Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(2.31305\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.31305 | 1.03443 | 0.517214 | − | 0.855856i | \(-0.326969\pi\) | ||||
0.517214 | + | 0.855856i | \(0.326969\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.58648 | 1.73353 | 0.866763 | − | 0.498720i | \(-0.166196\pi\) | ||||
0.866763 | + | 0.498720i | \(0.166196\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.21418 | 0.969110 | 0.484555 | − | 0.874761i | \(-0.338981\pi\) | ||||
0.484555 | + | 0.874761i | \(0.338981\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.90839 | −1.63869 | −0.819346 | − | 0.573299i | \(-0.805663\pi\) | ||||
−0.819346 | + | 0.573299i | \(0.805663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.31305 | 0.597227 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.31037 | 1.53049 | 0.765244 | − | 0.643740i | \(-0.222618\pi\) | ||||
0.765244 | + | 0.643740i | \(0.222618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.08386 | −1.62515 | −0.812574 | − | 0.582858i | \(-0.801934\pi\) | ||||
−0.812574 | + | 0.582858i | \(0.801934\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58648 | 1.00085 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.12084 | −0.233711 | −0.116855 | − | 0.993149i | \(-0.537281\pi\) | ||||
−0.116855 | + | 0.993149i | \(0.537281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.350210 | 0.0700420 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0956753 | −0.0177665 | −0.00888323 | − | 0.999961i | \(-0.502828\pi\) | ||||
−0.00888323 | + | 0.999961i | \(0.502828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.81707 | 0.865172 | 0.432586 | − | 0.901593i | \(-0.357601\pi\) | ||||
0.432586 | + | 0.901593i | \(0.357601\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.21418 | 0.559516 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.6088 | 1.79321 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.60986 | 0.593458 | 0.296729 | − | 0.954962i | \(-0.404104\pi\) | ||||
0.296729 | + | 0.954962i | \(0.404104\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.90839 | −0.946100 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.59300 | 1.34200 | 0.671001 | − | 0.741457i | \(-0.265865\pi\) | ||||
0.671001 | + | 0.741457i | \(0.265865\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.44278 | −1.28751 | −0.643756 | − | 0.765231i | \(-0.722625\pi\) | ||||
−0.643756 | + | 0.765231i | \(0.722625\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.31305 | 0.344809 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.42753 | 0.937551 | 0.468776 | − | 0.883317i | \(-0.344695\pi\) | ||||
0.468776 | + | 0.883317i | \(0.344695\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.0358 | 2.00511 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.31037 | 0.883628 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.56167 | 0.351873 | 0.175936 | − | 0.984402i | \(-0.443705\pi\) | ||||
0.175936 | + | 0.984402i | \(0.443705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.43455 | 1.00248 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.08386 | −0.938280 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.13741 | 0.799022 | 0.399511 | − | 0.916728i | \(-0.369180\pi\) | ||||
0.399511 | + | 0.916728i | \(0.369180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.66615 | −0.725476 | −0.362738 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362738 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.58648 | 0.577842 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.6664 | −1.69511 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.24652 | −1.12964 | −0.564821 | − | 0.825213i | \(-0.691055\pi\) | ||||
−0.564821 | + | 0.825213i | \(0.691055\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.12084 | −0.134933 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.95267 | −0.943808 | −0.471904 | − | 0.881650i | \(-0.656433\pi\) | ||||
−0.471904 | + | 0.881650i | \(0.656433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.9676 | 1.75182 | 0.875911 | − | 0.482473i | \(-0.160261\pi\) | ||||
0.875911 | + | 0.482473i | \(0.160261\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.350210 | 0.0404388 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.7417 | 1.67998 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4092 | 1.50866 | 0.754328 | − | 0.656498i | \(-0.227963\pi\) | ||||
0.754328 | + | 0.656498i | \(0.227963\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.20203 | −0.351468 | −0.175734 | − | 0.984438i | \(-0.556230\pi\) | ||||
−0.175734 | + | 0.984438i | \(0.556230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.5962 | 1.58318 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0956753 | −0.0102575 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.0148 | −1.69756 | −0.848780 | − | 0.528746i | \(-0.822662\pi\) | ||||
−0.848780 | + | 0.528746i | \(0.822662\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.0987 | −2.84072 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.81707 | 0.499507 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.3853 | −1.68110 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.476438 | 0.0483749 | 0.0241875 | − | 0.999707i | \(-0.492300\pi\) | ||||
0.0241875 | + | 0.999707i | \(0.492300\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.21418 | 0.323037 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.3819 | −1.53056 | −0.765278 | − | 0.643699i | \(-0.777399\pi\) | ||||
−0.765278 | + | 0.643699i | \(0.777399\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.09569 | 0.797692 | 0.398846 | − | 0.917018i | \(-0.369411\pi\) | ||||
0.398846 | + | 0.917018i | \(0.369411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.6088 | 1.03531 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.87538 | −0.277974 | −0.138987 | − | 0.990294i | \(-0.544385\pi\) | ||||
−0.138987 | + | 0.990294i | \(0.544385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.95551 | 0.378869 | 0.189435 | − | 0.981893i | \(-0.439335\pi\) | ||||
0.189435 | + | 0.981893i | \(0.439335\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.60986 | 0.342633 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.7456 | −1.19900 | −0.599501 | − | 0.800374i | \(-0.704634\pi\) | ||||
−0.599501 | + | 0.800374i | \(0.704634\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.59255 | −0.241757 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.90839 | −0.546231 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.9424 | 2.65314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.669077 | −0.0608252 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.59300 | 0.774805 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.7552 | −0.961975 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.45367 | 0.572671 | 0.286335 | − | 0.958129i | \(-0.407563\pi\) | ||||
0.286335 | + | 0.958129i | \(0.407563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.44278 | −0.743345 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.69274 | 0.759488 | 0.379744 | − | 0.925092i | \(-0.376012\pi\) | ||||
0.379744 | + | 0.925092i | \(0.376012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −32.4900 | −2.81724 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.31305 | 0.199076 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.18280 | 0.699104 | 0.349552 | − | 0.936917i | \(-0.386334\pi\) | ||||
0.349552 | + | 0.936917i | \(0.386334\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00849 | −0.679271 | −0.339636 | − | 0.940557i | \(-0.610304\pi\) | ||||
−0.339636 | + | 0.940557i | \(0.610304\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.42753 | 0.541295 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.9906 | −1.58807 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.221302 | −0.0183781 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.0358 | 1.15765 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.2148 | −1.00067 | −0.500336 | − | 0.865831i | \(-0.666790\pi\) | ||||
−0.500336 | + | 0.865831i | \(0.666790\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.8534 | 1.20875 | 0.604377 | − | 0.796698i | \(-0.293422\pi\) | ||||
0.604377 | + | 0.796698i | \(0.293422\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.31037 | 0.510163 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.1421 | 0.894958 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.3909 | −1.14852 | −0.574259 | − | 0.818674i | \(-0.694710\pi\) | ||||
−0.574259 | + | 0.818674i | \(0.694710\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.56167 | 0.203154 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.14070 | −0.405144 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.84431 | 0.771066 | 0.385533 | − | 0.922694i | \(-0.374018\pi\) | ||||
0.385533 | + | 0.922694i | \(0.374018\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.43455 | 0.578779 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.9091 | 1.68531 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.08386 | −0.541716 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.4914 | −1.63396 | −0.816981 | − | 0.576665i | \(-0.804354\pi\) | ||||
−0.816981 | + | 0.576665i | \(0.804354\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.60623 | 0.121420 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.13741 | 0.461316 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.7394 | −0.952190 | −0.476095 | − | 0.879394i | \(-0.657948\pi\) | ||||
−0.476095 | + | 0.879394i | \(0.657948\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1252 | 1.19858 | 0.599288 | − | 0.800534i | \(-0.295451\pi\) | ||||
0.599288 | + | 0.800534i | \(0.295451\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.66615 | −0.418854 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.34980 | 0.613890 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.2826 | 1.48321 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.58648 | 0.333617 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.06940 | −0.222094 | −0.111047 | − | 0.993815i | \(-0.535420\pi\) | ||||
−0.111047 | + | 0.993815i | \(0.535420\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.3544 | −1.46514 | −0.732572 | − | 0.680689i | \(-0.761680\pi\) | ||||
−0.732572 | + | 0.680689i | \(0.761680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.6664 | −0.978672 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.35545 | −0.452807 | −0.226404 | − | 0.974034i | \(-0.572697\pi\) | ||||
−0.226404 | + | 0.974034i | \(0.572697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8698 | −0.912315 | −0.456158 | − | 0.889899i | \(-0.650775\pi\) | ||||
−0.456158 | + | 0.889899i | \(0.650775\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.24652 | −0.652200 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.438813 | −0.0307986 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.8761 | 1.38820 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.12084 | −0.0779035 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.7688 | −1.57495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.5752 | 0.865714 | 0.432857 | − | 0.901463i | \(-0.357506\pi\) | ||||
0.432857 | + | 0.901463i | \(0.357506\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.95267 | −0.544908 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.5286 | −1.33184 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.0934 | 1.49980 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.9676 | 1.01141 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37.2841 | −2.50800 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4007 | −0.897375 | −0.448688 | − | 0.893689i | \(-0.648108\pi\) | ||||
−0.448688 | + | 0.893689i | \(0.648108\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.350210 | 0.0233473 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.2416 | 1.60897 | 0.804486 | − | 0.593972i | \(-0.202441\pi\) | ||||
0.804486 | + | 0.593972i | \(0.202441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.58387 | 0.104665 | 0.0523325 | − | 0.998630i | \(-0.483334\pi\) | ||||
0.0523325 | + | 0.998630i | \(0.483334\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.7417 | 0.969936 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0966 | 1.18554 | 0.592772 | − | 0.805370i | \(-0.298033\pi\) | ||||
0.592772 | + | 0.805370i | \(0.298033\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.8672 | 0.969829 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.4092 | 0.871023 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8153 | 0.958321 | 0.479161 | − | 0.877727i | \(-0.340941\pi\) | ||||
0.479161 | + | 0.877727i | \(0.340941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.7654 | −1.85294 | −0.926472 | − | 0.376363i | \(-0.877175\pi\) | ||||
−0.926472 | + | 0.376363i | \(0.877175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 32.4655 | 2.07415 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.8542 | 2.66312 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.20203 | −0.202920 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.2143 | 1.52839 | 0.764196 | − | 0.644985i | \(-0.223136\pi\) | ||||
0.764196 | + | 0.644985i | \(0.223136\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.60257 | −0.226491 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.5962 | 0.914050 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.609749 | −0.0380351 | −0.0190175 | − | 0.999819i | \(-0.506054\pi\) | ||||
−0.0190175 | + | 0.999819i | \(0.506054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.5566 | 1.02878 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0956753 | −0.00592216 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.6789 | −0.966801 | −0.483401 | − | 0.875399i | \(-0.660599\pi\) | ||||
−0.483401 | + | 0.875399i | \(0.660599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.92528 | 0.363987 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.0148 | −0.980087 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.4228 | −1.30617 | −0.653087 | − | 0.757283i | \(-0.726526\pi\) | ||||
−0.653087 | + | 0.757283i | \(0.726526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2126 | −0.741864 | −0.370932 | − | 0.928660i | \(-0.620962\pi\) | ||||
−0.370932 | + | 0.928660i | \(0.620962\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.0987 | −1.64009 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.12564 | 0.0678784 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4046 | 0.865489 | 0.432744 | − | 0.901517i | \(-0.357545\pi\) | ||||
0.432744 | + | 0.901517i | \(0.357545\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.81707 | 0.288391 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.73061 | 0.282204 | 0.141102 | − | 0.989995i | \(-0.454935\pi\) | ||||
0.141102 | + | 0.989995i | \(0.454935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.9197 | −1.12466 | −0.562329 | − | 0.826914i | \(-0.690094\pi\) | ||||
−0.562329 | + | 0.826914i | \(0.690094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.3853 | −0.970583 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39.4116 | 2.32639 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.8207 | 1.34239 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.476438 | 0.0279293 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.27544 | 0.249774 | 0.124887 | − | 0.992171i | \(-0.460143\pi\) | ||||
0.124887 | + | 0.992171i | \(0.460143\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1961 | 0.826531 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.21418 | 0.186505 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.62234 | 0.382980 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −38.7226 | −2.23193 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.3819 | −0.883667 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.1061 | −0.750453 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.2247 | 1.15429 | 0.577143 | − | 0.816643i | \(-0.304167\pi\) | ||||
0.577143 | + | 0.816643i | \(0.304167\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.09569 | 0.460548 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.1435 | −1.08553 | −0.542763 | − | 0.839886i | \(-0.682622\pi\) | ||||
−0.542763 | + | 0.839886i | \(0.682622\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.2504 | −1.54028 | −0.770141 | − | 0.637874i | \(-0.779814\pi\) | ||||
−0.770141 | + | 0.637874i | \(0.779814\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.6088 | 0.597736 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.80299 | 0.325928 | 0.162964 | − | 0.986632i | \(-0.447895\pi\) | ||||
0.162964 | + | 0.986632i | \(0.447895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.307517 | −0.0172177 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.87538 | −0.160488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −44.7017 | −2.48727 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.06918 | −0.114777 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.95551 | 0.218740 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.4797 | 1.62527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.6624 | −0.586056 | −0.293028 | − | 0.956104i | \(-0.594663\pi\) | ||||
−0.293028 | + | 0.956104i | \(0.594663\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.60986 | 0.197819 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.3877 | −1.16853 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0252 | −1.25426 | −0.627132 | − | 0.778913i | \(-0.715771\pi\) | ||||
−0.627132 | + | 0.778913i | \(0.715771\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.7456 | −0.692244 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.4829 | 0.838447 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 32.2695 | 1.74239 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.59255 | −0.139578 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.3802 | −0.557238 | −0.278619 | − | 0.960402i | \(-0.589877\pi\) | ||||
−0.278619 | + | 0.960402i | \(0.589877\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.7466 | 1.69935 | 0.849677 | − | 0.527303i | \(-0.176797\pi\) | ||||
0.849677 | + | 0.527303i | \(0.176797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.90839 | −0.315367 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.5012 | 1.57019 | 0.785094 | − | 0.619376i | \(-0.212615\pi\) | ||||
0.785094 | + | 0.619376i | \(0.212615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.3949 | −0.976302 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.9424 | 1.53179 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.5925 | 1.93128 | 0.965639 | − | 0.259888i | \(-0.0836855\pi\) | ||||
0.965639 | + | 0.259888i | \(0.0836855\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.1810 | 1.64111 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.669077 | −0.0351174 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.6208 | 1.81213 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.2131 | 0.689718 | 0.344859 | − | 0.938655i | \(-0.387927\pi\) | ||||
0.344859 | + | 0.938655i | \(0.387927\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.59300 | 0.447334 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.7491 | 0.609980 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.4903 | 0.543169 | 0.271585 | − | 0.962415i | \(-0.412452\pi\) | ||||
0.271585 | + | 0.962415i | \(0.412452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.7552 | −0.555396 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.565287 | 0.0291138 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.9819 | 0.975035 | 0.487517 | − | 0.873113i | \(-0.337903\pi\) | ||||
0.487517 | + | 0.873113i | \(0.337903\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.45367 | 0.330632 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.61342 | −0.389028 | −0.194514 | − | 0.980900i | \(-0.562313\pi\) | ||||
−0.194514 | + | 0.980900i | \(0.562313\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.0984 | 1.73782 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.44278 | −0.429170 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.1854 | 0.567124 | 0.283562 | − | 0.958954i | \(-0.408484\pi\) | ||||
0.283562 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.07289 | −0.357691 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.69274 | 0.438491 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 31.0162 | 1.56060 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4789 | 0.726675 | 0.363338 | − | 0.931658i | \(-0.381637\pi\) | ||||
0.363338 | + | 0.931658i | \(0.381637\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.4900 | −1.62653 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.3950 | −0.918602 | −0.459301 | − | 0.888281i | \(-0.651900\pi\) | ||||
−0.459301 | + | 0.888281i | \(0.651900\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.4611 | −1.41775 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.31305 | 0.114936 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.6027 | 0.575126 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.8381 | −1.57429 | −0.787146 | − | 0.616767i | \(-0.788442\pi\) | ||||
−0.787146 | + | 0.616767i | \(0.788442\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.18280 | 0.403628 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.1491 | 1.38513 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.40646 | −0.363569 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.00849 | −0.392177 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.5931 | −1.73883 | −0.869417 | − | 0.494078i | \(-0.835506\pi\) | ||||
−0.869417 | + | 0.494078i | \(0.835506\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.2164 | −1.32644 | −0.663222 | − | 0.748423i | \(-0.730812\pi\) | ||||
−0.663222 | + | 0.748423i | \(0.730812\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.42753 | 0.312517 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.20995 | 0.107198 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.9877 | −1.25763 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.9906 | −0.916875 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.7305 | 0.565036 | 0.282518 | − | 0.959262i | \(-0.408830\pi\) | ||||
0.282518 | + | 0.959262i | \(0.408830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.60527 | −0.317429 | −0.158715 | − | 0.987325i | \(-0.550735\pi\) | ||||
−0.158715 | + | 0.987325i | \(0.550735\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.221302 | −0.0106106 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.93985 | 0.379814 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.99747 | −0.429426 | −0.214713 | − | 0.976677i | \(-0.568882\pi\) | ||||
−0.214713 | + | 0.976677i | \(0.568882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.0358 | 0.668371 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.4240 | −0.542771 | −0.271385 | − | 0.962471i | \(-0.587482\pi\) | ||||
−0.271385 | + | 0.962471i | \(0.587482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.0430 | −1.75600 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.2148 | −0.577738 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.51165 | −0.401690 | −0.200845 | − | 0.979623i | \(-0.564369\pi\) | ||||
−0.200845 | + | 0.979623i | \(0.564369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.6194 | 1.30055 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.8534 | 0.697875 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −62.6807 | −2.93852 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.37503 | 0.391767 | 0.195884 | − | 0.980627i | \(-0.437243\pi\) | ||||
0.195884 | + | 0.980627i | \(0.437243\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.31037 | 0.294543 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.6981 | −0.684557 | −0.342279 | − | 0.939599i | \(-0.611199\pi\) | ||||
−0.342279 | + | 0.939599i | \(0.611199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.96089 | −0.416448 | −0.208224 | − | 0.978081i | \(-0.566768\pi\) | ||||
−0.208224 | + | 0.978081i | \(0.566768\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.1421 | 0.516704 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.5404 | 0.626576 | 0.313288 | − | 0.949658i | \(-0.398570\pi\) | ||||
0.313288 | + | 0.949658i | \(0.398570\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −42.4090 | −1.95827 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.3909 | −0.663097 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.1366 | −1.24774 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.48084 | −0.113829 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.56167 | 0.117291 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.28706 | −0.378646 | −0.189323 | − | 0.981915i | \(-0.560629\pi\) | ||||
−0.189323 | + | 0.981915i | \(0.560629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.3285 | −0.972495 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.14070 | −0.233910 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.10203 | 0.0500404 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.4042 | −1.64963 | −0.824815 | − | 0.565402i | \(-0.808721\pi\) | ||||
−0.824815 | + | 0.565402i | \(0.808721\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.84431 | 0.445175 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.7273 | 1.16105 | 0.580527 | − | 0.814241i | \(-0.302846\pi\) | ||||
0.580527 | + | 0.814241i | \(0.302846\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.603746 | −0.0271914 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.43455 | 0.334158 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.4747 | −1.63612 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.6775 | −1.55238 | −0.776190 | − | 0.630499i | \(-0.782850\pi\) | ||||
−0.776190 | + | 0.630499i | \(0.782850\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.6211 | −0.562748 | −0.281374 | − | 0.959598i | \(-0.590790\pi\) | ||||
−0.281374 | + | 0.959598i | \(0.590790\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.5792 | −1.58325 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.9091 | 0.973017 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.2360 | 1.29586 | 0.647931 | − | 0.761699i | \(-0.275635\pi\) | ||||
0.647931 | + | 0.761699i | \(0.275635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 68.6484 | 3.03683 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.08386 | −0.312760 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.7258 | 0.825155 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.6592 | 0.908591 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.4914 | −0.943368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.0135 | −1.27110 | −0.635551 | − | 0.772059i | \(-0.719227\pi\) | ||||
−0.635551 | + | 0.772059i | \(0.719227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5844 | 0.594003 | 0.297001 | − | 0.954877i | \(-0.404013\pi\) | ||||
0.297001 | + | 0.954877i | \(0.404013\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.60623 | 0.0701016 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.3975 | 1.32414 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7437 | −0.945379 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.13741 | 0.266341 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −50.7708 | −2.19913 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.65091 | −0.287544 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.7394 | −0.549747 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 45.1135 | 1.94318 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.2472 | 1.25743 | 0.628717 | − | 0.777634i | \(-0.283581\pi\) | ||||
0.628717 | + | 0.777634i | \(0.283581\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.1252 | 0.691998 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.14930 | 0.391913 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7016 | −0.671353 | −0.335676 | − | 0.941977i | \(-0.608965\pi\) | ||||
−0.335676 | + | 0.941977i | \(0.608965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.66615 | −0.241825 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.677751 | 0.0288731 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 61.5011 | 2.61529 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.34980 | 0.354429 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.6588 | −0.960083 | −0.480041 | − | 0.877246i | \(-0.659378\pi\) | ||||
−0.480041 | + | 0.877246i | \(0.659378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 49.8832 | 2.10984 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.2826 | 0.856333 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.2384 | −1.44298 | −0.721488 | − | 0.692427i | \(-0.756542\pi\) | ||||
−0.721488 | + | 0.692427i | \(0.756542\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.4812 | −1.24028 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.58648 | 0.192614 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.2105 | −1.47610 | −0.738050 | − | 0.674746i | \(-0.764253\pi\) | ||||
−0.738050 | + | 0.674746i | \(0.764253\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.6184 | 1.61613 | 0.808065 | − | 0.589093i | \(-0.200515\pi\) | ||||
0.808065 | + | 0.589093i | \(0.200515\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.06940 | −0.128226 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.392528 | −0.0163696 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −42.9247 | −1.78698 | −0.893490 | − | 0.449084i | \(-0.851750\pi\) | ||||
−0.893490 | + | 0.449084i | \(0.851750\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.3544 | −0.845901 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6860 | −0.609280 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.23366 | 0.341003 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.6664 | −0.565037 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.7904 | 0.693013 | 0.346507 | − | 0.938048i | \(-0.387368\pi\) | ||||
0.346507 | + | 0.938048i | \(0.387368\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.1235 | −1.40603 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.35545 | −0.261428 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.96900 | −0.0808573 | −0.0404287 | − | 0.999182i | \(-0.512872\pi\) | ||||
−0.0404287 | + | 0.999182i | \(0.512872\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 66.9452 | 2.74449 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.8698 | −0.526725 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.97393 | 0.0806528 | 0.0403264 | − | 0.999187i | \(-0.487160\pi\) | ||||
0.0403264 | + | 0.999187i | \(0.487160\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.9942 | 0.897160 | 0.448580 | − | 0.893743i | \(-0.351930\pi\) | ||||
0.448580 | + | 0.893743i | \(0.351930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.24652 | −0.376548 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.54761 | −0.0629193 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8801 | 0.563378 | 0.281689 | − | 0.959506i | \(-0.409105\pi\) | ||||
0.281689 | + | 0.959506i | \(0.409105\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.438813 | −0.0177816 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.9763 | −1.53636 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.7685 | 1.44468 | 0.722338 | − | 0.691540i | \(-0.243067\pi\) | ||||
0.722338 | + | 0.691540i | \(0.243067\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.8761 | 0.801480 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.5812 | −0.868825 | −0.434413 | − | 0.900714i | \(-0.643044\pi\) | ||||
−0.434413 | + | 0.900714i | \(0.643044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.1766 | 1.41387 | 0.706933 | − | 0.707280i | \(-0.250078\pi\) | ||||
0.706933 | + | 0.707280i | \(0.250078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.12084 | −0.0449776 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −73.4513 | −2.94277 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.6284 | −1.06514 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −22.7688 | −0.909297 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.7796 | 0.908281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.6537 | 1.14068 | 0.570342 | − | 0.821407i | \(-0.306811\pi\) | ||||
0.570342 | + | 0.821407i | \(0.306811\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.5752 | 0.499820 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9277 | 0.592387 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −82.9290 | −3.28577 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.95267 | −0.314603 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.25764 | 0.247162 | 0.123581 | − | 0.992334i | \(-0.460562\pi\) | ||||
0.123581 | + | 0.992334i | \(0.460562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.84712 | −0.151716 | −0.0758578 | − | 0.997119i | \(-0.524170\pi\) | ||||
−0.0758578 | + | 0.997119i | \(0.524170\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.5286 | −0.768937 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.4438 | −0.960986 | −0.480493 | − | 0.876998i | \(-0.659542\pi\) | ||||
−0.480493 | + | 0.876998i | \(0.659542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.7267 | 0.774341 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.0934 | 0.865909 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.9659 | 1.87705 | 0.938525 | − | 0.345212i | \(-0.112193\pi\) | ||||
0.938525 | + | 0.345212i | \(0.112193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.1068 | 0.785636 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.9676 | 0.583940 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.0165 | 0.546006 | 0.273003 | − | 0.962013i | \(-0.411983\pi\) | ||||
0.273003 | + | 0.962013i | \(0.411983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7905 | −0.653075 | −0.326538 | − | 0.945184i | \(-0.605882\pi\) | ||||
−0.326538 | + | 0.945184i | \(0.605882\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −37.2841 | −1.44799 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −75.1510 | −2.91423 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.107236 | 0.00415221 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.4007 | −0.518100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.2120 | −0.703066 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −51.0281 | −1.96699 | −0.983494 | − | 0.180939i | \(-0.942086\pi\) | ||||
−0.983494 | + | 0.180939i | \(0.942086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.350210 | 0.0134796 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.3164 | 0.934556 | 0.467278 | − | 0.884111i | \(-0.345235\pi\) | ||||
0.467278 | + | 0.884111i | \(0.345235\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.18517 | 0.0838592 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.2416 | 0.928940 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.89320 | 0.187233 | 0.0936165 | − | 0.995608i | \(-0.470157\pi\) | ||||
0.0936165 | + | 0.995608i | \(0.470157\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.9272 | 0.723173 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.58387 | 0.0604284 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.1354 | −0.576611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0140 | 0.913536 | 0.456768 | − | 0.889586i | \(-0.349007\pi\) | ||||
0.456768 | + | 0.889586i | \(0.349007\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.7417 | 0.559993 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.5240 | −0.702657 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.2250 | 2.05392 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.0966 | 0.684475 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.0044 | 0.717785 | 0.358893 | − | 0.933379i | \(-0.383154\pi\) | ||||
0.358893 | + | 0.933379i | \(0.383154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.5718 | −0.964457 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.8672 | 0.559931 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −70.5488 | −2.65326 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.6743 | 1.26467 | 0.632333 | − | 0.774697i | \(-0.282098\pi\) | ||||
0.632333 | + | 0.774697i | \(0.282098\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4092 | 0.502885 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.39915 | −0.202200 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.9263 | −1.64275 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.8153 | 0.553287 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.8777 | 1.18884 | 0.594419 | − | 0.804155i | \(-0.297382\pi\) | ||||
0.594419 | + | 0.804155i | \(0.297382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.1307 | 1.38282 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.7654 | −1.06980 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0335065 | −0.00124440 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5765 | 0.540614 | 0.270307 | − | 0.962774i | \(-0.412875\pi\) | ||||
0.270307 | + | 0.962774i | \(0.412875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.2770 | −1.97052 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.08605 | 0.0770501 | 0.0385251 | − | 0.999258i | \(-0.487734\pi\) | ||||
0.0385251 | + | 0.999258i | \(0.487734\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 32.4655 | 1.19751 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.7200 | −1.09475 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.9185 | 0.659142 | 0.329571 | − | 0.944131i | \(-0.393096\pi\) | ||||
0.329571 | + | 0.944131i | \(0.393096\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 41.8542 | 1.53755 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.3924 | 1.51854 | 0.759270 | − | 0.650776i | \(-0.225556\pi\) | ||||
0.759270 | + | 0.650776i | \(0.225556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.2534 | −1.03512 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.20203 | −0.117156 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.1879 | −0.481875 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.50906 | 0.0550663 | 0.0275332 | − | 0.999621i | \(-0.491235\pi\) | ||||
0.0275332 | + | 0.999621i | \(0.491235\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.2143 | 0.882417 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.3567 | 1.25037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.8730 | −1.04941 | −0.524704 | − | 0.851285i | \(-0.675824\pi\) | ||||
−0.524704 | + | 0.851285i | \(0.675824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.60257 | −0.130765 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.2833 | −0.554019 | −0.277009 | − | 0.960867i | \(-0.589343\pi\) | ||||
−0.277009 | + | 0.960867i | \(0.589343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.1419 | 0.656780 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.5962 | 0.527727 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.2622 | −1.30935 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0530 | −1.08374 | −0.541869 | − | 0.840463i | \(-0.682283\pi\) | ||||
−0.541869 | + | 0.840463i | \(0.682283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.609749 | −0.0219596 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.7691 | −1.32249 | −0.661247 | − | 0.750168i | \(-0.729972\pi\) | ||||
−0.661247 | + | 0.750168i | \(0.729972\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.68699 | 0.0605983 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.5566 | 0.593964 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −60.8716 | −2.18095 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.5613 | −0.914654 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0956753 | −0.00341916 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.2869 | −1.18806 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.24409 | 0.186932 | 0.0934658 | − | 0.995622i | \(-0.470205\pi\) | ||||
0.0934658 | + | 0.995622i | \(0.470205\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.6789 | −0.558183 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −58.4573 | −2.07850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.4778 | 1.18883 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.92528 | 0.210148 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.4374 | −0.723928 | −0.361964 | − | 0.932192i | \(-0.617894\pi\) | ||||
−0.361964 | + | 0.932192i | \(0.617894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.5600 | 1.43491 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.0148 | −0.565853 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.1084 | 1.69771 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.8907 | −0.419092 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.4228 | −0.754120 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.2523 | −1.38004 | −0.690019 | − | 0.723791i | \(-0.742398\pi\) | ||||
−0.690019 | + | 0.723791i | \(0.742398\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.47145 | −0.121899 | −0.0609495 | − | 0.998141i | \(-0.519413\pi\) | ||||
−0.0609495 | + | 0.998141i | \(0.519413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.2126 | −0.428315 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.7704 | 0.797612 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59.8074 | 2.09240 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27.0987 | −0.946906 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.2347 | −1.43910 | −0.719551 | − | 0.694440i | \(-0.755652\pi\) | ||||
−0.719551 | + | 0.694440i | \(0.755652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.6439 | 0.963607 | 0.481803 | − | 0.876279i | \(-0.339982\pi\) | ||||
0.481803 | + | 0.876279i | \(0.339982\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.12564 | 0.0391896 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.1297 | −1.60409 | −0.802043 | − | 0.597266i | \(-0.796254\pi\) | ||||
−0.802043 | + | 0.597266i | \(0.796254\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.2938 | −1.57312 | −0.786559 | − | 0.617515i | \(-0.788139\pi\) | ||||
−0.786559 | + | 0.617515i | \(0.788139\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.4046 | 0.499690 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 88.5710 | 3.06880 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.31305 | 0.0800465 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.81707 | 0.166502 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.7011 | 1.81945 | 0.909723 | − | 0.415216i | \(-0.136294\pi\) | ||||
0.909723 | + | 0.415216i | \(0.136294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9908 | −0.999684 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.73061 | 0.162931 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 50.6769 | 1.74334 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.06871 | −0.105442 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.9197 | −0.649321 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.04607 | −0.138697 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.3615 | 1.17651 | 0.588257 | − | 0.808674i | \(-0.299814\pi\) | ||||
0.588257 | + | 0.808674i | \(0.299814\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.3853 | −0.560367 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.28567 | 0.317192 | 0.158596 | − | 0.987344i | \(-0.449303\pi\) | ||||
0.158596 | + | 0.987344i | \(0.449303\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.8965 | 0.610622 | 0.305311 | − | 0.952253i | \(-0.401240\pi\) | ||||
0.305311 | + | 0.952253i | \(0.401240\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.4116 | 1.34314 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.3429 | −0.998845 | −0.499422 | − | 0.866359i | \(-0.666454\pi\) | ||||
−0.499422 | + | 0.866359i | \(0.666454\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.7108 | −1.69022 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.8207 | 0.775032 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.0996 | 1.46205 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.6321 | 1.85114 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.476438 | 0.0161250 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −49.3285 | −1.66761 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.6823 | −1.47505 | −0.737523 | − | 0.675322i | \(-0.764005\pi\) | ||||
−0.737523 | + | 0.675322i | \(0.764005\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.27544 | 0.144207 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.1789 | −0.747227 | −0.373614 | − | 0.927584i | \(-0.621881\pi\) | ||||
−0.373614 | + | 0.927584i | \(0.621881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.72940 | 0.260115 | 0.130057 | − | 0.991506i | \(-0.458484\pi\) | ||||
0.130057 | + | 0.991506i | \(0.458484\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1961 | 0.477198 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.0092 | −0.806150 | −0.403075 | − | 0.915167i | \(-0.632059\pi\) | ||||
−0.403075 | + | 0.915167i | \(0.632059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.5996 | 0.992740 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.21418 | 0.107679 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.5317 | −1.52366 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29.4670 | −0.984972 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.62234 | 0.221114 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.460875 | −0.0153710 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.1651 | 0.538537 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −38.7226 | −1.28861 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.2984 | 1.23984 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.6999 | 0.587715 | 0.293857 | − | 0.955849i | \(-0.405061\pi\) | ||||
0.293857 | + | 0.955849i | \(0.405061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.3819 | −0.510186 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.84469 | −0.326169 | −0.163085 | − | 0.986612i | \(-0.552144\pi\) | ||||
−0.163085 | + | 0.986612i | \(0.552144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.2919 | −0.340612 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.1061 | −0.433274 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.8691 | 1.31659 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.2682 | −0.536638 | −0.268319 | − | 0.963330i | \(-0.586468\pi\) | ||||
−0.268319 | + | 0.963330i | \(0.586468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.2247 | 0.666428 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.9875 | 1.54661 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.26421 | 0.0415670 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.09569 | 0.265897 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.38263 | −0.0453625 | −0.0226812 | − | 0.999743i | \(-0.507220\pi\) | ||||
−0.0226812 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −99.4276 | −3.25861 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.1435 | −0.626729 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.9148 | 1.53428 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.9877 | 1.56769 | 0.783845 | − | 0.620956i | \(-0.213256\pi\) | ||||
0.783845 | + | 0.620956i | \(0.213256\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.2504 | −0.889282 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.3869 | 1.25138 | 0.625688 | − | 0.780073i | \(-0.284818\pi\) | ||||
0.625688 | + | 0.780073i | \(0.284818\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.63135 | −0.313640 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.6088 | 0.345103 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.9162 | −1.52457 | −0.762285 | − | 0.647241i | \(-0.775923\pi\) | ||||
−0.762285 | + | 0.647241i | \(0.775923\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −88.4342 | −2.87070 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.80299 | 0.188175 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.6138 | 0.700139 | 0.350070 | − | 0.936724i | \(-0.386158\pi\) | ||||
0.350070 | + | 0.936724i | \(0.386158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.09968 | −0.229740 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.307517 | −0.00994062 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.5302 | 1.21191 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.79581 | −0.251478 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.87538 | −0.0926579 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −47.0809 | −1.51559 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.9732 | 1.25330 | 0.626648 | − | 0.779303i | \(-0.284427\pi\) | ||||
0.626648 | + | 0.779303i | \(0.284427\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44.7017 | −1.43603 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.0949 | −0.997882 | −0.498941 | − | 0.866636i | \(-0.666278\pi\) | ||||
−0.498941 | + | 0.866636i | \(0.666278\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.7308 | −1.17753 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.06918 | −0.0662667 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.3796 | −0.811966 | −0.405983 | − | 0.913881i | \(-0.633071\pi\) | ||||
−0.405983 | + | 0.913881i | \(0.633071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.4742 | −1.64512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.95551 | 0.126290 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.01822 | −0.287636 | −0.143818 | − | 0.989604i | \(-0.545938\pi\) | ||||
−0.143818 | + | 0.989604i | \(0.545938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.7005 | −0.468397 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.4797 | 0.938350 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.46297 | 0.300905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.25211 | −0.103307 | −0.0516534 | − | 0.998665i | \(-0.516449\pi\) | ||||
−0.0516534 | + | 0.998665i | \(0.516449\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.6624 | −0.338360 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.7685 | −0.943725 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.1469 | 1.39815 | 0.699073 | − | 0.715051i | \(-0.253596\pi\) | ||||
0.699073 | + | 0.715051i | \(0.253596\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.60986 | 0.114211 |
(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 | 4008.2.a.l.1.9 | ✓ | 12 | |
4.3 | odd | 2 | 8016.2.a.bf.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8016.2.a.bf.1.9 | 12 | 4.3 | odd | 2 |