LMFDB - Embedded newform 552.2.q.c.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(25,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [30,0,3,0,-2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			49.1
Character	$\chi$	$=$	552.49
Dual form			552.2.q.c.169.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.415415 + 0.909632i) q^{3} +(-2.29838 + 2.65247i) q^{5} +(-2.05854 + 1.32294i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(0.516583 - 3.59291i) q^{11} +(-1.06754 - 0.686067i) q^{13} +(-1.45799 - 3.19256i) q^{15} +(-3.04373 - 0.893720i) q^{17} +(5.42582 - 1.59316i) q^{19} +(-0.348244 - 2.42209i) q^{21} +(-2.27256 - 4.22321i) q^{23} +(-1.04148 - 7.24368i) q^{25} +(0.959493 - 0.281733i) q^{27} +(-3.58685 - 1.05319i) q^{29} +(1.20314 + 2.63450i) q^{31} +(3.05363 + 1.96245i) q^{33} +(1.22224 - 8.50086i) q^{35} +(0.367275 + 0.423858i) q^{37} +(1.06754 - 0.686067i) q^{39} +(-6.77685 + 7.82090i) q^{41} +(1.22675 - 2.68620i) q^{43} +3.50972 q^{45} -11.8576 q^{47} +(-0.420491 + 0.920747i) q^{49} +(2.07737 - 2.39741i) q^{51} +(-9.81751 + 6.30933i) q^{53} +(8.34280 + 9.62810i) q^{55} +(-0.804773 + 5.59732i) q^{57} +(9.75532 + 6.26936i) q^{59} +(-2.34534 - 5.13557i) q^{61} +(2.34787 + 0.689398i) q^{63} +(4.27339 - 1.25478i) q^{65} +(-1.66547 - 11.5836i) q^{67} +(4.78562 - 0.312806i) q^{69} +(-0.110048 - 0.765404i) q^{71} +(-13.7538 + 4.03848i) q^{73} +(7.02173 + 2.06177i) q^{75} +(3.68982 + 8.07957i) q^{77} +(-5.98253 - 3.84474i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-2.61290 - 3.01545i) q^{83} +(9.36622 - 6.01931i) q^{85} +(2.44805 - 2.82520i) q^{87} +(3.55432 - 7.78287i) q^{89} +3.10521 q^{91} -2.89622 q^{93} +(-8.24477 + 18.0535i) q^{95} +(-5.63529 + 6.50347i) q^{97} +(-3.05363 + 1.96245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$		0			0
$5$	−2.29838	+	2.65247i	−1.02787	+	1.18622i	−0.0455569	+	0.998962i	$0.514506\pi$
$5$	−2.29838	+	2.65247i	−1.02787	+	1.18622i	−0.982310	+	0.187260i	$0.940039\pi$
$6$		0			0
$7$	−2.05854	+	1.32294i	−0.778056	+	0.500026i	−0.868388	−	0.495886i	$-0.834844\pi$
$7$	−2.05854	+	1.32294i	−0.778056	+	0.500026i	0.0903320	+	0.995912i	$0.471207\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	0.516583	−	3.59291i	0.155756	−	1.08330i	−0.750590	−	0.660768i	$-0.770231\pi$
$11$	0.516583	−	3.59291i	0.155756	−	1.08330i	0.906346	−	0.422536i	$-0.138860\pi$
$12$		0			0
$13$	−1.06754	−	0.686067i	−0.296083	−	0.190281i	0.384162	−	0.923266i	$-0.374490\pi$
$13$	−1.06754	−	0.686067i	−0.296083	−	0.190281i	−0.680245	+	0.732985i	$0.738127\pi$
$14$		0			0
$15$	−1.45799	−	3.19256i	−0.376452	−	0.824315i
$16$		0			0
$17$	−3.04373	−	0.893720i	−0.738213	−	0.216759i	−0.109054	−	0.994036i	$-0.534782\pi$
$17$	−3.04373	−	0.893720i	−0.738213	−	0.216759i	−0.629159	+	0.777277i	$0.716600\pi$
$18$		0			0
$19$	5.42582	−	1.59316i	1.24477	−	0.365497i	0.407963	−	0.912998i	$-0.366239\pi$
$19$	5.42582	−	1.59316i	1.24477	−	0.365497i	0.836805	+	0.547502i	$0.184421\pi$
$20$		0			0
$21$	−0.348244	−	2.42209i	−0.0759930	−	0.528543i
$22$		0			0
$23$	−2.27256	−	4.22321i	−0.473861	−	0.880600i
$23$	−2.27256	−	4.22321i	−0.473861	−	0.880600i
$24$		0			0
$25$	−1.04148	−	7.24368i	−0.208297	−	1.44874i
$26$		0			0
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$		0			0
$29$	−3.58685	−	1.05319i	−0.666061	−	0.195573i	−0.0688125	−	0.997630i	$-0.521921\pi$
$29$	−3.58685	−	1.05319i	−0.666061	−	0.195573i	−0.597248	+	0.802057i	$0.703739\pi$
$30$		0			0
$31$	1.20314	+	2.63450i	0.216089	+	0.473170i	0.986372	−	0.164533i	$-0.0526118\pi$
$31$	1.20314	+	2.63450i	0.216089	+	0.473170i	−0.770282	+	0.637703i	$0.779885\pi$
$32$		0			0
$33$	3.05363	+	1.96245i	0.531569	+	0.341619i
$34$		0			0
$35$	1.22224	−	8.50086i	0.206596	−	1.43691i
$36$		0			0
$37$	0.367275	+	0.423858i	0.0603797	+	0.0696818i	0.785136	−	0.619324i	$-0.212593\pi$
$37$	0.367275	+	0.423858i	0.0603797	+	0.0696818i	−0.724756	+	0.689005i	$0.758048\pi$
$38$		0			0
$39$	1.06754	−	0.686067i	0.170943	−	0.109859i
$40$		0			0
$41$	−6.77685	+	7.82090i	−1.05837	+	1.22142i	−0.0839966	+	0.996466i	$0.526768\pi$
$41$	−6.77685	+	7.82090i	−1.05837	+	1.22142i	−0.974369	+	0.224954i	$0.927777\pi$
$42$		0			0
$43$	1.22675	−	2.68620i	0.187077	−	0.409642i	−0.792734	−	0.609568i	$-0.791343\pi$
$43$	1.22675	−	2.68620i	0.187077	−	0.409642i	0.979811	+	0.199926i	$0.0640703\pi$
$44$		0			0
$45$	3.50972			0.523199
$46$		0			0
$47$	−11.8576			−1.72961			−0.864804	−	0.502110i	$-0.832557\pi$
$47$	−11.8576			−1.72961			−0.864804	+	0.502110i	$0.832557\pi$
$48$		0			0
$49$	−0.420491	+	0.920747i	−0.0600702	+	0.131535i
$50$		0			0
$51$	2.07737	−	2.39741i	0.290890	−	0.335705i
$52$		0			0
$53$	−9.81751	+	6.30933i	−1.34854	+	0.866653i	−0.997566	−	0.0697323i	$-0.977785\pi$
$53$	−9.81751	+	6.30933i	−1.34854	+	0.866653i	−0.350973	+	0.936386i	$0.614149\pi$
$54$		0			0
$55$	8.34280	+	9.62810i	1.12494	+	1.29825i
$56$		0			0
$57$	−0.804773	+	5.59732i	−0.106595	+	0.741383i
$58$		0			0
$59$	9.75532	+	6.26936i	1.27003	+	0.816201i	0.989624	−	0.143679i	$-0.0458932\pi$
$59$	9.75532	+	6.26936i	1.27003	+	0.816201i	0.280410	+	0.959880i	$0.409530\pi$
$60$		0			0
$61$	−2.34534	−	5.13557i	−0.300289	−	0.657542i	0.697994	−	0.716103i	$-0.254076\pi$
$61$	−2.34534	−	5.13557i	−0.300289	−	0.657542i	−0.998284	+	0.0585611i	$0.981349\pi$
$62$		0			0
$63$	2.34787	+	0.689398i	0.295804	+	0.0868560i
$64$		0			0
$65$	4.27339	−	1.25478i	0.530049	−	0.155636i
$66$		0			0
$67$	−1.66547	−	11.5836i	−0.203469	−	1.41516i	−0.793890	−	0.608062i	$-0.791947\pi$
$67$	−1.66547	−	11.5836i	−0.203469	−	1.41516i	0.590421	−	0.807096i	$-0.298962\pi$
$68$		0			0
$69$	4.78562	−	0.312806i	0.576121	−	0.0376575i
$70$		0			0
$71$	−0.110048	−	0.765404i	−0.0130603	−	0.0908367i	0.982249	−	0.187583i	$-0.0600654\pi$
$71$	−0.110048	−	0.765404i	−0.0130603	−	0.0908367i	−0.995309	+	0.0967466i	$0.969156\pi$
$72$		0			0
$73$	−13.7538	+	4.03848i	−1.60976	+	0.472668i	−0.958240	−	0.285964i	$-0.907686\pi$
$73$	−13.7538	+	4.03848i	−1.60976	+	0.472668i	−0.651519	+	0.758632i	$0.725868\pi$
$74$		0			0
$75$	7.02173	+	2.06177i	0.810800	+	0.238072i
$76$		0			0
$77$	3.68982	+	8.07957i	0.420494	+	0.920753i
$78$		0			0
$79$	−5.98253	−	3.84474i	−0.673087	−	0.432567i	0.158950	−	0.987287i	$-0.449189\pi$
$79$	−5.98253	−	3.84474i	−0.673087	−	0.432567i	−0.832037	+	0.554720i	$0.812825\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	−2.61290	−	3.01545i	−0.286804	−	0.330989i	0.594005	−	0.804461i	$-0.297546\pi$
$83$	−2.61290	−	3.01545i	−0.286804	−	0.330989i	−0.880809	+	0.473472i	$0.843000\pi$
$84$		0			0
$85$	9.36622	−	6.01931i	1.01591	−	0.652885i
$86$		0			0
$87$	2.44805	−	2.82520i	0.262458	−	0.302893i
$88$		0			0
$89$	3.55432	−	7.78287i	0.376757	−	0.824983i	−0.622350	−	0.782739i	$-0.713822\pi$
$89$	3.55432	−	7.78287i	0.376757	−	0.824983i	0.999107	−	0.0422438i	$-0.0134506\pi$
$90$		0			0
$91$	3.10521			0.325514
$92$		0			0
$93$	−2.89622			−0.300325
$94$		0			0
$95$	−8.24477	+	18.0535i	−0.845896	+	1.85225i
$96$		0			0
$97$	−5.63529	+	6.50347i	−0.572177	+	0.660328i	−0.965904	−	0.258900i	$-0.916640\pi$
$97$	−5.63529	+	6.50347i	−0.572177	+	0.660328i	0.393727	+	0.919227i	$0.371186\pi$
$98$		0			0
$99$	−3.05363	+	1.96245i	−0.306902	+	0.197234i
$100$		0			0
$101$	7.01701	+	8.09806i	0.698219	+	0.805787i	0.988511	−	0.151151i	$-0.0482979\pi$
$101$	7.01701	+	8.09806i	0.698219	+	0.805787i	−0.290292	+	0.956938i	$0.593752\pi$
$102$		0			0
$103$	−0.132448	+	0.921197i	−0.0130505	+	0.0907683i	−0.995306	−	0.0967810i	$-0.969145\pi$
$103$	−0.132448	+	0.921197i	−0.0130505	+	0.0907683i	0.982255	+	0.187549i	$0.0600544\pi$
$104$		0			0
$105$	7.22492	+	4.64317i	0.705080	+	0.453127i
$106$		0			0
$107$	−2.32137	−	5.08310i	−0.224415	−	0.491401i	0.763613	−	0.645674i	$-0.223424\pi$
$107$	−2.32137	−	5.08310i	−0.224415	−	0.491401i	−0.988028	+	0.154273i	$0.950696\pi$
$108$		0			0
$109$	15.2551	+	4.47929i	1.46117	+	0.429039i	0.913218	−	0.407470i	$-0.133589\pi$
$109$	15.2551	+	4.47929i	1.46117	+	0.429039i	0.547953	+	0.836509i	$0.315407\pi$
$110$		0			0
$111$	−0.538127	+	0.158008i	−0.0510767	+	0.0149975i
$112$		0			0
$113$	−0.809546	−	5.63052i	−0.0761557	−	0.529674i	−0.991811	−	0.127711i	$-0.959237\pi$
$113$	−0.809546	−	5.63052i	−0.0761557	−	0.529674i	0.915656	−	0.401963i	$-0.131672\pi$
$114$		0			0
$115$	16.4251	+	3.67865i	1.53165	+	0.343035i
$116$		0			0
$117$	0.180596	+	1.25607i	0.0166961	+	0.116124i
$118$		0			0
$119$	7.44799	−	2.18693i	0.682756	−	0.200475i
$120$		0			0
$121$	−2.08774	−	0.613016i	−0.189795	−	0.0557287i
$122$		0			0
$123$	−4.29894	−	9.41336i	−0.387622	−	0.848774i
$124$		0			0
$125$	6.84455	+	4.39873i	0.612195	+	0.393434i
$126$		0			0
$127$	−1.39870	+	9.72815i	−0.124114	+	0.863234i	0.828703	+	0.559689i	$0.189079\pi$
$127$	−1.39870	+	9.72815i	−0.124114	+	0.863234i	−0.952817	+	0.303545i	$0.901830\pi$
$128$		0			0
$129$	1.93384	+	2.23178i	0.170265	+	0.196497i
$130$		0			0
$131$	−14.7823	+	9.50001i	−1.29154	+	0.830019i	−0.992264	−	0.124149i	$-0.960380\pi$
$131$	−14.7823	+	9.50001i	−1.29154	+	0.830019i	−0.299272	+	0.954168i	$0.596744\pi$
$132$		0			0
$133$	−9.06161	+	10.4577i	−0.785741	+	0.906793i
$134$		0			0
$135$	−1.45799	+	3.19256i	−0.125484	+	0.274772i
$136$		0			0
$137$	−3.59670			−0.307287			−0.153643	−	0.988126i	$-0.549101\pi$
$137$	−3.59670			−0.307287			−0.153643	+	0.988126i	$0.549101\pi$
$138$		0			0
$139$	−4.59723			−0.389932			−0.194966	−	0.980810i	$-0.562460\pi$
$139$	−4.59723			−0.389932			−0.194966	+	0.980810i	$0.562460\pi$
$140$		0			0
$141$	4.92582	−	10.7860i	0.414829	−	0.908349i
$142$		0			0
$143$	−3.01645	+	3.48117i	−0.252248	+	0.291110i
$144$		0			0
$145$	11.0375	−	7.09337i	0.916615	−	0.589073i
$146$		0			0
$147$	−0.662863	−	0.764984i	−0.0546720	−	0.0630949i
$148$		0			0
$149$	−1.15315	+	8.02034i	−0.0944697	+	0.657051i	0.886477	+	0.462773i	$0.153146\pi$
$149$	−1.15315	+	8.02034i	−0.0944697	+	0.657051i	−0.980946	+	0.194278i	$0.937764\pi$
$150$		0			0
$151$	7.47081	+	4.80120i	0.607966	+	0.390716i	0.808094	−	0.589054i	$-0.200499\pi$
$151$	7.47081	+	4.80120i	0.607966	+	0.390716i	−0.200128	+	0.979770i	$0.564136\pi$
$152$		0			0
$153$	1.31779	+	2.88556i	0.106537	+	0.233284i
$154$		0			0
$155$	−9.75320	−	2.86380i	−0.783396	−	0.230026i
$156$		0			0
$157$	21.0092	−	6.16886i	1.67672	−	0.492329i	0.701332	−	0.712835i	$-0.252589\pi$
$157$	21.0092	−	6.16886i	1.67672	−	0.492329i	0.975386	+	0.220506i	$0.0707708\pi$
$158$		0			0
$159$	−1.66083	−	11.5513i	−0.131712	−	0.916079i
$160$		0			0
$161$	10.2652	+	5.68719i	0.809013	+	0.448213i
$162$		0			0
$163$	1.60254	+	11.1459i	0.125520	+	0.873014i	0.951134	+	0.308778i	$0.0999200\pi$
$163$	1.60254	+	11.1459i	0.125520	+	0.873014i	−0.825614	+	0.564236i	$0.809171\pi$
$164$		0			0
$165$	−12.2238	+	3.58922i	−0.951618	+	0.279420i
$166$		0			0
$167$	10.8435	+	3.18393i	0.839092	+	0.246380i	0.672918	−	0.739717i	$-0.265041\pi$
$167$	10.8435	+	3.18393i	0.839092	+	0.246380i	0.166174	+	0.986096i	$0.446859\pi$
$168$		0			0
$169$	−4.73144	−	10.3604i	−0.363957	−	0.796954i
$170$		0			0
$171$	−4.75719	−	3.05726i	−0.363791	−	0.233794i
$172$		0			0
$173$	3.01076	−	20.9403i	0.228904	−	1.59206i	−0.473836	−	0.880613i	$-0.657131\pi$
$173$	3.01076	−	20.9403i	0.228904	−	1.59206i	0.702740	−	0.711447i	$-0.251960\pi$
$174$		0			0
$175$	11.7269	+	13.5336i	0.886473	+	1.02304i
$176$		0			0
$177$	−9.75532	+	6.26936i	−0.733255	+	0.471234i
$178$		0			0
$179$	6.66146	−	7.68773i	0.497901	−	0.574608i	−0.450059	−	0.892999i	$-0.648597\pi$
$179$	6.66146	−	7.68773i	0.497901	−	0.574608i	0.947960	+	0.318391i	$0.103142\pi$
$180$		0			0
$181$	−4.42318	+	9.68542i	−0.328772	+	0.719911i	−0.999768	−	0.0215503i	$-0.993140\pi$
$181$	−4.42318	+	9.68542i	−0.328772	+	0.719911i	0.670995	+	0.741462i	$0.265867\pi$
$182$		0			0
$183$	5.64576			0.417347
$184$		0			0
$185$	−1.96841			−0.144720
$186$		0			0
$187$	−4.78340	+	10.4742i	−0.349797	+	0.765948i
$188$		0			0
$189$	−1.60244	+	1.84931i	−0.116560	+	0.134518i
$190$		0			0
$191$	−8.60852	+	5.53236i	−0.622890	+	0.400307i	−0.813671	−	0.581325i	$-0.802534\pi$
$191$	−8.60852	+	5.53236i	−0.622890	+	0.400307i	0.190781	+	0.981633i	$0.438898\pi$
$192$		0			0
$193$	6.64157	+	7.66478i	0.478071	+	0.551723i	0.942639	−	0.333814i	$-0.108336\pi$
$193$	6.64157	+	7.66478i	0.478071	+	0.551723i	−0.464568	+	0.885537i	$0.653790\pi$
$194$		0			0
$195$	−0.633842	+	4.40847i	−0.0453903	+	0.315697i
$196$		0			0
$197$	−17.7533	−	11.4093i	−1.26487	−	0.812881i	−0.275925	−	0.961179i	$-0.588984\pi$
$197$	−17.7533	−	11.4093i	−1.26487	−	0.812881i	−0.988943	+	0.148298i	$0.952620\pi$
$198$		0			0
$199$	2.47795	+	5.42595i	0.175657	+	0.384635i	0.976898	−	0.213707i	$-0.0685537\pi$
$199$	2.47795	+	5.42595i	0.175657	+	0.384635i	−0.801241	+	0.598342i	$0.795826\pi$
$200$		0			0
$201$	11.2286	+	3.29703i	0.792007	+	0.232554i
$202$		0			0
$203$	8.77699	−	2.57716i	0.616024	−	0.180881i
$204$		0			0
$205$	−5.16895	−	35.9508i	−0.361015	−	2.51091i
$206$		0			0
$207$	−1.70348	+	4.48310i	−0.118400	+	0.311597i
$208$		0			0
$209$	−2.92121	−	20.3175i	−0.202065	−	1.40539i
$210$		0			0
$211$	−18.4390	+	5.41417i	−1.26939	+	0.372727i	−0.845982	−	0.533212i	$-0.820985\pi$
$211$	−18.4390	+	5.41417i	−1.26939	+	0.372727i	−0.423409	+	0.905939i	$0.639167\pi$
$212$		0			0
$213$	0.741951	+	0.217857i	0.0508377	+	0.0149273i
$214$		0			0
$215$	4.30554	+	9.42782i	0.293635	+	0.642972i
$216$		0			0
$217$	−5.96200	−	3.83155i	−0.404727	−	0.260102i
$218$		0			0
$219$	2.04000	−	14.1885i	0.137851	−	0.958772i
$220$		0			0
$221$	2.63616	+	3.04229i	0.177327	+	0.204646i
$222$		0			0
$223$	0.265575	−	0.170675i	0.0177842	−	0.0114292i	−0.531718	−	0.846921i	$-0.678454\pi$
$223$	0.265575	−	0.170675i	0.0177842	−	0.0114292i	0.549503	+	0.835492i	$0.314817\pi$
$224$		0			0
$225$	−4.79238	+	5.53070i	−0.319492	+	0.368714i
$226$		0			0
$227$	11.1097	−	24.3269i	0.737377	−	1.61463i	−0.0504439	−	0.998727i	$-0.516064\pi$
$227$	11.1097	−	24.3269i	0.737377	−	1.61463i	0.787821	−	0.615904i	$-0.211209\pi$
$228$		0			0
$229$	−25.3339			−1.67411			−0.837057	−	0.547116i	$-0.815726\pi$
$229$	−25.3339			−1.67411			−0.837057	+	0.547116i	$0.815726\pi$
$230$		0			0
$231$	−8.88224			−0.584409
$232$		0			0
$233$	−9.93226	+	21.7486i	−0.650684	+	1.42480i	0.240270	+	0.970706i	$0.422764\pi$
$233$	−9.93226	+	21.7486i	−0.650684	+	1.42480i	−0.890954	+	0.454093i	$0.849963\pi$
$234$		0			0
$235$	27.2533	−	31.4519i	1.77781	−	2.05170i
$236$		0			0
$237$	5.98253	−	3.84474i	0.388607	−	0.249743i
$238$		0			0
$239$	−0.935153	−	1.07922i	−0.0604900	−	0.0698092i	0.724698	−	0.689067i	$-0.241979\pi$
$239$	−0.935153	−	1.07922i	−0.0604900	−	0.0698092i	−0.785188	+	0.619257i	$0.787434\pi$
$240$		0			0
$241$	−0.0338900	+	0.235710i	−0.00218305	+	0.0151834i	−0.990884	−	0.134719i	$-0.956987\pi$
$241$	−0.0338900	+	0.235710i	−0.00218305	+	0.0151834i	0.988701	+	0.149902i	$0.0478959\pi$
$242$		0			0
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$		0			0
$245$	−1.47581	−	3.23157i	−0.0942859	−	0.206457i
$246$		0			0
$247$	−6.88530	−	2.02171i	−0.438101	−	0.128638i
$248$		0			0
$249$	3.82839	−	1.12412i	0.242615	−	0.0712381i
$250$		0			0
$251$	2.88789	+	20.0857i	0.182282	+	1.26780i	0.851350	+	0.524598i	$0.175784\pi$
$251$	2.88789	+	20.0857i	0.182282	+	1.26780i	−0.669068	+	0.743201i	$0.733306\pi$
$252$		0			0
$253$	−16.3476	+	5.98346i	−1.02776	+	0.376177i
$254$		0			0
$255$	1.58448	+	11.0203i	0.0992242	+	0.690120i
$256$		0			0
$257$	15.9917	−	4.69557i	0.997532	−	0.292902i	0.258089	−	0.966121i	$-0.416907\pi$
$257$	15.9917	−	4.69557i	0.997532	−	0.292902i	0.739443	+	0.673219i	$0.235089\pi$
$258$		0			0
$259$	−1.31679	−	0.386645i	−0.0818215	−	0.0240250i
$260$		0			0
$261$	1.55293	+	3.40045i	0.0961242	+	0.210483i
$262$		0			0
$263$	−14.2732	−	9.17281i	−0.880122	−	0.565620i	0.0207113	−	0.999785i	$-0.493407\pi$
$263$	−14.2732	−	9.17281i	−0.880122	−	0.565620i	−0.900833	+	0.434166i	$0.857043\pi$
$264$		0			0
$265$	5.82905	−	40.5419i	0.358076	−	2.49047i
$266$		0			0
$267$	5.60303	+	6.46624i	0.342900	+	0.395728i
$268$		0			0
$269$	3.58110	−	2.30144i	0.218344	−	0.140321i	−0.426897	−	0.904300i	$-0.640393\pi$
$269$	3.58110	−	2.30144i	0.218344	−	0.140321i	0.645241	+	0.763979i	$0.276757\pi$
$270$		0			0
$271$	−3.90435	+	4.50586i	−0.237172	+	0.273712i	−0.861841	−	0.507178i	$-0.830689\pi$
$271$	−3.90435	+	4.50586i	−0.237172	+	0.273712i	0.624669	+	0.780890i	$0.285234\pi$
$272$		0			0
$273$	−1.28995	+	2.82460i	−0.0780713	+	0.170952i
$274$		0			0
$275$	−26.5639			−1.60186
$276$		0			0
$277$	19.8240			1.19111			0.595553	−	0.803316i	$-0.296933\pi$
$277$	19.8240			1.19111			0.595553	+	0.803316i	$0.296933\pi$
$278$		0			0
$279$	1.20314	−	2.63450i	0.0720298	−	0.157723i
$280$		0			0
$281$	7.56805	−	8.73400i	0.451472	−	0.521027i	−0.483693	−	0.875237i	$-0.660705\pi$
$281$	7.56805	−	8.73400i	0.451472	−	0.521027i	0.935166	+	0.354211i	$0.115251\pi$
$282$		0			0
$283$	−23.2358	+	14.9327i	−1.38122	+	0.887659i	−0.999332	−	0.0365476i	$-0.988364\pi$
$283$	−23.2358	+	14.9327i	−1.38122	+	0.887659i	−0.381893	+	0.924207i	$0.624728\pi$
$284$		0			0
$285$	−12.9971	−	14.9994i	−0.769880	−	0.888489i
$286$		0			0
$287$	3.60381	−	25.0651i	0.212726	−	1.47954i
$288$		0			0
$289$	−5.83575	−	3.75041i	−0.343279	−	0.220612i
$290$		0			0
$291$	−3.57478	−	7.82768i	−0.209557	−	0.458867i
$292$		0			0
$293$	17.6302	+	5.17670i	1.02997	+	0.302426i	0.752698	−	0.658366i	$-0.228752\pi$
$293$	17.6302	+	5.17670i	1.02997	+	0.302426i	0.277270	+	0.960792i	$0.410570\pi$
$294$		0			0
$295$	−39.0508	+	11.4663i	−2.27362	+	0.667596i
$296$		0			0
$297$	−0.516583	−	3.59291i	−0.0299752	−	0.208482i
$298$		0			0
$299$	−0.471356	+	6.06757i	−0.0272592	+	0.350897i
$300$		0			0
$301$	1.02838	+	7.15257i	0.0592751	+	0.412267i
$302$		0			0
$303$	−10.2812	+	3.01884i	−0.590641	+	0.173428i
$304$		0			0
$305$	19.0124	+	5.58255i	1.08865	+	0.319656i
$306$		0			0
$307$	4.63405	+	10.1472i	0.264479	+	0.579129i	0.994552	−	0.104240i	$-0.0332411\pi$
$307$	4.63405	+	10.1472i	0.264479	+	0.579129i	−0.730073	+	0.683369i	$0.760514\pi$
$308$		0			0
$309$	−0.782930	−	0.503158i	−0.0445393	−	0.0286237i
$310$		0			0
$311$	3.08650	−	21.4671i	0.175019	−	1.21729i	−0.693067	−	0.720873i	$-0.743741\pi$
$311$	3.08650	−	21.4671i	0.175019	−	1.21729i	0.868086	−	0.496413i	$-0.165350\pi$
$312$		0			0
$313$	−11.4658	−	13.2322i	−0.648083	−	0.747927i	0.332699	−	0.943033i	$-0.392041\pi$
$313$	−11.4658	−	13.2322i	−0.648083	−	0.747927i	−0.980782	+	0.195105i	$0.937495\pi$
$314$		0			0
$315$	−7.22492	+	4.64317i	−0.407078	+	0.261613i
$316$		0			0
$317$	−18.5905	+	21.4546i	−1.04415	+	1.20501i	−0.0658429	+	0.997830i	$0.520974\pi$
$317$	−18.5905	+	21.4546i	−1.04415	+	1.20501i	−0.978303	+	0.207179i	$0.933572\pi$
$318$		0			0
$319$	−5.63693	+	12.3432i	−0.315608	+	0.691085i
$320$		0			0
$321$	5.58808			0.311896
$322$		0			0
$323$	−17.9386			−0.998129
$324$		0			0
$325$	−3.85782	+	8.44745i	−0.213993	+	0.468580i
$326$		0			0
$327$	−10.4117	+	12.0157i	−0.575768	+	0.664472i
$328$		0			0
$329$	24.4094	−	15.6869i	1.34573	−	0.864849i
$330$		0			0
$331$	−17.9331	−	20.6959i	−0.985691	−	1.13755i	−0.990493	−	0.137560i	$-0.956074\pi$
$331$	−17.9331	−	20.6959i	−0.985691	−	1.13755i	0.00480243	−	0.999988i	$-0.498471\pi$
$332$		0			0
$333$	0.0798165	−	0.555136i	0.00437392	−	0.0304213i
$334$		0			0
$335$	34.5530	+	22.2058i	1.88783	+	1.21324i
$336$		0			0
$337$	4.56933	+	10.0054i	0.248907	+	0.545031i	0.992305	−	0.123819i	$-0.0395141\pi$
$337$	4.56933	+	10.0054i	0.248907	+	0.545031i	−0.743397	+	0.668850i	$0.766787\pi$
$338$		0			0
$339$	5.45800	+	1.60261i	0.296438	+	0.0870419i
$340$		0			0
$341$	10.0870	−	2.96182i	0.546244	−	0.160392i
$342$		0			0
$343$	−2.79020	−	19.4063i	−0.150657	−	1.04784i
$344$		0			0
$345$	−10.1695	+	13.4127i	−0.547506	+	0.722114i
$346$		0			0
$347$	0.678050	+	4.71594i	0.0363996	+	0.253165i	0.999894	−	0.0145639i	$-0.00463598\pi$
$347$	0.678050	+	4.71594i	0.0363996	+	0.253165i	−0.963494	+	0.267729i	$0.913727\pi$
$348$		0			0
$349$	−7.96416	+	2.33849i	−0.426312	+	0.125176i	−0.487848	−	0.872928i	$-0.662218\pi$
$349$	−7.96416	+	2.33849i	−0.426312	+	0.125176i	0.0615367	+	0.998105i	$0.480400\pi$
$350$		0			0
$351$	−1.21759	−	0.357515i	−0.0649899	−	0.0190828i
$352$		0			0
$353$	13.4551	+	29.4626i	0.716145	+	1.56814i	0.819229	+	0.573466i	$0.194402\pi$
$353$	13.4551	+	29.4626i	0.716145	+	1.56814i	−0.103085	+	0.994673i	$0.532871\pi$
$354$		0			0
$355$	2.28315	+	1.46729i	0.121177	+	0.0778756i
$356$		0			0
$357$	−1.10471	+	7.68341i	−0.0584674	+	0.406649i
$358$		0			0
$359$	−4.96350	−	5.72818i	−0.261963	−	0.302322i	0.609496	−	0.792789i	$-0.291372\pi$
$359$	−4.96350	−	5.72818i	−0.261963	−	0.302322i	−0.871460	+	0.490467i	$0.836826\pi$
$360$		0			0
$361$	10.9175	−	7.01625i	0.574605	−	0.369277i
$362$		0			0
$363$	1.42490	−	1.64442i	0.0747878	−	0.0863097i
$364$		0			0
$365$	20.8995	−	45.7635i	1.09393	−	2.39537i
$366$		0			0
$367$	−31.6972			−1.65458			−0.827291	−	0.561774i	$-0.810119\pi$
$367$	−31.6972			−1.65458			−0.827291	+	0.561774i	$0.810119\pi$
$368$		0			0
$369$	10.3485			0.538723
$370$		0			0
$371$	11.8629	−	25.9761i	0.615889	−	1.34861i
$372$		0			0
$373$	−9.46556	+	10.9238i	−0.490108	+	0.565615i	−0.945895	−	0.324474i	$-0.894813\pi$
$373$	−9.46556	+	10.9238i	−0.490108	+	0.565615i	0.455786	+	0.890089i	$0.349358\pi$
$374$		0			0
$375$	−6.84455	+	4.39873i	−0.353451	+	0.227149i
$376$		0			0
$377$	3.10654	+	3.58514i	0.159995	+	0.184644i
$378$		0			0
$379$	1.19331	−	8.29968i	0.0612964	−	0.426326i	−0.935948	−	0.352138i	$-0.885455\pi$
$379$	1.19331	−	8.29968i	0.0612964	−	0.426326i	0.997244	−	0.0741874i	$-0.0236363\pi$
$380$		0			0
$381$	−8.26800	−	5.31352i	−0.423582	−	0.272220i
$382$		0			0
$383$	8.09331	+	17.7219i	0.413549	+	0.905546i	0.995715	+	0.0924757i	$0.0294781\pi$
$383$	8.09331	+	17.7219i	0.413549	+	0.905546i	−0.582166	+	0.813070i	$0.697795\pi$
$384$		0			0
$385$	−29.9115	−	8.78280i	−1.52443	−	0.447613i
$386$		0			0
$387$	−2.83344	+	0.831974i	−0.144032	+	0.0422916i
$388$		0			0
$389$	3.08550	+	21.4601i	0.156441	+	1.08807i	0.905125	+	0.425145i	$0.139777\pi$
$389$	3.08550	+	21.4601i	0.156441	+	1.08807i	−0.748684	+	0.662927i	$0.769314\pi$
$390$		0			0
$391$	3.14269	+	14.8853i	0.158932	+	0.752784i
$392$		0			0
$393$	−2.50072	−	17.3929i	−0.126145	−	0.877355i
$394$		0			0
$395$	23.9482	−	7.03182i	1.20496	−	0.353809i
$396$		0			0
$397$	21.5975	+	6.34161i	1.08395	+	0.318276i	0.774457	−	0.632626i	$-0.218023\pi$
$397$	21.5975	+	6.34161i	1.08395	+	0.318276i	0.309492	+	0.950902i	$0.399841\pi$
$398$		0			0
$399$	−5.74829	−	12.5870i	−0.287774	−	0.630138i
$400$		0			0
$401$	−10.8294	−	6.95964i	−0.540795	−	0.347548i	0.241555	−	0.970387i	$-0.422343\pi$
$401$	−10.8294	−	6.95964i	−0.540795	−	0.347548i	−0.782350	+	0.622839i	$0.785979\pi$
$402$		0			0
$403$	0.523046	−	3.63787i	0.0260548	−	0.181215i
$404$		0			0
$405$	−2.29838	−	2.65247i	−0.114207	−	0.131802i
$406$		0			0
$407$	1.71261	−	1.10063i	0.0848911	−	0.0545562i
$408$		0			0
$409$	22.7662	−	26.2736i	1.12572	−	1.29915i	0.176578	−	0.984287i	$-0.443497\pi$
$409$	22.7662	−	26.2736i	1.12572	−	1.29915i	0.949138	−	0.314859i	$-0.101957\pi$
$410$		0			0
$411$	1.49412	−	3.27167i	0.0736997	−	0.161380i
$412$		0			0
$413$	−28.3758			−1.39628
$414$		0			0
$415$	14.0039			0.687422
$416$		0			0
$417$	1.90976	−	4.18179i	0.0935213	−	0.204783i
$418$		0			0
$419$	17.6919	−	20.4176i	0.864307	−	0.997463i	−0.135671	−	0.990754i	$-0.543319\pi$
$419$	17.6919	−	20.4176i	0.864307	−	0.997463i	0.999977	−	0.00670920i	$-0.00213562\pi$
$420$		0			0
$421$	12.9955	−	8.35171i	0.633363	−	0.407037i	−0.184191	−	0.982891i	$-0.558966\pi$
$421$	12.9955	−	8.35171i	0.633363	−	0.407037i	0.817553	+	0.575853i	$0.195330\pi$
$422$		0			0
$423$	7.76507	+	8.96137i	0.377551	+	0.435717i
$424$		0			0
$425$	−3.30383	+	22.9786i	−0.160259	+	1.11463i
$426$		0			0
$427$	11.6220	+	7.46904i	0.562430	+	0.361452i
$428$		0			0
$429$	−1.91350	−	4.18999i	−0.0923849	−	0.202295i
$430$		0			0
$431$	−3.11328	−	0.914140i	−0.149961	−	0.0440326i	0.205890	−	0.978575i	$-0.433991\pi$
$431$	−3.11328	−	0.914140i	−0.149961	−	0.0440326i	−0.355852	+	0.934542i	$0.615809\pi$
$432$		0			0
$433$	−13.4286	+	3.94300i	−0.645339	+	0.189489i	−0.587993	−	0.808866i	$-0.700082\pi$
$433$	−13.4286	+	3.94300i	−0.645339	+	0.189489i	−0.0573457	+	0.998354i	$0.518264\pi$
$434$		0			0
$435$	1.86721	+	12.9868i	0.0895261	+	0.622668i
$436$		0			0
$437$	−19.0587	−	19.2938i	−0.911703	−	0.922948i
$438$		0			0
$439$	−2.79383	−	19.4315i	−0.133342	−	0.927414i	−0.941155	−	0.337975i	$-0.890258\pi$
$439$	−2.79383	−	19.4315i	−0.133342	−	0.927414i	0.807813	−	0.589439i	$-0.200651\pi$
$440$		0			0
$441$	0.971218	−	0.285175i	0.0462485	−	0.0135798i
$442$		0			0
$443$	24.3705	+	7.15583i	1.15788	+	0.339984i	0.803608	−	0.595159i	$-0.202911\pi$
$443$	24.3705	+	7.15583i	1.15788	+	0.339984i	0.354271	+	0.935143i	$0.384729\pi$
$444$		0			0
$445$	12.4747	+	27.3157i	0.591356	+	1.29489i
$446$		0			0
$447$	−6.81652	−	4.38071i	−0.322410	−	0.207200i
$448$		0			0
$449$	−1.49936	+	10.4283i	−0.0707591	+	0.492140i	0.923368	+	0.383917i	$0.125425\pi$
$449$	−1.49936	+	10.4283i	−0.0707591	+	0.492140i	−0.994127	+	0.108223i	$0.965484\pi$
$450$		0			0
$451$	24.5990	+	28.3888i	1.15832	+	1.33678i
$452$		0			0
$453$	−7.47081	+	4.80120i	−0.351009	+	0.225580i
$454$		0			0
$455$	−7.13695	+	8.23648i	−0.334585	+	0.386132i
$456$		0			0
$457$	−12.5634	+	27.5100i	−0.587691	+	1.28686i	0.349136	+	0.937072i	$0.386475\pi$
$457$	−12.5634	+	27.5100i	−0.587691	+	1.28686i	−0.936827	+	0.349792i	$0.886252\pi$
$458$		0			0
$459$	−3.17223			−0.148067
$460$		0			0
$461$	−20.0214			−0.932491			−0.466245	−	0.884655i	$-0.654394\pi$
$461$	−20.0214			−0.932491			−0.466245	+	0.884655i	$0.654394\pi$
$462$		0			0
$463$	4.12893	−	9.04111i	0.191888	−	0.420176i	−0.789095	−	0.614272i	$-0.789450\pi$
$463$	4.12893	−	9.04111i	0.191888	−	0.420176i	0.980983	+	0.194096i	$0.0621772\pi$
$464$		0			0
$465$	6.65663	−	7.68216i	0.308694	−	0.356252i
$466$		0			0
$467$	27.4856	−	17.6639i	1.27188	−	0.817388i	0.282017	−	0.959409i	$-0.408997\pi$
$467$	27.4856	−	17.6639i	1.27188	−	0.817388i	0.989864	+	0.142021i	$0.0453602\pi$
$468$		0			0
$469$	18.7529	+	21.6419i	0.865926	+	0.999332i
$470$		0			0
$471$	−3.11615	+	21.6733i	−0.143585	+	0.998653i
$472$		0			0
$473$	−9.01756	−	5.79524i	−0.414628	−	0.266465i
$474$		0			0
$475$	−17.1913	−	37.6436i	−0.788790	−	1.72721i
$476$		0			0
$477$	11.1974	+	3.28785i	0.512693	+	0.150540i
$478$		0			0
$479$	9.09607	−	2.67085i	0.415610	−	0.122034i	−0.0672406	−	0.997737i	$-0.521420\pi$
$479$	9.09607	−	2.67085i	0.415610	−	0.122034i	0.482851	+	0.875703i	$0.339601\pi$
$480$		0			0
$481$	−0.101286	−	0.704461i	−0.00461825	−	0.0321207i
$482$		0			0
$483$	−9.43758	+	6.97504i	−0.429425	+	0.317375i
$484$		0			0
$485$	−4.29824	−	29.8949i	−0.195173	−	1.35746i
$486$		0			0
$487$	17.6216	−	5.17416i	0.798509	−	0.234463i	0.143071	−	0.989712i	$-0.454302\pi$
$487$	17.6216	−	5.17416i	0.798509	−	0.234463i	0.655438	+	0.755249i	$0.272484\pi$
$488$		0			0
$489$	−10.8044	−	3.17245i	−0.488591	−	0.143463i
$490$		0			0
$491$	9.39577	+	20.5739i	0.424025	+	0.928485i	0.994259	+	0.107003i	$0.0341254\pi$
$491$	9.39577	+	20.5739i	0.424025	+	0.928485i	−0.570234	+	0.821483i	$0.693147\pi$
$492$		0			0
$493$	9.97614	+	6.41127i	0.449303	+	0.288749i
$494$		0			0
$495$	1.81306	−	12.6101i	0.0814912	−	0.566783i
$496$		0			0
$497$	1.23913	+	1.43003i	0.0555824	+	0.0641455i
$498$		0			0
$499$	12.8226	−	8.24060i	0.574020	−	0.368900i	−0.221194	−	0.975230i	$-0.570995\pi$
$499$	12.8226	−	8.24060i	0.574020	−	0.368900i	0.795213	+	0.606330i	$0.207359\pi$
$500$		0			0
$501$	−7.40074	+	8.54091i	−0.330641	+	0.381580i
$502$		0			0
$503$	−11.3672	+	24.8908i	−0.506841	+	1.10983i	0.467345	+	0.884075i	$0.345211\pi$
$503$	−11.3672	+	24.8908i	−0.506841	+	1.10983i	−0.974185	+	0.225751i	$0.927516\pi$
$504$		0			0
$505$	−37.6077			−1.67352
$506$		0			0
$507$	11.3897			0.505833
$508$		0			0
$509$	5.96078	−	13.0523i	0.264207	−	0.578532i	−0.730309	−	0.683117i	$-0.760624\pi$
$509$	5.96078	−	13.0523i	0.264207	−	0.578532i	0.994516	+	0.104584i	$0.0333512\pi$
$510$		0			0
$511$	22.9701	−	26.5089i	1.01614	−	1.17268i
$512$		0			0
$513$	4.75719	−	3.05726i	0.210035	−	0.134981i
$514$		0			0
$515$	−2.13903	−	2.46858i	−0.0942571	−	0.108779i
$516$		0			0
$517$	−6.12543	+	42.6033i	−0.269396	+	1.87369i
$518$		0			0
$519$	17.7972	+	11.4376i	0.781212	+	0.502054i
$520$		0			0
$521$	16.1919	+	35.4554i	0.709381	+	1.55333i	0.828213	+	0.560413i	$0.189358\pi$
$521$	16.1919	+	35.4554i	0.709381	+	1.55333i	−0.118832	+	0.992914i	$0.537915\pi$
$522$		0			0
$523$	32.4675	+	9.53331i	1.41970	+	0.416863i	0.899403	−	0.437121i	$-0.144002\pi$
$523$	32.4675	+	9.53331i	1.41970	+	0.416863i	0.520301	+	0.853983i	$0.325820\pi$
$524$		0			0
$525$	−17.1821	+	5.04513i	−0.749890	+	0.220188i
$526$		0			0
$527$	−1.30752	−	9.09397i	−0.0569563	−	0.396140i
$528$		0			0
$529$	−12.6710	+	19.1950i	−0.550912	+	0.834563i
$530$		0			0
$531$	−1.65031	−	11.4781i	−0.0716172	−	0.498109i
$532$		0			0
$533$	12.6002	−	3.69976i	0.545776	−	0.160254i
$534$		0			0
$535$	18.8182	+	5.52551i	0.813580	+	0.238889i
$536$		0			0
$537$	4.22574	+	9.25308i	0.182354	+	0.399300i
$538$		0			0
$539$	3.09095	+	1.98643i	0.133136	+	0.0855616i
$540$		0			0
$541$	−4.94069	+	34.3632i	−0.212417	+	1.47739i	0.552636	+	0.833423i	$0.313622\pi$
$541$	−4.94069	+	34.3632i	−0.212417	+	1.47739i	−0.765053	+	0.643968i	$0.777287\pi$
$542$		0			0
$543$	−6.97271	−	8.04693i	−0.299228	−	0.345327i
$544$		0			0
$545$	−46.9432	+	30.1686i	−2.01083	+	1.29228i
$546$		0			0
$547$	−9.22896	+	10.6508i	−0.394602	+	0.455395i	−0.917933	−	0.396734i	$-0.870143\pi$
$547$	−9.22896	+	10.6508i	−0.394602	+	0.455395i	0.523332	+	0.852129i	$0.324689\pi$
$548$		0			0
$549$	−2.34534	+	5.13557i	−0.100096	+	0.219181i
$550$		0			0
$551$	−21.1395			−0.900572
$552$		0			0
$553$	17.4017			0.739994
$554$		0			0
$555$	0.817707	−	1.79053i	0.0347097	−	0.0760037i
$556$		0			0
$557$	11.2096	−	12.9366i	0.474968	−	0.548142i	−0.466819	−	0.884353i	$-0.654600\pi$
$557$	11.2096	−	12.9366i	0.474968	−	0.548142i	0.941787	+	0.336211i	$0.109146\pi$
$558$		0			0
$559$	−3.15251	+	2.02600i	−0.133337	+	0.0856906i
$560$		0			0
$561$	−7.54055	−	8.70226i	−0.318362	−	0.367410i
$562$		0			0
$563$	−5.10761	+	35.5242i	−0.215260	+	1.49717i	0.539957	+	0.841693i	$0.318441\pi$
$563$	−5.10761	+	35.5242i	−0.215260	+	1.49717i	−0.755217	+	0.655475i	$0.772469\pi$
$564$		0			0
$565$	16.7954	+	10.7938i	0.706589	+	0.454097i
$566$		0			0
$567$	−1.01652	−	2.22586i	−0.0426897	−	0.0934775i
$568$		0			0
$569$	9.76922	+	2.86850i	0.409547	+	0.120254i	0.480015	−	0.877260i	$-0.340631\pi$
$569$	9.76922	+	2.86850i	0.409547	+	0.120254i	−0.0704682	+	0.997514i	$0.522449\pi$
$570$		0			0
$571$	1.96770	−	0.577770i	0.0823458	−	0.0241789i	−0.240300	−	0.970699i	$-0.577246\pi$
$571$	1.96770	−	0.577770i	0.0823458	−	0.0241789i	0.322646	+	0.946520i	$0.395428\pi$
$572$		0			0
$573$	−1.45630	−	10.1288i	−0.0608379	−	0.423137i
$574$		0			0
$575$	−28.2247	+	20.8601i	−1.17705	+	0.869925i
$576$		0			0
$577$	1.29934	+	9.03714i	0.0540924	+	0.376221i	0.998829	+	0.0483893i	$0.0154088\pi$
$577$	1.29934	+	9.03714i	0.0540924	+	0.376221i	−0.944736	+	0.327832i	$0.893682\pi$
$578$		0			0
$579$	−9.73114	+	2.85732i	−0.404412	+	0.118746i
$580$		0			0
$581$	9.36805	+	2.75071i	0.388652	+	0.114119i
$582$		0			0
$583$	17.5973	+	38.5328i	0.728806	+	1.59586i
$584$		0			0
$585$	−3.74677	−	2.40791i	−0.154910	−	0.0995546i
$586$		0			0
$587$	0.370355	−	2.57588i	0.0152862	−	0.106318i	−0.980750	−	0.195268i	$-0.937442\pi$
$587$	0.370355	−	2.57588i	0.0152862	−	0.106318i	0.996036	+	0.0889505i	$0.0283513\pi$
$588$		0			0
$589$	10.7252	+	12.3775i	0.441923	+	0.510007i
$590$		0			0
$591$	17.7533	−	11.4093i	0.730271	−	0.469317i
$592$		0			0
$593$	−8.01595	+	9.25090i	−0.329176	+	0.379889i	−0.896078	−	0.443896i	$-0.853596\pi$
$593$	−8.01595	+	9.25090i	−0.329176	+	0.379889i	0.566903	+	0.823785i	$0.308141\pi$
$594$		0			0
$595$	−11.3176	+	24.7820i	−0.463975	+	1.01596i
$596$		0			0
$597$	−5.96499			−0.244131
$598$		0			0
$599$	12.1215			0.495270			0.247635	−	0.968853i	$-0.420347\pi$
$599$	12.1215			0.495270			0.247635	+	0.968853i	$0.420347\pi$
$600$		0			0
$601$	−13.8159	+	30.2527i	−0.563564	+	1.23403i	0.386590	+	0.922252i	$0.373653\pi$
$601$	−13.8159	+	30.2527i	−0.563564	+	1.23403i	−0.950154	+	0.311781i	$0.899074\pi$
$602$		0			0
$603$	−7.66363	+	8.84430i	−0.312087	+	0.360168i
$604$		0			0
$605$	6.42443	−	4.12873i	0.261190	−	0.167857i
$606$		0			0
$607$	−9.71185	−	11.2081i	−0.394192	−	0.454922i	0.523611	−	0.851957i	$-0.324584\pi$
$607$	−9.71185	−	11.2081i	−0.394192	−	0.454922i	−0.917803	+	0.397036i	$0.870039\pi$
$608$		0			0
$609$	−1.30183	+	9.05442i	−0.0527528	+	0.366904i
$610$		0			0
$611$	12.6585	+	8.13510i	0.512106	+	0.329111i
$612$		0			0
$613$	−13.2703	−	29.0578i	−0.535980	−	1.17363i	−0.963027	−	0.269404i	$-0.913173\pi$
$613$	−13.2703	−	29.0578i	−0.535980	−	1.17363i	0.427047	−	0.904230i	$-0.359554\pi$
$614$		0			0
$615$	34.8493	+	10.2327i	1.40526	+	0.412621i
$616$		0			0
$617$	44.9152	−	13.1883i	1.80822	−	0.530941i	0.809776	−	0.586739i	$-0.199589\pi$
$617$	44.9152	−	13.1883i	1.80822	−	0.530941i	0.998442	+	0.0557986i	$0.0177705\pi$
$618$		0			0
$619$	−2.13534	−	14.8516i	−0.0858266	−	0.596937i	−0.986663	−	0.162778i	$-0.947955\pi$
$619$	−2.13534	−	14.8516i	−0.0858266	−	0.596937i	0.900836	−	0.434159i	$-0.142954\pi$
$620$		0			0
$621$	−3.37032	−	3.41189i	−0.135246	−	0.136914i
$622$		0			0
$623$	2.97959	+	20.7235i	0.119375	+	0.830271i
$624$		0			0
$625$	7.70976	−	2.26379i	0.308391	−	0.0905516i
$626$		0			0
$627$	19.6950	+	5.78296i	0.786541	+	0.230949i
$628$		0			0
$629$	−0.739076	−	1.61835i	−0.0294689	−	0.0645279i
$630$		0			0
$631$	−32.9969	−	21.2058i	−1.31359	−	0.844190i	−0.318964	−	0.947767i	$-0.603335\pi$
$631$	−32.9969	−	21.2058i	−1.31359	−	0.844190i	−0.994621	+	0.103577i	$0.966971\pi$
$632$		0			0
$633$	2.73492	−	19.0218i	0.108703	−	0.756049i
$634$		0			0
$635$	−22.5889	−	26.0690i	−0.896414	−	1.03452i
$636$		0			0
$637$	1.08059	−	0.694450i	0.0428144	−	0.0275151i
$638$		0			0
$639$	−0.506387	+	0.584402i	−0.0200324	+	0.0231186i
$640$		0			0
$641$	−11.5294	+	25.2459i	−0.455384	+	0.997153i	0.533131	+	0.846033i	$0.321015\pi$
$641$	−11.5294	+	25.2459i	−0.455384	+	0.997153i	−0.988515	+	0.151120i	$0.951712\pi$
$642$		0			0
$643$	−1.26270			−0.0497958			−0.0248979	−	0.999690i	$-0.507926\pi$
$643$	−1.26270			−0.0497958			−0.0248979	+	0.999690i	$0.507926\pi$
$644$		0			0
$645$	−10.3644			−0.408099
$646$		0			0
$647$	5.24476	−	11.4844i	0.206193	−	0.451499i	−0.778078	−	0.628168i	$-0.783805\pi$
$647$	5.24476	−	11.4844i	0.206193	−	0.451499i	0.984270	+	0.176669i	$0.0565323\pi$
$648$		0			0
$649$	27.5647	−	31.8114i	1.08201	−	1.24871i
$650$		0			0
$651$	5.96200	−	3.83155i	0.233669	−	0.150170i
$652$		0			0
$653$	−28.6300	−	33.0408i	−1.12038	−	1.29299i	−0.951602	−	0.307333i	$-0.900564\pi$
$653$	−28.6300	−	33.0408i	−1.12038	−	1.29299i	−0.168777	−	0.985654i	$-0.553982\pi$
$654$		0			0
$655$	8.77684	−	61.0443i	0.342940	−	2.38520i
$656$		0			0
$657$	12.0589	+	7.74978i	0.470462	+	0.302348i
$658$		0			0
$659$	−3.31001	−	7.24790i	−0.128940	−	0.282338i	0.834141	−	0.551551i	$-0.185964\pi$
$659$	−3.31001	−	7.24790i	−0.128940	−	0.282338i	−0.963081	+	0.269213i	$0.913237\pi$
$660$		0			0
$661$	−12.6323	−	3.70918i	−0.491339	−	0.144270i	0.0266715	−	0.999644i	$-0.491509\pi$
$661$	−12.6323	−	3.70918i	−0.491339	−	0.144270i	−0.518011	+	0.855374i	$0.673327\pi$
$662$		0			0
$663$	−3.86246	+	1.13412i	−0.150005	+	0.0440456i
$664$		0			0
$665$	−6.91162	−	48.0713i	−0.268021	−	1.86413i
$666$		0			0
$667$	3.70346	+	17.5414i	0.143398	+	0.679207i
$668$		0			0
$669$	0.0449274	+	0.312477i	0.00173699	+	0.0120810i
$670$		0			0
$671$	−19.6632	+	5.77364i	−0.759090	+	0.222889i
$672$		0			0
$673$	−34.9936	−	10.2750i	−1.34890	−	0.396074i	−0.474065	−	0.880490i	$-0.657214\pi$
$673$	−34.9936	−	10.2750i	−1.34890	−	0.396074i	−0.874838	+	0.484416i	$0.839032\pi$
$674$		0			0
$675$	−3.04008	−	6.65684i	−0.117013	−	0.256222i
$676$		0			0
$677$	8.29781	+	5.33268i	0.318911	+	0.204951i	0.690295	−	0.723528i	$-0.257481\pi$
$677$	8.29781	+	5.33268i	0.318911	+	0.204951i	−0.371385	+	0.928479i	$0.621117\pi$
$678$		0			0
$679$	2.99675	−	20.8429i	0.115005	−	0.799876i
$680$		0			0
$681$	17.5134	+	20.2115i	0.671113	+	0.774506i
$682$		0			0
$683$	−2.38499	+	1.53274i	−0.0912591	+	0.0586487i	−0.585475	−	0.810691i	$-0.699092\pi$
$683$	−2.38499	+	1.53274i	−0.0912591	+	0.0586487i	0.494215	+	0.869339i	$0.335455\pi$
$684$		0			0
$685$	8.26659	−	9.54015i	0.315850	−	0.364510i
$686$		0			0
$687$	10.5241	−	23.0446i	0.401519	−	0.879205i
$688$		0			0
$689$	14.8092			0.564186
$690$		0			0
$691$	−35.4217			−1.34750			−0.673752	−	0.738957i	$-0.735318\pi$
$691$	−35.4217			−1.34750			−0.673752	+	0.738957i	$0.735318\pi$
$692$		0			0
$693$	3.68982	−	8.07957i	0.140165	−	0.306918i
$694$		0			0
$695$	10.5662	−	12.1940i	0.400799	−	0.462546i
$696$		0			0
$697$	27.6166	−	17.7481i	1.04605	−	0.672258i
$698$		0			0
$699$	−15.6572	−	18.0694i	−0.592211	−	0.683447i
$700$		0			0
$701$	2.56956	−	17.8717i	0.0970508	−	0.675003i	−0.881979	−	0.471288i	$-0.843789\pi$
$701$	2.56956	−	17.8717i	0.0970508	−	0.675003i	0.979030	−	0.203715i	$-0.0653017\pi$
$702$		0			0
$703$	2.66804	+	1.71465i	0.100627	+	0.0646691i
$704$		0			0
$705$	17.2883	+	37.8560i	0.651114	+	1.42574i
$706$		0			0
$707$	−25.1581	−	7.38709i	−0.946168	−	0.277820i
$708$		0			0
$709$	37.1662	−	10.9130i	1.39581	−	0.409845i	0.504564	−	0.863374i	$-0.331653\pi$
$709$	37.1662	−	10.9130i	1.39581	−	0.409845i	0.891242	+	0.453529i	$0.149835\pi$
$710$		0			0
$711$	1.01206	+	7.03906i	0.0379554	+	0.263985i
$712$		0			0
$713$	8.39184	−	11.0681i	0.314277	−	0.414505i
$714$		0			0
$715$	−2.30076	−	16.0021i	−0.0860434	−	0.598445i
$716$		0			0
$717$	1.37017	−	0.402319i	0.0511701	−	0.0150249i
$718$		0			0
$719$	49.1790	+	14.4402i	1.83407	+	0.538530i	0.999915	−	0.0130060i	$-0.00414007\pi$
$719$	49.1790	+	14.4402i	1.83407	+	0.538530i	0.834151	+	0.551536i	$0.185958\pi$
$720$		0			0
$721$	−0.946043	−	2.07155i	−0.0352325	−	0.0771484i
$722$		0			0
$723$	−0.200331	−	0.128745i	−0.00745040	−	0.00478808i
$724$		0			0
$725$	−3.89335	+	27.0789i	−0.144595	+	1.00568i
$726$		0			0
$727$	−32.4331	−	37.4298i	−1.20288	−	1.38819i	−0.900415	−	0.435031i	$-0.856737\pi$
$727$	−32.4331	−	37.4298i	−1.20288	−	1.38819i	−0.302461	−	0.953162i	$-0.597808\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	−6.13460	+	7.07970i	−0.226896	+	0.261852i
$732$		0			0
$733$	−13.8110	+	30.2418i	−0.510120	+	1.11701i	0.462926	+	0.886397i	$0.346800\pi$
$733$	−13.8110	+	30.2418i	−0.510120	+	1.11701i	−0.973046	+	0.230610i	$0.925928\pi$
$734$		0			0
$735$	3.55261			0.131040
$736$		0			0
$737$	−42.4791			−1.56474
$738$		0			0
$739$	16.3928	−	35.8953i	0.603020	−	1.32043i	−0.324227	−	0.945979i	$-0.605104\pi$
$739$	16.3928	−	35.8953i	0.603020	−	1.32043i	0.927247	−	0.374451i	$-0.122169\pi$
$740$		0			0
$741$	4.69926	−	5.42324i	0.172632	−	0.199228i
$742$		0			0
$743$	28.4816	−	18.3040i	1.04489	−	0.671508i	0.0986965	−	0.995118i	$-0.468533\pi$
$743$	28.4816	−	18.3040i	1.04489	−	0.671508i	0.946191	+	0.323609i	$0.104896\pi$
$744$		0			0
$745$	−18.6233	−	21.4925i	−0.682307	−	0.787424i
$746$		0			0
$747$	−0.567839	+	3.94940i	−0.0207761	+	0.144501i
$748$		0			0
$749$	11.5033	+	7.39272i	0.420321	+	0.270124i
$750$		0			0
$751$	−11.8182	−	25.8781i	−0.431251	−	0.944307i	−0.993122	−	0.117083i	$-0.962646\pi$
$751$	−11.8182	−	25.8781i	−0.431251	−	0.944307i	0.561872	−	0.827224i	$-0.310081\pi$
$752$		0			0
$753$	−19.4703	−	5.71699i	−0.709537	−	0.208339i
$754$		0			0
$755$	−29.9058	+	8.78114i	−1.08838	+	0.319578i
$756$		0			0
$757$	3.15222	+	21.9241i	0.114569	+	0.796847i	0.963378	+	0.268147i	$0.0864112\pi$
$757$	3.15222	+	21.9241i	0.114569	+	0.796847i	−0.848809	+	0.528700i	$0.822680\pi$
$758$		0			0
$759$	1.34828	−	17.3559i	0.0489396	−	0.629979i
$760$		0			0
$761$	−4.00085	−	27.8265i	−0.145031	−	1.00871i	−0.924203	−	0.381901i	$-0.875269\pi$
$761$	−4.00085	−	27.8265i	−0.145031	−	1.00871i	0.779172	−	0.626810i	$-0.215640\pi$
$762$		0			0
$763$	−37.3291	+	10.9608i	−1.35140	+	0.396808i
$764$		0			0
$765$	−10.6827	−	3.13671i	−0.386232	−	0.113408i
$766$		0			0
$767$	−6.11300	−	13.3856i	−0.220728	−	0.483326i
$768$		0			0
$769$	−15.8579	−	10.1913i	−0.571852	−	0.367507i	0.222530	−	0.974926i	$-0.428569\pi$
$769$	−15.8579	−	10.1913i	−0.571852	−	0.367507i	−0.794382	+	0.607419i	$0.792205\pi$
$770$		0			0
$771$	−2.37193	+	16.4971i	−0.0854230	+	0.594130i
$772$		0			0
$773$	10.5832	+	12.2137i	0.380651	+	0.439295i	0.913452	−	0.406946i	$-0.133406\pi$
$773$	10.5832	+	12.2137i	0.380651	+	0.439295i	−0.532801	+	0.846240i	$0.678861\pi$
$774$		0			0
$775$	17.8304	−	11.4589i	0.640488	−	0.411616i
$776$		0			0
$777$	0.898720	−	1.03718i	0.0322414	−	0.0372086i
$778$		0			0
$779$	−24.3100	+	53.2314i	−0.870995	+	1.90721i
$780$		0			0
$781$	−2.80688			−0.100438
$782$		0			0
$783$	−3.73827			−0.133595
$784$		0			0
$785$	−31.9244	+	69.9048i	−1.13943	+	2.49501i
$786$		0			0
$787$	7.88438	−	9.09906i	0.281048	−	0.324346i	−0.597621	−	0.801779i	$-0.703887\pi$
$787$	7.88438	−	9.09906i	0.281048	−	0.324346i	0.878668	+	0.477433i	$0.158433\pi$
$788$		0			0
$789$	14.2732	−	9.17281i	0.508139	−	0.326561i
$790$		0			0
$791$	9.11535	+	10.5197i	0.324104	+	0.374037i
$792$		0			0
$793$	−1.01960	+	7.09148i	−0.0362071	+	0.251826i
$794$		0			0
$795$	34.4568	+	22.1440i	1.22206	+	0.785367i
$796$		0			0
$797$	−18.6721	−	40.8863i	−0.661401	−	1.44827i	−0.881210	−	0.472724i	$-0.843271\pi$
$797$	−18.6721	−	40.8863i	−0.661401	−	1.44827i	0.219809	−	0.975543i	$-0.429457\pi$
$798$		0			0
$799$	36.0913	+	10.5974i	1.27682	+	0.374908i
$800$		0			0
$801$	−8.20948	+	2.41052i	−0.290068	+	0.0851716i
$802$		0			0
$803$	7.40492	+	51.5024i	0.261314	+	1.81748i
$804$		0			0
$805$	−38.6785	+	14.1569i	−1.36324	+	0.498966i
$806$		0			0
$807$	0.605815	+	4.21354i	0.0213257	+	0.148324i
$808$		0			0
$809$	−19.0920	+	5.60591i	−0.671238	+	0.197093i	−0.599554	−	0.800334i	$-0.704655\pi$
$809$	−19.0920	+	5.60591i	−0.671238	+	0.197093i	−0.0716836	+	0.997427i	$0.522837\pi$
$810$		0			0
$811$	−31.3402	−	9.20230i	−1.10050	−	0.323137i	−0.319450	−	0.947603i	$-0.603498\pi$
$811$	−31.3402	−	9.20230i	−1.10050	−	0.323137i	−0.781052	+	0.624466i	$0.785316\pi$
$812$		0			0
$813$	−2.47675	−	5.42332i	−0.0868634	−	0.190204i
$814$		0			0
$815$	−33.2474	−	21.3668i	−1.16461	−	0.748447i
$816$		0			0
$817$	2.37655	−	16.5292i	0.0831448	−	0.578285i
$818$		0			0
$819$	−2.03348	−	2.34676i	−0.0710555	−	0.0820024i
$820$		0			0
$821$	−11.3204	+	7.27518i	−0.395085	+	0.253905i	−0.723066	−	0.690779i	$-0.757268\pi$
$821$	−11.3204	+	7.27518i	−0.395085	+	0.253905i	0.327982	+	0.944684i	$0.393632\pi$
$822$		0			0
$823$	12.2385	−	14.1239i	0.426606	−	0.492329i	−0.501232	−	0.865313i	$-0.667120\pi$
$823$	12.2385	−	14.1239i	0.426606	−	0.492329i	0.927838	+	0.372984i	$0.121665\pi$
$824$		0			0
$825$	11.0351	−	24.1634i	0.384191	−	0.841261i
$826$		0			0
$827$	−18.1631			−0.631594			−0.315797	−	0.948827i	$-0.602272\pi$
$827$	−18.1631			−0.631594			−0.315797	+	0.948827i	$0.602272\pi$
$828$		0			0
$829$	37.8172			1.31345			0.656723	−	0.754132i	$-0.271942\pi$
$829$	37.8172			1.31345			0.656723	+	0.754132i	$0.271942\pi$
$830$		0			0
$831$	−8.23517	+	18.0325i	−0.285675	+	0.625541i
$832$		0			0
$833$	2.10275	−	2.42671i	0.0728561	−	0.0840804i
$834$		0			0
$835$	−33.3677	+	21.4441i	−1.15474	+	0.742104i
$836$		0			0
$837$	1.89662	+	2.18882i	0.0655569	+	0.0756567i
$838$		0			0
$839$	4.59025	−	31.9259i	0.158473	−	1.10220i	−0.742976	−	0.669318i	$-0.766586\pi$
$839$	4.59025	−	31.9259i	0.158473	−	1.10220i	0.901449	−	0.432885i	$-0.142505\pi$
$840$		0			0
$841$	−12.6401	−	8.12330i	−0.435866	−	0.280114i
$842$		0			0
$843$	4.80084	+	10.5124i	0.165350	+	0.362065i
$844$		0			0
$845$	38.3554	+	11.2621i	1.31946	+	0.387430i
$846$		0			0
$847$	5.10869	−	1.50005i	0.175537	−	0.0515422i
$848$		0			0
$849$	−3.93080	−	27.3393i	−0.134905	−	0.938282i
$850$		0			0
$851$	0.955387	−	2.51432i	0.0327503	−	0.0861898i
$852$		0			0
$853$	−1.97706	−	13.7508i	−0.0676933	−	0.470817i	−0.995267	−	0.0971771i	$-0.969019\pi$
$853$	−1.97706	−	13.7508i	−0.0676933	−	0.470817i	0.927574	−	0.373640i	$-0.121890\pi$
$854$		0			0
$855$	19.0431	−	5.59157i	0.651261	−	0.191228i
$856$		0			0
$857$	−33.4741	−	9.82889i	−1.14345	−	0.335749i	−0.345472	−	0.938429i	$-0.612281\pi$
$857$	−33.4741	−	9.82889i	−1.14345	−	0.335749i	−0.797983	+	0.602680i	$0.794099\pi$
$858$		0			0
$859$	1.26281	+	2.76518i	0.0430866	+	0.0943466i	0.929951	−	0.367683i	$-0.119849\pi$
$859$	1.26281	+	2.76518i	0.0430866	+	0.0943466i	−0.886865	+	0.462029i	$0.847121\pi$
$860$		0			0
$861$	21.3029	+	13.6905i	0.726001	+	0.466572i
$862$		0			0
$863$	3.47453	−	24.1659i	0.118275	−	0.822617i	−0.841180	−	0.540755i	$-0.818139\pi$
$863$	3.47453	−	24.1659i	0.118275	−	0.822617i	0.959455	−	0.281863i	$-0.0909522\pi$
$864$		0			0
$865$	48.6236	+	56.1147i	1.65325	+	1.90796i
$866$		0			0
$867$	5.83575	−	3.75041i	0.198192	−	0.127371i
$868$		0			0
$869$	−16.9043	+	19.5086i	−0.573438	+	0.661783i
$870$		0			0
$871$	−6.16915	+	13.5085i	−0.209034	+	0.457720i
$872$		0			0
$873$	8.60533			0.291246
$874$		0			0
$875$	−19.9091			−0.673050
$876$		0			0
$877$	−7.75427	+	16.9795i	−0.261843	+	0.573356i	−0.994198	−	0.107567i	$-0.965694\pi$
$877$	−7.75427	+	16.9795i	−0.261843	+	0.573356i	0.732355	+	0.680923i	$0.238421\pi$
$878$		0			0
$879$	−12.0327	+	13.8865i	−0.405854	+	0.468381i
$880$		0			0
$881$	0.407658	−	0.261986i	0.0137343	−	0.00882652i	−0.533756	−	0.845639i	$-0.679220\pi$
$881$	0.407658	−	0.261986i	0.0137343	−	0.00882652i	0.547490	+	0.836812i	$0.315583\pi$
$882$		0			0
$883$	31.6473	+	36.5229i	1.06502	+	1.22909i	0.972382	+	0.233395i	$0.0749834\pi$
$883$	31.6473	+	36.5229i	1.06502	+	1.22909i	0.0926345	+	0.995700i	$0.470471\pi$
$884$		0			0
$885$	5.79212	−	40.2851i	0.194700	−	1.35417i
$886$		0			0
$887$	−9.98107	−	6.41445i	−0.335132	−	0.215376i	0.362241	−	0.932084i	$-0.382012\pi$
$887$	−9.98107	−	6.41445i	−0.335132	−	0.215376i	−0.697373	+	0.716708i	$0.745648\pi$
$888$		0			0
$889$	−9.99053	−	21.8762i	−0.335072	−	0.733705i
$890$		0			0
$891$	3.48282	+	1.02265i	0.116679	+	0.0342601i
$892$		0			0
$893$	−64.3371	+	18.8911i	−2.15296	+	0.632166i
$894$		0			0
$895$	5.08094	+	35.3387i	0.169837	+	1.18124i
$896$		0			0
$897$	−5.32345	−	2.94932i	−0.177745	−	0.0984750i
$898$		0			0
$899$	−1.54083	−	10.7167i	−0.0513894	−	0.357421i
$900$		0			0
$901$	35.5206	−	10.4298i	1.18336	−	0.347467i
$902$		0			0
$903$	−6.93342	−	2.03583i	−0.230730	−	0.0677483i
$904$		0			0
$905$	−15.5242	−	33.9931i	−0.516040	−	1.12997i
$906$		0			0
$907$	17.2104	+	11.0605i	0.571462	+	0.367256i	0.794232	−	0.607615i	$-0.207874\pi$
$907$	17.2104	+	11.0605i	0.571462	+	0.367256i	−0.222770	+	0.974871i	$0.571510\pi$
$908$		0			0
$909$	1.52494	−	10.6062i	0.0505791	−	0.351786i
$910$		0			0
$911$	−7.35328	−	8.48614i	−0.243625	−	0.281158i	0.620747	−	0.784011i	$-0.286829\pi$
$911$	−7.35328	−	8.48614i	−0.243625	−	0.281158i	−0.864372	+	0.502853i	$0.832284\pi$
$912$		0			0
$913$	−12.1840	+	7.83021i	−0.403233	+	0.259142i
$914$		0			0
$915$	−12.9761	+	14.9752i	−0.428977	+	0.495066i
$916$		0			0
$917$	17.8620	−	39.1123i	0.589855	−	1.29160i
$918$		0			0
$919$	−15.5940			−0.514399			−0.257200	−	0.966358i	$-0.582800\pi$
$919$	−15.5940			−0.514399			−0.257200	+	0.966358i	$0.582800\pi$
$920$		0			0
$921$	−11.1552			−0.367578
$922$		0			0
$923$	−0.407637	+	0.892600i	−0.0134175	+	0.0293803i
$924$		0			0
$925$	2.68778	−	3.10187i	0.0883737	−	0.101989i
$926$		0			0
$927$	0.782930	−	0.503158i	0.0257148	−	0.0165259i
$928$		0			0
$929$	−11.9711	−	13.8154i	−0.392758	−	0.453267i	0.524589	−	0.851356i	$-0.324219\pi$
$929$	−11.9711	−	13.8154i	−0.392758	−	0.453267i	−0.917347	+	0.398089i	$0.869674\pi$
$930$		0			0
$931$	−0.814607	+	5.66572i	−0.0266977	+	0.185686i
$932$		0			0
$933$	18.2450	+	11.7253i	0.597313	+	0.383870i
$934$		0			0
$935$	−16.7884	−	36.7615i	−0.549040	−	1.20223i
$936$		0			0
$937$	−32.1451	−	9.43864i	−1.05013	−	0.308347i	−0.289262	−	0.957250i	$-0.593410\pi$
$937$	−32.1451	−	9.43864i	−1.05013	−	0.308347i	−0.760871	+	0.648903i	$0.775228\pi$
$938$		0			0
$939$	16.7995	−	4.93277i	0.548230	−	0.160975i
$940$		0			0
$941$	−7.98942	−	55.5677i	−0.260448	−	1.81145i	−0.529480	−	0.848323i	$-0.677613\pi$
$941$	−7.98942	−	55.5677i	−0.260448	−	1.81145i	0.269032	−	0.963131i	$-0.413296\pi$
$942$		0			0
$943$	48.4301	+	10.8466i	1.57710	+	0.353214i
$944$		0			0
$945$	−1.22224	−	8.50086i	−0.0397594	−	0.276533i
$946$		0			0
$947$	−37.6807	+	11.0640i	−1.22446	+	0.359533i	−0.829155	−	0.559018i	$-0.811178\pi$
$947$	−37.6807	+	11.0640i	−1.22446	+	0.359533i	−0.395302	+	0.918551i	$0.629360\pi$
$948$		0			0
$949$	17.4534	+	5.12478i	0.566561	+	0.166357i
$950$		0			0
$951$	−11.7930	−	25.8231i	−0.382414	−	0.837370i
$952$		0			0
$953$	−17.1159	−	10.9997i	−0.554438	−	0.356316i	0.233224	−	0.972423i	$-0.425072\pi$
$953$	−17.1159	−	10.9997i	−0.554438	−	0.356316i	−0.787662	+	0.616107i	$0.788709\pi$
$954$		0			0
$955$	5.11122	−	35.5493i	0.165395	−	1.15035i
$956$		0			0
$957$	−8.88607	−	10.2551i	−0.287246	−	0.331499i
$958$		0			0
$959$	7.40396	−	4.75824i	0.239086	−	0.153651i
$960$		0			0
$961$	14.8076	−	17.0889i	0.477666	−	0.551255i
$962$		0			0
$963$	−2.32137	+	5.08310i	−0.0748052	+	0.163800i
$964$		0			0
$965$	−35.5955			−1.14586
$966$		0			0
$967$	5.66729			0.182248			0.0911239	−	0.995840i	$-0.470954\pi$
$967$	5.66729			0.182248			0.0911239	+	0.995840i	$0.470954\pi$
$968$		0			0
$969$	7.45195	−	16.3175i	0.239391	−	0.524194i
$970$		0			0
$971$	−9.50053	+	10.9642i	−0.304886	+	0.351858i	−0.887431	−	0.460941i	$-0.847512\pi$
$971$	−9.50053	+	10.9642i	−0.304886	+	0.351858i	0.582544	+	0.812799i	$0.302057\pi$
$972$		0			0
$973$	9.46360	−	6.08189i	0.303389	−	0.194976i
$974$		0			0
$975$	−6.08148	−	7.01840i	−0.194763	−	0.224769i
$976$		0			0
$977$	−3.20624	+	22.2999i	−0.102577	+	0.713436i	0.872020	+	0.489470i	$0.162810\pi$
$977$	−3.20624	+	22.2999i	−0.102577	+	0.713436i	−0.974597	+	0.223966i	$0.928099\pi$
$978$		0			0
$979$	−26.1271	−	16.7908i	−0.835025	−	0.536638i
$980$		0			0
$981$	−6.60473	−	14.4623i	−0.210873	−	0.461747i
$982$		0			0
$983$	43.6709	+	12.8229i	1.39288	+	0.408988i	0.890235	−	0.455502i	$-0.150540\pi$
$983$	43.6709	+	12.8229i	1.39288	+	0.408988i	0.502650	+	0.864490i	$0.332359\pi$
$984$		0			0
$985$	71.0667	−	20.8671i	2.26437	−	0.664880i
$986$		0			0
$987$	4.12933	+	28.7201i	0.131438	+	0.914171i
$988$		0			0
$989$	−14.1322	+	0.923736i	−0.449379	+	0.0293731i
$990$		0			0
$991$	0.355063	+	2.46952i	0.0112790	+	0.0784469i	0.994683	−	0.102980i	$-0.0328376\pi$
$991$	0.355063	+	2.46952i	0.0112790	+	0.0784469i	−0.983405	+	0.181427i	$0.941929\pi$
$992$		0			0
$993$	26.2753	−	7.71512i	0.833821	−	0.244832i
$994$		0			0
$995$	−20.0874	−	5.89821i	−0.636815	−	0.186986i
$996$		0			0
$997$	17.0870	+	37.4152i	0.541149	+	1.18495i	0.960794	+	0.277263i	$0.0894275\pi$
$997$	17.0870	+	37.4152i	0.541149	+	1.18495i	−0.419645	+	0.907689i	$0.637845\pi$
$998$		0			0
$999$	0.471813	+	0.303216i	0.0149275	+	0.00959331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.49.1	✓	30
23.8	even	11	inner	552.2.q.c.169.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.49.1	✓	30	1.1	even	1	trivial
552.2.q.c.169.1	yes	30	23.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{3} +(-2.29838 + 2.65247i) q^{5} +(-2.05854 + 1.32294i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(0.516583 - 3.59291i) q^{11} +(-1.06754 - 0.686067i) q^{13} +(-1.45799 - 3.19256i) q^{15} +(-3.04373 - 0.893720i) q^{17} +(5.42582 - 1.59316i) q^{19} +(-0.348244 - 2.42209i) q^{21} +(-2.27256 - 4.22321i) q^{23} +(-1.04148 - 7.24368i) q^{25} +(0.959493 - 0.281733i) q^{27} +(-3.58685 - 1.05319i) q^{29} +(1.20314 + 2.63450i) q^{31} +(3.05363 + 1.96245i) q^{33} +(1.22224 - 8.50086i) q^{35} +(0.367275 + 0.423858i) q^{37} +(1.06754 - 0.686067i) q^{39} +(-6.77685 + 7.82090i) q^{41} +(1.22675 - 2.68620i) q^{43} +3.50972 q^{45} -11.8576 q^{47} +(-0.420491 + 0.920747i) q^{49} +(2.07737 - 2.39741i) q^{51} +(-9.81751 + 6.30933i) q^{53} +(8.34280 + 9.62810i) q^{55} +(-0.804773 + 5.59732i) q^{57} +(9.75532 + 6.26936i) q^{59} +(-2.34534 - 5.13557i) q^{61} +(2.34787 + 0.689398i) q^{63} +(4.27339 - 1.25478i) q^{65} +(-1.66547 - 11.5836i) q^{67} +(4.78562 - 0.312806i) q^{69} +(-0.110048 - 0.765404i) q^{71} +(-13.7538 + 4.03848i) q^{73} +(7.02173 + 2.06177i) q^{75} +(3.68982 + 8.07957i) q^{77} +(-5.98253 - 3.84474i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-2.61290 - 3.01545i) q^{83} +(9.36622 - 6.01931i) q^{85} +(2.44805 - 2.82520i) q^{87} +(3.55432 - 7.78287i) q^{89} +3.10521 q^{91} -2.89622 q^{93} +(-8.24477 + 18.0535i) q^{95} +(-5.63529 + 6.50347i) q^{97} +(-3.05363 + 1.96245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37}+ \cdots - 9 q^{99}+O(q^{100}) \) 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

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Database

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