Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.732051 | −0.422650 | −0.211325 | − | 0.977416i | \(-0.567778\pi\) | ||||
−0.211325 | + | 0.977416i | \(0.567778\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.732051 | −0.298858 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.732051 | −0.211325 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.732051 | 0.189015 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.46410 | −1.81031 | −0.905155 | − | 0.425081i | \(-0.860246\pi\) | ||||
−0.905155 | + | 0.425081i | \(0.860246\pi\) | |||||||
\(18\) | −2.46410 | −0.580794 | ||||||||
\(19\) | −2.73205 | −0.626775 | −0.313388 | − | 0.949625i | \(-0.601464\pi\) | ||||
−0.313388 | + | 0.949625i | \(0.601464\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0.732051 | 0.159747 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.19615 | −0.457929 | −0.228965 | − | 0.973435i | \(-0.573534\pi\) | ||||
−0.228965 | + | 0.973435i | \(0.573534\pi\) | |||||||
\(24\) | −0.732051 | −0.149429 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −9.66025 | −1.79386 | −0.896932 | − | 0.442168i | \(-0.854209\pi\) | ||||
−0.896932 | + | 0.442168i | \(0.854209\pi\) | |||||||
\(30\) | 0.732051 | 0.133654 | ||||||||
\(31\) | 7.46410 | 1.34059 | 0.670296 | − | 0.742094i | \(-0.266167\pi\) | ||||
0.670296 | + | 0.742094i | \(0.266167\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.46410 | −1.28008 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −2.46410 | −0.410684 | ||||||||
\(37\) | 0.732051 | 0.120348 | 0.0601742 | − | 0.998188i | \(-0.480834\pi\) | ||||
0.0601742 | + | 0.998188i | \(0.480834\pi\) | |||||||
\(38\) | −2.73205 | −0.443197 | ||||||||
\(39\) | 2.92820 | 0.468888 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 8.19615 | 1.28002 | 0.640012 | − | 0.768365i | \(-0.278929\pi\) | ||||
0.640012 | + | 0.768365i | \(0.278929\pi\) | |||||||
\(42\) | 0.732051 | 0.112958 | ||||||||
\(43\) | −8.92820 | −1.36154 | −0.680769 | − | 0.732498i | \(-0.738354\pi\) | ||||
−0.680769 | + | 0.732498i | \(0.738354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.46410 | 0.367327 | ||||||||
\(46\) | −2.19615 | −0.323805 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | −0.732051 | −0.105662 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 5.46410 | 0.765127 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | 8.73205 | 1.19944 | 0.599720 | − | 0.800210i | \(-0.295279\pi\) | ||||
0.599720 | + | 0.800210i | \(0.295279\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −9.66025 | −1.26845 | ||||||||
\(59\) | −12.3923 | −1.61334 | −0.806670 | − | 0.591002i | \(-0.798733\pi\) | ||||
−0.806670 | + | 0.591002i | \(0.798733\pi\) | |||||||
\(60\) | 0.732051 | 0.0945074 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 7.46410 | 0.947942 | ||||||||
\(63\) | 2.46410 | 0.310448 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8564 | −1.44849 | −0.724245 | − | 0.689542i | \(-0.757812\pi\) | ||||
−0.724245 | + | 0.689542i | \(0.757812\pi\) | |||||||
\(68\) | −7.46410 | −0.905155 | ||||||||
\(69\) | 1.60770 | 0.193544 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 14.9282 | 1.77165 | 0.885826 | − | 0.464018i | \(-0.153593\pi\) | ||||
0.885826 | + | 0.464018i | \(0.153593\pi\) | |||||||
\(72\) | −2.46410 | −0.290397 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0.732051 | 0.0850992 | ||||||||
\(75\) | −0.732051 | −0.0845299 | ||||||||
\(76\) | −2.73205 | −0.313388 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.92820 | 0.331554 | ||||||||
\(79\) | 9.66025 | 1.08686 | 0.543432 | − | 0.839453i | \(-0.317125\pi\) | ||||
0.543432 | + | 0.839453i | \(0.317125\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 8.19615 | 0.905114 | ||||||||
\(83\) | −1.07180 | −0.117645 | −0.0588225 | − | 0.998268i | \(-0.518735\pi\) | ||||
−0.0588225 | + | 0.998268i | \(0.518735\pi\) | |||||||
\(84\) | 0.732051 | 0.0798733 | ||||||||
\(85\) | 7.46410 | 0.809595 | ||||||||
\(86\) | −8.92820 | −0.962753 | ||||||||
\(87\) | 7.07180 | 0.758176 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.92820 | 0.522388 | 0.261194 | − | 0.965286i | \(-0.415884\pi\) | ||||
0.261194 | + | 0.965286i | \(0.415884\pi\) | |||||||
\(90\) | 2.46410 | 0.259739 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | −2.19615 | −0.228965 | ||||||||
\(93\) | −5.46410 | −0.566601 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 2.73205 | 0.280302 | ||||||||
\(96\) | −0.732051 | −0.0747146 | ||||||||
\(97\) | −0.732051 | −0.0743285 | −0.0371642 | − | 0.999309i | \(-0.511832\pi\) | ||||
−0.0371642 | + | 0.999309i | \(0.511832\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.00000 | −0.796030 | −0.398015 | − | 0.917379i | \(-0.630301\pi\) | ||||
−0.398015 | + | 0.917379i | \(0.630301\pi\) | |||||||
\(102\) | 5.46410 | 0.541027 | ||||||||
\(103\) | −18.3923 | −1.81225 | −0.906124 | − | 0.423013i | \(-0.860973\pi\) | ||||
−0.906124 | + | 0.423013i | \(0.860973\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | −0.732051 | −0.0714408 | ||||||||
\(106\) | 8.73205 | 0.848132 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | 13.2679 | 1.27084 | 0.635420 | − | 0.772167i | \(-0.280827\pi\) | ||||
0.635420 | + | 0.772167i | \(0.280827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.535898 | −0.0508652 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 2.00000 | 0.187317 | ||||||||
\(115\) | 2.19615 | 0.204792 | ||||||||
\(116\) | −9.66025 | −0.896932 | ||||||||
\(117\) | 9.85641 | 0.911225 | ||||||||
\(118\) | −12.3923 | −1.14080 | ||||||||
\(119\) | 7.46410 | 0.684233 | ||||||||
\(120\) | 0.732051 | 0.0668268 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 8.00000 | 0.724286 | ||||||||
\(123\) | −6.00000 | −0.541002 | ||||||||
\(124\) | 7.46410 | 0.670296 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.46410 | 0.219520 | ||||||||
\(127\) | 12.3923 | 1.09964 | 0.549820 | − | 0.835283i | \(-0.314696\pi\) | ||||
0.549820 | + | 0.835283i | \(0.314696\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.53590 | 0.575454 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | 0.196152 | 0.0171379 | 0.00856896 | − | 0.999963i | \(-0.497272\pi\) | ||||
0.00856896 | + | 0.999963i | \(0.497272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.73205 | 0.236899 | ||||||||
\(134\) | −11.8564 | −1.02424 | ||||||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | −7.46410 | −0.640041 | ||||||||
\(137\) | 19.8564 | 1.69645 | 0.848224 | − | 0.529638i | \(-0.177672\pi\) | ||||
0.848224 | + | 0.529638i | \(0.177672\pi\) | |||||||
\(138\) | 1.60770 | 0.136856 | ||||||||
\(139\) | −13.6603 | −1.15865 | −0.579324 | − | 0.815097i | \(-0.696683\pi\) | ||||
−0.579324 | + | 0.815097i | \(0.696683\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −4.39230 | −0.369899 | ||||||||
\(142\) | 14.9282 | 1.25275 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.46410 | −0.205342 | ||||||||
\(145\) | 9.66025 | 0.802240 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | −0.732051 | −0.0603785 | ||||||||
\(148\) | 0.732051 | 0.0601742 | ||||||||
\(149\) | −12.1962 | −0.999148 | −0.499574 | − | 0.866271i | \(-0.666510\pi\) | ||||
−0.499574 | + | 0.866271i | \(0.666510\pi\) | |||||||
\(150\) | −0.732051 | −0.0597717 | ||||||||
\(151\) | 12.1962 | 0.992509 | 0.496254 | − | 0.868177i | \(-0.334708\pi\) | ||||
0.496254 | + | 0.868177i | \(0.334708\pi\) | |||||||
\(152\) | −2.73205 | −0.221599 | ||||||||
\(153\) | 18.3923 | 1.48693 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.46410 | −0.599531 | ||||||||
\(156\) | 2.92820 | 0.234444 | ||||||||
\(157\) | −23.4641 | −1.87264 | −0.936320 | − | 0.351149i | \(-0.885791\pi\) | ||||
−0.936320 | + | 0.351149i | \(0.885791\pi\) | |||||||
\(158\) | 9.66025 | 0.768529 | ||||||||
\(159\) | −6.39230 | −0.506943 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 2.19615 | 0.173081 | ||||||||
\(162\) | 4.46410 | 0.350733 | ||||||||
\(163\) | −0.928203 | −0.0727025 | −0.0363512 | − | 0.999339i | \(-0.511574\pi\) | ||||
−0.0363512 | + | 0.999339i | \(0.511574\pi\) | |||||||
\(164\) | 8.19615 | 0.640012 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.07180 | −0.0831876 | ||||||||
\(167\) | −18.9282 | −1.46471 | −0.732354 | − | 0.680924i | \(-0.761578\pi\) | ||||
−0.732354 | + | 0.680924i | \(0.761578\pi\) | |||||||
\(168\) | 0.732051 | 0.0564789 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 7.46410 | 0.572470 | ||||||||
\(171\) | 6.73205 | 0.514813 | ||||||||
\(172\) | −8.92820 | −0.680769 | ||||||||
\(173\) | 8.92820 | 0.678799 | 0.339399 | − | 0.940642i | \(-0.389776\pi\) | ||||
0.339399 | + | 0.940642i | \(0.389776\pi\) | |||||||
\(174\) | 7.07180 | 0.536112 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.07180 | 0.681878 | ||||||||
\(178\) | 4.92820 | 0.369384 | ||||||||
\(179\) | −14.3923 | −1.07573 | −0.537866 | − | 0.843031i | \(-0.680769\pi\) | ||||
−0.537866 | + | 0.843031i | \(0.680769\pi\) | |||||||
\(180\) | 2.46410 | 0.183663 | ||||||||
\(181\) | 8.92820 | 0.663628 | 0.331814 | − | 0.943345i | \(-0.392339\pi\) | ||||
0.331814 | + | 0.943345i | \(0.392339\pi\) | |||||||
\(182\) | 4.00000 | 0.296500 | ||||||||
\(183\) | −5.85641 | −0.432918 | ||||||||
\(184\) | −2.19615 | −0.161903 | ||||||||
\(185\) | −0.732051 | −0.0538214 | ||||||||
\(186\) | −5.46410 | −0.400647 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | −4.00000 | −0.290957 | ||||||||
\(190\) | 2.73205 | 0.198204 | ||||||||
\(191\) | 0.392305 | 0.0283862 | 0.0141931 | − | 0.999899i | \(-0.495482\pi\) | ||||
0.0141931 | + | 0.999899i | \(0.495482\pi\) | |||||||
\(192\) | −0.732051 | −0.0528312 | ||||||||
\(193\) | 16.0000 | 1.15171 | 0.575853 | − | 0.817554i | \(-0.304670\pi\) | ||||
0.575853 | + | 0.817554i | \(0.304670\pi\) | |||||||
\(194\) | −0.732051 | −0.0525582 | ||||||||
\(195\) | −2.92820 | −0.209693 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −3.46410 | −0.246807 | −0.123404 | − | 0.992357i | \(-0.539381\pi\) | ||||
−0.123404 | + | 0.992357i | \(0.539381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.8564 | 1.83291 | 0.916456 | − | 0.400135i | \(-0.131037\pi\) | ||||
0.916456 | + | 0.400135i | \(0.131037\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 8.67949 | 0.612204 | ||||||||
\(202\) | −8.00000 | −0.562878 | ||||||||
\(203\) | 9.66025 | 0.678017 | ||||||||
\(204\) | 5.46410 | 0.382564 | ||||||||
\(205\) | −8.19615 | −0.572444 | ||||||||
\(206\) | −18.3923 | −1.28145 | ||||||||
\(207\) | 5.41154 | 0.376128 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.732051 | −0.0505163 | ||||||||
\(211\) | −13.8564 | −0.953914 | −0.476957 | − | 0.878927i | \(-0.658260\pi\) | ||||
−0.476957 | + | 0.878927i | \(0.658260\pi\) | |||||||
\(212\) | 8.73205 | 0.599720 | ||||||||
\(213\) | −10.9282 | −0.748788 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 8.92820 | 0.608898 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | −7.46410 | −0.506696 | ||||||||
\(218\) | 13.2679 | 0.898619 | ||||||||
\(219\) | −4.39230 | −0.296804 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.8564 | 2.00836 | ||||||||
\(222\) | −0.535898 | −0.0359671 | ||||||||
\(223\) | −4.53590 | −0.303746 | −0.151873 | − | 0.988400i | \(-0.548531\pi\) | ||||
−0.151873 | + | 0.988400i | \(0.548531\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 18.0000 | 1.19734 | ||||||||
\(227\) | −11.3205 | −0.751369 | −0.375684 | − | 0.926748i | \(-0.622592\pi\) | ||||
−0.375684 | + | 0.926748i | \(0.622592\pi\) | |||||||
\(228\) | 2.00000 | 0.132453 | ||||||||
\(229\) | −11.3205 | −0.748080 | −0.374040 | − | 0.927413i | \(-0.622028\pi\) | ||||
−0.374040 | + | 0.927413i | \(0.622028\pi\) | |||||||
\(230\) | 2.19615 | 0.144810 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.66025 | −0.634227 | ||||||||
\(233\) | 3.85641 | 0.252642 | 0.126321 | − | 0.991989i | \(-0.459683\pi\) | ||||
0.126321 | + | 0.991989i | \(0.459683\pi\) | |||||||
\(234\) | 9.85641 | 0.644333 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | −12.3923 | −0.806670 | ||||||||
\(237\) | −7.07180 | −0.459363 | ||||||||
\(238\) | 7.46410 | 0.483826 | ||||||||
\(239\) | 18.0526 | 1.16772 | 0.583861 | − | 0.811853i | \(-0.301541\pi\) | ||||
0.583861 | + | 0.811853i | \(0.301541\pi\) | |||||||
\(240\) | 0.732051 | 0.0472537 | ||||||||
\(241\) | −28.9808 | −1.86681 | −0.933407 | − | 0.358818i | \(-0.883180\pi\) | ||||
−0.933407 | + | 0.358818i | \(0.883180\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2679 | −0.979439 | ||||||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 10.9282 | 0.695345 | ||||||||
\(248\) | 7.46410 | 0.473971 | ||||||||
\(249\) | 0.784610 | 0.0497226 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 16.7846 | 1.05944 | 0.529718 | − | 0.848174i | \(-0.322298\pi\) | ||||
0.529718 | + | 0.848174i | \(0.322298\pi\) | |||||||
\(252\) | 2.46410 | 0.155224 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.3923 | 0.777562 | ||||||||
\(255\) | −5.46410 | −0.342175 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.1962 | −1.13504 | −0.567522 | − | 0.823358i | \(-0.692098\pi\) | ||||
−0.567522 | + | 0.823358i | \(0.692098\pi\) | |||||||
\(258\) | 6.53590 | 0.406907 | ||||||||
\(259\) | −0.732051 | −0.0454874 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 23.8038 | 1.47342 | ||||||||
\(262\) | 0.196152 | 0.0121183 | ||||||||
\(263\) | −7.60770 | −0.469111 | −0.234555 | − | 0.972103i | \(-0.575363\pi\) | ||||
−0.234555 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.73205 | −0.536406 | ||||||||
\(266\) | 2.73205 | 0.167513 | ||||||||
\(267\) | −3.60770 | −0.220787 | ||||||||
\(268\) | −11.8564 | −0.724245 | ||||||||
\(269\) | 16.3923 | 0.999456 | 0.499728 | − | 0.866182i | \(-0.333433\pi\) | ||||
0.499728 | + | 0.866182i | \(0.333433\pi\) | |||||||
\(270\) | −4.00000 | −0.243432 | ||||||||
\(271\) | −11.6077 | −0.705117 | −0.352559 | − | 0.935790i | \(-0.614688\pi\) | ||||
−0.352559 | + | 0.935790i | \(0.614688\pi\) | |||||||
\(272\) | −7.46410 | −0.452578 | ||||||||
\(273\) | −2.92820 | −0.177223 | ||||||||
\(274\) | 19.8564 | 1.19957 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.60770 | 0.0967719 | ||||||||
\(277\) | −17.3205 | −1.04069 | −0.520344 | − | 0.853957i | \(-0.674196\pi\) | ||||
−0.520344 | + | 0.853957i | \(0.674196\pi\) | |||||||
\(278\) | −13.6603 | −0.819288 | ||||||||
\(279\) | −18.3923 | −1.10112 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −11.3205 | −0.675325 | −0.337662 | − | 0.941267i | \(-0.609636\pi\) | ||||
−0.337662 | + | 0.941267i | \(0.609636\pi\) | |||||||
\(282\) | −4.39230 | −0.261558 | ||||||||
\(283\) | 2.53590 | 0.150744 | 0.0753718 | − | 0.997156i | \(-0.475986\pi\) | ||||
0.0753718 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(284\) | 14.9282 | 0.885826 | ||||||||
\(285\) | −2.00000 | −0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.19615 | −0.483804 | ||||||||
\(288\) | −2.46410 | −0.145199 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | 9.66025 | 0.567270 | ||||||||
\(291\) | 0.535898 | 0.0314149 | ||||||||
\(292\) | 6.00000 | 0.351123 | ||||||||
\(293\) | 27.7128 | 1.61900 | 0.809500 | − | 0.587120i | \(-0.199738\pi\) | ||||
0.809500 | + | 0.587120i | \(0.199738\pi\) | |||||||
\(294\) | −0.732051 | −0.0426941 | ||||||||
\(295\) | 12.3923 | 0.721508 | ||||||||
\(296\) | 0.732051 | 0.0425496 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.1962 | −0.706504 | ||||||||
\(299\) | 8.78461 | 0.508027 | ||||||||
\(300\) | −0.732051 | −0.0422650 | ||||||||
\(301\) | 8.92820 | 0.514613 | ||||||||
\(302\) | 12.1962 | 0.701810 | ||||||||
\(303\) | 5.85641 | 0.336442 | ||||||||
\(304\) | −2.73205 | −0.156694 | ||||||||
\(305\) | −8.00000 | −0.458079 | ||||||||
\(306\) | 18.3923 | 1.05142 | ||||||||
\(307\) | −6.53590 | −0.373023 | −0.186512 | − | 0.982453i | \(-0.559718\pi\) | ||||
−0.186512 | + | 0.982453i | \(0.559718\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4641 | 0.765946 | ||||||||
\(310\) | −7.46410 | −0.423932 | ||||||||
\(311\) | −17.3205 | −0.982156 | −0.491078 | − | 0.871116i | \(-0.663397\pi\) | ||||
−0.491078 | + | 0.871116i | \(0.663397\pi\) | |||||||
\(312\) | 2.92820 | 0.165777 | ||||||||
\(313\) | 0.732051 | 0.0413780 | 0.0206890 | − | 0.999786i | \(-0.493414\pi\) | ||||
0.0206890 | + | 0.999786i | \(0.493414\pi\) | |||||||
\(314\) | −23.4641 | −1.32416 | ||||||||
\(315\) | −2.46410 | −0.138836 | ||||||||
\(316\) | 9.66025 | 0.543432 | ||||||||
\(317\) | 26.5885 | 1.49336 | 0.746678 | − | 0.665185i | \(-0.231647\pi\) | ||||
0.746678 | + | 0.665185i | \(0.231647\pi\) | |||||||
\(318\) | −6.39230 | −0.358463 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −1.46410 | −0.0817182 | ||||||||
\(322\) | 2.19615 | 0.122387 | ||||||||
\(323\) | 20.3923 | 1.13466 | ||||||||
\(324\) | 4.46410 | 0.248006 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | −0.928203 | −0.0514084 | ||||||||
\(327\) | −9.71281 | −0.537120 | ||||||||
\(328\) | 8.19615 | 0.452557 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3923 | 1.45065 | 0.725326 | − | 0.688405i | \(-0.241689\pi\) | ||||
0.725326 | + | 0.688405i | \(0.241689\pi\) | |||||||
\(332\) | −1.07180 | −0.0588225 | ||||||||
\(333\) | −1.80385 | −0.0988502 | ||||||||
\(334\) | −18.9282 | −1.03571 | ||||||||
\(335\) | 11.8564 | 0.647785 | ||||||||
\(336\) | 0.732051 | 0.0399366 | ||||||||
\(337\) | −0.143594 | −0.00782204 | −0.00391102 | − | 0.999992i | \(-0.501245\pi\) | ||||
−0.00391102 | + | 0.999992i | \(0.501245\pi\) | |||||||
\(338\) | 3.00000 | 0.163178 | ||||||||
\(339\) | −13.1769 | −0.715672 | ||||||||
\(340\) | 7.46410 | 0.404798 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.73205 | 0.364028 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.92820 | −0.481376 | ||||||||
\(345\) | −1.60770 | −0.0865554 | ||||||||
\(346\) | 8.92820 | 0.479983 | ||||||||
\(347\) | 8.92820 | 0.479291 | 0.239646 | − | 0.970860i | \(-0.422969\pi\) | ||||
0.239646 | + | 0.970860i | \(0.422969\pi\) | |||||||
\(348\) | 7.07180 | 0.379088 | ||||||||
\(349\) | 1.46410 | 0.0783716 | 0.0391858 | − | 0.999232i | \(-0.487524\pi\) | ||||
0.0391858 | + | 0.999232i | \(0.487524\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −16.0000 | −0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.9808 | −1.43604 | −0.718021 | − | 0.696022i | \(-0.754952\pi\) | ||||
−0.718021 | + | 0.696022i | \(0.754952\pi\) | |||||||
\(354\) | 9.07180 | 0.482161 | ||||||||
\(355\) | −14.9282 | −0.792307 | ||||||||
\(356\) | 4.92820 | 0.261194 | ||||||||
\(357\) | −5.46410 | −0.289191 | ||||||||
\(358\) | −14.3923 | −0.760657 | ||||||||
\(359\) | 34.4449 | 1.81793 | 0.908965 | − | 0.416872i | \(-0.136874\pi\) | ||||
0.908965 | + | 0.416872i | \(0.136874\pi\) | |||||||
\(360\) | 2.46410 | 0.129870 | ||||||||
\(361\) | −11.5359 | −0.607153 | ||||||||
\(362\) | 8.92820 | 0.469256 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | −5.85641 | −0.306119 | ||||||||
\(367\) | 6.39230 | 0.333676 | 0.166838 | − | 0.985984i | \(-0.446644\pi\) | ||||
0.166838 | + | 0.985984i | \(0.446644\pi\) | |||||||
\(368\) | −2.19615 | −0.114482 | ||||||||
\(369\) | −20.1962 | −1.05137 | ||||||||
\(370\) | −0.732051 | −0.0380575 | ||||||||
\(371\) | −8.73205 | −0.453345 | ||||||||
\(372\) | −5.46410 | −0.283300 | ||||||||
\(373\) | 1.32051 | 0.0683733 | 0.0341867 | − | 0.999415i | \(-0.489116\pi\) | ||||
0.0341867 | + | 0.999415i | \(0.489116\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.732051 | 0.0378029 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 38.6410 | 1.99011 | ||||||||
\(378\) | −4.00000 | −0.205738 | ||||||||
\(379\) | 2.14359 | 0.110109 | 0.0550545 | − | 0.998483i | \(-0.482467\pi\) | ||||
0.0550545 | + | 0.998483i | \(0.482467\pi\) | |||||||
\(380\) | 2.73205 | 0.140151 | ||||||||
\(381\) | −9.07180 | −0.464762 | ||||||||
\(382\) | 0.392305 | 0.0200721 | ||||||||
\(383\) | −3.46410 | −0.177007 | −0.0885037 | − | 0.996076i | \(-0.528208\pi\) | ||||
−0.0885037 | + | 0.996076i | \(0.528208\pi\) | |||||||
\(384\) | −0.732051 | −0.0373573 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | 22.0000 | 1.11832 | ||||||||
\(388\) | −0.732051 | −0.0371642 | ||||||||
\(389\) | 5.60770 | 0.284321 | 0.142161 | − | 0.989844i | \(-0.454595\pi\) | ||||
0.142161 | + | 0.989844i | \(0.454595\pi\) | |||||||
\(390\) | −2.92820 | −0.148275 | ||||||||
\(391\) | 16.3923 | 0.828994 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −0.143594 | −0.00724334 | ||||||||
\(394\) | −3.46410 | −0.174519 | ||||||||
\(395\) | −9.66025 | −0.486060 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.535898 | 0.0268960 | 0.0134480 | − | 0.999910i | \(-0.495719\pi\) | ||||
0.0134480 | + | 0.999910i | \(0.495719\pi\) | |||||||
\(398\) | 25.8564 | 1.29606 | ||||||||
\(399\) | −2.00000 | −0.100125 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −0.392305 | −0.0195908 | −0.00979538 | − | 0.999952i | \(-0.503118\pi\) | ||||
−0.00979538 | + | 0.999952i | \(0.503118\pi\) | |||||||
\(402\) | 8.67949 | 0.432894 | ||||||||
\(403\) | −29.8564 | −1.48725 | ||||||||
\(404\) | −8.00000 | −0.398015 | ||||||||
\(405\) | −4.46410 | −0.221823 | ||||||||
\(406\) | 9.66025 | 0.479430 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.46410 | 0.270513 | ||||||||
\(409\) | −19.8038 | −0.979237 | −0.489619 | − | 0.871937i | \(-0.662864\pi\) | ||||
−0.489619 | + | 0.871937i | \(0.662864\pi\) | |||||||
\(410\) | −8.19615 | −0.404779 | ||||||||
\(411\) | −14.5359 | −0.717003 | ||||||||
\(412\) | −18.3923 | −0.906124 | ||||||||
\(413\) | 12.3923 | 0.609785 | ||||||||
\(414\) | 5.41154 | 0.265963 | ||||||||
\(415\) | 1.07180 | 0.0526124 | ||||||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | 10.0000 | 0.489702 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1436 | 0.495547 | 0.247773 | − | 0.968818i | \(-0.420301\pi\) | ||||
0.247773 | + | 0.968818i | \(0.420301\pi\) | |||||||
\(420\) | −0.732051 | −0.0357204 | ||||||||
\(421\) | −24.2487 | −1.18181 | −0.590905 | − | 0.806741i | \(-0.701229\pi\) | ||||
−0.590905 | + | 0.806741i | \(0.701229\pi\) | |||||||
\(422\) | −13.8564 | −0.674519 | ||||||||
\(423\) | −14.7846 | −0.718852 | ||||||||
\(424\) | 8.73205 | 0.424066 | ||||||||
\(425\) | −7.46410 | −0.362062 | ||||||||
\(426\) | −10.9282 | −0.529473 | ||||||||
\(427\) | −8.00000 | −0.387147 | ||||||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.92820 | 0.430556 | ||||||||
\(431\) | 13.2679 | 0.639095 | 0.319547 | − | 0.947570i | \(-0.396469\pi\) | ||||
0.319547 | + | 0.947570i | \(0.396469\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | −32.7321 | −1.57300 | −0.786501 | − | 0.617589i | \(-0.788110\pi\) | ||||
−0.786501 | + | 0.617589i | \(0.788110\pi\) | |||||||
\(434\) | −7.46410 | −0.358288 | ||||||||
\(435\) | −7.07180 | −0.339067 | ||||||||
\(436\) | 13.2679 | 0.635420 | ||||||||
\(437\) | 6.00000 | 0.287019 | ||||||||
\(438\) | −4.39230 | −0.209872 | ||||||||
\(439\) | 22.5359 | 1.07558 | 0.537790 | − | 0.843079i | \(-0.319259\pi\) | ||||
0.537790 | + | 0.843079i | \(0.319259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46410 | −0.117338 | ||||||||
\(442\) | 29.8564 | 1.42012 | ||||||||
\(443\) | −15.0718 | −0.716083 | −0.358041 | − | 0.933706i | \(-0.616555\pi\) | ||||
−0.358041 | + | 0.933706i | \(0.616555\pi\) | |||||||
\(444\) | −0.535898 | −0.0254326 | ||||||||
\(445\) | −4.92820 | −0.233619 | ||||||||
\(446\) | −4.53590 | −0.214781 | ||||||||
\(447\) | 8.92820 | 0.422290 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 38.2487 | 1.80507 | 0.902534 | − | 0.430618i | \(-0.141704\pi\) | ||||
0.902534 | + | 0.430618i | \(0.141704\pi\) | |||||||
\(450\) | −2.46410 | −0.116159 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 18.0000 | 0.846649 | ||||||||
\(453\) | −8.92820 | −0.419484 | ||||||||
\(454\) | −11.3205 | −0.531298 | ||||||||
\(455\) | −4.00000 | −0.187523 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | −11.8564 | −0.554619 | −0.277310 | − | 0.960781i | \(-0.589443\pi\) | ||||
−0.277310 | + | 0.960781i | \(0.589443\pi\) | |||||||
\(458\) | −11.3205 | −0.528973 | ||||||||
\(459\) | −29.8564 | −1.39358 | ||||||||
\(460\) | 2.19615 | 0.102396 | ||||||||
\(461\) | 39.3205 | 1.83134 | 0.915669 | − | 0.401932i | \(-0.131661\pi\) | ||||
0.915669 | + | 0.401932i | \(0.131661\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.5885 | 1.79336 | 0.896679 | − | 0.442682i | \(-0.145973\pi\) | ||||
0.896679 | + | 0.442682i | \(0.145973\pi\) | |||||||
\(464\) | −9.66025 | −0.448466 | ||||||||
\(465\) | 5.46410 | 0.253392 | ||||||||
\(466\) | 3.85641 | 0.178645 | ||||||||
\(467\) | 9.41154 | 0.435514 | 0.217757 | − | 0.976003i | \(-0.430126\pi\) | ||||
0.217757 | + | 0.976003i | \(0.430126\pi\) | |||||||
\(468\) | 9.85641 | 0.455613 | ||||||||
\(469\) | 11.8564 | 0.547478 | ||||||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | 17.1769 | 0.791470 | ||||||||
\(472\) | −12.3923 | −0.570402 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −7.07180 | −0.324818 | ||||||||
\(475\) | −2.73205 | −0.125355 | ||||||||
\(476\) | 7.46410 | 0.342117 | ||||||||
\(477\) | −21.5167 | −0.985180 | ||||||||
\(478\) | 18.0526 | 0.825705 | ||||||||
\(479\) | −35.7128 | −1.63176 | −0.815880 | − | 0.578221i | \(-0.803747\pi\) | ||||
−0.815880 | + | 0.578221i | \(0.803747\pi\) | |||||||
\(480\) | 0.732051 | 0.0334134 | ||||||||
\(481\) | −2.92820 | −0.133515 | ||||||||
\(482\) | −28.9808 | −1.32004 | ||||||||
\(483\) | −1.60770 | −0.0731527 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.732051 | 0.0332407 | ||||||||
\(486\) | −15.2679 | −0.692568 | ||||||||
\(487\) | 8.05256 | 0.364896 | 0.182448 | − | 0.983215i | \(-0.441598\pi\) | ||||
0.182448 | + | 0.983215i | \(0.441598\pi\) | |||||||
\(488\) | 8.00000 | 0.362143 | ||||||||
\(489\) | 0.679492 | 0.0307277 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 22.9282 | 1.03474 | 0.517368 | − | 0.855763i | \(-0.326912\pi\) | ||||
0.517368 | + | 0.855763i | \(0.326912\pi\) | |||||||
\(492\) | −6.00000 | −0.270501 | ||||||||
\(493\) | 72.1051 | 3.24745 | ||||||||
\(494\) | 10.9282 | 0.491683 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.46410 | 0.335148 | ||||||||
\(497\) | −14.9282 | −0.669621 | ||||||||
\(498\) | 0.784610 | 0.0351592 | ||||||||
\(499\) | −1.60770 | −0.0719703 | −0.0359852 | − | 0.999352i | \(-0.511457\pi\) | ||||
−0.0359852 | + | 0.999352i | \(0.511457\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 13.8564 | 0.619059 | ||||||||
\(502\) | 16.7846 | 0.749134 | ||||||||
\(503\) | 37.8564 | 1.68793 | 0.843967 | − | 0.536395i | \(-0.180214\pi\) | ||||
0.843967 | + | 0.536395i | \(0.180214\pi\) | |||||||
\(504\) | 2.46410 | 0.109760 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.19615 | −0.0975346 | ||||||||
\(508\) | 12.3923 | 0.549820 | ||||||||
\(509\) | 12.9282 | 0.573033 | 0.286516 | − | 0.958075i | \(-0.407503\pi\) | ||||
0.286516 | + | 0.958075i | \(0.407503\pi\) | |||||||
\(510\) | −5.46410 | −0.241954 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −10.9282 | −0.482492 | ||||||||
\(514\) | −18.1962 | −0.802598 | ||||||||
\(515\) | 18.3923 | 0.810462 | ||||||||
\(516\) | 6.53590 | 0.287727 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.732051 | −0.0321645 | ||||||||
\(519\) | −6.53590 | −0.286894 | ||||||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | 24.2487 | 1.06236 | 0.531178 | − | 0.847260i | \(-0.321750\pi\) | ||||
0.531178 | + | 0.847260i | \(0.321750\pi\) | |||||||
\(522\) | 23.8038 | 1.04187 | ||||||||
\(523\) | 21.4641 | 0.938560 | 0.469280 | − | 0.883050i | \(-0.344514\pi\) | ||||
0.469280 | + | 0.883050i | \(0.344514\pi\) | |||||||
\(524\) | 0.196152 | 0.00856896 | ||||||||
\(525\) | 0.732051 | 0.0319493 | ||||||||
\(526\) | −7.60770 | −0.331711 | ||||||||
\(527\) | −55.7128 | −2.42689 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | −8.73205 | −0.379296 | ||||||||
\(531\) | 30.5359 | 1.32515 | ||||||||
\(532\) | 2.73205 | 0.118449 | ||||||||
\(533\) | −32.7846 | −1.42006 | ||||||||
\(534\) | −3.60770 | −0.156120 | ||||||||
\(535\) | −2.00000 | −0.0864675 | ||||||||
\(536\) | −11.8564 | −0.512119 | ||||||||
\(537\) | 10.5359 | 0.454658 | ||||||||
\(538\) | 16.3923 | 0.706722 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | 9.26795 | 0.398460 | 0.199230 | − | 0.979953i | \(-0.436156\pi\) | ||||
0.199230 | + | 0.979953i | \(0.436156\pi\) | |||||||
\(542\) | −11.6077 | −0.498593 | ||||||||
\(543\) | −6.53590 | −0.280482 | ||||||||
\(544\) | −7.46410 | −0.320021 | ||||||||
\(545\) | −13.2679 | −0.568337 | ||||||||
\(546\) | −2.92820 | −0.125316 | ||||||||
\(547\) | 31.7128 | 1.35594 | 0.677971 | − | 0.735089i | \(-0.262859\pi\) | ||||
0.677971 | + | 0.735089i | \(0.262859\pi\) | |||||||
\(548\) | 19.8564 | 0.848224 | ||||||||
\(549\) | −19.7128 | −0.841322 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.3923 | 1.12435 | ||||||||
\(552\) | 1.60770 | 0.0684280 | ||||||||
\(553\) | −9.66025 | −0.410796 | ||||||||
\(554\) | −17.3205 | −0.735878 | ||||||||
\(555\) | 0.535898 | 0.0227476 | ||||||||
\(556\) | −13.6603 | −0.579324 | ||||||||
\(557\) | −16.9282 | −0.717271 | −0.358635 | − | 0.933478i | \(-0.616758\pi\) | ||||
−0.358635 | + | 0.933478i | \(0.616758\pi\) | |||||||
\(558\) | −18.3923 | −0.778608 | ||||||||
\(559\) | 35.7128 | 1.51049 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.3205 | −0.477527 | ||||||||
\(563\) | 15.7128 | 0.662216 | 0.331108 | − | 0.943593i | \(-0.392578\pi\) | ||||
0.331108 | + | 0.943593i | \(0.392578\pi\) | |||||||
\(564\) | −4.39230 | −0.184949 | ||||||||
\(565\) | −18.0000 | −0.757266 | ||||||||
\(566\) | 2.53590 | 0.106592 | ||||||||
\(567\) | −4.46410 | −0.187475 | ||||||||
\(568\) | 14.9282 | 0.626373 | ||||||||
\(569\) | 6.14359 | 0.257553 | 0.128776 | − | 0.991674i | \(-0.458895\pi\) | ||||
0.128776 | + | 0.991674i | \(0.458895\pi\) | |||||||
\(570\) | −2.00000 | −0.0837708 | ||||||||
\(571\) | 15.3205 | 0.641143 | 0.320572 | − | 0.947224i | \(-0.396125\pi\) | ||||
0.320572 | + | 0.947224i | \(0.396125\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.287187 | −0.0119974 | ||||||||
\(574\) | −8.19615 | −0.342101 | ||||||||
\(575\) | −2.19615 | −0.0915859 | ||||||||
\(576\) | −2.46410 | −0.102671 | ||||||||
\(577\) | 4.73205 | 0.196998 | 0.0984989 | − | 0.995137i | \(-0.468596\pi\) | ||||
0.0984989 | + | 0.995137i | \(0.468596\pi\) | |||||||
\(578\) | 38.7128 | 1.61024 | ||||||||
\(579\) | −11.7128 | −0.486768 | ||||||||
\(580\) | 9.66025 | 0.401120 | ||||||||
\(581\) | 1.07180 | 0.0444656 | ||||||||
\(582\) | 0.535898 | 0.0222137 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | −9.85641 | −0.407512 | ||||||||
\(586\) | 27.7128 | 1.14481 | ||||||||
\(587\) | 23.2679 | 0.960371 | 0.480186 | − | 0.877167i | \(-0.340569\pi\) | ||||
0.480186 | + | 0.877167i | \(0.340569\pi\) | |||||||
\(588\) | −0.732051 | −0.0301893 | ||||||||
\(589\) | −20.3923 | −0.840250 | ||||||||
\(590\) | 12.3923 | 0.510183 | ||||||||
\(591\) | 2.53590 | 0.104313 | ||||||||
\(592\) | 0.732051 | 0.0300871 | ||||||||
\(593\) | −40.6410 | −1.66893 | −0.834463 | − | 0.551064i | \(-0.814222\pi\) | ||||
−0.834463 | + | 0.551064i | \(0.814222\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.46410 | −0.305998 | ||||||||
\(596\) | −12.1962 | −0.499574 | ||||||||
\(597\) | −18.9282 | −0.774680 | ||||||||
\(598\) | 8.78461 | 0.359229 | ||||||||
\(599\) | −33.0718 | −1.35128 | −0.675638 | − | 0.737233i | \(-0.736132\pi\) | ||||
−0.675638 | + | 0.737233i | \(0.736132\pi\) | |||||||
\(600\) | −0.732051 | −0.0298858 | ||||||||
\(601\) | −27.1244 | −1.10643 | −0.553213 | − | 0.833040i | \(-0.686598\pi\) | ||||
−0.553213 | + | 0.833040i | \(0.686598\pi\) | |||||||
\(602\) | 8.92820 | 0.363886 | ||||||||
\(603\) | 29.2154 | 1.18974 | ||||||||
\(604\) | 12.1962 | 0.496254 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.85641 | 0.237900 | ||||||||
\(607\) | −10.0000 | −0.405887 | −0.202944 | − | 0.979190i | \(-0.565051\pi\) | ||||
−0.202944 | + | 0.979190i | \(0.565051\pi\) | |||||||
\(608\) | −2.73205 | −0.110799 | ||||||||
\(609\) | −7.07180 | −0.286564 | ||||||||
\(610\) | −8.00000 | −0.323911 | ||||||||
\(611\) | −24.0000 | −0.970936 | ||||||||
\(612\) | 18.3923 | 0.743465 | ||||||||
\(613\) | 13.7128 | 0.553855 | 0.276928 | − | 0.960891i | \(-0.410684\pi\) | ||||
0.276928 | + | 0.960891i | \(0.410684\pi\) | |||||||
\(614\) | −6.53590 | −0.263767 | ||||||||
\(615\) | 6.00000 | 0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.6077 | 0.708859 | 0.354430 | − | 0.935083i | \(-0.384675\pi\) | ||||
0.354430 | + | 0.935083i | \(0.384675\pi\) | |||||||
\(618\) | 13.4641 | 0.541606 | ||||||||
\(619\) | 18.9282 | 0.760789 | 0.380394 | − | 0.924824i | \(-0.375788\pi\) | ||||
0.380394 | + | 0.924824i | \(0.375788\pi\) | |||||||
\(620\) | −7.46410 | −0.299766 | ||||||||
\(621\) | −8.78461 | −0.352514 | ||||||||
\(622\) | −17.3205 | −0.694489 | ||||||||
\(623\) | −4.92820 | −0.197444 | ||||||||
\(624\) | 2.92820 | 0.117222 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.732051 | 0.0292586 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.4641 | −0.936320 | ||||||||
\(629\) | −5.46410 | −0.217868 | ||||||||
\(630\) | −2.46410 | −0.0981722 | ||||||||
\(631\) | 1.85641 | 0.0739024 | 0.0369512 | − | 0.999317i | \(-0.488235\pi\) | ||||
0.0369512 | + | 0.999317i | \(0.488235\pi\) | |||||||
\(632\) | 9.66025 | 0.384264 | ||||||||
\(633\) | 10.1436 | 0.403172 | ||||||||
\(634\) | 26.5885 | 1.05596 | ||||||||
\(635\) | −12.3923 | −0.491774 | ||||||||
\(636\) | −6.39230 | −0.253471 | ||||||||
\(637\) | −4.00000 | −0.158486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.7846 | −1.45518 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 3.85641 | 0.152319 | 0.0761594 | − | 0.997096i | \(-0.475734\pi\) | ||||
0.0761594 | + | 0.997096i | \(0.475734\pi\) | |||||||
\(642\) | −1.46410 | −0.0577835 | ||||||||
\(643\) | −6.19615 | −0.244352 | −0.122176 | − | 0.992508i | \(-0.538987\pi\) | ||||
−0.122176 | + | 0.992508i | \(0.538987\pi\) | |||||||
\(644\) | 2.19615 | 0.0865405 | ||||||||
\(645\) | −6.53590 | −0.257351 | ||||||||
\(646\) | 20.3923 | 0.802325 | ||||||||
\(647\) | −26.3923 | −1.03759 | −0.518794 | − | 0.854899i | \(-0.673619\pi\) | ||||
−0.518794 | + | 0.854899i | \(0.673619\pi\) | |||||||
\(648\) | 4.46410 | 0.175366 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | −0.156893 | ||||||||
\(651\) | 5.46410 | 0.214155 | ||||||||
\(652\) | −0.928203 | −0.0363512 | ||||||||
\(653\) | −31.2679 | −1.22361 | −0.611805 | − | 0.791009i | \(-0.709556\pi\) | ||||
−0.611805 | + | 0.791009i | \(0.709556\pi\) | |||||||
\(654\) | −9.71281 | −0.379801 | ||||||||
\(655\) | −0.196152 | −0.00766431 | ||||||||
\(656\) | 8.19615 | 0.320006 | ||||||||
\(657\) | −14.7846 | −0.576803 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | −19.6077 | −0.763807 | −0.381904 | − | 0.924202i | \(-0.624731\pi\) | ||||
−0.381904 | + | 0.924202i | \(0.624731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | 26.3923 | 1.02577 | ||||||||
\(663\) | −21.8564 | −0.848832 | ||||||||
\(664\) | −1.07180 | −0.0415938 | ||||||||
\(665\) | −2.73205 | −0.105944 | ||||||||
\(666\) | −1.80385 | −0.0698977 | ||||||||
\(667\) | 21.2154 | 0.821463 | ||||||||
\(668\) | −18.9282 | −0.732354 | ||||||||
\(669\) | 3.32051 | 0.128378 | ||||||||
\(670\) | 11.8564 | 0.458053 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.732051 | 0.0282395 | ||||||||
\(673\) | 16.1436 | 0.622290 | 0.311145 | − | 0.950362i | \(-0.399288\pi\) | ||||
0.311145 | + | 0.950362i | \(0.399288\pi\) | |||||||
\(674\) | −0.143594 | −0.00553102 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −0.928203 | −0.0356737 | −0.0178369 | − | 0.999841i | \(-0.505678\pi\) | ||||
−0.0178369 | + | 0.999841i | \(0.505678\pi\) | |||||||
\(678\) | −13.1769 | −0.506056 | ||||||||
\(679\) | 0.732051 | 0.0280935 | ||||||||
\(680\) | 7.46410 | 0.286235 | ||||||||
\(681\) | 8.28719 | 0.317566 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.3923 | 0.856818 | 0.428409 | − | 0.903585i | \(-0.359074\pi\) | ||||
0.428409 | + | 0.903585i | \(0.359074\pi\) | |||||||
\(684\) | 6.73205 | 0.257406 | ||||||||
\(685\) | −19.8564 | −0.758674 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 8.28719 | 0.316176 | ||||||||
\(688\) | −8.92820 | −0.340385 | ||||||||
\(689\) | −34.9282 | −1.33066 | ||||||||
\(690\) | −1.60770 | −0.0612039 | ||||||||
\(691\) | −1.07180 | −0.0407731 | −0.0203865 | − | 0.999792i | \(-0.506490\pi\) | ||||
−0.0203865 | + | 0.999792i | \(0.506490\pi\) | |||||||
\(692\) | 8.92820 | 0.339399 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.92820 | 0.338910 | ||||||||
\(695\) | 13.6603 | 0.518163 | ||||||||
\(696\) | 7.07180 | 0.268056 | ||||||||
\(697\) | −61.1769 | −2.31724 | ||||||||
\(698\) | 1.46410 | 0.0554171 | ||||||||
\(699\) | −2.82309 | −0.106779 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −34.7321 | −1.31181 | −0.655906 | − | 0.754843i | \(-0.727713\pi\) | ||||
−0.655906 | + | 0.754843i | \(0.727713\pi\) | |||||||
\(702\) | −16.0000 | −0.603881 | ||||||||
\(703\) | −2.00000 | −0.0754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.39230 | 0.165424 | ||||||||
\(706\) | −26.9808 | −1.01543 | ||||||||
\(707\) | 8.00000 | 0.300871 | ||||||||
\(708\) | 9.07180 | 0.340939 | ||||||||
\(709\) | 23.8564 | 0.895946 | 0.447973 | − | 0.894047i | \(-0.352146\pi\) | ||||
0.447973 | + | 0.894047i | \(0.352146\pi\) | |||||||
\(710\) | −14.9282 | −0.560245 | ||||||||
\(711\) | −23.8038 | −0.892714 | ||||||||
\(712\) | 4.92820 | 0.184692 | ||||||||
\(713\) | −16.3923 | −0.613897 | ||||||||
\(714\) | −5.46410 | −0.204489 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.3923 | −0.537866 | ||||||||
\(717\) | −13.2154 | −0.493538 | ||||||||
\(718\) | 34.4449 | 1.28547 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 2.46410 | 0.0918316 | ||||||||
\(721\) | 18.3923 | 0.684965 | ||||||||
\(722\) | −11.5359 | −0.429322 | ||||||||
\(723\) | 21.2154 | 0.789009 | ||||||||
\(724\) | 8.92820 | 0.331814 | ||||||||
\(725\) | −9.66025 | −0.358773 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.71281 | 0.360228 | 0.180114 | − | 0.983646i | \(-0.442353\pi\) | ||||
0.180114 | + | 0.983646i | \(0.442353\pi\) | |||||||
\(728\) | 4.00000 | 0.148250 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | 66.6410 | 2.46481 | ||||||||
\(732\) | −5.85641 | −0.216459 | ||||||||
\(733\) | −24.1436 | −0.891764 | −0.445882 | − | 0.895092i | \(-0.647110\pi\) | ||||
−0.445882 | + | 0.895092i | \(0.647110\pi\) | |||||||
\(734\) | 6.39230 | 0.235944 | ||||||||
\(735\) | 0.732051 | 0.0270021 | ||||||||
\(736\) | −2.19615 | −0.0809513 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −20.1962 | −0.743431 | ||||||||
\(739\) | −17.8564 | −0.656859 | −0.328429 | − | 0.944529i | \(-0.606519\pi\) | ||||
−0.328429 | + | 0.944529i | \(0.606519\pi\) | |||||||
\(740\) | −0.732051 | −0.0269107 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | −8.73205 | −0.320564 | ||||||||
\(743\) | 24.3923 | 0.894867 | 0.447433 | − | 0.894317i | \(-0.352338\pi\) | ||||
0.447433 | + | 0.894317i | \(0.352338\pi\) | |||||||
\(744\) | −5.46410 | −0.200324 | ||||||||
\(745\) | 12.1962 | 0.446832 | ||||||||
\(746\) | 1.32051 | 0.0483472 | ||||||||
\(747\) | 2.64102 | 0.0966297 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.00000 | −0.0730784 | ||||||||
\(750\) | 0.732051 | 0.0267307 | ||||||||
\(751\) | 49.8564 | 1.81929 | 0.909643 | − | 0.415391i | \(-0.136355\pi\) | ||||
0.909643 | + | 0.415391i | \(0.136355\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | −12.2872 | −0.447770 | ||||||||
\(754\) | 38.6410 | 1.40722 | ||||||||
\(755\) | −12.1962 | −0.443863 | ||||||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | −27.6603 | −1.00533 | −0.502665 | − | 0.864482i | \(-0.667647\pi\) | ||||
−0.502665 | + | 0.864482i | \(0.667647\pi\) | |||||||
\(758\) | 2.14359 | 0.0778588 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.73205 | 0.0991019 | ||||||||
\(761\) | 3.41154 | 0.123668 | 0.0618342 | − | 0.998086i | \(-0.480305\pi\) | ||||
0.0618342 | + | 0.998086i | \(0.480305\pi\) | |||||||
\(762\) | −9.07180 | −0.328637 | ||||||||
\(763\) | −13.2679 | −0.480332 | ||||||||
\(764\) | 0.392305 | 0.0141931 | ||||||||
\(765\) | −18.3923 | −0.664975 | ||||||||
\(766\) | −3.46410 | −0.125163 | ||||||||
\(767\) | 49.5692 | 1.78984 | ||||||||
\(768\) | −0.732051 | −0.0264156 | ||||||||
\(769\) | −6.73205 | −0.242764 | −0.121382 | − | 0.992606i | \(-0.538733\pi\) | ||||
−0.121382 | + | 0.992606i | \(0.538733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.3205 | 0.479726 | ||||||||
\(772\) | 16.0000 | 0.575853 | ||||||||
\(773\) | 9.71281 | 0.349346 | 0.174673 | − | 0.984627i | \(-0.444113\pi\) | ||||
0.174673 | + | 0.984627i | \(0.444113\pi\) | |||||||
\(774\) | 22.0000 | 0.790774 | ||||||||
\(775\) | 7.46410 | 0.268118 | ||||||||
\(776\) | −0.732051 | −0.0262791 | ||||||||
\(777\) | 0.535898 | 0.0192252 | ||||||||
\(778\) | 5.60770 | 0.201046 | ||||||||
\(779\) | −22.3923 | −0.802288 | ||||||||
\(780\) | −2.92820 | −0.104846 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 16.3923 | 0.586188 | ||||||||
\(783\) | −38.6410 | −1.38092 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 23.4641 | 0.837470 | ||||||||
\(786\) | −0.143594 | −0.00512181 | ||||||||
\(787\) | 36.7846 | 1.31123 | 0.655615 | − | 0.755095i | \(-0.272410\pi\) | ||||
0.655615 | + | 0.755095i | \(0.272410\pi\) | |||||||
\(788\) | −3.46410 | −0.123404 | ||||||||
\(789\) | 5.56922 | 0.198269 | ||||||||
\(790\) | −9.66025 | −0.343696 | ||||||||
\(791\) | −18.0000 | −0.640006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.0000 | −1.13635 | ||||||||
\(794\) | 0.535898 | 0.0190183 | ||||||||
\(795\) | 6.39230 | 0.226712 | ||||||||
\(796\) | 25.8564 | 0.916456 | ||||||||
\(797\) | −2.39230 | −0.0847398 | −0.0423699 | − | 0.999102i | \(-0.513491\pi\) | ||||
−0.0423699 | + | 0.999102i | \(0.513491\pi\) | |||||||
\(798\) | −2.00000 | −0.0707992 | ||||||||
\(799\) | −44.7846 | −1.58437 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −12.1436 | −0.429073 | ||||||||
\(802\) | −0.392305 | −0.0138528 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.67949 | 0.306102 | ||||||||
\(805\) | −2.19615 | −0.0774042 | ||||||||
\(806\) | −29.8564 | −1.05165 | ||||||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | −8.00000 | −0.281439 | ||||||||
\(809\) | −32.1051 | −1.12876 | −0.564378 | − | 0.825517i | \(-0.690884\pi\) | ||||
−0.564378 | + | 0.825517i | \(0.690884\pi\) | |||||||
\(810\) | −4.46410 | −0.156853 | ||||||||
\(811\) | −6.73205 | −0.236394 | −0.118197 | − | 0.992990i | \(-0.537711\pi\) | ||||
−0.118197 | + | 0.992990i | \(0.537711\pi\) | |||||||
\(812\) | 9.66025 | 0.339008 | ||||||||
\(813\) | 8.49742 | 0.298018 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.928203 | 0.0325135 | ||||||||
\(816\) | 5.46410 | 0.191282 | ||||||||
\(817\) | 24.3923 | 0.853379 | ||||||||
\(818\) | −19.8038 | −0.692425 | ||||||||
\(819\) | −9.85641 | −0.344411 | ||||||||
\(820\) | −8.19615 | −0.286222 | ||||||||
\(821\) | −49.3731 | −1.72313 | −0.861566 | − | 0.507646i | \(-0.830516\pi\) | ||||
−0.861566 | + | 0.507646i | \(0.830516\pi\) | |||||||
\(822\) | −14.5359 | −0.506998 | ||||||||
\(823\) | 40.0526 | 1.39614 | 0.698072 | − | 0.716027i | \(-0.254041\pi\) | ||||
0.698072 | + | 0.716027i | \(0.254041\pi\) | |||||||
\(824\) | −18.3923 | −0.640726 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.3923 | 0.431183 | ||||||||
\(827\) | −20.7846 | −0.722752 | −0.361376 | − | 0.932420i | \(-0.617693\pi\) | ||||
−0.361376 | + | 0.932420i | \(0.617693\pi\) | |||||||
\(828\) | 5.41154 | 0.188064 | ||||||||
\(829\) | 24.3923 | 0.847180 | 0.423590 | − | 0.905854i | \(-0.360770\pi\) | ||||
0.423590 | + | 0.905854i | \(0.360770\pi\) | |||||||
\(830\) | 1.07180 | 0.0372026 | ||||||||
\(831\) | 12.6795 | 0.439847 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | −7.46410 | −0.258616 | ||||||||
\(834\) | 10.0000 | 0.346272 | ||||||||
\(835\) | 18.9282 | 0.655037 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.8564 | 1.03199 | ||||||||
\(838\) | 10.1436 | 0.350405 | ||||||||
\(839\) | 20.2487 | 0.699063 | 0.349532 | − | 0.936925i | \(-0.386341\pi\) | ||||
0.349532 | + | 0.936925i | \(0.386341\pi\) | |||||||
\(840\) | −0.732051 | −0.0252582 | ||||||||
\(841\) | 64.3205 | 2.21795 | ||||||||
\(842\) | −24.2487 | −0.835666 | ||||||||
\(843\) | 8.28719 | 0.285426 | ||||||||
\(844\) | −13.8564 | −0.476957 | ||||||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | −14.7846 | −0.508305 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.73205 | 0.299860 | ||||||||
\(849\) | −1.85641 | −0.0637117 | ||||||||
\(850\) | −7.46410 | −0.256017 | ||||||||
\(851\) | −1.60770 | −0.0551111 | ||||||||
\(852\) | −10.9282 | −0.374394 | ||||||||
\(853\) | −44.6410 | −1.52848 | −0.764240 | − | 0.644932i | \(-0.776886\pi\) | ||||
−0.764240 | + | 0.644932i | \(0.776886\pi\) | |||||||
\(854\) | −8.00000 | −0.273754 | ||||||||
\(855\) | −6.73205 | −0.230231 | ||||||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | 11.0718 | 0.378205 | 0.189103 | − | 0.981957i | \(-0.439442\pi\) | ||||
0.189103 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.9282 | 0.918778 | 0.459389 | − | 0.888235i | \(-0.348068\pi\) | ||||
0.459389 | + | 0.888235i | \(0.348068\pi\) | |||||||
\(860\) | 8.92820 | 0.304449 | ||||||||
\(861\) | 6.00000 | 0.204479 | ||||||||
\(862\) | 13.2679 | 0.451908 | ||||||||
\(863\) | −11.6603 | −0.396920 | −0.198460 | − | 0.980109i | \(-0.563594\pi\) | ||||
−0.198460 | + | 0.980109i | \(0.563594\pi\) | |||||||
\(864\) | 4.00000 | 0.136083 | ||||||||
\(865\) | −8.92820 | −0.303568 | ||||||||
\(866\) | −32.7321 | −1.11228 | ||||||||
\(867\) | −28.3397 | −0.962468 | ||||||||
\(868\) | −7.46410 | −0.253348 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −7.07180 | −0.239756 | ||||||||
\(871\) | 47.4256 | 1.60696 | ||||||||
\(872\) | 13.2679 | 0.449309 | ||||||||
\(873\) | 1.80385 | 0.0610510 | ||||||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −4.39230 | −0.148402 | ||||||||
\(877\) | 17.6077 | 0.594570 | 0.297285 | − | 0.954789i | \(-0.403919\pi\) | ||||
0.297285 | + | 0.954789i | \(0.403919\pi\) | |||||||
\(878\) | 22.5359 | 0.760550 | ||||||||
\(879\) | −20.2872 | −0.684270 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.7128 | 1.94439 | 0.972197 | − | 0.234164i | \(-0.0752354\pi\) | ||||
0.972197 | + | 0.234164i | \(0.0752354\pi\) | |||||||
\(882\) | −2.46410 | −0.0829706 | ||||||||
\(883\) | −22.6795 | −0.763226 | −0.381613 | − | 0.924322i | \(-0.624631\pi\) | ||||
−0.381613 | + | 0.924322i | \(0.624631\pi\) | |||||||
\(884\) | 29.8564 | 1.00418 | ||||||||
\(885\) | −9.07180 | −0.304945 | ||||||||
\(886\) | −15.0718 | −0.506347 | ||||||||
\(887\) | −22.6410 | −0.760211 | −0.380105 | − | 0.924943i | \(-0.624112\pi\) | ||||
−0.380105 | + | 0.924943i | \(0.624112\pi\) | |||||||
\(888\) | −0.535898 | −0.0179836 | ||||||||
\(889\) | −12.3923 | −0.415625 | ||||||||
\(890\) | −4.92820 | −0.165194 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.53590 | −0.151873 | ||||||||
\(893\) | −16.3923 | −0.548548 | ||||||||
\(894\) | 8.92820 | 0.298604 | ||||||||
\(895\) | 14.3923 | 0.481082 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −6.43078 | −0.214718 | ||||||||
\(898\) | 38.2487 | 1.27638 | ||||||||
\(899\) | −72.1051 | −2.40484 | ||||||||
\(900\) | −2.46410 | −0.0821367 | ||||||||
\(901\) | −65.1769 | −2.17136 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.53590 | −0.217501 | ||||||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | −8.92820 | −0.296784 | ||||||||
\(906\) | −8.92820 | −0.296620 | ||||||||
\(907\) | 25.3205 | 0.840754 | 0.420377 | − | 0.907350i | \(-0.361898\pi\) | ||||
0.420377 | + | 0.907350i | \(0.361898\pi\) | |||||||
\(908\) | −11.3205 | −0.375684 | ||||||||
\(909\) | 19.7128 | 0.653833 | ||||||||
\(910\) | −4.00000 | −0.132599 | ||||||||
\(911\) | −47.0333 | −1.55828 | −0.779142 | − | 0.626848i | \(-0.784345\pi\) | ||||
−0.779142 | + | 0.626848i | \(0.784345\pi\) | |||||||
\(912\) | 2.00000 | 0.0662266 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −11.8564 | −0.392175 | ||||||||
\(915\) | 5.85641 | 0.193607 | ||||||||
\(916\) | −11.3205 | −0.374040 | ||||||||
\(917\) | −0.196152 | −0.00647752 | ||||||||
\(918\) | −29.8564 | −0.985408 | ||||||||
\(919\) | −37.3731 | −1.23282 | −0.616412 | − | 0.787424i | \(-0.711414\pi\) | ||||
−0.616412 | + | 0.787424i | \(0.711414\pi\) | |||||||
\(920\) | 2.19615 | 0.0724050 | ||||||||
\(921\) | 4.78461 | 0.157658 | ||||||||
\(922\) | 39.3205 | 1.29495 | ||||||||
\(923\) | −59.7128 | −1.96547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.732051 | 0.0240697 | ||||||||
\(926\) | 38.5885 | 1.26810 | ||||||||
\(927\) | 45.3205 | 1.48852 | ||||||||
\(928\) | −9.66025 | −0.317113 | ||||||||
\(929\) | 12.2487 | 0.401867 | 0.200934 | − | 0.979605i | \(-0.435602\pi\) | ||||
0.200934 | + | 0.979605i | \(0.435602\pi\) | |||||||
\(930\) | 5.46410 | 0.179175 | ||||||||
\(931\) | −2.73205 | −0.0895393 | ||||||||
\(932\) | 3.85641 | 0.126321 | ||||||||
\(933\) | 12.6795 | 0.415108 | ||||||||
\(934\) | 9.41154 | 0.307955 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.85641 | 0.322167 | ||||||||
\(937\) | 41.3205 | 1.34988 | 0.674941 | − | 0.737872i | \(-0.264169\pi\) | ||||
0.674941 | + | 0.737872i | \(0.264169\pi\) | |||||||
\(938\) | 11.8564 | 0.387125 | ||||||||
\(939\) | −0.535898 | −0.0174884 | ||||||||
\(940\) | −6.00000 | −0.195698 | ||||||||
\(941\) | −6.92820 | −0.225853 | −0.112926 | − | 0.993603i | \(-0.536022\pi\) | ||||
−0.112926 | + | 0.993603i | \(0.536022\pi\) | |||||||
\(942\) | 17.1769 | 0.559654 | ||||||||
\(943\) | −18.0000 | −0.586161 | ||||||||
\(944\) | −12.3923 | −0.403335 | ||||||||
\(945\) | 4.00000 | 0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.3923 | −0.597670 | −0.298835 | − | 0.954305i | \(-0.596598\pi\) | ||||
−0.298835 | + | 0.954305i | \(0.596598\pi\) | |||||||
\(948\) | −7.07180 | −0.229681 | ||||||||
\(949\) | −24.0000 | −0.779073 | ||||||||
\(950\) | −2.73205 | −0.0886394 | ||||||||
\(951\) | −19.4641 | −0.631167 | ||||||||
\(952\) | 7.46410 | 0.241913 | ||||||||
\(953\) | 46.6410 | 1.51085 | 0.755425 | − | 0.655235i | \(-0.227430\pi\) | ||||
0.755425 | + | 0.655235i | \(0.227430\pi\) | |||||||
\(954\) | −21.5167 | −0.696628 | ||||||||
\(955\) | −0.392305 | −0.0126947 | ||||||||
\(956\) | 18.0526 | 0.583861 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.7128 | −1.15383 | ||||||||
\(959\) | −19.8564 | −0.641197 | ||||||||
\(960\) | 0.732051 | 0.0236268 | ||||||||
\(961\) | 24.7128 | 0.797188 | ||||||||
\(962\) | −2.92820 | −0.0944091 | ||||||||
\(963\) | −4.92820 | −0.158809 | ||||||||
\(964\) | −28.9808 | −0.933407 | ||||||||
\(965\) | −16.0000 | −0.515058 | ||||||||
\(966\) | −1.60770 | −0.0517267 | ||||||||
\(967\) | −15.6077 | −0.501910 | −0.250955 | − | 0.967999i | \(-0.580745\pi\) | ||||
−0.250955 | + | 0.967999i | \(0.580745\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.9282 | −0.479563 | ||||||||
\(970\) | 0.732051 | 0.0235047 | ||||||||
\(971\) | 24.3923 | 0.782786 | 0.391393 | − | 0.920224i | \(-0.371993\pi\) | ||||
0.391393 | + | 0.920224i | \(0.371993\pi\) | |||||||
\(972\) | −15.2679 | −0.489720 | ||||||||
\(973\) | 13.6603 | 0.437928 | ||||||||
\(974\) | 8.05256 | 0.258021 | ||||||||
\(975\) | 2.92820 | 0.0937776 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | 4.14359 | 0.132565 | 0.0662827 | − | 0.997801i | \(-0.478886\pi\) | ||||
0.0662827 | + | 0.997801i | \(0.478886\pi\) | |||||||
\(978\) | 0.679492 | 0.0217278 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −32.6936 | −1.04383 | ||||||||
\(982\) | 22.9282 | 0.731668 | ||||||||
\(983\) | 20.5359 | 0.654993 | 0.327497 | − | 0.944852i | \(-0.393795\pi\) | ||||
0.327497 | + | 0.944852i | \(0.393795\pi\) | |||||||
\(984\) | −6.00000 | −0.191273 | ||||||||
\(985\) | 3.46410 | 0.110375 | ||||||||
\(986\) | 72.1051 | 2.29629 | ||||||||
\(987\) | 4.39230 | 0.139809 | ||||||||
\(988\) | 10.9282 | 0.347672 | ||||||||
\(989\) | 19.6077 | 0.623488 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.3923 | −0.774847 | −0.387424 | − | 0.921902i | \(-0.626635\pi\) | ||||
−0.387424 | + | 0.921902i | \(0.626635\pi\) | |||||||
\(992\) | 7.46410 | 0.236985 | ||||||||
\(993\) | −19.3205 | −0.613118 | ||||||||
\(994\) | −14.9282 | −0.473494 | ||||||||
\(995\) | −25.8564 | −0.819703 | ||||||||
\(996\) | 0.784610 | 0.0248613 | ||||||||
\(997\) | 3.85641 | 0.122134 | 0.0610668 | − | 0.998134i | \(-0.480550\pi\) | ||||
0.0610668 | + | 0.998134i | \(0.480550\pi\) | |||||||
\(998\) | −1.60770 | −0.0508907 | ||||||||
\(999\) | 2.92820 | 0.0926443 |
(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 | 8470.2.a.cd.1.1 | yes | 2 | |
11.10 | odd | 2 | 8470.2.a.bs.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bs.1.1 | ✓ | 2 | 11.10 | odd | 2 | ||
8470.2.a.cd.1.1 | yes | 2 | 1.1 | even | 1 | trivial |