Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(719,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.719");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bq (of order \(6\), degree \(2\), not 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: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 719.9 | ||
Character | \(\chi\) | \(=\) | 1120.719 |
Dual form | 1120.2.bq.b.1039.9 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −0.929162 | − | 1.60936i | −0.536452 | − | 0.929162i | −0.999092 | − | 0.0426153i | \(-0.986431\pi\) |
0.462640 | − | 0.886546i | \(-0.346902\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.698124 | − | 2.12429i | −0.312211 | − | 0.950013i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.10610 | − | 2.40345i | 0.418066 | − | 0.908417i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.226682 | + | 0.392626i | −0.0755608 | + | 0.130875i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61069 | − | 2.78980i | −0.485642 | − | 0.841157i | 0.514222 | − | 0.857657i | \(-0.328081\pi\) |
−0.999864 | + | 0.0165005i | \(0.994747\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.668981i | − | 0.185542i | −0.995687 | − | 0.0927710i | \(-0.970428\pi\) | ||
0.995687 | − | 0.0927710i | \(-0.0295724\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.77007 | + | 3.09734i | −0.715230 | + | 0.799730i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.62295 | − | 2.81103i | −0.393624 | − | 0.681776i | 0.599301 | − | 0.800524i | \(-0.295445\pi\) |
−0.992924 | + | 0.118748i | \(0.962112\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.77054 | + | 3.33162i | 1.32385 | + | 0.764326i | 0.984341 | − | 0.176276i | \(-0.0564052\pi\) |
0.339511 | + | 0.940602i | \(0.389738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.89574 | + | 0.453085i | −1.06834 | + | 0.0988712i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.41240 | − | 7.64251i | 0.920050 | − | 1.59357i | 0.120715 | − | 0.992687i | \(-0.461481\pi\) |
0.799335 | − | 0.600886i | \(-0.205185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.02524 | + | 2.96604i | −0.805049 | + | 0.593208i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.73247 | −0.910764 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.17360i | − | 0.589322i | −0.955602 | − | 0.294661i | \(-0.904793\pi\) | ||
0.955602 | − | 0.294661i | \(-0.0952068\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.58684 | + | 4.48053i | 0.464609 | + | 0.804727i | 0.999184 | − | 0.0403943i | \(-0.0128614\pi\) |
−0.534574 | + | 0.845121i | \(0.679528\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.99319 | + | 5.18435i | −0.521047 | + | 0.902480i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.87782 | − | 0.671772i | −0.993532 | − | 0.113550i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.15890 | − | 2.00727i | 0.190522 | − | 0.329994i | −0.754901 | − | 0.655838i | \(-0.772315\pi\) |
0.945423 | + | 0.325845i | \(0.105649\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.07663 | + | 0.621591i | −0.172398 | + | 0.0995343i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.34903i | 1.46007i | 0.683408 | + | 0.730036i | \(0.260497\pi\) | ||||
−0.683408 | + | 0.730036i | \(0.739503\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.84531i | 1.04390i | 0.852976 | + | 0.521950i | \(0.174795\pi\) | ||||
−0.852976 | + | 0.521950i | \(0.825205\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.992304 | + | 0.207439i | 0.147924 | + | 0.0309231i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.12812 | + | 1.80602i | 0.456284 | + | 0.263436i | 0.710480 | − | 0.703717i | \(-0.248478\pi\) |
−0.254197 | + | 0.967153i | \(0.581811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.55310 | − | 5.31689i | −0.650442 | − | 0.759556i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.01597 | + | 5.22381i | −0.422320 | + | 0.731480i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.0130049 | − | 0.0225252i | −0.00178637 | − | 0.00309408i | 0.865131 | − | 0.501546i | \(-0.167235\pi\) |
−0.866917 | + | 0.498452i | \(0.833902\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.80189 | + | 5.36921i | −0.647487 | + | 0.723984i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.3825i | − | 1.64010i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0160236 | + | 0.00925120i | −0.00208609 | + | 0.00120440i | −0.501043 | − | 0.865423i | \(-0.667050\pi\) |
0.498957 | + | 0.866627i | \(0.333717\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.897835 | − | 1.55510i | 0.114956 | − | 0.199110i | −0.802806 | − | 0.596240i | \(-0.796661\pi\) |
0.917762 | + | 0.397130i | \(0.129994\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.692921 | + | 0.979101i | 0.0872998 | + | 0.123355i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.42111 | + | 0.467032i | −0.176267 | + | 0.0579282i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.14522 | + | 2.39324i | −0.506419 | + | 0.292381i | −0.731360 | − | 0.681991i | \(-0.761114\pi\) |
0.224942 | + | 0.974372i | \(0.427781\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.3993 | −1.97425 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.13591i | − | 0.965555i | −0.875743 | − | 0.482778i | \(-0.839628\pi\) | ||
0.875743 | − | 0.482778i | \(-0.160372\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.30342 | + | 10.9178i | 0.737760 | + | 1.27784i | 0.953502 | + | 0.301387i | \(0.0974495\pi\) |
−0.215742 | + | 0.976450i | \(0.569217\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.51352 | + | 3.72212i | 0.983056 | + | 0.429793i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.48672 | + | 0.785418i | −0.967151 | + | 0.0895067i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5306 | − | 7.81192i | −1.52232 | − | 0.878910i | −0.999652 | − | 0.0263718i | \(-0.991605\pi\) |
−0.522665 | − | 0.852538i | \(-0.675062\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.07728 | + | 8.79410i | 0.564142 | + | 0.977123i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.60312 | −0.724787 | −0.362393 | − | 0.932025i | \(-0.618040\pi\) | ||||
−0.362393 | + | 0.932025i | \(0.618040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.83844 | + | 5.41008i | −0.524802 | + | 0.586805i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.10745 | + | 2.94879i | −0.547576 | + | 0.316143i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.31681 | − | 0.760263i | −0.139582 | − | 0.0805877i | 0.428583 | − | 0.903503i | \(-0.359013\pi\) |
−0.568165 | + | 0.822915i | \(0.692346\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.60786 | − | 0.739958i | −0.168549 | − | 0.0775687i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.80718 | − | 8.32628i | 0.498481 | − | 0.863395i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.04879 | − | 14.5842i | 0.312799 | − | 1.49631i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.1700 | −1.23568 | −0.617839 | − | 0.786305i | \(-0.711992\pi\) | ||||
−0.617839 | + | 0.786305i | \(0.711992\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.46046 | 0.146782 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.06658 | + | 12.2397i | 0.703151 | + | 1.21789i | 0.967355 | + | 0.253426i | \(0.0815574\pi\) |
−0.264204 | + | 0.964467i | \(0.585109\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.433570 | + | 0.250322i | 0.0427209 | + | 0.0246649i | 0.521208 | − | 0.853429i | \(-0.325481\pi\) |
−0.478487 | + | 0.878094i | \(0.658815\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.38032 | + | 10.0837i | 0.427476 | + | 0.984066i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0652 | + | 9.27527i | 1.55309 | + | 0.896674i | 0.997888 | + | 0.0649558i | \(0.0206907\pi\) |
0.555197 | + | 0.831719i | \(0.312643\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.92950 | − | 2.26870i | 0.376378 | − | 0.217302i | −0.299863 | − | 0.953982i | \(-0.596941\pi\) |
0.676241 | + | 0.736680i | \(0.263608\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.30722 | −0.408823 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.94668i | − | 0.653489i | −0.945113 | − | 0.326744i | \(-0.894048\pi\) | ||
0.945113 | − | 0.326744i | \(-0.105952\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.3153 | − | 4.03782i | −1.80116 | − | 0.376529i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.262659 | + | 0.151646i | 0.0242828 | + | 0.0140197i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.55131 | + | 0.791396i | −0.783897 | + | 0.0725471i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.311339 | − | 0.539255i | 0.0283036 | − | 0.0490232i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.0459 | − | 8.68675i | 1.35664 | − | 0.783258i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.11086 | + | 6.48013i | 0.814901 | + | 0.579601i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.54642 | −0.492166 | −0.246083 | − | 0.969249i | \(-0.579144\pi\) | ||||
−0.246083 | + | 0.969249i | \(0.579144\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.0165 | − | 6.36040i | 0.969951 | − | 0.560002i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.39758 | − | 0.806895i | −0.122107 | − | 0.0704987i | 0.437702 | − | 0.899120i | \(-0.355792\pi\) |
−0.559810 | + | 0.828621i | \(0.689126\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.3901 | − | 10.1841i | 1.24778 | − | 0.883071i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.30385 | + | 10.0532i | 0.284350 | + | 0.865238i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.25548 | − | 4.18895i | 0.619877 | − | 0.357886i | −0.156944 | − | 0.987607i | \(-0.550164\pi\) |
0.776821 | + | 0.629721i | \(0.216831\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.1284i | − | 0.859077i | −0.903048 | − | 0.429539i | \(-0.858676\pi\) | ||
0.903048 | − | 0.429539i | \(-0.141324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 6.71235i | − | 0.565282i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.86632 | + | 1.07752i | −0.156070 | + | 0.0901070i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.74165 | + | 2.21557i | −0.559864 | + | 0.183993i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.32620 | + | 12.2678i | −0.356819 | + | 1.01183i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.14985 | − | 1.24122i | −0.176123 | − | 0.101684i | 0.409347 | − | 0.912379i | \(-0.365757\pi\) |
−0.585470 | + | 0.810694i | \(0.699090\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.38942 | − | 1.37954i | 0.194449 | − | 0.112265i | −0.399615 | − | 0.916683i | \(-0.630856\pi\) |
0.594063 | + | 0.804418i | \(0.297523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.47158 | 0.118970 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.71203 | − | 8.62317i | 0.619445 | − | 0.692629i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.55831 | − | 2.63174i | 0.363793 | − | 0.210036i | −0.306951 | − | 0.951725i | \(-0.599309\pi\) |
0.670743 | + | 0.741690i | \(0.265975\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0241674 | + | 0.0418591i | −0.00191660 | + | 0.00331964i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.4878 | − | 19.0583i | −1.06299 | − | 1.50201i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.72563 | + | 2.15099i | 0.291814 | + | 0.168479i | 0.638760 | − | 0.769406i | \(-0.279448\pi\) |
−0.346946 | + | 0.937885i | \(0.612781\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.1027 | + | 2.73909i | 1.02004 | + | 0.213237i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.88102i | − | 0.300322i | −0.988662 | − | 0.150161i | \(-0.952021\pi\) | ||
0.988662 | − | 0.150161i | \(-0.0479792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5525 | 0.965574 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.61616 | + | 1.51044i | −0.200063 | + | 0.115506i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.3964 | + | 8.31178i | 1.09454 | + | 0.631933i | 0.934781 | − | 0.355223i | \(-0.115595\pi\) |
0.159758 | + | 0.987156i | \(0.448929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.67640 | + | 12.9552i | 0.202317 | + | 0.979320i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0297769 | + | 0.0171917i | 0.00223817 | + | 0.00129221i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.95928 | − | 13.7859i | −0.594905 | − | 1.03040i | −0.993560 | − | 0.113304i | \(-0.963856\pi\) |
0.398656 | − | 0.917101i | \(-0.369477\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.50289 | 0.557685 | 0.278843 | − | 0.960337i | \(-0.410049\pi\) | ||||
0.278843 | + | 0.960337i | \(0.410049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.33693 | −0.246673 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.07309 | − | 1.06052i | −0.372981 | − | 0.0779708i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.22815 | + | 9.05542i | −0.382320 | + | 0.662198i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.23458 | + | 11.3742i | −0.380759 | + | 0.827354i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.2310 | + | 7.06156i | 0.885002 | + | 0.510956i | 0.872304 | − | 0.488963i | \(-0.162625\pi\) |
0.0126977 | + | 0.999919i | \(0.495958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.10077 | + | 4.09963i | −0.511124 | + | 0.295098i | −0.733296 | − | 0.679910i | \(-0.762019\pi\) |
0.222171 | + | 0.975008i | \(0.428686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.07206 | + | 1.85313i | 0.148383 | + | 0.132705i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.63166 | −0.472486 | −0.236243 | − | 0.971694i | \(-0.575916\pi\) | ||||
−0.236243 | + | 0.971694i | \(0.575916\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.78141 | + | 3.08549i | 0.126281 | + | 0.218725i | 0.922233 | − | 0.386635i | \(-0.126363\pi\) |
−0.795952 | + | 0.605360i | \(0.793029\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.70315 | + | 4.44742i | 0.543338 | + | 0.313697i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.62757 | − | 3.51031i | −0.535350 | − | 0.246375i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.8601 | − | 6.52678i | 1.38709 | − | 0.455850i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00043 | + | 3.46485i | 0.139039 | + | 0.240823i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 21.4649i | − | 1.48476i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5590 | 0.933438 | 0.466719 | − | 0.884406i | \(-0.345436\pi\) | ||||
0.466719 | + | 0.884406i | \(0.345436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.0936 | + | 7.55958i | −0.897157 | + | 0.517974i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.5414 | − | 4.77888i | 0.991718 | − | 0.325917i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.6300 | − | 1.26141i | 0.925265 | − | 0.0856303i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.7138 | − | 20.2889i | 0.791545 | − | 1.37100i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.88053 | + | 1.08572i | −0.126498 | + | 0.0730337i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5244i | 1.17352i | 0.809760 | + | 0.586761i | \(0.199597\pi\) | ||||
−0.809760 | + | 0.586761i | \(0.800403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.252091 | − | 2.25276i | −0.0168061 | − | 0.150184i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.47563 | − | 9.48408i | −0.363431 | − | 0.629480i | 0.625092 | − | 0.780551i | \(-0.285061\pi\) |
−0.988523 | + | 0.151071i | \(0.951728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.35182 | − | 16.1978i | 0.617985 | − | 1.07038i | −0.371867 | − | 0.928286i | \(-0.621282\pi\) |
0.989853 | − | 0.142096i | \(-0.0453842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.14955 | + | 12.9284i | 0.601996 | + | 0.850624i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.70368 | + | 2.13832i | 0.242636 | + | 0.140086i | 0.616388 | − | 0.787443i | \(-0.288595\pi\) |
−0.373752 | + | 0.927529i | \(0.621929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.65270 | − | 7.90588i | 0.107811 | − | 0.515723i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 29.0342i | 1.88597i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.1064i | − | 1.62400i | −0.583658 | − | 0.812000i | \(-0.698379\pi\) | ||
0.583658 | − | 0.812000i | \(-0.301621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.69808 | − | 0.980389i | 0.109383 | − | 0.0631524i | −0.444310 | − | 0.895873i | \(-0.646551\pi\) |
0.553694 | + | 0.832721i | \(0.313218\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.33652 | − | 4.04696i | 0.149888 | − | 0.259613i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.11601 | + | 13.3840i | −0.518513 | + | 0.855070i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.22879 | − | 3.86038i | 0.141815 | − | 0.245630i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.13537 | + | 10.6268i | 0.388813 | + | 0.673444i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 10.2716i | − | 0.648336i | −0.945999 | − | 0.324168i | \(-0.894916\pi\) | ||
0.945999 | − | 0.324168i | \(-0.105084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.4281 | −1.78726 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.2024 | + | 2.75993i | 0.826768 | + | 0.172834i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.42809 | − | 7.66968i | 0.276217 | − | 0.478422i | −0.694225 | − | 0.719759i | \(-0.744253\pi\) |
0.970441 | + | 0.241337i | \(0.0775859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.54252 | − | 5.00559i | −0.220121 | − | 0.311032i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.24604 | + | 0.719399i | 0.0771277 | + | 0.0445297i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.21178 | + | 10.7591i | 0.383035 | + | 0.663436i | 0.991494 | − | 0.130149i | \(-0.0415455\pi\) |
−0.608459 | + | 0.793585i | \(0.708212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0387711 | + | 0.0433517i | −0.00238169 | + | 0.00266307i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.82563i | 0.172926i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.6032 | − | 23.5615i | −0.829403 | − | 1.43657i | −0.898507 | − | 0.438959i | \(-0.855347\pi\) |
0.0691035 | − | 0.997609i | \(-0.477986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.19784 | − | 9.00292i | 0.315746 | − | 0.546889i | −0.663850 | − | 0.747866i | \(-0.731078\pi\) |
0.979596 | + | 0.200978i | \(0.0644118\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.303105 | + | 3.27516i | 0.0183448 | + | 0.198221i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.7581 | + | 6.45225i | 0.889947 | + | 0.389085i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.2142 | − | 17.6915i | −0.613711 | − | 1.06298i | −0.990609 | − | 0.136724i | \(-0.956343\pi\) |
0.376898 | − | 0.926255i | \(-0.376991\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.34556 | −0.140425 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.1658 | −1.85919 | −0.929597 | − | 0.368578i | \(-0.879845\pi\) | ||||
−0.929597 | + | 0.368578i | \(0.879845\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.09232 | + | 12.2843i | 0.421594 | + | 0.730223i | 0.996096 | − | 0.0882807i | \(-0.0281373\pi\) |
−0.574501 | + | 0.818504i | \(0.694804\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −26.3040 | + | 8.64449i | −1.55811 | + | 0.512056i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.4699 | + | 10.3409i | 1.32635 | + | 0.610406i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.23206 | − | 5.59809i | 0.190121 | − | 0.329299i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.3079 | + | 19.5859i | 0.662881 | + | 1.14814i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.3400i | 0.779333i | 0.920956 | + | 0.389666i | \(0.127410\pi\) | ||||
−0.920956 | + | 0.389666i | \(0.872590\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0308387 | + | 0.0275802i | 0.00179550 | + | 0.00160578i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.62256 | + | 13.2027i | 0.442306 | + | 0.766096i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.11269 | − | 2.95181i | −0.295675 | − | 0.170708i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.4523 | + | 7.57158i | 0.948296 | + | 0.436418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.1320 | − | 22.7453i | 0.754413 | − | 1.30668i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.93028 | − | 0.821615i | −0.225047 | − | 0.0470455i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5134 | 0.885395 | 0.442697 | − | 0.896671i | \(-0.354022\pi\) | ||||
0.442697 | + | 0.896671i | \(0.354022\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 0.930357i | − | 0.0529262i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.58870 | + | 7.94786i | 0.260201 | + | 0.450682i | 0.966295 | − | 0.257436i | \(-0.0828778\pi\) |
−0.706094 | + | 0.708118i | \(0.749544\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.2088 | − | 28.0744i | 0.916175 | − | 1.58686i | 0.111002 | − | 0.993820i | \(-0.464594\pi\) |
0.805172 | − | 0.593041i | \(-0.202073\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.59615 | − | 2.15550i | 0.0899330 | − | 0.121449i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.205982 | − | 0.356772i | 0.0115691 | − | 0.0200383i | −0.860183 | − | 0.509986i | \(-0.829651\pi\) |
0.871752 | + | 0.489947i | \(0.162984\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.85371 | + | 5.11169i | −0.495713 | + | 0.286200i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 34.4729i | − | 1.92409i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 21.6282i | − | 1.20343i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.98423 | + | 2.69281i | 0.110065 | + | 0.149370i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.30229 | − | 4.21598i | −0.403817 | − | 0.233144i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.80069 | − | 5.52064i | 0.430066 | − | 0.304363i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.7269 | + | 25.5078i | −0.809465 | + | 1.40203i | 0.103770 | + | 0.994601i | \(0.466909\pi\) |
−0.913235 | + | 0.407433i | \(0.866424\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.525405 | + | 0.910027i | 0.0287920 | + | 0.0498692i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.97783 | + | 7.13488i | 0.435875 | + | 0.389820i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.726788i | − | 0.0395906i | −0.999804 | − | 0.0197953i | \(-0.993699\pi\) | ||
0.999804 | − | 0.0197953i | \(-0.00630146\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.1797 | + | 6.45459i | −0.607197 | + | 0.350565i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.33319 | − | 14.4335i | 0.451268 | − | 0.781619i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8150 | + | 5.06212i | −0.961921 | + | 0.273329i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.4488 | + | 34.8370i | 0.616382 | + | 1.87556i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.4004 | − | 8.31409i | 0.773056 | − | 0.446324i | −0.0609078 | − | 0.998143i | \(-0.519400\pi\) |
0.833964 | + | 0.551819i | \(0.186066\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.3428 | −1.78480 | −0.892401 | − | 0.451244i | \(-0.850980\pi\) | ||||
−0.892401 | + | 0.451244i | \(0.850980\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.16593i | 0.168985i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.25151 | + | 7.36384i | 0.226285 | + | 0.391938i | 0.956704 | − | 0.291062i | \(-0.0940085\pi\) |
−0.730419 | + | 0.682999i | \(0.760675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.2831 | + | 5.67988i | −0.917290 | + | 0.301457i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.21918 | + | 13.0268i | 0.487931 | + | 0.689449i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.2304 | + | 16.2989i | 1.48995 | + | 0.860220i | 0.999934 | − | 0.0114955i | \(-0.00365922\pi\) |
0.490012 | + | 0.871716i | \(0.336993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.6994 | + | 21.9960i | 0.668389 | + | 1.15768i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.15714 | −0.0607340 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.7921 | − | 21.0123i | 0.983625 | − | 1.09984i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.02375 | + | 1.74576i | −0.157838 | + | 0.0911280i | −0.576839 | − | 0.816858i | \(-0.695714\pi\) |
0.419000 | + | 0.907986i | \(0.362381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.67067 | − | 2.11926i | −0.191087 | − | 0.110324i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0685228 | + | 0.00634157i | −0.00355753 | + | 0.000329238i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.1896 | + | 21.1129i | −0.631151 | + | 1.09319i | 0.356165 | + | 0.934423i | \(0.384084\pi\) |
−0.987317 | + | 0.158763i | \(0.949249\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.96337 | − | 20.6837i | 0.101388 | − | 1.06810i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.12308 | −0.109344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.6902 | 1.73055 | 0.865274 | − | 0.501299i | \(-0.167144\pi\) | ||||
0.865274 | + | 0.501299i | \(0.167144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.15352 | + | 8.92617i | 0.264023 | + | 0.457301i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.7966 | − | 7.38811i | −0.653875 | − | 0.377515i | 0.136064 | − | 0.990700i | \(-0.456555\pi\) |
−0.789939 | + | 0.613185i | \(0.789888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.59324 | + | 17.4800i | 0.386987 | + | 0.890861i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.68764 | − | 1.55171i | −0.136621 | − | 0.0788779i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.178263 | − | 0.102920i | 0.00903829 | − | 0.00521826i | −0.495474 | − | 0.868623i | \(-0.665006\pi\) |
0.504512 | + | 0.863404i | \(0.331672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.6445 | −1.44861 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.99894i | 0.151277i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.14874 | + | 34.1968i | −0.359692 | + | 1.72063i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.39175 | − | 2.53558i | −0.220416 | − | 0.127257i | 0.385727 | − | 0.922613i | \(-0.373951\pi\) |
−0.606143 | + | 0.795356i | \(0.707284\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −29.7605 | − | 13.6962i | −1.48989 | − | 0.685668i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.62688 | + | 16.6743i | −0.480744 | + | 0.832672i | −0.999756 | − | 0.0220944i | \(-0.992967\pi\) |
0.519012 | + | 0.854767i | \(0.326300\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.99739 | − | 1.73054i | 0.149311 | − | 0.0862045i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.1367 | − | 16.9250i | 0.752148 | − | 0.841010i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.46653 | −0.370102 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.9967 | + | 10.9678i | −0.939327 | + | 0.542321i | −0.889749 | − | 0.456450i | \(-0.849121\pi\) |
−0.0495776 | + | 0.998770i | \(0.515788\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.4830 | − | 7.78442i | −0.665068 | − | 0.383977i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.00451114 | + | 0.0487445i | 0.000221979 | + | 0.00239856i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.60980 | + | 14.0270i | 0.226286 | + | 0.688557i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.3001 | + | 9.41089i | −0.798222 | + | 0.460853i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 20.3822i | − | 0.995734i | −0.867253 | − | 0.497867i | \(-0.834117\pi\) | ||
0.867253 | − | 0.497867i | \(-0.165883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 21.2887i | − | 1.03755i | −0.854912 | − | 0.518774i | \(-0.826389\pi\) | ||
0.854912 | − | 0.518774i | \(-0.173611\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.41818 | + | 0.818788i | −0.0689544 | + | 0.0398108i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.8704 | + | 6.50136i | 0.721321 | + | 0.315362i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.74449 | − | 3.87798i | −0.132815 | − | 0.187669i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.46823 | + | 2.00239i | 0.167448 | + | 0.0966761i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.7227 | + | 10.8096i | −0.901842 | + | 0.520679i | −0.877797 | − | 0.479032i | \(-0.840988\pi\) |
−0.0240450 | + | 0.999711i | \(0.507654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.8068 | −1.43243 | −0.716213 | − | 0.697882i | \(-0.754126\pi\) | ||||
−0.716213 | + | 0.697882i | \(0.754126\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.82972 | + | 8.79110i | 0.471299 | + | 0.421501i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 50.9239 | − | 29.4009i | 2.43602 | − | 1.40644i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.9755 | + | 25.9383i | −0.714740 | + | 1.23797i | 0.248320 | + | 0.968678i | \(0.420122\pi\) |
−0.963060 | + | 0.269288i | \(0.913212\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.11965 | − | 0.582416i | 0.148555 | − | 0.0277341i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.1133 | − | 18.5406i | −1.52575 | − | 0.880893i | −0.999533 | − | 0.0305429i | \(-0.990276\pi\) |
−0.526218 | − | 0.850350i | \(-0.676390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.695721 | + | 3.32806i | −0.0329803 | + | 0.157765i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.61317i | 0.218195i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.1980 | 0.811625 | 0.405813 | − | 0.913956i | \(-0.366989\pi\) | ||||
0.405813 | + | 0.913956i | \(0.366989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.0819 | − | 15.0584i | 1.22815 | − | 0.709073i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.44032 | − | 2.56362i | −0.208625 | − | 0.120449i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.449403 | + | 3.93215i | −0.0210683 | + | 0.184342i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.54674 | + | 4.93447i | 0.399800 | + | 0.230825i | 0.686398 | − | 0.727226i | \(-0.259191\pi\) |
−0.286598 | + | 0.958051i | \(0.592524\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.68057 | + | 13.3031i | 0.358498 | + | 0.620937i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.0434 | −0.886938 | −0.443469 | − | 0.896290i | \(-0.646252\pi\) | ||||
−0.443469 | + | 0.896290i | \(0.646252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.5965 | −0.724831 | −0.362415 | − | 0.932017i | \(-0.618048\pi\) | ||||
−0.362415 | + | 0.932017i | \(0.618048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21.0435 | − | 4.39908i | −0.975867 | − | 0.204002i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.3528 | − | 19.6636i | 0.525343 | − | 0.909921i | −0.474221 | − | 0.880406i | \(-0.657270\pi\) |
0.999564 | − | 0.0295151i | \(-0.00939632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.16701 | + | 12.6100i | 0.0538876 | + | 0.582274i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.47081 | − | 4.89062i | −0.390314 | − | 0.225348i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.0970 | − | 11.0257i | 0.878083 | − | 0.506961i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.1095 | + | 3.70506i | −1.51917 | + | 0.170000i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.0117920 | 0.000539917 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.2162 | − | 29.8193i | −0.786626 | − | 1.36248i | −0.928023 | − | 0.372523i | \(-0.878493\pi\) |
0.141397 | − | 0.989953i | \(-0.454841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.34283 | − | 0.775282i | −0.0612277 | − | 0.0353498i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.1393 | + | 39.4149i | −0.825366 | + | 1.79344i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.49618 | + | 25.8527i | 0.385792 | + | 1.17391i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.417834 | + | 0.723709i | 0.0189338 | + | 0.0327944i | 0.875337 | − | 0.483513i | \(-0.160639\pi\) |
−0.856403 | + | 0.516308i | \(0.827306\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.99448i | − | 0.361523i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.3101 | −1.27762 | −0.638809 | − | 0.769365i | \(-0.720573\pi\) | ||||
−0.638809 | + | 0.769365i | \(0.720573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.92109 | + | 5.15060i | −0.401786 | + | 0.231971i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.01958 | − | 3.10245i | −0.0458269 | − | 0.139445i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.5542 | − | 8.99911i | −0.877127 | − | 0.403665i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.19914 | + | 3.80903i | −0.0984472 | + | 0.170516i | −0.911042 | − | 0.412313i | \(-0.864721\pi\) |
0.812595 | + | 0.582829i | \(0.198054\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.24594 | + | 3.60609i | −0.279048 | + | 0.161108i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.2435i | 0.947200i | 0.880740 | + | 0.473600i | \(0.157046\pi\) | ||||
−0.880740 | + | 0.473600i | \(0.842954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.0673 | − | 23.5563i | 0.937482 | − | 1.04824i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.6633 | − | 20.2014i | −0.517984 | − | 0.897174i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.64622 | + | 8.04750i | −0.205940 | + | 0.356699i | −0.950432 | − | 0.310933i | \(-0.899359\pi\) |
0.744492 | + | 0.667632i | \(0.232692\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.2126 | − | 3.07372i | 1.46924 | − | 0.135973i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.3089 | − | 15.7668i | −1.20572 | − | 0.696121i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.229071 | − | 1.09579i | 0.0100941 | − | 0.0482861i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.6358i | − | 0.511742i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 30.8919i | − | 1.35601i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.2972 | − | 11.1412i | 0.845425 | − | 0.488106i | −0.0136798 | − | 0.999906i | \(-0.504355\pi\) |
0.859104 | + | 0.511800i | \(0.171021\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.18906 | − | 2.05951i | 0.0519939 | − | 0.0900560i | −0.838857 | − | 0.544352i | \(-0.816776\pi\) |
0.890851 | + | 0.454296i | \(0.150109\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.3627 | − | 16.3447i | 0.801413 | − | 0.713343i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.39662 | − | 14.5434i | 0.365762 | − | 0.633519i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.4386 | − | 47.5251i | −1.19298 | − | 2.06631i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 0.00838834i | − | 0.000364023i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.25432 | 0.270905 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.48786 | − | 40.6026i | 0.366962 | − | 1.75540i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.7909 | + | 25.6186i | −0.638275 | + | 1.10552i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.49943 | + | 21.2661i | −0.323023 | + | 0.915996i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.1918 | + | 10.5031i | 0.782128 | + | 0.451562i | 0.837184 | − | 0.546922i | \(-0.184200\pi\) |
−0.0550562 | + | 0.998483i | \(0.517534\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.97140 | − | 12.0748i | −0.299171 | − | 0.518180i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.56266 | − | 6.76358i | −0.323949 | − | 0.289720i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.9270i | − | 0.638234i | −0.947715 | − | 0.319117i | \(-0.896614\pi\) | ||
0.947715 | − | 0.319117i | \(-0.103386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.407047 | + | 0.705026i | 0.0173723 | + | 0.0300898i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.5732 | − | 18.3134i | 0.450434 | − | 0.780175i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.7417 | + | 23.8794i | −1.43485 | + | 1.01546i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.00698 | + | 9.14980i | 0.127639 | + | 0.388387i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.63827 | − | 2.83757i | −0.0694157 | − | 0.120232i | 0.829229 | − | 0.558910i | \(-0.188780\pi\) |
−0.898644 | + | 0.438678i | \(0.855447\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.57938 | 0.193687 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.4312 | 0.820385 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.29192 | + | 7.43383i | 0.180883 | + | 0.313299i | 0.942181 | − | 0.335103i | \(-0.108771\pi\) |
−0.761298 | + | 0.648402i | \(0.775438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.7568 | + | 4.84965i | −0.620823 | + | 0.204026i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.7521 | − | 2.47582i | 1.12348 | − | 0.103975i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.8908 | + | 22.3275i | −0.540411 | + | 0.936019i | 0.458470 | + | 0.888710i | \(0.348398\pi\) |
−0.998880 | + | 0.0473086i | \(0.984936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.5532 | + | 26.9389i | 0.650881 | + | 1.12736i | 0.982909 | + | 0.184089i | \(0.0589336\pi\) |
−0.332029 | + | 0.943269i | \(0.607733\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 26.2453i | − | 1.09641i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.90699 | + | 43.8503i | 0.204636 | + | 1.82869i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.1101 | + | 17.5112i | 0.420889 | + | 0.729001i | 0.996027 | − | 0.0890553i | \(-0.0283848\pi\) |
−0.575137 | + | 0.818057i | \(0.695051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.1955 | + | 7.61844i | 0.548387 | + | 0.316611i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.30370 | + | 15.8702i | −0.303008 | + | 0.658409i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0418939 | + | 0.0725624i | −0.00173507 | + | 0.00300523i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.138772 | − | 0.663833i | 0.00573753 | − | 0.0274461i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.6836 | −0.894976 | −0.447488 | − | 0.894290i | \(-0.647681\pi\) | ||||
−0.447488 | + | 0.894290i | \(0.647681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.4734i | 1.42045i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.16188 | + | 10.6727i | 0.253466 | + | 0.439016i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.9180 | − | 25.8387i | 0.612609 | − | 1.06107i | −0.378190 | − | 0.925728i | \(-0.623453\pi\) |
0.990799 | − | 0.135342i | \(-0.0432133\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.65103 | + | 17.6130i | 0.313662 | + | 0.722062i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.31044 | − | 5.73384i | 0.135487 | − | 0.234671i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.90813 | − | 3.98841i | 0.282259 | − | 0.162962i | −0.352187 | − | 0.935930i | \(-0.614562\pi\) |
0.634445 | + | 0.772968i | \(0.281229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.8990i | 1.74989i | 0.484224 | + | 0.874944i | \(0.339102\pi\) | ||||
−0.484224 | + | 0.874944i | \(0.660898\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2.17002i | − | 0.0883702i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.36289 | − | 0.284909i | −0.0554094 | − | 0.0115832i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.6567 | − | 14.2355i | −1.00078 | − | 0.577802i | −0.0923032 | − | 0.995731i | \(-0.529423\pi\) |
−0.908480 | + | 0.417929i | \(0.862756\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.43791 | + | 15.5371i | 0.0582670 | + | 0.629596i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.20820 | − | 2.09266i | 0.0488783 | − | 0.0846598i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6922 | − | 23.7156i | −0.553022 | − | 0.957863i | −0.998054 | − | 0.0623483i | \(-0.980141\pi\) |
0.445032 | − | 0.895515i | \(-0.353192\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28.9571 | − | 25.8975i | −1.16766 | − | 1.04429i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.4349i | 1.06423i | 0.846673 | + | 0.532114i | \(0.178602\pi\) | ||||
−0.846673 | + | 0.532114i | \(0.821398\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.44010 | − | 3.71819i | 0.258850 | − | 0.149447i | −0.364960 | − | 0.931023i | \(-0.618917\pi\) |
0.623810 | + | 0.781576i | \(0.285584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.8816 | + | 36.1679i | −0.837949 | + | 1.45137i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.28377 | + | 2.32396i | −0.131562 | + | 0.0931076i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.40519 | − | 23.8781i | 0.296208 | − | 0.955124i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −34.5446 | + | 19.9443i | −1.37958 | + | 0.796500i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.52335 | −0.299976 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 23.0524i | − | 0.917701i | −0.888514 | − | 0.458850i | \(-0.848261\pi\) | ||
0.888514 | − | 0.458850i | \(-0.151739\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.5985 | − | 21.8212i | −0.500744 | − | 0.867315i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.87209 | + | 11.7822i | 0.153659 | + | 0.467564i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.55690 | + | 3.04593i | −0.140929 | + | 0.120684i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.19437 | + | 1.84427i | 0.126367 | + | 0.0729581i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.04336 | + | 7.00330i | 0.159703 | + | 0.276614i | 0.934762 | − | 0.355276i | \(-0.115613\pi\) |
−0.775059 | + | 0.631889i | \(0.782280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.3144 | 0.879995 | 0.439998 | − | 0.897999i | \(-0.354979\pi\) | ||||
0.439998 | + | 0.897999i | \(0.354979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.2023 | − | 18.9620i | −0.834838 | − | 0.746628i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.37529 | − | 0.794021i | 0.0540681 | − | 0.0312162i | −0.472722 | − | 0.881211i | \(-0.656729\pi\) |
0.526790 | + | 0.849995i | \(0.323395\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0516180 | + | 0.0298017i | 0.00202618 | + | 0.00116982i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.6945 | − | 20.7635i | −0.575924 | − | 0.813784i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.2296 | − | 38.5028i | 0.869912 | − | 1.50673i | 0.00782554 | − | 0.999969i | \(-0.497509\pi\) |
0.862086 | − | 0.506762i | \(-0.169158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.738395 | + | 3.53219i | −0.0288515 | + | 0.138014i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.71550 | −0.222983 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.14200 | −0.239259 | −0.119629 | − | 0.992819i | \(-0.538171\pi\) | ||||
−0.119629 | + | 0.992819i | \(0.538171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.19173 | + | 7.26029i | 0.163039 | + | 0.282393i | 0.935957 | − | 0.352114i | \(-0.114537\pi\) |
−0.772918 | + | 0.634506i | \(0.781204\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.49463 | + | 2.01762i | 0.135720 | + | 0.0783581i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −31.6801 | − | 23.4591i | −1.22850 | − | 0.909706i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.2543 | − | 14.0032i | −0.939128 | − | 0.542206i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.2030 | − | 16.2830i | 1.09039 | − | 0.629538i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.78454 | −0.223310 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5.56001i | − | 0.214323i | −0.994242 | − | 0.107161i | \(-0.965824\pi\) | ||
0.994242 | − | 0.107161i | \(-0.0341761\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.0494 | − | 14.0367i | 0.733210 | − | 0.540273i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5074 | − | 7.79851i | −0.519132 | − | 0.299721i | 0.217447 | − | 0.976072i | \(-0.430227\pi\) |
−0.736579 | + | 0.676351i | \(0.763560\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.4612 | + | 29.2500i | −0.516594 | + | 1.12251i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1755 | + | 17.6245i | −0.389926 | + | 0.675371i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.9790 | + | 8.07076i | −0.534890 | + | 0.308819i | −0.743006 | − | 0.669285i | \(-0.766600\pi\) |
0.208115 | + | 0.978104i | \(0.433267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.9638 | − | 12.4883i | −0.533529 | − | 0.477155i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.7574 | −1.32608 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0150689 | + | 0.00870005i | −0.000574081 | + | 0.000331446i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.5750 | − | 7.26020i | −0.478377 | − | 0.276191i | 0.241363 | − | 0.970435i | \(-0.422406\pi\) |
−0.719740 | + | 0.694244i | \(0.755739\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.61541 | − | 3.51014i | 0.0613645 | − | 0.133339i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.5156 | + | 7.07086i | −0.816135 | + | 0.268213i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.2804 | − | 15.1730i | 0.995442 | − | 0.574719i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 7.94737i | − | 0.300597i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 50.0391i | − | 1.88995i | −0.327140 | − | 0.944976i | \(-0.606085\pi\) | ||
0.327140 | − | 0.944976i | \(-0.393915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3749 | − | 7.72203i | 0.504446 | − | 0.291242i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.2590 | + | 4.68606i | −0.537025 | + | 0.176487i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.2337 | − | 3.44586i | 1.40032 | − | 0.129595i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.6072 | − | 14.2069i | −0.924141 | − | 0.533553i | −0.0391872 | − | 0.999232i | \(-0.512477\pi\) |
−0.884954 | + | 0.465679i | \(0.845810\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.13432 | − | 3.54165i | 0.230055 | − | 0.132822i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.6567 | 1.70986 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.59190 | + | 3.21237i | 0.134329 | + | 0.120136i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.4051 | + | 23.3279i | −1.50896 | + | 0.871197i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.99938 | + | 12.1233i | −0.261033 | + | 0.452122i | −0.966517 | − | 0.256604i | \(-0.917396\pi\) |
0.705484 | + | 0.708726i | \(0.250730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.08121 | − | 0.765181i | 0.0402662 | − | 0.0284968i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.15559 | − | 1.82188i | −0.117358 | − | 0.0677564i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.41303 | + | 12.7745i | 0.349591 | + | 0.474433i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27.8172i | − | 1.03168i | −0.856684 | − | 0.515842i | \(-0.827479\pi\) | ||
0.856684 | − | 0.515842i | \(-0.172521\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.7797 | 0.806654 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.2424 | − | 11.1096i | 0.711705 | − | 0.410903i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.1317 | + | 23.1700i | 1.48230 | + | 0.855804i | 0.999798 | − | 0.0200925i | \(-0.00639608\pi\) |
0.482498 | + | 0.875897i | \(0.339729\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.0806 | + | 0.625674i | 1.07266 | + | 0.0230783i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.3533 | + | 7.70955i | 0.491877 | + | 0.283985i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.81690 | + | 8.34311i | 0.177192 | + | 0.306906i | 0.940918 | − | 0.338635i | \(-0.109965\pi\) |
−0.763725 | + | 0.645541i | \(0.776632\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.28362 | −0.304307 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.6002 | 1.19599 | 0.597993 | − | 0.801501i | \(-0.295965\pi\) | ||||
0.597993 | + | 0.801501i | \(0.295965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.13585 | + | 5.43344i | −0.0416142 | + | 0.199066i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.49681 | − | 2.59255i | 0.0547655 | − | 0.0948566i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40.0623 | − | 28.3526i | 1.46385 | − | 1.03598i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.64496 | − | 2.68177i | −0.169497 | − | 0.0978591i | 0.412852 | − | 0.910798i | \(-0.364533\pi\) |
−0.582349 | + | 0.812939i | \(0.697866\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.5306 | + | 9.54396i | −0.602409 | + | 0.347801i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.59865 | − | 4.11275i | −0.167362 | − | 0.149678i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.4301 | 0.524470 | 0.262235 | − | 0.965004i | \(-0.415540\pi\) | ||||
0.262235 | + | 0.965004i | \(0.415540\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.4143 | + | 45.7509i | 0.958778 | + | 1.66065i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.5866 | − | 8.42159i | −0.528765 | − | 0.305283i | 0.211748 | − | 0.977324i | \(-0.432084\pi\) |
−0.740513 | + | 0.672042i | \(0.765418\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.10628 | − | 11.9537i | −0.0400500 | − | 0.432755i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.02734 | − | 3.12606i | −0.0371437 | − | 0.113023i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.00618888 | + | 0.0107195i | 0.000223467 | + | 0.000387057i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.2864i | 1.92156i | 0.277315 | + | 0.960779i | \(0.410555\pi\) | ||||
−0.277315 | + | 0.960779i | \(0.589445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.4577 | −0.592708 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.228998 | − | 0.132212i | 0.00823647 | − | 0.00475533i | −0.495876 | − | 0.868393i | \(-0.665153\pi\) |
0.504113 | + | 0.863638i | \(0.331820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.7021 | − | 10.3626i | −0.851404 | − | 0.372235i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.76421 | + | 10.3522i | −0.170915 | + | 0.371382i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.1474 | + | 53.9489i | −1.11597 | + | 1.93292i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.6976 | + | 13.1045i | −0.812183 | + | 0.468914i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.0190i | 0.536734i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.77286 | − | 7.84590i | −0.313117 | − | 0.280032i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.22171 | + | 12.5084i | 0.257426 | + | 0.445875i | 0.965552 | − | 0.260211i | \(-0.0837922\pi\) |
−0.708126 | + | 0.706087i | \(0.750459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.5435 | − | 19.9939i | 0.410960 | − | 0.711803i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.6960 | − | 7.68371i | −0.593640 | − | 0.273201i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.04033 | − | 0.600634i | −0.0369432 | − | 0.0213292i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.105793 | + | 0.0221157i | 0.00375209 | + | 0.000784364i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.3379i | 1.21631i | 0.793818 | + | 0.608156i | \(0.208091\pi\) | ||||
−0.793818 | + | 0.608156i | \(0.791909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.7244i | − | 0.414778i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.596997 | − | 0.344676i | 0.0210938 | − | 0.0121785i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.3057 | − | 35.1706i | 0.716574 | − | 1.24114i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.0693 | + | 41.9571i | −1.09505 | + | 1.47879i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.2792 | + | 43.7848i | −0.889870 | + | 1.54130i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.65907 | + | 14.9980i | 0.304437 | + | 0.527300i | 0.977136 | − | 0.212616i | \(-0.0681984\pi\) |
−0.672699 | + | 0.739916i | \(0.734865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.3807i | 0.891236i | 0.895223 | + | 0.445618i | \(0.147016\pi\) | ||||
−0.895223 | + | 0.445618i | \(0.852984\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.3185 | −0.677530 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.96839 | − | 9.41600i | 0.0689497 | − | 0.329828i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.8060 | + | 39.5011i | −0.797880 | + | 1.38197i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.655000 | − | 0.463551i | 0.0228875 | − | 0.0161978i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.2636 | − | 11.6992i | −0.707206 | − | 0.408306i | 0.102820 | − | 0.994700i | \(-0.467214\pi\) |
−0.810026 | + | 0.586394i | \(0.800547\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.67683 | − | 16.7608i | −0.337313 | − | 0.584243i | 0.646613 | − | 0.762818i | \(-0.276185\pi\) |
−0.983926 | + | 0.178575i | \(0.942851\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.32870 | − | 29.7462i | −0.115890 | − | 1.03563i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 29.0919i | − | 1.01162i | −0.862644 | − | 0.505812i | \(-0.831193\pi\) | ||
0.862644 | − | 0.505812i | \(-0.168807\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.3551 | − | 23.1317i | −0.463841 | − | 0.803397i | 0.535307 | − | 0.844658i | \(-0.320196\pi\) |
−0.999148 | + | 0.0412606i | \(0.986863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.9813 | + | 32.8765i | −0.658453 | + | 1.14047i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.55651 | + | 21.4280i | −0.261817 | + | 0.742435i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.24442 | + | 2.70943i | −0.285310 | + | 0.0937638i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.2421 | − | 21.2040i | −0.423150 | − | 0.732917i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.7914 | 0.855896 | 0.427948 | − | 0.903803i | \(-0.359237\pi\) | ||||
0.427948 | + | 0.903803i | \(0.359237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9283 | 0.652699 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.9580 | + | 50.1568i | 0.997367 | + | 1.72749i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.76318 | − | 26.6651i | −0.301463 | − | 0.917308i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.951699 | − | 1.34476i | −0.0327008 | − | 0.0462064i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.1798 | − | 22.8281i | 0.452330 | − | 0.783459i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.2271 | − | 17.7138i | −0.350579 | − | 0.607221i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.6858i | 1.73545i | 0.497047 | + | 0.867724i | \(0.334418\pi\) | ||||
−0.497047 | + | 0.867724i | \(0.665582\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.03502 | + | 4.50301i | 0.172194 | + | 0.154000i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.5812 | − | 18.3272i | −0.361448 | − | 0.626047i | 0.626751 | − | 0.779219i | \(-0.284384\pi\) |
−0.988199 | + | 0.153173i | \(0.951051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.47660 | − | 1.42986i | −0.0845003 | − | 0.0487863i | 0.457154 | − | 0.889387i | \(-0.348869\pi\) |
−0.541655 | + | 0.840601i | \(0.682202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.23590 | − | 45.7704i | −0.144359 | − | 1.55985i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.07596 | − | 10.5239i | 0.206828 | − | 0.358237i | −0.743886 | − | 0.668307i | \(-0.767019\pi\) |
0.950714 | + | 0.310070i | \(0.100353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.60616 | − | 36.3849i | 0.258617 | − | 1.23712i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0124 | −0.407963 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.3304i | 1.70734i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.60103 | + | 2.77307i | 0.0542489 | + | 0.0939619i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.75873 | − | 4.77826i | 0.0933688 | − | 0.161720i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.6522 | − | 14.7298i | 0.867201 | − | 0.497958i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.6594 | + | 28.8550i | −0.562549 | + | 0.974363i | 0.434725 | + | 0.900563i | \(0.356846\pi\) |
−0.997273 | + | 0.0737992i | \(0.976488\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.4688 | − | 12.3950i | 0.724126 | − | 0.418074i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 19.5712i | − | 0.659372i | −0.944091 | − | 0.329686i | \(-0.893057\pi\) | ||
0.944091 | − | 0.329686i | \(-0.106943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.7210i | 1.43768i | 0.695178 | + | 0.718838i | \(0.255325\pi\) | ||||
−0.695178 | + | 0.718838i | \(0.744675\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0157323 | − | 0.0752569i | 0.000528834 | − | 0.00252973i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.02603 | − | 1.74708i | −0.101604 | − | 0.0586613i | 0.448337 | − | 0.893865i | \(-0.352017\pi\) |
−0.549941 | + | 0.835203i | \(0.685350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.13489 | + | 13.3305i | −0.205757 | + | 0.447091i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.3559 | − | 28.3292i | 0.547942 | − | 0.949064i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0340 | + | 20.8434i | 0.402701 | + | 0.697499i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.7287 | + | 26.5321i | −0.793162 | + | 0.886870i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.9708i | 0.366306i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.2194 | − | 8.20958i | 0.474244 | − | 0.273805i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0422128 | + | 0.0731146i | −0.00140631 | + | 0.00243580i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.10150 | − | 33.5128i | −0.103212 | − | 1.11524i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.23795 | − | 15.9383i | −0.174115 | − | 0.529808i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.3487 | − | 10.5936i | 0.609258 | − | 0.351755i | −0.163417 | − | 0.986557i | \(-0.552252\pi\) |
0.772675 | + | 0.634802i | \(0.218918\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.40748 | −0.212523 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.1566i | 0.469030i | 0.972112 | + | 0.234515i | \(0.0753502\pi\) | ||||
−0.972112 | + | 0.234515i | \(0.924650\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6356 | + | 18.4214i | 0.351987 | + | 0.609659i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.32960 | + | 7.08863i | 0.0770140 | + | 0.234343i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.48519 | + | 2.46651i | −0.115091 | + | 0.0814513i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4716 | + | 14.7060i | 0.840230 | + | 0.485107i | 0.857342 | − | 0.514746i | \(-0.172114\pi\) |
−0.0171122 | + | 0.999854i | \(0.505447\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.4144 | − | 24.9665i | −0.474972 | − | 0.822675i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.44277 | −0.179151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.28880 | + | 11.5171i | 0.0423755 | + | 0.378680i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.196565 | + | 0.113487i | −0.00645606 | + | 0.00372741i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.8894 | + | 9.75112i | 0.554125 | + | 0.319924i | 0.750784 | − | 0.660548i | \(-0.229676\pi\) |
−0.196659 | + | 0.980472i | \(0.563009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.55994 | − | 45.8505i | −0.280541 | − | 1.50269i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.52728 | − | 14.7697i | 0.279171 | − | 0.483538i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.8863 | + | 4.78431i | 0.748461 | + | 0.156464i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.05387 | −0.0670971 | −0.0335485 | − | 0.999437i | \(-0.510681\pi\) | ||||
−0.0335485 | + | 0.999437i | \(0.510681\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −60.2423 | −1.96593 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.1289 | + | 26.2040i | 0.493187 | + | 0.854226i | 0.999969 | − | 0.00784879i | \(-0.00249837\pi\) |
−0.506782 | + | 0.862074i | \(0.669165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 71.4500 | + | 41.2517i | 2.32673 | + | 1.34334i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27.8166 | + | 3.17914i | 0.904874 | + | 0.103418i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.8806 | + | 20.1383i | 1.13347 | + | 0.654407i | 0.944804 | − | 0.327635i | \(-0.106252\pi\) |
0.188662 | + | 0.982042i | \(0.439585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.30383 | − | 4.21687i | 0.237092 | − | 0.136885i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.765564 | −0.0248251 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.4230i | 1.47140i | 0.677309 | + | 0.735698i | \(0.263146\pi\) | ||||
−0.677309 | + | 0.735698i | \(0.736854\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.46208 | − | 30.9120i | 0.209108 | − | 1.00029i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.4531 | + | 9.49917i | 0.531852 | + | 0.307065i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.04265 | − | 22.0715i | −0.0659605 | − | 0.712727i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.11656 | − | 3.66599i | 0.0682761 | − | 0.118258i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.28342 | + | 4.20508i | −0.234705 | + | 0.135507i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.6660 | + | 12.2221i | 0.439925 | + | 0.393442i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.7807 | 1.69731 | 0.848656 | − | 0.528945i | \(-0.177412\pi\) | ||||
0.848656 | + | 0.528945i | \(0.177412\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.8075 | + | 20.0961i | −1.11818 | + | 0.645580i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.0287 | + | 15.0277i | 0.835300 | + | 0.482261i | 0.855664 | − | 0.517532i | \(-0.173149\pi\) |
−0.0203639 | + | 0.999793i | \(0.506482\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.3430 | − | 11.2030i | −0.780400 | − | 0.359151i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.49002 | − | 5.69538i | 0.0797446 | − | 0.182398i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.9900 | − | 21.3562i | 1.18341 | − | 0.683245i | 0.226613 | − | 0.973985i | \(-0.427235\pi\) |
0.956802 | + | 0.290740i | \(0.0939015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.89820i | 0.156547i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.05710i | 0.0656781i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.5472 | + | 6.08944i | −0.336404 | + | 0.194223i | −0.658681 | − | 0.752423i | \(-0.728885\pi\) |
0.322277 | + | 0.946646i | \(0.395552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.62972 | + | 14.0876i | 0.147515 | + | 0.448868i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.1328 | − | 7.42451i | −0.513512 | − | 0.236325i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52.3153 | + | 30.2043i | 1.66353 | + | 0.960440i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8998 | − | 9.75712i | 0.536841 | − | 0.309945i | −0.206957 | − | 0.978350i | \(-0.566356\pi\) |
0.743798 | + | 0.668405i | \(0.233023\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 54.7348 | 1.73696 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.31085 | − | 5.93830i | 0.168365 | − | 0.188257i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.7749 | − | 14.8811i | 0.816298 | − | 0.471290i | −0.0328401 | − | 0.999461i | \(-0.510455\pi\) |
0.849138 | + | 0.528171i | \(0.177122\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.48446 | + | 9.49936i | −0.173521 | + | 0.300547i |
(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 | 1120.2.bq.b.719.9 | 80 | ||
4.3 | odd | 2 | 280.2.ba.b.19.39 | yes | 80 | ||
5.4 | even | 2 | inner | 1120.2.bq.b.719.31 | 80 | ||
7.3 | odd | 6 | inner | 1120.2.bq.b.1039.32 | 80 | ||
8.3 | odd | 2 | inner | 1120.2.bq.b.719.10 | 80 | ||
8.5 | even | 2 | 280.2.ba.b.19.25 | yes | 80 | ||
20.19 | odd | 2 | 280.2.ba.b.19.2 | ✓ | 80 | ||
28.3 | even | 6 | 280.2.ba.b.59.16 | yes | 80 | ||
35.24 | odd | 6 | inner | 1120.2.bq.b.1039.10 | 80 | ||
40.19 | odd | 2 | inner | 1120.2.bq.b.719.32 | 80 | ||
40.29 | even | 2 | 280.2.ba.b.19.16 | yes | 80 | ||
56.3 | even | 6 | inner | 1120.2.bq.b.1039.31 | 80 | ||
56.45 | odd | 6 | 280.2.ba.b.59.2 | yes | 80 | ||
140.59 | even | 6 | 280.2.ba.b.59.25 | yes | 80 | ||
280.59 | even | 6 | inner | 1120.2.bq.b.1039.9 | 80 | ||
280.269 | odd | 6 | 280.2.ba.b.59.39 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.ba.b.19.2 | ✓ | 80 | 20.19 | odd | 2 | ||
280.2.ba.b.19.16 | yes | 80 | 40.29 | even | 2 | ||
280.2.ba.b.19.25 | yes | 80 | 8.5 | even | 2 | ||
280.2.ba.b.19.39 | yes | 80 | 4.3 | odd | 2 | ||
280.2.ba.b.59.2 | yes | 80 | 56.45 | odd | 6 | ||
280.2.ba.b.59.16 | yes | 80 | 28.3 | even | 6 | ||
280.2.ba.b.59.25 | yes | 80 | 140.59 | even | 6 | ||
280.2.ba.b.59.39 | yes | 80 | 280.269 | odd | 6 | ||
1120.2.bq.b.719.9 | 80 | 1.1 | even | 1 | trivial | ||
1120.2.bq.b.719.10 | 80 | 8.3 | odd | 2 | inner | ||
1120.2.bq.b.719.31 | 80 | 5.4 | even | 2 | inner | ||
1120.2.bq.b.719.32 | 80 | 40.19 | odd | 2 | inner | ||
1120.2.bq.b.1039.9 | 80 | 280.59 | even | 6 | inner | ||
1120.2.bq.b.1039.10 | 80 | 35.24 | odd | 6 | inner | ||
1120.2.bq.b.1039.31 | 80 | 56.3 | even | 6 | inner | ||
1120.2.bq.b.1039.32 | 80 | 7.3 | odd | 6 | inner |