Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 15 x^{10} + 30 x^{9} + 74 x^{8} - 149 x^{7} - 140 x^{6} + 278 x^{5} + 126 x^{4} - 211 x^{3} - 64 x^{2} + 53 x + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.48589\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.48589 | 1.75779 | 0.878896 | − | 0.477014i | \(-0.158281\pi\) | ||||
0.878896 | + | 0.477014i | \(0.158281\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.17966 | 2.08983 | ||||||||
\(5\) | 1.76717 | 0.790303 | 0.395152 | − | 0.918616i | \(-0.370692\pi\) | ||||
0.395152 | + | 0.918616i | \(0.370692\pi\) | |||||||
\(6\) | 2.48589 | 1.01486 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.41840 | 1.91569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.39300 | 1.38919 | ||||||||
\(11\) | 0.293529 | 0.0885023 | 0.0442511 | − | 0.999020i | \(-0.485910\pi\) | ||||
0.0442511 | + | 0.999020i | \(0.485910\pi\) | |||||||
\(12\) | 4.17966 | 1.20656 | ||||||||
\(13\) | 6.33387 | 1.75670 | 0.878350 | − | 0.478019i | \(-0.158645\pi\) | ||||
0.878350 | + | 0.478019i | \(0.158645\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.76717 | 0.456282 | ||||||||
\(16\) | 5.11024 | 1.27756 | ||||||||
\(17\) | 1.00183 | 0.242979 | 0.121490 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121490 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(18\) | 2.48589 | 0.585930 | ||||||||
\(19\) | −5.87506 | −1.34783 | −0.673916 | − | 0.738808i | \(-0.735389\pi\) | ||||
−0.673916 | + | 0.738808i | \(0.735389\pi\) | |||||||
\(20\) | 7.38618 | 1.65160 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.729681 | 0.155569 | ||||||||
\(23\) | 0.838269 | 0.174791 | 0.0873956 | − | 0.996174i | \(-0.472146\pi\) | ||||
0.0873956 | + | 0.996174i | \(0.472146\pi\) | |||||||
\(24\) | 5.41840 | 1.10603 | ||||||||
\(25\) | −1.87710 | −0.375421 | ||||||||
\(26\) | 15.7453 | 3.08791 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.34260 | 0.435009 | 0.217505 | − | 0.976059i | \(-0.430208\pi\) | ||||
0.217505 | + | 0.976059i | \(0.430208\pi\) | |||||||
\(30\) | 4.39300 | 0.802048 | ||||||||
\(31\) | −1.39480 | −0.250514 | −0.125257 | − | 0.992124i | \(-0.539976\pi\) | ||||
−0.125257 | + | 0.992124i | \(0.539976\pi\) | |||||||
\(32\) | 1.86671 | 0.329990 | ||||||||
\(33\) | 0.293529 | 0.0510968 | ||||||||
\(34\) | 2.49044 | 0.427106 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.17966 | 0.696610 | ||||||||
\(37\) | −0.691089 | −0.113614 | −0.0568072 | − | 0.998385i | \(-0.518092\pi\) | ||||
−0.0568072 | + | 0.998385i | \(0.518092\pi\) | |||||||
\(38\) | −14.6048 | −2.36921 | ||||||||
\(39\) | 6.33387 | 1.01423 | ||||||||
\(40\) | 9.57525 | 1.51398 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.408550 | −0.0623034 | −0.0311517 | − | 0.999515i | \(-0.509917\pi\) | ||||
−0.0311517 | + | 0.999515i | \(0.509917\pi\) | |||||||
\(44\) | 1.22685 | 0.184955 | ||||||||
\(45\) | 1.76717 | 0.263434 | ||||||||
\(46\) | 2.08385 | 0.307247 | ||||||||
\(47\) | 11.0390 | 1.61021 | 0.805103 | − | 0.593135i | \(-0.202110\pi\) | ||||
0.805103 | + | 0.593135i | \(0.202110\pi\) | |||||||
\(48\) | 5.11024 | 0.737600 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.66628 | −0.659911 | ||||||||
\(51\) | 1.00183 | 0.140284 | ||||||||
\(52\) | 26.4734 | 3.67120 | ||||||||
\(53\) | −9.65969 | −1.32686 | −0.663430 | − | 0.748238i | \(-0.730900\pi\) | ||||
−0.663430 | + | 0.748238i | \(0.730900\pi\) | |||||||
\(54\) | 2.48589 | 0.338287 | ||||||||
\(55\) | 0.518716 | 0.0699436 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.87506 | −0.778171 | ||||||||
\(58\) | 5.82344 | 0.764655 | ||||||||
\(59\) | −1.49818 | −0.195047 | −0.0975233 | − | 0.995233i | \(-0.531092\pi\) | ||||
−0.0975233 | + | 0.995233i | \(0.531092\pi\) | |||||||
\(60\) | 7.38618 | 0.953552 | ||||||||
\(61\) | 12.8700 | 1.64783 | 0.823916 | − | 0.566712i | \(-0.191785\pi\) | ||||
0.823916 | + | 0.566712i | \(0.191785\pi\) | |||||||
\(62\) | −3.46733 | −0.440351 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.58005 | −0.697506 | ||||||||
\(65\) | 11.1930 | 1.38833 | ||||||||
\(66\) | 0.729681 | 0.0898175 | ||||||||
\(67\) | −6.48266 | −0.791983 | −0.395992 | − | 0.918254i | \(-0.629599\pi\) | ||||
−0.395992 | + | 0.918254i | \(0.629599\pi\) | |||||||
\(68\) | 4.18730 | 0.507785 | ||||||||
\(69\) | 0.838269 | 0.100916 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.1061 | −1.31805 | −0.659023 | − | 0.752122i | \(-0.729030\pi\) | ||||
−0.659023 | + | 0.752122i | \(0.729030\pi\) | |||||||
\(72\) | 5.41840 | 0.638565 | ||||||||
\(73\) | 4.74670 | 0.555559 | 0.277780 | − | 0.960645i | \(-0.410402\pi\) | ||||
0.277780 | + | 0.960645i | \(0.410402\pi\) | |||||||
\(74\) | −1.71797 | −0.199710 | ||||||||
\(75\) | −1.87710 | −0.216749 | ||||||||
\(76\) | −24.5558 | −2.81674 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 15.7453 | 1.78281 | ||||||||
\(79\) | 1.80292 | 0.202844 | 0.101422 | − | 0.994844i | \(-0.467661\pi\) | ||||
0.101422 | + | 0.994844i | \(0.467661\pi\) | |||||||
\(80\) | 9.03067 | 1.00966 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.48589 | −0.274521 | ||||||||
\(83\) | 11.4808 | 1.26018 | 0.630090 | − | 0.776522i | \(-0.283018\pi\) | ||||
0.630090 | + | 0.776522i | \(0.283018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.77040 | 0.192027 | ||||||||
\(86\) | −1.01561 | −0.109516 | ||||||||
\(87\) | 2.34260 | 0.251153 | ||||||||
\(88\) | 1.59046 | 0.169543 | ||||||||
\(89\) | −15.8082 | −1.67566 | −0.837831 | − | 0.545929i | \(-0.816177\pi\) | ||||
−0.837831 | + | 0.545929i | \(0.816177\pi\) | |||||||
\(90\) | 4.39300 | 0.463063 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.50368 | 0.365284 | ||||||||
\(93\) | −1.39480 | −0.144634 | ||||||||
\(94\) | 27.4418 | 2.83041 | ||||||||
\(95\) | −10.3822 | −1.06520 | ||||||||
\(96\) | 1.86671 | 0.190520 | ||||||||
\(97\) | 9.27612 | 0.941848 | 0.470924 | − | 0.882174i | \(-0.343921\pi\) | ||||
0.470924 | + | 0.882174i | \(0.343921\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.293529 | 0.0295008 | ||||||||
\(100\) | −7.84565 | −0.784565 | ||||||||
\(101\) | −12.8057 | −1.27421 | −0.637107 | − | 0.770775i | \(-0.719869\pi\) | ||||
−0.637107 | + | 0.770775i | \(0.719869\pi\) | |||||||
\(102\) | 2.49044 | 0.246590 | ||||||||
\(103\) | 3.88886 | 0.383181 | 0.191590 | − | 0.981475i | \(-0.438636\pi\) | ||||
0.191590 | + | 0.981475i | \(0.438636\pi\) | |||||||
\(104\) | 34.3194 | 3.36530 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −24.0130 | −2.33234 | ||||||||
\(107\) | −16.5858 | −1.60341 | −0.801703 | − | 0.597723i | \(-0.796072\pi\) | ||||
−0.801703 | + | 0.597723i | \(0.796072\pi\) | |||||||
\(108\) | 4.17966 | 0.402188 | ||||||||
\(109\) | 4.13025 | 0.395606 | 0.197803 | − | 0.980242i | \(-0.436619\pi\) | ||||
0.197803 | + | 0.980242i | \(0.436619\pi\) | |||||||
\(110\) | 1.28947 | 0.122946 | ||||||||
\(111\) | −0.691089 | −0.0655953 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.33895 | 0.220030 | 0.110015 | − | 0.993930i | \(-0.464910\pi\) | ||||
0.110015 | + | 0.993930i | \(0.464910\pi\) | |||||||
\(114\) | −14.6048 | −1.36786 | ||||||||
\(115\) | 1.48137 | 0.138138 | ||||||||
\(116\) | 9.79125 | 0.909095 | ||||||||
\(117\) | 6.33387 | 0.585566 | ||||||||
\(118\) | −3.72432 | −0.342851 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 9.57525 | 0.874096 | ||||||||
\(121\) | −10.9138 | −0.992167 | ||||||||
\(122\) | 31.9934 | 2.89654 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −5.82980 | −0.523532 | ||||||||
\(125\) | −12.1530 | −1.08700 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.9908 | −1.06401 | −0.532006 | − | 0.846741i | \(-0.678562\pi\) | ||||
−0.532006 | + | 0.846741i | \(0.678562\pi\) | |||||||
\(128\) | −17.6048 | −1.55606 | ||||||||
\(129\) | −0.408550 | −0.0359709 | ||||||||
\(130\) | 27.8247 | 2.44039 | ||||||||
\(131\) | 11.6217 | 1.01540 | 0.507698 | − | 0.861535i | \(-0.330497\pi\) | ||||
0.507698 | + | 0.861535i | \(0.330497\pi\) | |||||||
\(132\) | 1.22685 | 0.106784 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −16.1152 | −1.39214 | ||||||||
\(135\) | 1.76717 | 0.152094 | ||||||||
\(136\) | 5.42831 | 0.465473 | ||||||||
\(137\) | 4.19260 | 0.358198 | 0.179099 | − | 0.983831i | \(-0.442682\pi\) | ||||
0.179099 | + | 0.983831i | \(0.442682\pi\) | |||||||
\(138\) | 2.08385 | 0.177389 | ||||||||
\(139\) | −13.9015 | −1.17911 | −0.589554 | − | 0.807729i | \(-0.700696\pi\) | ||||
−0.589554 | + | 0.807729i | \(0.700696\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0390 | 0.929653 | ||||||||
\(142\) | −27.6085 | −2.31685 | ||||||||
\(143\) | 1.85917 | 0.155472 | ||||||||
\(144\) | 5.11024 | 0.425853 | ||||||||
\(145\) | 4.13977 | 0.343789 | ||||||||
\(146\) | 11.7998 | 0.976557 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.88852 | −0.237435 | ||||||||
\(149\) | 19.7434 | 1.61744 | 0.808720 | − | 0.588194i | \(-0.200161\pi\) | ||||
0.808720 | + | 0.588194i | \(0.200161\pi\) | |||||||
\(150\) | −4.66628 | −0.381000 | ||||||||
\(151\) | 0.568140 | 0.0462346 | 0.0231173 | − | 0.999733i | \(-0.492641\pi\) | ||||
0.0231173 | + | 0.999733i | \(0.492641\pi\) | |||||||
\(152\) | −31.8335 | −2.58203 | ||||||||
\(153\) | 1.00183 | 0.0809930 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.46486 | −0.197982 | ||||||||
\(156\) | 26.4734 | 2.11957 | ||||||||
\(157\) | −21.6089 | −1.72458 | −0.862290 | − | 0.506415i | \(-0.830970\pi\) | ||||
−0.862290 | + | 0.506415i | \(0.830970\pi\) | |||||||
\(158\) | 4.48185 | 0.356557 | ||||||||
\(159\) | −9.65969 | −0.766063 | ||||||||
\(160\) | 3.29879 | 0.260792 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.48589 | 0.195310 | ||||||||
\(163\) | −5.82941 | −0.456595 | −0.228297 | − | 0.973591i | \(-0.573316\pi\) | ||||
−0.228297 | + | 0.973591i | \(0.573316\pi\) | |||||||
\(164\) | −4.17966 | −0.326377 | ||||||||
\(165\) | 0.518716 | 0.0403820 | ||||||||
\(166\) | 28.5400 | 2.21513 | ||||||||
\(167\) | 14.9641 | 1.15795 | 0.578977 | − | 0.815344i | \(-0.303452\pi\) | ||||
0.578977 | + | 0.815344i | \(0.303452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.1179 | 2.08599 | ||||||||
\(170\) | 4.40103 | 0.337544 | ||||||||
\(171\) | −5.87506 | −0.449277 | ||||||||
\(172\) | −1.70760 | −0.130203 | ||||||||
\(173\) | 2.55467 | 0.194228 | 0.0971142 | − | 0.995273i | \(-0.469039\pi\) | ||||
0.0971142 | + | 0.995273i | \(0.469039\pi\) | |||||||
\(174\) | 5.82344 | 0.441474 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.50000 | 0.113067 | ||||||||
\(177\) | −1.49818 | −0.112610 | ||||||||
\(178\) | −39.2974 | −2.94546 | ||||||||
\(179\) | 11.4969 | 0.859315 | 0.429658 | − | 0.902992i | \(-0.358634\pi\) | ||||
0.429658 | + | 0.902992i | \(0.358634\pi\) | |||||||
\(180\) | 7.38618 | 0.550533 | ||||||||
\(181\) | 10.4879 | 0.779561 | 0.389780 | − | 0.920908i | \(-0.372551\pi\) | ||||
0.389780 | + | 0.920908i | \(0.372551\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8700 | 0.951376 | ||||||||
\(184\) | 4.54208 | 0.334847 | ||||||||
\(185\) | −1.22127 | −0.0897898 | ||||||||
\(186\) | −3.46733 | −0.254237 | ||||||||
\(187\) | 0.294065 | 0.0215042 | ||||||||
\(188\) | 46.1393 | 3.36506 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.8092 | −1.87239 | ||||||||
\(191\) | −5.06053 | −0.366167 | −0.183083 | − | 0.983097i | \(-0.558608\pi\) | ||||
−0.183083 | + | 0.983097i | \(0.558608\pi\) | |||||||
\(192\) | −5.58005 | −0.402705 | ||||||||
\(193\) | 3.54687 | 0.255310 | 0.127655 | − | 0.991819i | \(-0.459255\pi\) | ||||
0.127655 | + | 0.991819i | \(0.459255\pi\) | |||||||
\(194\) | 23.0594 | 1.65557 | ||||||||
\(195\) | 11.1930 | 0.801550 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.6617 | −1.25835 | −0.629173 | − | 0.777265i | \(-0.716606\pi\) | ||||
−0.629173 | + | 0.777265i | \(0.716606\pi\) | |||||||
\(198\) | 0.729681 | 0.0518562 | ||||||||
\(199\) | −15.1642 | −1.07496 | −0.537481 | − | 0.843276i | \(-0.680624\pi\) | ||||
−0.537481 | + | 0.843276i | \(0.680624\pi\) | |||||||
\(200\) | −10.1709 | −0.719191 | ||||||||
\(201\) | −6.48266 | −0.457252 | ||||||||
\(202\) | −31.8336 | −2.23980 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.18730 | 0.293170 | ||||||||
\(205\) | −1.76717 | −0.123425 | ||||||||
\(206\) | 9.66728 | 0.673551 | ||||||||
\(207\) | 0.838269 | 0.0582638 | ||||||||
\(208\) | 32.3676 | 2.24429 | ||||||||
\(209\) | −1.72450 | −0.119286 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.89154 | 0.474433 | 0.237217 | − | 0.971457i | \(-0.423765\pi\) | ||||
0.237217 | + | 0.971457i | \(0.423765\pi\) | |||||||
\(212\) | −40.3742 | −2.77291 | ||||||||
\(213\) | −11.1061 | −0.760975 | ||||||||
\(214\) | −41.2304 | −2.81845 | ||||||||
\(215\) | −0.721979 | −0.0492386 | ||||||||
\(216\) | 5.41840 | 0.368676 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.2674 | 0.695393 | ||||||||
\(219\) | 4.74670 | 0.320752 | ||||||||
\(220\) | 2.16806 | 0.146170 | ||||||||
\(221\) | 6.34545 | 0.426841 | ||||||||
\(222\) | −1.71797 | −0.115303 | ||||||||
\(223\) | −17.7285 | −1.18719 | −0.593594 | − | 0.804764i | \(-0.702292\pi\) | ||||
−0.593594 | + | 0.804764i | \(0.702292\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.87710 | −0.125140 | ||||||||
\(226\) | 5.81438 | 0.386767 | ||||||||
\(227\) | 6.90430 | 0.458254 | 0.229127 | − | 0.973397i | \(-0.426413\pi\) | ||||
0.229127 | + | 0.973397i | \(0.426413\pi\) | |||||||
\(228\) | −24.5558 | −1.62625 | ||||||||
\(229\) | 14.1972 | 0.938175 | 0.469088 | − | 0.883152i | \(-0.344583\pi\) | ||||
0.469088 | + | 0.883152i | \(0.344583\pi\) | |||||||
\(230\) | 3.68252 | 0.242818 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.6931 | 0.833344 | ||||||||
\(233\) | 1.41764 | 0.0928725 | 0.0464363 | − | 0.998921i | \(-0.485214\pi\) | ||||
0.0464363 | + | 0.998921i | \(0.485214\pi\) | |||||||
\(234\) | 15.7453 | 1.02930 | ||||||||
\(235\) | 19.5078 | 1.27255 | ||||||||
\(236\) | −6.26189 | −0.407614 | ||||||||
\(237\) | 1.80292 | 0.117112 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.91363 | 0.123782 | 0.0618912 | − | 0.998083i | \(-0.480287\pi\) | ||||
0.0618912 | + | 0.998083i | \(0.480287\pi\) | |||||||
\(240\) | 9.03067 | 0.582928 | ||||||||
\(241\) | −8.74190 | −0.563115 | −0.281558 | − | 0.959544i | \(-0.590851\pi\) | ||||
−0.281558 | + | 0.959544i | \(0.590851\pi\) | |||||||
\(242\) | −27.1306 | −1.74402 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 53.7921 | 3.44369 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.48589 | −0.158495 | ||||||||
\(247\) | −37.2119 | −2.36774 | ||||||||
\(248\) | −7.55760 | −0.479908 | ||||||||
\(249\) | 11.4808 | 0.727566 | ||||||||
\(250\) | −30.2111 | −1.91072 | ||||||||
\(251\) | 16.3935 | 1.03475 | 0.517373 | − | 0.855760i | \(-0.326910\pi\) | ||||
0.517373 | + | 0.855760i | \(0.326910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.246056 | 0.0154694 | ||||||||
\(254\) | −29.8079 | −1.87031 | ||||||||
\(255\) | 1.77040 | 0.110867 | ||||||||
\(256\) | −32.6036 | −2.03772 | ||||||||
\(257\) | −5.79030 | −0.361189 | −0.180594 | − | 0.983558i | \(-0.557802\pi\) | ||||
−0.180594 | + | 0.983558i | \(0.557802\pi\) | |||||||
\(258\) | −1.01561 | −0.0632293 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 46.7831 | 2.90136 | ||||||||
\(261\) | 2.34260 | 0.145003 | ||||||||
\(262\) | 28.8904 | 1.78485 | ||||||||
\(263\) | 7.57467 | 0.467074 | 0.233537 | − | 0.972348i | \(-0.424970\pi\) | ||||
0.233537 | + | 0.972348i | \(0.424970\pi\) | |||||||
\(264\) | 1.59046 | 0.0978859 | ||||||||
\(265\) | −17.0703 | −1.04862 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.8082 | −0.967444 | ||||||||
\(268\) | −27.0953 | −1.65511 | ||||||||
\(269\) | −24.0489 | −1.46629 | −0.733144 | − | 0.680073i | \(-0.761948\pi\) | ||||
−0.733144 | + | 0.680073i | \(0.761948\pi\) | |||||||
\(270\) | 4.39300 | 0.267349 | ||||||||
\(271\) | 14.6082 | 0.887385 | 0.443693 | − | 0.896179i | \(-0.353668\pi\) | ||||
0.443693 | + | 0.896179i | \(0.353668\pi\) | |||||||
\(272\) | 5.11958 | 0.310420 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.4223 | 0.629637 | ||||||||
\(275\) | −0.550984 | −0.0332256 | ||||||||
\(276\) | 3.50368 | 0.210897 | ||||||||
\(277\) | 13.2496 | 0.796094 | 0.398047 | − | 0.917365i | \(-0.369688\pi\) | ||||
0.398047 | + | 0.917365i | \(0.369688\pi\) | |||||||
\(278\) | −34.5576 | −2.07263 | ||||||||
\(279\) | −1.39480 | −0.0835047 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2773 | 0.911366 | 0.455683 | − | 0.890142i | \(-0.349395\pi\) | ||||
0.455683 | + | 0.890142i | \(0.349395\pi\) | |||||||
\(282\) | 27.4418 | 1.63414 | ||||||||
\(283\) | 27.9553 | 1.66177 | 0.830885 | − | 0.556444i | \(-0.187834\pi\) | ||||
0.830885 | + | 0.556444i | \(0.187834\pi\) | |||||||
\(284\) | −46.4196 | −2.75449 | ||||||||
\(285\) | −10.3822 | −0.614991 | ||||||||
\(286\) | 4.62170 | 0.273287 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.86671 | 0.109997 | ||||||||
\(289\) | −15.9963 | −0.940961 | ||||||||
\(290\) | 10.2910 | 0.604309 | ||||||||
\(291\) | 9.27612 | 0.543776 | ||||||||
\(292\) | 19.8396 | 1.16102 | ||||||||
\(293\) | 10.3302 | 0.603498 | 0.301749 | − | 0.953387i | \(-0.402430\pi\) | ||||
0.301749 | + | 0.953387i | \(0.402430\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.64754 | −0.154146 | ||||||||
\(296\) | −3.74460 | −0.217650 | ||||||||
\(297\) | 0.293529 | 0.0170323 | ||||||||
\(298\) | 49.0799 | 2.84312 | ||||||||
\(299\) | 5.30949 | 0.307056 | ||||||||
\(300\) | −7.84565 | −0.452969 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.41233 | 0.0812707 | ||||||||
\(303\) | −12.8057 | −0.735668 | ||||||||
\(304\) | −30.0230 | −1.72194 | ||||||||
\(305\) | 22.7435 | 1.30229 | ||||||||
\(306\) | 2.49044 | 0.142369 | ||||||||
\(307\) | −19.9196 | −1.13687 | −0.568437 | − | 0.822727i | \(-0.692452\pi\) | ||||
−0.568437 | + | 0.822727i | \(0.692452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.88886 | 0.221229 | ||||||||
\(310\) | −6.12737 | −0.348011 | ||||||||
\(311\) | −19.0288 | −1.07903 | −0.539513 | − | 0.841977i | \(-0.681392\pi\) | ||||
−0.539513 | + | 0.841977i | \(0.681392\pi\) | |||||||
\(312\) | 34.3194 | 1.94296 | ||||||||
\(313\) | 30.7830 | 1.73996 | 0.869979 | − | 0.493090i | \(-0.164133\pi\) | ||||
0.869979 | + | 0.493090i | \(0.164133\pi\) | |||||||
\(314\) | −53.7175 | −3.03145 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.53557 | 0.423909 | ||||||||
\(317\) | −3.77693 | −0.212134 | −0.106067 | − | 0.994359i | \(-0.533826\pi\) | ||||
−0.106067 | + | 0.994359i | \(0.533826\pi\) | |||||||
\(318\) | −24.0130 | −1.34658 | ||||||||
\(319\) | 0.687619 | 0.0384993 | ||||||||
\(320\) | −9.86091 | −0.551242 | ||||||||
\(321\) | −16.5858 | −0.925726 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.88580 | −0.327495 | ||||||||
\(324\) | 4.17966 | 0.232203 | ||||||||
\(325\) | −11.8893 | −0.659501 | ||||||||
\(326\) | −14.4913 | −0.802598 | ||||||||
\(327\) | 4.13025 | 0.228403 | ||||||||
\(328\) | −5.41840 | −0.299181 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.28947 | 0.0709831 | ||||||||
\(331\) | −10.2326 | −0.562434 | −0.281217 | − | 0.959644i | \(-0.590738\pi\) | ||||
−0.281217 | + | 0.959644i | \(0.590738\pi\) | |||||||
\(332\) | 47.9858 | 2.63356 | ||||||||
\(333\) | −0.691089 | −0.0378715 | ||||||||
\(334\) | 37.1991 | 2.03544 | ||||||||
\(335\) | −11.4560 | −0.625907 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36.0266 | 1.96249 | 0.981247 | − | 0.192753i | \(-0.0617416\pi\) | ||||
0.981247 | + | 0.192753i | \(0.0617416\pi\) | |||||||
\(338\) | 67.4122 | 3.66674 | ||||||||
\(339\) | 2.33895 | 0.127034 | ||||||||
\(340\) | 7.39968 | 0.401304 | ||||||||
\(341\) | −0.409415 | −0.0221711 | ||||||||
\(342\) | −14.6048 | −0.789736 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.21369 | −0.119354 | ||||||||
\(345\) | 1.48137 | 0.0797541 | ||||||||
\(346\) | 6.35065 | 0.341413 | ||||||||
\(347\) | 8.72186 | 0.468214 | 0.234107 | − | 0.972211i | \(-0.424783\pi\) | ||||
0.234107 | + | 0.972211i | \(0.424783\pi\) | |||||||
\(348\) | 9.79125 | 0.524866 | ||||||||
\(349\) | 25.6152 | 1.37115 | 0.685576 | − | 0.728001i | \(-0.259550\pi\) | ||||
0.685576 | + | 0.728001i | \(0.259550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.33387 | 0.338077 | ||||||||
\(352\) | 0.547932 | 0.0292049 | ||||||||
\(353\) | 3.43415 | 0.182781 | 0.0913906 | − | 0.995815i | \(-0.470869\pi\) | ||||
0.0913906 | + | 0.995815i | \(0.470869\pi\) | |||||||
\(354\) | −3.72432 | −0.197945 | ||||||||
\(355\) | −19.6263 | −1.04166 | ||||||||
\(356\) | −66.0728 | −3.50185 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.5799 | 1.51050 | ||||||||
\(359\) | −34.2365 | −1.80693 | −0.903467 | − | 0.428658i | \(-0.858987\pi\) | ||||
−0.903467 | + | 0.428658i | \(0.858987\pi\) | |||||||
\(360\) | 9.57525 | 0.504660 | ||||||||
\(361\) | 15.5164 | 0.816651 | ||||||||
\(362\) | 26.0718 | 1.37031 | ||||||||
\(363\) | −10.9138 | −0.572828 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.38823 | 0.439060 | ||||||||
\(366\) | 31.9934 | 1.67232 | ||||||||
\(367\) | −15.7607 | −0.822700 | −0.411350 | − | 0.911478i | \(-0.634943\pi\) | ||||
−0.411350 | + | 0.911478i | \(0.634943\pi\) | |||||||
\(368\) | 4.28376 | 0.223306 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −3.03595 | −0.157832 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.82980 | −0.302261 | ||||||||
\(373\) | −34.4113 | −1.78175 | −0.890876 | − | 0.454247i | \(-0.849908\pi\) | ||||
−0.890876 | + | 0.454247i | \(0.849908\pi\) | |||||||
\(374\) | 0.731015 | 0.0377999 | ||||||||
\(375\) | −12.1530 | −0.627579 | ||||||||
\(376\) | 59.8138 | 3.08466 | ||||||||
\(377\) | 14.8377 | 0.764180 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.4556 | 1.05073 | 0.525366 | − | 0.850877i | \(-0.323929\pi\) | ||||
0.525366 | + | 0.850877i | \(0.323929\pi\) | |||||||
\(380\) | −43.3943 | −2.22608 | ||||||||
\(381\) | −11.9908 | −0.614308 | ||||||||
\(382\) | −12.5799 | −0.643645 | ||||||||
\(383\) | −30.8234 | −1.57500 | −0.787502 | − | 0.616312i | \(-0.788626\pi\) | ||||
−0.787502 | + | 0.616312i | \(0.788626\pi\) | |||||||
\(384\) | −17.6048 | −0.898392 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.81715 | 0.448781 | ||||||||
\(387\) | −0.408550 | −0.0207678 | ||||||||
\(388\) | 38.7710 | 1.96830 | ||||||||
\(389\) | 24.5119 | 1.24280 | 0.621401 | − | 0.783493i | \(-0.286564\pi\) | ||||
0.621401 | + | 0.783493i | \(0.286564\pi\) | |||||||
\(390\) | 27.8247 | 1.40896 | ||||||||
\(391\) | 0.839802 | 0.0424706 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.6217 | 0.586239 | ||||||||
\(394\) | −43.9052 | −2.21191 | ||||||||
\(395\) | 3.18606 | 0.160308 | ||||||||
\(396\) | 1.22685 | 0.0616516 | ||||||||
\(397\) | 13.5526 | 0.680188 | 0.340094 | − | 0.940391i | \(-0.389541\pi\) | ||||
0.340094 | + | 0.940391i | \(0.389541\pi\) | |||||||
\(398\) | −37.6966 | −1.88956 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.59245 | −0.479623 | ||||||||
\(401\) | 19.7195 | 0.984746 | 0.492373 | − | 0.870384i | \(-0.336130\pi\) | ||||
0.492373 | + | 0.870384i | \(0.336130\pi\) | |||||||
\(402\) | −16.1152 | −0.803753 | ||||||||
\(403\) | −8.83450 | −0.440078 | ||||||||
\(404\) | −53.5235 | −2.66289 | ||||||||
\(405\) | 1.76717 | 0.0878115 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.202855 | −0.0100551 | ||||||||
\(408\) | 5.42831 | 0.268741 | ||||||||
\(409\) | −15.1964 | −0.751415 | −0.375707 | − | 0.926738i | \(-0.622600\pi\) | ||||
−0.375707 | + | 0.926738i | \(0.622600\pi\) | |||||||
\(410\) | −4.39300 | −0.216955 | ||||||||
\(411\) | 4.19260 | 0.206806 | ||||||||
\(412\) | 16.2541 | 0.800782 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.08385 | 0.102416 | ||||||||
\(415\) | 20.2885 | 0.995925 | ||||||||
\(416\) | 11.8235 | 0.579694 | ||||||||
\(417\) | −13.9015 | −0.680758 | ||||||||
\(418\) | −4.28692 | −0.209680 | ||||||||
\(419\) | −38.4758 | −1.87966 | −0.939832 | − | 0.341637i | \(-0.889019\pi\) | ||||
−0.939832 | + | 0.341637i | \(0.889019\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.0584 | −1.90359 | −0.951795 | − | 0.306734i | \(-0.900764\pi\) | ||||
−0.951795 | + | 0.306734i | \(0.900764\pi\) | |||||||
\(422\) | 17.1316 | 0.833955 | ||||||||
\(423\) | 11.0390 | 0.536735 | ||||||||
\(424\) | −52.3401 | −2.54186 | ||||||||
\(425\) | −1.88053 | −0.0912193 | ||||||||
\(426\) | −27.6085 | −1.33763 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −69.3228 | −3.35084 | ||||||||
\(429\) | 1.85917 | 0.0897617 | ||||||||
\(430\) | −1.79476 | −0.0865511 | ||||||||
\(431\) | 1.05223 | 0.0506840 | 0.0253420 | − | 0.999679i | \(-0.491933\pi\) | ||||
0.0253420 | + | 0.999679i | \(0.491933\pi\) | |||||||
\(432\) | 5.11024 | 0.245867 | ||||||||
\(433\) | 24.7423 | 1.18904 | 0.594520 | − | 0.804081i | \(-0.297342\pi\) | ||||
0.594520 | + | 0.804081i | \(0.297342\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.13977 | 0.198487 | ||||||||
\(436\) | 17.2630 | 0.826749 | ||||||||
\(437\) | −4.92489 | −0.235589 | ||||||||
\(438\) | 11.7998 | 0.563815 | ||||||||
\(439\) | −13.9212 | −0.664421 | −0.332210 | − | 0.943205i | \(-0.607794\pi\) | ||||
−0.332210 | + | 0.943205i | \(0.607794\pi\) | |||||||
\(440\) | 2.81061 | 0.133991 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.7741 | 0.750298 | ||||||||
\(443\) | 7.20423 | 0.342283 | 0.171142 | − | 0.985246i | \(-0.445254\pi\) | ||||
0.171142 | + | 0.985246i | \(0.445254\pi\) | |||||||
\(444\) | −2.88852 | −0.137083 | ||||||||
\(445\) | −27.9357 | −1.32428 | ||||||||
\(446\) | −44.0712 | −2.08683 | ||||||||
\(447\) | 19.7434 | 0.933830 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.5965 | −1.25517 | −0.627584 | − | 0.778549i | \(-0.715956\pi\) | ||||
−0.627584 | + | 0.778549i | \(0.715956\pi\) | |||||||
\(450\) | −4.66628 | −0.219970 | ||||||||
\(451\) | −0.293529 | −0.0138217 | ||||||||
\(452\) | 9.77601 | 0.459825 | ||||||||
\(453\) | 0.568140 | 0.0266935 | ||||||||
\(454\) | 17.1633 | 0.805515 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −31.8335 | −1.49074 | ||||||||
\(457\) | 22.2276 | 1.03976 | 0.519881 | − | 0.854238i | \(-0.325976\pi\) | ||||
0.519881 | + | 0.854238i | \(0.325976\pi\) | |||||||
\(458\) | 35.2926 | 1.64912 | ||||||||
\(459\) | 1.00183 | 0.0467613 | ||||||||
\(460\) | 6.19161 | 0.288685 | ||||||||
\(461\) | 1.88110 | 0.0876114 | 0.0438057 | − | 0.999040i | \(-0.486052\pi\) | ||||
0.0438057 | + | 0.999040i | \(0.486052\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.16637 | −0.425997 | −0.212999 | − | 0.977053i | \(-0.568323\pi\) | ||||
−0.212999 | + | 0.977053i | \(0.568323\pi\) | |||||||
\(464\) | 11.9712 | 0.555750 | ||||||||
\(465\) | −2.46486 | −0.114305 | ||||||||
\(466\) | 3.52409 | 0.163250 | ||||||||
\(467\) | −33.7593 | −1.56220 | −0.781098 | − | 0.624409i | \(-0.785340\pi\) | ||||
−0.781098 | + | 0.624409i | \(0.785340\pi\) | |||||||
\(468\) | 26.4734 | 1.22373 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 48.4944 | 2.23688 | ||||||||
\(471\) | −21.6089 | −0.995687 | ||||||||
\(472\) | −8.11775 | −0.373650 | ||||||||
\(473\) | −0.119921 | −0.00551399 | ||||||||
\(474\) | 4.48185 | 0.205858 | ||||||||
\(475\) | 11.0281 | 0.506004 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.65969 | −0.442287 | ||||||||
\(478\) | 4.75707 | 0.217583 | ||||||||
\(479\) | −7.16053 | −0.327173 | −0.163587 | − | 0.986529i | \(-0.552306\pi\) | ||||
−0.163587 | + | 0.986529i | \(0.552306\pi\) | |||||||
\(480\) | 3.29879 | 0.150569 | ||||||||
\(481\) | −4.37727 | −0.199586 | ||||||||
\(482\) | −21.7314 | −0.989839 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −45.6161 | −2.07346 | ||||||||
\(485\) | 16.3925 | 0.744345 | ||||||||
\(486\) | 2.48589 | 0.112762 | ||||||||
\(487\) | −10.9331 | −0.495424 | −0.247712 | − | 0.968834i | \(-0.579679\pi\) | ||||
−0.247712 | + | 0.968834i | \(0.579679\pi\) | |||||||
\(488\) | 69.7347 | 3.15674 | ||||||||
\(489\) | −5.82941 | −0.263615 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.5154 | 1.10637 | 0.553183 | − | 0.833060i | \(-0.313413\pi\) | ||||
0.553183 | + | 0.833060i | \(0.313413\pi\) | |||||||
\(492\) | −4.17966 | −0.188434 | ||||||||
\(493\) | 2.34688 | 0.105698 | ||||||||
\(494\) | −92.5047 | −4.16199 | ||||||||
\(495\) | 0.518716 | 0.0233145 | ||||||||
\(496\) | −7.12778 | −0.320047 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 28.5400 | 1.27891 | ||||||||
\(499\) | −37.4506 | −1.67652 | −0.838261 | − | 0.545270i | \(-0.816427\pi\) | ||||
−0.838261 | + | 0.545270i | \(0.816427\pi\) | |||||||
\(500\) | −50.7955 | −2.27164 | ||||||||
\(501\) | 14.9641 | 0.668545 | ||||||||
\(502\) | 40.7524 | 1.81887 | ||||||||
\(503\) | −11.7824 | −0.525352 | −0.262676 | − | 0.964884i | \(-0.584605\pi\) | ||||
−0.262676 | + | 0.964884i | \(0.584605\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.6299 | −1.00702 | ||||||||
\(506\) | 0.611669 | 0.0271920 | ||||||||
\(507\) | 27.1179 | 1.20435 | ||||||||
\(508\) | −50.1175 | −2.22360 | ||||||||
\(509\) | 44.4596 | 1.97064 | 0.985319 | − | 0.170723i | \(-0.0546104\pi\) | ||||
0.985319 | + | 0.170723i | \(0.0546104\pi\) | |||||||
\(510\) | 4.40103 | 0.194881 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −45.8394 | −2.02583 | ||||||||
\(513\) | −5.87506 | −0.259390 | ||||||||
\(514\) | −14.3941 | −0.634894 | ||||||||
\(515\) | 6.87228 | 0.302829 | ||||||||
\(516\) | −1.70760 | −0.0751730 | ||||||||
\(517\) | 3.24027 | 0.142507 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.55467 | 0.112138 | ||||||||
\(520\) | 60.6484 | 2.65961 | ||||||||
\(521\) | 10.0439 | 0.440031 | 0.220015 | − | 0.975496i | \(-0.429389\pi\) | ||||
0.220015 | + | 0.975496i | \(0.429389\pi\) | |||||||
\(522\) | 5.82344 | 0.254885 | ||||||||
\(523\) | −29.9705 | −1.31052 | −0.655259 | − | 0.755405i | \(-0.727440\pi\) | ||||
−0.655259 | + | 0.755405i | \(0.727440\pi\) | |||||||
\(524\) | 48.5749 | 2.12200 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.8298 | 0.821019 | ||||||||
\(527\) | −1.39735 | −0.0608696 | ||||||||
\(528\) | 1.50000 | 0.0652793 | ||||||||
\(529\) | −22.2973 | −0.969448 | ||||||||
\(530\) | −42.4350 | −1.84326 | ||||||||
\(531\) | −1.49818 | −0.0650155 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.33387 | −0.274350 | ||||||||
\(534\) | −39.2974 | −1.70056 | ||||||||
\(535\) | −29.3099 | −1.26718 | ||||||||
\(536\) | −35.1257 | −1.51720 | ||||||||
\(537\) | 11.4969 | 0.496126 | ||||||||
\(538\) | −59.7830 | −2.57743 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.38618 | 0.317851 | ||||||||
\(541\) | 5.69166 | 0.244704 | 0.122352 | − | 0.992487i | \(-0.460956\pi\) | ||||
0.122352 | + | 0.992487i | \(0.460956\pi\) | |||||||
\(542\) | 36.3144 | 1.55984 | ||||||||
\(543\) | 10.4879 | 0.450080 | ||||||||
\(544\) | 1.87012 | 0.0801807 | ||||||||
\(545\) | 7.29886 | 0.312649 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.2276 | −1.67725 | −0.838625 | − | 0.544710i | \(-0.816640\pi\) | ||||
−0.838625 | + | 0.544710i | \(0.816640\pi\) | |||||||
\(548\) | 17.5236 | 0.748573 | ||||||||
\(549\) | 12.8700 | 0.549277 | ||||||||
\(550\) | −1.36969 | −0.0584036 | ||||||||
\(551\) | −13.7629 | −0.586319 | ||||||||
\(552\) | 4.54208 | 0.193324 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 32.9372 | 1.39937 | ||||||||
\(555\) | −1.22127 | −0.0518402 | ||||||||
\(556\) | −58.1035 | −2.46414 | ||||||||
\(557\) | −14.4005 | −0.610170 | −0.305085 | − | 0.952325i | \(-0.598685\pi\) | ||||
−0.305085 | + | 0.952325i | \(0.598685\pi\) | |||||||
\(558\) | −3.46733 | −0.146784 | ||||||||
\(559\) | −2.58771 | −0.109448 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.294065 | 0.0124155 | ||||||||
\(562\) | 37.9777 | 1.60199 | ||||||||
\(563\) | 5.77006 | 0.243179 | 0.121590 | − | 0.992580i | \(-0.461201\pi\) | ||||
0.121590 | + | 0.992580i | \(0.461201\pi\) | |||||||
\(564\) | 46.1393 | 1.94282 | ||||||||
\(565\) | 4.13333 | 0.173890 | ||||||||
\(566\) | 69.4939 | 2.92105 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −60.1771 | −2.52497 | ||||||||
\(569\) | 16.3956 | 0.687340 | 0.343670 | − | 0.939091i | \(-0.388330\pi\) | ||||
0.343670 | + | 0.939091i | \(0.388330\pi\) | |||||||
\(570\) | −25.8092 | −1.08103 | ||||||||
\(571\) | 7.21318 | 0.301862 | 0.150931 | − | 0.988544i | \(-0.451773\pi\) | ||||
0.150931 | + | 0.988544i | \(0.451773\pi\) | |||||||
\(572\) | 7.77071 | 0.324910 | ||||||||
\(573\) | −5.06053 | −0.211407 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.57352 | −0.0656203 | ||||||||
\(576\) | −5.58005 | −0.232502 | ||||||||
\(577\) | −47.7149 | −1.98640 | −0.993199 | − | 0.116433i | \(-0.962854\pi\) | ||||
−0.993199 | + | 0.116433i | \(0.962854\pi\) | |||||||
\(578\) | −39.7652 | −1.65401 | ||||||||
\(579\) | 3.54687 | 0.147403 | ||||||||
\(580\) | 17.3028 | 0.718461 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 23.0594 | 0.955845 | ||||||||
\(583\) | −2.83540 | −0.117430 | ||||||||
\(584\) | 25.7195 | 1.06428 | ||||||||
\(585\) | 11.1930 | 0.462775 | ||||||||
\(586\) | 25.6798 | 1.06082 | ||||||||
\(587\) | 10.7984 | 0.445698 | 0.222849 | − | 0.974853i | \(-0.428464\pi\) | ||||
0.222849 | + | 0.974853i | \(0.428464\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.19455 | 0.337651 | ||||||||
\(590\) | −6.58151 | −0.270956 | ||||||||
\(591\) | −17.6617 | −0.726506 | ||||||||
\(592\) | −3.53163 | −0.145149 | ||||||||
\(593\) | −27.3645 | −1.12373 | −0.561863 | − | 0.827230i | \(-0.689915\pi\) | ||||
−0.561863 | + | 0.827230i | \(0.689915\pi\) | |||||||
\(594\) | 0.729681 | 0.0299392 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 82.5206 | 3.38018 | ||||||||
\(597\) | −15.1642 | −0.620630 | ||||||||
\(598\) | 13.1988 | 0.539740 | ||||||||
\(599\) | 25.8885 | 1.05777 | 0.528887 | − | 0.848692i | \(-0.322610\pi\) | ||||
0.528887 | + | 0.848692i | \(0.322610\pi\) | |||||||
\(600\) | −10.1709 | −0.415225 | ||||||||
\(601\) | 15.1127 | 0.616459 | 0.308230 | − | 0.951312i | \(-0.400263\pi\) | ||||
0.308230 | + | 0.951312i | \(0.400263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.48266 | −0.263994 | ||||||||
\(604\) | 2.37463 | 0.0966224 | ||||||||
\(605\) | −19.2866 | −0.784113 | ||||||||
\(606\) | −31.8336 | −1.29315 | ||||||||
\(607\) | −12.5002 | −0.507369 | −0.253685 | − | 0.967287i | \(-0.581643\pi\) | ||||
−0.253685 | + | 0.967287i | \(0.581643\pi\) | |||||||
\(608\) | −10.9670 | −0.444771 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 56.5378 | 2.28915 | ||||||||
\(611\) | 69.9197 | 2.82865 | ||||||||
\(612\) | 4.18730 | 0.169262 | ||||||||
\(613\) | 9.60492 | 0.387939 | 0.193970 | − | 0.981008i | \(-0.437864\pi\) | ||||
0.193970 | + | 0.981008i | \(0.437864\pi\) | |||||||
\(614\) | −49.5181 | −1.99839 | ||||||||
\(615\) | −1.76717 | −0.0712593 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.72064 | 0.149787 | 0.0748936 | − | 0.997192i | \(-0.476138\pi\) | ||||
0.0748936 | + | 0.997192i | \(0.476138\pi\) | |||||||
\(618\) | 9.66728 | 0.388875 | ||||||||
\(619\) | 34.8001 | 1.39874 | 0.699368 | − | 0.714762i | \(-0.253465\pi\) | ||||
0.699368 | + | 0.714762i | \(0.253465\pi\) | |||||||
\(620\) | −10.3023 | −0.413749 | ||||||||
\(621\) | 0.838269 | 0.0336386 | ||||||||
\(622\) | −47.3036 | −1.89670 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 32.3676 | 1.29574 | ||||||||
\(625\) | −12.0910 | −0.483639 | ||||||||
\(626\) | 76.5232 | 3.05848 | ||||||||
\(627\) | −1.72450 | −0.0688699 | ||||||||
\(628\) | −90.3180 | −3.60408 | ||||||||
\(629\) | −0.692353 | −0.0276059 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.9796 | −0.795377 | −0.397688 | − | 0.917521i | \(-0.630187\pi\) | ||||
−0.397688 | + | 0.917521i | \(0.630187\pi\) | |||||||
\(632\) | 9.76892 | 0.388587 | ||||||||
\(633\) | 6.89154 | 0.273914 | ||||||||
\(634\) | −9.38905 | −0.372887 | ||||||||
\(635\) | −21.1898 | −0.840892 | ||||||||
\(636\) | −40.3742 | −1.60094 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.70935 | 0.0676737 | ||||||||
\(639\) | −11.1061 | −0.439349 | ||||||||
\(640\) | −31.1107 | −1.22976 | ||||||||
\(641\) | 19.8441 | 0.783794 | 0.391897 | − | 0.920009i | \(-0.371819\pi\) | ||||
0.391897 | + | 0.920009i | \(0.371819\pi\) | |||||||
\(642\) | −41.2304 | −1.62723 | ||||||||
\(643\) | −45.1521 | −1.78062 | −0.890312 | − | 0.455352i | \(-0.849513\pi\) | ||||
−0.890312 | + | 0.455352i | \(0.849513\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.721979 | −0.0284279 | ||||||||
\(646\) | −14.6315 | −0.575668 | ||||||||
\(647\) | 24.8685 | 0.977683 | 0.488841 | − | 0.872373i | \(-0.337420\pi\) | ||||
0.488841 | + | 0.872373i | \(0.337420\pi\) | |||||||
\(648\) | 5.41840 | 0.212855 | ||||||||
\(649\) | −0.439759 | −0.0172621 | ||||||||
\(650\) | −29.5556 | −1.15927 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.3649 | −0.954205 | ||||||||
\(653\) | −26.2667 | −1.02789 | −0.513947 | − | 0.857822i | \(-0.671817\pi\) | ||||
−0.513947 | + | 0.857822i | \(0.671817\pi\) | |||||||
\(654\) | 10.2674 | 0.401485 | ||||||||
\(655\) | 20.5376 | 0.802470 | ||||||||
\(656\) | −5.11024 | −0.199521 | ||||||||
\(657\) | 4.74670 | 0.185186 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.06739 | 0.275307 | 0.137653 | − | 0.990480i | \(-0.456044\pi\) | ||||
0.137653 | + | 0.990480i | \(0.456044\pi\) | |||||||
\(660\) | 2.16806 | 0.0843915 | ||||||||
\(661\) | 21.1380 | 0.822174 | 0.411087 | − | 0.911596i | \(-0.365149\pi\) | ||||
0.411087 | + | 0.911596i | \(0.365149\pi\) | |||||||
\(662\) | −25.4371 | −0.988641 | ||||||||
\(663\) | 6.34545 | 0.246437 | ||||||||
\(664\) | 62.2075 | 2.41412 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.71797 | −0.0665701 | ||||||||
\(667\) | 1.96373 | 0.0760358 | ||||||||
\(668\) | 62.5447 | 2.41993 | ||||||||
\(669\) | −17.7285 | −0.685424 | ||||||||
\(670\) | −28.4783 | −1.10021 | ||||||||
\(671\) | 3.77771 | 0.145837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.2461 | 1.66701 | 0.833506 | − | 0.552510i | \(-0.186330\pi\) | ||||
0.833506 | + | 0.552510i | \(0.186330\pi\) | |||||||
\(674\) | 89.5583 | 3.44966 | ||||||||
\(675\) | −1.87710 | −0.0722497 | ||||||||
\(676\) | 113.344 | 4.35937 | ||||||||
\(677\) | −5.05319 | −0.194210 | −0.0971049 | − | 0.995274i | \(-0.530958\pi\) | ||||
−0.0971049 | + | 0.995274i | \(0.530958\pi\) | |||||||
\(678\) | 5.81438 | 0.223300 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 9.59275 | 0.367865 | ||||||||
\(681\) | 6.90430 | 0.264573 | ||||||||
\(682\) | −1.01776 | −0.0389721 | ||||||||
\(683\) | 4.29790 | 0.164455 | 0.0822273 | − | 0.996614i | \(-0.473797\pi\) | ||||
0.0822273 | + | 0.996614i | \(0.473797\pi\) | |||||||
\(684\) | −24.5558 | −0.938913 | ||||||||
\(685\) | 7.40904 | 0.283085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.1972 | 0.541656 | ||||||||
\(688\) | −2.08779 | −0.0795963 | ||||||||
\(689\) | −61.1832 | −2.33090 | ||||||||
\(690\) | 3.68252 | 0.140191 | ||||||||
\(691\) | 1.35475 | 0.0515370 | 0.0257685 | − | 0.999668i | \(-0.491797\pi\) | ||||
0.0257685 | + | 0.999668i | \(0.491797\pi\) | |||||||
\(692\) | 10.6777 | 0.405904 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.6816 | 0.823023 | ||||||||
\(695\) | −24.5663 | −0.931853 | ||||||||
\(696\) | 12.6931 | 0.481132 | ||||||||
\(697\) | −1.00183 | −0.0379469 | ||||||||
\(698\) | 63.6767 | 2.41020 | ||||||||
\(699\) | 1.41764 | 0.0536200 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.4004 | −1.63921 | −0.819605 | − | 0.572929i | \(-0.805807\pi\) | ||||
−0.819605 | + | 0.572929i | \(0.805807\pi\) | |||||||
\(702\) | 15.7453 | 0.594269 | ||||||||
\(703\) | 4.06019 | 0.153133 | ||||||||
\(704\) | −1.63791 | −0.0617309 | ||||||||
\(705\) | 19.5078 | 0.734708 | ||||||||
\(706\) | 8.53692 | 0.321291 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.26189 | −0.235336 | ||||||||
\(709\) | 40.2824 | 1.51284 | 0.756419 | − | 0.654087i | \(-0.226947\pi\) | ||||
0.756419 | + | 0.654087i | \(0.226947\pi\) | |||||||
\(710\) | −48.7889 | −1.83102 | ||||||||
\(711\) | 1.80292 | 0.0676146 | ||||||||
\(712\) | −85.6550 | −3.21006 | ||||||||
\(713\) | −1.16922 | −0.0437877 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.28548 | 0.122870 | ||||||||
\(716\) | 48.0530 | 1.79582 | ||||||||
\(717\) | 1.91363 | 0.0714658 | ||||||||
\(718\) | −85.1083 | −3.17621 | ||||||||
\(719\) | −31.2329 | −1.16479 | −0.582394 | − | 0.812906i | \(-0.697884\pi\) | ||||
−0.582394 | + | 0.812906i | \(0.697884\pi\) | |||||||
\(720\) | 9.03067 | 0.336553 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 38.5720 | 1.43550 | ||||||||
\(723\) | −8.74190 | −0.325115 | ||||||||
\(724\) | 43.8359 | 1.62915 | ||||||||
\(725\) | −4.39729 | −0.163311 | ||||||||
\(726\) | −27.1306 | −1.00691 | ||||||||
\(727\) | 33.0217 | 1.22471 | 0.612354 | − | 0.790584i | \(-0.290223\pi\) | ||||
0.612354 | + | 0.790584i | \(0.290223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 20.8522 | 0.771776 | ||||||||
\(731\) | −0.409297 | −0.0151384 | ||||||||
\(732\) | 53.7921 | 1.98821 | ||||||||
\(733\) | 9.34705 | 0.345241 | 0.172621 | − | 0.984988i | \(-0.444777\pi\) | ||||
0.172621 | + | 0.984988i | \(0.444777\pi\) | |||||||
\(734\) | −39.1793 | −1.44613 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.56480 | 0.0576794 | ||||||||
\(737\) | −1.90285 | −0.0700923 | ||||||||
\(738\) | −2.48589 | −0.0915070 | ||||||||
\(739\) | −48.8290 | −1.79620 | −0.898101 | − | 0.439789i | \(-0.855053\pi\) | ||||
−0.898101 | + | 0.439789i | \(0.855053\pi\) | |||||||
\(740\) | −5.10451 | −0.187645 | ||||||||
\(741\) | −37.2119 | −1.36701 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.2245 | 0.521845 | 0.260923 | − | 0.965360i | \(-0.415973\pi\) | ||||
0.260923 | + | 0.965360i | \(0.415973\pi\) | |||||||
\(744\) | −7.55760 | −0.277075 | ||||||||
\(745\) | 34.8899 | 1.27827 | ||||||||
\(746\) | −85.5429 | −3.13195 | ||||||||
\(747\) | 11.4808 | 0.420060 | ||||||||
\(748\) | 1.22909 | 0.0449401 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −30.2111 | −1.10315 | ||||||||
\(751\) | −6.47294 | −0.236201 | −0.118100 | − | 0.993002i | \(-0.537680\pi\) | ||||
−0.118100 | + | 0.993002i | \(0.537680\pi\) | |||||||
\(752\) | 56.4120 | 2.05714 | ||||||||
\(753\) | 16.3935 | 0.597411 | ||||||||
\(754\) | 36.8849 | 1.34327 | ||||||||
\(755\) | 1.00400 | 0.0365393 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.8314 | 1.04790 | 0.523948 | − | 0.851751i | \(-0.324459\pi\) | ||||
0.523948 | + | 0.851751i | \(0.324459\pi\) | |||||||
\(758\) | 50.8503 | 1.84697 | ||||||||
\(759\) | 0.246056 | 0.00893128 | ||||||||
\(760\) | −56.2552 | −2.04059 | ||||||||
\(761\) | −34.6531 | −1.25617 | −0.628087 | − | 0.778143i | \(-0.716162\pi\) | ||||
−0.628087 | + | 0.778143i | \(0.716162\pi\) | |||||||
\(762\) | −29.8079 | −1.07982 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −21.1513 | −0.765227 | ||||||||
\(765\) | 1.77040 | 0.0640090 | ||||||||
\(766\) | −76.6238 | −2.76853 | ||||||||
\(767\) | −9.48929 | −0.342638 | ||||||||
\(768\) | −32.6036 | −1.17648 | ||||||||
\(769\) | −23.0565 | −0.831438 | −0.415719 | − | 0.909493i | \(-0.636470\pi\) | ||||
−0.415719 | + | 0.909493i | \(0.636470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.79030 | −0.208532 | ||||||||
\(772\) | 14.8247 | 0.533554 | ||||||||
\(773\) | 13.9342 | 0.501180 | 0.250590 | − | 0.968093i | \(-0.419375\pi\) | ||||
0.250590 | + | 0.968093i | \(0.419375\pi\) | |||||||
\(774\) | −1.01561 | −0.0365054 | ||||||||
\(775\) | 2.61819 | 0.0940481 | ||||||||
\(776\) | 50.2618 | 1.80429 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 60.9339 | 2.18459 | ||||||||
\(779\) | 5.87506 | 0.210496 | ||||||||
\(780\) | 46.7831 | 1.67510 | ||||||||
\(781\) | −3.25995 | −0.116650 | ||||||||
\(782\) | 2.08766 | 0.0746545 | ||||||||
\(783\) | 2.34260 | 0.0837175 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.1867 | −1.36294 | ||||||||
\(786\) | 28.8904 | 1.03049 | ||||||||
\(787\) | −7.78663 | −0.277564 | −0.138782 | − | 0.990323i | \(-0.544319\pi\) | ||||
−0.138782 | + | 0.990323i | \(0.544319\pi\) | |||||||
\(788\) | −73.8200 | −2.62973 | ||||||||
\(789\) | 7.57467 | 0.269665 | ||||||||
\(790\) | 7.92020 | 0.281788 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.59046 | 0.0565144 | ||||||||
\(793\) | 81.5168 | 2.89475 | ||||||||
\(794\) | 33.6904 | 1.19563 | ||||||||
\(795\) | −17.0703 | −0.605422 | ||||||||
\(796\) | −63.3813 | −2.24649 | ||||||||
\(797\) | −12.2136 | −0.432628 | −0.216314 | − | 0.976324i | \(-0.569404\pi\) | ||||
−0.216314 | + | 0.976324i | \(0.569404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0592 | 0.391246 | ||||||||
\(800\) | −3.50400 | −0.123885 | ||||||||
\(801\) | −15.8082 | −0.558554 | ||||||||
\(802\) | 49.0206 | 1.73098 | ||||||||
\(803\) | 1.39329 | 0.0491683 | ||||||||
\(804\) | −27.0953 | −0.955578 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.9616 | −0.773565 | ||||||||
\(807\) | −24.0489 | −0.846562 | ||||||||
\(808\) | −69.3864 | −2.44101 | ||||||||
\(809\) | 40.8740 | 1.43705 | 0.718527 | − | 0.695499i | \(-0.244817\pi\) | ||||
0.718527 | + | 0.695499i | \(0.244817\pi\) | |||||||
\(810\) | 4.39300 | 0.154354 | ||||||||
\(811\) | −22.6939 | −0.796891 | −0.398446 | − | 0.917192i | \(-0.630450\pi\) | ||||
−0.398446 | + | 0.917192i | \(0.630450\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.6082 | 0.512332 | ||||||||
\(814\) | −0.504275 | −0.0176748 | ||||||||
\(815\) | −10.3016 | −0.360848 | ||||||||
\(816\) | 5.11958 | 0.179221 | ||||||||
\(817\) | 2.40026 | 0.0839745 | ||||||||
\(818\) | −37.7767 | −1.32083 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.38618 | −0.257937 | ||||||||
\(821\) | 23.5550 | 0.822077 | 0.411038 | − | 0.911618i | \(-0.365166\pi\) | ||||
0.411038 | + | 0.911618i | \(0.365166\pi\) | |||||||
\(822\) | 10.4223 | 0.363521 | ||||||||
\(823\) | 38.9259 | 1.35687 | 0.678436 | − | 0.734659i | \(-0.262658\pi\) | ||||
0.678436 | + | 0.734659i | \(0.262658\pi\) | |||||||
\(824\) | 21.0714 | 0.734057 | ||||||||
\(825\) | −0.550984 | −0.0191828 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.6495 | 0.961468 | 0.480734 | − | 0.876867i | \(-0.340370\pi\) | ||||
0.480734 | + | 0.876867i | \(0.340370\pi\) | |||||||
\(828\) | 3.50368 | 0.121761 | ||||||||
\(829\) | 5.42158 | 0.188299 | 0.0941496 | − | 0.995558i | \(-0.469987\pi\) | ||||
0.0941496 | + | 0.995558i | \(0.469987\pi\) | |||||||
\(830\) | 50.4351 | 1.75063 | ||||||||
\(831\) | 13.2496 | 0.459625 | ||||||||
\(832\) | −35.3433 | −1.22531 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −34.5576 | −1.19663 | ||||||||
\(835\) | 26.4441 | 0.915135 | ||||||||
\(836\) | −7.20783 | −0.249288 | ||||||||
\(837\) | −1.39480 | −0.0482114 | ||||||||
\(838\) | −95.6466 | −3.30406 | ||||||||
\(839\) | 21.8886 | 0.755680 | 0.377840 | − | 0.925871i | \(-0.376667\pi\) | ||||
0.377840 | + | 0.925871i | \(0.376667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.5122 | −0.810767 | ||||||||
\(842\) | −97.0950 | −3.34611 | ||||||||
\(843\) | 15.2773 | 0.526178 | ||||||||
\(844\) | 28.8043 | 0.991485 | ||||||||
\(845\) | 47.9220 | 1.64857 | ||||||||
\(846\) | 27.4418 | 0.943469 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −49.3634 | −1.69514 | ||||||||
\(849\) | 27.9553 | 0.959424 | ||||||||
\(850\) | −4.67481 | −0.160345 | ||||||||
\(851\) | −0.579319 | −0.0198588 | ||||||||
\(852\) | −46.4196 | −1.59031 | ||||||||
\(853\) | −12.9626 | −0.443831 | −0.221915 | − | 0.975066i | \(-0.571231\pi\) | ||||
−0.221915 | + | 0.975066i | \(0.571231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.3822 | −0.355065 | ||||||||
\(856\) | −89.8683 | −3.07163 | ||||||||
\(857\) | 42.7269 | 1.45952 | 0.729762 | − | 0.683702i | \(-0.239631\pi\) | ||||
0.729762 | + | 0.683702i | \(0.239631\pi\) | |||||||
\(858\) | 4.62170 | 0.157782 | ||||||||
\(859\) | 33.9106 | 1.15701 | 0.578507 | − | 0.815678i | \(-0.303636\pi\) | ||||
0.578507 | + | 0.815678i | \(0.303636\pi\) | |||||||
\(860\) | −3.01763 | −0.102900 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.61572 | 0.0890919 | ||||||||
\(863\) | −20.2687 | −0.689955 | −0.344978 | − | 0.938611i | \(-0.612113\pi\) | ||||
−0.344978 | + | 0.938611i | \(0.612113\pi\) | |||||||
\(864\) | 1.86671 | 0.0635066 | ||||||||
\(865\) | 4.51455 | 0.153499 | ||||||||
\(866\) | 61.5067 | 2.09008 | ||||||||
\(867\) | −15.9963 | −0.543264 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.529208 | 0.0179521 | ||||||||
\(870\) | 10.2910 | 0.348898 | ||||||||
\(871\) | −41.0603 | −1.39128 | ||||||||
\(872\) | 22.3793 | 0.757860 | ||||||||
\(873\) | 9.27612 | 0.313949 | ||||||||
\(874\) | −12.2427 | −0.414117 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.8396 | 0.670318 | ||||||||
\(877\) | −5.45153 | −0.184085 | −0.0920425 | − | 0.995755i | \(-0.529340\pi\) | ||||
−0.0920425 | + | 0.995755i | \(0.529340\pi\) | |||||||
\(878\) | −34.6065 | −1.16791 | ||||||||
\(879\) | 10.3302 | 0.348430 | ||||||||
\(880\) | 2.65076 | 0.0893572 | ||||||||
\(881\) | 52.0187 | 1.75256 | 0.876278 | − | 0.481806i | \(-0.160019\pi\) | ||||
0.876278 | + | 0.481806i | \(0.160019\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.9846 | −0.638882 | −0.319441 | − | 0.947606i | \(-0.603495\pi\) | ||||
−0.319441 | + | 0.947606i | \(0.603495\pi\) | |||||||
\(884\) | 26.5218 | 0.892025 | ||||||||
\(885\) | −2.64754 | −0.0889962 | ||||||||
\(886\) | 17.9089 | 0.601662 | ||||||||
\(887\) | −41.7572 | −1.40207 | −0.701035 | − | 0.713127i | \(-0.747278\pi\) | ||||
−0.701035 | + | 0.713127i | \(0.747278\pi\) | |||||||
\(888\) | −3.74460 | −0.125661 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −69.4453 | −2.32781 | ||||||||
\(891\) | 0.293529 | 0.00983359 | ||||||||
\(892\) | −74.0991 | −2.48102 | ||||||||
\(893\) | −64.8549 | −2.17029 | ||||||||
\(894\) | 49.0799 | 1.64148 | ||||||||
\(895\) | 20.3169 | 0.679120 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.30949 | 0.177279 | ||||||||
\(898\) | −66.1161 | −2.20632 | ||||||||
\(899\) | −3.26746 | −0.108976 | ||||||||
\(900\) | −7.84565 | −0.261522 | ||||||||
\(901\) | −9.67735 | −0.322399 | ||||||||
\(902\) | −0.729681 | −0.0242957 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.6734 | 0.421510 | ||||||||
\(905\) | 18.5340 | 0.616090 | ||||||||
\(906\) | 1.41233 | 0.0469217 | ||||||||
\(907\) | 6.25865 | 0.207815 | 0.103908 | − | 0.994587i | \(-0.466865\pi\) | ||||
0.103908 | + | 0.994587i | \(0.466865\pi\) | |||||||
\(908\) | 28.8576 | 0.957673 | ||||||||
\(909\) | −12.8057 | −0.424738 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.44814 | 0.0479789 | 0.0239895 | − | 0.999712i | \(-0.492363\pi\) | ||||
0.0239895 | + | 0.999712i | \(0.492363\pi\) | |||||||
\(912\) | −30.0230 | −0.994161 | ||||||||
\(913\) | 3.36994 | 0.111529 | ||||||||
\(914\) | 55.2554 | 1.82769 | ||||||||
\(915\) | 22.7435 | 0.751876 | ||||||||
\(916\) | 59.3393 | 1.96063 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.49044 | 0.0821967 | ||||||||
\(919\) | 48.5596 | 1.60183 | 0.800916 | − | 0.598776i | \(-0.204346\pi\) | ||||
0.800916 | + | 0.598776i | \(0.204346\pi\) | |||||||
\(920\) | 8.02664 | 0.264630 | ||||||||
\(921\) | −19.9196 | −0.656375 | ||||||||
\(922\) | 4.67620 | 0.154002 | ||||||||
\(923\) | −70.3443 | −2.31541 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.29725 | 0.0426532 | ||||||||
\(926\) | −22.7866 | −0.748814 | ||||||||
\(927\) | 3.88886 | 0.127727 | ||||||||
\(928\) | 4.37294 | 0.143549 | ||||||||
\(929\) | 12.0033 | 0.393814 | 0.196907 | − | 0.980422i | \(-0.436910\pi\) | ||||
0.196907 | + | 0.980422i | \(0.436910\pi\) | |||||||
\(930\) | −6.12737 | −0.200924 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.92524 | 0.194088 | ||||||||
\(933\) | −19.0288 | −0.622976 | ||||||||
\(934\) | −83.9221 | −2.74601 | ||||||||
\(935\) | 0.519664 | 0.0169948 | ||||||||
\(936\) | 34.3194 | 1.12177 | ||||||||
\(937\) | 23.2643 | 0.760013 | 0.380007 | − | 0.924984i | \(-0.375922\pi\) | ||||
0.380007 | + | 0.924984i | \(0.375922\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.7830 | 1.00456 | ||||||||
\(940\) | 81.5362 | 2.65942 | ||||||||
\(941\) | 29.8756 | 0.973918 | 0.486959 | − | 0.873425i | \(-0.338106\pi\) | ||||
0.486959 | + | 0.873425i | \(0.338106\pi\) | |||||||
\(942\) | −53.7175 | −1.75021 | ||||||||
\(943\) | −0.838269 | −0.0272978 | ||||||||
\(944\) | −7.65607 | −0.249184 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.298112 | −0.00969244 | ||||||||
\(947\) | −12.3349 | −0.400830 | −0.200415 | − | 0.979711i | \(-0.564229\pi\) | ||||
−0.200415 | + | 0.979711i | \(0.564229\pi\) | |||||||
\(948\) | 7.53557 | 0.244744 | ||||||||
\(949\) | 30.0650 | 0.975950 | ||||||||
\(950\) | 27.4147 | 0.889449 | ||||||||
\(951\) | −3.77693 | −0.122475 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.1038 | 1.07234 | 0.536169 | − | 0.844111i | \(-0.319871\pi\) | ||||
0.536169 | + | 0.844111i | \(0.319871\pi\) | |||||||
\(954\) | −24.0130 | −0.777448 | ||||||||
\(955\) | −8.94282 | −0.289383 | ||||||||
\(956\) | 7.99832 | 0.258684 | ||||||||
\(957\) | 0.687619 | 0.0222276 | ||||||||
\(958\) | −17.8003 | −0.575102 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.86091 | −0.318259 | ||||||||
\(961\) | −29.0545 | −0.937243 | ||||||||
\(962\) | −10.8814 | −0.350831 | ||||||||
\(963\) | −16.5858 | −0.534468 | ||||||||
\(964\) | −36.5382 | −1.17682 | ||||||||
\(965\) | 6.26794 | 0.201772 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.206392 | 0.00663711 | 0.00331856 | − | 0.999994i | \(-0.498944\pi\) | ||||
0.00331856 | + | 0.999994i | \(0.498944\pi\) | |||||||
\(968\) | −59.1356 | −1.90069 | ||||||||
\(969\) | −5.88580 | −0.189079 | ||||||||
\(970\) | 40.7500 | 1.30840 | ||||||||
\(971\) | 19.7601 | 0.634133 | 0.317067 | − | 0.948403i | \(-0.397302\pi\) | ||||
0.317067 | + | 0.948403i | \(0.397302\pi\) | |||||||
\(972\) | 4.17966 | 0.134063 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27.1784 | −0.870852 | ||||||||
\(975\) | −11.8893 | −0.380763 | ||||||||
\(976\) | 65.7687 | 2.10520 | ||||||||
\(977\) | 43.0318 | 1.37671 | 0.688354 | − | 0.725375i | \(-0.258333\pi\) | ||||
0.688354 | + | 0.725375i | \(0.258333\pi\) | |||||||
\(978\) | −14.4913 | −0.463380 | ||||||||
\(979\) | −4.64015 | −0.148300 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.13025 | 0.131869 | ||||||||
\(982\) | 60.9428 | 1.94476 | ||||||||
\(983\) | −58.2137 | −1.85673 | −0.928365 | − | 0.371670i | \(-0.878785\pi\) | ||||
−0.928365 | + | 0.371670i | \(0.878785\pi\) | |||||||
\(984\) | −5.41840 | −0.172732 | ||||||||
\(985\) | −31.2113 | −0.994475 | ||||||||
\(986\) | 5.83409 | 0.185795 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −155.533 | −4.94817 | ||||||||
\(989\) | −0.342475 | −0.0108901 | ||||||||
\(990\) | 1.28947 | 0.0409821 | ||||||||
\(991\) | 56.9979 | 1.81060 | 0.905300 | − | 0.424774i | \(-0.139646\pi\) | ||||
0.905300 | + | 0.424774i | \(0.139646\pi\) | |||||||
\(992\) | −2.60369 | −0.0826672 | ||||||||
\(993\) | −10.2326 | −0.324721 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.7978 | −0.849547 | ||||||||
\(996\) | 47.9858 | 1.52049 | ||||||||
\(997\) | 48.8707 | 1.54775 | 0.773875 | − | 0.633338i | \(-0.218316\pi\) | ||||
0.773875 | + | 0.633338i | \(0.218316\pi\) | |||||||
\(998\) | −93.0983 | −2.94697 | ||||||||
\(999\) | −0.691089 | −0.0218651 |
(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 | 6027.2.a.bg.1.12 | 12 | ||
7.2 | even | 3 | 861.2.i.e.739.1 | yes | 24 | ||
7.4 | even | 3 | 861.2.i.e.247.1 | ✓ | 24 | ||
7.6 | odd | 2 | 6027.2.a.bf.1.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.e.247.1 | ✓ | 24 | 7.4 | even | 3 | ||
861.2.i.e.739.1 | yes | 24 | 7.2 | even | 3 | ||
6027.2.a.bf.1.12 | 12 | 7.6 | odd | 2 | |||
6027.2.a.bg.1.12 | 12 | 1.1 | even | 1 | trivial |