Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(93,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, 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("322.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.310217769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.4 | ||
Root | \(-0.198169 + 0.343239i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.277 |
Dual form | 322.2.e.a.93.4 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.563379 | − | 0.975800i | 0.325267 | − | 0.563379i | −0.656300 | − | 0.754500i | \(-0.727879\pi\) |
0.981566 | + | 0.191122i | \(0.0612126\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.858079 | − | 1.48624i | −0.383745 | − | 0.664665i | 0.607849 | − | 0.794052i | \(-0.292032\pi\) |
−0.991594 | + | 0.129387i | \(0.958699\pi\) | |||||||
\(6\) | −1.12676 | −0.459997 | ||||||||
\(7\) | 0.779537 | − | 2.52830i | 0.294637 | − | 0.955609i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.865209 | + | 1.49859i | 0.288403 | + | 0.499529i | ||||
\(10\) | −0.858079 | + | 1.48624i | −0.271349 | + | 0.469989i | ||||
\(11\) | 1.82493 | − | 3.16087i | 0.550236 | − | 0.953037i | −0.448021 | − | 0.894023i | \(-0.647871\pi\) |
0.998257 | − | 0.0590137i | \(-0.0187956\pi\) | |||||||
\(12\) | 0.563379 | + | 0.975800i | 0.162633 | + | 0.281689i | ||||
\(13\) | −3.79833 | −1.05347 | −0.526733 | − | 0.850031i | \(-0.676583\pi\) | ||||
−0.526733 | + | 0.850031i | \(0.676583\pi\) | |||||||
\(14\) | −2.57934 | + | 0.589053i | −0.689359 | + | 0.157431i | ||||
\(15\) | −1.93369 | −0.499278 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.08850 | + | 3.61738i | −0.506535 | + | 0.877345i | 0.493436 | + | 0.869782i | \(0.335741\pi\) |
−0.999971 | + | 0.00756264i | \(0.997593\pi\) | |||||||
\(18\) | 0.865209 | − | 1.49859i | 0.203932 | − | 0.353220i | ||||
\(19\) | −4.06135 | − | 7.03447i | −0.931739 | − | 1.61382i | −0.780349 | − | 0.625345i | \(-0.784958\pi\) |
−0.151390 | − | 0.988474i | \(-0.548375\pi\) | |||||||
\(20\) | 1.71616 | 0.383745 | ||||||||
\(21\) | −2.02795 | − | 2.18506i | −0.442534 | − | 0.476820i | ||||
\(22\) | −3.64985 | −0.778151 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | ||||
\(24\) | 0.563379 | − | 0.975800i | 0.114999 | − | 0.199184i | ||||
\(25\) | 1.02740 | − | 1.77951i | 0.205480 | − | 0.355902i | ||||
\(26\) | 1.89916 | + | 3.28945i | 0.372457 | + | 0.645114i | ||||
\(27\) | 5.33003 | 1.02577 | ||||||||
\(28\) | 1.79981 | + | 1.93925i | 0.340132 | + | 0.366484i | ||||
\(29\) | 2.80694 | 0.521235 | 0.260618 | − | 0.965442i | \(-0.416074\pi\) | ||||
0.260618 | + | 0.965442i | \(0.416074\pi\) | |||||||
\(30\) | 0.966847 | + | 1.67463i | 0.176521 | + | 0.305744i | ||||
\(31\) | −4.27150 | + | 7.39846i | −0.767185 | + | 1.32880i | 0.171899 | + | 0.985115i | \(0.445010\pi\) |
−0.939084 | + | 0.343688i | \(0.888324\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.05625 | − | 3.56153i | −0.357947 | − | 0.619982i | ||||
\(34\) | 4.17700 | 0.716349 | ||||||||
\(35\) | −4.42656 | + | 1.01091i | −0.748226 | + | 0.170875i | ||||
\(36\) | −1.73042 | −0.288403 | ||||||||
\(37\) | −4.46765 | − | 7.73820i | −0.734477 | − | 1.27215i | −0.954952 | − | 0.296759i | \(-0.904094\pi\) |
0.220475 | − | 0.975393i | \(-0.429239\pi\) | |||||||
\(38\) | −4.06135 | + | 7.03447i | −0.658839 | + | 1.14114i | ||||
\(39\) | −2.13990 | + | 3.70641i | −0.342658 | + | 0.593501i | ||||
\(40\) | −0.858079 | − | 1.48624i | −0.135674 | − | 0.234995i | ||||
\(41\) | 10.0518 | 1.56983 | 0.784917 | − | 0.619601i | \(-0.212706\pi\) | ||||
0.784917 | + | 0.619601i | \(0.212706\pi\) | |||||||
\(42\) | −0.878349 | + | 2.84878i | −0.135532 | + | 0.439577i | ||||
\(43\) | 8.11069 | 1.23687 | 0.618434 | − | 0.785837i | \(-0.287767\pi\) | ||||
0.618434 | + | 0.785837i | \(0.287767\pi\) | |||||||
\(44\) | 1.82493 | + | 3.16087i | 0.275118 | + | 0.476518i | ||||
\(45\) | 1.48484 | − | 2.57181i | 0.221346 | − | 0.383383i | ||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | 1.47568 | + | 2.55596i | 0.215250 | + | 0.372825i | 0.953350 | − | 0.301867i | \(-0.0976099\pi\) |
−0.738100 | + | 0.674692i | \(0.764277\pi\) | |||||||
\(48\) | −1.12676 | −0.162633 | ||||||||
\(49\) | −5.78464 | − | 3.94181i | −0.826378 | − | 0.563116i | ||||
\(50\) | −2.05480 | −0.290593 | ||||||||
\(51\) | 2.35323 | + | 4.07591i | 0.329518 | + | 0.570742i | ||||
\(52\) | 1.89916 | − | 3.28945i | 0.263367 | − | 0.456165i | ||||
\(53\) | −1.52740 | + | 2.64553i | −0.209804 | + | 0.363392i | −0.951653 | − | 0.307176i | \(-0.900616\pi\) |
0.741848 | + | 0.670568i | \(0.233949\pi\) | |||||||
\(54\) | −2.66502 | − | 4.61594i | −0.362663 | − | 0.628150i | ||||
\(55\) | −6.26373 | −0.844601 | ||||||||
\(56\) | 0.779537 | − | 2.52830i | 0.104170 | − | 0.337859i | ||||
\(57\) | −9.15232 | −1.21225 | ||||||||
\(58\) | −1.40347 | − | 2.43088i | −0.184284 | − | 0.319190i | ||||
\(59\) | −2.09451 | + | 3.62779i | −0.272682 | + | 0.472299i | −0.969548 | − | 0.244903i | \(-0.921244\pi\) |
0.696866 | + | 0.717201i | \(0.254577\pi\) | |||||||
\(60\) | 0.966847 | − | 1.67463i | 0.124819 | − | 0.216194i | ||||
\(61\) | 5.65778 | + | 9.79957i | 0.724405 | + | 1.25471i | 0.959218 | + | 0.282666i | \(0.0912188\pi\) |
−0.234813 | + | 0.972040i | \(0.575448\pi\) | |||||||
\(62\) | 8.54301 | 1.08496 | ||||||||
\(63\) | 4.46335 | − | 1.01931i | 0.562329 | − | 0.128421i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.25927 | + | 5.64522i | 0.404262 | + | 0.700203i | ||||
\(66\) | −2.05625 | + | 3.56153i | −0.253107 | + | 0.438394i | ||||
\(67\) | 6.61841 | − | 11.4634i | 0.808567 | − | 1.40048i | −0.105290 | − | 0.994442i | \(-0.533577\pi\) |
0.913856 | − | 0.406037i | \(-0.133090\pi\) | |||||||
\(68\) | −2.08850 | − | 3.61738i | −0.253268 | − | 0.438672i | ||||
\(69\) | 1.12676 | 0.135646 | ||||||||
\(70\) | 3.08875 | + | 3.32806i | 0.369177 | + | 0.397780i | ||||
\(71\) | 14.3054 | 1.69773 | 0.848867 | − | 0.528607i | \(-0.177285\pi\) | ||||
0.848867 | + | 0.528607i | \(0.177285\pi\) | |||||||
\(72\) | 0.865209 | + | 1.49859i | 0.101966 | + | 0.176610i | ||||
\(73\) | 2.13049 | − | 3.69011i | 0.249355 | − | 0.431895i | −0.713992 | − | 0.700154i | \(-0.753115\pi\) |
0.963347 | + | 0.268259i | \(0.0864482\pi\) | |||||||
\(74\) | −4.46765 | + | 7.73820i | −0.519354 | + | 0.899547i | ||||
\(75\) | −1.15763 | − | 2.00507i | −0.133672 | − | 0.231526i | ||||
\(76\) | 8.12271 | 0.931739 | ||||||||
\(77\) | −6.56903 | − | 7.07798i | −0.748610 | − | 0.806611i | ||||
\(78\) | 4.27979 | 0.484591 | ||||||||
\(79\) | 6.72409 | + | 11.6465i | 0.756519 | + | 1.31033i | 0.944615 | + | 0.328179i | \(0.106435\pi\) |
−0.188096 | + | 0.982151i | \(0.560232\pi\) | |||||||
\(80\) | −0.858079 | + | 1.48624i | −0.0959362 | + | 0.166166i | ||||
\(81\) | 0.407198 | − | 0.705288i | 0.0452442 | − | 0.0783653i | ||||
\(82\) | −5.02592 | − | 8.70515i | −0.555020 | − | 0.961323i | ||||
\(83\) | 9.43848 | 1.03601 | 0.518004 | − | 0.855378i | \(-0.326675\pi\) | ||||
0.518004 | + | 0.855378i | \(0.326675\pi\) | |||||||
\(84\) | 2.90629 | − | 0.663720i | 0.317103 | − | 0.0724177i | ||||
\(85\) | 7.16839 | 0.777521 | ||||||||
\(86\) | −4.05534 | − | 7.02406i | −0.437299 | − | 0.757424i | ||||
\(87\) | 1.58137 | − | 2.73901i | 0.169540 | − | 0.293653i | ||||
\(88\) | 1.82493 | − | 3.16087i | 0.194538 | − | 0.336949i | ||||
\(89\) | −1.97918 | − | 3.42805i | −0.209793 | − | 0.363372i | 0.741856 | − | 0.670559i | \(-0.233946\pi\) |
−0.951649 | + | 0.307187i | \(0.900612\pi\) | |||||||
\(90\) | −2.96967 | −0.313031 | ||||||||
\(91\) | −2.96094 | + | 9.60333i | −0.310391 | + | 1.00670i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 4.81295 | + | 8.33627i | 0.499079 | + | 0.864431i | ||||
\(94\) | 1.47568 | − | 2.55596i | 0.152205 | − | 0.263627i | ||||
\(95\) | −6.96993 | + | 12.0723i | −0.715100 | + | 1.23859i | ||||
\(96\) | 0.563379 | + | 0.975800i | 0.0574996 | + | 0.0995922i | ||||
\(97\) | 0.121105 | 0.0122964 | 0.00614819 | − | 0.999981i | \(-0.498043\pi\) | ||||
0.00614819 | + | 0.999981i | \(0.498043\pi\) | |||||||
\(98\) | −0.521390 | + | 6.98056i | −0.0526683 | + | 0.705143i | ||||
\(99\) | 6.31577 | 0.634759 | ||||||||
\(100\) | 1.02740 | + | 1.77951i | 0.102740 | + | 0.177951i | ||||
\(101\) | 1.86148 | − | 3.22418i | 0.185224 | − | 0.320818i | −0.758428 | − | 0.651757i | \(-0.774032\pi\) |
0.943652 | + | 0.330939i | \(0.107366\pi\) | |||||||
\(102\) | 2.35323 | − | 4.07591i | 0.233004 | − | 0.403576i | ||||
\(103\) | −7.56418 | − | 13.1015i | −0.745321 | − | 1.29093i | −0.950045 | − | 0.312114i | \(-0.898963\pi\) |
0.204724 | − | 0.978820i | \(-0.434370\pi\) | |||||||
\(104\) | −3.79833 | −0.372457 | ||||||||
\(105\) | −1.50739 | + | 4.88897i | −0.147106 | + | 0.477114i | ||||
\(106\) | 3.05480 | 0.296708 | ||||||||
\(107\) | 6.86772 | + | 11.8952i | 0.663927 | + | 1.14996i | 0.979575 | + | 0.201079i | \(0.0644449\pi\) |
−0.315648 | + | 0.948876i | \(0.602222\pi\) | |||||||
\(108\) | −2.66502 | + | 4.61594i | −0.256441 | + | 0.444169i | ||||
\(109\) | −4.69467 | + | 8.13140i | −0.449668 | + | 0.778847i | −0.998364 | − | 0.0571745i | \(-0.981791\pi\) |
0.548697 | + | 0.836022i | \(0.315124\pi\) | |||||||
\(110\) | 3.13186 | + | 5.42455i | 0.298611 | + | 0.517210i | ||||
\(111\) | −10.0679 | −0.955604 | ||||||||
\(112\) | −2.57934 | + | 0.589053i | −0.243725 | + | 0.0556603i | ||||
\(113\) | −9.39338 | −0.883655 | −0.441828 | − | 0.897100i | \(-0.645670\pi\) | ||||
−0.441828 | + | 0.897100i | \(0.645670\pi\) | |||||||
\(114\) | 4.57616 | + | 7.92614i | 0.428597 | + | 0.742351i | ||||
\(115\) | 0.858079 | − | 1.48624i | 0.0800163 | − | 0.138592i | ||||
\(116\) | −1.40347 | + | 2.43088i | −0.130309 | + | 0.225701i | ||||
\(117\) | −3.28635 | − | 5.69212i | −0.303823 | − | 0.526237i | ||||
\(118\) | 4.18902 | 0.385630 | ||||||||
\(119\) | 7.51779 | + | 8.10024i | 0.689154 | + | 0.742548i | ||||
\(120\) | −1.93369 | −0.176521 | ||||||||
\(121\) | −1.16071 | − | 2.01041i | −0.105519 | − | 0.182765i | ||||
\(122\) | 5.65778 | − | 9.79957i | 0.512232 | − | 0.887211i | ||||
\(123\) | 5.66299 | − | 9.80859i | 0.510615 | − | 0.884411i | ||||
\(124\) | −4.27150 | − | 7.39846i | −0.383592 | − | 0.664401i | ||||
\(125\) | −12.1072 | −1.08290 | ||||||||
\(126\) | −3.11442 | − | 3.35572i | −0.277455 | − | 0.298951i | ||||
\(127\) | 2.53575 | 0.225012 | 0.112506 | − | 0.993651i | \(-0.464112\pi\) | ||||
0.112506 | + | 0.993651i | \(0.464112\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.56939 | − | 7.91441i | 0.402312 | − | 0.696825i | ||||
\(130\) | 3.25927 | − | 5.64522i | 0.285857 | − | 0.495118i | ||||
\(131\) | 2.63129 | + | 4.55753i | 0.229897 | + | 0.398193i | 0.957777 | − | 0.287511i | \(-0.0928278\pi\) |
−0.727881 | + | 0.685704i | \(0.759494\pi\) | |||||||
\(132\) | 4.11250 | 0.357947 | ||||||||
\(133\) | −20.9513 | + | 4.78471i | −1.81670 | + | 0.414887i | ||||
\(134\) | −13.2368 | −1.14349 | ||||||||
\(135\) | −4.57359 | − | 7.92169i | −0.393632 | − | 0.681791i | ||||
\(136\) | −2.08850 | + | 3.61738i | −0.179087 | + | 0.310188i | ||||
\(137\) | 6.92566 | − | 11.9956i | 0.591699 | − | 1.02485i | −0.402305 | − | 0.915506i | \(-0.631791\pi\) |
0.994004 | − | 0.109347i | \(-0.0348760\pi\) | |||||||
\(138\) | −0.563379 | − | 0.975800i | −0.0479580 | − | 0.0830656i | ||||
\(139\) | −9.65665 | −0.819067 | −0.409533 | − | 0.912295i | \(-0.634308\pi\) | ||||
−0.409533 | + | 0.912295i | \(0.634308\pi\) | |||||||
\(140\) | 1.33781 | − | 4.33897i | 0.113066 | − | 0.366710i | ||||
\(141\) | 3.32547 | 0.280055 | ||||||||
\(142\) | −7.15268 | − | 12.3888i | −0.600239 | − | 1.03965i | ||||
\(143\) | −6.93167 | + | 12.0060i | −0.579655 | + | 1.00399i | ||||
\(144\) | 0.865209 | − | 1.49859i | 0.0721008 | − | 0.124882i | ||||
\(145\) | −2.40857 | − | 4.17177i | −0.200021 | − | 0.346447i | ||||
\(146\) | −4.26097 | −0.352641 | ||||||||
\(147\) | −7.10537 | + | 3.42392i | −0.586041 | + | 0.282400i | ||||
\(148\) | 8.93530 | 0.734477 | ||||||||
\(149\) | 4.78066 | + | 8.28034i | 0.391647 | + | 0.678352i | 0.992667 | − | 0.120882i | \(-0.0385722\pi\) |
−0.601020 | + | 0.799234i | \(0.705239\pi\) | |||||||
\(150\) | −1.15763 | + | 2.00507i | −0.0945201 | + | 0.163714i | ||||
\(151\) | −3.62836 | + | 6.28451i | −0.295272 | + | 0.511426i | −0.975048 | − | 0.221994i | \(-0.928744\pi\) |
0.679776 | + | 0.733420i | \(0.262077\pi\) | |||||||
\(152\) | −4.06135 | − | 7.03447i | −0.329419 | − | 0.570571i | ||||
\(153\) | −7.22795 | −0.584345 | ||||||||
\(154\) | −2.84520 | + | 9.22794i | −0.229272 | + | 0.743608i | ||||
\(155\) | 14.6612 | 1.17761 | ||||||||
\(156\) | −2.13990 | − | 3.70641i | −0.171329 | − | 0.296750i | ||||
\(157\) | 1.37755 | − | 2.38598i | 0.109940 | − | 0.190422i | −0.805806 | − | 0.592180i | \(-0.798267\pi\) |
0.915746 | + | 0.401758i | \(0.131601\pi\) | |||||||
\(158\) | 6.72409 | − | 11.6465i | 0.534940 | − | 0.926543i | ||||
\(159\) | 1.72101 | + | 2.98087i | 0.136485 | + | 0.236399i | ||||
\(160\) | 1.71616 | 0.135674 | ||||||||
\(161\) | 2.57934 | − | 0.589053i | 0.203281 | − | 0.0464239i | ||||
\(162\) | −0.814396 | −0.0639850 | ||||||||
\(163\) | −10.1420 | − | 17.5665i | −0.794386 | − | 1.37592i | −0.923228 | − | 0.384252i | \(-0.874459\pi\) |
0.128842 | − | 0.991665i | \(-0.458874\pi\) | |||||||
\(164\) | −5.02592 | + | 8.70515i | −0.392459 | + | 0.679758i | ||||
\(165\) | −3.52885 | + | 6.11215i | −0.274721 | + | 0.475830i | ||||
\(166\) | −4.71924 | − | 8.17397i | −0.366284 | − | 0.634423i | ||||
\(167\) | −0.325472 | −0.0251858 | −0.0125929 | − | 0.999921i | \(-0.504009\pi\) | ||||
−0.0125929 | + | 0.999921i | \(0.504009\pi\) | |||||||
\(168\) | −2.02795 | − | 2.18506i | −0.156459 | − | 0.168581i | ||||
\(169\) | 1.42730 | 0.109792 | ||||||||
\(170\) | −3.58419 | − | 6.20801i | −0.274895 | − | 0.476132i | ||||
\(171\) | 7.02784 | − | 12.1726i | 0.537433 | − | 0.930861i | ||||
\(172\) | −4.05534 | + | 7.02406i | −0.309217 | + | 0.535580i | ||||
\(173\) | −6.70089 | − | 11.6063i | −0.509459 | − | 0.882410i | −0.999940 | − | 0.0109575i | \(-0.996512\pi\) |
0.490480 | − | 0.871452i | \(-0.336821\pi\) | |||||||
\(174\) | −3.16274 | −0.239766 | ||||||||
\(175\) | −3.69824 | − | 3.98477i | −0.279561 | − | 0.301220i | ||||
\(176\) | −3.64985 | −0.275118 | ||||||||
\(177\) | 2.36000 | + | 4.08764i | 0.177389 | + | 0.307246i | ||||
\(178\) | −1.97918 | + | 3.42805i | −0.148346 | + | 0.256943i | ||||
\(179\) | −10.4273 | + | 18.0606i | −0.779370 | + | 1.34991i | 0.152935 | + | 0.988236i | \(0.451128\pi\) |
−0.932305 | + | 0.361673i | \(0.882206\pi\) | |||||||
\(180\) | 1.48484 | + | 2.57181i | 0.110673 | + | 0.191692i | ||||
\(181\) | 1.57738 | 0.117246 | 0.0586229 | − | 0.998280i | \(-0.481329\pi\) | ||||
0.0586229 | + | 0.998280i | \(0.481329\pi\) | |||||||
\(182\) | 9.79720 | − | 2.23742i | 0.726217 | − | 0.165848i | ||||
\(183\) | 12.7499 | 0.942500 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | −7.66719 | + | 13.2800i | −0.563703 | + | 0.976363i | ||||
\(186\) | 4.81295 | − | 8.33627i | 0.352902 | − | 0.611245i | ||||
\(187\) | 7.62271 | + | 13.2029i | 0.557428 | + | 0.965493i | ||||
\(188\) | −2.95137 | −0.215250 | ||||||||
\(189\) | 4.15496 | − | 13.4759i | 0.302229 | − | 0.980231i | ||||
\(190\) | 13.9399 | 1.01130 | ||||||||
\(191\) | −3.13049 | − | 5.42216i | −0.226514 | − | 0.392334i | 0.730259 | − | 0.683171i | \(-0.239400\pi\) |
−0.956773 | + | 0.290837i | \(0.906066\pi\) | |||||||
\(192\) | 0.563379 | − | 0.975800i | 0.0406583 | − | 0.0704223i | ||||
\(193\) | −6.51789 | + | 11.2893i | −0.469168 | + | 0.812623i | −0.999379 | − | 0.0352433i | \(-0.988779\pi\) |
0.530211 | + | 0.847866i | \(0.322113\pi\) | |||||||
\(194\) | −0.0605527 | − | 0.104880i | −0.00434743 | − | 0.00752997i | ||||
\(195\) | 7.34481 | 0.525972 | ||||||||
\(196\) | 6.30603 | − | 3.03874i | 0.450431 | − | 0.217053i | ||||
\(197\) | −21.2551 | −1.51436 | −0.757182 | − | 0.653204i | \(-0.773425\pi\) | ||||
−0.757182 | + | 0.653204i | \(0.773425\pi\) | |||||||
\(198\) | −3.15789 | − | 5.46962i | −0.224421 | − | 0.388709i | ||||
\(199\) | −2.36862 | + | 4.10257i | −0.167907 | + | 0.290824i | −0.937684 | − | 0.347490i | \(-0.887034\pi\) |
0.769777 | + | 0.638313i | \(0.220368\pi\) | |||||||
\(200\) | 1.02740 | − | 1.77951i | 0.0726481 | − | 0.125830i | ||||
\(201\) | −7.45734 | − | 12.9165i | −0.526000 | − | 0.911058i | ||||
\(202\) | −3.72296 | −0.261947 | ||||||||
\(203\) | 2.18811 | − | 7.09679i | 0.153575 | − | 0.498097i | ||||
\(204\) | −4.70646 | −0.329518 | ||||||||
\(205\) | −8.62528 | − | 14.9394i | −0.602416 | − | 1.04341i | ||||
\(206\) | −7.56418 | + | 13.1015i | −0.527021 | + | 0.912828i | ||||
\(207\) | −0.865209 | + | 1.49859i | −0.0601362 | + | 0.104159i | ||||
\(208\) | 1.89916 | + | 3.28945i | 0.131683 | + | 0.228082i | ||||
\(209\) | −29.6467 | −2.05070 | ||||||||
\(210\) | 4.98766 | − | 1.13905i | 0.344181 | − | 0.0786018i | ||||
\(211\) | 16.7617 | 1.15392 | 0.576962 | − | 0.816771i | \(-0.304238\pi\) | ||||
0.576962 | + | 0.816771i | \(0.304238\pi\) | |||||||
\(212\) | −1.52740 | − | 2.64553i | −0.104902 | − | 0.181696i | ||||
\(213\) | 8.05933 | − | 13.9592i | 0.552216 | − | 0.956467i | ||||
\(214\) | 6.86772 | − | 11.8952i | 0.469467 | − | 0.813142i | ||||
\(215\) | −6.95962 | − | 12.0544i | −0.474642 | − | 0.822104i | ||||
\(216\) | 5.33003 | 0.362663 | ||||||||
\(217\) | 15.3758 | + | 16.5670i | 1.04377 | + | 1.12464i | ||||
\(218\) | 9.38933 | 0.635926 | ||||||||
\(219\) | −2.40054 | − | 4.15786i | −0.162214 | − | 0.280962i | ||||
\(220\) | 3.13186 | − | 5.42455i | 0.211150 | − | 0.365723i | ||||
\(221\) | 7.93280 | − | 13.7400i | 0.533618 | − | 0.924253i | ||||
\(222\) | 5.03396 | + | 8.71907i | 0.337857 | + | 0.585185i | ||||
\(223\) | 1.23469 | 0.0826812 | 0.0413406 | − | 0.999145i | \(-0.486837\pi\) | ||||
0.0413406 | + | 0.999145i | \(0.486837\pi\) | |||||||
\(224\) | 1.79981 | + | 1.93925i | 0.120255 | + | 0.129572i | ||||
\(225\) | 3.55566 | 0.237044 | ||||||||
\(226\) | 4.69669 | + | 8.13491i | 0.312419 | + | 0.541126i | ||||
\(227\) | −11.5210 | + | 19.9550i | −0.764678 | + | 1.32446i | 0.175739 | + | 0.984437i | \(0.443768\pi\) |
−0.940417 | + | 0.340024i | \(0.889565\pi\) | |||||||
\(228\) | 4.57616 | − | 7.92614i | 0.303064 | − | 0.524922i | ||||
\(229\) | 2.41831 | + | 4.18864i | 0.159807 | + | 0.276793i | 0.934799 | − | 0.355178i | \(-0.115580\pi\) |
−0.774992 | + | 0.631971i | \(0.782246\pi\) | |||||||
\(230\) | −1.71616 | −0.113160 | ||||||||
\(231\) | −10.6075 | + | 2.42248i | −0.697925 | + | 0.159387i | ||||
\(232\) | 2.80694 | 0.184284 | ||||||||
\(233\) | 6.62724 | + | 11.4787i | 0.434165 | + | 0.751996i | 0.997227 | − | 0.0744188i | \(-0.0237101\pi\) |
−0.563062 | + | 0.826415i | \(0.690377\pi\) | |||||||
\(234\) | −3.28635 | + | 5.69212i | −0.214835 | + | 0.372106i | ||||
\(235\) | 2.53251 | − | 4.38643i | 0.165202 | − | 0.286139i | ||||
\(236\) | −2.09451 | − | 3.62779i | −0.136341 | − | 0.236149i | ||||
\(237\) | 15.1528 | 0.984282 | ||||||||
\(238\) | 3.25612 | − | 10.5607i | 0.211063 | − | 0.684550i | ||||
\(239\) | −5.40250 | −0.349459 | −0.174729 | − | 0.984616i | \(-0.555905\pi\) | ||||
−0.174729 | + | 0.984616i | \(0.555905\pi\) | |||||||
\(240\) | 0.966847 | + | 1.67463i | 0.0624097 | + | 0.108097i | ||||
\(241\) | 8.61037 | − | 14.9136i | 0.554643 | − | 0.960670i | −0.443288 | − | 0.896379i | \(-0.646188\pi\) |
0.997931 | − | 0.0642905i | \(-0.0204784\pi\) | |||||||
\(242\) | −1.16071 | + | 2.01041i | −0.0746134 | + | 0.129234i | ||||
\(243\) | 7.53624 | + | 13.0531i | 0.483450 | + | 0.837359i | ||||
\(244\) | −11.3156 | −0.724405 | ||||||||
\(245\) | −0.894788 | + | 11.9797i | −0.0571659 | + | 0.765358i | ||||
\(246\) | −11.3260 | −0.722118 | ||||||||
\(247\) | 15.4264 | + | 26.7192i | 0.981556 | + | 1.70010i | ||||
\(248\) | −4.27150 | + | 7.39846i | −0.271241 | + | 0.469803i | ||||
\(249\) | 5.31744 | − | 9.21007i | 0.336979 | − | 0.583665i | ||||
\(250\) | 6.05358 | + | 10.4851i | 0.382862 | + | 0.663136i | ||||
\(251\) | 16.9165 | 1.06776 | 0.533879 | − | 0.845561i | \(-0.320734\pi\) | ||||
0.533879 | + | 0.845561i | \(0.320734\pi\) | |||||||
\(252\) | −1.34893 | + | 4.37502i | −0.0849743 | + | 0.275601i | ||||
\(253\) | 3.64985 | 0.229464 | ||||||||
\(254\) | −1.26788 | − | 2.19602i | −0.0795536 | − | 0.137791i | ||||
\(255\) | 4.03852 | − | 6.99491i | 0.252902 | − | 0.438039i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.13308 | + | 10.6228i | 0.382571 | + | 0.662633i | 0.991429 | − | 0.130646i | \(-0.0417053\pi\) |
−0.608858 | + | 0.793279i | \(0.708372\pi\) | |||||||
\(258\) | −9.13878 | −0.568955 | ||||||||
\(259\) | −23.0472 | + | 5.26336i | −1.43208 | + | 0.327050i | ||||
\(260\) | −6.51854 | −0.404262 | ||||||||
\(261\) | 2.42859 | + | 4.20644i | 0.150326 | + | 0.260372i | ||||
\(262\) | 2.63129 | − | 4.55753i | 0.162562 | − | 0.281565i | ||||
\(263\) | −6.52900 | + | 11.3086i | −0.402596 | + | 0.697316i | −0.994038 | − | 0.109031i | \(-0.965225\pi\) |
0.591443 | + | 0.806347i | \(0.298559\pi\) | |||||||
\(264\) | −2.05625 | − | 3.56153i | −0.126553 | − | 0.219197i | ||||
\(265\) | 5.24252 | 0.322045 | ||||||||
\(266\) | 14.6193 | + | 15.7520i | 0.896367 | + | 0.965815i | ||||
\(267\) | −4.46012 | −0.272955 | ||||||||
\(268\) | 6.61841 | + | 11.4634i | 0.404283 | + | 0.700239i | ||||
\(269\) | −1.78352 | + | 3.08915i | −0.108743 | + | 0.188349i | −0.915261 | − | 0.402860i | \(-0.868016\pi\) |
0.806518 | + | 0.591209i | \(0.201349\pi\) | |||||||
\(270\) | −4.57359 | + | 7.92169i | −0.278340 | + | 0.482099i | ||||
\(271\) | −0.988595 | − | 1.71230i | −0.0600529 | − | 0.104015i | 0.834436 | − | 0.551105i | \(-0.185794\pi\) |
−0.894489 | + | 0.447090i | \(0.852460\pi\) | |||||||
\(272\) | 4.17700 | 0.253268 | ||||||||
\(273\) | 7.70280 | + | 8.29959i | 0.466195 | + | 0.502314i | ||||
\(274\) | −13.8513 | −0.836789 | ||||||||
\(275\) | −3.74986 | − | 6.49494i | −0.226125 | − | 0.391660i | ||||
\(276\) | −0.563379 | + | 0.975800i | −0.0339114 | + | 0.0587363i | ||||
\(277\) | 5.46819 | − | 9.47119i | 0.328552 | − | 0.569069i | −0.653673 | − | 0.756777i | \(-0.726773\pi\) |
0.982225 | + | 0.187709i | \(0.0601061\pi\) | |||||||
\(278\) | 4.82833 | + | 8.36291i | 0.289584 | + | 0.501574i | ||||
\(279\) | −14.7830 | −0.885034 | ||||||||
\(280\) | −4.42656 | + | 1.01091i | −0.264538 | + | 0.0604133i | ||||
\(281\) | −4.58034 | −0.273240 | −0.136620 | − | 0.990624i | \(-0.543624\pi\) | ||||
−0.136620 | + | 0.990624i | \(0.543624\pi\) | |||||||
\(282\) | −1.66274 | − | 2.87994i | −0.0990145 | − | 0.171498i | ||||
\(283\) | 7.54044 | − | 13.0604i | 0.448233 | − | 0.776361i | −0.550039 | − | 0.835139i | \(-0.685387\pi\) |
0.998271 | + | 0.0587778i | \(0.0187203\pi\) | |||||||
\(284\) | −7.15268 | + | 12.3888i | −0.424433 | + | 0.735140i | ||||
\(285\) | 7.85342 | + | 13.6025i | 0.465196 | + | 0.805744i | ||||
\(286\) | 13.8633 | 0.819757 | ||||||||
\(287\) | 7.83579 | − | 25.4141i | 0.462532 | − | 1.50015i | ||||
\(288\) | −1.73042 | −0.101966 | ||||||||
\(289\) | −0.223647 | − | 0.387368i | −0.0131557 | − | 0.0227863i | ||||
\(290\) | −2.40857 | + | 4.17177i | −0.141436 | + | 0.244975i | ||||
\(291\) | 0.0682282 | − | 0.118175i | 0.00399961 | − | 0.00692752i | ||||
\(292\) | 2.13049 | + | 3.69011i | 0.124677 | + | 0.215947i | ||||
\(293\) | 14.5555 | 0.850344 | 0.425172 | − | 0.905113i | \(-0.360214\pi\) | ||||
0.425172 | + | 0.905113i | \(0.360214\pi\) | |||||||
\(294\) | 6.51789 | + | 4.44147i | 0.380131 | + | 0.259032i | ||||
\(295\) | 7.18902 | 0.418561 | ||||||||
\(296\) | −4.46765 | − | 7.73820i | −0.259677 | − | 0.449773i | ||||
\(297\) | 9.72692 | − | 16.8475i | 0.564413 | − | 0.977592i | ||||
\(298\) | 4.78066 | − | 8.28034i | 0.276936 | − | 0.479667i | ||||
\(299\) | −1.89916 | − | 3.28945i | −0.109832 | − | 0.190234i | ||||
\(300\) | 2.31526 | 0.133672 | ||||||||
\(301\) | 6.32258 | − | 20.5063i | 0.364428 | − | 1.18196i | ||||
\(302\) | 7.25672 | 0.417577 | ||||||||
\(303\) | −2.09744 | − | 3.63286i | −0.120495 | − | 0.208703i | ||||
\(304\) | −4.06135 | + | 7.03447i | −0.232935 | + | 0.403455i | ||||
\(305\) | 9.70966 | − | 16.8176i | 0.555973 | − | 0.962974i | ||||
\(306\) | 3.61398 | + | 6.25959i | 0.206597 | + | 0.357837i | ||||
\(307\) | −12.7024 | −0.724965 | −0.362482 | − | 0.931991i | \(-0.618071\pi\) | ||||
−0.362482 | + | 0.931991i | \(0.618071\pi\) | |||||||
\(308\) | 9.41423 | − | 2.14996i | 0.536425 | − | 0.122505i | ||||
\(309\) | −17.0460 | −0.969712 | ||||||||
\(310\) | −7.33058 | − | 12.6969i | −0.416349 | − | 0.721137i | ||||
\(311\) | 4.60947 | − | 7.98383i | 0.261379 | − | 0.452722i | −0.705230 | − | 0.708979i | \(-0.749156\pi\) |
0.966609 | + | 0.256257i | \(0.0824894\pi\) | |||||||
\(312\) | −2.13990 | + | 3.70641i | −0.121148 | + | 0.209834i | ||||
\(313\) | 7.82833 | + | 13.5591i | 0.442483 | + | 0.766403i | 0.997873 | − | 0.0651867i | \(-0.0207643\pi\) |
−0.555390 | + | 0.831590i | \(0.687431\pi\) | |||||||
\(314\) | −2.75509 | −0.155479 | ||||||||
\(315\) | −5.34484 | − | 5.75894i | −0.301147 | − | 0.324480i | ||||
\(316\) | −13.4482 | −0.756519 | ||||||||
\(317\) | −5.51911 | − | 9.55938i | −0.309984 | − | 0.536908i | 0.668374 | − | 0.743825i | \(-0.266990\pi\) |
−0.978359 | + | 0.206917i | \(0.933657\pi\) | |||||||
\(318\) | 1.72101 | − | 2.98087i | 0.0965094 | − | 0.167159i | ||||
\(319\) | 5.12245 | − | 8.87235i | 0.286802 | − | 0.496756i | ||||
\(320\) | −0.858079 | − | 1.48624i | −0.0479681 | − | 0.0830832i | ||||
\(321\) | 15.4765 | 0.863814 | ||||||||
\(322\) | −1.79981 | − | 1.93925i | −0.100299 | − | 0.108070i | ||||
\(323\) | 33.9285 | 1.88783 | ||||||||
\(324\) | 0.407198 | + | 0.705288i | 0.0226221 | + | 0.0391827i | ||||
\(325\) | −3.90240 | + | 6.75916i | −0.216466 | + | 0.374931i | ||||
\(326\) | −10.1420 | + | 17.5665i | −0.561716 | + | 0.972921i | ||||
\(327\) | 5.28975 | + | 9.16211i | 0.292524 | + | 0.506666i | ||||
\(328\) | 10.0518 | 0.555020 | ||||||||
\(329\) | 7.61259 | − | 1.73851i | 0.419696 | − | 0.0958472i | ||||
\(330\) | 7.05770 | 0.388513 | ||||||||
\(331\) | 7.84574 | + | 13.5892i | 0.431241 | + | 0.746931i | 0.996980 | − | 0.0776528i | \(-0.0247426\pi\) |
−0.565740 | + | 0.824584i | \(0.691409\pi\) | |||||||
\(332\) | −4.71924 | + | 8.17397i | −0.259002 | + | 0.448605i | ||||
\(333\) | 7.73090 | − | 13.3903i | 0.423651 | − | 0.733785i | ||||
\(334\) | 0.162736 | + | 0.281867i | 0.00890451 | + | 0.0154231i | ||||
\(335\) | −22.7165 | −1.24113 | ||||||||
\(336\) | −0.878349 | + | 2.84878i | −0.0479179 | + | 0.155414i | ||||
\(337\) | 5.18787 | 0.282601 | 0.141301 | − | 0.989967i | \(-0.454872\pi\) | ||||
0.141301 | + | 0.989967i | \(0.454872\pi\) | |||||||
\(338\) | −0.713651 | − | 1.23608i | −0.0388175 | − | 0.0672339i | ||||
\(339\) | −5.29203 | + | 9.16606i | −0.287424 | + | 0.497832i | ||||
\(340\) | −3.58419 | + | 6.20801i | −0.194380 | + | 0.336676i | ||||
\(341\) | 15.5904 | + | 27.0033i | 0.844265 | + | 1.46231i | ||||
\(342\) | −14.0557 | −0.760045 | ||||||||
\(343\) | −14.4755 | + | 11.5525i | −0.781601 | + | 0.623779i | ||||
\(344\) | 8.11069 | 0.437299 | ||||||||
\(345\) | −0.966847 | − | 1.67463i | −0.0520533 | − | 0.0901589i | ||||
\(346\) | −6.70089 | + | 11.6063i | −0.360242 | + | 0.623958i | ||||
\(347\) | 8.87970 | − | 15.3801i | 0.476687 | − | 0.825646i | −0.522956 | − | 0.852360i | \(-0.675171\pi\) |
0.999643 | + | 0.0267134i | \(0.00850415\pi\) | |||||||
\(348\) | 1.58137 | + | 2.73901i | 0.0847702 | + | 0.146826i | ||||
\(349\) | −15.3654 | −0.822488 | −0.411244 | − | 0.911525i | \(-0.634906\pi\) | ||||
−0.411244 | + | 0.911525i | \(0.634906\pi\) | |||||||
\(350\) | −1.60179 | + | 5.19516i | −0.0856194 | + | 0.277693i | ||||
\(351\) | −20.2452 | −1.08061 | ||||||||
\(352\) | 1.82493 | + | 3.16087i | 0.0972689 | + | 0.168475i | ||||
\(353\) | 13.2323 | − | 22.9190i | 0.704283 | − | 1.21985i | −0.262666 | − | 0.964887i | \(-0.584602\pi\) |
0.966950 | − | 0.254968i | \(-0.0820648\pi\) | |||||||
\(354\) | 2.36000 | − | 4.08764i | 0.125433 | − | 0.217256i | ||||
\(355\) | −12.2751 | − | 21.2612i | −0.651496 | − | 1.12842i | ||||
\(356\) | 3.95837 | 0.209793 | ||||||||
\(357\) | 12.1396 | − | 2.77235i | 0.642495 | − | 0.146729i | ||||
\(358\) | 20.8545 | 1.10220 | ||||||||
\(359\) | −3.75001 | − | 6.49521i | −0.197918 | − | 0.342804i | 0.749935 | − | 0.661511i | \(-0.230085\pi\) |
−0.947853 | + | 0.318707i | \(0.896751\pi\) | |||||||
\(360\) | 1.48484 | − | 2.57181i | 0.0782578 | − | 0.135546i | ||||
\(361\) | −23.4892 | + | 40.6845i | −1.23627 | + | 2.14129i | ||||
\(362\) | −0.788691 | − | 1.36605i | −0.0414527 | − | 0.0717981i | ||||
\(363\) | −2.61568 | −0.137288 | ||||||||
\(364\) | −6.83626 | − | 7.36591i | −0.358317 | − | 0.386079i | ||||
\(365\) | −7.31251 | −0.382754 | ||||||||
\(366\) | −6.37495 | − | 11.0417i | −0.333224 | − | 0.577161i | ||||
\(367\) | 0.805459 | − | 1.39510i | 0.0420446 | − | 0.0728234i | −0.844237 | − | 0.535970i | \(-0.819946\pi\) |
0.886282 | + | 0.463146i | \(0.153280\pi\) | |||||||
\(368\) | 0.500000 | − | 0.866025i | 0.0260643 | − | 0.0451447i | ||||
\(369\) | 8.69695 | + | 15.0636i | 0.452745 | + | 0.784177i | ||||
\(370\) | 15.3344 | 0.797197 | ||||||||
\(371\) | 5.49805 | + | 5.92402i | 0.285444 | + | 0.307560i | ||||
\(372\) | −9.62589 | −0.499079 | ||||||||
\(373\) | −9.05039 | − | 15.6757i | −0.468612 | − | 0.811659i | 0.530745 | − | 0.847532i | \(-0.321912\pi\) |
−0.999356 | + | 0.0358726i | \(0.988579\pi\) | |||||||
\(374\) | 7.62271 | − | 13.2029i | 0.394161 | − | 0.682707i | ||||
\(375\) | −6.82091 | + | 11.8142i | −0.352230 | + | 0.610081i | ||||
\(376\) | 1.47568 | + | 2.55596i | 0.0761025 | + | 0.131813i | ||||
\(377\) | −10.6617 | −0.549104 | ||||||||
\(378\) | −13.7480 | + | 3.13967i | −0.707120 | + | 0.161487i | ||||
\(379\) | −10.3909 | −0.533747 | −0.266873 | − | 0.963732i | \(-0.585991\pi\) | ||||
−0.266873 | + | 0.963732i | \(0.585991\pi\) | |||||||
\(380\) | −6.96993 | − | 12.0723i | −0.357550 | − | 0.619294i | ||||
\(381\) | 1.42859 | − | 2.47439i | 0.0731888 | − | 0.126767i | ||||
\(382\) | −3.13049 | + | 5.42216i | −0.160170 | + | 0.277422i | ||||
\(383\) | 3.69781 | + | 6.40480i | 0.188949 | + | 0.327270i | 0.944900 | − | 0.327359i | \(-0.106158\pi\) |
−0.755951 | + | 0.654628i | \(0.772825\pi\) | |||||||
\(384\) | −1.12676 | −0.0574996 | ||||||||
\(385\) | −4.88281 | + | 15.8366i | −0.248851 | + | 0.807108i | ||||
\(386\) | 13.0358 | 0.663504 | ||||||||
\(387\) | 7.01744 | + | 12.1546i | 0.356717 | + | 0.617851i | ||||
\(388\) | −0.0605527 | + | 0.104880i | −0.00307410 | + | 0.00532449i | ||||
\(389\) | −2.03971 | + | 3.53288i | −0.103417 | + | 0.179124i | −0.913090 | − | 0.407757i | \(-0.866311\pi\) |
0.809673 | + | 0.586881i | \(0.199644\pi\) | |||||||
\(390\) | −3.67240 | − | 6.36079i | −0.185959 | − | 0.322091i | ||||
\(391\) | −4.17700 | −0.211240 | ||||||||
\(392\) | −5.78464 | − | 3.94181i | −0.292169 | − | 0.199092i | ||||
\(393\) | 5.92965 | 0.299111 | ||||||||
\(394\) | 10.6276 | + | 18.4075i | 0.535409 | + | 0.927355i | ||||
\(395\) | 11.5396 | − | 19.9872i | 0.580621 | − | 1.00566i | ||||
\(396\) | −3.15789 | + | 5.46962i | −0.158690 | + | 0.274859i | ||||
\(397\) | −4.43055 | − | 7.67394i | −0.222363 | − | 0.385144i | 0.733162 | − | 0.680054i | \(-0.238044\pi\) |
−0.955525 | + | 0.294910i | \(0.904710\pi\) | |||||||
\(398\) | 4.73724 | 0.237456 | ||||||||
\(399\) | −7.13457 | + | 23.1398i | −0.357175 | + | 1.15844i | ||||
\(400\) | −2.05480 | −0.102740 | ||||||||
\(401\) | −8.30173 | − | 14.3790i | −0.414569 | − | 0.718054i | 0.580814 | − | 0.814036i | \(-0.302734\pi\) |
−0.995383 | + | 0.0959821i | \(0.969401\pi\) | |||||||
\(402\) | −7.45734 | + | 12.9165i | −0.371938 | + | 0.644216i | ||||
\(403\) | 16.2246 | − | 28.1018i | 0.808204 | − | 1.39985i | ||||
\(404\) | 1.86148 | + | 3.22418i | 0.0926121 | + | 0.160409i | ||||
\(405\) | −1.39763 | −0.0694489 | ||||||||
\(406\) | −7.24006 | + | 1.65343i | −0.359318 | + | 0.0820586i | ||||
\(407\) | −32.6125 | −1.61654 | ||||||||
\(408\) | 2.35323 | + | 4.07591i | 0.116502 | + | 0.201788i | ||||
\(409\) | −16.8717 | + | 29.2227i | −0.834253 | + | 1.44497i | 0.0603848 | + | 0.998175i | \(0.480767\pi\) |
−0.894637 | + | 0.446793i | \(0.852566\pi\) | |||||||
\(410\) | −8.62528 | + | 14.9394i | −0.425972 | + | 0.737805i | ||||
\(411\) | −7.80354 | − | 13.5161i | −0.384920 | − | 0.666701i | ||||
\(412\) | 15.1284 | 0.745321 | ||||||||
\(413\) | 7.53942 | + | 8.12355i | 0.370991 | + | 0.399734i | ||||
\(414\) | 1.73042 | 0.0850454 | ||||||||
\(415\) | −8.09897 | − | 14.0278i | −0.397563 | − | 0.688599i | ||||
\(416\) | 1.89916 | − | 3.28945i | 0.0931142 | − | 0.161279i | ||||
\(417\) | −5.44035 | + | 9.42296i | −0.266415 | + | 0.461445i | ||||
\(418\) | 14.8233 | + | 25.6748i | 0.725034 | + | 1.25579i | ||||
\(419\) | 36.5806 | 1.78708 | 0.893539 | − | 0.448985i | \(-0.148214\pi\) | ||||
0.893539 | + | 0.448985i | \(0.148214\pi\) | |||||||
\(420\) | −3.48028 | − | 3.74992i | −0.169820 | − | 0.182977i | ||||
\(421\) | −32.7603 | −1.59664 | −0.798321 | − | 0.602233i | \(-0.794278\pi\) | ||||
−0.798321 | + | 0.602233i | \(0.794278\pi\) | |||||||
\(422\) | −8.38086 | − | 14.5161i | −0.407974 | − | 0.706631i | ||||
\(423\) | −2.55355 | + | 4.42288i | −0.124158 | + | 0.215048i | ||||
\(424\) | −1.52740 | + | 2.64553i | −0.0741771 | + | 0.128478i | ||||
\(425\) | 4.29144 | + | 7.43300i | 0.208166 | + | 0.360553i | ||||
\(426\) | −16.1187 | −0.780952 | ||||||||
\(427\) | 29.1867 | − | 6.66547i | 1.41245 | − | 0.322565i | ||||
\(428\) | −13.7354 | −0.663927 | ||||||||
\(429\) | 7.81031 | + | 13.5279i | 0.377085 | + | 0.653131i | ||||
\(430\) | −6.95962 | + | 12.0544i | −0.335622 | + | 0.581315i | ||||
\(431\) | 8.85968 | − | 15.3454i | 0.426756 | − | 0.739163i | −0.569827 | − | 0.821765i | \(-0.692990\pi\) |
0.996583 | + | 0.0826019i | \(0.0263230\pi\) | |||||||
\(432\) | −2.66502 | − | 4.61594i | −0.128221 | − | 0.222085i | ||||
\(433\) | −4.51989 | −0.217212 | −0.108606 | − | 0.994085i | \(-0.534639\pi\) | ||||
−0.108606 | + | 0.994085i | \(0.534639\pi\) | |||||||
\(434\) | 6.65959 | − | 21.5993i | 0.319671 | − | 1.03680i | ||||
\(435\) | −5.42776 | −0.260241 | ||||||||
\(436\) | −4.69467 | − | 8.13140i | −0.224834 | − | 0.389424i | ||||
\(437\) | 4.06135 | − | 7.03447i | 0.194281 | − | 0.336504i | ||||
\(438\) | −2.40054 | + | 4.15786i | −0.114702 | + | 0.198670i | ||||
\(439\) | −3.19897 | − | 5.54078i | −0.152679 | − | 0.264447i | 0.779533 | − | 0.626361i | \(-0.215457\pi\) |
−0.932211 | + | 0.361914i | \(0.882123\pi\) | |||||||
\(440\) | −6.26373 | −0.298611 | ||||||||
\(441\) | 0.902222 | − | 12.0793i | 0.0429630 | − | 0.575204i | ||||
\(442\) | −15.8656 | −0.754650 | ||||||||
\(443\) | 8.56844 | + | 14.8410i | 0.407099 | + | 0.705116i | 0.994563 | − | 0.104134i | \(-0.0332070\pi\) |
−0.587464 | + | 0.809250i | \(0.699874\pi\) | |||||||
\(444\) | 5.03396 | − | 8.71907i | 0.238901 | − | 0.413789i | ||||
\(445\) | −3.39660 | + | 5.88308i | −0.161014 | + | 0.278885i | ||||
\(446\) | −0.617347 | − | 1.06928i | −0.0292322 | − | 0.0506317i | ||||
\(447\) | 10.7733 | 0.509559 | ||||||||
\(448\) | 0.779537 | − | 2.52830i | 0.0368297 | − | 0.119451i | ||||
\(449\) | −13.2695 | −0.626226 | −0.313113 | − | 0.949716i | \(-0.601372\pi\) | ||||
−0.313113 | + | 0.949716i | \(0.601372\pi\) | |||||||
\(450\) | −1.77783 | − | 3.07929i | −0.0838078 | − | 0.145159i | ||||
\(451\) | 18.3439 | − | 31.7725i | 0.863779 | − | 1.49611i | ||||
\(452\) | 4.69669 | − | 8.13491i | 0.220914 | − | 0.382634i | ||||
\(453\) | 4.08828 | + | 7.08111i | 0.192084 | + | 0.332700i | ||||
\(454\) | 23.0421 | 1.08142 | ||||||||
\(455\) | 16.8135 | − | 3.83976i | 0.788231 | − | 0.180011i | ||||
\(456\) | −9.15232 | −0.428597 | ||||||||
\(457\) | 15.2314 | + | 26.3815i | 0.712494 | + | 1.23408i | 0.963918 | + | 0.266199i | \(0.0857679\pi\) |
−0.251424 | + | 0.967877i | \(0.580899\pi\) | |||||||
\(458\) | 2.41831 | − | 4.18864i | 0.113000 | − | 0.195722i | ||||
\(459\) | −11.1318 | + | 19.2808i | −0.519586 | + | 0.899950i | ||||
\(460\) | 0.858079 | + | 1.48624i | 0.0400082 | + | 0.0692962i | ||||
\(461\) | 13.1239 | 0.611239 | 0.305620 | − | 0.952154i | \(-0.401136\pi\) | ||||
0.305620 | + | 0.952154i | \(0.401136\pi\) | |||||||
\(462\) | 7.40170 | + | 7.97516i | 0.344358 | + | 0.371038i | ||||
\(463\) | −21.3453 | −0.991998 | −0.495999 | − | 0.868323i | \(-0.665198\pi\) | ||||
−0.495999 | + | 0.868323i | \(0.665198\pi\) | |||||||
\(464\) | −1.40347 | − | 2.43088i | −0.0651544 | − | 0.112851i | ||||
\(465\) | 8.25978 | − | 14.3064i | 0.383038 | − | 0.663442i | ||||
\(466\) | 6.62724 | − | 11.4787i | 0.307001 | − | 0.531741i | ||||
\(467\) | −11.1802 | − | 19.3647i | −0.517358 | − | 0.896091i | −0.999797 | − | 0.0201608i | \(-0.993582\pi\) |
0.482439 | − | 0.875930i | \(-0.339751\pi\) | |||||||
\(468\) | 6.57270 | 0.303823 | ||||||||
\(469\) | −23.8237 | − | 25.6695i | −1.10008 | − | 1.18531i | ||||
\(470\) | −5.06501 | −0.233632 | ||||||||
\(471\) | −1.55216 | − | 2.68842i | −0.0715198 | − | 0.123876i | ||||
\(472\) | −2.09451 | + | 3.62779i | −0.0964075 | + | 0.166983i | ||||
\(473\) | 14.8014 | − | 25.6368i | 0.680570 | − | 1.17878i | ||||
\(474\) | −7.57642 | − | 13.1227i | −0.347996 | − | 0.602747i | ||||
\(475\) | −16.6905 | −0.765814 | ||||||||
\(476\) | −10.7739 | + | 2.46047i | −0.493821 | + | 0.112776i | ||||
\(477\) | −5.28608 | −0.242033 | ||||||||
\(478\) | 2.70125 | + | 4.67871i | 0.123552 | + | 0.213999i | ||||
\(479\) | 8.73350 | − | 15.1269i | 0.399044 | − | 0.691164i | −0.594564 | − | 0.804048i | \(-0.702675\pi\) |
0.993608 | + | 0.112884i | \(0.0360088\pi\) | |||||||
\(480\) | 0.966847 | − | 1.67463i | 0.0441303 | − | 0.0764360i | ||||
\(481\) | 16.9696 | + | 29.3922i | 0.773747 | + | 1.34017i | ||||
\(482\) | −17.2207 | −0.784383 | ||||||||
\(483\) | 0.878349 | − | 2.84878i | 0.0399663 | − | 0.129624i | ||||
\(484\) | 2.32142 | 0.105519 | ||||||||
\(485\) | −0.103918 | − | 0.179991i | −0.00471867 | − | 0.00817298i | ||||
\(486\) | 7.53624 | − | 13.0531i | 0.341851 | − | 0.592103i | ||||
\(487\) | 2.89533 | − | 5.01486i | 0.131200 | − | 0.227245i | −0.792939 | − | 0.609301i | \(-0.791450\pi\) |
0.924139 | + | 0.382055i | \(0.124784\pi\) | |||||||
\(488\) | 5.65778 | + | 9.79957i | 0.256116 | + | 0.443606i | ||||
\(489\) | −22.8552 | −1.03355 | ||||||||
\(490\) | 10.8222 | − | 5.21496i | 0.488895 | − | 0.235588i | ||||
\(491\) | −8.47054 | −0.382270 | −0.191135 | − | 0.981564i | \(-0.561217\pi\) | ||||
−0.191135 | + | 0.981564i | \(0.561217\pi\) | |||||||
\(492\) | 5.66299 | + | 9.80859i | 0.255307 | + | 0.442205i | ||||
\(493\) | −5.86228 | + | 10.1538i | −0.264024 | + | 0.457303i | ||||
\(494\) | 15.4264 | − | 26.7192i | 0.694065 | − | 1.20216i | ||||
\(495\) | −5.41943 | − | 9.38674i | −0.243585 | − | 0.421902i | ||||
\(496\) | 8.54301 | 0.383592 | ||||||||
\(497\) | 11.1516 | − | 36.1683i | 0.500216 | − | 1.62237i | ||||
\(498\) | −10.6349 | −0.476560 | ||||||||
\(499\) | 1.26100 | + | 2.18412i | 0.0564502 | + | 0.0977746i | 0.892870 | − | 0.450315i | \(-0.148688\pi\) |
−0.836419 | + | 0.548090i | \(0.815355\pi\) | |||||||
\(500\) | 6.05358 | − | 10.4851i | 0.270724 | − | 0.468908i | ||||
\(501\) | −0.183364 | + | 0.317596i | −0.00819209 | + | 0.0141891i | ||||
\(502\) | −8.45824 | − | 14.6501i | −0.377510 | − | 0.653866i | ||||
\(503\) | 8.34455 | 0.372065 | 0.186033 | − | 0.982544i | \(-0.440437\pi\) | ||||
0.186033 | + | 0.982544i | \(0.440437\pi\) | |||||||
\(504\) | 4.46335 | − | 1.01931i | 0.198813 | − | 0.0454036i | ||||
\(505\) | −6.38919 | −0.284315 | ||||||||
\(506\) | −1.82493 | − | 3.16087i | −0.0811279 | − | 0.140518i | ||||
\(507\) | 0.804111 | − | 1.39276i | 0.0357118 | − | 0.0618547i | ||||
\(508\) | −1.26788 | + | 2.19602i | −0.0562529 | + | 0.0974329i | ||||
\(509\) | 8.43774 | + | 14.6146i | 0.373996 | + | 0.647781i | 0.990176 | − | 0.139825i | \(-0.0446539\pi\) |
−0.616180 | + | 0.787605i | \(0.711321\pi\) | |||||||
\(510\) | −8.07703 | −0.357657 | ||||||||
\(511\) | −7.66893 | − | 8.26310i | −0.339253 | − | 0.365538i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −21.6472 | − | 37.4940i | −0.955745 | − | 1.65540i | ||||
\(514\) | 6.13308 | − | 10.6228i | 0.270519 | − | 0.468552i | ||||
\(515\) | −12.9813 | + | 22.4843i | −0.572026 | + | 0.990778i | ||||
\(516\) | 4.56939 | + | 7.91441i | 0.201156 | + | 0.348413i | ||||
\(517\) | 10.7720 | 0.473754 | ||||||||
\(518\) | 16.0818 | + | 17.3278i | 0.706594 | + | 0.761339i | ||||
\(519\) | −15.1006 | −0.662841 | ||||||||
\(520\) | 3.25927 | + | 5.64522i | 0.142928 | + | 0.247559i | ||||
\(521\) | −3.43970 | + | 5.95774i | −0.150696 | + | 0.261013i | −0.931484 | − | 0.363783i | \(-0.881485\pi\) |
0.780787 | + | 0.624797i | \(0.214818\pi\) | |||||||
\(522\) | 2.42859 | − | 4.20644i | 0.106296 | − | 0.184111i | ||||
\(523\) | −10.6428 | − | 18.4338i | −0.465375 | − | 0.806053i | 0.533843 | − | 0.845583i | \(-0.320747\pi\) |
−0.999218 | + | 0.0395302i | \(0.987414\pi\) | |||||||
\(524\) | −5.26258 | −0.229897 | ||||||||
\(525\) | −5.97185 | + | 1.36381i | −0.260633 | + | 0.0595216i | ||||
\(526\) | 13.0580 | 0.569356 | ||||||||
\(527\) | −17.8421 | − | 30.9033i | −0.777212 | − | 1.34617i | ||||
\(528\) | −2.05625 | + | 3.56153i | −0.0894867 | + | 0.154996i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −2.62126 | − | 4.54016i | −0.113860 | − | 0.197212i | ||||
\(531\) | −7.24875 | −0.314569 | ||||||||
\(532\) | 6.33195 | − | 20.5367i | 0.274525 | − | 0.890378i | ||||
\(533\) | −38.1802 | −1.65377 | ||||||||
\(534\) | 2.23006 | + | 3.86258i | 0.0965041 | + | 0.167150i | ||||
\(535\) | 11.7861 | − | 20.4141i | 0.509557 | − | 0.882579i | ||||
\(536\) | 6.61841 | − | 11.4634i | 0.285872 | − | 0.495144i | ||||
\(537\) | 11.7490 | + | 20.3499i | 0.507007 | + | 0.878161i | ||||
\(538\) | 3.56705 | 0.153786 | ||||||||
\(539\) | −23.0161 | + | 11.0910i | −0.991373 | + | 0.477721i | ||||
\(540\) | 9.14718 | 0.393632 | ||||||||
\(541\) | 22.2528 | + | 38.5429i | 0.956721 | + | 1.65709i | 0.730379 | + | 0.683042i | \(0.239343\pi\) |
0.226342 | + | 0.974048i | \(0.427323\pi\) | |||||||
\(542\) | −0.988595 | + | 1.71230i | −0.0424638 | + | 0.0735494i | ||||
\(543\) | 0.888663 | − | 1.53921i | 0.0381362 | − | 0.0660538i | ||||
\(544\) | −2.08850 | − | 3.61738i | −0.0895436 | − | 0.155094i | ||||
\(545\) | 16.1136 | 0.690230 | ||||||||
\(546\) | 3.33626 | − | 10.8206i | 0.142779 | − | 0.463080i | ||||
\(547\) | 4.70118 | 0.201008 | 0.100504 | − | 0.994937i | \(-0.467954\pi\) | ||||
0.100504 | + | 0.994937i | \(0.467954\pi\) | |||||||
\(548\) | 6.92566 | + | 11.9956i | 0.295850 | + | 0.512426i | ||||
\(549\) | −9.79034 | + | 16.9574i | −0.417841 | + | 0.723722i | ||||
\(550\) | −3.74986 | + | 6.49494i | −0.159894 | + | 0.276945i | ||||
\(551\) | −11.4000 | − | 19.7453i | −0.485655 | − | 0.841179i | ||||
\(552\) | 1.12676 | 0.0479580 | ||||||||
\(553\) | 34.6875 | − | 7.92169i | 1.47506 | − | 0.336865i | ||||
\(554\) | −10.9364 | −0.464643 | ||||||||
\(555\) | 8.63907 | + | 14.9633i | 0.366708 | + | 0.635157i | ||||
\(556\) | 4.82833 | − | 8.36291i | 0.204767 | − | 0.354666i | ||||
\(557\) | −11.6577 | + | 20.1917i | −0.493951 | + | 0.855548i | −0.999976 | − | 0.00697093i | \(-0.997781\pi\) |
0.506025 | + | 0.862519i | \(0.331114\pi\) | |||||||
\(558\) | 7.39149 | + | 12.8024i | 0.312907 | + | 0.541970i | ||||
\(559\) | −30.8071 | −1.30300 | ||||||||
\(560\) | 3.08875 | + | 3.32806i | 0.130524 | + | 0.140636i | ||||
\(561\) | 17.1779 | 0.725251 | ||||||||
\(562\) | 2.29017 | + | 3.96669i | 0.0966050 | + | 0.167325i | ||||
\(563\) | −19.6307 | + | 34.0014i | −0.827335 | + | 1.43299i | 0.0727857 | + | 0.997348i | \(0.476811\pi\) |
−0.900121 | + | 0.435639i | \(0.856522\pi\) | |||||||
\(564\) | −1.66274 | + | 2.87994i | −0.0700138 | + | 0.121267i | ||||
\(565\) | 8.06027 | + | 13.9608i | 0.339098 | + | 0.587335i | ||||
\(566\) | −15.0809 | −0.633896 | ||||||||
\(567\) | −1.46576 | − | 1.57932i | −0.0615560 | − | 0.0663251i | ||||
\(568\) | 14.3054 | 0.600239 | ||||||||
\(569\) | −14.2620 | − | 24.7026i | −0.597895 | − | 1.03559i | −0.993131 | − | 0.117006i | \(-0.962670\pi\) |
0.395236 | − | 0.918580i | \(-0.370663\pi\) | |||||||
\(570\) | 7.85342 | − | 13.6025i | 0.328943 | − | 0.569747i | ||||
\(571\) | −5.73892 | + | 9.94011i | −0.240167 | + | 0.415981i | −0.960762 | − | 0.277376i | \(-0.910535\pi\) |
0.720595 | + | 0.693356i | \(0.243869\pi\) | |||||||
\(572\) | −6.93167 | − | 12.0060i | −0.289828 | − | 0.501996i | ||||
\(573\) | −7.05460 | −0.294710 | ||||||||
\(574\) | −25.9272 | + | 5.92107i | −1.08218 | + | 0.247141i | ||||
\(575\) | 2.05480 | 0.0856911 | ||||||||
\(576\) | 0.865209 | + | 1.49859i | 0.0360504 | + | 0.0624411i | ||||
\(577\) | −11.4092 | + | 19.7613i | −0.474970 | + | 0.822672i | −0.999589 | − | 0.0286648i | \(-0.990874\pi\) |
0.524619 | + | 0.851337i | \(0.324208\pi\) | |||||||
\(578\) | −0.223647 | + | 0.387368i | −0.00930248 | + | 0.0161124i | ||||
\(579\) | 7.34408 | + | 12.7203i | 0.305209 | + | 0.528638i | ||||
\(580\) | 4.81715 | 0.200021 | ||||||||
\(581\) | 7.35765 | − | 23.8634i | 0.305247 | − | 0.990019i | ||||
\(582\) | −0.136456 | −0.00565630 | ||||||||
\(583\) | 5.57478 | + | 9.65581i | 0.230884 | + | 0.399903i | ||||
\(584\) | 2.13049 | − | 3.69011i | 0.0881602 | − | 0.152698i | ||||
\(585\) | −5.63990 | + | 9.76859i | −0.233181 | + | 0.403881i | ||||
\(586\) | −7.27777 | − | 12.6055i | −0.300642 | − | 0.520727i | ||||
\(587\) | 20.6525 | 0.852422 | 0.426211 | − | 0.904624i | \(-0.359848\pi\) | ||||
0.426211 | + | 0.904624i | \(0.359848\pi\) | |||||||
\(588\) | 0.587480 | − | 7.86539i | 0.0242272 | − | 0.324363i | ||||
\(589\) | 69.3924 | 2.85926 | ||||||||
\(590\) | −3.59451 | − | 6.22587i | −0.147984 | − | 0.256315i | ||||
\(591\) | −11.9747 | + | 20.7407i | −0.492572 | + | 0.853160i | ||||
\(592\) | −4.46765 | + | 7.73820i | −0.183619 | + | 0.318038i | ||||
\(593\) | 3.83376 | + | 6.64027i | 0.157434 | + | 0.272683i | 0.933943 | − | 0.357423i | \(-0.116345\pi\) |
−0.776509 | + | 0.630106i | \(0.783011\pi\) | |||||||
\(594\) | −19.4538 | −0.798200 | ||||||||
\(595\) | 5.58803 | − | 18.1239i | 0.229087 | − | 0.743006i | ||||
\(596\) | −9.56131 | −0.391647 | ||||||||
\(597\) | 2.66886 | + | 4.62260i | 0.109229 | + | 0.189190i | ||||
\(598\) | −1.89916 | + | 3.28945i | −0.0776626 | + | 0.134516i | ||||
\(599\) | −18.7730 | + | 32.5158i | −0.767043 | + | 1.32856i | 0.172117 | + | 0.985077i | \(0.444939\pi\) |
−0.939160 | + | 0.343481i | \(0.888394\pi\) | |||||||
\(600\) | −1.15763 | − | 2.00507i | −0.0472600 | − | 0.0818568i | ||||
\(601\) | −16.2537 | −0.663003 | −0.331501 | − | 0.943455i | \(-0.607555\pi\) | ||||
−0.331501 | + | 0.943455i | \(0.607555\pi\) | |||||||
\(602\) | −20.9203 | + | 4.77763i | −0.852646 | + | 0.194722i | ||||
\(603\) | 22.9052 | 0.932773 | ||||||||
\(604\) | −3.62836 | − | 6.28451i | −0.147636 | − | 0.255713i | ||||
\(605\) | −1.99197 | + | 3.45019i | −0.0809849 | + | 0.140270i | ||||
\(606\) | −2.09744 | + | 3.63286i | −0.0852025 | + | 0.147575i | ||||
\(607\) | −2.16135 | − | 3.74356i | −0.0877264 | − | 0.151947i | 0.818823 | − | 0.574046i | \(-0.194627\pi\) |
−0.906550 | + | 0.422099i | \(0.861293\pi\) | |||||||
\(608\) | 8.12271 | 0.329419 | ||||||||
\(609\) | −5.69231 | − | 6.13334i | −0.230664 | − | 0.248535i | ||||
\(610\) | −19.4193 | −0.786265 | ||||||||
\(611\) | −5.60513 | − | 9.70837i | −0.226759 | − | 0.392758i | ||||
\(612\) | 3.61398 | − | 6.25959i | 0.146086 | − | 0.253029i | ||||
\(613\) | −20.0725 | + | 34.7666i | −0.810720 | + | 1.40421i | 0.101640 | + | 0.994821i | \(0.467591\pi\) |
−0.912360 | + | 0.409388i | \(0.865742\pi\) | |||||||
\(614\) | 6.35121 | + | 11.0006i | 0.256314 | + | 0.443949i | ||||
\(615\) | −19.4372 | −0.783783 | ||||||||
\(616\) | −6.56903 | − | 7.07798i | −0.264674 | − | 0.285180i | ||||
\(617\) | −27.7668 | −1.11785 | −0.558925 | − | 0.829218i | \(-0.688786\pi\) | ||||
−0.558925 | + | 0.829218i | \(0.688786\pi\) | |||||||
\(618\) | 8.52299 | + | 14.7623i | 0.342845 | + | 0.593825i | ||||
\(619\) | 8.36648 | − | 14.4912i | 0.336277 | − | 0.582450i | −0.647452 | − | 0.762106i | \(-0.724165\pi\) |
0.983729 | + | 0.179657i | \(0.0574987\pi\) | |||||||
\(620\) | −7.33058 | + | 12.6969i | −0.294403 | + | 0.509921i | ||||
\(621\) | 2.66502 | + | 4.61594i | 0.106943 | + | 0.185231i | ||||
\(622\) | −9.21894 | −0.369646 | ||||||||
\(623\) | −10.2100 | + | 2.33169i | −0.409055 | + | 0.0934172i | ||||
\(624\) | 4.27979 | 0.171329 | ||||||||
\(625\) | 5.25190 | + | 9.09656i | 0.210076 | + | 0.363862i | ||||
\(626\) | 7.82833 | − | 13.5591i | 0.312883 | − | 0.541929i | ||||
\(627\) | −16.7023 | + | 28.9292i | −0.667026 | + | 1.15532i | ||||
\(628\) | 1.37755 | + | 2.38598i | 0.0549701 | + | 0.0952110i | ||||
\(629\) | 37.3227 | 1.48815 | ||||||||
\(630\) | −2.31497 | + | 7.50824i | −0.0922306 | + | 0.299135i | ||||
\(631\) | 16.4804 | 0.656073 | 0.328037 | − | 0.944665i | \(-0.393613\pi\) | ||||
0.328037 | + | 0.944665i | \(0.393613\pi\) | |||||||
\(632\) | 6.72409 | + | 11.6465i | 0.267470 | + | 0.463272i | ||||
\(633\) | 9.44319 | − | 16.3561i | 0.375333 | − | 0.650096i | ||||
\(634\) | −5.51911 | + | 9.55938i | −0.219192 | + | 0.379651i | ||||
\(635\) | −2.17588 | − | 3.76873i | −0.0863470 | − | 0.149557i | ||||
\(636\) | −3.44202 | −0.136485 | ||||||||
\(637\) | 21.9720 | + | 14.9723i | 0.870561 | + | 0.593224i | ||||
\(638\) | −10.2449 | −0.405600 | ||||||||
\(639\) | 12.3771 | + | 21.4378i | 0.489632 | + | 0.848067i | ||||
\(640\) | −0.858079 | + | 1.48624i | −0.0339186 | + | 0.0587487i | ||||
\(641\) | −0.882551 | + | 1.52862i | −0.0348587 | + | 0.0603770i | −0.882928 | − | 0.469508i | \(-0.844431\pi\) |
0.848070 | + | 0.529885i | \(0.177765\pi\) | |||||||
\(642\) | −7.73825 | − | 13.4030i | −0.305404 | − | 0.528976i | ||||
\(643\) | −8.26706 | −0.326021 | −0.163010 | − | 0.986624i | \(-0.552120\pi\) | ||||
−0.163010 | + | 0.986624i | \(0.552120\pi\) | |||||||
\(644\) | −0.779537 | + | 2.52830i | −0.0307181 | + | 0.0996291i | ||||
\(645\) | −15.6836 | −0.617541 | ||||||||
\(646\) | −16.9643 | − | 29.3830i | −0.667450 | − | 1.15606i | ||||
\(647\) | 7.76187 | − | 13.4439i | 0.305150 | − | 0.528536i | −0.672144 | − | 0.740420i | \(-0.734627\pi\) |
0.977295 | + | 0.211884i | \(0.0679599\pi\) | |||||||
\(648\) | 0.407198 | − | 0.705288i | 0.0159963 | − | 0.0277063i | ||||
\(649\) | 7.64464 | + | 13.2409i | 0.300079 | + | 0.519751i | ||||
\(650\) | 7.80480 | 0.306130 | ||||||||
\(651\) | 24.8285 | − | 5.67016i | 0.973105 | − | 0.222231i | ||||
\(652\) | 20.2841 | 0.794386 | ||||||||
\(653\) | −9.92962 | − | 17.1986i | −0.388576 | − | 0.673033i | 0.603682 | − | 0.797225i | \(-0.293700\pi\) |
−0.992258 | + | 0.124192i | \(0.960366\pi\) | |||||||
\(654\) | 5.28975 | − | 9.16211i | 0.206846 | − | 0.358267i | ||||
\(655\) | 4.51571 | − | 7.82144i | 0.176443 | − | 0.305609i | ||||
\(656\) | −5.02592 | − | 8.70515i | −0.196229 | − | 0.339879i | ||||
\(657\) | 7.37327 | 0.287659 | ||||||||
\(658\) | −5.31189 | − | 5.72344i | −0.207079 | − | 0.223123i | ||||
\(659\) | −1.62164 | −0.0631702 | −0.0315851 | − | 0.999501i | \(-0.510056\pi\) | ||||
−0.0315851 | + | 0.999501i | \(0.510056\pi\) | |||||||
\(660\) | −3.52885 | − | 6.11215i | −0.137360 | − | 0.237915i | ||||
\(661\) | 4.53150 | − | 7.84879i | 0.176255 | − | 0.305283i | −0.764340 | − | 0.644814i | \(-0.776935\pi\) |
0.940595 | + | 0.339531i | \(0.110268\pi\) | |||||||
\(662\) | 7.84574 | − | 13.5892i | 0.304933 | − | 0.528160i | ||||
\(663\) | −8.93834 | − | 15.4817i | −0.347136 | − | 0.601258i | ||||
\(664\) | 9.43848 | 0.366284 | ||||||||
\(665\) | 25.0891 | + | 27.0329i | 0.972912 | + | 1.04829i | ||||
\(666\) | −15.4618 | −0.599133 | ||||||||
\(667\) | 1.40347 | + | 2.43088i | 0.0543425 | + | 0.0941240i | ||||
\(668\) | 0.162736 | − | 0.281867i | 0.00629644 | − | 0.0109058i | ||||
\(669\) | 0.695600 | − | 1.20481i | 0.0268934 | − | 0.0465808i | ||||
\(670\) | 11.3582 | + | 19.6730i | 0.438807 | + | 0.760036i | ||||
\(671\) | 41.3002 | 1.59438 | ||||||||
\(672\) | 2.90629 | − | 0.663720i | 0.112113 | − | 0.0256035i | ||||
\(673\) | 8.45539 | 0.325931 | 0.162966 | − | 0.986632i | \(-0.447894\pi\) | ||||
0.162966 | + | 0.986632i | \(0.447894\pi\) | |||||||
\(674\) | −2.59393 | − | 4.49282i | −0.0999146 | − | 0.173057i | ||||
\(675\) | 5.47607 | − | 9.48484i | 0.210774 | − | 0.365072i | ||||
\(676\) | −0.713651 | + | 1.23608i | −0.0274481 | + | 0.0475415i | ||||
\(677\) | 15.3193 | + | 26.5338i | 0.588767 | + | 1.01978i | 0.994394 | + | 0.105736i | \(0.0337199\pi\) |
−0.405627 | + | 0.914039i | \(0.632947\pi\) | |||||||
\(678\) | 10.5841 | 0.406478 | ||||||||
\(679\) | 0.0944061 | − | 0.306191i | 0.00362297 | − | 0.0117505i | ||||
\(680\) | 7.16839 | 0.274895 | ||||||||
\(681\) | 12.9814 | + | 22.4845i | 0.497448 | + | 0.861606i | ||||
\(682\) | 15.5904 | − | 27.0033i | 0.596986 | − | 1.03401i | ||||
\(683\) | 14.5152 | − | 25.1411i | 0.555410 | − | 0.961998i | −0.442462 | − | 0.896787i | \(-0.645895\pi\) |
0.997872 | − | 0.0652106i | \(-0.0207719\pi\) | |||||||
\(684\) | 7.02784 | + | 12.1726i | 0.268716 | + | 0.465430i | ||||
\(685\) | −23.7711 | −0.908246 | ||||||||
\(686\) | 17.2425 | + | 6.75983i | 0.658323 | + | 0.258092i | ||||
\(687\) | 5.44971 | 0.207919 | ||||||||
\(688\) | −4.05534 | − | 7.02406i | −0.154609 | − | 0.267790i | ||||
\(689\) | 5.80157 | − | 10.0486i | 0.221022 | − | 0.382821i | ||||
\(690\) | −0.966847 | + | 1.67463i | −0.0368072 | + | 0.0637520i | ||||
\(691\) | −11.1056 | − | 19.2355i | −0.422477 | − | 0.731751i | 0.573704 | − | 0.819062i | \(-0.305506\pi\) |
−0.996181 | + | 0.0873113i | \(0.972173\pi\) | |||||||
\(692\) | 13.4018 | 0.509459 | ||||||||
\(693\) | 4.92338 | − | 15.9682i | 0.187024 | − | 0.606582i | ||||
\(694\) | −17.7594 | −0.674137 | ||||||||
\(695\) | 8.28617 | + | 14.3521i | 0.314313 | + | 0.544405i | ||||
\(696\) | 1.58137 | − | 2.73901i | 0.0599416 | − | 0.103822i | ||||
\(697\) | −20.9933 | + | 36.3614i | −0.795176 | + | 1.37729i | ||||
\(698\) | 7.68268 | + | 13.3068i | 0.290794 | + | 0.503669i | ||||
\(699\) | 14.9346 | 0.564878 | ||||||||
\(700\) | 5.30003 | − | 1.21039i | 0.200322 | − | 0.0457483i | ||||
\(701\) | −2.49593 | −0.0942699 | −0.0471350 | − | 0.998889i | \(-0.515009\pi\) | ||||
−0.0471350 | + | 0.998889i | \(0.515009\pi\) | |||||||
\(702\) | 10.1226 | + | 17.5329i | 0.382053 | + | 0.661736i | ||||
\(703\) | −36.2894 | + | 62.8551i | −1.36868 | + | 2.37063i | ||||
\(704\) | 1.82493 | − | 3.16087i | 0.0687795 | − | 0.119130i | ||||
\(705\) | −2.85352 | − | 4.94244i | −0.107470 | − | 0.186143i | ||||
\(706\) | −26.4646 | −0.996007 | ||||||||
\(707\) | −6.70061 | − | 7.21975i | −0.252002 | − | 0.271527i | ||||
\(708\) | −4.72000 | −0.177389 | ||||||||
\(709\) | 20.0638 | + | 34.7515i | 0.753510 | + | 1.30512i | 0.946111 | + | 0.323841i | \(0.104974\pi\) |
−0.192601 | + | 0.981277i | \(0.561692\pi\) | |||||||
\(710\) | −12.2751 | + | 21.2612i | −0.460677 | + | 0.797917i | ||||
\(711\) | −11.6355 | + | 20.1533i | −0.436365 | + | 0.755806i | ||||
\(712\) | −1.97918 | − | 3.42805i | −0.0741731 | − | 0.128472i | ||||
\(713\) | −8.54301 | −0.319938 | ||||||||
\(714\) | −8.47072 | − | 9.12701i | −0.317009 | − | 0.341570i | ||||
\(715\) | 23.7917 | 0.889759 | ||||||||
\(716\) | −10.4273 | − | 18.0606i | −0.389685 | − | 0.674955i | ||||
\(717\) | −3.04365 | + | 5.27176i | −0.113667 | + | 0.196878i | ||||
\(718\) | −3.75001 | + | 6.49521i | −0.139949 | + | 0.242399i | ||||
\(719\) | −5.69592 | − | 9.86562i | −0.212422 | − | 0.367926i | 0.740050 | − | 0.672552i | \(-0.234802\pi\) |
−0.952472 | + | 0.304626i | \(0.901468\pi\) | |||||||
\(720\) | −2.96967 | −0.110673 | ||||||||
\(721\) | −39.0213 | + | 8.91141i | −1.45323 | + | 0.331878i | ||||
\(722\) | 46.9784 | 1.74836 | ||||||||
\(723\) | −9.70180 | − | 16.8040i | −0.360814 | − | 0.624948i | ||||
\(724\) | −0.788691 | + | 1.36605i | −0.0293115 | + | 0.0507689i | ||||
\(725\) | 2.88385 | − | 4.99497i | 0.107103 | − | 0.185508i | ||||
\(726\) | 1.30784 | + | 2.26525i | 0.0485385 | + | 0.0840712i | ||||
\(727\) | −22.5154 | −0.835051 | −0.417526 | − | 0.908665i | \(-0.637103\pi\) | ||||
−0.417526 | + | 0.908665i | \(0.637103\pi\) | |||||||
\(728\) | −2.96094 | + | 9.60333i | −0.109740 | + | 0.355923i | ||||
\(729\) | 19.4262 | 0.719489 | ||||||||
\(730\) | 3.65625 | + | 6.33282i | 0.135324 | + | 0.234388i | ||||
\(731\) | −16.9392 | + | 29.3395i | −0.626517 | + | 1.08516i | ||||
\(732\) | −6.37495 | + | 11.0417i | −0.235625 | + | 0.408114i | ||||
\(733\) | 6.17468 | + | 10.6949i | 0.228067 | + | 0.395024i | 0.957235 | − | 0.289311i | \(-0.0934261\pi\) |
−0.729168 | + | 0.684335i | \(0.760093\pi\) | |||||||
\(734\) | −1.61092 | −0.0594600 | ||||||||
\(735\) | 11.1857 | + | 7.62226i | 0.412592 | + | 0.281151i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −24.1562 | − | 41.8398i | −0.889805 | − | 1.54119i | ||||
\(738\) | 8.69695 | − | 15.0636i | 0.320139 | − | 0.554497i | ||||
\(739\) | 4.74812 | − | 8.22398i | 0.174662 | − | 0.302524i | −0.765382 | − | 0.643576i | \(-0.777450\pi\) |
0.940044 | + | 0.341052i | \(0.110783\pi\) | |||||||
\(740\) | −7.66719 | − | 13.2800i | −0.281852 | − | 0.488181i | ||||
\(741\) | 34.7635 | 1.27707 | ||||||||
\(742\) | 2.38133 | − | 7.72346i | 0.0874214 | − | 0.283537i | ||||
\(743\) | −31.7348 | −1.16424 | −0.582118 | − | 0.813104i | \(-0.697776\pi\) | ||||
−0.582118 | + | 0.813104i | \(0.697776\pi\) | |||||||
\(744\) | 4.81295 | + | 8.33627i | 0.176451 | + | 0.305622i | ||||
\(745\) | 8.20437 | − | 14.2104i | 0.300585 | − | 0.520628i | ||||
\(746\) | −9.05039 | + | 15.6757i | −0.331358 | + | 0.573930i | ||||
\(747\) | 8.16626 | + | 14.1444i | 0.298788 | + | 0.517516i | ||||
\(748\) | −15.2454 | −0.557428 | ||||||||
\(749\) | 35.4284 | − | 8.09090i | 1.29453 | − | 0.295635i | ||||
\(750\) | 13.6418 | 0.498129 | ||||||||
\(751\) | 0.729462 | + | 1.26346i | 0.0266184 | + | 0.0461045i | 0.879028 | − | 0.476771i | \(-0.158193\pi\) |
−0.852409 | + | 0.522875i | \(0.824859\pi\) | |||||||
\(752\) | 1.47568 | − | 2.55596i | 0.0538126 | − | 0.0932062i | ||||
\(753\) | 9.53038 | − | 16.5071i | 0.347306 | − | 0.601552i | ||||
\(754\) | 5.33083 | + | 9.23328i | 0.194138 | + | 0.336256i | ||||
\(755\) | 12.4537 | 0.453236 | ||||||||
\(756\) | 9.59303 | + | 10.3363i | 0.348895 | + | 0.375927i | ||||
\(757\) | 13.7895 | 0.501186 | 0.250593 | − | 0.968092i | \(-0.419374\pi\) | ||||
0.250593 | + | 0.968092i | \(0.419374\pi\) | |||||||
\(758\) | 5.19547 | + | 8.99882i | 0.188708 | + | 0.326852i | ||||
\(759\) | 2.05625 | − | 3.56153i | 0.0746371 | − | 0.129275i | ||||
\(760\) | −6.96993 | + | 12.0723i | −0.252826 | + | 0.437907i | ||||
\(761\) | 2.63708 | + | 4.56756i | 0.0955942 | + | 0.165574i | 0.909856 | − | 0.414923i | \(-0.136192\pi\) |
−0.814262 | + | 0.580497i | \(0.802858\pi\) | |||||||
\(762\) | −2.85718 | −0.103505 | ||||||||
\(763\) | 16.8990 | + | 18.2083i | 0.611785 | + | 0.659184i | ||||
\(764\) | 6.26097 | 0.226514 | ||||||||
\(765\) | 6.20216 | + | 10.7424i | 0.224239 | + | 0.388394i | ||||
\(766\) | 3.69781 | − | 6.40480i | 0.133607 | − | 0.231415i | ||||
\(767\) | 7.95563 | − | 13.7796i | 0.287261 | − | 0.497551i | ||||
\(768\) | 0.563379 | + | 0.975800i | 0.0203292 | + | 0.0352112i | ||||
\(769\) | −4.68371 | −0.168899 | −0.0844495 | − | 0.996428i | \(-0.526913\pi\) | ||||
−0.0844495 | + | 0.996428i | \(0.526913\pi\) | |||||||
\(770\) | 16.1563 | − | 3.68967i | 0.582233 | − | 0.132966i | ||||
\(771\) | 13.8210 | 0.497751 | ||||||||
\(772\) | −6.51789 | − | 11.2893i | −0.234584 | − | 0.406311i | ||||
\(773\) | 4.20158 | − | 7.27735i | 0.151120 | − | 0.261748i | −0.780519 | − | 0.625132i | \(-0.785045\pi\) |
0.931640 | + | 0.363384i | \(0.118379\pi\) | |||||||
\(774\) | 7.01744 | − | 12.1546i | 0.252237 | − | 0.436887i | ||||
\(775\) | 8.77708 | + | 15.2024i | 0.315282 | + | 0.546085i | ||||
\(776\) | 0.121105 | 0.00434743 | ||||||||
\(777\) | −7.84831 | + | 25.4547i | −0.281557 | + | 0.913184i | ||||
\(778\) | 4.07942 | 0.146254 | ||||||||
\(779\) | −40.8241 | − | 70.7094i | −1.46268 | − | 2.53343i | ||||
\(780\) | −3.67240 | + | 6.36079i | −0.131493 | + | 0.227753i | ||||
\(781\) | 26.1062 | − | 45.2173i | 0.934154 | − | 1.61800i | ||||
\(782\) | 2.08850 | + | 3.61738i | 0.0746845 | + | 0.129357i | ||||
\(783\) | 14.9611 | 0.534665 | ||||||||
\(784\) | −0.521390 | + | 6.98056i | −0.0186211 | + | 0.249306i | ||||
\(785\) | −4.72818 | −0.168756 | ||||||||
\(786\) | −2.96482 | − | 5.13522i | −0.105752 | − | 0.183167i | ||||
\(787\) | −12.4682 | + | 21.5956i | −0.444444 | + | 0.769800i | −0.998013 | − | 0.0630033i | \(-0.979932\pi\) |
0.553569 | + | 0.832803i | \(0.313265\pi\) | |||||||
\(788\) | 10.6276 | − | 18.4075i | 0.378591 | − | 0.655739i | ||||
\(789\) | 7.35660 | + | 12.7420i | 0.261902 | + | 0.453627i | ||||
\(790\) | −23.0792 | −0.821122 | ||||||||
\(791\) | −7.32249 | + | 23.7493i | −0.260358 | + | 0.844429i | ||||
\(792\) | 6.31577 | 0.224421 | ||||||||
\(793\) | −21.4901 | − | 37.2220i | −0.763137 | − | 1.32179i | ||||
\(794\) | −4.43055 | + | 7.67394i | −0.157234 | + | 0.272338i | ||||
\(795\) | 2.95352 | − | 5.11565i | 0.104751 | − | 0.181434i | ||||
\(796\) | −2.36862 | − | 4.10257i | −0.0839535 | − | 0.145412i | ||||
\(797\) | −5.67934 | −0.201173 | −0.100586 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100586 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(798\) | 23.6070 | − | 5.39120i | 0.835678 | − | 0.190846i | ||||
\(799\) | −12.3278 | −0.436128 | ||||||||
\(800\) | 1.02740 | + | 1.77951i | 0.0363241 | + | 0.0629151i | ||||
\(801\) | 3.42482 | − | 5.93196i | 0.121010 | − | 0.209595i | ||||
\(802\) | −8.30173 | + | 14.3790i | −0.293144 | + | 0.507741i | ||||
\(803\) | −7.77596 | − | 13.4684i | −0.274408 | − | 0.475288i | ||||
\(804\) | 14.9147 | 0.526000 | ||||||||
\(805\) | −3.08875 | − | 3.32806i | −0.108864 | − | 0.117299i | ||||
\(806\) | −32.4491 | −1.14297 | ||||||||
\(807\) | 2.00960 | + | 3.48073i | 0.0707412 | + | 0.122527i | ||||
\(808\) | 1.86148 | − | 3.22418i | 0.0654866 | − | 0.113426i | ||||
\(809\) | 9.10604 | − | 15.7721i | 0.320151 | − | 0.554518i | −0.660368 | − | 0.750942i | \(-0.729600\pi\) |
0.980519 | + | 0.196424i | \(0.0629329\pi\) | |||||||
\(810\) | 0.698817 | + | 1.21039i | 0.0245539 | + | 0.0425286i | ||||
\(811\) | 39.0257 | 1.37038 | 0.685188 | − | 0.728366i | \(-0.259720\pi\) | ||||
0.685188 | + | 0.728366i | \(0.259720\pi\) | |||||||
\(812\) | 5.05194 | + | 5.44336i | 0.177288 | + | 0.191024i | ||||
\(813\) | −2.22781 | −0.0781328 | ||||||||
\(814\) | 16.3063 | + | 28.2433i | 0.571534 | + | 0.989926i | ||||
\(815\) | −17.4054 | + | 30.1470i | −0.609683 | + | 1.05600i | ||||
\(816\) | 2.35323 | − | 4.07591i | 0.0823795 | − | 0.142686i | ||||
\(817\) | −32.9404 | − | 57.0544i | −1.15244 | − | 1.99608i | ||||
\(818\) | 33.7434 | 1.17981 | ||||||||
\(819\) | −16.9533 | + | 3.87167i | −0.592395 | + | 0.135287i | ||||
\(820\) | 17.2506 | 0.602416 | ||||||||
\(821\) | −5.83009 | − | 10.0980i | −0.203472 | − | 0.352423i | 0.746173 | − | 0.665752i | \(-0.231889\pi\) |
−0.949645 | + | 0.313329i | \(0.898556\pi\) | |||||||
\(822\) | −7.80354 | + | 13.5161i | −0.272180 | + | 0.471429i | ||||
\(823\) | 26.8214 | − | 46.4559i | 0.934934 | − | 1.61935i | 0.160181 | − | 0.987088i | \(-0.448792\pi\) |
0.774752 | − | 0.632265i | \(-0.217875\pi\) | |||||||
\(824\) | −7.56418 | − | 13.1015i | −0.263511 | − | 0.456414i | ||||
\(825\) | −8.45036 | −0.294204 | ||||||||
\(826\) | 3.26549 | − | 10.5911i | 0.113621 | − | 0.368512i | ||||
\(827\) | −8.37095 | −0.291086 | −0.145543 | − | 0.989352i | \(-0.546493\pi\) | ||||
−0.145543 | + | 0.989352i | \(0.546493\pi\) | |||||||
\(828\) | −0.865209 | − | 1.49859i | −0.0300681 | − | 0.0520795i | ||||
\(829\) | 21.8638 | − | 37.8693i | 0.759362 | − | 1.31525i | −0.183814 | − | 0.982961i | \(-0.558845\pi\) |
0.943176 | − | 0.332293i | \(-0.107822\pi\) | |||||||
\(830\) | −8.09897 | + | 14.0278i | −0.281119 | + | 0.486913i | ||||
\(831\) | −6.16133 | − | 10.6717i | −0.213734 | − | 0.370198i | ||||
\(832\) | −3.79833 | −0.131683 | ||||||||
\(833\) | 26.3403 | − | 12.6928i | 0.912636 | − | 0.439780i | ||||
\(834\) | 10.8807 | 0.376768 | ||||||||
\(835\) | 0.279281 | + | 0.483728i | 0.00966491 | + | 0.0167401i | ||||
\(836\) | 14.8233 | − | 25.6748i | 0.512676 | − | 0.887981i | ||||
\(837\) | −22.7673 | + | 39.4340i | −0.786951 | + | 1.36304i | ||||
\(838\) | −18.2903 | − | 31.6797i | −0.631828 | − | 1.09436i | ||||
\(839\) | −20.3471 | −0.702460 | −0.351230 | − | 0.936289i | \(-0.614236\pi\) | ||||
−0.351230 | + | 0.936289i | \(0.614236\pi\) | |||||||
\(840\) | −1.50739 | + | 4.88897i | −0.0520098 | + | 0.168685i | ||||
\(841\) | −21.1211 | −0.728314 | ||||||||
\(842\) | 16.3802 | + | 28.3713i | 0.564498 | + | 0.977739i | ||||
\(843\) | −2.58046 | + | 4.46950i | −0.0888759 | + | 0.153938i | ||||
\(844\) | −8.38086 | + | 14.5161i | −0.288481 | + | 0.499664i | ||||
\(845\) | −1.22474 | − | 2.12131i | −0.0421323 | − | 0.0729752i | ||||
\(846\) | 5.10710 | 0.175586 | ||||||||
\(847\) | −5.98775 | + | 1.36744i | −0.205742 | + | 0.0469859i | ||||
\(848\) | 3.05480 | 0.104902 | ||||||||
\(849\) | −8.49624 | − | 14.7159i | −0.291590 | − | 0.505049i | ||||
\(850\) | 4.29144 | − | 7.43300i | 0.147195 | − | 0.254950i | ||||
\(851\) | 4.46765 | − | 7.73820i | 0.153149 | − | 0.265262i | ||||
\(852\) | 8.05933 | + | 13.9592i | 0.276108 | + | 0.478233i | ||||
\(853\) | 10.3309 | 0.353724 | 0.176862 | − | 0.984236i | \(-0.443405\pi\) | ||||
0.176862 | + | 0.984236i | \(0.443405\pi\) | |||||||
\(854\) | −20.3658 | − | 21.9437i | −0.696905 | − | 0.750899i | ||||
\(855\) | −24.1218 | −0.824948 | ||||||||
\(856\) | 6.86772 | + | 11.8952i | 0.234734 | + | 0.406571i | ||||
\(857\) | −23.3108 | + | 40.3756i | −0.796283 | + | 1.37920i | 0.125738 | + | 0.992064i | \(0.459870\pi\) |
−0.922021 | + | 0.387140i | \(0.873463\pi\) | |||||||
\(858\) | 7.81031 | − | 13.5279i | 0.266640 | − | 0.461833i | ||||
\(859\) | 5.12762 | + | 8.88130i | 0.174952 | + | 0.303026i | 0.940145 | − | 0.340775i | \(-0.110690\pi\) |
−0.765193 | + | 0.643801i | \(0.777356\pi\) | |||||||
\(860\) | 13.9192 | 0.474642 | ||||||||
\(861\) | −20.3846 | − | 21.9639i | −0.694705 | − | 0.748529i | ||||
\(862\) | −17.7194 | −0.603524 | ||||||||
\(863\) | 19.6952 | + | 34.1130i | 0.670431 | + | 1.16122i | 0.977782 | + | 0.209625i | \(0.0672242\pi\) |
−0.307351 | + | 0.951596i | \(0.599442\pi\) | |||||||
\(864\) | −2.66502 | + | 4.61594i | −0.0906657 | + | 0.157038i | ||||
\(865\) | −11.4998 | + | 19.9182i | −0.391005 | + | 0.677240i | ||||
\(866\) | 2.25994 | + | 3.91434i | 0.0767960 | + | 0.133015i | ||||
\(867\) | −0.503991 | −0.0171164 | ||||||||
\(868\) | −22.0354 | + | 5.03228i | −0.747929 | + | 0.170807i | ||||
\(869\) | 49.0839 | 1.66506 | ||||||||
\(870\) | 2.71388 | + | 4.70058i | 0.0920091 | + | 0.159364i | ||||
\(871\) | −25.1389 | + | 43.5418i | −0.851798 | + | 1.47536i | ||||
\(872\) | −4.69467 | + | 8.13140i | −0.158981 | + | 0.275364i | ||||
\(873\) | 0.104781 | + | 0.181487i | 0.00354632 | + | 0.00614240i | ||||
\(874\) | −8.12271 | −0.274755 | ||||||||
\(875\) | −9.43798 | + | 30.6106i | −0.319062 | + | 1.03483i | ||||
\(876\) | 4.80108 | 0.162214 | ||||||||
\(877\) | −21.6309 | − | 37.4659i | −0.730424 | − | 1.26513i | −0.956702 | − | 0.291069i | \(-0.905989\pi\) |
0.226278 | − | 0.974063i | \(-0.427344\pi\) | |||||||
\(878\) | −3.19897 | + | 5.54078i | −0.107960 | + | 0.186992i | ||||
\(879\) | 8.20028 | − | 14.2033i | 0.276589 | − | 0.479065i | ||||
\(880\) | 3.13186 | + | 5.42455i | 0.105575 | + | 0.182861i | ||||
\(881\) | 27.5229 | 0.927272 | 0.463636 | − | 0.886026i | \(-0.346545\pi\) | ||||
0.463636 | + | 0.886026i | \(0.346545\pi\) | |||||||
\(882\) | −10.9121 | + | 5.25829i | −0.367429 | + | 0.177056i | ||||
\(883\) | −20.9321 | −0.704421 | −0.352210 | − | 0.935921i | \(-0.614570\pi\) | ||||
−0.352210 | + | 0.935921i | \(0.614570\pi\) | |||||||
\(884\) | 7.93280 | + | 13.7400i | 0.266809 | + | 0.462127i | ||||
\(885\) | 4.05014 | − | 7.01504i | 0.136144 | − | 0.235808i | ||||
\(886\) | 8.56844 | − | 14.8410i | 0.287863 | − | 0.498593i | ||||
\(887\) | 25.0642 | + | 43.4125i | 0.841575 | + | 1.45765i | 0.888563 | + | 0.458755i | \(0.151704\pi\) |
−0.0469884 | + | 0.998895i | \(0.514962\pi\) | |||||||
\(888\) | −10.0679 | −0.337857 | ||||||||
\(889\) | 1.97671 | − | 6.41115i | 0.0662968 | − | 0.215023i | ||||
\(890\) | 6.79319 | 0.227708 | ||||||||
\(891\) | −1.48621 | − | 2.57420i | −0.0497900 | − | 0.0862388i | ||||
\(892\) | −0.617347 | + | 1.06928i | −0.0206703 | + | 0.0358020i | ||||
\(893\) | 11.9865 | − | 20.7613i | 0.401114 | − | 0.694750i | ||||
\(894\) | −5.38664 | − | 9.32993i | −0.180156 | − | 0.312040i | ||||
\(895\) | 35.7897 | 1.19632 | ||||||||
\(896\) | −2.57934 | + | 0.589053i | −0.0861698 | + | 0.0196789i | ||||
\(897\) | −4.27979 | −0.142898 | ||||||||
\(898\) | 6.63475 | + | 11.4917i | 0.221404 | + | 0.383484i | ||||
\(899\) | −11.9898 | + | 20.7670i | −0.399884 | + | 0.692619i | ||||
\(900\) | −1.77783 | + | 3.07929i | −0.0592610 | + | 0.102643i | ||||
\(901\) | −6.37994 | − | 11.0504i | −0.212547 | − | 0.368142i | ||||
\(902\) | −36.6877 | −1.22157 | ||||||||
\(903\) | −16.4480 | − | 17.7224i | −0.547356 | − | 0.589764i | ||||
\(904\) | −9.39338 | −0.312419 | ||||||||
\(905\) | −1.35352 | − | 2.34436i | −0.0449925 | − | 0.0779293i | ||||
\(906\) | 4.08828 | − | 7.08111i | 0.135824 | − | 0.235254i | ||||
\(907\) | 20.8613 | − | 36.1329i | 0.692689 | − | 1.19977i | −0.278265 | − | 0.960504i | \(-0.589759\pi\) |
0.970954 | − | 0.239268i | \(-0.0769073\pi\) | |||||||
\(908\) | −11.5210 | − | 19.9550i | −0.382339 | − | 0.662230i | ||||
\(909\) | 6.44228 | 0.213677 | ||||||||
\(910\) | −11.7321 | − | 12.6411i | −0.388915 | − | 0.419048i | ||||
\(911\) | 28.5662 | 0.946440 | 0.473220 | − | 0.880944i | \(-0.343092\pi\) | ||||
0.473220 | + | 0.880944i | \(0.343092\pi\) | |||||||
\(912\) | 4.57616 | + | 7.92614i | 0.151532 | + | 0.262461i | ||||
\(913\) | 17.2245 | − | 29.8338i | 0.570049 | − | 0.987354i | ||||
\(914\) | 15.2314 | − | 26.3815i | 0.503810 | − | 0.872624i | ||||
\(915\) | −10.9404 | − | 18.9494i | −0.361679 | − | 0.626447i | ||||
\(916\) | −4.83663 | −0.159807 | ||||||||
\(917\) | 13.5740 | − | 3.09994i | 0.448253 | − | 0.102369i | ||||
\(918\) | 22.2635 | 0.734806 | ||||||||
\(919\) | −8.48538 | − | 14.6971i | −0.279907 | − | 0.484813i | 0.691454 | − | 0.722420i | \(-0.256970\pi\) |
−0.971361 | + | 0.237607i | \(0.923637\pi\) | |||||||
\(920\) | 0.858079 | − | 1.48624i | 0.0282900 | − | 0.0489998i | ||||
\(921\) | −7.15627 | + | 12.3950i | −0.235807 | + | 0.408430i | ||||
\(922\) | −6.56193 | − | 11.3656i | −0.216106 | − | 0.374306i | ||||
\(923\) | −54.3364 | −1.78851 | ||||||||
\(924\) | 3.20584 | − | 10.3976i | 0.105465 | − | 0.342057i | ||||
\(925\) | −18.3602 | −0.603681 | ||||||||
\(926\) | 10.6726 | + | 18.4855i | 0.350724 | + | 0.607472i | ||||
\(927\) | 13.0892 | − | 22.6712i | 0.429906 | − | 0.744618i | ||||
\(928\) | −1.40347 | + | 2.43088i | −0.0460711 | + | 0.0797975i | ||||
\(929\) | −17.3867 | − | 30.1146i | −0.570438 | − | 0.988027i | −0.996521 | − | 0.0833434i | \(-0.973440\pi\) |
0.426083 | − | 0.904684i | \(-0.359893\pi\) | |||||||
\(930\) | −16.5196 | −0.541698 | ||||||||
\(931\) | −4.23510 | + | 56.7010i | −0.138800 | + | 1.85830i | ||||
\(932\) | −13.2545 | −0.434165 | ||||||||
\(933\) | −5.19375 | − | 8.99584i | −0.170036 | − | 0.294511i | ||||
\(934\) | −11.1802 | + | 19.3647i | −0.365827 | + | 0.633632i | ||||
\(935\) | 13.0818 | − | 22.6583i | 0.427820 | − | 0.741006i | ||||
\(936\) | −3.28635 | − | 5.69212i | −0.107418 | − | 0.186053i | ||||
\(937\) | −49.0341 | −1.60187 | −0.800937 | − | 0.598749i | \(-0.795665\pi\) | ||||
−0.800937 | + | 0.598749i | \(0.795665\pi\) | |||||||
\(938\) | −10.3186 | + | 33.4667i | −0.336914 | + | 1.09273i | ||||
\(939\) | 17.6412 | 0.575700 | ||||||||
\(940\) | 2.53251 | + | 4.38643i | 0.0826012 | + | 0.143070i | ||||
\(941\) | −17.4632 | + | 30.2472i | −0.569285 | + | 0.986030i | 0.427352 | + | 0.904085i | \(0.359446\pi\) |
−0.996637 | + | 0.0819447i | \(0.973887\pi\) | |||||||
\(942\) | −1.55216 | + | 2.68842i | −0.0505721 | + | 0.0875935i | ||||
\(943\) | 5.02592 | + | 8.70515i | 0.163667 | + | 0.283479i | ||||
\(944\) | 4.18902 | 0.136341 | ||||||||
\(945\) | −23.5937 | + | 5.38817i | −0.767504 | + | 0.175277i | ||||
\(946\) | −29.6028 | −0.962471 | ||||||||
\(947\) | 0.183796 | + | 0.318345i | 0.00597258 | + | 0.0103448i | 0.868996 | − | 0.494819i | \(-0.164766\pi\) |
−0.863024 | + | 0.505163i | \(0.831432\pi\) | |||||||
\(948\) | −7.57642 | + | 13.1227i | −0.246071 | + | 0.426207i | ||||
\(949\) | −8.09229 | + | 14.0163i | −0.262687 | + | 0.454987i | ||||
\(950\) | 8.34527 | + | 14.4544i | 0.270756 | + | 0.468964i | ||||
\(951\) | −12.4374 | −0.403310 | ||||||||
\(952\) | 7.51779 | + | 8.10024i | 0.243653 | + | 0.262530i | ||||
\(953\) | 39.2201 | 1.27047 | 0.635233 | − | 0.772321i | \(-0.280904\pi\) | ||||
0.635233 | + | 0.772321i | \(0.280904\pi\) | |||||||
\(954\) | 2.64304 | + | 4.57788i | 0.0855716 | + | 0.148214i | ||||
\(955\) | −5.37241 | + | 9.30529i | −0.173847 | + | 0.301112i | ||||
\(956\) | 2.70125 | − | 4.67871i | 0.0873647 | − | 0.151320i | ||||
\(957\) | −5.77176 | − | 9.99698i | −0.186575 | − | 0.323157i | ||||
\(958\) | −17.4670 | −0.564333 | ||||||||
\(959\) | −24.9297 | − | 26.8612i | −0.805022 | − | 0.867393i | ||||
\(960\) | −1.93369 | −0.0624097 | ||||||||
\(961\) | −20.9915 | − | 36.3583i | −0.677145 | − | 1.17285i | ||||
\(962\) | 16.9696 | − | 29.3922i | 0.547122 | − | 0.947643i | ||||
\(963\) | −11.8840 | + | 20.5837i | −0.382957 | + | 0.663302i | ||||
\(964\) | 8.61037 | + | 14.9136i | 0.277321 | + | 0.480335i | ||||
\(965\) | 22.3715 | 0.720163 | ||||||||
\(966\) | −2.90629 | + | 0.663720i | −0.0935085 | + | 0.0213548i | ||||
\(967\) | 20.3070 | 0.653030 | 0.326515 | − | 0.945192i | \(-0.394126\pi\) | ||||
0.326515 | + | 0.945192i | \(0.394126\pi\) | |||||||
\(968\) | −1.16071 | − | 2.01041i | −0.0373067 | − | 0.0646171i | ||||
\(969\) | 19.1146 | − | 33.1075i | 0.614049 | − | 1.06356i | ||||
\(970\) | −0.103918 | + | 0.179991i | −0.00333661 | + | 0.00577917i | ||||
\(971\) | −11.9692 | − | 20.7312i | −0.384110 | − | 0.665297i | 0.607536 | − | 0.794292i | \(-0.292158\pi\) |
−0.991645 | + | 0.128995i | \(0.958825\pi\) | |||||||
\(972\) | −15.0725 | −0.483450 | ||||||||
\(973\) | −7.52772 | + | 24.4150i | −0.241328 | + | 0.782708i | ||||
\(974\) | −5.79067 | −0.185545 | ||||||||
\(975\) | 4.39706 | + | 7.61593i | 0.140819 | + | 0.243905i | ||||
\(976\) | 5.65778 | − | 9.79957i | 0.181101 | − | 0.313677i | ||||
\(977\) | −4.27141 | + | 7.39830i | −0.136655 | + | 0.236693i | −0.926228 | − | 0.376963i | \(-0.876968\pi\) |
0.789574 | + | 0.613656i | \(0.210302\pi\) | |||||||
\(978\) | 11.4276 | + | 19.7932i | 0.365415 | + | 0.632917i | ||||
\(979\) | −14.4475 | −0.461743 | ||||||||
\(980\) | −9.92737 | − | 6.76478i | −0.317118 | − | 0.216093i | ||||
\(981\) | −16.2475 | −0.518742 | ||||||||
\(982\) | 4.23527 | + | 7.33570i | 0.135153 | + | 0.234092i | ||||
\(983\) | −15.1512 | + | 26.2426i | −0.483248 | + | 0.837011i | −0.999815 | − | 0.0192364i | \(-0.993876\pi\) |
0.516567 | + | 0.856247i | \(0.327210\pi\) | |||||||
\(984\) | 5.66299 | − | 9.80859i | 0.180530 | − | 0.312686i | ||||
\(985\) | 18.2386 | + | 31.5901i | 0.581129 | + | 1.00655i | ||||
\(986\) | 11.7246 | 0.373386 | ||||||||
\(987\) | 2.59233 | − | 8.40780i | 0.0825147 | − | 0.267623i | ||||
\(988\) | −30.8527 | −0.981556 | ||||||||
\(989\) | 4.05534 | + | 7.02406i | 0.128952 | + | 0.223352i | ||||
\(990\) | −5.41943 | + | 9.38674i | −0.172241 | + | 0.298330i | ||||
\(991\) | 16.2905 | − | 28.2160i | 0.517486 | − | 0.896311i | −0.482308 | − | 0.876002i | \(-0.660201\pi\) |
0.999794 | − | 0.0203096i | \(-0.00646520\pi\) | |||||||
\(992\) | −4.27150 | − | 7.39846i | −0.135620 | − | 0.234901i | ||||
\(993\) | 17.6805 | 0.561073 | ||||||||
\(994\) | −36.8984 | + | 8.42661i | −1.17035 | + | 0.267276i | ||||
\(995\) | 8.12986 | 0.257734 | ||||||||
\(996\) | 5.31744 | + | 9.21007i | 0.168489 | + | 0.291832i | ||||
\(997\) | 0.465561 | − | 0.806375i | 0.0147445 | − | 0.0255381i | −0.858559 | − | 0.512715i | \(-0.828640\pi\) |
0.873303 | + | 0.487177i | \(0.161973\pi\) | |||||||
\(998\) | 1.26100 | − | 2.18412i | 0.0399163 | − | 0.0691371i | ||||
\(999\) | −23.8127 | − | 41.2448i | −0.753401 | − | 1.30493i |
(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 | 322.2.e.a.277.4 | yes | 8 | |
7.2 | even | 3 | inner | 322.2.e.a.93.4 | ✓ | 8 | |
7.3 | odd | 6 | 2254.2.a.x.1.4 | 4 | |||
7.4 | even | 3 | 2254.2.a.z.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.e.a.93.4 | ✓ | 8 | 7.2 | even | 3 | inner | |
322.2.e.a.277.4 | yes | 8 | 1.1 | even | 1 | trivial | |
2254.2.a.x.1.4 | 4 | 7.3 | odd | 6 | |||
2254.2.a.z.1.1 | 4 | 7.4 | even | 3 |