Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3475,2,Mod(1,3475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3475.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3475 = 5^{2} \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3475.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: | \(27.7480147024\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{7} - x^{6} - 11x^{5} + 8x^{4} + 35x^{3} - 10x^{2} - 32x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 139) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.48318\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.48318 | 1.75587 | 0.877935 | − | 0.478779i | \(-0.158921\pi\) | ||||
0.877935 | + | 0.478779i | \(0.158921\pi\) | |||||||
\(3\) | −1.56460 | −0.903322 | −0.451661 | − | 0.892190i | \(-0.649168\pi\) | ||||
−0.451661 | + | 0.892190i | \(0.649168\pi\) | |||||||
\(4\) | 4.16616 | 2.08308 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.88518 | −1.58612 | ||||||||
\(7\) | 3.67776 | 1.39006 | 0.695031 | − | 0.718980i | \(-0.255391\pi\) | ||||
0.695031 | + | 0.718980i | \(0.255391\pi\) | |||||||
\(8\) | 5.37897 | 1.90175 | ||||||||
\(9\) | −0.552027 | −0.184009 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.01926 | 1.51336 | 0.756682 | − | 0.653783i | \(-0.226819\pi\) | ||||
0.756682 | + | 0.653783i | \(0.226819\pi\) | |||||||
\(12\) | −6.51838 | −1.88169 | ||||||||
\(13\) | −1.93452 | −0.536539 | −0.268270 | − | 0.963344i | \(-0.586452\pi\) | ||||
−0.268270 | + | 0.963344i | \(0.586452\pi\) | |||||||
\(14\) | 9.13252 | 2.44077 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.02459 | 1.25615 | ||||||||
\(17\) | 0.320577 | 0.0777514 | 0.0388757 | − | 0.999244i | \(-0.487622\pi\) | ||||
0.0388757 | + | 0.999244i | \(0.487622\pi\) | |||||||
\(18\) | −1.37078 | −0.323096 | ||||||||
\(19\) | −2.85843 | −0.655768 | −0.327884 | − | 0.944718i | \(-0.606336\pi\) | ||||
−0.327884 | + | 0.944718i | \(0.606336\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.75422 | −1.25567 | ||||||||
\(22\) | 12.4637 | 2.65727 | ||||||||
\(23\) | 1.64820 | 0.343674 | 0.171837 | − | 0.985125i | \(-0.445030\pi\) | ||||
0.171837 | + | 0.985125i | \(0.445030\pi\) | |||||||
\(24\) | −8.41593 | −1.71789 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.80375 | −0.942094 | ||||||||
\(27\) | 5.55750 | 1.06954 | ||||||||
\(28\) | 15.3221 | 2.89561 | ||||||||
\(29\) | 8.72513 | 1.62022 | 0.810108 | − | 0.586280i | \(-0.199408\pi\) | ||||
0.810108 | + | 0.586280i | \(0.199408\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.09788 | 0.197185 | 0.0985924 | − | 0.995128i | \(-0.468566\pi\) | ||||
0.0985924 | + | 0.995128i | \(0.468566\pi\) | |||||||
\(32\) | 1.71901 | 0.303882 | ||||||||
\(33\) | −7.85313 | −1.36705 | ||||||||
\(34\) | 0.796050 | 0.136521 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.29983 | −0.383306 | ||||||||
\(37\) | 4.88302 | 0.802763 | 0.401382 | − | 0.915911i | \(-0.368530\pi\) | ||||
0.401382 | + | 0.915911i | \(0.368530\pi\) | |||||||
\(38\) | −7.09798 | −1.15144 | ||||||||
\(39\) | 3.02675 | 0.484668 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.59487 | −1.49847 | −0.749233 | − | 0.662306i | \(-0.769578\pi\) | ||||
−0.749233 | + | 0.662306i | \(0.769578\pi\) | |||||||
\(42\) | −14.2887 | −2.20480 | ||||||||
\(43\) | 5.85039 | 0.892176 | 0.446088 | − | 0.894989i | \(-0.352817\pi\) | ||||
0.446088 | + | 0.894989i | \(0.352817\pi\) | |||||||
\(44\) | 20.9111 | 3.15246 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.09278 | 0.603447 | ||||||||
\(47\) | 6.33260 | 0.923704 | 0.461852 | − | 0.886957i | \(-0.347185\pi\) | ||||
0.461852 | + | 0.886957i | \(0.347185\pi\) | |||||||
\(48\) | −7.86147 | −1.13471 | ||||||||
\(49\) | 6.52589 | 0.932270 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.501575 | −0.0702346 | ||||||||
\(52\) | −8.05953 | −1.11766 | ||||||||
\(53\) | −6.55399 | −0.900259 | −0.450130 | − | 0.892963i | \(-0.648622\pi\) | ||||
−0.450130 | + | 0.892963i | \(0.648622\pi\) | |||||||
\(54\) | 13.8003 | 1.87798 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19.7825 | 2.64355 | ||||||||
\(57\) | 4.47230 | 0.592370 | ||||||||
\(58\) | 21.6660 | 2.84489 | ||||||||
\(59\) | −6.51771 | −0.848534 | −0.424267 | − | 0.905537i | \(-0.639468\pi\) | ||||
−0.424267 | + | 0.905537i | \(0.639468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3143 | −1.32062 | −0.660308 | − | 0.750995i | \(-0.729574\pi\) | ||||
−0.660308 | + | 0.750995i | \(0.729574\pi\) | |||||||
\(62\) | 2.72623 | 0.346231 | ||||||||
\(63\) | −2.03022 | −0.255784 | ||||||||
\(64\) | −5.78057 | −0.722571 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −19.5007 | −2.40037 | ||||||||
\(67\) | 0.221404 | 0.0270488 | 0.0135244 | − | 0.999909i | \(-0.495695\pi\) | ||||
0.0135244 | + | 0.999909i | \(0.495695\pi\) | |||||||
\(68\) | 1.33558 | 0.161963 | ||||||||
\(69\) | −2.57878 | −0.310448 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.41910 | −0.524451 | −0.262225 | − | 0.965007i | \(-0.584456\pi\) | ||||
−0.262225 | + | 0.965007i | \(0.584456\pi\) | |||||||
\(72\) | −2.96933 | −0.349939 | ||||||||
\(73\) | 1.92636 | 0.225464 | 0.112732 | − | 0.993625i | \(-0.464040\pi\) | ||||
0.112732 | + | 0.993625i | \(0.464040\pi\) | |||||||
\(74\) | 12.1254 | 1.40955 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.9087 | −1.36602 | ||||||||
\(77\) | 18.4596 | 2.10367 | ||||||||
\(78\) | 7.51595 | 0.851014 | ||||||||
\(79\) | 16.5019 | 1.85661 | 0.928305 | − | 0.371820i | \(-0.121266\pi\) | ||||
0.928305 | + | 0.371820i | \(0.121266\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.03919 | −0.782132 | ||||||||
\(82\) | −23.8257 | −2.63111 | ||||||||
\(83\) | 11.1705 | 1.22612 | 0.613061 | − | 0.790036i | \(-0.289938\pi\) | ||||
0.613061 | + | 0.790036i | \(0.289938\pi\) | |||||||
\(84\) | −23.9730 | −2.61567 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.5276 | 1.56655 | ||||||||
\(87\) | −13.6513 | −1.46358 | ||||||||
\(88\) | 26.9984 | 2.87804 | ||||||||
\(89\) | 5.44197 | 0.576848 | 0.288424 | − | 0.957503i | \(-0.406869\pi\) | ||||
0.288424 | + | 0.957503i | \(0.406869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.11469 | −0.745822 | ||||||||
\(92\) | 6.86668 | 0.715901 | ||||||||
\(93\) | −1.71774 | −0.178121 | ||||||||
\(94\) | 15.7249 | 1.62190 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.68957 | −0.274503 | ||||||||
\(97\) | −3.46235 | −0.351548 | −0.175774 | − | 0.984431i | \(-0.556243\pi\) | ||||
−0.175774 | + | 0.984431i | \(0.556243\pi\) | |||||||
\(98\) | 16.2049 | 1.63695 | ||||||||
\(99\) | −2.77077 | −0.278473 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.21196 | 0.817120 | 0.408560 | − | 0.912731i | \(-0.366031\pi\) | ||||
0.408560 | + | 0.912731i | \(0.366031\pi\) | |||||||
\(102\) | −1.24550 | −0.123323 | ||||||||
\(103\) | 4.39161 | 0.432718 | 0.216359 | − | 0.976314i | \(-0.430582\pi\) | ||||
0.216359 | + | 0.976314i | \(0.430582\pi\) | |||||||
\(104\) | −10.4057 | −1.02036 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.2747 | −1.58074 | ||||||||
\(107\) | 1.46816 | 0.141932 | 0.0709660 | − | 0.997479i | \(-0.477392\pi\) | ||||
0.0709660 | + | 0.997479i | \(0.477392\pi\) | |||||||
\(108\) | 23.1535 | 2.22794 | ||||||||
\(109\) | −10.9449 | −1.04833 | −0.524166 | − | 0.851616i | \(-0.675623\pi\) | ||||
−0.524166 | + | 0.851616i | \(0.675623\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.63997 | −0.725154 | ||||||||
\(112\) | 18.4792 | 1.74612 | ||||||||
\(113\) | −15.7092 | −1.47779 | −0.738897 | − | 0.673819i | \(-0.764653\pi\) | ||||
−0.738897 | + | 0.673819i | \(0.764653\pi\) | |||||||
\(114\) | 11.1055 | 1.04013 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 36.3503 | 3.37504 | ||||||||
\(117\) | 1.06791 | 0.0987280 | ||||||||
\(118\) | −16.1846 | −1.48992 | ||||||||
\(119\) | 1.17900 | 0.108079 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.1930 | 1.29027 | ||||||||
\(122\) | −25.6123 | −2.31883 | ||||||||
\(123\) | 15.0121 | 1.35360 | ||||||||
\(124\) | 4.57394 | 0.410752 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.04140 | −0.449123 | ||||||||
\(127\) | 8.77542 | 0.778692 | 0.389346 | − | 0.921091i | \(-0.372701\pi\) | ||||
0.389346 | + | 0.921091i | \(0.372701\pi\) | |||||||
\(128\) | −17.7922 | −1.57262 | ||||||||
\(129\) | −9.15352 | −0.805923 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.17930 | 0.365147 | 0.182574 | − | 0.983192i | \(-0.441557\pi\) | ||||
0.182574 | + | 0.983192i | \(0.441557\pi\) | |||||||
\(132\) | −32.7174 | −2.84769 | ||||||||
\(133\) | −10.5126 | −0.911558 | ||||||||
\(134\) | 0.549785 | 0.0474942 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.72437 | 0.147864 | ||||||||
\(137\) | 8.14588 | 0.695950 | 0.347975 | − | 0.937504i | \(-0.386869\pi\) | ||||
0.347975 | + | 0.937504i | \(0.386869\pi\) | |||||||
\(138\) | −6.40356 | −0.545107 | ||||||||
\(139\) | 1.00000 | 0.0848189 | ||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.90798 | −0.834402 | ||||||||
\(142\) | −10.9734 | −0.920868 | ||||||||
\(143\) | −9.70986 | −0.811979 | ||||||||
\(144\) | −2.77371 | −0.231142 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.78350 | 0.395885 | ||||||||
\(147\) | −10.2104 | −0.842140 | ||||||||
\(148\) | 20.3435 | 1.67222 | ||||||||
\(149\) | 0.336484 | 0.0275658 | 0.0137829 | − | 0.999905i | \(-0.495613\pi\) | ||||
0.0137829 | + | 0.999905i | \(0.495613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6069 | 1.43283 | 0.716413 | − | 0.697677i | \(-0.245783\pi\) | ||||
0.716413 | + | 0.697677i | \(0.245783\pi\) | |||||||
\(152\) | −15.3754 | −1.24711 | ||||||||
\(153\) | −0.176967 | −0.0143070 | ||||||||
\(154\) | 45.8385 | 3.69377 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 12.6099 | 1.00960 | ||||||||
\(157\) | −5.49163 | −0.438280 | −0.219140 | − | 0.975693i | \(-0.570325\pi\) | ||||
−0.219140 | + | 0.975693i | \(0.570325\pi\) | |||||||
\(158\) | 40.9771 | 3.25997 | ||||||||
\(159\) | 10.2544 | 0.813224 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.06168 | 0.477728 | ||||||||
\(162\) | −17.4795 | −1.37332 | ||||||||
\(163\) | 3.37555 | 0.264393 | 0.132197 | − | 0.991224i | \(-0.457797\pi\) | ||||
0.132197 | + | 0.991224i | \(0.457797\pi\) | |||||||
\(164\) | −39.9738 | −3.12143 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.7383 | 2.15291 | ||||||||
\(167\) | −2.95641 | −0.228774 | −0.114387 | − | 0.993436i | \(-0.536490\pi\) | ||||
−0.114387 | + | 0.993436i | \(0.536490\pi\) | |||||||
\(168\) | −30.9517 | −2.38798 | ||||||||
\(169\) | −9.25763 | −0.712126 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.57793 | 0.120667 | ||||||||
\(172\) | 24.3737 | 1.85848 | ||||||||
\(173\) | −23.9199 | −1.81860 | −0.909298 | − | 0.416145i | \(-0.863381\pi\) | ||||
−0.909298 | + | 0.416145i | \(0.863381\pi\) | |||||||
\(174\) | −33.8987 | −2.56985 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.2197 | 1.90101 | ||||||||
\(177\) | 10.1976 | 0.766500 | ||||||||
\(178\) | 13.5134 | 1.01287 | ||||||||
\(179\) | 0.981994 | 0.0733977 | 0.0366989 | − | 0.999326i | \(-0.488316\pi\) | ||||
0.0366989 | + | 0.999326i | \(0.488316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.43082 | 0.552328 | 0.276164 | − | 0.961111i | \(-0.410937\pi\) | ||||
0.276164 | + | 0.961111i | \(0.410937\pi\) | |||||||
\(182\) | −17.6670 | −1.30957 | ||||||||
\(183\) | 16.1378 | 1.19294 | ||||||||
\(184\) | 8.86562 | 0.653582 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.26545 | −0.312758 | ||||||||
\(187\) | 1.60906 | 0.117666 | ||||||||
\(188\) | 26.3826 | 1.92415 | ||||||||
\(189\) | 20.4391 | 1.48673 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.4018 | 1.04208 | 0.521040 | − | 0.853532i | \(-0.325544\pi\) | ||||
0.521040 | + | 0.853532i | \(0.325544\pi\) | |||||||
\(192\) | 9.04428 | 0.652714 | ||||||||
\(193\) | 10.7996 | 0.777370 | 0.388685 | − | 0.921371i | \(-0.372929\pi\) | ||||
0.388685 | + | 0.921371i | \(0.372929\pi\) | |||||||
\(194\) | −8.59762 | −0.617273 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 27.1879 | 1.94199 | ||||||||
\(197\) | −23.3541 | −1.66391 | −0.831954 | − | 0.554844i | \(-0.812778\pi\) | ||||
−0.831954 | + | 0.554844i | \(0.812778\pi\) | |||||||
\(198\) | −6.88030 | −0.488962 | ||||||||
\(199\) | −19.1019 | −1.35410 | −0.677048 | − | 0.735939i | \(-0.736741\pi\) | ||||
−0.677048 | + | 0.735939i | \(0.736741\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.346409 | −0.0244338 | ||||||||
\(202\) | 20.3917 | 1.43476 | ||||||||
\(203\) | 32.0889 | 2.25220 | ||||||||
\(204\) | −2.08964 | −0.146304 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.9051 | 0.759797 | ||||||||
\(207\) | −0.909852 | −0.0632391 | ||||||||
\(208\) | −9.72017 | −0.673973 | ||||||||
\(209\) | −14.3472 | −0.992416 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.95125 | −0.272015 | −0.136008 | − | 0.990708i | \(-0.543427\pi\) | ||||
−0.136008 | + | 0.990708i | \(0.543427\pi\) | |||||||
\(212\) | −27.3050 | −1.87531 | ||||||||
\(213\) | 6.91413 | 0.473748 | ||||||||
\(214\) | 3.64569 | 0.249214 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 29.8936 | 2.03400 | ||||||||
\(217\) | 4.03773 | 0.274099 | ||||||||
\(218\) | −27.1781 | −1.84073 | ||||||||
\(219\) | −3.01399 | −0.203666 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.620163 | −0.0417167 | ||||||||
\(222\) | −18.9714 | −1.27328 | ||||||||
\(223\) | −8.53385 | −0.571469 | −0.285734 | − | 0.958309i | \(-0.592238\pi\) | ||||
−0.285734 | + | 0.958309i | \(0.592238\pi\) | |||||||
\(224\) | 6.32211 | 0.422414 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −39.0086 | −2.59481 | ||||||||
\(227\) | 6.89031 | 0.457326 | 0.228663 | − | 0.973506i | \(-0.426565\pi\) | ||||
0.228663 | + | 0.973506i | \(0.426565\pi\) | |||||||
\(228\) | 18.6323 | 1.23396 | ||||||||
\(229\) | 5.62355 | 0.371615 | 0.185807 | − | 0.982586i | \(-0.440510\pi\) | ||||
0.185807 | + | 0.982586i | \(0.440510\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.8819 | −1.90029 | ||||||||
\(232\) | 46.9322 | 3.08125 | ||||||||
\(233\) | 1.43017 | 0.0936935 | 0.0468468 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468468 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(234\) | 2.65180 | 0.173354 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −27.1539 | −1.76757 | ||||||||
\(237\) | −25.8189 | −1.67712 | ||||||||
\(238\) | 2.92768 | 0.189773 | ||||||||
\(239\) | 11.4060 | 0.737796 | 0.368898 | − | 0.929470i | \(-0.379735\pi\) | ||||
0.368898 | + | 0.929470i | \(0.379735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5641 | 1.06699 | 0.533493 | − | 0.845804i | \(-0.320879\pi\) | ||||
0.533493 | + | 0.845804i | \(0.320879\pi\) | |||||||
\(242\) | 35.2436 | 2.26555 | ||||||||
\(243\) | −5.65899 | −0.363025 | ||||||||
\(244\) | −42.9712 | −2.75095 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 37.2778 | 2.37674 | ||||||||
\(247\) | 5.52968 | 0.351845 | ||||||||
\(248\) | 5.90545 | 0.374997 | ||||||||
\(249\) | −17.4774 | −1.10758 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.14003 | 0.450674 | 0.225337 | − | 0.974281i | \(-0.427652\pi\) | ||||
0.225337 | + | 0.974281i | \(0.427652\pi\) | |||||||
\(252\) | −8.45823 | −0.532818 | ||||||||
\(253\) | 8.27275 | 0.520104 | ||||||||
\(254\) | 21.7909 | 1.36728 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.6200 | −2.03875 | ||||||||
\(257\) | −23.1376 | −1.44328 | −0.721641 | − | 0.692268i | \(-0.756612\pi\) | ||||
−0.721641 | + | 0.692268i | \(0.756612\pi\) | |||||||
\(258\) | −22.7298 | −1.41510 | ||||||||
\(259\) | 17.9586 | 1.11589 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.81651 | −0.298134 | ||||||||
\(262\) | 10.3779 | 0.641151 | ||||||||
\(263\) | −28.9163 | −1.78306 | −0.891528 | − | 0.452966i | \(-0.850366\pi\) | ||||
−0.891528 | + | 0.452966i | \(0.850366\pi\) | |||||||
\(264\) | −42.2417 | −2.59980 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −26.1046 | −1.60058 | ||||||||
\(267\) | −8.51451 | −0.521079 | ||||||||
\(268\) | 0.922405 | 0.0563449 | ||||||||
\(269\) | 4.15750 | 0.253487 | 0.126744 | − | 0.991936i | \(-0.459547\pi\) | ||||
0.126744 | + | 0.991936i | \(0.459547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.73906 | −0.470115 | −0.235057 | − | 0.971982i | \(-0.575528\pi\) | ||||
−0.235057 | + | 0.971982i | \(0.575528\pi\) | |||||||
\(272\) | 1.61077 | 0.0976672 | ||||||||
\(273\) | 11.1316 | 0.673718 | ||||||||
\(274\) | 20.2277 | 1.22200 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.7436 | −0.646689 | ||||||||
\(277\) | −3.93125 | −0.236206 | −0.118103 | − | 0.993001i | \(-0.537681\pi\) | ||||
−0.118103 | + | 0.993001i | \(0.537681\pi\) | |||||||
\(278\) | 2.48318 | 0.148931 | ||||||||
\(279\) | −0.606059 | −0.0362838 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5398 | −0.807717 | −0.403859 | − | 0.914821i | \(-0.632331\pi\) | ||||
−0.403859 | + | 0.914821i | \(0.632331\pi\) | |||||||
\(282\) | −24.6033 | −1.46510 | ||||||||
\(283\) | −19.1993 | −1.14128 | −0.570641 | − | 0.821200i | \(-0.693305\pi\) | ||||
−0.570641 | + | 0.821200i | \(0.693305\pi\) | |||||||
\(284\) | −18.4107 | −1.09247 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.1113 | −1.42573 | ||||||||
\(287\) | −35.2876 | −2.08296 | ||||||||
\(288\) | −0.948942 | −0.0559169 | ||||||||
\(289\) | −16.8972 | −0.993955 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.41719 | 0.317561 | ||||||||
\(292\) | 8.02554 | 0.469659 | ||||||||
\(293\) | 25.5252 | 1.49120 | 0.745598 | − | 0.666396i | \(-0.232164\pi\) | ||||
0.745598 | + | 0.666396i | \(0.232164\pi\) | |||||||
\(294\) | −25.3542 | −1.47869 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 26.2656 | 1.52666 | ||||||||
\(297\) | 27.8945 | 1.61861 | ||||||||
\(298\) | 0.835549 | 0.0484020 | ||||||||
\(299\) | −3.18848 | −0.184395 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.5163 | 1.24018 | ||||||||
\(302\) | 43.7209 | 2.51586 | ||||||||
\(303\) | −12.8484 | −0.738123 | ||||||||
\(304\) | −14.3624 | −0.823742 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.439441 | −0.0251212 | ||||||||
\(307\) | −6.77909 | −0.386903 | −0.193452 | − | 0.981110i | \(-0.561968\pi\) | ||||
−0.193452 | + | 0.981110i | \(0.561968\pi\) | |||||||
\(308\) | 76.9058 | 4.38211 | ||||||||
\(309\) | −6.87111 | −0.390884 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.0482 | −1.81729 | −0.908643 | − | 0.417573i | \(-0.862881\pi\) | ||||
−0.908643 | + | 0.417573i | \(0.862881\pi\) | |||||||
\(312\) | 16.2808 | 0.921718 | ||||||||
\(313\) | −2.35936 | −0.133359 | −0.0666795 | − | 0.997774i | \(-0.521240\pi\) | ||||
−0.0666795 | + | 0.997774i | \(0.521240\pi\) | |||||||
\(314\) | −13.6367 | −0.769563 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 68.7496 | 3.86747 | ||||||||
\(317\) | −8.05786 | −0.452574 | −0.226287 | − | 0.974061i | \(-0.572659\pi\) | ||||
−0.226287 | + | 0.974061i | \(0.572659\pi\) | |||||||
\(318\) | 25.4634 | 1.42792 | ||||||||
\(319\) | 43.7937 | 2.45198 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.29708 | −0.128210 | ||||||||
\(322\) | 15.0522 | 0.838828 | ||||||||
\(323\) | −0.916347 | −0.0509869 | ||||||||
\(324\) | −29.3264 | −1.62924 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.38208 | 0.464241 | ||||||||
\(327\) | 17.1244 | 0.946981 | ||||||||
\(328\) | −51.6104 | −2.84971 | ||||||||
\(329\) | 23.2897 | 1.28400 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.67255 | −0.531651 | −0.265826 | − | 0.964021i | \(-0.585645\pi\) | ||||
−0.265826 | + | 0.964021i | \(0.585645\pi\) | |||||||
\(332\) | 46.5381 | 2.55411 | ||||||||
\(333\) | −2.69556 | −0.147716 | ||||||||
\(334\) | −7.34128 | −0.401697 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −28.9126 | −1.57731 | ||||||||
\(337\) | 11.2077 | 0.610521 | 0.305261 | − | 0.952269i | \(-0.401256\pi\) | ||||
0.305261 | + | 0.952269i | \(0.401256\pi\) | |||||||
\(338\) | −22.9883 | −1.25040 | ||||||||
\(339\) | 24.5786 | 1.33492 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.51054 | 0.298412 | ||||||||
\(342\) | 3.91828 | 0.211876 | ||||||||
\(343\) | −1.74367 | −0.0941491 | ||||||||
\(344\) | 31.4691 | 1.69670 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −59.3973 | −3.19322 | ||||||||
\(347\) | −2.42372 | −0.130112 | −0.0650561 | − | 0.997882i | \(-0.520723\pi\) | ||||
−0.0650561 | + | 0.997882i | \(0.520723\pi\) | |||||||
\(348\) | −56.8737 | −3.04875 | ||||||||
\(349\) | −19.8877 | −1.06457 | −0.532283 | − | 0.846567i | \(-0.678666\pi\) | ||||
−0.532283 | + | 0.846567i | \(0.678666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.7511 | −0.573851 | ||||||||
\(352\) | 8.62818 | 0.459883 | ||||||||
\(353\) | −2.50948 | −0.133566 | −0.0667831 | − | 0.997768i | \(-0.521274\pi\) | ||||
−0.0667831 | + | 0.997768i | \(0.521274\pi\) | |||||||
\(354\) | 25.3225 | 1.34587 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 22.6721 | 1.20162 | ||||||||
\(357\) | −1.84467 | −0.0976303 | ||||||||
\(358\) | 2.43847 | 0.128877 | ||||||||
\(359\) | −11.0468 | −0.583029 | −0.291515 | − | 0.956566i | \(-0.594159\pi\) | ||||
−0.291515 | + | 0.956566i | \(0.594159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.8294 | −0.569968 | ||||||||
\(362\) | 18.4520 | 0.969817 | ||||||||
\(363\) | −22.2063 | −1.16553 | ||||||||
\(364\) | −29.6410 | −1.55361 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 40.0731 | 2.09465 | ||||||||
\(367\) | −28.7068 | −1.49848 | −0.749242 | − | 0.662296i | \(-0.769582\pi\) | ||||
−0.749242 | + | 0.662296i | \(0.769582\pi\) | |||||||
\(368\) | 8.28154 | 0.431705 | ||||||||
\(369\) | 5.29662 | 0.275731 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.1040 | −1.25142 | ||||||||
\(372\) | −7.15639 | −0.371042 | ||||||||
\(373\) | −36.5928 | −1.89470 | −0.947350 | − | 0.320199i | \(-0.896250\pi\) | ||||
−0.947350 | + | 0.320199i | \(0.896250\pi\) | |||||||
\(374\) | 3.99558 | 0.206607 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 34.0628 | 1.75666 | ||||||||
\(377\) | −16.8789 | −0.869310 | ||||||||
\(378\) | 50.7540 | 2.61050 | ||||||||
\(379\) | −2.73973 | −0.140730 | −0.0703652 | − | 0.997521i | \(-0.522416\pi\) | ||||
−0.0703652 | + | 0.997521i | \(0.522416\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.7300 | −0.703410 | ||||||||
\(382\) | 35.7623 | 1.82976 | ||||||||
\(383\) | −38.8075 | −1.98297 | −0.991486 | − | 0.130216i | \(-0.958433\pi\) | ||||
−0.991486 | + | 0.130216i | \(0.958433\pi\) | |||||||
\(384\) | 27.8377 | 1.42059 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.8172 | 1.36496 | ||||||||
\(387\) | −3.22957 | −0.164168 | ||||||||
\(388\) | −14.4247 | −0.732304 | ||||||||
\(389\) | −28.4346 | −1.44169 | −0.720846 | − | 0.693095i | \(-0.756247\pi\) | ||||
−0.720846 | + | 0.693095i | \(0.756247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.528376 | 0.0267211 | ||||||||
\(392\) | 35.1025 | 1.77295 | ||||||||
\(393\) | −6.53893 | −0.329845 | ||||||||
\(394\) | −57.9923 | −2.92161 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −11.5435 | −0.580081 | ||||||||
\(397\) | 14.3578 | 0.720598 | 0.360299 | − | 0.932837i | \(-0.382675\pi\) | ||||
0.360299 | + | 0.932837i | \(0.382675\pi\) | |||||||
\(398\) | −47.4333 | −2.37762 | ||||||||
\(399\) | 16.4480 | 0.823431 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.9135 | −1.14425 | −0.572123 | − | 0.820168i | \(-0.693880\pi\) | ||||
−0.572123 | + | 0.820168i | \(0.693880\pi\) | |||||||
\(402\) | −0.860194 | −0.0429026 | ||||||||
\(403\) | −2.12387 | −0.105797 | ||||||||
\(404\) | 34.2124 | 1.70213 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 79.6824 | 3.95457 | ||||||||
\(407\) | 24.5091 | 1.21487 | ||||||||
\(408\) | −2.69796 | −0.133569 | ||||||||
\(409\) | 10.2648 | 0.507560 | 0.253780 | − | 0.967262i | \(-0.418326\pi\) | ||||
0.253780 | + | 0.967262i | \(0.418326\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.7450 | −0.628667 | ||||||||
\(412\) | 18.2961 | 0.901387 | ||||||||
\(413\) | −23.9706 | −1.17951 | ||||||||
\(414\) | −2.25932 | −0.111040 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.32547 | −0.163044 | ||||||||
\(417\) | −1.56460 | −0.0766188 | ||||||||
\(418\) | −35.6266 | −1.74255 | ||||||||
\(419\) | −33.3063 | −1.62712 | −0.813559 | − | 0.581482i | \(-0.802473\pi\) | ||||
−0.813559 | + | 0.581482i | \(0.802473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.57798 | 0.125643 | 0.0628215 | − | 0.998025i | \(-0.479990\pi\) | ||||
0.0628215 | + | 0.998025i | \(0.479990\pi\) | |||||||
\(422\) | −9.81165 | −0.477624 | ||||||||
\(423\) | −3.49576 | −0.169970 | ||||||||
\(424\) | −35.2537 | −1.71207 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 17.1690 | 0.831840 | ||||||||
\(427\) | −37.9336 | −1.83574 | ||||||||
\(428\) | 6.11658 | 0.295656 | ||||||||
\(429\) | 15.1920 | 0.733479 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.9552 | 1.63556 | 0.817781 | − | 0.575529i | \(-0.195204\pi\) | ||||
0.817781 | + | 0.575529i | \(0.195204\pi\) | |||||||
\(432\) | 27.9242 | 1.34350 | ||||||||
\(433\) | 27.5099 | 1.32204 | 0.661020 | − | 0.750368i | \(-0.270124\pi\) | ||||
0.661020 | + | 0.750368i | \(0.270124\pi\) | |||||||
\(434\) | 10.0264 | 0.481282 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −45.5982 | −2.18376 | ||||||||
\(437\) | −4.71127 | −0.225370 | ||||||||
\(438\) | −7.48426 | −0.357612 | ||||||||
\(439\) | −6.88770 | −0.328732 | −0.164366 | − | 0.986399i | \(-0.552558\pi\) | ||||
−0.164366 | + | 0.986399i | \(0.552558\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.60247 | −0.171546 | ||||||||
\(442\) | −1.53997 | −0.0732491 | ||||||||
\(443\) | 26.6821 | 1.26770 | 0.633851 | − | 0.773455i | \(-0.281473\pi\) | ||||
0.633851 | + | 0.773455i | \(0.281473\pi\) | |||||||
\(444\) | −31.8294 | −1.51055 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −21.1911 | −1.00343 | ||||||||
\(447\) | −0.526463 | −0.0249008 | ||||||||
\(448\) | −21.2595 | −1.00442 | ||||||||
\(449\) | −21.2689 | −1.00374 | −0.501871 | − | 0.864942i | \(-0.667355\pi\) | ||||
−0.501871 | + | 0.864942i | \(0.667355\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.1591 | −2.26772 | ||||||||
\(452\) | −65.4469 | −3.07837 | ||||||||
\(453\) | −27.5477 | −1.29430 | ||||||||
\(454\) | 17.1099 | 0.803005 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.0563 | 1.12654 | ||||||||
\(457\) | −15.5804 | −0.728823 | −0.364411 | − | 0.931238i | \(-0.618730\pi\) | ||||
−0.364411 | + | 0.931238i | \(0.618730\pi\) | |||||||
\(458\) | 13.9643 | 0.652508 | ||||||||
\(459\) | 1.78161 | 0.0831584 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.61982 | −0.354890 | −0.177445 | − | 0.984131i | \(-0.556783\pi\) | ||||
−0.177445 | + | 0.984131i | \(0.556783\pi\) | |||||||
\(462\) | −71.7189 | −3.33666 | ||||||||
\(463\) | −27.8633 | −1.29492 | −0.647459 | − | 0.762100i | \(-0.724168\pi\) | ||||
−0.647459 | + | 0.762100i | \(0.724168\pi\) | |||||||
\(464\) | 43.8402 | 2.03523 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.55136 | 0.164514 | ||||||||
\(467\) | −20.6076 | −0.953607 | −0.476804 | − | 0.879010i | \(-0.658205\pi\) | ||||
−0.476804 | + | 0.879010i | \(0.658205\pi\) | |||||||
\(468\) | 4.44908 | 0.205659 | ||||||||
\(469\) | 0.814270 | 0.0375995 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.59220 | 0.395908 | ||||||||
\(472\) | −35.0586 | −1.61370 | ||||||||
\(473\) | 29.3646 | 1.35019 | ||||||||
\(474\) | −64.1128 | −2.94480 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.91193 | 0.225138 | ||||||||
\(477\) | 3.61798 | 0.165656 | ||||||||
\(478\) | 28.3232 | 1.29547 | ||||||||
\(479\) | 8.70849 | 0.397901 | 0.198951 | − | 0.980010i | \(-0.436247\pi\) | ||||
0.198951 | + | 0.980010i | \(0.436247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.44630 | −0.430714 | ||||||||
\(482\) | 41.1316 | 1.87349 | ||||||||
\(483\) | −9.48411 | −0.431542 | ||||||||
\(484\) | 59.1302 | 2.68774 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.0523 | −0.637424 | ||||||||
\(487\) | 0.792885 | 0.0359291 | 0.0179645 | − | 0.999839i | \(-0.494281\pi\) | ||||
0.0179645 | + | 0.999839i | \(0.494281\pi\) | |||||||
\(488\) | −55.4805 | −2.51148 | ||||||||
\(489\) | −5.28138 | −0.238832 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.15362 | −0.187450 | −0.0937252 | − | 0.995598i | \(-0.529878\pi\) | ||||
−0.0937252 | + | 0.995598i | \(0.529878\pi\) | |||||||
\(492\) | 62.5430 | 2.81965 | ||||||||
\(493\) | 2.79708 | 0.125974 | ||||||||
\(494\) | 13.7312 | 0.617795 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.51639 | 0.247693 | ||||||||
\(497\) | −16.2524 | −0.729019 | ||||||||
\(498\) | −43.3994 | −1.94477 | ||||||||
\(499\) | 9.15019 | 0.409619 | 0.204809 | − | 0.978802i | \(-0.434343\pi\) | ||||
0.204809 | + | 0.978802i | \(0.434343\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.62560 | 0.206656 | ||||||||
\(502\) | 17.7299 | 0.791326 | ||||||||
\(503\) | 18.4456 | 0.822450 | 0.411225 | − | 0.911534i | \(-0.365101\pi\) | ||||
0.411225 | + | 0.911534i | \(0.365101\pi\) | |||||||
\(504\) | −10.9205 | −0.486437 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.5427 | 0.913234 | ||||||||
\(507\) | 14.4845 | 0.643279 | ||||||||
\(508\) | 36.5598 | 1.62208 | ||||||||
\(509\) | 30.4642 | 1.35030 | 0.675152 | − | 0.737679i | \(-0.264078\pi\) | ||||
0.675152 | + | 0.737679i | \(0.264078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.08469 | 0.313408 | ||||||||
\(512\) | −45.4169 | −2.00716 | ||||||||
\(513\) | −15.8857 | −0.701371 | ||||||||
\(514\) | −57.4546 | −2.53421 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −38.1351 | −1.67880 | ||||||||
\(517\) | 31.7849 | 1.39790 | ||||||||
\(518\) | 44.5942 | 1.95936 | ||||||||
\(519\) | 37.4251 | 1.64278 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4940 | 0.459749 | 0.229875 | − | 0.973220i | \(-0.426168\pi\) | ||||
0.229875 | + | 0.973220i | \(0.426168\pi\) | |||||||
\(522\) | −11.9602 | −0.523486 | ||||||||
\(523\) | −11.7187 | −0.512423 | −0.256211 | − | 0.966621i | \(-0.582474\pi\) | ||||
−0.256211 | + | 0.966621i | \(0.582474\pi\) | |||||||
\(524\) | 17.4116 | 0.760631 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −71.8043 | −3.13081 | ||||||||
\(527\) | 0.351955 | 0.0153314 | ||||||||
\(528\) | −39.4588 | −1.71722 | ||||||||
\(529\) | −20.2834 | −0.881888 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.59795 | 0.156138 | ||||||||
\(532\) | −43.7972 | −1.89885 | ||||||||
\(533\) | 18.5615 | 0.803986 | ||||||||
\(534\) | −21.1430 | −0.914948 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.19092 | 0.0514401 | ||||||||
\(537\) | −1.53643 | −0.0663018 | ||||||||
\(538\) | 10.3238 | 0.445091 | ||||||||
\(539\) | 32.7551 | 1.41086 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.46252 | −0.148865 | −0.0744326 | − | 0.997226i | \(-0.523715\pi\) | ||||
−0.0744326 | + | 0.997226i | \(0.523715\pi\) | |||||||
\(542\) | −19.2175 | −0.825460 | ||||||||
\(543\) | −11.6263 | −0.498930 | ||||||||
\(544\) | 0.551077 | 0.0236272 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 27.6418 | 1.18296 | ||||||||
\(547\) | 17.5518 | 0.750459 | 0.375230 | − | 0.926932i | \(-0.377564\pi\) | ||||
0.375230 | + | 0.926932i | \(0.377564\pi\) | |||||||
\(548\) | 33.9371 | 1.44972 | ||||||||
\(549\) | 5.69380 | 0.243005 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.9402 | −1.06249 | ||||||||
\(552\) | −13.8711 | −0.590395 | ||||||||
\(553\) | 60.6900 | 2.58080 | ||||||||
\(554\) | −9.76198 | −0.414747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.16616 | 0.176685 | ||||||||
\(557\) | 38.0718 | 1.61315 | 0.806577 | − | 0.591129i | \(-0.201318\pi\) | ||||
0.806577 | + | 0.591129i | \(0.201318\pi\) | |||||||
\(558\) | −1.50495 | −0.0637096 | ||||||||
\(559\) | −11.3177 | −0.478688 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.51754 | −0.106290 | ||||||||
\(562\) | −33.6217 | −1.41825 | ||||||||
\(563\) | 37.7706 | 1.59184 | 0.795921 | − | 0.605400i | \(-0.206987\pi\) | ||||
0.795921 | + | 0.605400i | \(0.206987\pi\) | |||||||
\(564\) | −41.2783 | −1.73813 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −47.6753 | −2.00394 | ||||||||
\(567\) | −25.8884 | −1.08721 | ||||||||
\(568\) | −23.7702 | −0.997375 | ||||||||
\(569\) | 18.5035 | 0.775709 | 0.387854 | − | 0.921721i | \(-0.373216\pi\) | ||||
0.387854 | + | 0.921721i | \(0.373216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7650 | 1.12008 | 0.560040 | − | 0.828466i | \(-0.310786\pi\) | ||||
0.560040 | + | 0.828466i | \(0.310786\pi\) | |||||||
\(572\) | −40.4529 | −1.69142 | ||||||||
\(573\) | −22.5331 | −0.941335 | ||||||||
\(574\) | −87.6253 | −3.65741 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.19103 | 0.132960 | ||||||||
\(577\) | 10.4962 | 0.436961 | 0.218480 | − | 0.975841i | \(-0.429890\pi\) | ||||
0.218480 | + | 0.975841i | \(0.429890\pi\) | |||||||
\(578\) | −41.9588 | −1.74526 | ||||||||
\(579\) | −16.8970 | −0.702215 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.0824 | 1.70438 | ||||||||
\(582\) | 13.4518 | 0.557597 | ||||||||
\(583\) | −32.8962 | −1.36242 | ||||||||
\(584\) | 10.3618 | 0.428776 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 63.3835 | 2.61835 | ||||||||
\(587\) | 13.6306 | 0.562596 | 0.281298 | − | 0.959621i | \(-0.409235\pi\) | ||||
0.281298 | + | 0.959621i | \(0.409235\pi\) | |||||||
\(588\) | −42.5382 | −1.75425 | ||||||||
\(589\) | −3.13821 | −0.129308 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.5398 | 1.50305 | ||||||||
\(592\) | 24.5352 | 1.00839 | ||||||||
\(593\) | 19.8228 | 0.814025 | 0.407012 | − | 0.913423i | \(-0.366571\pi\) | ||||
0.407012 | + | 0.913423i | \(0.366571\pi\) | |||||||
\(594\) | 69.2671 | 2.84206 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.40185 | 0.0574219 | ||||||||
\(597\) | 29.8868 | 1.22319 | ||||||||
\(598\) | −7.91756 | −0.323773 | ||||||||
\(599\) | 39.6002 | 1.61802 | 0.809010 | − | 0.587794i | \(-0.200004\pi\) | ||||
0.809010 | + | 0.587794i | \(0.200004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.01537 | 0.286163 | 0.143082 | − | 0.989711i | \(-0.454299\pi\) | ||||
0.143082 | + | 0.989711i | \(0.454299\pi\) | |||||||
\(602\) | 53.4288 | 2.17760 | ||||||||
\(603\) | −0.122221 | −0.00497722 | ||||||||
\(604\) | 73.3530 | 2.98469 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −31.9049 | −1.29605 | ||||||||
\(607\) | 35.2836 | 1.43212 | 0.716058 | − | 0.698041i | \(-0.245945\pi\) | ||||
0.716058 | + | 0.698041i | \(0.245945\pi\) | |||||||
\(608\) | −4.91368 | −0.199276 | ||||||||
\(609\) | −50.2063 | −2.03446 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2505 | −0.495603 | ||||||||
\(612\) | −0.737275 | −0.0298026 | ||||||||
\(613\) | −29.2541 | −1.18156 | −0.590782 | − | 0.806831i | \(-0.701181\pi\) | ||||
−0.590782 | + | 0.806831i | \(0.701181\pi\) | |||||||
\(614\) | −16.8337 | −0.679352 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 99.2936 | 4.00065 | ||||||||
\(617\) | 7.71652 | 0.310656 | 0.155328 | − | 0.987863i | \(-0.450357\pi\) | ||||
0.155328 | + | 0.987863i | \(0.450357\pi\) | |||||||
\(618\) | −17.0622 | −0.686341 | ||||||||
\(619\) | −13.6849 | −0.550041 | −0.275021 | − | 0.961438i | \(-0.588685\pi\) | ||||
−0.275021 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.15988 | 0.367573 | ||||||||
\(622\) | −79.5813 | −3.19092 | ||||||||
\(623\) | 20.0142 | 0.801853 | ||||||||
\(624\) | 15.2082 | 0.608814 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.85871 | −0.234161 | ||||||||
\(627\) | 22.4476 | 0.896471 | ||||||||
\(628\) | −22.8790 | −0.912973 | ||||||||
\(629\) | 1.56538 | 0.0624160 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.67134 | 0.265582 | 0.132791 | − | 0.991144i | \(-0.457606\pi\) | ||||
0.132791 | + | 0.991144i | \(0.457606\pi\) | |||||||
\(632\) | 88.7632 | 3.53081 | ||||||||
\(633\) | 6.18212 | 0.245717 | ||||||||
\(634\) | −20.0091 | −0.794662 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 42.7214 | 1.69401 | ||||||||
\(637\) | −12.6245 | −0.500199 | ||||||||
\(638\) | 108.747 | 4.30535 | ||||||||
\(639\) | 2.43946 | 0.0965037 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 50.3780 | 1.98981 | 0.994905 | − | 0.100820i | \(-0.0321465\pi\) | ||||
0.994905 | + | 0.100820i | \(0.0321465\pi\) | |||||||
\(642\) | −5.70405 | −0.225121 | ||||||||
\(643\) | −20.6698 | −0.815136 | −0.407568 | − | 0.913175i | \(-0.633623\pi\) | ||||
−0.407568 | + | 0.913175i | \(0.633623\pi\) | |||||||
\(644\) | 25.2540 | 0.995146 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.27545 | −0.0895264 | ||||||||
\(647\) | −31.4817 | −1.23767 | −0.618836 | − | 0.785520i | \(-0.712396\pi\) | ||||
−0.618836 | + | 0.785520i | \(0.712396\pi\) | |||||||
\(648\) | −37.8635 | −1.48742 | ||||||||
\(649\) | −32.7141 | −1.28414 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.31743 | −0.247600 | ||||||||
\(652\) | 14.0631 | 0.550753 | ||||||||
\(653\) | −9.35717 | −0.366174 | −0.183087 | − | 0.983097i | \(-0.558609\pi\) | ||||
−0.183087 | + | 0.983097i | \(0.558609\pi\) | |||||||
\(654\) | 42.5229 | 1.66278 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −48.2103 | −1.88230 | ||||||||
\(657\) | −1.06340 | −0.0414874 | ||||||||
\(658\) | 57.8325 | 2.25455 | ||||||||
\(659\) | 31.4427 | 1.22483 | 0.612416 | − | 0.790535i | \(-0.290198\pi\) | ||||
0.612416 | + | 0.790535i | \(0.290198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.2818 | −0.788871 | −0.394435 | − | 0.918924i | \(-0.629060\pi\) | ||||
−0.394435 | + | 0.918924i | \(0.629060\pi\) | |||||||
\(662\) | −24.0186 | −0.933511 | ||||||||
\(663\) | 0.970307 | 0.0376836 | ||||||||
\(664\) | 60.0858 | 2.33178 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.69355 | −0.259370 | ||||||||
\(667\) | 14.3808 | 0.556826 | ||||||||
\(668\) | −12.3169 | −0.476555 | ||||||||
\(669\) | 13.3521 | 0.516221 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −51.7704 | −1.99857 | ||||||||
\(672\) | −9.89158 | −0.381576 | ||||||||
\(673\) | −11.5905 | −0.446782 | −0.223391 | − | 0.974729i | \(-0.571713\pi\) | ||||
−0.223391 | + | 0.974729i | \(0.571713\pi\) | |||||||
\(674\) | 27.8307 | 1.07200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −38.5688 | −1.48342 | ||||||||
\(677\) | 34.8510 | 1.33943 | 0.669717 | − | 0.742617i | \(-0.266416\pi\) | ||||
0.669717 | + | 0.742617i | \(0.266416\pi\) | |||||||
\(678\) | 61.0329 | 2.34395 | ||||||||
\(679\) | −12.7337 | −0.488674 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.7806 | −0.413113 | ||||||||
\(682\) | 13.6836 | 0.523974 | ||||||||
\(683\) | −12.7665 | −0.488497 | −0.244248 | − | 0.969713i | \(-0.578541\pi\) | ||||
−0.244248 | + | 0.969713i | \(0.578541\pi\) | |||||||
\(684\) | 6.57391 | 0.251360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.32983 | −0.165314 | ||||||||
\(687\) | −8.79861 | −0.335688 | ||||||||
\(688\) | 29.3958 | 1.12071 | ||||||||
\(689\) | 12.6788 | 0.483025 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.25420 | −0.123796 | −0.0618978 | − | 0.998082i | \(-0.519715\pi\) | ||||
−0.0618978 | + | 0.998082i | \(0.519715\pi\) | |||||||
\(692\) | −99.6542 | −3.78828 | ||||||||
\(693\) | −10.1902 | −0.387094 | ||||||||
\(694\) | −6.01853 | −0.228460 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −73.4301 | −2.78336 | ||||||||
\(697\) | −3.07590 | −0.116508 | ||||||||
\(698\) | −49.3847 | −1.86924 | ||||||||
\(699\) | −2.23764 | −0.0846354 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.7274 | −0.405168 | −0.202584 | − | 0.979265i | \(-0.564934\pi\) | ||||
−0.202584 | + | 0.979265i | \(0.564934\pi\) | |||||||
\(702\) | −26.6969 | −1.00761 | ||||||||
\(703\) | −13.9578 | −0.526427 | ||||||||
\(704\) | −29.0142 | −1.09351 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.23148 | −0.234525 | ||||||||
\(707\) | 30.2016 | 1.13585 | ||||||||
\(708\) | 42.4849 | 1.59668 | ||||||||
\(709\) | −30.3373 | −1.13934 | −0.569670 | − | 0.821873i | \(-0.692929\pi\) | ||||
−0.569670 | + | 0.821873i | \(0.692929\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.10950 | −0.341633 | ||||||||
\(712\) | 29.2722 | 1.09702 | ||||||||
\(713\) | 1.80953 | 0.0677673 | ||||||||
\(714\) | −4.58064 | −0.171426 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.09115 | 0.152893 | ||||||||
\(717\) | −17.8459 | −0.666467 | ||||||||
\(718\) | −27.4312 | −1.02372 | ||||||||
\(719\) | −16.5155 | −0.615924 | −0.307962 | − | 0.951399i | \(-0.599647\pi\) | ||||
−0.307962 | + | 0.951399i | \(0.599647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.1513 | 0.601504 | ||||||||
\(722\) | −26.8913 | −1.00079 | ||||||||
\(723\) | −25.9162 | −0.963833 | ||||||||
\(724\) | 30.9580 | 1.15054 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −55.1422 | −2.04652 | ||||||||
\(727\) | 0.711471 | 0.0263870 | 0.0131935 | − | 0.999913i | \(-0.495800\pi\) | ||||
0.0131935 | + | 0.999913i | \(0.495800\pi\) | |||||||
\(728\) | −38.2697 | −1.41837 | ||||||||
\(729\) | 29.9716 | 1.11006 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.87550 | 0.0693680 | ||||||||
\(732\) | 67.2328 | 2.48500 | ||||||||
\(733\) | 50.8654 | 1.87876 | 0.939378 | − | 0.342884i | \(-0.111404\pi\) | ||||
0.939378 | + | 0.342884i | \(0.111404\pi\) | |||||||
\(734\) | −71.2841 | −2.63114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.83328 | 0.104436 | ||||||||
\(737\) | 1.11128 | 0.0409347 | ||||||||
\(738\) | 13.1525 | 0.484148 | ||||||||
\(739\) | 34.1665 | 1.25684 | 0.628418 | − | 0.777876i | \(-0.283703\pi\) | ||||
0.628418 | + | 0.777876i | \(0.283703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.65174 | −0.317830 | ||||||||
\(742\) | −59.8544 | −2.19732 | ||||||||
\(743\) | 42.4874 | 1.55871 | 0.779356 | − | 0.626581i | \(-0.215546\pi\) | ||||
0.779356 | + | 0.626581i | \(0.215546\pi\) | |||||||
\(744\) | −9.23967 | −0.338743 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −90.8662 | −3.32685 | ||||||||
\(747\) | −6.16642 | −0.225617 | ||||||||
\(748\) | 6.70361 | 0.245108 | ||||||||
\(749\) | 5.39952 | 0.197294 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.8677 | −1.05340 | −0.526700 | − | 0.850052i | \(-0.676571\pi\) | ||||
−0.526700 | + | 0.850052i | \(0.676571\pi\) | |||||||
\(752\) | 31.8187 | 1.16031 | ||||||||
\(753\) | −11.1713 | −0.407104 | ||||||||
\(754\) | −41.9134 | −1.52640 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 85.1528 | 3.09698 | ||||||||
\(757\) | −22.2621 | −0.809131 | −0.404566 | − | 0.914509i | \(-0.632577\pi\) | ||||
−0.404566 | + | 0.914509i | \(0.632577\pi\) | |||||||
\(758\) | −6.80323 | −0.247104 | ||||||||
\(759\) | −12.9435 | −0.469821 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.10166 | −0.0399351 | −0.0199675 | − | 0.999801i | \(-0.506356\pi\) | ||||
−0.0199675 | + | 0.999801i | \(0.506356\pi\) | |||||||
\(762\) | −34.0941 | −1.23510 | ||||||||
\(763\) | −40.2527 | −1.45724 | ||||||||
\(764\) | 60.0004 | 2.17074 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −96.3659 | −3.48184 | ||||||||
\(767\) | 12.6086 | 0.455272 | ||||||||
\(768\) | 51.0373 | 1.84165 | ||||||||
\(769\) | −30.6128 | −1.10393 | −0.551963 | − | 0.833869i | \(-0.686121\pi\) | ||||
−0.551963 | + | 0.833869i | \(0.686121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.2010 | 1.30375 | ||||||||
\(772\) | 44.9928 | 1.61932 | ||||||||
\(773\) | 22.3697 | 0.804583 | 0.402291 | − | 0.915512i | \(-0.368214\pi\) | ||||
0.402291 | + | 0.915512i | \(0.368214\pi\) | |||||||
\(774\) | −8.01960 | −0.288259 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.6239 | −0.668558 | ||||||||
\(777\) | −28.0979 | −1.00801 | ||||||||
\(778\) | −70.6082 | −2.53143 | ||||||||
\(779\) | 27.4262 | 0.982647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.1806 | −0.793685 | ||||||||
\(782\) | 1.31205 | 0.0469188 | ||||||||
\(783\) | 48.4899 | 1.73289 | ||||||||
\(784\) | 32.7899 | 1.17107 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.2373 | −0.579166 | ||||||||
\(787\) | −13.7579 | −0.490416 | −0.245208 | − | 0.969471i | \(-0.578856\pi\) | ||||
−0.245208 | + | 0.969471i | \(0.578856\pi\) | |||||||
\(788\) | −97.2969 | −3.46606 | ||||||||
\(789\) | 45.2424 | 1.61067 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −57.7745 | −2.05422 | ||||||||
\(792\) | −14.9039 | −0.529586 | ||||||||
\(793\) | 19.9533 | 0.708563 | ||||||||
\(794\) | 35.6530 | 1.26528 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −79.5815 | −2.82069 | ||||||||
\(797\) | 13.2106 | 0.467942 | 0.233971 | − | 0.972244i | \(-0.424828\pi\) | ||||
0.233971 | + | 0.972244i | \(0.424828\pi\) | |||||||
\(798\) | 40.8433 | 1.44584 | ||||||||
\(799\) | 2.03009 | 0.0718193 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00411 | −0.106145 | ||||||||
\(802\) | −56.8983 | −2.00915 | ||||||||
\(803\) | 9.66892 | 0.341209 | ||||||||
\(804\) | −1.44319 | −0.0508976 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.27394 | −0.185767 | ||||||||
\(807\) | −6.50482 | −0.228981 | ||||||||
\(808\) | 44.1718 | 1.55396 | ||||||||
\(809\) | −34.1325 | −1.20004 | −0.600018 | − | 0.799986i | \(-0.704840\pi\) | ||||
−0.600018 | + | 0.799986i | \(0.704840\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.3883 | 1.31288 | 0.656441 | − | 0.754377i | \(-0.272061\pi\) | ||||
0.656441 | + | 0.754377i | \(0.272061\pi\) | |||||||
\(812\) | 133.688 | 4.69152 | ||||||||
\(813\) | 12.1085 | 0.424665 | ||||||||
\(814\) | 60.8605 | 2.13316 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.52021 | −0.0882250 | ||||||||
\(817\) | −16.7229 | −0.585061 | ||||||||
\(818\) | 25.4892 | 0.891209 | ||||||||
\(819\) | 3.92750 | 0.137238 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 56.5411 | 1.97330 | 0.986649 | − | 0.162861i | \(-0.0520723\pi\) | ||||
0.986649 | + | 0.162861i | \(0.0520723\pi\) | |||||||
\(822\) | −31.6482 | −1.10386 | ||||||||
\(823\) | −20.3282 | −0.708595 | −0.354297 | − | 0.935133i | \(-0.615280\pi\) | ||||
−0.354297 | + | 0.935133i | \(0.615280\pi\) | |||||||
\(824\) | 23.6223 | 0.822922 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −59.5231 | −2.07107 | ||||||||
\(827\) | −6.50545 | −0.226217 | −0.113108 | − | 0.993583i | \(-0.536081\pi\) | ||||
−0.113108 | + | 0.993583i | \(0.536081\pi\) | |||||||
\(828\) | −3.79059 | −0.131732 | ||||||||
\(829\) | −29.5602 | −1.02667 | −0.513334 | − | 0.858189i | \(-0.671590\pi\) | ||||
−0.513334 | + | 0.858189i | \(0.671590\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.15083 | 0.213370 | ||||||||
\(832\) | 11.1826 | 0.387688 | ||||||||
\(833\) | 2.09205 | 0.0724853 | ||||||||
\(834\) | −3.88518 | −0.134533 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −59.7727 | −2.06728 | ||||||||
\(837\) | 6.10146 | 0.210897 | ||||||||
\(838\) | −82.7054 | −2.85701 | ||||||||
\(839\) | 20.3869 | 0.703834 | 0.351917 | − | 0.936031i | \(-0.385530\pi\) | ||||
0.351917 | + | 0.936031i | \(0.385530\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.1280 | 1.62510 | ||||||||
\(842\) | 6.40158 | 0.220613 | ||||||||
\(843\) | 21.1844 | 0.729629 | ||||||||
\(844\) | −16.4616 | −0.566630 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.68060 | −0.298445 | ||||||||
\(847\) | 52.1983 | 1.79355 | ||||||||
\(848\) | −32.9311 | −1.13086 | ||||||||
\(849\) | 30.0393 | 1.03094 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.04820 | 0.275889 | ||||||||
\(852\) | 28.8054 | 0.986856 | ||||||||
\(853\) | 20.9930 | 0.718788 | 0.359394 | − | 0.933186i | \(-0.382983\pi\) | ||||
0.359394 | + | 0.933186i | \(0.382983\pi\) | |||||||
\(854\) | −94.1959 | −3.22332 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.89716 | 0.269920 | ||||||||
\(857\) | 6.26547 | 0.214024 | 0.107012 | − | 0.994258i | \(-0.465872\pi\) | ||||
0.107012 | + | 0.994258i | \(0.465872\pi\) | |||||||
\(858\) | 37.7245 | 1.28789 | ||||||||
\(859\) | −28.1468 | −0.960355 | −0.480177 | − | 0.877171i | \(-0.659428\pi\) | ||||
−0.480177 | + | 0.877171i | \(0.659428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 55.2109 | 1.88158 | ||||||||
\(862\) | 84.3166 | 2.87184 | ||||||||
\(863\) | −28.3593 | −0.965361 | −0.482680 | − | 0.875797i | \(-0.660337\pi\) | ||||
−0.482680 | + | 0.875797i | \(0.660337\pi\) | |||||||
\(864\) | 9.55342 | 0.325014 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 68.3119 | 2.32133 | ||||||||
\(867\) | 26.4374 | 0.897861 | ||||||||
\(868\) | 16.8218 | 0.570971 | ||||||||
\(869\) | 82.8273 | 2.80973 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.428310 | −0.0145127 | ||||||||
\(872\) | −58.8722 | −1.99367 | ||||||||
\(873\) | 1.91131 | 0.0646881 | ||||||||
\(874\) | −11.6989 | −0.395721 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.5568 | −0.424254 | ||||||||
\(877\) | 40.6994 | 1.37432 | 0.687160 | − | 0.726506i | \(-0.258857\pi\) | ||||
0.687160 | + | 0.726506i | \(0.258857\pi\) | |||||||
\(878\) | −17.1034 | −0.577211 | ||||||||
\(879\) | −39.9367 | −1.34703 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.7228 | −1.23722 | −0.618612 | − | 0.785697i | \(-0.712305\pi\) | ||||
−0.618612 | + | 0.785697i | \(0.712305\pi\) | |||||||
\(882\) | −8.94556 | −0.301213 | ||||||||
\(883\) | 6.46902 | 0.217700 | 0.108850 | − | 0.994058i | \(-0.465283\pi\) | ||||
0.108850 | + | 0.994058i | \(0.465283\pi\) | |||||||
\(884\) | −2.58370 | −0.0868992 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 66.2562 | 2.22592 | ||||||||
\(887\) | −9.69577 | −0.325552 | −0.162776 | − | 0.986663i | \(-0.552045\pi\) | ||||
−0.162776 | + | 0.986663i | \(0.552045\pi\) | |||||||
\(888\) | −41.0951 | −1.37906 | ||||||||
\(889\) | 32.2738 | 1.08243 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.3315 | −1.18365 | ||||||||
\(892\) | −35.5534 | −1.19042 | ||||||||
\(893\) | −18.1013 | −0.605736 | ||||||||
\(894\) | −1.30730 | −0.0437226 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −65.4354 | −2.18604 | ||||||||
\(897\) | 4.98869 | 0.166568 | ||||||||
\(898\) | −52.8145 | −1.76244 | ||||||||
\(899\) | 9.57914 | 0.319482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.10106 | −0.0699964 | ||||||||
\(902\) | −119.588 | −3.98183 | ||||||||
\(903\) | −33.6644 | −1.12028 | ||||||||
\(904\) | −84.4990 | −2.81040 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −68.4057 | −2.27263 | ||||||||
\(907\) | 0.218135 | 0.00724306 | 0.00362153 | − | 0.999993i | \(-0.498847\pi\) | ||||
0.00362153 | + | 0.999993i | \(0.498847\pi\) | |||||||
\(908\) | 28.7062 | 0.952647 | ||||||||
\(909\) | −4.53322 | −0.150358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.4478 | 0.544938 | 0.272469 | − | 0.962165i | \(-0.412160\pi\) | ||||
0.272469 | + | 0.962165i | \(0.412160\pi\) | |||||||
\(912\) | 22.4715 | 0.744104 | ||||||||
\(913\) | 56.0677 | 1.85557 | ||||||||
\(914\) | −38.6890 | −1.27972 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.4286 | 0.774104 | ||||||||
\(917\) | 15.3704 | 0.507577 | ||||||||
\(918\) | 4.42405 | 0.146015 | ||||||||
\(919\) | −37.9728 | −1.25261 | −0.626304 | − | 0.779579i | \(-0.715433\pi\) | ||||
−0.626304 | + | 0.779579i | \(0.715433\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.6066 | 0.349498 | ||||||||
\(922\) | −18.9214 | −0.623142 | ||||||||
\(923\) | 8.54884 | 0.281389 | ||||||||
\(924\) | −120.327 | −3.95846 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −69.1895 | −2.27371 | ||||||||
\(927\) | −2.42429 | −0.0796240 | ||||||||
\(928\) | 14.9986 | 0.492354 | ||||||||
\(929\) | 10.2888 | 0.337566 | 0.168783 | − | 0.985653i | \(-0.446016\pi\) | ||||
0.168783 | + | 0.985653i | \(0.446016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.6538 | −0.611353 | ||||||||
\(932\) | 5.95832 | 0.195171 | ||||||||
\(933\) | 50.1426 | 1.64160 | ||||||||
\(934\) | −51.1724 | −1.67441 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.74424 | 0.187756 | ||||||||
\(937\) | −57.3195 | −1.87255 | −0.936274 | − | 0.351272i | \(-0.885749\pi\) | ||||
−0.936274 | + | 0.351272i | \(0.885749\pi\) | |||||||
\(938\) | 2.02198 | 0.0660198 | ||||||||
\(939\) | 3.69146 | 0.120466 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7662 | −0.383567 | −0.191784 | − | 0.981437i | \(-0.561427\pi\) | ||||
−0.191784 | + | 0.981437i | \(0.561427\pi\) | |||||||
\(942\) | 21.3360 | 0.695163 | ||||||||
\(943\) | −15.8143 | −0.514984 | ||||||||
\(944\) | −32.7488 | −1.06588 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 72.9176 | 2.37075 | ||||||||
\(947\) | −14.6619 | −0.476449 | −0.238225 | − | 0.971210i | \(-0.576565\pi\) | ||||
−0.238225 | + | 0.971210i | \(0.576565\pi\) | |||||||
\(948\) | −107.566 | −3.49357 | ||||||||
\(949\) | −3.72659 | −0.120970 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.6073 | 0.408820 | ||||||||
\(952\) | 6.34183 | 0.205540 | ||||||||
\(953\) | −34.3227 | −1.11182 | −0.555911 | − | 0.831242i | \(-0.687631\pi\) | ||||
−0.555911 | + | 0.831242i | \(0.687631\pi\) | |||||||
\(954\) | 8.98408 | 0.290870 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 47.5195 | 1.53689 | ||||||||
\(957\) | −68.5196 | −2.21493 | ||||||||
\(958\) | 21.6247 | 0.698663 | ||||||||
\(959\) | 29.9586 | 0.967413 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7947 | −0.961118 | ||||||||
\(962\) | −23.4568 | −0.756278 | ||||||||
\(963\) | −0.810462 | −0.0261168 | ||||||||
\(964\) | 69.0087 | 2.22262 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −23.5507 | −0.757732 | ||||||||
\(967\) | −61.3511 | −1.97292 | −0.986459 | − | 0.164009i | \(-0.947557\pi\) | ||||
−0.986459 | + | 0.164009i | \(0.947557\pi\) | |||||||
\(968\) | 76.3435 | 2.45377 | ||||||||
\(969\) | 1.43372 | 0.0460576 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.4895 | 0.432897 | 0.216449 | − | 0.976294i | \(-0.430553\pi\) | ||||
0.216449 | + | 0.976294i | \(0.430553\pi\) | |||||||
\(972\) | −23.5763 | −0.756210 | ||||||||
\(973\) | 3.67776 | 0.117903 | ||||||||
\(974\) | 1.96887 | 0.0630868 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −51.8254 | −1.65889 | ||||||||
\(977\) | 33.5320 | 1.07278 | 0.536392 | − | 0.843969i | \(-0.319787\pi\) | ||||
0.536392 | + | 0.843969i | \(0.319787\pi\) | |||||||
\(978\) | −13.1146 | −0.419359 | ||||||||
\(979\) | 27.3147 | 0.872980 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.04188 | 0.192902 | ||||||||
\(982\) | −10.3142 | −0.329139 | ||||||||
\(983\) | −49.4173 | −1.57617 | −0.788084 | − | 0.615567i | \(-0.788927\pi\) | ||||
−0.788084 | + | 0.615567i | \(0.788927\pi\) | |||||||
\(984\) | 80.7497 | 2.57421 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.94564 | 0.221194 | ||||||||
\(987\) | −36.4391 | −1.15987 | ||||||||
\(988\) | 23.0376 | 0.732923 | ||||||||
\(989\) | 9.64263 | 0.306618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6910 | 0.466675 | 0.233338 | − | 0.972396i | \(-0.425035\pi\) | ||||
0.233338 | + | 0.972396i | \(0.425035\pi\) | |||||||
\(992\) | 1.88727 | 0.0599208 | ||||||||
\(993\) | 15.1337 | 0.480253 | ||||||||
\(994\) | −40.3575 | −1.28006 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −72.8136 | −2.30719 | ||||||||
\(997\) | 44.2589 | 1.40169 | 0.700847 | − | 0.713312i | \(-0.252806\pi\) | ||||
0.700847 | + | 0.713312i | \(0.252806\pi\) | |||||||
\(998\) | 22.7215 | 0.719238 | ||||||||
\(999\) | 27.1374 | 0.858589 |
(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 | 3475.2.a.e.1.7 | 7 | ||
5.4 | even | 2 | 139.2.a.c.1.1 | ✓ | 7 | ||
15.14 | odd | 2 | 1251.2.a.k.1.7 | 7 | |||
20.19 | odd | 2 | 2224.2.a.o.1.2 | 7 | |||
35.34 | odd | 2 | 6811.2.a.p.1.1 | 7 | |||
40.19 | odd | 2 | 8896.2.a.bd.1.6 | 7 | |||
40.29 | even | 2 | 8896.2.a.be.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
139.2.a.c.1.1 | ✓ | 7 | 5.4 | even | 2 | ||
1251.2.a.k.1.7 | 7 | 15.14 | odd | 2 | |||
2224.2.a.o.1.2 | 7 | 20.19 | odd | 2 | |||
3475.2.a.e.1.7 | 7 | 1.1 | even | 1 | trivial | ||
6811.2.a.p.1.1 | 7 | 35.34 | odd | 2 | |||
8896.2.a.bd.1.6 | 7 | 40.19 | odd | 2 | |||
8896.2.a.be.1.2 | 7 | 40.29 | even | 2 |