Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(364,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.69570878012\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 727.12 | ||
Character | \(\chi\) | \(=\) | 1089.727 |
Dual form | 1089.2.e.o.364.12 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.338834 | − | 0.586878i | 0.239592 | − | 0.414986i | −0.721005 | − | 0.692930i | \(-0.756320\pi\) |
0.960597 | + | 0.277944i | \(0.0896530\pi\) | |||||||
\(3\) | 0.461570 | + | 1.66942i | 0.266488 | + | 0.963838i | ||||
\(4\) | 0.770383 | + | 1.33434i | 0.385191 | + | 0.667171i | ||||
\(5\) | −0.145397 | − | 0.251836i | −0.0650237 | − | 0.112624i | 0.831681 | − | 0.555254i | \(-0.187379\pi\) |
−0.896705 | + | 0.442630i | \(0.854046\pi\) | |||||||
\(6\) | 1.13614 | + | 0.294770i | 0.463827 | + | 0.120339i | ||||
\(7\) | 1.67774 | − | 2.90594i | 0.634128 | − | 1.09834i | −0.352571 | − | 0.935785i | \(-0.614693\pi\) |
0.986699 | − | 0.162557i | \(-0.0519740\pi\) | |||||||
\(8\) | 2.39947 | 0.848339 | ||||||||
\(9\) | −2.57391 | + | 1.54111i | −0.857968 | + | 0.513702i | ||||
\(10\) | −0.197063 | −0.0623166 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.87199 | + | 1.90198i | −0.540396 | + | 0.549055i | ||||
\(13\) | 2.09336 | + | 3.62580i | 0.580593 | + | 1.00562i | 0.995409 | + | 0.0957108i | \(0.0305124\pi\) |
−0.414817 | + | 0.909905i | \(0.636154\pi\) | |||||||
\(14\) | −1.13695 | − | 1.96926i | −0.303864 | − | 0.526308i | ||||
\(15\) | 0.353308 | − | 0.358969i | 0.0912236 | − | 0.0926853i | ||||
\(16\) | −0.727744 | + | 1.26049i | −0.181936 | + | 0.315122i | ||||
\(17\) | −3.48327 | −0.844818 | −0.422409 | − | 0.906405i | \(-0.638815\pi\) | ||||
−0.422409 | + | 0.906405i | \(0.638815\pi\) | |||||||
\(18\) | 0.0323148 | + | 2.03275i | 0.00761667 | + | 0.479124i | ||||
\(19\) | 6.07908 | 1.39464 | 0.697318 | − | 0.716762i | \(-0.254377\pi\) | ||||
0.697318 | + | 0.716762i | \(0.254377\pi\) | |||||||
\(20\) | 0.224023 | − | 0.388020i | 0.0500931 | − | 0.0867638i | ||||
\(21\) | 5.62562 | + | 1.45956i | 1.22761 | + | 0.318502i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.34545 | + | 5.79449i | 0.697575 | + | 1.20824i | 0.969305 | + | 0.245862i | \(0.0790709\pi\) |
−0.271730 | + | 0.962374i | \(0.587596\pi\) | |||||||
\(24\) | 1.10752 | + | 4.00571i | 0.226072 | + | 0.817662i | ||||
\(25\) | 2.45772 | − | 4.25689i | 0.491544 | − | 0.851379i | ||||
\(26\) | 2.83720 | 0.556422 | ||||||||
\(27\) | −3.76079 | − | 3.58559i | −0.723764 | − | 0.690047i | ||||
\(28\) | 5.17002 | 0.977042 | ||||||||
\(29\) | −0.829864 | + | 1.43737i | −0.154102 | + | 0.266912i | −0.932732 | − | 0.360571i | \(-0.882582\pi\) |
0.778630 | + | 0.627484i | \(0.215915\pi\) | |||||||
\(30\) | −0.0909583 | − | 0.328980i | −0.0166066 | − | 0.0600632i | ||||
\(31\) | −0.981505 | − | 1.70002i | −0.176284 | − | 0.305332i | 0.764321 | − | 0.644836i | \(-0.223074\pi\) |
−0.940605 | + | 0.339504i | \(0.889741\pi\) | |||||||
\(32\) | 2.89263 | + | 5.01019i | 0.511350 | + | 0.885685i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.18025 | + | 2.04426i | −0.202412 | + | 0.350587i | ||||
\(35\) | −0.975759 | −0.164933 | ||||||||
\(36\) | −4.03926 | − | 2.24723i | −0.673209 | − | 0.374538i | ||||
\(37\) | −2.53648 | −0.416995 | −0.208497 | − | 0.978023i | \(-0.566857\pi\) | ||||
−0.208497 | + | 0.978023i | \(0.566857\pi\) | |||||||
\(38\) | 2.05980 | − | 3.56768i | 0.334144 | − | 0.578754i | ||||
\(39\) | −5.08674 | + | 5.16825i | −0.814530 | + | 0.827582i | ||||
\(40\) | −0.348876 | − | 0.604271i | −0.0551622 | − | 0.0955437i | ||||
\(41\) | −3.24317 | − | 5.61734i | −0.506499 | − | 0.877281i | −0.999972 | − | 0.00752028i | \(-0.997606\pi\) |
0.493473 | − | 0.869761i | \(-0.335727\pi\) | |||||||
\(42\) | 2.76274 | − | 2.80701i | 0.426300 | − | 0.433130i | ||||
\(43\) | 0.0247979 | − | 0.0429513i | 0.00378165 | − | 0.00655001i | −0.864128 | − | 0.503271i | \(-0.832130\pi\) |
0.867910 | + | 0.496721i | \(0.165463\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.762345 | + | 0.424128i | 0.113644 | + | 0.0632253i | ||||
\(46\) | 4.53422 | 0.668534 | ||||||||
\(47\) | −0.674704 | + | 1.16862i | −0.0984157 | + | 0.170461i | −0.911029 | − | 0.412342i | \(-0.864711\pi\) |
0.812613 | + | 0.582803i | \(0.198044\pi\) | |||||||
\(48\) | −2.44019 | − | 0.633103i | −0.352211 | − | 0.0913806i | ||||
\(49\) | −2.12965 | − | 3.68867i | −0.304236 | − | 0.526952i | ||||
\(50\) | −1.66552 | − | 2.88476i | −0.235540 | − | 0.407967i | ||||
\(51\) | −1.60778 | − | 5.81503i | −0.225134 | − | 0.814267i | ||||
\(52\) | −3.22537 | + | 5.58651i | −0.447278 | + | 0.774709i | ||||
\(53\) | −1.87766 | −0.257916 | −0.128958 | − | 0.991650i | \(-0.541163\pi\) | ||||
−0.128958 | + | 0.991650i | \(0.541163\pi\) | |||||||
\(54\) | −3.37859 | + | 0.992204i | −0.459768 | + | 0.135022i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.02569 | − | 6.97270i | 0.537955 | − | 0.931766i | ||||
\(57\) | 2.80592 | + | 10.1485i | 0.371653 | + | 1.34420i | ||||
\(58\) | 0.562373 | + | 0.974058i | 0.0738432 | + | 0.127900i | ||||
\(59\) | 7.28706 | + | 12.6216i | 0.948694 | + | 1.64319i | 0.748180 | + | 0.663496i | \(0.230928\pi\) |
0.200515 | + | 0.979691i | \(0.435739\pi\) | |||||||
\(60\) | 0.751169 | + | 0.194890i | 0.0969755 | + | 0.0251602i | ||||
\(61\) | 1.92957 | − | 3.34212i | 0.247056 | − | 0.427914i | −0.715651 | − | 0.698458i | \(-0.753870\pi\) |
0.962708 | + | 0.270544i | \(0.0872034\pi\) | |||||||
\(62\) | −1.33027 | −0.168945 | ||||||||
\(63\) | 0.160007 | + | 10.0652i | 0.0201590 | + | 1.26810i | ||||
\(64\) | 1.00952 | 0.126190 | ||||||||
\(65\) | 0.608737 | − | 1.05436i | 0.0755046 | − | 0.130778i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.46764 | + | 7.73818i | 0.545809 | + | 0.945369i | 0.998556 | + | 0.0537300i | \(0.0171110\pi\) |
−0.452746 | + | 0.891639i | \(0.649556\pi\) | |||||||
\(68\) | −2.68345 | − | 4.64788i | −0.325416 | − | 0.563638i | ||||
\(69\) | −8.12926 | + | 8.25952i | −0.978648 | + | 0.994330i | ||||
\(70\) | −0.330621 | + | 0.572652i | −0.0395167 | + | 0.0684450i | ||||
\(71\) | −11.1283 | −1.32068 | −0.660340 | − | 0.750967i | \(-0.729588\pi\) | ||||
−0.660340 | + | 0.750967i | \(0.729588\pi\) | |||||||
\(72\) | −6.17600 | + | 3.69783i | −0.727848 | + | 0.435794i | ||||
\(73\) | −1.25869 | −0.147318 | −0.0736591 | − | 0.997283i | \(-0.523468\pi\) | ||||
−0.0736591 | + | 0.997283i | \(0.523468\pi\) | |||||||
\(74\) | −0.859446 | + | 1.48860i | −0.0999086 | + | 0.173047i | ||||
\(75\) | 8.24094 | + | 2.13810i | 0.951582 | + | 0.246887i | ||||
\(76\) | 4.68321 | + | 8.11157i | 0.537202 | + | 0.930460i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.30957 | + | 4.73648i | 0.148280 | + | 0.536300i | ||||
\(79\) | 1.05357 | − | 1.82483i | 0.118535 | − | 0.205309i | −0.800652 | − | 0.599130i | \(-0.795513\pi\) |
0.919188 | + | 0.393820i | \(0.128847\pi\) | |||||||
\(80\) | 0.423248 | 0.0473206 | ||||||||
\(81\) | 4.24998 | − | 7.93333i | 0.472220 | − | 0.881481i | ||||
\(82\) | −4.39559 | −0.485412 | ||||||||
\(83\) | 4.68763 | − | 8.11922i | 0.514535 | − | 0.891200i | −0.485323 | − | 0.874335i | \(-0.661298\pi\) |
0.999858 | − | 0.0168653i | \(-0.00536866\pi\) | |||||||
\(84\) | 2.38633 | + | 8.63092i | 0.260370 | + | 0.941710i | ||||
\(85\) | 0.506459 | + | 0.877212i | 0.0549332 | + | 0.0951470i | ||||
\(86\) | −0.0168048 | − | 0.0291068i | −0.00181211 | − | 0.00313866i | ||||
\(87\) | −2.78260 | − | 0.721943i | −0.298326 | − | 0.0774004i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.41413 | −0.891896 | −0.445948 | − | 0.895059i | \(-0.647133\pi\) | ||||
−0.445948 | + | 0.895059i | \(0.647133\pi\) | |||||||
\(90\) | 0.507220 | − | 0.303694i | 0.0534657 | − | 0.0320122i | ||||
\(91\) | 14.0485 | 1.47268 | ||||||||
\(92\) | −5.15456 | + | 8.92795i | −0.537400 | + | 0.930803i | ||||
\(93\) | 2.38500 | − | 2.42322i | 0.247313 | − | 0.251276i | ||||
\(94\) | 0.457226 | + | 0.791938i | 0.0471593 | + | 0.0816822i | ||||
\(95\) | −0.883882 | − | 1.53093i | −0.0906844 | − | 0.157070i | ||||
\(96\) | −7.02894 | + | 7.14157i | −0.717388 | + | 0.728883i | ||||
\(97\) | −0.491742 | + | 0.851722i | −0.0499288 | + | 0.0864793i | −0.889910 | − | 0.456137i | \(-0.849233\pi\) |
0.839981 | + | 0.542616i | \(0.182566\pi\) | |||||||
\(98\) | −2.88640 | −0.291570 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.57354 | 0.757354 | ||||||||
\(101\) | −1.95582 | + | 3.38758i | −0.194611 | + | 0.337077i | −0.946773 | − | 0.321902i | \(-0.895678\pi\) |
0.752162 | + | 0.658979i | \(0.229011\pi\) | |||||||
\(102\) | −3.95749 | − | 1.02676i | −0.391850 | − | 0.101665i | ||||
\(103\) | −7.73117 | − | 13.3908i | −0.761775 | − | 1.31943i | −0.941935 | − | 0.335795i | \(-0.890995\pi\) |
0.180160 | − | 0.983637i | \(-0.442338\pi\) | |||||||
\(104\) | 5.02294 | + | 8.69998i | 0.492539 | + | 0.853103i | ||||
\(105\) | −0.450381 | − | 1.62895i | −0.0439527 | − | 0.158969i | ||||
\(106\) | −0.636215 | + | 1.10196i | −0.0617946 | + | 0.107031i | ||||
\(107\) | −6.26446 | −0.605609 | −0.302804 | − | 0.953053i | \(-0.597923\pi\) | ||||
−0.302804 | + | 0.953053i | \(0.597923\pi\) | |||||||
\(108\) | 1.88716 | − | 7.78045i | 0.181592 | − | 0.748675i | ||||
\(109\) | −3.09153 | −0.296115 | −0.148057 | − | 0.988979i | \(-0.547302\pi\) | ||||
−0.148057 | + | 0.988979i | \(0.547302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.17076 | − | 4.23444i | −0.111124 | − | 0.401915i | ||||
\(112\) | 2.44194 | + | 4.22956i | 0.230741 | + | 0.399656i | ||||
\(113\) | −7.97205 | − | 13.8080i | −0.749948 | − | 1.29895i | −0.947847 | − | 0.318725i | \(-0.896745\pi\) |
0.197899 | − | 0.980222i | \(-0.436588\pi\) | |||||||
\(114\) | 6.90669 | + | 1.79193i | 0.646870 | + | 0.167830i | ||||
\(115\) | 0.972840 | − | 1.68501i | 0.0907178 | − | 0.157128i | ||||
\(116\) | −2.55725 | −0.237435 | ||||||||
\(117\) | −10.9758 | − | 6.10638i | −1.01472 | − | 0.564535i | ||||
\(118\) | 9.87642 | 0.909199 | ||||||||
\(119\) | −5.84404 | + | 10.1222i | −0.535722 | + | 0.927898i | ||||
\(120\) | 0.847750 | − | 0.861333i | 0.0773886 | − | 0.0786286i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.30761 | − | 2.26485i | −0.118385 | − | 0.205050i | ||||
\(123\) | 7.88073 | − | 8.00701i | 0.710582 | − | 0.721968i | ||||
\(124\) | 1.51227 | − | 2.61933i | 0.135806 | − | 0.235222i | ||||
\(125\) | −2.88336 | −0.257895 | ||||||||
\(126\) | 5.96126 | + | 3.31653i | 0.531071 | + | 0.295460i | ||||
\(127\) | 18.5061 | 1.64215 | 0.821075 | − | 0.570821i | \(-0.193375\pi\) | ||||
0.821075 | + | 0.570821i | \(0.193375\pi\) | |||||||
\(128\) | −5.44321 | + | 9.42791i | −0.481116 | + | 0.833318i | ||||
\(129\) | 0.0831496 | + | 0.0215731i | 0.00732092 | + | 0.00189940i | ||||
\(130\) | −0.412522 | − | 0.714509i | −0.0361806 | − | 0.0626666i | ||||
\(131\) | −0.432321 | − | 0.748803i | −0.0377721 | − | 0.0654232i | 0.846521 | − | 0.532355i | \(-0.178693\pi\) |
−0.884293 | + | 0.466932i | \(0.845359\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.1991 | − | 17.6654i | 0.884377 | − | 1.53179i | ||||
\(134\) | 6.05516 | 0.523086 | ||||||||
\(135\) | −0.356171 | + | 1.46844i | −0.0306543 | + | 0.126383i | ||||
\(136\) | −8.35799 | −0.716692 | ||||||||
\(137\) | 6.18908 | − | 10.7198i | 0.528769 | − | 0.915855i | −0.470668 | − | 0.882310i | \(-0.655987\pi\) |
0.999437 | − | 0.0335444i | \(-0.0106795\pi\) | |||||||
\(138\) | 2.09286 | + | 7.56950i | 0.178156 | + | 0.644358i | ||||
\(139\) | −0.332985 | − | 0.576746i | −0.0282434 | − | 0.0489190i | 0.851558 | − | 0.524260i | \(-0.175658\pi\) |
−0.879802 | + | 0.475341i | \(0.842325\pi\) | |||||||
\(140\) | −0.751707 | − | 1.30200i | −0.0635309 | − | 0.110039i | ||||
\(141\) | −2.26234 | − | 0.586961i | −0.190523 | − | 0.0494310i | ||||
\(142\) | −3.77063 | + | 6.53093i | −0.316425 | + | 0.548063i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.0694052 | − | 4.36591i | −0.00578377 | − | 0.363826i | ||||
\(145\) | 0.482640 | 0.0400811 | ||||||||
\(146\) | −0.426487 | + | 0.738697i | −0.0352963 | + | 0.0611350i | ||||
\(147\) | 5.17494 | − | 5.25786i | 0.426822 | − | 0.433661i | ||||
\(148\) | −1.95406 | − | 3.38453i | −0.160623 | − | 0.278207i | ||||
\(149\) | −6.02662 | − | 10.4384i | −0.493720 | − | 0.855148i | 0.506254 | − | 0.862384i | \(-0.331030\pi\) |
−0.999974 | + | 0.00723647i | \(0.997697\pi\) | |||||||
\(150\) | 4.04712 | − | 4.11197i | 0.330446 | − | 0.335741i | ||||
\(151\) | 10.2525 | − | 17.7578i | 0.834333 | − | 1.44511i | −0.0602386 | − | 0.998184i | \(-0.519186\pi\) |
0.894572 | − | 0.446924i | \(-0.147481\pi\) | |||||||
\(152\) | 14.5865 | 1.18312 | ||||||||
\(153\) | 8.96561 | − | 5.36810i | 0.724827 | − | 0.433985i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.285417 | + | 0.494356i | −0.0229252 | + | 0.0397076i | ||||
\(156\) | −10.8149 | − | 2.80592i | −0.865888 | − | 0.224654i | ||||
\(157\) | 4.22762 | + | 7.32245i | 0.337401 | + | 0.584395i | 0.983943 | − | 0.178483i | \(-0.0571190\pi\) |
−0.646542 | + | 0.762878i | \(0.723786\pi\) | |||||||
\(158\) | −0.713969 | − | 1.23663i | −0.0568003 | − | 0.0983811i | ||||
\(159\) | −0.866671 | − | 3.13459i | −0.0687315 | − | 0.248589i | ||||
\(160\) | 0.841163 | − | 1.45694i | 0.0664998 | − | 0.115181i | ||||
\(161\) | 22.4513 | 1.76941 | ||||||||
\(162\) | −3.21586 | − | 5.18230i | −0.252662 | − | 0.407160i | ||||
\(163\) | −23.2731 | −1.82289 | −0.911446 | − | 0.411419i | \(-0.865033\pi\) | ||||
−0.911446 | + | 0.411419i | \(0.865033\pi\) | |||||||
\(164\) | 4.99697 | − | 8.65500i | 0.390198 | − | 0.675842i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.17666 | − | 5.50214i | −0.246557 | − | 0.427049i | ||||
\(167\) | −9.78866 | − | 16.9545i | −0.757469 | − | 1.31198i | −0.944137 | − | 0.329553i | \(-0.893102\pi\) |
0.186668 | − | 0.982423i | \(-0.440231\pi\) | |||||||
\(168\) | 13.4985 | + | 3.50216i | 1.04143 | + | 0.270198i | ||||
\(169\) | −2.26428 | + | 3.92185i | −0.174176 | + | 0.301681i | ||||
\(170\) | 0.686422 | 0.0526462 | ||||||||
\(171\) | −15.6470 | + | 9.36851i | −1.19655 | + | 0.716428i | ||||
\(172\) | 0.0764156 | 0.00582664 | ||||||||
\(173\) | 8.95509 | − | 15.5107i | 0.680843 | − | 1.17925i | −0.293881 | − | 0.955842i | \(-0.594947\pi\) |
0.974724 | − | 0.223413i | \(-0.0717197\pi\) | |||||||
\(174\) | −1.36653 | + | 1.38843i | −0.103597 | + | 0.105257i | ||||
\(175\) | −8.24685 | − | 14.2840i | −0.623403 | − | 1.07977i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.7071 | + | 17.9909i | −1.33095 | + | 1.35228i | ||||
\(178\) | −2.85100 | + | 4.93807i | −0.213691 | + | 0.370124i | ||||
\(179\) | 9.44944 | 0.706284 | 0.353142 | − | 0.935570i | \(-0.385113\pi\) | ||||
0.353142 | + | 0.935570i | \(0.385113\pi\) | |||||||
\(180\) | 0.0213652 | + | 1.34397i | 0.00159247 | + | 0.100174i | ||||
\(181\) | 11.0798 | 0.823555 | 0.411777 | − | 0.911284i | \(-0.364908\pi\) | ||||
0.411777 | + | 0.911284i | \(0.364908\pi\) | |||||||
\(182\) | 4.76010 | − | 8.24474i | 0.352842 | − | 0.611141i | ||||
\(183\) | 6.47002 | + | 1.67864i | 0.478277 | + | 0.124088i | ||||
\(184\) | 8.02730 | + | 13.9037i | 0.591780 | + | 1.02499i | ||||
\(185\) | 0.368797 | + | 0.638776i | 0.0271145 | + | 0.0469637i | ||||
\(186\) | −0.614014 | − | 2.22078i | −0.0450217 | − | 0.162835i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.07912 | −0.151636 | ||||||||
\(189\) | −16.7292 | + | 4.91292i | −1.21687 | + | 0.357362i | ||||
\(190\) | −1.19796 | −0.0869090 | ||||||||
\(191\) | 2.26860 | − | 3.92932i | 0.164150 | − | 0.284316i | −0.772203 | − | 0.635376i | \(-0.780845\pi\) |
0.936353 | + | 0.351060i | \(0.114179\pi\) | |||||||
\(192\) | 0.465965 | + | 1.68531i | 0.0336282 | + | 0.121627i | ||||
\(193\) | 6.74928 | + | 11.6901i | 0.485824 | + | 0.841471i | 0.999867 | − | 0.0162928i | \(-0.00518639\pi\) |
−0.514044 | + | 0.857764i | \(0.671853\pi\) | |||||||
\(194\) | 0.333238 | + | 0.577185i | 0.0239251 | + | 0.0414395i | ||||
\(195\) | 2.04115 | + | 0.529573i | 0.146170 | + | 0.0379235i | ||||
\(196\) | 3.28129 | − | 5.68337i | 0.234378 | − | 0.405955i | ||||
\(197\) | −1.70047 | −0.121153 | −0.0605766 | − | 0.998164i | \(-0.519294\pi\) | ||||
−0.0605766 | + | 0.998164i | \(0.519294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1442 | −0.719105 | −0.359552 | − | 0.933125i | \(-0.617071\pi\) | ||||
−0.359552 | + | 0.933125i | \(0.617071\pi\) | |||||||
\(200\) | 5.89721 | − | 10.2143i | 0.416996 | − | 0.722258i | ||||
\(201\) | −10.8561 | + | 11.0301i | −0.765732 | + | 0.778001i | ||||
\(202\) | 1.32540 | + | 2.29566i | 0.0932547 | + | 0.161522i | ||||
\(203\) | 2.78460 | + | 4.82307i | 0.195441 | + | 0.338513i | ||||
\(204\) | 6.52064 | − | 6.62512i | 0.456536 | − | 0.463851i | ||||
\(205\) | −0.943098 | + | 1.63349i | −0.0658688 | + | 0.114088i | ||||
\(206\) | −10.4783 | −0.730061 | ||||||||
\(207\) | −17.5408 | − | 9.75878i | −1.21917 | − | 0.678282i | ||||
\(208\) | −6.09371 | −0.422523 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.10860 | − | 0.287624i | −0.0765006 | − | 0.0198480i | ||||
\(211\) | −5.33769 | − | 9.24514i | −0.367461 | − | 0.636462i | 0.621707 | − | 0.783250i | \(-0.286440\pi\) |
−0.989168 | + | 0.146788i | \(0.953106\pi\) | |||||||
\(212\) | −1.44651 | − | 2.50544i | −0.0993470 | − | 0.172074i | ||||
\(213\) | −5.13647 | − | 18.5777i | −0.351945 | − | 1.27292i | ||||
\(214\) | −2.12262 | + | 3.67648i | −0.145099 | + | 0.251319i | ||||
\(215\) | −0.0144222 | −0.000983588 | ||||||||
\(216\) | −9.02388 | − | 8.60350i | −0.613998 | − | 0.585394i | ||||
\(217\) | −6.58686 | −0.447145 | ||||||||
\(218\) | −1.04752 | + | 1.81435i | −0.0709467 | + | 0.122883i | ||||
\(219\) | −0.580973 | − | 2.10128i | −0.0392585 | − | 0.141991i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.29173 | − | 12.6296i | −0.490495 | − | 0.849562i | ||||
\(222\) | −2.88180 | − | 0.747678i | −0.193414 | − | 0.0501809i | ||||
\(223\) | −1.41869 | + | 2.45725i | −0.0950028 | + | 0.164550i | −0.909610 | − | 0.415464i | \(-0.863619\pi\) |
0.814607 | + | 0.580013i | \(0.196953\pi\) | |||||||
\(224\) | 19.4124 | 1.29705 | ||||||||
\(225\) | 0.234394 | + | 14.7445i | 0.0156262 | + | 0.982963i | ||||
\(226\) | −10.8048 | −0.718726 | ||||||||
\(227\) | 3.24294 | − | 5.61693i | 0.215241 | − | 0.372809i | −0.738106 | − | 0.674685i | \(-0.764280\pi\) |
0.953347 | + | 0.301876i | \(0.0976129\pi\) | |||||||
\(228\) | −11.3800 | + | 11.5623i | −0.753656 | + | 0.765732i | ||||
\(229\) | 12.8202 | + | 22.2052i | 0.847181 | + | 1.46736i | 0.883714 | + | 0.468028i | \(0.155035\pi\) |
−0.0365331 | + | 0.999332i | \(0.511631\pi\) | |||||||
\(230\) | −0.659263 | − | 1.14188i | −0.0434705 | − | 0.0752932i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.99123 | + | 3.44891i | −0.130731 | + | 0.226432i | ||||
\(233\) | 0.649882 | 0.0425752 | 0.0212876 | − | 0.999773i | \(-0.493223\pi\) | ||||
0.0212876 | + | 0.999773i | \(0.493223\pi\) | |||||||
\(234\) | −7.30270 | + | 4.37244i | −0.477392 | + | 0.285835i | ||||
\(235\) | 0.392401 | 0.0255974 | ||||||||
\(236\) | −11.2276 | + | 19.4469i | −0.730858 | + | 1.26588i | ||||
\(237\) | 3.53270 | + | 0.916554i | 0.229473 | + | 0.0595366i | ||||
\(238\) | 3.96032 | + | 6.85948i | 0.256710 | + | 0.444634i | ||||
\(239\) | −8.46729 | − | 14.6658i | −0.547703 | − | 0.948650i | −0.998431 | − | 0.0559887i | \(-0.982169\pi\) |
0.450728 | − | 0.892661i | \(-0.351164\pi\) | |||||||
\(240\) | 0.195359 | + | 0.706578i | 0.0126104 | + | 0.0456094i | ||||
\(241\) | 12.2496 | − | 21.2170i | 0.789069 | − | 1.36671i | −0.137469 | − | 0.990506i | \(-0.543897\pi\) |
0.926538 | − | 0.376201i | \(-0.122770\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2057 | + | 3.43319i | 0.975446 | + | 0.220240i | ||||
\(244\) | 5.94603 | 0.380656 | ||||||||
\(245\) | −0.619292 | + | 1.07264i | −0.0395651 | + | 0.0685288i | ||||
\(246\) | −2.02888 | − | 7.33808i | −0.129356 | − | 0.467859i | ||||
\(247\) | 12.7257 | + | 22.0415i | 0.809715 | + | 1.40247i | ||||
\(248\) | −2.35509 | − | 4.07913i | −0.149548 | − | 0.259025i | ||||
\(249\) | 15.7180 | + | 4.07802i | 0.996090 | + | 0.258434i | ||||
\(250\) | −0.976981 | + | 1.69218i | −0.0617897 | + | 0.107023i | ||||
\(251\) | 17.8710 | 1.12801 | 0.564005 | − | 0.825771i | \(-0.309260\pi\) | ||||
0.564005 | + | 0.825771i | \(0.309260\pi\) | |||||||
\(252\) | −13.3071 | + | 7.96755i | −0.838271 | + | 0.501909i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.27050 | − | 10.8608i | 0.393446 | − | 0.681468i | ||||
\(255\) | −1.23067 | + | 1.25039i | −0.0770673 | + | 0.0783022i | ||||
\(256\) | 4.69821 | + | 8.13755i | 0.293638 | + | 0.508597i | ||||
\(257\) | 0.623376 | + | 1.07972i | 0.0388851 | + | 0.0673510i | 0.884813 | − | 0.465946i | \(-0.154286\pi\) |
−0.845928 | + | 0.533297i | \(0.820953\pi\) | |||||||
\(258\) | 0.0408347 | − | 0.0414890i | 0.00254226 | − | 0.00258299i | ||||
\(259\) | −4.25556 | + | 7.37085i | −0.264428 | + | 0.458002i | ||||
\(260\) | 1.87584 | 0.116335 | ||||||||
\(261\) | −0.0791445 | − | 4.97855i | −0.00489892 | − | 0.308165i | ||||
\(262\) | −0.585941 | −0.0361996 | ||||||||
\(263\) | −8.39035 | + | 14.5325i | −0.517371 | + | 0.896113i | 0.482425 | + | 0.875937i | \(0.339756\pi\) |
−0.999796 | + | 0.0201758i | \(0.993577\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.273006 | + | 0.472861i | 0.0167707 | + | 0.0290476i | ||||
\(266\) | −6.91164 | − | 11.9713i | −0.423780 | − | 0.734008i | ||||
\(267\) | −3.88371 | − | 14.0467i | −0.237679 | − | 0.859643i | ||||
\(268\) | −6.88359 | + | 11.9227i | −0.420482 | + | 0.728296i | ||||
\(269\) | 21.9703 | 1.33955 | 0.669777 | − | 0.742563i | \(-0.266390\pi\) | ||||
0.669777 | + | 0.742563i | \(0.266390\pi\) | |||||||
\(270\) | 0.741111 | + | 0.706586i | 0.0451026 | + | 0.0430014i | ||||
\(271\) | −10.1083 | −0.614037 | −0.307018 | − | 0.951704i | \(-0.599331\pi\) | ||||
−0.307018 | + | 0.951704i | \(0.599331\pi\) | |||||||
\(272\) | 2.53493 | − | 4.39063i | 0.153703 | − | 0.266221i | ||||
\(273\) | 6.48436 | + | 23.4527i | 0.392451 | + | 1.41942i | ||||
\(274\) | −4.19415 | − | 7.26448i | −0.253378 | − | 0.438863i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.2837 | − | 4.48422i | −1.04035 | − | 0.269919i | ||||
\(277\) | 3.88655 | − | 6.73171i | 0.233520 | − | 0.404469i | −0.725321 | − | 0.688411i | \(-0.758309\pi\) |
0.958842 | + | 0.283941i | \(0.0916421\pi\) | |||||||
\(278\) | −0.451306 | −0.0270676 | ||||||||
\(279\) | 5.14621 | + | 2.86308i | 0.308095 | + | 0.171408i | ||||
\(280\) | −2.34130 | −0.139919 | ||||||||
\(281\) | −16.1452 | + | 27.9643i | −0.963142 | + | 1.66821i | −0.248615 | + | 0.968602i | \(0.579975\pi\) |
−0.714527 | + | 0.699608i | \(0.753358\pi\) | |||||||
\(282\) | −1.11103 | + | 1.12884i | −0.0661611 | + | 0.0672212i | ||||
\(283\) | −6.26153 | − | 10.8453i | −0.372209 | − | 0.644685i | 0.617696 | − | 0.786417i | \(-0.288066\pi\) |
−0.989905 | + | 0.141732i | \(0.954733\pi\) | |||||||
\(284\) | −8.57301 | − | 14.8489i | −0.508715 | − | 0.881120i | ||||
\(285\) | 2.14778 | − | 2.18220i | 0.127224 | − | 0.129262i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.7649 | −1.28474 | ||||||||
\(288\) | −15.1666 | − | 8.43790i | −0.893701 | − | 0.497208i | ||||
\(289\) | −4.86682 | −0.286283 | ||||||||
\(290\) | 0.163535 | − | 0.283251i | 0.00960311 | − | 0.0166331i | ||||
\(291\) | −1.64885 | − | 0.427793i | −0.0966575 | − | 0.0250776i | ||||
\(292\) | −0.969671 | − | 1.67952i | −0.0567457 | − | 0.0982865i | ||||
\(293\) | −9.19219 | − | 15.9213i | −0.537013 | − | 0.930134i | −0.999063 | − | 0.0432803i | \(-0.986219\pi\) |
0.462050 | − | 0.886854i | \(-0.347114\pi\) | |||||||
\(294\) | −1.33228 | − | 4.81860i | −0.0776999 | − | 0.281026i | ||||
\(295\) | 2.11904 | − | 3.67028i | 0.123375 | − | 0.213692i | ||||
\(296\) | −6.08619 | −0.353753 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.16810 | −0.473166 | ||||||||
\(299\) | −14.0064 | + | 24.2599i | −0.810014 | + | 1.40299i | ||||
\(300\) | 3.49572 | + | 12.6434i | 0.201826 | + | 0.729966i | ||||
\(301\) | −0.0832092 | − | 0.144123i | −0.00479610 | − | 0.00830709i | ||||
\(302\) | −6.94777 | − | 12.0339i | −0.399799 | − | 0.692473i | ||||
\(303\) | −6.55803 | − | 1.70147i | −0.376749 | − | 0.0977470i | ||||
\(304\) | −4.42401 | + | 7.66261i | −0.253734 | + | 0.439481i | ||||
\(305\) | −1.12222 | −0.0642581 | ||||||||
\(306\) | −0.112561 | − | 7.08062i | −0.00643469 | − | 0.404772i | ||||
\(307\) | −8.42389 | −0.480777 | −0.240388 | − | 0.970677i | \(-0.577275\pi\) | ||||
−0.240388 | + | 0.970677i | \(0.577275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.7863 | − | 19.0873i | 1.06872 | − | 1.08584i | ||||
\(310\) | 0.193418 | + | 0.335010i | 0.0109854 | + | 0.0190273i | ||||
\(311\) | −5.65168 | − | 9.78899i | −0.320477 | − | 0.555083i | 0.660109 | − | 0.751170i | \(-0.270510\pi\) |
−0.980587 | + | 0.196087i | \(0.937177\pi\) | |||||||
\(312\) | −12.2055 | + | 12.4010i | −0.690998 | + | 0.702070i | ||||
\(313\) | −3.05532 | + | 5.29197i | −0.172697 | + | 0.299120i | −0.939362 | − | 0.342928i | \(-0.888581\pi\) |
0.766665 | + | 0.642047i | \(0.221915\pi\) | |||||||
\(314\) | 5.72985 | 0.323354 | ||||||||
\(315\) | 2.51151 | − | 1.50375i | 0.141508 | − | 0.0847266i | ||||
\(316\) | 3.24660 | 0.182635 | ||||||||
\(317\) | 0.414288 | − | 0.717568i | 0.0232687 | − | 0.0403026i | −0.854157 | − | 0.520016i | \(-0.825926\pi\) |
0.877425 | + | 0.479713i | \(0.159259\pi\) | |||||||
\(318\) | −2.13328 | − | 0.553477i | −0.119629 | − | 0.0310375i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.146782 | − | 0.254234i | −0.00820535 | − | 0.0142121i | ||||
\(321\) | −2.89149 | − | 10.4580i | −0.161387 | − | 0.583709i | ||||
\(322\) | 7.60726 | − | 13.1762i | 0.423936 | − | 0.734278i | ||||
\(323\) | −21.1751 | −1.17821 | ||||||||
\(324\) | 13.8599 | − | 0.440775i | 0.769993 | − | 0.0244875i | ||||
\(325\) | 20.5795 | 1.14155 | ||||||||
\(326\) | −7.88574 | + | 13.6585i | −0.436751 | + | 0.756474i | ||||
\(327\) | −1.42696 | − | 5.16105i | −0.0789110 | − | 0.285407i | ||||
\(328\) | −7.78188 | − | 13.4786i | −0.429683 | − | 0.744232i | ||||
\(329\) | 2.26396 | + | 3.92130i | 0.124816 | + | 0.216188i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.09227 | + | 7.08802i | −0.224931 | + | 0.389593i | −0.956299 | − | 0.292391i | \(-0.905549\pi\) |
0.731367 | + | 0.681984i | \(0.238882\pi\) | |||||||
\(332\) | 14.4451 | 0.792777 | ||||||||
\(333\) | 6.52866 | − | 3.90899i | 0.357768 | − | 0.214211i | ||||
\(334\) | −13.2669 | −0.725935 | ||||||||
\(335\) | 1.29917 | − | 2.25022i | 0.0709811 | − | 0.122943i | ||||
\(336\) | −5.93377 | + | 6.02885i | −0.323714 | + | 0.328901i | ||||
\(337\) | −1.25242 | − | 2.16926i | −0.0682239 | − | 0.118167i | 0.829896 | − | 0.557919i | \(-0.188400\pi\) |
−0.898120 | + | 0.439751i | \(0.855067\pi\) | |||||||
\(338\) | 1.53443 | + | 2.65772i | 0.0834622 | + | 0.144561i | ||||
\(339\) | 19.3716 | − | 19.6820i | 1.05212 | − | 1.06898i | ||||
\(340\) | −0.780334 | + | 1.35158i | −0.0423195 | + | 0.0732996i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.196444 | + | 12.3572i | 0.0106225 | + | 0.668203i | ||||
\(343\) | 9.19637 | 0.496558 | ||||||||
\(344\) | 0.0595018 | − | 0.103060i | 0.00320812 | − | 0.00555663i | ||||
\(345\) | 3.26202 | + | 0.846326i | 0.175621 | + | 0.0455646i | ||||
\(346\) | −6.06858 | − | 10.5111i | −0.326249 | − | 0.565080i | ||||
\(347\) | −15.7632 | − | 27.3027i | −0.846213 | − | 1.46568i | −0.884563 | − | 0.466420i | \(-0.845544\pi\) |
0.0383501 | − | 0.999264i | \(-0.487790\pi\) | |||||||
\(348\) | −1.18035 | − | 4.26912i | −0.0632735 | − | 0.228849i | ||||
\(349\) | −4.37596 | + | 7.57939i | −0.234240 | + | 0.405715i | −0.959052 | − | 0.283232i | \(-0.908593\pi\) |
0.724812 | + | 0.688947i | \(0.241927\pi\) | |||||||
\(350\) | −11.1773 | −0.597450 | ||||||||
\(351\) | 5.12796 | − | 21.1418i | 0.273711 | − | 1.12847i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.219931 | + | 0.380932i | −0.0117058 | + | 0.0202750i | −0.871819 | − | 0.489828i | \(-0.837059\pi\) |
0.860113 | + | 0.510103i | \(0.170393\pi\) | |||||||
\(354\) | 4.55867 | + | 16.4879i | 0.242290 | + | 0.876320i | ||||
\(355\) | 1.61802 | + | 2.80249i | 0.0858755 | + | 0.148741i | ||||
\(356\) | −6.48210 | − | 11.2273i | −0.343550 | − | 0.595047i | ||||
\(357\) | −19.5956 | − | 5.08404i | −1.03711 | − | 0.269076i | ||||
\(358\) | 3.20179 | − | 5.54567i | 0.169220 | − | 0.293098i | ||||
\(359\) | −16.7381 | −0.883404 | −0.441702 | − | 0.897162i | \(-0.645625\pi\) | ||||
−0.441702 | + | 0.897162i | \(0.645625\pi\) | |||||||
\(360\) | 1.82922 | + | 1.01768i | 0.0964084 | + | 0.0536365i | ||||
\(361\) | 17.9552 | 0.945009 | ||||||||
\(362\) | 3.75422 | − | 6.50249i | 0.197317 | − | 0.341763i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.8227 | + | 18.7455i | 0.567263 | + | 0.982529i | ||||
\(365\) | 0.183010 | + | 0.316983i | 0.00957918 | + | 0.0165916i | ||||
\(366\) | 3.17742 | − | 3.22833i | 0.166086 | − | 0.168748i | ||||
\(367\) | 7.37439 | − | 12.7728i | 0.384940 | − | 0.666735i | −0.606821 | − | 0.794839i | \(-0.707556\pi\) |
0.991761 | + | 0.128103i | \(0.0408888\pi\) | |||||||
\(368\) | −9.73853 | −0.507656 | ||||||||
\(369\) | 17.0045 | + | 9.46043i | 0.885221 | + | 0.492490i | ||||
\(370\) | 0.499845 | 0.0259857 | ||||||||
\(371\) | −3.15023 | + | 5.45636i | −0.163552 | + | 0.283280i | ||||
\(372\) | 5.07077 | + | 1.31560i | 0.262907 | + | 0.0682108i | ||||
\(373\) | 11.8254 | + | 20.4822i | 0.612296 | + | 1.06053i | 0.990852 | + | 0.134950i | \(0.0430873\pi\) |
−0.378556 | + | 0.925578i | \(0.623579\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.33087 | − | 4.81353i | −0.0687260 | − | 0.248569i | ||||
\(376\) | −1.61893 | + | 2.80407i | −0.0834899 | + | 0.144609i | ||||
\(377\) | −6.94880 | −0.357882 | ||||||||
\(378\) | −2.78513 | + | 11.4826i | −0.143252 | + | 0.590603i | ||||
\(379\) | −11.4766 | −0.589514 | −0.294757 | − | 0.955572i | \(-0.595239\pi\) | ||||
−0.294757 | + | 0.955572i | \(0.595239\pi\) | |||||||
\(380\) | 1.36185 | − | 2.35880i | 0.0698617 | − | 0.121004i | ||||
\(381\) | 8.54186 | + | 30.8944i | 0.437613 | + | 1.58277i | ||||
\(382\) | −1.53736 | − | 2.66278i | −0.0786580 | − | 0.136240i | ||||
\(383\) | 3.96434 | + | 6.86643i | 0.202568 | + | 0.350858i | 0.949355 | − | 0.314205i | \(-0.101738\pi\) |
−0.746787 | + | 0.665063i | \(0.768405\pi\) | |||||||
\(384\) | −18.2515 | − | 4.73534i | −0.931395 | − | 0.241649i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.14755 | 0.465598 | ||||||||
\(387\) | 0.00236499 | + | 0.148769i | 0.000120219 | + | 0.00756235i | ||||
\(388\) | −1.51532 | −0.0769286 | ||||||||
\(389\) | −4.52549 | + | 7.83839i | −0.229452 | + | 0.397422i | −0.957646 | − | 0.287949i | \(-0.907027\pi\) |
0.728194 | + | 0.685371i | \(0.240360\pi\) | |||||||
\(390\) | 1.00241 | − | 1.01847i | 0.0507588 | − | 0.0515721i | ||||
\(391\) | −11.6531 | − | 20.1838i | −0.589324 | − | 1.02074i | ||||
\(392\) | −5.11003 | − | 8.85083i | −0.258095 | − | 0.447034i | ||||
\(393\) | 1.05052 | − | 1.06735i | 0.0529916 | − | 0.0538407i | ||||
\(394\) | −0.576176 | + | 0.997966i | −0.0290273 | + | 0.0502768i | ||||
\(395\) | −0.612743 | −0.0308305 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.38182 | 0.270106 | 0.135053 | − | 0.990838i | \(-0.456880\pi\) | ||||
0.135053 | + | 0.990838i | \(0.456880\pi\) | |||||||
\(398\) | −3.43721 | + | 5.95342i | −0.172292 | + | 0.298418i | ||||
\(399\) | 34.1986 | + | 8.87277i | 1.71207 | + | 0.444194i | ||||
\(400\) | 3.57718 | + | 6.19586i | 0.178859 | + | 0.309793i | ||||
\(401\) | 7.83416 | + | 13.5692i | 0.391219 | + | 0.677611i | 0.992611 | − | 0.121343i | \(-0.0387201\pi\) |
−0.601392 | + | 0.798954i | \(0.705387\pi\) | |||||||
\(402\) | 2.79488 | + | 10.1086i | 0.139396 | + | 0.504171i | ||||
\(403\) | 4.10928 | − | 7.11748i | 0.204698 | − | 0.354547i | ||||
\(404\) | −6.02692 | −0.299850 | ||||||||
\(405\) | −2.61583 | + | 0.0831892i | −0.129982 | + | 0.00413370i | ||||
\(406\) | 3.77407 | 0.187304 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.85780 | − | 13.9530i | −0.190990 | − | 0.690775i | ||||
\(409\) | −11.3706 | − | 19.6945i | −0.562242 | − | 0.973832i | −0.997300 | − | 0.0734296i | \(-0.976606\pi\) |
0.435058 | − | 0.900402i | \(-0.356728\pi\) | |||||||
\(410\) | 0.639108 | + | 1.10697i | 0.0315633 | + | 0.0546692i | ||||
\(411\) | 20.7525 | + | 5.38421i | 1.02365 | + | 0.265584i | ||||
\(412\) | 11.9119 | − | 20.6320i | 0.586858 | − | 1.01647i | ||||
\(413\) | 48.9033 | 2.40637 | ||||||||
\(414\) | −11.6706 | + | 6.98771i | −0.573581 | + | 0.343427i | ||||
\(415\) | −2.72628 | −0.133828 | ||||||||
\(416\) | −12.1106 | + | 20.9762i | −0.593773 | + | 1.02844i | ||||
\(417\) | 0.809134 | − | 0.822099i | 0.0396235 | − | 0.0402584i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.5131 | + | 33.7978i | 0.953279 | + | 1.65113i | 0.738257 | + | 0.674519i | \(0.235649\pi\) |
0.215022 | + | 0.976609i | \(0.431018\pi\) | |||||||
\(420\) | 1.82661 | − | 1.85588i | 0.0891293 | − | 0.0905575i | ||||
\(421\) | −12.0938 | + | 20.9470i | −0.589414 | + | 1.02090i | 0.404895 | + | 0.914363i | \(0.367308\pi\) |
−0.994309 | + | 0.106532i | \(0.966025\pi\) | |||||||
\(422\) | −7.23436 | −0.352163 | ||||||||
\(423\) | −0.0643468 | − | 4.04771i | −0.00312865 | − | 0.196807i | ||||
\(424\) | −4.50537 | −0.218800 | ||||||||
\(425\) | −8.56090 | + | 14.8279i | −0.415265 | + | 0.719260i | ||||
\(426\) | −12.6433 | − | 3.28028i | −0.612568 | − | 0.158930i | ||||
\(427\) | −6.47465 | − | 11.2144i | −0.313330 | − | 0.542704i | ||||
\(428\) | −4.82603 | − | 8.35894i | −0.233275 | − | 0.404044i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.00488675 | + | 0.00846409i | −0.000235660 | + | 0.000408175i | ||||
\(431\) | 12.2455 | 0.589844 | 0.294922 | − | 0.955521i | \(-0.404706\pi\) | ||||
0.294922 | + | 0.955521i | \(0.404706\pi\) | |||||||
\(432\) | 7.25649 | − | 2.13104i | 0.349128 | − | 0.102530i | ||||
\(433\) | −7.13183 | −0.342734 | −0.171367 | − | 0.985207i | \(-0.554818\pi\) | ||||
−0.171367 | + | 0.985207i | \(0.554818\pi\) | |||||||
\(434\) | −2.23185 | + | 3.86568i | −0.107132 | + | 0.185559i | ||||
\(435\) | 0.222772 | + | 0.805728i | 0.0106811 | + | 0.0386317i | ||||
\(436\) | −2.38166 | − | 4.12515i | −0.114061 | − | 0.197559i | ||||
\(437\) | 20.3373 | + | 35.2252i | 0.972863 | + | 1.68505i | ||||
\(438\) | −1.43005 | − | 0.371024i | −0.0683303 | − | 0.0177282i | ||||
\(439\) | −9.59720 | + | 16.6228i | −0.458049 | + | 0.793365i | −0.998858 | − | 0.0477810i | \(-0.984785\pi\) |
0.540808 | + | 0.841146i | \(0.318118\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.1662 | + | 6.21225i | 0.531721 | + | 0.295822i | ||||
\(442\) | −9.88275 | −0.470075 | ||||||||
\(443\) | 4.82527 | − | 8.35762i | 0.229256 | − | 0.397083i | −0.728332 | − | 0.685224i | \(-0.759704\pi\) |
0.957588 | + | 0.288142i | \(0.0930375\pi\) | |||||||
\(444\) | 4.74826 | − | 4.82434i | 0.225342 | − | 0.228953i | ||||
\(445\) | 1.22339 | + | 2.11898i | 0.0579944 | + | 0.100449i | ||||
\(446\) | 0.961405 | + | 1.66520i | 0.0455238 | + | 0.0788496i | ||||
\(447\) | 14.6444 | − | 14.8790i | 0.692654 | − | 0.703753i | ||||
\(448\) | 1.69372 | − | 2.93361i | 0.0800207 | − | 0.138600i | ||||
\(449\) | −15.3818 | −0.725912 | −0.362956 | − | 0.931806i | \(-0.618233\pi\) | ||||
−0.362956 | + | 0.931806i | \(0.618233\pi\) | |||||||
\(450\) | 8.73262 | + | 4.85837i | 0.411660 | + | 0.229026i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.2831 | − | 21.2749i | 0.577747 | − | 1.00069i | ||||
\(453\) | 34.3774 | + | 8.91916i | 1.61519 | + | 0.419059i | ||||
\(454\) | −2.19764 | − | 3.80642i | −0.103140 | − | 0.178644i | ||||
\(455\) | −2.04261 | − | 3.53791i | −0.0957591 | − | 0.165860i | ||||
\(456\) | 6.73271 | + | 24.3510i | 0.315288 | + | 1.14034i | ||||
\(457\) | −9.54887 | + | 16.5391i | −0.446678 | + | 0.773668i | −0.998167 | − | 0.0605134i | \(-0.980726\pi\) |
0.551490 | + | 0.834182i | \(0.314060\pi\) | |||||||
\(458\) | 17.3757 | 0.811911 | ||||||||
\(459\) | 13.0999 | + | 12.4896i | 0.611449 | + | 0.582964i | ||||
\(460\) | 2.99784 | 0.139775 | ||||||||
\(461\) | 4.18590 | − | 7.25020i | 0.194957 | − | 0.337675i | −0.751929 | − | 0.659244i | \(-0.770877\pi\) |
0.946886 | + | 0.321568i | \(0.104210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.1298 | − | 24.4735i | −0.656665 | − | 1.13738i | −0.981474 | − | 0.191598i | \(-0.938633\pi\) |
0.324808 | − | 0.945780i | \(-0.394700\pi\) | |||||||
\(464\) | −1.20786 | − | 2.09207i | −0.0560733 | − | 0.0971218i | ||||
\(465\) | −0.957026 | − | 0.248299i | −0.0443810 | − | 0.0115146i | ||||
\(466\) | 0.220202 | − | 0.381402i | 0.0102007 | − | 0.0176681i | ||||
\(467\) | −8.22408 | −0.380565 | −0.190282 | − | 0.981729i | \(-0.560940\pi\) | ||||
−0.190282 | + | 0.981729i | \(0.560940\pi\) | |||||||
\(468\) | −0.307605 | − | 19.3498i | −0.0142190 | − | 0.894444i | ||||
\(469\) | 29.9822 | 1.38445 | ||||||||
\(470\) | 0.132959 | − | 0.230292i | 0.00613294 | − | 0.0106226i | ||||
\(471\) | −10.2729 | + | 10.4375i | −0.473349 | + | 0.480934i | ||||
\(472\) | 17.4850 | + | 30.2850i | 0.804815 | + | 1.39398i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.73491 | − | 1.76270i | 0.0796868 | − | 0.0809637i | ||||
\(475\) | 14.9407 | − | 25.8780i | 0.685525 | − | 1.18736i | ||||
\(476\) | −18.0086 | −0.825422 | ||||||||
\(477\) | 4.83291 | − | 2.89367i | 0.221284 | − | 0.132492i | ||||
\(478\) | −11.4760 | −0.524901 | ||||||||
\(479\) | −15.2111 | + | 26.3463i | −0.695012 | + | 1.20380i | 0.275165 | + | 0.961397i | \(0.411267\pi\) |
−0.970177 | + | 0.242398i | \(0.922066\pi\) | |||||||
\(480\) | 2.82049 | + | 0.731773i | 0.128737 | + | 0.0334007i | ||||
\(481\) | −5.30975 | − | 9.19677i | −0.242104 | − | 0.419336i | ||||
\(482\) | −8.30120 | − | 14.3781i | −0.378109 | − | 0.654905i | ||||
\(483\) | 10.3628 | + | 37.4805i | 0.471525 | + | 1.70542i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.285992 | 0.0129862 | ||||||||
\(486\) | 7.16708 | − | 7.76061i | 0.325105 | − | 0.352028i | ||||
\(487\) | −22.2893 | −1.01002 | −0.505012 | − | 0.863112i | \(-0.668512\pi\) | ||||
−0.505012 | + | 0.863112i | \(0.668512\pi\) | |||||||
\(488\) | 4.62994 | − | 8.01929i | 0.209588 | − | 0.363016i | ||||
\(489\) | −10.7422 | − | 38.8526i | −0.485779 | − | 1.75697i | ||||
\(490\) | 0.419675 | + | 0.726898i | 0.0189590 | + | 0.0328379i | ||||
\(491\) | −16.1829 | − | 28.0296i | −0.730325 | − | 1.26496i | −0.956744 | − | 0.290930i | \(-0.906035\pi\) |
0.226419 | − | 0.974030i | \(-0.427298\pi\) | |||||||
\(492\) | 16.7553 | + | 4.34713i | 0.755386 | + | 0.195984i | ||||
\(493\) | 2.89064 | − | 5.00674i | 0.130188 | − | 0.225492i | ||||
\(494\) | 17.2476 | 0.776005 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.85714 | 0.128289 | ||||||||
\(497\) | −18.6704 | + | 32.3380i | −0.837480 | + | 1.45056i | ||||
\(498\) | 7.71911 | − | 7.84280i | 0.345902 | − | 0.351444i | ||||
\(499\) | −0.130887 | − | 0.226703i | −0.00585931 | − | 0.0101486i | 0.863081 | − | 0.505066i | \(-0.168532\pi\) |
−0.868940 | + | 0.494917i | \(0.835198\pi\) | |||||||
\(500\) | −2.22129 | − | 3.84738i | −0.0993391 | − | 0.172060i | ||||
\(501\) | 23.7859 | − | 24.1670i | 1.06268 | − | 1.07970i | ||||
\(502\) | 6.05532 | − | 10.4881i | 0.270262 | − | 0.468108i | ||||
\(503\) | 18.0436 | 0.804525 | 0.402263 | − | 0.915524i | \(-0.368224\pi\) | ||||
0.402263 | + | 0.915524i | \(0.368224\pi\) | |||||||
\(504\) | 0.383932 | + | 24.1511i | 0.0171017 | + | 1.07577i | ||||
\(505\) | 1.13748 | 0.0506174 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.59233 | − | 1.96982i | −0.337187 | − | 0.0874828i | ||||
\(508\) | 14.2568 | + | 24.6934i | 0.632542 | + | 1.09559i | ||||
\(509\) | 2.12639 | + | 3.68302i | 0.0942506 | + | 0.163247i | 0.909296 | − | 0.416151i | \(-0.136621\pi\) |
−0.815045 | + | 0.579398i | \(0.803288\pi\) | |||||||
\(510\) | 0.316832 | + | 1.14593i | 0.0140296 | + | 0.0507424i | ||||
\(511\) | −2.11176 | + | 3.65767i | −0.0934186 | + | 0.161806i | ||||
\(512\) | −15.4052 | −0.680819 | ||||||||
\(513\) | −22.8621 | − | 21.7971i | −1.00939 | − | 0.962365i | ||||
\(514\) | 0.844884 | 0.0372662 | ||||||||
\(515\) | −2.24818 | + | 3.89397i | −0.0990668 | + | 0.171589i | ||||
\(516\) | 0.0352712 | + | 0.127570i | 0.00155273 | + | 0.00561593i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.88386 | + | 4.99500i | 0.126710 | + | 0.219468i | ||||
\(519\) | 30.0272 | + | 7.79051i | 1.31805 | + | 0.341965i | ||||
\(520\) | 1.46064 | − | 2.52991i | 0.0640535 | − | 0.110944i | ||||
\(521\) | 13.7326 | 0.601635 | 0.300817 | − | 0.953682i | \(-0.402741\pi\) | ||||
0.300817 | + | 0.953682i | \(0.402741\pi\) | |||||||
\(522\) | −2.94862 | − | 1.64046i | −0.129058 | − | 0.0718009i | ||||
\(523\) | −26.0362 | −1.13849 | −0.569243 | − | 0.822170i | \(-0.692764\pi\) | ||||
−0.569243 | + | 0.822170i | \(0.692764\pi\) | |||||||
\(524\) | 0.666106 | − | 1.15373i | 0.0290990 | − | 0.0504009i | ||||
\(525\) | 20.0394 | − | 20.3605i | 0.874590 | − | 0.888604i | ||||
\(526\) | 5.68588 | + | 9.84823i | 0.247916 | + | 0.429403i | ||||
\(527\) | 3.41885 | + | 5.92162i | 0.148927 | + | 0.257950i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.8841 | + | 18.8518i | −0.473222 | + | 0.819644i | ||||
\(530\) | 0.370016 | 0.0160725 | ||||||||
\(531\) | −38.2074 | − | 21.2566i | −1.65806 | − | 0.922456i | ||||
\(532\) | 31.4289 | 1.36262 | ||||||||
\(533\) | 13.5782 | − | 23.5182i | 0.588139 | − | 1.01869i | ||||
\(534\) | −9.55963 | − | 2.48023i | −0.413686 | − | 0.107330i | ||||
\(535\) | 0.910837 | + | 1.57762i | 0.0393789 | + | 0.0682063i | ||||
\(536\) | 10.7200 | + | 18.5675i | 0.463031 | + | 0.801994i | ||||
\(537\) | 4.36158 | + | 15.7751i | 0.188216 | + | 0.680744i | ||||
\(538\) | 7.44430 | − | 12.8939i | 0.320946 | − | 0.555895i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.23378 | + | 0.656004i | −0.0961268 | + | 0.0282299i | ||||
\(541\) | −15.1235 | −0.650211 | −0.325106 | − | 0.945678i | \(-0.605400\pi\) | ||||
−0.325106 | + | 0.945678i | \(0.605400\pi\) | |||||||
\(542\) | −3.42505 | + | 5.93236i | −0.147118 | + | 0.254816i | ||||
\(543\) | 5.11411 | + | 18.4968i | 0.219467 | + | 0.793774i | ||||
\(544\) | −10.0758 | − | 17.4519i | −0.431998 | − | 0.748242i | ||||
\(545\) | 0.449500 | + | 0.778557i | 0.0192545 | + | 0.0333497i | ||||
\(546\) | 15.9610 | + | 4.14107i | 0.683069 | + | 0.177221i | ||||
\(547\) | −11.1215 | + | 19.2630i | −0.475521 | + | 0.823627i | −0.999607 | − | 0.0280389i | \(-0.991074\pi\) |
0.524086 | + | 0.851665i | \(0.324407\pi\) | |||||||
\(548\) | 19.0718 | 0.814709 | ||||||||
\(549\) | 0.184024 | + | 11.5760i | 0.00785395 | + | 0.494050i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.04481 | + | 8.73786i | −0.214916 | + | 0.372245i | ||||
\(552\) | −19.5059 | + | 19.8184i | −0.830226 | + | 0.843529i | ||||
\(553\) | −3.53523 | − | 6.12320i | −0.150333 | − | 0.260385i | ||||
\(554\) | −2.63380 | − | 4.56187i | −0.111899 | − | 0.193815i | ||||
\(555\) | −0.896157 | + | 0.910517i | −0.0380398 | + | 0.0386493i | ||||
\(556\) | 0.513051 | − | 0.888630i | 0.0217582 | − | 0.0376863i | ||||
\(557\) | 35.8076 | 1.51722 | 0.758609 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758609 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(558\) | 3.42399 | − | 2.05009i | 0.144949 | − | 0.0867872i | ||||
\(559\) | 0.207644 | 0.00878239 | ||||||||
\(560\) | 0.710102 | − | 1.22993i | 0.0300073 | − | 0.0519742i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.9411 | + | 18.9505i | 0.461522 | + | 0.799380i | ||||
\(563\) | 16.8060 | + | 29.1089i | 0.708289 | + | 1.22679i | 0.965491 | + | 0.260435i | \(0.0838660\pi\) |
−0.257202 | + | 0.966358i | \(0.582801\pi\) | |||||||
\(564\) | −0.959661 | − | 3.47092i | −0.0404090 | − | 0.146152i | ||||
\(565\) | −2.31823 | + | 4.01530i | −0.0975288 | + | 0.168925i | ||||
\(566\) | −8.48648 | −0.356713 | ||||||||
\(567\) | −15.9234 | − | 25.6603i | −0.668719 | − | 1.07763i | ||||
\(568\) | −26.7019 | −1.12039 | ||||||||
\(569\) | −11.3739 | + | 19.7001i | −0.476817 | + | 0.825872i | −0.999647 | − | 0.0265652i | \(-0.991543\pi\) |
0.522830 | + | 0.852437i | \(0.324876\pi\) | |||||||
\(570\) | −0.552942 | − | 1.99989i | −0.0231602 | − | 0.0837663i | ||||
\(571\) | −17.6597 | − | 30.5875i | −0.739035 | − | 1.28005i | −0.952930 | − | 0.303190i | \(-0.901948\pi\) |
0.213895 | − | 0.976857i | \(-0.431385\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.60679 | + | 1.97357i | 0.317778 | + | 0.0824472i | ||||
\(574\) | −7.37468 | + | 12.7733i | −0.307813 | + | 0.533148i | ||||
\(575\) | 32.8887 | 1.37155 | ||||||||
\(576\) | −2.59841 | + | 1.55578i | −0.108267 | + | 0.0648242i | ||||
\(577\) | 29.5174 | 1.22883 | 0.614413 | − | 0.788984i | \(-0.289393\pi\) | ||||
0.614413 | + | 0.788984i | \(0.289393\pi\) | |||||||
\(578\) | −1.64904 | + | 2.85623i | −0.0685912 | + | 0.118803i | ||||
\(579\) | −16.4004 | + | 16.6632i | −0.681576 | + | 0.692497i | ||||
\(580\) | 0.371818 | + | 0.644007i | 0.0154389 | + | 0.0267409i | ||||
\(581\) | −15.7293 | − | 27.2440i | −0.652561 | − | 1.13027i | ||||
\(582\) | −0.809750 | + | 0.822725i | −0.0335652 | + | 0.0341031i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3.02018 | −0.124976 | ||||||||
\(585\) | 0.0580555 | + | 3.65196i | 0.00240030 | + | 0.150990i | ||||
\(586\) | −12.4585 | −0.514657 | ||||||||
\(587\) | 16.5389 | − | 28.6462i | 0.682632 | − | 1.18235i | −0.291542 | − | 0.956558i | \(-0.594168\pi\) |
0.974175 | − | 0.225796i | \(-0.0724983\pi\) | |||||||
\(588\) | 11.0025 | + | 2.85457i | 0.453734 | + | 0.117721i | ||||
\(589\) | −5.96664 | − | 10.3345i | −0.245851 | − | 0.425827i | ||||
\(590\) | −1.43601 | − | 2.48724i | −0.0591195 | − | 0.102398i | ||||
\(591\) | −0.784884 | − | 2.83878i | −0.0322858 | − | 0.116772i | ||||
\(592\) | 1.84591 | − | 3.19720i | 0.0758663 | − | 0.131404i | ||||
\(593\) | 9.74358 | 0.400121 | 0.200060 | − | 0.979784i | \(-0.435886\pi\) | ||||
0.200060 | + | 0.979784i | \(0.435886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.39883 | 0.139339 | ||||||||
\(596\) | 9.28561 | − | 16.0831i | 0.380353 | − | 0.658791i | ||||
\(597\) | −4.68227 | − | 16.9349i | −0.191633 | − | 0.693101i | ||||
\(598\) | 9.49173 | + | 16.4402i | 0.388146 | + | 0.672288i | ||||
\(599\) | −13.9289 | − | 24.1256i | −0.569120 | − | 0.985744i | −0.996653 | − | 0.0817449i | \(-0.973951\pi\) |
0.427533 | − | 0.904000i | \(-0.359383\pi\) | |||||||
\(600\) | 19.7739 | + | 5.13030i | 0.807264 | + | 0.209444i | ||||
\(601\) | −10.6596 | + | 18.4630i | −0.434815 | + | 0.753122i | −0.997281 | − | 0.0736992i | \(-0.976520\pi\) |
0.562466 | + | 0.826821i | \(0.309853\pi\) | |||||||
\(602\) | −0.112777 | −0.00459643 | ||||||||
\(603\) | −23.4247 | − | 13.0322i | −0.953926 | − | 0.530714i | ||||
\(604\) | 31.5933 | 1.28551 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.22064 | + | 3.27225i | −0.130830 | + | 0.132926i | ||||
\(607\) | 9.57155 | + | 16.5784i | 0.388497 | + | 0.672897i | 0.992248 | − | 0.124277i | \(-0.0396610\pi\) |
−0.603750 | + | 0.797173i | \(0.706328\pi\) | |||||||
\(608\) | 17.5845 | + | 30.4573i | 0.713148 | + | 1.23521i | ||||
\(609\) | −6.76642 | + | 6.87484i | −0.274189 | + | 0.278583i | ||||
\(610\) | −0.380246 | + | 0.658606i | −0.0153957 | + | 0.0266662i | ||||
\(611\) | −5.64959 | −0.228558 | ||||||||
\(612\) | 14.0698 | + | 7.82770i | 0.568739 | + | 0.316416i | ||||
\(613\) | −6.05388 | −0.244514 | −0.122257 | − | 0.992498i | \(-0.539013\pi\) | ||||
−0.122257 | + | 0.992498i | \(0.539013\pi\) | |||||||
\(614\) | −2.85430 | + | 4.94380i | −0.115190 | + | 0.199515i | ||||
\(615\) | −3.16229 | − | 0.820451i | −0.127516 | − | 0.0330838i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.1632 | + | 26.2634i | 0.610448 | + | 1.05733i | 0.991165 | + | 0.132635i | \(0.0423438\pi\) |
−0.380717 | + | 0.924692i | \(0.624323\pi\) | |||||||
\(618\) | −4.83649 | − | 17.4927i | −0.194552 | − | 0.703661i | ||||
\(619\) | 2.33034 | − | 4.03627i | 0.0936642 | − | 0.162231i | −0.815386 | − | 0.578918i | \(-0.803475\pi\) |
0.909050 | + | 0.416686i | \(0.136809\pi\) | |||||||
\(620\) | −0.879520 | −0.0353224 | ||||||||
\(621\) | 8.19515 | − | 33.7873i | 0.328860 | − | 1.35584i | ||||
\(622\) | −7.65993 | −0.307135 | ||||||||
\(623\) | −14.1168 | + | 24.4509i | −0.565576 | + | 0.979606i | ||||
\(624\) | −2.81268 | − | 10.1729i | −0.112597 | − | 0.407243i | ||||
\(625\) | −11.8694 | − | 20.5583i | −0.474775 | − | 0.822334i | ||||
\(626\) | 2.07050 | + | 3.58620i | 0.0827536 | + | 0.143334i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.51377 | + | 11.2822i | −0.259928 | + | 0.450208i | ||||
\(629\) | 8.83525 | 0.352284 | ||||||||
\(630\) | −0.0315314 | − | 1.98347i | −0.00125624 | − | 0.0790234i | ||||
\(631\) | 49.0740 | 1.95360 | 0.976802 | − | 0.214146i | \(-0.0686968\pi\) | ||||
0.976802 | + | 0.214146i | \(0.0686968\pi\) | |||||||
\(632\) | 2.52800 | − | 4.37862i | 0.100558 | − | 0.174172i | ||||
\(633\) | 12.9703 | − | 13.1781i | 0.515522 | − | 0.523783i | ||||
\(634\) | −0.280750 | − | 0.486273i | −0.0111500 | − | 0.0193124i | ||||
\(635\) | −2.69074 | − | 4.66049i | −0.106779 | − | 0.184946i | ||||
\(636\) | 3.51495 | − | 3.57127i | 0.139377 | − | 0.141610i | ||||
\(637\) | 8.91624 | − | 15.4434i | 0.353274 | − | 0.611889i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.6431 | − | 17.1498i | 1.13310 | − | 0.678437i | ||||
\(640\) | 3.16571 | 0.125136 | ||||||||
\(641\) | −14.3613 | + | 24.8746i | −0.567239 | + | 0.982487i | 0.429598 | + | 0.903020i | \(0.358655\pi\) |
−0.996837 | + | 0.0794670i | \(0.974678\pi\) | |||||||
\(642\) | −7.11731 | − | 1.84658i | −0.280898 | − | 0.0728786i | ||||
\(643\) | −6.51054 | − | 11.2766i | −0.256751 | − | 0.444705i | 0.708619 | − | 0.705591i | \(-0.249319\pi\) |
−0.965370 | + | 0.260886i | \(0.915985\pi\) | |||||||
\(644\) | 17.2961 | + | 29.9576i | 0.681560 | + | 1.18050i | ||||
\(645\) | −0.00665687 | − | 0.0240767i | −0.000262114 | − | 0.000948020i | ||||
\(646\) | −7.17484 | + | 12.4272i | −0.282290 | + | 0.488941i | ||||
\(647\) | 36.6127 | 1.43939 | 0.719696 | − | 0.694289i | \(-0.244281\pi\) | ||||
0.719696 | + | 0.694289i | \(0.244281\pi\) | |||||||
\(648\) | 10.1977 | − | 19.0357i | 0.400603 | − | 0.747795i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.97305 | − | 12.0777i | 0.273506 | − | 0.473726i | ||||
\(651\) | −3.04030 | − | 10.9962i | −0.119159 | − | 0.430976i | ||||
\(652\) | −17.9292 | − | 31.0543i | −0.702162 | − | 1.21618i | ||||
\(653\) | 5.83469 | + | 10.1060i | 0.228329 | + | 0.395478i | 0.957313 | − | 0.289053i | \(-0.0933404\pi\) |
−0.728984 | + | 0.684531i | \(0.760007\pi\) | |||||||
\(654\) | −3.51241 | − | 0.911290i | −0.137346 | − | 0.0356343i | ||||
\(655\) | −0.125717 | + | 0.217748i | −0.00491216 | + | 0.00850811i | ||||
\(656\) | 9.44080 | 0.368601 | ||||||||
\(657\) | 3.23974 | − | 1.93977i | 0.126394 | − | 0.0756778i | ||||
\(658\) | 3.06843 | 0.119620 | ||||||||
\(659\) | −19.8661 | + | 34.4091i | −0.773873 | + | 1.34039i | 0.161553 | + | 0.986864i | \(0.448350\pi\) |
−0.935426 | + | 0.353523i | \(0.884984\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.7410 | − | 18.6039i | −0.417775 | − | 0.723607i | 0.577940 | − | 0.816079i | \(-0.303857\pi\) |
−0.995715 | + | 0.0924716i | \(0.970523\pi\) | |||||||
\(662\) | 2.77320 | + | 4.80333i | 0.107784 | + | 0.186687i | ||||
\(663\) | 17.7185 | − | 18.0024i | 0.688129 | − | 0.699156i | ||||
\(664\) | 11.2478 | − | 19.4818i | 0.436500 | − | 0.756040i | ||||
\(665\) | −5.93171 | −0.230022 | ||||||||
\(666\) | −0.0819658 | − | 5.15603i | −0.00317611 | − | 0.199792i | ||||
\(667\) | −11.1051 | −0.429990 | ||||||||
\(668\) | 15.0820 | − | 26.1228i | 0.583541 | − | 1.01072i | ||||
\(669\) | −4.75700 | − | 1.23420i | −0.183916 | − | 0.0477168i | ||||
\(670\) | −0.880405 | − | 1.52491i | −0.0340130 | − | 0.0589123i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 8.96019 | + | 32.4074i | 0.345647 | + | 1.25014i | ||||
\(673\) | −10.2554 | + | 17.7629i | −0.395316 | + | 0.684708i | −0.993141 | − | 0.116919i | \(-0.962698\pi\) |
0.597825 | + | 0.801626i | \(0.296032\pi\) | |||||||
\(674\) | −1.69746 | −0.0653836 | ||||||||
\(675\) | −24.5064 | + | 7.19690i | −0.943254 | + | 0.277009i | ||||
\(676\) | −6.97745 | −0.268364 | ||||||||
\(677\) | 0.591492 | − | 1.02450i | 0.0227329 | − | 0.0393745i | −0.854435 | − | 0.519558i | \(-0.826097\pi\) |
0.877168 | + | 0.480184i | \(0.159430\pi\) | |||||||
\(678\) | −4.98719 | − | 18.0378i | −0.191532 | − | 0.692736i | ||||
\(679\) | 1.65003 | + | 2.85794i | 0.0633225 | + | 0.109678i | ||||
\(680\) | 1.21523 | + | 2.10484i | 0.0466020 | + | 0.0807170i | ||||
\(681\) | 10.8738 | + | 2.82120i | 0.416687 | + | 0.108109i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.06013 | −0.231884 | −0.115942 | − | 0.993256i | \(-0.536989\pi\) | ||||
−0.115942 | + | 0.993256i | \(0.536989\pi\) | |||||||
\(684\) | −24.5549 | − | 13.6611i | −0.938882 | − | 0.522344i | ||||
\(685\) | −3.59951 | −0.137530 | ||||||||
\(686\) | 3.11605 | − | 5.39715i | 0.118971 | − | 0.206064i | ||||
\(687\) | −31.1523 | + | 31.6515i | −1.18853 | + | 1.20758i | ||||
\(688\) | 0.0360931 | + | 0.0625151i | 0.00137604 | + | 0.00238336i | ||||
\(689\) | −3.93061 | − | 6.80801i | −0.149744 | − | 0.259364i | ||||
\(690\) | 1.60197 | − | 1.62764i | 0.0609861 | − | 0.0619633i | ||||
\(691\) | −21.4146 | + | 37.0912i | −0.814650 | + | 1.41101i | 0.0949295 | + | 0.995484i | \(0.469737\pi\) |
−0.909579 | + | 0.415531i | \(0.863596\pi\) | |||||||
\(692\) | 27.5954 | 1.04902 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.3645 | −0.810984 | ||||||||
\(695\) | −0.0968302 | + | 0.167715i | −0.00367298 | + | 0.00636179i | ||||
\(696\) | −6.67676 | − | 1.73228i | −0.253082 | − | 0.0656618i | ||||
\(697\) | 11.2969 | + | 19.5667i | 0.427899 | + | 0.741143i | ||||
\(698\) | 2.96545 | + | 5.13631i | 0.112244 | + | 0.194412i | ||||
\(699\) | 0.299966 | + | 1.08492i | 0.0113458 | + | 0.0410356i | ||||
\(700\) | 12.7065 | − | 22.0082i | 0.480259 | − | 0.831833i | ||||
\(701\) | 3.89209 | 0.147002 | 0.0735011 | − | 0.997295i | \(-0.476583\pi\) | ||||
0.0735011 | + | 0.997295i | \(0.476583\pi\) | |||||||
\(702\) | −10.6701 | − | 10.1731i | −0.402718 | − | 0.383957i | ||||
\(703\) | −15.4195 | −0.581556 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.181121 | + | 0.655081i | 0.00682140 | + | 0.0246718i | ||||
\(706\) | 0.149041 | + | 0.258146i | 0.00560922 | + | 0.00971545i | ||||
\(707\) | 6.56273 | + | 11.3670i | 0.246817 | + | 0.427499i | ||||
\(708\) | −37.6473 | − | 9.76753i | −1.41487 | − | 0.367086i | ||||
\(709\) | −11.0746 | + | 19.1818i | −0.415917 | + | 0.720389i | −0.995524 | − | 0.0945071i | \(-0.969873\pi\) |
0.579608 | + | 0.814896i | \(0.303206\pi\) | |||||||
\(710\) | 2.19296 | 0.0823004 | ||||||||
\(711\) | 0.100479 | + | 6.32060i | 0.00376826 | + | 0.237041i | ||||
\(712\) | −20.1894 | −0.756630 | ||||||||
\(713\) | 6.56716 | − | 11.3746i | 0.245942 | − | 0.425984i | ||||
\(714\) | −9.62336 | + | 9.77756i | −0.360145 | + | 0.365916i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.27968 | + | 12.6088i | 0.272054 | + | 0.471212i | ||||
\(717\) | 20.5750 | − | 20.9047i | 0.768389 | − | 0.780701i | ||||
\(718\) | −5.67145 | + | 9.82323i | −0.211657 | + | 0.366600i | ||||
\(719\) | −37.5592 | −1.40072 | −0.700362 | − | 0.713788i | \(-0.746978\pi\) | ||||
−0.700362 | + | 0.713788i | \(0.746978\pi\) | |||||||
\(720\) | −1.08940 | + | 0.652271i | −0.0405996 | + | 0.0243087i | ||||
\(721\) | −51.8837 | −1.93225 | ||||||||
\(722\) | 6.08383 | − | 10.5375i | 0.226417 | − | 0.392165i | ||||
\(723\) | 41.0741 | + | 10.6566i | 1.52756 | + | 0.396324i | ||||
\(724\) | 8.53568 | + | 14.7842i | 0.317226 | + | 0.549452i | ||||
\(725\) | 4.07914 | + | 7.06529i | 0.151496 | + | 0.262398i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.2388 | − | 24.6624i | 0.528090 | − | 0.914678i | −0.471374 | − | 0.881933i | \(-0.656242\pi\) |
0.999464 | − | 0.0327447i | \(-0.0104248\pi\) | |||||||
\(728\) | 33.7088 | 1.24933 | ||||||||
\(729\) | 1.28707 | + | 26.9693i | 0.0476691 | + | 0.998863i | ||||
\(730\) | 0.248040 | 0.00918038 | ||||||||
\(731\) | −0.0863780 | + | 0.149611i | −0.00319481 | + | 0.00553356i | ||||
\(732\) | 2.74451 | + | 9.92641i | 0.101440 | + | 0.366891i | ||||
\(733\) | 7.94821 | + | 13.7667i | 0.293574 | + | 0.508485i | 0.974652 | − | 0.223726i | \(-0.0718220\pi\) |
−0.681078 | + | 0.732211i | \(0.738489\pi\) | |||||||
\(734\) | −4.99739 | − | 8.65574i | −0.184457 | − | 0.319489i | ||||
\(735\) | −2.07654 | − | 0.538755i | −0.0765943 | − | 0.0198723i | ||||
\(736\) | −19.3543 | + | 33.5227i | −0.713411 | + | 1.23566i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 11.3138 | − | 6.77408i | 0.416468 | − | 0.249357i | ||||
\(739\) | −36.3058 | −1.33553 | −0.667766 | − | 0.744371i | \(-0.732749\pi\) | ||||
−0.667766 | + | 0.744371i | \(0.732749\pi\) | |||||||
\(740\) | −0.568230 | + | 0.984204i | −0.0208886 | + | 0.0361801i | ||||
\(741\) | −30.9227 | + | 31.4182i | −1.13597 | + | 1.15418i | ||||
\(742\) | 2.13481 | + | 3.69760i | 0.0783714 | + | 0.135743i | ||||
\(743\) | 20.9153 | + | 36.2264i | 0.767308 | + | 1.32902i | 0.939018 | + | 0.343869i | \(0.111738\pi\) |
−0.171710 | + | 0.985148i | \(0.554929\pi\) | |||||||
\(744\) | 5.72273 | − | 5.81443i | 0.209806 | − | 0.213167i | ||||
\(745\) | −1.75251 | + | 3.03544i | −0.0642070 | + | 0.111210i | ||||
\(746\) | 16.0274 | 0.586805 | ||||||||
\(747\) | 0.447062 | + | 28.1223i | 0.0163571 | + | 1.02894i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.5102 | + | 18.2041i | −0.384033 | + | 0.665165i | ||||
\(750\) | −3.27590 | − | 0.849928i | −0.119619 | − | 0.0310350i | ||||
\(751\) | −8.99786 | − | 15.5848i | −0.328337 | − | 0.568696i | 0.653845 | − | 0.756628i | \(-0.273155\pi\) |
−0.982182 | + | 0.187933i | \(0.939821\pi\) | |||||||
\(752\) | −0.982023 | − | 1.70091i | −0.0358107 | − | 0.0620260i | ||||
\(753\) | 8.24874 | + | 29.8342i | 0.300601 | + | 1.08722i | ||||
\(754\) | −2.35449 | + | 4.07810i | −0.0857456 | + | 0.148516i | ||||
\(755\) | −5.96272 | −0.217006 | ||||||||
\(756\) | −19.4434 | − | 18.5376i | −0.707148 | − | 0.674205i | ||||
\(757\) | 27.2640 | 0.990928 | 0.495464 | − | 0.868628i | \(-0.334998\pi\) | ||||
0.495464 | + | 0.868628i | \(0.334998\pi\) | |||||||
\(758\) | −3.88867 | + | 6.73538i | −0.141243 | + | 0.244640i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.12084 | − | 3.67341i | −0.0769311 | − | 0.133249i | ||||
\(761\) | −0.262219 | − | 0.454176i | −0.00950543 | − | 0.0164639i | 0.861234 | − | 0.508209i | \(-0.169692\pi\) |
−0.870739 | + | 0.491745i | \(0.836359\pi\) | |||||||
\(762\) | 21.0255 | + | 5.45504i | 0.761674 | + | 0.197615i | ||||
\(763\) | −5.18679 | + | 8.98379i | −0.187775 | + | 0.325235i | ||||
\(764\) | 6.99075 | 0.252916 | ||||||||
\(765\) | −2.65545 | − | 1.47735i | −0.0960082 | − | 0.0534139i | ||||
\(766\) | 5.37301 | 0.194135 | ||||||||
\(767\) | −30.5088 | + | 52.8428i | −1.10161 | + | 1.90804i | ||||
\(768\) | −11.4164 | + | 11.5993i | −0.411954 | + | 0.418555i | ||||
\(769\) | −0.597250 | − | 1.03447i | −0.0215374 | − | 0.0373038i | 0.855056 | − | 0.518536i | \(-0.173523\pi\) |
−0.876593 | + | 0.481232i | \(0.840189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.51477 | + | 1.53904i | −0.0545530 | + | 0.0554272i | ||||
\(772\) | −10.3991 | + | 18.0117i | −0.374270 | + | 0.648255i | ||||
\(773\) | 28.6486 | 1.03042 | 0.515209 | − | 0.857065i | \(-0.327714\pi\) | ||||
0.515209 | + | 0.857065i | \(0.327714\pi\) | |||||||
\(774\) | 0.0881106 | + | 0.0490200i | 0.00316707 | + | 0.00176199i | ||||
\(775\) | −9.64906 | −0.346604 | ||||||||
\(776\) | −1.17992 | + | 2.04368i | −0.0423566 | + | 0.0733638i | ||||
\(777\) | −14.2693 | − | 3.70214i | −0.511907 | − | 0.132814i | ||||
\(778\) | 3.06679 | + | 5.31183i | 0.109950 | + | 0.190438i | ||||
\(779\) | −19.7155 | − | 34.1482i | −0.706381 | − | 1.22349i | ||||
\(780\) | 0.865833 | + | 3.13156i | 0.0310018 | + | 0.112128i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −15.7939 | −0.564789 | ||||||||
\(783\) | 8.27475 | − | 2.43008i | 0.295715 | − | 0.0868439i | ||||
\(784\) | 6.19936 | 0.221406 | ||||||||
\(785\) | 1.22937 | − | 2.12933i | 0.0438781 | − | 0.0759990i | ||||
\(786\) | −0.270453 | − | 0.978180i | −0.00964675 | − | 0.0348905i | ||||
\(787\) | 5.75380 | + | 9.96587i | 0.205101 | + | 0.355245i | 0.950165 | − | 0.311748i | \(-0.100914\pi\) |
−0.745064 | + | 0.666993i | \(0.767581\pi\) | |||||||
\(788\) | −1.31001 | − | 2.26900i | −0.0466671 | − | 0.0808298i | ||||
\(789\) | −28.1336 | − | 7.29921i | −1.00158 | − | 0.259859i | ||||
\(790\) | −0.207619 | + | 0.359606i | −0.00738673 | + | 0.0127942i | ||||
\(791\) | −53.5003 | −1.90225 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1571 | 0.573756 | ||||||||
\(794\) | 1.82354 | − | 3.15847i | 0.0647152 | − | 0.112090i | ||||
\(795\) | −0.663390 | + | 0.674020i | −0.0235280 | + | 0.0239050i | ||||
\(796\) | −7.81493 | − | 13.5359i | −0.276993 | − | 0.479766i | ||||
\(797\) | −0.670392 | − | 1.16115i | −0.0237465 | − | 0.0411301i | 0.853908 | − | 0.520424i | \(-0.174226\pi\) |
−0.877654 | + | 0.479294i | \(0.840893\pi\) | |||||||
\(798\) | 16.7949 | − | 17.0640i | 0.594533 | − | 0.604059i | ||||
\(799\) | 2.35018 | − | 4.07063i | 0.0831433 | − | 0.144008i | ||||
\(800\) | 28.4371 | 1.00540 | ||||||||
\(801\) | 21.6572 | − | 12.9671i | 0.765218 | − | 0.458169i | ||||
\(802\) | 10.6179 | 0.374932 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −23.0813 | − | 5.98840i | −0.814013 | − | 0.211195i | ||||
\(805\) | −3.26435 | − | 5.65403i | −0.115053 | − | 0.199278i | ||||
\(806\) | −2.78473 | − | 4.82329i | −0.0980879 | − | 0.169893i | ||||
\(807\) | 10.1408 | + | 36.6776i | 0.356975 | + | 1.29111i | ||||
\(808\) | −4.69292 | + | 8.12838i | −0.165096 | + | 0.285955i | ||||
\(809\) | 29.7375 | 1.04551 | 0.522757 | − | 0.852482i | \(-0.324904\pi\) | ||||
0.522757 | + | 0.852482i | \(0.324904\pi\) | |||||||
\(810\) | −0.837511 | + | 1.56336i | −0.0294272 | + | 0.0549309i | ||||
\(811\) | −28.5904 | −1.00395 | −0.501973 | − | 0.864883i | \(-0.667392\pi\) | ||||
−0.501973 | + | 0.864883i | \(0.667392\pi\) | |||||||
\(812\) | −4.29041 | + | 7.43121i | −0.150564 | + | 0.260784i | ||||
\(813\) | −4.66570 | − | 16.8750i | −0.163633 | − | 0.591832i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.38385 | + | 5.86101i | 0.118531 | + | 0.205302i | ||||
\(816\) | 8.49983 | + | 2.20527i | 0.297554 | + | 0.0771999i | ||||
\(817\) | 0.150749 | − | 0.261104i | 0.00527403 | − | 0.00913488i | ||||
\(818\) | −15.4111 | −0.538835 | ||||||||
\(819\) | −36.1594 | + | 21.6502i | −1.26351 | + | 0.756519i | ||||
\(820\) | −2.90619 | −0.101488 | ||||||||
\(821\) | −7.76988 | + | 13.4578i | −0.271171 | + | 0.469681i | −0.969162 | − | 0.246425i | \(-0.920744\pi\) |
0.697991 | + | 0.716106i | \(0.254077\pi\) | |||||||
\(822\) | 10.1915 | − | 10.3548i | 0.355471 | − | 0.361167i | ||||
\(823\) | 20.2888 | + | 35.1413i | 0.707225 | + | 1.22495i | 0.965883 | + | 0.258980i | \(0.0833865\pi\) |
−0.258658 | + | 0.965969i | \(0.583280\pi\) | |||||||
\(824\) | −18.5507 | − | 32.1307i | −0.646244 | − | 1.11933i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.5701 | − | 28.7003i | 0.576548 | − | 0.998610i | ||||
\(827\) | 2.54353 | 0.0884472 | 0.0442236 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442236 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(828\) | −0.491592 | − | 30.9234i | −0.0170840 | − | 1.07466i | ||||
\(829\) | −14.3710 | −0.499127 | −0.249564 | − | 0.968358i | \(-0.580287\pi\) | ||||
−0.249564 | + | 0.968358i | \(0.580287\pi\) | |||||||
\(830\) | −0.923757 | + | 1.59999i | −0.0320641 | + | 0.0555366i | ||||
\(831\) | 13.0319 | + | 3.38112i | 0.452073 | + | 0.117290i | ||||
\(832\) | 2.11329 | + | 3.66032i | 0.0732651 | + | 0.126899i | ||||
\(833\) | 7.41816 | + | 12.8486i | 0.257024 | + | 0.445178i | ||||
\(834\) | −0.208310 | − | 0.753419i | −0.00721318 | − | 0.0260888i | ||||
\(835\) | −2.84649 | + | 4.93027i | −0.0985069 | + | 0.170619i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.40433 | + | 9.91268i | −0.0831059 | + | 0.342632i | ||||
\(838\) | 26.4469 | 0.913593 | ||||||||
\(839\) | −18.7905 | + | 32.5461i | −0.648721 | + | 1.12362i | 0.334708 | + | 0.942322i | \(0.391362\pi\) |
−0.983429 | + | 0.181296i | \(0.941971\pi\) | |||||||
\(840\) | −1.08067 | − | 3.90861i | −0.0372868 | − | 0.134860i | ||||
\(841\) | 13.1227 | + | 22.7291i | 0.452505 | + | 0.783762i | ||||
\(842\) | 8.19557 | + | 14.1951i | 0.282438 | + | 0.489197i | ||||
\(843\) | −54.1362 | − | 14.0456i | −1.86455 | − | 0.483755i | ||||
\(844\) | 8.22412 | − | 14.2446i | 0.283086 | − | 0.490319i | ||||
\(845\) | 1.31688 | 0.0453022 | ||||||||
\(846\) | −2.39732 | − | 1.33374i | −0.0824215 | − | 0.0458549i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.36645 | − | 2.36677i | 0.0469242 | − | 0.0812751i | ||||
\(849\) | 15.2152 | − | 15.4590i | 0.522183 | − | 0.530550i | ||||
\(850\) | 5.80146 | + | 10.0484i | 0.198988 | + | 0.344658i | ||||
\(851\) | −8.48567 | − | 14.6976i | −0.290885 | − | 0.503828i | ||||
\(852\) | 20.8319 | − | 21.1657i | 0.713690 | − | 0.725126i | ||||
\(853\) | 17.5579 | − | 30.4111i | 0.601170 | − | 1.04126i | −0.391474 | − | 0.920189i | \(-0.628035\pi\) |
0.992644 | − | 0.121068i | \(-0.0386318\pi\) | |||||||
\(854\) | −8.77534 | −0.300286 | ||||||||
\(855\) | 4.63435 | + | 2.57831i | 0.158492 | + | 0.0881763i | ||||
\(856\) | −15.0314 | −0.513762 | ||||||||
\(857\) | 14.5051 | − | 25.1236i | 0.495486 | − | 0.858206i | −0.504501 | − | 0.863411i | \(-0.668323\pi\) |
0.999986 | + | 0.00520496i | \(0.00165680\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.95891 | + | 3.39292i | 0.0668370 | + | 0.115765i | 0.897507 | − | 0.440999i | \(-0.145376\pi\) |
−0.830670 | + | 0.556764i | \(0.812043\pi\) | |||||||
\(860\) | −0.0111106 | − | 0.0192442i | −0.000378869 | − | 0.000656221i | ||||
\(861\) | −10.0460 | − | 36.3346i | −0.342367 | − | 1.23828i | ||||
\(862\) | 4.14919 | − | 7.18661i | 0.141322 | − | 0.244777i | ||||
\(863\) | −15.5259 | −0.528507 | −0.264253 | − | 0.964453i | \(-0.585126\pi\) | ||||
−0.264253 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(864\) | 7.08591 | − | 29.2141i | 0.241067 | − | 0.993883i | ||||
\(865\) | −5.20819 | −0.177084 | ||||||||
\(866\) | −2.41651 | + | 4.18551i | −0.0821163 | + | 0.142230i | ||||
\(867\) | −2.24638 | − | 8.12475i | −0.0762910 | − | 0.275931i | ||||
\(868\) | −5.07440 | − | 8.78912i | −0.172236 | − | 0.298322i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.548347 | + | 0.142268i | 0.0185907 | + | 0.00482333i | ||||
\(871\) | −18.7047 | + | 32.3975i | −0.633786 | + | 1.09775i | ||||
\(872\) | −7.41801 | −0.251206 | ||||||||
\(873\) | −0.0468976 | − | 2.95008i | −0.00158724 | − | 0.0998451i | ||||
\(874\) | 27.5639 | 0.932361 | ||||||||
\(875\) | −4.83754 | + | 8.37886i | −0.163539 | + | 0.283257i | ||||
\(876\) | 2.35625 | − | 2.39400i | 0.0796102 | − | 0.0808858i | ||||
\(877\) | −17.0122 | − | 29.4659i | −0.574460 | − | 0.994994i | −0.996100 | − | 0.0882306i | \(-0.971879\pi\) |
0.421640 | − | 0.906763i | \(-0.361455\pi\) | |||||||
\(878\) | 6.50372 | + | 11.2648i | 0.219490 | + | 0.380168i | ||||
\(879\) | 22.3365 | − | 22.6944i | 0.753392 | − | 0.765464i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.8513 | −0.837261 | −0.418630 | − | 0.908157i | \(-0.637490\pi\) | ||||
−0.418630 | + | 0.908157i | \(0.637490\pi\) | |||||||
\(882\) | 7.42931 | − | 4.44825i | 0.250158 | − | 0.149780i | ||||
\(883\) | 23.5034 | 0.790952 | 0.395476 | − | 0.918476i | \(-0.370580\pi\) | ||||
0.395476 | + | 0.918476i | \(0.370580\pi\) | |||||||
\(884\) | 11.2348 | − | 19.4593i | 0.377869 | − | 0.654488i | ||||
\(885\) | 7.10532 | + | 1.84347i | 0.238843 | + | 0.0619674i | ||||
\(886\) | −3.26994 | − | 5.66370i | −0.109856 | − | 0.190276i | ||||
\(887\) | 18.9872 | + | 32.8867i | 0.637527 | + | 1.10423i | 0.985974 | + | 0.166900i | \(0.0533757\pi\) |
−0.348447 | + | 0.937328i | \(0.613291\pi\) | |||||||
\(888\) | −2.80921 | − | 10.1604i | −0.0942708 | − | 0.340961i | ||||
\(889\) | 31.0485 | − | 53.7775i | 1.04133 | − | 1.80364i | ||||
\(890\) | 1.65811 | 0.0555800 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.37175 | −0.146377 | ||||||||
\(893\) | −4.10158 | + | 7.10414i | −0.137254 | + | 0.237731i | ||||
\(894\) | −3.77016 | − | 13.6360i | −0.126093 | − | 0.456055i | ||||
\(895\) | −1.37392 | − | 2.37971i | −0.0459252 | − | 0.0795448i | ||||
\(896\) | 18.2646 | + | 31.6353i | 0.610178 | + | 1.05686i | ||||
\(897\) | −46.9648 | − | 12.1850i | −1.56811 | − | 0.406844i | ||||
\(898\) | −5.21189 | + | 9.02725i | −0.173923 | + | 0.301243i | ||||
\(899\) | 3.25806 | 0.108662 | ||||||||
\(900\) | −19.4936 | + | 11.6716i | −0.649785 | + | 0.389054i | ||||
\(901\) | 6.54039 | 0.217892 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.202194 | − | 0.205434i | 0.00672859 | − | 0.00683640i | ||||
\(904\) | −19.1287 | − | 33.1318i | −0.636210 | − | 1.10195i | ||||
\(905\) | −1.61097 | − | 2.79029i | −0.0535506 | − | 0.0927523i | ||||
\(906\) | 16.8827 | − | 17.1532i | 0.560890 | − | 0.569877i | ||||
\(907\) | 9.17576 | − | 15.8929i | 0.304676 | − | 0.527715i | −0.672513 | − | 0.740085i | \(-0.734785\pi\) |
0.977189 | + | 0.212371i | \(0.0681184\pi\) | |||||||
\(908\) | 9.99321 | 0.331636 | ||||||||
\(909\) | −0.186527 | − | 11.7334i | −0.00618672 | − | 0.389173i | ||||
\(910\) | −2.76843 | −0.0917725 | ||||||||
\(911\) | −1.05480 | + | 1.82697i | −0.0349472 | + | 0.0605303i | −0.882970 | − | 0.469429i | \(-0.844460\pi\) |
0.848023 | + | 0.529960i | \(0.177793\pi\) | |||||||
\(912\) | −14.8341 | − | 3.84868i | −0.491206 | − | 0.127443i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.47097 | + | 11.2081i | 0.214041 | + | 0.370730i | ||||
\(915\) | −0.517983 | − | 1.87345i | −0.0171240 | − | 0.0619344i | ||||
\(916\) | −19.7529 | + | 34.2130i | −0.652653 | + | 1.13043i | ||||
\(917\) | −2.90130 | −0.0958093 | ||||||||
\(918\) | 11.7685 | − | 3.45612i | 0.388420 | − | 0.114069i | ||||
\(919\) | −11.0435 | −0.364290 | −0.182145 | − | 0.983272i | \(-0.558304\pi\) | ||||
−0.182145 | + | 0.983272i | \(0.558304\pi\) | |||||||
\(920\) | 2.33430 | − | 4.04312i | 0.0769595 | − | 0.133298i | ||||
\(921\) | −3.88822 | − | 14.0630i | −0.128121 | − | 0.463391i | ||||
\(922\) | −2.83666 | − | 4.91323i | −0.0934203 | − | 0.161809i | ||||
\(923\) | −23.2954 | − | 40.3488i | −0.766777 | − | 1.32810i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.23395 | + | 10.7975i | −0.204971 | + | 0.355020i | ||||
\(926\) | −19.1506 | −0.629327 | ||||||||
\(927\) | 40.5359 | + | 22.5520i | 1.33137 | + | 0.740706i | ||||
\(928\) | −9.60197 | −0.315200 | ||||||||
\(929\) | −7.77092 | + | 13.4596i | −0.254956 | + | 0.441596i | −0.964884 | − | 0.262678i | \(-0.915394\pi\) |
0.709928 | + | 0.704275i | \(0.248728\pi\) | |||||||
\(930\) | −0.469995 | + | 0.477526i | −0.0154117 | + | 0.0156587i | ||||
\(931\) | −12.9463 | − | 22.4237i | −0.424298 | − | 0.734906i | ||||
\(932\) | 0.500658 | + | 0.867165i | 0.0163996 | + | 0.0284049i | ||||
\(933\) | 13.7333 | − | 13.9533i | 0.449607 | − | 0.456811i | ||||
\(934\) | −2.78660 | + | 4.82653i | −0.0911803 | + | 0.157929i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −26.3362 | − | 14.6520i | −0.860825 | − | 0.478917i | ||||
\(937\) | −22.4663 | −0.733941 | −0.366971 | − | 0.930232i | \(-0.619605\pi\) | ||||
−0.366971 | + | 0.930232i | \(0.619605\pi\) | |||||||
\(938\) | 10.1590 | − | 17.5959i | 0.331704 | − | 0.574527i | ||||
\(939\) | −10.2448 | − | 2.65799i | −0.334325 | − | 0.0867401i | ||||
\(940\) | 0.302299 | + | 0.523597i | 0.00985990 | + | 0.0170778i | ||||
\(941\) | −2.60544 | − | 4.51276i | −0.0849350 | − | 0.147112i | 0.820429 | − | 0.571749i | \(-0.193735\pi\) |
−0.905364 | + | 0.424637i | \(0.860402\pi\) | |||||||
\(942\) | 2.64473 | + | 9.56550i | 0.0861699 | + | 0.311661i | ||||
\(943\) | 21.6998 | − | 37.5851i | 0.706642 | − | 1.22394i | ||||
\(944\) | −21.2124 | −0.690406 | ||||||||
\(945\) | 3.66962 | + | 3.49867i | 0.119373 | + | 0.113812i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.81080 | − | 15.2608i | 0.286312 | − | 0.495908i | −0.686614 | − | 0.727022i | \(-0.740904\pi\) |
0.972927 | + | 0.231114i | \(0.0742371\pi\) | |||||||
\(948\) | 1.49853 | + | 5.41992i | 0.0486701 | + | 0.176031i | ||||
\(949\) | −2.63488 | − | 4.56375i | −0.0855319 | − | 0.148146i | ||||
\(950\) | −10.1248 | − | 17.5367i | −0.328493 | − | 0.568966i | ||||
\(951\) | 1.38914 | + | 0.360411i | 0.0450460 | + | 0.0116871i | ||||
\(952\) | −14.0226 | + | 24.2878i | −0.454474 | + | 0.787172i | ||||
\(953\) | 46.6714 | 1.51183 | 0.755917 | − | 0.654667i | \(-0.227191\pi\) | ||||
0.755917 | + | 0.654667i | \(0.227191\pi\) | |||||||
\(954\) | −0.0606761 | − | 3.81681i | −0.00196446 | − | 0.123574i | ||||
\(955\) | −1.31939 | −0.0426945 | ||||||||
\(956\) | 13.0461 | − | 22.5965i | 0.421941 | − | 0.730823i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.3081 | + | 17.8541i | 0.333039 | + | 0.576840i | ||||
\(959\) | −20.7674 | − | 35.9702i | −0.670614 | − | 1.16154i | ||||
\(960\) | 0.356672 | − | 0.362387i | 0.0115115 | − | 0.0116960i | ||||
\(961\) | 13.5733 | − | 23.5096i | 0.437848 | − | 0.758375i | ||||
\(962\) | −7.19651 | −0.232025 | ||||||||
\(963\) | 16.1241 | − | 9.65421i | 0.519593 | − | 0.311103i | ||||
\(964\) | 37.7476 | 1.21577 | ||||||||
\(965\) | 1.96266 | − | 3.39942i | 0.0631801 | − | 0.109431i | ||||
\(966\) | 25.5078 | + | 6.61796i | 0.820699 | + | 0.212929i | ||||
\(967\) | −0.286105 | − | 0.495548i | −0.00920051 | − | 0.0159357i | 0.861388 | − | 0.507947i | \(-0.169595\pi\) |
−0.870589 | + | 0.492011i | \(0.836262\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.77379 | − | 35.3500i | −0.313979 | − | 1.13561i | ||||
\(970\) | 0.0969039 | − | 0.167843i | 0.00311140 | − | 0.00538910i | ||||
\(971\) | 37.1703 | 1.19285 | 0.596426 | − | 0.802668i | \(-0.296587\pi\) | ||||
0.596426 | + | 0.802668i | \(0.296587\pi\) | |||||||
\(972\) | 7.13315 | + | 22.9345i | 0.228796 | + | 0.735623i | ||||
\(973\) | −2.23465 | −0.0716397 | ||||||||
\(974\) | −7.55238 | + | 13.0811i | −0.241994 | + | 0.419146i | ||||
\(975\) | 9.49890 | + | 34.3558i | 0.304208 | + | 1.10027i | ||||
\(976\) | 2.80847 | + | 4.86441i | 0.0898968 | + | 0.155706i | ||||
\(977\) | 8.02404 | + | 13.8980i | 0.256712 | + | 0.444638i | 0.965359 | − | 0.260925i | \(-0.0840275\pi\) |
−0.708647 | + | 0.705563i | \(0.750694\pi\) | |||||||
\(978\) | −26.4416 | − | 6.86022i | −0.845508 | − | 0.219366i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.90837 | −0.0609605 | ||||||||
\(981\) | 7.95730 | − | 4.76438i | 0.254057 | − | 0.152115i | ||||
\(982\) | −21.9333 | −0.699920 | ||||||||
\(983\) | −22.9464 | + | 39.7443i | −0.731877 | + | 1.26765i | 0.224203 | + | 0.974542i | \(0.428022\pi\) |
−0.956080 | + | 0.293105i | \(0.905311\pi\) | |||||||
\(984\) | 18.9095 | − | 19.2125i | 0.602814 | − | 0.612473i | ||||
\(985\) | 0.247243 | + | 0.428238i | 0.00787782 | + | 0.0136448i | ||||
\(986\) | −1.95890 | − | 3.39291i | −0.0623840 | − | 0.108052i | ||||
\(987\) | −5.50130 | + | 5.58945i | −0.175108 | + | 0.177914i | ||||
\(988\) | −19.6073 | + | 33.9608i | −0.623791 | + | 1.08044i | ||||
\(989\) | 0.331841 | 0.0105519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.3187 | −0.899573 | −0.449786 | − | 0.893136i | \(-0.648500\pi\) | ||||
−0.449786 | + | 0.893136i | \(0.648500\pi\) | |||||||
\(992\) | 5.67827 | − | 9.83505i | 0.180285 | − | 0.312263i | ||||
\(993\) | −13.7217 | − | 3.56008i | −0.435446 | − | 0.112976i | ||||
\(994\) | 12.6523 | + | 21.9145i | 0.401307 | + | 0.695084i | ||||
\(995\) | 1.47494 | + | 2.55468i | 0.0467589 | + | 0.0809887i | ||||
\(996\) | 6.66743 | + | 24.1149i | 0.211265 | + | 0.764109i | ||||
\(997\) | −17.5735 | + | 30.4382i | −0.556558 | + | 0.963987i | 0.441222 | + | 0.897398i | \(0.354545\pi\) |
−0.997780 | + | 0.0665894i | \(0.978788\pi\) | |||||||
\(998\) | −0.177396 | −0.00561538 | ||||||||
\(999\) | 9.53916 | + | 9.09478i | 0.301806 | + | 0.287746i |
(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 | 1089.2.e.o.727.12 | 36 | ||
9.2 | odd | 6 | 9801.2.a.cn.1.12 | 18 | |||
9.4 | even | 3 | inner | 1089.2.e.o.364.12 | 36 | ||
9.7 | even | 3 | 9801.2.a.co.1.7 | 18 | |||
11.7 | odd | 10 | 99.2.m.b.16.4 | ✓ | 72 | ||
11.8 | odd | 10 | 99.2.m.b.97.6 | yes | 72 | ||
11.10 | odd | 2 | 1089.2.e.p.727.7 | 36 | |||
33.8 | even | 10 | 297.2.n.b.262.4 | 72 | |||
33.29 | even | 10 | 297.2.n.b.181.6 | 72 | |||
99.7 | odd | 30 | 891.2.f.f.82.6 | 36 | |||
99.29 | even | 30 | 891.2.f.e.82.4 | 36 | |||
99.40 | odd | 30 | 99.2.m.b.49.6 | yes | 72 | ||
99.41 | even | 30 | 297.2.n.b.64.6 | 72 | |||
99.43 | odd | 6 | 9801.2.a.cm.1.12 | 18 | |||
99.52 | odd | 30 | 891.2.f.f.163.6 | 36 | |||
99.65 | even | 6 | 9801.2.a.cp.1.7 | 18 | |||
99.74 | even | 30 | 891.2.f.e.163.4 | 36 | |||
99.76 | odd | 6 | 1089.2.e.p.364.7 | 36 | |||
99.85 | odd | 30 | 99.2.m.b.31.4 | yes | 72 | ||
99.95 | even | 30 | 297.2.n.b.280.4 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.16.4 | ✓ | 72 | 11.7 | odd | 10 | ||
99.2.m.b.31.4 | yes | 72 | 99.85 | odd | 30 | ||
99.2.m.b.49.6 | yes | 72 | 99.40 | odd | 30 | ||
99.2.m.b.97.6 | yes | 72 | 11.8 | odd | 10 | ||
297.2.n.b.64.6 | 72 | 99.41 | even | 30 | |||
297.2.n.b.181.6 | 72 | 33.29 | even | 10 | |||
297.2.n.b.262.4 | 72 | 33.8 | even | 10 | |||
297.2.n.b.280.4 | 72 | 99.95 | even | 30 | |||
891.2.f.e.82.4 | 36 | 99.29 | even | 30 | |||
891.2.f.e.163.4 | 36 | 99.74 | even | 30 | |||
891.2.f.f.82.6 | 36 | 99.7 | odd | 30 | |||
891.2.f.f.163.6 | 36 | 99.52 | odd | 30 | |||
1089.2.e.o.364.12 | 36 | 9.4 | even | 3 | inner | ||
1089.2.e.o.727.12 | 36 | 1.1 | even | 1 | trivial | ||
1089.2.e.p.364.7 | 36 | 99.76 | odd | 6 | |||
1089.2.e.p.727.7 | 36 | 11.10 | odd | 2 | |||
9801.2.a.cm.1.12 | 18 | 99.43 | odd | 6 | |||
9801.2.a.cn.1.12 | 18 | 9.2 | odd | 6 | |||
9801.2.a.co.1.7 | 18 | 9.7 | even | 3 | |||
9801.2.a.cp.1.7 | 18 | 99.65 | even | 6 |