Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,2,Mod(431,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, 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("2160.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.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: | \(17.2476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 431.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.431 |
Dual form | 2160.2.h.a.431.2 |
$q$-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 \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.73205i | − 1.78855i | −0.447521 | − | 0.894274i | \(-0.647693\pi\) | ||||
0.447521 | − | 0.894274i | \(-0.352307\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.73205 | −1.42677 | −0.713384 | − | 0.700774i | \(-0.752838\pi\) | ||||
−0.713384 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.19615 | 1.71850 | 0.859252 | − | 0.511553i | \(-0.170930\pi\) | ||||
0.859252 | + | 0.511553i | \(0.170930\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.19615i | 1.26025i | 0.776493 | + | 0.630126i | \(0.216997\pi\) | ||||
−0.776493 | + | 0.630126i | \(0.783003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.464102i | − 0.106472i | −0.998582 | − | 0.0532361i | \(-0.983046\pi\) | ||||
0.998582 | − | 0.0532361i | \(-0.0169536\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.26795 | 0.889929 | 0.444964 | − | 0.895548i | \(-0.353216\pi\) | ||||
0.444964 | + | 0.895548i | \(0.353216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.19615i | − 1.52199i | −0.648759 | − | 0.760994i | \(-0.724712\pi\) | ||||
0.648759 | − | 0.760994i | \(-0.275288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.464102i | − 0.0833551i | −0.999131 | − | 0.0416776i | \(-0.986730\pi\) | ||||
0.999131 | − | 0.0416776i | \(-0.0132702\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.73205 | 0.799863 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 2.19615i | − 0.342981i | −0.985186 | − | 0.171491i | \(-0.945142\pi\) | ||||
0.985186 | − | 0.171491i | \(-0.0548583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.66025i | − 0.863181i | −0.902070 | − | 0.431590i | \(-0.857953\pi\) | ||||
0.902070 | − | 0.431590i | \(-0.142047\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.46410 | −1.38048 | −0.690241 | − | 0.723580i | \(-0.742495\pi\) | ||||
−0.690241 | + | 0.723580i | \(0.742495\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.3923 | −2.19890 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.1962i | − 1.53791i | −0.639303 | − | 0.768955i | \(-0.720777\pi\) | ||||
0.639303 | − | 0.768955i | \(-0.279223\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 4.73205i | − 0.638070i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.66025 | 0.736902 | 0.368451 | − | 0.929647i | \(-0.379888\pi\) | ||||
0.368451 | + | 0.929647i | \(0.379888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.19615i | 0.768538i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.3923i | − 1.26962i | −0.772667 | − | 0.634811i | \(-0.781078\pi\) | ||||
0.772667 | − | 0.634811i | \(-0.218922\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.73205 | −0.561591 | −0.280796 | − | 0.959768i | \(-0.590598\pi\) | ||||
−0.280796 | + | 0.959768i | \(0.590598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.19615 | −0.491122 | −0.245561 | − | 0.969381i | \(-0.578972\pi\) | ||||
−0.245561 | + | 0.969381i | \(0.578972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.3923i | 2.55184i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 9.92820i | − 1.11701i | −0.829501 | − | 0.558505i | \(-0.811375\pi\) | ||||
0.829501 | − | 0.558505i | \(-0.188625\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.19615 | −0.570352 | −0.285176 | − | 0.958475i | \(-0.592052\pi\) | ||||
−0.285176 | + | 0.958475i | \(0.592052\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.19615 | −0.563602 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 14.1962i | − 1.50479i | −0.658713 | − | 0.752395i | \(-0.728899\pi\) | ||||
0.658713 | − | 0.752395i | \(-0.271101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 29.3205i | − 3.07362i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.464102 | 0.0476158 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.39230i | 0.437051i | 0.975831 | + | 0.218525i | \(0.0701246\pi\) | ||||
−0.975831 | + | 0.218525i | \(0.929875\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 9.46410i | − 0.932526i | −0.884646 | − | 0.466263i | \(-0.845600\pi\) | ||||
0.884646 | − | 0.466263i | \(-0.154400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.9282 | 1.82986 | 0.914929 | − | 0.403614i | \(-0.132246\pi\) | ||||
0.914929 | + | 0.403614i | \(0.132246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3923 | 1.09118 | 0.545592 | − | 0.838051i | \(-0.316305\pi\) | ||||
0.545592 | + | 0.838051i | \(0.316305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000i | 1.12887i | 0.825479 | + | 0.564433i | \(0.190905\pi\) | ||||
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.26795i | 0.397988i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.5885 | 2.25402 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3923 | 1.03566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000i | 1.59724i | 0.601834 | + | 0.798621i | \(0.294437\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.928203 | −0.0810975 | −0.0405487 | − | 0.999178i | \(-0.512911\pi\) | ||||
−0.0405487 | + | 0.999178i | \(0.512911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.19615 | −0.190431 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 5.19615i | − 0.443937i | −0.975054 | − | 0.221969i | \(-0.928752\pi\) | ||||
0.975054 | − | 0.221969i | \(-0.0712483\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 19.8564i | − 1.68420i | −0.539323 | − | 0.842099i | \(-0.681320\pi\) | ||||
0.539323 | − | 0.842099i | \(-0.318680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29.3205 | −2.45190 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.19615 | 0.680653 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.80385i | 0.803162i | 0.915823 | + | 0.401581i | \(0.131539\pi\) | ||||
−0.915823 | + | 0.401581i | \(0.868461\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.9282i | 1.54036i | 0.637829 | + | 0.770178i | \(0.279832\pi\) | ||||
−0.637829 | + | 0.770178i | \(0.720168\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.464102 | 0.0372775 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1962 | 1.29259 | 0.646297 | − | 0.763086i | \(-0.276317\pi\) | ||||
0.646297 | + | 0.763086i | \(0.276317\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 20.1962i | − 1.59168i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 10.3923i | − 0.813988i | −0.913431 | − | 0.406994i | \(-0.866577\pi\) | ||||
0.913431 | − | 0.406994i | \(-0.133423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.6603 | −1.13444 | −0.567222 | − | 0.823565i | \(-0.691982\pi\) | ||||
−0.567222 | + | 0.823565i | \(0.691982\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.3923 | 1.95325 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 17.1962i | − 1.30740i | −0.756754 | − | 0.653700i | \(-0.773216\pi\) | ||||
0.756754 | − | 0.653700i | \(-0.226784\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.73205i | 0.357709i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.85641 | 0.138754 | 0.0693772 | − | 0.997591i | \(-0.477899\pi\) | ||||
0.0693772 | + | 0.997591i | \(0.477899\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3923 | −1.14410 | −0.572051 | − | 0.820218i | \(-0.693852\pi\) | ||||
−0.572051 | + | 0.820218i | \(0.693852\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000i | 0.147043i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 24.5885i | − 1.79809i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.0000 | 1.30243 | 0.651217 | − | 0.758891i | \(-0.274259\pi\) | ||||
0.651217 | + | 0.758891i | \(0.274259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.80385 | −0.129844 | −0.0649219 | − | 0.997890i | \(-0.520680\pi\) | ||||
−0.0649219 | + | 0.997890i | \(0.520680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 17.1962i | − 1.22518i | −0.790403 | − | 0.612588i | \(-0.790129\pi\) | ||||
0.790403 | − | 0.612588i | \(-0.209871\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3923i | 0.736691i | 0.929689 | + | 0.368345i | \(0.120076\pi\) | ||||
−0.929689 | + | 0.368345i | \(0.879924\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −38.7846 | −2.72215 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.19615 | 0.153386 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.19615i | 0.151911i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000i | 0.619586i | 0.950804 | + | 0.309793i | \(0.100260\pi\) | ||||
−0.950804 | + | 0.309793i | \(0.899740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.66025 | 0.386026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.19615 | −0.149085 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 32.1962i | 2.16575i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.928203i | 0.0621571i | 0.999517 | + | 0.0310785i | \(0.00989420\pi\) | ||||
−0.999517 | + | 0.0310785i | \(0.990106\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.26795 | 0.283274 | 0.141637 | − | 0.989919i | \(-0.454763\pi\) | ||||
0.141637 | + | 0.989919i | \(0.454763\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.00000 | −0.330409 | −0.165205 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165205 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7846i | 0.968572i | 0.874910 | + | 0.484286i | \(0.160921\pi\) | ||||
−0.874910 | + | 0.484286i | \(0.839079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 9.46410i | − 0.617370i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3205 | 1.89659 | 0.948293 | − | 0.317396i | \(-0.102809\pi\) | ||||
0.948293 | + | 0.317396i | \(0.102809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.39230 | −0.218518 | −0.109259 | − | 0.994013i | \(-0.534848\pi\) | ||||
−0.109259 | + | 0.994013i | \(0.534848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 15.3923i | − 0.983378i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.87564i | − 0.182973i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.3205 | −0.714544 | −0.357272 | − | 0.934000i | \(-0.616293\pi\) | ||||
−0.357272 | + | 0.934000i | \(0.616293\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.1962 | −1.26972 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 9.58846i | − 0.598112i | −0.954236 | − | 0.299056i | \(-0.903328\pi\) | ||||
0.954236 | − | 0.299056i | \(-0.0966717\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.46410i | − 0.588071i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.3205 | −0.698052 | −0.349026 | − | 0.937113i | \(-0.613488\pi\) | ||||
−0.349026 | + | 0.937113i | \(0.613488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.1962 | 0.687774 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7846i | 0.901434i | 0.892667 | + | 0.450717i | \(0.148832\pi\) | ||||
−0.892667 | + | 0.450717i | \(0.851168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 17.5359i | − 1.06523i | −0.846358 | − | 0.532615i | \(-0.821209\pi\) | ||||
0.846358 | − | 0.532615i | \(-0.178791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.73205 | 0.285353 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.1962 | −1.69414 | −0.847071 | − | 0.531479i | \(-0.821636\pi\) | ||||
−0.847071 | + | 0.531479i | \(0.821636\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 12.5885i | − 0.750964i | −0.926830 | − | 0.375482i | \(-0.877477\pi\) | ||||
0.926830 | − | 0.375482i | \(-0.122523\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.2679i | 0.788698i | 0.918961 | + | 0.394349i | \(0.129030\pi\) | ||||
−0.918961 | + | 0.394349i | \(0.870970\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3923 | −0.613438 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0000 | −0.588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.8038i | 0.748009i | 0.927427 | + | 0.374004i | \(0.122016\pi\) | ||||
−0.927427 | + | 0.374004i | \(0.877984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.66025i | 0.329553i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.4449 | 1.52935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.7846 | −1.54384 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 1.00000i | − 0.0572598i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8564i | 1.13326i | 0.823971 | + | 0.566632i | \(0.191754\pi\) | ||||
−0.823971 | + | 0.566632i | \(0.808246\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.7321 | −1.28902 | −0.644508 | − | 0.764597i | \(-0.722938\pi\) | ||||
−0.644508 | + | 0.764597i | \(0.722938\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.00000 | 0.452187 | 0.226093 | − | 0.974106i | \(-0.427405\pi\) | ||||
0.226093 | + | 0.974106i | \(0.427405\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 18.8038i | − 1.05613i | −0.849204 | − | 0.528065i | \(-0.822918\pi\) | ||||
0.849204 | − | 0.528065i | \(-0.177082\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38.7846i | 2.17152i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.41154 | 0.134182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.19615 | −0.343701 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 44.7846i | 2.46906i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.53590i | 0.469175i | 0.972095 | + | 0.234588i | \(0.0753740\pi\) | ||||
−0.972095 | + | 0.234588i | \(0.924626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.3923 | 0.567792 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.58846 | −0.141002 | −0.0705011 | − | 0.997512i | \(-0.522460\pi\) | ||||
−0.0705011 | + | 0.997512i | \(0.522460\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.19615i | 0.118928i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 39.7128i | 2.14429i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3923 | 0.557888 | 0.278944 | − | 0.960307i | \(-0.410016\pi\) | ||||
0.278944 | + | 0.960307i | \(0.410016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.6077 | 0.674874 | 0.337437 | − | 0.941348i | \(-0.390440\pi\) | ||||
0.337437 | + | 0.941348i | \(0.390440\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.3923i | 1.19182i | 0.803050 | + | 0.595911i | \(0.203209\pi\) | ||||
−0.803050 | + | 0.595911i | \(0.796791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4.73205i | − 0.251151i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.7128 | 1.14596 | 0.572979 | − | 0.819570i | \(-0.305788\pi\) | ||||
0.572979 | + | 0.819570i | \(0.305788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7846 | 0.988664 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.19615i | − 0.219637i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.58846i | 0.343915i | 0.985104 | + | 0.171957i | \(0.0550091\pi\) | ||||
−0.985104 | + | 0.171957i | \(0.944991\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −52.9808 | −2.75062 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.39230 | −0.434537 | −0.217269 | − | 0.976112i | \(-0.569715\pi\) | ||||
−0.217269 | + | 0.976112i | \(0.569715\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 50.7846i | − 2.61554i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0000i | 1.38690i | 0.720506 | + | 0.693448i | \(0.243909\pi\) | ||||
−0.720506 | + | 0.693448i | \(0.756091\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.33975 | 0.170653 | 0.0853265 | − | 0.996353i | \(-0.472807\pi\) | ||||
0.0853265 | + | 0.996353i | \(0.472807\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.3923 | −1.14122 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.58846i | 0.334048i | 0.985953 | + | 0.167024i | \(0.0534157\pi\) | ||||
−0.985953 | + | 0.167024i | \(0.946584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.1769i | 1.12153i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.92820 | 0.499542 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.5885 | 1.33444 | 0.667218 | − | 0.744862i | \(-0.267485\pi\) | ||||
0.667218 | + | 0.744862i | \(0.267485\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3923i | 0.518967i | 0.965748 | + | 0.259483i | \(0.0835523\pi\) | ||||
−0.965748 | + | 0.259483i | \(0.916448\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.87564i | − 0.143246i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.46410 | −0.469118 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.78461 | 0.187137 | 0.0935685 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935685 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 26.7846i | − 1.31798i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 5.19615i | − 0.255069i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.9808 | 1.70892 | 0.854461 | − | 0.519515i | \(-0.173888\pi\) | ||||
0.854461 | + | 0.519515i | \(0.173888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.1769 | 1.56821 | 0.784103 | − | 0.620630i | \(-0.213123\pi\) | ||||
0.784103 | + | 0.620630i | \(0.213123\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 5.19615i | − 0.252050i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.73205i | 0.229000i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1244 | 0.728515 | 0.364257 | − | 0.931298i | \(-0.381323\pi\) | ||||
0.364257 | + | 0.931298i | \(0.381323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.5885 | 1.27776 | 0.638880 | − | 0.769307i | \(-0.279398\pi\) | ||||
0.638880 | + | 0.769307i | \(0.279398\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.98076i | − 0.0947527i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.7128i | 1.46584i | 0.680313 | + | 0.732921i | \(0.261844\pi\) | ||||
−0.680313 | + | 0.732921i | \(0.738156\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.5167 | −0.784730 | −0.392365 | − | 0.919810i | \(-0.628343\pi\) | ||||
−0.392365 | + | 0.919810i | \(0.628343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1962 | 0.672962 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 28.9808i | − 1.36769i | −0.729629 | − | 0.683843i | \(-0.760307\pi\) | ||||
0.729629 | − | 0.683843i | \(-0.239693\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3923i | 0.489355i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.3205 | 1.37457 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.784610 | 0.0367025 | 0.0183512 | − | 0.999832i | \(-0.494158\pi\) | ||||
0.0183512 | + | 0.999832i | \(0.494158\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 22.3923i | − 1.04291i | −0.853278 | − | 0.521457i | \(-0.825389\pi\) | ||||
0.853278 | − | 0.521457i | \(-0.174611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.928203i | 0.0431373i | 0.999767 | + | 0.0215686i | \(0.00686604\pi\) | ||||
−0.999767 | + | 0.0215686i | \(0.993134\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.7321 | −1.46838 | −0.734192 | − | 0.678942i | \(-0.762439\pi\) | ||||
−0.734192 | + | 0.678942i | \(0.762439\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −49.1769 | −2.27078 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.7846i | 1.23156i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.464102i | 0.0212944i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.8038 | −0.996243 | −0.498122 | − | 0.867107i | \(-0.665977\pi\) | ||||
−0.498122 | + | 0.867107i | \(0.665977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.3923 | 0.565040 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 8.00000i | − 0.363261i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.9808i | 0.769472i | 0.923027 | + | 0.384736i | \(0.125707\pi\) | ||||
−0.923027 | + | 0.384736i | \(0.874293\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.78461 | −0.125668 | −0.0628338 | − | 0.998024i | \(-0.520014\pi\) | ||||
−0.0628338 | + | 0.998024i | \(0.520014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.5885 | 1.91809 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.3923i | 1.00443i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 35.5359i | − 1.59081i | −0.606081 | − | 0.795403i | \(-0.707259\pi\) | ||||
0.606081 | − | 0.795403i | \(-0.292741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.41154 | 0.107525 | 0.0537627 | − | 0.998554i | \(-0.482879\pi\) | ||||
0.0537627 | + | 0.998554i | \(0.482879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.39230 | −0.195455 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 4.39230i | − 0.194685i | −0.995251 | − | 0.0973427i | \(-0.968966\pi\) | ||||
0.995251 | − | 0.0973427i | \(-0.0310343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.8564i | 0.878396i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.46410 | 0.417038 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.7846 | 1.96962 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.58846i | 0.288646i | 0.989531 | + | 0.144323i | \(0.0461004\pi\) | ||||
−0.989531 | + | 0.144323i | \(0.953900\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 23.6603i | − 1.03459i | −0.855807 | − | 0.517295i | \(-0.826939\pi\) | ||||
0.855807 | − | 0.517295i | \(-0.173061\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.41154 | 0.105048 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.78461 | −0.208027 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13.6077i | − 0.589415i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.9282i | 0.818338i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 72.8372 | 3.13732 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0000 | 0.687894 | 0.343947 | − | 0.938989i | \(-0.388236\pi\) | ||||
0.343947 | + | 0.938989i | \(0.388236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.3923i | 0.487993i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.7321i | 0.971952i | 0.873972 | + | 0.485976i | \(0.161536\pi\) | ||||
−0.873972 | + | 0.485976i | \(0.838464\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.80385 | −0.162049 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −46.9808 | −1.99783 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.3923i | 1.45725i | 0.684914 | + | 0.728624i | \(0.259840\pi\) | ||||
−0.684914 | + | 0.728624i | \(0.740160\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 35.0718i | − 1.48338i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.85641 | −0.0782382 | −0.0391191 | − | 0.999235i | \(-0.512455\pi\) | ||||
−0.0391191 | + | 0.999235i | \(0.512455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0000 | −0.504844 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.1962i | 1.34973i | 0.737940 | + | 0.674866i | \(0.235799\pi\) | ||||
−0.737940 | + | 0.674866i | \(0.764201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 0.464102i | − 0.0194220i | −0.999953 | − | 0.00971102i | \(-0.996909\pi\) | ||||
0.999953 | − | 0.00971102i | \(-0.00309116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.26795 | −0.177986 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.58846 | −0.191020 | −0.0955100 | − | 0.995428i | \(-0.530448\pi\) | ||||
−0.0955100 | + | 0.995428i | \(0.530448\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.5885i | 1.02010i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.9808i | 2.19424i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.19615 | 0.214468 | 0.107234 | − | 0.994234i | \(-0.465801\pi\) | ||||
0.107234 | + | 0.994234i | \(0.465801\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.215390 | −0.00887500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 23.1962i | − 0.952552i | −0.879296 | − | 0.476276i | \(-0.841986\pi\) | ||||
0.879296 | − | 0.476276i | \(-0.158014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.5885i | 1.00803i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.4115 | −0.466263 | −0.233131 | − | 0.972445i | \(-0.574897\pi\) | ||||
−0.233131 | + | 0.972445i | \(0.574897\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.1769 | −1.31252 | −0.656262 | − | 0.754533i | \(-0.727863\pi\) | ||||
−0.656262 | + | 0.754533i | \(0.727863\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.3923i | 0.463163i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7321i | 0.922665i | 0.887227 | + | 0.461333i | \(0.152629\pi\) | ||||
−0.887227 | + | 0.461333i | \(0.847371\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −58.6410 | −2.37236 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.1769 | 1.34000 | 0.670001 | − | 0.742360i | \(-0.266293\pi\) | ||||
0.670001 | + | 0.742360i | \(0.266293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.58846i | 0.144466i | 0.997388 | + | 0.0722329i | \(0.0230125\pi\) | ||||
−0.997388 | + | 0.0722329i | \(0.976988\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.53590i | 0.343087i | 0.985177 | + | 0.171543i | \(0.0548754\pi\) | ||||
−0.985177 | + | 0.171543i | \(0.945125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −67.1769 | −2.69139 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.3923i | 0.414368i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.7846i | 1.90228i | 0.308767 | + | 0.951138i | \(0.400084\pi\) | ||||
−0.308767 | + | 0.951138i | \(0.599916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.0000 | −0.714308 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −95.3731 | −3.77882 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 16.3923i | − 0.647457i | −0.946150 | − | 0.323729i | \(-0.895064\pi\) | ||||
0.946150 | − | 0.323729i | \(-0.104936\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.58846i | 0.259823i | 0.991526 | + | 0.129912i | \(0.0414694\pi\) | ||||
−0.991526 | + | 0.129912i | \(0.958531\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.05256 | −0.277265 | −0.138632 | − | 0.990344i | \(-0.544271\pi\) | ||||
−0.138632 | + | 0.990344i | \(0.544271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.7846 | −1.05139 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.41154i | 0.0943710i | 0.998886 | + | 0.0471855i | \(0.0150252\pi\) | ||||
−0.998886 | + | 0.0471855i | \(0.984975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 0.928203i | − 0.0362679i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.5885 | 0.957830 | 0.478915 | − | 0.877861i | \(-0.341030\pi\) | ||||
0.478915 | + | 0.877861i | \(0.341030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.00000 | −0.155582 | −0.0777910 | − | 0.996970i | \(-0.524787\pi\) | ||||
−0.0777910 | + | 0.996970i | \(0.524787\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 2.19615i | − 0.0851631i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 34.9808i | − 1.35446i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.73205 | 0.182679 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5885 | 0.562344 | 0.281172 | − | 0.959657i | \(-0.409277\pi\) | ||||
0.281172 | + | 0.959657i | \(0.409277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.8564i | 1.45280i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.6603 | −1.24971 | −0.624855 | − | 0.780741i | \(-0.714842\pi\) | ||||
−0.624855 | + | 0.780741i | \(0.714842\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.19615 | 0.198535 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 69.3731i | − 2.64290i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 27.0000i | − 1.02713i | −0.858051 | − | 0.513564i | \(-0.828325\pi\) | ||||
0.858051 | − | 0.513564i | \(-0.171675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.8564 | 0.753196 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.4115 | 0.432243 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000i | 0.226617i | 0.993560 | + | 0.113308i | \(0.0361448\pi\) | ||||
−0.993560 | + | 0.113308i | \(0.963855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 0.928203i | − 0.0350078i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.7846 | 0.781686 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.0000 | 1.05156 | 0.525781 | − | 0.850620i | \(-0.323773\pi\) | ||||
0.525781 | + | 0.850620i | \(0.323773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.98076i | − 0.0741801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 29.3205i | − 1.09652i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.9282 | 1.37719 | 0.688595 | − | 0.725146i | \(-0.258228\pi\) | ||||
0.688595 | + | 0.725146i | \(0.258228\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.7846 | −1.66787 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.19615i | 0.304397i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.7128i | 1.47287i | 0.676510 | + | 0.736433i | \(0.263492\pi\) | ||||
−0.676510 | + | 0.736433i | \(0.736508\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.4115 | 1.08783 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.3923 | −1.34418 | −0.672090 | − | 0.740469i | \(-0.734603\pi\) | ||||
−0.672090 | + | 0.740469i | \(0.734603\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 49.1769i | 1.81145i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.3923i | 0.713357i | 0.934227 | + | 0.356679i | \(0.116091\pi\) | ||||
−0.934227 | + | 0.356679i | \(0.883909\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.1051 | −1.83818 | −0.919089 | − | 0.394049i | \(-0.871074\pi\) | ||||
−0.919089 | + | 0.394049i | \(0.871074\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.80385 | −0.359185 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 89.5692i | − 3.27279i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 48.7128i | − 1.77756i | −0.458338 | − | 0.888778i | \(-0.651555\pi\) | ||||
0.458338 | − | 0.888778i | \(-0.348445\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.9282 | −0.688868 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.0000 | 1.23575 | 0.617876 | − | 0.786276i | \(-0.287994\pi\) | ||||
0.617876 | + | 0.786276i | \(0.287994\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 45.3731i | − 1.64477i | −0.568930 | − | 0.822386i | \(-0.692642\pi\) | ||||
0.568930 | − | 0.822386i | \(-0.307358\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 53.9090i | − 1.95164i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.0718 | 1.26637 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.0000 | −0.468792 | −0.234396 | − | 0.972141i | \(-0.575311\pi\) | ||||
−0.234396 | + | 0.972141i | \(0.575311\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.1962i | 0.834308i | 0.908836 | + | 0.417154i | \(0.136972\pi\) | ||||
−0.908836 | + | 0.417154i | \(0.863028\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.464102i | 0.0166710i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.01924 | −0.0365180 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.3923 | 0.801260 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1962i | 0.578065i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.1244i | 0.539125i | 0.962983 | + | 0.269563i | \(0.0868791\pi\) | ||||
−0.962983 | + | 0.269563i | \(0.913121\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.7846 | 2.01903 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.19615 | −0.220032 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.7654i | 1.44398i | 0.691902 | + | 0.721992i | \(0.256773\pi\) | ||||
−0.691902 | + | 0.721992i | \(0.743227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 49.1769i | − 1.73975i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.8564 | 0.700717 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.1962 | 0.711821 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 5.41154i | − 0.190260i | −0.995465 | − | 0.0951299i | \(-0.969673\pi\) | ||||
0.995465 | − | 0.0951299i | \(-0.0303266\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0718i | 0.599472i | 0.954022 | + | 0.299736i | \(0.0968986\pi\) | ||||
−0.954022 | + | 0.299736i | \(0.903101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.3923 | 0.364027 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.62693 | −0.0919048 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.3923i | 0.362694i | 0.983419 | + | 0.181347i | \(0.0580457\pi\) | ||||
−0.983419 | + | 0.181347i | \(0.941954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3.80385i | − 0.132594i | −0.997800 | − | 0.0662969i | \(-0.978882\pi\) | ||||
0.997800 | − | 0.0662969i | \(-0.0211184\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.7321 | −1.10343 | −0.551716 | − | 0.834032i | \(-0.686027\pi\) | ||||
−0.551716 | + | 0.834032i | \(0.686027\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.1769 | 1.01336 | 0.506678 | − | 0.862135i | \(-0.330873\pi\) | ||||
0.506678 | + | 0.862135i | \(0.330873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 79.9808i | − 2.77117i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 14.6603i | − 0.507339i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.9282 | 0.653474 | 0.326737 | − | 0.945115i | \(-0.394051\pi\) | ||||
0.326737 | + | 0.945115i | \(0.394051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −38.1769 | −1.31645 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.3923i | 0.873522i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 53.9090i | − 1.85233i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.53590 | 0.292607 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.784610 | −0.0268645 | −0.0134323 | − | 0.999910i | \(-0.504276\pi\) | ||||
−0.0134323 | + | 0.999910i | \(0.504276\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.8038i | 0.437371i | 0.975795 | + | 0.218686i | \(0.0701769\pi\) | ||||
−0.975795 | + | 0.218686i | \(0.929823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.24871i | − 0.110845i | −0.998463 | − | 0.0554223i | \(-0.982349\pi\) | ||||
0.998463 | − | 0.0554223i | \(-0.0176505\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.1962 | −1.40233 | −0.701167 | − | 0.712997i | \(-0.747337\pi\) | ||||
−0.701167 | + | 0.712997i | \(0.747337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.1962 | 0.584687 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.9808i | 1.59371i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 64.3923i | − 2.18185i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.73205 | −0.159973 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.41154 | 0.250270 | 0.125135 | − | 0.992140i | \(-0.460064\pi\) | ||||
0.125135 | + | 0.992140i | \(0.460064\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.4115i | 0.384465i | 0.981349 | + | 0.192232i | \(0.0615727\pi\) | ||||
−0.981349 | + | 0.192232i | \(0.938427\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 4.73205i | − 0.159246i | −0.996825 | − | 0.0796231i | \(-0.974628\pi\) | ||||
0.996825 | − | 0.0796231i | \(-0.0253717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.5167 | −1.15896 | −0.579478 | − | 0.814988i | \(-0.696744\pi\) | ||||
−0.579478 | + | 0.814988i | \(0.696744\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 85.1769 | 2.85674 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.39230i | 0.146983i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.85641i | 0.0620528i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.80385 | −0.126865 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.1769 | 1.93815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 15.3923i | − 0.511658i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 18.9282i | − 0.628501i | −0.949340 | − | 0.314250i | \(-0.898247\pi\) | ||||
0.949340 | − | 0.314250i | \(-0.101753\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.51666 | 0.249038 | 0.124519 | − | 0.992217i | \(-0.460261\pi\) | ||||
0.124519 | + | 0.992217i | \(0.460261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.5885 | 0.813759 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.39230i | 0.145047i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 21.7128i | − 0.716240i | −0.933676 | − | 0.358120i | \(-0.883418\pi\) | ||||
0.933676 | − | 0.358120i | \(-0.116582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.3205 | −0.965096 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.80385i | 0.321654i | 0.986983 | + | 0.160827i | \(0.0514161\pi\) | ||||
−0.986983 | + | 0.160827i | \(0.948584\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.14359i | 0.234122i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.5885 | 0.804129 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.1769 | 1.08384 | 0.541921 | − | 0.840429i | \(-0.317697\pi\) | ||||
0.541921 | + | 0.840429i | \(0.317697\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 55.1769i | − 1.79872i | −0.437213 | − | 0.899358i | \(-0.644034\pi\) | ||||
0.437213 | − | 0.899358i | \(-0.355966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 9.37307i | − 0.305229i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7654 | 1.51967 | 0.759835 | − | 0.650116i | \(-0.225280\pi\) | ||||
0.759835 | + | 0.650116i | \(0.225280\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.0000 | −0.843996 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.0000i | 0.582466i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.5885 | −0.794003 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7846 | 0.993052 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.80385i | − 0.0580679i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 29.3205i | − 0.942884i | −0.881897 | − | 0.471442i | \(-0.843734\pi\) | ||||
0.881897 | − | 0.471442i | \(-0.156266\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.3205 | −0.940940 | −0.470470 | − | 0.882416i | \(-0.655916\pi\) | ||||
−0.470470 | + | 0.882416i | \(0.655916\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −93.9615 | −3.01227 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.1769i | 0.997438i | 0.866764 | + | 0.498719i | \(0.166196\pi\) | ||||
−0.866764 | + | 0.498719i | \(0.833804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 67.1769i | 2.14698i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.7321 | 0.437984 | 0.218992 | − | 0.975727i | \(-0.429723\pi\) | ||||
0.218992 | + | 0.975727i | \(0.429723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.1962 | 0.547915 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 24.1577i | − 0.768169i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.0718i | 1.39999i | 0.714149 | + | 0.699993i | \(0.246814\pi\) | ||||
−0.714149 | + | 0.699993i | \(0.753186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3923 | −0.329458 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.1962 | −1.52639 | −0.763194 | − | 0.646170i | \(-0.776370\pi\) | ||||
−0.763194 | + | 0.646170i | \(0.776370\pi\) | |||||||
\(998\) | 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 | 2160.2.h.a.431.3 | yes | 4 | |
3.2 | odd | 2 | 2160.2.h.f.431.1 | yes | 4 | ||
4.3 | odd | 2 | 2160.2.h.f.431.4 | yes | 4 | ||
12.11 | even | 2 | inner | 2160.2.h.a.431.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2160.2.h.a.431.2 | ✓ | 4 | 12.11 | even | 2 | inner | |
2160.2.h.a.431.3 | yes | 4 | 1.1 | even | 1 | trivial | |
2160.2.h.f.431.1 | yes | 4 | 3.2 | odd | 2 | ||
2160.2.h.f.431.4 | yes | 4 | 4.3 | odd | 2 |