Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
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: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.46410 | −1.54919 | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.46410 | 1.09545 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.46410 | −0.894427 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.46410 | 1.56777 | 0.783887 | − | 0.620903i | \(-0.213234\pi\) | ||||
0.783887 | + | 0.620903i | \(0.213234\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 7.46410 | 1.71238 | 0.856191 | − | 0.516659i | \(-0.172825\pi\) | ||||
0.856191 | + | 0.516659i | \(0.172825\pi\) | |||||||
\(20\) | −3.46410 | −0.774597 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | 5.73205 | 1.19522 | 0.597608 | − | 0.801789i | \(-0.296118\pi\) | ||||
0.597608 | + | 0.801789i | \(0.296118\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 3.46410 | 0.632456 | ||||||||
\(31\) | −6.46410 | −1.16099 | −0.580493 | − | 0.814265i | \(-0.697140\pi\) | ||||
−0.580493 | + | 0.814265i | \(0.697140\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | −6.46410 | −1.10858 | ||||||||
\(35\) | −3.46410 | −0.585540 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.92820 | −0.810192 | −0.405096 | − | 0.914274i | \(-0.632762\pi\) | ||||
−0.405096 | + | 0.914274i | \(0.632762\pi\) | |||||||
\(38\) | −7.46410 | −1.21084 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.46410 | 0.547723 | ||||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 4.46410 | 0.680769 | 0.340385 | − | 0.940286i | \(-0.389443\pi\) | ||||
0.340385 | + | 0.940286i | \(0.389443\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | −3.46410 | −0.516398 | ||||||||
\(46\) | −5.73205 | −0.845145 | ||||||||
\(47\) | −0.535898 | −0.0781688 | −0.0390844 | − | 0.999236i | \(-0.512444\pi\) | ||||
−0.0390844 | + | 0.999236i | \(0.512444\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.00000 | −0.989949 | ||||||||
\(51\) | 6.46410 | 0.905155 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.26795 | −1.13569 | −0.567845 | − | 0.823135i | \(-0.692223\pi\) | ||||
−0.567845 | + | 0.823135i | \(0.692223\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −13.8564 | −1.86840 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 7.46410 | 0.988644 | ||||||||
\(58\) | −8.00000 | −1.05045 | ||||||||
\(59\) | 6.26795 | 0.816017 | 0.408009 | − | 0.912978i | \(-0.366223\pi\) | ||||
0.408009 | + | 0.912978i | \(0.366223\pi\) | |||||||
\(60\) | −3.46410 | −0.447214 | ||||||||
\(61\) | −5.19615 | −0.665299 | −0.332650 | − | 0.943051i | \(-0.607943\pi\) | ||||
−0.332650 | + | 0.943051i | \(0.607943\pi\) | |||||||
\(62\) | 6.46410 | 0.820942 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | −7.19615 | −0.879150 | −0.439575 | − | 0.898206i | \(-0.644871\pi\) | ||||
−0.439575 | + | 0.898206i | \(0.644871\pi\) | |||||||
\(68\) | 6.46410 | 0.783887 | ||||||||
\(69\) | 5.73205 | 0.690058 | ||||||||
\(70\) | 3.46410 | 0.414039 | ||||||||
\(71\) | 1.92820 | 0.228836 | 0.114418 | − | 0.993433i | \(-0.463500\pi\) | ||||
0.114418 | + | 0.993433i | \(0.463500\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −10.9282 | −1.27905 | −0.639525 | − | 0.768771i | \(-0.720869\pi\) | ||||
−0.639525 | + | 0.768771i | \(0.720869\pi\) | |||||||
\(74\) | 4.92820 | 0.572892 | ||||||||
\(75\) | 7.00000 | 0.808290 | ||||||||
\(76\) | 7.46410 | 0.856191 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.46410 | −1.06479 | −0.532397 | − | 0.846495i | \(-0.678709\pi\) | ||||
−0.532397 | + | 0.846495i | \(0.678709\pi\) | |||||||
\(80\) | −3.46410 | −0.387298 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.92820 | −0.765092 | ||||||||
\(83\) | 1.73205 | 0.190117 | 0.0950586 | − | 0.995472i | \(-0.469696\pi\) | ||||
0.0950586 | + | 0.995472i | \(0.469696\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −22.3923 | −2.42879 | ||||||||
\(86\) | −4.46410 | −0.481376 | ||||||||
\(87\) | 8.00000 | 0.857690 | ||||||||
\(88\) | −4.00000 | −0.426401 | ||||||||
\(89\) | −11.7321 | −1.24359 | −0.621797 | − | 0.783178i | \(-0.713597\pi\) | ||||
−0.621797 | + | 0.783178i | \(0.713597\pi\) | |||||||
\(90\) | 3.46410 | 0.365148 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.73205 | 0.597608 | ||||||||
\(93\) | −6.46410 | −0.670296 | ||||||||
\(94\) | 0.535898 | 0.0552737 | ||||||||
\(95\) | −25.8564 | −2.65281 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 12.3923 | 1.25825 | 0.629124 | − | 0.777305i | \(-0.283414\pi\) | ||||
0.629124 | + | 0.777305i | \(0.283414\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 7.00000 | 0.700000 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | −6.46410 | −0.640041 | ||||||||
\(103\) | 10.6603 | 1.05039 | 0.525193 | − | 0.850983i | \(-0.323993\pi\) | ||||
0.525193 | + | 0.850983i | \(0.323993\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.46410 | −0.338062 | ||||||||
\(106\) | 8.26795 | 0.803054 | ||||||||
\(107\) | 8.53590 | 0.825196 | 0.412598 | − | 0.910913i | \(-0.364621\pi\) | ||||
0.412598 | + | 0.910913i | \(0.364621\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −12.0000 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(110\) | 13.8564 | 1.32116 | ||||||||
\(111\) | −4.92820 | −0.467764 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −4.39230 | −0.413193 | −0.206597 | − | 0.978426i | \(-0.566239\pi\) | ||||
−0.206597 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(114\) | −7.46410 | −0.699077 | ||||||||
\(115\) | −19.8564 | −1.85162 | ||||||||
\(116\) | 8.00000 | 0.742781 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.26795 | −0.577011 | ||||||||
\(119\) | 6.46410 | 0.592563 | ||||||||
\(120\) | 3.46410 | 0.316228 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 5.19615 | 0.470438 | ||||||||
\(123\) | 6.92820 | 0.624695 | ||||||||
\(124\) | −6.46410 | −0.580493 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 5.07180 | 0.450049 | 0.225025 | − | 0.974353i | \(-0.427754\pi\) | ||||
0.225025 | + | 0.974353i | \(0.427754\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.46410 | 0.393042 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.0000 | 1.66004 | 0.830019 | − | 0.557735i | \(-0.188330\pi\) | ||||
0.830019 | + | 0.557735i | \(0.188330\pi\) | |||||||
\(132\) | 4.00000 | 0.348155 | ||||||||
\(133\) | 7.46410 | 0.647220 | ||||||||
\(134\) | 7.19615 | 0.621653 | ||||||||
\(135\) | −3.46410 | −0.298142 | ||||||||
\(136\) | −6.46410 | −0.554292 | ||||||||
\(137\) | 13.8564 | 1.18383 | 0.591916 | − | 0.805999i | \(-0.298372\pi\) | ||||
0.591916 | + | 0.805999i | \(0.298372\pi\) | |||||||
\(138\) | −5.73205 | −0.487945 | ||||||||
\(139\) | 2.92820 | 0.248367 | 0.124183 | − | 0.992259i | \(-0.460369\pi\) | ||||
0.124183 | + | 0.992259i | \(0.460369\pi\) | |||||||
\(140\) | −3.46410 | −0.292770 | ||||||||
\(141\) | −0.535898 | −0.0451308 | ||||||||
\(142\) | −1.92820 | −0.161811 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −27.7128 | −2.30142 | ||||||||
\(146\) | 10.9282 | 0.904425 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −4.92820 | −0.405096 | ||||||||
\(149\) | −11.5359 | −0.945058 | −0.472529 | − | 0.881315i | \(-0.656659\pi\) | ||||
−0.472529 | + | 0.881315i | \(0.656659\pi\) | |||||||
\(150\) | −7.00000 | −0.571548 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | −7.46410 | −0.605419 | ||||||||
\(153\) | 6.46410 | 0.522592 | ||||||||
\(154\) | −4.00000 | −0.322329 | ||||||||
\(155\) | 22.3923 | 1.79859 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.92820 | −0.233696 | −0.116848 | − | 0.993150i | \(-0.537279\pi\) | ||||
−0.116848 | + | 0.993150i | \(0.537279\pi\) | |||||||
\(158\) | 9.46410 | 0.752923 | ||||||||
\(159\) | −8.26795 | −0.655691 | ||||||||
\(160\) | 3.46410 | 0.273861 | ||||||||
\(161\) | 5.73205 | 0.451749 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −1.33975 | −0.104937 | −0.0524685 | − | 0.998623i | \(-0.516709\pi\) | ||||
−0.0524685 | + | 0.998623i | \(0.516709\pi\) | |||||||
\(164\) | 6.92820 | 0.541002 | ||||||||
\(165\) | −13.8564 | −1.07872 | ||||||||
\(166\) | −1.73205 | −0.134433 | ||||||||
\(167\) | 20.0000 | 1.54765 | 0.773823 | − | 0.633402i | \(-0.218342\pi\) | ||||
0.773823 | + | 0.633402i | \(0.218342\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 22.3923 | 1.71741 | ||||||||
\(171\) | 7.46410 | 0.570794 | ||||||||
\(172\) | 4.46410 | 0.340385 | ||||||||
\(173\) | 1.07180 | 0.0814872 | 0.0407436 | − | 0.999170i | \(-0.487027\pi\) | ||||
0.0407436 | + | 0.999170i | \(0.487027\pi\) | |||||||
\(174\) | −8.00000 | −0.606478 | ||||||||
\(175\) | 7.00000 | 0.529150 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 6.26795 | 0.471128 | ||||||||
\(178\) | 11.7321 | 0.879354 | ||||||||
\(179\) | −16.9282 | −1.26527 | −0.632637 | − | 0.774449i | \(-0.718027\pi\) | ||||
−0.632637 | + | 0.774449i | \(0.718027\pi\) | |||||||
\(180\) | −3.46410 | −0.258199 | ||||||||
\(181\) | 24.7846 | 1.84223 | 0.921113 | − | 0.389296i | \(-0.127282\pi\) | ||||
0.921113 | + | 0.389296i | \(0.127282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.19615 | −0.384111 | ||||||||
\(184\) | −5.73205 | −0.422572 | ||||||||
\(185\) | 17.0718 | 1.25514 | ||||||||
\(186\) | 6.46410 | 0.473971 | ||||||||
\(187\) | 25.8564 | 1.89081 | ||||||||
\(188\) | −0.535898 | −0.0390844 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 25.8564 | 1.87582 | ||||||||
\(191\) | −26.5167 | −1.91868 | −0.959339 | − | 0.282256i | \(-0.908917\pi\) | ||||
−0.959339 | + | 0.282256i | \(0.908917\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 17.8564 | 1.28533 | 0.642666 | − | 0.766146i | \(-0.277828\pi\) | ||||
0.642666 | + | 0.766146i | \(0.277828\pi\) | |||||||
\(194\) | −12.3923 | −0.889716 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −2.60770 | −0.185791 | −0.0928953 | − | 0.995676i | \(-0.529612\pi\) | ||||
−0.0928953 | + | 0.995676i | \(0.529612\pi\) | |||||||
\(198\) | −4.00000 | −0.284268 | ||||||||
\(199\) | −22.1244 | −1.56835 | −0.784177 | − | 0.620537i | \(-0.786915\pi\) | ||||
−0.784177 | + | 0.620537i | \(0.786915\pi\) | |||||||
\(200\) | −7.00000 | −0.494975 | ||||||||
\(201\) | −7.19615 | −0.507577 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 6.46410 | 0.452578 | ||||||||
\(205\) | −24.0000 | −1.67623 | ||||||||
\(206\) | −10.6603 | −0.742735 | ||||||||
\(207\) | 5.73205 | 0.398405 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.8564 | 2.06521 | ||||||||
\(210\) | 3.46410 | 0.239046 | ||||||||
\(211\) | −9.07180 | −0.624528 | −0.312264 | − | 0.949995i | \(-0.601087\pi\) | ||||
−0.312264 | + | 0.949995i | \(0.601087\pi\) | |||||||
\(212\) | −8.26795 | −0.567845 | ||||||||
\(213\) | 1.92820 | 0.132118 | ||||||||
\(214\) | −8.53590 | −0.583502 | ||||||||
\(215\) | −15.4641 | −1.05464 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −6.46410 | −0.438812 | ||||||||
\(218\) | 12.0000 | 0.812743 | ||||||||
\(219\) | −10.9282 | −0.738460 | ||||||||
\(220\) | −13.8564 | −0.934199 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.92820 | 0.330759 | ||||||||
\(223\) | 7.53590 | 0.504641 | 0.252321 | − | 0.967644i | \(-0.418806\pi\) | ||||
0.252321 | + | 0.967644i | \(0.418806\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 4.39230 | 0.292172 | ||||||||
\(227\) | −13.3205 | −0.884113 | −0.442057 | − | 0.896987i | \(-0.645751\pi\) | ||||
−0.442057 | + | 0.896987i | \(0.645751\pi\) | |||||||
\(228\) | 7.46410 | 0.494322 | ||||||||
\(229\) | 19.9282 | 1.31689 | 0.658446 | − | 0.752628i | \(-0.271214\pi\) | ||||
0.658446 | + | 0.752628i | \(0.271214\pi\) | |||||||
\(230\) | 19.8564 | 1.30929 | ||||||||
\(231\) | 4.00000 | 0.263181 | ||||||||
\(232\) | −8.00000 | −0.525226 | ||||||||
\(233\) | 13.4641 | 0.882063 | 0.441031 | − | 0.897492i | \(-0.354613\pi\) | ||||
0.441031 | + | 0.897492i | \(0.354613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.85641 | 0.121099 | ||||||||
\(236\) | 6.26795 | 0.408009 | ||||||||
\(237\) | −9.46410 | −0.614759 | ||||||||
\(238\) | −6.46410 | −0.419005 | ||||||||
\(239\) | 12.8564 | 0.831612 | 0.415806 | − | 0.909453i | \(-0.363500\pi\) | ||||
0.415806 | + | 0.909453i | \(0.363500\pi\) | |||||||
\(240\) | −3.46410 | −0.223607 | ||||||||
\(241\) | −15.8564 | −1.02140 | −0.510700 | − | 0.859759i | \(-0.670614\pi\) | ||||
−0.510700 | + | 0.859759i | \(0.670614\pi\) | |||||||
\(242\) | −5.00000 | −0.321412 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.19615 | −0.332650 | ||||||||
\(245\) | −3.46410 | −0.221313 | ||||||||
\(246\) | −6.92820 | −0.441726 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.46410 | 0.410471 | ||||||||
\(249\) | 1.73205 | 0.109764 | ||||||||
\(250\) | 6.92820 | 0.438178 | ||||||||
\(251\) | −10.0718 | −0.635726 | −0.317863 | − | 0.948137i | \(-0.602965\pi\) | ||||
−0.317863 | + | 0.948137i | \(0.602965\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 22.9282 | 1.44148 | ||||||||
\(254\) | −5.07180 | −0.318233 | ||||||||
\(255\) | −22.3923 | −1.40226 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.464102 | 0.0289499 | 0.0144749 | − | 0.999895i | \(-0.495392\pi\) | ||||
0.0144749 | + | 0.999895i | \(0.495392\pi\) | |||||||
\(258\) | −4.46410 | −0.277923 | ||||||||
\(259\) | −4.92820 | −0.306224 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | 0.495188 | ||||||||
\(262\) | −19.0000 | −1.17382 | ||||||||
\(263\) | −17.3205 | −1.06803 | −0.534014 | − | 0.845476i | \(-0.679317\pi\) | ||||
−0.534014 | + | 0.845476i | \(0.679317\pi\) | |||||||
\(264\) | −4.00000 | −0.246183 | ||||||||
\(265\) | 28.6410 | 1.75940 | ||||||||
\(266\) | −7.46410 | −0.457653 | ||||||||
\(267\) | −11.7321 | −0.717990 | ||||||||
\(268\) | −7.19615 | −0.439575 | ||||||||
\(269\) | 22.3923 | 1.36528 | 0.682641 | − | 0.730753i | \(-0.260831\pi\) | ||||
0.682641 | + | 0.730753i | \(0.260831\pi\) | |||||||
\(270\) | 3.46410 | 0.210819 | ||||||||
\(271\) | 12.4641 | 0.757140 | 0.378570 | − | 0.925573i | \(-0.376416\pi\) | ||||
0.378570 | + | 0.925573i | \(0.376416\pi\) | |||||||
\(272\) | 6.46410 | 0.391944 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.8564 | −0.837096 | ||||||||
\(275\) | 28.0000 | 1.68846 | ||||||||
\(276\) | 5.73205 | 0.345029 | ||||||||
\(277\) | 7.32051 | 0.439847 | 0.219923 | − | 0.975517i | \(-0.429419\pi\) | ||||
0.219923 | + | 0.975517i | \(0.429419\pi\) | |||||||
\(278\) | −2.92820 | −0.175622 | ||||||||
\(279\) | −6.46410 | −0.386996 | ||||||||
\(280\) | 3.46410 | 0.207020 | ||||||||
\(281\) | −2.39230 | −0.142713 | −0.0713565 | − | 0.997451i | \(-0.522733\pi\) | ||||
−0.0713565 | + | 0.997451i | \(0.522733\pi\) | |||||||
\(282\) | 0.535898 | 0.0319123 | ||||||||
\(283\) | −11.4641 | −0.681470 | −0.340735 | − | 0.940159i | \(-0.610676\pi\) | ||||
−0.340735 | + | 0.940159i | \(0.610676\pi\) | |||||||
\(284\) | 1.92820 | 0.114418 | ||||||||
\(285\) | −25.8564 | −1.53160 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.92820 | 0.408959 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 24.7846 | 1.45792 | ||||||||
\(290\) | 27.7128 | 1.62735 | ||||||||
\(291\) | 12.3923 | 0.726450 | ||||||||
\(292\) | −10.9282 | −0.639525 | ||||||||
\(293\) | 33.4641 | 1.95499 | 0.977497 | − | 0.210950i | \(-0.0676557\pi\) | ||||
0.977497 | + | 0.210950i | \(0.0676557\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −21.7128 | −1.26417 | ||||||||
\(296\) | 4.92820 | 0.286446 | ||||||||
\(297\) | 4.00000 | 0.232104 | ||||||||
\(298\) | 11.5359 | 0.668257 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.00000 | 0.404145 | ||||||||
\(301\) | 4.46410 | 0.257307 | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.46410 | 0.428096 | ||||||||
\(305\) | 18.0000 | 1.03068 | ||||||||
\(306\) | −6.46410 | −0.369528 | ||||||||
\(307\) | −22.0000 | −1.25561 | −0.627803 | − | 0.778372i | \(-0.716046\pi\) | ||||
−0.627803 | + | 0.778372i | \(0.716046\pi\) | |||||||
\(308\) | 4.00000 | 0.227921 | ||||||||
\(309\) | 10.6603 | 0.606441 | ||||||||
\(310\) | −22.3923 | −1.27180 | ||||||||
\(311\) | 13.3205 | 0.755337 | 0.377668 | − | 0.925941i | \(-0.376726\pi\) | ||||
0.377668 | + | 0.925941i | \(0.376726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.679492 | 0.0384072 | 0.0192036 | − | 0.999816i | \(-0.493887\pi\) | ||||
0.0192036 | + | 0.999816i | \(0.493887\pi\) | |||||||
\(314\) | 2.92820 | 0.165248 | ||||||||
\(315\) | −3.46410 | −0.195180 | ||||||||
\(316\) | −9.46410 | −0.532397 | ||||||||
\(317\) | 16.4641 | 0.924716 | 0.462358 | − | 0.886693i | \(-0.347003\pi\) | ||||
0.462358 | + | 0.886693i | \(0.347003\pi\) | |||||||
\(318\) | 8.26795 | 0.463644 | ||||||||
\(319\) | 32.0000 | 1.79166 | ||||||||
\(320\) | −3.46410 | −0.193649 | ||||||||
\(321\) | 8.53590 | 0.476427 | ||||||||
\(322\) | −5.73205 | −0.319435 | ||||||||
\(323\) | 48.2487 | 2.68463 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.33975 | 0.0742017 | ||||||||
\(327\) | −12.0000 | −0.663602 | ||||||||
\(328\) | −6.92820 | −0.382546 | ||||||||
\(329\) | −0.535898 | −0.0295450 | ||||||||
\(330\) | 13.8564 | 0.762770 | ||||||||
\(331\) | 21.3205 | 1.17188 | 0.585941 | − | 0.810354i | \(-0.300725\pi\) | ||||
0.585941 | + | 0.810354i | \(0.300725\pi\) | |||||||
\(332\) | 1.73205 | 0.0950586 | ||||||||
\(333\) | −4.92820 | −0.270064 | ||||||||
\(334\) | −20.0000 | −1.09435 | ||||||||
\(335\) | 24.9282 | 1.36197 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.39230 | −0.238557 | ||||||||
\(340\) | −22.3923 | −1.21439 | ||||||||
\(341\) | −25.8564 | −1.40020 | ||||||||
\(342\) | −7.46410 | −0.403612 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −4.46410 | −0.240688 | ||||||||
\(345\) | −19.8564 | −1.06903 | ||||||||
\(346\) | −1.07180 | −0.0576202 | ||||||||
\(347\) | 25.7128 | 1.38034 | 0.690168 | − | 0.723649i | \(-0.257537\pi\) | ||||
0.690168 | + | 0.723649i | \(0.257537\pi\) | |||||||
\(348\) | 8.00000 | 0.428845 | ||||||||
\(349\) | −35.6410 | −1.90782 | −0.953910 | − | 0.300093i | \(-0.902982\pi\) | ||||
−0.953910 | + | 0.300093i | \(0.902982\pi\) | |||||||
\(350\) | −7.00000 | −0.374166 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | −0.213201 | ||||||||
\(353\) | −9.33975 | −0.497105 | −0.248552 | − | 0.968618i | \(-0.579955\pi\) | ||||
−0.248552 | + | 0.968618i | \(0.579955\pi\) | |||||||
\(354\) | −6.26795 | −0.333138 | ||||||||
\(355\) | −6.67949 | −0.354511 | ||||||||
\(356\) | −11.7321 | −0.621797 | ||||||||
\(357\) | 6.46410 | 0.342117 | ||||||||
\(358\) | 16.9282 | 0.894683 | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 3.46410 | 0.182574 | ||||||||
\(361\) | 36.7128 | 1.93225 | ||||||||
\(362\) | −24.7846 | −1.30265 | ||||||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.8564 | 1.98149 | ||||||||
\(366\) | 5.19615 | 0.271607 | ||||||||
\(367\) | −33.0526 | −1.72533 | −0.862665 | − | 0.505776i | \(-0.831206\pi\) | ||||
−0.862665 | + | 0.505776i | \(0.831206\pi\) | |||||||
\(368\) | 5.73205 | 0.298804 | ||||||||
\(369\) | 6.92820 | 0.360668 | ||||||||
\(370\) | −17.0718 | −0.887520 | ||||||||
\(371\) | −8.26795 | −0.429251 | ||||||||
\(372\) | −6.46410 | −0.335148 | ||||||||
\(373\) | −26.2487 | −1.35911 | −0.679553 | − | 0.733626i | \(-0.737826\pi\) | ||||
−0.679553 | + | 0.733626i | \(0.737826\pi\) | |||||||
\(374\) | −25.8564 | −1.33700 | ||||||||
\(375\) | −6.92820 | −0.357771 | ||||||||
\(376\) | 0.535898 | 0.0276368 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 9.60770 | 0.493514 | 0.246757 | − | 0.969077i | \(-0.420635\pi\) | ||||
0.246757 | + | 0.969077i | \(0.420635\pi\) | |||||||
\(380\) | −25.8564 | −1.32641 | ||||||||
\(381\) | 5.07180 | 0.259836 | ||||||||
\(382\) | 26.5167 | 1.35671 | ||||||||
\(383\) | 7.32051 | 0.374060 | 0.187030 | − | 0.982354i | \(-0.440114\pi\) | ||||
0.187030 | + | 0.982354i | \(0.440114\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −13.8564 | −0.706188 | ||||||||
\(386\) | −17.8564 | −0.908867 | ||||||||
\(387\) | 4.46410 | 0.226923 | ||||||||
\(388\) | 12.3923 | 0.629124 | ||||||||
\(389\) | −14.6603 | −0.743304 | −0.371652 | − | 0.928372i | \(-0.621209\pi\) | ||||
−0.371652 | + | 0.928372i | \(0.621209\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.0526 | 1.87383 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 19.0000 | 0.958423 | ||||||||
\(394\) | 2.60770 | 0.131374 | ||||||||
\(395\) | 32.7846 | 1.64957 | ||||||||
\(396\) | 4.00000 | 0.201008 | ||||||||
\(397\) | 29.7846 | 1.49485 | 0.747423 | − | 0.664348i | \(-0.231291\pi\) | ||||
0.747423 | + | 0.664348i | \(0.231291\pi\) | |||||||
\(398\) | 22.1244 | 1.10899 | ||||||||
\(399\) | 7.46410 | 0.373672 | ||||||||
\(400\) | 7.00000 | 0.350000 | ||||||||
\(401\) | −16.3923 | −0.818593 | −0.409296 | − | 0.912402i | \(-0.634226\pi\) | ||||
−0.409296 | + | 0.912402i | \(0.634226\pi\) | |||||||
\(402\) | 7.19615 | 0.358911 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.46410 | −0.172133 | ||||||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | −19.7128 | −0.977128 | ||||||||
\(408\) | −6.46410 | −0.320021 | ||||||||
\(409\) | 6.39230 | 0.316079 | 0.158040 | − | 0.987433i | \(-0.449483\pi\) | ||||
0.158040 | + | 0.987433i | \(0.449483\pi\) | |||||||
\(410\) | 24.0000 | 1.18528 | ||||||||
\(411\) | 13.8564 | 0.683486 | ||||||||
\(412\) | 10.6603 | 0.525193 | ||||||||
\(413\) | 6.26795 | 0.308426 | ||||||||
\(414\) | −5.73205 | −0.281715 | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.92820 | 0.143395 | ||||||||
\(418\) | −29.8564 | −1.46032 | ||||||||
\(419\) | −5.00000 | −0.244266 | −0.122133 | − | 0.992514i | \(-0.538973\pi\) | ||||
−0.122133 | + | 0.992514i | \(0.538973\pi\) | |||||||
\(420\) | −3.46410 | −0.169031 | ||||||||
\(421\) | −1.60770 | −0.0783543 | −0.0391771 | − | 0.999232i | \(-0.512474\pi\) | ||||
−0.0391771 | + | 0.999232i | \(0.512474\pi\) | |||||||
\(422\) | 9.07180 | 0.441608 | ||||||||
\(423\) | −0.535898 | −0.0260563 | ||||||||
\(424\) | 8.26795 | 0.401527 | ||||||||
\(425\) | 45.2487 | 2.19488 | ||||||||
\(426\) | −1.92820 | −0.0934218 | ||||||||
\(427\) | −5.19615 | −0.251459 | ||||||||
\(428\) | 8.53590 | 0.412598 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.4641 | 0.745745 | ||||||||
\(431\) | −4.85641 | −0.233925 | −0.116962 | − | 0.993136i | \(-0.537316\pi\) | ||||
−0.116962 | + | 0.993136i | \(0.537316\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 9.85641 | 0.473669 | 0.236834 | − | 0.971550i | \(-0.423890\pi\) | ||||
0.236834 | + | 0.971550i | \(0.423890\pi\) | |||||||
\(434\) | 6.46410 | 0.310287 | ||||||||
\(435\) | −27.7128 | −1.32873 | ||||||||
\(436\) | −12.0000 | −0.574696 | ||||||||
\(437\) | 42.7846 | 2.04667 | ||||||||
\(438\) | 10.9282 | 0.522170 | ||||||||
\(439\) | −13.6077 | −0.649460 | −0.324730 | − | 0.945807i | \(-0.605273\pi\) | ||||
−0.324730 | + | 0.945807i | \(0.605273\pi\) | |||||||
\(440\) | 13.8564 | 0.660578 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.3923 | −1.06389 | −0.531945 | − | 0.846779i | \(-0.678539\pi\) | ||||
−0.531945 | + | 0.846779i | \(0.678539\pi\) | |||||||
\(444\) | −4.92820 | −0.233882 | ||||||||
\(445\) | 40.6410 | 1.92657 | ||||||||
\(446\) | −7.53590 | −0.356835 | ||||||||
\(447\) | −11.5359 | −0.545629 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | −7.00000 | −0.329983 | ||||||||
\(451\) | 27.7128 | 1.30495 | ||||||||
\(452\) | −4.39230 | −0.206597 | ||||||||
\(453\) | −12.0000 | −0.563809 | ||||||||
\(454\) | 13.3205 | 0.625162 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.46410 | −0.349539 | ||||||||
\(457\) | −1.19615 | −0.0559537 | −0.0279768 | − | 0.999609i | \(-0.508906\pi\) | ||||
−0.0279768 | + | 0.999609i | \(0.508906\pi\) | |||||||
\(458\) | −19.9282 | −0.931184 | ||||||||
\(459\) | 6.46410 | 0.301718 | ||||||||
\(460\) | −19.8564 | −0.925810 | ||||||||
\(461\) | −5.07180 | −0.236217 | −0.118109 | − | 0.993001i | \(-0.537683\pi\) | ||||
−0.118109 | + | 0.993001i | \(0.537683\pi\) | |||||||
\(462\) | −4.00000 | −0.186097 | ||||||||
\(463\) | 8.24871 | 0.383350 | 0.191675 | − | 0.981458i | \(-0.438608\pi\) | ||||
0.191675 | + | 0.981458i | \(0.438608\pi\) | |||||||
\(464\) | 8.00000 | 0.371391 | ||||||||
\(465\) | 22.3923 | 1.03842 | ||||||||
\(466\) | −13.4641 | −0.623712 | ||||||||
\(467\) | −39.6410 | −1.83437 | −0.917184 | − | 0.398465i | \(-0.869543\pi\) | ||||
−0.917184 | + | 0.398465i | \(0.869543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.19615 | −0.332287 | ||||||||
\(470\) | −1.85641 | −0.0856296 | ||||||||
\(471\) | −2.92820 | −0.134924 | ||||||||
\(472\) | −6.26795 | −0.288506 | ||||||||
\(473\) | 17.8564 | 0.821038 | ||||||||
\(474\) | 9.46410 | 0.434701 | ||||||||
\(475\) | 52.2487 | 2.39734 | ||||||||
\(476\) | 6.46410 | 0.296282 | ||||||||
\(477\) | −8.26795 | −0.378563 | ||||||||
\(478\) | −12.8564 | −0.588038 | ||||||||
\(479\) | −4.39230 | −0.200690 | −0.100345 | − | 0.994953i | \(-0.531995\pi\) | ||||
−0.100345 | + | 0.994953i | \(0.531995\pi\) | |||||||
\(480\) | 3.46410 | 0.158114 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15.8564 | 0.722240 | ||||||||
\(483\) | 5.73205 | 0.260817 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | −42.9282 | −1.94927 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 0.392305 | 0.0177770 | 0.00888851 | − | 0.999960i | \(-0.497171\pi\) | ||||
0.00888851 | + | 0.999960i | \(0.497171\pi\) | |||||||
\(488\) | 5.19615 | 0.235219 | ||||||||
\(489\) | −1.33975 | −0.0605854 | ||||||||
\(490\) | 3.46410 | 0.156492 | ||||||||
\(491\) | −9.85641 | −0.444813 | −0.222407 | − | 0.974954i | \(-0.571391\pi\) | ||||
−0.222407 | + | 0.974954i | \(0.571391\pi\) | |||||||
\(492\) | 6.92820 | 0.312348 | ||||||||
\(493\) | 51.7128 | 2.32903 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.8564 | −0.622799 | ||||||||
\(496\) | −6.46410 | −0.290247 | ||||||||
\(497\) | 1.92820 | 0.0864917 | ||||||||
\(498\) | −1.73205 | −0.0776151 | ||||||||
\(499\) | −0.267949 | −0.0119951 | −0.00599753 | − | 0.999982i | \(-0.501909\pi\) | ||||
−0.00599753 | + | 0.999982i | \(0.501909\pi\) | |||||||
\(500\) | −6.92820 | −0.309839 | ||||||||
\(501\) | 20.0000 | 0.893534 | ||||||||
\(502\) | 10.0718 | 0.449526 | ||||||||
\(503\) | −6.92820 | −0.308913 | −0.154457 | − | 0.988000i | \(-0.549363\pi\) | ||||
−0.154457 | + | 0.988000i | \(0.549363\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.9282 | −1.01928 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.07180 | 0.225025 | ||||||||
\(509\) | 34.2487 | 1.51805 | 0.759024 | − | 0.651063i | \(-0.225677\pi\) | ||||
0.759024 | + | 0.651063i | \(0.225677\pi\) | |||||||
\(510\) | 22.3923 | 0.991548 | ||||||||
\(511\) | −10.9282 | −0.483435 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.46410 | 0.329548 | ||||||||
\(514\) | −0.464102 | −0.0204706 | ||||||||
\(515\) | −36.9282 | −1.62725 | ||||||||
\(516\) | 4.46410 | 0.196521 | ||||||||
\(517\) | −2.14359 | −0.0942751 | ||||||||
\(518\) | 4.92820 | 0.216533 | ||||||||
\(519\) | 1.07180 | 0.0470467 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | −8.00000 | −0.350150 | ||||||||
\(523\) | 14.9282 | 0.652765 | 0.326382 | − | 0.945238i | \(-0.394170\pi\) | ||||
0.326382 | + | 0.945238i | \(0.394170\pi\) | |||||||
\(524\) | 19.0000 | 0.830019 | ||||||||
\(525\) | 7.00000 | 0.305505 | ||||||||
\(526\) | 17.3205 | 0.755210 | ||||||||
\(527\) | −41.7846 | −1.82017 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | 9.85641 | 0.428539 | ||||||||
\(530\) | −28.6410 | −1.24409 | ||||||||
\(531\) | 6.26795 | 0.272006 | ||||||||
\(532\) | 7.46410 | 0.323610 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 11.7321 | 0.507695 | ||||||||
\(535\) | −29.5692 | −1.27839 | ||||||||
\(536\) | 7.19615 | 0.310826 | ||||||||
\(537\) | −16.9282 | −0.730506 | ||||||||
\(538\) | −22.3923 | −0.965401 | ||||||||
\(539\) | 4.00000 | 0.172292 | ||||||||
\(540\) | −3.46410 | −0.149071 | ||||||||
\(541\) | −17.3205 | −0.744667 | −0.372333 | − | 0.928099i | \(-0.621442\pi\) | ||||
−0.372333 | + | 0.928099i | \(0.621442\pi\) | |||||||
\(542\) | −12.4641 | −0.535379 | ||||||||
\(543\) | 24.7846 | 1.06361 | ||||||||
\(544\) | −6.46410 | −0.277146 | ||||||||
\(545\) | 41.5692 | 1.78063 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 13.8564 | 0.591916 | ||||||||
\(549\) | −5.19615 | −0.221766 | ||||||||
\(550\) | −28.0000 | −1.19392 | ||||||||
\(551\) | 59.7128 | 2.54385 | ||||||||
\(552\) | −5.73205 | −0.243972 | ||||||||
\(553\) | −9.46410 | −0.402455 | ||||||||
\(554\) | −7.32051 | −0.311019 | ||||||||
\(555\) | 17.0718 | 0.724657 | ||||||||
\(556\) | 2.92820 | 0.124183 | ||||||||
\(557\) | 24.6077 | 1.04266 | 0.521331 | − | 0.853355i | \(-0.325436\pi\) | ||||
0.521331 | + | 0.853355i | \(0.325436\pi\) | |||||||
\(558\) | 6.46410 | 0.273647 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.46410 | −0.146385 | ||||||||
\(561\) | 25.8564 | 1.09166 | ||||||||
\(562\) | 2.39230 | 0.100913 | ||||||||
\(563\) | −13.8564 | −0.583978 | −0.291989 | − | 0.956422i | \(-0.594317\pi\) | ||||
−0.291989 | + | 0.956422i | \(0.594317\pi\) | |||||||
\(564\) | −0.535898 | −0.0225654 | ||||||||
\(565\) | 15.2154 | 0.640116 | ||||||||
\(566\) | 11.4641 | 0.481872 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −1.92820 | −0.0809056 | ||||||||
\(569\) | 15.4641 | 0.648289 | 0.324144 | − | 0.946008i | \(-0.394924\pi\) | ||||
0.324144 | + | 0.946008i | \(0.394924\pi\) | |||||||
\(570\) | 25.8564 | 1.08301 | ||||||||
\(571\) | −3.39230 | −0.141964 | −0.0709818 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709818 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.5167 | −1.10775 | ||||||||
\(574\) | −6.92820 | −0.289178 | ||||||||
\(575\) | 40.1244 | 1.67330 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 1.21539 | 0.0505974 | 0.0252987 | − | 0.999680i | \(-0.491946\pi\) | ||||
0.0252987 | + | 0.999680i | \(0.491946\pi\) | |||||||
\(578\) | −24.7846 | −1.03090 | ||||||||
\(579\) | 17.8564 | 0.742087 | ||||||||
\(580\) | −27.7128 | −1.15071 | ||||||||
\(581\) | 1.73205 | 0.0718576 | ||||||||
\(582\) | −12.3923 | −0.513678 | ||||||||
\(583\) | −33.0718 | −1.36969 | ||||||||
\(584\) | 10.9282 | 0.452212 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −33.4641 | −1.38239 | ||||||||
\(587\) | −8.12436 | −0.335328 | −0.167664 | − | 0.985844i | \(-0.553622\pi\) | ||||
−0.167664 | + | 0.985844i | \(0.553622\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −48.2487 | −1.98805 | ||||||||
\(590\) | 21.7128 | 0.893902 | ||||||||
\(591\) | −2.60770 | −0.107266 | ||||||||
\(592\) | −4.92820 | −0.202548 | ||||||||
\(593\) | 4.26795 | 0.175264 | 0.0876318 | − | 0.996153i | \(-0.472070\pi\) | ||||
0.0876318 | + | 0.996153i | \(0.472070\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | −22.3923 | −0.917995 | ||||||||
\(596\) | −11.5359 | −0.472529 | ||||||||
\(597\) | −22.1244 | −0.905490 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.0526 | −0.778466 | −0.389233 | − | 0.921139i | \(-0.627260\pi\) | ||||
−0.389233 | + | 0.921139i | \(0.627260\pi\) | |||||||
\(600\) | −7.00000 | −0.285774 | ||||||||
\(601\) | −24.2487 | −0.989126 | −0.494563 | − | 0.869142i | \(-0.664672\pi\) | ||||
−0.494563 | + | 0.869142i | \(0.664672\pi\) | |||||||
\(602\) | −4.46410 | −0.181943 | ||||||||
\(603\) | −7.19615 | −0.293050 | ||||||||
\(604\) | −12.0000 | −0.488273 | ||||||||
\(605\) | −17.3205 | −0.704179 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.1962 | −0.616793 | −0.308396 | − | 0.951258i | \(-0.599792\pi\) | ||||
−0.308396 | + | 0.951258i | \(0.599792\pi\) | |||||||
\(608\) | −7.46410 | −0.302709 | ||||||||
\(609\) | 8.00000 | 0.324176 | ||||||||
\(610\) | −18.0000 | −0.728799 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.46410 | 0.261296 | ||||||||
\(613\) | −34.3923 | −1.38909 | −0.694546 | − | 0.719448i | \(-0.744395\pi\) | ||||
−0.694546 | + | 0.719448i | \(0.744395\pi\) | |||||||
\(614\) | 22.0000 | 0.887848 | ||||||||
\(615\) | −24.0000 | −0.967773 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | −5.85641 | −0.235770 | −0.117885 | − | 0.993027i | \(-0.537611\pi\) | ||||
−0.117885 | + | 0.993027i | \(0.537611\pi\) | |||||||
\(618\) | −10.6603 | −0.428818 | ||||||||
\(619\) | 30.7846 | 1.23734 | 0.618669 | − | 0.785652i | \(-0.287672\pi\) | ||||
0.618669 | + | 0.785652i | \(0.287672\pi\) | |||||||
\(620\) | 22.3923 | 0.899297 | ||||||||
\(621\) | 5.73205 | 0.230019 | ||||||||
\(622\) | −13.3205 | −0.534104 | ||||||||
\(623\) | −11.7321 | −0.470035 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −0.679492 | −0.0271580 | ||||||||
\(627\) | 29.8564 | 1.19235 | ||||||||
\(628\) | −2.92820 | −0.116848 | ||||||||
\(629\) | −31.8564 | −1.27020 | ||||||||
\(630\) | 3.46410 | 0.138013 | ||||||||
\(631\) | −34.9282 | −1.39047 | −0.695235 | − | 0.718783i | \(-0.744700\pi\) | ||||
−0.695235 | + | 0.718783i | \(0.744700\pi\) | |||||||
\(632\) | 9.46410 | 0.376462 | ||||||||
\(633\) | −9.07180 | −0.360572 | ||||||||
\(634\) | −16.4641 | −0.653873 | ||||||||
\(635\) | −17.5692 | −0.697213 | ||||||||
\(636\) | −8.26795 | −0.327846 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −32.0000 | −1.26689 | ||||||||
\(639\) | 1.92820 | 0.0762785 | ||||||||
\(640\) | 3.46410 | 0.136931 | ||||||||
\(641\) | −26.6410 | −1.05226 | −0.526128 | − | 0.850405i | \(-0.676357\pi\) | ||||
−0.526128 | + | 0.850405i | \(0.676357\pi\) | |||||||
\(642\) | −8.53590 | −0.336885 | ||||||||
\(643\) | −20.2487 | −0.798531 | −0.399266 | − | 0.916835i | \(-0.630735\pi\) | ||||
−0.399266 | + | 0.916835i | \(0.630735\pi\) | |||||||
\(644\) | 5.73205 | 0.225874 | ||||||||
\(645\) | −15.4641 | −0.608898 | ||||||||
\(646\) | −48.2487 | −1.89832 | ||||||||
\(647\) | 37.3205 | 1.46722 | 0.733610 | − | 0.679570i | \(-0.237834\pi\) | ||||
0.733610 | + | 0.679570i | \(0.237834\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 25.0718 | 0.984154 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.46410 | −0.253348 | ||||||||
\(652\) | −1.33975 | −0.0524685 | ||||||||
\(653\) | −37.5885 | −1.47095 | −0.735475 | − | 0.677552i | \(-0.763041\pi\) | ||||
−0.735475 | + | 0.677552i | \(0.763041\pi\) | |||||||
\(654\) | 12.0000 | 0.469237 | ||||||||
\(655\) | −65.8179 | −2.57172 | ||||||||
\(656\) | 6.92820 | 0.270501 | ||||||||
\(657\) | −10.9282 | −0.426350 | ||||||||
\(658\) | 0.535898 | 0.0208915 | ||||||||
\(659\) | 1.60770 | 0.0626269 | 0.0313135 | − | 0.999510i | \(-0.490031\pi\) | ||||
0.0313135 | + | 0.999510i | \(0.490031\pi\) | |||||||
\(660\) | −13.8564 | −0.539360 | ||||||||
\(661\) | 50.7128 | 1.97250 | 0.986250 | − | 0.165261i | \(-0.0528466\pi\) | ||||
0.986250 | + | 0.165261i | \(0.0528466\pi\) | |||||||
\(662\) | −21.3205 | −0.828645 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.73205 | −0.0672166 | ||||||||
\(665\) | −25.8564 | −1.00267 | ||||||||
\(666\) | 4.92820 | 0.190964 | ||||||||
\(667\) | 45.8564 | 1.77557 | ||||||||
\(668\) | 20.0000 | 0.773823 | ||||||||
\(669\) | 7.53590 | 0.291355 | ||||||||
\(670\) | −24.9282 | −0.963061 | ||||||||
\(671\) | −20.7846 | −0.802381 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 39.6410 | 1.52805 | 0.764024 | − | 0.645187i | \(-0.223221\pi\) | ||||
0.764024 | + | 0.645187i | \(0.223221\pi\) | |||||||
\(674\) | −6.00000 | −0.231111 | ||||||||
\(675\) | 7.00000 | 0.269430 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.07180 | 0.0411925 | 0.0205962 | − | 0.999788i | \(-0.493444\pi\) | ||||
0.0205962 | + | 0.999788i | \(0.493444\pi\) | |||||||
\(678\) | 4.39230 | 0.168685 | ||||||||
\(679\) | 12.3923 | 0.475573 | ||||||||
\(680\) | 22.3923 | 0.858706 | ||||||||
\(681\) | −13.3205 | −0.510443 | ||||||||
\(682\) | 25.8564 | 0.990093 | ||||||||
\(683\) | −51.1769 | −1.95823 | −0.979115 | − | 0.203307i | \(-0.934831\pi\) | ||||
−0.979115 | + | 0.203307i | \(0.934831\pi\) | |||||||
\(684\) | 7.46410 | 0.285397 | ||||||||
\(685\) | −48.0000 | −1.83399 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 19.9282 | 0.760308 | ||||||||
\(688\) | 4.46410 | 0.170192 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 19.8564 | 0.755920 | ||||||||
\(691\) | 41.1769 | 1.56644 | 0.783222 | − | 0.621742i | \(-0.213575\pi\) | ||||
0.783222 | + | 0.621742i | \(0.213575\pi\) | |||||||
\(692\) | 1.07180 | 0.0407436 | ||||||||
\(693\) | 4.00000 | 0.151947 | ||||||||
\(694\) | −25.7128 | −0.976045 | ||||||||
\(695\) | −10.1436 | −0.384768 | ||||||||
\(696\) | −8.00000 | −0.303239 | ||||||||
\(697\) | 44.7846 | 1.69634 | ||||||||
\(698\) | 35.6410 | 1.34903 | ||||||||
\(699\) | 13.4641 | 0.509259 | ||||||||
\(700\) | 7.00000 | 0.264575 | ||||||||
\(701\) | −2.12436 | −0.0802358 | −0.0401179 | − | 0.999195i | \(-0.512773\pi\) | ||||
−0.0401179 | + | 0.999195i | \(0.512773\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.7846 | −1.38736 | ||||||||
\(704\) | 4.00000 | 0.150756 | ||||||||
\(705\) | 1.85641 | 0.0699163 | ||||||||
\(706\) | 9.33975 | 0.351506 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.26795 | 0.235564 | ||||||||
\(709\) | 7.71281 | 0.289661 | 0.144830 | − | 0.989456i | \(-0.453736\pi\) | ||||
0.144830 | + | 0.989456i | \(0.453736\pi\) | |||||||
\(710\) | 6.67949 | 0.250677 | ||||||||
\(711\) | −9.46410 | −0.354932 | ||||||||
\(712\) | 11.7321 | 0.439677 | ||||||||
\(713\) | −37.0526 | −1.38763 | ||||||||
\(714\) | −6.46410 | −0.241913 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.9282 | −0.632637 | ||||||||
\(717\) | 12.8564 | 0.480131 | ||||||||
\(718\) | 8.00000 | 0.298557 | ||||||||
\(719\) | 34.5359 | 1.28797 | 0.643986 | − | 0.765037i | \(-0.277280\pi\) | ||||
0.643986 | + | 0.765037i | \(0.277280\pi\) | |||||||
\(720\) | −3.46410 | −0.129099 | ||||||||
\(721\) | 10.6603 | 0.397009 | ||||||||
\(722\) | −36.7128 | −1.36631 | ||||||||
\(723\) | −15.8564 | −0.589706 | ||||||||
\(724\) | 24.7846 | 0.921113 | ||||||||
\(725\) | 56.0000 | 2.07979 | ||||||||
\(726\) | −5.00000 | −0.185567 | ||||||||
\(727\) | −22.9090 | −0.849646 | −0.424823 | − | 0.905276i | \(-0.639664\pi\) | ||||
−0.424823 | + | 0.905276i | \(0.639664\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −37.8564 | −1.40113 | ||||||||
\(731\) | 28.8564 | 1.06729 | ||||||||
\(732\) | −5.19615 | −0.192055 | ||||||||
\(733\) | 4.85641 | 0.179375 | 0.0896877 | − | 0.995970i | \(-0.471413\pi\) | ||||
0.0896877 | + | 0.995970i | \(0.471413\pi\) | |||||||
\(734\) | 33.0526 | 1.21999 | ||||||||
\(735\) | −3.46410 | −0.127775 | ||||||||
\(736\) | −5.73205 | −0.211286 | ||||||||
\(737\) | −28.7846 | −1.06029 | ||||||||
\(738\) | −6.92820 | −0.255031 | ||||||||
\(739\) | 7.73205 | 0.284428 | 0.142214 | − | 0.989836i | \(-0.454578\pi\) | ||||
0.142214 | + | 0.989836i | \(0.454578\pi\) | |||||||
\(740\) | 17.0718 | 0.627572 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.26795 | 0.303526 | ||||||||
\(743\) | −1.78461 | −0.0654710 | −0.0327355 | − | 0.999464i | \(-0.510422\pi\) | ||||
−0.0327355 | + | 0.999464i | \(0.510422\pi\) | |||||||
\(744\) | 6.46410 | 0.236985 | ||||||||
\(745\) | 39.9615 | 1.46408 | ||||||||
\(746\) | 26.2487 | 0.961034 | ||||||||
\(747\) | 1.73205 | 0.0633724 | ||||||||
\(748\) | 25.8564 | 0.945404 | ||||||||
\(749\) | 8.53590 | 0.311895 | ||||||||
\(750\) | 6.92820 | 0.252982 | ||||||||
\(751\) | 29.3205 | 1.06992 | 0.534960 | − | 0.844877i | \(-0.320327\pi\) | ||||
0.534960 | + | 0.844877i | \(0.320327\pi\) | |||||||
\(752\) | −0.535898 | −0.0195422 | ||||||||
\(753\) | −10.0718 | −0.367037 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.5692 | 1.51286 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 19.8564 | 0.721693 | 0.360847 | − | 0.932625i | \(-0.382488\pi\) | ||||
0.360847 | + | 0.932625i | \(0.382488\pi\) | |||||||
\(758\) | −9.60770 | −0.348967 | ||||||||
\(759\) | 22.9282 | 0.832241 | ||||||||
\(760\) | 25.8564 | 0.937910 | ||||||||
\(761\) | −6.92820 | −0.251147 | −0.125574 | − | 0.992084i | \(-0.540077\pi\) | ||||
−0.125574 | + | 0.992084i | \(0.540077\pi\) | |||||||
\(762\) | −5.07180 | −0.183732 | ||||||||
\(763\) | −12.0000 | −0.434429 | ||||||||
\(764\) | −26.5167 | −0.959339 | ||||||||
\(765\) | −22.3923 | −0.809595 | ||||||||
\(766\) | −7.32051 | −0.264501 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −42.6410 | −1.53767 | −0.768837 | − | 0.639445i | \(-0.779164\pi\) | ||||
−0.768837 | + | 0.639445i | \(0.779164\pi\) | |||||||
\(770\) | 13.8564 | 0.499350 | ||||||||
\(771\) | 0.464102 | 0.0167142 | ||||||||
\(772\) | 17.8564 | 0.642666 | ||||||||
\(773\) | 12.9282 | 0.464995 | 0.232498 | − | 0.972597i | \(-0.425310\pi\) | ||||
0.232498 | + | 0.972597i | \(0.425310\pi\) | |||||||
\(774\) | −4.46410 | −0.160459 | ||||||||
\(775\) | −45.2487 | −1.62538 | ||||||||
\(776\) | −12.3923 | −0.444858 | ||||||||
\(777\) | −4.92820 | −0.176798 | ||||||||
\(778\) | 14.6603 | 0.525596 | ||||||||
\(779\) | 51.7128 | 1.85280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.71281 | 0.275986 | ||||||||
\(782\) | −37.0526 | −1.32500 | ||||||||
\(783\) | 8.00000 | 0.285897 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.1436 | 0.362040 | ||||||||
\(786\) | −19.0000 | −0.677708 | ||||||||
\(787\) | 8.39230 | 0.299153 | 0.149577 | − | 0.988750i | \(-0.452209\pi\) | ||||
0.149577 | + | 0.988750i | \(0.452209\pi\) | |||||||
\(788\) | −2.60770 | −0.0928953 | ||||||||
\(789\) | −17.3205 | −0.616626 | ||||||||
\(790\) | −32.7846 | −1.16642 | ||||||||
\(791\) | −4.39230 | −0.156172 | ||||||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −29.7846 | −1.05702 | ||||||||
\(795\) | 28.6410 | 1.01579 | ||||||||
\(796\) | −22.1244 | −0.784177 | ||||||||
\(797\) | 42.2487 | 1.49653 | 0.748263 | − | 0.663402i | \(-0.230888\pi\) | ||||
0.748263 | + | 0.663402i | \(0.230888\pi\) | |||||||
\(798\) | −7.46410 | −0.264226 | ||||||||
\(799\) | −3.46410 | −0.122551 | ||||||||
\(800\) | −7.00000 | −0.247487 | ||||||||
\(801\) | −11.7321 | −0.414532 | ||||||||
\(802\) | 16.3923 | 0.578832 | ||||||||
\(803\) | −43.7128 | −1.54259 | ||||||||
\(804\) | −7.19615 | −0.253789 | ||||||||
\(805\) | −19.8564 | −0.699846 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.3923 | 0.788246 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.7128 | 0.552433 | 0.276217 | − | 0.961095i | \(-0.410919\pi\) | ||||
0.276217 | + | 0.961095i | \(0.410919\pi\) | |||||||
\(810\) | 3.46410 | 0.121716 | ||||||||
\(811\) | 2.14359 | 0.0752717 | 0.0376359 | − | 0.999292i | \(-0.488017\pi\) | ||||
0.0376359 | + | 0.999292i | \(0.488017\pi\) | |||||||
\(812\) | 8.00000 | 0.280745 | ||||||||
\(813\) | 12.4641 | 0.437135 | ||||||||
\(814\) | 19.7128 | 0.690934 | ||||||||
\(815\) | 4.64102 | 0.162568 | ||||||||
\(816\) | 6.46410 | 0.226289 | ||||||||
\(817\) | 33.3205 | 1.16574 | ||||||||
\(818\) | −6.39230 | −0.223502 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | −31.2487 | −1.09059 | −0.545294 | − | 0.838245i | \(-0.683582\pi\) | ||||
−0.545294 | + | 0.838245i | \(0.683582\pi\) | |||||||
\(822\) | −13.8564 | −0.483298 | ||||||||
\(823\) | 23.6077 | 0.822913 | 0.411456 | − | 0.911430i | \(-0.365020\pi\) | ||||
0.411456 | + | 0.911430i | \(0.365020\pi\) | |||||||
\(824\) | −10.6603 | −0.371368 | ||||||||
\(825\) | 28.0000 | 0.974835 | ||||||||
\(826\) | −6.26795 | −0.218090 | ||||||||
\(827\) | 36.3923 | 1.26548 | 0.632742 | − | 0.774363i | \(-0.281929\pi\) | ||||
0.632742 | + | 0.774363i | \(0.281929\pi\) | |||||||
\(828\) | 5.73205 | 0.199203 | ||||||||
\(829\) | 7.21539 | 0.250601 | 0.125300 | − | 0.992119i | \(-0.460011\pi\) | ||||
0.125300 | + | 0.992119i | \(0.460011\pi\) | |||||||
\(830\) | 6.00000 | 0.208263 | ||||||||
\(831\) | 7.32051 | 0.253946 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.46410 | 0.223968 | ||||||||
\(834\) | −2.92820 | −0.101395 | ||||||||
\(835\) | −69.2820 | −2.39760 | ||||||||
\(836\) | 29.8564 | 1.03261 | ||||||||
\(837\) | −6.46410 | −0.223432 | ||||||||
\(838\) | 5.00000 | 0.172722 | ||||||||
\(839\) | 1.60770 | 0.0555038 | 0.0277519 | − | 0.999615i | \(-0.491165\pi\) | ||||
0.0277519 | + | 0.999615i | \(0.491165\pi\) | |||||||
\(840\) | 3.46410 | 0.119523 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 1.60770 | 0.0554048 | ||||||||
\(843\) | −2.39230 | −0.0823954 | ||||||||
\(844\) | −9.07180 | −0.312264 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.535898 | 0.0184246 | ||||||||
\(847\) | 5.00000 | 0.171802 | ||||||||
\(848\) | −8.26795 | −0.283923 | ||||||||
\(849\) | −11.4641 | −0.393447 | ||||||||
\(850\) | −45.2487 | −1.55202 | ||||||||
\(851\) | −28.2487 | −0.968353 | ||||||||
\(852\) | 1.92820 | 0.0660592 | ||||||||
\(853\) | 47.6410 | 1.63120 | 0.815599 | − | 0.578618i | \(-0.196408\pi\) | ||||
0.815599 | + | 0.578618i | \(0.196408\pi\) | |||||||
\(854\) | 5.19615 | 0.177809 | ||||||||
\(855\) | −25.8564 | −0.884270 | ||||||||
\(856\) | −8.53590 | −0.291751 | ||||||||
\(857\) | −33.7128 | −1.15161 | −0.575804 | − | 0.817588i | \(-0.695311\pi\) | ||||
−0.575804 | + | 0.817588i | \(0.695311\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.8564 | −0.541014 | −0.270507 | − | 0.962718i | \(-0.587191\pi\) | ||||
−0.270507 | + | 0.962718i | \(0.587191\pi\) | |||||||
\(860\) | −15.4641 | −0.527321 | ||||||||
\(861\) | 6.92820 | 0.236113 | ||||||||
\(862\) | 4.85641 | 0.165410 | ||||||||
\(863\) | 42.9282 | 1.46129 | 0.730647 | − | 0.682756i | \(-0.239219\pi\) | ||||
0.730647 | + | 0.682756i | \(0.239219\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −3.71281 | −0.126239 | ||||||||
\(866\) | −9.85641 | −0.334934 | ||||||||
\(867\) | 24.7846 | 0.841729 | ||||||||
\(868\) | −6.46410 | −0.219406 | ||||||||
\(869\) | −37.8564 | −1.28419 | ||||||||
\(870\) | 27.7128 | 0.939552 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12.0000 | 0.406371 | ||||||||
\(873\) | 12.3923 | 0.419416 | ||||||||
\(874\) | −42.7846 | −1.44721 | ||||||||
\(875\) | −6.92820 | −0.234216 | ||||||||
\(876\) | −10.9282 | −0.369230 | ||||||||
\(877\) | 25.7128 | 0.868260 | 0.434130 | − | 0.900850i | \(-0.357056\pi\) | ||||
0.434130 | + | 0.900850i | \(0.357056\pi\) | |||||||
\(878\) | 13.6077 | 0.459237 | ||||||||
\(879\) | 33.4641 | 1.12872 | ||||||||
\(880\) | −13.8564 | −0.467099 | ||||||||
\(881\) | 32.0333 | 1.07923 | 0.539615 | − | 0.841912i | \(-0.318570\pi\) | ||||
0.539615 | + | 0.841912i | \(0.318570\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −0.320508 | −0.0107860 | −0.00539298 | − | 0.999985i | \(-0.501717\pi\) | ||||
−0.00539298 | + | 0.999985i | \(0.501717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.7128 | −0.729868 | ||||||||
\(886\) | 22.3923 | 0.752284 | ||||||||
\(887\) | 11.8564 | 0.398099 | 0.199050 | − | 0.979989i | \(-0.436215\pi\) | ||||
0.199050 | + | 0.979989i | \(0.436215\pi\) | |||||||
\(888\) | 4.92820 | 0.165380 | ||||||||
\(889\) | 5.07180 | 0.170103 | ||||||||
\(890\) | −40.6410 | −1.36229 | ||||||||
\(891\) | 4.00000 | 0.134005 | ||||||||
\(892\) | 7.53590 | 0.252321 | ||||||||
\(893\) | −4.00000 | −0.133855 | ||||||||
\(894\) | 11.5359 | 0.385818 | ||||||||
\(895\) | 58.6410 | 1.96015 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | 0.600668 | ||||||||
\(899\) | −51.7128 | −1.72472 | ||||||||
\(900\) | 7.00000 | 0.233333 | ||||||||
\(901\) | −53.4449 | −1.78051 | ||||||||
\(902\) | −27.7128 | −0.922736 | ||||||||
\(903\) | 4.46410 | 0.148556 | ||||||||
\(904\) | 4.39230 | 0.146086 | ||||||||
\(905\) | −85.8564 | −2.85396 | ||||||||
\(906\) | 12.0000 | 0.398673 | ||||||||
\(907\) | −18.4641 | −0.613090 | −0.306545 | − | 0.951856i | \(-0.599173\pi\) | ||||
−0.306545 | + | 0.951856i | \(0.599173\pi\) | |||||||
\(908\) | −13.3205 | −0.442057 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.1769 | 0.900411 | 0.450206 | − | 0.892925i | \(-0.351351\pi\) | ||||
0.450206 | + | 0.892925i | \(0.351351\pi\) | |||||||
\(912\) | 7.46410 | 0.247161 | ||||||||
\(913\) | 6.92820 | 0.229290 | ||||||||
\(914\) | 1.19615 | 0.0395652 | ||||||||
\(915\) | 18.0000 | 0.595062 | ||||||||
\(916\) | 19.9282 | 0.658446 | ||||||||
\(917\) | 19.0000 | 0.627435 | ||||||||
\(918\) | −6.46410 | −0.213347 | ||||||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | 19.8564 | 0.654646 | ||||||||
\(921\) | −22.0000 | −0.724925 | ||||||||
\(922\) | 5.07180 | 0.167031 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.00000 | 0.131590 | ||||||||
\(925\) | −34.4974 | −1.13427 | ||||||||
\(926\) | −8.24871 | −0.271069 | ||||||||
\(927\) | 10.6603 | 0.350129 | ||||||||
\(928\) | −8.00000 | −0.262613 | ||||||||
\(929\) | 5.87564 | 0.192774 | 0.0963868 | − | 0.995344i | \(-0.469271\pi\) | ||||
0.0963868 | + | 0.995344i | \(0.469271\pi\) | |||||||
\(930\) | −22.3923 | −0.734273 | ||||||||
\(931\) | 7.46410 | 0.244626 | ||||||||
\(932\) | 13.4641 | 0.441031 | ||||||||
\(933\) | 13.3205 | 0.436094 | ||||||||
\(934\) | 39.6410 | 1.29709 | ||||||||
\(935\) | −89.5692 | −2.92923 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.9282 | −1.46774 | −0.733870 | − | 0.679290i | \(-0.762288\pi\) | ||||
−0.733870 | + | 0.679290i | \(0.762288\pi\) | |||||||
\(938\) | 7.19615 | 0.234963 | ||||||||
\(939\) | 0.679492 | 0.0221744 | ||||||||
\(940\) | 1.85641 | 0.0605493 | ||||||||
\(941\) | −19.6077 | −0.639193 | −0.319596 | − | 0.947554i | \(-0.603547\pi\) | ||||
−0.319596 | + | 0.947554i | \(0.603547\pi\) | |||||||
\(942\) | 2.92820 | 0.0954060 | ||||||||
\(943\) | 39.7128 | 1.29323 | ||||||||
\(944\) | 6.26795 | 0.204004 | ||||||||
\(945\) | −3.46410 | −0.112687 | ||||||||
\(946\) | −17.8564 | −0.580562 | ||||||||
\(947\) | 30.2487 | 0.982951 | 0.491476 | − | 0.870891i | \(-0.336458\pi\) | ||||
0.491476 | + | 0.870891i | \(0.336458\pi\) | |||||||
\(948\) | −9.46410 | −0.307380 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −52.2487 | −1.69517 | ||||||||
\(951\) | 16.4641 | 0.533885 | ||||||||
\(952\) | −6.46410 | −0.209503 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 8.26795 | 0.267685 | ||||||||
\(955\) | 91.8564 | 2.97240 | ||||||||
\(956\) | 12.8564 | 0.415806 | ||||||||
\(957\) | 32.0000 | 1.03441 | ||||||||
\(958\) | 4.39230 | 0.141909 | ||||||||
\(959\) | 13.8564 | 0.447447 | ||||||||
\(960\) | −3.46410 | −0.111803 | ||||||||
\(961\) | 10.7846 | 0.347891 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.53590 | 0.275065 | ||||||||
\(964\) | −15.8564 | −0.510700 | ||||||||
\(965\) | −61.8564 | −1.99123 | ||||||||
\(966\) | −5.73205 | −0.184426 | ||||||||
\(967\) | 16.5359 | 0.531759 | 0.265879 | − | 0.964006i | \(-0.414338\pi\) | ||||
0.265879 | + | 0.964006i | \(0.414338\pi\) | |||||||
\(968\) | −5.00000 | −0.160706 | ||||||||
\(969\) | 48.2487 | 1.54997 | ||||||||
\(970\) | 42.9282 | 1.37834 | ||||||||
\(971\) | 23.9282 | 0.767893 | 0.383946 | − | 0.923355i | \(-0.374565\pi\) | ||||
0.383946 | + | 0.923355i | \(0.374565\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 2.92820 | 0.0938739 | ||||||||
\(974\) | −0.392305 | −0.0125703 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.19615 | −0.166325 | ||||||||
\(977\) | 25.8564 | 0.827220 | 0.413610 | − | 0.910454i | \(-0.364268\pi\) | ||||
0.413610 | + | 0.910454i | \(0.364268\pi\) | |||||||
\(978\) | 1.33975 | 0.0428404 | ||||||||
\(979\) | −46.9282 | −1.49983 | ||||||||
\(980\) | −3.46410 | −0.110657 | ||||||||
\(981\) | −12.0000 | −0.383131 | ||||||||
\(982\) | 9.85641 | 0.314531 | ||||||||
\(983\) | 19.0718 | 0.608296 | 0.304148 | − | 0.952625i | \(-0.401628\pi\) | ||||
0.304148 | + | 0.952625i | \(0.401628\pi\) | |||||||
\(984\) | −6.92820 | −0.220863 | ||||||||
\(985\) | 9.03332 | 0.287826 | ||||||||
\(986\) | −51.7128 | −1.64687 | ||||||||
\(987\) | −0.535898 | −0.0170578 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.5885 | 0.813666 | ||||||||
\(990\) | 13.8564 | 0.440386 | ||||||||
\(991\) | 0.143594 | 0.00456140 | 0.00228070 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228070 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(992\) | 6.46410 | 0.205235 | ||||||||
\(993\) | 21.3205 | 0.676586 | ||||||||
\(994\) | −1.92820 | −0.0611589 | ||||||||
\(995\) | 76.6410 | 2.42968 | ||||||||
\(996\) | 1.73205 | 0.0548821 | ||||||||
\(997\) | 33.9808 | 1.07618 | 0.538091 | − | 0.842887i | \(-0.319146\pi\) | ||||
0.538091 | + | 0.842887i | \(0.319146\pi\) | |||||||
\(998\) | 0.267949 | 0.00848178 | ||||||||
\(999\) | −4.92820 | −0.155921 |
(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 | 7098.2.a.bn.1.1 | 2 | ||
13.6 | odd | 12 | 546.2.s.c.127.2 | yes | 4 | ||
13.11 | odd | 12 | 546.2.s.c.43.2 | ✓ | 4 | ||
13.12 | even | 2 | 7098.2.a.bz.1.2 | 2 | |||
39.11 | even | 12 | 1638.2.bj.e.1135.1 | 4 | |||
39.32 | even | 12 | 1638.2.bj.e.127.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.c.43.2 | ✓ | 4 | 13.11 | odd | 12 | ||
546.2.s.c.127.2 | yes | 4 | 13.6 | odd | 12 | ||
1638.2.bj.e.127.1 | 4 | 39.32 | even | 12 | |||
1638.2.bj.e.1135.1 | 4 | 39.11 | even | 12 | |||
7098.2.a.bn.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7098.2.a.bz.1.2 | 2 | 13.12 | even | 2 |