Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(229,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.f (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.10 | ||
Character | \(\chi\) | \(=\) | 690.229 |
Dual form | 690.3.f.a.229.12 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 4.91938 | − | 0.894267i | 0.983876 | − | 0.178853i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −6.65471 | −0.950673 | −0.475336 | − | 0.879804i | \(-0.657674\pi\) | ||||
−0.475336 | + | 0.879804i | \(0.657674\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −1.26468 | − | 6.95705i | −0.126468 | − | 0.695705i | ||||
\(11\) | − | 10.9802i | − | 0.998199i | −0.866545 | − | 0.499100i | \(-0.833664\pi\) | ||
0.866545 | − | 0.499100i | \(-0.166336\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 2.68725i | 0.206711i | 0.994644 | + | 0.103356i | \(0.0329580\pi\) | ||||
−0.994644 | + | 0.103356i | \(0.967042\pi\) | |||||||
\(14\) | 9.41118i | 0.672227i | ||||||||
\(15\) | −1.54892 | − | 8.52061i | −0.103261 | − | 0.568041i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −26.7003 | −1.57061 | −0.785304 | − | 0.619111i | \(-0.787493\pi\) | ||||
−0.785304 | + | 0.619111i | \(0.787493\pi\) | |||||||
\(18\) | 4.24264i | 0.235702i | ||||||||
\(19\) | 21.8613i | 1.15059i | 0.817944 | + | 0.575297i | \(0.195114\pi\) | ||||
−0.817944 | + | 0.575297i | \(0.804886\pi\) | |||||||
\(20\) | −9.83876 | + | 1.78853i | −0.491938 | + | 0.0894267i | ||||
\(21\) | 11.5263i | 0.548871i | ||||||||
\(22\) | −15.5283 | −0.705833 | ||||||||
\(23\) | −7.63499 | − | 21.6958i | −0.331956 | − | 0.943295i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | 23.4006 | − | 8.79847i | 0.936023 | − | 0.351939i | ||||
\(26\) | 3.80034 | 0.146167 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 13.3094 | 0.475336 | ||||||||
\(29\) | −24.5688 | −0.847202 | −0.423601 | − | 0.905849i | \(-0.639234\pi\) | ||||
−0.423601 | + | 0.905849i | \(0.639234\pi\) | |||||||
\(30\) | −12.0500 | + | 2.19050i | −0.401666 | + | 0.0730166i | ||||
\(31\) | 19.2480 | 0.620902 | 0.310451 | − | 0.950589i | \(-0.399520\pi\) | ||||
0.310451 | + | 0.950589i | \(0.399520\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | −19.0182 | −0.576310 | ||||||||
\(34\) | 37.7600i | 1.11059i | ||||||||
\(35\) | −32.7370 | + | 5.95108i | −0.935344 | + | 0.170031i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −22.7782 | −0.615627 | −0.307814 | − | 0.951447i | \(-0.599597\pi\) | ||||
−0.307814 | + | 0.951447i | \(0.599597\pi\) | |||||||
\(38\) | 30.9165 | 0.813593 | ||||||||
\(39\) | 4.65445 | 0.119345 | ||||||||
\(40\) | 2.52937 | + | 13.9141i | 0.0632342 | + | 0.347853i | ||||
\(41\) | −66.8030 | −1.62934 | −0.814671 | − | 0.579924i | \(-0.803082\pi\) | ||||
−0.814671 | + | 0.579924i | \(0.803082\pi\) | |||||||
\(42\) | 16.3006 | 0.388110 | ||||||||
\(43\) | −41.3259 | −0.961067 | −0.480534 | − | 0.876976i | \(-0.659557\pi\) | ||||
−0.480534 | + | 0.876976i | \(0.659557\pi\) | |||||||
\(44\) | 21.9604i | 0.499100i | ||||||||
\(45\) | −14.7581 | + | 2.68280i | −0.327959 | + | 0.0596178i | ||||
\(46\) | −30.6825 | + | 10.7975i | −0.667010 | + | 0.234728i | ||||
\(47\) | 3.50098i | 0.0744889i | 0.999306 | + | 0.0372445i | \(0.0118580\pi\) | ||||
−0.999306 | + | 0.0372445i | \(0.988142\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | −4.71486 | −0.0962216 | ||||||||
\(50\) | −12.4429 | − | 33.0934i | −0.248858 | − | 0.661868i | ||||
\(51\) | 46.2463i | 0.906791i | ||||||||
\(52\) | − | 5.37449i | − | 0.103356i | ||||||
\(53\) | −18.9181 | −0.356946 | −0.178473 | − | 0.983945i | \(-0.557116\pi\) | ||||
−0.178473 | + | 0.983945i | \(0.557116\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | −9.81922 | − | 54.0157i | −0.178531 | − | 0.982104i | ||||
\(56\) | − | 18.8224i | − | 0.336114i | ||||||
\(57\) | 37.8649 | 0.664296 | ||||||||
\(58\) | 34.7456i | 0.599062i | ||||||||
\(59\) | 62.7409 | 1.06341 | 0.531703 | − | 0.846931i | \(-0.321552\pi\) | ||||
0.531703 | + | 0.846931i | \(0.321552\pi\) | |||||||
\(60\) | 3.09783 | + | 17.0412i | 0.0516305 | + | 0.284020i | ||||
\(61\) | 77.7774i | 1.27504i | 0.770434 | + | 0.637520i | \(0.220040\pi\) | ||||
−0.770434 | + | 0.637520i | \(0.779960\pi\) | |||||||
\(62\) | − | 27.2207i | − | 0.439044i | ||||||
\(63\) | 19.9641 | 0.316891 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 2.40311 | + | 13.2196i | 0.0369710 | + | 0.203378i | ||||
\(66\) | 26.8959i | 0.407513i | ||||||||
\(67\) | 7.04561 | 0.105158 | 0.0525791 | − | 0.998617i | \(-0.483256\pi\) | ||||
0.0525791 | + | 0.998617i | \(0.483256\pi\) | |||||||
\(68\) | 53.4007 | 0.785304 | ||||||||
\(69\) | −37.5782 | + | 13.2242i | −0.544612 | + | 0.191655i | ||||
\(70\) | 8.41610 | + | 46.2972i | 0.120230 | + | 0.661388i | ||||
\(71\) | 104.609 | 1.47337 | 0.736685 | − | 0.676236i | \(-0.236390\pi\) | ||||
0.736685 | + | 0.676236i | \(0.236390\pi\) | |||||||
\(72\) | − | 8.48528i | − | 0.117851i | ||||||
\(73\) | − | 111.643i | − | 1.52935i | −0.644414 | − | 0.764677i | \(-0.722899\pi\) | ||
0.644414 | − | 0.764677i | \(-0.277101\pi\) | |||||||
\(74\) | 32.2132i | 0.435314i | ||||||||
\(75\) | −15.2394 | − | 40.5310i | −0.203192 | − | 0.540413i | ||||
\(76\) | − | 43.7226i | − | 0.575297i | ||||||
\(77\) | 73.0700i | 0.948960i | ||||||||
\(78\) | − | 6.58238i | − | 0.0843895i | ||||||
\(79\) | 111.861i | 1.41596i | 0.706232 | + | 0.707980i | \(0.250393\pi\) | ||||
−0.706232 | + | 0.707980i | \(0.749607\pi\) | |||||||
\(80\) | 19.6775 | − | 3.57707i | 0.245969 | − | 0.0447133i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 94.4737i | 1.15212i | ||||||||
\(83\) | 13.4125 | 0.161596 | 0.0807982 | − | 0.996730i | \(-0.474253\pi\) | ||||
0.0807982 | + | 0.996730i | \(0.474253\pi\) | |||||||
\(84\) | − | 23.0526i | − | 0.274436i | ||||||
\(85\) | −131.349 | + | 23.8772i | −1.54528 | + | 0.280908i | ||||
\(86\) | 58.4436i | 0.679577i | ||||||||
\(87\) | 42.5545i | 0.489132i | ||||||||
\(88\) | 31.0567 | 0.352917 | ||||||||
\(89\) | − | 55.4626i | − | 0.623175i | −0.950217 | − | 0.311588i | \(-0.899139\pi\) | ||
0.950217 | − | 0.311588i | \(-0.100861\pi\) | |||||||
\(90\) | 3.79405 | + | 20.8712i | 0.0421561 | + | 0.231902i | ||||
\(91\) | − | 17.8828i | − | 0.196515i | ||||||
\(92\) | 15.2700 | + | 43.3916i | 0.165978 | + | 0.471647i | ||||
\(93\) | − | 33.3385i | − | 0.358478i | ||||||
\(94\) | 4.95113 | 0.0526716 | ||||||||
\(95\) | 19.5498 | + | 107.544i | 0.205788 | + | 1.13204i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −61.5740 | −0.634783 | −0.317392 | − | 0.948295i | \(-0.602807\pi\) | ||||
−0.317392 | + | 0.948295i | \(0.602807\pi\) | |||||||
\(98\) | 6.66782i | 0.0680389i | ||||||||
\(99\) | 32.9406i | 0.332733i | ||||||||
\(100\) | −46.8011 | + | 17.5969i | −0.468011 | + | 0.175969i | ||||
\(101\) | −56.2343 | −0.556776 | −0.278388 | − | 0.960469i | \(-0.589800\pi\) | ||||
−0.278388 | + | 0.960469i | \(0.589800\pi\) | |||||||
\(102\) | 65.4022 | 0.641198 | ||||||||
\(103\) | −127.954 | −1.24227 | −0.621136 | − | 0.783702i | \(-0.713329\pi\) | ||||
−0.621136 | + | 0.783702i | \(0.713329\pi\) | |||||||
\(104\) | −7.60068 | −0.0730834 | ||||||||
\(105\) | 10.3076 | + | 56.7022i | 0.0981674 | + | 0.540021i | ||||
\(106\) | 26.7543i | 0.252399i | ||||||||
\(107\) | 60.7658 | 0.567905 | 0.283952 | − | 0.958838i | \(-0.408354\pi\) | ||||
0.283952 | + | 0.958838i | \(0.408354\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | 14.0645i | 0.129032i | 0.997917 | + | 0.0645162i | \(0.0205504\pi\) | ||||
−0.997917 | + | 0.0645162i | \(0.979450\pi\) | |||||||
\(110\) | −76.3897 | + | 13.8865i | −0.694452 | + | 0.126241i | ||||
\(111\) | 39.4530i | 0.355432i | ||||||||
\(112\) | −26.6188 | −0.237668 | ||||||||
\(113\) | −1.76140 | −0.0155876 | −0.00779382 | − | 0.999970i | \(-0.502481\pi\) | ||||
−0.00779382 | + | 0.999970i | \(0.502481\pi\) | |||||||
\(114\) | − | 53.5490i | − | 0.469728i | ||||||
\(115\) | −56.9612 | − | 99.9021i | −0.495315 | − | 0.868714i | ||||
\(116\) | 49.1377 | 0.423601 | ||||||||
\(117\) | − | 8.06174i | − | 0.0689037i | ||||||
\(118\) | − | 88.7291i | − | 0.751941i | ||||||
\(119\) | 177.683 | 1.49313 | ||||||||
\(120\) | 24.0999 | − | 4.38099i | 0.200833 | − | 0.0365083i | ||||
\(121\) | 0.435445 | 0.00359872 | ||||||||
\(122\) | 109.994 | 0.901589 | ||||||||
\(123\) | 115.706i | 0.940701i | ||||||||
\(124\) | −38.4959 | −0.310451 | ||||||||
\(125\) | 107.248 | − | 64.2094i | 0.857985 | − | 0.513675i | ||||
\(126\) | − | 28.2335i | − | 0.224076i | ||||||
\(127\) | 60.2924i | 0.474743i | 0.971419 | + | 0.237371i | \(0.0762859\pi\) | ||||
−0.971419 | + | 0.237371i | \(0.923714\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 71.5785i | 0.554872i | ||||||||
\(130\) | 18.6953 | − | 3.39852i | 0.143810 | − | 0.0261424i | ||||
\(131\) | −18.3256 | −0.139890 | −0.0699449 | − | 0.997551i | \(-0.522282\pi\) | ||||
−0.0699449 | + | 0.997551i | \(0.522282\pi\) | |||||||
\(132\) | 38.0365 | 0.288155 | ||||||||
\(133\) | − | 145.481i | − | 1.09384i | ||||||
\(134\) | − | 9.96399i | − | 0.0743581i | ||||||
\(135\) | 4.64675 | + | 25.5618i | 0.0344203 | + | 0.189347i | ||||
\(136\) | − | 75.5199i | − | 0.555294i | ||||||
\(137\) | −134.685 | −0.983105 | −0.491552 | − | 0.870848i | \(-0.663570\pi\) | ||||
−0.491552 | + | 0.870848i | \(0.663570\pi\) | |||||||
\(138\) | 18.7018 | + | 53.1436i | 0.135520 | + | 0.385099i | ||||
\(139\) | −184.379 | −1.32647 | −0.663233 | − | 0.748413i | \(-0.730816\pi\) | ||||
−0.663233 | + | 0.748413i | \(0.730816\pi\) | |||||||
\(140\) | 65.4741 | − | 11.9022i | 0.467672 | − | 0.0850155i | ||||
\(141\) | 6.06388 | 0.0430062 | ||||||||
\(142\) | − | 147.940i | − | 1.04183i | ||||||
\(143\) | 29.5065 | 0.206339 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | −120.863 | + | 21.9711i | −0.833541 | + | 0.151525i | ||||
\(146\) | −157.887 | −1.08142 | ||||||||
\(147\) | 8.16637i | 0.0555536i | ||||||||
\(148\) | 45.5564 | 0.307814 | ||||||||
\(149\) | − | 124.082i | − | 0.832766i | −0.909189 | − | 0.416383i | \(-0.863298\pi\) | ||
0.909189 | − | 0.416383i | \(-0.136702\pi\) | |||||||
\(150\) | −57.3195 | + | 21.5518i | −0.382130 | + | 0.143678i | ||||
\(151\) | 295.727 | 1.95846 | 0.979229 | − | 0.202759i | \(-0.0649907\pi\) | ||||
0.979229 | + | 0.202759i | \(0.0649907\pi\) | |||||||
\(152\) | −61.8331 | −0.406797 | ||||||||
\(153\) | 80.1010 | 0.523536 | ||||||||
\(154\) | 103.337 | 0.671016 | ||||||||
\(155\) | 94.6880 | − | 17.2128i | 0.610891 | − | 0.111050i | ||||
\(156\) | −9.30889 | −0.0596724 | ||||||||
\(157\) | −235.853 | −1.50225 | −0.751125 | − | 0.660160i | \(-0.770489\pi\) | ||||
−0.751125 | + | 0.660160i | \(0.770489\pi\) | |||||||
\(158\) | 158.195 | 1.00124 | ||||||||
\(159\) | 32.7672i | 0.206083i | ||||||||
\(160\) | −5.05874 | − | 27.8282i | −0.0316171 | − | 0.173926i | ||||
\(161\) | 50.8086 | + | 144.379i | 0.315581 | + | 0.896765i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | − | 241.368i | − | 1.48079i | −0.672174 | − | 0.740393i | \(-0.734639\pi\) | ||
0.672174 | − | 0.740393i | \(-0.265361\pi\) | |||||||
\(164\) | 133.606 | 0.814671 | ||||||||
\(165\) | −93.5580 | + | 17.0074i | −0.567018 | + | 0.103075i | ||||
\(166\) | − | 18.9681i | − | 0.114266i | ||||||
\(167\) | − | 108.519i | − | 0.649816i | −0.945746 | − | 0.324908i | \(-0.894667\pi\) | ||
0.945746 | − | 0.324908i | \(-0.105333\pi\) | |||||||
\(168\) | −32.6013 | −0.194055 | ||||||||
\(169\) | 161.779 | 0.957270 | ||||||||
\(170\) | 33.7675 | + | 185.756i | 0.198632 | + | 1.09268i | ||||
\(171\) | − | 65.5839i | − | 0.383532i | ||||||
\(172\) | 82.6518 | 0.480534 | ||||||||
\(173\) | − | 275.166i | − | 1.59055i | −0.606247 | − | 0.795276i | \(-0.707326\pi\) | ||
0.606247 | − | 0.795276i | \(-0.292674\pi\) | |||||||
\(174\) | 60.1811 | 0.345869 | ||||||||
\(175\) | −155.724 | + | 58.5513i | −0.889851 | + | 0.334579i | ||||
\(176\) | − | 43.9208i | − | 0.249550i | ||||||
\(177\) | − | 108.670i | − | 0.613957i | ||||||
\(178\) | −78.4360 | −0.440652 | ||||||||
\(179\) | 90.2015 | 0.503919 | 0.251959 | − | 0.967738i | \(-0.418925\pi\) | ||||
0.251959 | + | 0.967738i | \(0.418925\pi\) | |||||||
\(180\) | 29.5163 | − | 5.36560i | 0.163979 | − | 0.0298089i | ||||
\(181\) | − | 50.3982i | − | 0.278443i | −0.990261 | − | 0.139222i | \(-0.955540\pi\) | ||
0.990261 | − | 0.139222i | \(-0.0444600\pi\) | |||||||
\(182\) | −25.2901 | −0.138957 | ||||||||
\(183\) | 134.714 | 0.736144 | ||||||||
\(184\) | 61.3649 | − | 21.5950i | 0.333505 | − | 0.117364i | ||||
\(185\) | −112.055 | + | 20.3698i | −0.605700 | + | 0.110107i | ||||
\(186\) | −47.1477 | −0.253482 | ||||||||
\(187\) | 293.175i | 1.56778i | ||||||||
\(188\) | − | 7.00196i | − | 0.0372445i | ||||||
\(189\) | − | 34.5789i | − | 0.182957i | ||||||
\(190\) | 152.090 | − | 27.6476i | 0.800475 | − | 0.145514i | ||||
\(191\) | − | 326.515i | − | 1.70950i | −0.519039 | − | 0.854750i | \(-0.673710\pi\) | ||
0.519039 | − | 0.854750i | \(-0.326290\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | − | 96.3354i | − | 0.499147i | −0.968356 | − | 0.249574i | \(-0.919710\pi\) | ||
0.968356 | − | 0.249574i | \(-0.0802905\pi\) | |||||||
\(194\) | 87.0788i | 0.448860i | ||||||||
\(195\) | 22.8970 | − | 4.16231i | 0.117420 | − | 0.0213452i | ||||
\(196\) | 9.42972 | 0.0481108 | ||||||||
\(197\) | − | 3.71172i | − | 0.0188412i | −0.999956 | − | 0.00942062i | \(-0.997001\pi\) | ||
0.999956 | − | 0.00942062i | \(-0.00299872\pi\) | |||||||
\(198\) | 46.5850 | 0.235278 | ||||||||
\(199\) | − | 291.255i | − | 1.46359i | −0.681524 | − | 0.731796i | \(-0.738683\pi\) | ||
0.681524 | − | 0.731796i | \(-0.261317\pi\) | |||||||
\(200\) | 24.8858 | + | 66.1868i | 0.124429 | + | 0.330934i | ||||
\(201\) | − | 12.2033i | − | 0.0607132i | ||||||
\(202\) | 79.5274i | 0.393700i | ||||||||
\(203\) | 163.498 | 0.805411 | ||||||||
\(204\) | − | 92.4927i | − | 0.453395i | ||||||
\(205\) | −328.629 | + | 59.7397i | −1.60307 | + | 0.291413i | ||||
\(206\) | 180.954i | 0.878420i | ||||||||
\(207\) | 22.9050 | + | 65.0873i | 0.110652 | + | 0.314432i | ||||
\(208\) | 10.7490i | 0.0516778i | ||||||||
\(209\) | 240.041 | 1.14852 | ||||||||
\(210\) | 80.1890 | − | 14.5771i | 0.381852 | − | 0.0694148i | ||||
\(211\) | −302.726 | −1.43472 | −0.717361 | − | 0.696702i | \(-0.754650\pi\) | ||||
−0.717361 | + | 0.696702i | \(0.754650\pi\) | |||||||
\(212\) | 37.8363 | 0.178473 | ||||||||
\(213\) | − | 181.189i | − | 0.850650i | ||||||
\(214\) | − | 85.9358i | − | 0.401569i | ||||||
\(215\) | −203.298 | + | 36.9564i | −0.945571 | + | 0.171890i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −128.090 | −0.590275 | ||||||||
\(218\) | 19.8903 | 0.0912397 | ||||||||
\(219\) | −193.371 | −0.882973 | ||||||||
\(220\) | 19.6384 | + | 108.031i | 0.0892656 | + | 0.491052i | ||||
\(221\) | − | 71.7503i | − | 0.324662i | ||||||
\(222\) | 55.7950 | 0.251329 | ||||||||
\(223\) | − | 92.7845i | − | 0.416074i | −0.978121 | − | 0.208037i | \(-0.933293\pi\) | ||
0.978121 | − | 0.208037i | \(-0.0667074\pi\) | |||||||
\(224\) | 37.6447i | 0.168057i | ||||||||
\(225\) | −70.2017 | + | 26.3954i | −0.312008 | + | 0.117313i | ||||
\(226\) | 2.49100i | 0.0110221i | ||||||||
\(227\) | −142.941 | −0.629695 | −0.314848 | − | 0.949142i | \(-0.601953\pi\) | ||||
−0.314848 | + | 0.949142i | \(0.601953\pi\) | |||||||
\(228\) | −75.7298 | −0.332148 | ||||||||
\(229\) | − | 350.149i | − | 1.52904i | −0.644603 | − | 0.764518i | \(-0.722977\pi\) | ||
0.644603 | − | 0.764518i | \(-0.277023\pi\) | |||||||
\(230\) | −141.283 | + | 80.5553i | −0.614273 | + | 0.350241i | ||||
\(231\) | 126.561 | 0.547883 | ||||||||
\(232\) | − | 69.4912i | − | 0.299531i | ||||||
\(233\) | 67.8477i | 0.291192i | 0.989344 | + | 0.145596i | \(0.0465099\pi\) | ||||
−0.989344 | + | 0.145596i | \(0.953490\pi\) | |||||||
\(234\) | −11.4010 | −0.0487223 | ||||||||
\(235\) | 3.13081 | + | 17.2226i | 0.0133226 | + | 0.0732879i | ||||
\(236\) | −125.482 | −0.531703 | ||||||||
\(237\) | 193.749 | 0.817505 | ||||||||
\(238\) | − | 251.282i | − | 1.05580i | ||||||
\(239\) | −334.991 | −1.40164 | −0.700818 | − | 0.713340i | \(-0.747182\pi\) | ||||
−0.700818 | + | 0.713340i | \(0.747182\pi\) | |||||||
\(240\) | −6.19566 | − | 34.0825i | −0.0258153 | − | 0.142010i | ||||
\(241\) | 53.0754i | 0.220230i | 0.993919 | + | 0.110115i | \(0.0351219\pi\) | ||||
−0.993919 | + | 0.110115i | \(0.964878\pi\) | |||||||
\(242\) | − | 0.615812i | − | 0.00254468i | ||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | − | 155.555i | − | 0.637520i | ||||||
\(245\) | −23.1942 | + | 4.21634i | −0.0946701 | + | 0.0172095i | ||||
\(246\) | 163.633 | 0.665176 | ||||||||
\(247\) | −58.7467 | −0.237841 | ||||||||
\(248\) | 54.4415i | 0.219522i | ||||||||
\(249\) | − | 23.2311i | − | 0.0932977i | ||||||
\(250\) | −90.8058 | − | 151.672i | −0.363223 | − | 0.606687i | ||||
\(251\) | − | 287.306i | − | 1.14464i | −0.820029 | − | 0.572322i | \(-0.806043\pi\) | ||
0.820029 | − | 0.572322i | \(-0.193957\pi\) | |||||||
\(252\) | −39.9282 | −0.158445 | ||||||||
\(253\) | −238.224 | + | 83.8336i | −0.941596 | + | 0.331358i | ||||
\(254\) | 85.2663 | 0.335694 | ||||||||
\(255\) | 41.3565 | + | 227.503i | 0.162183 | + | 0.892169i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 304.797i | 1.18598i | 0.805210 | + | 0.592990i | \(0.202053\pi\) | ||||
−0.805210 | + | 0.592990i | \(0.797947\pi\) | |||||||
\(258\) | 101.227 | 0.392354 | ||||||||
\(259\) | 151.582 | 0.585260 | ||||||||
\(260\) | −4.80623 | − | 26.4392i | −0.0184855 | − | 0.101689i | ||||
\(261\) | 73.7065 | 0.282401 | ||||||||
\(262\) | 25.9163i | 0.0989171i | ||||||||
\(263\) | 167.430 | 0.636617 | 0.318308 | − | 0.947987i | \(-0.396885\pi\) | ||||
0.318308 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(264\) | − | 53.7917i | − | 0.203757i | ||||||
\(265\) | −93.0655 | + | 16.9179i | −0.351191 | + | 0.0638410i | ||||
\(266\) | −205.741 | −0.773461 | ||||||||
\(267\) | −96.0641 | −0.359791 | ||||||||
\(268\) | −14.0912 | −0.0525791 | ||||||||
\(269\) | 293.666 | 1.09170 | 0.545848 | − | 0.837884i | \(-0.316208\pi\) | ||||
0.545848 | + | 0.837884i | \(0.316208\pi\) | |||||||
\(270\) | 36.1499 | − | 6.57149i | 0.133889 | − | 0.0243389i | ||||
\(271\) | 145.730 | 0.537750 | 0.268875 | − | 0.963175i | \(-0.413348\pi\) | ||||
0.268875 | + | 0.963175i | \(0.413348\pi\) | |||||||
\(272\) | −106.801 | −0.392652 | ||||||||
\(273\) | −30.9740 | −0.113458 | ||||||||
\(274\) | 190.474i | 0.695160i | ||||||||
\(275\) | −96.6089 | − | 256.943i | −0.351305 | − | 0.934337i | ||||
\(276\) | 75.1564 | − | 26.4484i | 0.272306 | − | 0.0958274i | ||||
\(277\) | 395.777i | 1.42880i | 0.699738 | + | 0.714399i | \(0.253300\pi\) | ||||
−0.699738 | + | 0.714399i | \(0.746700\pi\) | |||||||
\(278\) | 260.751i | 0.937953i | ||||||||
\(279\) | −57.7439 | −0.206967 | ||||||||
\(280\) | −16.8322 | − | 92.5943i | −0.0601150 | − | 0.330694i | ||||
\(281\) | 26.8272i | 0.0954704i | 0.998860 | + | 0.0477352i | \(0.0152004\pi\) | ||||
−0.998860 | + | 0.0477352i | \(0.984800\pi\) | |||||||
\(282\) | − | 8.57562i | − | 0.0304100i | ||||||
\(283\) | 213.545 | 0.754576 | 0.377288 | − | 0.926096i | \(-0.376857\pi\) | ||||
0.377288 | + | 0.926096i | \(0.376857\pi\) | |||||||
\(284\) | −209.218 | −0.736685 | ||||||||
\(285\) | 186.272 | − | 33.8613i | 0.653585 | − | 0.118812i | ||||
\(286\) | − | 41.7284i | − | 0.145904i | ||||||
\(287\) | 444.554 | 1.54897 | ||||||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | 423.908 | 1.46681 | ||||||||
\(290\) | 31.0718 | + | 170.927i | 0.107144 | + | 0.589403i | ||||
\(291\) | 106.649i | 0.366492i | ||||||||
\(292\) | 223.286i | 0.764677i | ||||||||
\(293\) | 64.7200 | 0.220887 | 0.110444 | − | 0.993882i | \(-0.464773\pi\) | ||||
0.110444 | + | 0.993882i | \(0.464773\pi\) | |||||||
\(294\) | 11.5490 | 0.0392823 | ||||||||
\(295\) | 308.646 | − | 56.1071i | 1.04626 | − | 0.190194i | ||||
\(296\) | − | 64.4265i | − | 0.217657i | ||||||
\(297\) | 57.0547 | 0.192103 | ||||||||
\(298\) | −175.479 | −0.588854 | ||||||||
\(299\) | 58.3019 | − | 20.5171i | 0.194990 | − | 0.0686190i | ||||
\(300\) | 30.4788 | + | 81.0620i | 0.101596 | + | 0.270207i | ||||
\(301\) | 275.012 | 0.913660 | ||||||||
\(302\) | − | 418.221i | − | 1.38484i | ||||||
\(303\) | 97.4007i | 0.321455i | ||||||||
\(304\) | 87.4452i | 0.287649i | ||||||||
\(305\) | 69.5537 | + | 382.616i | 0.228045 | + | 1.25448i | ||||
\(306\) | − | 113.280i | − | 0.370196i | ||||||
\(307\) | − | 401.291i | − | 1.30714i | −0.756868 | − | 0.653568i | \(-0.773271\pi\) | ||
0.756868 | − | 0.653568i | \(-0.226729\pi\) | |||||||
\(308\) | − | 146.140i | − | 0.474480i | ||||||
\(309\) | 221.623i | 0.717227i | ||||||||
\(310\) | −24.3426 | − | 133.909i | −0.0785245 | − | 0.431965i | ||||
\(311\) | −177.603 | −0.571069 | −0.285535 | − | 0.958368i | \(-0.592171\pi\) | ||||
−0.285535 | + | 0.958368i | \(0.592171\pi\) | |||||||
\(312\) | 13.1648i | 0.0421947i | ||||||||
\(313\) | −254.363 | −0.812661 | −0.406331 | − | 0.913726i | \(-0.633192\pi\) | ||||
−0.406331 | + | 0.913726i | \(0.633192\pi\) | |||||||
\(314\) | 333.547i | 1.06225i | ||||||||
\(315\) | 98.2111 | − | 17.8533i | 0.311781 | − | 0.0566770i | ||||
\(316\) | − | 223.722i | − | 0.707980i | ||||||
\(317\) | − | 353.112i | − | 1.11392i | −0.830540 | − | 0.556959i | \(-0.811968\pi\) | ||
0.830540 | − | 0.556959i | \(-0.188032\pi\) | |||||||
\(318\) | 46.3398 | 0.145723 | ||||||||
\(319\) | 269.771i | 0.845676i | ||||||||
\(320\) | −39.3550 | + | 7.15413i | −0.122984 | + | 0.0223567i | ||||
\(321\) | − | 105.249i | − | 0.327880i | ||||||
\(322\) | 204.183 | − | 71.8542i | 0.634108 | − | 0.223150i | ||||
\(323\) | − | 583.704i | − | 1.80713i | ||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 23.6437 | + | 62.8831i | 0.0727497 | + | 0.193486i | ||||
\(326\) | −341.346 | −1.04707 | ||||||||
\(327\) | 24.3605 | 0.0744969 | ||||||||
\(328\) | − | 188.947i | − | 0.576059i | ||||||
\(329\) | − | 23.2980i | − | 0.0708146i | ||||||
\(330\) | 24.0521 | + | 132.311i | 0.0728851 | + | 0.400942i | ||||
\(331\) | −120.997 | −0.365549 | −0.182774 | − | 0.983155i | \(-0.558508\pi\) | ||||
−0.182774 | + | 0.983155i | \(0.558508\pi\) | |||||||
\(332\) | −26.8250 | −0.0807982 | ||||||||
\(333\) | 68.3346 | 0.205209 | ||||||||
\(334\) | −153.469 | −0.459489 | ||||||||
\(335\) | 34.6600 | − | 6.30065i | 0.103463 | − | 0.0188079i | ||||
\(336\) | 46.1052i | 0.137218i | ||||||||
\(337\) | 110.729 | 0.328573 | 0.164286 | − | 0.986413i | \(-0.447468\pi\) | ||||
0.164286 | + | 0.986413i | \(0.447468\pi\) | |||||||
\(338\) | − | 228.790i | − | 0.676892i | ||||||
\(339\) | 3.05084i | 0.00899953i | ||||||||
\(340\) | 262.698 | − | 47.7544i | 0.772641 | − | 0.140454i | ||||
\(341\) | − | 211.346i | − | 0.619784i | ||||||
\(342\) | −92.7496 | −0.271198 | ||||||||
\(343\) | 357.457 | 1.04215 | ||||||||
\(344\) | − | 116.887i | − | 0.339789i | ||||||
\(345\) | −173.035 | + | 98.6597i | −0.501552 | + | 0.285970i | ||||
\(346\) | −389.143 | −1.12469 | ||||||||
\(347\) | 334.500i | 0.963978i | 0.876177 | + | 0.481989i | \(0.160086\pi\) | ||||
−0.876177 | + | 0.481989i | \(0.839914\pi\) | |||||||
\(348\) | − | 85.1090i | − | 0.244566i | ||||||
\(349\) | −550.891 | −1.57848 | −0.789242 | − | 0.614083i | \(-0.789526\pi\) | ||||
−0.789242 | + | 0.614083i | \(0.789526\pi\) | |||||||
\(350\) | 82.8040 | + | 220.227i | 0.236583 | + | 0.629220i | ||||
\(351\) | −13.9633 | −0.0397816 | ||||||||
\(352\) | −62.1133 | −0.176458 | ||||||||
\(353\) | − | 406.298i | − | 1.15099i | −0.817807 | − | 0.575493i | \(-0.804810\pi\) | ||
0.817807 | − | 0.575493i | \(-0.195190\pi\) | |||||||
\(354\) | −153.683 | −0.434133 | ||||||||
\(355\) | 514.612 | − | 93.5486i | 1.44961 | − | 0.263517i | ||||
\(356\) | 110.925i | 0.311588i | ||||||||
\(357\) | − | 307.756i | − | 0.862061i | ||||||
\(358\) | − | 127.564i | − | 0.356324i | ||||||
\(359\) | 377.504i | 1.05154i | 0.850626 | + | 0.525771i | \(0.176223\pi\) | ||||
−0.850626 | + | 0.525771i | \(0.823777\pi\) | |||||||
\(360\) | −7.58810 | − | 41.7423i | −0.0210781 | − | 0.115951i | ||||
\(361\) | −116.917 | −0.323868 | ||||||||
\(362\) | −71.2739 | −0.196889 | ||||||||
\(363\) | − | 0.754212i | − | 0.00207772i | ||||||
\(364\) | 35.7657i | 0.0982573i | ||||||||
\(365\) | −99.8385 | − | 549.213i | −0.273530 | − | 1.50469i | ||||
\(366\) | − | 190.515i | − | 0.520533i | ||||||
\(367\) | −345.082 | −0.940279 | −0.470139 | − | 0.882592i | \(-0.655796\pi\) | ||||
−0.470139 | + | 0.882592i | \(0.655796\pi\) | |||||||
\(368\) | −30.5400 | − | 86.7831i | −0.0829890 | − | 0.235824i | ||||
\(369\) | 200.409 | 0.543114 | ||||||||
\(370\) | 28.8072 | + | 158.469i | 0.0778574 | + | 0.428295i | ||||
\(371\) | 125.895 | 0.339339 | ||||||||
\(372\) | 66.6769i | 0.179239i | ||||||||
\(373\) | 91.3305 | 0.244854 | 0.122427 | − | 0.992478i | \(-0.460932\pi\) | ||||
0.122427 | + | 0.992478i | \(0.460932\pi\) | |||||||
\(374\) | 414.612 | 1.10859 | ||||||||
\(375\) | −111.214 | − | 185.759i | −0.296570 | − | 0.495358i | ||||
\(376\) | −9.90227 | −0.0263358 | ||||||||
\(377\) | − | 66.0225i | − | 0.175126i | ||||||
\(378\) | −48.9019 | −0.129370 | ||||||||
\(379\) | − | 424.858i | − | 1.12100i | −0.828155 | − | 0.560499i | \(-0.810609\pi\) | ||
0.828155 | − | 0.560499i | \(-0.189391\pi\) | |||||||
\(380\) | −39.0997 | − | 215.088i | −0.102894 | − | 0.566021i | ||||
\(381\) | 104.429 | 0.274093 | ||||||||
\(382\) | −461.761 | −1.20880 | ||||||||
\(383\) | 535.544 | 1.39829 | 0.699143 | − | 0.714982i | \(-0.253565\pi\) | ||||
0.699143 | + | 0.714982i | \(0.253565\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | 65.3440 | + | 359.459i | 0.169725 | + | 0.933659i | ||||
\(386\) | −136.239 | −0.352950 | ||||||||
\(387\) | 123.978 | 0.320356 | ||||||||
\(388\) | 123.148 | 0.317392 | ||||||||
\(389\) | 725.538i | 1.86514i | 0.360993 | + | 0.932568i | \(0.382438\pi\) | ||||
−0.360993 | + | 0.932568i | \(0.617562\pi\) | |||||||
\(390\) | −5.88640 | − | 32.3812i | −0.0150933 | − | 0.0830288i | ||||
\(391\) | 203.857 | + | 579.285i | 0.521373 | + | 1.48155i | ||||
\(392\) | − | 13.3356i | − | 0.0340195i | ||||||
\(393\) | 31.7408i | 0.0807655i | ||||||||
\(394\) | −5.24917 | −0.0133228 | ||||||||
\(395\) | 100.033 | + | 550.286i | 0.253249 | + | 1.39313i | ||||
\(396\) | − | 65.8811i | − | 0.166367i | ||||||
\(397\) | 721.320i | 1.81693i | 0.417964 | + | 0.908463i | \(0.362744\pi\) | ||||
−0.417964 | + | 0.908463i | \(0.637256\pi\) | |||||||
\(398\) | −411.896 | −1.03492 | ||||||||
\(399\) | −251.980 | −0.631528 | ||||||||
\(400\) | 93.6023 | − | 35.1939i | 0.234006 | − | 0.0879847i | ||||
\(401\) | 458.171i | 1.14257i | 0.820751 | + | 0.571286i | \(0.193555\pi\) | ||||
−0.820751 | + | 0.571286i | \(0.806445\pi\) | |||||||
\(402\) | −17.2581 | −0.0429307 | ||||||||
\(403\) | 51.7240i | 0.128347i | ||||||||
\(404\) | 112.469 | 0.278388 | ||||||||
\(405\) | 44.2744 | − | 8.04840i | 0.109320 | − | 0.0198726i | ||||
\(406\) | − | 231.222i | − | 0.569512i | ||||||
\(407\) | 250.109i | 0.614518i | ||||||||
\(408\) | −130.804 | −0.320599 | ||||||||
\(409\) | −499.936 | −1.22234 | −0.611169 | − | 0.791500i | \(-0.709301\pi\) | ||||
−0.611169 | + | 0.791500i | \(0.709301\pi\) | |||||||
\(410\) | 84.4847 | + | 464.752i | 0.206060 | + | 1.13354i | ||||
\(411\) | 233.282i | 0.567596i | ||||||||
\(412\) | 255.908 | 0.621136 | ||||||||
\(413\) | −417.523 | −1.01095 | ||||||||
\(414\) | 92.0474 | − | 32.3925i | 0.222337 | − | 0.0782428i | ||||
\(415\) | 65.9811 | − | 11.9943i | 0.158991 | − | 0.0289020i | ||||
\(416\) | 15.2014 | 0.0365417 | ||||||||
\(417\) | 319.353i | 0.765836i | ||||||||
\(418\) | − | 339.470i | − | 0.812128i | ||||||
\(419\) | 413.532i | 0.986950i | 0.869760 | + | 0.493475i | \(0.164274\pi\) | ||||
−0.869760 | + | 0.493475i | \(0.835726\pi\) | |||||||
\(420\) | −20.6152 | − | 113.404i | −0.0490837 | − | 0.270010i | ||||
\(421\) | − | 523.778i | − | 1.24413i | −0.782966 | − | 0.622064i | \(-0.786294\pi\) | ||
0.782966 | − | 0.622064i | \(-0.213706\pi\) | |||||||
\(422\) | 428.120i | 1.01450i | ||||||||
\(423\) | − | 10.5029i | − | 0.0248296i | ||||||
\(424\) | − | 53.5086i | − | 0.126200i | ||||||
\(425\) | −624.803 | + | 234.922i | −1.47012 | + | 0.552758i | ||||
\(426\) | −256.239 | −0.601501 | ||||||||
\(427\) | − | 517.586i | − | 1.21215i | ||||||
\(428\) | −121.532 | −0.283952 | ||||||||
\(429\) | − | 51.1067i | − | 0.119130i | ||||||
\(430\) | 52.2642 | + | 287.506i | 0.121545 | + | 0.668620i | ||||
\(431\) | − | 129.957i | − | 0.301523i | −0.988570 | − | 0.150762i | \(-0.951827\pi\) | ||
0.988570 | − | 0.150762i | \(-0.0481726\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | 302.337 | 0.698239 | 0.349119 | − | 0.937078i | \(-0.386481\pi\) | ||||
0.349119 | + | 0.937078i | \(0.386481\pi\) | |||||||
\(434\) | 181.146i | 0.417387i | ||||||||
\(435\) | 38.0551 | + | 209.342i | 0.0874829 | + | 0.481245i | ||||
\(436\) | − | 28.1291i | − | 0.0645162i | ||||||
\(437\) | 474.298 | − | 166.911i | 1.08535 | − | 0.381947i | ||||
\(438\) | 273.468i | 0.624356i | ||||||||
\(439\) | −124.955 | −0.284634 | −0.142317 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142317 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(440\) | 152.779 | − | 27.7729i | 0.347226 | − | 0.0631203i | ||||
\(441\) | 14.1446 | 0.0320739 | ||||||||
\(442\) | −101.470 | −0.229571 | ||||||||
\(443\) | 516.339i | 1.16555i | 0.812633 | + | 0.582776i | \(0.198033\pi\) | ||||
−0.812633 | + | 0.582776i | \(0.801967\pi\) | |||||||
\(444\) | − | 78.9060i | − | 0.177716i | ||||||
\(445\) | −49.5984 | − | 272.842i | −0.111457 | − | 0.613127i | ||||
\(446\) | −131.217 | −0.294209 | ||||||||
\(447\) | −214.917 | −0.480798 | ||||||||
\(448\) | 53.2377 | 0.118834 | ||||||||
\(449\) | 45.4215 | 0.101162 | 0.0505808 | − | 0.998720i | \(-0.483893\pi\) | ||||
0.0505808 | + | 0.998720i | \(0.483893\pi\) | |||||||
\(450\) | 37.3288 | + | 99.2802i | 0.0829528 | + | 0.220623i | ||||
\(451\) | 733.510i | 1.62641i | ||||||||
\(452\) | 3.52281 | 0.00779382 | ||||||||
\(453\) | − | 512.214i | − | 1.13072i | ||||||
\(454\) | 202.149i | 0.445262i | ||||||||
\(455\) | −15.9920 | − | 87.9724i | −0.0351473 | − | 0.193346i | ||||
\(456\) | 107.098i | 0.234864i | ||||||||
\(457\) | −102.958 | −0.225290 | −0.112645 | − | 0.993635i | \(-0.535932\pi\) | ||||
−0.112645 | + | 0.993635i | \(0.535932\pi\) | |||||||
\(458\) | −495.186 | −1.08119 | ||||||||
\(459\) | − | 138.739i | − | 0.302264i | ||||||
\(460\) | 113.922 | + | 199.804i | 0.247657 | + | 0.434357i | ||||
\(461\) | 110.027 | 0.238669 | 0.119335 | − | 0.992854i | \(-0.461924\pi\) | ||||
0.119335 | + | 0.992854i | \(0.461924\pi\) | |||||||
\(462\) | − | 178.984i | − | 0.387411i | ||||||
\(463\) | 81.3171i | 0.175631i | 0.996137 | + | 0.0878154i | \(0.0279886\pi\) | ||||
−0.996137 | + | 0.0878154i | \(0.972011\pi\) | |||||||
\(464\) | −98.2754 | −0.211800 | ||||||||
\(465\) | −29.8135 | − | 164.005i | −0.0641150 | − | 0.352698i | ||||
\(466\) | 95.9511 | 0.205904 | ||||||||
\(467\) | 807.265 | 1.72862 | 0.864309 | − | 0.502961i | \(-0.167756\pi\) | ||||
0.864309 | + | 0.502961i | \(0.167756\pi\) | |||||||
\(468\) | 16.1235i | 0.0344519i | ||||||||
\(469\) | −46.8864 | −0.0999711 | ||||||||
\(470\) | 24.3565 | − | 4.42763i | 0.0518223 | − | 0.00942050i | ||||
\(471\) | 408.510i | 0.867325i | ||||||||
\(472\) | 177.458i | 0.375971i | ||||||||
\(473\) | 453.766i | 0.959336i | ||||||||
\(474\) | − | 274.002i | − | 0.578063i | ||||||
\(475\) | 192.346 | + | 511.567i | 0.404939 | + | 1.07698i | ||||
\(476\) | −355.366 | −0.746567 | ||||||||
\(477\) | 56.7544 | 0.118982 | ||||||||
\(478\) | 473.749i | 0.991107i | ||||||||
\(479\) | − | 496.522i | − | 1.03658i | −0.855205 | − | 0.518290i | \(-0.826569\pi\) | ||
0.855205 | − | 0.518290i | \(-0.173431\pi\) | |||||||
\(480\) | −48.1999 | + | 8.76199i | −0.100416 | + | 0.0182541i | ||||
\(481\) | − | 61.2106i | − | 0.127257i | ||||||
\(482\) | 75.0600 | 0.155726 | ||||||||
\(483\) | 250.072 | − | 88.0031i | 0.517747 | − | 0.182201i | ||||
\(484\) | −0.870889 | −0.00179936 | ||||||||
\(485\) | −302.906 | + | 55.0636i | −0.624548 | + | 0.113533i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 196.039i | 0.402543i | 0.979535 | + | 0.201272i | \(0.0645074\pi\) | ||||
−0.979535 | + | 0.201272i | \(0.935493\pi\) | |||||||
\(488\) | −219.988 | −0.450794 | ||||||||
\(489\) | −418.062 | −0.854932 | ||||||||
\(490\) | 5.96280 | + | 32.8015i | 0.0121690 | + | 0.0669419i | ||||
\(491\) | 103.195 | 0.210173 | 0.105086 | − | 0.994463i | \(-0.466488\pi\) | ||||
0.105086 | + | 0.994463i | \(0.466488\pi\) | |||||||
\(492\) | − | 231.412i | − | 0.470350i | ||||||
\(493\) | 655.996 | 1.33062 | ||||||||
\(494\) | 83.0803i | 0.168179i | ||||||||
\(495\) | 29.4577 | + | 162.047i | 0.0595104 | + | 0.327368i | ||||
\(496\) | 76.9919 | 0.155226 | ||||||||
\(497\) | −696.144 | −1.40069 | ||||||||
\(498\) | −32.8538 | −0.0659714 | ||||||||
\(499\) | −820.456 | −1.64420 | −0.822101 | − | 0.569342i | \(-0.807198\pi\) | ||||
−0.822101 | + | 0.569342i | \(0.807198\pi\) | |||||||
\(500\) | −214.496 | + | 128.419i | −0.428992 | + | 0.256837i | ||||
\(501\) | −187.961 | −0.375171 | ||||||||
\(502\) | −406.312 | −0.809386 | ||||||||
\(503\) | −146.500 | −0.291253 | −0.145627 | − | 0.989340i | \(-0.546520\pi\) | ||||
−0.145627 | + | 0.989340i | \(0.546520\pi\) | |||||||
\(504\) | 56.4671i | 0.112038i | ||||||||
\(505\) | −276.638 | + | 50.2885i | −0.547798 | + | 0.0995812i | ||||
\(506\) | 118.559 | + | 336.899i | 0.234306 | + | 0.665809i | ||||
\(507\) | − | 280.209i | − | 0.552680i | ||||||
\(508\) | − | 120.585i | − | 0.237371i | ||||||
\(509\) | −138.422 | −0.271949 | −0.135974 | − | 0.990712i | \(-0.543416\pi\) | ||||
−0.135974 | + | 0.990712i | \(0.543416\pi\) | |||||||
\(510\) | 321.738 | − | 58.4870i | 0.630859 | − | 0.114680i | ||||
\(511\) | 742.950i | 1.45391i | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −113.595 | −0.221432 | ||||||||
\(514\) | 431.048 | 0.838615 | ||||||||
\(515\) | −629.455 | + | 114.425i | −1.22224 | + | 0.222185i | ||||
\(516\) | − | 143.157i | − | 0.277436i | ||||||
\(517\) | 38.4414 | 0.0743548 | ||||||||
\(518\) | − | 214.370i | − | 0.413841i | ||||||
\(519\) | −476.601 | −0.918306 | ||||||||
\(520\) | −37.3906 | + | 6.79703i | −0.0719050 | + | 0.0130712i | ||||
\(521\) | 833.697i | 1.60019i | 0.599876 | + | 0.800093i | \(0.295217\pi\) | ||||
−0.599876 | + | 0.800093i | \(0.704783\pi\) | |||||||
\(522\) | − | 104.237i | − | 0.199687i | ||||||
\(523\) | 747.765 | 1.42976 | 0.714881 | − | 0.699247i | \(-0.246481\pi\) | ||||
0.714881 | + | 0.699247i | \(0.246481\pi\) | |||||||
\(524\) | 36.6511 | 0.0699449 | ||||||||
\(525\) | 101.414 | + | 269.722i | 0.193169 | + | 0.513756i | ||||
\(526\) | − | 236.782i | − | 0.450156i | ||||||
\(527\) | −513.927 | −0.975194 | ||||||||
\(528\) | −76.0730 | −0.144078 | ||||||||
\(529\) | −412.414 | + | 331.294i | −0.779610 | + | 0.626265i | ||||
\(530\) | 23.9255 | + | 131.615i | 0.0451424 | + | 0.248329i | ||||
\(531\) | −188.223 | −0.354468 | ||||||||
\(532\) | 290.961i | 0.546919i | ||||||||
\(533\) | − | 179.516i | − | 0.336803i | ||||||
\(534\) | 135.855i | 0.254410i | ||||||||
\(535\) | 298.930 | − | 54.3408i | 0.558748 | − | 0.101572i | ||||
\(536\) | 19.9280i | 0.0371791i | ||||||||
\(537\) | − | 156.234i | − | 0.290938i | ||||||
\(538\) | − | 415.307i | − | 0.771945i | ||||||
\(539\) | 51.7700i | 0.0960483i | ||||||||
\(540\) | −9.29349 | − | 51.1237i | −0.0172102 | − | 0.0946735i | ||||
\(541\) | 295.029 | 0.545340 | 0.272670 | − | 0.962108i | \(-0.412093\pi\) | ||||
0.272670 | + | 0.962108i | \(0.412093\pi\) | |||||||
\(542\) | − | 206.094i | − | 0.380246i | ||||||
\(543\) | −87.2923 | −0.160759 | ||||||||
\(544\) | 151.040i | 0.277647i | ||||||||
\(545\) | 12.5774 | + | 69.1888i | 0.0230779 | + | 0.126952i | ||||
\(546\) | 43.8038i | 0.0802268i | ||||||||
\(547\) | 491.725i | 0.898948i | 0.893293 | + | 0.449474i | \(0.148389\pi\) | ||||
−0.893293 | + | 0.449474i | \(0.851611\pi\) | |||||||
\(548\) | 269.371 | 0.491552 | ||||||||
\(549\) | − | 233.332i | − | 0.425013i | ||||||
\(550\) | −363.372 | + | 136.626i | −0.660676 | + | 0.248410i | ||||
\(551\) | − | 537.107i | − | 0.974786i | ||||||
\(552\) | −37.4036 | − | 106.287i | −0.0677602 | − | 0.192549i | ||||
\(553\) | − | 744.401i | − | 1.34611i | ||||||
\(554\) | 559.713 | 1.01031 | ||||||||
\(555\) | 35.2815 | + | 194.084i | 0.0635703 | + | 0.349701i | ||||
\(556\) | 368.758 | 0.663233 | ||||||||
\(557\) | 510.871 | 0.917183 | 0.458592 | − | 0.888647i | \(-0.348354\pi\) | ||||
0.458592 | + | 0.888647i | \(0.348354\pi\) | |||||||
\(558\) | 81.6622i | 0.146348i | ||||||||
\(559\) | − | 111.053i | − | 0.198663i | ||||||
\(560\) | −130.948 | + | 23.8043i | −0.233836 | + | 0.0425077i | ||||
\(561\) | 507.793 | 0.905158 | ||||||||
\(562\) | 37.9394 | 0.0675078 | ||||||||
\(563\) | 243.665 | 0.432797 | 0.216398 | − | 0.976305i | \(-0.430569\pi\) | ||||
0.216398 | + | 0.976305i | \(0.430569\pi\) | |||||||
\(564\) | −12.1278 | −0.0215031 | ||||||||
\(565\) | −8.66501 | + | 1.57517i | −0.0153363 | + | 0.00278790i | ||||
\(566\) | − | 301.998i | − | 0.533566i | ||||||
\(567\) | −59.8924 | −0.105630 | ||||||||
\(568\) | 295.880i | 0.520915i | ||||||||
\(569\) | − | 971.291i | − | 1.70701i | −0.521081 | − | 0.853507i | \(-0.674471\pi\) | ||
0.521081 | − | 0.853507i | \(-0.325529\pi\) | |||||||
\(570\) | −47.8871 | − | 263.428i | −0.0840125 | − | 0.462154i | ||||
\(571\) | 179.364i | 0.314123i | 0.987589 | + | 0.157062i | \(0.0502022\pi\) | ||||
−0.987589 | + | 0.157062i | \(0.949798\pi\) | |||||||
\(572\) | −59.0129 | −0.103169 | ||||||||
\(573\) | −565.540 | −0.986981 | ||||||||
\(574\) | − | 628.695i | − | 1.09529i | ||||||
\(575\) | −369.553 | − | 440.518i | −0.642701 | − | 0.766117i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | − | 339.485i | − | 0.588363i | −0.955750 | − | 0.294181i | \(-0.904953\pi\) | ||
0.955750 | − | 0.294181i | \(-0.0950470\pi\) | |||||||
\(578\) | − | 599.496i | − | 1.03719i | ||||||
\(579\) | −166.858 | −0.288183 | ||||||||
\(580\) | 241.727 | − | 43.9422i | 0.416771 | − | 0.0757624i | ||||
\(581\) | −89.2562 | −0.153625 | ||||||||
\(582\) | 150.825 | 0.259149 | ||||||||
\(583\) | 207.725i | 0.356303i | ||||||||
\(584\) | 315.774 | 0.540708 | ||||||||
\(585\) | −7.20934 | − | 39.6587i | −0.0123237 | − | 0.0677927i | ||||
\(586\) | − | 91.5279i | − | 0.156191i | ||||||
\(587\) | 798.800i | 1.36082i | 0.732832 | + | 0.680409i | \(0.238198\pi\) | ||||
−0.732832 | + | 0.680409i | \(0.761802\pi\) | |||||||
\(588\) | − | 16.3327i | − | 0.0277768i | ||||||
\(589\) | 420.786i | 0.714407i | ||||||||
\(590\) | −79.3474 | − | 436.492i | −0.134487 | − | 0.739817i | ||||
\(591\) | −6.42889 | −0.0108780 | ||||||||
\(592\) | −91.1128 | −0.153907 | ||||||||
\(593\) | − | 1121.35i | − | 1.89098i | −0.325657 | − | 0.945488i | \(-0.605585\pi\) | ||
0.325657 | − | 0.945488i | \(-0.394415\pi\) | |||||||
\(594\) | − | 80.6876i | − | 0.135838i | ||||||
\(595\) | 874.090 | − | 158.896i | 1.46906 | − | 0.267052i | ||||
\(596\) | 248.164i | 0.416383i | ||||||||
\(597\) | −504.468 | −0.845005 | ||||||||
\(598\) | −29.0155 | − | 82.4513i | −0.0485210 | − | 0.137878i | ||||
\(599\) | 1047.06 | 1.74801 | 0.874004 | − | 0.485919i | \(-0.161515\pi\) | ||||
0.874004 | + | 0.485919i | \(0.161515\pi\) | |||||||
\(600\) | 114.639 | − | 43.1035i | 0.191065 | − | 0.0718392i | ||||
\(601\) | 329.240 | 0.547820 | 0.273910 | − | 0.961755i | \(-0.411683\pi\) | ||||
0.273910 | + | 0.961755i | \(0.411683\pi\) | |||||||
\(602\) | − | 388.925i | − | 0.646055i | ||||||
\(603\) | −21.1368 | −0.0350528 | ||||||||
\(604\) | −591.454 | −0.979229 | ||||||||
\(605\) | 2.14212 | − | 0.389404i | 0.00354069 | − | 0.000643642i | ||||
\(606\) | 137.745 | 0.227303 | ||||||||
\(607\) | 524.433i | 0.863976i | 0.901879 | + | 0.431988i | \(0.142188\pi\) | ||||
−0.901879 | + | 0.431988i | \(0.857812\pi\) | |||||||
\(608\) | 123.666 | 0.203398 | ||||||||
\(609\) | − | 283.188i | − | 0.465004i | ||||||
\(610\) | 541.101 | − | 98.3638i | 0.887052 | − | 0.161252i | ||||
\(611\) | −9.40799 | −0.0153977 | ||||||||
\(612\) | −160.202 | −0.261768 | ||||||||
\(613\) | −233.266 | −0.380532 | −0.190266 | − | 0.981733i | \(-0.560935\pi\) | ||||
−0.190266 | + | 0.981733i | \(0.560935\pi\) | |||||||
\(614\) | −567.511 | −0.924285 | ||||||||
\(615\) | 103.472 | + | 569.203i | 0.168247 | + | 0.925533i | ||||
\(616\) | −206.673 | −0.335508 | ||||||||
\(617\) | 280.650 | 0.454863 | 0.227431 | − | 0.973794i | \(-0.426967\pi\) | ||||
0.227431 | + | 0.973794i | \(0.426967\pi\) | |||||||
\(618\) | 313.422 | 0.507156 | ||||||||
\(619\) | 613.679i | 0.991405i | 0.868492 | + | 0.495702i | \(0.165089\pi\) | ||||
−0.868492 | + | 0.495702i | \(0.834911\pi\) | |||||||
\(620\) | −189.376 | + | 34.4256i | −0.305445 | + | 0.0555252i | ||||
\(621\) | 112.735 | − | 39.6726i | 0.181537 | − | 0.0638850i | ||||
\(622\) | 251.168i | 0.403807i | ||||||||
\(623\) | 369.088i | 0.592436i | ||||||||
\(624\) | 18.6178 | 0.0298362 | ||||||||
\(625\) | 470.174 | − | 411.779i | 0.752278 | − | 0.658846i | ||||
\(626\) | 359.724i | 0.574638i | ||||||||
\(627\) | − | 415.764i | − | 0.663100i | ||||||
\(628\) | 471.707 | 0.751125 | ||||||||
\(629\) | 608.185 | 0.966909 | ||||||||
\(630\) | −25.2483 | − | 138.891i | −0.0400767 | − | 0.220463i | ||||
\(631\) | − | 102.785i | − | 0.162893i | −0.996678 | − | 0.0814464i | \(-0.974046\pi\) | ||
0.996678 | − | 0.0814464i | \(-0.0259539\pi\) | |||||||
\(632\) | −316.390 | −0.500618 | ||||||||
\(633\) | 524.337i | 0.828337i | ||||||||
\(634\) | −499.376 | −0.787660 | ||||||||
\(635\) | 53.9174 | + | 296.601i | 0.0849094 | + | 0.467088i | ||||
\(636\) | − | 65.5344i | − | 0.103041i | ||||||
\(637\) | − | 12.6700i | − | 0.0198901i | ||||||
\(638\) | 381.513 | 0.597983 | ||||||||
\(639\) | −313.828 | −0.491123 | ||||||||
\(640\) | 10.1175 | + | 55.6564i | 0.0158085 | + | 0.0869632i | ||||
\(641\) | 96.0151i | 0.149790i | 0.997191 | + | 0.0748948i | \(0.0238621\pi\) | ||||
−0.997191 | + | 0.0748948i | \(0.976138\pi\) | |||||||
\(642\) | −148.845 | −0.231846 | ||||||||
\(643\) | −620.769 | −0.965427 | −0.482713 | − | 0.875778i | \(-0.660349\pi\) | ||||
−0.482713 | + | 0.875778i | \(0.660349\pi\) | |||||||
\(644\) | −101.617 | − | 288.758i | −0.157791 | − | 0.448382i | ||||
\(645\) | 64.0103 | + | 352.122i | 0.0992408 | + | 0.545926i | ||||
\(646\) | −825.482 | −1.27784 | ||||||||
\(647\) | − | 1267.27i | − | 1.95869i | −0.202193 | − | 0.979346i | \(-0.564807\pi\) | ||
0.202193 | − | 0.979346i | \(-0.435193\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | − | 688.907i | − | 1.06149i | ||||||
\(650\) | 88.9301 | − | 33.4372i | 0.136816 | − | 0.0514418i | ||||
\(651\) | 221.858i | 0.340795i | ||||||||
\(652\) | 482.736i | 0.740393i | ||||||||
\(653\) | 27.5591i | 0.0422038i | 0.999777 | + | 0.0211019i | \(0.00671744\pi\) | ||||
−0.999777 | + | 0.0211019i | \(0.993283\pi\) | |||||||
\(654\) | − | 34.4509i | − | 0.0526773i | ||||||
\(655\) | −90.1504 | + | 16.3879i | −0.137634 | + | 0.0250198i | ||||
\(656\) | −267.212 | −0.407335 | ||||||||
\(657\) | 334.928i | 0.509785i | ||||||||
\(658\) | −32.9484 | −0.0500735 | ||||||||
\(659\) | − | 575.719i | − | 0.873626i | −0.899552 | − | 0.436813i | \(-0.856107\pi\) | ||
0.899552 | − | 0.436813i | \(-0.143893\pi\) | |||||||
\(660\) | 187.116 | − | 34.0148i | 0.283509 | − | 0.0515375i | ||||
\(661\) | − | 556.994i | − | 0.842653i | −0.906909 | − | 0.421327i | \(-0.861565\pi\) | ||
0.906909 | − | 0.421327i | \(-0.138435\pi\) | |||||||
\(662\) | 171.115i | 0.258482i | ||||||||
\(663\) | −124.275 | −0.187444 | ||||||||
\(664\) | 37.9363i | 0.0571329i | ||||||||
\(665\) | −130.098 | − | 715.674i | −0.195637 | − | 1.07620i | ||||
\(666\) | − | 96.6397i | − | 0.145105i | ||||||
\(667\) | 187.583 | + | 533.040i | 0.281234 | + | 0.799161i | ||||
\(668\) | 217.038i | 0.324908i | ||||||||
\(669\) | −160.707 | −0.240220 | ||||||||
\(670\) | −8.91046 | − | 49.0166i | −0.0132992 | − | 0.0731592i | ||||
\(671\) | 854.011 | 1.27274 | ||||||||
\(672\) | 65.2026 | 0.0970276 | ||||||||
\(673\) | 644.574i | 0.957762i | 0.877880 | + | 0.478881i | \(0.158957\pi\) | ||||
−0.877880 | + | 0.478881i | \(0.841043\pi\) | |||||||
\(674\) | − | 156.594i | − | 0.232336i | ||||||
\(675\) | 45.7182 | + | 121.593i | 0.0677307 | + | 0.180138i | ||||
\(676\) | −323.557 | −0.478635 | ||||||||
\(677\) | −1135.00 | −1.67652 | −0.838260 | − | 0.545270i | \(-0.816427\pi\) | ||||
−0.838260 | + | 0.545270i | \(0.816427\pi\) | |||||||
\(678\) | 4.31454 | 0.00636363 | ||||||||
\(679\) | 409.757 | 0.603471 | ||||||||
\(680\) | −67.5350 | − | 371.511i | −0.0993161 | − | 0.546340i | ||||
\(681\) | 247.581i | 0.363555i | ||||||||
\(682\) | −298.889 | −0.438253 | ||||||||
\(683\) | 336.175i | 0.492203i | 0.969244 | + | 0.246101i | \(0.0791496\pi\) | ||||
−0.969244 | + | 0.246101i | \(0.920850\pi\) | |||||||
\(684\) | 131.168i | 0.191766i | ||||||||
\(685\) | −662.568 | + | 120.445i | −0.967253 | + | 0.175832i | ||||
\(686\) | − | 505.520i | − | 0.736910i | ||||||
\(687\) | −606.476 | −0.882789 | ||||||||
\(688\) | −165.304 | −0.240267 | ||||||||
\(689\) | − | 50.8377i | − | 0.0737848i | ||||||
\(690\) | 139.526 | + | 244.709i | 0.202211 | + | 0.354651i | ||||
\(691\) | 876.008 | 1.26774 | 0.633870 | − | 0.773440i | \(-0.281465\pi\) | ||||
0.633870 | + | 0.773440i | \(0.281465\pi\) | |||||||
\(692\) | 550.331i | 0.795276i | ||||||||
\(693\) | − | 219.210i | − | 0.316320i | ||||||
\(694\) | 473.055 | 0.681636 | ||||||||
\(695\) | −907.029 | + | 164.884i | −1.30508 | + | 0.237243i | ||||
\(696\) | −120.362 | −0.172934 | ||||||||
\(697\) | 1783.66 | 2.55906 | ||||||||
\(698\) | 779.077i | 1.11616i | ||||||||
\(699\) | 117.516 | 0.168120 | ||||||||
\(700\) | 311.448 | − | 117.103i | 0.444926 | − | 0.167289i | ||||
\(701\) | − | 1042.02i | − | 1.48647i | −0.669029 | − | 0.743236i | \(-0.733290\pi\) | ||
0.669029 | − | 0.743236i | \(-0.266710\pi\) | |||||||
\(702\) | 19.7471i | 0.0281298i | ||||||||
\(703\) | − | 497.961i | − | 0.708337i | ||||||
\(704\) | 87.8415i | 0.124775i | ||||||||
\(705\) | 29.8305 | − | 5.42272i | 0.0423128 | − | 0.00769180i | ||||
\(706\) | −574.592 | −0.813869 | ||||||||
\(707\) | 374.223 | 0.529311 | ||||||||
\(708\) | 217.341i | 0.306979i | ||||||||
\(709\) | 284.090i | 0.400692i | 0.979725 | + | 0.200346i | \(0.0642066\pi\) | ||||
−0.979725 | + | 0.200346i | \(0.935793\pi\) | |||||||
\(710\) | −132.298 | − | 727.772i | −0.186335 | − | 1.02503i | ||||
\(711\) | − | 335.583i | − | 0.471987i | ||||||
\(712\) | 156.872 | 0.220326 | ||||||||
\(713\) | −146.958 | − | 417.600i | −0.206112 | − | 0.585694i | ||||
\(714\) | −435.232 | −0.609569 | ||||||||
\(715\) | 145.153 | − | 26.3866i | 0.203012 | − | 0.0369044i | ||||
\(716\) | −180.403 | −0.251959 | ||||||||
\(717\) | 580.222i | 0.809235i | ||||||||
\(718\) | 533.871 | 0.743553 | ||||||||
\(719\) | −354.612 | −0.493202 | −0.246601 | − | 0.969117i | \(-0.579314\pi\) | ||||
−0.246601 | + | 0.969117i | \(0.579314\pi\) | |||||||
\(720\) | −59.0325 | + | 10.7312i | −0.0819896 | + | 0.0149044i | ||||
\(721\) | 851.497 | 1.18099 | ||||||||
\(722\) | 165.345i | 0.229010i | ||||||||
\(723\) | 91.9293 | 0.127150 | ||||||||
\(724\) | 100.796i | 0.139222i | ||||||||
\(725\) | −574.925 | + | 216.168i | −0.793000 | + | 0.298163i | ||||
\(726\) | −1.06662 | −0.00146917 | ||||||||
\(727\) | −75.5220 | −0.103882 | −0.0519408 | − | 0.998650i | \(-0.516541\pi\) | ||||
−0.0519408 | + | 0.998650i | \(0.516541\pi\) | |||||||
\(728\) | 50.5803 | 0.0694784 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −776.705 | + | 141.193i | −1.06398 | + | 0.193415i | ||||
\(731\) | 1103.42 | 1.50946 | ||||||||
\(732\) | −269.429 | −0.368072 | ||||||||
\(733\) | −1193.82 | −1.62868 | −0.814338 | − | 0.580390i | \(-0.802900\pi\) | ||||
−0.814338 | + | 0.580390i | \(0.802900\pi\) | |||||||
\(734\) | 488.020i | 0.664878i | ||||||||
\(735\) | 7.30291 | + | 40.1735i | 0.00993594 | + | 0.0546578i | ||||
\(736\) | −122.730 | + | 43.1900i | −0.166753 | + | 0.0586821i | ||||
\(737\) | − | 77.3621i | − | 0.104969i | ||||||
\(738\) | − | 283.421i | − | 0.384039i | ||||||
\(739\) | −1258.10 | −1.70243 | −0.851216 | − | 0.524815i | \(-0.824134\pi\) | ||||
−0.851216 | + | 0.524815i | \(0.824134\pi\) | |||||||
\(740\) | 224.109 | − | 40.7396i | 0.302850 | − | 0.0550535i | ||||
\(741\) | 101.752i | 0.137317i | ||||||||
\(742\) | − | 178.042i | − | 0.239949i | ||||||
\(743\) | 670.264 | 0.902105 | 0.451052 | − | 0.892497i | \(-0.351049\pi\) | ||||
0.451052 | + | 0.892497i | \(0.351049\pi\) | |||||||
\(744\) | 94.2954 | 0.126741 | ||||||||
\(745\) | −110.963 | − | 610.407i | −0.148943 | − | 0.819338i | ||||
\(746\) | − | 129.161i | − | 0.173138i | ||||||
\(747\) | −40.2375 | −0.0538654 | ||||||||
\(748\) | − | 586.349i | − | 0.783890i | ||||||
\(749\) | −404.379 | −0.539891 | ||||||||
\(750\) | −262.703 | + | 157.280i | −0.350271 | + | 0.209707i | ||||
\(751\) | 567.949i | 0.756257i | 0.925753 | + | 0.378129i | \(0.123432\pi\) | ||||
−0.925753 | + | 0.378129i | \(0.876568\pi\) | |||||||
\(752\) | 14.0039i | 0.0186222i | ||||||||
\(753\) | −497.628 | −0.660861 | ||||||||
\(754\) | −93.3699 | −0.123833 | ||||||||
\(755\) | 1454.79 | − | 264.459i | 1.92688 | − | 0.350277i | ||||
\(756\) | 69.1578i | 0.0914785i | ||||||||
\(757\) | −335.085 | −0.442648 | −0.221324 | − | 0.975200i | \(-0.571038\pi\) | ||||
−0.221324 | + | 0.975200i | \(0.571038\pi\) | |||||||
\(758\) | −600.840 | −0.792665 | ||||||||
\(759\) | 145.204 | + | 412.616i | 0.191310 | + | 0.543631i | ||||
\(760\) | −304.180 | + | 55.2953i | −0.400237 | + | 0.0727569i | ||||
\(761\) | −1035.35 | −1.36051 | −0.680255 | − | 0.732976i | \(-0.738131\pi\) | ||||
−0.680255 | + | 0.732976i | \(0.738131\pi\) | |||||||
\(762\) | − | 147.686i | − | 0.193813i | ||||||
\(763\) | − | 93.5954i | − | 0.122668i | ||||||
\(764\) | 653.029i | 0.854750i | ||||||||
\(765\) | 394.047 | − | 71.6316i | 0.515094 | − | 0.0936361i | ||||
\(766\) | − | 757.373i | − | 0.988738i | ||||||
\(767\) | 168.600i | 0.219818i | ||||||||
\(768\) | − | 27.7128i | − | 0.0360844i | ||||||
\(769\) | 691.450i | 0.899155i | 0.893241 | + | 0.449577i | \(0.148425\pi\) | ||||
−0.893241 | + | 0.449577i | \(0.851575\pi\) | |||||||
\(770\) | 508.351 | − | 92.4104i | 0.660197 | − | 0.120014i | ||||
\(771\) | 527.924 | 0.684726 | ||||||||
\(772\) | 192.671i | 0.249574i | ||||||||
\(773\) | −739.787 | −0.957033 | −0.478517 | − | 0.878079i | \(-0.658825\pi\) | ||||
−0.478517 | + | 0.878079i | \(0.658825\pi\) | |||||||
\(774\) | − | 175.331i | − | 0.226526i | ||||||
\(775\) | 450.413 | − | 169.353i | 0.581179 | − | 0.218520i | ||||
\(776\) | − | 174.158i | − | 0.224430i | ||||||
\(777\) | − | 262.548i | − | 0.337900i | ||||||
\(778\) | 1026.07 | 1.31885 | ||||||||
\(779\) | − | 1460.40i | − | 1.87471i | ||||||
\(780\) | −45.7940 | + | 8.32463i | −0.0587102 | + | 0.0106726i | ||||
\(781\) | − | 1148.63i | − | 1.47072i | ||||||
\(782\) | 819.232 | − | 288.297i | 1.04761 | − | 0.368666i | ||||
\(783\) | − | 127.663i | − | 0.163044i | ||||||
\(784\) | −18.8594 | −0.0240554 | ||||||||
\(785\) | −1160.25 | + | 210.916i | −1.47803 | + | 0.268682i | ||||
\(786\) | 44.8883 | 0.0571098 | ||||||||
\(787\) | 1337.12 | 1.69901 | 0.849503 | − | 0.527583i | \(-0.176902\pi\) | ||||
0.849503 | + | 0.527583i | \(0.176902\pi\) | |||||||
\(788\) | 7.42345i | 0.00942062i | ||||||||
\(789\) | − | 289.998i | − | 0.367551i | ||||||
\(790\) | 778.222 | − | 141.469i | 0.985091 | − | 0.179074i | ||||
\(791\) | 11.7216 | 0.0148188 | ||||||||
\(792\) | −93.1700 | −0.117639 | ||||||||
\(793\) | −209.007 | −0.263565 | ||||||||
\(794\) | 1020.10 | 1.28476 | ||||||||
\(795\) | 29.3026 | + | 161.194i | 0.0368586 | + | 0.202760i | ||||
\(796\) | 582.509i | 0.731796i | ||||||||
\(797\) | −890.671 | −1.11753 | −0.558765 | − | 0.829326i | \(-0.688725\pi\) | ||||
−0.558765 | + | 0.829326i | \(0.688725\pi\) | |||||||
\(798\) | 356.353i | 0.446558i | ||||||||
\(799\) | − | 93.4773i | − | 0.116993i | ||||||
\(800\) | −49.7717 | − | 132.374i | −0.0622146 | − | 0.165467i | ||||
\(801\) | 166.388i | 0.207725i | ||||||||
\(802\) | 647.952 | 0.807921 | ||||||||
\(803\) | −1225.86 | −1.52660 | ||||||||
\(804\) | 24.4067i | 0.0303566i | ||||||||
\(805\) | 379.060 | + | 664.819i | 0.470882 | + | 0.825862i | ||||
\(806\) | 73.1488 | 0.0907553 | ||||||||
\(807\) | − | 508.645i | − | 0.630291i | ||||||
\(808\) | − | 159.055i | − | 0.196850i | ||||||
\(809\) | 38.5042 | 0.0475948 | 0.0237974 | − | 0.999717i | \(-0.492424\pi\) | ||||
0.0237974 | + | 0.999717i | \(0.492424\pi\) | |||||||
\(810\) | −11.3822 | − | 62.6135i | −0.0140520 | − | 0.0773006i | ||||
\(811\) | 257.237 | 0.317185 | 0.158593 | − | 0.987344i | \(-0.449304\pi\) | ||||
0.158593 | + | 0.987344i | \(0.449304\pi\) | |||||||
\(812\) | −326.997 | −0.402706 | ||||||||
\(813\) | − | 252.412i | − | 0.310470i | ||||||
\(814\) | 353.707 | 0.434530 | ||||||||
\(815\) | −215.847 | − | 1187.38i | −0.264843 | − | 1.45691i | ||||
\(816\) | 184.985i | 0.226698i | ||||||||
\(817\) | − | 903.438i | − | 1.10580i | ||||||
\(818\) | 707.017i | 0.864324i | ||||||||
\(819\) | 53.6485i | 0.0655049i | ||||||||
\(820\) | 657.259 | − | 119.479i | 0.801535 | − | 0.145707i | ||||
\(821\) | 504.663 | 0.614693 | 0.307347 | − | 0.951598i | \(-0.400559\pi\) | ||||
0.307347 | + | 0.951598i | \(0.400559\pi\) | |||||||
\(822\) | 329.910 | 0.401351 | ||||||||
\(823\) | 1466.35i | 1.78172i | 0.454282 | + | 0.890858i | \(0.349896\pi\) | ||||
−0.454282 | + | 0.890858i | \(0.650104\pi\) | |||||||
\(824\) | − | 361.909i | − | 0.439210i | ||||||
\(825\) | −445.038 | + | 167.332i | −0.539440 | + | 0.202826i | ||||
\(826\) | 590.466i | 0.714850i | ||||||||
\(827\) | −140.719 | −0.170156 | −0.0850780 | − | 0.996374i | \(-0.527114\pi\) | ||||
−0.0850780 | + | 0.996374i | \(0.527114\pi\) | |||||||
\(828\) | −45.8099 | − | 130.175i | −0.0553260 | − | 0.157216i | ||||
\(829\) | −437.909 | −0.528238 | −0.264119 | − | 0.964490i | \(-0.585081\pi\) | ||||
−0.264119 | + | 0.964490i | \(0.585081\pi\) | |||||||
\(830\) | −16.9626 | − | 93.3114i | −0.0204368 | − | 0.112423i | ||||
\(831\) | 685.506 | 0.824917 | ||||||||
\(832\) | − | 21.4980i | − | 0.0258389i | ||||||
\(833\) | 125.888 | 0.151126 | ||||||||
\(834\) | 451.634 | 0.541528 | ||||||||
\(835\) | −97.0451 | − | 533.847i | −0.116222 | − | 0.639338i | ||||
\(836\) | −480.082 | −0.574261 | ||||||||
\(837\) | 100.015i | 0.119493i | ||||||||
\(838\) | 584.823 | 0.697879 | ||||||||
\(839\) | 166.341i | 0.198261i | 0.995074 | + | 0.0991306i | \(0.0316062\pi\) | ||||
−0.995074 | + | 0.0991306i | \(0.968394\pi\) | |||||||
\(840\) | −160.378 | + | 29.1542i | −0.190926 | + | 0.0347074i | ||||
\(841\) | −237.372 | −0.282250 | ||||||||
\(842\) | −740.734 | −0.879731 | ||||||||
\(843\) | 46.4660 | 0.0551199 | ||||||||
\(844\) | 605.453 | 0.717361 | ||||||||
\(845\) | 795.851 | − | 144.673i | 0.941835 | − | 0.171211i | ||||
\(846\) | −14.8534 | −0.0175572 | ||||||||
\(847\) | −2.89776 | −0.00342120 | ||||||||
\(848\) | −75.6726 | −0.0892365 | ||||||||
\(849\) | − | 369.871i | − | 0.435655i | ||||||
\(850\) | 332.230 | + | 883.605i | 0.390859 | + | 1.03954i | ||||
\(851\) | 173.911 | + | 494.191i | 0.204361 | + | 0.580718i | ||||
\(852\) | 362.377i | 0.425325i | ||||||||
\(853\) | 409.500i | 0.480071i | 0.970764 | + | 0.240035i | \(0.0771591\pi\) | ||||
−0.970764 | + | 0.240035i | \(0.922841\pi\) | |||||||
\(854\) | −731.977 | −0.857116 | ||||||||
\(855\) | −58.6495 | − | 322.632i | −0.0685959 | − | 0.377347i | ||||
\(856\) | 171.872i | 0.200785i | ||||||||
\(857\) | − | 684.144i | − | 0.798301i | −0.916886 | − | 0.399150i | \(-0.869305\pi\) | ||
0.916886 | − | 0.399150i | \(-0.130695\pi\) | |||||||
\(858\) | −72.2758 | −0.0842375 | ||||||||
\(859\) | −758.159 | −0.882607 | −0.441304 | − | 0.897358i | \(-0.645484\pi\) | ||||
−0.441304 | + | 0.897358i | \(0.645484\pi\) | |||||||
\(860\) | 406.595 | − | 73.9127i | 0.472785 | − | 0.0859450i | ||||
\(861\) | − | 769.991i | − | 0.894298i | ||||||
\(862\) | −183.786 | −0.213209 | ||||||||
\(863\) | 436.885i | 0.506239i | 0.967435 | + | 0.253120i | \(0.0814566\pi\) | ||||
−0.967435 | + | 0.253120i | \(0.918543\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | −246.071 | − | 1353.64i | −0.284476 | − | 1.56491i | ||||
\(866\) | − | 427.570i | − | 0.493730i | ||||||
\(867\) | − | 734.230i | − | 0.846862i | ||||||
\(868\) | 256.179 | 0.295137 | ||||||||
\(869\) | 1228.25 | 1.41341 | ||||||||
\(870\) | 296.054 | − | 53.8180i | 0.340292 | − | 0.0618597i | ||||
\(871\) | 18.9333i | 0.0217374i | ||||||||
\(872\) | −39.7805 | −0.0456199 | ||||||||
\(873\) | 184.722 | 0.211594 | ||||||||
\(874\) | −236.047 | − | 670.759i | −0.270077 | − | 0.767458i | ||||
\(875\) | −713.705 | + | 427.295i | −0.815663 | + | 0.488337i | ||||
\(876\) | 386.742 | 0.441486 | ||||||||
\(877\) | 659.296i | 0.751763i | 0.926668 | + | 0.375881i | \(0.122660\pi\) | ||||
−0.926668 | + | 0.375881i | \(0.877340\pi\) | |||||||
\(878\) | 176.712i | 0.201267i | ||||||||
\(879\) | − | 112.098i | − | 0.127529i | ||||||
\(880\) | −39.2769 | − | 216.063i | −0.0446328 | − | 0.245526i | ||||
\(881\) | 373.491i | 0.423939i | 0.977276 | + | 0.211970i | \(0.0679878\pi\) | ||||
−0.977276 | + | 0.211970i | \(0.932012\pi\) | |||||||
\(882\) | − | 20.0034i | − | 0.0226796i | ||||||
\(883\) | 990.692i | 1.12196i | 0.827829 | + | 0.560981i | \(0.189576\pi\) | ||||
−0.827829 | + | 0.560981i | \(0.810424\pi\) | |||||||
\(884\) | 143.501i | 0.162331i | ||||||||
\(885\) | −97.1804 | − | 534.591i | −0.109808 | − | 0.604058i | ||||
\(886\) | 730.214 | 0.824169 | ||||||||
\(887\) | − | 897.114i | − | 1.01140i | −0.862709 | − | 0.505701i | \(-0.831234\pi\) | ||
0.862709 | − | 0.505701i | \(-0.168766\pi\) | |||||||
\(888\) | −111.590 | −0.125664 | ||||||||
\(889\) | − | 401.228i | − | 0.451325i | ||||||
\(890\) | −385.856 | + | 70.1427i | −0.433546 | + | 0.0788120i | ||||
\(891\) | − | 98.8217i | − | 0.110911i | ||||||
\(892\) | 185.569i | 0.208037i | ||||||||
\(893\) | −76.5360 | −0.0857066 | ||||||||
\(894\) | 303.938i | 0.339975i | ||||||||
\(895\) | 443.735 | − | 80.6642i | 0.495793 | − | 0.0901276i | ||||
\(896\) | − | 75.2894i | − | 0.0840284i | ||||||
\(897\) | −35.5366 | − | 100.982i | −0.0396172 | − | 0.112577i | ||||
\(898\) | − | 64.2357i | − | 0.0715320i | ||||||
\(899\) | −472.900 | −0.526029 | ||||||||
\(900\) | 140.403 | − | 52.7908i | 0.156004 | − | 0.0586565i | ||||
\(901\) | 505.121 | 0.560622 | ||||||||
\(902\) | 1037.34 | 1.15004 | ||||||||
\(903\) | − | 476.334i | − | 0.527502i | ||||||
\(904\) | − | 4.98200i | − | 0.00551107i | ||||||
\(905\) | −45.0695 | − | 247.928i | −0.0498005 | − | 0.273954i | ||||
\(906\) | −724.380 | −0.799537 | ||||||||
\(907\) | 1061.17 | 1.16998 | 0.584990 | − | 0.811040i | \(-0.301098\pi\) | ||||
0.584990 | + | 0.811040i | \(0.301098\pi\) | |||||||
\(908\) | 285.882 | 0.314848 | ||||||||
\(909\) | 168.703 | 0.185592 | ||||||||
\(910\) | −124.412 | + | 22.6161i | −0.136716 | + | 0.0248529i | ||||
\(911\) | − | 1270.71i | − | 1.39485i | −0.716658 | − | 0.697425i | \(-0.754329\pi\) | ||
0.716658 | − | 0.697425i | \(-0.245671\pi\) | |||||||
\(912\) | 151.460 | 0.166074 | ||||||||
\(913\) | − | 147.272i | − | 0.161305i | ||||||
\(914\) | 145.604i | 0.159304i | ||||||||
\(915\) | 662.711 | − | 120.471i | 0.724275 | − | 0.131662i | ||||
\(916\) | 700.298i | 0.764518i | ||||||||
\(917\) | 121.951 | 0.132989 | ||||||||
\(918\) | −196.207 | −0.213733 | ||||||||
\(919\) | − | 1226.21i | − | 1.33428i | −0.744931 | − | 0.667142i | \(-0.767518\pi\) | ||
0.744931 | − | 0.667142i | \(-0.232482\pi\) | |||||||
\(920\) | 282.566 | − | 161.111i | 0.307137 | − | 0.175120i | ||||
\(921\) | −695.056 | −0.754675 | ||||||||
\(922\) | − | 155.601i | − | 0.168765i | ||||||
\(923\) | 281.111i | 0.304562i | ||||||||
\(924\) | −253.122 | −0.273941 | ||||||||
\(925\) | −533.023 | + | 200.413i | −0.576241 | + | 0.216663i | ||||
\(926\) | 115.000 | 0.124190 | ||||||||
\(927\) | 383.862 | 0.414091 | ||||||||
\(928\) | 138.982i | 0.149765i | ||||||||
\(929\) | 1836.08 | 1.97640 | 0.988200 | − | 0.153168i | \(-0.0489477\pi\) | ||||
0.988200 | + | 0.153168i | \(0.0489477\pi\) | |||||||
\(930\) | −231.937 | + | 42.1626i | −0.249395 | + | 0.0453361i | ||||
\(931\) | − | 103.073i | − | 0.110712i | ||||||
\(932\) | − | 135.695i | − | 0.145596i | ||||||
\(933\) | 307.617i | 0.329707i | ||||||||
\(934\) | − | 1141.64i | − | 1.22232i | ||||||
\(935\) | 262.176 | + | 1442.24i | 0.280402 | + | 1.54250i | ||||
\(936\) | 22.8020 | 0.0243611 | ||||||||
\(937\) | −179.352 | −0.191411 | −0.0957053 | − | 0.995410i | \(-0.530511\pi\) | ||||
−0.0957053 | + | 0.995410i | \(0.530511\pi\) | |||||||
\(938\) | 66.3075i | 0.0706902i | ||||||||
\(939\) | 440.570i | 0.469190i | ||||||||
\(940\) | −6.26162 | − | 34.4453i | −0.00666130 | − | 0.0366439i | ||||
\(941\) | 1098.28i | 1.16714i | 0.812064 | + | 0.583568i | \(0.198344\pi\) | ||||
−0.812064 | + | 0.583568i | \(0.801656\pi\) | |||||||
\(942\) | 577.720 | 0.613291 | ||||||||
\(943\) | 510.040 | + | 1449.34i | 0.540870 | + | 1.53695i | ||||
\(944\) | 250.964 | 0.265851 | ||||||||
\(945\) | −30.9227 | − | 170.107i | −0.0327225 | − | 0.180007i | ||||
\(946\) | 641.722 | 0.678353 | ||||||||
\(947\) | − | 91.9245i | − | 0.0970691i | −0.998822 | − | 0.0485346i | \(-0.984545\pi\) | ||
0.998822 | − | 0.0485346i | \(-0.0154551\pi\) | |||||||
\(948\) | −387.497 | −0.408753 | ||||||||
\(949\) | 300.012 | 0.316134 | ||||||||
\(950\) | 723.465 | − | 272.018i | 0.761542 | − | 0.286335i | ||||
\(951\) | −611.608 | −0.643121 | ||||||||
\(952\) | 502.563i | 0.527902i | ||||||||
\(953\) | 1516.37 | 1.59115 | 0.795577 | − | 0.605853i | \(-0.207168\pi\) | ||||
0.795577 | + | 0.605853i | \(0.207168\pi\) | |||||||
\(954\) | − | 80.2629i | − | 0.0841330i | ||||||
\(955\) | −291.991 | − | 1606.25i | −0.305750 | − | 1.68194i | ||||
\(956\) | 669.982 | 0.700818 | ||||||||
\(957\) | 467.256 | 0.488251 | ||||||||
\(958\) | −702.188 | −0.732973 | ||||||||
\(959\) | 896.292 | 0.934611 | ||||||||
\(960\) | 12.3913 | + | 68.1649i | 0.0129076 | + | 0.0710051i | ||||
\(961\) | −590.516 | −0.614480 | ||||||||
\(962\) | −86.5649 | −0.0899843 | ||||||||
\(963\) | −182.297 | −0.189302 | ||||||||
\(964\) | − | 106.151i | − | 0.110115i | ||||||
\(965\) | −86.1495 | − | 473.910i | −0.0892741 | − | 0.491099i | ||||
\(966\) | −124.455 | − | 353.655i | −0.128836 | − | 0.366103i | ||||
\(967\) | − | 464.442i | − | 0.480292i | −0.970737 | − | 0.240146i | \(-0.922805\pi\) | ||
0.970737 | − | 0.240146i | \(-0.0771953\pi\) | |||||||
\(968\) | 1.23162i | 0.00127234i | ||||||||
\(969\) | −1011.00 | −1.04335 | ||||||||
\(970\) | 77.8716 | + | 428.373i | 0.0802800 | + | 0.441622i | ||||
\(971\) | − | 1386.72i | − | 1.42813i | −0.700077 | − | 0.714067i | \(-0.746851\pi\) | ||
0.700077 | − | 0.714067i | \(-0.253149\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 1226.99 | 1.26104 | ||||||||
\(974\) | 277.240 | 0.284641 | ||||||||
\(975\) | 108.917 | − | 40.9520i | 0.111709 | − | 0.0420021i | ||||
\(976\) | 311.110i | 0.318760i | ||||||||
\(977\) | −1217.04 | −1.24569 | −0.622845 | − | 0.782345i | \(-0.714023\pi\) | ||||
−0.622845 | + | 0.782345i | \(0.714023\pi\) | |||||||
\(978\) | 591.229i | 0.604528i | ||||||||
\(979\) | −608.990 | −0.622053 | ||||||||
\(980\) | 46.3883 | − | 8.43268i | 0.0473350 | − | 0.00860477i | ||||
\(981\) | − | 42.1936i | − | 0.0430108i | ||||||
\(982\) | − | 145.939i | − | 0.148614i | ||||||
\(983\) | −793.530 | −0.807253 | −0.403627 | − | 0.914924i | \(-0.632250\pi\) | ||||
−0.403627 | + | 0.914924i | \(0.632250\pi\) | |||||||
\(984\) | −327.267 | −0.332588 | ||||||||
\(985\) | −3.31927 | − | 18.2594i | −0.00336982 | − | 0.0185374i | ||||
\(986\) | − | 927.719i | − | 0.940891i | ||||||
\(987\) | −40.3533 | −0.0408848 | ||||||||
\(988\) | 117.493 | 0.118920 | ||||||||
\(989\) | 315.523 | + | 896.598i | 0.319032 | + | 0.906570i | ||||
\(990\) | 229.169 | − | 41.6594i | 0.231484 | − | 0.0420802i | ||||
\(991\) | −901.021 | −0.909204 | −0.454602 | − | 0.890695i | \(-0.650219\pi\) | ||||
−0.454602 | + | 0.890695i | \(0.650219\pi\) | |||||||
\(992\) | − | 108.883i | − | 0.109761i | ||||||
\(993\) | 209.572i | 0.211050i | ||||||||
\(994\) | 984.496i | 0.990439i | ||||||||
\(995\) | −260.459 | − | 1432.79i | −0.261768 | − | 1.43999i | ||||
\(996\) | 46.4622i | 0.0466488i | ||||||||
\(997\) | − | 398.753i | − | 0.399953i | −0.979801 | − | 0.199976i | \(-0.935913\pi\) | ||
0.979801 | − | 0.199976i | \(-0.0640865\pi\) | |||||||
\(998\) | 1160.30i | 1.16263i | ||||||||
\(999\) | − | 118.359i | − | 0.118477i |
(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 | 690.3.f.a.229.10 | yes | 48 | |
5.4 | even | 2 | inner | 690.3.f.a.229.11 | yes | 48 | |
23.22 | odd | 2 | inner | 690.3.f.a.229.9 | ✓ | 48 | |
115.114 | odd | 2 | inner | 690.3.f.a.229.12 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.f.a.229.9 | ✓ | 48 | 23.22 | odd | 2 | inner | |
690.3.f.a.229.10 | yes | 48 | 1.1 | even | 1 | trivial | |
690.3.f.a.229.11 | yes | 48 | 5.4 | even | 2 | inner | |
690.3.f.a.229.12 | yes | 48 | 115.114 | odd | 2 | inner |