LMFDB - Embedded newform 552.2.q.c.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	552.25
Dual form			552.2.q.c.265.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{3} +(-3.30472 - 0.970352i) q^{5} +(1.20819 - 1.39433i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{3} +(-3.30472 - 0.970352i) q^{5} +(1.20819 - 1.39433i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(1.75329 - 1.12677i) q^{11} +(3.23909 + 3.73811i) q^{13} +(0.490165 - 3.40917i) q^{15} +(3.08844 - 6.76275i) q^{17} +(0.0456185 + 0.0998907i) q^{19} +(1.55208 + 0.997461i) q^{21} +(1.89050 - 4.40749i) q^{23} +(5.77330 + 3.71027i) q^{25} +(-0.415415 - 0.909632i) q^{27} +(2.05743 - 4.50514i) q^{29} +(0.687579 - 4.78222i) q^{31} +(1.36482 + 1.57509i) q^{33} +(-5.34572 + 3.43549i) q^{35} +(4.85951 - 1.42688i) q^{37} +(-3.23909 + 3.73811i) q^{39} +(9.62979 + 2.82756i) q^{41} +(0.383056 + 2.66421i) q^{43} +3.44423 q^{45} -13.2801 q^{47} +(0.511781 + 3.55952i) q^{49} +(7.13345 + 2.09457i) q^{51} +(-4.97734 + 5.74416i) q^{53} +(-6.88749 + 2.02235i) q^{55} +(-0.0923817 + 0.0593701i) q^{57} +(9.04058 + 10.4334i) q^{59} +(0.993721 - 6.91148i) q^{61} +(-0.766424 + 1.67824i) q^{63} +(-7.07699 - 15.4964i) q^{65} +(-3.38571 - 2.17586i) q^{67} +(4.63168 + 1.24401i) q^{69} +(-9.77019 - 6.27892i) q^{71} +(0.296845 + 0.649999i) q^{73} +(-2.85088 + 6.24256i) q^{75} +(0.547223 - 3.80602i) q^{77} +(-8.89515 - 10.2656i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-1.15678 + 0.339661i) q^{83} +(-16.7687 + 19.3521i) q^{85} +(4.75209 + 1.39534i) q^{87} +(0.207767 + 1.44505i) q^{89} +9.12560 q^{91} +4.83140 q^{93} +(-0.0538272 - 0.374376i) q^{95} +(2.46065 + 0.722511i) q^{97} +(-1.36482 + 1.57509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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 $

$2$		0			0
$2$		0			0
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$		0			0
$5$	−3.30472	−	0.970352i	−1.47791	−	0.433955i	−0.559252	−	0.828998i	$-0.688911\pi$
$5$	−3.30472	−	0.970352i	−1.47791	−	0.433955i	−0.918663	+	0.395043i	$0.870730\pi$
$6$		0			0
$7$	1.20819	−	1.39433i	0.456654	−	0.527007i	−0.479997	−	0.877270i	$-0.659362\pi$
$7$	1.20819	−	1.39433i	0.456654	−	0.527007i	0.936651	+	0.350263i	$0.113908\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	1.75329	−	1.12677i	0.528637	−	0.339734i	−0.248943	−	0.968518i	$-0.580083\pi$
$11$	1.75329	−	1.12677i	0.528637	−	0.339734i	0.777580	+	0.628784i	$0.216447\pi$
$12$		0			0
$13$	3.23909	+	3.73811i	0.898362	+	1.03676i	0.999124	+	0.0418544i	$0.0133266\pi$
$13$	3.23909	+	3.73811i	0.898362	+	1.03676i	−0.100762	+	0.994911i	$0.532128\pi$
$14$		0			0
$15$	0.490165	−	3.40917i	0.126560	−	0.880245i
$16$		0			0
$17$	3.08844	−	6.76275i	0.749058	−	1.64021i	−0.0189940	−	0.999820i	$-0.506046\pi$
$17$	3.08844	−	6.76275i	0.749058	−	1.64021i	0.768052	−	0.640388i	$-0.221226\pi$
$18$		0			0
$19$	0.0456185	+	0.0998907i	0.0104656	+	0.0229165i	0.914793	−	0.403924i	$-0.132354\pi$
$19$	0.0456185	+	0.0998907i	0.0104656	+	0.0229165i	−0.904327	+	0.426840i	$0.859627\pi$
$20$		0			0
$21$	1.55208	+	0.997461i	0.338692	+	0.217664i
$22$		0			0
$23$	1.89050	−	4.40749i	0.394197	−	0.919026i
$23$	1.89050	−	4.40749i	0.394197	−	0.919026i
$24$		0			0
$25$	5.77330	+	3.71027i	1.15466	+	0.742055i
$26$		0			0
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$		0			0
$29$	2.05743	−	4.50514i	0.382055	−	0.836583i	−0.616724	−	0.787179i	$-0.711541\pi$
$29$	2.05743	−	4.50514i	0.382055	−	0.836583i	0.998779	−	0.0494039i	$-0.0157322\pi$
$30$		0			0
$31$	0.687579	−	4.78222i	0.123493	−	0.858912i	−0.830057	−	0.557678i	$-0.811692\pi$
$31$	0.687579	−	4.78222i	0.123493	−	0.858912i	0.953550	−	0.301234i	$-0.0973985\pi$
$32$		0			0
$33$	1.36482	+	1.57509i	0.237585	+	0.274188i
$34$		0			0
$35$	−5.34572	+	3.43549i	−0.903592	+	0.580703i
$36$		0			0
$37$	4.85951	−	1.42688i	0.798899	−	0.234578i	0.143292	−	0.989680i	$-0.454231\pi$
$37$	4.85951	−	1.42688i	0.798899	−	0.234578i	0.655607	+	0.755103i	$0.272413\pi$
$38$		0			0
$39$	−3.23909	+	3.73811i	−0.518670	+	0.598577i
$40$		0			0
$41$	9.62979	+	2.82756i	1.50392	+	0.441591i	0.926953	−	0.375177i	$-0.122418\pi$
$41$	9.62979	+	2.82756i	1.50392	+	0.441591i	0.576967	+	0.816768i	$0.304236\pi$
$42$		0			0
$43$	0.383056	+	2.66421i	0.0584155	+	0.406289i	0.997959	+	0.0638589i	$0.0203408\pi$
$43$	0.383056	+	2.66421i	0.0584155	+	0.406289i	−0.939543	+	0.342430i	$0.888750\pi$
$44$		0			0
$45$	3.44423			0.513436
$46$		0			0
$47$	−13.2801			−1.93710			−0.968550	−	0.248821i	$-0.919957\pi$
$47$	−13.2801			−1.93710			−0.968550	+	0.248821i	$0.919957\pi$
$48$		0			0
$49$	0.511781	+	3.55952i	0.0731116	+	0.508502i
$50$		0			0
$51$	7.13345	+	2.09457i	0.998882	+	0.293298i
$52$		0			0
$53$	−4.97734	+	5.74416i	−0.683691	+	0.789021i	−0.986453	−	0.164045i	$-0.947546\pi$
$53$	−4.97734	+	5.74416i	−0.683691	+	0.789021i	0.302762	+	0.953066i	$0.402091\pi$
$54$		0			0
$55$	−6.88749	+	2.02235i	−0.928709	+	0.272694i
$56$		0			0
$57$	−0.0923817	+	0.0593701i	−0.0122363	+	0.00786377i
$58$		0			0
$59$	9.04058	+	10.4334i	1.17698	+	1.35831i	0.920011	+	0.391892i	$0.128179\pi$
$59$	9.04058	+	10.4334i	1.17698	+	1.35831i	0.256972	+	0.966419i	$0.417275\pi$
$60$		0			0
$61$	0.993721	−	6.91148i	0.127233	−	0.884924i	−0.821807	−	0.569767i	$-0.807034\pi$
$61$	0.993721	−	6.91148i	0.127233	−	0.884924i	0.949039	−	0.315157i	$-0.102057\pi$
$62$		0			0
$63$	−0.766424	+	1.67824i	−0.0965604	+	0.211438i
$64$		0			0
$65$	−7.07699	−	15.4964i	−0.877793	−	1.92210i
$66$		0			0
$67$	−3.38571	−	2.17586i	−0.413630	−	0.265824i	0.317234	−	0.948347i	$-0.397246\pi$
$67$	−3.38571	−	2.17586i	−0.413630	−	0.265824i	−0.730864	+	0.682524i	$0.760882\pi$
$68$		0			0
$69$	4.63168	+	1.24401i	0.557589	+	0.149761i
$70$		0			0
$71$	−9.77019	−	6.27892i	−1.15951	−	0.745171i	−0.187998	−	0.982169i	$-0.560200\pi$
$71$	−9.77019	−	6.27892i	−1.15951	−	0.745171i	−0.971510	+	0.236999i	$0.923836\pi$
$72$		0			0
$73$	0.296845	+	0.649999i	0.0347430	+	0.0760766i	0.926208	−	0.377013i	$-0.123049\pi$
$73$	0.296845	+	0.649999i	0.0347430	+	0.0760766i	−0.891465	+	0.453090i	$0.850322\pi$
$74$		0			0
$75$	−2.85088	+	6.24256i	−0.329192	+	0.720829i
$76$		0			0
$77$	0.547223	−	3.80602i	0.0623618	−	0.433736i
$78$		0			0
$79$	−8.89515	−	10.2656i	−1.00078	−	1.15497i	−0.987907	−	0.155048i	$-0.950447\pi$
$79$	−8.89515	−	10.2656i	−1.00078	−	1.15497i	−0.0128760	−	0.999917i	$-0.504099\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	−1.15678	+	0.339661i	−0.126973	+	0.0372827i	−0.344602	−	0.938749i	$-0.611986\pi$
$83$	−1.15678	+	0.339661i	−0.126973	+	0.0372827i	0.217629	+	0.976032i	$0.430168\pi$
$84$		0			0
$85$	−16.7687	+	19.3521i	−1.81882	+	2.09903i
$86$		0			0
$87$	4.75209	+	1.39534i	0.509477	+	0.149596i
$88$		0			0
$89$	0.207767	+	1.44505i	0.0220232	+	0.153175i	0.997866	−	0.0653008i	$-0.0208007\pi$
$89$	0.207767	+	1.44505i	0.0220232	+	0.153175i	−0.975842	+	0.218476i	$0.929892\pi$
$90$		0			0
$91$	9.12560			0.956622
$92$		0			0
$93$	4.83140			0.500993
$94$		0			0
$95$	−0.0538272	−	0.374376i	−0.00552255	−	0.0384102i
$96$		0			0
$97$	2.46065	+	0.722511i	0.249841	+	0.0733599i	0.404255	−	0.914646i	$-0.367531\pi$
$97$	2.46065	+	0.722511i	0.249841	+	0.0733599i	−0.154414	+	0.988006i	$0.549349\pi$
$98$		0			0
$99$	−1.36482	+	1.57509i	−0.137170	+	0.158302i
$100$		0			0
$101$	−6.93348	+	2.03585i	−0.689907	+	0.202575i	−0.607849	−	0.794053i	$-0.707967\pi$
$101$	−6.93348	+	2.03585i	−0.689907	+	0.202575i	−0.0820579	+	0.996628i	$0.526149\pi$
$102$		0			0
$103$	5.02023	−	3.22630i	0.494658	−	0.317897i	−0.269418	−	0.963023i	$-0.586831\pi$
$103$	5.02023	−	3.22630i	0.494658	−	0.317897i	0.764076	+	0.645126i	$0.223195\pi$
$104$		0			0
$105$	−4.16129	−	4.80239i	−0.406101	−	0.468665i
$106$		0			0
$107$	1.08818	−	7.56845i	0.105198	−	0.731670i	−0.867135	−	0.498073i	$-0.834041\pi$
$107$	1.08818	−	7.56845i	0.105198	−	0.731670i	0.972333	−	0.233597i	$-0.0750497\pi$
$108$		0			0
$109$	4.88500	−	10.6966i	0.467898	−	1.02455i	−0.517718	−	0.855551i	$-0.673218\pi$
$109$	4.88500	−	10.6966i	0.467898	−	1.02455i	0.985616	−	0.169002i	$-0.0540543\pi$
$110$		0			0
$111$	2.10394	+	4.60698i	0.199697	+	0.437275i
$112$		0			0
$113$	3.28043	+	2.10821i	0.308597	+	0.198323i	0.685768	−	0.727820i	$-0.259467\pi$
$113$	3.28043	+	2.10821i	0.308597	+	0.198323i	−0.377171	+	0.926144i	$0.623103\pi$
$114$		0			0
$115$	−10.5244	+	12.7311i	−0.981405	+	1.18718i
$116$		0			0
$117$	−4.16103	−	2.67413i	−0.384687	−	0.247224i
$118$		0			0
$119$	−5.69806	−	12.4770i	−0.522340	−	1.14377i
$120$		0			0
$121$	−2.76515	+	6.05484i	−0.251378	+	0.550440i
$122$		0			0
$123$	−1.42832	+	9.93417i	−0.128787	+	0.895734i
$124$		0			0
$125$	−4.20138	−	4.84865i	−0.375783	−	0.433677i
$126$		0			0
$127$	9.49496	−	6.10204i	0.842542	−	0.541469i	−0.0466987	−	0.998909i	$-0.514870\pi$
$127$	9.49496	−	6.10204i	0.842542	−	0.541469i	0.889240	+	0.457440i	$0.151234\pi$
$128$		0			0
$129$	−2.58258	+	0.758314i	−0.227384	+	0.0667658i
$130$		0			0
$131$	1.00266	−	1.15713i	0.0876025	−	0.101099i	−0.710256	−	0.703944i	$-0.751421\pi$
$131$	1.00266	−	1.15713i	0.0876025	−	0.101099i	0.797858	+	0.602845i	$0.205966\pi$
$132$		0			0
$133$	0.194396	+	0.0570799i	0.0168563	+	0.00494946i
$134$		0			0
$135$	0.490165	+	3.40917i	0.0421867	+	0.293415i
$136$		0			0
$137$	1.88696			0.161214			0.0806070	−	0.996746i	$-0.474314\pi$
$137$	1.88696			0.161214			0.0806070	+	0.996746i	$0.474314\pi$
$138$		0			0
$139$	−9.86622			−0.836842			−0.418421	−	0.908253i	$-0.637416\pi$
$139$	−9.86622			−0.836842			−0.418421	+	0.908253i	$0.637416\pi$
$140$		0			0
$141$	−1.88995	−	13.1449i	−0.159163	−	1.10700i
$142$		0			0
$143$	9.89106	+	2.90428i	0.827132	+	0.242868i
$144$		0			0
$145$	−11.1708	+	12.8918i	−0.927683	+	1.07060i
$146$		0			0
$147$	−3.45045	+	1.01314i	−0.284588	+	0.0835627i
$148$		0			0
$149$	−10.1432	+	6.51861i	−0.830960	+	0.534025i	−0.885583	−	0.464482i	$-0.846241\pi$
$149$	−10.1432	+	6.51861i	−0.830960	+	0.534025i	0.0546231	+	0.998507i	$0.482604\pi$
$150$		0			0
$151$	4.32571	+	4.99213i	0.352021	+	0.406254i	0.903951	−	0.427637i	$-0.140654\pi$
$151$	4.32571	+	4.99213i	0.352021	+	0.406254i	−0.551930	+	0.833891i	$0.686108\pi$
$152$		0			0
$153$	−1.05805	+	7.35893i	−0.0855386	+	0.594934i
$154$		0			0
$155$	−6.91269	+	15.1367i	−0.555241	+	1.21581i
$156$		0			0
$157$	6.54932	+	14.3410i	0.522693	+	1.14454i	0.968410	+	0.249364i	$0.0802215\pi$
$157$	6.54932	+	14.3410i	0.522693	+	1.14454i	−0.445717	+	0.895174i	$0.647051\pi$
$158$		0			0
$159$	−6.39404	−	4.10920i	−0.507081	−	0.325881i
$160$		0			0
$161$	−3.86140	−	7.96108i	−0.304321	−	0.627421i
$162$		0			0
$163$	6.44316	+	4.14077i	0.504667	+	0.324330i	0.768081	−	0.640353i	$-0.221212\pi$
$163$	6.44316	+	4.14077i	0.504667	+	0.324330i	−0.263414	+	0.964683i	$0.584848\pi$
$164$		0			0
$165$	−2.98196	−	6.52958i	−0.232145	−	0.508327i
$166$		0			0
$167$	−1.39039	+	3.04454i	−0.107592	+	0.235593i	−0.955768	−	0.294120i	$-0.904973\pi$
$167$	−1.39039	+	3.04454i	−0.107592	+	0.235593i	0.848176	+	0.529714i	$0.177701\pi$
$168$		0			0
$169$	−1.63166	+	11.3485i	−0.125513	+	0.872959i
$170$		0			0
$171$	−0.0719131	−	0.0829922i	−0.00549933	−	0.00634657i
$172$		0			0
$173$	−8.26759	+	5.31325i	−0.628573	+	0.403959i	−0.815781	−	0.578361i	$-0.803693\pi$
$173$	−8.26759	+	5.31325i	−0.628573	+	0.403959i	0.187208	+	0.982320i	$0.440056\pi$
$174$		0			0
$175$	12.1486	−	3.56715i	0.918347	−	0.269651i
$176$		0			0
$177$	−9.04058	+	10.4334i	−0.679532	+	0.784221i
$178$		0			0
$179$	−11.9835	−	3.51867i	−0.895688	−	0.262998i	−0.198683	−	0.980064i	$-0.563666\pi$
$179$	−11.9835	−	3.51867i	−0.895688	−	0.262998i	−0.697005	+	0.717066i	$0.745484\pi$
$180$		0			0
$181$	2.86274	+	19.9108i	0.212786	+	1.47996i	0.763796	+	0.645458i	$0.223333\pi$
$181$	2.86274	+	19.9108i	0.212786	+	1.47996i	−0.551011	+	0.834498i	$0.685758\pi$
$182$		0			0
$183$	6.98255			0.516165
$184$		0			0
$185$	−17.4439			−1.28250
$186$		0			0
$187$	−2.20513	−	15.3370i	−0.161255	−	1.12155i
$188$		0			0
$189$	−1.77023	−	0.519786i	−0.128765	−	0.0378088i
$190$		0			0
$191$	−4.93777	+	5.69849i	−0.357284	+	0.412328i	−0.905728	−	0.423859i	$-0.860675\pi$
$191$	−4.93777	+	5.69849i	−0.357284	+	0.412328i	0.548444	+	0.836188i	$0.315221\pi$
$192$		0			0
$193$	25.0809	−	7.36443i	1.80537	−	0.530103i	0.807179	−	0.590307i	$-0.200993\pi$
$193$	25.0809	−	7.36443i	1.80537	−	0.530103i	0.998186	+	0.0602034i	$0.0191749\pi$
$194$		0			0
$195$	14.3316	−	9.21033i	1.02630	−	0.659566i
$196$		0			0
$197$	14.1048	+	16.2778i	1.00493	+	1.15975i	0.987132	+	0.159906i	$0.0511191\pi$
$197$	14.1048	+	16.2778i	1.00493	+	1.15975i	0.0177947	+	0.999842i	$0.494335\pi$
$198$		0			0
$199$	−1.12432	+	7.81982i	−0.0797009	+	0.554332i	0.910373	+	0.413788i	$0.135794\pi$
$199$	−1.12432	+	7.81982i	−0.0797009	+	0.554332i	−0.990074	+	0.140544i	$0.955115\pi$
$200$		0			0
$201$	1.67188	−	3.66090i	0.117925	−	0.258220i
$202$		0			0
$203$	−3.79587	−	8.31181i	−0.266418	−	0.583374i
$204$		0			0
$205$	−29.0800	−	18.6886i	−2.03103	−	1.30527i
$206$		0			0
$207$	−0.572188	+	4.76158i	−0.0397698	+	0.330952i
$208$		0			0
$209$	0.192536	+	0.123736i	0.0133180	+	0.00855898i
$210$		0			0
$211$	−8.20128	−	17.9583i	−0.564599	−	1.23630i	−0.949623	−	0.313393i	$-0.898534\pi$
$211$	−8.20128	−	17.9583i	−0.564599	−	1.23630i	0.385024	−	0.922907i	$-0.374193\pi$
$212$		0			0
$213$	4.82457	−	10.5643i	0.330574	−	0.723856i
$214$		0			0
$215$	1.31933	−	9.17617i	0.0899778	−	0.625809i
$216$		0			0
$217$	−5.83726	−	6.73655i	−0.396259	−	0.457307i
$218$		0			0
$219$	−0.601137	+	0.386328i	−0.0406211	+	0.0261056i
$220$		0			0
$221$	35.2836	−	10.3602i	2.37343	−	0.696903i
$222$		0			0
$223$	−1.76114	+	2.03247i	−0.117935	+	0.136104i	−0.811647	−	0.584148i	$-0.801429\pi$
$223$	−1.76114	+	2.03247i	−0.117935	+	0.136104i	0.693712	+	0.720253i	$0.255974\pi$
$224$		0			0
$225$	−6.58474	−	1.93346i	−0.438983	−	0.128897i
$226$		0			0
$227$	1.93626	+	13.4670i	0.128514	+	0.893836i	0.947439	+	0.319936i	$0.103661\pi$
$227$	1.93626	+	13.4670i	0.128514	+	0.893836i	−0.818925	+	0.573900i	$0.805430\pi$
$228$		0			0
$229$	8.43839			0.557624			0.278812	−	0.960346i	$-0.410059\pi$
$229$	8.43839			0.557624			0.278812	+	0.960346i	$0.410059\pi$
$230$		0			0
$231$	3.84516			0.252993
$232$		0			0
$233$	−2.27331	−	15.8112i	−0.148930	−	1.03583i	−0.917976	−	0.396636i	$-0.870177\pi$
$233$	−2.27331	−	15.8112i	−0.148930	−	1.03583i	0.769046	−	0.639193i	$-0.220732\pi$
$234$		0			0
$235$	43.8869	+	12.8864i	2.86287	+	0.840613i
$236$		0			0
$237$	8.89515	−	10.2656i	0.577802	−	0.666819i
$238$		0			0
$239$	21.4288	−	6.29206i	1.38611	−	0.407000i	0.498220	−	0.867050i	$-0.333987\pi$
$239$	21.4288	−	6.29206i	1.38611	−	0.407000i	0.887893	+	0.460051i	$0.152169\pi$
$240$		0			0
$241$	6.66310	−	4.28211i	0.429208	−	0.275835i	−0.308150	−	0.951338i	$-0.599710\pi$
$241$	6.66310	−	4.28211i	0.429208	−	0.275835i	0.737357	+	0.675503i	$0.236073\pi$
$242$		0			0
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$		0			0
$245$	1.76269	−	12.2598i	0.112614	−	0.783250i
$246$		0			0
$247$	−0.225640	+	0.494082i	−0.0143571	+	0.0314377i
$248$		0			0
$249$	−0.500831	−	1.09667i	−0.0317389	−	0.0694984i
$250$		0			0
$251$	13.6544	+	8.77516i	0.861859	+	0.553883i	0.895253	−	0.445559i	$-0.146995\pi$
$251$	13.6544	+	8.77516i	0.861859	+	0.553883i	−0.0333935	+	0.999442i	$0.510631\pi$
$252$		0			0
$253$	−1.65164	−	9.85778i	−0.103838	−	0.619753i
$254$		0			0
$255$	−21.5415	−	13.8439i	−1.34898	−	0.866939i
$256$		0			0
$257$	12.5270	+	27.4304i	0.781416	+	1.71106i	0.699734	+	0.714403i	$0.253302\pi$
$257$	12.5270	+	27.4304i	0.781416	+	1.71106i	0.0816816	+	0.996658i	$0.473971\pi$
$258$		0			0
$259$	3.88168	−	8.49970i	0.241196	−	0.528146i
$260$		0			0
$261$	−0.704843	+	4.90229i	−0.0436287	+	0.303444i
$262$		0			0
$263$	20.6347	+	23.8137i	1.27239	+	1.46842i	0.815347	+	0.578972i	$0.196546\pi$
$263$	20.6347	+	23.8137i	1.27239	+	1.46842i	0.457043	+	0.889445i	$0.348909\pi$
$264$		0			0
$265$	22.0226	−	14.1530i	1.35284	−	0.869415i
$266$		0			0
$267$	−1.40077	+	0.411304i	−0.0857259	+	0.0251714i
$268$		0			0
$269$	−5.80135	+	6.69512i	−0.353715	+	0.408208i	−0.904524	−	0.426423i	$-0.859774\pi$
$269$	−5.80135	+	6.69512i	−0.353715	+	0.408208i	0.550809	+	0.834631i	$0.314319\pi$
$270$		0			0
$271$	−14.2800	−	4.19298i	−0.867446	−	0.254705i	−0.182417	−	0.983221i	$-0.558392\pi$
$271$	−14.2800	−	4.19298i	−0.867446	−	0.254705i	−0.685029	+	0.728516i	$0.740210\pi$
$272$		0			0
$273$	1.29871	+	9.03271i	0.0786014	+	0.546684i
$274$		0			0
$275$	14.3029			0.862497
$276$		0			0
$277$	−32.4585			−1.95024			−0.975120	−	0.221678i	$-0.928847\pi$
$277$	−32.4585			−1.95024			−0.975120	+	0.221678i	$0.928847\pi$
$278$		0			0
$279$	0.687579	+	4.78222i	0.0411643	+	0.286304i
$280$		0			0
$281$	−19.8029	−	5.81464i	−1.18134	−	0.346872i	−0.368649	−	0.929569i	$-0.620180\pi$
$281$	−19.8029	−	5.81464i	−1.18134	−	0.346872i	−0.812690	+	0.582696i	$0.801998\pi$
$282$		0			0
$283$	−3.29890	+	3.80713i	−0.196099	+	0.226310i	−0.845280	−	0.534324i	$-0.820566\pi$
$283$	−3.29890	+	3.80713i	−0.196099	+	0.226310i	0.649181	+	0.760634i	$0.275112\pi$
$284$		0			0
$285$	0.362905	−	0.106559i	0.0214967	−	0.00631199i
$286$		0			0
$287$	15.5772	−	10.0108i	0.919492	−	0.590922i
$288$		0			0
$289$	−25.0637	−	28.9250i	−1.47433	−	1.70147i
$290$		0			0
$291$	−0.364971	+	2.53843i	−0.0213950	+	0.148805i
$292$		0			0
$293$	8.48792	−	18.5859i	0.495869	−	1.08580i	−0.481920	−	0.876215i	$-0.660061\pi$
$293$	8.48792	−	18.5859i	0.495869	−	1.08580i	0.977790	−	0.209588i	$-0.0672121\pi$
$294$		0			0
$295$	−19.7525	−	43.2519i	−1.15003	−	2.51822i
$296$		0			0
$297$	−1.75329	−	1.12677i	−0.101736	−	0.0653819i
$298$		0			0
$299$	22.5992	−	7.20937i	1.30695	−	0.416929i
$300$		0			0
$301$	4.17759	+	2.68478i	0.240792	+	0.154748i
$302$		0			0
$303$	−3.00187	−	6.57317i	−0.172453	−	0.377619i
$304$		0			0
$305$	−9.99053	+	21.8762i	−0.572056	+	1.25263i
$306$		0			0
$307$	1.08404	−	7.53967i	0.0618695	−	0.430312i	−0.935220	−	0.354068i	$-0.884798\pi$
$307$	1.08404	−	7.53967i	0.0618695	−	0.430312i	0.997089	−	0.0762438i	$-0.0242927\pi$
$308$		0			0
$309$	3.90792	+	4.50998i	0.222314	+	0.256564i
$310$		0			0
$311$	−9.15822	+	5.88563i	−0.519315	+	0.333744i	−0.773901	−	0.633307i	$-0.781697\pi$
$311$	−9.15822	+	5.88563i	−0.519315	+	0.333744i	0.254586	+	0.967050i	$0.418061\pi$
$312$		0			0
$313$	−3.08439	+	0.905659i	−0.174340	+	0.0511909i	−0.367737	−	0.929930i	$-0.619867\pi$
$313$	−3.08439	+	0.905659i	−0.174340	+	0.0511909i	0.193397	+	0.981120i	$0.438049\pi$
$314$		0			0
$315$	4.16129	−	4.80239i	0.234462	−	0.270584i
$316$		0			0
$317$	0.424328	+	0.124594i	0.0238326	+	0.00699789i	0.293627	−	0.955920i	$-0.405138\pi$
$317$	0.424328	+	0.124594i	0.0238326	+	0.00699789i	−0.269795	+	0.962918i	$0.586956\pi$
$318$		0			0
$319$	−1.46899	−	10.2171i	−0.0822478	−	0.572046i
$320$		0			0
$321$	7.64628			0.426774
$322$		0			0
$323$	0.816426			0.0454272
$324$		0			0
$325$	4.83083	+	33.5991i	0.267966	+	1.86374i
$326$		0			0
$327$	11.2830	+	3.31298i	0.623950	+	0.183208i
$328$		0			0
$329$	−16.0449	+	18.5168i	−0.884584	+	1.02086i
$330$		0			0
$331$	−22.4909	+	6.60394i	−1.23621	+	0.362985i	−0.833592	−	0.552381i	$-0.813719\pi$
$331$	−22.4909	+	6.60394i	−1.23621	+	0.362985i	−0.402622	+	0.915366i	$0.631901\pi$
$332$		0			0
$333$	−4.26067	+	2.73817i	−0.233483	+	0.150051i
$334$		0			0
$335$	9.07745	+	10.4759i	0.495954	+	0.572362i
$336$		0			0
$337$	2.29301	−	15.9483i	0.124908	−	0.868757i	−0.826962	−	0.562257i	$-0.809933\pi$
$337$	2.29301	−	15.9483i	0.124908	−	0.868757i	0.951871	−	0.306500i	$-0.0991579\pi$
$338$		0			0
$339$	−1.61989	+	3.54707i	−0.0879806	+	0.192651i
$340$		0			0
$341$	−4.18294	−	9.15936i	−0.226519	−	0.496007i
$342$		0			0
$343$	16.4460	+	10.5692i	0.888002	+	0.570684i
$344$		0			0
$345$	−14.0993	−	8.60545i	−0.759079	−	0.463302i
$346$		0			0
$347$	6.02498	+	3.87202i	0.323438	+	0.207861i	0.692276	−	0.721633i	$-0.256608\pi$
$347$	6.02498	+	3.87202i	0.323438	+	0.207861i	−0.368838	+	0.929494i	$0.620244\pi$
$348$		0			0
$349$	10.1941	+	22.3220i	0.545678	+	1.19487i	0.958771	+	0.284179i	$0.0917210\pi$
$349$	10.1941	+	22.3220i	0.545678	+	1.19487i	−0.413093	+	0.910689i	$0.635552\pi$
$350$		0			0
$351$	2.05474	−	4.49925i	0.109674	−	0.240152i
$352$		0			0
$353$	1.22803	−	8.54117i	0.0653617	−	0.454600i	−0.930689	−	0.365812i	$-0.880791\pi$
$353$	1.22803	−	8.54117i	0.0653617	−	0.454600i	0.996050	−	0.0887886i	$-0.0282995\pi$
$354$		0			0
$355$	26.1949	+	30.2306i	1.39028	+	1.60447i
$356$		0			0
$357$	11.5391	−	7.41572i	0.610713	−	0.392482i
$358$		0			0
$359$	1.82556	−	0.536033i	0.0963494	−	0.0282907i	−0.233203	−	0.972428i	$-0.574921\pi$
$359$	1.82556	−	0.536033i	0.0963494	−	0.0282907i	0.329552	+	0.944137i	$0.393102\pi$
$360$		0			0
$361$	12.4345	−	14.3501i	0.654445	−	0.755270i
$362$		0			0
$363$	−6.38673	−	1.87531i	−0.335217	−	0.0984285i
$364$		0			0
$365$	−0.350259	−	2.43611i	−0.0183334	−	0.127512i
$366$		0			0
$367$	1.32075			0.0689425			0.0344712	−	0.999406i	$-0.489025\pi$
$367$	1.32075			0.0689425			0.0344712	+	0.999406i	$0.489025\pi$
$368$		0			0
$369$	−10.0363			−0.522470
$370$		0			0
$371$	1.99566	+	13.8801i	0.103609	+	0.720619i
$372$		0			0
$373$	−20.7612	−	6.09604i	−1.07497	−	0.315641i	−0.304108	−	0.952638i	$-0.598358\pi$
$373$	−20.7612	−	6.09604i	−1.07497	−	0.315641i	−0.770867	+	0.636997i	$0.780177\pi$
$374$		0			0
$375$	4.20138	−	4.84865i	0.216958	−	0.250383i
$376$		0			0
$377$	23.5049	−	6.90166i	1.21056	−	0.355454i
$378$		0			0
$379$	−19.3421	+	12.4304i	−0.993535	+	0.638506i	−0.933082	−	0.359665i	$-0.882891\pi$
$379$	−19.3421	+	12.4304i	−0.993535	+	0.638506i	−0.0604537	+	0.998171i	$0.519255\pi$
$380$		0			0
$381$	7.39120	+	8.52991i	0.378663	+	0.437000i
$382$		0			0
$383$	0.634088	−	4.41018i	0.0324004	−	0.225350i	−0.967187	−	0.254065i	$-0.918232\pi$
$383$	0.634088	−	4.41018i	0.0324004	−	0.225350i	0.999588	+	0.0287150i	$0.00914153\pi$
$384$		0			0
$385$	−5.50159	+	12.0468i	−0.280387	+	0.613962i
$386$		0			0
$387$	−1.11813	−	2.44837i	−0.0568380	−	0.124458i
$388$		0			0
$389$	−13.1264	−	8.43586i	−0.665537	−	0.427715i	0.163777	−	0.986497i	$-0.447632\pi$
$389$	−13.1264	−	8.43586i	−0.665537	−	0.427715i	−0.829314	+	0.558782i	$0.811269\pi$
$390$		0			0
$391$	−23.9681	−	26.3973i	−1.21212	−	1.33497i
$392$		0			0
$393$	1.28804	+	0.827774i	0.0649731	+	0.0417557i
$394$		0			0
$395$	19.4348	+	42.5562i	0.977869	+	2.14123i
$396$		0			0
$397$	−5.51507	+	12.0763i	−0.276793	+	0.606093i	−0.996064	−	0.0886369i	$-0.971749\pi$
$397$	−5.51507	+	12.0763i	−0.276793	+	0.606093i	0.719271	+	0.694730i	$0.244476\pi$
$398$		0			0
$399$	−0.0288334	+	0.200541i	−0.00144348	+	0.0100396i
$400$		0			0
$401$	8.30961	+	9.58980i	0.414962	+	0.478892i	0.924296	−	0.381677i	$-0.124653\pi$
$401$	8.30961	+	9.58980i	0.414962	+	0.478892i	−0.509333	+	0.860569i	$0.670108\pi$
$402$		0			0
$403$	20.1036	−	12.9198i	1.00143	−	0.643581i
$404$		0			0
$405$	−3.30472	+	0.970352i	−0.164213	+	0.0482172i
$406$		0			0
$407$	6.91236	−	7.97729i	0.342633	−	0.395420i
$408$		0			0
$409$	5.53919	+	1.62645i	0.273895	+	0.0804229i	0.415796	−	0.909458i	$-0.363503\pi$
$409$	5.53919	+	1.62645i	0.273895	+	0.0804229i	−0.141900	+	0.989881i	$0.545321\pi$
$410$		0			0
$411$	0.268543	+	1.86775i	0.0132462	+	0.0921295i
$412$		0			0
$413$	25.4703			1.25331
$414$		0			0
$415$	4.15242			0.203834
$416$		0			0
$417$	−1.40411	−	9.76579i	−0.0687595	−	0.478233i
$418$		0			0
$419$	−35.2394	−	10.3472i	−1.72156	−	0.505494i	−0.736310	−	0.676644i	$-0.763434\pi$
$419$	−35.2394	−	10.3472i	−1.72156	−	0.505494i	−0.985245	+	0.171150i	$0.945252\pi$
$420$		0			0
$421$	15.3269	−	17.6882i	0.746987	−	0.862069i	−0.247286	−	0.968943i	$-0.579539\pi$
$421$	15.3269	−	17.6882i	0.746987	−	0.862069i	0.994273	+	0.106874i	$0.0340841\pi$
$422$		0			0
$423$	12.7421	−	3.74143i	0.619544	−	0.181915i
$424$		0			0
$425$	42.9222	−	27.5844i	2.08203	−	1.33804i
$426$		0			0
$427$	−8.43626	−	9.73597i	−0.408259	−	0.471157i
$428$		0			0
$429$	−1.46707	+	10.2037i	−0.0708308	+	0.492639i
$430$		0			0
$431$	−15.9121	+	34.8427i	−0.766461	+	1.67832i	−0.0321681	+	0.999482i	$0.510241\pi$
$431$	−15.9121	+	34.8427i	−0.766461	+	1.67832i	−0.734293	+	0.678833i	$0.762486\pi$
$432$		0			0
$433$	5.85137	+	12.8127i	0.281199	+	0.615740i	0.996547	−	0.0830284i	$-0.0264592\pi$
$433$	5.85137	+	12.8127i	0.281199	+	0.615740i	−0.715348	+	0.698768i	$0.753732\pi$
$434$		0			0
$435$	−14.3503	−	9.22239i	−0.688045	−	0.442180i
$436$		0			0
$437$	0.526510	−	0.0122200i	0.0251864	−	0.000584563i
$438$		0			0
$439$	−21.9406	−	14.1003i	−1.04717	−	0.672973i	−0.100417	−	0.994945i	$-0.532018\pi$
$439$	−21.9406	−	14.1003i	−1.04717	−	0.672973i	−0.946749	+	0.321973i	$0.895654\pi$
$440$		0			0
$441$	−1.49388	−	3.27115i	−0.0711372	−	0.155769i
$442$		0			0
$443$	−10.1954	+	22.3247i	−0.484396	+	1.06068i	0.496835	+	0.867845i	$0.334495\pi$
$443$	−10.1954	+	22.3247i	−0.484396	+	1.06068i	−0.981231	+	0.192834i	$0.938232\pi$
$444$		0			0
$445$	0.715597	−	4.97708i	0.0339225	−	0.235936i
$446$		0			0
$447$	−7.89578	−	9.11222i	−0.373458	−	0.430993i
$448$		0			0
$449$	−25.3826	+	16.3124i	−1.19788	+	0.769831i	−0.978588	−	0.205828i	$-0.934011\pi$
$449$	−25.3826	+	16.3124i	−1.19788	+	0.769831i	−0.219292	+	0.975659i	$0.570375\pi$
$450$		0			0
$451$	20.0698	−	5.89303i	0.945051	−	0.277492i
$452$		0			0
$453$	−4.32571	+	4.99213i	−0.203239	+	0.234551i
$454$		0			0
$455$	−30.1575	−	8.85504i	−1.41381	−	0.415131i
$456$		0			0
$457$	−0.468656	−	3.25958i	−0.0219228	−	0.152477i	0.975920	−	0.218130i	$-0.0699958\pi$
$457$	−0.468656	−	3.25958i	−0.0219228	−	0.152477i	−0.997842	+	0.0656538i	$0.979087\pi$
$458$		0			0
$459$	−7.43460			−0.347017
$460$		0			0
$461$	21.9422			1.02195			0.510975	−	0.859595i	$-0.329284\pi$
$461$	21.9422			1.02195			0.510975	+	0.859595i	$0.329284\pi$
$462$		0			0
$463$	1.03212	+	7.17852i	0.0479665	+	0.333614i	0.999648	+	0.0265276i	$0.00844498\pi$
$463$	1.03212	+	7.17852i	0.0479665	+	0.333614i	−0.951682	+	0.307086i	$0.900646\pi$
$464$		0			0
$465$	−15.9664	−	4.68816i	−0.740424	−	0.217408i
$466$		0			0
$467$	−7.10436	+	8.19887i	−0.328751	+	0.379398i	−0.895930	−	0.444196i	$-0.853489\pi$
$467$	−7.10436	+	8.19887i	−0.328751	+	0.379398i	0.567179	+	0.823595i	$0.308035\pi$
$468$		0			0
$469$	−7.12445	+	2.09193i	−0.328977	+	0.0965963i
$470$		0			0
$471$	−13.2630	+	8.52360i	−0.611126	+	0.392747i
$472$		0			0
$473$	3.67357	+	4.23952i	0.168911	+	0.194933i
$474$		0			0
$475$	−0.107252	+	0.745956i	−0.00492107	+	0.0342268i
$476$		0			0
$477$	3.15741	−	6.91376i	0.144568	−	0.316559i
$478$		0			0
$479$	−14.2887	−	31.2878i	−0.652866	−	1.42958i	−0.889023	−	0.457863i	$-0.848615\pi$
$479$	−14.2887	−	31.2878i	−0.652866	−	1.42958i	0.236157	−	0.971715i	$-0.424112\pi$
$480$		0			0
$481$	21.0742	+	13.5436i	0.960902	+	0.617534i
$482$		0			0
$483$	7.33051	−	4.95508i	0.333550	−	0.225464i
$484$		0			0
$485$	−7.43065	−	4.77539i	−0.337409	−	0.216839i
$486$		0			0
$487$	10.0493	+	22.0049i	0.455378	+	0.997138i	0.988517	+	0.151110i	$0.0482849\pi$
$487$	10.0493	+	22.0049i	0.455378	+	0.997138i	−0.533139	+	0.846028i	$0.678988\pi$
$488$		0			0
$489$	−3.18166	+	6.96687i	−0.143880	+	0.315053i
$490$		0			0
$491$	3.71270	−	25.8224i	0.167552	−	1.16535i	−0.716372	−	0.697718i	$-0.754199\pi$
$491$	3.71270	−	25.8224i	0.167552	−	1.16535i	0.883924	−	0.467630i	$-0.154892\pi$
$492$		0			0
$493$	−24.1129	−	27.8277i	−1.08599	−	1.25330i
$494$		0			0
$495$	6.03874	−	3.88086i	0.271421	−	0.174432i
$496$		0			0
$497$	−20.5591	+	6.03671i	−0.922204	+	0.270783i
$498$		0			0
$499$	−20.5327	+	23.6960i	−0.919168	+	1.06078i	0.0787892	+	0.996891i	$0.474895\pi$
$499$	−20.5327	+	23.6960i	−0.919168	+	1.06078i	−0.997957	+	0.0638852i	$0.979651\pi$
$500$		0			0
$501$	−3.21142	−	0.942959i	−0.143476	−	0.0421283i
$502$		0			0
$503$	1.88383	+	13.1023i	0.0839957	+	0.584203i	0.987737	+	0.156125i	$0.0499002\pi$
$503$	1.88383	+	13.1023i	0.0839957	+	0.584203i	−0.903742	+	0.428078i	$0.859191\pi$
$504$		0			0
$505$	24.8887			1.10753
$506$		0			0
$507$	−11.4652			−0.509186
$508$		0			0
$509$	1.60552	+	11.1666i	0.0711633	+	0.494952i	0.993967	+	0.109681i	$0.0349829\pi$
$509$	1.60552	+	11.1666i	0.0711633	+	0.494952i	−0.922804	+	0.385271i	$0.874108\pi$
$510$		0			0
$511$	1.26496	+	0.371425i	0.0559584	+	0.0164309i
$512$		0			0
$513$	0.0719131	−	0.0829922i	0.00317504	−	0.00366419i
$514$		0			0
$515$	−19.7211	+	5.79063i	−0.869015	+	0.255166i
$516$		0			0
$517$	−23.2838	+	14.9636i	−1.02402	+	0.658099i
$518$		0			0
$519$	−6.43577	−	7.42728i	−0.282499	−	0.326021i
$520$		0			0
$521$	−4.81537	+	33.4916i	−0.210965	+	1.46730i	0.558977	+	0.829183i	$0.311194\pi$
$521$	−4.81537	+	33.4916i	−0.210965	+	1.46730i	−0.769943	+	0.638113i	$0.779715\pi$
$522$		0			0
$523$	−11.0795	+	24.2607i	−0.484473	+	1.06085i	0.496736	+	0.867902i	$0.334532\pi$
$523$	−11.0795	+	24.2607i	−0.484473	+	1.06085i	−0.981209	+	0.192947i	$0.938196\pi$
$524$		0			0
$525$	5.25977	+	11.5173i	0.229555	+	0.502655i
$526$		0			0
$527$	−30.2174	−	19.4195i	−1.31629	−	0.845929i
$528$		0			0
$529$	−15.8520	−	16.6647i	−0.689218	−	0.724554i
$530$		0			0
$531$	−11.6138	−	7.46373i	−0.503996	−	0.323898i
$532$		0			0
$533$	20.6220	+	45.1559i	0.893239	+	1.95592i
$534$		0			0
$535$	−10.9402	+	23.9557i	−0.472986	+	1.03569i
$536$		0			0
$537$	1.77743	−	12.3623i	0.0767016	−	0.533471i
$538$		0			0
$539$	4.90806	+	5.66420i	0.211405	+	0.243975i
$540$		0			0
$541$	37.6935	−	24.2242i	1.62057	−	1.04148i	0.664948	−	0.746890i	$-0.268454\pi$
$541$	37.6935	−	24.2242i	1.62057	−	1.04148i	0.955624	−	0.294588i	$-0.0951825\pi$
$542$		0			0
$543$	−19.3007	+	5.66720i	−0.828272	+	0.243203i
$544$		0			0
$545$	−26.5230	+	30.6092i	−1.13612	+	1.31115i
$546$		0			0
$547$	4.02184	+	1.18092i	0.171961	+	0.0504924i	0.366580	−	0.930387i	$-0.380529\pi$
$547$	4.02184	+	1.18092i	0.171961	+	0.0504924i	−0.194618	+	0.980879i	$0.562347\pi$
$548$		0			0
$549$	0.993721	+	6.91148i	0.0424110	+	0.294975i
$550$		0			0
$551$	0.543878			0.0231700
$552$		0			0
$553$	−25.0606			−1.06569
$554$		0			0
$555$	−2.48252	−	17.2663i	−0.105377	−	0.732915i
$556$		0			0
$557$	−12.2795	−	3.60559i	−0.520299	−	0.152774i	0.0110298	−	0.999939i	$-0.496489\pi$
$557$	−12.2795	−	3.60559i	−0.520299	−	0.152774i	−0.531329	+	0.847166i	$0.678307\pi$
$558$		0			0
$559$	−8.71837	+	10.0615i	−0.368748	+	0.425557i
$560$		0			0
$561$	14.8671	−	4.36537i	0.627689	−	0.184306i
$562$		0			0
$563$	24.5510	−	15.7780i	1.03470	−	0.664963i	0.0910314	−	0.995848i	$-0.470984\pi$
$563$	24.5510	−	15.7780i	1.03470	−	0.664963i	0.943671	+	0.330885i	$0.107347\pi$
$564$		0			0
$565$	−8.79520	−	10.1502i	−0.370017	−	0.427022i
$566$		0			0
$567$	0.262565	−	1.82618i	0.0110267	−	0.0766924i
$568$		0			0
$569$	5.10737	−	11.1836i	0.214112	−	0.468840i	−0.771851	−	0.635803i	$-0.780669\pi$
$569$	5.10737	−	11.1836i	0.214112	−	0.468840i	0.985963	+	0.166963i	$0.0533962\pi$
$570$		0			0
$571$	−13.5292	−	29.6249i	−0.566180	−	1.23976i	−0.948806	−	0.315859i	$-0.897708\pi$
$571$	−13.5292	−	29.6249i	−0.566180	−	1.23976i	0.382626	−	0.923903i	$-0.375020\pi$
$572$		0			0
$573$	−6.34320	−	4.07653i	−0.264991	−	0.170299i
$574$		0			0
$575$	27.2674	−	18.4315i	1.13713	−	0.768647i
$576$		0			0
$577$	19.6303	+	12.6156i	0.817221	+	0.525196i	0.881194	−	0.472755i	$-0.156741\pi$
$577$	19.6303	+	12.6156i	0.817221	+	0.525196i	−0.0639723	+	0.997952i	$0.520377\pi$
$578$		0			0
$579$	10.8589	+	23.7776i	0.451279	+	0.988163i
$580$		0			0
$581$	−0.924013	+	2.02331i	−0.0383345	+	0.0839409i
$582$		0			0
$583$	−2.25437	+	15.6795i	−0.0933666	+	0.649379i
$584$		0			0
$585$	11.1562	+	12.8749i	0.461251	+	0.532312i
$586$		0			0
$587$	18.7185	−	12.0296i	0.772593	−	0.496515i	−0.0939748	−	0.995575i	$-0.529957\pi$
$587$	18.7185	−	12.0296i	0.772593	−	0.496515i	0.866568	+	0.499059i	$0.166321\pi$
$588$		0			0
$589$	0.509066	−	0.149475i	0.0209757	−	0.00615902i
$590$		0			0
$591$	−14.1048	+	16.2778i	−0.580195	+	0.669581i
$592$		0			0
$593$	−20.9244	−	6.14395i	−0.859261	−	0.252302i	−0.177720	−	0.984081i	$-0.556872\pi$
$593$	−20.9244	−	6.14395i	−0.859261	−	0.252302i	−0.681542	+	0.731779i	$0.738690\pi$
$594$		0			0
$595$	6.72337	+	46.7621i	0.275631	+	1.91706i
$596$		0			0
$597$	−7.90023			−0.323335
$598$		0			0
$599$	−32.2379			−1.31721			−0.658603	−	0.752491i	$-0.728852\pi$
$599$	−32.2379			−1.31721			−0.658603	+	0.752491i	$0.728852\pi$
$600$		0			0
$601$	−2.13029	−	14.8165i	−0.0868964	−	0.604378i	−0.986013	−	0.166668i	$-0.946699\pi$
$601$	−2.13029	−	14.8165i	−0.0868964	−	0.604378i	0.899117	−	0.437709i	$-0.144210\pi$
$602$		0			0
$603$	3.86157	+	1.13386i	0.157255	+	0.0461744i
$604$		0			0
$605$	15.0134	−	17.3264i	0.610380	−	0.704417i
$606$		0			0
$607$	−6.96786	+	2.04595i	−0.282817	+	0.0830425i	−0.420065	−	0.907494i	$-0.637993\pi$
$607$	−6.96786	+	2.04595i	−0.282817	+	0.0830425i	0.137248	+	0.990537i	$0.456174\pi$
$608$		0			0
$609$	7.68699	−	4.94013i	0.311493	−	0.200184i
$610$		0			0
$611$	−43.0154	−	49.6424i	−1.74022	−	2.00832i
$612$		0			0
$613$	−0.0124466	+	0.0865682i	−0.000502714	+	0.00349646i	−0.990071	−	0.140566i	$-0.955108\pi$
$613$	−0.0124466	+	0.0865682i	−0.000502714	+	0.00349646i	0.989569	+	0.144063i	$0.0460167\pi$
$614$		0			0
$615$	14.3598	−	31.4437i	0.579044	−	1.26793i
$616$		0			0
$617$	8.27862	+	18.1277i	0.333285	+	0.729792i	0.999878	−	0.0156299i	$-0.00497537\pi$
$617$	8.27862	+	18.1277i	0.333285	+	0.729792i	−0.666593	+	0.745422i	$0.732248\pi$
$618$		0			0
$619$	−28.0805	−	18.0462i	−1.12865	−	0.725339i	−0.163372	−	0.986565i	$-0.552237\pi$
$619$	−28.0805	−	18.0462i	−1.12865	−	0.725339i	−0.965278	+	0.261225i	$0.915873\pi$
$620$		0			0
$621$	−4.79454	+	0.111279i	−0.192398	+	0.00446547i
$622$		0			0
$623$	2.26589	+	1.45620i	0.0907811	+	0.0583415i
$624$		0			0
$625$	−5.07494	−	11.1126i	−0.202998	−	0.444503i
$626$		0			0
$627$	−0.0950754	+	0.208186i	−0.00379695	+	0.00831415i
$628$		0			0
$629$	5.35869	−	37.2705i	0.213665	−	1.48607i
$630$		0			0
$631$	25.9057	+	29.8967i	1.03129	+	1.19017i	0.981510	+	0.191410i	$0.0613061\pi$
$631$	25.9057	+	29.8967i	1.03129	+	1.19017i	0.0497787	+	0.998760i	$0.484148\pi$
$632$		0			0
$633$	16.6083	−	10.6735i	0.660122	−	0.424235i
$634$		0			0
$635$	−37.2993	+	10.9521i	−1.48018	+	0.434619i
$636$		0			0
$637$	−11.6482	+	13.4427i	−0.461517	+	0.532619i
$638$		0			0
$639$	11.1434	+	3.27200i	0.440826	+	0.129438i
$640$		0			0
$641$	6.11081	+	42.5016i	0.241363	+	1.67871i	0.645302	+	0.763928i	$0.276732\pi$
$641$	6.11081	+	42.5016i	0.241363	+	1.67871i	−0.403939	+	0.914786i	$0.632359\pi$
$642$		0			0
$643$	25.8215			1.01830			0.509150	−	0.860678i	$-0.329960\pi$
$643$	25.8215			1.01830			0.509150	+	0.860678i	$0.329960\pi$
$644$		0			0
$645$	9.27053			0.365027
$646$		0			0
$647$	1.60863	+	11.1883i	0.0632419	+	0.439857i	0.996700	+	0.0811709i	$0.0258660\pi$
$647$	1.60863	+	11.1883i	0.0632419	+	0.439857i	−0.933458	+	0.358686i	$0.883225\pi$
$648$		0			0
$649$	27.6068	+	8.10609i	1.08366	+	0.318192i
$650$		0			0
$651$	5.83726	−	6.73655i	0.228780	−	0.264026i
$652$		0			0
$653$	−3.19575	+	0.938356i	−0.125059	+	0.0367207i	−0.343663	−	0.939093i	$-0.611668\pi$
$653$	−3.19575	+	0.938356i	−0.125059	+	0.0367207i	0.218604	+	0.975814i	$0.429850\pi$
$654$		0			0
$655$	−4.43631	+	2.85105i	−0.173341	+	0.111400i
$656$		0			0
$657$	−0.467946	−	0.540039i	−0.0182563	−	0.0210689i
$658$		0			0
$659$	7.07617	−	49.2159i	0.275649	−	1.91718i	−0.108862	−	0.994057i	$-0.534721\pi$
$659$	7.07617	−	49.2159i	0.275649	−	1.91718i	0.384510	−	0.923121i	$-0.374370\pi$
$660$		0			0
$661$	−13.1348	+	28.7612i	−0.510884	+	1.11868i	0.461892	+	0.886936i	$0.347171\pi$
$661$	−13.1348	+	28.7612i	−0.510884	+	1.11868i	−0.972777	+	0.231744i	$0.925557\pi$
$662$		0			0
$663$	15.2761	+	33.4501i	0.593276	+	1.29909i
$664$		0			0
$665$	−0.587037	−	0.377266i	−0.0227643	−	0.0146297i
$666$		0			0
$667$	−15.9668	−	17.5851i	−0.618237	−	0.680897i
$668$		0			0
$669$	−2.26242	−	1.45397i	−0.0874701	−	0.0562136i
$670$		0			0
$671$	−6.04537	−	13.2375i	−0.233379	−	0.511029i
$672$		0			0
$673$	−4.49612	+	9.84514i	−0.173313	+	0.379502i	−0.976277	−	0.216525i	$-0.930528\pi$
$673$	−4.49612	+	9.84514i	−0.173313	+	0.379502i	0.802964	+	0.596027i	$0.203255\pi$
$674$		0			0
$675$	0.976669	−	6.79288i	0.0375920	−	0.261458i
$676$		0			0
$677$	27.1897	+	31.3786i	1.04499	+	1.20598i	0.978082	+	0.208218i	$0.0667664\pi$
$677$	27.1897	+	31.3786i	1.04499	+	1.20598i	0.0669031	+	0.997759i	$0.478688\pi$
$678$		0			0
$679$	3.98035	−	2.55802i	0.152752	−	0.0981677i
$680$		0			0
$681$	−13.0544	+	3.83311i	−0.500244	+	0.146885i
$682$		0			0
$683$	13.0537	−	15.0647i	0.499484	−	0.576436i	−0.448891	−	0.893587i	$-0.648181\pi$
$683$	13.0537	−	15.0647i	0.499484	−	0.576436i	0.948375	+	0.317151i	$0.102726\pi$
$684$		0			0
$685$	−6.23587	−	1.83102i	−0.238260	−	0.0699596i
$686$		0			0
$687$	1.20091	+	8.35250i	0.0458175	+	0.318668i
$688$		0			0
$689$	−37.5944			−1.43223
$690$		0			0
$691$	18.9745			0.721823			0.360911	−	0.932600i	$-0.382466\pi$
$691$	18.9745			0.721823			0.360911	+	0.932600i	$0.382466\pi$
$692$		0			0
$693$	0.547223	+	3.80602i	0.0207873	+	0.144579i
$694$		0			0
$695$	32.6051	+	9.57371i	1.23678	+	0.363151i
$696$		0			0
$697$	48.8631	−	56.3911i	1.85082	−	2.13596i
$698$		0			0
$699$	15.3268	−	4.50035i	0.579712	−	0.170219i
$700$		0			0
$701$	17.9741	−	11.5513i	0.678873	−	0.436285i	−0.155242	−	0.987877i	$-0.549616\pi$
$701$	17.9741	−	11.5513i	0.678873	−	0.436285i	0.834114	+	0.551591i	$0.185979\pi$
$702$		0			0
$703$	0.364216	+	0.420328i	0.0137367	+	0.0158530i
$704$		0			0
$705$	−6.50944	+	45.2741i	−0.245160	+	1.70512i
$706$		0			0
$707$	−5.53833	+	12.1272i	−0.208290	+	0.456092i
$708$		0			0
$709$	−12.9256	−	28.3031i	−0.485430	−	1.06294i	−0.980935	−	0.194339i	$-0.937744\pi$
$709$	−12.9256	−	28.3031i	−0.485430	−	1.06294i	0.495504	−	0.868606i	$-0.334983\pi$
$710$		0			0
$711$	11.4270	+	7.34367i	0.428545	+	0.275409i
$712$		0			0
$713$	−19.7777	−	12.0713i	−0.740682	−	0.452074i
$714$		0			0
$715$	−29.8690	−	19.1956i	−1.11704	−	0.717875i
$716$		0			0
$717$	9.27765	+	20.3152i	0.346480	+	0.758686i
$718$		0			0
$719$	10.3887	−	22.7482i	0.387435	−	0.848364i	−0.610956	−	0.791664i	$-0.709215\pi$
$719$	10.3887	−	22.7482i	0.387435	−	0.848364i	0.998391	−	0.0566998i	$-0.0180578\pi$
$720$		0			0
$721$	1.56687	−	10.8978i	0.0583534	−	0.405857i
$722$		0			0
$723$	5.18679	+	5.98587i	0.192899	+	0.222617i
$724$		0			0
$725$	28.5934	−	18.3759i	1.06193	−	0.682464i
$726$		0			0
$727$	15.9701	−	4.68924i	0.592297	−	0.173914i	0.0281715	−	0.999603i	$-0.491032\pi$
$727$	15.9701	−	4.68924i	0.592297	−	0.173914i	0.564126	+	0.825689i	$0.309213\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	19.2004	+	5.63776i	0.710154	+	0.208520i
$732$		0			0
$733$	−1.90536	−	13.2521i	−0.0703760	−	0.489476i	−0.994276	−	0.106842i	$-0.965926\pi$
$733$	−1.90536	−	13.2521i	−0.0703760	−	0.489476i	0.923900	−	0.382634i	$-0.124983\pi$
$734$		0			0
$735$	12.3859			0.456860
$736$		0			0
$737$	−8.38783			−0.308970
$738$		0			0
$739$	1.56378	+	10.8763i	0.0575245	+	0.400091i	0.998158	+	0.0606676i	$0.0193230\pi$
$739$	1.56378	+	10.8763i	0.0575245	+	0.400091i	−0.940634	+	0.339424i	$0.889768\pi$
$740$		0			0
$741$	−0.521165	−	0.153028i	−0.0191455	−	0.00562162i
$742$		0			0
$743$	11.5906	−	13.3763i	0.425219	−	0.490728i	−0.502201	−	0.864751i	$-0.667476\pi$
$743$	11.5906	−	13.3763i	0.425219	−	0.490728i	0.927420	+	0.374023i	$0.122022\pi$
$744$		0			0
$745$	39.8456	−	11.6997i	1.45983	−	0.428645i
$746$		0			0
$747$	1.01423	−	0.651805i	0.0371087	−	0.0238483i
$748$		0			0
$749$	−9.23818	−	10.6614i	−0.337556	−	0.389560i
$750$		0			0
$751$	−3.07756	+	21.4049i	−0.112302	+	0.781076i	0.853369	+	0.521307i	$0.174556\pi$
$751$	−3.07756	+	21.4049i	−0.112302	+	0.781076i	−0.965671	+	0.259769i	$0.916354\pi$
$752$		0			0
$753$	−6.74262	+	14.7643i	−0.245715	+	0.538040i
$754$		0			0
$755$	−9.45111	−	20.6950i	−0.343961	−	0.753170i
$756$		0			0
$757$	−36.4082	−	23.3982i	−1.32328	−	0.850421i	−0.327741	−	0.944768i	$-0.606287\pi$
$757$	−36.4082	−	23.3982i	−1.32328	−	0.850421i	−0.995539	+	0.0943470i	$0.969924\pi$
$758$		0			0
$759$	9.52239	−	3.03774i	0.345641	−	0.110263i
$760$		0			0
$761$	27.7133	+	17.8103i	1.00461	+	0.645622i	0.935992	−	0.352021i	$-0.114505\pi$
$761$	27.7133	+	17.8103i	1.00461	+	0.645622i	0.0686156	+	0.997643i	$0.478142\pi$
$762$		0			0
$763$	−9.01262	−	19.7349i	−0.326279	−	0.714451i
$764$		0			0
$765$	10.6373	−	23.2925i	0.384593	−	0.842141i
$766$		0			0
$767$	−9.71788	+	67.5894i	−0.350892	+	2.44051i
$768$		0			0
$769$	−5.55431	−	6.41002i	−0.200294	−	0.231151i	0.646713	−	0.762733i	$-0.276143\pi$
$769$	−5.55431	−	6.41002i	−0.200294	−	0.231151i	−0.847007	+	0.531582i	$0.821598\pi$
$770$		0			0
$771$	−25.3684	+	16.3033i	−0.913621	+	0.587149i
$772$		0			0
$773$	33.7394	−	9.90679i	1.21352	−	0.356323i	0.388515	−	0.921443i	$-0.372988\pi$
$773$	33.7394	−	9.90679i	1.21352	−	0.356323i	0.825009	+	0.565120i	$0.191170\pi$
$774$		0			0
$775$	21.7129	−	25.0581i	0.779952	−	0.900113i
$776$		0			0
$777$	8.96561	+	2.63254i	0.321639	+	0.0944419i
$778$		0			0
$779$	0.156850	+	1.09092i	0.00561973	+	0.0390861i
$780$		0			0
$781$	−24.2049			−0.866119
$782$		0			0
$783$	−4.95271			−0.176995
$784$		0			0
$785$	−7.72782	−	53.7481i	−0.275818	−	1.91835i
$786$		0			0
$787$	15.2561	+	4.47961i	0.543823	+	0.159681i	0.542094	−	0.840318i	$-0.317632\pi$
$787$	15.2561	+	4.47961i	0.543823	+	0.159681i	0.00172861	+	0.999999i	$0.499450\pi$
$788$		0			0
$789$	−20.6347	+	23.8137i	−0.734615	+	0.847791i
$790$		0			0
$791$	6.90293	−	2.02688i	0.245440	−	0.0720676i
$792$		0			0
$793$	29.0546	−	18.6723i	1.03176	−	0.663072i
$794$		0			0
$795$	17.1431	+	19.7842i	0.608004	+	0.701674i
$796$		0			0
$797$	−4.42060	+	30.7459i	−0.156586	+	1.08908i	0.748281	+	0.663382i	$0.230880\pi$
$797$	−4.42060	+	30.7459i	−0.156586	+	1.08908i	−0.904867	+	0.425695i	$0.860030\pi$
$798$		0			0
$799$	−41.0148	+	89.8099i	−1.45100	+	3.17724i
$800$		0			0
$801$	−0.606468	−	1.32798i	−0.0214285	−	0.0469218i
$802$		0			0
$803$	1.25285	+	0.805161i	0.0442123	+	0.0284135i
$804$		0			0
$805$	5.03580	+	30.0560i	0.177488	+	1.05934i
$806$		0			0
$807$	−7.45259	−	4.78949i	−0.262344	−	0.168598i
$808$		0			0
$809$	−16.3836	−	35.8750i	−0.576015	−	1.26130i	−0.943532	−	0.331281i	$-0.892519\pi$
$809$	−16.3836	−	35.8750i	−0.576015	−	1.26130i	0.367517	−	0.930017i	$-0.380208\pi$
$810$		0			0
$811$	−2.03197	+	4.44939i	−0.0713521	+	0.156239i	−0.941947	−	0.335761i	$-0.891007\pi$
$811$	−2.03197	+	4.44939i	−0.0713521	+	0.156239i	0.870595	+	0.492000i	$0.163734\pi$
$812$		0			0
$813$	2.11805	−	14.7313i	0.0742831	−	0.516651i
$814$		0			0
$815$	−17.2748	−	19.9362i	−0.605110	−	0.698334i
$816$		0			0
$817$	−0.248656	+	0.159801i	−0.00869936	+	0.00559074i
$818$		0			0
$819$	−8.75594	+	2.57098i	−0.305957	+	0.0898372i
$820$		0			0
$821$	−7.06226	+	8.15028i	−0.246475	+	0.284447i	−0.865484	−	0.500937i	$-0.832989\pi$
$821$	−7.06226	+	8.15028i	−0.246475	+	0.284447i	0.619009	+	0.785384i	$0.287534\pi$
$822$		0			0
$823$	45.6527	+	13.4048i	1.59135	+	0.467263i	0.953123	−	0.302584i	$-0.0978492\pi$
$823$	45.6527	+	13.4048i	1.59135	+	0.467263i	0.638229	+	0.769847i	$0.279667\pi$
$824$		0			0
$825$	2.03551	+	14.1573i	0.0708675	+	0.492894i
$826$		0			0
$827$	13.0441			0.453589			0.226794	−	0.973943i	$-0.427175\pi$
$827$	13.0441			0.453589			0.226794	+	0.973943i	$0.427175\pi$
$828$		0			0
$829$	−21.0911			−0.732524			−0.366262	−	0.930512i	$-0.619363\pi$
$829$	−21.0911			−0.732524			−0.366262	+	0.930512i	$0.619363\pi$
$830$		0			0
$831$	−4.61932	−	32.1281i	−0.160242	−	1.11451i
$832$		0			0
$833$	25.6527	+	7.53232i	0.888814	+	0.260979i
$834$		0			0
$835$	7.54913	−	8.71216i	0.261249	−	0.301497i
$836$		0			0
$837$	−4.63569	+	1.36116i	−0.160233	+	0.0470486i
$838$		0			0
$839$	−29.3252	+	18.8462i	−1.01242	+	0.650642i	−0.938018	−	0.346586i	$-0.887341\pi$
$839$	−29.3252	+	18.8462i	−1.01242	+	0.650642i	−0.0744007	+	0.997228i	$0.523704\pi$
$840$		0			0
$841$	2.92769	+	3.37874i	0.100955	+	0.116508i
$842$		0			0
$843$	2.93722	−	20.4288i	0.101163	−	0.703605i
$844$		0			0
$845$	16.4042	−	35.9202i	0.564321	−	1.23569i
$846$		0			0
$847$	5.10160	+	11.1709i	0.175293	+	0.383838i
$848$		0			0
$849$	−4.23786	−	2.72351i	−0.145443	−	0.0934706i
$850$		0			0
$851$	2.89794	−	24.1158i	0.0993401	−	0.826679i
$852$		0			0
$853$	2.22166	+	1.42778i	0.0760683	+	0.0488862i	0.578122	−	0.815950i	$-0.303786\pi$
$853$	2.22166	+	1.42778i	0.0760683	+	0.0488862i	−0.502054	+	0.864836i	$0.667422\pi$
$854$		0			0
$855$	0.157121	+	0.344047i	0.00537342	+	0.0117661i
$856$		0			0
$857$	−10.6272	+	23.2704i	−0.363019	+	0.794900i	0.636698	+	0.771113i	$0.280300\pi$
$857$	−10.6272	+	23.2704i	−0.363019	+	0.794900i	−0.999717	+	0.0237874i	$0.992428\pi$
$858$		0			0
$859$	−4.77006	+	33.1765i	−0.162752	+	1.13197i	0.730663	+	0.682738i	$0.239211\pi$
$859$	−4.77006	+	33.1765i	−0.162752	+	1.13197i	−0.893416	+	0.449230i	$0.851698\pi$
$860$		0			0
$861$	12.1258	+	13.9939i	0.413247	+	0.476912i
$862$		0			0
$863$	7.93646	−	5.10045i	0.270160	−	0.173621i	−0.398546	−	0.917149i	$-0.630485\pi$
$863$	7.93646	−	5.10045i	0.270160	−	0.173621i	0.668706	+	0.743527i	$0.266849\pi$
$864$		0			0
$865$	32.4778	−	9.53633i	1.10428	−	0.324245i
$866$		0			0
$867$	25.0637	−	28.9250i	0.851206	−	0.982344i
$868$		0			0
$869$	−27.1627	−	7.97569i	−0.921432	−	0.270557i
$870$		0			0
$871$	−2.83300	−	19.7040i	−0.0959926	−	0.667643i
$872$		0			0
$873$	−2.56453			−0.0867962
$874$		0			0
$875$	−11.8367			−0.400153
$876$		0			0
$877$	3.45777	+	24.0493i	0.116761	+	0.812089i	0.961084	+	0.276255i	$0.0890934\pi$
$877$	3.45777	+	24.0493i	0.116761	+	0.812089i	−0.844324	+	0.535834i	$0.819997\pi$
$878$		0			0
$879$	19.6047	+	5.75647i	0.661251	+	0.194161i
$880$		0			0
$881$	−17.2648	+	19.9247i	−0.581667	+	0.671280i	−0.967962	−	0.251096i	$-0.919209\pi$
$881$	−17.2648	+	19.9247i	−0.581667	+	0.671280i	0.386295	+	0.922375i	$0.373755\pi$
$882$		0			0
$883$	−29.2301	+	8.58272i	−0.983670	+	0.288832i	−0.733739	−	0.679432i	$-0.762226\pi$
$883$	−29.2301	+	8.58272i	−0.983670	+	0.288832i	−0.249932	+	0.968263i	$0.580408\pi$
$884$		0			0
$885$	40.0006	−	25.7068i	1.34461	−	0.864126i
$886$		0			0
$887$	1.59665	+	1.84263i	0.0536103	+	0.0618695i	0.781921	−	0.623377i	$-0.214240\pi$
$887$	1.59665	+	1.84263i	0.0536103	+	0.0618695i	−0.728311	+	0.685247i	$0.759694\pi$
$888$		0			0
$889$	2.96349	−	20.6115i	0.0993923	−	0.691289i
$890$		0			0
$891$	0.865783	−	1.89580i	0.0290048	−	0.0635117i
$892$		0			0
$893$	−0.605818	−	1.32656i	−0.0202729	−	0.0443915i
$894$		0			0
$895$	36.1877	+	23.2564i	1.20962	+	0.777376i
$896$		0			0
$897$	10.3522	+	21.3432i	0.345650	+	0.712628i
$898$		0			0
$899$	−20.1299	−	12.9367i	−0.671371	−	0.431464i
$900$		0			0
$901$	23.4741	+	51.4011i	0.782035	+	1.71242i
$902$		0			0
$903$	−2.06292	+	4.51715i	−0.0686495	+	0.150321i
$904$		0			0
$905$	9.85993	−	68.5773i	0.327755	−	2.27959i
$906$		0			0
$907$	−36.9530	−	42.6460i	−1.22700	−	1.41604i	−0.877825	−	0.478981i	$-0.841006\pi$
$907$	−36.9530	−	42.6460i	−1.22700	−	1.41604i	−0.349178	−	0.937056i	$-0.613539\pi$
$908$		0			0
$909$	6.07906	−	3.90677i	0.201630	−	0.129579i
$910$		0			0
$911$	41.2652	−	12.1165i	1.36718	−	0.401439i	0.485889	−	0.874021i	$-0.338496\pi$
$911$	41.2652	−	12.1165i	1.36718	−	0.401439i	0.881287	+	0.472582i	$0.156678\pi$
$912$		0			0
$913$	−1.64545	+	1.89895i	−0.0544564	+	0.0628461i
$914$		0			0
$915$	−23.0753	−	6.77553i	−0.762848	−	0.223992i
$916$		0			0
$917$	−0.402013	−	2.79606i	−0.0132756	−	0.0923341i
$918$		0			0
$919$	2.89616			0.0955355			0.0477678	−	0.998858i	$-0.484789\pi$
$919$	2.89616			0.0955355			0.0477678	+	0.998858i	$0.484789\pi$
$920$		0			0
$921$	7.61720			0.250995
$922$		0			0
$923$	−8.17524	−	56.8600i	−0.269091	−	1.87157i
$924$		0			0
$925$	33.3495	+	9.79231i	1.09653	+	0.321969i
$926$		0			0
$927$	−3.90792	+	4.50998i	−0.128353	+	0.148127i
$928$		0			0
$929$	20.6597	−	6.06622i	0.677821	−	0.199026i	0.0753384	−	0.997158i	$-0.475996\pi$
$929$	20.6597	−	6.06622i	0.677821	−	0.199026i	0.602483	+	0.798132i	$0.294178\pi$
$930$		0			0
$931$	−0.332216	+	0.213502i	−0.0108879	+	0.00699725i
$932$		0			0
$933$	−7.12908	−	8.22739i	−0.233395	−	0.269353i
$934$		0			0
$935$	−7.59498	+	52.8243i	−0.248383	+	1.72754i
$936$		0			0
$937$	4.69146	−	10.2729i	0.153263	−	0.335600i	−0.817389	−	0.576086i	$-0.804579\pi$
$937$	4.69146	−	10.2729i	0.153263	−	0.335600i	0.970653	+	0.240486i	$0.0773068\pi$
$938$		0			0
$939$	−1.33539	−	2.92411i	−0.0435790	−	0.0954246i
$940$		0			0
$941$	−29.9455	−	19.2448i	−0.976195	−	0.627362i	−0.0477604	−	0.998859i	$-0.515208\pi$
$941$	−29.9455	−	19.2448i	−0.976195	−	0.627362i	−0.928434	+	0.371497i	$0.878845\pi$
$942$		0			0
$943$	30.6676	−	37.0977i	0.998674	−	1.20807i
$944$		0			0
$945$	5.34572	+	3.43549i	0.173896	+	0.111756i
$946$		0			0
$947$	0.795603	+	1.74213i	0.0258536	+	0.0566116i	0.922118	−	0.386908i	$-0.126457\pi$
$947$	0.795603	+	1.74213i	0.0258536	+	0.0566116i	−0.896265	+	0.443520i	$0.853730\pi$
$948$		0			0
$949$	−1.46826	+	3.21504i	−0.0476617	+	0.104365i
$950$		0			0
$951$	−0.0629376	+	0.437741i	−0.00204089	+	0.0141947i
$952$		0			0
$953$	−30.6808	−	35.4075i	−0.993848	−	1.14696i	−0.989141	−	0.146973i	$-0.953047\pi$
$953$	−30.6808	−	35.4075i	−0.993848	−	1.14696i	−0.00470745	−	0.999989i	$-0.501498\pi$
$954$		0			0
$955$	21.8475	−	14.0405i	0.706967	−	0.454340i
$956$		0			0
$957$	9.90401	−	2.90808i	0.320151	−	0.0940049i
$958$		0			0
$959$	2.27981	−	2.63104i	0.0736190	−	0.0849608i
$960$		0			0
$961$	7.34742	+	2.15740i	0.237013	+	0.0695934i
$962$		0			0
$963$	1.08818	+	7.56845i	0.0350661	+	0.243890i
$964$		0			0
$965$	−90.0315			−2.89822
$966$		0			0
$967$	28.1196			0.904266			0.452133	−	0.891950i	$-0.350663\pi$
$967$	28.1196			0.904266			0.452133	+	0.891950i	$0.350663\pi$
$968$		0			0
$969$	0.116190	+	0.808116i	0.00373255	+	0.0259604i
$970$		0			0
$971$	−18.9721	−	5.57072i	−0.608844	−	0.178773i	−0.0372457	−	0.999306i	$-0.511858\pi$
$971$	−18.9721	−	5.57072i	−0.608844	−	0.178773i	−0.571599	+	0.820533i	$0.693677\pi$
$972$		0			0
$973$	−11.9203	+	13.7567i	−0.382147	+	0.441021i
$974$		0			0
$975$	−32.5696	+	9.56331i	−1.04306	+	0.306271i
$976$		0			0
$977$	−18.4883	+	11.8817i	−0.591494	+	0.380130i	−0.801877	−	0.597489i	$-0.796165\pi$
$977$	−18.4883	+	11.8817i	−0.591494	+	0.380130i	0.210383	+	0.977619i	$0.432529\pi$
$978$		0			0
$979$	1.99251	+	2.29948i	0.0636810	+	0.0734918i
$980$		0			0
$981$	−1.67352	+	11.6396i	−0.0534315	+	0.371624i
$982$		0			0
$983$	14.5538	−	31.8684i	0.464194	−	1.01644i	−0.522318	−	0.852751i	$-0.674932\pi$
$983$	14.5538	−	31.8684i	0.464194	−	1.01644i	0.986512	−	0.163692i	$-0.0523402\pi$
$984$		0			0
$985$	−30.8172	−	67.4803i	−0.981918	−	2.15010i
$986$		0			0
$987$	−20.6117	−	13.2464i	−0.656079	−	0.421636i
$988$		0			0
$989$	12.4667	+	3.34838i	0.396417	+	0.106472i
$990$		0			0
$991$	32.3429	+	20.7856i	1.02741	+	0.660275i	0.941841	−	0.336058i	$-0.109094\pi$
$991$	32.3429	+	20.7856i	1.02741	+	0.660275i	0.0855662	+	0.996332i	$0.472730\pi$
$992$		0			0
$993$	−9.73751	−	21.3222i	−0.309011	−	0.676639i
$994$		0			0
$995$	11.3035	−	24.7513i	0.358346	−	0.784669i
$996$		0			0
$997$	1.66444	−	11.5764i	0.0527134	−	0.366629i	−0.946342	−	0.323168i	$-0.895252\pi$
$997$	1.66444	−	11.5764i	0.0527134	−	0.366629i	0.999055	−	0.0434618i	$-0.0138387\pi$
$998$		0			0
$999$	−3.31665	−	3.82762i	−0.104934	−	0.121101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.25.1	✓	30
23.12	even	11	inner	552.2.q.c.265.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.25.1	✓	30	1.1	even	1	trivial
552.2.q.c.265.1	yes	30	23.12	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{3} +(-3.30472 - 0.970352i) q^{5} +(1.20819 - 1.39433i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{3} +(-3.30472 - 0.970352i) q^{5} +(1.20819 - 1.39433i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(1.75329 - 1.12677i) q^{11} +(3.23909 + 3.73811i) q^{13} +(0.490165 - 3.40917i) q^{15} +(3.08844 - 6.76275i) q^{17} +(0.0456185 + 0.0998907i) q^{19} +(1.55208 + 0.997461i) q^{21} +(1.89050 - 4.40749i) q^{23} +(5.77330 + 3.71027i) q^{25} +(-0.415415 - 0.909632i) q^{27} +(2.05743 - 4.50514i) q^{29} +(0.687579 - 4.78222i) q^{31} +(1.36482 + 1.57509i) q^{33} +(-5.34572 + 3.43549i) q^{35} +(4.85951 - 1.42688i) q^{37} +(-3.23909 + 3.73811i) q^{39} +(9.62979 + 2.82756i) q^{41} +(0.383056 + 2.66421i) q^{43} +3.44423 q^{45} -13.2801 q^{47} +(0.511781 + 3.55952i) q^{49} +(7.13345 + 2.09457i) q^{51} +(-4.97734 + 5.74416i) q^{53} +(-6.88749 + 2.02235i) q^{55} +(-0.0923817 + 0.0593701i) q^{57} +(9.04058 + 10.4334i) q^{59} +(0.993721 - 6.91148i) q^{61} +(-0.766424 + 1.67824i) q^{63} +(-7.07699 - 15.4964i) q^{65} +(-3.38571 - 2.17586i) q^{67} +(4.63168 + 1.24401i) q^{69} +(-9.77019 - 6.27892i) q^{71} +(0.296845 + 0.649999i) q^{73} +(-2.85088 + 6.24256i) q^{75} +(0.547223 - 3.80602i) q^{77} +(-8.89515 - 10.2656i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-1.15678 + 0.339661i) q^{83} +(-16.7687 + 19.3521i) q^{85} +(4.75209 + 1.39534i) q^{87} +(0.207767 + 1.44505i) q^{89} +9.12560 q^{91} +4.83140 q^{93} +(-0.0538272 - 0.374376i) q^{95} +(2.46065 + 0.722511i) q^{97} +(-1.36482 + 1.57509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more