Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(61\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73344 | −1.22572 | −0.612862 | − | 0.790190i | \(-0.709982\pi\) | ||||
−0.612862 | + | 0.790190i | \(0.709982\pi\) | |||||||
\(3\) | −1.78807 | −1.03234 | −0.516172 | − | 0.856485i | \(-0.672644\pi\) | ||||
−0.516172 | + | 0.856485i | \(0.672644\pi\) | |||||||
\(4\) | 1.00480 | 0.502399 | ||||||||
\(5\) | −2.76512 | −1.23660 | −0.618299 | − | 0.785943i | \(-0.712178\pi\) | ||||
−0.618299 | + | 0.785943i | \(0.712178\pi\) | |||||||
\(6\) | 3.09951 | 1.26537 | ||||||||
\(7\) | −4.11682 | −1.55601 | −0.778005 | − | 0.628258i | \(-0.783768\pi\) | ||||
−0.778005 | + | 0.628258i | \(0.783768\pi\) | |||||||
\(8\) | 1.72512 | 0.609922 | ||||||||
\(9\) | 0.197207 | 0.0657357 | ||||||||
\(10\) | 4.79315 | 1.51573 | ||||||||
\(11\) | −1.99041 | −0.600131 | −0.300066 | − | 0.953919i | \(-0.597009\pi\) | ||||
−0.300066 | + | 0.953919i | \(0.597009\pi\) | |||||||
\(12\) | −1.79665 | −0.518649 | ||||||||
\(13\) | −4.67393 | −1.29631 | −0.648157 | − | 0.761506i | \(-0.724460\pi\) | ||||
−0.648157 | + | 0.761506i | \(0.724460\pi\) | |||||||
\(14\) | 7.13623 | 1.90724 | ||||||||
\(15\) | 4.94423 | 1.27660 | ||||||||
\(16\) | −4.99998 | −1.24999 | ||||||||
\(17\) | −2.57995 | −0.625730 | −0.312865 | − | 0.949798i | \(-0.601289\pi\) | ||||
−0.312865 | + | 0.949798i | \(0.601289\pi\) | |||||||
\(18\) | −0.341846 | −0.0805738 | ||||||||
\(19\) | −2.14491 | −0.492076 | −0.246038 | − | 0.969260i | \(-0.579129\pi\) | ||||
−0.246038 | + | 0.969260i | \(0.579129\pi\) | |||||||
\(20\) | −2.77838 | −0.621265 | ||||||||
\(21\) | 7.36117 | 1.60634 | ||||||||
\(22\) | 3.45025 | 0.735595 | ||||||||
\(23\) | −1.75275 | −0.365474 | −0.182737 | − | 0.983162i | \(-0.558496\pi\) | ||||
−0.182737 | + | 0.983162i | \(0.558496\pi\) | |||||||
\(24\) | −3.08464 | −0.629649 | ||||||||
\(25\) | 2.64587 | 0.529174 | ||||||||
\(26\) | 8.10195 | 1.58892 | ||||||||
\(27\) | 5.01160 | 0.964483 | ||||||||
\(28\) | −4.13657 | −0.781738 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −8.57050 | −1.56475 | ||||||||
\(31\) | 6.89231 | 1.23790 | 0.618948 | − | 0.785432i | \(-0.287559\pi\) | ||||
0.618948 | + | 0.785432i | \(0.287559\pi\) | |||||||
\(32\) | 5.21690 | 0.922226 | ||||||||
\(33\) | 3.55900 | 0.619542 | ||||||||
\(34\) | 4.47218 | 0.766972 | ||||||||
\(35\) | 11.3835 | 1.92416 | ||||||||
\(36\) | 0.198153 | 0.0330255 | ||||||||
\(37\) | 5.25840 | 0.864476 | 0.432238 | − | 0.901759i | \(-0.357724\pi\) | ||||
0.432238 | + | 0.901759i | \(0.357724\pi\) | |||||||
\(38\) | 3.71806 | 0.603149 | ||||||||
\(39\) | 8.35733 | 1.33824 | ||||||||
\(40\) | −4.77016 | −0.754228 | ||||||||
\(41\) | −6.91323 | −1.07967 | −0.539833 | − | 0.841772i | \(-0.681513\pi\) | ||||
−0.539833 | + | 0.841772i | \(0.681513\pi\) | |||||||
\(42\) | −12.7601 | −1.96893 | ||||||||
\(43\) | −4.92517 | −0.751081 | −0.375541 | − | 0.926806i | \(-0.622543\pi\) | ||||
−0.375541 | + | 0.926806i | \(0.622543\pi\) | |||||||
\(44\) | −1.99996 | −0.301505 | ||||||||
\(45\) | −0.545301 | −0.0812886 | ||||||||
\(46\) | 3.03828 | 0.447970 | ||||||||
\(47\) | −4.03679 | −0.588827 | −0.294413 | − | 0.955678i | \(-0.595124\pi\) | ||||
−0.294413 | + | 0.955678i | \(0.595124\pi\) | |||||||
\(48\) | 8.94033 | 1.29043 | ||||||||
\(49\) | 9.94817 | 1.42117 | ||||||||
\(50\) | −4.58644 | −0.648621 | ||||||||
\(51\) | 4.61314 | 0.645969 | ||||||||
\(52\) | −4.69635 | −0.651267 | ||||||||
\(53\) | 6.90102 | 0.947928 | 0.473964 | − | 0.880544i | \(-0.342823\pi\) | ||||
0.473964 | + | 0.880544i | \(0.342823\pi\) | |||||||
\(54\) | −8.68728 | −1.18219 | ||||||||
\(55\) | 5.50372 | 0.742121 | ||||||||
\(56\) | −7.10200 | −0.949044 | ||||||||
\(57\) | 3.83526 | 0.507992 | ||||||||
\(58\) | 1.73344 | 0.227611 | ||||||||
\(59\) | −11.1107 | −1.44649 | −0.723243 | − | 0.690594i | \(-0.757349\pi\) | ||||
−0.723243 | + | 0.690594i | \(0.757349\pi\) | |||||||
\(60\) | 4.96795 | 0.641360 | ||||||||
\(61\) | −3.54169 | −0.453467 | −0.226734 | − | 0.973957i | \(-0.572805\pi\) | ||||
−0.226734 | + | 0.973957i | \(0.572805\pi\) | |||||||
\(62\) | −11.9474 | −1.51732 | ||||||||
\(63\) | −0.811866 | −0.102285 | ||||||||
\(64\) | 0.956800 | 0.119600 | ||||||||
\(65\) | 12.9240 | 1.60302 | ||||||||
\(66\) | −6.16929 | −0.759388 | ||||||||
\(67\) | 8.82546 | 1.07820 | 0.539101 | − | 0.842241i | \(-0.318764\pi\) | ||||
0.539101 | + | 0.842241i | \(0.318764\pi\) | |||||||
\(68\) | −2.59233 | −0.314366 | ||||||||
\(69\) | 3.13405 | 0.377295 | ||||||||
\(70\) | −19.7325 | −2.35849 | ||||||||
\(71\) | 1.32126 | 0.156805 | 0.0784025 | − | 0.996922i | \(-0.475018\pi\) | ||||
0.0784025 | + | 0.996922i | \(0.475018\pi\) | |||||||
\(72\) | 0.340206 | 0.0400936 | ||||||||
\(73\) | 1.21852 | 0.142616 | 0.0713082 | − | 0.997454i | \(-0.477283\pi\) | ||||
0.0713082 | + | 0.997454i | \(0.477283\pi\) | |||||||
\(74\) | −9.11510 | −1.05961 | ||||||||
\(75\) | −4.73101 | −0.546290 | ||||||||
\(76\) | −2.15520 | −0.247218 | ||||||||
\(77\) | 8.19415 | 0.933810 | ||||||||
\(78\) | −14.4869 | −1.64032 | ||||||||
\(79\) | −13.8652 | −1.55996 | −0.779981 | − | 0.625804i | \(-0.784771\pi\) | ||||
−0.779981 | + | 0.625804i | \(0.784771\pi\) | |||||||
\(80\) | 13.8255 | 1.54574 | ||||||||
\(81\) | −9.55273 | −1.06141 | ||||||||
\(82\) | 11.9836 | 1.32337 | ||||||||
\(83\) | 14.0747 | 1.54490 | 0.772451 | − | 0.635075i | \(-0.219031\pi\) | ||||
0.772451 | + | 0.635075i | \(0.219031\pi\) | |||||||
\(84\) | 7.39648 | 0.807023 | ||||||||
\(85\) | 7.13386 | 0.773776 | ||||||||
\(86\) | 8.53746 | 0.920618 | ||||||||
\(87\) | 1.78807 | 0.191702 | ||||||||
\(88\) | −3.43369 | −0.366033 | ||||||||
\(89\) | 7.91115 | 0.838580 | 0.419290 | − | 0.907852i | \(-0.362279\pi\) | ||||
0.419290 | + | 0.907852i | \(0.362279\pi\) | |||||||
\(90\) | 0.945244 | 0.0996374 | ||||||||
\(91\) | 19.2417 | 2.01708 | ||||||||
\(92\) | −1.76116 | −0.183614 | ||||||||
\(93\) | −12.3240 | −1.27793 | ||||||||
\(94\) | 6.99752 | 0.721739 | ||||||||
\(95\) | 5.93093 | 0.608500 | ||||||||
\(96\) | −9.32820 | −0.952055 | ||||||||
\(97\) | 17.0121 | 1.72731 | 0.863657 | − | 0.504079i | \(-0.168168\pi\) | ||||
0.863657 | + | 0.504079i | \(0.168168\pi\) | |||||||
\(98\) | −17.2445 | −1.74196 | ||||||||
\(99\) | −0.392523 | −0.0394501 | ||||||||
\(100\) | 2.65856 | 0.265856 | ||||||||
\(101\) | 1.60717 | 0.159919 | 0.0799596 | − | 0.996798i | \(-0.474521\pi\) | ||||
0.0799596 | + | 0.996798i | \(0.474521\pi\) | |||||||
\(102\) | −7.99658 | −0.791780 | ||||||||
\(103\) | 8.06634 | 0.794800 | 0.397400 | − | 0.917646i | \(-0.369913\pi\) | ||||
0.397400 | + | 0.917646i | \(0.369913\pi\) | |||||||
\(104\) | −8.06308 | −0.790650 | ||||||||
\(105\) | −20.3545 | −1.98639 | ||||||||
\(106\) | −11.9625 | −1.16190 | ||||||||
\(107\) | 12.4805 | 1.20654 | 0.603270 | − | 0.797537i | \(-0.293864\pi\) | ||||
0.603270 | + | 0.797537i | \(0.293864\pi\) | |||||||
\(108\) | 5.03564 | 0.484555 | ||||||||
\(109\) | −6.69103 | −0.640884 | −0.320442 | − | 0.947268i | \(-0.603831\pi\) | ||||
−0.320442 | + | 0.947268i | \(0.603831\pi\) | |||||||
\(110\) | −9.54033 | −0.909635 | ||||||||
\(111\) | −9.40241 | −0.892438 | ||||||||
\(112\) | 20.5840 | 1.94500 | ||||||||
\(113\) | 16.2832 | 1.53179 | 0.765897 | − | 0.642964i | \(-0.222295\pi\) | ||||
0.765897 | + | 0.642964i | \(0.222295\pi\) | |||||||
\(114\) | −6.64817 | −0.622658 | ||||||||
\(115\) | 4.84656 | 0.451944 | ||||||||
\(116\) | −1.00480 | −0.0932931 | ||||||||
\(117\) | −0.921732 | −0.0852142 | ||||||||
\(118\) | 19.2596 | 1.77299 | ||||||||
\(119\) | 10.6212 | 0.973642 | ||||||||
\(120\) | 8.52939 | 0.778623 | ||||||||
\(121\) | −7.03827 | −0.639843 | ||||||||
\(122\) | 6.13929 | 0.555825 | ||||||||
\(123\) | 12.3614 | 1.11459 | ||||||||
\(124\) | 6.92537 | 0.621917 | ||||||||
\(125\) | 6.50945 | 0.582223 | ||||||||
\(126\) | 1.40732 | 0.125374 | ||||||||
\(127\) | −1.13446 | −0.100667 | −0.0503337 | − | 0.998732i | \(-0.516028\pi\) | ||||
−0.0503337 | + | 0.998732i | \(0.516028\pi\) | |||||||
\(128\) | −12.0923 | −1.06882 | ||||||||
\(129\) | 8.80656 | 0.775375 | ||||||||
\(130\) | −22.4028 | −1.96486 | ||||||||
\(131\) | −17.6223 | −1.53967 | −0.769834 | − | 0.638244i | \(-0.779661\pi\) | ||||
−0.769834 | + | 0.638244i | \(0.779661\pi\) | |||||||
\(132\) | 3.57607 | 0.311257 | ||||||||
\(133\) | 8.83020 | 0.765675 | ||||||||
\(134\) | −15.2984 | −1.32158 | ||||||||
\(135\) | −13.8577 | −1.19268 | ||||||||
\(136\) | −4.45072 | −0.381646 | ||||||||
\(137\) | −16.1735 | −1.38180 | −0.690898 | − | 0.722952i | \(-0.742785\pi\) | ||||
−0.690898 | + | 0.722952i | \(0.742785\pi\) | |||||||
\(138\) | −5.43267 | −0.462460 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | 11.4381 | 0.966695 | ||||||||
\(141\) | 7.21808 | 0.607872 | ||||||||
\(142\) | −2.29032 | −0.192200 | ||||||||
\(143\) | 9.30303 | 0.777959 | ||||||||
\(144\) | −0.986031 | −0.0821693 | ||||||||
\(145\) | 2.76512 | 0.229630 | ||||||||
\(146\) | −2.11222 | −0.174808 | ||||||||
\(147\) | −17.7881 | −1.46713 | ||||||||
\(148\) | 5.28363 | 0.434312 | ||||||||
\(149\) | 4.67382 | 0.382895 | 0.191447 | − | 0.981503i | \(-0.438682\pi\) | ||||
0.191447 | + | 0.981503i | \(0.438682\pi\) | |||||||
\(150\) | 8.20089 | 0.669600 | ||||||||
\(151\) | 2.36916 | 0.192799 | 0.0963996 | − | 0.995343i | \(-0.469267\pi\) | ||||
0.0963996 | + | 0.995343i | \(0.469267\pi\) | |||||||
\(152\) | −3.70023 | −0.300128 | ||||||||
\(153\) | −0.508785 | −0.0411328 | ||||||||
\(154\) | −14.2040 | −1.14459 | ||||||||
\(155\) | −19.0580 | −1.53078 | ||||||||
\(156\) | 8.39742 | 0.672332 | ||||||||
\(157\) | 9.65761 | 0.770761 | 0.385381 | − | 0.922758i | \(-0.374070\pi\) | ||||
0.385381 | + | 0.922758i | \(0.374070\pi\) | |||||||
\(158\) | 24.0345 | 1.91208 | ||||||||
\(159\) | −12.3395 | −0.978589 | ||||||||
\(160\) | −14.4253 | −1.14042 | ||||||||
\(161\) | 7.21575 | 0.568681 | ||||||||
\(162\) | 16.5590 | 1.30100 | ||||||||
\(163\) | 1.40430 | 0.109994 | 0.0549968 | − | 0.998487i | \(-0.482485\pi\) | ||||
0.0549968 | + | 0.998487i | \(0.482485\pi\) | |||||||
\(164\) | −6.94640 | −0.542423 | ||||||||
\(165\) | −9.84105 | −0.766125 | ||||||||
\(166\) | −24.3976 | −1.89362 | ||||||||
\(167\) | 23.2591 | 1.79984 | 0.899922 | − | 0.436050i | \(-0.143623\pi\) | ||||
0.899922 | + | 0.436050i | \(0.143623\pi\) | |||||||
\(168\) | 12.6989 | 0.979741 | ||||||||
\(169\) | 8.84561 | 0.680432 | ||||||||
\(170\) | −12.3661 | −0.948436 | ||||||||
\(171\) | −0.422992 | −0.0323470 | ||||||||
\(172\) | −4.94880 | −0.377342 | ||||||||
\(173\) | 3.38728 | 0.257530 | 0.128765 | − | 0.991675i | \(-0.458899\pi\) | ||||
0.128765 | + | 0.991675i | \(0.458899\pi\) | |||||||
\(174\) | −3.09951 | −0.234973 | ||||||||
\(175\) | −10.8926 | −0.823400 | ||||||||
\(176\) | 9.95200 | 0.750161 | ||||||||
\(177\) | 19.8667 | 1.49327 | ||||||||
\(178\) | −13.7135 | −1.02787 | ||||||||
\(179\) | 15.7211 | 1.17505 | 0.587524 | − | 0.809207i | \(-0.300103\pi\) | ||||
0.587524 | + | 0.809207i | \(0.300103\pi\) | |||||||
\(180\) | −0.547917 | −0.0408393 | ||||||||
\(181\) | −17.1928 | −1.27793 | −0.638965 | − | 0.769236i | \(-0.720637\pi\) | ||||
−0.638965 | + | 0.769236i | \(0.720637\pi\) | |||||||
\(182\) | −33.3542 | −2.47238 | ||||||||
\(183\) | 6.33280 | 0.468134 | ||||||||
\(184\) | −3.02370 | −0.222910 | ||||||||
\(185\) | −14.5401 | −1.06901 | ||||||||
\(186\) | 21.3628 | 1.56639 | ||||||||
\(187\) | 5.13516 | 0.375520 | ||||||||
\(188\) | −4.05616 | −0.295826 | ||||||||
\(189\) | −20.6318 | −1.50075 | ||||||||
\(190\) | −10.2809 | −0.745853 | ||||||||
\(191\) | 4.86513 | 0.352028 | 0.176014 | − | 0.984388i | \(-0.443680\pi\) | ||||
0.176014 | + | 0.984388i | \(0.443680\pi\) | |||||||
\(192\) | −1.71083 | −0.123468 | ||||||||
\(193\) | −25.5427 | −1.83860 | −0.919302 | − | 0.393553i | \(-0.871246\pi\) | ||||
−0.919302 | + | 0.393553i | \(0.871246\pi\) | |||||||
\(194\) | −29.4893 | −2.11721 | ||||||||
\(195\) | −23.1090 | −1.65487 | ||||||||
\(196\) | 9.99590 | 0.713993 | ||||||||
\(197\) | −3.93826 | −0.280590 | −0.140295 | − | 0.990110i | \(-0.544805\pi\) | ||||
−0.140295 | + | 0.990110i | \(0.544805\pi\) | |||||||
\(198\) | 0.680413 | 0.0483549 | ||||||||
\(199\) | 8.92493 | 0.632671 | 0.316336 | − | 0.948647i | \(-0.397547\pi\) | ||||
0.316336 | + | 0.948647i | \(0.397547\pi\) | |||||||
\(200\) | 4.56444 | 0.322755 | ||||||||
\(201\) | −15.7806 | −1.11308 | ||||||||
\(202\) | −2.78592 | −0.196017 | ||||||||
\(203\) | 4.11682 | 0.288944 | ||||||||
\(204\) | 4.63527 | 0.324534 | ||||||||
\(205\) | 19.1159 | 1.33511 | ||||||||
\(206\) | −13.9825 | −0.974205 | ||||||||
\(207\) | −0.345655 | −0.0240247 | ||||||||
\(208\) | 23.3695 | 1.62039 | ||||||||
\(209\) | 4.26925 | 0.295310 | ||||||||
\(210\) | 35.2832 | 2.43477 | ||||||||
\(211\) | −16.7727 | −1.15468 | −0.577341 | − | 0.816503i | \(-0.695910\pi\) | ||||
−0.577341 | + | 0.816503i | \(0.695910\pi\) | |||||||
\(212\) | 6.93413 | 0.476238 | ||||||||
\(213\) | −2.36252 | −0.161877 | ||||||||
\(214\) | −21.6342 | −1.47888 | ||||||||
\(215\) | 13.6187 | 0.928785 | ||||||||
\(216\) | 8.64561 | 0.588259 | ||||||||
\(217\) | −28.3744 | −1.92618 | ||||||||
\(218\) | 11.5985 | 0.785547 | ||||||||
\(219\) | −2.17879 | −0.147229 | ||||||||
\(220\) | 5.53012 | 0.372841 | ||||||||
\(221\) | 12.0585 | 0.811143 | ||||||||
\(222\) | 16.2985 | 1.09388 | ||||||||
\(223\) | −9.42187 | −0.630935 | −0.315468 | − | 0.948936i | \(-0.602161\pi\) | ||||
−0.315468 | + | 0.948936i | \(0.602161\pi\) | |||||||
\(224\) | −21.4770 | −1.43499 | ||||||||
\(225\) | 0.521784 | 0.0347856 | ||||||||
\(226\) | −28.2258 | −1.87756 | ||||||||
\(227\) | −18.5748 | −1.23285 | −0.616426 | − | 0.787413i | \(-0.711420\pi\) | ||||
−0.616426 | + | 0.787413i | \(0.711420\pi\) | |||||||
\(228\) | 3.85366 | 0.255215 | ||||||||
\(229\) | −0.969783 | −0.0640851 | −0.0320425 | − | 0.999487i | \(-0.510201\pi\) | ||||
−0.0320425 | + | 0.999487i | \(0.510201\pi\) | |||||||
\(230\) | −8.40120 | −0.553959 | ||||||||
\(231\) | −14.6517 | −0.964014 | ||||||||
\(232\) | −1.72512 | −0.113260 | ||||||||
\(233\) | −9.93912 | −0.651134 | −0.325567 | − | 0.945519i | \(-0.605555\pi\) | ||||
−0.325567 | + | 0.945519i | \(0.605555\pi\) | |||||||
\(234\) | 1.59776 | 0.104449 | ||||||||
\(235\) | 11.1622 | 0.728142 | ||||||||
\(236\) | −11.1640 | −0.726713 | ||||||||
\(237\) | 24.7921 | 1.61042 | ||||||||
\(238\) | −18.4111 | −1.19342 | ||||||||
\(239\) | −11.8610 | −0.767227 | −0.383613 | − | 0.923494i | \(-0.625320\pi\) | ||||
−0.383613 | + | 0.923494i | \(0.625320\pi\) | |||||||
\(240\) | −24.7210 | −1.59574 | ||||||||
\(241\) | 7.98266 | 0.514208 | 0.257104 | − | 0.966384i | \(-0.417232\pi\) | ||||
0.257104 | + | 0.966384i | \(0.417232\pi\) | |||||||
\(242\) | 12.2004 | 0.784270 | ||||||||
\(243\) | 2.04619 | 0.131263 | ||||||||
\(244\) | −3.55868 | −0.227821 | ||||||||
\(245\) | −27.5079 | −1.75741 | ||||||||
\(246\) | −21.4276 | −1.36618 | ||||||||
\(247\) | 10.0252 | 0.637885 | ||||||||
\(248\) | 11.8901 | 0.755019 | ||||||||
\(249\) | −25.1666 | −1.59487 | ||||||||
\(250\) | −11.2837 | −0.713644 | ||||||||
\(251\) | 20.3390 | 1.28379 | 0.641893 | − | 0.766794i | \(-0.278149\pi\) | ||||
0.641893 | + | 0.766794i | \(0.278149\pi\) | |||||||
\(252\) | −0.815761 | −0.0513881 | ||||||||
\(253\) | 3.48869 | 0.219332 | ||||||||
\(254\) | 1.96652 | 0.123390 | ||||||||
\(255\) | −12.7559 | −0.798804 | ||||||||
\(256\) | 19.0477 | 1.19048 | ||||||||
\(257\) | 23.5156 | 1.46686 | 0.733432 | − | 0.679762i | \(-0.237917\pi\) | ||||
0.733432 | + | 0.679762i | \(0.237917\pi\) | |||||||
\(258\) | −15.2656 | −0.950395 | ||||||||
\(259\) | −21.6479 | −1.34513 | ||||||||
\(260\) | 12.9860 | 0.805355 | ||||||||
\(261\) | −0.197207 | −0.0122068 | ||||||||
\(262\) | 30.5471 | 1.88721 | ||||||||
\(263\) | −18.5188 | −1.14192 | −0.570958 | − | 0.820979i | \(-0.693428\pi\) | ||||
−0.570958 | + | 0.820979i | \(0.693428\pi\) | |||||||
\(264\) | 6.13970 | 0.377872 | ||||||||
\(265\) | −19.0821 | −1.17221 | ||||||||
\(266\) | −15.3066 | −0.938507 | ||||||||
\(267\) | −14.1457 | −0.865704 | ||||||||
\(268\) | 8.86780 | 0.541687 | ||||||||
\(269\) | 25.9852 | 1.58434 | 0.792171 | − | 0.610299i | \(-0.208951\pi\) | ||||
0.792171 | + | 0.610299i | \(0.208951\pi\) | |||||||
\(270\) | 24.0213 | 1.46189 | ||||||||
\(271\) | −20.3772 | −1.23783 | −0.618913 | − | 0.785459i | \(-0.712427\pi\) | ||||
−0.618913 | + | 0.785459i | \(0.712427\pi\) | |||||||
\(272\) | 12.8997 | 0.782159 | ||||||||
\(273\) | −34.4056 | −2.08232 | ||||||||
\(274\) | 28.0357 | 1.69370 | ||||||||
\(275\) | −5.26636 | −0.317574 | ||||||||
\(276\) | 3.14908 | 0.189553 | ||||||||
\(277\) | 1.82620 | 0.109726 | 0.0548628 | − | 0.998494i | \(-0.482528\pi\) | ||||
0.0548628 | + | 0.998494i | \(0.482528\pi\) | |||||||
\(278\) | 1.73344 | 0.103965 | ||||||||
\(279\) | 1.35921 | 0.0813739 | ||||||||
\(280\) | 19.6378 | 1.17359 | ||||||||
\(281\) | 3.64692 | 0.217557 | 0.108778 | − | 0.994066i | \(-0.465306\pi\) | ||||
0.108778 | + | 0.994066i | \(0.465306\pi\) | |||||||
\(282\) | −12.5121 | −0.745083 | ||||||||
\(283\) | −1.75521 | −0.104337 | −0.0521683 | − | 0.998638i | \(-0.516613\pi\) | ||||
−0.0521683 | + | 0.998638i | \(0.516613\pi\) | |||||||
\(284\) | 1.32760 | 0.0787787 | ||||||||
\(285\) | −10.6049 | −0.628182 | ||||||||
\(286\) | −16.1262 | −0.953563 | ||||||||
\(287\) | 28.4605 | 1.67997 | ||||||||
\(288\) | 1.02881 | 0.0606232 | ||||||||
\(289\) | −10.3439 | −0.608462 | ||||||||
\(290\) | −4.79315 | −0.281463 | ||||||||
\(291\) | −30.4188 | −1.78318 | ||||||||
\(292\) | 1.22436 | 0.0716503 | ||||||||
\(293\) | 10.6127 | 0.620003 | 0.310002 | − | 0.950736i | \(-0.399670\pi\) | ||||
0.310002 | + | 0.950736i | \(0.399670\pi\) | |||||||
\(294\) | 30.8345 | 1.79830 | ||||||||
\(295\) | 30.7223 | 1.78872 | ||||||||
\(296\) | 9.07137 | 0.527263 | ||||||||
\(297\) | −9.97514 | −0.578816 | ||||||||
\(298\) | −8.10177 | −0.469323 | ||||||||
\(299\) | 8.19224 | 0.473769 | ||||||||
\(300\) | −4.75370 | −0.274455 | ||||||||
\(301\) | 20.2760 | 1.16869 | ||||||||
\(302\) | −4.10678 | −0.236319 | ||||||||
\(303\) | −2.87373 | −0.165092 | ||||||||
\(304\) | 10.7245 | 0.615092 | ||||||||
\(305\) | 9.79319 | 0.560756 | ||||||||
\(306\) | 0.881946 | 0.0504175 | ||||||||
\(307\) | −0.258382 | −0.0147467 | −0.00737333 | − | 0.999973i | \(-0.502347\pi\) | ||||
−0.00737333 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(308\) | 8.23346 | 0.469145 | ||||||||
\(309\) | −14.4232 | −0.820507 | ||||||||
\(310\) | 33.0359 | 1.87631 | ||||||||
\(311\) | 24.4312 | 1.38536 | 0.692682 | − | 0.721243i | \(-0.256429\pi\) | ||||
0.692682 | + | 0.721243i | \(0.256429\pi\) | |||||||
\(312\) | 14.4174 | 0.816224 | ||||||||
\(313\) | 10.9772 | 0.620467 | 0.310234 | − | 0.950660i | \(-0.399593\pi\) | ||||
0.310234 | + | 0.950660i | \(0.399593\pi\) | |||||||
\(314\) | −16.7408 | −0.944741 | ||||||||
\(315\) | 2.24490 | 0.126486 | ||||||||
\(316\) | −13.9318 | −0.783723 | ||||||||
\(317\) | −26.5903 | −1.49346 | −0.746729 | − | 0.665129i | \(-0.768377\pi\) | ||||
−0.746729 | + | 0.665129i | \(0.768377\pi\) | |||||||
\(318\) | 21.3898 | 1.19948 | ||||||||
\(319\) | 1.99041 | 0.111442 | ||||||||
\(320\) | −2.64566 | −0.147897 | ||||||||
\(321\) | −22.3161 | −1.24556 | ||||||||
\(322\) | −12.5080 | −0.697046 | ||||||||
\(323\) | 5.53376 | 0.307907 | ||||||||
\(324\) | −9.59856 | −0.533253 | ||||||||
\(325\) | −12.3666 | −0.685976 | ||||||||
\(326\) | −2.43427 | −0.134822 | ||||||||
\(327\) | 11.9641 | 0.661614 | ||||||||
\(328\) | −11.9262 | −0.658512 | ||||||||
\(329\) | 16.6187 | 0.916220 | ||||||||
\(330\) | 17.0588 | 0.939057 | ||||||||
\(331\) | −23.1894 | −1.27461 | −0.637304 | − | 0.770613i | \(-0.719950\pi\) | ||||
−0.637304 | + | 0.770613i | \(0.719950\pi\) | |||||||
\(332\) | 14.1422 | 0.776156 | ||||||||
\(333\) | 1.03700 | 0.0568270 | ||||||||
\(334\) | −40.3182 | −2.20611 | ||||||||
\(335\) | −24.4034 | −1.33330 | ||||||||
\(336\) | −36.8057 | −2.00791 | ||||||||
\(337\) | 12.7774 | 0.696029 | 0.348015 | − | 0.937489i | \(-0.386856\pi\) | ||||
0.348015 | + | 0.937489i | \(0.386856\pi\) | |||||||
\(338\) | −15.3333 | −0.834021 | ||||||||
\(339\) | −29.1155 | −1.58134 | ||||||||
\(340\) | 7.16809 | 0.388744 | ||||||||
\(341\) | −13.7185 | −0.742899 | ||||||||
\(342\) | 0.733229 | 0.0396485 | ||||||||
\(343\) | −12.1371 | −0.655341 | ||||||||
\(344\) | −8.49650 | −0.458101 | ||||||||
\(345\) | −8.66601 | −0.466562 | ||||||||
\(346\) | −5.87164 | −0.315661 | ||||||||
\(347\) | −16.1604 | −0.867536 | −0.433768 | − | 0.901025i | \(-0.642816\pi\) | ||||
−0.433768 | + | 0.901025i | \(0.642816\pi\) | |||||||
\(348\) | 1.79665 | 0.0963106 | ||||||||
\(349\) | −27.3766 | −1.46544 | −0.732719 | − | 0.680531i | \(-0.761749\pi\) | ||||
−0.732719 | + | 0.680531i | \(0.761749\pi\) | |||||||
\(350\) | 18.8815 | 1.00926 | ||||||||
\(351\) | −23.4239 | −1.25027 | ||||||||
\(352\) | −10.3838 | −0.553457 | ||||||||
\(353\) | −8.09900 | −0.431066 | −0.215533 | − | 0.976497i | \(-0.569149\pi\) | ||||
−0.215533 | + | 0.976497i | \(0.569149\pi\) | |||||||
\(354\) | −34.4376 | −1.83034 | ||||||||
\(355\) | −3.65345 | −0.193905 | ||||||||
\(356\) | 7.94910 | 0.421302 | ||||||||
\(357\) | −18.9915 | −1.00513 | ||||||||
\(358\) | −27.2515 | −1.44028 | ||||||||
\(359\) | 4.45481 | 0.235116 | 0.117558 | − | 0.993066i | \(-0.462493\pi\) | ||||
0.117558 | + | 0.993066i | \(0.462493\pi\) | |||||||
\(360\) | −0.940709 | −0.0495797 | ||||||||
\(361\) | −14.3994 | −0.757861 | ||||||||
\(362\) | 29.8026 | 1.56639 | ||||||||
\(363\) | 12.5849 | 0.660538 | ||||||||
\(364\) | 19.3340 | 1.01338 | ||||||||
\(365\) | −3.36934 | −0.176359 | ||||||||
\(366\) | −10.9775 | −0.573803 | ||||||||
\(367\) | −1.13040 | −0.0590064 | −0.0295032 | − | 0.999565i | \(-0.509393\pi\) | ||||
−0.0295032 | + | 0.999565i | \(0.509393\pi\) | |||||||
\(368\) | 8.76372 | 0.456840 | ||||||||
\(369\) | −1.36334 | −0.0709726 | ||||||||
\(370\) | 25.2043 | 1.31031 | ||||||||
\(371\) | −28.4102 | −1.47499 | ||||||||
\(372\) | −12.3831 | −0.642033 | ||||||||
\(373\) | −21.0857 | −1.09178 | −0.545889 | − | 0.837857i | \(-0.683808\pi\) | ||||
−0.545889 | + | 0.837857i | \(0.683808\pi\) | |||||||
\(374\) | −8.90147 | −0.460284 | ||||||||
\(375\) | −11.6394 | −0.601055 | ||||||||
\(376\) | −6.96395 | −0.359138 | ||||||||
\(377\) | 4.67393 | 0.240720 | ||||||||
\(378\) | 35.7639 | 1.83950 | ||||||||
\(379\) | 35.6204 | 1.82970 | 0.914848 | − | 0.403798i | \(-0.132310\pi\) | ||||
0.914848 | + | 0.403798i | \(0.132310\pi\) | |||||||
\(380\) | 5.95938 | 0.305710 | ||||||||
\(381\) | 2.02850 | 0.103923 | ||||||||
\(382\) | −8.43339 | −0.431490 | ||||||||
\(383\) | −1.78014 | −0.0909608 | −0.0454804 | − | 0.998965i | \(-0.514482\pi\) | ||||
−0.0454804 | + | 0.998965i | \(0.514482\pi\) | |||||||
\(384\) | 21.6220 | 1.10339 | ||||||||
\(385\) | −22.6578 | −1.15475 | ||||||||
\(386\) | 44.2766 | 2.25362 | ||||||||
\(387\) | −0.971279 | −0.0493729 | ||||||||
\(388\) | 17.0937 | 0.867801 | ||||||||
\(389\) | 1.43693 | 0.0728552 | 0.0364276 | − | 0.999336i | \(-0.488402\pi\) | ||||
0.0364276 | + | 0.999336i | \(0.488402\pi\) | |||||||
\(390\) | 40.0579 | 2.02841 | ||||||||
\(391\) | 4.52201 | 0.228688 | ||||||||
\(392\) | 17.1618 | 0.866801 | ||||||||
\(393\) | 31.5100 | 1.58947 | ||||||||
\(394\) | 6.82673 | 0.343926 | ||||||||
\(395\) | 38.3390 | 1.92904 | ||||||||
\(396\) | −0.394406 | −0.0198197 | ||||||||
\(397\) | −38.4081 | −1.92765 | −0.963823 | − | 0.266543i | \(-0.914119\pi\) | ||||
−0.963823 | + | 0.266543i | \(0.914119\pi\) | |||||||
\(398\) | −15.4708 | −0.775480 | ||||||||
\(399\) | −15.7890 | −0.790441 | ||||||||
\(400\) | −13.2293 | −0.661464 | ||||||||
\(401\) | −15.8959 | −0.793804 | −0.396902 | − | 0.917861i | \(-0.629915\pi\) | ||||
−0.396902 | + | 0.917861i | \(0.629915\pi\) | |||||||
\(402\) | 27.3546 | 1.36432 | ||||||||
\(403\) | −32.2142 | −1.60470 | ||||||||
\(404\) | 1.61488 | 0.0803432 | ||||||||
\(405\) | 26.4144 | 1.31254 | ||||||||
\(406\) | −7.13623 | −0.354165 | ||||||||
\(407\) | −10.4664 | −0.518799 | ||||||||
\(408\) | 7.95822 | 0.393991 | ||||||||
\(409\) | −6.52618 | −0.322699 | −0.161349 | − | 0.986897i | \(-0.551585\pi\) | ||||
−0.161349 | + | 0.986897i | \(0.551585\pi\) | |||||||
\(410\) | −33.1362 | −1.63648 | ||||||||
\(411\) | 28.9194 | 1.42649 | ||||||||
\(412\) | 8.10503 | 0.399306 | ||||||||
\(413\) | 45.7406 | 2.25075 | ||||||||
\(414\) | 0.599171 | 0.0294476 | ||||||||
\(415\) | −38.9182 | −1.91042 | ||||||||
\(416\) | −24.3834 | −1.19549 | ||||||||
\(417\) | 1.78807 | 0.0875623 | ||||||||
\(418\) | −7.40047 | −0.361969 | ||||||||
\(419\) | 17.4463 | 0.852308 | 0.426154 | − | 0.904651i | \(-0.359868\pi\) | ||||
0.426154 | + | 0.904651i | \(0.359868\pi\) | |||||||
\(420\) | −20.4521 | −0.997962 | ||||||||
\(421\) | 21.5524 | 1.05040 | 0.525201 | − | 0.850978i | \(-0.323990\pi\) | ||||
0.525201 | + | 0.850978i | \(0.323990\pi\) | |||||||
\(422\) | 29.0744 | 1.41532 | ||||||||
\(423\) | −0.796084 | −0.0387069 | ||||||||
\(424\) | 11.9051 | 0.578162 | ||||||||
\(425\) | −6.82621 | −0.331120 | ||||||||
\(426\) | 4.09527 | 0.198416 | ||||||||
\(427\) | 14.5805 | 0.705599 | ||||||||
\(428\) | 12.5404 | 0.606164 | ||||||||
\(429\) | −16.6345 | −0.803122 | ||||||||
\(430\) | −23.6071 | −1.13843 | ||||||||
\(431\) | −17.7399 | −0.854501 | −0.427250 | − | 0.904133i | \(-0.640518\pi\) | ||||
−0.427250 | + | 0.904133i | \(0.640518\pi\) | |||||||
\(432\) | −25.0579 | −1.20560 | ||||||||
\(433\) | −33.3143 | −1.60098 | −0.800492 | − | 0.599344i | \(-0.795428\pi\) | ||||
−0.800492 | + | 0.599344i | \(0.795428\pi\) | |||||||
\(434\) | 49.1851 | 2.36096 | ||||||||
\(435\) | −4.94423 | −0.237058 | ||||||||
\(436\) | −6.72313 | −0.321979 | ||||||||
\(437\) | 3.75949 | 0.179841 | ||||||||
\(438\) | 3.77680 | 0.180462 | ||||||||
\(439\) | 39.5485 | 1.88754 | 0.943772 | − | 0.330596i | \(-0.107250\pi\) | ||||
0.943772 | + | 0.330596i | \(0.107250\pi\) | |||||||
\(440\) | 9.49456 | 0.452636 | ||||||||
\(441\) | 1.96185 | 0.0934215 | ||||||||
\(442\) | −20.9026 | −0.994237 | ||||||||
\(443\) | 35.8764 | 1.70454 | 0.852269 | − | 0.523104i | \(-0.175226\pi\) | ||||
0.852269 | + | 0.523104i | \(0.175226\pi\) | |||||||
\(444\) | −9.44752 | −0.448360 | ||||||||
\(445\) | −21.8753 | −1.03699 | ||||||||
\(446\) | 16.3322 | 0.773352 | ||||||||
\(447\) | −8.35714 | −0.395279 | ||||||||
\(448\) | −3.93897 | −0.186099 | ||||||||
\(449\) | −28.0027 | −1.32153 | −0.660765 | − | 0.750592i | \(-0.729768\pi\) | ||||
−0.660765 | + | 0.750592i | \(0.729768\pi\) | |||||||
\(450\) | −0.904479 | −0.0426376 | ||||||||
\(451\) | 13.7602 | 0.647941 | ||||||||
\(452\) | 16.3613 | 0.769571 | ||||||||
\(453\) | −4.23623 | −0.199035 | ||||||||
\(454\) | 32.1982 | 1.51114 | ||||||||
\(455\) | −53.2056 | −2.49431 | ||||||||
\(456\) | 6.61628 | 0.309835 | ||||||||
\(457\) | −17.0996 | −0.799885 | −0.399942 | − | 0.916540i | \(-0.630970\pi\) | ||||
−0.399942 | + | 0.916540i | \(0.630970\pi\) | |||||||
\(458\) | 1.68106 | 0.0785506 | ||||||||
\(459\) | −12.9297 | −0.603506 | ||||||||
\(460\) | 4.86981 | 0.227056 | ||||||||
\(461\) | 16.1459 | 0.751990 | 0.375995 | − | 0.926622i | \(-0.377301\pi\) | ||||
0.375995 | + | 0.926622i | \(0.377301\pi\) | |||||||
\(462\) | 25.3979 | 1.18161 | ||||||||
\(463\) | −10.3594 | −0.481444 | −0.240722 | − | 0.970594i | \(-0.577384\pi\) | ||||
−0.240722 | + | 0.970594i | \(0.577384\pi\) | |||||||
\(464\) | 4.99998 | 0.232118 | ||||||||
\(465\) | 34.0772 | 1.58029 | ||||||||
\(466\) | 17.2288 | 0.798110 | ||||||||
\(467\) | 10.9627 | 0.507291 | 0.253646 | − | 0.967297i | \(-0.418370\pi\) | ||||
0.253646 | + | 0.967297i | \(0.418370\pi\) | |||||||
\(468\) | −0.926154 | −0.0428115 | ||||||||
\(469\) | −36.3328 | −1.67769 | ||||||||
\(470\) | −19.3489 | −0.892500 | ||||||||
\(471\) | −17.2685 | −0.795692 | ||||||||
\(472\) | −19.1672 | −0.882243 | ||||||||
\(473\) | 9.80310 | 0.450747 | ||||||||
\(474\) | −42.9754 | −1.97393 | ||||||||
\(475\) | −5.67515 | −0.260394 | ||||||||
\(476\) | 10.6721 | 0.489157 | ||||||||
\(477\) | 1.36093 | 0.0623127 | ||||||||
\(478\) | 20.5603 | 0.940408 | ||||||||
\(479\) | 30.5134 | 1.39419 | 0.697096 | − | 0.716978i | \(-0.254475\pi\) | ||||
0.697096 | + | 0.716978i | \(0.254475\pi\) | |||||||
\(480\) | 25.7936 | 1.17731 | ||||||||
\(481\) | −24.5774 | −1.12063 | ||||||||
\(482\) | −13.8374 | −0.630277 | ||||||||
\(483\) | −12.9023 | −0.587075 | ||||||||
\(484\) | −7.07203 | −0.321456 | ||||||||
\(485\) | −47.0404 | −2.13599 | ||||||||
\(486\) | −3.54693 | −0.160892 | ||||||||
\(487\) | 12.1141 | 0.548942 | 0.274471 | − | 0.961595i | \(-0.411497\pi\) | ||||
0.274471 | + | 0.961595i | \(0.411497\pi\) | |||||||
\(488\) | −6.10984 | −0.276579 | ||||||||
\(489\) | −2.51100 | −0.113551 | ||||||||
\(490\) | 47.6831 | 2.15410 | ||||||||
\(491\) | 22.9920 | 1.03762 | 0.518808 | − | 0.854891i | \(-0.326376\pi\) | ||||
0.518808 | + | 0.854891i | \(0.326376\pi\) | |||||||
\(492\) | 12.4207 | 0.559967 | ||||||||
\(493\) | 2.57995 | 0.116195 | ||||||||
\(494\) | −17.3780 | −0.781871 | ||||||||
\(495\) | 1.08537 | 0.0487839 | ||||||||
\(496\) | −34.4614 | −1.54736 | ||||||||
\(497\) | −5.43940 | −0.243990 | ||||||||
\(498\) | 43.6247 | 1.95487 | ||||||||
\(499\) | 1.13345 | 0.0507403 | 0.0253702 | − | 0.999678i | \(-0.491924\pi\) | ||||
0.0253702 | + | 0.999678i | \(0.491924\pi\) | |||||||
\(500\) | 6.54068 | 0.292508 | ||||||||
\(501\) | −41.5890 | −1.85806 | ||||||||
\(502\) | −35.2564 | −1.57357 | ||||||||
\(503\) | −11.3333 | −0.505329 | −0.252664 | − | 0.967554i | \(-0.581307\pi\) | ||||
−0.252664 | + | 0.967554i | \(0.581307\pi\) | |||||||
\(504\) | −1.40056 | −0.0623861 | ||||||||
\(505\) | −4.44401 | −0.197756 | ||||||||
\(506\) | −6.04742 | −0.268841 | ||||||||
\(507\) | −15.8166 | −0.702440 | ||||||||
\(508\) | −1.13991 | −0.0505751 | ||||||||
\(509\) | 31.3002 | 1.38735 | 0.693677 | − | 0.720286i | \(-0.255989\pi\) | ||||
0.693677 | + | 0.720286i | \(0.255989\pi\) | |||||||
\(510\) | 22.1115 | 0.979113 | ||||||||
\(511\) | −5.01640 | −0.221913 | ||||||||
\(512\) | −8.83326 | −0.390378 | ||||||||
\(513\) | −10.7494 | −0.474599 | ||||||||
\(514\) | −40.7628 | −1.79797 | ||||||||
\(515\) | −22.3044 | −0.982847 | ||||||||
\(516\) | 8.84881 | 0.389547 | ||||||||
\(517\) | 8.03487 | 0.353373 | ||||||||
\(518\) | 37.5252 | 1.64876 | ||||||||
\(519\) | −6.05671 | −0.265860 | ||||||||
\(520\) | 22.2954 | 0.977716 | ||||||||
\(521\) | 25.8744 | 1.13358 | 0.566788 | − | 0.823863i | \(-0.308186\pi\) | ||||
0.566788 | + | 0.823863i | \(0.308186\pi\) | |||||||
\(522\) | 0.341846 | 0.0149622 | ||||||||
\(523\) | −15.6465 | −0.684173 | −0.342086 | − | 0.939668i | \(-0.611134\pi\) | ||||
−0.342086 | + | 0.939668i | \(0.611134\pi\) | |||||||
\(524\) | −17.7068 | −0.773527 | ||||||||
\(525\) | 19.4767 | 0.850032 | ||||||||
\(526\) | 32.1011 | 1.39967 | ||||||||
\(527\) | −17.7818 | −0.774588 | ||||||||
\(528\) | −17.7949 | −0.774424 | ||||||||
\(529\) | −19.9279 | −0.866429 | ||||||||
\(530\) | 33.0776 | 1.43680 | ||||||||
\(531\) | −2.19110 | −0.0950858 | ||||||||
\(532\) | 8.87256 | 0.384674 | ||||||||
\(533\) | 32.3120 | 1.39959 | ||||||||
\(534\) | 24.5207 | 1.06111 | ||||||||
\(535\) | −34.5101 | −1.49200 | ||||||||
\(536\) | 15.2250 | 0.657618 | ||||||||
\(537\) | −28.1104 | −1.21305 | ||||||||
\(538\) | −45.0436 | −1.94197 | ||||||||
\(539\) | −19.8009 | −0.852887 | ||||||||
\(540\) | −13.9241 | −0.599199 | ||||||||
\(541\) | −29.2020 | −1.25549 | −0.627746 | − | 0.778418i | \(-0.716022\pi\) | ||||
−0.627746 | + | 0.778418i | \(0.716022\pi\) | |||||||
\(542\) | 35.3226 | 1.51723 | ||||||||
\(543\) | 30.7420 | 1.31926 | ||||||||
\(544\) | −13.4593 | −0.577064 | ||||||||
\(545\) | 18.5015 | 0.792516 | ||||||||
\(546\) | 59.6398 | 2.55235 | ||||||||
\(547\) | 4.68008 | 0.200106 | 0.100053 | − | 0.994982i | \(-0.468099\pi\) | ||||
0.100053 | + | 0.994982i | \(0.468099\pi\) | |||||||
\(548\) | −16.2511 | −0.694213 | ||||||||
\(549\) | −0.698447 | −0.0298090 | ||||||||
\(550\) | 9.12890 | 0.389258 | ||||||||
\(551\) | 2.14491 | 0.0913762 | ||||||||
\(552\) | 5.40661 | 0.230120 | ||||||||
\(553\) | 57.0806 | 2.42732 | ||||||||
\(554\) | −3.16560 | −0.134493 | ||||||||
\(555\) | 25.9988 | 1.10359 | ||||||||
\(556\) | −1.00480 | −0.0426129 | ||||||||
\(557\) | −3.30413 | −0.140001 | −0.0700003 | − | 0.997547i | \(-0.522300\pi\) | ||||
−0.0700003 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(558\) | −2.35611 | −0.0997420 | ||||||||
\(559\) | 23.0199 | 0.973637 | ||||||||
\(560\) | −56.9171 | −2.40519 | ||||||||
\(561\) | −9.18204 | −0.387666 | ||||||||
\(562\) | −6.32170 | −0.266665 | ||||||||
\(563\) | 12.0632 | 0.508404 | 0.254202 | − | 0.967151i | \(-0.418187\pi\) | ||||
0.254202 | + | 0.967151i | \(0.418187\pi\) | |||||||
\(564\) | 7.25271 | 0.305394 | ||||||||
\(565\) | −45.0249 | −1.89421 | ||||||||
\(566\) | 3.04255 | 0.127888 | ||||||||
\(567\) | 39.3268 | 1.65157 | ||||||||
\(568\) | 2.27934 | 0.0956388 | ||||||||
\(569\) | −40.9608 | −1.71717 | −0.858584 | − | 0.512673i | \(-0.828655\pi\) | ||||
−0.858584 | + | 0.512673i | \(0.828655\pi\) | |||||||
\(570\) | 18.3830 | 0.769978 | ||||||||
\(571\) | 2.49342 | 0.104346 | 0.0521731 | − | 0.998638i | \(-0.483385\pi\) | ||||
0.0521731 | + | 0.998638i | \(0.483385\pi\) | |||||||
\(572\) | 9.34767 | 0.390846 | ||||||||
\(573\) | −8.69921 | −0.363415 | ||||||||
\(574\) | −49.3344 | −2.05918 | ||||||||
\(575\) | −4.63755 | −0.193399 | ||||||||
\(576\) | 0.188688 | 0.00786199 | ||||||||
\(577\) | 25.4492 | 1.05946 | 0.529732 | − | 0.848165i | \(-0.322292\pi\) | ||||
0.529732 | + | 0.848165i | \(0.322292\pi\) | |||||||
\(578\) | 17.9304 | 0.745806 | ||||||||
\(579\) | 45.6722 | 1.89807 | ||||||||
\(580\) | 2.77838 | 0.115366 | ||||||||
\(581\) | −57.9430 | −2.40388 | ||||||||
\(582\) | 52.7291 | 2.18569 | ||||||||
\(583\) | −13.7359 | −0.568881 | ||||||||
\(584\) | 2.10208 | 0.0869848 | ||||||||
\(585\) | 2.54870 | 0.105376 | ||||||||
\(586\) | −18.3965 | −0.759953 | ||||||||
\(587\) | 29.2319 | 1.20653 | 0.603264 | − | 0.797542i | \(-0.293867\pi\) | ||||
0.603264 | + | 0.797542i | \(0.293867\pi\) | |||||||
\(588\) | −17.8734 | −0.737087 | ||||||||
\(589\) | −14.7834 | −0.609139 | ||||||||
\(590\) | −53.2551 | −2.19248 | ||||||||
\(591\) | 7.04191 | 0.289665 | ||||||||
\(592\) | −26.2919 | −1.08059 | ||||||||
\(593\) | 28.0472 | 1.15176 | 0.575880 | − | 0.817534i | \(-0.304659\pi\) | ||||
0.575880 | + | 0.817534i | \(0.304659\pi\) | |||||||
\(594\) | 17.2913 | 0.709469 | ||||||||
\(595\) | −29.3688 | −1.20400 | ||||||||
\(596\) | 4.69625 | 0.192366 | ||||||||
\(597\) | −15.9584 | −0.653135 | ||||||||
\(598\) | −14.2007 | −0.580710 | ||||||||
\(599\) | 24.6296 | 1.00634 | 0.503169 | − | 0.864188i | \(-0.332167\pi\) | ||||
0.503169 | + | 0.864188i | \(0.332167\pi\) | |||||||
\(600\) | −8.16155 | −0.333194 | ||||||||
\(601\) | −35.0948 | −1.43155 | −0.715774 | − | 0.698332i | \(-0.753926\pi\) | ||||
−0.715774 | + | 0.698332i | \(0.753926\pi\) | |||||||
\(602\) | −35.1471 | −1.43249 | ||||||||
\(603\) | 1.74044 | 0.0708763 | ||||||||
\(604\) | 2.38052 | 0.0968621 | ||||||||
\(605\) | 19.4616 | 0.791228 | ||||||||
\(606\) | 4.98143 | 0.202357 | ||||||||
\(607\) | 14.8389 | 0.602293 | 0.301147 | − | 0.953578i | \(-0.402631\pi\) | ||||
0.301147 | + | 0.953578i | \(0.402631\pi\) | |||||||
\(608\) | −11.1898 | −0.453805 | ||||||||
\(609\) | −7.36117 | −0.298290 | ||||||||
\(610\) | −16.9759 | −0.687332 | ||||||||
\(611\) | 18.8677 | 0.763304 | ||||||||
\(612\) | −0.511226 | −0.0206651 | ||||||||
\(613\) | 27.5300 | 1.11193 | 0.555963 | − | 0.831207i | \(-0.312350\pi\) | ||||
0.555963 | + | 0.831207i | \(0.312350\pi\) | |||||||
\(614\) | 0.447889 | 0.0180753 | ||||||||
\(615\) | −34.1806 | −1.37830 | ||||||||
\(616\) | 14.1359 | 0.569551 | ||||||||
\(617\) | −27.9004 | −1.12323 | −0.561613 | − | 0.827400i | \(-0.689819\pi\) | ||||
−0.561613 | + | 0.827400i | \(0.689819\pi\) | |||||||
\(618\) | 25.0017 | 1.00572 | ||||||||
\(619\) | 16.9797 | 0.682470 | 0.341235 | − | 0.939978i | \(-0.389155\pi\) | ||||
0.341235 | + | 0.939978i | \(0.389155\pi\) | |||||||
\(620\) | −19.1495 | −0.769061 | ||||||||
\(621\) | −8.78409 | −0.352493 | ||||||||
\(622\) | −42.3498 | −1.69807 | ||||||||
\(623\) | −32.5688 | −1.30484 | ||||||||
\(624\) | −41.7865 | −1.67280 | ||||||||
\(625\) | −31.2287 | −1.24915 | ||||||||
\(626\) | −19.0282 | −0.760521 | ||||||||
\(627\) | −7.63373 | −0.304862 | ||||||||
\(628\) | 9.70395 | 0.387230 | ||||||||
\(629\) | −13.5664 | −0.540929 | ||||||||
\(630\) | −3.89139 | −0.155037 | ||||||||
\(631\) | 0.523279 | 0.0208314 | 0.0104157 | − | 0.999946i | \(-0.496685\pi\) | ||||
0.0104157 | + | 0.999946i | \(0.496685\pi\) | |||||||
\(632\) | −23.9192 | −0.951454 | ||||||||
\(633\) | 29.9909 | 1.19203 | ||||||||
\(634\) | 46.0925 | 1.83057 | ||||||||
\(635\) | 3.13692 | 0.124485 | ||||||||
\(636\) | −12.3987 | −0.491642 | ||||||||
\(637\) | −46.4971 | −1.84228 | ||||||||
\(638\) | −3.45025 | −0.136597 | ||||||||
\(639\) | 0.260563 | 0.0103077 | ||||||||
\(640\) | 33.4367 | 1.32170 | ||||||||
\(641\) | −13.3609 | −0.527726 | −0.263863 | − | 0.964560i | \(-0.584997\pi\) | ||||
−0.263863 | + | 0.964560i | \(0.584997\pi\) | |||||||
\(642\) | 38.6836 | 1.52672 | ||||||||
\(643\) | −9.81732 | −0.387157 | −0.193579 | − | 0.981085i | \(-0.562009\pi\) | ||||
−0.193579 | + | 0.981085i | \(0.562009\pi\) | |||||||
\(644\) | 7.25037 | 0.285705 | ||||||||
\(645\) | −24.3512 | −0.958826 | ||||||||
\(646\) | −9.59242 | −0.377409 | ||||||||
\(647\) | 6.90779 | 0.271573 | 0.135787 | − | 0.990738i | \(-0.456644\pi\) | ||||
0.135787 | + | 0.990738i | \(0.456644\pi\) | |||||||
\(648\) | −16.4796 | −0.647380 | ||||||||
\(649\) | 22.1148 | 0.868081 | ||||||||
\(650\) | 21.4367 | 0.840817 | ||||||||
\(651\) | 50.7355 | 1.98848 | ||||||||
\(652\) | 1.41104 | 0.0552607 | ||||||||
\(653\) | 13.6257 | 0.533214 | 0.266607 | − | 0.963805i | \(-0.414097\pi\) | ||||
0.266607 | + | 0.963805i | \(0.414097\pi\) | |||||||
\(654\) | −20.7389 | −0.810956 | ||||||||
\(655\) | 48.7277 | 1.90395 | ||||||||
\(656\) | 34.5660 | 1.34958 | ||||||||
\(657\) | 0.240300 | 0.00937499 | ||||||||
\(658\) | −28.8075 | −1.12303 | ||||||||
\(659\) | −13.6298 | −0.530942 | −0.265471 | − | 0.964119i | \(-0.585527\pi\) | ||||
−0.265471 | + | 0.964119i | \(0.585527\pi\) | |||||||
\(660\) | −9.88826 | −0.384900 | ||||||||
\(661\) | 29.9549 | 1.16511 | 0.582556 | − | 0.812791i | \(-0.302053\pi\) | ||||
0.582556 | + | 0.812791i | \(0.302053\pi\) | |||||||
\(662\) | 40.1974 | 1.56232 | ||||||||
\(663\) | −21.5615 | −0.837379 | ||||||||
\(664\) | 24.2806 | 0.942269 | ||||||||
\(665\) | −24.4165 | −0.946832 | ||||||||
\(666\) | −1.79756 | −0.0696542 | ||||||||
\(667\) | 1.75275 | 0.0678668 | ||||||||
\(668\) | 23.3707 | 0.904240 | ||||||||
\(669\) | 16.8470 | 0.651343 | ||||||||
\(670\) | 42.3017 | 1.63426 | ||||||||
\(671\) | 7.04942 | 0.272140 | ||||||||
\(672\) | 38.4025 | 1.48141 | ||||||||
\(673\) | −10.3738 | −0.399882 | −0.199941 | − | 0.979808i | \(-0.564075\pi\) | ||||
−0.199941 | + | 0.979808i | \(0.564075\pi\) | |||||||
\(674\) | −22.1488 | −0.853139 | ||||||||
\(675\) | 13.2600 | 0.510379 | ||||||||
\(676\) | 8.88805 | 0.341848 | ||||||||
\(677\) | −12.4111 | −0.476997 | −0.238498 | − | 0.971143i | \(-0.576655\pi\) | ||||
−0.238498 | + | 0.971143i | \(0.576655\pi\) | |||||||
\(678\) | 50.4699 | 1.93828 | ||||||||
\(679\) | −70.0356 | −2.68772 | ||||||||
\(680\) | 12.3068 | 0.471943 | ||||||||
\(681\) | 33.2131 | 1.27273 | ||||||||
\(682\) | 23.7802 | 0.910590 | ||||||||
\(683\) | 37.1084 | 1.41991 | 0.709956 | − | 0.704246i | \(-0.248715\pi\) | ||||
0.709956 | + | 0.704246i | \(0.248715\pi\) | |||||||
\(684\) | −0.425021 | −0.0162511 | ||||||||
\(685\) | 44.7216 | 1.70873 | ||||||||
\(686\) | 21.0388 | 0.803267 | ||||||||
\(687\) | 1.73404 | 0.0661579 | ||||||||
\(688\) | 24.6257 | 0.938847 | ||||||||
\(689\) | −32.2549 | −1.22881 | ||||||||
\(690\) | 15.0220 | 0.571876 | ||||||||
\(691\) | 15.0165 | 0.571253 | 0.285627 | − | 0.958341i | \(-0.407798\pi\) | ||||
0.285627 | + | 0.958341i | \(0.407798\pi\) | |||||||
\(692\) | 3.40353 | 0.129383 | ||||||||
\(693\) | 1.61595 | 0.0613847 | ||||||||
\(694\) | 28.0130 | 1.06336 | ||||||||
\(695\) | 2.76512 | 0.104887 | ||||||||
\(696\) | 3.08464 | 0.116923 | ||||||||
\(697\) | 17.8358 | 0.675579 | ||||||||
\(698\) | 47.4556 | 1.79622 | ||||||||
\(699\) | 17.7719 | 0.672194 | ||||||||
\(700\) | −10.9448 | −0.413675 | ||||||||
\(701\) | −32.5487 | −1.22935 | −0.614673 | − | 0.788782i | \(-0.710712\pi\) | ||||
−0.614673 | + | 0.788782i | \(0.710712\pi\) | |||||||
\(702\) | 40.6037 | 1.53249 | ||||||||
\(703\) | −11.2788 | −0.425388 | ||||||||
\(704\) | −1.90442 | −0.0717757 | ||||||||
\(705\) | −19.9588 | −0.751693 | ||||||||
\(706\) | 14.0391 | 0.528368 | ||||||||
\(707\) | −6.61641 | −0.248836 | ||||||||
\(708\) | 19.9620 | 0.750218 | ||||||||
\(709\) | 39.9748 | 1.50128 | 0.750642 | − | 0.660709i | \(-0.229744\pi\) | ||||
0.750642 | + | 0.660709i | \(0.229744\pi\) | |||||||
\(710\) | 6.33301 | 0.237674 | ||||||||
\(711\) | −2.73433 | −0.102545 | ||||||||
\(712\) | 13.6477 | 0.511468 | ||||||||
\(713\) | −12.0805 | −0.452418 | ||||||||
\(714\) | 32.9205 | 1.23202 | ||||||||
\(715\) | −25.7240 | −0.962022 | ||||||||
\(716\) | 15.7965 | 0.590343 | ||||||||
\(717\) | 21.2084 | 0.792043 | ||||||||
\(718\) | −7.72213 | −0.288187 | ||||||||
\(719\) | 0.921437 | 0.0343638 | 0.0171819 | − | 0.999852i | \(-0.494531\pi\) | ||||
0.0171819 | + | 0.999852i | \(0.494531\pi\) | |||||||
\(720\) | 2.72649 | 0.101610 | ||||||||
\(721\) | −33.2076 | −1.23672 | ||||||||
\(722\) | 24.9604 | 0.928928 | ||||||||
\(723\) | −14.2736 | −0.530840 | ||||||||
\(724\) | −17.2753 | −0.642031 | ||||||||
\(725\) | −2.64587 | −0.0982651 | ||||||||
\(726\) | −21.8152 | −0.809637 | ||||||||
\(727\) | 21.5936 | 0.800862 | 0.400431 | − | 0.916327i | \(-0.368860\pi\) | ||||
0.400431 | + | 0.916327i | \(0.368860\pi\) | |||||||
\(728\) | 33.1942 | 1.23026 | ||||||||
\(729\) | 24.9995 | 0.925906 | ||||||||
\(730\) | 5.84053 | 0.216168 | ||||||||
\(731\) | 12.7067 | 0.469974 | ||||||||
\(732\) | 6.36319 | 0.235190 | ||||||||
\(733\) | −22.0973 | −0.816183 | −0.408092 | − | 0.912941i | \(-0.633806\pi\) | ||||
−0.408092 | + | 0.912941i | \(0.633806\pi\) | |||||||
\(734\) | 1.95947 | 0.0723255 | ||||||||
\(735\) | 49.1861 | 1.81426 | ||||||||
\(736\) | −9.14392 | −0.337050 | ||||||||
\(737\) | −17.5663 | −0.647062 | ||||||||
\(738\) | 2.36326 | 0.0869928 | ||||||||
\(739\) | 42.3637 | 1.55837 | 0.779187 | − | 0.626792i | \(-0.215632\pi\) | ||||
0.779187 | + | 0.626792i | \(0.215632\pi\) | |||||||
\(740\) | −14.6099 | −0.537069 | ||||||||
\(741\) | −17.9257 | −0.658518 | ||||||||
\(742\) | 49.2473 | 1.80792 | ||||||||
\(743\) | 2.31320 | 0.0848630 | 0.0424315 | − | 0.999099i | \(-0.486490\pi\) | ||||
0.0424315 | + | 0.999099i | \(0.486490\pi\) | |||||||
\(744\) | −21.2603 | −0.779440 | ||||||||
\(745\) | −12.9237 | −0.473486 | ||||||||
\(746\) | 36.5508 | 1.33822 | ||||||||
\(747\) | 2.77564 | 0.101555 | ||||||||
\(748\) | 5.15980 | 0.188661 | ||||||||
\(749\) | −51.3801 | −1.87739 | ||||||||
\(750\) | 20.1761 | 0.736727 | ||||||||
\(751\) | −18.2167 | −0.664736 | −0.332368 | − | 0.943150i | \(-0.607848\pi\) | ||||
−0.332368 | + | 0.943150i | \(0.607848\pi\) | |||||||
\(752\) | 20.1839 | 0.736030 | ||||||||
\(753\) | −36.3676 | −1.32531 | ||||||||
\(754\) | −8.10195 | −0.295056 | ||||||||
\(755\) | −6.55100 | −0.238415 | ||||||||
\(756\) | −20.7308 | −0.753972 | ||||||||
\(757\) | 12.5485 | 0.456083 | 0.228041 | − | 0.973651i | \(-0.426768\pi\) | ||||
0.228041 | + | 0.973651i | \(0.426768\pi\) | |||||||
\(758\) | −61.7456 | −2.24270 | ||||||||
\(759\) | −6.23804 | −0.226427 | ||||||||
\(760\) | 10.2316 | 0.371137 | ||||||||
\(761\) | 24.6831 | 0.894763 | 0.447382 | − | 0.894343i | \(-0.352357\pi\) | ||||
0.447382 | + | 0.894343i | \(0.352357\pi\) | |||||||
\(762\) | −3.51628 | −0.127381 | ||||||||
\(763\) | 27.5457 | 0.997223 | ||||||||
\(764\) | 4.88847 | 0.176859 | ||||||||
\(765\) | 1.40685 | 0.0508647 | ||||||||
\(766\) | 3.08575 | 0.111493 | ||||||||
\(767\) | 51.9305 | 1.87510 | ||||||||
\(768\) | −34.0587 | −1.22899 | ||||||||
\(769\) | −35.7018 | −1.28744 | −0.643720 | − | 0.765261i | \(-0.722610\pi\) | ||||
−0.643720 | + | 0.765261i | \(0.722610\pi\) | |||||||
\(770\) | 39.2758 | 1.41540 | ||||||||
\(771\) | −42.0477 | −1.51431 | ||||||||
\(772\) | −25.6652 | −0.923712 | ||||||||
\(773\) | −7.51031 | −0.270127 | −0.135064 | − | 0.990837i | \(-0.543124\pi\) | ||||
−0.135064 | + | 0.990837i | \(0.543124\pi\) | |||||||
\(774\) | 1.68365 | 0.0605175 | ||||||||
\(775\) | 18.2361 | 0.655062 | ||||||||
\(776\) | 29.3479 | 1.05353 | ||||||||
\(777\) | 38.7080 | 1.38864 | ||||||||
\(778\) | −2.49082 | −0.0893003 | ||||||||
\(779\) | 14.8283 | 0.531278 | ||||||||
\(780\) | −23.2199 | −0.831404 | ||||||||
\(781\) | −2.62986 | −0.0941036 | ||||||||
\(782\) | −7.83862 | −0.280308 | ||||||||
\(783\) | −5.01160 | −0.179100 | ||||||||
\(784\) | −49.7406 | −1.77645 | ||||||||
\(785\) | −26.7044 | −0.953122 | ||||||||
\(786\) | −54.6205 | −1.94825 | ||||||||
\(787\) | 4.92388 | 0.175518 | 0.0877588 | − | 0.996142i | \(-0.472030\pi\) | ||||
0.0877588 | + | 0.996142i | \(0.472030\pi\) | |||||||
\(788\) | −3.95716 | −0.140968 | ||||||||
\(789\) | 33.1129 | 1.17885 | ||||||||
\(790\) | −66.4582 | −2.36448 | ||||||||
\(791\) | −67.0349 | −2.38349 | ||||||||
\(792\) | −0.677149 | −0.0240614 | ||||||||
\(793\) | 16.5536 | 0.587836 | ||||||||
\(794\) | 66.5779 | 2.36276 | ||||||||
\(795\) | 34.1202 | 1.21012 | ||||||||
\(796\) | 8.96774 | 0.317853 | ||||||||
\(797\) | −44.0689 | −1.56100 | −0.780499 | − | 0.625157i | \(-0.785035\pi\) | ||||
−0.780499 | + | 0.625157i | \(0.785035\pi\) | |||||||
\(798\) | 27.3693 | 0.968862 | ||||||||
\(799\) | 10.4147 | 0.368446 | ||||||||
\(800\) | 13.8032 | 0.488018 | ||||||||
\(801\) | 1.56014 | 0.0551247 | ||||||||
\(802\) | 27.5545 | 0.972985 | ||||||||
\(803\) | −2.42534 | −0.0855885 | ||||||||
\(804\) | −15.8563 | −0.559208 | ||||||||
\(805\) | −19.9524 | −0.703230 | ||||||||
\(806\) | 55.8412 | 1.96692 | ||||||||
\(807\) | −46.4634 | −1.63559 | ||||||||
\(808\) | 2.77256 | 0.0975382 | ||||||||
\(809\) | 35.8140 | 1.25915 | 0.629577 | − | 0.776938i | \(-0.283228\pi\) | ||||
0.629577 | + | 0.776938i | \(0.283228\pi\) | |||||||
\(810\) | −45.7877 | −1.60881 | ||||||||
\(811\) | −28.5435 | −1.00230 | −0.501149 | − | 0.865361i | \(-0.667089\pi\) | ||||
−0.501149 | + | 0.865361i | \(0.667089\pi\) | |||||||
\(812\) | 4.13657 | 0.145165 | ||||||||
\(813\) | 36.4359 | 1.27786 | ||||||||
\(814\) | 18.1428 | 0.635905 | ||||||||
\(815\) | −3.88307 | −0.136018 | ||||||||
\(816\) | −23.0656 | −0.807458 | ||||||||
\(817\) | 10.5640 | 0.369589 | ||||||||
\(818\) | 11.3127 | 0.395540 | ||||||||
\(819\) | 3.79460 | 0.132594 | ||||||||
\(820\) | 19.2076 | 0.670759 | ||||||||
\(821\) | 0.641300 | 0.0223815 | 0.0111908 | − | 0.999937i | \(-0.496438\pi\) | ||||
0.0111908 | + | 0.999937i | \(0.496438\pi\) | |||||||
\(822\) | −50.1300 | −1.74848 | ||||||||
\(823\) | 17.8126 | 0.620907 | 0.310453 | − | 0.950589i | \(-0.399519\pi\) | ||||
0.310453 | + | 0.950589i | \(0.399519\pi\) | |||||||
\(824\) | 13.9154 | 0.484766 | ||||||||
\(825\) | 9.41664 | 0.327845 | ||||||||
\(826\) | −79.2883 | −2.75879 | ||||||||
\(827\) | 38.6438 | 1.34378 | 0.671889 | − | 0.740652i | \(-0.265483\pi\) | ||||
0.671889 | + | 0.740652i | \(0.265483\pi\) | |||||||
\(828\) | −0.347313 | −0.0120700 | ||||||||
\(829\) | 39.9589 | 1.38783 | 0.693916 | − | 0.720056i | \(-0.255884\pi\) | ||||
0.693916 | + | 0.720056i | \(0.255884\pi\) | |||||||
\(830\) | 67.4622 | 2.34165 | ||||||||
\(831\) | −3.26538 | −0.113275 | ||||||||
\(832\) | −4.47202 | −0.155039 | ||||||||
\(833\) | −25.6658 | −0.889267 | ||||||||
\(834\) | −3.09951 | −0.107327 | ||||||||
\(835\) | −64.3142 | −2.22568 | ||||||||
\(836\) | 4.28973 | 0.148363 | ||||||||
\(837\) | 34.5415 | 1.19393 | ||||||||
\(838\) | −30.2420 | −1.04469 | ||||||||
\(839\) | −1.46409 | −0.0505462 | −0.0252731 | − | 0.999681i | \(-0.508046\pi\) | ||||
−0.0252731 | + | 0.999681i | \(0.508046\pi\) | |||||||
\(840\) | −35.1139 | −1.21155 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −37.3598 | −1.28750 | ||||||||
\(843\) | −6.52096 | −0.224594 | ||||||||
\(844\) | −16.8532 | −0.580111 | ||||||||
\(845\) | −24.4591 | −0.841420 | ||||||||
\(846\) | 1.37996 | 0.0474440 | ||||||||
\(847\) | 28.9753 | 0.995602 | ||||||||
\(848\) | −34.5049 | −1.18490 | ||||||||
\(849\) | 3.13845 | 0.107711 | ||||||||
\(850\) | 11.8328 | 0.405861 | ||||||||
\(851\) | −9.21668 | −0.315944 | ||||||||
\(852\) | −2.37385 | −0.0813268 | ||||||||
\(853\) | 57.5784 | 1.97145 | 0.985723 | − | 0.168376i | \(-0.0538522\pi\) | ||||
0.985723 | + | 0.168376i | \(0.0538522\pi\) | |||||||
\(854\) | −25.2743 | −0.864870 | ||||||||
\(855\) | 1.16962 | 0.0400002 | ||||||||
\(856\) | 21.5304 | 0.735894 | ||||||||
\(857\) | 8.96067 | 0.306091 | 0.153045 | − | 0.988219i | \(-0.451092\pi\) | ||||
0.153045 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(858\) | 28.8348 | 0.984405 | ||||||||
\(859\) | −37.8543 | −1.29157 | −0.645786 | − | 0.763518i | \(-0.723470\pi\) | ||||
−0.645786 | + | 0.763518i | \(0.723470\pi\) | |||||||
\(860\) | 13.6840 | 0.466620 | ||||||||
\(861\) | −50.8895 | −1.73431 | ||||||||
\(862\) | 30.7510 | 1.04738 | ||||||||
\(863\) | 14.1478 | 0.481596 | 0.240798 | − | 0.970575i | \(-0.422591\pi\) | ||||
0.240798 | + | 0.970575i | \(0.422591\pi\) | |||||||
\(864\) | 26.1450 | 0.889471 | ||||||||
\(865\) | −9.36623 | −0.318461 | ||||||||
\(866\) | 57.7482 | 1.96236 | ||||||||
\(867\) | 18.4956 | 0.628142 | ||||||||
\(868\) | −28.5105 | −0.967709 | ||||||||
\(869\) | 27.5975 | 0.936182 | ||||||||
\(870\) | 8.57050 | 0.290567 | ||||||||
\(871\) | −41.2496 | −1.39769 | ||||||||
\(872\) | −11.5428 | −0.390889 | ||||||||
\(873\) | 3.35490 | 0.113546 | ||||||||
\(874\) | −6.51684 | −0.220435 | ||||||||
\(875\) | −26.7982 | −0.905944 | ||||||||
\(876\) | −2.18925 | −0.0739678 | ||||||||
\(877\) | 1.85034 | 0.0624817 | 0.0312408 | − | 0.999512i | \(-0.490054\pi\) | ||||
0.0312408 | + | 0.999512i | \(0.490054\pi\) | |||||||
\(878\) | −68.5547 | −2.31361 | ||||||||
\(879\) | −18.9764 | −0.640057 | ||||||||
\(880\) | −27.5184 | −0.927647 | ||||||||
\(881\) | −53.7460 | −1.81075 | −0.905375 | − | 0.424613i | \(-0.860410\pi\) | ||||
−0.905375 | + | 0.424613i | \(0.860410\pi\) | |||||||
\(882\) | −3.40074 | −0.114509 | ||||||||
\(883\) | 28.7143 | 0.966312 | 0.483156 | − | 0.875534i | \(-0.339490\pi\) | ||||
0.483156 | + | 0.875534i | \(0.339490\pi\) | |||||||
\(884\) | 12.1164 | 0.407517 | ||||||||
\(885\) | −54.9337 | −1.84658 | ||||||||
\(886\) | −62.1894 | −2.08929 | ||||||||
\(887\) | −13.0560 | −0.438377 | −0.219188 | − | 0.975683i | \(-0.570341\pi\) | ||||
−0.219188 | + | 0.975683i | \(0.570341\pi\) | |||||||
\(888\) | −16.2203 | −0.544317 | ||||||||
\(889\) | 4.67038 | 0.156639 | ||||||||
\(890\) | 37.9193 | 1.27106 | ||||||||
\(891\) | 19.0139 | 0.636988 | ||||||||
\(892\) | −9.46708 | −0.316981 | ||||||||
\(893\) | 8.65856 | 0.289748 | ||||||||
\(894\) | 14.4866 | 0.484503 | ||||||||
\(895\) | −43.4706 | −1.45306 | ||||||||
\(896\) | 49.7820 | 1.66310 | ||||||||
\(897\) | −14.6483 | −0.489093 | ||||||||
\(898\) | 48.5409 | 1.61983 | ||||||||
\(899\) | −6.89231 | −0.229871 | ||||||||
\(900\) | 0.524288 | 0.0174763 | ||||||||
\(901\) | −17.8043 | −0.593147 | ||||||||
\(902\) | −23.8524 | −0.794197 | ||||||||
\(903\) | −36.2550 | −1.20649 | ||||||||
\(904\) | 28.0904 | 0.934274 | ||||||||
\(905\) | 47.5401 | 1.58029 | ||||||||
\(906\) | 7.34323 | 0.243962 | ||||||||
\(907\) | 43.7318 | 1.45209 | 0.726045 | − | 0.687648i | \(-0.241357\pi\) | ||||
0.726045 | + | 0.687648i | \(0.241357\pi\) | |||||||
\(908\) | −18.6639 | −0.619383 | ||||||||
\(909\) | 0.316945 | 0.0105124 | ||||||||
\(910\) | 92.2284 | 3.05734 | ||||||||
\(911\) | −5.69697 | −0.188749 | −0.0943746 | − | 0.995537i | \(-0.530085\pi\) | ||||
−0.0943746 | + | 0.995537i | \(0.530085\pi\) | |||||||
\(912\) | −19.1762 | −0.634987 | ||||||||
\(913\) | −28.0145 | −0.927143 | ||||||||
\(914\) | 29.6410 | 0.980438 | ||||||||
\(915\) | −17.5109 | −0.578894 | ||||||||
\(916\) | −0.974435 | −0.0321962 | ||||||||
\(917\) | 72.5478 | 2.39574 | ||||||||
\(918\) | 22.4128 | 0.739732 | ||||||||
\(919\) | 29.1840 | 0.962691 | 0.481345 | − | 0.876531i | \(-0.340148\pi\) | ||||
0.481345 | + | 0.876531i | \(0.340148\pi\) | |||||||
\(920\) | 8.36090 | 0.275651 | ||||||||
\(921\) | 0.462007 | 0.0152236 | ||||||||
\(922\) | −27.9879 | −0.921732 | ||||||||
\(923\) | −6.17549 | −0.203269 | ||||||||
\(924\) | −14.7220 | −0.484319 | ||||||||
\(925\) | 13.9130 | 0.457458 | ||||||||
\(926\) | 17.9574 | 0.590117 | ||||||||
\(927\) | 1.59074 | 0.0522467 | ||||||||
\(928\) | −5.21690 | −0.171253 | ||||||||
\(929\) | 27.8507 | 0.913750 | 0.456875 | − | 0.889531i | \(-0.348969\pi\) | ||||
0.456875 | + | 0.889531i | \(0.348969\pi\) | |||||||
\(930\) | −59.0706 | −1.93700 | ||||||||
\(931\) | −21.3379 | −0.699323 | ||||||||
\(932\) | −9.98681 | −0.327129 | ||||||||
\(933\) | −43.6847 | −1.43017 | ||||||||
\(934\) | −19.0031 | −0.621799 | ||||||||
\(935\) | −14.1993 | −0.464367 | ||||||||
\(936\) | −1.59010 | −0.0519740 | ||||||||
\(937\) | −13.5946 | −0.444116 | −0.222058 | − | 0.975033i | \(-0.571277\pi\) | ||||
−0.222058 | + | 0.975033i | \(0.571277\pi\) | |||||||
\(938\) | 62.9805 | 2.05639 | ||||||||
\(939\) | −19.6280 | −0.640536 | ||||||||
\(940\) | 11.2157 | 0.365817 | ||||||||
\(941\) | 47.4444 | 1.54664 | 0.773322 | − | 0.634014i | \(-0.218594\pi\) | ||||
0.773322 | + | 0.634014i | \(0.218594\pi\) | |||||||
\(942\) | 29.9339 | 0.975298 | ||||||||
\(943\) | 12.1172 | 0.394590 | ||||||||
\(944\) | 55.5531 | 1.80810 | ||||||||
\(945\) | 57.0494 | 1.85582 | ||||||||
\(946\) | −16.9930 | −0.552492 | ||||||||
\(947\) | 31.7174 | 1.03068 | 0.515338 | − | 0.856987i | \(-0.327666\pi\) | ||||
0.515338 | + | 0.856987i | \(0.327666\pi\) | |||||||
\(948\) | 24.9110 | 0.809072 | ||||||||
\(949\) | −5.69525 | −0.184876 | ||||||||
\(950\) | 9.83750 | 0.319171 | ||||||||
\(951\) | 47.5453 | 1.54176 | ||||||||
\(952\) | 18.3228 | 0.593846 | ||||||||
\(953\) | −3.23737 | −0.104869 | −0.0524343 | − | 0.998624i | \(-0.516698\pi\) | ||||
−0.0524343 | + | 0.998624i | \(0.516698\pi\) | |||||||
\(954\) | −2.35909 | −0.0763782 | ||||||||
\(955\) | −13.4527 | −0.435318 | ||||||||
\(956\) | −11.9179 | −0.385454 | ||||||||
\(957\) | −3.55900 | −0.115046 | ||||||||
\(958\) | −52.8930 | −1.70889 | ||||||||
\(959\) | 66.5834 | 2.15009 | ||||||||
\(960\) | 4.73064 | 0.152681 | ||||||||
\(961\) | 16.5039 | 0.532384 | ||||||||
\(962\) | 42.6033 | 1.37359 | ||||||||
\(963\) | 2.46125 | 0.0793127 | ||||||||
\(964\) | 8.02095 | 0.258338 | ||||||||
\(965\) | 70.6285 | 2.27361 | ||||||||
\(966\) | 22.3653 | 0.719592 | ||||||||
\(967\) | 41.2621 | 1.32690 | 0.663450 | − | 0.748221i | \(-0.269092\pi\) | ||||
0.663450 | + | 0.748221i | \(0.269092\pi\) | |||||||
\(968\) | −12.1419 | −0.390254 | ||||||||
\(969\) | −9.89478 | −0.317866 | ||||||||
\(970\) | 81.5414 | 2.61814 | ||||||||
\(971\) | 14.4091 | 0.462411 | 0.231206 | − | 0.972905i | \(-0.425733\pi\) | ||||
0.231206 | + | 0.972905i | \(0.425733\pi\) | |||||||
\(972\) | 2.05600 | 0.0659463 | ||||||||
\(973\) | 4.11682 | 0.131979 | ||||||||
\(974\) | −20.9990 | −0.672851 | ||||||||
\(975\) | 22.1124 | 0.708163 | ||||||||
\(976\) | 17.7084 | 0.566831 | ||||||||
\(977\) | 43.1375 | 1.38009 | 0.690045 | − | 0.723766i | \(-0.257591\pi\) | ||||
0.690045 | + | 0.723766i | \(0.257591\pi\) | |||||||
\(978\) | 4.35266 | 0.139183 | ||||||||
\(979\) | −15.7464 | −0.503258 | ||||||||
\(980\) | −27.6398 | −0.882922 | ||||||||
\(981\) | −1.31952 | −0.0421290 | ||||||||
\(982\) | −39.8552 | −1.27183 | ||||||||
\(983\) | −23.1476 | −0.738293 | −0.369146 | − | 0.929371i | \(-0.620350\pi\) | ||||
−0.369146 | + | 0.929371i | \(0.620350\pi\) | |||||||
\(984\) | 21.3248 | 0.679811 | ||||||||
\(985\) | 10.8898 | 0.346977 | ||||||||
\(986\) | −4.47218 | −0.142423 | ||||||||
\(987\) | −29.7155 | −0.945855 | ||||||||
\(988\) | 10.0733 | 0.320473 | ||||||||
\(989\) | 8.63259 | 0.274501 | ||||||||
\(990\) | −1.88142 | −0.0597955 | ||||||||
\(991\) | −32.6835 | −1.03823 | −0.519113 | − | 0.854706i | \(-0.673738\pi\) | ||||
−0.519113 | + | 0.854706i | \(0.673738\pi\) | |||||||
\(992\) | 35.9565 | 1.14162 | ||||||||
\(993\) | 41.4644 | 1.31583 | ||||||||
\(994\) | 9.42884 | 0.299065 | ||||||||
\(995\) | −24.6785 | −0.782360 | ||||||||
\(996\) | −25.2874 | −0.801261 | ||||||||
\(997\) | 18.0248 | 0.570852 | 0.285426 | − | 0.958401i | \(-0.407865\pi\) | ||||
0.285426 | + | 0.958401i | \(0.407865\pi\) | |||||||
\(998\) | −1.96477 | −0.0621936 | ||||||||
\(999\) | 26.3530 | 0.833773 |
(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 | 4031.2.a.c.1.14 | ✓ | 61 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.c.1.14 | ✓ | 61 | 1.1 | even | 1 | trivial |