Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(1,4056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.3873230598\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.27700337.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 19x^{4} + 17x^{3} + 103x^{2} - 71x - 127 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.920510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.72245 | 1.21752 | 0.608758 | − | 0.793356i | \(-0.291668\pi\) | ||||
0.608758 | + | 0.793356i | \(0.291668\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.31535 | 1.25308 | 0.626542 | − | 0.779388i | \(-0.284470\pi\) | ||||
0.626542 | + | 0.779388i | \(0.284470\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.656645 | 0.197986 | 0.0989930 | − | 0.995088i | \(-0.468438\pi\) | ||||
0.0989930 | + | 0.995088i | \(0.468438\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.72245 | 0.702933 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.16749 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.77137 | 1.55346 | 0.776729 | − | 0.629835i | \(-0.216878\pi\) | ||||
0.776729 | + | 0.629835i | \(0.216878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.31535 | 0.723468 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.90073 | 1.43890 | 0.719451 | − | 0.694543i | \(-0.244393\pi\) | ||||
0.719451 | + | 0.694543i | \(0.244393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.41172 | 0.482344 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.82010 | −1.08077 | −0.540383 | − | 0.841419i | \(-0.681721\pi\) | ||||
−0.540383 | + | 0.841419i | \(0.681721\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.969574 | −0.174141 | −0.0870703 | − | 0.996202i | \(-0.527750\pi\) | ||||
−0.0870703 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.656645 | 0.114307 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.02586 | 1.52565 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.93482 | −1.63327 | −0.816637 | − | 0.577151i | \(-0.804164\pi\) | ||||
−0.816637 | + | 0.577151i | \(0.804164\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5937 | 1.65445 | 0.827227 | − | 0.561869i | \(-0.189917\pi\) | ||||
0.827227 | + | 0.561869i | \(0.189917\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.07523 | −0.773965 | −0.386983 | − | 0.922087i | \(-0.626483\pi\) | ||||
−0.386983 | + | 0.922087i | \(0.626483\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.72245 | 0.405839 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.24364 | −1.20246 | −0.601229 | − | 0.799077i | \(-0.705322\pi\) | ||||
−0.601229 | + | 0.799077i | \(0.705322\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.99153 | 0.570218 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.16749 | −0.163481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.841166 | 0.115543 | 0.0577715 | − | 0.998330i | \(-0.481601\pi\) | ||||
0.0577715 | + | 0.998330i | \(0.481601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.78768 | 0.241051 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.77137 | 0.896889 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.128144 | 0.0166829 | 0.00834145 | − | 0.999965i | \(-0.497345\pi\) | ||||
0.00834145 | + | 0.999965i | \(0.497345\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7223 | 1.50089 | 0.750443 | − | 0.660935i | \(-0.229840\pi\) | ||||
0.750443 | + | 0.660935i | \(0.229840\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.31535 | 0.417694 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.9422 | −1.94765 | −0.973824 | − | 0.227303i | \(-0.927009\pi\) | ||||
−0.973824 | + | 0.227303i | \(0.927009\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.90073 | 0.830750 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.32056 | 0.631434 | 0.315717 | − | 0.948853i | \(-0.397755\pi\) | ||||
0.315717 | + | 0.948853i | \(0.397755\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.75917 | −0.439977 | −0.219989 | − | 0.975502i | \(-0.570602\pi\) | ||||
−0.219989 | + | 0.975502i | \(0.570602\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.41172 | 0.278482 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.17701 | 0.248093 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.17759 | 0.244998 | 0.122499 | − | 0.992469i | \(-0.460909\pi\) | ||||
0.122499 | + | 0.992469i | \(0.460909\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8237 | −1.18806 | −0.594029 | − | 0.804444i | \(-0.702464\pi\) | ||||
−0.594029 | + | 0.804444i | \(0.702464\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.17843 | −0.344749 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.82010 | −0.623980 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.09193 | −0.433743 | −0.216872 | − | 0.976200i | \(-0.569585\pi\) | ||||
−0.216872 | + | 0.976200i | \(0.569585\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.969574 | −0.100540 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.4347 | 1.89136 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.5008 | 1.67540 | 0.837702 | − | 0.546127i | \(-0.183899\pi\) | ||||
0.837702 | + | 0.546127i | \(0.183899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.656645 | 0.0659953 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.4134 | 1.43419 | 0.717096 | − | 0.696975i | \(-0.245471\pi\) | ||||
0.717096 | + | 0.696975i | \(0.245471\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.7309 | −1.55001 | −0.775007 | − | 0.631953i | \(-0.782253\pi\) | ||||
−0.775007 | + | 0.631953i | \(0.782253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.02586 | 0.880834 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.27509 | 0.896656 | 0.448328 | − | 0.893869i | \(-0.352020\pi\) | ||||
0.448328 | + | 0.893869i | \(0.352020\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.82889 | 0.845655 | 0.422827 | − | 0.906210i | \(-0.361038\pi\) | ||||
0.422827 | + | 0.906210i | \(0.361038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.93482 | −0.942971 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.45873 | 0.607586 | 0.303793 | − | 0.952738i | \(-0.401747\pi\) | ||||
0.303793 | + | 0.952738i | \(0.401747\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.7869 | 1.75189 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.87063 | −0.354820 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5688 | −0.960802 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.5937 | 0.955199 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.04645 | −0.630254 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.90436 | −0.435191 | −0.217596 | − | 0.976039i | \(-0.569821\pi\) | ||||
−0.217596 | + | 0.976039i | \(0.569821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.07523 | −0.446849 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.9311 | −1.21717 | −0.608584 | − | 0.793489i | \(-0.708262\pi\) | ||||
−0.608584 | + | 0.793489i | \(0.708262\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.4494 | 1.94661 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.72245 | 0.234311 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.4589 | −1.49161 | −0.745806 | − | 0.666163i | \(-0.767936\pi\) | ||||
−0.745806 | + | 0.666163i | \(0.767936\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.93881 | 0.842999 | 0.421499 | − | 0.906829i | \(-0.361504\pi\) | ||||
0.421499 | + | 0.906829i | \(0.361504\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.24364 | −0.694239 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.8449 | −1.31585 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.99153 | 0.329216 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.7938 | −1.21196 | −0.605979 | − | 0.795481i | \(-0.707218\pi\) | ||||
−0.605979 | + | 0.795481i | \(0.707218\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5920 | −0.943340 | −0.471670 | − | 0.881775i | \(-0.656349\pi\) | ||||
−0.471670 | + | 0.881775i | \(0.656349\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.16749 | −0.0943859 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.63961 | −0.212019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.3811 | −1.30735 | −0.653677 | − | 0.756773i | \(-0.726775\pi\) | ||||
−0.653677 | + | 0.756773i | \(0.726775\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.841166 | 0.0667088 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.8783 | 1.80306 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.2719 | −1.66615 | −0.833073 | − | 0.553163i | \(-0.813421\pi\) | ||||
−0.833073 | + | 0.553163i | \(0.813421\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.78768 | 0.139171 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5498 | −0.816367 | −0.408183 | − | 0.912900i | \(-0.633838\pi\) | ||||
−0.408183 | + | 0.912900i | \(0.633838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.77137 | 0.517819 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.4284 | 1.55314 | 0.776569 | − | 0.630032i | \(-0.216958\pi\) | ||||
0.776569 | + | 0.630032i | \(0.216958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.99570 | 0.604418 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.128144 | 0.00963188 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.71037 | −0.426813 | −0.213406 | − | 0.976964i | \(-0.568456\pi\) | ||||
−0.213406 | + | 0.976964i | \(0.568456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.70324 | 0.349589 | 0.174795 | − | 0.984605i | \(-0.444074\pi\) | ||||
0.174795 | + | 0.984605i | \(0.444074\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7223 | 0.866537 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.0470 | −1.98854 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.766626 | −0.0560613 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.31535 | 0.241156 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.7128 | 1.06458 | 0.532292 | − | 0.846561i | \(-0.321331\pi\) | ||||
0.532292 | + | 0.846561i | \(0.321331\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.50643 | 0.108435 | 0.0542177 | − | 0.998529i | \(-0.482734\pi\) | ||||
0.0542177 | + | 0.998529i | \(0.482734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4470 | −1.24305 | −0.621524 | − | 0.783395i | \(-0.713486\pi\) | ||||
−0.621524 | + | 0.783395i | \(0.713486\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.4032 | 1.23368 | 0.616841 | − | 0.787088i | \(-0.288412\pi\) | ||||
0.616841 | + | 0.787088i | \(0.288412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.9422 | −1.12448 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.2957 | −1.35429 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.8407 | 2.01432 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.90073 | 0.479634 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.44638 | 0.307563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.4002 | −0.853662 | −0.426831 | − | 0.904331i | \(-0.640370\pi\) | ||||
−0.426831 | + | 0.904331i | \(0.640370\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.32056 | 0.364559 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.8170 | −0.942315 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.21447 | −0.218213 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.75917 | −0.254021 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5356 | −0.839448 | −0.419724 | − | 0.907652i | \(-0.637873\pi\) | ||||
−0.419724 | + | 0.907652i | \(0.637873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.41172 | 0.160781 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.16802 | 0.0775243 | 0.0387622 | − | 0.999248i | \(-0.487659\pi\) | ||||
0.0387622 | + | 0.999248i | \(0.487659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.9158 | 1.44824 | 0.724119 | − | 0.689675i | \(-0.242247\pi\) | ||||
0.724119 | + | 0.689675i | \(0.242247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.17701 | 0.143237 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00659 | −0.196968 | −0.0984842 | − | 0.995139i | \(-0.531399\pi\) | ||||
−0.0984842 | + | 0.995139i | \(0.531399\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.4429 | −1.46401 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.17759 | 0.141450 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7853 | 0.827015 | 0.413508 | − | 0.910501i | \(-0.364303\pi\) | ||||
0.413508 | + | 0.910501i | \(0.364303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.6123 | 1.52100 | 0.760499 | − | 0.649339i | \(-0.224954\pi\) | ||||
0.760499 | + | 0.649339i | \(0.224954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.8667 | 0.694249 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.8237 | −0.685926 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.22001 | 0.518843 | 0.259421 | − | 0.965764i | \(-0.416468\pi\) | ||||
0.259421 | + | 0.965764i | \(0.416468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.53133 | 0.284882 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.17843 | −0.199041 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.7850 | 1.73318 | 0.866592 | − | 0.499018i | \(-0.166306\pi\) | ||||
0.866592 | + | 0.499018i | \(0.166306\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.9374 | −2.04663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.82010 | −0.360255 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.5270 | 0.649120 | 0.324560 | − | 0.945865i | \(-0.394784\pi\) | ||||
0.324560 | + | 0.945865i | \(0.394784\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.29003 | 0.140676 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.09193 | −0.250422 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.51426 | −0.153297 | −0.0766486 | − | 0.997058i | \(-0.524422\pi\) | ||||
−0.0766486 | + | 0.997058i | \(0.524422\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.83460 | −0.293681 | −0.146841 | − | 0.989160i | \(-0.546910\pi\) | ||||
−0.146841 | + | 0.989160i | \(0.546910\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.58365 | 0.0954974 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4274 | −0.926941 | −0.463471 | − | 0.886112i | \(-0.653396\pi\) | ||||
−0.463471 | + | 0.886112i | \(0.653396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.969574 | −0.0580469 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.10796 | −0.364370 | −0.182185 | − | 0.983264i | \(-0.558317\pi\) | ||||
−0.182185 | + | 0.983264i | \(0.558317\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3138 | 0.672538 | 0.336269 | − | 0.941766i | \(-0.390835\pi\) | ||||
0.336269 | + | 0.941766i | \(0.390835\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.4347 | 1.09198 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.1217 | 2.07317 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6370 | −0.919822 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.5008 | 0.967295 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.0013 | 1.63585 | 0.817927 | − | 0.575322i | \(-0.195123\pi\) | ||||
0.817927 | + | 0.575322i | \(0.195123\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.348865 | 0.0203117 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.656645 | 0.0381024 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.8261 | −0.969843 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.4134 | 0.828031 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.9134 | 1.82735 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6077 | 1.06199 | 0.530997 | − | 0.847373i | \(-0.321817\pi\) | ||||
0.530997 | + | 0.847373i | \(0.321817\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.7309 | −0.894900 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.9076 | 1.46909 | 0.734543 | − | 0.678563i | \(-0.237397\pi\) | ||||
0.734543 | + | 0.678563i | \(0.237397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.799031 | −0.0451639 | −0.0225819 | − | 0.999745i | \(-0.507189\pi\) | ||||
−0.0225819 | + | 0.999745i | \(0.507189\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.02586 | 0.508550 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.7072 | 1.83702 | 0.918509 | − | 0.395400i | \(-0.129394\pi\) | ||||
0.918509 | + | 0.395400i | \(0.129394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.82174 | −0.213976 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.27509 | 0.517685 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.90550 | −0.439874 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.82889 | 0.488239 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.3305 | −1.50678 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.69662 | 0.313115 | 0.156557 | − | 0.987669i | \(-0.449960\pi\) | ||||
0.156557 | + | 0.987669i | \(0.449960\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.93482 | −0.544425 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −43.4018 | −2.37129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4046 | −0.566773 | −0.283387 | − | 0.959006i | \(-0.591458\pi\) | ||||
−0.283387 | + | 0.959006i | \(0.591458\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.45873 | 0.350790 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.636666 | −0.0344774 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.97413 | −0.538553 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.7869 | 1.01145 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.76863 | 0.524408 | 0.262204 | − | 0.965013i | \(-0.415551\pi\) | ||||
0.262204 | + | 0.965013i | \(0.415551\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.11185 | −0.327160 | −0.163580 | − | 0.986530i | \(-0.552304\pi\) | ||||
−0.163580 | + | 0.986530i | \(0.552304\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1136 | 1.12376 | 0.561882 | − | 0.827217i | \(-0.310077\pi\) | ||||
0.561882 | + | 0.827217i | \(0.310077\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.4849 | 0.768781 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.87063 | −0.204856 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.37346 | 0.125267 | 0.0626333 | − | 0.998037i | \(-0.480050\pi\) | ||||
0.0626333 | + | 0.998037i | \(0.480050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.8514 | 1.41323 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.5688 | −0.554719 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2341 | −0.535679 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.1977 | −1.78511 | −0.892553 | − | 0.450943i | \(-0.851088\pi\) | ||||
−0.892553 | + | 0.450943i | \(0.851088\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.5937 | 0.551484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.78876 | 0.144785 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.01148 | 0.207707 | 0.103853 | − | 0.994593i | \(-0.466883\pi\) | ||||
0.103853 | + | 0.994593i | \(0.466883\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.04645 | −0.363877 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.282802 | −0.0145265 | −0.00726327 | − | 0.999974i | \(-0.502312\pi\) | ||||
−0.00726327 | + | 0.999974i | \(0.502312\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.90436 | −0.251258 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.7130 | −0.598508 | −0.299254 | − | 0.954173i | \(-0.596738\pi\) | ||||
−0.299254 | + | 0.954173i | \(0.596738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.92679 | 0.302057 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.07523 | −0.257988 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.7485 | −0.595672 | −0.297836 | − | 0.954617i | \(-0.596265\pi\) | ||||
−0.297836 | + | 0.954617i | \(0.596265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.05653 | −0.407436 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.9311 | −0.702733 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.92838 | 0.298289 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.55897 | −0.0782427 | −0.0391213 | − | 0.999234i | \(-0.512456\pi\) | ||||
−0.0391213 | + | 0.999234i | \(0.512456\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.4494 | 1.12388 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.75468 | −0.287375 | −0.143687 | − | 0.989623i | \(-0.545896\pi\) | ||||
−0.143687 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.72245 | 0.135280 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.52365 | −0.323365 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.5609 | 1.11557 | 0.557783 | − | 0.829987i | \(-0.311652\pi\) | ||||
0.557783 | + | 0.829987i | \(0.311652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.4589 | −0.861183 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.424841 | 0.0209051 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.4670 | −1.44648 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.93881 | 0.486706 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.5676 | 0.711675 | 0.355837 | − | 0.934548i | \(-0.384196\pi\) | ||||
0.355837 | + | 0.934548i | \(0.384196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.2281 | −1.96060 | −0.980298 | − | 0.197525i | \(-0.936710\pi\) | ||||
−0.980298 | + | 0.197525i | \(0.936710\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.24364 | −0.400819 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.81566 | −0.136580 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.8635 | 1.88074 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.9559 | −0.720402 | −0.360201 | − | 0.932875i | \(-0.617292\pi\) | ||||
−0.360201 | + | 0.932875i | \(0.617292\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.1200 | −1.44748 | −0.723738 | − | 0.690074i | \(-0.757578\pi\) | ||||
−0.723738 | + | 0.690074i | \(0.757578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.8449 | −0.759706 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 46.7274 | 2.23527 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.7914 | 0.515043 | 0.257522 | − | 0.966273i | \(-0.417094\pi\) | ||||
0.257522 | + | 0.966273i | \(0.417094\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.99153 | 0.190073 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.6498 | 1.45622 | 0.728108 | − | 0.685463i | \(-0.240400\pi\) | ||||
0.728108 | + | 0.685463i | \(0.240400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.1401 | −0.528089 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.7938 | −0.699724 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.3953 | 0.584970 | 0.292485 | − | 0.956270i | \(-0.405518\pi\) | ||||
0.292485 | + | 0.956270i | \(0.405518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.95628 | 0.327558 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.5920 | −0.544638 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.5121 | 1.00629 | 0.503147 | − | 0.864201i | \(-0.332175\pi\) | ||||
0.503147 | + | 0.864201i | \(0.332175\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.16749 | −0.0544938 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.2208 | −0.941777 | −0.470889 | − | 0.882193i | \(-0.656067\pi\) | ||||
−0.470889 | + | 0.882193i | \(0.656067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.2424 | −0.522477 | −0.261239 | − | 0.965274i | \(-0.584131\pi\) | ||||
−0.261239 | + | 0.965274i | \(0.584131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.63961 | −0.122409 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.1166 | −1.25481 | −0.627403 | − | 0.778695i | \(-0.715882\pi\) | ||||
−0.627403 | + | 0.778695i | \(0.715882\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −52.8539 | −2.44057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.3811 | −0.754802 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.33262 | −0.153234 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.3307 | 0.749302 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.841166 | 0.0385144 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.8701 | −0.633743 | −0.316872 | − | 0.948468i | \(-0.602632\pi\) | ||||
−0.316872 | + | 0.948468i | \(0.602632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.8783 | 1.04100 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.9226 | 2.03983 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.0497164 | −0.00225287 | −0.00112643 | − | 0.999999i | \(-0.500359\pi\) | ||||
−0.00112643 | + | 0.999999i | \(0.500359\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.2719 | −0.961950 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.9646 | −0.991248 | −0.495624 | − | 0.868537i | \(-0.665061\pi\) | ||||
−0.495624 | + | 0.868537i | \(0.665061\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.79491 | 0.306027 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.78768 | 0.0803503 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.6395 | 0.791240 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.8347 | −1.60418 | −0.802091 | − | 0.597202i | \(-0.796279\pi\) | ||||
−0.802091 | + | 0.597202i | \(0.796279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.5498 | −0.471329 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.104369 | −0.00465358 | −0.00232679 | − | 0.999997i | \(-0.500741\pi\) | ||||
−0.00232679 | + | 0.999997i | \(0.500741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.2399 | 1.74615 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.19452 | 0.0529464 | 0.0264732 | − | 0.999650i | \(-0.491572\pi\) | ||||
0.0264732 | + | 0.999650i | \(0.491572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4629 | −0.551328 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.77137 | 0.298963 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.8266 | −1.88717 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.41314 | −0.238070 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.4284 | 0.896705 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.8446 | 1.00084 | 0.500420 | − | 0.865783i | \(-0.333179\pi\) | ||||
0.500420 | + | 0.865783i | \(0.333179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.3582 | 1.67728 | 0.838642 | − | 0.544682i | \(-0.183350\pi\) | ||||
0.838642 | + | 0.544682i | \(0.183350\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.99570 | 0.348961 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.13197 | 0.0493093 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.6201 | 1.07044 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.128144 | 0.00556097 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.2509 | 1.09169 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.71037 | −0.246420 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.62102 | 0.112895 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.5126 | −0.451970 | −0.225985 | − | 0.974131i | \(-0.572560\pi\) | ||||
−0.225985 | + | 0.974131i | \(0.572560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.70324 | 0.201835 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.0362 | 1.02960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.9358 | 1.02342 | 0.511711 | − | 0.859158i | \(-0.329012\pi\) | ||||
0.511711 | + | 0.859158i | \(0.329012\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.7223 | 0.500296 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.4100 | −1.67892 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.21948 | 0.307003 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.0470 | −1.14808 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.843060 | 0.0357216 | 0.0178608 | − | 0.999840i | \(-0.494314\pi\) | ||||
0.0178608 | + | 0.999840i | \(0.494314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.766626 | −0.0323670 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4169 | −0.776179 | −0.388090 | − | 0.921622i | \(-0.626865\pi\) | ||||
−0.388090 | + | 0.921622i | \(0.626865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.5836 | 0.739746 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.31535 | 0.139231 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.6396 | −1.15871 | −0.579356 | − | 0.815075i | \(-0.696696\pi\) | ||||
−0.579356 | + | 0.815075i | \(0.696696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.23866 | 0.344777 | 0.172389 | − | 0.985029i | \(-0.444852\pi\) | ||||
0.172389 | + | 0.985029i | \(0.444852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.7128 | 0.614638 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.6426 | 0.694046 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.60340 | −0.108381 | −0.0541906 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541906 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.50643 | 0.0626052 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −35.8844 | −1.48874 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.552348 | 0.0228759 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.62011 | −0.355790 | −0.177895 | − | 0.984049i | \(-0.556929\pi\) | ||||
−0.177895 | + | 0.984049i | \(0.556929\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.56534 | −0.270520 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.4470 | −0.717674 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.3090 | 1.61423 | 0.807114 | − | 0.590395i | \(-0.201028\pi\) | ||||
0.807114 | + | 0.590395i | \(0.201028\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.5376 | −0.431999 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.4032 | 0.712266 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.7451 | 1.58308 | 0.791542 | − | 0.611115i | \(-0.209279\pi\) | ||||
0.791542 | + | 0.611115i | \(0.209279\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.5673 | −1.28766 | −0.643828 | − | 0.765170i | \(-0.722655\pi\) | ||||
−0.643828 | + | 0.765170i | \(0.722655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.9422 | −0.649216 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.7731 | −1.16979 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.5512 | −1.60533 | −0.802667 | − | 0.596427i | \(-0.796586\pi\) | ||||
−0.802667 | + | 0.596427i | \(0.796586\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.2957 | −0.781899 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.8092 | −1.72905 | −0.864524 | − | 0.502592i | \(-0.832380\pi\) | ||||
−0.864524 | + | 0.502592i | \(0.832380\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.8407 | 1.16297 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.9368 | 0.802626 | 0.401313 | − | 0.915941i | \(-0.368554\pi\) | ||||
0.401313 | + | 0.915941i | \(0.368554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.1555 | 1.53360 | 0.766799 | − | 0.641887i | \(-0.221848\pi\) | ||||
0.766799 | + | 0.641887i | \(0.221848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.90073 | 0.276917 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.5662 | −0.543516 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2422 | −1.24969 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.44638 | 0.177571 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.5988 | 0.462474 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.6027 | −1.21827 | −0.609137 | − | 0.793065i | \(-0.708484\pi\) | ||||
−0.609137 | + | 0.793065i | \(0.708484\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.4002 | −0.492862 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.3519 | −0.529852 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.32056 | 0.210478 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.7211 | 1.01592 | 0.507962 | − | 0.861379i | \(-0.330399\pi\) | ||||
0.507962 | + | 0.861379i | \(0.330399\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.1373 | −1.18850 | −0.594249 | − | 0.804281i | \(-0.702551\pi\) | ||||
−0.594249 | + | 0.804281i | \(0.702551\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.8170 | −0.544046 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.75127 | 0.265420 | 0.132710 | − | 0.991155i | \(-0.457632\pi\) | ||||
0.132710 | + | 0.991155i | \(0.457632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0841450 | 0.00330298 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.21447 | −0.125985 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.20999 | −0.0473507 | −0.0236754 | − | 0.999720i | \(-0.507537\pi\) | ||||
−0.0236754 | + | 0.999720i | \(0.507537\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.9268 | −1.48192 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.75917 | −0.146659 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.6149 | −0.530361 | −0.265181 | − | 0.964199i | \(-0.585432\pi\) | ||||
−0.265181 | + | 0.964199i | \(0.585432\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7711 | −0.418949 | −0.209474 | − | 0.977814i | \(-0.567175\pi\) | ||||
−0.209474 | + | 0.977814i | \(0.567175\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 61.1174 | 2.37003 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.1629 | −1.55512 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.5356 | −0.484655 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.69739 | 0.297155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.0338 | −1.77447 | −0.887236 | − | 0.461316i | \(-0.847377\pi\) | ||||
−0.887236 | + | 0.461316i | \(0.847377\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.41172 | 0.0928272 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.84261 | 0.0708172 | 0.0354086 | − | 0.999373i | \(-0.488727\pi\) | ||||
0.0354086 | + | 0.999373i | \(0.488727\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 54.7059 | 2.09942 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.16802 | 0.0447587 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.7758 | −0.909757 | −0.454878 | − | 0.890554i | \(-0.650317\pi\) | ||||
−0.454878 | + | 0.890554i | \(0.650317\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −47.5309 | −1.81606 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.9158 | 0.836140 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.67973 | 0.0639001 | 0.0319501 | − | 0.999489i | \(-0.489828\pi\) | ||||
0.0319501 | + | 0.999489i | \(0.489828\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.17701 | 0.0826976 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.0579 | 1.02636 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.3680 | −0.468471 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.00659 | −0.113720 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.8738 | 0.675086 | 0.337543 | − | 0.941310i | \(-0.390404\pi\) | ||||
0.337543 | + | 0.941310i | \(0.390404\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −67.2723 | −2.53722 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.4429 | −0.845247 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.7856 | 1.79716 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.27227 | 0.160448 | 0.0802242 | − | 0.996777i | \(-0.474436\pi\) | ||||
0.0802242 | + | 0.996777i | \(0.474436\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.17759 | 0.0816661 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.69077 | −0.250571 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.7853 | 0.477478 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.5341 | −1.02685 | −0.513424 | − | 0.858135i | \(-0.671623\pi\) | ||||
−0.513424 | + | 0.858135i | \(0.671623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.1534 | −1.94230 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.6123 | 0.878149 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.0365 | −0.521301 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.2674 | −1.04838 | −0.524189 | − | 0.851602i | \(-0.675631\pi\) | ||||
−0.524189 | + | 0.851602i | \(0.675631\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.92528 | 0.219154 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.2904 | 0.934123 | 0.467062 | − | 0.884225i | \(-0.345313\pi\) | ||||
0.467062 | + | 0.884225i | \(0.345313\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.8667 | 0.400825 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.4684 | −0.385607 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.06509 | 0.296679 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.2716 | −0.523575 | −0.261787 | − | 0.965126i | \(-0.584312\pi\) | ||||
−0.261787 | + | 0.965126i | \(0.584312\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.2754 | −1.47558 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.8237 | −0.396019 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.7501 | 1.12359 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.0043 | 1.20434 | 0.602171 | − | 0.798367i | \(-0.294302\pi\) | ||||
0.602171 | + | 0.798367i | \(0.294302\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.22001 | 0.299554 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.5585 | −1.14853 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.2365 | 1.28069 | 0.640347 | − | 0.768086i | \(-0.278791\pi\) | ||||
0.640347 | + | 0.768086i | \(0.278791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.53133 | 0.164477 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.7212 | 1.11364 | 0.556822 | − | 0.830632i | \(-0.312021\pi\) | ||||
0.556822 | + | 0.830632i | \(0.312021\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.2709 | 1.05968 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.17843 | −0.114916 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.95972 | −0.250974 | −0.125487 | − | 0.992095i | \(-0.540049\pi\) | ||||
−0.125487 | + | 0.992095i | \(0.540049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.7850 | 1.00065 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.5717 | −1.45926 | −0.729632 | − | 0.683840i | \(-0.760308\pi\) | ||||
−0.729632 | + | 0.683840i | \(0.760308\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.33834 | −0.0839957 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.9374 | −1.18162 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 71.7336 | 2.57012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.49372 | 0.125015 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.82010 | −0.207993 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.5967 | −1.59172 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.88731 | −0.174214 | −0.0871068 | − | 0.996199i | \(-0.527762\pi\) | ||||
−0.0871068 | + | 0.996199i | \(0.527762\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.5270 | 0.374769 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.4129 | 0.761356 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.29003 | 0.0812191 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.5982 | −0.871314 | −0.435657 | − | 0.900113i | \(-0.643484\pi\) | ||||
−0.435657 | + | 0.900113i | \(0.643484\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.62436 | 0.340485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.09193 | −0.144581 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.46844 | −0.0871093 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 62.2850 | 2.19526 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.51426 | −0.0885061 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.6525 | 0.479996 | 0.239998 | − | 0.970773i | \(-0.422853\pi\) | ||||
0.239998 | + | 0.970773i | \(0.422853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.2951 | −1.55541 | −0.777706 | − | 0.628628i | \(-0.783617\pi\) | ||||
−0.777706 | + | 0.628628i | \(0.783617\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.83460 | −0.169557 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −57.9117 | −2.02856 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.3662 | −1.20232 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.2133 | 1.12425 | 0.562127 | − | 0.827051i | \(-0.309983\pi\) | ||||
0.562127 | + | 0.827051i | \(0.309983\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.6321 | −0.998052 | −0.499026 | − | 0.866587i | \(-0.666309\pi\) | ||||
−0.499026 | + | 0.866587i | \(0.666309\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.58365 | 0.0551355 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.8863 | −1.42176 | −0.710879 | − | 0.703315i | \(-0.751702\pi\) | ||||
−0.710879 | + | 0.703315i | \(0.751702\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.7016 | 0.371681 | 0.185841 | − | 0.982580i | \(-0.440499\pi\) | ||||
0.185841 | + | 0.982580i | \(0.440499\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.4274 | −0.535170 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.66007 | −0.161462 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.7212 | −0.993939 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.969574 | −0.0335134 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.1362 | −0.557085 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.87357 | 0.168054 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.10796 | −0.210369 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.0393 | −1.20396 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.3138 | 0.388290 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −68.5575 | −2.35012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.7776 | −0.540215 | −0.270108 | − | 0.962830i | \(-0.587059\pi\) | ||||
−0.270108 | + | 0.962830i | \(0.587059\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.4347 | 0.630453 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.5463 | 0.736006 | 0.368003 | − | 0.929825i | \(-0.380042\pi\) | ||||
0.368003 | + | 0.929825i | \(0.380042\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.07749 | −0.139122 | −0.0695611 | − | 0.997578i | \(-0.522160\pi\) | ||||
−0.0695611 | + | 0.997578i | \(0.522160\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.1217 | 1.19694 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.5883 | 0.598712 | 0.299356 | − | 0.954141i | \(-0.403228\pi\) | ||||
0.299356 | + | 0.954141i | \(0.403228\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.6151 | 1.89097 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.6370 | −0.531059 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.42991 | 0.0485062 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.5008 | 0.558468 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.3614 | −0.789761 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.07451 | −0.171354 | −0.0856770 | − | 0.996323i | \(-0.527305\pi\) | ||||
−0.0856770 | + | 0.996323i | \(0.527305\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.0013 | 0.944461 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.8471 | 1.67939 | 0.839696 | − | 0.543057i | \(-0.182733\pi\) | ||||
0.839696 | + | 0.543057i | \(0.182733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.7712 | 1.57398 | 0.786989 | − | 0.616967i | \(-0.211639\pi\) | ||||
0.786989 | + | 0.616967i | \(0.211639\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.348865 | 0.0117270 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.5889 | −0.657730 | −0.328865 | − | 0.944377i | \(-0.606666\pi\) | ||||
−0.328865 | + | 0.944377i | \(0.606666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.2596 | −0.545331 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.656645 | 0.0219984 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −55.8207 | −1.86797 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.5462 | −0.519651 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.64302 | 0.188205 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.982053 | −0.0327169 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.8261 | −0.559939 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.8043 | 0.425630 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.5223 | −0.581818 | −0.290909 | − | 0.956751i | \(-0.593958\pi\) | ||||
−0.290909 | + | 0.956751i | \(0.593958\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.4134 | 0.478064 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.6916 | −0.387360 | −0.193680 | − | 0.981065i | \(-0.562042\pi\) | ||||
−0.193680 | + | 0.981065i | \(0.562042\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.10735 | −0.235219 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.9134 | 1.05502 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −46.1865 | −1.52521 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.7980 | −1.41177 | −0.705887 | − | 0.708324i | \(-0.749452\pi\) | ||||
−0.705887 | + | 0.708324i | \(0.749452\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.6077 | 0.613143 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.9600 | −0.787801 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.7309 | −0.516671 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.8135 | −0.912532 | −0.456266 | − | 0.889843i | \(-0.650813\pi\) | ||||
−0.456266 | + | 0.889843i | \(0.650813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.0281 | 0.885810 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.9076 | 0.848177 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.08710 | −0.0682555 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.2544 | 1.57640 | 0.788201 | − | 0.615417i | \(-0.211013\pi\) | ||||
0.788201 | + | 0.615417i | \(0.211013\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.799031 | −0.0260754 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.8449 | 0.451332 | 0.225666 | − | 0.974205i | \(-0.427544\pi\) | ||||
0.225666 | + | 0.974205i | \(0.427544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 73.1041 | 2.38060 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.02586 | 0.293611 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.6924 | 0.607422 | 0.303711 | − | 0.952764i | \(-0.401774\pi\) | ||||
0.303711 | + | 0.952764i | \(0.401774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.7072 | 1.06060 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.2242 | 1.43256 | 0.716281 | − | 0.697812i | \(-0.245843\pi\) | ||||
0.716281 | + | 0.697812i | \(0.245843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.0550 | 1.29615 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.82174 | −0.123539 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −57.8822 | −1.86911 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0599 | −0.969675 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.27509 | 0.298885 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.10118 | 0.132022 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.5221 | −1.17447 | −0.587235 | − | 0.809416i | \(-0.699784\pi\) | ||||
−0.587235 | + | 0.809416i | \(0.699784\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.90550 | −0.253961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.0922 | 1.09407 | 0.547035 | − | 0.837110i | \(-0.315756\pi\) | ||||
0.547035 | + | 0.837110i | \(0.315756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.9506 | 1.05635 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 59.7205 | 1.91063 | 0.955315 | − | 0.295591i | \(-0.0955166\pi\) | ||||
0.955315 | + | 0.295591i | \(0.0955166\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.68694 | −0.0858751 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.82889 | 0.281885 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.8000 | 1.58837 | 0.794186 | − | 0.607674i | \(-0.207897\pi\) | ||||
0.794186 | + | 0.607674i | \(0.207897\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.4986 | −1.51343 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.3305 | −0.869940 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.0228 | −1.11366 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.1731 | −0.545522 | −0.272761 | − | 0.962082i | \(-0.587937\pi\) | ||||
−0.272761 | + | 0.962082i | \(0.587937\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.69662 | 0.180777 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 47.3794 | 1.50203 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.9494 | −1.10686 | −0.553430 | − | 0.832896i | \(-0.686681\pi\) | ||||
−0.553430 | + | 0.832896i | \(0.686681\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.93482 | −0.314324 |
(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 | 4056.2.a.bi.1.5 | yes | 6 | |
4.3 | odd | 2 | 8112.2.a.cu.1.5 | 6 | |||
13.5 | odd | 4 | 4056.2.c.r.337.3 | 12 | |||
13.8 | odd | 4 | 4056.2.c.r.337.10 | 12 | |||
13.12 | even | 2 | 4056.2.a.bh.1.2 | ✓ | 6 | ||
52.51 | odd | 2 | 8112.2.a.ct.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4056.2.a.bh.1.2 | ✓ | 6 | 13.12 | even | 2 | ||
4056.2.a.bi.1.5 | yes | 6 | 1.1 | even | 1 | trivial | |
4056.2.c.r.337.3 | 12 | 13.5 | odd | 4 | |||
4056.2.c.r.337.10 | 12 | 13.8 | odd | 4 | |||
8112.2.a.ct.1.2 | 6 | 52.51 | odd | 2 | |||
8112.2.a.cu.1.5 | 6 | 4.3 | odd | 2 |