Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(47,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.13 | ||
Character | \(\chi\) | \(=\) | 276.47 |
Dual form | 276.2.c.a.47.14 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.456308 | − | 1.33857i | 0.322659 | − | 0.946515i | ||||
\(3\) | 0.784130 | − | 1.54439i | 0.452718 | − | 0.891654i | ||||
\(4\) | −1.58357 | − | 1.22161i | −0.791783 | − | 0.610803i | ||||
\(5\) | − | 1.42397i | − | 0.636817i | −0.947954 | − | 0.318408i | \(-0.896852\pi\) | ||
0.947954 | − | 0.318408i | \(-0.103148\pi\) | |||||||
\(6\) | −1.70948 | − | 1.75433i | −0.697891 | − | 0.716204i | ||||
\(7\) | 1.12562i | 0.425445i | 0.977113 | + | 0.212723i | \(0.0682330\pi\) | ||||
−0.977113 | + | 0.212723i | \(0.931767\pi\) | |||||||
\(8\) | −2.35780 | + | 1.56229i | −0.833610 | + | 0.552354i | ||||
\(9\) | −1.77028 | − | 2.42200i | −0.590094 | − | 0.807335i | ||||
\(10\) | −1.90608 | − | 0.649767i | −0.602757 | − | 0.205474i | ||||
\(11\) | −1.68304 | −0.507456 | −0.253728 | − | 0.967276i | \(-0.581657\pi\) | ||||
−0.253728 | + | 0.967276i | \(0.581657\pi\) | |||||||
\(12\) | −3.12836 | + | 1.48775i | −0.903079 | + | 0.429475i | ||||
\(13\) | 5.14341 | 1.42652 | 0.713262 | − | 0.700897i | \(-0.247217\pi\) | ||||
0.713262 | + | 0.700897i | \(0.247217\pi\) | |||||||
\(14\) | 1.50673 | + | 0.513630i | 0.402690 | + | 0.137273i | ||||
\(15\) | −2.19916 | − | 1.11657i | −0.567820 | − | 0.288298i | ||||
\(16\) | 1.01536 | + | 3.86898i | 0.253841 | + | 0.967246i | ||||
\(17\) | − | 4.65065i | − | 1.12795i | −0.825793 | − | 0.563974i | \(-0.809272\pi\) | ||
0.825793 | − | 0.563974i | \(-0.190728\pi\) | |||||||
\(18\) | −4.04983 | + | 1.26447i | −0.954554 | + | 0.298039i | ||||
\(19\) | 5.86444i | 1.34540i | 0.739918 | + | 0.672698i | \(0.234865\pi\) | ||||
−0.739918 | + | 0.672698i | \(0.765135\pi\) | |||||||
\(20\) | −1.73952 | + | 2.25494i | −0.388969 | + | 0.504221i | ||||
\(21\) | 1.73840 | + | 0.882634i | 0.379350 | + | 0.192606i | ||||
\(22\) | −0.767985 | + | 2.25288i | −0.163735 | + | 0.480315i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0.563966 | + | 4.86641i | 0.115119 | + | 0.993352i | ||||
\(25\) | 2.97232 | 0.594465 | ||||||||
\(26\) | 2.34698 | − | 6.88484i | 0.460280 | − | 1.35023i | ||||
\(27\) | −5.12865 | + | 0.834839i | −0.987009 | + | 0.160665i | ||||
\(28\) | 1.37507 | − | 1.78250i | 0.259863 | − | 0.336860i | ||||
\(29\) | − | 3.67220i | − | 0.681911i | −0.940080 | − | 0.340955i | \(-0.889250\pi\) | ||
0.940080 | − | 0.340955i | \(-0.110750\pi\) | |||||||
\(30\) | −2.49811 | + | 2.43424i | −0.456091 | + | 0.444429i | ||||
\(31\) | − | 3.79271i | − | 0.681191i | −0.940210 | − | 0.340595i | \(-0.889371\pi\) | ||
0.940210 | − | 0.340595i | \(-0.110629\pi\) | |||||||
\(32\) | 5.64224 | + | 0.406310i | 0.997417 | + | 0.0718262i | ||||
\(33\) | −1.31972 | + | 2.59927i | −0.229734 | + | 0.452475i | ||||
\(34\) | −6.22524 | − | 2.12213i | −1.06762 | − | 0.363942i | ||||
\(35\) | 1.60285 | 0.270931 | ||||||||
\(36\) | −0.155376 | + | 5.99799i | −0.0258960 | + | 0.999665i | ||||
\(37\) | −2.52020 | −0.414319 | −0.207159 | − | 0.978307i | \(-0.566422\pi\) | ||||
−0.207159 | + | 0.978307i | \(0.566422\pi\) | |||||||
\(38\) | 7.85000 | + | 2.67599i | 1.27344 | + | 0.434103i | ||||
\(39\) | 4.03310 | − | 7.94343i | 0.645813 | − | 1.27197i | ||||
\(40\) | 2.22465 | + | 3.35743i | 0.351748 | + | 0.530856i | ||||
\(41\) | 8.23771i | 1.28651i | 0.765650 | + | 0.643257i | \(0.222417\pi\) | ||||
−0.765650 | + | 0.643257i | \(0.777583\pi\) | |||||||
\(42\) | 1.97472 | − | 1.92423i | 0.304705 | − | 0.296914i | ||||
\(43\) | − | 3.72497i | − | 0.568052i | −0.958817 | − | 0.284026i | \(-0.908330\pi\) | ||
0.958817 | − | 0.284026i | \(-0.0916703\pi\) | |||||||
\(44\) | 2.66521 | + | 2.05601i | 0.401795 | + | 0.309955i | ||||
\(45\) | −3.44885 | + | 2.52082i | −0.514124 | + | 0.375781i | ||||
\(46\) | 0.456308 | − | 1.33857i | 0.0672790 | − | 0.197362i | ||||
\(47\) | 7.62360 | 1.11202 | 0.556008 | − | 0.831177i | \(-0.312332\pi\) | ||||
0.556008 | + | 0.831177i | \(0.312332\pi\) | |||||||
\(48\) | 6.77140 | + | 1.46567i | 0.977367 | + | 0.211551i | ||||
\(49\) | 5.73298 | 0.818996 | ||||||||
\(50\) | 1.35629 | − | 3.97868i | 0.191809 | − | 0.562670i | ||||
\(51\) | −7.18241 | − | 3.64671i | −1.00574 | − | 0.510642i | ||||
\(52\) | −8.14493 | − | 6.28321i | −1.12950 | − | 0.871325i | ||||
\(53\) | − | 2.23179i | − | 0.306560i | −0.988183 | − | 0.153280i | \(-0.951016\pi\) | ||
0.988183 | − | 0.153280i | \(-0.0489837\pi\) | |||||||
\(54\) | −1.22275 | + | 7.24603i | −0.166395 | + | 0.986059i | ||||
\(55\) | 2.39659i | 0.323156i | ||||||||
\(56\) | −1.75855 | − | 2.65400i | −0.234996 | − | 0.354655i | ||||
\(57\) | 9.05699 | + | 4.59848i | 1.19963 | + | 0.609084i | ||||
\(58\) | −4.91552 | − | 1.67565i | −0.645439 | − | 0.220024i | ||||
\(59\) | −3.98448 | −0.518735 | −0.259367 | − | 0.965779i | \(-0.583514\pi\) | ||||
−0.259367 | + | 0.965779i | \(0.583514\pi\) | |||||||
\(60\) | 2.11850 | + | 4.45467i | 0.273497 | + | 0.575095i | ||||
\(61\) | −7.14195 | −0.914433 | −0.457217 | − | 0.889355i | \(-0.651154\pi\) | ||||
−0.457217 | + | 0.889355i | \(0.651154\pi\) | |||||||
\(62\) | −5.07682 | − | 1.73064i | −0.644757 | − | 0.219792i | ||||
\(63\) | 2.72626 | − | 1.99267i | 0.343477 | − | 0.251052i | ||||
\(64\) | 3.11848 | − | 7.36716i | 0.389810 | − | 0.920895i | ||||
\(65\) | − | 7.32404i | − | 0.908435i | ||||||
\(66\) | 2.87712 | + | 2.95262i | 0.354149 | + | 0.363442i | ||||
\(67\) | 12.2990i | 1.50257i | 0.659981 | + | 0.751283i | \(0.270565\pi\) | ||||
−0.659981 | + | 0.751283i | \(0.729435\pi\) | |||||||
\(68\) | −5.68125 | + | 7.36460i | −0.688953 | + | 0.893090i | ||||
\(69\) | 0.784130 | − | 1.54439i | 0.0943981 | − | 0.185923i | ||||
\(70\) | 0.731392 | − | 2.14553i | 0.0874180 | − | 0.256440i | ||||
\(71\) | −3.55458 | −0.421851 | −0.210925 | − | 0.977502i | \(-0.567648\pi\) | ||||
−0.210925 | + | 0.977502i | \(0.567648\pi\) | |||||||
\(72\) | 7.95786 | + | 2.94491i | 0.937842 | + | 0.347061i | ||||
\(73\) | 13.8147 | 1.61689 | 0.808447 | − | 0.588570i | \(-0.200309\pi\) | ||||
0.808447 | + | 0.588570i | \(0.200309\pi\) | |||||||
\(74\) | −1.14999 | + | 3.37348i | −0.133683 | + | 0.392159i | ||||
\(75\) | 2.33069 | − | 4.59043i | 0.269125 | − | 0.530057i | ||||
\(76\) | 7.16403 | − | 9.28673i | 0.821771 | − | 1.06526i | ||||
\(77\) | − | 1.89447i | − | 0.215895i | ||||||
\(78\) | −8.79254 | − | 9.02326i | −0.995559 | − | 1.02168i | ||||
\(79\) | − | 5.27297i | − | 0.593255i | −0.954993 | − | 0.296628i | \(-0.904138\pi\) | ||
0.954993 | − | 0.296628i | \(-0.0958620\pi\) | |||||||
\(80\) | 5.50930 | − | 1.44584i | 0.615958 | − | 0.161650i | ||||
\(81\) | −2.73221 | + | 8.57526i | −0.303579 | + | 0.952806i | ||||
\(82\) | 11.0268 | + | 3.75894i | 1.21771 | + | 0.415105i | ||||
\(83\) | 12.9095 | 1.41700 | 0.708502 | − | 0.705709i | \(-0.249371\pi\) | ||||
0.708502 | + | 0.705709i | \(0.249371\pi\) | |||||||
\(84\) | −1.67464 | − | 3.52135i | −0.182718 | − | 0.384210i | ||||
\(85\) | −6.62236 | −0.718296 | ||||||||
\(86\) | −4.98615 | − | 1.69973i | −0.537670 | − | 0.183287i | ||||
\(87\) | −5.67131 | − | 2.87948i | −0.608028 | − | 0.308713i | ||||
\(88\) | 3.96828 | − | 2.62940i | 0.423020 | − | 0.280295i | ||||
\(89\) | 15.9010i | 1.68550i | 0.538303 | + | 0.842751i | \(0.319065\pi\) | ||||
−0.538303 | + | 0.842751i | \(0.680935\pi\) | |||||||
\(90\) | 1.80057 | + | 5.76681i | 0.189796 | + | 0.607876i | ||||
\(91\) | 5.78953i | 0.606908i | ||||||||
\(92\) | −1.58357 | − | 1.22161i | −0.165098 | − | 0.127361i | ||||
\(93\) | −5.85742 | − | 2.97398i | −0.607386 | − | 0.308387i | ||||
\(94\) | 3.47871 | − | 10.2048i | 0.358802 | − | 1.05254i | ||||
\(95\) | 8.35076 | 0.856770 | ||||||||
\(96\) | 5.05175 | − | 8.39522i | 0.515592 | − | 0.856834i | ||||
\(97\) | −11.9616 | −1.21451 | −0.607256 | − | 0.794506i | \(-0.707730\pi\) | ||||
−0.607256 | + | 0.794506i | \(0.707730\pi\) | |||||||
\(98\) | 2.61600 | − | 7.67402i | 0.264256 | − | 0.775193i | ||||
\(99\) | 2.97946 | + | 4.07633i | 0.299447 | + | 0.409687i | ||||
\(100\) | −4.70687 | − | 3.63101i | −0.470687 | − | 0.363101i | ||||
\(101\) | − | 1.11023i | − | 0.110472i | −0.998473 | − | 0.0552362i | \(-0.982409\pi\) | ||
0.998473 | − | 0.0552362i | \(-0.0175912\pi\) | |||||||
\(102\) | −8.15879 | + | 7.95017i | −0.807840 | + | 0.787184i | ||||
\(103\) | 16.6642i | 1.64197i | 0.570949 | + | 0.820985i | \(0.306575\pi\) | ||||
−0.570949 | + | 0.820985i | \(0.693425\pi\) | |||||||
\(104\) | −12.1271 | + | 8.03551i | −1.18916 | + | 0.787947i | ||||
\(105\) | 1.25684 | − | 2.47542i | 0.122655 | − | 0.241576i | ||||
\(106\) | −2.98742 | − | 1.01838i | −0.290164 | − | 0.0989143i | ||||
\(107\) | −5.17617 | −0.500400 | −0.250200 | − | 0.968194i | \(-0.580496\pi\) | ||||
−0.250200 | + | 0.968194i | \(0.580496\pi\) | |||||||
\(108\) | 9.14140 | + | 4.94316i | 0.879631 | + | 0.475656i | ||||
\(109\) | −1.88125 | −0.180191 | −0.0900953 | − | 0.995933i | \(-0.528717\pi\) | ||||
−0.0900953 | + | 0.995933i | \(0.528717\pi\) | |||||||
\(110\) | 3.20802 | + | 1.09358i | 0.305873 | + | 0.104269i | ||||
\(111\) | −1.97617 | + | 3.89218i | −0.187569 | + | 0.369429i | ||||
\(112\) | −4.35501 | + | 1.14291i | −0.411510 | + | 0.107995i | ||||
\(113\) | 10.8879i | 1.02425i | 0.858911 | + | 0.512124i | \(0.171141\pi\) | ||||
−0.858911 | + | 0.512124i | \(0.828859\pi\) | |||||||
\(114\) | 10.2882 | − | 10.0251i | 0.963577 | − | 0.938939i | ||||
\(115\) | − | 1.42397i | − | 0.132785i | ||||||
\(116\) | −4.48598 | + | 5.81517i | −0.416513 | + | 0.539925i | ||||
\(117\) | −9.10528 | − | 12.4574i | −0.841783 | − | 1.15168i | ||||
\(118\) | −1.81815 | + | 5.33352i | −0.167374 | + | 0.490990i | ||||
\(119\) | 5.23487 | 0.479880 | ||||||||
\(120\) | 6.92960 | − | 0.803069i | 0.632583 | − | 0.0733098i | ||||
\(121\) | −8.16737 | −0.742488 | ||||||||
\(122\) | −3.25893 | + | 9.56004i | −0.295050 | + | 0.865525i | ||||
\(123\) | 12.7222 | + | 6.45944i | 1.14713 | + | 0.582428i | ||||
\(124\) | −4.63319 | + | 6.00600i | −0.416073 | + | 0.539355i | ||||
\(125\) | − | 11.3523i | − | 1.01538i | ||||||
\(126\) | −1.42332 | − | 4.55858i | −0.126799 | − | 0.406110i | ||||
\(127\) | − | 8.80731i | − | 0.781523i | −0.920492 | − | 0.390761i | \(-0.872212\pi\) | ||
0.920492 | − | 0.390761i | \(-0.127788\pi\) | |||||||
\(128\) | −8.43851 | − | 7.53601i | −0.745866 | − | 0.666096i | ||||
\(129\) | −5.75280 | − | 2.92086i | −0.506506 | − | 0.257167i | ||||
\(130\) | −9.80377 | − | 3.34202i | −0.859848 | − | 0.293114i | ||||
\(131\) | −18.3393 | −1.60231 | −0.801155 | − | 0.598457i | \(-0.795781\pi\) | ||||
−0.801155 | + | 0.598457i | \(0.795781\pi\) | |||||||
\(132\) | 5.26515 | − | 2.50394i | 0.458273 | − | 0.217940i | ||||
\(133\) | −6.60114 | −0.572392 | ||||||||
\(134\) | 16.4632 | + | 5.61215i | 1.42220 | + | 0.484816i | ||||
\(135\) | 1.18878 | + | 7.30302i | 0.102314 | + | 0.628544i | ||||
\(136\) | 7.26567 | + | 10.9653i | 0.623026 | + | 0.940268i | ||||
\(137\) | − | 5.76597i | − | 0.492620i | −0.969191 | − | 0.246310i | \(-0.920782\pi\) | ||
0.969191 | − | 0.246310i | \(-0.0792181\pi\) | |||||||
\(138\) | −1.70948 | − | 1.75433i | −0.145520 | − | 0.149339i | ||||
\(139\) | 2.41616i | 0.204936i | 0.994736 | + | 0.102468i | \(0.0326739\pi\) | ||||
−0.994736 | + | 0.102468i | \(0.967326\pi\) | |||||||
\(140\) | −2.53821 | − | 1.95805i | −0.214518 | − | 0.165485i | ||||
\(141\) | 5.97789 | − | 11.7738i | 0.503429 | − | 0.991534i | ||||
\(142\) | −1.62198 | + | 4.75807i | −0.136114 | + | 0.399288i | ||||
\(143\) | −8.65657 | −0.723899 | ||||||||
\(144\) | 7.57322 | − | 9.30840i | 0.631102 | − | 0.775700i | ||||
\(145\) | −5.22909 | −0.434252 | ||||||||
\(146\) | 6.30378 | − | 18.4921i | 0.521704 | − | 1.53041i | ||||
\(147\) | 4.49540 | − | 8.85395i | 0.370774 | − | 0.730261i | ||||
\(148\) | 3.99091 | + | 3.07869i | 0.328050 | + | 0.253067i | ||||
\(149\) | 17.0925i | 1.40027i | 0.714008 | + | 0.700137i | \(0.246878\pi\) | ||||
−0.714008 | + | 0.700137i | \(0.753122\pi\) | |||||||
\(150\) | −5.08112 | − | 5.21445i | −0.414872 | − | 0.425758i | ||||
\(151\) | − | 6.22274i | − | 0.506399i | −0.967414 | − | 0.253200i | \(-0.918517\pi\) | ||
0.967414 | − | 0.253200i | \(-0.0814829\pi\) | |||||||
\(152\) | −9.16198 | − | 13.8272i | −0.743135 | − | 1.12153i | ||||
\(153\) | −11.2639 | + | 8.23295i | −0.910631 | + | 0.665595i | ||||
\(154\) | −2.53589 | − | 0.864461i | −0.204348 | − | 0.0696603i | ||||
\(155\) | −5.40068 | −0.433793 | ||||||||
\(156\) | −16.0904 | + | 7.65209i | −1.28826 | + | 0.612657i | ||||
\(157\) | −12.6190 | −1.00711 | −0.503553 | − | 0.863964i | \(-0.667974\pi\) | ||||
−0.503553 | + | 0.863964i | \(0.667974\pi\) | |||||||
\(158\) | −7.05826 | − | 2.40610i | −0.561525 | − | 0.191419i | ||||
\(159\) | −3.44676 | − | 1.75001i | −0.273346 | − | 0.138785i | ||||
\(160\) | 0.578572 | − | 8.03436i | 0.0457401 | − | 0.635172i | ||||
\(161\) | 1.12562i | 0.0887114i | ||||||||
\(162\) | 10.2319 | + | 7.57023i | 0.803894 | + | 0.594773i | ||||
\(163\) | 14.7432i | 1.15478i | 0.816469 | + | 0.577390i | \(0.195929\pi\) | ||||
−0.816469 | + | 0.577390i | \(0.804071\pi\) | |||||||
\(164\) | 10.0632 | − | 13.0450i | 0.785806 | − | 1.01864i | ||||
\(165\) | 3.70127 | + | 1.87924i | 0.288144 | + | 0.146299i | ||||
\(166\) | 5.89072 | − | 17.2804i | 0.457209 | − | 1.34122i | ||||
\(167\) | −21.1334 | −1.63535 | −0.817674 | − | 0.575681i | \(-0.804737\pi\) | ||||
−0.817674 | + | 0.575681i | \(0.804737\pi\) | |||||||
\(168\) | −5.47774 | + | 0.634813i | −0.422617 | + | 0.0489769i | ||||
\(169\) | 13.4547 | 1.03497 | ||||||||
\(170\) | −3.02184 | + | 8.86452i | −0.231764 | + | 0.679878i | ||||
\(171\) | 14.2037 | − | 10.3817i | 1.08618 | − | 0.793909i | ||||
\(172\) | −4.55044 | + | 5.89873i | −0.346968 | + | 0.449774i | ||||
\(173\) | 1.66069i | 0.126260i | 0.998005 | + | 0.0631299i | \(0.0201083\pi\) | ||||
−0.998005 | + | 0.0631299i | \(0.979892\pi\) | |||||||
\(174\) | −6.44227 | + | 6.27754i | −0.488387 | + | 0.475899i | ||||
\(175\) | 3.34571i | 0.252912i | ||||||||
\(176\) | −1.70890 | − | 6.51166i | −0.128813 | − | 0.490835i | ||||
\(177\) | −3.12435 | + | 6.15358i | −0.234840 | + | 0.462532i | ||||
\(178\) | 21.2847 | + | 7.25575i | 1.59535 | + | 0.543842i | ||||
\(179\) | −0.693693 | −0.0518491 | −0.0259245 | − | 0.999664i | \(-0.508253\pi\) | ||||
−0.0259245 | + | 0.999664i | \(0.508253\pi\) | |||||||
\(180\) | 8.54093 | + | 0.221250i | 0.636603 | + | 0.0164910i | ||||
\(181\) | 8.70102 | 0.646742 | 0.323371 | − | 0.946272i | \(-0.395184\pi\) | ||||
0.323371 | + | 0.946272i | \(0.395184\pi\) | |||||||
\(182\) | 7.74973 | + | 2.64181i | 0.574448 | + | 0.195824i | ||||
\(183\) | −5.60022 | + | 11.0300i | −0.413980 | + | 0.815358i | ||||
\(184\) | −2.35780 | + | 1.56229i | −0.173820 | + | 0.115174i | ||||
\(185\) | 3.58868i | 0.263845i | ||||||||
\(186\) | −6.65368 | + | 6.48355i | −0.487871 | + | 0.475397i | ||||
\(187\) | 7.82723i | 0.572384i | ||||||||
\(188\) | −12.0725 | − | 9.31303i | −0.880476 | − | 0.679223i | ||||
\(189\) | −0.939713 | − | 5.77292i | −0.0683541 | − | 0.419918i | ||||
\(190\) | 3.81052 | − | 11.1781i | 0.276444 | − | 0.810946i | ||||
\(191\) | 11.9566 | 0.865150 | 0.432575 | − | 0.901598i | \(-0.357605\pi\) | ||||
0.432575 | + | 0.901598i | \(0.357605\pi\) | |||||||
\(192\) | −8.93248 | − | 10.5930i | −0.644646 | − | 0.764481i | ||||
\(193\) | −11.3568 | −0.817480 | −0.408740 | − | 0.912651i | \(-0.634032\pi\) | ||||
−0.408740 | + | 0.912651i | \(0.634032\pi\) | |||||||
\(194\) | −5.45815 | + | 16.0114i | −0.391873 | + | 1.14955i | ||||
\(195\) | −11.3112 | − | 5.74299i | −0.810009 | − | 0.411264i | ||||
\(196\) | −9.07854 | − | 7.00343i | −0.648467 | − | 0.500245i | ||||
\(197\) | 4.63430i | 0.330180i | 0.986278 | + | 0.165090i | \(0.0527915\pi\) | ||||
−0.986278 | + | 0.165090i | \(0.947208\pi\) | |||||||
\(198\) | 6.81603 | − | 2.12816i | 0.484394 | − | 0.151242i | ||||
\(199\) | − | 18.1750i | − | 1.28839i | −0.764861 | − | 0.644196i | \(-0.777192\pi\) | ||
0.764861 | − | 0.644196i | \(-0.222808\pi\) | |||||||
\(200\) | −7.00816 | + | 4.64364i | −0.495551 | + | 0.328355i | ||||
\(201\) | 18.9945 | + | 9.64403i | 1.33977 | + | 0.680238i | ||||
\(202\) | −1.48613 | − | 0.506608i | −0.104564 | − | 0.0356448i | ||||
\(203\) | 4.13351 | 0.290116 | ||||||||
\(204\) | 6.91898 | + | 14.5489i | 0.484426 | + | 1.01863i | ||||
\(205\) | 11.7302 | 0.819274 | ||||||||
\(206\) | 22.3063 | + | 7.60400i | 1.55415 | + | 0.529796i | ||||
\(207\) | −1.77028 | − | 2.42200i | −0.123043 | − | 0.168341i | ||||
\(208\) | 5.22242 | + | 19.8998i | 0.362110 | + | 1.37980i | ||||
\(209\) | − | 9.87010i | − | 0.682729i | ||||||
\(210\) | −2.74003 | − | 2.81193i | −0.189080 | − | 0.194041i | ||||
\(211\) | − | 12.9459i | − | 0.891231i | −0.895225 | − | 0.445615i | \(-0.852985\pi\) | ||
0.895225 | − | 0.445615i | \(-0.147015\pi\) | |||||||
\(212\) | −2.72637 | + | 3.53419i | −0.187248 | + | 0.242729i | ||||
\(213\) | −2.78725 | + | 5.48965i | −0.190979 | + | 0.376145i | ||||
\(214\) | −2.36193 | + | 6.92870i | −0.161458 | + | 0.473636i | ||||
\(215\) | −5.30423 | −0.361745 | ||||||||
\(216\) | 10.7881 | − | 9.98084i | 0.734036 | − | 0.679110i | ||||
\(217\) | 4.26916 | 0.289809 | ||||||||
\(218\) | −0.858427 | + | 2.51819i | −0.0581400 | + | 0.170553i | ||||
\(219\) | 10.8325 | − | 21.3353i | 0.731996 | − | 1.44171i | ||||
\(220\) | 2.92769 | − | 3.79516i | 0.197385 | − | 0.255870i | ||||
\(221\) | − | 23.9202i | − | 1.60905i | ||||||
\(222\) | 4.30823 | + | 4.42128i | 0.289149 | + | 0.296737i | ||||
\(223\) | − | 1.17720i | − | 0.0788314i | −0.999223 | − | 0.0394157i | \(-0.987450\pi\) | ||
0.999223 | − | 0.0394157i | \(-0.0125497\pi\) | |||||||
\(224\) | −0.457352 | + | 6.35103i | −0.0305581 | + | 0.424346i | ||||
\(225\) | −5.26185 | − | 7.19898i | −0.350790 | − | 0.479932i | ||||
\(226\) | 14.5743 | + | 4.96824i | 0.969467 | + | 0.330483i | ||||
\(227\) | −23.4475 | −1.55626 | −0.778132 | − | 0.628101i | \(-0.783832\pi\) | ||||
−0.778132 | + | 0.628101i | \(0.783832\pi\) | |||||||
\(228\) | −8.72480 | − | 18.3461i | −0.577814 | − | 1.21500i | ||||
\(229\) | 27.6644 | 1.82811 | 0.914057 | − | 0.405586i | \(-0.132933\pi\) | ||||
0.914057 | + | 0.405586i | \(0.132933\pi\) | |||||||
\(230\) | −1.90608 | − | 0.649767i | −0.125683 | − | 0.0428444i | ||||
\(231\) | −2.92580 | − | 1.48551i | −0.192503 | − | 0.0977393i | ||||
\(232\) | 5.73706 | + | 8.65833i | 0.376656 | + | 0.568447i | ||||
\(233\) | 13.5634i | 0.888566i | 0.895887 | + | 0.444283i | \(0.146541\pi\) | ||||
−0.895887 | + | 0.444283i | \(0.853459\pi\) | |||||||
\(234\) | −20.8299 | + | 6.50371i | −1.36169 | + | 0.425161i | ||||
\(235\) | − | 10.8557i | − | 0.708151i | ||||||
\(236\) | 6.30968 | + | 4.86746i | 0.410725 | + | 0.316844i | ||||
\(237\) | −8.14352 | − | 4.13469i | −0.528978 | − | 0.268577i | ||||
\(238\) | 2.38871 | − | 7.00727i | 0.154837 | − | 0.454214i | ||||
\(239\) | 29.8334 | 1.92976 | 0.964882 | − | 0.262683i | \(-0.0846075\pi\) | ||||
0.964882 | + | 0.262683i | \(0.0846075\pi\) | |||||||
\(240\) | 2.08706 | − | 9.64223i | 0.134719 | − | 0.622403i | ||||
\(241\) | 19.2786 | 1.24184 | 0.620922 | − | 0.783873i | \(-0.286759\pi\) | ||||
0.620922 | + | 0.783873i | \(0.286759\pi\) | |||||||
\(242\) | −3.72684 | + | 10.9326i | −0.239570 | + | 0.702777i | ||||
\(243\) | 11.1011 | + | 10.9437i | 0.712138 | + | 0.702039i | ||||
\(244\) | 11.3098 | + | 8.72465i | 0.724033 | + | 0.558538i | ||||
\(245\) | − | 8.16356i | − | 0.521551i | ||||||
\(246\) | 14.4517 | − | 14.0822i | 0.921407 | − | 0.897847i | ||||
\(247\) | 30.1632i | 1.91924i | ||||||||
\(248\) | 5.92532 | + | 8.94246i | 0.376258 | + | 0.567847i | ||||
\(249\) | 10.1227 | − | 19.9373i | 0.641503 | − | 1.26348i | ||||
\(250\) | −15.1959 | − | 5.18015i | −0.961074 | − | 0.327622i | ||||
\(251\) | −12.7274 | −0.803345 | −0.401673 | − | 0.915783i | \(-0.631571\pi\) | ||||
−0.401673 | + | 0.915783i | \(0.631571\pi\) | |||||||
\(252\) | −6.75147 | − | 0.174894i | −0.425302 | − | 0.0110173i | ||||
\(253\) | −1.68304 | −0.105812 | ||||||||
\(254\) | −11.7893 | − | 4.01885i | −0.739723 | − | 0.252165i | ||||
\(255\) | −5.19279 | + | 10.2275i | −0.325185 | + | 0.640471i | ||||
\(256\) | −13.9381 | + | 7.85684i | −0.871130 | + | 0.491052i | ||||
\(257\) | 15.8466i | 0.988484i | 0.869324 | + | 0.494242i | \(0.164554\pi\) | ||||
−0.869324 | + | 0.494242i | \(0.835446\pi\) | |||||||
\(258\) | −6.53484 | + | 6.36775i | −0.406841 | + | 0.396439i | ||||
\(259\) | − | 2.83679i | − | 0.176270i | ||||||
\(260\) | −8.94708 | + | 11.5981i | −0.554874 | + | 0.719283i | ||||
\(261\) | −8.89409 | + | 6.50083i | −0.550530 | + | 0.402391i | ||||
\(262\) | −8.36836 | + | 24.5485i | −0.516999 | + | 1.51661i | ||||
\(263\) | 24.4640 | 1.50852 | 0.754258 | − | 0.656578i | \(-0.227997\pi\) | ||||
0.754258 | + | 0.656578i | \(0.227997\pi\) | |||||||
\(264\) | −0.949179 | − | 8.19037i | −0.0584179 | − | 0.504082i | ||||
\(265\) | −3.17799 | −0.195223 | ||||||||
\(266\) | −3.01216 | + | 8.83613i | −0.184687 | + | 0.541778i | ||||
\(267\) | 24.5573 | + | 12.4684i | 1.50288 | + | 0.763056i | ||||
\(268\) | 15.0246 | − | 19.4763i | 0.917771 | − | 1.18971i | ||||
\(269\) | 2.06964i | 0.126188i | 0.998008 | + | 0.0630941i | \(0.0200968\pi\) | ||||
−0.998008 | + | 0.0630941i | \(0.979903\pi\) | |||||||
\(270\) | 10.3181 | + | 1.74115i | 0.627939 | + | 0.105963i | ||||
\(271\) | − | 23.7171i | − | 1.44071i | −0.693604 | − | 0.720357i | \(-0.743978\pi\) | ||
0.693604 | − | 0.720357i | \(-0.256022\pi\) | |||||||
\(272\) | 17.9933 | − | 4.72209i | 1.09100 | − | 0.286319i | ||||
\(273\) | 8.94130 | + | 4.53975i | 0.541152 | + | 0.274758i | ||||
\(274\) | −7.71818 | − | 2.63106i | −0.466272 | − | 0.158948i | ||||
\(275\) | −5.00254 | −0.301665 | ||||||||
\(276\) | −3.12836 | + | 1.48775i | −0.188305 | + | 0.0895518i | ||||
\(277\) | −13.0359 | −0.783250 | −0.391625 | − | 0.920125i | \(-0.628087\pi\) | ||||
−0.391625 | + | 0.920125i | \(0.628087\pi\) | |||||||
\(278\) | 3.23421 | + | 1.10251i | 0.193975 | + | 0.0661244i | ||||
\(279\) | −9.18596 | + | 6.71416i | −0.549949 | + | 0.401966i | ||||
\(280\) | −3.77920 | + | 2.50412i | −0.225850 | + | 0.149650i | ||||
\(281\) | 14.5979i | 0.870838i | 0.900228 | + | 0.435419i | \(0.143400\pi\) | ||||
−0.900228 | + | 0.435419i | \(0.856600\pi\) | |||||||
\(282\) | −13.0324 | − | 13.3743i | −0.776067 | − | 0.796431i | ||||
\(283\) | − | 22.7921i | − | 1.35485i | −0.735593 | − | 0.677424i | \(-0.763096\pi\) | ||
0.735593 | − | 0.677424i | \(-0.236904\pi\) | |||||||
\(284\) | 5.62891 | + | 4.34229i | 0.334014 | + | 0.257668i | ||||
\(285\) | 6.54808 | − | 12.8968i | 0.387875 | − | 0.763942i | ||||
\(286\) | −3.95006 | + | 11.5875i | −0.233572 | + | 0.685181i | ||||
\(287\) | −9.27255 | −0.547341 | ||||||||
\(288\) | −9.00427 | − | 14.3848i | −0.530582 | − | 0.847634i | ||||
\(289\) | −4.62851 | −0.272265 | ||||||||
\(290\) | −2.38607 | + | 6.99952i | −0.140115 | + | 0.411026i | ||||
\(291\) | −9.37941 | + | 18.4733i | −0.549831 | + | 1.08292i | ||||
\(292\) | −21.8766 | − | 16.8762i | −1.28023 | − | 0.987602i | ||||
\(293\) | − | 27.1247i | − | 1.58464i | −0.610106 | − | 0.792320i | \(-0.708873\pi\) | ||
0.610106 | − | 0.792320i | \(-0.291127\pi\) | |||||||
\(294\) | −9.80039 | − | 10.0576i | −0.571570 | − | 0.586568i | ||||
\(295\) | 5.67375i | 0.330339i | ||||||||
\(296\) | 5.94214 | − | 3.93730i | 0.345380 | − | 0.228851i | ||||
\(297\) | 8.63173 | − | 1.40507i | 0.500864 | − | 0.0815304i | ||||
\(298\) | 22.8796 | + | 7.79946i | 1.32538 | + | 0.451811i | ||||
\(299\) | 5.14341 | 0.297451 | ||||||||
\(300\) | −9.29848 | + | 4.42206i | −0.536848 | + | 0.255308i | ||||
\(301\) | 4.19291 | 0.241675 | ||||||||
\(302\) | −8.32960 | − | 2.83949i | −0.479315 | − | 0.163394i | ||||
\(303\) | −1.71463 | − | 0.870567i | −0.0985031 | − | 0.0500127i | ||||
\(304\) | −22.6894 | + | 5.95453i | −1.30133 | + | 0.341516i | ||||
\(305\) | 10.1699i | 0.582326i | ||||||||
\(306\) | 5.88062 | + | 18.8343i | 0.336173 | + | 1.07669i | ||||
\(307\) | − | 18.0198i | − | 1.02844i | −0.857658 | − | 0.514221i | \(-0.828081\pi\) | ||
0.857658 | − | 0.514221i | \(-0.171919\pi\) | |||||||
\(308\) | −2.31429 | + | 3.00002i | −0.131869 | + | 0.170942i | ||||
\(309\) | 25.7360 | + | 13.0669i | 1.46407 | + | 0.743349i | ||||
\(310\) | −2.46438 | + | 7.22922i | −0.139967 | + | 0.410592i | ||||
\(311\) | 15.4078 | 0.873697 | 0.436848 | − | 0.899535i | \(-0.356095\pi\) | ||||
0.436848 | + | 0.899535i | \(0.356095\pi\) | |||||||
\(312\) | 2.90071 | + | 25.0299i | 0.164220 | + | 1.41704i | ||||
\(313\) | −1.19493 | −0.0675416 | −0.0337708 | − | 0.999430i | \(-0.510752\pi\) | ||||
−0.0337708 | + | 0.999430i | \(0.510752\pi\) | |||||||
\(314\) | −5.75815 | + | 16.8915i | −0.324951 | + | 0.953241i | ||||
\(315\) | −2.83749 | − | 3.88210i | −0.159874 | − | 0.218732i | ||||
\(316\) | −6.44148 | + | 8.35009i | −0.362362 | + | 0.469729i | ||||
\(317\) | − | 4.92932i | − | 0.276858i | −0.990372 | − | 0.138429i | \(-0.955795\pi\) | ||
0.990372 | − | 0.138429i | \(-0.0442053\pi\) | |||||||
\(318\) | −3.91531 | + | 3.81520i | −0.219560 | + | 0.213946i | ||||
\(319\) | 6.18047i | 0.346040i | ||||||||
\(320\) | −10.4906 | − | 4.44060i | −0.586441 | − | 0.248237i | ||||
\(321\) | −4.05879 | + | 7.99403i | −0.226540 | + | 0.446183i | ||||
\(322\) | 1.50673 | + | 0.513630i | 0.0839667 | + | 0.0286235i | ||||
\(323\) | 27.2734 | 1.51754 | ||||||||
\(324\) | 14.8022 | − | 10.2418i | 0.822345 | − | 0.568989i | ||||
\(325\) | 15.2879 | 0.848019 | ||||||||
\(326\) | 19.7349 | + | 6.72746i | 1.09302 | + | 0.372600i | ||||
\(327\) | −1.47514 | + | 2.90538i | −0.0815755 | + | 0.160668i | ||||
\(328\) | −12.8697 | − | 19.4229i | −0.710612 | − | 1.07245i | ||||
\(329\) | 8.58129i | 0.473102i | ||||||||
\(330\) | 4.20442 | − | 4.09692i | 0.231446 | − | 0.225528i | ||||
\(331\) | − | 12.5469i | − | 0.689639i | −0.938669 | − | 0.344819i | \(-0.887940\pi\) | ||
0.938669 | − | 0.344819i | \(-0.112060\pi\) | |||||||
\(332\) | −20.4431 | − | 15.7703i | −1.12196 | − | 0.865510i | ||||
\(333\) | 4.46147 | + | 6.10394i | 0.244487 | + | 0.334494i | ||||
\(334\) | −9.64332 | + | 28.2886i | −0.527659 | + | 1.54788i | ||||
\(335\) | 17.5134 | 0.956859 | ||||||||
\(336\) | −1.64979 | + | 7.62203i | −0.0900035 | + | 0.415816i | ||||
\(337\) | 21.1109 | 1.14998 | 0.574991 | − | 0.818160i | \(-0.305006\pi\) | ||||
0.574991 | + | 0.818160i | \(0.305006\pi\) | |||||||
\(338\) | 6.13947 | − | 18.0101i | 0.333943 | − | 0.979618i | ||||
\(339\) | 16.8152 | + | 8.53754i | 0.913275 | + | 0.463695i | ||||
\(340\) | 10.4869 | + | 8.08991i | 0.568734 | + | 0.438737i | ||||
\(341\) | 6.38328i | 0.345674i | ||||||||
\(342\) | −7.41543 | − | 23.7500i | −0.400981 | − | 1.28425i | ||||
\(343\) | 14.3325i | 0.773883i | ||||||||
\(344\) | 5.81949 | + | 8.78274i | 0.313766 | + | 0.473534i | ||||
\(345\) | −2.19916 | − | 1.11657i | −0.118399 | − | 0.0601143i | ||||
\(346\) | 2.22296 | + | 0.757786i | 0.119507 | + | 0.0407388i | ||||
\(347\) | 1.73613 | 0.0932006 | 0.0466003 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466003 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(348\) | 5.46330 | + | 11.4880i | 0.292864 | + | 0.615819i | ||||
\(349\) | −14.9792 | −0.801820 | −0.400910 | − | 0.916117i | \(-0.631306\pi\) | ||||
−0.400910 | + | 0.916117i | \(0.631306\pi\) | |||||||
\(350\) | 4.47849 | + | 1.52668i | 0.239385 | + | 0.0816042i | ||||
\(351\) | −26.3787 | + | 4.29392i | −1.40799 | + | 0.229192i | ||||
\(352\) | −9.49613 | − | 0.683837i | −0.506145 | − | 0.0364487i | ||||
\(353\) | 0.688688i | 0.0366551i | 0.999832 | + | 0.0183276i | \(0.00583417\pi\) | ||||
−0.999832 | + | 0.0183276i | \(0.994166\pi\) | |||||||
\(354\) | 6.81137 | + | 6.99010i | 0.362020 | + | 0.371520i | ||||
\(355\) | 5.06159i | 0.268642i | ||||||||
\(356\) | 19.4247 | − | 25.1803i | 1.02951 | − | 1.33455i | ||||
\(357\) | 4.10482 | − | 8.08468i | 0.217250 | − | 0.427887i | ||||
\(358\) | −0.316538 | + | 0.928561i | −0.0167295 | + | 0.0490759i | ||||
\(359\) | −29.0421 | −1.53278 | −0.766392 | − | 0.642373i | \(-0.777950\pi\) | ||||
−0.766392 | + | 0.642373i | \(0.777950\pi\) | |||||||
\(360\) | 4.19345 | − | 11.3317i | 0.221014 | − | 0.597234i | ||||
\(361\) | −15.3917 | −0.810088 | ||||||||
\(362\) | 3.97035 | − | 11.6470i | 0.208677 | − | 0.612151i | ||||
\(363\) | −6.40428 | + | 12.6136i | −0.336137 | + | 0.662043i | ||||
\(364\) | 7.07252 | − | 9.16811i | 0.370701 | − | 0.480539i | ||||
\(365\) | − | 19.6717i | − | 1.02966i | ||||||
\(366\) | 12.2090 | + | 12.5294i | 0.638175 | + | 0.654921i | ||||
\(367\) | − | 12.6525i | − | 0.660457i | −0.943901 | − | 0.330229i | \(-0.892874\pi\) | ||
0.943901 | − | 0.330229i | \(-0.107126\pi\) | |||||||
\(368\) | 1.01536 | + | 3.86898i | 0.0529294 | + | 0.201685i | ||||
\(369\) | 19.9518 | − | 14.5831i | 1.03865 | − | 0.759164i | ||||
\(370\) | 4.80372 | + | 1.63754i | 0.249733 | + | 0.0851318i | ||||
\(371\) | 2.51215 | 0.130425 | ||||||||
\(372\) | 5.64259 | + | 11.8649i | 0.292555 | + | 0.615169i | ||||
\(373\) | −22.3439 | −1.15693 | −0.578463 | − | 0.815709i | \(-0.696347\pi\) | ||||
−0.578463 | + | 0.815709i | \(0.696347\pi\) | |||||||
\(374\) | 10.4773 | + | 3.57163i | 0.541770 | + | 0.184684i | ||||
\(375\) | −17.5324 | − | 8.90168i | −0.905369 | − | 0.459681i | ||||
\(376\) | −17.9750 | + | 11.9103i | −0.926988 | + | 0.614227i | ||||
\(377\) | − | 18.8876i | − | 0.972762i | ||||||
\(378\) | −8.15629 | − | 1.37635i | −0.419514 | − | 0.0707920i | ||||
\(379\) | − | 3.26510i | − | 0.167717i | −0.996478 | − | 0.0838585i | \(-0.973276\pi\) | ||
0.996478 | − | 0.0838585i | \(-0.0267244\pi\) | |||||||
\(380\) | −13.2240 | − | 10.2013i | −0.678376 | − | 0.523317i | ||||
\(381\) | −13.6019 | − | 6.90608i | −0.696848 | − | 0.353809i | ||||
\(382\) | 5.45589 | − | 16.0048i | 0.279148 | − | 0.818877i | ||||
\(383\) | −37.8875 | −1.93596 | −0.967979 | − | 0.251030i | \(-0.919231\pi\) | ||||
−0.967979 | + | 0.251030i | \(0.919231\pi\) | |||||||
\(384\) | −18.2554 | + | 7.12314i | −0.931594 | + | 0.363501i | ||||
\(385\) | −2.69766 | −0.137485 | ||||||||
\(386\) | −5.18219 | + | 15.2019i | −0.263767 | + | 0.773757i | ||||
\(387\) | −9.02189 | + | 6.59424i | −0.458608 | + | 0.335204i | ||||
\(388\) | 18.9419 | + | 14.6123i | 0.961630 | + | 0.741827i | ||||
\(389\) | 0.929471i | 0.0471261i | 0.999722 | + | 0.0235630i | \(0.00750104\pi\) | ||||
−0.999722 | + | 0.0235630i | \(0.992499\pi\) | |||||||
\(390\) | −12.8488 | + | 12.5203i | −0.650624 | + | 0.633989i | ||||
\(391\) | − | 4.65065i | − | 0.235193i | ||||||
\(392\) | −13.5172 | + | 8.95659i | −0.682723 | + | 0.452376i | ||||
\(393\) | −14.3804 | + | 28.3230i | −0.725394 | + | 1.42871i | ||||
\(394\) | 6.20336 | + | 2.11467i | 0.312521 | + | 0.106536i | ||||
\(395\) | −7.50852 | −0.377795 | ||||||||
\(396\) | 0.261504 | − | 10.0949i | 0.0131411 | − | 0.507286i | ||||
\(397\) | −12.6204 | −0.633398 | −0.316699 | − | 0.948526i | \(-0.602575\pi\) | ||||
−0.316699 | + | 0.948526i | \(0.602575\pi\) | |||||||
\(398\) | −24.3286 | − | 8.29340i | −1.21948 | − | 0.415710i | ||||
\(399\) | −5.17615 | + | 10.1947i | −0.259132 | + | 0.510375i | ||||
\(400\) | 3.01798 | + | 11.4999i | 0.150899 | + | 0.574994i | ||||
\(401\) | − | 11.5308i | − | 0.575823i | −0.957657 | − | 0.287911i | \(-0.907039\pi\) | ||
0.957657 | − | 0.287911i | \(-0.0929609\pi\) | |||||||
\(402\) | 21.5766 | − | 21.0249i | 1.07614 | − | 1.04863i | ||||
\(403\) | − | 19.5074i | − | 0.971735i | ||||||
\(404\) | −1.35627 | + | 1.75813i | −0.0674768 | + | 0.0874701i | ||||
\(405\) | 12.2109 | + | 3.89057i | 0.606763 | + | 0.193324i | ||||
\(406\) | 1.88615 | − | 5.53301i | 0.0936082 | − | 0.274599i | ||||
\(407\) | 4.24160 | 0.210249 | ||||||||
\(408\) | 22.6319 | − | 2.62281i | 1.12045 | − | 0.129848i | ||||
\(409\) | 23.2167 | 1.14799 | 0.573996 | − | 0.818858i | \(-0.305393\pi\) | ||||
0.573996 | + | 0.818858i | \(0.305393\pi\) | |||||||
\(410\) | 5.35259 | − | 15.7018i | 0.264346 | − | 0.775455i | ||||
\(411\) | −8.90490 | − | 4.52127i | −0.439246 | − | 0.223018i | ||||
\(412\) | 20.3570 | − | 26.3888i | 1.00292 | − | 1.30008i | ||||
\(413\) | − | 4.48501i | − | 0.220693i | ||||||
\(414\) | −4.04983 | + | 1.26447i | −0.199038 | + | 0.0621455i | ||||
\(415\) | − | 18.3827i | − | 0.902372i | ||||||
\(416\) | 29.0204 | + | 2.08982i | 1.42284 | + | 0.102462i | ||||
\(417\) | 3.73149 | + | 1.89458i | 0.182732 | + | 0.0927781i | ||||
\(418\) | −13.2119 | − | 4.50381i | −0.646213 | − | 0.220288i | ||||
\(419\) | −29.3409 | −1.43339 | −0.716697 | − | 0.697384i | \(-0.754347\pi\) | ||||
−0.716697 | + | 0.697384i | \(0.754347\pi\) | |||||||
\(420\) | −5.01427 | + | 2.38463i | −0.244672 | + | 0.116358i | ||||
\(421\) | −25.5900 | −1.24718 | −0.623591 | − | 0.781751i | \(-0.714327\pi\) | ||||
−0.623591 | + | 0.781751i | \(0.714327\pi\) | |||||||
\(422\) | −17.3290 | − | 5.90731i | −0.843564 | − | 0.287563i | ||||
\(423\) | −13.4959 | − | 18.4644i | −0.656194 | − | 0.897770i | ||||
\(424\) | 3.48671 | + | 5.26213i | 0.169330 | + | 0.255552i | ||||
\(425\) | − | 13.8232i | − | 0.670525i | ||||||
\(426\) | 6.07647 | + | 6.23592i | 0.294406 | + | 0.302131i | ||||
\(427\) | − | 8.03914i | − | 0.389041i | ||||||
\(428\) | 8.19681 | + | 6.32324i | 0.396208 | + | 0.305645i | ||||
\(429\) | −6.78787 | + | 13.3691i | −0.327722 | + | 0.645467i | ||||
\(430\) | −2.42036 | + | 7.10010i | −0.116720 | + | 0.342397i | ||||
\(431\) | 18.0908 | 0.871401 | 0.435700 | − | 0.900092i | \(-0.356501\pi\) | ||||
0.435700 | + | 0.900092i | \(0.356501\pi\) | |||||||
\(432\) | −8.43742 | − | 18.9950i | −0.405945 | − | 0.913897i | ||||
\(433\) | −2.87373 | −0.138103 | −0.0690514 | − | 0.997613i | \(-0.521997\pi\) | ||||
−0.0690514 | + | 0.997613i | \(0.521997\pi\) | |||||||
\(434\) | 1.94805 | − | 5.71459i | 0.0935094 | − | 0.274309i | ||||
\(435\) | −4.10028 | + | 8.07575i | −0.196593 | + | 0.387202i | ||||
\(436\) | 2.97908 | + | 2.29814i | 0.142672 | + | 0.110061i | ||||
\(437\) | 5.86444i | 0.280534i | ||||||||
\(438\) | −23.6160 | − | 24.2357i | −1.12842 | − | 1.15803i | ||||
\(439\) | − | 27.8221i | − | 1.32788i | −0.747787 | − | 0.663939i | \(-0.768884\pi\) | ||
0.747787 | − | 0.663939i | \(-0.231116\pi\) | |||||||
\(440\) | −3.74418 | − | 5.65069i | −0.178497 | − | 0.269386i | ||||
\(441\) | −10.1490 | − | 13.8853i | −0.483285 | − | 0.661204i | ||||
\(442\) | −32.0189 | − | 10.9150i | −1.52299 | − | 0.519172i | ||||
\(443\) | −3.54917 | −0.168626 | −0.0843131 | − | 0.996439i | \(-0.526870\pi\) | ||||
−0.0843131 | + | 0.996439i | \(0.526870\pi\) | |||||||
\(444\) | 7.88409 | − | 3.74942i | 0.374162 | − | 0.177940i | ||||
\(445\) | 22.6425 | 1.07336 | ||||||||
\(446\) | −1.57578 | − | 0.537168i | −0.0746152 | − | 0.0254356i | ||||
\(447\) | 26.3975 | + | 13.4028i | 1.24856 | + | 0.633929i | ||||
\(448\) | 8.29264 | + | 3.51023i | 0.391790 | + | 0.165843i | ||||
\(449\) | − | 12.1412i | − | 0.572980i | −0.958083 | − | 0.286490i | \(-0.907511\pi\) | ||
0.958083 | − | 0.286490i | \(-0.0924885\pi\) | |||||||
\(450\) | −12.0374 | + | 3.75843i | −0.567448 | + | 0.177174i | ||||
\(451\) | − | 13.8644i | − | 0.652850i | ||||||
\(452\) | 13.3007 | − | 17.2417i | 0.625614 | − | 0.810983i | ||||
\(453\) | −9.61033 | − | 4.87943i | −0.451533 | − | 0.229256i | ||||
\(454\) | −10.6993 | + | 31.3862i | −0.502142 | + | 1.47303i | ||||
\(455\) | 8.24409 | 0.386489 | ||||||||
\(456\) | −28.5388 | + | 3.30735i | −1.33645 | + | 0.154881i | ||||
\(457\) | −28.7263 | −1.34376 | −0.671879 | − | 0.740660i | \(-0.734513\pi\) | ||||
−0.671879 | + | 0.740660i | \(0.734513\pi\) | |||||||
\(458\) | 12.6235 | − | 37.0308i | 0.589856 | − | 1.73034i | ||||
\(459\) | 3.88254 | + | 23.8515i | 0.181222 | + | 1.11329i | ||||
\(460\) | −1.73952 | + | 2.25494i | −0.0811057 | + | 0.105137i | ||||
\(461\) | − | 22.0190i | − | 1.02553i | −0.858530 | − | 0.512763i | \(-0.828622\pi\) | ||
0.858530 | − | 0.512763i | \(-0.171378\pi\) | |||||||
\(462\) | −3.32353 | + | 3.23855i | −0.154625 | + | 0.150671i | ||||
\(463\) | 25.7220i | 1.19540i | 0.801719 | + | 0.597701i | \(0.203919\pi\) | ||||
−0.801719 | + | 0.597701i | \(0.796081\pi\) | |||||||
\(464\) | 14.2077 | − | 3.72861i | 0.659575 | − | 0.173097i | ||||
\(465\) | −4.23484 | + | 8.34076i | −0.196386 | + | 0.386794i | ||||
\(466\) | 18.1556 | + | 6.18907i | 0.841041 | + | 0.286703i | ||||
\(467\) | 18.8463 | 0.872105 | 0.436052 | − | 0.899921i | \(-0.356376\pi\) | ||||
0.436052 | + | 0.899921i | \(0.356376\pi\) | |||||||
\(468\) | −0.799161 | + | 30.8501i | −0.0369412 | + | 1.42605i | ||||
\(469\) | −13.8441 | −0.639259 | ||||||||
\(470\) | −14.5312 | − | 4.95356i | −0.670275 | − | 0.228491i | ||||
\(471\) | −9.89493 | + | 19.4887i | −0.455934 | + | 0.897990i | ||||
\(472\) | 9.39461 | − | 6.22492i | 0.432422 | − | 0.286525i | ||||
\(473\) | 6.26928i | 0.288262i | ||||||||
\(474\) | −9.25055 | + | 9.01402i | −0.424892 | + | 0.414028i | ||||
\(475\) | 17.4310i | 0.799790i | ||||||||
\(476\) | −8.28976 | − | 6.39494i | −0.379961 | − | 0.293112i | ||||
\(477\) | −5.40541 | + | 3.95090i | −0.247497 | + | 0.180899i | ||||
\(478\) | 13.6132 | − | 39.9343i | 0.622655 | − | 1.82655i | ||||
\(479\) | 0.112079 | 0.00512102 | 0.00256051 | − | 0.999997i | \(-0.499185\pi\) | ||||
0.00256051 | + | 0.999997i | \(0.499185\pi\) | |||||||
\(480\) | −11.9545 | − | 7.19352i | −0.545646 | − | 0.328338i | ||||
\(481\) | −12.9624 | −0.591036 | ||||||||
\(482\) | 8.79698 | − | 25.8058i | 0.400691 | − | 1.17542i | ||||
\(483\) | 1.73840 | + | 0.882634i | 0.0790999 | + | 0.0401612i | ||||
\(484\) | 12.9336 | + | 9.97730i | 0.587890 | + | 0.453514i | ||||
\(485\) | 17.0328i | 0.773421i | ||||||||
\(486\) | 19.7145 | − | 9.86600i | 0.894269 | − | 0.447531i | ||||
\(487\) | 27.4672i | 1.24466i | 0.782756 | + | 0.622329i | \(0.213813\pi\) | ||||
−0.782756 | + | 0.622329i | \(0.786187\pi\) | |||||||
\(488\) | 16.8393 | − | 11.1578i | 0.762280 | − | 0.505091i | ||||
\(489\) | 22.7693 | + | 11.5606i | 1.02966 | + | 0.522789i | ||||
\(490\) | −10.9275 | − | 3.72510i | −0.493656 | − | 0.168283i | ||||
\(491\) | 11.2094 | 0.505875 | 0.252938 | − | 0.967483i | \(-0.418603\pi\) | ||||
0.252938 | + | 0.967483i | \(0.418603\pi\) | |||||||
\(492\) | −12.2556 | − | 25.7705i | −0.552526 | − | 1.16182i | ||||
\(493\) | −17.0781 | −0.769159 | ||||||||
\(494\) | 40.3757 | + | 13.7637i | 1.81659 | + | 0.619259i | ||||
\(495\) | 5.80456 | − | 4.24264i | 0.260895 | − | 0.190693i | ||||
\(496\) | 14.6739 | − | 3.85097i | 0.658879 | − | 0.172914i | ||||
\(497\) | − | 4.00111i | − | 0.179474i | ||||||
\(498\) | −22.0685 | − | 22.6476i | −0.988915 | − | 1.01486i | ||||
\(499\) | − | 0.0293070i | − | 0.00131196i | −1.00000 | 0.000655980i | \(-0.999791\pi\) | |||
1.00000 | 0.000655980i | \(-0.000208805\pi\) | ||||||||
\(500\) | −13.8680 | + | 17.9771i | −0.620198 | + | 0.803962i | ||||
\(501\) | −16.5713 | + | 32.6382i | −0.740351 | + | 1.45817i | ||||
\(502\) | −5.80761 | + | 17.0366i | −0.259206 | + | 0.760379i | ||||
\(503\) | 34.0242 | 1.51706 | 0.758532 | − | 0.651636i | \(-0.225917\pi\) | ||||
0.758532 | + | 0.651636i | \(0.225917\pi\) | |||||||
\(504\) | −3.31486 | + | 8.95754i | −0.147656 | + | 0.399000i | ||||
\(505\) | −1.58093 | −0.0703506 | ||||||||
\(506\) | −0.767985 | + | 2.25288i | −0.0341411 | + | 0.100153i | ||||
\(507\) | 10.5502 | − | 20.7792i | 0.468551 | − | 0.922838i | ||||
\(508\) | −10.7591 | + | 13.9470i | −0.477356 | + | 0.618796i | ||||
\(509\) | − | 3.40402i | − | 0.150880i | −0.997150 | − | 0.0754402i | \(-0.975964\pi\) | ||
0.997150 | − | 0.0754402i | \(-0.0240362\pi\) | |||||||
\(510\) | 11.3208 | + | 11.6178i | 0.501292 | + | 0.514446i | ||||
\(511\) | 15.5502i | 0.687899i | ||||||||
\(512\) | 4.15691 | + | 22.2423i | 0.183711 | + | 0.982980i | ||||
\(513\) | −4.89587 | − | 30.0767i | −0.216158 | − | 1.32792i | ||||
\(514\) | 21.2119 | + | 7.23093i | 0.935615 | + | 0.318943i | ||||
\(515\) | 23.7292 | 1.04563 | ||||||||
\(516\) | 5.54181 | + | 11.6530i | 0.243965 | + | 0.512996i | ||||
\(517\) | −12.8308 | −0.564300 | ||||||||
\(518\) | −3.79726 | − | 1.29445i | −0.166842 | − | 0.0568750i | ||||
\(519\) | 2.56475 | + | 1.30220i | 0.112580 | + | 0.0571601i | ||||
\(520\) | 11.4423 | + | 17.2686i | 0.501778 | + | 0.757280i | ||||
\(521\) | 18.1993i | 0.797324i | 0.917098 | + | 0.398662i | \(0.130525\pi\) | ||||
−0.917098 | + | 0.398662i | \(0.869475\pi\) | |||||||
\(522\) | 4.64340 | + | 14.8718i | 0.203236 | + | 0.650920i | ||||
\(523\) | 3.70416i | 0.161972i | 0.996715 | + | 0.0809859i | \(0.0258069\pi\) | ||||
−0.996715 | + | 0.0809859i | \(0.974193\pi\) | |||||||
\(524\) | 29.0415 | + | 22.4034i | 1.26868 | + | 0.978695i | ||||
\(525\) | 5.16708 | + | 2.62347i | 0.225510 | + | 0.114498i | ||||
\(526\) | 11.1631 | − | 32.7469i | 0.486735 | − | 1.42783i | ||||
\(527\) | −17.6385 | −0.768347 | ||||||||
\(528\) | −11.3965 | − | 2.46678i | −0.495971 | − | 0.107353i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −1.45014 | + | 4.25398i | −0.0629902 | + | 0.184781i | ||||
\(531\) | 7.05364 | + | 9.65042i | 0.306102 | + | 0.418792i | ||||
\(532\) | 10.4533 | + | 8.06399i | 0.453210 | + | 0.349618i | ||||
\(533\) | 42.3699i | 1.83525i | ||||||||
\(534\) | 27.8957 | − | 27.1824i | 1.20716 | − | 1.17630i | ||||
\(535\) | 7.37069i | 0.318663i | ||||||||
\(536\) | −19.2147 | − | 28.9987i | −0.829948 | − | 1.25255i | ||||
\(537\) | −0.543946 | + | 1.07133i | −0.0234730 | + | 0.0462314i | ||||
\(538\) | 2.77037 | + | 0.944394i | 0.119439 | + | 0.0407157i | ||||
\(539\) | −9.64883 | −0.415605 | ||||||||
\(540\) | 7.03889 | − | 13.0170i | 0.302906 | − | 0.560164i | ||||
\(541\) | −33.2070 | −1.42768 | −0.713840 | − | 0.700309i | \(-0.753046\pi\) | ||||
−0.713840 | + | 0.700309i | \(0.753046\pi\) | |||||||
\(542\) | −31.7472 | − | 10.8223i | −1.36366 | − | 0.464858i | ||||
\(543\) | 6.82273 | − | 13.4378i | 0.292791 | − | 0.576670i | ||||
\(544\) | 1.88961 | − | 26.2401i | 0.0810162 | − | 1.12503i | ||||
\(545\) | 2.67883i | 0.114748i | ||||||||
\(546\) | 10.1568 | − | 9.89708i | 0.434670 | − | 0.423556i | ||||
\(547\) | 3.26242i | 0.139491i | 0.997565 | + | 0.0697456i | \(0.0222188\pi\) | ||||
−0.997565 | + | 0.0697456i | \(0.977781\pi\) | |||||||
\(548\) | −7.04374 | + | 9.13079i | −0.300893 | + | 0.390048i | ||||
\(549\) | 12.6433 | + | 17.2978i | 0.539601 | + | 0.738254i | ||||
\(550\) | −2.28270 | + | 6.69628i | −0.0973347 | + | 0.285530i | ||||
\(551\) | 21.5354 | 0.917439 | ||||||||
\(552\) | 0.563966 | + | 4.86641i | 0.0240040 | + | 0.207128i | ||||
\(553\) | 5.93537 | 0.252398 | ||||||||
\(554\) | −5.94837 | + | 17.4495i | −0.252722 | + | 0.741358i | ||||
\(555\) | 5.54232 | + | 2.81399i | 0.235258 | + | 0.119447i | ||||
\(556\) | 2.95159 | − | 3.82615i | 0.125175 | − | 0.162265i | ||||
\(557\) | 9.81979i | 0.416078i | 0.978121 | + | 0.208039i | \(0.0667081\pi\) | ||||
−0.978121 | + | 0.208039i | \(0.933292\pi\) | |||||||
\(558\) | 4.79578 | + | 15.3598i | 0.203022 | + | 0.650233i | ||||
\(559\) | − | 19.1590i | − | 0.810341i | ||||||
\(560\) | 1.62747 | + | 6.20139i | 0.0687731 | + | 0.262056i | ||||
\(561\) | 12.0883 | + | 6.13756i | 0.510368 | + | 0.259128i | ||||
\(562\) | 19.5404 | + | 6.66115i | 0.824262 | + | 0.280983i | ||||
\(563\) | −40.6115 | −1.71157 | −0.855786 | − | 0.517329i | \(-0.826926\pi\) | ||||
−0.855786 | + | 0.517329i | \(0.826926\pi\) | |||||||
\(564\) | −23.8493 | + | 11.3420i | −1.00424 | + | 0.477584i | ||||
\(565\) | 15.5040 | 0.652258 | ||||||||
\(566\) | −30.5089 | − | 10.4002i | −1.28239 | − | 0.437153i | ||||
\(567\) | −9.65250 | − | 3.07543i | −0.405367 | − | 0.129156i | ||||
\(568\) | 8.38100 | − | 5.55329i | 0.351659 | − | 0.233011i | ||||
\(569\) | 9.32103i | 0.390758i | 0.980728 | + | 0.195379i | \(0.0625937\pi\) | ||||
−0.980728 | + | 0.195379i | \(0.937406\pi\) | |||||||
\(570\) | −14.2754 | − | 14.6500i | −0.597932 | − | 0.613622i | ||||
\(571\) | 45.0437i | 1.88502i | 0.334178 | + | 0.942510i | \(0.391541\pi\) | ||||
−0.334178 | + | 0.942510i | \(0.608459\pi\) | |||||||
\(572\) | 13.7082 | + | 10.5749i | 0.573171 | + | 0.442159i | ||||
\(573\) | 9.37553 | − | 18.4657i | 0.391668 | − | 0.771414i | ||||
\(574\) | −4.23114 | + | 12.4120i | −0.176604 | + | 0.518067i | ||||
\(575\) | 2.97232 | 0.123954 | ||||||||
\(576\) | −23.3639 | + | 5.48898i | −0.973495 | + | 0.228708i | ||||
\(577\) | 18.7099 | 0.778902 | 0.389451 | − | 0.921047i | \(-0.372665\pi\) | ||||
0.389451 | + | 0.921047i | \(0.372665\pi\) | |||||||
\(578\) | −2.11203 | + | 6.19561i | −0.0878487 | + | 0.257703i | ||||
\(579\) | −8.90520 | + | 17.5393i | −0.370087 | + | 0.728909i | ||||
\(580\) | 8.28060 | + | 6.38788i | 0.343833 | + | 0.265242i | ||||
\(581\) | 14.5312i | 0.602858i | ||||||||
\(582\) | 20.4480 | + | 20.9846i | 0.847597 | + | 0.869838i | ||||
\(583\) | 3.75620i | 0.155566i | ||||||||
\(584\) | −32.5725 | + | 21.5827i | −1.34786 | + | 0.893098i | ||||
\(585\) | −17.7388 | + | 12.9656i | −0.733411 | + | 0.536062i | ||||
\(586\) | −36.3084 | − | 12.3772i | −1.49989 | − | 0.511297i | ||||
\(587\) | −4.79917 | −0.198083 | −0.0990415 | − | 0.995083i | \(-0.531578\pi\) | ||||
−0.0990415 | + | 0.995083i | \(0.531578\pi\) | |||||||
\(588\) | −17.9348 | + | 8.52921i | −0.739618 | + | 0.351739i | ||||
\(589\) | 22.2421 | 0.916470 | ||||||||
\(590\) | 7.59475 | + | 2.58898i | 0.312671 | + | 0.106587i | ||||
\(591\) | 7.15717 | + | 3.63389i | 0.294407 | + | 0.149478i | ||||
\(592\) | −2.55892 | − | 9.75062i | −0.105171 | − | 0.400748i | ||||
\(593\) | − | 37.6994i | − | 1.54813i | −0.633106 | − | 0.774065i | \(-0.718220\pi\) | ||
0.633106 | − | 0.774065i | \(-0.281780\pi\) | |||||||
\(594\) | 2.05794 | − | 12.1954i | 0.0844382 | − | 0.500382i | ||||
\(595\) | − | 7.45427i | − | 0.305595i | ||||||
\(596\) | 20.8803 | − | 27.0672i | 0.855291 | − | 1.10871i | ||||
\(597\) | −28.0693 | − | 14.2516i | −1.14880 | − | 0.583277i | ||||
\(598\) | 2.34698 | − | 6.88484i | 0.0959751 | − | 0.281542i | ||||
\(599\) | 40.4030 | 1.65082 | 0.825411 | − | 0.564532i | \(-0.190943\pi\) | ||||
0.825411 | + | 0.564532i | \(0.190943\pi\) | |||||||
\(600\) | 1.67629 | + | 14.4645i | 0.0684343 | + | 0.590512i | ||||
\(601\) | −8.44230 | −0.344369 | −0.172184 | − | 0.985065i | \(-0.555082\pi\) | ||||
−0.172184 | + | 0.985065i | \(0.555082\pi\) | |||||||
\(602\) | 1.91326 | − | 5.61252i | 0.0779785 | − | 0.228749i | ||||
\(603\) | 29.7883 | − | 21.7727i | 1.21307 | − | 0.886654i | ||||
\(604\) | −7.60173 | + | 9.85412i | −0.309310 | + | 0.400958i | ||||
\(605\) | 11.6301i | 0.472829i | ||||||||
\(606\) | −1.94772 | + | 1.89792i | −0.0791207 | + | 0.0770976i | ||||
\(607\) | 29.3385i | 1.19081i | 0.803425 | + | 0.595406i | \(0.203009\pi\) | ||||
−0.803425 | + | 0.595406i | \(0.796991\pi\) | |||||||
\(608\) | −2.38278 | + | 33.0886i | −0.0966347 | + | 1.34192i | ||||
\(609\) | 3.24121 | − | 6.38375i | 0.131340 | − | 0.258683i | ||||
\(610\) | 13.6132 | + | 4.64060i | 0.551181 | + | 0.187893i | ||||
\(611\) | 39.2113 | 1.58632 | ||||||||
\(612\) | 27.8945 | + | 0.722598i | 1.12757 | + | 0.0292093i | ||||
\(613\) | 22.9467 | 0.926809 | 0.463404 | − | 0.886147i | \(-0.346628\pi\) | ||||
0.463404 | + | 0.886147i | \(0.346628\pi\) | |||||||
\(614\) | −24.1208 | − | 8.22256i | −0.973436 | − | 0.331835i | ||||
\(615\) | 9.19801 | − | 18.1160i | 0.370900 | − | 0.730509i | ||||
\(616\) | 2.95972 | + | 4.46678i | 0.119250 | + | 0.179972i | ||||
\(617\) | 45.6198i | 1.83658i | 0.395905 | + | 0.918292i | \(0.370431\pi\) | ||||
−0.395905 | + | 0.918292i | \(0.629569\pi\) | |||||||
\(618\) | 29.2345 | − | 28.4870i | 1.17599 | − | 1.14592i | ||||
\(619\) | − | 29.6236i | − | 1.19067i | −0.803476 | − | 0.595337i | \(-0.797019\pi\) | ||
0.803476 | − | 0.595337i | \(-0.202981\pi\) | |||||||
\(620\) | 8.55234 | + | 6.59750i | 0.343470 | + | 0.264962i | ||||
\(621\) | −5.12865 | + | 0.834839i | −0.205806 | + | 0.0335009i | ||||
\(622\) | 7.03071 | − | 20.6245i | 0.281906 | − | 0.826967i | ||||
\(623\) | −17.8985 | −0.717089 | ||||||||
\(624\) | 34.8281 | + | 7.53854i | 1.39424 | + | 0.301783i | ||||
\(625\) | −1.30368 | −0.0521472 | ||||||||
\(626\) | −0.545258 | + | 1.59951i | −0.0217929 | + | 0.0639292i | ||||
\(627\) | −15.2433 | − | 7.73944i | −0.608758 | − | 0.309083i | ||||
\(628\) | 19.9830 | + | 15.4154i | 0.797409 | + | 0.615143i | ||||
\(629\) | 11.7206i | 0.467330i | ||||||||
\(630\) | −6.49125 | + | 2.02676i | −0.258618 | + | 0.0807480i | ||||
\(631\) | − | 21.9242i | − | 0.872788i | −0.899756 | − | 0.436394i | \(-0.856255\pi\) | ||
0.899756 | − | 0.436394i | \(-0.143745\pi\) | |||||||
\(632\) | 8.23792 | + | 12.4326i | 0.327687 | + | 0.494543i | ||||
\(633\) | −19.9935 | − | 10.1512i | −0.794669 | − | 0.403476i | ||||
\(634\) | −6.59827 | − | 2.24929i | −0.262051 | − | 0.0893307i | ||||
\(635\) | −12.5413 | −0.497687 | ||||||||
\(636\) | 3.32034 | + | 6.98184i | 0.131660 | + | 0.276848i | ||||
\(637\) | 29.4870 | 1.16832 | ||||||||
\(638\) | 8.27302 | + | 2.82020i | 0.327532 | + | 0.111653i | ||||
\(639\) | 6.29260 | + | 8.60920i | 0.248931 | + | 0.340575i | ||||
\(640\) | −10.7310 | + | 12.0161i | −0.424181 | + | 0.474980i | ||||
\(641\) | − | 31.3286i | − | 1.23741i | −0.785625 | − | 0.618704i | \(-0.787658\pi\) | ||
0.785625 | − | 0.618704i | \(-0.212342\pi\) | |||||||
\(642\) | 8.84855 | + | 9.08074i | 0.349224 | + | 0.358388i | ||||
\(643\) | 14.2291i | 0.561141i | 0.959833 | + | 0.280570i | \(0.0905236\pi\) | ||||
−0.959833 | + | 0.280570i | \(0.909476\pi\) | |||||||
\(644\) | 1.37507 | − | 1.78250i | 0.0541852 | − | 0.0702402i | ||||
\(645\) | −4.15920 | + | 8.19179i | −0.163768 | + | 0.322552i | ||||
\(646\) | 12.4451 | − | 36.5076i | 0.489646 | − | 1.43637i | ||||
\(647\) | −22.6877 | −0.891944 | −0.445972 | − | 0.895047i | \(-0.647142\pi\) | ||||
−0.445972 | + | 0.895047i | \(0.647142\pi\) | |||||||
\(648\) | −6.95505 | − | 24.4873i | −0.273220 | − | 0.961951i | ||||
\(649\) | 6.70604 | 0.263235 | ||||||||
\(650\) | 6.97598 | − | 20.4640i | 0.273620 | − | 0.802663i | ||||
\(651\) | 3.34757 | − | 6.59324i | 0.131202 | − | 0.258410i | ||||
\(652\) | 18.0104 | − | 23.3469i | 0.705342 | − | 0.914335i | ||||
\(653\) | 47.5253i | 1.85981i | 0.367799 | + | 0.929905i | \(0.380111\pi\) | ||||
−0.367799 | + | 0.929905i | \(0.619889\pi\) | |||||||
\(654\) | 3.21595 | + | 3.30033i | 0.125753 | + | 0.129053i | ||||
\(655\) | 26.1145i | 1.02038i | ||||||||
\(656\) | −31.8716 | + | 8.36426i | −1.24438 | + | 0.326570i | ||||
\(657\) | −24.4560 | − | 33.4594i | −0.954119 | − | 1.30537i | ||||
\(658\) | 11.4867 | + | 3.91571i | 0.447798 | + | 0.152650i | ||||
\(659\) | −19.0539 | −0.742236 | −0.371118 | − | 0.928586i | \(-0.621025\pi\) | ||||
−0.371118 | + | 0.928586i | \(0.621025\pi\) | |||||||
\(660\) | −3.56552 | − | 7.49739i | −0.138788 | − | 0.291836i | ||||
\(661\) | 8.25746 | 0.321178 | 0.160589 | − | 0.987021i | \(-0.448661\pi\) | ||||
0.160589 | + | 0.987021i | \(0.448661\pi\) | |||||||
\(662\) | −16.7949 | − | 5.72524i | −0.652754 | − | 0.222518i | ||||
\(663\) | −36.9421 | − | 18.7565i | −1.43471 | − | 0.728443i | ||||
\(664\) | −30.4381 | + | 20.1685i | −1.18123 | + | 0.782688i | ||||
\(665\) | 9.39980i | 0.364509i | ||||||||
\(666\) | 10.2064 | − | 3.18673i | 0.395489 | − | 0.123483i | ||||
\(667\) | − | 3.67220i | − | 0.142188i | ||||||
\(668\) | 33.4661 | + | 25.8166i | 1.29484 | + | 0.998875i | ||||
\(669\) | −1.81806 | − | 0.923081i | −0.0702904 | − | 0.0356884i | ||||
\(670\) | 7.99150 | − | 23.4430i | 0.308739 | − | 0.905681i | ||||
\(671\) | 12.0202 | 0.464035 | ||||||||
\(672\) | 9.44985 | + | 5.68636i | 0.364536 | + | 0.219356i | ||||
\(673\) | −30.1539 | −1.16235 | −0.581174 | − | 0.813779i | \(-0.697407\pi\) | ||||
−0.581174 | + | 0.813779i | \(0.697407\pi\) | |||||||
\(674\) | 9.63305 | − | 28.2585i | 0.371051 | − | 1.08848i | ||||
\(675\) | −15.2440 | + | 2.48141i | −0.586742 | + | 0.0955096i | ||||
\(676\) | −21.3063 | − | 16.4363i | −0.819474 | − | 0.632164i | ||||
\(677\) | − | 49.3523i | − | 1.89676i | −0.317133 | − | 0.948381i | \(-0.602720\pi\) | ||
0.317133 | − | 0.948381i | \(-0.397280\pi\) | |||||||
\(678\) | 19.1010 | − | 18.6126i | 0.733571 | − | 0.714814i | ||||
\(679\) | − | 13.4642i | − | 0.516708i | ||||||
\(680\) | 15.6142 | − | 10.3461i | 0.598778 | − | 0.396754i | ||||
\(681\) | −18.3859 | + | 36.2120i | −0.704548 | + | 1.38765i | ||||
\(682\) | 8.54451 | + | 2.91274i | 0.327186 | + | 0.111535i | ||||
\(683\) | −5.73685 | −0.219514 | −0.109757 | − | 0.993958i | \(-0.535007\pi\) | ||||
−0.109757 | + | 0.993958i | \(0.535007\pi\) | |||||||
\(684\) | −35.1749 | − | 0.911192i | −1.34494 | − | 0.0348403i | ||||
\(685\) | −8.21054 | −0.313708 | ||||||||
\(686\) | 19.1851 | + | 6.54004i | 0.732492 | + | 0.249700i | ||||
\(687\) | 21.6925 | − | 42.7246i | 0.827619 | − | 1.63004i | ||||
\(688\) | 14.4118 | − | 3.78219i | 0.549446 | − | 0.144195i | ||||
\(689\) | − | 11.4790i | − | 0.437316i | ||||||
\(690\) | −2.49811 | + | 2.43424i | −0.0951014 | + | 0.0926698i | ||||
\(691\) | − | 6.45669i | − | 0.245624i | −0.992430 | − | 0.122812i | \(-0.960809\pi\) | ||
0.992430 | − | 0.122812i | \(-0.0391912\pi\) | |||||||
\(692\) | 2.02871 | − | 2.62981i | 0.0771199 | − | 0.0999704i | ||||
\(693\) | −4.58841 | + | 3.35374i | −0.174299 | + | 0.127398i | ||||
\(694\) | 0.792212 | − | 2.32395i | 0.0300720 | − | 0.0882158i | ||||
\(695\) | 3.44053 | 0.130507 | ||||||||
\(696\) | 17.8704 | − | 2.07100i | 0.677377 | − | 0.0785010i | ||||
\(697\) | 38.3107 | 1.45112 | ||||||||
\(698\) | −6.83514 | + | 20.0508i | −0.258714 | + | 0.758935i | ||||
\(699\) | 20.9471 | + | 10.6354i | 0.792293 | + | 0.402269i | ||||
\(700\) | 4.08714 | − | 5.29816i | 0.154479 | − | 0.200251i | ||||
\(701\) | 7.50410i | 0.283426i | 0.989908 | + | 0.141713i | \(0.0452610\pi\) | ||||
−0.989908 | + | 0.141713i | \(0.954739\pi\) | |||||||
\(702\) | −6.28910 | + | 37.2693i | −0.237367 | + | 1.40664i | ||||
\(703\) | − | 14.7796i | − | 0.557422i | ||||||
\(704\) | −5.24853 | + | 12.3992i | −0.197811 | + | 0.467314i | ||||
\(705\) | −16.7655 | − | 8.51231i | −0.631425 | − | 0.320592i | ||||
\(706\) | 0.921860 | + | 0.314254i | 0.0346947 | + | 0.0118271i | ||||
\(707\) | 1.24970 | 0.0469999 | ||||||||
\(708\) | 12.4649 | − | 5.92789i | 0.468458 | − | 0.222784i | ||||
\(709\) | 38.2988 | 1.43834 | 0.719170 | − | 0.694834i | \(-0.244522\pi\) | ||||
0.719170 | + | 0.694834i | \(0.244522\pi\) | |||||||
\(710\) | 6.77532 | + | 2.30965i | 0.254273 | + | 0.0866795i | ||||
\(711\) | −12.7712 | + | 9.33464i | −0.478956 | + | 0.350076i | ||||
\(712\) | −24.8420 | − | 37.4914i | −0.930994 | − | 1.40505i | ||||
\(713\) | − | 3.79271i | − | 0.142038i | ||||||
\(714\) | −8.94889 | − | 9.18371i | −0.334904 | − | 0.343692i | ||||
\(715\) | 12.3267i | 0.460991i | ||||||||
\(716\) | 1.09851 | + | 0.847419i | 0.0410532 | + | 0.0316695i | ||||
\(717\) | 23.3933 | − | 46.0745i | 0.873638 | − | 1.72068i | ||||
\(718\) | −13.2522 | + | 38.8751i | −0.494566 | + | 1.45080i | ||||
\(719\) | −42.9789 | −1.60284 | −0.801422 | − | 0.598100i | \(-0.795923\pi\) | ||||
−0.801422 | + | 0.598100i | \(0.795923\pi\) | |||||||
\(720\) | −13.2548 | − | 10.7840i | −0.493979 | − | 0.401896i | ||||
\(721\) | −18.7576 | −0.698568 | ||||||||
\(722\) | −7.02335 | + | 20.6029i | −0.261382 | + | 0.766761i | ||||
\(723\) | 15.1169 | − | 29.7737i | 0.562204 | − | 1.10729i | ||||
\(724\) | −13.7786 | − | 10.6292i | −0.512079 | − | 0.395032i | ||||
\(725\) | − | 10.9150i | − | 0.405372i | ||||||
\(726\) | 13.9619 | + | 14.3283i | 0.518176 | + | 0.531773i | ||||
\(727\) | − | 18.6182i | − | 0.690511i | −0.938509 | − | 0.345255i | \(-0.887792\pi\) | ||
0.938509 | − | 0.345255i | \(-0.112208\pi\) | |||||||
\(728\) | −9.04495 | − | 13.6506i | −0.335228 | − | 0.505924i | ||||
\(729\) | 25.6061 | − | 8.56319i | 0.948374 | − | 0.317155i | ||||
\(730\) | −26.3321 | − | 8.97636i | −0.974593 | − | 0.332230i | ||||
\(731\) | −17.3235 | −0.640733 | ||||||||
\(732\) | 22.3426 | − | 10.6254i | 0.825805 | − | 0.392727i | ||||
\(733\) | −6.88546 | −0.254320 | −0.127160 | − | 0.991882i | \(-0.540586\pi\) | ||||
−0.127160 | + | 0.991882i | \(0.540586\pi\) | |||||||
\(734\) | −16.9364 | − | 5.77346i | −0.625133 | − | 0.213102i | ||||
\(735\) | −12.6077 | − | 6.40129i | −0.465043 | − | 0.236115i | ||||
\(736\) | 5.64224 | + | 0.406310i | 0.207976 | + | 0.0149768i | ||||
\(737\) | − | 20.6998i | − | 0.762486i | ||||||
\(738\) | −10.4164 | − | 33.3613i | −0.383432 | − | 1.22805i | ||||
\(739\) | − | 4.21689i | − | 0.155121i | −0.996988 | − | 0.0775603i | \(-0.975287\pi\) | ||
0.996988 | − | 0.0775603i | \(-0.0247130\pi\) | |||||||
\(740\) | 4.38395 | − | 5.68291i | 0.161157 | − | 0.208908i | ||||
\(741\) | 46.5838 | + | 23.6519i | 1.71130 | + | 0.868873i | ||||
\(742\) | 1.14632 | − | 3.36271i | 0.0420826 | − | 0.123449i | ||||
\(743\) | 47.4143 | 1.73946 | 0.869731 | − | 0.493527i | \(-0.164293\pi\) | ||||
0.869731 | + | 0.493527i | \(0.164293\pi\) | |||||||
\(744\) | 18.4569 | − | 2.13896i | 0.676662 | − | 0.0784181i | ||||
\(745\) | 24.3392 | 0.891718 | ||||||||
\(746\) | −10.1957 | + | 29.9091i | −0.373292 | + | 1.09505i | ||||
\(747\) | −22.8535 | − | 31.2669i | −0.836165 | − | 1.14400i | ||||
\(748\) | 9.56178 | − | 12.3949i | 0.349613 | − | 0.453204i | ||||
\(749\) | − | 5.82642i | − | 0.212893i | ||||||
\(750\) | −19.9157 | + | 19.4065i | −0.727220 | + | 0.708626i | ||||
\(751\) | 12.0897i | 0.441158i | 0.975369 | + | 0.220579i | \(0.0707947\pi\) | ||||
−0.975369 | + | 0.220579i | \(0.929205\pi\) | |||||||
\(752\) | 7.74072 | + | 29.4956i | 0.282275 | + | 1.07559i | ||||
\(753\) | −9.97992 | + | 19.6560i | −0.363689 | + | 0.716306i | ||||
\(754\) | −25.2825 | − | 8.61858i | −0.920735 | − | 0.313870i | ||||
\(755\) | −8.86096 | −0.322483 | ||||||||
\(756\) | −5.56413 | + | 10.2898i | −0.202365 | + | 0.374235i | ||||
\(757\) | 3.14493 | 0.114304 | 0.0571522 | − | 0.998365i | \(-0.481798\pi\) | ||||
0.0571522 | + | 0.998365i | \(0.481798\pi\) | |||||||
\(758\) | −4.37058 | − | 1.48989i | −0.158747 | − | 0.0541153i | ||||
\(759\) | −1.31972 | + | 2.59927i | −0.0479029 | + | 0.0943476i | ||||
\(760\) | −19.6895 | + | 13.0463i | −0.714212 | + | 0.473240i | ||||
\(761\) | − | 20.3562i | − | 0.737910i | −0.929447 | − | 0.368955i | \(-0.879716\pi\) | ||
0.929447 | − | 0.368955i | \(-0.120284\pi\) | |||||||
\(762\) | −15.4510 | + | 15.0559i | −0.559730 | + | 0.545418i | ||||
\(763\) | − | 2.11757i | − | 0.0766612i | ||||||
\(764\) | −18.9341 | − | 14.6062i | −0.685011 | − | 0.528436i | ||||
\(765\) | 11.7234 | + | 16.0394i | 0.423862 | + | 0.579905i | ||||
\(766\) | −17.2884 | + | 50.7152i | −0.624654 | + | 1.83241i | ||||
\(767\) | −20.4938 | −0.739988 | ||||||||
\(768\) | 1.20476 | + | 27.6866i | 0.0434731 | + | 0.999055i | ||||
\(769\) | −29.0487 | −1.04752 | −0.523762 | − | 0.851865i | \(-0.675472\pi\) | ||||
−0.523762 | + | 0.851865i | \(0.675472\pi\) | |||||||
\(770\) | −1.23096 | + | 3.61102i | −0.0443608 | + | 0.130132i | ||||
\(771\) | 24.4733 | + | 12.4258i | 0.881385 | + | 0.447504i | ||||
\(772\) | 17.9842 | + | 13.8735i | 0.647266 | + | 0.499319i | ||||
\(773\) | 10.1707i | 0.365813i | 0.983130 | + | 0.182907i | \(0.0585506\pi\) | ||||
−0.983130 | + | 0.182907i | \(0.941449\pi\) | |||||||
\(774\) | 4.71013 | + | 15.0855i | 0.169302 | + | 0.542236i | ||||
\(775\) | − | 11.2732i | − | 0.404944i | ||||||
\(776\) | 28.2030 | − | 18.6875i | 1.01243 | − | 0.670841i | ||||
\(777\) | −4.38112 | − | 2.22442i | −0.157172 | − | 0.0798004i | ||||
\(778\) | 1.24417 | + | 0.424125i | 0.0446055 | + | 0.0152056i | ||||
\(779\) | −48.3096 | −1.73087 | ||||||||
\(780\) | 10.8963 | + | 22.9122i | 0.390150 | + | 0.820388i | ||||
\(781\) | 5.98250 | 0.214071 | ||||||||
\(782\) | −6.22524 | − | 2.12213i | −0.222614 | − | 0.0758871i | ||||
\(783\) | 3.06570 | + | 18.8334i | 0.109559 | + | 0.673052i | ||||
\(784\) | 5.82105 | + | 22.1808i | 0.207894 | + | 0.792171i | ||||
\(785\) | 17.9690i | 0.641342i | ||||||||
\(786\) | 31.3506 | + | 32.1732i | 1.11824 | + | 1.14758i | ||||
\(787\) | 39.7585i | 1.41724i | 0.705591 | + | 0.708619i | \(0.250681\pi\) | ||||
−0.705591 | + | 0.708619i | \(0.749319\pi\) | |||||||
\(788\) | 5.66129 | − | 7.33872i | 0.201675 | − | 0.261431i | ||||
\(789\) | 19.1830 | − | 37.7820i | 0.682931 | − | 1.34507i | ||||
\(790\) | −3.42620 | + | 10.0507i | −0.121899 | + | 0.357589i | ||||
\(791\) | −12.2557 | −0.435762 | ||||||||
\(792\) | −13.3934 | − | 4.95641i | −0.475914 | − | 0.176118i | ||||
\(793\) | −36.7340 | −1.30446 | ||||||||
\(794\) | −5.75878 | + | 16.8933i | −0.204371 | + | 0.599521i | ||||
\(795\) | −2.49196 | + | 4.90806i | −0.0883807 | + | 0.174071i | ||||
\(796\) | −22.2027 | + | 28.7813i | −0.786953 | + | 1.02013i | ||||
\(797\) | − | 1.92774i | − | 0.0682842i | −0.999417 | − | 0.0341421i | \(-0.989130\pi\) | ||
0.999417 | − | 0.0341421i | \(-0.0108699\pi\) | |||||||
\(798\) | 11.2845 | + | 11.5806i | 0.399467 | + | 0.409949i | ||||
\(799\) | − | 35.4547i | − | 1.25430i | ||||||
\(800\) | 16.7706 | + | 1.20769i | 0.592929 | + | 0.0426982i | ||||
\(801\) | 38.5123 | − | 28.1492i | 1.36076 | − | 0.994604i | ||||
\(802\) | −15.4349 | − | 5.26162i | −0.545025 | − | 0.185794i | ||||
\(803\) | −23.2508 | −0.820502 | ||||||||
\(804\) | −18.2978 | − | 38.4757i | −0.645315 | − | 1.35693i | ||||
\(805\) | 1.60285 | 0.0564929 | ||||||||
\(806\) | −26.1122 | − | 8.90141i | −0.919762 | − | 0.313539i | ||||
\(807\) | 3.19633 | + | 1.62287i | 0.112516 | + | 0.0571276i | ||||
\(808\) | 1.73451 | + | 2.61771i | 0.0610198 | + | 0.0920908i | ||||
\(809\) | − | 26.8795i | − | 0.945032i | −0.881322 | − | 0.472516i | \(-0.843346\pi\) | ||
0.881322 | − | 0.472516i | \(-0.156654\pi\) | |||||||
\(810\) | 10.7797 | − | 14.5699i | 0.378761 | − | 0.511933i | ||||
\(811\) | 33.4488i | 1.17454i | 0.809389 | + | 0.587272i | \(0.199798\pi\) | ||||
−0.809389 | + | 0.587272i | \(0.800202\pi\) | |||||||
\(812\) | −6.54569 | − | 5.04952i | −0.229709 | − | 0.177203i | ||||
\(813\) | −36.6285 | − | 18.5973i | −1.28462 | − | 0.652236i | ||||
\(814\) | 1.93548 | − | 5.67771i | 0.0678385 | − | 0.199003i | ||||
\(815\) | 20.9939 | 0.735383 | ||||||||
\(816\) | 6.81632 | − | 31.4914i | 0.238619 | − | 1.10242i | ||||
\(817\) | 21.8449 | 0.764255 | ||||||||
\(818\) | 10.5940 | − | 31.0773i | 0.370409 | − | 1.08659i | ||||
\(819\) | 14.0223 | − | 10.2491i | 0.489978 | − | 0.358133i | ||||
\(820\) | −18.5756 | − | 14.3297i | −0.648687 | − | 0.500415i | ||||
\(821\) | 6.68055i | 0.233153i | 0.993182 | + | 0.116576i | \(0.0371920\pi\) | ||||
−0.993182 | + | 0.116576i | \(0.962808\pi\) | |||||||
\(822\) | −10.1154 | + | 9.85679i | −0.352816 | + | 0.343795i | ||||
\(823\) | 3.67845i | 0.128223i | 0.997943 | + | 0.0641113i | \(0.0204213\pi\) | ||||
−0.997943 | + | 0.0641113i | \(0.979579\pi\) | |||||||
\(824\) | −26.0343 | − | 39.2909i | −0.906949 | − | 1.36876i | ||||
\(825\) | −3.92264 | + | 7.72588i | −0.136569 | + | 0.268981i | ||||
\(826\) | −6.00353 | − | 2.04655i | −0.208889 | − | 0.0712085i | ||||
\(827\) | −29.3519 | −1.02067 | −0.510334 | − | 0.859977i | \(-0.670478\pi\) | ||||
−0.510334 | + | 0.859977i | \(0.670478\pi\) | |||||||
\(828\) | −0.155376 | + | 5.99799i | −0.00539968 | + | 0.208444i | ||||
\(829\) | 13.3676 | 0.464274 | 0.232137 | − | 0.972683i | \(-0.425428\pi\) | ||||
0.232137 | + | 0.972683i | \(0.425428\pi\) | |||||||
\(830\) | −24.6066 | − | 8.38818i | −0.854109 | − | 0.291158i | ||||
\(831\) | −10.2218 | + | 20.1325i | −0.354591 | + | 0.698388i | ||||
\(832\) | 16.0396 | − | 37.8923i | 0.556073 | − | 1.31368i | ||||
\(833\) | − | 26.6620i | − | 0.923785i | ||||||
\(834\) | 4.23875 | − | 4.13037i | 0.146776 | − | 0.143023i | ||||
\(835\) | 30.0932i | 1.04142i | ||||||||
\(836\) | −12.0574 | + | 15.6300i | −0.417013 | + | 0.540573i | ||||
\(837\) | 3.16630 | + | 19.4515i | 0.109443 | + | 0.672341i | ||||
\(838\) | −13.3885 | + | 39.2749i | −0.462497 | + | 1.35673i | ||||
\(839\) | 7.53668 | 0.260195 | 0.130098 | − | 0.991501i | \(-0.458471\pi\) | ||||
0.130098 | + | 0.991501i | \(0.458471\pi\) | |||||||
\(840\) | 0.903952 | + | 7.80011i | 0.0311893 | + | 0.269129i | ||||
\(841\) | 15.5149 | 0.534998 | ||||||||
\(842\) | −11.6769 | + | 34.2542i | −0.402414 | + | 1.18048i | ||||
\(843\) | 22.5449 | + | 11.4467i | 0.776487 | + | 0.394244i | ||||
\(844\) | −15.8147 | + | 20.5006i | −0.544366 | + | 0.705661i | ||||
\(845\) | − | 19.1590i | − | 0.659088i | ||||||
\(846\) | −30.8743 | + | 9.63985i | −1.06148 | + | 0.331425i | ||||
\(847\) | − | 9.19337i | − | 0.315888i | ||||||
\(848\) | 8.63477 | − | 2.26608i | 0.296519 | − | 0.0778174i | ||||
\(849\) | −35.1999 | − | 17.8719i | −1.20806 | − | 0.613364i | ||||
\(850\) | −18.5034 | − | 6.30765i | −0.634662 | − | 0.216351i | ||||
\(851\) | −2.52020 | −0.0863914 | ||||||||
\(852\) | 11.1200 | − | 5.28831i | 0.380964 | − | 0.181175i | ||||
\(853\) | 36.6618 | 1.25528 | 0.627638 | − | 0.778506i | \(-0.284022\pi\) | ||||
0.627638 | + | 0.778506i | \(0.284022\pi\) | |||||||
\(854\) | −10.7610 | − | 3.66832i | −0.368234 | − | 0.125527i | ||||
\(855\) | −14.7832 | − | 20.2256i | −0.505575 | − | 0.691700i | ||||
\(856\) | 12.2044 | − | 8.08670i | 0.417138 | − | 0.276398i | ||||
\(857\) | 22.2605i | 0.760404i | 0.924903 | + | 0.380202i | \(0.124146\pi\) | ||||
−0.924903 | + | 0.380202i | \(0.875854\pi\) | |||||||
\(858\) | 14.7982 | + | 15.1865i | 0.505202 | + | 0.518459i | ||||
\(859\) | 19.7600i | 0.674201i | 0.941469 | + | 0.337100i | \(0.109446\pi\) | ||||
−0.941469 | + | 0.337100i | \(0.890554\pi\) | |||||||
\(860\) | 8.39959 | + | 6.47967i | 0.286424 | + | 0.220955i | ||||
\(861\) | −7.27088 | + | 14.3204i | −0.247791 | + | 0.488039i | ||||
\(862\) | 8.25496 | − | 24.2158i | 0.281165 | − | 0.824794i | ||||
\(863\) | 40.1334 | 1.36616 | 0.683078 | − | 0.730345i | \(-0.260641\pi\) | ||||
0.683078 | + | 0.730345i | \(0.260641\pi\) | |||||||
\(864\) | −29.2763 | + | 2.62654i | −0.996000 | + | 0.0893568i | ||||
\(865\) | 2.36476 | 0.0804044 | ||||||||
\(866\) | −1.31131 | + | 3.84671i | −0.0445600 | + | 0.130716i | ||||
\(867\) | −3.62935 | + | 7.14823i | −0.123259 | + | 0.242766i | ||||
\(868\) | −6.76049 | − | 5.21522i | −0.229466 | − | 0.177016i | ||||
\(869\) | 8.87462i | 0.301051i | ||||||||
\(870\) | 8.93900 | + | 9.17356i | 0.303061 | + | 0.311013i | ||||
\(871\) | 63.2589i | 2.14345i | ||||||||
\(872\) | 4.43561 | − | 2.93906i | 0.150209 | − | 0.0995290i | ||||
\(873\) | 21.1753 | + | 28.9709i | 0.716676 | + | 0.980518i | ||||
\(874\) | 7.85000 | + | 2.67599i | 0.265530 | + | 0.0905168i | ||||
\(875\) | 12.7784 | 0.431989 | ||||||||
\(876\) | −43.2174 | + | 20.5528i | −1.46018 | + | 0.694416i | ||||
\(877\) | −6.22608 | −0.210240 | −0.105120 | − | 0.994460i | \(-0.533523\pi\) | ||||
−0.105120 | + | 0.994460i | \(0.533523\pi\) | |||||||
\(878\) | −37.2420 | − | 12.6955i | −1.25686 | − | 0.428451i | ||||
\(879\) | −41.8911 | − | 21.2693i | −1.41295 | − | 0.717394i | ||||
\(880\) | −9.27238 | + | 2.43341i | −0.312572 | + | 0.0820302i | ||||
\(881\) | 18.1502i | 0.611496i | 0.952112 | + | 0.305748i | \(0.0989066\pi\) | ||||
−0.952112 | + | 0.305748i | \(0.901093\pi\) | |||||||
\(882\) | −23.2176 | + | 7.24920i | −0.781776 | + | 0.244093i | ||||
\(883\) | − | 7.83604i | − | 0.263704i | −0.991269 | − | 0.131852i | \(-0.957908\pi\) | ||
0.991269 | − | 0.131852i | \(-0.0420923\pi\) | |||||||
\(884\) | −29.2210 | + | 37.8792i | −0.982809 | + | 1.27401i | ||||
\(885\) | 8.76249 | + | 4.44896i | 0.294548 | + | 0.149550i | ||||
\(886\) | −1.61952 | + | 4.75083i | −0.0544087 | + | 0.159607i | ||||
\(887\) | 10.4966 | 0.352443 | 0.176221 | − | 0.984351i | \(-0.443613\pi\) | ||||
0.176221 | + | 0.984351i | \(0.443613\pi\) | |||||||
\(888\) | −1.42131 | − | 12.2643i | −0.0476960 | − | 0.411564i | ||||
\(889\) | 9.91371 | 0.332495 | ||||||||
\(890\) | 10.3319 | − | 30.3086i | 0.346327 | − | 1.01595i | ||||
\(891\) | 4.59842 | − | 14.4325i | 0.154053 | − | 0.483507i | ||||
\(892\) | −1.43808 | + | 1.86418i | −0.0481504 | + | 0.0624174i | ||||
\(893\) | 44.7082i | 1.49610i | ||||||||
\(894\) | 29.9860 | − | 29.2193i | 1.00288 | − | 0.977239i | ||||
\(895\) | 0.987795i | 0.0330184i | ||||||||
\(896\) | 8.48270 | − | 9.49858i | 0.283387 | − | 0.317325i | ||||
\(897\) | 4.03310 | − | 7.94343i | 0.134661 | − | 0.265223i | ||||
\(898\) | −16.2519 | − | 5.54014i | −0.542334 | − | 0.184877i | ||||
\(899\) | −13.9276 | −0.464511 | ||||||||
\(900\) | −0.461827 | + | 17.8280i | −0.0153942 | + | 0.594265i | ||||
\(901\) | −10.3793 | −0.345784 | ||||||||
\(902\) | −18.5586 | − | 6.32644i | −0.617932 | − | 0.210648i | ||||
\(903\) | 3.28778 | − | 6.47548i | 0.109411 | − | 0.215491i | ||||
\(904\) | −17.0101 | − | 25.6716i | −0.565748 | − | 0.853823i | ||||
\(905\) | − | 12.3900i | − | 0.411856i | ||||||
\(906\) | −10.9168 | + | 10.6376i | −0.362685 | + | 0.353412i | ||||
\(907\) | − | 5.19923i | − | 0.172637i | −0.996268 | − | 0.0863187i | \(-0.972490\pi\) | ||
0.996268 | − | 0.0863187i | \(-0.0275103\pi\) | |||||||
\(908\) | 37.1306 | + | 28.6436i | 1.23222 | + | 0.950570i | ||||
\(909\) | −2.68899 | + | 1.96542i | −0.0891881 | + | 0.0651890i | ||||
\(910\) | 3.76185 | − | 11.0353i | 0.124704 | − | 0.365818i | ||||
\(911\) | 30.3688 | 1.00616 | 0.503081 | − | 0.864239i | \(-0.332200\pi\) | ||||
0.503081 | + | 0.864239i | \(0.332200\pi\) | |||||||
\(912\) | −8.59534 | + | 39.7105i | −0.284620 | + | 1.31494i | ||||
\(913\) | −21.7273 | −0.719067 | ||||||||
\(914\) | −13.1080 | + | 38.4523i | −0.433575 | + | 1.27189i | ||||
\(915\) | 15.7063 | + | 7.97452i | 0.519234 | + | 0.263629i | ||||
\(916\) | −43.8084 | − | 33.7949i | −1.44747 | − | 1.11662i | ||||
\(917\) | − | 20.6431i | − | 0.681695i | ||||||
\(918\) | 33.6987 | + | 5.68657i | 1.11222 | + | 0.187685i | ||||
\(919\) | − | 11.0039i | − | 0.362984i | −0.983392 | − | 0.181492i | \(-0.941907\pi\) | ||
0.983392 | − | 0.181492i | \(-0.0580926\pi\) | |||||||
\(920\) | 2.22465 | + | 3.35743i | 0.0733446 | + | 0.110691i | ||||
\(921\) | −27.8295 | − | 14.1298i | −0.917014 | − | 0.465593i | ||||
\(922\) | −29.4741 | − | 10.0474i | −0.970677 | − | 0.330895i | ||||
\(923\) | −18.2826 | −0.601781 | ||||||||
\(924\) | 2.81849 | + | 5.92657i | 0.0927215 | + | 0.194970i | ||||
\(925\) | −7.49086 | −0.246298 | ||||||||
\(926\) | 34.4308 | + | 11.7371i | 1.13147 | + | 0.385706i | ||||
\(927\) | 40.3607 | − | 29.5003i | 1.32562 | − | 0.968916i | ||||
\(928\) | 1.49205 | − | 20.7195i | 0.0489791 | − | 0.680149i | ||||
\(929\) | − | 56.7119i | − | 1.86066i | −0.366729 | − | 0.930328i | \(-0.619522\pi\) | ||
0.366729 | − | 0.930328i | \(-0.380478\pi\) | |||||||
\(930\) | 9.23235 | + | 9.47460i | 0.302741 | + | 0.310685i | ||||
\(931\) | 33.6207i | 1.10187i | ||||||||
\(932\) | 16.5691 | − | 21.4785i | 0.542738 | − | 0.703551i | ||||
\(933\) | 12.0817 | − | 23.7957i | 0.395538 | − | 0.779035i | ||||
\(934\) | 8.59974 | − | 25.2272i | 0.281392 | − | 0.825461i | ||||
\(935\) | 11.1457 | 0.364503 | ||||||||
\(936\) | 40.9305 | + | 15.1469i | 1.33786 | + | 0.495092i | ||||
\(937\) | −34.7161 | −1.13413 | −0.567064 | − | 0.823674i | \(-0.691921\pi\) | ||||
−0.567064 | + | 0.823674i | \(0.691921\pi\) | |||||||
\(938\) | −6.31715 | + | 18.5313i | −0.206262 | + | 0.605069i | ||||
\(939\) | −0.936982 | + | 1.84544i | −0.0305773 | + | 0.0602237i | ||||
\(940\) | −13.2614 | + | 17.1908i | −0.432540 | + | 0.560702i | ||||
\(941\) | − | 10.5373i | − | 0.343507i | −0.985140 | − | 0.171754i | \(-0.945057\pi\) | ||
0.985140 | − | 0.171754i | \(-0.0549433\pi\) | |||||||
\(942\) | 21.5719 | + | 22.1379i | 0.702850 | + | 0.721293i | ||||
\(943\) | 8.23771i | 0.268257i | ||||||||
\(944\) | −4.04569 | − | 15.4159i | −0.131676 | − | 0.501744i | ||||
\(945\) | −8.22044 | + | 1.33812i | −0.267411 | + | 0.0435290i | ||||
\(946\) | 8.39190 | + | 2.86072i | 0.272844 | + | 0.0930101i | ||||
\(947\) | −4.19362 | −0.136274 | −0.0681372 | − | 0.997676i | \(-0.521706\pi\) | ||||
−0.0681372 | + | 0.997676i | \(0.521706\pi\) | |||||||
\(948\) | 7.84484 | + | 16.4957i | 0.254789 | + | 0.535756i | ||||
\(949\) | 71.0549 | 2.30654 | ||||||||
\(950\) | 23.3327 | + | 7.95391i | 0.757013 | + | 0.258059i | ||||
\(951\) | −7.61280 | − | 3.86523i | −0.246862 | − | 0.125339i | ||||
\(952\) | −12.3428 | + | 8.17840i | −0.400032 | + | 0.265064i | ||||
\(953\) | − | 2.24336i | − | 0.0726695i | −0.999340 | − | 0.0363347i | \(-0.988432\pi\) | ||
0.999340 | − | 0.0363347i | \(-0.0115683\pi\) | |||||||
\(954\) | 2.82204 | + | 9.03837i | 0.0913670 | + | 0.292628i | ||||
\(955\) | − | 17.0258i | − | 0.550942i | ||||||
\(956\) | −47.2432 | − | 36.4447i | −1.52795 | − | 1.17870i | ||||
\(957\) | 9.54505 | + | 4.84629i | 0.308548 | + | 0.156658i | ||||
\(958\) | 0.0511425 | − | 0.150026i | 0.00165234 | − | 0.00484712i | ||||
\(959\) | 6.49030 | 0.209583 | ||||||||
\(960\) | −15.0840 | + | 12.7195i | −0.486834 | + | 0.410521i | ||||
\(961\) | 16.6154 | 0.535979 | ||||||||
\(962\) | −5.91486 | + | 17.3512i | −0.190703 | + | 0.559425i | ||||
\(963\) | 9.16328 | + | 12.5367i | 0.295283 | + | 0.403990i | ||||
\(964\) | −30.5289 | − | 23.5508i | −0.983270 | − | 0.758521i | ||||
\(965\) | 16.1717i | 0.520585i | ||||||||
\(966\) | 1.97472 | − | 1.92423i | 0.0635355 | − | 0.0619109i | ||||
\(967\) | 6.60501i | 0.212403i | 0.994345 | + | 0.106201i | \(0.0338688\pi\) | ||||
−0.994345 | + | 0.106201i | \(0.966131\pi\) | |||||||
\(968\) | 19.2571 | − | 12.7598i | 0.618945 | − | 0.410117i | ||||
\(969\) | 21.3859 | − | 42.1208i | 0.687015 | − | 1.35312i | ||||
\(970\) | 22.7997 | + | 7.77222i | 0.732055 | + | 0.249551i | ||||
\(971\) | 31.3795 | 1.00702 | 0.503508 | − | 0.863990i | \(-0.332042\pi\) | ||||
0.503508 | + | 0.863990i | \(0.332042\pi\) | |||||||
\(972\) | −4.21049 | − | 30.8913i | −0.135051 | − | 0.990839i | ||||
\(973\) | −2.71968 | −0.0871890 | ||||||||
\(974\) | 36.7669 | + | 12.5335i | 1.17809 | + | 0.401599i | ||||
\(975\) | 11.9877 | − | 23.6104i | 0.383913 | − | 0.756139i | ||||
\(976\) | −7.25167 | − | 27.6321i | −0.232120 | − | 0.884482i | ||||
\(977\) | − | 33.9220i | − | 1.08526i | −0.839971 | − | 0.542631i | \(-0.817428\pi\) | ||
0.839971 | − | 0.542631i | \(-0.182572\pi\) | |||||||
\(978\) | 25.8646 | − | 25.2032i | 0.827058 | − | 0.805911i | ||||
\(979\) | − | 26.7620i | − | 0.855318i | ||||||
\(980\) | −9.97264 | + | 12.9275i | −0.318564 | + | 0.412955i | ||||
\(981\) | 3.33033 | + | 4.55638i | 0.106329 | + | 0.145474i | ||||
\(982\) | 5.11496 | − | 15.0047i | 0.163225 | − | 0.478819i | ||||
\(983\) | −47.8056 | −1.52476 | −0.762381 | − | 0.647128i | \(-0.775970\pi\) | ||||
−0.762381 | + | 0.647128i | \(0.775970\pi\) | |||||||
\(984\) | −40.0881 | + | 4.64579i | −1.27796 | + | 0.148102i | ||||
\(985\) | 6.59908 | 0.210264 | ||||||||
\(986\) | −7.79288 | + | 22.8603i | −0.248176 | + | 0.728021i | ||||
\(987\) | 13.2529 | + | 6.72885i | 0.421843 | + | 0.214182i | ||||
\(988\) | 36.8475 | − | 47.7655i | 1.17228 | − | 1.51962i | ||||
\(989\) | − | 3.72497i | − | 0.118447i | ||||||
\(990\) | −3.03043 | − | 9.70579i | −0.0963133 | − | 0.308470i | ||||
\(991\) | − | 58.8306i | − | 1.86881i | −0.356207 | − | 0.934407i | \(-0.615930\pi\) | ||
0.356207 | − | 0.934407i | \(-0.384070\pi\) | |||||||
\(992\) | 1.54102 | − | 21.3994i | 0.0489273 | − | 0.679431i | ||||
\(993\) | −19.3773 | − | 9.83838i | −0.614919 | − | 0.312212i | ||||
\(994\) | −5.35579 | − | 1.82574i | −0.169875 | − | 0.0579089i | ||||
\(995\) | −25.8806 | −0.820469 | ||||||||
\(996\) | −40.3856 | + | 19.2061i | −1.27967 | + | 0.608569i | ||||
\(997\) | 7.97211 | 0.252479 | 0.126240 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126240 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(998\) | −0.0392296 | − | 0.0133730i | −0.00124179 | − | 0.000423315i | ||||
\(999\) | 12.9252 | − | 2.10396i | 0.408936 | − | 0.0665665i |
(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 | 276.2.c.a.47.13 | ✓ | 22 | |
3.2 | odd | 2 | 276.2.c.b.47.10 | yes | 22 | ||
4.3 | odd | 2 | 276.2.c.b.47.9 | yes | 22 | ||
12.11 | even | 2 | inner | 276.2.c.a.47.14 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.c.a.47.13 | ✓ | 22 | 1.1 | even | 1 | trivial | |
276.2.c.a.47.14 | yes | 22 | 12.11 | even | 2 | inner | |
276.2.c.b.47.9 | yes | 22 | 4.3 | odd | 2 | ||
276.2.c.b.47.10 | yes | 22 | 3.2 | odd | 2 |