Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.d.2591.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.14626i | − 1.40705i | −0.710669 | − | 0.703526i | \(-0.751608\pi\) | ||||
0.710669 | − | 0.703526i | \(-0.248392\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.04989 | −0.618065 | −0.309032 | − | 0.951052i | \(-0.600005\pi\) | ||||
−0.309032 | + | 0.951052i | \(0.600005\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949 | 0.679366 | 0.339683 | − | 0.940540i | \(-0.389680\pi\) | ||||
0.339683 | + | 0.940540i | \(0.389680\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.14626i | − 0.763081i | −0.924352 | − | 0.381541i | \(-0.875394\pi\) | ||||
0.924352 | − | 0.381541i | \(-0.124606\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.44949i | 1.02078i | 0.859942 | + | 0.510391i | \(0.170499\pi\) | ||||
−0.859942 | + | 0.510391i | \(0.829501\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.89898 | −0.979796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.778539i | − 0.144571i | −0.997384 | − | 0.0722855i | \(-0.976971\pi\) | ||||
0.997384 | − | 0.0722855i | \(-0.0230293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.449490i | 0.0807307i | 0.999185 | + | 0.0403654i | \(0.0128522\pi\) | ||||
−0.999185 | + | 0.0403654i | \(0.987148\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.14626 | 0.531816 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 2.51059i | − 0.392088i | −0.980595 | − | 0.196044i | \(-0.937190\pi\) | ||||
0.980595 | − | 0.196044i | \(-0.0628096\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.34847i | 0.663135i | 0.943431 | + | 0.331568i | \(0.107578\pi\) | ||||
−0.943431 | + | 0.331568i | \(0.892422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.38891 | −1.07778 | −0.538891 | − | 0.842375i | \(-0.681157\pi\) | ||||
−0.538891 | + | 0.842375i | \(0.681157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 6.29253i | − 0.864345i | −0.901791 | − | 0.432173i | \(-0.857747\pi\) | ||||
0.901791 | − | 0.432173i | \(-0.142253\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.44949i | 0.869649i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.83183 | −0.759239 | −0.379620 | − | 0.925143i | \(-0.623945\pi\) | ||||
−0.379620 | + | 0.925143i | \(0.623945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.34847 | −0.684801 | −0.342401 | − | 0.939554i | \(-0.611240\pi\) | ||||
−0.342401 | + | 0.939554i | \(0.611240\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 7.70674i | − 0.955904i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.8990 | 1.50971 | 0.754856 | − | 0.655891i | \(-0.227707\pi\) | ||||
0.754856 | + | 0.655891i | \(0.227707\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.04989i | − 0.233606i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 13.4495i | − 1.51319i | −0.653886 | − | 0.756593i | \(-0.726863\pi\) | ||||
0.653886 | − | 0.756593i | \(-0.273137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.75323 | −0.741263 | −0.370632 | − | 0.928780i | \(-0.620859\pi\) | ||||
−0.370632 | + | 0.928780i | \(0.620859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.89898 | −1.07370 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.1421i | 1.49906i | 0.661968 | + | 0.749532i | \(0.269721\pi\) | ||||
−0.661968 | + | 0.749532i | \(0.730279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.44949i | 0.256776i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.9993 | 1.43629 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.2474 | −1.24354 | −0.621770 | − | 0.783200i | \(-0.713586\pi\) | ||||
−0.621770 | + | 0.783200i | \(0.713586\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.2419i | 1.81514i | 0.419903 | + | 0.907569i | \(0.362064\pi\) | ||||
−0.419903 | + | 0.907569i | \(0.637936\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 12.8990i | − 1.27097i | −0.772111 | − | 0.635487i | \(-0.780799\pi\) | ||||
0.772111 | − | 0.635487i | \(-0.219201\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.1421 | −1.36717 | −0.683586 | − | 0.729870i | \(-0.739581\pi\) | ||||
−0.683586 | + | 0.729870i | \(0.739581\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 11.1708i | − 1.05086i | −0.850835 | − | 0.525432i | \(-0.823904\pi\) | ||||
0.850835 | − | 0.525432i | \(-0.176096\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.89898i | 0.829834i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.14626 | 0.288418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.79796 | −0.617996 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 0.317837i | − 0.0284282i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.24745i | 0.820578i | 0.911955 | + | 0.410289i | \(0.134572\pi\) | ||||
−0.911955 | + | 0.410289i | \(0.865428\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.73545 | −0.413738 | −0.206869 | − | 0.978369i | \(-0.566327\pi\) | ||||
−0.206869 | + | 0.978369i | \(0.566327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.44949 | −0.385820 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11.8065i | − 1.00870i | −0.863500 | − | 0.504349i | \(-0.831732\pi\) | ||||
0.863500 | − | 0.504349i | \(-0.168268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2474i | 1.03882i | 0.854527 | + | 0.519408i | \(0.173847\pi\) | ||||
−0.854527 | + | 0.519408i | \(0.826153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.02118 | −0.419892 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.44949 | −0.203419 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.97129i | − 0.243418i | −0.992566 | − | 0.121709i | \(-0.961163\pi\) | ||||
0.992566 | − | 0.121709i | \(-0.0388374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.24745i | 0.589789i | 0.955530 | + | 0.294895i | \(0.0952845\pi\) | ||||
−0.955530 | + | 0.294895i | \(0.904715\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.41421 | 0.113592 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.651531 | 0.0519978 | 0.0259989 | − | 0.999662i | \(-0.491723\pi\) | ||||
0.0259989 | + | 0.999662i | \(0.491723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 2.82843i | − 0.222911i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2474i | 1.03762i | 0.854889 | + | 0.518810i | \(0.173625\pi\) | ||||
−0.854889 | + | 0.518810i | \(0.826375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.2453 | 1.64401 | 0.822006 | − | 0.569479i | \(-0.192855\pi\) | ||||
0.822006 | + | 0.569479i | \(0.192855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.19275i | 0.166712i | 0.996520 | + | 0.0833559i | \(0.0265638\pi\) | ||||
−0.996520 | + | 0.0833559i | \(0.973436\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.89898i | − 0.370328i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.04989 | −0.153216 | −0.0766079 | − | 0.997061i | \(-0.524409\pi\) | ||||
−0.0766079 | + | 0.997061i | \(0.524409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.69694 | −0.349121 | −0.174560 | − | 0.984646i | \(-0.555850\pi\) | ||||
−0.174560 | + | 0.984646i | \(0.555850\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.0239i | 1.61923i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.44949i | 0.471633i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.73545 | 0.342645 | 0.171323 | − | 0.985215i | \(-0.445196\pi\) | ||||
0.171323 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | −0.791797 | −0.395899 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395899 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.70674i | 0.549083i | 0.961575 | + | 0.274541i | \(0.0885260\pi\) | ||||
−0.961575 | + | 0.274541i | \(0.911474\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000i | 0.708881i | 0.935079 | + | 0.354441i | \(0.115329\pi\) | ||||
−0.935079 | + | 0.354441i | \(0.884671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.778539 | 0.0546427 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.89898 | −0.551689 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 9.12096i | − 0.630910i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00000i | 0.413057i | 0.978441 | + | 0.206529i | \(0.0662166\pi\) | ||||
−0.978441 | + | 0.206529i | \(0.933783\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.6814 | 0.933066 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.449490 | −0.0305134 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 7.70674i | − 0.518412i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 6.24745i | − 0.418360i | −0.977877 | − | 0.209180i | \(-0.932921\pi\) | ||||
0.977877 | − | 0.209180i | \(-0.0670795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.75663 | −0.647570 | −0.323785 | − | 0.946131i | \(-0.604955\pi\) | ||||
−0.323785 | + | 0.946131i | \(0.604955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.6969 | −1.10336 | −0.551682 | − | 0.834054i | \(-0.686014\pi\) | ||||
−0.551682 | + | 0.834054i | \(0.686014\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.9063i | 1.04206i | 0.853540 | + | 0.521028i | \(0.174451\pi\) | ||||
−0.853540 | + | 0.521028i | \(0.825549\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.2474i | 1.51650i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.4634 | 1.12961 | 0.564806 | − | 0.825224i | \(-0.308951\pi\) | ||||
0.564806 | + | 0.825224i | \(0.308951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.2474 | −1.81958 | −0.909789 | − | 0.415071i | \(-0.863757\pi\) | ||||
−0.909789 | + | 0.415071i | \(0.863757\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.14626i | 0.201007i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.8990i | 0.693485i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7600 | −0.805406 | −0.402703 | − | 0.915331i | \(-0.631929\pi\) | ||||
−0.402703 | + | 0.915331i | \(0.631929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.79796 | 0.364515 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.6848i | 1.04077i | 0.853931 | + | 0.520386i | \(0.174212\pi\) | ||||
−0.853931 | + | 0.520386i | \(0.825788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7.00000i | − 0.434959i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.07107 | 0.436021 | 0.218010 | − | 0.975946i | \(-0.430043\pi\) | ||||
0.218010 | + | 0.975946i | \(0.430043\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.7980 | −1.21618 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.72452i | 0.592915i | 0.955046 | + | 0.296457i | \(0.0958052\pi\) | ||||
−0.955046 | + | 0.296457i | \(0.904195\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6969i | 0.771284i | 0.922648 | + | 0.385642i | \(0.126020\pi\) | ||||
−0.922648 | + | 0.385642i | \(0.873980\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.0424 | 0.605577 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7980 | −0.648786 | −0.324393 | − | 0.945922i | \(-0.605160\pi\) | ||||
−0.324393 | + | 0.945922i | \(0.605160\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 8.48528i | − 0.506189i | −0.967442 | − | 0.253095i | \(-0.918552\pi\) | ||||
0.967442 | − | 0.253095i | \(-0.0814484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7.75255i | − 0.460841i | −0.973091 | − | 0.230421i | \(-0.925990\pi\) | ||||
0.973091 | − | 0.230421i | \(-0.0740102\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.51059 | 0.148195 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.10102 | 0.417707 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 10.3602i | − 0.605249i | −0.953110 | − | 0.302625i | \(-0.902137\pi\) | ||||
0.953110 | − | 0.302625i | \(-0.0978628\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.3485i | 1.06829i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.92820 | −0.400668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.34847 | −0.250642 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.8277i | 0.963551i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4.89898i | − 0.279600i | −0.990180 | − | 0.139800i | \(-0.955354\pi\) | ||||
0.990180 | − | 0.139800i | \(-0.0446459\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0458 | 0.739757 | 0.369879 | − | 0.929080i | \(-0.379399\pi\) | ||||
0.369879 | + | 0.929080i | \(0.379399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.89898 | −0.163860 | −0.0819300 | − | 0.996638i | \(-0.526108\pi\) | ||||
−0.0819300 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.9985i | 1.57255i | 0.617874 | + | 0.786277i | \(0.287994\pi\) | ||||
−0.617874 | + | 0.786277i | \(0.712006\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.59592i | 0.0893543i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9993 | 0.778940 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0000 | −0.665640 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 7.38891i | − 0.407364i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 17.2474i | − 0.948006i | −0.880523 | − | 0.474003i | \(-0.842809\pi\) | ||||
0.880523 | − | 0.474003i | \(-0.157191\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.1701 | 1.37519 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.00000 | 0.163420 | 0.0817102 | − | 0.996656i | \(-0.473962\pi\) | ||||
0.0817102 | + | 0.996656i | \(0.473962\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 0.921404i | − 0.0498968i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.4128 | 1.57896 | 0.789480 | − | 0.613777i | \(-0.210350\pi\) | ||||
0.789480 | + | 0.613777i | \(0.210350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.7980 | 1.80916 | 0.904582 | − | 0.426300i | \(-0.140183\pi\) | ||||
0.904582 | + | 0.426300i | \(0.140183\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7525i | 1.10454i | 0.833664 | + | 0.552272i | \(0.186239\pi\) | ||||
−0.833664 | + | 0.552272i | \(0.813761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.0915 | −1.37706 | −0.688529 | − | 0.725209i | \(-0.741743\pi\) | ||||
−0.688529 | + | 0.725209i | \(0.741743\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.797959 | −0.0419978 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 40.5836i | − 2.12424i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.6969i | 0.871573i | 0.900050 | + | 0.435787i | \(0.143530\pi\) | ||||
−0.900050 | + | 0.435787i | \(0.856470\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.29253 | 0.326692 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.2929 | −1.82739 | −0.913697 | − | 0.406395i | \(-0.866786\pi\) | ||||
−0.913697 | + | 0.406395i | \(0.866786\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.90702i | − 0.0982167i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0454i | 0.567364i | 0.958918 | + | 0.283682i | \(0.0915561\pi\) | ||||
−0.958918 | + | 0.283682i | \(0.908444\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4887 | 0.587044 | 0.293522 | − | 0.955952i | \(-0.405173\pi\) | ||||
0.293522 | + | 0.955952i | \(0.405173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.44949 | −0.328696 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.07107i | 0.358517i | 0.983802 | + | 0.179259i | \(0.0573699\pi\) | ||||
−0.983802 | + | 0.179259i | \(0.942630\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.89898i | 0.450041i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −42.3157 | −2.12913 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.8990 | −1.24964 | −0.624822 | − | 0.780767i | \(-0.714828\pi\) | ||||
−0.624822 | + | 0.780767i | \(0.714828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 22.9774i | − 1.14743i | −0.819053 | − | 0.573717i | \(-0.805501\pi\) | ||||
0.819053 | − | 0.573717i | \(-0.194499\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.10102i | 0.0548457i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.3492 | 0.711264 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.7980 | 0.682265 | 0.341133 | − | 0.940015i | \(-0.389189\pi\) | ||||
0.341133 | + | 0.940015i | \(0.389189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.83183i | − 0.286965i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.2474i | 1.04300i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.63907 | −0.177780 | −0.0888902 | − | 0.996041i | \(-0.528332\pi\) | ||||
−0.0888902 | + | 0.996041i | \(0.528332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8990 | 0.823606 | 0.411803 | − | 0.911273i | \(-0.364899\pi\) | ||||
0.411803 | + | 0.911273i | \(0.364899\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.4135i | 0.747664i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.34847i | − 0.258831i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.2979 | 1.94108 | 0.970540 | − | 0.240940i | \(-0.0774556\pi\) | ||||
0.970540 | + | 0.240940i | \(0.0774556\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.8434 | −1.81864 | −0.909318 | − | 0.416102i | \(-0.863396\pi\) | ||||
−0.909318 | + | 0.416102i | \(0.863396\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 12.5851i | − 0.602025i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.00000i | 0.0954548i | 0.998860 | + | 0.0477274i | \(0.0151979\pi\) | ||||
−0.998860 | + | 0.0477274i | \(0.984802\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.6841 | −1.45785 | −0.728923 | − | 0.684596i | \(-0.759979\pi\) | ||||
−0.728923 | + | 0.684596i | \(0.759979\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.4949 | 2.10926 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.8209i | 0.510670i | 0.966853 | + | 0.255335i | \(0.0821857\pi\) | ||||
−0.966853 | + | 0.255335i | \(0.917814\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.14643i | 0.242336i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.70674 | 0.361298 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.3939 | 1.74921 | 0.874606 | − | 0.484835i | \(-0.161120\pi\) | ||||
0.874606 | + | 0.484835i | \(0.161120\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.953512i | 0.0444095i | 0.999753 | + | 0.0222047i | \(0.00706857\pi\) | ||||
−0.999753 | + | 0.0222047i | \(0.992931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.8434i | 1.61931i | 0.586907 | + | 0.809654i | \(0.300345\pi\) | ||||
−0.586907 | + | 0.809654i | \(0.699655\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.7272 | −1.23679 | −0.618393 | − | 0.785869i | \(-0.712216\pi\) | ||||
−0.618393 | + | 0.785869i | \(0.712216\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 8.91388i | − 0.409860i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 21.7980i | − 1.00016i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.8024 | −1.04187 | −0.520934 | − | 0.853597i | \(-0.674416\pi\) | ||||
−0.520934 | + | 0.853597i | \(0.674416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.1464 | −0.781810 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 38.5337i | 1.74973i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 25.7980i | − 1.16902i | −0.811388 | − | 0.584509i | \(-0.801287\pi\) | ||||
0.811388 | − | 0.584509i | \(-0.198713\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8851 | −0.491238 | −0.245619 | − | 0.969366i | \(-0.578991\pi\) | ||||
−0.245619 | + | 0.969366i | \(0.578991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.44949 | −0.110319 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5505i | 0.740903i | 0.928852 | + | 0.370451i | \(0.120797\pi\) | ||||
−0.928852 | + | 0.370451i | \(0.879203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.7956 | −0.748878 | −0.374439 | − | 0.927251i | \(-0.622165\pi\) | ||||
−0.374439 | + | 0.927251i | \(0.622165\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 57.3939 | 2.55399 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 33.9732i | − 1.50584i | −0.658114 | − | 0.752919i | \(-0.728645\pi\) | ||||
0.658114 | − | 0.752919i | \(-0.271355\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8990i | 0.570617i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −40.5836 | −1.78833 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.1464 | 0.666139 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.9097i | 0.828449i | 0.910175 | + | 0.414224i | \(0.135947\pi\) | ||||
−0.910175 | + | 0.414224i | \(0.864053\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 40.7423i | − 1.78154i | −0.454456 | − | 0.890769i | \(-0.650166\pi\) | ||||
0.454456 | − | 0.890769i | \(-0.349834\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.41421 | 0.0616041 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 6.14966i | − 0.266372i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 44.4949i | 1.92368i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.04989 | 0.0882949 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.5959 | −1.57338 | −0.786691 | − | 0.617347i | \(-0.788207\pi\) | ||||
−0.786691 | + | 0.617347i | \(0.788207\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 22.0239i | − 0.943398i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.04541i | 0.130212i | 0.997878 | + | 0.0651061i | \(0.0207386\pi\) | ||||
−0.997878 | + | 0.0651061i | \(0.979261\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.46410 | 0.147576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.4495 | 0.571930 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 16.3991i | − 0.694852i | −0.937707 | − | 0.347426i | \(-0.887056\pi\) | ||||
0.937707 | − | 0.347426i | \(-0.112944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6515i | 0.450512i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.4838 | −1.53761 | −0.768805 | − | 0.639483i | \(-0.779148\pi\) | ||||
−0.768805 | + | 0.639483i | \(0.779148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.1464 | −1.47862 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 13.5707i | − 0.568912i | −0.958689 | − | 0.284456i | \(-0.908187\pi\) | ||||
0.958689 | − | 0.284456i | \(-0.0918130\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 7.44949i | − 0.311751i | −0.987777 | − | 0.155876i | \(-0.950180\pi\) | ||||
0.987777 | − | 0.155876i | \(-0.0498199\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.8564 | 0.577852 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.89898 | −0.120686 | −0.0603430 | − | 0.998178i | \(-0.519219\pi\) | ||||
−0.0603430 | + | 0.998178i | \(0.519219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.75323i | − 0.280171i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.8990i | 0.534221i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.48528 | 0.350225 | 0.175113 | − | 0.984548i | \(-0.443971\pi\) | ||||
0.175113 | + | 0.984548i | \(0.443971\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 35.8803i | − 1.47343i | −0.676206 | − | 0.736713i | \(-0.736377\pi\) | ||||
0.676206 | − | 0.736713i | \(-0.263623\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 9.89898i | − 0.405819i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.3636 | −0.546022 | −0.273011 | − | 0.962011i | \(-0.588020\pi\) | ||||
−0.273011 | + | 0.962011i | \(0.588020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.2474 | −1.47856 | −0.739282 | − | 0.673396i | \(-0.764835\pi\) | ||||
−0.739282 | + | 0.673396i | \(0.764835\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.3882i | 0.869553i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 23.8434i | − 0.967772i | −0.875131 | − | 0.483886i | \(-0.839225\pi\) | ||||
0.875131 | − | 0.483886i | \(-0.160775\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.0990 | −0.732209 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.0000 | −0.807792 | −0.403896 | − | 0.914805i | \(-0.632344\pi\) | ||||
−0.403896 | + | 0.914805i | \(0.632344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 11.5994i | − 0.466976i | −0.972360 | − | 0.233488i | \(-0.924986\pi\) | ||||
0.972360 | − | 0.233488i | \(-0.0750139\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1464i | 1.25188i | 0.779871 | + | 0.625940i | \(0.215285\pi\) | ||||
−0.779871 | + | 0.625940i | \(0.784715\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.1421 | −0.566593 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.4949 | −1.01980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.0239i | 0.878148i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 5.44949i | − 0.216941i | −0.994100 | − | 0.108470i | \(-0.965405\pi\) | ||||
0.994100 | − | 0.108470i | \(-0.0345953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 29.0949 | 1.15460 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.44949 | −0.0970523 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 29.4128i | − 1.16173i | −0.813998 | − | 0.580867i | \(-0.802714\pi\) | ||||
0.813998 | − | 0.580867i | \(-0.197286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 15.3031i | − 0.603494i | −0.953388 | − | 0.301747i | \(-0.902430\pi\) | ||||
0.953388 | − | 0.301747i | \(-0.0975698\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.0409 | −1.49554 | −0.747771 | − | 0.663957i | \(-0.768876\pi\) | ||||
−0.747771 | + | 0.663957i | \(0.768876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.9546 | 0.469259 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.34242i | 0.326464i | 0.986588 | + | 0.163232i | \(0.0521919\pi\) | ||||
−0.986588 | + | 0.163232i | \(0.947808\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8990i | 0.582151i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.90702 | −0.0742871 | −0.0371435 | − | 0.999310i | \(-0.511826\pi\) | ||||
−0.0371435 | + | 0.999310i | \(0.511826\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.7423 | 1.04016 | 0.520078 | − | 0.854119i | \(-0.325903\pi\) | ||||
0.520078 | + | 0.854119i | \(0.325903\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.9993i | 0.542868i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.20204i | 0.0852634i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.9638 | 0.423251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.2929 | 1.78446 | 0.892229 | − | 0.451583i | \(-0.149140\pi\) | ||||
0.892229 | + | 0.451583i | \(0.149140\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.94258i | 0.228392i | 0.993458 | + | 0.114196i | \(0.0364292\pi\) | ||||
−0.993458 | + | 0.114196i | \(0.963571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 12.2474i | − 0.470014i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2986 | −1.00629 | −0.503144 | − | 0.864203i | \(-0.667823\pi\) | ||||
−0.503144 | + | 0.864203i | \(0.667823\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.1464 | −1.41929 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 15.4135i | − 0.587207i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2474i | 1.07458i | 0.843396 | + | 0.537292i | \(0.180553\pi\) | ||||
−0.843396 | + | 0.537292i | \(0.819447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.5337 | 1.46167 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.89898 | −0.299195 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 15.5563i | − 0.587555i | −0.955874 | − | 0.293778i | \(-0.905087\pi\) | ||||
0.955874 | − | 0.293778i | \(-0.0949125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 31.1464i | − 1.17471i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.2419 | −0.686058 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.0000 | 1.31445 | 0.657226 | − | 0.753693i | \(-0.271730\pi\) | ||||
0.657226 | + | 0.753693i | \(0.271730\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.27135i | − 0.0476124i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.7980i | 0.590810i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.23171 | −0.344285 | −0.172142 | − | 0.985072i | \(-0.555069\pi\) | ||||
−0.172142 | + | 0.985072i | \(0.555069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8990 | 0.480383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.81405i | 0.141650i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 42.2474i | − 1.56687i | −0.621473 | − | 0.783436i | \(-0.713465\pi\) | ||||
0.621473 | − | 0.783436i | \(-0.286535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.6814 | 0.506026 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.8990 | 1.58451 | 0.792255 | − | 0.610190i | \(-0.208907\pi\) | ||||
0.792255 | + | 0.610190i | \(0.208907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 16.3991i | − 0.604069i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 39.5959i | − 1.45656i | −0.685280 | − | 0.728280i | \(-0.740320\pi\) | ||||
0.685280 | − | 0.728280i | \(-0.259680\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.2556 | 1.14666 | 0.573328 | − | 0.819326i | \(-0.305652\pi\) | ||||
0.573328 | + | 0.819326i | \(0.305652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.34847 | −0.342501 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 14.1421i | − 0.516742i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 33.3939i | − 1.21856i | −0.792955 | − | 0.609280i | \(-0.791459\pi\) | ||||
0.792955 | − | 0.609280i | \(-0.208541\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.8024 | 0.829864 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.3031 | −0.883310 | −0.441655 | − | 0.897185i | \(-0.645608\pi\) | ||||
−0.441655 | + | 0.897185i | \(0.645608\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 2.79632i | − 0.101366i | −0.998715 | − | 0.0506832i | \(-0.983860\pi\) | ||||
0.998715 | − | 0.0506832i | \(-0.0161399\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.00000i | 0.253417i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.2850 | −0.515801 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.1010 | −0.905166 | −0.452583 | − | 0.891722i | \(-0.649497\pi\) | ||||
−0.452583 | + | 0.891722i | \(0.649497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 32.0662i | − 1.15334i | −0.816977 | − | 0.576671i | \(-0.804352\pi\) | ||||
0.816977 | − | 0.576671i | \(-0.195648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 2.20204i | − 0.0790996i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.1708 | 0.400237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 2.04989i | − 0.0731636i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4.49490i | − 0.160226i | −0.996786 | − | 0.0801129i | \(-0.974472\pi\) | ||||
0.996786 | − | 0.0801129i | \(-0.0255281\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1708 | 0.397189 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.1010 | −0.465231 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 36.1981i | − 1.28220i | −0.767456 | − | 0.641101i | \(-0.778478\pi\) | ||||
0.767456 | − | 0.641101i | \(-0.221522\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.2474i | 0.822436i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.4415 | −0.933099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.89898 | −0.313648 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.4203i | 0.753097i | 0.926397 | + | 0.376549i | \(0.122889\pi\) | ||||
−0.926397 | + | 0.376549i | \(0.877111\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 36.7423i | − 1.29020i | −0.764099 | − | 0.645099i | \(-0.776816\pi\) | ||||
0.764099 | − | 0.645099i | \(-0.223184\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41.6800 | 1.45999 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.3485 | −0.676917 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0560i | 0.769758i | 0.922967 | + | 0.384879i | \(0.125757\pi\) | ||||
−0.922967 | + | 0.384879i | \(0.874243\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.3485i | 0.848734i | 0.905490 | + | 0.424367i | \(0.139503\pi\) | ||||
−0.905490 | + | 0.424367i | \(0.860497\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.9766 | −1.28580 | −0.642902 | − | 0.765949i | \(-0.722270\pi\) | ||||
−0.642902 | + | 0.765949i | \(0.722270\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0454 | 1.32137 | 0.660686 | − | 0.750663i | \(-0.270266\pi\) | ||||
0.660686 | + | 0.750663i | \(0.270266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.14626i | 0.109012i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 66.8434i | − 2.31321i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.7238 | −0.819036 | −0.409518 | − | 0.912302i | \(-0.634303\pi\) | ||||
−0.409518 | + | 0.912302i | \(0.634303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.3939 | 0.979099 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.0239i | 0.757643i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 6.79796i | − 0.233581i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.7990 | 0.678701 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.1010 | 1.27031 | 0.635157 | − | 0.772383i | \(-0.280935\pi\) | ||||
0.635157 | + | 0.772383i | \(0.280935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.8085i | 1.46231i | 0.682212 | + | 0.731155i | \(0.261018\pi\) | ||||
−0.682212 | + | 0.731155i | \(0.738982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 22.4949i | − 0.767516i | −0.923434 | − | 0.383758i | \(-0.874630\pi\) | ||||
0.923434 | − | 0.383758i | \(-0.125370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.0915 | 0.888166 | 0.444083 | − | 0.895986i | \(-0.353530\pi\) | ||||
0.444083 | + | 0.895986i | \(0.353530\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.89898 | 0.234572 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.5699i | 0.935246i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5959i | 0.663982i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.317837 | 0.0107449 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.2020 | −0.648407 | −0.324203 | − | 0.945987i | \(-0.605096\pi\) | ||||
−0.324203 | + | 0.945987i | \(0.605096\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.49966i | 0.252670i | 0.991988 | + | 0.126335i | \(0.0403214\pi\) | ||||
−0.991988 | + | 0.126335i | \(0.959679\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.0454i | 1.24668i | 0.781952 | + | 0.623339i | \(0.214224\pi\) | ||||
−0.781952 | + | 0.623339i | \(0.785776\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.0458 | 0.438034 | 0.219017 | − | 0.975721i | \(-0.429715\pi\) | ||||
0.219017 | + | 0.975721i | \(0.429715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.24745 | −0.310149 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 32.8769i | − 1.10018i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.44949i | 0.215583i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.349945 | 0.0116713 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.7980 | −0.659566 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.7778i | 0.491231i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.9444i | 1.85760i | 0.370578 | + | 0.928801i | \(0.379160\pi\) | ||||
−0.370578 | + | 0.928801i | \(0.620840\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.70674 | −0.255336 | −0.127668 | − | 0.991817i | \(-0.540749\pi\) | ||||
−0.127668 | + | 0.991817i | \(0.540749\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8434 | 0.458149 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.73545i | − 0.156378i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 37.2474i | − 1.22868i | −0.789041 | − | 0.614340i | \(-0.789422\pi\) | ||||
0.789041 | − | 0.614340i | \(-0.210578\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.2929 | 1.12754 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.8885i | 0.455667i | 0.973700 | + | 0.227834i | \(0.0731643\pi\) | ||||
−0.973700 | + | 0.227834i | \(0.926836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.44949i | − 0.145826i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.2918 | 0.663613 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.651531 | 0.0212846 | 0.0106423 | − | 0.999943i | \(-0.496612\pi\) | ||||
0.0106423 | + | 0.999943i | \(0.496612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 22.3096i | − 0.727272i | −0.931541 | − | 0.363636i | \(-0.881535\pi\) | ||||
0.931541 | − | 0.363636i | \(-0.118465\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.10102i | 0.231241i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.9842 | −0.941859 | −0.470929 | − | 0.882171i | \(-0.656081\pi\) | ||||
−0.470929 | + | 0.882171i | \(0.656081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.5959 | 1.02565 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 2.25697i | − 0.0731104i | −0.999332 | − | 0.0365552i | \(-0.988362\pi\) | ||||
0.999332 | − | 0.0365552i | \(-0.0116385\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 14.8990i | − 0.482120i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.8065 | 0.381252 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7980 | 0.993483 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 34.6089i | 1.11410i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4.89898i | − 0.157541i | −0.996893 | − | 0.0787703i | \(-0.974901\pi\) | ||||
0.996893 | − | 0.0787703i | \(-0.0250994\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.8221 | −1.79142 | −0.895708 | − | 0.444642i | \(-0.853331\pi\) | ||||
−0.895708 | + | 0.444642i | \(0.853331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.2474 | −0.392635 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 43.7620i | − 1.40007i | −0.714109 | − | 0.700035i | \(-0.753168\pi\) | ||||
0.714109 | − | 0.700035i | \(-0.246832\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 28.9898i | − 0.926518i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.1735 | 0.898596 | 0.449298 | − | 0.893382i | \(-0.351674\pi\) | ||||
0.449298 | + | 0.893382i | \(0.351674\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.2474 | 0.772588 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 12.2993i | − 0.391096i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.5505i | 0.462212i | 0.972929 | + | 0.231106i | \(0.0742344\pi\) | ||||
−0.972929 | + | 0.231106i | \(0.925766\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.4626 | 0.997433 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.2474 | 1.02129 | 0.510643 | − | 0.859793i | \(-0.329407\pi\) | ||||
0.510643 | + | 0.859793i | \(0.329407\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6048.2.h.d.2591.2 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.d.2591.8 | yes | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.d.2591.1 | ✓ | 8 | |
12.11 | even | 2 | inner | 6048.2.h.d.2591.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.d.2591.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
6048.2.h.d.2591.2 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.d.2591.7 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.d.2591.8 | yes | 8 | 3.2 | odd | 2 | inner |