Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(701,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 701.1 | ||
Character | \(\chi\) | \(=\) | 1620.701 |
Dual form | 1620.3.o.g.1241.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.93649 | − | 1.11803i | −0.387298 | − | 0.223607i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.26486 | − | 3.92285i | −0.323551 | − | 0.560407i | 0.657667 | − | 0.753309i | \(-0.271543\pi\) |
−0.981218 | + | 0.192902i | \(0.938210\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.9226 | − | 7.46089i | 1.17479 | − | 0.678263i | 0.219983 | − | 0.975504i | \(-0.429400\pi\) |
0.954803 | + | 0.297241i | \(0.0960664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.82703 | + | 13.5568i | −0.602079 | + | 1.04283i | 0.390427 | + | 0.920634i | \(0.372327\pi\) |
−0.992506 | + | 0.122197i | \(0.961006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.53594i | 0.443290i | 0.975127 | + | 0.221645i | \(0.0711427\pi\) | ||||
−0.975127 | + | 0.221645i | \(0.928857\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.77167 | 0.514299 | 0.257149 | − | 0.966372i | \(-0.417217\pi\) | ||||
0.257149 | + | 0.966372i | \(0.417217\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.38708 | − | 5.41963i | −0.408134 | − | 0.235636i | 0.281854 | − | 0.959457i | \(-0.409051\pi\) |
−0.689988 | + | 0.723821i | \(0.742384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.94676 | − | 2.27866i | 0.136095 | − | 0.0785746i | −0.430407 | − | 0.902635i | \(-0.641630\pi\) |
0.566502 | + | 0.824061i | \(0.308296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 24.4879 | − | 42.4143i | 0.789932 | − | 1.36820i | −0.136077 | − | 0.990698i | \(-0.543449\pi\) |
0.926008 | − | 0.377503i | \(-0.123217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.1288i | 0.289393i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 21.4786 | 0.580502 | 0.290251 | − | 0.956951i | \(-0.406261\pi\) | ||||
0.290251 | + | 0.956951i | \(0.406261\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 45.6430 | + | 26.3520i | 1.11324 | + | 0.642731i | 0.939667 | − | 0.342089i | \(-0.111135\pi\) |
0.173576 | + | 0.984821i | \(0.444468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20.5817 | − | 35.6486i | −0.478644 | − | 0.829036i | 0.521056 | − | 0.853523i | \(-0.325538\pi\) |
−0.999700 | + | 0.0244863i | \(0.992205\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −32.2207 | + | 18.6026i | −0.685547 | + | 0.395801i | −0.801942 | − | 0.597402i | \(-0.796200\pi\) |
0.116394 | + | 0.993203i | \(0.462866\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.2408 | − | 24.6659i | 0.290629 | − | 0.503385i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 81.8456i | 1.54426i | 0.635466 | + | 0.772129i | \(0.280808\pi\) | ||||
−0.635466 | + | 0.772129i | \(0.719192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −33.3661 | −0.606657 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −70.3732 | − | 40.6300i | −1.19277 | − | 0.688644i | −0.233834 | − | 0.972277i | \(-0.575127\pi\) |
−0.958933 | + | 0.283632i | \(0.908460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −24.5444 | − | 42.5121i | −0.402367 | − | 0.696920i | 0.591644 | − | 0.806199i | \(-0.298479\pi\) |
−0.994011 | + | 0.109279i | \(0.965146\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 30.3139 | − | 17.5018i | 0.466368 | − | 0.269258i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23.2834 | − | 40.3280i | 0.347513 | − | 0.601910i | −0.638294 | − | 0.769793i | \(-0.720360\pi\) |
0.985807 | + | 0.167882i | \(0.0536929\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 17.4203i | − | 0.245356i | −0.992446 | − | 0.122678i | \(-0.960852\pi\) | ||
0.992446 | − | 0.122678i | \(-0.0391483\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −101.619 | −1.39205 | −0.696023 | − | 0.718019i | \(-0.745049\pi\) | ||||
−0.696023 | + | 0.718019i | \(0.745049\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −58.5359 | − | 33.7957i | −0.760207 | − | 0.438905i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −28.7070 | − | 49.7219i | −0.363379 | − | 0.629391i | 0.625135 | − | 0.780516i | \(-0.285044\pi\) |
−0.988515 | + | 0.151125i | \(0.951710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 75.2273 | − | 43.4325i | 0.906353 | − | 0.523283i | 0.0270968 | − | 0.999633i | \(-0.491374\pi\) |
0.879256 | + | 0.476350i | \(0.158040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.42543 | − | 14.5933i | 0.0991227 | − | 0.171686i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 41.3946i | − | 0.465108i | −0.972584 | − | 0.232554i | \(-0.925292\pi\) | ||
0.972584 | − | 0.232554i | \(-0.0747082\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 70.9084 | 0.779213 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.9228 | − | 10.9251i | −0.199187 | − | 0.115001i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −90.4805 | − | 156.717i | −0.932789 | − | 1.61564i | −0.778530 | − | 0.627607i | \(-0.784034\pi\) |
−0.154259 | − | 0.988031i | \(-0.549299\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 55.2853 | − | 31.9190i | 0.547379 | − | 0.316029i | −0.200685 | − | 0.979656i | \(-0.564317\pi\) |
0.748064 | + | 0.663626i | \(0.230983\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6921 | − | 23.7155i | 0.132933 | − | 0.230247i | −0.791873 | − | 0.610686i | \(-0.790894\pi\) |
0.924806 | + | 0.380439i | \(0.124227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.87078i | 0.0361755i | 0.999836 | + | 0.0180878i | \(0.00575783\pi\) | ||||
−0.999836 | + | 0.0180878i | \(0.994242\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −65.8864 | −0.604462 | −0.302231 | − | 0.953235i | \(-0.597731\pi\) | ||||
−0.302231 | + | 0.953235i | \(0.597731\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.3675 | − | 10.6045i | −0.162544 | − | 0.0938450i | 0.416521 | − | 0.909126i | \(-0.363249\pi\) |
−0.579066 | + | 0.815281i | \(0.696582\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.1187 | + | 20.9902i | 0.105380 | + | 0.182523i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29.5623 | − | 17.0678i | 0.248423 | − | 0.143427i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 50.8298 | − | 88.0398i | 0.420081 | − | 0.727602i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 46.5874 | 0.366830 | 0.183415 | − | 0.983036i | \(-0.441285\pi\) | ||||
0.183415 | + | 0.983036i | \(0.441285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −120.460 | − | 69.5474i | −0.919539 | − | 0.530896i | −0.0360513 | − | 0.999350i | \(-0.511478\pi\) |
−0.883488 | + | 0.468454i | \(0.844811\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.1315 | − | 38.3328i | −0.166402 | − | 0.288217i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 184.463 | − | 106.500i | 1.34645 | − | 0.777371i | 0.358702 | − | 0.933452i | \(-0.383220\pi\) |
0.987744 | + | 0.156081i | \(0.0498862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 126.328 | − | 218.807i | 0.908835 | − | 1.57415i | 0.0931489 | − | 0.995652i | \(-0.470307\pi\) |
0.815686 | − | 0.578495i | \(-0.196360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 233.586i | 1.63347i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.1905 | −0.0702793 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −77.7390 | − | 44.8827i | −0.521738 | − | 0.301226i | 0.215907 | − | 0.976414i | \(-0.430729\pi\) |
−0.737646 | + | 0.675188i | \(0.764062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −94.4037 | − | 163.512i | −0.625190 | − | 1.08286i | −0.988504 | − | 0.151194i | \(-0.951688\pi\) |
0.363314 | − | 0.931667i | \(-0.381645\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −94.8411 | + | 54.7566i | −0.611878 | + | 0.353268i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 65.9966 | − | 114.309i | 0.420361 | − | 0.728086i | −0.575614 | − | 0.817722i | \(-0.695237\pi\) |
0.995975 | + | 0.0896356i | \(0.0285703\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 49.0988i | 0.304962i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 173.331 | 1.06338 | 0.531691 | − | 0.846939i | \(-0.321557\pi\) | ||||
0.531691 | + | 0.846939i | \(0.321557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.6383 | + | 13.0702i | 0.135559 | + | 0.0782648i | 0.566246 | − | 0.824237i | \(-0.308395\pi\) |
−0.430687 | + | 0.902501i | \(0.641729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −38.0247 | − | 65.8607i | −0.224998 | − | 0.389709i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −203.324 | + | 117.389i | −1.17529 | + | 0.678551i | −0.954919 | − | 0.296866i | \(-0.904059\pi\) |
−0.220366 | + | 0.975417i | \(0.570725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.3243 | − | 19.6142i | 0.0647102 | − | 0.112081i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 170.441i | 0.952184i | 0.879395 | + | 0.476092i | \(0.157947\pi\) | ||||
−0.879395 | + | 0.476092i | \(0.842053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4034 | −0.118251 | −0.0591254 | − | 0.998251i | \(-0.518831\pi\) | ||||
−0.0591254 | + | 0.998251i | \(0.518831\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −41.5931 | − | 24.0138i | −0.224827 | − | 0.129804i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 56.2248 | + | 97.3842i | 0.300667 | + | 0.520771i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 160.046 | − | 92.4025i | 0.837936 | − | 0.483783i | −0.0186261 | − | 0.999827i | \(-0.505929\pi\) |
0.856562 | + | 0.516044i | \(0.172596\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 190.160 | − | 329.367i | 0.985286 | − | 1.70657i | 0.344628 | − | 0.938740i | \(-0.388005\pi\) |
0.640658 | − | 0.767826i | \(-0.278661\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 79.3079i | 0.402578i | 0.979532 | + | 0.201289i | \(0.0645131\pi\) | ||||
−0.979532 | + | 0.201289i | \(0.935487\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −87.2272 | −0.438328 | −0.219164 | − | 0.975688i | \(-0.570333\pi\) | ||||
−0.219164 | + | 0.975688i | \(0.570333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.8777 | − | 10.3217i | −0.0880675 | − | 0.0508458i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −58.9248 | − | 102.061i | −0.287438 | − | 0.497857i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 126.276 | − | 72.9054i | 0.604191 | − | 0.348830i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −168.236 | + | 291.393i | −0.797327 | + | 1.38101i | 0.124024 | + | 0.992279i | \(0.460420\pi\) |
−0.921351 | + | 0.388732i | \(0.872913\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 92.0442i | 0.428113i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −221.846 | −1.02233 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −102.163 | − | 58.9840i | −0.462277 | − | 0.266896i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −41.8581 | − | 72.5004i | −0.187705 | − | 0.325114i | 0.756780 | − | 0.653670i | \(-0.226771\pi\) |
−0.944485 | + | 0.328556i | \(0.893438\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 271.315 | − | 156.644i | 1.19522 | − | 0.690060i | 0.235734 | − | 0.971818i | \(-0.424251\pi\) |
0.959486 | + | 0.281757i | \(0.0909173\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −112.802 | + | 195.379i | −0.492586 | + | 0.853184i | −0.999964 | − | 0.00853978i | \(-0.997282\pi\) |
0.507377 | + | 0.861724i | \(0.330615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 62.6406i | 0.268844i | 0.990924 | + | 0.134422i | \(0.0429177\pi\) | ||||
−0.990924 | + | 0.134422i | \(0.957082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 83.1936 | 0.354015 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 91.1510 | + | 52.6260i | 0.381385 | + | 0.220193i | 0.678421 | − | 0.734674i | \(-0.262665\pi\) |
−0.297036 | + | 0.954866i | \(0.595998\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −135.295 | − | 234.337i | −0.561389 | − | 0.972354i | −0.997376 | − | 0.0724007i | \(-0.976934\pi\) |
0.435987 | − | 0.899953i | \(-0.356399\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −55.1545 | + | 31.8435i | −0.225121 | + | 0.129973i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −76.4832 | + | 132.473i | −0.309648 | + | 0.536327i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.05439i | 0.0161529i | 0.999967 | + | 0.00807647i | \(0.00257085\pi\) | ||||
−0.999967 | + | 0.00807647i | \(0.997429\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −161.741 | −0.639293 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 33.6710 | + | 19.4400i | 0.131016 | + | 0.0756418i | 0.564075 | − | 0.825723i | \(-0.309233\pi\) |
−0.433060 | + | 0.901365i | \(0.642566\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −48.6459 | − | 84.2572i | −0.187822 | − | 0.325317i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −113.246 | + | 65.3825i | −0.430593 | + | 0.248603i | −0.699599 | − | 0.714536i | \(-0.746638\pi\) |
0.269006 | + | 0.963138i | \(0.413305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 91.5062 | − | 158.493i | 0.345306 | − | 0.598088i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 327.701i | − | 1.21822i | −0.793086 | − | 0.609109i | \(-0.791527\pi\) | ||
0.793086 | − | 0.609109i | \(-0.208473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 151.222 | 0.558016 | 0.279008 | − | 0.960289i | \(-0.409994\pi\) | ||||
0.279008 | + | 0.960289i | \(0.409994\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 64.6132 | + | 37.3045i | 0.234957 | + | 0.135653i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −182.096 | − | 315.400i | −0.657388 | − | 1.13863i | −0.981289 | − | 0.192538i | \(-0.938328\pi\) |
0.323902 | − | 0.946091i | \(-0.395005\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 103.822 | − | 59.9418i | 0.369474 | − | 0.213316i | −0.303755 | − | 0.952750i | \(-0.598240\pi\) |
0.673229 | + | 0.739434i | \(0.264907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 210.787 | − | 365.094i | 0.744831 | − | 1.29008i | −0.205443 | − | 0.978669i | \(-0.565864\pi\) |
0.950274 | − | 0.311416i | \(-0.100803\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 238.734i | − | 0.831826i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 232.210 | 0.803494 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 283.065 | + | 163.428i | 0.966093 | + | 0.557774i | 0.898043 | − | 0.439908i | \(-0.144989\pi\) |
0.0680502 | + | 0.997682i | \(0.478322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 90.8515 | + | 157.359i | 0.307971 | + | 0.533421i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 146.946 | − | 84.8393i | 0.491458 | − | 0.283743i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −93.2293 | + | 161.478i | −0.309732 | + | 0.536471i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 109.766i | 0.359888i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 157.856 | 0.514190 | 0.257095 | − | 0.966386i | \(-0.417235\pi\) | ||||
0.257095 | + | 0.966386i | \(0.417235\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −380.038 | − | 219.415i | −1.22199 | − | 0.705514i | −0.256645 | − | 0.966506i | \(-0.582617\pi\) |
−0.965341 | + | 0.260992i | \(0.915950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 203.852 | + | 353.082i | 0.651284 | + | 1.12806i | 0.982812 | + | 0.184611i | \(0.0591026\pi\) |
−0.331528 | + | 0.943446i | \(0.607564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −380.871 | + | 219.896i | −1.20149 | + | 0.693678i | −0.960885 | − | 0.276946i | \(-0.910678\pi\) |
−0.240600 | + | 0.970624i | \(0.577344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.0017 | − | 58.8927i | 0.106588 | − | 0.184617i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 73.6387i | 0.227984i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −78.2703 | −0.240832 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 145.951 | + | 84.2647i | 0.443619 | + | 0.256124i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.744429 | + | 1.28939i | 0.00224903 | + | 0.00389543i | 0.867148 | − | 0.498051i | \(-0.165951\pi\) |
−0.864899 | + | 0.501946i | \(0.832617\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −90.1761 | + | 52.0632i | −0.269183 | + | 0.155413i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −62.7444 | + | 108.677i | −0.186185 | + | 0.322482i | −0.943975 | − | 0.330016i | \(-0.892946\pi\) |
0.757790 | + | 0.652499i | \(0.226279\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 730.806i | − | 2.14313i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −350.970 | −1.02324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −171.620 | − | 99.0848i | −0.494582 | − | 0.285547i | 0.231892 | − | 0.972742i | \(-0.425509\pi\) |
−0.726473 | + | 0.687195i | \(0.758842\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.8274 | − | 58.5908i | −0.0969267 | − | 0.167882i | 0.813484 | − | 0.581587i | \(-0.197568\pi\) |
−0.910411 | + | 0.413705i | \(0.864235\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −495.143 | + | 285.871i | −1.40267 | + | 0.809833i | −0.994666 | − | 0.103147i | \(-0.967109\pi\) |
−0.408005 | + | 0.912980i | \(0.633776\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.4765 | + | 33.7343i | −0.0548634 | + | 0.0950262i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 648.758i | 1.80713i | 0.428455 | + | 0.903563i | \(0.359058\pi\) | ||||
−0.428455 | + | 0.903563i | \(0.640942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −265.514 | −0.735497 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 196.785 | + | 113.614i | 0.539137 | + | 0.311271i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 256.297 | + | 443.919i | 0.698356 | + | 1.20959i | 0.969036 | + | 0.246919i | \(0.0794181\pi\) |
−0.270680 | + | 0.962669i | \(0.587249\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 321.068 | − | 185.369i | 0.865413 | − | 0.499646i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −93.2229 | + | 161.467i | −0.249927 | + | 0.432887i | −0.963505 | − | 0.267689i | \(-0.913740\pi\) |
0.713578 | + | 0.700576i | \(0.247073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 71.3406i | 0.189232i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 257.240 | 0.678735 | 0.339367 | − | 0.940654i | \(-0.389787\pi\) | ||||
0.339367 | + | 0.940654i | \(0.389787\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −226.437 | − | 130.733i | −0.591219 | − | 0.341341i | 0.174360 | − | 0.984682i | \(-0.444214\pi\) |
−0.765579 | + | 0.643341i | \(0.777548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 75.5695 | + | 130.890i | 0.196284 | + | 0.339975i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −350.519 | + | 202.372i | −0.901077 | + | 0.520237i | −0.877549 | − | 0.479486i | \(-0.840823\pi\) |
−0.0235274 | + | 0.999723i | \(0.507490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.8420 | − | 70.7405i | 0.104455 | − | 0.180922i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 128.381i | 0.325016i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 289.798 | 0.729970 | 0.364985 | − | 0.931013i | \(-0.381074\pi\) | ||||
0.364985 | + | 0.931013i | \(0.381074\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 666.871 | + | 385.018i | 1.66302 | + | 0.960146i | 0.971261 | + | 0.238019i | \(0.0764979\pi\) |
0.691760 | + | 0.722127i | \(0.256835\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 383.335 | + | 663.955i | 0.951202 | + | 1.64753i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 277.560 | − | 160.249i | 0.681966 | − | 0.393733i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −253.671 | + | 439.371i | −0.620222 | + | 1.07426i | 0.369222 | + | 0.929341i | \(0.379624\pi\) |
−0.989444 | + | 0.144915i | \(0.953709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 368.085i | 0.891246i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −194.236 | −0.468038 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −189.672 | − | 109.507i | −0.452677 | − | 0.261353i | 0.256283 | − | 0.966602i | \(-0.417502\pi\) |
−0.708960 | + | 0.705249i | \(0.750835\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 181.027 | + | 313.547i | 0.429992 | + | 0.744768i | 0.996872 | − | 0.0790326i | \(-0.0251831\pi\) |
−0.566880 | + | 0.823800i | \(0.691850\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −32.6316 | + | 18.8398i | −0.0767801 | + | 0.0443290i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −111.179 | + | 192.568i | −0.260372 | + | 0.450978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 619.958i | − | 1.43842i | −0.694794 | − | 0.719209i | \(-0.744504\pi\) | ||
0.694794 | − | 0.719209i | \(-0.255496\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −506.921 | −1.17072 | −0.585359 | − | 0.810774i | \(-0.699047\pi\) | ||||
−0.585359 | + | 0.810774i | \(0.699047\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −91.7275 | − | 52.9589i | −0.209903 | − | 0.121187i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 287.794 | + | 498.475i | 0.655568 | + | 1.13548i | 0.981751 | + | 0.190171i | \(0.0609042\pi\) |
−0.326183 | + | 0.945307i | \(0.605762\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −419.097 | + | 241.966i | −0.946042 | + | 0.546198i | −0.891849 | − | 0.452333i | \(-0.850592\pi\) |
−0.0541930 | + | 0.998530i | \(0.517259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −46.2805 | + | 80.1602i | −0.104001 | + | 0.180135i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 560.721i | − | 1.24882i | −0.781096 | − | 0.624411i | \(-0.785339\pi\) | ||
0.781096 | − | 0.624411i | \(-0.214661\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 786.437 | 1.74376 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −137.314 | − | 79.2780i | −0.301788 | − | 0.174237i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −254.138 | − | 440.180i | −0.556101 | − | 0.963195i | −0.997817 | − | 0.0660398i | \(-0.978964\pi\) |
0.441716 | − | 0.897155i | \(-0.354370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 508.162 | − | 293.388i | 1.10230 | − | 0.636416i | 0.165479 | − | 0.986213i | \(-0.447083\pi\) |
0.936825 | + | 0.349797i | \(0.113750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −83.9079 | + | 145.333i | −0.181226 | + | 0.313893i | −0.942298 | − | 0.334774i | \(-0.891340\pi\) |
0.761072 | + | 0.648667i | \(0.224673\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 896.380i | − | 1.91944i | −0.280953 | − | 0.959721i | \(-0.590651\pi\) | ||
0.280953 | − | 0.959721i | \(-0.409349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −210.934 | −0.449753 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −531.940 | − | 307.116i | −1.12461 | − | 0.649293i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.4292 | + | 42.3126i | 0.0514299 | + | 0.0890791i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.4303 | − | 24.4971i | 0.0885810 | − | 0.0511423i | −0.455055 | − | 0.890463i | \(-0.650380\pi\) |
0.543636 | + | 0.839321i | \(0.317047\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −168.113 | + | 291.181i | −0.349508 | + | 0.605366i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 404.641i | 0.834312i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 338.170 | 0.694393 | 0.347197 | − | 0.937792i | \(-0.387134\pi\) | ||||
0.347197 | + | 0.937792i | \(0.387134\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 645.469 | + | 372.662i | 1.31460 | + | 0.758986i | 0.982855 | − | 0.184383i | \(-0.0590286\pi\) |
0.331747 | + | 0.943368i | \(0.392362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.1719 | + | 29.7425i | 0.0348314 | + | 0.0603297i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −68.3372 | + | 39.4545i | −0.137499 | + | 0.0793854i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −224.102 | + | 388.157i | −0.449103 | + | 0.777869i | −0.998328 | − | 0.0578054i | \(-0.981590\pi\) |
0.549225 | + | 0.835675i | \(0.314923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 869.698i | 1.72902i | 0.502615 | + | 0.864511i | \(0.332371\pi\) | ||||
−0.502615 | + | 0.864511i | \(0.667629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −142.746 | −0.282665 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 627.704 | + | 362.405i | 1.23321 | + | 0.711994i | 0.967698 | − | 0.252113i | \(-0.0811255\pi\) |
0.265513 | + | 0.964107i | \(0.414459\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 230.153 | + | 398.638i | 0.450398 | + | 0.780113i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −53.0295 | + | 30.6166i | −0.102970 | + | 0.0594496i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −277.585 | + | 480.791i | −0.536914 | + | 0.929963i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 847.907i | − | 1.62746i | −0.581242 | − | 0.813731i | \(-0.697433\pi\) | ||
0.581242 | − | 0.813731i | \(-0.302567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −208.461 | −0.398588 | −0.199294 | − | 0.979940i | \(-0.563865\pi\) | ||||
−0.199294 | + | 0.979940i | \(0.563865\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 319.631 | + | 184.539i | 0.606511 | + | 0.350169i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −205.755 | − | 356.378i | −0.388951 | − | 0.673683i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −714.498 | + | 412.515i | −1.34052 | + | 0.773950i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.32767 | − | 7.49574i | 0.00808910 | − | 0.0140107i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 424.997i | − | 0.788492i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 427.550 | 0.790295 | 0.395147 | − | 0.918618i | \(-0.370694\pi\) | ||||
0.395147 | + | 0.918618i | \(0.370694\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 127.588 | + | 73.6632i | 0.234107 | + | 0.135162i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 165.569 | + | 286.774i | 0.302685 | + | 0.524266i | 0.976743 | − | 0.214412i | \(-0.0687836\pi\) |
−0.674058 | + | 0.738678i | \(0.735450\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.5665 | − | 22.2664i | 0.0699936 | − | 0.0404108i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −130.034 | + | 225.226i | −0.235144 | + | 0.407281i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 889.916i | − | 1.59769i | −0.601534 | − | 0.798847i | \(-0.705444\pi\) | ||
0.601534 | − | 0.798847i | \(-0.294556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 644.374 | 1.15273 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 501.920 | + | 289.784i | 0.891511 | + | 0.514714i | 0.874436 | − | 0.485140i | \(-0.161231\pi\) |
0.0170743 | + | 0.999854i | \(0.494565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.7124 | + | 41.0710i | 0.0419688 | + | 0.0726920i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −428.063 | + | 247.142i | −0.752307 | + | 0.434345i | −0.826527 | − | 0.562897i | \(-0.809687\pi\) |
0.0742198 | + | 0.997242i | \(0.476353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −164.165 | + | 284.342i | −0.287504 | + | 0.497972i | −0.973213 | − | 0.229904i | \(-0.926159\pi\) |
0.685709 | + | 0.727875i | \(0.259492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 54.1963i | − | 0.0942545i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 271.036 | 0.469734 | 0.234867 | − | 0.972028i | \(-0.424535\pi\) | ||||
0.234867 | + | 0.972028i | \(0.424535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −340.758 | − | 196.737i | −0.586503 | − | 0.338618i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 610.642 | + | 1057.66i | 1.04741 | + | 1.81417i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −376.662 | + | 217.466i | −0.641673 | + | 0.370470i | −0.785259 | − | 0.619168i | \(-0.787470\pi\) |
0.143585 | + | 0.989638i | \(0.454137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 239.288 | − | 414.458i | 0.406261 | − | 0.703664i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 735.060i | 1.23956i | 0.784775 | + | 0.619780i | \(0.212778\pi\) | ||||
−0.784775 | + | 0.619780i | \(0.787222\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −76.3296 | −0.128285 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 438.530 | + | 253.185i | 0.732103 | + | 0.422680i | 0.819191 | − | 0.573521i | \(-0.194423\pi\) |
−0.0870882 | + | 0.996201i | \(0.527756\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −432.447 | − | 749.020i | −0.719546 | − | 1.24629i | −0.961180 | − | 0.275922i | \(-0.911017\pi\) |
0.241634 | − | 0.970367i | \(-0.422317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −196.863 | + | 113.659i | −0.325393 | + | 0.187866i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −141.662 | + | 245.365i | −0.233380 | + | 0.404226i | −0.958801 | − | 0.284080i | \(-0.908312\pi\) |
0.725421 | + | 0.688306i | \(0.241645\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 582.414i | − | 0.953214i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1170.79 | −1.90994 | −0.954971 | − | 0.296698i | \(-0.904114\pi\) | ||||
−0.954971 | + | 0.296698i | \(0.904114\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 543.687 | + | 313.898i | 0.881178 | + | 0.508748i | 0.871047 | − | 0.491200i | \(-0.163442\pi\) |
0.0101314 | + | 0.999949i | \(0.496775\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 130.204 | + | 225.520i | 0.210345 | + | 0.364329i | 0.951823 | − | 0.306649i | \(-0.0992078\pi\) |
−0.741477 | + | 0.670978i | \(0.765874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −162.385 | + | 93.7528i | −0.260650 | + | 0.150486i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 161.861i | 0.257331i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 604.324 | 0.957723 | 0.478862 | − | 0.877890i | \(-0.341050\pi\) | ||||
0.478862 | + | 0.877890i | \(0.341050\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −90.2162 | − | 52.0863i | −0.142073 | − | 0.0820257i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 222.927 | + | 386.121i | 0.349964 | + | 0.606155i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −237.935 | + | 137.372i | −0.371193 | + | 0.214309i | −0.673980 | − | 0.738750i | \(-0.735417\pi\) |
0.302786 | + | 0.953058i | \(0.402083\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 66.9700 | − | 115.995i | 0.104152 | − | 0.180397i | −0.809239 | − | 0.587479i | \(-0.800120\pi\) |
0.913392 | + | 0.407082i | \(0.133454\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 918.547i | 1.41970i | 0.704352 | + | 0.709851i | \(0.251238\pi\) | ||||
−0.704352 | + | 0.709851i | \(0.748762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1212.54 | −1.86833 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1014.31 | + | 585.613i | 1.55331 | + | 0.896804i | 0.997869 | + | 0.0652482i | \(0.0207839\pi\) |
0.555441 | + | 0.831556i | \(0.312549\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 155.513 | + | 269.356i | 0.237424 | + | 0.411230i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 332.558 | − | 192.002i | 0.504640 | − | 0.291354i | −0.225987 | − | 0.974130i | \(-0.572561\pi\) |
0.730628 | + | 0.682776i | \(0.239228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −252.259 | + | 436.925i | −0.381632 | + | 0.661006i | −0.991296 | − | 0.131654i | \(-0.957971\pi\) |
0.609664 | + | 0.792660i | \(0.291304\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 98.9749i | 0.148834i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −49.3981 | −0.0740601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −634.356 | − | 366.246i | −0.945390 | − | 0.545821i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 303.578 | + | 525.813i | 0.451082 | + | 0.781298i | 0.998454 | − | 0.0555924i | \(-0.0177047\pi\) |
−0.547371 | + | 0.836890i | \(0.684371\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 701.540 | − | 405.035i | 1.03625 | − | 0.598278i | 0.117480 | − | 0.993075i | \(-0.462518\pi\) |
0.918768 | + | 0.394797i | \(0.129185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −409.851 | + | 709.883i | −0.603610 | + | 1.04548i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1095.97i | 1.60465i | 0.596889 | + | 0.802324i | \(0.296403\pi\) | ||||
−0.596889 | + | 0.802324i | \(0.703597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −476.282 | −0.695302 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1109.57 | − | 640.608i | −1.61040 | − | 0.929765i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −495.310 | − | 857.902i | −0.716802 | − | 1.24154i | −0.962260 | − | 0.272130i | \(-0.912272\pi\) |
0.245458 | − | 0.969407i | \(-0.421062\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −489.266 | + | 282.478i | −0.703980 | + | 0.406443i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −198.587 | + | 343.962i | −0.284917 | + | 0.493490i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 302.260i | − | 0.431184i | −0.976484 | − | 0.215592i | \(-0.930832\pi\) | ||
0.976484 | − | 0.215592i | \(-0.0691680\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 209.882 | 0.298551 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −250.427 | − | 144.584i | −0.354210 | − | 0.204503i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 454.761 | + | 787.670i | 0.641412 | + | 1.11096i | 0.985118 | + | 0.171881i | \(0.0549845\pi\) |
−0.343705 | + | 0.939078i | \(0.611682\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −459.739 | + | 265.431i | −0.644796 | + | 0.372273i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 261.158 | − | 452.338i | 0.365255 | − | 0.632641i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 779.361i | − | 1.08395i | −0.840394 | − | 0.541976i | \(-0.817677\pi\) | ||
0.840394 | − | 0.541976i | \(-0.182323\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −124.043 | −0.172043 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.7338 | + | 11.3933i | 0.0272190 | + | 0.0157149i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −96.5145 | − | 167.168i | −0.132757 | − | 0.229942i | 0.791981 | − | 0.610545i | \(-0.209050\pi\) |
−0.924738 | + | 0.380603i | \(0.875716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 268.645 | − | 155.102i | 0.367504 | − | 0.212178i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 429.154 | − | 743.317i | 0.585477 | − | 1.01408i | −0.409339 | − | 0.912382i | \(-0.634241\pi\) |
0.994816 | − | 0.101693i | \(-0.0324259\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 694.859i | − | 0.942821i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 977.178 | 1.32230 | 0.661149 | − | 0.750255i | \(-0.270069\pi\) | ||||
0.661149 | + | 0.750255i | \(0.270069\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −156.349 | − | 90.2680i | −0.210429 | − | 0.121491i | 0.391082 | − | 0.920356i | \(-0.372101\pi\) |
−0.601511 | + | 0.798865i | \(0.705434\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 100.361 | + | 173.830i | 0.134712 | + | 0.233329i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1845 | − | 8.76677i | 0.0202730 | − | 0.0117046i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −700.877 | + | 1213.95i | −0.933258 | + | 1.61645i | −0.155547 | + | 0.987829i | \(0.549714\pi\) |
−0.777711 | + | 0.628622i | \(0.783619\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 422.186i | 0.559187i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −69.2097 | −0.0914262 | −0.0457131 | − | 0.998955i | \(-0.514556\pi\) | ||||
−0.0457131 | + | 0.998955i | \(0.514556\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −236.592 | − | 136.597i | −0.310897 | − | 0.179496i | 0.336431 | − | 0.941708i | \(-0.390780\pi\) |
−0.647328 | + | 0.762212i | \(0.724113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 149.223 | + | 258.462i | 0.195574 | + | 0.338745i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1101.63 | − | 636.024i | 1.43628 | − | 0.829236i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 154.379 | − | 267.393i | 0.200753 | − | 0.347715i | −0.748018 | − | 0.663678i | \(-0.768994\pi\) |
0.948771 | + | 0.315963i | \(0.102328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 764.959i | − | 0.989597i | −0.869008 | − | 0.494799i | \(-0.835242\pi\) | ||
0.869008 | − | 0.494799i | \(-0.164758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 244.879 | 0.315973 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 446.008 | + | 257.503i | 0.572539 | + | 0.330556i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −129.971 | − | 225.116i | −0.166416 | − | 0.288241i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −255.604 | + | 147.573i | −0.325610 | + | 0.187991i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 566.734 | − | 981.612i | 0.720120 | − | 1.24728i | −0.240832 | − | 0.970567i | \(-0.577420\pi\) |
0.960952 | − | 0.276717i | \(-0.0892464\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 96.0706i | 0.121455i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 768.438 | 0.969026 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 452.278 | + | 261.123i | 0.567476 | + | 0.327632i | 0.756141 | − | 0.654409i | \(-0.227083\pi\) |
−0.188665 | + | 0.982042i | \(0.560416\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −140.188 | − | 242.813i | −0.175455 | − | 0.303897i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1313.19 | + | 758.171i | −1.63536 | + | 0.944173i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54.8941 | − | 95.0794i | 0.0681915 | − | 0.118111i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 198.946i | − | 0.245916i | −0.992412 | − | 0.122958i | \(-0.960762\pi\) | ||
0.992412 | − | 0.122958i | \(-0.0392380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1256.10 | 1.54883 | 0.774415 | − | 0.632678i | \(-0.218044\pi\) | ||||
0.774415 | + | 0.632678i | \(0.218044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −335.654 | − | 193.790i | −0.411846 | − | 0.237779i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −201.118 | − | 348.346i | −0.246166 | − | 0.426372i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1201.66 | − | 693.781i | 1.46366 | − | 0.845044i | 0.464482 | − | 0.885583i | \(-0.346241\pi\) |
0.999178 | + | 0.0405384i | \(0.0129073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 503.241 | − | 871.639i | 0.611471 | − | 1.05910i | −0.379521 | − | 0.925183i | \(-0.623911\pi\) |
0.990993 | − | 0.133916i | \(-0.0427554\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 768.926i | − | 0.929778i | −0.885369 | − | 0.464889i | \(-0.846094\pi\) | ||
0.885369 | − | 0.464889i | \(-0.153906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −602.188 | −0.726403 | −0.363201 | − | 0.931711i | \(-0.618316\pi\) | ||||
−0.363201 | + | 0.931711i | \(0.618316\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 185.880 | + | 107.318i | 0.223146 | + | 0.128833i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.2259 | − | 50.6208i | −0.0350011 | − | 0.0606237i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1111.05 | − | 641.464i | 1.32425 | − | 0.764558i | 0.339850 | − | 0.940480i | \(-0.389624\pi\) |
0.984404 | + | 0.175922i | \(0.0562905\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −410.115 | + | 710.341i | −0.487652 | + | 0.844638i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 170.052i | 0.201245i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −460.489 | −0.543671 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −201.621 | − | 116.406i | −0.236923 | − | 0.136787i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −599.045 | − | 1037.58i | −0.702281 | − | 1.21639i | −0.967664 | − | 0.252243i | \(-0.918832\pi\) |
0.265383 | − | 0.964143i | \(-0.414502\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −481.135 | + | 277.783i | −0.561418 | + | 0.324135i | −0.753714 | − | 0.657202i | \(-0.771740\pi\) |
0.192297 | + | 0.981337i | \(0.438406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 290.615 | − | 503.360i | 0.338318 | − | 0.585984i | −0.645799 | − | 0.763508i | \(-0.723475\pi\) |
0.984116 | + | 0.177524i | \(0.0568088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1487.60i | 1.72375i | 0.507120 | + | 0.861876i | \(0.330710\pi\) | ||||
−0.507120 | + | 0.861876i | \(0.669290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 524.981 | 0.606915 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −741.940 | − | 428.359i | −0.853786 | − | 0.492933i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 364.479 | + | 631.297i | 0.418461 | + | 0.724795i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −43.8588 | + | 25.3219i | −0.0501243 | + | 0.0289393i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −520.859 | + | 902.155i | −0.593910 | + | 1.02868i | 0.399789 | + | 0.916607i | \(0.369083\pi\) |
−0.993700 | + | 0.112076i | \(0.964250\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1205.55i | − | 1.36839i | −0.729299 | − | 0.684196i | \(-0.760153\pi\) | ||
0.729299 | − | 0.684196i | \(-0.239847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 75.6957 | 0.0857256 | 0.0428628 | − | 0.999081i | \(-0.486352\pi\) | ||||
0.0428628 | + | 0.999081i | \(0.486352\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1307.91 | − | 755.124i | −1.47454 | − | 0.851324i | −0.474948 | − | 0.880014i | \(-0.657533\pi\) |
−0.999588 | + | 0.0286903i | \(0.990866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −105.514 | − | 182.756i | −0.118688 | − | 0.205574i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −314.850 | + | 181.779i | −0.352576 | + | 0.203560i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 190.559 | − | 330.057i | 0.212915 | − | 0.368779i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 223.199i | − | 0.248274i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −616.784 | −0.684554 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.4475 | + | 23.9297i | 0.0457983 | + | 0.0264417i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 176.596 | + | 305.873i | 0.194703 | + | 0.337235i | 0.946803 | − | 0.321813i | \(-0.104292\pi\) |
−0.752100 | + | 0.659049i | \(0.770959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 849.700 | − | 490.575i | 0.932712 | − | 0.538501i | 0.0450436 | − | 0.998985i | \(-0.485657\pi\) |
0.887668 | + | 0.460484i | \(0.152324\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 648.090 | − | 1122.52i | 0.709847 | − | 1.22949i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 630.060i | 0.687088i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −303.202 | −0.329926 | −0.164963 | − | 0.986300i | \(-0.552750\pi\) | ||||
−0.164963 | + | 0.986300i | \(0.552750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 236.164 | + | 136.349i | 0.255865 | + | 0.147724i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53.6964 | + | 93.0050i | 0.0580502 | + | 0.100546i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −69.3559 | + | 40.0426i | −0.0746565 | + | 0.0431030i | −0.536864 | − | 0.843669i | \(-0.680391\pi\) |
0.462207 | + | 0.886772i | \(0.347058\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 139.157 | − | 241.027i | 0.149470 | − | 0.258890i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 251.445i | − | 0.268925i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −367.445 | −0.392150 | −0.196075 | − | 0.980589i | \(-0.562820\pi\) | ||||
−0.196075 | + | 0.980589i | \(0.562820\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 583.005 | + | 336.598i | 0.619559 | + | 0.357702i | 0.776697 | − | 0.629874i | \(-0.216894\pi\) |
−0.157138 | + | 0.987577i | \(0.550227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −285.636 | − | 494.736i | −0.302902 | − | 0.524641i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 866.108 | − | 500.048i | 0.914581 | − | 0.528034i | 0.0326790 | − | 0.999466i | \(-0.489596\pi\) |
0.881902 | + | 0.471432i | \(0.156263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 795.378 | − | 1377.63i | 0.838122 | − | 1.45167i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1800.63i | 1.88943i | 0.327889 | + | 0.944716i | \(0.393663\pi\) | ||||
−0.327889 | + | 0.944716i | \(0.606337\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −413.236 | −0.432708 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −835.565 | − | 482.414i | −0.871288 | − | 0.503038i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −718.812 | − | 1245.02i | −0.747984 | − | 1.29555i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −736.487 | + | 425.211i | −0.763199 | + | 0.440633i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 236.137 | − | 409.001i | 0.244196 | − | 0.422959i | −0.717710 | − | 0.696343i | \(-0.754809\pi\) |
0.961905 | + | 0.273383i | \(0.0881428\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 350.248i | 0.360708i | 0.983602 | + | 0.180354i | \(0.0577244\pi\) | ||||
−0.983602 | + | 0.180354i | \(0.942276\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1144.46 | −1.17622 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1157.45 | + | 668.251i | 1.18469 | + | 0.683983i | 0.957096 | − | 0.289772i | \(-0.0935795\pi\) |
0.227598 | + | 0.973755i | \(0.426913\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −308.840 | − | 534.927i | −0.315465 | − | 0.546402i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1174.62 | + | 678.167i | −1.19493 | + | 0.689895i | −0.959421 | − | 0.281976i | \(-0.909010\pi\) |
−0.235512 | + | 0.971871i | \(0.575677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 88.6690 | − | 153.579i | 0.0900193 | − | 0.155918i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 446.181i | 0.451144i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1699.68 | −1.71512 | −0.857558 | − | 0.514388i | \(-0.828019\pi\) | ||||
−0.857558 | + | 0.514388i | \(0.828019\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 168.915 | + | 97.5229i | 0.169764 | + | 0.0980130i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −816.024 | − | 1413.40i | −0.818480 | − | 1.41765i | −0.906802 | − | 0.421557i | \(-0.861484\pi\) |
0.0883222 | − | 0.996092i | \(-0.471849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.3.o.g.701.1 | 32 | ||
3.2 | odd | 2 | inner | 1620.3.o.g.701.16 | 32 | ||
9.2 | odd | 6 | inner | 1620.3.o.g.1241.1 | 32 | ||
9.4 | even | 3 | 1620.3.g.c.161.14 | yes | 16 | ||
9.5 | odd | 6 | 1620.3.g.c.161.6 | ✓ | 16 | ||
9.7 | even | 3 | inner | 1620.3.o.g.1241.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.3.g.c.161.6 | ✓ | 16 | 9.5 | odd | 6 | ||
1620.3.g.c.161.14 | yes | 16 | 9.4 | even | 3 | ||
1620.3.o.g.701.1 | 32 | 1.1 | even | 1 | trivial | ||
1620.3.o.g.701.16 | 32 | 3.2 | odd | 2 | inner | ||
1620.3.o.g.1241.1 | 32 | 9.2 | odd | 6 | inner | ||
1620.3.o.g.1241.16 | 32 | 9.7 | even | 3 | inner |