Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(323,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.e (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.11 | ||
Character | \(\chi\) | \(=\) | 756.323 |
Dual form | 756.2.e.b.323.12 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0572568 | − | 1.41305i | −0.0404867 | − | 0.999180i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99344 | + | 0.161814i | −0.996722 | + | 0.0809069i | ||||
\(5\) | 0.386370i | 0.172790i | 0.996261 | + | 0.0863950i | \(0.0275347\pi\) | ||||
−0.996261 | + | 0.0863950i | \(0.972465\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0.342790 | + | 2.80758i | 0.121195 | + | 0.992629i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.545962 | − | 0.0221223i | 0.172648 | − | 0.00699569i | ||||
\(11\) | −3.49674 | −1.05431 | −0.527153 | − | 0.849771i | \(-0.676740\pi\) | ||||
−0.527153 | + | 0.849771i | \(0.676740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.33247 | 1.47896 | 0.739481 | − | 0.673178i | \(-0.235071\pi\) | ||||
0.739481 | + | 0.673178i | \(0.235071\pi\) | |||||||
\(14\) | 1.41305 | − | 0.0572568i | 0.377655 | − | 0.0153025i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.94763 | − | 0.645134i | 0.986908 | − | 0.161283i | ||||
\(17\) | − | 4.58027i | − | 1.11088i | −0.831557 | − | 0.555439i | \(-0.812550\pi\) | ||
0.831557 | − | 0.555439i | \(-0.187450\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.22605i | − | 1.42835i | −0.699965 | − | 0.714177i | \(-0.746801\pi\) | ||
0.699965 | − | 0.714177i | \(-0.253199\pi\) | |||||||
\(20\) | −0.0625201 | − | 0.770207i | −0.0139799 | − | 0.172224i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.200212 | + | 4.94108i | 0.0426853 | + | 1.05344i | ||||
\(23\) | 8.20171 | 1.71017 | 0.855087 | − | 0.518484i | \(-0.173503\pi\) | ||||
0.855087 | + | 0.518484i | \(0.173503\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.85072 | 0.970144 | ||||||||
\(26\) | −0.305320 | − | 7.53507i | −0.0598782 | − | 1.47775i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.161814 | − | 1.99344i | −0.0305800 | − | 0.376725i | ||||
\(29\) | − | 6.76887i | − | 1.25695i | −0.777831 | − | 0.628474i | \(-0.783680\pi\) | ||
0.777831 | − | 0.628474i | \(-0.216320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.47346i | 1.70148i | 0.525584 | + | 0.850742i | \(0.323847\pi\) | ||||
−0.525584 | + | 0.850742i | \(0.676153\pi\) | |||||||
\(32\) | −1.13764 | − | 5.54128i | −0.201108 | − | 0.979569i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.47216 | + | 0.262251i | −1.10997 | + | 0.0449757i | ||||
\(35\) | −0.386370 | −0.0653085 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.41693 | 0.726139 | 0.363070 | − | 0.931762i | \(-0.381729\pi\) | ||||
0.363070 | + | 0.931762i | \(0.381729\pi\) | |||||||
\(38\) | −8.79775 | + | 0.356484i | −1.42718 | + | 0.0578293i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.08476 | + | 0.132444i | −0.171516 | + | 0.0209412i | ||||
\(41\) | − | 4.43840i | − | 0.693162i | −0.938020 | − | 0.346581i | \(-0.887343\pi\) | ||
0.938020 | − | 0.346581i | \(-0.112657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.95948i | 0.298818i | 0.988775 | + | 0.149409i | \(0.0477371\pi\) | ||||
−0.988775 | + | 0.149409i | \(0.952263\pi\) | |||||||
\(44\) | 6.97054 | − | 0.565820i | 1.05085 | − | 0.0853006i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.469604 | − | 11.5895i | −0.0692393 | − | 1.70877i | ||||
\(47\) | 0.996370 | 0.145336 | 0.0726678 | − | 0.997356i | \(-0.476849\pi\) | ||||
0.0726678 | + | 0.997356i | \(0.476849\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −0.277737 | − | 6.85433i | −0.0392779 | − | 0.969348i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.6300 | + | 0.862868i | −1.47411 | + | 0.119658i | ||||
\(53\) | 1.92203i | 0.264011i | 0.991249 | + | 0.132005i | \(0.0421416\pi\) | ||||
−0.991249 | + | 0.132005i | \(0.957858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.35103i | − | 0.182173i | ||||||
\(56\) | −2.80758 | + | 0.342790i | −0.375178 | + | 0.0458072i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.56478 | + | 0.387564i | −1.25592 | + | 0.0508896i | ||||
\(59\) | −5.78408 | −0.753023 | −0.376512 | − | 0.926412i | \(-0.622876\pi\) | ||||
−0.376512 | + | 0.926412i | \(0.622876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.68946 | 0.856498 | 0.428249 | − | 0.903661i | \(-0.359131\pi\) | ||||
0.428249 | + | 0.903661i | \(0.359131\pi\) | |||||||
\(62\) | 13.3865 | − | 0.542420i | 1.70009 | − | 0.0688874i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.76499 | + | 1.92482i | −0.970624 | + | 0.240602i | ||||
\(65\) | 2.06031i | 0.255550i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.49626i | − | 0.427136i | −0.976928 | − | 0.213568i | \(-0.931491\pi\) | ||
0.976928 | − | 0.213568i | \(-0.0685085\pi\) | |||||||
\(68\) | 0.741151 | + | 9.13050i | 0.0898777 | + | 1.10724i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0221223 | + | 0.545962i | 0.00264412 | + | 0.0652549i | ||||
\(71\) | −12.0342 | −1.42820 | −0.714100 | − | 0.700044i | \(-0.753164\pi\) | ||||
−0.714100 | + | 0.700044i | \(0.753164\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.14330 | 0.953101 | 0.476551 | − | 0.879147i | \(-0.341887\pi\) | ||||
0.476551 | + | 0.879147i | \(0.341887\pi\) | |||||||
\(74\) | −0.252899 | − | 6.24137i | −0.0293990 | − | 0.725544i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00746 | + | 12.4113i | 0.115564 | + | 1.42367i | ||||
\(77\) | − | 3.49674i | − | 0.398490i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.0625i | − | 1.35713i | −0.734540 | − | 0.678566i | \(-0.762602\pi\) | ||
0.734540 | − | 0.678566i | \(-0.237398\pi\) | |||||||
\(80\) | 0.249260 | + | 1.52525i | 0.0278682 | + | 0.170528i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.27170 | + | 0.254129i | −0.692593 | + | 0.0280638i | ||||
\(83\) | 11.4944 | 1.26168 | 0.630838 | − | 0.775915i | \(-0.282711\pi\) | ||||
0.630838 | + | 0.775915i | \(0.282711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.76968 | 0.191949 | ||||||||
\(86\) | 2.76885 | − | 0.112194i | 0.298573 | − | 0.0120981i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.19865 | − | 9.81736i | −0.127776 | − | 1.04653i | ||||
\(89\) | 0.206472i | 0.0218860i | 0.999940 | + | 0.0109430i | \(0.00348334\pi\) | ||||
−0.999940 | + | 0.0109430i | \(0.996517\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.33247i | 0.558995i | ||||||||
\(92\) | −16.3496 | + | 1.32715i | −1.70457 | + | 0.138365i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.0570490 | − | 1.40792i | −0.00588415 | − | 0.145216i | ||||
\(95\) | 2.40556 | 0.246805 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.99826 | −0.913635 | −0.456818 | − | 0.889560i | \(-0.651011\pi\) | ||||
−0.456818 | + | 0.889560i | \(0.651011\pi\) | |||||||
\(98\) | 0.0572568 | + | 1.41305i | 0.00578381 | + | 0.142740i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.66963 | + | 0.784914i | −0.966963 | + | 0.0784914i | ||||
\(101\) | 5.94651i | 0.591700i | 0.955234 | + | 0.295850i | \(0.0956028\pi\) | ||||
−0.955234 | + | 0.295850i | \(0.904397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9130i | 1.07529i | 0.843172 | + | 0.537644i | \(0.180686\pi\) | ||||
−0.843172 | + | 0.537644i | \(0.819314\pi\) | |||||||
\(104\) | 1.82792 | + | 14.9713i | 0.179242 | + | 1.46806i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.71593 | − | 0.110049i | 0.263794 | − | 0.0106889i | ||||
\(107\) | −2.37293 | −0.229400 | −0.114700 | − | 0.993400i | \(-0.536591\pi\) | ||||
−0.114700 | + | 0.993400i | \(0.536591\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.49012 | −0.334293 | −0.167146 | − | 0.985932i | \(-0.553455\pi\) | ||||
−0.167146 | + | 0.985932i | \(0.553455\pi\) | |||||||
\(110\) | −1.90908 | + | 0.0773559i | −0.182024 | + | 0.00737560i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.645134 | + | 3.94763i | 0.0609594 | + | 0.373016i | ||||
\(113\) | 19.0081i | 1.78813i | 0.447935 | + | 0.894066i | \(0.352160\pi\) | ||||
−0.447935 | + | 0.894066i | \(0.647840\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.16890i | 0.295501i | ||||||||
\(116\) | 1.09530 | + | 13.4934i | 0.101696 | + | 1.25283i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.331178 | + | 8.17322i | 0.0304874 | + | 0.752406i | ||||
\(119\) | 4.58027 | 0.419872 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.22716 | 0.111560 | ||||||||
\(122\) | −0.383017 | − | 9.45257i | −0.0346767 | − | 0.855795i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.53294 | − | 18.8848i | −0.137662 | − | 1.69591i | ||||
\(125\) | 3.80602i | 0.340421i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.29024i | − | 0.646904i | −0.946245 | − | 0.323452i | \(-0.895157\pi\) | ||
0.946245 | − | 0.323452i | \(-0.104843\pi\) | |||||||
\(128\) | 3.16447 | + | 10.8621i | 0.279702 | + | 0.960087i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.91133 | − | 0.117967i | 0.255340 | − | 0.0103464i | ||||
\(131\) | 13.1755 | 1.15115 | 0.575574 | − | 0.817749i | \(-0.304778\pi\) | ||||
0.575574 | + | 0.817749i | \(0.304778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.22605 | 0.539867 | ||||||||
\(134\) | −4.94041 | + | 0.200185i | −0.426786 | + | 0.0172933i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.8595 | − | 1.57007i | 1.10269 | − | 0.134632i | ||||
\(137\) | 5.32595i | 0.455027i | 0.973775 | + | 0.227513i | \(0.0730595\pi\) | ||||
−0.973775 | + | 0.227513i | \(0.926940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.71810i | 0.739459i | 0.929139 | + | 0.369730i | \(0.120550\pi\) | ||||
−0.929139 | + | 0.369730i | \(0.879450\pi\) | |||||||
\(140\) | 0.770207 | − | 0.0625201i | 0.0650944 | − | 0.00528391i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.689041 | + | 17.0050i | 0.0578231 | + | 1.42703i | ||||
\(143\) | −18.6462 | −1.55928 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.61529 | 0.217188 | ||||||||
\(146\) | −0.466259 | − | 11.5069i | −0.0385879 | − | 0.952320i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.80491 | + | 0.714721i | −0.723759 | + | 0.0587497i | ||||
\(149\) | − | 5.27938i | − | 0.432503i | −0.976338 | − | 0.216252i | \(-0.930617\pi\) | ||
0.976338 | − | 0.216252i | \(-0.0693832\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.0546i | − | 1.22513i | −0.790422 | − | 0.612563i | \(-0.790139\pi\) | ||
0.790422 | − | 0.612563i | \(-0.209861\pi\) | |||||||
\(152\) | 17.4801 | − | 2.13423i | 1.41783 | − | 0.173109i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.94108 | + | 0.200212i | −0.398163 | + | 0.0161335i | ||||
\(155\) | −3.66026 | −0.293999 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.68524 | −0.453732 | −0.226866 | − | 0.973926i | \(-0.572848\pi\) | ||||
−0.226866 | + | 0.973926i | \(0.572848\pi\) | |||||||
\(158\) | −17.0449 | + | 0.690657i | −1.35602 | + | 0.0549457i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.14099 | − | 0.439549i | 0.169260 | − | 0.0347494i | ||||
\(161\) | 8.20171i | 0.646385i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.5536i | − | 1.53156i | −0.643103 | − | 0.765780i | \(-0.722353\pi\) | ||
0.643103 | − | 0.765780i | \(-0.277647\pi\) | |||||||
\(164\) | 0.718195 | + | 8.84770i | 0.0560816 | + | 0.690889i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.658133 | − | 16.2422i | −0.0510810 | − | 1.26064i | ||||
\(167\) | 6.27919 | 0.485899 | 0.242949 | − | 0.970039i | \(-0.421885\pi\) | ||||
0.242949 | + | 0.970039i | \(0.421885\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.4353 | 1.18733 | ||||||||
\(170\) | −0.101326 | − | 2.50065i | −0.00777136 | − | 0.191791i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.317071 | − | 3.90611i | −0.0241764 | − | 0.297838i | ||||
\(173\) | − | 6.12181i | − | 0.465433i | −0.972545 | − | 0.232716i | \(-0.925239\pi\) | ||
0.972545 | − | 0.232716i | \(-0.0747614\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.85072i | 0.366680i | ||||||||
\(176\) | −13.8038 | + | 2.25586i | −1.04050 | + | 0.170042i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.291757 | − | 0.0118220i | 0.0218681 | − | 0.000886093i | ||||
\(179\) | −18.1104 | −1.35363 | −0.676816 | − | 0.736152i | \(-0.736641\pi\) | ||||
−0.676816 | + | 0.736152i | \(0.736641\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.16529 | 0.458262 | 0.229131 | − | 0.973396i | \(-0.426412\pi\) | ||||
0.229131 | + | 0.973396i | \(0.426412\pi\) | |||||||
\(182\) | 7.53507 | − | 0.305320i | 0.558537 | − | 0.0226318i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.81146 | + | 23.0269i | 0.207264 | + | 1.69757i | ||||
\(185\) | 1.70657i | 0.125470i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0160i | 1.17120i | ||||||||
\(188\) | −1.98621 | + | 0.161227i | −0.144859 | + | 0.0117587i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.137735 | − | 3.39919i | −0.00999233 | − | 0.246603i | ||||
\(191\) | 17.9832 | 1.30122 | 0.650610 | − | 0.759412i | \(-0.274513\pi\) | ||||
0.650610 | + | 0.759412i | \(0.274513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.5475 | 1.11913 | 0.559565 | − | 0.828786i | \(-0.310968\pi\) | ||||
0.559565 | + | 0.828786i | \(0.310968\pi\) | |||||||
\(194\) | 0.515212 | + | 12.7150i | 0.0369900 | + | 0.912886i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.99344 | − | 0.161814i | 0.142389 | − | 0.0115581i | ||||
\(197\) | − | 15.2391i | − | 1.08574i | −0.839815 | − | 0.542872i | \(-0.817337\pi\) | ||
0.839815 | − | 0.542872i | \(-0.182663\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5459i | 1.52735i | 0.645601 | + | 0.763675i | \(0.276607\pi\) | ||||
−0.645601 | + | 0.763675i | \(0.723393\pi\) | |||||||
\(200\) | 1.66278 | + | 13.6188i | 0.117576 | + | 0.962992i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 8.40274 | − | 0.340478i | 0.591215 | − | 0.0239560i | ||||
\(203\) | 6.76887 | 0.475082 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.71487 | 0.119771 | ||||||||
\(206\) | 15.4206 | − | 0.624842i | 1.07441 | − | 0.0435348i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 21.0506 | − | 3.44016i | 1.45960 | − | 0.238532i | ||||
\(209\) | 21.7709i | 1.50592i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1173i | 0.696503i | 0.937401 | + | 0.348251i | \(0.113224\pi\) | ||||
−0.937401 | + | 0.348251i | \(0.886776\pi\) | |||||||
\(212\) | −0.311011 | − | 3.83145i | −0.0213603 | − | 0.263145i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.135866 | + | 3.35307i | 0.00928762 | + | 0.229211i | ||||
\(215\) | −0.757085 | −0.0516327 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.47346 | −0.643100 | ||||||||
\(218\) | 0.199833 | + | 4.93173i | 0.0135344 | + | 0.334019i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.218616 | + | 2.69321i | 0.0147391 | + | 0.181576i | ||||
\(221\) | − | 24.4241i | − | 1.64295i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.80598i | − | 0.321832i | −0.986968 | − | 0.160916i | \(-0.948555\pi\) | ||
0.986968 | − | 0.160916i | \(-0.0514449\pi\) | |||||||
\(224\) | 5.54128 | − | 1.13764i | 0.370242 | − | 0.0760116i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 26.8595 | − | 1.08834i | 1.78667 | − | 0.0723955i | ||||
\(227\) | 2.62950 | 0.174526 | 0.0872630 | − | 0.996185i | \(-0.472188\pi\) | ||||
0.0872630 | + | 0.996185i | \(0.472188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0616 | −0.730973 | −0.365487 | − | 0.930817i | \(-0.619097\pi\) | ||||
−0.365487 | + | 0.930817i | \(0.619097\pi\) | |||||||
\(230\) | 4.47782 | − | 0.181441i | 0.295259 | − | 0.0119639i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.0041 | − | 2.32030i | 1.24768 | − | 0.152335i | ||||
\(233\) | 20.8133i | 1.36352i | 0.731575 | + | 0.681761i | \(0.238786\pi\) | ||||
−0.731575 | + | 0.681761i | \(0.761214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.384968i | 0.0251125i | ||||||||
\(236\) | 11.5302 | − | 0.935944i | 0.750554 | − | 0.0609248i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.262251 | − | 6.47216i | −0.0169992 | − | 0.419528i | ||||
\(239\) | −26.4240 | −1.70923 | −0.854614 | − | 0.519263i | \(-0.826206\pi\) | ||||
−0.854614 | + | 0.519263i | \(0.826206\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4304 | −1.38045 | −0.690226 | − | 0.723594i | \(-0.742489\pi\) | ||||
−0.690226 | + | 0.723594i | \(0.742489\pi\) | |||||||
\(242\) | −0.0702631 | − | 1.73404i | −0.00451668 | − | 0.111468i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.3351 | + | 1.08245i | −0.853690 | + | 0.0692966i | ||||
\(245\) | − | 0.386370i | − | 0.0246843i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 33.2002i | − | 2.11248i | ||||||
\(248\) | −26.5975 | + | 3.24741i | −1.68894 | + | 0.206210i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.37812 | − | 0.217921i | 0.340142 | − | 0.0137825i | ||||
\(251\) | −8.66366 | −0.546845 | −0.273423 | − | 0.961894i | \(-0.588156\pi\) | ||||
−0.273423 | + | 0.961894i | \(0.588156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.6792 | −1.80305 | ||||||||
\(254\) | −10.3015 | + | 0.417416i | −0.646374 | + | 0.0261910i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.1676 | − | 5.09350i | 0.947975 | − | 0.318344i | ||||
\(257\) | 30.9680i | 1.93173i | 0.259049 | + | 0.965864i | \(0.416591\pi\) | ||||
−0.259049 | + | 0.965864i | \(0.583409\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.41693i | 0.274455i | ||||||||
\(260\) | −0.333386 | − | 4.10711i | −0.0206758 | − | 0.254712i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.754387 | − | 18.6177i | −0.0466062 | − | 1.15021i | ||||
\(263\) | 15.7715 | 0.972514 | 0.486257 | − | 0.873816i | \(-0.338362\pi\) | ||||
0.486257 | + | 0.873816i | \(0.338362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.742614 | −0.0456184 | ||||||||
\(266\) | −0.356484 | − | 8.79775i | −0.0218574 | − | 0.539425i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.565744 | + | 6.96960i | 0.0345583 | + | 0.425736i | ||||
\(269\) | 5.55063i | 0.338428i | 0.985579 | + | 0.169214i | \(0.0541229\pi\) | ||||
−0.985579 | + | 0.169214i | \(0.945877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.57901i | 0.581884i | 0.956741 | + | 0.290942i | \(0.0939686\pi\) | ||||
−0.956741 | + | 0.290942i | \(0.906031\pi\) | |||||||
\(272\) | −2.95488 | − | 18.0812i | −0.179166 | − | 1.09633i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.52585 | − | 0.304947i | 0.454653 | − | 0.0184225i | ||||
\(275\) | −16.9617 | −1.02283 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.8684 | −1.43411 | −0.717057 | − | 0.697015i | \(-0.754511\pi\) | ||||
−0.717057 | + | 0.697015i | \(0.754511\pi\) | |||||||
\(278\) | 12.3191 | − | 0.499170i | 0.738853 | − | 0.0299382i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.132444 | − | 1.08476i | −0.00791503 | − | 0.0648271i | ||||
\(281\) | − | 8.73238i | − | 0.520930i | −0.965483 | − | 0.260465i | \(-0.916124\pi\) | ||
0.965483 | − | 0.260465i | \(-0.0838759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.18895i | − | 0.0706760i | −0.999375 | − | 0.0353380i | \(-0.988749\pi\) | ||
0.999375 | − | 0.0353380i | \(-0.0112508\pi\) | |||||||
\(284\) | 23.9895 | − | 1.94730i | 1.42352 | − | 0.115551i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.06762 | + | 26.3481i | 0.0631299 | + | 1.55800i | ||||
\(287\) | 4.43840 | 0.261990 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.97884 | −0.234049 | ||||||||
\(290\) | −0.149743 | − | 3.69555i | −0.00879322 | − | 0.217010i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.2332 | + | 1.31770i | −0.949977 | + | 0.0771125i | ||||
\(293\) | − | 5.50536i | − | 0.321627i | −0.986985 | − | 0.160813i | \(-0.948588\pi\) | ||
0.986985 | − | 0.160813i | \(-0.0514117\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.23480i | − | 0.130115i | ||||||
\(296\) | 1.51408 | + | 12.4009i | 0.0880041 | + | 0.720787i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.46004 | + | 0.302280i | −0.432149 | + | 0.0175106i | ||||
\(299\) | 43.7354 | 2.52928 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.95948 | −0.112943 | ||||||||
\(302\) | −21.2730 | + | 0.861978i | −1.22412 | + | 0.0496013i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.01664 | − | 24.5782i | −0.230370 | − | 1.40965i | ||||
\(305\) | 2.58461i | 0.147994i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.4222i | − | 1.10849i | −0.832355 | − | 0.554243i | \(-0.813008\pi\) | ||
0.832355 | − | 0.554243i | \(-0.186992\pi\) | |||||||
\(308\) | 0.565820 | + | 6.97054i | 0.0322406 | + | 0.397184i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.209575 | + | 5.17215i | 0.0119031 | + | 0.293758i | ||||
\(311\) | 19.9681 | 1.13229 | 0.566143 | − | 0.824307i | \(-0.308435\pi\) | ||||
0.566143 | + | 0.824307i | \(0.308435\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6381 | −1.16654 | −0.583268 | − | 0.812280i | \(-0.698226\pi\) | ||||
−0.583268 | + | 0.812280i | \(0.698226\pi\) | |||||||
\(314\) | 0.325519 | + | 8.03356i | 0.0183701 | + | 0.453360i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.95187 | + | 24.0458i | 0.109801 | + | 1.35268i | ||||
\(317\) | − | 27.4374i | − | 1.54104i | −0.637418 | − | 0.770518i | \(-0.719997\pi\) | ||
0.637418 | − | 0.770518i | \(-0.280003\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.6689i | 1.32521i | ||||||||
\(320\) | −0.743693 | − | 3.00016i | −0.0415737 | − | 0.167714i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.5895 | − | 0.469604i | 0.645855 | − | 0.0261700i | ||||
\(323\) | −28.5170 | −1.58673 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.8663 | 1.43481 | ||||||||
\(326\) | −27.6304 | + | 1.11958i | −1.53030 | + | 0.0620078i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.4612 | − | 1.52144i | 0.688052 | − | 0.0840074i | ||||
\(329\) | 0.996370i | 0.0549317i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.0348i | − | 1.15618i | −0.815975 | − | 0.578088i | \(-0.803799\pi\) | ||
0.815975 | − | 0.578088i | \(-0.196201\pi\) | |||||||
\(332\) | −22.9135 | + | 1.85996i | −1.25754 | + | 0.102078i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.359527 | − | 8.87284i | −0.0196724 | − | 0.485500i | ||||
\(335\) | 1.35085 | 0.0738049 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.7637 | −1.07660 | −0.538298 | − | 0.842755i | \(-0.680932\pi\) | ||||
−0.538298 | + | 0.842755i | \(0.680932\pi\) | |||||||
\(338\) | −0.883773 | − | 21.8108i | −0.0480709 | − | 1.18635i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.52775 | + | 0.286359i | −0.191319 | + | 0.0155300i | ||||
\(341\) | − | 33.1262i | − | 1.79388i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −5.50139 | + | 0.671690i | −0.296615 | + | 0.0362151i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.65045 | + | 0.350515i | −0.465051 | + | 0.0188438i | ||||
\(347\) | −0.272222 | −0.0146136 | −0.00730682 | − | 0.999973i | \(-0.502326\pi\) | ||||
−0.00730682 | + | 0.999973i | \(0.502326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.92498 | 0.263628 | 0.131814 | − | 0.991274i | \(-0.457920\pi\) | ||||
0.131814 | + | 0.991274i | \(0.457920\pi\) | |||||||
\(350\) | 6.85433 | − | 0.277737i | 0.366379 | − | 0.0148456i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.97802 | + | 19.3764i | 0.212029 | + | 1.03276i | ||||
\(353\) | 2.99080i | 0.159184i | 0.996828 | + | 0.0795922i | \(0.0253618\pi\) | ||||
−0.996828 | + | 0.0795922i | \(0.974638\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.64967i | − | 0.246779i | ||||||
\(356\) | −0.0334101 | − | 0.411591i | −0.00177073 | − | 0.0218143i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.03694 | + | 25.5909i | 0.0548040 | + | 1.35252i | ||||
\(359\) | −9.86716 | −0.520769 | −0.260385 | − | 0.965505i | \(-0.583849\pi\) | ||||
−0.260385 | + | 0.965505i | \(0.583849\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.7637 | −1.04020 | ||||||||
\(362\) | −0.353004 | − | 8.71188i | −0.0185535 | − | 0.457886i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.862868 | − | 10.6300i | −0.0452266 | − | 0.557162i | ||||
\(365\) | 3.14633i | 0.164686i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8605i | 1.24551i | 0.782418 | + | 0.622754i | \(0.213986\pi\) | ||||
−0.782418 | + | 0.622754i | \(0.786014\pi\) | |||||||
\(368\) | 32.3773 | − | 5.29120i | 1.68779 | − | 0.275823i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.41148 | − | 0.0977128i | 0.125367 | − | 0.00507985i | ||||
\(371\) | −1.92203 | −0.0997867 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.4683 | −1.47403 | −0.737016 | − | 0.675876i | \(-0.763766\pi\) | ||||
−0.737016 | + | 0.675876i | \(0.763766\pi\) | |||||||
\(374\) | 22.6314 | − | 0.917024i | 1.17024 | − | 0.0474182i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.341546 | + | 2.79739i | 0.0176139 | + | 0.144264i | ||||
\(377\) | − | 36.0948i | − | 1.85898i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11.0145i | − | 0.565779i | −0.959153 | − | 0.282889i | \(-0.908707\pi\) | ||
0.959153 | − | 0.282889i | \(-0.0912929\pi\) | |||||||
\(380\) | −4.79535 | + | 0.389253i | −0.245996 | + | 0.0199683i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.02966 | − | 25.4113i | −0.0526821 | − | 1.30015i | ||||
\(383\) | −12.6616 | −0.646976 | −0.323488 | − | 0.946232i | \(-0.604856\pi\) | ||||
−0.323488 | + | 0.946232i | \(0.604856\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.35103 | 0.0688551 | ||||||||
\(386\) | −0.890198 | − | 21.9694i | −0.0453099 | − | 1.11821i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.9375 | − | 1.45604i | 0.910640 | − | 0.0739194i | ||||
\(389\) | 21.5099i | 1.09060i | 0.838242 | + | 0.545298i | \(0.183584\pi\) | ||||
−0.838242 | + | 0.545298i | \(0.816416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 37.5660i | − | 1.89980i | ||||||
\(392\) | −0.342790 | − | 2.80758i | −0.0173135 | − | 0.141804i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.5337 | + | 0.872545i | −1.08485 | + | 0.0439582i | ||||
\(395\) | 4.66057 | 0.234499 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.09412 | −0.0549124 | −0.0274562 | − | 0.999623i | \(-0.508741\pi\) | ||||
−0.0274562 | + | 0.999623i | \(0.508741\pi\) | |||||||
\(398\) | 30.4455 | − | 1.23365i | 1.52610 | − | 0.0618373i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.1489 | − | 3.12936i | 0.957443 | − | 0.156468i | ||||
\(401\) | − | 2.97516i | − | 0.148573i | −0.997237 | − | 0.0742863i | \(-0.976332\pi\) | ||
0.997237 | − | 0.0742863i | \(-0.0236679\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 50.5169i | 2.51643i | ||||||||
\(404\) | −0.962228 | − | 11.8540i | −0.0478726 | − | 0.589760i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.387564 | − | 9.56478i | −0.0192345 | − | 0.474692i | ||||
\(407\) | −15.4448 | −0.765573 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.9391 | −0.985923 | −0.492962 | − | 0.870051i | \(-0.664086\pi\) | ||||
−0.492962 | + | 0.870051i | \(0.664086\pi\) | |||||||
\(410\) | −0.0981877 | − | 2.42320i | −0.00484914 | − | 0.119673i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.76587 | − | 21.7544i | −0.0869983 | − | 1.07176i | ||||
\(413\) | − | 5.78408i | − | 0.284616i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.44110i | 0.218005i | ||||||||
\(416\) | −6.06642 | − | 29.5487i | −0.297431 | − | 1.44875i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.7634 | − | 1.24653i | 1.50469 | − | 0.0609698i | ||||
\(419\) | 27.5046 | 1.34369 | 0.671845 | − | 0.740692i | \(-0.265502\pi\) | ||||
0.671845 | + | 0.740692i | \(0.265502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4219 | 0.654142 | 0.327071 | − | 0.945000i | \(-0.393938\pi\) | ||||
0.327071 | + | 0.945000i | \(0.393938\pi\) | |||||||
\(422\) | 14.2963 | − | 0.579284i | 0.695932 | − | 0.0281991i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.39624 | + | 0.658852i | −0.262065 | + | 0.0319967i | ||||
\(425\) | − | 22.2176i | − | 1.07771i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.68946i | 0.323726i | ||||||||
\(428\) | 4.73030 | − | 0.383973i | 0.228647 | − | 0.0185600i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0433482 | + | 1.06980i | 0.00209044 | + | 0.0515904i | ||||
\(431\) | −5.42483 | −0.261305 | −0.130652 | − | 0.991428i | \(-0.541707\pi\) | ||||
−0.130652 | + | 0.991428i | \(0.541707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.2723 | −1.64702 | −0.823511 | − | 0.567300i | \(-0.807988\pi\) | ||||
−0.823511 | + | 0.567300i | \(0.807988\pi\) | |||||||
\(434\) | 0.542420 | + | 13.3865i | 0.0260370 | + | 0.642573i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.95735 | − | 0.564750i | 0.333197 | − | 0.0270466i | ||||
\(437\) | − | 51.0643i | − | 2.44274i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.87818i | − | 0.185096i | −0.995708 | − | 0.0925478i | \(-0.970499\pi\) | ||
0.995708 | − | 0.0925478i | \(-0.0295011\pi\) | |||||||
\(440\) | 3.79313 | − | 0.463121i | 0.180831 | − | 0.0220784i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −34.5126 | + | 1.39845i | −1.64160 | + | 0.0665174i | ||||
\(443\) | −9.48942 | −0.450856 | −0.225428 | − | 0.974260i | \(-0.572378\pi\) | ||||
−0.225428 | + | 0.974260i | \(0.572378\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0797748 | −0.00378169 | ||||||||
\(446\) | −6.79111 | + | 0.275175i | −0.321568 | + | 0.0130299i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.92482 | − | 7.76499i | −0.0909392 | − | 0.366861i | ||||
\(449\) | 18.2662i | 0.862038i | 0.902343 | + | 0.431019i | \(0.141846\pi\) | ||||
−0.902343 | + | 0.431019i | \(0.858154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.5199i | 0.730804i | ||||||||
\(452\) | −3.07578 | − | 37.8916i | −0.144672 | − | 1.78227i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.150557 | − | 3.71563i | −0.00706598 | − | 0.174383i | ||||
\(455\) | −2.06031 | −0.0965887 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.62419 | −0.169533 | −0.0847663 | − | 0.996401i | \(-0.527014\pi\) | ||||
−0.0847663 | + | 0.996401i | \(0.527014\pi\) | |||||||
\(458\) | 0.633353 | + | 15.6307i | 0.0295947 | + | 0.730374i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.512771 | − | 6.31702i | −0.0239081 | − | 0.294532i | ||||
\(461\) | 9.53162i | 0.443932i | 0.975054 | + | 0.221966i | \(0.0712473\pi\) | ||||
−0.975054 | + | 0.221966i | \(0.928753\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 41.9466i | − | 1.94943i | −0.223461 | − | 0.974713i | \(-0.571735\pi\) | ||
0.223461 | − | 0.974713i | \(-0.428265\pi\) | |||||||
\(464\) | −4.36683 | − | 26.7210i | −0.202725 | − | 1.24049i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.4103 | − | 1.19170i | 1.36240 | − | 0.0552045i | ||||
\(467\) | 8.02448 | 0.371329 | 0.185664 | − | 0.982613i | \(-0.440556\pi\) | ||||
0.185664 | + | 0.982613i | \(0.440556\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.49626 | 0.161442 | ||||||||
\(470\) | 0.543980 | − | 0.0220420i | 0.0250919 | − | 0.00101672i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.98272 | − | 16.2393i | −0.0912623 | − | 0.747472i | ||||
\(473\) | − | 6.85178i | − | 0.315045i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 30.2008i | − | 1.38571i | ||||||
\(476\) | −9.13050 | + | 0.741151i | −0.418496 | + | 0.0339706i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.51296 | + | 37.3386i | 0.0692010 | + | 1.70783i | ||||
\(479\) | −17.1710 | −0.784563 | −0.392281 | − | 0.919845i | \(-0.628314\pi\) | ||||
−0.392281 | + | 0.919845i | \(0.628314\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.5532 | 1.07393 | ||||||||
\(482\) | 1.22703 | + | 30.2823i | 0.0558899 | + | 1.37932i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.44627 | + | 0.198571i | −0.111194 | + | 0.00902596i | ||||
\(485\) | − | 3.47666i | − | 0.157867i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.5764i | 1.43086i | 0.698682 | + | 0.715432i | \(0.253770\pi\) | ||||
−0.698682 | + | 0.715432i | \(0.746230\pi\) | |||||||
\(488\) | 2.29308 | + | 18.7812i | 0.103803 | + | 0.850184i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.545962 | + | 0.0221223i | −0.0246640 | + | 0.000999385i | ||||
\(491\) | 16.0782 | 0.725599 | 0.362800 | − | 0.931867i | \(-0.381821\pi\) | ||||
0.362800 | + | 0.931867i | \(0.381821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.0032 | −1.39631 | ||||||||
\(494\) | −46.9137 | + | 1.90094i | −2.11075 | + | 0.0855273i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.11165 | + | 37.3977i | 0.274421 | + | 1.67921i | ||||
\(497\) | − | 12.0342i | − | 0.539809i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.6396i | − | 0.744889i | −0.928054 | − | 0.372445i | \(-0.878520\pi\) | ||
0.928054 | − | 0.372445i | \(-0.121480\pi\) | |||||||
\(500\) | −0.615868 | − | 7.58709i | −0.0275424 | − | 0.339305i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.496053 | + | 12.2422i | 0.0221399 | + | 0.546397i | ||||
\(503\) | 20.1267 | 0.897407 | 0.448704 | − | 0.893681i | \(-0.351886\pi\) | ||||
0.448704 | + | 0.893681i | \(0.351886\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.29755 | −0.102240 | ||||||||
\(506\) | 1.64208 | + | 40.5253i | 0.0729993 | + | 1.80157i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.17966 | + | 14.5327i | 0.0523391 | + | 0.644784i | ||||
\(509\) | 37.6363i | 1.66820i | 0.551612 | + | 0.834101i | \(0.314013\pi\) | ||||
−0.551612 | + | 0.834101i | \(0.685987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.14330i | 0.360238i | ||||||||
\(512\) | −8.06584 | − | 21.1410i | −0.356463 | − | 0.934309i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 43.7594 | − | 1.77313i | 1.93014 | − | 0.0782092i | ||||
\(515\) | −4.21645 | −0.185799 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.48404 | −0.153228 | ||||||||
\(518\) | 6.24137 | − | 0.252899i | 0.274230 | − | 0.0111118i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.78448 | + | 0.706253i | −0.253666 | + | 0.0309712i | ||||
\(521\) | 36.2014i | 1.58601i | 0.609213 | + | 0.793007i | \(0.291485\pi\) | ||||
−0.609213 | + | 0.793007i | \(0.708515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.8379i | 1.91690i | 0.285268 | + | 0.958448i | \(0.407917\pi\) | ||||
−0.285268 | + | 0.958448i | \(0.592083\pi\) | |||||||
\(524\) | −26.2646 | + | 2.13198i | −1.14738 | + | 0.0931359i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.903027 | − | 22.2860i | −0.0393739 | − | 0.971717i | ||||
\(527\) | 43.3910 | 1.89014 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.2681 | 1.92470 | ||||||||
\(530\) | 0.0425197 | + | 1.04935i | 0.00184694 | + | 0.0455810i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.4113 | + | 1.00746i | −0.538097 | + | 0.0436790i | ||||
\(533\) | − | 23.6676i | − | 1.02516i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.916828i | − | 0.0396379i | ||||||
\(536\) | 9.81603 | − | 1.19848i | 0.423988 | − | 0.0517666i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.84334 | − | 0.317811i | 0.338150 | − | 0.0137018i | ||||
\(539\) | 3.49674 | 0.150615 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.6236 | 1.31661 | 0.658307 | − | 0.752750i | \(-0.271273\pi\) | ||||
0.658307 | + | 0.752750i | \(0.271273\pi\) | |||||||
\(542\) | 13.5357 | − | 0.548464i | 0.581407 | − | 0.0235585i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25.3805 | + | 5.21068i | −1.08818 | + | 0.223406i | ||||
\(545\) | − | 1.34848i | − | 0.0577624i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.4353i | − | 0.916507i | −0.888822 | − | 0.458254i | \(-0.848475\pi\) | ||
0.888822 | − | 0.458254i | \(-0.151525\pi\) | |||||||
\(548\) | −0.861813 | − | 10.6170i | −0.0368148 | − | 0.453535i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.971171 | + | 23.9678i | 0.0414109 | + | 1.02199i | ||||
\(551\) | −42.1433 | −1.79537 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0625 | 0.512948 | ||||||||
\(554\) | 1.36663 | + | 33.7273i | 0.0580625 | + | 1.43294i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.41071 | − | 17.3790i | −0.0598274 | − | 0.737035i | ||||
\(557\) | 4.24025i | 0.179665i | 0.995957 | + | 0.0898326i | \(0.0286332\pi\) | ||||
−0.995957 | + | 0.0898326i | \(0.971367\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4489i | 0.441940i | ||||||||
\(560\) | −1.52525 | + | 0.249260i | −0.0644535 | + | 0.0105332i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.3393 | + | 0.499988i | −0.520503 | + | 0.0210907i | ||||
\(563\) | −31.5890 | −1.33132 | −0.665658 | − | 0.746257i | \(-0.731849\pi\) | ||||
−0.665658 | + | 0.746257i | \(0.731849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.34417 | −0.308971 | ||||||||
\(566\) | −1.68006 | + | 0.0680757i | −0.0706181 | + | 0.00286144i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.12521 | − | 33.7870i | −0.173090 | − | 1.41767i | ||||
\(569\) | 12.1710i | 0.510234i | 0.966910 | + | 0.255117i | \(0.0821141\pi\) | ||||
−0.966910 | + | 0.255117i | \(0.917886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.04693i | − | 0.127510i | −0.997966 | − | 0.0637551i | \(-0.979692\pi\) | ||
0.997966 | − | 0.0637551i | \(-0.0203076\pi\) | |||||||
\(572\) | 37.1702 | − | 3.01722i | 1.55417 | − | 0.126156i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.254129 | − | 6.27170i | −0.0106071 | − | 0.261776i | ||||
\(575\) | 39.7842 | 1.65912 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.1633 | 1.58876 | 0.794381 | − | 0.607420i | \(-0.207796\pi\) | ||||
0.794381 | + | 0.607420i | \(0.207796\pi\) | |||||||
\(578\) | 0.227815 | + | 5.62231i | 0.00947587 | + | 0.233857i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.21343 | + | 0.423190i | −0.216476 | + | 0.0175720i | ||||
\(581\) | 11.4944i | 0.476868i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.72082i | − | 0.278348i | ||||||
\(584\) | 2.79144 | + | 22.8630i | 0.115511 | + | 0.946076i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.77938 | + | 0.315220i | −0.321363 | + | 0.0130216i | ||||
\(587\) | −21.5383 | −0.888982 | −0.444491 | − | 0.895783i | \(-0.646616\pi\) | ||||
−0.444491 | + | 0.895783i | \(0.646616\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58.9822 | 2.43032 | ||||||||
\(590\) | −3.15789 | + | 0.127957i | −0.130008 | + | 0.00526792i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.4364 | − | 2.84951i | 0.716633 | − | 0.117114i | ||||
\(593\) | 23.8264i | 0.978434i | 0.872162 | + | 0.489217i | \(0.162717\pi\) | ||||
−0.872162 | + | 0.489217i | \(0.837283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.76968i | 0.0725497i | ||||||||
\(596\) | 0.854276 | + | 10.5241i | 0.0349925 | + | 0.431085i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.50415 | − | 61.8005i | −0.102402 | − | 2.52721i | ||||
\(599\) | −17.2409 | −0.704446 | −0.352223 | − | 0.935916i | \(-0.614574\pi\) | ||||
−0.352223 | + | 0.935916i | \(0.614574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.3544 | 1.44214 | 0.721068 | − | 0.692864i | \(-0.243651\pi\) | ||||
0.721068 | + | 0.692864i | \(0.243651\pi\) | |||||||
\(602\) | 0.112194 | + | 2.76885i | 0.00457267 | + | 0.112850i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.43604 | + | 30.0105i | 0.0991212 | + | 1.22111i | ||||
\(605\) | 0.474137i | 0.0192764i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0905i | 0.653091i | 0.945181 | + | 0.326546i | \(0.105885\pi\) | ||||
−0.945181 | + | 0.326546i | \(0.894115\pi\) | |||||||
\(608\) | −34.5003 | + | 7.08299i | −1.39917 | + | 0.287253i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.65219 | − | 0.147986i | 0.147873 | − | 0.00599179i | ||||
\(611\) | 5.31312 | 0.214946 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.2454 | −1.26199 | −0.630995 | − | 0.775787i | \(-0.717353\pi\) | ||||
−0.630995 | + | 0.775787i | \(0.717353\pi\) | |||||||
\(614\) | −27.4447 | + | 1.11205i | −1.10758 | + | 0.0448789i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.81736 | − | 1.19865i | 0.395553 | − | 0.0482948i | ||||
\(617\) | − | 13.4327i | − | 0.540782i | −0.962751 | − | 0.270391i | \(-0.912847\pi\) | ||
0.962751 | − | 0.270391i | \(-0.0871529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 0.489134i | − | 0.0196599i | −0.999952 | − | 0.00982997i | \(-0.996871\pi\) | ||
0.999952 | − | 0.00982997i | \(-0.00312903\pi\) | |||||||
\(620\) | 7.29652 | − | 0.592281i | 0.293035 | − | 0.0237866i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.14331 | − | 28.2160i | −0.0458425 | − | 1.13136i | ||||
\(623\) | −0.206472 | −0.00827214 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.7831 | 0.911322 | ||||||||
\(626\) | 1.18167 | + | 29.1628i | 0.0472291 | + | 1.16558i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.3332 | − | 0.919951i | 0.452244 | − | 0.0367101i | ||||
\(629\) | − | 20.2307i | − | 0.806652i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.6454i | 0.981118i | 0.871408 | + | 0.490559i | \(0.163207\pi\) | ||||
−0.871408 | + | 0.490559i | \(0.836793\pi\) | |||||||
\(632\) | 33.8663 | − | 4.13489i | 1.34713 | − | 0.164477i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −38.7705 | + | 1.57098i | −1.53977 | + | 0.0623915i | ||||
\(635\) | 2.81673 | 0.111779 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.33247 | −0.211280 | ||||||||
\(638\) | 33.4455 | − | 1.35521i | 1.32412 | − | 0.0536532i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.19681 | + | 1.22266i | −0.165893 | + | 0.0483298i | ||||
\(641\) | 34.9422i | 1.38014i | 0.723745 | + | 0.690068i | \(0.242419\pi\) | ||||
−0.723745 | + | 0.690068i | \(0.757581\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.2972i | − | 0.642701i | −0.946960 | − | 0.321350i | \(-0.895863\pi\) | ||
0.946960 | − | 0.321350i | \(-0.104137\pi\) | |||||||
\(644\) | −1.32715 | − | 16.3496i | −0.0522971 | − | 0.644266i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.63279 | + | 40.2960i | 0.0642413 | + | 1.58543i | ||||
\(647\) | −7.61731 | −0.299467 | −0.149734 | − | 0.988726i | \(-0.547842\pi\) | ||||
−0.149734 | + | 0.988726i | \(0.547842\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.2254 | 0.793916 | ||||||||
\(650\) | −1.48102 | − | 36.5505i | −0.0580905 | − | 1.43363i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.16405 | + | 38.9791i | 0.123914 | + | 1.52654i | ||||
\(653\) | 38.8914i | 1.52194i | 0.648788 | + | 0.760969i | \(0.275276\pi\) | ||||
−0.648788 | + | 0.760969i | \(0.724724\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.09062i | 0.198907i | ||||||||
\(656\) | −2.86336 | − | 17.5212i | −0.111795 | − | 0.684087i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.40792 | − | 0.0570490i | 0.0548866 | − | 0.00222400i | ||||
\(659\) | 2.21194 | 0.0861648 | 0.0430824 | − | 0.999072i | \(-0.486282\pi\) | ||||
0.0430824 | + | 0.999072i | \(0.486282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0793 | 0.664308 | 0.332154 | − | 0.943225i | \(-0.392225\pi\) | ||||
0.332154 | + | 0.943225i | \(0.392225\pi\) | |||||||
\(662\) | −29.7233 | + | 1.20438i | −1.15523 | + | 0.0468097i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.94017 | + | 32.2715i | 0.152908 | + | 1.25238i | ||||
\(665\) | 2.40556i | 0.0932837i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 55.5163i | − | 2.14960i | ||||||
\(668\) | −12.5172 | + | 1.01606i | −0.484306 | + | 0.0393126i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.0773454 | − | 1.90883i | −0.00298811 | − | 0.0737444i | ||||
\(671\) | −23.3913 | −0.903010 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.8342 | −0.571818 | −0.285909 | − | 0.958257i | \(-0.592295\pi\) | ||||
−0.285909 | + | 0.958257i | \(0.592295\pi\) | |||||||
\(674\) | 1.13160 | + | 27.9271i | 0.0435878 | + | 1.07571i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.7693 | + | 2.49764i | −1.18343 | + | 0.0960630i | ||||
\(677\) | − | 30.8678i | − | 1.18634i | −0.805076 | − | 0.593172i | \(-0.797875\pi\) | ||
0.805076 | − | 0.593172i | \(-0.202125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.99826i | − | 0.345322i | ||||||
\(680\) | 0.606628 | + | 4.96851i | 0.0232631 | + | 0.190534i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −46.8091 | + | 1.89670i | −1.79241 | + | 0.0726283i | ||||
\(683\) | 39.6035 | 1.51539 | 0.757694 | − | 0.652611i | \(-0.226326\pi\) | ||||
0.757694 | + | 0.652611i | \(0.226326\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.05779 | −0.0786240 | ||||||||
\(686\) | −1.41305 | + | 0.0572568i | −0.0539507 | + | 0.00218607i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.26413 | + | 7.73531i | 0.0481944 | + | 0.294906i | ||||
\(689\) | 10.2492i | 0.390462i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.9714i | 1.21625i | 0.793841 | + | 0.608125i | \(0.208078\pi\) | ||||
−0.793841 | + | 0.608125i | \(0.791922\pi\) | |||||||
\(692\) | 0.990594 | + | 12.2035i | 0.0376567 | + | 0.463907i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.0155866 | + | 0.384664i | 0.000591658 | + | 0.0146017i | ||||
\(695\) | −3.36841 | −0.127771 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.3290 | −0.770018 | ||||||||
\(698\) | −0.281989 | − | 6.95927i | −0.0106734 | − | 0.263412i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.784914 | − | 9.66963i | −0.0296669 | − | 0.365478i | ||||
\(701\) | 19.3239i | 0.729852i | 0.931037 | + | 0.364926i | \(0.118906\pi\) | ||||
−0.931037 | + | 0.364926i | \(0.881094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 27.5001i | − | 1.03718i | ||||||
\(704\) | 27.1521 | − | 6.73058i | 1.02333 | − | 0.253668i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.22617 | − | 0.171244i | 0.159054 | − | 0.00644485i | ||||
\(707\) | −5.94651 | −0.223642 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0015 | −0.638503 | −0.319252 | − | 0.947670i | \(-0.603432\pi\) | ||||
−0.319252 | + | 0.947670i | \(0.603432\pi\) | |||||||
\(710\) | −6.57023 | + | 0.266225i | −0.246576 | + | 0.00999125i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.579688 | + | 0.0707767i | −0.0217247 | + | 0.00265247i | ||||
\(713\) | 77.6986i | 2.90983i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 7.20435i | − | 0.269427i | ||||||
\(716\) | 36.1020 | − | 2.93051i | 1.34919 | − | 0.109518i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.564962 | + | 13.9428i | 0.0210842 | + | 0.520342i | ||||
\(719\) | 5.89884 | 0.219990 | 0.109995 | − | 0.993932i | \(-0.464917\pi\) | ||||
0.109995 | + | 0.993932i | \(0.464917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.9130 | −0.406421 | ||||||||
\(722\) | 1.13161 | + | 27.9272i | 0.0421141 | + | 1.03934i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.2901 | + | 0.997629i | −0.456760 | + | 0.0370766i | ||||
\(725\) | − | 32.8339i | − | 1.21942i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.8081i | 0.512112i | 0.966662 | + | 0.256056i | \(0.0824232\pi\) | ||||
−0.966662 | + | 0.256056i | \(0.917577\pi\) | |||||||
\(728\) | −14.9713 | + | 1.82792i | −0.554874 | + | 0.0677471i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.44593 | − | 0.180149i | 0.164551 | − | 0.00666760i | ||||
\(731\) | 8.97494 | 0.331950 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.4952 | −1.01556 | −0.507779 | − | 0.861488i | \(-0.669533\pi\) | ||||
−0.507779 | + | 0.861488i | \(0.669533\pi\) | |||||||
\(734\) | 33.7162 | − | 1.36618i | 1.24449 | − | 0.0504265i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.33057 | − | 45.4480i | −0.343929 | − | 1.67523i | ||||
\(737\) | 12.2255i | 0.450332i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12.9652i | − | 0.476931i | −0.971151 | − | 0.238465i | \(-0.923356\pi\) | ||
0.971151 | − | 0.238465i | \(-0.0766444\pi\) | |||||||
\(740\) | −0.276147 | − | 3.40195i | −0.0101514 | − | 0.125058i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.110049 | + | 2.71593i | 0.00404003 | + | 0.0997049i | ||||
\(743\) | 16.0988 | 0.590608 | 0.295304 | − | 0.955403i | \(-0.404579\pi\) | ||||
0.295304 | + | 0.955403i | \(0.404579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.03979 | 0.0747323 | ||||||||
\(746\) | 1.63000 | + | 40.2272i | 0.0596786 | + | 1.47282i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.59161 | − | 31.9269i | −0.0947586 | − | 1.16736i | ||||
\(749\) | − | 2.37293i | − | 0.0867049i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 6.94450i | − | 0.253409i | −0.991941 | − | 0.126704i | \(-0.959560\pi\) | ||
0.991941 | − | 0.126704i | \(-0.0404399\pi\) | |||||||
\(752\) | 3.93330 | − | 0.642792i | 0.143433 | − | 0.0234402i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −51.0039 | + | 2.06667i | −1.85745 | + | 0.0752638i | ||||
\(755\) | 5.81665 | 0.211689 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.5620 | −0.601956 | −0.300978 | − | 0.953631i | \(-0.597313\pi\) | ||||
−0.300978 | + | 0.953631i | \(0.597313\pi\) | |||||||
\(758\) | −15.5641 | + | 0.630657i | −0.565315 | + | 0.0229065i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.824602 | + | 6.75380i | 0.0299115 | + | 0.244986i | ||||
\(761\) | 20.2273i | 0.733238i | 0.930371 | + | 0.366619i | \(0.119485\pi\) | ||||
−0.930371 | + | 0.366619i | \(0.880515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.49012i | − | 0.126351i | ||||||
\(764\) | −35.8485 | + | 2.90993i | −1.29695 | + | 0.105278i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.724961 | + | 17.8915i | 0.0261939 | + | 0.646446i | ||||
\(767\) | −30.8434 | −1.11369 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.2180 | 0.873322 | 0.436661 | − | 0.899626i | \(-0.356161\pi\) | ||||
0.436661 | + | 0.899626i | \(0.356161\pi\) | |||||||
\(770\) | −0.0773559 | − | 1.90908i | −0.00278771 | − | 0.0687986i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −30.9930 | + | 2.51580i | −1.11546 | + | 0.0905455i | ||||
\(773\) | − | 43.4363i | − | 1.56230i | −0.624346 | − | 0.781148i | \(-0.714635\pi\) | ||
0.624346 | − | 0.781148i | \(-0.285365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.9531i | 1.65068i | ||||||||
\(776\) | −3.08451 | − | 25.2633i | −0.110728 | − | 0.906900i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.3947 | − | 1.23159i | 1.08970 | − | 0.0441546i | ||||
\(779\) | −27.6337 | −0.990080 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.0805 | 1.50576 | ||||||||
\(782\) | −53.0828 | + | 2.15091i | −1.89824 | + | 0.0769164i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.94763 | + | 0.645134i | −0.140987 | + | 0.0230405i | ||||
\(785\) | − | 2.19661i | − | 0.0784003i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.0714i | 1.49968i | 0.661617 | + | 0.749842i | \(0.269870\pi\) | ||||
−0.661617 | + | 0.749842i | \(0.730130\pi\) | |||||||
\(788\) | 2.46591 | + | 30.3784i | 0.0878443 | + | 1.08218i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.266849 | − | 6.58564i | −0.00949408 | − | 0.234307i | ||||
\(791\) | −19.0081 | −0.675850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.6714 | 1.26673 | ||||||||
\(794\) | 0.0626459 | + | 1.54605i | 0.00222322 | + | 0.0548674i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.48643 | − | 42.9506i | −0.123573 | − | 1.52234i | ||||
\(797\) | − | 39.4905i | − | 1.39883i | −0.714718 | − | 0.699413i | \(-0.753445\pi\) | ||
0.714718 | − | 0.699413i | \(-0.246555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.56364i | − | 0.161450i | ||||||
\(800\) | −5.51836 | − | 26.8792i | −0.195103 | − | 0.950323i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.20407 | + | 0.170348i | −0.148451 | + | 0.00601521i | ||||
\(803\) | −28.4750 | −1.00486 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.16890 | −0.111689 | ||||||||
\(806\) | 71.3832 | − | 2.89244i | 2.51436 | − | 0.101882i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.6953 | + | 2.03840i | −0.587338 | + | 0.0717108i | ||||
\(809\) | − | 5.57369i | − | 0.195960i | −0.995188 | − | 0.0979802i | \(-0.968762\pi\) | ||
0.995188 | − | 0.0979802i | \(-0.0312382\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.0725i | − | 0.985757i | −0.870098 | − | 0.492879i | \(-0.835945\pi\) | ||
0.870098 | − | 0.492879i | \(-0.164055\pi\) | |||||||
\(812\) | −13.4934 | + | 1.09530i | −0.473524 | + | 0.0384374i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.884323 | + | 21.8244i | 0.0309955 | + | 0.764945i | ||||
\(815\) | 7.55495 | 0.264638 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.1998 | 0.426818 | ||||||||
\(818\) | 1.14165 | + | 28.1750i | 0.0399167 | + | 0.985115i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.41849 | + | 0.277489i | −0.119379 | + | 0.00969034i | ||||
\(821\) | − | 55.1825i | − | 1.92588i | −0.269709 | − | 0.962942i | \(-0.586928\pi\) | ||
0.269709 | − | 0.962942i | \(-0.413072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0505i | 0.350340i | 0.984538 | + | 0.175170i | \(0.0560475\pi\) | ||||
−0.984538 | + | 0.175170i | \(0.943953\pi\) | |||||||
\(824\) | −30.6390 | + | 3.74086i | −1.06736 | + | 0.130319i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.17322 | + | 0.331178i | −0.284383 | + | 0.0115232i | ||||
\(827\) | −1.70986 | −0.0594577 | −0.0297288 | − | 0.999558i | \(-0.509464\pi\) | ||||
−0.0297288 | + | 0.999558i | \(0.509464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.6507 | 1.20347 | 0.601734 | − | 0.798697i | \(-0.294477\pi\) | ||||
0.601734 | + | 0.798697i | \(0.294477\pi\) | |||||||
\(830\) | 6.27551 | − | 0.254283i | 0.217826 | − | 0.00882629i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −41.4066 | + | 10.2640i | −1.43552 | + | 0.355842i | ||||
\(833\) | 4.58027i | 0.158697i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.42609i | 0.0839584i | ||||||||
\(836\) | −3.52283 | − | 43.3990i | −0.121840 | − | 1.50098i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.57483 | − | 38.8655i | −0.0544015 | − | 1.34259i | ||||
\(839\) | 28.4935 | 0.983707 | 0.491853 | − | 0.870678i | \(-0.336320\pi\) | ||||
0.491853 | + | 0.870678i | \(0.336320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.8176 | −0.579917 | ||||||||
\(842\) | −0.768494 | − | 18.9658i | −0.0264840 | − | 0.653606i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.63712 | − | 20.1682i | −0.0563519 | − | 0.694220i | ||||
\(845\) | 5.96372i | 0.205158i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.22716i | 0.0421656i | ||||||||
\(848\) | 1.23996 | + | 7.58746i | 0.0425806 | + | 0.260554i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −31.3946 | + | 1.27211i | −1.07683 | + | 0.0436329i | ||||
\(851\) | 36.2264 | 1.24183 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.2012 | 0.862874 | 0.431437 | − | 0.902143i | \(-0.358007\pi\) | ||||
0.431437 | + | 0.902143i | \(0.358007\pi\) | |||||||
\(854\) | 9.45257 | − | 0.383017i | 0.323460 | − | 0.0131066i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.813416 | − | 6.66218i | −0.0278020 | − | 0.227709i | ||||
\(857\) | 40.0177i | 1.36698i | 0.729961 | + | 0.683489i | \(0.239538\pi\) | ||||
−0.729961 | + | 0.683489i | \(0.760462\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.4904i | 0.733242i | 0.930370 | + | 0.366621i | \(0.119485\pi\) | ||||
−0.930370 | + | 0.366621i | \(0.880515\pi\) | |||||||
\(860\) | 1.50921 | − | 0.122507i | 0.0514635 | − | 0.00417745i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.310608 | + | 7.66558i | 0.0105794 | + | 0.261091i | ||||
\(863\) | 34.6137 | 1.17827 | 0.589133 | − | 0.808036i | \(-0.299470\pi\) | ||||
0.589133 | + | 0.808036i | \(0.299470\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.36528 | 0.0804221 | ||||||||
\(866\) | 1.96232 | + | 48.4286i | 0.0666825 | + | 1.64567i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.8848 | − | 1.53294i | 0.640992 | − | 0.0520313i | ||||
\(869\) | 42.1792i | 1.43083i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 18.6437i | − | 0.631718i | ||||||
\(872\) | −1.19638 | − | 9.79878i | −0.0405145 | − | 0.331829i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −72.1566 | + | 2.92378i | −2.44073 | + | 0.0988982i | ||||
\(875\) | −3.80602 | −0.128667 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.62230 | 0.257387 | 0.128693 | − | 0.991684i | \(-0.458922\pi\) | ||||
0.128693 | + | 0.991684i | \(0.458922\pi\) | |||||||
\(878\) | −5.48008 | + | 0.222052i | −0.184944 | + | 0.00749390i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.871598 | − | 5.33339i | −0.0293816 | − | 0.179788i | ||||
\(881\) | 32.5174i | 1.09554i | 0.836629 | + | 0.547769i | \(0.184523\pi\) | ||||
−0.836629 | + | 0.547769i | \(0.815477\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16.9931i | − | 0.571864i | −0.958250 | − | 0.285932i | \(-0.907697\pi\) | ||
0.958250 | − | 0.285932i | \(-0.0923032\pi\) | |||||||
\(884\) | 3.95216 | + | 48.6881i | 0.132926 | + | 1.63756i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.543334 | + | 13.4091i | 0.0182536 | + | 0.450486i | ||||
\(887\) | −12.9685 | −0.435439 | −0.217719 | − | 0.976011i | \(-0.569862\pi\) | ||||
−0.217719 | + | 0.976011i | \(0.569862\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.29024 | 0.244507 | ||||||||
\(890\) | 0.00456765 | + | 0.112726i | 0.000153108 | + | 0.00377859i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.777675 | + | 9.58045i | 0.0260385 | + | 0.320777i | ||||
\(893\) | − | 6.20345i | − | 0.207591i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.99730i | − | 0.233894i | ||||||
\(896\) | −10.8621 | + | 3.16447i | −0.362879 | + | 0.105718i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.8112 | − | 1.04587i | 0.861331 | − | 0.0349010i | ||||
\(899\) | 64.1246 | 2.13867 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.80340 | 0.293284 | ||||||||
\(902\) | 21.9305 | − | 0.888620i | 0.730205 | − | 0.0295878i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −53.3667 | + | 6.51579i | −1.77495 | + | 0.216712i | ||||
\(905\) | 2.38208i | 0.0791831i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.6698i | 0.586718i | 0.956002 | + | 0.293359i | \(0.0947731\pi\) | ||||
−0.956002 | + | 0.293359i | \(0.905227\pi\) | |||||||
\(908\) | −5.24176 | + | 0.425490i | −0.173954 | + | 0.0141204i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.117967 | + | 2.91133i | 0.00391056 | + | 0.0965095i | ||||
\(911\) | 30.2405 | 1.00191 | 0.500957 | − | 0.865472i | \(-0.332982\pi\) | ||||
0.500957 | + | 0.865472i | \(0.332982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.1929 | −1.33019 | ||||||||
\(914\) | 0.207510 | + | 5.12118i | 0.00686381 | + | 0.169394i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.0507 | − | 1.78993i | 0.728577 | − | 0.0591408i | ||||
\(917\) | 13.1755i | 0.435093i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 17.1414i | − | 0.565441i | −0.959202 | − | 0.282721i | \(-0.908763\pi\) | ||
0.959202 | − | 0.282721i | \(-0.0912370\pi\) | |||||||
\(920\) | −8.89692 | + | 1.08627i | −0.293323 | + | 0.0358131i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.4687 | − | 0.545750i | 0.443568 | − | 0.0179733i | ||||
\(923\) | −64.1722 | −2.11225 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.4253 | 0.704460 | ||||||||
\(926\) | −59.2729 | + | 2.40173i | −1.94783 | + | 0.0789258i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −37.5082 | + | 7.70052i | −1.23127 | + | 0.252782i | ||||
\(929\) | − | 19.9342i | − | 0.654021i | −0.945021 | − | 0.327011i | \(-0.893959\pi\) | ||
0.945021 | − | 0.327011i | \(-0.106041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.22605i | 0.204051i | ||||||||
\(932\) | −3.36787 | − | 41.4901i | −0.110318 | − | 1.35905i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.459456 | − | 11.3390i | −0.0150339 | − | 0.371024i | ||||
\(935\) | −6.18810 | −0.202372 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.1107 | 0.330303 | 0.165152 | − | 0.986268i | \(-0.447189\pi\) | ||||
0.165152 | + | 0.986268i | \(0.447189\pi\) | |||||||
\(938\) | −0.200185 | − | 4.94041i | −0.00653626 | − | 0.161310i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0622931 | − | 0.767411i | −0.00203178 | − | 0.0250302i | ||||
\(941\) | 40.1540i | 1.30898i | 0.756069 | + | 0.654492i | \(0.227117\pi\) | ||||
−0.756069 | + | 0.654492i | \(0.772883\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 36.4025i | − | 1.18543i | ||||||
\(944\) | −22.8334 | + | 3.73150i | −0.743165 | + | 0.121450i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.68194 | + | 0.392311i | −0.314787 | + | 0.0127551i | ||||
\(947\) | −28.7212 | −0.933312 | −0.466656 | − | 0.884439i | \(-0.654541\pi\) | ||||
−0.466656 | + | 0.884439i | \(0.654541\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.4239 | 1.40960 | ||||||||
\(950\) | −42.6754 | + | 1.72920i | −1.38457 | + | 0.0561027i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.57007 | + | 12.8595i | 0.0508862 | + | 0.416777i | ||||
\(953\) | 3.42678i | 0.111004i | 0.998459 | + | 0.0555022i | \(0.0176760\pi\) | ||||
−0.998459 | + | 0.0555022i | \(0.982324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.94818i | 0.224838i | ||||||||
\(956\) | 52.6748 | − | 4.27578i | 1.70363 | − | 0.138288i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.983156 | + | 24.2635i | 0.0317643 | + | 0.783920i | ||||
\(959\) | −5.32595 | −0.171984 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −58.7464 | −1.89504 | ||||||||
\(962\) | −1.34858 | − | 33.2819i | −0.0434799 | − | 1.07305i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 42.7202 | − | 3.46773i | 1.37593 | − | 0.111688i | ||||
\(965\) | 6.00708i | 0.193375i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.4049i | 1.00991i | 0.863145 | + | 0.504956i | \(0.168491\pi\) | ||||
−0.863145 | + | 0.504956i | \(0.831509\pi\) | |||||||
\(968\) | 0.420657 | + | 3.44534i | 0.0135204 | + | 0.110737i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.91271 | + | 0.199062i | −0.157738 | + | 0.00639151i | ||||
\(971\) | −20.9930 | −0.673696 | −0.336848 | − | 0.941559i | \(-0.609361\pi\) | ||||
−0.336848 | + | 0.941559i | \(0.609361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.71810 | −0.279489 | ||||||||
\(974\) | 44.6192 | − | 1.80797i | 1.42969 | − | 0.0579309i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.4075 | − | 4.31560i | 0.845284 | − | 0.138139i | ||||
\(977\) | − | 1.40360i | − | 0.0449052i | −0.999748 | − | 0.0224526i | \(-0.992853\pi\) | ||
0.999748 | − | 0.0224526i | \(-0.00714748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.721979i | − | 0.0230746i | ||||||
\(980\) | 0.0625201 | + | 0.770207i | 0.00199713 | + | 0.0246034i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.920586 | − | 22.7194i | −0.0293771 | − | 0.725004i | ||||
\(983\) | 8.34663 | 0.266216 | 0.133108 | − | 0.991102i | \(-0.457504\pi\) | ||||
0.133108 | + | 0.991102i | \(0.457504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.88795 | 0.187606 | ||||||||
\(986\) | 1.77515 | + | 43.8092i | 0.0565321 | + | 1.39517i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.37226 | + | 66.1828i | 0.170914 | + | 2.10556i | ||||
\(989\) | 16.0711i | 0.511031i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.5476i | 0.335056i | 0.985867 | + | 0.167528i | \(0.0535785\pi\) | ||||
−0.985867 | + | 0.167528i | \(0.946421\pi\) | |||||||
\(992\) | 52.4951 | − | 10.7774i | 1.66672 | − | 0.342182i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.0050 | + | 0.689041i | −0.539366 | + | 0.0218551i | ||||
\(995\) | −8.32470 | −0.263911 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.14520 | 0.0362688 | 0.0181344 | − | 0.999836i | \(-0.494227\pi\) | ||||
0.0181344 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(998\) | −23.5126 | + | 0.952728i | −0.744279 | + | 0.0301581i | ||||
\(999\) | 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 | 756.2.e.b.323.11 | ✓ | 24 | |
3.2 | odd | 2 | inner | 756.2.e.b.323.14 | yes | 24 | |
4.3 | odd | 2 | inner | 756.2.e.b.323.13 | yes | 24 | |
12.11 | even | 2 | inner | 756.2.e.b.323.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.e.b.323.11 | ✓ | 24 | 1.1 | even | 1 | trivial | |
756.2.e.b.323.12 | yes | 24 | 12.11 | even | 2 | inner | |
756.2.e.b.323.13 | yes | 24 | 4.3 | odd | 2 | inner | |
756.2.e.b.323.14 | yes | 24 | 3.2 | odd | 2 | inner |