Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(-2.06929\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.06929 | 1.19470 | 0.597352 | − | 0.801979i | \(-0.296219\pi\) | ||||
0.597352 | + | 0.801979i | \(0.296219\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.835530 | −0.315800 | −0.157900 | − | 0.987455i | \(-0.550472\pi\) | ||||
−0.157900 | + | 0.987455i | \(0.550472\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.28196 | 0.427318 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.16889 | −1.55848 | −0.779239 | − | 0.626727i | \(-0.784394\pi\) | ||||
−0.779239 | + | 0.626727i | \(0.784394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.52286 | 1.25441 | 0.627207 | − | 0.778852i | \(-0.284198\pi\) | ||||
0.627207 | + | 0.778852i | \(0.284198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.06929 | 0.534288 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.30666 | −1.28705 | −0.643527 | − | 0.765424i | \(-0.722529\pi\) | ||||
−0.643527 | + | 0.765424i | \(0.722529\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.46213 | −1.48251 | −0.741257 | − | 0.671221i | \(-0.765770\pi\) | ||||
−0.741257 | + | 0.671221i | \(0.765770\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.72895 | −0.377288 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.32449 | −1.11023 | −0.555116 | − | 0.831773i | \(-0.687326\pi\) | ||||
−0.555116 | + | 0.831773i | \(0.687326\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.55513 | −0.684185 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.21060 | 1.33898 | 0.669488 | − | 0.742823i | \(-0.266514\pi\) | ||||
0.669488 | + | 0.742823i | \(0.266514\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.66896 | 1.37739 | 0.688693 | − | 0.725053i | \(-0.258185\pi\) | ||||
0.688693 | + | 0.725053i | \(0.258185\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.6959 | −1.86192 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.835530 | −0.141230 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.65331 | 1.25820 | 0.629098 | − | 0.777326i | \(-0.283424\pi\) | ||||
0.629098 | + | 0.777326i | \(0.283424\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.35910 | 1.49865 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.14014 | −0.490408 | −0.245204 | − | 0.969472i | \(-0.578855\pi\) | ||||
−0.245204 | + | 0.969472i | \(0.578855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.02225 | 1.22338 | 0.611691 | − | 0.791097i | \(-0.290490\pi\) | ||||
0.611691 | + | 0.791097i | \(0.290490\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.28196 | 0.191103 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1777 | −1.77630 | −0.888152 | − | 0.459551i | \(-0.848010\pi\) | ||||
−0.888152 | + | 0.459551i | \(0.848010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.30189 | −0.900270 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.9810 | −1.53765 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.3115 | 1.55375 | 0.776877 | − | 0.629653i | \(-0.216803\pi\) | ||||
0.776877 | + | 0.629653i | \(0.216803\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.16889 | −0.696973 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.3720 | −1.77117 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.74516 | −1.00833 | −0.504167 | − | 0.863606i | \(-0.668200\pi\) | ||||
−0.504167 | + | 0.863606i | \(0.668200\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1168 | 1.29532 | 0.647661 | − | 0.761929i | \(-0.275747\pi\) | ||||
0.647661 | + | 0.761929i | \(0.275747\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.07111 | −0.134947 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.52286 | 0.560991 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.34910 | −0.653497 | −0.326748 | − | 0.945111i | \(-0.605953\pi\) | ||||
−0.326748 | + | 0.945111i | \(0.605953\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.0179 | −1.32640 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5813 | −1.37445 | −0.687224 | − | 0.726446i | \(-0.741171\pi\) | ||||
−0.687224 | + | 0.726446i | \(0.741171\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.45002 | −0.989000 | −0.494500 | − | 0.869178i | \(-0.664649\pi\) | ||||
−0.494500 | + | 0.869178i | \(0.664649\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.06929 | 0.238941 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.31876 | 0.492168 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7154 | −1.43060 | −0.715299 | − | 0.698818i | \(-0.753710\pi\) | ||||
−0.715299 | + | 0.698818i | \(0.753710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2025 | −1.24472 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.2329 | −1.56227 | −0.781134 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781134 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.30666 | −0.575588 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.9208 | 1.59968 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.3014 | −1.72795 | −0.863974 | − | 0.503536i | \(-0.832032\pi\) | ||||
−0.863974 | + | 0.503536i | \(0.832032\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.77898 | −0.396145 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.8693 | 1.64557 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.46213 | −0.663001 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9093 | −1.31074 | −0.655372 | − | 0.755306i | \(-0.727488\pi\) | ||||
−0.655372 | + | 0.755306i | \(0.727488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.62628 | −0.665967 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.2443 | −1.51686 | −0.758432 | − | 0.651752i | \(-0.774034\pi\) | ||||
−0.758432 | + | 0.651752i | \(0.774034\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.56124 | 0.745031 | 0.372515 | − | 0.928026i | \(-0.378495\pi\) | ||||
0.372515 | + | 0.928026i | \(0.378495\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.72895 | −0.168728 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.6019 | −1.02493 | −0.512463 | − | 0.858709i | \(-0.671267\pi\) | ||||
−0.512463 | + | 0.858709i | \(0.671267\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.61594 | −0.250561 | −0.125281 | − | 0.992121i | \(-0.539983\pi\) | ||||
−0.125281 | + | 0.992121i | \(0.539983\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.8369 | 1.50317 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.3961 | 1.16613 | 0.583064 | − | 0.812426i | \(-0.301854\pi\) | ||||
0.583064 | + | 0.812426i | \(0.301854\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.32449 | −0.496511 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.79810 | 0.536035 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.43387 | 0.406452 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.7174 | 1.42886 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.49786 | −0.585893 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6039 | −1.02968 | −0.514838 | − | 0.857287i | \(-0.672148\pi\) | ||||
−0.514838 | + | 0.857287i | \(0.672148\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.6003 | 1.46158 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.3615 | 1.08003 | 0.540013 | − | 0.841657i | \(-0.318419\pi\) | ||||
0.540013 | + | 0.841657i | \(0.318419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.39930 | 0.468179 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.55513 | −0.305977 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.32336 | 0.198498 | 0.0992491 | − | 0.995063i | \(-0.468356\pi\) | ||||
0.0992491 | + | 0.995063i | \(0.468356\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.0803 | 1.61837 | 0.809183 | − | 0.587557i | \(-0.199910\pi\) | ||||
0.809183 | + | 0.587557i | \(0.199910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −25.1992 | −2.12216 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.3781 | −1.95498 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.21060 | 0.598808 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.0404 | −1.07556 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.4699 | −1.18542 | −0.592712 | − | 0.805415i | \(-0.701943\pi\) | ||||
−0.592712 | + | 0.805415i | \(0.701943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.80290 | −0.549982 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.66896 | 0.615986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8769 | −1.10750 | −0.553749 | − | 0.832684i | \(-0.686803\pi\) | ||||
−0.553749 | + | 0.832684i | \(0.686803\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.4067 | 1.85628 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.44877 | 0.350612 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.22611 | 0.174362 | 0.0871812 | − | 0.996192i | \(-0.472214\pi\) | ||||
0.0871812 | + | 0.996192i | \(0.472214\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.6959 | −0.832676 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.2210 | −1.48736 | −0.743682 | − | 0.668534i | \(-0.766922\pi\) | ||||
−0.743682 | + | 0.668534i | \(0.766922\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.45624 | 0.573557 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.28416 | −0.633506 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.9144 | −1.05790 | −0.528948 | − | 0.848654i | \(-0.677413\pi\) | ||||
−0.528948 | + | 0.848654i | \(0.677413\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.835530 | −0.0631601 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.0270 | −1.20466 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.5790 | 1.46341 | 0.731703 | − | 0.681623i | \(-0.238726\pi\) | ||||
0.731703 | + | 0.681623i | \(0.238726\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2953 | 1.28555 | 0.642774 | − | 0.766056i | \(-0.277783\pi\) | ||||
0.642774 | + | 0.766056i | \(0.277783\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.9345 | 1.54753 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.65331 | 0.562682 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.4295 | 2.00585 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.97042 | 0.216066 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.13159 | 0.226594 | 0.113297 | − | 0.993561i | \(-0.463859\pi\) | ||||
0.113297 | + | 0.993561i | \(0.463859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.32113 | −0.239060 | −0.119530 | − | 0.992831i | \(-0.538139\pi\) | ||||
−0.119530 | + | 0.992831i | \(0.538139\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.35910 | 0.670219 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.47516 | −0.105101 | −0.0525503 | − | 0.998618i | \(-0.516735\pi\) | ||||
−0.0525503 | + | 0.998618i | \(0.516735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5686 | 1.03274 | 0.516371 | − | 0.856365i | \(-0.327282\pi\) | ||||
0.516371 | + | 0.856365i | \(0.327282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.0688 | −0.780735 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.02467 | −0.422849 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.14014 | −0.219317 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.82576 | −0.474423 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.4020 | 2.31047 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.78970 | −0.605108 | −0.302554 | − | 0.953132i | \(-0.597839\pi\) | ||||
−0.302554 | + | 0.953132i | \(0.597839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.9650 | −1.64206 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.02225 | 0.547113 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.40764 | −0.434979 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.4855 | −1.18156 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.0013 | −1.61450 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.60000 | −0.308039 | −0.154019 | − | 0.988068i | \(-0.549222\pi\) | ||||
−0.154019 | + | 0.988068i | \(0.549222\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.28196 | 0.0854637 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.7763 | 0.715250 | 0.357625 | − | 0.933865i | \(-0.383587\pi\) | ||||
0.357625 | + | 0.933865i | \(0.383587\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.39513 | −0.554766 | −0.277383 | − | 0.960759i | \(-0.589467\pi\) | ||||
−0.277383 | + | 0.960759i | \(0.589467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.93676 | 0.587996 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.1187 | −0.924947 | −0.462473 | − | 0.886633i | \(-0.653038\pi\) | ||||
−0.462473 | + | 0.886633i | \(0.653038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1777 | −0.794387 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.3119 | −1.70914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.4588 | −0.870575 | −0.435287 | − | 0.900292i | \(-0.643353\pi\) | ||||
−0.435287 | + | 0.900292i | \(0.643353\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.39148 | 0.604958 | 0.302479 | − | 0.953156i | \(-0.402186\pi\) | ||||
0.302479 | + | 0.953156i | \(0.402186\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.5157 | −0.802884 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.30189 | −0.402613 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.2273 | −1.85969 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.4520 | −1.86645 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.91069 | 0.183721 | 0.0918606 | − | 0.995772i | \(-0.470719\pi\) | ||||
0.0918606 | + | 0.995772i | \(0.470719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.5217 | 1.73027 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.9810 | −0.687657 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1799 | −0.697386 | −0.348693 | − | 0.937237i | \(-0.613374\pi\) | ||||
−0.348693 | + | 0.937237i | \(0.613374\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.39456 | −0.397339 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.24367 | 0.572169 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.2666 | 0.941378 | 0.470689 | − | 0.882299i | \(-0.344005\pi\) | ||||
0.470689 | + | 0.882299i | \(0.344005\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.3115 | 0.694860 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −33.7324 | −2.06439 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.2376 | 0.990023 | 0.495011 | − | 0.868887i | \(-0.335164\pi\) | ||||
0.495011 | + | 0.868887i | \(0.335164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.6327 | 1.80006 | 0.900030 | − | 0.435827i | \(-0.143544\pi\) | ||||
0.900030 | + | 0.435827i | \(0.143544\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.81980 | −0.473276 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.16889 | −0.311696 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.52014 | −0.211505 | −0.105752 | − | 0.994392i | \(-0.533725\pi\) | ||||
−0.105752 | + | 0.994392i | \(0.533725\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.83127 | 0.588582 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.54474 | −0.569392 | −0.284696 | − | 0.958618i | \(-0.591893\pi\) | ||||
−0.284696 | + | 0.958618i | \(0.591893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1609 | 0.604002 | 0.302001 | − | 0.953308i | \(-0.402345\pi\) | ||||
0.302001 | + | 0.953308i | \(0.402345\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.3720 | −0.792090 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.62368 | 0.154871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1606 | 0.656506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −26.7131 | −1.56595 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.2837 | 1.41867 | 0.709334 | − | 0.704873i | \(-0.248996\pi\) | ||||
0.709334 | + | 0.704873i | \(0.248996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.74516 | −0.450941 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.3761 | 1.06629 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.0819 | −1.39269 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.70283 | −0.386344 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.5449 | −1.81220 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.1168 | 0.579285 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.63111 | −0.207238 | −0.103619 | − | 0.994617i | \(-0.533042\pi\) | ||||
−0.103619 | + | 0.994617i | \(0.533042\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.6464 | 0.890092 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5499 | 0.938458 | 0.469229 | − | 0.883077i | \(-0.344532\pi\) | ||||
0.469229 | + | 0.883077i | \(0.344532\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.6185 | 1.33500 | 0.667499 | − | 0.744611i | \(-0.267365\pi\) | ||||
0.667499 | + | 0.744611i | \(0.267365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.07111 | −0.0603503 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.4797 | 1.31875 | 0.659377 | − | 0.751813i | \(-0.270820\pi\) | ||||
0.659377 | + | 0.751813i | \(0.270820\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.2708 | −2.08676 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.9384 | −1.22448 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.2923 | 1.90808 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.52286 | 0.250883 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.41313 | −0.299347 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.1748 | 0.560957 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4491 | −0.629302 | −0.314651 | − | 0.949207i | \(-0.601887\pi\) | ||||
−0.314651 | + | 0.949207i | \(0.601887\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.81120 | 0.537650 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.34910 | −0.292253 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.3593 | −1.10904 | −0.554521 | − | 0.832169i | \(-0.687099\pi\) | ||||
−0.554521 | + | 0.832169i | \(0.687099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.6512 | 1.39318 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −39.6400 | −2.14663 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1141 | 0.600106 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.0179 | −0.593184 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.0321 | 1.71957 | 0.859787 | − | 0.510653i | \(-0.170596\pi\) | ||||
0.859787 | + | 0.510653i | \(0.170596\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.48515 | 0.293614 | 0.146807 | − | 0.989165i | \(-0.453100\pi\) | ||||
0.146807 | + | 0.989165i | \(0.453100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.0793 | −0.858252 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.04362 | −0.481343 | −0.240672 | − | 0.970607i | \(-0.577368\pi\) | ||||
−0.240672 | + | 0.970607i | \(0.577368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.5813 | −0.614671 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.17495 | 0.485590 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.9220 | 0.893110 | 0.446555 | − | 0.894756i | \(-0.352651\pi\) | ||||
0.446555 | + | 0.894756i | \(0.352651\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.7591 | 1.19785 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.5239 | 1.70706 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.45002 | −0.442294 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.38029 | −0.124250 | −0.0621251 | − | 0.998068i | \(-0.519788\pi\) | ||||
−0.0621251 | + | 0.998068i | \(0.519788\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.02552 | −0.209560 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.45109 | −0.490676 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.65463 | −0.0856736 | −0.0428368 | − | 0.999082i | \(-0.513640\pi\) | ||||
−0.0428368 | + | 0.999082i | \(0.513640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.06929 | 0.106858 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.6125 | 1.67963 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.2563 | 0.783665 | 0.391832 | − | 0.920037i | \(-0.371841\pi\) | ||||
0.391832 | + | 0.920037i | \(0.371841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.0117 | −1.23016 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.0927 | −1.12889 | −0.564443 | − | 0.825472i | \(-0.690909\pi\) | ||||
−0.564443 | + | 0.825472i | \(0.690909\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.31876 | 0.220104 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.2842 | 0.522773 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.8242 | 1.05583 | 0.527915 | − | 0.849297i | \(-0.322974\pi\) | ||||
0.527915 | + | 0.849297i | \(0.322974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.2552 | 1.42893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.5794 | 1.29031 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.7154 | −0.639783 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.91881 | −0.0963023 | −0.0481511 | − | 0.998840i | \(-0.515333\pi\) | ||||
−0.0481511 | + | 0.998840i | \(0.515333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.1727 | 0.559335 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.66802 | −0.233110 | −0.116555 | − | 0.993184i | \(-0.537185\pi\) | ||||
−0.116555 | + | 0.993184i | \(0.537185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.6856 | 1.72781 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.2025 | −0.556655 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −39.5591 | −1.96087 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.0822 | −1.19079 | −0.595393 | − | 0.803435i | \(-0.703004\pi\) | ||||
−0.595393 | + | 0.803435i | \(0.703004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.80771 | 0.237147 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.47131 | 0.318432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.2329 | −0.698667 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 39.4825 | 1.93347 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.5364 | 0.905564 | 0.452782 | − | 0.891621i | \(-0.350432\pi\) | ||||
0.452782 | + | 0.891621i | \(0.350432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.5023 | 1.63280 | 0.816400 | − | 0.577487i | \(-0.195967\pi\) | ||||
0.816400 | + | 0.577487i | \(0.195967\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.6113 | −0.759047 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.30666 | −0.257411 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.45287 | −0.409063 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −48.3761 | −2.33562 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.0155 | 1.54213 | 0.771065 | − | 0.636756i | \(-0.219724\pi\) | ||||
0.771065 | + | 0.636756i | \(0.219724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.02308 | −0.0972232 | −0.0486116 | − | 0.998818i | \(-0.515480\pi\) | ||||
−0.0486116 | + | 0.998818i | \(0.515480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.9208 | 0.715399 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.4075 | 1.64594 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.818067 | 0.0390442 | 0.0195221 | − | 0.999809i | \(-0.493786\pi\) | ||||
0.0195221 | + | 0.999809i | \(0.493786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.07874 | −0.384702 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.02456 | 0.143701 | 0.0718506 | − | 0.997415i | \(-0.477110\pi\) | ||||
0.0718506 | + | 0.997415i | \(0.477110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.3014 | −0.772762 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.9425 | −1.41623 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.8233 | −1.40745 | −0.703724 | − | 0.710474i | \(-0.748481\pi\) | ||||
−0.703724 | + | 0.710474i | \(0.748481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.2311 | 0.764290 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.06929 | 0.0972237 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.77898 | −0.177161 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.7034 | 0.781350 | 0.390675 | − | 0.920529i | \(-0.372242\pi\) | ||||
0.390675 | + | 0.920529i | \(0.372242\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.8659 | 0.880583 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.8849 | 1.34530 | 0.672652 | − | 0.739959i | \(-0.265155\pi\) | ||||
0.672652 | + | 0.739959i | \(0.265155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.2501 | −1.68469 | −0.842343 | − | 0.538942i | \(-0.818824\pi\) | ||||
−0.842343 | + | 0.538942i | \(0.818824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.8693 | 0.735921 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.4982 | 1.45756 | 0.728782 | − | 0.684746i | \(-0.240087\pi\) | ||||
0.728782 | + | 0.684746i | \(0.240087\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.46933 | 0.206375 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.7153 | −1.32313 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.4661 | −1.90661 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.46213 | −0.296503 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.5008 | 0.663947 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.6813 | 1.44756 | 0.723778 | − | 0.690033i | \(-0.242404\pi\) | ||||
0.723778 | + | 0.690033i | \(0.242404\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.6148 | 1.57830 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.20578 | 0.418878 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.9093 | −0.586183 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.69086 | −0.212563 | −0.106282 | − | 0.994336i | \(-0.533894\pi\) | ||||
−0.106282 | + | 0.994336i | \(0.533894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.60647 | 0.208312 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.9410 | −0.674276 | −0.337138 | − | 0.941455i | \(-0.609459\pi\) | ||||
−0.337138 | + | 0.941455i | \(0.609459\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.2642 | −1.72333 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.62628 | −0.297829 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.67652 | 0.434051 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.6274 | −1.10247 | −0.551237 | − | 0.834349i | \(-0.685844\pi\) | ||||
−0.551237 | + | 0.834349i | \(0.685844\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.7737 | −1.77696 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.20454 | 0.365823 | 0.182911 | − | 0.983129i | \(-0.441448\pi\) | ||||
0.182911 | + | 0.983129i | \(0.441448\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.2443 | −0.678363 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.4291 | 0.685231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.51038 | −0.199919 | −0.0999595 | − | 0.994992i | \(-0.531871\pi\) | ||||
−0.0999595 | + | 0.994992i | \(0.531871\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.06024 | 0.312327 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.9737 | 1.01431 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.56124 | 0.333188 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 62.9453 | 2.76833 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.7930 | −1.26387 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.8532 | −1.35170 | −0.675851 | − | 0.737038i | \(-0.736224\pi\) | ||||
−0.675851 | + | 0.737038i | \(0.736224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.0957 | −0.922450 | −0.461225 | − | 0.887283i | \(-0.652590\pi\) | ||||
−0.461225 | + | 0.887283i | \(0.652590\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.72895 | −0.0754576 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −40.6965 | −1.77277 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.35017 | 0.232616 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.92895 | −0.430880 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.2024 | −0.615175 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.6019 | −0.458361 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40.5147 | 1.74834 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.5738 | 1.40305 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.8673 | −1.28409 | −0.642047 | − | 0.766666i | \(-0.721914\pi\) | ||||
−0.642047 | + | 0.766666i | \(0.721914\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.7889 | 1.53585 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.61594 | −0.112054 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.72185 | −0.0736210 | −0.0368105 | − | 0.999322i | \(-0.511720\pi\) | ||||
−0.0368105 | + | 0.999322i | \(0.511720\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.9693 | 0.553515 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.5959 | −1.98505 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6241 | 0.451784 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.8369 | 0.672239 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.38990 | 0.313120 | 0.156560 | − | 0.987668i | \(-0.449960\pi\) | ||||
0.156560 | + | 0.987668i | \(0.449960\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.2835 | 1.53463 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 56.7596 | 2.39639 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.76351 | 0.0743232 | 0.0371616 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371616 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.3961 | 0.521509 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.35998 | 0.393082 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.7925 | −0.997433 | −0.498716 | − | 0.866765i | \(-0.666195\pi\) | ||||
−0.498716 | + | 0.866765i | \(0.666195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.6514 | −1.03163 | −0.515814 | − | 0.856700i | \(-0.672511\pi\) | ||||
−0.515814 | + | 0.856700i | \(0.672511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.48017 | 0.270713 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.32449 | −0.222046 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.6431 | −0.526340 | −0.263170 | − | 0.964749i | \(-0.584768\pi\) | ||||
−0.263170 | + | 0.964749i | \(0.584768\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.87237 | −0.285606 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.8920 | 0.493365 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −58.4679 | −2.42149 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.79810 | 0.239722 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.223982 | 0.00924472 | 0.00462236 | − | 0.999989i | \(-0.498529\pi\) | ||||
0.00462236 | + | 0.999989i | \(0.498529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.5578 | −2.04199 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.05253 | −0.125564 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.35704 | −0.137857 | −0.0689286 | − | 0.997622i | \(-0.521958\pi\) | ||||
−0.0689286 | + | 0.997622i | \(0.521958\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.43387 | 0.181771 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.1467 | 1.23382 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.1903 | 1.51956 | 0.759778 | − | 0.650182i | \(-0.225307\pi\) | ||||
0.759778 | + | 0.650182i | \(0.225307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.7225 | 0.722914 | 0.361457 | − | 0.932389i | \(-0.382279\pi\) | ||||
0.361457 | + | 0.932389i | \(0.382279\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.85731 | −0.279251 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.7174 | 0.639004 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0325 | 0.650740 | 0.325370 | − | 0.945587i | \(-0.394511\pi\) | ||||
0.325370 | + | 0.945587i | \(0.394511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.4668 | −0.505180 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −55.0781 | −2.22822 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.0279 | 1.01087 | 0.505434 | − | 0.862865i | \(-0.331332\pi\) | ||||
0.505434 | + | 0.862865i | \(0.331332\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.49786 | −0.262019 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.6646 | 1.19425 | 0.597126 | − | 0.802147i | \(-0.296309\pi\) | ||||
0.597126 | + | 0.802147i | \(0.296309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8356 | 0.475714 | 0.237857 | − | 0.971300i | \(-0.423555\pi\) | ||||
0.237857 | + | 0.971300i | \(0.423555\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.9292 | 0.759604 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.6203 | 0.545687 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 69.1184 | 2.76032 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40.6135 | −1.61937 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.4927 | −1.37313 | −0.686566 | − | 0.727067i | \(-0.740883\pi\) | ||||
−0.686566 | + | 0.727067i | \(0.740883\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.1884 | −0.722925 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.6039 | −0.460485 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.5026 | −1.12931 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.8467 | −0.587327 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.6030 | −0.813770 | −0.406885 | − | 0.913479i | \(-0.633385\pi\) | ||||
−0.406885 | + | 0.913479i | \(0.633385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.88259 | 0.350295 | 0.175148 | − | 0.984542i | \(-0.443960\pi\) | ||||
0.175148 | + | 0.984542i | \(0.443960\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.6003 | 0.653638 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.4768 | 0.765713 | 0.382857 | − | 0.923808i | \(-0.374940\pi\) | ||||
0.382857 | + | 0.923808i | \(0.374940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0339 | 1.57147 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.2593 | −0.519672 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.9684 | −1.64235 | −0.821175 | − | 0.570676i | \(-0.806681\pi\) | ||||
−0.821175 | + | 0.570676i | \(0.806681\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.3615 | 0.483002 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.8325 | −0.422618 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.9151 | −1.67174 | −0.835868 | − | 0.548930i | \(-0.815035\pi\) | ||||
−0.835868 | + | 0.548930i | \(0.815035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.9219 | 1.20272 | 0.601362 | − | 0.798977i | \(-0.294625\pi\) | ||||
0.601362 | + | 0.798977i | \(0.294625\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −49.6655 | −1.92885 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.39930 | 0.209376 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.3928 | −1.48657 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.51873 | −0.368015 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.2925 | −2.01873 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.4204 | 0.902789 | 0.451394 | − | 0.892325i | \(-0.350927\pi\) | ||||
0.451394 | + | 0.892325i | \(0.350927\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.55513 | −0.136837 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.3253 | 1.01176 | 0.505881 | − | 0.862603i | \(-0.331167\pi\) | ||||
0.505881 | + | 0.862603i | \(0.331167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.7861 | 0.413934 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.2993 | 0.854512 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.78192 | 0.0681833 | 0.0340917 | − | 0.999419i | \(-0.489146\pi\) | ||||
0.0340917 | + | 0.999419i | \(0.489146\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.32336 | 0.0887711 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.3720 | −0.662781 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 51.1603 | 1.94905 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.9347 | −1.93765 | −0.968824 | − | 0.247752i | \(-0.920308\pi\) | ||||
−0.968824 | + | 0.247752i | \(0.920308\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.53646 | 0.210313 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.0803 | 0.723755 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.6637 | 0.631181 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.2157 | −1.10504 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.2992 | 0.464533 | 0.232266 | − | 0.972652i | \(-0.425386\pi\) | ||||
0.232266 | + | 0.972652i | \(0.425386\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49.4567 | −1.86529 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.1992 | −0.949057 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.7371 | 0.479027 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.2798 | 0.836737 | 0.418368 | − | 0.908277i | \(-0.362602\pi\) | ||||
0.418368 | + | 0.908277i | \(0.362602\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.3006 | −0.611321 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.8333 | −1.52922 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.3781 | −0.874293 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.8501 | −1.04008 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.9514 | −1.75099 | −0.875495 | − | 0.483227i | \(-0.839465\pi\) | ||||
−0.875495 | + | 0.483227i | \(0.839465\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.31764 | −0.235281 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.4337 | 0.722746 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.21060 | 0.267795 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.02745 | −0.0381060 | −0.0190530 | − | 0.999818i | \(-0.506065\pi\) | ||||
−0.0190530 | + | 0.999818i | \(0.506065\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.70872 | 0.285508 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.5713 | −1.57456 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.14311 | 0.0791576 | 0.0395788 | − | 0.999216i | \(-0.487398\pi\) | ||||
0.0395788 | + | 0.999216i | \(0.487398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.0404 | −0.481004 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.6489 | 1.01846 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.3022 | 1.00433 | 0.502163 | − | 0.864773i | \(-0.332538\pi\) | ||||
0.502163 | + | 0.864773i | \(0.332538\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −60.4797 | −2.22178 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.7468 | 0.504322 | 0.252161 | − | 0.967685i | \(-0.418859\pi\) | ||||
0.252161 | + | 0.967685i | \(0.418859\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.4699 | −0.530137 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.2460 | −0.667586 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.85822 | 0.323672 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.8584 | −1.78287 | −0.891433 | − | 0.453152i | \(-0.850300\pi\) | ||||
−0.891433 | + | 0.453152i | \(0.850300\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.02306 | 0.219493 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.67603 | 0.206299 | 0.103149 | − | 0.994666i | \(-0.467108\pi\) | ||||
0.103149 | + | 0.994666i | \(0.467108\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 56.9503 | 2.06717 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.5687 | 1.07186 | 0.535932 | − | 0.844261i | \(-0.319960\pi\) | ||||
0.535932 | + | 0.844261i | \(0.319960\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.18569 | 0.0791274 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.80290 | −0.245959 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.0303 | −1.26487 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.5967 | −1.28365 | −0.641824 | − | 0.766852i | \(-0.721822\pi\) | ||||
−0.641824 | + | 0.766852i | \(0.721822\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.1345 | −0.833170 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.2990 | 1.48542 | 0.742710 | − | 0.669613i | \(-0.233540\pi\) | ||||
0.742710 | + | 0.669613i | \(0.233540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.66896 | 0.275477 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.2322 | −0.474702 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.2920 | 0.727037 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.8624 | 2.14205 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.6346 | −0.916107 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.8769 | −0.495288 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.71524 | −0.0967879 | −0.0483939 | − | 0.998828i | \(-0.515410\pi\) | ||||
−0.0483939 | + | 0.998828i | \(0.515410\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.5910 | 1.12467 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3573 | −0.368264 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.7568 | 1.62487 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.4067 | 0.830152 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.18113 | −0.218947 | −0.109473 | − | 0.993990i | \(-0.534916\pi\) | ||||
−0.109473 | + | 0.993990i | \(0.534916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 64.6230 | 2.28620 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.8977 | −0.738384 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 43.6772 | 1.54133 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.44877 | 0.156798 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.6002 | 1.18278 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4970 | 0.580003 | 0.290002 | − | 0.957026i | \(-0.406344\pi\) | ||||
0.290002 | + | 0.957026i | \(0.406344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.38782 | −0.0838478 | −0.0419239 | − | 0.999121i | \(-0.513349\pi\) | ||||
−0.0419239 | + | 0.999121i | \(0.513349\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 61.3187 | 2.15054 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.22611 | 0.0779773 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.8408 | −1.81368 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.84448 | −0.169280 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.8720 | −0.553938 | −0.276969 | − | 0.960879i | \(-0.589330\pi\) | ||||
−0.276969 | + | 0.960879i | \(0.589330\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.6087 | 0.962378 | 0.481189 | − | 0.876617i | \(-0.340205\pi\) | ||||
0.481189 | + | 0.876617i | \(0.340205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.6959 | −0.372384 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.41744 | −0.257930 | −0.128965 | − | 0.991649i | \(-0.541165\pi\) | ||||
−0.128965 | + | 0.991649i | \(0.541165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.22470 | 0.0772672 | 0.0386336 | − | 0.999253i | \(-0.487699\pi\) | ||||
0.0386336 | + | 0.999253i | \(0.487699\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.28419 | −0.252686 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.4420 | 1.15870 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.2210 | −0.665169 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.2642 | −0.942387 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.71578 | −0.0592352 | −0.0296176 | − | 0.999561i | \(-0.509429\pi\) | ||||
−0.0296176 | + | 0.999561i | \(0.509429\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.9928 | 0.792856 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.7508 | −0.680255 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.45624 | 0.256502 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.1324 | −0.451233 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.0258 | 0.721604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.7499 | −1.39689 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.1804 | −0.348571 | −0.174285 | − | 0.984695i | \(-0.555762\pi\) | ||||
−0.174285 | + | 0.984695i | \(0.555762\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.28416 | −0.283312 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.11763 | 0.243134 | 0.121567 | − | 0.992583i | \(-0.461208\pi\) | ||||
0.121567 | + | 0.992583i | \(0.461208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.2733 | 1.57882 | 0.789412 | − | 0.613864i | \(-0.210386\pi\) | ||||
0.789412 | + | 0.613864i | \(0.210386\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.42916 | 0.185025 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.4586 | 0.390054 | 0.195027 | − | 0.980798i | \(-0.437521\pi\) | ||||
0.195027 | + | 0.980798i | \(0.437521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.9144 | −0.473105 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.0945 | 0.784331 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 65.7247 | 2.22956 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.1932 | −0.819756 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.5492 | −0.560105 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.835530 | −0.0282461 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.2457 | −0.953791 | −0.476896 | − | 0.878960i | \(-0.658238\pi\) | ||||
−0.476896 | + | 0.878960i | \(0.658238\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.2499 | 1.69489 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.8395 | −0.702100 | −0.351050 | − | 0.936357i | \(-0.614175\pi\) | ||||
−0.351050 | + | 0.936357i | \(0.614175\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.1261 | −0.946520 | −0.473260 | − | 0.880923i | \(-0.656923\pi\) | ||||
−0.473260 | + | 0.880923i | \(0.656923\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0270 | −0.538741 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.6378 | −0.357183 | −0.178592 | − | 0.983923i | \(-0.557154\pi\) | ||||
−0.178592 | + | 0.983923i | \(0.557154\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.69537 | 0.325172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 57.9043 | 1.93987 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 78.6940 | 2.63339 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.5790 | 0.654455 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −49.8324 | −1.66386 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.2978 | 1.84429 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −60.0262 | −1.99976 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.8701 | −0.461567 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.2953 | 0.574915 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.37638 | −0.0457019 | −0.0228509 | − | 0.999739i | \(-0.507274\pi\) | ||||
−0.0228509 | + | 0.999739i | \(0.507274\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.5425 | −0.648184 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.2833 | −0.738278 | −0.369139 | − | 0.929374i | \(-0.620347\pi\) | ||||
−0.369139 | + | 0.929374i | \(0.620347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 73.5684 | 2.43476 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.9345 | 0.692075 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3284 | −0.341073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.6587 | −0.978349 | −0.489174 | − | 0.872186i | \(-0.662702\pi\) | ||||
−0.489174 | + | 0.872186i | \(0.662702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.51381 | −0.247589 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −52.3806 | −1.72413 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.65331 | 0.251639 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.69317 | 0.318365 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.5991 | 0.446171 | 0.223085 | − | 0.974799i | \(-0.428387\pi\) | ||||
0.223085 | + | 0.974799i | \(0.428387\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.7236 | 1.33466 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.2465 | 1.12118 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.4295 | 0.897041 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.3218 | 1.70928 | 0.854640 | − | 0.519222i | \(-0.173778\pi\) | ||||
0.854640 | + | 0.519222i | \(0.173778\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.8735 | 1.59493 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.7630 | −0.611656 | −0.305828 | − | 0.952087i | \(-0.598933\pi\) | ||||
−0.305828 | + | 0.952087i | \(0.598933\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.7197 | 0.544467 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.97042 | 0.0966277 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.85285 | 0.0602095 | 0.0301047 | − | 0.999547i | \(-0.490416\pi\) | ||||
0.0301047 | + | 0.999547i | \(0.490416\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.2182 | −1.24062 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.5864 | 1.57552 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.4953 | −0.501943 | −0.250971 | − | 0.967995i | \(-0.580750\pi\) | ||||
−0.250971 | + | 0.967995i | \(0.580750\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.13159 | 0.101336 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −77.1241 | −2.49307 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.94124 | −0.0626858 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.8130 | 0.897192 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.5912 | −0.437970 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.32113 | −0.106911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.2727 | −0.812714 | −0.406357 | − | 0.913714i | \(-0.633201\pi\) | ||||
−0.406357 | + | 0.913714i | \(0.633201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 70.9607 | 2.27959 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.7912 | −0.474673 | −0.237336 | − | 0.971428i | \(-0.576274\pi\) | ||||
−0.237336 | + | 0.971428i | \(0.576274\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.9421 | −0.511081 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.35910 | 0.299731 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.6952 | −0.630104 | −0.315052 | − | 0.949074i | \(-0.602022\pi\) | ||||
−0.315052 | + | 0.949074i | \(0.602022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 84.2603 | 2.69297 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.35352 | −0.107070 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.4893 | 0.398348 | 0.199174 | − | 0.979964i | \(-0.436174\pi\) | ||||
0.199174 | + | 0.979964i | \(0.436174\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.47516 | −0.0470024 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.0547 | 0.670178 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.7144 | −1.35824 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6774 | 0.942734 | 0.471367 | − | 0.881937i | \(-0.343761\pi\) | ||||
0.471367 | + | 0.881937i | \(0.343761\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.6916 | −0.751830 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.5686 | 0.461856 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.4881 | 1.50396 | 0.751981 | − | 0.659185i | \(-0.229098\pi\) | ||||
0.751981 | + | 0.659185i | \(0.229098\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.2085 | −0.860839 |
(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 | 6040.2.a.p.1.17 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.17 | ✓ | 19 | 1.1 | even | 1 | trivial |