Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.23607 | 1.58114 | 0.790569 | − | 0.612372i | \(-0.209785\pi\) | ||||
0.790569 | + | 0.612372i | \(0.209785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.00000 | 1.50000 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.47214 | 1.41421 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.23607 | −0.897524 | −0.448762 | − | 0.893651i | \(-0.648135\pi\) | ||||
−0.448762 | + | 0.893651i | \(0.648135\pi\) | |||||||
\(14\) | −2.23607 | −0.597614 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.23607 | −0.784862 | −0.392431 | − | 0.919781i | \(-0.628366\pi\) | ||||
−0.392431 | + | 0.919781i | \(0.628366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.47214 | −1.48481 | −0.742405 | − | 0.669951i | \(-0.766315\pi\) | ||||
−0.742405 | + | 0.669951i | \(0.766315\pi\) | |||||||
\(20\) | 6.00000 | 1.34164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.47214 | −0.515476 | −0.257738 | − | 0.966215i | \(-0.582977\pi\) | ||||
−0.257738 | + | 0.966215i | \(0.582977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −7.23607 | −1.41911 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.00000 | −0.566947 | ||||||||
\(29\) | 8.47214 | 1.57324 | 0.786618 | − | 0.617440i | \(-0.211830\pi\) | ||||
0.786618 | + | 0.617440i | \(0.211830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76393 | −0.496417 | −0.248208 | − | 0.968707i | \(-0.579842\pi\) | ||||
−0.248208 | + | 0.968707i | \(0.579842\pi\) | |||||||
\(32\) | −6.70820 | −1.18585 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.23607 | −1.24098 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.47214 | −1.39281 | −0.696405 | − | 0.717649i | \(-0.745218\pi\) | ||||
−0.696405 | + | 0.717649i | \(0.745218\pi\) | |||||||
\(38\) | −14.4721 | −2.34769 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.47214 | 0.707107 | ||||||||
\(41\) | −11.2361 | −1.75478 | −0.877390 | − | 0.479779i | \(-0.840717\pi\) | ||||
−0.877390 | + | 0.479779i | \(0.840717\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.52786 | −0.815039 | ||||||||
\(47\) | −2.76393 | −0.403161 | −0.201580 | − | 0.979472i | \(-0.564608\pi\) | ||||
−0.201580 | + | 0.979472i | \(0.564608\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.23607 | −0.316228 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.70820 | −1.34629 | ||||||||
\(53\) | 0.472136 | 0.0648529 | 0.0324264 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324264 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18.9443 | 2.48750 | ||||||||
\(59\) | 1.23607 | 0.160922 | 0.0804612 | − | 0.996758i | \(-0.474361\pi\) | ||||
0.0804612 | + | 0.996758i | \(0.474361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23607 | 0.926484 | 0.463242 | − | 0.886232i | \(-0.346686\pi\) | ||||
0.463242 | + | 0.886232i | \(0.346686\pi\) | |||||||
\(62\) | −6.18034 | −0.784904 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0000 | −1.62500 | ||||||||
\(65\) | −6.47214 | −0.802770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4721 | 1.76805 | 0.884026 | − | 0.467437i | \(-0.154823\pi\) | ||||
0.884026 | + | 0.467437i | \(0.154823\pi\) | |||||||
\(68\) | −9.70820 | −1.17729 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.47214 | −0.534522 | ||||||||
\(71\) | 10.4721 | 1.24281 | 0.621407 | − | 0.783488i | \(-0.286561\pi\) | ||||
0.621407 | + | 0.783488i | \(0.286561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.763932 | 0.0894115 | 0.0447057 | − | 0.999000i | \(-0.485765\pi\) | ||||
0.0447057 | + | 0.999000i | \(0.485765\pi\) | |||||||
\(74\) | −18.9443 | −2.20223 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −19.4164 | −2.22721 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.94427 | 1.00631 | 0.503155 | − | 0.864196i | \(-0.332173\pi\) | ||||
0.503155 | + | 0.864196i | \(0.332173\pi\) | |||||||
\(80\) | −2.00000 | −0.223607 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −25.1246 | −2.77455 | ||||||||
\(83\) | −11.4164 | −1.25311 | −0.626557 | − | 0.779376i | \(-0.715536\pi\) | ||||
−0.626557 | + | 0.779376i | \(0.715536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.47214 | −0.702002 | ||||||||
\(86\) | −17.8885 | −1.92897 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.23607 | 0.339232 | ||||||||
\(92\) | −7.41641 | −0.773214 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.18034 | −0.637453 | ||||||||
\(95\) | −12.9443 | −1.32805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.4164 | 1.76837 | 0.884184 | − | 0.467139i | \(-0.154715\pi\) | ||||
0.884184 | + | 0.467139i | \(0.154715\pi\) | |||||||
\(98\) | 2.23607 | 0.225877 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | −4.76393 | −0.474029 | −0.237014 | − | 0.971506i | \(-0.576169\pi\) | ||||
−0.237014 | + | 0.971506i | \(0.576169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.70820 | 0.759512 | 0.379756 | − | 0.925087i | \(-0.376008\pi\) | ||||
0.379756 | + | 0.925087i | \(0.376008\pi\) | |||||||
\(104\) | −7.23607 | −0.709555 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.05573 | 0.102541 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.47214 | 0.428353 | 0.214176 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214176 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.94427 | −0.461056 | ||||||||
\(116\) | 25.4164 | 2.35985 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.76393 | 0.254441 | ||||||||
\(119\) | 3.23607 | 0.296650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 16.1803 | 1.46490 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.29180 | −0.744625 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.05573 | −0.271152 | −0.135576 | − | 0.990767i | \(-0.543288\pi\) | ||||
−0.135576 | + | 0.990767i | \(0.543288\pi\) | |||||||
\(128\) | −15.6525 | −1.38350 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.4721 | −1.26929 | ||||||||
\(131\) | 21.8885 | 1.91241 | 0.956205 | − | 0.292696i | \(-0.0945525\pi\) | ||||
0.956205 | + | 0.292696i | \(0.0945525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.47214 | 0.561205 | ||||||||
\(134\) | 32.3607 | 2.79554 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.23607 | −0.620488 | ||||||||
\(137\) | −16.4721 | −1.40731 | −0.703655 | − | 0.710542i | \(-0.748450\pi\) | ||||
−0.703655 | + | 0.710542i | \(0.748450\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.52786 | 0.129592 | 0.0647959 | − | 0.997899i | \(-0.479360\pi\) | ||||
0.0647959 | + | 0.997899i | \(0.479360\pi\) | |||||||
\(140\) | −6.00000 | −0.507093 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 23.4164 | 1.96506 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.9443 | 1.40715 | ||||||||
\(146\) | 1.70820 | 0.141372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −25.4164 | −2.08922 | ||||||||
\(149\) | 14.0000 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | −14.4721 | −1.17385 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.52786 | −0.444009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9443 | 0.873448 | 0.436724 | − | 0.899596i | \(-0.356139\pi\) | ||||
0.436724 | + | 0.899596i | \(0.356139\pi\) | |||||||
\(158\) | 20.0000 | 1.59111 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.4164 | −1.06066 | ||||||||
\(161\) | 2.47214 | 0.194832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.41641 | −0.267594 | −0.133797 | − | 0.991009i | \(-0.542717\pi\) | ||||
−0.133797 | + | 0.991009i | \(0.542717\pi\) | |||||||
\(164\) | −33.7082 | −2.63217 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.5279 | −1.98135 | ||||||||
\(167\) | 4.94427 | 0.382599 | 0.191300 | − | 0.981532i | \(-0.438730\pi\) | ||||
0.191300 | + | 0.981532i | \(0.438730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.52786 | −0.194451 | ||||||||
\(170\) | −14.4721 | −1.10996 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −24.0000 | −1.82998 | ||||||||
\(173\) | −12.7639 | −0.970424 | −0.485212 | − | 0.874397i | \(-0.661258\pi\) | ||||
−0.485212 | + | 0.874397i | \(0.661258\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.47214 | −0.335201 | ||||||||
\(179\) | 8.94427 | 0.668526 | 0.334263 | − | 0.942480i | \(-0.391513\pi\) | ||||
0.334263 | + | 0.942480i | \(0.391513\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.4164 | −1.88919 | −0.944593 | − | 0.328243i | \(-0.893544\pi\) | ||||
−0.944593 | + | 0.328243i | \(0.893544\pi\) | |||||||
\(182\) | 7.23607 | 0.536373 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.52786 | −0.407520 | ||||||||
\(185\) | −16.9443 | −1.24577 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.29180 | −0.604741 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −28.9443 | −2.09984 | ||||||||
\(191\) | 3.05573 | 0.221105 | 0.110552 | − | 0.993870i | \(-0.464738\pi\) | ||||
0.110552 | + | 0.993870i | \(0.464738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8885 | −0.855756 | −0.427878 | − | 0.903836i | \(-0.640739\pi\) | ||||
−0.427878 | + | 0.903836i | \(0.640739\pi\) | |||||||
\(194\) | 38.9443 | 2.79604 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.18034 | −0.154560 | −0.0772801 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772801 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(200\) | −2.23607 | −0.158114 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.6525 | −0.749506 | ||||||||
\(203\) | −8.47214 | −0.594627 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.4721 | −1.56952 | ||||||||
\(206\) | 17.2361 | 1.20089 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.23607 | 0.224381 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8885 | 0.956127 | 0.478063 | − | 0.878325i | \(-0.341339\pi\) | ||||
0.478063 | + | 0.878325i | \(0.341339\pi\) | |||||||
\(212\) | 1.41641 | 0.0972793 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.94427 | −0.611418 | ||||||||
\(215\) | −16.0000 | −1.09119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.76393 | 0.187628 | ||||||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4721 | 0.704432 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1803 | −0.681726 | −0.340863 | − | 0.940113i | \(-0.610719\pi\) | ||||
−0.340863 | + | 0.940113i | \(0.610719\pi\) | |||||||
\(224\) | 6.70820 | 0.448211 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.47214 | −0.297482 | ||||||||
\(227\) | 5.88854 | 0.390836 | 0.195418 | − | 0.980720i | \(-0.437394\pi\) | ||||
0.195418 | + | 0.980720i | \(0.437394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.47214 | −0.295527 | −0.147764 | − | 0.989023i | \(-0.547207\pi\) | ||||
−0.147764 | + | 0.989023i | \(0.547207\pi\) | |||||||
\(230\) | −11.0557 | −0.728993 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.9443 | 1.24375 | ||||||||
\(233\) | 9.41641 | 0.616889 | 0.308445 | − | 0.951242i | \(-0.400192\pi\) | ||||
0.308445 | + | 0.951242i | \(0.400192\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.52786 | −0.360598 | ||||||||
\(236\) | 3.70820 | 0.241384 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.23607 | 0.469045 | ||||||||
\(239\) | −9.88854 | −0.639637 | −0.319818 | − | 0.947479i | \(-0.603622\pi\) | ||||
−0.319818 | + | 0.947479i | \(0.603622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1246 | 0.845431 | 0.422715 | − | 0.906263i | \(-0.361077\pi\) | ||||
0.422715 | + | 0.906263i | \(0.361077\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 21.7082 | 1.38973 | ||||||||
\(245\) | 2.00000 | 0.127775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.9443 | 1.33265 | ||||||||
\(248\) | −6.18034 | −0.392452 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −26.8328 | −1.69706 | ||||||||
\(251\) | −4.29180 | −0.270896 | −0.135448 | − | 0.990784i | \(-0.543247\pi\) | ||||
−0.135448 | + | 0.990784i | \(0.543247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.83282 | −0.428729 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.47214 | 0.526433 | ||||||||
\(260\) | −19.4164 | −1.20415 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 48.9443 | 3.02379 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.944272 | 0.0580062 | ||||||||
\(266\) | 14.4721 | 0.887344 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 43.4164 | 2.65208 | ||||||||
\(269\) | −13.4164 | −0.818013 | −0.409006 | − | 0.912532i | \(-0.634125\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4721 | 0.636137 | 0.318068 | − | 0.948068i | \(-0.396966\pi\) | ||||
0.318068 | + | 0.948068i | \(0.396966\pi\) | |||||||
\(272\) | 3.23607 | 0.196215 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −36.8328 | −2.22515 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8885 | 1.19499 | 0.597493 | − | 0.801874i | \(-0.296163\pi\) | ||||
0.597493 | + | 0.801874i | \(0.296163\pi\) | |||||||
\(278\) | 3.41641 | 0.204903 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.47214 | −0.267261 | ||||||||
\(281\) | −3.52786 | −0.210455 | −0.105227 | − | 0.994448i | \(-0.533557\pi\) | ||||
−0.105227 | + | 0.994448i | \(0.533557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.8885 | −1.77669 | −0.888345 | − | 0.459177i | \(-0.848144\pi\) | ||||
−0.888345 | + | 0.459177i | \(0.848144\pi\) | |||||||
\(284\) | 31.4164 | 1.86422 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.2361 | 0.663244 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.52786 | −0.383992 | ||||||||
\(290\) | 37.8885 | 2.22489 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.29180 | 0.134117 | ||||||||
\(293\) | −25.1246 | −1.46780 | −0.733898 | − | 0.679260i | \(-0.762301\pi\) | ||||
−0.733898 | + | 0.679260i | \(0.762301\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.47214 | 0.143933 | ||||||||
\(296\) | −18.9443 | −1.10111 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 31.3050 | 1.81345 | ||||||||
\(299\) | 8.00000 | 0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | −20.0000 | −1.15087 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.47214 | 0.371202 | ||||||||
\(305\) | 14.4721 | 0.828672 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.94427 | 0.510477 | 0.255238 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255238 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.3607 | −0.702039 | ||||||||
\(311\) | 8.29180 | 0.470185 | 0.235092 | − | 0.971973i | \(-0.424461\pi\) | ||||
0.235092 | + | 0.971973i | \(0.424461\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9443 | 0.844700 | 0.422350 | − | 0.906433i | \(-0.361205\pi\) | ||||
0.422350 | + | 0.906433i | \(0.361205\pi\) | |||||||
\(314\) | 24.4721 | 1.38104 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.8328 | 1.50946 | ||||||||
\(317\) | −14.0000 | −0.786318 | −0.393159 | − | 0.919470i | \(-0.628618\pi\) | ||||
−0.393159 | + | 0.919470i | \(0.628618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −26.0000 | −1.45344 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.52786 | 0.308056 | ||||||||
\(323\) | 20.9443 | 1.16537 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.23607 | 0.179505 | ||||||||
\(326\) | −7.63932 | −0.423103 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −25.1246 | −1.38727 | ||||||||
\(329\) | 2.76393 | 0.152381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.8885 | −0.763383 | −0.381692 | − | 0.924290i | \(-0.624658\pi\) | ||||
−0.381692 | + | 0.924290i | \(0.624658\pi\) | |||||||
\(332\) | −34.2492 | −1.87967 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.0557 | 0.604943 | ||||||||
\(335\) | 28.9443 | 1.58139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.5279 | 0.627963 | 0.313981 | − | 0.949429i | \(-0.398337\pi\) | ||||
0.313981 | + | 0.949429i | \(0.398337\pi\) | |||||||
\(338\) | −5.65248 | −0.307454 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19.4164 | −1.05300 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −17.8885 | −0.964486 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.5410 | −1.53437 | ||||||||
\(347\) | 20.9443 | 1.12435 | 0.562174 | − | 0.827019i | \(-0.309965\pi\) | ||||
0.562174 | + | 0.827019i | \(0.309965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.23607 | 0.387338 | 0.193669 | − | 0.981067i | \(-0.437961\pi\) | ||||
0.193669 | + | 0.981067i | \(0.437961\pi\) | |||||||
\(350\) | 2.23607 | 0.119523 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.8885 | −1.05856 | −0.529280 | − | 0.848447i | \(-0.677538\pi\) | ||||
−0.529280 | + | 0.848447i | \(0.677538\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.9443 | 1.11161 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.0000 | 1.05703 | ||||||||
\(359\) | −24.9443 | −1.31651 | −0.658254 | − | 0.752796i | \(-0.728705\pi\) | ||||
−0.658254 | + | 0.752796i | \(0.728705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.8885 | 1.20466 | ||||||||
\(362\) | −56.8328 | −2.98707 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.70820 | 0.508848 | ||||||||
\(365\) | 1.52786 | 0.0799721 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1246 | −1.20709 | −0.603547 | − | 0.797327i | \(-0.706247\pi\) | ||||
−0.603547 | + | 0.797327i | \(0.706247\pi\) | |||||||
\(368\) | 2.47214 | 0.128869 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −37.8885 | −1.96973 | ||||||||
\(371\) | −0.472136 | −0.0245121 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.18034 | −0.318727 | ||||||||
\(377\) | −27.4164 | −1.41202 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.3050 | 1.91623 | 0.958113 | − | 0.286389i | \(-0.0924551\pi\) | ||||
0.958113 | + | 0.286389i | \(0.0924551\pi\) | |||||||
\(380\) | −38.8328 | −1.99208 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.83282 | 0.349597 | ||||||||
\(383\) | 4.65248 | 0.237730 | 0.118865 | − | 0.992910i | \(-0.462074\pi\) | ||||
0.118865 | + | 0.992910i | \(0.462074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.5836 | −1.35307 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 52.2492 | 2.65255 | ||||||||
\(389\) | −15.8885 | −0.805581 | −0.402791 | − | 0.915292i | \(-0.631960\pi\) | ||||
−0.402791 | + | 0.915292i | \(0.631960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 2.23607 | 0.112938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.47214 | −0.225303 | ||||||||
\(395\) | 17.8885 | 0.900070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.8885 | −1.80119 | −0.900597 | − | 0.434655i | \(-0.856870\pi\) | ||||
−0.900597 | + | 0.434655i | \(0.856870\pi\) | |||||||
\(398\) | −4.87539 | −0.244381 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −22.9443 | −1.14578 | −0.572891 | − | 0.819631i | \(-0.694178\pi\) | ||||
−0.572891 | + | 0.819631i | \(0.694178\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.94427 | 0.445546 | ||||||||
\(404\) | −14.2918 | −0.711043 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.9443 | −0.940188 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.12461 | −0.451183 | −0.225592 | − | 0.974222i | \(-0.572431\pi\) | ||||
−0.225592 | + | 0.974222i | \(0.572431\pi\) | |||||||
\(410\) | −50.2492 | −2.48163 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 23.1246 | 1.13927 | ||||||||
\(413\) | −1.23607 | −0.0608229 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.8328 | −1.12082 | ||||||||
\(416\) | 21.7082 | 1.06433 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.6525 | −1.20435 | −0.602176 | − | 0.798363i | \(-0.705700\pi\) | ||||
−0.602176 | + | 0.798363i | \(0.705700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3607 | 1.08979 | 0.544896 | − | 0.838503i | \(-0.316569\pi\) | ||||
0.544896 | + | 0.838503i | \(0.316569\pi\) | |||||||
\(422\) | 31.0557 | 1.51177 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.05573 | 0.0512707 | ||||||||
\(425\) | 3.23607 | 0.156972 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.23607 | −0.350178 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −35.7771 | −1.72532 | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.47214 | −0.407145 | −0.203572 | − | 0.979060i | \(-0.565255\pi\) | ||||
−0.203572 | + | 0.979060i | \(0.565255\pi\) | |||||||
\(434\) | 6.18034 | 0.296666 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.4164 | 0.642529 | ||||||||
\(437\) | 16.0000 | 0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4721 | −0.499808 | −0.249904 | − | 0.968271i | \(-0.580399\pi\) | ||||
−0.249904 | + | 0.968271i | \(0.580399\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.4164 | 1.11380 | ||||||||
\(443\) | 24.9443 | 1.18514 | 0.592569 | − | 0.805520i | \(-0.298114\pi\) | ||||
0.592569 | + | 0.805520i | \(0.298114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.00000 | −0.189618 | ||||||||
\(446\) | −22.7639 | −1.07790 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.0000 | 0.614192 | ||||||||
\(449\) | 28.4721 | 1.34368 | 0.671842 | − | 0.740695i | \(-0.265504\pi\) | ||||
0.671842 | + | 0.740695i | \(0.265504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.1672 | 0.617967 | ||||||||
\(455\) | 6.47214 | 0.303418 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.8328 | 1.34874 | 0.674371 | − | 0.738393i | \(-0.264415\pi\) | ||||
0.674371 | + | 0.738393i | \(0.264415\pi\) | |||||||
\(458\) | −10.0000 | −0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.8328 | −0.691584 | ||||||||
\(461\) | −12.1803 | −0.567295 | −0.283647 | − | 0.958929i | \(-0.591545\pi\) | ||||
−0.283647 | + | 0.958929i | \(0.591545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.52786 | −0.256902 | −0.128451 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128451 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(464\) | −8.47214 | −0.393309 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.0557 | 0.975388 | ||||||||
\(467\) | −24.0689 | −1.11378 | −0.556888 | − | 0.830588i | \(-0.688005\pi\) | ||||
−0.556888 | + | 0.830588i | \(0.688005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.4721 | −0.668261 | ||||||||
\(470\) | −12.3607 | −0.570156 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.76393 | 0.127220 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.47214 | 0.296962 | ||||||||
\(476\) | 9.70820 | 0.444975 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.1115 | −1.01135 | ||||||||
\(479\) | 13.5279 | 0.618104 | 0.309052 | − | 0.951045i | \(-0.399988\pi\) | ||||
0.309052 | + | 0.951045i | \(0.399988\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.4164 | 1.25008 | ||||||||
\(482\) | 29.3475 | 1.33674 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.8328 | 1.58168 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.3607 | −1.64766 | −0.823830 | − | 0.566837i | \(-0.808167\pi\) | ||||
−0.823830 | + | 0.566837i | \(0.808167\pi\) | |||||||
\(488\) | 16.1803 | 0.732450 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.47214 | 0.202031 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.4164 | −1.23477 | ||||||||
\(494\) | 46.8328 | 2.10711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.76393 | 0.124104 | ||||||||
\(497\) | −10.4721 | −0.469739 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.52786 | 0.0683966 | 0.0341983 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341983 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(500\) | −36.0000 | −1.60997 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.59675 | −0.428324 | ||||||||
\(503\) | 23.4164 | 1.04409 | 0.522043 | − | 0.852919i | \(-0.325170\pi\) | ||||
0.522043 | + | 0.852919i | \(0.325170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.52786 | −0.423984 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.16718 | −0.406728 | ||||||||
\(509\) | −40.4721 | −1.79390 | −0.896948 | − | 0.442136i | \(-0.854221\pi\) | ||||
−0.896948 | + | 0.442136i | \(0.854221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.763932 | −0.0337944 | ||||||||
\(512\) | 11.1803 | 0.494106 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.4164 | 0.591772 | ||||||||
\(515\) | 15.4164 | 0.679328 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 18.9443 | 0.832364 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.4721 | −0.634645 | ||||||||
\(521\) | −30.3607 | −1.33013 | −0.665063 | − | 0.746787i | \(-0.731595\pi\) | ||||
−0.665063 | + | 0.746787i | \(0.731595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −44.0000 | −1.92399 | −0.961993 | − | 0.273075i | \(-0.911959\pi\) | ||||
−0.961993 | + | 0.273075i | \(0.911959\pi\) | |||||||
\(524\) | 65.6656 | 2.86862 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.94427 | 0.389619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 2.11146 | 0.0917158 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 19.4164 | 0.841808 | ||||||||
\(533\) | 36.3607 | 1.57496 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.00000 | −0.345870 | ||||||||
\(536\) | 32.3607 | 1.39777 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.0000 | −1.29339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.8328 | −0.895673 | −0.447836 | − | 0.894116i | \(-0.647805\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(542\) | 23.4164 | 1.00582 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.7082 | 0.930732 | ||||||||
\(545\) | 8.94427 | 0.383131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | −49.4164 | −2.11096 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54.8328 | −2.33596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.94427 | −0.380349 | ||||||||
\(554\) | 44.4721 | 1.88944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.58359 | 0.194388 | ||||||||
\(557\) | −38.9443 | −1.65012 | −0.825061 | − | 0.565044i | \(-0.808859\pi\) | ||||
−0.825061 | + | 0.565044i | \(0.808859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.8885 | 1.09497 | ||||||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.88854 | −0.332758 | ||||||||
\(563\) | 12.5836 | 0.530335 | 0.265168 | − | 0.964202i | \(-0.414573\pi\) | ||||
0.265168 | + | 0.964202i | \(0.414573\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.00000 | −0.168281 | ||||||||
\(566\) | −66.8328 | −2.80919 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.4164 | 0.982531 | ||||||||
\(569\) | 7.52786 | 0.315584 | 0.157792 | − | 0.987472i | \(-0.449562\pi\) | ||||
0.157792 | + | 0.987472i | \(0.449562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0557 | 0.630063 | 0.315031 | − | 0.949081i | \(-0.397985\pi\) | ||||
0.315031 | + | 0.949081i | \(0.397985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25.1246 | 1.04868 | ||||||||
\(575\) | 2.47214 | 0.103095 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.5279 | −0.812956 | −0.406478 | − | 0.913661i | \(-0.633243\pi\) | ||||
−0.406478 | + | 0.913661i | \(0.633243\pi\) | |||||||
\(578\) | −14.5967 | −0.607145 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 50.8328 | 2.11072 | ||||||||
\(581\) | 11.4164 | 0.473632 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.70820 | 0.0706860 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −56.1803 | −2.32079 | ||||||||
\(587\) | −27.1246 | −1.11955 | −0.559776 | − | 0.828644i | \(-0.689113\pi\) | ||||
−0.559776 | + | 0.828644i | \(0.689113\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8885 | 0.737085 | ||||||||
\(590\) | 5.52786 | 0.227579 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.47214 | 0.348203 | ||||||||
\(593\) | −45.7082 | −1.87701 | −0.938505 | − | 0.345264i | \(-0.887789\pi\) | ||||
−0.938505 | + | 0.345264i | \(0.887789\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.47214 | 0.265332 | ||||||||
\(596\) | 42.0000 | 1.72039 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.8885 | 0.731517 | ||||||||
\(599\) | 23.4164 | 0.956768 | 0.478384 | − | 0.878151i | \(-0.341223\pi\) | ||||
0.478384 | + | 0.878151i | \(0.341223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1246 | 1.51434 | 0.757172 | − | 0.653215i | \(-0.226580\pi\) | ||||
0.757172 | + | 0.653215i | \(0.226580\pi\) | |||||||
\(602\) | 17.8885 | 0.729083 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −26.8328 | −1.09181 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.9443 | −0.525392 | −0.262696 | − | 0.964879i | \(-0.584612\pi\) | ||||
−0.262696 | + | 0.964879i | \(0.584612\pi\) | |||||||
\(608\) | 43.4164 | 1.76077 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.3607 | 1.31025 | ||||||||
\(611\) | 8.94427 | 0.361847 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.3050 | −0.618161 | −0.309081 | − | 0.951036i | \(-0.600021\pi\) | ||||
−0.309081 | + | 0.951036i | \(0.600021\pi\) | |||||||
\(614\) | 20.0000 | 0.807134 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.58359 | −0.265045 | −0.132523 | − | 0.991180i | \(-0.542308\pi\) | ||||
−0.132523 | + | 0.991180i | \(0.542308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1246 | 0.447136 | 0.223568 | − | 0.974688i | \(-0.428230\pi\) | ||||
0.223568 | + | 0.974688i | \(0.428230\pi\) | |||||||
\(620\) | −16.5836 | −0.666013 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.5410 | 0.743427 | ||||||||
\(623\) | 2.00000 | 0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 33.4164 | 1.33559 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 32.8328 | 1.31017 | ||||||||
\(629\) | 27.4164 | 1.09316 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | −0.955425 | −0.477712 | − | 0.878516i | \(-0.658534\pi\) | ||||
−0.477712 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(632\) | 20.0000 | 0.795557 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −31.3050 | −1.24328 | ||||||||
\(635\) | −6.11146 | −0.242526 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.23607 | −0.128218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −31.3050 | −1.23744 | ||||||||
\(641\) | 15.5279 | 0.613314 | 0.306657 | − | 0.951820i | \(-0.400790\pi\) | ||||
0.306657 | + | 0.951820i | \(0.400790\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.1246 | 0.438712 | 0.219356 | − | 0.975645i | \(-0.429604\pi\) | ||||
0.219356 | + | 0.975645i | \(0.429604\pi\) | |||||||
\(644\) | 7.41641 | 0.292247 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 46.8328 | 1.84261 | ||||||||
\(647\) | −36.0689 | −1.41801 | −0.709007 | − | 0.705201i | \(-0.750857\pi\) | ||||
−0.709007 | + | 0.705201i | \(0.750857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 7.23607 | 0.283822 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.2492 | −0.401391 | ||||||||
\(653\) | −25.0557 | −0.980506 | −0.490253 | − | 0.871580i | \(-0.663096\pi\) | ||||
−0.490253 | + | 0.871580i | \(0.663096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.7771 | 1.71051 | ||||||||
\(656\) | 11.2361 | 0.438695 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.18034 | 0.240935 | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.8328 | −1.58821 | −0.794106 | − | 0.607779i | \(-0.792061\pi\) | ||||
−0.794106 | + | 0.607779i | \(0.792061\pi\) | |||||||
\(662\) | −31.0557 | −1.20702 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25.5279 | −0.990673 | ||||||||
\(665\) | 12.9443 | 0.501957 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.9443 | −0.810965 | ||||||||
\(668\) | 14.8328 | 0.573899 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 64.7214 | 2.50040 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.4164 | 0.825542 | 0.412771 | − | 0.910835i | \(-0.364561\pi\) | ||||
0.412771 | + | 0.910835i | \(0.364561\pi\) | |||||||
\(674\) | 25.7771 | 0.992896 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.58359 | −0.291677 | ||||||||
\(677\) | −9.70820 | −0.373117 | −0.186558 | − | 0.982444i | \(-0.559733\pi\) | ||||
−0.186558 | + | 0.982444i | \(0.559733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.4164 | −0.668380 | ||||||||
\(680\) | −14.4721 | −0.554981 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.88854 | 0.225319 | 0.112659 | − | 0.993634i | \(-0.464063\pi\) | ||||
0.112659 | + | 0.993634i | \(0.464063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.9443 | −1.25874 | ||||||||
\(686\) | −2.23607 | −0.0853735 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | −1.52786 | −0.0582070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.5410 | 0.705334 | 0.352667 | − | 0.935749i | \(-0.385275\pi\) | ||||
0.352667 | + | 0.935749i | \(0.385275\pi\) | |||||||
\(692\) | −38.2918 | −1.45564 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.8328 | 1.77775 | ||||||||
\(695\) | 3.05573 | 0.115910 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.3607 | 1.37726 | ||||||||
\(698\) | 16.1803 | 0.612435 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.00000 | 0.113389 | ||||||||
\(701\) | −15.5279 | −0.586479 | −0.293240 | − | 0.956039i | \(-0.594733\pi\) | ||||
−0.293240 | + | 0.956039i | \(0.594733\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.8328 | 2.06806 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −44.4721 | −1.67373 | ||||||||
\(707\) | 4.76393 | 0.179166 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9443 | −0.561244 | −0.280622 | − | 0.959818i | \(-0.590541\pi\) | ||||
−0.280622 | + | 0.959818i | \(0.590541\pi\) | |||||||
\(710\) | 46.8328 | 1.75760 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.47214 | −0.167600 | ||||||||
\(713\) | 6.83282 | 0.255891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.8328 | 1.00279 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −55.7771 | −2.08158 | ||||||||
\(719\) | 51.4853 | 1.92008 | 0.960039 | − | 0.279867i | \(-0.0902905\pi\) | ||||
0.960039 | + | 0.279867i | \(0.0902905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.70820 | −0.287069 | ||||||||
\(722\) | 51.1803 | 1.90474 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −76.2492 | −2.83378 | ||||||||
\(725\) | −8.47214 | −0.314647 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.0132 | 0.927687 | 0.463843 | − | 0.885917i | \(-0.346470\pi\) | ||||
0.463843 | + | 0.885917i | \(0.346470\pi\) | |||||||
\(728\) | 7.23607 | 0.268187 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.41641 | 0.126447 | ||||||||
\(731\) | 25.8885 | 0.957522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.76393 | −0.323703 | −0.161852 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161852 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(734\) | −51.7082 | −1.90858 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.5836 | 0.611279 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.9443 | −0.917590 | −0.458795 | − | 0.888542i | \(-0.651719\pi\) | ||||
−0.458795 | + | 0.888542i | \(0.651719\pi\) | |||||||
\(740\) | −50.8328 | −1.86865 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.05573 | −0.0387570 | ||||||||
\(743\) | 1.88854 | 0.0692840 | 0.0346420 | − | 0.999400i | \(-0.488971\pi\) | ||||
0.0346420 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.0000 | 1.02584 | ||||||||
\(746\) | −13.4164 | −0.491210 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.5279 | 1.07749 | 0.538744 | − | 0.842470i | \(-0.318899\pi\) | ||||
0.538744 | + | 0.842470i | \(0.318899\pi\) | |||||||
\(752\) | 2.76393 | 0.100790 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −61.3050 | −2.23259 | ||||||||
\(755\) | −17.8885 | −0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8885 | 0.577479 | 0.288739 | − | 0.957408i | \(-0.406764\pi\) | ||||
0.288739 | + | 0.957408i | \(0.406764\pi\) | |||||||
\(758\) | 83.4164 | 3.02982 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −28.9443 | −1.04992 | ||||||||
\(761\) | −31.5967 | −1.14538 | −0.572691 | − | 0.819772i | \(-0.694100\pi\) | ||||
−0.572691 | + | 0.819772i | \(0.694100\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.47214 | −0.161902 | ||||||||
\(764\) | 9.16718 | 0.331657 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.4033 | 0.375885 | ||||||||
\(767\) | −4.00000 | −0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.2918 | −0.659619 | −0.329810 | − | 0.944047i | \(-0.606985\pi\) | ||||
−0.329810 | + | 0.944047i | \(0.606985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −35.6656 | −1.28363 | ||||||||
\(773\) | 38.3607 | 1.37974 | 0.689869 | − | 0.723934i | \(-0.257668\pi\) | ||||
0.689869 | + | 0.723934i | \(0.257668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.76393 | 0.0992834 | ||||||||
\(776\) | 38.9443 | 1.39802 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.5279 | −1.27374 | ||||||||
\(779\) | 72.7214 | 2.60551 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 17.8885 | 0.639693 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 21.8885 | 0.781236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.4164 | 1.54763 | 0.773814 | − | 0.633413i | \(-0.218347\pi\) | ||||
0.773814 | + | 0.633413i | \(0.218347\pi\) | |||||||
\(788\) | −6.00000 | −0.213741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 40.0000 | 1.42314 | ||||||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.4164 | −0.831541 | ||||||||
\(794\) | −80.2492 | −2.84794 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.54102 | −0.231840 | ||||||||
\(797\) | 14.9443 | 0.529353 | 0.264677 | − | 0.964337i | \(-0.414735\pi\) | ||||
0.264677 | + | 0.964337i | \(0.414735\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.94427 | 0.316426 | ||||||||
\(800\) | 6.70820 | 0.237171 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −51.3050 | −1.81164 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.94427 | 0.174263 | ||||||||
\(806\) | 20.0000 | 0.704470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.6525 | −0.374753 | ||||||||
\(809\) | 21.0557 | 0.740280 | 0.370140 | − | 0.928976i | \(-0.379310\pi\) | ||||
0.370140 | + | 0.928976i | \(0.379310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.8328 | 1.22315 | 0.611573 | − | 0.791188i | \(-0.290537\pi\) | ||||
0.611573 | + | 0.791188i | \(0.290537\pi\) | |||||||
\(812\) | −25.4164 | −0.891941 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.83282 | −0.239343 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.7771 | 1.81145 | ||||||||
\(818\) | −20.4033 | −0.713383 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −67.4164 | −2.35428 | ||||||||
\(821\) | 44.8328 | 1.56468 | 0.782338 | − | 0.622854i | \(-0.214027\pi\) | ||||
0.782338 | + | 0.622854i | \(0.214027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1115 | −0.491894 | −0.245947 | − | 0.969283i | \(-0.579099\pi\) | ||||
−0.245947 | + | 0.969283i | \(0.579099\pi\) | |||||||
\(824\) | 17.2361 | 0.600447 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.76393 | −0.0961695 | ||||||||
\(827\) | −12.9443 | −0.450116 | −0.225058 | − | 0.974345i | \(-0.572257\pi\) | ||||
−0.225058 | + | 0.974345i | \(0.572257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.8328 | 1.27926 | 0.639628 | − | 0.768684i | \(-0.279088\pi\) | ||||
0.639628 | + | 0.768684i | \(0.279088\pi\) | |||||||
\(830\) | −51.0557 | −1.77217 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 42.0689 | 1.45848 | ||||||||
\(833\) | −3.23607 | −0.112123 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.88854 | 0.342207 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −55.1246 | −1.90425 | ||||||||
\(839\) | −44.0689 | −1.52143 | −0.760713 | − | 0.649088i | \(-0.775151\pi\) | ||||
−0.760713 | + | 0.649088i | \(0.775151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7771 | 1.47507 | ||||||||
\(842\) | 50.0000 | 1.72311 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 41.6656 | 1.43419 | ||||||||
\(845\) | −5.05573 | −0.173922 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.472136 | −0.0162132 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.23607 | 0.248195 | ||||||||
\(851\) | 20.9443 | 0.717960 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.6525 | 1.04952 | 0.524760 | − | 0.851250i | \(-0.324155\pi\) | ||||
0.524760 | + | 0.851250i | \(0.324155\pi\) | |||||||
\(854\) | −16.1803 | −0.553680 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.94427 | −0.305709 | ||||||||
\(857\) | 15.2361 | 0.520454 | 0.260227 | − | 0.965547i | \(-0.416203\pi\) | ||||
0.260227 | + | 0.965547i | \(0.416203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.5410 | −0.905568 | −0.452784 | − | 0.891620i | \(-0.649569\pi\) | ||||
−0.452784 | + | 0.891620i | \(0.649569\pi\) | |||||||
\(860\) | −48.0000 | −1.63679 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.8328 | 0.913929 | ||||||||
\(863\) | 3.05573 | 0.104018 | 0.0520091 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520091 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.5279 | −0.867973 | ||||||||
\(866\) | −18.9443 | −0.643753 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.29180 | 0.281442 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.8328 | −1.58687 | ||||||||
\(872\) | 10.0000 | 0.338643 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 35.7771 | 1.21018 | ||||||||
\(875\) | 12.0000 | 0.405674 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.5836 | −0.492453 | −0.246226 | − | 0.969212i | \(-0.579191\pi\) | ||||
−0.246226 | + | 0.969212i | \(0.579191\pi\) | |||||||
\(878\) | −23.4164 | −0.790265 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.58359 | −0.0870434 | −0.0435217 | − | 0.999052i | \(-0.513858\pi\) | ||||
−0.0435217 | + | 0.999052i | \(0.513858\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.94427 | −0.300999 | −0.150499 | − | 0.988610i | \(-0.548088\pi\) | ||||
−0.150499 | + | 0.988610i | \(0.548088\pi\) | |||||||
\(884\) | 31.4164 | 1.05665 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 55.7771 | 1.87387 | ||||||||
\(887\) | −4.36068 | −0.146417 | −0.0732086 | − | 0.997317i | \(-0.523324\pi\) | ||||
−0.0732086 | + | 0.997317i | \(0.523324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.05573 | 0.102486 | ||||||||
\(890\) | −8.94427 | −0.299813 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.5410 | −1.02259 | ||||||||
\(893\) | 17.8885 | 0.598617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.8885 | 0.597948 | ||||||||
\(896\) | 15.6525 | 0.522913 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 63.6656 | 2.12455 | ||||||||
\(899\) | −23.4164 | −0.780981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.52786 | −0.0509005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.47214 | −0.148741 | ||||||||
\(905\) | −50.8328 | −1.68974 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.4721 | 0.746175 | 0.373088 | − | 0.927796i | \(-0.378299\pi\) | ||||
0.373088 | + | 0.927796i | \(0.378299\pi\) | |||||||
\(908\) | 17.6656 | 0.586255 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14.4721 | 0.479747 | ||||||||
\(911\) | −42.4721 | −1.40716 | −0.703582 | − | 0.710614i | \(-0.748417\pi\) | ||||
−0.703582 | + | 0.710614i | \(0.748417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 64.4721 | 2.13255 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.4164 | −0.443291 | ||||||||
\(917\) | −21.8885 | −0.722823 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.8885 | −1.38178 | −0.690888 | − | 0.722962i | \(-0.742780\pi\) | ||||
−0.690888 | + | 0.722962i | \(0.742780\pi\) | |||||||
\(920\) | −11.0557 | −0.364497 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.2361 | −0.896972 | ||||||||
\(923\) | −33.8885 | −1.11546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.47214 | 0.278562 | ||||||||
\(926\) | −12.3607 | −0.406197 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −56.8328 | −1.86563 | ||||||||
\(929\) | 52.2492 | 1.71424 | 0.857121 | − | 0.515116i | \(-0.172251\pi\) | ||||
0.857121 | + | 0.515116i | \(0.172251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.47214 | −0.212116 | ||||||||
\(932\) | 28.2492 | 0.925334 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −53.8197 | −1.76103 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6525 | 0.348001 | 0.174001 | − | 0.984746i | \(-0.444331\pi\) | ||||
0.174001 | + | 0.984746i | \(0.444331\pi\) | |||||||
\(938\) | −32.3607 | −1.05661 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.5836 | −0.540897 | ||||||||
\(941\) | 7.59675 | 0.247647 | 0.123823 | − | 0.992304i | \(-0.460484\pi\) | ||||
0.123823 | + | 0.992304i | \(0.460484\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.7771 | 0.904546 | ||||||||
\(944\) | −1.23607 | −0.0402306 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.16718 | 0.167911 | 0.0839555 | − | 0.996470i | \(-0.473245\pi\) | ||||
0.0839555 | + | 0.996470i | \(0.473245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.47214 | −0.0802489 | ||||||||
\(950\) | 14.4721 | 0.469538 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.23607 | 0.234522 | ||||||||
\(953\) | 22.9443 | 0.743238 | 0.371619 | − | 0.928385i | \(-0.378803\pi\) | ||||
0.371619 | + | 0.928385i | \(0.378803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.11146 | 0.197762 | ||||||||
\(956\) | −29.6656 | −0.959455 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.2492 | 0.977308 | ||||||||
\(959\) | 16.4721 | 0.531913 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3607 | −0.753570 | ||||||||
\(962\) | 61.3050 | 1.97655 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 39.3738 | 1.26815 | ||||||||
\(965\) | −23.7771 | −0.765412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.8885 | 0.446625 | 0.223313 | − | 0.974747i | \(-0.428313\pi\) | ||||
0.223313 | + | 0.974747i | \(0.428313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 77.8885 | 2.50085 | ||||||||
\(971\) | −11.1246 | −0.357006 | −0.178503 | − | 0.983939i | \(-0.557125\pi\) | ||||
−0.178503 | + | 0.983939i | \(0.557125\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.52786 | −0.0489811 | ||||||||
\(974\) | −81.3050 | −2.60518 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.23607 | −0.231621 | ||||||||
\(977\) | −22.9443 | −0.734052 | −0.367026 | − | 0.930211i | \(-0.619624\pi\) | ||||
−0.367026 | + | 0.930211i | \(0.619624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.00000 | 0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.8197 | −0.695939 | −0.347970 | − | 0.937506i | \(-0.613129\pi\) | ||||
−0.347970 | + | 0.937506i | \(0.613129\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.00000 | −0.127451 | ||||||||
\(986\) | −61.3050 | −1.95235 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 62.8328 | 1.99898 | ||||||||
\(989\) | 19.7771 | 0.628875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.2492 | 1.72328 | 0.861642 | − | 0.507517i | \(-0.169437\pi\) | ||||
0.861642 | + | 0.507517i | \(0.169437\pi\) | |||||||
\(992\) | 18.5410 | 0.588678 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.4164 | −0.742723 | ||||||||
\(995\) | −4.36068 | −0.138243 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.34752 | −0.0426765 | −0.0213383 | − | 0.999772i | \(-0.506793\pi\) | ||||
−0.0213383 | + | 0.999772i | \(0.506793\pi\) | |||||||
\(998\) | 3.41641 | 0.108145 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.bl.1.2 | 2 | ||
3.2 | odd | 2 | 847.2.a.f.1.1 | 2 | |||
11.10 | odd | 2 | 693.2.a.h.1.1 | 2 | |||
21.20 | even | 2 | 5929.2.a.m.1.1 | 2 | |||
33.2 | even | 10 | 847.2.f.a.323.1 | 4 | |||
33.5 | odd | 10 | 847.2.f.m.729.1 | 4 | |||
33.8 | even | 10 | 847.2.f.n.372.1 | 4 | |||
33.14 | odd | 10 | 847.2.f.b.372.1 | 4 | |||
33.17 | even | 10 | 847.2.f.a.729.1 | 4 | |||
33.20 | odd | 10 | 847.2.f.m.323.1 | 4 | |||
33.26 | odd | 10 | 847.2.f.b.148.1 | 4 | |||
33.29 | even | 10 | 847.2.f.n.148.1 | 4 | |||
33.32 | even | 2 | 77.2.a.d.1.2 | ✓ | 2 | ||
77.76 | even | 2 | 4851.2.a.y.1.1 | 2 | |||
132.131 | odd | 2 | 1232.2.a.m.1.2 | 2 | |||
165.32 | odd | 4 | 1925.2.b.h.1849.3 | 4 | |||
165.98 | odd | 4 | 1925.2.b.h.1849.2 | 4 | |||
165.164 | even | 2 | 1925.2.a.r.1.1 | 2 | |||
231.32 | even | 6 | 539.2.e.i.177.1 | 4 | |||
231.65 | even | 6 | 539.2.e.i.67.1 | 4 | |||
231.131 | odd | 6 | 539.2.e.j.67.1 | 4 | |||
231.164 | odd | 6 | 539.2.e.j.177.1 | 4 | |||
231.230 | odd | 2 | 539.2.a.f.1.2 | 2 | |||
264.131 | odd | 2 | 4928.2.a.bv.1.1 | 2 | |||
264.197 | even | 2 | 4928.2.a.bm.1.2 | 2 | |||
924.923 | even | 2 | 8624.2.a.ce.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.d.1.2 | ✓ | 2 | 33.32 | even | 2 | ||
539.2.a.f.1.2 | 2 | 231.230 | odd | 2 | |||
539.2.e.i.67.1 | 4 | 231.65 | even | 6 | |||
539.2.e.i.177.1 | 4 | 231.32 | even | 6 | |||
539.2.e.j.67.1 | 4 | 231.131 | odd | 6 | |||
539.2.e.j.177.1 | 4 | 231.164 | odd | 6 | |||
693.2.a.h.1.1 | 2 | 11.10 | odd | 2 | |||
847.2.a.f.1.1 | 2 | 3.2 | odd | 2 | |||
847.2.f.a.323.1 | 4 | 33.2 | even | 10 | |||
847.2.f.a.729.1 | 4 | 33.17 | even | 10 | |||
847.2.f.b.148.1 | 4 | 33.26 | odd | 10 | |||
847.2.f.b.372.1 | 4 | 33.14 | odd | 10 | |||
847.2.f.m.323.1 | 4 | 33.20 | odd | 10 | |||
847.2.f.m.729.1 | 4 | 33.5 | odd | 10 | |||
847.2.f.n.148.1 | 4 | 33.29 | even | 10 | |||
847.2.f.n.372.1 | 4 | 33.8 | even | 10 | |||
1232.2.a.m.1.2 | 2 | 132.131 | odd | 2 | |||
1925.2.a.r.1.1 | 2 | 165.164 | even | 2 | |||
1925.2.b.h.1849.2 | 4 | 165.98 | odd | 4 | |||
1925.2.b.h.1849.3 | 4 | 165.32 | odd | 4 | |||
4851.2.a.y.1.1 | 2 | 77.76 | even | 2 | |||
4928.2.a.bm.1.2 | 2 | 264.197 | even | 2 | |||
4928.2.a.bv.1.1 | 2 | 264.131 | odd | 2 | |||
5929.2.a.m.1.1 | 2 | 21.20 | even | 2 | |||
7623.2.a.bl.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8624.2.a.ce.1.1 | 2 | 924.923 | even | 2 |