0821325 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.00969 | −0.0869677 | ||||||||
\(535\) | −52.6805 | −2.27758 | ||||||||
\(536\) | 34.4306 | 1.48717 | ||||||||
\(537\) | 6.46144 | 0.278832 | ||||||||
\(538\) | −16.3327 | −0.704154 | ||||||||
\(539\) | −2.15883 | −0.0929875 | ||||||||
\(540\) | −4.13706 | −0.178031 | ||||||||
\(541\) | −22.5652 | −0.970155 | −0.485078 | − | 0.874471i | \(-0.661209\pi\) | ||||
−0.485078 | + | 0.874471i | \(0.661209\pi\) | |||||||
\(542\) | −13.6310 | −0.585503 | ||||||||
\(543\) | −0.576728 | −0.0247498 | ||||||||
\(544\) | −4.67456 | −0.200420 | ||||||||
\(545\) | 43.5870 | 1.86706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.1739 | 1.41841 | 0.709207 | − | 0.705001i | \(-0.249053\pi\) | ||||
0.709207 | + | 0.705001i | \(0.249053\pi\) | |||||||
\(548\) | 16.7711 | 0.716425 | ||||||||
\(549\) | −10.0858 | −0.430449 | ||||||||
\(550\) | 7.43727 | 0.317126 | ||||||||
\(551\) | 3.45148 | 0.147038 | ||||||||
\(552\) | 8.14914 | 0.346851 | ||||||||
\(553\) | −1.33513 | −0.0567753 | ||||||||
\(554\) | 12.2392 | 0.519994 | ||||||||
\(555\) | −32.7778 | −1.39134 | ||||||||
\(556\) | −18.4558 | −0.782700 | ||||||||
\(557\) | −23.2838 | −0.986567 | −0.493283 | − | 0.869869i | \(-0.664203\pi\) | ||||
−0.493283 | + | 0.869869i | \(0.664203\pi\) | |||||||
\(558\) | −5.02715 | −0.212816 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.69202 | −0.0715010 | ||||||||
\(561\) | −1.73125 | −0.0730934 | ||||||||
\(562\) | 7.86294 | 0.331678 | ||||||||
\(563\) | 3.26577 | 0.137636 | 0.0688178 | − | 0.997629i | \(-0.478077\pi\) | ||||
0.0688178 | + | 0.997629i | \(0.478077\pi\) | |||||||
\(564\) | −12.4276 | −0.523296 | ||||||||
\(565\) | 49.6021 | 2.08677 | ||||||||
\(566\) | −3.76271 | −0.158158 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 38.0248 | 1.59548 | ||||||||
\(569\) | −22.0780 | −0.925557 | −0.462779 | − | 0.886474i | \(-0.653148\pi\) | ||||
−0.462779 | + | 0.886474i | \(0.653148\pi\) | |||||||
\(570\) | −3.41358 | −0.142979 | ||||||||
\(571\) | −10.8649 | −0.454680 | −0.227340 | − | 0.973815i | \(-0.573003\pi\) | ||||
−0.227340 | + | 0.973815i | \(0.573003\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.12498 | −0.381202 | ||||||||
\(574\) | 4.17629 | 0.174315 | ||||||||
\(575\) | 13.0043 | 0.542317 | ||||||||
\(576\) | 3.56465 | 0.148527 | ||||||||
\(577\) | −10.5526 | −0.439309 | −0.219655 | − | 0.975578i | \(-0.570493\pi\) | ||||
−0.219655 | + | 0.975578i | \(0.570493\pi\) | |||||||
\(578\) | 13.1172 | 0.545604 | ||||||||
\(579\) | −7.26636 | −0.301979 | ||||||||
\(580\) | −10.2276 | −0.424678 | ||||||||
\(581\) | 8.92692 | 0.370351 | ||||||||
\(582\) | 1.86294 | 0.0772212 | ||||||||
\(583\) | −2.63342 | −0.109065 | ||||||||
\(584\) | 27.2567 | 1.12789 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.8761 | −0.697145 | ||||||||
\(587\) | 1.95971 | 0.0808857 | 0.0404429 | − | 0.999182i | \(-0.487123\pi\) | ||||
0.0404429 | + | 0.999182i | \(0.487123\pi\) | |||||||
\(588\) | −1.35690 | −0.0559574 | ||||||||
\(589\) | 8.75196 | 0.360618 | ||||||||
\(590\) | −21.1032 | −0.868805 | ||||||||
\(591\) | −5.65519 | −0.232623 | ||||||||
\(592\) | −5.96615 | −0.245207 | ||||||||
\(593\) | −40.9178 | −1.68029 | −0.840147 | − | 0.542359i | \(-0.817531\pi\) | ||||
−0.840147 | + | 0.542359i | \(0.817531\pi\) | |||||||
\(594\) | 1.73125 | 0.0710341 | ||||||||
\(595\) | −2.44504 | −0.100237 | ||||||||
\(596\) | 11.3099 | 0.463271 | ||||||||
\(597\) | 17.2892 | 0.707600 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.7875 | 0.645058 | 0.322529 | − | 0.946560i | \(-0.395467\pi\) | ||||
0.322529 | + | 0.946560i | \(0.395467\pi\) | |||||||
\(600\) | 11.5646 | 0.472125 | ||||||||
\(601\) | −14.1782 | −0.578341 | −0.289171 | − | 0.957278i | \(-0.593380\pi\) | ||||
−0.289171 | + | 0.957278i | \(0.593380\pi\) | |||||||
\(602\) | −6.92154 | −0.282101 | ||||||||
\(603\) | 12.7899 | 0.520843 | ||||||||
\(604\) | 15.5797 | 0.633930 | ||||||||
\(605\) | −19.3284 | −0.785812 | ||||||||
\(606\) | −11.8465 | −0.481233 | ||||||||
\(607\) | −33.6222 | −1.36468 | −0.682341 | − | 0.731034i | \(-0.739038\pi\) | ||||
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(608\) | −8.13813 | −0.330045 | ||||||||
\(609\) | −2.47219 | −0.100178 | ||||||||
\(610\) | 24.6601 | 0.998458 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.08815 | −0.0439857 | ||||||||
\(613\) | −38.7157 | −1.56371 | −0.781856 | − | 0.623459i | \(-0.785727\pi\) | ||||
−0.781856 | + | 0.623459i | \(0.785727\pi\) | |||||||
\(614\) | −10.2760 | −0.414707 | ||||||||
\(615\) | 15.8780 | 0.640263 | ||||||||
\(616\) | 5.81163 | 0.234157 | ||||||||
\(617\) | −28.1696 | −1.13406 | −0.567032 | − | 0.823695i | \(-0.691909\pi\) | ||||
−0.567032 | + | 0.823695i | \(0.691909\pi\) | |||||||
\(618\) | 8.15106 | 0.327884 | ||||||||
\(619\) | 13.0556 | 0.524750 | 0.262375 | − | 0.964966i | \(-0.415494\pi\) | ||||
0.262375 | + | 0.964966i | \(0.415494\pi\) | |||||||
\(620\) | −25.9342 | −1.04154 | ||||||||
\(621\) | 3.02715 | 0.121475 | ||||||||
\(622\) | −7.34827 | −0.294639 | ||||||||
\(623\) | −2.50604 | −0.100402 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.0248 | −1.12099 | ||||||||
\(626\) | −8.87608 | −0.354760 | ||||||||
\(627\) | −3.01400 | −0.120368 | ||||||||
\(628\) | 4.06159 | 0.162075 | ||||||||
\(629\) | −8.62133 | −0.343755 | ||||||||
\(630\) | 2.44504 | 0.0974128 | ||||||||
\(631\) | 26.9869 | 1.07433 | 0.537165 | − | 0.843477i | \(-0.319495\pi\) | ||||
0.537165 | + | 0.843477i | \(0.319495\pi\) | |||||||
\(632\) | 3.59419 | 0.142969 | ||||||||
\(633\) | 9.16852 | 0.364416 | ||||||||
\(634\) | −12.7845 | −0.507737 | ||||||||
\(635\) | −13.7549 | −0.545848 | ||||||||
\(636\) | −1.65519 | −0.0656324 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.27998 | 0.169446 | ||||||||
\(639\) | 14.1250 | 0.558776 | ||||||||
\(640\) | 26.8291 | 1.06051 | ||||||||
\(641\) | 40.1323 | 1.58513 | 0.792565 | − | 0.609788i | \(-0.208745\pi\) | ||||
0.792565 | + | 0.609788i | \(0.208745\pi\) | |||||||
\(642\) | 13.8562 | 0.546862 | ||||||||
\(643\) | 34.7560 | 1.37064 | 0.685322 | − | 0.728241i | \(-0.259662\pi\) | ||||
0.685322 | + | 0.728241i | \(0.259662\pi\) | |||||||
\(644\) | 4.10752 | 0.161859 | ||||||||
\(645\) | −26.3153 | −1.03616 | ||||||||
\(646\) | −0.897853 | −0.0353256 | ||||||||
\(647\) | −4.08947 | −0.160774 | −0.0803869 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803869 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(648\) | 2.69202 | 0.105753 | ||||||||
\(649\) | −18.6329 | −0.731407 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.26875 | −0.245692 | ||||||||
\(652\) | −21.2155 | −0.830864 | ||||||||
\(653\) | −14.2319 | −0.556938 | −0.278469 | − | 0.960445i | \(-0.589827\pi\) | ||||
−0.278469 | + | 0.960445i | \(0.589827\pi\) | |||||||
\(654\) | −11.4644 | −0.448294 | ||||||||
\(655\) | 3.19806 | 0.124959 | ||||||||
\(656\) | 2.89008 | 0.112839 | ||||||||
\(657\) | 10.1250 | 0.395013 | ||||||||
\(658\) | 7.34481 | 0.286331 | ||||||||
\(659\) | 23.0696 | 0.898665 | 0.449332 | − | 0.893365i | \(-0.351662\pi\) | ||||
0.449332 | + | 0.893365i | \(0.351662\pi\) | |||||||
\(660\) | 8.93123 | 0.347648 | ||||||||
\(661\) | 11.3545 | 0.441639 | 0.220819 | − | 0.975315i | \(-0.429127\pi\) | ||||
0.220819 | + | 0.975315i | \(0.429127\pi\) | |||||||
\(662\) | 4.27221 | 0.166044 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.0315 | −0.932601 | ||||||||
\(665\) | −4.25667 | −0.165067 | ||||||||
\(666\) | 8.62133 | 0.334070 | ||||||||
\(667\) | 7.48368 | 0.289769 | ||||||||
\(668\) | −9.09352 | −0.351839 | ||||||||
\(669\) | 19.0978 | 0.738365 | ||||||||
\(670\) | −31.2717 | −1.20813 | ||||||||
\(671\) | 21.7735 | 0.840555 | ||||||||
\(672\) | 5.82908 | 0.224862 | ||||||||
\(673\) | 47.0960 | 1.81542 | 0.907709 | − | 0.419600i | \(-0.137829\pi\) | ||||
0.907709 | + | 0.419600i | \(0.137829\pi\) | |||||||
\(674\) | 23.7323 | 0.914135 | ||||||||
\(675\) | 4.29590 | 0.165349 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.0653 | −0.771173 | −0.385586 | − | 0.922672i | \(-0.626001\pi\) | ||||
−0.385586 | + | 0.922672i | \(0.626001\pi\) | |||||||
\(678\) | −13.0465 | −0.501049 | ||||||||
\(679\) | 2.32304 | 0.0891502 | ||||||||
\(680\) | 6.58211 | 0.252412 | ||||||||
\(681\) | 27.9463 | 1.07090 | ||||||||
\(682\) | 10.8528 | 0.415574 | ||||||||
\(683\) | 33.9715 | 1.29988 | 0.649942 | − | 0.759984i | \(-0.274793\pi\) | ||||
0.649942 | + | 0.759984i | \(0.274793\pi\) | |||||||
\(684\) | −1.89440 | −0.0724340 | ||||||||
\(685\) | −37.6843 | −1.43984 | ||||||||
\(686\) | 0.801938 | 0.0306181 | ||||||||
\(687\) | 19.8388 | 0.756896 | ||||||||
\(688\) | −4.78986 | −0.182612 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.40150 | −0.281770 | ||||||||
\(691\) | 33.7845 | 1.28522 | 0.642611 | − | 0.766193i | \(-0.277851\pi\) | ||||
0.642611 | + | 0.766193i | \(0.277851\pi\) | |||||||
\(692\) | 9.56789 | 0.363717 | ||||||||
\(693\) | 2.15883 | 0.0820073 | ||||||||
\(694\) | −16.2567 | −0.617095 | ||||||||
\(695\) | 41.4698 | 1.57304 | ||||||||
\(696\) | 6.65519 | 0.252264 | ||||||||
\(697\) | 4.17629 | 0.158188 | ||||||||
\(698\) | 9.64933 | 0.365233 | ||||||||
\(699\) | −5.71379 | −0.216115 | ||||||||
\(700\) | 5.82908 | 0.220319 | ||||||||
\(701\) | −2.13036 | −0.0804625 | −0.0402313 | − | 0.999190i | \(-0.512809\pi\) | ||||
−0.0402313 | + | 0.999190i | \(0.512809\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0092 | −0.566083 | ||||||||
\(704\) | −7.69548 | −0.290034 | ||||||||
\(705\) | 27.9245 | 1.05170 | ||||||||
\(706\) | 27.8146 | 1.04682 | ||||||||
\(707\) | −14.7724 | −0.555573 | ||||||||
\(708\) | −11.7114 | −0.440141 | ||||||||
\(709\) | −30.2180 | −1.13486 | −0.567431 | − | 0.823421i | \(-0.692063\pi\) | ||||
−0.567431 | + | 0.823421i | \(0.692063\pi\) | |||||||
\(710\) | −34.5362 | −1.29612 | ||||||||
\(711\) | 1.33513 | 0.0500711 | ||||||||
\(712\) | 6.74632 | 0.252829 | ||||||||
\(713\) | 18.9764 | 0.710673 | ||||||||
\(714\) | 0.643104 | 0.0240676 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.76749 | −0.327657 | ||||||||
\(717\) | −11.3840 | −0.425145 | ||||||||
\(718\) | −23.7366 | −0.885843 | ||||||||
\(719\) | 9.88577 | 0.368677 | 0.184339 | − | 0.982863i | \(-0.440986\pi\) | ||||
0.184339 | + | 0.982863i | \(0.440986\pi\) | |||||||
\(720\) | 1.69202 | 0.0630579 | ||||||||
\(721\) | 10.1642 | 0.378535 | ||||||||
\(722\) | 13.6737 | 0.508883 | ||||||||
\(723\) | 26.4403 | 0.983324 | ||||||||
\(724\) | 0.782560 | 0.0290836 | ||||||||
\(725\) | 10.6203 | 0.394427 | ||||||||
\(726\) | 5.08383 | 0.188679 | ||||||||
\(727\) | −23.5579 | −0.873716 | −0.436858 | − | 0.899531i | \(-0.643909\pi\) | ||||
−0.436858 | + | 0.899531i | \(0.643909\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −24.7560 | −0.916261 | ||||||||
\(731\) | −6.92154 | −0.256003 | ||||||||
\(732\) | 13.6853 | 0.505824 | ||||||||
\(733\) | −0.958852 | −0.0354160 | −0.0177080 | − | 0.999843i | \(-0.505637\pi\) | ||||
−0.0177080 | + | 0.999843i | \(0.505637\pi\) | |||||||
\(734\) | −27.0543 | −0.998592 | ||||||||
\(735\) | 3.04892 | 0.112461 | ||||||||
\(736\) | −17.6455 | −0.650422 | ||||||||
\(737\) | −27.6112 | −1.01707 | ||||||||
\(738\) | −4.17629 | −0.153731 | ||||||||
\(739\) | 2.06339 | 0.0759031 | 0.0379515 | − | 0.999280i | \(-0.487917\pi\) | ||||
0.0379515 | + | 0.999280i | \(0.487917\pi\) | |||||||
\(740\) | 44.4760 | 1.63497 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.978230 | 0.0359119 | ||||||||
\(743\) | −43.4494 | −1.59400 | −0.797001 | − | 0.603978i | \(-0.793582\pi\) | ||||
−0.797001 | + | 0.603978i | \(0.793582\pi\) | |||||||
\(744\) | 16.8756 | 0.618690 | ||||||||
\(745\) | −25.4131 | −0.931064 | ||||||||
\(746\) | −19.7138 | −0.721773 | ||||||||
\(747\) | −8.92692 | −0.326619 | ||||||||
\(748\) | 2.34913 | 0.0858926 | ||||||||
\(749\) | 17.2784 | 0.631340 | ||||||||
\(750\) | 1.72156 | 0.0628625 | ||||||||
\(751\) | −33.7778 | −1.23257 | −0.616284 | − | 0.787524i | \(-0.711363\pi\) | ||||
−0.616284 | + | 0.787524i | \(0.711363\pi\) | |||||||
\(752\) | 5.08277 | 0.185350 | ||||||||
\(753\) | −22.5972 | −0.823487 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35.0073 | −1.27405 | ||||||||
\(756\) | 1.35690 | 0.0493498 | ||||||||
\(757\) | −45.0525 | −1.63746 | −0.818730 | − | 0.574178i | \(-0.805322\pi\) | ||||
−0.818730 | + | 0.574178i | \(0.805322\pi\) | |||||||
\(758\) | −1.54958 | −0.0562833 | ||||||||
\(759\) | −6.53511 | −0.237209 | ||||||||
\(760\) | 11.4590 | 0.415663 | ||||||||
\(761\) | −18.8605 | −0.683694 | −0.341847 | − | 0.939756i | \(-0.611052\pi\) | ||||
−0.341847 | + | 0.939756i | \(0.611052\pi\) | |||||||
\(762\) | 3.61788 | 0.131062 | ||||||||
\(763\) | −14.2959 | −0.517546 | ||||||||
\(764\) | 12.3817 | 0.447952 | ||||||||
\(765\) | 2.44504 | 0.0884007 | ||||||||
\(766\) | 15.2078 | 0.549478 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −14.1860 | −0.511892 | ||||||||
\(769\) | 6.20642 | 0.223809 | 0.111905 | − | 0.993719i | \(-0.464305\pi\) | ||||
0.111905 | + | 0.993719i | \(0.464305\pi\) | |||||||
\(770\) | −5.27844 | −0.190222 | ||||||||
\(771\) | 11.0392 | 0.397568 | ||||||||
\(772\) | 9.85969 | 0.354858 | ||||||||
\(773\) | −14.9299 | −0.536991 | −0.268496 | − | 0.963281i | \(-0.586526\pi\) | ||||
−0.268496 | + | 0.963281i | \(0.586526\pi\) | |||||||
\(774\) | 6.92154 | 0.248790 | ||||||||
\(775\) | 26.9299 | 0.967351 | ||||||||
\(776\) | −6.25368 | −0.224494 | ||||||||
\(777\) | 10.7506 | 0.385677 | ||||||||
\(778\) | −14.0108 | −0.502310 | ||||||||
\(779\) | 7.27067 | 0.260499 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.4935 | −1.09114 | ||||||||
\(782\) | −1.94677 | −0.0696164 | ||||||||
\(783\) | 2.47219 | 0.0883488 | ||||||||
\(784\) | 0.554958 | 0.0198199 | ||||||||
\(785\) | −9.12631 | −0.325732 | ||||||||
\(786\) | −0.841166 | −0.0300034 | ||||||||
\(787\) | 48.2174 | 1.71877 | 0.859383 | − | 0.511332i | \(-0.170848\pi\) | ||||
0.859383 | + | 0.511332i | \(0.170848\pi\) | |||||||
\(788\) | 7.67350 | 0.273357 | ||||||||
\(789\) | −14.2470 | −0.507206 | ||||||||
\(790\) | −3.26444 | −0.116143 | ||||||||
\(791\) | −16.2687 | −0.578450 | ||||||||
\(792\) | −5.81163 | −0.206507 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21.8291 | −0.774685 | ||||||||
\(795\) | 3.71917 | 0.131905 | ||||||||
\(796\) | −23.4596 | −0.831505 | ||||||||
\(797\) | 23.5284 | 0.833419 | 0.416709 | − | 0.909040i | \(-0.363183\pi\) | ||||
0.416709 | + | 0.909040i | \(0.363183\pi\) | |||||||
\(798\) | 1.11960 | 0.0396336 | ||||||||
\(799\) | 7.34481 | 0.259841 | ||||||||
\(800\) | −25.0411 | −0.885338 | ||||||||
\(801\) | 2.50604 | 0.0885466 | ||||||||
\(802\) | 17.1032 | 0.603935 | ||||||||
\(803\) | −21.8582 | −0.771357 | ||||||||
\(804\) | −17.3545 | −0.612046 | ||||||||
\(805\) | −9.22952 | −0.325298 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.3666 | 0.716938 | ||||||||
\(808\) | 39.7676 | 1.39902 | ||||||||
\(809\) | −47.3997 | −1.66648 | −0.833242 | − | 0.552908i | \(-0.813518\pi\) | ||||
−0.833242 | + | 0.552908i | \(0.813518\pi\) | |||||||
\(810\) | −2.44504 | −0.0859100 | ||||||||
\(811\) | −14.4125 | −0.506092 | −0.253046 | − | 0.967454i | \(-0.581432\pi\) | ||||
−0.253046 | + | 0.967454i | \(0.581432\pi\) | |||||||
\(812\) | 3.35450 | 0.117720 | ||||||||
\(813\) | 16.9976 | 0.596132 | ||||||||
\(814\) | −18.6120 | −0.652351 | ||||||||
\(815\) | 47.6708 | 1.66984 | ||||||||
\(816\) | 0.445042 | 0.0155796 | ||||||||
\(817\) | −12.0500 | −0.421576 | ||||||||
\(818\) | 21.8605 | 0.764336 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.5448 | −0.752377 | ||||||||
\(821\) | −19.9409 | −0.695943 | −0.347971 | − | 0.937505i | \(-0.613129\pi\) | ||||
−0.347971 | + | 0.937505i | \(0.613129\pi\) | |||||||
\(822\) | 9.91185 | 0.345716 | ||||||||
\(823\) | 31.3961 | 1.09440 | 0.547200 | − | 0.837002i | \(-0.315694\pi\) | ||||
0.547200 | + | 0.837002i | \(0.315694\pi\) | |||||||
\(824\) | −27.3623 | −0.953210 | ||||||||
\(825\) | −9.27413 | −0.322884 | ||||||||
\(826\) | 6.92154 | 0.240831 | ||||||||
\(827\) | 15.5109 | 0.539368 | 0.269684 | − | 0.962949i | \(-0.413081\pi\) | ||||
0.269684 | + | 0.962949i | \(0.413081\pi\) | |||||||
\(828\) | −4.10752 | −0.142746 | ||||||||
\(829\) | −37.5362 | −1.30369 | −0.651843 | − | 0.758354i | \(-0.726004\pi\) | ||||
−0.651843 | + | 0.758354i | \(0.726004\pi\) | |||||||
\(830\) | 21.8267 | 0.757616 | ||||||||
\(831\) | −15.2620 | −0.529434 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.801938 | 0.0277855 | ||||||||
\(834\) | −10.9075 | −0.377697 | ||||||||
\(835\) | 20.4330 | 0.707112 | ||||||||
\(836\) | 4.08968 | 0.141445 | ||||||||
\(837\) | 6.26875 | 0.216680 | ||||||||
\(838\) | −21.8920 | −0.756247 | ||||||||
\(839\) | −27.6122 | −0.953280 | −0.476640 | − | 0.879099i | \(-0.658146\pi\) | ||||
−0.476640 | + | 0.879099i | \(0.658146\pi\) | |||||||
\(840\) | −8.20775 | −0.283194 | ||||||||
\(841\) | −22.8883 | −0.789251 | ||||||||
\(842\) | 0.655186 | 0.0225792 | ||||||||
\(843\) | −9.80492 | −0.337699 | ||||||||
\(844\) | −12.4407 | −0.428228 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.34481 | −0.252520 | ||||||||
\(847\) | 6.33944 | 0.217826 | ||||||||
\(848\) | 0.676956 | 0.0232468 | ||||||||
\(849\) | 4.69202 | 0.161030 | ||||||||
\(850\) | −2.76271 | −0.0947601 | ||||||||
\(851\) | −32.5437 | −1.11558 | ||||||||
\(852\) | −19.1661 | −0.656621 | ||||||||
\(853\) | 30.2314 | 1.03510 | 0.517552 | − | 0.855652i | \(-0.326843\pi\) | ||||
0.517552 | + | 0.855652i | \(0.326843\pi\) | |||||||
\(854\) | −8.08815 | −0.276771 | ||||||||
\(855\) | 4.25667 | 0.145575 | ||||||||
\(856\) | −46.5139 | −1.58981 | ||||||||
\(857\) | −14.4179 | −0.492506 | −0.246253 | − | 0.969206i | \(-0.579199\pi\) | ||||
−0.246253 | + | 0.969206i | \(0.579199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.8062 | −0.573422 | −0.286711 | − | 0.958017i | \(-0.592562\pi\) | ||||
−0.286711 | + | 0.958017i | \(0.592562\pi\) | |||||||
\(860\) | 35.7071 | 1.21760 | ||||||||
\(861\) | −5.20775 | −0.177480 | ||||||||
\(862\) | 22.9051 | 0.780152 | ||||||||
\(863\) | −17.9608 | −0.611392 | −0.305696 | − | 0.952129i | \(-0.598889\pi\) | ||||
−0.305696 | + | 0.952129i | \(0.598889\pi\) | |||||||
\(864\) | −5.82908 | −0.198309 | ||||||||
\(865\) | −21.4989 | −0.730983 | ||||||||
\(866\) | 10.0252 | 0.340671 | ||||||||
\(867\) | −16.3569 | −0.555509 | ||||||||
\(868\) | 8.50604 | 0.288714 | ||||||||
\(869\) | −2.88231 | −0.0977758 | ||||||||
\(870\) | −6.04461 | −0.204931 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 38.4849 | 1.30326 | ||||||||
\(873\) | −2.32304 | −0.0786231 | ||||||||
\(874\) | −3.38921 | −0.114642 | ||||||||
\(875\) | 2.14675 | 0.0725735 | ||||||||
\(876\) | −13.7385 | −0.464182 | ||||||||
\(877\) | −20.3744 | −0.687993 | −0.343997 | − | 0.938971i | \(-0.611781\pi\) | ||||
−0.343997 | + | 0.938971i | \(0.611781\pi\) | |||||||
\(878\) | −3.43642 | −0.115973 | ||||||||
\(879\) | 21.0441 | 0.709801 | ||||||||
\(880\) | −3.65279 | −0.123136 | ||||||||
\(881\) | 11.0425 | 0.372030 | 0.186015 | − | 0.982547i | \(-0.440443\pi\) | ||||
0.186015 | + | 0.982547i | \(0.440443\pi\) | |||||||
\(882\) | −0.801938 | −0.0270026 | ||||||||
\(883\) | −53.5260 | −1.80129 | −0.900647 | − | 0.434552i | \(-0.856907\pi\) | ||||
−0.900647 | + | 0.434552i | \(0.856907\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.3153 | 0.884578 | ||||||||
\(886\) | 14.0920 | 0.473429 | ||||||||
\(887\) | 39.7706 | 1.33537 | 0.667683 | − | 0.744446i | \(-0.267286\pi\) | ||||
0.667683 | + | 0.744446i | \(0.267286\pi\) | |||||||
\(888\) | −28.9409 | −0.971194 | ||||||||
\(889\) | 4.51142 | 0.151308 | ||||||||
\(890\) | −6.12737 | −0.205390 | ||||||||
\(891\) | −2.15883 | −0.0723236 | ||||||||
\(892\) | −25.9138 | −0.867657 | ||||||||
\(893\) | 12.7869 | 0.427896 | ||||||||
\(894\) | 6.68425 | 0.223555 | ||||||||
\(895\) | 19.7004 | 0.658511 | ||||||||
\(896\) | −8.79954 | −0.293972 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.0877 | −0.603593 | ||||||||
\(899\) | 15.4975 | 0.516872 | ||||||||
\(900\) | −5.82908 | −0.194303 | ||||||||
\(901\) | 0.978230 | 0.0325896 | ||||||||
\(902\) | 9.01592 | 0.300197 | ||||||||
\(903\) | 8.63102 | 0.287222 | ||||||||
\(904\) | 43.7958 | 1.45663 | ||||||||
\(905\) | −1.75840 | −0.0584511 | ||||||||
\(906\) | 9.20775 | 0.305907 | ||||||||
\(907\) | −13.5381 | −0.449525 | −0.224762 | − | 0.974414i | \(-0.572161\pi\) | ||||
−0.224762 | + | 0.974414i | \(0.572161\pi\) | |||||||
\(908\) | −37.9202 | −1.25843 | ||||||||
\(909\) | 14.7724 | 0.489970 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.19434 | −0.138965 | −0.0694824 | − | 0.997583i | \(-0.522135\pi\) | ||||
−0.0694824 | + | 0.997583i | \(0.522135\pi\) | |||||||
\(912\) | 0.774791 | 0.0256559 | ||||||||
\(913\) | 19.2717 | 0.637801 | ||||||||
\(914\) | −19.0457 | −0.629975 | ||||||||
\(915\) | −30.7506 | −1.01658 | ||||||||
\(916\) | −26.9191 | −0.889434 | ||||||||
\(917\) | −1.04892 | −0.0346383 | ||||||||
\(918\) | −0.643104 | −0.0212256 | ||||||||
\(919\) | 1.94630 | 0.0642024 | 0.0321012 | − | 0.999485i | \(-0.489780\pi\) | ||||
0.0321012 | + | 0.999485i | \(0.489780\pi\) | |||||||
\(920\) | 24.8461 | 0.819151 | ||||||||
\(921\) | 12.8140 | 0.422236 | ||||||||
\(922\) | 10.7987 | 0.355636 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.92931 | −0.0963673 | ||||||||
\(925\) | −46.1836 | −1.51851 | ||||||||
\(926\) | 20.2534 | 0.665569 | ||||||||
\(927\) | −10.1642 | −0.333836 | ||||||||
\(928\) | −14.4106 | −0.473051 | ||||||||
\(929\) | 24.5948 | 0.806928 | 0.403464 | − | 0.914995i | \(-0.367806\pi\) | ||||
0.403464 | + | 0.914995i | \(0.367806\pi\) | |||||||
\(930\) | −15.3274 | −0.502604 | ||||||||
\(931\) | 1.39612 | 0.0457561 | ||||||||
\(932\) | 7.75302 | 0.253959 | ||||||||
\(933\) | 9.16315 | 0.299988 | ||||||||
\(934\) | 27.2446 | 0.891470 | ||||||||
\(935\) | −5.27844 | −0.172623 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.88663 | −0.322982 | −0.161491 | − | 0.986874i | \(-0.551630\pi\) | ||||
−0.161491 | + | 0.986874i | \(0.551630\pi\) | |||||||
\(938\) | 10.2567 | 0.334892 | ||||||||
\(939\) | 11.0683 | 0.361200 | ||||||||
\(940\) | −37.8907 | −1.23586 | ||||||||
\(941\) | −23.1468 | −0.754563 | −0.377281 | − | 0.926099i | \(-0.623141\pi\) | ||||
−0.377281 | + | 0.926099i | \(0.623141\pi\) | |||||||
\(942\) | 2.40044 | 0.0782104 | ||||||||
\(943\) | 15.7646 | 0.513367 | ||||||||
\(944\) | 4.78986 | 0.155897 | ||||||||
\(945\) | −3.04892 | −0.0991813 | ||||||||
\(946\) | −14.9425 | −0.485821 | ||||||||
\(947\) | −14.2903 | −0.464371 | −0.232185 | − | 0.972672i | \(-0.574588\pi\) | ||||
−0.232185 | + | 0.972672i | \(0.574588\pi\) | |||||||
\(948\) | −1.81163 | −0.0588389 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.80971 | −0.156048 | ||||||||
\(951\) | 15.9420 | 0.516954 | ||||||||
\(952\) | −2.15883 | −0.0699682 | ||||||||
\(953\) | −51.5411 | −1.66958 | −0.834790 | − | 0.550569i | \(-0.814411\pi\) | ||||
−0.834790 | + | 0.550569i | \(0.814411\pi\) | |||||||
\(954\) | −0.978230 | −0.0316714 | ||||||||
\(955\) | −27.8213 | −0.900277 | ||||||||
\(956\) | 15.4470 | 0.499590 | ||||||||
\(957\) | −5.33704 | −0.172522 | ||||||||
\(958\) | −0.260980 | −0.00843189 | ||||||||
\(959\) | 12.3599 | 0.399121 | ||||||||
\(960\) | 10.8683 | 0.350773 | ||||||||
\(961\) | 8.29722 | 0.267652 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.2784 | −0.556790 | ||||||||
\(964\) | −35.8767 | −1.15551 | ||||||||
\(965\) | −22.1545 | −0.713179 | ||||||||
\(966\) | 2.42758 | 0.0781062 | ||||||||
\(967\) | 20.0944 | 0.646192 | 0.323096 | − | 0.946366i | \(-0.395276\pi\) | ||||
0.323096 | + | 0.946366i | \(0.395276\pi\) | |||||||
\(968\) | −17.0659 | −0.548519 | ||||||||
\(969\) | 1.11960 | 0.0359669 | ||||||||
\(970\) | 5.67994 | 0.182372 | ||||||||
\(971\) | −37.9181 | −1.21685 | −0.608425 | − | 0.793612i | \(-0.708198\pi\) | ||||
−0.608425 | + | 0.793612i | \(0.708198\pi\) | |||||||
\(972\) | −1.35690 | −0.0435225 | ||||||||
\(973\) | −13.6015 | −0.436044 | ||||||||
\(974\) | 8.31575 | 0.266454 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.59717 | −0.179161 | ||||||||
\(977\) | 2.92931 | 0.0937170 | 0.0468585 | − | 0.998902i | \(-0.485079\pi\) | ||||
0.0468585 | + | 0.998902i | \(0.485079\pi\) | |||||||
\(978\) | −12.5386 | −0.400939 | ||||||||
\(979\) | −5.41013 | −0.172908 | ||||||||
\(980\) | −4.13706 | −0.132154 | ||||||||
\(981\) | 14.2959 | 0.456433 | ||||||||
\(982\) | 12.5657 | 0.400988 | ||||||||
\(983\) | −59.9879 | −1.91332 | −0.956659 | − | 0.291211i | \(-0.905942\pi\) | ||||
−0.956659 | + | 0.291211i | \(0.905942\pi\) | |||||||
\(984\) | 14.0194 | 0.446921 | ||||||||
\(985\) | −17.2422 | −0.549382 | ||||||||
\(986\) | −1.58987 | −0.0506319 | ||||||||
\(987\) | −9.15883 | −0.291529 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.1274 | −0.830802 | ||||||||
\(990\) | 5.27844 | 0.167760 | ||||||||
\(991\) | 8.83818 | 0.280754 | 0.140377 | − | 0.990098i | \(-0.455169\pi\) | ||||
0.140377 | + | 0.990098i | \(0.455169\pi\) | |||||||
\(992\) | −36.5411 | −1.16018 | ||||||||
\(993\) | −5.32736 | −0.169059 | ||||||||
\(994\) | 11.3274 | 0.359282 | ||||||||
\(995\) | 52.7133 | 1.67112 | ||||||||
\(996\) | 12.1129 | 0.383812 | ||||||||
\(997\) | −31.7077 | −1.00419 | −0.502096 | − | 0.864812i | \(-0.667438\pi\) | ||||
−0.502096 | + | 0.864812i | \(0.667438\pi\) | |||||||
\(998\) | 17.2978 | 0.547553 | ||||||||
\(999\) | −10.7506 | −0.340135 |
(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 | 3549.2.a.u.1.1 | 3 | ||
13.4 | even | 6 | 273.2.k.c.211.1 | yes | 6 | ||
13.10 | even | 6 | 273.2.k.c.22.1 | ✓ | 6 | ||
13.12 | even | 2 | 3549.2.a.i.1.3 | 3 | |||
39.17 | odd | 6 | 819.2.o.e.757.3 | 6 | |||
39.23 | odd | 6 | 819.2.o.e.568.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.k.c.22.1 | ✓ | 6 | 13.10 | even | 6 | ||
273.2.k.c.211.1 | yes | 6 | 13.4 | even | 6 | ||
819.2.o.e.568.3 | 6 | 39.23 | odd | 6 | |||
819.2.o.e.757.3 | 6 | 39.17 | odd | 6 | |||
3549.2.a.i.1.3 | 3 | 13.12 | even | 2 | |||
3549.2.a.u.1.1 | 3 | 1.1 | even | 1 | trivial |