LMFDB - Embedded newform 465.2.k.b.32.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(32,465)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("465.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,0,0,-4,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.16
Character	$\chi$	$=$	465.32
Dual form			465.2.k.b.218.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.150369 - 0.150369i) q^{2} +(-1.62789 - 0.591574i) q^{3} +1.95478i q^{4} +(-0.684260 + 2.12880i) q^{5} +(-0.333740 + 0.155831i) q^{6} +(-0.387197 - 0.387197i) q^{7} +(0.594677 + 0.594677i) q^{8} +(2.30008 + 1.92604i) q^{9} +(0.217214 + 0.422998i) q^{10} -5.94154i q^{11} +(1.15640 - 3.18217i) q^{12} +(-2.75083 + 2.75083i) q^{13} -0.116445 q^{14} +(2.37325 - 3.06067i) q^{15} -3.73071 q^{16} +(-4.13991 + 4.13991i) q^{17} +(0.635479 - 0.0562442i) q^{18} +1.21724i q^{19} +(-4.16133 - 1.33758i) q^{20} +(0.401260 + 0.859371i) q^{21} +(-0.893425 - 0.893425i) q^{22} +(-6.27242 - 6.27242i) q^{23} +(-0.616276 - 1.31987i) q^{24} +(-4.06358 - 2.91331i) q^{25} +0.827280i q^{26} +(-2.60489 - 4.49606i) q^{27} +(0.756883 - 0.756883i) q^{28} +2.83642 q^{29} +(-0.103368 - 0.817094i) q^{30} -1.00000 q^{31} +(-1.75034 + 1.75034i) q^{32} +(-3.51486 + 9.67221i) q^{33} +1.24503i q^{34} +(1.08921 - 0.559321i) q^{35} +(-3.76498 + 4.49615i) q^{36} +(3.46533 + 3.46533i) q^{37} +(0.183035 + 0.183035i) q^{38} +(6.10537 - 2.85074i) q^{39} +(-1.67286 + 0.859035i) q^{40} +6.88424i q^{41} +(0.189560 + 0.0688858i) q^{42} +(-4.32117 + 4.32117i) q^{43} +11.6144 q^{44} +(-5.67401 + 3.57850i) q^{45} -1.88636 q^{46} +(-3.93745 + 3.93745i) q^{47} +(6.07321 + 2.20699i) q^{48} -6.70016i q^{49} +(-1.04911 + 0.172965i) q^{50} +(9.18839 - 4.29027i) q^{51} +(-5.37726 - 5.37726i) q^{52} +(-4.51366 - 4.51366i) q^{53} +(-1.06776 - 0.284373i) q^{54} +(12.6484 + 4.06556i) q^{55} -0.460514i q^{56} +(0.720087 - 1.98154i) q^{57} +(0.426510 - 0.426510i) q^{58} -4.65734 q^{59} +(5.98293 + 4.63917i) q^{60} +0.744831 q^{61} +(-0.150369 + 0.150369i) q^{62} +(-0.144827 - 1.63634i) q^{63} -6.93503i q^{64} +(-3.97368 - 7.73824i) q^{65} +(0.925875 + 1.98293i) q^{66} +(5.51708 + 5.51708i) q^{67} +(-8.09260 - 8.09260i) q^{68} +(6.50024 + 13.9214i) q^{69} +(0.0796786 - 0.247888i) q^{70} +4.91796i q^{71} +(0.222433 + 2.51318i) q^{72} +(9.51707 - 9.51707i) q^{73} +1.04216 q^{74} +(4.89164 + 7.14646i) q^{75} -2.37943 q^{76} +(-2.30055 + 2.30055i) q^{77} +(0.489397 - 1.34672i) q^{78} +3.31966i q^{79} +(2.55278 - 7.94194i) q^{80} +(1.58074 + 8.86009i) q^{81} +(1.03518 + 1.03518i) q^{82} +(4.12394 + 4.12394i) q^{83} +(-1.67988 + 0.784374i) q^{84} +(-5.98026 - 11.6458i) q^{85} +1.29954i q^{86} +(-4.61739 - 1.67795i) q^{87} +(3.53330 - 3.53330i) q^{88} -3.87913 q^{89} +(-0.315100 + 1.39129i) q^{90} +2.13022 q^{91} +(12.2612 - 12.2612i) q^{92} +(1.62789 + 0.591574i) q^{93} +1.18414i q^{94} +(-2.59126 - 0.832908i) q^{95} +(3.88482 - 1.81391i) q^{96} +(5.32691 + 5.32691i) q^{97} +(-1.00750 - 1.00750i) q^{98} +(11.4436 - 13.6660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40}+ \cdots + 56 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.150369	−	0.150369i	0.106327	−	0.106327i	−0.651942	−	0.758269i	$-0.726045\pi$
$2$	0.150369	−	0.150369i	0.106327	−	0.106327i	0.758269	+	0.651942i	$0.226045\pi$
$3$	−1.62789	−	0.591574i	−0.939865	−	0.341545i
$3$	−1.62789	−	0.591574i	−0.939865	−	0.341545i
$4$			1.95478i			0.977389i
$5$	−0.684260	+	2.12880i	−0.306010	+	0.952028i
$5$	−0.684260	+	2.12880i	−0.306010	+	0.952028i
$6$	−0.333740	+	0.155831i	−0.136249	+	0.0636176i
$7$	−0.387197	−	0.387197i	−0.146347	−	0.146347i	0.630137	−	0.776484i	$-0.282999\pi$
$7$	−0.387197	−	0.387197i	−0.146347	−	0.146347i	−0.776484	+	0.630137i	$0.782999\pi$
$8$	0.594677	+	0.594677i	0.210250	+	0.210250i
$9$	2.30008	+	1.92604i	0.766694	+	0.642013i
$10$	0.217214	+	0.422998i	0.0686892	+	0.133764i
$11$		−	5.94154i		−	1.79144i	−0.444616	−	0.895721i	$-0.646660\pi$
$11$		−	5.94154i		−	1.79144i	0.444616	−	0.895721i	$-0.353340\pi$
$12$	1.15640	−	3.18217i	0.333823	−	0.918614i
$13$	−2.75083	+	2.75083i	−0.762942	+	0.762942i	−0.976853	−	0.213911i	$-0.931380\pi$
$13$	−2.75083	+	2.75083i	−0.762942	+	0.762942i	0.213911	+	0.976853i	$0.431380\pi$
$14$	−0.116445			−0.0311212
$15$	2.37325	−	3.06067i	0.612769	−	0.790262i
$16$	−3.73071			−0.932679
$17$	−4.13991	+	4.13991i	−1.00408	+	1.00408i	−0.00408352	+	0.999992i	$0.501300\pi$
$17$	−4.13991	+	4.13991i	−1.00408	+	1.00408i	−0.999992	+	0.00408352i	$0.998700\pi$
$18$	0.635479	−	0.0562442i	0.149784	−	0.0132569i
$19$			1.21724i			0.279254i	0.990204	+	0.139627i	$0.0445903\pi$
$19$			1.21724i			0.279254i	−0.990204	+	0.139627i	$0.955410\pi$
$20$	−4.16133	−	1.33758i	−0.930502	−	0.299091i
$21$	0.401260	+	0.859371i	0.0875621	+	0.187530i
$22$	−0.893425	−	0.893425i	−0.190479	−	0.190479i
$23$	−6.27242	−	6.27242i	−1.30789	−	1.30789i	−0.922936	−	0.384954i	$-0.874217\pi$
$23$	−6.27242	−	6.27242i	−1.30789	−	1.30789i	−0.384954	−	0.922936i	$-0.625783\pi$
$24$	−0.616276	−	1.31987i	−0.125797	−	0.269417i
$25$	−4.06358	−	2.91331i	−0.812715	−	0.582661i
$26$			0.827280i			0.162243i
$27$	−2.60489	−	4.49606i	−0.501312	−	0.865267i
$28$	0.756883	−	0.756883i	0.143038	−	0.143038i
$29$	2.83642			0.526709			0.263355	−	0.964699i	$-0.415171\pi$
$29$	2.83642			0.526709			0.263355	+	0.964699i	$0.415171\pi$
$30$	−0.103368	−	0.817094i	−0.0188723	−	0.149180i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−1.75034	+	1.75034i	−0.309419	+	0.309419i
$33$	−3.51486	+	9.67221i	−0.611859	+	1.68371i
$34$			1.24503i			0.213521i
$35$	1.08921	−	0.559321i	0.184110	−	0.0945425i
$36$	−3.76498	+	4.49615i	−0.627497	+	0.749358i
$37$	3.46533	+	3.46533i	0.569697	+	0.569697i	0.932043	−	0.362347i	$-0.118024\pi$
$37$	3.46533	+	3.46533i	0.569697	+	0.569697i	−0.362347	+	0.932043i	$0.618024\pi$
$38$	0.183035	+	0.183035i	0.0296922	+	0.0296922i
$39$	6.10537	−	2.85074i	0.977642	−	0.456483i
$40$	−1.67286	+	0.859035i	−0.264503	+	0.135825i
$41$			6.88424i			1.07514i	0.843220	+	0.537568i	$0.180657\pi$
$41$			6.88424i			1.07514i	−0.843220	+	0.537568i	$0.819343\pi$
$42$	0.189560	+	0.0688858i	0.0292498	+	0.0106293i
$43$	−4.32117	+	4.32117i	−0.658972	+	0.658972i	−0.955137	−	0.296165i	$-0.904292\pi$
$43$	−4.32117	+	4.32117i	−0.658972	+	0.658972i	0.296165	+	0.955137i	$0.404292\pi$
$44$	11.6144			1.75094
$45$	−5.67401	+	3.57850i	−0.845831	+	0.533451i
$46$	−1.88636			−0.278128
$47$	−3.93745	+	3.93745i	−0.574335	+	0.574335i	−0.933337	−	0.359002i	$-0.883117\pi$
$47$	−3.93745	+	3.93745i	−0.574335	+	0.574335i	0.359002	+	0.933337i	$0.383117\pi$
$48$	6.07321	+	2.20699i	0.876592	+	0.318552i
$49$		−	6.70016i		−	0.957165i
$50$	−1.04911	+	0.172965i	−0.148366	+	0.0244610i
$51$	9.18839	−	4.29027i	1.28663	−	0.600758i
$52$	−5.37726	−	5.37726i	−0.745691	−	0.745691i
$53$	−4.51366	−	4.51366i	−0.619999	−	0.619999i	0.325532	−	0.945531i	$-0.394457\pi$
$53$	−4.51366	−	4.51366i	−0.619999	−	0.619999i	−0.945531	+	0.325532i	$0.894457\pi$
$54$	−1.06776	−	0.284373i	−0.145304	−	0.0386982i
$55$	12.6484	+	4.06556i	1.70550	+	0.548200i
$56$		−	0.460514i		−	0.0615388i
$57$	0.720087	−	1.98154i	0.0953778	−	0.262461i
$58$	0.426510	−	0.426510i	0.0560035	−	0.0560035i
$59$	−4.65734			−0.606334			−0.303167	−	0.952937i	$-0.598044\pi$
$59$	−4.65734			−0.606334			−0.303167	+	0.952937i	$0.598044\pi$
$60$	5.98293	+	4.63917i	0.772393	+	0.598914i
$61$	0.744831			0.0953658			0.0476829	−	0.998863i	$-0.484816\pi$
$61$	0.744831			0.0953658			0.0476829	+	0.998863i	$0.484816\pi$
$62$	−0.150369	+	0.150369i	−0.0190969	+	0.0190969i
$63$	−0.144827	−	1.63634i	−0.0182465	−	0.206159i
$64$		−	6.93503i		−	0.866879i
$65$	−3.97368	−	7.73824i	−0.492874	−	0.959811i
$66$	0.925875	+	1.98293i	0.113967	+	0.244082i
$67$	5.51708	+	5.51708i	0.674019	+	0.674019i	0.958640	−	0.284621i	$-0.0918677\pi$
$67$	5.51708	+	5.51708i	0.674019	+	0.674019i	−0.284621	+	0.958640i	$0.591868\pi$
$68$	−8.09260	−	8.09260i	−0.981372	−	0.981372i
$69$	6.50024	+	13.9214i	0.782537	+	1.67594i
$70$	0.0796786	−	0.247888i	0.00952342	−	0.0296283i
$71$			4.91796i			0.583655i	0.956471	+	0.291827i	$0.0942633\pi$
$71$			4.91796i			0.583655i	−0.956471	+	0.291827i	$0.905737\pi$
$72$	0.222433	+	2.51318i	0.0262140	+	0.296181i
$73$	9.51707	−	9.51707i	1.11389	−	1.11389i	0.121270	−	0.992620i	$-0.461303\pi$
$73$	9.51707	−	9.51707i	1.11389	−	1.11389i	0.992620	−	0.121270i	$-0.0386966\pi$
$74$	1.04216			0.121148
$75$	4.89164	+	7.14646i	0.564838	+	0.825202i
$76$	−2.37943			−0.272940
$77$	−2.30055	+	2.30055i	−0.262171	+	0.262171i
$78$	0.489397	−	1.34672i	0.0554133	−	0.152486i
$79$			3.31966i			0.373491i	0.982408	+	0.186745i	$0.0597939\pi$
$79$			3.31966i			0.373491i	−0.982408	+	0.186745i	$0.940206\pi$
$80$	2.55278	−	7.94194i	0.285409	−	0.887936i
$81$	1.58074	+	8.86009i	0.175638	+	0.984455i
$82$	1.03518	+	1.03518i	0.114316	+	0.114316i
$83$	4.12394	+	4.12394i	0.452661	+	0.452661i	0.896237	−	0.443576i	$-0.146290\pi$
$83$	4.12394	+	4.12394i	0.452661	+	0.452661i	−0.443576	+	0.896237i	$0.646290\pi$
$84$	−1.67988	+	0.784374i	−0.183290	+	0.0855822i
$85$	−5.98026	−	11.6458i	−0.648650	−	1.26317i
$86$			1.29954i			0.140133i
$87$	−4.61739	−	1.67795i	−0.495036	−	0.179895i
$88$	3.53330	−	3.53330i	0.376651	−	0.376651i
$89$	−3.87913			−0.411187			−0.205593	−	0.978638i	$-0.565912\pi$
$89$	−3.87913			−0.411187			−0.205593	+	0.978638i	$0.565912\pi$
$90$	−0.315100	+	1.39129i	−0.0332145	+	0.146655i
$91$	2.13022			0.223308
$92$	12.2612	−	12.2612i	1.27832	−	1.27832i
$93$	1.62789	+	0.591574i	0.168805	+	0.0613434i
$94$			1.18414i			0.122135i
$95$	−2.59126	−	0.832908i	−0.265857	−	0.0854546i
$96$	3.88482	−	1.81391i	0.396493	−	0.185132i
$97$	5.32691	+	5.32691i	0.540865	+	0.540865i	0.923783	−	0.382917i	$-0.125081\pi$
$97$	5.32691	+	5.32691i	0.540865	+	0.540865i	−0.382917	+	0.923783i	$0.625081\pi$
$98$	−1.00750	−	1.00750i	−0.101773	−	0.101773i
$99$	11.4436	−	13.6660i	1.15013	−	1.37349i
$100$	5.69487	−	7.94339i	0.569487	−	0.794339i
$101$			3.06803i			0.305280i	0.988282	+	0.152640i	$0.0487775\pi$
$101$			3.06803i			0.305280i	−0.988282	+	0.152640i	$0.951223\pi$
$102$	0.736527	−	2.02678i	0.0729271	−	0.200681i
$103$	6.09837	−	6.09837i	0.600890	−	0.600890i	−0.339658	−	0.940549i	$-0.610311\pi$
$103$	6.09837	−	6.09837i	0.600890	−	0.600890i	0.940549	+	0.339658i	$0.110311\pi$
$104$	−3.27171			−0.320817
$105$	−2.10399	+	0.266169i	−0.205329	+	0.0259754i
$106$	−1.35743			−0.131845
$107$	−6.95342	+	6.95342i	−0.672212	+	0.672212i	−0.958226	−	0.286013i	$-0.907670\pi$
$107$	−6.95342	+	6.95342i	−0.672212	+	0.672212i	0.286013	+	0.958226i	$0.407670\pi$
$108$	8.78879	−	5.09199i	0.845702	−	0.489977i
$109$			18.0090i			1.72495i	0.506103	+	0.862473i	$0.331085\pi$
$109$			18.0090i			1.72495i	−0.506103	+	0.862473i	$0.668915\pi$
$110$	2.51326	−	1.29059i	0.239630	−	0.123053i
$111$	−3.59119	−	7.69119i	−0.340861	−	0.730016i
$112$	1.44452	+	1.44452i	0.136494	+	0.136494i
$113$	−5.26302	−	5.26302i	−0.495104	−	0.495104i	0.414806	−	0.909910i	$-0.363849\pi$
$113$	−5.26302	−	5.26302i	−0.495104	−	0.495104i	−0.909910	+	0.414806i	$0.863849\pi$
$114$	−0.189683	−	0.406241i	−0.0177655	−	0.0380480i
$115$	17.6447	−	9.06076i	1.64538	−	0.844920i
$116$			5.54457i			0.514800i
$117$	−11.6253	+	1.02892i	−1.07476	+	0.0951238i
$118$	−0.700320	+	0.700320i	−0.0644697	+	0.0644697i
$119$	3.20592			0.293886
$120$	3.23143	−	0.408796i	0.294987	−	0.0373178i
$121$	−24.3019			−2.20927
$122$	0.112000	−	0.112000i	0.0101400	−	0.0101400i
$123$	4.07253	−	11.2068i	0.367208	−	1.01048i
$124$		−	1.95478i		−	0.175544i
$125$	8.98239	−	6.65708i	0.803409	−	0.595427i
$126$	−0.267833	−	0.224278i	−0.0238604	−	0.0199802i
$127$	4.38475	+	4.38475i	0.389084	+	0.389084i	0.874361	−	0.485277i	$-0.161281\pi$
$127$	4.38475	+	4.38475i	0.389084	+	0.389084i	−0.485277	+	0.874361i	$0.661281\pi$
$128$	−4.54349	−	4.54349i	−0.401592	−	0.401592i
$129$	9.59070	−	4.47812i	0.844414	−	0.394276i
$130$	−1.76111	−	0.566075i	−0.154460	−	0.0496480i
$131$			12.5892i			1.09993i	0.835189	+	0.549963i	$0.185358\pi$
$131$			12.5892i			1.09993i	−0.835189	+	0.549963i	$0.814642\pi$
$132$	−18.9070	−	6.87078i	−1.64564	−	0.598024i
$133$	0.471311	−	0.471311i	0.0408678	−	0.0408678i
$134$	1.65920			0.143333
$135$	11.3536	−	2.46882i	0.977165	−	0.212482i
$136$	−4.92382			−0.422214
$137$	−7.88928	+	7.88928i	−0.674027	+	0.674027i	−0.958642	−	0.284615i	$-0.908134\pi$
$137$	−7.88928	+	7.88928i	−0.674027	+	0.674027i	0.284615	+	0.958642i	$0.408134\pi$
$138$	3.07079	+	1.11592i	0.261403	+	0.0949935i
$139$			17.9929i			1.52614i	0.646316	+	0.763070i	$0.276309\pi$
$139$			17.9929i			1.52614i	−0.646316	+	0.763070i	$0.723691\pi$
$140$	1.09335	+	2.12916i	0.0924048	+	0.179947i
$141$	8.73904	−	4.08046i	0.735960	−	0.343636i
$142$	0.739510	+	0.739510i	0.0620583	+	0.0620583i
$143$	16.3442	+	16.3442i	1.36677	+	1.36677i
$144$	−8.58094	−	7.18550i	−0.715079	−	0.598792i
$145$	−1.94085	+	6.03816i	−0.161179	+	0.501442i
$146$		−	2.86215i		−	0.236873i
$147$	−3.96364	+	10.9071i	−0.326915	+	0.899607i
$148$	−6.77395	+	6.77395i	−0.556816	+	0.556816i
$149$	4.60051			0.376888			0.188444	−	0.982084i	$-0.439656\pi$
$149$	4.60051			0.376888			0.188444	+	0.982084i	$0.439656\pi$
$150$	1.81016	+	0.339056i	0.147799	+	0.0276838i
$151$	6.31707			0.514076			0.257038	−	0.966401i	$-0.417253\pi$
$151$	6.31707			0.514076			0.257038	+	0.966401i	$0.417253\pi$
$152$	−0.723864	+	0.723864i	−0.0587131	+	0.0587131i
$153$	−17.4957	+	1.54849i	−1.41445	+	0.125188i
$154$			0.691863i			0.0557519i
$155$	0.684260	−	2.12880i	0.0549611	−	0.170989i
$156$	5.57256	+	11.9347i	0.446162	+	0.955537i
$157$	−7.07817	−	7.07817i	−0.564899	−	0.564899i	0.365796	−	0.930695i	$-0.380797\pi$
$157$	−7.07817	−	7.07817i	−0.564899	−	0.564899i	−0.930695	+	0.365796i	$0.880797\pi$
$158$	0.499174	+	0.499174i	0.0397122	+	0.0397122i
$159$	4.67760	+	10.0179i	0.370958	+	0.794473i
$160$	−2.52843	−	4.92381i	−0.199890	−	0.389261i
$161$			4.85732i			0.382810i
$162$	1.56998	+	1.09459i	0.123349	+	0.0859992i
$163$	−6.57855	+	6.57855i	−0.515272	+	0.515272i	−0.916137	−	0.400865i	$-0.868710\pi$
$163$	−6.57855	+	6.57855i	−0.515272	+	0.515272i	0.400865	+	0.916137i	$0.368710\pi$
$164$	−13.4572			−1.05083
$165$	−18.1851	−	14.1007i	−1.41571	−	1.09774i
$166$	1.24023			0.0962603
$167$	0.410469	−	0.410469i	0.0317630	−	0.0317630i	−0.691047	−	0.722810i	$-0.742850\pi$
$167$	0.410469	−	0.410469i	0.0317630	−	0.0317630i	0.722810	+	0.691047i	$0.242850\pi$
$168$	−0.272428	+	0.749668i	−0.0210183	+	0.0578381i
$169$		−	2.13410i		−	0.164161i
$170$	−2.65042	−	0.851924i	−0.203278	−	0.0653396i
$171$	−2.34445	+	2.79975i	−0.179285	+	0.214102i
$172$	−8.44693	−	8.44693i	−0.644072	−	0.644072i
$173$	15.4838	+	15.4838i	1.17721	+	1.17721i	0.980453	+	0.196756i	$0.0630405\pi$
$173$	15.4838	+	15.4838i	1.17721	+	1.17721i	0.196756	+	0.980453i	$0.436959\pi$
$174$	−0.946625	+	0.442001i	−0.0717635	+	0.0335080i
$175$	0.445381	+	2.70142i	0.0336676	+	0.204209i
$176$			22.1662i			1.67084i
$177$	7.58165	+	2.75516i	0.569872	+	0.207090i
$178$	−0.583302	+	0.583302i	−0.0437203	+	0.0437203i
$179$	−12.8633			−0.961447			−0.480723	−	0.876872i	$-0.659626\pi$
$179$	−12.8633			−0.961447			−0.480723	+	0.876872i	$0.659626\pi$
$180$	−6.99517	−	11.0914i	−0.521389	−	0.826706i
$181$	1.90600			0.141672			0.0708359	−	0.997488i	$-0.477433\pi$
$181$	1.90600			0.141672			0.0708359	+	0.997488i	$0.477433\pi$
$182$	0.320320	−	0.320320i	0.0237437	−	0.0237437i
$183$	−1.21251	−	0.440622i	−0.0896310	−	0.0325717i
$184$		−	7.46013i		−	0.549968i
$185$	−9.74818	+	5.00581i	−0.716701	+	0.368034i
$186$	0.333740	−	0.155831i	0.0244710	−	0.0114261i
$187$	24.5974	+	24.5974i	1.79874	+	1.79874i
$188$	−7.69683	−	7.69683i	−0.561349	−	0.561349i
$189$	−0.732252	+	2.74946i	−0.0532635	+	0.199994i
$190$	−0.514889	+	0.264402i	−0.0373540	+	0.0191817i
$191$		−	22.1386i		−	1.60189i	−0.598738	−	0.800945i	$-0.704331\pi$
$191$		−	22.1386i		−	1.60189i	0.598738	−	0.800945i	$-0.295669\pi$
$192$	−4.10259	+	11.2895i	−0.296079	+	0.814750i
$193$	11.1630	−	11.1630i	0.803532	−	0.803532i	−0.180114	−	0.983646i	$-0.557647\pi$
$193$	11.1630	−	11.1630i	0.803532	−	0.803532i	0.983646	+	0.180114i	$0.0576466\pi$
$194$	1.60201			0.115017
$195$	1.89099	+	14.9478i	0.135416	+	1.07043i
$196$	13.0973			0.935523
$197$	3.08689	−	3.08689i	0.219932	−	0.219932i	−0.588538	−	0.808470i	$-0.700296\pi$
$197$	3.08689	−	3.08689i	0.219932	−	0.219932i	0.808470	+	0.588538i	$0.200296\pi$
$198$	−0.334178	−	3.77572i	−0.0237490	−	0.268329i
$199$		−	26.9148i		−	1.90794i	−0.299907	−	0.953968i	$-0.596956\pi$
$199$		−	26.9148i		−	1.90794i	0.299907	−	0.953968i	$-0.403044\pi$
$200$	−0.684039	−	4.14899i	−0.0483689	−	0.293378i
$201$	−5.71747	−	12.2450i	−0.403279	−	0.863695i
$202$	0.461337	+	0.461337i	0.0324595	+	0.0324595i
$203$	−1.09825	−	1.09825i	−0.0770821	−	0.0770821i
$204$	8.38653	+	17.9613i	0.587174	+	1.25754i
$205$	−14.6552	−	4.71061i	−1.02356	−	0.329003i
$206$		−	1.83402i		−	0.127782i
$207$	−2.34614	−	26.5080i	−0.163068	−	1.84243i
$208$	10.2625	−	10.2625i	0.711580	−	0.711580i
$209$	7.23228			0.500267
$210$	−0.276352	+	0.356400i	−0.0190701	+	0.0245939i
$211$	−16.3188			−1.12344			−0.561718	−	0.827329i	$-0.689859\pi$
$211$	−16.3188			−1.12344			−0.561718	+	0.827329i	$0.689859\pi$
$212$	8.82320	−	8.82320i	0.605980	−	0.605980i
$213$	2.90934	−	8.00592i	0.199345	−	0.548557i
$214$			2.09116i			0.142949i
$215$	−6.24210	−	12.1557i	−0.425708	−	0.829012i
$216$	1.12463	−	4.22277i	0.0765215	−	0.287323i
$217$	0.387197	+	0.387197i	0.0262846	+	0.0262846i
$218$	2.70799	+	2.70799i	0.183408	+	0.183408i
$219$	−21.1228	+	9.86274i	−1.42735	+	0.666462i
$220$	−7.94727	+	24.7247i	−0.535805	+	1.66694i
$221$		−	22.7763i		−	1.53210i
$222$	−1.69652	−	0.616514i	−0.113863	−	0.0413777i
$223$	−2.38293	+	2.38293i	−0.159573	+	0.159573i	−0.782377	−	0.622805i	$-0.785993\pi$
$223$	−2.38293	+	2.38293i	−0.159573	+	0.159573i	0.622805	+	0.782377i	$0.285993\pi$
$224$	1.35545			0.0905649
$225$	−3.73541	−	14.5274i	−0.249027	−	0.968496i
$226$	−1.58279			−0.105286
$227$	−5.53741	+	5.53741i	−0.367531	+	0.367531i	−0.866576	−	0.499045i	$-0.833684\pi$
$227$	−5.53741	+	5.53741i	−0.367531	+	0.367531i	0.499045	+	0.866576i	$0.333684\pi$
$228$	3.87346	+	1.40761i	0.256526	+	0.0932212i
$229$			16.0544i			1.06090i	0.847715	+	0.530452i	$0.177978\pi$
$229$			16.0544i			1.06090i	−0.847715	+	0.530452i	$0.822022\pi$
$230$	1.29076	−	4.01568i	0.0851102	−	0.264786i
$231$	5.10599	−	2.38410i	0.335949	−	0.156862i
$232$	1.68675	+	1.68675i	0.110741	+	0.110741i
$233$	3.58715	+	3.58715i	0.235002	+	0.235002i	0.814777	−	0.579775i	$-0.196859\pi$
$233$	3.58715	+	3.58715i	0.235002	+	0.235002i	−0.579775	+	0.814777i	$0.696859\pi$
$234$	−1.59337	+	1.90281i	−0.104162	+	0.124391i
$235$	−5.68780	−	11.0763i	−0.371031	−	0.722536i
$236$		−	9.10406i		−	0.592624i
$237$	1.96382	−	5.40405i	0.127564	−	0.351031i
$238$	0.482071	−	0.482071i	0.0312480	−	0.0312480i
$239$	12.0021			0.776352			0.388176	−	0.921585i	$-0.373105\pi$
$239$	12.0021			0.776352			0.388176	+	0.921585i	$0.373105\pi$
$240$	−8.85390	+	11.4185i	−0.571517	+	0.737060i
$241$	−14.8788			−0.958430			−0.479215	−	0.877698i	$-0.659079\pi$
$241$	−14.8788			−0.958430			−0.479215	+	0.877698i	$0.659079\pi$
$242$	−3.65426	+	3.65426i	−0.234905	+	0.234905i
$243$	2.66812	−	15.3584i	0.171160	−	0.985243i
$244$			1.45598i			0.0932095i
$245$	14.2633	+	4.58465i	0.911248	+	0.292903i
$246$	−1.07278	−	2.29754i	−0.0683977	−	0.146486i
$247$	−3.34841	−	3.34841i	−0.213054	−	0.213054i
$248$	−0.594677	−	0.594677i	−0.0377620	−	0.0377620i
$249$	−4.27372	−	9.15295i	−0.270836	−	0.580045i
$250$	0.349655	−	2.35170i	0.0221141	−	0.148734i
$251$			25.4696i			1.60763i	0.594882	+	0.803813i	$0.297199\pi$
$251$			25.4696i			1.60763i	−0.594882	+	0.803813i	$0.702801\pi$
$252$	3.19868	−	0.283105i	0.201498	−	0.0178340i
$253$	−37.2679	+	37.2679i	−2.34301	+	2.34301i
$254$	1.31866			0.0827404
$255$	2.84588	+	22.4959i	0.178216	+	1.40875i
$256$	12.5037			0.781479
$257$	−10.4714	+	10.4714i	−0.653188	+	0.653188i	−0.953759	−	0.300572i	$-0.902823\pi$
$257$	−10.4714	+	10.4714i	−0.653188	+	0.653188i	0.300572	+	0.953759i	$0.402823\pi$
$258$	0.768775	−	2.11552i	0.0478619	−	0.131706i
$259$		−	2.68353i		−	0.166746i
$260$	15.1265	−	7.76766i	0.938108	−	0.481730i
$261$	6.52399	+	5.46305i	0.403825	+	0.338154i
$262$	1.89303	+	1.89303i	0.116952	+	0.116952i
$263$	−3.06882	−	3.06882i	−0.189232	−	0.189232i	0.606132	−	0.795364i	$-0.292720\pi$
$263$	−3.06882	−	3.06882i	−0.189232	−	0.189232i	−0.795364	+	0.606132i	$0.792720\pi$
$264$	−7.84205	+	3.66163i	−0.482645	+	0.225358i
$265$	12.6972	−	6.52016i	0.779983	−	0.400530i
$266$		−	0.141741i		−	0.00869072i
$267$	6.31481	+	2.29479i	0.386460	+	0.140439i
$268$	−10.7847	+	10.7847i	−0.658779	+	0.658779i
$269$	25.2332			1.53850			0.769248	−	0.638950i	$-0.220631\pi$
$269$	25.2332			1.53850			0.769248	+	0.638950i	$0.220631\pi$
$270$	1.33600	−	2.07847i	0.0813065	−	0.126492i
$271$	−12.5505			−0.762388			−0.381194	−	0.924495i	$-0.624487\pi$
$271$	−12.5505			−0.762388			−0.381194	+	0.924495i	$0.624487\pi$
$272$	15.4448	−	15.4448i	0.936479	−	0.936479i
$273$	−3.46778	−	1.26018i	−0.209879	−	0.0762698i
$274$			2.37261i			0.143335i
$275$	−17.3095	+	24.1439i	−1.04380	+	1.45593i
$276$	−27.2133	+	12.7065i	−1.63805	+	0.764843i
$277$	−8.03940	−	8.03940i	−0.483041	−	0.483041i	0.423061	−	0.906101i	$-0.360956\pi$
$277$	−8.03940	−	8.03940i	−0.483041	−	0.483041i	−0.906101	+	0.423061i	$0.860956\pi$
$278$	2.70558	+	2.70558i	0.162270	+	0.162270i
$279$	−2.30008	−	1.92604i	−0.137702	−	0.115309i
$280$	0.980342	+	0.315111i	0.0585866	+	0.0188315i
$281$		−	25.6247i		−	1.52864i	−0.644835	−	0.764322i	$-0.723074\pi$
$281$		−	25.6247i		−	1.52864i	0.644835	−	0.764322i	$-0.276926\pi$
$282$	0.700507	−	1.92766i	0.0417146	−	0.114790i
$283$	5.80564	−	5.80564i	0.345109	−	0.345109i	−0.513175	−	0.858284i	$-0.671531\pi$
$283$	5.80564	−	5.80564i	0.345109	−	0.345109i	0.858284	+	0.513175i	$0.171531\pi$
$284$	−9.61353			−0.570458
$285$	3.72557	+	2.88881i	0.220684	+	0.171118i
$286$	4.91532			0.290649
$287$	2.66555	−	2.66555i	0.157343	−	0.157343i
$288$	−7.39714	+	0.654698i	−0.435881	+	0.0385785i
$289$		−	17.2777i		−	1.01633i
$290$	0.616111	+	1.19980i	0.0361793	+	0.0704546i
$291$	−5.52038	−	11.8229i	−0.323611	−	0.693071i
$292$	18.6038	+	18.6038i	1.08870	+	1.08870i
$293$	3.49594	+	3.49594i	0.204235	+	0.204235i	0.801812	−	0.597577i	$-0.203870\pi$
$293$	3.49594	+	3.49594i	0.204235	+	0.204235i	−0.597577	+	0.801812i	$0.703870\pi$
$294$	1.04409	+	2.23611i	0.0608926	+	0.130413i
$295$	3.18683	−	9.91454i	0.185544	−	0.577247i
$296$			4.12151i			0.239558i
$297$	−26.7135	+	15.4771i	−1.55008	+	0.898072i
$298$	0.691775	−	0.691775i	0.0400734	−	0.0400734i
$299$	34.5087			1.99569
$300$	−13.9697	+	9.56207i	−0.806544	+	0.552066i
$301$	3.34628			0.192877
$302$	0.949893	−	0.949893i	0.0546602	−	0.0546602i
$303$	1.81496	−	4.99442i	0.104267	−	0.286922i
$304$		−	4.54117i		−	0.260454i
$305$	−0.509658	+	1.58560i	−0.0291829	+	0.0907909i
$306$	−2.39798	+	2.86367i	−0.137083	+	0.163705i
$307$	−21.3502	−	21.3502i	−1.21852	−	1.21852i	−0.968150	−	0.250370i	$-0.919448\pi$
$307$	−21.3502	−	21.3502i	−1.21852	−	1.21852i	−0.250370	−	0.968150i	$-0.580552\pi$
$308$	−4.49706	−	4.49706i	−0.256244	−	0.256244i
$309$	−13.5351	+	6.31987i	−0.769987	+	0.359525i
$310$	−0.217214	−	0.422998i	−0.0123369	−	0.0240247i
$311$		−	14.4807i		−	0.821128i	−0.911832	−	0.410564i	$-0.865332\pi$
$311$		−	14.4807i		−	0.821128i	0.911832	−	0.410564i	$-0.134668\pi$
$312$	5.32599	+	1.93546i	0.301525	+	0.109574i
$313$	−15.6700	+	15.6700i	−0.885720	+	0.885720i	−0.994109	−	0.108389i	$-0.965431\pi$
$313$	−15.6700	+	15.6700i	−0.885720	+	0.885720i	0.108389	+	0.994109i	$0.465431\pi$
$314$	−2.12868			−0.120128
$315$	3.58254	+	0.811374i	0.201853	+	0.0457157i
$316$	−6.48919			−0.365046
$317$	1.91432	−	1.91432i	0.107519	−	0.107519i	−0.651301	−	0.758820i	$-0.725776\pi$
$317$	1.91432	−	1.91432i	0.107519	−	0.107519i	0.758820	+	0.651301i	$0.225776\pi$
$318$	2.20976	+	0.803021i	0.123917	+	0.0450312i
$319$		−	16.8527i		−	0.943570i
$320$	14.7633	+	4.74537i	0.825293	+	0.265274i
$321$	15.4329	−	7.20597i	0.861380	−	0.402198i
$322$	0.730392	+	0.730392i	0.0407031	+	0.0407031i
$323$	−5.03926	−	5.03926i	−0.280392	−	0.280392i
$324$	−17.3195	+	3.09000i	−0.962195	+	0.171667i
$325$	19.1922	−	3.16419i	1.06459	−	0.175518i
$326$			1.97842i			0.109575i
$327$	10.6536	−	29.3167i	0.589147	−	1.62122i
$328$	−4.09390	+	4.09390i	−0.226048	+	0.226048i
$329$	3.04913			0.168104
$330$	−4.85480	+	0.614163i	−0.267248	+	0.0338086i
$331$	−19.9462			−1.09634			−0.548170	−	0.836367i	$-0.684675\pi$
$331$	−19.9462			−1.09634			−0.548170	+	0.836367i	$0.684675\pi$
$332$	−8.06139	+	8.06139i	−0.442426	+	0.442426i
$333$	1.29618	+	14.6449i	0.0710300	+	0.802536i
$334$		−	0.123444i		−	0.00675454i
$335$	−15.5199	+	7.96965i	−0.847942	+	0.435428i
$336$	−1.49699	−	3.20607i	−0.0816673	−	0.174905i
$337$	−3.51648	−	3.51648i	−0.191555	−	0.191555i	0.604813	−	0.796368i	$-0.293248\pi$
$337$	−3.51648	−	3.51648i	−0.191555	−	0.191555i	−0.796368	+	0.604813i	$0.793248\pi$
$338$	−0.320903	−	0.320903i	−0.0174548	−	0.0174548i
$339$	5.45418	+	11.6811i	0.296230	+	0.634431i
$340$	22.7650	−	11.6901i	1.23460	−	0.633984i
$341$			5.94154i			0.321753i
$342$	0.0684627	+	0.773529i	0.00370204	+	0.0418277i
$343$	−5.30465	+	5.30465i	−0.286424	+	0.286424i
$344$	−5.13940			−0.277098
$345$	−34.0838	+	4.31182i	−1.83501	+	0.232140i
$346$	4.65656			0.250338
$347$	5.30489	−	5.30489i	0.284781	−	0.284781i	−0.550231	−	0.835012i	$-0.685460\pi$
$347$	5.30489	−	5.30489i	0.284781	−	0.284781i	0.835012	+	0.550231i	$0.185460\pi$
$348$	3.28002	−	9.02597i	0.175828	−	0.483843i
$349$			18.3193i			0.980610i	0.871551	+	0.490305i	$0.163115\pi$
$349$			18.3193i			0.980610i	−0.871551	+	0.490305i	$0.836885\pi$
$350$	0.473183	+	0.339240i	0.0252927	+	0.0181331i
$351$	19.5335	+	5.20226i	1.04262	+	0.277676i
$352$	10.3997	+	10.3997i	0.554307	+	0.554307i
$353$	−22.8752	−	22.8752i	−1.21752	−	1.21752i	−0.968497	−	0.249024i	$-0.919890\pi$
$353$	−22.8752	−	22.8752i	−1.21752	−	1.21752i	−0.249024	−	0.968497i	$-0.580110\pi$
$354$	1.55434	−	0.725756i	0.0826122	−	0.0385735i
$355$	−10.4694	−	3.36517i	−0.555656	−	0.178604i
$356$		−	7.58284i		−	0.401889i
$357$	−5.21889	−	1.89654i	−0.276213	−	0.100375i
$358$	−1.93424	+	1.93424i	−0.102228	+	0.102228i
$359$	−15.1609			−0.800161			−0.400080	−	0.916480i	$-0.631018\pi$
$359$	−15.1609			−0.800161			−0.400080	+	0.916480i	$0.631018\pi$
$360$	−5.50225	−	1.24615i	−0.289994	−	0.0656779i
$361$	17.5183			0.922017
$362$	0.286603	−	0.286603i	0.0150635	−	0.0150635i
$363$	39.5610	+	14.3764i	2.07641	+	0.754565i
$364$			4.16411i			0.218259i
$365$	13.7478	+	26.7721i	0.719592	+	1.40132i
$366$	−0.248580	+	0.116068i	−0.0129935	+	0.00606695i
$367$	1.01193	+	1.01193i	0.0528225	+	0.0528225i	0.733025	−	0.680202i	$-0.238108\pi$
$367$	1.01193	+	1.01193i	0.0528225	+	0.0528225i	−0.680202	+	0.733025i	$0.738108\pi$
$368$	23.4006	+	23.4006i	1.21984	+	1.21984i
$369$	−13.2593	+	15.8343i	−0.690252	+	0.824301i
$370$	−0.713108	+	2.21855i	−0.0370727	+	0.115337i
$371$			3.49535i			0.181469i
$372$	−1.15640	+	3.18217i	−0.0599563	+	0.164988i
$373$	15.2384	−	15.2384i	0.789015	−	0.789015i	−0.192317	−	0.981333i	$-0.561600\pi$
$373$	15.2384	−	15.2384i	0.789015	−	0.789015i	0.981333	+	0.192317i	$0.0616003\pi$
$374$	7.39740			0.382510
$375$	−18.5605	+	5.52328i	−0.958462	+	0.285221i
$376$	−4.68302			−0.241508
$377$	−7.80249	+	7.80249i	−0.401849	+	0.401849i
$378$	0.303327	+	0.523543i	0.0156014	+	0.0269282i
$379$		−	12.6527i		−	0.649926i	−0.945727	−	0.324963i	$-0.894648\pi$
$379$		−	12.6527i		−	0.649926i	0.945727	−	0.324963i	$-0.105352\pi$
$380$	1.62815	−	5.06533i	0.0835224	−	0.259846i
$381$	−4.54401	−	9.73182i	−0.232797	−	0.498576i
$382$	−3.32896	−	3.32896i	−0.170324	−	0.170324i
$383$	15.8313	+	15.8313i	0.808941	+	0.808941i	0.984474	−	0.175533i	$-0.0561648\pi$
$383$	15.8313	+	15.8313i	0.808941	+	0.808941i	−0.175533	+	0.984474i	$0.556165\pi$
$384$	4.70852	+	10.0841i	0.240280	+	0.514604i
$385$	−3.32323	−	6.47157i	−0.169367	−	0.329822i
$386$		−	3.35715i		−	0.170874i
$387$	−18.2618	+	1.61629i	−0.928299	+	0.0821608i
$388$	−10.4129	+	10.4129i	−0.528636	+	0.528636i
$389$	−15.1891			−0.770119			−0.385059	−	0.922892i	$-0.625819\pi$
$389$	−15.1891			−0.770119			−0.385059	+	0.922892i	$0.625819\pi$
$390$	2.53203	+	1.96334i	0.128214	+	0.0994175i
$391$	51.9345			2.62644
$392$	3.98443	−	3.98443i	0.201244	−	0.201244i
$393$	7.44745	−	20.4939i	0.375674	−	1.03378i
$394$		−	0.928346i		−	0.0467694i
$395$	−7.06689	−	2.27151i	−0.355574	−	0.114292i
$396$	26.7141	+	22.3698i	1.34243	+	1.12412i
$397$	−0.341751	−	0.341751i	−0.0171520	−	0.0171520i	0.698479	−	0.715631i	$-0.253861\pi$
$397$	−0.341751	−	0.341751i	−0.0171520	−	0.0171520i	−0.715631	+	0.698479i	$0.753861\pi$
$398$	−4.04715	−	4.04715i	−0.202865	−	0.202865i
$399$	−1.04606	+	0.488429i	−0.0523685	+	0.0244520i
$400$	15.1600	+	10.8687i	0.758002	+	0.543436i
$401$			24.8749i			1.24219i	0.783733	+	0.621097i	$0.213313\pi$
$401$			24.8749i			1.24219i	−0.783733	+	0.621097i	$0.786687\pi$
$402$	−2.70100	−	0.981539i	−0.134714	−	0.0489547i
$403$	2.75083	−	2.75083i	0.137028	−	0.137028i
$404$	−5.99731			−0.298377
$405$	−19.9430	−	2.69753i	−0.990976	−	0.134041i
$406$	−0.330286			−0.0163918
$407$	20.5894	−	20.5894i	1.02058	−	1.02058i
$408$	8.01545	+	2.91280i	0.396824	+	0.144205i
$409$		−	35.0261i		−	1.73193i	−0.500107	−	0.865964i	$-0.666706\pi$
$409$		−	35.0261i		−	1.73193i	0.500107	−	0.865964i	$-0.333294\pi$
$410$	−2.91202	+	1.49535i	−0.143814	+	0.0738503i
$411$	17.5100	−	8.17583i	0.863706	−	0.403284i
$412$	11.9210	+	11.9210i	0.587304	+	0.587304i
$413$	1.80331	+	1.80331i	0.0887349	+	0.0887349i
$414$	−4.33878	−	3.63320i	−0.213239	−	0.178562i
$415$	−11.6009	+	5.95719i	−0.569465	+	0.292427i
$416$		−	9.62976i		−	0.472138i
$417$	10.6441	−	29.2906i	0.521246	−	1.43437i
$418$	1.08751	−	1.08751i	0.0531920	−	0.0531920i
$419$	−11.3426			−0.554122			−0.277061	−	0.960852i	$-0.589360\pi$
$419$	−11.3426			−0.554122			−0.277061	+	0.960852i	$0.589360\pi$
$420$	−0.520301	−	4.11284i	−0.0253881	−	0.200686i
$421$	7.44294			0.362747			0.181373	−	0.983414i	$-0.441946\pi$
$421$	7.44294			0.362747			0.181373	+	0.983414i	$0.441946\pi$
$422$	−2.45385	+	2.45385i	−0.119452	+	0.119452i
$423$	−16.6401	+	1.47277i	−0.809070	+	0.0716083i
$424$		−	5.36834i		−	0.260710i
$425$	28.8836	−	4.76201i	1.40106	−	0.230992i
$426$	−0.766370	−	1.64132i	−0.0371307	−	0.0795222i
$427$	−0.288396	−	0.288396i	−0.0139565	−	0.0139565i
$428$	−13.5924	−	13.5924i	−0.657013	−	0.657013i
$429$	−16.9378	−	36.2753i	−0.817764	−	1.75139i
$430$	−2.76647	−	0.889225i	−0.133411	−	0.0428822i
$431$		−	22.7224i		−	1.09450i	−0.836970	−	0.547249i	$-0.815675\pi$
$431$		−	22.7224i		−	1.09450i	0.836970	−	0.547249i	$-0.184325\pi$
$432$	9.71811	+	16.7735i	0.467563	+	0.807016i
$433$	−5.15688	+	5.15688i	−0.247824	+	0.247824i	−0.820077	−	0.572253i	$-0.806069\pi$
$433$	−5.15688	+	5.15688i	−0.247824	+	0.247824i	0.572253	+	0.820077i	$0.306069\pi$
$434$	0.116445			0.00558954
$435$	6.73152	−	8.68134i	0.322751	−	0.416238i
$436$	−35.2035			−1.68594
$437$	7.63503	−	7.63503i	0.365233	−	0.365233i
$438$	−1.69317	+	4.65928i	−0.0809030	+	0.222629i
$439$		−	14.9779i		−	0.714858i	−0.933940	−	0.357429i	$-0.883653\pi$
$439$		−	14.9779i		−	0.714858i	0.933940	−	0.357429i	$-0.116347\pi$
$440$	5.10399	+	9.93938i	0.243323	+	0.473841i
$441$	12.9048	−	15.4109i	0.614513	−	0.733852i
$442$	−3.42486	−	3.42486i	−0.162904	−	0.162904i
$443$	13.6735	+	13.6735i	0.649648	+	0.649648i	0.952908	−	0.303260i	$-0.0980751\pi$
$443$	13.6735	+	13.6735i	0.649648	+	0.649648i	−0.303260	+	0.952908i	$0.598075\pi$
$444$	15.0346	−	7.01999i	0.713509	−	0.333154i
$445$	2.65433	−	8.25789i	0.125827	−	0.391461i
$446$			0.716638i			0.0339338i
$447$	−7.48914	−	2.72154i	−0.354224	−	0.128724i
$448$	−2.68522	+	2.68522i	−0.126865	+	0.126865i
$449$	−1.47057			−0.0694006			−0.0347003	−	0.999398i	$-0.511048\pi$
$449$	−1.47057			−0.0694006			−0.0347003	+	0.999398i	$0.511048\pi$
$450$	−2.74617	−	1.62279i	−0.129456	−	0.0764991i
$451$	40.9030			1.92605
$452$	10.2880	−	10.2880i	0.483909	−	0.483909i
$453$	−10.2835	−	3.73701i	−0.483162	−	0.175580i
$454$			1.66531i			0.0781569i
$455$	−1.45763	+	4.53482i	−0.0683346	+	0.212595i
$456$	1.60659	−	0.750155i	0.0752356	−	0.0351292i
$457$	12.9890	+	12.9890i	0.607602	+	0.607602i	0.942319	−	0.334717i	$-0.108641\pi$
$457$	12.9890	+	12.9890i	0.607602	+	0.607602i	−0.334717	+	0.942319i	$0.608641\pi$
$458$	2.41408	+	2.41408i	0.112803	+	0.112803i
$459$	29.3973	+	7.82924i	1.37215	+	0.365438i
$460$	17.7118	+	34.4915i	0.825816	+	1.60817i
$461$		−	16.5999i		−	0.773133i	−0.922262	−	0.386567i	$-0.873661\pi$
$461$		−	16.5999i		−	0.773133i	0.922262	−	0.386567i	$-0.126339\pi$
$462$	0.409288	−	1.12628i	0.0190418	−	0.0523993i
$463$	−2.21616	+	2.21616i	−0.102994	+	0.102994i	−0.756726	−	0.653732i	$-0.773202\pi$
$463$	−2.21616	+	2.21616i	−0.102994	+	0.102994i	0.653732	+	0.756726i	$0.273202\pi$
$464$	−10.5819			−0.491251
$465$	−2.37325	+	3.06067i	−0.110057	+	0.141935i
$466$	1.07879			0.0499742
$467$	6.70869	−	6.70869i	0.310441	−	0.310441i	−0.534639	−	0.845080i	$-0.679553\pi$
$467$	6.70869	−	6.70869i	0.310441	−	0.310441i	0.845080	+	0.534639i	$0.179553\pi$
$468$	−2.01131	−	22.7249i	−0.0929730	−	1.05046i
$469$		−	4.27239i		−	0.197281i
$470$	−2.52080	−	0.810261i	−0.116276	−	0.0373745i
$471$	7.33525	+	15.7098i	0.337991	+	0.723868i
$472$	−2.76961	−	2.76961i	−0.127482	−	0.127482i
$473$	25.6744	+	25.6744i	1.18051	+	1.18051i
$474$	−0.517305	−	1.10790i	−0.0237606	−	0.0508876i
$475$	3.54619	−	4.94634i	0.162710	−	0.226954i
$476$			6.26686i			0.287241i
$477$	−1.68829	−	19.0753i	−0.0773016	−	0.873397i
$478$	1.80475	−	1.80475i	0.0825473	−	0.0825473i
$479$	17.5332			0.801112			0.400556	−	0.916272i	$-0.368817\pi$
$479$	17.5332			0.801112			0.400556	+	0.916272i	$0.368817\pi$
$480$	1.20323	+	9.51119i	0.0549195	+	0.434125i
$481$	−19.0651			−0.869292
$482$	−2.23732	+	2.23732i	−0.101907	+	0.101907i
$483$	2.87346	−	7.90720i	0.130747	−	0.359790i
$484$		−	47.5049i		−	2.15931i
$485$	−14.9849	+	7.69493i	−0.680430	+	0.349409i
$486$	−1.90823	−	2.71064i	−0.0865591	−	0.122957i
$487$	16.5622	+	16.5622i	0.750506	+	0.750506i	0.974574	−	0.224067i	$-0.0719336\pi$
$487$	16.5622	+	16.5622i	0.750506	+	0.750506i	−0.224067	+	0.974574i	$0.571934\pi$
$488$	0.442934	+	0.442934i	0.0200507	+	0.0200507i
$489$	14.6009	−	6.81749i	0.660275	−	0.308298i
$490$	2.83415	−	1.45537i	0.128034	−	0.0657469i
$491$			43.8967i			1.98103i	0.137409	+	0.990514i	$0.456123\pi$
$491$			43.8967i			1.98103i	−0.137409	+	0.990514i	$0.543877\pi$
$492$	21.9068	+	7.96090i	0.987636	+	0.358905i
$493$	−11.7425	+	11.7425i	−0.528856	+	0.528856i
$494$	−1.00700			−0.0453069
$495$	21.2618	+	33.7124i	0.955647	+	1.51526i
$496$	3.73071			0.167514
$497$	1.90422	−	1.90422i	0.0854159	−	0.0854159i
$498$	−2.01896	−	0.733686i	−0.0904717	−	0.0328773i
$499$			2.06424i			0.0924083i	0.998932	+	0.0462041i	$0.0147125\pi$
$499$			2.06424i			0.0924083i	−0.998932	+	0.0462041i	$0.985288\pi$
$500$	13.0131	+	17.5586i	0.581964	+	0.785243i
$501$	−0.911023	+	0.425377i	−0.0407015	+	0.0190045i
$502$	3.82984	+	3.82984i	0.170934	+	0.170934i
$503$	−3.64758	−	3.64758i	−0.162637	−	0.162637i	0.621097	−	0.783734i	$-0.286687\pi$
$503$	−3.64758	−	3.64758i	−0.162637	−	0.162637i	−0.783734	+	0.621097i	$0.786687\pi$
$504$	0.886968	−	1.05922i	0.0395087	−	0.0471814i
$505$	−6.53121	−	2.09933i	−0.290635	−	0.0934189i
$506$			11.2079i			0.498251i
$507$	−1.26248	+	3.47409i	−0.0560686	+	0.154290i
$508$	−8.57122	+	8.57122i	−0.380286	+	0.380286i
$509$	2.71268			0.120237			0.0601187	−	0.998191i	$-0.480852\pi$
$509$	2.71268			0.120237			0.0601187	+	0.998191i	$0.480852\pi$
$510$	3.81063	+	2.95476i	0.168737	+	0.130839i
$511$	−7.36996			−0.326028
$512$	10.9672	−	10.9672i	0.484684	−	0.484684i
$513$	5.47278	−	3.17078i	0.241629	−	0.139993i
$514$			3.14915i			0.138903i
$515$	8.80934	+	17.1551i	0.388186	+	0.755943i
$516$	8.75373	+	18.7477i	0.385361	+	0.825321i
$517$	23.3945	+	23.3945i	1.02889	+	1.02889i
$518$	−0.403520	−	0.403520i	−0.0177297	−	0.0177297i
$519$	−16.0461	−	34.3657i	−0.704347	−	1.50849i
$520$	2.23870	−	6.96481i	0.0981735	−	0.305427i
$521$		−	2.76763i		−	0.121252i	−0.998161	−	0.0606260i	$-0.980690\pi$
$521$		−	2.76763i		−	0.121252i	0.998161	−	0.0606260i	$-0.0193097\pi$
$522$	1.80248	−	0.159532i	0.0788925	−	0.00698253i
$523$	19.8821	−	19.8821i	0.869385	−	0.869385i	−0.123019	−	0.992404i	$-0.539258\pi$
$523$	19.8821	−	19.8821i	0.869385	−	0.869385i	0.992404	+	0.123019i	$0.0392576\pi$
$524$	−24.6091			−1.07506
$525$	0.873060	−	4.66111i	0.0381034	−	0.203428i
$526$	−0.922914			−0.0402410
$527$	4.13991	−	4.13991i	0.180337	−	0.180337i
$528$	13.1129	−	36.0842i	0.570668	−	1.57036i
$529$			55.6865i			2.42115i
$530$	0.928836	−	2.88970i	0.0403461	−	0.125521i
$531$	−10.7123	−	8.97022i	−0.464872	−	0.389274i
$532$	0.921308	+	0.921308i	0.0399438	+	0.0399438i
$533$	−18.9373	−	18.9373i	−0.820267	−	0.820267i
$534$	1.29462	−	0.604487i	0.0560237	−	0.0261587i
$535$	−10.0445	−	19.5604i	−0.434261	−	0.845669i
$536$			6.56177i			0.283425i
$537$	20.9401	+	7.60958i	0.903630	+	0.328378i
$538$	3.79430	−	3.79430i	0.163584	−	0.163584i
$539$	−39.8093			−1.71471
$540$	4.82600	+	22.1938i	0.207678	+	0.955070i
$541$	−21.0674			−0.905757			−0.452879	−	0.891572i	$-0.649603\pi$
$541$	−21.0674			−0.905757			−0.452879	+	0.891572i	$0.649603\pi$
$542$	−1.88721	+	1.88721i	−0.0810625	+	0.0810625i
$543$	−3.10276	−	1.12754i	−0.133152	−	0.0483873i
$544$		−	14.4925i		−	0.621360i
$545$	−38.3375	−	12.3228i	−1.64220	−	0.527851i
$546$	−0.710940	+	0.331954i	−0.0304254	+	0.0142063i
$547$	−7.80186	−	7.80186i	−0.333584	−	0.333584i	0.520362	−	0.853946i	$-0.325797\pi$
$547$	−7.80186	−	7.80186i	−0.333584	−	0.333584i	−0.853946	+	0.520362i	$0.825797\pi$
$548$	−15.4218	−	15.4218i	−0.658787	−	0.658787i
$549$	1.71317	+	1.43457i	0.0731163	+	0.0612261i
$550$	1.02768	+	6.23332i	0.0438205	+	0.265790i
$551$			3.45260i			0.147086i
$552$	−4.41322	+	12.1443i	−0.187839	+	0.516896i
$553$	1.28536	−	1.28536i	0.0546591	−	0.0546591i
$554$	−2.41776			−0.102721
$555$	18.8303	−	2.38215i	0.799303	−	0.101117i
$556$	−35.1722			−1.49163
$557$	2.73515	−	2.73515i	0.115892	−	0.115892i	−0.646782	−	0.762675i	$-0.723886\pi$
$557$	2.73515	−	2.73515i	0.115892	−	0.115892i	0.762675	+	0.646782i	$0.223886\pi$
$558$	−0.635479	+	0.0562442i	−0.0269020	+	0.00238101i
$559$		−	23.7736i		−	1.00552i
$560$	−4.06352	+	2.08667i	−0.171715	+	0.0881777i
$561$	−25.4908	−	54.5932i	−1.07622	−	2.30493i
$562$	−3.85317	−	3.85317i	−0.162536	−	0.162536i
$563$	−18.9526	−	18.9526i	−0.798756	−	0.798756i	0.184144	−	0.982899i	$-0.441049\pi$
$563$	−18.9526	−	18.9526i	−0.798756	−	0.798756i	−0.982899	+	0.184144i	$0.941049\pi$
$564$	7.97639	+	17.0829i	0.335866	+	0.719319i
$565$	14.8052	−	7.60264i	0.622859	−	0.319846i
$566$		−	1.74598i		−	0.0733890i
$567$	2.81854	−	4.04266i	0.118368	−	0.169776i
$568$	−2.92460	+	2.92460i	−0.122713	+	0.122713i
$569$	−10.1657			−0.426168			−0.213084	−	0.977034i	$-0.568351\pi$
$569$	−10.1657			−0.426168			−0.213084	+	0.977034i	$0.568351\pi$
$570$	0.994599	−	0.125823i	0.0416592	−	0.00527015i
$571$	34.6026			1.44808			0.724038	−	0.689760i	$-0.242284\pi$
$571$	34.6026			1.44808			0.724038	+	0.689760i	$0.242284\pi$
$572$	−31.9492	+	31.9492i	−1.33586	+	1.33586i
$573$	−13.0966	+	36.0392i	−0.547118	+	1.50556i
$574$		−	0.801634i		−	0.0334596i
$575$	7.21498	+	43.7619i	0.300885	+	1.82500i
$576$	13.3572	−	15.9511i	0.556548	−	0.664631i
$577$	−2.15736	−	2.15736i	−0.0898119	−	0.0898119i	0.660773	−	0.750585i	$-0.270228\pi$
$577$	−2.15736	−	2.15736i	−0.0898119	−	0.0898119i	−0.750585	+	0.660773i	$0.770228\pi$
$578$	−2.59803	−	2.59803i	−0.108064	−	0.108064i
$579$	−24.7760	+	11.5685i	−1.02965	+	0.480769i
$580$	−11.8033	−	3.79393i	−0.490104	−	0.157534i
$581$		−	3.19355i		−	0.132491i
$582$	−2.60790	−	0.947705i	−0.108101	−	0.0392836i
$583$	−26.8181	+	26.8181i	−1.11069	+	1.11069i
$584$	11.3192			0.468391
$585$	5.76438	−	25.4520i	0.238328	−	1.05231i
$586$	1.05136			0.0434315
$587$	14.1634	−	14.1634i	0.584588	−	0.584588i	−0.351573	−	0.936161i	$-0.614353\pi$
$587$	14.1634	−	14.1634i	0.584588	−	0.584588i	0.936161	+	0.351573i	$0.114353\pi$
$588$	−21.3211	−	7.74803i	−0.879266	−	0.319524i
$589$		−	1.21724i		−	0.0501555i
$590$	−1.01164	−	1.97004i	−0.0416486	−	0.0811054i
$591$	−6.85125	+	3.19901i	−0.281823	+	0.131589i
$592$	−12.9282	−	12.9282i	−0.531344	−	0.531344i
$593$	19.3823	+	19.3823i	0.795937	+	0.795937i	0.982452	−	0.186515i	$-0.0597194\pi$
$593$	19.3823	+	19.3823i	0.795937	+	0.795937i	−0.186515	+	0.982452i	$0.559719\pi$
$594$	−1.68961	+	6.34417i	−0.0693257	+	0.260304i
$595$	−2.19368	+	6.82475i	−0.0899322	+	0.279788i
$596$			8.99297i			0.368366i
$597$	−15.9221	+	43.8144i	−0.651647	+	1.79320i
$598$	5.18905	−	5.18905i	0.212196	−	0.212196i
$599$	14.3410			0.585959			0.292979	−	0.956119i	$-0.405353\pi$
$599$	14.3410			0.585959			0.292979	+	0.956119i	$0.405353\pi$
$600$	−1.34089	+	7.15878i	−0.0547417	+	0.292256i
$601$	−34.6467			−1.41327			−0.706634	−	0.707579i	$-0.749787\pi$
$601$	−34.6467			−1.41327			−0.706634	+	0.707579i	$0.749787\pi$
$602$	0.503178	−	0.503178i	0.0205080	−	0.0205080i
$603$	2.06361	+	23.3159i	0.0840369	+	0.949495i
$604$			12.3485i			0.502452i
$605$	16.6288	−	51.7340i	0.676059	−	2.10328i
$606$	−0.478093	−	1.02392i	−0.0194212	−	0.0415940i
$607$	11.0616	+	11.0616i	0.448977	+	0.448977i	0.895014	−	0.446037i	$-0.147165\pi$
$607$	11.0616	+	11.0616i	0.448977	+	0.448977i	−0.446037	+	0.895014i	$0.647165\pi$
$608$	−2.13058	−	2.13058i	−0.0864065	−	0.0864065i
$609$	1.13814	+	2.43753i	0.0461198	+	0.0987739i
$610$	0.161788	+	0.315062i	0.00655060	+	0.0127565i
$611$		−	21.6625i		−	0.876369i
$612$	−3.02696	−	34.2003i	−0.122358	−	1.38247i
$613$	27.2713	−	27.2713i	1.10148	−	1.10148i	0.107245	−	0.994233i	$-0.465797\pi$
$613$	27.2713	−	27.2713i	1.10148	−	1.10148i	0.994233	−	0.107245i	$-0.0342029\pi$
$614$	−6.42083			−0.259124
$615$	21.0704	+	16.3380i	0.849640	+	0.658811i
$616$	−2.73616			−0.110243
$617$	4.99456	−	4.99456i	0.201073	−	0.201073i	−0.599387	−	0.800460i	$-0.704589\pi$
$617$	4.99456	−	4.99456i	0.201073	−	0.201073i	0.800460	+	0.599387i	$0.204589\pi$
$618$	−1.08496	+	2.98558i	−0.0436433	+	0.120098i
$619$		−	5.68333i		−	0.228432i	−0.993456	−	0.114216i	$-0.963564\pi$
$619$		−	5.68333i		−	0.228432i	0.993456	−	0.114216i	$-0.0364357\pi$
$620$	4.16133	+	1.33758i	0.167123	+	0.0537184i
$621$	−11.8622	+	44.5401i	−0.476013	+	1.78733i
$622$	−2.17746	−	2.17746i	−0.0873082	−	0.0873082i
$623$	1.50199	+	1.50199i	0.0601758	+	0.0601758i
$624$	−22.7774	+	10.6353i	−0.911826	+	0.425752i
$625$	8.02530	+	23.6769i	0.321012	+	0.947075i
$626$			4.71257i			0.188352i
$627$	−11.7734	−	4.27843i	−0.470184	−	0.170864i
$628$	13.8363	−	13.8363i	0.552127	−	0.552127i
$629$	−28.6923			−1.14404
$630$	0.660709	−	0.416698i	0.0263233	−	0.0166016i
$631$	−3.36174			−0.133829			−0.0669144	−	0.997759i	$-0.521315\pi$
$631$	−3.36174			−0.133829			−0.0669144	+	0.997759i	$0.521315\pi$
$632$	−1.97412	+	1.97412i	−0.0785264	+	0.0785264i
$633$	26.5654	+	9.65380i	1.05588	+	0.383704i
$634$		−	0.575710i		−	0.0228644i
$635$	−12.3346	+	6.33395i	−0.489483	+	0.251355i
$636$	−19.5828	+	9.14367i	−0.776509	+	0.362570i
$637$	18.4310	+	18.4310i	0.730262	+	0.730262i
$638$	−2.53413	−	2.53413i	−0.100327	−	0.100327i
$639$	−9.47219	+	11.3117i	−0.374714	+	0.447484i
$640$	12.7811	−	6.56326i	0.505218	−	0.259435i
$641$		−	15.8897i		−	0.627606i	−0.949488	−	0.313803i	$-0.898397\pi$
$641$		−	15.8897i		−	0.627606i	0.949488	−	0.313803i	$-0.101603\pi$
$642$	1.23708	−	3.40419i	0.0488235	−	0.134353i
$643$	−18.6741	+	18.6741i	−0.736436	+	0.736436i	−0.971886	−	0.235450i	$-0.924344\pi$
$643$	−18.6741	+	18.6741i	−0.736436	+	0.736436i	0.235450	+	0.971886i	$0.424344\pi$
$644$	−9.49498			−0.374155
$645$	2.97048	+	23.4809i	0.116963	+	0.924559i
$646$	−1.51550			−0.0596265
$647$	−7.58920	+	7.58920i	−0.298362	+	0.298362i	−0.840372	−	0.542010i	$-0.817664\pi$
$647$	−7.58920	+	7.58920i	−0.298362	+	0.298362i	0.542010	+	0.840372i	$0.317664\pi$
$648$	−4.32886	+	6.20893i	−0.170054	+	0.243910i
$649$			27.6718i			1.08621i
$650$	2.41012	−	3.36171i	0.0945326	−	0.131857i
$651$	−0.401260	−	0.859371i	−0.0157266	−	0.0336814i
$652$	−12.8596	−	12.8596i	−0.503621	−	0.503621i
$653$	26.7830	+	26.7830i	1.04810	+	1.04810i	0.998783	+	0.0493152i	$0.0157039\pi$
$653$	26.7830	+	26.7830i	1.04810	+	1.04810i	0.0493152	+	0.998783i	$0.484296\pi$
$654$	−2.80635	−	6.01031i	−0.109737	−	0.235022i
$655$	−26.7999	−	8.61430i	−1.04716	−	0.336589i
$656$		−	25.6831i		−	1.00276i
$657$	40.2203	−	3.55977i	1.56914	−	0.138880i
$658$	0.458496	−	0.458496i	0.0178740	−	0.0178740i
$659$	−18.9035			−0.736377			−0.368189	−	0.929751i	$-0.620022\pi$
$659$	−18.9035			−0.736377			−0.368189	+	0.929751i	$0.620022\pi$
$660$	27.5638	−	35.5478i	1.07292	−	1.38370i
$661$	−7.52825			−0.292815			−0.146408	−	0.989224i	$-0.546771\pi$
$661$	−7.52825			−0.292815			−0.146408	+	0.989224i	$0.546771\pi$
$662$	−2.99929	+	2.99929i	−0.116571	+	0.116571i
$663$	−13.4739	+	37.0775i	−0.523283	+	1.43997i
$664$			4.90482i			0.190344i
$665$	0.680827	+	1.32583i	0.0264013	+	0.0514133i
$666$	2.39705	+	2.00724i	0.0928838	+	0.0777789i
$667$	−17.7912	−	17.7912i	−0.688878	−	0.688878i
$668$	0.802376	+	0.802376i	0.0310448	+	0.0310448i
$669$	5.28883	−	2.46948i	0.204478	−	0.0954754i
$670$	−1.13532	+	3.53210i	−0.0438614	+	0.136457i
$671$		−	4.42544i		−	0.170842i
$672$	−2.20653	−	0.801849i	−0.0851188	−	0.0309320i
$673$	27.1168	−	27.1168i	1.04527	−	1.04527i	0.0463492	−	0.998925i	$-0.485241\pi$
$673$	27.1168	−	27.1168i	1.04527	−	1.04527i	0.998925	−	0.0463492i	$-0.0147587\pi$
$674$	−1.05754			−0.0407349
$675$	−2.51321	+	25.8589i	−0.0967334	+	0.995310i
$676$	4.17169			0.160450
$677$	11.0573	−	11.0573i	0.424965	−	0.424965i	−0.461944	−	0.886909i	$-0.652848\pi$
$677$	11.0573	−	11.0573i	0.424965	−	0.424965i	0.886909	+	0.461944i	$0.152848\pi$
$678$	2.57662	+	0.936340i	0.0989545	+	0.0359599i
$679$		−	4.12512i		−	0.158308i
$680$	3.36917	−	10.4818i	0.129202	−	0.401959i
$681$	12.2901	−	5.73853i	0.470958	−	0.219901i
$682$	0.893425	+	0.893425i	0.0342110	+	0.0342110i
$683$	−5.35568	−	5.35568i	−0.204930	−	0.204930i	0.597179	−	0.802108i	$-0.296288\pi$
$683$	−5.35568	−	5.35568i	−0.204930	−	0.204930i	−0.802108	+	0.597179i	$0.796288\pi$
$684$	−5.47289	−	4.58288i	−0.209261	−	0.175231i
$685$	−11.3964	−	22.1930i	−0.435433	−	0.847952i
$686$			1.59531i			0.0609094i
$687$	9.49735	−	26.1348i	0.362347	−	0.997106i
$688$	16.1210	−	16.1210i	0.614609	−	0.614609i
$689$	24.8326			0.946047
$690$	−4.47679	+	5.77352i	−0.170429	+	0.219794i
$691$	−45.9628			−1.74851			−0.874254	−	0.485469i	$-0.838649\pi$
$691$	−45.9628			−1.74851			−0.874254	+	0.485469i	$0.838649\pi$
$692$	−30.2673	+	30.2673i	−1.15059	+	1.15059i
$693$	−9.72238	+	0.860498i	−0.369323	+	0.0326876i
$694$		−	1.59538i		−	0.0605599i
$695$	−38.3033	−	12.3118i	−1.45293	−	0.467015i
$696$	−1.74802	−	3.74369i	−0.0662584	−	0.141904i
$697$	−28.5001	−	28.5001i	−1.07952	−	1.07952i
$698$	2.75466	+	2.75466i	0.104265	+	0.104265i
$699$	−3.71744	−	7.96157i	−0.140606	−	0.301134i
$700$	−5.28069	+	0.870621i	−0.199591	+	0.0329064i
$701$		−	16.2166i		−	0.612492i	−0.951952	−	0.306246i	$-0.900927\pi$
$701$		−	16.2166i		−	0.612492i	0.951952	−	0.306246i	$-0.0990730\pi$
$702$	3.71950	−	2.15498i	0.140383	−	0.0813343i
$703$	−4.21814	+	4.21814i	−0.159090	+	0.159090i
$704$	−41.2048			−1.55296
$705$	2.70670	+	21.3957i	0.101940	+	0.805811i
$706$	−6.87944			−0.258911
$707$	1.18793	−	1.18793i	0.0446767	−	0.0446767i
$708$	−5.38573	+	14.8205i	−0.202408	+	0.556987i
$709$			10.3445i			0.388495i	0.980953	+	0.194248i	$0.0622266\pi$
$709$			10.3445i			0.388495i	−0.980953	+	0.194248i	$0.937773\pi$
$710$	−2.08029	+	1.06825i	−0.0780718	+	0.0400908i
$711$	−6.39379	+	7.63548i	−0.239786	+	0.286353i
$712$	−2.30683	−	2.30683i	−0.0864521	−	0.0864521i
$713$	6.27242	+	6.27242i	0.234904	+	0.234904i
$714$	−1.06994	+	0.499580i	−0.0400416	+	0.0186963i
$715$	−45.9771	+	23.6098i	−1.71945	+	0.882956i
$716$		−	25.1449i		−	0.939708i
$717$	−19.5382	−	7.10014i	−0.729667	−	0.265160i
$718$	−2.27973	+	2.27973i	−0.0850788	+	0.0850788i
$719$	−47.9026			−1.78647			−0.893233	−	0.449595i	$-0.851568\pi$
$719$	−47.9026			−1.78647			−0.893233	+	0.449595i	$0.851568\pi$
$720$	21.1681	−	13.3504i	0.788888	−	0.497538i
$721$	−4.72254			−0.175877
$722$	2.63422	−	2.63422i	0.0980355	−	0.0980355i
$723$	24.2212	+	8.80193i	0.900795	+	0.327347i
$724$			3.72580i			0.138468i
$725$	−11.5260	−	8.26335i	−0.428065	−	0.306893i
$726$	8.11052	−	3.78699i	0.301010	−	0.140548i
$727$	19.1390	+	19.1390i	0.709826	+	0.709826i	0.966498	−	0.256672i	$-0.0826261\pi$
$727$	19.1390	+	19.1390i	0.709826	+	0.709826i	−0.256672	+	0.966498i	$0.582626\pi$
$728$	1.26679	+	1.26679i	0.0469505	+	0.0469505i
$729$	−13.4291	+	23.4235i	−0.497373	+	0.867537i
$730$	6.09295	+	1.95846i	0.225510	+	0.0724857i
$731$		−	35.7785i		−	1.32332i
$732$	0.861319	−	2.37018i	0.0318353	−	0.0876044i
$733$	−16.4809	+	16.4809i	−0.608734	+	0.608734i	−0.942615	−	0.333881i	$-0.891642\pi$
$733$	−16.4809	+	16.4809i	−0.608734	+	0.608734i	0.333881	+	0.942615i	$0.391642\pi$
$734$	0.304327			0.0112329
$735$	−20.5070	−	15.9011i	−0.756411	−	0.586522i
$736$	21.9577			0.809372
$737$	32.7800	−	32.7800i	1.20747	−	1.20747i
$738$	0.387199	+	4.37478i	0.0142530	+	0.161038i
$739$		−	10.1260i		−	0.372491i	−0.982503	−	0.186245i	$-0.940368\pi$
$739$		−	10.1260i		−	0.372491i	0.982503	−	0.186245i	$-0.0596319\pi$
$740$	−9.78524	−	19.0555i	−0.359713	−	0.700495i
$741$	3.47003	+	7.43170i	0.127475	+	0.273010i
$742$	0.525593	+	0.525593i	0.0192951	+	0.0192951i
$743$	25.7772	+	25.7772i	0.945673	+	0.945673i	0.998598	−	0.0529252i	$-0.0168545\pi$
$743$	25.7772	+	25.7772i	0.945673	+	0.945673i	−0.0529252	+	0.998598i	$0.516854\pi$
$744$	0.616276	+	1.31987i	0.0225938	+	0.0483887i
$745$	−3.14794	+	9.79356i	−0.115332	+	0.358808i
$746$		−	4.58278i		−	0.167787i
$747$	1.54252	+	17.4283i	0.0564379	+	0.637667i
$748$	−48.0825	+	48.0825i	−1.75807	+	1.75807i
$749$	5.38468			0.196752
$750$	−1.96040	+	3.62146i	−0.0715838	+	0.132237i
$751$	49.0297			1.78912			0.894560	−	0.446948i	$-0.147489\pi$
$751$	49.0297			1.78912			0.894560	+	0.446948i	$0.147489\pi$
$752$	14.6895	−	14.6895i	0.535670	−	0.535670i
$753$	15.0672	−	41.4618i	0.549077	−	1.51095i
$754$			2.34651i			0.0854549i
$755$	−4.32252	+	13.4478i	−0.157313	+	0.489415i
$756$	−5.37459	−	1.43139i	−0.195472	−	0.0520592i
$757$	−17.5977	−	17.5977i	−0.639599	−	0.639599i	0.310858	−	0.950456i	$-0.399384\pi$
$757$	−17.5977	−	17.5977i	−0.639599	−	0.639599i	−0.950456	+	0.310858i	$0.899384\pi$
$758$	−1.90258	−	1.90258i	−0.0691047	−	0.0691047i
$759$	82.7148	−	38.6214i	3.00236	−	1.40187i
$760$	−1.04565	−	2.03627i	−0.0379297	−	0.0738634i
$761$			12.2728i			0.444890i	0.974945	+	0.222445i	$0.0714038\pi$
$761$			12.2728i			0.444890i	−0.974945	+	0.222445i	$0.928596\pi$
$762$	−2.14665	−	0.780087i	−0.0777648	−	0.0282596i
$763$	6.97301	−	6.97301i	0.252440	−	0.252440i
$764$	43.2760			1.56567
$765$	8.67521	−	38.3045i	0.313653	−	1.38490i
$766$	4.76108			0.172025
$767$	12.8115	−	12.8115i	0.462598	−	0.462598i
$768$	−20.3546	−	7.39684i	−0.734485	−	0.266911i
$769$			34.1804i			1.23258i	0.787520	+	0.616289i	$0.211365\pi$
$769$			34.1804i			1.23258i	−0.787520	+	0.616289i	$0.788635\pi$
$770$	−1.47284	−	0.473414i	−0.0530774	−	0.0170607i
$771$	23.2409	−	10.8517i	0.837002	−	0.390815i
$772$	21.8212	+	21.8212i	0.785363	+	0.785363i
$773$	−28.9943	−	28.9943i	−1.04285	−	1.04285i	−0.999040	−	0.0438138i	$-0.986049\pi$
$773$	−28.9943	−	28.9943i	−1.04285	−	1.04285i	−0.0438138	−	0.999040i	$-0.513951\pi$
$774$	−2.50297	+	2.98905i	−0.0899674	+	0.107439i
$775$	4.06358	+	2.91331i	0.145968	+	0.104649i
$776$			6.33558i			0.227434i
$777$	−1.58751	+	4.36850i	−0.0569515	+	0.156719i
$778$	−2.28398	+	2.28398i	−0.0818845	+	0.0818845i
$779$	−8.37976			−0.300236
$780$	−29.2196	+	3.69646i	−1.04623	+	0.132355i
$781$	29.2203			1.04558
$782$	7.80935	−	7.80935i	0.279262	−	0.279262i
$783$	−7.38857	−	12.7527i	−0.264046	−	0.455744i
$784$			24.9964i			0.892728i
$785$	19.9113	−	10.2247i	0.710665	−	0.364935i
$786$	−1.96179	−	4.20152i	−0.0699747	−	0.149863i
$787$	28.9823	+	28.9823i	1.03311	+	1.03311i	0.999433	+	0.0336749i	$0.0107211\pi$
$787$	28.9823	+	28.9823i	1.03311	+	1.03311i	0.0336749	+	0.999433i	$0.489279\pi$
$788$	6.03418	+	6.03418i	0.214959	+	0.214959i
$789$	3.18029	+	6.81116i	0.113221	+	0.242484i
$790$	−1.40421	+	0.721077i	−0.0499595	+	0.0256548i
$791$			4.07565i			0.144913i
$792$	14.9321	−	1.32160i	0.530591	−	0.0469609i
$793$	−2.04890	+	2.04890i	−0.0727586	+	0.0727586i
$794$	−0.102778			−0.00364744
$795$	−24.5269	+	3.10280i	−0.869878	+	0.110045i
$796$	52.6124			1.86480
$797$	−38.6866	+	38.6866i	−1.37035	+	1.37035i	−0.510428	+	0.859921i	$0.670513\pi$
$797$	−38.6866	+	38.6866i	−1.37035	+	1.37035i	−0.859921	+	0.510428i	$0.829487\pi$
$798$	−0.0838505	+	0.230740i	−0.00296827	+	0.00816810i
$799$		−	32.6013i		−	1.15335i
$800$	12.2119	−	2.01336i	0.431756	−	0.0711831i
$801$	−8.92231	−	7.47136i	−0.315254	−	0.263987i
$802$	3.74043	+	3.74043i	0.132079	+	0.132079i
$803$	−56.5461	−	56.5461i	−1.99547	−	1.99547i
$804$	23.9362	−	11.1764i	0.844166	−	0.394161i
$805$	−10.3403	−	3.32367i	−0.364446	−	0.117144i
$806$		−	0.827280i		−	0.0291397i
$807$	−41.0770	−	14.9273i	−1.44598	−	0.525466i
$808$	−1.82448	+	1.82448i	−0.0641851	+	0.0641851i
$809$	−28.5690			−1.00443			−0.502216	−	0.864742i	$-0.667482\pi$
$809$	−28.5690			−1.00443			−0.502216	+	0.864742i	$0.667482\pi$
$810$	−3.40444	+	2.59319i	−0.119620	+	0.0911154i
$811$	−16.6652			−0.585196			−0.292598	−	0.956236i	$-0.594520\pi$
$811$	−16.6652			−0.585196			−0.292598	+	0.956236i	$0.594520\pi$
$812$	2.14684	−	2.14684i	0.0753392	−	0.0753392i
$813$	20.4309	+	7.42454i	0.716542	+	0.260390i
$814$		−	6.19203i		−	0.217031i
$815$	−9.50298	−	18.5059i	−0.332875	−	0.648232i
$816$	−34.2793	+	16.0058i	−1.20001	+	0.560314i
$817$	−5.25990	−	5.25990i	−0.184020	−	0.184020i
$818$	−5.26684	−	5.26684i	−0.184151	−	0.184151i
$819$	4.89968	+	4.10289i	0.171209	+	0.143367i
$820$	9.20819	−	28.6476i	0.321564	−	1.00042i
$821$			4.02639i			0.140522i	0.997529	+	0.0702609i	$0.0223832\pi$
$821$			4.02639i			0.140522i	−0.997529	+	0.0702609i	$0.977617\pi$
$822$	1.40358	−	3.86236i	0.0489553	−	0.134715i
$823$	−16.6083	+	16.6083i	−0.578928	+	0.578928i	−0.934608	−	0.355680i	$-0.884249\pi$
$823$	−16.6083	+	16.6083i	−0.578928	+	0.578928i	0.355680	+	0.934608i	$0.384249\pi$
$824$	7.25312			0.252675
$825$	42.4610	−	29.0639i	1.47830	−	1.01187i
$826$	0.542323			0.0188698
$827$	−32.5604	+	32.5604i	−1.13224	+	1.13224i	−0.142433	+	0.989804i	$0.545493\pi$
$827$	−32.5604	+	32.5604i	−1.13224	+	1.13224i	−0.989804	+	0.142433i	$0.954507\pi$
$828$	51.8173	−	4.58618i	1.80077	−	0.159381i
$829$			39.3477i			1.36660i	0.730137	+	0.683301i	$0.239456\pi$
$829$			39.3477i			1.36660i	−0.730137	+	0.683301i	$0.760544\pi$
$830$	−0.848638	+	2.64020i	−0.0294567	+	0.0916425i
$831$	8.33140	+	17.8432i	0.289013	+	0.618974i
$832$	19.0771	+	19.0771i	0.661379	+	0.661379i
$833$	27.7380	+	27.7380i	0.961066	+	0.961066i
$834$	−2.80385	−	6.00496i	−0.0970894	−	0.207935i
$835$	0.592939	+	1.15467i	0.0205195	+	0.0399591i
$836$			14.1375i			0.488956i
$837$	2.60489	+	4.49606i	0.0900383	+	0.155406i
$838$	−1.70558	+	1.70558i	−0.0589182	+	0.0589182i
$839$	−23.7421			−0.819667			−0.409834	−	0.912160i	$-0.634413\pi$
$839$	−23.7421			−0.819667			−0.409834	+	0.912160i	$0.634413\pi$
$840$	−1.40948	−	1.09291i	−0.0486317	−	0.0377091i
$841$	−20.9547			−0.722577
$842$	1.11919	−	1.11919i	0.0385698	−	0.0385698i
$843$	−15.1589	+	41.7144i	−0.522101	+	1.43672i
$844$		−	31.8997i		−	1.09803i
$845$	4.54307	+	1.46028i	0.156286	+	0.0502351i
$846$	−2.28070	+	2.72362i	−0.0784122	+	0.0936400i
$847$	9.40963	+	9.40963i	0.323319	+	0.323319i
$848$	16.8392	+	16.8392i	0.578260	+	0.578260i
$849$	−12.8854	+	6.01650i	−0.442227	+	0.206486i
$850$	3.62715	−	5.05927i	0.124410	−	0.173532i
$851$		−	43.4720i		−	1.49020i
$852$	15.6498	+	5.68711i	0.536153	+	0.194837i
$853$	31.5646	−	31.5646i	1.08075	−	1.08075i	0.0843126	−	0.996439i	$-0.473131\pi$
$853$	31.5646	−	31.5646i	1.08075	−	1.08075i	0.996439	−	0.0843126i	$-0.0268694\pi$
$854$	−0.0867318			−0.00296790
$855$	−4.35589	−	6.90662i	−0.148968	−	0.236201i
$856$	−8.27008			−0.282665
$857$	−35.6222	+	35.6222i	−1.21683	+	1.21683i	−0.248098	+	0.968735i	$0.579805\pi$
$857$	−35.6222	+	35.6222i	−1.21683	+	1.21683i	−0.968735	+	0.248098i	$0.920195\pi$
$858$	−8.00162	−	2.90777i	−0.273171	−	0.0992698i
$859$			32.8366i			1.12037i	0.828368	+	0.560184i	$0.189270\pi$
$859$			32.8366i			1.12037i	−0.828368	+	0.560184i	$0.810730\pi$
$860$	23.7617	−	12.2019i	0.810268	−	0.416082i
$861$	−5.91611	+	2.76237i	−0.201620	+	0.0941412i
$862$	−3.41674	−	3.41674i	−0.116375	−	0.116375i
$863$	7.37506	+	7.37506i	0.251050	+	0.251050i	0.821401	−	0.570351i	$-0.193193\pi$
$863$	7.37506	+	7.37506i	0.251050	+	0.251050i	−0.570351	+	0.821401i	$0.693193\pi$
$864$	12.4291	+	3.31018i	0.422846	+	0.112615i
$865$	−43.5567	+	22.3669i	−1.48097	+	0.760497i
$866$			1.55087i			0.0527008i
$867$	−10.2210	+	28.1262i	−0.347124	+	0.955217i
$868$	−0.756883	+	0.756883i	−0.0256903	+	0.0256903i
$869$	19.7239			0.669087
$870$	−0.293194	−	2.31762i	−0.00994019	−	0.0785747i
$871$	−30.3531			−1.02848
$872$	−10.7095	+	10.7095i	−0.362670	+	0.362670i
$873$	1.99248	+	22.5122i	0.0674352	+	0.761921i
$874$		−	2.29615i		−	0.0776684i
$875$	−6.05555	−	0.900351i	−0.204715	−	0.0304374i
$876$	−19.2795	−	41.2905i	−0.651393	−	1.39508i
$877$	12.7700	+	12.7700i	0.431213	+	0.431213i	0.889041	−	0.457828i	$-0.151373\pi$
$877$	12.7700	+	12.7700i	0.431213	+	0.431213i	−0.457828	+	0.889041i	$0.651373\pi$
$878$	−2.25222	−	2.25222i	−0.0760088	−	0.0760088i
$879$	−3.62292	−	7.75913i	−0.122198	−	0.261709i
$880$	−47.1874	−	15.1674i	−1.59069	−	0.511295i
$881$		−	0.0959314i		−	0.00323201i	−0.999999	−	0.00161601i	$-0.999486\pi$
$881$		−	0.0959314i		−	0.00323201i	0.999999	−	0.00161601i	$-0.000514391\pi$
$882$	−0.376845	−	4.25781i	−0.0126890	−	0.143368i
$883$	2.39245	−	2.39245i	0.0805123	−	0.0805123i	−0.665704	−	0.746216i	$-0.731869\pi$
$883$	2.39245	−	2.39245i	0.0805123	−	0.0805123i	0.746216	+	0.665704i	$0.231869\pi$
$884$	44.5227			1.49746
$885$	−11.0530	+	14.2546i	−0.371543	+	0.479162i
$886$	4.11215			0.138150
$887$	10.2230	−	10.2230i	0.343256	−	0.343256i	−0.514334	−	0.857590i	$-0.671961\pi$
$887$	10.2230	−	10.2230i	0.343256	−	0.343256i	0.857590	+	0.514334i	$0.171961\pi$
$888$	2.43818	−	6.70938i	0.0818198	−	0.225152i
$889$		−	3.39552i		−	0.113882i
$890$	−0.842602	−	1.64086i	−0.0282441	−	0.0550018i
$891$	52.6426	−	9.39204i	1.76359	−	0.314645i
$892$	−4.65809	−	4.65809i	−0.155964	−	0.155964i
$893$	−4.79281	−	4.79281i	−0.160385	−	0.160385i
$894$	−1.53537	+	0.716901i	−0.0513505	+	0.0239767i
$895$	8.80183	−	27.3833i	0.294213	−	0.915324i
$896$			3.51845i			0.117543i
$897$	−56.1765	−	20.4144i	−1.87568	−	0.681618i
$898$	−0.221129	+	0.221129i	−0.00737917	+	0.00737917i
$899$	−2.83642			−0.0945998
$900$	28.3979	−	7.30190i	0.946598	−	0.243397i
$901$	37.3723			1.24505
$902$	6.15055	−	6.15055i	0.204791	−	0.204791i
$903$	−5.44740	−	1.97957i	−0.181278	−	0.0658761i
$904$		−	6.25960i		−	0.208191i
$905$	−1.30420	+	4.05749i	−0.0433530	+	0.134875i
$906$	−2.10826	+	0.984394i	−0.0700422	+	0.0327043i
$907$	33.6412	+	33.6412i	1.11704	+	1.11704i	0.992174	+	0.124865i	$0.0398499\pi$
$907$	33.6412	+	33.6412i	1.11704	+	1.11704i	0.124865	+	0.992174i	$0.460150\pi$
$908$	−10.8244	−	10.8244i	−0.359220	−	0.359220i
$909$	−5.90914	+	7.05671i	−0.195994	+	0.234056i
$910$	0.462715	+	0.901079i	0.0153388	+	0.0298705i
$911$			19.7839i			0.655470i	0.944770	+	0.327735i	$0.106285\pi$
$911$			19.7839i			0.655470i	−0.944770	+	0.327735i	$0.893715\pi$
$912$	−2.68644	+	7.39255i	−0.0889569	+	0.244792i
$913$	24.5026	−	24.5026i	0.810916	−	0.810916i
$914$	3.90631			0.129209
$915$	1.76767	−	2.27968i	0.0584372	−	0.0753639i
$916$	−31.3827			−1.03692
$917$	4.87450	−	4.87450i	0.160970	−	0.160970i
$918$	5.59773	−	3.24317i	0.184752	−	0.107041i
$919$			6.29613i			0.207690i	0.994593	+	0.103845i	$0.0331146\pi$
$919$			6.29613i			0.207690i	−0.994593	+	0.103845i	$0.966885\pi$
$920$	15.8811	+	5.10467i	0.523585	+	0.168296i
$921$	22.1257	+	47.3861i	0.729065	+	1.56142i
$922$	−2.49611	−	2.49611i	−0.0822050	−	0.0822050i
$923$	−13.5285	−	13.5285i	−0.445295	−	0.445295i
$924$	4.66039	+	9.98107i	0.153316	+	0.328353i
$925$	−3.98607	−	24.1772i	−0.131061	−	0.794942i
$926$			0.666486i			0.0219021i
$927$	25.7725	−	2.28104i	0.846479	−	0.0749192i
$928$	−4.96469	+	4.96469i	−0.162974	+	0.162974i
$929$	28.8485			0.946487			0.473244	−	0.880932i	$-0.343083\pi$
$929$	28.8485			0.946487			0.473244	+	0.880932i	$0.343083\pi$
$930$	0.103368	+	0.817094i	0.00338956	+	0.0267936i
$931$	8.15569			0.267292
$932$	−7.01209	+	7.01209i	−0.229689	+	0.229689i
$933$	−8.56643	+	23.5731i	−0.280452	+	0.771750i
$934$		−	2.01756i		−	0.0660166i
$935$	−69.1941	+	35.5320i	−2.26289	+	1.16202i
$936$	−7.52519	−	6.30144i	−0.245969	−	0.205969i
$937$	−9.12232	−	9.12232i	−0.298013	−	0.298013i	0.542222	−	0.840235i	$-0.317583\pi$
$937$	−9.12232	−	9.12232i	−0.298013	−	0.298013i	−0.840235	+	0.542222i	$0.817583\pi$
$938$	−0.642437	−	0.642437i	−0.0209763	−	0.0209763i
$939$	34.7790	−	16.2391i	1.13497	−	0.529944i
$940$	21.6517	−	11.1184i	0.706199	−	0.362642i
$941$		−	6.71081i		−	0.218766i	−0.994000	−	0.109383i	$-0.965112\pi$
$941$		−	6.71081i		−	0.218766i	0.994000	−	0.109383i	$-0.0348875\pi$
$942$	3.46526	+	1.25927i	0.112904	+	0.0410293i
$943$	43.1808	−	43.1808i	1.40616	−	1.40616i
$944$	17.3752			0.565514
$945$	−5.35201	−	3.44017i	−0.174101	−	0.111909i
$946$	7.72129			0.251041
$947$	2.03973	−	2.03973i	0.0662825	−	0.0662825i	−0.673188	−	0.739471i	$-0.735076\pi$
$947$	2.03973	−	2.03973i	0.0662825	−	0.0662825i	0.739471	+	0.673188i	$0.235076\pi$
$948$	10.5637	+	3.83884i	0.343094	+	0.124680i
$949$			52.3596i			1.69967i
$950$	−0.210540	−	1.27702i	−0.00683082	−	0.0414319i
$951$	−4.24877	+	1.98385i	−0.137776	+	0.0643307i
$952$	1.90649	+	1.90649i	0.0617895	+	0.0617895i
$953$	5.00183	+	5.00183i	0.162025	+	0.162025i	0.783463	−	0.621438i	$-0.213451\pi$
$953$	5.00183	+	5.00183i	0.162025	+	0.162025i	−0.621438	+	0.783463i	$0.713451\pi$
$954$	−3.12220	−	2.61447i	−0.101085	−	0.0846465i
$955$	47.1286	+	15.1485i	1.52504	+	0.490195i
$956$			23.4615i			0.758798i
$957$	−9.96962	+	27.4344i	−0.322272	+	0.886829i
$958$	2.63645	−	2.63645i	0.0851800	−	0.0851800i
$959$	6.10941			0.197283
$960$	−21.2259	−	16.4585i	−0.685061	−	0.531197i
$961$	1.00000			0.0322581
$962$	−2.86680	+	2.86680i	−0.0924293	+	0.0924293i
$963$	−29.3860	+	2.60086i	−0.946950	+	0.0838116i
$964$		−	29.0848i		−	0.936759i
$965$	16.1254	+	31.4023i	0.519096	+	1.01087i
$966$	−0.756920	−	1.62108i	−0.0243535	−	0.0521574i
$967$	−33.2417	−	33.2417i	−1.06898	−	1.06898i	−0.997437	−	0.0715442i	$-0.977207\pi$
$967$	−33.2417	−	33.2417i	−1.06898	−	1.06898i	−0.0715442	−	0.997437i	$-0.522793\pi$
$968$	−14.4518	−	14.4518i	−0.464499	−	0.464499i
$969$	5.22229	+	11.1845i	0.167764	+	0.359297i
$970$	−1.09619	+	3.41035i	−0.0351965	+	0.109500i
$971$			10.7794i			0.345926i	0.984928	+	0.172963i	$0.0553342\pi$
$971$			10.7794i			0.345926i	−0.984928	+	0.172963i	$0.944666\pi$
$972$	30.0223	+	5.21558i	0.962966	+	0.167290i
$973$	6.96680	−	6.96680i	0.223345	−	0.223345i
$974$	4.98090			0.159598
$975$	−33.1147	−	6.20263i	−1.06052	−	0.198643i
$976$	−2.77875			−0.0889456
$977$	−28.5232	+	28.5232i	−0.912536	+	0.912536i	−0.996471	−	0.0839348i	$-0.973251\pi$
$977$	−28.5232	+	28.5232i	−0.912536	+	0.912536i	0.0839348	+	0.996471i	$0.473251\pi$
$978$	1.17038	−	3.22067i	0.0374248	−	0.102986i
$979$			23.0480i			0.736618i
$980$	−8.96198	+	27.8816i	−0.286280	+	0.890644i
$981$	−34.6860	+	41.4221i	−1.10744	+	1.32250i
$982$	6.60071	+	6.60071i	0.210637	+	0.210637i
$983$	6.03258	+	6.03258i	0.192409	+	0.192409i	0.796736	−	0.604327i	$-0.206558\pi$
$983$	6.03258	+	6.03258i	0.192409	+	0.192409i	−0.604327	+	0.796736i	$0.706558\pi$
$984$	9.08627	−	4.24259i	0.289660	−	0.135249i
$985$	4.45913	+	8.68360i	0.142080	+	0.276683i
$986$			3.53142i			0.112463i
$987$	−4.96366	−	1.80379i	−0.157995	−	0.0574152i
$988$	6.54541	−	6.54541i	0.208237	−	0.208237i
$989$	54.2084			1.72373
$990$	8.26642	+	1.87218i	0.262724	+	0.0595018i
$991$	−41.5159			−1.31880			−0.659399	−	0.751793i	$-0.729189\pi$
$991$	−41.5159			−1.31880			−0.659399	+	0.751793i	$0.729189\pi$
$992$	1.75034	−	1.75034i	0.0555733	−	0.0555733i
$993$	32.4702	+	11.7996i	1.03041	+	0.374450i
$994$		−	0.572672i		−	0.0181640i
$995$	57.2961	+	18.4167i	1.81641	+	0.583849i
$996$	17.8920	−	8.35418i	0.566929	−	0.264712i
$997$	−22.6987	−	22.6987i	−0.718876	−	0.718876i	0.249499	−	0.968375i	$-0.419734\pi$
$997$	−22.6987	−	22.6987i	−0.718876	−	0.718876i	−0.968375	+	0.249499i	$0.919734\pi$
$998$	0.310399	+	0.310399i	0.00982550	+	0.00982550i
$999$	6.55351	−	24.6071i	0.207344	−	0.778536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.b.32.16	yes	60
3.2	odd	2	inner	465.2.k.b.32.15	✓	60
5.3	odd	4	inner	465.2.k.b.218.15	yes	60
15.8	even	4	inner	465.2.k.b.218.16	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.b.32.15	✓	60	3.2	odd	2	inner
465.2.k.b.32.16	yes	60	1.1	even	1	trivial
465.2.k.b.218.15	yes	60	5.3	odd	4	inner
465.2.k.b.218.16	yes	60	15.8	even	4	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.150369 - 0.150369i) q^{2} +(-1.62789 - 0.591574i) q^{3} +1.95478i q^{4} +(-0.684260 + 2.12880i) q^{5} +(-0.333740 + 0.155831i) q^{6} +(-0.387197 - 0.387197i) q^{7} +(0.594677 + 0.594677i) q^{8} +(2.30008 + 1.92604i) q^{9} +(0.217214 + 0.422998i) q^{10} -5.94154i q^{11} +(1.15640 - 3.18217i) q^{12} +(-2.75083 + 2.75083i) q^{13} -0.116445 q^{14} +(2.37325 - 3.06067i) q^{15} -3.73071 q^{16} +(-4.13991 + 4.13991i) q^{17} +(0.635479 - 0.0562442i) q^{18} +1.21724i q^{19} +(-4.16133 - 1.33758i) q^{20} +(0.401260 + 0.859371i) q^{21} +(-0.893425 - 0.893425i) q^{22} +(-6.27242 - 6.27242i) q^{23} +(-0.616276 - 1.31987i) q^{24} +(-4.06358 - 2.91331i) q^{25} +0.827280i q^{26} +(-2.60489 - 4.49606i) q^{27} +(0.756883 - 0.756883i) q^{28} +2.83642 q^{29} +(-0.103368 - 0.817094i) q^{30} -1.00000 q^{31} +(-1.75034 + 1.75034i) q^{32} +(-3.51486 + 9.67221i) q^{33} +1.24503i q^{34} +(1.08921 - 0.559321i) q^{35} +(-3.76498 + 4.49615i) q^{36} +(3.46533 + 3.46533i) q^{37} +(0.183035 + 0.183035i) q^{38} +(6.10537 - 2.85074i) q^{39} +(-1.67286 + 0.859035i) q^{40} +6.88424i q^{41} +(0.189560 + 0.0688858i) q^{42} +(-4.32117 + 4.32117i) q^{43} +11.6144 q^{44} +(-5.67401 + 3.57850i) q^{45} -1.88636 q^{46} +(-3.93745 + 3.93745i) q^{47} +(6.07321 + 2.20699i) q^{48} -6.70016i q^{49} +(-1.04911 + 0.172965i) q^{50} +(9.18839 - 4.29027i) q^{51} +(-5.37726 - 5.37726i) q^{52} +(-4.51366 - 4.51366i) q^{53} +(-1.06776 - 0.284373i) q^{54} +(12.6484 + 4.06556i) q^{55} -0.460514i q^{56} +(0.720087 - 1.98154i) q^{57} +(0.426510 - 0.426510i) q^{58} -4.65734 q^{59} +(5.98293 + 4.63917i) q^{60} +0.744831 q^{61} +(-0.150369 + 0.150369i) q^{62} +(-0.144827 - 1.63634i) q^{63} -6.93503i q^{64} +(-3.97368 - 7.73824i) q^{65} +(0.925875 + 1.98293i) q^{66} +(5.51708 + 5.51708i) q^{67} +(-8.09260 - 8.09260i) q^{68} +(6.50024 + 13.9214i) q^{69} +(0.0796786 - 0.247888i) q^{70} +4.91796i q^{71} +(0.222433 + 2.51318i) q^{72} +(9.51707 - 9.51707i) q^{73} +1.04216 q^{74} +(4.89164 + 7.14646i) q^{75} -2.37943 q^{76} +(-2.30055 + 2.30055i) q^{77} +(0.489397 - 1.34672i) q^{78} +3.31966i q^{79} +(2.55278 - 7.94194i) q^{80} +(1.58074 + 8.86009i) q^{81} +(1.03518 + 1.03518i) q^{82} +(4.12394 + 4.12394i) q^{83} +(-1.67988 + 0.784374i) q^{84} +(-5.98026 - 11.6458i) q^{85} +1.29954i q^{86} +(-4.61739 - 1.67795i) q^{87} +(3.53330 - 3.53330i) q^{88} -3.87913 q^{89} +(-0.315100 + 1.39129i) q^{90} +2.13022 q^{91} +(12.2612 - 12.2612i) q^{92} +(1.62789 + 0.591574i) q^{93} +1.18414i q^{94} +(-2.59126 - 0.832908i) q^{95} +(3.88482 - 1.81391i) q^{96} +(5.32691 + 5.32691i) q^{97} +(-1.00750 - 1.00750i) q^{98} +(11.4436 - 13.6660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6} + 16 q^{10} - 12 q^{13} - 8 q^{15} - 60 q^{16} + 34 q^{18} - 4 q^{21} + 8 q^{22} + 8 q^{25} - 6 q^{27} - 80 q^{28} - 54 q^{30} - 60 q^{31} + 10 q^{33} + 28 q^{36} - 12 q^{37} + 60 q^{40}+ \cdots + 56 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 + 16 * q^10 - 12 * q^13 - 8 * q^15 - 60 * q^16 + 34 * q^18 - 4 * q^21 + 8 * q^22 + 8 * q^25 - 6 * q^27 - 80 * q^28 - 54 * q^30 - 60 * q^31 + 10 * q^33 + 28 * q^36 - 12 * q^37 + 60 * q^40 - 12 * q^42 - 24 * q^43 - 58 * q^45 + 8 * q^46 + 80 * q^48 + 32 * q^51 + 52 * q^52 + 64 * q^55 - 14 * q^57 - 48 * q^58 - 108 * q^60 - 56 * q^61 + 62 * q^63 + 40 * q^66 + 104 * q^67 + 108 * q^70 - 76 * q^72 - 108 * q^73 - 38 * q^75 - 120 * q^76 + 112 * q^78 + 60 * q^81 + 20 * q^82 + 48 * q^85 - 110 * q^87 - 28 * q^88 - 82 * q^90 - 32 * q^91 + 120 * q^96 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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