Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(265,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.265");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.t (of order \(6\), degree \(2\), 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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 265.9 | ||
Character | \(\chi\) | \(=\) | 684.265 |
Dual form | 684.3.t.a.493.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −2.57066 | + | 1.54651i | −0.856888 | + | 0.515503i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.45280 | − | 2.51632i | 0.290560 | − | 0.503265i | −0.683382 | − | 0.730061i | \(-0.739492\pi\) |
0.973942 | + | 0.226796i | \(0.0728251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.663126 | − | 1.14857i | −0.0947323 | − | 0.164081i | 0.814765 | − | 0.579792i | \(-0.196866\pi\) |
−0.909497 | + | 0.415711i | \(0.863533\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.21662 | − | 7.95111i | 0.468513 | − | 0.883457i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.65951 | − | 6.33846i | −0.332683 | − | 0.576224i | 0.650354 | − | 0.759631i | \(-0.274621\pi\) |
−0.983037 | + | 0.183408i | \(0.941287\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.0381 | + | 9.25959i | 1.23370 | + | 0.712276i | 0.967799 | − | 0.251725i | \(-0.0809977\pi\) |
0.265899 | + | 0.964001i | \(0.414331\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.156859 | + | 8.71539i | 0.0104573 | + | 0.581026i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −16.5415 | −0.973030 | −0.486515 | − | 0.873672i | \(-0.661732\pi\) | ||||
−0.486515 | + | 0.873672i | \(0.661732\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.9944 | + | 0.459853i | −0.999707 | + | 0.0242028i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.48095 | + | 1.92705i | 0.165759 | + | 0.0917644i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.86716 | − | 4.96607i | 0.124659 | − | 0.215916i | −0.796940 | − | 0.604058i | \(-0.793550\pi\) |
0.921600 | + | 0.388142i | \(0.126883\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.27875 | + | 14.3392i | 0.331150 | + | 0.573568i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.45697 | + | 26.9607i | 0.0539619 | + | 0.998543i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.50630 | − | 1.44701i | 0.0864241 | − | 0.0498970i | −0.456165 | − | 0.889895i | \(-0.650777\pi\) |
0.542589 | + | 0.839998i | \(0.317444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.2594 | − | 16.3156i | −0.911594 | − | 0.526309i | −0.0306505 | − | 0.999530i | \(-0.509758\pi\) |
−0.880944 | + | 0.473221i | \(0.843091\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 19.2099 | + | 10.6346i | 0.582117 | + | 0.322260i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.85356 | −0.110102 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12.1535i | 0.328473i | 0.986421 | + | 0.164237i | \(0.0525160\pi\) | ||||
−0.986421 | + | 0.164237i | \(0.947484\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −55.5485 | + | 0.999762i | −1.42432 | + | 0.0256349i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −43.8411 | − | 25.3117i | −1.06929 | − | 0.617358i | −0.141306 | − | 0.989966i | \(-0.545130\pi\) |
−0.927989 | + | 0.372608i | \(0.878464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −32.6098 | − | 56.4819i | −0.758368 | − | 1.31353i | −0.943682 | − | 0.330853i | \(-0.892664\pi\) |
0.185314 | − | 0.982679i | \(-0.440670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.8817 | − | 22.1617i | −0.308481 | − | 0.492483i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.40712 | − | 7.63335i | −0.0937685 | − | 0.162412i | 0.815325 | − | 0.579003i | \(-0.196558\pi\) |
−0.909094 | + | 0.416591i | \(0.863225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.6205 | − | 40.9120i | 0.482052 | − | 0.834938i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42.5226 | − | 25.5816i | 0.833777 | − | 0.501600i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26.3085i | 0.496387i | 0.968710 | + | 0.248194i | \(0.0798370\pi\) | ||||
−0.968710 | + | 0.248194i | \(0.920163\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −21.2662 | −0.386657 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 48.1171 | − | 30.5572i | 0.844160 | − | 0.536091i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −44.3022 | − | 25.5779i | −0.750885 | − | 0.433523i | 0.0751288 | − | 0.997174i | \(-0.476063\pi\) |
−0.826013 | + | 0.563650i | \(0.809397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.58788 | − | 7.94644i | −0.0752111 | − | 0.130269i | 0.825967 | − | 0.563719i | \(-0.190630\pi\) |
−0.901178 | + | 0.433449i | \(0.857296\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.9285 | + | 0.429519i | −0.189342 | + | 0.00681776i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 46.6002 | − | 26.9047i | 0.716927 | − | 0.413918i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.04428 | − | 5.22172i | −0.134989 | − | 0.0779361i | 0.430985 | − | 0.902359i | \(-0.358166\pi\) |
−0.565974 | + | 0.824423i | \(0.691500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.309569 | + | 17.2002i | 0.00448651 | + | 0.249278i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 46.2556i | − | 0.651487i | −0.945458 | − | 0.325744i | \(-0.894385\pi\) | ||
0.945458 | − | 0.325744i | \(-0.105615\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −32.7798 | −0.449038 | −0.224519 | − | 0.974470i | \(-0.572081\pi\) | ||||
−0.224519 | + | 0.974470i | \(0.572081\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −43.4576 | − | 24.0581i | −0.579434 | − | 0.320775i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.85344 | + | 8.40640i | −0.0630317 | + | 0.109174i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −46.4522 | + | 26.8192i | −0.588002 | + | 0.339483i | −0.764307 | − | 0.644852i | \(-0.776919\pi\) |
0.176305 | + | 0.984336i | \(0.443586\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −45.4403 | − | 67.0535i | −0.560991 | − | 0.827822i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −52.4783 | − | 90.8950i | −0.632268 | − | 1.09512i | −0.987087 | − | 0.160185i | \(-0.948791\pi\) |
0.354819 | − | 0.934935i | \(-0.384543\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.0315 | + | 41.6238i | −0.282724 | + | 0.489692i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.20503 | + | 7.59580i | −0.0483337 | + | 0.0873080i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 58.3307i | − | 0.655402i | −0.944782 | − | 0.327701i | \(-0.893726\pi\) | ||
0.944782 | − | 0.327701i | \(-0.106274\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 24.5611i | − | 0.269902i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 97.8777 | − | 1.76160i | 1.05245 | − | 0.0189419i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.4380 | + | 48.4642i | −0.278294 | + | 0.510150i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −102.545 | + | 59.2042i | −1.05716 | + | 0.610353i | −0.924646 | − | 0.380828i | \(-0.875639\pi\) |
−0.132516 | + | 0.991181i | \(0.542306\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −65.8286 | + | 2.37033i | −0.664935 | + | 0.0239427i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −64.0887 | − | 111.005i | −0.634542 | − | 1.09906i | −0.986612 | − | 0.163085i | \(-0.947855\pi\) |
0.352070 | − | 0.935974i | \(-0.385478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.07819 | − | 0.622493i | −0.0104679 | − | 0.00604362i | 0.494757 | − | 0.869031i | \(-0.335257\pi\) |
−0.505225 | + | 0.862988i | \(0.668590\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.90620 | − | 5.95957i | 0.0943448 | − | 0.0567578i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 132.982i | − | 1.24282i | −0.783485 | − | 0.621411i | \(-0.786560\pi\) | ||
0.783485 | − | 0.621411i | \(-0.213440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 93.1878i | 0.854934i | 0.904031 | + | 0.427467i | \(0.140594\pi\) | ||||
−0.904031 | + | 0.427467i | \(0.859406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.7955 | − | 31.2426i | −0.169329 | − | 0.281465i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −46.9613 | − | 27.1131i | −0.415587 | − | 0.239939i | 0.277600 | − | 0.960697i | \(-0.410461\pi\) |
−0.693187 | + | 0.720757i | \(0.743794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.33083 | − | 14.4294i | −0.0724420 | − | 0.125473i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 141.250 | − | 88.4764i | 1.20727 | − | 0.756209i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.9691 | + | 18.9991i | 0.0921774 | + | 0.159656i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 33.7159 | − | 58.3977i | 0.278644 | − | 0.482626i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 151.845 | − | 2.73291i | 1.23452 | − | 0.0222188i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 120.749 | 0.965995 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 225.693i | 1.77711i | 0.458772 | + | 0.888554i | \(0.348289\pi\) | ||||
−0.458772 | + | 0.888554i | \(0.651711\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 171.179 | + | 94.7645i | 1.32697 | + | 0.734608i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −24.3115 | + | 42.1088i | −0.185584 | + | 0.321441i | −0.943773 | − | 0.330594i | \(-0.892751\pi\) |
0.758189 | + | 0.652035i | \(0.226084\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.1239 | + | 21.5115i | 0.0986758 | + | 0.161740i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 69.9584 | + | 35.5022i | 0.518211 | + | 0.262979i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3479 | + | 19.6552i | 0.0828315 | + | 0.143468i | 0.904465 | − | 0.426548i | \(-0.140270\pi\) |
−0.821634 | + | 0.570016i | \(0.806937\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −82.3364 | + | 142.611i | −0.592348 | + | 1.02598i | 0.401567 | + | 0.915830i | \(0.368466\pi\) |
−0.993915 | + | 0.110148i | \(0.964868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.1343 | + | 12.8071i | 0.164073 | + | 0.0908307i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 135.542i | − | 0.947848i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.40888i | − | 0.0579922i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.55032 | + | 141.700i | 0.0173491 | + | 0.963947i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6141 | + | 30.5085i | −0.118216 | + | 0.204755i | −0.919061 | − | 0.394116i | \(-0.871051\pi\) |
0.800845 | + | 0.598872i | \(0.204384\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −210.694 | + | 121.644i | −1.39533 | + | 0.805592i | −0.993898 | − | 0.110299i | \(-0.964819\pi\) |
−0.401428 | + | 0.915891i | \(0.631486\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −69.7492 | + | 131.523i | −0.455877 | + | 0.859630i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −82.1106 | + | 47.4066i | −0.529746 | + | 0.305849i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 99.9191 | − | 173.065i | 0.636427 | − | 1.10232i | −0.349783 | − | 0.936831i | \(-0.613745\pi\) |
0.986211 | − | 0.165494i | \(-0.0529219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −40.6864 | − | 67.6304i | −0.255889 | − | 0.425348i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.60516 | −0.0472370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −58.9658 | −0.361753 | −0.180877 | − | 0.983506i | \(-0.557893\pi\) | ||||
−0.180877 | + | 0.983506i | \(0.557893\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 54.6681 | − | 32.8883i | 0.331322 | − | 0.199323i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 71.0960 | + | 41.0473i | 0.425725 | + | 0.245792i | 0.697524 | − | 0.716562i | \(-0.254285\pi\) |
−0.271799 | + | 0.962354i | \(0.587619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 86.9800 | + | 150.654i | 0.514674 | + | 0.891442i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −76.4359 | + | 152.966i | −0.446993 | + | 0.894537i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −34.2663 | + | 19.7837i | −0.198071 | + | 0.114356i | −0.595755 | − | 0.803166i | \(-0.703147\pi\) |
0.397684 | + | 0.917522i | \(0.369814\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.9797 | − | 19.0174i | 0.0627412 | − | 0.108671i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 153.442 | − | 2.76166i | 0.866906 | − | 0.0156026i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 137.422i | − | 0.767720i | −0.923391 | − | 0.383860i | \(-0.874595\pi\) | ||
0.923391 | − | 0.383860i | \(-0.125405\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 140.483i | 0.776152i | 0.921627 | + | 0.388076i | \(0.126860\pi\) | ||||
−0.921627 | + | 0.388076i | \(0.873140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.0831 | + | 13.3324i | 0.131602 | + | 0.0728547i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 30.5821 | + | 17.6566i | 0.165309 | + | 0.0954411i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 60.5339 | + | 104.848i | 0.323710 | + | 0.560683i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 30.0000 | − | 19.5518i | 0.158730 | − | 0.103448i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 158.930 | + | 275.275i | 0.832096 | + | 1.44123i | 0.896373 | + | 0.443300i | \(0.146192\pi\) |
−0.0642776 | + | 0.997932i | \(0.520474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −132.898 | − | 76.7287i | −0.688591 | − | 0.397558i | 0.114493 | − | 0.993424i | \(-0.463476\pi\) |
−0.803084 | + | 0.595866i | \(0.796809\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −78.1852 | + | 141.231i | −0.400950 | + | 0.724259i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 248.770 | 1.26279 | 0.631396 | − | 0.775460i | \(-0.282482\pi\) | ||||
0.631396 | + | 0.775460i | \(0.282482\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 122.997 | 0.618076 | 0.309038 | − | 0.951050i | \(-0.399993\pi\) | ||||
0.309038 | + | 0.951050i | \(0.399993\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.3252 | − | 0.563792i | 0.155847 | − | 0.00280493i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.32399 | − | 1.91910i | −0.0163743 | − | 0.00945371i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −127.385 | + | 73.5456i | −0.621389 | + | 0.358759i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −27.3961 | − | 43.7371i | −0.132348 | − | 0.211291i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 72.4251 | + | 118.713i | 0.346532 | + | 0.568003i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 166.537 | + | 96.1504i | 0.789276 | + | 0.455689i | 0.839708 | − | 0.543039i | \(-0.182726\pi\) |
−0.0504313 | + | 0.998728i | \(0.516060\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 71.5347 | + | 118.907i | 0.335844 | + | 0.558251i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −189.502 | −0.881406 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 43.2772i | 0.199434i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 84.2658 | − | 50.6943i | 0.384775 | − | 0.231481i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −265.294 | − | 153.168i | −1.20043 | − | 0.693066i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.7205 | + | 13.1177i | −0.101886 | + | 0.0588237i | −0.550077 | − | 0.835114i | \(-0.685402\pi\) |
0.448191 | + | 0.893938i | \(0.352068\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 148.921 | − | 5.36229i | 0.661871 | − | 0.0238324i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 363.943 | − | 210.123i | 1.60327 | − | 0.925651i | 0.612449 | − | 0.790510i | \(-0.290185\pi\) |
0.990826 | − | 0.135141i | \(-0.0431487\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 84.3954 | − | 146.177i | 0.368539 | − | 0.638328i | −0.620798 | − | 0.783970i | \(-0.713191\pi\) |
0.989337 | + | 0.145642i | \(0.0465248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.524028 | − | 29.1159i | −0.00226852 | − | 0.126043i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 403.689 | 1.73257 | 0.866284 | − | 0.499551i | \(-0.166502\pi\) | ||||
0.866284 | + | 0.499551i | \(0.166502\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.6106 | −0.108981 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 77.9368 | − | 140.782i | 0.328847 | − | 0.594016i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −104.337 | + | 180.717i | −0.436557 | + | 0.756139i | −0.997421 | − | 0.0717689i | \(-0.977136\pi\) |
0.560864 | + | 0.827908i | \(0.310469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −79.6486 | + | 45.9851i | −0.330492 | + | 0.190810i | −0.656060 | − | 0.754709i | \(-0.727778\pi\) |
0.325567 | + | 0.945519i | \(0.394445\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 220.511 | + | 102.098i | 0.907451 | + | 0.420157i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −68.6318 | − | 118.874i | −0.280130 | − | 0.485199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −308.892 | − | 168.506i | −1.25058 | − | 0.682209i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 275.474 | + | 152.502i | 1.10632 | + | 0.612459i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4421 | −0.0734744 | −0.0367372 | − | 0.999325i | \(-0.511696\pi\) | ||||
−0.0367372 | + | 0.999325i | \(0.511696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −41.9697 | −0.165888 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.59469 | − | 144.166i | −0.0101753 | − | 0.565356i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −176.738 | − | 102.040i | −0.687696 | − | 0.397042i | 0.115052 | − | 0.993359i | \(-0.463296\pi\) |
−0.802748 | + | 0.596318i | \(0.796630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.9591 | − | 8.05931i | 0.0538963 | − | 0.0311170i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.937256 | − | 26.0293i | −0.00359102 | − | 0.0997293i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −243.146 | − | 421.141i | −0.924508 | − | 1.60130i | −0.792350 | − | 0.610067i | \(-0.791143\pi\) |
−0.132158 | − | 0.991229i | \(-0.542191\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 66.2008 | + | 38.2210i | 0.249814 | + | 0.144230i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 90.2091 | + | 149.949i | 0.337862 | + | 0.561606i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 463.171i | − | 1.72183i | −0.508752 | − | 0.860913i | \(-0.669893\pi\) | ||
0.508752 | − | 0.860913i | \(-0.330107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 172.822 | 0.637719 | 0.318859 | − | 0.947802i | \(-0.396700\pi\) | ||||
0.318859 | + | 0.947802i | \(0.396700\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 37.9840 | + | 63.1383i | 0.139136 | + | 0.231276i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 60.5923 | − | 104.949i | 0.220336 | − | 0.381633i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 144.894 | + | 250.964i | 0.523083 | + | 0.906007i | 0.999639 | + | 0.0268627i | \(0.00855168\pi\) |
−0.476556 | + | 0.879144i | \(0.658115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −248.886 | + | 155.897i | −0.892065 | + | 0.558771i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −454.513 | + | 262.413i | −1.61748 | + | 0.933855i | −0.629916 | + | 0.776663i | \(0.716911\pi\) |
−0.987568 | + | 0.157191i | \(0.949756\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −180.446 | + | 312.542i | −0.637620 | + | 1.10439i | 0.348334 | + | 0.937371i | \(0.386748\pi\) |
−0.985954 | + | 0.167019i | \(0.946586\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.98725 | − | 165.472i | −0.0245167 | − | 0.580603i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 67.1393i | 0.233935i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3785 | −0.0532126 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 172.048 | − | 310.780i | 0.591230 | − | 1.06797i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −496.429 | − | 286.613i | −1.69430 | − | 0.978203i | −0.950974 | − | 0.309271i | \(-0.899915\pi\) |
−0.743323 | − | 0.668932i | \(-0.766752\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −128.724 | + | 74.3191i | −0.436354 | + | 0.251929i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 165.557 | − | 107.898i | 0.557432 | − | 0.363292i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 91.9676 | − | 53.0975i | 0.307584 | − | 0.177584i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −43.2489 | + | 74.9093i | −0.143684 | + | 0.248868i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 336.421 | + | 186.242i | 1.11030 | + | 0.614662i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.6611 | −0.0874134 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 354.493i | − | 1.15470i | −0.816496 | − | 0.577351i | \(-0.804087\pi\) | ||
0.816496 | − | 0.577351i | \(-0.195913\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.73436 | − | 0.0672109i | 0.0120853 | − | 0.000217511i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −222.647 | + | 385.635i | −0.715906 | + | 1.23998i | 0.246704 | + | 0.969091i | \(0.420653\pi\) |
−0.962609 | + | 0.270894i | \(0.912681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 82.2430 | + | 142.449i | 0.262757 | + | 0.455109i | 0.966974 | − | 0.254877i | \(-0.0820349\pi\) |
−0.704217 | + | 0.709985i | \(0.748702\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.2490 | + | 30.6401i | −0.0515841 | + | 0.0972701i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 257.031 | − | 148.397i | 0.810822 | − | 0.468128i | −0.0364192 | − | 0.999337i | \(-0.511595\pi\) |
0.847241 | + | 0.531208i | \(0.178262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.3437 | − | 10.5907i | −0.0575036 | − | 0.0331997i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 205.658 | + | 341.852i | 0.640679 | + | 1.06496i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 314.197 | − | 7.60666i | 0.972745 | − | 0.0235500i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 306.631i | 0.943480i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −144.116 | − | 239.554i | −0.440721 | − | 0.732582i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.84495 | + | 10.1238i | −0.0177658 | + | 0.0307713i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 293.764 | − | 169.605i | 0.887504 | − | 0.512401i | 0.0143790 | − | 0.999897i | \(-0.495423\pi\) |
0.873125 | + | 0.487496i | \(0.162090\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 96.6338 | + | 51.2467i | 0.290192 | + | 0.153894i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.2791 | + | 15.1722i | −0.0784450 | + | 0.0452902i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 207.414 | + | 119.750i | 0.615472 | + | 0.355343i | 0.775104 | − | 0.631834i | \(-0.217698\pi\) |
−0.159632 | + | 0.987177i | \(0.551031\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 162.652 | − | 2.92742i | 0.479801 | − | 0.00863545i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 238.828i | 0.700376i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −127.640 | −0.372128 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 43.7310 | + | 24.2095i | 0.126756 | + | 0.0701723i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −124.105 | + | 214.957i | −0.357652 | + | 0.619472i | −0.987568 | − | 0.157191i | \(-0.949756\pi\) |
0.629916 | + | 0.776664i | \(0.283089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −300.432 | − | 520.364i | −0.860838 | − | 1.49101i | −0.871122 | − | 0.491068i | \(-0.836607\pi\) |
0.0102838 | − | 0.999947i | \(-0.496727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −226.278 | + | 445.888i | −0.644666 | + | 1.27034i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −103.500 | − | 179.267i | −0.293200 | − | 0.507837i | 0.681365 | − | 0.731944i | \(-0.261387\pi\) |
−0.974565 | + | 0.224107i | \(0.928054\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −116.394 | − | 67.2001i | −0.327870 | − | 0.189296i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −57.5801 | − | 31.8763i | −0.161289 | − | 0.0892895i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 218.156 | 0.607676 | 0.303838 | − | 0.952724i | \(-0.401732\pi\) | ||||
0.303838 | + | 0.952724i | \(0.401732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 360.577 | − | 17.4693i | 0.998828 | − | 0.0483914i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.64033 | + | 202.263i | 0.0100284 | + | 0.557198i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −47.6225 | + | 82.4845i | −0.130473 | + | 0.225985i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −100.949 | − | 174.848i | −0.275064 | − | 0.476425i | 0.695087 | − | 0.718925i | \(-0.255366\pi\) |
−0.970151 | + | 0.242500i | \(0.922032\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −386.117 | + | 241.856i | −1.04639 | + | 0.655436i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.2172 | − | 17.4459i | 0.0814479 | − | 0.0470239i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 210.083 | + | 121.292i | 0.563226 | + | 0.325179i | 0.754439 | − | 0.656370i | \(-0.227909\pi\) |
−0.191213 | + | 0.981549i | \(0.561242\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −310.406 | + | 186.740i | −0.827750 | + | 0.497974i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 53.5949 | 0.142162 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 89.6768i | 0.236614i | 0.992977 | + | 0.118307i | \(0.0377467\pi\) | ||||
−0.992977 | + | 0.118307i | \(0.962253\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −349.036 | − | 580.180i | −0.916105 | − | 1.52278i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 424.451 | + | 245.057i | 1.10823 | + | 0.639835i | 0.938369 | − | 0.345634i | \(-0.112336\pi\) |
0.169857 | + | 0.985469i | \(0.445669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.1021 | + | 24.4256i | 0.0366290 | + | 0.0634432i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −586.597 | + | 21.1220i | −1.51575 | + | 0.0545788i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.5170 | − | 63.2493i | −0.0938740 | − | 0.162594i | 0.815264 | − | 0.579089i | \(-0.196592\pi\) |
−0.909138 | + | 0.416495i | \(0.863258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −47.4272 | + | 82.1463i | −0.121297 | + | 0.210093i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.62493 | − | 145.846i | −0.00667920 | − | 0.371108i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 155.852i | 0.394561i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 310.040 | 0.780958 | 0.390479 | − | 0.920612i | \(-0.372309\pi\) | ||||
0.390479 | + | 0.920612i | \(0.372309\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −67.0048 | − | 35.0025i | −0.167932 | − | 0.0877256i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 162.090 | + | 93.5826i | 0.404214 | + | 0.233373i | 0.688301 | − | 0.725425i | \(-0.258357\pi\) |
−0.284087 | + | 0.958799i | \(0.591690\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −302.151 | − | 523.341i | −0.749755 | − | 1.29861i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −234.744 | + | 16.9271i | −0.579615 | + | 0.0417953i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 77.0345 | − | 44.4759i | 0.189274 | − | 0.109277i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 60.9834 | + | 35.2088i | 0.149104 | + | 0.0860850i | 0.572696 | − | 0.819768i | \(-0.305898\pi\) |
−0.423592 | + | 0.905853i | \(0.639231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −59.5686 | − | 32.9772i | −0.144936 | − | 0.0802364i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 67.8455i | 0.164275i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −304.962 | −0.734847 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.88990 | − | 493.939i | −0.0213187 | − | 1.18450i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 115.222 | − | 199.571i | 0.274994 | − | 0.476303i | −0.695140 | − | 0.718875i | \(-0.744657\pi\) |
0.970134 | + | 0.242571i | \(0.0779908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −107.934 | + | 62.3157i | −0.256375 | + | 0.148018i | −0.622680 | − | 0.782477i | \(-0.713956\pi\) |
0.366305 | + | 0.930495i | \(0.380623\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −79.2767 | + | 2.85457i | −0.187415 | + | 0.00674839i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −136.943 | − | 237.192i | −0.322219 | − | 0.558099i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.08469 | + | 10.5390i | −0.0142499 | + | 0.0246815i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 209.618 | + | 348.434i | 0.488619 | + | 0.812200i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 684.497i | 1.58816i | 0.607813 | + | 0.794080i | \(0.292047\pi\) | ||||
−0.607813 | + | 0.794080i | \(0.707953\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 250.418i | 0.578333i | 0.957279 | + | 0.289166i | \(0.0933781\pi\) | ||||
−0.957279 | + | 0.289166i | \(0.906622\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.0044 | + | 21.6164i | 0.0298952 | + | 0.0496928i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −52.1765 | + | 95.6462i | −0.119397 | + | 0.218870i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 45.8879 | − | 26.4934i | 0.104528 | − | 0.0603495i | −0.446824 | − | 0.894622i | \(-0.647445\pi\) |
0.551353 | + | 0.834272i | \(0.314112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −225.697 | − | 360.319i | −0.511784 | − | 0.817051i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −261.160 | − | 452.343i | −0.589527 | − | 1.02109i | −0.994294 | − | 0.106671i | \(-0.965981\pi\) |
0.404768 | − | 0.914419i | \(-0.367352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −146.779 | − | 84.7429i | −0.329840 | − | 0.190433i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.90180 | − | 105.668i | −0.00425460 | − | 0.236393i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 552.299i | − | 1.23006i | −0.788502 | − | 0.615032i | \(-0.789143\pi\) | ||
0.788502 | − | 0.615032i | \(-0.210857\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 370.513i | 0.821537i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 353.500 | − | 638.547i | 0.780352 | − | 1.40960i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −61.8037 | − | 35.6824i | −0.135832 | − | 0.0784228i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −176.969 | − | 306.519i | −0.387240 | − | 0.670719i | 0.604837 | − | 0.796349i | \(-0.293238\pi\) |
−0.992077 | + | 0.125630i | \(0.959905\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.1005 | − | 445.970i | −0.0525066 | − | 0.971612i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 49.3548 | + | 85.4849i | 0.107060 | + | 0.185434i | 0.914578 | − | 0.404409i | \(-0.132523\pi\) |
−0.807518 | + | 0.589843i | \(0.799190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 61.1161 | − | 105.856i | 0.132000 | − | 0.228631i | −0.792447 | − | 0.609940i | \(-0.791193\pi\) |
0.924448 | + | 0.381309i | \(0.124527\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 137.764 | − | 248.851i | 0.296266 | − | 0.535164i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −180.368 | −0.386228 | −0.193114 | − | 0.981176i | \(-0.561859\pi\) | ||||
−0.193114 | + | 0.981176i | \(0.561859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.8506i | 0.0295323i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.7883 | + | 599.418i | 0.0229051 | + | 1.27265i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −238.672 | + | 413.392i | −0.504592 | + | 0.873980i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −163.844 | − | 268.558i | −0.344935 | − | 0.565386i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 209.182 | + | 110.933i | 0.438537 | + | 0.232564i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −335.479 | − | 581.067i | −0.700374 | − | 1.21308i | −0.968335 | − | 0.249654i | \(-0.919683\pi\) |
0.267961 | − | 0.963430i | \(-0.413650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −112.536 | + | 194.919i | −0.233964 | + | 0.405237i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.5503 | − | 11.7615i | 0.0404768 | − | 0.0243509i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 344.047i | 0.709376i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 415.292i | − | 0.852755i | −0.904545 | − | 0.426378i | \(-0.859790\pi\) | ||
0.904545 | − | 0.426378i | \(-0.140210\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 151.581 | − | 91.1912i | 0.309982 | − | 0.186485i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −120.766 | + | 209.174i | −0.245960 | + | 0.426015i | −0.962401 | − | 0.271632i | \(-0.912437\pi\) |
0.716441 | + | 0.697648i | \(0.245770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.4580 | + | 23.9358i | −0.0840932 | + | 0.0485512i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −89.6712 | + | 169.090i | −0.181154 | + | 0.341595i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −53.1277 | + | 30.6733i | −0.106897 | + | 0.0617169i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.5201 | + | 70.1828i | −0.0812025 | + | 0.140647i | −0.903767 | − | 0.428025i | \(-0.859209\pi\) |
0.822564 | + | 0.568672i | \(0.192543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −246.244 | + | 4.43190i | −0.491505 | + | 0.00884610i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 611.143 | 1.21500 | 0.607498 | − | 0.794321i | \(-0.292173\pi\) | ||||
0.607498 | + | 0.794321i | \(0.292173\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −372.432 | −0.737490 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −456.584 | − | 252.765i | −0.900560 | − | 0.498550i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 647.042 | + | 373.570i | 1.27120 | + | 0.733929i | 0.975214 | − | 0.221262i | \(-0.0710177\pi\) |
0.295988 | + | 0.955192i | \(0.404351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.7371 | + | 37.6498i | 0.0425384 | + | 0.0736787i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −40.0723 | − | 511.433i | −0.0781136 | − | 0.996944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.13279 | + | 1.80872i | −0.00608309 | + | 0.00351207i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.2558 | + | 55.8687i | −0.0623903 | + | 0.108063i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.4915 | − | 103.850i | 0.110774 | − | 0.200097i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 412.618i | 0.791974i | 0.918256 | + | 0.395987i | \(0.129597\pi\) | ||||
−0.918256 | + | 0.395987i | \(0.870403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 732.398i | − | 1.40038i | −0.713957 | − | 0.700190i | \(-0.753099\pi\) | ||
0.713957 | − | 0.700190i | \(-0.246901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.18548 | + | 65.8676i | 0.00225807 | + | 0.125462i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 467.453 | + | 269.884i | 0.887008 | + | 0.512115i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 248.059 | + | 429.650i | 0.468920 | + | 0.812194i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −390.178 | + | 244.400i | −0.734798 | + | 0.460263i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −468.751 | − | 811.901i | −0.879458 | − | 1.52327i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −334.626 | − | 193.196i | −0.625468 | − | 0.361114i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 212.524 | + | 353.265i | 0.395762 | + | 0.657850i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −345.758 | −0.641481 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 256.682 | 0.474458 | 0.237229 | − | 0.971454i | \(-0.423761\pi\) | ||||
0.237229 | + | 0.971454i | \(0.423761\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −217.259 | − | 361.136i | −0.400109 | − | 0.665075i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 234.491 | + | 135.383i | 0.430258 | + | 0.248409i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 779.393 | − | 449.983i | 1.42485 | − | 0.822638i | 0.428143 | − | 0.903711i | \(-0.359168\pi\) |
0.996708 | + | 0.0810730i | \(0.0258347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −82.5283 | + | 2.97165i | −0.150325 | + | 0.00541284i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.9403 | + | 28.6377i | −0.0851911 | + | 0.0519741i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 61.6073 | + | 35.5690i | 0.111406 | + | 0.0643201i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −105.922 | + | 1.90639i | −0.190851 | + | 0.00343494i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.5151 | 0.0332407 | 0.0166204 | − | 0.999862i | \(-0.494709\pi\) | ||||
0.0166204 | + | 0.999862i | \(0.494709\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1207.81i | − | 2.16067i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −317.760 | − | 175.912i | −0.566417 | − | 0.313569i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −217.520 | − | 125.585i | −0.386359 | − | 0.223065i | 0.294222 | − | 0.955737i | \(-0.404939\pi\) |
−0.680581 | + | 0.732672i | \(0.738273\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −136.451 | + | 78.7799i | −0.241506 | + | 0.139433i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −46.8829 | + | 96.6563i | −0.0826860 | + | 0.170470i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −376.237 | + | 217.220i | −0.661225 | + | 0.381758i | −0.792744 | − | 0.609555i | \(-0.791348\pi\) |
0.131519 | + | 0.991314i | \(0.458015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.6699 | − | 80.8346i | 0.0817335 | − | 0.141567i | −0.822261 | − | 0.569110i | \(-0.807288\pi\) |
0.903995 | + | 0.427544i | \(0.140621\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −834.272 | − | 461.853i | −1.45597 | − | 0.806026i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 94.9460 | 0.165124 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −553.366 | −0.959040 | −0.479520 | − | 0.877531i | \(-0.659189\pi\) | ||||
−0.479520 | + | 0.877531i | \(0.659189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 460.298 | − | 8.28443i | 0.794987 | − | 0.0143082i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −69.5994 | + | 120.550i | −0.119792 | + | 0.207487i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 166.756 | − | 96.2764i | 0.286030 | − | 0.165140i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.4266 | − | 483.970i | −0.0297891 | − | 0.827300i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 87.0791 | + | 150.825i | 0.148346 | + | 0.256943i | 0.930616 | − | 0.365996i | \(-0.119272\pi\) |
−0.782270 | + | 0.622939i | \(0.785938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 544.274 | + | 296.910i | 0.924065 | + | 0.504092i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −639.504 | + | 384.725i | −1.08207 | + | 0.650973i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 206.615 | 0.348423 | 0.174212 | − | 0.984708i | \(-0.444262\pi\) | ||||
0.174212 | + | 0.984708i | \(0.444262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 63.7437 | 0.107132 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −316.184 | + | 190.216i | −0.529622 | + | 0.318620i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.4371 | − | 17.5729i | −0.0508132 | − | 0.0293370i | 0.474378 | − | 0.880321i | \(-0.342673\pi\) |
−0.525191 | + | 0.850984i | \(0.676006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 53.9451 | − | 31.1452i | 0.0897590 | − | 0.0518224i | −0.454449 | − | 0.890773i | \(-0.650164\pi\) |
0.544208 | + | 0.838951i | \(0.316830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −79.6547 | + | 49.8941i | −0.132097 | + | 0.0827431i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −97.9650 | − | 169.680i | −0.161926 | − | 0.280463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −408.713 | − | 235.970i | −0.673333 | − | 0.388749i | 0.124006 | − | 0.992282i | \(-0.460426\pi\) |
−0.797338 | + | 0.603533i | \(0.793759\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.5128 | − | 0.207207i | 0.0189044 | − | 0.000340241i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 163.232i | − | 0.267156i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −259.476 | −0.423289 | −0.211645 | − | 0.977347i | \(-0.567882\pi\) | ||||
−0.211645 | + | 0.977347i | \(0.567882\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 213.724 | − | 386.062i | 0.347519 | − | 0.627744i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −447.580 | + | 775.232i | −0.725414 | + | 1.25645i | 0.233390 | + | 0.972383i | \(0.425018\pi\) |
−0.958803 | + | 0.284070i | \(0.908315\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 249.739 | + | 432.560i | 0.403455 | + | 0.698804i | 0.994140 | − | 0.108098i | \(-0.0344759\pi\) |
−0.590686 | + | 0.806902i | \(0.701143\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 138.066 | + | 70.0652i | 0.222328 | + | 0.112826i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −66.9969 | + | 38.6807i | −0.107539 | + | 0.0620877i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.5439 | + | 54.6356i | −0.0504702 | + | 0.0874170i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −369.771 | − | 193.164i | −0.589746 | − | 0.308077i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 201.037i | − | 0.319614i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.8556 | −0.0742561 | −0.0371280 | − | 0.999311i | \(-0.511821\pi\) | ||||
−0.0371280 | + | 0.999311i | \(0.511821\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −576.809 | + | 10.3814i | −0.911230 | + | 0.0164003i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 567.916 | + | 327.886i | 0.894355 | + | 0.516356i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 757.656 | − | 437.433i | 1.18941 | − | 0.686708i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −367.783 | − | 195.042i | −0.575561 | − | 0.305230i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −235.482 | + | 135.955i | −0.367366 | + | 0.212099i | −0.672307 | − | 0.740272i | \(-0.734697\pi\) |
0.304941 | + | 0.952371i | \(0.401363\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 404.629 | − | 700.837i | 0.629283 | − | 1.08995i | −0.358413 | − | 0.933563i | \(-0.616682\pi\) |
0.987696 | − | 0.156386i | \(-0.0499845\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 487.146 | − | 293.067i | 0.755266 | − | 0.454368i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.2587 | 0.0714972 | 0.0357486 | − | 0.999361i | \(-0.488618\pi\) | ||||
0.0357486 | + | 0.999361i | \(0.488618\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 374.410i | 0.576903i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −66.9286 | − | 111.251i | −0.102809 | − | 0.170893i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 349.601 | − | 605.526i | 0.535376 | − | 0.927298i | −0.463769 | − | 0.885956i | \(-0.653503\pi\) |
0.999145 | − | 0.0413423i | \(-0.0131634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 70.6396 | + | 122.351i | 0.107847 | + | 0.186796i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −138.220 | + | 260.636i | −0.210380 | + | 0.396706i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 226.326 | − | 130.670i | 0.343439 | − | 0.198285i | −0.318353 | − | 0.947972i | \(-0.603130\pi\) |
0.661792 | + | 0.749688i | \(0.269796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 321.288 | + | 185.496i | 0.486063 | + | 0.280629i | 0.722940 | − | 0.690911i | \(-0.242790\pi\) |
−0.236877 | + | 0.971540i | \(0.576124\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 918.857 | − | 16.5376i | 1.38591 | − | 0.0249436i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 73.1962 | − | 1.77207i | 0.110069 | − | 0.00266477i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16.5953i | − | 0.0248805i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.1201 | − | 68.8586i | 0.0569807 | − | 0.102928i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.5788 | + | 58.1602i | −0.0500429 | + | 0.0866769i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 951.502 | − | 549.350i | 1.41382 | − | 0.816270i | 0.418076 | − | 0.908412i | \(-0.362705\pi\) |
0.995746 | + | 0.0921420i | \(0.0293714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −374.533 | + | 244.092i | −0.554863 | + | 0.361618i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −182.351 | + | 105.281i | −0.269352 | + | 0.155510i | −0.628593 | − | 0.777734i | \(-0.716369\pi\) |
0.359241 | + | 0.933245i | \(0.383036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 136.000 | + | 78.5197i | 0.200295 | + | 0.115640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −610.619 | + | 1103.00i | −0.896650 | + | 1.61967i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 739.534i | 1.08277i | 0.840774 | + | 0.541386i | \(0.182100\pi\) | ||||
−0.840774 | + | 0.541386i | \(0.817900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 65.9450 | 0.0962701 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.11221 | + | 506.291i | 0.0132638 | + | 0.736959i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −243.606 | + | 421.938i | −0.353565 | + | 0.612392i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 294.555 | + | 510.184i | 0.426273 | + | 0.738326i | 0.996538 | − | 0.0831341i | \(-0.0264930\pi\) |
−0.570265 | + | 0.821460i | \(0.693160\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.3751 | + | 74.0368i | 0.0669194 | + | 0.106835i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 239.237 | + | 414.370i | 0.344225 | + | 0.596216i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 725.198 | + | 418.693i | 1.04046 | + | 0.600708i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1037.75 | + | 624.308i | −1.48462 | + | 0.893145i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1159.94 | 1.65469 | 0.827345 | − | 0.561694i | \(-0.189850\pi\) | ||||
0.827345 | + | 0.561694i | \(0.189850\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.58882 | − | 230.849i | −0.00794996 | − | 0.328377i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 65.8363 | − | 39.6071i | 0.0933849 | − | 0.0561803i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −84.9979 | + | 147.221i | −0.120223 | + | 0.208233i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −544.899 | − | 943.793i | −0.768546 | − | 1.33116i | −0.938351 | − | 0.345683i | \(-0.887647\pi\) |
0.169806 | − | 0.985478i | \(-0.445686\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.3713 | + | 482.433i | 0.0244322 | + | 0.678527i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −162.049 | + | 93.5589i | −0.227277 | + | 0.131219i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −341.068 | − | 196.916i | −0.477019 | − | 0.275407i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.2653 | − | 625.921i | −0.0157118 | − | 0.872973i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 788.886 | 1.09720 | 0.548599 | − | 0.836085i | \(-0.315161\pi\) | ||||
0.548599 | + | 0.836085i | \(0.315161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.65117i | 0.00229011i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 133.633 | − | 241.390i | 0.184832 | − | 0.333872i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.4980 | + | 23.9589i | 0.0572386 | + | 0.0330467i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 538.278 | + | 932.324i | 0.740409 | + | 1.28243i | 0.952309 | + | 0.305135i | \(0.0987016\pi\) |
−0.211900 | + | 0.977291i | \(0.567965\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −724.754 | + | 78.5619i | −0.994176 | + | 0.107767i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 539.416 | + | 934.296i | 0.737915 | + | 1.27811i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 538.967 | − | 933.518i | 0.735289 | − | 1.27356i | −0.219307 | − | 0.975656i | \(-0.570380\pi\) |
0.954596 | − | 0.297903i | \(-0.0962871\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 360.269 | + | 199.445i | 0.490161 | + | 0.271353i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 76.4358i | 0.103712i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 825.434 | 1.11696 | 0.558480 | − | 0.829518i | \(-0.311385\pi\) | ||||
0.558480 | + | 0.829518i | \(0.311385\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1054.65 | − | 44.5341i | 1.42328 | − | 0.0601000i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −64.5430 | − | 37.2639i | −0.0868681 | − | 0.0501533i | 0.455937 | − | 0.890012i | \(-0.349304\pi\) |
−0.542805 | + | 0.839859i | \(0.682638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.1796 | + | 88.6456i | 0.0686974 | + | 0.118987i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −943.997 | + | 33.9911i | −1.26372 | + | 0.0455035i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −152.739 | + | 88.1839i | −0.203924 | + | 0.117735i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −462.816 | − | 267.207i | −0.616266 | − | 0.355801i | 0.159148 | − | 0.987255i | \(-0.449125\pi\) |
−0.775414 | + | 0.631453i | \(0.782459\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 47.4084 | − | 28.5208i | 0.0629593 | − | 0.0378763i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 706.900i | 0.936291i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −372.882 | −0.492579 | −0.246289 | − | 0.969196i | \(-0.579211\pi\) | ||||
−0.246289 | + | 0.969196i | \(0.579211\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 107.890 | − | 64.9065i | 0.142147 | − | 0.0855158i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −437.900 | + | 758.465i | −0.575427 | + | 0.996669i | 0.420568 | + | 0.907261i | \(0.361831\pi\) |
−0.995995 | + | 0.0894081i | \(0.971502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 107.033 | − | 61.7953i | 0.140279 | − | 0.0809899i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 229.624 | + | 366.589i | 0.300162 | + | 0.479201i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −473.681 | − | 820.440i | −0.617577 | − | 1.06967i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −343.462 | + | 594.894i | −0.446635 | + | 0.773594i | −0.998164 | − | 0.0605610i | \(-0.980711\pi\) |
0.551530 | + | 0.834155i | \(0.314044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 612.139 | − | 11.0173i | 0.793954 | − | 0.0142896i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1020.13i | 1.31970i | 0.751398 | + | 0.659850i | \(0.229380\pi\) | ||||
−0.751398 | + | 0.659850i | \(0.770620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 540.290i | − | 0.697149i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.4204 | + | 42.3057i | −0.0301421 | + | 0.0544475i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 844.376 | + | 460.620i | 1.08392 | + | 0.591297i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −293.189 | + | 169.273i | −0.375402 | + | 0.216739i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.6640 | + | 65.4632i | 0.0544879 | + | 0.0836056i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −290.325 | − | 502.858i | −0.369841 | − | 0.640583i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 428.852 | + | 247.598i | 0.544920 | + | 0.314609i | 0.747070 | − | 0.664745i | \(-0.231460\pi\) |
−0.202151 | + | 0.979354i | \(0.564793\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1276.34 | + | 706.584i | 1.61767 | + | 0.895543i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 71.9178i | 0.0909200i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 169.927i | − | 0.214284i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −229.289 | + | 4.12674i | −0.288414 | + | 0.00519087i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1145.16 | − | 661.160i | −1.43684 | − | 0.829561i | −0.439212 | − | 0.898383i | \(-0.644742\pi\) |
−0.997629 | + | 0.0688225i | \(0.978076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 72.9004 | + | 126.267i | 0.0912395 | + | 0.158031i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −463.794 | − | 245.958i | −0.579019 | − | 0.307064i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 119.958 | + | 207.773i | 0.149387 | + | 0.258746i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.0488 | + | 19.1371i | −0.0137252 | + | 0.0237727i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 716.299 | + | 1190.66i | 0.887607 | + | 1.47541i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1170.22 | 1.44650 | 0.723250 | − | 0.690586i | \(-0.242647\pi\) | ||||
0.723250 | + | 0.690586i | \(0.242647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 951.145i | − | 1.17281i | −0.810020 | − | 0.586403i | \(-0.800544\pi\) | ||
0.810020 | − | 0.586403i | \(-0.199456\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −444.267 | + | 267.271i | −0.546453 | + | 0.328746i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −85.6655 | + | 148.377i | −0.105111 | + | 0.182058i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 645.379 | + | 1057.85i | 0.789937 | + | 1.29479i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −195.288 | − | 103.565i | −0.238447 | − | 0.126453i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −522.954 | − | 905.783i | −0.636972 | − | 1.10327i | −0.986094 | − | 0.166190i | \(-0.946853\pi\) |
0.349122 | − | 0.937077i | \(-0.386480\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 221.025 | − | 382.827i | 0.268560 | − | 0.465160i | −0.699930 | − | 0.714212i | \(-0.746785\pi\) |
0.968490 | + | 0.249051i | \(0.0801188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.54218 | + | 363.495i | 0.00792992 | + | 0.440600i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 837.366i | 1.01253i | 0.862377 | + | 0.506267i | \(0.168975\pi\) | ||||
−0.862377 | + | 0.506267i | \(0.831025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 333.104i | 0.401814i | 0.979610 | + | 0.200907i | \(0.0643890\pi\) | ||||
−0.979610 | + | 0.200907i | \(0.935611\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −760.592 | − | 421.064i | −0.915273 | − | 0.506695i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −390.719 | + | 676.745i | −0.469051 | + | 0.812420i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 206.577 | − | 119.267i | 0.247397 | − | 0.142835i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 398.706 | − | 785.664i | 0.476351 | − | 0.938667i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 410.267 | − | 236.868i | 0.488995 | − | 0.282322i | −0.235162 | − | 0.971956i | \(-0.575562\pi\) |
0.724158 | + | 0.689634i | \(0.242229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −416.312 | + | 721.074i | −0.495021 | + | 0.857401i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 762.575 | − | 1377.48i | 0.904597 | − | 1.63403i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 505.458 | 0.598175 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −89.4317 | −0.105586 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.4829 | − | 1082.50i | −0.0229480 | − | 1.27503i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 60.3552 | + | 34.8461i | 0.0709226 | + | 0.0409472i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6335 | + | 51.3267i | 0.0347403 | + | 0.0601720i | 0.882873 | − | 0.469612i | \(-0.155606\pi\) |
−0.848132 | + | 0.529784i | \(0.822273\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 273.865 | + | 414.566i | 0.320311 | + | 0.484873i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −565.033 | + | 326.222i | −0.659316 | + | 0.380656i | −0.792016 | − | 0.610500i | \(-0.790968\pi\) |
0.132701 | + | 0.991156i | \(0.457635\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −124.886 | + | 216.309i | −0.145385 | + | 0.251815i | −0.929517 | − | 0.368780i | \(-0.879776\pi\) |
0.784131 | + | 0.620595i | \(0.213109\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −103.832 | − | 172.593i | −0.120594 | − | 0.200456i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1259.81i | 1.45980i | 0.683553 | + | 0.729901i | \(0.260434\pi\) | ||||
−0.683553 | + | 0.729901i | \(0.739566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 114.967i | 0.132910i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.5328 | − | 23.7829i | 0.0455972 | − | 0.0274313i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 339.985 | + | 196.290i | 0.391237 | + | 0.225881i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −96.7020 | − | 167.493i | −0.111024 | − | 0.192299i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 38.3476 | + | 1064.99i | 0.0439263 | + | 1.21991i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −80.0721 | − | 138.689i | −0.0915110 | − | 0.158502i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 543.869 | + | 314.003i | 0.620147 | + | 0.358042i | 0.776926 | − | 0.629591i | \(-0.216778\pi\) |
−0.156779 | + | 0.987634i | \(0.550111\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1719.40 | − | 30.9458i | 1.95609 | − | 0.0352057i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1307.34 | −1.48393 | −0.741963 | − | 0.670441i | \(-0.766105\pi\) | ||||
−0.741963 | + | 0.670441i | \(0.766105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1325.22 | 1.50081 | 0.750405 | − | 0.660978i | \(-0.229858\pi\) | ||||
0.750405 | + | 0.660978i | \(0.229858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 215.972 | − | 390.123i | 0.244036 | − | 0.440817i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 664.056 | + | 383.393i | 0.748654 | + | 0.432236i | 0.825207 | − | 0.564830i | \(-0.191058\pi\) |
−0.0765534 | + | 0.997065i | \(0.524392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 259.224 | − | 149.663i | 0.291590 | − | 0.168350i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −258.727 | + | 533.405i | −0.290378 | + | 0.598659i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 87.2209 | + | 142.965i | 0.0976718 | + | 0.160095i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −345.798 | − | 199.646i | −0.386366 | − | 0.223069i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −154.302 | + | 278.724i | −0.172020 | + | 0.310730i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −94.4354 | −0.105045 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 435.183i | − | 0.483000i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.66960 | − | 259.451i | −0.00517121 | − | 0.287322i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 353.502 | + | 204.094i | 0.390610 | + | 0.225519i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 501.802 | − | 289.716i | 0.553255 | − | 0.319422i | −0.197179 | − | 0.980368i | \(-0.563178\pi\) |
0.750434 | + | 0.660946i | \(0.229845\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1152.85 | + | 41.5114i | −1.26826 | + | 0.0456671i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1480.53 | − | 854.782i | 1.62517 | − | 0.938290i | 0.639658 | − | 0.768659i | \(-0.279076\pi\) |
0.985508 | − | 0.169631i | \(-0.0542575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −384.090 | + | 665.263i | −0.420690 | + | 0.728656i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 68.5366 | − | 41.2316i | 0.0749034 | − | 0.0450619i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 64.4865 | 0.0703233 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −517.810 | −0.563449 | −0.281725 | − | 0.959495i | \(-0.590906\pi\) | ||||
−0.281725 | + | 0.959495i | \(0.590906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 548.227 | + | 911.283i | 0.595252 | + | 0.989449i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 428.308 | − | 741.851i | 0.464039 | − | 0.803738i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −174.272 | + | 100.616i | −0.188402 | + | 0.108774i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.49583 | + | 5.94799i | −0.0102436 | + | 0.00641639i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 355.354 | + | 615.492i | 0.382513 | + | 0.662531i | 0.991421 | − | 0.130709i | \(-0.0417255\pi\) |
−0.608908 | + | 0.793241i | \(0.708392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −429.845 | + | 787.961i | −0.461703 | + | 0.846360i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0393 | − | 1335.66i | −0.0257656 | − | 1.43158i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 351.774 | 0.376229 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −742.921 | −0.792872 | −0.396436 | − | 0.918062i | \(-0.629753\pi\) | ||||
−0.396436 | + | 0.918062i | \(0.629753\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −431.718 | − | 238.999i | −0.459763 | − | 0.254525i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1363.82 | − | 787.404i | −1.44933 | − | 0.836773i | −0.450892 | − | 0.892578i | \(-0.648894\pi\) |
−0.998442 | + | 0.0558053i | \(0.982227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −251.399 | + | 145.145i | −0.266595 | + | 0.153919i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.61453 | − | 103.895i | −0.00594130 | − | 0.109941i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 525.446 | + | 910.099i | 0.554853 | + | 0.961034i | 0.997915 | + | 0.0645429i | \(0.0205589\pi\) |
−0.443062 | + | 0.896491i | \(0.646108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −525.725 | − | 303.527i | −0.553978 | − | 0.319839i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −431.242 | + | 778.978i | −0.453462 | + | 0.819115i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 485.193i | − | 0.509122i | −0.967057 | − | 0.254561i | \(-0.918069\pi\) | ||
0.967057 | − | 0.254561i | \(-0.0819310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 923.576 | 0.967095 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 63.5340 | − | 1.14348i | 0.0663887 | − | 0.00119486i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.0502 | − | 26.0677i | 0.0156936 | − | 0.0271822i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.8965 | + | 89.8874i | 0.0540026 | + | 0.0935353i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1057.35 | − | 560.734i | −1.09798 | − | 0.582278i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −386.148 | + | 222.943i | −0.400154 | + | 0.231029i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 400.703 | − | 694.038i | 0.414377 | − | 0.717723i | −0.580985 | − | 0.813914i | \(-0.697333\pi\) |
0.995363 | + | 0.0961912i | \(0.0306660\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −795.930 | + | 505.462i | −0.821393 | + | 0.521633i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1333.51i | − | 1.37333i | −0.726972 | − | 0.686667i | \(-0.759073\pi\) | ||
0.726972 | − | 0.686667i | \(-0.240927\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 218.398 | 0.224458 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −474.208 | − | 788.245i | −0.486367 | − | 0.808457i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −663.222 | − | 382.911i | −0.678835 | − | 0.391926i | 0.120581 | − | 0.992704i | \(-0.461524\pi\) |
−0.799416 | + | 0.600778i | \(0.794858\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −369.727 | + | 213.462i | −0.377658 | + | 0.218041i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 740.946 | + | 392.937i | 0.755297 | + | 0.400547i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 999.494 | − | 577.058i | 1.01678 | − | 0.587038i | 0.103610 | − | 0.994618i | \(-0.466961\pi\) |
0.913169 | + | 0.407580i | \(0.133627\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 361.413 | − | 625.986i | 0.366917 | − | 0.635519i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.631082 | − | 35.0640i | −0.000639394 | − | 0.0355259i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −373.991 | −0.378150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 486.461i | 0.490879i | 0.969412 | + | 0.245440i | \(0.0789323\pi\) | ||||
−0.969412 | + | 0.245440i | \(0.921068\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −492.873 | + | 890.305i | −0.496347 | + | 0.896581i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 178.690 | − | 309.501i | 0.179588 | − | 0.311056i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 533.786 | + | 924.544i | 0.535392 | + | 0.927326i | 0.999144 | + | 0.0413613i | \(0.0131695\pi\) |
−0.463752 | + | 0.885965i | \(0.653497\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −327.666 | + | 17.7073i | −0.327994 | + | 0.0177250i |
(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 | 684.3.t.a.265.9 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.t.a.37.13 | 80 | |||
9.2 | odd | 6 | 2052.3.t.a.721.14 | 80 | |||
9.7 | even | 3 | inner | 684.3.t.a.493.32 | yes | 80 | |
19.18 | odd | 2 | inner | 684.3.t.a.265.32 | yes | 80 | |
57.56 | even | 2 | 2052.3.t.a.37.14 | 80 | |||
171.56 | even | 6 | 2052.3.t.a.721.13 | 80 | |||
171.151 | odd | 6 | inner | 684.3.t.a.493.9 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.t.a.265.9 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.t.a.265.32 | yes | 80 | 19.18 | odd | 2 | inner | |
684.3.t.a.493.9 | yes | 80 | 171.151 | odd | 6 | inner | |
684.3.t.a.493.32 | yes | 80 | 9.7 | even | 3 | inner | |
2052.3.t.a.37.13 | 80 | 3.2 | odd | 2 | |||
2052.3.t.a.37.14 | 80 | 57.56 | even | 2 | |||
2052.3.t.a.721.13 | 80 | 171.56 | even | 6 | |||
2052.3.t.a.721.14 | 80 | 9.2 | odd | 6 |