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: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.473.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 5x - 1 \) |
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 | \(-2.12842\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12842 | −1.50502 | −0.752510 | − | 0.658581i | \(-0.771157\pi\) | ||||
−0.752510 | + | 0.658581i | \(0.771157\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.53017 | 1.26508 | ||||||||
\(5\) | 2.65859 | 1.18896 | 0.594478 | − | 0.804112i | \(-0.297359\pi\) | ||||
0.594478 | + | 0.804112i | \(0.297359\pi\) | |||||||
\(6\) | 2.12842 | 0.868923 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.12842 | −0.398956 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.65859 | −1.78940 | ||||||||
\(11\) | 0.658587 | 0.198571 | 0.0992857 | − | 0.995059i | \(-0.468344\pi\) | ||||
0.0992857 | + | 0.995059i | \(0.468344\pi\) | |||||||
\(12\) | −2.53017 | −0.730397 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.12842 | 0.568844 | ||||||||
\(15\) | −2.65859 | −0.686444 | ||||||||
\(16\) | −2.65859 | −0.664647 | ||||||||
\(17\) | 6.12842 | 1.48636 | 0.743180 | − | 0.669092i | \(-0.233317\pi\) | ||||
0.743180 | + | 0.669092i | \(0.233317\pi\) | |||||||
\(18\) | −2.12842 | −0.501673 | ||||||||
\(19\) | −5.25684 | −1.20600 | −0.603001 | − | 0.797741i | \(-0.706028\pi\) | ||||
−0.603001 | + | 0.797741i | \(0.706028\pi\) | |||||||
\(20\) | 6.72667 | 1.50413 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.40175 | −0.298854 | ||||||||
\(23\) | −3.53017 | −0.736091 | −0.368045 | − | 0.929808i | \(-0.619973\pi\) | ||||
−0.368045 | + | 0.929808i | \(0.619973\pi\) | |||||||
\(24\) | 1.12842 | 0.230338 | ||||||||
\(25\) | 2.06808 | 0.413617 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.53017 | −0.478157 | ||||||||
\(29\) | 0.871581 | 0.161849 | 0.0809243 | − | 0.996720i | \(-0.474213\pi\) | ||||
0.0809243 | + | 0.996720i | \(0.474213\pi\) | |||||||
\(30\) | 5.65859 | 1.03311 | ||||||||
\(31\) | 5.91542 | 1.06244 | 0.531221 | − | 0.847233i | \(-0.321733\pi\) | ||||
0.531221 | + | 0.847233i | \(0.321733\pi\) | |||||||
\(32\) | 7.91542 | 1.39926 | ||||||||
\(33\) | −0.658587 | −0.114645 | ||||||||
\(34\) | −13.0438 | −2.23700 | ||||||||
\(35\) | −2.65859 | −0.449383 | ||||||||
\(36\) | 2.53017 | 0.421695 | ||||||||
\(37\) | −1.46208 | −0.240365 | −0.120183 | − | 0.992752i | \(-0.538348\pi\) | ||||
−0.120183 | + | 0.992752i | \(0.538348\pi\) | |||||||
\(38\) | 11.1888 | 1.81506 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00000 | −0.474342 | ||||||||
\(41\) | −10.5137 | −1.64196 | −0.820980 | − | 0.570957i | \(-0.806572\pi\) | ||||
−0.820980 | + | 0.570957i | \(0.806572\pi\) | |||||||
\(42\) | −2.12842 | −0.328422 | ||||||||
\(43\) | −3.53017 | −0.538346 | −0.269173 | − | 0.963092i | \(-0.586750\pi\) | ||||
−0.269173 | + | 0.963092i | \(0.586750\pi\) | |||||||
\(44\) | 1.66633 | 0.251209 | ||||||||
\(45\) | 2.65859 | 0.396319 | ||||||||
\(46\) | 7.51368 | 1.10783 | ||||||||
\(47\) | −8.71892 | −1.27179 | −0.635893 | − | 0.771777i | \(-0.719368\pi\) | ||||
−0.635893 | + | 0.771777i | \(0.719368\pi\) | |||||||
\(48\) | 2.65859 | 0.383734 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.40175 | −0.622501 | ||||||||
\(51\) | −6.12842 | −0.858150 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.93966 | −0.266433 | −0.133217 | − | 0.991087i | \(-0.542531\pi\) | ||||
−0.133217 | + | 0.991087i | \(0.542531\pi\) | |||||||
\(54\) | 2.12842 | 0.289641 | ||||||||
\(55\) | 1.75091 | 0.236093 | ||||||||
\(56\) | 1.12842 | 0.150791 | ||||||||
\(57\) | 5.25684 | 0.696285 | ||||||||
\(58\) | −1.85509 | −0.243585 | ||||||||
\(59\) | −13.9077 | −1.81063 | −0.905313 | − | 0.424746i | \(-0.860363\pi\) | ||||
−0.905313 | + | 0.424746i | \(0.860363\pi\) | |||||||
\(60\) | −6.72667 | −0.868409 | ||||||||
\(61\) | 8.19650 | 1.04945 | 0.524727 | − | 0.851270i | \(-0.324167\pi\) | ||||
0.524727 | + | 0.851270i | \(0.324167\pi\) | |||||||
\(62\) | −12.5905 | −1.59900 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −11.5302 | −1.44127 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.40175 | 0.172543 | ||||||||
\(67\) | −13.3853 | −1.63527 | −0.817635 | − | 0.575737i | \(-0.804715\pi\) | ||||
−0.817635 | + | 0.575737i | \(0.804715\pi\) | |||||||
\(68\) | 15.5059 | 1.88037 | ||||||||
\(69\) | 3.53017 | 0.424982 | ||||||||
\(70\) | 5.65859 | 0.676330 | ||||||||
\(71\) | −4.27333 | −0.507151 | −0.253575 | − | 0.967316i | \(-0.581607\pi\) | ||||
−0.253575 | + | 0.967316i | \(0.581607\pi\) | |||||||
\(72\) | −1.12842 | −0.132985 | ||||||||
\(73\) | 3.46983 | 0.406113 | 0.203057 | − | 0.979167i | \(-0.434912\pi\) | ||||
0.203057 | + | 0.979167i | \(0.434912\pi\) | |||||||
\(74\) | 3.11193 | 0.361754 | ||||||||
\(75\) | −2.06808 | −0.238802 | ||||||||
\(76\) | −13.3007 | −1.52569 | ||||||||
\(77\) | −0.658587 | −0.0750529 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.85509 | 0.546240 | 0.273120 | − | 0.961980i | \(-0.411944\pi\) | ||||
0.273120 | + | 0.961980i | \(0.411944\pi\) | |||||||
\(80\) | −7.06808 | −0.790236 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 22.3775 | 2.47118 | ||||||||
\(83\) | −15.8551 | −1.74032 | −0.870161 | − | 0.492767i | \(-0.835985\pi\) | ||||
−0.870161 | + | 0.492767i | \(0.835985\pi\) | |||||||
\(84\) | 2.53017 | 0.276064 | ||||||||
\(85\) | 16.2929 | 1.76722 | ||||||||
\(86\) | 7.51368 | 0.810221 | ||||||||
\(87\) | −0.871581 | −0.0934433 | ||||||||
\(88\) | −0.743162 | −0.0792213 | ||||||||
\(89\) | 9.51368 | 1.00845 | 0.504224 | − | 0.863573i | \(-0.331779\pi\) | ||||
0.504224 | + | 0.863573i | \(0.331779\pi\) | |||||||
\(90\) | −5.65859 | −0.596467 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.93192 | −0.931217 | ||||||||
\(93\) | −5.91542 | −0.613401 | ||||||||
\(94\) | 18.5575 | 1.91406 | ||||||||
\(95\) | −13.9758 | −1.43388 | ||||||||
\(96\) | −7.91542 | −0.807865 | ||||||||
\(97\) | −2.97576 | −0.302143 | −0.151071 | − | 0.988523i | \(-0.548272\pi\) | ||||
−0.151071 | + | 0.988523i | \(0.548272\pi\) | |||||||
\(98\) | −2.12842 | −0.215003 | ||||||||
\(99\) | 0.658587 | 0.0661905 | ||||||||
\(100\) | 5.23260 | 0.523260 | ||||||||
\(101\) | −9.24035 | −0.919449 | −0.459724 | − | 0.888062i | \(-0.652052\pi\) | ||||
−0.459724 | + | 0.888062i | \(0.652052\pi\) | |||||||
\(102\) | 13.0438 | 1.29153 | ||||||||
\(103\) | 13.3775 | 1.31813 | 0.659063 | − | 0.752088i | \(-0.270953\pi\) | ||||
0.659063 | + | 0.752088i | \(0.270953\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.65859 | 0.259452 | ||||||||
\(106\) | 4.12842 | 0.400988 | ||||||||
\(107\) | 9.84734 | 0.951978 | 0.475989 | − | 0.879451i | \(-0.342090\pi\) | ||||
0.475989 | + | 0.879451i | \(0.342090\pi\) | |||||||
\(108\) | −2.53017 | −0.243466 | ||||||||
\(109\) | −6.32492 | −0.605818 | −0.302909 | − | 0.953020i | \(-0.597958\pi\) | ||||
−0.302909 | + | 0.953020i | \(0.597958\pi\) | |||||||
\(110\) | −3.72667 | −0.355324 | ||||||||
\(111\) | 1.46208 | 0.138775 | ||||||||
\(112\) | 2.65859 | 0.251213 | ||||||||
\(113\) | 13.2326 | 1.24482 | 0.622409 | − | 0.782692i | \(-0.286154\pi\) | ||||
0.622409 | + | 0.782692i | \(0.286154\pi\) | |||||||
\(114\) | −11.1888 | −1.04792 | ||||||||
\(115\) | −9.38526 | −0.875180 | ||||||||
\(116\) | 2.20525 | 0.204752 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 29.6014 | 2.72503 | ||||||||
\(119\) | −6.12842 | −0.561791 | ||||||||
\(120\) | 3.00000 | 0.273861 | ||||||||
\(121\) | −10.5663 | −0.960569 | ||||||||
\(122\) | −17.4456 | −1.57945 | ||||||||
\(123\) | 10.5137 | 0.947986 | ||||||||
\(124\) | 14.9670 | 1.34408 | ||||||||
\(125\) | −7.79475 | −0.697184 | ||||||||
\(126\) | 2.12842 | 0.189615 | ||||||||
\(127\) | −12.1119 | −1.07476 | −0.537380 | − | 0.843340i | \(-0.680586\pi\) | ||||
−0.537380 | + | 0.843340i | \(0.680586\pi\) | |||||||
\(128\) | 8.71018 | 0.769878 | ||||||||
\(129\) | 3.53017 | 0.310814 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.34141 | −0.291941 | −0.145970 | − | 0.989289i | \(-0.546630\pi\) | ||||
−0.145970 | + | 0.989289i | \(0.546630\pi\) | |||||||
\(132\) | −1.66633 | −0.145036 | ||||||||
\(133\) | 5.25684 | 0.455826 | ||||||||
\(134\) | 28.4894 | 2.46111 | ||||||||
\(135\) | −2.65859 | −0.228815 | ||||||||
\(136\) | −6.91542 | −0.592993 | ||||||||
\(137\) | −1.80350 | −0.154083 | −0.0770416 | − | 0.997028i | \(-0.524547\pi\) | ||||
−0.0770416 | + | 0.997028i | \(0.524547\pi\) | |||||||
\(138\) | −7.51368 | −0.639607 | ||||||||
\(139\) | −1.12842 | −0.0957113 | −0.0478556 | − | 0.998854i | \(-0.515239\pi\) | ||||
−0.0478556 | + | 0.998854i | \(0.515239\pi\) | |||||||
\(140\) | −6.72667 | −0.568507 | ||||||||
\(141\) | 8.71892 | 0.734266 | ||||||||
\(142\) | 9.09544 | 0.763272 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.65859 | −0.221549 | ||||||||
\(145\) | 2.31717 | 0.192431 | ||||||||
\(146\) | −7.38526 | −0.611208 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −3.69932 | −0.304082 | ||||||||
\(149\) | −13.8396 | −1.13378 | −0.566892 | − | 0.823792i | \(-0.691854\pi\) | ||||
−0.566892 | + | 0.823792i | \(0.691854\pi\) | |||||||
\(150\) | 4.40175 | 0.359401 | ||||||||
\(151\) | 7.57401 | 0.616364 | 0.308182 | − | 0.951327i | \(-0.400279\pi\) | ||||
0.308182 | + | 0.951327i | \(0.400279\pi\) | |||||||
\(152\) | 5.93192 | 0.481142 | ||||||||
\(153\) | 6.12842 | 0.495453 | ||||||||
\(154\) | 1.40175 | 0.112956 | ||||||||
\(155\) | 15.7267 | 1.26320 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.36877 | 0.588092 | 0.294046 | − | 0.955791i | \(-0.404998\pi\) | ||||
0.294046 | + | 0.955791i | \(0.404998\pi\) | |||||||
\(158\) | −10.3337 | −0.822102 | ||||||||
\(159\) | 1.93966 | 0.153825 | ||||||||
\(160\) | 21.0438 | 1.66366 | ||||||||
\(161\) | 3.53017 | 0.278216 | ||||||||
\(162\) | −2.12842 | −0.167224 | ||||||||
\(163\) | 21.1207 | 1.65430 | 0.827149 | − | 0.561982i | \(-0.189961\pi\) | ||||
0.827149 | + | 0.561982i | \(0.189961\pi\) | |||||||
\(164\) | −26.6014 | −2.07722 | ||||||||
\(165\) | −1.75091 | −0.136308 | ||||||||
\(166\) | 33.7463 | 2.61922 | ||||||||
\(167\) | 7.12067 | 0.551014 | 0.275507 | − | 0.961299i | \(-0.411154\pi\) | ||||
0.275507 | + | 0.961299i | \(0.411154\pi\) | |||||||
\(168\) | −1.12842 | −0.0870594 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −34.6782 | −2.65970 | ||||||||
\(171\) | −5.25684 | −0.402000 | ||||||||
\(172\) | −8.93192 | −0.681052 | ||||||||
\(173\) | −4.59050 | −0.349009 | −0.174505 | − | 0.984656i | \(-0.555832\pi\) | ||||
−0.174505 | + | 0.984656i | \(0.555832\pi\) | |||||||
\(174\) | 1.85509 | 0.140634 | ||||||||
\(175\) | −2.06808 | −0.156332 | ||||||||
\(176\) | −1.75091 | −0.131980 | ||||||||
\(177\) | 13.9077 | 1.04536 | ||||||||
\(178\) | −20.2491 | −1.51773 | ||||||||
\(179\) | 21.2161 | 1.58577 | 0.792883 | − | 0.609374i | \(-0.208579\pi\) | ||||
0.792883 | + | 0.609374i | \(0.208579\pi\) | |||||||
\(180\) | 6.72667 | 0.501376 | ||||||||
\(181\) | −17.6179 | −1.30952 | −0.654762 | − | 0.755835i | \(-0.727231\pi\) | ||||
−0.654762 | + | 0.755835i | \(0.727231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.19650 | −0.605903 | ||||||||
\(184\) | 3.98351 | 0.293668 | ||||||||
\(185\) | −3.88708 | −0.285784 | ||||||||
\(186\) | 12.5905 | 0.923180 | ||||||||
\(187\) | 4.03610 | 0.295149 | ||||||||
\(188\) | −22.0603 | −1.60892 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 29.7463 | 2.15802 | ||||||||
\(191\) | −2.30068 | −0.166472 | −0.0832358 | − | 0.996530i | \(-0.526525\pi\) | ||||
−0.0832358 | + | 0.996530i | \(0.526525\pi\) | |||||||
\(192\) | 11.5302 | 0.832118 | ||||||||
\(193\) | 23.2249 | 1.67176 | 0.835881 | − | 0.548911i | \(-0.184958\pi\) | ||||
0.835881 | + | 0.548911i | \(0.184958\pi\) | |||||||
\(194\) | 6.33367 | 0.454731 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.53017 | 0.180726 | ||||||||
\(197\) | 11.3337 | 0.807490 | 0.403745 | − | 0.914872i | \(-0.367708\pi\) | ||||
0.403745 | + | 0.914872i | \(0.367708\pi\) | |||||||
\(198\) | −1.40175 | −0.0996179 | ||||||||
\(199\) | −15.8144 | −1.12105 | −0.560525 | − | 0.828137i | \(-0.689401\pi\) | ||||
−0.560525 | + | 0.828137i | \(0.689401\pi\) | |||||||
\(200\) | −2.33367 | −0.165015 | ||||||||
\(201\) | 13.3853 | 0.944123 | ||||||||
\(202\) | 19.6673 | 1.38379 | ||||||||
\(203\) | −0.871581 | −0.0611730 | ||||||||
\(204\) | −15.5059 | −1.08563 | ||||||||
\(205\) | −27.9515 | −1.95222 | ||||||||
\(206\) | −28.4729 | −1.98380 | ||||||||
\(207\) | −3.53017 | −0.245364 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.46208 | −0.239477 | ||||||||
\(210\) | −5.65859 | −0.390480 | ||||||||
\(211\) | 6.60600 | 0.454776 | 0.227388 | − | 0.973804i | \(-0.426981\pi\) | ||||
0.227388 | + | 0.973804i | \(0.426981\pi\) | |||||||
\(212\) | −4.90768 | −0.337061 | ||||||||
\(213\) | 4.27333 | 0.292804 | ||||||||
\(214\) | −20.9593 | −1.43275 | ||||||||
\(215\) | −9.38526 | −0.640069 | ||||||||
\(216\) | 1.12842 | 0.0767792 | ||||||||
\(217\) | −5.91542 | −0.401565 | ||||||||
\(218\) | 13.4621 | 0.911767 | ||||||||
\(219\) | −3.46983 | −0.234470 | ||||||||
\(220\) | 4.43010 | 0.298677 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.11193 | −0.208859 | ||||||||
\(223\) | 9.80350 | 0.656491 | 0.328245 | − | 0.944592i | \(-0.393543\pi\) | ||||
0.328245 | + | 0.944592i | \(0.393543\pi\) | |||||||
\(224\) | −7.91542 | −0.528872 | ||||||||
\(225\) | 2.06808 | 0.137872 | ||||||||
\(226\) | −28.1645 | −1.87348 | ||||||||
\(227\) | 16.2929 | 1.08140 | 0.540700 | − | 0.841215i | \(-0.318159\pi\) | ||||
0.540700 | + | 0.841215i | \(0.318159\pi\) | |||||||
\(228\) | 13.3007 | 0.880859 | ||||||||
\(229\) | 23.1919 | 1.53256 | 0.766281 | − | 0.642506i | \(-0.222105\pi\) | ||||
0.766281 | + | 0.642506i | \(0.222105\pi\) | |||||||
\(230\) | 19.9758 | 1.31716 | ||||||||
\(231\) | 0.658587 | 0.0433318 | ||||||||
\(232\) | −0.983509 | −0.0645705 | ||||||||
\(233\) | −2.60699 | −0.170790 | −0.0853949 | − | 0.996347i | \(-0.527215\pi\) | ||||
−0.0853949 | + | 0.996347i | \(0.527215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.1800 | −1.51210 | ||||||||
\(236\) | −35.1888 | −2.29059 | ||||||||
\(237\) | −4.85509 | −0.315372 | ||||||||
\(238\) | 13.0438 | 0.845507 | ||||||||
\(239\) | −15.7432 | −1.01834 | −0.509170 | − | 0.860666i | \(-0.670048\pi\) | ||||
−0.509170 | + | 0.860666i | \(0.670048\pi\) | |||||||
\(240\) | 7.06808 | 0.456243 | ||||||||
\(241\) | −29.8669 | −1.92390 | −0.961950 | − | 0.273227i | \(-0.911909\pi\) | ||||
−0.961950 | + | 0.273227i | \(0.911909\pi\) | |||||||
\(242\) | 22.4894 | 1.44568 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 20.7385 | 1.32765 | ||||||||
\(245\) | 2.65859 | 0.169851 | ||||||||
\(246\) | −22.3775 | −1.42674 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.67508 | −0.423868 | ||||||||
\(249\) | 15.8551 | 1.00478 | ||||||||
\(250\) | 16.5905 | 1.04928 | ||||||||
\(251\) | −20.7189 | −1.30777 | −0.653883 | − | 0.756595i | \(-0.726861\pi\) | ||||
−0.653883 | + | 0.756595i | \(0.726861\pi\) | |||||||
\(252\) | −2.53017 | −0.159386 | ||||||||
\(253\) | −2.32492 | −0.146167 | ||||||||
\(254\) | 25.7793 | 1.61753 | ||||||||
\(255\) | −16.2929 | −1.02030 | ||||||||
\(256\) | 4.52142 | 0.282589 | ||||||||
\(257\) | 10.6508 | 0.664381 | 0.332191 | − | 0.943212i | \(-0.392212\pi\) | ||||
0.332191 | + | 0.943212i | \(0.392212\pi\) | |||||||
\(258\) | −7.51368 | −0.467781 | ||||||||
\(259\) | 1.46208 | 0.0908495 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.871581 | 0.0539495 | ||||||||
\(262\) | 7.11193 | 0.439376 | ||||||||
\(263\) | −23.6782 | −1.46006 | −0.730030 | − | 0.683415i | \(-0.760494\pi\) | ||||
−0.730030 | + | 0.683415i | \(0.760494\pi\) | |||||||
\(264\) | 0.743162 | 0.0457385 | ||||||||
\(265\) | −5.15677 | −0.316778 | ||||||||
\(266\) | −11.1888 | −0.686027 | ||||||||
\(267\) | −9.51368 | −0.582228 | ||||||||
\(268\) | −33.8669 | −2.06875 | ||||||||
\(269\) | −0.477581 | −0.0291186 | −0.0145593 | − | 0.999894i | \(-0.504635\pi\) | ||||
−0.0145593 | + | 0.999894i | \(0.504635\pi\) | |||||||
\(270\) | 5.65859 | 0.344371 | ||||||||
\(271\) | 20.6421 | 1.25392 | 0.626959 | − | 0.779052i | \(-0.284299\pi\) | ||||
0.626959 | + | 0.779052i | \(0.284299\pi\) | |||||||
\(272\) | −16.2929 | −0.987904 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.83860 | 0.231898 | ||||||||
\(275\) | 1.36201 | 0.0821324 | ||||||||
\(276\) | 8.93192 | 0.537638 | ||||||||
\(277\) | −26.3600 | −1.58382 | −0.791910 | − | 0.610638i | \(-0.790913\pi\) | ||||
−0.791910 | + | 0.610638i | \(0.790913\pi\) | |||||||
\(278\) | 2.40175 | 0.144047 | ||||||||
\(279\) | 5.91542 | 0.354147 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | −0.205246 | −0.0122439 | −0.00612197 | − | 0.999981i | \(-0.501949\pi\) | ||||
−0.00612197 | + | 0.999981i | \(0.501949\pi\) | |||||||
\(282\) | −18.5575 | −1.10508 | ||||||||
\(283\) | 1.41824 | 0.0843056 | 0.0421528 | − | 0.999111i | \(-0.486578\pi\) | ||||
0.0421528 | + | 0.999111i | \(0.486578\pi\) | |||||||
\(284\) | −10.8122 | −0.641588 | ||||||||
\(285\) | 13.9758 | 0.827853 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.5137 | 0.620603 | ||||||||
\(288\) | 7.91542 | 0.466421 | ||||||||
\(289\) | 20.5575 | 1.20927 | ||||||||
\(290\) | −4.93192 | −0.289612 | ||||||||
\(291\) | 2.97576 | 0.174442 | ||||||||
\(292\) | 8.77926 | 0.513767 | ||||||||
\(293\) | −30.6256 | −1.78917 | −0.894583 | − | 0.446901i | \(-0.852528\pi\) | ||||
−0.894583 | + | 0.446901i | \(0.852528\pi\) | |||||||
\(294\) | 2.12842 | 0.124132 | ||||||||
\(295\) | −36.9748 | −2.15275 | ||||||||
\(296\) | 1.64984 | 0.0958952 | ||||||||
\(297\) | −0.658587 | −0.0382151 | ||||||||
\(298\) | 29.4565 | 1.70637 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.23260 | −0.302104 | ||||||||
\(301\) | 3.53017 | 0.203475 | ||||||||
\(302\) | −16.1207 | −0.927640 | ||||||||
\(303\) | 9.24035 | 0.530844 | ||||||||
\(304\) | 13.9758 | 0.801565 | ||||||||
\(305\) | 21.7911 | 1.24776 | ||||||||
\(306\) | −13.0438 | −0.745667 | ||||||||
\(307\) | −4.47858 | −0.255606 | −0.127803 | − | 0.991800i | \(-0.540792\pi\) | ||||
−0.127803 | + | 0.991800i | \(0.540792\pi\) | |||||||
\(308\) | −1.66633 | −0.0949482 | ||||||||
\(309\) | −13.3775 | −0.761020 | ||||||||
\(310\) | −33.4729 | −1.90114 | ||||||||
\(311\) | 0.675078 | 0.0382802 | 0.0191401 | − | 0.999817i | \(-0.493907\pi\) | ||||
0.0191401 | + | 0.999817i | \(0.493907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0242 | 0.566604 | 0.283302 | − | 0.959031i | \(-0.408570\pi\) | ||||
0.283302 | + | 0.959031i | \(0.408570\pi\) | |||||||
\(314\) | −15.6838 | −0.885089 | ||||||||
\(315\) | −2.65859 | −0.149794 | ||||||||
\(316\) | 12.2842 | 0.691040 | ||||||||
\(317\) | −27.1558 | −1.52522 | −0.762610 | − | 0.646859i | \(-0.776082\pi\) | ||||
−0.762610 | + | 0.646859i | \(0.776082\pi\) | |||||||
\(318\) | −4.12842 | −0.231510 | ||||||||
\(319\) | 0.574012 | 0.0321385 | ||||||||
\(320\) | −30.6540 | −1.71361 | ||||||||
\(321\) | −9.84734 | −0.549625 | ||||||||
\(322\) | −7.51368 | −0.418721 | ||||||||
\(323\) | −32.2161 | −1.79255 | ||||||||
\(324\) | 2.53017 | 0.140565 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −44.9536 | −2.48975 | ||||||||
\(327\) | 6.32492 | 0.349769 | ||||||||
\(328\) | 11.8638 | 0.655071 | ||||||||
\(329\) | 8.71892 | 0.480690 | ||||||||
\(330\) | 3.72667 | 0.205146 | ||||||||
\(331\) | −23.8112 | −1.30878 | −0.654392 | − | 0.756155i | \(-0.727075\pi\) | ||||
−0.654392 | + | 0.756155i | \(0.727075\pi\) | |||||||
\(332\) | −40.1160 | −2.20165 | ||||||||
\(333\) | −1.46208 | −0.0801217 | ||||||||
\(334\) | −15.1558 | −0.829287 | ||||||||
\(335\) | −35.5859 | −1.94426 | ||||||||
\(336\) | −2.65859 | −0.145038 | ||||||||
\(337\) | −21.4894 | −1.17060 | −0.585302 | − | 0.810815i | \(-0.699024\pi\) | ||||
−0.585302 | + | 0.810815i | \(0.699024\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.2326 | −0.718696 | ||||||||
\(340\) | 41.2239 | 2.23568 | ||||||||
\(341\) | 3.89582 | 0.210971 | ||||||||
\(342\) | 11.1888 | 0.605019 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.98351 | 0.214776 | ||||||||
\(345\) | 9.38526 | 0.505285 | ||||||||
\(346\) | 9.77051 | 0.525266 | ||||||||
\(347\) | −19.6266 | −1.05361 | −0.526806 | − | 0.849986i | \(-0.676610\pi\) | ||||
−0.526806 | + | 0.849986i | \(0.676610\pi\) | |||||||
\(348\) | −2.20525 | −0.118214 | ||||||||
\(349\) | −27.0799 | −1.44956 | −0.724778 | − | 0.688983i | \(-0.758058\pi\) | ||||
−0.724778 | + | 0.688983i | \(0.758058\pi\) | |||||||
\(350\) | 4.40175 | 0.235283 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.21299 | 0.277854 | ||||||||
\(353\) | 1.67408 | 0.0891025 | 0.0445512 | − | 0.999007i | \(-0.485814\pi\) | ||||
0.0445512 | + | 0.999007i | \(0.485814\pi\) | |||||||
\(354\) | −29.6014 | −1.57329 | ||||||||
\(355\) | −11.3610 | −0.602980 | ||||||||
\(356\) | 24.0712 | 1.27577 | ||||||||
\(357\) | 6.12842 | 0.324350 | ||||||||
\(358\) | −45.1568 | −2.38661 | ||||||||
\(359\) | −20.1207 | −1.06193 | −0.530964 | − | 0.847394i | \(-0.678170\pi\) | ||||
−0.530964 | + | 0.847394i | \(0.678170\pi\) | |||||||
\(360\) | −3.00000 | −0.158114 | ||||||||
\(361\) | 8.63435 | 0.454439 | ||||||||
\(362\) | 37.4982 | 1.97086 | ||||||||
\(363\) | 10.5663 | 0.554585 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.22485 | 0.482851 | ||||||||
\(366\) | 17.4456 | 0.911896 | ||||||||
\(367\) | 16.7112 | 0.872316 | 0.436158 | − | 0.899870i | \(-0.356339\pi\) | ||||
0.436158 | + | 0.899870i | \(0.356339\pi\) | |||||||
\(368\) | 9.38526 | 0.489240 | ||||||||
\(369\) | −10.5137 | −0.547320 | ||||||||
\(370\) | 8.27333 | 0.430110 | ||||||||
\(371\) | 1.93966 | 0.100702 | ||||||||
\(372\) | −14.9670 | −0.776004 | ||||||||
\(373\) | 16.2852 | 0.843215 | 0.421607 | − | 0.906778i | \(-0.361466\pi\) | ||||
0.421607 | + | 0.906778i | \(0.361466\pi\) | |||||||
\(374\) | −8.59050 | −0.444204 | ||||||||
\(375\) | 7.79475 | 0.402519 | ||||||||
\(376\) | 9.83860 | 0.507387 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.12842 | −0.109474 | ||||||||
\(379\) | −27.5255 | −1.41389 | −0.706946 | − | 0.707268i | \(-0.749928\pi\) | ||||
−0.706946 | + | 0.707268i | \(0.749928\pi\) | |||||||
\(380\) | −35.3610 | −1.81398 | ||||||||
\(381\) | 12.1119 | 0.620513 | ||||||||
\(382\) | 4.89682 | 0.250543 | ||||||||
\(383\) | −12.2413 | −0.625503 | −0.312752 | − | 0.949835i | \(-0.601251\pi\) | ||||
−0.312752 | + | 0.949835i | \(0.601251\pi\) | |||||||
\(384\) | −8.71018 | −0.444489 | ||||||||
\(385\) | −1.75091 | −0.0892346 | ||||||||
\(386\) | −49.4322 | −2.51603 | ||||||||
\(387\) | −3.53017 | −0.179449 | ||||||||
\(388\) | −7.52917 | −0.382236 | ||||||||
\(389\) | −2.77051 | −0.140471 | −0.0702353 | − | 0.997530i | \(-0.522375\pi\) | ||||
−0.0702353 | + | 0.997530i | \(0.522375\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.6343 | −1.09410 | ||||||||
\(392\) | −1.12842 | −0.0569938 | ||||||||
\(393\) | 3.34141 | 0.168552 | ||||||||
\(394\) | −24.1228 | −1.21529 | ||||||||
\(395\) | 12.9077 | 0.649456 | ||||||||
\(396\) | 1.66633 | 0.0837365 | ||||||||
\(397\) | −0.812241 | −0.0407652 | −0.0203826 | − | 0.999792i | \(-0.506488\pi\) | ||||
−0.0203826 | + | 0.999792i | \(0.506488\pi\) | |||||||
\(398\) | 33.6596 | 1.68720 | ||||||||
\(399\) | −5.25684 | −0.263171 | ||||||||
\(400\) | −5.49818 | −0.274909 | ||||||||
\(401\) | 9.76277 | 0.487529 | 0.243765 | − | 0.969834i | \(-0.421618\pi\) | ||||
0.243765 | + | 0.969834i | \(0.421618\pi\) | |||||||
\(402\) | −28.4894 | −1.42092 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −23.3796 | −1.16318 | ||||||||
\(405\) | 2.65859 | 0.132106 | ||||||||
\(406\) | 1.85509 | 0.0920665 | ||||||||
\(407\) | −0.962909 | −0.0477296 | ||||||||
\(408\) | 6.91542 | 0.342365 | ||||||||
\(409\) | −18.8231 | −0.930742 | −0.465371 | − | 0.885116i | \(-0.654079\pi\) | ||||
−0.465371 | + | 0.885116i | \(0.654079\pi\) | |||||||
\(410\) | 59.4925 | 2.93813 | ||||||||
\(411\) | 1.80350 | 0.0889600 | ||||||||
\(412\) | 33.8473 | 1.66754 | ||||||||
\(413\) | 13.9077 | 0.684352 | ||||||||
\(414\) | 7.51368 | 0.369277 | ||||||||
\(415\) | −42.1521 | −2.06917 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.12842 | 0.0552589 | ||||||||
\(418\) | 7.36877 | 0.360418 | ||||||||
\(419\) | −12.5224 | −0.611760 | −0.305880 | − | 0.952070i | \(-0.598951\pi\) | ||||
−0.305880 | + | 0.952070i | \(0.598951\pi\) | |||||||
\(420\) | 6.72667 | 0.328228 | ||||||||
\(421\) | −27.5771 | −1.34403 | −0.672013 | − | 0.740539i | \(-0.734570\pi\) | ||||
−0.672013 | + | 0.740539i | \(0.734570\pi\) | |||||||
\(422\) | −14.0603 | −0.684446 | ||||||||
\(423\) | −8.71892 | −0.423929 | ||||||||
\(424\) | 2.18875 | 0.106295 | ||||||||
\(425\) | 12.6741 | 0.614783 | ||||||||
\(426\) | −9.09544 | −0.440675 | ||||||||
\(427\) | −8.19650 | −0.396657 | ||||||||
\(428\) | 24.9154 | 1.20433 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.9758 | 0.963317 | ||||||||
\(431\) | −0.888072 | −0.0427769 | −0.0213885 | − | 0.999771i | \(-0.506809\pi\) | ||||
−0.0213885 | + | 0.999771i | \(0.506809\pi\) | |||||||
\(432\) | 2.65859 | 0.127911 | ||||||||
\(433\) | 26.8308 | 1.28941 | 0.644704 | − | 0.764432i | \(-0.276981\pi\) | ||||
0.644704 | + | 0.764432i | \(0.276981\pi\) | |||||||
\(434\) | 12.5905 | 0.604363 | ||||||||
\(435\) | −2.31717 | −0.111100 | ||||||||
\(436\) | −16.0031 | −0.766410 | ||||||||
\(437\) | 18.5575 | 0.887727 | ||||||||
\(438\) | 7.38526 | 0.352881 | ||||||||
\(439\) | −34.0041 | −1.62293 | −0.811464 | − | 0.584403i | \(-0.801329\pi\) | ||||
−0.811464 | + | 0.584403i | \(0.801329\pi\) | |||||||
\(440\) | −1.97576 | −0.0941907 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.9670 | −0.996173 | −0.498087 | − | 0.867127i | \(-0.665964\pi\) | ||||
−0.498087 | + | 0.867127i | \(0.665964\pi\) | |||||||
\(444\) | 3.69932 | 0.175562 | ||||||||
\(445\) | 25.2929 | 1.19900 | ||||||||
\(446\) | −20.8660 | −0.988031 | ||||||||
\(447\) | 13.8396 | 0.654590 | ||||||||
\(448\) | 11.5302 | 0.544749 | ||||||||
\(449\) | −17.8221 | −0.841077 | −0.420539 | − | 0.907275i | \(-0.638159\pi\) | ||||
−0.420539 | + | 0.907275i | \(0.638159\pi\) | |||||||
\(450\) | −4.40175 | −0.207500 | ||||||||
\(451\) | −6.92417 | −0.326046 | ||||||||
\(452\) | 33.4807 | 1.57480 | ||||||||
\(453\) | −7.57401 | −0.355858 | ||||||||
\(454\) | −34.6782 | −1.62753 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.93192 | −0.277787 | ||||||||
\(457\) | 41.0557 | 1.92050 | 0.960252 | − | 0.279133i | \(-0.0900472\pi\) | ||||
0.960252 | + | 0.279133i | \(0.0900472\pi\) | |||||||
\(458\) | −49.3620 | −2.30654 | ||||||||
\(459\) | −6.12842 | −0.286050 | ||||||||
\(460\) | −23.7463 | −1.10718 | ||||||||
\(461\) | 35.9876 | 1.67611 | 0.838055 | − | 0.545585i | \(-0.183693\pi\) | ||||
0.838055 | + | 0.545585i | \(0.183693\pi\) | |||||||
\(462\) | −1.40175 | −0.0652152 | ||||||||
\(463\) | 13.1527 | 0.611256 | 0.305628 | − | 0.952151i | \(-0.401134\pi\) | ||||
0.305628 | + | 0.952151i | \(0.401134\pi\) | |||||||
\(464\) | −2.31717 | −0.107572 | ||||||||
\(465\) | −15.7267 | −0.729307 | ||||||||
\(466\) | 5.54878 | 0.257042 | ||||||||
\(467\) | 19.4729 | 0.901100 | 0.450550 | − | 0.892751i | \(-0.351228\pi\) | ||||
0.450550 | + | 0.892751i | \(0.351228\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.3853 | 0.618074 | ||||||||
\(470\) | 49.3368 | 2.27574 | ||||||||
\(471\) | −7.36877 | −0.339535 | ||||||||
\(472\) | 15.6937 | 0.722361 | ||||||||
\(473\) | −2.32492 | −0.106900 | ||||||||
\(474\) | 10.3337 | 0.474641 | ||||||||
\(475\) | −10.8716 | −0.498822 | ||||||||
\(476\) | −15.5059 | −0.710713 | ||||||||
\(477\) | −1.93966 | −0.0888111 | ||||||||
\(478\) | 33.5080 | 1.53262 | ||||||||
\(479\) | −5.04384 | −0.230459 | −0.115230 | − | 0.993339i | \(-0.536760\pi\) | ||||
−0.115230 | + | 0.993339i | \(0.536760\pi\) | |||||||
\(480\) | −21.0438 | −0.960516 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 63.5694 | 2.89551 | ||||||||
\(483\) | −3.53017 | −0.160628 | ||||||||
\(484\) | −26.7344 | −1.21520 | ||||||||
\(485\) | −7.91132 | −0.359234 | ||||||||
\(486\) | 2.12842 | 0.0965470 | ||||||||
\(487\) | 12.4941 | 0.566160 | 0.283080 | − | 0.959096i | \(-0.408644\pi\) | ||||
0.283080 | + | 0.959096i | \(0.408644\pi\) | |||||||
\(488\) | −9.24909 | −0.418687 | ||||||||
\(489\) | −21.1207 | −0.955110 | ||||||||
\(490\) | −5.65859 | −0.255629 | ||||||||
\(491\) | −0.0680836 | −0.00307257 | −0.00153629 | − | 0.999999i | \(-0.500489\pi\) | ||||
−0.00153629 | + | 0.999999i | \(0.500489\pi\) | |||||||
\(492\) | 26.6014 | 1.19928 | ||||||||
\(493\) | 5.34141 | 0.240565 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.75091 | 0.0786976 | ||||||||
\(496\) | −15.7267 | −0.706148 | ||||||||
\(497\) | 4.27333 | 0.191685 | ||||||||
\(498\) | −33.7463 | −1.51221 | ||||||||
\(499\) | 2.14392 | 0.0959748 | 0.0479874 | − | 0.998848i | \(-0.484719\pi\) | ||||
0.0479874 | + | 0.998848i | \(0.484719\pi\) | |||||||
\(500\) | −19.7220 | −0.881996 | ||||||||
\(501\) | −7.12067 | −0.318128 | ||||||||
\(502\) | 44.0985 | 1.96821 | ||||||||
\(503\) | −22.7824 | −1.01582 | −0.507908 | − | 0.861411i | \(-0.669581\pi\) | ||||
−0.507908 | + | 0.861411i | \(0.669581\pi\) | |||||||
\(504\) | 1.12842 | 0.0502638 | ||||||||
\(505\) | −24.5663 | −1.09318 | ||||||||
\(506\) | 4.94841 | 0.219984 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −30.6452 | −1.35966 | ||||||||
\(509\) | −25.9515 | −1.15028 | −0.575140 | − | 0.818055i | \(-0.695053\pi\) | ||||
−0.575140 | + | 0.818055i | \(0.695053\pi\) | |||||||
\(510\) | 34.6782 | 1.53558 | ||||||||
\(511\) | −3.46983 | −0.153496 | ||||||||
\(512\) | −27.0438 | −1.19518 | ||||||||
\(513\) | 5.25684 | 0.232095 | ||||||||
\(514\) | −22.6694 | −0.999906 | ||||||||
\(515\) | 35.5653 | 1.56719 | ||||||||
\(516\) | 8.93192 | 0.393206 | ||||||||
\(517\) | −5.74217 | −0.252540 | ||||||||
\(518\) | −3.11193 | −0.136730 | ||||||||
\(519\) | 4.59050 | 0.201501 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0077 | −0.482258 | −0.241129 | − | 0.970493i | \(-0.577518\pi\) | ||||
−0.241129 | + | 0.970493i | \(0.577518\pi\) | |||||||
\(522\) | −1.85509 | −0.0811951 | ||||||||
\(523\) | −24.0031 | −1.04958 | −0.524791 | − | 0.851231i | \(-0.675857\pi\) | ||||
−0.524791 | + | 0.851231i | \(0.675857\pi\) | |||||||
\(524\) | −8.45434 | −0.369329 | ||||||||
\(525\) | 2.06808 | 0.0902586 | ||||||||
\(526\) | 50.3971 | 2.19742 | ||||||||
\(527\) | 36.2522 | 1.57917 | ||||||||
\(528\) | 1.75091 | 0.0761986 | ||||||||
\(529\) | −10.5379 | −0.458170 | ||||||||
\(530\) | 10.9758 | 0.476757 | ||||||||
\(531\) | −13.9077 | −0.603542 | ||||||||
\(532\) | 13.3007 | 0.576658 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 20.2491 | 0.876264 | ||||||||
\(535\) | 26.1800 | 1.13186 | ||||||||
\(536\) | 15.1042 | 0.652401 | ||||||||
\(537\) | −21.2161 | −0.915543 | ||||||||
\(538\) | 1.01649 | 0.0438241 | ||||||||
\(539\) | 0.658587 | 0.0283673 | ||||||||
\(540\) | −6.72667 | −0.289470 | ||||||||
\(541\) | 7.12842 | 0.306475 | 0.153237 | − | 0.988189i | \(-0.451030\pi\) | ||||
0.153237 | + | 0.988189i | \(0.451030\pi\) | |||||||
\(542\) | −43.9350 | −1.88717 | ||||||||
\(543\) | 17.6179 | 0.756055 | ||||||||
\(544\) | 48.5090 | 2.07981 | ||||||||
\(545\) | −16.8154 | −0.720291 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.6540 | 1.26791 | 0.633956 | − | 0.773369i | \(-0.281430\pi\) | ||||
0.633956 | + | 0.773369i | \(0.281430\pi\) | |||||||
\(548\) | −4.56315 | −0.194928 | ||||||||
\(549\) | 8.19650 | 0.349818 | ||||||||
\(550\) | −2.89893 | −0.123611 | ||||||||
\(551\) | −4.58176 | −0.195190 | ||||||||
\(552\) | −3.98351 | −0.169549 | ||||||||
\(553\) | −4.85509 | −0.206459 | ||||||||
\(554\) | 56.1052 | 2.38368 | ||||||||
\(555\) | 3.88708 | 0.164997 | ||||||||
\(556\) | −2.85509 | −0.121083 | ||||||||
\(557\) | −8.61474 | −0.365018 | −0.182509 | − | 0.983204i | \(-0.558422\pi\) | ||||
−0.182509 | + | 0.983204i | \(0.558422\pi\) | |||||||
\(558\) | −12.5905 | −0.532998 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7.06808 | 0.298681 | ||||||||
\(561\) | −4.03610 | −0.170404 | ||||||||
\(562\) | 0.436849 | 0.0184274 | ||||||||
\(563\) | 35.6694 | 1.50329 | 0.751644 | − | 0.659569i | \(-0.229261\pi\) | ||||
0.751644 | + | 0.659569i | \(0.229261\pi\) | |||||||
\(564\) | 22.0603 | 0.928908 | ||||||||
\(565\) | 35.1800 | 1.48003 | ||||||||
\(566\) | −3.01861 | −0.126882 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 4.82211 | 0.202331 | ||||||||
\(569\) | −11.3765 | −0.476928 | −0.238464 | − | 0.971151i | \(-0.576644\pi\) | ||||
−0.238464 | + | 0.971151i | \(0.576644\pi\) | |||||||
\(570\) | −29.7463 | −1.24593 | ||||||||
\(571\) | 24.6266 | 1.03059 | 0.515296 | − | 0.857013i | \(-0.327682\pi\) | ||||
0.515296 | + | 0.857013i | \(0.327682\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.30068 | 0.0961124 | ||||||||
\(574\) | −22.3775 | −0.934019 | ||||||||
\(575\) | −7.30068 | −0.304459 | ||||||||
\(576\) | −11.5302 | −0.480424 | ||||||||
\(577\) | 18.0438 | 0.751175 | 0.375588 | − | 0.926787i | \(-0.377441\pi\) | ||||
0.375588 | + | 0.926787i | \(0.377441\pi\) | |||||||
\(578\) | −43.7550 | −1.81997 | ||||||||
\(579\) | −23.2249 | −0.965192 | ||||||||
\(580\) | 5.86284 | 0.243441 | ||||||||
\(581\) | 15.8551 | 0.657780 | ||||||||
\(582\) | −6.33367 | −0.262539 | ||||||||
\(583\) | −1.27744 | −0.0529061 | ||||||||
\(584\) | −3.91542 | −0.162021 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 65.1841 | 2.69273 | ||||||||
\(587\) | −46.1723 | −1.90573 | −0.952867 | − | 0.303390i | \(-0.901882\pi\) | ||||
−0.952867 | + | 0.303390i | \(0.901882\pi\) | |||||||
\(588\) | −2.53017 | −0.104342 | ||||||||
\(589\) | −31.0964 | −1.28131 | ||||||||
\(590\) | 78.6978 | 3.23994 | ||||||||
\(591\) | −11.3337 | −0.466205 | ||||||||
\(592\) | 3.88708 | 0.159758 | ||||||||
\(593\) | 37.8505 | 1.55433 | 0.777166 | − | 0.629296i | \(-0.216657\pi\) | ||||
0.777166 | + | 0.629296i | \(0.216657\pi\) | |||||||
\(594\) | 1.40175 | 0.0575144 | ||||||||
\(595\) | −16.2929 | −0.667945 | ||||||||
\(596\) | −35.0165 | −1.43433 | ||||||||
\(597\) | 15.8144 | 0.647239 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.68283 | −0.150476 | −0.0752381 | − | 0.997166i | \(-0.523972\pi\) | ||||
−0.0752381 | + | 0.997166i | \(0.523972\pi\) | |||||||
\(600\) | 2.33367 | 0.0952715 | ||||||||
\(601\) | 2.65859 | 0.108446 | 0.0542230 | − | 0.998529i | \(-0.482732\pi\) | ||||
0.0542230 | + | 0.998529i | \(0.482732\pi\) | |||||||
\(602\) | −7.51368 | −0.306235 | ||||||||
\(603\) | −13.3853 | −0.545090 | ||||||||
\(604\) | 19.1635 | 0.779753 | ||||||||
\(605\) | −28.0913 | −1.14207 | ||||||||
\(606\) | −19.6673 | −0.798931 | ||||||||
\(607\) | 44.7298 | 1.81553 | 0.907763 | − | 0.419484i | \(-0.137789\pi\) | ||||
0.907763 | + | 0.419484i | \(0.137789\pi\) | |||||||
\(608\) | −41.6101 | −1.68751 | ||||||||
\(609\) | 0.871581 | 0.0353182 | ||||||||
\(610\) | −46.3806 | −1.87790 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.5059 | 0.626790 | ||||||||
\(613\) | 43.0031 | 1.73688 | 0.868440 | − | 0.495795i | \(-0.165123\pi\) | ||||
0.868440 | + | 0.495795i | \(0.165123\pi\) | |||||||
\(614\) | 9.53229 | 0.384692 | ||||||||
\(615\) | 27.9515 | 1.12711 | ||||||||
\(616\) | 0.743162 | 0.0299428 | ||||||||
\(617\) | −13.1723 | −0.530295 | −0.265148 | − | 0.964208i | \(-0.585421\pi\) | ||||
−0.265148 | + | 0.964208i | \(0.585421\pi\) | |||||||
\(618\) | 28.4729 | 1.14535 | ||||||||
\(619\) | −24.7705 | −0.995611 | −0.497806 | − | 0.867289i | \(-0.665861\pi\) | ||||
−0.497806 | + | 0.867289i | \(0.665861\pi\) | |||||||
\(620\) | 39.7911 | 1.59805 | ||||||||
\(621\) | 3.53017 | 0.141661 | ||||||||
\(622\) | −1.43685 | −0.0576124 | ||||||||
\(623\) | −9.51368 | −0.381157 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0634 | −1.24254 | ||||||||
\(626\) | −21.3358 | −0.852749 | ||||||||
\(627\) | 3.46208 | 0.138262 | ||||||||
\(628\) | 18.6442 | 0.743985 | ||||||||
\(629\) | −8.96026 | −0.357269 | ||||||||
\(630\) | 5.65859 | 0.225443 | ||||||||
\(631\) | −4.43374 | −0.176504 | −0.0882521 | − | 0.996098i | \(-0.528128\pi\) | ||||
−0.0882521 | + | 0.996098i | \(0.528128\pi\) | |||||||
\(632\) | −5.47858 | −0.217926 | ||||||||
\(633\) | −6.60600 | −0.262565 | ||||||||
\(634\) | 57.7989 | 2.29549 | ||||||||
\(635\) | −32.2006 | −1.27784 | ||||||||
\(636\) | 4.90768 | 0.194602 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.22174 | −0.0483690 | ||||||||
\(639\) | −4.27333 | −0.169050 | ||||||||
\(640\) | 23.1568 | 0.915352 | ||||||||
\(641\) | −12.4698 | −0.492529 | −0.246264 | − | 0.969203i | \(-0.579203\pi\) | ||||
−0.246264 | + | 0.969203i | \(0.579203\pi\) | |||||||
\(642\) | 20.9593 | 0.827196 | ||||||||
\(643\) | −38.0274 | −1.49965 | −0.749826 | − | 0.661635i | \(-0.769863\pi\) | ||||
−0.749826 | + | 0.661635i | \(0.769863\pi\) | |||||||
\(644\) | 8.93192 | 0.351967 | ||||||||
\(645\) | 9.38526 | 0.369544 | ||||||||
\(646\) | 68.5694 | 2.69783 | ||||||||
\(647\) | 12.1888 | 0.479189 | 0.239595 | − | 0.970873i | \(-0.422985\pi\) | ||||
0.239595 | + | 0.970873i | \(0.422985\pi\) | |||||||
\(648\) | −1.12842 | −0.0443285 | ||||||||
\(649\) | −9.15941 | −0.359538 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.91542 | 0.231844 | ||||||||
\(652\) | 53.4388 | 2.09283 | ||||||||
\(653\) | 11.3290 | 0.443339 | 0.221670 | − | 0.975122i | \(-0.428849\pi\) | ||||
0.221670 | + | 0.975122i | \(0.428849\pi\) | |||||||
\(654\) | −13.4621 | −0.526409 | ||||||||
\(655\) | −8.88344 | −0.347105 | ||||||||
\(656\) | 27.9515 | 1.09132 | ||||||||
\(657\) | 3.46983 | 0.135371 | ||||||||
\(658\) | −18.5575 | −0.723447 | ||||||||
\(659\) | 42.2929 | 1.64750 | 0.823749 | − | 0.566954i | \(-0.191878\pi\) | ||||
0.823749 | + | 0.566954i | \(0.191878\pi\) | |||||||
\(660\) | −4.43010 | −0.172441 | ||||||||
\(661\) | 15.3533 | 0.597173 | 0.298586 | − | 0.954383i | \(-0.403485\pi\) | ||||
0.298586 | + | 0.954383i | \(0.403485\pi\) | |||||||
\(662\) | 50.6803 | 1.96975 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.8912 | 0.694313 | ||||||||
\(665\) | 13.9758 | 0.541957 | ||||||||
\(666\) | 3.11193 | 0.120585 | ||||||||
\(667\) | −3.07683 | −0.119135 | ||||||||
\(668\) | 18.0165 | 0.697079 | ||||||||
\(669\) | −9.80350 | −0.379025 | ||||||||
\(670\) | 75.7416 | 2.92615 | ||||||||
\(671\) | 5.39811 | 0.208392 | ||||||||
\(672\) | 7.91542 | 0.305344 | ||||||||
\(673\) | 38.7814 | 1.49491 | 0.747456 | − | 0.664311i | \(-0.231275\pi\) | ||||
0.747456 | + | 0.664311i | \(0.231275\pi\) | |||||||
\(674\) | 45.7385 | 1.76178 | ||||||||
\(675\) | −2.06808 | −0.0796006 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.4729 | −0.825272 | −0.412636 | − | 0.910896i | \(-0.635392\pi\) | ||||
−0.412636 | + | 0.910896i | \(0.635392\pi\) | |||||||
\(678\) | 28.1645 | 1.08165 | ||||||||
\(679\) | 2.97576 | 0.114199 | ||||||||
\(680\) | −18.3853 | −0.705042 | ||||||||
\(681\) | −16.2929 | −0.624347 | ||||||||
\(682\) | −8.29194 | −0.317515 | ||||||||
\(683\) | −5.15266 | −0.197161 | −0.0985805 | − | 0.995129i | \(-0.531430\pi\) | ||||
−0.0985805 | + | 0.995129i | \(0.531430\pi\) | |||||||
\(684\) | −13.3007 | −0.508564 | ||||||||
\(685\) | −4.79475 | −0.183198 | ||||||||
\(686\) | 2.12842 | 0.0812634 | ||||||||
\(687\) | −23.1919 | −0.884825 | ||||||||
\(688\) | 9.38526 | 0.357810 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −19.9758 | −0.760464 | ||||||||
\(691\) | −24.2852 | −0.923852 | −0.461926 | − | 0.886918i | \(-0.652841\pi\) | ||||
−0.461926 | + | 0.886918i | \(0.652841\pi\) | |||||||
\(692\) | −11.6147 | −0.441526 | ||||||||
\(693\) | −0.658587 | −0.0250176 | ||||||||
\(694\) | 41.7736 | 1.58571 | ||||||||
\(695\) | −3.00000 | −0.113796 | ||||||||
\(696\) | 0.983509 | 0.0372798 | ||||||||
\(697\) | −64.4322 | −2.44054 | ||||||||
\(698\) | 57.6375 | 2.18161 | ||||||||
\(699\) | 2.60699 | 0.0986056 | ||||||||
\(700\) | −5.23260 | −0.197774 | ||||||||
\(701\) | −1.31307 | −0.0495938 | −0.0247969 | − | 0.999693i | \(-0.507894\pi\) | ||||
−0.0247969 | + | 0.999693i | \(0.507894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.68594 | 0.289881 | ||||||||
\(704\) | −7.59362 | −0.286195 | ||||||||
\(705\) | 23.1800 | 0.873010 | ||||||||
\(706\) | −3.56315 | −0.134101 | ||||||||
\(707\) | 9.24035 | 0.347519 | ||||||||
\(708\) | 35.1888 | 1.32247 | ||||||||
\(709\) | −32.7715 | −1.23076 | −0.615380 | − | 0.788231i | \(-0.710997\pi\) | ||||
−0.615380 | + | 0.788231i | \(0.710997\pi\) | |||||||
\(710\) | 24.1810 | 0.907497 | ||||||||
\(711\) | 4.85509 | 0.182080 | ||||||||
\(712\) | −10.7354 | −0.402327 | ||||||||
\(713\) | −20.8824 | −0.782054 | ||||||||
\(714\) | −13.0438 | −0.488154 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 53.6803 | 2.00613 | ||||||||
\(717\) | 15.7432 | 0.587939 | ||||||||
\(718\) | 42.8252 | 1.59822 | ||||||||
\(719\) | −46.4642 | −1.73282 | −0.866411 | − | 0.499331i | \(-0.833579\pi\) | ||||
−0.866411 | + | 0.499331i | \(0.833579\pi\) | |||||||
\(720\) | −7.06808 | −0.263412 | ||||||||
\(721\) | −13.3775 | −0.498204 | ||||||||
\(722\) | −18.3775 | −0.683940 | ||||||||
\(723\) | 29.8669 | 1.11076 | ||||||||
\(724\) | −44.5761 | −1.65666 | ||||||||
\(725\) | 1.80250 | 0.0669433 | ||||||||
\(726\) | −22.4894 | −0.834661 | ||||||||
\(727\) | 19.5059 | 0.723435 | 0.361717 | − | 0.932288i | \(-0.382191\pi\) | ||||
0.361717 | + | 0.932288i | \(0.382191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.6343 | −0.726700 | ||||||||
\(731\) | −21.6343 | −0.800175 | ||||||||
\(732\) | −20.7385 | −0.766518 | ||||||||
\(733\) | 21.6849 | 0.800952 | 0.400476 | − | 0.916307i | \(-0.368845\pi\) | ||||
0.400476 | + | 0.916307i | \(0.368845\pi\) | |||||||
\(734\) | −35.5684 | −1.31285 | ||||||||
\(735\) | −2.65859 | −0.0980635 | ||||||||
\(736\) | −27.9428 | −1.02998 | ||||||||
\(737\) | −8.81535 | −0.324718 | ||||||||
\(738\) | 22.3775 | 0.823727 | ||||||||
\(739\) | 44.3554 | 1.63164 | 0.815820 | − | 0.578306i | \(-0.196286\pi\) | ||||
0.815820 | + | 0.578306i | \(0.196286\pi\) | |||||||
\(740\) | −9.83496 | −0.361540 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.12842 | −0.151559 | ||||||||
\(743\) | 15.8112 | 0.580058 | 0.290029 | − | 0.957018i | \(-0.406335\pi\) | ||||
0.290029 | + | 0.957018i | \(0.406335\pi\) | |||||||
\(744\) | 6.67508 | 0.244720 | ||||||||
\(745\) | −36.7938 | −1.34802 | ||||||||
\(746\) | −34.6617 | −1.26905 | ||||||||
\(747\) | −15.8551 | −0.580107 | ||||||||
\(748\) | 10.2120 | 0.373388 | ||||||||
\(749\) | −9.84734 | −0.359814 | ||||||||
\(750\) | −16.5905 | −0.605800 | ||||||||
\(751\) | −11.4008 | −0.416019 | −0.208010 | − | 0.978127i | \(-0.566699\pi\) | ||||
−0.208010 | + | 0.978127i | \(0.566699\pi\) | |||||||
\(752\) | 23.1800 | 0.845288 | ||||||||
\(753\) | 20.7189 | 0.755039 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.1362 | 0.732830 | ||||||||
\(756\) | 2.53017 | 0.0920213 | ||||||||
\(757\) | 0.623486 | 0.0226610 | 0.0113305 | − | 0.999936i | \(-0.496393\pi\) | ||||
0.0113305 | + | 0.999936i | \(0.496393\pi\) | |||||||
\(758\) | 58.5859 | 2.12793 | ||||||||
\(759\) | 2.32492 | 0.0843893 | ||||||||
\(760\) | 15.7705 | 0.572057 | ||||||||
\(761\) | 36.2929 | 1.31562 | 0.657809 | − | 0.753185i | \(-0.271483\pi\) | ||||
0.657809 | + | 0.753185i | \(0.271483\pi\) | |||||||
\(762\) | −25.7793 | −0.933884 | ||||||||
\(763\) | 6.32492 | 0.228978 | ||||||||
\(764\) | −5.82111 | −0.210600 | ||||||||
\(765\) | 16.2929 | 0.589072 | ||||||||
\(766\) | 26.0547 | 0.941395 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −4.52142 | −0.163153 | ||||||||
\(769\) | −35.1305 | −1.26684 | −0.633420 | − | 0.773808i | \(-0.718349\pi\) | ||||
−0.633420 | + | 0.773808i | \(0.718349\pi\) | |||||||
\(770\) | 3.72667 | 0.134300 | ||||||||
\(771\) | −10.6508 | −0.383581 | ||||||||
\(772\) | 58.7628 | 2.11492 | ||||||||
\(773\) | 51.7901 | 1.86276 | 0.931381 | − | 0.364047i | \(-0.118605\pi\) | ||||
0.931381 | + | 0.364047i | \(0.118605\pi\) | |||||||
\(774\) | 7.51368 | 0.270074 | ||||||||
\(775\) | 12.2336 | 0.439444 | ||||||||
\(776\) | 3.35790 | 0.120542 | ||||||||
\(777\) | −1.46208 | −0.0524520 | ||||||||
\(778\) | 5.89682 | 0.211411 | ||||||||
\(779\) | 55.2687 | 1.98021 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.81436 | −0.100706 | ||||||||
\(782\) | 46.0470 | 1.64664 | ||||||||
\(783\) | −0.871581 | −0.0311478 | ||||||||
\(784\) | −2.65859 | −0.0949495 | ||||||||
\(785\) | 19.5905 | 0.699215 | ||||||||
\(786\) | −7.11193 | −0.253674 | ||||||||
\(787\) | 32.0041 | 1.14082 | 0.570412 | − | 0.821359i | \(-0.306784\pi\) | ||||
0.570412 | + | 0.821359i | \(0.306784\pi\) | |||||||
\(788\) | 28.6761 | 1.02154 | ||||||||
\(789\) | 23.6782 | 0.842966 | ||||||||
\(790\) | −27.4729 | −0.977444 | ||||||||
\(791\) | −13.2326 | −0.470497 | ||||||||
\(792\) | −0.743162 | −0.0264071 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.72879 | 0.0613524 | ||||||||
\(795\) | 5.15677 | 0.182892 | ||||||||
\(796\) | −40.0130 | −1.41822 | ||||||||
\(797\) | 15.0264 | 0.532261 | 0.266130 | − | 0.963937i | \(-0.414255\pi\) | ||||
0.266130 | + | 0.963937i | \(0.414255\pi\) | |||||||
\(798\) | 11.1888 | 0.396078 | ||||||||
\(799\) | −53.4332 | −1.89033 | ||||||||
\(800\) | 16.3698 | 0.578758 | ||||||||
\(801\) | 9.51368 | 0.336149 | ||||||||
\(802\) | −20.7793 | −0.733741 | ||||||||
\(803\) | 2.28519 | 0.0806425 | ||||||||
\(804\) | 33.8669 | 1.19440 | ||||||||
\(805\) | 9.38526 | 0.330787 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.477581 | 0.0168116 | ||||||||
\(808\) | 10.4270 | 0.366820 | ||||||||
\(809\) | −52.4729 | −1.84485 | −0.922425 | − | 0.386176i | \(-0.873796\pi\) | ||||
−0.922425 | + | 0.386176i | \(0.873796\pi\) | |||||||
\(810\) | −5.65859 | −0.198822 | ||||||||
\(811\) | 29.6627 | 1.04160 | 0.520799 | − | 0.853679i | \(-0.325634\pi\) | ||||
0.520799 | + | 0.853679i | \(0.325634\pi\) | |||||||
\(812\) | −2.20525 | −0.0773890 | ||||||||
\(813\) | −20.6421 | −0.723950 | ||||||||
\(814\) | 2.04947 | 0.0718340 | ||||||||
\(815\) | 56.1511 | 1.96689 | ||||||||
\(816\) | 16.2929 | 0.570367 | ||||||||
\(817\) | 18.5575 | 0.649245 | ||||||||
\(818\) | 40.0634 | 1.40079 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −70.7220 | −2.46972 | ||||||||
\(821\) | 5.77614 | 0.201589 | 0.100794 | − | 0.994907i | \(-0.467862\pi\) | ||||
0.100794 | + | 0.994907i | \(0.467862\pi\) | |||||||
\(822\) | −3.83860 | −0.133886 | ||||||||
\(823\) | −11.2568 | −0.392389 | −0.196194 | − | 0.980565i | \(-0.562858\pi\) | ||||
−0.196194 | + | 0.980565i | \(0.562858\pi\) | |||||||
\(824\) | −15.0954 | −0.525874 | ||||||||
\(825\) | −1.36201 | −0.0474192 | ||||||||
\(826\) | −29.6014 | −1.02996 | ||||||||
\(827\) | −20.0644 | −0.697709 | −0.348855 | − | 0.937177i | \(-0.613429\pi\) | ||||
−0.348855 | + | 0.937177i | \(0.613429\pi\) | |||||||
\(828\) | −8.93192 | −0.310406 | ||||||||
\(829\) | −31.6617 | −1.09966 | −0.549828 | − | 0.835278i | \(-0.685307\pi\) | ||||
−0.549828 | + | 0.835278i | \(0.685307\pi\) | |||||||
\(830\) | 89.7174 | 3.11414 | ||||||||
\(831\) | 26.3600 | 0.914419 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.12842 | 0.212337 | ||||||||
\(834\) | −2.40175 | −0.0831658 | ||||||||
\(835\) | 18.9309 | 0.655132 | ||||||||
\(836\) | −8.75965 | −0.302959 | ||||||||
\(837\) | −5.91542 | −0.204467 | ||||||||
\(838\) | 26.6530 | 0.920711 | ||||||||
\(839\) | 12.0506 | 0.416033 | 0.208016 | − | 0.978125i | \(-0.433299\pi\) | ||||
0.208016 | + | 0.978125i | \(0.433299\pi\) | |||||||
\(840\) | −3.00000 | −0.103510 | ||||||||
\(841\) | −28.2403 | −0.973805 | ||||||||
\(842\) | 58.6957 | 2.02279 | ||||||||
\(843\) | 0.205246 | 0.00706905 | ||||||||
\(844\) | 16.7143 | 0.575329 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.5575 | 0.638021 | ||||||||
\(847\) | 10.5663 | 0.363061 | ||||||||
\(848\) | 5.15677 | 0.177084 | ||||||||
\(849\) | −1.41824 | −0.0486739 | ||||||||
\(850\) | −26.9758 | −0.925261 | ||||||||
\(851\) | 5.16140 | 0.176931 | ||||||||
\(852\) | 10.8122 | 0.370421 | ||||||||
\(853\) | −36.1764 | −1.23866 | −0.619328 | − | 0.785133i | \(-0.712595\pi\) | ||||
−0.619328 | + | 0.785133i | \(0.712595\pi\) | |||||||
\(854\) | 17.4456 | 0.596976 | ||||||||
\(855\) | −13.9758 | −0.477961 | ||||||||
\(856\) | −11.1119 | −0.379798 | ||||||||
\(857\) | −30.6869 | −1.04825 | −0.524123 | − | 0.851643i | \(-0.675607\pi\) | ||||
−0.524123 | + | 0.851643i | \(0.675607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.93291 | −0.202428 | −0.101214 | − | 0.994865i | \(-0.532273\pi\) | ||||
−0.101214 | + | 0.994865i | \(0.532273\pi\) | |||||||
\(860\) | −23.7463 | −0.809741 | ||||||||
\(861\) | −10.5137 | −0.358305 | ||||||||
\(862\) | 1.89019 | 0.0643801 | ||||||||
\(863\) | −16.8299 | −0.572895 | −0.286447 | − | 0.958096i | \(-0.592474\pi\) | ||||
−0.286447 | + | 0.958096i | \(0.592474\pi\) | |||||||
\(864\) | −7.91542 | −0.269288 | ||||||||
\(865\) | −12.2043 | −0.414957 | ||||||||
\(866\) | −57.1073 | −1.94058 | ||||||||
\(867\) | −20.5575 | −0.698170 | ||||||||
\(868\) | −14.9670 | −0.508014 | ||||||||
\(869\) | 3.19750 | 0.108468 | ||||||||
\(870\) | 4.93192 | 0.167208 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 7.13716 | 0.241695 | ||||||||
\(873\) | −2.97576 | −0.100714 | ||||||||
\(874\) | −39.4982 | −1.33605 | ||||||||
\(875\) | 7.79475 | 0.263511 | ||||||||
\(876\) | −8.77926 | −0.296624 | ||||||||
\(877\) | 51.8679 | 1.75146 | 0.875728 | − | 0.482805i | \(-0.160382\pi\) | ||||
0.875728 | + | 0.482805i | \(0.160382\pi\) | |||||||
\(878\) | 72.3750 | 2.44254 | ||||||||
\(879\) | 30.6256 | 1.03298 | ||||||||
\(880\) | −4.65495 | −0.156918 | ||||||||
\(881\) | −16.2609 | −0.547845 | −0.273923 | − | 0.961752i | \(-0.588321\pi\) | ||||
−0.273923 | + | 0.961752i | \(0.588321\pi\) | |||||||
\(882\) | −2.12842 | −0.0716676 | ||||||||
\(883\) | −21.5049 | −0.723699 | −0.361849 | − | 0.932237i | \(-0.617855\pi\) | ||||
−0.361849 | + | 0.932237i | \(0.617855\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.9748 | 1.24289 | ||||||||
\(886\) | 44.6266 | 1.49926 | ||||||||
\(887\) | 0.634347 | 0.0212993 | 0.0106496 | − | 0.999943i | \(-0.496610\pi\) | ||||
0.0106496 | + | 0.999943i | \(0.496610\pi\) | |||||||
\(888\) | −1.64984 | −0.0553651 | ||||||||
\(889\) | 12.1119 | 0.406221 | ||||||||
\(890\) | −53.8340 | −1.80452 | ||||||||
\(891\) | 0.658587 | 0.0220635 | ||||||||
\(892\) | 24.8045 | 0.830516 | ||||||||
\(893\) | 45.8340 | 1.53378 | ||||||||
\(894\) | −29.4565 | −0.985171 | ||||||||
\(895\) | 56.4049 | 1.88541 | ||||||||
\(896\) | −8.71018 | −0.290987 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.9329 | 1.26584 | ||||||||
\(899\) | 5.15577 | 0.171955 | ||||||||
\(900\) | 5.23260 | 0.174420 | ||||||||
\(901\) | −11.8871 | −0.396016 | ||||||||
\(902\) | 14.7375 | 0.490706 | ||||||||
\(903\) | −3.53017 | −0.117477 | ||||||||
\(904\) | −14.9319 | −0.496628 | ||||||||
\(905\) | −46.8386 | −1.55697 | ||||||||
\(906\) | 16.1207 | 0.535573 | ||||||||
\(907\) | −24.3533 | −0.808637 | −0.404319 | − | 0.914618i | \(-0.632491\pi\) | ||||
−0.404319 | + | 0.914618i | \(0.632491\pi\) | |||||||
\(908\) | 41.2239 | 1.36806 | ||||||||
\(909\) | −9.24035 | −0.306483 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.71217 | −0.0898582 | −0.0449291 | − | 0.998990i | \(-0.514306\pi\) | ||||
−0.0449291 | + | 0.998990i | \(0.514306\pi\) | |||||||
\(912\) | −13.9758 | −0.462784 | ||||||||
\(913\) | −10.4420 | −0.345578 | ||||||||
\(914\) | −87.3837 | −2.89040 | ||||||||
\(915\) | −21.7911 | −0.720392 | ||||||||
\(916\) | 58.6793 | 1.93882 | ||||||||
\(917\) | 3.34141 | 0.110343 | ||||||||
\(918\) | 13.0438 | 0.430511 | ||||||||
\(919\) | 4.97576 | 0.164135 | 0.0820676 | − | 0.996627i | \(-0.473848\pi\) | ||||
0.0820676 | + | 0.996627i | \(0.473848\pi\) | |||||||
\(920\) | 10.5905 | 0.349159 | ||||||||
\(921\) | 4.47858 | 0.147574 | ||||||||
\(922\) | −76.5967 | −2.52258 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.66633 | 0.0548184 | ||||||||
\(925\) | −3.02371 | −0.0994190 | ||||||||
\(926\) | −27.9944 | −0.919952 | ||||||||
\(927\) | 13.3775 | 0.439375 | ||||||||
\(928\) | 6.89893 | 0.226469 | ||||||||
\(929\) | −50.6334 | −1.66123 | −0.830613 | − | 0.556850i | \(-0.812010\pi\) | ||||
−0.830613 | + | 0.556850i | \(0.812010\pi\) | |||||||
\(930\) | 33.4729 | 1.09762 | ||||||||
\(931\) | −5.25684 | −0.172286 | ||||||||
\(932\) | −6.59613 | −0.216064 | ||||||||
\(933\) | −0.675078 | −0.0221011 | ||||||||
\(934\) | −41.4466 | −1.35617 | ||||||||
\(935\) | 10.7303 | 0.350919 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.5018 | 0.637097 | 0.318548 | − | 0.947907i | \(-0.396805\pi\) | ||||
0.318548 | + | 0.947907i | \(0.396805\pi\) | |||||||
\(938\) | −28.4894 | −0.930213 | ||||||||
\(939\) | −10.0242 | −0.327129 | ||||||||
\(940\) | −58.6493 | −1.91293 | ||||||||
\(941\) | 9.95827 | 0.324630 | 0.162315 | − | 0.986739i | \(-0.448104\pi\) | ||||
0.162315 | + | 0.986739i | \(0.448104\pi\) | |||||||
\(942\) | 15.6838 | 0.511007 | ||||||||
\(943\) | 37.1150 | 1.20863 | ||||||||
\(944\) | 36.9748 | 1.20343 | ||||||||
\(945\) | 2.65859 | 0.0864838 | ||||||||
\(946\) | 4.94841 | 0.160887 | ||||||||
\(947\) | −60.0186 | −1.95034 | −0.975171 | − | 0.221452i | \(-0.928921\pi\) | ||||
−0.975171 | + | 0.221452i | \(0.928921\pi\) | |||||||
\(948\) | −12.2842 | −0.398972 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 23.1393 | 0.750737 | ||||||||
\(951\) | 27.1558 | 0.880586 | ||||||||
\(952\) | 6.91542 | 0.224130 | ||||||||
\(953\) | −1.59925 | −0.0518047 | −0.0259023 | − | 0.999664i | \(-0.508246\pi\) | ||||
−0.0259023 | + | 0.999664i | \(0.508246\pi\) | |||||||
\(954\) | 4.12842 | 0.133663 | ||||||||
\(955\) | −6.11656 | −0.197927 | ||||||||
\(956\) | −39.8328 | −1.28829 | ||||||||
\(957\) | −0.574012 | −0.0185552 | ||||||||
\(958\) | 10.7354 | 0.346845 | ||||||||
\(959\) | 1.80350 | 0.0582380 | ||||||||
\(960\) | 30.6540 | 0.989352 | ||||||||
\(961\) | 3.99225 | 0.128782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.84734 | 0.317326 | ||||||||
\(964\) | −75.5684 | −2.43389 | ||||||||
\(965\) | 61.7453 | 1.98765 | ||||||||
\(966\) | 7.51368 | 0.241749 | ||||||||
\(967\) | −29.7705 | −0.957355 | −0.478678 | − | 0.877991i | \(-0.658884\pi\) | ||||
−0.478678 | + | 0.877991i | \(0.658884\pi\) | |||||||
\(968\) | 11.9232 | 0.383225 | ||||||||
\(969\) | 32.2161 | 1.03493 | ||||||||
\(970\) | 16.8386 | 0.540655 | ||||||||
\(971\) | 36.1810 | 1.16110 | 0.580552 | − | 0.814223i | \(-0.302837\pi\) | ||||
0.580552 | + | 0.814223i | \(0.302837\pi\) | |||||||
\(972\) | −2.53017 | −0.0811552 | ||||||||
\(973\) | 1.12842 | 0.0361755 | ||||||||
\(974\) | −26.5926 | −0.852083 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21.7911 | −0.697517 | ||||||||
\(977\) | 4.30068 | 0.137591 | 0.0687955 | − | 0.997631i | \(-0.478084\pi\) | ||||
0.0687955 | + | 0.997631i | \(0.478084\pi\) | |||||||
\(978\) | 44.9536 | 1.43746 | ||||||||
\(979\) | 6.26558 | 0.200249 | ||||||||
\(980\) | 6.72667 | 0.214876 | ||||||||
\(981\) | −6.32492 | −0.201939 | ||||||||
\(982\) | 0.144911 | 0.00462428 | ||||||||
\(983\) | −7.42599 | −0.236852 | −0.118426 | − | 0.992963i | \(-0.537785\pi\) | ||||
−0.118426 | + | 0.992963i | \(0.537785\pi\) | |||||||
\(984\) | −11.8638 | −0.378205 | ||||||||
\(985\) | 30.1315 | 0.960070 | ||||||||
\(986\) | −11.3688 | −0.362055 | ||||||||
\(987\) | −8.71892 | −0.277526 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.4621 | 0.396271 | ||||||||
\(990\) | −3.72667 | −0.118441 | ||||||||
\(991\) | 10.2764 | 0.326442 | 0.163221 | − | 0.986590i | \(-0.447812\pi\) | ||||
0.163221 | + | 0.986590i | \(0.447812\pi\) | |||||||
\(992\) | 46.8231 | 1.48663 | ||||||||
\(993\) | 23.8112 | 0.755627 | ||||||||
\(994\) | −9.09544 | −0.288490 | ||||||||
\(995\) | −42.0438 | −1.33288 | ||||||||
\(996\) | 40.1160 | 1.27113 | ||||||||
\(997\) | −23.3894 | −0.740749 | −0.370374 | − | 0.928883i | \(-0.620771\pi\) | ||||
−0.370374 | + | 0.928883i | \(0.620771\pi\) | |||||||
\(998\) | −4.56315 | −0.144444 | ||||||||
\(999\) | 1.46208 | 0.0462583 |
(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.l.1.1 | 3 | ||
13.4 | even | 6 | 273.2.k.b.211.1 | yes | 6 | ||
13.10 | even | 6 | 273.2.k.b.22.1 | ✓ | 6 | ||
13.12 | even | 2 | 3549.2.a.m.1.3 | 3 | |||
39.17 | odd | 6 | 819.2.o.f.757.3 | 6 | |||
39.23 | odd | 6 | 819.2.o.f.568.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.k.b.22.1 | ✓ | 6 | 13.10 | even | 6 | ||
273.2.k.b.211.1 | yes | 6 | 13.4 | even | 6 | ||
819.2.o.f.568.3 | 6 | 39.23 | odd | 6 | |||
819.2.o.f.757.3 | 6 | 39.17 | odd | 6 | |||
3549.2.a.l.1.1 | 3 | 1.1 | even | 1 | trivial | ||
3549.2.a.m.1.3 | 3 | 13.12 | even | 2 |