LMFDB - Embedded newform 95.2.p.a.54.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [95,2,Mod(4,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 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("95.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.p (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			54.3
Character	$\chi$	$=$	95.54
Dual form			95.2.p.a.44.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04072 + 1.24028i) q^{2} +(0.406515 + 1.11689i) q^{3} +(-0.107903 - 0.611947i) q^{4} +(2.23519 + 0.0626993i) q^{5} +(-1.80832 - 0.658176i) q^{6} +(-1.93288 + 1.11595i) q^{7} +(-1.93303 - 1.11604i) q^{8} +(1.21594 - 1.02030i) q^{9} +(-2.40397 + 2.70701i) q^{10} +(-2.82239 + 4.88852i) q^{11} +(0.639613 - 0.369281i) q^{12} +(1.60766 - 4.41702i) q^{13} +(0.627496 - 3.55871i) q^{14} +(0.838609 + 2.52195i) q^{15} +(4.56376 - 1.66107i) q^{16} +(-0.505129 + 0.601990i) q^{17} +2.56995i q^{18} +(2.63014 - 3.47597i) q^{19} +(-0.202814 - 1.37458i) q^{20} +(-2.03214 - 1.70517i) q^{21} +(-3.12582 - 8.58813i) q^{22} +(5.05247 - 0.890886i) q^{23} +(0.460684 - 2.61267i) q^{24} +(4.99214 + 0.280289i) q^{25} +(3.80521 + 6.59082i) q^{26} +(4.72186 + 2.72616i) q^{27} +(0.891466 + 1.06241i) q^{28} +(-2.32611 + 1.95184i) q^{29} +(-4.00068 - 1.58453i) q^{30} +(-4.05208 - 7.01841i) q^{31} +(-1.16257 + 3.19413i) q^{32} +(-6.60729 - 1.16504i) q^{33} +(-0.220938 - 1.25300i) q^{34} +(-4.39033 + 2.37317i) q^{35} +(-0.755571 - 0.634000i) q^{36} +0.985141i q^{37} +(1.57393 + 6.87961i) q^{38} +5.58687 q^{39} +(-4.25071 - 2.61575i) q^{40} +(-1.33247 + 0.484978i) q^{41} +(4.22977 - 0.745823i) q^{42} +(-1.49862 - 0.264247i) q^{43} +(3.29606 + 1.19967i) q^{44} +(2.78183 - 2.20432i) q^{45} +(-4.15324 + 7.19363i) q^{46} +(-0.617523 - 0.735935i) q^{47} +(3.71047 + 4.42197i) q^{48} +(-1.00930 + 1.74817i) q^{49} +(-5.54304 + 5.89994i) q^{50} +(-0.877699 - 0.319456i) q^{51} +(-2.87645 - 0.507196i) q^{52} +(-4.34421 + 0.766002i) q^{53} +(-8.29533 + 3.01925i) q^{54} +(-6.61508 + 10.7498i) q^{55} +4.98176 q^{56} +(4.95147 + 1.52455i) q^{57} -4.91635i q^{58} +(-7.56739 - 6.34980i) q^{59} +(1.45281 - 0.785309i) q^{60} +(0.363973 + 2.06420i) q^{61} +(12.9219 + 2.27847i) q^{62} +(-1.21168 + 3.32905i) q^{63} +(2.10495 + 3.64588i) q^{64} +(3.87038 - 9.77207i) q^{65} +(8.32130 - 6.98240i) q^{66} +(2.08785 + 2.48820i) q^{67} +(0.422891 + 0.244156i) q^{68} +(3.04892 + 5.28089i) q^{69} +(1.62570 - 7.91504i) q^{70} +(1.24628 - 7.06798i) q^{71} +(-3.48914 + 0.615230i) q^{72} +(-5.18587 - 14.2481i) q^{73} +(-1.22185 - 1.02525i) q^{74} +(1.71633 + 5.68961i) q^{75} +(-2.41091 - 1.23444i) q^{76} -12.5986i q^{77} +(-5.81435 + 6.92928i) q^{78} +(1.25893 - 0.458214i) q^{79} +(10.3050 - 3.42667i) q^{80} +(-0.298427 + 1.69246i) q^{81} +(0.785214 - 2.15736i) q^{82} +(-6.51723 + 3.76273i) q^{83} +(-0.824199 + 1.42756i) q^{84} +(-1.16680 + 1.31389i) q^{85} +(1.88738 - 1.58370i) q^{86} +(-3.12559 - 1.80456i) q^{87} +(10.9115 - 6.29977i) q^{88} +(3.19776 + 1.16389i) q^{89} +(-0.161134 + 5.74433i) q^{90} +(1.82175 + 10.3317i) q^{91} +(-1.09035 - 2.99571i) q^{92} +(6.19156 - 7.37882i) q^{93} +1.55543 q^{94} +(6.09681 - 7.60453i) q^{95} -4.04009 q^{96} +(-8.20200 + 9.77477i) q^{97} +(-1.11781 - 3.07117i) q^{98} +(1.55588 + 8.82385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) $ 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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 $

$2$	−1.04072	+	1.24028i	−0.735899	+	0.877010i	−0.996072	−	0.0885521i	$-0.971776\pi$
$2$	−1.04072	+	1.24028i	−0.735899	+	0.877010i	0.260173	+	0.965562i	$0.416220\pi$
$3$	0.406515	+	1.11689i	0.234701	+	0.644837i	0.999999	+	0.00116068i	$0.000369458\pi$
$3$	0.406515	+	1.11689i	0.234701	+	0.644837i	−0.765298	+	0.643676i	$0.777408\pi$
$4$	−0.107903	−	0.611947i	−0.0539514	−	0.305973i
$5$	2.23519	+	0.0626993i	0.999607	+	0.0280400i
$5$	2.23519	+	0.0626993i	0.999607	+	0.0280400i
$6$	−1.80832	−	0.658176i	−0.738245	−	0.268699i
$7$	−1.93288	+	1.11595i	−0.730562	+	0.421790i	−0.818628	−	0.574325i	$-0.805265\pi$
$7$	−1.93288	+	1.11595i	−0.730562	+	0.421790i	0.0880659	+	0.996115i	$0.471931\pi$
$8$	−1.93303	−	1.11604i	−0.683429	−	0.394578i
$9$	1.21594	−	1.02030i	0.405314	−	0.340099i
$10$	−2.40397	+	2.70701i	−0.760201	+	0.856031i
$11$	−2.82239	+	4.88852i	−0.850983	+	1.47395i	0.0293397	+	0.999569i	$0.490660\pi$
$11$	−2.82239	+	4.88852i	−0.850983	+	1.47395i	−0.880322	+	0.474376i	$0.842674\pi$
$12$	0.639613	−	0.369281i	0.184640	−	0.106602i
$13$	1.60766	−	4.41702i	0.445886	−	1.22506i	−0.489678	−	0.871903i	$-0.662886\pi$
$13$	1.60766	−	4.41702i	0.445886	−	1.22506i	0.935564	−	0.353158i	$-0.114892\pi$
$14$	0.627496	−	3.55871i	0.167705	−	0.951105i
$15$	0.838609	+	2.52195i	0.216528	+	0.651164i
$16$	4.56376	−	1.66107i	1.14094	−	0.415268i
$17$	−0.505129	+	0.601990i	−0.122512	+	0.146004i	−0.823814	−	0.566860i	$-0.808158\pi$
$17$	−0.505129	+	0.601990i	−0.122512	+	0.146004i	0.701302	+	0.712864i	$0.252602\pi$
$18$			2.56995i			0.605743i
$19$	2.63014	−	3.47597i	0.603396	−	0.797442i
$19$	2.63014	−	3.47597i	0.603396	−	0.797442i
$20$	−0.202814	−	1.37458i	−0.0453507	−	0.307366i
$21$	−2.03214	−	1.70517i	−0.443450	−	0.372098i
$22$	−3.12582	−	8.58813i	−0.666428	−	1.83099i
$23$	5.05247	−	0.890886i	1.05351	−	0.185763i	0.380036	−	0.924972i	$-0.375912\pi$
$23$	5.05247	−	0.890886i	1.05351	−	0.185763i	0.673476	+	0.739209i	$0.264800\pi$
$24$	0.460684	−	2.61267i	0.0940367	−	0.533309i
$25$	4.99214	+	0.280289i	0.998428	+	0.0560579i
$26$	3.80521	+	6.59082i	0.746264	+	1.29257i
$27$	4.72186	+	2.72616i	0.908721	+	0.524651i
$28$	0.891466	+	1.06241i	0.168471	+	0.200776i
$29$	−2.32611	+	1.95184i	−0.431949	+	0.362448i	−0.832686	−	0.553745i	$-0.813198\pi$
$29$	−2.32611	+	1.95184i	−0.431949	+	0.362448i	0.400738	+	0.916193i	$0.368754\pi$
$30$	−4.00068	−	1.58453i	−0.730420	−	0.289294i
$31$	−4.05208	−	7.01841i	−0.727775	−	1.26054i	−0.957822	−	0.287364i	$-0.907221\pi$
$31$	−4.05208	−	7.01841i	−0.727775	−	1.26054i	0.230047	−	0.973180i	$-0.426112\pi$
$32$	−1.16257	+	3.19413i	−0.205515	+	0.564647i
$33$	−6.60729	−	1.16504i	−1.15018	−	0.202808i
$34$	−0.220938	−	1.25300i	−0.0378906	−	0.214888i
$35$	−4.39033	+	2.37317i	−0.742101	+	0.401139i
$36$	−0.755571	−	0.634000i	−0.125929	−	0.105667i
$37$			0.985141i			0.161956i	0.996716	+	0.0809781i	$0.0258044\pi$
$37$			0.985141i			0.161956i	−0.996716	+	0.0809781i	$0.974196\pi$
$38$	1.57393	+	6.87961i	0.255326	+	1.11602i
$39$	5.58687			0.894615
$40$	−4.25071	−	2.61575i	−0.672097	−	0.413586i
$41$	−1.33247	+	0.484978i	−0.208096	+	0.0757409i	−0.443965	−	0.896044i	$-0.646429\pi$
$41$	−1.33247	+	0.484978i	−0.208096	+	0.0757409i	0.235869	+	0.971785i	$0.424206\pi$
$42$	4.22977	−	0.745823i	0.652668	−	0.115083i
$43$	−1.49862	−	0.264247i	−0.228537	−	0.0402973i	0.0582066	−	0.998305i	$-0.481462\pi$
$43$	−1.49862	−	0.264247i	−0.228537	−	0.0402973i	−0.286744	+	0.958007i	$0.592573\pi$
$44$	3.29606	+	1.19967i	0.496900	+	0.180857i
$45$	2.78183	−	2.20432i	0.414691	−	0.328600i
$46$	−4.15324	+	7.19363i	−0.612363	+	1.06064i
$47$	−0.617523	−	0.735935i	−0.0900749	−	0.107347i	0.719124	−	0.694881i	$-0.244543\pi$
$47$	−0.617523	−	0.735935i	−0.0900749	−	0.107347i	−0.809199	+	0.587534i	$0.800099\pi$
$48$	3.71047	+	4.42197i	0.535561	+	0.638256i
$49$	−1.00930	+	1.74817i	−0.144186	+	0.249738i
$50$	−5.54304	+	5.89994i	−0.783905	+	0.834378i
$51$	−0.877699	−	0.319456i	−0.122902	−	0.0447328i
$52$	−2.87645	−	0.507196i	−0.398892	−	0.0703355i
$53$	−4.34421	+	0.766002i	−0.596723	+	0.105218i	−0.463849	−	0.885914i	$-0.653532\pi$
$53$	−4.34421	+	0.766002i	−0.596723	+	0.105218i	−0.132875	+	0.991133i	$0.542421\pi$
$54$	−8.29533	+	3.01925i	−1.12885	+	0.410868i
$55$	−6.61508	+	10.7498i	−0.891977	+	1.44950i
$56$	4.98176			0.665716
$57$	4.95147	+	1.52455i	0.655838	+	0.201932i
$58$		−	4.91635i		−	0.645548i
$59$	−7.56739	−	6.34980i	−0.985191	−	0.826673i	−0.000326502	−	1.00000i	$-0.500104\pi$
$59$	−7.56739	−	6.34980i	−0.985191	−	0.826673i	−0.984864	+	0.173327i	$0.944548\pi$
$60$	1.45281	−	0.785309i	0.187557	−	0.101383i
$61$	0.363973	+	2.06420i	0.0466020	+	0.264293i	0.999202	−	0.0399312i	$-0.0127139\pi$
$61$	0.363973	+	2.06420i	0.0466020	+	0.264293i	−0.952600	+	0.304224i	$0.901603\pi$
$62$	12.9219	+	2.27847i	1.64108	+	0.289366i
$63$	−1.21168	+	3.32905i	−0.152657	+	0.419421i
$64$	2.10495	+	3.64588i	0.263118	+	0.455735i
$65$	3.87038	−	9.77207i	0.480061	−	1.21208i
$66$	8.32130	−	6.98240i	1.02428	−	0.859474i
$67$	2.08785	+	2.48820i	0.255071	+	0.303982i	0.878350	−	0.478017i	$-0.158644\pi$
$67$	2.08785	+	2.48820i	0.255071	+	0.303982i	−0.623279	+	0.781999i	$0.714200\pi$
$68$	0.422891	+	0.244156i	0.0512830	+	0.0296083i
$69$	3.04892	+	5.28089i	0.367047	+	0.635745i
$70$	1.62570	−	7.91504i	0.194308	−	0.946028i
$71$	1.24628	−	7.06798i	0.147906	−	0.838815i	−0.817082	−	0.576521i	$-0.804410\pi$
$71$	1.24628	−	7.06798i	0.147906	−	0.838815i	0.964988	−	0.262294i	$-0.0844790\pi$
$72$	−3.48914	+	0.615230i	−0.411199	+	0.0725056i
$73$	−5.18587	−	14.2481i	−0.606960	−	1.66761i	−0.736829	−	0.676079i	$-0.763678\pi$
$73$	−5.18587	−	14.2481i	−0.606960	−	1.66761i	0.129869	−	0.991531i	$-0.458544\pi$
$74$	−1.22185	−	1.02525i	−0.142037	−	0.119183i
$75$	1.71633	+	5.68961i	0.198184	+	0.656980i
$76$	−2.41091	−	1.23444i	−0.276550	−	0.141600i
$77$		−	12.5986i		−	1.43574i
$78$	−5.81435	+	6.92928i	−0.658346	+	0.784586i
$79$	1.25893	−	0.458214i	0.141641	−	0.0515531i	−0.270227	−	0.962797i	$-0.587099\pi$
$79$	1.25893	−	0.458214i	0.141641	−	0.0515531i	0.411868	+	0.911244i	$0.364877\pi$
$80$	10.3050	−	3.42667i	1.15214	−	0.383113i
$81$	−0.298427	+	1.69246i	−0.0331585	+	0.188051i
$82$	0.785214	−	2.15736i	0.0867123	−	0.238240i
$83$	−6.51723	+	3.76273i	−0.715359	+	0.413013i	−0.813042	−	0.582205i	$-0.802190\pi$
$83$	−6.51723	+	3.76273i	−0.715359	+	0.413013i	0.0976829	+	0.995218i	$0.468857\pi$
$84$	−0.824199	+	1.42756i	−0.0899275	+	0.155759i
$85$	−1.16680	+	1.31389i	−0.126558	+	0.142511i
$86$	1.88738	−	1.58370i	0.203522	−	0.170775i
$87$	−3.12559	−	1.80456i	−0.335099	−	0.193469i
$88$	10.9115	−	6.29977i	1.16317	−	0.671558i
$89$	3.19776	+	1.16389i	0.338962	+	0.123372i	0.505892	−	0.862597i	$-0.331163\pi$
$89$	3.19776	+	1.16389i	0.338962	+	0.123372i	−0.166930	+	0.985969i	$0.553386\pi$
$90$	−0.161134	+	5.74433i	−0.0169850	+	0.605505i
$91$	1.82175	+	10.3317i	0.190971	+	1.08305i
$92$	−1.09035	−	2.99571i	−0.113677	−	0.312324i
$93$	6.19156	−	7.37882i	0.642035	−	0.765148i
$94$	1.55543			0.160431
$95$	6.09681	−	7.60453i	0.625519	−	0.780209i
$96$	−4.04009			−0.412340
$97$	−8.20200	+	9.77477i	−0.832787	+	0.992477i	0.167191	+	0.985924i	$0.446530\pi$
$97$	−8.20200	+	9.77477i	−0.832787	+	0.992477i	−0.999979	+	0.00655264i	$0.997914\pi$
$98$	−1.11781	−	3.07117i	−0.112916	−	0.310235i
$99$	1.55588	+	8.82385i	0.156372	+	0.886830i
$100$	−0.367143	−	3.08517i	−0.0367143	−	0.308517i
$101$	−5.23691	−	1.90608i	−0.521092	−	0.189662i	0.0680647	−	0.997681i	$-0.478318\pi$
$101$	−5.23691	−	1.90608i	−0.521092	−	0.189662i	−0.589156	+	0.808019i	$0.700540\pi$
$102$	1.30965	−	0.756128i	0.129675	−	0.0748679i
$103$	2.86453	+	1.65384i	0.282251	+	0.162958i	0.634442	−	0.772971i	$-0.281230\pi$
$103$	2.86453	+	1.65384i	0.282251	+	0.162958i	−0.352191	+	0.935928i	$0.614563\pi$
$104$	−8.03721	+	6.74402i	−0.788114	+	0.661306i
$105$	−4.43531	−	3.93879i	−0.432842	−	0.384386i
$106$	3.57104	−	6.18523i	0.346850	−	0.600763i
$107$	−5.77870	+	3.33633i	−0.558648	+	0.322536i	−0.752603	−	0.658475i	$-0.771202\pi$
$107$	−5.77870	+	3.33633i	−0.558648	+	0.322536i	0.193955	+	0.981010i	$0.437869\pi$
$108$	1.15877	−	3.18368i	0.111502	−	0.306350i
$109$	−2.72302	+	15.4430i	−0.260818	+	1.47917i	0.519866	+	0.854248i	$0.325982\pi$
$109$	−2.72302	+	15.4430i	−0.260818	+	1.47917i	−0.780684	+	0.624925i	$0.785129\pi$
$110$	−6.44833	−	19.3921i	−0.614825	−	1.84896i
$111$	−1.10029	+	0.400474i	−0.104435	+	0.0380114i
$112$	−6.96755	+	8.30360i	−0.658371	+	0.784616i
$113$			6.58139i			0.619125i	0.950879	+	0.309562i	$0.100183\pi$
$113$			6.58139i			0.619125i	−0.950879	+	0.309562i	$0.899817\pi$
$114$	−7.04395	+	4.55458i	−0.659726	+	0.426575i
$115$	11.3491	−	1.67451i	1.05831	−	0.156149i
$116$	1.44542	+	1.21285i	0.134204	+	0.112610i
$117$	−2.55185	−	7.01114i	−0.235918	−	0.648180i
$118$	15.7510	−	2.77733i	1.45000	−	0.255674i
$119$	0.304565	−	1.72728i	0.0279195	−	0.158339i
$120$	1.19353	−	5.81092i	0.108954	−	0.530462i
$121$	−10.4318	−	18.0684i	−0.948343	−	1.64258i
$122$	−2.93897	−	1.69682i	−0.266082	−	0.153623i
$123$	−1.08334	−	1.29107i	−0.0976810	−	0.116412i
$124$	−3.85766	+	3.23696i	−0.346428	+	0.290688i
$125$	11.1408	+	0.939503i	0.996463	+	0.0840317i
$126$	−2.86794	−	4.96742i	−0.255497	−	0.442533i
$127$	−0.456461	+	1.25412i	−0.0405044	+	0.111285i	−0.958296	−	0.285778i	$-0.907748\pi$
$127$	−0.456461	+	1.25412i	−0.0405044	+	0.111285i	0.917792	+	0.397062i	$0.129970\pi$
$128$	−13.4075	−	2.36411i	−1.18507	−	0.208960i
$129$	−0.314076	−	1.78121i	−0.0276529	−	0.156827i
$130$	8.09213	+	14.9703i	0.709727	+	1.31298i
$131$	10.5552	+	8.85684i	0.922210	+	0.773826i	0.974402	−	0.224811i	$-0.0721765\pi$
$131$	10.5552	+	8.85684i	0.922210	+	0.773826i	−0.0521924	+	0.998637i	$0.516621\pi$
$132$			4.16902i			0.362867i
$133$	−1.20475	+	9.65376i	−0.104465	+	0.837087i
$134$	−5.25892			−0.454302
$135$	10.3833	+	6.38955i	0.893653	+	0.549925i
$136$	1.64827	−	0.599922i	0.141338	−	0.0514429i
$137$	−11.5639	+	2.03902i	−0.987969	+	0.174206i	−0.644207	−	0.764851i	$-0.722813\pi$
$137$	−11.5639	+	2.03902i	−0.987969	+	0.174206i	−0.343762	+	0.939057i	$0.611701\pi$
$138$	−9.72285	−	1.71440i	−0.827664	−	0.145940i
$139$	−8.77809	−	3.19496i	−0.744548	−	0.270993i	−0.0582382	−	0.998303i	$-0.518548\pi$
$139$	−8.77809	−	3.19496i	−0.744548	−	0.270993i	−0.686310	+	0.727309i	$0.740771\pi$
$140$	1.92598	+	2.43058i	0.162775	+	0.205421i
$141$	0.570926	−	0.988874i	0.0480807	−	0.0832782i
$142$	7.46925	+	8.90151i	0.626806	+	0.746998i
$143$	17.0553	+	20.3257i	1.42623	+	1.69972i
$144$	3.85449	−	6.67616i	0.321207	−	0.556347i
$145$	−5.32168	+	4.21689i	−0.441942	+	0.350194i
$146$	23.0686	+	8.39629i	1.90917	+	0.694882i
$147$	−2.36281	−	0.416627i	−0.194881	−	0.0343628i
$148$	0.602854	−	0.106299i	0.0495543	−	0.00873776i
$149$	16.9364	−	6.16435i	1.38748	−	0.505003i	0.463046	−	0.886334i	$-0.346756\pi$
$149$	16.9364	−	6.16435i	1.38748	−	0.505003i	0.924439	+	0.381331i	$0.124534\pi$
$150$	−8.84292	−	3.79256i	−0.722021	−	0.309661i
$151$	−13.0159			−1.05922			−0.529611	−	0.848241i	$-0.677662\pi$
$151$	−13.0159			−1.05922			−0.529611	+	0.848241i	$0.677662\pi$
$152$	−8.96345	+	3.78382i	−0.727032	+	0.306908i
$153$			1.24737i			0.100844i
$154$	15.6258	+	13.1116i	1.25916	+	1.05656i
$155$	−8.61711	−	15.9415i	−0.692143	−	1.28045i
$156$	−0.602838	−	3.41887i	−0.0482657	−	0.273728i
$157$	10.3475	+	1.82454i	0.825821	+	0.145614i	0.570558	−	0.821257i	$-0.306727\pi$
$157$	10.3475	+	1.82454i	0.825821	+	0.145614i	0.255263	+	0.966872i	$0.417838\pi$
$158$	−0.741880	+	2.03830i	−0.0590208	+	0.162158i
$159$	−2.62153	−	4.54062i	−0.207901	−	0.360094i
$160$	−2.79883	+	7.06658i	−0.221267	+	0.558662i
$161$	−8.77165	+	7.36029i	−0.691303	+	0.580072i
$162$	−1.78855	−	2.13151i	−0.140522	−	0.167467i
$163$	−3.13838	−	1.81195i	−0.245817	−	0.141923i	0.372030	−	0.928221i	$-0.378662\pi$
$163$	−3.13838	−	1.81195i	−0.245817	−	0.141923i	−0.617847	+	0.786298i	$0.711995\pi$
$164$	0.440558	+	0.763068i	0.0344018	+	0.0595856i
$165$	−14.6955	−	3.01836i	−1.14404	−	0.234979i
$166$	2.11577	−	11.9991i	0.164216	−	0.931313i
$167$	10.4783	−	1.84761i	0.810835	−	0.142972i	0.247166	−	0.968973i	$-0.420501\pi$
$167$	10.4783	−	1.84761i	0.810835	−	0.142972i	0.563669	+	0.826001i	$0.309389\pi$
$168$	2.02516	+	5.56409i	0.156245	+	0.429279i
$169$	−6.96691	−	5.84593i	−0.535916	−	0.449687i
$170$	−0.415276	−	2.81455i	−0.0318502	−	0.215866i
$171$	−0.348416	−	6.91011i	−0.0266440	−	0.528429i
$172$			0.945588i			0.0721004i
$173$	12.4770	−	14.8695i	0.948611	−	1.13051i	−0.0427156	−	0.999087i	$-0.513601\pi$
$173$	12.4770	−	14.8695i	0.948611	−	1.13051i	0.991326	−	0.131423i	$-0.0419546\pi$
$174$	5.49102	−	1.99857i	0.416273	−	0.151511i
$175$	−9.96202	+	5.02922i	−0.753058	+	0.380173i
$176$	−4.76052	+	26.9982i	−0.358838	+	2.03507i
$177$	4.01577	−	11.0332i	0.301844	−	0.829309i
$178$	−4.77152	+	2.75484i	−0.357640	+	0.206484i
$179$	1.03526	−	1.79312i	0.0773789	−	0.134024i	−0.824739	−	0.565513i	$-0.808678\pi$
$179$	1.03526	−	1.79312i	0.0773789	−	0.134024i	0.902118	+	0.431489i	$0.142012\pi$
$180$	−1.64909	−	1.46448i	−0.122916	−	0.109156i
$181$	16.5714	−	13.9051i	1.23174	−	1.03356i	0.233619	−	0.972328i	$-0.424943\pi$
$181$	16.5714	−	13.9051i	1.23174	−	1.03356i	0.998124	−	0.0612273i	$-0.0195014\pi$
$182$	−14.7101	−	8.49287i	−1.09038	−	0.629533i
$183$	−2.15752	+	1.24564i	−0.159488	+	0.0920807i
$184$	−10.7608	−	3.91662i	−0.793299	−	0.288737i
$185$	−0.0617676	+	2.20198i	−0.00454125	+	0.161892i
$186$	2.70812	+	15.3585i	0.198569	+	1.12614i
$187$	−1.51717	−	4.16839i	−0.110946	−	0.304823i
$188$	−0.383721	+	0.457300i	−0.0279857	+	0.0333521i
$189$	−12.1691			−0.885169
$190$	3.08669	+	15.4759i	0.223932	+	1.12274i
$191$	−22.4061			−1.62125			−0.810626	−	0.585565i	$-0.800873\pi$
$191$	−22.4061			−1.62125			−0.810626	+	0.585565i	$0.800873\pi$
$192$	−3.21635	+	3.83310i	−0.232120	+	0.276630i
$193$	6.70316	+	18.4168i	0.482504	+	1.32567i	0.907339	+	0.420399i	$0.138110\pi$
$193$	6.70316	+	18.4168i	0.482504	+	1.32567i	−0.424835	+	0.905271i	$0.639668\pi$
$194$	−3.58747	−	20.3455i	−0.257565	−	1.46073i
$195$	12.4877	+	0.350292i	0.894263	+	0.0250850i
$196$	1.17869	+	0.429009i	0.0841923	+	0.0306435i
$197$	13.3885	−	7.72984i	0.953890	−	0.550729i	0.0596028	−	0.998222i	$-0.481017\pi$
$197$	13.3885	−	7.72984i	0.953890	−	0.550729i	0.894287	+	0.447494i	$0.147683\pi$
$198$	−12.5633	−	7.25341i	−0.892833	−	0.515477i
$199$	1.05175	−	0.882524i	0.0745566	−	0.0625604i	−0.604748	−	0.796417i	$-0.706726\pi$
$199$	1.05175	−	0.882524i	0.0745566	−	0.0625604i	0.679304	+	0.733857i	$0.262282\pi$
$200$	−9.33714	−	6.11321i	−0.660235	−	0.432269i
$201$	−1.93031	+	3.34339i	−0.136153	+	0.235824i
$202$	7.81421	−	4.51154i	0.549806	−	0.317431i
$203$	2.31795	−	6.36852i	0.162688	−	0.446982i
$204$	−0.100784	+	0.571575i	−0.00705630	+	0.0400183i
$205$	−3.00872	+	1.00047i	−0.210138	+	0.0698761i
$206$	−5.03239	+	1.83164i	−0.350623	+	0.127617i
$207$	5.23454	−	6.23829i	0.363826	−	0.433591i
$208$		−	22.8287i		−	1.58288i
$209$	9.56906	+	22.6681i	0.661905	+	1.56798i
$210$	9.50110	−	1.40185i	0.655638	−	0.0967370i
$211$	7.33250	+	6.15270i	0.504790	+	0.423569i	0.859291	−	0.511486i	$-0.170905\pi$
$211$	7.33250	+	6.15270i	0.504790	+	0.423569i	−0.354501	+	0.935056i	$0.615349\pi$
$212$	0.937505	+	2.57577i	0.0643881	+	0.176905i
$213$	8.40079	−	1.48129i	0.575613	−	0.101496i
$214$	1.87601	−	10.6394i	0.128241	−	0.727293i
$215$	−3.33313	−	0.684604i	−0.227318	−	0.0466896i
$216$	−6.08499	−	10.5395i	−0.414031	−	0.717123i
$217$	15.6644	+	9.04385i	1.06337	+	0.613936i
$218$	−16.3198	−	19.4491i	−1.10531	−	1.31726i
$219$	13.8054	−	11.5841i	0.932882	−	0.782781i
$220$	7.29210	+	2.88814i	0.491633	+	0.194719i
$221$	1.84692	+	3.19896i	0.124237	+	0.215186i
$222$	0.648396	−	1.78145i	0.0435175	−	0.119563i
$223$	−6.43818	−	1.13522i	−0.431132	−	0.0760203i	−0.0461291	−	0.998935i	$-0.514689\pi$
$223$	−6.43818	−	1.13522i	−0.431132	−	0.0760203i	−0.385003	+	0.922915i	$0.625800\pi$
$224$	−1.31738	−	7.47124i	−0.0880213	−	0.499194i
$225$	6.35614	−	4.75265i	0.423742	−	0.316843i
$226$	−8.16276	−	6.84937i	−0.542979	−	0.455613i
$227$			8.88867i			0.589962i	0.955503	+	0.294981i	$0.0953133\pi$
$227$			8.88867i			0.589962i	−0.955503	+	0.294981i	$0.904687\pi$
$228$	0.398666	−	3.19454i	0.0264023	−	0.211563i
$229$	7.22494			0.477438			0.238719	−	0.971089i	$-0.423273\pi$
$229$	7.22494			0.477438			0.238719	+	0.971089i	$0.423273\pi$
$230$	−9.73432	+	15.8187i	−0.641862	+	1.04306i
$231$	14.0713	−	5.12152i	0.925821	−	0.336971i
$232$	6.67477	−	1.17694i	0.438220	−	0.0772701i
$233$	−24.5985	−	4.33738i	−1.61150	−	0.284151i	−0.705910	−	0.708302i	$-0.749462\pi$
$233$	−24.5985	−	4.33738i	−1.61150	−	0.284151i	−0.905592	+	0.424151i	$0.860573\pi$
$234$	11.3515	+	4.13162i	0.742073	+	0.270092i
$235$	−1.33414	−	1.68367i	−0.0870295	−	0.109831i
$236$	−3.06920	+	5.31600i	−0.199788	+	0.346042i
$237$	1.02355	+	1.21982i	0.0664866	+	0.0792357i
$238$	1.82534	+	2.17535i	0.118319	+	0.141007i
$239$	8.40936	−	14.5654i	0.543956	−	0.942160i	−0.454715	−	0.890637i	$-0.650259\pi$
$239$	8.40936	−	14.5654i	0.543956	−	0.942160i	0.998672	−	0.0515232i	$-0.0164076\pi$
$240$	8.01635	+	10.1166i	0.517453	+	0.653022i
$241$	10.1922	+	3.70965i	0.656536	+	0.238959i	0.648740	−	0.761010i	$-0.275296\pi$
$241$	10.1922	+	3.70965i	0.656536	+	0.238959i	0.00779570	+	0.999970i	$0.497519\pi$
$242$	33.2664	+	5.86576i	2.13844	+	0.377065i
$243$	14.0969	−	2.48566i	0.904315	−	0.159455i
$244$	1.22390	−	0.445465i	0.0783524	−	0.0285179i
$245$	−2.36560	+	3.84420i	−0.151132	+	0.245597i
$246$	2.72873			0.173978
$247$	−11.1250	−	17.2056i	−0.707869	−	1.09476i
$248$			18.0891i			1.14866i
$249$	−6.85191	−	5.74943i	−0.434222	−	0.364355i
$250$	−12.7597	+	12.8399i	−0.806993	+	0.812069i
$251$	1.10625	+	6.27388i	0.0698262	+	0.396004i	0.999611	+	0.0278997i	$0.00888191\pi$
$251$	1.10625	+	6.27388i	0.0698262	+	0.396004i	−0.929785	+	0.368104i	$0.880007\pi$
$252$	2.16795	+	0.382267i	0.136568	+	0.0240806i
$253$	−9.90491	+	27.2135i	−0.622717	+	1.71090i
$254$	−1.08041	−	1.87132i	−0.0677909	−	0.117417i
$255$	−1.94179	−	0.769076i	−0.121600	−	0.0481614i
$256$	10.4357	−	8.75656i	0.652229	−	0.547285i
$257$	−8.77180	−	10.4538i	−0.547170	−	0.652092i	0.419609	−	0.907705i	$-0.362167\pi$
$257$	−8.77180	−	10.4538i	−0.547170	−	0.652092i	−0.966779	+	0.255613i	$0.917723\pi$
$258$	2.53607	+	1.46420i	0.157889	+	0.0911571i
$259$	−1.09937	−	1.90416i	−0.0683115	−	0.118319i
$260$	−6.39761	−	1.31403i	−0.396763	−	0.0814927i
$261$	−0.836964	+	4.74666i	−0.0518068	+	0.293811i
$262$	−21.9699	+	3.87389i	−1.35731	+	0.239330i
$263$	−3.49596	−	9.60508i	−0.215570	−	0.592274i	0.784025	−	0.620730i	$-0.213163\pi$
$263$	−3.49596	−	9.60508i	−0.215570	−	0.592274i	−0.999595	+	0.0284550i	$0.990941\pi$
$264$	11.4719	+	9.62603i	0.706044	+	0.592441i
$265$	−9.75816	+	1.43978i	−0.599439	+	0.0884450i
$266$	−10.7195	−	11.5411i	−0.657258	−	0.707628i
$267$			4.04469i			0.247531i
$268$	1.29736	−	1.54613i	0.0792490	−	0.0944452i
$269$	−13.5785	+	4.94217i	−0.827895	+	0.301329i	−0.720995	−	0.692941i	$-0.756315\pi$
$269$	−13.5785	+	4.94217i	−0.827895	+	0.301329i	−0.106900	+	0.994270i	$0.534093\pi$
$270$	−18.7309	+	6.22849i	−1.13993	+	0.379054i
$271$	−2.81404	+	15.9592i	−0.170941	+	0.969453i	0.771785	+	0.635884i	$0.219364\pi$
$271$	−2.81404	+	15.9592i	−0.170941	+	0.969453i	−0.942725	+	0.333570i	$0.891747\pi$
$272$	−1.30534	+	3.58639i	−0.0791479	+	0.217457i
$273$	−10.7988	+	6.23467i	−0.653571	+	0.377340i
$274$	9.50578	−	16.4645i	0.574265	−	0.994657i
$275$	−15.4600	+	23.6131i	−0.932271	+	1.42392i
$276$	2.90264	−	2.43560i	0.174718	−	0.146606i
$277$	24.7634	+	14.2971i	1.48789	+	0.859032i	0.999904	−	0.0138211i	$-0.00439952\pi$
$277$	24.7634	+	14.2971i	1.48789	+	0.859032i	0.487983	+	0.872853i	$0.337733\pi$
$278$	13.0982	−	7.56223i	0.785576	−	0.453552i
$279$	−12.0880	−	4.39966i	−0.723687	−	0.263401i
$280$	11.1352	+	0.312353i	0.665455	+	0.0186667i
$281$	1.24639	+	7.06866i	0.0743537	+	0.421681i	0.999150	+	0.0412185i	$0.0131240\pi$
$281$	1.24639	+	7.06866i	0.0743537	+	0.421681i	−0.924796	+	0.380462i	$0.875765\pi$
$282$	0.632306	+	1.73725i	0.0376533	+	0.103452i
$283$	6.66290	−	7.94053i	0.396068	−	0.472016i	−0.530749	−	0.847529i	$-0.678089\pi$
$283$	6.66290	−	7.94053i	0.396068	−	0.472016i	0.926817	+	0.375514i	$0.122534\pi$
$284$	−4.45970			−0.264635
$285$	10.9719	+	3.71811i	0.649918	+	0.220242i
$286$	−42.9592			−2.54023
$287$	2.03429	−	2.42438i	0.120080	−	0.143106i
$288$	1.84534	+	5.07004i	0.108738	+	0.298755i
$289$	2.84478	+	16.1336i	0.167340	+	0.949033i
$290$	0.308251	−	10.9890i	0.0181012	−	0.645294i
$291$	−14.2516	−	5.18715i	−0.835442	−	0.304076i
$292$	−8.15949	+	4.71088i	−0.477498	+	0.275684i
$293$	7.87266	+	4.54528i	0.459926	+	0.265538i	0.712013	−	0.702166i	$-0.247784\pi$
$293$	7.87266	+	4.54528i	0.459926	+	0.265538i	−0.252087	+	0.967704i	$0.581117\pi$
$294$	2.97575	−	2.49695i	0.173549	−	0.145625i
$295$	−16.5164	−	14.6675i	−0.961624	−	0.853973i
$296$	1.09945	−	1.90431i	0.0639044	−	0.110686i
$297$	−26.6538	+	15.3886i	−1.54661	+	0.892937i
$298$	−9.98051	+	27.4212i	−0.578156	+	1.58847i
$299$	4.18761	−	23.7491i	0.242175	−	1.37345i
$300$	3.29654	−	1.66422i	0.190326	−	0.0960841i
$301$	3.19155	−	1.16163i	0.183958	−	0.0669551i
$302$	13.5459	−	16.1434i	0.779480	−	0.928948i
$303$		−	6.62390i		−	0.380533i
$304$	6.22951	−	20.2323i	0.357287	−	1.16040i
$305$	0.684125	+	4.63669i	0.0391729	+	0.265496i
$306$	−1.54708	−	1.29816i	−0.0884409	−	0.0742108i
$307$	5.01541	+	13.7797i	0.286245	+	0.786450i	0.996584	+	0.0825907i	$0.0263194\pi$
$307$	5.01541	+	13.7797i	0.286245	+	0.786450i	−0.710339	+	0.703860i	$0.751458\pi$
$308$	−7.70967	+	1.35942i	−0.439299	+	0.0774603i
$309$	−0.682682	+	3.87168i	−0.0388364	+	0.220252i
$310$	28.7399	+	5.90301i	1.63232	+	0.335268i
$311$	15.7905	+	27.3500i	0.895400	+	1.55088i	0.833309	+	0.552807i	$0.186443\pi$
$311$	15.7905	+	27.3500i	0.895400	+	1.55088i	0.0620906	+	0.998071i	$0.480223\pi$
$312$	−10.7996	−	6.23514i	−0.611406	−	0.352995i
$313$	5.77911	+	6.88727i	0.326654	+	0.389292i	0.904230	−	0.427046i	$-0.140446\pi$
$313$	5.77911	+	6.88727i	0.326654	+	0.389292i	−0.577576	+	0.816337i	$0.696001\pi$
$314$	−13.0318	+	10.9350i	−0.735426	+	0.617095i
$315$	−2.91705	+	7.36509i	−0.164357	+	0.414976i
$316$	−0.416244	−	0.720957i	−0.0234156	−	0.0405570i
$317$	−3.56399	+	9.79199i	−0.200174	+	0.549973i	−0.998644	−	0.0520614i	$-0.983421\pi$
$317$	−3.56399	+	9.79199i	−0.200174	+	0.549973i	0.798470	+	0.602035i	$0.205643\pi$
$318$	8.35991	+	1.47408i	0.468800	+	0.0826621i
$319$	−2.97642	−	16.8801i	−0.166648	−	0.945106i
$320$	4.47636	+	8.28120i	0.250236	+	0.462933i
$321$	−6.07545	−	5.09791i	−0.339098	−	0.284537i
$322$		−	18.5393i		−	1.03315i
$323$	0.763934	+	3.33913i	0.0425064	+	0.185794i
$324$	1.06790			0.0593276
$325$	9.26372	−	21.5998i	0.513859	−	1.19814i
$326$	5.51349	−	2.00675i	0.305364	−	0.111143i
$327$	−18.3551	+	3.23650i	−1.01504	+	0.178979i
$328$	3.11695	+	0.549603i	0.172105	+	0.0303467i
$329$	2.01487	+	0.733352i	0.111083	+	0.0404310i
$330$	19.0375	−	15.0852i	1.04798	−	0.830416i
$331$	2.01528	−	3.49056i	0.110770	−	0.191859i	−0.805311	−	0.592852i	$-0.798002\pi$
$331$	2.01528	−	3.49056i	0.110770	−	0.191859i	0.916081	+	0.400994i	$0.131335\pi$
$332$	3.00582	+	3.58219i	0.164966	+	0.196598i
$333$	1.00514	+	1.19788i	0.0550812	+	0.0656432i
$334$	−8.61341	+	14.9189i	−0.471305	+	0.816324i
$335$	4.51072	+	5.69250i	0.246447	+	0.311015i
$336$	−12.1066	−	4.40645i	−0.660470	−	0.240392i
$337$	−24.4051	−	4.30328i	−1.32943	−	0.234414i	−0.536590	−	0.843843i	$-0.680288\pi$
$337$	−24.4051	−	4.30328i	−1.32943	−	0.234414i	−0.792841	+	0.609429i	$0.791399\pi$
$338$	14.5012	−	2.55695i	0.788760	−	0.139080i
$339$	−7.35069	+	2.67543i	−0.399235	+	0.145310i
$340$	0.929932	+	0.572250i	0.0504326	+	0.0310346i
$341$	45.7462			2.47730
$342$	8.93307	+	6.75934i	0.483045	+	0.365503i
$343$		−	20.1287i		−	1.08685i
$344$	2.60197	+	2.18331i	0.140289	+	0.117716i
$345$	6.48381	+	11.9950i	0.349077	+	0.645787i
$346$	5.45732	+	30.9500i	0.293387	+	1.66388i
$347$	−28.1891	−	4.97049i	−1.51327	−	0.266830i	−0.645485	−	0.763773i	$-0.723345\pi$
$347$	−28.1891	−	4.97049i	−1.51327	−	0.266830i	−0.867783	+	0.496943i	$0.834456\pi$
$348$	−0.767036	+	2.10741i	−0.0411174	+	0.112969i
$349$	5.11084	+	8.85223i	0.273577	+	0.473849i	0.969775	−	0.244001i	$-0.0784599\pi$
$349$	5.11084	+	8.85223i	0.273577	+	0.473849i	−0.696198	+	0.717850i	$0.745127\pi$
$350$	4.13002	−	17.5897i	0.220759	−	0.940208i
$351$	19.6327	−	16.4738i	1.04791	−	0.879305i
$352$	−12.3333	−	14.6983i	−0.657369	−	0.783422i
$353$	−15.4082	−	8.89593i	−0.820096	−	0.473483i	0.0303537	−	0.999539i	$-0.490337\pi$
$353$	−15.4082	−	8.89593i	−0.820096	−	0.473483i	−0.850450	+	0.526057i	$0.823670\pi$
$354$	9.50501	+	16.4632i	0.505186	+	0.875007i
$355$	3.22882	−	15.7201i	0.171368	−	0.834338i
$356$	0.367192	−	2.08245i	0.0194611	−	0.110369i
$357$	2.05299	−	0.361997i	0.108656	−	0.0191589i
$358$	1.14656	+	3.15014i	0.0605975	+	0.166490i
$359$	0.659251	+	0.553177i	0.0347939	+	0.0291956i	0.660019	−	0.751249i	$-0.270548\pi$
$359$	0.659251	+	0.553177i	0.0347939	+	0.0291956i	−0.625225	+	0.780445i	$0.714993\pi$
$360$	−7.83747	+	1.15639i	−0.413071	+	0.0609470i
$361$	−5.16469	−	18.2846i	−0.271826	−	0.962346i
$362$			35.0244i			1.84084i
$363$	15.9397	−	18.9962i	0.836618	−	0.997042i
$364$	6.12586	−	2.22963i	0.321082	−	0.116864i
$365$	−10.6981	−	32.1723i	−0.559962	−	1.68397i
$366$	0.700422	−	3.97229i	0.0366116	−	0.207635i
$367$	7.28874	−	20.0256i	0.380469	−	1.04533i	−0.590690	−	0.806899i	$-0.701144\pi$
$367$	7.28874	−	20.0256i	0.380469	−	1.04533i	0.971159	−	0.238432i	$-0.0766334\pi$
$368$	21.5784	−	12.4583i	1.12485	−	0.649434i
$369$	−1.12538	+	1.94922i	−0.0585850	+	0.101472i
$370$	−2.66678	−	2.36825i	−0.138639	−	0.123119i
$371$	7.54204	−	6.32852i	0.391563	−	0.328561i
$372$	−5.18353	−	2.99271i	−0.268753	−	0.155165i
$373$	12.2737	−	7.08623i	0.635509	−	0.366911i	−0.147374	−	0.989081i	$-0.547082\pi$
$373$	12.2737	−	7.08623i	0.635509	−	0.366911i	0.782882	+	0.622170i	$0.213749\pi$
$374$	6.74891	+	2.45640i	0.348978	+	0.127018i
$375$	3.47958	+	12.8250i	0.179685	+	0.662279i
$376$	0.372360	+	2.11176i	0.0192030	+	0.108906i
$377$	4.88171	+	13.4124i	0.251421	+	0.690774i
$378$	12.6646	−	15.0930i	0.651395	−	0.776302i
$379$	3.54496			0.182092			0.0910462	−	0.995847i	$-0.470979\pi$
$379$	3.54496			0.182092			0.0910462	+	0.995847i	$0.470979\pi$
$380$	−5.31143	−	2.91037i	−0.272471	−	0.149299i
$381$	−1.58627			−0.0812671
$382$	23.3185	−	27.7899i	1.19308	−	1.42185i
$383$	2.63645	+	7.24358i	0.134716	+	0.370130i	0.988647	−	0.150257i	$-0.0480101\pi$
$383$	2.63645	+	7.24358i	0.134716	+	0.370130i	−0.853931	+	0.520387i	$0.825788\pi$
$384$	−2.80991	−	15.9358i	−0.143392	−	0.813219i
$385$	0.789923	−	28.1603i	0.0402582	−	1.43518i
$386$	−29.8181	−	10.8529i	−1.51770	−	0.552398i
$387$	−2.09185	+	1.20773i	−0.106335	+	0.0613923i
$388$	6.86665	+	3.96447i	0.348602	+	0.201265i
$389$	−1.37878	+	1.15693i	−0.0699070	+	0.0586589i	−0.677072	−	0.735917i	$-0.736751\pi$
$389$	−1.37878	+	1.15693i	−0.0699070	+	0.0586589i	0.607165	+	0.794576i	$0.292307\pi$
$390$	−13.4306	+	15.1237i	−0.680087	+	0.765818i
$391$	−2.01584	+	3.49155i	−0.101946	+	0.176575i
$392$	3.90203	−	2.25284i	0.197082	−	0.113786i
$393$	−5.60129	+	15.3894i	−0.282548	+	0.776293i
$394$	−4.34647	+	24.6500i	−0.218972	+	1.24185i
$395$	2.84268	−	0.945260i	0.143031	−	0.0475612i
$396$	5.23184	−	1.90423i	0.262910	−	0.0956914i
$397$	−11.3616	+	13.5403i	−0.570224	+	0.679567i	−0.971677	−	0.236313i	$-0.924061\pi$
$397$	−11.3616	+	13.5403i	−0.570224	+	0.679567i	0.401453	+	0.915880i	$0.368505\pi$
$398$			2.22292i			0.111425i
$399$	−11.2719	+	2.57882i	−0.564303	+	0.129102i
$400$	23.2485	−	7.01313i	1.16243	−	0.350657i
$401$	−20.7714	−	17.4293i	−1.03727	−	0.870375i	−0.0455746	−	0.998961i	$-0.514512\pi$
$401$	−20.7714	−	17.4293i	−1.03727	−	0.870375i	−0.991698	+	0.128586i	$0.958956\pi$
$402$	−2.13783	−	5.87364i	−0.106625	−	0.292951i
$403$	−37.5148	+	6.61488i	−1.86875	+	0.329510i
$404$	−0.601342	+	3.41038i	−0.0299179	+	0.169673i
$405$	−0.773156	+	3.76426i	−0.0384184	+	0.187048i
$406$	5.48641	+	9.50273i	0.272286	+	0.471613i
$407$	−4.81588	−	2.78045i	−0.238715	−	0.137822i
$408$	1.34009	+	1.59706i	0.0663446	+	0.0790664i
$409$	−25.9468	+	21.7720i	−1.28299	+	1.07655i	−0.290162	+	0.956977i	$0.593709\pi$
$409$	−25.9468	+	21.7720i	−1.28299	+	1.07655i	−0.992825	+	0.119577i	$0.961846\pi$
$410$	1.89037	−	4.77287i	0.0933585	−	0.235715i
$411$	−6.97826	−	12.0867i	−0.344212	−	0.596193i
$412$	0.702970	−	1.93140i	0.0346329	−	0.0951530i
$413$	21.7130	+	3.82858i	1.06843	+	0.188392i
$414$	2.28953	+	12.9846i	0.112524	+	0.638158i
$415$	−14.8032	+	8.00178i	−0.726659	+	0.392792i
$416$	12.2395	+	10.2702i	0.600091	+	0.503536i
$417$		−	11.1030i		−	0.543714i
$418$	−38.0734	−	11.7227i	−1.86223	−	0.573378i
$419$	23.2338			1.13505			0.567524	−	0.823357i	$-0.307901\pi$
$419$	23.2338			1.13505			0.567524	+	0.823357i	$0.307901\pi$
$420$	−1.93175	+	3.13918i	−0.0942596	+	0.153176i
$421$	−18.1808	+	6.61727i	−0.886077	+	0.322506i	−0.744660	−	0.667444i	$-0.767388\pi$
$421$	−18.1808	+	6.61727i	−0.886077	+	0.322506i	−0.141418	+	0.989950i	$0.545166\pi$
$422$	−15.2621	+	2.69113i	−0.742949	+	0.131002i
$423$	−1.50175	−	0.264798i	−0.0730173	−	0.0128749i
$424$	9.25238	+	3.36759i	0.449335	+	0.163545i
$425$	−2.69041	+	2.86363i	−0.130504	+	0.138907i
$426$	−6.90564	+	11.9609i	−0.334580	+	0.579509i
$427$	−3.00706	−	3.58367i	−0.145522	−	0.173426i
$428$	2.66520	+	3.17626i	0.128827	+	0.153530i
$429$	−15.7683	+	27.3115i	−0.761302	+	1.31861i
$430$	4.31795	−	3.42153i	0.208230	−	0.165001i
$431$	12.2685	+	4.46538i	0.590955	+	0.215090i	0.620149	−	0.784484i	$-0.287072\pi$
$431$	12.2685	+	4.46538i	0.590955	+	0.215090i	−0.0291947	+	0.999574i	$0.509294\pi$
$432$	26.0778	+	4.59821i	1.25467	+	0.221232i
$433$	5.74031	−	1.01217i	0.275862	−	0.0486418i	−0.0340058	−	0.999422i	$-0.510826\pi$
$433$	5.74031	−	1.01217i	0.275862	−	0.0486418i	0.309867	+	0.950780i	$0.399715\pi$
$434$	−27.5191	+	10.0161i	−1.32096	+	0.480790i
$435$	−6.87315	−	4.22951i	−0.329542	−	0.202789i
$436$	9.74413			0.466659
$437$	10.1920	−	19.9054i	0.487550	−	0.952203i
$438$			29.1783i			1.39419i
$439$	4.97166	+	4.17172i	0.237284	+	0.199105i	0.753674	−	0.657249i	$-0.228280\pi$
$439$	4.97166	+	4.17172i	0.237284	+	0.199105i	−0.516390	+	0.856354i	$0.672724\pi$
$440$	24.7843	−	13.3970i	1.18155	−	0.638679i
$441$	0.556393	+	3.15546i	0.0264949	+	0.150260i
$442$	−5.88973	−	1.03852i	−0.280146	−	0.0493973i
$443$	3.14771	−	8.64826i	0.149552	−	0.410891i	−0.842183	−	0.539191i	$-0.818730\pi$
$443$	3.14771	−	8.64826i	0.149552	−	0.410891i	0.991735	+	0.128300i	$0.0409522\pi$
$444$	0.363794	+	0.630109i	0.0172649	+	0.0299037i
$445$	7.07463	+	2.80201i	0.335369	+	0.132828i
$446$	8.10832	−	6.80369i	0.383940	−	0.322164i
$447$	13.7698	+	16.4102i	0.651289	+	0.776177i
$448$	−8.13724	−	4.69804i	−0.384449	−	0.221961i
$449$	−8.73231	−	15.1248i	−0.412103	−	0.713783i	0.583017	−	0.812460i	$-0.301872\pi$
$449$	−8.73231	−	15.1248i	−0.412103	−	0.713783i	−0.995120	+	0.0986770i	$0.968539\pi$
$450$	−0.720330	+	12.8296i	−0.0339567	+	0.604791i
$451$	1.38991	−	7.88259i	0.0654485	−	0.371177i
$452$	4.02746	−	0.710150i	0.189436	−	0.0334026i
$453$	−5.29117	−	14.5374i	−0.248601	−	0.683025i
$454$	−11.0244	−	9.25060i	−0.517402	−	0.434152i
$455$	3.42417	+	23.2074i	0.160528	+	1.08798i
$456$	−7.86988	−	8.47301i	−0.368541	−	0.396785i
$457$		−	0.381827i		−	0.0178611i	−0.999960	−	0.00893055i	$-0.997157\pi$
$457$		−	0.381827i		−	0.0178611i	0.999960	−	0.00893055i	$-0.00284272\pi$
$458$	−7.51913	+	8.96095i	−0.351346	+	0.418718i
$459$	−4.02627	+	1.46544i	−0.187930	+	0.0684010i
$460$	−2.24931	−	6.76434i	−0.104875	−	0.315389i
$461$	1.47897	−	8.38766i	0.0688826	−	0.390652i	−0.930802	−	0.365525i	$-0.880890\pi$
$461$	1.47897	−	8.38766i	0.0688826	−	0.390652i	0.999684	−	0.0251278i	$-0.00799928\pi$
$462$	−8.29210	+	22.7824i	−0.385783	+	1.05993i
$463$	−32.0583	+	18.5089i	−1.48988	+	0.860181i	−0.999933	−	0.0115723i	$-0.996316\pi$
$463$	−32.0583	+	18.5089i	−1.48988	+	0.860181i	−0.489945	+	0.871754i	$0.662983\pi$
$464$	−7.37368	+	12.7716i	−0.342314	+	0.592906i
$465$	14.3020	−	16.1048i	0.663237	−	0.746844i
$466$	30.9797	−	25.9950i	1.43511	−	1.20420i
$467$	22.4636	+	12.9694i	1.03949	+	0.600151i	0.919689	−	0.392647i	$-0.128440\pi$
$467$	22.4636	+	12.9694i	1.03949	+	0.600151i	0.119803	+	0.992798i	$0.461774\pi$
$468$	−4.01509	+	2.31812i	−0.185598	+	0.107155i
$469$	−6.81228	−	2.47947i	−0.314562	−	0.114491i
$470$	3.47668	+	0.0975244i	0.160367	+	0.00449847i
$471$	2.16860	+	12.2987i	0.0999237	+	0.566696i
$472$	7.54140	+	20.7198i	0.347121	+	0.953707i
$473$	5.52147	−	6.58023i	0.253877	−	0.302559i
$474$	−2.57814			−0.118418
$475$	14.1043	−	16.6153i	0.647150	−	0.762362i
$476$	−1.08986			−0.0499539
$477$	−4.50077	+	5.36380i	−0.206076	+	0.245592i
$478$	9.31344	+	25.5885i	0.425987	+	1.17039i
$479$	−2.05579	−	11.6589i	−0.0939313	−	0.532711i	−0.995070	−	0.0991792i	$-0.968378\pi$
$479$	−2.05579	−	11.6589i	−0.0939313	−	0.532711i	0.901138	−	0.433532i	$-0.142733\pi$
$480$	−9.03036	−	0.253311i	−0.412178	−	0.0115620i
$481$	4.35139	+	1.58378i	0.198406	+	0.0722139i
$482$	−15.2082	+	8.78045i	−0.692714	+	0.399938i
$483$	−11.7864	−	6.80490i	−0.536302	−	0.309634i
$484$	−9.93126	+	8.33332i	−0.451421	+	0.378787i
$485$	−18.9459	+	21.3342i	−0.860289	+	0.968736i
$486$	−11.5880	+	20.0709i	−0.525641	+	0.910436i
$487$	25.4449	−	14.6906i	1.15302	−	0.665696i	0.203398	−	0.979096i	$-0.434801\pi$
$487$	25.4449	−	14.6906i	1.15302	−	0.665696i	0.949621	+	0.313400i	$0.101468\pi$
$488$	1.60014	−	4.39636i	0.0724351	−	0.199014i
$489$	0.747946	−	4.24181i	0.0338233	−	0.191821i
$490$	−2.30597	−	6.93473i	−0.104173	−	0.313279i
$491$	4.52780	−	1.64798i	0.204337	−	0.0743725i	−0.237824	−	0.971308i	$-0.576434\pi$
$491$	4.52780	−	1.64798i	0.204337	−	0.0743725i	0.442161	+	0.896936i	$0.354212\pi$
$492$	−0.673170	+	0.802253i	−0.0303489	+	0.0361684i
$493$		−	2.38623i		−	0.107470i
$494$	32.9177	+	4.10801i	1.48104	+	0.184828i
$495$	2.92444	+	19.8205i	0.131444	+	0.890866i
$496$	−30.1508	−	25.2995i	−1.35381	−	1.13598i
$497$	5.47862	+	15.0524i	0.245750	+	0.675191i
$498$	14.2618	−	2.51474i	0.639087	−	0.112688i
$499$	−0.0326851	+	0.185366i	−0.00146318	+	0.00829813i	−0.985531	−	0.169498i	$-0.945786\pi$
$499$	−0.0326851	+	0.185366i	−0.00146318	+	0.00829813i	0.984067	+	0.177796i	$0.0568966\pi$
$500$	−0.627196	−	6.91895i	−0.0280491	−	0.309425i
$501$	6.32316	+	10.9520i	0.282498	+	0.489301i
$502$	−8.93266	−	5.15728i	−0.398684	−	0.230181i
$503$	−1.46289	−	1.74340i	−0.0652269	−	0.0777343i	0.732444	−	0.680827i	$-0.238379\pi$
$503$	−1.46289	−	1.74340i	−0.0652269	−	0.0777343i	−0.797671	+	0.603093i	$0.793935\pi$
$504$	6.05754	−	5.08288i	0.269824	−	0.226410i
$505$	−11.5860	−	4.58879i	−0.515569	−	0.204199i
$506$	−23.4442	−	40.6065i	−1.04222	−	1.80518i
$507$	3.69711	−	10.1577i	0.164194	−	0.451121i
$508$	0.816707	+	0.144007i	0.0362355	+	0.00638930i
$509$	0.742270	+	4.20962i	0.0329006	+	0.186588i	0.996829	−	0.0795731i	$-0.0253557\pi$
$509$	0.742270	+	4.20962i	0.0329006	+	0.186588i	−0.963928	+	0.266161i	$0.914245\pi$
$510$	2.97473	−	1.60798i	0.131723	−	0.0712023i
$511$	25.9238	+	21.7527i	1.14680	+	0.962282i
$512$		−	5.17245i		−	0.228592i
$513$	21.8952	−	9.24281i	0.966697	−	0.408080i
$514$	22.0946			0.974552
$515$	6.29908	+	3.87625i	0.277571	+	0.170808i
$516$	−1.05612	+	0.384396i	−0.0464930	+	0.0169221i
$517$	5.34052	−	0.941679i	0.234876	−	0.0414150i
$518$	3.50583	+	0.618172i	0.154037	+	0.0271609i
$519$	21.6797	+	7.89078i	0.951635	+	0.346367i
$520$	−18.3875	+	14.5702i	−0.806347	+	0.638947i
$521$	−16.1637	+	27.9963i	−0.708143	+	1.22654i	0.257402	+	0.966304i	$0.417134\pi$
$521$	−16.1637	+	27.9963i	−0.708143	+	1.22654i	−0.965545	+	0.260236i	$0.916200\pi$
$522$	−5.01614	−	5.97800i	−0.219550	−	0.261650i
$523$	−18.9726	−	22.6107i	−0.829613	−	0.988695i	−0.999995	−	0.00331656i	$-0.998944\pi$
$523$	−18.9726	−	22.6107i	−0.829613	−	0.988695i	0.170381	−	0.985378i	$-0.445500\pi$
$524$	4.28099	−	7.41488i	0.187016	−	0.323921i
$525$	−9.66679	−	9.08203i	−0.421893	−	0.396372i
$526$	15.5513	+	5.66021i	0.678069	+	0.246797i
$527$	6.27183	+	1.10589i	0.273205	+	0.0481735i
$528$	−32.0893	+	5.65821i	−1.39651	+	0.246242i
$529$	3.12081	−	1.13588i	0.135687	−	0.0493861i
$530$	8.36977	−	13.6013i	0.363559	−	0.590801i
$531$	−15.6802			−0.680463
$532$	6.03758	−	0.304422i	0.261762	−	0.0131984i
$533$			6.66521i			0.288702i
$534$	−5.01654	−	4.20938i	−0.217087	−	0.182158i
$535$	−13.1257	+	7.09502i	−0.567472	+	0.306744i
$536$	−1.25895	−	7.13988i	−0.0543785	−	0.308396i
$537$	2.42357	+	0.427341i	0.104585	+	0.0184411i
$538$	8.00171	−	21.9845i	0.344978	−	0.947820i
$539$	−5.69730	−	9.86802i	−0.245400	−	0.425046i
$540$	2.78968	−	7.04348i	0.120049	−	0.303103i
$541$	14.4594	−	12.1328i	0.621656	−	0.521632i	−0.276667	−	0.960966i	$-0.589230\pi$
$541$	14.4594	−	12.1328i	0.621656	−	0.521632i	0.898324	+	0.439334i	$0.144786\pi$
$542$	−16.8653	−	20.0992i	−0.724425	−	0.863336i
$543$	22.2670	+	12.8558i	0.955567	+	0.551697i
$544$	−1.33558	−	2.31330i	−0.0572627	−	0.0991819i
$545$	−7.05473	+	34.3473i	−0.302192	+	1.47128i
$546$	3.50574	−	19.8820i	0.150032	−	0.850872i
$547$	24.7374	−	4.36188i	1.05770	−	0.186500i	0.382362	−	0.924012i	$-0.375111\pi$
$547$	24.7374	−	4.36188i	1.05770	−	0.186500i	0.675334	+	0.737512i	$0.264000\pi$
$548$	2.49555	+	6.85647i	0.106605	+	0.292894i
$549$	2.54866	+	2.13858i	0.108774	+	0.0912725i
$550$	−13.1974	−	43.7492i	−0.562738	−	1.86547i
$551$	0.666523	+	13.2191i	0.0283949	+	0.563153i
$552$		−	13.6108i		−	0.579315i
$553$	−1.92203	+	2.29058i	−0.0817328	+	0.0974054i
$554$	−43.5042	+	15.8342i	−1.84831	+	0.672731i
$555$	−2.48448	+	0.826148i	−0.105460	+	0.0350680i
$556$	−1.00797	+	5.71647i	−0.0427473	+	0.242432i
$557$	−9.63578	+	26.4741i	−0.408281	+	1.12174i	0.549812	+	0.835288i	$0.314699\pi$
$557$	−9.63578	+	26.4741i	−0.408281	+	1.12174i	−0.958094	+	0.286455i	$0.907523\pi$
$558$	18.0370	−	10.4136i	0.763566	−	0.440845i
$559$	−3.57646	+	6.19461i	−0.151268	+	0.262004i
$560$	−16.0944	+	18.1232i	−0.680113	+	0.765847i
$561$	4.03888	−	3.38902i	0.170522	−	0.143085i
$562$	−10.0643	−	5.81060i	−0.424535	−	0.245105i
$563$	−17.6927	+	10.2149i	−0.745656	+	0.430505i	−0.824122	−	0.566412i	$-0.808331\pi$
$563$	−17.6927	+	10.2149i	−0.745656	+	0.430505i	0.0784660	+	0.996917i	$0.474998\pi$
$564$	−0.666742	−	0.242674i	−0.0280749	−	0.0102184i
$565$	−0.412648	+	14.7106i	−0.0173602	+	0.618881i
$566$	2.91428	+	16.5277i	0.122496	+	0.694711i
$567$	−1.31188	−	3.60436i	−0.0550938	−	0.151369i
$568$	−10.2972	+	12.2717i	−0.432061	+	0.514910i
$569$	35.8386			1.50243			0.751217	−	0.660056i	$-0.229467\pi$
$569$	35.8386			1.50243			0.751217	+	0.660056i	$0.229467\pi$
$570$	−16.0301	+	9.73869i	−0.671428	+	0.407909i
$571$	−2.82827			−0.118359			−0.0591797	−	0.998247i	$-0.518848\pi$
$571$	−2.82827			−0.118359			−0.0591797	+	0.998247i	$0.518848\pi$
$572$	10.5979	−	12.6301i	0.443121	−	0.528091i
$573$	−9.10843	−	25.0252i	−0.380510	−	1.04544i
$574$	0.889778	+	5.04618i	0.0371386	+	0.210624i
$575$	25.4723	−	3.03127i	1.06227	−	0.126413i
$576$	6.27938	+	2.28551i	0.261641	+	0.0952294i
$577$	37.5103	−	21.6566i	1.56157	−	0.901575i	0.564476	−	0.825449i	$-0.309078\pi$
$577$	37.5103	−	21.6566i	1.56157	−	0.901575i	0.997098	−	0.0761261i	$-0.0242552\pi$
$578$	−22.9707	−	13.2622i	−0.955457	−	0.551633i
$579$	−17.8446	+	14.9734i	−0.741596	+	0.622273i
$580$	3.15474	+	2.80157i	0.130993	+	0.116329i
$581$	8.39804	−	14.5458i	0.348409	−	0.603463i
$582$	21.2654	−	12.2776i	0.881479	−	0.508922i
$583$	8.51645	−	23.3987i	0.352715	−	0.969077i
$584$	−5.87690	+	33.3296i	−0.243188	+	1.37919i
$585$	−5.26427	−	15.8312i	−0.217651	−	0.654541i
$586$	−13.8306	+	5.03394i	−0.571338	+	0.207950i
$587$	15.7959	−	18.8249i	0.651968	−	0.776985i	−0.334242	−	0.942487i	$-0.608480\pi$
$587$	15.7959	−	18.8249i	0.651968	−	0.776985i	0.986209	+	0.165502i	$0.0529246\pi$
$588$			1.49087i			0.0614824i
$589$	−35.0533	−	4.37452i	−1.44435	−	0.180249i
$590$	35.3807	−	5.22029i	1.45660	−	0.214916i
$591$	14.0760	+	11.8112i	0.579010	+	0.485847i
$592$	1.63639	+	4.49595i	0.0672553	+	0.184782i
$593$	−0.308954	+	0.0544770i	−0.0126872	+	0.00223710i	−0.179988	−	0.983669i	$-0.557606\pi$
$593$	−0.308954	+	0.0544770i	−0.0126872	+	0.00223710i	0.167301	+	0.985906i	$0.446495\pi$
$594$	8.65296	−	49.0734i	0.355035	−	2.01351i
$595$	0.789060	−	3.84169i	0.0323483	−	0.157494i
$596$	−5.59974	−	9.69903i	−0.229374	−	0.397288i
$597$	1.41323	+	0.815931i	0.0578398	+	0.0333938i
$598$	25.0974	+	29.9099i	1.02631	+	1.22311i
$599$	−18.7653	+	15.7460i	−0.766731	+	0.643364i	−0.939869	−	0.341534i	$-0.889054\pi$
$599$	−18.7653	+	15.7460i	−0.766731	+	0.643364i	0.173139	+	0.984897i	$0.444609\pi$
$600$	3.03210	−	12.9137i	0.123785	−	0.527198i
$601$	3.91522	+	6.78137i	0.159705	+	0.276618i	0.934762	−	0.355273i	$-0.115612\pi$
$601$	3.91522	+	6.78137i	0.159705	+	0.276618i	−0.775057	+	0.631891i	$0.782279\pi$
$602$	−1.88076	+	5.16734i	−0.0766539	+	0.210605i
$603$	5.07741	+	0.895284i	0.206768	+	0.0364588i
$604$	1.40445	+	7.96506i	0.0571464	+	0.324094i
$605$	−22.1841	−	41.0403i	−0.901912	−	1.66852i
$606$	8.21549	+	6.89361i	0.333731	+	0.280034i
$607$			12.4142i			0.503876i	0.967743	+	0.251938i	$0.0810680\pi$
$607$			12.4142i			0.503876i	−0.967743	+	0.251938i	$0.918932\pi$
$608$	8.04496	+	12.4421i	0.326266	+	0.504592i
$609$	8.05522			0.326414
$610$	−6.46277	−	3.97698i	−0.261670	−	0.161023i
$611$	−4.24341	+	1.54447i	−0.171670	+	0.0624827i
$612$	0.763323	−	0.134594i	0.0308555	−	0.00544066i
$613$	1.04244	+	0.183811i	0.0421039	+	0.00742405i	0.194660	−	0.980871i	$-0.437640\pi$
$613$	1.04244	+	0.183811i	0.0421039	+	0.00742405i	−0.152557	+	0.988295i	$0.548751\pi$
$614$	−22.3103	−	8.12030i	−0.900372	−	0.327709i
$615$	−2.34051	−	2.95371i	−0.0943784	−	0.119105i
$616$	−14.0605	+	24.3535i	−0.566513	+	0.981229i
$617$	−18.3761	−	21.8998i	−0.739794	−	0.881652i	0.256598	−	0.966518i	$-0.417398\pi$
$617$	−18.3761	−	21.8998i	−0.739794	−	0.881652i	−0.996392	+	0.0848661i	$0.972954\pi$
$618$	−4.09149	−	4.87604i	−0.164584	−	0.196143i
$619$	4.70978	−	8.15758i	0.189302	−	0.327881i	−0.755716	−	0.654900i	$-0.772711\pi$
$619$	4.70978	−	8.15758i	0.189302	−	0.327881i	0.945018	+	0.327019i	$0.106044\pi$
$620$	−8.82556	+	6.99335i	−0.354443	+	0.280860i
$621$	26.2857	+	9.56722i	1.05481	+	0.383919i
$622$	−50.3552	−	8.87898i	−2.01906	−	0.356015i
$623$	−7.47975	+	1.31888i	−0.299670	+	0.0528399i
$624$	25.4971	−	9.28019i	1.02070	−	0.371505i
$625$	24.8429	+	2.79849i	0.993715	+	0.111939i
$626$	−14.5566			−0.581797
$627$	−21.4278	+	19.9025i	−0.855743	+	0.794829i
$628$		−	6.52899i		−	0.260535i
$629$	−0.593045	−	0.497624i	−0.0236462	−	0.0198416i
$630$	−6.09894	−	11.2829i	−0.242987	−	0.449523i
$631$	−6.88134	−	39.0260i	−0.273942	−	1.55360i	−0.742304	−	0.670064i	$-0.766267\pi$
$631$	−6.88134	−	39.0260i	−0.273942	−	1.55360i	0.468362	−	0.883537i	$-0.344844\pi$
$632$	−2.94493	−	0.519271i	−0.117143	−	0.0206555i
$633$	−3.89112	+	10.6908i	−0.154658	+	0.424920i
$634$	−8.43570	−	14.6111i	−0.335024	−	0.580279i
$635$	−1.09891	+	2.77457i	−0.0436089	+	0.110105i
$636$	−2.49575	+	2.09418i	−0.0989628	+	0.0830396i
$637$	6.09907	+	7.26858i	0.241654	+	0.287992i
$638$	24.0337	+	13.8759i	0.951503	+	0.549350i
$639$	−5.69604	−	9.86584i	−0.225332	−	0.390286i
$640$	−29.8201	−	6.12487i	−1.17874	−	0.242107i
$641$	3.41320	−	19.3572i	0.134813	−	0.764565i	−0.840176	−	0.542314i	$-0.817548\pi$
$641$	3.41320	−	19.3572i	0.134813	−	0.764565i	0.974989	−	0.222251i	$-0.0713405\pi$
$642$	12.6457	−	2.22977i	0.499084	−	0.0880020i
$643$	9.81994	+	26.9801i	0.387261	+	1.06399i	0.968229	+	0.250064i	$0.0804516\pi$
$643$	9.81994	+	26.9801i	0.387261	+	1.06399i	−0.580969	+	0.813926i	$0.697326\pi$
$644$	5.45059	+	4.57359i	0.214783	+	0.180225i
$645$	−0.590339	−	4.00104i	−0.0232446	−	0.157541i
$646$	−4.93650	−	2.52760i	−0.194224	−	0.0994472i
$647$		−	17.4412i		−	0.685686i	−0.939393	−	0.342843i	$-0.888610\pi$
$647$		−	17.4412i		−	0.685686i	0.939393	−	0.342843i	$-0.111390\pi$
$648$	2.46571	−	2.93852i	0.0968624	−	0.115436i
$649$	52.3993	−	19.0718i	2.05685	−	0.748633i
$650$	17.1488	+	33.9689i	0.672632	+	1.33237i
$651$	−3.73317	+	21.1719i	−0.146315	+	0.829791i
$652$	−0.770175	+	2.11604i	−0.0301624	+	0.0828704i
$653$	26.2837	−	15.1749i	1.02856	−	0.593839i	0.111988	−	0.993710i	$-0.464278\pi$
$653$	26.2837	−	15.1749i	1.02856	−	0.593839i	0.916572	+	0.399871i	$0.130945\pi$
$654$	15.0883	−	26.1338i	0.590000	−	1.02191i
$655$	23.0375	+	20.4585i	0.900149	+	0.799381i
$656$	−5.27547	+	4.42665i	−0.205973	+	0.172832i
$657$	−20.8430	−	12.0337i	−0.813163	−	0.469480i
$658$	−3.00647	+	1.73579i	−0.117204	+	0.0676680i
$659$	6.14432	+	2.23635i	0.239349	+	0.0871158i	0.458909	−	0.888483i	$-0.348240\pi$
$659$	6.14432	+	2.23635i	0.239349	+	0.0871158i	−0.219561	+	0.975599i	$0.570462\pi$
$660$	−0.261395	+	9.31855i	−0.0101748	+	0.362724i
$661$	4.13276	+	23.4381i	0.160746	+	0.911635i	0.953343	+	0.301889i	$0.0976174\pi$
$661$	4.13276	+	23.4381i	0.160746	+	0.911635i	−0.792597	+	0.609746i	$0.791272\pi$
$662$	2.23194	+	6.13220i	0.0867467	+	0.238335i
$663$	−2.82209	+	3.36324i	−0.109601	+	0.130617i
$664$	16.7973			0.651863
$665$	−3.29813	+	21.5024i	−0.127896	+	0.833828i
$666$	−2.53176			−0.0981039
$667$	−10.0137	+	11.9339i	−0.387734	+	0.462083i
$668$	−2.26127	−	6.21280i	−0.0874913	−	0.240380i
$669$	−1.34929	−	7.65223i	−0.0521667	−	0.295852i
$670$	−11.7547	−	0.329731i	−0.454123	−	0.0127386i
$671$	−11.1181	−	4.04667i	−0.429211	−	0.156220i
$672$	7.80903	−	4.50854i	0.301240	−	0.173921i
$673$	43.2343	+	24.9614i	1.66656	+	0.962189i	0.969471	+	0.245206i	$0.0788555\pi$
$673$	43.2343	+	24.9614i	1.66656	+	0.962189i	0.697090	+	0.716984i	$0.254478\pi$
$674$	30.7361	−	25.7906i	1.18391	−	0.993418i
$675$	22.8080	+	14.9329i	0.877882	+	0.574767i
$676$	−2.82565	+	4.89417i	−0.108679	+	0.188237i
$677$	−29.9494	+	17.2913i	−1.15105	+	0.664558i	−0.949143	−	0.314847i	$-0.898047\pi$
$677$	−29.9494	+	17.2913i	−1.15105	+	0.664558i	−0.201906	+	0.979405i	$0.564714\pi$
$678$	4.33171	−	11.9013i	0.166358	−	0.457066i
$679$	4.94536	−	28.0465i	0.189786	−	1.07633i
$680$	3.72181	−	1.23759i	0.142725	−	0.0474595i
$681$	−9.92767	+	3.61338i	−0.380429	+	0.138465i
$682$	−47.6089	+	56.7381i	−1.82304	+	2.17261i
$683$			21.1277i			0.808429i	0.914664	+	0.404214i	$0.132455\pi$
$683$			21.1277i			0.808429i	−0.914664	+	0.404214i	$0.867545\pi$
$684$	−4.19102	+	0.958831i	−0.160248	+	0.0366618i
$685$	−25.9753	+	3.83256i	−0.992466	+	0.146435i
$686$	24.9652	+	20.9483i	0.953174	+	0.799808i
$687$	2.93705	+	8.06947i	0.112055	+	0.307869i
$688$	−7.27827	+	1.28336i	−0.277482	+	0.0489275i
$689$	−3.60059	+	20.4199i	−0.137171	+	0.777938i
$690$	−21.6249	−	4.44163i	−0.823247	−	0.169090i
$691$	−13.9430	−	24.1500i	−0.530418	−	0.918711i	−0.999370	−	0.0354873i	$-0.988702\pi$
$691$	−13.9430	−	24.1500i	−0.530418	−	0.918711i	0.468952	−	0.883224i	$-0.344632\pi$
$692$	−10.4457	−	6.03081i	−0.397085	−	0.229257i
$693$	−12.8543	−	15.3192i	−0.488295	−	0.581928i
$694$	35.5017	−	29.7894i	1.34762	−	1.13079i
$695$	−19.4204	−	7.69173i	−0.736656	−	0.291764i
$696$	4.02791	+	6.97655i	0.152678	+	0.264445i
$697$	0.381116	−	1.04711i	0.0144358	−	0.0396620i
$698$	−16.2982	−	2.87381i	−0.616895	−	0.108775i
$699$	−5.15528	−	29.2370i	−0.194991	−	1.10585i
$700$	4.15254	+	5.55356i	0.156951	+	0.209905i
$701$	−30.1319	−	25.2837i	−1.13807	−	0.954952i	−0.138694	−	0.990335i	$-0.544290\pi$
$701$	−30.1319	−	25.2837i	−1.13807	−	0.954952i	−0.999374	+	0.0353834i	$0.988735\pi$
$702$			41.4946i			1.56611i
$703$	3.42432	+	2.59106i	0.129151	+	0.0977237i
$704$	−23.7639			−0.895637
$705$	1.33813	−	2.17452i	0.0503969	−	0.0818973i
$706$	27.0690	−	9.85232i	1.01876	−	0.370797i
$707$	12.2494	−	2.15990i	0.460687	−	0.0812316i
$708$	−7.18507	−	1.26692i	−0.270031	−	0.0476138i
$709$	4.02970	+	1.46669i	0.151339	+	0.0550828i	0.416579	−	0.909100i	$-0.363229\pi$
$709$	4.02970	+	1.46669i	0.151339	+	0.0550828i	−0.265240	+	0.964182i	$0.585451\pi$
$710$	16.1371	+	20.3649i	0.605613	+	0.764280i
$711$	1.06328	−	1.84165i	0.0398759	−	0.0690671i
$712$	−4.88243	−	5.81865i	−0.182977	−	0.218063i
$713$	−26.7256	−	31.8503i	−1.00088	−	1.19280i
$714$	−1.68760	+	2.92302i	−0.0631570	+	0.109391i
$715$	36.8473	+	46.5010i	1.37801	+	1.73904i
$716$	−1.20900	−	0.440041i	−0.0451825	−	0.0164451i
$717$	19.6865	+	3.47127i	0.735207	+	0.129637i
$718$	−1.37219	+	0.241954i	−0.0512096	+	0.00902964i
$719$	−3.69536	+	1.34500i	−0.137814	+	0.0501600i	−0.410006	−	0.912083i	$-0.634473\pi$
$719$	−3.69536	+	1.34500i	−0.137814	+	0.0501600i	0.272193	+	0.962243i	$0.412251\pi$
$720$	9.03409	−	14.6808i	0.336681	−	0.547122i
$721$	−7.38242			−0.274936
$722$	28.0530	+	12.6234i	1.04402	+	0.469795i
$723$			12.8916i			0.479443i
$724$	−10.2973	−	8.64043i	−0.382695	−	0.321119i
$725$	−12.1594	+	9.09188i	−0.451587	+	0.337664i
$726$	6.97186	+	39.5394i	0.258750	+	1.46744i
$727$	−19.7527	−	3.48294i	−0.732587	−	0.129175i	−0.205104	−	0.978740i	$-0.565753\pi$
$727$	−19.7527	−	3.48294i	−0.732587	−	0.129175i	−0.527483	+	0.849565i	$0.676864\pi$
$728$	8.00900	−	22.0046i	0.296833	−	0.815543i
$729$	11.0847	+	19.1992i	0.410543	+	0.711081i
$730$	51.0363	+	20.2137i	1.88894	+	0.748142i
$731$	0.916071	−	0.768675i	0.0338821	−	0.0284305i
$732$	0.995070	+	1.18588i	0.0367789	+	0.0438313i
$733$	−0.178212	−	0.102891i	−0.00658241	−	0.00380036i	0.496705	−	0.867919i	$-0.334543\pi$
$733$	−0.178212	−	0.102891i	−0.00658241	−	0.00380036i	−0.503288	+	0.864119i	$0.667876\pi$
$734$	17.2519	+	29.8811i	0.636778	+	1.10293i
$735$	−5.25520	−	1.07939i	−0.193841	−	0.0398138i
$736$	−3.02823	+	17.1739i	−0.111622	+	0.633039i
$737$	−18.0563	+	3.18382i	−0.665114	+	0.117278i
$738$	−1.24637	−	3.42438i	−0.0458795	−	0.126053i
$739$	−24.9819	−	20.9623i	−0.918976	−	0.771112i	0.0548297	−	0.998496i	$-0.482538\pi$
$739$	−24.9819	−	20.9623i	−0.918976	−	0.771112i	−0.973805	+	0.227384i	$0.926983\pi$
$740$	1.35416	−	0.199801i	0.0497798	−	0.00734482i
$741$	14.6943	−	19.4198i	0.539807	−	0.713403i
$742$			15.9404i			0.585192i
$743$	−19.0010	+	22.6445i	−0.697078	+	0.830745i	−0.992192	−	0.124717i	$-0.960198\pi$
$743$	−19.0010	+	22.6445i	−0.697078	+	0.830745i	0.295114	+	0.955462i	$0.404642\pi$
$744$	−20.2035	+	7.35347i	−0.740696	+	0.269591i
$745$	38.2426	−	12.7166i	1.40110	−	0.465900i
$746$	−3.98457	+	22.5976i	−0.145885	+	0.827357i
$747$	−4.08549	+	11.2248i	−0.149480	+	0.410693i
$748$	−2.38712	+	1.37821i	−0.0872819	+	0.0503922i
$749$	7.44637	−	12.8975i	0.272085	−	0.471264i
$750$	−19.5278	−	9.03153i	−0.713055	−	0.329785i
$751$	−28.3787	+	23.8126i	−1.03555	+	0.868932i	−0.991501	−	0.130097i	$-0.958471\pi$
$751$	−28.3787	+	23.8126i	−1.03555	+	0.868932i	−0.0440520	+	0.999029i	$0.514027\pi$
$752$	−4.04067	−	2.33288i	−0.147348	−	0.0850714i
$753$	−6.55753	+	3.78599i	−0.238970	+	0.137969i
$754$	−21.7156	−	7.90384i	−0.790836	−	0.287841i
$755$	−29.0931	−	0.816089i	−1.05880	−	0.0297005i
$756$	1.31308	+	7.44682i	0.0477561	+	0.270838i
$757$	−10.4480	−	28.7057i	−0.379740	−	1.04333i	−0.971464	−	0.237187i	$-0.923775\pi$
$757$	−10.4480	−	28.7057i	−0.379740	−	1.04333i	0.591724	−	0.806141i	$-0.298447\pi$
$758$	−3.68931	+	4.39674i	−0.134002	+	0.159697i
$759$	−34.4210			−1.24940
$760$	−20.2722	+	7.89554i	−0.735351	+	0.286401i
$761$	−46.0692			−1.67001			−0.835004	−	0.550244i	$-0.814535\pi$
$761$	−46.0692			−1.67001			−0.835004	+	0.550244i	$0.814535\pi$
$762$	1.65086	−	1.96742i	0.0598044	−	0.0712720i
$763$	−11.9704	−	32.8883i	−0.433357	−	1.19064i
$764$	2.41768	+	13.7114i	0.0874687	+	0.496060i
$765$	−0.0782091	+	2.78810i	−0.00282765	+	0.100804i
$766$	−11.7279	−	4.26859i	−0.423745	−	0.154231i
$767$	−40.2130	+	23.2170i	−1.45201	+	0.838317i
$768$	14.0224	+	8.09582i	0.505989	+	0.292133i
$769$	−11.2761	+	9.46178i	−0.406627	+	0.341200i	−0.823048	−	0.567971i	$-0.807728\pi$
$769$	−11.2761	+	9.46178i	−0.406627	+	0.341200i	0.416422	+	0.909172i	$0.363284\pi$
$770$	34.1045	+	30.2866i	1.22904	+	1.09145i
$771$	8.10991	−	14.0468i	0.292071	−	0.505882i
$772$	10.5468	−	6.08920i	0.379588	−	0.219155i
$773$	−3.03195	+	8.33022i	−0.109052	+	0.299617i	−0.982200	−	0.187837i	$-0.939852\pi$
$773$	−3.03195	+	8.33022i	−0.109052	+	0.299617i	0.873148	+	0.487454i	$0.162074\pi$
$774$	0.679102	−	3.85138i	0.0244098	−	0.138435i
$775$	−18.2614	−	36.1726i	−0.655967	−	1.29936i
$776$	26.7637	−	9.74119i	0.960761	−	0.349688i
$777$	1.67983	−	2.00195i	0.0602636	−	0.0718194i
$778$		−	2.91412i		−	0.104476i
$779$	−1.81881	+	5.90717i	−0.0651656	+	0.211646i
$780$	−1.13310	−	7.67961i	−0.0405714	−	0.274974i
$781$	31.0345	+	26.0410i	1.11050	+	0.931822i
$782$	−2.23257	−	6.13393i	−0.0798364	−	0.219349i
$783$	−16.3046	+	2.87494i	−0.582679	+	0.102742i
$784$	−1.70239	+	9.65474i	−0.0607997	+	0.344812i
$785$	23.0142	+	4.72698i	0.821413	+	0.168713i
$786$	−13.2578	−	22.9632i	−0.472890	−	0.819070i
$787$	−11.4182	−	6.59229i	−0.407014	−	0.234990i	0.282492	−	0.959270i	$-0.408839\pi$
$787$	−11.4182	−	6.59229i	−0.407014	−	0.234990i	−0.689506	+	0.724280i	$0.742172\pi$
$788$	−6.17491	−	7.35897i	−0.219972	−	0.262152i
$789$	9.30666	−	7.80921i	0.331326	−	0.278015i
$790$	−1.78604	+	4.50947i	−0.0635445	+	0.160440i
$791$	−7.34451	−	12.7211i	−0.261141	−	0.452309i
$792$	6.84016	−	18.7932i	0.243054	−	0.667787i
$793$	9.70274	+	1.71085i	0.344554	+	0.0607542i
$794$	−4.96946	−	28.1832i	−0.176360	−	1.00018i
$795$	−5.57491	−	10.3135i	−0.197722	−	0.365782i
$796$	−0.653544	−	0.548389i	−0.0231643	−	0.0194371i
$797$		−	38.1858i		−	1.35261i	−0.736621	−	0.676306i	$-0.763580\pi$
$797$		−	38.1858i		−	1.35261i	0.736621	−	0.676306i	$-0.236420\pi$
$798$	8.53245	−	16.6642i	0.302046	−	0.589905i
$799$	0.754954			0.0267084
$800$	−6.69897	+	15.6197i	−0.236844	+	0.552238i
$801$	5.07581	−	1.84744i	0.179345	−	0.0652762i
$802$	43.2343	−	7.62337i	1.52666	−	0.269191i
$803$	84.2886	+	14.8623i	2.97448	+	0.524481i
$804$	2.25426	+	0.820484i	0.0795016	+	0.0289362i
$805$	−20.0678	+	15.9017i	−0.707296	+	0.560460i
$806$	30.8381	−	53.4131i	1.08622	−	1.88140i
$807$	−11.0397	−	13.1566i	−0.388616	−	0.463135i
$808$	7.99585	+	9.52908i	0.281293	+	0.335232i
$809$	21.8833	−	37.9031i	0.769377	−	1.33260i	−0.168524	−	0.985698i	$-0.553900\pi$
$809$	21.8833	−	37.9031i	0.769377	−	1.33260i	0.937901	−	0.346903i	$-0.112767\pi$
$810$	−3.86410	−	4.87646i	−0.135770	−	0.171341i
$811$	5.59328	+	2.03579i	0.196407	+	0.0714862i	0.438351	−	0.898804i	$-0.355563\pi$
$811$	5.59328	+	2.03579i	0.196407	+	0.0714862i	−0.241944	+	0.970290i	$0.577785\pi$
$812$	−4.14731	−	0.731282i	−0.145542	−	0.0256630i
$813$	−18.9686	+	3.34468i	−0.665260	+	0.117303i
$814$	8.46052	−	3.07938i	0.296541	−	0.107932i
$815$	−6.90127	−	4.24682i	−0.241741	−	0.148759i
$816$	−4.53625			−0.158800
$817$	−4.86010	+	4.51415i	−0.170033	+	0.157930i
$818$		−	54.8398i		−	1.91743i
$819$	12.7565	+	10.7040i	0.445749	+	0.374028i
$820$	0.936886	+	1.73322i	0.0327175	+	0.0605268i
$821$	−1.38401	−	7.84911i	−0.0483023	−	0.273936i	0.951085	−	0.308928i	$-0.0999703\pi$
$821$	−1.38401	−	7.84911i	−0.0483023	−	0.273936i	−0.999388	+	0.0349926i	$0.988859\pi$
$822$	22.2533	+	3.92385i	0.776172	+	0.136860i
$823$	9.64179	−	26.4906i	0.336092	−	0.923404i	−0.650400	−	0.759592i	$-0.725399\pi$
$823$	9.64179	−	26.4906i	0.336092	−	0.923404i	0.986492	−	0.163812i	$-0.0523791\pi$
$824$	−3.69149	−	6.39384i	−0.128599	−	0.222740i
$825$	−32.6579	−	7.66801i	−1.13700	−	0.266966i
$826$	−27.3456	+	22.9457i	−0.951475	+	0.798382i
$827$	35.0380	+	41.7566i	1.21839	+	1.45202i	0.853600	+	0.520929i	$0.174415\pi$
$827$	35.0380	+	41.7566i	1.21839	+	1.45202i	0.364789	+	0.931090i	$0.381141\pi$
$828$	−4.38232	−	2.53013i	−0.152296	−	0.0879282i
$829$	4.20261	+	7.27913i	0.145963	+	0.252815i	0.929732	−	0.368238i	$-0.120039\pi$
$829$	4.20261	+	7.27913i	0.145963	+	0.252815i	−0.783769	+	0.621052i	$0.786705\pi$
$830$	5.48148	−	26.6877i	0.190265	−	0.926342i
$831$	−5.90166	+	33.4700i	−0.204726	+	1.16106i
$832$	19.4880	−	3.43625i	0.675623	−	0.119131i
$833$	−0.542549	−	1.49064i	−0.0187982	−	0.0516477i
$834$	13.7708	+	11.5551i	0.476843	+	0.400119i
$835$	23.5368	−	3.47277i	0.814525	−	0.120180i
$836$	12.8391	−	8.30170i	0.444050	−	0.287120i
$837$		−	44.1865i		−	1.52731i
$838$	−24.1799	+	28.8165i	−0.835280	+	0.995448i
$839$	35.4409	−	12.8994i	1.22356	−	0.445338i	0.352171	−	0.935936i	$-0.385444\pi$
$839$	35.4409	−	12.8994i	1.22356	−	0.445338i	0.871386	+	0.490597i	$0.163221\pi$
$840$	4.17775	+	12.5638i	0.144146	+	0.433491i
$841$	−3.43468	+	19.4790i	−0.118437	+	0.671690i
$842$	10.7138	−	29.4360i	0.369222	−	1.01443i
$843$	−7.38824	+	4.26560i	−0.254464	+	0.146915i
$844$	2.97393	−	5.15099i	0.102367	−	0.177304i
$845$	−15.2058	−	13.5036i	−0.523096	−	0.464537i
$846$	1.89132	−	1.58700i	0.0650248	−	0.0545623i
$847$	40.3268	+	23.2827i	1.38565	+	0.800003i
$848$	−18.5536	+	10.7119i	−0.637132	+	0.367848i
$849$	11.5773	+	4.21378i	0.397331	+	0.144617i
$850$	−0.751751	−	6.31709i	−0.0257848	−	0.216674i
$851$	0.877648	+	4.97739i	0.0300854	+	0.170623i
$852$	−1.81294	−	4.98100i	−0.0621102	−	0.170646i
$853$	−26.5455	+	31.6357i	−0.908902	+	1.08319i	0.0873063	+	0.996182i	$0.472174\pi$
$853$	−26.5455	+	31.6357i	−0.908902	+	1.08319i	−0.996208	+	0.0870051i	$0.972270\pi$
$854$	7.57426			0.259186
$855$	−0.345516	−	15.4672i	−0.0118164	−	0.528969i
$856$	14.8939			0.509062
$857$	−2.20780	+	2.63115i	−0.0754170	+	0.0898785i	−0.802434	−	0.596741i	$-0.796462\pi$
$857$	−2.20780	+	2.63115i	−0.0754170	+	0.0898785i	0.727017	+	0.686620i	$0.240906\pi$
$858$	−17.4636	−	47.9807i	−0.596196	−	1.63803i
$859$	5.26017	+	29.8319i	0.179475	+	1.01785i	0.932851	+	0.360262i	$0.117313\pi$
$859$	5.26017	+	29.8319i	0.179475	+	1.01785i	−0.753377	+	0.657589i	$0.771576\pi$
$860$	−0.0592877	+	2.11357i	−0.00202169	+	0.0720721i
$861$	3.53473	+	1.28654i	0.120463	+	0.0438451i
$862$	−18.3064	+	10.5692i	−0.623519	+	0.359989i
$863$	−20.6624	−	11.9295i	−0.703358	−	0.406084i	0.105239	−	0.994447i	$-0.466439\pi$
$863$	−20.6624	−	11.9295i	−0.703358	−	0.406084i	−0.808597	+	0.588363i	$0.799773\pi$
$864$	−14.1972	+	11.9129i	−0.482998	+	0.405283i
$865$	28.8208	−	32.4539i	0.979937	−	1.10347i
$866$	−4.71867	+	8.17297i	−0.160347	+	0.277729i
$867$	−16.8630	+	9.73585i	−0.572697	+	0.330647i
$868$	3.84412	−	10.5616i	0.130478	−	0.358485i
$869$	−1.31321	+	7.44757i	−0.0445475	+	0.252642i
$870$	12.3988	−	4.12290i	0.420358	−	0.139779i
$871$	14.3470	−	5.22188i	0.486129	−	0.176936i
$872$	22.4986	−	26.8128i	0.761900	−	0.907997i
$873$			20.2540i			0.685496i
$874$	14.0812	+	33.3568i	0.476304	+	1.12831i
$875$	−22.5823	+	10.6166i	−0.763422	+	0.358908i
$876$	−8.57849	−	7.19821i	−0.289840	−	0.243205i
$877$	4.54055	+	12.4751i	0.153324	+	0.421253i	0.992445	−	0.122691i	$-0.0391525\pi$
$877$	4.54055	+	12.4751i	0.153324	+	0.421253i	−0.839121	+	0.543944i	$0.816930\pi$
$878$	−10.3482	+	1.82466i	−0.349234	+	0.0615794i
$879$	−1.87623	+	10.6406i	−0.0632836	+	0.358899i
$880$	−12.3334	+	60.0477i	−0.415760	+	2.02421i
$881$	−10.0999	−	17.4935i	−0.340274	−	0.589371i	0.644210	−	0.764849i	$-0.277186\pi$
$881$	−10.0999	−	17.4935i	−0.340274	−	0.589371i	−0.984483	+	0.175478i	$0.943853\pi$
$882$	−4.49270	−	2.59386i	−0.151277	−	0.0873400i
$883$	37.4427	+	44.6225i	1.26005	+	1.50167i	0.781922	+	0.623376i	$0.214239\pi$
$883$	37.4427	+	44.6225i	1.26005	+	1.50167i	0.478126	+	0.878291i	$0.341316\pi$
$884$	1.75831	−	1.47540i	0.0591383	−	0.0496229i
$885$	9.66778	−	24.4096i	0.324979	−	0.820519i
$886$	7.45038	+	12.9044i	0.250300	+	0.433533i
$887$	15.7612	−	43.3035i	0.529208	−	1.45399i	−0.330797	−	0.943702i	$-0.607317\pi$
$887$	15.7612	−	43.3035i	0.529208	−	1.45399i	0.860005	−	0.510286i	$-0.170460\pi$
$888$	2.57385	+	0.453838i	0.0863726	+	0.0152298i
$889$	−0.517247	−	2.93345i	−0.0173479	−	0.0983849i
$890$	−10.8380	+	5.85841i	−0.363289	+	0.196374i
$891$	−7.43136	−	6.23565i	−0.248960	−	0.208902i
$892$			4.06232i			0.136016i
$893$	−4.18226	+	0.210874i	−0.139954	+	0.00705664i
$894$	−34.6837			−1.16000
$895$	2.42643	−	3.94305i	0.0811065	−	0.131802i
$896$	28.5534	−	10.3926i	0.953903	−	0.347192i
$897$	28.2275	−	4.97726i	0.942487	−	0.166186i
$898$	27.8468	+	4.91015i	0.929261	+	0.163854i
$899$	23.1244	+	8.41660i	0.771243	+	0.280709i
$900$	−3.59421	−	3.37679i	−0.119807	−	0.112560i
$901$	1.73326	−	3.00210i	0.0577434	−	0.100015i
$902$	8.33011	+	9.92744i	0.277362	+	0.330548i
$903$	2.59482	+	3.09239i	0.0863503	+	0.102908i
$904$	7.34506	−	12.7220i	0.244293	−	0.423128i
$905$	37.9121	−	30.0414i	1.26024	−	0.998611i
$906$	23.5370	+	8.56677i	0.781965	+	0.284612i
$907$	−43.0236	−	7.58622i	−1.42857	−	0.251896i	−0.594743	−	0.803916i	$-0.702746\pi$
$907$	−43.0236	−	7.58622i	−1.42857	−	0.251896i	−0.833831	+	0.552020i	$0.813857\pi$
$908$	5.43939	−	0.959112i	0.180513	−	0.0318292i
$909$	−8.31255	+	3.02552i	−0.275710	+	0.100350i
$910$	−32.3473	−	19.9055i	−1.07230	−	0.659860i
$911$	−30.7689			−1.01942			−0.509709	−	0.860347i	$-0.670247\pi$
$911$	−30.7689			−1.01942			−0.509709	+	0.860347i	$0.670247\pi$
$912$	25.1297	−	1.26707i	0.832127	−	0.0419568i
$913$		−	42.4795i		−	1.40587i
$914$	0.473572	+	0.397374i	0.0156644	+	0.0131440i
$915$	−4.90056	+	2.64898i	−0.162008	+	0.0875724i
$916$	−0.779591	−	4.42128i	−0.0257584	−	0.146083i
$917$	−30.2857	−	5.34019i	−1.00012	−	0.176349i
$918$	2.37265	−	6.51881i	0.0783093	−	0.215153i
$919$	6.04713	+	10.4739i	0.199476	+	0.345503i	0.948359	−	0.317200i	$-0.102743\pi$
$919$	6.04713	+	10.4739i	0.199476	+	0.345503i	−0.748882	+	0.662703i	$0.769409\pi$
$920$	−23.8069	−	9.42908i	−0.784891	−	0.310868i
$921$	−13.3516	+	11.2033i	−0.439950	+	0.369162i
$922$	8.86385	+	10.5635i	0.291915	+	0.347891i
$923$	−29.2158	−	16.8678i	−0.961650	−	0.555209i
$924$	−4.65242	−	8.05824i	−0.153054	−	0.265096i
$925$	−0.276125	+	4.91796i	−0.00907892	+	0.161702i
$926$	10.4075	−	59.0238i	0.342012	−	1.93964i
$927$	5.17052	−	0.911702i	0.169822	−	0.0299442i
$928$	−3.53016	−	9.69905i	−0.115883	−	0.318387i
$929$	−12.2297	−	10.2619i	−0.401242	−	0.336682i	0.419731	−	0.907648i	$-0.362124\pi$
$929$	−12.2297	−	10.2619i	−0.401242	−	0.336682i	−0.820974	+	0.570966i	$0.806569\pi$
$930$	5.09020	+	34.4990i	0.166914	+	1.13127i
$931$	3.42195	+	8.10624i	0.112150	+	0.265671i
$932$			15.5210i			0.508407i
$933$	−24.1279	+	28.7545i	−0.789912	+	0.941380i
$934$	−39.4639	+	14.3637i	−1.29130	+	0.469995i
$935$	−3.12980	−	9.41226i	−0.102356	−	0.307814i
$936$	−2.89189	+	16.4007i	−0.0945242	+	0.536074i
$937$	1.22430	−	3.36373i	0.0399961	−	0.109888i	−0.918087	−	0.396379i	$-0.870267\pi$
$937$	1.22430	−	3.36373i	0.0399961	−	0.109888i	0.958083	+	0.286491i	$0.0924888\pi$
$938$	10.1649	−	5.86870i	0.331895	−	0.191620i
$939$	−5.34304	+	9.25441i	−0.174363	+	0.302006i
$940$	−0.886360	+	0.998094i	−0.0289099	+	0.0325542i
$941$	26.5863	−	22.3086i	0.866689	−	0.727238i	−0.0967092	−	0.995313i	$-0.530832\pi$
$941$	26.5863	−	22.3086i	0.866689	−	0.727238i	0.963398	+	0.268074i	$0.0863872\pi$
$942$	−17.5108	−	10.1098i	−0.570531	−	0.329396i
$943$	−6.30018	+	3.63741i	−0.205162	+	0.118450i
$944$	−45.0833	−	16.4090i	−1.46733	−	0.534066i
$945$	−27.2002	−	0.762992i	−0.884821	−	0.0248201i
$946$	2.41503	+	13.6963i	0.0785195	+	0.445306i
$947$	15.3805	+	42.2576i	0.499800	+	1.37319i	0.891469	+	0.453082i	$0.149676\pi$
$947$	15.3805	+	42.2576i	0.499800	+	1.37319i	−0.391669	+	0.920106i	$0.628102\pi$
$948$	0.636020	−	0.757979i	0.0206570	−	0.0246180i
$949$	−71.2711			−2.31356
$950$	5.92901	+	34.7851i	0.192362	+	1.12858i
$951$	−12.3854			−0.401624
$952$	−2.51644	+	2.99897i	−0.0815582	+	0.0971972i
$953$	−0.572365	−	1.57256i	−0.0185407	−	0.0509402i	0.930077	−	0.367365i	$-0.119740\pi$
$953$	−0.572365	−	1.57256i	−0.0185407	−	0.0509402i	−0.948618	+	0.316424i	$0.897518\pi$
$954$	−1.96859	−	11.1644i	−0.0637354	−	0.361461i
$955$	−50.0820	−	1.40485i	−1.62061	−	0.0454598i
$956$	−9.82067	−	3.57443i	−0.317623	−	0.115605i
$957$	17.6433	−	10.1864i	0.570327	−	0.329278i
$958$	16.5998	+	9.58393i	0.536317	+	0.309643i
$959$	20.0762	−	16.8459i	0.648294	−	0.543984i
$960$	−7.42949	+	8.36604i	−0.239786	+	0.270013i
$961$	−17.3387	+	30.0315i	−0.559313	+	0.968758i
$962$	−6.49289	+	3.74867i	−0.209339	+	0.120862i
$963$	−3.62252	+	9.95279i	−0.116734	+	0.320724i
$964$	1.17034	−	6.63735i	0.0376942	−	0.213775i
$965$	13.8281	+	41.5853i	0.445143	+	1.33868i
$966$	20.7063	−	7.53649i	0.666216	−	0.242483i
$967$	−11.6789	+	13.9183i	−0.375568	+	0.447584i	−0.920410	−	0.390954i	$-0.872145\pi$
$967$	−11.6789	+	13.9183i	−0.375568	+	0.447584i	0.544842	+	0.838538i	$0.316589\pi$
$968$			46.5689i			1.49678i
$969$	−3.41889	+	2.21064i	−0.109831	+	0.0710159i
$970$	−6.74302	−	45.7011i	−0.216505	−	1.46737i
$971$	3.56175	+	2.98867i	0.114302	+	0.0959108i	0.698147	−	0.715954i	$-0.254008\pi$
$971$	3.56175	+	2.98867i	0.114302	+	0.0959108i	−0.583845	+	0.811865i	$0.698453\pi$
$972$	−3.04218	−	8.35833i	−0.0975781	−	0.268094i
$973$	20.5325	−	3.62043i	0.658240	−	0.116066i
$974$	−8.26050	+	46.8476i	−0.264683	+	1.50109i
$975$	27.8904	+	1.56594i	0.893208	+	0.0501502i
$976$	5.08987	+	8.81591i	0.162923	+	0.282190i
$977$	11.8979	+	6.86928i	0.380649	+	0.219768i	0.678100	−	0.734969i	$-0.262803\pi$
$977$	11.8979	+	6.86928i	0.380649	+	0.219768i	−0.297452	+	0.954737i	$0.596137\pi$
$978$	4.48263	+	5.34219i	0.143339	+	0.170825i
$979$	−14.7150	+	12.3474i	−0.470295	+	0.394624i
$980$	2.60770	+	1.03282i	0.0832999	+	0.0329922i
$981$	12.4454	+	21.5561i	0.397352	+	0.688234i
$982$	−2.66820	+	7.33082i	−0.0851457	+	0.233936i
$983$	8.28423	+	1.46073i	0.264226	+	0.0465901i	0.304191	−	0.952611i	$-0.401614\pi$
$983$	8.28423	+	1.46073i	0.264226	+	0.0465901i	−0.0399657	+	0.999201i	$0.512725\pi$
$984$	0.653241	+	3.70471i	0.0208246	+	0.118102i
$985$	30.4104	−	16.4382i	0.968957	−	0.523765i
$986$	2.95959	+	2.48339i	0.0942526	+	0.0790873i
$987$			2.54850i			0.0811198i
$988$	−9.32848	+	8.66446i	−0.296778	+	0.275653i
$989$	−7.80714			−0.248253
$990$	−27.6265	−	17.0004i	−0.878028	−	0.540310i
$991$	−17.4575	+	6.35400i	−0.554555	+	0.201841i	−0.604069	−	0.796932i	$-0.706455\pi$
$991$	−17.4575	+	6.35400i	−0.554555	+	0.201841i	0.0495142	+	0.998773i	$0.484233\pi$
$992$	27.1285	−	4.78348i	0.861330	−	0.151876i
$993$	4.71781	+	0.831878i	0.149715	+	0.0263988i
$994$	−24.3708	−	8.87026i	−0.772996	−	0.281348i
$995$	2.40619	−	1.90666i	0.0762815	−	0.0604453i
$996$	−2.77901	+	4.81338i	−0.0880562	+	0.152518i
$997$	24.7222	+	29.4628i	0.782960	+	0.933096i	0.999063	−	0.0432750i	$-0.0137792\pi$
$997$	24.7222	+	29.4628i	0.782960	+	0.933096i	−0.216103	+	0.976371i	$0.569335\pi$
$998$	−0.195890	−	0.233452i	−0.00620079	−	0.00738981i
$999$	−2.68566	+	4.65169i	−0.0849704	+	0.147173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.p.a.54.3	yes	48
3.2	odd	2		855.2.da.b.244.6		48
5.2	odd	4		475.2.l.f.301.3		48
5.3	odd	4		475.2.l.f.301.6		48
5.4	even	2	inner	95.2.p.a.54.6	yes	48
15.14	odd	2		855.2.da.b.244.3		48
19.5	even	9		1805.2.b.k.1084.19		24
19.6	even	9	inner	95.2.p.a.44.6	yes	48
19.14	odd	18		1805.2.b.l.1084.6		24
57.44	odd	18		855.2.da.b.424.3		48
95.14	odd	18		1805.2.b.l.1084.19		24
95.24	even	18		1805.2.b.k.1084.6		24
95.33	even	36		9025.2.a.ct.1.6		24
95.43	odd	36		9025.2.a.cu.1.19		24
95.44	even	18	inner	95.2.p.a.44.3	✓	48
95.52	even	36		9025.2.a.ct.1.19		24
95.62	odd	36		9025.2.a.cu.1.6		24
95.63	odd	36		475.2.l.f.101.6		48
95.82	odd	36		475.2.l.f.101.3		48
285.44	odd	18		855.2.da.b.424.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.3	✓	48	95.44	even	18	inner
95.2.p.a.44.6	yes	48	19.6	even	9	inner
95.2.p.a.54.3	yes	48	1.1	even	1	trivial
95.2.p.a.54.6	yes	48	5.4	even	2	inner
475.2.l.f.101.3		48	95.82	odd	36
475.2.l.f.101.6		48	95.63	odd	36
475.2.l.f.301.3		48	5.2	odd	4
475.2.l.f.301.6		48	5.3	odd	4
855.2.da.b.244.3		48	15.14	odd	2
855.2.da.b.244.6		48	3.2	odd	2
855.2.da.b.424.3		48	57.44	odd	18
855.2.da.b.424.6		48	285.44	odd	18
1805.2.b.k.1084.6		24	95.24	even	18
1805.2.b.k.1084.19		24	19.5	even	9
1805.2.b.l.1084.6		24	19.14	odd	18
1805.2.b.l.1084.19		24	95.14	odd	18
9025.2.a.ct.1.6		24	95.33	even	36
9025.2.a.ct.1.19		24	95.52	even	36
9025.2.a.cu.1.6		24	95.62	odd	36
9025.2.a.cu.1.19		24	95.43	odd	36

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04072 + 1.24028i) q^{2} +(0.406515 + 1.11689i) q^{3} +(-0.107903 - 0.611947i) q^{4} +(2.23519 + 0.0626993i) q^{5} +(-1.80832 - 0.658176i) q^{6} +(-1.93288 + 1.11595i) q^{7} +(-1.93303 - 1.11604i) q^{8} +(1.21594 - 1.02030i) q^{9} +(-2.40397 + 2.70701i) q^{10} +(-2.82239 + 4.88852i) q^{11} +(0.639613 - 0.369281i) q^{12} +(1.60766 - 4.41702i) q^{13} +(0.627496 - 3.55871i) q^{14} +(0.838609 + 2.52195i) q^{15} +(4.56376 - 1.66107i) q^{16} +(-0.505129 + 0.601990i) q^{17} +2.56995i q^{18} +(2.63014 - 3.47597i) q^{19} +(-0.202814 - 1.37458i) q^{20} +(-2.03214 - 1.70517i) q^{21} +(-3.12582 - 8.58813i) q^{22} +(5.05247 - 0.890886i) q^{23} +(0.460684 - 2.61267i) q^{24} +(4.99214 + 0.280289i) q^{25} +(3.80521 + 6.59082i) q^{26} +(4.72186 + 2.72616i) q^{27} +(0.891466 + 1.06241i) q^{28} +(-2.32611 + 1.95184i) q^{29} +(-4.00068 - 1.58453i) q^{30} +(-4.05208 - 7.01841i) q^{31} +(-1.16257 + 3.19413i) q^{32} +(-6.60729 - 1.16504i) q^{33} +(-0.220938 - 1.25300i) q^{34} +(-4.39033 + 2.37317i) q^{35} +(-0.755571 - 0.634000i) q^{36} +0.985141i q^{37} +(1.57393 + 6.87961i) q^{38} +5.58687 q^{39} +(-4.25071 - 2.61575i) q^{40} +(-1.33247 + 0.484978i) q^{41} +(4.22977 - 0.745823i) q^{42} +(-1.49862 - 0.264247i) q^{43} +(3.29606 + 1.19967i) q^{44} +(2.78183 - 2.20432i) q^{45} +(-4.15324 + 7.19363i) q^{46} +(-0.617523 - 0.735935i) q^{47} +(3.71047 + 4.42197i) q^{48} +(-1.00930 + 1.74817i) q^{49} +(-5.54304 + 5.89994i) q^{50} +(-0.877699 - 0.319456i) q^{51} +(-2.87645 - 0.507196i) q^{52} +(-4.34421 + 0.766002i) q^{53} +(-8.29533 + 3.01925i) q^{54} +(-6.61508 + 10.7498i) q^{55} +4.98176 q^{56} +(4.95147 + 1.52455i) q^{57} -4.91635i q^{58} +(-7.56739 - 6.34980i) q^{59} +(1.45281 - 0.785309i) q^{60} +(0.363973 + 2.06420i) q^{61} +(12.9219 + 2.27847i) q^{62} +(-1.21168 + 3.32905i) q^{63} +(2.10495 + 3.64588i) q^{64} +(3.87038 - 9.77207i) q^{65} +(8.32130 - 6.98240i) q^{66} +(2.08785 + 2.48820i) q^{67} +(0.422891 + 0.244156i) q^{68} +(3.04892 + 5.28089i) q^{69} +(1.62570 - 7.91504i) q^{70} +(1.24628 - 7.06798i) q^{71} +(-3.48914 + 0.615230i) q^{72} +(-5.18587 - 14.2481i) q^{73} +(-1.22185 - 1.02525i) q^{74} +(1.71633 + 5.68961i) q^{75} +(-2.41091 - 1.23444i) q^{76} -12.5986i q^{77} +(-5.81435 + 6.92928i) q^{78} +(1.25893 - 0.458214i) q^{79} +(10.3050 - 3.42667i) q^{80} +(-0.298427 + 1.69246i) q^{81} +(0.785214 - 2.15736i) q^{82} +(-6.51723 + 3.76273i) q^{83} +(-0.824199 + 1.42756i) q^{84} +(-1.16680 + 1.31389i) q^{85} +(1.88738 - 1.58370i) q^{86} +(-3.12559 - 1.80456i) q^{87} +(10.9115 - 6.29977i) q^{88} +(3.19776 + 1.16389i) q^{89} +(-0.161134 + 5.74433i) q^{90} +(1.82175 + 10.3317i) q^{91} +(-1.09035 - 2.99571i) q^{92} +(6.19156 - 7.37882i) q^{93} +1.55543 q^{94} +(6.09681 - 7.60453i) q^{95} -4.04009 q^{96} +(-8.20200 + 9.77477i) q^{97} +(-1.11781 - 3.07117i) q^{98} +(1.55588 + 8.82385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 18 q^{4} - 6 q^{5} - 6 q^{6} - 12 q^{9} - 15 q^{10} - 12 q^{11} + 6 q^{14} + 3 q^{15} - 42 q^{16} + 12 q^{19} + 42 q^{20} - 54 q^{21} + 24 q^{24} + 12 q^{25} + 12 q^{26} + 18 q^{30} - 42 q^{31} - 36 q^{34}+ \cdots - 36 q^{99}+O(q^{100}) \) 48 * q - 18 * q^4 - 6 * q^5 - 6 * q^6 - 12 * q^9 - 15 * q^10 - 12 * q^11 + 6 * q^14 + 3 * q^15 - 42 * q^16 + 12 * q^19 + 42 * q^20 - 54 * q^21 + 24 * q^24 + 12 * q^25 + 12 * q^26 + 18 * q^30 - 42 * q^31 - 36 * q^34 + 6 * q^35 + 18 * q^36 - 48 * q^39 + 66 * q^40 + 6 * q^41 - 6 * q^44 - 9 * q^45 - 6 * q^46 + 12 * q^49 - 18 * q^50 + 108 * q^51 + 24 * q^54 + 36 * q^56 - 36 * q^59 - 114 * q^60 + 48 * q^61 - 18 * q^65 + 180 * q^66 + 66 * q^69 - 123 * q^70 - 24 * q^71 + 84 * q^74 + 72 * q^75 + 66 * q^76 + 48 * q^79 - 39 * q^80 - 78 * q^81 - 54 * q^84 - 84 * q^85 - 42 * q^86 - 12 * q^89 + 18 * q^90 - 30 * q^91 - 72 * q^94 - 63 * q^95 - 240 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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