Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(626,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.626");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 626.10 | ||
Character | \(\chi\) | \(=\) | 1045.626 |
Dual form | 1045.2.f.b.626.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.83534 | −1.29778 | −0.648892 | − | 0.760880i | \(-0.724767\pi\) | ||||
−0.648892 | + | 0.760880i | \(0.724767\pi\) | |||||||
\(3\) | − | 0.556027i | − | 0.321023i | −0.987034 | − | 0.160511i | \(-0.948686\pi\) | ||
0.987034 | − | 0.160511i | \(-0.0513143\pi\) | |||||||
\(4\) | 1.36849 | 0.684245 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.02050i | 0.416618i | ||||||||
\(7\) | 4.08954i | 1.54570i | 0.634589 | + | 0.772850i | \(0.281170\pi\) | ||||
−0.634589 | + | 0.772850i | \(0.718830\pi\) | |||||||
\(8\) | 1.15904 | 0.409782 | ||||||||
\(9\) | 2.69083 | 0.896945 | ||||||||
\(10\) | −1.83534 | −0.580387 | ||||||||
\(11\) | 2.99061 | + | 1.43396i | 0.901704 | + | 0.432354i | ||||
\(12\) | − | 0.760918i | − | 0.219658i | ||||||
\(13\) | 5.36672 | 1.48846 | 0.744231 | − | 0.667923i | \(-0.232816\pi\) | ||||
0.744231 | + | 0.667923i | \(0.232816\pi\) | |||||||
\(14\) | − | 7.50571i | − | 2.00599i | ||||||
\(15\) | − | 0.556027i | − | 0.143566i | ||||||
\(16\) | −4.86421 | −1.21605 | ||||||||
\(17\) | 5.36655i | 1.30158i | 0.759258 | + | 0.650790i | \(0.225562\pi\) | ||||
−0.759258 | + | 0.650790i | \(0.774438\pi\) | |||||||
\(18\) | −4.93861 | −1.16404 | ||||||||
\(19\) | 0.797318 | − | 4.28536i | 0.182917 | − | 0.983128i | ||||
\(20\) | 1.36849 | 0.306004 | ||||||||
\(21\) | 2.27389 | 0.496205 | ||||||||
\(22\) | −5.48881 | − | 2.63180i | −1.17022 | − | 0.561102i | ||||
\(23\) | −1.90493 | −0.397205 | −0.198603 | − | 0.980080i | \(-0.563640\pi\) | ||||
−0.198603 | + | 0.980080i | \(0.563640\pi\) | |||||||
\(24\) | − | 0.644456i | − | 0.131549i | ||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.84979 | −1.93170 | ||||||||
\(27\) | − | 3.16426i | − | 0.608962i | ||||||
\(28\) | 5.59649i | 1.05764i | ||||||||
\(29\) | −8.05184 | −1.49519 | −0.747595 | − | 0.664155i | \(-0.768792\pi\) | ||||
−0.747595 | + | 0.664155i | \(0.768792\pi\) | |||||||
\(30\) | 1.02050i | 0.186317i | ||||||||
\(31\) | 5.60442i | 1.00658i | 0.864117 | + | 0.503292i | \(0.167878\pi\) | ||||
−0.864117 | + | 0.503292i | \(0.832122\pi\) | |||||||
\(32\) | 6.60944 | 1.16839 | ||||||||
\(33\) | 0.797318 | − | 1.66286i | 0.138795 | − | 0.289467i | ||||
\(34\) | − | 9.84947i | − | 1.68917i | ||||||
\(35\) | 4.08954i | 0.691258i | ||||||||
\(36\) | 3.68238 | 0.613730 | ||||||||
\(37\) | 3.42346i | 0.562813i | 0.959589 | + | 0.281407i | \(0.0908010\pi\) | ||||
−0.959589 | + | 0.281407i | \(0.909199\pi\) | |||||||
\(38\) | −1.46335 | + | 7.86511i | −0.237387 | + | 1.27589i | ||||
\(39\) | − | 2.98404i | − | 0.477830i | ||||||
\(40\) | 1.15904 | 0.183260 | ||||||||
\(41\) | −9.21852 | −1.43969 | −0.719846 | − | 0.694134i | \(-0.755787\pi\) | ||||
−0.719846 | + | 0.694134i | \(0.755787\pi\) | |||||||
\(42\) | −4.17338 | −0.643967 | ||||||||
\(43\) | 6.62567i | 1.01041i | 0.863001 | + | 0.505203i | \(0.168582\pi\) | ||||
−0.863001 | + | 0.505203i | \(0.831418\pi\) | |||||||
\(44\) | 4.09263 | + | 1.96235i | 0.616987 | + | 0.295836i | ||||
\(45\) | 2.69083 | 0.401126 | ||||||||
\(46\) | 3.49620 | 0.515487 | ||||||||
\(47\) | 7.01016 | 1.02254 | 0.511268 | − | 0.859421i | \(-0.329176\pi\) | ||||
0.511268 | + | 0.859421i | \(0.329176\pi\) | |||||||
\(48\) | 2.70464i | 0.390381i | ||||||||
\(49\) | −9.72432 | −1.38919 | ||||||||
\(50\) | −1.83534 | −0.259557 | ||||||||
\(51\) | 2.98395 | 0.417836 | ||||||||
\(52\) | 7.34431 | 1.01847 | ||||||||
\(53\) | − | 7.74220i | − | 1.06347i | −0.846910 | − | 0.531736i | \(-0.821540\pi\) | ||
0.846910 | − | 0.531736i | \(-0.178460\pi\) | |||||||
\(54\) | 5.80751i | 0.790301i | ||||||||
\(55\) | 2.99061 | + | 1.43396i | 0.403254 | + | 0.193354i | ||||
\(56\) | 4.73993i | 0.633399i | ||||||||
\(57\) | −2.38278 | − | 0.443331i | −0.315606 | − | 0.0587206i | ||||
\(58\) | 14.7779 | 1.94043 | ||||||||
\(59\) | 3.01488i | 0.392504i | 0.980554 | + | 0.196252i | \(0.0628770\pi\) | ||||
−0.980554 | + | 0.196252i | \(0.937123\pi\) | |||||||
\(60\) | − | 0.760918i | − | 0.0982341i | ||||||
\(61\) | − | 7.25535i | − | 0.928953i | −0.885586 | − | 0.464476i | \(-0.846243\pi\) | ||
0.885586 | − | 0.464476i | \(-0.153757\pi\) | |||||||
\(62\) | − | 10.2860i | − | 1.30633i | ||||||
\(63\) | 11.0043i | 1.38641i | ||||||||
\(64\) | −2.40217 | −0.300271 | ||||||||
\(65\) | 5.36672 | 0.665660 | ||||||||
\(66\) | −1.46335 | + | 3.05193i | −0.180126 | + | 0.375666i | ||||
\(67\) | − | 6.53890i | − | 0.798854i | −0.916765 | − | 0.399427i | \(-0.869209\pi\) | ||
0.916765 | − | 0.399427i | \(-0.130791\pi\) | |||||||
\(68\) | 7.34407i | 0.890600i | ||||||||
\(69\) | 1.05919i | 0.127512i | ||||||||
\(70\) | − | 7.50571i | − | 0.897104i | ||||||
\(71\) | − | 0.908694i | − | 0.107842i | −0.998545 | − | 0.0539211i | \(-0.982828\pi\) | ||
0.998545 | − | 0.0539211i | \(-0.0171719\pi\) | |||||||
\(72\) | 3.11878 | 0.367551 | ||||||||
\(73\) | − | 9.46787i | − | 1.10813i | −0.832473 | − | 0.554065i | \(-0.813076\pi\) | ||
0.832473 | − | 0.554065i | \(-0.186924\pi\) | |||||||
\(74\) | − | 6.28323i | − | 0.730411i | ||||||
\(75\) | − | 0.556027i | − | 0.0642045i | ||||||
\(76\) | 1.09112 | − | 5.86447i | 0.125160 | − | 0.672701i | ||||
\(77\) | −5.86421 | + | 12.2302i | −0.668289 | + | 1.39376i | ||||
\(78\) | 5.47675i | 0.620120i | ||||||||
\(79\) | 9.42033 | 1.05987 | 0.529935 | − | 0.848038i | \(-0.322216\pi\) | ||||
0.529935 | + | 0.848038i | \(0.322216\pi\) | |||||||
\(80\) | −4.86421 | −0.543836 | ||||||||
\(81\) | 6.31309 | 0.701454 | ||||||||
\(82\) | 16.9192 | 1.86841 | ||||||||
\(83\) | − | 3.44016i | − | 0.377606i | −0.982015 | − | 0.188803i | \(-0.939539\pi\) | ||
0.982015 | − | 0.188803i | \(-0.0604608\pi\) | |||||||
\(84\) | 3.11180 | 0.339526 | ||||||||
\(85\) | 5.36655i | 0.582084i | ||||||||
\(86\) | − | 12.1604i | − | 1.31129i | ||||||
\(87\) | 4.47704i | 0.479990i | ||||||||
\(88\) | 3.46623 | + | 1.66201i | 0.369502 | + | 0.177171i | ||||
\(89\) | − | 6.38503i | − | 0.676812i | −0.941000 | − | 0.338406i | \(-0.890112\pi\) | ||
0.941000 | − | 0.338406i | \(-0.109888\pi\) | |||||||
\(90\) | −4.93861 | −0.520575 | ||||||||
\(91\) | 21.9474i | 2.30071i | ||||||||
\(92\) | −2.60688 | −0.271786 | ||||||||
\(93\) | 3.11621 | 0.323136 | ||||||||
\(94\) | −12.8661 | −1.32703 | ||||||||
\(95\) | 0.797318 | − | 4.28536i | 0.0818031 | − | 0.439668i | ||||
\(96\) | − | 3.67503i | − | 0.375081i | ||||||
\(97\) | 12.5270i | 1.27192i | 0.771720 | + | 0.635962i | \(0.219396\pi\) | ||||
−0.771720 | + | 0.635962i | \(0.780604\pi\) | |||||||
\(98\) | 17.8475 | 1.80287 | ||||||||
\(99\) | 8.04724 | + | 3.85854i | 0.808779 | + | 0.387797i | ||||
\(100\) | 1.36849 | 0.136849 | ||||||||
\(101\) | − | 19.3531i | − | 1.92571i | −0.270022 | − | 0.962854i | \(-0.587031\pi\) | ||
0.270022 | − | 0.962854i | \(-0.412969\pi\) | |||||||
\(102\) | −5.47657 | −0.542262 | ||||||||
\(103\) | 19.1440i | 1.88632i | 0.332343 | + | 0.943159i | \(0.392161\pi\) | ||||
−0.332343 | + | 0.943159i | \(0.607839\pi\) | |||||||
\(104\) | 6.22023 | 0.609944 | ||||||||
\(105\) | 2.27389 | 0.221909 | ||||||||
\(106\) | 14.2096i | 1.38016i | ||||||||
\(107\) | 2.16802 | 0.209590 | 0.104795 | − | 0.994494i | \(-0.466581\pi\) | ||||
0.104795 | + | 0.994494i | \(0.466581\pi\) | |||||||
\(108\) | − | 4.33026i | − | 0.416679i | ||||||
\(109\) | −15.5057 | −1.48518 | −0.742589 | − | 0.669747i | \(-0.766403\pi\) | ||||
−0.742589 | + | 0.669747i | \(0.766403\pi\) | |||||||
\(110\) | −5.48881 | − | 2.63180i | −0.523337 | − | 0.250933i | ||||
\(111\) | 1.90354 | 0.180676 | ||||||||
\(112\) | − | 19.8924i | − | 1.87965i | ||||||
\(113\) | 14.5570i | 1.36941i | 0.728820 | + | 0.684706i | \(0.240069\pi\) | ||||
−0.728820 | + | 0.684706i | \(0.759931\pi\) | |||||||
\(114\) | 4.37321 | + | 0.813665i | 0.409589 | + | 0.0762067i | ||||
\(115\) | −1.90493 | −0.177635 | ||||||||
\(116\) | −11.0189 | −1.02308 | ||||||||
\(117\) | 14.4410 | 1.33507 | ||||||||
\(118\) | − | 5.53334i | − | 0.509385i | ||||||
\(119\) | −21.9467 | −2.01185 | ||||||||
\(120\) | − | 0.644456i | − | 0.0588306i | ||||||
\(121\) | 6.88754 | + | 8.57681i | 0.626140 | + | 0.779710i | ||||
\(122\) | 13.3161i | 1.20558i | ||||||||
\(123\) | 5.12575i | 0.462173i | ||||||||
\(124\) | 7.66960i | 0.688750i | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | − | 20.1966i | − | 1.79926i | ||||||
\(127\) | 10.9929 | 0.975462 | 0.487731 | − | 0.872994i | \(-0.337825\pi\) | ||||
0.487731 | + | 0.872994i | \(0.337825\pi\) | |||||||
\(128\) | −8.81007 | −0.778708 | ||||||||
\(129\) | 3.68406 | 0.324363 | ||||||||
\(130\) | −9.84979 | −0.863884 | ||||||||
\(131\) | 7.82540i | 0.683708i | 0.939753 | + | 0.341854i | \(0.111055\pi\) | ||||
−0.939753 | + | 0.341854i | \(0.888945\pi\) | |||||||
\(132\) | 1.09112 | − | 2.27561i | 0.0949700 | − | 0.198067i | ||||
\(133\) | 17.5251 | + | 3.26066i | 1.51962 | + | 0.282735i | ||||
\(134\) | 12.0011i | 1.03674i | ||||||||
\(135\) | − | 3.16426i | − | 0.272336i | ||||||
\(136\) | 6.22003i | 0.533363i | ||||||||
\(137\) | −16.0753 | −1.37341 | −0.686705 | − | 0.726937i | \(-0.740943\pi\) | ||||
−0.686705 | + | 0.726937i | \(0.740943\pi\) | |||||||
\(138\) | − | 1.94398i | − | 0.165483i | ||||||
\(139\) | 14.9215i | 1.26562i | 0.774306 | + | 0.632811i | \(0.218099\pi\) | ||||
−0.774306 | + | 0.632811i | \(0.781901\pi\) | |||||||
\(140\) | 5.59649i | 0.472990i | ||||||||
\(141\) | − | 3.89784i | − | 0.328257i | ||||||
\(142\) | 1.66777i | 0.139956i | ||||||||
\(143\) | 16.0498 | + | 7.69564i | 1.34215 | + | 0.643542i | ||||
\(144\) | −13.0888 | −1.09073 | ||||||||
\(145\) | −8.05184 | −0.668669 | ||||||||
\(146\) | 17.3768i | 1.43812i | ||||||||
\(147\) | 5.40699i | 0.445961i | ||||||||
\(148\) | 4.68497i | 0.385102i | ||||||||
\(149\) | − | 6.23473i | − | 0.510769i | −0.966840 | − | 0.255384i | \(-0.917798\pi\) | ||
0.966840 | − | 0.255384i | \(-0.0822020\pi\) | |||||||
\(150\) | 1.02050i | 0.0833236i | ||||||||
\(151\) | 7.01213 | 0.570639 | 0.285319 | − | 0.958432i | \(-0.407900\pi\) | ||||
0.285319 | + | 0.958432i | \(0.407900\pi\) | |||||||
\(152\) | 0.924122 | − | 4.96689i | 0.0749562 | − | 0.402868i | ||||
\(153\) | 14.4405i | 1.16744i | ||||||||
\(154\) | 10.7629 | − | 22.4467i | 0.867296 | − | 1.80881i | ||||
\(155\) | 5.60442i | 0.450158i | ||||||||
\(156\) | − | 4.08364i | − | 0.326953i | ||||||
\(157\) | 9.47616 | 0.756280 | 0.378140 | − | 0.925749i | \(-0.376564\pi\) | ||||
0.378140 | + | 0.925749i | \(0.376564\pi\) | |||||||
\(158\) | −17.2895 | −1.37548 | ||||||||
\(159\) | −4.30487 | −0.341399 | ||||||||
\(160\) | 6.60944 | 0.522522 | ||||||||
\(161\) | − | 7.79028i | − | 0.613960i | ||||||
\(162\) | −11.5867 | −0.910336 | ||||||||
\(163\) | 1.79960 | 0.140956 | 0.0704778 | − | 0.997513i | \(-0.477548\pi\) | ||||
0.0704778 | + | 0.997513i | \(0.477548\pi\) | |||||||
\(164\) | −12.6155 | −0.985102 | ||||||||
\(165\) | 0.797318 | − | 1.66286i | 0.0620711 | − | 0.129454i | ||||
\(166\) | 6.31387i | 0.490051i | ||||||||
\(167\) | −16.2612 | −1.25833 | −0.629166 | − | 0.777271i | \(-0.716603\pi\) | ||||
−0.629166 | + | 0.777271i | \(0.716603\pi\) | |||||||
\(168\) | 2.63553 | 0.203335 | ||||||||
\(169\) | 15.8017 | 1.21552 | ||||||||
\(170\) | − | 9.84947i | − | 0.755420i | ||||||
\(171\) | 2.14545 | − | 11.5312i | 0.164067 | − | 0.881812i | ||||
\(172\) | 9.06717i | 0.691365i | ||||||||
\(173\) | 17.5756 | 1.33625 | 0.668123 | − | 0.744051i | \(-0.267098\pi\) | ||||
0.668123 | + | 0.744051i | \(0.267098\pi\) | |||||||
\(174\) | − | 8.21692i | − | 0.622923i | ||||||
\(175\) | 4.08954i | 0.309140i | ||||||||
\(176\) | −14.5470 | − | 6.97507i | −1.09652 | − | 0.525765i | ||||
\(177\) | 1.67635 | 0.126003 | ||||||||
\(178\) | 11.7187i | 0.878356i | ||||||||
\(179\) | − | 24.1500i | − | 1.80506i | −0.430632 | − | 0.902528i | \(-0.641709\pi\) | ||
0.430632 | − | 0.902528i | \(-0.358291\pi\) | |||||||
\(180\) | 3.68238 | 0.274468 | ||||||||
\(181\) | − | 12.2267i | − | 0.908804i | −0.890797 | − | 0.454402i | \(-0.849853\pi\) | ||
0.890797 | − | 0.454402i | \(-0.150147\pi\) | |||||||
\(182\) | − | 40.2811i | − | 2.98583i | ||||||
\(183\) | −4.03417 | −0.298215 | ||||||||
\(184\) | −2.20788 | −0.162767 | ||||||||
\(185\) | 3.42346i | 0.251698i | ||||||||
\(186\) | −5.71932 | −0.419361 | ||||||||
\(187\) | −7.69539 | + | 16.0493i | −0.562743 | + | 1.17364i | ||||
\(188\) | 9.59334 | 0.699666 | ||||||||
\(189\) | 12.9404 | 0.941272 | ||||||||
\(190\) | −1.46335 | + | 7.86511i | −0.106163 | + | 0.570595i | ||||
\(191\) | −2.74212 | −0.198413 | −0.0992065 | − | 0.995067i | \(-0.531630\pi\) | ||||
−0.0992065 | + | 0.995067i | \(0.531630\pi\) | |||||||
\(192\) | 1.33567i | 0.0963937i | ||||||||
\(193\) | −2.80307 | −0.201770 | −0.100885 | − | 0.994898i | \(-0.532167\pi\) | ||||
−0.100885 | + | 0.994898i | \(0.532167\pi\) | |||||||
\(194\) | − | 22.9914i | − | 1.65068i | ||||||
\(195\) | − | 2.98404i | − | 0.213692i | ||||||
\(196\) | −13.3076 | −0.950546 | ||||||||
\(197\) | − | 27.3376i | − | 1.94772i | −0.227140 | − | 0.973862i | \(-0.572938\pi\) | ||
0.227140 | − | 0.973862i | \(-0.427062\pi\) | |||||||
\(198\) | −14.7695 | − | 7.08174i | −1.04962 | − | 0.503278i | ||||
\(199\) | −10.9591 | −0.776872 | −0.388436 | − | 0.921476i | \(-0.626985\pi\) | ||||
−0.388436 | + | 0.921476i | \(0.626985\pi\) | |||||||
\(200\) | 1.15904 | 0.0819563 | ||||||||
\(201\) | −3.63581 | −0.256450 | ||||||||
\(202\) | 35.5197i | 2.49916i | ||||||||
\(203\) | − | 32.9283i | − | 2.31112i | ||||||
\(204\) | 4.08350 | 0.285903 | ||||||||
\(205\) | −9.21852 | −0.643849 | ||||||||
\(206\) | − | 35.1359i | − | 2.44803i | ||||||
\(207\) | −5.12585 | −0.356271 | ||||||||
\(208\) | −26.1049 | −1.81005 | ||||||||
\(209\) | 8.52948 | − | 11.6725i | 0.589997 | − | 0.807406i | ||||
\(210\) | −4.17338 | −0.287991 | ||||||||
\(211\) | 6.28757 | 0.432854 | 0.216427 | − | 0.976299i | \(-0.430560\pi\) | ||||
0.216427 | + | 0.976299i | \(0.430560\pi\) | |||||||
\(212\) | − | 10.5951i | − | 0.727676i | ||||||
\(213\) | −0.505258 | −0.0346197 | ||||||||
\(214\) | −3.97906 | −0.272003 | ||||||||
\(215\) | 6.62567i | 0.451867i | ||||||||
\(216\) | − | 3.66749i | − | 0.249541i | ||||||
\(217\) | −22.9195 | −1.55588 | ||||||||
\(218\) | 28.4583 | 1.92744 | ||||||||
\(219\) | −5.26440 | −0.355735 | ||||||||
\(220\) | 4.09263 | + | 1.96235i | 0.275925 | + | 0.132302i | ||||
\(221\) | 28.8008i | 1.93735i | ||||||||
\(222\) | −3.49365 | −0.234478 | ||||||||
\(223\) | 22.8453i | 1.52983i | 0.644130 | + | 0.764916i | \(0.277220\pi\) | ||||
−0.644130 | + | 0.764916i | \(0.722780\pi\) | |||||||
\(224\) | 27.0295i | 1.80599i | ||||||||
\(225\) | 2.69083 | 0.179389 | ||||||||
\(226\) | − | 26.7172i | − | 1.77720i | ||||||
\(227\) | −20.2532 | −1.34425 | −0.672126 | − | 0.740437i | \(-0.734619\pi\) | ||||
−0.672126 | + | 0.740437i | \(0.734619\pi\) | |||||||
\(228\) | −3.26081 | − | 0.606694i | −0.215952 | − | 0.0401793i | ||||
\(229\) | 8.42267 | 0.556586 | 0.278293 | − | 0.960496i | \(-0.410231\pi\) | ||||
0.278293 | + | 0.960496i | \(0.410231\pi\) | |||||||
\(230\) | 3.49620 | 0.230533 | ||||||||
\(231\) | 6.80034 | + | 3.26066i | 0.447430 | + | 0.214536i | ||||
\(232\) | −9.33239 | −0.612701 | ||||||||
\(233\) | 12.1491i | 0.795913i | 0.917404 | + | 0.397957i | \(0.130281\pi\) | ||||
−0.917404 | + | 0.397957i | \(0.869719\pi\) | |||||||
\(234\) | −26.5041 | −1.73263 | ||||||||
\(235\) | 7.01016 | 0.457292 | ||||||||
\(236\) | 4.12583i | 0.268569i | ||||||||
\(237\) | − | 5.23796i | − | 0.340242i | ||||||
\(238\) | 40.2798 | 2.61095 | ||||||||
\(239\) | 9.71140i | 0.628178i | 0.949394 | + | 0.314089i | \(0.101699\pi\) | ||||
−0.949394 | + | 0.314089i | \(0.898301\pi\) | |||||||
\(240\) | 2.70464i | 0.174584i | ||||||||
\(241\) | 10.4015 | 0.670022 | 0.335011 | − | 0.942214i | \(-0.391260\pi\) | ||||
0.335011 | + | 0.942214i | \(0.391260\pi\) | |||||||
\(242\) | −12.6410 | − | 15.7414i | −0.812596 | − | 1.01190i | ||||
\(243\) | − | 13.0030i | − | 0.834144i | ||||||
\(244\) | − | 9.92888i | − | 0.635632i | ||||||
\(245\) | −9.72432 | −0.621264 | ||||||||
\(246\) | − | 9.40752i | − | 0.599801i | ||||||
\(247\) | 4.27899 | − | 22.9983i | 0.272265 | − | 1.46335i | ||||
\(248\) | 6.49573i | 0.412479i | ||||||||
\(249\) | −1.91282 | −0.121220 | ||||||||
\(250\) | −1.83534 | −0.116077 | ||||||||
\(251\) | 14.3271 | 0.904316 | 0.452158 | − | 0.891938i | \(-0.350654\pi\) | ||||
0.452158 | + | 0.891938i | \(0.350654\pi\) | |||||||
\(252\) | 15.0592i | 0.948643i | ||||||||
\(253\) | −5.69691 | − | 2.73158i | −0.358161 | − | 0.171733i | ||||
\(254\) | −20.1758 | −1.26594 | ||||||||
\(255\) | 2.98395 | 0.186862 | ||||||||
\(256\) | 20.9738 | 1.31087 | ||||||||
\(257\) | 7.82897i | 0.488358i | 0.969730 | + | 0.244179i | \(0.0785184\pi\) | ||||
−0.969730 | + | 0.244179i | \(0.921482\pi\) | |||||||
\(258\) | −6.76151 | −0.420953 | ||||||||
\(259\) | −14.0004 | −0.869941 | ||||||||
\(260\) | 7.34431 | 0.455475 | ||||||||
\(261\) | −21.6662 | −1.34110 | ||||||||
\(262\) | − | 14.3623i | − | 0.887306i | ||||||
\(263\) | − | 4.23088i | − | 0.260887i | −0.991456 | − | 0.130444i | \(-0.958360\pi\) | ||
0.991456 | − | 0.130444i | \(-0.0416402\pi\) | |||||||
\(264\) | 0.924122 | − | 1.92732i | 0.0568758 | − | 0.118618i | ||||
\(265\) | − | 7.74220i | − | 0.475599i | ||||||
\(266\) | −32.1647 | − | 5.98444i | −1.97214 | − | 0.366930i | ||||
\(267\) | −3.55025 | −0.217272 | ||||||||
\(268\) | − | 8.94842i | − | 0.546612i | ||||||
\(269\) | − | 22.3455i | − | 1.36243i | −0.732083 | − | 0.681215i | \(-0.761452\pi\) | ||
0.732083 | − | 0.681215i | \(-0.238548\pi\) | |||||||
\(270\) | 5.80751i | 0.353434i | ||||||||
\(271\) | 14.8331i | 0.901044i | 0.892765 | + | 0.450522i | \(0.148762\pi\) | ||||
−0.892765 | + | 0.450522i | \(0.851238\pi\) | |||||||
\(272\) | − | 26.1040i | − | 1.58279i | ||||||
\(273\) | 12.2034 | 0.738581 | ||||||||
\(274\) | 29.5038 | 1.78239 | ||||||||
\(275\) | 2.99061 | + | 1.43396i | 0.180341 | + | 0.0864708i | ||||
\(276\) | 1.44949i | 0.0872493i | ||||||||
\(277\) | − | 19.4975i | − | 1.17149i | −0.810494 | − | 0.585747i | \(-0.800801\pi\) | ||
0.810494 | − | 0.585747i | \(-0.199199\pi\) | |||||||
\(278\) | − | 27.3860i | − | 1.64251i | ||||||
\(279\) | 15.0806i | 0.902850i | ||||||||
\(280\) | 4.73993i | 0.283265i | ||||||||
\(281\) | 20.7464 | 1.23763 | 0.618813 | − | 0.785538i | \(-0.287614\pi\) | ||||
0.618813 | + | 0.785538i | \(0.287614\pi\) | |||||||
\(282\) | 7.15388i | 0.426007i | ||||||||
\(283\) | 3.16295i | 0.188018i | 0.995571 | + | 0.0940088i | \(0.0299682\pi\) | ||||
−0.995571 | + | 0.0940088i | \(0.970032\pi\) | |||||||
\(284\) | − | 1.24354i | − | 0.0737905i | ||||||
\(285\) | −2.38278 | − | 0.443331i | −0.141143 | − | 0.0262606i | ||||
\(286\) | −29.4569 | − | 14.1242i | −1.74182 | − | 0.835179i | ||||
\(287\) | − | 37.6995i | − | 2.22533i | ||||||
\(288\) | 17.7849 | 1.04798 | ||||||||
\(289\) | −11.7999 | −0.694109 | ||||||||
\(290\) | 14.7779 | 0.867789 | ||||||||
\(291\) | 6.96535 | 0.408316 | ||||||||
\(292\) | − | 12.9567i | − | 0.758233i | ||||||
\(293\) | −13.1728 | −0.769561 | −0.384780 | − | 0.923008i | \(-0.625723\pi\) | ||||
−0.384780 | + | 0.923008i | \(0.625723\pi\) | |||||||
\(294\) | − | 9.92369i | − | 0.578761i | ||||||
\(295\) | 3.01488i | 0.175533i | ||||||||
\(296\) | 3.96792i | 0.230631i | ||||||||
\(297\) | 4.53741 | − | 9.46308i | 0.263287 | − | 0.549103i | ||||
\(298\) | 11.4429i | 0.662868i | ||||||||
\(299\) | −10.2232 | −0.591224 | ||||||||
\(300\) | − | 0.760918i | − | 0.0439316i | ||||||
\(301\) | −27.0959 | −1.56178 | ||||||||
\(302\) | −12.8697 | −0.740567 | ||||||||
\(303\) | −10.7609 | −0.618196 | ||||||||
\(304\) | −3.87833 | + | 20.8449i | −0.222437 | + | 1.19554i | ||||
\(305\) | − | 7.25535i | − | 0.415440i | ||||||
\(306\) | − | 26.5033i | − | 1.51509i | ||||||
\(307\) | 25.5176 | 1.45637 | 0.728184 | − | 0.685382i | \(-0.240365\pi\) | ||||
0.728184 | + | 0.685382i | \(0.240365\pi\) | |||||||
\(308\) | −8.02512 | + | 16.7370i | −0.457274 | + | 0.953677i | ||||
\(309\) | 10.6446 | 0.605550 | ||||||||
\(310\) | − | 10.2860i | − | 0.584208i | ||||||
\(311\) | 2.64178 | 0.149802 | 0.0749009 | − | 0.997191i | \(-0.476136\pi\) | ||||
0.0749009 | + | 0.997191i | \(0.476136\pi\) | |||||||
\(312\) | − | 3.45862i | − | 0.195806i | ||||||
\(313\) | −22.5891 | −1.27681 | −0.638406 | − | 0.769700i | \(-0.720406\pi\) | ||||
−0.638406 | + | 0.769700i | \(0.720406\pi\) | |||||||
\(314\) | −17.3920 | −0.981488 | ||||||||
\(315\) | 11.0043i | 0.620020i | ||||||||
\(316\) | 12.8916 | 0.725211 | ||||||||
\(317\) | − | 9.60819i | − | 0.539650i | −0.962909 | − | 0.269825i | \(-0.913034\pi\) | ||
0.962909 | − | 0.269825i | \(-0.0869658\pi\) | |||||||
\(318\) | 7.90093 | 0.443062 | ||||||||
\(319\) | −24.0800 | − | 11.5460i | −1.34822 | − | 0.646451i | ||||
\(320\) | −2.40217 | −0.134285 | ||||||||
\(321\) | − | 1.20548i | − | 0.0672831i | ||||||
\(322\) | 14.2978i | 0.796788i | ||||||||
\(323\) | 22.9976 | + | 4.27885i | 1.27962 | + | 0.238081i | ||||
\(324\) | 8.63940 | 0.479967 | ||||||||
\(325\) | 5.36672 | 0.297692 | ||||||||
\(326\) | −3.30289 | −0.182930 | ||||||||
\(327\) | 8.62160i | 0.476776i | ||||||||
\(328\) | −10.6846 | −0.589959 | ||||||||
\(329\) | 28.6683i | 1.58053i | ||||||||
\(330\) | −1.46335 | + | 3.05193i | −0.0805550 | + | 0.168003i | ||||
\(331\) | − | 18.3796i | − | 1.01023i | −0.863051 | − | 0.505116i | \(-0.831450\pi\) | ||
0.863051 | − | 0.505116i | \(-0.168550\pi\) | |||||||
\(332\) | − | 4.70782i | − | 0.258375i | ||||||
\(333\) | 9.21196i | 0.504812i | ||||||||
\(334\) | 29.8450 | 1.63304 | ||||||||
\(335\) | − | 6.53890i | − | 0.357258i | ||||||
\(336\) | −11.0607 | −0.603411 | ||||||||
\(337\) | 16.8472 | 0.917727 | 0.458863 | − | 0.888507i | \(-0.348257\pi\) | ||||
0.458863 | + | 0.888507i | \(0.348257\pi\) | |||||||
\(338\) | −29.0016 | −1.57748 | ||||||||
\(339\) | 8.09411 | 0.439612 | ||||||||
\(340\) | 7.34407i | 0.398288i | ||||||||
\(341\) | −8.03649 | + | 16.7607i | −0.435200 | + | 0.907640i | ||||
\(342\) | −3.93764 | + | 21.1637i | −0.212923 | + | 1.14440i | ||||
\(343\) | − | 11.1412i | − | 0.601569i | ||||||
\(344\) | 7.67940i | 0.414046i | ||||||||
\(345\) | 1.05919i | 0.0570250i | ||||||||
\(346\) | −32.2572 | −1.73416 | ||||||||
\(347\) | 13.4799i | 0.723641i | 0.932248 | + | 0.361820i | \(0.117845\pi\) | ||||
−0.932248 | + | 0.361820i | \(0.882155\pi\) | |||||||
\(348\) | 6.12679i | 0.328431i | ||||||||
\(349\) | − | 17.8479i | − | 0.955376i | −0.878530 | − | 0.477688i | \(-0.841475\pi\) | ||
0.878530 | − | 0.477688i | \(-0.158525\pi\) | |||||||
\(350\) | − | 7.50571i | − | 0.401197i | ||||||
\(351\) | − | 16.9817i | − | 0.906416i | ||||||
\(352\) | 19.7663 | + | 9.47764i | 1.05355 | + | 0.505160i | ||||
\(353\) | 8.97800 | 0.477851 | 0.238925 | − | 0.971038i | \(-0.423205\pi\) | ||||
0.238925 | + | 0.971038i | \(0.423205\pi\) | |||||||
\(354\) | −3.07669 | −0.163524 | ||||||||
\(355\) | − | 0.908694i | − | 0.0482285i | ||||||
\(356\) | − | 8.73786i | − | 0.463105i | ||||||
\(357\) | 12.2030i | 0.645850i | ||||||||
\(358\) | 44.3236i | 2.34257i | ||||||||
\(359\) | − | 6.55754i | − | 0.346094i | −0.984914 | − | 0.173047i | \(-0.944639\pi\) | ||
0.984914 | − | 0.173047i | \(-0.0553612\pi\) | |||||||
\(360\) | 3.11878 | 0.164374 | ||||||||
\(361\) | −17.7286 | − | 6.83359i | −0.933082 | − | 0.359662i | ||||
\(362\) | 22.4402i | 1.17943i | ||||||||
\(363\) | 4.76894 | − | 3.82966i | 0.250305 | − | 0.201005i | ||||
\(364\) | 30.0348i | 1.57425i | ||||||||
\(365\) | − | 9.46787i | − | 0.495571i | ||||||
\(366\) | 7.40410 | 0.387019 | ||||||||
\(367\) | 7.89395 | 0.412061 | 0.206030 | − | 0.978546i | \(-0.433945\pi\) | ||||
0.206030 | + | 0.978546i | \(0.433945\pi\) | |||||||
\(368\) | 9.26598 | 0.483023 | ||||||||
\(369\) | −24.8055 | −1.29132 | ||||||||
\(370\) | − | 6.28323i | − | 0.326650i | ||||||
\(371\) | 31.6620 | 1.64381 | ||||||||
\(372\) | 4.26450 | 0.221104 | ||||||||
\(373\) | −8.28038 | −0.428742 | −0.214371 | − | 0.976752i | \(-0.568770\pi\) | ||||
−0.214371 | + | 0.976752i | \(0.568770\pi\) | |||||||
\(374\) | 14.1237 | − | 29.4560i | 0.730319 | − | 1.52313i | ||||
\(375\) | − | 0.556027i | − | 0.0287131i | ||||||
\(376\) | 8.12503 | 0.419017 | ||||||||
\(377\) | −43.2120 | −2.22553 | ||||||||
\(378\) | −23.7500 | −1.22157 | ||||||||
\(379\) | − | 2.52457i | − | 0.129679i | −0.997896 | − | 0.0648393i | \(-0.979347\pi\) | ||
0.997896 | − | 0.0648393i | \(-0.0206535\pi\) | |||||||
\(380\) | 1.09112 | − | 5.86447i | 0.0559734 | − | 0.300841i | ||||
\(381\) | − | 6.11235i | − | 0.313145i | ||||||
\(382\) | 5.03274 | 0.257497 | ||||||||
\(383\) | − | 1.62674i | − | 0.0831225i | −0.999136 | − | 0.0415613i | \(-0.986767\pi\) | ||
0.999136 | − | 0.0415613i | \(-0.0132332\pi\) | |||||||
\(384\) | 4.89864i | 0.249983i | ||||||||
\(385\) | −5.86421 | + | 12.2302i | −0.298868 | + | 0.623310i | ||||
\(386\) | 5.14461 | 0.261854 | ||||||||
\(387\) | 17.8286i | 0.906278i | ||||||||
\(388\) | 17.1431i | 0.870308i | ||||||||
\(389\) | 1.52255 | 0.0771964 | 0.0385982 | − | 0.999255i | \(-0.487711\pi\) | ||||
0.0385982 | + | 0.999255i | \(0.487711\pi\) | |||||||
\(390\) | 5.47675i | 0.277326i | ||||||||
\(391\) | − | 10.2229i | − | 0.516994i | ||||||
\(392\) | −11.2709 | −0.569264 | ||||||||
\(393\) | 4.35113 | 0.219486 | ||||||||
\(394\) | 50.1739i | 2.52773i | ||||||||
\(395\) | 9.42033 | 0.473988 | ||||||||
\(396\) | 11.0126 | + | 5.28037i | 0.553403 | + | 0.265349i | ||||
\(397\) | 26.5187 | 1.33093 | 0.665467 | − | 0.746427i | \(-0.268232\pi\) | ||||
0.665467 | + | 0.746427i | \(0.268232\pi\) | |||||||
\(398\) | 20.1138 | 1.00821 | ||||||||
\(399\) | 1.81302 | − | 9.74445i | 0.0907644 | − | 0.487833i | ||||
\(400\) | −4.86421 | −0.243211 | ||||||||
\(401\) | − | 0.583132i | − | 0.0291202i | −0.999894 | − | 0.0145601i | \(-0.995365\pi\) | ||
0.999894 | − | 0.0145601i | \(-0.00463479\pi\) | |||||||
\(402\) | 6.67296 | 0.332817 | ||||||||
\(403\) | 30.0774i | 1.49826i | ||||||||
\(404\) | − | 26.4846i | − | 1.31766i | ||||||
\(405\) | 6.31309 | 0.313700 | ||||||||
\(406\) | 60.4348i | 2.99933i | ||||||||
\(407\) | −4.90909 | + | 10.2382i | −0.243335 | + | 0.507491i | ||||
\(408\) | 3.45851 | 0.171222 | ||||||||
\(409\) | −7.96701 | −0.393943 | −0.196972 | − | 0.980409i | \(-0.563111\pi\) | ||||
−0.196972 | + | 0.980409i | \(0.563111\pi\) | |||||||
\(410\) | 16.9192 | 0.835578 | ||||||||
\(411\) | 8.93833i | 0.440895i | ||||||||
\(412\) | 26.1984i | 1.29070i | ||||||||
\(413\) | −12.3295 | −0.606693 | ||||||||
\(414\) | 9.40769 | 0.462363 | ||||||||
\(415\) | − | 3.44016i | − | 0.168871i | ||||||
\(416\) | 35.4710 | 1.73911 | ||||||||
\(417\) | 8.29674 | 0.406293 | ||||||||
\(418\) | −15.6545 | + | 21.4231i | −0.765689 | + | 1.04784i | ||||
\(419\) | −2.93792 | −0.143527 | −0.0717634 | − | 0.997422i | \(-0.522863\pi\) | ||||
−0.0717634 | + | 0.997422i | \(0.522863\pi\) | |||||||
\(420\) | 3.11180 | 0.151840 | ||||||||
\(421\) | 3.30643i | 0.161146i | 0.996749 | + | 0.0805728i | \(0.0256749\pi\) | ||||
−0.996749 | + | 0.0805728i | \(0.974325\pi\) | |||||||
\(422\) | −11.5399 | −0.561752 | ||||||||
\(423\) | 18.8632 | 0.917159 | ||||||||
\(424\) | − | 8.97350i | − | 0.435792i | ||||||
\(425\) | 5.36655i | 0.260316i | ||||||||
\(426\) | 0.927324 | 0.0449290 | ||||||||
\(427\) | 29.6710 | 1.43588 | ||||||||
\(428\) | 2.96691 | 0.143411 | ||||||||
\(429\) | 4.27899 | − | 8.92413i | 0.206591 | − | 0.430861i | ||||
\(430\) | − | 12.1604i | − | 0.586426i | ||||||
\(431\) | 9.10067 | 0.438364 | 0.219182 | − | 0.975684i | \(-0.429661\pi\) | ||||
0.219182 | + | 0.975684i | \(0.429661\pi\) | |||||||
\(432\) | 15.3916i | 0.740530i | ||||||||
\(433\) | − | 36.6982i | − | 1.76360i | −0.471621 | − | 0.881801i | \(-0.656331\pi\) | ||
0.471621 | − | 0.881801i | \(-0.343669\pi\) | |||||||
\(434\) | 42.0652 | 2.01919 | ||||||||
\(435\) | 4.47704i | 0.214658i | ||||||||
\(436\) | −21.2194 | −1.01623 | ||||||||
\(437\) | −1.51883 | + | 8.16330i | −0.0726557 | + | 0.390503i | ||||
\(438\) | 9.66198 | 0.461667 | ||||||||
\(439\) | 32.3779 | 1.54531 | 0.772657 | − | 0.634824i | \(-0.218927\pi\) | ||||
0.772657 | + | 0.634824i | \(0.218927\pi\) | |||||||
\(440\) | 3.46623 | + | 1.66201i | 0.165246 | + | 0.0792331i | ||||
\(441\) | −26.1665 | −1.24603 | ||||||||
\(442\) | − | 52.8594i | − | 2.51426i | ||||||
\(443\) | −29.7753 | −1.41467 | −0.707333 | − | 0.706880i | \(-0.750102\pi\) | ||||
−0.707333 | + | 0.706880i | \(0.750102\pi\) | |||||||
\(444\) | 2.60497 | 0.123627 | ||||||||
\(445\) | − | 6.38503i | − | 0.302680i | ||||||
\(446\) | − | 41.9290i | − | 1.98539i | ||||||
\(447\) | −3.46668 | −0.163968 | ||||||||
\(448\) | − | 9.82375i | − | 0.464128i | ||||||
\(449\) | 21.3178i | 1.00605i | 0.864273 | + | 0.503023i | \(0.167779\pi\) | ||||
−0.864273 | + | 0.503023i | \(0.832221\pi\) | |||||||
\(450\) | −4.93861 | −0.232808 | ||||||||
\(451\) | −27.5690 | − | 13.2189i | −1.29818 | − | 0.622456i | ||||
\(452\) | 19.9212i | 0.937014i | ||||||||
\(453\) | − | 3.89894i | − | 0.183188i | ||||||
\(454\) | 37.1716 | 1.74455 | ||||||||
\(455\) | 21.9474i | 1.02891i | ||||||||
\(456\) | −2.76173 | − | 0.513837i | −0.129330 | − | 0.0240626i | ||||
\(457\) | 2.19241i | 0.102557i | 0.998684 | + | 0.0512783i | \(0.0163296\pi\) | ||||
−0.998684 | + | 0.0512783i | \(0.983670\pi\) | |||||||
\(458\) | −15.4585 | −0.722329 | ||||||||
\(459\) | 16.9812 | 0.792612 | ||||||||
\(460\) | −2.60688 | −0.121546 | ||||||||
\(461\) | 0.666820i | 0.0310569i | 0.999879 | + | 0.0155285i | \(0.00494306\pi\) | ||||
−0.999879 | + | 0.0155285i | \(0.995057\pi\) | |||||||
\(462\) | −12.4810 | − | 5.98444i | −0.580667 | − | 0.278421i | ||||
\(463\) | 7.79469 | 0.362250 | 0.181125 | − | 0.983460i | \(-0.442026\pi\) | ||||
0.181125 | + | 0.983460i | \(0.442026\pi\) | |||||||
\(464\) | 39.1659 | 1.81823 | ||||||||
\(465\) | 3.11621 | 0.144511 | ||||||||
\(466\) | − | 22.2978i | − | 1.03292i | ||||||
\(467\) | 12.3550 | 0.571720 | 0.285860 | − | 0.958271i | \(-0.407721\pi\) | ||||
0.285860 | + | 0.958271i | \(0.407721\pi\) | |||||||
\(468\) | 19.7623 | 0.913513 | ||||||||
\(469\) | 26.7411 | 1.23479 | ||||||||
\(470\) | −12.8661 | −0.593467 | ||||||||
\(471\) | − | 5.26900i | − | 0.242783i | ||||||
\(472\) | 3.49436i | 0.160841i | ||||||||
\(473\) | −9.50092 | + | 19.8148i | −0.436853 | + | 0.911087i | ||||
\(474\) | 9.61346i | 0.441561i | ||||||||
\(475\) | 0.797318 | − | 4.28536i | 0.0365835 | − | 0.196626i | ||||
\(476\) | −30.0339 | −1.37660 | ||||||||
\(477\) | − | 20.8330i | − | 0.953876i | ||||||
\(478\) | − | 17.8238i | − | 0.815240i | ||||||
\(479\) | − | 12.7066i | − | 0.580581i | −0.956939 | − | 0.290290i | \(-0.906248\pi\) | ||
0.956939 | − | 0.290290i | \(-0.0937519\pi\) | |||||||
\(480\) | − | 3.67503i | − | 0.167741i | ||||||
\(481\) | 18.3728i | 0.837726i | ||||||||
\(482\) | −19.0904 | −0.869545 | ||||||||
\(483\) | −4.33161 | −0.197095 | ||||||||
\(484\) | 9.42554 | + | 11.7373i | 0.428434 | + | 0.533513i | ||||
\(485\) | 12.5270i | 0.568822i | ||||||||
\(486\) | 23.8650i | 1.08254i | ||||||||
\(487\) | − | 1.56912i | − | 0.0711038i | −0.999368 | − | 0.0355519i | \(-0.988681\pi\) | ||
0.999368 | − | 0.0355519i | \(-0.0113189\pi\) | |||||||
\(488\) | − | 8.40923i | − | 0.380668i | ||||||
\(489\) | − | 1.00063i | − | 0.0452499i | ||||||
\(490\) | 17.8475 | 0.806267 | ||||||||
\(491\) | 13.6611i | 0.616517i | 0.951303 | + | 0.308258i | \(0.0997461\pi\) | ||||
−0.951303 | + | 0.308258i | \(0.900254\pi\) | |||||||
\(492\) | 7.01454i | 0.316240i | ||||||||
\(493\) | − | 43.2106i | − | 1.94611i | ||||||
\(494\) | −7.85342 | + | 42.2099i | −0.353342 | + | 1.89911i | ||||
\(495\) | 8.04724 | + | 3.85854i | 0.361697 | + | 0.173428i | ||||
\(496\) | − | 27.2611i | − | 1.22406i | ||||||
\(497\) | 3.71614 | 0.166692 | ||||||||
\(498\) | 3.51068 | 0.157318 | ||||||||
\(499\) | 36.6887 | 1.64241 | 0.821205 | − | 0.570633i | \(-0.193302\pi\) | ||||
0.821205 | + | 0.570633i | \(0.193302\pi\) | |||||||
\(500\) | 1.36849 | 0.0612008 | ||||||||
\(501\) | 9.04169i | 0.403953i | ||||||||
\(502\) | −26.2951 | −1.17361 | ||||||||
\(503\) | − | 39.8719i | − | 1.77780i | −0.458102 | − | 0.888899i | \(-0.651471\pi\) | ||
0.458102 | − | 0.888899i | \(-0.348529\pi\) | |||||||
\(504\) | 12.7544i | 0.568124i | ||||||||
\(505\) | − | 19.3531i | − | 0.861203i | ||||||
\(506\) | 10.4558 | + | 5.01339i | 0.464816 | + | 0.222873i | ||||
\(507\) | − | 8.78619i | − | 0.390208i | ||||||
\(508\) | 15.0437 | 0.667456 | ||||||||
\(509\) | 11.2708i | 0.499571i | 0.968301 | + | 0.249786i | \(0.0803602\pi\) | ||||
−0.968301 | + | 0.249786i | \(0.919640\pi\) | |||||||
\(510\) | −5.47657 | −0.242507 | ||||||||
\(511\) | 38.7192 | 1.71284 | ||||||||
\(512\) | −20.8741 | −0.922514 | ||||||||
\(513\) | −13.5600 | − | 2.52292i | −0.598688 | − | 0.111390i | ||||
\(514\) | − | 14.3689i | − | 0.633783i | ||||||
\(515\) | 19.1440i | 0.843587i | ||||||||
\(516\) | 5.04160 | 0.221944 | ||||||||
\(517\) | 20.9647 | + | 10.0523i | 0.922025 | + | 0.442098i | ||||
\(518\) | 25.6955 | 1.12900 | ||||||||
\(519\) | − | 9.77249i | − | 0.428965i | ||||||
\(520\) | 6.22023 | 0.272775 | ||||||||
\(521\) | 10.8381i | 0.474825i | 0.971409 | + | 0.237413i | \(0.0762994\pi\) | ||||
−0.971409 | + | 0.237413i | \(0.923701\pi\) | |||||||
\(522\) | 39.7649 | 1.74046 | ||||||||
\(523\) | 8.09479 | 0.353960 | 0.176980 | − | 0.984214i | \(-0.443367\pi\) | ||||
0.176980 | + | 0.984214i | \(0.443367\pi\) | |||||||
\(524\) | 10.7090i | 0.467824i | ||||||||
\(525\) | 2.27389 | 0.0992409 | ||||||||
\(526\) | 7.76513i | 0.338576i | ||||||||
\(527\) | −30.0764 | −1.31015 | ||||||||
\(528\) | −3.87833 | + | 8.08852i | −0.168783 | + | 0.352008i | ||||
\(529\) | −19.3712 | −0.842228 | ||||||||
\(530\) | 14.2096i | 0.617226i | ||||||||
\(531\) | 8.11253i | 0.352054i | ||||||||
\(532\) | 23.9830 | + | 4.46219i | 1.03979 | + | 0.193460i | ||||
\(533\) | −49.4733 | −2.14292 | ||||||||
\(534\) | 6.51594 | 0.281972 | ||||||||
\(535\) | 2.16802 | 0.0937315 | ||||||||
\(536\) | − | 7.57883i | − | 0.327356i | ||||||
\(537\) | −13.4281 | −0.579463 | ||||||||
\(538\) | 41.0117i | 1.76814i | ||||||||
\(539\) | −29.0817 | − | 13.9442i | −1.25264 | − | 0.600621i | ||||
\(540\) | − | 4.33026i | − | 0.186345i | ||||||
\(541\) | 29.3769i | 1.26301i | 0.775371 | + | 0.631506i | \(0.217563\pi\) | ||||
−0.775371 | + | 0.631506i | \(0.782437\pi\) | |||||||
\(542\) | − | 27.2238i | − | 1.16936i | ||||||
\(543\) | −6.79838 | −0.291747 | ||||||||
\(544\) | 35.4699i | 1.52076i | ||||||||
\(545\) | −15.5057 | −0.664192 | ||||||||
\(546\) | −22.3974 | −0.958519 | ||||||||
\(547\) | −14.2016 | −0.607215 | −0.303608 | − | 0.952797i | \(-0.598191\pi\) | ||||
−0.303608 | + | 0.952797i | \(0.598191\pi\) | |||||||
\(548\) | −21.9990 | −0.939749 | ||||||||
\(549\) | − | 19.5229i | − | 0.833219i | ||||||
\(550\) | −5.48881 | − | 2.63180i | −0.234044 | − | 0.112220i | ||||
\(551\) | −6.41988 | + | 34.5050i | −0.273496 | + | 1.46996i | ||||
\(552\) | 1.22764i | 0.0522520i | ||||||||
\(553\) | 38.5248i | 1.63824i | ||||||||
\(554\) | 35.7847i | 1.52035i | ||||||||
\(555\) | 1.90354 | 0.0808007 | ||||||||
\(556\) | 20.4199i | 0.865996i | ||||||||
\(557\) | 38.6125i | 1.63606i | 0.575173 | + | 0.818032i | \(0.304935\pi\) | ||||
−0.575173 | + | 0.818032i | \(0.695065\pi\) | |||||||
\(558\) | − | 27.6780i | − | 1.17170i | ||||||
\(559\) | 35.5582i | 1.50395i | ||||||||
\(560\) | − | 19.8924i | − | 0.840607i | ||||||
\(561\) | 8.92384 | + | 4.27885i | 0.376765 | + | 0.180653i | ||||
\(562\) | −38.0768 | −1.60617 | ||||||||
\(563\) | −44.7052 | −1.88410 | −0.942049 | − | 0.335474i | \(-0.891104\pi\) | ||||
−0.942049 | + | 0.335474i | \(0.891104\pi\) | |||||||
\(564\) | − | 5.33416i | − | 0.224609i | ||||||
\(565\) | 14.5570i | 0.612420i | ||||||||
\(566\) | − | 5.80510i | − | 0.244006i | ||||||
\(567\) | 25.8176i | 1.08424i | ||||||||
\(568\) | − | 1.05321i | − | 0.0441917i | ||||||
\(569\) | 12.2282 | 0.512633 | 0.256316 | − | 0.966593i | \(-0.417491\pi\) | ||||
0.256316 | + | 0.966593i | \(0.417491\pi\) | |||||||
\(570\) | 4.37321 | + | 0.813665i | 0.183174 | + | 0.0340807i | ||||
\(571\) | − | 12.7770i | − | 0.534699i | −0.963600 | − | 0.267350i | \(-0.913852\pi\) | ||
0.963600 | − | 0.267350i | \(-0.0861479\pi\) | |||||||
\(572\) | 21.9640 | + | 10.5314i | 0.918361 | + | 0.440340i | ||||
\(573\) | 1.52469i | 0.0636950i | ||||||||
\(574\) | 69.1916i | 2.88800i | ||||||||
\(575\) | −1.90493 | −0.0794410 | ||||||||
\(576\) | −6.46383 | −0.269326 | ||||||||
\(577\) | −44.8565 | −1.86740 | −0.933700 | − | 0.358057i | \(-0.883439\pi\) | ||||
−0.933700 | + | 0.358057i | \(0.883439\pi\) | |||||||
\(578\) | 21.6568 | 0.900804 | ||||||||
\(579\) | 1.55859i | 0.0647726i | ||||||||
\(580\) | −11.0189 | −0.457534 | ||||||||
\(581\) | 14.0686 | 0.583666 | ||||||||
\(582\) | −12.7838 | −0.529907 | ||||||||
\(583\) | 11.1020 | − | 23.1539i | 0.459796 | − | 0.958938i | ||||
\(584\) | − | 10.9736i | − | 0.454092i | ||||||
\(585\) | 14.4410 | 0.597060 | ||||||||
\(586\) | 24.1766 | 0.998724 | ||||||||
\(587\) | 3.53027 | 0.145710 | 0.0728550 | − | 0.997343i | \(-0.476789\pi\) | ||||
0.0728550 | + | 0.997343i | \(0.476789\pi\) | |||||||
\(588\) | 7.39941i | 0.305147i | ||||||||
\(589\) | 24.0169 | + | 4.46851i | 0.989601 | + | 0.184122i | ||||
\(590\) | − | 5.53334i | − | 0.227804i | ||||||
\(591\) | −15.2005 | −0.625263 | ||||||||
\(592\) | − | 16.6524i | − | 0.684411i | ||||||
\(593\) | 3.72182i | 0.152837i | 0.997076 | + | 0.0764185i | \(0.0243485\pi\) | ||||
−0.997076 | + | 0.0764185i | \(0.975652\pi\) | |||||||
\(594\) | −8.32770 | + | 17.3680i | −0.341690 | + | 0.712618i | ||||
\(595\) | −21.9467 | −0.899727 | ||||||||
\(596\) | − | 8.53217i | − | 0.349491i | ||||||
\(597\) | 6.09358i | 0.249393i | ||||||||
\(598\) | 18.7631 | 0.767282 | ||||||||
\(599\) | − | 12.0519i | − | 0.492428i | −0.969216 | − | 0.246214i | \(-0.920813\pi\) | ||
0.969216 | − | 0.246214i | \(-0.0791866\pi\) | |||||||
\(600\) | − | 0.644456i | − | 0.0263098i | ||||||
\(601\) | 24.0531 | 0.981148 | 0.490574 | − | 0.871400i | \(-0.336787\pi\) | ||||
0.490574 | + | 0.871400i | \(0.336787\pi\) | |||||||
\(602\) | 49.7304 | 2.02686 | ||||||||
\(603\) | − | 17.5951i | − | 0.716527i | ||||||
\(604\) | 9.59603 | 0.390457 | ||||||||
\(605\) | 6.88754 | + | 8.57681i | 0.280019 | + | 0.348697i | ||||
\(606\) | 19.7499 | 0.802285 | ||||||||
\(607\) | 17.0902 | 0.693672 | 0.346836 | − | 0.937926i | \(-0.387256\pi\) | ||||
0.346836 | + | 0.937926i | \(0.387256\pi\) | |||||||
\(608\) | 5.26982 | − | 28.3238i | 0.213720 | − | 1.14868i | ||||
\(609\) | −18.3090 | −0.741920 | ||||||||
\(610\) | 13.3161i | 0.539152i | ||||||||
\(611\) | 37.6216 | 1.52201 | ||||||||
\(612\) | 19.7617i | 0.798818i | ||||||||
\(613\) | − | 45.1575i | − | 1.82389i | −0.410307 | − | 0.911947i | \(-0.634579\pi\) | ||
0.410307 | − | 0.911947i | \(-0.365421\pi\) | |||||||
\(614\) | −46.8337 | −1.89005 | ||||||||
\(615\) | 5.12575i | 0.206690i | ||||||||
\(616\) | −6.79684 | + | 14.1753i | −0.273853 | + | 0.571139i | ||||
\(617\) | 15.4937 | 0.623753 | 0.311877 | − | 0.950123i | \(-0.399042\pi\) | ||||
0.311877 | + | 0.950123i | \(0.399042\pi\) | |||||||
\(618\) | −19.5365 | −0.785874 | ||||||||
\(619\) | −23.4826 | −0.943847 | −0.471924 | − | 0.881639i | \(-0.656440\pi\) | ||||
−0.471924 | + | 0.881639i | \(0.656440\pi\) | |||||||
\(620\) | 7.66960i | 0.308018i | ||||||||
\(621\) | 6.02769i | 0.241883i | ||||||||
\(622\) | −4.84859 | −0.194411 | ||||||||
\(623\) | 26.1118 | 1.04615 | ||||||||
\(624\) | 14.5150i | 0.581066i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 41.4588 | 1.65703 | ||||||||
\(627\) | −6.49024 | − | 4.74262i | −0.259195 | − | 0.189402i | ||||
\(628\) | 12.9680 | 0.517481 | ||||||||
\(629\) | −18.3722 | −0.732546 | ||||||||
\(630\) | − | 20.1966i | − | 0.804653i | ||||||
\(631\) | 27.0277 | 1.07596 | 0.537979 | − | 0.842958i | \(-0.319188\pi\) | ||||
0.537979 | + | 0.842958i | \(0.319188\pi\) | |||||||
\(632\) | 10.9185 | 0.434315 | ||||||||
\(633\) | − | 3.49606i | − | 0.138956i | ||||||
\(634\) | 17.6343i | 0.700349i | ||||||||
\(635\) | 10.9929 | 0.436240 | ||||||||
\(636\) | −5.89118 | −0.233600 | ||||||||
\(637\) | −52.1877 | −2.06775 | ||||||||
\(638\) | 44.1950 | + | 21.1909i | 1.74970 | + | 0.838954i | ||||
\(639\) | − | 2.44514i | − | 0.0967284i | ||||||
\(640\) | −8.81007 | −0.348249 | ||||||||
\(641\) | 10.3415i | 0.408465i | 0.978922 | + | 0.204233i | \(0.0654699\pi\) | ||||
−0.978922 | + | 0.204233i | \(0.934530\pi\) | |||||||
\(642\) | 2.21246i | 0.0873190i | ||||||||
\(643\) | 32.8621 | 1.29596 | 0.647978 | − | 0.761659i | \(-0.275615\pi\) | ||||
0.647978 | + | 0.761659i | \(0.275615\pi\) | |||||||
\(644\) | − | 10.6609i | − | 0.420099i | ||||||
\(645\) | 3.68406 | 0.145060 | ||||||||
\(646\) | −42.2085 | − | 7.85316i | −1.66067 | − | 0.308978i | ||||
\(647\) | −2.08256 | −0.0818737 | −0.0409369 | − | 0.999162i | \(-0.513034\pi\) | ||||
−0.0409369 | + | 0.999162i | \(0.513034\pi\) | |||||||
\(648\) | 7.31710 | 0.287443 | ||||||||
\(649\) | −4.32320 | + | 9.01634i | −0.169700 | + | 0.353922i | ||||
\(650\) | −9.84979 | −0.386340 | ||||||||
\(651\) | 12.7439i | 0.499471i | ||||||||
\(652\) | 2.46274 | 0.0964482 | ||||||||
\(653\) | −25.5955 | −1.00163 | −0.500815 | − | 0.865555i | \(-0.666966\pi\) | ||||
−0.500815 | + | 0.865555i | \(0.666966\pi\) | |||||||
\(654\) | − | 15.8236i | − | 0.618752i | ||||||
\(655\) | 7.82540i | 0.305764i | ||||||||
\(656\) | 44.8409 | 1.75074 | ||||||||
\(657\) | − | 25.4765i | − | 0.993932i | ||||||
\(658\) | − | 52.6162i | − | 2.05119i | ||||||
\(659\) | −6.55507 | −0.255349 | −0.127675 | − | 0.991816i | \(-0.540751\pi\) | ||||
−0.127675 | + | 0.991816i | \(0.540751\pi\) | |||||||
\(660\) | 1.09112 | − | 2.27561i | 0.0424719 | − | 0.0885781i | ||||
\(661\) | − | 44.6883i | − | 1.73817i | −0.494660 | − | 0.869086i | \(-0.664707\pi\) | ||
0.494660 | − | 0.869086i | \(-0.335293\pi\) | |||||||
\(662\) | 33.7328i | 1.31106i | ||||||||
\(663\) | 16.0140 | 0.621933 | ||||||||
\(664\) | − | 3.98727i | − | 0.154736i | ||||||
\(665\) | 17.5251 | + | 3.26066i | 0.679595 | + | 0.126443i | ||||
\(666\) | − | 16.9071i | − | 0.655138i | ||||||
\(667\) | 15.3382 | 0.593897 | ||||||||
\(668\) | −22.2533 | −0.861008 | ||||||||
\(669\) | 12.7026 | 0.491111 | ||||||||
\(670\) | 12.0011i | 0.463644i | ||||||||
\(671\) | 10.4039 | − | 21.6980i | 0.401636 | − | 0.837640i | ||||
\(672\) | 15.0292 | 0.579763 | ||||||||
\(673\) | −21.4395 | −0.826432 | −0.413216 | − | 0.910633i | \(-0.635594\pi\) | ||||
−0.413216 | + | 0.910633i | \(0.635594\pi\) | |||||||
\(674\) | −30.9205 | −1.19101 | ||||||||
\(675\) | − | 3.16426i | − | 0.121792i | ||||||
\(676\) | 21.6245 | 0.831712 | ||||||||
\(677\) | −17.0149 | −0.653935 | −0.326968 | − | 0.945036i | \(-0.606027\pi\) | ||||
−0.326968 | + | 0.945036i | \(0.606027\pi\) | |||||||
\(678\) | −14.8555 | −0.570522 | ||||||||
\(679\) | −51.2296 | −1.96601 | ||||||||
\(680\) | 6.22003i | 0.238527i | ||||||||
\(681\) | 11.2613i | 0.431535i | ||||||||
\(682\) | 14.7497 | − | 30.7616i | 0.564796 | − | 1.17792i | ||||
\(683\) | 6.01886i | 0.230305i | 0.993348 | + | 0.115153i | \(0.0367357\pi\) | ||||
−0.993348 | + | 0.115153i | \(0.963264\pi\) | |||||||
\(684\) | 2.93603 | − | 15.7803i | 0.112262 | − | 0.603375i | ||||
\(685\) | −16.0753 | −0.614207 | ||||||||
\(686\) | 20.4480i | 0.780707i | ||||||||
\(687\) | − | 4.68324i | − | 0.178677i | ||||||
\(688\) | − | 32.2287i | − | 1.22871i | ||||||
\(689\) | − | 41.5502i | − | 1.58294i | ||||||
\(690\) | − | 1.94398i | − | 0.0740062i | ||||||
\(691\) | −51.1113 | −1.94436 | −0.972182 | − | 0.234226i | \(-0.924744\pi\) | ||||
−0.972182 | + | 0.234226i | \(0.924744\pi\) | |||||||
\(692\) | 24.0520 | 0.914320 | ||||||||
\(693\) | −15.7796 | + | 32.9095i | −0.599418 | + | 1.25013i | ||||
\(694\) | − | 24.7403i | − | 0.939130i | ||||||
\(695\) | 14.9215i | 0.566004i | ||||||||
\(696\) | 5.18906i | 0.196691i | ||||||||
\(697\) | − | 49.4717i | − | 1.87387i | ||||||
\(698\) | 32.7570i | 1.23987i | ||||||||
\(699\) | 6.75522 | 0.255506 | ||||||||
\(700\) | 5.59649i | 0.211528i | ||||||||
\(701\) | − | 6.49530i | − | 0.245324i | −0.992449 | − | 0.122662i | \(-0.960857\pi\) | ||
0.992449 | − | 0.122662i | \(-0.0391431\pi\) | |||||||
\(702\) | 31.1673i | 1.17633i | ||||||||
\(703\) | 14.6708 | + | 2.72959i | 0.553318 | + | 0.102948i | ||||
\(704\) | −7.18395 | − | 3.44460i | −0.270755 | − | 0.129823i | ||||
\(705\) | − | 3.89784i | − | 0.146801i | ||||||
\(706\) | −16.4777 | −0.620148 | ||||||||
\(707\) | 79.1454 | 2.97657 | ||||||||
\(708\) | 2.29408 | 0.0862166 | ||||||||
\(709\) | 4.65020 | 0.174642 | 0.0873209 | − | 0.996180i | \(-0.472169\pi\) | ||||
0.0873209 | + | 0.996180i | \(0.472169\pi\) | |||||||
\(710\) | 1.66777i | 0.0625902i | ||||||||
\(711\) | 25.3485 | 0.950644 | ||||||||
\(712\) | − | 7.40049i | − | 0.277345i | ||||||
\(713\) | − | 10.6760i | − | 0.399820i | ||||||
\(714\) | − | 22.3967i | − | 0.838174i | ||||||
\(715\) | 16.0498 | + | 7.69564i | 0.600228 | + | 0.287801i | ||||
\(716\) | − | 33.0490i | − | 1.23510i | ||||||
\(717\) | 5.39980 | 0.201659 | ||||||||
\(718\) | 12.0353i | 0.449155i | ||||||||
\(719\) | −14.4010 | −0.537066 | −0.268533 | − | 0.963271i | \(-0.586539\pi\) | ||||
−0.268533 | + | 0.963271i | \(0.586539\pi\) | |||||||
\(720\) | −13.0888 | −0.487790 | ||||||||
\(721\) | −78.2902 | −2.91568 | ||||||||
\(722\) | 32.5380 | + | 12.5420i | 1.21094 | + | 0.466764i | ||||
\(723\) | − | 5.78354i | − | 0.215092i | ||||||
\(724\) | − | 16.7321i | − | 0.621845i | ||||||
\(725\) | −8.05184 | −0.299038 | ||||||||
\(726\) | −8.75265 | + | 7.02875i | −0.324841 | + | 0.260861i | ||||
\(727\) | −6.68089 | −0.247781 | −0.123890 | − | 0.992296i | \(-0.539537\pi\) | ||||
−0.123890 | + | 0.992296i | \(0.539537\pi\) | |||||||
\(728\) | 25.4379i | 0.942791i | ||||||||
\(729\) | 11.7092 | 0.433675 | ||||||||
\(730\) | 17.3768i | 0.643145i | ||||||||
\(731\) | −35.5570 | −1.31512 | ||||||||
\(732\) | −5.52073 | −0.204052 | ||||||||
\(733\) | − | 16.2583i | − | 0.600514i | −0.953858 | − | 0.300257i | \(-0.902928\pi\) | ||
0.953858 | − | 0.300257i | \(-0.0970724\pi\) | |||||||
\(734\) | −14.4881 | −0.534766 | ||||||||
\(735\) | 5.40699i | 0.199440i | ||||||||
\(736\) | −12.5905 | −0.464092 | ||||||||
\(737\) | 9.37649 | − | 19.5553i | 0.345387 | − | 0.720330i | ||||
\(738\) | 45.5267 | 1.67586 | ||||||||
\(739\) | 20.5139i | 0.754616i | 0.926088 | + | 0.377308i | \(0.123150\pi\) | ||||
−0.926088 | + | 0.377308i | \(0.876850\pi\) | |||||||
\(740\) | 4.68497i | 0.172223i | ||||||||
\(741\) | −12.7877 | − | 2.37923i | −0.469768 | − | 0.0874033i | ||||
\(742\) | −58.1107 | −2.13331 | ||||||||
\(743\) | −6.96289 | −0.255444 | −0.127722 | − | 0.991810i | \(-0.540766\pi\) | ||||
−0.127722 | + | 0.991810i | \(0.540766\pi\) | |||||||
\(744\) | 3.61180 | 0.132415 | ||||||||
\(745\) | − | 6.23473i | − | 0.228423i | ||||||
\(746\) | 15.1974 | 0.556415 | ||||||||
\(747\) | − | 9.25689i | − | 0.338692i | ||||||
\(748\) | −10.5311 | + | 21.9633i | −0.385054 | + | 0.803057i | ||||
\(749\) | 8.86618i | 0.323963i | ||||||||
\(750\) | 1.02050i | 0.0372635i | ||||||||
\(751\) | − | 24.7078i | − | 0.901599i | −0.892625 | − | 0.450800i | \(-0.851139\pi\) | ||
0.892625 | − | 0.450800i | \(-0.148861\pi\) | |||||||
\(752\) | −34.0989 | −1.24346 | ||||||||
\(753\) | − | 7.96624i | − | 0.290306i | ||||||
\(754\) | 79.3090 | 2.88826 | ||||||||
\(755\) | 7.01213 | 0.255198 | ||||||||
\(756\) | 17.7088 | 0.644061 | ||||||||
\(757\) | 33.3132 | 1.21079 | 0.605395 | − | 0.795925i | \(-0.293015\pi\) | ||||
0.605395 | + | 0.795925i | \(0.293015\pi\) | |||||||
\(758\) | 4.63346i | 0.168295i | ||||||||
\(759\) | −1.51883 | + | 3.16763i | −0.0551302 | + | 0.114978i | ||||
\(760\) | 0.924122 | − | 4.96689i | 0.0335214 | − | 0.180168i | ||||
\(761\) | − | 28.7548i | − | 1.04236i | −0.853447 | − | 0.521180i | \(-0.825492\pi\) | ||
0.853447 | − | 0.521180i | \(-0.174508\pi\) | |||||||
\(762\) | 11.2183i | 0.406395i | ||||||||
\(763\) | − | 63.4112i | − | 2.29564i | ||||||
\(764\) | −3.75257 | −0.135763 | ||||||||
\(765\) | 14.4405i | 0.522097i | ||||||||
\(766\) | 2.98563i | 0.107875i | ||||||||
\(767\) | 16.1800i | 0.584226i | ||||||||
\(768\) | − | 11.6620i | − | 0.420817i | ||||||
\(769\) | 15.9549i | 0.575349i | 0.957728 | + | 0.287675i | \(0.0928822\pi\) | ||||
−0.957728 | + | 0.287675i | \(0.907118\pi\) | |||||||
\(770\) | 10.7629 | − | 22.4467i | 0.387866 | − | 0.808923i | ||||
\(771\) | 4.35312 | 0.156774 | ||||||||
\(772\) | −3.83598 | −0.138060 | ||||||||
\(773\) | 47.0295i | 1.69153i | 0.533553 | + | 0.845767i | \(0.320856\pi\) | ||||
−0.533553 | + | 0.845767i | \(0.679144\pi\) | |||||||
\(774\) | − | 32.7216i | − | 1.17615i | ||||||
\(775\) | 5.60442i | 0.201317i | ||||||||
\(776\) | 14.5193i | 0.521211i | ||||||||
\(777\) | 7.78459i | 0.279271i | ||||||||
\(778\) | −2.79441 | −0.100184 | ||||||||
\(779\) | −7.35010 | + | 39.5047i | −0.263345 | + | 1.41540i | ||||
\(780\) | − | 4.08364i | − | 0.146218i | ||||||
\(781\) | 1.30303 | − | 2.71755i | 0.0466259 | − | 0.0972417i | ||||
\(782\) | 18.7625i | 0.670947i | ||||||||
\(783\) | 25.4781i | 0.910514i | ||||||||
\(784\) | 47.3012 | 1.68933 | ||||||||
\(785\) | 9.47616 | 0.338219 | ||||||||
\(786\) | −7.98583 | −0.284845 | ||||||||
\(787\) | −26.7602 | −0.953899 | −0.476950 | − | 0.878931i | \(-0.658258\pi\) | ||||
−0.476950 | + | 0.878931i | \(0.658258\pi\) | |||||||
\(788\) | − | 37.4113i | − | 1.33272i | ||||||
\(789\) | −2.35249 | −0.0837507 | ||||||||
\(790\) | −17.2895 | −0.615135 | ||||||||
\(791\) | −59.5316 | −2.11670 | ||||||||
\(792\) | 9.32706 | + | 4.47219i | 0.331423 | + | 0.158912i | ||||
\(793\) | − | 38.9375i | − | 1.38271i | ||||||
\(794\) | −48.6709 | −1.72727 | ||||||||
\(795\) | −4.30487 | −0.152678 | ||||||||
\(796\) | −14.9975 | −0.531571 | ||||||||
\(797\) | − | 47.7999i | − | 1.69316i | −0.532262 | − | 0.846579i | \(-0.678658\pi\) | ||
0.532262 | − | 0.846579i | \(-0.321342\pi\) | |||||||
\(798\) | −3.32751 | + | 17.8844i | −0.117793 | + | 0.633102i | ||||
\(799\) | 37.6204i | 1.33091i | ||||||||
\(800\) | 6.60944 | 0.233679 | ||||||||
\(801\) | − | 17.1811i | − | 0.607063i | ||||||
\(802\) | 1.07025i | 0.0377918i | ||||||||
\(803\) | 13.5765 | − | 28.3148i | 0.479105 | − | 0.999206i | ||||
\(804\) | −4.97557 | −0.175475 | ||||||||
\(805\) | − | 7.79028i | − | 0.274571i | ||||||
\(806\) | − | 55.2023i | − | 1.94442i | ||||||
\(807\) | −12.4247 | −0.437371 | ||||||||
\(808\) | − | 22.4310i | − | 0.789120i | ||||||
\(809\) | − | 34.4405i | − | 1.21086i | −0.795897 | − | 0.605432i | \(-0.793000\pi\) | ||
0.795897 | − | 0.605432i | \(-0.207000\pi\) | |||||||
\(810\) | −11.5867 | −0.407115 | ||||||||
\(811\) | −28.9085 | −1.01511 | −0.507557 | − | 0.861618i | \(-0.669451\pi\) | ||||
−0.507557 | + | 0.861618i | \(0.669451\pi\) | |||||||
\(812\) | − | 45.0621i | − | 1.58137i | ||||||
\(813\) | 8.24759 | 0.289256 | ||||||||
\(814\) | 9.00987 | − | 18.7907i | 0.315796 | − | 0.658614i | ||||
\(815\) | 1.79960 | 0.0630372 | ||||||||
\(816\) | −14.5146 | −0.508111 | ||||||||
\(817\) | 28.3934 | + | 5.28277i | 0.993358 | + | 0.184821i | ||||
\(818\) | 14.6222 | 0.511254 | ||||||||
\(819\) | 59.0569i | 2.06361i | ||||||||
\(820\) | −12.6155 | −0.440551 | ||||||||
\(821\) | − | 2.02869i | − | 0.0708019i | −0.999373 | − | 0.0354009i | \(-0.988729\pi\) | ||
0.999373 | − | 0.0354009i | \(-0.0112708\pi\) | |||||||
\(822\) | − | 16.4049i | − | 0.572187i | ||||||
\(823\) | −21.2219 | −0.739750 | −0.369875 | − | 0.929081i | \(-0.620600\pi\) | ||||
−0.369875 | + | 0.929081i | \(0.620600\pi\) | |||||||
\(824\) | 22.1886i | 0.772978i | ||||||||
\(825\) | 0.797318 | − | 1.66286i | 0.0277591 | − | 0.0578935i | ||||
\(826\) | 22.6288 | 0.787357 | ||||||||
\(827\) | 18.2806 | 0.635679 | 0.317840 | − | 0.948144i | \(-0.397043\pi\) | ||||
0.317840 | + | 0.948144i | \(0.397043\pi\) | |||||||
\(828\) | −7.01467 | −0.243777 | ||||||||
\(829\) | 9.24614i | 0.321132i | 0.987025 | + | 0.160566i | \(0.0513319\pi\) | ||||
−0.987025 | + | 0.160566i | \(0.948668\pi\) | |||||||
\(830\) | 6.31387i | 0.219158i | ||||||||
\(831\) | −10.8412 | −0.376076 | ||||||||
\(832\) | −12.8918 | −0.446941 | ||||||||
\(833\) | − | 52.1861i | − | 1.80814i | ||||||
\(834\) | −15.2274 | −0.527281 | ||||||||
\(835\) | −16.2612 | −0.562743 | ||||||||
\(836\) | 11.6725 | − | 15.9737i | 0.403702 | − | 0.552464i | ||||
\(837\) | 17.7338 | 0.612971 | ||||||||
\(838\) | 5.39210 | 0.186267 | ||||||||
\(839\) | − | 51.4071i | − | 1.77477i | −0.461028 | − | 0.887386i | \(-0.652519\pi\) | ||
0.461028 | − | 0.887386i | \(-0.347481\pi\) | |||||||
\(840\) | 2.63553 | 0.0909344 | ||||||||
\(841\) | 35.8322 | 1.23559 | ||||||||
\(842\) | − | 6.06844i | − | 0.209132i | ||||||
\(843\) | − | 11.5356i | − | 0.397306i | ||||||
\(844\) | 8.60448 | 0.296178 | ||||||||
\(845\) | 15.8017 | 0.543596 | ||||||||
\(846\) | −34.6204 | −1.19027 | ||||||||
\(847\) | −35.0752 | + | 28.1669i | −1.20520 | + | 0.967825i | ||||
\(848\) | 37.6597i | 1.29324i | ||||||||
\(849\) | 1.75868 | 0.0603579 | ||||||||
\(850\) | − | 9.84947i | − | 0.337834i | ||||||
\(851\) | − | 6.52145i | − | 0.223552i | ||||||
\(852\) | −0.691442 | −0.0236884 | ||||||||
\(853\) | − | 27.7719i | − | 0.950890i | −0.879745 | − | 0.475445i | \(-0.842287\pi\) | ||
0.879745 | − | 0.475445i | \(-0.157713\pi\) | |||||||
\(854\) | −54.4566 | −1.86347 | ||||||||
\(855\) | 2.14545 | − | 11.5312i | 0.0733729 | − | 0.394358i | ||||
\(856\) | 2.51281 | 0.0858861 | ||||||||
\(857\) | −11.5029 | −0.392931 | −0.196465 | − | 0.980511i | \(-0.562946\pi\) | ||||
−0.196465 | + | 0.980511i | \(0.562946\pi\) | |||||||
\(858\) | −7.85342 | + | 16.3788i | −0.268111 | + | 0.559165i | ||||
\(859\) | −43.7925 | −1.49418 | −0.747090 | − | 0.664723i | \(-0.768550\pi\) | ||||
−0.747090 | + | 0.664723i | \(0.768550\pi\) | |||||||
\(860\) | 9.06717i | 0.309188i | ||||||||
\(861\) | −20.9619 | −0.714381 | ||||||||
\(862\) | −16.7029 | −0.568902 | ||||||||
\(863\) | − | 18.5796i | − | 0.632457i | −0.948683 | − | 0.316228i | \(-0.897583\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102417\pi\) | |||||||
\(864\) | − | 20.9140i | − | 0.711508i | ||||||
\(865\) | 17.5756 | 0.597587 | ||||||||
\(866\) | 67.3539i | 2.28878i | ||||||||
\(867\) | 6.56104i | 0.222825i | ||||||||
\(868\) | −31.3651 | −1.06460 | ||||||||
\(869\) | 28.1726 | + | 13.5083i | 0.955689 | + | 0.458239i | ||||
\(870\) | − | 8.21692i | − | 0.278580i | ||||||
\(871\) | − | 35.0925i | − | 1.18906i | ||||||
\(872\) | −17.9717 | −0.608599 | ||||||||
\(873\) | 33.7081i | 1.14085i | ||||||||
\(874\) | 2.78758 | − | 14.9825i | 0.0942914 | − | 0.506789i | ||||
\(875\) | 4.08954i | 0.138252i | ||||||||
\(876\) | −7.20428 | −0.243410 | ||||||||
\(877\) | 41.3037 | 1.39473 | 0.697364 | − | 0.716717i | \(-0.254356\pi\) | ||||
0.697364 | + | 0.716717i | \(0.254356\pi\) | |||||||
\(878\) | −59.4246 | −2.00548 | ||||||||
\(879\) | 7.32441i | 0.247046i | ||||||||
\(880\) | −14.5470 | − | 6.97507i | −0.490379 | − | 0.235129i | ||||
\(881\) | 11.1721 | 0.376399 | 0.188199 | − | 0.982131i | \(-0.439735\pi\) | ||||
0.188199 | + | 0.982131i | \(0.439735\pi\) | |||||||
\(882\) | 48.0246 | 1.61707 | ||||||||
\(883\) | −28.6532 | −0.964255 | −0.482128 | − | 0.876101i | \(-0.660136\pi\) | ||||
−0.482128 | + | 0.876101i | \(0.660136\pi\) | |||||||
\(884\) | 39.4136i | 1.32562i | ||||||||
\(885\) | 1.67635 | 0.0563500 | ||||||||
\(886\) | 54.6479 | 1.83593 | ||||||||
\(887\) | 49.6519 | 1.66715 | 0.833575 | − | 0.552407i | \(-0.186291\pi\) | ||||
0.833575 | + | 0.552407i | \(0.186291\pi\) | |||||||
\(888\) | 2.20627 | 0.0740376 | ||||||||
\(889\) | 44.9559i | 1.50777i | ||||||||
\(890\) | 11.7187i | 0.392813i | ||||||||
\(891\) | 18.8800 | + | 9.05268i | 0.632504 | + | 0.303276i | ||||
\(892\) | 31.2635i | 1.04678i | ||||||||
\(893\) | 5.58933 | − | 30.0410i | 0.187040 | − | 1.00528i | ||||
\(894\) | 6.36255 | 0.212796 | ||||||||
\(895\) | − | 24.1500i | − | 0.807245i | ||||||
\(896\) | − | 36.0291i | − | 1.20365i | ||||||
\(897\) | 5.68439i | 0.189796i | ||||||||
\(898\) | − | 39.1254i | − | 1.30563i | ||||||
\(899\) | − | 45.1259i | − | 1.50503i | ||||||
\(900\) | 3.68238 | 0.122746 | ||||||||
\(901\) | 41.5489 | 1.38419 | ||||||||
\(902\) | 50.5987 | + | 24.2613i | 1.68475 | + | 0.807814i | ||||
\(903\) | 15.0661i | 0.501368i | ||||||||
\(904\) | 16.8722i | 0.561160i | ||||||||
\(905\) | − | 12.2267i | − | 0.406429i | ||||||
\(906\) | 7.15589i | 0.237739i | ||||||||
\(907\) | 20.0790i | 0.666714i | 0.942801 | + | 0.333357i | \(0.108181\pi\) | ||||
−0.942801 | + | 0.333357i | \(0.891819\pi\) | |||||||
\(908\) | −27.7163 | −0.919798 | ||||||||
\(909\) | − | 52.0761i | − | 1.72725i | ||||||
\(910\) | − | 40.2811i | − | 1.33530i | ||||||
\(911\) | 40.9514i | 1.35678i | 0.734702 | + | 0.678390i | \(0.237322\pi\) | ||||
−0.734702 | + | 0.678390i | \(0.762678\pi\) | |||||||
\(912\) | 11.5903 | + | 2.15646i | 0.383794 | + | 0.0714074i | ||||
\(913\) | 4.93303 | − | 10.2882i | 0.163259 | − | 0.340489i | ||||
\(914\) | − | 4.02383i | − | 0.133096i | ||||||
\(915\) | −4.03417 | −0.133366 | ||||||||
\(916\) | 11.5264 | 0.380841 | ||||||||
\(917\) | −32.0023 | −1.05681 | ||||||||
\(918\) | −31.1663 | −1.02864 | ||||||||
\(919\) | − | 12.5429i | − | 0.413754i | −0.978367 | − | 0.206877i | \(-0.933670\pi\) | ||
0.978367 | − | 0.206877i | \(-0.0663299\pi\) | |||||||
\(920\) | −2.20788 | −0.0727917 | ||||||||
\(921\) | − | 14.1885i | − | 0.467527i | ||||||
\(922\) | − | 1.22385i | − | 0.0403052i | ||||||
\(923\) | − | 4.87671i | − | 0.160519i | ||||||
\(924\) | 9.30620 | + | 4.46219i | 0.306152 | + | 0.146795i | ||||
\(925\) | 3.42346i | 0.112563i | ||||||||
\(926\) | −14.3059 | −0.470123 | ||||||||
\(927\) | 51.5134i | 1.69192i | ||||||||
\(928\) | −53.2181 | −1.74697 | ||||||||
\(929\) | 30.1376 | 0.988782 | 0.494391 | − | 0.869240i | \(-0.335391\pi\) | ||||
0.494391 | + | 0.869240i | \(0.335391\pi\) | |||||||
\(930\) | −5.71932 | −0.187544 | ||||||||
\(931\) | −7.75338 | + | 41.6722i | −0.254107 | + | 1.36575i | ||||
\(932\) | 16.6259i | 0.544600i | ||||||||
\(933\) | − | 1.46890i | − | 0.0480898i | ||||||
\(934\) | −22.6756 | −0.741970 | ||||||||
\(935\) | −7.69539 | + | 16.0493i | −0.251666 | + | 0.524868i | ||||
\(936\) | 16.7376 | 0.547086 | ||||||||
\(937\) | − | 27.6531i | − | 0.903386i | −0.892173 | − | 0.451693i | \(-0.850820\pi\) | ||
0.892173 | − | 0.451693i | \(-0.149180\pi\) | |||||||
\(938\) | −49.0791 | −1.60249 | ||||||||
\(939\) | 12.5602i | 0.409885i | ||||||||
\(940\) | 9.59334 | 0.312900 | ||||||||
\(941\) | 45.3025 | 1.47682 | 0.738410 | − | 0.674352i | \(-0.235577\pi\) | ||||
0.738410 | + | 0.674352i | \(0.235577\pi\) | |||||||
\(942\) | 9.67043i | 0.315080i | ||||||||
\(943\) | 17.5606 | 0.571853 | ||||||||
\(944\) | − | 14.6650i | − | 0.477305i | ||||||
\(945\) | 12.9404 | 0.420950 | ||||||||
\(946\) | 17.4375 | − | 36.3671i | 0.566941 | − | 1.18239i | ||||
\(947\) | −9.89509 | −0.321547 | −0.160774 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160774 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(948\) | − | 7.16810i | − | 0.232809i | ||||||
\(949\) | − | 50.8115i | − | 1.64941i | ||||||
\(950\) | −1.46335 | + | 7.86511i | −0.0474775 | + | 0.255178i | ||||
\(951\) | −5.34242 | −0.173240 | ||||||||
\(952\) | −25.4371 | −0.824420 | ||||||||
\(953\) | −8.39491 | −0.271938 | −0.135969 | − | 0.990713i | \(-0.543415\pi\) | ||||
−0.135969 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(954\) | 38.2357i | 1.23793i | ||||||||
\(955\) | −2.74212 | −0.0887330 | ||||||||
\(956\) | 13.2900i | 0.429828i | ||||||||
\(957\) | −6.41988 | + | 13.3891i | −0.207525 | + | 0.432809i | ||||
\(958\) | 23.3211i | 0.753469i | ||||||||
\(959\) | − | 65.7407i | − | 2.12288i | ||||||
\(960\) | 1.33567i | 0.0431086i | ||||||||
\(961\) | −0.409517 | −0.0132102 | ||||||||
\(962\) | − | 33.7204i | − | 1.08719i | ||||||
\(963\) | 5.83377 | 0.187991 | ||||||||
\(964\) | 14.2344 | 0.458460 | ||||||||
\(965\) | −2.80307 | −0.0902341 | ||||||||
\(966\) | 7.94999 | 0.255787 | ||||||||
\(967\) | − | 22.4769i | − | 0.722809i | −0.932409 | − | 0.361405i | \(-0.882297\pi\) | ||
0.932409 | − | 0.361405i | \(-0.117703\pi\) | |||||||
\(968\) | 7.98292 | + | 9.94085i | 0.256581 | + | 0.319511i | ||||
\(969\) | 2.37916 | − | 12.7873i | 0.0764295 | − | 0.410787i | ||||
\(970\) | − | 22.9914i | − | 0.738208i | ||||||
\(971\) | 17.9797i | 0.576997i | 0.957480 | + | 0.288498i | \(0.0931560\pi\) | ||||
−0.957480 | + | 0.288498i | \(0.906844\pi\) | |||||||
\(972\) | − | 17.7945i | − | 0.570759i | ||||||
\(973\) | −61.0219 | −1.95627 | ||||||||
\(974\) | 2.87989i | 0.0922775i | ||||||||
\(975\) | − | 2.98404i | − | 0.0955659i | ||||||
\(976\) | 35.2916i | 1.12966i | ||||||||
\(977\) | − | 13.1960i | − | 0.422179i | −0.977467 | − | 0.211089i | \(-0.932299\pi\) | ||
0.977467 | − | 0.211089i | \(-0.0677011\pi\) | |||||||
\(978\) | 1.83650i | 0.0587246i | ||||||||
\(979\) | 9.15585 | − | 19.0952i | 0.292622 | − | 0.610284i | ||||
\(980\) | −13.3076 | −0.425097 | ||||||||
\(981\) | −41.7233 | −1.33212 | ||||||||
\(982\) | − | 25.0728i | − | 0.800106i | ||||||
\(983\) | 9.75240i | 0.311053i | 0.987832 | + | 0.155527i | \(0.0497074\pi\) | ||||
−0.987832 | + | 0.155527i | \(0.950293\pi\) | |||||||
\(984\) | 5.94094i | 0.189390i | ||||||||
\(985\) | − | 27.3376i | − | 0.871049i | ||||||
\(986\) | 79.3064i | 2.52563i | ||||||||
\(987\) | 15.9404 | 0.507387 | ||||||||
\(988\) | 5.85575 | − | 31.4730i | 0.186296 | − | 1.00129i | ||||
\(989\) | − | 12.6214i | − | 0.401338i | ||||||
\(990\) | −14.7695 | − | 7.08174i | −0.469405 | − | 0.225073i | ||||
\(991\) | − | 15.9412i | − | 0.506390i | −0.967415 | − | 0.253195i | \(-0.918519\pi\) | ||
0.967415 | − | 0.253195i | \(-0.0814814\pi\) | |||||||
\(992\) | 37.0421i | 1.17609i | ||||||||
\(993\) | −10.2195 | −0.324307 | ||||||||
\(994\) | −6.82039 | −0.216330 | ||||||||
\(995\) | −10.9591 | −0.347428 | ||||||||
\(996\) | −2.61768 | −0.0829443 | ||||||||
\(997\) | 11.8297i | 0.374650i | 0.982298 | + | 0.187325i | \(0.0599818\pi\) | ||||
−0.982298 | + | 0.187325i | \(0.940018\pi\) | |||||||
\(998\) | −67.3364 | −2.13150 | ||||||||
\(999\) | 10.8327 | 0.342732 |
(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 | 1045.2.f.b.626.10 | yes | 40 | |
11.10 | odd | 2 | inner | 1045.2.f.b.626.32 | yes | 40 | |
19.18 | odd | 2 | inner | 1045.2.f.b.626.31 | yes | 40 | |
209.208 | even | 2 | inner | 1045.2.f.b.626.9 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.f.b.626.9 | ✓ | 40 | 209.208 | even | 2 | inner | |
1045.2.f.b.626.10 | yes | 40 | 1.1 | even | 1 | trivial | |
1045.2.f.b.626.31 | yes | 40 | 19.18 | odd | 2 | inner | |
1045.2.f.b.626.32 | yes | 40 | 11.10 | odd | 2 | inner |