Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.6 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.5 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.28216 | −1.64108 | −0.820540 | − | 0.571589i | \(-0.806327\pi\) | ||||
−0.820540 | + | 0.571589i | \(0.806327\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 6.77257 | 1.69314 | ||||||||
\(5\) | − | 2.78765i | − | 0.557530i | −0.960359 | − | 0.278765i | \(-0.910075\pi\) | ||
0.960359 | − | 0.278765i | \(-0.0899251\pi\) | |||||||
\(6\) | −5.68487 | −0.947478 | ||||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | −9.10001 | −1.13750 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 9.14952i | 0.914952i | ||||||||
\(11\) | − | 7.34623i | − | 0.667839i | −0.942602 | − | 0.333919i | \(-0.891629\pi\) | ||
0.942602 | − | 0.333919i | \(-0.108371\pi\) | |||||||
\(12\) | 11.7304 | 0.977536 | ||||||||
\(13\) | 3.74384 | 0.287987 | 0.143994 | − | 0.989579i | \(-0.454006\pi\) | ||||
0.143994 | + | 0.989579i | \(0.454006\pi\) | |||||||
\(14\) | 8.68378i | 0.620270i | ||||||||
\(15\) | − | 4.82836i | − | 0.321890i | ||||||
\(16\) | 2.77741 | 0.173588 | ||||||||
\(17\) | − | 19.4029i | − | 1.14135i | −0.821177 | − | 0.570673i | \(-0.806682\pi\) | ||
0.821177 | − | 0.570673i | \(-0.193318\pi\) | |||||||
\(18\) | −9.84648 | −0.547027 | ||||||||
\(19\) | 7.40141i | 0.389548i | 0.980848 | + | 0.194774i | \(0.0623973\pi\) | ||||
−0.980848 | + | 0.194774i | \(0.937603\pi\) | |||||||
\(20\) | − | 18.8796i | − | 0.943978i | ||||||
\(21\) | − | 4.58258i | − | 0.218218i | ||||||
\(22\) | 24.1115i | 1.09598i | ||||||||
\(23\) | −19.1329 | − | 12.7646i | −0.831863 | − | 0.554981i | ||||
\(24\) | −15.7617 | −0.656737 | ||||||||
\(25\) | 17.2290 | 0.689160 | ||||||||
\(26\) | −12.2879 | −0.472610 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | − | 17.9185i | − | 0.639948i | ||||||
\(29\) | −40.6316 | −1.40109 | −0.700544 | − | 0.713609i | \(-0.747059\pi\) | ||||
−0.700544 | + | 0.713609i | \(0.747059\pi\) | |||||||
\(30\) | 15.8474i | 0.528248i | ||||||||
\(31\) | 8.80682 | 0.284091 | 0.142045 | − | 0.989860i | \(-0.454632\pi\) | ||||
0.142045 | + | 0.989860i | \(0.454632\pi\) | |||||||
\(32\) | 27.2841 | 0.852629 | ||||||||
\(33\) | − | 12.7240i | − | 0.385577i | ||||||
\(34\) | 63.6834i | 1.87304i | ||||||||
\(35\) | −7.37544 | −0.210727 | ||||||||
\(36\) | 20.3177 | 0.564381 | ||||||||
\(37\) | 22.4788i | 0.607535i | 0.952746 | + | 0.303767i | \(0.0982446\pi\) | ||||
−0.952746 | + | 0.303767i | \(0.901755\pi\) | |||||||
\(38\) | − | 24.2926i | − | 0.639279i | ||||||
\(39\) | 6.48451 | 0.166270 | ||||||||
\(40\) | 25.3677i | 0.634192i | ||||||||
\(41\) | −0.856967 | −0.0209016 | −0.0104508 | − | 0.999945i | \(-0.503327\pi\) | ||||
−0.0104508 | + | 0.999945i | \(0.503327\pi\) | |||||||
\(42\) | 15.0407i | 0.358113i | ||||||||
\(43\) | 40.9123i | 0.951448i | 0.879595 | + | 0.475724i | \(0.157814\pi\) | ||||
−0.879595 | + | 0.475724i | \(0.842186\pi\) | |||||||
\(44\) | − | 49.7528i | − | 1.13075i | ||||||
\(45\) | − | 8.36296i | − | 0.185843i | ||||||
\(46\) | 62.7971 | + | 41.8953i | 1.36515 | + | 0.910768i | ||||
\(47\) | 16.9402 | 0.360429 | 0.180214 | − | 0.983627i | \(-0.442321\pi\) | ||||
0.180214 | + | 0.983627i | \(0.442321\pi\) | |||||||
\(48\) | 4.81062 | 0.100221 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | −56.5483 | −1.13097 | ||||||||
\(51\) | − | 33.6068i | − | 0.658957i | ||||||
\(52\) | 25.3554 | 0.487604 | ||||||||
\(53\) | − | 34.8928i | − | 0.658354i | −0.944268 | − | 0.329177i | \(-0.893229\pi\) | ||
0.944268 | − | 0.329177i | \(-0.106771\pi\) | |||||||
\(54\) | −17.0546 | −0.315826 | ||||||||
\(55\) | −20.4787 | −0.372341 | ||||||||
\(56\) | 24.0764i | 0.429935i | ||||||||
\(57\) | 12.8196i | 0.224905i | ||||||||
\(58\) | 133.359 | 2.29930 | ||||||||
\(59\) | −27.4908 | −0.465945 | −0.232973 | − | 0.972483i | \(-0.574845\pi\) | ||||
−0.232973 | + | 0.972483i | \(0.574845\pi\) | |||||||
\(60\) | − | 32.7004i | − | 0.545006i | ||||||
\(61\) | − | 94.2762i | − | 1.54551i | −0.634704 | − | 0.772756i | \(-0.718878\pi\) | ||
0.634704 | − | 0.772756i | \(-0.281122\pi\) | |||||||
\(62\) | −28.9054 | −0.466216 | ||||||||
\(63\) | − | 7.93725i | − | 0.125988i | ||||||
\(64\) | −100.661 | −1.57282 | ||||||||
\(65\) | − | 10.4365i | − | 0.160562i | ||||||
\(66\) | 41.7623i | 0.632762i | ||||||||
\(67\) | − | 61.9795i | − | 0.925067i | −0.886602 | − | 0.462533i | \(-0.846941\pi\) | ||
0.886602 | − | 0.462533i | \(-0.153059\pi\) | |||||||
\(68\) | − | 131.407i | − | 1.93246i | ||||||
\(69\) | −33.1391 | − | 22.1089i | −0.480276 | − | 0.320418i | ||||
\(70\) | 24.2074 | 0.345819 | ||||||||
\(71\) | −77.3081 | −1.08885 | −0.544423 | − | 0.838811i | \(-0.683251\pi\) | ||||
−0.544423 | + | 0.838811i | \(0.683251\pi\) | |||||||
\(72\) | −27.3000 | −0.379167 | ||||||||
\(73\) | −132.608 | −1.81654 | −0.908272 | − | 0.418379i | \(-0.862598\pi\) | ||||
−0.908272 | + | 0.418379i | \(0.862598\pi\) | |||||||
\(74\) | − | 73.7790i | − | 0.997013i | ||||||
\(75\) | 29.8415 | 0.397887 | ||||||||
\(76\) | 50.1265i | 0.659560i | ||||||||
\(77\) | −19.4363 | −0.252419 | ||||||||
\(78\) | −21.2832 | −0.272862 | ||||||||
\(79\) | − | 124.048i | − | 1.57023i | −0.619351 | − | 0.785114i | \(-0.712604\pi\) | ||
0.619351 | − | 0.785114i | \(-0.287396\pi\) | |||||||
\(80\) | − | 7.74246i | − | 0.0967808i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 2.81270 | 0.0343012 | ||||||||
\(83\) | − | 59.1946i | − | 0.713188i | −0.934259 | − | 0.356594i | \(-0.883938\pi\) | ||
0.934259 | − | 0.356594i | \(-0.116062\pi\) | |||||||
\(84\) | − | 31.0358i | − | 0.369474i | ||||||
\(85\) | −54.0885 | −0.636335 | ||||||||
\(86\) | − | 134.281i | − | 1.56140i | ||||||
\(87\) | −70.3760 | −0.808919 | ||||||||
\(88\) | 66.8508i | 0.759668i | ||||||||
\(89\) | − | 66.6559i | − | 0.748943i | −0.927238 | − | 0.374471i | \(-0.877824\pi\) | ||
0.927238 | − | 0.374471i | \(-0.122176\pi\) | |||||||
\(90\) | 27.4486i | 0.304984i | ||||||||
\(91\) | − | 9.90526i | − | 0.108849i | ||||||
\(92\) | −129.579 | − | 86.4489i | −1.40846 | − | 0.939662i | ||||
\(93\) | 15.2539 | 0.164020 | ||||||||
\(94\) | −55.6003 | −0.591492 | ||||||||
\(95\) | 20.6325 | 0.217185 | ||||||||
\(96\) | 47.2575 | 0.492266 | ||||||||
\(97\) | − | 7.24707i | − | 0.0747120i | −0.999302 | − | 0.0373560i | \(-0.988106\pi\) | ||
0.999302 | − | 0.0373560i | \(-0.0118936\pi\) | |||||||
\(98\) | 22.9751 | 0.234440 | ||||||||
\(99\) | − | 22.0387i | − | 0.222613i | ||||||
\(100\) | 116.685 | 1.16685 | ||||||||
\(101\) | 20.6541 | 0.204496 | 0.102248 | − | 0.994759i | \(-0.467396\pi\) | ||||
0.102248 | + | 0.994759i | \(0.467396\pi\) | |||||||
\(102\) | 110.303i | 1.08140i | ||||||||
\(103\) | 117.447i | 1.14026i | 0.821553 | + | 0.570132i | \(0.193108\pi\) | ||||
−0.821553 | + | 0.570132i | \(0.806892\pi\) | |||||||
\(104\) | −34.0689 | −0.327586 | ||||||||
\(105\) | −12.7746 | −0.121663 | ||||||||
\(106\) | 114.524i | 1.08041i | ||||||||
\(107\) | − | 85.9178i | − | 0.802970i | −0.915866 | − | 0.401485i | \(-0.868494\pi\) | ||
0.915866 | − | 0.401485i | \(-0.131506\pi\) | |||||||
\(108\) | 35.1913 | 0.325845 | ||||||||
\(109\) | − | 191.485i | − | 1.75674i | −0.477977 | − | 0.878372i | \(-0.658630\pi\) | ||
0.477977 | − | 0.878372i | \(-0.341370\pi\) | |||||||
\(110\) | 67.2144 | 0.611040 | ||||||||
\(111\) | 38.9344i | 0.350760i | ||||||||
\(112\) | − | 7.34834i | − | 0.0656102i | ||||||
\(113\) | 133.624i | 1.18251i | 0.806483 | + | 0.591257i | \(0.201368\pi\) | ||||
−0.806483 | + | 0.591257i | \(0.798632\pi\) | |||||||
\(114\) | − | 42.0760i | − | 0.369088i | ||||||
\(115\) | −35.5832 | + | 53.3357i | −0.309419 | + | 0.463789i | ||||
\(116\) | −275.180 | −2.37224 | ||||||||
\(117\) | 11.2315 | 0.0959958 | ||||||||
\(118\) | 90.2291 | 0.764654 | ||||||||
\(119\) | −51.3352 | −0.431388 | ||||||||
\(120\) | 43.9381i | 0.366151i | ||||||||
\(121\) | 67.0329 | 0.553991 | ||||||||
\(122\) | 309.429i | 2.53631i | ||||||||
\(123\) | −1.48431 | −0.0120676 | ||||||||
\(124\) | 59.6448 | 0.481006 | ||||||||
\(125\) | − | 117.720i | − | 0.941758i | ||||||
\(126\) | 26.0513i | 0.206757i | ||||||||
\(127\) | −5.96059 | −0.0469337 | −0.0234669 | − | 0.999725i | \(-0.507470\pi\) | ||||
−0.0234669 | + | 0.999725i | \(0.507470\pi\) | |||||||
\(128\) | 221.247 | 1.72849 | ||||||||
\(129\) | 70.8621i | 0.549319i | ||||||||
\(130\) | 34.2543i | 0.263495i | ||||||||
\(131\) | 67.0342 | 0.511711 | 0.255856 | − | 0.966715i | \(-0.417643\pi\) | ||||
0.255856 | + | 0.966715i | \(0.417643\pi\) | |||||||
\(132\) | − | 86.1744i | − | 0.652837i | ||||||
\(133\) | 19.5823 | 0.147235 | ||||||||
\(134\) | 203.427i | 1.51811i | ||||||||
\(135\) | − | 14.4851i | − | 0.107297i | ||||||
\(136\) | 176.567i | 1.29828i | ||||||||
\(137\) | − | 2.58095i | − | 0.0188391i | −0.999956 | − | 0.00941953i | \(-0.997002\pi\) | ||
0.999956 | − | 0.00941953i | \(-0.00299837\pi\) | |||||||
\(138\) | 108.768 | + | 72.5648i | 0.788172 | + | 0.525832i | ||||
\(139\) | 22.8055 | 0.164069 | 0.0820343 | − | 0.996630i | \(-0.473858\pi\) | ||||
0.0820343 | + | 0.996630i | \(0.473858\pi\) | |||||||
\(140\) | −49.9506 | −0.356790 | ||||||||
\(141\) | 29.3412 | 0.208094 | ||||||||
\(142\) | 253.738 | 1.78688 | ||||||||
\(143\) | − | 27.5031i | − | 0.192329i | ||||||
\(144\) | 8.33224 | 0.0578628 | ||||||||
\(145\) | 113.267i | 0.781150i | ||||||||
\(146\) | 435.240 | 2.98109 | ||||||||
\(147\) | −12.1244 | −0.0824786 | ||||||||
\(148\) | 152.239i | 1.02864i | ||||||||
\(149\) | 131.419i | 0.882006i | 0.897506 | + | 0.441003i | \(0.145377\pi\) | ||||
−0.897506 | + | 0.441003i | \(0.854623\pi\) | |||||||
\(150\) | −97.9445 | −0.652964 | ||||||||
\(151\) | −99.7634 | −0.660685 | −0.330342 | − | 0.943861i | \(-0.607164\pi\) | ||||
−0.330342 | + | 0.943861i | \(0.607164\pi\) | |||||||
\(152\) | − | 67.3529i | − | 0.443111i | ||||||
\(153\) | − | 58.2087i | − | 0.380449i | ||||||
\(154\) | 63.7930 | 0.414240 | ||||||||
\(155\) | − | 24.5503i | − | 0.158389i | ||||||
\(156\) | 43.9168 | 0.281518 | ||||||||
\(157\) | 31.6630i | 0.201675i | 0.994903 | + | 0.100838i | \(0.0321523\pi\) | ||||
−0.994903 | + | 0.100838i | \(0.967848\pi\) | |||||||
\(158\) | 407.145i | 2.57687i | ||||||||
\(159\) | − | 60.4361i | − | 0.380101i | ||||||
\(160\) | − | 76.0587i | − | 0.475367i | ||||||
\(161\) | −33.7719 | + | 50.6208i | −0.209763 | + | 0.314415i | ||||
\(162\) | −29.5394 | −0.182342 | ||||||||
\(163\) | 105.168 | 0.645201 | 0.322601 | − | 0.946535i | \(-0.395443\pi\) | ||||
0.322601 | + | 0.946535i | \(0.395443\pi\) | |||||||
\(164\) | −5.80387 | −0.0353894 | ||||||||
\(165\) | −35.4702 | −0.214971 | ||||||||
\(166\) | 194.286i | 1.17040i | ||||||||
\(167\) | 69.6119 | 0.416837 | 0.208419 | − | 0.978040i | \(-0.433168\pi\) | ||||
0.208419 | + | 0.978040i | \(0.433168\pi\) | |||||||
\(168\) | 41.7015i | 0.248223i | ||||||||
\(169\) | −154.984 | −0.917063 | ||||||||
\(170\) | 177.527 | 1.04428 | ||||||||
\(171\) | 22.2042i | 0.129849i | ||||||||
\(172\) | 277.081i | 1.61094i | ||||||||
\(173\) | 93.3923 | 0.539840 | 0.269920 | − | 0.962883i | \(-0.413003\pi\) | ||||
0.269920 | + | 0.962883i | \(0.413003\pi\) | |||||||
\(174\) | 230.985 | 1.32750 | ||||||||
\(175\) | − | 45.5836i | − | 0.260478i | ||||||
\(176\) | − | 20.4035i | − | 0.115929i | ||||||
\(177\) | −47.6154 | −0.269014 | ||||||||
\(178\) | 218.775i | 1.22907i | ||||||||
\(179\) | −18.6887 | −0.104406 | −0.0522032 | − | 0.998636i | \(-0.516624\pi\) | ||||
−0.0522032 | + | 0.998636i | \(0.516624\pi\) | |||||||
\(180\) | − | 56.6387i | − | 0.314659i | ||||||
\(181\) | 141.499i | 0.781761i | 0.920441 | + | 0.390881i | \(0.127829\pi\) | ||||
−0.920441 | + | 0.390881i | \(0.872171\pi\) | |||||||
\(182\) | 32.5106i | 0.178630i | ||||||||
\(183\) | − | 163.291i | − | 0.892301i | ||||||
\(184\) | 174.109 | + | 116.158i | 0.946246 | + | 0.631292i | ||||
\(185\) | 62.6630 | 0.338719 | ||||||||
\(186\) | −50.0656 | −0.269170 | ||||||||
\(187\) | −142.538 | −0.762235 | ||||||||
\(188\) | 114.728 | 0.610257 | ||||||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | −67.7193 | −0.356417 | ||||||||
\(191\) | 289.469i | 1.51554i | 0.652519 | + | 0.757772i | \(0.273712\pi\) | ||||
−0.652519 | + | 0.757772i | \(0.726288\pi\) | |||||||
\(192\) | −174.349 | −0.908069 | ||||||||
\(193\) | 157.578 | 0.816465 | 0.408233 | − | 0.912878i | \(-0.366145\pi\) | ||||
0.408233 | + | 0.912878i | \(0.366145\pi\) | |||||||
\(194\) | 23.7860i | 0.122608i | ||||||||
\(195\) | − | 18.0766i | − | 0.0927004i | ||||||
\(196\) | −47.4080 | −0.241877 | ||||||||
\(197\) | −7.97780 | −0.0404964 | −0.0202482 | − | 0.999795i | \(-0.506446\pi\) | ||||
−0.0202482 | + | 0.999795i | \(0.506446\pi\) | |||||||
\(198\) | 72.3345i | 0.365326i | ||||||||
\(199\) | − | 299.579i | − | 1.50542i | −0.658350 | − | 0.752712i | \(-0.728745\pi\) | ||
0.658350 | − | 0.752712i | \(-0.271255\pi\) | |||||||
\(200\) | −156.784 | −0.783920 | ||||||||
\(201\) | − | 107.352i | − | 0.534088i | ||||||
\(202\) | −67.7900 | −0.335594 | ||||||||
\(203\) | 107.501i | 0.529562i | ||||||||
\(204\) | − | 227.604i | − | 1.11571i | ||||||
\(205\) | 2.38893i | 0.0116533i | ||||||||
\(206\) | − | 385.480i | − | 1.87126i | ||||||
\(207\) | −57.3986 | − | 38.2937i | −0.277288 | − | 0.184994i | ||||
\(208\) | 10.3982 | 0.0499912 | ||||||||
\(209\) | 54.3724 | 0.260155 | ||||||||
\(210\) | 41.9284 | 0.199659 | ||||||||
\(211\) | 141.461 | 0.670433 | 0.335216 | − | 0.942141i | \(-0.391191\pi\) | ||||
0.335216 | + | 0.942141i | \(0.391191\pi\) | |||||||
\(212\) | − | 236.314i | − | 1.11469i | ||||||
\(213\) | −133.902 | −0.628646 | ||||||||
\(214\) | 281.996i | 1.31774i | ||||||||
\(215\) | 114.049 | 0.530461 | ||||||||
\(216\) | −47.2850 | −0.218912 | ||||||||
\(217\) | − | 23.3006i | − | 0.107376i | ||||||
\(218\) | 628.485i | 2.88296i | ||||||||
\(219\) | −229.683 | −1.04878 | ||||||||
\(220\) | −138.694 | −0.630425 | ||||||||
\(221\) | − | 72.6412i | − | 0.328693i | ||||||
\(222\) | − | 127.789i | − | 0.575626i | ||||||
\(223\) | 142.812 | 0.640412 | 0.320206 | − | 0.947348i | \(-0.396248\pi\) | ||||
0.320206 | + | 0.947348i | \(0.396248\pi\) | |||||||
\(224\) | − | 72.1870i | − | 0.322264i | ||||||
\(225\) | 51.6870 | 0.229720 | ||||||||
\(226\) | − | 438.576i | − | 1.94060i | ||||||
\(227\) | 220.920i | 0.973218i | 0.873620 | + | 0.486609i | \(0.161766\pi\) | ||||
−0.873620 | + | 0.486609i | \(0.838234\pi\) | |||||||
\(228\) | 86.8217i | 0.380797i | ||||||||
\(229\) | − | 342.678i | − | 1.49641i | −0.663468 | − | 0.748205i | \(-0.730916\pi\) | ||
0.663468 | − | 0.748205i | \(-0.269084\pi\) | |||||||
\(230\) | 116.790 | − | 175.056i | 0.507781 | − | 0.761115i | ||||
\(231\) | −33.6646 | −0.145734 | ||||||||
\(232\) | 369.748 | 1.59374 | ||||||||
\(233\) | −57.8140 | −0.248129 | −0.124064 | − | 0.992274i | \(-0.539593\pi\) | ||||
−0.124064 | + | 0.992274i | \(0.539593\pi\) | |||||||
\(234\) | −36.8636 | −0.157537 | ||||||||
\(235\) | − | 47.2233i | − | 0.200950i | ||||||
\(236\) | −186.183 | −0.788912 | ||||||||
\(237\) | − | 214.857i | − | 0.906572i | ||||||
\(238\) | 168.490 | 0.707943 | ||||||||
\(239\) | −369.300 | −1.54519 | −0.772595 | − | 0.634899i | \(-0.781042\pi\) | ||||
−0.772595 | + | 0.634899i | \(0.781042\pi\) | |||||||
\(240\) | − | 13.4103i | − | 0.0558764i | ||||||
\(241\) | − | 37.1026i | − | 0.153953i | −0.997033 | − | 0.0769763i | \(-0.975473\pi\) | ||
0.997033 | − | 0.0769763i | \(-0.0245266\pi\) | |||||||
\(242\) | −220.013 | −0.909144 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | − | 638.492i | − | 2.61677i | ||||||
\(245\) | 19.5136i | 0.0796472i | ||||||||
\(246\) | 4.87174 | 0.0198038 | ||||||||
\(247\) | 27.7096i | 0.112185i | ||||||||
\(248\) | −80.1421 | −0.323154 | ||||||||
\(249\) | − | 102.528i | − | 0.411759i | ||||||
\(250\) | 386.375i | 1.54550i | ||||||||
\(251\) | 196.331i | 0.782196i | 0.920349 | + | 0.391098i | \(0.127905\pi\) | ||||
−0.920349 | + | 0.391098i | \(0.872095\pi\) | |||||||
\(252\) | − | 53.7556i | − | 0.213316i | ||||||
\(253\) | −93.7714 | + | 140.554i | −0.370638 | + | 0.555551i | ||||
\(254\) | 19.5636 | 0.0770220 | ||||||||
\(255\) | −93.6841 | −0.367388 | ||||||||
\(256\) | −323.527 | −1.26378 | ||||||||
\(257\) | 319.634 | 1.24371 | 0.621856 | − | 0.783131i | \(-0.286379\pi\) | ||||
0.621856 | + | 0.783131i | \(0.286379\pi\) | |||||||
\(258\) | − | 232.581i | − | 0.901476i | ||||||
\(259\) | 59.4733 | 0.229627 | ||||||||
\(260\) | − | 70.6820i | − | 0.271854i | ||||||
\(261\) | −121.895 | −0.467030 | ||||||||
\(262\) | −220.017 | −0.839759 | ||||||||
\(263\) | 208.330i | 0.792131i | 0.918222 | + | 0.396065i | \(0.129625\pi\) | ||||
−0.918222 | + | 0.396065i | \(0.870375\pi\) | |||||||
\(264\) | 115.789i | 0.438594i | ||||||||
\(265\) | −97.2690 | −0.367053 | ||||||||
\(266\) | −64.2722 | −0.241625 | ||||||||
\(267\) | − | 115.451i | − | 0.432402i | ||||||
\(268\) | − | 419.760i | − | 1.56627i | ||||||
\(269\) | −17.4800 | −0.0649815 | −0.0324908 | − | 0.999472i | \(-0.510344\pi\) | ||||
−0.0324908 | + | 0.999472i | \(0.510344\pi\) | |||||||
\(270\) | 47.5423i | 0.176083i | ||||||||
\(271\) | −76.9658 | −0.284007 | −0.142003 | − | 0.989866i | \(-0.545354\pi\) | ||||
−0.142003 | + | 0.989866i | \(0.545354\pi\) | |||||||
\(272\) | − | 53.8898i | − | 0.198124i | ||||||
\(273\) | − | 17.1564i | − | 0.0628440i | ||||||
\(274\) | 8.47109i | 0.0309164i | ||||||||
\(275\) | − | 126.568i | − | 0.460248i | ||||||
\(276\) | −224.437 | − | 149.734i | −0.813176 | − | 0.542514i | ||||
\(277\) | 326.944 | 1.18031 | 0.590153 | − | 0.807292i | \(-0.299068\pi\) | ||||
0.590153 | + | 0.807292i | \(0.299068\pi\) | |||||||
\(278\) | −74.8514 | −0.269250 | ||||||||
\(279\) | 26.4204 | 0.0946969 | ||||||||
\(280\) | 67.1165 | 0.239702 | ||||||||
\(281\) | − | 195.830i | − | 0.696903i | −0.937327 | − | 0.348452i | \(-0.886708\pi\) | ||
0.937327 | − | 0.348452i | \(-0.113292\pi\) | |||||||
\(282\) | −96.3025 | −0.341498 | ||||||||
\(283\) | 359.211i | 1.26930i | 0.772802 | + | 0.634648i | \(0.218855\pi\) | ||||
−0.772802 | + | 0.634648i | \(0.781145\pi\) | |||||||
\(284\) | −523.575 | −1.84357 | ||||||||
\(285\) | 35.7366 | 0.125392 | ||||||||
\(286\) | 90.2694i | 0.315627i | ||||||||
\(287\) | 2.26732i | 0.00790007i | ||||||||
\(288\) | 81.8524 | 0.284210 | ||||||||
\(289\) | −87.4721 | −0.302672 | ||||||||
\(290\) | − | 371.759i | − | 1.28193i | ||||||
\(291\) | − | 12.5523i | − | 0.0431350i | ||||||
\(292\) | −898.095 | −3.07567 | ||||||||
\(293\) | 59.6930i | 0.203730i | 0.994798 | + | 0.101865i | \(0.0324810\pi\) | ||||
−0.994798 | + | 0.101865i | \(0.967519\pi\) | |||||||
\(294\) | 39.7941 | 0.135354 | ||||||||
\(295\) | 76.6347i | 0.259779i | ||||||||
\(296\) | − | 204.557i | − | 0.691072i | ||||||
\(297\) | − | 38.1721i | − | 0.128526i | ||||||
\(298\) | − | 431.338i | − | 1.44744i | ||||||
\(299\) | −71.6303 | − | 47.7884i | −0.239566 | − | 0.159827i | ||||
\(300\) | 202.104 | 0.673679 | ||||||||
\(301\) | 108.244 | 0.359614 | ||||||||
\(302\) | 327.439 | 1.08424 | ||||||||
\(303\) | 35.7739 | 0.118066 | ||||||||
\(304\) | 20.5568i | 0.0676209i | ||||||||
\(305\) | −262.809 | −0.861670 | ||||||||
\(306\) | 191.050i | 0.624347i | ||||||||
\(307\) | 168.152 | 0.547727 | 0.273864 | − | 0.961769i | \(-0.411698\pi\) | ||||
0.273864 | + | 0.961769i | \(0.411698\pi\) | |||||||
\(308\) | −131.634 | −0.427382 | ||||||||
\(309\) | 203.424i | 0.658331i | ||||||||
\(310\) | 80.5781i | 0.259929i | ||||||||
\(311\) | 495.245 | 1.59243 | 0.796214 | − | 0.605015i | \(-0.206833\pi\) | ||||
0.796214 | + | 0.605015i | \(0.206833\pi\) | |||||||
\(312\) | −59.0092 | −0.189132 | ||||||||
\(313\) | 370.674i | 1.18426i | 0.805842 | + | 0.592130i | \(0.201713\pi\) | ||||
−0.805842 | + | 0.592130i | \(0.798287\pi\) | |||||||
\(314\) | − | 103.923i | − | 0.330965i | ||||||
\(315\) | −22.1263 | −0.0702422 | ||||||||
\(316\) | − | 840.124i | − | 2.65862i | ||||||
\(317\) | 275.198 | 0.868131 | 0.434066 | − | 0.900881i | \(-0.357079\pi\) | ||||
0.434066 | + | 0.900881i | \(0.357079\pi\) | |||||||
\(318\) | 198.361i | 0.623776i | ||||||||
\(319\) | 298.489i | 0.935702i | ||||||||
\(320\) | 280.607i | 0.876896i | ||||||||
\(321\) | − | 148.814i | − | 0.463595i | ||||||
\(322\) | 110.845 | − | 166.145i | 0.344238 | − | 0.515980i | ||||
\(323\) | 143.609 | 0.444609 | ||||||||
\(324\) | 60.9531 | 0.188127 | ||||||||
\(325\) | 64.5025 | 0.198469 | ||||||||
\(326\) | −345.177 | −1.05883 | ||||||||
\(327\) | − | 331.662i | − | 1.01426i | ||||||
\(328\) | 7.79841 | 0.0237756 | ||||||||
\(329\) | − | 44.8194i | − | 0.136229i | ||||||
\(330\) | 116.419 | 0.352784 | ||||||||
\(331\) | 83.7782 | 0.253106 | 0.126553 | − | 0.991960i | \(-0.459609\pi\) | ||||
0.126553 | + | 0.991960i | \(0.459609\pi\) | |||||||
\(332\) | − | 400.900i | − | 1.20753i | ||||||
\(333\) | 67.4364i | 0.202512i | ||||||||
\(334\) | −228.477 | −0.684064 | ||||||||
\(335\) | −172.777 | −0.515753 | ||||||||
\(336\) | − | 12.7277i | − | 0.0378801i | ||||||
\(337\) | − | 519.798i | − | 1.54243i | −0.636576 | − | 0.771214i | \(-0.719650\pi\) | ||
0.636576 | − | 0.771214i | \(-0.280350\pi\) | |||||||
\(338\) | 508.681 | 1.50497 | ||||||||
\(339\) | 231.444i | 0.682725i | ||||||||
\(340\) | −366.318 | −1.07741 | ||||||||
\(341\) | − | 64.6969i | − | 0.189727i | ||||||
\(342\) | − | 72.8778i | − | 0.213093i | ||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 372.302i | − | 1.08227i | ||||||
\(345\) | −61.6318 | + | 92.3802i | −0.178643 | + | 0.267769i | ||||
\(346\) | −306.528 | −0.885920 | ||||||||
\(347\) | 47.0383 | 0.135557 | 0.0677785 | − | 0.997700i | \(-0.478409\pi\) | ||||
0.0677785 | + | 0.997700i | \(0.478409\pi\) | |||||||
\(348\) | −476.626 | −1.36961 | ||||||||
\(349\) | −149.404 | −0.428092 | −0.214046 | − | 0.976824i | \(-0.568664\pi\) | ||||
−0.214046 | + | 0.976824i | \(0.568664\pi\) | |||||||
\(350\) | 149.613i | 0.427465i | ||||||||
\(351\) | 19.4535 | 0.0554232 | ||||||||
\(352\) | − | 200.435i | − | 0.569419i | ||||||
\(353\) | 311.382 | 0.882102 | 0.441051 | − | 0.897482i | \(-0.354606\pi\) | ||||
0.441051 | + | 0.897482i | \(0.354606\pi\) | |||||||
\(354\) | 156.281 | 0.441473 | ||||||||
\(355\) | 215.508i | 0.607065i | ||||||||
\(356\) | − | 451.432i | − | 1.26807i | ||||||
\(357\) | −88.9152 | −0.249062 | ||||||||
\(358\) | 61.3394 | 0.171339 | ||||||||
\(359\) | − | 309.900i | − | 0.863230i | −0.902058 | − | 0.431615i | \(-0.857944\pi\) | ||
0.902058 | − | 0.431615i | \(-0.142056\pi\) | |||||||
\(360\) | 76.1030i | 0.211397i | ||||||||
\(361\) | 306.219 | 0.848253 | ||||||||
\(362\) | − | 464.422i | − | 1.28293i | ||||||
\(363\) | 116.104 | 0.319847 | ||||||||
\(364\) | − | 67.0840i | − | 0.184297i | ||||||
\(365\) | 369.664i | 1.01278i | ||||||||
\(366\) | 535.947i | 1.46434i | ||||||||
\(367\) | 60.4009i | 0.164580i | 0.996608 | + | 0.0822900i | \(0.0262234\pi\) | ||||
−0.996608 | + | 0.0822900i | \(0.973777\pi\) | |||||||
\(368\) | −53.1398 | − | 35.4525i | −0.144402 | − | 0.0963382i | ||||
\(369\) | −2.57090 | −0.00696721 | ||||||||
\(370\) | −205.670 | −0.555865 | ||||||||
\(371\) | −92.3176 | −0.248835 | ||||||||
\(372\) | 103.308 | 0.277709 | ||||||||
\(373\) | 160.463i | 0.430196i | 0.976592 | + | 0.215098i | \(0.0690070\pi\) | ||||
−0.976592 | + | 0.215098i | \(0.930993\pi\) | |||||||
\(374\) | 467.833 | 1.25089 | ||||||||
\(375\) | − | 203.897i | − | 0.543724i | ||||||
\(376\) | −154.156 | −0.409988 | ||||||||
\(377\) | −152.118 | −0.403496 | ||||||||
\(378\) | 45.1222i | 0.119371i | ||||||||
\(379\) | − | 190.016i | − | 0.501362i | −0.968070 | − | 0.250681i | \(-0.919345\pi\) | ||
0.968070 | − | 0.250681i | \(-0.0806546\pi\) | |||||||
\(380\) | 139.735 | 0.367725 | ||||||||
\(381\) | −10.3240 | −0.0270972 | ||||||||
\(382\) | − | 950.083i | − | 2.48713i | ||||||
\(383\) | 513.529i | 1.34081i | 0.741997 | + | 0.670404i | \(0.233879\pi\) | ||||
−0.741997 | + | 0.670404i | \(0.766121\pi\) | |||||||
\(384\) | 383.212 | 0.997947 | ||||||||
\(385\) | 54.1816i | 0.140731i | ||||||||
\(386\) | −517.195 | −1.33988 | ||||||||
\(387\) | 122.737i | 0.317149i | ||||||||
\(388\) | − | 49.0812i | − | 0.126498i | ||||||
\(389\) | 390.284i | 1.00330i | 0.865070 | + | 0.501651i | \(0.167274\pi\) | ||||
−0.865070 | + | 0.501651i | \(0.832726\pi\) | |||||||
\(390\) | 59.3302i | 0.152129i | ||||||||
\(391\) | −247.669 | + | 371.233i | −0.633425 | + | 0.949444i | ||||
\(392\) | 63.7001 | 0.162500 | ||||||||
\(393\) | 116.107 | 0.295437 | ||||||||
\(394\) | 26.1844 | 0.0664579 | ||||||||
\(395\) | −345.803 | −0.875450 | ||||||||
\(396\) | − | 149.258i | − | 0.376915i | ||||||
\(397\) | −552.158 | −1.39082 | −0.695412 | − | 0.718611i | \(-0.744778\pi\) | ||||
−0.695412 | + | 0.718611i | \(0.744778\pi\) | |||||||
\(398\) | 983.267i | 2.47052i | ||||||||
\(399\) | 33.9175 | 0.0850063 | ||||||||
\(400\) | 47.8520 | 0.119630 | ||||||||
\(401\) | 41.0185i | 0.102291i | 0.998691 | + | 0.0511453i | \(0.0162871\pi\) | ||||
−0.998691 | + | 0.0511453i | \(0.983713\pi\) | |||||||
\(402\) | 352.345i | 0.876480i | ||||||||
\(403\) | 32.9713 | 0.0818146 | ||||||||
\(404\) | 139.881 | 0.346241 | ||||||||
\(405\) | − | 25.0889i | − | 0.0619478i | ||||||
\(406\) | − | 352.836i | − | 0.869053i | ||||||
\(407\) | 165.134 | 0.405735 | ||||||||
\(408\) | 305.822i | 0.749564i | ||||||||
\(409\) | −211.284 | −0.516586 | −0.258293 | − | 0.966067i | \(-0.583160\pi\) | ||||
−0.258293 | + | 0.966067i | \(0.583160\pi\) | |||||||
\(410\) | − | 7.84083i | − | 0.0191240i | ||||||
\(411\) | − | 4.47034i | − | 0.0108767i | ||||||
\(412\) | 795.419i | 1.93063i | ||||||||
\(413\) | 72.7338i | 0.176111i | ||||||||
\(414\) | 188.391 | + | 125.686i | 0.455051 | + | 0.303589i | ||||
\(415\) | −165.014 | −0.397624 | ||||||||
\(416\) | 102.147 | 0.245546 | ||||||||
\(417\) | 39.5004 | 0.0947251 | ||||||||
\(418\) | −178.459 | −0.426935 | ||||||||
\(419\) | − | 48.5428i | − | 0.115854i | −0.998321 | − | 0.0579270i | \(-0.981551\pi\) | ||
0.998321 | − | 0.0579270i | \(-0.0184491\pi\) | |||||||
\(420\) | −86.5170 | −0.205993 | ||||||||
\(421\) | − | 190.130i | − | 0.451616i | −0.974172 | − | 0.225808i | \(-0.927498\pi\) | ||
0.974172 | − | 0.225808i | \(-0.0725022\pi\) | |||||||
\(422\) | −464.299 | −1.10023 | ||||||||
\(423\) | 50.8205 | 0.120143 | ||||||||
\(424\) | 317.525i | 0.748879i | ||||||||
\(425\) | − | 334.292i | − | 0.786570i | ||||||
\(426\) | 439.486 | 1.03166 | ||||||||
\(427\) | −249.431 | −0.584148 | ||||||||
\(428\) | − | 581.884i | − | 1.35954i | ||||||
\(429\) | − | 47.6367i | − | 0.111041i | ||||||
\(430\) | −374.328 | −0.870529 | ||||||||
\(431\) | − | 528.069i | − | 1.22522i | −0.790386 | − | 0.612609i | \(-0.790120\pi\) | ||
0.790386 | − | 0.612609i | \(-0.209880\pi\) | |||||||
\(432\) | 14.4319 | 0.0334071 | ||||||||
\(433\) | − | 570.370i | − | 1.31725i | −0.752471 | − | 0.658625i | \(-0.771138\pi\) | ||
0.752471 | − | 0.658625i | \(-0.228862\pi\) | |||||||
\(434\) | 76.4764i | 0.176213i | ||||||||
\(435\) | 196.184i | 0.450997i | ||||||||
\(436\) | − | 1296.85i | − | 2.97442i | ||||||
\(437\) | 94.4757 | − | 141.610i | 0.216192 | − | 0.324050i | ||||
\(438\) | 753.858 | 1.72114 | ||||||||
\(439\) | 477.624 | 1.08798 | 0.543991 | − | 0.839091i | \(-0.316913\pi\) | ||||
0.543991 | + | 0.839091i | \(0.316913\pi\) | |||||||
\(440\) | 186.357 | 0.423538 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | 238.420i | 0.539412i | ||||||||
\(443\) | 665.292 | 1.50179 | 0.750894 | − | 0.660423i | \(-0.229623\pi\) | ||||
0.750894 | + | 0.660423i | \(0.229623\pi\) | |||||||
\(444\) | 263.686i | 0.593887i | ||||||||
\(445\) | −185.814 | −0.417558 | ||||||||
\(446\) | −468.731 | −1.05097 | ||||||||
\(447\) | 227.624i | 0.509227i | ||||||||
\(448\) | 266.323i | 0.594470i | ||||||||
\(449\) | 576.679 | 1.28436 | 0.642181 | − | 0.766553i | \(-0.278030\pi\) | ||||
0.642181 | + | 0.766553i | \(0.278030\pi\) | |||||||
\(450\) | −169.645 | −0.376989 | ||||||||
\(451\) | 6.29547i | 0.0139589i | ||||||||
\(452\) | 904.978i | 2.00216i | ||||||||
\(453\) | −172.795 | −0.381446 | ||||||||
\(454\) | − | 725.096i | − | 1.59713i | ||||||
\(455\) | −27.6124 | −0.0606866 | ||||||||
\(456\) | − | 116.659i | − | 0.255830i | ||||||
\(457\) | 505.790i | 1.10676i | 0.832928 | + | 0.553381i | \(0.186663\pi\) | ||||
−0.832928 | + | 0.553381i | \(0.813337\pi\) | |||||||
\(458\) | 1124.72i | 2.45573i | ||||||||
\(459\) | − | 100.820i | − | 0.219652i | ||||||
\(460\) | −240.989 | + | 361.220i | −0.523890 | + | 0.785261i | ||||
\(461\) | −723.295 | −1.56897 | −0.784485 | − | 0.620148i | \(-0.787073\pi\) | ||||
−0.784485 | + | 0.620148i | \(0.787073\pi\) | |||||||
\(462\) | 110.493 | 0.239162 | ||||||||
\(463\) | 622.083 | 1.34359 | 0.671796 | − | 0.740737i | \(-0.265523\pi\) | ||||
0.671796 | + | 0.740737i | \(0.265523\pi\) | |||||||
\(464\) | −112.851 | −0.243213 | ||||||||
\(465\) | − | 42.5224i | − | 0.0914461i | ||||||
\(466\) | 189.755 | 0.407199 | ||||||||
\(467\) | 401.686i | 0.860140i | 0.902795 | + | 0.430070i | \(0.141511\pi\) | ||||
−0.902795 | + | 0.430070i | \(0.858489\pi\) | |||||||
\(468\) | 76.0662 | 0.162535 | ||||||||
\(469\) | −163.982 | −0.349642 | ||||||||
\(470\) | 154.994i | 0.329775i | ||||||||
\(471\) | 54.8420i | 0.116437i | ||||||||
\(472\) | 250.166 | 0.530014 | ||||||||
\(473\) | 300.551 | 0.635414 | ||||||||
\(474\) | 705.196i | 1.48776i | ||||||||
\(475\) | 127.519i | 0.268461i | ||||||||
\(476\) | −347.671 | −0.730402 | ||||||||
\(477\) | − | 104.678i | − | 0.219451i | ||||||
\(478\) | 1212.10 | 2.53578 | ||||||||
\(479\) | − | 52.7804i | − | 0.110189i | −0.998481 | − | 0.0550944i | \(-0.982454\pi\) | ||
0.998481 | − | 0.0550944i | \(-0.0175460\pi\) | |||||||
\(480\) | − | 131.738i | − | 0.274453i | ||||||
\(481\) | 84.1569i | 0.174962i | ||||||||
\(482\) | 121.777i | 0.252649i | ||||||||
\(483\) | −58.4946 | + | 87.6777i | −0.121107 | + | 0.181527i | ||||
\(484\) | 453.985 | 0.937986 | ||||||||
\(485\) | −20.2023 | −0.0416542 | ||||||||
\(486\) | −51.1638 | −0.105275 | ||||||||
\(487\) | 629.626 | 1.29287 | 0.646434 | − | 0.762970i | \(-0.276260\pi\) | ||||
0.646434 | + | 0.762970i | \(0.276260\pi\) | |||||||
\(488\) | 857.914i | 1.75802i | ||||||||
\(489\) | 182.156 | 0.372507 | ||||||||
\(490\) | − | 64.0466i | − | 0.130707i | ||||||
\(491\) | 25.7496 | 0.0524432 | 0.0262216 | − | 0.999656i | \(-0.491652\pi\) | ||||
0.0262216 | + | 0.999656i | \(0.491652\pi\) | |||||||
\(492\) | −10.0526 | −0.0204321 | ||||||||
\(493\) | 788.370i | 1.59913i | ||||||||
\(494\) | − | 90.9475i | − | 0.184104i | ||||||
\(495\) | −61.4362 | −0.124114 | ||||||||
\(496\) | 24.4602 | 0.0493148 | ||||||||
\(497\) | 204.538i | 0.411545i | ||||||||
\(498\) | 336.514i | 0.675730i | ||||||||
\(499\) | 262.836 | 0.526725 | 0.263363 | − | 0.964697i | \(-0.415168\pi\) | ||||
0.263363 | + | 0.964697i | \(0.415168\pi\) | |||||||
\(500\) | − | 797.265i | − | 1.59453i | ||||||
\(501\) | 120.571 | 0.240661 | ||||||||
\(502\) | − | 644.390i | − | 1.28365i | ||||||
\(503\) | 757.291i | 1.50555i | 0.658279 | + | 0.752774i | \(0.271285\pi\) | ||||
−0.658279 | + | 0.752774i | \(0.728715\pi\) | |||||||
\(504\) | 72.2291i | 0.143312i | ||||||||
\(505\) | − | 57.5764i | − | 0.114013i | ||||||
\(506\) | 307.773 | − | 461.322i | 0.608246 | − | 0.911703i | ||||
\(507\) | −268.440 | −0.529467 | ||||||||
\(508\) | −40.3685 | −0.0794655 | ||||||||
\(509\) | −460.495 | −0.904706 | −0.452353 | − | 0.891839i | \(-0.649415\pi\) | ||||
−0.452353 | + | 0.891839i | \(0.649415\pi\) | |||||||
\(510\) | 307.486 | 0.602914 | ||||||||
\(511\) | 350.847i | 0.686589i | ||||||||
\(512\) | 176.877 | 0.345463 | ||||||||
\(513\) | 38.4588i | 0.0749685i | ||||||||
\(514\) | −1049.09 | −2.04103 | ||||||||
\(515\) | 327.402 | 0.635732 | ||||||||
\(516\) | 479.919i | 0.930075i | ||||||||
\(517\) | − | 124.446i | − | 0.240708i | ||||||
\(518\) | −195.201 | −0.376835 | ||||||||
\(519\) | 161.760 | 0.311677 | ||||||||
\(520\) | 94.9724i | 0.182639i | ||||||||
\(521\) | 292.391i | 0.561211i | 0.959823 | + | 0.280606i | \(0.0905353\pi\) | ||||
−0.959823 | + | 0.280606i | \(0.909465\pi\) | |||||||
\(522\) | 400.078 | 0.766433 | ||||||||
\(523\) | − | 128.901i | − | 0.246465i | −0.992378 | − | 0.123233i | \(-0.960674\pi\) | ||
0.992378 | − | 0.123233i | \(-0.0393262\pi\) | |||||||
\(524\) | 453.994 | 0.866400 | ||||||||
\(525\) | − | 78.9532i | − | 0.150387i | ||||||
\(526\) | − | 683.773i | − | 1.29995i | ||||||
\(527\) | − | 170.878i | − | 0.324246i | ||||||
\(528\) | − | 35.3399i | − | 0.0669316i | ||||||
\(529\) | 203.132 | + | 488.445i | 0.383992 | + | 0.923336i | ||||
\(530\) | 319.252 | 0.602363 | ||||||||
\(531\) | −82.4723 | −0.155315 | ||||||||
\(532\) | 132.622 | 0.249290 | ||||||||
\(533\) | −3.20834 | −0.00601940 | ||||||||
\(534\) | 378.930i | 0.709607i | ||||||||
\(535\) | −239.509 | −0.447680 | ||||||||
\(536\) | 564.014i | 1.05226i | ||||||||
\(537\) | −32.3698 | −0.0602790 | ||||||||
\(538\) | 57.3722 | 0.106640 | ||||||||
\(539\) | 51.4236i | 0.0954056i | ||||||||
\(540\) | − | 98.1011i | − | 0.181669i | ||||||
\(541\) | −890.548 | −1.64612 | −0.823058 | − | 0.567958i | \(-0.807734\pi\) | ||||
−0.823058 | + | 0.567958i | \(0.807734\pi\) | |||||||
\(542\) | 252.614 | 0.466078 | ||||||||
\(543\) | 245.083i | 0.451350i | ||||||||
\(544\) | − | 529.391i | − | 0.973145i | ||||||
\(545\) | −533.794 | −0.979439 | ||||||||
\(546\) | 56.3101i | 0.103132i | ||||||||
\(547\) | 451.013 | 0.824522 | 0.412261 | − | 0.911066i | \(-0.364739\pi\) | ||||
0.412261 | + | 0.911066i | \(0.364739\pi\) | |||||||
\(548\) | − | 17.4797i | − | 0.0318972i | ||||||
\(549\) | − | 282.829i | − | 0.515170i | ||||||
\(550\) | 415.417i | 0.755303i | ||||||||
\(551\) | − | 300.731i | − | 0.545791i | ||||||
\(552\) | 301.566 | + | 201.191i | 0.546315 | + | 0.364476i | ||||
\(553\) | −328.200 | −0.593490 | ||||||||
\(554\) | −1073.08 | −1.93697 | ||||||||
\(555\) | 108.536 | 0.195560 | ||||||||
\(556\) | 154.452 | 0.277792 | ||||||||
\(557\) | − | 798.237i | − | 1.43310i | −0.697536 | − | 0.716550i | \(-0.745720\pi\) | ||
0.697536 | − | 0.716550i | \(-0.254280\pi\) | |||||||
\(558\) | −86.7161 | −0.155405 | ||||||||
\(559\) | 153.169i | 0.274005i | ||||||||
\(560\) | −20.4846 | −0.0365797 | ||||||||
\(561\) | −246.883 | −0.440077 | ||||||||
\(562\) | 642.745i | 1.14367i | ||||||||
\(563\) | − | 743.196i | − | 1.32006i | −0.751238 | − | 0.660032i | \(-0.770543\pi\) | ||
0.751238 | − | 0.660032i | \(-0.229457\pi\) | |||||||
\(564\) | 198.715 | 0.352332 | ||||||||
\(565\) | 372.498 | 0.659288 | ||||||||
\(566\) | − | 1178.99i | − | 2.08301i | ||||||
\(567\) | − | 23.8118i | − | 0.0419961i | ||||||
\(568\) | 703.505 | 1.23856 | ||||||||
\(569\) | − | 1101.92i | − | 1.93658i | −0.249824 | − | 0.968291i | \(-0.580373\pi\) | ||
0.249824 | − | 0.968291i | \(-0.419627\pi\) | |||||||
\(570\) | −117.293 | −0.205778 | ||||||||
\(571\) | − | 713.916i | − | 1.25029i | −0.780509 | − | 0.625145i | \(-0.785040\pi\) | ||
0.780509 | − | 0.625145i | \(-0.214960\pi\) | |||||||
\(572\) | − | 186.266i | − | 0.325641i | ||||||
\(573\) | 501.375i | 0.875000i | ||||||||
\(574\) | − | 7.44171i | − | 0.0129646i | ||||||
\(575\) | −329.640 | − | 219.921i | −0.573287 | − | 0.382470i | ||||
\(576\) | −301.982 | −0.524274 | ||||||||
\(577\) | −606.046 | −1.05034 | −0.525170 | − | 0.850997i | \(-0.675998\pi\) | ||||
−0.525170 | + | 0.850997i | \(0.675998\pi\) | |||||||
\(578\) | 287.097 | 0.496708 | ||||||||
\(579\) | 272.933 | 0.471386 | ||||||||
\(580\) | 767.107i | 1.32260i | ||||||||
\(581\) | −156.614 | −0.269560 | ||||||||
\(582\) | 41.1986i | 0.0707880i | ||||||||
\(583\) | −256.330 | −0.439675 | ||||||||
\(584\) | 1206.73 | 2.06632 | ||||||||
\(585\) | − | 31.3095i | − | 0.0535206i | ||||||
\(586\) | − | 195.922i | − | 0.334338i | ||||||
\(587\) | −1038.80 | −1.76967 | −0.884835 | − | 0.465905i | \(-0.845729\pi\) | ||||
−0.884835 | + | 0.465905i | \(0.845729\pi\) | |||||||
\(588\) | −82.1130 | −0.139648 | ||||||||
\(589\) | 65.1828i | 0.110667i | ||||||||
\(590\) | − | 251.527i | − | 0.426318i | ||||||
\(591\) | −13.8180 | −0.0233806 | ||||||||
\(592\) | 62.4329i | 0.105461i | ||||||||
\(593\) | −623.644 | −1.05168 | −0.525838 | − | 0.850585i | \(-0.676248\pi\) | ||||
−0.525838 | + | 0.850585i | \(0.676248\pi\) | |||||||
\(594\) | 125.287i | 0.210921i | ||||||||
\(595\) | 143.105i | 0.240512i | ||||||||
\(596\) | 890.044i | 1.49336i | ||||||||
\(597\) | − | 518.887i | − | 0.869157i | ||||||
\(598\) | 235.102 | + | 156.849i | 0.393147 | + | 0.262290i | ||||
\(599\) | 932.541 | 1.55683 | 0.778415 | − | 0.627750i | \(-0.216024\pi\) | ||||
0.778415 | + | 0.627750i | \(0.216024\pi\) | |||||||
\(600\) | −271.558 | −0.452597 | ||||||||
\(601\) | −321.981 | −0.535742 | −0.267871 | − | 0.963455i | \(-0.586320\pi\) | ||||
−0.267871 | + | 0.963455i | \(0.586320\pi\) | |||||||
\(602\) | −355.273 | −0.590154 | ||||||||
\(603\) | − | 185.938i | − | 0.308356i | ||||||
\(604\) | −675.654 | −1.11863 | ||||||||
\(605\) | − | 186.865i | − | 0.308867i | ||||||
\(606\) | −117.416 | −0.193755 | ||||||||
\(607\) | 1116.54 | 1.83944 | 0.919722 | − | 0.392571i | \(-0.128414\pi\) | ||||
0.919722 | + | 0.392571i | \(0.128414\pi\) | |||||||
\(608\) | 201.941i | 0.332140i | ||||||||
\(609\) | 186.197i | 0.305743i | ||||||||
\(610\) | 862.582 | 1.41407 | ||||||||
\(611\) | 63.4212 | 0.103799 | ||||||||
\(612\) | − | 394.222i | − | 0.644154i | ||||||
\(613\) | − | 984.755i | − | 1.60645i | −0.595675 | − | 0.803226i | \(-0.703115\pi\) | ||
0.595675 | − | 0.803226i | \(-0.296885\pi\) | |||||||
\(614\) | −551.903 | −0.898864 | ||||||||
\(615\) | 4.13774i | 0.00672803i | ||||||||
\(616\) | 176.870 | 0.287127 | ||||||||
\(617\) | − | 308.789i | − | 0.500469i | −0.968185 | − | 0.250235i | \(-0.919492\pi\) | ||
0.968185 | − | 0.250235i | \(-0.0805077\pi\) | |||||||
\(618\) | − | 667.671i | − | 1.08037i | ||||||
\(619\) | 889.616i | 1.43718i | 0.695432 | + | 0.718591i | \(0.255213\pi\) | ||||
−0.695432 | + | 0.718591i | \(0.744787\pi\) | |||||||
\(620\) | − | 166.269i | − | 0.268176i | ||||||
\(621\) | −99.4172 | − | 66.3266i | −0.160092 | − | 0.106806i | ||||
\(622\) | −1625.47 | −2.61330 | ||||||||
\(623\) | −176.355 | −0.283074 | ||||||||
\(624\) | 18.0102 | 0.0288625 | ||||||||
\(625\) | 102.563 | 0.164101 | ||||||||
\(626\) | − | 1216.61i | − | 1.94347i | ||||||
\(627\) | 94.1758 | 0.150201 | ||||||||
\(628\) | 214.440i | 0.341465i | ||||||||
\(629\) | 436.153 | 0.693408 | ||||||||
\(630\) | 72.6221 | 0.115273 | ||||||||
\(631\) | − | 55.1014i | − | 0.0873240i | −0.999046 | − | 0.0436620i | \(-0.986098\pi\) | ||
0.999046 | − | 0.0436620i | \(-0.0139025\pi\) | |||||||
\(632\) | 1128.84i | 1.78614i | ||||||||
\(633\) | 245.018 | 0.387075 | ||||||||
\(634\) | −903.242 | −1.42467 | ||||||||
\(635\) | 16.6160i | 0.0261670i | ||||||||
\(636\) | − | 409.307i | − | 0.643565i | ||||||
\(637\) | −26.2068 | −0.0411411 | ||||||||
\(638\) | − | 979.688i | − | 1.53556i | ||||||
\(639\) | −231.924 | −0.362949 | ||||||||
\(640\) | − | 616.761i | − | 0.963689i | ||||||
\(641\) | − | 146.120i | − | 0.227957i | −0.993483 | − | 0.113978i | \(-0.963641\pi\) | ||
0.993483 | − | 0.113978i | \(-0.0363595\pi\) | |||||||
\(642\) | 488.431i | 0.760796i | ||||||||
\(643\) | 1114.71i | 1.73360i | 0.498653 | + | 0.866802i | \(0.333828\pi\) | ||||
−0.498653 | + | 0.866802i | \(0.666172\pi\) | |||||||
\(644\) | −228.722 | + | 342.833i | −0.355159 | + | 0.532349i | ||||
\(645\) | 197.539 | 0.306262 | ||||||||
\(646\) | −471.347 | −0.729639 | ||||||||
\(647\) | −362.955 | −0.560981 | −0.280491 | − | 0.959857i | \(-0.590497\pi\) | ||||
−0.280491 | + | 0.959857i | \(0.590497\pi\) | |||||||
\(648\) | −81.9001 | −0.126389 | ||||||||
\(649\) | 201.954i | 0.311176i | ||||||||
\(650\) | −211.708 | −0.325704 | ||||||||
\(651\) | − | 40.3579i | − | 0.0619937i | ||||||
\(652\) | 712.256 | 1.09242 | ||||||||
\(653\) | −231.202 | −0.354061 | −0.177030 | − | 0.984205i | \(-0.556649\pi\) | ||||
−0.177030 | + | 0.984205i | \(0.556649\pi\) | |||||||
\(654\) | 1088.57i | 1.66448i | ||||||||
\(655\) | − | 186.868i | − | 0.285295i | ||||||
\(656\) | −2.38015 | −0.00362828 | ||||||||
\(657\) | −397.823 | −0.605515 | ||||||||
\(658\) | 147.105i | 0.223563i | ||||||||
\(659\) | 348.022i | 0.528107i | 0.964508 | + | 0.264053i | \(0.0850595\pi\) | ||||
−0.964508 | + | 0.264053i | \(0.914941\pi\) | |||||||
\(660\) | −240.224 | −0.363976 | ||||||||
\(661\) | − | 1125.69i | − | 1.70302i | −0.524340 | − | 0.851509i | \(-0.675688\pi\) | ||
0.524340 | − | 0.851509i | \(-0.324312\pi\) | |||||||
\(662\) | −274.973 | −0.415368 | ||||||||
\(663\) | − | 125.818i | − | 0.189771i | ||||||
\(664\) | 538.672i | 0.811253i | ||||||||
\(665\) | − | 54.5886i | − | 0.0820881i | ||||||
\(666\) | − | 221.337i | − | 0.332338i | ||||||
\(667\) | 777.398 | + | 518.644i | 1.16551 | + | 0.777578i | ||||
\(668\) | 471.451 | 0.705765 | ||||||||
\(669\) | 247.357 | 0.369742 | ||||||||
\(670\) | 567.082 | 0.846392 | ||||||||
\(671\) | −692.574 | −1.03215 | ||||||||
\(672\) | − | 125.032i | − | 0.186059i | ||||||
\(673\) | 971.764 | 1.44393 | 0.721964 | − | 0.691930i | \(-0.243239\pi\) | ||||
0.721964 | + | 0.691930i | \(0.243239\pi\) | |||||||
\(674\) | 1706.06i | 2.53125i | ||||||||
\(675\) | 89.5245 | 0.132629 | ||||||||
\(676\) | −1049.64 | −1.55272 | ||||||||
\(677\) | − | 432.134i | − | 0.638307i | −0.947703 | − | 0.319154i | \(-0.896601\pi\) | ||
0.947703 | − | 0.319154i | \(-0.103399\pi\) | |||||||
\(678\) | − | 759.635i | − | 1.12041i | ||||||
\(679\) | −19.1739 | −0.0282385 | ||||||||
\(680\) | 492.206 | 0.723833 | ||||||||
\(681\) | 382.645i | 0.561888i | ||||||||
\(682\) | 212.345i | 0.311357i | ||||||||
\(683\) | 924.855 | 1.35411 | 0.677054 | − | 0.735934i | \(-0.263257\pi\) | ||||
0.677054 | + | 0.735934i | \(0.263257\pi\) | |||||||
\(684\) | 150.380i | 0.219853i | ||||||||
\(685\) | −7.19479 | −0.0105033 | ||||||||
\(686\) | − | 60.7864i | − | 0.0886100i | ||||||
\(687\) | − | 593.535i | − | 0.863952i | ||||||
\(688\) | 113.630i | 0.165160i | ||||||||
\(689\) | − | 130.633i | − | 0.189598i | ||||||
\(690\) | 202.285 | − | 303.207i | 0.293167 | − | 0.439430i | ||||
\(691\) | 604.638 | 0.875019 | 0.437510 | − | 0.899214i | \(-0.355861\pi\) | ||||
0.437510 | + | 0.899214i | \(0.355861\pi\) | |||||||
\(692\) | 632.506 | 0.914026 | ||||||||
\(693\) | −58.3089 | −0.0841398 | ||||||||
\(694\) | −154.387 | −0.222460 | ||||||||
\(695\) | − | 63.5739i | − | 0.0914733i | ||||||
\(696\) | 640.422 | 0.920147 | ||||||||
\(697\) | 16.6276i | 0.0238560i | ||||||||
\(698\) | 490.368 | 0.702533 | ||||||||
\(699\) | −100.137 | −0.143257 | ||||||||
\(700\) | − | 308.718i | − | 0.441026i | ||||||
\(701\) | − | 711.153i | − | 1.01448i | −0.861804 | − | 0.507242i | \(-0.830665\pi\) | ||
0.861804 | − | 0.507242i | \(-0.169335\pi\) | |||||||
\(702\) | −63.8496 | −0.0909539 | ||||||||
\(703\) | −166.375 | −0.236664 | ||||||||
\(704\) | 739.475i | 1.05039i | ||||||||
\(705\) | − | 81.7931i | − | 0.116019i | ||||||
\(706\) | −1022.01 | −1.44760 | ||||||||
\(707\) | − | 54.6456i | − | 0.0772922i | ||||||
\(708\) | −322.479 | −0.455478 | ||||||||
\(709\) | 331.156i | 0.467075i | 0.972348 | + | 0.233537i | \(0.0750301\pi\) | ||||
−0.972348 | + | 0.233537i | \(0.924970\pi\) | |||||||
\(710\) | − | 707.332i | − | 0.996242i | ||||||
\(711\) | − | 372.144i | − | 0.523409i | ||||||
\(712\) | 606.570i | 0.851924i | ||||||||
\(713\) | −168.499 | − | 112.415i | −0.236325 | − | 0.157665i | ||||
\(714\) | 291.834 | 0.408731 | ||||||||
\(715\) | −76.6690 | −0.107229 | ||||||||
\(716\) | −126.571 | −0.176775 | ||||||||
\(717\) | −639.647 | −0.892116 | ||||||||
\(718\) | 1017.14i | 1.41663i | ||||||||
\(719\) | −576.485 | −0.801787 | −0.400894 | − | 0.916125i | \(-0.631300\pi\) | ||||
−0.400894 | + | 0.916125i | \(0.631300\pi\) | |||||||
\(720\) | − | 23.2274i | − | 0.0322603i | ||||||
\(721\) | 310.736 | 0.430979 | ||||||||
\(722\) | −1005.06 | −1.39205 | ||||||||
\(723\) | − | 64.2636i | − | 0.0888846i | ||||||
\(724\) | 958.310i | 1.32363i | ||||||||
\(725\) | −700.041 | −0.965574 | ||||||||
\(726\) | −381.073 | −0.524894 | ||||||||
\(727\) | 1023.00i | 1.40715i | 0.710621 | + | 0.703575i | \(0.248414\pi\) | ||||
−0.710621 | + | 0.703575i | \(0.751586\pi\) | |||||||
\(728\) | 90.1380i | 0.123816i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 1213.30i | − | 1.66205i | ||||||
\(731\) | 793.816 | 1.08593 | ||||||||
\(732\) | − | 1105.90i | − | 1.51079i | ||||||
\(733\) | − | 1229.83i | − | 1.67780i | −0.544284 | − | 0.838901i | \(-0.683199\pi\) | ||
0.544284 | − | 0.838901i | \(-0.316801\pi\) | |||||||
\(734\) | − | 198.245i | − | 0.270089i | ||||||
\(735\) | 33.7985i | 0.0459843i | ||||||||
\(736\) | −522.023 | − | 348.270i | −0.709271 | − | 0.473193i | ||||
\(737\) | −455.315 | −0.617796 | ||||||||
\(738\) | 8.43810 | 0.0114337 | ||||||||
\(739\) | 293.034 | 0.396527 | 0.198264 | − | 0.980149i | \(-0.436470\pi\) | ||||
0.198264 | + | 0.980149i | \(0.436470\pi\) | |||||||
\(740\) | 424.390 | 0.573500 | ||||||||
\(741\) | 47.9945i | 0.0647699i | ||||||||
\(742\) | 303.001 | 0.408357 | ||||||||
\(743\) | 1145.14i | 1.54124i | 0.637294 | + | 0.770621i | \(0.280054\pi\) | ||||
−0.637294 | + | 0.770621i | \(0.719946\pi\) | |||||||
\(744\) | −138.810 | −0.186573 | ||||||||
\(745\) | 366.350 | 0.491745 | ||||||||
\(746\) | − | 526.665i | − | 0.705985i | ||||||
\(747\) | − | 177.584i | − | 0.237729i | ||||||
\(748\) | −965.349 | −1.29057 | ||||||||
\(749\) | −227.317 | −0.303494 | ||||||||
\(750\) | 669.221i | 0.892295i | ||||||||
\(751\) | 909.316i | 1.21081i | 0.795919 | + | 0.605404i | \(0.206988\pi\) | ||||
−0.795919 | + | 0.605404i | \(0.793012\pi\) | |||||||
\(752\) | 47.0498 | 0.0625662 | ||||||||
\(753\) | 340.056i | 0.451601i | ||||||||
\(754\) | 499.275 | 0.662169 | ||||||||
\(755\) | 278.106i | 0.368352i | ||||||||
\(756\) | − | 93.1074i | − | 0.123158i | ||||||
\(757\) | − | 703.956i | − | 0.929929i | −0.885329 | − | 0.464964i | \(-0.846067\pi\) | ||
0.885329 | − | 0.464964i | \(-0.153933\pi\) | |||||||
\(758\) | 623.664i | 0.822775i | ||||||||
\(759\) | −162.417 | + | 243.447i | −0.213988 | + | 0.320747i | ||||
\(760\) | −187.756 | −0.247048 | ||||||||
\(761\) | 261.889 | 0.344138 | 0.172069 | − | 0.985085i | \(-0.444955\pi\) | ||||
0.172069 | + | 0.985085i | \(0.444955\pi\) | |||||||
\(762\) | 33.8851 | 0.0444687 | ||||||||
\(763\) | −506.622 | −0.663987 | ||||||||
\(764\) | 1960.45i | 2.56603i | ||||||||
\(765\) | −162.266 | −0.212112 | ||||||||
\(766\) | − | 1685.48i | − | 2.20037i | ||||||
\(767\) | −102.921 | −0.134186 | ||||||||
\(768\) | −560.365 | −0.729642 | ||||||||
\(769\) | 438.046i | 0.569631i | 0.958582 | + | 0.284816i | \(0.0919324\pi\) | ||||
−0.958582 | + | 0.284816i | \(0.908068\pi\) | |||||||
\(770\) | − | 177.833i | − | 0.230952i | ||||||
\(771\) | 553.623 | 0.718058 | ||||||||
\(772\) | 1067.21 | 1.38239 | ||||||||
\(773\) | 837.173i | 1.08302i | 0.840695 | + | 0.541509i | \(0.182147\pi\) | ||||
−0.840695 | + | 0.541509i | \(0.817853\pi\) | |||||||
\(774\) | − | 402.842i | − | 0.520467i | ||||||
\(775\) | 151.733 | 0.195784 | ||||||||
\(776\) | 65.9484i | 0.0849850i | ||||||||
\(777\) | 103.011 | 0.132575 | ||||||||
\(778\) | − | 1280.98i | − | 1.64650i | ||||||
\(779\) | − | 6.34276i | − | 0.00814218i | ||||||
\(780\) | − | 122.425i | − | 0.156955i | ||||||
\(781\) | 567.923i | 0.727174i | ||||||||
\(782\) | 812.890 | − | 1218.44i | 1.03950 | − | 1.55811i | ||||
\(783\) | −211.128 | −0.269640 | ||||||||
\(784\) | −19.4419 | −0.0247983 | ||||||||
\(785\) | 88.2656 | 0.112440 | ||||||||
\(786\) | −381.080 | −0.484835 | ||||||||
\(787\) | 1233.03i | 1.56675i | 0.621549 | + | 0.783375i | \(0.286503\pi\) | ||||
−0.621549 | + | 0.783375i | \(0.713497\pi\) | |||||||
\(788\) | −54.0302 | −0.0685662 | ||||||||
\(789\) | 360.839i | 0.457337i | ||||||||
\(790\) | 1134.98 | 1.43668 | ||||||||
\(791\) | 353.536 | 0.446948 | ||||||||
\(792\) | 200.552i | 0.253223i | ||||||||
\(793\) | − | 352.954i | − | 0.445088i | ||||||
\(794\) | 1812.27 | 2.28245 | ||||||||
\(795\) | −168.475 | −0.211918 | ||||||||
\(796\) | − | 2028.92i | − | 2.54890i | ||||||
\(797\) | 324.595i | 0.407271i | 0.979047 | + | 0.203635i | \(0.0652757\pi\) | ||||
−0.979047 | + | 0.203635i | \(0.934724\pi\) | |||||||
\(798\) | −111.323 | −0.139502 | ||||||||
\(799\) | − | 328.688i | − | 0.411374i | ||||||
\(800\) | 470.078 | 0.587598 | ||||||||
\(801\) | − | 199.968i | − | 0.249648i | ||||||
\(802\) | − | 134.629i | − | 0.167867i | ||||||
\(803\) | 974.167i | 1.21316i | ||||||||
\(804\) | − | 727.046i | − | 0.904286i | ||||||
\(805\) | 141.113 | + | 94.1442i | 0.175296 | + | 0.116949i | ||||
\(806\) | −108.217 | −0.134264 | ||||||||
\(807\) | −30.2763 | −0.0375171 | ||||||||
\(808\) | −187.952 | −0.232614 | ||||||||
\(809\) | 821.535 | 1.01549 | 0.507747 | − | 0.861506i | \(-0.330478\pi\) | ||||
0.507747 | + | 0.861506i | \(0.330478\pi\) | |||||||
\(810\) | 82.3457i | 0.101661i | ||||||||
\(811\) | −286.315 | −0.353040 | −0.176520 | − | 0.984297i | \(-0.556484\pi\) | ||||
−0.176520 | + | 0.984297i | \(0.556484\pi\) | |||||||
\(812\) | 728.058i | 0.896623i | ||||||||
\(813\) | −133.309 | −0.163971 | ||||||||
\(814\) | −541.997 | −0.665844 | ||||||||
\(815\) | − | 293.171i | − | 0.359719i | ||||||
\(816\) | − | 93.3399i | − | 0.114387i | ||||||
\(817\) | −302.808 | −0.370634 | ||||||||
\(818\) | 693.467 | 0.847759 | ||||||||
\(819\) | − | 29.7158i | − | 0.0362830i | ||||||
\(820\) | 16.1792i | 0.0197307i | ||||||||
\(821\) | −347.091 | −0.422766 | −0.211383 | − | 0.977403i | \(-0.567797\pi\) | ||||
−0.211383 | + | 0.977403i | \(0.567797\pi\) | |||||||
\(822\) | 14.6724i | 0.0178496i | ||||||||
\(823\) | −627.377 | −0.762305 | −0.381153 | − | 0.924512i | \(-0.624473\pi\) | ||||
−0.381153 | + | 0.924512i | \(0.624473\pi\) | |||||||
\(824\) | − | 1068.77i | − | 1.29705i | ||||||
\(825\) | − | 219.222i | − | 0.265724i | ||||||
\(826\) | − | 238.724i | − | 0.289012i | ||||||
\(827\) | 434.650i | 0.525574i | 0.964854 | + | 0.262787i | \(0.0846417\pi\) | ||||
−0.964854 | + | 0.262787i | \(0.915358\pi\) | |||||||
\(828\) | −388.736 | − | 259.347i | −0.469488 | − | 0.313221i | ||||
\(829\) | −200.868 | −0.242301 | −0.121151 | − | 0.992634i | \(-0.538658\pi\) | ||||
−0.121151 | + | 0.992634i | \(0.538658\pi\) | |||||||
\(830\) | 541.602 | 0.652533 | ||||||||
\(831\) | 566.284 | 0.681449 | ||||||||
\(832\) | −376.856 | −0.452953 | ||||||||
\(833\) | 135.820i | 0.163049i | ||||||||
\(834\) | −129.646 | −0.155451 | ||||||||
\(835\) | − | 194.054i | − | 0.232400i | ||||||
\(836\) | 368.241 | 0.440480 | ||||||||
\(837\) | 45.7616 | 0.0546733 | ||||||||
\(838\) | 159.325i | 0.190126i | ||||||||
\(839\) | − | 1097.49i | − | 1.30809i | −0.756454 | − | 0.654046i | \(-0.773070\pi\) | ||
0.756454 | − | 0.654046i | \(-0.226930\pi\) | |||||||
\(840\) | 116.249 | 0.138392 | ||||||||
\(841\) | 809.925 | 0.963050 | ||||||||
\(842\) | 624.038i | 0.741138i | ||||||||
\(843\) | − | 339.187i | − | 0.402357i | ||||||
\(844\) | 958.057 | 1.13514 | ||||||||
\(845\) | 432.041i | 0.511291i | ||||||||
\(846\) | −166.801 | −0.197164 | ||||||||
\(847\) | − | 177.352i | − | 0.209389i | ||||||
\(848\) | − | 96.9117i | − | 0.114283i | ||||||
\(849\) | 622.171i | 0.732828i | ||||||||
\(850\) | 1097.20i | 1.29082i | ||||||||
\(851\) | 286.932 | − | 430.083i | 0.337170 | − | 0.505386i | ||||
\(852\) | −906.858 | −1.06439 | ||||||||
\(853\) | 424.358 | 0.497488 | 0.248744 | − | 0.968569i | \(-0.419982\pi\) | ||||
0.248744 | + | 0.968569i | \(0.419982\pi\) | |||||||
\(854\) | 818.673 | 0.958634 | ||||||||
\(855\) | 61.8976 | 0.0723949 | ||||||||
\(856\) | 781.853i | 0.913379i | ||||||||
\(857\) | 1606.59 | 1.87467 | 0.937335 | − | 0.348430i | \(-0.113285\pi\) | ||||
0.937335 | + | 0.348430i | \(0.113285\pi\) | |||||||
\(858\) | 156.351i | 0.182228i | ||||||||
\(859\) | 1235.99 | 1.43887 | 0.719436 | − | 0.694559i | \(-0.244400\pi\) | ||||
0.719436 | + | 0.694559i | \(0.244400\pi\) | |||||||
\(860\) | 772.406 | 0.898146 | ||||||||
\(861\) | 3.92712i | 0.00456111i | ||||||||
\(862\) | 1733.21i | 2.01068i | ||||||||
\(863\) | −307.747 | −0.356601 | −0.178300 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178300 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(864\) | 141.773 | 0.164089 | ||||||||
\(865\) | − | 260.345i | − | 0.300977i | ||||||
\(866\) | 1872.04i | 2.16171i | ||||||||
\(867\) | −151.506 | −0.174748 | ||||||||
\(868\) | − | 157.805i | − | 0.181803i | ||||||
\(869\) | −911.285 | −1.04866 | ||||||||
\(870\) | − | 643.906i | − | 0.740122i | ||||||
\(871\) | − | 232.041i | − | 0.266408i | ||||||
\(872\) | 1742.52i | 1.99830i | ||||||||
\(873\) | − | 21.7412i | − | 0.0249040i | ||||||
\(874\) | −310.084 | + | 464.787i | −0.354788 | + | 0.531792i | ||||
\(875\) | −311.457 | −0.355951 | ||||||||
\(876\) | −1555.55 | −1.77574 | ||||||||
\(877\) | −104.777 | −0.119472 | −0.0597362 | − | 0.998214i | \(-0.519026\pi\) | ||||
−0.0597362 | + | 0.998214i | \(0.519026\pi\) | |||||||
\(878\) | −1567.64 | −1.78546 | ||||||||
\(879\) | 103.391i | 0.117624i | ||||||||
\(880\) | −56.8779 | −0.0646340 | ||||||||
\(881\) | 1184.55i | 1.34455i | 0.740301 | + | 0.672276i | \(0.234683\pi\) | ||||
−0.740301 | + | 0.672276i | \(0.765317\pi\) | |||||||
\(882\) | 68.9253 | 0.0781466 | ||||||||
\(883\) | −898.241 | −1.01726 | −0.508630 | − | 0.860985i | \(-0.669848\pi\) | ||||
−0.508630 | + | 0.860985i | \(0.669848\pi\) | |||||||
\(884\) | − | 491.968i | − | 0.556525i | ||||||
\(885\) | 132.735i | 0.149983i | ||||||||
\(886\) | −2183.59 | −2.46455 | ||||||||
\(887\) | −1301.00 | −1.46675 | −0.733373 | − | 0.679827i | \(-0.762055\pi\) | ||||
−0.733373 | + | 0.679827i | \(0.762055\pi\) | |||||||
\(888\) | − | 354.303i | − | 0.398990i | ||||||
\(889\) | 15.7702i | 0.0177393i | ||||||||
\(890\) | 609.870 | 0.685247 | ||||||||
\(891\) | − | 66.1160i | − | 0.0742043i | ||||||
\(892\) | 967.203 | 1.08431 | ||||||||
\(893\) | 125.381i | 0.140404i | ||||||||
\(894\) | − | 747.099i | − | 0.835681i | ||||||
\(895\) | 52.0977i | 0.0582097i | ||||||||
\(896\) | − | 585.365i | − | 0.653310i | ||||||
\(897\) | −124.067 | − | 82.7720i | −0.138314 | − | 0.0922764i | ||||
\(898\) | −1892.75 | −2.10774 | ||||||||
\(899\) | −357.835 | −0.398037 | ||||||||
\(900\) | 350.054 | 0.388948 | ||||||||
\(901\) | −677.021 | −0.751411 | ||||||||
\(902\) | − | 20.6627i | − | 0.0229077i | ||||||
\(903\) | 187.484 | 0.207623 | ||||||||
\(904\) | − | 1215.98i | − | 1.34511i | ||||||
\(905\) | 394.449 | 0.435856 | ||||||||
\(906\) | 567.141 | 0.625984 | ||||||||
\(907\) | 886.325i | 0.977205i | 0.872506 | + | 0.488603i | \(0.162493\pi\) | ||||
−0.872506 | + | 0.488603i | \(0.837507\pi\) | |||||||
\(908\) | 1496.20i | 1.64780i | ||||||||
\(909\) | 61.9622 | 0.0681653 | ||||||||
\(910\) | 90.6283 | 0.0995916 | ||||||||
\(911\) | 1148.22i | 1.26039i | 0.776437 | + | 0.630195i | \(0.217025\pi\) | ||||
−0.776437 | + | 0.630195i | \(0.782975\pi\) | |||||||
\(912\) | 35.6054i | 0.0390410i | ||||||||
\(913\) | −434.857 | −0.476295 | ||||||||
\(914\) | − | 1660.08i | − | 1.81628i | ||||||
\(915\) | −455.199 | −0.497485 | ||||||||
\(916\) | − | 2320.81i | − | 2.53363i | ||||||
\(917\) | − | 177.356i | − | 0.193409i | ||||||
\(918\) | 330.909i | 0.360467i | ||||||||
\(919\) | 180.919i | 0.196865i | 0.995144 | + | 0.0984324i | \(0.0313828\pi\) | ||||
−0.995144 | + | 0.0984324i | \(0.968617\pi\) | |||||||
\(920\) | 323.807 | − | 485.356i | 0.351964 | − | 0.527561i | ||||
\(921\) | 291.248 | 0.316231 | ||||||||
\(922\) | 2373.97 | 2.57480 | ||||||||
\(923\) | −289.429 | −0.313574 | ||||||||
\(924\) | −227.996 | −0.246749 | ||||||||
\(925\) | 387.287i | 0.418688i | ||||||||
\(926\) | −2041.77 | −2.20494 | ||||||||
\(927\) | 352.341i | 0.380088i | ||||||||
\(928\) | −1108.60 | −1.19461 | ||||||||
\(929\) | 1319.40 | 1.42024 | 0.710118 | − | 0.704083i | \(-0.248642\pi\) | ||||
0.710118 | + | 0.704083i | \(0.248642\pi\) | |||||||
\(930\) | 139.565i | 0.150070i | ||||||||
\(931\) | − | 51.8098i | − | 0.0556497i | ||||||
\(932\) | −391.549 | −0.420117 | ||||||||
\(933\) | 857.790 | 0.919389 | ||||||||
\(934\) | − | 1318.40i | − | 1.41156i | ||||||
\(935\) | 397.347i | 0.424970i | ||||||||
\(936\) | −102.207 | −0.109195 | ||||||||
\(937\) | − | 539.214i | − | 0.575469i | −0.957710 | − | 0.287734i | \(-0.907098\pi\) | ||
0.957710 | − | 0.287734i | \(-0.0929020\pi\) | |||||||
\(938\) | 538.216 | 0.573791 | ||||||||
\(939\) | 642.026i | 0.683733i | ||||||||
\(940\) | − | 319.823i | − | 0.340237i | ||||||
\(941\) | − | 1615.46i | − | 1.71674i | −0.513028 | − | 0.858372i | \(-0.671476\pi\) | ||
0.513028 | − | 0.858372i | \(-0.328524\pi\) | |||||||
\(942\) | − | 180.000i | − | 0.191083i | ||||||
\(943\) | 16.3962 | + | 10.9388i | 0.0173873 | + | 0.0116000i | ||||
\(944\) | −76.3532 | −0.0808827 | ||||||||
\(945\) | −38.3239 | −0.0405544 | ||||||||
\(946\) | −986.456 | −1.04276 | ||||||||
\(947\) | 678.516 | 0.716490 | 0.358245 | − | 0.933628i | \(-0.383375\pi\) | ||||
0.358245 | + | 0.933628i | \(0.383375\pi\) | |||||||
\(948\) | − | 1455.14i | − | 1.53495i | ||||||
\(949\) | −496.462 | −0.523142 | ||||||||
\(950\) | − | 418.537i | − | 0.440565i | ||||||
\(951\) | 476.656 | 0.501216 | ||||||||
\(952\) | 467.151 | 0.490705 | ||||||||
\(953\) | − | 613.791i | − | 0.644062i | −0.946729 | − | 0.322031i | \(-0.895634\pi\) | ||
0.946729 | − | 0.322031i | \(-0.104366\pi\) | |||||||
\(954\) | 343.571i | 0.360137i | ||||||||
\(955\) | 806.939 | 0.844962 | ||||||||
\(956\) | −2501.11 | −2.61623 | ||||||||
\(957\) | 516.998i | 0.540228i | ||||||||
\(958\) | 173.234i | 0.180829i | ||||||||
\(959\) | −6.82855 | −0.00712049 | ||||||||
\(960\) | 486.025i | 0.506276i | ||||||||
\(961\) | −883.440 | −0.919292 | ||||||||
\(962\) | − | 276.216i | − | 0.287127i | ||||||
\(963\) | − | 257.753i | − | 0.267657i | ||||||
\(964\) | − | 251.280i | − | 0.260664i | ||||||
\(965\) | − | 439.272i | − | 0.455204i | ||||||
\(966\) | 191.988 | − | 287.772i | 0.198746 | − | 0.297901i | ||||
\(967\) | 1383.87 | 1.43110 | 0.715549 | − | 0.698562i | \(-0.246176\pi\) | ||||
0.715549 | + | 0.698562i | \(0.246176\pi\) | |||||||
\(968\) | −610.001 | −0.630166 | ||||||||
\(969\) | 248.738 | 0.256695 | ||||||||
\(970\) | 66.3072 | 0.0683579 | ||||||||
\(971\) | 1031.26i | 1.06206i | 0.847353 | + | 0.531030i | \(0.178195\pi\) | ||||
−0.847353 | + | 0.531030i | \(0.821805\pi\) | |||||||
\(972\) | 105.574 | 0.108615 | ||||||||
\(973\) | − | 60.3378i | − | 0.0620121i | ||||||
\(974\) | −2066.53 | −2.12170 | ||||||||
\(975\) | 111.722 | 0.114586 | ||||||||
\(976\) | − | 261.844i | − | 0.268283i | ||||||
\(977\) | − | 991.160i | − | 1.01449i | −0.861801 | − | 0.507247i | \(-0.830663\pi\) | ||
0.861801 | − | 0.507247i | \(-0.169337\pi\) | |||||||
\(978\) | −597.865 | −0.611314 | ||||||||
\(979\) | −489.670 | −0.500173 | ||||||||
\(980\) | 132.157i | 0.134854i | ||||||||
\(981\) | − | 574.455i | − | 0.585582i | ||||||
\(982\) | −84.5143 | −0.0860634 | ||||||||
\(983\) | − | 1914.93i | − | 1.94804i | −0.226453 | − | 0.974022i | \(-0.572713\pi\) | ||
0.226453 | − | 0.974022i | \(-0.427287\pi\) | |||||||
\(984\) | 13.5072 | 0.0137269 | ||||||||
\(985\) | 22.2393i | 0.0225780i | ||||||||
\(986\) | − | 2587.56i | − | 2.62430i | ||||||
\(987\) | − | 77.6295i | − | 0.0786520i | ||||||
\(988\) | 187.666i | 0.189945i | ||||||||
\(989\) | 522.227 | − | 782.768i | 0.528035 | − | 0.791475i | ||||
\(990\) | 201.643 | 0.203680 | ||||||||
\(991\) | −51.8628 | −0.0523338 | −0.0261669 | − | 0.999658i | \(-0.508330\pi\) | ||||
−0.0261669 | + | 0.999658i | \(0.508330\pi\) | |||||||
\(992\) | 240.286 | 0.242224 | ||||||||
\(993\) | 145.108 | 0.146131 | ||||||||
\(994\) | − | 671.326i | − | 0.675379i | ||||||
\(995\) | −835.123 | −0.839320 | ||||||||
\(996\) | − | 694.379i | − | 0.697167i | ||||||
\(997\) | −625.045 | −0.626926 | −0.313463 | − | 0.949600i | \(-0.601489\pi\) | ||||
−0.313463 | + | 0.949600i | \(0.601489\pi\) | |||||||
\(998\) | −862.669 | −0.864398 | ||||||||
\(999\) | 116.803i | 0.116920i |
(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 | 483.3.f.a.22.6 | yes | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.5 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.5 | ✓ | 48 | 23.22 | odd | 2 | inner | |
483.3.f.a.22.6 | yes | 48 | 1.1 | even | 1 | trivial |