Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, 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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.751024\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.751024 | −0.531054 | −0.265527 | − | 0.964103i | \(-0.585546\pi\) | ||||
−0.265527 | + | 0.964103i | \(0.585546\pi\) | |||||||
\(3\) | 2.33152 | 1.34610 | 0.673050 | − | 0.739597i | \(-0.264984\pi\) | ||||
0.673050 | + | 0.739597i | \(0.264984\pi\) | |||||||
\(4\) | −1.43596 | −0.717981 | ||||||||
\(5\) | 4.26543 | 1.90756 | 0.953779 | − | 0.300509i | \(-0.0971565\pi\) | ||||
0.953779 | + | 0.300509i | \(0.0971565\pi\) | |||||||
\(6\) | −1.75102 | −0.714853 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.58049 | 0.912341 | ||||||||
\(9\) | 2.43596 | 0.811988 | ||||||||
\(10\) | −3.20344 | −1.01302 | ||||||||
\(11\) | 4.09899 | 1.23589 | 0.617946 | − | 0.786220i | \(-0.287965\pi\) | ||||
0.617946 | + | 0.786220i | \(0.287965\pi\) | |||||||
\(12\) | −3.34797 | −0.966475 | ||||||||
\(13\) | −2.18699 | −0.606561 | −0.303281 | − | 0.952901i | \(-0.598082\pi\) | ||||
−0.303281 | + | 0.952901i | \(0.598082\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.94491 | 2.56777 | ||||||||
\(16\) | 0.933914 | 0.233479 | ||||||||
\(17\) | 0.590042 | 0.143106 | 0.0715531 | − | 0.997437i | \(-0.477204\pi\) | ||||
0.0715531 | + | 0.997437i | \(0.477204\pi\) | |||||||
\(18\) | −1.82947 | −0.431209 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −6.12500 | −1.36959 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.07844 | −0.656326 | ||||||||
\(23\) | −4.36988 | −0.911182 | −0.455591 | − | 0.890189i | \(-0.650572\pi\) | ||||
−0.455591 | + | 0.890189i | \(0.650572\pi\) | |||||||
\(24\) | 6.01645 | 1.22810 | ||||||||
\(25\) | 13.1939 | 2.63878 | ||||||||
\(26\) | 1.64248 | 0.322117 | ||||||||
\(27\) | −1.31506 | −0.253084 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.36442 | −1.36754 | −0.683769 | − | 0.729698i | \(-0.739661\pi\) | ||||
−0.683769 | + | 0.729698i | \(0.739661\pi\) | |||||||
\(30\) | −7.46887 | −1.36362 | ||||||||
\(31\) | 4.51850 | 0.811547 | 0.405773 | − | 0.913974i | \(-0.367002\pi\) | ||||
0.405773 | + | 0.913974i | \(0.367002\pi\) | |||||||
\(32\) | −5.86237 | −1.03633 | ||||||||
\(33\) | 9.55686 | 1.66364 | ||||||||
\(34\) | −0.443136 | −0.0759972 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.49795 | −0.582992 | ||||||||
\(37\) | 8.95446 | 1.47210 | 0.736052 | − | 0.676924i | \(-0.236688\pi\) | ||||
0.736052 | + | 0.676924i | \(0.236688\pi\) | |||||||
\(38\) | 0.751024 | 0.121832 | ||||||||
\(39\) | −5.09899 | −0.816492 | ||||||||
\(40\) | 11.0069 | 1.74034 | ||||||||
\(41\) | −2.17744 | −0.340058 | −0.170029 | − | 0.985439i | \(-0.554386\pi\) | ||||
−0.170029 | + | 0.985439i | \(0.554386\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.69594 | −1.32612 | −0.663059 | − | 0.748567i | \(-0.730742\pi\) | ||||
−0.663059 | + | 0.748567i | \(0.730742\pi\) | |||||||
\(44\) | −5.88600 | −0.887348 | ||||||||
\(45\) | 10.3904 | 1.54891 | ||||||||
\(46\) | 3.28188 | 0.483887 | ||||||||
\(47\) | −11.8333 | −1.72606 | −0.863032 | − | 0.505150i | \(-0.831437\pi\) | ||||
−0.863032 | + | 0.505150i | \(0.831437\pi\) | |||||||
\(48\) | 2.17744 | 0.314286 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9.90893 | −1.40133 | ||||||||
\(51\) | 1.37569 | 0.192635 | ||||||||
\(52\) | 3.14043 | 0.435500 | ||||||||
\(53\) | 4.40996 | 0.605754 | 0.302877 | − | 0.953030i | \(-0.402053\pi\) | ||||
0.302877 | + | 0.953030i | \(0.402053\pi\) | |||||||
\(54\) | 0.987643 | 0.134401 | ||||||||
\(55\) | 17.4840 | 2.35754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.33152 | −0.308817 | ||||||||
\(58\) | 5.53086 | 0.726237 | ||||||||
\(59\) | 10.7178 | 1.39534 | 0.697672 | − | 0.716417i | \(-0.254219\pi\) | ||||
0.697672 | + | 0.716417i | \(0.254219\pi\) | |||||||
\(60\) | −14.2805 | −1.84361 | ||||||||
\(61\) | −2.43051 | −0.311195 | −0.155597 | − | 0.987821i | \(-0.549730\pi\) | ||||
−0.155597 | + | 0.987821i | \(0.549730\pi\) | |||||||
\(62\) | −3.39350 | −0.430975 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.53496 | 0.316869 | ||||||||
\(65\) | −9.32844 | −1.15705 | ||||||||
\(66\) | −7.17744 | −0.883481 | ||||||||
\(67\) | −5.65348 | −0.690682 | −0.345341 | − | 0.938477i | \(-0.612237\pi\) | ||||
−0.345341 | + | 0.938477i | \(0.612237\pi\) | |||||||
\(68\) | −0.847279 | −0.102748 | ||||||||
\(69\) | −10.1884 | −1.22654 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.32434 | 0.987918 | 0.493959 | − | 0.869485i | \(-0.335549\pi\) | ||||
0.493959 | + | 0.869485i | \(0.335549\pi\) | |||||||
\(72\) | 6.28598 | 0.740810 | ||||||||
\(73\) | −10.6795 | −1.24994 | −0.624970 | − | 0.780649i | \(-0.714889\pi\) | ||||
−0.624970 | + | 0.780649i | \(0.714889\pi\) | |||||||
\(74\) | −6.72502 | −0.781768 | ||||||||
\(75\) | 30.7618 | 3.55206 | ||||||||
\(76\) | 1.43596 | 0.164716 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.82947 | 0.433602 | ||||||||
\(79\) | 8.56377 | 0.963499 | 0.481750 | − | 0.876309i | \(-0.340002\pi\) | ||||
0.481750 | + | 0.876309i | \(0.340002\pi\) | |||||||
\(80\) | 3.98355 | 0.445374 | ||||||||
\(81\) | −10.3740 | −1.15266 | ||||||||
\(82\) | 1.63531 | 0.180589 | ||||||||
\(83\) | −4.25826 | −0.467404 | −0.233702 | − | 0.972308i | \(-0.575084\pi\) | ||||
−0.233702 | + | 0.972308i | \(0.575084\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.51678 | 0.272983 | ||||||||
\(86\) | 6.53086 | 0.704241 | ||||||||
\(87\) | −17.1703 | −1.84085 | ||||||||
\(88\) | 10.5774 | 1.12756 | ||||||||
\(89\) | 3.79110 | 0.401856 | 0.200928 | − | 0.979606i | \(-0.435604\pi\) | ||||
0.200928 | + | 0.979606i | \(0.435604\pi\) | |||||||
\(90\) | −7.80346 | −0.822557 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.27498 | 0.654212 | ||||||||
\(93\) | 10.5350 | 1.09242 | ||||||||
\(94\) | 8.88709 | 0.916633 | ||||||||
\(95\) | −4.26543 | −0.437624 | ||||||||
\(96\) | −13.6682 | −1.39501 | ||||||||
\(97\) | 2.11026 | 0.214265 | 0.107132 | − | 0.994245i | \(-0.465833\pi\) | ||||
0.107132 | + | 0.994245i | \(0.465833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.98499 | 1.00353 | ||||||||
\(100\) | −18.9459 | −1.89459 | ||||||||
\(101\) | 15.0606 | 1.49859 | 0.749294 | − | 0.662237i | \(-0.230393\pi\) | ||||
0.749294 | + | 0.662237i | \(0.230393\pi\) | |||||||
\(102\) | −1.03318 | −0.102300 | ||||||||
\(103\) | 4.89383 | 0.482204 | 0.241102 | − | 0.970500i | \(-0.422491\pi\) | ||||
0.241102 | + | 0.970500i | \(0.422491\pi\) | |||||||
\(104\) | −5.64350 | −0.553391 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.31198 | −0.321688 | ||||||||
\(107\) | 0.888650 | 0.0859090 | 0.0429545 | − | 0.999077i | \(-0.486323\pi\) | ||||
0.0429545 | + | 0.999077i | \(0.486323\pi\) | |||||||
\(108\) | 1.88838 | 0.181709 | ||||||||
\(109\) | −1.11135 | −0.106448 | −0.0532240 | − | 0.998583i | \(-0.516950\pi\) | ||||
−0.0532240 | + | 0.998583i | \(0.516950\pi\) | |||||||
\(110\) | −13.1309 | −1.25198 | ||||||||
\(111\) | 20.8775 | 1.98160 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9161 | −1.21504 | −0.607522 | − | 0.794303i | \(-0.707836\pi\) | ||||
−0.607522 | + | 0.794303i | \(0.707836\pi\) | |||||||
\(114\) | 1.75102 | 0.163998 | ||||||||
\(115\) | −18.6394 | −1.73813 | ||||||||
\(116\) | 10.5750 | 0.981867 | ||||||||
\(117\) | −5.32742 | −0.492520 | ||||||||
\(118\) | −8.04936 | −0.741004 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 25.6628 | 2.34268 | ||||||||
\(121\) | 5.80174 | 0.527431 | ||||||||
\(122\) | 1.82537 | 0.165261 | ||||||||
\(123\) | −5.07672 | −0.457753 | ||||||||
\(124\) | −6.48840 | −0.582676 | ||||||||
\(125\) | 34.9505 | 3.12606 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.11373 | −0.276299 | −0.138149 | − | 0.990411i | \(-0.544115\pi\) | ||||
−0.138149 | + | 0.990411i | \(0.544115\pi\) | |||||||
\(128\) | 9.82094 | 0.868056 | ||||||||
\(129\) | −20.2747 | −1.78509 | ||||||||
\(130\) | 7.00588 | 0.614457 | ||||||||
\(131\) | 3.70721 | 0.323900 | 0.161950 | − | 0.986799i | \(-0.448222\pi\) | ||||
0.161950 | + | 0.986799i | \(0.448222\pi\) | |||||||
\(132\) | −13.7233 | −1.19446 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.24590 | 0.366790 | ||||||||
\(135\) | −5.60930 | −0.482772 | ||||||||
\(136\) | 1.52260 | 0.130562 | ||||||||
\(137\) | 1.16098 | 0.0991894 | 0.0495947 | − | 0.998769i | \(-0.484207\pi\) | ||||
0.0495947 | + | 0.998769i | \(0.484207\pi\) | |||||||
\(138\) | 7.65176 | 0.651361 | ||||||||
\(139\) | −4.24633 | −0.360169 | −0.180084 | − | 0.983651i | \(-0.557637\pi\) | ||||
−0.180084 | + | 0.983651i | \(0.557637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.5895 | −2.32346 | ||||||||
\(142\) | −6.25178 | −0.524638 | ||||||||
\(143\) | −8.96444 | −0.749644 | ||||||||
\(144\) | 2.27498 | 0.189582 | ||||||||
\(145\) | −31.4124 | −2.60866 | ||||||||
\(146\) | 8.02055 | 0.663785 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.8583 | −1.05694 | ||||||||
\(149\) | −23.9932 | −1.96560 | −0.982799 | − | 0.184677i | \(-0.940876\pi\) | ||||
−0.982799 | + | 0.184677i | \(0.940876\pi\) | |||||||
\(150\) | −23.1028 | −1.88634 | ||||||||
\(151\) | 8.50069 | 0.691776 | 0.345888 | − | 0.938276i | \(-0.387578\pi\) | ||||
0.345888 | + | 0.938276i | \(0.387578\pi\) | |||||||
\(152\) | −2.58049 | −0.209305 | ||||||||
\(153\) | 1.43732 | 0.116201 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.2734 | 1.54807 | ||||||||
\(156\) | 7.32196 | 0.586226 | ||||||||
\(157\) | 4.43877 | 0.354252 | 0.177126 | − | 0.984188i | \(-0.443320\pi\) | ||||
0.177126 | + | 0.984188i | \(0.443320\pi\) | |||||||
\(158\) | −6.43160 | −0.511670 | ||||||||
\(159\) | 10.2819 | 0.815406 | ||||||||
\(160\) | −25.0055 | −1.97686 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.79110 | 0.612127 | ||||||||
\(163\) | −0.146906 | −0.0115066 | −0.00575329 | − | 0.999983i | \(-0.501831\pi\) | ||||
−0.00575329 | + | 0.999983i | \(0.501831\pi\) | |||||||
\(164\) | 3.12672 | 0.244156 | ||||||||
\(165\) | 40.7641 | 3.17348 | ||||||||
\(166\) | 3.19805 | 0.248217 | ||||||||
\(167\) | 0.885641 | 0.0685329 | 0.0342665 | − | 0.999413i | \(-0.489091\pi\) | ||||
0.0342665 | + | 0.999413i | \(0.489091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.21709 | −0.632084 | ||||||||
\(170\) | −1.89017 | −0.144969 | ||||||||
\(171\) | −2.43596 | −0.186283 | ||||||||
\(172\) | 12.4870 | 0.952128 | ||||||||
\(173\) | 24.2638 | 1.84474 | 0.922371 | − | 0.386305i | \(-0.126249\pi\) | ||||
0.922371 | + | 0.386305i | \(0.126249\pi\) | |||||||
\(174\) | 12.8953 | 0.977589 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.82811 | 0.288555 | ||||||||
\(177\) | 24.9888 | 1.87827 | ||||||||
\(178\) | −2.84721 | −0.213408 | ||||||||
\(179\) | −12.9466 | −0.967677 | −0.483838 | − | 0.875157i | \(-0.660758\pi\) | ||||
−0.483838 | + | 0.875157i | \(0.660758\pi\) | |||||||
\(180\) | −14.9203 | −1.11209 | ||||||||
\(181\) | 18.6034 | 1.38278 | 0.691391 | − | 0.722481i | \(-0.256998\pi\) | ||||
0.691391 | + | 0.722481i | \(0.256998\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.66677 | −0.418899 | ||||||||
\(184\) | −11.2764 | −0.831309 | ||||||||
\(185\) | 38.1946 | 2.80813 | ||||||||
\(186\) | −7.91201 | −0.580136 | ||||||||
\(187\) | 2.41858 | 0.176864 | ||||||||
\(188\) | 16.9922 | 1.23928 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.20344 | 0.232402 | ||||||||
\(191\) | −23.2888 | −1.68512 | −0.842559 | − | 0.538605i | \(-0.818952\pi\) | ||||
−0.842559 | + | 0.538605i | \(0.818952\pi\) | |||||||
\(192\) | 5.91029 | 0.426538 | ||||||||
\(193\) | 3.18843 | 0.229509 | 0.114754 | − | 0.993394i | \(-0.463392\pi\) | ||||
0.114754 | + | 0.993394i | \(0.463392\pi\) | |||||||
\(194\) | −1.58486 | −0.113786 | ||||||||
\(195\) | −21.7494 | −1.55751 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.25178 | −0.587915 | −0.293958 | − | 0.955818i | \(-0.594972\pi\) | ||||
−0.293958 | + | 0.955818i | \(0.594972\pi\) | |||||||
\(198\) | −7.49897 | −0.532929 | ||||||||
\(199\) | −19.6024 | −1.38958 | −0.694789 | − | 0.719214i | \(-0.744502\pi\) | ||||
−0.694789 | + | 0.719214i | \(0.744502\pi\) | |||||||
\(200\) | 34.0467 | 2.40747 | ||||||||
\(201\) | −13.1812 | −0.929728 | ||||||||
\(202\) | −11.3109 | −0.795832 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.97544 | −0.138309 | ||||||||
\(205\) | −9.28770 | −0.648681 | ||||||||
\(206\) | −3.67539 | −0.256076 | ||||||||
\(207\) | −10.6449 | −0.739869 | ||||||||
\(208\) | −2.04246 | −0.141619 | ||||||||
\(209\) | −4.09899 | −0.283533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.49078 | 0.653372 | 0.326686 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326686 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(212\) | −6.33254 | −0.434920 | ||||||||
\(213\) | 19.4083 | 1.32984 | ||||||||
\(214\) | −0.667398 | −0.0456224 | ||||||||
\(215\) | −37.0919 | −2.52965 | ||||||||
\(216\) | −3.39350 | −0.230899 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.834651 | 0.0565297 | ||||||||
\(219\) | −24.8994 | −1.68254 | ||||||||
\(220\) | −25.1063 | −1.69267 | ||||||||
\(221\) | −1.29041 | −0.0868027 | ||||||||
\(222\) | −15.6795 | −1.05234 | ||||||||
\(223\) | −18.8829 | −1.26449 | −0.632247 | − | 0.774767i | \(-0.717867\pi\) | ||||
−0.632247 | + | 0.774767i | \(0.717867\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 32.1398 | 2.14265 | ||||||||
\(226\) | 9.70030 | 0.645255 | ||||||||
\(227\) | −20.5405 | −1.36332 | −0.681660 | − | 0.731669i | \(-0.738742\pi\) | ||||
−0.681660 | + | 0.731669i | \(0.738742\pi\) | |||||||
\(228\) | 3.34797 | 0.221725 | ||||||||
\(229\) | −6.98499 | −0.461581 | −0.230791 | − | 0.973003i | \(-0.574131\pi\) | ||||
−0.230791 | + | 0.973003i | \(0.574131\pi\) | |||||||
\(230\) | 13.9986 | 0.923043 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.0038 | −1.24766 | ||||||||
\(233\) | 19.5265 | 1.27922 | 0.639612 | − | 0.768698i | \(-0.279095\pi\) | ||||
0.639612 | + | 0.768698i | \(0.279095\pi\) | |||||||
\(234\) | 4.00102 | 0.261555 | ||||||||
\(235\) | −50.4741 | −3.29257 | ||||||||
\(236\) | −15.3904 | −1.00183 | ||||||||
\(237\) | 19.9666 | 1.29697 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.8056 | −1.15175 | −0.575873 | − | 0.817539i | \(-0.695338\pi\) | ||||
−0.575873 | + | 0.817539i | \(0.695338\pi\) | |||||||
\(240\) | 9.28770 | 0.599518 | ||||||||
\(241\) | −15.2268 | −0.980844 | −0.490422 | − | 0.871485i | \(-0.663157\pi\) | ||||
−0.490422 | + | 0.871485i | \(0.663157\pi\) | |||||||
\(242\) | −4.35725 | −0.280095 | ||||||||
\(243\) | −20.2419 | −1.29852 | ||||||||
\(244\) | 3.49012 | 0.223432 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.81274 | 0.243092 | ||||||||
\(247\) | 2.18699 | 0.139155 | ||||||||
\(248\) | 11.6600 | 0.740408 | ||||||||
\(249\) | −9.92819 | −0.629173 | ||||||||
\(250\) | −26.2486 | −1.66011 | ||||||||
\(251\) | −6.70311 | −0.423097 | −0.211548 | − | 0.977368i | \(-0.567851\pi\) | ||||
−0.211548 | + | 0.977368i | \(0.567851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.9121 | −1.12612 | ||||||||
\(254\) | 2.33848 | 0.146730 | ||||||||
\(255\) | 5.86792 | 0.367463 | ||||||||
\(256\) | −12.4457 | −0.777854 | ||||||||
\(257\) | −8.25135 | −0.514705 | −0.257353 | − | 0.966318i | \(-0.582850\pi\) | ||||
−0.257353 | + | 0.966318i | \(0.582850\pi\) | |||||||
\(258\) | 15.2268 | 0.947979 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.3953 | 0.830741 | ||||||||
\(261\) | −17.9395 | −1.11042 | ||||||||
\(262\) | −2.78420 | −0.172009 | ||||||||
\(263\) | −0.700305 | −0.0431827 | −0.0215913 | − | 0.999767i | \(-0.506873\pi\) | ||||
−0.0215913 | + | 0.999767i | \(0.506873\pi\) | |||||||
\(264\) | 24.6614 | 1.51780 | ||||||||
\(265\) | 18.8104 | 1.15551 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.83902 | 0.540939 | ||||||||
\(268\) | 8.11819 | 0.495897 | ||||||||
\(269\) | −13.9652 | −0.851473 | −0.425736 | − | 0.904847i | \(-0.639985\pi\) | ||||
−0.425736 | + | 0.904847i | \(0.639985\pi\) | |||||||
\(270\) | 4.21272 | 0.256378 | ||||||||
\(271\) | 8.32570 | 0.505750 | 0.252875 | − | 0.967499i | \(-0.418624\pi\) | ||||
0.252875 | + | 0.967499i | \(0.418624\pi\) | |||||||
\(272\) | 0.551049 | 0.0334122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.871925 | −0.0526749 | ||||||||
\(275\) | 54.0817 | 3.26125 | ||||||||
\(276\) | 14.6302 | 0.880635 | ||||||||
\(277\) | −15.1501 | −0.910280 | −0.455140 | − | 0.890420i | \(-0.650411\pi\) | ||||
−0.455140 | + | 0.890420i | \(0.650411\pi\) | |||||||
\(278\) | 3.18909 | 0.191269 | ||||||||
\(279\) | 11.0069 | 0.658966 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2038 | −0.608708 | −0.304354 | − | 0.952559i | \(-0.598441\pi\) | ||||
−0.304354 | + | 0.952559i | \(0.598441\pi\) | |||||||
\(282\) | 20.7204 | 1.23388 | ||||||||
\(283\) | 6.29116 | 0.373971 | 0.186985 | − | 0.982363i | \(-0.440128\pi\) | ||||
0.186985 | + | 0.982363i | \(0.440128\pi\) | |||||||
\(284\) | −11.9534 | −0.709306 | ||||||||
\(285\) | −9.94491 | −0.589086 | ||||||||
\(286\) | 6.73251 | 0.398102 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −14.2805 | −0.841488 | ||||||||
\(289\) | −16.6519 | −0.979521 | ||||||||
\(290\) | 23.5915 | 1.38534 | ||||||||
\(291\) | 4.92011 | 0.288422 | ||||||||
\(292\) | 15.3353 | 0.897433 | ||||||||
\(293\) | 1.48286 | 0.0866294 | 0.0433147 | − | 0.999061i | \(-0.486208\pi\) | ||||
0.0433147 | + | 0.999061i | \(0.486208\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.7162 | 2.66170 | ||||||||
\(296\) | 23.1069 | 1.34306 | ||||||||
\(297\) | −5.39043 | −0.312784 | ||||||||
\(298\) | 18.0195 | 1.04384 | ||||||||
\(299\) | 9.55686 | 0.552688 | ||||||||
\(300\) | −44.1727 | −2.55031 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.38422 | −0.367371 | ||||||||
\(303\) | 35.1141 | 2.01725 | ||||||||
\(304\) | −0.933914 | −0.0535637 | ||||||||
\(305\) | −10.3672 | −0.593622 | ||||||||
\(306\) | −1.07946 | −0.0617088 | ||||||||
\(307\) | −29.9624 | −1.71004 | −0.855022 | − | 0.518592i | \(-0.826456\pi\) | ||||
−0.855022 | + | 0.518592i | \(0.826456\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.4100 | 0.649095 | ||||||||
\(310\) | −14.4748 | −0.822111 | ||||||||
\(311\) | 4.38115 | 0.248432 | 0.124216 | − | 0.992255i | \(-0.460358\pi\) | ||||
0.124216 | + | 0.992255i | \(0.460358\pi\) | |||||||
\(312\) | −13.1579 | −0.744920 | ||||||||
\(313\) | 20.4536 | 1.15611 | 0.578053 | − | 0.815999i | \(-0.303813\pi\) | ||||
0.578053 | + | 0.815999i | \(0.303813\pi\) | |||||||
\(314\) | −3.33362 | −0.188127 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.2972 | −0.691774 | ||||||||
\(317\) | −8.81648 | −0.495183 | −0.247591 | − | 0.968865i | \(-0.579639\pi\) | ||||
−0.247591 | + | 0.968865i | \(0.579639\pi\) | |||||||
\(318\) | −7.72194 | −0.433025 | ||||||||
\(319\) | −30.1867 | −1.69013 | ||||||||
\(320\) | 10.8127 | 0.604447 | ||||||||
\(321\) | 2.07190 | 0.115642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.590042 | −0.0328308 | ||||||||
\(324\) | 14.8966 | 0.827591 | ||||||||
\(325\) | −28.8549 | −1.60058 | ||||||||
\(326\) | 0.110330 | 0.00611062 | ||||||||
\(327\) | −2.59113 | −0.143290 | ||||||||
\(328\) | −5.61885 | −0.310249 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −30.6148 | −1.68529 | ||||||||
\(331\) | 12.0580 | 0.662767 | 0.331383 | − | 0.943496i | \(-0.392485\pi\) | ||||
0.331383 | + | 0.943496i | \(0.392485\pi\) | |||||||
\(332\) | 6.11470 | 0.335588 | ||||||||
\(333\) | 21.8127 | 1.19533 | ||||||||
\(334\) | −0.665138 | −0.0363947 | ||||||||
\(335\) | −24.1145 | −1.31752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.5871 | 1.50277 | 0.751383 | − | 0.659866i | \(-0.229387\pi\) | ||||
0.751383 | + | 0.659866i | \(0.229387\pi\) | |||||||
\(338\) | 6.17123 | 0.335671 | ||||||||
\(339\) | −30.1141 | −1.63557 | ||||||||
\(340\) | −3.61401 | −0.195997 | ||||||||
\(341\) | 18.5213 | 1.00299 | ||||||||
\(342\) | 1.82947 | 0.0989262 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −22.4398 | −1.20987 | ||||||||
\(345\) | −43.4581 | −2.33970 | ||||||||
\(346\) | −18.2227 | −0.979658 | ||||||||
\(347\) | 0.991536 | 0.0532284 | 0.0266142 | − | 0.999646i | \(-0.491527\pi\) | ||||
0.0266142 | + | 0.999646i | \(0.491527\pi\) | |||||||
\(348\) | 24.6559 | 1.32169 | ||||||||
\(349\) | 31.6583 | 1.69463 | 0.847316 | − | 0.531090i | \(-0.178217\pi\) | ||||
0.847316 | + | 0.531090i | \(0.178217\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.87602 | 0.153511 | ||||||||
\(352\) | −24.0298 | −1.28079 | ||||||||
\(353\) | 8.90381 | 0.473902 | 0.236951 | − | 0.971522i | \(-0.423852\pi\) | ||||
0.236951 | + | 0.971522i | \(0.423852\pi\) | |||||||
\(354\) | −18.7672 | −0.997466 | ||||||||
\(355\) | 35.5069 | 1.88451 | ||||||||
\(356\) | −5.44389 | −0.288525 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.72323 | 0.513889 | ||||||||
\(359\) | −21.6998 | −1.14527 | −0.572635 | − | 0.819811i | \(-0.694079\pi\) | ||||
−0.572635 | + | 0.819811i | \(0.694079\pi\) | |||||||
\(360\) | 26.8124 | 1.41314 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −13.9716 | −0.734332 | ||||||||
\(363\) | 13.5269 | 0.709976 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −45.5526 | −2.38433 | ||||||||
\(366\) | 4.25588 | 0.222458 | ||||||||
\(367\) | 12.7772 | 0.666964 | 0.333482 | − | 0.942757i | \(-0.391776\pi\) | ||||
0.333482 | + | 0.942757i | \(0.391776\pi\) | |||||||
\(368\) | −4.08109 | −0.212742 | ||||||||
\(369\) | −5.30415 | −0.276123 | ||||||||
\(370\) | −28.6851 | −1.49127 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −15.1278 | −0.784340 | ||||||||
\(373\) | −13.2182 | −0.684415 | −0.342207 | − | 0.939624i | \(-0.611175\pi\) | ||||
−0.342207 | + | 0.939624i | \(0.611175\pi\) | |||||||
\(374\) | −1.81641 | −0.0939244 | ||||||||
\(375\) | 81.4875 | 4.20800 | ||||||||
\(376\) | −30.5357 | −1.57476 | ||||||||
\(377\) | 16.1059 | 0.829496 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.72767 | −0.0887443 | −0.0443722 | − | 0.999015i | \(-0.514129\pi\) | ||||
−0.0443722 | + | 0.999015i | \(0.514129\pi\) | |||||||
\(380\) | 6.12500 | 0.314206 | ||||||||
\(381\) | −7.25970 | −0.371926 | ||||||||
\(382\) | 17.4904 | 0.894889 | ||||||||
\(383\) | −4.85563 | −0.248111 | −0.124056 | − | 0.992275i | \(-0.539590\pi\) | ||||
−0.124056 | + | 0.992275i | \(0.539590\pi\) | |||||||
\(384\) | 22.8977 | 1.16849 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.39459 | −0.121881 | ||||||||
\(387\) | −21.1830 | −1.07679 | ||||||||
\(388\) | −3.03026 | −0.153838 | ||||||||
\(389\) | 10.6299 | 0.538955 | 0.269477 | − | 0.963007i | \(-0.413149\pi\) | ||||
0.269477 | + | 0.963007i | \(0.413149\pi\) | |||||||
\(390\) | 16.3343 | 0.827120 | ||||||||
\(391\) | −2.57841 | −0.130396 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.64341 | 0.436002 | ||||||||
\(394\) | 6.19729 | 0.312215 | ||||||||
\(395\) | 36.5281 | 1.83793 | ||||||||
\(396\) | −14.3381 | −0.720516 | ||||||||
\(397\) | 12.7514 | 0.639974 | 0.319987 | − | 0.947422i | \(-0.396322\pi\) | ||||
0.319987 | + | 0.947422i | \(0.396322\pi\) | |||||||
\(398\) | 14.7219 | 0.737941 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.3220 | 0.616098 | ||||||||
\(401\) | 19.2514 | 0.961367 | 0.480683 | − | 0.876894i | \(-0.340389\pi\) | ||||
0.480683 | + | 0.876894i | \(0.340389\pi\) | |||||||
\(402\) | 9.89938 | 0.493736 | ||||||||
\(403\) | −9.88190 | −0.492253 | ||||||||
\(404\) | −21.6265 | −1.07596 | ||||||||
\(405\) | −44.2495 | −2.19877 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.7043 | 1.81936 | ||||||||
\(408\) | 3.54996 | 0.175749 | ||||||||
\(409\) | 3.13980 | 0.155253 | 0.0776266 | − | 0.996983i | \(-0.475266\pi\) | ||||
0.0776266 | + | 0.996983i | \(0.475266\pi\) | |||||||
\(410\) | 6.97529 | 0.344485 | ||||||||
\(411\) | 2.70685 | 0.133519 | ||||||||
\(412\) | −7.02736 | −0.346213 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.99455 | 0.392910 | ||||||||
\(415\) | −18.1633 | −0.891601 | ||||||||
\(416\) | 12.8209 | 0.628598 | ||||||||
\(417\) | −9.90038 | −0.484823 | ||||||||
\(418\) | 3.07844 | 0.150572 | ||||||||
\(419\) | 12.4881 | 0.610085 | 0.305043 | − | 0.952339i | \(-0.401329\pi\) | ||||
0.305043 | + | 0.952339i | \(0.401329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.5141 | −0.707376 | −0.353688 | − | 0.935364i | \(-0.615072\pi\) | ||||
−0.353688 | + | 0.935364i | \(0.615072\pi\) | |||||||
\(422\) | −7.12780 | −0.346976 | ||||||||
\(423\) | −28.8255 | −1.40154 | ||||||||
\(424\) | 11.3799 | 0.552655 | ||||||||
\(425\) | 7.78495 | 0.377626 | ||||||||
\(426\) | −14.5761 | −0.706215 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.27607 | −0.0616811 | ||||||||
\(429\) | −20.9007 | −1.00910 | ||||||||
\(430\) | 27.8569 | 1.34338 | ||||||||
\(431\) | 23.6671 | 1.14001 | 0.570003 | − | 0.821643i | \(-0.306942\pi\) | ||||
0.570003 | + | 0.821643i | \(0.306942\pi\) | |||||||
\(432\) | −1.22815 | −0.0590896 | ||||||||
\(433\) | 4.61912 | 0.221981 | 0.110990 | − | 0.993821i | \(-0.464598\pi\) | ||||
0.110990 | + | 0.993821i | \(0.464598\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −73.2385 | −3.51152 | ||||||||
\(436\) | 1.59586 | 0.0764277 | ||||||||
\(437\) | 4.36988 | 0.209040 | ||||||||
\(438\) | 18.7000 | 0.893522 | ||||||||
\(439\) | 18.9603 | 0.904925 | 0.452462 | − | 0.891783i | \(-0.350546\pi\) | ||||
0.452462 | + | 0.891783i | \(0.350546\pi\) | |||||||
\(440\) | 45.1172 | 2.15088 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.969132 | 0.0460969 | ||||||||
\(443\) | −22.4689 | −1.06753 | −0.533764 | − | 0.845633i | \(-0.679223\pi\) | ||||
−0.533764 | + | 0.845633i | \(0.679223\pi\) | |||||||
\(444\) | −29.9793 | −1.42275 | ||||||||
\(445\) | 16.1707 | 0.766564 | ||||||||
\(446\) | 14.1815 | 0.671515 | ||||||||
\(447\) | −55.9405 | −2.64589 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7360 | 0.742629 | 0.371314 | − | 0.928507i | \(-0.378907\pi\) | ||||
0.371314 | + | 0.928507i | \(0.378907\pi\) | |||||||
\(450\) | −24.1378 | −1.13787 | ||||||||
\(451\) | −8.92529 | −0.420276 | ||||||||
\(452\) | 18.5470 | 0.872379 | ||||||||
\(453\) | 19.8195 | 0.931201 | ||||||||
\(454\) | 15.4264 | 0.723997 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.01645 | −0.281746 | ||||||||
\(457\) | 22.8566 | 1.06919 | 0.534594 | − | 0.845109i | \(-0.320464\pi\) | ||||
0.534594 | + | 0.845109i | \(0.320464\pi\) | |||||||
\(458\) | 5.24590 | 0.245125 | ||||||||
\(459\) | −0.775942 | −0.0362179 | ||||||||
\(460\) | 26.7655 | 1.24795 | ||||||||
\(461\) | 26.0021 | 1.21104 | 0.605519 | − | 0.795831i | \(-0.292965\pi\) | ||||
0.605519 | + | 0.795831i | \(0.292965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.3481 | 0.945654 | 0.472827 | − | 0.881155i | \(-0.343233\pi\) | ||||
0.472827 | + | 0.881155i | \(0.343233\pi\) | |||||||
\(464\) | −6.87774 | −0.319291 | ||||||||
\(465\) | 44.9361 | 2.08386 | ||||||||
\(466\) | −14.6649 | −0.679337 | ||||||||
\(467\) | 15.1302 | 0.700141 | 0.350071 | − | 0.936723i | \(-0.386158\pi\) | ||||
0.350071 | + | 0.936723i | \(0.386158\pi\) | |||||||
\(468\) | 7.64997 | 0.353620 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 37.9073 | 1.74853 | ||||||||
\(471\) | 10.3491 | 0.476859 | ||||||||
\(472\) | 27.6573 | 1.27303 | ||||||||
\(473\) | −35.6446 | −1.63894 | ||||||||
\(474\) | −14.9954 | −0.688760 | ||||||||
\(475\) | −13.1939 | −0.605377 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7425 | 0.491865 | ||||||||
\(478\) | 13.3724 | 0.611640 | ||||||||
\(479\) | 27.9265 | 1.27599 | 0.637997 | − | 0.770039i | \(-0.279763\pi\) | ||||
0.637997 | + | 0.770039i | \(0.279763\pi\) | |||||||
\(480\) | −58.3008 | −2.66106 | ||||||||
\(481\) | −19.5833 | −0.892921 | ||||||||
\(482\) | 11.4357 | 0.520881 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.33109 | −0.378686 | ||||||||
\(485\) | 9.00118 | 0.408722 | ||||||||
\(486\) | 15.2021 | 0.689584 | ||||||||
\(487\) | 0.660652 | 0.0299370 | 0.0149685 | − | 0.999888i | \(-0.495235\pi\) | ||||
0.0149685 | + | 0.999888i | \(0.495235\pi\) | |||||||
\(488\) | −6.27190 | −0.283916 | ||||||||
\(489\) | −0.342514 | −0.0154890 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.09463 | −0.229917 | −0.114959 | − | 0.993370i | \(-0.536674\pi\) | ||||
−0.114959 | + | 0.993370i | \(0.536674\pi\) | |||||||
\(492\) | 7.28999 | 0.328658 | ||||||||
\(493\) | −4.34532 | −0.195703 | ||||||||
\(494\) | −1.64248 | −0.0738987 | ||||||||
\(495\) | 42.5903 | 1.91429 | ||||||||
\(496\) | 4.21989 | 0.189479 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.45631 | 0.334125 | ||||||||
\(499\) | −12.7990 | −0.572963 | −0.286482 | − | 0.958086i | \(-0.592486\pi\) | ||||
−0.286482 | + | 0.958086i | \(0.592486\pi\) | |||||||
\(500\) | −50.1876 | −2.24446 | ||||||||
\(501\) | 2.06488 | 0.0922522 | ||||||||
\(502\) | 5.03420 | 0.224687 | ||||||||
\(503\) | 32.1398 | 1.43304 | 0.716522 | − | 0.697565i | \(-0.245733\pi\) | ||||
0.716522 | + | 0.697565i | \(0.245733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 64.2401 | 2.85865 | ||||||||
\(506\) | 13.4524 | 0.598033 | ||||||||
\(507\) | −19.1583 | −0.850848 | ||||||||
\(508\) | 4.47120 | 0.198377 | ||||||||
\(509\) | 36.4645 | 1.61626 | 0.808130 | − | 0.589004i | \(-0.200480\pi\) | ||||
0.808130 | + | 0.589004i | \(0.200480\pi\) | |||||||
\(510\) | −4.40695 | −0.195143 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.2949 | −0.454973 | ||||||||
\(513\) | 1.31506 | 0.0580614 | ||||||||
\(514\) | 6.19697 | 0.273336 | ||||||||
\(515\) | 20.8743 | 0.919832 | ||||||||
\(516\) | 29.1137 | 1.28166 | ||||||||
\(517\) | −48.5046 | −2.13323 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 56.5714 | 2.48321 | ||||||||
\(520\) | −24.0720 | −1.05562 | ||||||||
\(521\) | 35.5212 | 1.55621 | 0.778107 | − | 0.628132i | \(-0.216180\pi\) | ||||
0.778107 | + | 0.628132i | \(0.216180\pi\) | |||||||
\(522\) | 13.4730 | 0.589696 | ||||||||
\(523\) | 14.1623 | 0.619273 | 0.309636 | − | 0.950855i | \(-0.399793\pi\) | ||||
0.309636 | + | 0.950855i | \(0.399793\pi\) | |||||||
\(524\) | −5.32341 | −0.232554 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.525946 | 0.0229323 | ||||||||
\(527\) | 2.66611 | 0.116137 | ||||||||
\(528\) | 8.92529 | 0.388424 | ||||||||
\(529\) | −3.90417 | −0.169747 | ||||||||
\(530\) | −14.1270 | −0.613639 | ||||||||
\(531\) | 26.1083 | 1.13300 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.76202 | 0.206266 | ||||||||
\(534\) | −6.63832 | −0.287268 | ||||||||
\(535\) | 3.79047 | 0.163876 | ||||||||
\(536\) | −14.5888 | −0.630138 | ||||||||
\(537\) | −30.1853 | −1.30259 | ||||||||
\(538\) | 10.4882 | 0.452178 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.05475 | 0.346621 | ||||||||
\(541\) | −16.7454 | −0.719940 | −0.359970 | − | 0.932964i | \(-0.617213\pi\) | ||||
−0.359970 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(542\) | −6.25280 | −0.268581 | ||||||||
\(543\) | 43.3742 | 1.86136 | ||||||||
\(544\) | −3.45905 | −0.148305 | ||||||||
\(545\) | −4.74039 | −0.203056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.3888 | −1.76966 | −0.884829 | − | 0.465917i | \(-0.845725\pi\) | ||||
−0.884829 | + | 0.465917i | \(0.845725\pi\) | |||||||
\(548\) | −1.66713 | −0.0712161 | ||||||||
\(549\) | −5.92063 | −0.252686 | ||||||||
\(550\) | −40.6166 | −1.73190 | ||||||||
\(551\) | 7.36442 | 0.313735 | ||||||||
\(552\) | −26.2912 | −1.11903 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 11.3781 | 0.483408 | ||||||||
\(555\) | 89.0514 | 3.78002 | ||||||||
\(556\) | 6.09757 | 0.258594 | ||||||||
\(557\) | 37.6750 | 1.59634 | 0.798172 | − | 0.602430i | \(-0.205801\pi\) | ||||
0.798172 | + | 0.602430i | \(0.205801\pi\) | |||||||
\(558\) | −8.26645 | −0.349947 | ||||||||
\(559\) | 19.0179 | 0.804372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.63895 | 0.238077 | ||||||||
\(562\) | 7.66330 | 0.323257 | ||||||||
\(563\) | −3.45814 | −0.145743 | −0.0728717 | − | 0.997341i | \(-0.523216\pi\) | ||||
−0.0728717 | + | 0.997341i | \(0.523216\pi\) | |||||||
\(564\) | 39.6175 | 1.66820 | ||||||||
\(565\) | −55.0927 | −2.31777 | ||||||||
\(566\) | −4.72482 | −0.198599 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.4809 | 0.901318 | ||||||||
\(569\) | 7.69204 | 0.322467 | 0.161234 | − | 0.986916i | \(-0.448453\pi\) | ||||
0.161234 | + | 0.986916i | \(0.448453\pi\) | |||||||
\(570\) | 7.46887 | 0.312837 | ||||||||
\(571\) | −0.417131 | −0.0174564 | −0.00872819 | − | 0.999962i | \(-0.502778\pi\) | ||||
−0.00872819 | + | 0.999962i | \(0.502778\pi\) | |||||||
\(572\) | 12.8726 | 0.538231 | ||||||||
\(573\) | −54.2982 | −2.26834 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −57.6557 | −2.40441 | ||||||||
\(576\) | 6.17506 | 0.257294 | ||||||||
\(577\) | 23.2905 | 0.969596 | 0.484798 | − | 0.874626i | \(-0.338893\pi\) | ||||
0.484798 | + | 0.874626i | \(0.338893\pi\) | |||||||
\(578\) | 12.5059 | 0.520179 | ||||||||
\(579\) | 7.43388 | 0.308942 | ||||||||
\(580\) | 45.1071 | 1.87297 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.69512 | −0.153168 | ||||||||
\(583\) | 18.0764 | 0.748647 | ||||||||
\(584\) | −27.5583 | −1.14037 | ||||||||
\(585\) | −22.7237 | −0.939511 | ||||||||
\(586\) | −1.11366 | −0.0460049 | ||||||||
\(587\) | −30.5061 | −1.25912 | −0.629562 | − | 0.776951i | \(-0.716766\pi\) | ||||
−0.629562 | + | 0.776951i | \(0.716766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.51850 | −0.186182 | ||||||||
\(590\) | −34.3340 | −1.41351 | ||||||||
\(591\) | −19.2392 | −0.791393 | ||||||||
\(592\) | 8.36270 | 0.343705 | ||||||||
\(593\) | −32.6861 | −1.34226 | −0.671129 | − | 0.741341i | \(-0.734190\pi\) | ||||
−0.671129 | + | 0.741341i | \(0.734190\pi\) | |||||||
\(594\) | 4.04834 | 0.166105 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34.4533 | 1.41126 | ||||||||
\(597\) | −45.7033 | −1.87051 | ||||||||
\(598\) | −7.17744 | −0.293507 | ||||||||
\(599\) | −20.3738 | −0.832451 | −0.416225 | − | 0.909262i | \(-0.636647\pi\) | ||||
−0.416225 | + | 0.909262i | \(0.636647\pi\) | |||||||
\(600\) | 79.3804 | 3.24069 | ||||||||
\(601\) | 12.3891 | 0.505363 | 0.252682 | − | 0.967549i | \(-0.418687\pi\) | ||||
0.252682 | + | 0.967549i | \(0.418687\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.7717 | −0.560826 | ||||||||
\(604\) | −12.2067 | −0.496683 | ||||||||
\(605\) | 24.7469 | 1.00611 | ||||||||
\(606\) | −26.3715 | −1.07127 | ||||||||
\(607\) | −33.3480 | −1.35355 | −0.676776 | − | 0.736189i | \(-0.736624\pi\) | ||||
−0.676776 | + | 0.736189i | \(0.736624\pi\) | |||||||
\(608\) | 5.86237 | 0.237751 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.78599 | 0.315245 | ||||||||
\(611\) | 25.8793 | 1.04696 | ||||||||
\(612\) | −2.06394 | −0.0834298 | ||||||||
\(613\) | −38.7985 | −1.56706 | −0.783528 | − | 0.621356i | \(-0.786582\pi\) | ||||
−0.783528 | + | 0.621356i | \(0.786582\pi\) | |||||||
\(614\) | 22.5025 | 0.908126 | ||||||||
\(615\) | −21.6544 | −0.873190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.98936 | 0.0800887 | 0.0400443 | − | 0.999198i | \(-0.487250\pi\) | ||||
0.0400443 | + | 0.999198i | \(0.487250\pi\) | |||||||
\(618\) | −8.56922 | −0.344705 | ||||||||
\(619\) | 13.0014 | 0.522572 | 0.261286 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261286 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(620\) | −27.6758 | −1.11149 | ||||||||
\(621\) | 5.74666 | 0.230605 | ||||||||
\(622\) | −3.29035 | −0.131931 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.76202 | −0.190633 | ||||||||
\(625\) | 83.1093 | 3.32437 | ||||||||
\(626\) | −15.3611 | −0.613955 | ||||||||
\(627\) | −9.55686 | −0.381664 | ||||||||
\(628\) | −6.37391 | −0.254347 | ||||||||
\(629\) | 5.28351 | 0.210667 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9918 | −0.596814 | −0.298407 | − | 0.954439i | \(-0.596455\pi\) | ||||
−0.298407 | + | 0.954439i | \(0.596455\pi\) | |||||||
\(632\) | 22.0987 | 0.879040 | ||||||||
\(633\) | 22.1279 | 0.879505 | ||||||||
\(634\) | 6.62139 | 0.262969 | ||||||||
\(635\) | −13.2814 | −0.527056 | ||||||||
\(636\) | −14.7644 | −0.585447 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.6710 | 0.897552 | ||||||||
\(639\) | 20.2778 | 0.802177 | ||||||||
\(640\) | 41.8905 | 1.65587 | ||||||||
\(641\) | 24.0547 | 0.950105 | 0.475053 | − | 0.879957i | \(-0.342429\pi\) | ||||
0.475053 | + | 0.879957i | \(0.342429\pi\) | |||||||
\(642\) | −1.55605 | −0.0614123 | ||||||||
\(643\) | −24.3676 | −0.960964 | −0.480482 | − | 0.877005i | \(-0.659538\pi\) | ||||
−0.480482 | + | 0.877005i | \(0.659538\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −86.4803 | −3.40516 | ||||||||
\(646\) | 0.443136 | 0.0174350 | ||||||||
\(647\) | 38.2402 | 1.50338 | 0.751688 | − | 0.659519i | \(-0.229240\pi\) | ||||
0.751688 | + | 0.659519i | \(0.229240\pi\) | |||||||
\(648\) | −26.7699 | −1.05162 | ||||||||
\(649\) | 43.9324 | 1.72450 | ||||||||
\(650\) | 21.6707 | 0.849995 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.210952 | 0.00826151 | ||||||||
\(653\) | 21.1624 | 0.828147 | 0.414074 | − | 0.910243i | \(-0.364106\pi\) | ||||
0.414074 | + | 0.910243i | \(0.364106\pi\) | |||||||
\(654\) | 1.94600 | 0.0760947 | ||||||||
\(655\) | 15.8128 | 0.617858 | ||||||||
\(656\) | −2.03354 | −0.0793963 | ||||||||
\(657\) | −26.0148 | −1.01493 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.6069 | 0.958548 | 0.479274 | − | 0.877665i | \(-0.340900\pi\) | ||||
0.479274 | + | 0.877665i | \(0.340900\pi\) | |||||||
\(660\) | −58.5358 | −2.27850 | ||||||||
\(661\) | 38.1953 | 1.48562 | 0.742812 | − | 0.669500i | \(-0.233492\pi\) | ||||
0.742812 | + | 0.669500i | \(0.233492\pi\) | |||||||
\(662\) | −9.05584 | −0.351965 | ||||||||
\(663\) | −3.00862 | −0.116845 | ||||||||
\(664\) | −10.9884 | −0.426432 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.3819 | −0.634786 | ||||||||
\(667\) | 32.1816 | 1.24608 | ||||||||
\(668\) | −1.27175 | −0.0492054 | ||||||||
\(669\) | −44.0258 | −1.70214 | ||||||||
\(670\) | 18.1106 | 0.699673 | ||||||||
\(671\) | −9.96264 | −0.384603 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0333 | −1.08060 | −0.540302 | − | 0.841471i | \(-0.681690\pi\) | ||||
−0.540302 | + | 0.841471i | \(0.681690\pi\) | |||||||
\(674\) | −20.7186 | −0.798050 | ||||||||
\(675\) | −17.3508 | −0.667832 | ||||||||
\(676\) | 11.7994 | 0.453824 | ||||||||
\(677\) | 5.23635 | 0.201249 | 0.100625 | − | 0.994924i | \(-0.467916\pi\) | ||||
0.100625 | + | 0.994924i | \(0.467916\pi\) | |||||||
\(678\) | 22.6164 | 0.868578 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.49454 | 0.249054 | ||||||||
\(681\) | −47.8905 | −1.83517 | ||||||||
\(682\) | −13.9099 | −0.532639 | ||||||||
\(683\) | −1.25171 | −0.0478955 | −0.0239478 | − | 0.999713i | \(-0.507624\pi\) | ||||
−0.0239478 | + | 0.999713i | \(0.507624\pi\) | |||||||
\(684\) | 3.49795 | 0.133748 | ||||||||
\(685\) | 4.95209 | 0.189210 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.2856 | −0.621335 | ||||||||
\(688\) | −8.12126 | −0.309620 | ||||||||
\(689\) | −9.64452 | −0.367427 | ||||||||
\(690\) | 32.6380 | 1.24251 | ||||||||
\(691\) | −50.8050 | −1.93271 | −0.966357 | − | 0.257204i | \(-0.917199\pi\) | ||||
−0.966357 | + | 0.257204i | \(0.917199\pi\) | |||||||
\(692\) | −34.8419 | −1.32449 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.744668 | −0.0282672 | ||||||||
\(695\) | −18.1124 | −0.687043 | ||||||||
\(696\) | −44.3077 | −1.67948 | ||||||||
\(697\) | −1.28478 | −0.0486645 | ||||||||
\(698\) | −23.7762 | −0.899941 | ||||||||
\(699\) | 45.5263 | 1.72196 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.998799 | 0.0377241 | 0.0188621 | − | 0.999822i | \(-0.493996\pi\) | ||||
0.0188621 | + | 0.999822i | \(0.493996\pi\) | |||||||
\(702\) | −2.15996 | −0.0815225 | ||||||||
\(703\) | −8.95446 | −0.337724 | ||||||||
\(704\) | 10.3908 | 0.391617 | ||||||||
\(705\) | −117.681 | −4.43213 | ||||||||
\(706\) | −6.68698 | −0.251668 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −35.8830 | −1.34857 | ||||||||
\(709\) | −13.9625 | −0.524371 | −0.262185 | − | 0.965017i | \(-0.584443\pi\) | ||||
−0.262185 | + | 0.965017i | \(0.584443\pi\) | |||||||
\(710\) | −26.6665 | −1.00078 | ||||||||
\(711\) | 20.8610 | 0.782349 | ||||||||
\(712\) | 9.78291 | 0.366630 | ||||||||
\(713\) | −19.7453 | −0.739467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.2372 | −1.42999 | ||||||||
\(716\) | 18.5909 | 0.694774 | ||||||||
\(717\) | −41.5140 | −1.55037 | ||||||||
\(718\) | 16.2970 | 0.608200 | ||||||||
\(719\) | 18.5694 | 0.692521 | 0.346260 | − | 0.938138i | \(-0.387451\pi\) | ||||
0.346260 | + | 0.938138i | \(0.387451\pi\) | |||||||
\(720\) | 9.70377 | 0.361638 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.751024 | −0.0279502 | ||||||||
\(723\) | −35.5015 | −1.32032 | ||||||||
\(724\) | −26.7138 | −0.992811 | ||||||||
\(725\) | −97.1654 | −3.60863 | ||||||||
\(726\) | −10.1590 | −0.377036 | ||||||||
\(727\) | −32.1991 | −1.19420 | −0.597099 | − | 0.802168i | \(-0.703680\pi\) | ||||
−0.597099 | + | 0.802168i | \(0.703680\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.0724 | −0.595272 | ||||||||
\(730\) | 34.2111 | 1.26621 | ||||||||
\(731\) | −5.13097 | −0.189776 | ||||||||
\(732\) | 8.13727 | 0.300762 | ||||||||
\(733\) | 9.55623 | 0.352968 | 0.176484 | − | 0.984304i | \(-0.443528\pi\) | ||||
0.176484 | + | 0.984304i | \(0.443528\pi\) | |||||||
\(734\) | −9.59598 | −0.354194 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.6179 | 0.944287 | ||||||||
\(737\) | −23.1736 | −0.853609 | ||||||||
\(738\) | 3.98355 | 0.146636 | ||||||||
\(739\) | −20.2850 | −0.746194 | −0.373097 | − | 0.927792i | \(-0.621704\pi\) | ||||
−0.373097 | + | 0.927792i | \(0.621704\pi\) | |||||||
\(740\) | −54.8461 | −2.01618 | ||||||||
\(741\) | 5.09899 | 0.187316 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.965374 | 0.0354161 | 0.0177081 | − | 0.999843i | \(-0.494363\pi\) | ||||
0.0177081 | + | 0.999843i | \(0.494363\pi\) | |||||||
\(744\) | 27.1854 | 0.996664 | ||||||||
\(745\) | −102.341 | −3.74949 | ||||||||
\(746\) | 9.92722 | 0.363461 | ||||||||
\(747\) | −10.3730 | −0.379527 | ||||||||
\(748\) | −3.47299 | −0.126985 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −61.1991 | −2.23468 | ||||||||
\(751\) | −0.657779 | −0.0240027 | −0.0120013 | − | 0.999928i | \(-0.503820\pi\) | ||||
−0.0120013 | + | 0.999928i | \(0.503820\pi\) | |||||||
\(752\) | −11.0513 | −0.402999 | ||||||||
\(753\) | −15.6284 | −0.569531 | ||||||||
\(754\) | −12.0959 | −0.440507 | ||||||||
\(755\) | 36.2591 | 1.31960 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.47679 | −0.0536749 | −0.0268375 | − | 0.999640i | \(-0.508544\pi\) | ||||
−0.0268375 | + | 0.999640i | \(0.508544\pi\) | |||||||
\(758\) | 1.29752 | 0.0471281 | ||||||||
\(759\) | −41.7623 | −1.51588 | ||||||||
\(760\) | −11.0069 | −0.399262 | ||||||||
\(761\) | 18.4847 | 0.670070 | 0.335035 | − | 0.942206i | \(-0.391252\pi\) | ||||
0.335035 | + | 0.942206i | \(0.391252\pi\) | |||||||
\(762\) | 5.45221 | 0.197513 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 33.4418 | 1.20988 | ||||||||
\(765\) | 6.13079 | 0.221659 | ||||||||
\(766\) | 3.64669 | 0.131760 | ||||||||
\(767\) | −23.4398 | −0.846362 | ||||||||
\(768\) | −29.0173 | −1.04707 | ||||||||
\(769\) | −4.34052 | −0.156523 | −0.0782617 | − | 0.996933i | \(-0.524937\pi\) | ||||
−0.0782617 | + | 0.996933i | \(0.524937\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.2382 | −0.692845 | ||||||||
\(772\) | −4.57847 | −0.164783 | ||||||||
\(773\) | 33.5513 | 1.20676 | 0.603379 | − | 0.797455i | \(-0.293821\pi\) | ||||
0.603379 | + | 0.797455i | \(0.293821\pi\) | |||||||
\(774\) | 15.9089 | 0.571835 | ||||||||
\(775\) | 59.6166 | 2.14149 | ||||||||
\(776\) | 5.44551 | 0.195483 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.98328 | −0.286214 | ||||||||
\(779\) | 2.17744 | 0.0780147 | ||||||||
\(780\) | 31.2313 | 1.11826 | ||||||||
\(781\) | 34.1214 | 1.22096 | ||||||||
\(782\) | 1.93645 | 0.0692473 | ||||||||
\(783\) | 9.68467 | 0.346102 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.9333 | 0.675757 | ||||||||
\(786\) | −6.49141 | −0.231541 | ||||||||
\(787\) | −42.0571 | −1.49917 | −0.749587 | − | 0.661906i | \(-0.769748\pi\) | ||||
−0.749587 | + | 0.661906i | \(0.769748\pi\) | |||||||
\(788\) | 11.8493 | 0.422112 | ||||||||
\(789\) | −1.63277 | −0.0581282 | ||||||||
\(790\) | −27.4335 | −0.976041 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 25.7662 | 0.915562 | ||||||||
\(793\) | 5.31549 | 0.188759 | ||||||||
\(794\) | −9.57660 | −0.339861 | ||||||||
\(795\) | 43.8566 | 1.55544 | ||||||||
\(796\) | 28.1483 | 0.997691 | ||||||||
\(797\) | 2.71101 | 0.0960289 | 0.0480145 | − | 0.998847i | \(-0.484711\pi\) | ||||
0.0480145 | + | 0.998847i | \(0.484711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.98214 | −0.247010 | ||||||||
\(800\) | −77.3475 | −2.73465 | ||||||||
\(801\) | 9.23499 | 0.326302 | ||||||||
\(802\) | −14.4582 | −0.510538 | ||||||||
\(803\) | −43.7751 | −1.54479 | ||||||||
\(804\) | 18.9277 | 0.667528 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.42155 | 0.261413 | ||||||||
\(807\) | −32.5601 | −1.14617 | ||||||||
\(808\) | 38.8638 | 1.36722 | ||||||||
\(809\) | 13.3158 | 0.468159 | 0.234079 | − | 0.972217i | \(-0.424792\pi\) | ||||
0.234079 | + | 0.972217i | \(0.424792\pi\) | |||||||
\(810\) | 33.2324 | 1.16767 | ||||||||
\(811\) | −15.1310 | −0.531320 | −0.265660 | − | 0.964067i | \(-0.585590\pi\) | ||||
−0.265660 | + | 0.964067i | \(0.585590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.4115 | 0.680791 | ||||||||
\(814\) | −27.5658 | −0.966181 | ||||||||
\(815\) | −0.626618 | −0.0219495 | ||||||||
\(816\) | 1.28478 | 0.0449763 | ||||||||
\(817\) | 8.69594 | 0.304232 | ||||||||
\(818\) | −2.35807 | −0.0824478 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.3368 | 0.465741 | ||||||||
\(821\) | −24.3734 | −0.850639 | −0.425319 | − | 0.905043i | \(-0.639838\pi\) | ||||
−0.425319 | + | 0.905043i | \(0.639838\pi\) | |||||||
\(822\) | −2.03291 | −0.0709058 | ||||||||
\(823\) | 11.7877 | 0.410892 | 0.205446 | − | 0.978668i | \(-0.434135\pi\) | ||||
0.205446 | + | 0.978668i | \(0.434135\pi\) | |||||||
\(824\) | 12.6285 | 0.439934 | ||||||||
\(825\) | 126.092 | 4.38997 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.5429 | 0.610028 | 0.305014 | − | 0.952348i | \(-0.401339\pi\) | ||||
0.305014 | + | 0.952348i | \(0.401339\pi\) | |||||||
\(828\) | 15.2856 | 0.531212 | ||||||||
\(829\) | 50.9728 | 1.77036 | 0.885180 | − | 0.465249i | \(-0.154035\pi\) | ||||
0.885180 | + | 0.465249i | \(0.154035\pi\) | |||||||
\(830\) | 13.6411 | 0.473488 | ||||||||
\(831\) | −35.3226 | −1.22533 | ||||||||
\(832\) | −5.54391 | −0.192201 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.43542 | 0.257468 | ||||||||
\(835\) | 3.77764 | 0.130731 | ||||||||
\(836\) | 5.88600 | 0.203572 | ||||||||
\(837\) | −5.94211 | −0.205389 | ||||||||
\(838\) | −9.37889 | −0.323988 | ||||||||
\(839\) | −5.84311 | −0.201727 | −0.100863 | − | 0.994900i | \(-0.532160\pi\) | ||||
−0.100863 | + | 0.994900i | \(0.532160\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.2347 | 0.870163 | ||||||||
\(842\) | 10.9005 | 0.375655 | ||||||||
\(843\) | −23.7903 | −0.819382 | ||||||||
\(844\) | −13.6284 | −0.469109 | ||||||||
\(845\) | −35.0494 | −1.20574 | ||||||||
\(846\) | 21.6486 | 0.744295 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.11852 | 0.141431 | ||||||||
\(849\) | 14.6679 | 0.503403 | ||||||||
\(850\) | −5.84669 | −0.200540 | ||||||||
\(851\) | −39.1299 | −1.34136 | ||||||||
\(852\) | −27.8696 | −0.954798 | ||||||||
\(853\) | −37.0096 | −1.26719 | −0.633593 | − | 0.773667i | \(-0.718421\pi\) | ||||
−0.633593 | + | 0.773667i | \(0.718421\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.3904 | −0.355345 | ||||||||
\(856\) | 2.29315 | 0.0783784 | ||||||||
\(857\) | 40.1269 | 1.37071 | 0.685355 | − | 0.728209i | \(-0.259647\pi\) | ||||
0.685355 | + | 0.728209i | \(0.259647\pi\) | |||||||
\(858\) | 15.6970 | 0.535885 | ||||||||
\(859\) | −14.4388 | −0.492644 | −0.246322 | − | 0.969188i | \(-0.579222\pi\) | ||||
−0.246322 | + | 0.969188i | \(0.579222\pi\) | |||||||
\(860\) | 53.2626 | 1.81624 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.7746 | −0.605405 | ||||||||
\(863\) | 30.6183 | 1.04226 | 0.521130 | − | 0.853477i | \(-0.325511\pi\) | ||||
0.521130 | + | 0.853477i | \(0.325511\pi\) | |||||||
\(864\) | 7.70938 | 0.262279 | ||||||||
\(865\) | 103.496 | 3.51895 | ||||||||
\(866\) | −3.46907 | −0.117884 | ||||||||
\(867\) | −38.8240 | −1.31853 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.1028 | 1.19078 | ||||||||
\(870\) | 55.0039 | 1.86481 | ||||||||
\(871\) | 12.3641 | 0.418941 | ||||||||
\(872\) | −2.86783 | −0.0971169 | ||||||||
\(873\) | 5.14052 | 0.173980 | ||||||||
\(874\) | −3.28188 | −0.111011 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 35.7546 | 1.20804 | ||||||||
\(877\) | −16.0685 | −0.542596 | −0.271298 | − | 0.962495i | \(-0.587453\pi\) | ||||
−0.271298 | + | 0.962495i | \(0.587453\pi\) | |||||||
\(878\) | −14.2396 | −0.480564 | ||||||||
\(879\) | 3.45730 | 0.116612 | ||||||||
\(880\) | 16.3285 | 0.550435 | ||||||||
\(881\) | −40.2468 | −1.35595 | −0.677975 | − | 0.735085i | \(-0.737142\pi\) | ||||
−0.677975 | + | 0.735085i | \(0.737142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.564426 | −0.0189944 | −0.00949722 | − | 0.999955i | \(-0.503023\pi\) | ||||
−0.00949722 | + | 0.999955i | \(0.503023\pi\) | |||||||
\(884\) | 1.85299 | 0.0623227 | ||||||||
\(885\) | 106.588 | 3.58292 | ||||||||
\(886\) | 16.8747 | 0.566915 | ||||||||
\(887\) | −35.5836 | −1.19478 | −0.597390 | − | 0.801951i | \(-0.703796\pi\) | ||||
−0.597390 | + | 0.801951i | \(0.703796\pi\) | |||||||
\(888\) | 53.8741 | 1.80790 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.1446 | −0.407087 | ||||||||
\(891\) | −42.5228 | −1.42457 | ||||||||
\(892\) | 27.1152 | 0.907883 | ||||||||
\(893\) | 11.8333 | 0.395986 | ||||||||
\(894\) | 42.0127 | 1.40511 | ||||||||
\(895\) | −55.2229 | −1.84590 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.2820 | 0.743973 | ||||||||
\(898\) | −11.8181 | −0.394376 | ||||||||
\(899\) | −33.2762 | −1.10982 | ||||||||
\(900\) | −46.1516 | −1.53839 | ||||||||
\(901\) | 2.60206 | 0.0866872 | ||||||||
\(902\) | 6.70311 | 0.223189 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33.3299 | −1.10854 | ||||||||
\(905\) | 79.3516 | 2.63774 | ||||||||
\(906\) | −14.8849 | −0.494518 | ||||||||
\(907\) | 30.3682 | 1.00836 | 0.504179 | − | 0.863599i | \(-0.331795\pi\) | ||||
0.504179 | + | 0.863599i | \(0.331795\pi\) | |||||||
\(908\) | 29.4954 | 0.978839 | ||||||||
\(909\) | 36.6871 | 1.21684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.9947 | 0.596191 | 0.298096 | − | 0.954536i | \(-0.403649\pi\) | ||||
0.298096 | + | 0.954536i | \(0.403649\pi\) | |||||||
\(912\) | −2.17744 | −0.0721021 | ||||||||
\(913\) | −17.4546 | −0.577662 | ||||||||
\(914\) | −17.1659 | −0.567797 | ||||||||
\(915\) | −24.1712 | −0.799075 | ||||||||
\(916\) | 10.0302 | 0.331407 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.582751 | 0.0192336 | ||||||||
\(919\) | 41.9568 | 1.38403 | 0.692014 | − | 0.721884i | \(-0.256724\pi\) | ||||
0.692014 | + | 0.721884i | \(0.256724\pi\) | |||||||
\(920\) | −48.0988 | −1.58577 | ||||||||
\(921\) | −69.8578 | −2.30189 | ||||||||
\(922\) | −19.5282 | −0.643127 | ||||||||
\(923\) | −18.2052 | −0.599232 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 118.144 | 3.88456 | ||||||||
\(926\) | −15.2819 | −0.502194 | ||||||||
\(927\) | 11.9212 | 0.391543 | ||||||||
\(928\) | 43.1730 | 1.41722 | ||||||||
\(929\) | −19.1145 | −0.627127 | −0.313563 | − | 0.949567i | \(-0.601523\pi\) | ||||
−0.313563 | + | 0.949567i | \(0.601523\pi\) | |||||||
\(930\) | −33.7481 | −1.10664 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −28.0393 | −0.918458 | ||||||||
\(933\) | 10.2147 | 0.334415 | ||||||||
\(934\) | −11.3631 | −0.371813 | ||||||||
\(935\) | 10.3163 | 0.337378 | ||||||||
\(936\) | −13.7474 | −0.449346 | ||||||||
\(937\) | 44.3779 | 1.44976 | 0.724881 | − | 0.688874i | \(-0.241895\pi\) | ||||
0.724881 | + | 0.688874i | \(0.241895\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 47.6879 | 1.55623 | ||||||||
\(940\) | 72.4789 | 2.36400 | ||||||||
\(941\) | −37.6172 | −1.22628 | −0.613142 | − | 0.789973i | \(-0.710095\pi\) | ||||
−0.613142 | + | 0.789973i | \(0.710095\pi\) | |||||||
\(942\) | −7.77239 | −0.253238 | ||||||||
\(943\) | 9.51513 | 0.309855 | ||||||||
\(944\) | 10.0096 | 0.325783 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.7699 | 0.870366 | ||||||||
\(947\) | 29.1696 | 0.947883 | 0.473942 | − | 0.880556i | \(-0.342831\pi\) | ||||
0.473942 | + | 0.880556i | \(0.342831\pi\) | |||||||
\(948\) | −28.6712 | −0.931198 | ||||||||
\(949\) | 23.3559 | 0.758164 | ||||||||
\(950\) | 9.90893 | 0.321488 | ||||||||
\(951\) | −20.5558 | −0.666566 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.0234 | 0.810586 | 0.405293 | − | 0.914187i | \(-0.367170\pi\) | ||||
0.405293 | + | 0.914187i | \(0.367170\pi\) | |||||||
\(954\) | −8.06787 | −0.261207 | ||||||||
\(955\) | −99.3367 | −3.21446 | ||||||||
\(956\) | 25.5681 | 0.826933 | ||||||||
\(957\) | −70.3808 | −2.27509 | ||||||||
\(958\) | −20.9735 | −0.677622 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 25.2099 | 0.813647 | ||||||||
\(961\) | −10.5831 | −0.341392 | ||||||||
\(962\) | 14.7075 | 0.474190 | ||||||||
\(963\) | 2.16472 | 0.0697571 | ||||||||
\(964\) | 21.8651 | 0.704228 | ||||||||
\(965\) | 13.6000 | 0.437801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8469 | −0.927655 | −0.463828 | − | 0.885926i | \(-0.653524\pi\) | ||||
−0.463828 | + | 0.885926i | \(0.653524\pi\) | |||||||
\(968\) | 14.9713 | 0.481197 | ||||||||
\(969\) | −1.37569 | −0.0441936 | ||||||||
\(970\) | −6.76010 | −0.217054 | ||||||||
\(971\) | 3.19928 | 0.102670 | 0.0513348 | − | 0.998681i | \(-0.483652\pi\) | ||||
0.0513348 | + | 0.998681i | \(0.483652\pi\) | |||||||
\(972\) | 29.0666 | 0.932312 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.496166 | −0.0158982 | ||||||||
\(975\) | −67.2755 | −2.15454 | ||||||||
\(976\) | −2.26989 | −0.0726573 | ||||||||
\(977\) | −54.4969 | −1.74351 | −0.871755 | − | 0.489943i | \(-0.837018\pi\) | ||||
−0.871755 | + | 0.489943i | \(0.837018\pi\) | |||||||
\(978\) | 0.257236 | 0.00822551 | ||||||||
\(979\) | 15.5397 | 0.496651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.70721 | −0.0864345 | ||||||||
\(982\) | 3.82619 | 0.122099 | ||||||||
\(983\) | −5.45760 | −0.174070 | −0.0870352 | − | 0.996205i | \(-0.527739\pi\) | ||||
−0.0870352 | + | 0.996205i | \(0.527739\pi\) | |||||||
\(984\) | −13.1004 | −0.417627 | ||||||||
\(985\) | −35.1974 | −1.12148 | ||||||||
\(986\) | 3.26344 | 0.103929 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.14043 | −0.0999104 | ||||||||
\(989\) | 38.0002 | 1.20834 | ||||||||
\(990\) | −31.9863 | −1.01659 | ||||||||
\(991\) | 34.2911 | 1.08929 | 0.544646 | − | 0.838666i | \(-0.316664\pi\) | ||||
0.544646 | + | 0.838666i | \(0.316664\pi\) | |||||||
\(992\) | −26.4891 | −0.841031 | ||||||||
\(993\) | 28.1134 | 0.892151 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −83.6127 | −2.65070 | ||||||||
\(996\) | 14.2565 | 0.451735 | ||||||||
\(997\) | 23.2138 | 0.735188 | 0.367594 | − | 0.929986i | \(-0.380182\pi\) | ||||
0.367594 | + | 0.929986i | \(0.380182\pi\) | |||||||
\(998\) | 9.61238 | 0.304275 | ||||||||
\(999\) | −11.7757 | −0.372566 |
(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 | 931.2.a.m.1.2 | yes | 4 | |
3.2 | odd | 2 | 8379.2.a.bu.1.3 | 4 | |||
7.2 | even | 3 | 931.2.f.n.704.3 | 8 | |||
7.3 | odd | 6 | 931.2.f.o.324.3 | 8 | |||
7.4 | even | 3 | 931.2.f.n.324.3 | 8 | |||
7.5 | odd | 6 | 931.2.f.o.704.3 | 8 | |||
7.6 | odd | 2 | 931.2.a.l.1.2 | ✓ | 4 | ||
21.20 | even | 2 | 8379.2.a.bv.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
931.2.a.l.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
931.2.a.m.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
931.2.f.n.324.3 | 8 | 7.4 | even | 3 | |||
931.2.f.n.704.3 | 8 | 7.2 | even | 3 | |||
931.2.f.o.324.3 | 8 | 7.3 | odd | 6 | |||
931.2.f.o.704.3 | 8 | 7.5 | odd | 6 | |||
8379.2.a.bu.1.3 | 4 | 3.2 | odd | 2 | |||
8379.2.a.bv.1.3 | 4 | 21.20 | even | 2 |