LMFDB - Embedded newform 460.2.s.a.449.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			449.9
Character	$\chi$	$=$	460.449
Dual form			460.2.s.a.209.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30292 + 0.187332i) q^{3} +(2.16868 + 0.544811i) q^{5} +(-1.39279 + 1.20686i) q^{7} +(-1.21597 - 0.357042i) q^{9} +O(q^{10})$	\(q+(1.30292 + 0.187332i) q^{3} +(2.16868 + 0.544811i) q^{5} +(-1.39279 + 1.20686i) q^{7} +(-1.21597 - 0.357042i) q^{9} +(2.33946 + 1.50348i) q^{11} +(3.29071 + 2.85142i) q^{13} +(2.72356 + 1.11611i) q^{15} +(2.24721 - 1.02627i) q^{17} +(1.00865 - 2.20863i) q^{19} +(-2.04078 + 1.31153i) q^{21} +(-3.31979 + 3.46107i) q^{23} +(4.40636 + 2.36304i) q^{25} +(-5.10952 - 2.33344i) q^{27} +(-4.15493 - 9.09802i) q^{29} +(-0.166336 - 1.15689i) q^{31} +(2.76648 + 2.39717i) q^{33} +(-3.67803 + 1.85849i) q^{35} +(-0.164958 + 0.561797i) q^{37} +(3.75337 + 4.33162i) q^{39} +(4.48704 - 1.31751i) q^{41} +(0.0602290 + 0.00865962i) q^{43} +(-2.44254 - 1.43679i) q^{45} +2.80626i q^{47} +(-0.512849 + 3.56695i) q^{49} +(3.12019 - 0.916169i) q^{51} +(3.24540 - 2.81215i) q^{53} +(4.25443 + 4.53513i) q^{55} +(1.72794 - 2.68872i) q^{57} +(3.19702 - 3.68956i) q^{59} +(-0.684457 - 4.76050i) q^{61} +(2.12450 - 0.970224i) q^{63} +(5.58302 + 7.97663i) q^{65} +(-8.23855 - 12.8194i) q^{67} +(-4.97378 + 3.88760i) q^{69} +(-8.56338 + 5.50335i) q^{71} +(-9.37936 - 4.28341i) q^{73} +(5.29846 + 3.90431i) q^{75} +(-5.07286 + 0.729368i) q^{77} +(-8.09041 + 9.33683i) q^{79} +(-3.02179 - 1.94198i) q^{81} +(-1.30211 + 4.43458i) q^{83} +(5.43261 - 1.00134i) q^{85} +(-3.70919 - 12.6323i) q^{87} +(0.218274 - 1.51813i) q^{89} -8.02452 q^{91} -1.53849i q^{93} +(3.39073 - 4.24030i) q^{95} +(-4.98862 - 16.9897i) q^{97} +(-2.30791 - 2.66348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{10}{11}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.30292	+	0.187332i	0.752241	+	0.108156i	0.507760	−	0.861498i	$-0.330474\pi$
$3$	1.30292	+	0.187332i	0.752241	+	0.108156i	0.244480	+	0.969654i	$0.421383\pi$
$4$		0			0
$5$	2.16868	+	0.544811i	0.969864	+	0.243647i
$5$	2.16868	+	0.544811i	0.969864	+	0.243647i
$6$		0			0
$7$	−1.39279	+	1.20686i	−0.526425	+	0.456150i	−0.877073	−	0.480357i	$-0.840507\pi$
$7$	−1.39279	+	1.20686i	−0.526425	+	0.456150i	0.350648	+	0.936507i	$0.385961\pi$
$8$		0			0
$9$	−1.21597	−	0.357042i	−0.405324	−	0.119014i
$10$		0			0
$11$	2.33946	+	1.50348i	0.705373	+	0.453316i	0.843521	−	0.537096i	$-0.180479\pi$
$11$	2.33946	+	1.50348i	0.705373	+	0.453316i	−0.138148	+	0.990412i	$0.544115\pi$
$12$		0			0
$13$	3.29071	+	2.85142i	0.912678	+	0.790840i	0.978341	−	0.207002i	$-0.0663705\pi$
$13$	3.29071	+	2.85142i	0.912678	+	0.790840i	−0.0656622	+	0.997842i	$0.520916\pi$
$14$		0			0
$15$	2.72356	+	1.11611i	0.703219	+	0.288178i
$16$		0			0
$17$	2.24721	−	1.02627i	0.545029	−	0.248906i	−0.123820	−	0.992305i	$-0.539515\pi$
$17$	2.24721	−	1.02627i	0.545029	−	0.248906i	0.668849	+	0.743398i	$0.266787\pi$
$18$		0			0
$19$	1.00865	−	2.20863i	0.231400	−	0.506695i	−0.757939	−	0.652325i	$-0.773794\pi$
$19$	1.00865	−	2.20863i	0.231400	−	0.506695i	0.989339	+	0.145630i	$0.0465209\pi$
$20$		0			0
$21$	−2.04078	+	1.31153i	−0.445334	+	0.286199i
$22$		0			0
$23$	−3.31979	+	3.46107i	−0.692223	+	0.721683i
$23$	−3.31979	+	3.46107i	−0.692223	+	0.721683i
$24$		0			0
$25$	4.40636	+	2.36304i	0.881272	+	0.472609i
$26$		0			0
$27$	−5.10952	−	2.33344i	−0.983328	−	0.449071i
$28$		0			0
$29$	−4.15493	−	9.09802i	−0.771550	−	1.68946i	−0.723210	−	0.690629i	$-0.757334\pi$
$29$	−4.15493	−	9.09802i	−0.771550	−	1.68946i	−0.0483408	−	0.998831i	$-0.515393\pi$
$30$		0			0
$31$	−0.166336	−	1.15689i	−0.0298748	−	0.207784i	0.969417	−	0.245421i	$-0.0789261\pi$
$31$	−0.166336	−	1.15689i	−0.0298748	−	0.207784i	−0.999291	+	0.0376369i	$0.988017\pi$
$32$		0			0
$33$	2.76648	+	2.39717i	0.481582	+	0.417293i
$34$		0			0
$35$	−3.67803	+	1.85849i	−0.621700	+	0.314142i
$36$		0			0
$37$	−0.164958	+	0.561797i	−0.0271190	+	0.0923588i	−0.971941	−	0.235227i	$-0.924417\pi$
$37$	−0.164958	+	0.561797i	−0.0271190	+	0.0923588i	0.944822	+	0.327585i	$0.106235\pi$
$38$		0			0
$39$	3.75337	+	4.33162i	0.601020	+	0.693614i
$40$		0			0
$41$	4.48704	−	1.31751i	0.700758	−	0.205761i	0.0881030	−	0.996111i	$-0.471920\pi$
$41$	4.48704	−	1.31751i	0.700758	−	0.205761i	0.612655	+	0.790350i	$0.290101\pi$
$42$		0			0
$43$	0.0602290	+	0.00865962i	0.00918483	+	0.00132058i	0.146906	−	0.989150i	$-0.453069\pi$
$43$	0.0602290	+	0.00865962i	0.00918483	+	0.00132058i	−0.137721	+	0.990471i	$0.543978\pi$
$44$		0			0
$45$	−2.44254	−	1.43679i	−0.364112	−	0.214183i
$46$		0			0
$47$			2.80626i			0.409334i	0.978832	+	0.204667i	$0.0656112\pi$
$47$			2.80626i			0.409334i	−0.978832	+	0.204667i	$0.934389\pi$
$48$		0			0
$49$	−0.512849	+	3.56695i	−0.0732642	+	0.509564i
$50$		0			0
$51$	3.12019	−	0.916169i	0.436913	−	0.128289i
$52$		0			0
$53$	3.24540	−	2.81215i	0.445790	−	0.386279i	−0.402836	−	0.915272i	$-0.631976\pi$
$53$	3.24540	−	2.81215i	0.445790	−	0.386279i	0.848626	+	0.528993i	$0.177430\pi$
$54$		0			0
$55$	4.25443	+	4.53513i	0.573667	+	0.611517i
$56$		0			0
$57$	1.72794	−	2.68872i	0.228871	−	0.356130i
$58$		0			0
$59$	3.19702	−	3.68956i	0.416217	−	0.480340i	−0.508464	−	0.861083i	$-0.669786\pi$
$59$	3.19702	−	3.68956i	0.416217	−	0.480340i	0.924681	+	0.380743i	$0.124332\pi$
$60$		0			0
$61$	−0.684457	−	4.76050i	−0.0876358	−	0.609520i	−0.985554	−	0.169359i	$-0.945830\pi$
$61$	−0.684457	−	4.76050i	−0.0876358	−	0.609520i	0.897919	−	0.440161i	$-0.145079\pi$
$62$		0			0
$63$	2.12450	−	0.970224i	0.267661	−	0.122237i
$64$		0			0
$65$	5.58302	+	7.97663i	0.692488	+	0.989379i
$66$		0			0
$67$	−8.23855	−	12.8194i	−1.00650	−	1.56614i	−0.810668	−	0.585506i	$-0.800896\pi$
$67$	−8.23855	−	12.8194i	−1.00650	−	1.56614i	−0.195831	−	0.980638i	$-0.562741\pi$
$68$		0			0
$69$	−4.97378	+	3.88760i	−0.598773	+	0.468012i
$70$		0			0
$71$	−8.56338	+	5.50335i	−1.01629	+	0.653127i	−0.939013	−	0.343883i	$-0.888258\pi$
$71$	−8.56338	+	5.50335i	−1.01629	+	0.653127i	−0.0772732	+	0.997010i	$0.524621\pi$
$72$		0			0
$73$	−9.37936	−	4.28341i	−1.09777	−	0.501335i	−0.217622	−	0.976033i	$-0.569830\pi$
$73$	−9.37936	−	4.28341i	−1.09777	−	0.501335i	−0.880149	+	0.474698i	$0.842557\pi$
$74$		0			0
$75$	5.29846	+	3.90431i	0.611814	+	0.450830i
$76$		0			0
$77$	−5.07286	+	0.729368i	−0.578106	+	0.0831191i
$78$		0			0
$79$	−8.09041	+	9.33683i	−0.910242	+	1.05048i	0.0882779	+	0.996096i	$0.471864\pi$
$79$	−8.09041	+	9.33683i	−0.910242	+	1.05048i	−0.998520	+	0.0543799i	$0.982682\pi$
$80$		0			0
$81$	−3.02179	−	1.94198i	−0.335754	−	0.215776i
$82$		0			0
$83$	−1.30211	+	4.43458i	−0.142925	+	0.486759i	−0.999575	−	0.0291392i	$-0.990723\pi$
$83$	−1.30211	+	4.43458i	−0.142925	+	0.486759i	0.856650	+	0.515898i	$0.172542\pi$
$84$		0			0
$85$	5.43261	−	1.00134i	0.589249	−	0.108611i
$86$		0			0
$87$	−3.70919	−	12.6323i	−0.397667	−	1.35433i
$88$		0			0
$89$	0.218274	−	1.51813i	0.0231370	−	0.160921i	−0.974977	−	0.222304i	$-0.928642\pi$
$89$	0.218274	−	1.51813i	0.0231370	−	0.160921i	0.998114	+	0.0613833i	$0.0195512\pi$
$90$		0			0
$91$	−8.02452			−0.841199
$92$		0			0
$93$		−	1.53849i		−	0.159534i
$94$		0			0
$95$	3.39073	−	4.24030i	0.347881	−	0.435046i
$96$		0			0
$97$	−4.98862	−	16.9897i	−0.506518	−	1.72504i	−0.673598	−	0.739098i	$-0.735252\pi$
$97$	−4.98862	−	16.9897i	−0.506518	−	1.72504i	0.167080	−	0.985943i	$-0.446566\pi$
$98$		0			0
$99$	−2.30791	−	2.66348i	−0.231954	−	0.267689i
$100$		0			0
$101$	13.5501	+	3.97867i	1.34828	+	0.395892i	0.874618	−	0.484813i	$-0.161112\pi$
$101$	13.5501	+	3.97867i	1.34828	+	0.395892i	0.473666	+	0.880704i	$0.342930\pi$
$102$		0			0
$103$	6.69130	−	10.4119i	0.659314	−	1.02591i	−0.337114	−	0.941464i	$-0.609451\pi$
$103$	6.69130	−	10.4119i	0.659314	−	1.02591i	0.996428	−	0.0844482i	$-0.0269127\pi$
$104$		0			0
$105$	−5.14033	+	1.73245i	−0.501645	+	0.169070i
$106$		0			0
$107$	−16.2467	+	2.33592i	−1.57062	+	0.225822i	−0.871942	−	0.489610i	$-0.837139\pi$
$107$	−16.2467	+	2.33592i	−1.57062	+	0.225822i	−0.698683	+	0.715432i	$0.746230\pi$
$108$		0			0
$109$	−1.81048	−	3.96439i	−0.173412	−	0.379720i	0.802891	−	0.596125i	$-0.203294\pi$
$109$	−1.81048	−	3.96439i	−0.173412	−	0.379720i	−0.976304	+	0.216406i	$0.930567\pi$
$110$		0			0
$111$	−0.320170	+	0.701074i	−0.0303892	+	0.0665430i
$112$		0			0
$113$	4.15185	+	6.46040i	0.390573	+	0.607743i	0.979741	−	0.200267i	$-0.0641809\pi$
$113$	4.15185	+	6.46040i	0.390573	+	0.607743i	−0.589168	+	0.808010i	$0.700545\pi$
$114$		0			0
$115$	−9.08519	+	5.69731i	−0.847198	+	0.531277i
$116$		0			0
$117$	−2.98334	−	4.64217i	−0.275810	−	0.429168i
$118$		0			0
$119$	−1.89133	+	4.14144i	−0.173378	+	0.379645i
$120$		0			0
$121$	−1.35695	−	2.97130i	−0.123359	−	0.270118i
$122$		0			0
$123$	6.09307	−	0.876051i	0.549393	−	0.0789908i
$124$		0			0
$125$	8.26858	+	7.52533i	0.739565	+	0.673086i
$126$		0			0
$127$	−5.04253	+	7.84633i	−0.447452	+	0.696249i	−0.989570	−	0.144053i	$-0.953986\pi$
$127$	−5.04253	+	7.84633i	−0.447452	+	0.696249i	0.542118	+	0.840303i	$0.317623\pi$
$128$		0			0
$129$	0.0768513	+	0.0225656i	0.00676638	+	0.00198679i
$130$		0			0
$131$	−1.69341	−	1.95430i	−0.147954	−	0.170748i	0.676935	−	0.736043i	$-0.263308\pi$
$131$	−1.69341	−	1.95430i	−0.147954	−	0.170748i	−0.824889	+	0.565295i	$0.808762\pi$
$132$		0			0
$133$	1.26067	+	4.29346i	0.109314	+	0.372290i
$134$		0			0
$135$	−9.80965	−	7.84422i	−0.844280	−	0.675123i
$136$		0			0
$137$		−	14.1049i		−	1.20507i	−0.798094	−	0.602533i	$-0.794158\pi$
$137$		−	14.1049i		−	1.20507i	0.798094	−	0.602533i	$-0.205842\pi$
$138$		0			0
$139$	8.71522			0.739216			0.369608	−	0.929188i	$-0.379492\pi$
$139$	8.71522			0.739216			0.369608	+	0.929188i	$0.379492\pi$
$140$		0			0
$141$	−0.525700	+	3.65632i	−0.0442719	+	0.307918i
$142$		0			0
$143$	3.41143	+	11.6183i	0.285279	+	0.971569i
$144$		0			0
$145$	−4.05401	−	21.9944i	−0.336667	−	1.82653i
$146$		0			0
$147$	−1.33640	+	4.55137i	−0.110225	+	0.375391i
$148$		0			0
$149$	13.1093	+	8.42487i	1.07396	+	0.690192i	0.953154	−	0.302484i	$-0.0978159\pi$
$149$	13.1093	+	8.42487i	1.07396	+	0.690192i	0.120805	+	0.992676i	$0.461452\pi$
$150$		0			0
$151$	−10.9610	+	12.6497i	−0.891993	+	1.02942i	0.107387	+	0.994217i	$0.465752\pi$
$151$	−10.9610	+	12.6497i	−0.891993	+	1.02942i	−0.999380	+	0.0351978i	$0.988794\pi$
$152$		0			0
$153$	−3.09897	+	0.445564i	−0.250537	+	0.0360217i
$154$		0			0
$155$	0.269558	−	2.59955i	0.0216514	−	0.208801i
$156$		0			0
$157$	−1.41937	−	0.648203i	−0.113278	−	0.0517323i	0.357970	−	0.933733i	$-0.383469\pi$
$157$	−1.41937	−	0.648203i	−0.113278	−	0.0517323i	−0.471248	+	0.882001i	$0.656196\pi$
$158$		0			0
$159$	4.75530	−	3.05604i	0.377120	−	0.242360i
$160$		0			0
$161$	0.446737	−	8.82706i	0.0352078	−	0.695670i
$162$		0			0
$163$	−7.78590	−	12.1151i	−0.609839	−	0.948928i	−0.999608	−	0.0280150i	$-0.991081\pi$
$163$	−7.78590	−	12.1151i	−0.609839	−	0.948928i	0.389769	−	0.920913i	$-0.372555\pi$
$164$		0			0
$165$	4.69361	+	6.70590i	0.365397	+	0.522053i
$166$		0			0
$167$	−7.17514	+	3.27678i	−0.555229	+	0.253565i	−0.673210	−	0.739451i	$-0.735085\pi$
$167$	−7.17514	+	3.27678i	−0.555229	+	0.253565i	0.117981	+	0.993016i	$0.462358\pi$
$168$		0			0
$169$	0.848102	+	5.89868i	0.0652386	+	0.453744i
$170$		0			0
$171$	−2.01507	+	2.32551i	−0.154096	+	0.177836i
$172$		0			0
$173$	−8.04455	+	12.5176i	−0.611616	+	0.951693i	0.387934	+	0.921687i	$0.373189\pi$
$173$	−8.04455	+	12.5176i	−0.611616	+	0.951693i	−0.999550	+	0.0300055i	$0.990448\pi$
$174$		0			0
$175$	−8.98900	+	2.02663i	−0.679504	+	0.153199i
$176$		0			0
$177$	4.85664	−	4.20830i	0.365047	−	0.316315i
$178$		0			0
$179$	3.42930	−	1.00693i	0.256318	−	0.0752618i	−0.151049	−	0.988526i	$-0.548265\pi$
$179$	3.42930	−	1.00693i	0.256318	−	0.0752618i	0.407367	+	0.913264i	$0.366447\pi$
$180$		0			0
$181$	1.77943	−	12.3762i	0.132264	−	0.919918i	−0.810329	−	0.585975i	$-0.800712\pi$
$181$	1.77943	−	12.3762i	0.132264	−	0.919918i	0.942593	−	0.333943i	$-0.108379\pi$
$182$		0			0
$183$		−	6.33077i		−	0.467984i
$184$		0			0
$185$	−0.663815	+	1.12849i	−0.0488047	+	0.0829680i
$186$		0			0
$187$	6.80023	+	0.977725i	0.497282	+	0.0714983i
$188$		0			0
$189$	9.93263	−	2.91648i	0.722492	−	0.212143i
$190$		0			0
$191$	5.31319	+	6.13174i	0.384449	+	0.443677i	0.914682	−	0.404174i	$-0.132441\pi$
$191$	5.31319	+	6.13174i	0.384449	+	0.443677i	−0.530233	+	0.847852i	$0.677896\pi$
$192$		0			0
$193$	1.06732	−	3.63497i	0.0768276	−	0.261651i	−0.912118	−	0.409927i	$-0.865554\pi$
$193$	1.06732	−	3.63497i	0.0768276	−	0.261651i	0.988946	+	0.148276i	$0.0473724\pi$
$194$		0			0
$195$	5.77995	+	11.4388i	0.413911	+	0.819148i
$196$		0			0
$197$	13.7908	+	11.9498i	0.982552	+	0.851386i	0.988898	−	0.148594i	$-0.0474748\pi$
$197$	13.7908	+	11.9498i	0.982552	+	0.851386i	−0.00634675	+	0.999980i	$0.502020\pi$
$198$		0			0
$199$	0.0932702	+	0.648709i	0.00661175	+	0.0459857i	0.992860	−	0.119284i	$-0.0380598\pi$
$199$	0.0932702	+	0.648709i	0.00661175	+	0.0459857i	−0.986248	+	0.165269i	$0.947151\pi$
$200$		0			0
$201$	−8.33268	−	18.2460i	−0.587742	−	1.28698i
$202$		0			0
$203$	16.7670	+	7.65722i	1.17681	+	0.537431i
$204$		0			0
$205$	10.4488	−	0.412679i	0.729774	−	0.0288228i
$206$		0			0
$207$	5.27252	−	3.02327i	0.366465	−	0.210132i
$208$		0			0
$209$	5.68033	−	3.65053i	0.392917	−	0.252512i
$210$		0			0
$211$	−7.44165	+	16.2949i	−0.512304	+	1.12179i	0.459967	+	0.887936i	$0.347861\pi$
$211$	−7.44165	+	16.2949i	−0.512304	+	1.12179i	−0.972272	+	0.233854i	$0.924866\pi$
$212$		0			0
$213$	−12.1883	+	5.56623i	−0.835131	+	0.381392i
$214$		0			0
$215$	0.125900	+	0.0515934i	0.00858628	+	0.00351864i
$216$		0			0
$217$	1.62787	+	1.41056i	0.110507	+	0.0957552i
$218$		0			0
$219$	−11.4181	−	7.33799i	−0.771566	−	0.495855i
$220$		0			0
$221$	10.3212	+	3.03059i	0.694281	+	0.203859i
$222$		0			0
$223$	4.68799	−	4.06216i	0.313931	−	0.272023i	−0.483615	−	0.875281i	$-0.660677\pi$
$223$	4.68799	−	4.06216i	0.313931	−	0.272023i	0.797546	+	0.603258i	$0.206131\pi$
$224$		0			0
$225$	−4.51431	−	4.44665i	−0.300954	−	0.296444i
$226$		0			0
$227$	−1.59277	−	0.229005i	−0.105716	−	0.0151996i	0.0892539	−	0.996009i	$-0.471552\pi$
$227$	−1.59277	−	0.229005i	−0.105716	−	0.0151996i	−0.194970	+	0.980809i	$0.562461\pi$
$228$		0			0
$229$	−10.2130			−0.674894			−0.337447	−	0.941345i	$-0.609563\pi$
$229$	−10.2130			−0.674894			−0.337447	+	0.941345i	$0.609563\pi$
$230$		0			0
$231$	−6.74616			−0.443865
$232$		0			0
$233$	23.1258	+	3.32498i	1.51502	+	0.217827i	0.849114	−	0.528209i	$-0.177136\pi$
$233$	23.1258	+	3.32498i	1.51502	+	0.217827i	0.665906	+	0.746036i	$0.268045\pi$
$234$		0			0
$235$	−1.52888	+	6.08587i	−0.0997331	+	0.396999i
$236$		0			0
$237$	−12.2902	+	10.6496i	−0.798337	+	0.691763i
$238$		0			0
$239$	24.1837	+	7.10099i	1.56432	+	0.459325i	0.945340	−	0.326085i	$-0.105730\pi$
$239$	24.1837	+	7.10099i	1.56432	+	0.459325i	0.618976	+	0.785410i	$0.287548\pi$
$240$		0			0
$241$	13.7092	+	8.81037i	0.883088	+	0.567526i	0.901730	−	0.432300i	$-0.142298\pi$
$241$	13.7092	+	8.81037i	0.883088	+	0.567526i	−0.0186419	+	0.999826i	$0.505934\pi$
$242$		0			0
$243$	9.16209	+	7.93899i	0.587748	+	0.509287i
$244$		0			0
$245$	−3.05552	+	7.45617i	−0.195210	+	0.476357i
$246$		0			0
$247$	9.61690	−	4.39189i	0.611909	−	0.279449i
$248$		0			0
$249$	−2.52728	+	5.53398i	−0.160160	+	0.350702i
$250$		0			0
$251$	22.8507	−	14.6853i	1.44232	−	0.926926i	0.442784	−	0.896628i	$-0.353991\pi$
$251$	22.8507	−	14.6853i	1.44232	−	0.926926i	0.999541	−	0.0302973i	$-0.00964542\pi$
$252$		0			0
$253$	−12.9702	+	3.10581i	−0.815426	+	0.195260i
$254$		0			0
$255$	7.26583	−	0.286967i	0.455004	−	0.0179706i
$256$		0			0
$257$	13.6420	+	6.23007i	0.850962	+	0.388621i	0.792650	−	0.609677i	$-0.208701\pi$
$257$	13.6420	+	6.23007i	0.850962	+	0.388621i	0.0583120	+	0.998298i	$0.481428\pi$
$258$		0			0
$259$	−0.448257	−	0.981546i	−0.0278533	−	0.0609903i
$260$		0			0
$261$	1.80390	+	12.5464i	0.111659	+	0.776605i
$262$		0			0
$263$	1.85173	+	1.60453i	0.114182	+	0.0989397i	0.710081	−	0.704120i	$-0.248658\pi$
$263$	1.85173	+	1.60453i	0.114182	+	0.0989397i	−0.595898	+	0.803060i	$0.703204\pi$
$264$		0			0
$265$	8.57033	−	4.33054i	0.526471	−	0.266023i
$266$		0			0
$267$	0.568786	−	1.93711i	0.0348091	−	0.118549i
$268$		0			0
$269$	−1.47476	−	1.70197i	−0.0899180	−	0.103771i	0.709007	−	0.705201i	$-0.249143\pi$
$269$	−1.47476	−	1.70197i	−0.0899180	−	0.103771i	−0.798925	+	0.601430i	$0.794598\pi$
$270$		0			0
$271$	23.9375	−	7.02867i	1.45410	−	0.426962i	0.543203	−	0.839601i	$-0.317211\pi$
$271$	23.9375	−	7.02867i	1.45410	−	0.426962i	0.910894	+	0.412640i	$0.135393\pi$
$272$		0			0
$273$	−10.4553	−	1.50325i	−0.632784	−	0.0909806i
$274$		0			0
$275$	6.75571	+	12.1531i	0.407385	+	0.732860i
$276$		0			0
$277$			15.1928i			0.912848i	0.889762	+	0.456424i	$0.150870\pi$
$277$			15.1928i			0.912848i	−0.889762	+	0.456424i	$0.849130\pi$
$278$		0			0
$279$	−0.210799	+	1.46614i	−0.0126202	+	0.0877753i
$280$		0			0
$281$	−12.8418	+	3.77068i	−0.766075	+	0.224940i	−0.641347	−	0.767251i	$-0.721624\pi$
$281$	−12.8418	+	3.77068i	−0.766075	+	0.224940i	−0.124728	+	0.992191i	$0.539806\pi$
$282$		0			0
$283$	8.01404	−	6.94420i	0.476385	−	0.412790i	−0.383292	−	0.923627i	$-0.625210\pi$
$283$	8.01404	−	6.94420i	0.476385	−	0.412790i	0.859678	+	0.510837i	$0.170664\pi$
$284$		0			0
$285$	5.21219	−	4.88958i	0.308743	−	0.289634i
$286$		0			0
$287$	−4.65945	+	7.25025i	−0.275039	+	0.427969i
$288$		0			0
$289$	−7.13590	+	8.23527i	−0.419759	+	0.484428i
$290$		0			0
$291$	−3.31707	−	23.0707i	−0.194450	−	1.35243i
$292$		0			0
$293$	−30.7962	+	14.0641i	−1.79913	+	0.821636i	−0.837935	+	0.545770i	$0.816237\pi$
$293$	−30.7962	+	14.0641i	−1.79913	+	0.821636i	−0.961196	+	0.275865i	$0.911036\pi$
$294$		0			0
$295$	8.94344	−	6.25971i	0.520707	−	0.364455i
$296$		0			0
$297$	−8.44524	−	13.1411i	−0.490043	−	0.762521i
$298$		0			0
$299$	−20.7934	+	1.92329i	−1.20251	+	0.111227i
$300$		0			0
$301$	−0.0943372	+	0.0606269i	−0.00543751	+	0.00349447i
$302$		0			0
$303$	16.9093	+	7.72224i	0.971416	+	0.443631i
$304$		0			0
$305$	1.10921	−	10.6969i	0.0635130	−	0.612504i
$306$		0			0
$307$	18.8433	−	2.70925i	1.07544	−	0.154625i	0.418237	−	0.908338i	$-0.362648\pi$
$307$	18.8433	−	2.70925i	1.07544	−	0.154625i	0.657204	+	0.753713i	$0.271739\pi$
$308$		0			0
$309$	10.6687	−	12.3123i	0.606921	−	0.700424i
$310$		0			0
$311$	−5.30678	−	3.41046i	−0.300920	−	0.193389i	0.381464	−	0.924384i	$-0.375420\pi$
$311$	−5.30678	−	3.41046i	−0.300920	−	0.193389i	−0.682383	+	0.730994i	$0.739057\pi$
$312$		0			0
$313$	−0.725536	+	2.47095i	−0.0410097	+	0.139666i	−0.977453	−	0.211152i	$-0.932278\pi$
$313$	−0.725536	+	2.47095i	−0.0410097	+	0.139666i	0.936443	+	0.350819i	$0.114097\pi$
$314$		0			0
$315$	5.13594	−	0.946659i	0.289378	−	0.0533382i
$316$		0			0
$317$	8.92626	+	30.4000i	0.501349	+	1.70744i	0.688615	+	0.725128i	$0.258219\pi$
$317$	8.92626	+	30.4000i	0.501349	+	1.70744i	−0.187266	+	0.982309i	$0.559963\pi$
$318$		0			0
$319$	3.95840	−	27.5313i	0.221628	−	1.54146i
$320$		0			0
$321$	−21.6057			−1.20591
$322$		0			0
$323$		−	5.99841i		−	0.333760i
$324$		0			0
$325$	7.76203	+	20.3405i	0.430560	+	1.12829i
$326$		0			0
$327$	−1.61625	−	5.50444i	−0.0893788	−	0.304396i
$328$		0			0
$329$	−3.38676	−	3.90852i	−0.186718	−	0.215484i
$330$		0			0
$331$	2.02240	+	0.593829i	0.111161	+	0.0326398i	0.336840	−	0.941562i	$-0.390642\pi$
$331$	2.02240	+	0.593829i	0.111161	+	0.0326398i	−0.225679	+	0.974202i	$0.572460\pi$
$332$		0			0
$333$	0.401170	−	0.624233i	0.0219840	−	0.0342077i
$334$		0			0
$335$	−10.8826	−	32.2897i	−0.594581	−	1.76418i
$336$		0			0
$337$	−19.9308	+	2.86562i	−1.08570	+	0.156100i	−0.661854	−	0.749633i	$-0.730230\pi$
$337$	−19.9308	+	2.86562i	−1.08570	+	0.156100i	−0.423848	+	0.905733i	$0.639321\pi$
$338$		0			0
$339$	4.19928	+	9.19515i	0.228074	+	0.499412i
$340$		0			0
$341$	1.35022	−	2.95658i	0.0731188	−	0.160108i
$342$		0			0
$343$	−10.5650	−	16.4395i	−0.570458	−	0.887650i
$344$		0			0
$345$	−12.9046	+	5.72119i	−0.694758	+	0.308019i
$346$		0			0
$347$	0.843816	+	1.31300i	0.0452984	+	0.0704857i	0.863164	−	0.504923i	$-0.168479\pi$
$347$	0.843816	+	1.31300i	0.0452984	+	0.0704857i	−0.817866	+	0.575409i	$0.804843\pi$
$348$		0			0
$349$	−8.62730	+	18.8912i	−0.461809	+	1.01122i	0.525263	+	0.850940i	$0.323967\pi$
$349$	−8.62730	+	18.8912i	−0.461809	+	1.01122i	−0.987072	+	0.160280i	$0.948760\pi$
$350$		0			0
$351$	−10.1603	−	22.2481i	−0.542319	−	1.18751i
$352$		0			0
$353$	−10.0713	+	1.44803i	−0.536040	+	0.0770709i	−0.405018	−	0.914309i	$-0.632735\pi$
$353$	−10.0713	+	1.44803i	−0.536040	+	0.0770709i	−0.131022	+	0.991380i	$0.541826\pi$
$354$		0			0
$355$	−21.5695	+	7.26959i	−1.14479	+	0.385830i
$356$		0			0
$357$	−3.24008	+	5.04166i	−0.171483	+	0.266833i
$358$		0			0
$359$	−20.2952	−	5.95921i	−1.07114	−	0.314515i	−0.301811	−	0.953368i	$-0.597591\pi$
$359$	−20.2952	−	5.95921i	−1.07114	−	0.314515i	−0.769329	+	0.638853i	$0.779409\pi$
$360$		0			0
$361$	8.58166	+	9.90377i	0.451666	+	0.521251i
$362$		0			0
$363$	−1.21137	−	4.12556i	−0.0635806	−	0.216536i
$364$		0			0
$365$	−18.0072	−	14.3993i	−0.942540	−	0.753696i
$366$		0			0
$367$			19.9966i			1.04381i	0.853002	+	0.521907i	$0.174779\pi$
$367$			19.9966i			1.04381i	−0.853002	+	0.521907i	$0.825221\pi$
$368$		0			0
$369$	−5.92653			−0.308523
$370$		0			0
$371$	−1.12628	+	7.83348i	−0.0584738	+	0.406694i
$372$		0			0
$373$	−9.76806	−	33.2670i	−0.505771	−	1.72250i	−0.675824	−	0.737063i	$-0.736212\pi$
$373$	−9.76806	−	33.2670i	−0.505771	−	1.72250i	0.170053	−	0.985435i	$-0.445606\pi$
$374$		0			0
$375$	9.36357	+	11.3539i	0.483532	+	0.586311i
$376$		0			0
$377$	12.2696	−	41.7863i	0.631915	−	2.15211i
$378$		0			0
$379$	−14.5811	−	9.37073i	−0.748983	−	0.481342i	0.109626	−	0.993973i	$-0.465035\pi$
$379$	−14.5811	−	9.37073i	−0.748983	−	0.481342i	−0.858609	+	0.512631i	$0.828671\pi$
$380$		0			0
$381$	−8.03988	+	9.27851i	−0.411895	+	0.475353i
$382$		0			0
$383$	34.9226	−	5.02111i	1.78446	−	0.256567i	0.830611	−	0.556853i	$-0.187992\pi$
$383$	34.9226	−	5.02111i	1.78446	−	0.256567i	0.953849	+	0.300287i	$0.0970824\pi$
$384$		0			0
$385$	−11.3988	−	1.18199i	−0.580936	−	0.0602396i
$386$		0			0
$387$	−0.0701450	−	0.0320341i	−0.00356567	−	0.00162839i
$388$		0			0
$389$	12.5992	−	8.09703i	0.638806	−	0.410536i	−0.180754	−	0.983528i	$-0.557854\pi$
$389$	12.5992	−	8.09703i	0.638806	−	0.410536i	0.819561	+	0.572992i	$0.194218\pi$
$390$		0			0
$391$	−3.90827	+	11.1847i	−0.197650	+	0.565637i
$392$		0			0
$393$	−1.84027	−	2.86352i	−0.0928294	−	0.144445i
$394$		0			0
$395$	−22.6323	+	15.8409i	−1.13876	+	0.797041i
$396$		0			0
$397$	3.53811	−	1.61580i	0.177573	−	0.0810948i	−0.324645	−	0.945836i	$-0.605245\pi$
$397$	3.53811	−	1.61580i	0.177573	−	0.0810948i	0.502218	+	0.864741i	$0.332518\pi$
$398$		0			0
$399$	0.838256	+	5.83020i	0.0419653	+	0.291875i
$400$		0			0
$401$	−19.2368	+	22.2004i	−0.960639	+	1.10864i	0.0333811	+	0.999443i	$0.489372\pi$
$401$	−19.2368	+	22.2004i	−0.960639	+	1.10864i	−0.994020	+	0.109194i	$0.965173\pi$
$402$		0			0
$403$	2.75141	−	4.28128i	0.137058	−	0.213266i
$404$		0			0
$405$	−5.49528	−	5.85785i	−0.273063	−	0.291079i
$406$		0			0
$407$	−1.23056	+	1.06629i	−0.0609967	+	0.0528540i
$408$		0			0
$409$	−5.97942	+	1.75571i	−0.295663	+	0.0868145i	−0.426200	−	0.904629i	$-0.640148\pi$
$409$	−5.97942	+	1.75571i	−0.295663	+	0.0868145i	0.130537	+	0.991443i	$0.458330\pi$
$410$		0			0
$411$	2.64230	−	18.3776i	0.130335	−	0.906500i
$412$		0			0
$413$			8.99715i			0.442721i
$414$		0			0
$415$	−5.23987	+	8.90779i	−0.257215	+	0.437266i
$416$		0			0
$417$	11.3552	+	1.63264i	0.556068	+	0.0799505i
$418$		0			0
$419$	20.5083	−	6.02179i	1.00190	−	0.294184i	0.260663	−	0.965430i	$-0.416059\pi$
$419$	20.5083	−	6.02179i	1.00190	−	0.294184i	0.741235	+	0.671246i	$0.234241\pi$
$420$		0			0
$421$	18.7761	+	21.6688i	0.915092	+	1.05607i	0.998226	+	0.0595342i	$0.0189615\pi$
$421$	18.7761	+	21.6688i	0.915092	+	1.05607i	−0.0831342	+	0.996538i	$0.526493\pi$
$422$		0			0
$423$	1.00195	−	3.41233i	0.0487165	−	0.165913i
$424$		0			0
$425$	12.3271	+	0.788156i	0.597954	+	0.0382312i
$426$		0			0
$427$	6.69856	+	5.80434i	0.324166	+	0.280892i
$428$		0			0
$429$	2.26835	+	15.7768i	0.109517	+	0.761709i
$430$		0			0
$431$	−3.49149	−	7.64529i	−0.168179	−	0.368261i	0.806711	−	0.590946i	$-0.201245\pi$
$431$	−3.49149	−	7.64529i	−0.168179	−	0.368261i	−0.974891	+	0.222685i	$0.928518\pi$
$432$		0			0
$433$	−35.0380	−	16.0013i	−1.68382	−	0.768974i	−0.999197	−	0.0400752i	$-0.987240\pi$
$433$	−35.0380	−	16.0013i	−1.68382	−	0.768974i	−0.684621	−	0.728899i	$-0.740032\pi$
$434$		0			0
$435$	−1.16181	−	29.4163i	−0.0557046	−	1.41040i
$436$		0			0
$437$	4.29574	+	10.8232i	0.205493	+	0.517744i
$438$		0			0
$439$	3.28690	−	2.11236i	0.156875	−	0.100818i	−0.459848	−	0.887998i	$-0.652096\pi$
$439$	3.28690	−	2.11236i	0.156875	−	0.100818i	0.616723	+	0.787180i	$0.288460\pi$
$440$		0			0
$441$	1.89716	−	4.15420i	0.0903410	−	0.197819i
$442$		0			0
$443$	5.42381	−	2.47697i	0.257693	−	0.117684i	−0.282380	−	0.959303i	$-0.591124\pi$
$443$	5.42381	−	2.47697i	0.257693	−	0.117684i	0.540073	+	0.841618i	$0.318397\pi$
$444$		0			0
$445$	1.30046	−	3.17342i	0.0616477	−	0.150434i
$446$		0			0
$447$	15.5022	+	13.4327i	0.733228	+	0.635346i
$448$		0			0
$449$	−23.4690	−	15.0826i	−1.10757	−	0.711791i	−0.146806	−	0.989165i	$-0.546899\pi$
$449$	−23.4690	−	15.0826i	−1.10757	−	0.711791i	−0.960762	+	0.277374i	$0.910536\pi$
$450$		0			0
$451$	12.4781	+	3.66390i	0.587571	+	0.172526i
$452$		0			0
$453$	−16.6510	+	14.4282i	−0.782331	+	0.677894i
$454$		0			0
$455$	−17.4026	−	4.37185i	−0.815848	−	0.204956i
$456$		0			0
$457$	14.6111	+	2.10076i	0.683477	+	0.0982692i	0.475303	−	0.879822i	$-0.342339\pi$
$457$	14.6111	+	2.10076i	0.683477	+	0.0982692i	0.208175	+	0.978092i	$0.433248\pi$
$458$		0			0
$459$	−13.8769			−0.647718
$460$		0			0
$461$	17.2587			0.803817			0.401909	−	0.915680i	$-0.368347\pi$
$461$	17.2587			0.803817			0.401909	+	0.915680i	$0.368347\pi$
$462$		0			0
$463$	−0.978550	−	0.140694i	−0.0454771	−	0.00653862i	0.119539	−	0.992830i	$-0.461858\pi$
$463$	−0.978550	−	0.140694i	−0.0454771	−	0.00653862i	−0.165016	+	0.986291i	$0.552768\pi$
$464$		0			0
$465$	0.838189	−	3.33651i	0.0388701	−	0.154727i
$466$		0			0
$467$	11.8571	−	10.2742i	0.548679	−	0.475433i	−0.335852	−	0.941915i	$-0.609024\pi$
$467$	11.8571	−	10.2742i	0.548679	−	0.475433i	0.884531	+	0.466482i	$0.154479\pi$
$468$		0			0
$469$	26.9458	+	7.91201i	1.24424	+	0.365343i
$470$		0			0
$471$	−1.72789	−	1.11045i	−0.0796171	−	0.0511668i
$472$		0			0
$473$	0.127884	+	0.110812i	0.00588009	+	0.00509513i
$474$		0			0
$475$	9.66357	−	7.34856i	0.443395	−	0.337175i
$476$		0			0
$477$	−4.95037	+	2.26076i	−0.226662	+	0.103513i
$478$		0			0
$479$	−6.53266	+	14.3045i	−0.298485	+	0.653591i	−0.998145	−	0.0608851i	$-0.980608\pi$
$479$	−6.53266	+	14.3045i	−0.298485	+	0.653591i	0.699660	+	0.714476i	$0.253335\pi$
$480$		0			0
$481$	−2.14475	+	1.37834i	−0.0977920	+	0.0628471i
$482$		0			0
$483$	2.23565	−	11.4173i	0.101726	−	0.519503i
$484$		0			0
$485$	−1.56256	−	39.5631i	−0.0709523	−	1.79647i
$486$		0			0
$487$	14.1927	+	6.48160i	0.643134	+	0.293709i	0.710158	−	0.704042i	$-0.248623\pi$
$487$	14.1927	+	6.48160i	0.643134	+	0.293709i	−0.0670245	+	0.997751i	$0.521351\pi$
$488$		0			0
$489$	−7.87486	−	17.2435i	−0.356114	−	0.779780i
$490$		0			0
$491$	5.30629	+	36.9060i	0.239469	+	1.66555i	0.654744	+	0.755850i	$0.272776\pi$
$491$	5.30629	+	36.9060i	0.239469	+	1.66555i	−0.415275	+	0.909696i	$0.636315\pi$
$492$		0			0
$493$	−18.6740	−	16.1811i	−0.841034	−	0.728760i
$494$		0			0
$495$	−3.55404	−	7.03361i	−0.159742	−	0.316137i
$496$		0			0
$497$	5.28522	−	17.9998i	0.237074	−	0.807401i
$498$		0			0
$499$	−14.5650	−	16.8090i	−0.652021	−	0.752472i	0.329431	−	0.944180i	$-0.393143\pi$
$499$	−14.5650	−	16.8090i	−0.652021	−	0.752472i	−0.981452	+	0.191707i	$0.938598\pi$
$500$		0			0
$501$	−9.96248	+	2.92525i	−0.445091	+	0.130690i
$502$		0			0
$503$	−27.6917	−	3.98147i	−1.23471	−	0.177525i	−0.506115	−	0.862466i	$-0.668919\pi$
$503$	−27.6917	−	3.98147i	−1.23471	−	0.177525i	−0.728599	+	0.684941i	$0.759828\pi$
$504$		0			0
$505$	27.2182	+	16.0107i	1.21119	+	0.712467i
$506$		0			0
$507$			7.84438i			0.348381i
$508$		0			0
$509$	−3.99932	+	27.8159i	−0.177267	+	1.23292i	0.685786	+	0.727803i	$0.259459\pi$
$509$	−3.99932	+	27.8159i	−0.177267	+	1.23292i	−0.863053	+	0.505114i	$0.831450\pi$
$510$		0			0
$511$	18.2330	−	5.35368i	0.806578	−	0.236833i
$512$		0			0
$513$	−10.3074	+	8.93144i	−0.455084	+	0.394333i
$514$		0			0
$515$	20.1838	−	18.9345i	0.889405	−	0.834355i
$516$		0			0
$517$	−4.21915	+	6.56512i	−0.185558	+	0.288734i
$518$		0			0
$519$	−12.8263	+	14.8024i	−0.563013	+	0.649752i
$520$		0			0
$521$	1.60915	+	11.1919i	0.0704981	+	0.490325i	0.994229	+	0.107282i	$0.0342147\pi$
$521$	1.60915	+	11.1919i	0.0704981	+	0.490325i	−0.923731	+	0.383043i	$0.874876\pi$
$522$		0			0
$523$	−6.52525	+	2.97998i	−0.285329	+	0.130305i	−0.552939	−	0.833222i	$-0.686494\pi$
$523$	−6.52525	+	2.97998i	−0.285329	+	0.130305i	0.267609	+	0.963527i	$0.413766\pi$
$524$		0			0
$525$	−12.0916	+	0.956619i	−0.527720	+	0.0417503i
$526$		0			0
$527$	−1.56107	−	2.42907i	−0.0680012	−	0.105812i
$528$		0			0
$529$	−0.958043	−	22.9800i	−0.0416541	−	0.999132i
$530$		0			0
$531$	−5.20483	+	3.34494i	−0.225870	+	0.145158i
$532$		0			0
$533$	18.5223	+	8.45887i	0.802291	+	0.366394i
$534$		0			0
$535$	−36.5065	−	3.78550i	−1.57831	−	0.163662i
$536$		0			0
$537$	4.65673	−	0.669537i	0.200953	−	0.0288927i
$538$		0			0
$539$	−6.56262	+	7.57367i	−0.282672	+	0.326221i
$540$		0			0
$541$	−37.6697	−	24.2088i	−1.61955	−	1.04082i	−0.956288	−	0.292427i	$-0.905537\pi$
$541$	−37.6697	−	24.2088i	−1.61955	−	1.04082i	−0.663257	−	0.748391i	$-0.730827\pi$
$542$		0			0
$543$	4.63692	−	15.7919i	0.198989	−	0.677695i
$544$		0			0
$545$	−1.76650	−	9.58387i	−0.0756687	−	0.410528i
$546$		0			0
$547$	8.33566	+	28.3886i	0.356407	+	1.21381i	0.921367	+	0.388693i	$0.127073\pi$
$547$	8.33566	+	28.3886i	0.356407	+	1.21381i	−0.564961	+	0.825118i	$0.691109\pi$
$548$		0			0
$549$	−0.867418	+	6.03303i	−0.0370205	+	0.257483i
$550$		0			0
$551$	−24.2851			−1.03458
$552$		0			0
$553$		−	22.7682i		−	0.968204i
$554$		0			0
$555$	−1.07630	+	1.34597i	−0.0456863	+	0.0571334i
$556$		0			0
$557$	3.64530	+	12.4147i	0.154456	+	0.526029i	0.999969	−	0.00792635i	$-0.00252306\pi$
$557$	3.64530	+	12.4147i	0.154456	+	0.526029i	−0.845512	+	0.533956i	$0.820705\pi$
$558$		0			0
$559$	0.173504	+	0.200234i	0.00733843	+	0.00846900i
$560$		0			0
$561$	8.67699	+	2.54779i	0.366343	+	0.107568i
$562$		0			0
$563$	8.35542	−	13.0013i	0.352139	−	0.547939i	−0.619323	−	0.785137i	$-0.712593\pi$
$563$	8.35542	−	13.0013i	0.352139	−	0.547939i	0.971461	+	0.237198i	$0.0762290\pi$
$564$		0			0
$565$	5.48434	+	16.2725i	0.230728	+	0.684590i
$566$		0			0
$567$	6.55242	−	0.942095i	0.275176	−	0.0395643i
$568$		0			0
$569$	−9.18510	−	20.1126i	−0.385059	−	0.843163i	−0.998569	−	0.0534754i	$-0.982970\pi$
$569$	−9.18510	−	20.1126i	−0.385059	−	0.843163i	0.613510	−	0.789687i	$-0.289757\pi$
$570$		0			0
$571$	6.74197	−	14.7629i	0.282143	−	0.617807i	−0.714504	−	0.699631i	$-0.753348\pi$
$571$	6.74197	−	14.7629i	0.282143	−	0.617807i	0.996647	+	0.0818248i	$0.0260748\pi$
$572$		0			0
$573$	5.77398	+	8.98449i	0.241212	+	0.375333i
$574$		0			0
$575$	−22.8068	+	7.40594i	−0.951111	+	0.308849i
$576$		0			0
$577$	15.9755	+	24.8584i	0.665070	+	1.03487i	0.995837	+	0.0911571i	$0.0290565\pi$
$577$	15.9755	+	24.8584i	0.665070	+	1.03487i	−0.330766	+	0.943713i	$0.607307\pi$
$578$		0			0
$579$	2.07158	−	4.53613i	0.0860920	−	0.188515i
$580$		0			0
$581$	−3.53835	−	7.74791i	−0.146796	−	0.321437i
$582$		0			0
$583$	11.8205	−	1.69953i	0.489555	−	0.0703873i
$584$		0			0
$585$	−3.94081	−	11.6927i	−0.162932	−	0.483435i
$586$		0			0
$587$	−20.4215	+	31.7764i	−0.842884	+	1.31155i	0.105496	+	0.994420i	$0.466357\pi$
$587$	−20.4215	+	31.7764i	−0.842884	+	1.31155i	−0.948381	+	0.317134i	$0.897279\pi$
$588$		0			0
$589$	−2.72292	−	0.799522i	−0.112196	−	0.0329437i
$590$		0			0
$591$	15.7297	+	18.1530i	0.647033	+	0.746716i
$592$		0			0
$593$	−1.46341	−	4.98393i	−0.0600952	−	0.204665i	0.923973	−	0.382458i	$-0.124922\pi$
$593$	−1.46341	−	4.98393i	−0.0600952	−	0.204665i	−0.984068	+	0.177793i	$0.943104\pi$
$594$		0			0
$595$	−6.35800	+	7.95105i	−0.260653	+	0.325961i
$596$		0			0
$597$			0.862687i			0.0353074i
$598$		0			0
$599$	−8.38442			−0.342578			−0.171289	−	0.985221i	$-0.554793\pi$
$599$	−8.38442			−0.342578			−0.171289	+	0.985221i	$0.554793\pi$
$600$		0			0
$601$	−1.04873	+	7.29406i	−0.0427785	+	0.297531i	0.957189	+	0.289464i	$0.0934770\pi$
$601$	−1.04873	+	7.29406i	−0.0427785	+	0.297531i	−0.999967	+	0.00806713i	$0.997432\pi$
$602$		0			0
$603$	5.44078	+	18.5296i	0.221566	+	0.754584i
$604$		0			0
$605$	−1.32399	−	7.18308i	−0.0538278	−	0.292034i
$606$		0			0
$607$	6.84101	−	23.2983i	0.277668	−	0.945651i	−0.696069	−	0.717975i	$-0.745069\pi$
$607$	6.84101	−	23.2983i	0.277668	−	0.945651i	0.973737	−	0.227676i	$-0.0731126\pi$
$608$		0			0
$609$	20.4116	+	13.1177i	0.827118	+	0.531557i
$610$		0			0
$611$	−8.00180	+	9.23457i	−0.323718	+	0.373591i
$612$		0			0
$613$	11.6430	−	1.67402i	0.470258	−	0.0676129i	0.0968876	−	0.995295i	$-0.469111\pi$
$613$	11.6430	−	1.67402i	0.470258	−	0.0676129i	0.373370	+	0.927682i	$0.378202\pi$
$614$		0			0
$615$	13.6912	+	1.41970i	0.552083	+	0.0572477i
$616$		0			0
$617$	−2.56100	−	1.16957i	−0.103102	−	0.0470852i	0.363196	−	0.931713i	$-0.381685\pi$
$617$	−2.56100	−	1.16957i	−0.103102	−	0.0470852i	−0.466298	+	0.884627i	$0.654413\pi$
$618$		0			0
$619$	31.5668	−	20.2867i	1.26878	−	0.815393i	0.279316	−	0.960199i	$-0.409892\pi$
$619$	31.5668	−	20.2867i	1.26878	−	0.815393i	0.989460	+	0.144806i	$0.0462560\pi$
$620$		0			0
$621$	25.0387	−	9.93791i	1.00477	−	0.398794i
$622$		0			0
$623$	1.52816	+	2.37786i	0.0612243	+	0.0952669i
$624$		0			0
$625$	13.8320	+	20.8249i	0.553282	+	0.832994i
$626$		0			0
$627$	8.08487	−	3.69224i	0.322879	−	0.147454i
$628$		0			0
$629$	0.205857	+	1.43177i	0.00820805	+	0.0570883i
$630$		0			0
$631$	8.59012	−	9.91353i	0.341967	−	0.394651i	−0.558550	−	0.829471i	$-0.688642\pi$
$631$	8.59012	−	9.91353i	0.341967	−	0.394651i	0.900518	+	0.434819i	$0.143188\pi$
$632$		0			0
$633$	−12.7484	+	19.8369i	−0.506705	+	0.788448i
$634$		0			0
$635$	−15.2104	+	14.2690i	−0.603607	+	0.566247i
$636$		0			0
$637$	−11.8585	+	10.2754i	−0.469850	+	0.407128i
$638$		0			0
$639$	12.3778	−	3.63444i	0.489657	−	0.143776i
$640$		0			0
$641$	6.15504	−	42.8092i	0.243109	−	1.69086i	−0.393219	−	0.919445i	$-0.628639\pi$
$641$	6.15504	−	42.8092i	0.243109	−	1.69086i	0.636329	−	0.771418i	$-0.280452\pi$
$642$		0			0
$643$			12.2873i			0.484563i	0.970206	+	0.242281i	$0.0778957\pi$
$643$			12.2873i			0.484563i	−0.970206	+	0.242281i	$0.922104\pi$
$644$		0			0
$645$	0.154372	+	0.0908069i	0.00607839	+	0.00357552i
$646$		0			0
$647$	−37.4761	−	5.38825i	−1.47334	−	0.211834i	−0.641616	−	0.767026i	$-0.721736\pi$
$647$	−37.4761	−	5.38825i	−1.47334	−	0.211834i	−0.831722	+	0.555192i	$0.812645\pi$
$648$		0			0
$649$	13.0265	−	3.82492i	0.511334	−	0.150141i
$650$		0			0
$651$	1.85675	+	2.14280i	0.0727717	+	0.0839830i
$652$		0			0
$653$	−2.09560	+	7.13696i	−0.0820072	+	0.279291i	−0.990280	−	0.139087i	$-0.955583\pi$
$653$	−2.09560	+	7.13696i	−0.0820072	+	0.279291i	0.908273	+	0.418378i	$0.137401\pi$
$654$		0			0
$655$	−2.60774	−	5.16083i	−0.101893	−	0.201650i
$656$		0			0
$657$	9.87569	+	8.55734i	0.385288	+	0.333854i
$658$		0			0
$659$	0.990860	+	6.89159i	0.0385984	+	0.268458i	0.999977	−	0.00677116i	$-0.00215534\pi$
$659$	0.990860	+	6.89159i	0.0385984	+	0.268458i	−0.961379	+	0.275229i	$0.911246\pi$
$660$		0			0
$661$	−3.82568	−	8.37708i	−0.148802	−	0.325831i	0.820523	−	0.571613i	$-0.193682\pi$
$661$	−3.82568	−	8.37708i	−0.148802	−	0.325831i	−0.969325	+	0.245783i	$0.920955\pi$
$662$		0			0
$663$	12.8800	+	5.88210i	0.500218	+	0.228442i
$664$		0			0
$665$	0.394875	+	9.99798i	0.0153126	+	0.387705i
$666$		0			0
$667$	45.2824	+	15.8230i	1.75334	+	0.612668i
$668$		0			0
$669$	6.86904	−	4.41446i	0.265572	−	0.170673i
$670$		0			0
$671$	5.55606	−	12.1661i	0.214489	−	0.469666i
$672$		0			0
$673$	−45.2580	+	20.6686i	−1.74457	+	0.796718i	−0.754472	+	0.656333i	$0.772107\pi$
$673$	−45.2580	+	20.6686i	−1.74457	+	0.796718i	−0.990097	+	0.140385i	$0.955166\pi$
$674$		0			0
$675$	−17.0004	−	22.3560i	−0.654345	−	0.860483i
$676$		0			0
$677$	27.0003	+	23.3959i	1.03771	+	0.899177i	0.994996	−	0.0999102i	$-0.0318555\pi$
$677$	27.0003	+	23.3959i	1.03771	+	0.899177i	0.0427095	+	0.999088i	$0.486401\pi$
$678$		0			0
$679$	27.4523	+	17.6425i	1.05352	+	0.677057i
$680$		0			0
$681$	−2.03235	−	0.596751i	−0.0778797	−	0.0228676i
$682$		0			0
$683$	16.4297	−	14.2364i	0.628666	−	0.544742i	−0.281198	−	0.959650i	$-0.590732\pi$
$683$	16.4297	−	14.2364i	0.628666	−	0.544742i	0.909863	+	0.414908i	$0.136186\pi$
$684$		0			0
$685$	7.68453	−	30.5891i	0.293611	−	1.16875i
$686$		0			0
$687$	−13.3067	−	1.91322i	−0.507683	−	0.0729938i
$688$		0			0
$689$	18.6983			0.712348
$690$		0			0
$691$	−31.4654			−1.19700			−0.598501	−	0.801122i	$-0.704237\pi$
$691$	−31.4654			−1.19700			−0.598501	+	0.801122i	$0.704237\pi$
$692$		0			0
$693$	6.42888	+	0.924333i	0.244213	+	0.0351125i
$694$		0			0
$695$	18.9005	+	4.74815i	0.716939	+	0.180108i
$696$		0			0
$697$	8.73121	−	7.56564i	0.330718	−	0.286569i
$698$		0			0
$699$	29.5081	+	8.66437i	1.11610	+	0.327717i
$700$		0			0
$701$	−15.1027	−	9.70589i	−0.570420	−	0.366586i	0.223412	−	0.974724i	$-0.428280\pi$
$701$	−15.1027	−	9.70589i	−0.570420	−	0.366586i	−0.793832	+	0.608138i	$0.791917\pi$
$702$		0			0
$703$	1.07442	+	0.930988i	0.0405224	+	0.0351129i
$704$		0			0
$705$	−3.13208	+	7.64300i	−0.117961	+	0.287852i
$706$		0			0
$707$	−23.6741	+	10.8116i	−0.890357	+	0.406612i
$708$		0			0
$709$	1.72571	−	3.77878i	0.0648105	−	0.141915i	−0.874455	−	0.485107i	$-0.838781\pi$
$709$	1.72571	−	3.77878i	0.0648105	−	0.141915i	0.939265	+	0.343192i	$0.111508\pi$
$710$		0			0
$711$	13.1714	−	8.46472i	0.493965	−	0.317452i
$712$		0			0
$713$	4.55628	+	3.26493i	0.170634	+	0.122273i
$714$		0			0
$715$	1.06855	+	27.0549i	0.0399614	+	1.01180i
$716$		0			0
$717$	30.1792	+	13.7824i	1.12706	+	0.514713i
$718$		0			0
$719$	6.81934	+	14.9323i	0.254318	+	0.556879i	0.993128	−	0.117035i	$-0.0373389\pi$
$719$	6.81934	+	14.9323i	0.254318	+	0.556879i	−0.738809	+	0.673914i	$0.764612\pi$
$720$		0			0
$721$	3.24608	+	22.5770i	0.120890	+	0.840812i
$722$		0			0
$723$	16.2115	+	14.0474i	0.602913	+	0.522427i
$724$		0			0
$725$	3.19091	−	49.9074i	0.118508	−	1.85352i
$726$		0			0
$727$	−8.96402	+	30.5287i	−0.332457	+	1.13225i	0.608453	+	0.793590i	$0.291790\pi$
$727$	−8.96402	+	30.5287i	−0.332457	+	1.13225i	−0.940910	+	0.338656i	$0.890028\pi$
$728$		0			0
$729$	17.5070	+	20.2042i	0.648408	+	0.748303i
$730$		0			0
$731$	0.144234	−	0.0423510i	0.00533469	−	0.00156641i
$732$		0			0
$733$	−5.75880	−	0.827990i	−0.212706	−	0.0305825i	0.0351379	−	0.999382i	$-0.488813\pi$
$733$	−5.75880	−	0.827990i	−0.212706	−	0.0305825i	−0.247844	+	0.968800i	$0.579722\pi$
$734$		0			0
$735$	−5.37787	+	9.14239i	−0.198366	+	0.337222i
$736$		0			0
$737$		−	42.3770i		−	1.56098i
$738$		0			0
$739$	−3.93500	+	27.3685i	−0.144751	+	1.00677i	0.779887	+	0.625921i	$0.215277\pi$
$739$	−3.93500	+	27.3685i	−0.144751	+	1.00677i	−0.924638	+	0.380847i	$0.875632\pi$
$740$		0			0
$741$	13.3528	−	3.92073i	0.490527	−	0.144032i
$742$		0			0
$743$	−7.27245	+	6.30161i	−0.266800	+	0.231184i	−0.777978	−	0.628291i	$-0.783755\pi$
$743$	−7.27245	+	6.30161i	−0.266800	+	0.231184i	0.511178	+	0.859475i	$0.329209\pi$
$744$		0			0
$745$	23.8400	+	25.4130i	0.873432	+	0.931059i
$746$		0			0
$747$	3.16666	−	4.92743i	0.115862	−	0.180285i
$748$		0			0
$749$	19.8091	−	22.8609i	0.723808	−	0.835318i
$750$		0			0
$751$	−7.06502	−	49.1383i	−0.257806	−	1.79308i	−0.548381	−	0.836229i	$-0.684756\pi$
$751$	−7.06502	−	49.1383i	−0.257806	−	1.79308i	0.290575	−	0.956852i	$-0.406153\pi$
$752$		0			0
$753$	32.5237	−	14.8531i	1.18523	−	0.541275i
$754$		0			0
$755$	−30.6626	+	21.4614i	−1.11593	+	0.781061i
$756$		0			0
$757$	6.40403	+	9.96487i	0.232758	+	0.362179i	0.937911	−	0.346877i	$-0.112758\pi$
$757$	6.40403	+	9.96487i	0.232758	+	0.362179i	−0.705152	+	0.709056i	$0.749121\pi$
$758$		0			0
$759$	−17.4809	+	1.61690i	−0.634516	+	0.0586897i
$760$		0			0
$761$	23.2504	−	14.9421i	0.842826	−	0.541651i	−0.0465039	−	0.998918i	$-0.514808\pi$
$761$	23.2504	−	14.9421i	0.842826	−	0.541651i	0.889329	+	0.457267i	$0.151172\pi$
$762$		0			0
$763$	7.30608	+	3.33657i	0.264498	+	0.120792i
$764$		0			0
$765$	−6.96342	−	0.722065i	−0.251763	−	0.0261063i
$766$		0			0
$767$	21.0410	−	3.02523i	0.759745	−	0.109235i
$768$		0			0
$769$	−23.6630	+	27.3086i	−0.853310	+	0.984772i	−0.999990	−	0.00441179i	$-0.998596\pi$
$769$	−23.6630	+	27.3086i	−0.853310	+	0.984772i	0.146680	+	0.989184i	$0.453141\pi$
$770$		0			0
$771$	16.6073	+	10.6728i	0.598097	+	0.384373i
$772$		0			0
$773$	−6.34228	+	21.5998i	−0.228116	+	0.776892i	0.763288	+	0.646058i	$0.223584\pi$
$773$	−6.34228	+	21.5998i	−0.228116	+	0.776892i	−0.991404	+	0.130834i	$0.958235\pi$
$774$		0			0
$775$	2.00085	−	5.49074i	0.0718726	−	0.197233i
$776$		0			0
$777$	−0.400168	−	1.36285i	−0.0143560	−	0.0488919i
$778$		0			0
$779$	1.61595	−	11.2391i	0.0578973	−	0.402684i
$780$		0			0
$781$	−28.3078			−1.01293
$782$		0			0
$783$			56.1818i			2.00777i
$784$		0			0
$785$	−2.72501	−	2.17903i	−0.0972597	−	0.0777731i
$786$		0			0
$787$	−6.16475	−	20.9952i	−0.219749	−	0.748398i	−0.993392	−	0.114775i	$-0.963385\pi$
$787$	−6.16475	−	20.9952i	−0.219749	−	0.748398i	0.773642	−	0.633623i	$-0.218433\pi$
$788$		0			0
$789$	2.11207	+	2.43746i	0.0751918	+	0.0867760i
$790$		0			0
$791$	−13.5794	−	3.98728i	−0.482829	−	0.141772i
$792$		0			0
$793$	11.3218	−	17.6171i	0.402050	−	0.625602i
$794$		0			0
$795$	11.9777	−	4.03685i	0.424805	−	0.143172i
$796$		0			0
$797$	−5.26347	+	0.756773i	−0.186442	+	0.0268063i	−0.234903	−	0.972019i	$-0.575477\pi$
$797$	−5.26347	+	0.756773i	−0.186442	+	0.0268063i	0.0484614	+	0.998825i	$0.484568\pi$
$798$		0			0
$799$	2.87997	+	6.30625i	0.101886	+	0.223099i
$800$		0			0
$801$	−0.807450	+	1.76807i	−0.0285298	+	0.0624716i
$802$		0			0
$803$	−15.5026	−	24.1225i	−0.547075	−	0.851266i
$804$		0			0
$805$	5.77791	−	18.8997i	0.203645	−	0.666127i
$806$		0			0
$807$	−1.60267	−	2.49380i	−0.0564165	−	0.0877858i
$808$		0			0
$809$	−3.91336	+	8.56907i	−0.137586	+	0.301272i	−0.965866	−	0.259043i	$-0.916593\pi$
$809$	−3.91336	+	8.56907i	−0.137586	+	0.301272i	0.828279	+	0.560315i	$0.189320\pi$
$810$		0			0
$811$	19.3651	+	42.4037i	0.680001	+	1.48899i	0.862642	+	0.505815i	$0.168808\pi$
$811$	19.3651	+	42.4037i	0.680001	+	1.48899i	−0.182641	+	0.983180i	$0.558465\pi$
$812$		0			0
$813$	32.5053	−	4.67355i	1.14001	−	0.163909i
$814$		0			0
$815$	−10.2847	−	30.5156i	−0.360257	−	1.06892i
$816$		0			0
$817$	0.0798758	−	0.124289i	0.00279450	−	0.00434833i
$818$		0			0
$819$	9.75761	+	2.86509i	0.340958	+	0.100114i
$820$		0			0
$821$	15.7175	+	18.1389i	0.548544	+	0.633053i	0.960543	−	0.278131i	$-0.0897149\pi$
$821$	15.7175	+	18.1389i	0.548544	+	0.633053i	−0.411999	+	0.911184i	$0.635169\pi$
$822$		0			0
$823$	−15.0146	−	51.1349i	−0.523375	−	1.78245i	−0.617135	−	0.786857i	$-0.711707\pi$
$823$	−15.0146	−	51.1349i	−0.523375	−	1.78245i	0.0937603	−	0.995595i	$-0.470111\pi$
$824$		0			0
$825$	6.52549	+	17.1001i	0.227188	+	0.595349i
$826$		0			0
$827$		−	13.4385i		−	0.467301i	−0.972321	−	0.233651i	$-0.924933\pi$
$827$		−	13.4385i		−	0.467301i	0.972321	−	0.233651i	$-0.0750672\pi$
$828$		0			0
$829$	−11.1831			−0.388406			−0.194203	−	0.980961i	$-0.562212\pi$
$829$	−11.1831			−0.388406			−0.194203	+	0.980961i	$0.562212\pi$
$830$		0			0
$831$	−2.84609	+	19.7950i	−0.0987299	+	0.686681i
$832$		0			0
$833$	2.50816	+	8.54200i	0.0869025	+	0.295963i
$834$		0			0
$835$	−17.3458	+	3.19719i	−0.600277	+	0.110643i
$836$		0			0
$837$	−1.84964	+	6.29929i	−0.0639329	+	0.217735i
$838$		0			0
$839$	8.18494	+	5.26014i	0.282576	+	0.181600i	0.674249	−	0.738504i	$-0.264467\pi$
$839$	8.18494	+	5.26014i	0.282576	+	0.181600i	−0.391674	+	0.920104i	$0.628104\pi$
$840$		0			0
$841$	−46.5196	+	53.6864i	−1.60412	+	1.85126i
$842$		0			0
$843$	−17.4381	+	2.50723i	−0.600602	+	0.0863535i
$844$		0			0
$845$	−1.37440	+	13.2544i	−0.0472809	+	0.455966i
$846$		0			0
$847$	5.47588	+	2.50075i	0.188153	+	0.0859268i
$848$		0			0
$849$	11.7425	−	7.54646i	0.403002	−	0.258994i
$850$		0			0
$851$	−1.39679	−	2.43598i	−0.0478814	−	0.0835042i
$852$		0			0
$853$	−6.67245	−	10.3825i	−0.228460	−	0.355491i	0.708031	−	0.706181i	$-0.249584\pi$
$853$	−6.67245	−	10.3825i	−0.228460	−	0.355491i	−0.936492	+	0.350690i	$0.885947\pi$
$854$		0			0
$855$	−5.63700	+	3.94546i	−0.192781	+	0.134932i
$856$		0			0
$857$	21.9401	−	10.0197i	0.749460	−	0.342267i	−0.00379760	−	0.999993i	$-0.501209\pi$
$857$	21.9401	−	10.0197i	0.749460	−	0.342267i	0.753257	+	0.657726i	$0.228482\pi$
$858$		0			0
$859$	−7.73871	−	53.8239i	−0.264041	−	1.83645i	−0.501630	−	0.865082i	$-0.667266\pi$
$859$	−7.73871	−	53.8239i	−0.264041	−	1.83645i	0.237588	−	0.971366i	$-0.423643\pi$
$860$		0			0
$861$	−7.42909	+	8.57363i	−0.253183	+	0.292189i
$862$		0			0
$863$	9.98322	−	15.5342i	0.339833	−	0.528790i	−0.628709	−	0.777641i	$-0.716416\pi$
$863$	9.98322	−	15.5342i	0.339833	−	0.528790i	0.968542	+	0.248850i	$0.0800527\pi$
$864$		0			0
$865$	−24.2658	+	22.7638i	−0.825061	+	0.773994i
$866$		0			0
$867$	−10.8402	+	9.39311i	−0.368154	+	0.319007i
$868$		0			0
$869$	−32.9649	+	9.67937i	−1.11826	+	0.328350i
$870$		0			0
$871$	9.44287	−	65.6766i	0.319959	−	2.22537i
$872$		0			0
$873$			22.4402i			0.759484i
$874$		0			0
$875$	−20.5984	−	0.502181i	−0.696353	−	0.0169768i
$876$		0			0
$877$	−26.8480	−	3.86017i	−0.906594	−	0.130349i	−0.326783	−	0.945099i	$-0.605965\pi$
$877$	−26.8480	−	3.86017i	−0.906594	−	0.130349i	−0.579811	+	0.814751i	$0.696874\pi$
$878$		0			0
$879$	−42.7596	+	12.5553i	−1.44224	+	0.423481i
$880$		0			0
$881$	−8.00953	−	9.24349i	−0.269848	−	0.311421i	0.604611	−	0.796521i	$-0.293329\pi$
$881$	−8.00953	−	9.24349i	−0.269848	−	0.311421i	−0.874459	+	0.485100i	$0.838783\pi$
$882$		0			0
$883$	8.65272	−	29.4685i	0.291187	−	0.991692i	−0.675846	−	0.737043i	$-0.736222\pi$
$883$	8.65272	−	29.4685i	0.291187	−	0.991692i	0.967033	−	0.254650i	$-0.0819602\pi$
$884$		0			0
$885$	12.8252	−	6.48051i	0.431115	−	0.217840i
$886$		0			0
$887$	−37.3985	−	32.4060i	−1.25572	−	1.08809i	−0.992358	−	0.123389i	$-0.960624\pi$
$887$	−37.3985	−	32.4060i	−1.25572	−	1.08809i	−0.263360	−	0.964698i	$-0.584831\pi$
$888$		0			0
$889$	−2.44623	−	17.0139i	−0.0820440	−	0.570629i
$890$		0			0
$891$	−4.14961	−	9.08639i	−0.139017	−	0.304405i
$892$		0			0
$893$	6.19799	+	2.83053i	0.207408	+	0.0947200i
$894$		0			0
$895$	7.98565	−	0.315397i	0.266931	−	0.0105426i
$896$		0			0
$897$	−27.4524	−	1.38936i	−0.916610	−	0.0463895i
$898$		0			0
$899$	−9.83430	+	6.32012i	−0.327992	+	0.210788i
$900$		0			0
$901$	4.40707	−	9.65014i	0.146821	−	0.321493i
$902$		0			0
$903$	−0.134271	+	0.0613196i	−0.00446826	+	0.00204059i
$904$		0			0
$905$	10.6017	−	25.8706i	0.352413	−	0.859969i
$906$		0			0
$907$	25.8229	+	22.3757i	0.857437	+	0.742973i	0.968014	−	0.250894i	$-0.0807247\pi$
$907$	25.8229	+	22.3757i	0.857437	+	0.742973i	−0.110578	+	0.993867i	$0.535270\pi$
$908$		0			0
$909$	−15.0560	−	9.67590i	−0.499376	−	0.320929i
$910$		0			0
$911$	14.3177	+	4.20405i	0.474366	+	0.139287i	0.510172	−	0.860072i	$-0.329582\pi$
$911$	14.3177	+	4.20405i	0.474366	+	0.139287i	−0.0358059	+	0.999359i	$0.511400\pi$
$912$		0			0
$913$	−9.71354	+	8.41683i	−0.321471	+	0.278556i
$914$		0			0
$915$	3.44908	−	13.7294i	0.114023	−	0.453881i
$916$		0			0
$917$	4.71712	+	0.678220i	0.155773	+	0.0223968i
$918$		0			0
$919$	36.1615			1.19286			0.596430	−	0.802665i	$-0.296586\pi$
$919$	36.1615			1.19286			0.596430	+	0.802665i	$0.296586\pi$
$920$		0			0
$921$	25.0588			0.825714
$922$		0			0
$923$	−43.8719	−	6.30783i	−1.44406	−	0.207625i
$924$		0			0
$925$	−2.05442	+	2.08567i	−0.0675488	+	0.0685766i
$926$		0			0
$927$	−11.8539	+	10.2715i	−0.389334	+	0.337360i
$928$		0			0
$929$	−35.4116	−	10.3978i	−1.16182	−	0.341140i	−0.356678	−	0.934227i	$-0.616091\pi$
$929$	−35.4116	−	10.3978i	−1.16182	−	0.341140i	−0.805138	+	0.593088i	$0.797909\pi$
$930$		0			0
$931$	7.36079	+	4.73050i	0.241240	+	0.155036i
$932$		0			0
$933$	−6.27542	−	5.43768i	−0.205448	−	0.178022i
$934$		0			0
$935$	14.2149	+	5.82521i	0.464875	+	0.190505i
$936$		0			0
$937$	−30.0162	+	13.7079i	−0.980586	+	0.447819i	−0.840199	−	0.542278i	$-0.817562\pi$
$937$	−30.0162	+	13.7079i	−0.980586	+	0.447819i	−0.140387	+	0.990097i	$0.544835\pi$
$938$		0			0
$939$	−1.40820	+	3.08353i	−0.0459549	+	0.100627i
$940$		0			0
$941$	−13.0479	+	8.38535i	−0.425348	+	0.273355i	−0.735753	−	0.677250i	$-0.763172\pi$
$941$	−13.0479	+	8.38535i	−0.425348	+	0.273355i	0.310405	+	0.950604i	$0.399535\pi$
$942$		0			0
$943$	−10.3360	+	19.9039i	−0.336587	+	0.648159i
$944$		0			0
$945$	23.1296	−	0.913516i	0.752407	−	0.0297167i
$946$		0			0
$947$	−48.5881	−	22.1894i	−1.57890	−	0.721060i	−0.583082	−	0.812413i	$-0.698153\pi$
$947$	−48.5881	−	22.1894i	−1.57890	−	0.721060i	−0.995819	+	0.0913537i	$0.970881\pi$
$948$		0			0
$949$	−18.6510	−	40.8399i	−0.605436	−	1.32572i
$950$		0			0
$951$	5.93531	+	41.2810i	0.192466	+	1.33863i
$952$		0			0
$953$	7.67355	+	6.64916i	0.248571	+	0.215388i	0.770230	−	0.637766i	$-0.220141\pi$
$953$	7.67355	+	6.64916i	0.248571	+	0.215388i	−0.521660	+	0.853154i	$0.674687\pi$
$954$		0			0
$955$	8.18197	+	16.1925i	0.264762	+	0.523977i
$956$		0			0
$957$	10.3150	−	35.1295i	0.333435	−	1.13558i
$958$		0			0
$959$	17.0227	+	19.6452i	0.549691	+	0.634378i
$960$		0			0
$961$	28.4336	−	8.34884i	0.917211	−	0.269318i
$962$		0			0
$963$	20.5895	+	2.96033i	0.663488	+	0.0953952i
$964$		0			0
$965$	4.29506	−	7.30161i	0.138263	−	0.235047i
$966$		0			0
$967$		−	48.4239i		−	1.55721i	−0.627516	−	0.778604i	$-0.715928\pi$
$967$		−	48.4239i		−	1.55721i	0.627516	−	0.778604i	$-0.284072\pi$
$968$		0			0
$969$	1.12369	−	7.81544i	0.0360982	−	0.251068i
$970$		0			0
$971$	7.46918	−	2.19315i	0.239697	−	0.0703815i	−0.159677	−	0.987169i	$-0.551045\pi$
$971$	7.46918	−	2.19315i	0.239697	−	0.0703815i	0.399375	+	0.916788i	$0.369227\pi$
$972$		0			0
$973$	−12.1385	+	10.5181i	−0.389142	+	0.337193i
$974$		0			0
$975$	6.30289	+	27.9560i	0.201854	+	0.895310i
$976$		0			0
$977$	32.1932	−	50.0935i	1.02995	−	1.60263i	0.258853	−	0.965917i	$-0.416656\pi$
$977$	32.1932	−	50.0935i	1.02995	−	1.60263i	0.771097	−	0.636717i	$-0.219708\pi$
$978$		0			0
$979$	2.79311	−	3.22343i	0.0892683	−	0.103021i
$980$		0			0
$981$	0.786038	+	5.46701i	0.0250962	+	0.174548i
$982$		0			0
$983$	−10.7406	+	4.90507i	−0.342572	+	0.156448i	−0.579270	−	0.815136i	$-0.696662\pi$
$983$	−10.7406	+	4.90507i	−0.342572	+	0.156448i	0.236697	+	0.971583i	$0.423935\pi$
$984$		0			0
$985$	23.3974	+	33.4286i	0.745504	+	1.06512i
$986$		0			0
$987$	−3.68048	−	5.72694i	−0.117151	−	0.182290i
$988$		0			0
$989$	−0.229919	+	0.179709i	−0.00731099	+	0.00571440i
$990$		0			0
$991$	−16.4746	+	10.5876i	−0.523333	+	0.336326i	−0.775489	−	0.631361i	$-0.782497\pi$
$991$	−16.4746	+	10.5876i	−0.523333	+	0.336326i	0.252156	+	0.967687i	$0.418860\pi$
$992$		0			0
$993$	2.52378	+	1.15257i	0.0800896	+	0.0365757i
$994$		0			0
$995$	−0.151150	+	1.45766i	−0.00479179	+	0.0462108i
$996$		0			0
$997$	−30.6798	+	4.41109i	−0.971639	+	0.139701i	−0.609813	−	0.792545i	$-0.708756\pi$
$997$	−30.6798	+	4.41109i	−0.971639	+	0.139701i	−0.361826	+	0.932246i	$0.617846\pi$
$998$		0			0
$999$	2.15378	−	2.48559i	0.0681425	−	0.0786407i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.449.9	yes	120
5.4	even	2	inner	460.2.s.a.449.4	yes	120
23.2	even	11	inner	460.2.s.a.209.4	✓	120
115.94	even	22	inner	460.2.s.a.209.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.209.4	✓	120	23.2	even	11	inner
460.2.s.a.209.9	yes	120	115.94	even	22	inner
460.2.s.a.449.4	yes	120	5.4	even	2	inner
460.2.s.a.449.9	yes	120	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30292 + 0.187332i) q^{3} +(2.16868 + 0.544811i) q^{5} +(-1.39279 + 1.20686i) q^{7} +(-1.21597 - 0.357042i) q^{9} +O(q^{10})\)	\(q+(1.30292 + 0.187332i) q^{3} +(2.16868 + 0.544811i) q^{5} +(-1.39279 + 1.20686i) q^{7} +(-1.21597 - 0.357042i) q^{9} +(2.33946 + 1.50348i) q^{11} +(3.29071 + 2.85142i) q^{13} +(2.72356 + 1.11611i) q^{15} +(2.24721 - 1.02627i) q^{17} +(1.00865 - 2.20863i) q^{19} +(-2.04078 + 1.31153i) q^{21} +(-3.31979 + 3.46107i) q^{23} +(4.40636 + 2.36304i) q^{25} +(-5.10952 - 2.33344i) q^{27} +(-4.15493 - 9.09802i) q^{29} +(-0.166336 - 1.15689i) q^{31} +(2.76648 + 2.39717i) q^{33} +(-3.67803 + 1.85849i) q^{35} +(-0.164958 + 0.561797i) q^{37} +(3.75337 + 4.33162i) q^{39} +(4.48704 - 1.31751i) q^{41} +(0.0602290 + 0.00865962i) q^{43} +(-2.44254 - 1.43679i) q^{45} +2.80626i q^{47} +(-0.512849 + 3.56695i) q^{49} +(3.12019 - 0.916169i) q^{51} +(3.24540 - 2.81215i) q^{53} +(4.25443 + 4.53513i) q^{55} +(1.72794 - 2.68872i) q^{57} +(3.19702 - 3.68956i) q^{59} +(-0.684457 - 4.76050i) q^{61} +(2.12450 - 0.970224i) q^{63} +(5.58302 + 7.97663i) q^{65} +(-8.23855 - 12.8194i) q^{67} +(-4.97378 + 3.88760i) q^{69} +(-8.56338 + 5.50335i) q^{71} +(-9.37936 - 4.28341i) q^{73} +(5.29846 + 3.90431i) q^{75} +(-5.07286 + 0.729368i) q^{77} +(-8.09041 + 9.33683i) q^{79} +(-3.02179 - 1.94198i) q^{81} +(-1.30211 + 4.43458i) q^{83} +(5.43261 - 1.00134i) q^{85} +(-3.70919 - 12.6323i) q^{87} +(0.218274 - 1.51813i) q^{89} -8.02452 q^{91} -1.53849i q^{93} +(3.39073 - 4.24030i) q^{95} +(-4.98862 - 16.9897i) q^{97} +(-2.30791 - 2.66348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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