Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4x^{10} - 6x^{9} + 37x^{8} - 2x^{7} - 109x^{6} + 55x^{5} + 115x^{4} - 76x^{3} - 29x^{2} + 14x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.14470\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14470 | −0.809429 | −0.404714 | − | 0.914443i | \(-0.632629\pi\) | ||||
−0.404714 | + | 0.914443i | \(0.632629\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.689651 | −0.344825 | ||||||||
\(5\) | 1.33318 | 0.596216 | 0.298108 | − | 0.954532i | \(-0.403645\pi\) | ||||
0.298108 | + | 0.954532i | \(0.403645\pi\) | |||||||
\(6\) | −1.14470 | −0.467324 | ||||||||
\(7\) | −3.52170 | −1.33108 | −0.665538 | − | 0.746364i | \(-0.731798\pi\) | ||||
−0.665538 | + | 0.746364i | \(0.731798\pi\) | |||||||
\(8\) | 3.07886 | 1.08854 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.52610 | −0.482594 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.689651 | −0.199085 | ||||||||
\(13\) | −5.11237 | −1.41792 | −0.708958 | − | 0.705250i | \(-0.750835\pi\) | ||||
−0.708958 | + | 0.705250i | \(0.750835\pi\) | |||||||
\(14\) | 4.03130 | 1.07741 | ||||||||
\(15\) | 1.33318 | 0.344225 | ||||||||
\(16\) | −2.14508 | −0.536270 | ||||||||
\(17\) | 1.76849 | 0.428923 | 0.214461 | − | 0.976732i | \(-0.431200\pi\) | ||||
0.214461 | + | 0.976732i | \(0.431200\pi\) | |||||||
\(18\) | −1.14470 | −0.269810 | ||||||||
\(19\) | 7.94593 | 1.82292 | 0.911461 | − | 0.411386i | \(-0.134955\pi\) | ||||
0.911461 | + | 0.411386i | \(0.134955\pi\) | |||||||
\(20\) | −0.919427 | −0.205590 | ||||||||
\(21\) | −3.52170 | −0.768497 | ||||||||
\(22\) | 1.14470 | 0.244052 | ||||||||
\(23\) | 2.83929 | 0.592033 | 0.296016 | − | 0.955183i | \(-0.404342\pi\) | ||||
0.296016 | + | 0.955183i | \(0.404342\pi\) | |||||||
\(24\) | 3.07886 | 0.628469 | ||||||||
\(25\) | −3.22263 | −0.644527 | ||||||||
\(26\) | 5.85216 | 1.14770 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.42874 | 0.458989 | ||||||||
\(29\) | 9.92659 | 1.84332 | 0.921661 | − | 0.387996i | \(-0.126833\pi\) | ||||
0.921661 | + | 0.387996i | \(0.126833\pi\) | |||||||
\(30\) | −1.52610 | −0.278626 | ||||||||
\(31\) | −4.21272 | −0.756628 | −0.378314 | − | 0.925677i | \(-0.623496\pi\) | ||||
−0.378314 | + | 0.925677i | \(0.623496\pi\) | |||||||
\(32\) | −3.70223 | −0.654468 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −2.02440 | −0.347182 | ||||||||
\(35\) | −4.69505 | −0.793608 | ||||||||
\(36\) | −0.689651 | −0.114942 | ||||||||
\(37\) | −9.46041 | −1.55528 | −0.777641 | − | 0.628708i | \(-0.783584\pi\) | ||||
−0.777641 | + | 0.628708i | \(0.783584\pi\) | |||||||
\(38\) | −9.09575 | −1.47553 | ||||||||
\(39\) | −5.11237 | −0.818635 | ||||||||
\(40\) | 4.10467 | 0.649005 | ||||||||
\(41\) | −4.92390 | −0.768984 | −0.384492 | − | 0.923128i | \(-0.625623\pi\) | ||||
−0.384492 | + | 0.923128i | \(0.625623\pi\) | |||||||
\(42\) | 4.03130 | 0.622043 | ||||||||
\(43\) | −5.08527 | −0.775496 | −0.387748 | − | 0.921765i | \(-0.626747\pi\) | ||||
−0.387748 | + | 0.921765i | \(0.626747\pi\) | |||||||
\(44\) | 0.689651 | 0.103969 | ||||||||
\(45\) | 1.33318 | 0.198739 | ||||||||
\(46\) | −3.25015 | −0.479208 | ||||||||
\(47\) | −6.83907 | −0.997580 | −0.498790 | − | 0.866723i | \(-0.666222\pi\) | ||||
−0.498790 | + | 0.866723i | \(0.666222\pi\) | |||||||
\(48\) | −2.14508 | −0.309616 | ||||||||
\(49\) | 5.40234 | 0.771763 | ||||||||
\(50\) | 3.68897 | 0.521699 | ||||||||
\(51\) | 1.76849 | 0.247639 | ||||||||
\(52\) | 3.52575 | 0.488933 | ||||||||
\(53\) | 2.41931 | 0.332318 | 0.166159 | − | 0.986099i | \(-0.446863\pi\) | ||||
0.166159 | + | 0.986099i | \(0.446863\pi\) | |||||||
\(54\) | −1.14470 | −0.155775 | ||||||||
\(55\) | −1.33318 | −0.179766 | ||||||||
\(56\) | −10.8428 | −1.44893 | ||||||||
\(57\) | 7.94593 | 1.05246 | ||||||||
\(58\) | −11.3630 | −1.49204 | ||||||||
\(59\) | −5.09379 | −0.663155 | −0.331577 | − | 0.943428i | \(-0.607581\pi\) | ||||
−0.331577 | + | 0.943428i | \(0.607581\pi\) | |||||||
\(60\) | −0.919427 | −0.118698 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 4.82233 | 0.612436 | ||||||||
\(63\) | −3.52170 | −0.443692 | ||||||||
\(64\) | 8.52812 | 1.06602 | ||||||||
\(65\) | −6.81570 | −0.845384 | ||||||||
\(66\) | 1.14470 | 0.140903 | ||||||||
\(67\) | −14.9335 | −1.82441 | −0.912206 | − | 0.409732i | \(-0.865622\pi\) | ||||
−0.912206 | + | 0.409732i | \(0.865622\pi\) | |||||||
\(68\) | −1.21964 | −0.147903 | ||||||||
\(69\) | 2.83929 | 0.341810 | ||||||||
\(70\) | 5.37445 | 0.642369 | ||||||||
\(71\) | −1.73224 | −0.205579 | −0.102789 | − | 0.994703i | \(-0.532777\pi\) | ||||
−0.102789 | + | 0.994703i | \(0.532777\pi\) | |||||||
\(72\) | 3.07886 | 0.362847 | ||||||||
\(73\) | −0.272088 | −0.0318455 | −0.0159228 | − | 0.999873i | \(-0.505069\pi\) | ||||
−0.0159228 | + | 0.999873i | \(0.505069\pi\) | |||||||
\(74\) | 10.8294 | 1.25889 | ||||||||
\(75\) | −3.22263 | −0.372118 | ||||||||
\(76\) | −5.47992 | −0.628590 | ||||||||
\(77\) | 3.52170 | 0.401334 | ||||||||
\(78\) | 5.85216 | 0.662626 | ||||||||
\(79\) | 14.9608 | 1.68323 | 0.841613 | − | 0.540081i | \(-0.181606\pi\) | ||||
0.841613 | + | 0.540081i | \(0.181606\pi\) | |||||||
\(80\) | −2.85978 | −0.319733 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.63642 | 0.622438 | ||||||||
\(83\) | −12.0244 | −1.31985 | −0.659924 | − | 0.751333i | \(-0.729411\pi\) | ||||
−0.659924 | + | 0.751333i | \(0.729411\pi\) | |||||||
\(84\) | 2.42874 | 0.264997 | ||||||||
\(85\) | 2.35772 | 0.255731 | ||||||||
\(86\) | 5.82113 | 0.627709 | ||||||||
\(87\) | 9.92659 | 1.06424 | ||||||||
\(88\) | −3.07886 | −0.328207 | ||||||||
\(89\) | −13.3848 | −1.41879 | −0.709396 | − | 0.704811i | \(-0.751032\pi\) | ||||
−0.709396 | + | 0.704811i | \(0.751032\pi\) | |||||||
\(90\) | −1.52610 | −0.160865 | ||||||||
\(91\) | 18.0042 | 1.88735 | ||||||||
\(92\) | −1.95812 | −0.204148 | ||||||||
\(93\) | −4.21272 | −0.436839 | ||||||||
\(94\) | 7.82871 | 0.807470 | ||||||||
\(95\) | 10.5933 | 1.08685 | ||||||||
\(96\) | −3.70223 | −0.377857 | ||||||||
\(97\) | −1.16994 | −0.118790 | −0.0593949 | − | 0.998235i | \(-0.518917\pi\) | ||||
−0.0593949 | + | 0.998235i | \(0.518917\pi\) | |||||||
\(98\) | −6.18408 | −0.624687 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 2.22249 | 0.222249 | ||||||||
\(101\) | 1.20636 | 0.120037 | 0.0600186 | − | 0.998197i | \(-0.480884\pi\) | ||||
0.0600186 | + | 0.998197i | \(0.480884\pi\) | |||||||
\(102\) | −2.02440 | −0.200446 | ||||||||
\(103\) | −7.97633 | −0.785931 | −0.392966 | − | 0.919553i | \(-0.628551\pi\) | ||||
−0.392966 | + | 0.919553i | \(0.628551\pi\) | |||||||
\(104\) | −15.7403 | −1.54346 | ||||||||
\(105\) | −4.69505 | −0.458190 | ||||||||
\(106\) | −2.76940 | −0.268988 | ||||||||
\(107\) | 13.1670 | 1.27290 | 0.636451 | − | 0.771317i | \(-0.280402\pi\) | ||||
0.636451 | + | 0.771317i | \(0.280402\pi\) | |||||||
\(108\) | −0.689651 | −0.0663617 | ||||||||
\(109\) | −7.42870 | −0.711540 | −0.355770 | − | 0.934574i | \(-0.615781\pi\) | ||||
−0.355770 | + | 0.934574i | \(0.615781\pi\) | |||||||
\(110\) | 1.52610 | 0.145508 | ||||||||
\(111\) | −9.46041 | −0.897943 | ||||||||
\(112\) | 7.55432 | 0.713816 | ||||||||
\(113\) | −5.85940 | −0.551206 | −0.275603 | − | 0.961271i | \(-0.588878\pi\) | ||||
−0.275603 | + | 0.961271i | \(0.588878\pi\) | |||||||
\(114\) | −9.09575 | −0.851895 | ||||||||
\(115\) | 3.78528 | 0.352979 | ||||||||
\(116\) | −6.84588 | −0.635624 | ||||||||
\(117\) | −5.11237 | −0.472639 | ||||||||
\(118\) | 5.83088 | 0.536776 | ||||||||
\(119\) | −6.22810 | −0.570929 | ||||||||
\(120\) | 4.10467 | 0.374703 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.14470 | −0.103637 | ||||||||
\(123\) | −4.92390 | −0.443973 | ||||||||
\(124\) | 2.90531 | 0.260904 | ||||||||
\(125\) | −10.9622 | −0.980493 | ||||||||
\(126\) | 4.03130 | 0.359137 | ||||||||
\(127\) | −5.94779 | −0.527781 | −0.263890 | − | 0.964553i | \(-0.585006\pi\) | ||||
−0.263890 | + | 0.964553i | \(0.585006\pi\) | |||||||
\(128\) | −2.35773 | −0.208396 | ||||||||
\(129\) | −5.08527 | −0.447733 | ||||||||
\(130\) | 7.80197 | 0.684278 | ||||||||
\(131\) | −19.8009 | −1.73002 | −0.865008 | − | 0.501758i | \(-0.832687\pi\) | ||||
−0.865008 | + | 0.501758i | \(0.832687\pi\) | |||||||
\(132\) | 0.689651 | 0.0600264 | ||||||||
\(133\) | −27.9832 | −2.42645 | ||||||||
\(134\) | 17.0944 | 1.47673 | ||||||||
\(135\) | 1.33318 | 0.114742 | ||||||||
\(136\) | 5.44494 | 0.466900 | ||||||||
\(137\) | −17.3461 | −1.48198 | −0.740988 | − | 0.671519i | \(-0.765642\pi\) | ||||
−0.740988 | + | 0.671519i | \(0.765642\pi\) | |||||||
\(138\) | −3.25015 | −0.276671 | ||||||||
\(139\) | 10.2385 | 0.868417 | 0.434209 | − | 0.900812i | \(-0.357028\pi\) | ||||
0.434209 | + | 0.900812i | \(0.357028\pi\) | |||||||
\(140\) | 3.23794 | 0.273656 | ||||||||
\(141\) | −6.83907 | −0.575953 | ||||||||
\(142\) | 1.98290 | 0.166401 | ||||||||
\(143\) | 5.11237 | 0.427518 | ||||||||
\(144\) | −2.14508 | −0.178757 | ||||||||
\(145\) | 13.2339 | 1.09902 | ||||||||
\(146\) | 0.311461 | 0.0257767 | ||||||||
\(147\) | 5.40234 | 0.445577 | ||||||||
\(148\) | 6.52438 | 0.536301 | ||||||||
\(149\) | 11.0748 | 0.907280 | 0.453640 | − | 0.891185i | \(-0.350125\pi\) | ||||
0.453640 | + | 0.891185i | \(0.350125\pi\) | |||||||
\(150\) | 3.68897 | 0.301203 | ||||||||
\(151\) | −0.576802 | −0.0469395 | −0.0234698 | − | 0.999725i | \(-0.507471\pi\) | ||||
−0.0234698 | + | 0.999725i | \(0.507471\pi\) | |||||||
\(152\) | 24.4644 | 1.98432 | ||||||||
\(153\) | 1.76849 | 0.142974 | ||||||||
\(154\) | −4.03130 | −0.324852 | ||||||||
\(155\) | −5.61631 | −0.451113 | ||||||||
\(156\) | 3.52575 | 0.282286 | ||||||||
\(157\) | 0.409551 | 0.0326857 | 0.0163429 | − | 0.999866i | \(-0.494798\pi\) | ||||
0.0163429 | + | 0.999866i | \(0.494798\pi\) | |||||||
\(158\) | −17.1258 | −1.36245 | ||||||||
\(159\) | 2.41931 | 0.191864 | ||||||||
\(160\) | −4.93573 | −0.390204 | ||||||||
\(161\) | −9.99911 | −0.788041 | ||||||||
\(162\) | −1.14470 | −0.0899365 | ||||||||
\(163\) | 10.7263 | 0.840146 | 0.420073 | − | 0.907490i | \(-0.362004\pi\) | ||||
0.420073 | + | 0.907490i | \(0.362004\pi\) | |||||||
\(164\) | 3.39577 | 0.265165 | ||||||||
\(165\) | −1.33318 | −0.103788 | ||||||||
\(166\) | 13.7644 | 1.06832 | ||||||||
\(167\) | −9.02703 | −0.698533 | −0.349266 | − | 0.937023i | \(-0.613569\pi\) | ||||
−0.349266 | + | 0.937023i | \(0.613569\pi\) | |||||||
\(168\) | −10.8428 | −0.836540 | ||||||||
\(169\) | 13.1363 | 1.01049 | ||||||||
\(170\) | −2.69889 | −0.206996 | ||||||||
\(171\) | 7.94593 | 0.607641 | ||||||||
\(172\) | 3.50706 | 0.267411 | ||||||||
\(173\) | 1.04546 | 0.0794852 | 0.0397426 | − | 0.999210i | \(-0.487346\pi\) | ||||
0.0397426 | + | 0.999210i | \(0.487346\pi\) | |||||||
\(174\) | −11.3630 | −0.861428 | ||||||||
\(175\) | 11.3491 | 0.857914 | ||||||||
\(176\) | 2.14508 | 0.161692 | ||||||||
\(177\) | −5.09379 | −0.382873 | ||||||||
\(178\) | 15.3217 | 1.14841 | ||||||||
\(179\) | −19.9008 | −1.48745 | −0.743727 | − | 0.668483i | \(-0.766944\pi\) | ||||
−0.743727 | + | 0.668483i | \(0.766944\pi\) | |||||||
\(180\) | −0.919427 | −0.0685301 | ||||||||
\(181\) | 25.4805 | 1.89395 | 0.946975 | − | 0.321308i | \(-0.104122\pi\) | ||||
0.946975 | + | 0.321308i | \(0.104122\pi\) | |||||||
\(182\) | −20.6095 | −1.52768 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 8.74177 | 0.644452 | ||||||||
\(185\) | −12.6124 | −0.927284 | ||||||||
\(186\) | 4.82233 | 0.353590 | ||||||||
\(187\) | −1.76849 | −0.129325 | ||||||||
\(188\) | 4.71656 | 0.343991 | ||||||||
\(189\) | −3.52170 | −0.256166 | ||||||||
\(190\) | −12.1263 | −0.879731 | ||||||||
\(191\) | −3.08595 | −0.223291 | −0.111646 | − | 0.993748i | \(-0.535612\pi\) | ||||
−0.111646 | + | 0.993748i | \(0.535612\pi\) | |||||||
\(192\) | 8.52812 | 0.615464 | ||||||||
\(193\) | −20.2049 | −1.45438 | −0.727190 | − | 0.686437i | \(-0.759174\pi\) | ||||
−0.727190 | + | 0.686437i | \(0.759174\pi\) | |||||||
\(194\) | 1.33924 | 0.0961518 | ||||||||
\(195\) | −6.81570 | −0.488083 | ||||||||
\(196\) | −3.72573 | −0.266123 | ||||||||
\(197\) | 20.4684 | 1.45832 | 0.729158 | − | 0.684346i | \(-0.239912\pi\) | ||||
0.729158 | + | 0.684346i | \(0.239912\pi\) | |||||||
\(198\) | 1.14470 | 0.0813506 | ||||||||
\(199\) | −7.13828 | −0.506019 | −0.253009 | − | 0.967464i | \(-0.581420\pi\) | ||||
−0.253009 | + | 0.967464i | \(0.581420\pi\) | |||||||
\(200\) | −9.92203 | −0.701593 | ||||||||
\(201\) | −14.9335 | −1.05332 | ||||||||
\(202\) | −1.38093 | −0.0971616 | ||||||||
\(203\) | −34.9584 | −2.45360 | ||||||||
\(204\) | −1.21964 | −0.0853921 | ||||||||
\(205\) | −6.56444 | −0.458481 | ||||||||
\(206\) | 9.13055 | 0.636155 | ||||||||
\(207\) | 2.83929 | 0.197344 | ||||||||
\(208\) | 10.9665 | 0.760387 | ||||||||
\(209\) | −7.94593 | −0.549632 | ||||||||
\(210\) | 5.37445 | 0.370872 | ||||||||
\(211\) | 2.60205 | 0.179133 | 0.0895664 | − | 0.995981i | \(-0.471452\pi\) | ||||
0.0895664 | + | 0.995981i | \(0.471452\pi\) | |||||||
\(212\) | −1.66848 | −0.114592 | ||||||||
\(213\) | −1.73224 | −0.118691 | ||||||||
\(214\) | −15.0723 | −1.03032 | ||||||||
\(215\) | −6.77957 | −0.462363 | ||||||||
\(216\) | 3.07886 | 0.209490 | ||||||||
\(217\) | 14.8359 | 1.00713 | ||||||||
\(218\) | 8.50367 | 0.575941 | ||||||||
\(219\) | −0.272088 | −0.0183860 | ||||||||
\(220\) | 0.919427 | 0.0619878 | ||||||||
\(221\) | −9.04120 | −0.608177 | ||||||||
\(222\) | 10.8294 | 0.726821 | ||||||||
\(223\) | 14.8878 | 0.996959 | 0.498480 | − | 0.866901i | \(-0.333892\pi\) | ||||
0.498480 | + | 0.866901i | \(0.333892\pi\) | |||||||
\(224\) | 13.0381 | 0.871146 | ||||||||
\(225\) | −3.22263 | −0.214842 | ||||||||
\(226\) | 6.70729 | 0.446162 | ||||||||
\(227\) | −24.1004 | −1.59960 | −0.799800 | − | 0.600267i | \(-0.795061\pi\) | ||||
−0.799800 | + | 0.600267i | \(0.795061\pi\) | |||||||
\(228\) | −5.47992 | −0.362916 | ||||||||
\(229\) | −13.3300 | −0.880872 | −0.440436 | − | 0.897784i | \(-0.645176\pi\) | ||||
−0.440436 | + | 0.897784i | \(0.645176\pi\) | |||||||
\(230\) | −4.33303 | −0.285712 | ||||||||
\(231\) | 3.52170 | 0.231711 | ||||||||
\(232\) | 30.5626 | 2.00653 | ||||||||
\(233\) | 2.31713 | 0.151801 | 0.0759003 | − | 0.997115i | \(-0.475817\pi\) | ||||
0.0759003 | + | 0.997115i | \(0.475817\pi\) | |||||||
\(234\) | 5.85216 | 0.382567 | ||||||||
\(235\) | −9.11770 | −0.594773 | ||||||||
\(236\) | 3.51293 | 0.228672 | ||||||||
\(237\) | 14.9608 | 0.971811 | ||||||||
\(238\) | 7.12934 | 0.462126 | ||||||||
\(239\) | −13.3420 | −0.863021 | −0.431510 | − | 0.902108i | \(-0.642019\pi\) | ||||
−0.431510 | + | 0.902108i | \(0.642019\pi\) | |||||||
\(240\) | −2.85978 | −0.184598 | ||||||||
\(241\) | −14.0952 | −0.907951 | −0.453975 | − | 0.891014i | \(-0.649995\pi\) | ||||
−0.453975 | + | 0.891014i | \(0.649995\pi\) | |||||||
\(242\) | −1.14470 | −0.0735844 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.689651 | −0.0441503 | ||||||||
\(245\) | 7.20228 | 0.460137 | ||||||||
\(246\) | 5.63642 | 0.359365 | ||||||||
\(247\) | −40.6226 | −2.58475 | ||||||||
\(248\) | −12.9704 | −0.823620 | ||||||||
\(249\) | −12.0244 | −0.762014 | ||||||||
\(250\) | 12.5485 | 0.793639 | ||||||||
\(251\) | −10.1102 | −0.638150 | −0.319075 | − | 0.947730i | \(-0.603372\pi\) | ||||
−0.319075 | + | 0.947730i | \(0.603372\pi\) | |||||||
\(252\) | 2.42874 | 0.152996 | ||||||||
\(253\) | −2.83929 | −0.178505 | ||||||||
\(254\) | 6.80846 | 0.427201 | ||||||||
\(255\) | 2.35772 | 0.147646 | ||||||||
\(256\) | −14.3573 | −0.897334 | ||||||||
\(257\) | 5.00734 | 0.312349 | 0.156175 | − | 0.987729i | \(-0.450084\pi\) | ||||
0.156175 | + | 0.987729i | \(0.450084\pi\) | |||||||
\(258\) | 5.82113 | 0.362408 | ||||||||
\(259\) | 33.3167 | 2.07020 | ||||||||
\(260\) | 4.70045 | 0.291510 | ||||||||
\(261\) | 9.92659 | 0.614441 | ||||||||
\(262\) | 22.6662 | 1.40032 | ||||||||
\(263\) | −11.7522 | −0.724670 | −0.362335 | − | 0.932048i | \(-0.618020\pi\) | ||||
−0.362335 | + | 0.932048i | \(0.618020\pi\) | |||||||
\(264\) | −3.07886 | −0.189491 | ||||||||
\(265\) | 3.22538 | 0.198133 | ||||||||
\(266\) | 32.0325 | 1.96404 | ||||||||
\(267\) | −13.3848 | −0.819139 | ||||||||
\(268\) | 10.2989 | 0.629103 | ||||||||
\(269\) | 25.2506 | 1.53956 | 0.769779 | − | 0.638311i | \(-0.220367\pi\) | ||||
0.769779 | + | 0.638311i | \(0.220367\pi\) | |||||||
\(270\) | −1.52610 | −0.0928753 | ||||||||
\(271\) | −0.247119 | −0.0150114 | −0.00750571 | − | 0.999972i | \(-0.502389\pi\) | ||||
−0.00750571 | + | 0.999972i | \(0.502389\pi\) | |||||||
\(272\) | −3.79356 | −0.230019 | ||||||||
\(273\) | 18.0042 | 1.08966 | ||||||||
\(274\) | 19.8561 | 1.19955 | ||||||||
\(275\) | 3.22263 | 0.194332 | ||||||||
\(276\) | −1.95812 | −0.117865 | ||||||||
\(277\) | −8.44029 | −0.507128 | −0.253564 | − | 0.967319i | \(-0.581603\pi\) | ||||
−0.253564 | + | 0.967319i | \(0.581603\pi\) | |||||||
\(278\) | −11.7201 | −0.702922 | ||||||||
\(279\) | −4.21272 | −0.252209 | ||||||||
\(280\) | −14.4554 | −0.863874 | ||||||||
\(281\) | 17.3091 | 1.03257 | 0.516286 | − | 0.856416i | \(-0.327314\pi\) | ||||
0.516286 | + | 0.856416i | \(0.327314\pi\) | |||||||
\(282\) | 7.82871 | 0.466193 | ||||||||
\(283\) | −17.2268 | −1.02403 | −0.512013 | − | 0.858978i | \(-0.671100\pi\) | ||||
−0.512013 | + | 0.858978i | \(0.671100\pi\) | |||||||
\(284\) | 1.19464 | 0.0708888 | ||||||||
\(285\) | 10.5933 | 0.627496 | ||||||||
\(286\) | −5.85216 | −0.346045 | ||||||||
\(287\) | 17.3405 | 1.02358 | ||||||||
\(288\) | −3.70223 | −0.218156 | ||||||||
\(289\) | −13.8724 | −0.816025 | ||||||||
\(290\) | −15.1489 | −0.889576 | ||||||||
\(291\) | −1.16994 | −0.0685833 | ||||||||
\(292\) | 0.187646 | 0.0109811 | ||||||||
\(293\) | 20.3320 | 1.18781 | 0.593905 | − | 0.804535i | \(-0.297586\pi\) | ||||
0.593905 | + | 0.804535i | \(0.297586\pi\) | |||||||
\(294\) | −6.18408 | −0.360663 | ||||||||
\(295\) | −6.79093 | −0.395383 | ||||||||
\(296\) | −29.1273 | −1.69299 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −12.6773 | −0.734378 | ||||||||
\(299\) | −14.5155 | −0.839453 | ||||||||
\(300\) | 2.22249 | 0.128316 | ||||||||
\(301\) | 17.9088 | 1.03224 | ||||||||
\(302\) | 0.660268 | 0.0379942 | ||||||||
\(303\) | 1.20636 | 0.0693035 | ||||||||
\(304\) | −17.0447 | −0.977579 | ||||||||
\(305\) | 1.33318 | 0.0763376 | ||||||||
\(306\) | −2.02440 | −0.115727 | ||||||||
\(307\) | −15.3499 | −0.876063 | −0.438031 | − | 0.898960i | \(-0.644324\pi\) | ||||
−0.438031 | + | 0.898960i | \(0.644324\pi\) | |||||||
\(308\) | −2.42874 | −0.138390 | ||||||||
\(309\) | −7.97633 | −0.453758 | ||||||||
\(310\) | 6.42902 | 0.365144 | ||||||||
\(311\) | 9.55462 | 0.541793 | 0.270896 | − | 0.962608i | \(-0.412680\pi\) | ||||
0.270896 | + | 0.962608i | \(0.412680\pi\) | |||||||
\(312\) | −15.7403 | −0.891117 | ||||||||
\(313\) | 15.5623 | 0.879635 | 0.439817 | − | 0.898087i | \(-0.355043\pi\) | ||||
0.439817 | + | 0.898087i | \(0.355043\pi\) | |||||||
\(314\) | −0.468815 | −0.0264568 | ||||||||
\(315\) | −4.69505 | −0.264536 | ||||||||
\(316\) | −10.3178 | −0.580419 | ||||||||
\(317\) | 15.1622 | 0.851596 | 0.425798 | − | 0.904818i | \(-0.359993\pi\) | ||||
0.425798 | + | 0.904818i | \(0.359993\pi\) | |||||||
\(318\) | −2.76940 | −0.155300 | ||||||||
\(319\) | −9.92659 | −0.555783 | ||||||||
\(320\) | 11.3695 | 0.635575 | ||||||||
\(321\) | 13.1670 | 0.734910 | ||||||||
\(322\) | 11.4460 | 0.637863 | ||||||||
\(323\) | 14.0523 | 0.781893 | ||||||||
\(324\) | −0.689651 | −0.0383139 | ||||||||
\(325\) | 16.4753 | 0.913886 | ||||||||
\(326\) | −12.2784 | −0.680038 | ||||||||
\(327\) | −7.42870 | −0.410808 | ||||||||
\(328\) | −15.1600 | −0.837070 | ||||||||
\(329\) | 24.0851 | 1.32785 | ||||||||
\(330\) | 1.52610 | 0.0840088 | ||||||||
\(331\) | −31.4774 | −1.73015 | −0.865077 | − | 0.501639i | \(-0.832731\pi\) | ||||
−0.865077 | + | 0.501639i | \(0.832731\pi\) | |||||||
\(332\) | 8.29262 | 0.455117 | ||||||||
\(333\) | −9.46041 | −0.518428 | ||||||||
\(334\) | 10.3333 | 0.565412 | ||||||||
\(335\) | −19.9090 | −1.08774 | ||||||||
\(336\) | 7.55432 | 0.412122 | ||||||||
\(337\) | 5.47362 | 0.298167 | 0.149083 | − | 0.988825i | \(-0.452368\pi\) | ||||
0.149083 | + | 0.988825i | \(0.452368\pi\) | |||||||
\(338\) | −15.0372 | −0.817918 | ||||||||
\(339\) | −5.85940 | −0.318239 | ||||||||
\(340\) | −1.62600 | −0.0881823 | ||||||||
\(341\) | 4.21272 | 0.228132 | ||||||||
\(342\) | −9.09575 | −0.491842 | ||||||||
\(343\) | 5.62647 | 0.303801 | ||||||||
\(344\) | −15.6568 | −0.844159 | ||||||||
\(345\) | 3.78528 | 0.203793 | ||||||||
\(346\) | −1.19675 | −0.0643376 | ||||||||
\(347\) | 20.0402 | 1.07581 | 0.537906 | − | 0.843005i | \(-0.319215\pi\) | ||||
0.537906 | + | 0.843005i | \(0.319215\pi\) | |||||||
\(348\) | −6.84588 | −0.366978 | ||||||||
\(349\) | −4.99181 | −0.267205 | −0.133603 | − | 0.991035i | \(-0.542655\pi\) | ||||
−0.133603 | + | 0.991035i | \(0.542655\pi\) | |||||||
\(350\) | −12.9914 | −0.694420 | ||||||||
\(351\) | −5.11237 | −0.272878 | ||||||||
\(352\) | 3.70223 | 0.197329 | ||||||||
\(353\) | 4.32905 | 0.230412 | 0.115206 | − | 0.993342i | \(-0.463247\pi\) | ||||
0.115206 | + | 0.993342i | \(0.463247\pi\) | |||||||
\(354\) | 5.83088 | 0.309908 | ||||||||
\(355\) | −2.30938 | −0.122569 | ||||||||
\(356\) | 9.23087 | 0.489235 | ||||||||
\(357\) | −6.22810 | −0.329626 | ||||||||
\(358\) | 22.7805 | 1.20399 | ||||||||
\(359\) | −13.5801 | −0.716731 | −0.358366 | − | 0.933581i | \(-0.616666\pi\) | ||||
−0.358366 | + | 0.933581i | \(0.616666\pi\) | |||||||
\(360\) | 4.10467 | 0.216335 | ||||||||
\(361\) | 44.1379 | 2.32304 | ||||||||
\(362\) | −29.1676 | −1.53302 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −12.4166 | −0.650808 | ||||||||
\(365\) | −0.362742 | −0.0189868 | ||||||||
\(366\) | −1.14470 | −0.0598347 | ||||||||
\(367\) | 15.9859 | 0.834459 | 0.417230 | − | 0.908801i | \(-0.363001\pi\) | ||||
0.417230 | + | 0.908801i | \(0.363001\pi\) | |||||||
\(368\) | −6.09051 | −0.317490 | ||||||||
\(369\) | −4.92390 | −0.256328 | ||||||||
\(370\) | 14.4375 | 0.750570 | ||||||||
\(371\) | −8.52008 | −0.442341 | ||||||||
\(372\) | 2.90531 | 0.150633 | ||||||||
\(373\) | −4.07689 | −0.211093 | −0.105547 | − | 0.994414i | \(-0.533659\pi\) | ||||
−0.105547 | + | 0.994414i | \(0.533659\pi\) | |||||||
\(374\) | 2.02440 | 0.104679 | ||||||||
\(375\) | −10.9622 | −0.566088 | ||||||||
\(376\) | −21.0565 | −1.08591 | ||||||||
\(377\) | −50.7484 | −2.61368 | ||||||||
\(378\) | 4.03130 | 0.207348 | ||||||||
\(379\) | −8.06236 | −0.414136 | −0.207068 | − | 0.978327i | \(-0.566392\pi\) | ||||
−0.207068 | + | 0.978327i | \(0.566392\pi\) | |||||||
\(380\) | −7.30571 | −0.374775 | ||||||||
\(381\) | −5.94779 | −0.304714 | ||||||||
\(382\) | 3.53250 | 0.180738 | ||||||||
\(383\) | −4.49317 | −0.229591 | −0.114795 | − | 0.993389i | \(-0.536621\pi\) | ||||
−0.114795 | + | 0.993389i | \(0.536621\pi\) | |||||||
\(384\) | −2.35773 | −0.120317 | ||||||||
\(385\) | 4.69505 | 0.239282 | ||||||||
\(386\) | 23.1286 | 1.17722 | ||||||||
\(387\) | −5.08527 | −0.258499 | ||||||||
\(388\) | 0.806852 | 0.0409617 | ||||||||
\(389\) | 21.7065 | 1.10056 | 0.550282 | − | 0.834979i | \(-0.314520\pi\) | ||||
0.550282 | + | 0.834979i | \(0.314520\pi\) | |||||||
\(390\) | 7.80197 | 0.395068 | ||||||||
\(391\) | 5.02127 | 0.253936 | ||||||||
\(392\) | 16.6330 | 0.840095 | ||||||||
\(393\) | −19.8009 | −0.998825 | ||||||||
\(394\) | −23.4303 | −1.18040 | ||||||||
\(395\) | 19.9455 | 1.00357 | ||||||||
\(396\) | 0.689651 | 0.0346562 | ||||||||
\(397\) | −0.434918 | −0.0218279 | −0.0109140 | − | 0.999940i | \(-0.503474\pi\) | ||||
−0.0109140 | + | 0.999940i | \(0.503474\pi\) | |||||||
\(398\) | 8.17122 | 0.409586 | ||||||||
\(399\) | −27.9832 | −1.40091 | ||||||||
\(400\) | 6.91281 | 0.345641 | ||||||||
\(401\) | 23.6376 | 1.18041 | 0.590203 | − | 0.807255i | \(-0.299048\pi\) | ||||
0.590203 | + | 0.807255i | \(0.299048\pi\) | |||||||
\(402\) | 17.0944 | 0.852591 | ||||||||
\(403\) | 21.5370 | 1.07284 | ||||||||
\(404\) | −0.831966 | −0.0413919 | ||||||||
\(405\) | 1.33318 | 0.0662462 | ||||||||
\(406\) | 40.0171 | 1.98602 | ||||||||
\(407\) | 9.46041 | 0.468935 | ||||||||
\(408\) | 5.44494 | 0.269565 | ||||||||
\(409\) | −32.9182 | −1.62770 | −0.813849 | − | 0.581076i | \(-0.802632\pi\) | ||||
−0.813849 | + | 0.581076i | \(0.802632\pi\) | |||||||
\(410\) | 7.51435 | 0.371107 | ||||||||
\(411\) | −17.3461 | −0.855619 | ||||||||
\(412\) | 5.50088 | 0.271009 | ||||||||
\(413\) | 17.9388 | 0.882709 | ||||||||
\(414\) | −3.25015 | −0.159736 | ||||||||
\(415\) | −16.0307 | −0.786914 | ||||||||
\(416\) | 18.9272 | 0.927981 | ||||||||
\(417\) | 10.2385 | 0.501381 | ||||||||
\(418\) | 9.09575 | 0.444888 | ||||||||
\(419\) | 28.6995 | 1.40206 | 0.701030 | − | 0.713132i | \(-0.252724\pi\) | ||||
0.701030 | + | 0.713132i | \(0.252724\pi\) | |||||||
\(420\) | 3.23794 | 0.157995 | ||||||||
\(421\) | 36.0867 | 1.75876 | 0.879380 | − | 0.476120i | \(-0.157957\pi\) | ||||
0.879380 | + | 0.476120i | \(0.157957\pi\) | |||||||
\(422\) | −2.97858 | −0.144995 | ||||||||
\(423\) | −6.83907 | −0.332527 | ||||||||
\(424\) | 7.44871 | 0.361742 | ||||||||
\(425\) | −5.69921 | −0.276452 | ||||||||
\(426\) | 1.98290 | 0.0960719 | ||||||||
\(427\) | −3.52170 | −0.170427 | ||||||||
\(428\) | −9.08063 | −0.438929 | ||||||||
\(429\) | 5.11237 | 0.246828 | ||||||||
\(430\) | 7.76061 | 0.374250 | ||||||||
\(431\) | 32.5593 | 1.56833 | 0.784163 | − | 0.620555i | \(-0.213093\pi\) | ||||
0.784163 | + | 0.620555i | \(0.213093\pi\) | |||||||
\(432\) | −2.14508 | −0.103205 | ||||||||
\(433\) | −29.5779 | −1.42142 | −0.710711 | − | 0.703484i | \(-0.751627\pi\) | ||||
−0.710711 | + | 0.703484i | \(0.751627\pi\) | |||||||
\(434\) | −16.9828 | −0.815199 | ||||||||
\(435\) | 13.2339 | 0.634518 | ||||||||
\(436\) | 5.12320 | 0.245357 | ||||||||
\(437\) | 22.5608 | 1.07923 | ||||||||
\(438\) | 0.311461 | 0.0148822 | ||||||||
\(439\) | 20.9170 | 0.998316 | 0.499158 | − | 0.866511i | \(-0.333643\pi\) | ||||
0.499158 | + | 0.866511i | \(0.333643\pi\) | |||||||
\(440\) | −4.10467 | −0.195682 | ||||||||
\(441\) | 5.40234 | 0.257254 | ||||||||
\(442\) | 10.3495 | 0.492276 | ||||||||
\(443\) | 13.9300 | 0.661833 | 0.330917 | − | 0.943660i | \(-0.392642\pi\) | ||||
0.330917 | + | 0.943660i | \(0.392642\pi\) | |||||||
\(444\) | 6.52438 | 0.309633 | ||||||||
\(445\) | −17.8444 | −0.845905 | ||||||||
\(446\) | −17.0421 | −0.806967 | ||||||||
\(447\) | 11.0748 | 0.523818 | ||||||||
\(448\) | −30.0334 | −1.41895 | ||||||||
\(449\) | −15.8421 | −0.747633 | −0.373817 | − | 0.927503i | \(-0.621951\pi\) | ||||
−0.373817 | + | 0.927503i | \(0.621951\pi\) | |||||||
\(450\) | 3.68897 | 0.173900 | ||||||||
\(451\) | 4.92390 | 0.231858 | ||||||||
\(452\) | 4.04094 | 0.190070 | ||||||||
\(453\) | −0.576802 | −0.0271005 | ||||||||
\(454\) | 27.5879 | 1.29476 | ||||||||
\(455\) | 24.0028 | 1.12527 | ||||||||
\(456\) | 24.4644 | 1.14565 | ||||||||
\(457\) | 31.1875 | 1.45889 | 0.729444 | − | 0.684040i | \(-0.239779\pi\) | ||||
0.729444 | + | 0.684040i | \(0.239779\pi\) | |||||||
\(458\) | 15.2589 | 0.713003 | ||||||||
\(459\) | 1.76849 | 0.0825462 | ||||||||
\(460\) | −2.61052 | −0.121716 | ||||||||
\(461\) | −38.3496 | −1.78612 | −0.893059 | − | 0.449940i | \(-0.851445\pi\) | ||||
−0.893059 | + | 0.449940i | \(0.851445\pi\) | |||||||
\(462\) | −4.03130 | −0.187553 | ||||||||
\(463\) | 3.32069 | 0.154325 | 0.0771627 | − | 0.997019i | \(-0.475414\pi\) | ||||
0.0771627 | + | 0.997019i | \(0.475414\pi\) | |||||||
\(464\) | −21.2933 | −0.988519 | ||||||||
\(465\) | −5.61631 | −0.260450 | ||||||||
\(466\) | −2.65244 | −0.122872 | ||||||||
\(467\) | −16.9438 | −0.784068 | −0.392034 | − | 0.919951i | \(-0.628228\pi\) | ||||
−0.392034 | + | 0.919951i | \(0.628228\pi\) | |||||||
\(468\) | 3.52575 | 0.162978 | ||||||||
\(469\) | 52.5911 | 2.42843 | ||||||||
\(470\) | 10.4371 | 0.481426 | ||||||||
\(471\) | 0.409551 | 0.0188711 | ||||||||
\(472\) | −15.6830 | −0.721870 | ||||||||
\(473\) | 5.08527 | 0.233821 | ||||||||
\(474\) | −17.1258 | −0.786612 | ||||||||
\(475\) | −25.6068 | −1.17492 | ||||||||
\(476\) | 4.29521 | 0.196871 | ||||||||
\(477\) | 2.41931 | 0.110773 | ||||||||
\(478\) | 15.2726 | 0.698554 | ||||||||
\(479\) | −5.47364 | −0.250097 | −0.125049 | − | 0.992151i | \(-0.539909\pi\) | ||||
−0.125049 | + | 0.992151i | \(0.539909\pi\) | |||||||
\(480\) | −4.93573 | −0.225284 | ||||||||
\(481\) | 48.3652 | 2.20526 | ||||||||
\(482\) | 16.1348 | 0.734921 | ||||||||
\(483\) | −9.99911 | −0.454975 | ||||||||
\(484\) | −0.689651 | −0.0313478 | ||||||||
\(485\) | −1.55974 | −0.0708243 | ||||||||
\(486\) | −1.14470 | −0.0519249 | ||||||||
\(487\) | 37.1479 | 1.68333 | 0.841666 | − | 0.539998i | \(-0.181575\pi\) | ||||
0.841666 | + | 0.539998i | \(0.181575\pi\) | |||||||
\(488\) | 3.07886 | 0.139373 | ||||||||
\(489\) | 10.7263 | 0.485059 | ||||||||
\(490\) | −8.24449 | −0.372448 | ||||||||
\(491\) | −36.9552 | −1.66777 | −0.833883 | − | 0.551941i | \(-0.813887\pi\) | ||||
−0.833883 | + | 0.551941i | \(0.813887\pi\) | |||||||
\(492\) | 3.39577 | 0.153093 | ||||||||
\(493\) | 17.5551 | 0.790643 | ||||||||
\(494\) | 46.5009 | 2.09217 | ||||||||
\(495\) | −1.33318 | −0.0599219 | ||||||||
\(496\) | 9.03664 | 0.405757 | ||||||||
\(497\) | 6.10041 | 0.273641 | ||||||||
\(498\) | 13.7644 | 0.616796 | ||||||||
\(499\) | −20.2310 | −0.905662 | −0.452831 | − | 0.891596i | \(-0.649586\pi\) | ||||
−0.452831 | + | 0.891596i | \(0.649586\pi\) | |||||||
\(500\) | 7.56012 | 0.338099 | ||||||||
\(501\) | −9.02703 | −0.403298 | ||||||||
\(502\) | 11.5732 | 0.516537 | ||||||||
\(503\) | −19.6455 | −0.875952 | −0.437976 | − | 0.898987i | \(-0.644304\pi\) | ||||
−0.437976 | + | 0.898987i | \(0.644304\pi\) | |||||||
\(504\) | −10.8428 | −0.482976 | ||||||||
\(505\) | 1.60829 | 0.0715681 | ||||||||
\(506\) | 3.25015 | 0.144487 | ||||||||
\(507\) | 13.1363 | 0.583405 | ||||||||
\(508\) | 4.10189 | 0.181992 | ||||||||
\(509\) | 35.8608 | 1.58950 | 0.794752 | − | 0.606935i | \(-0.207601\pi\) | ||||
0.794752 | + | 0.606935i | \(0.207601\pi\) | |||||||
\(510\) | −2.69889 | −0.119509 | ||||||||
\(511\) | 0.958213 | 0.0423888 | ||||||||
\(512\) | 21.1504 | 0.934723 | ||||||||
\(513\) | 7.94593 | 0.350822 | ||||||||
\(514\) | −5.73193 | −0.252825 | ||||||||
\(515\) | −10.6339 | −0.468585 | ||||||||
\(516\) | 3.50706 | 0.154390 | ||||||||
\(517\) | 6.83907 | 0.300782 | ||||||||
\(518\) | −38.1378 | −1.67568 | ||||||||
\(519\) | 1.04546 | 0.0458908 | ||||||||
\(520\) | −20.9846 | −0.920235 | ||||||||
\(521\) | −22.2297 | −0.973900 | −0.486950 | − | 0.873430i | \(-0.661891\pi\) | ||||
−0.486950 | + | 0.873430i | \(0.661891\pi\) | |||||||
\(522\) | −11.3630 | −0.497346 | ||||||||
\(523\) | 8.21955 | 0.359416 | 0.179708 | − | 0.983720i | \(-0.442485\pi\) | ||||
0.179708 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(524\) | 13.6557 | 0.596553 | ||||||||
\(525\) | 11.3491 | 0.495317 | ||||||||
\(526\) | 13.4528 | 0.586569 | ||||||||
\(527\) | −7.45018 | −0.324535 | ||||||||
\(528\) | 2.14508 | 0.0933527 | ||||||||
\(529\) | −14.9384 | −0.649497 | ||||||||
\(530\) | −3.69210 | −0.160375 | ||||||||
\(531\) | −5.09379 | −0.221052 | ||||||||
\(532\) | 19.2986 | 0.836700 | ||||||||
\(533\) | 25.1728 | 1.09036 | ||||||||
\(534\) | 15.3217 | 0.663035 | ||||||||
\(535\) | 17.5540 | 0.758924 | ||||||||
\(536\) | −45.9780 | −1.98595 | ||||||||
\(537\) | −19.9008 | −0.858782 | ||||||||
\(538\) | −28.9045 | −1.24616 | ||||||||
\(539\) | −5.40234 | −0.232695 | ||||||||
\(540\) | −0.919427 | −0.0395659 | ||||||||
\(541\) | 9.01502 | 0.387586 | 0.193793 | − | 0.981042i | \(-0.437921\pi\) | ||||
0.193793 | + | 0.981042i | \(0.437921\pi\) | |||||||
\(542\) | 0.282879 | 0.0121507 | ||||||||
\(543\) | 25.4805 | 1.09347 | ||||||||
\(544\) | −6.54737 | −0.280716 | ||||||||
\(545\) | −9.90378 | −0.424231 | ||||||||
\(546\) | −20.6095 | −0.882006 | ||||||||
\(547\) | 21.1680 | 0.905079 | 0.452540 | − | 0.891744i | \(-0.350518\pi\) | ||||
0.452540 | + | 0.891744i | \(0.350518\pi\) | |||||||
\(548\) | 11.9627 | 0.511022 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −3.68897 | −0.157298 | ||||||||
\(551\) | 78.8761 | 3.36023 | ||||||||
\(552\) | 8.74177 | 0.372074 | ||||||||
\(553\) | −52.6875 | −2.24050 | ||||||||
\(554\) | 9.66164 | 0.410484 | ||||||||
\(555\) | −12.6124 | −0.535368 | ||||||||
\(556\) | −7.06098 | −0.299452 | ||||||||
\(557\) | 13.3758 | 0.566749 | 0.283375 | − | 0.959009i | \(-0.408546\pi\) | ||||
0.283375 | + | 0.959009i | \(0.408546\pi\) | |||||||
\(558\) | 4.82233 | 0.204145 | ||||||||
\(559\) | 25.9978 | 1.09959 | ||||||||
\(560\) | 10.0713 | 0.425588 | ||||||||
\(561\) | −1.76849 | −0.0746659 | ||||||||
\(562\) | −19.8138 | −0.835793 | ||||||||
\(563\) | 1.28336 | 0.0540874 | 0.0270437 | − | 0.999634i | \(-0.491391\pi\) | ||||
0.0270437 | + | 0.999634i | \(0.491391\pi\) | |||||||
\(564\) | 4.71656 | 0.198603 | ||||||||
\(565\) | −7.81163 | −0.328638 | ||||||||
\(566\) | 19.7196 | 0.828876 | ||||||||
\(567\) | −3.52170 | −0.147897 | ||||||||
\(568\) | −5.33331 | −0.223781 | ||||||||
\(569\) | −13.6521 | −0.572324 | −0.286162 | − | 0.958181i | \(-0.592380\pi\) | ||||
−0.286162 | + | 0.958181i | \(0.592380\pi\) | |||||||
\(570\) | −12.1263 | −0.507913 | ||||||||
\(571\) | 11.7612 | 0.492191 | 0.246095 | − | 0.969246i | \(-0.420852\pi\) | ||||
0.246095 | + | 0.969246i | \(0.420852\pi\) | |||||||
\(572\) | −3.52575 | −0.147419 | ||||||||
\(573\) | −3.08595 | −0.128917 | ||||||||
\(574\) | −19.8497 | −0.828512 | ||||||||
\(575\) | −9.14999 | −0.381581 | ||||||||
\(576\) | 8.52812 | 0.355338 | ||||||||
\(577\) | −4.18009 | −0.174019 | −0.0870096 | − | 0.996207i | \(-0.527731\pi\) | ||||
−0.0870096 | + | 0.996207i | \(0.527731\pi\) | |||||||
\(578\) | 15.8798 | 0.660514 | ||||||||
\(579\) | −20.2049 | −0.839686 | ||||||||
\(580\) | −9.12678 | −0.378969 | ||||||||
\(581\) | 42.3462 | 1.75682 | ||||||||
\(582\) | 1.33924 | 0.0555133 | ||||||||
\(583\) | −2.41931 | −0.100198 | ||||||||
\(584\) | −0.837721 | −0.0346651 | ||||||||
\(585\) | −6.81570 | −0.281795 | ||||||||
\(586\) | −23.2742 | −0.961447 | ||||||||
\(587\) | 29.1341 | 1.20249 | 0.601246 | − | 0.799064i | \(-0.294671\pi\) | ||||
0.601246 | + | 0.799064i | \(0.294671\pi\) | |||||||
\(588\) | −3.72573 | −0.153646 | ||||||||
\(589\) | −33.4740 | −1.37927 | ||||||||
\(590\) | 7.77361 | 0.320034 | ||||||||
\(591\) | 20.4684 | 0.841959 | ||||||||
\(592\) | 20.2934 | 0.834052 | ||||||||
\(593\) | 12.7057 | 0.521761 | 0.260880 | − | 0.965371i | \(-0.415987\pi\) | ||||
0.260880 | + | 0.965371i | \(0.415987\pi\) | |||||||
\(594\) | 1.14470 | 0.0469678 | ||||||||
\(595\) | −8.30317 | −0.340397 | ||||||||
\(596\) | −7.63772 | −0.312853 | ||||||||
\(597\) | −7.13828 | −0.292150 | ||||||||
\(598\) | 16.6160 | 0.679478 | ||||||||
\(599\) | −16.5948 | −0.678046 | −0.339023 | − | 0.940778i | \(-0.610096\pi\) | ||||
−0.339023 | + | 0.940778i | \(0.610096\pi\) | |||||||
\(600\) | −9.92203 | −0.405065 | ||||||||
\(601\) | 30.7501 | 1.25432 | 0.627161 | − | 0.778889i | \(-0.284217\pi\) | ||||
0.627161 | + | 0.778889i | \(0.284217\pi\) | |||||||
\(602\) | −20.5003 | −0.835528 | ||||||||
\(603\) | −14.9335 | −0.608137 | ||||||||
\(604\) | 0.397792 | 0.0161859 | ||||||||
\(605\) | 1.33318 | 0.0542014 | ||||||||
\(606\) | −1.38093 | −0.0560962 | ||||||||
\(607\) | −21.0480 | −0.854312 | −0.427156 | − | 0.904178i | \(-0.640484\pi\) | ||||
−0.427156 | + | 0.904178i | \(0.640484\pi\) | |||||||
\(608\) | −29.4177 | −1.19304 | ||||||||
\(609\) | −34.9584 | −1.41659 | ||||||||
\(610\) | −1.52610 | −0.0617898 | ||||||||
\(611\) | 34.9638 | 1.41449 | ||||||||
\(612\) | −1.21964 | −0.0493011 | ||||||||
\(613\) | 27.1514 | 1.09664 | 0.548318 | − | 0.836270i | \(-0.315268\pi\) | ||||
0.548318 | + | 0.836270i | \(0.315268\pi\) | |||||||
\(614\) | 17.5711 | 0.709110 | ||||||||
\(615\) | −6.56444 | −0.264704 | ||||||||
\(616\) | 10.8428 | 0.436869 | ||||||||
\(617\) | 26.8583 | 1.08127 | 0.540636 | − | 0.841256i | \(-0.318183\pi\) | ||||
0.540636 | + | 0.841256i | \(0.318183\pi\) | |||||||
\(618\) | 9.13055 | 0.367285 | ||||||||
\(619\) | −14.0051 | −0.562914 | −0.281457 | − | 0.959574i | \(-0.590818\pi\) | ||||
−0.281457 | + | 0.959574i | \(0.590818\pi\) | |||||||
\(620\) | 3.87329 | 0.155555 | ||||||||
\(621\) | 2.83929 | 0.113937 | ||||||||
\(622\) | −10.9372 | −0.438543 | ||||||||
\(623\) | 47.1374 | 1.88852 | ||||||||
\(624\) | 10.9665 | 0.439009 | ||||||||
\(625\) | 1.49855 | 0.0599419 | ||||||||
\(626\) | −17.8143 | −0.712002 | ||||||||
\(627\) | −7.94593 | −0.317330 | ||||||||
\(628\) | −0.282447 | −0.0112709 | ||||||||
\(629\) | −16.7307 | −0.667096 | ||||||||
\(630\) | 5.37445 | 0.214123 | ||||||||
\(631\) | 24.5099 | 0.975723 | 0.487862 | − | 0.872921i | \(-0.337777\pi\) | ||||
0.487862 | + | 0.872921i | \(0.337777\pi\) | |||||||
\(632\) | 46.0623 | 1.83226 | ||||||||
\(633\) | 2.60205 | 0.103422 | ||||||||
\(634\) | −17.3563 | −0.689307 | ||||||||
\(635\) | −7.92946 | −0.314671 | ||||||||
\(636\) | −1.66848 | −0.0661595 | ||||||||
\(637\) | −27.6188 | −1.09430 | ||||||||
\(638\) | 11.3630 | 0.449866 | ||||||||
\(639\) | −1.73224 | −0.0685263 | ||||||||
\(640\) | −3.14327 | −0.124249 | ||||||||
\(641\) | 1.69206 | 0.0668324 | 0.0334162 | − | 0.999442i | \(-0.489361\pi\) | ||||
0.0334162 | + | 0.999442i | \(0.489361\pi\) | |||||||
\(642\) | −15.0723 | −0.594857 | ||||||||
\(643\) | −23.6988 | −0.934591 | −0.467295 | − | 0.884101i | \(-0.654772\pi\) | ||||
−0.467295 | + | 0.884101i | \(0.654772\pi\) | |||||||
\(644\) | 6.89589 | 0.271736 | ||||||||
\(645\) | −6.77957 | −0.266945 | ||||||||
\(646\) | −16.0858 | −0.632887 | ||||||||
\(647\) | −3.21842 | −0.126529 | −0.0632646 | − | 0.997997i | \(-0.520151\pi\) | ||||
−0.0632646 | + | 0.997997i | \(0.520151\pi\) | |||||||
\(648\) | 3.07886 | 0.120949 | ||||||||
\(649\) | 5.09379 | 0.199949 | ||||||||
\(650\) | −18.8594 | −0.739725 | ||||||||
\(651\) | 14.8359 | 0.581466 | ||||||||
\(652\) | −7.39738 | −0.289704 | ||||||||
\(653\) | 1.62340 | 0.0635286 | 0.0317643 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317643 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(654\) | 8.50367 | 0.332520 | ||||||||
\(655\) | −26.3982 | −1.03146 | ||||||||
\(656\) | 10.5622 | 0.412384 | ||||||||
\(657\) | −0.272088 | −0.0106152 | ||||||||
\(658\) | −27.5703 | −1.07480 | ||||||||
\(659\) | −21.7938 | −0.848965 | −0.424483 | − | 0.905436i | \(-0.639544\pi\) | ||||
−0.424483 | + | 0.905436i | \(0.639544\pi\) | |||||||
\(660\) | 0.919427 | 0.0357887 | ||||||||
\(661\) | 33.5998 | 1.30688 | 0.653440 | − | 0.756979i | \(-0.273325\pi\) | ||||
0.653440 | + | 0.756979i | \(0.273325\pi\) | |||||||
\(662\) | 36.0323 | 1.40044 | ||||||||
\(663\) | −9.04120 | −0.351131 | ||||||||
\(664\) | −37.0214 | −1.43671 | ||||||||
\(665\) | −37.3065 | −1.44669 | ||||||||
\(666\) | 10.8294 | 0.419630 | ||||||||
\(667\) | 28.1845 | 1.09131 | ||||||||
\(668\) | 6.22550 | 0.240872 | ||||||||
\(669\) | 14.8878 | 0.575595 | ||||||||
\(670\) | 22.7899 | 0.880450 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 13.0381 | 0.502956 | ||||||||
\(673\) | 23.6911 | 0.913225 | 0.456613 | − | 0.889666i | \(-0.349063\pi\) | ||||
0.456613 | + | 0.889666i | \(0.349063\pi\) | |||||||
\(674\) | −6.26568 | −0.241345 | ||||||||
\(675\) | −3.22263 | −0.124039 | ||||||||
\(676\) | −9.05949 | −0.348442 | ||||||||
\(677\) | 20.4021 | 0.784115 | 0.392058 | − | 0.919941i | \(-0.371763\pi\) | ||||
0.392058 | + | 0.919941i | \(0.371763\pi\) | |||||||
\(678\) | 6.70729 | 0.257592 | ||||||||
\(679\) | 4.12018 | 0.158118 | ||||||||
\(680\) | 7.25908 | 0.278373 | ||||||||
\(681\) | −24.1004 | −0.923529 | ||||||||
\(682\) | −4.82233 | −0.184656 | ||||||||
\(683\) | 14.2024 | 0.543441 | 0.271720 | − | 0.962376i | \(-0.412407\pi\) | ||||
0.271720 | + | 0.962376i | \(0.412407\pi\) | |||||||
\(684\) | −5.47992 | −0.209530 | ||||||||
\(685\) | −23.1254 | −0.883577 | ||||||||
\(686\) | −6.44065 | −0.245905 | ||||||||
\(687\) | −13.3300 | −0.508572 | ||||||||
\(688\) | 10.9083 | 0.415876 | ||||||||
\(689\) | −12.3684 | −0.471199 | ||||||||
\(690\) | −4.33303 | −0.164956 | ||||||||
\(691\) | −35.6324 | −1.35552 | −0.677759 | − | 0.735284i | \(-0.737049\pi\) | ||||
−0.677759 | + | 0.735284i | \(0.737049\pi\) | |||||||
\(692\) | −0.721005 | −0.0274085 | ||||||||
\(693\) | 3.52170 | 0.133778 | ||||||||
\(694\) | −22.9401 | −0.870793 | ||||||||
\(695\) | 13.6497 | 0.517764 | ||||||||
\(696\) | 30.5626 | 1.15847 | ||||||||
\(697\) | −8.70789 | −0.329835 | ||||||||
\(698\) | 5.71414 | 0.216284 | ||||||||
\(699\) | 2.31713 | 0.0876421 | ||||||||
\(700\) | −7.82694 | −0.295830 | ||||||||
\(701\) | −8.93051 | −0.337301 | −0.168650 | − | 0.985676i | \(-0.553941\pi\) | ||||
−0.168650 | + | 0.985676i | \(0.553941\pi\) | |||||||
\(702\) | 5.85216 | 0.220875 | ||||||||
\(703\) | −75.1718 | −2.83516 | ||||||||
\(704\) | −8.52812 | −0.321416 | ||||||||
\(705\) | −9.11770 | −0.343392 | ||||||||
\(706\) | −4.95548 | −0.186502 | ||||||||
\(707\) | −4.24843 | −0.159779 | ||||||||
\(708\) | 3.51293 | 0.132024 | ||||||||
\(709\) | −37.0126 | −1.39004 | −0.695019 | − | 0.718992i | \(-0.744604\pi\) | ||||
−0.695019 | + | 0.718992i | \(0.744604\pi\) | |||||||
\(710\) | 2.64356 | 0.0992111 | ||||||||
\(711\) | 14.9608 | 0.561075 | ||||||||
\(712\) | −41.2100 | −1.54441 | ||||||||
\(713\) | −11.9611 | −0.447948 | ||||||||
\(714\) | 7.12934 | 0.266809 | ||||||||
\(715\) | 6.81570 | 0.254893 | ||||||||
\(716\) | 13.7246 | 0.512912 | ||||||||
\(717\) | −13.3420 | −0.498265 | ||||||||
\(718\) | 15.5452 | 0.580143 | ||||||||
\(719\) | −24.6974 | −0.921058 | −0.460529 | − | 0.887645i | \(-0.652340\pi\) | ||||
−0.460529 | + | 0.887645i | \(0.652340\pi\) | |||||||
\(720\) | −2.85978 | −0.106578 | ||||||||
\(721\) | 28.0902 | 1.04613 | ||||||||
\(722\) | −50.5248 | −1.88034 | ||||||||
\(723\) | −14.0952 | −0.524206 | ||||||||
\(724\) | −17.5726 | −0.653082 | ||||||||
\(725\) | −31.9898 | −1.18807 | ||||||||
\(726\) | −1.14470 | −0.0424840 | ||||||||
\(727\) | −22.5756 | −0.837282 | −0.418641 | − | 0.908152i | \(-0.637493\pi\) | ||||
−0.418641 | + | 0.908152i | \(0.637493\pi\) | |||||||
\(728\) | 55.4324 | 2.05446 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.415233 | 0.0153685 | ||||||||
\(731\) | −8.99327 | −0.332628 | ||||||||
\(732\) | −0.689651 | −0.0254902 | ||||||||
\(733\) | 36.8572 | 1.36135 | 0.680676 | − | 0.732585i | \(-0.261686\pi\) | ||||
0.680676 | + | 0.732585i | \(0.261686\pi\) | |||||||
\(734\) | −18.2992 | −0.675435 | ||||||||
\(735\) | 7.20228 | 0.265660 | ||||||||
\(736\) | −10.5117 | −0.387466 | ||||||||
\(737\) | 14.9335 | 0.550081 | ||||||||
\(738\) | 5.63642 | 0.207479 | ||||||||
\(739\) | 9.87637 | 0.363308 | 0.181654 | − | 0.983362i | \(-0.441855\pi\) | ||||
0.181654 | + | 0.983362i | \(0.441855\pi\) | |||||||
\(740\) | 8.69816 | 0.319751 | ||||||||
\(741\) | −40.6226 | −1.49231 | ||||||||
\(742\) | 9.75298 | 0.358043 | ||||||||
\(743\) | −25.0671 | −0.919622 | −0.459811 | − | 0.888017i | \(-0.652083\pi\) | ||||
−0.459811 | + | 0.888017i | \(0.652083\pi\) | |||||||
\(744\) | −12.9704 | −0.475517 | ||||||||
\(745\) | 14.7646 | 0.540934 | ||||||||
\(746\) | 4.66684 | 0.170865 | ||||||||
\(747\) | −12.0244 | −0.439949 | ||||||||
\(748\) | 1.21964 | 0.0445946 | ||||||||
\(749\) | −46.3702 | −1.69433 | ||||||||
\(750\) | 12.5485 | 0.458208 | ||||||||
\(751\) | −9.07144 | −0.331021 | −0.165511 | − | 0.986208i | \(-0.552927\pi\) | ||||
−0.165511 | + | 0.986208i | \(0.552927\pi\) | |||||||
\(752\) | 14.6704 | 0.534973 | ||||||||
\(753\) | −10.1102 | −0.368436 | ||||||||
\(754\) | 58.0920 | 2.11559 | ||||||||
\(755\) | −0.768980 | −0.0279861 | ||||||||
\(756\) | 2.42874 | 0.0883324 | ||||||||
\(757\) | 29.3753 | 1.06766 | 0.533832 | − | 0.845591i | \(-0.320752\pi\) | ||||
0.533832 | + | 0.845591i | \(0.320752\pi\) | |||||||
\(758\) | 9.22902 | 0.335213 | ||||||||
\(759\) | −2.83929 | −0.103060 | ||||||||
\(760\) | 32.6154 | 1.18308 | ||||||||
\(761\) | 35.8397 | 1.29919 | 0.649594 | − | 0.760281i | \(-0.274939\pi\) | ||||
0.649594 | + | 0.760281i | \(0.274939\pi\) | |||||||
\(762\) | 6.80846 | 0.246645 | ||||||||
\(763\) | 26.1616 | 0.947114 | ||||||||
\(764\) | 2.12823 | 0.0769965 | ||||||||
\(765\) | 2.35772 | 0.0852435 | ||||||||
\(766\) | 5.14336 | 0.185837 | ||||||||
\(767\) | 26.0413 | 0.940298 | ||||||||
\(768\) | −14.3573 | −0.518076 | ||||||||
\(769\) | −20.3758 | −0.734772 | −0.367386 | − | 0.930069i | \(-0.619747\pi\) | ||||
−0.367386 | + | 0.930069i | \(0.619747\pi\) | |||||||
\(770\) | −5.37445 | −0.193682 | ||||||||
\(771\) | 5.00734 | 0.180335 | ||||||||
\(772\) | 13.9343 | 0.501507 | ||||||||
\(773\) | −43.4010 | −1.56103 | −0.780513 | − | 0.625140i | \(-0.785042\pi\) | ||||
−0.780513 | + | 0.625140i | \(0.785042\pi\) | |||||||
\(774\) | 5.82113 | 0.209236 | ||||||||
\(775\) | 13.5761 | 0.487667 | ||||||||
\(776\) | −3.60209 | −0.129307 | ||||||||
\(777\) | 33.3167 | 1.19523 | ||||||||
\(778\) | −24.8476 | −0.890829 | ||||||||
\(779\) | −39.1250 | −1.40180 | ||||||||
\(780\) | 4.70045 | 0.168303 | ||||||||
\(781\) | 1.73224 | 0.0619843 | ||||||||
\(782\) | −5.74787 | −0.205543 | ||||||||
\(783\) | 9.92659 | 0.354748 | ||||||||
\(784\) | −11.5885 | −0.413873 | ||||||||
\(785\) | 0.546004 | 0.0194877 | ||||||||
\(786\) | 22.6662 | 0.808478 | ||||||||
\(787\) | 14.3584 | 0.511823 | 0.255912 | − | 0.966700i | \(-0.417624\pi\) | ||||
0.255912 | + | 0.966700i | \(0.417624\pi\) | |||||||
\(788\) | −14.1161 | −0.502864 | ||||||||
\(789\) | −11.7522 | −0.418388 | ||||||||
\(790\) | −22.8317 | −0.812315 | ||||||||
\(791\) | 20.6350 | 0.733697 | ||||||||
\(792\) | −3.07886 | −0.109402 | ||||||||
\(793\) | −5.11237 | −0.181546 | ||||||||
\(794\) | 0.497853 | 0.0176682 | ||||||||
\(795\) | 3.22538 | 0.114392 | ||||||||
\(796\) | 4.92292 | 0.174488 | ||||||||
\(797\) | −34.5788 | −1.22484 | −0.612421 | − | 0.790532i | \(-0.709804\pi\) | ||||
−0.612421 | + | 0.790532i | \(0.709804\pi\) | |||||||
\(798\) | 32.0325 | 1.13394 | ||||||||
\(799\) | −12.0948 | −0.427885 | ||||||||
\(800\) | 11.9309 | 0.421822 | ||||||||
\(801\) | −13.3848 | −0.472930 | ||||||||
\(802\) | −27.0581 | −0.955455 | ||||||||
\(803\) | 0.272088 | 0.00960179 | ||||||||
\(804\) | 10.2989 | 0.363213 | ||||||||
\(805\) | −13.3306 | −0.469842 | ||||||||
\(806\) | −24.6535 | −0.868383 | ||||||||
\(807\) | 25.2506 | 0.888864 | ||||||||
\(808\) | 3.71421 | 0.130665 | ||||||||
\(809\) | 7.62680 | 0.268144 | 0.134072 | − | 0.990972i | \(-0.457195\pi\) | ||||
0.134072 | + | 0.990972i | \(0.457195\pi\) | |||||||
\(810\) | −1.52610 | −0.0536216 | ||||||||
\(811\) | 19.4077 | 0.681496 | 0.340748 | − | 0.940155i | \(-0.389320\pi\) | ||||
0.340748 | + | 0.940155i | \(0.389320\pi\) | |||||||
\(812\) | 24.1091 | 0.846064 | ||||||||
\(813\) | −0.247119 | −0.00866685 | ||||||||
\(814\) | −10.8294 | −0.379570 | ||||||||
\(815\) | 14.3000 | 0.500908 | ||||||||
\(816\) | −3.79356 | −0.132801 | ||||||||
\(817\) | −40.4072 | −1.41367 | ||||||||
\(818\) | 37.6816 | 1.31751 | ||||||||
\(819\) | 18.0042 | 0.629118 | ||||||||
\(820\) | 4.52717 | 0.158096 | ||||||||
\(821\) | 4.76831 | 0.166415 | 0.0832076 | − | 0.996532i | \(-0.473484\pi\) | ||||
0.0832076 | + | 0.996532i | \(0.473484\pi\) | |||||||
\(822\) | 19.8561 | 0.692562 | ||||||||
\(823\) | −39.4737 | −1.37597 | −0.687984 | − | 0.725726i | \(-0.741504\pi\) | ||||
−0.687984 | + | 0.725726i | \(0.741504\pi\) | |||||||
\(824\) | −24.5580 | −0.855518 | ||||||||
\(825\) | 3.22263 | 0.112198 | ||||||||
\(826\) | −20.5346 | −0.714490 | ||||||||
\(827\) | 2.07065 | 0.0720036 | 0.0360018 | − | 0.999352i | \(-0.488538\pi\) | ||||
0.0360018 | + | 0.999352i | \(0.488538\pi\) | |||||||
\(828\) | −1.95812 | −0.0680493 | ||||||||
\(829\) | 2.50352 | 0.0869507 | 0.0434753 | − | 0.999055i | \(-0.486157\pi\) | ||||
0.0434753 | + | 0.999055i | \(0.486157\pi\) | |||||||
\(830\) | 18.3504 | 0.636951 | ||||||||
\(831\) | −8.44029 | −0.292790 | ||||||||
\(832\) | −43.5989 | −1.51152 | ||||||||
\(833\) | 9.55401 | 0.331027 | ||||||||
\(834\) | −11.7201 | −0.405832 | ||||||||
\(835\) | −12.0346 | −0.416476 | ||||||||
\(836\) | 5.47992 | 0.189527 | ||||||||
\(837\) | −4.21272 | −0.145613 | ||||||||
\(838\) | −32.8524 | −1.13487 | ||||||||
\(839\) | 12.2823 | 0.424032 | 0.212016 | − | 0.977266i | \(-0.431997\pi\) | ||||
0.212016 | + | 0.977266i | \(0.431997\pi\) | |||||||
\(840\) | −14.4554 | −0.498758 | ||||||||
\(841\) | 69.5373 | 2.39784 | ||||||||
\(842\) | −41.3087 | −1.42359 | ||||||||
\(843\) | 17.3091 | 0.596155 | ||||||||
\(844\) | −1.79451 | −0.0617695 | ||||||||
\(845\) | 17.5131 | 0.602469 | ||||||||
\(846\) | 7.82871 | 0.269157 | ||||||||
\(847\) | −3.52170 | −0.121007 | ||||||||
\(848\) | −5.18962 | −0.178212 | ||||||||
\(849\) | −17.2268 | −0.591222 | ||||||||
\(850\) | 6.52392 | 0.223768 | ||||||||
\(851\) | −26.8609 | −0.920778 | ||||||||
\(852\) | 1.19464 | 0.0409276 | ||||||||
\(853\) | 55.1509 | 1.88833 | 0.944166 | − | 0.329470i | \(-0.106870\pi\) | ||||
0.944166 | + | 0.329470i | \(0.106870\pi\) | |||||||
\(854\) | 4.03130 | 0.137948 | ||||||||
\(855\) | 10.5933 | 0.362285 | ||||||||
\(856\) | 40.5393 | 1.38560 | ||||||||
\(857\) | −45.0798 | −1.53990 | −0.769948 | − | 0.638106i | \(-0.779718\pi\) | ||||
−0.769948 | + | 0.638106i | \(0.779718\pi\) | |||||||
\(858\) | −5.85216 | −0.199789 | ||||||||
\(859\) | 10.3830 | 0.354264 | 0.177132 | − | 0.984187i | \(-0.443318\pi\) | ||||
0.177132 | + | 0.984187i | \(0.443318\pi\) | |||||||
\(860\) | 4.67553 | 0.159434 | ||||||||
\(861\) | 17.3405 | 0.590962 | ||||||||
\(862\) | −37.2708 | −1.26945 | ||||||||
\(863\) | −56.8511 | −1.93523 | −0.967617 | − | 0.252421i | \(-0.918773\pi\) | ||||
−0.967617 | + | 0.252421i | \(0.918773\pi\) | |||||||
\(864\) | −3.70223 | −0.125952 | ||||||||
\(865\) | 1.39379 | 0.0473903 | ||||||||
\(866\) | 33.8579 | 1.15054 | ||||||||
\(867\) | −13.8724 | −0.471132 | ||||||||
\(868\) | −10.2316 | −0.347283 | ||||||||
\(869\) | −14.9608 | −0.507512 | ||||||||
\(870\) | −15.1489 | −0.513597 | ||||||||
\(871\) | 76.3454 | 2.58686 | ||||||||
\(872\) | −22.8719 | −0.774540 | ||||||||
\(873\) | −1.16994 | −0.0395966 | ||||||||
\(874\) | −25.8255 | −0.873560 | ||||||||
\(875\) | 38.6057 | 1.30511 | ||||||||
\(876\) | 0.187646 | 0.00633997 | ||||||||
\(877\) | 11.5941 | 0.391506 | 0.195753 | − | 0.980653i | \(-0.437285\pi\) | ||||
0.195753 | + | 0.980653i | \(0.437285\pi\) | |||||||
\(878\) | −23.9438 | −0.808066 | ||||||||
\(879\) | 20.3320 | 0.685782 | ||||||||
\(880\) | 2.85978 | 0.0964030 | ||||||||
\(881\) | −4.12729 | −0.139052 | −0.0695259 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695259 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(882\) | −6.18408 | −0.208229 | ||||||||
\(883\) | −16.0992 | −0.541782 | −0.270891 | − | 0.962610i | \(-0.587318\pi\) | ||||
−0.270891 | + | 0.962610i | \(0.587318\pi\) | |||||||
\(884\) | 6.23527 | 0.209715 | ||||||||
\(885\) | −6.79093 | −0.228275 | ||||||||
\(886\) | −15.9457 | −0.535707 | ||||||||
\(887\) | 16.9188 | 0.568077 | 0.284038 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284038 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(888\) | −29.1273 | −0.977447 | ||||||||
\(889\) | 20.9463 | 0.702516 | ||||||||
\(890\) | 20.4266 | 0.684700 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −10.2674 | −0.343777 | ||||||||
\(893\) | −54.3428 | −1.81851 | ||||||||
\(894\) | −12.6773 | −0.423994 | ||||||||
\(895\) | −26.5313 | −0.886844 | ||||||||
\(896\) | 8.30320 | 0.277390 | ||||||||
\(897\) | −14.5155 | −0.484659 | ||||||||
\(898\) | 18.1345 | 0.605156 | ||||||||
\(899\) | −41.8180 | −1.39471 | ||||||||
\(900\) | 2.22249 | 0.0740831 | ||||||||
\(901\) | 4.27854 | 0.142539 | ||||||||
\(902\) | −5.63642 | −0.187672 | ||||||||
\(903\) | 17.9088 | 0.595966 | ||||||||
\(904\) | −18.0403 | −0.600010 | ||||||||
\(905\) | 33.9700 | 1.12920 | ||||||||
\(906\) | 0.660268 | 0.0219359 | ||||||||
\(907\) | 24.6453 | 0.818334 | 0.409167 | − | 0.912459i | \(-0.365819\pi\) | ||||
0.409167 | + | 0.912459i | \(0.365819\pi\) | |||||||
\(908\) | 16.6209 | 0.551582 | ||||||||
\(909\) | 1.20636 | 0.0400124 | ||||||||
\(910\) | −27.4762 | −0.910826 | ||||||||
\(911\) | −40.8445 | −1.35324 | −0.676620 | − | 0.736333i | \(-0.736556\pi\) | ||||
−0.676620 | + | 0.736333i | \(0.736556\pi\) | |||||||
\(912\) | −17.0447 | −0.564405 | ||||||||
\(913\) | 12.0244 | 0.397949 | ||||||||
\(914\) | −35.7005 | −1.18087 | ||||||||
\(915\) | 1.33318 | 0.0440735 | ||||||||
\(916\) | 9.19305 | 0.303747 | ||||||||
\(917\) | 69.7329 | 2.30278 | ||||||||
\(918\) | −2.02440 | −0.0668153 | ||||||||
\(919\) | 18.4138 | 0.607416 | 0.303708 | − | 0.952765i | \(-0.401775\pi\) | ||||
0.303708 | + | 0.952765i | \(0.401775\pi\) | |||||||
\(920\) | 11.6543 | 0.384232 | ||||||||
\(921\) | −15.3499 | −0.505795 | ||||||||
\(922\) | 43.8989 | 1.44573 | ||||||||
\(923\) | 8.85584 | 0.291494 | ||||||||
\(924\) | −2.42874 | −0.0798997 | ||||||||
\(925\) | 30.4875 | 1.00242 | ||||||||
\(926\) | −3.80121 | −0.124915 | ||||||||
\(927\) | −7.97633 | −0.261977 | ||||||||
\(928\) | −36.7505 | −1.20639 | ||||||||
\(929\) | −6.06386 | −0.198949 | −0.0994744 | − | 0.995040i | \(-0.531716\pi\) | ||||
−0.0994744 | + | 0.995040i | \(0.531716\pi\) | |||||||
\(930\) | 6.42902 | 0.210816 | ||||||||
\(931\) | 42.9266 | 1.40686 | ||||||||
\(932\) | −1.59801 | −0.0523447 | ||||||||
\(933\) | 9.55462 | 0.312804 | ||||||||
\(934\) | 19.3957 | 0.634647 | ||||||||
\(935\) | −2.35772 | −0.0771056 | ||||||||
\(936\) | −15.7403 | −0.514486 | ||||||||
\(937\) | 32.3089 | 1.05549 | 0.527743 | − | 0.849404i | \(-0.323039\pi\) | ||||
0.527743 | + | 0.849404i | \(0.323039\pi\) | |||||||
\(938\) | −60.2013 | −1.96564 | ||||||||
\(939\) | 15.5623 | 0.507857 | ||||||||
\(940\) | 6.28802 | 0.205093 | ||||||||
\(941\) | 32.3579 | 1.05484 | 0.527419 | − | 0.849605i | \(-0.323160\pi\) | ||||
0.527419 | + | 0.849605i | \(0.323160\pi\) | |||||||
\(942\) | −0.468815 | −0.0152748 | ||||||||
\(943\) | −13.9804 | −0.455264 | ||||||||
\(944\) | 10.9266 | 0.355630 | ||||||||
\(945\) | −4.69505 | −0.152730 | ||||||||
\(946\) | −5.82113 | −0.189261 | ||||||||
\(947\) | 13.7872 | 0.448025 | 0.224013 | − | 0.974586i | \(-0.428084\pi\) | ||||
0.224013 | + | 0.974586i | \(0.428084\pi\) | |||||||
\(948\) | −10.3178 | −0.335105 | ||||||||
\(949\) | 1.39102 | 0.0451543 | ||||||||
\(950\) | 29.3123 | 0.951016 | ||||||||
\(951\) | 15.1622 | 0.491669 | ||||||||
\(952\) | −19.1754 | −0.621479 | ||||||||
\(953\) | −51.7560 | −1.67654 | −0.838270 | − | 0.545256i | \(-0.816433\pi\) | ||||
−0.838270 | + | 0.545256i | \(0.816433\pi\) | |||||||
\(954\) | −2.76940 | −0.0896626 | ||||||||
\(955\) | −4.11412 | −0.133130 | ||||||||
\(956\) | 9.20130 | 0.297591 | ||||||||
\(957\) | −9.92659 | −0.320881 | ||||||||
\(958\) | 6.26571 | 0.202436 | ||||||||
\(959\) | 61.0876 | 1.97262 | ||||||||
\(960\) | 11.3695 | 0.366949 | ||||||||
\(961\) | −13.2529 | −0.427514 | ||||||||
\(962\) | −55.3638 | −1.78500 | ||||||||
\(963\) | 13.1670 | 0.424301 | ||||||||
\(964\) | 9.72075 | 0.313084 | ||||||||
\(965\) | −26.9367 | −0.867124 | ||||||||
\(966\) | 11.4460 | 0.368270 | ||||||||
\(967\) | −44.6069 | −1.43446 | −0.717231 | − | 0.696836i | \(-0.754591\pi\) | ||||
−0.717231 | + | 0.696836i | \(0.754591\pi\) | |||||||
\(968\) | 3.07886 | 0.0989582 | ||||||||
\(969\) | 14.0523 | 0.451426 | ||||||||
\(970\) | 1.78545 | 0.0573272 | ||||||||
\(971\) | 16.2610 | 0.521839 | 0.260920 | − | 0.965361i | \(-0.415974\pi\) | ||||
0.260920 | + | 0.965361i | \(0.415974\pi\) | |||||||
\(972\) | −0.689651 | −0.0221206 | ||||||||
\(973\) | −36.0568 | −1.15593 | ||||||||
\(974\) | −42.5234 | −1.36254 | ||||||||
\(975\) | 16.4753 | 0.527632 | ||||||||
\(976\) | −2.14508 | −0.0686624 | ||||||||
\(977\) | −37.5432 | −1.20111 | −0.600557 | − | 0.799582i | \(-0.705054\pi\) | ||||
−0.600557 | + | 0.799582i | \(0.705054\pi\) | |||||||
\(978\) | −12.2784 | −0.392620 | ||||||||
\(979\) | 13.3848 | 0.427782 | ||||||||
\(980\) | −4.96706 | −0.158667 | ||||||||
\(981\) | −7.42870 | −0.237180 | ||||||||
\(982\) | 42.3028 | 1.34994 | ||||||||
\(983\) | 52.4689 | 1.67350 | 0.836750 | − | 0.547585i | \(-0.184453\pi\) | ||||
0.836750 | + | 0.547585i | \(0.184453\pi\) | |||||||
\(984\) | −15.1600 | −0.483283 | ||||||||
\(985\) | 27.2881 | 0.869470 | ||||||||
\(986\) | −20.0954 | −0.639969 | ||||||||
\(987\) | 24.0851 | 0.766637 | ||||||||
\(988\) | 28.0154 | 0.891288 | ||||||||
\(989\) | −14.4386 | −0.459119 | ||||||||
\(990\) | 1.52610 | 0.0485025 | ||||||||
\(991\) | −45.0110 | −1.42982 | −0.714910 | − | 0.699216i | \(-0.753532\pi\) | ||||
−0.714910 | + | 0.699216i | \(0.753532\pi\) | |||||||
\(992\) | 15.5965 | 0.495188 | ||||||||
\(993\) | −31.4774 | −0.998905 | ||||||||
\(994\) | −6.98317 | −0.221493 | ||||||||
\(995\) | −9.51660 | −0.301696 | ||||||||
\(996\) | 8.29262 | 0.262762 | ||||||||
\(997\) | −11.8012 | −0.373747 | −0.186873 | − | 0.982384i | \(-0.559835\pi\) | ||||
−0.186873 | + | 0.982384i | \(0.559835\pi\) | |||||||
\(998\) | 23.1585 | 0.733069 | ||||||||
\(999\) | −9.46041 | −0.299314 |
(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 | 2013.2.a.a.1.5 | ✓ | 11 | |
3.2 | odd | 2 | 6039.2.a.d.1.7 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.a.1.5 | ✓ | 11 | 1.1 | even | 1 | trivial | |
6039.2.a.d.1.7 | 11 | 3.2 | odd | 2 |