Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
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: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.381966 | 0.270091 | 0.135045 | − | 0.990839i | \(-0.456882\pi\) | ||||
0.135045 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(3\) | 2.23607 | 1.29099 | 0.645497 | − | 0.763763i | \(-0.276650\pi\) | ||||
0.645497 | + | 0.763763i | \(0.276650\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | 2.23607 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0.854102 | 0.348686 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.47214 | −0.520479 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0.854102 | 0.270091 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | −4.14590 | −1.19682 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.00000 | 1.29099 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −7.47214 | −1.81226 | −0.906130 | − | 0.423000i | \(-0.860977\pi\) | ||||
−0.906130 | + | 0.423000i | \(0.860977\pi\) | |||||||
\(18\) | 0.763932 | 0.180061 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | −4.14590 | −0.927051 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.14590 | 0.244306 | ||||||||
\(23\) | −3.76393 | −0.784834 | −0.392417 | − | 0.919787i | \(-0.628361\pi\) | ||||
−0.392417 | + | 0.919787i | \(0.628361\pi\) | |||||||
\(24\) | −3.29180 | −0.671935 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | 1.90983 | 0.348686 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | 4.14590 | 0.732898 | ||||||||
\(33\) | 6.70820 | 1.16775 | ||||||||
\(34\) | −2.85410 | −0.489474 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.70820 | −0.618034 | ||||||||
\(37\) | 8.70820 | 1.43162 | 0.715810 | − | 0.698295i | \(-0.246058\pi\) | ||||
0.715810 | + | 0.698295i | \(0.246058\pi\) | |||||||
\(38\) | −1.14590 | −0.185889 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.29180 | −0.520479 | ||||||||
\(41\) | −4.47214 | −0.698430 | −0.349215 | − | 0.937043i | \(-0.613552\pi\) | ||||
−0.349215 | + | 0.937043i | \(0.613552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −5.56231 | −0.838549 | ||||||||
\(45\) | 4.47214 | 0.666667 | ||||||||
\(46\) | −1.43769 | −0.211976 | ||||||||
\(47\) | −1.47214 | −0.214733 | −0.107367 | − | 0.994220i | \(-0.534242\pi\) | ||||
−0.107367 | + | 0.994220i | \(0.534242\pi\) | |||||||
\(48\) | 7.03444 | 1.01533 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.7082 | −2.33962 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.47214 | 0.202213 | 0.101107 | − | 0.994876i | \(-0.467762\pi\) | ||||
0.101107 | + | 0.994876i | \(0.467762\pi\) | |||||||
\(54\) | −0.854102 | −0.116229 | ||||||||
\(55\) | 6.70820 | 0.904534 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.70820 | −0.888523 | ||||||||
\(58\) | −1.70820 | −0.224298 | ||||||||
\(59\) | −7.47214 | −0.972789 | −0.486395 | − | 0.873739i | \(-0.661688\pi\) | ||||
−0.486395 | + | 0.873739i | \(0.661688\pi\) | |||||||
\(60\) | −9.27051 | −1.19682 | ||||||||
\(61\) | 3.00000 | 0.384111 | 0.192055 | − | 0.981384i | \(-0.438485\pi\) | ||||
0.192055 | + | 0.981384i | \(0.438485\pi\) | |||||||
\(62\) | −1.90983 | −0.242549 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.56231 | 0.315398 | ||||||||
\(67\) | 3.00000 | 0.366508 | 0.183254 | − | 0.983066i | \(-0.441337\pi\) | ||||
0.183254 | + | 0.983066i | \(0.441337\pi\) | |||||||
\(68\) | 13.8541 | 1.68006 | ||||||||
\(69\) | −8.41641 | −1.01322 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.94427 | −1.06149 | −0.530745 | − | 0.847532i | \(-0.678088\pi\) | ||||
−0.530745 | + | 0.847532i | \(0.678088\pi\) | |||||||
\(72\) | −2.94427 | −0.346986 | ||||||||
\(73\) | −10.7082 | −1.25330 | −0.626650 | − | 0.779301i | \(-0.715575\pi\) | ||||
−0.626650 | + | 0.779301i | \(0.715575\pi\) | |||||||
\(74\) | 3.32624 | 0.386667 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.56231 | 0.638040 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7082 | 1.20477 | 0.602384 | − | 0.798207i | \(-0.294218\pi\) | ||||
0.602384 | + | 0.798207i | \(0.294218\pi\) | |||||||
\(80\) | 7.03444 | 0.786475 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −1.70820 | −0.188640 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.7082 | −1.81226 | ||||||||
\(86\) | −3.05573 | −0.329508 | ||||||||
\(87\) | −10.0000 | −1.07211 | ||||||||
\(88\) | −4.41641 | −0.470791 | ||||||||
\(89\) | 2.23607 | 0.237023 | 0.118511 | − | 0.992953i | \(-0.462188\pi\) | ||||
0.118511 | + | 0.992953i | \(0.462188\pi\) | |||||||
\(90\) | 1.70820 | 0.180061 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.97871 | 0.727581 | ||||||||
\(93\) | −11.1803 | −1.15935 | ||||||||
\(94\) | −0.562306 | −0.0579974 | ||||||||
\(95\) | −6.70820 | −0.688247 | ||||||||
\(96\) | 9.27051 | 0.946167 | ||||||||
\(97\) | 17.4164 | 1.76837 | 0.884184 | − | 0.467139i | \(-0.154715\pi\) | ||||
0.884184 | + | 0.467139i | \(0.154715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | −0.895533 | −0.447767 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | −6.38197 | −0.631909 | ||||||||
\(103\) | 10.7082 | 1.05511 | 0.527555 | − | 0.849521i | \(-0.323109\pi\) | ||||
0.527555 | + | 0.849521i | \(0.323109\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.562306 | 0.0546160 | ||||||||
\(107\) | −14.2361 | −1.37625 | −0.688126 | − | 0.725591i | \(-0.741567\pi\) | ||||
−0.688126 | + | 0.725591i | \(0.741567\pi\) | |||||||
\(108\) | 4.14590 | 0.398939 | ||||||||
\(109\) | −10.7082 | −1.02566 | −0.512830 | − | 0.858490i | \(-0.671403\pi\) | ||||
−0.512830 | + | 0.858490i | \(0.671403\pi\) | |||||||
\(110\) | 2.56231 | 0.244306 | ||||||||
\(111\) | 19.4721 | 1.84821 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.9443 | −1.40584 | −0.702919 | − | 0.711269i | \(-0.748121\pi\) | ||||
−0.702919 | + | 0.711269i | \(0.748121\pi\) | |||||||
\(114\) | −2.56231 | −0.239982 | ||||||||
\(115\) | −8.41641 | −0.784834 | ||||||||
\(116\) | 8.29180 | 0.769874 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.85410 | −0.262741 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.36068 | −0.671935 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 1.14590 | 0.103745 | ||||||||
\(123\) | −10.0000 | −0.901670 | ||||||||
\(124\) | 9.27051 | 0.832516 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4164 | 1.36798 | 0.683992 | − | 0.729489i | \(-0.260242\pi\) | ||||
0.683992 | + | 0.729489i | \(0.260242\pi\) | |||||||
\(128\) | −10.0902 | −0.891853 | ||||||||
\(129\) | −17.8885 | −1.57500 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.76393 | −0.328856 | −0.164428 | − | 0.986389i | \(-0.552578\pi\) | ||||
−0.164428 | + | 0.986389i | \(0.552578\pi\) | |||||||
\(132\) | −12.4377 | −1.08256 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.14590 | 0.0989905 | ||||||||
\(135\) | −5.00000 | −0.430331 | ||||||||
\(136\) | 11.0000 | 0.943242 | ||||||||
\(137\) | 3.76393 | 0.321574 | 0.160787 | − | 0.986989i | \(-0.448597\pi\) | ||||
0.160787 | + | 0.986989i | \(0.448597\pi\) | |||||||
\(138\) | −3.21478 | −0.273660 | ||||||||
\(139\) | 3.41641 | 0.289776 | 0.144888 | − | 0.989448i | \(-0.453718\pi\) | ||||
0.144888 | + | 0.989448i | \(0.453718\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.29180 | −0.277219 | ||||||||
\(142\) | −3.41641 | −0.286699 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.29180 | 0.524316 | ||||||||
\(145\) | −10.0000 | −0.830455 | ||||||||
\(146\) | −4.09017 | −0.338505 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.1459 | −1.32718 | ||||||||
\(149\) | 12.7082 | 1.04110 | 0.520548 | − | 0.853832i | \(-0.325728\pi\) | ||||
0.520548 | + | 0.853832i | \(0.325728\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.41641 | 0.522160 | 0.261080 | − | 0.965317i | \(-0.415921\pi\) | ||||
0.261080 | + | 0.965317i | \(0.415921\pi\) | |||||||
\(152\) | 4.41641 | 0.358218 | ||||||||
\(153\) | −14.9443 | −1.20817 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.1803 | −0.898027 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00000 | 0.558661 | 0.279330 | − | 0.960195i | \(-0.409888\pi\) | ||||
0.279330 | + | 0.960195i | \(0.409888\pi\) | |||||||
\(158\) | 4.09017 | 0.325396 | ||||||||
\(159\) | 3.29180 | 0.261056 | ||||||||
\(160\) | 9.27051 | 0.732898 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.20163 | −0.330111 | ||||||||
\(163\) | −10.4164 | −0.815876 | −0.407938 | − | 0.913010i | \(-0.633752\pi\) | ||||
−0.407938 | + | 0.913010i | \(0.633752\pi\) | |||||||
\(164\) | 8.29180 | 0.647480 | ||||||||
\(165\) | 15.0000 | 1.16775 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.5279 | −1.04682 | −0.523409 | − | 0.852082i | \(-0.675340\pi\) | ||||
−0.523409 | + | 0.852082i | \(0.675340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.38197 | −0.489474 | ||||||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | 14.8328 | 1.13099 | ||||||||
\(173\) | 10.4164 | 0.791945 | 0.395972 | − | 0.918262i | \(-0.370408\pi\) | ||||
0.395972 | + | 0.918262i | \(0.370408\pi\) | |||||||
\(174\) | −3.81966 | −0.289568 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.43769 | 0.711393 | ||||||||
\(177\) | −16.7082 | −1.25587 | ||||||||
\(178\) | 0.854102 | 0.0640176 | ||||||||
\(179\) | 20.1246 | 1.50418 | 0.752092 | − | 0.659058i | \(-0.229045\pi\) | ||||
0.752092 | + | 0.659058i | \(0.229045\pi\) | |||||||
\(180\) | −8.29180 | −0.618034 | ||||||||
\(181\) | 1.41641 | 0.105281 | 0.0526404 | − | 0.998614i | \(-0.483236\pi\) | ||||
0.0526404 | + | 0.998614i | \(0.483236\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.70820 | 0.495885 | ||||||||
\(184\) | 5.54102 | 0.408489 | ||||||||
\(185\) | 19.4721 | 1.43162 | ||||||||
\(186\) | −4.27051 | −0.313129 | ||||||||
\(187\) | −22.4164 | −1.63925 | ||||||||
\(188\) | 2.72949 | 0.199069 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.56231 | −0.185889 | ||||||||
\(191\) | −11.1803 | −0.808981 | −0.404491 | − | 0.914542i | \(-0.632551\pi\) | ||||
−0.404491 | + | 0.914542i | \(0.632551\pi\) | |||||||
\(192\) | −10.5279 | −0.759783 | ||||||||
\(193\) | 12.7082 | 0.914757 | 0.457378 | − | 0.889272i | \(-0.348789\pi\) | ||||
0.457378 | + | 0.889272i | \(0.348789\pi\) | |||||||
\(194\) | 6.65248 | 0.477620 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.9443 | 1.91970 | 0.959850 | − | 0.280514i | \(-0.0905049\pi\) | ||||
0.959850 | + | 0.280514i | \(0.0905049\pi\) | |||||||
\(198\) | 2.29180 | 0.162871 | ||||||||
\(199\) | −7.29180 | −0.516902 | −0.258451 | − | 0.966024i | \(-0.583212\pi\) | ||||
−0.258451 | + | 0.966024i | \(0.583212\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.70820 | 0.473160 | ||||||||
\(202\) | −3.43769 | −0.241875 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 30.9787 | 2.16894 | ||||||||
\(205\) | −10.0000 | −0.698430 | ||||||||
\(206\) | 4.09017 | 0.284976 | ||||||||
\(207\) | −7.52786 | −0.523223 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.00000 | −0.622543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −2.72949 | −0.187462 | ||||||||
\(213\) | −20.0000 | −1.37038 | ||||||||
\(214\) | −5.43769 | −0.371713 | ||||||||
\(215\) | −17.8885 | −1.21999 | ||||||||
\(216\) | 3.29180 | 0.223978 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.09017 | −0.277021 | ||||||||
\(219\) | −23.9443 | −1.61800 | ||||||||
\(220\) | −12.4377 | −0.838549 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.43769 | 0.499185 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.70820 | −0.379704 | ||||||||
\(227\) | 11.9443 | 0.792769 | 0.396385 | − | 0.918085i | \(-0.370265\pi\) | ||||
0.396385 | + | 0.918085i | \(0.370265\pi\) | |||||||
\(228\) | 12.4377 | 0.823706 | ||||||||
\(229\) | 16.1246 | 1.06554 | 0.532772 | − | 0.846259i | \(-0.321150\pi\) | ||||
0.532772 | + | 0.846259i | \(0.321150\pi\) | |||||||
\(230\) | −3.21478 | −0.211976 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.58359 | 0.432234 | ||||||||
\(233\) | −5.94427 | −0.389422 | −0.194711 | − | 0.980861i | \(-0.562377\pi\) | ||||
−0.194711 | + | 0.980861i | \(0.562377\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.29180 | −0.214733 | ||||||||
\(236\) | 13.8541 | 0.901825 | ||||||||
\(237\) | 23.9443 | 1.55535 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.41641 | 0.479728 | 0.239864 | − | 0.970807i | \(-0.422897\pi\) | ||||
0.239864 | + | 0.970807i | \(0.422897\pi\) | |||||||
\(240\) | 15.7295 | 1.01533 | ||||||||
\(241\) | 8.70820 | 0.560945 | 0.280472 | − | 0.959862i | \(-0.409509\pi\) | ||||
0.280472 | + | 0.959862i | \(0.409509\pi\) | |||||||
\(242\) | −0.763932 | −0.0491074 | ||||||||
\(243\) | −17.8885 | −1.14755 | ||||||||
\(244\) | −5.56231 | −0.356090 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.81966 | −0.243533 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 7.36068 | 0.467404 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.27051 | −0.270091 | ||||||||
\(251\) | 10.4721 | 0.660995 | 0.330498 | − | 0.943807i | \(-0.392783\pi\) | ||||
0.330498 | + | 0.943807i | \(0.392783\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.2918 | −0.709909 | ||||||||
\(254\) | 5.88854 | 0.369480 | ||||||||
\(255\) | −37.3607 | −2.33962 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | −17.9443 | −1.11933 | −0.559666 | − | 0.828718i | \(-0.689071\pi\) | ||||
−0.559666 | + | 0.828718i | \(0.689071\pi\) | |||||||
\(258\) | −6.83282 | −0.425393 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.94427 | −0.553637 | ||||||||
\(262\) | −1.43769 | −0.0888210 | ||||||||
\(263\) | −14.1246 | −0.870961 | −0.435480 | − | 0.900198i | \(-0.643421\pi\) | ||||
−0.435480 | + | 0.900198i | \(0.643421\pi\) | |||||||
\(264\) | −9.87539 | −0.607788 | ||||||||
\(265\) | 3.29180 | 0.202213 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.00000 | 0.305995 | ||||||||
\(268\) | −5.56231 | −0.339772 | ||||||||
\(269\) | 4.52786 | 0.276069 | 0.138034 | − | 0.990427i | \(-0.455922\pi\) | ||||
0.138034 | + | 0.990427i | \(0.455922\pi\) | |||||||
\(270\) | −1.90983 | −0.116229 | ||||||||
\(271\) | −6.41641 | −0.389769 | −0.194885 | − | 0.980826i | \(-0.562433\pi\) | ||||
−0.194885 | + | 0.980826i | \(0.562433\pi\) | |||||||
\(272\) | −23.5066 | −1.42530 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.43769 | 0.0868543 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 15.6049 | 0.939303 | ||||||||
\(277\) | 26.4164 | 1.58721 | 0.793604 | − | 0.608435i | \(-0.208202\pi\) | ||||
0.793604 | + | 0.608435i | \(0.208202\pi\) | |||||||
\(278\) | 1.30495 | 0.0782658 | ||||||||
\(279\) | −10.0000 | −0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.05573 | −0.540219 | −0.270110 | − | 0.962830i | \(-0.587060\pi\) | ||||
−0.270110 | + | 0.962830i | \(0.587060\pi\) | |||||||
\(282\) | −1.25735 | −0.0748744 | ||||||||
\(283\) | −14.1246 | −0.839621 | −0.419811 | − | 0.907612i | \(-0.637903\pi\) | ||||
−0.419811 | + | 0.907612i | \(0.637903\pi\) | |||||||
\(284\) | 16.5836 | 0.984055 | ||||||||
\(285\) | −15.0000 | −0.888523 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.29180 | 0.488599 | ||||||||
\(289\) | 38.8328 | 2.28428 | ||||||||
\(290\) | −3.81966 | −0.224298 | ||||||||
\(291\) | 38.9443 | 2.28295 | ||||||||
\(292\) | 19.8541 | 1.16187 | ||||||||
\(293\) | −2.94427 | −0.172006 | −0.0860031 | − | 0.996295i | \(-0.527409\pi\) | ||||
−0.0860031 | + | 0.996295i | \(0.527409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.7082 | −0.972789 | ||||||||
\(296\) | −12.8197 | −0.745128 | ||||||||
\(297\) | −6.70820 | −0.389249 | ||||||||
\(298\) | 4.85410 | 0.281191 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.45085 | 0.141031 | ||||||||
\(303\) | −20.1246 | −1.15613 | ||||||||
\(304\) | −9.43769 | −0.541289 | ||||||||
\(305\) | 6.70820 | 0.384111 | ||||||||
\(306\) | −5.70820 | −0.326316 | ||||||||
\(307\) | 7.41641 | 0.423277 | 0.211638 | − | 0.977348i | \(-0.432120\pi\) | ||||
0.211638 | + | 0.977348i | \(0.432120\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.9443 | 1.36214 | ||||||||
\(310\) | −4.27051 | −0.242549 | ||||||||
\(311\) | −32.2361 | −1.82794 | −0.913970 | − | 0.405782i | \(-0.866999\pi\) | ||||
−0.913970 | + | 0.405782i | \(0.866999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.4164 | −1.83228 | −0.916142 | − | 0.400854i | \(-0.868713\pi\) | ||||
−0.916142 | + | 0.400854i | \(0.868713\pi\) | |||||||
\(314\) | 2.67376 | 0.150889 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.8541 | −1.11688 | ||||||||
\(317\) | 3.76393 | 0.211403 | 0.105702 | − | 0.994398i | \(-0.466291\pi\) | ||||
0.105702 | + | 0.994398i | \(0.466291\pi\) | |||||||
\(318\) | 1.25735 | 0.0705089 | ||||||||
\(319\) | −13.4164 | −0.751175 | ||||||||
\(320\) | −10.5279 | −0.588525 | ||||||||
\(321\) | −31.8328 | −1.77673 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.4164 | 1.24728 | ||||||||
\(324\) | 20.3951 | 1.13306 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.97871 | −0.220361 | ||||||||
\(327\) | −23.9443 | −1.32412 | ||||||||
\(328\) | 6.58359 | 0.363518 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.72949 | 0.315398 | ||||||||
\(331\) | 28.4164 | 1.56191 | 0.780954 | − | 0.624589i | \(-0.214734\pi\) | ||||
0.780954 | + | 0.624589i | \(0.214734\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.4164 | 0.954413 | ||||||||
\(334\) | −5.16718 | −0.282736 | ||||||||
\(335\) | 6.70820 | 0.366508 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −33.4164 | −1.81493 | ||||||||
\(340\) | 30.9787 | 1.68006 | ||||||||
\(341\) | −15.0000 | −0.812296 | ||||||||
\(342\) | −2.29180 | −0.123926 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.7771 | 0.634978 | ||||||||
\(345\) | −18.8197 | −1.01322 | ||||||||
\(346\) | 3.97871 | 0.213897 | ||||||||
\(347\) | −35.0689 | −1.88260 | −0.941298 | − | 0.337576i | \(-0.890393\pi\) | ||||
−0.941298 | + | 0.337576i | \(0.890393\pi\) | |||||||
\(348\) | 18.5410 | 0.993903 | ||||||||
\(349\) | 2.58359 | 0.138297 | 0.0691483 | − | 0.997606i | \(-0.477972\pi\) | ||||
0.0691483 | + | 0.997606i | \(0.477972\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.4377 | 0.662931 | ||||||||
\(353\) | −30.7082 | −1.63443 | −0.817216 | − | 0.576331i | \(-0.804484\pi\) | ||||
−0.817216 | + | 0.576331i | \(0.804484\pi\) | |||||||
\(354\) | −6.38197 | −0.339198 | ||||||||
\(355\) | −20.0000 | −1.06149 | ||||||||
\(356\) | −4.14590 | −0.219732 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.68692 | 0.406266 | ||||||||
\(359\) | 5.94427 | 0.313727 | 0.156863 | − | 0.987620i | \(-0.449862\pi\) | ||||
0.156863 | + | 0.987620i | \(0.449862\pi\) | |||||||
\(360\) | −6.58359 | −0.346986 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 0.541020 | 0.0284354 | ||||||||
\(363\) | −4.47214 | −0.234726 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.9443 | −1.25330 | ||||||||
\(366\) | 2.56231 | 0.133934 | ||||||||
\(367\) | 0.708204 | 0.0369679 | 0.0184840 | − | 0.999829i | \(-0.494116\pi\) | ||||
0.0184840 | + | 0.999829i | \(0.494116\pi\) | |||||||
\(368\) | −11.8409 | −0.617252 | ||||||||
\(369\) | −8.94427 | −0.465620 | ||||||||
\(370\) | 7.43769 | 0.386667 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 20.7295 | 1.07477 | ||||||||
\(373\) | −28.4164 | −1.47135 | −0.735673 | − | 0.677337i | \(-0.763134\pi\) | ||||
−0.735673 | + | 0.677337i | \(0.763134\pi\) | |||||||
\(374\) | −8.56231 | −0.442746 | ||||||||
\(375\) | −25.0000 | −1.29099 | ||||||||
\(376\) | 2.16718 | 0.111764 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4164 | −0.586421 | −0.293211 | − | 0.956048i | \(-0.594724\pi\) | ||||
−0.293211 | + | 0.956048i | \(0.594724\pi\) | |||||||
\(380\) | 12.4377 | 0.638040 | ||||||||
\(381\) | 34.4721 | 1.76606 | ||||||||
\(382\) | −4.27051 | −0.218498 | ||||||||
\(383\) | −15.0000 | −0.766464 | −0.383232 | − | 0.923652i | \(-0.625189\pi\) | ||||
−0.383232 | + | 0.923652i | \(0.625189\pi\) | |||||||
\(384\) | −22.5623 | −1.15138 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.85410 | 0.247067 | ||||||||
\(387\) | −16.0000 | −0.813326 | ||||||||
\(388\) | −32.2918 | −1.63937 | ||||||||
\(389\) | −7.47214 | −0.378852 | −0.189426 | − | 0.981895i | \(-0.560663\pi\) | ||||
−0.189426 | + | 0.981895i | \(0.560663\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.1246 | 1.42232 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.41641 | −0.424552 | ||||||||
\(394\) | 10.2918 | 0.518493 | ||||||||
\(395\) | 23.9443 | 1.20477 | ||||||||
\(396\) | −11.1246 | −0.559033 | ||||||||
\(397\) | −14.1246 | −0.708894 | −0.354447 | − | 0.935076i | \(-0.615331\pi\) | ||||
−0.354447 | + | 0.935076i | \(0.615331\pi\) | |||||||
\(398\) | −2.78522 | −0.139610 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.76393 | −0.487587 | −0.243794 | − | 0.969827i | \(-0.578392\pi\) | ||||
−0.243794 | + | 0.969827i | \(0.578392\pi\) | |||||||
\(402\) | 2.56231 | 0.127796 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.6869 | 0.830205 | ||||||||
\(405\) | −24.5967 | −1.22222 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.1246 | 1.29495 | ||||||||
\(408\) | 24.5967 | 1.21772 | ||||||||
\(409\) | 4.70820 | 0.232806 | 0.116403 | − | 0.993202i | \(-0.462864\pi\) | ||||
0.116403 | + | 0.993202i | \(0.462864\pi\) | |||||||
\(410\) | −3.81966 | −0.188640 | ||||||||
\(411\) | 8.41641 | 0.415151 | ||||||||
\(412\) | −19.8541 | −0.978141 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.87539 | −0.141318 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.63932 | 0.374099 | ||||||||
\(418\) | −3.43769 | −0.168143 | ||||||||
\(419\) | 15.0557 | 0.735520 | 0.367760 | − | 0.929921i | \(-0.380125\pi\) | ||||
0.367760 | + | 0.929921i | \(0.380125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4164 | 0.653876 | 0.326938 | − | 0.945046i | \(-0.393983\pi\) | ||||
0.326938 | + | 0.945046i | \(0.393983\pi\) | |||||||
\(422\) | 1.52786 | 0.0743753 | ||||||||
\(423\) | −2.94427 | −0.143155 | ||||||||
\(424\) | −2.16718 | −0.105248 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.63932 | −0.370126 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 26.3951 | 1.27586 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.83282 | −0.329508 | ||||||||
\(431\) | −13.3607 | −0.643561 | −0.321781 | − | 0.946814i | \(-0.604281\pi\) | ||||
−0.321781 | + | 0.946814i | \(0.604281\pi\) | |||||||
\(432\) | −7.03444 | −0.338445 | ||||||||
\(433\) | 2.58359 | 0.124160 | 0.0620798 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620798 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.3607 | −1.07211 | ||||||||
\(436\) | 19.8541 | 0.950839 | ||||||||
\(437\) | 11.2918 | 0.540160 | ||||||||
\(438\) | −9.14590 | −0.437008 | ||||||||
\(439\) | −16.1246 | −0.769586 | −0.384793 | − | 0.923003i | \(-0.625727\pi\) | ||||
−0.384793 | + | 0.923003i | \(0.625727\pi\) | |||||||
\(440\) | −9.87539 | −0.470791 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.23607 | −0.106239 | −0.0531194 | − | 0.998588i | \(-0.516916\pi\) | ||||
−0.0531194 | + | 0.998588i | \(0.516916\pi\) | |||||||
\(444\) | −36.1033 | −1.71339 | ||||||||
\(445\) | 5.00000 | 0.237023 | ||||||||
\(446\) | 1.52786 | 0.0723465 | ||||||||
\(447\) | 28.4164 | 1.34405 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3607 | −0.488951 | −0.244475 | − | 0.969656i | \(-0.578616\pi\) | ||||
−0.244475 | + | 0.969656i | \(0.578616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.4164 | −0.631754 | ||||||||
\(452\) | 27.7082 | 1.30328 | ||||||||
\(453\) | 14.3475 | 0.674105 | ||||||||
\(454\) | 4.56231 | 0.214120 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.87539 | 0.462457 | ||||||||
\(457\) | −34.1246 | −1.59628 | −0.798141 | − | 0.602471i | \(-0.794183\pi\) | ||||
−0.798141 | + | 0.602471i | \(0.794183\pi\) | |||||||
\(458\) | 6.15905 | 0.287794 | ||||||||
\(459\) | 16.7082 | 0.779872 | ||||||||
\(460\) | 15.6049 | 0.727581 | ||||||||
\(461\) | 10.3607 | 0.482545 | 0.241272 | − | 0.970457i | \(-0.422435\pi\) | ||||
0.241272 | + | 0.970457i | \(0.422435\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(464\) | −14.0689 | −0.653132 | ||||||||
\(465\) | −25.0000 | −1.15935 | ||||||||
\(466\) | −2.27051 | −0.105179 | ||||||||
\(467\) | −21.6525 | −1.00196 | −0.500979 | − | 0.865460i | \(-0.667026\pi\) | ||||
−0.500979 | + | 0.865460i | \(0.667026\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.25735 | −0.0579974 | ||||||||
\(471\) | 15.6525 | 0.721228 | ||||||||
\(472\) | 11.0000 | 0.506316 | ||||||||
\(473\) | −24.0000 | −1.10352 | ||||||||
\(474\) | 9.14590 | 0.420085 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.94427 | 0.134809 | ||||||||
\(478\) | 2.83282 | 0.129570 | ||||||||
\(479\) | 29.8328 | 1.36310 | 0.681548 | − | 0.731773i | \(-0.261307\pi\) | ||||
0.681548 | + | 0.731773i | \(0.261307\pi\) | |||||||
\(480\) | 20.7295 | 0.946167 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.32624 | 0.151506 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.70820 | 0.168555 | ||||||||
\(485\) | 38.9443 | 1.76837 | ||||||||
\(486\) | −6.83282 | −0.309943 | ||||||||
\(487\) | −31.8328 | −1.44248 | −0.721241 | − | 0.692684i | \(-0.756428\pi\) | ||||
−0.721241 | + | 0.692684i | \(0.756428\pi\) | |||||||
\(488\) | −4.41641 | −0.199921 | ||||||||
\(489\) | −23.2918 | −1.05329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.4721 | −1.55571 | −0.777853 | − | 0.628446i | \(-0.783691\pi\) | ||||
−0.777853 | + | 0.628446i | \(0.783691\pi\) | |||||||
\(492\) | 18.5410 | 0.835894 | ||||||||
\(493\) | 33.4164 | 1.50500 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.4164 | 0.603023 | ||||||||
\(496\) | −15.7295 | −0.706275 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.416408 | 0.0186410 | 0.00932049 | − | 0.999957i | \(-0.497033\pi\) | ||||
0.00932049 | + | 0.999957i | \(0.497033\pi\) | |||||||
\(500\) | 20.7295 | 0.927051 | ||||||||
\(501\) | −30.2492 | −1.35144 | ||||||||
\(502\) | 4.00000 | 0.178529 | ||||||||
\(503\) | 3.05573 | 0.136248 | 0.0681241 | − | 0.997677i | \(-0.478299\pi\) | ||||
0.0681241 | + | 0.997677i | \(0.478299\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.1246 | −0.895533 | ||||||||
\(506\) | −4.31308 | −0.191740 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −28.5836 | −1.26819 | ||||||||
\(509\) | 15.7639 | 0.698724 | 0.349362 | − | 0.936988i | \(-0.386398\pi\) | ||||
0.349362 | + | 0.936988i | \(0.386398\pi\) | |||||||
\(510\) | −14.2705 | −0.631909 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.3050 | 0.985749 | ||||||||
\(513\) | 6.70820 | 0.296174 | ||||||||
\(514\) | −6.85410 | −0.302321 | ||||||||
\(515\) | 23.9443 | 1.05511 | ||||||||
\(516\) | 33.1672 | 1.46010 | ||||||||
\(517\) | −4.41641 | −0.194233 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.2918 | 1.02240 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0557281 | −0.00244149 | −0.00122075 | − | 0.999999i | \(-0.500389\pi\) | ||||
−0.00122075 | + | 0.999999i | \(0.500389\pi\) | |||||||
\(522\) | −3.41641 | −0.149532 | ||||||||
\(523\) | 19.2918 | 0.843571 | 0.421786 | − | 0.906696i | \(-0.361403\pi\) | ||||
0.421786 | + | 0.906696i | \(0.361403\pi\) | |||||||
\(524\) | 6.97871 | 0.304867 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.39512 | −0.235238 | ||||||||
\(527\) | 37.3607 | 1.62746 | ||||||||
\(528\) | 21.1033 | 0.918404 | ||||||||
\(529\) | −8.83282 | −0.384035 | ||||||||
\(530\) | 1.25735 | 0.0546160 | ||||||||
\(531\) | −14.9443 | −0.648526 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.90983 | 0.0826464 | ||||||||
\(535\) | −31.8328 | −1.37625 | ||||||||
\(536\) | −4.41641 | −0.190760 | ||||||||
\(537\) | 45.0000 | 1.94189 | ||||||||
\(538\) | 1.72949 | 0.0745636 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.27051 | 0.398939 | ||||||||
\(541\) | −14.7082 | −0.632355 | −0.316178 | − | 0.948700i | \(-0.602400\pi\) | ||||
−0.316178 | + | 0.948700i | \(0.602400\pi\) | |||||||
\(542\) | −2.45085 | −0.105273 | ||||||||
\(543\) | 3.16718 | 0.135917 | ||||||||
\(544\) | −30.9787 | −1.32820 | ||||||||
\(545\) | −23.9443 | −1.02566 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.4164 | −1.34327 | −0.671634 | − | 0.740883i | \(-0.734407\pi\) | ||||
−0.671634 | + | 0.740883i | \(0.734407\pi\) | |||||||
\(548\) | −6.97871 | −0.298116 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.4164 | 0.571558 | ||||||||
\(552\) | 12.3901 | 0.527358 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.0902 | 0.428690 | ||||||||
\(555\) | 43.5410 | 1.84821 | ||||||||
\(556\) | −6.33437 | −0.268637 | ||||||||
\(557\) | 5.29180 | 0.224221 | 0.112110 | − | 0.993696i | \(-0.464239\pi\) | ||||
0.112110 | + | 0.993696i | \(0.464239\pi\) | |||||||
\(558\) | −3.81966 | −0.161699 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −50.1246 | −2.11626 | ||||||||
\(562\) | −3.45898 | −0.145908 | ||||||||
\(563\) | −36.5967 | −1.54237 | −0.771185 | − | 0.636612i | \(-0.780335\pi\) | ||||
−0.771185 | + | 0.636612i | \(0.780335\pi\) | |||||||
\(564\) | 6.10333 | 0.256996 | ||||||||
\(565\) | −33.4164 | −1.40584 | ||||||||
\(566\) | −5.39512 | −0.226774 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.1672 | 0.552483 | ||||||||
\(569\) | 16.5279 | 0.692884 | 0.346442 | − | 0.938071i | \(-0.387390\pi\) | ||||
0.346442 | + | 0.938071i | \(0.387390\pi\) | |||||||
\(570\) | −5.72949 | −0.239982 | ||||||||
\(571\) | 4.12461 | 0.172610 | 0.0863048 | − | 0.996269i | \(-0.472494\pi\) | ||||
0.0863048 | + | 0.996269i | \(0.472494\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.0000 | −1.04439 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −9.41641 | −0.392350 | ||||||||
\(577\) | 32.7082 | 1.36166 | 0.680830 | − | 0.732441i | \(-0.261619\pi\) | ||||
0.680830 | + | 0.732441i | \(0.261619\pi\) | |||||||
\(578\) | 14.8328 | 0.616964 | ||||||||
\(579\) | 28.4164 | 1.18095 | ||||||||
\(580\) | 18.5410 | 0.769874 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.8754 | 0.616605 | ||||||||
\(583\) | 4.41641 | 0.182909 | ||||||||
\(584\) | 15.7639 | 0.652316 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.12461 | −0.0464573 | ||||||||
\(587\) | 41.8885 | 1.72893 | 0.864463 | − | 0.502697i | \(-0.167659\pi\) | ||||
0.864463 | + | 0.502697i | \(0.167659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.0000 | 0.618064 | ||||||||
\(590\) | −6.38197 | −0.262741 | ||||||||
\(591\) | 60.2492 | 2.47832 | ||||||||
\(592\) | 27.3951 | 1.12593 | ||||||||
\(593\) | −32.2361 | −1.32378 | −0.661888 | − | 0.749602i | \(-0.730245\pi\) | ||||
−0.661888 | + | 0.749602i | \(0.730245\pi\) | |||||||
\(594\) | −2.56231 | −0.105133 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −23.5623 | −0.965150 | ||||||||
\(597\) | −16.3050 | −0.667317 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.0689 | 1.67803 | 0.839015 | − | 0.544109i | \(-0.183132\pi\) | ||||
0.839015 | + | 0.544109i | \(0.183132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.00000 | 0.244339 | ||||||||
\(604\) | −11.8967 | −0.484069 | ||||||||
\(605\) | −4.47214 | −0.181818 | ||||||||
\(606\) | −7.68692 | −0.312260 | ||||||||
\(607\) | −16.1246 | −0.654478 | −0.327239 | − | 0.944942i | \(-0.606118\pi\) | ||||
−0.327239 | + | 0.944942i | \(0.606118\pi\) | |||||||
\(608\) | −12.4377 | −0.504415 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.56231 | 0.103745 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 27.7082 | 1.12004 | ||||||||
\(613\) | −22.1246 | −0.893605 | −0.446802 | − | 0.894633i | \(-0.647437\pi\) | ||||
−0.446802 | + | 0.894633i | \(0.647437\pi\) | |||||||
\(614\) | 2.83282 | 0.114323 | ||||||||
\(615\) | −22.3607 | −0.901670 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.47214 | −0.180041 | −0.0900207 | − | 0.995940i | \(-0.528693\pi\) | ||||
−0.0900207 | + | 0.995940i | \(0.528693\pi\) | |||||||
\(618\) | 9.14590 | 0.367902 | ||||||||
\(619\) | −17.0000 | −0.683288 | −0.341644 | − | 0.939829i | \(-0.610984\pi\) | ||||
−0.341644 | + | 0.939829i | \(0.610984\pi\) | |||||||
\(620\) | 20.7295 | 0.832516 | ||||||||
\(621\) | 8.41641 | 0.337739 | ||||||||
\(622\) | −12.3131 | −0.493710 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | −12.3820 | −0.494883 | ||||||||
\(627\) | −20.1246 | −0.803700 | ||||||||
\(628\) | −12.9787 | −0.517907 | ||||||||
\(629\) | −65.0689 | −2.59447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.8328 | 1.22744 | 0.613718 | − | 0.789526i | \(-0.289673\pi\) | ||||
0.613718 | + | 0.789526i | \(0.289673\pi\) | |||||||
\(632\) | −15.7639 | −0.627056 | ||||||||
\(633\) | 8.94427 | 0.355503 | ||||||||
\(634\) | 1.43769 | 0.0570981 | ||||||||
\(635\) | 34.4721 | 1.36798 | ||||||||
\(636\) | −6.10333 | −0.242013 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.12461 | −0.202885 | ||||||||
\(639\) | −17.8885 | −0.707660 | ||||||||
\(640\) | −22.5623 | −0.891853 | ||||||||
\(641\) | −5.94427 | −0.234785 | −0.117392 | − | 0.993086i | \(-0.537453\pi\) | ||||
−0.117392 | + | 0.993086i | \(0.537453\pi\) | |||||||
\(642\) | −12.1591 | −0.479880 | ||||||||
\(643\) | 18.8328 | 0.742694 | 0.371347 | − | 0.928494i | \(-0.378896\pi\) | ||||
0.371347 | + | 0.928494i | \(0.378896\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.0000 | −1.57500 | ||||||||
\(646\) | 8.56231 | 0.336879 | ||||||||
\(647\) | 15.7639 | 0.619744 | 0.309872 | − | 0.950778i | \(-0.399714\pi\) | ||||
0.309872 | + | 0.950778i | \(0.399714\pi\) | |||||||
\(648\) | 16.1935 | 0.636141 | ||||||||
\(649\) | −22.4164 | −0.879921 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.3131 | 0.756359 | ||||||||
\(653\) | 13.4721 | 0.527205 | 0.263603 | − | 0.964631i | \(-0.415089\pi\) | ||||
0.263603 | + | 0.964631i | \(0.415089\pi\) | |||||||
\(654\) | −9.14590 | −0.357633 | ||||||||
\(655\) | −8.41641 | −0.328856 | ||||||||
\(656\) | −14.0689 | −0.549298 | ||||||||
\(657\) | −21.4164 | −0.835534 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.94427 | 0.348419 | 0.174210 | − | 0.984709i | \(-0.444263\pi\) | ||||
0.174210 | + | 0.984709i | \(0.444263\pi\) | |||||||
\(660\) | −27.8115 | −1.08256 | ||||||||
\(661\) | −6.70820 | −0.260919 | −0.130459 | − | 0.991454i | \(-0.541645\pi\) | ||||
−0.130459 | + | 0.991454i | \(0.541645\pi\) | |||||||
\(662\) | 10.8541 | 0.421857 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.65248 | 0.257778 | ||||||||
\(667\) | 16.8328 | 0.651769 | ||||||||
\(668\) | 25.0820 | 0.970453 | ||||||||
\(669\) | 8.94427 | 0.345806 | ||||||||
\(670\) | 2.56231 | 0.0989905 | ||||||||
\(671\) | 9.00000 | 0.347441 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4164 | 0.671353 | 0.335677 | − | 0.941977i | \(-0.391035\pi\) | ||||
0.335677 | + | 0.941977i | \(0.391035\pi\) | |||||||
\(674\) | 6.87539 | 0.264830 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.8885 | 1.26401 | 0.632005 | − | 0.774965i | \(-0.282232\pi\) | ||||
0.632005 | + | 0.774965i | \(0.282232\pi\) | |||||||
\(678\) | −12.7639 | −0.490196 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 24.5967 | 0.943242 | ||||||||
\(681\) | 26.7082 | 1.02346 | ||||||||
\(682\) | −5.72949 | −0.219394 | ||||||||
\(683\) | 4.52786 | 0.173254 | 0.0866270 | − | 0.996241i | \(-0.472391\pi\) | ||||
0.0866270 | + | 0.996241i | \(0.472391\pi\) | |||||||
\(684\) | 11.1246 | 0.425360 | ||||||||
\(685\) | 8.41641 | 0.321574 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.0557 | 1.37561 | ||||||||
\(688\) | −25.1672 | −0.959490 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.18847 | −0.273660 | ||||||||
\(691\) | −1.83282 | −0.0697236 | −0.0348618 | − | 0.999392i | \(-0.511099\pi\) | ||||
−0.0348618 | + | 0.999392i | \(0.511099\pi\) | |||||||
\(692\) | −19.3131 | −0.734173 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.3951 | −0.508472 | ||||||||
\(695\) | 7.63932 | 0.289776 | ||||||||
\(696\) | 14.7214 | 0.558012 | ||||||||
\(697\) | 33.4164 | 1.26574 | ||||||||
\(698\) | 0.986844 | 0.0373526 | ||||||||
\(699\) | −13.2918 | −0.502742 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.3607 | 0.844551 | 0.422276 | − | 0.906467i | \(-0.361231\pi\) | ||||
0.422276 | + | 0.906467i | \(0.361231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.1246 | −0.985308 | ||||||||
\(704\) | −14.1246 | −0.532341 | ||||||||
\(705\) | −7.36068 | −0.277219 | ||||||||
\(706\) | −11.7295 | −0.441445 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 30.9787 | 1.16425 | ||||||||
\(709\) | 9.87539 | 0.370878 | 0.185439 | − | 0.982656i | \(-0.440629\pi\) | ||||
0.185439 | + | 0.982656i | \(0.440629\pi\) | |||||||
\(710\) | −7.63932 | −0.286699 | ||||||||
\(711\) | 21.4164 | 0.803178 | ||||||||
\(712\) | −3.29180 | −0.123365 | ||||||||
\(713\) | 18.8197 | 0.704802 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −37.3131 | −1.39446 | ||||||||
\(717\) | 16.5836 | 0.619326 | ||||||||
\(718\) | 2.27051 | 0.0847347 | ||||||||
\(719\) | 11.2918 | 0.421113 | 0.210556 | − | 0.977582i | \(-0.432472\pi\) | ||||
0.210556 | + | 0.977582i | \(0.432472\pi\) | |||||||
\(720\) | 14.0689 | 0.524316 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.81966 | −0.142153 | ||||||||
\(723\) | 19.4721 | 0.724177 | ||||||||
\(724\) | −2.62616 | −0.0976006 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.70820 | −0.0633974 | ||||||||
\(727\) | 14.8328 | 0.550119 | 0.275059 | − | 0.961427i | \(-0.411302\pi\) | ||||
0.275059 | + | 0.961427i | \(0.411302\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | −9.14590 | −0.338505 | ||||||||
\(731\) | 59.7771 | 2.21094 | ||||||||
\(732\) | −12.4377 | −0.459710 | ||||||||
\(733\) | −15.2918 | −0.564815 | −0.282408 | − | 0.959294i | \(-0.591133\pi\) | ||||
−0.282408 | + | 0.959294i | \(0.591133\pi\) | |||||||
\(734\) | 0.270510 | 0.00998470 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.6049 | −0.575203 | ||||||||
\(737\) | 9.00000 | 0.331519 | ||||||||
\(738\) | −3.41641 | −0.125760 | ||||||||
\(739\) | −35.8328 | −1.31813 | −0.659066 | − | 0.752085i | \(-0.729048\pi\) | ||||
−0.659066 | + | 0.752085i | \(0.729048\pi\) | |||||||
\(740\) | −36.1033 | −1.32718 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.0557 | −0.552341 | −0.276171 | − | 0.961109i | \(-0.589065\pi\) | ||||
−0.276171 | + | 0.961109i | \(0.589065\pi\) | |||||||
\(744\) | 16.4590 | 0.603415 | ||||||||
\(745\) | 28.4164 | 1.04110 | ||||||||
\(746\) | −10.8541 | −0.397397 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 41.5623 | 1.51967 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.54915 | −0.348686 | ||||||||
\(751\) | 30.1246 | 1.09926 | 0.549631 | − | 0.835407i | \(-0.314768\pi\) | ||||
0.549631 | + | 0.835407i | \(0.314768\pi\) | |||||||
\(752\) | −4.63119 | −0.168882 | ||||||||
\(753\) | 23.4164 | 0.853341 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.3475 | 0.522160 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.832816 | 0.0302692 | 0.0151346 | − | 0.999885i | \(-0.495182\pi\) | ||||
0.0151346 | + | 0.999885i | \(0.495182\pi\) | |||||||
\(758\) | −4.36068 | −0.158387 | ||||||||
\(759\) | −25.2492 | −0.916489 | ||||||||
\(760\) | 9.87539 | 0.358218 | ||||||||
\(761\) | −33.5410 | −1.21586 | −0.607931 | − | 0.793990i | \(-0.708000\pi\) | ||||
−0.607931 | + | 0.793990i | \(0.708000\pi\) | |||||||
\(762\) | 13.1672 | 0.476997 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.7295 | 0.749967 | ||||||||
\(765\) | −33.4164 | −1.20817 | ||||||||
\(766\) | −5.72949 | −0.207015 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 12.4377 | 0.448807 | ||||||||
\(769\) | −46.0000 | −1.65880 | −0.829401 | − | 0.558653i | \(-0.811318\pi\) | ||||
−0.829401 | + | 0.558653i | \(0.811318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.1246 | −1.44505 | ||||||||
\(772\) | −23.5623 | −0.848026 | ||||||||
\(773\) | −11.0689 | −0.398120 | −0.199060 | − | 0.979987i | \(-0.563789\pi\) | ||||
−0.199060 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(774\) | −6.11146 | −0.219672 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25.6393 | −0.920398 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.85410 | −0.102325 | ||||||||
\(779\) | 13.4164 | 0.480693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.8328 | −0.960154 | ||||||||
\(782\) | 10.7426 | 0.384156 | ||||||||
\(783\) | 10.0000 | 0.357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.6525 | 0.558661 | ||||||||
\(786\) | −3.21478 | −0.114667 | ||||||||
\(787\) | 6.41641 | 0.228720 | 0.114360 | − | 0.993439i | \(-0.463518\pi\) | ||||
0.114360 | + | 0.993439i | \(0.463518\pi\) | |||||||
\(788\) | −49.9574 | −1.77966 | ||||||||
\(789\) | −31.5836 | −1.12441 | ||||||||
\(790\) | 9.14590 | 0.325396 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8.83282 | −0.313860 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5.39512 | −0.191466 | ||||||||
\(795\) | 7.36068 | 0.261056 | ||||||||
\(796\) | 13.5197 | 0.479194 | ||||||||
\(797\) | 26.9443 | 0.954415 | 0.477208 | − | 0.878791i | \(-0.341649\pi\) | ||||
0.477208 | + | 0.878791i | \(0.341649\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0000 | 0.389152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.47214 | 0.158015 | ||||||||
\(802\) | −3.72949 | −0.131693 | ||||||||
\(803\) | −32.1246 | −1.13365 | ||||||||
\(804\) | −12.4377 | −0.438644 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.1246 | 0.356403 | ||||||||
\(808\) | 13.2492 | 0.466106 | ||||||||
\(809\) | −4.41641 | −0.155273 | −0.0776363 | − | 0.996982i | \(-0.524737\pi\) | ||||
−0.0776363 | + | 0.996982i | \(0.524737\pi\) | |||||||
\(810\) | −9.39512 | −0.330111 | ||||||||
\(811\) | −38.8328 | −1.36360 | −0.681802 | − | 0.731536i | \(-0.738804\pi\) | ||||
−0.681802 | + | 0.731536i | \(0.738804\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.3475 | −0.503190 | ||||||||
\(814\) | 9.97871 | 0.349754 | ||||||||
\(815\) | −23.2918 | −0.815876 | ||||||||
\(816\) | −52.5623 | −1.84005 | ||||||||
\(817\) | 24.0000 | 0.839654 | ||||||||
\(818\) | 1.79837 | 0.0628787 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.5410 | 0.647480 | ||||||||
\(821\) | −33.7639 | −1.17837 | −0.589185 | − | 0.807998i | \(-0.700551\pi\) | ||||
−0.589185 | + | 0.807998i | \(0.700551\pi\) | |||||||
\(822\) | 3.21478 | 0.112128 | ||||||||
\(823\) | −6.12461 | −0.213491 | −0.106745 | − | 0.994286i | \(-0.534043\pi\) | ||||
−0.106745 | + | 0.994286i | \(0.534043\pi\) | |||||||
\(824\) | −15.7639 | −0.549163 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.8328 | 0.933068 | 0.466534 | − | 0.884503i | \(-0.345502\pi\) | ||||
0.466534 | + | 0.884503i | \(0.345502\pi\) | |||||||
\(828\) | 13.9574 | 0.485054 | ||||||||
\(829\) | −25.0000 | −0.868286 | −0.434143 | − | 0.900844i | \(-0.642949\pi\) | ||||
−0.434143 | + | 0.900844i | \(0.642949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 59.0689 | 2.04908 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.91796 | 0.101041 | ||||||||
\(835\) | −30.2492 | −1.04682 | ||||||||
\(836\) | 16.6869 | 0.577129 | ||||||||
\(837\) | 11.1803 | 0.386449 | ||||||||
\(838\) | 5.75078 | 0.198657 | ||||||||
\(839\) | −29.8885 | −1.03187 | −0.515934 | − | 0.856629i | \(-0.672555\pi\) | ||||
−0.515934 | + | 0.856629i | \(0.672555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 5.12461 | 0.176606 | ||||||||
\(843\) | −20.2492 | −0.697420 | ||||||||
\(844\) | −7.41641 | −0.255283 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.12461 | −0.0386650 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.63119 | 0.159036 | ||||||||
\(849\) | −31.5836 | −1.08395 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.7771 | −1.12358 | ||||||||
\(852\) | 37.0820 | 1.27041 | ||||||||
\(853\) | −28.2492 | −0.967235 | −0.483617 | − | 0.875279i | \(-0.660677\pi\) | ||||
−0.483617 | + | 0.875279i | \(0.660677\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.4164 | −0.458831 | ||||||||
\(856\) | 20.9574 | 0.716310 | ||||||||
\(857\) | 43.3607 | 1.48117 | 0.740586 | − | 0.671961i | \(-0.234548\pi\) | ||||
0.740586 | + | 0.671961i | \(0.234548\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.29180 | 0.248793 | 0.124396 | − | 0.992233i | \(-0.460301\pi\) | ||||
0.124396 | + | 0.992233i | \(0.460301\pi\) | |||||||
\(860\) | 33.1672 | 1.13099 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.10333 | −0.173820 | ||||||||
\(863\) | −6.05573 | −0.206139 | −0.103070 | − | 0.994674i | \(-0.532866\pi\) | ||||
−0.103070 | + | 0.994674i | \(0.532866\pi\) | |||||||
\(864\) | −9.27051 | −0.315389 | ||||||||
\(865\) | 23.2918 | 0.791945 | ||||||||
\(866\) | 0.986844 | 0.0335343 | ||||||||
\(867\) | 86.8328 | 2.94900 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.1246 | 1.08975 | ||||||||
\(870\) | −8.54102 | −0.289568 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 15.7639 | 0.533834 | ||||||||
\(873\) | 34.8328 | 1.17891 | ||||||||
\(874\) | 4.31308 | 0.145892 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.3951 | 1.49997 | ||||||||
\(877\) | 8.12461 | 0.274349 | 0.137174 | − | 0.990547i | \(-0.456198\pi\) | ||||
0.137174 | + | 0.990547i | \(0.456198\pi\) | |||||||
\(878\) | −6.15905 | −0.207858 | ||||||||
\(879\) | −6.58359 | −0.222059 | ||||||||
\(880\) | 21.1033 | 0.711393 | ||||||||
\(881\) | −19.3050 | −0.650400 | −0.325200 | − | 0.945645i | \(-0.605432\pi\) | ||||
−0.325200 | + | 0.945645i | \(0.605432\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −37.3607 | −1.25587 | ||||||||
\(886\) | −0.854102 | −0.0286941 | ||||||||
\(887\) | −15.7639 | −0.529301 | −0.264651 | − | 0.964344i | \(-0.585257\pi\) | ||||
−0.264651 | + | 0.964344i | \(0.585257\pi\) | |||||||
\(888\) | −28.6656 | −0.961956 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.90983 | 0.0640176 | ||||||||
\(891\) | −33.0000 | −1.10554 | ||||||||
\(892\) | −7.41641 | −0.248320 | ||||||||
\(893\) | 4.41641 | 0.147789 | ||||||||
\(894\) | 10.8541 | 0.363015 | ||||||||
\(895\) | 45.0000 | 1.50418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.95743 | −0.132061 | ||||||||
\(899\) | 22.3607 | 0.745770 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0000 | −0.366463 | ||||||||
\(902\) | −5.12461 | −0.170631 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.0000 | 0.731709 | ||||||||
\(905\) | 3.16718 | 0.105281 | ||||||||
\(906\) | 5.48027 | 0.182070 | ||||||||
\(907\) | 5.29180 | 0.175711 | 0.0878556 | − | 0.996133i | \(-0.471999\pi\) | ||||
0.0878556 | + | 0.996133i | \(0.471999\pi\) | |||||||
\(908\) | −22.1459 | −0.734937 | ||||||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.2492 | 1.53231 | 0.766153 | − | 0.642659i | \(-0.222169\pi\) | ||||
0.766153 | + | 0.642659i | \(0.222169\pi\) | |||||||
\(912\) | −21.1033 | −0.698801 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −13.0344 | −0.431141 | ||||||||
\(915\) | 15.0000 | 0.495885 | ||||||||
\(916\) | −29.8967 | −0.987814 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.38197 | 0.210636 | ||||||||
\(919\) | −20.1246 | −0.663850 | −0.331925 | − | 0.943306i | \(-0.607698\pi\) | ||||
−0.331925 | + | 0.943306i | \(0.607698\pi\) | |||||||
\(920\) | 12.3901 | 0.408489 | ||||||||
\(921\) | 16.5836 | 0.546448 | ||||||||
\(922\) | 3.95743 | 0.130331 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.16718 | 0.301252 | ||||||||
\(927\) | 21.4164 | 0.703407 | ||||||||
\(928\) | −18.5410 | −0.608639 | ||||||||
\(929\) | 47.1803 | 1.54794 | 0.773968 | − | 0.633224i | \(-0.218269\pi\) | ||||
0.773968 | + | 0.633224i | \(0.218269\pi\) | |||||||
\(930\) | −9.54915 | −0.313129 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.0213 | 0.361014 | ||||||||
\(933\) | −72.0820 | −2.35986 | ||||||||
\(934\) | −8.27051 | −0.270619 | ||||||||
\(935\) | −50.1246 | −1.63925 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.41641 | −0.0462720 | −0.0231360 | − | 0.999732i | \(-0.507365\pi\) | ||||
−0.0231360 | + | 0.999732i | \(0.507365\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −72.4853 | −2.36547 | ||||||||
\(940\) | 6.10333 | 0.199069 | ||||||||
\(941\) | −45.7639 | −1.49186 | −0.745931 | − | 0.666023i | \(-0.767995\pi\) | ||||
−0.745931 | + | 0.666023i | \(0.767995\pi\) | |||||||
\(942\) | 5.97871 | 0.194797 | ||||||||
\(943\) | 16.8328 | 0.548152 | ||||||||
\(944\) | −23.5066 | −0.765074 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.16718 | −0.298051 | ||||||||
\(947\) | 31.4721 | 1.02271 | 0.511354 | − | 0.859370i | \(-0.329144\pi\) | ||||
0.511354 | + | 0.859370i | \(0.329144\pi\) | |||||||
\(948\) | −44.3951 | −1.44189 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.41641 | 0.272921 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.7771 | 0.964574 | 0.482287 | − | 0.876013i | \(-0.339806\pi\) | ||||
0.482287 | + | 0.876013i | \(0.339806\pi\) | |||||||
\(954\) | 1.12461 | 0.0364107 | ||||||||
\(955\) | −25.0000 | −0.808981 | ||||||||
\(956\) | −13.7508 | −0.444732 | ||||||||
\(957\) | −30.0000 | −0.969762 | ||||||||
\(958\) | 11.3951 | 0.368160 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −23.5410 | −0.759783 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.4721 | −0.917502 | ||||||||
\(964\) | −16.1459 | −0.520024 | ||||||||
\(965\) | 28.4164 | 0.914757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.4164 | −1.39618 | −0.698089 | − | 0.716011i | \(-0.745966\pi\) | ||||
−0.698089 | + | 0.716011i | \(0.745966\pi\) | |||||||
\(968\) | 2.94427 | 0.0946325 | ||||||||
\(969\) | 50.1246 | 1.61023 | ||||||||
\(970\) | 14.8754 | 0.477620 | ||||||||
\(971\) | −24.7082 | −0.792924 | −0.396462 | − | 0.918051i | \(-0.629762\pi\) | ||||
−0.396462 | + | 0.918051i | \(0.629762\pi\) | |||||||
\(972\) | 33.1672 | 1.06384 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12.1591 | −0.389601 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.43769 | 0.302093 | ||||||||
\(977\) | 33.6525 | 1.07664 | 0.538319 | − | 0.842741i | \(-0.319060\pi\) | ||||
0.538319 | + | 0.842741i | \(0.319060\pi\) | |||||||
\(978\) | −8.89667 | −0.284484 | ||||||||
\(979\) | 6.70820 | 0.214395 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.4164 | −0.683773 | ||||||||
\(982\) | −13.1672 | −0.420182 | ||||||||
\(983\) | 1.47214 | 0.0469538 | 0.0234769 | − | 0.999724i | \(-0.492526\pi\) | ||||
0.0234769 | + | 0.999724i | \(0.492526\pi\) | |||||||
\(984\) | 14.7214 | 0.469300 | ||||||||
\(985\) | 60.2492 | 1.91970 | ||||||||
\(986\) | 12.7639 | 0.406486 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.1115 | 0.957489 | ||||||||
\(990\) | 5.12461 | 0.162871 | ||||||||
\(991\) | 17.2918 | 0.549292 | 0.274646 | − | 0.961545i | \(-0.411439\pi\) | ||||
0.274646 | + | 0.961545i | \(0.411439\pi\) | |||||||
\(992\) | −20.7295 | −0.658162 | ||||||||
\(993\) | 63.5410 | 2.01641 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.3050 | −0.516902 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.416408 | −0.0131878 | −0.00659388 | − | 0.999978i | \(-0.502099\pi\) | ||||
−0.00659388 | + | 0.999978i | \(0.502099\pi\) | |||||||
\(998\) | 0.159054 | 0.00503476 | ||||||||
\(999\) | −19.4721 | −0.616071 |
(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 | 8281.2.a.z.1.1 | 2 | ||
7.2 | even | 3 | 1183.2.e.d.508.2 | 4 | |||
7.4 | even | 3 | 1183.2.e.d.170.2 | 4 | |||
7.6 | odd | 2 | 8281.2.a.ba.1.1 | 2 | |||
13.12 | even | 2 | 637.2.a.f.1.2 | 2 | |||
39.38 | odd | 2 | 5733.2.a.v.1.1 | 2 | |||
91.12 | odd | 6 | 637.2.e.h.508.1 | 4 | |||
91.25 | even | 6 | 91.2.e.b.79.1 | yes | 4 | ||
91.38 | odd | 6 | 637.2.e.h.79.1 | 4 | |||
91.51 | even | 6 | 91.2.e.b.53.1 | ✓ | 4 | ||
91.90 | odd | 2 | 637.2.a.e.1.2 | 2 | |||
273.116 | odd | 6 | 819.2.j.c.352.2 | 4 | |||
273.233 | odd | 6 | 819.2.j.c.235.2 | 4 | |||
273.272 | even | 2 | 5733.2.a.w.1.1 | 2 | |||
364.51 | odd | 6 | 1456.2.r.j.417.2 | 4 | |||
364.207 | odd | 6 | 1456.2.r.j.625.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.b.53.1 | ✓ | 4 | 91.51 | even | 6 | ||
91.2.e.b.79.1 | yes | 4 | 91.25 | even | 6 | ||
637.2.a.e.1.2 | 2 | 91.90 | odd | 2 | |||
637.2.a.f.1.2 | 2 | 13.12 | even | 2 | |||
637.2.e.h.79.1 | 4 | 91.38 | odd | 6 | |||
637.2.e.h.508.1 | 4 | 91.12 | odd | 6 | |||
819.2.j.c.235.2 | 4 | 273.233 | odd | 6 | |||
819.2.j.c.352.2 | 4 | 273.116 | odd | 6 | |||
1183.2.e.d.170.2 | 4 | 7.4 | even | 3 | |||
1183.2.e.d.508.2 | 4 | 7.2 | even | 3 | |||
1456.2.r.j.417.2 | 4 | 364.51 | odd | 6 | |||
1456.2.r.j.625.2 | 4 | 364.207 | odd | 6 | |||
5733.2.a.v.1.1 | 2 | 39.38 | odd | 2 | |||
5733.2.a.w.1.1 | 2 | 273.272 | even | 2 | |||
8281.2.a.z.1.1 | 2 | 1.1 | even | 1 | trivial | ||
8281.2.a.ba.1.1 | 2 | 7.6 | odd | 2 |