LMFDB - Embedded newform 273.2.cd.e.242.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			242.3
Character	$\chi$	$=$	273.242
Dual form			273.2.cd.e.44.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41247 - 0.646418i) q^{2} +(0.872737 + 1.49611i) q^{3} +(3.67009 + 2.11892i) q^{4} +(-1.51647 - 0.406338i) q^{5} +(-1.13834 - 4.17346i) q^{6} +(-1.79039 + 1.94795i) q^{7} +(-3.95215 - 3.95215i) q^{8} +(-1.47666 + 2.61141i) q^{9} +O(q^{10})$	\(q+(-2.41247 - 0.646418i) q^{2} +(0.872737 + 1.49611i) q^{3} +(3.67009 + 2.11892i) q^{4} +(-1.51647 - 0.406338i) q^{5} +(-1.13834 - 4.17346i) q^{6} +(-1.79039 + 1.94795i) q^{7} +(-3.95215 - 3.95215i) q^{8} +(-1.47666 + 2.61141i) q^{9} +(3.39578 + 1.96055i) q^{10} +(-1.16460 + 0.312052i) q^{11} +(0.0328833 + 7.34010i) q^{12} +(-1.67805 - 3.19126i) q^{13} +(5.57845 - 3.54202i) q^{14} +(-0.715558 - 2.62343i) q^{15} +(2.74184 + 4.74900i) q^{16} +(-0.0180259 + 0.0312218i) q^{17} +(5.25046 - 5.34540i) q^{18} +(0.354340 - 1.32242i) q^{19} +(-4.70459 - 4.70459i) q^{20} +(-4.47687 - 0.978568i) q^{21} +3.01126 q^{22} +(-2.87493 - 4.97952i) q^{23} +(2.46365 - 9.36202i) q^{24} +(-2.19554 - 1.26760i) q^{25} +(1.98535 + 8.78353i) q^{26} +(-5.19568 + 0.0698330i) q^{27} +(-10.6984 + 3.35543i) q^{28} +10.4846i q^{29} +(0.0304256 + 6.79149i) q^{30} +(-1.26381 + 0.338636i) q^{31} +(-0.651571 - 2.43170i) q^{32} +(-1.48325 - 1.47002i) q^{33} +(0.0636693 - 0.0636693i) q^{34} +(3.50661 - 2.22651i) q^{35} +(-10.9529 + 6.45517i) q^{36} +(-9.47419 - 2.53860i) q^{37} +(-1.70967 + 2.96123i) q^{38} +(3.30997 - 5.29567i) q^{39} +(4.38743 + 7.59925i) q^{40} +(-2.92653 + 2.92653i) q^{41} +(10.1677 + 5.25470i) q^{42} +4.27650i q^{43} +(-4.93538 - 1.32243i) q^{44} +(3.30044 - 3.36012i) q^{45} +(3.71681 + 13.8713i) q^{46} +(-0.106809 + 0.398617i) q^{47} +(-4.71210 + 8.24670i) q^{48} +(-0.589001 - 6.97518i) q^{49} +(4.47727 + 4.47727i) q^{50} +(-0.0624430 + 0.000279742i) q^{51} +(0.603453 - 15.2679i) q^{52} +(-7.13704 - 4.12057i) q^{53} +(12.5796 + 3.19012i) q^{54} +1.89288 q^{55} +(14.7745 - 0.622688i) q^{56} +(2.28772 - 0.623990i) q^{57} +(6.77746 - 25.2938i) q^{58} +(7.56335 - 2.02659i) q^{59} +(2.93270 - 11.1444i) q^{60} +(5.41126 + 9.37258i) q^{61} +3.26779 q^{62} +(-2.44309 - 7.55191i) q^{63} -4.67977i q^{64} +(1.24799 + 5.52132i) q^{65} +(2.62804 + 4.50517i) q^{66} +(3.10471 - 0.831905i) q^{67} +(-0.132313 + 0.0763912i) q^{68} +(4.94083 - 8.64701i) q^{69} +(-9.89883 + 3.10464i) q^{70} +(5.73066 - 5.73066i) q^{71} +(16.1567 - 4.48470i) q^{72} +(3.30991 + 12.3528i) q^{73} +(21.2152 + 12.2486i) q^{74} +(-0.0196717 - 4.39104i) q^{75} +(4.10256 - 4.10256i) q^{76} +(1.47722 - 2.82727i) q^{77} +(-11.4084 + 10.6360i) q^{78} +(1.15250 + 1.99619i) q^{79} +(-2.22823 - 8.31585i) q^{80} +(-4.63894 - 7.71234i) q^{81} +(8.95193 - 5.16840i) q^{82} +(-9.19760 + 9.19760i) q^{83} +(-14.3570 - 13.0776i) q^{84} +(0.0400225 - 0.0400225i) q^{85} +(2.76441 - 10.3169i) q^{86} +(-15.6861 + 9.15032i) q^{87} +(5.83593 + 3.36938i) q^{88} +(-1.95890 + 7.31073i) q^{89} +(-10.1342 + 5.97270i) q^{90} +(9.22078 + 2.44485i) q^{91} -24.3670i q^{92} +(-1.60960 - 1.59525i) q^{93} +(0.515347 - 0.892608i) q^{94} +(-1.07470 + 1.86143i) q^{95} +(3.06942 - 3.09705i) q^{96} +(12.3676 + 12.3676i) q^{97} +(-3.08794 + 17.2081i) q^{98} +(0.904816 - 3.50203i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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 $

$2$	−2.41247	−	0.646418i	−1.70587	−	0.457087i	−0.731465	−	0.681879i	$-0.761163\pi$
$2$	−2.41247	−	0.646418i	−1.70587	−	0.457087i	−0.974407	+	0.224793i	$0.927830\pi$
$3$	0.872737	+	1.49611i	0.503875	+	0.863777i
$3$	0.872737	+	1.49611i	0.503875	+	0.863777i
$4$	3.67009	+	2.11892i	1.83504	+	1.05946i
$5$	−1.51647	−	0.406338i	−0.678188	−	0.181720i	−0.0967477	−	0.995309i	$-0.530844\pi$
$5$	−1.51647	−	0.406338i	−0.678188	−	0.181720i	−0.581440	+	0.813589i	$0.697511\pi$
$6$	−1.13834	−	4.17346i	−0.464724	−	1.70381i
$7$	−1.79039	+	1.94795i	−0.676704	+	0.736255i
$7$	−1.79039	+	1.94795i	−0.676704	+	0.736255i
$8$	−3.95215	−	3.95215i	−1.39730	−	1.39730i
$9$	−1.47666	+	2.61141i	−0.492221	+	0.870471i
$10$	3.39578	+	1.96055i	1.07384	+	0.619982i
$11$	−1.16460	+	0.312052i	−0.351139	+	0.0940874i	−0.430077	−	0.902792i	$-0.641514\pi$
$11$	−1.16460	+	0.312052i	−0.351139	+	0.0940874i	0.0789383	+	0.996880i	$0.474847\pi$
$12$	0.0328833	+	7.34010i	0.00949260	+	2.11890i
$13$	−1.67805	−	3.19126i	−0.465407	−	0.885097i
$13$	−1.67805	−	3.19126i	−0.465407	−	0.885097i
$14$	5.57845	−	3.54202i	1.49090	−	0.946644i
$15$	−0.715558	−	2.62343i	−0.184756	−	0.677367i
$16$	2.74184	+	4.74900i	0.685459	+	1.18725i
$17$	−0.0180259	+	0.0312218i	−0.00437193	+	0.00757241i	−0.868203	−	0.496209i	$-0.834725\pi$
$17$	−0.0180259	+	0.0312218i	−0.00437193	+	0.00757241i	0.863831	+	0.503781i	$0.168058\pi$
$18$	5.25046	−	5.34540i	1.23755	−	1.25992i
$19$	0.354340	−	1.32242i	0.0812912	−	0.303383i	−0.913295	−	0.407299i	$-0.866471\pi$
$19$	0.354340	−	1.32242i	0.0812912	−	0.303383i	0.994586	+	0.103916i	$0.0331373\pi$
$20$	−4.70459	−	4.70459i	−1.05198	−	1.05198i
$21$	−4.47687	−	0.978568i	−0.976934	−	0.213541i
$22$	3.01126			0.642004
$23$	−2.87493	−	4.97952i	−0.599464	−	1.03830i	−0.992900	−	0.118950i	$-0.962047\pi$
$23$	−2.87493	−	4.97952i	−0.599464	−	1.03830i	0.393436	−	0.919352i	$-0.371286\pi$
$24$	2.46365	−	9.36202i	0.502890	−	1.91101i
$25$	−2.19554	−	1.26760i	−0.439108	−	0.253519i
$26$	1.98535	+	8.78353i	0.389359	+	1.72259i
$27$	−5.19568	+	0.0698330i	−0.999910	+	0.0134394i
$28$	−10.6984	+	3.35543i	−2.02182	+	0.634117i
$29$			10.4846i			1.94695i	0.228798	+	0.973474i	$0.426520\pi$
$29$			10.4846i			1.94695i	−0.228798	+	0.973474i	$0.573480\pi$
$30$	0.0304256	+	6.79149i	0.00555493	+	1.23995i
$31$	−1.26381	+	0.338636i	−0.226986	+	0.0608208i	−0.370519	−	0.928825i	$-0.620820\pi$
$31$	−1.26381	+	0.338636i	−0.226986	+	0.0608208i	0.143533	+	0.989646i	$0.454154\pi$
$32$	−0.651571	−	2.43170i	−0.115183	−	0.429867i
$33$	−1.48325	−	1.47002i	−0.258200	−	0.255897i
$34$	0.0636693	−	0.0636693i	0.0109192	−	0.0109192i
$35$	3.50661	−	2.22651i	0.592725	−	0.376349i
$36$	−10.9529	+	6.45517i	−1.82548	+	1.07586i
$37$	−9.47419	−	2.53860i	−1.55755	−	0.417343i	−0.625661	−	0.780095i	$-0.715171\pi$
$37$	−9.47419	−	2.53860i	−1.55755	−	0.417343i	−0.931886	+	0.362752i	$0.881837\pi$
$38$	−1.70967	+	2.96123i	−0.277345	+	0.480375i
$39$	3.30997	−	5.29567i	0.530019	−	0.847986i
$40$	4.38743	+	7.59925i	0.693713	+	1.20155i
$41$	−2.92653	+	2.92653i	−0.457048	+	0.457048i	−0.897685	−	0.440637i	$-0.854752\pi$
$41$	−2.92653	+	2.92653i	−0.457048	+	0.457048i	0.440637	+	0.897685i	$0.354752\pi$
$42$	10.1677	+	5.25470i	1.56892	+	0.810817i
$43$			4.27650i			0.652160i	0.945342	+	0.326080i	$0.105728\pi$
$43$			4.27650i			0.652160i	−0.945342	+	0.326080i	$0.894272\pi$
$44$	−4.93538	−	1.32243i	−0.744037	−	0.199364i
$45$	3.30044	−	3.36012i	0.492000	−	0.500897i
$46$	3.71681	+	13.8713i	0.548014	+	2.04522i
$47$	−0.106809	+	0.398617i	−0.0155797	+	0.0581443i	−0.973278	−	0.229630i	$-0.926249\pi$
$47$	−0.106809	+	0.398617i	−0.0155797	+	0.0581443i	0.957698	+	0.287774i	$0.0929152\pi$
$48$	−4.71210	+	8.24670i	−0.680133	+	1.19031i
$49$	−0.589001	−	6.97518i	−0.0841430	−	0.996454i
$50$	4.47727	+	4.47727i	0.633182	+	0.633182i
$51$	−0.0624430		0.000279742i	−0.00874377		3.91717e-5i
$52$	0.603453	−	15.2679i	0.0836839	−	2.11727i
$53$	−7.13704	−	4.12057i	−0.980348	−	0.566004i	−0.0779726	−	0.996956i	$-0.524845\pi$
$53$	−7.13704	−	4.12057i	−0.980348	−	0.566004i	−0.902375	+	0.430952i	$0.858178\pi$
$54$	12.5796	+	3.19012i	1.71186	+	0.434120i
$55$	1.89288			0.255236
$56$	14.7745	−	0.622688i	1.97432	−	0.0832102i
$57$	2.28772	−	0.623990i	0.303016	−	0.0826495i
$58$	6.77746	−	25.2938i	0.889924	−	3.32124i
$59$	7.56335	−	2.02659i	0.984665	−	0.263840i	0.269657	−	0.962956i	$-0.413090\pi$
$59$	7.56335	−	2.02659i	0.984665	−	0.263840i	0.715008	+	0.699116i	$0.246423\pi$
$60$	2.93270	−	11.1444i	0.378609	−	1.43874i
$61$	5.41126	+	9.37258i	0.692841	+	1.20004i	0.970903	+	0.239473i	$0.0769745\pi$
$61$	5.41126	+	9.37258i	0.692841	+	1.20004i	−0.278062	+	0.960563i	$0.589692\pi$
$62$	3.26779			0.415010
$63$	−2.44309	−	7.55191i	−0.307801	−	0.951451i
$64$		−	4.67977i		−	0.584971i
$65$	1.24799	+	5.52132i	0.154794	+	0.684836i
$66$	2.62804	+	4.50517i	0.323489	+	0.554548i
$67$	3.10471	−	0.831905i	0.379301	−	0.101633i	−0.0641309	−	0.997941i	$-0.520428\pi$
$67$	3.10471	−	0.831905i	0.379301	−	0.101633i	0.443432	+	0.896308i	$0.353761\pi$
$68$	−0.132313	+	0.0763912i	−0.0160454	+	0.00926379i
$69$	4.94083	−	8.64701i	0.594806	−	1.04098i
$70$	−9.89883	+	3.10464i	−1.18314	+	0.371076i
$71$	5.73066	−	5.73066i	0.680105	−	0.680105i	−0.279919	−	0.960024i	$-0.590308\pi$
$71$	5.73066	−	5.73066i	0.680105	−	0.680105i	0.960024	+	0.279919i	$0.0903076\pi$
$72$	16.1567	−	4.48470i	1.90408	−	0.528527i
$73$	3.30991	+	12.3528i	0.387396	+	1.44578i	0.834356	+	0.551227i	$0.185840\pi$
$73$	3.30991	+	12.3528i	0.387396	+	1.44578i	−0.446960	+	0.894554i	$0.647493\pi$
$74$	21.2152	+	12.2486i	2.46621	+	1.42387i
$75$	−0.0196717	−	4.39104i	−0.00227149	−	0.507034i
$76$	4.10256	−	4.10256i	0.470596	−	0.470596i
$77$	1.47722	−	2.82727i	0.168345	−	0.322197i
$78$	−11.4084	+	10.6360i	−1.29175	+	1.20429i
$79$	1.15250	+	1.99619i	0.129667	+	0.224589i	0.923547	−	0.383484i	$-0.125276\pi$
$79$	1.15250	+	1.99619i	0.129667	+	0.224589i	−0.793881	+	0.608073i	$0.791943\pi$
$80$	−2.22823	−	8.31585i	−0.249123	−	0.929740i
$81$	−4.63894	−	7.71234i	−0.515438	−	0.856927i
$82$	8.95193	−	5.16840i	0.988575	−	0.570754i
$83$	−9.19760	+	9.19760i	−1.00957	+	1.00957i	−0.00961355	+	0.999954i	$0.503060\pi$
$83$	−9.19760	+	9.19760i	−1.00957	+	1.00957i	−0.999954	+	0.00961355i	$0.996940\pi$
$84$	−14.3570	−	13.0776i	−1.56648	−	1.42688i
$85$	0.0400225	−	0.0400225i	0.00434105	−	0.00434105i
$86$	2.76441	−	10.3169i	0.298094	−	1.11250i
$87$	−15.6861	+	9.15032i	−1.68173	+	0.981018i
$88$	5.83593	+	3.36938i	0.622113	+	0.359177i
$89$	−1.95890	+	7.31073i	−0.207643	+	0.774936i	0.780984	+	0.624551i	$0.214718\pi$
$89$	−1.95890	+	7.31073i	−0.207643	+	0.774936i	−0.988628	+	0.150385i	$0.951949\pi$
$90$	−10.1342	+	5.97270i	−1.06824	+	0.629578i
$91$	9.22078	+	2.44485i	0.966600	+	0.256290i
$92$		−	24.3670i		−	2.54044i
$93$	−1.60960	−	1.59525i	−0.166908	−	0.165419i
$94$	0.515347	−	0.892608i	0.0531540	−	0.0920655i
$95$	−1.07470	+	1.86143i	−0.110261	+	0.190978i
$96$	3.06942	−	3.09705i	0.313272	−	0.316091i
$97$	12.3676	+	12.3676i	1.25574	+	1.25574i	0.953106	+	0.302635i	$0.0978664\pi$
$97$	12.3676	+	12.3676i	1.25574	+	1.25574i	0.302635	+	0.953106i	$0.402134\pi$
$98$	−3.08794	+	17.2081i	−0.311929	+	1.73828i
$99$	0.904816	−	3.50203i	0.0909375	−	0.351968i
$100$	−5.37188	−	9.30437i	−0.537188	−	0.930437i
$101$	2.70146	−	4.67907i	0.268805	−	0.465585i	−0.699748	−	0.714390i	$-0.746704\pi$
$101$	2.70146	−	4.67907i	0.268805	−	0.465585i	0.968554	+	0.248805i	$0.0800378\pi$
$102$	0.150823	+	0.0396894i	0.0149337	+	0.00392984i
$103$	−13.0145	+	7.51391i	−1.28236	+	0.740368i	−0.977278	−	0.211960i	$-0.932015\pi$
$103$	−13.0145	+	7.51391i	−1.28236	+	0.740368i	−0.305077	+	0.952328i	$0.598682\pi$
$104$	−5.98043	+	19.2442i	−0.586430	+	1.88705i
$105$	6.39144	+	3.30310i	0.623741	+	0.322349i
$106$	14.5543	+	14.5543i	1.41363	+	1.41363i
$107$	13.8001	−	7.96747i	1.33410	−	0.770244i	0.348177	−	0.937429i	$-0.386801\pi$
$107$	13.8001	−	7.96747i	1.33410	−	0.770244i	0.985926	+	0.167185i	$0.0534676\pi$
$108$	−19.2166	−	10.7530i	−1.84912	−	1.03470i
$109$	−5.35365	+	1.43451i	−0.512787	+	0.137401i	−0.505928	−	0.862576i	$-0.668850\pi$
$109$	−5.35365	+	1.43451i	−0.512787	+	0.137401i	−0.00685882	+	0.999976i	$0.502183\pi$
$110$	−4.56651	−	1.22359i	−0.435399	−	0.116665i
$111$	−4.47046	−	16.3899i	−0.424317	−	1.55566i
$112$	−14.1598	−	3.16161i	−1.33797	−	0.298744i
$113$		−	7.44891i		−	0.700734i	−0.936612	−	0.350367i	$-0.886057\pi$
$113$		−	7.44891i		−	0.700734i	0.936612	−	0.350367i	$-0.113943\pi$
$114$	−5.92240	+	0.0265321i	−0.554684	+	0.00248496i
$115$	2.33639	+	8.71951i	0.217869	+	0.813099i
$116$	−22.2162	+	38.4795i	−2.06272	+	3.57273i
$117$	10.8116	+	0.330332i	0.999534	+	0.0305392i
$118$	−19.5564			−1.80031
$119$	−0.0285450	−	0.0910128i	−0.00261672	−	0.00834313i
$120$	−7.54020	+	13.1962i	−0.688323	+	1.20464i
$121$	−8.26737	+	4.77317i	−0.751579	+	0.433925i
$122$	−6.99588	−	26.1090i	−0.633377	−	2.36379i
$123$	−6.93250	−	1.82431i	−0.625082	−	0.164492i
$124$	−5.35582	−	1.43509i	−0.480967	−	0.128875i
$125$	8.36509	+	8.36509i	0.748197	+	0.748197i
$126$	1.01218	+	19.7980i	0.0901725	+	1.76374i
$127$		−	6.26805i		−	0.556199i	−0.960552	−	0.278100i	$-0.910295\pi$
$127$		−	6.26805i		−	0.556199i	0.960552	−	0.278100i	$-0.0897045\pi$
$128$	−4.32823	+	16.1532i	−0.382565	+	1.42775i
$129$	−6.39809	+	3.73226i	−0.563321	+	0.328607i
$130$	0.558351	−	14.1267i	0.0489706	−	1.23900i
$131$	0.222042	−	0.128196i	0.0193999	−	0.0112006i	−0.490269	−	0.871571i	$-0.663101\pi$
$131$	0.222042	−	0.128196i	0.0193999	−	0.0112006i	0.509669	+	0.860371i	$0.329768\pi$
$132$	−2.32879	−	8.53798i	−0.202695	−	0.743136i
$133$	1.94159	+	3.05788i	0.168357	+	0.265152i
$134$	−8.02777			−0.693494
$135$	7.90750	+	2.00530i	0.680569	+	0.172589i
$136$	0.194634	−	0.0521522i	0.0166898	−	0.00447201i
$137$	1.29326	−	0.346527i	0.110490	−	0.0296058i	−0.203150	−	0.979148i	$-0.565118\pi$
$137$	1.29326	−	0.346527i	0.110490	−	0.0296058i	0.313641	+	0.949542i	$0.398451\pi$
$138$	−17.5092	+	17.6668i	−1.49048	+	1.50389i
$139$	19.1985			1.62840			0.814200	−	0.580585i	$-0.197176\pi$
$139$	19.1985			1.62840			0.814200	+	0.580585i	$0.197176\pi$
$140$	17.5874	−	0.741241i	1.48640	−	0.0626463i
$141$	−0.689590	+	0.188090i	−0.0580740	+	0.0158401i
$142$	−17.5294	+	10.1206i	−1.47104	+	0.849304i
$143$	2.95009	+	3.19289i	0.246699	+	0.267003i
$144$	−16.4504	+	0.147397i	−1.37086	+	0.0122831i
$145$	4.26031	−	15.8997i	0.353799	−	1.32040i
$146$		−	31.9402i		−	2.64339i
$147$	9.92155	−	6.96870i	0.818316	−	0.574769i
$148$	−29.3920	−	29.3920i	−2.41600	−	2.41600i
$149$	−2.23177	−	0.598001i	−0.182834	−	0.0489901i	0.166240	−	0.986085i	$-0.446837\pi$
$149$	−2.23177	−	0.598001i	−0.182834	−	0.0489901i	−0.349074	+	0.937095i	$0.613504\pi$
$150$	−2.79099	+	10.6059i	−0.227883	+	0.865972i
$151$	−3.87535	−	14.4630i	−0.315371	−	1.17698i	−0.923643	−	0.383253i	$-0.874804\pi$
$151$	−3.87535	−	14.4630i	−0.315371	−	1.17698i	0.608272	−	0.793729i	$-0.291863\pi$
$152$	−6.62679	+	3.82598i	−0.537504	+	0.310328i
$153$	−0.0549148	−	0.0931772i	−0.00443960	−	0.00753293i
$154$	−5.39134	+	5.86579i	−0.434447	+	0.472678i
$155$	2.05413			0.164992
$156$	23.3690	−	12.4220i	1.87102	−	0.994555i
$157$	−3.71827	+	6.44023i	−0.296750	+	0.513986i	−0.975390	−	0.220484i	$-0.929236\pi$
$157$	−3.71827	+	6.44023i	−0.296750	+	0.513986i	0.678640	+	0.734471i	$0.262570\pi$
$158$	−1.49000	−	5.56075i	−0.118538	−	0.442389i
$159$	−0.0639466	−	14.2739i	−0.00507130	−	1.13200i
$160$			3.95237i			0.312462i
$161$	14.8471	+	3.31508i	1.17011	+	0.261265i
$162$	6.20589	+	21.6045i	0.487580	+	1.69741i
$163$	−3.78189	−	1.01335i	−0.296220	−	0.0793720i	0.107648	−	0.994189i	$-0.465668\pi$
$163$	−3.78189	−	1.01335i	−0.296220	−	0.0793720i	−0.403868	+	0.914817i	$0.632335\pi$
$164$	−16.9417	+	4.53952i	−1.32293	+	0.354477i
$165$	1.65198	+	2.83195i	0.128607	+	0.220467i
$166$	28.1344	−	16.2434i	2.18365	−	1.26073i
$167$	2.45941	+	2.45941i	0.190315	+	0.190315i	0.795832	−	0.605517i	$-0.207034\pi$
$167$	2.45941	+	2.45941i	0.190315	+	0.190315i	−0.605517	+	0.795832i	$0.707034\pi$
$168$	13.8258	+	21.5607i	1.06669	+	1.66345i
$169$	−7.36829	+	10.7102i	−0.566792	+	0.823861i
$170$	−0.122424	+	0.0706816i	−0.00938951	+	0.00542103i
$171$	2.93013	+	2.87809i	0.224073	+	0.220093i
$172$	−9.06158	+	15.6951i	−0.690939	+	1.19674i
$173$	−7.04136	−	12.1960i	−0.535344	−	0.927244i	−0.999147	−	0.0413048i	$-0.986849\pi$
$173$	−7.04136	−	12.1960i	−0.535344	−	0.927244i	0.463802	−	0.885939i	$-0.346485\pi$
$174$	43.7572	−	11.9351i	3.31722	−	0.904794i
$175$	6.40009	−	2.00731i	0.483801	−	0.151738i
$176$	−4.67507	−	4.67507i	−0.352396	−	0.352396i
$177$	9.63281	+	9.54689i	0.724047	+	0.717588i
$178$	9.45158	−	16.3706i	0.708426	−	1.22703i
$179$	−9.70396	+	16.8077i	−0.725308	+	1.25627i	0.233539	+	0.972347i	$0.424969\pi$
$179$	−9.70396	+	16.8077i	−0.725308	+	1.25627i	−0.958847	+	0.283923i	$0.908364\pi$
$180$	19.2327	−	5.33854i	1.43352	−	0.397911i
$181$		−	1.45258i		−	0.107969i	−0.998542	−	0.0539846i	$-0.982808\pi$
$181$		−	1.45258i		−	0.107969i	0.998542	−	0.0539846i	$-0.0171922\pi$
$182$	−20.6644	−	11.8586i	−1.53175	−	0.879018i
$183$	−9.29976	+	16.2756i	−0.687458	+	1.20313i
$184$	−8.31767	+	31.0420i	−0.613187	+	2.28844i
$185$	13.3358	+	7.69945i	0.980470	+	0.566075i
$186$	2.85192	+	4.88896i	0.209113	+	0.358476i
$187$	0.0112501	−	0.0419858i	0.000822687	−	0.00307031i
$188$	−1.23664	+	1.23664i	−0.0901912	+	0.0901912i
$189$	9.16627	−	10.2459i	0.666748	−	0.745283i
$190$	3.79593	−	3.79593i	0.275386	−	0.275386i
$191$	−11.9389	+	6.89292i	−0.863867	+	0.498754i	−0.865305	−	0.501245i	$-0.832876\pi$
$191$	−11.9389	+	6.89292i	−0.863867	+	0.498754i	0.00143823	+	0.999999i	$0.499542\pi$
$192$	7.00143	−	4.08420i	0.505284	−	0.294752i
$193$	−0.977701	−	3.64883i	−0.0703764	−	0.262648i	0.921769	−	0.387740i	$-0.126744\pi$
$193$	−0.977701	−	3.64883i	−0.0703764	−	0.262648i	−0.992145	+	0.125092i	$0.960078\pi$
$194$	−21.8418	−	37.8311i	−1.56815	−	2.71612i
$195$	−7.17131	+	6.68579i	−0.513548	+	0.478779i
$196$	12.6182	−	26.8475i	0.901299	−	1.91768i
$197$	−11.8814	+	11.8814i	−0.846517	+	0.846517i	−0.989697	−	0.143180i	$-0.954267\pi$
$197$	−11.8814	+	11.8814i	−0.846517	+	0.846517i	0.143180	+	0.989697i	$0.454267\pi$
$198$	−4.44662	+	7.86365i	−0.316007	+	0.558845i
$199$	−5.29617	−	3.05774i	−0.375435	−	0.216758i	0.300395	−	0.953815i	$-0.402881\pi$
$199$	−5.29617	−	3.05774i	−0.375435	−	0.216758i	−0.675830	+	0.737057i	$0.736215\pi$
$200$	3.66738	+	13.6868i	0.259323	+	0.967806i
$201$	3.95421	+	3.91894i	0.278909	+	0.276421i
$202$	−9.54182	+	9.54182i	−0.671360	+	0.671360i
$203$	−20.4235	−	18.7716i	−1.43345	−	1.31751i
$204$	−0.229764	−	0.131285i	−0.0160867	−	0.00919182i
$205$	5.62718	−	3.24885i	0.393019	−	0.226910i
$206$	36.2541	−	9.71426i	2.52594	−	0.676825i
$207$	17.2489	−	0.154552i	1.19888	−	0.0107421i
$208$	10.5544	−	16.7190i	0.731813	−	1.15925i
$209$			1.65065i			0.114178i
$210$	−13.2839	−	12.1002i	−0.916679	−	0.834990i
$211$	−17.6101			−1.21233			−0.606165	−	0.795339i	$-0.707293\pi$
$211$	−17.6101			−1.21233			−0.606165	+	0.795339i	$0.707293\pi$
$212$	−17.4624	−	30.2457i	−1.19932	−	2.07728i
$213$	13.5750	+	3.57232i	0.930146	+	0.244771i
$214$	−38.4425	+	10.3006i	−2.62788	+	0.704137i
$215$	1.73771	−	6.48520i	0.118511	−	0.442287i
$216$	20.8101	+	20.2581i	1.41595	+	1.37839i
$217$	1.60306	−	3.06812i	0.108823	−	0.208277i
$218$	13.8428			0.937553
$219$	−15.5923	+	15.7327i	−1.05363	+	1.06312i
$220$	6.94703	+	4.01087i	0.468369	+	0.270413i
$221$	0.129885	+	0.00513364i	0.00873704	+	0.000345326i
$222$	0.190084	+	42.4299i	0.0127576	+	2.84771i
$223$	−10.9938	−	10.9938i	−0.736200	−	0.736200i	0.235641	−	0.971840i	$-0.424281\pi$
$223$	−10.9938	−	10.9938i	−0.736200	−	0.736200i	−0.971840	+	0.235641i	$0.924281\pi$
$224$	5.90339	+	3.08446i	0.394437	+	0.206089i
$225$	6.55229	−	3.86165i	0.436819	−	0.257443i
$226$	−4.81511	+	17.9702i	−0.320296	+	1.19536i
$227$	1.89023	+	7.05442i	0.125459	+	0.468218i	0.999856	−	0.0169930i	$-0.00540930\pi$
$227$	1.89023	+	7.05442i	0.125459	+	0.468218i	−0.874397	+	0.485211i	$0.838743\pi$
$228$	9.71831	+	2.55741i	0.643611	+	0.169368i
$229$	15.2787	+	4.09391i	1.00964	+	0.270533i	0.725480	−	0.688243i	$-0.241618\pi$
$229$	15.2787	+	4.09391i	1.00964	+	0.270533i	0.284163	+	0.958776i	$0.408284\pi$
$230$		−	22.5458i		−	1.48663i
$231$	5.51911	−	0.257384i	0.363131	−	0.0169346i
$232$	41.4368	−	41.4368i	2.72046	−	2.72046i
$233$	3.48710	+	6.03983i	0.228447	+	0.395682i	0.957348	−	0.288937i	$-0.0933018\pi$
$233$	3.48710	+	6.03983i	0.228447	+	0.395682i	−0.728901	+	0.684619i	$0.759968\pi$
$234$	−25.8691	−	7.78574i	−1.69112	−	0.508970i
$235$	0.323947	−	0.561093i	0.0211320	−	0.0366017i
$236$	32.0524	+	8.58840i	2.08643	+	0.559057i
$237$	−1.98068	+	3.46641i	−0.128659	+	0.225168i
$238$	0.0100315	+	0.238017i	0.000650248	+	0.0154284i
$239$	13.0198	−	13.0198i	0.842178	−	0.842178i	−0.146964	−	0.989142i	$-0.546950\pi$
$239$	13.0198	−	13.0198i	0.842178	−	0.842178i	0.989142	+	0.146964i	$0.0469500\pi$
$240$	10.4967	−	10.5912i	0.677561	−	0.683659i
$241$	1.29014	+	4.81487i	0.0831053	+	0.310153i	0.994949	−	0.100385i	$-0.0320075\pi$
$241$	1.29014	+	4.81487i	0.0831053	+	0.310153i	−0.911843	+	0.410538i	$0.865341\pi$
$242$	23.0302	−	6.17093i	1.48044	−	0.396682i
$243$	7.48990	−	13.6712i	0.480478	−	0.877007i
$244$			45.8642i			2.93616i
$245$	−1.94108	+	10.8170i	−0.124011	+	0.691074i
$246$	15.5451	+	8.88238i	0.991122	+	0.566320i
$247$	−4.81477	+	1.08829i	−0.306357	+	0.0692461i
$248$	6.33309	+	3.65641i	0.402152	+	0.232182i
$249$	−21.7877	−	5.73349i	−1.38074	−	0.363345i
$250$	−14.7732	−	25.5879i	−0.934336	−	1.61832i
$251$	−13.9661			−0.881532			−0.440766	−	0.897622i	$-0.645293\pi$
$251$	−13.9661			−0.881532			−0.440766	+	0.897622i	$0.645293\pi$
$252$	7.03557	−	32.8929i	0.443199	−	2.07206i
$253$	4.90200	+	4.90200i	0.308186	+	0.308186i
$254$	−4.05178	+	15.1215i	−0.254231	+	0.948804i
$255$	0.0948070	+	0.0249488i	0.00593704	+	0.00156235i
$256$	16.2037	−	28.0655i	1.01273	−	1.75410i
$257$	5.91465	+	10.2445i	0.368945	+	0.639032i	0.989401	−	0.145209i	$-0.0463856\pi$
$257$	5.91465	+	10.2445i	0.368945	+	0.639032i	−0.620456	+	0.784242i	$0.713052\pi$
$258$	17.8478	−	4.86810i	1.11115	−	0.303075i
$259$	21.9076	−	13.9101i	1.36127	−	0.864334i
$260$	−7.11904	+	22.9081i	−0.441504	+	1.42070i
$261$	−27.3797	−	15.4823i	−1.69476	−	0.958328i
$262$	−0.618538	+	0.165737i	−0.0382134	+	0.0102393i
$263$	−11.4822	−	6.62925i	−0.708023	−	0.408777i	0.102306	−	0.994753i	$-0.467378\pi$
$263$	−11.4822	−	6.62925i	−0.708023	−	0.408777i	−0.810329	+	0.585976i	$0.800711\pi$
$264$	0.0522889	+	11.6718i	0.00321816	+	0.718347i
$265$	9.14879	+	9.14879i	0.562006	+	0.562006i
$266$	−2.70735	−	8.63210i	−0.165998	−	0.529268i
$267$	−12.6472	+	3.44961i	−0.773998	+	0.211113i
$268$	13.1573	+	3.52549i	0.803710	+	0.215353i
$269$	2.34154	+	1.35189i	0.142766	+	0.0824259i	0.569682	−	0.821866i	$-0.307067\pi$
$269$	2.34154	+	1.35189i	0.142766	+	0.0824259i	−0.426916	+	0.904291i	$0.640400\pi$
$270$	−17.7803	−	9.94928i	−1.08208	−	0.605494i
$271$	−16.1143	−	4.31781i	−0.978874	−	0.262289i	−0.266304	−	0.963889i	$-0.585802\pi$
$271$	−16.1143	−	4.31781i	−0.978874	−	0.262289i	−0.712570	+	0.701601i	$0.752469\pi$
$272$	−0.197697			−0.0119871
$273$	4.38956	+	15.9290i	0.265668	+	0.964065i
$274$	−3.34394			−0.202015
$275$	2.95247	+	0.791113i	0.178041	+	0.0477059i
$276$	36.4556	−	21.2660i	2.19437	−	1.28006i
$277$	15.2886	+	8.82686i	0.918601	+	0.530354i	0.883188	−	0.469018i	$-0.155392\pi$
$277$	15.2886	+	8.82686i	0.918601	+	0.530354i	0.0354123	+	0.999373i	$0.488726\pi$
$278$	−46.3158	−	12.4103i	−2.77784	−	0.744320i
$279$	0.981897	−	3.80037i	0.0587846	−	0.227522i
$280$	−22.6581	−	5.05914i	−1.35408	−	0.302342i
$281$	−3.81908	−	3.81908i	−0.227827	−	0.227827i	0.583957	−	0.811784i	$-0.301504\pi$
$281$	−3.81908	−	3.81908i	−0.227827	−	0.227827i	−0.811784	+	0.583957i	$0.801504\pi$
$282$	1.78520	−	0.00799761i	0.106307	−	0.000476251i
$283$	−7.52530	−	4.34473i	−0.447332	−	0.258268i	0.259370	−	0.965778i	$-0.416485\pi$
$283$	−7.52530	−	4.34473i	−0.447332	−	0.258268i	−0.706703	+	0.707510i	$0.749818\pi$
$284$	33.1749	−	8.88918i	1.96857	−	0.527476i
$285$	−3.72282	+	0.0166781i	−0.220521	+	0.000987923i
$286$	−5.05305	−	9.60973i	−0.298793	−	0.568235i
$287$	−0.461095	−	10.9404i	−0.0272176	−	0.645790i
$288$	7.31231	+	1.88927i	0.430882	+	0.111326i
$289$	8.49935	+	14.7213i	0.499962	+	0.865959i
$290$	−20.5557	+	35.6035i	−1.20707	+	2.09071i
$291$	−7.70959	+	29.2969i	−0.451944	+	1.71742i
$292$	−14.0269	+	52.3491i	−0.820862	+	3.06350i
$293$	16.1414	+	16.1414i	0.942993	+	0.942993i	0.998460	−	0.0554676i	$-0.0176649\pi$
$293$	16.1414	+	16.1414i	0.942993	+	0.942993i	−0.0554676	+	0.998460i	$0.517665\pi$
$294$	−28.4401	+	10.3983i	−1.65866	+	0.606440i
$295$	−12.2931			−0.715733
$296$	27.4105	+	47.4763i	1.59320	+	2.75951i
$297$	6.02908	−	1.70265i	0.349843	−	0.0987980i
$298$	4.99751	+	2.88531i	0.289498	+	0.167142i
$299$	−11.0667	+	17.5305i	−0.640002	+	1.01382i
$300$	9.23208	−	16.1572i	0.533015	−	0.932835i
$301$	−8.33040	−	7.65661i	−0.480156	−	0.441319i
$302$			37.3966i			2.15193i
$303$	9.35804	−	0.0419236i	0.537605	−	0.00240845i
$304$	7.25169	−	1.94308i	0.415913	−	0.111444i
$305$	−4.39760	−	16.4121i	−0.251806	−	0.939753i
$306$	0.0722487	+	0.260285i	0.00413019	+	0.0148795i
$307$	−3.45895	+	3.45895i	−0.197413	+	0.197413i	−0.798890	−	0.601477i	$-0.794579\pi$
$307$	−3.45895	+	3.45895i	−0.197413	+	0.197413i	0.601477	+	0.798890i	$0.294579\pi$
$308$	11.4123	−	7.24620i	0.650276	−	0.412890i
$309$	−22.5998	−	12.9134i	−1.28566	−	0.734616i
$310$	−4.95552	−	1.32783i	−0.281455	−	0.0754156i
$311$	8.03426	−	13.9157i	0.455581	−	0.789090i	−0.543140	−	0.839642i	$-0.682765\pi$
$311$	8.03426	−	13.9157i	0.455581	−	0.789090i	0.998721	+	0.0505523i	$0.0160982\pi$
$312$	−34.0108	+	7.84780i	−1.92548	+	0.444294i
$313$	−10.5954	−	18.3517i	−0.598886	−	1.03730i	−0.992986	−	0.118234i	$-0.962277\pi$
$313$	−10.5954	−	18.3517i	−0.598886	−	1.03730i	0.394100	−	0.919068i	$-0.371056\pi$
$314$	13.1333	−	13.1333i	0.741154	−	0.741154i
$315$	0.636258	+	12.4450i	0.0358491	+	0.701196i
$316$			9.76826i			0.549508i
$317$	−7.43321	−	1.99172i	−0.417490	−	0.111866i	0.0439577	−	0.999033i	$-0.486003\pi$
$317$	−7.43321	−	1.99172i	−0.417490	−	0.111866i	−0.461448	+	0.887167i	$0.652670\pi$
$318$	−9.07266	+	34.4767i	−0.508770	+	1.93336i
$319$	−3.27176	−	12.2104i	−0.183183	−	0.683649i
$320$	−1.90157	+	7.09675i	−0.106301	+	0.396720i
$321$	23.9640	+	13.6928i	1.33754	+	0.764260i
$322$	−33.6752	−	17.5950i	−1.87664	−	0.980528i
$323$	0.0349009	+	0.0349009i	0.00194194	+	0.00194194i
$324$	−0.683433	−	38.1345i	−0.0379685	−	2.11858i
$325$	−0.361002	+	9.13364i	−0.0200248	+	0.506643i
$326$	8.46862	+	4.88936i	0.469034	+	0.270797i
$327$	−6.81850	−	6.75768i	−0.377064	−	0.373701i
$328$	23.1322			1.27726
$329$	−0.585256	−	0.921740i	−0.0322662	−	0.0508172i
$330$	−2.15474	−	7.89985i	−0.118614	−	0.434872i
$331$	−1.45525	+	5.43106i	−0.0799876	+	0.298518i	−0.994318	−	0.106451i	$-0.966051\pi$
$331$	−1.45525	+	5.43106i	−0.0799876	+	0.298518i	0.914330	+	0.404969i	$0.132718\pi$
$332$	−53.2450	+	14.2669i	−2.92220	+	0.783001i
$333$	20.6195	−	20.9923i	1.12994	−	1.15037i
$334$	−4.34343	−	7.52304i	−0.237662	−	0.411642i
$335$	−5.04625			−0.275706
$336$	−7.62764	−	23.9437i	−0.416122	−	1.30624i
$337$			0.688603i			0.0375106i	0.999824	+	0.0187553i	$0.00597034\pi$
$337$			0.688603i			0.0375106i	−0.999824	+	0.0187553i	$0.994030\pi$
$338$	24.6990	−	21.0750i	1.34345	−	1.14633i
$339$	11.1443	−	6.50093i	0.605278	−	0.353082i
$340$	0.231691	−	0.0620813i	0.0125652	−	0.00336683i
$341$	1.36615	−	0.788748i	0.0739812	−	0.0427131i
$342$	−5.20839	−	8.83738i	−0.281638	−	0.477871i
$343$	14.6418	+	11.3409i	0.790584	+	0.612354i
$344$	16.9014	−	16.9014i	0.911261	−	0.911261i
$345$	−11.0063	+	11.1053i	−0.592557	+	0.597890i
$346$	9.10332	+	33.9741i	0.489398	+	1.82646i
$347$	−20.6195	−	11.9047i	−1.10691	−	0.639076i	−0.168884	−	0.985636i	$-0.554016\pi$
$347$	−20.6195	−	11.9047i	−1.10691	−	0.639076i	−0.938028	+	0.346560i	$0.887350\pi$
$348$	−76.9582	+	0.344770i	−4.12539	+	0.0184816i
$349$	2.59131	−	2.59131i	0.138710	−	0.138710i	−0.634342	−	0.773052i	$-0.718729\pi$
$349$	2.59131	−	2.59131i	0.138710	−	0.138710i	0.773052	+	0.634342i	$0.218729\pi$
$350$	−16.7376	+	0.705425i	−0.894660	+	0.0377065i
$351$	8.94147	+	16.4636i	0.477261	+	0.878762i
$352$	1.51763	+	2.62862i	0.0808902	+	0.140106i
$353$	−4.54981	−	16.9801i	−0.242162	−	0.903760i	−0.974789	−	0.223130i	$-0.928373\pi$
$353$	−4.54981	−	16.9801i	−0.242162	−	0.903760i	0.732627	−	0.680630i	$-0.238294\pi$
$354$	−17.0676	−	29.2584i	−0.907130	−	1.55506i
$355$	−11.0190	+	6.36182i	−0.584827	+	0.337650i
$356$	−22.6802	+	22.6802i	−1.20205	+	1.20205i
$357$	0.111253	−	0.122137i	0.00588811	−	0.00646415i
$358$	34.2753	−	34.2753i	1.81151	−	1.81151i
$359$	3.65645	−	13.6461i	0.192980	−	0.720211i	−0.799801	−	0.600266i	$-0.795061\pi$
$359$	3.65645	−	13.6461i	0.192980	−	0.720211i	0.992781	−	0.119945i	$-0.0382719\pi$
$360$	−26.3235	+	0.235861i	−1.38737	+	0.0124310i
$361$	14.8313	+	8.56283i	0.780592	+	0.450675i
$362$	−0.938973	+	3.50429i	−0.0493513	+	0.184182i
$363$	−14.3564	−	8.20314i	−0.753516	−	0.430553i
$364$	28.6606	+	28.5109i	1.50222	+	1.49438i
$365$		−	20.0776i		−	1.05091i
$366$	32.9562	−	33.2528i	1.72265	−	1.73815i
$367$	10.2912	−	17.8249i	0.537196	−	0.930450i	−0.461858	−	0.886954i	$-0.652817\pi$
$367$	10.2912	−	17.8249i	0.537196	−	0.930450i	0.999054	−	0.0434961i	$-0.0138496\pi$
$368$	15.7652	−	27.3061i	0.821816	−	1.42343i
$369$	−3.32088	−	11.9639i	−0.172878	−	0.622815i
$370$	−27.1952	−	27.1952i	−1.41381	−	1.41381i
$371$	20.8047	−	6.52515i	1.08013	−	0.338769i
$372$	−2.52718	−	9.26532i	−0.131028	−	0.480385i
$373$	7.56634	+	13.1053i	0.391770	+	0.678566i	0.992683	−	0.120749i	$-0.0385295\pi$
$373$	7.56634	+	13.1053i	0.391770	+	0.678566i	−0.600913	+	0.799314i	$0.705196\pi$
$374$	−0.0542808	+	0.0940172i	−0.00280680	+	0.00486151i
$375$	−5.21454	+	19.8156i	−0.269278	+	1.02327i
$376$	1.99752	−	1.15327i	0.103014	−	0.0594754i
$377$	33.4592	−	17.5937i	1.72324	−	0.906124i
$378$	−28.7365	+	18.7928i	−1.47805	+	0.966595i
$379$	4.95373	+	4.95373i	0.254456	+	0.254456i	0.822795	−	0.568339i	$-0.192414\pi$
$379$	4.95373	+	4.95373i	0.254456	+	0.254456i	−0.568339	+	0.822795i	$0.692414\pi$
$380$	−7.88845	+	4.55440i	−0.404669	+	0.233636i
$381$	9.37766	−	5.47035i	0.480432	−	0.280255i
$382$	33.2579	−	8.91142i	1.70162	−	0.455948i
$383$	33.7026	+	9.03057i	1.72212	+	0.461441i	0.978344	−	0.206988i	$-0.0663660\pi$
$383$	33.7026	+	9.03057i	1.72212	+	0.461441i	0.743777	+	0.668428i	$0.233033\pi$
$384$	−27.9443	+	7.62198i	−1.42602	+	0.388957i
$385$	−3.38899	+	3.68723i	−0.172719	+	0.187919i
$386$			9.43468i			0.480213i
$387$	−11.1677	−	6.31494i	−0.567686	−	0.321007i
$388$	19.1842	+	71.5963i	0.973929	+	3.63475i
$389$	−16.1151	+	27.9122i	−0.817070	+	1.41521i	0.0907622	+	0.995873i	$0.471070\pi$
$389$	−16.1151	+	27.9122i	−0.817070	+	1.41521i	−0.907832	+	0.419334i	$0.862264\pi$
$390$	21.6224	−	11.4936i	1.09489	−	0.581999i
$391$	0.207293			0.0104833
$392$	−25.2391	+	29.8948i	−1.27477	+	1.50991i
$393$	0.385580	+	0.220317i	0.0194499	+	0.0111135i
$394$	36.3439	−	20.9832i	1.83098	−	1.05712i
$395$	−0.936611	−	3.49548i	−0.0471260	−	0.175877i
$396$	10.7413	−	10.9355i	0.539771	−	0.549531i
$397$	−17.3918	−	4.66013i	−0.872871	−	0.233885i	−0.205542	−	0.978648i	$-0.565896\pi$
$397$	−17.3918	−	4.66013i	−0.872871	−	0.233885i	−0.667329	+	0.744763i	$0.732562\pi$
$398$	10.8002	+	10.8002i	0.541367	+	0.541367i
$399$	−2.88041	+	5.57354i	−0.144201	+	0.279026i
$400$		−	13.9022i		−	0.695108i
$401$	5.92706	−	22.1201i	0.295983	−	1.10462i	−0.644450	−	0.764646i	$-0.722914\pi$
$401$	5.92706	−	22.1201i	0.295983	−	1.10462i	0.940434	−	0.339978i	$-0.110420\pi$
$402$	−7.00613	−	12.0104i	−0.349434	−	0.599024i
$403$	3.20141	+	3.46489i	0.159473	+	0.172598i
$404$	19.8292	−	11.4484i	0.986539	−	0.569578i
$405$	3.90102	+	13.5806i	0.193843	+	0.674823i
$406$	37.1367	+	58.4880i	1.84307	+	2.90271i
$407$	11.8258			0.586182
$408$	0.247890	+	0.245679i	0.0122724	+	0.0121629i
$409$	−13.2802	+	3.55843i	−0.656665	+	0.175953i	−0.571741	−	0.820434i	$-0.693732\pi$
$409$	−13.2802	+	3.55843i	−0.656665	+	0.175953i	−0.0849248	+	0.996387i	$0.527065\pi$
$410$	−15.6755	+	4.20024i	−0.774157	+	0.207435i
$411$	1.64711	+	1.63242i	0.0812460	+	0.0805213i
$412$	−63.6857			−3.13757
$413$	−9.59366	+	18.3614i	−0.472073	+	0.903506i
$414$	−41.7122	−	10.7771i	−2.05004	−	0.529667i
$415$	17.6853	−	10.2106i	0.868135	−	0.501218i
$416$	−6.66681	+	6.15984i	−0.326867	+	0.302011i
$417$	16.7553	+	28.7230i	0.820509	+	1.40657i
$418$	1.06701	−	3.98214i	0.0521893	−	0.194773i
$419$			11.5025i			0.561936i	0.959717	+	0.280968i	$0.0906554\pi$
$419$			11.5025i			0.561936i	−0.959717	+	0.280968i	$0.909345\pi$
$420$	16.4581	+	25.6656i	0.803073	+	1.25235i
$421$	−14.5632	−	14.5632i	−0.709769	−	0.709769i	0.256717	−	0.966487i	$-0.417359\pi$
$421$	−14.5632	−	14.5632i	−0.709769	−	0.709769i	−0.966487	+	0.256717i	$0.917359\pi$
$422$	42.4838	+	11.3835i	2.06808	+	0.554140i
$423$	−0.883233	−	0.867546i	−0.0429443	−	0.0421815i
$424$	11.9215	+	44.4918i	0.578961	+	2.16071i
$425$	0.0791534	−	0.0456992i	0.00383950	−	0.00221674i
$426$	−30.4401	−	17.3932i	−1.47483	−	0.842705i
$427$	−27.9456	−	6.23973i	−1.35238	−	0.301961i
$428$	67.5299			3.26418
$429$	−2.20225	+	7.20020i	−0.106325	+	0.347629i
$430$	−8.38431	+	14.5221i	−0.404327	+	0.700315i
$431$	−9.12622	−	34.0595i	−0.439594	−	1.64059i	−0.729826	−	0.683633i	$-0.760399\pi$
$431$	−9.12622	−	34.0595i	−0.439594	−	1.64059i	0.290232	−	0.956956i	$-0.406268\pi$
$432$	−14.5773	−	24.4828i	−0.701353	−	1.17793i
$433$		−	22.4893i		−	1.08077i	−0.841418	−	0.540384i	$-0.818279\pi$
$433$		−	22.4893i		−	1.08077i	0.841418	−	0.540384i	$-0.181721\pi$
$434$	−5.85062	+	6.36548i	−0.280839	+	0.305553i
$435$	27.5057	−	7.50237i	1.31880	−	0.359711i
$436$	−22.6880	−	6.07923i	−1.08656	−	0.291142i
$437$	−7.60370	+	2.03740i	−0.363734	+	0.0974623i
$438$	47.7859	−	27.8754i	2.28330	−	1.33194i
$439$	23.9899	−	13.8506i	1.14498	−	0.661052i	0.197318	−	0.980340i	$-0.436777\pi$
$439$	23.9899	−	13.8506i	1.14498	−	0.661052i	0.947658	+	0.319288i	$0.103444\pi$
$440$	−7.48094	−	7.48094i	−0.356640	−	0.356640i
$441$	19.0848	+	8.76185i	0.908800	+	0.417231i
$442$	−0.310026	−	0.0963451i	−0.0147464	−	0.00458267i
$443$	−4.82478	+	2.78559i	−0.229232	+	0.132347i	−0.610218	−	0.792234i	$-0.708918\pi$
$443$	−4.82478	+	2.78559i	−0.229232	+	0.132347i	0.380985	+	0.924581i	$0.375585\pi$
$444$	18.3220	−	69.6249i	0.869525	−	3.30425i
$445$	5.94126	−	10.2906i	0.281643	−	0.487819i
$446$	19.4156	+	33.6288i	0.919355	+	1.59237i
$447$	−1.05307	−	3.86086i	−0.0498087	−	0.182612i
$448$	9.11594	+	8.37861i	0.430688	+	0.395852i
$449$	−3.83218	−	3.83218i	−0.180852	−	0.180852i	0.610875	−	0.791727i	$-0.290818\pi$
$449$	−3.83218	−	3.83218i	−0.180852	−	0.180852i	−0.791727	+	0.610875i	$0.790818\pi$
$450$	−18.3034	+	5.08058i	−0.862831	+	0.239501i
$451$	2.49500	−	4.32146i	0.117485	−	0.203490i
$452$	15.7837	−	27.3381i	0.742402	−	1.28588i
$453$	18.2560	−	18.4203i	0.857742	−	0.865462i
$454$		−	18.2404i		−	0.856066i
$455$	−12.9896	−	7.45431i	−0.608964	−	0.349463i
$456$	−11.5075	−	6.57530i	−0.538888	−	0.307917i
$457$	0.693229	−	2.58717i	0.0324279	−	0.121023i	−0.947815	−	0.318822i	$-0.896713\pi$
$457$	0.693229	−	2.58717i	0.0324279	−	0.121023i	0.980243	+	0.197799i	$0.0633795\pi$
$458$	−34.2129	−	19.7528i	−1.59866	−	0.922989i
$459$	0.0914767	−	0.163478i	0.00426977	−	0.00763048i
$460$	−9.90125	+	36.9520i	−0.461648	+	1.72290i
$461$	−19.4233	+	19.4233i	−0.904632	+	0.904632i	−0.995833	−	0.0912008i	$-0.970929\pi$
$461$	−19.4233	+	19.4233i	−0.904632	+	0.904632i	0.0912008	+	0.995833i	$0.470929\pi$
$462$	−13.4811	−	2.94673i	−0.627195	−	0.137094i
$463$	0.0917473	−	0.0917473i	0.00426386	−	0.00426386i	−0.704972	−	0.709235i	$-0.749040\pi$
$463$	0.0917473	−	0.0917473i	0.00426386	−	0.00426386i	0.709235	+	0.704972i	$0.249040\pi$
$464$	−49.7915	+	28.7471i	−2.31151	+	1.33455i
$465$	1.79272	+	3.07320i	0.0831352	+	0.142516i
$466$	−4.50825	−	16.8250i	−0.208841	−	0.779404i
$467$	5.55944	+	9.62924i	0.257260	+	0.445588i	0.965507	−	0.260377i	$-0.0838469\pi$
$467$	5.55944	+	9.62924i	0.257260	+	0.445588i	−0.708247	+	0.705965i	$0.750514\pi$
$468$	38.9796	+	24.1213i	1.80183	+	1.11501i
$469$	−3.93814	+	7.53725i	−0.181846	+	0.348038i
$470$	−1.14421	+	1.14421i	−0.0527786	+	0.0527786i
$471$	−12.8803	+	0.0577033i	−0.593494	+	0.00265883i
$472$	−37.9009	−	21.8821i	−1.74453	−	1.00721i
$473$	−1.33449	−	4.98039i	−0.0613600	−	0.228999i
$474$	7.01909	−	7.08226i	0.322397	−	0.325299i
$475$	−2.45426	+	2.45426i	−0.112609	+	0.112609i
$476$	0.0880867	−	0.394510i	0.00403745	−	0.0180823i
$477$	21.2995	−	12.5531i	0.975237	−	0.574765i
$478$	−39.8259	+	22.9935i	−1.82160	+	1.05170i
$479$	−12.8400	+	3.44047i	−0.586674	+	0.157199i	−0.539933	−	0.841708i	$-0.681550\pi$
$479$	−12.8400	+	3.44047i	−0.586674	+	0.157199i	−0.0467415	+	0.998907i	$0.514884\pi$
$480$	−5.91315	+	3.44937i	−0.269897	+	0.157442i
$481$	7.79683	+	34.4945i	0.355505	+	1.57281i
$482$		−	12.4497i		−	0.567067i
$483$	7.99789	+	25.1060i	0.363917	+	1.14236i
$484$	−40.4560			−1.83891
$485$	−13.7297	−	23.7806i	−0.623436	−	1.07982i
$486$	−26.9064	+	28.1397i	−1.22050	+	1.27644i
$487$	−20.3455	+	5.45155i	−0.921941	+	0.247033i	−0.688415	−	0.725317i	$-0.741693\pi$
$487$	−20.3455	+	5.45155i	−0.921941	+	0.247033i	−0.233526	+	0.972351i	$0.575026\pi$
$488$	15.6557	−	58.4279i	0.708701	−	2.64491i
$489$	−1.78451	−	6.54249i	−0.0806982	−	0.295862i
$490$	11.6751	−	24.8409i	0.527427	−	1.12220i
$491$	−15.9278			−0.718812			−0.359406	−	0.933181i	$-0.617021\pi$
$491$	−15.9278			−0.718812			−0.359406	+	0.933181i	$0.617021\pi$
$492$	−21.5773	−	21.3848i	−0.972779	−	0.964102i
$493$	−0.327349	−	0.188995i	−0.0147431	−	0.00851192i
$494$	12.3190	+	0.486900i	0.554257	+	0.0219067i
$495$	−2.79514	+	4.94309i	−0.125632	+	0.222175i
$496$	−5.07333	−	5.07333i	−0.227799	−	0.227799i
$497$	0.902905	+	21.4232i	0.0405008	+	0.960960i
$498$	48.8557	+	27.9158i	2.18928	+	1.25094i
$499$	−1.55937	+	5.81965i	−0.0698071	+	0.260523i	−0.992006	−	0.126193i	$-0.959724\pi$
$499$	−1.55937	+	5.81965i	−0.0698071	+	0.260523i	0.922199	+	0.386716i	$0.126391\pi$
$500$	12.9756	+	48.4256i	0.580287	+	2.16566i
$501$	−1.53312	+	5.82595i	−0.0684946	+	0.260284i
$502$	33.6927	+	9.02794i	1.50378	+	0.402937i
$503$		−	4.55024i		−	0.202885i	−0.994841	−	0.101443i	$-0.967654\pi$
$503$		−	4.55024i		−	0.202885i	0.994841	−	0.101443i	$-0.0323458\pi$
$504$	−20.1908	+	39.5017i	−0.899370	+	1.75955i
$505$	−5.99798	+	5.99798i	−0.266907	+	0.266907i
$506$	−8.65717	−	14.9947i	−0.384858	−	0.666594i
$507$	−22.4542	−	1.67656i	−0.997224	−	0.0744588i
$508$	13.2815	−	23.0043i	0.589272	−	1.02065i
$509$	−6.89545	−	1.84763i	−0.305635	−	0.0818947i	0.102742	−	0.994708i	$-0.467238\pi$
$509$	−6.89545	−	1.84763i	−0.305635	−	0.0818947i	−0.408377	+	0.912813i	$0.633905\pi$
$510$	−0.212591	−	0.121473i	−0.00941370	−	0.00537892i
$511$	−29.9886	−	15.6687i	−1.32662	−	0.693144i
$512$	−33.5830	+	33.5830i	−1.48417	+	1.48417i
$513$	−1.74869	+	6.89560i	−0.0772066	+	0.304448i
$514$	−7.64667	−	28.5378i	−0.337280	−	1.25875i
$515$	22.7893	−	6.10638i	1.00422	−	0.269079i
$516$	−31.3899	+	0.140625i	−1.38186	+	0.00619069i
$517$		−	0.497558i		−	0.0218826i
$518$	−61.8430	+	19.3963i	−2.71723	+	0.852223i
$519$	12.1012	−	21.1785i	0.531185	−	0.929633i
$520$	16.8889	−	26.7533i	0.740625	−	1.17321i
$521$	−19.7436	−	11.3990i	−0.864981	−	0.499397i	0.000695975	−	1.00000i	$-0.499778\pi$
$521$	−19.7436	−	11.3990i	−0.864981	−	0.499397i	−0.865677	+	0.500603i	$0.833112\pi$
$522$	56.0446	+	55.0492i	2.45300	+	2.40944i
$523$	11.4263	+	19.7909i	0.499637	+	0.865396i	1.00000		0.000419527i	$-0.000133540\pi$
$523$	11.4263	+	19.7909i	0.499637	+	0.865396i	−0.500363	+	0.865816i	$0.666800\pi$
$524$	1.08655			0.0474663
$525$	8.58873	+	7.82336i	0.374843	+	0.341439i
$526$	23.4152	+	23.4152i	1.02095	+	1.02095i
$527$	0.0122085	−	0.0455626i	0.000531808	−	0.00198474i
$528$	2.91429	−	11.0745i	0.126828	−	0.481955i
$529$	−5.03042	+	8.71295i	−0.218714	+	0.378824i
$530$	−16.1572	−	27.9851i	−0.701824	−	1.21560i
$531$	−5.87624	+	22.7436i	−0.255007	+	0.986989i
$532$	0.646386	+	15.3368i	0.0280244	+	0.664932i
$533$	14.2502	+	4.42846i	0.617245	+	0.191818i
$534$	32.7409	−	0.146678i	1.41684	−	0.00634737i
$535$	−24.1649	+	6.47497i	−1.04474	+	0.279938i
$536$	−15.5581	−	8.98247i	−0.672007	−	0.387984i
$537$	−33.6152	+	0.150594i	−1.45060	+	0.00649863i
$538$	−4.77499	−	4.77499i	−0.205864	−	0.205864i
$539$	2.86257	+	7.93946i	0.123300	+	0.341977i
$540$	24.7721	+	24.1150i	1.06602	+	1.03775i
$541$	−28.9391	−	7.75421i	−1.24419	−	0.333380i	−0.424101	−	0.905615i	$-0.639410\pi$
$541$	−28.9391	−	7.75421i	−1.24419	−	0.333380i	−0.820089	+	0.572235i	$0.806076\pi$
$542$	36.0841	+	20.8332i	1.54994	+	0.894861i
$543$	2.17321	−	1.26772i	0.0932613	−	0.0544030i
$544$	0.0876672	+	0.0234904i	0.00375870	+	0.00100714i
$545$	8.70158			0.372735
$546$	−0.292882	−	41.2656i	−0.0125342	−	1.76600i
$547$	32.7019			1.39823			0.699115	−	0.715009i	$-0.253577\pi$
$547$	32.7019			1.39823			0.699115	+	0.715009i	$0.253577\pi$
$548$	5.48062	+	1.46853i	0.234121	+	0.0627324i
$549$	−32.4663	+	0.290901i	−1.38563	+	0.0124153i
$550$	−6.61136	−	3.81707i	−0.281909	−	0.162760i
$551$	13.8650	+	3.71513i	0.590671	+	0.158270i
$552$	−53.7012	+	14.6473i	−2.28567	+	0.623432i
$553$	−5.95191	−	1.32895i	−0.253101	−	0.0565127i
$554$	−31.1773	−	31.1773i	−1.32460	−	1.32460i
$555$	0.119487	+	26.6714i	0.00507193	+	1.13214i
$556$	70.4603	+	40.6803i	2.98818	+	1.72523i
$557$	−10.5760	+	2.83384i	−0.448121	+	0.120074i	−0.475820	−	0.879543i	$-0.657849\pi$
$557$	−10.5760	+	2.83384i	−0.448121	+	0.120074i	0.0276991	+	0.999616i	$0.491182\pi$
$558$	−4.82542	+	8.53354i	−0.204276	+	0.361254i
$559$	13.6474	−	7.17618i	0.577225	−	0.303520i
$560$	20.1882	+	10.5482i	0.853109	+	0.445741i
$561$	0.0726336	−	0.0198113i	0.00306659	−	0.000836433i
$562$	6.74467	+	11.6821i	0.284507	+	0.492780i
$563$	−4.34682	+	7.52891i	−0.183197	+	0.317306i	−0.942967	−	0.332885i	$-0.891978\pi$
$563$	−4.34682	+	7.52891i	−0.183197	+	0.317306i	0.759771	+	0.650191i	$0.225311\pi$
$564$	−2.92940	−	0.770882i	−0.123350	−	0.0324600i
$565$	−3.02678	+	11.2961i	−0.127337	+	0.475230i
$566$	15.3460	+	15.3460i	0.645041	+	0.645041i
$567$	23.3288	+	4.77170i	0.979716	+	0.200392i
$568$	−45.2969			−1.90061
$569$	4.99492	+	8.65145i	0.209398	+	0.362688i	0.951525	−	0.307571i	$-0.0995163\pi$
$569$	4.99492	+	8.65145i	0.209398	+	0.362688i	−0.742127	+	0.670259i	$0.766183\pi$
$570$	8.99196	+	2.36626i	0.376632	+	0.0991119i
$571$	38.7624	+	22.3795i	1.62216	+	0.936553i	0.986342	+	0.164711i	$0.0526691\pi$
$571$	38.7624	+	22.3795i	1.62216	+	0.936553i	0.635815	+	0.771842i	$0.280664\pi$
$572$	4.06160	+	17.9692i	0.169824	+	0.751330i
$573$	−20.7320	−	11.8461i	−0.866093	−	0.494879i
$574$	−5.95968	+	26.6913i	−0.248752	+	1.11408i
$575$			14.5770i			0.607903i
$576$	12.2208	+	6.91043i	0.509200	+	0.287935i
$577$	40.0417	−	10.7291i	1.66696	−	0.446660i	0.702670	−	0.711515i	$-0.251991\pi$
$577$	40.0417	−	10.7291i	1.66696	−	0.446660i	0.964288	+	0.264855i	$0.0853242\pi$
$578$	−10.9883	−	41.0088i	−0.457052	−	1.70574i
$579$	4.60576	−	4.64721i	0.191409	−	0.193131i
$580$	49.3259	−	49.3259i	2.04815	−	2.04815i
$581$	−1.44914	−	34.3837i	−0.0601206	−	1.42648i
$582$	37.5372	−	65.6943i	1.55597	−	2.72311i
$583$	9.59760	+	2.57167i	0.397492	+	0.106508i
$584$	35.7387	−	61.9012i	1.47888	−	2.56149i
$585$	−16.2613	−	4.89411i	−0.672322	−	0.202347i
$586$	−28.5066	−	49.3748i	−1.17759	−	2.03965i
$587$	−12.5328	+	12.5328i	−0.517284	+	0.517284i	−0.916749	−	0.399465i	$-0.869196\pi$
$587$	−12.5328	+	12.5328i	−0.517284	+	0.517284i	0.399465	+	0.916749i	$0.369196\pi$
$588$	51.1791	−	4.55269i	2.11059	−	0.187750i
$589$			1.79127i			0.0738080i
$590$	29.6567	+	7.94650i	1.22095	+	0.327152i
$591$	−28.1452	−	7.40651i	−1.15774	−	0.304663i
$592$	−13.9208	−	51.9533i	−0.572143	−	2.13527i
$593$	8.92468	−	33.3074i	0.366493	−	1.36777i	−0.498893	−	0.866664i	$-0.666260\pi$
$593$	8.92468	−	33.3074i	0.366493	−	1.36777i	0.865386	−	0.501106i	$-0.167073\pi$
$594$	−15.6456	+	0.210286i	−0.641946	+	0.00862813i
$595$	0.00630582	+	0.149618i	0.000258513	+	0.00613372i
$596$	−6.92367	−	6.92367i	−0.283604	−	0.283604i
$597$	−0.0474527	−	10.5922i	−0.00194211	−	0.433511i
$598$	38.0300	−	35.1381i	1.55516	−	1.43690i
$599$	3.63222	+	2.09706i	0.148409	+	0.0856837i	0.572365	−	0.819999i	$-0.306026\pi$
$599$	3.63222	+	2.09706i	0.148409	+	0.0856837i	−0.423957	+	0.905682i	$0.639359\pi$
$600$	−17.2763	+	17.4318i	−0.705302	+	0.711650i
$601$	3.92273			0.160011			0.0800057	−	0.996794i	$-0.474506\pi$
$601$	3.92273			0.160011			0.0800057	+	0.996794i	$0.474506\pi$
$602$	15.1474	+	23.8562i	0.617363	+	0.972307i
$603$	−2.41216	+	9.33612i	−0.0982308	+	0.380196i
$604$	16.4231	−	61.2920i	0.668248	−	2.49394i
$605$	14.4768	−	3.87904i	0.588565	−	0.157706i
$606$	−22.6031	−	5.94807i	−0.918186	−	0.241624i
$607$	14.5482	+	25.1983i	0.590495	+	1.02277i	0.994166	+	0.107863i	$0.0344008\pi$
$607$	14.5482	+	25.1983i	0.590495	+	1.02277i	−0.403671	+	0.914904i	$0.632266\pi$
$608$	−3.44659			−0.139778
$609$	10.2599	−	46.9384i	0.415753	−	1.90204i
$610$			42.4363i			1.71819i
$611$	1.45132	−	0.328044i	0.0587143	−	0.0132712i
$612$	−0.00410667	−	0.458329i	−0.000166002	−	0.0185268i
$613$	−23.9305	+	6.41217i	−0.966545	+	0.258985i	−0.707368	−	0.706845i	$-0.750118\pi$
$613$	−23.9305	+	6.41217i	−0.966545	+	0.258985i	−0.259176	+	0.965830i	$0.583451\pi$
$614$	10.5805	−	6.10867i	0.426995	−	0.246526i
$615$	9.77167	+	5.58346i	0.394032	+	0.225147i
$616$	−17.0120	+	5.33559i	−0.685432	+	0.214977i
$617$	−5.99264	+	5.99264i	−0.241255	+	0.241255i	−0.817369	−	0.576114i	$-0.804568\pi$
$617$	−5.99264	+	5.99264i	−0.241255	+	0.241255i	0.576114	+	0.817369i	$0.304568\pi$
$618$	46.1739	+	45.7620i	1.85739	+	1.84082i
$619$	−12.0209	−	44.8625i	−0.483160	−	1.80318i	−0.588209	−	0.808709i	$-0.700167\pi$
$619$	−12.0209	−	44.8625i	−0.483160	−	1.80318i	0.105049	−	0.994467i	$-0.466500\pi$
$620$	7.53884	+	4.35255i	0.302767	+	0.174803i
$621$	15.2849	+	25.6712i	0.613364	+	1.03015i
$622$	−28.3778	+	28.3778i	−1.13785	+	1.13785i
$623$	−10.7337	−	16.9049i	−0.430037	−	0.677281i
$624$	34.2245	+	1.19917i	1.37008	+	0.0480051i
$625$	−2.94842	−	5.10681i	−0.117937	−	0.204272i
$626$	13.6981	+	51.1220i	0.547486	+	2.04325i
$627$	−2.46955	+	1.44058i	−0.0986243	+	0.0575314i
$628$	−27.2927	+	15.7575i	−1.08910	+	0.628791i
$629$	0.250041	−	0.250041i	0.00996978	−	0.00996978i
$630$	6.50972	−	30.4344i	0.259354	−	1.21254i
$631$	12.6139	−	12.6139i	0.502153	−	0.502153i	−0.409953	−	0.912106i	$-0.634455\pi$
$631$	12.6139	−	12.6139i	0.502153	−	0.502153i	0.912106	+	0.409953i	$0.134455\pi$
$632$	3.33439	−	12.4441i	0.132635	−	0.495000i
$633$	−15.3690	−	26.3466i	−0.610862	−	1.04718i
$634$	16.6449	+	9.60992i	0.661052	+	0.381659i
$635$	−2.54695	+	9.50534i	−0.101073	+	0.377208i
$636$	30.0107	−	52.5221i	1.19000	−	2.08263i
$637$	−21.2712	+	13.5844i	−0.842797	+	0.538232i
$638$			31.5720i			1.24995i
$639$	6.50287	+	23.4274i	0.257249	+	0.926772i
$640$	13.1273	−	22.7372i	0.518902	−	0.898765i
$641$	−0.927763	+	1.60693i	−0.0366444	+	0.0634700i	−0.883766	−	0.467929i	$-0.845000\pi$
$641$	−0.927763	+	1.60693i	−0.0366444	+	0.0634700i	0.847122	+	0.531399i	$0.178334\pi$
$642$	−48.9610	−	48.5243i	−1.93234	−	1.91510i
$643$	7.69902	+	7.69902i	0.303620	+	0.303620i	0.842428	−	0.538809i	$-0.181125\pi$
$643$	7.69902	+	7.69902i	0.303620	+	0.303620i	−0.538809	+	0.842428i	$0.681125\pi$
$644$	47.4657	+	43.6265i	1.87041	+	1.71912i
$645$	11.2191	−	3.06008i	0.441752	−	0.120491i
$646$	−0.0616367	−	0.106758i	−0.00242506	−	0.00420033i
$647$	11.9903	−	20.7677i	0.471385	−	0.816463i	−0.528079	−	0.849195i	$-0.677087\pi$
$647$	11.9903	−	20.7677i	0.471385	−	0.816463i	0.999464	+	0.0327320i	$0.0104208\pi$
$648$	−12.1465	+	48.8141i	−0.477161	+	1.91760i
$649$	−8.17584	+	4.72033i	−0.320930	+	0.185289i
$650$	6.77505	−	21.8012i	0.265740	−	0.855115i
$651$	5.98928	−	0.279310i	0.234738	−	0.0109470i
$652$	−11.7326	−	11.7326i	−0.459485	−	0.459485i
$653$	15.8664	−	9.16049i	0.620902	−	0.358478i	−0.156318	−	0.987707i	$-0.549963\pi$
$653$	15.8664	−	9.16049i	0.620902	−	0.358478i	0.777220	+	0.629229i	$0.216629\pi$
$654$	12.0811	+	20.7103i	0.472409	+	0.809836i
$655$	−0.388813	+	0.104182i	−0.0151922	+	0.00407073i
$656$	−21.9222	−	5.87403i	−0.855917	−	0.229342i
$657$	−37.1457	−	9.59730i	−1.44919	−	0.374426i
$658$	0.816080	+	2.60199i	0.0318141	+	0.101436i
$659$			21.7738i			0.848188i	0.905618	+	0.424094i	$0.139407\pi$
$659$			21.7738i			0.848188i	−0.905618	+	0.424094i	$0.860593\pi$
$660$	0.0622441	+	13.8939i	0.00242285	+	0.540820i
$661$	8.04549	+	30.0262i	0.312933	+	1.16788i	0.925898	+	0.377773i	$0.123310\pi$
$661$	8.04549	+	30.0262i	0.312933	+	1.16788i	−0.612965	+	0.790110i	$0.710023\pi$
$662$	7.02147	−	12.1615i	0.272897	−	0.472672i
$663$	0.105675	+	0.198803i	0.00410409	+	0.00772085i
$664$	72.7006			2.82133
$665$	−1.70184	−	5.42614i	−0.0659945	−	0.210417i
$666$	−63.3137	+	37.3145i	−2.45336	+	1.44591i
$667$	52.2085	−	30.1426i	2.02152	−	1.16712i
$668$	3.81493	+	14.2375i	0.147604	+	0.550867i
$669$	6.85319	−	26.0426i	0.264960	−	1.00686i
$670$	12.1739	+	3.26199i	0.470319	+	0.126022i
$671$	−9.22667	−	9.22667i	−0.356192	−	0.356192i
$672$	0.537422	+	11.5240i	0.0207315	+	0.444548i
$673$		−	29.8707i		−	1.15143i	−0.817650	−	0.575716i	$-0.804724\pi$
$673$		−	29.8707i		−	1.15143i	0.817650	−	0.575716i	$-0.195276\pi$
$674$	0.445125	−	1.66123i	0.0171456	−	0.0639882i
$675$	11.4959	+	6.43271i	0.442476	+	0.247595i
$676$	−49.7364	+	23.6945i	−1.91294	+	0.911326i
$677$	−6.67032	+	3.85111i	−0.256361	+	0.148010i	−0.622673	−	0.782482i	$-0.713953\pi$
$677$	−6.67032	+	3.85111i	−0.256361	+	0.148010i	0.366312	+	0.930492i	$0.380620\pi$
$678$	−31.0877	+	8.47937i	−1.19392	+	0.325648i
$679$	−46.2344	+	1.94860i	−1.77431	+	0.0747805i
$680$	−0.316350			−0.0121315
$681$	−8.90449	+	8.98463i	−0.341221	+	0.344292i
$682$	−3.80565	+	1.01972i	−0.145726	+	0.0390472i
$683$	7.68744	−	2.05984i	0.294152	−	0.0788177i	−0.108725	−	0.994072i	$-0.534677\pi$
$683$	7.68744	−	2.05984i	0.294152	−	0.0788177i	0.402877	+	0.915254i	$0.368010\pi$
$684$	4.65538	+	16.7716i	0.178003	+	0.641276i
$685$	−2.10200			−0.0803131
$686$	−27.9919	−	36.8244i	−1.06874	−	1.40596i
$687$	7.20934	+	26.4314i	0.275053	+	1.00842i
$688$	−20.3091	+	11.7255i	−0.774277	+	0.447029i
$689$	−1.17351	+	29.6907i	−0.0447070	+	1.13112i
$690$	33.7309	−	19.6766i	1.28411	−	0.749074i
$691$	6.46768	−	24.1377i	0.246042	−	0.918241i	−0.726815	−	0.686833i	$-0.759000\pi$
$691$	6.46768	−	24.1377i	0.246042	−	0.918241i	0.972857	−	0.231408i	$-0.0743331\pi$
$692$		−	59.6804i		−	2.26871i
$693$	5.20181	+	8.03255i	0.197600	+	0.305131i
$694$	42.0484	+	42.0484i	1.59614	+	1.59614i
$695$	−29.1141	−	7.80110i	−1.10436	−	0.295913i
$696$	98.1573	+	25.8304i	3.72064	+	0.979100i
$697$	−0.0386182	−	0.144125i	−0.00146277	−	0.00545913i
$698$	−7.92652	+	4.57638i	−0.300023	+	0.173218i
$699$	−5.99290	+	10.4882i	−0.226672	+	0.396702i
$700$	27.7422	+	6.19432i	1.04856	+	0.234123i
$701$	−39.3491			−1.48619			−0.743097	−	0.669184i	$-0.766644\pi$
$701$	−39.3491			−1.48619			−0.743097	+	0.669184i	$0.766644\pi$
$702$	−10.9286	−	45.4978i	−0.412475	−	1.71720i
$703$	−6.71417	+	11.6293i	−0.253230	+	0.438607i
$704$	1.46033	+	5.45004i	0.0550384	+	0.205406i
$705$	1.12217	−	0.00502729i	0.0422635	−	0.000189339i
$706$			43.9050i			1.65239i
$707$	4.27791	+	13.6397i	0.160887	+	0.512972i
$708$	15.1241	+	55.4491i	0.568399	+	2.08390i
$709$	−23.9497	−	6.41730i	−0.899450	−	0.241007i	−0.220670	−	0.975349i	$-0.570824\pi$
$709$	−23.9497	−	6.41730i	−0.899450	−	0.241007i	−0.678780	+	0.734342i	$0.737491\pi$
$710$	30.6953	−	8.22479i	1.15198	−	0.308671i
$711$	−6.91474	+	0.0619567i	−0.259323	+	0.00232356i
$712$	36.6350	−	21.1512i	1.37295	−	0.792675i
$713$	5.31960	+	5.31960i	0.199220	+	0.199220i
$714$	−0.347344	+	0.222735i	−0.0129990	+	0.00833564i
$715$	−3.17635	−	6.04067i	−0.118789	−	0.225908i
$716$	−71.2287	+	41.1239i	−2.66194	+	1.53687i
$717$	30.8418	+	8.11611i	1.15181	+	0.303102i
$718$	−17.6421	+	30.5570i	−0.658398	+	1.14038i
$719$	−6.84162	−	11.8500i	−0.255149	−	0.441931i	0.709787	−	0.704417i	$-0.248791\pi$
$719$	−6.84162	−	11.8500i	−0.255149	−	0.441931i	−0.964936	+	0.262485i	$0.915458\pi$
$720$	25.0064	+	6.46088i	0.931935	+	0.240783i
$721$	8.66430	−	38.8044i	0.322675	−	1.44515i
$722$	−30.2447	−	30.2447i	−1.12559	−	1.12559i
$723$	−6.07760	+	6.13230i	−0.226028	+	0.228063i
$724$	3.07790	−	5.33108i	0.114389	−	0.198128i
$725$	13.2903	−	23.0194i	0.493589	−	0.854921i
$726$	29.3317	+	29.0700i	1.08860	+	1.07889i
$727$			32.3518i			1.19986i	0.800051	+	0.599931i	$0.204805\pi$
$727$			32.3518i			1.19986i	−0.800051	+	0.599931i	$0.795195\pi$
$728$	−26.7795	−	46.1043i	−0.992513	−	1.70874i
$729$	26.9902	−	0.725661i	0.999639	−	0.0268763i
$730$	−12.9785	+	48.4365i	−0.480357	+	1.79272i
$731$	−0.133520	−	0.0770879i	−0.00493842	−	0.00285120i
$732$	−68.6177	+	40.0274i	−2.53618	+	1.47945i
$733$	4.40270	−	16.4311i	0.162618	−	0.606897i	−0.835714	−	0.549164i	$-0.814946\pi$
$733$	4.40270	−	16.4311i	0.162618	−	0.606897i	0.998332	−	0.0577329i	$-0.0183872\pi$
$734$	−36.3495	+	36.3495i	−1.34168	+	1.34168i
$735$	−17.8774	+	6.53635i	−0.659419	+	0.241097i
$736$	−10.2355	+	10.2355i	−0.377284	+	0.377284i
$737$	−3.35614	+	1.93767i	−0.123625	+	0.0713748i
$738$	0.277845	+	31.0091i	0.0102276	+	1.14146i
$739$	−6.32510	−	23.6056i	−0.232672	−	0.868345i	−0.979184	−	0.202973i	$-0.934940\pi$
$739$	−6.32510	−	23.6056i	−0.232672	−	0.868345i	0.746512	−	0.665372i	$-0.231727\pi$
$740$	32.6291	+	56.5153i	1.19947	+	2.07754i
$741$	−5.83022	−	6.25362i	−0.214179	−	0.229732i
$742$	−54.4087	+	2.29312i	−1.99741	+	0.0841832i
$743$	25.2907	−	25.2907i	0.927826	−	0.927826i	−0.0697391	−	0.997565i	$-0.522217\pi$
$743$	25.2907	−	25.2907i	0.927826	−	0.927826i	0.997565	+	0.0697391i	$0.0222167\pi$
$744$	0.0567434	+	12.6661i	0.00208031	+	0.464360i
$745$	3.14143	+	1.81371i	0.115093	+	0.0664491i
$746$	−9.78204	−	36.5071i	−0.358146	−	1.33662i
$747$	−10.4370	−	37.6004i	−0.381869	−	1.37573i
$748$	0.130254	−	0.130254i	0.00476254	−	0.00476254i
$749$	−9.18729	+	41.1467i	−0.335696	+	1.50347i
$750$	25.3891	−	44.4337i	0.927077	−	1.62249i
$751$	4.79468	−	2.76821i	0.174960	−	0.101013i	−0.409962	−	0.912102i	$-0.634458\pi$
$751$	4.79468	−	2.76821i	0.174960	−	0.101013i	0.584923	+	0.811089i	$0.301125\pi$
$752$	−2.18589	+	0.585707i	−0.0797111	+	0.0213585i
$753$	−12.1887	−	20.8947i	−0.444182	−	0.761447i
$754$	−92.0921	+	20.8157i	−3.35380	+	0.758062i
$755$			23.5075i			0.855525i
$756$	55.3514	−	18.1809i	2.01311	−	0.661232i
$757$	13.3974			0.486938			0.243469	−	0.969909i	$-0.421715\pi$
$757$	13.3974			0.486938			0.243469	+	0.969909i	$0.421715\pi$
$758$	−8.74852	−	15.1529i	−0.317761	−	0.550378i
$759$	−3.05575	+	11.6121i	−0.110917	+	0.421491i
$760$	11.6040	−	3.10928i	0.420921	−	0.112786i
$761$	−3.76270	+	14.0426i	−0.136398	+	0.509044i	0.863590	+	0.504194i	$0.168210\pi$
$761$	−3.76270	+	14.0426i	−0.136398	+	0.509044i	−0.999988	+	0.00484983i	$0.998456\pi$
$762$	−26.1594	+	7.13515i	−0.947656	+	0.258479i
$763$	6.79079	−	12.9970i	0.245843	−	0.470522i
$764$	−58.4223			−2.11364
$765$	0.0454155	+	0.163615i	0.00164200	+	0.00591551i
$766$	−75.4688	−	43.5719i	−2.72680	−	1.57432i
$767$	−19.1591	−	20.7359i	−0.691794	−	0.748730i
$768$	56.1305	−	0.251462i	2.02544	−	0.00907387i
$769$	−10.0440	−	10.0440i	−0.362197	−	0.362197i	0.502424	−	0.864621i	$-0.332442\pi$
$769$	−10.0440	−	10.0440i	−0.362197	−	0.362197i	−0.864621	+	0.502424i	$0.832442\pi$
$770$	10.5593	−	6.70461i	0.380532	−	0.241617i
$771$	−10.1649	+	17.7897i	−0.366079	+	0.640679i
$772$	4.14335	−	15.4632i	0.149122	−	0.556532i
$773$	6.82014	+	25.4531i	0.245303	+	0.915485i	0.973231	+	0.229830i	$0.0738172\pi$
$773$	6.82014	+	25.4531i	0.245303	+	0.915485i	−0.727927	+	0.685654i	$0.759516\pi$
$774$	22.8596	+	22.4536i	0.821671	+	0.807078i
$775$	3.20399	+	0.858507i	0.115091	+	0.0308385i
$776$		−	97.7574i		−	3.50929i
$777$	39.9305	+	20.6361i	1.43250	+	0.740317i
$778$	56.9202	−	56.9202i	2.04069	−	2.04069i
$779$	2.83311	+	4.90708i	0.101507	+	0.175814i
$780$	−40.4860	+	9.34193i	−1.44963	+	0.334495i
$781$	−4.88564	+	8.46217i	−0.174822	+	0.302800i
$782$	−0.500087	−	0.133998i	−0.0178831	−	0.00479176i
$783$	−0.732174	−	54.4748i	−0.0261658	−	1.94677i
$784$	31.5102	−	21.9219i	1.12536	−	0.782927i
$785$	8.25557	−	8.25557i	0.294654	−	0.294654i
$786$	−0.787781	−	0.780754i	−0.0280992	−	0.0278486i
$787$	0.846065	+	3.15756i	0.0301590	+	0.112555i	0.979364	−	0.202102i	$-0.0647772\pi$
$787$	0.846065	+	3.15756i	0.0301590	+	0.112555i	−0.949206	+	0.314657i	$0.898111\pi$
$788$	−68.7817	+	18.4300i	−2.45025	+	0.656542i
$789$	−0.102879	−	22.9642i	−0.00366257	−	0.817546i
$790$			9.03817i			0.321564i
$791$	14.5101	+	13.3365i	0.515919	+	0.474190i
$792$	−17.4165	+	10.2646i	−0.618870	+	0.364736i
$793$	20.8300	−	32.9964i	0.739694	−	1.17174i
$794$	38.9448	+	22.4848i	1.38210	+	0.797955i
$795$	−5.70307	+	21.6720i	−0.202267	+	0.768628i
$796$	−12.9583	−	22.4444i	−0.459293	−	0.795519i
$797$	36.6002			1.29645			0.648223	−	0.761451i	$-0.275513\pi$
$797$	36.6002			1.29645			0.648223	+	0.761451i	$0.275513\pi$
$798$	10.5517	−	11.5840i	0.373527	−	0.410070i
$799$	−0.0105202	−	0.0105202i	−0.000372179	−	0.000372179i
$800$	−1.65186	+	6.16482i	−0.0584020	+	0.217959i
$801$	−16.1987	−	15.9110i	−0.572352	−	0.562187i
$802$	−28.5976	+	49.5326i	−1.00982	+	1.74906i
$803$	−7.70942	−	13.3531i	−0.272059	−	0.471221i
$804$	6.20836	+	22.7615i	0.218952	+	0.802737i
$805$	−21.1682	−	11.0602i	−0.746081	−	0.389820i
$806$	−5.48352	−	10.4284i	−0.193149	−	0.367324i
$807$	0.0209797	+	4.68302i	0.000738522	+	0.164850i
$808$	−29.1689	+	7.81580i	−1.02616	+	0.274959i
$809$	15.4915	+	8.94404i	0.544654	+	0.314456i	0.746963	−	0.664866i	$-0.231511\pi$
$809$	15.4915	+	8.94404i	0.544654	+	0.314456i	−0.202309	+	0.979322i	$0.564845\pi$
$810$	−0.632352	−	35.2843i	−0.0222186	−	1.23976i
$811$	−1.18970	−	1.18970i	−0.0417760	−	0.0417760i	0.685910	−	0.727686i	$-0.259404\pi$
$811$	−1.18970	−	1.18970i	−0.0417760	−	0.0417760i	−0.727686	+	0.685910i	$0.759404\pi$
$812$	−35.1805	−	112.169i	−1.23459	−	3.93637i
$813$	−7.60364	−	27.8770i	−0.266671	−	0.977689i
$814$	−28.5293	−	7.64440i	−0.999951	−	0.267936i
$815$	5.32337	+	3.07345i	0.186470	+	0.107658i
$816$	−0.172537	−	0.295775i	−0.00604000	−	0.0103542i
$817$	5.65531	+	1.51534i	0.197854	+	0.0530149i
$818$	34.3384			1.20061
$819$	−20.0005	+	20.4690i	−0.698873	+	0.715246i
$820$	27.5363			0.961609
$821$	−23.9604	−	6.42017i	−0.836224	−	0.224066i	−0.184797	−	0.982777i	$-0.559163\pi$
$821$	−23.9604	−	6.42017i	−0.836224	−	0.224066i	−0.651427	+	0.758711i	$0.725829\pi$
$822$	−2.91837	−	5.00288i	−0.101790	−	0.174495i
$823$	−26.6801	−	15.4038i	−0.930011	−	0.536942i	−0.0431963	−	0.999067i	$-0.513754\pi$
$823$	−26.6801	−	15.4038i	−0.930011	−	0.536942i	−0.886815	+	0.462124i	$0.847087\pi$
$824$	81.1313	+	21.7391i	2.82634	+	0.757316i
$825$	1.39314	+	5.10765i	0.0485031	+	0.177825i
$826$	35.0135	−	38.0948i	1.21828	−	1.32549i
$827$	27.8830	+	27.8830i	0.969587	+	0.969587i	0.999551	−	0.0299638i	$-0.00953920\pi$
$827$	27.8830	+	27.8830i	0.969587	+	0.969587i	−0.0299638	+	0.999551i	$0.509539\pi$
$828$	63.6323	+	35.9819i	2.21138	+	1.25046i
$829$	−10.8992	−	6.29266i	−0.378545	−	0.218553i	0.298640	−	0.954366i	$-0.403467\pi$
$829$	−10.8992	−	6.29266i	−0.378545	−	0.218553i	−0.677185	+	0.735813i	$0.736800\pi$
$830$	−49.2654	+	13.2006i	−1.71003	+	0.458200i
$831$	0.136983	+	30.5768i	0.00475188	+	1.06070i
$832$	−14.9344	+	7.85289i	−0.517756	+	0.272250i
$833$	0.228395	+	0.107344i	0.00791342	+	0.00371926i
$834$	−21.8544	−	80.1243i	−0.756757	−	2.77448i
$835$	−2.73028	−	4.72898i	−0.0944852	−	0.163653i
$836$	−3.49761	+	6.05803i	−0.120967	+	0.209522i
$837$	6.54269	−	1.84770i	0.226148	−	0.0638658i
$838$	7.43545	−	27.7495i	0.256853	−	0.958590i
$839$	31.6664	+	31.6664i	1.09325	+	1.09325i	0.995180	+	0.0980660i	$0.0312656\pi$
$839$	31.6664	+	31.6664i	1.09325	+	1.09325i	0.0980660	+	0.995180i	$0.468734\pi$
$840$	−12.2056	−	38.3143i	−0.421132	−	1.32197i
$841$	−80.9276			−2.79061
$842$	25.7194	+	44.5473i	0.886349	+	1.53520i
$843$	2.38069	−	9.04679i	0.0819954	−	0.311588i
$844$	−64.6306	−	37.3145i	−2.22468	−	1.28442i
$845$	15.5258	−	13.2477i	0.534104	−	0.455735i
$846$	1.56997	+	2.66386i	0.0539768	+	0.0915855i
$847$	5.50394	−	24.6503i	0.189118	−	0.846993i
$848$		−	45.1917i		−	1.55189i
$849$	−0.0674253	−	15.0504i	−0.00231403	−	0.516530i
$850$	−0.220496	+	0.0590816i	−0.00756294	+	0.00202648i
$851$	14.5966	+	54.4752i	0.500365	+	1.86739i
$852$	42.2521	+	41.8752i	1.44753	+	1.43462i
$853$	−24.8739	+	24.8739i	−0.851667	+	0.851667i	−0.990338	−	0.138672i	$-0.955717\pi$
$853$	−24.8739	+	24.8739i	−0.851667	+	0.851667i	0.138672	+	0.990338i	$0.455717\pi$
$854$	63.3843	+	33.1177i	2.16896	+	1.13326i
$855$	−3.27399	−	5.55517i	−0.111968	−	0.189983i
$856$	−86.0285	−	23.0513i	−2.94039	−	0.787876i
$857$	−19.8450	+	34.3725i	−0.677891	+	1.17414i	0.297724	+	0.954652i	$0.403772\pi$
$857$	−19.8450	+	34.3725i	−0.677891	+	1.17414i	−0.975615	+	0.219489i	$0.929561\pi$
$858$	9.96718	−	15.9467i	0.340274	−	0.544410i
$859$	4.10807	+	7.11539i	0.140166	+	0.242774i	0.927559	−	0.373677i	$-0.121903\pi$
$859$	4.10807	+	7.11539i	0.140166	+	0.242774i	−0.787393	+	0.616451i	$0.788570\pi$
$860$	20.1192	−	20.1192i	0.686059	−	0.686059i
$861$	15.9655	−	10.2379i	0.544104	−	0.348907i
$862$			88.0668i			2.99957i
$863$	51.2884	+	13.7427i	1.74588	+	0.467806i	0.983738	−	0.179609i	$-0.0574832\pi$
$863$	51.2884	+	13.7427i	1.74588	+	0.467806i	0.762138	+	0.647415i	$0.224150\pi$
$864$	3.55517	+	12.5888i	0.120949	+	0.428281i
$865$	5.72234	+	21.3561i	0.194566	+	0.726128i
$866$	−14.5375	+	54.2547i	−0.494005	+	1.84365i
$867$	−14.6069	+	25.5637i	−0.496077	+	0.868190i
$868$	12.3845	−	7.86349i	0.420357	−	0.266904i
$869$	−1.96512	−	1.96512i	−0.0666620	−	0.0666620i
$870$	−71.2063	+	0.319001i	−2.41412	+	0.0108152i
$871$	−7.86469	−	8.51196i	−0.266485	−	0.288417i
$872$	26.8278	+	15.4891i	0.908505	+	0.524525i
$873$	−50.5597	+	14.0342i	−1.71119	+	0.474984i
$874$	19.6607			0.665032
$875$	−31.2716	+	1.31798i	−1.05717	+	0.0445558i
$876$	−90.5616	+	24.7013i	−3.05979	+	0.834578i
$877$	−9.59166	+	35.7966i	−0.323887	+	1.20876i	0.591538	+	0.806277i	$0.298521\pi$
$877$	−9.59166	+	35.7966i	−0.323887	+	1.20876i	−0.915426	+	0.402487i	$0.868146\pi$
$878$	−66.8281	+	17.9065i	−2.25534	+	0.604316i
$879$	−10.0621	+	38.2365i	−0.339385	+	1.28969i
$880$	5.18996	+	8.98928i	0.174954	+	0.303029i
$881$	14.5052			0.488693			0.244346	−	0.969688i	$-0.421427\pi$
$881$	14.5052			0.488693			0.244346	+	0.969688i	$0.421427\pi$
$882$	−40.3776	−	33.4744i	−1.35959	−	1.12714i
$883$		−	8.89008i		−	0.299175i	−0.988748	−	0.149588i	$-0.952205\pi$
$883$		−	8.89008i		−	0.299175i	0.988748	−	0.149588i	$-0.0477946\pi$
$884$	0.465813	+	0.294058i	0.0156670	+	0.00989025i
$885$	−10.7287	−	18.3918i	−0.360640	−	0.618234i
$886$	13.4403	−	3.60131i	0.451535	−	0.120989i
$887$	−0.844045	+	0.487309i	−0.0283402	+	0.0163622i	−0.514103	−	0.857728i	$-0.671875\pi$
$887$	−0.844045	+	0.487309i	−0.0283402	+	0.0163622i	0.485763	+	0.874091i	$0.338542\pi$
$888$	−47.1075	+	82.4433i	−1.58082	+	2.76662i
$889$	12.2098	+	11.2223i	0.409505	+	0.376382i
$890$	−20.9851	+	20.9851i	−0.703422	+	0.703422i
$891$	7.80915	+	7.53417i	0.261616	+	0.252404i
$892$	−17.0532	−	63.6433i	−0.570982	−	2.13093i
$893$	0.489291	+	0.282492i	0.0163735	+	0.00945325i
$894$	0.0447768	+	9.99492i	0.00149756	+	0.334280i
$895$	21.5454	−	21.5454i	0.720185	−	0.720185i
$896$	−23.7163	−	37.3517i	−0.792307	−	1.24783i
$897$	−35.8858	−	1.25738i	−1.19819	−	0.0419826i
$898$	6.76781	+	11.7222i	0.225845	+	0.391174i
$899$	−3.55047	−	13.2505i	−0.118415	−	0.441930i
$900$	32.2300	−	0.288784i	1.07433	−	0.00962613i
$901$	0.257304	−	0.148554i	0.00857202	−	0.00494906i
$902$	−8.81257	+	8.81257i	−0.293426	+	0.293426i
$903$	4.18484	−	19.1453i	0.139263	−	0.637117i
$904$	−29.4392	+	29.4392i	−0.979133	+	0.979133i
$905$	−0.590238	+	2.20280i	−0.0196202	+	0.0732234i
$906$	−55.9492	+	32.6374i	−1.85879	+	1.08430i
$907$	1.79669	+	1.03732i	0.0596580	+	0.0344436i	0.529532	−	0.848290i	$-0.322367\pi$
$907$	1.79669	+	1.03732i	0.0596580	+	0.0344436i	−0.469874	+	0.882733i	$0.655701\pi$
$908$	−8.01050	+	29.8956i	−0.265838	+	0.992120i
$909$	8.22983	+	13.9640i	0.272966	+	0.463157i
$910$	26.5185	+	26.3800i	0.879079	+	0.874489i
$911$			16.7050i			0.553460i	0.960948	+	0.276730i	$0.0892508\pi$
$911$			16.7050i			0.553460i	−0.960948	+	0.276730i	$0.910749\pi$
$912$	9.23588	+	9.15349i	0.305830	+	0.303102i
$913$	7.84135	−	13.5816i	0.259511	−	0.449486i
$914$	−3.34478	+	5.79334i	−0.110636	+	0.191627i
$915$	20.7163	−	20.9027i	0.684858	−	0.691022i
$916$	47.3993	+	47.3993i	1.56612	+	1.56612i
$917$	−0.147823	+	0.662048i	−0.00488155	+	0.0218628i
$918$	−0.326359	+	0.335252i	−0.0107715	+	0.0110650i
$919$	6.01586	+	10.4198i	0.198445	+	0.343717i	0.948024	−	0.318198i	$-0.103078\pi$
$919$	6.01586	+	10.4198i	0.198445	+	0.343717i	−0.749579	+	0.661914i	$0.769744\pi$
$920$	25.2271	−	43.6946i	0.831712	−	1.44057i
$921$	−8.19371	−	2.15620i	−0.269992	−	0.0710492i
$922$	59.4135	−	34.3024i	1.95668	−	1.12969i
$923$	−27.9044	−	8.67170i	−0.918484	−	0.285432i
$924$	20.8010	+	10.7500i	0.684302	+	0.353648i
$925$	17.5830	+	17.5830i	0.578127	+	0.578127i
$926$	−0.280645	+	0.162030i	−0.00922255	+	0.00532464i
$927$	−0.403936	−	45.0817i	−0.0132670	−	1.48068i
$928$	25.4955	−	6.83149i	0.836929	−	0.224254i
$929$	−33.4348	−	8.95882i	−1.09696	−	0.293929i	−0.335433	−	0.942064i	$-0.608883\pi$
$929$	−33.4348	−	8.95882i	−1.09696	−	0.293929i	−0.761526	+	0.648135i	$0.775549\pi$
$930$	−2.33829	−	8.57283i	−0.0766757	−	0.281114i
$931$	−9.43279	−	1.69268i	−0.309147	−	0.0554754i
$932$			29.5556i			0.968126i
$933$	27.8312	−	0.124683i	0.911153	−	0.00408193i
$934$	−7.18745	−	26.8239i	−0.235181	−	0.877706i
$935$	−0.0341209	+	0.0590991i	−0.00111587	+	0.00193275i
$936$	−41.4236	−	44.0346i	−1.35397	−	1.43932i
$937$	−2.71343			−0.0886440			−0.0443220	−	0.999017i	$-0.514113\pi$
$937$	−2.71343			−0.0886440			−0.0443220	+	0.999017i	$0.514113\pi$
$938$	14.3728	−	15.6377i	0.469290	−	0.510588i
$939$	18.2091	−	31.8680i	0.594233	−	1.03997i
$940$	2.37783	−	1.37284i	0.0775562	−	0.0447771i
$941$	−8.33651	−	31.1123i	−0.271763	−	1.01423i	−0.957980	−	0.286835i	$-0.907397\pi$
$941$	−8.33651	−	31.1123i	−0.271763	−	1.01423i	0.686217	−	0.727397i	$-0.259270\pi$
$942$	31.1107	+	8.18688i	1.01364	+	0.266743i
$943$	22.9863	+	6.15916i	0.748537	+	0.200570i
$944$	30.3618	+	30.3618i	0.988191	+	0.988191i
$945$	−18.0637	+	11.8131i	−0.587614	+	0.384281i
$946$			12.8777i			0.418689i
$947$	4.69062	−	17.5056i	0.152425	−	0.568857i	−0.846887	−	0.531772i	$-0.821526\pi$
$947$	4.69062	−	17.5056i	0.152425	−	0.568857i	0.999312	−	0.0370847i	$-0.0118071\pi$
$948$	−14.6143	+	8.52512i	−0.474652	+	0.276883i
$949$	33.8667	−	31.2913i	1.09936	−	1.01576i
$950$	7.50729	−	4.33434i	0.243569	−	0.140624i
$951$	−3.50741	−	12.8591i	−0.113735	−	0.416985i
$952$	−0.246882	+	0.472511i	−0.00800150	+	0.0153142i
$953$	−55.7076			−1.80455			−0.902273	−	0.431165i	$-0.858103\pi$
$953$	−55.7076			−1.80455			−0.902273	+	0.431165i	$0.858103\pi$
$954$	−59.4988	+	16.5154i	−1.92635	+	0.534707i
$955$	20.9059	−	5.60171i	0.676498	−	0.181267i
$956$	75.3715	−	20.1957i	2.43769	−	0.653177i
$957$	15.4126	−	15.5513i	0.498219	−	0.502703i
$958$	33.2000			1.07264
$959$	−1.64042	+	3.13961i	−0.0529718	+	0.101383i
$960$	−12.2771	+	3.34865i	−0.396240	+	0.108077i
$961$	−25.3643	+	14.6441i	−0.818202	+	0.472389i
$962$	3.48830	−	88.2568i	0.112467	−	2.84551i
$963$	0.428318	+	47.8029i	0.0138024	+	1.54043i
$964$	−5.46742	+	20.4047i	−0.176094	+	0.657191i
$965$			5.93063i			0.190914i
$966$	−3.06566	−	65.7374i	−0.0986360	−	2.11507i
$967$	−19.7857	−	19.7857i	−0.636264	−	0.636264i	0.313368	−	0.949632i	$-0.398543\pi$
$967$	−19.7857	−	19.7857i	−0.636264	−	0.636264i	−0.949632	+	0.313368i	$0.898543\pi$
$968$	51.5382	+	13.8096i	1.65650	+	0.443858i
$969$	−0.0217561	+	0.0826747i	−0.000698908	+	0.00265590i
$970$	17.7503	+	66.2451i	0.569929	+	2.12700i
$971$	−21.4276	+	12.3712i	−0.687645	+	0.397012i	−0.802729	−	0.596344i	$-0.796619\pi$
$971$	−21.4276	+	12.3712i	−0.687645	+	0.397012i	0.115084	+	0.993356i	$0.463286\pi$
$972$	56.4568	−	34.3039i	1.81085	−	1.10030i
$973$	−34.3729	+	37.3978i	−1.10194	+	1.19892i
$974$	52.6067			1.68563
$975$	−13.9799	+	7.43116i	−0.447716	+	0.237988i
$976$	−29.6736	+	51.3961i	−0.949828	+	1.64515i
$977$	5.40842	+	20.1845i	0.173031	+	0.645759i	0.996879	+	0.0789482i	$0.0251562\pi$
$977$	5.40842	+	20.1845i	0.173031	+	0.645759i	−0.823848	+	0.566811i	$0.808177\pi$
$978$	0.0758774	+	16.9371i	0.00242629	+	0.541588i
$979$		−	9.12532i		−	0.291647i
$980$	−30.0444	+	35.5864i	−0.959732	+	1.13676i
$981$	4.15945	−	16.0989i	0.132801	−	0.513997i
$982$	38.4253	+	10.2960i	1.22620	+	0.328560i
$983$	1.90251	−	0.509776i	0.0606807	−	0.0162593i	−0.228351	−	0.973579i	$-0.573333\pi$
$983$	1.90251	−	0.509776i	0.0606807	−	0.0162593i	0.289032	+	0.957320i	$0.406667\pi$
$984$	20.1883	+	34.6082i	0.643580	+	1.10327i
$985$	22.8458	−	13.1900i	0.727927	−	0.420269i
$986$	0.667549	+	0.667549i	0.0212591	+	0.0212591i
$987$	0.868246	−	1.68004i	0.0276366	−	0.0534763i
$988$	−19.9766	−	6.20803i	−0.635541	−	0.197504i
$989$	21.2949	−	12.2946i	0.677139	−	0.390946i
$990$	9.93849	−	10.1182i	0.315866	−	0.321577i
$991$	25.7506	−	44.6013i	0.817994	−	1.41681i	−0.0891632	−	0.996017i	$-0.528419\pi$
$991$	25.7506	−	44.6013i	0.817994	−	1.41681i	0.907158	−	0.420791i	$-0.138247\pi$
$992$	1.64692	+	2.85255i	0.0522897	+	0.0905685i
$993$	−9.39548	+	2.56268i	−0.298156	+	0.0813241i
$994$	11.6701	−	52.2663i	0.370153	−	1.65779i
$995$	6.78902	+	6.78902i	0.215227	+	0.215227i
$996$	−67.8137	−	67.2088i	−2.14876	−	2.12959i
$997$	−15.2981	+	26.4970i	−0.484494	+	0.839168i	−0.999841	−	0.0178130i	$-0.994330\pi$
$997$	−15.2981	+	26.4970i	−0.484494	+	0.839168i	0.515347	+	0.856981i	$0.327663\pi$
$998$	7.52386	−	13.0317i	0.238164	−	0.412512i
$999$	49.4021	+	12.5282i	1.56301	+	0.396373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.242.3	yes	112
3.2	odd	2	inner	273.2.cd.e.242.26	yes	112
7.2	even	3	inner	273.2.cd.e.86.26	yes	112
13.5	odd	4	inner	273.2.cd.e.200.3	yes	112
21.2	odd	6	inner	273.2.cd.e.86.3	yes	112
39.5	even	4	inner	273.2.cd.e.200.26	yes	112
91.44	odd	12	inner	273.2.cd.e.44.26	yes	112
273.44	even	12	inner	273.2.cd.e.44.3	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.3	✓	112	273.44	even	12	inner
273.2.cd.e.44.26	yes	112	91.44	odd	12	inner
273.2.cd.e.86.3	yes	112	21.2	odd	6	inner
273.2.cd.e.86.26	yes	112	7.2	even	3	inner
273.2.cd.e.200.3	yes	112	13.5	odd	4	inner
273.2.cd.e.200.26	yes	112	39.5	even	4	inner
273.2.cd.e.242.3	yes	112	1.1	even	1	trivial
273.2.cd.e.242.26	yes	112	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.41247 - 0.646418i) q^{2} +(0.872737 + 1.49611i) q^{3} +(3.67009 + 2.11892i) q^{4} +(-1.51647 - 0.406338i) q^{5} +(-1.13834 - 4.17346i) q^{6} +(-1.79039 + 1.94795i) q^{7} +(-3.95215 - 3.95215i) q^{8} +(-1.47666 + 2.61141i) q^{9} +O(q^{10})\)	\(q+(-2.41247 - 0.646418i) q^{2} +(0.872737 + 1.49611i) q^{3} +(3.67009 + 2.11892i) q^{4} +(-1.51647 - 0.406338i) q^{5} +(-1.13834 - 4.17346i) q^{6} +(-1.79039 + 1.94795i) q^{7} +(-3.95215 - 3.95215i) q^{8} +(-1.47666 + 2.61141i) q^{9} +(3.39578 + 1.96055i) q^{10} +(-1.16460 + 0.312052i) q^{11} +(0.0328833 + 7.34010i) q^{12} +(-1.67805 - 3.19126i) q^{13} +(5.57845 - 3.54202i) q^{14} +(-0.715558 - 2.62343i) q^{15} +(2.74184 + 4.74900i) q^{16} +(-0.0180259 + 0.0312218i) q^{17} +(5.25046 - 5.34540i) q^{18} +(0.354340 - 1.32242i) q^{19} +(-4.70459 - 4.70459i) q^{20} +(-4.47687 - 0.978568i) q^{21} +3.01126 q^{22} +(-2.87493 - 4.97952i) q^{23} +(2.46365 - 9.36202i) q^{24} +(-2.19554 - 1.26760i) q^{25} +(1.98535 + 8.78353i) q^{26} +(-5.19568 + 0.0698330i) q^{27} +(-10.6984 + 3.35543i) q^{28} +10.4846i q^{29} +(0.0304256 + 6.79149i) q^{30} +(-1.26381 + 0.338636i) q^{31} +(-0.651571 - 2.43170i) q^{32} +(-1.48325 - 1.47002i) q^{33} +(0.0636693 - 0.0636693i) q^{34} +(3.50661 - 2.22651i) q^{35} +(-10.9529 + 6.45517i) q^{36} +(-9.47419 - 2.53860i) q^{37} +(-1.70967 + 2.96123i) q^{38} +(3.30997 - 5.29567i) q^{39} +(4.38743 + 7.59925i) q^{40} +(-2.92653 + 2.92653i) q^{41} +(10.1677 + 5.25470i) q^{42} +4.27650i q^{43} +(-4.93538 - 1.32243i) q^{44} +(3.30044 - 3.36012i) q^{45} +(3.71681 + 13.8713i) q^{46} +(-0.106809 + 0.398617i) q^{47} +(-4.71210 + 8.24670i) q^{48} +(-0.589001 - 6.97518i) q^{49} +(4.47727 + 4.47727i) q^{50} +(-0.0624430 + 0.000279742i) q^{51} +(0.603453 - 15.2679i) q^{52} +(-7.13704 - 4.12057i) q^{53} +(12.5796 + 3.19012i) q^{54} +1.89288 q^{55} +(14.7745 - 0.622688i) q^{56} +(2.28772 - 0.623990i) q^{57} +(6.77746 - 25.2938i) q^{58} +(7.56335 - 2.02659i) q^{59} +(2.93270 - 11.1444i) q^{60} +(5.41126 + 9.37258i) q^{61} +3.26779 q^{62} +(-2.44309 - 7.55191i) q^{63} -4.67977i q^{64} +(1.24799 + 5.52132i) q^{65} +(2.62804 + 4.50517i) q^{66} +(3.10471 - 0.831905i) q^{67} +(-0.132313 + 0.0763912i) q^{68} +(4.94083 - 8.64701i) q^{69} +(-9.89883 + 3.10464i) q^{70} +(5.73066 - 5.73066i) q^{71} +(16.1567 - 4.48470i) q^{72} +(3.30991 + 12.3528i) q^{73} +(21.2152 + 12.2486i) q^{74} +(-0.0196717 - 4.39104i) q^{75} +(4.10256 - 4.10256i) q^{76} +(1.47722 - 2.82727i) q^{77} +(-11.4084 + 10.6360i) q^{78} +(1.15250 + 1.99619i) q^{79} +(-2.22823 - 8.31585i) q^{80} +(-4.63894 - 7.71234i) q^{81} +(8.95193 - 5.16840i) q^{82} +(-9.19760 + 9.19760i) q^{83} +(-14.3570 - 13.0776i) q^{84} +(0.0400225 - 0.0400225i) q^{85} +(2.76441 - 10.3169i) q^{86} +(-15.6861 + 9.15032i) q^{87} +(5.83593 + 3.36938i) q^{88} +(-1.95890 + 7.31073i) q^{89} +(-10.1342 + 5.97270i) q^{90} +(9.22078 + 2.44485i) q^{91} -24.3670i q^{92} +(-1.60960 - 1.59525i) q^{93} +(0.515347 - 0.892608i) q^{94} +(-1.07470 + 1.86143i) q^{95} +(3.06942 - 3.09705i) q^{96} +(12.3676 + 12.3676i) q^{97} +(-3.08794 + 17.2081i) q^{98} +(0.904816 - 3.50203i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

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