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 | 22.8 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.23657 | −1.61829 | −0.809143 | − | 0.587612i | \(-0.800068\pi\) | ||||
−0.809143 | + | 0.587612i | \(0.800068\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 6.47539 | 1.61885 | ||||||||
\(5\) | − | 4.61855i | − | 0.923711i | −0.886955 | − | 0.461855i | \(-0.847184\pi\) | ||
0.886955 | − | 0.461855i | \(-0.152816\pi\) | |||||||
\(6\) | 5.60591 | 0.934318 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | −8.01179 | −1.00147 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 14.9483i | 1.49483i | ||||||||
\(11\) | 2.93058i | 0.266416i | 0.991088 | + | 0.133208i | \(0.0425279\pi\) | ||||
−0.991088 | + | 0.133208i | \(0.957472\pi\) | |||||||
\(12\) | −11.2157 | −0.934643 | ||||||||
\(13\) | −15.4536 | −1.18874 | −0.594368 | − | 0.804193i | \(-0.702598\pi\) | ||||
−0.594368 | + | 0.804193i | \(0.702598\pi\) | |||||||
\(14\) | − | 8.56316i | − | 0.611654i | ||||||
\(15\) | 7.99957i | 0.533305i | ||||||||
\(16\) | 0.0291511 | 0.00182195 | ||||||||
\(17\) | − | 24.9051i | − | 1.46500i | −0.680764 | − | 0.732502i | \(-0.738352\pi\) | ||
0.680764 | − | 0.732502i | \(-0.261648\pi\) | |||||||
\(18\) | −9.70971 | −0.539429 | ||||||||
\(19\) | 15.1966i | 0.799824i | 0.916554 | + | 0.399912i | \(0.130959\pi\) | ||||
−0.916554 | + | 0.399912i | \(0.869041\pi\) | |||||||
\(20\) | − | 29.9070i | − | 1.49535i | ||||||
\(21\) | − | 4.58258i | − | 0.218218i | ||||||
\(22\) | − | 9.48503i | − | 0.431138i | ||||||
\(23\) | 19.6279 | − | 11.9895i | 0.853385 | − | 0.521281i | ||||
\(24\) | 13.8768 | 0.578201 | ||||||||
\(25\) | 3.66895 | 0.146758 | ||||||||
\(26\) | 50.0166 | 1.92372 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 17.1323i | 0.611867i | ||||||||
\(29\) | −2.82436 | −0.0973916 | −0.0486958 | − | 0.998814i | \(-0.515506\pi\) | ||||
−0.0486958 | + | 0.998814i | \(0.515506\pi\) | |||||||
\(30\) | − | 25.8912i | − | 0.863039i | ||||||
\(31\) | −9.30833 | −0.300269 | −0.150134 | − | 0.988666i | \(-0.547971\pi\) | ||||
−0.150134 | + | 0.988666i | \(0.547971\pi\) | |||||||
\(32\) | 31.9528 | 0.998525 | ||||||||
\(33\) | − | 5.07591i | − | 0.153815i | ||||||
\(34\) | 80.6071i | 2.37080i | ||||||||
\(35\) | 12.2195 | 0.349130 | ||||||||
\(36\) | 19.4262 | 0.539616 | ||||||||
\(37\) | − | 30.8753i | − | 0.834468i | −0.908799 | − | 0.417234i | \(-0.863000\pi\) | ||
0.908799 | − | 0.417234i | \(-0.137000\pi\) | |||||||
\(38\) | − | 49.1850i | − | 1.29434i | ||||||
\(39\) | 26.7664 | 0.686317 | ||||||||
\(40\) | 37.0029i | 0.925072i | ||||||||
\(41\) | −74.7145 | −1.82231 | −0.911153 | − | 0.412068i | \(-0.864807\pi\) | ||||
−0.911153 | + | 0.412068i | \(0.864807\pi\) | |||||||
\(42\) | 14.8318i | 0.353139i | ||||||||
\(43\) | − | 2.66427i | − | 0.0619597i | −0.999520 | − | 0.0309798i | \(-0.990137\pi\) | ||
0.999520 | − | 0.0309798i | \(-0.00986276\pi\) | |||||||
\(44\) | 18.9766i | 0.431287i | ||||||||
\(45\) | − | 13.8557i | − | 0.307904i | ||||||
\(46\) | −63.5270 | + | 38.8047i | −1.38102 | + | 0.843581i | ||||
\(47\) | 53.7831 | 1.14432 | 0.572161 | − | 0.820141i | \(-0.306105\pi\) | ||||
0.572161 | + | 0.820141i | \(0.306105\pi\) | |||||||
\(48\) | −0.0504912 | −0.00105190 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | −11.8748 | −0.237496 | ||||||||
\(51\) | 43.1369i | 0.845821i | ||||||||
\(52\) | −100.068 | −1.92438 | ||||||||
\(53\) | 1.59067i | 0.0300127i | 0.999887 | + | 0.0150063i | \(0.00477684\pi\) | ||||
−0.999887 | + | 0.0150063i | \(0.995223\pi\) | |||||||
\(54\) | 16.8177 | 0.311439 | ||||||||
\(55\) | 13.5350 | 0.246092 | ||||||||
\(56\) | − | 21.1972i | − | 0.378521i | ||||||
\(57\) | − | 26.3214i | − | 0.461778i | ||||||
\(58\) | 9.14123 | 0.157607 | ||||||||
\(59\) | −94.3907 | −1.59984 | −0.799921 | − | 0.600105i | \(-0.795125\pi\) | ||||
−0.799921 | + | 0.600105i | \(0.795125\pi\) | |||||||
\(60\) | 51.8004i | 0.863340i | ||||||||
\(61\) | 115.051i | 1.88609i | 0.332668 | + | 0.943044i | \(0.392051\pi\) | ||||
−0.332668 | + | 0.943044i | \(0.607949\pi\) | |||||||
\(62\) | 30.1271 | 0.485920 | ||||||||
\(63\) | 7.93725i | 0.125988i | ||||||||
\(64\) | −103.534 | −1.61772 | ||||||||
\(65\) | 71.3732i | 1.09805i | ||||||||
\(66\) | 16.4285i | 0.248917i | ||||||||
\(67\) | 112.901i | 1.68509i | 0.538629 | + | 0.842543i | \(0.318942\pi\) | ||||
−0.538629 | + | 0.842543i | \(0.681058\pi\) | |||||||
\(68\) | − | 161.270i | − | 2.37162i | ||||||
\(69\) | −33.9965 | + | 20.7663i | −0.492702 | + | 0.300962i | ||||
\(70\) | −39.5494 | −0.564992 | ||||||||
\(71\) | −15.5639 | −0.219210 | −0.109605 | − | 0.993975i | \(-0.534959\pi\) | ||||
−0.109605 | + | 0.993975i | \(0.534959\pi\) | |||||||
\(72\) | −24.0354 | −0.333825 | ||||||||
\(73\) | −65.7091 | −0.900125 | −0.450062 | − | 0.892997i | \(-0.648598\pi\) | ||||
−0.450062 | + | 0.892997i | \(0.648598\pi\) | |||||||
\(74\) | 99.9301i | 1.35041i | ||||||||
\(75\) | −6.35481 | −0.0847308 | ||||||||
\(76\) | 98.4043i | 1.29479i | ||||||||
\(77\) | −7.75358 | −0.100696 | ||||||||
\(78\) | −86.6313 | −1.11066 | ||||||||
\(79\) | − | 5.83968i | − | 0.0739200i | −0.999317 | − | 0.0369600i | \(-0.988233\pi\) | ||
0.999317 | − | 0.0369600i | \(-0.0117674\pi\) | |||||||
\(80\) | − | 0.134636i | − | 0.00168295i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 241.819 | 2.94901 | ||||||||
\(83\) | 54.9299i | 0.661805i | 0.943665 | + | 0.330903i | \(0.107353\pi\) | ||||
−0.943665 | + | 0.330903i | \(0.892647\pi\) | |||||||
\(84\) | − | 29.6740i | − | 0.353262i | ||||||
\(85\) | −115.025 | −1.35324 | ||||||||
\(86\) | 8.62308i | 0.100268i | ||||||||
\(87\) | 4.89193 | 0.0562291 | ||||||||
\(88\) | − | 23.4792i | − | 0.266809i | ||||||
\(89\) | 172.575i | 1.93904i | 0.245013 | + | 0.969520i | \(0.421208\pi\) | ||||
−0.245013 | + | 0.969520i | \(0.578792\pi\) | |||||||
\(90\) | 44.8448i | 0.498276i | ||||||||
\(91\) | − | 40.8863i | − | 0.449300i | ||||||
\(92\) | 127.098 | − | 77.6364i | 1.38150 | − | 0.843874i | ||||
\(93\) | 16.1225 | 0.173360 | ||||||||
\(94\) | −174.073 | −1.85184 | ||||||||
\(95\) | 70.1866 | 0.738806 | ||||||||
\(96\) | −55.3439 | −0.576499 | ||||||||
\(97\) | 1.81335i | 0.0186943i | 0.999956 | + | 0.00934717i | \(0.00297534\pi\) | ||||
−0.999956 | + | 0.00934717i | \(0.997025\pi\) | |||||||
\(98\) | 22.6560 | 0.231184 | ||||||||
\(99\) | 8.79173i | 0.0888054i | ||||||||
\(100\) | 23.7579 | 0.237579 | ||||||||
\(101\) | −33.3132 | −0.329834 | −0.164917 | − | 0.986307i | \(-0.552736\pi\) | ||||
−0.164917 | + | 0.986307i | \(0.552736\pi\) | |||||||
\(102\) | − | 139.616i | − | 1.36878i | ||||||
\(103\) | 112.394i | 1.09120i | 0.838045 | + | 0.545601i | \(0.183699\pi\) | ||||
−0.838045 | + | 0.545601i | \(0.816301\pi\) | |||||||
\(104\) | 123.811 | 1.19049 | ||||||||
\(105\) | −21.1649 | −0.201570 | ||||||||
\(106\) | − | 5.14832i | − | 0.0485691i | ||||||
\(107\) | − | 33.4623i | − | 0.312731i | −0.987699 | − | 0.156366i | \(-0.950022\pi\) | ||
0.987699 | − | 0.156366i | \(-0.0499778\pi\) | |||||||
\(108\) | −33.6471 | −0.311548 | ||||||||
\(109\) | − | 37.1568i | − | 0.340888i | −0.985367 | − | 0.170444i | \(-0.945480\pi\) | ||
0.985367 | − | 0.170444i | \(-0.0545202\pi\) | |||||||
\(110\) | −43.8071 | −0.398246 | ||||||||
\(111\) | 53.4776i | 0.481780i | ||||||||
\(112\) | 0.0771266i | 0.000688631i | ||||||||
\(113\) | 88.0058i | 0.778812i | 0.921066 | + | 0.389406i | \(0.127320\pi\) | ||||
−0.921066 | + | 0.389406i | \(0.872680\pi\) | |||||||
\(114\) | 85.1910i | 0.747289i | ||||||||
\(115\) | −55.3740 | − | 90.6524i | −0.481513 | − | 0.788281i | ||||
\(116\) | −18.2888 | −0.157662 | ||||||||
\(117\) | −46.3607 | −0.396246 | ||||||||
\(118\) | 305.502 | 2.58900 | ||||||||
\(119\) | 65.8927 | 0.553720 | ||||||||
\(120\) | − | 64.0909i | − | 0.534091i | ||||||
\(121\) | 112.412 | 0.929022 | ||||||||
\(122\) | − | 372.372i | − | 3.05223i | ||||||
\(123\) | 129.409 | 1.05211 | ||||||||
\(124\) | −60.2751 | −0.486089 | ||||||||
\(125\) | − | 132.409i | − | 1.05927i | ||||||
\(126\) | − | 25.6895i | − | 0.203885i | ||||||
\(127\) | −55.0491 | −0.433457 | −0.216729 | − | 0.976232i | \(-0.569539\pi\) | ||||
−0.216729 | + | 0.976232i | \(0.569539\pi\) | |||||||
\(128\) | 207.284 | 1.61941 | ||||||||
\(129\) | 4.61464i | 0.0357724i | ||||||||
\(130\) | − | 231.004i | − | 1.77696i | ||||||
\(131\) | −153.904 | −1.17484 | −0.587418 | − | 0.809284i | \(-0.699856\pi\) | ||||
−0.587418 | + | 0.809284i | \(0.699856\pi\) | |||||||
\(132\) | − | 32.8685i | − | 0.249004i | ||||||
\(133\) | −40.2066 | −0.302305 | ||||||||
\(134\) | − | 365.411i | − | 2.72695i | ||||||
\(135\) | 23.9987i | 0.177768i | ||||||||
\(136\) | 199.534i | 1.46716i | ||||||||
\(137\) | − | 159.358i | − | 1.16319i | −0.813477 | − | 0.581597i | \(-0.802428\pi\) | ||
0.813477 | − | 0.581597i | \(-0.197572\pi\) | |||||||
\(138\) | 110.032 | − | 67.2118i | 0.797333 | − | 0.487042i | ||||
\(139\) | 70.0443 | 0.503916 | 0.251958 | − | 0.967738i | \(-0.418926\pi\) | ||||
0.251958 | + | 0.967738i | \(0.418926\pi\) | |||||||
\(140\) | 79.1264 | 0.565188 | ||||||||
\(141\) | −93.1551 | −0.660674 | ||||||||
\(142\) | 50.3737 | 0.354744 | ||||||||
\(143\) | − | 45.2879i | − | 0.316699i | ||||||
\(144\) | 0.0874534 | 0.000607315 | ||||||||
\(145\) | 13.0444i | 0.0899617i | ||||||||
\(146\) | 212.672 | 1.45666 | ||||||||
\(147\) | 12.1244 | 0.0824786 | ||||||||
\(148\) | − | 199.930i | − | 1.35088i | ||||||
\(149\) | 267.897i | 1.79796i | 0.437985 | + | 0.898982i | \(0.355692\pi\) | ||||
−0.437985 | + | 0.898982i | \(0.644308\pi\) | |||||||
\(150\) | 20.5678 | 0.137119 | ||||||||
\(151\) | −3.63835 | −0.0240950 | −0.0120475 | − | 0.999927i | \(-0.503835\pi\) | ||||
−0.0120475 | + | 0.999927i | \(0.503835\pi\) | |||||||
\(152\) | − | 121.752i | − | 0.801002i | ||||||
\(153\) | − | 74.7153i | − | 0.488335i | ||||||
\(154\) | 25.0950 | 0.162955 | ||||||||
\(155\) | 42.9910i | 0.277361i | ||||||||
\(156\) | 173.323 | 1.11104 | ||||||||
\(157\) | 278.943i | 1.77671i | 0.459158 | + | 0.888354i | \(0.348151\pi\) | ||||
−0.459158 | + | 0.888354i | \(0.651849\pi\) | |||||||
\(158\) | 18.9005i | 0.119624i | ||||||||
\(159\) | − | 2.75512i | − | 0.0173278i | ||||||
\(160\) | − | 147.576i | − | 0.922349i | ||||||
\(161\) | 31.7211 | + | 51.9304i | 0.197026 | + | 0.322549i | ||||
\(162\) | −29.1291 | −0.179810 | ||||||||
\(163\) | 174.779 | 1.07226 | 0.536132 | − | 0.844134i | \(-0.319885\pi\) | ||||
0.536132 | + | 0.844134i | \(0.319885\pi\) | |||||||
\(164\) | −483.806 | −2.95004 | ||||||||
\(165\) | −23.4434 | −0.142081 | ||||||||
\(166\) | − | 177.784i | − | 1.07099i | ||||||
\(167\) | −283.198 | −1.69580 | −0.847898 | − | 0.530159i | \(-0.822132\pi\) | ||||
−0.847898 | + | 0.530159i | \(0.822132\pi\) | |||||||
\(168\) | 36.7146i | 0.218539i | ||||||||
\(169\) | 69.8130 | 0.413095 | ||||||||
\(170\) | 372.288 | 2.18993 | ||||||||
\(171\) | 45.5899i | 0.266608i | ||||||||
\(172\) | − | 17.2522i | − | 0.100303i | ||||||
\(173\) | 31.0358 | 0.179398 | 0.0896990 | − | 0.995969i | \(-0.471410\pi\) | ||||
0.0896990 | + | 0.995969i | \(0.471410\pi\) | |||||||
\(174\) | −15.8331 | −0.0909947 | ||||||||
\(175\) | 9.70713i | 0.0554693i | ||||||||
\(176\) | 0.0854297i | 0.000485396i | ||||||||
\(177\) | 163.489 | 0.923669 | ||||||||
\(178\) | − | 558.550i | − | 3.13792i | ||||||
\(179\) | −33.6434 | −0.187952 | −0.0939759 | − | 0.995574i | \(-0.529958\pi\) | ||||
−0.0939759 | + | 0.995574i | \(0.529958\pi\) | |||||||
\(180\) | − | 89.7209i | − | 0.498449i | ||||||
\(181\) | 45.3731i | 0.250680i | 0.992114 | + | 0.125340i | \(0.0400022\pi\) | ||||
−0.992114 | + | 0.125340i | \(0.959998\pi\) | |||||||
\(182\) | 132.331i | 0.727096i | ||||||||
\(183\) | − | 199.275i | − | 1.08893i | ||||||
\(184\) | −157.254 | + | 96.0570i | −0.854643 | + | 0.522049i | ||||
\(185\) | −142.599 | −0.770807 | ||||||||
\(186\) | −52.1816 | −0.280546 | ||||||||
\(187\) | 72.9863 | 0.390301 | ||||||||
\(188\) | 348.267 | 1.85248 | ||||||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | −227.164 | −1.19560 | ||||||||
\(191\) | − | 48.8754i | − | 0.255892i | −0.991781 | − | 0.127946i | \(-0.959162\pi\) | ||
0.991781 | − | 0.127946i | \(-0.0408385\pi\) | |||||||
\(192\) | 179.326 | 0.933992 | ||||||||
\(193\) | −234.618 | −1.21564 | −0.607818 | − | 0.794076i | \(-0.707955\pi\) | ||||
−0.607818 | + | 0.794076i | \(0.707955\pi\) | |||||||
\(194\) | − | 5.86904i | − | 0.0302528i | ||||||
\(195\) | − | 123.622i | − | 0.633959i | ||||||
\(196\) | −45.3278 | −0.231264 | ||||||||
\(197\) | −141.358 | −0.717554 | −0.358777 | − | 0.933423i | \(-0.616806\pi\) | ||||
−0.358777 | + | 0.933423i | \(0.616806\pi\) | |||||||
\(198\) | − | 28.4551i | − | 0.143713i | ||||||
\(199\) | − | 145.768i | − | 0.732504i | −0.930516 | − | 0.366252i | \(-0.880641\pi\) | ||
0.930516 | − | 0.366252i | \(-0.119359\pi\) | |||||||
\(200\) | −29.3949 | −0.146974 | ||||||||
\(201\) | − | 195.550i | − | 0.972885i | ||||||
\(202\) | 107.821 | 0.533765 | ||||||||
\(203\) | − | 7.47254i | − | 0.0368106i | ||||||
\(204\) | 279.328i | 1.36926i | ||||||||
\(205\) | 345.073i | 1.68328i | ||||||||
\(206\) | − | 363.771i | − | 1.76588i | ||||||
\(207\) | 58.8836 | − | 35.9684i | 0.284462 | − | 0.173760i | ||||
\(208\) | −0.450489 | −0.00216581 | ||||||||
\(209\) | −44.5350 | −0.213086 | ||||||||
\(210\) | 68.5016 | 0.326198 | ||||||||
\(211\) | 80.5589 | 0.381796 | 0.190898 | − | 0.981610i | \(-0.438860\pi\) | ||||
0.190898 | + | 0.981610i | \(0.438860\pi\) | |||||||
\(212\) | 10.3002i | 0.0485860i | ||||||||
\(213\) | 26.9575 | 0.126561 | ||||||||
\(214\) | 108.303i | 0.506089i | ||||||||
\(215\) | −12.3051 | −0.0572328 | ||||||||
\(216\) | 41.6305 | 0.192734 | ||||||||
\(217\) | − | 24.6275i | − | 0.113491i | ||||||
\(218\) | 120.261i | 0.551654i | ||||||||
\(219\) | 113.812 | 0.519687 | ||||||||
\(220\) | 87.6447 | 0.398385 | ||||||||
\(221\) | 384.873i | 1.74150i | ||||||||
\(222\) | − | 173.084i | − | 0.779658i | ||||||
\(223\) | 150.489 | 0.674837 | 0.337419 | − | 0.941355i | \(-0.390446\pi\) | ||||
0.337419 | + | 0.941355i | \(0.390446\pi\) | |||||||
\(224\) | 84.5392i | 0.377407i | ||||||||
\(225\) | 11.0069 | 0.0489193 | ||||||||
\(226\) | − | 284.837i | − | 1.26034i | ||||||
\(227\) | 132.755i | 0.584825i | 0.956292 | + | 0.292412i | \(0.0944580\pi\) | ||||
−0.956292 | + | 0.292412i | \(0.905542\pi\) | |||||||
\(228\) | − | 170.441i | − | 0.747549i | ||||||
\(229\) | − | 12.1580i | − | 0.0530918i | −0.999648 | − | 0.0265459i | \(-0.991549\pi\) | ||
0.999648 | − | 0.0265459i | \(-0.00845082\pi\) | |||||||
\(230\) | 179.222 | + | 293.403i | 0.779225 | + | 1.27566i | ||||
\(231\) | 13.4296 | 0.0581368 | ||||||||
\(232\) | 22.6281 | 0.0975351 | ||||||||
\(233\) | −134.094 | −0.575509 | −0.287755 | − | 0.957704i | \(-0.592909\pi\) | ||||
−0.287755 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(234\) | 150.050 | 0.641238 | ||||||||
\(235\) | − | 248.400i | − | 1.05702i | ||||||
\(236\) | −611.217 | −2.58990 | ||||||||
\(237\) | 10.1146i | 0.0426777i | ||||||||
\(238\) | −213.266 | −0.896077 | ||||||||
\(239\) | −92.0888 | −0.385309 | −0.192654 | − | 0.981267i | \(-0.561710\pi\) | ||||
−0.192654 | + | 0.981267i | \(0.561710\pi\) | |||||||
\(240\) | 0.233197i | 0.000971652i | ||||||||
\(241\) | 223.750i | 0.928422i | 0.885725 | + | 0.464211i | \(0.153662\pi\) | ||||
−0.885725 | + | 0.464211i | \(0.846338\pi\) | |||||||
\(242\) | −363.829 | −1.50342 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 745.003i | 3.05329i | ||||||||
\(245\) | 32.3299i | 0.131959i | ||||||||
\(246\) | −418.843 | −1.70261 | ||||||||
\(247\) | − | 234.843i | − | 0.950780i | ||||||
\(248\) | 74.5763 | 0.300711 | ||||||||
\(249\) | − | 95.1413i | − | 0.382094i | ||||||
\(250\) | 428.552i | 1.71421i | ||||||||
\(251\) | 129.429i | 0.515653i | 0.966191 | + | 0.257827i | \(0.0830063\pi\) | ||||
−0.966191 | + | 0.257827i | \(0.916994\pi\) | |||||||
\(252\) | 51.3968i | 0.203956i | ||||||||
\(253\) | 35.1360 | + | 57.5210i | 0.138878 | + | 0.227356i | ||||
\(254\) | 178.170 | 0.701458 | ||||||||
\(255\) | 199.230 | 0.781294 | ||||||||
\(256\) | −256.754 | −1.00295 | ||||||||
\(257\) | 233.113 | 0.907053 | 0.453527 | − | 0.891243i | \(-0.350166\pi\) | ||||
0.453527 | + | 0.891243i | \(0.350166\pi\) | |||||||
\(258\) | − | 14.9356i | − | 0.0578900i | ||||||
\(259\) | 81.6884 | 0.315399 | ||||||||
\(260\) | 462.170i | 1.77758i | ||||||||
\(261\) | −8.47307 | −0.0324639 | ||||||||
\(262\) | 498.120 | 1.90122 | ||||||||
\(263\) | 146.687i | 0.557747i | 0.960328 | + | 0.278873i | \(0.0899610\pi\) | ||||
−0.960328 | + | 0.278873i | \(0.910039\pi\) | |||||||
\(264\) | 40.6671i | 0.154042i | ||||||||
\(265\) | 7.34660 | 0.0277230 | ||||||||
\(266\) | 130.131 | 0.489216 | ||||||||
\(267\) | − | 298.908i | − | 1.11951i | ||||||
\(268\) | 731.077i | 2.72790i | ||||||||
\(269\) | 104.745 | 0.389386 | 0.194693 | − | 0.980864i | \(-0.437629\pi\) | ||||
0.194693 | + | 0.980864i | \(0.437629\pi\) | |||||||
\(270\) | − | 77.6736i | − | 0.287680i | ||||||
\(271\) | 263.606 | 0.972717 | 0.486358 | − | 0.873759i | \(-0.338325\pi\) | ||||
0.486358 | + | 0.873759i | \(0.338325\pi\) | |||||||
\(272\) | − | 0.726011i | − | 0.00266916i | ||||||
\(273\) | 70.8172i | 0.259404i | ||||||||
\(274\) | 515.772i | 1.88238i | ||||||||
\(275\) | 10.7521i | 0.0390987i | ||||||||
\(276\) | −220.140 | + | 134.470i | −0.797610 | + | 0.487211i | ||||
\(277\) | −380.816 | −1.37479 | −0.687394 | − | 0.726284i | \(-0.741246\pi\) | ||||
−0.687394 | + | 0.726284i | \(0.741246\pi\) | |||||||
\(278\) | −226.703 | −0.815480 | ||||||||
\(279\) | −27.9250 | −0.100090 | ||||||||
\(280\) | −97.9004 | −0.349644 | ||||||||
\(281\) | − | 47.2087i | − | 0.168003i | −0.996466 | − | 0.0840013i | \(-0.973230\pi\) | ||
0.996466 | − | 0.0840013i | \(-0.0267700\pi\) | |||||||
\(282\) | 301.503 | 1.06916 | ||||||||
\(283\) | − | 59.5032i | − | 0.210259i | −0.994459 | − | 0.105129i | \(-0.966474\pi\) | ||
0.994459 | − | 0.105129i | \(-0.0335257\pi\) | |||||||
\(284\) | −100.782 | −0.354868 | ||||||||
\(285\) | −121.567 | −0.426550 | ||||||||
\(286\) | 146.578i | 0.512509i | ||||||||
\(287\) | − | 197.676i | − | 0.688767i | ||||||
\(288\) | 95.8584 | 0.332842 | ||||||||
\(289\) | −331.263 | −1.14624 | ||||||||
\(290\) | − | 42.2193i | − | 0.145584i | ||||||
\(291\) | − | 3.14082i | − | 0.0107932i | ||||||
\(292\) | −425.492 | −1.45717 | ||||||||
\(293\) | − | 205.325i | − | 0.700768i | −0.936606 | − | 0.350384i | \(-0.886051\pi\) | ||
0.936606 | − | 0.350384i | \(-0.113949\pi\) | |||||||
\(294\) | −39.2413 | −0.133474 | ||||||||
\(295\) | 435.949i | 1.47779i | ||||||||
\(296\) | 247.366i | 0.835697i | ||||||||
\(297\) | − | 15.2277i | − | 0.0512718i | ||||||
\(298\) | − | 867.067i | − | 2.90962i | ||||||
\(299\) | −303.321 | + | 185.280i | −1.01445 | + | 0.619665i | ||||
\(300\) | −41.1499 | −0.137166 | ||||||||
\(301\) | 7.04898 | 0.0234185 | ||||||||
\(302\) | 11.7758 | 0.0389926 | ||||||||
\(303\) | 57.7001 | 0.190430 | ||||||||
\(304\) | 0.442999i | 0.00145724i | ||||||||
\(305\) | 531.371 | 1.74220 | ||||||||
\(306\) | 241.821i | 0.790265i | ||||||||
\(307\) | −188.680 | −0.614591 | −0.307296 | − | 0.951614i | \(-0.599424\pi\) | ||||
−0.307296 | + | 0.951614i | \(0.599424\pi\) | |||||||
\(308\) | −50.2075 | −0.163011 | ||||||||
\(309\) | − | 194.672i | − | 0.630006i | ||||||
\(310\) | − | 139.143i | − | 0.448850i | ||||||
\(311\) | −451.261 | −1.45100 | −0.725500 | − | 0.688222i | \(-0.758391\pi\) | ||||
−0.725500 | + | 0.688222i | \(0.758391\pi\) | |||||||
\(312\) | −214.447 | −0.687329 | ||||||||
\(313\) | − | 620.664i | − | 1.98295i | −0.130287 | − | 0.991476i | \(-0.541590\pi\) | ||
0.130287 | − | 0.991476i | \(-0.458410\pi\) | |||||||
\(314\) | − | 902.820i | − | 2.87522i | ||||||
\(315\) | 36.6586 | 0.116377 | ||||||||
\(316\) | − | 37.8142i | − | 0.119665i | ||||||
\(317\) | −240.848 | −0.759771 | −0.379886 | − | 0.925033i | \(-0.624037\pi\) | ||||
−0.379886 | + | 0.925033i | \(0.624037\pi\) | |||||||
\(318\) | 8.91715i | 0.0280414i | ||||||||
\(319\) | − | 8.27700i | − | 0.0259467i | ||||||
\(320\) | 478.178i | 1.49431i | ||||||||
\(321\) | 57.9583i | 0.180556i | ||||||||
\(322\) | −102.668 | − | 168.077i | −0.318844 | − | 0.521977i | ||||
\(323\) | 378.474 | 1.17175 | ||||||||
\(324\) | 58.2785 | 0.179872 | ||||||||
\(325\) | −56.6984 | −0.174457 | ||||||||
\(326\) | −565.685 | −1.73523 | ||||||||
\(327\) | 64.3575i | 0.196812i | ||||||||
\(328\) | 598.597 | 1.82499 | ||||||||
\(329\) | 142.297i | 0.432513i | ||||||||
\(330\) | 75.8761 | 0.229928 | ||||||||
\(331\) | −399.744 | −1.20769 | −0.603843 | − | 0.797103i | \(-0.706365\pi\) | ||||
−0.603843 | + | 0.797103i | \(0.706365\pi\) | |||||||
\(332\) | 355.692i | 1.07136i | ||||||||
\(333\) | − | 92.6259i | − | 0.278156i | ||||||
\(334\) | 916.591 | 2.74428 | ||||||||
\(335\) | 521.438 | 1.55653 | ||||||||
\(336\) | − | 0.133587i | − | 0.000397581i | ||||||
\(337\) | − | 380.934i | − | 1.13037i | −0.824965 | − | 0.565184i | \(-0.808805\pi\) | ||
0.824965 | − | 0.565184i | \(-0.191195\pi\) | |||||||
\(338\) | −225.955 | −0.668505 | ||||||||
\(339\) | − | 152.430i | − | 0.449647i | ||||||
\(340\) | −744.835 | −2.19069 | ||||||||
\(341\) | − | 27.2788i | − | 0.0799964i | ||||||
\(342\) | − | 147.555i | − | 0.431448i | ||||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | 21.3455i | 0.0620510i | ||||||||
\(345\) | 95.9105 | + | 157.014i | 0.278001 | + | 0.455114i | ||||
\(346\) | −100.450 | −0.290317 | ||||||||
\(347\) | 475.546 | 1.37045 | 0.685225 | − | 0.728331i | \(-0.259704\pi\) | ||||
0.685225 | + | 0.728331i | \(0.259704\pi\) | |||||||
\(348\) | 31.6772 | 0.0910263 | ||||||||
\(349\) | −167.751 | −0.480663 | −0.240331 | − | 0.970691i | \(-0.577256\pi\) | ||||
−0.240331 | + | 0.970691i | \(0.577256\pi\) | |||||||
\(350\) | − | 31.4178i | − | 0.0897652i | ||||||
\(351\) | 80.2991 | 0.228772 | ||||||||
\(352\) | 93.6402i | 0.266023i | ||||||||
\(353\) | −398.591 | −1.12915 | −0.564576 | − | 0.825381i | \(-0.690960\pi\) | ||||
−0.564576 | + | 0.825381i | \(0.690960\pi\) | |||||||
\(354\) | −529.145 | −1.49476 | ||||||||
\(355\) | 71.8828i | 0.202487i | ||||||||
\(356\) | 1117.49i | 3.13901i | ||||||||
\(357\) | −114.129 | −0.319690 | ||||||||
\(358\) | 108.889 | 0.304160 | ||||||||
\(359\) | − | 371.041i | − | 1.03354i | −0.856124 | − | 0.516770i | \(-0.827134\pi\) | ||
0.856124 | − | 0.516770i | \(-0.172866\pi\) | |||||||
\(360\) | 111.009i | 0.308357i | ||||||||
\(361\) | 130.062 | 0.360282 | ||||||||
\(362\) | − | 146.853i | − | 0.405672i | ||||||
\(363\) | −194.703 | −0.536371 | ||||||||
\(364\) | − | 264.755i | − | 0.727349i | ||||||
\(365\) | 303.481i | 0.831455i | ||||||||
\(366\) | 644.967i | 1.76221i | ||||||||
\(367\) | 513.182i | 1.39832i | 0.714967 | + | 0.699158i | \(0.246442\pi\) | ||||
−0.714967 | + | 0.699158i | \(0.753558\pi\) | |||||||
\(368\) | 0.572174 | − | 0.349506i | 0.00155482 | − | 0.000949745i | ||||
\(369\) | −224.144 | −0.607435 | ||||||||
\(370\) | 461.533 | 1.24739 | ||||||||
\(371\) | −4.20852 | −0.0113437 | ||||||||
\(372\) | 104.399 | 0.280644 | ||||||||
\(373\) | − | 463.384i | − | 1.24232i | −0.783685 | − | 0.621158i | \(-0.786662\pi\) | ||
0.783685 | − | 0.621158i | \(-0.213338\pi\) | |||||||
\(374\) | −236.225 | −0.631619 | ||||||||
\(375\) | 229.339i | 0.611572i | ||||||||
\(376\) | −430.899 | −1.14601 | ||||||||
\(377\) | 43.6464 | 0.115773 | ||||||||
\(378\) | 44.4955i | 0.117713i | ||||||||
\(379\) | − | 404.771i | − | 1.06800i | −0.845485 | − | 0.533998i | \(-0.820689\pi\) | ||
0.845485 | − | 0.533998i | \(-0.179311\pi\) | |||||||
\(380\) | 454.486 | 1.19601 | ||||||||
\(381\) | 95.3478 | 0.250257 | ||||||||
\(382\) | 158.189i | 0.414107i | ||||||||
\(383\) | − | 550.465i | − | 1.43725i | −0.695400 | − | 0.718623i | \(-0.744773\pi\) | ||
0.695400 | − | 0.718623i | \(-0.255227\pi\) | |||||||
\(384\) | −359.027 | −0.934966 | ||||||||
\(385\) | 35.8103i | 0.0930139i | ||||||||
\(386\) | 759.357 | 1.96725 | ||||||||
\(387\) | − | 7.99280i | − | 0.0206532i | ||||||
\(388\) | 11.7422i | 0.0302633i | ||||||||
\(389\) | 642.282i | 1.65111i | 0.564322 | + | 0.825555i | \(0.309138\pi\) | ||||
−0.564322 | + | 0.825555i | \(0.690862\pi\) | |||||||
\(390\) | 400.111i | 1.02593i | ||||||||
\(391\) | −298.598 | − | 488.834i | −0.763679 | − | 1.25021i | ||||
\(392\) | 56.0825 | 0.143068 | ||||||||
\(393\) | 266.569 | 0.678292 | ||||||||
\(394\) | 457.516 | 1.16121 | ||||||||
\(395\) | −26.9709 | −0.0682807 | ||||||||
\(396\) | 56.9299i | 0.143762i | ||||||||
\(397\) | 29.4833 | 0.0742652 | 0.0371326 | − | 0.999310i | \(-0.488178\pi\) | ||||
0.0371326 | + | 0.999310i | \(0.488178\pi\) | |||||||
\(398\) | 471.789i | 1.18540i | ||||||||
\(399\) | 69.6398 | 0.174536 | ||||||||
\(400\) | 0.106954 | 0.000267385 | ||||||||
\(401\) | 463.906i | 1.15687i | 0.815727 | + | 0.578437i | \(0.196337\pi\) | ||||
−0.815727 | + | 0.578437i | \(0.803663\pi\) | |||||||
\(402\) | 632.911i | 1.57441i | ||||||||
\(403\) | 143.847 | 0.356940 | ||||||||
\(404\) | −215.716 | −0.533951 | ||||||||
\(405\) | − | 41.5670i | − | 0.102635i | ||||||
\(406\) | 24.1854i | 0.0595700i | ||||||||
\(407\) | 90.4825 | 0.222316 | ||||||||
\(408\) | − | 345.604i | − | 0.847067i | ||||||
\(409\) | 372.076 | 0.909721 | 0.454860 | − | 0.890563i | \(-0.349689\pi\) | ||||
0.454860 | + | 0.890563i | \(0.349689\pi\) | |||||||
\(410\) | − | 1116.85i | − | 2.72403i | ||||||
\(411\) | 276.016i | 0.671571i | ||||||||
\(412\) | 727.795i | 1.76649i | ||||||||
\(413\) | − | 249.734i | − | 0.604684i | ||||||
\(414\) | −190.581 | + | 116.414i | −0.460340 | + | 0.281194i | ||||
\(415\) | 253.697 | 0.611317 | ||||||||
\(416\) | −493.785 | −1.18698 | ||||||||
\(417\) | −121.320 | −0.290936 | ||||||||
\(418\) | 144.141 | 0.344834 | ||||||||
\(419\) | 398.036i | 0.949966i | 0.879995 | + | 0.474983i | \(0.157546\pi\) | ||||
−0.879995 | + | 0.474983i | \(0.842454\pi\) | |||||||
\(420\) | −137.051 | −0.326312 | ||||||||
\(421\) | 419.454i | 0.996328i | 0.867083 | + | 0.498164i | \(0.165992\pi\) | ||||
−0.867083 | + | 0.498164i | \(0.834008\pi\) | |||||||
\(422\) | −260.735 | −0.617854 | ||||||||
\(423\) | 161.349 | 0.381441 | ||||||||
\(424\) | − | 12.7441i | − | 0.0300569i | ||||||
\(425\) | − | 91.3755i | − | 0.215001i | ||||||
\(426\) | −87.2498 | −0.204812 | ||||||||
\(427\) | −304.397 | −0.712874 | ||||||||
\(428\) | − | 216.681i | − | 0.506265i | ||||||
\(429\) | 78.4410i | 0.182846i | ||||||||
\(430\) | 39.8262 | 0.0926190 | ||||||||
\(431\) | − | 269.366i | − | 0.624979i | −0.949921 | − | 0.312490i | \(-0.898837\pi\) | ||
0.949921 | − | 0.312490i | \(-0.101163\pi\) | |||||||
\(432\) | −0.151474 | −0.000350634 | ||||||||
\(433\) | − | 358.912i | − | 0.828896i | −0.910073 | − | 0.414448i | \(-0.863975\pi\) | ||
0.910073 | − | 0.414448i | \(-0.136025\pi\) | |||||||
\(434\) | 79.7087i | 0.183661i | ||||||||
\(435\) | − | 22.5936i | − | 0.0519394i | ||||||
\(436\) | − | 240.605i | − | 0.551846i | ||||||
\(437\) | 182.200 | + | 298.278i | 0.416933 | + | 0.682558i | ||||
\(438\) | −368.359 | −0.841003 | ||||||||
\(439\) | −222.724 | −0.507345 | −0.253672 | − | 0.967290i | \(-0.581638\pi\) | ||||
−0.253672 | + | 0.967290i | \(0.581638\pi\) | |||||||
\(440\) | −108.440 | −0.246454 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | − | 1245.67i | − | 2.81825i | ||||||
\(443\) | 123.225 | 0.278160 | 0.139080 | − | 0.990281i | \(-0.455586\pi\) | ||||
0.139080 | + | 0.990281i | \(0.455586\pi\) | |||||||
\(444\) | 346.288i | 0.779929i | ||||||||
\(445\) | 797.045 | 1.79111 | ||||||||
\(446\) | −487.068 | −1.09208 | ||||||||
\(447\) | − | 464.011i | − | 1.03806i | ||||||
\(448\) | − | 273.926i | − | 0.611441i | ||||||
\(449\) | −462.304 | −1.02963 | −0.514815 | − | 0.857301i | \(-0.672139\pi\) | ||||
−0.514815 | + | 0.857301i | \(0.672139\pi\) | |||||||
\(450\) | −35.6245 | −0.0791655 | ||||||||
\(451\) | − | 218.957i | − | 0.485492i | ||||||
\(452\) | 569.872i | 1.26078i | ||||||||
\(453\) | 6.30180 | 0.0139113 | ||||||||
\(454\) | − | 429.672i | − | 0.946413i | ||||||
\(455\) | −188.836 | −0.415024 | ||||||||
\(456\) | 210.881i | 0.462459i | ||||||||
\(457\) | 710.676i | 1.55509i | 0.628828 | + | 0.777545i | \(0.283535\pi\) | ||||
−0.628828 | + | 0.777545i | \(0.716465\pi\) | |||||||
\(458\) | 39.3503i | 0.0859178i | ||||||||
\(459\) | 129.411i | 0.281940i | ||||||||
\(460\) | −358.568 | − | 587.010i | −0.779496 | − | 1.27611i | ||||
\(461\) | 326.628 | 0.708521 | 0.354261 | − | 0.935147i | \(-0.384733\pi\) | ||||
0.354261 | + | 0.935147i | \(0.384733\pi\) | |||||||
\(462\) | −43.4658 | −0.0940819 | ||||||||
\(463\) | 16.6115 | 0.0358779 | 0.0179390 | − | 0.999839i | \(-0.494290\pi\) | ||||
0.0179390 | + | 0.999839i | \(0.494290\pi\) | |||||||
\(464\) | −0.0823332 | −0.000177442 | ||||||||
\(465\) | − | 74.4626i | − | 0.160135i | ||||||
\(466\) | 434.004 | 0.931338 | ||||||||
\(467\) | − | 523.319i | − | 1.12060i | −0.828291 | − | 0.560299i | \(-0.810686\pi\) | ||
0.828291 | − | 0.560299i | \(-0.189314\pi\) | |||||||
\(468\) | −300.204 | −0.641461 | ||||||||
\(469\) | −298.707 | −0.636902 | ||||||||
\(470\) | 803.965i | 1.71056i | ||||||||
\(471\) | − | 483.144i | − | 1.02578i | ||||||
\(472\) | 756.238 | 1.60220 | ||||||||
\(473\) | 7.80784 | 0.0165071 | ||||||||
\(474\) | − | 32.7367i | − | 0.0690647i | ||||||
\(475\) | 55.7557i | 0.117381i | ||||||||
\(476\) | 426.681 | 0.896388 | ||||||||
\(477\) | 4.77201i | 0.0100042i | ||||||||
\(478\) | 298.052 | 0.623540 | ||||||||
\(479\) | − | 861.906i | − | 1.79939i | −0.436523 | − | 0.899693i | \(-0.643790\pi\) | ||
0.436523 | − | 0.899693i | \(-0.356210\pi\) | |||||||
\(480\) | 255.609i | 0.532518i | ||||||||
\(481\) | 477.134i | 0.991962i | ||||||||
\(482\) | − | 724.182i | − | 1.50245i | ||||||
\(483\) | −54.9426 | − | 89.9462i | −0.113753 | − | 0.186224i | ||||
\(484\) | 727.910 | 1.50395 | ||||||||
\(485\) | 8.37506 | 0.0172682 | ||||||||
\(486\) | 50.4532 | 0.103813 | ||||||||
\(487\) | −25.7518 | −0.0528785 | −0.0264393 | − | 0.999650i | \(-0.508417\pi\) | ||||
−0.0264393 | + | 0.999650i | \(0.508417\pi\) | |||||||
\(488\) | − | 921.767i | − | 1.88887i | ||||||
\(489\) | −302.726 | −0.619072 | ||||||||
\(490\) | − | 104.638i | − | 0.213547i | ||||||
\(491\) | 694.469 | 1.41440 | 0.707199 | − | 0.707015i | \(-0.249959\pi\) | ||||
0.707199 | + | 0.707015i | \(0.249959\pi\) | |||||||
\(492\) | 837.977 | 1.70320 | ||||||||
\(493\) | 70.3408i | 0.142679i | ||||||||
\(494\) | 760.085i | 1.53863i | ||||||||
\(495\) | 40.6051 | 0.0820305 | ||||||||
\(496\) | −0.271348 | −0.000547073 | ||||||||
\(497\) | − | 41.1782i | − | 0.0828536i | ||||||
\(498\) | 307.932i | 0.618337i | ||||||||
\(499\) | 807.321 | 1.61788 | 0.808939 | − | 0.587893i | \(-0.200042\pi\) | ||||
0.808939 | + | 0.587893i | \(0.200042\pi\) | |||||||
\(500\) | − | 857.401i | − | 1.71480i | ||||||
\(501\) | 490.513 | 0.979069 | ||||||||
\(502\) | − | 418.906i | − | 0.834474i | ||||||
\(503\) | − | 375.920i | − | 0.747355i | −0.927559 | − | 0.373678i | \(-0.878097\pi\) | ||
0.927559 | − | 0.373678i | \(-0.121903\pi\) | |||||||
\(504\) | − | 63.5916i | − | 0.126174i | ||||||
\(505\) | 153.859i | 0.304671i | ||||||||
\(506\) | −113.720 | − | 186.171i | −0.224744 | − | 0.367926i | ||||
\(507\) | −120.920 | −0.238500 | ||||||||
\(508\) | −356.464 | −0.701702 | ||||||||
\(509\) | 402.707 | 0.791173 | 0.395587 | − | 0.918429i | \(-0.370541\pi\) | ||||
0.395587 | + | 0.918429i | \(0.370541\pi\) | |||||||
\(510\) | −644.822 | −1.26436 | ||||||||
\(511\) | − | 173.850i | − | 0.340215i | ||||||
\(512\) | 1.86567 | 0.00364389 | ||||||||
\(513\) | − | 78.9641i | − | 0.153926i | ||||||
\(514\) | −754.486 | −1.46787 | ||||||||
\(515\) | 519.097 | 1.00796 | ||||||||
\(516\) | 29.8816i | 0.0579101i | ||||||||
\(517\) | 157.616i | 0.304866i | ||||||||
\(518\) | −264.390 | −0.510406 | ||||||||
\(519\) | −53.7557 | −0.103575 | ||||||||
\(520\) | − | 571.827i | − | 1.09967i | ||||||
\(521\) | − | 690.363i | − | 1.32507i | −0.749030 | − | 0.662537i | \(-0.769480\pi\) | ||
0.749030 | − | 0.662537i | \(-0.230520\pi\) | |||||||
\(522\) | 27.4237 | 0.0525358 | ||||||||
\(523\) | − | 274.655i | − | 0.525152i | −0.964911 | − | 0.262576i | \(-0.915428\pi\) | ||
0.964911 | − | 0.262576i | \(-0.0845721\pi\) | |||||||
\(524\) | −996.586 | −1.90188 | ||||||||
\(525\) | − | 16.8132i | − | 0.0320252i | ||||||
\(526\) | − | 474.764i | − | 0.902594i | ||||||
\(527\) | 231.825i | 0.439895i | ||||||||
\(528\) | − | 0.147969i | − | 0.000280243i | ||||||
\(529\) | 241.506 | − | 470.655i | 0.456533 | − | 0.889706i | ||||
\(530\) | −23.7778 | −0.0448638 | ||||||||
\(531\) | −283.172 | −0.533281 | ||||||||
\(532\) | −260.353 | −0.489386 | ||||||||
\(533\) | 1154.61 | 2.16624 | ||||||||
\(534\) | 967.437i | 1.81168i | ||||||||
\(535\) | −154.547 | −0.288873 | ||||||||
\(536\) | − | 904.537i | − | 1.68757i | ||||||
\(537\) | 58.2720 | 0.108514 | ||||||||
\(538\) | −339.014 | −0.630138 | ||||||||
\(539\) | − | 20.5140i | − | 0.0380595i | ||||||
\(540\) | 155.401i | 0.287780i | ||||||||
\(541\) | 582.111 | 1.07599 | 0.537995 | − | 0.842948i | \(-0.319182\pi\) | ||||
0.537995 | + | 0.842948i | \(0.319182\pi\) | |||||||
\(542\) | −853.181 | −1.57413 | ||||||||
\(543\) | − | 78.5885i | − | 0.144730i | ||||||
\(544\) | − | 795.787i | − | 1.46284i | ||||||
\(545\) | −171.611 | −0.314882 | ||||||||
\(546\) | − | 229.205i | − | 0.419789i | ||||||
\(547\) | −523.370 | −0.956800 | −0.478400 | − | 0.878142i | \(-0.658783\pi\) | ||||
−0.478400 | + | 0.878142i | \(0.658783\pi\) | |||||||
\(548\) | − | 1031.90i | − | 1.88304i | ||||||
\(549\) | 345.154i | 0.628696i | ||||||||
\(550\) | − | 34.8001i | − | 0.0632729i | ||||||
\(551\) | − | 42.9208i | − | 0.0778961i | ||||||
\(552\) | 272.372 | − | 166.376i | 0.493428 | − | 0.301405i | ||||
\(553\) | 15.4503 | 0.0279391 | ||||||||
\(554\) | 1232.54 | 2.22480 | ||||||||
\(555\) | 246.989 | 0.445026 | ||||||||
\(556\) | 453.565 | 0.815764 | ||||||||
\(557\) | 424.538i | 0.762187i | 0.924537 | + | 0.381093i | \(0.124452\pi\) | ||||
−0.924537 | + | 0.381093i | \(0.875548\pi\) | |||||||
\(558\) | 90.3812 | 0.161973 | ||||||||
\(559\) | 41.1724i | 0.0736537i | ||||||||
\(560\) | 0.356214 | 0.000636096 | ||||||||
\(561\) | −126.416 | −0.225340 | ||||||||
\(562\) | 152.794i | 0.271876i | ||||||||
\(563\) | − | 746.148i | − | 1.32531i | −0.748926 | − | 0.662654i | \(-0.769430\pi\) | ||
0.748926 | − | 0.662654i | \(-0.230570\pi\) | |||||||
\(564\) | −603.216 | −1.06953 | ||||||||
\(565\) | 406.460 | 0.719397 | ||||||||
\(566\) | 192.586i | 0.340259i | ||||||||
\(567\) | 23.8118i | 0.0419961i | ||||||||
\(568\) | 124.695 | 0.219533 | ||||||||
\(569\) | 292.834i | 0.514647i | 0.966325 | + | 0.257324i | \(0.0828407\pi\) | ||||
−0.966325 | + | 0.257324i | \(0.917159\pi\) | |||||||
\(570\) | 393.459 | 0.690279 | ||||||||
\(571\) | 959.451i | 1.68030i | 0.542355 | + | 0.840150i | \(0.317533\pi\) | ||||
−0.542355 | + | 0.840150i | \(0.682467\pi\) | |||||||
\(572\) | − | 293.257i | − | 0.512687i | ||||||
\(573\) | 84.6548i | 0.147740i | ||||||||
\(574\) | 639.793i | 1.11462i | ||||||||
\(575\) | 72.0136 | − | 43.9887i | 0.125241 | − | 0.0765021i | ||||
\(576\) | −310.602 | −0.539240 | ||||||||
\(577\) | 93.9124 | 0.162760 | 0.0813799 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813799 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(578\) | 1072.16 | 1.85494 | ||||||||
\(579\) | 406.370 | 0.701848 | ||||||||
\(580\) | 84.4679i | 0.145634i | ||||||||
\(581\) | −145.331 | −0.250139 | ||||||||
\(582\) | 10.1655i | 0.0174665i | ||||||||
\(583\) | −4.66159 | −0.00799586 | ||||||||
\(584\) | 526.448 | 0.901451 | ||||||||
\(585\) | 214.120i | 0.366016i | ||||||||
\(586\) | 664.549i | 1.13404i | ||||||||
\(587\) | −530.842 | −0.904330 | −0.452165 | − | 0.891934i | \(-0.649348\pi\) | ||||
−0.452165 | + | 0.891934i | \(0.649348\pi\) | |||||||
\(588\) | 78.5100 | 0.133520 | ||||||||
\(589\) | − | 141.455i | − | 0.240162i | ||||||
\(590\) | − | 1410.98i | − | 2.39149i | ||||||
\(591\) | 244.840 | 0.414280 | ||||||||
\(592\) | − | 0.900050i | − | 0.00152035i | ||||||
\(593\) | −836.235 | −1.41018 | −0.705089 | − | 0.709119i | \(-0.749093\pi\) | ||||
−0.705089 | + | 0.709119i | \(0.749093\pi\) | |||||||
\(594\) | 49.2856i | 0.0829725i | ||||||||
\(595\) | − | 304.329i | − | 0.511477i | ||||||
\(596\) | 1734.74i | 2.91063i | ||||||||
\(597\) | 252.478i | 0.422911i | ||||||||
\(598\) | 981.719 | − | 599.672i | 1.64167 | − | 1.00280i | ||||
\(599\) | 133.373 | 0.222659 | 0.111329 | − | 0.993784i | \(-0.464489\pi\) | ||||
0.111329 | + | 0.993784i | \(0.464489\pi\) | |||||||
\(600\) | 50.9134 | 0.0848556 | ||||||||
\(601\) | −873.614 | −1.45360 | −0.726800 | − | 0.686849i | \(-0.758993\pi\) | ||||
−0.726800 | + | 0.686849i | \(0.758993\pi\) | |||||||
\(602\) | −22.8145 | −0.0378979 | ||||||||
\(603\) | 338.702i | 0.561695i | ||||||||
\(604\) | −23.5597 | −0.0390062 | ||||||||
\(605\) | − | 519.180i | − | 0.858148i | ||||||
\(606\) | −186.751 | −0.308169 | ||||||||
\(607\) | −1197.84 | −1.97337 | −0.986687 | − | 0.162630i | \(-0.948002\pi\) | ||||
−0.986687 | + | 0.162630i | \(0.948002\pi\) | |||||||
\(608\) | 485.576i | 0.798644i | ||||||||
\(609\) | 12.9428i | 0.0212526i | ||||||||
\(610\) | −1719.82 | −2.81938 | ||||||||
\(611\) | −831.142 | −1.36030 | ||||||||
\(612\) | − | 483.811i | − | 0.790540i | ||||||
\(613\) | 439.201i | 0.716478i | 0.933630 | + | 0.358239i | \(0.116623\pi\) | ||||
−0.933630 | + | 0.358239i | \(0.883377\pi\) | |||||||
\(614\) | 610.675 | 0.994584 | ||||||||
\(615\) | − | 597.684i | − | 0.971845i | ||||||
\(616\) | 62.1201 | 0.100844 | ||||||||
\(617\) | − | 126.704i | − | 0.205355i | −0.994715 | − | 0.102677i | \(-0.967259\pi\) | ||
0.994715 | − | 0.102677i | \(-0.0327410\pi\) | |||||||
\(618\) | 630.070i | 1.01953i | ||||||||
\(619\) | 610.765i | 0.986697i | 0.869832 | + | 0.493348i | \(0.164227\pi\) | ||||
−0.869832 | + | 0.493348i | \(0.835773\pi\) | |||||||
\(620\) | 278.384i | 0.449006i | ||||||||
\(621\) | −101.989 | + | 62.2990i | −0.164234 | + | 0.100321i | ||||
\(622\) | 1460.54 | 2.34813 | ||||||||
\(623\) | −456.589 | −0.732888 | ||||||||
\(624\) | 0.780270 | 0.00125043 | ||||||||
\(625\) | −519.815 | −0.831704 | ||||||||
\(626\) | 2008.82i | 3.20898i | ||||||||
\(627\) | 77.1368 | 0.123025 | ||||||||
\(628\) | 1806.27i | 2.87622i | ||||||||
\(629\) | −768.952 | −1.22250 | ||||||||
\(630\) | −118.648 | −0.188331 | ||||||||
\(631\) | 943.021i | 1.49449i | 0.664551 | + | 0.747243i | \(0.268623\pi\) | ||||
−0.664551 | + | 0.747243i | \(0.731377\pi\) | |||||||
\(632\) | 46.7863i | 0.0740289i | ||||||||
\(633\) | −139.532 | −0.220430 | ||||||||
\(634\) | 779.520 | 1.22953 | ||||||||
\(635\) | 254.247i | 0.400389i | ||||||||
\(636\) | − | 17.8405i | − | 0.0280511i | ||||||
\(637\) | 108.175 | 0.169820 | ||||||||
\(638\) | 26.7891i | 0.0419892i | ||||||||
\(639\) | −46.6917 | −0.0730700 | ||||||||
\(640\) | − | 957.354i | − | 1.49587i | ||||||
\(641\) | − | 977.288i | − | 1.52463i | −0.647206 | − | 0.762315i | \(-0.724063\pi\) | ||
0.647206 | − | 0.762315i | \(-0.275937\pi\) | |||||||
\(642\) | − | 187.586i | − | 0.292190i | ||||||
\(643\) | − | 855.465i | − | 1.33043i | −0.746653 | − | 0.665214i | \(-0.768340\pi\) | ||
0.746653 | − | 0.665214i | \(-0.231660\pi\) | |||||||
\(644\) | 205.407 | + | 336.270i | 0.318955 | + | 0.522158i | ||||
\(645\) | 21.3130 | 0.0330434 | ||||||||
\(646\) | −1224.96 | −1.89622 | ||||||||
\(647\) | −357.779 | −0.552982 | −0.276491 | − | 0.961017i | \(-0.589172\pi\) | ||||
−0.276491 | + | 0.961017i | \(0.589172\pi\) | |||||||
\(648\) | −72.1061 | −0.111275 | ||||||||
\(649\) | − | 276.619i | − | 0.426224i | ||||||
\(650\) | 183.508 | 0.282321 | ||||||||
\(651\) | 42.6561i | 0.0655240i | ||||||||
\(652\) | 1131.76 | 1.73583 | ||||||||
\(653\) | 520.581 | 0.797215 | 0.398607 | − | 0.917122i | \(-0.369494\pi\) | ||||
0.398607 | + | 0.917122i | \(0.369494\pi\) | |||||||
\(654\) | − | 208.298i | − | 0.318498i | ||||||
\(655\) | 710.812i | 1.08521i | ||||||||
\(656\) | −2.17801 | −0.00332014 | ||||||||
\(657\) | −197.127 | −0.300042 | ||||||||
\(658\) | − | 460.554i | − | 0.699929i | ||||||
\(659\) | − | 636.441i | − | 0.965768i | −0.875684 | − | 0.482884i | \(-0.839589\pi\) | ||
0.875684 | − | 0.482884i | \(-0.160411\pi\) | |||||||
\(660\) | −151.805 | −0.230008 | ||||||||
\(661\) | 1033.29i | 1.56322i | 0.623766 | + | 0.781611i | \(0.285602\pi\) | ||||
−0.623766 | + | 0.781611i | \(0.714398\pi\) | |||||||
\(662\) | 1293.80 | 1.95438 | ||||||||
\(663\) | − | 666.619i | − | 1.00546i | ||||||
\(664\) | − | 440.086i | − | 0.662781i | ||||||
\(665\) | 185.696i | 0.279242i | ||||||||
\(666\) | 299.790i | 0.450136i | ||||||||
\(667\) | −55.4361 | + | 33.8625i | −0.0831126 | + | 0.0507684i | ||||
\(668\) | −1833.82 | −2.74524 | ||||||||
\(669\) | −260.654 | −0.389618 | ||||||||
\(670\) | −1687.67 | −2.51891 | ||||||||
\(671\) | −337.167 | −0.502484 | ||||||||
\(672\) | − | 146.426i | − | 0.217896i | ||||||
\(673\) | −468.106 | −0.695552 | −0.347776 | − | 0.937578i | \(-0.613063\pi\) | ||||
−0.347776 | + | 0.937578i | \(0.613063\pi\) | |||||||
\(674\) | 1232.92i | 1.82926i | ||||||||
\(675\) | −19.0644 | −0.0282436 | ||||||||
\(676\) | 452.067 | 0.668738 | ||||||||
\(677\) | 722.201i | 1.06677i | 0.845874 | + | 0.533383i | \(0.179080\pi\) | ||||
−0.845874 | + | 0.533383i | \(0.820920\pi\) | |||||||
\(678\) | 493.352i | 0.727658i | ||||||||
\(679\) | −4.79768 | −0.00706580 | ||||||||
\(680\) | 921.560 | 1.35524 | ||||||||
\(681\) | − | 229.939i | − | 0.337649i | ||||||
\(682\) | 88.2897i | 0.129457i | ||||||||
\(683\) | 551.975 | 0.808163 | 0.404081 | − | 0.914723i | \(-0.367591\pi\) | ||||
0.404081 | + | 0.914723i | \(0.367591\pi\) | |||||||
\(684\) | 295.213i | 0.431598i | ||||||||
\(685\) | −736.002 | −1.07446 | ||||||||
\(686\) | 59.9421i | 0.0873792i | ||||||||
\(687\) | 21.0583i | 0.0306526i | ||||||||
\(688\) | − | 0.0776663i | − | 0.000112887i | ||||||
\(689\) | − | 24.5816i | − | 0.0356772i | ||||||
\(690\) | −310.421 | − | 508.189i | −0.449886 | − | 0.736505i | ||||
\(691\) | −736.563 | −1.06594 | −0.532969 | − | 0.846135i | \(-0.678924\pi\) | ||||
−0.532969 | + | 0.846135i | \(0.678924\pi\) | |||||||
\(692\) | 200.969 | 0.290418 | ||||||||
\(693\) | −23.2607 | −0.0335653 | ||||||||
\(694\) | −1539.14 | −2.21778 | ||||||||
\(695\) | − | 323.504i | − | 0.465473i | ||||||
\(696\) | −39.1931 | −0.0563119 | ||||||||
\(697\) | 1860.77i | 2.66969i | ||||||||
\(698\) | 542.939 | 0.777849 | ||||||||
\(699\) | 232.257 | 0.332270 | ||||||||
\(700\) | 62.8575i | 0.0897964i | ||||||||
\(701\) | 327.666i | 0.467427i | 0.972306 | + | 0.233713i | \(0.0750877\pi\) | ||||
−0.972306 | + | 0.233713i | \(0.924912\pi\) | |||||||
\(702\) | −259.894 | −0.370219 | ||||||||
\(703\) | 469.201 | 0.667427 | ||||||||
\(704\) | − | 303.415i | − | 0.430987i | ||||||
\(705\) | 430.242i | 0.610272i | ||||||||
\(706\) | 1290.07 | 1.82729 | ||||||||
\(707\) | − | 88.1384i | − | 0.124665i | ||||||
\(708\) | 1058.66 | 1.49528 | ||||||||
\(709\) | − | 434.190i | − | 0.612398i | −0.951967 | − | 0.306199i | \(-0.900943\pi\) | ||
0.951967 | − | 0.306199i | \(-0.0990574\pi\) | |||||||
\(710\) | − | 232.654i | − | 0.327681i | ||||||
\(711\) | − | 17.5190i | − | 0.0246400i | ||||||
\(712\) | − | 1382.63i | − | 1.94190i | ||||||
\(713\) | −182.703 | + | 111.602i | −0.256245 | + | 0.156524i | ||||
\(714\) | 369.388 | 0.517350 | ||||||||
\(715\) | −209.165 | −0.292538 | ||||||||
\(716\) | −217.854 | −0.304265 | ||||||||
\(717\) | 159.503 | 0.222458 | ||||||||
\(718\) | 1200.90i | 1.67256i | ||||||||
\(719\) | 936.978 | 1.30317 | 0.651584 | − | 0.758577i | \(-0.274105\pi\) | ||||
0.651584 | + | 0.758577i | \(0.274105\pi\) | |||||||
\(720\) | − | 0.403908i | − | 0.000560984i | ||||||
\(721\) | −297.366 | −0.412436 | ||||||||
\(722\) | −420.954 | −0.583039 | ||||||||
\(723\) | − | 387.546i | − | 0.536025i | ||||||
\(724\) | 293.809i | 0.405813i | ||||||||
\(725\) | −10.3624 | −0.0142930 | ||||||||
\(726\) | 630.169 | 0.868002 | ||||||||
\(727\) | 815.192i | 1.12131i | 0.828050 | + | 0.560655i | \(0.189451\pi\) | ||||
−0.828050 | + | 0.560655i | \(0.810549\pi\) | |||||||
\(728\) | 327.573i | 0.449962i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 982.238i | − | 1.34553i | ||||||
\(731\) | −66.3538 | −0.0907712 | ||||||||
\(732\) | − | 1290.38i | − | 1.76282i | ||||||
\(733\) | − | 476.591i | − | 0.650192i | −0.945681 | − | 0.325096i | \(-0.894603\pi\) | ||
0.945681 | − | 0.325096i | \(-0.105397\pi\) | |||||||
\(734\) | − | 1660.95i | − | 2.26287i | ||||||
\(735\) | − | 55.9970i | − | 0.0761864i | ||||||
\(736\) | 627.165 | − | 383.097i | 0.852127 | − | 0.520512i | ||||
\(737\) | −330.864 | −0.448934 | ||||||||
\(738\) | 725.457 | 0.983004 | ||||||||
\(739\) | 858.892 | 1.16224 | 0.581118 | − | 0.813820i | \(-0.302616\pi\) | ||||
0.581118 | + | 0.813820i | \(0.302616\pi\) | |||||||
\(740\) | −923.386 | −1.24782 | ||||||||
\(741\) | 406.759i | 0.548933i | ||||||||
\(742\) | 13.6212 | 0.0183574 | ||||||||
\(743\) | 94.2457i | 0.126845i | 0.997987 | + | 0.0634224i | \(0.0202015\pi\) | ||||
−0.997987 | + | 0.0634224i | \(0.979798\pi\) | |||||||
\(744\) | −129.170 | −0.173616 | ||||||||
\(745\) | 1237.30 | 1.66080 | ||||||||
\(746\) | 1499.78i | 2.01042i | ||||||||
\(747\) | 164.790i | 0.220602i | ||||||||
\(748\) | 472.615 | 0.631838 | ||||||||
\(749\) | 88.5328 | 0.118201 | ||||||||
\(750\) | − | 742.273i | − | 0.989697i | ||||||
\(751\) | 383.210i | 0.510266i | 0.966906 | + | 0.255133i | \(0.0821193\pi\) | ||||
−0.966906 | + | 0.255133i | \(0.917881\pi\) | |||||||
\(752\) | 1.56784 | 0.00208489 | ||||||||
\(753\) | − | 224.178i | − | 0.297713i | ||||||
\(754\) | −141.265 | −0.187354 | ||||||||
\(755\) | 16.8039i | 0.0222568i | ||||||||
\(756\) | − | 89.0219i | − | 0.117754i | ||||||
\(757\) | 184.528i | 0.243763i | 0.992545 | + | 0.121881i | \(0.0388927\pi\) | ||||
−0.992545 | + | 0.121881i | \(0.961107\pi\) | |||||||
\(758\) | 1310.07i | 1.72832i | ||||||||
\(759\) | −60.8574 | − | 99.6293i | −0.0801810 | − | 0.131264i | ||||
\(760\) | −562.320 | −0.739895 | ||||||||
\(761\) | −244.980 | −0.321919 | −0.160960 | − | 0.986961i | \(-0.551459\pi\) | ||||
−0.160960 | + | 0.986961i | \(0.551459\pi\) | |||||||
\(762\) | −308.600 | −0.404987 | ||||||||
\(763\) | 98.3077 | 0.128844 | ||||||||
\(764\) | − | 316.488i | − | 0.414251i | ||||||
\(765\) | −345.076 | −0.451080 | ||||||||
\(766\) | 1781.62i | 2.32588i | ||||||||
\(767\) | 1458.67 | 1.90179 | ||||||||
\(768\) | 444.711 | 0.579051 | ||||||||
\(769\) | − | 51.1696i | − | 0.0665405i | −0.999446 | − | 0.0332702i | \(-0.989408\pi\) | ||
0.999446 | − | 0.0332702i | \(-0.0105922\pi\) | |||||||
\(770\) | − | 115.903i | − | 0.150523i | ||||||
\(771\) | −403.763 | −0.523688 | ||||||||
\(772\) | −1519.24 | −1.96793 | ||||||||
\(773\) | 1041.81i | 1.34775i | 0.738843 | + | 0.673877i | \(0.235372\pi\) | ||||
−0.738843 | + | 0.673877i | \(0.764628\pi\) | |||||||
\(774\) | 25.8693i | 0.0334228i | ||||||||
\(775\) | −34.1518 | −0.0440668 | ||||||||
\(776\) | − | 14.5282i | − | 0.0187219i | ||||||
\(777\) | −141.488 | −0.182096 | ||||||||
\(778\) | − | 2078.79i | − | 2.67197i | ||||||
\(779\) | − | 1135.41i | − | 1.45752i | ||||||
\(780\) | − | 800.501i | − | 1.02628i | ||||||
\(781\) | − | 45.6112i | − | 0.0584011i | ||||||
\(782\) | 966.435 | + | 1582.14i | 1.23585 | + | 2.02320i | ||||
\(783\) | 14.6758 | 0.0187430 | ||||||||
\(784\) | −0.204058 | −0.000260278 | ||||||||
\(785\) | 1288.31 | 1.64117 | ||||||||
\(786\) | −862.769 | −1.09767 | ||||||||
\(787\) | 437.311i | 0.555668i | 0.960629 | + | 0.277834i | \(0.0896166\pi\) | ||||
−0.960629 | + | 0.277834i | \(0.910383\pi\) | |||||||
\(788\) | −915.350 | −1.16161 | ||||||||
\(789\) | − | 254.070i | − | 0.322015i | ||||||
\(790\) | 87.2932 | 0.110498 | ||||||||
\(791\) | −232.841 | −0.294363 | ||||||||
\(792\) | − | 70.4375i | − | 0.0889363i | ||||||
\(793\) | − | 1777.95i | − | 2.24206i | ||||||
\(794\) | −95.4248 | −0.120182 | ||||||||
\(795\) | −12.7247 | −0.0160059 | ||||||||
\(796\) | − | 943.907i | − | 1.18581i | ||||||
\(797\) | − | 1171.76i | − | 1.47022i | −0.677950 | − | 0.735108i | \(-0.737131\pi\) | ||
0.677950 | − | 0.735108i | \(-0.262869\pi\) | |||||||
\(798\) | −225.394 | −0.282449 | ||||||||
\(799\) | − | 1339.47i | − | 1.67644i | ||||||
\(800\) | 117.233 | 0.146542 | ||||||||
\(801\) | 517.724i | 0.646347i | ||||||||
\(802\) | − | 1501.47i | − | 1.87215i | ||||||
\(803\) | − | 192.566i | − | 0.239808i | ||||||
\(804\) | − | 1266.26i | − | 1.57495i | ||||||
\(805\) | 239.844 | − | 146.506i | 0.297942 | − | 0.181995i | ||||
\(806\) | −465.571 | −0.577631 | ||||||||
\(807\) | −181.423 | −0.224812 | ||||||||
\(808\) | 266.898 | 0.330320 | ||||||||
\(809\) | −1573.47 | −1.94496 | −0.972479 | − | 0.232989i | \(-0.925149\pi\) | ||||
−0.972479 | + | 0.232989i | \(0.925149\pi\) | |||||||
\(810\) | 134.535i | 0.166092i | ||||||||
\(811\) | 580.336 | 0.715581 | 0.357791 | − | 0.933802i | \(-0.383530\pi\) | ||||
0.357791 | + | 0.933802i | \(0.383530\pi\) | |||||||
\(812\) | − | 48.3877i | − | 0.0595907i | ||||||
\(813\) | −456.579 | −0.561598 | ||||||||
\(814\) | −292.853 | −0.359770 | ||||||||
\(815\) | − | 807.227i | − | 0.990463i | ||||||
\(816\) | 1.25749i | 0.00154104i | ||||||||
\(817\) | 40.4879 | 0.0495568 | ||||||||
\(818\) | −1204.25 | −1.47219 | ||||||||
\(819\) | − | 122.659i | − | 0.149767i | ||||||
\(820\) | 2234.49i | 2.72498i | ||||||||
\(821\) | −1540.41 | −1.87626 | −0.938132 | − | 0.346279i | \(-0.887445\pi\) | ||||
−0.938132 | + | 0.346279i | \(0.887445\pi\) | |||||||
\(822\) | − | 893.344i | − | 1.08679i | ||||||
\(823\) | 1594.60 | 1.93754 | 0.968772 | − | 0.247951i | \(-0.0797574\pi\) | ||||
0.968772 | + | 0.247951i | \(0.0797574\pi\) | |||||||
\(824\) | − | 900.476i | − | 1.09281i | ||||||
\(825\) | − | 18.6233i | − | 0.0225737i | ||||||
\(826\) | 808.283i | 0.978551i | ||||||||
\(827\) | 805.566i | 0.974082i | 0.873379 | + | 0.487041i | \(0.161924\pi\) | ||||
−0.873379 | + | 0.487041i | \(0.838076\pi\) | |||||||
\(828\) | 381.294 | − | 232.909i | 0.460501 | − | 0.281291i | ||||
\(829\) | −513.777 | −0.619756 | −0.309878 | − | 0.950776i | \(-0.600288\pi\) | ||||
−0.309878 | + | 0.950776i | \(0.600288\pi\) | |||||||
\(830\) | −821.107 | −0.989286 | ||||||||
\(831\) | 659.594 | 0.793735 | ||||||||
\(832\) | 1599.97 | 1.92304 | ||||||||
\(833\) | 174.336i | 0.209286i | ||||||||
\(834\) | 392.662 | 0.470818 | ||||||||
\(835\) | 1307.97i | 1.56643i | ||||||||
\(836\) | −288.381 | −0.344954 | ||||||||
\(837\) | 48.3675 | 0.0577867 | ||||||||
\(838\) | − | 1288.27i | − | 1.53732i | ||||||
\(839\) | 957.631i | 1.14140i | 0.821160 | + | 0.570698i | \(0.193327\pi\) | ||||
−0.821160 | + | 0.570698i | \(0.806673\pi\) | |||||||
\(840\) | 169.569 | 0.201867 | ||||||||
\(841\) | −833.023 | −0.990515 | ||||||||
\(842\) | − | 1357.59i | − | 1.61234i | ||||||
\(843\) | 81.7679i | 0.0969963i | ||||||||
\(844\) | 521.650 | 0.618069 | ||||||||
\(845\) | − | 322.435i | − | 0.381580i | ||||||
\(846\) | −522.219 | −0.617280 | ||||||||
\(847\) | 297.413i | 0.351137i | ||||||||
\(848\) | 0.0463699i | 5.46814e-5i | ||||||||
\(849\) | 103.063i | 0.121393i | ||||||||
\(850\) | 295.743i | 0.347933i | ||||||||
\(851\) | −370.178 | − | 606.016i | −0.434992 | − | 0.712122i | ||||
\(852\) | 174.560 | 0.204883 | ||||||||
\(853\) | −694.747 | −0.814474 | −0.407237 | − | 0.913322i | \(-0.633508\pi\) | ||||
−0.407237 | + | 0.913322i | \(0.633508\pi\) | |||||||
\(854\) | 985.203 | 1.15363 | ||||||||
\(855\) | 210.560 | 0.246269 | ||||||||
\(856\) | 268.093i | 0.313192i | ||||||||
\(857\) | −198.585 | −0.231721 | −0.115861 | − | 0.993265i | \(-0.536963\pi\) | ||||
−0.115861 | + | 0.993265i | \(0.536963\pi\) | |||||||
\(858\) | − | 253.880i | − | 0.295897i | ||||||
\(859\) | −384.669 | −0.447811 | −0.223905 | − | 0.974611i | \(-0.571881\pi\) | ||||
−0.223905 | + | 0.974611i | \(0.571881\pi\) | |||||||
\(860\) | −79.6801 | −0.0926513 | ||||||||
\(861\) | 342.385i | 0.397660i | ||||||||
\(862\) | 871.822i | 1.01139i | ||||||||
\(863\) | 987.992 | 1.14483 | 0.572417 | − | 0.819963i | \(-0.306006\pi\) | ||||
0.572417 | + | 0.819963i | \(0.306006\pi\) | |||||||
\(864\) | −166.032 | −0.192166 | ||||||||
\(865\) | − | 143.341i | − | 0.165712i | ||||||
\(866\) | 1161.64i | 1.34139i | ||||||||
\(867\) | 573.765 | 0.661782 | ||||||||
\(868\) | − | 159.473i | − | 0.183725i | ||||||
\(869\) | 17.1136 | 0.0196935 | ||||||||
\(870\) | 73.1259i | 0.0840528i | ||||||||
\(871\) | − | 1744.72i | − | 2.00312i | ||||||
\(872\) | 297.693i | 0.341390i | ||||||||
\(873\) | 5.44005i | 0.00623145i | ||||||||
\(874\) | −589.702 | − | 965.397i | −0.674716 | − | 1.10457i | ||||
\(875\) | 350.322 | 0.400368 | ||||||||
\(876\) | 736.974 | 0.841295 | ||||||||
\(877\) | 391.192 | 0.446057 | 0.223028 | − | 0.974812i | \(-0.428406\pi\) | ||||
0.223028 | + | 0.974812i | \(0.428406\pi\) | |||||||
\(878\) | 720.863 | 0.821029 | ||||||||
\(879\) | 355.633i | 0.404589i | ||||||||
\(880\) | 0.394562 | 0.000448365 | ||||||||
\(881\) | − | 300.919i | − | 0.341565i | −0.985309 | − | 0.170783i | \(-0.945370\pi\) | ||
0.985309 | − | 0.170783i | \(-0.0546296\pi\) | |||||||
\(882\) | 67.9680 | 0.0770612 | ||||||||
\(883\) | 1588.28 | 1.79873 | 0.899366 | − | 0.437196i | \(-0.144028\pi\) | ||||
0.899366 | + | 0.437196i | \(0.144028\pi\) | |||||||
\(884\) | 2492.20i | 2.81923i | ||||||||
\(885\) | − | 755.085i | − | 0.853204i | ||||||
\(886\) | −398.826 | −0.450142 | ||||||||
\(887\) | 800.034 | 0.901955 | 0.450978 | − | 0.892535i | \(-0.351075\pi\) | ||||
0.450978 | + | 0.892535i | \(0.351075\pi\) | |||||||
\(888\) | − | 428.451i | − | 0.482490i | ||||||
\(889\) | − | 145.646i | − | 0.163831i | ||||||
\(890\) | −2579.69 | −2.89853 | ||||||||
\(891\) | 26.3752i | 0.0296018i | ||||||||
\(892\) | 974.474 | 1.09246 | ||||||||
\(893\) | 817.323i | 0.915256i | ||||||||
\(894\) | 1501.80i | 1.67987i | ||||||||
\(895\) | 155.384i | 0.173613i | ||||||||
\(896\) | 548.423i | 0.612079i | ||||||||
\(897\) | 525.367 | − | 320.914i | 0.585693 | − | 0.357764i | ||||
\(898\) | 1496.28 | 1.66623 | ||||||||
\(899\) | 26.2900 | 0.0292436 | ||||||||
\(900\) | 71.2737 | 0.0791930 | ||||||||
\(901\) | 39.6158 | 0.0439687 | ||||||||
\(902\) | 708.669i | 0.785665i | ||||||||
\(903\) | −12.2092 | −0.0135207 | ||||||||
\(904\) | − | 705.084i | − | 0.779960i | ||||||
\(905\) | 209.558 | 0.231556 | ||||||||
\(906\) | −20.3962 | −0.0225124 | ||||||||
\(907\) | − | 579.539i | − | 0.638963i | −0.947593 | − | 0.319481i | \(-0.896491\pi\) | ||
0.947593 | − | 0.319481i | \(-0.103509\pi\) | |||||||
\(908\) | 859.642i | 0.946743i | ||||||||
\(909\) | −99.9396 | −0.109945 | ||||||||
\(910\) | 611.180 | 0.671627 | ||||||||
\(911\) | 841.706i | 0.923936i | 0.886896 | + | 0.461968i | \(0.152857\pi\) | ||||
−0.886896 | + | 0.461968i | \(0.847143\pi\) | |||||||
\(912\) | − | 0.767298i | − | 0.000841335i | ||||||
\(913\) | −160.976 | −0.176316 | ||||||||
\(914\) | − | 2300.15i | − | 2.51658i | ||||||
\(915\) | −920.362 | −1.00586 | ||||||||
\(916\) | − | 78.7280i | − | 0.0859476i | ||||||
\(917\) | − | 407.190i | − | 0.444046i | ||||||
\(918\) | − | 418.847i | − | 0.456260i | ||||||
\(919\) | − | 583.667i | − | 0.635111i | −0.948240 | − | 0.317556i | \(-0.897138\pi\) | ||
0.948240 | − | 0.317556i | \(-0.102862\pi\) | |||||||
\(920\) | 443.644 | + | 726.288i | 0.482222 | + | 0.789443i | ||||
\(921\) | 326.803 | 0.354834 | ||||||||
\(922\) | −1057.16 | −1.14659 | ||||||||
\(923\) | 240.518 | 0.260583 | ||||||||
\(924\) | 86.9619 | 0.0941146 | ||||||||
\(925\) | − | 113.280i | − | 0.122465i | ||||||
\(926\) | −53.7643 | −0.0580608 | ||||||||
\(927\) | 337.182i | 0.363734i | ||||||||
\(928\) | −90.2461 | −0.0972480 | ||||||||
\(929\) | 1686.54 | 1.81543 | 0.907715 | − | 0.419587i | \(-0.137825\pi\) | ||||
0.907715 | + | 0.419587i | \(0.137825\pi\) | |||||||
\(930\) | 241.004i | 0.259144i | ||||||||
\(931\) | − | 106.377i | − | 0.114261i | ||||||
\(932\) | −868.309 | −0.931662 | ||||||||
\(933\) | 781.607 | 0.837735 | ||||||||
\(934\) | 1693.76i | 1.81345i | ||||||||
\(935\) | − | 337.091i | − | 0.360525i | ||||||
\(936\) | 371.432 | 0.396829 | ||||||||
\(937\) | − | 1127.48i | − | 1.20328i | −0.798766 | − | 0.601642i | \(-0.794513\pi\) | ||
0.798766 | − | 0.601642i | \(-0.205487\pi\) | |||||||
\(938\) | 966.787 | 1.03069 | ||||||||
\(939\) | 1075.02i | 1.14486i | ||||||||
\(940\) | − | 1608.49i | − | 1.71116i | ||||||
\(941\) | 1038.28i | 1.10338i | 0.834048 | + | 0.551692i | \(0.186018\pi\) | ||||
−0.834048 | + | 0.551692i | \(0.813982\pi\) | |||||||
\(942\) | 1563.73i | 1.66001i | ||||||||
\(943\) | −1466.49 | + | 895.787i | −1.55513 | + | 0.949933i | ||||
\(944\) | −2.75160 | −0.00291483 | ||||||||
\(945\) | −63.4946 | −0.0671901 | ||||||||
\(946\) | −25.2706 | −0.0267131 | ||||||||
\(947\) | −1646.42 | −1.73857 | −0.869284 | − | 0.494312i | \(-0.835420\pi\) | ||||
−0.869284 | + | 0.494312i | \(0.835420\pi\) | |||||||
\(948\) | 65.4962i | 0.0690888i | ||||||||
\(949\) | 1015.44 | 1.07001 | ||||||||
\(950\) | − | 180.457i | − | 0.189955i | ||||||
\(951\) | 417.160 | 0.438654 | ||||||||
\(952\) | −527.918 | −0.554536 | ||||||||
\(953\) | 1388.86i | 1.45735i | 0.684858 | + | 0.728676i | \(0.259864\pi\) | ||||
−0.684858 | + | 0.728676i | \(0.740136\pi\) | |||||||
\(954\) | − | 15.4450i | − | 0.0161897i | ||||||
\(955\) | −225.734 | −0.236371 | ||||||||
\(956\) | −596.312 | −0.623757 | ||||||||
\(957\) | 14.3362i | 0.0149803i | ||||||||
\(958\) | 2789.62i | 2.91192i | ||||||||
\(959\) | 421.621 | 0.439646 | ||||||||
\(960\) | − | 828.229i | − | 0.862738i | ||||||
\(961\) | −874.355 | −0.909839 | ||||||||
\(962\) | − | 1544.28i | − | 1.60528i | ||||||
\(963\) | − | 100.387i | − | 0.104244i | ||||||
\(964\) | 1448.87i | 1.50297i | ||||||||
\(965\) | 1083.60i | 1.12290i | ||||||||
\(966\) | 177.826 | + | 291.117i | 0.184084 | + | 0.301364i | ||||
\(967\) | −1907.18 | −1.97227 | −0.986133 | − | 0.165960i | \(-0.946928\pi\) | ||||
−0.986133 | + | 0.165960i | \(0.946928\pi\) | |||||||
\(968\) | −900.619 | −0.930391 | ||||||||
\(969\) | −655.536 | −0.676508 | ||||||||
\(970\) | −27.1065 | −0.0279448 | ||||||||
\(971\) | 1252.06i | 1.28946i | 0.764412 | + | 0.644728i | \(0.223029\pi\) | ||||
−0.764412 | + | 0.644728i | \(0.776971\pi\) | |||||||
\(972\) | −100.941 | −0.103849 | ||||||||
\(973\) | 185.320i | 0.190462i | ||||||||
\(974\) | 83.3476 | 0.0855725 | ||||||||
\(975\) | 98.2045 | 0.100723 | ||||||||
\(976\) | 3.35388i | 0.00343635i | ||||||||
\(977\) | − | 379.765i | − | 0.388705i | −0.980932 | − | 0.194353i | \(-0.937739\pi\) | ||
0.980932 | − | 0.194353i | \(-0.0622606\pi\) | |||||||
\(978\) | 979.796 | 1.00184 | ||||||||
\(979\) | −505.743 | −0.516592 | ||||||||
\(980\) | 209.349i | 0.213621i | ||||||||
\(981\) | − | 111.470i | − | 0.113629i | ||||||
\(982\) | −2247.70 | −2.28890 | ||||||||
\(983\) | − | 824.188i | − | 0.838442i | −0.907884 | − | 0.419221i | \(-0.862303\pi\) | ||
0.907884 | − | 0.419221i | \(-0.137697\pi\) | |||||||
\(984\) | −1036.80 | −1.05366 | ||||||||
\(985\) | 652.870i | 0.662813i | ||||||||
\(986\) | − | 227.663i | − | 0.230896i | ||||||
\(987\) | − | 246.465i | − | 0.249711i | ||||||
\(988\) | − | 1520.70i | − | 1.53917i | ||||||
\(989\) | −31.9431 | − | 52.2938i | −0.0322984 | − | 0.0528755i | ||||
\(990\) | −131.421 | −0.132749 | ||||||||
\(991\) | −213.523 | −0.215462 | −0.107731 | − | 0.994180i | \(-0.534359\pi\) | ||||
−0.107731 | + | 0.994180i | \(0.534359\pi\) | |||||||
\(992\) | −297.427 | −0.299826 | ||||||||
\(993\) | 692.377 | 0.697258 | ||||||||
\(994\) | 133.276i | 0.134081i | ||||||||
\(995\) | −673.239 | −0.676622 | ||||||||
\(996\) | − | 616.077i | − | 0.618552i | ||||||
\(997\) | −257.640 | −0.258415 | −0.129207 | − | 0.991618i | \(-0.541243\pi\) | ||||
−0.129207 | + | 0.991618i | \(0.541243\pi\) | |||||||
\(998\) | −2612.95 | −2.61819 | ||||||||
\(999\) | 160.433i | 0.160593i |
(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.22.8 | yes | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.7 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.7 | ✓ | 48 | 23.22 | odd | 2 | inner | |
483.3.f.a.22.8 | yes | 48 | 1.1 | even | 1 | trivial |