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 | 229.14 | ||
Character | \(\chi\) | \(=\) | 690.229 |
Dual form | 690.3.f.a.229.16 |
$q$-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 | ||||||||
\(5\) | 4.27075 | + | 2.60014i | 0.854150 | + | 0.520027i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 3.19570 | 0.456529 | 0.228264 | − | 0.973599i | \(-0.426695\pi\) | ||||
0.228264 | + | 0.973599i | \(0.426695\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 3.67715 | − | 6.03975i | 0.367715 | − | 0.603975i | ||||
\(11\) | − | 11.2032i | − | 1.01847i | −0.860628 | − | 0.509234i | \(-0.829929\pi\) | ||
0.860628 | − | 0.509234i | \(-0.170071\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | − | 14.7022i | − | 1.13094i | −0.824771 | − | 0.565468i | \(-0.808696\pi\) | ||
0.824771 | − | 0.565468i | \(-0.191304\pi\) | |||||||
\(14\) | − | 4.51940i | − | 0.322814i | ||||||
\(15\) | −4.50357 | + | 7.39715i | −0.300238 | + | 0.493144i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 10.6897 | 0.628808 | 0.314404 | − | 0.949289i | \(-0.398195\pi\) | ||||
0.314404 | + | 0.949289i | \(0.398195\pi\) | |||||||
\(18\) | 4.24264i | 0.235702i | ||||||||
\(19\) | − | 9.81553i | − | 0.516607i | −0.966064 | − | 0.258303i | \(-0.916837\pi\) | ||
0.966064 | − | 0.258303i | \(-0.0831634\pi\) | |||||||
\(20\) | −8.54150 | − | 5.20027i | −0.427075 | − | 0.260014i | ||||
\(21\) | 5.53511i | 0.263577i | ||||||||
\(22\) | −15.8437 | −0.720166 | ||||||||
\(23\) | −22.2781 | − | 5.71720i | −0.968613 | − | 0.248574i | ||||
\(24\) | −4.89898 | −0.204124 | ||||||||
\(25\) | 11.4786 | + | 22.2091i | 0.459143 | + | 0.888362i | ||||
\(26\) | −20.7920 | −0.799692 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −6.39140 | −0.228264 | ||||||||
\(29\) | 24.7684 | 0.854083 | 0.427042 | − | 0.904232i | \(-0.359556\pi\) | ||||
0.427042 | + | 0.904232i | \(0.359556\pi\) | |||||||
\(30\) | 10.4612 | + | 6.36901i | 0.348705 | + | 0.212300i | ||||
\(31\) | 37.7890 | 1.21900 | 0.609501 | − | 0.792786i | \(-0.291370\pi\) | ||||
0.609501 | + | 0.792786i | \(0.291370\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 19.4044 | 0.588013 | ||||||||
\(34\) | − | 15.1176i | − | 0.444635i | ||||||
\(35\) | 13.6480 | + | 8.30925i | 0.389944 | + | 0.237407i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 45.5299 | 1.23054 | 0.615269 | − | 0.788317i | \(-0.289047\pi\) | ||||
0.615269 | + | 0.788317i | \(0.289047\pi\) | |||||||
\(38\) | −13.8813 | −0.365296 | ||||||||
\(39\) | 25.4649 | 0.652946 | ||||||||
\(40\) | −7.35430 | + | 12.0795i | −0.183857 | + | 0.301988i | ||||
\(41\) | 57.0782 | 1.39215 | 0.696076 | − | 0.717968i | \(-0.254928\pi\) | ||||
0.696076 | + | 0.717968i | \(0.254928\pi\) | |||||||
\(42\) | 7.82783 | 0.186377 | ||||||||
\(43\) | −15.9581 | −0.371119 | −0.185560 | − | 0.982633i | \(-0.559410\pi\) | ||||
−0.185560 | + | 0.982633i | \(0.559410\pi\) | |||||||
\(44\) | 22.4063i | 0.509234i | ||||||||
\(45\) | −12.8122 | − | 7.80041i | −0.284717 | − | 0.173342i | ||||
\(46\) | −8.08534 | + | 31.5060i | −0.175768 | + | 0.684913i | ||||
\(47\) | 12.7398i | 0.271060i | 0.990773 | + | 0.135530i | \(0.0432737\pi\) | ||||
−0.990773 | + | 0.135530i | \(0.956726\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −38.7875 | −0.791582 | ||||||||
\(50\) | 31.4083 | − | 16.2332i | 0.628167 | − | 0.324663i | ||||
\(51\) | 18.5152i | 0.363043i | ||||||||
\(52\) | 29.4043i | 0.565468i | ||||||||
\(53\) | −62.0971 | −1.17164 | −0.585822 | − | 0.810440i | \(-0.699228\pi\) | ||||
−0.585822 | + | 0.810440i | \(0.699228\pi\) | |||||||
\(54\) | −7.34847 | −0.136083 | ||||||||
\(55\) | 29.1297 | − | 47.8459i | 0.529632 | − | 0.869925i | ||||
\(56\) | 9.03880i | 0.161407i | ||||||||
\(57\) | 17.0010 | 0.298263 | ||||||||
\(58\) | − | 35.0278i | − | 0.603928i | ||||||
\(59\) | 76.6723 | 1.29953 | 0.649765 | − | 0.760135i | \(-0.274867\pi\) | ||||
0.649765 | + | 0.760135i | \(0.274867\pi\) | |||||||
\(60\) | 9.00714 | − | 14.7943i | 0.150119 | − | 0.246572i | ||||
\(61\) | 39.0469i | 0.640113i | 0.947398 | + | 0.320057i | \(0.103702\pi\) | ||||
−0.947398 | + | 0.320057i | \(0.896298\pi\) | |||||||
\(62\) | − | 53.4418i | − | 0.861964i | ||||||
\(63\) | −9.58710 | −0.152176 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 38.2276 | − | 62.7892i | 0.588117 | − | 0.965988i | ||||
\(66\) | − | 27.4420i | − | 0.415788i | ||||||
\(67\) | 18.2212 | 0.271958 | 0.135979 | − | 0.990712i | \(-0.456582\pi\) | ||||
0.135979 | + | 0.990712i | \(0.456582\pi\) | |||||||
\(68\) | −21.3795 | −0.314404 | ||||||||
\(69\) | 9.90248 | − | 38.5868i | 0.143514 | − | 0.559229i | ||||
\(70\) | 11.7511 | − | 19.3012i | 0.167872 | − | 0.275732i | ||||
\(71\) | 94.9316 | 1.33707 | 0.668533 | − | 0.743683i | \(-0.266923\pi\) | ||||
0.668533 | + | 0.743683i | \(0.266923\pi\) | |||||||
\(72\) | − | 8.48528i | − | 0.117851i | ||||||
\(73\) | 8.59349i | 0.117719i | 0.998266 | + | 0.0588595i | \(0.0187464\pi\) | ||||
−0.998266 | + | 0.0588595i | \(0.981254\pi\) | |||||||
\(74\) | − | 64.3891i | − | 0.870122i | ||||||
\(75\) | −38.4672 | + | 19.8815i | −0.512896 | + | 0.265087i | ||||
\(76\) | 19.6311i | 0.258303i | ||||||||
\(77\) | − | 35.8019i | − | 0.464960i | ||||||
\(78\) | − | 36.0128i | − | 0.461702i | ||||||
\(79\) | − | 96.9457i | − | 1.22716i | −0.789632 | − | 0.613580i | \(-0.789729\pi\) | ||
0.789632 | − | 0.613580i | \(-0.210271\pi\) | |||||||
\(80\) | 17.0830 | + | 10.4005i | 0.213537 | + | 0.130007i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 80.7208i | − | 0.984400i | ||||||
\(83\) | −69.0270 | −0.831651 | −0.415825 | − | 0.909444i | \(-0.636507\pi\) | ||||
−0.415825 | + | 0.909444i | \(0.636507\pi\) | |||||||
\(84\) | − | 11.0702i | − | 0.131788i | ||||||
\(85\) | 45.6532 | + | 27.7948i | 0.537096 | + | 0.326997i | ||||
\(86\) | 22.5682i | 0.262421i | ||||||||
\(87\) | 42.9001i | 0.493105i | ||||||||
\(88\) | 31.6873 | 0.360083 | ||||||||
\(89\) | − | 91.6181i | − | 1.02942i | −0.857365 | − | 0.514708i | \(-0.827900\pi\) | ||
0.857365 | − | 0.514708i | \(-0.172100\pi\) | |||||||
\(90\) | −11.0314 | + | 18.1193i | −0.122572 | + | 0.201325i | ||||
\(91\) | − | 46.9837i | − | 0.516304i | ||||||
\(92\) | 44.5562 | + | 11.4344i | 0.484306 | + | 0.124287i | ||||
\(93\) | 65.4525i | 0.703791i | ||||||||
\(94\) | 18.0168 | 0.191668 | ||||||||
\(95\) | 25.5217 | − | 41.9196i | 0.268650 | − | 0.441259i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −99.7353 | −1.02820 | −0.514099 | − | 0.857731i | \(-0.671874\pi\) | ||||
−0.514099 | + | 0.857731i | \(0.671874\pi\) | |||||||
\(98\) | 54.8538i | 0.559733i | ||||||||
\(99\) | 33.6095i | 0.339490i | ||||||||
\(100\) | −22.9572 | − | 44.4181i | −0.229572 | − | 0.444181i | ||||
\(101\) | 24.8729 | 0.246267 | 0.123133 | − | 0.992390i | \(-0.460706\pi\) | ||||
0.123133 | + | 0.992390i | \(0.460706\pi\) | |||||||
\(102\) | 26.1844 | 0.256710 | ||||||||
\(103\) | −40.9185 | −0.397267 | −0.198633 | − | 0.980074i | \(-0.563650\pi\) | ||||
−0.198633 | + | 0.980074i | \(0.563650\pi\) | |||||||
\(104\) | 41.5840 | 0.399846 | ||||||||
\(105\) | −14.3921 | + | 23.6391i | −0.137067 | + | 0.225134i | ||||
\(106\) | 87.8185i | 0.828477i | ||||||||
\(107\) | 17.8171 | 0.166515 | 0.0832575 | − | 0.996528i | \(-0.473468\pi\) | ||||
0.0832575 | + | 0.996528i | \(0.473468\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | 73.8190i | 0.677239i | 0.940923 | + | 0.338619i | \(0.109960\pi\) | ||||
−0.940923 | + | 0.338619i | \(0.890040\pi\) | |||||||
\(110\) | −67.6643 | − | 41.1957i | −0.615130 | − | 0.374506i | ||||
\(111\) | 78.8602i | 0.710452i | ||||||||
\(112\) | 12.7828 | 0.114132 | ||||||||
\(113\) | 118.752 | 1.05090 | 0.525450 | − | 0.850824i | \(-0.323897\pi\) | ||||
0.525450 | + | 0.850824i | \(0.323897\pi\) | |||||||
\(114\) | − | 24.0430i | − | 0.210904i | ||||||
\(115\) | −80.2786 | − | 82.3428i | −0.698075 | − | 0.716024i | ||||
\(116\) | −49.5368 | −0.427042 | ||||||||
\(117\) | 44.1065i | 0.376978i | ||||||||
\(118\) | − | 108.431i | − | 0.918906i | ||||||
\(119\) | 34.1612 | 0.287069 | ||||||||
\(120\) | −20.9223 | − | 12.7380i | −0.174353 | − | 0.106150i | ||||
\(121\) | −4.51074 | −0.0372788 | ||||||||
\(122\) | 55.2207 | 0.452628 | ||||||||
\(123\) | 98.8624i | 0.803759i | ||||||||
\(124\) | −75.5781 | −0.609501 | ||||||||
\(125\) | −8.72443 | + | 124.695i | −0.0697955 | + | 0.997561i | ||||
\(126\) | 13.5582i | 0.107605i | ||||||||
\(127\) | − | 137.061i | − | 1.07922i | −0.841916 | − | 0.539609i | \(-0.818572\pi\) | ||
0.841916 | − | 0.539609i | \(-0.181428\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | − | 27.6403i | − | 0.214266i | ||||||
\(130\) | −88.7973 | − | 54.0620i | −0.683057 | − | 0.415862i | ||||
\(131\) | 56.4354 | 0.430805 | 0.215402 | − | 0.976525i | \(-0.430894\pi\) | ||||
0.215402 | + | 0.976525i | \(0.430894\pi\) | |||||||
\(132\) | −38.8089 | −0.294007 | ||||||||
\(133\) | − | 31.3675i | − | 0.235846i | ||||||
\(134\) | − | 25.7686i | − | 0.192303i | ||||||
\(135\) | 13.5107 | − | 22.1915i | 0.100079 | − | 0.164381i | ||||
\(136\) | 30.2352i | 0.222317i | ||||||||
\(137\) | 185.263 | 1.35228 | 0.676141 | − | 0.736772i | \(-0.263651\pi\) | ||||
0.676141 | + | 0.736772i | \(0.263651\pi\) | |||||||
\(138\) | −54.5700 | − | 14.0042i | −0.395435 | − | 0.101480i | ||||
\(139\) | −216.501 | −1.55756 | −0.778780 | − | 0.627297i | \(-0.784161\pi\) | ||||
−0.778780 | + | 0.627297i | \(0.784161\pi\) | |||||||
\(140\) | −27.2961 | − | 16.6185i | −0.194972 | − | 0.118704i | ||||
\(141\) | −22.0660 | −0.156496 | ||||||||
\(142\) | − | 134.254i | − | 0.945448i | ||||||
\(143\) | −164.711 | −1.15182 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 105.780 | + | 64.4012i | 0.729515 | + | 0.444147i | ||||
\(146\) | 12.1530 | 0.0832399 | ||||||||
\(147\) | − | 67.1819i | − | 0.457020i | ||||||
\(148\) | −91.0599 | −0.615269 | ||||||||
\(149\) | 42.7648i | 0.287012i | 0.989649 | + | 0.143506i | \(0.0458377\pi\) | ||||
−0.989649 | + | 0.143506i | \(0.954162\pi\) | |||||||
\(150\) | 28.1167 | + | 54.4009i | 0.187444 | + | 0.362672i | ||||
\(151\) | −232.802 | −1.54173 | −0.770867 | − | 0.636996i | \(-0.780177\pi\) | ||||
−0.770867 | + | 0.636996i | \(0.780177\pi\) | |||||||
\(152\) | 27.7625 | 0.182648 | ||||||||
\(153\) | −32.0692 | −0.209603 | ||||||||
\(154\) | −50.6316 | −0.328776 | ||||||||
\(155\) | 161.387 | + | 98.2566i | 1.04121 | + | 0.633914i | ||||
\(156\) | −50.9298 | −0.326473 | ||||||||
\(157\) | −225.331 | −1.43523 | −0.717613 | − | 0.696442i | \(-0.754765\pi\) | ||||
−0.717613 | + | 0.696442i | \(0.754765\pi\) | |||||||
\(158\) | −137.102 | −0.867733 | ||||||||
\(159\) | − | 107.555i | − | 0.676448i | ||||||
\(160\) | 14.7086 | − | 24.1590i | 0.0919287 | − | 0.150994i | ||||
\(161\) | −71.1941 | − | 18.2705i | −0.442199 | − | 0.113481i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 160.569i | 0.985086i | 0.870288 | + | 0.492543i | \(0.163933\pi\) | ||||
−0.870288 | + | 0.492543i | \(0.836067\pi\) | |||||||
\(164\) | −114.156 | −0.696076 | ||||||||
\(165\) | 82.8715 | + | 50.4542i | 0.502251 | + | 0.305783i | ||||
\(166\) | 97.6189i | 0.588066i | ||||||||
\(167\) | 168.699i | 1.01017i | 0.863069 | + | 0.505086i | \(0.168539\pi\) | ||||
−0.863069 | + | 0.505086i | \(0.831461\pi\) | |||||||
\(168\) | −15.6557 | −0.0931885 | ||||||||
\(169\) | −47.1534 | −0.279014 | ||||||||
\(170\) | 39.3078 | − | 64.5634i | 0.231222 | − | 0.379784i | ||||
\(171\) | 29.4466i | 0.172202i | ||||||||
\(172\) | 31.9162 | 0.185560 | ||||||||
\(173\) | − | 48.8655i | − | 0.282460i | −0.989977 | − | 0.141230i | \(-0.954894\pi\) | ||
0.989977 | − | 0.141230i | \(-0.0451057\pi\) | |||||||
\(174\) | 60.6700 | 0.348678 | ||||||||
\(175\) | 36.6821 | + | 70.9735i | 0.209612 | + | 0.405563i | ||||
\(176\) | − | 44.8126i | − | 0.254617i | ||||||
\(177\) | 132.800i | 0.750284i | ||||||||
\(178\) | −129.568 | −0.727908 | ||||||||
\(179\) | 141.731 | 0.791794 | 0.395897 | − | 0.918295i | \(-0.370434\pi\) | ||||
0.395897 | + | 0.918295i | \(0.370434\pi\) | |||||||
\(180\) | 25.6245 | + | 15.6008i | 0.142358 | + | 0.0866712i | ||||
\(181\) | − | 97.7581i | − | 0.540100i | −0.962846 | − | 0.270050i | \(-0.912960\pi\) | ||
0.962846 | − | 0.270050i | \(-0.0870402\pi\) | |||||||
\(182\) | −66.4449 | −0.365082 | ||||||||
\(183\) | −67.6312 | −0.369570 | ||||||||
\(184\) | 16.1707 | − | 63.0120i | 0.0878841 | − | 0.342456i | ||||
\(185\) | 194.447 | + | 118.384i | 1.05106 | + | 0.639914i | ||||
\(186\) | 92.5639 | 0.497655 | ||||||||
\(187\) | − | 119.759i | − | 0.640422i | ||||||
\(188\) | − | 25.4796i | − | 0.135530i | ||||||
\(189\) | − | 16.6053i | − | 0.0878590i | ||||||
\(190\) | −59.2833 | − | 36.0931i | −0.312018 | − | 0.189964i | ||||
\(191\) | 93.5071i | 0.489566i | 0.969578 | + | 0.244783i | \(0.0787167\pi\) | ||||
−0.969578 | + | 0.244783i | \(0.921283\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | − | 39.3466i | − | 0.203869i | −0.994791 | − | 0.101934i | \(-0.967497\pi\) | ||
0.994791 | − | 0.101934i | \(-0.0325031\pi\) | |||||||
\(194\) | 141.047i | 0.727046i | ||||||||
\(195\) | 108.754 | + | 66.2122i | 0.557713 | + | 0.339550i | ||||
\(196\) | 77.5750 | 0.395791 | ||||||||
\(197\) | 327.431i | 1.66209i | 0.556208 | + | 0.831043i | \(0.312256\pi\) | ||||
−0.556208 | + | 0.831043i | \(0.687744\pi\) | |||||||
\(198\) | 47.5310 | 0.240055 | ||||||||
\(199\) | − | 174.324i | − | 0.876001i | −0.898975 | − | 0.438000i | \(-0.855687\pi\) | ||
0.898975 | − | 0.438000i | \(-0.144313\pi\) | |||||||
\(200\) | −62.8167 | + | 32.4663i | −0.314083 | + | 0.162332i | ||||
\(201\) | 31.5600i | 0.157015i | ||||||||
\(202\) | − | 35.1756i | − | 0.174137i | ||||||
\(203\) | 79.1524 | 0.389913 | ||||||||
\(204\) | − | 37.0303i | − | 0.181521i | ||||||
\(205\) | 243.767 | + | 148.411i | 1.18911 | + | 0.723957i | ||||
\(206\) | 57.8674i | 0.280910i | ||||||||
\(207\) | 66.8343 | + | 17.1516i | 0.322871 | + | 0.0828580i | ||||
\(208\) | − | 58.8086i | − | 0.282734i | ||||||
\(209\) | −109.965 | −0.526148 | ||||||||
\(210\) | 33.4307 | + | 20.3534i | 0.159194 | + | 0.0969211i | ||||
\(211\) | −276.060 | −1.30834 | −0.654170 | − | 0.756348i | \(-0.726982\pi\) | ||||
−0.654170 | + | 0.756348i | \(0.726982\pi\) | |||||||
\(212\) | 124.194 | 0.585822 | ||||||||
\(213\) | 164.426i | 0.771955i | ||||||||
\(214\) | − | 25.1972i | − | 0.117744i | ||||||
\(215\) | −68.1531 | − | 41.4933i | −0.316991 | − | 0.192992i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 120.762 | 0.556509 | ||||||||
\(218\) | 104.396 | 0.478880 | ||||||||
\(219\) | −14.8844 | −0.0679651 | ||||||||
\(220\) | −58.2595 | + | 95.6917i | −0.264816 | + | 0.434962i | ||||
\(221\) | − | 157.162i | − | 0.711141i | ||||||
\(222\) | 111.525 | 0.502365 | ||||||||
\(223\) | − | 239.528i | − | 1.07412i | −0.843545 | − | 0.537059i | \(-0.819535\pi\) | ||
0.843545 | − | 0.537059i | \(-0.180465\pi\) | |||||||
\(224\) | − | 18.0776i | − | 0.0807036i | ||||||
\(225\) | −34.4357 | − | 66.6272i | −0.153048 | − | 0.296121i | ||||
\(226\) | − | 167.940i | − | 0.743099i | ||||||
\(227\) | −164.561 | −0.724936 | −0.362468 | − | 0.931996i | \(-0.618066\pi\) | ||||
−0.362468 | + | 0.931996i | \(0.618066\pi\) | |||||||
\(228\) | −34.0020 | −0.149132 | ||||||||
\(229\) | 88.8399i | 0.387947i | 0.981007 | + | 0.193974i | \(0.0621376\pi\) | ||||
−0.981007 | + | 0.193974i | \(0.937862\pi\) | |||||||
\(230\) | −116.450 | + | 113.531i | −0.506306 | + | 0.493614i | ||||
\(231\) | 62.0108 | 0.268445 | ||||||||
\(232\) | 70.0557i | 0.301964i | ||||||||
\(233\) | 206.041i | 0.884296i | 0.896942 | + | 0.442148i | \(0.145783\pi\) | ||||
−0.896942 | + | 0.442148i | \(0.854217\pi\) | |||||||
\(234\) | 62.3760 | 0.266564 | ||||||||
\(235\) | −33.1252 | + | 54.4085i | −0.140958 | + | 0.231526i | ||||
\(236\) | −153.345 | −0.649765 | ||||||||
\(237\) | 167.915 | 0.708501 | ||||||||
\(238\) | − | 48.3112i | − | 0.202988i | ||||||
\(239\) | 153.776 | 0.643413 | 0.321706 | − | 0.946839i | \(-0.395744\pi\) | ||||
0.321706 | + | 0.946839i | \(0.395744\pi\) | |||||||
\(240\) | −18.0143 | + | 29.5886i | −0.0750595 | + | 0.123286i | ||||
\(241\) | 390.573i | 1.62063i | 0.585991 | + | 0.810317i | \(0.300705\pi\) | ||||
−0.585991 | + | 0.810317i | \(0.699295\pi\) | |||||||
\(242\) | 6.37914i | 0.0263601i | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | − | 78.0938i | − | 0.320057i | ||||||
\(245\) | −165.652 | − | 100.853i | −0.676129 | − | 0.411644i | ||||
\(246\) | 139.813 | 0.568344 | ||||||||
\(247\) | −144.309 | −0.584249 | ||||||||
\(248\) | 106.884i | 0.430982i | ||||||||
\(249\) | − | 119.558i | − | 0.480154i | ||||||
\(250\) | 176.346 | + | 12.3382i | 0.705382 | + | 0.0493529i | ||||
\(251\) | − | 403.416i | − | 1.60723i | −0.595147 | − | 0.803617i | \(-0.702906\pi\) | ||
0.595147 | − | 0.803617i | \(-0.297094\pi\) | |||||||
\(252\) | 19.1742 | 0.0760881 | ||||||||
\(253\) | −64.0507 | + | 249.585i | −0.253165 | + | 0.986502i | ||||
\(254\) | −193.833 | −0.763122 | ||||||||
\(255\) | −48.1420 | + | 79.0736i | −0.188792 | + | 0.310093i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 310.575i | 1.20846i | 0.796809 | + | 0.604231i | \(0.206520\pi\) | ||||
−0.796809 | + | 0.604231i | \(0.793480\pi\) | |||||||
\(258\) | −39.0893 | −0.151509 | ||||||||
\(259\) | 145.500 | 0.561776 | ||||||||
\(260\) | −76.4552 | + | 125.578i | −0.294059 | + | 0.482994i | ||||
\(261\) | −74.3052 | −0.284694 | ||||||||
\(262\) | − | 79.8117i | − | 0.304625i | ||||||
\(263\) | −222.756 | −0.846980 | −0.423490 | − | 0.905901i | \(-0.639195\pi\) | ||||
−0.423490 | + | 0.905901i | \(0.639195\pi\) | |||||||
\(264\) | 54.8840i | 0.207894i | ||||||||
\(265\) | −265.201 | − | 161.461i | −1.00076 | − | 0.609286i | ||||
\(266\) | −44.3603 | −0.166768 | ||||||||
\(267\) | 158.687 | 0.594334 | ||||||||
\(268\) | −36.4423 | −0.135979 | ||||||||
\(269\) | 42.0265 | 0.156232 | 0.0781161 | − | 0.996944i | \(-0.475110\pi\) | ||||
0.0781161 | + | 0.996944i | \(0.475110\pi\) | |||||||
\(270\) | −31.3835 | − | 19.1070i | −0.116235 | − | 0.0707667i | ||||
\(271\) | 170.649 | 0.629700 | 0.314850 | − | 0.949141i | \(-0.398046\pi\) | ||||
0.314850 | + | 0.949141i | \(0.398046\pi\) | |||||||
\(272\) | 42.7590 | 0.157202 | ||||||||
\(273\) | 81.3781 | 0.298088 | ||||||||
\(274\) | − | 262.001i | − | 0.956208i | ||||||
\(275\) | 248.812 | − | 128.596i | 0.904769 | − | 0.467623i | ||||
\(276\) | −19.8050 | + | 77.1736i | −0.0717571 | + | 0.279614i | ||||
\(277\) | 412.691i | 1.48986i | 0.667143 | + | 0.744930i | \(0.267517\pi\) | ||||
−0.667143 | + | 0.744930i | \(0.732483\pi\) | |||||||
\(278\) | 306.178i | 1.10136i | ||||||||
\(279\) | −113.367 | −0.406334 | ||||||||
\(280\) | −23.5021 | + | 38.6025i | −0.0839361 | + | 0.137866i | ||||
\(281\) | − | 20.8145i | − | 0.0740729i | −0.999314 | − | 0.0370364i | \(-0.988208\pi\) | ||
0.999314 | − | 0.0370364i | \(-0.0117918\pi\) | |||||||
\(282\) | 31.2060i | 0.110660i | ||||||||
\(283\) | −402.588 | −1.42257 | −0.711286 | − | 0.702903i | \(-0.751887\pi\) | ||||
−0.711286 | + | 0.702903i | \(0.751887\pi\) | |||||||
\(284\) | −189.863 | −0.668533 | ||||||||
\(285\) | 72.6070 | + | 44.2049i | 0.254761 | + | 0.155105i | ||||
\(286\) | 232.936i | 0.814461i | ||||||||
\(287\) | 182.405 | 0.635557 | ||||||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | −174.729 | −0.604600 | ||||||||
\(290\) | 91.0771 | − | 149.595i | 0.314059 | − | 0.515845i | ||||
\(291\) | − | 172.747i | − | 0.593631i | ||||||
\(292\) | − | 17.1870i | − | 0.0588595i | ||||||
\(293\) | −107.231 | −0.365977 | −0.182988 | − | 0.983115i | \(-0.558577\pi\) | ||||
−0.182988 | + | 0.983115i | \(0.558577\pi\) | |||||||
\(294\) | −95.0096 | −0.323162 | ||||||||
\(295\) | 327.448 | + | 199.358i | 1.10999 | + | 0.675791i | ||||
\(296\) | 128.778i | 0.435061i | ||||||||
\(297\) | −58.2133 | −0.196004 | ||||||||
\(298\) | 60.4786 | 0.202948 | ||||||||
\(299\) | −84.0552 | + | 327.536i | −0.281121 | + | 1.09544i | ||||
\(300\) | 76.9344 | − | 39.7630i | 0.256448 | − | 0.132543i | ||||
\(301\) | −50.9974 | −0.169426 | ||||||||
\(302\) | 329.231i | 1.09017i | ||||||||
\(303\) | 43.0812i | 0.142182i | ||||||||
\(304\) | − | 39.2621i | − | 0.129152i | ||||||
\(305\) | −101.527 | + | 166.760i | −0.332876 | + | 0.546753i | ||||
\(306\) | 45.3527i | 0.148212i | ||||||||
\(307\) | − | 225.517i | − | 0.734582i | −0.930106 | − | 0.367291i | \(-0.880285\pi\) | ||
0.930106 | − | 0.367291i | \(-0.119715\pi\) | |||||||
\(308\) | 71.6039i | 0.232480i | ||||||||
\(309\) | − | 70.8729i | − | 0.229362i | ||||||
\(310\) | 138.956 | − | 228.236i | 0.448245 | − | 0.736246i | ||||
\(311\) | −284.663 | −0.915314 | −0.457657 | − | 0.889129i | \(-0.651311\pi\) | ||||
−0.457657 | + | 0.889129i | \(0.651311\pi\) | |||||||
\(312\) | 72.0256i | 0.230851i | ||||||||
\(313\) | 152.480 | 0.487158 | 0.243579 | − | 0.969881i | \(-0.421679\pi\) | ||||
0.243579 | + | 0.969881i | \(0.421679\pi\) | |||||||
\(314\) | 318.665i | 1.01486i | ||||||||
\(315\) | −40.9441 | − | 24.9278i | −0.129981 | − | 0.0791358i | ||||
\(316\) | 193.891i | 0.613580i | ||||||||
\(317\) | − | 570.042i | − | 1.79824i | −0.437704 | − | 0.899119i | \(-0.644208\pi\) | ||
0.437704 | − | 0.899119i | \(-0.355792\pi\) | |||||||
\(318\) | −152.106 | −0.478321 | ||||||||
\(319\) | − | 277.484i | − | 0.869857i | ||||||
\(320\) | −34.1660 | − | 20.8011i | −0.106769 | − | 0.0650034i | ||||
\(321\) | 30.8601i | 0.0961375i | ||||||||
\(322\) | −25.8383 | + | 100.684i | −0.0802432 | + | 0.312682i | ||||
\(323\) | − | 104.925i | − | 0.324847i | ||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 326.521 | − | 168.760i | 1.00468 | − | 0.519261i | ||||
\(326\) | 227.079 | 0.696561 | ||||||||
\(327\) | −127.858 | −0.391004 | ||||||||
\(328\) | 161.442i | 0.492200i | ||||||||
\(329\) | 40.7126i | 0.123747i | ||||||||
\(330\) | 71.3530 | − | 117.198i | 0.216221 | − | 0.355145i | ||||
\(331\) | 124.401 | 0.375835 | 0.187917 | − | 0.982185i | \(-0.439826\pi\) | ||||
0.187917 | + | 0.982185i | \(0.439826\pi\) | |||||||
\(332\) | 138.054 | 0.415825 | ||||||||
\(333\) | −136.590 | −0.410180 | ||||||||
\(334\) | 238.576 | 0.714300 | ||||||||
\(335\) | 77.8180 | + | 47.3775i | 0.232292 | + | 0.141425i | ||||
\(336\) | 22.1405i | 0.0658942i | ||||||||
\(337\) | −214.663 | −0.636983 | −0.318491 | − | 0.947926i | \(-0.603176\pi\) | ||||
−0.318491 | + | 0.947926i | \(0.603176\pi\) | |||||||
\(338\) | 66.6849i | 0.197293i | ||||||||
\(339\) | 205.684i | 0.606738i | ||||||||
\(340\) | −91.3064 | − | 55.5896i | −0.268548 | − | 0.163499i | ||||
\(341\) | − | 423.356i | − | 1.24151i | ||||||
\(342\) | 41.6438 | 0.121765 | ||||||||
\(343\) | −280.542 | −0.817908 | ||||||||
\(344\) | − | 45.1364i | − | 0.131210i | ||||||
\(345\) | 142.622 | − | 139.047i | 0.413397 | − | 0.403034i | ||||
\(346\) | −69.1063 | −0.199729 | ||||||||
\(347\) | − | 550.835i | − | 1.58742i | −0.608296 | − | 0.793710i | \(-0.708147\pi\) | ||
0.608296 | − | 0.793710i | \(-0.291853\pi\) | |||||||
\(348\) | − | 85.8003i | − | 0.246553i | ||||||
\(349\) | −369.105 | −1.05761 | −0.528804 | − | 0.848744i | \(-0.677359\pi\) | ||||
−0.528804 | + | 0.848744i | \(0.677359\pi\) | |||||||
\(350\) | 100.372 | − | 51.8763i | 0.286776 | − | 0.148218i | ||||
\(351\) | −76.3946 | −0.217649 | ||||||||
\(352\) | −63.3746 | −0.180042 | ||||||||
\(353\) | 414.260i | 1.17354i | 0.809753 | + | 0.586770i | \(0.199601\pi\) | ||||
−0.809753 | + | 0.586770i | \(0.800399\pi\) | |||||||
\(354\) | 187.808 | 0.530531 | ||||||||
\(355\) | 405.429 | + | 246.835i | 1.14205 | + | 0.695311i | ||||
\(356\) | 183.236i | 0.514708i | ||||||||
\(357\) | 59.1689i | 0.165739i | ||||||||
\(358\) | − | 200.438i | − | 0.559883i | ||||||
\(359\) | 285.478i | 0.795202i | 0.917558 | + | 0.397601i | \(0.130157\pi\) | ||||
−0.917558 | + | 0.397601i | \(0.869843\pi\) | |||||||
\(360\) | 22.0629 | − | 36.2385i | 0.0612858 | − | 0.100663i | ||||
\(361\) | 264.655 | 0.733118 | ||||||||
\(362\) | −138.251 | −0.381908 | ||||||||
\(363\) | − | 7.81282i | − | 0.0215229i | ||||||
\(364\) | 93.9673i | 0.258152i | ||||||||
\(365\) | −22.3442 | + | 36.7006i | −0.0612171 | + | 0.100550i | ||||
\(366\) | 95.6450i | 0.261325i | ||||||||
\(367\) | 273.124 | 0.744208 | 0.372104 | − | 0.928191i | \(-0.378637\pi\) | ||||
0.372104 | + | 0.928191i | \(0.378637\pi\) | |||||||
\(368\) | −89.1124 | − | 22.8688i | −0.242153 | − | 0.0621435i | ||||
\(369\) | −171.235 | −0.464051 | ||||||||
\(370\) | 167.420 | − | 274.989i | 0.452487 | − | 0.743215i | ||||
\(371\) | −198.444 | −0.534888 | ||||||||
\(372\) | − | 130.905i | − | 0.351895i | ||||||
\(373\) | −481.201 | −1.29008 | −0.645042 | − | 0.764147i | \(-0.723160\pi\) | ||||
−0.645042 | + | 0.764147i | \(0.723160\pi\) | |||||||
\(374\) | −169.365 | −0.452846 | ||||||||
\(375\) | −215.978 | − | 15.1112i | −0.575942 | − | 0.0402964i | ||||
\(376\) | −36.0336 | −0.0958341 | ||||||||
\(377\) | − | 364.149i | − | 0.965913i | ||||||
\(378\) | −23.4835 | −0.0621257 | ||||||||
\(379\) | 502.144i | 1.32492i | 0.749098 | + | 0.662459i | \(0.230487\pi\) | ||||
−0.749098 | + | 0.662459i | \(0.769513\pi\) | |||||||
\(380\) | −51.0434 | + | 83.8393i | −0.134325 | + | 0.220630i | ||||
\(381\) | 237.396 | 0.623087 | ||||||||
\(382\) | 132.239 | 0.346175 | ||||||||
\(383\) | −579.743 | −1.51369 | −0.756844 | − | 0.653595i | \(-0.773260\pi\) | ||||
−0.756844 | + | 0.653595i | \(0.773260\pi\) | |||||||
\(384\) | −19.5959 | −0.0510310 | ||||||||
\(385\) | 93.0899 | − | 152.901i | 0.241792 | − | 0.397145i | ||||
\(386\) | −55.6445 | −0.144157 | ||||||||
\(387\) | 47.8744 | 0.123706 | ||||||||
\(388\) | 199.471 | 0.514099 | ||||||||
\(389\) | − | 282.311i | − | 0.725736i | −0.931841 | − | 0.362868i | \(-0.881798\pi\) | ||
0.931841 | − | 0.362868i | \(-0.118202\pi\) | |||||||
\(390\) | 93.6381 | − | 153.802i | 0.240098 | − | 0.394363i | ||||
\(391\) | −238.147 | − | 61.1154i | −0.609072 | − | 0.156305i | ||||
\(392\) | − | 109.708i | − | 0.279866i | ||||||
\(393\) | 97.7490i | 0.248725i | ||||||||
\(394\) | 463.057 | 1.17527 | ||||||||
\(395\) | 252.072 | − | 414.031i | 0.638157 | − | 1.04818i | ||||
\(396\) | − | 67.2189i | − | 0.169745i | ||||||
\(397\) | 44.7863i | 0.112812i | 0.998408 | + | 0.0564059i | \(0.0179641\pi\) | ||||
−0.998408 | + | 0.0564059i | \(0.982036\pi\) | |||||||
\(398\) | −246.532 | −0.619426 | ||||||||
\(399\) | 54.3301 | 0.136166 | ||||||||
\(400\) | 45.9143 | + | 88.8362i | 0.114786 | + | 0.222091i | ||||
\(401\) | 176.453i | 0.440032i | 0.975496 | + | 0.220016i | \(0.0706110\pi\) | ||||
−0.975496 | + | 0.220016i | \(0.929389\pi\) | |||||||
\(402\) | 44.6325 | 0.111026 | ||||||||
\(403\) | − | 555.580i | − | 1.37861i | ||||||
\(404\) | −49.7459 | −0.123133 | ||||||||
\(405\) | 38.4367 | + | 23.4012i | 0.0949055 | + | 0.0577808i | ||||
\(406\) | − | 111.938i | − | 0.275710i | ||||||
\(407\) | − | 510.079i | − | 1.25327i | ||||||
\(408\) | −52.3688 | −0.128355 | ||||||||
\(409\) | 546.610 | 1.33645 | 0.668227 | − | 0.743957i | \(-0.267053\pi\) | ||||
0.668227 | + | 0.743957i | \(0.267053\pi\) | |||||||
\(410\) | 209.885 | − | 344.738i | 0.511915 | − | 0.840825i | ||||
\(411\) | 320.884i | 0.780741i | ||||||||
\(412\) | 81.8369 | 0.198633 | ||||||||
\(413\) | 245.021 | 0.593272 | ||||||||
\(414\) | 24.2560 | − | 94.5180i | 0.0585894 | − | 0.228304i | ||||
\(415\) | −294.797 | − | 179.480i | −0.710354 | − | 0.432481i | ||||
\(416\) | −83.1679 | −0.199923 | ||||||||
\(417\) | − | 374.990i | − | 0.899258i | ||||||
\(418\) | 155.514i | 0.372043i | ||||||||
\(419\) | 695.370i | 1.65959i | 0.558066 | + | 0.829797i | \(0.311544\pi\) | ||||
−0.558066 | + | 0.829797i | \(0.688456\pi\) | |||||||
\(420\) | 28.7841 | − | 47.2782i | 0.0685336 | − | 0.112567i | ||||
\(421\) | − | 376.599i | − | 0.894534i | −0.894400 | − | 0.447267i | \(-0.852397\pi\) | ||
0.894400 | − | 0.447267i | \(-0.147603\pi\) | |||||||
\(422\) | 390.407i | 0.925136i | ||||||||
\(423\) | − | 38.2194i | − | 0.0903533i | ||||||
\(424\) | − | 175.637i | − | 0.414238i | ||||||
\(425\) | 122.703 | + | 237.409i | 0.288713 | + | 0.558609i | ||||
\(426\) | 232.534 | 0.545855 | ||||||||
\(427\) | 124.782i | 0.292230i | ||||||||
\(428\) | −35.6342 | −0.0832575 | ||||||||
\(429\) | − | 285.287i | − | 0.665005i | ||||||
\(430\) | −58.6804 | + | 96.3831i | −0.136466 | + | 0.224147i | ||||
\(431\) | − | 717.791i | − | 1.66541i | −0.553718 | − | 0.832704i | \(-0.686792\pi\) | ||
0.553718 | − | 0.832704i | \(-0.313208\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | −426.428 | −0.984823 | −0.492411 | − | 0.870363i | \(-0.663884\pi\) | ||||
−0.492411 | + | 0.870363i | \(0.663884\pi\) | |||||||
\(434\) | − | 170.784i | − | 0.393511i | ||||||
\(435\) | −111.546 | + | 183.216i | −0.256428 | + | 0.421186i | ||||
\(436\) | − | 147.638i | − | 0.338619i | ||||||
\(437\) | −56.1173 | + | 218.671i | −0.128415 | + | 0.500392i | ||||
\(438\) | 21.0497i | 0.0480586i | ||||||||
\(439\) | −454.954 | −1.03634 | −0.518171 | − | 0.855277i | \(-0.673387\pi\) | ||||
−0.518171 | + | 0.855277i | \(0.673387\pi\) | |||||||
\(440\) | 135.329 | + | 82.3913i | 0.307565 | + | 0.187253i | ||||
\(441\) | 116.363 | 0.263861 | ||||||||
\(442\) | −222.261 | −0.502853 | ||||||||
\(443\) | − | 745.667i | − | 1.68322i | −0.540085 | − | 0.841611i | \(-0.681608\pi\) | ||
0.540085 | − | 0.841611i | \(-0.318392\pi\) | |||||||
\(444\) | − | 157.720i | − | 0.355226i | ||||||
\(445\) | 238.220 | − | 391.278i | 0.535325 | − | 0.879276i | ||||
\(446\) | −338.744 | −0.759516 | ||||||||
\(447\) | −74.0708 | −0.165707 | ||||||||
\(448\) | −25.5656 | −0.0570661 | ||||||||
\(449\) | 504.255 | 1.12306 | 0.561532 | − | 0.827455i | \(-0.310212\pi\) | ||||
0.561532 | + | 0.827455i | \(0.310212\pi\) | |||||||
\(450\) | −94.2250 | + | 48.6995i | −0.209389 | + | 0.108221i | ||||
\(451\) | − | 639.457i | − | 1.41786i | ||||||
\(452\) | −237.503 | −0.525450 | ||||||||
\(453\) | − | 403.225i | − | 0.890120i | ||||||
\(454\) | 232.724i | 0.512607i | ||||||||
\(455\) | 122.164 | − | 200.655i | 0.268492 | − | 0.441001i | ||||
\(456\) | 48.0861i | 0.105452i | ||||||||
\(457\) | −290.397 | −0.635443 | −0.317721 | − | 0.948184i | \(-0.602918\pi\) | ||||
−0.317721 | + | 0.948184i | \(0.602918\pi\) | |||||||
\(458\) | 125.639 | 0.274320 | ||||||||
\(459\) | − | 55.5455i | − | 0.121014i | ||||||
\(460\) | 160.557 | + | 164.686i | 0.349038 | + | 0.358012i | ||||
\(461\) | 537.525 | 1.16600 | 0.582999 | − | 0.812473i | \(-0.301879\pi\) | ||||
0.582999 | + | 0.812473i | \(0.301879\pi\) | |||||||
\(462\) | − | 87.6964i | − | 0.189819i | ||||||
\(463\) | 604.525i | 1.30567i | 0.757500 | + | 0.652835i | \(0.226420\pi\) | ||||
−0.757500 | + | 0.652835i | \(0.773580\pi\) | |||||||
\(464\) | 99.0737 | 0.213521 | ||||||||
\(465\) | −170.185 | + | 279.531i | −0.365990 | + | 0.601143i | ||||
\(466\) | 291.386 | 0.625292 | ||||||||
\(467\) | −42.4654 | −0.0909323 | −0.0454661 | − | 0.998966i | \(-0.514477\pi\) | ||||
−0.0454661 | + | 0.998966i | \(0.514477\pi\) | |||||||
\(468\) | − | 88.2129i | − | 0.188489i | ||||||
\(469\) | 58.2293 | 0.124156 | ||||||||
\(470\) | 76.9453 | + | 46.8462i | 0.163713 | + | 0.0996727i | ||||
\(471\) | − | 390.284i | − | 0.828628i | ||||||
\(472\) | 216.862i | 0.459453i | ||||||||
\(473\) | 178.781i | 0.377973i | ||||||||
\(474\) | − | 237.467i | − | 0.500986i | ||||||
\(475\) | 217.994 | − | 112.668i | 0.458934 | − | 0.237196i | ||||
\(476\) | −68.3224 | −0.143534 | ||||||||
\(477\) | 186.291 | 0.390548 | ||||||||
\(478\) | − | 217.472i | − | 0.454961i | ||||||
\(479\) | 411.978i | 0.860079i | 0.902810 | + | 0.430039i | \(0.141500\pi\) | ||||
−0.902810 | + | 0.430039i | \(0.858500\pi\) | |||||||
\(480\) | 41.8446 | + | 25.4760i | 0.0871763 | + | 0.0530751i | ||||
\(481\) | − | 669.388i | − | 1.39166i | ||||||
\(482\) | 552.353 | 1.14596 | ||||||||
\(483\) | 31.6454 | − | 123.312i | 0.0655183 | − | 0.255304i | ||||
\(484\) | 9.02147 | 0.0186394 | ||||||||
\(485\) | −425.944 | − | 259.325i | −0.878235 | − | 0.534691i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | − | 593.535i | − | 1.21876i | −0.792879 | − | 0.609379i | \(-0.791419\pi\) | ||
0.792879 | − | 0.609379i | \(-0.208581\pi\) | |||||||
\(488\) | −110.441 | −0.226314 | ||||||||
\(489\) | −278.114 | −0.568740 | ||||||||
\(490\) | −142.627 | + | 234.267i | −0.291076 | + | 0.478096i | ||||
\(491\) | −155.028 | −0.315739 | −0.157869 | − | 0.987460i | \(-0.550462\pi\) | ||||
−0.157869 | + | 0.987460i | \(0.550462\pi\) | |||||||
\(492\) | − | 197.725i | − | 0.401880i | ||||||
\(493\) | 264.768 | 0.537055 | ||||||||
\(494\) | 204.084i | 0.413126i | ||||||||
\(495\) | −87.3892 | + | 143.538i | −0.176544 | + | 0.289975i | ||||
\(496\) | 151.156 | 0.304750 | ||||||||
\(497\) | 303.373 | 0.610409 | ||||||||
\(498\) | −169.081 | −0.339520 | ||||||||
\(499\) | −4.87786 | −0.00977527 | −0.00488764 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488764 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(500\) | 17.4489 | − | 249.390i | 0.0348977 | − | 0.498781i | ||||
\(501\) | −292.195 | −0.583224 | ||||||||
\(502\) | −570.516 | −1.13649 | ||||||||
\(503\) | −385.678 | −0.766756 | −0.383378 | − | 0.923592i | \(-0.625239\pi\) | ||||
−0.383378 | + | 0.923592i | \(0.625239\pi\) | |||||||
\(504\) | − | 27.1164i | − | 0.0538024i | ||||||
\(505\) | 106.226 | + | 64.6730i | 0.210349 | + | 0.128065i | ||||
\(506\) | 352.967 | + | 90.5814i | 0.697562 | + | 0.179015i | ||||
\(507\) | − | 81.6720i | − | 0.161089i | ||||||
\(508\) | 274.121i | 0.539609i | ||||||||
\(509\) | 406.891 | 0.799392 | 0.399696 | − | 0.916648i | \(-0.369116\pi\) | ||||
0.399696 | + | 0.916648i | \(0.369116\pi\) | |||||||
\(510\) | 111.827 | + | 68.0830i | 0.219269 | + | 0.133496i | ||||
\(511\) | 27.4622i | 0.0537421i | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −51.0030 | −0.0994210 | ||||||||
\(514\) | 439.219 | 0.854511 | ||||||||
\(515\) | −174.752 | − | 106.394i | −0.339325 | − | 0.206589i | ||||
\(516\) | 55.2805i | 0.107133i | ||||||||
\(517\) | 142.726 | 0.276066 | ||||||||
\(518\) | − | 205.768i | − | 0.397236i | ||||||
\(519\) | 84.6376 | 0.163078 | ||||||||
\(520\) | 177.595 | + | 108.124i | 0.341528 | + | 0.207931i | ||||
\(521\) | − | 501.963i | − | 0.963461i | −0.876320 | − | 0.481730i | \(-0.840009\pi\) | ||
0.876320 | − | 0.481730i | \(-0.159991\pi\) | |||||||
\(522\) | 105.083i | 0.201309i | ||||||||
\(523\) | 217.341 | 0.415565 | 0.207783 | − | 0.978175i | \(-0.433375\pi\) | ||||
0.207783 | + | 0.978175i | \(0.433375\pi\) | |||||||
\(524\) | −112.871 | −0.215402 | ||||||||
\(525\) | −122.930 | + | 63.5353i | −0.234152 | + | 0.121020i | ||||
\(526\) | 315.024i | 0.598905i | ||||||||
\(527\) | 403.955 | 0.766518 | ||||||||
\(528\) | 77.6178 | 0.147003 | ||||||||
\(529\) | 463.627 | + | 254.737i | 0.876422 | + | 0.481544i | ||||
\(530\) | −228.340 | + | 375.051i | −0.430830 | + | 0.707643i | ||||
\(531\) | −230.017 | −0.433177 | ||||||||
\(532\) | 62.7350i | 0.117923i | ||||||||
\(533\) | − | 839.173i | − | 1.57443i | ||||||
\(534\) | − | 224.418i | − | 0.420258i | ||||||
\(535\) | 76.0924 | + | 46.3269i | 0.142229 | + | 0.0865923i | ||||
\(536\) | 51.5372i | 0.0961515i | ||||||||
\(537\) | 245.486i | 0.457143i | ||||||||
\(538\) | − | 59.4344i | − | 0.110473i | ||||||
\(539\) | 434.543i | 0.806201i | ||||||||
\(540\) | −27.0214 | + | 44.3829i | −0.0500396 | + | 0.0821906i | ||||
\(541\) | 140.244 | 0.259231 | 0.129616 | − | 0.991564i | \(-0.458626\pi\) | ||||
0.129616 | + | 0.991564i | \(0.458626\pi\) | |||||||
\(542\) | − | 241.334i | − | 0.445265i | ||||||
\(543\) | 169.322 | 0.311827 | ||||||||
\(544\) | − | 60.4703i | − | 0.111159i | ||||||
\(545\) | −191.939 | + | 315.262i | −0.352183 | + | 0.578463i | ||||
\(546\) | − | 115.086i | − | 0.210780i | ||||||
\(547\) | − | 83.5353i | − | 0.152715i | −0.997080 | − | 0.0763577i | \(-0.975671\pi\) | ||
0.997080 | − | 0.0763577i | \(-0.0243291\pi\) | |||||||
\(548\) | −370.525 | −0.676141 | ||||||||
\(549\) | − | 117.141i | − | 0.213371i | ||||||
\(550\) | −181.863 | − | 351.873i | −0.330660 | − | 0.639768i | ||||
\(551\) | − | 243.115i | − | 0.441225i | ||||||
\(552\) | 109.140 | + | 28.0084i | 0.197717 | + | 0.0507399i | ||||
\(553\) | − | 309.809i | − | 0.560234i | ||||||
\(554\) | 583.633 | 1.05349 | ||||||||
\(555\) | −205.047 | + | 336.792i | −0.369454 | + | 0.606832i | ||||
\(556\) | 433.002 | 0.778780 | ||||||||
\(557\) | 900.002 | 1.61580 | 0.807901 | − | 0.589318i | \(-0.200604\pi\) | ||||
0.807901 | + | 0.589318i | \(0.200604\pi\) | |||||||
\(558\) | 160.325i | 0.287321i | ||||||||
\(559\) | 234.619i | 0.419712i | ||||||||
\(560\) | 54.5921 | + | 33.2370i | 0.0974859 | + | 0.0593518i | ||||
\(561\) | 207.428 | 0.369748 | ||||||||
\(562\) | −29.4361 | −0.0523774 | ||||||||
\(563\) | −1.27327 | −0.00226159 | −0.00113079 | − | 0.999999i | \(-0.500360\pi\) | ||||
−0.00113079 | + | 0.999999i | \(0.500360\pi\) | |||||||
\(564\) | 44.1320 | 0.0782482 | ||||||||
\(565\) | 507.159 | + | 308.771i | 0.897626 | + | 0.546497i | ||||
\(566\) | 569.345i | 1.00591i | ||||||||
\(567\) | 28.7613 | 0.0507254 | ||||||||
\(568\) | 268.507i | 0.472724i | ||||||||
\(569\) | 1129.75i | 1.98550i | 0.120191 | + | 0.992751i | \(0.461649\pi\) | ||||
−0.120191 | + | 0.992751i | \(0.538351\pi\) | |||||||
\(570\) | 62.5152 | − | 102.682i | 0.109676 | − | 0.180143i | ||||
\(571\) | 153.556i | 0.268925i | 0.990919 | + | 0.134462i | \(0.0429307\pi\) | ||||
−0.990919 | + | 0.134462i | \(0.957069\pi\) | |||||||
\(572\) | 329.421 | 0.575911 | ||||||||
\(573\) | −161.959 | −0.282651 | ||||||||
\(574\) | − | 257.959i | − | 0.449407i | ||||||
\(575\) | −128.747 | − | 560.401i | −0.223908 | − | 0.974610i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 602.704i | 1.04455i | 0.852778 | + | 0.522274i | \(0.174916\pi\) | ||||
−0.852778 | + | 0.522274i | \(0.825084\pi\) | |||||||
\(578\) | 247.105i | 0.427517i | ||||||||
\(579\) | 68.1504 | 0.117704 | ||||||||
\(580\) | −211.559 | − | 128.802i | −0.364757 | − | 0.222073i | ||||
\(581\) | −220.590 | −0.379672 | ||||||||
\(582\) | −244.300 | −0.419760 | ||||||||
\(583\) | 695.683i | 1.19328i | ||||||||
\(584\) | −24.3060 | −0.0416199 | ||||||||
\(585\) | −114.683 | + | 188.368i | −0.196039 | + | 0.321996i | ||||
\(586\) | 151.648i | 0.258785i | ||||||||
\(587\) | − | 163.210i | − | 0.278042i | −0.990289 | − | 0.139021i | \(-0.955605\pi\) | ||
0.990289 | − | 0.139021i | \(-0.0443955\pi\) | |||||||
\(588\) | 134.364i | 0.228510i | ||||||||
\(589\) | − | 370.919i | − | 0.629744i | ||||||
\(590\) | 281.935 | − | 463.081i | 0.477856 | − | 0.784883i | ||||
\(591\) | −567.127 | −0.959606 | ||||||||
\(592\) | 182.120 | 0.307635 | ||||||||
\(593\) | 890.275i | 1.50131i | 0.660696 | + | 0.750653i | \(0.270261\pi\) | ||||
−0.660696 | + | 0.750653i | \(0.729739\pi\) | |||||||
\(594\) | 82.3261i | 0.138596i | ||||||||
\(595\) | 145.894 | + | 88.8238i | 0.245200 | + | 0.149284i | ||||
\(596\) | − | 85.5296i | − | 0.143506i | ||||||
\(597\) | 301.938 | 0.505759 | ||||||||
\(598\) | 463.206 | + | 118.872i | 0.774592 | + | 0.198783i | ||||
\(599\) | 643.232 | 1.07384 | 0.536921 | − | 0.843632i | \(-0.319587\pi\) | ||||
0.536921 | + | 0.843632i | \(0.319587\pi\) | |||||||
\(600\) | −56.2333 | − | 108.802i | −0.0937222 | − | 0.181336i | ||||
\(601\) | −185.138 | −0.308050 | −0.154025 | − | 0.988067i | \(-0.549224\pi\) | ||||
−0.154025 | + | 0.988067i | \(0.549224\pi\) | |||||||
\(602\) | 72.1212i | 0.119803i | ||||||||
\(603\) | −54.6635 | −0.0906525 | ||||||||
\(604\) | 465.604 | 0.770867 | ||||||||
\(605\) | −19.2642 | − | 11.7285i | −0.0318417 | − | 0.0193860i | ||||
\(606\) | 60.9260 | 0.100538 | ||||||||
\(607\) | 722.082i | 1.18959i | 0.803877 | + | 0.594796i | \(0.202767\pi\) | ||||
−0.803877 | + | 0.594796i | \(0.797233\pi\) | |||||||
\(608\) | −55.5250 | −0.0913240 | ||||||||
\(609\) | 137.096i | 0.225117i | ||||||||
\(610\) | 235.834 | + | 143.581i | 0.386612 | + | 0.235379i | ||||
\(611\) | 187.303 | 0.306551 | ||||||||
\(612\) | 64.1384 | 0.104801 | ||||||||
\(613\) | −779.332 | −1.27134 | −0.635671 | − | 0.771960i | \(-0.719276\pi\) | ||||
−0.635671 | + | 0.771960i | \(0.719276\pi\) | |||||||
\(614\) | −318.929 | −0.519428 | ||||||||
\(615\) | −257.056 | + | 422.216i | −0.417977 | + | 0.686531i | ||||
\(616\) | 101.263 | 0.164388 | ||||||||
\(617\) | −906.051 | −1.46848 | −0.734239 | − | 0.678891i | \(-0.762461\pi\) | ||||
−0.734239 | + | 0.678891i | \(0.762461\pi\) | |||||||
\(618\) | −100.229 | −0.162183 | ||||||||
\(619\) | − | 829.532i | − | 1.34012i | −0.742308 | − | 0.670058i | \(-0.766269\pi\) | ||
0.742308 | − | 0.670058i | \(-0.233731\pi\) | |||||||
\(620\) | −322.775 | − | 196.513i | −0.520605 | − | 0.316957i | ||||
\(621\) | −29.7074 | + | 115.760i | −0.0478381 | + | 0.186410i | ||||
\(622\) | 402.574i | 0.647225i | ||||||||
\(623\) | − | 292.784i | − | 0.469958i | ||||||
\(624\) | 101.860 | 0.163236 | ||||||||
\(625\) | −361.484 | + | 509.857i | −0.578375 | + | 0.815771i | ||||
\(626\) | − | 215.640i | − | 0.344473i | ||||||
\(627\) | − | 190.465i | − | 0.303772i | ||||||
\(628\) | 450.661 | 0.717613 | ||||||||
\(629\) | 486.703 | 0.773773 | ||||||||
\(630\) | −35.2532 | + | 57.9037i | −0.0559574 | + | 0.0919106i | ||||
\(631\) | 1078.38i | 1.70900i | 0.519451 | + | 0.854500i | \(0.326136\pi\) | ||||
−0.519451 | + | 0.854500i | \(0.673864\pi\) | |||||||
\(632\) | 274.204 | 0.433867 | ||||||||
\(633\) | − | 478.150i | − | 0.755370i | ||||||
\(634\) | −806.161 | −1.27155 | ||||||||
\(635\) | 356.377 | − | 585.352i | 0.561223 | − | 0.921814i | ||||
\(636\) | 215.111i | 0.338224i | ||||||||
\(637\) | 570.260i | 0.895227i | ||||||||
\(638\) | −392.422 | −0.615082 | ||||||||
\(639\) | −284.795 | −0.445688 | ||||||||
\(640\) | −29.4172 | + | 48.3180i | −0.0459644 | + | 0.0754969i | ||||
\(641\) | − | 744.723i | − | 1.16182i | −0.813970 | − | 0.580908i | \(-0.802698\pi\) | ||
0.813970 | − | 0.580908i | \(-0.197302\pi\) | |||||||
\(642\) | 43.6428 | 0.0679795 | ||||||||
\(643\) | 373.410 | 0.580731 | 0.290365 | − | 0.956916i | \(-0.406223\pi\) | ||||
0.290365 | + | 0.956916i | \(0.406223\pi\) | |||||||
\(644\) | 142.388 | + | 36.5409i | 0.221100 | + | 0.0567405i | ||||
\(645\) | 71.8685 | − | 118.045i | 0.111424 | − | 0.183015i | ||||
\(646\) | −148.387 | −0.229701 | ||||||||
\(647\) | 174.894i | 0.270315i | 0.990824 | + | 0.135157i | \(0.0431540\pi\) | ||||
−0.990824 | + | 0.135157i | \(0.956846\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | − | 858.971i | − | 1.32353i | ||||||
\(650\) | −238.663 | − | 461.770i | −0.367173 | − | 0.710416i | ||||
\(651\) | 209.167i | 0.321300i | ||||||||
\(652\) | − | 321.138i | − | 0.492543i | ||||||
\(653\) | 343.261i | 0.525668i | 0.964841 | + | 0.262834i | \(0.0846572\pi\) | ||||
−0.964841 | + | 0.262834i | \(0.915343\pi\) | |||||||
\(654\) | 180.819i | 0.276481i | ||||||||
\(655\) | 241.021 | + | 146.740i | 0.367972 | + | 0.224030i | ||||
\(656\) | 228.313 | 0.348038 | ||||||||
\(657\) | − | 25.7805i | − | 0.0392397i | ||||||
\(658\) | 57.5763 | 0.0875020 | ||||||||
\(659\) | 206.113i | 0.312766i | 0.987696 | + | 0.156383i | \(0.0499834\pi\) | ||||
−0.987696 | + | 0.156383i | \(0.950017\pi\) | |||||||
\(660\) | −165.743 | − | 100.908i | −0.251126 | − | 0.152891i | ||||
\(661\) | 876.964i | 1.32672i | 0.748299 | + | 0.663362i | \(0.230871\pi\) | ||||
−0.748299 | + | 0.663362i | \(0.769129\pi\) | |||||||
\(662\) | − | 175.930i | − | 0.265755i | ||||||
\(663\) | 272.213 | 0.410578 | ||||||||
\(664\) | − | 195.238i | − | 0.294033i | ||||||
\(665\) | 81.5597 | − | 133.963i | 0.122646 | − | 0.201448i | ||||
\(666\) | 193.167i | 0.290041i | ||||||||
\(667\) | −551.793 | − | 141.606i | −0.827276 | − | 0.212303i | ||||
\(668\) | − | 337.398i | − | 0.505086i | ||||||
\(669\) | 414.875 | 0.620142 | ||||||||
\(670\) | 67.0019 | − | 110.051i | 0.100003 | − | 0.164256i | ||||
\(671\) | 437.449 | 0.651935 | ||||||||
\(672\) | 31.3113 | 0.0465942 | ||||||||
\(673\) | 434.411i | 0.645485i | 0.946487 | + | 0.322743i | \(0.104605\pi\) | ||||
−0.946487 | + | 0.322743i | \(0.895395\pi\) | |||||||
\(674\) | 303.580i | 0.450415i | ||||||||
\(675\) | 115.402 | − | 59.6445i | 0.170965 | − | 0.0883622i | ||||
\(676\) | 94.3067 | 0.139507 | ||||||||
\(677\) | −665.420 | −0.982895 | −0.491447 | − | 0.870907i | \(-0.663532\pi\) | ||||
−0.491447 | + | 0.870907i | \(0.663532\pi\) | |||||||
\(678\) | 290.881 | 0.429028 | ||||||||
\(679\) | −318.724 | −0.469402 | ||||||||
\(680\) | −78.6155 | + | 129.127i | −0.115611 | + | 0.189892i | ||||
\(681\) | − | 285.027i | − | 0.418542i | ||||||
\(682\) | −598.716 | −0.877883 | ||||||||
\(683\) | − | 513.018i | − | 0.751124i | −0.926797 | − | 0.375562i | \(-0.877450\pi\) | ||
0.926797 | − | 0.375562i | \(-0.122550\pi\) | |||||||
\(684\) | − | 58.8932i | − | 0.0861011i | ||||||
\(685\) | 791.210 | + | 481.708i | 1.15505 | + | 0.703224i | ||||
\(686\) | 396.747i | 0.578348i | ||||||||
\(687\) | −153.875 | −0.223981 | ||||||||
\(688\) | −63.8325 | −0.0927798 | ||||||||
\(689\) | 912.961i | 1.32505i | ||||||||
\(690\) | −196.642 | − | 201.698i | −0.284988 | − | 0.292316i | ||||
\(691\) | −521.187 | −0.754251 | −0.377125 | − | 0.926162i | \(-0.623087\pi\) | ||||
−0.377125 | + | 0.926162i | \(0.623087\pi\) | |||||||
\(692\) | 97.7311i | 0.141230i | ||||||||
\(693\) | 107.406i | 0.154987i | ||||||||
\(694\) | −778.998 | −1.12248 | ||||||||
\(695\) | −924.620 | − | 562.932i | −1.33039 | − | 0.809973i | ||||
\(696\) | −121.340 | −0.174339 | ||||||||
\(697\) | 610.152 | 0.875397 | ||||||||
\(698\) | 521.993i | 0.747841i | ||||||||
\(699\) | −356.874 | −0.510549 | ||||||||
\(700\) | −73.3642 | − | 141.947i | −0.104806 | − | 0.202781i | ||||
\(701\) | 148.024i | 0.211161i | 0.994411 | + | 0.105580i | \(0.0336700\pi\) | ||||
−0.994411 | + | 0.105580i | \(0.966330\pi\) | |||||||
\(702\) | 108.038i | 0.153901i | ||||||||
\(703\) | − | 446.900i | − | 0.635705i | ||||||
\(704\) | 89.6253i | 0.127309i | ||||||||
\(705\) | −94.2383 | − | 57.3746i | −0.133671 | − | 0.0813824i | ||||
\(706\) | 585.852 | 0.829819 | ||||||||
\(707\) | 79.4864 | 0.112428 | ||||||||
\(708\) | − | 265.600i | − | 0.375142i | ||||||
\(709\) | 1053.52i | 1.48592i | 0.669336 | + | 0.742960i | \(0.266579\pi\) | ||||
−0.669336 | + | 0.742960i | \(0.733421\pi\) | |||||||
\(710\) | 349.078 | − | 573.363i | 0.491659 | − | 0.807554i | ||||
\(711\) | 290.837i | 0.409053i | ||||||||
\(712\) | 259.135 | 0.363954 | ||||||||
\(713\) | −841.868 | − | 216.047i | −1.18074 | − | 0.303012i | ||||
\(714\) | 83.6775 | 0.117195 | ||||||||
\(715\) | −703.437 | − | 428.270i | −0.983828 | − | 0.598979i | ||||
\(716\) | −283.462 | −0.395897 | ||||||||
\(717\) | 266.347i | 0.371474i | ||||||||
\(718\) | 403.726 | 0.562293 | ||||||||
\(719\) | −516.738 | −0.718689 | −0.359345 | − | 0.933205i | \(-0.617000\pi\) | ||||
−0.359345 | + | 0.933205i | \(0.617000\pi\) | |||||||
\(720\) | −51.2490 | − | 31.2016i | −0.0711791 | − | 0.0433356i | ||||
\(721\) | −130.763 | −0.181364 | ||||||||
\(722\) | − | 374.279i | − | 0.518392i | ||||||
\(723\) | −676.492 | −0.935674 | ||||||||
\(724\) | 195.516i | 0.270050i | ||||||||
\(725\) | 284.306 | + | 550.083i | 0.392147 | + | 0.758735i | ||||
\(726\) | −11.0490 | −0.0152190 | ||||||||
\(727\) | 348.090 | 0.478803 | 0.239401 | − | 0.970921i | \(-0.423049\pi\) | ||||
0.239401 | + | 0.970921i | \(0.423049\pi\) | |||||||
\(728\) | 132.890 | 0.182541 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 51.9025 | + | 31.5995i | 0.0710993 | + | 0.0432870i | ||||
\(731\) | −170.588 | −0.233363 | ||||||||
\(732\) | 135.262 | 0.184785 | ||||||||
\(733\) | 1172.59 | 1.59972 | 0.799858 | − | 0.600189i | \(-0.204908\pi\) | ||||
0.799858 | + | 0.600189i | \(0.204908\pi\) | |||||||
\(734\) | − | 386.256i | − | 0.526234i | ||||||
\(735\) | 174.682 | − | 286.917i | 0.237663 | − | 0.390363i | ||||
\(736\) | −32.3414 | + | 126.024i | −0.0439421 | + | 0.171228i | ||||
\(737\) | − | 204.134i | − | 0.276980i | ||||||
\(738\) | 242.162i | 0.328133i | ||||||||
\(739\) | −586.911 | −0.794196 | −0.397098 | − | 0.917776i | \(-0.629983\pi\) | ||||
−0.397098 | + | 0.917776i | \(0.629983\pi\) | |||||||
\(740\) | −388.894 | − | 236.768i | −0.525532 | − | 0.319957i | ||||
\(741\) | − | 249.951i | − | 0.337316i | ||||||
\(742\) | 280.642i | 0.378223i | ||||||||
\(743\) | 256.074 | 0.344648 | 0.172324 | − | 0.985040i | \(-0.444872\pi\) | ||||
0.172324 | + | 0.985040i | \(0.444872\pi\) | |||||||
\(744\) | −185.128 | −0.248828 | ||||||||
\(745\) | −111.194 | + | 182.638i | −0.149254 | + | 0.245151i | ||||
\(746\) | 680.521i | 0.912227i | ||||||||
\(747\) | 207.081 | 0.277217 | ||||||||
\(748\) | 239.518i | 0.320211i | ||||||||
\(749\) | 56.9381 | 0.0760188 | ||||||||
\(750\) | −21.3704 | + | 305.440i | −0.0284939 | + | 0.407253i | ||||
\(751\) | − | 839.297i | − | 1.11757i | −0.829312 | − | 0.558786i | \(-0.811267\pi\) | ||
0.829312 | − | 0.558786i | \(-0.188733\pi\) | |||||||
\(752\) | 50.9592i | 0.0677650i | ||||||||
\(753\) | 698.736 | 0.927937 | ||||||||
\(754\) | −514.985 | −0.683003 | ||||||||
\(755\) | −994.238 | − | 605.316i | −1.31687 | − | 0.801744i | ||||
\(756\) | 33.2107i | 0.0439295i | ||||||||
\(757\) | 979.027 | 1.29330 | 0.646649 | − | 0.762788i | \(-0.276170\pi\) | ||||
0.646649 | + | 0.762788i | \(0.276170\pi\) | |||||||
\(758\) | 710.139 | 0.936858 | ||||||||
\(759\) | −432.294 | − | 110.939i | −0.569557 | − | 0.146165i | ||||
\(760\) | 118.567 | + | 72.1863i | 0.156009 | + | 0.0949820i | ||||
\(761\) | 419.697 | 0.551507 | 0.275753 | − | 0.961228i | \(-0.411073\pi\) | ||||
0.275753 | + | 0.961228i | \(0.411073\pi\) | |||||||
\(762\) | − | 335.729i | − | 0.440589i | ||||||
\(763\) | 235.903i | 0.309179i | ||||||||
\(764\) | − | 187.014i | − | 0.244783i | ||||||
\(765\) | −136.960 | − | 83.3843i | −0.179032 | − | 0.108999i | ||||
\(766\) | 819.880i | 1.07034i | ||||||||
\(767\) | − | 1127.25i | − | 1.46968i | ||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | − | 215.482i | − | 0.280211i | −0.990137 | − | 0.140105i | \(-0.955256\pi\) | ||
0.990137 | − | 0.140105i | \(-0.0447442\pi\) | |||||||
\(770\) | −216.235 | − | 131.649i | −0.280824 | − | 0.170973i | ||||
\(771\) | −537.931 | −0.697706 | ||||||||
\(772\) | 78.6932i | 0.101934i | ||||||||
\(773\) | 1480.63 | 1.91543 | 0.957716 | − | 0.287715i | \(-0.0928956\pi\) | ||||
0.957716 | + | 0.287715i | \(0.0928956\pi\) | |||||||
\(774\) | − | 67.7046i | − | 0.0874736i | ||||||
\(775\) | 433.765 | + | 839.259i | 0.559696 | + | 1.08291i | ||||
\(776\) | − | 282.094i | − | 0.363523i | ||||||
\(777\) | 252.013i | 0.324342i | ||||||||
\(778\) | −399.249 | −0.513173 | ||||||||
\(779\) | − | 560.253i | − | 0.719195i | ||||||
\(780\) | −217.508 | − | 132.424i | −0.278857 | − | 0.169775i | ||||
\(781\) | − | 1063.53i | − | 1.36176i | ||||||
\(782\) | −86.4302 | + | 336.791i | −0.110525 | + | 0.430679i | ||||
\(783\) | − | 128.700i | − | 0.164368i | ||||||
\(784\) | −155.150 | −0.197895 | ||||||||
\(785\) | −962.330 | − | 585.890i | −1.22590 | − | 0.746357i | ||||
\(786\) | 138.238 | 0.175875 | ||||||||
\(787\) | −464.168 | −0.589795 | −0.294897 | − | 0.955529i | \(-0.595285\pi\) | ||||
−0.294897 | + | 0.955529i | \(0.595285\pi\) | |||||||
\(788\) | − | 654.862i | − | 0.831043i | ||||||
\(789\) | − | 385.824i | − | 0.489004i | ||||||
\(790\) | −585.528 | − | 356.484i | −0.741174 | − | 0.451245i | ||||
\(791\) | 379.495 | 0.479766 | ||||||||
\(792\) | −95.0619 | −0.120028 | ||||||||
\(793\) | 574.074 | 0.723926 | ||||||||
\(794\) | 63.3374 | 0.0797700 | ||||||||
\(795\) | 279.658 | − | 459.342i | 0.351772 | − | 0.577788i | ||||
\(796\) | 348.648i | 0.438000i | ||||||||
\(797\) | −584.750 | −0.733689 | −0.366844 | − | 0.930282i | \(-0.619562\pi\) | ||||
−0.366844 | + | 0.930282i | \(0.619562\pi\) | |||||||
\(798\) | − | 76.8343i | − | 0.0962836i | ||||||
\(799\) | 136.185i | 0.170445i | ||||||||
\(800\) | 125.633 | − | 64.9327i | 0.157042 | − | 0.0811658i | ||||
\(801\) | 274.854i | 0.343139i | ||||||||
\(802\) | 249.542 | 0.311150 | ||||||||
\(803\) | 96.2742 | 0.119893 | ||||||||
\(804\) | − | 63.1199i | − | 0.0785074i | ||||||
\(805\) | −256.546 | − | 263.143i | −0.318691 | − | 0.326886i | ||||
\(806\) | −785.709 | −0.974825 | ||||||||
\(807\) | 72.7920i | 0.0902007i | ||||||||
\(808\) | 70.3513i | 0.0870684i | ||||||||
\(809\) | −665.496 | −0.822615 | −0.411308 | − | 0.911497i | \(-0.634928\pi\) | ||||
−0.411308 | + | 0.911497i | \(0.634928\pi\) | |||||||
\(810\) | 33.0943 | − | 54.3578i | 0.0408572 | − | 0.0671083i | ||||
\(811\) | 858.250 | 1.05826 | 0.529131 | − | 0.848540i | \(-0.322518\pi\) | ||||
0.529131 | + | 0.848540i | \(0.322518\pi\) | |||||||
\(812\) | −158.305 | −0.194957 | ||||||||
\(813\) | 295.572i | 0.363557i | ||||||||
\(814\) | −721.361 | −0.886193 | ||||||||
\(815\) | −417.501 | + | 685.750i | −0.512272 | + | 0.841411i | ||||
\(816\) | 74.0607i | 0.0907607i | ||||||||
\(817\) | 156.637i | 0.191723i | ||||||||
\(818\) | − | 773.023i | − | 0.945016i | ||||||
\(819\) | 140.951i | 0.172101i | ||||||||
\(820\) | −487.534 | − | 296.822i | −0.594553 | − | 0.361979i | ||||
\(821\) | −1050.76 | −1.27985 | −0.639927 | − | 0.768436i | \(-0.721035\pi\) | ||||
−0.639927 | + | 0.768436i | \(0.721035\pi\) | |||||||
\(822\) | 453.799 | 0.552067 | ||||||||
\(823\) | 1241.28i | 1.50824i | 0.656739 | + | 0.754118i | \(0.271935\pi\) | ||||
−0.656739 | + | 0.754118i | \(0.728065\pi\) | |||||||
\(824\) | − | 115.735i | − | 0.140455i | ||||||
\(825\) | 222.735 | + | 430.954i | 0.269982 | + | 0.522369i | ||||
\(826\) | − | 346.513i | − | 0.419507i | ||||||
\(827\) | 615.457 | 0.744205 | 0.372102 | − | 0.928192i | \(-0.378637\pi\) | ||||
0.372102 | + | 0.928192i | \(0.378637\pi\) | |||||||
\(828\) | −133.669 | − | 34.3032i | −0.161435 | − | 0.0414290i | ||||
\(829\) | 1487.12 | 1.79387 | 0.896936 | − | 0.442159i | \(-0.145787\pi\) | ||||
0.896936 | + | 0.442159i | \(0.145787\pi\) | |||||||
\(830\) | −253.823 | + | 416.906i | −0.305810 | + | 0.502296i | ||||
\(831\) | −714.802 | −0.860171 | ||||||||
\(832\) | 117.617i | 0.141367i | ||||||||
\(833\) | −414.628 | −0.497753 | ||||||||
\(834\) | −530.316 | −0.635871 | ||||||||
\(835\) | −438.640 | + | 720.470i | −0.525317 | + | 0.862839i | ||||
\(836\) | 219.930 | 0.263074 | ||||||||
\(837\) | − | 196.358i | − | 0.234597i | ||||||
\(838\) | 983.401 | 1.17351 | ||||||||
\(839\) | 727.270i | 0.866830i | 0.901195 | + | 0.433415i | \(0.142692\pi\) | ||||
−0.901195 | + | 0.433415i | \(0.857308\pi\) | |||||||
\(840\) | −66.8614 | − | 40.7069i | −0.0795969 | − | 0.0484606i | ||||
\(841\) | −227.526 | −0.270542 | ||||||||
\(842\) | −532.591 | −0.632531 | ||||||||
\(843\) | 36.0517 | 0.0427660 | ||||||||
\(844\) | 552.119 | 0.654170 | ||||||||
\(845\) | −201.380 | − | 122.605i | −0.238320 | − | 0.145095i | ||||
\(846\) | −54.0504 | −0.0638894 | ||||||||
\(847\) | −14.4150 | −0.0170188 | ||||||||
\(848\) | −248.388 | −0.292911 | ||||||||
\(849\) | − | 697.303i | − | 0.821323i | ||||||
\(850\) | 335.747 | − | 173.528i | 0.394997 | − | 0.204151i | ||||
\(851\) | −1014.32 | − | 260.304i | −1.19192 | − | 0.305880i | ||||
\(852\) | − | 328.853i | − | 0.385978i | ||||||
\(853\) | − | 169.747i | − | 0.198999i | −0.995038 | − | 0.0994997i | \(-0.968276\pi\) | ||
0.995038 | − | 0.0994997i | \(-0.0317242\pi\) | |||||||
\(854\) | 176.469 | 0.206638 | ||||||||
\(855\) | −76.5651 | + | 125.759i | −0.0895499 | + | 0.147086i | ||||
\(856\) | 50.3944i | 0.0588719i | ||||||||
\(857\) | 370.253i | 0.432034i | 0.976390 | + | 0.216017i | \(0.0693066\pi\) | ||||
−0.976390 | + | 0.216017i | \(0.930693\pi\) | |||||||
\(858\) | −403.457 | −0.470229 | ||||||||
\(859\) | −457.241 | −0.532294 | −0.266147 | − | 0.963932i | \(-0.585751\pi\) | ||||
−0.266147 | + | 0.963932i | \(0.585751\pi\) | |||||||
\(860\) | 136.306 | + | 82.9866i | 0.158496 | + | 0.0964960i | ||||
\(861\) | 315.935i | 0.366939i | ||||||||
\(862\) | −1015.11 | −1.17762 | ||||||||
\(863\) | 1404.82i | 1.62783i | 0.580983 | + | 0.813916i | \(0.302668\pi\) | ||||
−0.580983 | + | 0.813916i | \(0.697332\pi\) | |||||||
\(864\) | −29.3939 | −0.0340207 | ||||||||
\(865\) | 127.057 | − | 208.692i | 0.146887 | − | 0.241263i | ||||
\(866\) | 603.061i | 0.696375i | ||||||||
\(867\) | − | 302.640i | − | 0.349066i | ||||||
\(868\) | −241.525 | −0.278254 | ||||||||
\(869\) | −1086.10 | −1.24982 | ||||||||
\(870\) | 259.106 | + | 157.750i | 0.297823 | + | 0.181322i | ||||
\(871\) | − | 267.890i | − | 0.307566i | ||||||
\(872\) | −208.792 | −0.239440 | ||||||||
\(873\) | 299.206 | 0.342733 | ||||||||
\(874\) | 309.248 | + | 79.3619i | 0.353831 | + | 0.0908031i | ||||
\(875\) | −27.8807 | + | 398.488i | −0.0318636 | + | 0.455415i | ||||
\(876\) | 29.7687 | 0.0339825 | ||||||||
\(877\) | − | 63.8174i | − | 0.0727679i | −0.999338 | − | 0.0363839i | \(-0.988416\pi\) | ||
0.999338 | − | 0.0363839i | \(-0.0115839\pi\) | |||||||
\(878\) | 643.402i | 0.732804i | ||||||||
\(879\) | − | 185.730i | − | 0.211297i | ||||||
\(880\) | 116.519 | − | 191.383i | 0.132408 | − | 0.217481i | ||||
\(881\) | 1395.77i | 1.58431i | 0.610323 | + | 0.792153i | \(0.291040\pi\) | ||||
−0.610323 | + | 0.792153i | \(0.708960\pi\) | |||||||
\(882\) | − | 164.561i | − | 0.186578i | ||||||
\(883\) | − | 322.412i | − | 0.365132i | −0.983194 | − | 0.182566i | \(-0.941560\pi\) | ||
0.983194 | − | 0.182566i | \(-0.0584404\pi\) | |||||||
\(884\) | 314.324i | 0.355571i | ||||||||
\(885\) | −345.299 | + | 567.156i | −0.390168 | + | 0.640855i | ||||
\(886\) | −1054.53 | −1.19022 | ||||||||
\(887\) | 563.100i | 0.634837i | 0.948286 | + | 0.317419i | \(0.102816\pi\) | ||||
−0.948286 | + | 0.317419i | \(0.897184\pi\) | |||||||
\(888\) | −223.050 | −0.251183 | ||||||||
\(889\) | − | 438.005i | − | 0.492694i | ||||||
\(890\) | −553.350 | − | 336.893i | −0.621742 | − | 0.378532i | ||||
\(891\) | − | 100.828i | − | 0.113163i | ||||||
\(892\) | 479.057i | 0.537059i | ||||||||
\(893\) | 125.048 | 0.140031 | ||||||||
\(894\) | 104.752i | 0.117172i | ||||||||
\(895\) | 605.298 | + | 368.520i | 0.676311 | + | 0.411755i | ||||
\(896\) | 36.1552i | 0.0403518i | ||||||||
\(897\) | −567.309 | − | 145.588i | −0.632452 | − | 0.162305i | ||||
\(898\) | − | 713.125i | − | 0.794126i | ||||||
\(899\) | 935.974 | 1.04113 | ||||||||
\(900\) | 68.8715 | + | 133.254i | 0.0765239 | + | 0.148060i | ||||
\(901\) | −663.802 | −0.736739 | ||||||||
\(902\) | −904.328 | −1.00258 | ||||||||
\(903\) | − | 88.3300i | − | 0.0978184i | ||||||
\(904\) | 335.881i | 0.371549i | ||||||||
\(905\) | 254.184 | − | 417.500i | 0.280867 | − | 0.461326i | ||||
\(906\) | −570.246 | −0.629410 | ||||||||
\(907\) | −1551.45 | −1.71053 | −0.855264 | − | 0.518193i | \(-0.826605\pi\) | ||||
−0.855264 | + | 0.518193i | \(0.826605\pi\) | |||||||
\(908\) | 329.121 | 0.362468 | ||||||||
\(909\) | −74.6188 | −0.0820889 | ||||||||
\(910\) | −283.770 | − | 172.766i | −0.311835 | − | 0.189853i | ||||
\(911\) | − | 1054.70i | − | 1.15774i | −0.815420 | − | 0.578870i | \(-0.803494\pi\) | ||
0.815420 | − | 0.578870i | \(-0.196506\pi\) | |||||||
\(912\) | 68.0040 | 0.0745658 | ||||||||
\(913\) | 773.320i | 0.847010i | ||||||||
\(914\) | 410.684i | 0.449326i | ||||||||
\(915\) | −288.836 | − | 175.850i | −0.315668 | − | 0.192186i | ||||
\(916\) | − | 177.680i | − | 0.193974i | ||||||
\(917\) | 180.351 | 0.196675 | ||||||||
\(918\) | −78.5532 | −0.0855700 | ||||||||
\(919\) | 855.524i | 0.930930i | 0.885066 | + | 0.465465i | \(0.154113\pi\) | ||||
−0.885066 | + | 0.465465i | \(0.845887\pi\) | |||||||
\(920\) | 232.901 | − | 227.062i | 0.253153 | − | 0.246807i | ||||
\(921\) | 390.606 | 0.424111 | ||||||||
\(922\) | − | 760.175i | − | 0.824485i | ||||||
\(923\) | − | 1395.70i | − | 1.51213i | ||||||
\(924\) | −124.022 | −0.134222 | ||||||||
\(925\) | 522.619 | + | 1011.18i | 0.564994 | + | 1.09316i | ||||
\(926\) | 854.927 | 0.923248 | ||||||||
\(927\) | 122.755 | 0.132422 | ||||||||
\(928\) | − | 140.111i | − | 0.150982i | ||||||
\(929\) | −1270.78 | −1.36790 | −0.683951 | − | 0.729528i | \(-0.739740\pi\) | ||||
−0.683951 | + | 0.729528i | \(0.739740\pi\) | |||||||
\(930\) | 395.317 | + | 240.679i | 0.425072 | + | 0.258794i | ||||
\(931\) | 380.720i | 0.408936i | ||||||||
\(932\) | − | 412.082i | − | 0.442148i | ||||||
\(933\) | − | 493.050i | − | 0.528457i | ||||||
\(934\) | 60.0551i | 0.0642988i | ||||||||
\(935\) | 311.389 | − | 511.460i | 0.333037 | − | 0.547016i | ||||
\(936\) | −124.752 | −0.133282 | ||||||||
\(937\) | 1051.53 | 1.12223 | 0.561116 | − | 0.827737i | \(-0.310372\pi\) | ||||
0.561116 | + | 0.827737i | \(0.310372\pi\) | |||||||
\(938\) | − | 82.3487i | − | 0.0877918i | ||||||
\(939\) | 264.104i | 0.281261i | ||||||||
\(940\) | 66.2505 | − | 108.817i | 0.0704792 | − | 0.115763i | ||||
\(941\) | 392.729i | 0.417353i | 0.977985 | + | 0.208677i | \(0.0669156\pi\) | ||||
−0.977985 | + | 0.208677i | \(0.933084\pi\) | |||||||
\(942\) | −551.945 | −0.585929 | ||||||||
\(943\) | −1271.59 | − | 326.328i | −1.34846 | − | 0.346053i | ||||
\(944\) | 306.689 | 0.324882 | ||||||||
\(945\) | 43.1762 | − | 70.9172i | 0.0456891 | − | 0.0750447i | ||||
\(946\) | 252.835 | 0.267267 | ||||||||
\(947\) | 405.516i | 0.428212i | 0.976810 | + | 0.214106i | \(0.0686837\pi\) | ||||
−0.976810 | + | 0.214106i | \(0.931316\pi\) | |||||||
\(948\) | −335.830 | −0.354251 | ||||||||
\(949\) | 126.343 | 0.133133 | ||||||||
\(950\) | −159.337 | − | 308.289i | −0.167723 | − | 0.324515i | ||||
\(951\) | 987.341 | 1.03821 | ||||||||
\(952\) | 96.6225i | 0.101494i | ||||||||
\(953\) | 762.883 | 0.800507 | 0.400254 | − | 0.916404i | \(-0.368922\pi\) | ||||
0.400254 | + | 0.916404i | \(0.368922\pi\) | |||||||
\(954\) | − | 263.456i | − | 0.276159i | ||||||
\(955\) | −243.131 | + | 399.345i | −0.254588 | + | 0.418162i | ||||
\(956\) | −307.551 | −0.321706 | ||||||||
\(957\) | 480.617 | 0.502212 | ||||||||
\(958\) | 582.625 | 0.608168 | ||||||||
\(959\) | 592.044 | 0.617356 | ||||||||
\(960\) | 36.0285 | − | 59.1772i | 0.0375297 | − | 0.0616429i | ||||
\(961\) | 467.011 | 0.485964 | ||||||||
\(962\) | −946.658 | −0.984052 | ||||||||
\(963\) | −53.4513 | −0.0555050 | ||||||||
\(964\) | − | 781.146i | − | 0.810317i | ||||||
\(965\) | 102.307 | − | 168.040i | 0.106017 | − | 0.174134i | ||||
\(966\) | −174.389 | − | 44.7533i | −0.180527 | − | 0.0463285i | ||||
\(967\) | 1235.35i | 1.27750i | 0.769413 | + | 0.638751i | \(0.220549\pi\) | ||||
−0.769413 | + | 0.638751i | \(0.779451\pi\) | |||||||
\(968\) | − | 12.7583i | − | 0.0131800i | ||||||
\(969\) | 181.736 | 0.187550 | ||||||||
\(970\) | −366.741 | + | 602.376i | −0.378084 | + | 0.621006i | ||||
\(971\) | 781.163i | 0.804493i | 0.915531 | + | 0.402247i | \(0.131771\pi\) | ||||
−0.915531 | + | 0.402247i | \(0.868229\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −691.871 | −0.711070 | ||||||||
\(974\) | −839.386 | −0.861792 | ||||||||
\(975\) | 292.301 | + | 565.551i | 0.299796 | + | 0.580052i | ||||
\(976\) | 156.188i | 0.160028i | ||||||||
\(977\) | 664.267 | 0.679905 | 0.339952 | − | 0.940443i | \(-0.389589\pi\) | ||||
0.339952 | + | 0.940443i | \(0.389589\pi\) | |||||||
\(978\) | 393.312i | 0.402160i | ||||||||
\(979\) | −1026.41 | −1.04843 | ||||||||
\(980\) | 331.303 | + | 201.706i | 0.338065 | + | 0.205822i | ||||
\(981\) | − | 221.457i | − | 0.225746i | ||||||
\(982\) | 219.242i | 0.223261i | ||||||||
\(983\) | 1687.78 | 1.71696 | 0.858482 | − | 0.512844i | \(-0.171408\pi\) | ||||
0.858482 | + | 0.512844i | \(0.171408\pi\) | |||||||
\(984\) | −279.625 | −0.284172 | ||||||||
\(985\) | −851.365 | + | 1398.38i | −0.864330 | + | 1.41967i | ||||
\(986\) | − | 374.438i | − | 0.379755i | ||||||
\(987\) | −70.5163 | −0.0714451 | ||||||||
\(988\) | 288.619 | 0.292124 | ||||||||
\(989\) | 355.517 | + | 91.2358i | 0.359471 | + | 0.0922505i | ||||
\(990\) | 202.993 | + | 123.587i | 0.205043 | + | 0.124835i | ||||
\(991\) | 1195.42 | 1.20627 | 0.603136 | − | 0.797638i | \(-0.293918\pi\) | ||||
0.603136 | + | 0.797638i | \(0.293918\pi\) | |||||||
\(992\) | − | 213.767i | − | 0.215491i | ||||||
\(993\) | 215.469i | 0.216988i | ||||||||
\(994\) | − | 429.034i | − | 0.431624i | ||||||
\(995\) | 453.267 | − | 744.495i | 0.455544 | − | 0.748236i | ||||
\(996\) | 239.117i | 0.240077i | ||||||||
\(997\) | 277.792i | 0.278628i | 0.990248 | + | 0.139314i | \(0.0444898\pi\) | ||||
−0.990248 | + | 0.139314i | \(0.955510\pi\) | |||||||
\(998\) | 6.89834i | 0.00691216i | ||||||||
\(999\) | − | 236.580i | − | 0.236817i |
(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.229.14 | yes | 48 | |
5.4 | even | 2 | inner | 690.3.f.a.229.15 | yes | 48 | |
23.22 | odd | 2 | inner | 690.3.f.a.229.13 | ✓ | 48 | |
115.114 | odd | 2 | inner | 690.3.f.a.229.16 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.f.a.229.13 | ✓ | 48 | 23.22 | odd | 2 | inner | |
690.3.f.a.229.14 | yes | 48 | 1.1 | even | 1 | trivial | |
690.3.f.a.229.15 | yes | 48 | 5.4 | even | 2 | inner | |
690.3.f.a.229.16 | yes | 48 | 115.114 | odd | 2 | inner |