Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(1151,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.c (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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.1151 |
Dual form | 1152.2.c.c.1151.4 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | − 3.41421i | − 1.52688i | −0.645877 | − | 0.763441i | \(-0.723508\pi\) | ||||
0.645877 | − | 0.763441i | \(-0.276492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.82843i | − 1.82497i | −0.409106 | − | 0.912487i | \(-0.634159\pi\) | ||||
0.409106 | − | 0.912487i | \(-0.365841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.41421i | − 1.31314i | −0.754265 | − | 0.656570i | \(-0.772007\pi\) | ||||
0.754265 | − | 0.656570i | \(-0.227993\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.65685i | 1.29777i | 0.760886 | + | 0.648886i | \(0.224765\pi\) | ||||
−0.760886 | + | 0.648886i | \(0.775235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.17157 | 0.244290 | 0.122145 | − | 0.992512i | \(-0.461023\pi\) | ||||
0.122145 | + | 0.992512i | \(0.461023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.65685 | −1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.585786i | − 0.108778i | −0.998520 | − | 0.0543889i | \(-0.982679\pi\) | ||||
0.998520 | − | 0.0543889i | \(-0.0173211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.17157i | 0.569631i | 0.958582 | + | 0.284816i | \(0.0919324\pi\) | ||||
−0.958582 | + | 0.284816i | \(0.908068\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.4853 | −2.78652 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.65685 | −0.601183 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 2.58579i | − 0.403832i | −0.979403 | − | 0.201916i | \(-0.935283\pi\) | ||||
0.979403 | − | 0.201916i | \(-0.0647168\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.65685i | 1.47266i | 0.676625 | + | 0.736328i | \(0.263442\pi\) | ||||
−0.676625 | + | 0.736328i | \(0.736558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.4853 | 1.82117 | 0.910583 | − | 0.413327i | \(-0.135633\pi\) | ||||
0.910583 | + | 0.413327i | \(0.135633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.3137 | −2.33053 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.07107i | 0.696565i | 0.937390 | + | 0.348282i | \(0.113235\pi\) | ||||
−0.937390 | + | 0.348282i | \(0.886765\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 9.65685i | − 1.30213i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.34315 | −0.305052 | −0.152526 | − | 0.988299i | \(-0.548741\pi\) | ||||
−0.152526 | + | 0.988299i | \(0.548741\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.65685 | −0.980360 | −0.490180 | − | 0.871621i | \(-0.663069\pi\) | ||||
−0.490180 | + | 0.871621i | \(0.663069\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.65685i | 1.19779i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 12.0000i | − 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48528 | −0.532305 | −0.266152 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266152 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 13.6569i | − 1.55634i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6.48528i | − 0.729651i | −0.931076 | − | 0.364826i | \(-0.881129\pi\) | ||||
0.931076 | − | 0.364826i | \(-0.118871\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.17157 | 0.567654 | 0.283827 | − | 0.958876i | \(-0.408396\pi\) | ||||
0.283827 | + | 0.958876i | \(0.408396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.4853 | −2.00501 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 12.2426i | − 1.29772i | −0.760909 | − | 0.648859i | \(-0.775247\pi\) | ||||
0.760909 | − | 0.648859i | \(-0.224753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.6569i | 1.43163i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.3137 | 1.98154 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6569 | 1.38664 | 0.693322 | − | 0.720628i | \(-0.256146\pi\) | ||||
0.693322 | + | 0.720628i | \(0.256146\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.7279i | − 1.06747i | −0.845652 | − | 0.533734i | \(-0.820788\pi\) | ||||
0.845652 | − | 0.533734i | \(-0.179212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 3.17157i | − 0.312504i | −0.987717 | − | 0.156252i | \(-0.950059\pi\) | ||||
0.987717 | − | 0.156252i | \(-0.0499413\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3137 | 1.09374 | 0.546869 | − | 0.837218i | \(-0.315820\pi\) | ||||
0.546869 | + | 0.837218i | \(0.315820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8284 | 1.03718 | 0.518588 | − | 0.855024i | \(-0.326458\pi\) | ||||
0.518588 | + | 0.855024i | \(0.326458\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 12.2426i | − 1.15169i | −0.817559 | − | 0.575845i | \(-0.804673\pi\) | ||||
0.817559 | − | 0.575845i | \(-0.195327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.00000i | − 0.373002i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.1421 | −2.39645 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.82843i | − 0.428454i | −0.976784 | − | 0.214227i | \(-0.931277\pi\) | ||||
0.976784 | − | 0.214227i | \(-0.0687232\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.65685 | −0.494242 | −0.247121 | − | 0.968985i | \(-0.579484\pi\) | ||||
−0.247121 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.3137 | 2.36840 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5858i | 0.904405i | 0.891915 | + | 0.452202i | \(0.149362\pi\) | ||||
−0.891915 | + | 0.452202i | \(0.850638\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000i | 1.01783i | 0.860818 | + | 0.508913i | \(0.169953\pi\) | ||||
−0.860818 | + | 0.508913i | \(0.830047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.00000 | −0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.72792i | 0.551173i | 0.961276 | + | 0.275586i | \(0.0888720\pi\) | ||||
−0.961276 | + | 0.275586i | \(0.911128\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.48528i | 0.527765i | 0.964555 | + | 0.263882i | \(0.0850031\pi\) | ||||
−0.964555 | + | 0.263882i | \(0.914997\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8284 | 0.869760 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.343146 | −0.0273860 | −0.0136930 | − | 0.999906i | \(-0.504359\pi\) | ||||
−0.0136930 | + | 0.999906i | \(0.504359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 5.65685i | − 0.445823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.65685i | − 0.129775i | −0.997893 | − | 0.0648874i | \(-0.979331\pi\) | ||||
0.997893 | − | 0.0648874i | \(-0.0206688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.65685 | −0.437741 | −0.218870 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218870 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.5858i | 1.56511i | 0.622582 | + | 0.782554i | \(0.286084\pi\) | ||||
−0.622582 | + | 0.782554i | \(0.713916\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 32.1421i | 2.42972i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.3137 | −1.44357 | −0.721787 | − | 0.692115i | \(-0.756679\pi\) | ||||
−0.721787 | + | 0.692115i | \(0.756679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.14214 | 0.456541 | 0.228271 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228271 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.4853i | 0.917936i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.3137i | − 1.11985i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3431 | −0.748404 | −0.374202 | − | 0.927347i | \(-0.622083\pi\) | ||||
−0.374202 | + | 0.927347i | \(0.622083\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.31371 | 0.382489 | 0.191245 | − | 0.981542i | \(-0.438748\pi\) | ||||
0.191245 | + | 0.981542i | \(0.438748\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 16.3848i | − 1.16737i | −0.811981 | − | 0.583683i | \(-0.801611\pi\) | ||||
0.811981 | − | 0.583683i | \(-0.198389\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.82843i | 0.342278i | 0.985247 | + | 0.171139i | \(0.0547447\pi\) | ||||
−0.985247 | + | 0.171139i | \(0.945255\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.82843 | −0.198517 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.82843 | −0.616604 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000i | 1.10674i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 23.3137i | − 1.60498i | −0.596664 | − | 0.802491i | \(-0.703508\pi\) | ||||
0.596664 | − | 0.802491i | \(-0.296492\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.9706 | 2.24857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.3137 | 1.03956 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.3137i | 1.03011i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.7990i | 1.19191i | 0.803018 | + | 0.595954i | \(0.203226\pi\) | ||||
−0.803018 | + | 0.595954i | \(0.796774\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.8284 | 1.78067 | 0.890333 | − | 0.455311i | \(-0.150472\pi\) | ||||
0.890333 | + | 0.455311i | \(0.150472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.17157 | 0.341747 | 0.170874 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170874 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8995i | 1.17263i | 0.810081 | + | 0.586317i | \(0.199423\pi\) | ||||
−0.810081 | + | 0.586317i | \(0.800577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 42.6274i | − 2.78071i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.9706 | 1.35083 | 0.675416 | − | 0.737437i | \(-0.263964\pi\) | ||||
0.675416 | + | 0.737437i | \(0.263964\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 55.6985i | 3.55845i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 16.0000i | − 1.01806i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.4853 | 1.54550 | 0.772749 | − | 0.634712i | \(-0.218881\pi\) | ||||
0.772749 | + | 0.634712i | \(0.218881\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.31371 | 0.208331 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.89949i | 0.617514i | 0.951141 | + | 0.308757i | \(0.0999129\pi\) | ||||
−0.951141 | + | 0.308757i | \(0.900087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.6569i | 1.09714i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.3431 | −1.13109 | −0.565543 | − | 0.824719i | \(-0.691334\pi\) | ||||
−0.565543 | + | 0.824719i | \(0.691334\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.3137 | 1.06357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 32.3848i | − 1.97453i | −0.159070 | − | 0.987267i | \(-0.550850\pi\) | ||||
0.159070 | − | 0.987267i | \(-0.449150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1.51472i | − 0.0920126i | −0.998941 | − | 0.0460063i | \(-0.985351\pi\) | ||||
0.998941 | − | 0.0460063i | \(-0.0146494\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.8284 | −1.13540 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.1716 | −1.27208 | −0.636038 | − | 0.771658i | \(-0.719428\pi\) | ||||
−0.636038 | + | 0.771658i | \(0.719428\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.10051i | 0.363926i | 0.983305 | + | 0.181963i | \(0.0582450\pi\) | ||||
−0.983305 | + | 0.181963i | \(0.941755\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.31371i | − 0.196980i | −0.995138 | − | 0.0984898i | \(-0.968599\pi\) | ||||
0.995138 | − | 0.0984898i | \(-0.0314012\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.4853 | −0.736983 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3137 | −0.724336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 28.8701i | − 1.68661i | −0.537438 | − | 0.843303i | \(-0.680608\pi\) | ||||
0.537438 | − | 0.843303i | \(-0.319392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000i | 0.465778i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.31371 | −0.191637 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 46.6274 | 2.68756 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.1421i | 1.49689i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.686292i | 0.0391687i | 0.999808 | + | 0.0195844i | \(0.00623429\pi\) | ||||
−0.999808 | + | 0.0195844i | \(0.993766\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6569 | −0.774409 | −0.387205 | − | 0.921994i | \(-0.626559\pi\) | ||||
−0.387205 | + | 0.921994i | \(0.626559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.31371 | 0.526442 | 0.263221 | − | 0.964736i | \(-0.415215\pi\) | ||||
0.263221 | + | 0.964736i | \(0.415215\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.2426i | 0.799946i | 0.916527 | + | 0.399973i | \(0.130981\pi\) | ||||
−0.916527 | + | 0.399973i | \(0.869019\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.65685i | − 0.0927660i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.6274 | 1.70416 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.8284 | 1.04441 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 60.2843i | − 3.32358i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.00000i | − 0.219860i | −0.993939 | − | 0.109930i | \(-0.964937\pi\) | ||||
0.993939 | − | 0.109930i | \(-0.0350627\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −40.9706 | −2.23846 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.3137 | 1.26998 | 0.634989 | − | 0.772521i | \(-0.281004\pi\) | ||||
0.634989 | + | 0.772521i | \(0.281004\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.97056i | 0.485783i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44.9706i | 2.42818i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.4853 | −0.884976 | −0.442488 | − | 0.896774i | \(-0.645904\pi\) | ||||
−0.442488 | + | 0.896774i | \(0.645904\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.6569 | 0.623977 | 0.311989 | − | 0.950086i | \(-0.399005\pi\) | ||||
0.311989 | + | 0.950086i | \(0.399005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 18.8701i | − 1.00435i | −0.864765 | − | 0.502176i | \(-0.832533\pi\) | ||||
0.864765 | − | 0.502176i | \(-0.167467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3137i | 0.812767i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.4853 | 1.08117 | 0.540586 | − | 0.841289i | \(-0.318203\pi\) | ||||
0.540586 | + | 0.841289i | \(0.318203\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | −0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 13.6569i | − 0.714832i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 20.8284i | − 1.08724i | −0.839333 | − | 0.543618i | \(-0.817054\pi\) | ||||
0.839333 | − | 0.543618i | \(-0.182946\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.4853 | 1.27121 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.9706 | 0.775146 | 0.387573 | − | 0.921839i | \(-0.373313\pi\) | ||||
0.387573 | + | 0.921839i | \(0.373313\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.65685i | 0.0853323i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.2843i | 1.04193i | 0.853577 | + | 0.520967i | \(0.174428\pi\) | ||||
−0.853577 | + | 0.520967i | \(0.825572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.6274 | −0.747426 | −0.373713 | − | 0.927544i | \(-0.621916\pi\) | ||||
−0.373713 | + | 0.927544i | \(0.621916\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −46.6274 | −2.37635 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.44365i | 0.123898i | 0.998079 | + | 0.0619490i | \(0.0197316\pi\) | ||||
−0.998079 | + | 0.0619490i | \(0.980268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 6.34315i | − 0.320787i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.1421 | −1.11409 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.9706 | −0.952105 | −0.476053 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476053 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 13.4142i | − 0.669874i | −0.942241 | − | 0.334937i | \(-0.891285\pi\) | ||||
0.942241 | − | 0.334937i | \(-0.108715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.97056i | − 0.446856i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.3431 | −0.512691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.3431 | 0.511436 | 0.255718 | − | 0.966751i | \(-0.417688\pi\) | ||||
0.255718 | + | 0.966751i | \(0.417688\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3137i | 0.556711i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 17.6569i | − 0.866741i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.7990 | 0.576418 | 0.288209 | − | 0.957567i | \(-0.406940\pi\) | ||||
0.288209 | + | 0.957567i | \(0.406940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.51472 | 0.366245 | 0.183122 | − | 0.983090i | \(-0.441380\pi\) | ||||
0.183122 | + | 0.983090i | \(0.441380\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 36.0416i | 1.74828i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.9706i | 1.78913i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.4853 | 1.37209 | 0.686044 | − | 0.727560i | \(-0.259346\pi\) | ||||
0.686044 | + | 0.727560i | \(0.259346\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.6274 | 1.37575 | 0.687873 | − | 0.725831i | \(-0.258545\pi\) | ||||
0.687873 | + | 0.725831i | \(0.258545\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.62742i | 0.317032i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.85786i | 0.375035i | 0.982261 | + | 0.187518i | \(0.0600442\pi\) | ||||
−0.982261 | + | 0.187518i | \(0.939956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.4558 | −0.829352 | −0.414676 | − | 0.909969i | \(-0.636105\pi\) | ||||
−0.414676 | + | 0.909969i | \(0.636105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.7990 | −1.98146 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 15.2721i | − 0.720734i | −0.932811 | − | 0.360367i | \(-0.882651\pi\) | ||||
0.932811 | − | 0.360367i | \(-0.117349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 7.31371i | − 0.344389i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 46.6274 | 2.18593 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.97056 | −0.419625 | −0.209813 | − | 0.977742i | \(-0.567285\pi\) | ||||
−0.209813 | + | 0.977742i | \(0.567285\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.10051i | 0.377278i | 0.982046 | + | 0.188639i | \(0.0604076\pi\) | ||||
−0.982046 | + | 0.188639i | \(0.939592\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 33.7990i | − 1.57077i | −0.619006 | − | 0.785386i | \(-0.712464\pi\) | ||||
0.619006 | − | 0.785386i | \(-0.287536\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.14214 | 0.284224 | 0.142112 | − | 0.989851i | \(-0.454611\pi\) | ||||
0.142112 | + | 0.989851i | \(0.454611\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −57.9411 | −2.67547 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.3137i | 1.25589i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 37.6569i | − 1.72781i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.17157 | 0.419060 | 0.209530 | − | 0.977802i | \(-0.432807\pi\) | ||||
0.209530 | + | 0.977802i | \(0.432807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3431 | 0.471607 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 46.6274i | − 2.11724i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.8284i | 1.30634i | 0.757211 | + | 0.653170i | \(0.226561\pi\) | ||||
−0.757211 | + | 0.653170i | \(0.773439\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.3137 | −1.59369 | −0.796843 | − | 0.604187i | \(-0.793498\pi\) | ||||
−0.796843 | + | 0.604187i | \(0.793498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.17157 | −0.142840 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.6569i | 0.971443i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.62742i | 0.296684i | 0.988936 | + | 0.148342i | \(0.0473936\pi\) | ||||
−0.988936 | + | 0.148342i | \(0.952606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.7990 | 0.704442 | 0.352221 | − | 0.935917i | \(-0.385427\pi\) | ||||
0.352221 | + | 0.935917i | \(0.385427\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.6274 | −1.62990 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 13.2721i | − 0.588275i | −0.955763 | − | 0.294137i | \(-0.904968\pi\) | ||||
0.955763 | − | 0.294137i | \(-0.0950323\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 19.3137i | − 0.854388i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.8284 | −0.477158 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.3137 | 1.55310 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 3.07107i | − 0.134546i | −0.997735 | − | 0.0672730i | \(-0.978570\pi\) | ||||
0.997735 | − | 0.0672730i | \(-0.0214298\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 45.6569i | − 1.99643i | −0.0596823 | − | 0.998217i | \(-0.519009\pi\) | ||||
0.0596823 | − | 0.998217i | \(-0.480991\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.1716 | 0.748005 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6274 | −0.940322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.31371i | 0.316792i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 38.6274i | − 1.67001i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −46.1421 | −1.98748 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.7990 | −1.53912 | −0.769559 | − | 0.638575i | \(-0.779524\pi\) | ||||
−0.769559 | + | 0.638575i | \(0.779524\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 36.9706i | − 1.58364i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.65685i | 0.412897i | 0.978457 | + | 0.206449i | \(0.0661906\pi\) | ||||
−0.978457 | + | 0.206449i | \(0.933809\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.31371 | 0.141169 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.3137 | −1.33159 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.07107i | 0.384353i | 0.981360 | + | 0.192177i | \(0.0615547\pi\) | ||||
−0.981360 | + | 0.192177i | \(0.938445\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 27.3137i | − 1.15525i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.4558 | 1.07284 | 0.536418 | − | 0.843952i | \(-0.319777\pi\) | ||||
0.536418 | + | 0.843952i | \(0.319777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.7990 | −1.75850 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 2.10051i | − 0.0880578i | −0.999030 | − | 0.0440289i | \(-0.985981\pi\) | ||||
0.999030 | − | 0.0440289i | \(-0.0140194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0000i | 1.00437i | 0.864761 | + | 0.502184i | \(0.167470\pi\) | ||||
−0.864761 | + | 0.502184i | \(0.832530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.79899 | −0.325240 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.3137 | −1.22035 | −0.610173 | − | 0.792268i | \(-0.708900\pi\) | ||||
−0.610173 | + | 0.792268i | \(0.708900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 24.9706i | − 1.03595i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.3431i | 0.594032i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.6569 | 1.22407 | 0.612035 | − | 0.790831i | \(-0.290351\pi\) | ||||
0.612035 | + | 0.790831i | \(0.290351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.9411 | −0.739251 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 15.0711i | − 0.618895i | −0.950917 | − | 0.309447i | \(-0.899856\pi\) | ||||
0.950917 | − | 0.309447i | \(-0.100144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 89.2548i | 3.65909i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.4853 | 1.81762 | 0.908810 | − | 0.417211i | \(-0.136992\pi\) | ||||
0.908810 | + | 0.417211i | \(0.136992\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.3137 | 0.869404 | 0.434702 | − | 0.900574i | \(-0.356854\pi\) | ||||
0.434702 | + | 0.900574i | \(0.356854\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.2426i | 0.416423i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1716i | 0.778150i | 0.921206 | + | 0.389075i | \(0.127205\pi\) | ||||
−0.921206 | + | 0.389075i | \(0.872795\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.3137 | −1.42864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.6569 | 0.470816 | 0.235408 | − | 0.971897i | \(-0.424357\pi\) | ||||
0.235408 | + | 0.971897i | \(0.424357\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 30.5858i | − 1.23134i | −0.788005 | − | 0.615669i | \(-0.788886\pi\) | ||||
0.788005 | − | 0.615669i | \(-0.211114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.9411i | 1.36421i | 0.731255 | + | 0.682105i | \(0.238935\pi\) | ||||
−0.731255 | + | 0.682105i | \(0.761065\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −59.1127 | −2.36830 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.7990i | 0.789437i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.51472i | 0.0603000i | 0.999545 | + | 0.0301500i | \(0.00959850\pi\) | ||||
−0.999545 | + | 0.0301500i | \(0.990402\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.4853 | −0.654198 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.1421 | 1.82822 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.8701i | 1.53527i | 0.640884 | + | 0.767637i | \(0.278568\pi\) | ||||
−0.640884 | + | 0.767637i | \(0.721432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.65685i | − 0.0653400i | −0.999466 | − | 0.0326700i | \(-0.989599\pi\) | ||||
0.999466 | − | 0.0326700i | \(-0.0104010\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.7990 | −0.935635 | −0.467817 | − | 0.883825i | \(-0.654960\pi\) | ||||
−0.467817 | + | 0.883825i | \(0.654960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.62742 | −0.260149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 30.7279i | − 1.20248i | −0.799070 | − | 0.601238i | \(-0.794674\pi\) | ||||
0.799070 | − | 0.601238i | \(-0.205326\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.3137i | 0.754649i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.9706 | 0.972715 | 0.486358 | − | 0.873760i | \(-0.338325\pi\) | ||||
0.486358 | + | 0.873760i | \(0.338325\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.65685 | 0.297817 | 0.148909 | − | 0.988851i | \(-0.452424\pi\) | ||||
0.148909 | + | 0.988851i | \(0.452424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 93.2548i | − 3.61627i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 0.686292i | − 0.0265733i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.6569 | −0.836054 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0000 | 0.693849 | 0.346925 | − | 0.937893i | \(-0.387226\pi\) | ||||
0.346925 | + | 0.937893i | \(0.387226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 6.72792i | − 0.258575i | −0.991607 | − | 0.129288i | \(-0.958731\pi\) | ||||
0.991607 | − | 0.129288i | \(-0.0412690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 65.9411i | − 2.53059i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.14214 | −0.235022 | −0.117511 | − | 0.993072i | \(-0.537492\pi\) | ||||
−0.117511 | + | 0.993072i | \(0.537492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.1421 | 1.38092 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 14.3431i | − 0.546430i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.9706i | 1.40643i | 0.710979 | + | 0.703213i | \(0.248252\pi\) | ||||
−0.710979 | + | 0.703213i | \(0.751748\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40.9706 | 1.55410 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0000 | −0.530288 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 22.2426i | − 0.840093i | −0.907503 | − | 0.420046i | \(-0.862014\pi\) | ||||
0.907503 | − | 0.420046i | \(-0.137986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 20.6863i | − 0.780198i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −51.7990 | −1.94810 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.0833 | −1.80580 | −0.902902 | − | 0.429846i | \(-0.858568\pi\) | ||||
−0.902902 | + | 0.429846i | \(0.858568\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.71573i | 0.139155i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.3137i | 1.02147i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5147 | 0.429427 | 0.214713 | − | 0.976677i | \(-0.431118\pi\) | ||||
0.214713 | + | 0.976677i | \(0.431118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.3137 | −0.570312 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.89949i | 0.144824i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 3.17157i | − 0.117627i | −0.998269 | − | 0.0588136i | \(-0.981268\pi\) | ||||
0.998269 | − | 0.0588136i | \(-0.0187317\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 52.2843 | 1.93380 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.51472 | −0.277562 | −0.138781 | − | 0.990323i | \(-0.544318\pi\) | ||||
−0.138781 | + | 0.990323i | \(0.544318\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 33.9411i | − 1.25024i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 8.00000i | − 0.294285i | −0.989115 | − | 0.147142i | \(-0.952992\pi\) | ||||
0.989115 | − | 0.147142i | \(-0.0470076\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9706 | 0.622590 | 0.311295 | − | 0.950313i | \(-0.399237\pi\) | ||||
0.311295 | + | 0.950313i | \(0.399237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.9706 | 0.841576 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 54.6274i | − 1.99604i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.1716i | 1.28343i | 0.766944 | + | 0.641714i | \(0.221777\pi\) | ||||
−0.766944 | + | 0.641714i | \(0.778223\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.1421 | 0.805835 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.4853 | 0.599168 | 0.299584 | − | 0.954070i | \(-0.403152\pi\) | ||||
0.299584 | + | 0.954070i | \(0.403152\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.6985i | 1.22157i | 0.791797 | + | 0.610785i | \(0.209146\pi\) | ||||
−0.791797 | + | 0.610785i | \(0.790854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 52.2843i | − 1.89282i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.62742 | 0.239302 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.31371 | 0.0473735 | 0.0236868 | − | 0.999719i | \(-0.492460\pi\) | ||||
0.0236868 | + | 0.999719i | \(0.492460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.4142i | 0.554411i | 0.960811 | + | 0.277205i | \(0.0894082\pi\) | ||||
−0.960811 | + | 0.277205i | \(0.910592\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 21.1127i | − 0.758391i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.6274 | 0.524082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6863 | −0.453951 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.17157i | 0.0418152i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 37.6569i | − 1.34232i | −0.741312 | − | 0.671161i | \(-0.765796\pi\) | ||||
0.741312 | − | 0.671161i | \(-0.234204\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.1127 | −2.10181 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.6569 | 0.769057 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.07107i | − 0.0379392i | −0.999820 | − | 0.0189696i | \(-0.993961\pi\) | ||||
0.999820 | − | 0.0189696i | \(-0.00603857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 67.5980i | − 2.39144i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.3137 | 0.399252 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.3137 | −0.680719 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.6690i | 1.78143i | 0.454563 | + | 0.890714i | \(0.349795\pi\) | ||||
−0.454563 | + | 0.890714i | \(0.650205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 47.5980i | − 1.67139i | −0.549193 | − | 0.835696i | \(-0.685065\pi\) | ||||
0.549193 | − | 0.835696i | \(-0.314935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.65685 | −0.198151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −54.6274 | −1.91117 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.58579i | 0.299646i | 0.988713 | + | 0.149823i | \(0.0478704\pi\) | ||||
−0.988713 | + | 0.149823i | \(0.952130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.4264i | 1.13031i | 0.824984 | + | 0.565157i | \(0.191184\pi\) | ||||
−0.824984 | + | 0.565157i | \(0.808816\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.9706 | −1.70287 | −0.851437 | − | 0.524457i | \(-0.824268\pi\) | ||||
−0.851437 | + | 0.524457i | \(0.824268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.7990 | −1.52120 | −0.760601 | − | 0.649220i | \(-0.775096\pi\) | ||||
−0.760601 | + | 0.649220i | \(0.775096\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 88.3259i | 3.06031i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.3137i | 0.668378i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.4853 | 0.707230 | 0.353615 | − | 0.935391i | \(-0.384952\pi\) | ||||
0.353615 | + | 0.935391i | \(0.384952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.6569 | 0.988167 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.0711i | 0.587263i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.4853i | 0.497720i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.28427 | −0.146863 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2843 | 0.489084 | 0.244542 | − | 0.969639i | \(-0.421362\pi\) | ||||
0.244542 | + | 0.969639i | \(0.421362\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.10051i | 0.0717519i | 0.999356 | + | 0.0358759i | \(0.0114221\pi\) | ||||
−0.999356 | + | 0.0358759i | \(0.988578\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.65685i | 0.329488i | 0.986336 | + | 0.164744i | \(0.0526797\pi\) | ||||
−0.986336 | + | 0.164744i | \(0.947320\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.9706 | 1.12233 | 0.561166 | − | 0.827704i | \(-0.310353\pi\) | ||||
0.561166 | + | 0.827704i | \(0.310353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 70.2843 | 2.38974 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 18.3431i | − 0.622249i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.9411i | 1.15005i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.3137 | 0.923372 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.9706 | −0.910731 | −0.455366 | − | 0.890305i | \(-0.650491\pi\) | ||||
−0.455366 | + | 0.890305i | \(0.650491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 12.7279i | − 0.428815i | −0.976744 | − | 0.214407i | \(-0.931218\pi\) | ||||
0.976744 | − | 0.214407i | \(-0.0687820\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 16.2843i | − 0.548009i | −0.961728 | − | 0.274005i | \(-0.911652\pi\) | ||||
0.961728 | − | 0.274005i | \(-0.0883484\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.6569 | 0.458552 | 0.229276 | − | 0.973361i | \(-0.426364\pi\) | ||||
0.229276 | + | 0.973361i | \(0.426364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.3137 | −0.781917 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 70.6274i | 2.36346i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 65.9411i | 2.20417i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.85786 | 0.0619632 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.4558 | 0.914687 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 20.9706i | − 0.697085i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.6569i | 0.851922i | 0.904742 | + | 0.425961i | \(0.140064\pi\) | ||||
−0.904742 | + | 0.425961i | \(0.859936\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.5980 | 1.84204 | 0.921022 | − | 0.389511i | \(-0.127356\pi\) | ||||
0.921022 | + | 0.389511i | \(0.127356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6274 | 0.484097 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.3137i | 0.901978i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 27.4558i | − 0.905685i | −0.891591 | − | 0.452842i | \(-0.850410\pi\) | ||||
0.891591 | − | 0.452842i | \(-0.149590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.6863 | 0.417574 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.3431 | 0.800398 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 8.72792i | − 0.286354i | −0.989697 | − | 0.143177i | \(-0.954268\pi\) | ||||
0.989697 | − | 0.143177i | \(-0.0457318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 92.2843i | − 3.02449i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −52.2843 | −1.70988 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.3726 | −0.371526 | −0.185763 | − | 0.982595i | \(-0.559476\pi\) | ||||
−0.185763 | + | 0.982595i | \(0.559476\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.7279i | 1.52329i | 0.647996 | + | 0.761643i | \(0.275607\pi\) | ||||
−0.647996 | + | 0.761643i | \(0.724393\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 3.02944i | − 0.0986521i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.5980 | −1.54673 | −0.773363 | − | 0.633963i | \(-0.781427\pi\) | ||||
−0.773363 | + | 0.633963i | \(0.781427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.3137 | −0.367259 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.5563i | 1.15178i | 0.817526 | + | 0.575892i | \(0.195345\pi\) | ||||
−0.817526 | + | 0.575892i | \(0.804655\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.3137i | 1.14272i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51.1127 | 1.65052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.9411 | 0.675520 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 18.1421i | − 0.584016i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0833i | 1.61057i | 0.592889 | + | 0.805285i | \(0.297987\pi\) | ||||
−0.592889 | + | 0.805285i | \(0.702013\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.8284 | −0.860965 | −0.430483 | − | 0.902599i | \(-0.641657\pi\) | ||||
−0.430483 | + | 0.902599i | \(0.641657\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.9411 | 1.85751 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 52.5269i | − 1.68048i | −0.542211 | − | 0.840242i | \(-0.682413\pi\) | ||||
0.542211 | − | 0.840242i | \(-0.317587\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 34.6274i | − 1.10670i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.6569 | −1.45623 | −0.728114 | − | 0.685456i | \(-0.759603\pi\) | ||||
−0.728114 | + | 0.685456i | \(0.759603\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −55.9411 | −1.78243 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3137i | 0.359755i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.7990i | 0.819532i | 0.912191 | + | 0.409766i | \(0.134390\pi\) | ||||
−0.912191 | + | 0.409766i | \(0.865610\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.4853 | 0.522619 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61.5980 | 1.95083 | 0.975414 | − | 0.220381i | \(-0.0707302\pi\) | ||||
0.975414 | + | 0.220381i | \(0.0707302\pi\) | |||||||
\(998\) | 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 | 1152.2.c.c.1151.1 | yes | 4 | |
3.2 | odd | 2 | 1152.2.c.b.1151.4 | yes | 4 | ||
4.3 | odd | 2 | 1152.2.c.b.1151.1 | yes | 4 | ||
8.3 | odd | 2 | 1152.2.c.a.1151.4 | yes | 4 | ||
8.5 | even | 2 | 1152.2.c.d.1151.4 | yes | 4 | ||
12.11 | even | 2 | inner | 1152.2.c.c.1151.4 | yes | 4 | |
16.3 | odd | 4 | 2304.2.f.b.1151.1 | 4 | |||
16.5 | even | 4 | 2304.2.f.g.1151.4 | 4 | |||
16.11 | odd | 4 | 2304.2.f.h.1151.3 | 4 | |||
16.13 | even | 4 | 2304.2.f.a.1151.2 | 4 | |||
24.5 | odd | 2 | 1152.2.c.a.1151.1 | ✓ | 4 | ||
24.11 | even | 2 | 1152.2.c.d.1151.1 | yes | 4 | ||
48.5 | odd | 4 | 2304.2.f.b.1151.2 | 4 | |||
48.11 | even | 4 | 2304.2.f.a.1151.1 | 4 | |||
48.29 | odd | 4 | 2304.2.f.h.1151.4 | 4 | |||
48.35 | even | 4 | 2304.2.f.g.1151.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.c.a.1151.1 | ✓ | 4 | 24.5 | odd | 2 | ||
1152.2.c.a.1151.4 | yes | 4 | 8.3 | odd | 2 | ||
1152.2.c.b.1151.1 | yes | 4 | 4.3 | odd | 2 | ||
1152.2.c.b.1151.4 | yes | 4 | 3.2 | odd | 2 | ||
1152.2.c.c.1151.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1152.2.c.c.1151.4 | yes | 4 | 12.11 | even | 2 | inner | |
1152.2.c.d.1151.1 | yes | 4 | 24.11 | even | 2 | ||
1152.2.c.d.1151.4 | yes | 4 | 8.5 | even | 2 | ||
2304.2.f.a.1151.1 | 4 | 48.11 | even | 4 | |||
2304.2.f.a.1151.2 | 4 | 16.13 | even | 4 | |||
2304.2.f.b.1151.1 | 4 | 16.3 | odd | 4 | |||
2304.2.f.b.1151.2 | 4 | 48.5 | odd | 4 | |||
2304.2.f.g.1151.3 | 4 | 48.35 | even | 4 | |||
2304.2.f.g.1151.4 | 4 | 16.5 | even | 4 | |||
2304.2.f.h.1151.3 | 4 | 16.11 | odd | 4 | |||
2304.2.f.h.1151.4 | 4 | 48.29 | odd | 4 |