Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, 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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.19520000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.15124\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.578669 | 0.334095 | 0.167047 | − | 0.985949i | \(-0.446577\pi\) | ||||
0.167047 | + | 0.985949i | \(0.446577\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.36891 | 0.612193 | 0.306097 | − | 0.952000i | \(-0.400977\pi\) | ||||
0.306097 | + | 0.952000i | \(0.400977\pi\) | |||||||
\(6\) | −0.578669 | −0.236241 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.66514 | −0.888381 | ||||||||
\(10\) | −1.36891 | −0.432886 | ||||||||
\(11\) | 1.62784 | 0.490812 | 0.245406 | − | 0.969420i | \(-0.421079\pi\) | ||||
0.245406 | + | 0.969420i | \(0.421079\pi\) | |||||||
\(12\) | 0.578669 | 0.167047 | ||||||||
\(13\) | 5.18824 | 1.43896 | 0.719480 | − | 0.694513i | \(-0.244380\pi\) | ||||
0.719480 | + | 0.694513i | \(0.244380\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0.792143 | 0.204531 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.257918 | 0.0625543 | 0.0312771 | − | 0.999511i | \(-0.490043\pi\) | ||||
0.0312771 | + | 0.999511i | \(0.490043\pi\) | |||||||
\(18\) | 2.66514 | 0.628180 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.36891 | 0.306097 | ||||||||
\(21\) | −0.578669 | −0.126276 | ||||||||
\(22\) | −1.62784 | −0.347057 | ||||||||
\(23\) | −0.275797 | −0.0575076 | −0.0287538 | − | 0.999587i | \(-0.509154\pi\) | ||||
−0.0287538 | + | 0.999587i | \(0.509154\pi\) | |||||||
\(24\) | −0.578669 | −0.118120 | ||||||||
\(25\) | −3.12610 | −0.625220 | ||||||||
\(26\) | −5.18824 | −1.01750 | ||||||||
\(27\) | −3.27824 | −0.630898 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −3.15414 | −0.585709 | −0.292854 | − | 0.956157i | \(-0.594605\pi\) | ||||
−0.292854 | + | 0.956157i | \(0.594605\pi\) | |||||||
\(30\) | −0.792143 | −0.144625 | ||||||||
\(31\) | −7.06316 | −1.26858 | −0.634291 | − | 0.773095i | \(-0.718708\pi\) | ||||
−0.634291 | + | 0.773095i | \(0.718708\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.941981 | 0.163978 | ||||||||
\(34\) | −0.257918 | −0.0442326 | ||||||||
\(35\) | −1.36891 | −0.231387 | ||||||||
\(36\) | −2.66514 | −0.444190 | ||||||||
\(37\) | −9.35193 | −1.53745 | −0.768724 | − | 0.639581i | \(-0.779108\pi\) | ||||
−0.768724 | + | 0.639581i | \(0.779108\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00228 | 0.480749 | ||||||||
\(40\) | −1.36891 | −0.216443 | ||||||||
\(41\) | −7.91308 | −1.23582 | −0.617908 | − | 0.786251i | \(-0.712020\pi\) | ||||
−0.617908 | + | 0.786251i | \(0.712020\pi\) | |||||||
\(42\) | 0.578669 | 0.0892906 | ||||||||
\(43\) | −2.96944 | −0.452835 | −0.226417 | − | 0.974030i | \(-0.572701\pi\) | ||||
−0.226417 | + | 0.974030i | \(0.572701\pi\) | |||||||
\(44\) | 1.62784 | 0.245406 | ||||||||
\(45\) | −3.64833 | −0.543860 | ||||||||
\(46\) | 0.275797 | 0.0406640 | ||||||||
\(47\) | −2.35659 | −0.343744 | −0.171872 | − | 0.985119i | \(-0.554982\pi\) | ||||
−0.171872 | + | 0.985119i | \(0.554982\pi\) | |||||||
\(48\) | 0.578669 | 0.0835237 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.12610 | 0.442097 | ||||||||
\(51\) | 0.149249 | 0.0208991 | ||||||||
\(52\) | 5.18824 | 0.719480 | ||||||||
\(53\) | −7.47738 | −1.02710 | −0.513549 | − | 0.858060i | \(-0.671669\pi\) | ||||
−0.513549 | + | 0.858060i | \(0.671669\pi\) | |||||||
\(54\) | 3.27824 | 0.446112 | ||||||||
\(55\) | 2.22836 | 0.300472 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.15414 | 0.414159 | ||||||||
\(59\) | −2.57219 | −0.334871 | −0.167435 | − | 0.985883i | \(-0.553549\pi\) | ||||
−0.167435 | + | 0.985883i | \(0.553549\pi\) | |||||||
\(60\) | 0.792143 | 0.102265 | ||||||||
\(61\) | 12.3032 | 1.57526 | 0.787630 | − | 0.616149i | \(-0.211308\pi\) | ||||
0.787630 | + | 0.616149i | \(0.211308\pi\) | |||||||
\(62\) | 7.06316 | 0.897022 | ||||||||
\(63\) | 2.66514 | 0.335776 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.10221 | 0.880921 | ||||||||
\(66\) | −0.941981 | −0.115950 | ||||||||
\(67\) | 3.59521 | 0.439225 | 0.219612 | − | 0.975587i | \(-0.429521\pi\) | ||||
0.219612 | + | 0.975587i | \(0.429521\pi\) | |||||||
\(68\) | 0.257918 | 0.0312771 | ||||||||
\(69\) | −0.159595 | −0.0192130 | ||||||||
\(70\) | 1.36891 | 0.163615 | ||||||||
\(71\) | 3.93297 | 0.466758 | 0.233379 | − | 0.972386i | \(-0.425022\pi\) | ||||
0.233379 | + | 0.972386i | \(0.425022\pi\) | |||||||
\(72\) | 2.66514 | 0.314090 | ||||||||
\(73\) | 1.56026 | 0.182614 | 0.0913072 | − | 0.995823i | \(-0.470895\pi\) | ||||
0.0913072 | + | 0.995823i | \(0.470895\pi\) | |||||||
\(74\) | 9.35193 | 1.08714 | ||||||||
\(75\) | −1.80898 | −0.208883 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.62784 | −0.185510 | ||||||||
\(78\) | −3.00228 | −0.339941 | ||||||||
\(79\) | −15.7365 | −1.77050 | −0.885248 | − | 0.465120i | \(-0.846011\pi\) | ||||
−0.885248 | + | 0.465120i | \(0.846011\pi\) | |||||||
\(80\) | 1.36891 | 0.153048 | ||||||||
\(81\) | 6.09841 | 0.677601 | ||||||||
\(82\) | 7.91308 | 0.873854 | ||||||||
\(83\) | 10.8657 | 1.19266 | 0.596331 | − | 0.802739i | \(-0.296625\pi\) | ||||
0.596331 | + | 0.802739i | \(0.296625\pi\) | |||||||
\(84\) | −0.578669 | −0.0631380 | ||||||||
\(85\) | 0.353065 | 0.0382953 | ||||||||
\(86\) | 2.96944 | 0.320202 | ||||||||
\(87\) | −1.82520 | −0.195682 | ||||||||
\(88\) | −1.62784 | −0.173528 | ||||||||
\(89\) | −0.947298 | −0.100413 | −0.0502067 | − | 0.998739i | \(-0.515988\pi\) | ||||
−0.0502067 | + | 0.998739i | \(0.515988\pi\) | |||||||
\(90\) | 3.64833 | 0.384567 | ||||||||
\(91\) | −5.18824 | −0.543876 | ||||||||
\(92\) | −0.275797 | −0.0287538 | ||||||||
\(93\) | −4.08723 | −0.423826 | ||||||||
\(94\) | 2.35659 | 0.243064 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.578669 | −0.0590602 | ||||||||
\(97\) | −4.32044 | −0.438675 | −0.219337 | − | 0.975649i | \(-0.570390\pi\) | ||||
−0.219337 | + | 0.975649i | \(0.570390\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −4.33843 | −0.436028 | ||||||||
\(100\) | −3.12610 | −0.312610 | ||||||||
\(101\) | 12.0383 | 1.19786 | 0.598928 | − | 0.800803i | \(-0.295593\pi\) | ||||
0.598928 | + | 0.800803i | \(0.295593\pi\) | |||||||
\(102\) | −0.149249 | −0.0147779 | ||||||||
\(103\) | −5.10605 | −0.503114 | −0.251557 | − | 0.967842i | \(-0.580943\pi\) | ||||
−0.251557 | + | 0.967842i | \(0.580943\pi\) | |||||||
\(104\) | −5.18824 | −0.508749 | ||||||||
\(105\) | −0.792143 | −0.0773053 | ||||||||
\(106\) | 7.47738 | 0.726268 | ||||||||
\(107\) | 4.21439 | 0.407420 | 0.203710 | − | 0.979031i | \(-0.434700\pi\) | ||||
0.203710 | + | 0.979031i | \(0.434700\pi\) | |||||||
\(108\) | −3.27824 | −0.315449 | ||||||||
\(109\) | 12.3453 | 1.18246 | 0.591232 | − | 0.806502i | \(-0.298642\pi\) | ||||
0.591232 | + | 0.806502i | \(0.298642\pi\) | |||||||
\(110\) | −2.22836 | −0.212466 | ||||||||
\(111\) | −5.41167 | −0.513653 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −15.3482 | −1.44384 | −0.721918 | − | 0.691979i | \(-0.756739\pi\) | ||||
−0.721918 | + | 0.691979i | \(0.756739\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.377540 | −0.0352058 | ||||||||
\(116\) | −3.15414 | −0.292854 | ||||||||
\(117\) | −13.8274 | −1.27834 | ||||||||
\(118\) | 2.57219 | 0.236789 | ||||||||
\(119\) | −0.257918 | −0.0236433 | ||||||||
\(120\) | −0.792143 | −0.0723125 | ||||||||
\(121\) | −8.35013 | −0.759103 | ||||||||
\(122\) | −12.3032 | −1.11388 | ||||||||
\(123\) | −4.57906 | −0.412880 | ||||||||
\(124\) | −7.06316 | −0.634291 | ||||||||
\(125\) | −11.1239 | −0.994948 | ||||||||
\(126\) | −2.66514 | −0.237430 | ||||||||
\(127\) | 12.5502 | 1.11365 | 0.556824 | − | 0.830630i | \(-0.312020\pi\) | ||||
0.556824 | + | 0.830630i | \(0.312020\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.71832 | −0.151290 | ||||||||
\(130\) | −7.10221 | −0.622905 | ||||||||
\(131\) | 8.20043 | 0.716475 | 0.358238 | − | 0.933630i | \(-0.383378\pi\) | ||||
0.358238 | + | 0.933630i | \(0.383378\pi\) | |||||||
\(132\) | 0.941981 | 0.0819890 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.59521 | −0.310579 | ||||||||
\(135\) | −4.48760 | −0.386231 | ||||||||
\(136\) | −0.257918 | −0.0221163 | ||||||||
\(137\) | 6.57313 | 0.561580 | 0.280790 | − | 0.959769i | \(-0.409403\pi\) | ||||
0.280790 | + | 0.959769i | \(0.409403\pi\) | |||||||
\(138\) | 0.159595 | 0.0135856 | ||||||||
\(139\) | −2.58506 | −0.219262 | −0.109631 | − | 0.993972i | \(-0.534967\pi\) | ||||
−0.109631 | + | 0.993972i | \(0.534967\pi\) | |||||||
\(140\) | −1.36891 | −0.115694 | ||||||||
\(141\) | −1.36369 | −0.114843 | ||||||||
\(142\) | −3.93297 | −0.330048 | ||||||||
\(143\) | 8.44563 | 0.706259 | ||||||||
\(144\) | −2.66514 | −0.222095 | ||||||||
\(145\) | −4.31772 | −0.358567 | ||||||||
\(146\) | −1.56026 | −0.129128 | ||||||||
\(147\) | 0.578669 | 0.0477278 | ||||||||
\(148\) | −9.35193 | −0.768724 | ||||||||
\(149\) | −16.4215 | −1.34530 | −0.672650 | − | 0.739960i | \(-0.734844\pi\) | ||||
−0.672650 | + | 0.739960i | \(0.734844\pi\) | |||||||
\(150\) | 1.80898 | 0.147702 | ||||||||
\(151\) | −1.43635 | −0.116889 | −0.0584443 | − | 0.998291i | \(-0.518614\pi\) | ||||
−0.0584443 | + | 0.998291i | \(0.518614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.687388 | −0.0555720 | ||||||||
\(154\) | 1.62784 | 0.131175 | ||||||||
\(155\) | −9.66880 | −0.776617 | ||||||||
\(156\) | 3.00228 | 0.240374 | ||||||||
\(157\) | −14.7226 | −1.17499 | −0.587495 | − | 0.809228i | \(-0.699886\pi\) | ||||
−0.587495 | + | 0.809228i | \(0.699886\pi\) | |||||||
\(158\) | 15.7365 | 1.25193 | ||||||||
\(159\) | −4.32693 | −0.343148 | ||||||||
\(160\) | −1.36891 | −0.108221 | ||||||||
\(161\) | 0.275797 | 0.0217358 | ||||||||
\(162\) | −6.09841 | −0.479136 | ||||||||
\(163\) | −23.3097 | −1.82576 | −0.912878 | − | 0.408234i | \(-0.866145\pi\) | ||||
−0.912878 | + | 0.408234i | \(0.866145\pi\) | |||||||
\(164\) | −7.91308 | −0.617908 | ||||||||
\(165\) | 1.28948 | 0.100386 | ||||||||
\(166\) | −10.8657 | −0.843340 | ||||||||
\(167\) | 17.9819 | 1.39148 | 0.695740 | − | 0.718294i | \(-0.255077\pi\) | ||||
0.695740 | + | 0.718294i | \(0.255077\pi\) | |||||||
\(168\) | 0.578669 | 0.0446453 | ||||||||
\(169\) | 13.9179 | 1.07060 | ||||||||
\(170\) | −0.353065 | −0.0270789 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.96944 | −0.226417 | ||||||||
\(173\) | −14.5104 | −1.10321 | −0.551603 | − | 0.834107i | \(-0.685984\pi\) | ||||
−0.551603 | + | 0.834107i | \(0.685984\pi\) | |||||||
\(174\) | 1.82520 | 0.138368 | ||||||||
\(175\) | 3.12610 | 0.236311 | ||||||||
\(176\) | 1.62784 | 0.122703 | ||||||||
\(177\) | −1.48845 | −0.111879 | ||||||||
\(178\) | 0.947298 | 0.0710030 | ||||||||
\(179\) | −22.6246 | −1.69104 | −0.845522 | − | 0.533941i | \(-0.820711\pi\) | ||||
−0.845522 | + | 0.533941i | \(0.820711\pi\) | |||||||
\(180\) | −3.64833 | −0.271930 | ||||||||
\(181\) | 26.7353 | 1.98722 | 0.993608 | − | 0.112883i | \(-0.0360084\pi\) | ||||
0.993608 | + | 0.112883i | \(0.0360084\pi\) | |||||||
\(182\) | 5.18824 | 0.384578 | ||||||||
\(183\) | 7.11946 | 0.526286 | ||||||||
\(184\) | 0.275797 | 0.0203320 | ||||||||
\(185\) | −12.8019 | −0.941215 | ||||||||
\(186\) | 4.08723 | 0.299691 | ||||||||
\(187\) | 0.419849 | 0.0307024 | ||||||||
\(188\) | −2.35659 | −0.171872 | ||||||||
\(189\) | 3.27824 | 0.238457 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2051 | 0.810772 | 0.405386 | − | 0.914146i | \(-0.367137\pi\) | ||||
0.405386 | + | 0.914146i | \(0.367137\pi\) | |||||||
\(192\) | 0.578669 | 0.0417619 | ||||||||
\(193\) | −1.14499 | −0.0824185 | −0.0412092 | − | 0.999151i | \(-0.513121\pi\) | ||||
−0.0412092 | + | 0.999151i | \(0.513121\pi\) | |||||||
\(194\) | 4.32044 | 0.310190 | ||||||||
\(195\) | 4.10983 | 0.294311 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.23216 | −0.301529 | −0.150764 | − | 0.988570i | \(-0.548173\pi\) | ||||
−0.150764 | + | 0.988570i | \(0.548173\pi\) | |||||||
\(198\) | 4.33843 | 0.308319 | ||||||||
\(199\) | −11.1242 | −0.788572 | −0.394286 | − | 0.918988i | \(-0.629008\pi\) | ||||
−0.394286 | + | 0.918988i | \(0.629008\pi\) | |||||||
\(200\) | 3.12610 | 0.221049 | ||||||||
\(201\) | 2.08044 | 0.146743 | ||||||||
\(202\) | −12.0383 | −0.847013 | ||||||||
\(203\) | 3.15414 | 0.221377 | ||||||||
\(204\) | 0.149249 | 0.0104495 | ||||||||
\(205\) | −10.8323 | −0.756558 | ||||||||
\(206\) | 5.10605 | 0.355755 | ||||||||
\(207\) | 0.735038 | 0.0510887 | ||||||||
\(208\) | 5.18824 | 0.359740 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.792143 | 0.0546631 | ||||||||
\(211\) | −26.2736 | −1.80875 | −0.904375 | − | 0.426738i | \(-0.859663\pi\) | ||||
−0.904375 | + | 0.426738i | \(0.859663\pi\) | |||||||
\(212\) | −7.47738 | −0.513549 | ||||||||
\(213\) | 2.27589 | 0.155941 | ||||||||
\(214\) | −4.21439 | −0.288089 | ||||||||
\(215\) | −4.06488 | −0.277222 | ||||||||
\(216\) | 3.27824 | 0.223056 | ||||||||
\(217\) | 7.06316 | 0.479479 | ||||||||
\(218\) | −12.3453 | −0.836128 | ||||||||
\(219\) | 0.902873 | 0.0610105 | ||||||||
\(220\) | 2.22836 | 0.150236 | ||||||||
\(221\) | 1.33814 | 0.0900131 | ||||||||
\(222\) | 5.41167 | 0.363208 | ||||||||
\(223\) | −13.1498 | −0.880574 | −0.440287 | − | 0.897857i | \(-0.645123\pi\) | ||||
−0.440287 | + | 0.897857i | \(0.645123\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 8.33150 | 0.555433 | ||||||||
\(226\) | 15.3482 | 1.02095 | ||||||||
\(227\) | 4.75659 | 0.315706 | 0.157853 | − | 0.987463i | \(-0.449543\pi\) | ||||
0.157853 | + | 0.987463i | \(0.449543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.6582 | −0.704313 | −0.352156 | − | 0.935941i | \(-0.614551\pi\) | ||||
−0.352156 | + | 0.935941i | \(0.614551\pi\) | |||||||
\(230\) | 0.377540 | 0.0248942 | ||||||||
\(231\) | −0.941981 | −0.0619778 | ||||||||
\(232\) | 3.15414 | 0.207079 | ||||||||
\(233\) | 1.58547 | 0.103868 | 0.0519339 | − | 0.998651i | \(-0.483461\pi\) | ||||
0.0519339 | + | 0.998651i | \(0.483461\pi\) | |||||||
\(234\) | 13.8274 | 0.903926 | ||||||||
\(235\) | −3.22595 | −0.210438 | ||||||||
\(236\) | −2.57219 | −0.167435 | ||||||||
\(237\) | −9.10623 | −0.591513 | ||||||||
\(238\) | 0.257918 | 0.0167183 | ||||||||
\(239\) | −13.6183 | −0.880894 | −0.440447 | − | 0.897779i | \(-0.645180\pi\) | ||||
−0.440447 | + | 0.897779i | \(0.645180\pi\) | |||||||
\(240\) | 0.792143 | 0.0511326 | ||||||||
\(241\) | −2.51719 | −0.162147 | −0.0810734 | − | 0.996708i | \(-0.525835\pi\) | ||||
−0.0810734 | + | 0.996708i | \(0.525835\pi\) | |||||||
\(242\) | 8.35013 | 0.536767 | ||||||||
\(243\) | 13.3637 | 0.857281 | ||||||||
\(244\) | 12.3032 | 0.787630 | ||||||||
\(245\) | 1.36891 | 0.0874562 | ||||||||
\(246\) | 4.57906 | 0.291950 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.06316 | 0.448511 | ||||||||
\(249\) | 6.28763 | 0.398462 | ||||||||
\(250\) | 11.1239 | 0.703535 | ||||||||
\(251\) | 15.5613 | 0.982219 | 0.491109 | − | 0.871098i | \(-0.336592\pi\) | ||||
0.491109 | + | 0.871098i | \(0.336592\pi\) | |||||||
\(252\) | 2.66514 | 0.167888 | ||||||||
\(253\) | −0.448953 | −0.0282255 | ||||||||
\(254\) | −12.5502 | −0.787468 | ||||||||
\(255\) | 0.204308 | 0.0127943 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.4424 | −1.08803 | −0.544013 | − | 0.839077i | \(-0.683096\pi\) | ||||
−0.544013 | + | 0.839077i | \(0.683096\pi\) | |||||||
\(258\) | 1.71832 | 0.106978 | ||||||||
\(259\) | 9.35193 | 0.581101 | ||||||||
\(260\) | 7.10221 | 0.440461 | ||||||||
\(261\) | 8.40622 | 0.520332 | ||||||||
\(262\) | −8.20043 | −0.506624 | ||||||||
\(263\) | −0.698187 | −0.0430521 | −0.0215260 | − | 0.999768i | \(-0.506852\pi\) | ||||
−0.0215260 | + | 0.999768i | \(0.506852\pi\) | |||||||
\(264\) | −0.941981 | −0.0579749 | ||||||||
\(265\) | −10.2358 | −0.628782 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.548172 | −0.0335476 | ||||||||
\(268\) | 3.59521 | 0.219612 | ||||||||
\(269\) | −16.1173 | −0.982688 | −0.491344 | − | 0.870966i | \(-0.663494\pi\) | ||||
−0.491344 | + | 0.870966i | \(0.663494\pi\) | |||||||
\(270\) | 4.48760 | 0.273107 | ||||||||
\(271\) | 20.6217 | 1.25268 | 0.626340 | − | 0.779550i | \(-0.284552\pi\) | ||||
0.626340 | + | 0.779550i | \(0.284552\pi\) | |||||||
\(272\) | 0.257918 | 0.0156386 | ||||||||
\(273\) | −3.00228 | −0.181706 | ||||||||
\(274\) | −6.57313 | −0.397097 | ||||||||
\(275\) | −5.08879 | −0.306866 | ||||||||
\(276\) | −0.159595 | −0.00960650 | ||||||||
\(277\) | −26.5364 | −1.59442 | −0.797208 | − | 0.603705i | \(-0.793690\pi\) | ||||
−0.797208 | + | 0.603705i | \(0.793690\pi\) | |||||||
\(278\) | 2.58506 | 0.155042 | ||||||||
\(279\) | 18.8243 | 1.12698 | ||||||||
\(280\) | 1.36891 | 0.0818077 | ||||||||
\(281\) | −8.20137 | −0.489253 | −0.244626 | − | 0.969617i | \(-0.578665\pi\) | ||||
−0.244626 | + | 0.969617i | \(0.578665\pi\) | |||||||
\(282\) | 1.36369 | 0.0812064 | ||||||||
\(283\) | 13.1749 | 0.783165 | 0.391582 | − | 0.920143i | \(-0.371928\pi\) | ||||
0.391582 | + | 0.920143i | \(0.371928\pi\) | |||||||
\(284\) | 3.93297 | 0.233379 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.44563 | −0.499401 | ||||||||
\(287\) | 7.91308 | 0.467094 | ||||||||
\(288\) | 2.66514 | 0.157045 | ||||||||
\(289\) | −16.9335 | −0.996087 | ||||||||
\(290\) | 4.31772 | 0.253545 | ||||||||
\(291\) | −2.50011 | −0.146559 | ||||||||
\(292\) | 1.56026 | 0.0913072 | ||||||||
\(293\) | −7.60243 | −0.444139 | −0.222069 | − | 0.975031i | \(-0.571281\pi\) | ||||
−0.222069 | + | 0.975031i | \(0.571281\pi\) | |||||||
\(294\) | −0.578669 | −0.0337487 | ||||||||
\(295\) | −3.52109 | −0.205006 | ||||||||
\(296\) | 9.35193 | 0.543570 | ||||||||
\(297\) | −5.33646 | −0.309653 | ||||||||
\(298\) | 16.4215 | 0.951271 | ||||||||
\(299\) | −1.43090 | −0.0827511 | ||||||||
\(300\) | −1.80898 | −0.104441 | ||||||||
\(301\) | 2.96944 | 0.171155 | ||||||||
\(302\) | 1.43635 | 0.0826527 | ||||||||
\(303\) | 6.96620 | 0.400198 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.8419 | 0.964363 | ||||||||
\(306\) | 0.687388 | 0.0392954 | ||||||||
\(307\) | 21.2034 | 1.21014 | 0.605072 | − | 0.796170i | \(-0.293144\pi\) | ||||
0.605072 | + | 0.796170i | \(0.293144\pi\) | |||||||
\(308\) | −1.62784 | −0.0927548 | ||||||||
\(309\) | −2.95471 | −0.168088 | ||||||||
\(310\) | 9.66880 | 0.549151 | ||||||||
\(311\) | 31.5530 | 1.78921 | 0.894604 | − | 0.446859i | \(-0.147458\pi\) | ||||
0.894604 | + | 0.446859i | \(0.147458\pi\) | |||||||
\(312\) | −3.00228 | −0.169970 | ||||||||
\(313\) | 2.14974 | 0.121510 | 0.0607552 | − | 0.998153i | \(-0.480649\pi\) | ||||
0.0607552 | + | 0.998153i | \(0.480649\pi\) | |||||||
\(314\) | 14.7226 | 0.830843 | ||||||||
\(315\) | 3.64833 | 0.205560 | ||||||||
\(316\) | −15.7365 | −0.885248 | ||||||||
\(317\) | 8.35113 | 0.469046 | 0.234523 | − | 0.972111i | \(-0.424647\pi\) | ||||
0.234523 | + | 0.972111i | \(0.424647\pi\) | |||||||
\(318\) | 4.32693 | 0.242642 | ||||||||
\(319\) | −5.13443 | −0.287473 | ||||||||
\(320\) | 1.36891 | 0.0765241 | ||||||||
\(321\) | 2.43873 | 0.136117 | ||||||||
\(322\) | −0.275797 | −0.0153696 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 6.09841 | 0.338800 | ||||||||
\(325\) | −16.2190 | −0.899666 | ||||||||
\(326\) | 23.3097 | 1.29100 | ||||||||
\(327\) | 7.14383 | 0.395055 | ||||||||
\(328\) | 7.91308 | 0.436927 | ||||||||
\(329\) | 2.35659 | 0.129923 | ||||||||
\(330\) | −1.28948 | −0.0709837 | ||||||||
\(331\) | 4.16252 | 0.228793 | 0.114396 | − | 0.993435i | \(-0.463507\pi\) | ||||
0.114396 | + | 0.993435i | \(0.463507\pi\) | |||||||
\(332\) | 10.8657 | 0.596331 | ||||||||
\(333\) | 24.9242 | 1.36584 | ||||||||
\(334\) | −17.9819 | −0.983925 | ||||||||
\(335\) | 4.92150 | 0.268890 | ||||||||
\(336\) | −0.578669 | −0.0315690 | ||||||||
\(337\) | 4.26524 | 0.232342 | 0.116171 | − | 0.993229i | \(-0.462938\pi\) | ||||
0.116171 | + | 0.993229i | \(0.462938\pi\) | |||||||
\(338\) | −13.9179 | −0.757032 | ||||||||
\(339\) | −8.88152 | −0.482378 | ||||||||
\(340\) | 0.353065 | 0.0191477 | ||||||||
\(341\) | −11.4977 | −0.622636 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.96944 | 0.160101 | ||||||||
\(345\) | −0.218471 | −0.0117621 | ||||||||
\(346\) | 14.5104 | 0.780085 | ||||||||
\(347\) | 20.2296 | 1.08598 | 0.542991 | − | 0.839739i | \(-0.317292\pi\) | ||||
0.542991 | + | 0.839739i | \(0.317292\pi\) | |||||||
\(348\) | −1.82520 | −0.0978411 | ||||||||
\(349\) | 7.80705 | 0.417902 | 0.208951 | − | 0.977926i | \(-0.432995\pi\) | ||||
0.208951 | + | 0.977926i | \(0.432995\pi\) | |||||||
\(350\) | −3.12610 | −0.167097 | ||||||||
\(351\) | −17.0083 | −0.907837 | ||||||||
\(352\) | −1.62784 | −0.0867642 | ||||||||
\(353\) | −25.5973 | −1.36241 | −0.681204 | − | 0.732093i | \(-0.738543\pi\) | ||||
−0.681204 | + | 0.732093i | \(0.738543\pi\) | |||||||
\(354\) | 1.48845 | 0.0791101 | ||||||||
\(355\) | 5.38386 | 0.285746 | ||||||||
\(356\) | −0.947298 | −0.0502067 | ||||||||
\(357\) | −0.149249 | −0.00789910 | ||||||||
\(358\) | 22.6246 | 1.19575 | ||||||||
\(359\) | −12.1661 | −0.642103 | −0.321052 | − | 0.947062i | \(-0.604036\pi\) | ||||
−0.321052 | + | 0.947062i | \(0.604036\pi\) | |||||||
\(360\) | 3.64833 | 0.192284 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −26.7353 | −1.40517 | ||||||||
\(363\) | −4.83197 | −0.253612 | ||||||||
\(364\) | −5.18824 | −0.271938 | ||||||||
\(365\) | 2.13585 | 0.111795 | ||||||||
\(366\) | −7.11946 | −0.372140 | ||||||||
\(367\) | 2.68751 | 0.140287 | 0.0701435 | − | 0.997537i | \(-0.477654\pi\) | ||||
0.0701435 | + | 0.997537i | \(0.477654\pi\) | |||||||
\(368\) | −0.275797 | −0.0143769 | ||||||||
\(369\) | 21.0895 | 1.09787 | ||||||||
\(370\) | 12.8019 | 0.665539 | ||||||||
\(371\) | 7.47738 | 0.388206 | ||||||||
\(372\) | −4.08723 | −0.211913 | ||||||||
\(373\) | −8.54484 | −0.442435 | −0.221218 | − | 0.975224i | \(-0.571003\pi\) | ||||
−0.221218 | + | 0.975224i | \(0.571003\pi\) | |||||||
\(374\) | −0.419849 | −0.0217099 | ||||||||
\(375\) | −6.43703 | −0.332407 | ||||||||
\(376\) | 2.35659 | 0.121532 | ||||||||
\(377\) | −16.3644 | −0.842811 | ||||||||
\(378\) | −3.27824 | −0.168615 | ||||||||
\(379\) | −31.1455 | −1.59984 | −0.799919 | − | 0.600108i | \(-0.795124\pi\) | ||||
−0.799919 | + | 0.600108i | \(0.795124\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.26240 | 0.372064 | ||||||||
\(382\) | −11.2051 | −0.573303 | ||||||||
\(383\) | −25.6663 | −1.31149 | −0.655743 | − | 0.754984i | \(-0.727644\pi\) | ||||
−0.655743 | + | 0.754984i | \(0.727644\pi\) | |||||||
\(384\) | −0.578669 | −0.0295301 | ||||||||
\(385\) | −2.22836 | −0.113568 | ||||||||
\(386\) | 1.14499 | 0.0582786 | ||||||||
\(387\) | 7.91397 | 0.402290 | ||||||||
\(388\) | −4.32044 | −0.219337 | ||||||||
\(389\) | −13.6211 | −0.690615 | −0.345307 | − | 0.938490i | \(-0.612225\pi\) | ||||
−0.345307 | + | 0.938490i | \(0.612225\pi\) | |||||||
\(390\) | −4.10983 | −0.208109 | ||||||||
\(391\) | −0.0711330 | −0.00359735 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 4.74534 | 0.239371 | ||||||||
\(394\) | 4.23216 | 0.213213 | ||||||||
\(395\) | −21.5418 | −1.08389 | ||||||||
\(396\) | −4.33843 | −0.218014 | ||||||||
\(397\) | −13.8436 | −0.694791 | −0.347396 | − | 0.937719i | \(-0.612934\pi\) | ||||
−0.347396 | + | 0.937719i | \(0.612934\pi\) | |||||||
\(398\) | 11.1242 | 0.557605 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.12610 | −0.156305 | ||||||||
\(401\) | 36.7080 | 1.83311 | 0.916556 | − | 0.399906i | \(-0.130957\pi\) | ||||
0.916556 | + | 0.399906i | \(0.130957\pi\) | |||||||
\(402\) | −2.08044 | −0.103763 | ||||||||
\(403\) | −36.6454 | −1.82544 | ||||||||
\(404\) | 12.0383 | 0.598928 | ||||||||
\(405\) | 8.34814 | 0.414823 | ||||||||
\(406\) | −3.15414 | −0.156537 | ||||||||
\(407\) | −15.2235 | −0.754599 | ||||||||
\(408\) | −0.149249 | −0.00738894 | ||||||||
\(409\) | 10.2376 | 0.506219 | 0.253110 | − | 0.967438i | \(-0.418547\pi\) | ||||
0.253110 | + | 0.967438i | \(0.418547\pi\) | |||||||
\(410\) | 10.8323 | 0.534967 | ||||||||
\(411\) | 3.80367 | 0.187621 | ||||||||
\(412\) | −5.10605 | −0.251557 | ||||||||
\(413\) | 2.57219 | 0.126569 | ||||||||
\(414\) | −0.735038 | −0.0361251 | ||||||||
\(415\) | 14.8741 | 0.730140 | ||||||||
\(416\) | −5.18824 | −0.254375 | ||||||||
\(417\) | −1.49590 | −0.0732544 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.2221 | 0.792502 | 0.396251 | − | 0.918142i | \(-0.370311\pi\) | ||||
0.396251 | + | 0.918142i | \(0.370311\pi\) | |||||||
\(420\) | −0.792143 | −0.0386526 | ||||||||
\(421\) | −11.8248 | −0.576305 | −0.288152 | − | 0.957585i | \(-0.593041\pi\) | ||||
−0.288152 | + | 0.957585i | \(0.593041\pi\) | |||||||
\(422\) | 26.2736 | 1.27898 | ||||||||
\(423\) | 6.28065 | 0.305376 | ||||||||
\(424\) | 7.47738 | 0.363134 | ||||||||
\(425\) | −0.806277 | −0.0391102 | ||||||||
\(426\) | −2.27589 | −0.110267 | ||||||||
\(427\) | −12.3032 | −0.595392 | ||||||||
\(428\) | 4.21439 | 0.203710 | ||||||||
\(429\) | 4.88723 | 0.235958 | ||||||||
\(430\) | 4.06488 | 0.196026 | ||||||||
\(431\) | −37.1721 | −1.79052 | −0.895259 | − | 0.445546i | \(-0.853009\pi\) | ||||
−0.895259 | + | 0.445546i | \(0.853009\pi\) | |||||||
\(432\) | −3.27824 | −0.157725 | ||||||||
\(433\) | 1.18587 | 0.0569892 | 0.0284946 | − | 0.999594i | \(-0.490929\pi\) | ||||
0.0284946 | + | 0.999594i | \(0.490929\pi\) | |||||||
\(434\) | −7.06316 | −0.339043 | ||||||||
\(435\) | −2.49853 | −0.119795 | ||||||||
\(436\) | 12.3453 | 0.591232 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.902873 | −0.0431410 | ||||||||
\(439\) | −28.6657 | −1.36814 | −0.684069 | − | 0.729417i | \(-0.739791\pi\) | ||||
−0.684069 | + | 0.729417i | \(0.739791\pi\) | |||||||
\(440\) | −2.22836 | −0.106233 | ||||||||
\(441\) | −2.66514 | −0.126912 | ||||||||
\(442\) | −1.33814 | −0.0636489 | ||||||||
\(443\) | 25.2457 | 1.19946 | 0.599731 | − | 0.800202i | \(-0.295274\pi\) | ||||
0.599731 | + | 0.800202i | \(0.295274\pi\) | |||||||
\(444\) | −5.41167 | −0.256827 | ||||||||
\(445\) | −1.29676 | −0.0614724 | ||||||||
\(446\) | 13.1498 | 0.622660 | ||||||||
\(447\) | −9.50261 | −0.449458 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 10.2395 | 0.483230 | 0.241615 | − | 0.970372i | \(-0.422323\pi\) | ||||
0.241615 | + | 0.970372i | \(0.422323\pi\) | |||||||
\(450\) | −8.33150 | −0.392750 | ||||||||
\(451\) | −12.8812 | −0.606554 | ||||||||
\(452\) | −15.3482 | −0.721918 | ||||||||
\(453\) | −0.831172 | −0.0390518 | ||||||||
\(454\) | −4.75659 | −0.223238 | ||||||||
\(455\) | −7.10221 | −0.332957 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5779 | −0.681927 | −0.340964 | − | 0.940076i | \(-0.610753\pi\) | ||||
−0.340964 | + | 0.940076i | \(0.610753\pi\) | |||||||
\(458\) | 10.6582 | 0.498024 | ||||||||
\(459\) | −0.845518 | −0.0394654 | ||||||||
\(460\) | −0.377540 | −0.0176029 | ||||||||
\(461\) | 34.8330 | 1.62234 | 0.811168 | − | 0.584814i | \(-0.198832\pi\) | ||||
0.811168 | + | 0.584814i | \(0.198832\pi\) | |||||||
\(462\) | 0.941981 | 0.0438249 | ||||||||
\(463\) | −0.367718 | −0.0170893 | −0.00854465 | − | 0.999963i | \(-0.502720\pi\) | ||||
−0.00854465 | + | 0.999963i | \(0.502720\pi\) | |||||||
\(464\) | −3.15414 | −0.146427 | ||||||||
\(465\) | −5.59504 | −0.259464 | ||||||||
\(466\) | −1.58547 | −0.0734456 | ||||||||
\(467\) | −19.4832 | −0.901574 | −0.450787 | − | 0.892632i | \(-0.648857\pi\) | ||||
−0.450787 | + | 0.892632i | \(0.648857\pi\) | |||||||
\(468\) | −13.8274 | −0.639172 | ||||||||
\(469\) | −3.59521 | −0.166011 | ||||||||
\(470\) | 3.22595 | 0.148802 | ||||||||
\(471\) | −8.51950 | −0.392558 | ||||||||
\(472\) | 2.57219 | 0.118395 | ||||||||
\(473\) | −4.83377 | −0.222257 | ||||||||
\(474\) | 9.10623 | 0.418263 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.257918 | −0.0118217 | ||||||||
\(477\) | 19.9283 | 0.912454 | ||||||||
\(478\) | 13.6183 | 0.622886 | ||||||||
\(479\) | −30.7828 | −1.40650 | −0.703250 | − | 0.710943i | \(-0.748269\pi\) | ||||
−0.703250 | + | 0.710943i | \(0.748269\pi\) | |||||||
\(480\) | −0.792143 | −0.0361562 | ||||||||
\(481\) | −48.5201 | −2.21233 | ||||||||
\(482\) | 2.51719 | 0.114655 | ||||||||
\(483\) | 0.159595 | 0.00726183 | ||||||||
\(484\) | −8.35013 | −0.379552 | ||||||||
\(485\) | −5.91428 | −0.268554 | ||||||||
\(486\) | −13.3637 | −0.606189 | ||||||||
\(487\) | 21.5085 | 0.974643 | 0.487321 | − | 0.873223i | \(-0.337974\pi\) | ||||
0.487321 | + | 0.873223i | \(0.337974\pi\) | |||||||
\(488\) | −12.3032 | −0.556938 | ||||||||
\(489\) | −13.4886 | −0.609975 | ||||||||
\(490\) | −1.36891 | −0.0618408 | ||||||||
\(491\) | 6.94462 | 0.313406 | 0.156703 | − | 0.987646i | \(-0.449913\pi\) | ||||
0.156703 | + | 0.987646i | \(0.449913\pi\) | |||||||
\(492\) | −4.57906 | −0.206440 | ||||||||
\(493\) | −0.813509 | −0.0366386 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.93890 | −0.266934 | ||||||||
\(496\) | −7.06316 | −0.317145 | ||||||||
\(497\) | −3.93297 | −0.176418 | ||||||||
\(498\) | −6.28763 | −0.281755 | ||||||||
\(499\) | −16.0613 | −0.719003 | −0.359502 | − | 0.933145i | \(-0.617053\pi\) | ||||
−0.359502 | + | 0.933145i | \(0.617053\pi\) | |||||||
\(500\) | −11.1239 | −0.497474 | ||||||||
\(501\) | 10.4056 | 0.464886 | ||||||||
\(502\) | −15.5613 | −0.694534 | ||||||||
\(503\) | 24.9929 | 1.11438 | 0.557190 | − | 0.830385i | \(-0.311879\pi\) | ||||
0.557190 | + | 0.830385i | \(0.311879\pi\) | |||||||
\(504\) | −2.66514 | −0.118715 | ||||||||
\(505\) | 16.4793 | 0.733320 | ||||||||
\(506\) | 0.448953 | 0.0199584 | ||||||||
\(507\) | 8.05384 | 0.357683 | ||||||||
\(508\) | 12.5502 | 0.556824 | ||||||||
\(509\) | 5.52919 | 0.245077 | 0.122538 | − | 0.992464i | \(-0.460897\pi\) | ||||
0.122538 | + | 0.992464i | \(0.460897\pi\) | |||||||
\(510\) | −0.204308 | −0.00904691 | ||||||||
\(511\) | −1.56026 | −0.0690218 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.4424 | 0.769350 | ||||||||
\(515\) | −6.98970 | −0.308003 | ||||||||
\(516\) | −1.71832 | −0.0756449 | ||||||||
\(517\) | −3.83616 | −0.168714 | ||||||||
\(518\) | −9.35193 | −0.410900 | ||||||||
\(519\) | −8.39673 | −0.368576 | ||||||||
\(520\) | −7.10221 | −0.311453 | ||||||||
\(521\) | 0.397939 | 0.0174340 | 0.00871701 | − | 0.999962i | \(-0.497225\pi\) | ||||
0.00871701 | + | 0.999962i | \(0.497225\pi\) | |||||||
\(522\) | −8.40622 | −0.367930 | ||||||||
\(523\) | −14.7312 | −0.644149 | −0.322074 | − | 0.946714i | \(-0.604380\pi\) | ||||
−0.322074 | + | 0.946714i | \(0.604380\pi\) | |||||||
\(524\) | 8.20043 | 0.358238 | ||||||||
\(525\) | 1.80898 | 0.0789502 | ||||||||
\(526\) | 0.698187 | 0.0304424 | ||||||||
\(527\) | −1.82172 | −0.0793552 | ||||||||
\(528\) | 0.941981 | 0.0409945 | ||||||||
\(529\) | −22.9239 | −0.996693 | ||||||||
\(530\) | 10.2358 | 0.444616 | ||||||||
\(531\) | 6.85526 | 0.297493 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −41.0550 | −1.77829 | ||||||||
\(534\) | 0.548172 | 0.0237217 | ||||||||
\(535\) | 5.76909 | 0.249420 | ||||||||
\(536\) | −3.59521 | −0.155289 | ||||||||
\(537\) | −13.0922 | −0.564969 | ||||||||
\(538\) | 16.1173 | 0.694865 | ||||||||
\(539\) | 1.62784 | 0.0701161 | ||||||||
\(540\) | −4.48760 | −0.193116 | ||||||||
\(541\) | −42.3044 | −1.81881 | −0.909403 | − | 0.415915i | \(-0.863461\pi\) | ||||
−0.909403 | + | 0.415915i | \(0.863461\pi\) | |||||||
\(542\) | −20.6217 | −0.885778 | ||||||||
\(543\) | 15.4709 | 0.663919 | ||||||||
\(544\) | −0.257918 | −0.0110581 | ||||||||
\(545\) | 16.8995 | 0.723896 | ||||||||
\(546\) | 3.00228 | 0.128486 | ||||||||
\(547\) | 8.11438 | 0.346946 | 0.173473 | − | 0.984839i | \(-0.444501\pi\) | ||||
0.173473 | + | 0.984839i | \(0.444501\pi\) | |||||||
\(548\) | 6.57313 | 0.280790 | ||||||||
\(549\) | −32.7897 | −1.39943 | ||||||||
\(550\) | 5.08879 | 0.216987 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.159595 | 0.00679282 | ||||||||
\(553\) | 15.7365 | 0.669184 | ||||||||
\(554\) | 26.5364 | 1.12742 | ||||||||
\(555\) | −7.40807 | −0.314455 | ||||||||
\(556\) | −2.58506 | −0.109631 | ||||||||
\(557\) | −9.74617 | −0.412959 | −0.206479 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206479 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(558\) | −18.8243 | −0.796897 | ||||||||
\(559\) | −15.4062 | −0.651611 | ||||||||
\(560\) | −1.36891 | −0.0578468 | ||||||||
\(561\) | 0.242954 | 0.0102575 | ||||||||
\(562\) | 8.20137 | 0.345954 | ||||||||
\(563\) | 25.7838 | 1.08666 | 0.543328 | − | 0.839520i | \(-0.317164\pi\) | ||||
0.543328 | + | 0.839520i | \(0.317164\pi\) | |||||||
\(564\) | −1.36369 | −0.0574216 | ||||||||
\(565\) | −21.0102 | −0.883906 | ||||||||
\(566\) | −13.1749 | −0.553781 | ||||||||
\(567\) | −6.09841 | −0.256109 | ||||||||
\(568\) | −3.93297 | −0.165024 | ||||||||
\(569\) | 38.7812 | 1.62579 | 0.812897 | − | 0.582407i | \(-0.197889\pi\) | ||||
0.812897 | + | 0.582407i | \(0.197889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5374 | 0.733918 | 0.366959 | − | 0.930237i | \(-0.380399\pi\) | ||||
0.366959 | + | 0.930237i | \(0.380399\pi\) | |||||||
\(572\) | 8.44563 | 0.353130 | ||||||||
\(573\) | 6.48404 | 0.270875 | ||||||||
\(574\) | −7.91308 | −0.330286 | ||||||||
\(575\) | 0.862168 | 0.0359549 | ||||||||
\(576\) | −2.66514 | −0.111048 | ||||||||
\(577\) | 18.6225 | 0.775265 | 0.387632 | − | 0.921814i | \(-0.373293\pi\) | ||||
0.387632 | + | 0.921814i | \(0.373293\pi\) | |||||||
\(578\) | 16.9335 | 0.704340 | ||||||||
\(579\) | −0.662573 | −0.0275356 | ||||||||
\(580\) | −4.31772 | −0.179283 | ||||||||
\(581\) | −10.8657 | −0.450784 | ||||||||
\(582\) | 2.50011 | 0.103633 | ||||||||
\(583\) | −12.1720 | −0.504112 | ||||||||
\(584\) | −1.56026 | −0.0645639 | ||||||||
\(585\) | −18.9284 | −0.782593 | ||||||||
\(586\) | 7.60243 | 0.314054 | ||||||||
\(587\) | −39.0644 | −1.61236 | −0.806180 | − | 0.591670i | \(-0.798469\pi\) | ||||
−0.806180 | + | 0.591670i | \(0.798469\pi\) | |||||||
\(588\) | 0.578669 | 0.0238639 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 3.52109 | 0.144961 | ||||||||
\(591\) | −2.44902 | −0.100739 | ||||||||
\(592\) | −9.35193 | −0.384362 | ||||||||
\(593\) | 36.8648 | 1.51385 | 0.756927 | − | 0.653499i | \(-0.226700\pi\) | ||||
0.756927 | + | 0.653499i | \(0.226700\pi\) | |||||||
\(594\) | 5.33646 | 0.218958 | ||||||||
\(595\) | −0.353065 | −0.0144743 | ||||||||
\(596\) | −16.4215 | −0.672650 | ||||||||
\(597\) | −6.43722 | −0.263458 | ||||||||
\(598\) | 1.43090 | 0.0585139 | ||||||||
\(599\) | 42.4517 | 1.73453 | 0.867265 | − | 0.497847i | \(-0.165876\pi\) | ||||
0.867265 | + | 0.497847i | \(0.165876\pi\) | |||||||
\(600\) | 1.80898 | 0.0738512 | ||||||||
\(601\) | 14.2391 | 0.580827 | 0.290413 | − | 0.956901i | \(-0.406207\pi\) | ||||
0.290413 | + | 0.956901i | \(0.406207\pi\) | |||||||
\(602\) | −2.96944 | −0.121025 | ||||||||
\(603\) | −9.58174 | −0.390199 | ||||||||
\(604\) | −1.43635 | −0.0584443 | ||||||||
\(605\) | −11.4305 | −0.464718 | ||||||||
\(606\) | −6.96620 | −0.282983 | ||||||||
\(607\) | −44.3153 | −1.79870 | −0.899352 | − | 0.437225i | \(-0.855961\pi\) | ||||
−0.899352 | + | 0.437225i | \(0.855961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.82520 | 0.0739609 | ||||||||
\(610\) | −16.8419 | −0.681908 | ||||||||
\(611\) | −12.2266 | −0.494634 | ||||||||
\(612\) | −0.687388 | −0.0277860 | ||||||||
\(613\) | −8.05804 | −0.325461 | −0.162731 | − | 0.986671i | \(-0.552030\pi\) | ||||
−0.162731 | + | 0.986671i | \(0.552030\pi\) | |||||||
\(614\) | −21.2034 | −0.855702 | ||||||||
\(615\) | −6.26829 | −0.252762 | ||||||||
\(616\) | 1.62784 | 0.0655876 | ||||||||
\(617\) | 44.2259 | 1.78047 | 0.890234 | − | 0.455503i | \(-0.150541\pi\) | ||||
0.890234 | + | 0.455503i | \(0.150541\pi\) | |||||||
\(618\) | 2.95471 | 0.118856 | ||||||||
\(619\) | 26.7726 | 1.07608 | 0.538042 | − | 0.842918i | \(-0.319164\pi\) | ||||
0.538042 | + | 0.842918i | \(0.319164\pi\) | |||||||
\(620\) | −9.66880 | −0.388308 | ||||||||
\(621\) | 0.904129 | 0.0362814 | ||||||||
\(622\) | −31.5530 | −1.26516 | ||||||||
\(623\) | 0.947298 | 0.0379527 | ||||||||
\(624\) | 3.00228 | 0.120187 | ||||||||
\(625\) | 0.402981 | 0.0161193 | ||||||||
\(626\) | −2.14974 | −0.0859208 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.7226 | −0.587495 | ||||||||
\(629\) | −2.41203 | −0.0961740 | ||||||||
\(630\) | −3.64833 | −0.145353 | ||||||||
\(631\) | −7.83816 | −0.312032 | −0.156016 | − | 0.987755i | \(-0.549865\pi\) | ||||
−0.156016 | + | 0.987755i | \(0.549865\pi\) | |||||||
\(632\) | 15.7365 | 0.625965 | ||||||||
\(633\) | −15.2037 | −0.604294 | ||||||||
\(634\) | −8.35113 | −0.331666 | ||||||||
\(635\) | 17.1800 | 0.681768 | ||||||||
\(636\) | −4.32693 | −0.171574 | ||||||||
\(637\) | 5.18824 | 0.205566 | ||||||||
\(638\) | 5.13443 | 0.203274 | ||||||||
\(639\) | −10.4819 | −0.414659 | ||||||||
\(640\) | −1.36891 | −0.0541107 | ||||||||
\(641\) | −8.40692 | −0.332053 | −0.166027 | − | 0.986121i | \(-0.553094\pi\) | ||||
−0.166027 | + | 0.986121i | \(0.553094\pi\) | |||||||
\(642\) | −2.43873 | −0.0962492 | ||||||||
\(643\) | 20.6578 | 0.814663 | 0.407332 | − | 0.913280i | \(-0.366459\pi\) | ||||
0.407332 | + | 0.913280i | \(0.366459\pi\) | |||||||
\(644\) | 0.275797 | 0.0108679 | ||||||||
\(645\) | −2.35222 | −0.0926185 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.1506 | 1.02809 | 0.514043 | − | 0.857765i | \(-0.328147\pi\) | ||||
0.514043 | + | 0.857765i | \(0.328147\pi\) | |||||||
\(648\) | −6.09841 | −0.239568 | ||||||||
\(649\) | −4.18712 | −0.164359 | ||||||||
\(650\) | 16.2190 | 0.636160 | ||||||||
\(651\) | 4.08723 | 0.160191 | ||||||||
\(652\) | −23.3097 | −0.912878 | ||||||||
\(653\) | −26.2233 | −1.02620 | −0.513099 | − | 0.858329i | \(-0.671503\pi\) | ||||
−0.513099 | + | 0.858329i | \(0.671503\pi\) | |||||||
\(654\) | −7.14383 | −0.279346 | ||||||||
\(655\) | 11.2256 | 0.438621 | ||||||||
\(656\) | −7.91308 | −0.308954 | ||||||||
\(657\) | −4.15831 | −0.162231 | ||||||||
\(658\) | −2.35659 | −0.0918695 | ||||||||
\(659\) | −35.3589 | −1.37739 | −0.688694 | − | 0.725052i | \(-0.741816\pi\) | ||||
−0.688694 | + | 0.725052i | \(0.741816\pi\) | |||||||
\(660\) | 1.28948 | 0.0501931 | ||||||||
\(661\) | −3.70891 | −0.144260 | −0.0721300 | − | 0.997395i | \(-0.522980\pi\) | ||||
−0.0721300 | + | 0.997395i | \(0.522980\pi\) | |||||||
\(662\) | −4.16252 | −0.161781 | ||||||||
\(663\) | 0.774341 | 0.0300729 | ||||||||
\(664\) | −10.8657 | −0.421670 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.9242 | −0.965794 | ||||||||
\(667\) | 0.869901 | 0.0336827 | ||||||||
\(668\) | 17.9819 | 0.695740 | ||||||||
\(669\) | −7.60937 | −0.294195 | ||||||||
\(670\) | −4.92150 | −0.190134 | ||||||||
\(671\) | 20.0276 | 0.773157 | ||||||||
\(672\) | 0.578669 | 0.0223226 | ||||||||
\(673\) | −4.64446 | −0.179031 | −0.0895154 | − | 0.995985i | \(-0.528532\pi\) | ||||
−0.0895154 | + | 0.995985i | \(0.528532\pi\) | |||||||
\(674\) | −4.26524 | −0.164291 | ||||||||
\(675\) | 10.2481 | 0.394450 | ||||||||
\(676\) | 13.9179 | 0.535302 | ||||||||
\(677\) | −16.2392 | −0.624122 | −0.312061 | − | 0.950062i | \(-0.601019\pi\) | ||||
−0.312061 | + | 0.950062i | \(0.601019\pi\) | |||||||
\(678\) | 8.88152 | 0.341093 | ||||||||
\(679\) | 4.32044 | 0.165803 | ||||||||
\(680\) | −0.353065 | −0.0135394 | ||||||||
\(681\) | 2.75249 | 0.105476 | ||||||||
\(682\) | 11.4977 | 0.440270 | ||||||||
\(683\) | 12.7728 | 0.488736 | 0.244368 | − | 0.969683i | \(-0.421419\pi\) | ||||
0.244368 | + | 0.969683i | \(0.421419\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.99799 | 0.343796 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −6.16756 | −0.235307 | ||||||||
\(688\) | −2.96944 | −0.113209 | ||||||||
\(689\) | −38.7945 | −1.47795 | ||||||||
\(690\) | 0.218471 | 0.00831703 | ||||||||
\(691\) | 17.7594 | 0.675599 | 0.337799 | − | 0.941218i | \(-0.390317\pi\) | ||||
0.337799 | + | 0.941218i | \(0.390317\pi\) | |||||||
\(692\) | −14.5104 | −0.551603 | ||||||||
\(693\) | 4.33843 | 0.164803 | ||||||||
\(694\) | −20.2296 | −0.767905 | ||||||||
\(695\) | −3.53871 | −0.134231 | ||||||||
\(696\) | 1.82520 | 0.0691841 | ||||||||
\(697\) | −2.04093 | −0.0773056 | ||||||||
\(698\) | −7.80705 | −0.295501 | ||||||||
\(699\) | 0.917465 | 0.0347017 | ||||||||
\(700\) | 3.12610 | 0.118155 | ||||||||
\(701\) | 15.7559 | 0.595092 | 0.297546 | − | 0.954707i | \(-0.403832\pi\) | ||||
0.297546 | + | 0.954707i | \(0.403832\pi\) | |||||||
\(702\) | 17.0083 | 0.641938 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.62784 | 0.0613516 | ||||||||
\(705\) | −1.86676 | −0.0703062 | ||||||||
\(706\) | 25.5973 | 0.963368 | ||||||||
\(707\) | −12.0383 | −0.452747 | ||||||||
\(708\) | −1.48845 | −0.0559393 | ||||||||
\(709\) | 12.1949 | 0.457989 | 0.228994 | − | 0.973428i | \(-0.426456\pi\) | ||||
0.228994 | + | 0.973428i | \(0.426456\pi\) | |||||||
\(710\) | −5.38386 | −0.202053 | ||||||||
\(711\) | 41.9400 | 1.57287 | ||||||||
\(712\) | 0.947298 | 0.0355015 | ||||||||
\(713\) | 1.94800 | 0.0729531 | ||||||||
\(714\) | 0.149249 | 0.00558551 | ||||||||
\(715\) | 11.5613 | 0.432367 | ||||||||
\(716\) | −22.6246 | −0.845522 | ||||||||
\(717\) | −7.88048 | −0.294302 | ||||||||
\(718\) | 12.1661 | 0.454036 | ||||||||
\(719\) | 27.5161 | 1.02618 | 0.513088 | − | 0.858336i | \(-0.328501\pi\) | ||||
0.513088 | + | 0.858336i | \(0.328501\pi\) | |||||||
\(720\) | −3.64833 | −0.135965 | ||||||||
\(721\) | 5.10605 | 0.190159 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.45662 | −0.0541724 | ||||||||
\(724\) | 26.7353 | 0.993608 | ||||||||
\(725\) | 9.86014 | 0.366197 | ||||||||
\(726\) | 4.83197 | 0.179331 | ||||||||
\(727\) | 0.500852 | 0.0185756 | 0.00928778 | − | 0.999957i | \(-0.497044\pi\) | ||||
0.00928778 | + | 0.999957i | \(0.497044\pi\) | |||||||
\(728\) | 5.18824 | 0.192289 | ||||||||
\(729\) | −10.5621 | −0.391188 | ||||||||
\(730\) | −2.13585 | −0.0790512 | ||||||||
\(731\) | −0.765871 | −0.0283268 | ||||||||
\(732\) | 7.11946 | 0.263143 | ||||||||
\(733\) | −24.5270 | −0.905924 | −0.452962 | − | 0.891530i | \(-0.649633\pi\) | ||||
−0.452962 | + | 0.891530i | \(0.649633\pi\) | |||||||
\(734\) | −2.68751 | −0.0991979 | ||||||||
\(735\) | 0.792143 | 0.0292186 | ||||||||
\(736\) | 0.275797 | 0.0101660 | ||||||||
\(737\) | 5.85243 | 0.215577 | ||||||||
\(738\) | −21.0895 | −0.776315 | ||||||||
\(739\) | −17.9155 | −0.659034 | −0.329517 | − | 0.944150i | \(-0.606886\pi\) | ||||
−0.329517 | + | 0.944150i | \(0.606886\pi\) | |||||||
\(740\) | −12.8019 | −0.470607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.47738 | −0.274503 | ||||||||
\(743\) | 33.3502 | 1.22350 | 0.611750 | − | 0.791051i | \(-0.290466\pi\) | ||||
0.611750 | + | 0.791051i | \(0.290466\pi\) | |||||||
\(744\) | 4.08723 | 0.149845 | ||||||||
\(745\) | −22.4795 | −0.823584 | ||||||||
\(746\) | 8.54484 | 0.312849 | ||||||||
\(747\) | −28.9586 | −1.05954 | ||||||||
\(748\) | 0.419849 | 0.0153512 | ||||||||
\(749\) | −4.21439 | −0.153990 | ||||||||
\(750\) | 6.43703 | 0.235047 | ||||||||
\(751\) | −40.9525 | −1.49438 | −0.747189 | − | 0.664612i | \(-0.768597\pi\) | ||||
−0.747189 | + | 0.664612i | \(0.768597\pi\) | |||||||
\(752\) | −2.35659 | −0.0859360 | ||||||||
\(753\) | 9.00483 | 0.328154 | ||||||||
\(754\) | 16.3644 | 0.595957 | ||||||||
\(755\) | −1.96623 | −0.0715583 | ||||||||
\(756\) | 3.27824 | 0.119229 | ||||||||
\(757\) | 27.6185 | 1.00381 | 0.501906 | − | 0.864922i | \(-0.332632\pi\) | ||||
0.501906 | + | 0.864922i | \(0.332632\pi\) | |||||||
\(758\) | 31.1455 | 1.13126 | ||||||||
\(759\) | −0.259795 | −0.00942998 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.9059 | −1.19284 | −0.596418 | − | 0.802674i | \(-0.703410\pi\) | ||||
−0.596418 | + | 0.802674i | \(0.703410\pi\) | |||||||
\(762\) | −7.26240 | −0.263089 | ||||||||
\(763\) | −12.3453 | −0.446929 | ||||||||
\(764\) | 11.2051 | 0.405386 | ||||||||
\(765\) | −0.940969 | −0.0340208 | ||||||||
\(766\) | 25.6663 | 0.927360 | ||||||||
\(767\) | −13.3452 | −0.481866 | ||||||||
\(768\) | 0.578669 | 0.0208809 | ||||||||
\(769\) | 46.4231 | 1.67406 | 0.837031 | − | 0.547156i | \(-0.184290\pi\) | ||||
0.837031 | + | 0.547156i | \(0.184290\pi\) | |||||||
\(770\) | 2.22836 | 0.0803045 | ||||||||
\(771\) | −10.0934 | −0.363504 | ||||||||
\(772\) | −1.14499 | −0.0412092 | ||||||||
\(773\) | −6.11539 | −0.219955 | −0.109978 | − | 0.993934i | \(-0.535078\pi\) | ||||
−0.109978 | + | 0.993934i | \(0.535078\pi\) | |||||||
\(774\) | −7.91397 | −0.284462 | ||||||||
\(775\) | 22.0801 | 0.793142 | ||||||||
\(776\) | 4.32044 | 0.155095 | ||||||||
\(777\) | 5.41167 | 0.194143 | ||||||||
\(778\) | 13.6211 | 0.488339 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 4.10983 | 0.147156 | ||||||||
\(781\) | 6.40225 | 0.229091 | ||||||||
\(782\) | 0.0711330 | 0.00254371 | ||||||||
\(783\) | 10.3400 | 0.369522 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −20.1538 | −0.719320 | ||||||||
\(786\) | −4.74534 | −0.169261 | ||||||||
\(787\) | 53.2270 | 1.89734 | 0.948669 | − | 0.316271i | \(-0.102431\pi\) | ||||
0.948669 | + | 0.316271i | \(0.102431\pi\) | |||||||
\(788\) | −4.23216 | −0.150764 | ||||||||
\(789\) | −0.404019 | −0.0143835 | ||||||||
\(790\) | 21.5418 | 0.766422 | ||||||||
\(791\) | 15.3482 | 0.545718 | ||||||||
\(792\) | 4.33843 | 0.154159 | ||||||||
\(793\) | 63.8318 | 2.26673 | ||||||||
\(794\) | 13.8436 | 0.491292 | ||||||||
\(795\) | −5.92316 | −0.210073 | ||||||||
\(796\) | −11.1242 | −0.394286 | ||||||||
\(797\) | −49.1901 | −1.74240 | −0.871201 | − | 0.490927i | \(-0.836658\pi\) | ||||
−0.871201 | + | 0.490927i | \(0.836658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.607807 | −0.0215027 | ||||||||
\(800\) | 3.12610 | 0.110524 | ||||||||
\(801\) | 2.52468 | 0.0892054 | ||||||||
\(802\) | −36.7080 | −1.29621 | ||||||||
\(803\) | 2.53985 | 0.0896294 | ||||||||
\(804\) | 2.08044 | 0.0733713 | ||||||||
\(805\) | 0.377540 | 0.0133065 | ||||||||
\(806\) | 36.6454 | 1.29078 | ||||||||
\(807\) | −9.32657 | −0.328311 | ||||||||
\(808\) | −12.0383 | −0.423506 | ||||||||
\(809\) | −2.51361 | −0.0883738 | −0.0441869 | − | 0.999023i | \(-0.514070\pi\) | ||||
−0.0441869 | + | 0.999023i | \(0.514070\pi\) | |||||||
\(810\) | −8.34814 | −0.293324 | ||||||||
\(811\) | −33.0435 | −1.16031 | −0.580156 | − | 0.814505i | \(-0.697009\pi\) | ||||
−0.580156 | + | 0.814505i | \(0.697009\pi\) | |||||||
\(812\) | 3.15414 | 0.110689 | ||||||||
\(813\) | 11.9331 | 0.418514 | ||||||||
\(814\) | 15.2235 | 0.533582 | ||||||||
\(815\) | −31.9087 | −1.11771 | ||||||||
\(816\) | 0.149249 | 0.00522477 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −10.2376 | −0.357951 | ||||||||
\(819\) | 13.8274 | 0.483169 | ||||||||
\(820\) | −10.8323 | −0.378279 | ||||||||
\(821\) | −26.6570 | −0.930337 | −0.465168 | − | 0.885222i | \(-0.654006\pi\) | ||||
−0.465168 | + | 0.885222i | \(0.654006\pi\) | |||||||
\(822\) | −3.80367 | −0.132668 | ||||||||
\(823\) | 49.4576 | 1.72398 | 0.861992 | − | 0.506921i | \(-0.169216\pi\) | ||||
0.861992 | + | 0.506921i | \(0.169216\pi\) | |||||||
\(824\) | 5.10605 | 0.177878 | ||||||||
\(825\) | −2.94473 | −0.102522 | ||||||||
\(826\) | −2.57219 | −0.0894980 | ||||||||
\(827\) | −52.4173 | −1.82273 | −0.911365 | − | 0.411600i | \(-0.864970\pi\) | ||||
−0.911365 | + | 0.411600i | \(0.864970\pi\) | |||||||
\(828\) | 0.735038 | 0.0255443 | ||||||||
\(829\) | −30.9801 | −1.07598 | −0.537992 | − | 0.842950i | \(-0.680817\pi\) | ||||
−0.537992 | + | 0.842950i | \(0.680817\pi\) | |||||||
\(830\) | −14.8741 | −0.516287 | ||||||||
\(831\) | −15.3558 | −0.532686 | ||||||||
\(832\) | 5.18824 | 0.179870 | ||||||||
\(833\) | 0.257918 | 0.00893633 | ||||||||
\(834\) | 1.49590 | 0.0517987 | ||||||||
\(835\) | 24.6155 | 0.851855 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.1548 | 0.800346 | ||||||||
\(838\) | −16.2221 | −0.560384 | ||||||||
\(839\) | 28.2511 | 0.975338 | 0.487669 | − | 0.873029i | \(-0.337847\pi\) | ||||
0.487669 | + | 0.873029i | \(0.337847\pi\) | |||||||
\(840\) | 0.792143 | 0.0273315 | ||||||||
\(841\) | −19.0514 | −0.656945 | ||||||||
\(842\) | 11.8248 | 0.407509 | ||||||||
\(843\) | −4.74588 | −0.163457 | ||||||||
\(844\) | −26.2736 | −0.904375 | ||||||||
\(845\) | 19.0522 | 0.655417 | ||||||||
\(846\) | −6.28065 | −0.215933 | ||||||||
\(847\) | 8.35013 | 0.286914 | ||||||||
\(848\) | −7.47738 | −0.256774 | ||||||||
\(849\) | 7.62389 | 0.261651 | ||||||||
\(850\) | 0.806277 | 0.0276551 | ||||||||
\(851\) | 2.57923 | 0.0884150 | ||||||||
\(852\) | 2.27589 | 0.0779707 | ||||||||
\(853\) | −10.7175 | −0.366959 | −0.183479 | − | 0.983024i | \(-0.558736\pi\) | ||||
−0.183479 | + | 0.983024i | \(0.558736\pi\) | |||||||
\(854\) | 12.3032 | 0.421006 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.21439 | −0.144045 | ||||||||
\(857\) | 37.1639 | 1.26949 | 0.634747 | − | 0.772720i | \(-0.281104\pi\) | ||||
0.634747 | + | 0.772720i | \(0.281104\pi\) | |||||||
\(858\) | −4.88723 | −0.166847 | ||||||||
\(859\) | −24.5057 | −0.836123 | −0.418062 | − | 0.908419i | \(-0.637290\pi\) | ||||
−0.418062 | + | 0.908419i | \(0.637290\pi\) | |||||||
\(860\) | −4.06488 | −0.138611 | ||||||||
\(861\) | 4.57906 | 0.156054 | ||||||||
\(862\) | 37.1721 | 1.26609 | ||||||||
\(863\) | 42.9929 | 1.46350 | 0.731748 | − | 0.681576i | \(-0.238705\pi\) | ||||
0.731748 | + | 0.681576i | \(0.238705\pi\) | |||||||
\(864\) | 3.27824 | 0.111528 | ||||||||
\(865\) | −19.8634 | −0.675375 | ||||||||
\(866\) | −1.18587 | −0.0402974 | ||||||||
\(867\) | −9.79888 | −0.332787 | ||||||||
\(868\) | 7.06316 | 0.239739 | ||||||||
\(869\) | −25.6165 | −0.868981 | ||||||||
\(870\) | 2.49853 | 0.0847081 | ||||||||
\(871\) | 18.6528 | 0.632027 | ||||||||
\(872\) | −12.3453 | −0.418064 | ||||||||
\(873\) | 11.5146 | 0.389710 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.1239 | 0.376055 | ||||||||
\(876\) | 0.902873 | 0.0305053 | ||||||||
\(877\) | 34.9372 | 1.17974 | 0.589872 | − | 0.807496i | \(-0.299178\pi\) | ||||
0.589872 | + | 0.807496i | \(0.299178\pi\) | |||||||
\(878\) | 28.6657 | 0.967420 | ||||||||
\(879\) | −4.39929 | −0.148385 | ||||||||
\(880\) | 2.22836 | 0.0751180 | ||||||||
\(881\) | −23.2171 | −0.782204 | −0.391102 | − | 0.920347i | \(-0.627906\pi\) | ||||
−0.391102 | + | 0.920347i | \(0.627906\pi\) | |||||||
\(882\) | 2.66514 | 0.0897400 | ||||||||
\(883\) | 27.2224 | 0.916108 | 0.458054 | − | 0.888924i | \(-0.348547\pi\) | ||||
0.458054 | + | 0.888924i | \(0.348547\pi\) | |||||||
\(884\) | 1.33814 | 0.0450065 | ||||||||
\(885\) | −2.03754 | −0.0684913 | ||||||||
\(886\) | −25.2457 | −0.848147 | ||||||||
\(887\) | 49.2391 | 1.65329 | 0.826644 | − | 0.562725i | \(-0.190247\pi\) | ||||
0.826644 | + | 0.562725i | \(0.190247\pi\) | |||||||
\(888\) | 5.41167 | 0.181604 | ||||||||
\(889\) | −12.5502 | −0.420919 | ||||||||
\(890\) | 1.29676 | 0.0434676 | ||||||||
\(891\) | 9.92724 | 0.332575 | ||||||||
\(892\) | −13.1498 | −0.440287 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 9.50261 | 0.317815 | ||||||||
\(895\) | −30.9710 | −1.03525 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −0.828018 | −0.0276467 | ||||||||
\(898\) | −10.2395 | −0.341695 | ||||||||
\(899\) | 22.2782 | 0.743019 | ||||||||
\(900\) | 8.33150 | 0.277717 | ||||||||
\(901\) | −1.92855 | −0.0642494 | ||||||||
\(902\) | 12.8812 | 0.428898 | ||||||||
\(903\) | 1.71832 | 0.0571821 | ||||||||
\(904\) | 15.3482 | 0.510473 | ||||||||
\(905\) | 36.5980 | 1.21656 | ||||||||
\(906\) | 0.831172 | 0.0276138 | ||||||||
\(907\) | 31.2791 | 1.03861 | 0.519303 | − | 0.854590i | \(-0.326191\pi\) | ||||
0.519303 | + | 0.854590i | \(0.326191\pi\) | |||||||
\(908\) | 4.75659 | 0.157853 | ||||||||
\(909\) | −32.0838 | −1.06415 | ||||||||
\(910\) | 7.10221 | 0.235436 | ||||||||
\(911\) | 4.77182 | 0.158098 | 0.0790488 | − | 0.996871i | \(-0.474812\pi\) | ||||
0.0790488 | + | 0.996871i | \(0.474812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6876 | 0.585374 | ||||||||
\(914\) | 14.5779 | 0.482195 | ||||||||
\(915\) | 9.74587 | 0.322189 | ||||||||
\(916\) | −10.6582 | −0.352156 | ||||||||
\(917\) | −8.20043 | −0.270802 | ||||||||
\(918\) | 0.845518 | 0.0279062 | ||||||||
\(919\) | 49.3170 | 1.62682 | 0.813409 | − | 0.581693i | \(-0.197609\pi\) | ||||
0.813409 | + | 0.581693i | \(0.197609\pi\) | |||||||
\(920\) | 0.377540 | 0.0124471 | ||||||||
\(921\) | 12.2698 | 0.404303 | ||||||||
\(922\) | −34.8330 | −1.14716 | ||||||||
\(923\) | 20.4052 | 0.671645 | ||||||||
\(924\) | −0.941981 | −0.0309889 | ||||||||
\(925\) | 29.2351 | 0.961243 | ||||||||
\(926\) | 0.367718 | 0.0120840 | ||||||||
\(927\) | 13.6084 | 0.446957 | ||||||||
\(928\) | 3.15414 | 0.103540 | ||||||||
\(929\) | 43.7705 | 1.43606 | 0.718031 | − | 0.696011i | \(-0.245043\pi\) | ||||
0.718031 | + | 0.696011i | \(0.245043\pi\) | |||||||
\(930\) | 5.59504 | 0.183468 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.58547 | 0.0519339 | ||||||||
\(933\) | 18.2588 | 0.597765 | ||||||||
\(934\) | 19.4832 | 0.637509 | ||||||||
\(935\) | 0.574734 | 0.0187958 | ||||||||
\(936\) | 13.8274 | 0.451963 | ||||||||
\(937\) | −53.3787 | −1.74381 | −0.871903 | − | 0.489678i | \(-0.837114\pi\) | ||||
−0.871903 | + | 0.489678i | \(0.837114\pi\) | |||||||
\(938\) | 3.59521 | 0.117388 | ||||||||
\(939\) | 1.24399 | 0.0405960 | ||||||||
\(940\) | −3.22595 | −0.105219 | ||||||||
\(941\) | 35.9659 | 1.17245 | 0.586227 | − | 0.810147i | \(-0.300613\pi\) | ||||
0.586227 | + | 0.810147i | \(0.300613\pi\) | |||||||
\(942\) | 8.51950 | 0.277580 | ||||||||
\(943\) | 2.18240 | 0.0710688 | ||||||||
\(944\) | −2.57219 | −0.0837177 | ||||||||
\(945\) | 4.48760 | 0.145982 | ||||||||
\(946\) | 4.83377 | 0.157159 | ||||||||
\(947\) | −36.2742 | −1.17875 | −0.589377 | − | 0.807858i | \(-0.700627\pi\) | ||||
−0.589377 | + | 0.807858i | \(0.700627\pi\) | |||||||
\(948\) | −9.10623 | −0.295757 | ||||||||
\(949\) | 8.09500 | 0.262775 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.83254 | 0.156706 | ||||||||
\(952\) | 0.257918 | 0.00835917 | ||||||||
\(953\) | −11.1181 | −0.360151 | −0.180075 | − | 0.983653i | \(-0.557634\pi\) | ||||
−0.180075 | + | 0.983653i | \(0.557634\pi\) | |||||||
\(954\) | −19.9283 | −0.645202 | ||||||||
\(955\) | 15.3387 | 0.496349 | ||||||||
\(956\) | −13.6183 | −0.440447 | ||||||||
\(957\) | −2.97114 | −0.0960433 | ||||||||
\(958\) | 30.7828 | 0.994546 | ||||||||
\(959\) | −6.57313 | −0.212257 | ||||||||
\(960\) | 0.792143 | 0.0255663 | ||||||||
\(961\) | 18.8883 | 0.609298 | ||||||||
\(962\) | 48.5201 | 1.56435 | ||||||||
\(963\) | −11.2319 | −0.361944 | ||||||||
\(964\) | −2.51719 | −0.0810734 | ||||||||
\(965\) | −1.56739 | −0.0504560 | ||||||||
\(966\) | −0.159595 | −0.00513489 | ||||||||
\(967\) | 51.5662 | 1.65826 | 0.829129 | − | 0.559057i | \(-0.188837\pi\) | ||||
0.829129 | + | 0.559057i | \(0.188837\pi\) | |||||||
\(968\) | 8.35013 | 0.268383 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.91428 | 0.189896 | ||||||||
\(971\) | 13.2758 | 0.426042 | 0.213021 | − | 0.977048i | \(-0.431670\pi\) | ||||
0.213021 | + | 0.977048i | \(0.431670\pi\) | |||||||
\(972\) | 13.3637 | 0.428641 | ||||||||
\(973\) | 2.58506 | 0.0828734 | ||||||||
\(974\) | −21.5085 | −0.689176 | ||||||||
\(975\) | −9.38541 | −0.300574 | ||||||||
\(976\) | 12.3032 | 0.393815 | ||||||||
\(977\) | 17.5847 | 0.562583 | 0.281291 | − | 0.959622i | \(-0.409237\pi\) | ||||
0.281291 | + | 0.959622i | \(0.409237\pi\) | |||||||
\(978\) | 13.4886 | 0.431318 | ||||||||
\(979\) | −1.54205 | −0.0492842 | ||||||||
\(980\) | 1.36891 | 0.0437281 | ||||||||
\(981\) | −32.9019 | −1.05048 | ||||||||
\(982\) | −6.94462 | −0.221612 | ||||||||
\(983\) | 50.5423 | 1.61205 | 0.806024 | − | 0.591883i | \(-0.201615\pi\) | ||||
0.806024 | + | 0.591883i | \(0.201615\pi\) | |||||||
\(984\) | 4.57906 | 0.145975 | ||||||||
\(985\) | −5.79343 | −0.184594 | ||||||||
\(986\) | 0.813509 | 0.0259074 | ||||||||
\(987\) | 1.36369 | 0.0434066 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.818961 | 0.0260414 | ||||||||
\(990\) | 5.93890 | 0.188751 | ||||||||
\(991\) | 45.7977 | 1.45481 | 0.727406 | − | 0.686208i | \(-0.240726\pi\) | ||||
0.727406 | + | 0.686208i | \(0.240726\pi\) | |||||||
\(992\) | 7.06316 | 0.224256 | ||||||||
\(993\) | 2.40872 | 0.0764385 | ||||||||
\(994\) | 3.93297 | 0.124746 | ||||||||
\(995\) | −15.2279 | −0.482758 | ||||||||
\(996\) | 6.28763 | 0.199231 | ||||||||
\(997\) | −14.4959 | −0.459088 | −0.229544 | − | 0.973298i | \(-0.573724\pi\) | ||||
−0.229544 | + | 0.973298i | \(0.573724\pi\) | |||||||
\(998\) | 16.0613 | 0.508412 | ||||||||
\(999\) | 30.6579 | 0.969973 |
(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 | 5054.2.a.bf.1.6 | ✓ | 8 | |
19.18 | odd | 2 | 5054.2.a.bi.1.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.bf.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5054.2.a.bi.1.3 | yes | 8 | 19.18 | odd | 2 |