Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2368,2,Mod(1,2368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2368, 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("2368.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2368 = 2^{6} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2368.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: | \(18.9085751986\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1184) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.14510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2368.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.14510 | −1.23848 | −0.619238 | − | 0.785204i | \(-0.712558\pi\) | ||||
−0.619238 | + | 0.785204i | \(0.712558\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.14510 | 1.40653 | 0.703266 | − | 0.710926i | \(-0.251724\pi\) | ||||
0.703266 | + | 0.710926i | \(0.251724\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.74657 | −0.660141 | −0.330070 | − | 0.943956i | \(-0.607072\pi\) | ||||
−0.330070 | + | 0.943956i | \(0.607072\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.60147 | 0.533822 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.89167 | −0.871872 | −0.435936 | − | 0.899978i | \(-0.643583\pi\) | ||||
−0.435936 | + | 0.899978i | \(0.643583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.39853 | 0.665234 | 0.332617 | − | 0.943062i | \(-0.392068\pi\) | ||||
0.332617 | + | 0.943062i | \(0.392068\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.74657 | −1.74196 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.49314 | −1.33228 | −0.666141 | − | 0.745826i | \(-0.732055\pi\) | ||||
−0.666141 | + | 0.745826i | \(0.732055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.74657 | 0.817568 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.60147 | 0.333929 | 0.166964 | − | 0.985963i | \(-0.446604\pi\) | ||||
0.166964 | + | 0.985963i | \(0.446604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89167 | 0.978334 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.00000 | 0.577350 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.89167 | 1.09406 | 0.547028 | − | 0.837114i | \(-0.315759\pi\) | ||||
0.547028 | + | 0.837114i | \(0.315759\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.94217 | −0.708035 | −0.354017 | − | 0.935239i | \(-0.615185\pi\) | ||||
−0.354017 | + | 0.935239i | \(0.615185\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.20293 | 1.07979 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.49314 | −0.928510 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.14510 | −0.823876 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.14510 | 0.959704 | 0.479852 | − | 0.877350i | \(-0.340690\pi\) | ||||
0.479852 | + | 0.877350i | \(0.340690\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.20293 | 0.793440 | 0.396720 | − | 0.917940i | \(-0.370148\pi\) | ||||
0.396720 | + | 0.917940i | \(0.370148\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.03677 | 0.750838 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.253432 | −0.0369668 | −0.0184834 | − | 0.999829i | \(-0.505884\pi\) | ||||
−0.0184834 | + | 0.999829i | \(0.505884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.94950 | −0.564214 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.7833 | 1.65000 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.543637 | −0.0746743 | −0.0373372 | − | 0.999303i | \(-0.511888\pi\) | ||||
−0.0373372 | + | 0.999303i | \(0.511888\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.09460 | −1.22632 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.29021 | −0.568252 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.6961 | 1.39251 | 0.696255 | − | 0.717795i | \(-0.254848\pi\) | ||||
0.696255 | + | 0.717795i | \(0.254848\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.63824 | −0.849939 | −0.424970 | − | 0.905208i | \(-0.639715\pi\) | ||||
−0.424970 | + | 0.905208i | \(0.639715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.79707 | −0.352398 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.54364 | 0.935673 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.14510 | 0.872913 | 0.436457 | − | 0.899725i | \(-0.356233\pi\) | ||||
0.436457 | + | 0.899725i | \(0.356233\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.43531 | −0.413562 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.03677 | 0.479077 | 0.239538 | − | 0.970887i | \(-0.423004\pi\) | ||||
0.239538 | + | 0.970887i | \(0.423004\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.18188 | 0.372410 | 0.186205 | − | 0.982511i | \(-0.440381\pi\) | ||||
0.186205 | + | 0.982511i | \(0.440381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.4931 | −1.21164 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.05050 | 0.575558 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.89167 | −1.11290 | −0.556450 | − | 0.830881i | \(-0.687837\pi\) | ||||
−0.556450 | + | 0.830881i | \(0.687837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2397 | −1.24886 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.03677 | 0.662622 | 0.331311 | − | 0.943522i | \(-0.392509\pi\) | ||||
0.331311 | + | 0.943522i | \(0.392509\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.2765 | −1.87390 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.6382 | −1.35496 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.50686 | 0.477727 | 0.238863 | − | 0.971053i | \(-0.423225\pi\) | ||||
0.238863 | + | 0.971053i | \(0.423225\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.18920 | −0.439148 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.45636 | 0.876884 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.29021 | 0.645361 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9863 | 1.31856 | 0.659278 | − | 0.751899i | \(-0.270862\pi\) | ||||
0.659278 | + | 0.751899i | \(0.270862\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.63091 | −0.465424 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.6172 | −1.65347 | −0.826736 | − | 0.562590i | \(-0.809805\pi\) | ||||
−0.826736 | + | 0.562590i | \(0.809805\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.13138 | 0.801208 | 0.400604 | − | 0.916251i | \(-0.368800\pi\) | ||||
0.400604 | + | 0.916251i | \(0.368800\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.7833 | 1.14994 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.3848 | −1.87400 | −0.937000 | − | 0.349329i | \(-0.886409\pi\) | ||||
−0.937000 | + | 0.349329i | \(0.886409\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.14510 | −0.203604 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.4794 | 1.92654 | 0.963270 | − | 0.268533i | \(-0.0865389\pi\) | ||||
0.963270 | + | 0.268533i | \(0.0865389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.03677 | 0.469682 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.84117 | 0.355116 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.59414 | 0.879493 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.63824 | −0.239840 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.1819 | −1.18857 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.340706 | −0.0304737 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.4426 | 1.63652 | 0.818260 | − | 0.574849i | \(-0.194939\pi\) | ||||
0.818260 | + | 0.574849i | \(0.194939\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.1608 | −0.982656 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3775 | 1.51828 | 0.759139 | − | 0.650929i | \(-0.225620\pi\) | ||||
0.759139 | + | 0.650929i | \(0.225620\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.49314 | −0.302893 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.43531 | 0.812062 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.84117 | −0.840788 | −0.420394 | − | 0.907342i | \(-0.638108\pi\) | ||||
−0.420394 | + | 0.907342i | \(0.638108\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.80440 | 0.577141 | 0.288571 | − | 0.957459i | \(-0.406820\pi\) | ||||
0.288571 | + | 0.957459i | \(0.406820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.543637 | 0.0457825 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.93577 | −0.579998 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.5299 | 1.53883 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.47208 | 0.698766 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.8201 | 1.13219 | 0.566094 | − | 0.824341i | \(-0.308454\pi\) | ||||
0.566094 | + | 0.824341i | \(0.308454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8706 | 0.884638 | 0.442319 | − | 0.896858i | \(-0.354156\pi\) | ||||
0.442319 | + | 0.896858i | \(0.354156\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.79707 | −0.711201 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.3985 | −0.995874 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.5162 | 1.79699 | 0.898494 | − | 0.438987i | \(-0.144663\pi\) | ||||
0.898494 | + | 0.438987i | \(0.144663\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.16616 | 0.0924823 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.79707 | −0.220440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0735 | 1.10233 | 0.551163 | − | 0.834398i | \(-0.314184\pi\) | ||||
0.551163 | + | 0.834398i | \(0.314184\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.5089 | 1.51876 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.7255 | 1.37164 | 0.685821 | − | 0.727771i | \(-0.259443\pi\) | ||||
0.685821 | + | 0.727771i | \(0.259443\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.24703 | −0.557464 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.20293 | 0.244934 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4564 | 1.17513 | 0.587563 | − | 0.809179i | \(-0.300088\pi\) | ||||
0.587563 | + | 0.809179i | \(0.300088\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.54364 | −0.645838 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.9442 | −1.72459 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.69607 | −0.351001 | −0.175500 | − | 0.984479i | \(-0.556154\pi\) | ||||
−0.175500 | + | 0.984479i | \(0.556154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.05050 | −0.226742 | −0.113371 | − | 0.993553i | \(-0.536165\pi\) | ||||
−0.113371 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.2397 | 1.05263 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.14510 | 0.231233 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8843 | 1.16158 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.23970 | −0.381132 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.73924 | 0.198204 | 0.0991022 | − | 0.995077i | \(-0.468403\pi\) | ||||
0.0991022 | + | 0.995077i | \(0.468403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0000 | 1.15171 | 0.575853 | − | 0.817554i | \(-0.304670\pi\) | ||||
0.575853 | + | 0.817554i | \(0.304670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.1819 | −1.15881 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.0230 | −1.64032 | −0.820162 | − | 0.572131i | \(-0.806117\pi\) | ||||
−0.820162 | + | 0.572131i | \(0.806117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.3270 | −1.08108 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.2902 | −0.722231 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.3270 | 1.34985 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.56469 | 0.178258 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.78334 | −0.400042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9652 | 1.03025 | 0.515124 | − | 0.857116i | \(-0.327746\pi\) | ||||
0.515124 | + | 0.857116i | \(0.327746\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.65929 | −0.593325 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.3638 | 1.11600 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.88527 | 0.467403 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.82545 | −0.461221 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.1755 | −0.886278 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.2260 | −1.48836 | −0.744181 | − | 0.667978i | \(-0.767160\pi\) | ||||
−0.744181 | + | 0.667978i | \(0.767160\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.83384 | 0.522256 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.6961 | −1.63914 | −0.819568 | − | 0.572982i | \(-0.805786\pi\) | ||||
−0.819568 | + | 0.572982i | \(0.805786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.92112 | 0.126951 | 0.0634755 | − | 0.997983i | \(-0.479782\pi\) | ||||
0.0634755 | + | 0.997983i | \(0.479782\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.8338 | −0.712815 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.4721 | 1.07912 | 0.539561 | − | 0.841947i | \(-0.318590\pi\) | ||||
0.539561 | + | 0.841947i | \(0.318590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.797069 | −0.0519950 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.2186 | 1.37830 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.52258 | −0.551280 | −0.275640 | − | 0.961261i | \(-0.588890\pi\) | ||||
−0.275640 | + | 0.961261i | \(0.588890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.17455 | 0.397738 | 0.198869 | − | 0.980026i | \(-0.436273\pi\) | ||||
0.198869 | + | 0.980026i | \(0.436273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1103 | 0.969328 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.4216 | −0.793586 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.79707 | 0.305230 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.9495 | −0.820641 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9725 | 1.63937 | 0.819686 | − | 0.572813i | \(-0.194148\pi\) | ||||
0.819686 | + | 0.572813i | \(0.194148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.63091 | −0.291143 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37.0598 | 2.32078 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.74657 | −0.108526 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.43531 | 0.584031 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.1524 | 1.11933 | 0.559663 | − | 0.828720i | \(-0.310930\pi\) | ||||
0.559663 | + | 0.828720i | \(0.310930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.70979 | −0.105032 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.66769 | −0.591653 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.6677 | 1.07722 | 0.538609 | − | 0.842556i | \(-0.318950\pi\) | ||||
0.538609 | + | 0.842556i | \(0.318950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.4426 | −0.998819 | −0.499409 | − | 0.866366i | \(-0.666450\pi\) | ||||
−0.499409 | + | 0.866366i | \(0.666450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.98627 | 0.543874 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.1451 | −0.852982 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3059 | 1.22006 | 0.610032 | − | 0.792376i | \(-0.291156\pi\) | ||||
0.610032 | + | 0.792376i | \(0.291156\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.31325 | −0.377965 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.5667 | 0.928630 | 0.464315 | − | 0.885670i | \(-0.346300\pi\) | ||||
0.464315 | + | 0.885670i | \(0.346300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.7833 | −1.29489 | −0.647443 | − | 0.762114i | \(-0.724161\pi\) | ||||
−0.647443 | + | 0.762114i | \(0.724161\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.4931 | −0.799264 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7328 | −0.633540 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.1745 | 0.774973 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.8569 | −1.63300 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.60879 | 0.444510 | 0.222255 | − | 0.974989i | \(-0.428658\pi\) | ||||
0.222255 | + | 0.974989i | \(0.428658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.6402 | 1.95861 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.67501 | −0.503375 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.84117 | 0.222141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.08727 | −0.523782 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.6456 | 2.04778 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.8779 | −1.19547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7392 | 0.669994 | 0.334997 | − | 0.942219i | \(-0.391265\pi\) | ||||
0.334997 | + | 0.942219i | \(0.391265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.4426 | −0.992277 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.5731 | −0.712954 | −0.356477 | − | 0.934304i | \(-0.616022\pi\) | ||||
−0.356477 | + | 0.934304i | \(0.616022\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4510 | −1.43858 | −0.719289 | − | 0.694711i | \(-0.755532\pi\) | ||||
−0.719289 | + | 0.694711i | \(0.755532\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.79707 | −0.495659 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.0735 | −0.902780 | −0.451390 | − | 0.892327i | \(-0.649072\pi\) | ||||
−0.451390 | + | 0.892327i | \(0.649072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.0368 | −0.953876 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 41.5824 | 2.32090 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.9863 | −0.611293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7328 | 0.650821 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.4510 | −1.18624 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.442636 | 0.0244033 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.08727 | −0.499482 | −0.249741 | − | 0.968313i | \(-0.580345\pi\) | ||||
−0.249741 | + | 0.968313i | \(0.580345\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.60147 | 0.0877598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.4721 | 1.22778 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.97895 | −0.325694 | −0.162847 | − | 0.986651i | \(-0.552068\pi\) | ||||
−0.162847 | + | 0.986651i | \(0.552068\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −43.9304 | −2.38597 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.3995 | 0.617316 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1240 | 1.03260 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.8044 | −0.581689 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.8706 | 1.22776 | 0.613880 | − | 0.789400i | \(-0.289608\pi\) | ||||
0.613880 | + | 0.789400i | \(0.289608\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.39121 | −0.449171 | −0.224585 | − | 0.974454i | \(-0.572103\pi\) | ||||
−0.224585 | + | 0.974454i | \(0.572103\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.19560 | 0.384073 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.8569 | −0.950426 | −0.475213 | − | 0.879871i | \(-0.657629\pi\) | ||||
−0.475213 | + | 0.879871i | \(0.657629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.6961 | 0.673837 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.5804 | −1.08923 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.03677 | 0.424165 | 0.212082 | − | 0.977252i | \(-0.431975\pi\) | ||||
0.212082 | + | 0.977252i | \(0.431975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.65929 | 0.297036 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0073 | 0.523807 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.6088 | −0.919172 | −0.459586 | − | 0.888133i | \(-0.652002\pi\) | ||||
−0.459586 | + | 0.888133i | \(0.652002\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.84117 | 0.512311 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.949499 | 0.0492956 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0084 | 0.777105 | 0.388553 | − | 0.921427i | \(-0.372975\pi\) | ||||
0.388553 | + | 0.921427i | \(0.372975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.730849 | 0.0377409 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.1314 | 0.727803 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.56469 | 0.285839 | 0.142920 | − | 0.989734i | \(-0.454351\pi\) | ||||
0.142920 | + | 0.989734i | \(0.454351\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.5613 | −2.02679 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.1745 | −1.33746 | −0.668728 | − | 0.743507i | \(-0.733161\pi\) | ||||
−0.668728 | + | 0.743507i | \(0.733161\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.8843 | 0.809541 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.33231 | 0.423555 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.5005 | −1.39433 | −0.697164 | − | 0.716911i | \(-0.745555\pi\) | ||||
−0.697164 | + | 0.716911i | \(0.745555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.79707 | −0.444887 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −37.2765 | −1.88035 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.1103 | −1.56533 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.8201 | −1.19550 | −0.597749 | − | 0.801684i | \(-0.703938\pi\) | ||||
−0.597749 | + | 0.801684i | \(0.703938\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.49314 | 0.375126 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.4373 | 1.22034 | 0.610170 | − | 0.792270i | \(-0.291101\pi\) | ||||
0.610170 | + | 0.792270i | \(0.291101\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.45543 | −0.471009 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −35.3500 | −1.75656 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.89167 | −0.143335 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.62252 | −0.426356 | −0.213178 | − | 0.977013i | \(-0.568381\pi\) | ||||
−0.213178 | + | 0.977013i | \(0.568381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.1103 | 1.04130 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.6814 | −0.919252 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.9863 | 0.931999 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.5961 | −0.714776 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.2186 | −0.499214 | −0.249607 | − | 0.968347i | \(-0.580301\pi\) | ||||
−0.249607 | + | 0.968347i | \(0.580301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.7339 | −1.44914 | −0.724571 | − | 0.689200i | \(-0.757962\pi\) | ||||
−0.724571 | + | 0.689200i | \(0.757962\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.405862 | −0.0197337 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.8706 | −1.30342 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.5941 | 0.561080 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.8779 | 0.718314 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6540 | −0.802193 | −0.401096 | − | 0.916036i | \(-0.631371\pi\) | ||||
−0.401096 | + | 0.916036i | \(0.631371\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0020 | 0.865121 | 0.432560 | − | 0.901605i | \(-0.357610\pi\) | ||||
0.432560 | + | 0.901605i | \(0.357610\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −39.7486 | −1.90580 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.20293 | 0.153217 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.587739 | 0.0280512 | 0.0140256 | − | 0.999902i | \(-0.495535\pi\) | ||||
0.0140256 | + | 0.999902i | \(0.495535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.32499 | −0.301190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.0388 | 0.714513 | 0.357257 | − | 0.934006i | \(-0.383712\pi\) | ||||
0.357257 | + | 0.934006i | \(0.383712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1745 | 0.671938 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.6456 | −1.40219 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.1608 | −0.526712 | −0.263356 | − | 0.964699i | \(-0.584829\pi\) | ||||
−0.263356 | + | 0.964699i | \(0.584829\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.7696 | −0.836738 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.3186 | −1.09560 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.1755 | −0.617676 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.9579 | −1.21426 | −0.607129 | − | 0.794603i | \(-0.707679\pi\) | ||||
−0.607129 | + | 0.794603i | \(0.707679\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.4794 | −0.769193 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.17455 | 0.194428 | 0.0972141 | − | 0.995263i | \(-0.469007\pi\) | ||||
0.0972141 | + | 0.995263i | \(0.469007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.10833 | 0.0979824 | 0.0489912 | − | 0.998799i | \(-0.484399\pi\) | ||||
0.0489912 | + | 0.998799i | \(0.484399\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 26.5961 | 1.23337 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.6677 | 1.55795 | 0.778977 | − | 0.627052i | \(-0.215739\pi\) | ||||
0.778977 | + | 0.627052i | \(0.215739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4794 | −0.576246 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −48.2995 | −2.22552 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.0452 | −0.691777 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.78334 | 0.448891 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.870616 | −0.0398628 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.10833 | −0.0963320 | −0.0481660 | − | 0.998839i | \(-0.515338\pi\) | ||||
−0.0481660 | + | 0.998839i | \(0.515338\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.39853 | 0.109364 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.00000 | 0.273009 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.8432 | 1.85459 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.7412 | 1.16645 | 0.583223 | − | 0.812312i | \(-0.301791\pi\) | ||||
0.583223 | + | 0.812312i | \(0.301791\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.1892 | −1.36520 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.5877 | −0.838853 | −0.419426 | − | 0.907789i | \(-0.637769\pi\) | ||||
−0.419426 | + | 0.907789i | \(0.637769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.3638 | −1.45759 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.5647 | −0.654634 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.05050 | −0.316258 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.9716 | 1.02835 | 0.514175 | − | 0.857685i | \(-0.328098\pi\) | ||||
0.514175 | + | 0.857685i | \(0.328098\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.0230 | −1.69874 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.9001 | −1.42235 | −0.711177 | − | 0.703013i | \(-0.751837\pi\) | ||||
−0.711177 | + | 0.703013i | \(0.751837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −52.2628 | −2.32566 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.5456 | 0.690406 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.3270 | 0.989626 | 0.494813 | − | 0.868999i | \(-0.335237\pi\) | ||||
0.494813 | + | 0.868999i | \(0.335237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.55736 | −0.245843 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.00000 | 0.264906 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.5740 | 1.12693 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.732841 | 0.0322303 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −33.1555 | −1.45536 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.110321 | −0.00483325 | −0.00241662 | − | 0.999997i | \(-0.500769\pi\) | ||||
−0.00241662 | + | 0.999997i | \(0.500769\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.9442 | −0.915824 | −0.457912 | − | 0.888997i | \(-0.651403\pi\) | ||||
−0.457912 | + | 0.888997i | \(0.651403\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.3270 | 0.799855 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.6549 | 0.943302 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4353 | −0.888492 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.1294 | 0.743352 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.7392 | 0.638427 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −60.9672 | −2.63584 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.0735 | 0.434706 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.4207 | 0.491922 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.5510 | −1.09852 | −0.549261 | − | 0.835651i | \(-0.685091\pi\) | ||||
−0.549261 | + | 0.835651i | \(0.685091\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.54364 | 0.280814 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.4510 | 1.34721 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.6823 | 0.499501 | 0.249750 | − | 0.968310i | \(-0.419651\pi\) | ||||
0.249750 | + | 0.968310i | \(0.419651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.6309 | −0.453716 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.7833 | 0.501987 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.2765 | 0.734671 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.74657 | −0.286376 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.6971 | 0.707480 | 0.353740 | − | 0.935344i | \(-0.384910\pi\) | ||||
0.353740 | + | 0.935344i | \(0.384910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.4794 | 0.527823 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.0735 | −1.43859 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.9588 | −1.47334 | −0.736669 | − | 0.676253i | \(-0.763603\pi\) | ||||
−0.736669 | + | 0.676253i | \(0.763603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 64.4098 | 2.70974 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.6309 | 0.824421 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.4931 | 0.817195 | 0.408597 | − | 0.912715i | \(-0.366018\pi\) | ||||
0.408597 | + | 0.912715i | \(0.366018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.9422 | 1.29489 | 0.647445 | − | 0.762112i | \(-0.275838\pi\) | ||||
0.647445 | + | 0.762112i | \(0.275838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.87595 | −0.245471 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.83384 | 0.326694 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.87062 | −0.369289 | −0.184644 | − | 0.982805i | \(-0.559113\pi\) | ||||
−0.184644 | + | 0.982805i | \(0.559113\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.3216 | −1.42636 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.5436 | −0.437424 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.57202 | 0.0651064 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0809 | 0.499483 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.1745 | 0.832693 | 0.416346 | − | 0.909206i | \(-0.363310\pi\) | ||||
0.416346 | + | 0.909206i | \(0.363310\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.88434 | −0.324869 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 49.3868 | 2.03150 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.5319 | −1.33593 | −0.667963 | − | 0.744195i | \(-0.732833\pi\) | ||||
−0.667963 | + | 0.744195i | \(0.732833\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.1745 | 1.23704 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.3216 | 1.40469 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.3554 | −0.545685 | −0.272843 | − | 0.962059i | \(-0.587964\pi\) | ||||
−0.272843 | + | 0.962059i | \(0.587964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.6099 | −1.04465 | −0.522324 | − | 0.852747i | \(-0.674935\pi\) | ||||
−0.522324 | + | 0.852747i | \(0.674935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.4426 | 0.465980 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.29753 | −0.337343 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.6015 | −1.52620 | −0.763098 | − | 0.646283i | \(-0.776323\pi\) | ||||
−0.763098 | + | 0.646283i | \(0.776323\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.0735 | 0.894465 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.607865 | −0.0245916 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.8201 | −1.28520 | −0.642601 | − | 0.766201i | \(-0.722145\pi\) | ||||
−0.642601 | + | 0.766201i | \(0.722145\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −41.4584 | −1.67176 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.8128 | 1.76384 | 0.881918 | − | 0.471402i | \(-0.156252\pi\) | ||||
0.881918 | + | 0.471402i | \(0.156252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.9063 | 1.16184 | 0.580922 | − | 0.813959i | \(-0.302692\pi\) | ||||
0.580922 | + | 0.813959i | \(0.302692\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.80440 | 0.192794 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.87154 | −0.315367 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.5299 | −1.02120 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.4059 | 0.495442 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.49314 | −0.219026 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.7907 | −1.42480 | −0.712402 | − | 0.701772i | \(-0.752393\pi\) | ||||
−0.712402 | + | 0.701772i | \(0.752393\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.1019 | −1.27594 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.0040 | 2.30182 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.47301 | −0.375334 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.46475 | 0.255742 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8412 | −0.507196 | −0.253598 | − | 0.967310i | \(-0.581614\pi\) | ||||
−0.253598 | + | 0.967310i | \(0.581614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.9579 | 0.865935 | 0.432967 | − | 0.901410i | \(-0.357467\pi\) | ||||
0.432967 | + | 0.901410i | \(0.357467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −35.1019 | −1.38214 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.4858 | 0.608810 | 0.304405 | − | 0.952543i | \(-0.401542\pi\) | ||||
0.304405 | + | 0.952543i | \(0.401542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.9295 | −1.21409 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.7696 | −0.578867 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.0525 | 0.902114 | 0.451057 | − | 0.892495i | \(-0.351047\pi\) | ||||
0.451057 | + | 0.892495i | \(0.351047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 54.6540 | 2.13551 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.09567 | 0.198801 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.05783 | 0.197025 | 0.0985125 | − | 0.995136i | \(-0.468592\pi\) | ||||
0.0985125 | + | 0.995136i | \(0.468592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.9789 | −1.36052 | −0.680262 | − | 0.732969i | \(-0.738134\pi\) | ||||
−0.680262 | + | 0.732969i | \(0.738134\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.2628 | 1.09763 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.9863 | −0.426029 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.43531 | 0.365337 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.6770 | 1.84330 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.1956 | 0.741038 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.73924 | 0.298326 | 0.149163 | − | 0.988813i | \(-0.452342\pi\) | ||||
0.149163 | + | 0.988813i | \(0.452342\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.6750 | 0.564842 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.5446 | 1.44295 | 0.721477 | − | 0.692438i | \(-0.243463\pi\) | ||||
0.721477 | + | 0.692438i | \(0.243463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.6814 | −0.870433 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 52.9756 | 2.03003 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.85596 | −0.185808 | −0.0929041 | − | 0.995675i | \(-0.529615\pi\) | ||||
−0.0929041 | + | 0.995675i | \(0.529615\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.9515 | −1.18260 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.12099 | −0.157226 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.30393 | −0.0496759 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.1471 | −0.918599 | −0.459299 | − | 0.888282i | \(-0.651899\pi\) | ||||
−0.459299 | + | 0.888282i | \(0.651899\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.08820 | 0.307245 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.4005 | 0.811768 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.7559 | −1.27860 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35.3343 | −1.33647 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0441 | 0.492669 | 0.246334 | − | 0.969185i | \(-0.420774\pi\) | ||||
0.246334 | + | 0.969185i | \(0.420774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.70979 | 0.0643946 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.0230 | 1.09152 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.5098 | −1.59649 | −0.798244 | − | 0.602334i | \(-0.794238\pi\) | ||||
−0.798244 | + | 0.602334i | \(0.794238\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.8412 | −0.594090 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.31325 | −0.236433 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.8137 | −0.815787 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.2818 | 0.682747 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.9220 | −1.00402 | −0.502011 | − | 0.864861i | \(-0.667406\pi\) | ||||
−0.502011 | + | 0.864861i | \(0.667406\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.2020 | −0.528910 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.2450 | −0.492588 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.8201 | 1.07035 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.4814 | 1.53846 | 0.769230 | − | 0.638972i | \(-0.220640\pi\) | ||||
0.769230 | + | 0.638972i | \(0.220640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.30592 | 0.0483676 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.5804 | −1.05708 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.5299 | 0.869097 | 0.434549 | − | 0.900648i | \(-0.356908\pi\) | ||||
0.434549 | + | 0.900648i | \(0.356908\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 26.6456 | 0.982837 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.6613 | −0.761068 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.3250 | −0.416596 | −0.208298 | − | 0.978065i | \(-0.566792\pi\) | ||||
−0.208298 | + | 0.978065i | \(0.566792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.2902 | −0.378020 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.3731 | 1.70126 | 0.850632 | − | 0.525762i | \(-0.176220\pi\) | ||||
0.850632 | + | 0.525762i | \(0.176220\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.4657 | 1.59246 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.66769 | 0.353722 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.8569 | 1.23710 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.9632 | −0.728468 | −0.364234 | − | 0.931307i | \(-0.618669\pi\) | ||||
−0.364234 | + | 0.931307i | \(0.618669\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −55.7138 | −2.03032 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.1892 | 1.24427 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2922 | 0.410422 | 0.205211 | − | 0.978718i | \(-0.434212\pi\) | ||||
0.205211 | + | 0.978718i | \(0.434212\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.93378 | 0.360573 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.5549 | 1.76012 | 0.880058 | − | 0.474867i | \(-0.157504\pi\) | ||||
0.880058 | + | 0.474867i | \(0.157504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.4657 | −0.632300 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.6677 | −1.00033 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.6549 | 0.926344 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.31859 | 0.263915 | 0.131958 | − | 0.991255i | \(-0.457874\pi\) | ||||
0.131958 | + | 0.991255i | \(0.457874\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.8706 | −0.463524 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.2711 | −1.26861 | −0.634307 | − | 0.773081i | \(-0.718715\pi\) | ||||
−0.634307 | + | 0.773081i | \(0.718715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.2838 | −0.692695 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.74657 | 0.134407 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.2902 | 0.440342 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6730 | −0.417694 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.6750 | 0.631653 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 70.8157 | 2.52752 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.9220 | 0.817083 | 0.408541 | − | 0.912740i | \(-0.366038\pi\) | ||||
0.408541 | + | 0.912740i | \(0.366038\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38.9388 | −1.38626 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.7687 | −1.27179 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.9220 | −0.565408 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.66769 | 0.130079 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.1819 | 0.785722 | 0.392861 | − | 0.919598i | \(-0.371485\pi\) | ||||
0.392861 | + | 0.919598i | \(0.371485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.39214 | 0.0492502 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.21759 | 0.255021 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.20094 | −0.324694 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.79707 | −0.310056 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.8990 | −1.33411 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.7098 | 0.974224 | 0.487112 | − | 0.873339i | \(-0.338050\pi\) | ||||
0.487112 | + | 0.873339i | \(0.338050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.4437 | 1.42017 | 0.710085 | − | 0.704116i | \(-0.248656\pi\) | ||||
0.710085 | + | 0.704116i | \(0.248656\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35.2711 | 1.23701 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.2628 | 1.55046 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4059 | 0.364055 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.70887 | −0.234427 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.93577 | −0.0675589 | −0.0337795 | − | 0.999429i | \(-0.510754\pi\) | ||||
−0.0337795 | + | 0.999429i | \(0.510754\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.3784 | −0.989209 | −0.494605 | − | 0.869118i | \(-0.664687\pi\) | ||||
−0.494605 | + | 0.869118i | \(0.664687\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.3427 | 1.05640 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.2902 | 0.566466 | 0.283233 | − | 0.959051i | \(-0.408593\pi\) | ||||
0.283233 | + | 0.959051i | \(0.408593\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6152 | 0.507607 | 0.253803 | − | 0.967256i | \(-0.418318\pi\) | ||||
0.253803 | + | 0.967256i | \(0.418318\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.5583 | −1.51102 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.6951 | 0.751692 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 55.7486 | 1.92926 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.8265 | −0.408784 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5215 | 0.777529 | 0.388765 | − | 0.921337i | \(-0.372902\pi\) | ||||
0.388765 | + | 0.921337i | \(0.372902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.71179 | 0.196958 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −33.3921 | −1.15009 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.7927 | −0.784091 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.60786 | 0.158328 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 46.7275 | 1.60368 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.60147 | 0.0548975 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.0578 | 0.755246 | 0.377623 | − | 0.925960i | \(-0.376742\pi\) | ||||
0.377623 | + | 0.925960i | \(0.376742\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.0735 | 0.344508 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.26182 | 0.316378 | 0.158189 | − | 0.987409i | \(-0.449434\pi\) | ||||
0.158189 | + | 0.987409i | \(0.449434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.8148 | 1.49494 | 0.747470 | − | 0.664295i | \(-0.231268\pi\) | ||||
0.747470 | + | 0.664295i | \(0.231268\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.0230 | 0.784623 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.231314 | 0.00787401 | 0.00393700 | − | 0.999992i | \(-0.498747\pi\) | ||||
0.00393700 | + | 0.999992i | \(0.498747\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.6118 | 1.65285 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.2608 | −0.959786 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.6035 | 0.970306 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.1378 | 0.580691 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.7971 | 0.703874 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.595066 | 0.0201169 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.1471 | −1.15307 | −0.576533 | − | 0.817074i | \(-0.695595\pi\) | ||||
−0.576533 | + | 0.817074i | \(0.695595\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.3216 | −0.550515 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.7118 | −1.37161 | −0.685807 | − | 0.727783i | \(-0.740551\pi\) | ||||
−0.685807 | + | 0.727783i | \(0.740551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.2206 | −1.21892 | −0.609461 | − | 0.792816i | \(-0.708614\pi\) | ||||
−0.609461 | + | 0.792816i | \(0.708614\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −72.1618 | −2.42569 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.36909 | −0.0795462 | −0.0397731 | − | 0.999209i | \(-0.512664\pi\) | ||||
−0.0397731 | + | 0.999209i | \(0.512664\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.2113 | −1.08033 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.5015 | 1.08884 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.506864 | −0.0169615 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.7696 | −0.493694 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.23970 | −0.275116 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.2260 | −0.774630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.98627 | 0.0994872 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.4931 | 0.648691 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.59414 | −0.318920 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.5667 | −1.11456 | −0.557282 | − | 0.830323i | \(-0.688156\pi\) | ||||
−0.557282 | + | 0.830323i | \(0.688156\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.6118 | −0.882659 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.92645 | −0.262615 | −0.131308 | − | 0.991342i | \(-0.541918\pi\) | ||||
−0.131308 | + | 0.991342i | \(0.541918\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.4564 | −0.577721 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 44.7853 | 1.48056 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.3510 | −1.00228 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.1819 | −0.829771 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.68234 | 0.318698 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.89167 | 0.160837 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.0221 | 0.427702 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.68035 | 0.153557 | 0.0767786 | − | 0.997048i | \(-0.475537\pi\) | ||||
0.0767786 | + | 0.997048i | \(0.475537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.89900 | −0.258879 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.9706 | 0.882976 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 49.9579 | 1.63380 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.1912 | 0.920966 | 0.460483 | − | 0.887668i | \(-0.347676\pi\) | ||||
0.460483 | + | 0.887668i | \(0.347676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.5951 | 1.78164 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.05584 | 0.0344193 | 0.0172096 | − | 0.999852i | \(-0.494522\pi\) | ||||
0.0172096 | + | 0.999852i | \(0.494522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.84117 | 0.320473 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.4794 | −0.536075 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.4794 | −1.51038 | −0.755189 | − | 0.655507i | \(-0.772455\pi\) | ||||
−0.755189 | + | 0.655507i | \(0.772455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.63184 | 0.247740 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.4794 | 1.11807 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.8358 | 0.383400 | 0.191700 | − | 0.981454i | \(-0.438600\pi\) | ||||
0.191700 | + | 0.981454i | \(0.438600\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.61519 | 0.278781 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 36.5456 | 1.18135 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.1883 | 0.555038 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4593 | −0.498687 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −31.0441 | −1.00038 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 50.3216 | 1.61991 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.2226 | −1.77584 | −0.887920 | − | 0.459998i | \(-0.847850\pi\) | ||||
−0.887920 | + | 0.459998i | \(0.847850\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.5667 | 0.757071 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.4353 | 1.84319 | 0.921593 | − | 0.388157i | \(-0.126888\pi\) | ||||
0.921593 | + | 0.388157i | \(0.126888\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.8843 | −0.380995 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.1681 | −0.806026 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.26182 | −0.168341 | −0.0841703 | − | 0.996451i | \(-0.526824\pi\) | ||||
−0.0841703 | + | 0.996451i | \(0.526824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.0324 | −0.416516 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.0147 | 0.511309 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.6770 | 1.83961 | 0.919805 | − | 0.392375i | \(-0.128346\pi\) | ||||
0.919805 | + | 0.392375i | \(0.128346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −72.4098 | −2.30717 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.949499 | −0.0302229 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.33231 | 0.264952 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.0250 | −0.922011 | −0.461005 | − | 0.887397i | \(-0.652511\pi\) | ||||
−0.461005 | + | 0.887397i | \(0.652511\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.4931 | 0.618596 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50.3216 | −1.59530 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0873 | 0.604500 | 0.302250 | − | 0.953229i | \(-0.402262\pi\) | ||||
0.302250 | + | 0.953229i | \(0.402262\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.00000 | 0.0949158 |
(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 | 2368.2.a.bd.1.1 | 3 | ||
4.3 | odd | 2 | 2368.2.a.bc.1.3 | 3 | |||
8.3 | odd | 2 | 1184.2.a.l.1.1 | ✓ | 3 | ||
8.5 | even | 2 | 1184.2.a.m.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1184.2.a.l.1.1 | ✓ | 3 | 8.3 | odd | 2 | ||
1184.2.a.m.1.3 | yes | 3 | 8.5 | even | 2 | ||
2368.2.a.bc.1.3 | 3 | 4.3 | odd | 2 | |||
2368.2.a.bd.1.1 | 3 | 1.1 | even | 1 | trivial |