LMFDB - Embedded newform 513.2.g.c.505.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(64,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-1,0,-17,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.6
Character	$\chi$	$=$	513.505
Dual form			513.2.g.c.64.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.616796 - 1.06832i) q^{2} +(0.239126 - 0.414178i) q^{4} +0.551543 q^{5} +(-1.62156 + 2.80862i) q^{7} -3.05715 q^{8} +(-0.340189 - 0.589225i) q^{10} +(-2.68677 + 4.65363i) q^{11} +(-1.76195 + 3.05178i) q^{13} +4.00069 q^{14} +(1.40739 + 2.43766i) q^{16} +(-2.60168 + 4.50624i) q^{17} +(0.164107 - 4.35581i) q^{19} +(0.131888 - 0.228437i) q^{20} +6.62876 q^{22} +(1.49233 - 2.58480i) q^{23} -4.69580 q^{25} +4.34704 q^{26} +(0.775514 + 1.34323i) q^{28} -5.49841 q^{29} +(-2.54567 - 4.40923i) q^{31} +(-1.32101 + 2.28806i) q^{32} +6.41881 q^{34} +(-0.894360 + 1.54908i) q^{35} +9.20826 q^{37} +(-4.75463 + 2.51133i) q^{38} -1.68615 q^{40} -1.71003 q^{41} +(1.79608 + 3.11091i) q^{43} +(1.28495 + 2.22561i) q^{44} -3.68186 q^{46} +10.6354 q^{47} +(-1.75891 - 3.04653i) q^{49} +(2.89635 + 5.01663i) q^{50} +(0.842653 + 1.45952i) q^{52} +(-0.562013 - 0.973435i) q^{53} +(-1.48187 + 2.56668i) q^{55} +(4.95735 - 8.58639i) q^{56} +(3.39140 + 5.87407i) q^{58} +7.77857 q^{59} -11.3745 q^{61} +(-3.14032 + 5.43919i) q^{62} +8.88872 q^{64} +(-0.971789 + 1.68319i) q^{65} +(-1.18630 + 2.05473i) q^{67} +(1.24426 + 2.15512i) q^{68} +2.20655 q^{70} +(0.507763 - 0.879471i) q^{71} +(-5.98562 + 10.3674i) q^{73} +(-5.67962 - 9.83738i) q^{74} +(-1.76484 - 1.10956i) q^{76} +(-8.71353 - 15.0923i) q^{77} +(0.568802 + 0.985193i) q^{79} +(0.776234 + 1.34448i) q^{80} +(1.05474 + 1.82686i) q^{82} +(1.14372 - 1.98099i) q^{83} +(-1.43494 + 2.48538i) q^{85} +(2.21563 - 3.83759i) q^{86} +(8.21387 - 14.2268i) q^{88} +(-1.12141 - 1.94234i) q^{89} +(-5.71420 - 9.89729i) q^{91} +(-0.713711 - 1.23618i) q^{92} +(-6.55987 - 11.3620i) q^{94} +(0.0905122 - 2.40242i) q^{95} +(-4.09100 - 7.08582i) q^{97} +(-2.16978 + 3.75817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) $ 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.616796	−	1.06832i	−0.436140	−	0.755418i	0.561247	−	0.827648i	$-0.310322\pi$
$2$	−0.616796	−	1.06832i	−0.436140	−	0.755418i	−0.997388	+	0.0722305i	$0.976988\pi$
$3$		0			0
$3$		0			0
$4$	0.239126	−	0.414178i	0.119563	−	0.207089i
$5$	0.551543			0.246658			0.123329	−	0.992366i	$-0.460643\pi$
$5$	0.551543			0.246658			0.123329	+	0.992366i	$0.460643\pi$
$6$		0			0
$7$	−1.62156	+	2.80862i	−0.612892	+	1.06156i	0.377858	+	0.925863i	$0.376661\pi$
$7$	−1.62156	+	2.80862i	−0.612892	+	1.06156i	−0.990750	+	0.135697i	$0.956673\pi$
$8$	−3.05715			−1.08087
$9$		0			0
$10$	−0.340189	−	0.589225i	−0.107577	−	0.186329i
$11$	−2.68677	+	4.65363i	−0.810093	+	1.40312i	0.102706	+	0.994712i	$0.467250\pi$
$11$	−2.68677	+	4.65363i	−0.810093	+	1.40312i	−0.912799	+	0.408410i	$0.866083\pi$
$12$		0			0
$13$	−1.76195	+	3.05178i	−0.488676	+	0.846411i	−0.999915	−	0.0130271i	$-0.995853\pi$
$13$	−1.76195	+	3.05178i	−0.488676	+	0.846411i	0.511239	+	0.859438i	$0.329187\pi$
$14$	4.00069			1.06923
$15$		0			0
$16$	1.40739	+	2.43766i	0.351846	+	0.609416i
$17$	−2.60168	+	4.50624i	−0.630999	+	1.09292i	0.356349	+	0.934353i	$0.384022\pi$
$17$	−2.60168	+	4.50624i	−0.630999	+	1.09292i	−0.987348	+	0.158570i	$0.949312\pi$
$18$		0			0
$19$	0.164107	−	4.35581i	0.0376488	−	0.999291i
$19$	0.164107	−	4.35581i	0.0376488	−	0.999291i
$20$	0.131888	−	0.228437i	0.0294911	−	0.0510801i
$21$		0			0
$22$	6.62876			1.41326
$23$	1.49233	−	2.58480i	0.311173	−	0.538967i	−0.667444	−	0.744660i	$-0.732612\pi$
$23$	1.49233	−	2.58480i	0.311173	−	0.538967i	0.978617	+	0.205693i	$0.0659449\pi$
$24$		0			0
$25$	−4.69580			−0.939160
$26$	4.34704			0.852525
$27$		0			0
$28$	0.775514	+	1.34323i	0.146558	+	0.253847i
$29$	−5.49841			−1.02103			−0.510515	−	0.859869i	$-0.670545\pi$
$29$	−5.49841			−1.02103			−0.510515	+	0.859869i	$0.670545\pi$
$30$		0			0
$31$	−2.54567	−	4.40923i	−0.457216	−	0.791921i	0.541597	−	0.840638i	$-0.317820\pi$
$31$	−2.54567	−	4.40923i	−0.457216	−	0.791921i	−0.998813	+	0.0487176i	$0.984487\pi$
$32$	−1.32101	+	2.28806i	−0.233524	+	0.404475i
$33$		0			0
$34$	6.41881			1.10082
$35$	−0.894360	+	1.54908i	−0.151174	+	0.261842i
$36$		0			0
$37$	9.20826			1.51383			0.756914	−	0.653514i	$-0.226706\pi$
$37$	9.20826			1.51383			0.756914	+	0.653514i	$0.226706\pi$
$38$	−4.75463	+	2.51133i	−0.771302	+	0.407391i
$39$		0			0
$40$	−1.68615			−0.266604
$41$	−1.71003			−0.267061			−0.133531	−	0.991045i	$-0.542631\pi$
$41$	−1.71003			−0.267061			−0.133531	+	0.991045i	$0.542631\pi$
$42$		0			0
$43$	1.79608	+	3.11091i	0.273900	+	0.474409i	0.969857	−	0.243675i	$-0.0783529\pi$
$43$	1.79608	+	3.11091i	0.273900	+	0.474409i	−0.695957	+	0.718083i	$0.745020\pi$
$44$	1.28495	+	2.22561i	0.193714	+	0.335523i
$45$		0			0
$46$	−3.68186			−0.542860
$47$	10.6354			1.55133			0.775666	−	0.631143i	$-0.217414\pi$
$47$	10.6354			1.55133			0.775666	+	0.631143i	$0.217414\pi$
$48$		0			0
$49$	−1.75891	−	3.04653i	−0.251273	−	0.435218i
$50$	2.89635	+	5.01663i	0.409606	+	0.709458i
$51$		0			0
$52$	0.842653	+	1.45952i	0.116855	+	0.202399i
$53$	−0.562013	−	0.973435i	−0.0771985	−	0.133712i	0.824842	−	0.565364i	$-0.191264\pi$
$53$	−0.562013	−	0.973435i	−0.0771985	−	0.133712i	−0.902040	+	0.431652i	$0.857931\pi$
$54$		0			0
$55$	−1.48187	+	2.56668i	−0.199815	+	0.346091i
$56$	4.95735	−	8.58639i	0.662454	−	1.14740i
$57$		0			0
$58$	3.39140	+	5.87407i	0.445312	+	0.771303i
$59$	7.77857			1.01268			0.506342	−	0.862333i	$-0.330997\pi$
$59$	7.77857			1.01268			0.506342	+	0.862333i	$0.330997\pi$
$60$		0			0
$61$	−11.3745			−1.45635			−0.728176	−	0.685391i	$-0.759631\pi$
$61$	−11.3745			−1.45635			−0.728176	+	0.685391i	$0.759631\pi$
$62$	−3.14032	+	5.43919i	−0.398820	+	0.690777i
$63$		0			0
$64$	8.88872			1.11109
$65$	−0.971789	+	1.68319i	−0.120536	+	0.208774i
$66$		0			0
$67$	−1.18630	+	2.05473i	−0.144929	+	0.251025i	−0.929347	−	0.369209i	$-0.879629\pi$
$67$	−1.18630	+	2.05473i	−0.144929	+	0.251025i	0.784417	+	0.620233i	$0.212962\pi$
$68$	1.24426	+	2.15512i	0.150888	+	0.261346i
$69$		0			0
$70$	2.20655			0.263733
$71$	0.507763	−	0.879471i	0.0602604	−	0.104374i	−0.834321	−	0.551278i	$-0.814140\pi$
$71$	0.507763	−	0.879471i	0.0602604	−	0.104374i	0.894582	+	0.446904i	$0.147474\pi$
$72$		0			0
$73$	−5.98562	+	10.3674i	−0.700564	+	1.21341i	0.267704	+	0.963501i	$0.413735\pi$
$73$	−5.98562	+	10.3674i	−0.700564	+	1.21341i	−0.968269	+	0.249912i	$0.919598\pi$
$74$	−5.67962	−	9.83738i	−0.660242	−	1.14357i
$75$		0			0
$76$	−1.76484	−	1.10956i	−0.202441	−	0.127275i
$77$	−8.71353	−	15.0923i	−0.992999	−	1.71992i
$78$		0			0
$79$	0.568802	+	0.985193i	0.0639952	+	0.110843i	0.896248	−	0.443554i	$-0.146282\pi$
$79$	0.568802	+	0.985193i	0.0639952	+	0.110843i	−0.832253	+	0.554397i	$0.812949\pi$
$80$	0.776234	+	1.34448i	0.0867856	+	0.150317i
$81$		0			0
$82$	1.05474	+	1.82686i	0.116476	+	0.201743i
$83$	1.14372	−	1.98099i	0.125540	−	0.217441i	−0.796404	−	0.604765i	$-0.793267\pi$
$83$	1.14372	−	1.98099i	0.125540	−	0.217441i	0.921944	+	0.387324i	$0.126600\pi$
$84$		0			0
$85$	−1.43494	+	2.48538i	−0.155641	+	0.269578i
$86$	2.21563	−	3.83759i	0.238918	−	0.413818i
$87$		0			0
$88$	8.21387	−	14.2268i	0.875601	−	1.51659i
$89$	−1.12141	−	1.94234i	−0.118870	−	0.205888i	0.800450	−	0.599399i	$-0.204594\pi$
$89$	−1.12141	−	1.94234i	−0.118870	−	0.205888i	−0.919320	+	0.393511i	$0.871260\pi$
$90$		0			0
$91$	−5.71420	−	9.89729i	−0.599011	−	1.03752i
$92$	−0.713711	−	1.23618i	−0.0744095	−	0.128881i
$93$		0			0
$94$	−6.55987	−	11.3620i	−0.676599	−	1.17190i
$95$	0.0905122	−	2.40242i	0.00928635	−	0.246483i
$96$		0			0
$97$	−4.09100	−	7.08582i	−0.415378	−	0.719456i	0.580090	−	0.814552i	$-0.303017\pi$
$97$	−4.09100	−	7.08582i	−0.415378	−	0.719456i	−0.995468	+	0.0950967i	$0.969684\pi$
$98$	−2.16978	+	3.75817i	−0.219181	+	0.379633i
$99$		0			0
$100$	−1.12289	+	1.94490i	−0.112289	+	0.194490i
$101$	−5.43430			−0.540733			−0.270366	−	0.962758i	$-0.587145\pi$
$101$	−5.43430			−0.540733			−0.270366	+	0.962758i	$0.587145\pi$
$102$		0			0
$103$	6.93864	+	12.0181i	0.683684	+	1.18418i	0.973848	+	0.227199i	$0.0729567\pi$
$103$	6.93864	+	12.0181i	0.683684	+	1.18418i	−0.290164	+	0.956977i	$0.593710\pi$
$104$	5.38653	−	9.32975i	0.528193	−	0.914857i
$105$		0			0
$106$	−0.693295	+	1.20082i	−0.0673387	+	0.116634i
$107$	15.8009			1.52753			0.763765	−	0.645494i	$-0.223348\pi$
$107$	15.8009			1.52753			0.763765	+	0.645494i	$0.223348\pi$
$108$		0			0
$109$	−3.79701	+	6.57662i	−0.363688	+	0.629926i	−0.988565	−	0.150798i	$-0.951816\pi$
$109$	−3.79701	+	6.57662i	−0.363688	+	0.629926i	0.624877	+	0.780723i	$0.285149\pi$
$110$	3.65605			0.348590
$111$		0			0
$112$	−9.12864			−0.862576
$113$	2.26572	+	3.92433i	0.213141	+	0.369170i	0.952696	−	0.303926i	$-0.0982974\pi$
$113$	2.26572	+	3.92433i	0.213141	+	0.369170i	−0.739555	+	0.673096i	$0.764964\pi$
$114$		0			0
$115$	0.823086	−	1.42563i	0.0767531	−	0.132940i
$116$	−1.31481	+	2.27732i	−0.122077	+	0.211444i
$117$		0			0
$118$	−4.79779	−	8.31001i	−0.441672	−	0.764999i
$119$	−8.43755	−	14.6143i	−0.773469	−	1.33969i
$120$		0			0
$121$	−8.93750	−	15.4802i	−0.812500	−	1.40729i
$122$	7.01572	+	12.1516i	0.635174	+	1.10015i
$123$		0			0
$124$	−2.43494			−0.218664
$125$	−5.34765			−0.478308
$126$		0			0
$127$	−5.24840	−	9.09049i	−0.465720	−	0.806651i	0.533514	−	0.845792i	$-0.320871\pi$
$127$	−5.24840	−	9.09049i	−0.465720	−	0.806651i	−0.999234	+	0.0391405i	$0.987538\pi$
$128$	−2.84050	−	4.91990i	−0.251067	−	0.434861i
$129$		0			0
$130$	2.39758			0.210282
$131$	0.563451			0.0492289			0.0246145	−	0.999697i	$-0.492164\pi$
$131$	0.563451			0.0492289			0.0246145	+	0.999697i	$0.492164\pi$
$132$		0			0
$133$	11.9677	+	7.52412i	1.03773	+	0.652424i
$134$	2.92681			0.252838
$135$		0			0
$136$	7.95372	−	13.7762i	0.682026	−	1.18130i
$137$	−17.2333			−1.47234			−0.736169	−	0.676798i	$-0.763367\pi$
$137$	−17.2333			−1.47234			−0.736169	+	0.676798i	$0.763367\pi$
$138$		0			0
$139$	−0.726237	+	1.25788i	−0.0615986	+	0.106692i	−0.895180	−	0.445705i	$-0.852953\pi$
$139$	−0.726237	+	1.25788i	−0.0615986	+	0.106692i	0.833582	+	0.552396i	$0.186287\pi$
$140$	0.427729	+	0.740849i	0.0361497	+	0.0626132i
$141$		0			0
$142$	−1.25274			−0.105128
$143$	−9.46790	−	16.3989i	−0.791745	−	1.37134i
$144$		0			0
$145$	−3.03261			−0.251845
$146$	14.7676			1.22218
$147$		0			0
$148$	2.20193	−	3.81386i	0.180998	−	0.313497i
$149$	−4.69012			−0.384230			−0.192115	−	0.981372i	$-0.561535\pi$
$149$	−4.69012			−0.384230			−0.192115	+	0.981372i	$0.561535\pi$
$150$		0			0
$151$	0.368885	−	0.638928i	0.0300195	−	0.0519953i	−0.850625	−	0.525772i	$-0.823776\pi$
$151$	0.368885	−	0.638928i	0.0300195	−	0.0519953i	0.880645	+	0.473777i	$0.157110\pi$
$152$	−0.501700	+	13.3164i	−0.0406933	+	1.08010i
$153$		0			0
$154$	−10.7489	+	18.6177i	−0.866174	+	1.50026i
$155$	−1.40405	−	2.43188i	−0.112776	−	0.195333i
$156$		0			0
$157$	5.41446			0.432121			0.216060	−	0.976380i	$-0.430679\pi$
$157$	5.41446			0.432121			0.216060	+	0.976380i	$0.430679\pi$
$158$	0.701669	−	1.21533i	0.0558218	−	0.0966862i
$159$		0			0
$160$	−0.728594	+	1.26196i	−0.0576005	+	0.0997669i
$161$	4.83981	+	8.38280i	0.381431	+	0.660657i
$162$		0			0
$163$	−10.0435			−0.786669			−0.393334	−	0.919395i	$-0.628679\pi$
$163$	−10.0435			−0.786669			−0.393334	+	0.919395i	$0.628679\pi$
$164$	−0.408912	+	0.708256i	−0.0319306	+	0.0553055i
$165$		0			0
$166$	−2.82177			−0.219012
$167$	−7.17245	+	12.4230i	−0.555021	+	0.961324i	0.442881	+	0.896580i	$0.353956\pi$
$167$	−7.17245	+	12.4230i	−0.555021	+	0.961324i	−0.997902	+	0.0647437i	$0.979377\pi$
$168$		0			0
$169$	0.291096	+	0.504193i	0.0223920	+	0.0387841i
$170$	3.54025			0.271525
$171$		0			0
$172$	1.71796			0.130993
$173$	2.04739	+	3.54619i	0.155660	+	0.269612i	0.933299	−	0.359100i	$-0.116916\pi$
$173$	2.04739	+	3.54619i	0.155660	+	0.269612i	−0.777639	+	0.628711i	$0.783583\pi$
$174$		0			0
$175$	7.61452	−	13.1887i	0.575604	−	0.996975i
$176$	−15.1253			−1.14011
$177$		0			0
$178$	−1.38337	+	2.39606i	−0.103688	+	0.179592i
$179$	−1.96134			−0.146597			−0.0732986	−	0.997310i	$-0.523353\pi$
$179$	−1.96134			−0.146597			−0.0732986	+	0.997310i	$0.523353\pi$
$180$		0			0
$181$	0.625824	+	1.08396i	0.0465172	+	0.0805701i	0.888347	−	0.459174i	$-0.151854\pi$
$181$	0.625824	+	1.08396i	0.0465172	+	0.0805701i	−0.841829	+	0.539744i	$0.818521\pi$
$182$	−7.04899	+	12.2092i	−0.522506	+	0.905007i
$183$		0			0
$184$	−4.56229	+	7.90211i	−0.336336	+	0.582551i
$185$	5.07875			0.373397
$186$		0			0
$187$	−13.9802	−	24.2145i	−1.02234	−	1.77074i
$188$	2.54320	−	4.40495i	0.185482	−	0.321264i
$189$		0			0
$190$	−2.62238	+	1.38510i	−0.190247	+	0.100486i
$191$	−8.35232	+	14.4666i	−0.604353	+	1.04677i	0.387801	+	0.921743i	$0.373235\pi$
$191$	−8.35232	+	14.4666i	−0.604353	+	1.04677i	−0.992153	+	0.125026i	$0.960098\pi$
$192$		0			0
$193$	24.7409			1.78089			0.890445	−	0.455091i	$-0.150393\pi$
$193$	24.7409			1.78089			0.890445	+	0.455091i	$0.150393\pi$
$194$	−5.04662	+	8.74100i	−0.362326	+	0.627567i
$195$		0			0
$196$	−1.68241			−0.120172
$197$	−3.02872			−0.215787			−0.107894	−	0.994162i	$-0.534411\pi$
$197$	−3.02872			−0.215787			−0.107894	+	0.994162i	$0.534411\pi$
$198$		0			0
$199$	8.82614	+	15.2873i	0.625668	+	1.08369i	0.988411	+	0.151800i	$0.0485069\pi$
$199$	8.82614	+	15.2873i	0.625668	+	1.08369i	−0.362743	+	0.931889i	$0.618160\pi$
$200$	14.3558			1.01511
$201$		0			0
$202$	3.35185	+	5.80558i	0.235835	+	0.408479i
$203$	8.91600	−	15.4430i	0.625781	−	1.08388i
$204$		0			0
$205$	−0.943153			−0.0658727
$206$	8.55944	−	14.8254i	0.596365	−	1.03293i
$207$		0			0
$208$	−9.91895			−0.687755
$209$	19.8294	+	12.4668i	1.37163	+	0.862344i
$210$		0			0
$211$	−8.12869			−0.559602			−0.279801	−	0.960058i	$-0.590269\pi$
$211$	−8.12869			−0.559602			−0.279801	+	0.960058i	$0.590269\pi$
$212$	−0.537568			−0.0369203
$213$		0			0
$214$	−9.74593	−	16.8804i	−0.666218	−	1.15392i
$215$	0.990617	+	1.71580i	0.0675595	+	0.117017i
$216$		0			0
$217$	16.5118			1.12090
$218$	9.36793			0.634476
$219$		0			0
$220$	0.708707	+	1.22752i	0.0477810	+	0.0827592i
$221$	−9.16802	−	15.8795i	−0.616708	−	1.06817i
$222$		0			0
$223$	2.90390	+	5.02970i	0.194459	+	0.336813i	0.946723	−	0.322049i	$-0.104371\pi$
$223$	2.90390	+	5.02970i	0.194459	+	0.336813i	−0.752264	+	0.658862i	$0.771038\pi$
$224$	−4.28420	−	7.42045i	−0.286250	−	0.495800i
$225$		0			0
$226$	2.79497	−	4.84103i	0.185918	−	0.322020i
$227$	5.88816	−	10.1986i	0.390811	−	0.676905i	−0.601746	−	0.798688i	$-0.705528\pi$
$227$	5.88816	−	10.1986i	0.390811	−	0.676905i	0.992557	+	0.121783i	$0.0388613\pi$
$228$		0			0
$229$	12.6223	+	21.8625i	0.834106	+	1.44471i	0.894756	+	0.446555i	$0.147349\pi$
$229$	12.6223	+	21.8625i	0.834106	+	1.44471i	−0.0606506	+	0.998159i	$0.519318\pi$
$230$	−2.03070			−0.133901
$231$		0			0
$232$	16.8095			1.10360
$233$	9.04140	−	15.6602i	0.592322	−	1.02593i	−0.401597	−	0.915816i	$-0.631545\pi$
$233$	9.04140	−	15.6602i	0.592322	−	1.02593i	0.993919	−	0.110115i	$-0.0351218\pi$
$234$		0			0
$235$	5.86588			0.382648
$236$	1.86006	−	3.22171i	0.121079	−	0.209716i
$237$		0			0
$238$	−10.4085	+	18.0280i	−0.674682	+	1.16858i
$239$	4.15871	+	7.20309i	0.269004	+	0.465929i	0.968605	−	0.248605i	$-0.0799720\pi$
$239$	4.15871	+	7.20309i	0.269004	+	0.465929i	−0.699601	+	0.714534i	$0.746639\pi$
$240$		0			0
$241$	19.7866			1.27456			0.637282	−	0.770630i	$-0.280058\pi$
$241$	19.7866			1.27456			0.637282	+	0.770630i	$0.280058\pi$
$242$	−11.0252	+	19.0962i	−0.708728	+	1.22755i
$243$		0			0
$244$	−2.71993	+	4.71106i	−0.174126	+	0.301594i
$245$	−0.970117	−	1.68029i	−0.0619785	−	0.107350i
$246$		0			0
$247$	13.0038	+	8.17552i	0.827413	+	0.520196i
$248$	7.78249	+	13.4797i	0.494189	+	0.855960i
$249$		0			0
$250$	3.29841	+	5.71301i	0.208610	+	0.361323i
$251$	−5.61049	−	9.71765i	−0.354131	−	0.613373i	0.632838	−	0.774284i	$-0.281890\pi$
$251$	−5.61049	−	9.71765i	−0.354131	−	0.613373i	−0.986969	+	0.160912i	$0.948557\pi$
$252$		0			0
$253$	8.01912	+	13.8895i	0.504158	+	0.873227i
$254$	−6.47438	+	11.2140i	−0.406239	+	0.703626i
$255$		0			0
$256$	5.38470	−	9.32657i	0.336544	−	0.582911i
$257$	−15.3868	+	26.6507i	−0.959800	+	1.66242i	−0.236820	+	0.971554i	$0.576105\pi$
$257$	−15.3868	+	26.6507i	−0.959800	+	1.66242i	−0.722980	+	0.690869i	$0.757228\pi$
$258$		0			0
$259$	−14.9317	+	25.8625i	−0.927814	+	1.60702i
$260$	0.464760	+	0.804987i	0.0288232	+	0.0499232i
$261$		0			0
$262$	−0.347534	−	0.601947i	−0.0214707	−	0.0371884i
$263$	11.0033	+	19.0582i	0.678491	+	1.17518i	0.975435	+	0.220286i	$0.0706992\pi$
$263$	11.0033	+	19.0582i	0.678491	+	1.17518i	−0.296944	+	0.954895i	$0.595967\pi$
$264$		0			0
$265$	−0.309974	−	0.536892i	−0.0190416	−	0.0329810i
$266$	0.656541	−	17.4262i	0.0402551	−	1.06847i
$267$		0			0
$268$	0.567348	+	0.982676i	0.0346563	+	0.0600265i
$269$	−4.69970	+	8.14012i	−0.286546	+	0.496312i	−0.972983	−	0.230877i	$-0.925840\pi$
$269$	−4.69970	+	8.14012i	−0.286546	+	0.496312i	0.686437	+	0.727189i	$0.259174\pi$
$270$		0			0
$271$	5.10799	−	8.84729i	0.310288	−	0.537435i	−0.668137	−	0.744039i	$-0.732908\pi$
$271$	5.10799	−	8.84729i	0.310288	−	0.537435i	0.978425	+	0.206604i	$0.0662412\pi$
$272$	−14.6463			−0.888059
$273$		0			0
$274$	10.6294	+	18.4107i	0.642146	+	1.11223i
$275$	12.6166	−	21.8525i	0.760807	−	1.31776i
$276$		0			0
$277$	−11.8449	+	20.5159i	−0.711688	+	1.23268i	0.252535	+	0.967588i	$0.418736\pi$
$277$	−11.8449	+	20.5159i	−0.711688	+	1.23268i	−0.964223	+	0.265092i	$0.914598\pi$
$278$	1.79176			0.107463
$279$		0			0
$280$	2.73419	−	4.73576i	0.163399	−	0.283016i
$281$	4.26690			0.254542			0.127271	−	0.991868i	$-0.459378\pi$
$281$	4.26690			0.254542			0.127271	+	0.991868i	$0.459378\pi$
$282$		0			0
$283$	−21.8728			−1.30020			−0.650102	−	0.759847i	$-0.725274\pi$
$283$	−21.8728			−1.30020			−0.650102	+	0.759847i	$0.725274\pi$
$284$	−0.242838	−	0.420608i	−0.0144098	−	0.0249585i
$285$		0			0
$286$	−11.6795	+	20.2295i	−0.690624	+	1.19620i
$287$	2.77291	−	4.80282i	0.163680	−	0.283502i
$288$		0			0
$289$	−5.03744	−	8.72510i	−0.296320	−	0.513241i
$290$	1.87050	+	3.23980i	0.109840	+	0.190248i
$291$		0			0
$292$	2.86263	+	4.95823i	0.167523	+	0.290158i
$293$	−0.0198641	−	0.0344056i	−0.00116047	−	0.00201000i	0.865445	−	0.501005i	$-0.167036\pi$
$293$	−0.0198641	−	0.0344056i	−0.00116047	−	0.00201000i	−0.866605	+	0.498995i	$0.833703\pi$
$294$		0			0
$295$	4.29022			0.249786
$296$	−28.1510			−1.63625
$297$		0			0
$298$	2.89285	+	5.01056i	0.167578	+	0.290254i
$299$	5.25882	+	9.10854i	0.304125	+	0.526760i
$300$		0			0
$301$	−11.6498			−0.671485
$302$	−0.910108			−0.0523708
$303$		0			0
$304$	10.8490	−	5.73027i	0.622231	−	0.328653i
$305$	−6.27351			−0.359220
$306$		0			0
$307$	7.73434	−	13.3963i	0.441422	−	0.764566i	−0.556373	−	0.830933i	$-0.687807\pi$
$307$	7.73434	−	13.3963i	0.441422	−	0.764566i	0.997795	+	0.0663669i	$0.0211408\pi$
$308$	−8.33452			−0.474903
$309$		0			0
$310$	−1.73202	+	2.99995i	−0.0983721	+	0.170385i
$311$	−6.04377	−	10.4681i	−0.342711	−	0.593593i	0.642224	−	0.766517i	$-0.278012\pi$
$311$	−6.04377	−	10.4681i	−0.342711	−	0.593593i	−0.984935	+	0.172924i	$0.944678\pi$
$312$		0			0
$313$	7.67487			0.433809			0.216905	−	0.976193i	$-0.430404\pi$
$313$	7.67487			0.433809			0.216905	+	0.976193i	$0.430404\pi$
$314$	−3.33962	−	5.78439i	−0.188465	−	0.326432i
$315$		0			0
$316$	0.544061			0.0306058
$317$	9.52242			0.534832			0.267416	−	0.963581i	$-0.413830\pi$
$317$	9.52242			0.534832			0.267416	+	0.963581i	$0.413830\pi$
$318$		0			0
$319$	14.7730	−	25.5876i	0.827128	−	1.43263i
$320$	4.90251			0.274059
$321$		0			0
$322$	5.97035	−	10.3410i	0.332715	−	0.576279i
$323$	19.2013	+	12.0719i	1.06839	+	0.671699i
$324$		0			0
$325$	8.27374	−	14.3305i	0.458945	−	0.794916i
$326$	6.19480	+	10.7297i	0.343098	+	0.594263i
$327$		0			0
$328$	5.22781			0.288657
$329$	−17.2459	+	29.8708i	−0.950800	+	1.64683i
$330$		0			0
$331$	4.84054	−	8.38406i	0.266060	−	0.460830i	−0.701781	−	0.712393i	$-0.747611\pi$
$331$	4.84054	−	8.38406i	0.266060	−	0.460830i	0.967841	+	0.251563i	$0.0809447\pi$
$332$	−0.546987	−	0.947410i	−0.0300198	−	0.0519959i
$333$		0			0
$334$	17.6957			0.968268
$335$	−0.654294	+	1.13327i	−0.0357479	+	0.0619171i
$336$		0			0
$337$	−30.3679			−1.65425			−0.827123	−	0.562021i	$-0.810024\pi$
$337$	−30.3679			−1.65425			−0.827123	+	0.562021i	$0.810024\pi$
$338$	0.359094	−	0.621969i	0.0195321	−	0.0338306i
$339$		0			0
$340$	0.686261	+	1.18864i	0.0372177	+	0.0644630i
$341$	27.3585			1.48155
$342$		0			0
$343$	−11.2931			−0.609770
$344$	−5.49090	−	9.51051i	−0.296049	−	0.512772i
$345$		0			0
$346$	2.52564	−	4.37454i	0.135780	−	0.235177i
$347$	8.24041			0.442369			0.221184	−	0.975232i	$-0.429008\pi$
$347$	8.24041			0.442369			0.221184	+	0.975232i	$0.429008\pi$
$348$		0			0
$349$	0.121550	−	0.210531i	0.00650642	−	0.0112695i	−0.862754	−	0.505624i	$-0.831262\pi$
$349$	0.121550	−	0.210531i	0.00650642	−	0.0112695i	0.869260	+	0.494355i	$0.164596\pi$
$350$	−18.7864			−1.00418
$351$		0			0
$352$	−7.09851	−	12.2950i	−0.378352	−	0.655325i
$353$	−5.37981	+	9.31810i	−0.286338	+	0.495952i	−0.972933	−	0.231088i	$-0.925771\pi$
$353$	−5.37981	+	9.31810i	−0.286338	+	0.495952i	0.686595	+	0.727040i	$0.259105\pi$
$354$		0			0
$355$	0.280053	−	0.485066i	0.0148637	−	0.0257446i
$356$	−1.07264			−0.0568495
$357$		0			0
$358$	1.20974	+	2.09534i	0.0639370	+	0.110742i
$359$	8.34473	−	14.4535i	0.440418	−	0.762827i	−0.557302	−	0.830310i	$-0.688164\pi$
$359$	8.34473	−	14.4535i	0.440418	−	0.762827i	0.997720	+	0.0674831i	$0.0214969\pi$
$360$		0			0
$361$	−18.9461	−	1.42964i	−0.997165	−	0.0752441i
$362$	0.772012	−	1.33716i	0.0405760	−	0.0702798i
$363$		0			0
$364$	−5.46565			−0.286478
$365$	−3.30133	+	5.71807i	−0.172799	+	0.299297i
$366$		0			0
$367$	−15.1697			−0.791853			−0.395927	−	0.918282i	$-0.629577\pi$
$367$	−15.1697			−0.791853			−0.395927	+	0.918282i	$0.629577\pi$
$368$	8.40115			0.437940
$369$		0			0
$370$	−3.13255	−	5.42574i	−0.162854	−	0.282071i
$371$	3.64535			0.189257
$372$		0			0
$373$	−15.4009	−	26.6751i	−0.797427	−	1.38118i	−0.921287	−	0.388884i	$-0.872861\pi$
$373$	−15.4009	−	26.6751i	−0.797427	−	1.38118i	0.123860	−	0.992300i	$-0.460473\pi$
$374$	−17.2459	+	29.8708i	−0.891764	+	1.54458i
$375$		0			0
$376$	−32.5140			−1.67678
$377$	9.68790	−	16.7799i	0.498952	−	0.864211i
$378$		0			0
$379$	22.2036			1.14052			0.570260	−	0.821464i	$-0.306842\pi$
$379$	22.2036			1.14052			0.570260	+	0.821464i	$0.306842\pi$
$380$	−0.973384	−	0.611968i	−0.0499336	−	0.0313933i
$381$		0			0
$382$	20.6067			1.05433
$383$	−3.10744			−0.158783			−0.0793913	−	0.996844i	$-0.525298\pi$
$383$	−3.10744			−0.158783			−0.0793913	+	0.996844i	$0.525298\pi$
$384$		0			0
$385$	−4.80589	−	8.32404i	−0.244931	−	0.424232i
$386$	−15.2601	−	26.4312i	−0.776718	−	1.34532i
$387$		0			0
$388$	−3.91305			−0.198655
$389$	1.09399			0.0554674			0.0277337	−	0.999615i	$-0.491171\pi$
$389$	1.09399			0.0554674			0.0277337	+	0.999615i	$0.491171\pi$
$390$		0			0
$391$	7.76513	+	13.4496i	0.392700	+	0.680176i
$392$	5.37726	+	9.31369i	0.271593	+	0.470413i
$393$		0			0
$394$	1.86810	+	3.23565i	0.0941137	+	0.163010i
$395$	0.313719	+	0.543377i	0.0157849	+	0.0273402i
$396$		0			0
$397$	−16.6030	+	28.7572i	−0.833279	+	1.44328i	0.0621458	+	0.998067i	$0.480206\pi$
$397$	−16.6030	+	28.7572i	−0.833279	+	1.44328i	−0.895424	+	0.445214i	$0.853128\pi$
$398$	10.8878	−	18.8583i	0.545758	−	0.945281i
$399$		0			0
$400$	−6.60880	−	11.4468i	−0.330440	−	0.572339i
$401$	−10.7068			−0.534671			−0.267336	−	0.963603i	$-0.586143\pi$
$401$	−10.7068			−0.534671			−0.267336	+	0.963603i	$0.586143\pi$
$402$		0			0
$403$	17.9413			0.893721
$404$	−1.29948	+	2.25077i	−0.0646516	+	0.111980i
$405$		0			0
$406$	−21.9974			−1.09171
$407$	−24.7405	+	42.8518i	−1.22634	+	2.12409i
$408$		0			0
$409$	5.61657	−	9.72818i	0.277721	−	0.481028i	−0.693097	−	0.720845i	$-0.743754\pi$
$409$	5.61657	−	9.72818i	0.277721	−	0.481028i	0.970818	+	0.239817i	$0.0770875\pi$
$410$	0.581733	+	1.00759i	0.0287297	+	0.0497614i
$411$		0			0
$412$	6.63683			0.326973
$413$	−12.6134	+	21.8471i	−0.620666	+	1.07502i
$414$		0			0
$415$	0.630812	−	1.09260i	0.0309654	−	0.0536336i
$416$	−4.65510	−	8.06287i	−0.228235	−	0.395315i
$417$		0			0
$418$	1.08783	−	28.8736i	0.0532074	−	1.41225i
$419$	3.31446	+	5.74081i	0.161922	+	0.280457i	0.935558	−	0.353173i	$-0.114897\pi$
$419$	3.31446	+	5.74081i	0.161922	+	0.280457i	−0.773636	+	0.633630i	$0.781564\pi$
$420$		0			0
$421$	7.08505	+	12.2717i	0.345304	+	0.598085i	0.985409	−	0.170203i	$-0.0544423\pi$
$421$	7.08505	+	12.2717i	0.345304	+	0.598085i	−0.640105	+	0.768288i	$0.721109\pi$
$422$	5.01374	+	8.68406i	0.244065	+	0.422733i
$423$		0			0
$424$	1.71816	+	2.97594i	0.0834412	+	0.144524i
$425$	12.2170	−	21.1604i	0.592609	−	1.02643i
$426$		0			0
$427$	18.4444	−	31.9466i	0.892586	−	1.54600i
$428$	3.77840	−	6.54439i	0.182636	−	0.316335i
$429$		0			0
$430$	1.22202	−	2.11660i	0.0589309	−	0.102071i
$431$	−6.14500	−	10.6434i	−0.295994	−	0.512677i	0.679222	−	0.733933i	$-0.262318\pi$
$431$	−6.14500	−	10.6434i	−0.295994	−	0.512677i	−0.975216	+	0.221256i	$0.928984\pi$
$432$		0			0
$433$	6.40711	+	11.0974i	0.307906	+	0.533309i	0.977904	−	0.209054i	$-0.0670384\pi$
$433$	6.40711	+	11.0974i	0.307906	+	0.533309i	−0.669998	+	0.742363i	$0.733705\pi$
$434$	−10.1844	−	17.6399i	−0.488868	−	0.846744i
$435$		0			0
$436$	1.81593	+	3.14528i	0.0869672	+	0.150632i
$437$	−11.0140	−	6.92450i	−0.526870	−	0.331244i
$438$		0			0
$439$	−3.27238	−	5.66793i	−0.156182	−	0.270516i	0.777307	−	0.629122i	$-0.216585\pi$
$439$	−3.27238	−	5.66793i	−0.156182	−	0.270516i	−0.933489	+	0.358606i	$0.883252\pi$
$440$	4.53030	−	7.84671i	0.215974	−	0.374077i
$441$		0			0
$442$	−11.3096	+	19.5888i	−0.537943	+	0.931744i
$443$	−4.62851			−0.219907			−0.109954	−	0.993937i	$-0.535070\pi$
$443$	−4.62851			−0.219907			−0.109954	+	0.993937i	$0.535070\pi$
$444$		0			0
$445$	−0.618507	−	1.07129i	−0.0293201	−	0.0507838i
$446$	3.58222	−	6.20459i	0.169623	−	0.293796i
$447$		0			0
$448$	−14.4136	+	24.9651i	−0.680978	+	1.17949i
$449$	−16.6475			−0.785642			−0.392821	−	0.919615i	$-0.628501\pi$
$449$	−16.6475			−0.785642			−0.392821	+	0.919615i	$0.628501\pi$
$450$		0			0
$451$	4.59445	−	7.95783i	0.216344	−	0.374719i
$452$	2.16716			0.101935
$453$		0			0
$454$	−14.5272			−0.681794
$455$	−3.15163	−	5.45878i	−0.147751	−	0.255912i
$456$		0			0
$457$	19.2727	−	33.3814i	0.901541	−	1.56151i	0.0760467	−	0.997104i	$-0.475770\pi$
$457$	19.2727	−	33.3814i	0.901541	−	1.56151i	0.825494	−	0.564411i	$-0.190896\pi$
$458$	15.5708	−	26.9694i	0.727575	−	1.26020i
$459$		0			0
$460$	−0.393642	−	0.681808i	−0.0183537	−	0.0317895i
$461$	−5.11154	−	8.85345i	−0.238068	−	0.412346i	0.722092	−	0.691797i	$-0.243181\pi$
$461$	−5.11154	−	8.85345i	−0.238068	−	0.412346i	−0.960160	+	0.279451i	$0.909848\pi$
$462$		0			0
$463$	4.51183	+	7.81472i	0.209683	+	0.363181i	0.951615	−	0.307294i	$-0.0994236\pi$
$463$	4.51183	+	7.81472i	0.209683	+	0.363181i	−0.741932	+	0.670475i	$0.766090\pi$
$464$	−7.73839	−	13.4033i	−0.359246	−	0.622232i
$465$		0			0
$466$	−22.3068			−1.03334
$467$	31.0166			1.43528			0.717639	−	0.696416i	$-0.245223\pi$
$467$	31.0166			1.43528			0.717639	+	0.696416i	$0.245223\pi$
$468$		0			0
$469$	−3.84730	−	6.66372i	−0.177652	−	0.307702i
$470$	−3.61805	−	6.26665i	−0.166888	−	0.289059i
$471$		0			0
$472$	−23.7803			−1.09457
$473$	−19.3027			−0.887538
$474$		0			0
$475$	−0.770614	+	20.4540i	−0.0353582	+	0.938494i
$476$	−8.07054			−0.369913
$477$		0			0
$478$	5.13015	−	8.88568i	0.234647	−	0.406421i
$479$	35.1079			1.60412			0.802060	−	0.597243i	$-0.203737\pi$
$479$	35.1079			1.60412			0.802060	+	0.597243i	$0.203737\pi$
$480$		0			0
$481$	−16.2245	+	28.1016i	−0.739771	+	1.28132i
$482$	−12.2043	−	21.1384i	−0.555889	−	0.962829i
$483$		0			0
$484$	−8.54875			−0.388580
$485$	−2.25636	−	3.90813i	−0.102456	−	0.177459i
$486$		0			0
$487$	23.8848			1.08232			0.541161	−	0.840919i	$-0.317985\pi$
$487$	23.8848			1.08232			0.541161	+	0.840919i	$0.317985\pi$
$488$	34.7735			1.57412
$489$		0			0
$490$	−1.19673	+	2.07279i	−0.0540626	+	0.0936392i
$491$	−35.8676			−1.61868			−0.809342	−	0.587338i	$-0.800176\pi$
$491$	−35.8676			−1.61868			−0.809342	+	0.587338i	$0.800176\pi$
$492$		0			0
$493$	14.3051	−	24.7771i	0.644269	−	1.11591i
$494$	0.713381	−	18.9349i	0.0320965	−	0.851921i
$495$		0			0
$496$	7.16548	−	12.4110i	0.321739	−	0.557269i
$497$	1.64674	+	2.85223i	0.0738662	+	0.127940i
$498$		0			0
$499$	−27.8941			−1.24871			−0.624355	−	0.781141i	$-0.714638\pi$
$499$	−27.8941			−1.24871			−0.624355	+	0.781141i	$0.714638\pi$
$500$	−1.27876	+	2.21488i	−0.0571880	+	0.0990525i
$501$		0			0
$502$	−6.92105	+	11.9876i	−0.308902	+	0.535033i
$503$	19.7196	+	34.1554i	0.879254	+	1.52291i	0.852161	+	0.523280i	$0.175292\pi$
$503$	19.7196	+	34.1554i	0.879254	+	1.52291i	0.0270935	+	0.999633i	$0.491375\pi$
$504$		0			0
$505$	−2.99725			−0.133376
$506$	9.89232	−	17.1340i	0.439767	−	0.761699i
$507$		0			0
$508$	−5.02011			−0.222731
$509$	9.56460	−	16.5664i	0.423943	−	0.734292i	−0.572378	−	0.819990i	$-0.693979\pi$
$509$	9.56460	−	16.5664i	0.423943	−	0.734292i	0.996321	+	0.0856985i	$0.0273122\pi$
$510$		0			0
$511$	−19.4121	−	33.6227i	−0.858741	−	1.48738i
$512$	−24.6471			−1.08926
$513$		0			0
$514$	37.9620			1.67443
$515$	3.82696	+	6.62848i	0.168636	+	0.292086i
$516$		0			0
$517$	−28.5749	+	49.4932i	−1.25672	+	2.17671i
$518$	36.8394			1.61863
$519$		0			0
$520$	2.97090	−	5.14576i	0.130283	−	0.225656i
$521$	33.0169			1.44650			0.723248	−	0.690589i	$-0.242648\pi$
$521$	33.0169			1.44650			0.723248	+	0.690589i	$0.242648\pi$
$522$		0			0
$523$	6.43545	+	11.1465i	0.281403	+	0.487404i	0.971730	−	0.236093i	$-0.0758670\pi$
$523$	6.43545	+	11.1465i	0.281403	+	0.487404i	−0.690328	+	0.723497i	$0.742534\pi$
$524$	0.134736	−	0.233369i	0.00588596	−	0.0101948i
$525$		0			0
$526$	13.5736	−	23.5101i	0.591835	−	1.02509i
$527$	26.4920			1.15401
$528$		0			0
$529$	7.04589	+	12.2038i	0.306343	+	0.530601i
$530$	−0.382382	+	0.662305i	−0.0166096	+	0.0287687i
$531$		0			0
$532$	5.97812	−	3.15756i	0.259184	−	0.136897i
$533$	3.01297	−	5.21862i	0.130506	−	0.226044i
$534$		0			0
$535$	8.71488			0.376777
$536$	3.62669	−	6.28161i	0.156649	−	0.271324i
$537$		0			0
$538$	11.5950			0.499897
$539$	18.9032			0.814219
$540$		0			0
$541$	−1.61584	−	2.79872i	−0.0694705	−	0.120326i	0.829198	−	0.558955i	$-0.188798\pi$
$541$	−1.61584	−	2.79872i	−0.0694705	−	0.120326i	−0.898668	+	0.438629i	$0.855464\pi$
$542$	−12.6023			−0.541317
$543$		0			0
$544$	−6.87369	−	11.9056i	−0.294707	−	0.510447i
$545$	−2.09422	+	3.62729i	−0.0897064	+	0.155376i
$546$		0			0
$547$	29.4688			1.26000			0.629998	−	0.776597i	$-0.283056\pi$
$547$	29.4688			1.26000			0.629998	+	0.776597i	$0.283056\pi$
$548$	−4.12092	+	7.13764i	−0.176037	+	0.304905i
$549$		0			0
$550$	−31.1273			−1.32727
$551$	−0.902329	+	23.9500i	−0.0384405	+	1.02031i
$552$		0			0
$553$	−3.68938			−0.156889
$554$	29.2234			1.24158
$555$		0			0
$556$	0.347324	+	0.601583i	0.0147298	+	0.0255128i
$557$	−13.2513	−	22.9520i	−0.561477	−	0.972506i	−0.997368	−	0.0725066i	$-0.976900\pi$
$557$	−13.2513	−	22.9520i	−0.561477	−	0.972506i	0.435891	−	0.899999i	$-0.356433\pi$
$558$		0			0
$559$	−12.6584			−0.535393
$560$	−5.03484			−0.212761
$561$		0			0
$562$	−2.63180	−	4.55842i	−0.111016	−	0.192285i
$563$	−9.60939	−	16.6440i	−0.404988	−	0.701459i	0.589332	−	0.807891i	$-0.299391\pi$
$563$	−9.60939	−	16.6440i	−0.404988	−	0.701459i	−0.994320	+	0.106432i	$0.966057\pi$
$564$		0			0
$565$	1.24964	+	2.16444i	0.0525727	+	0.0910586i
$566$	13.4911	+	23.3672i	0.567072	+	0.982197i
$567$		0			0
$568$	−1.55231	+	2.68867i	−0.0651334	+	0.112814i
$569$	22.9341	−	39.7230i	0.961446	−	1.66527i	0.242570	−	0.970134i	$-0.422009\pi$
$569$	22.9341	−	39.7230i	0.961446	−	1.66527i	0.718875	−	0.695139i	$-0.244657\pi$
$570$		0			0
$571$	−8.69243	−	15.0557i	−0.363767	−	0.630063i	0.624810	−	0.780776i	$-0.285176\pi$
$571$	−8.69243	−	15.0557i	−0.363767	−	0.630063i	−0.988577	+	0.150713i	$0.951843\pi$
$572$	−9.05607			−0.378654
$573$		0			0
$574$	−6.84128			−0.285549
$575$	−7.00770	+	12.1377i	−0.292241	+	0.506176i
$576$		0			0
$577$	11.7739			0.490155			0.245078	−	0.969503i	$-0.421187\pi$
$577$	11.7739			0.490155			0.245078	+	0.969503i	$0.421187\pi$
$578$	−6.21415	+	10.7632i	−0.258474	+	0.447691i
$579$		0			0
$580$	−0.725176	+	1.25604i	−0.0301113	+	0.0521543i
$581$	3.70923	+	6.42458i	0.153885	+	0.266536i
$582$		0			0
$583$	6.04001			0.250152
$584$	18.2990	−	31.6947i	0.757216	−	1.31154i
$585$		0			0
$586$	−0.0245042	+	0.0424425i	−0.00101226	+	0.00175328i
$587$	−6.94342	−	12.0264i	−0.286586	−	0.496381i	0.686407	−	0.727218i	$-0.259187\pi$
$587$	−6.94342	−	12.0264i	−0.286586	−	0.496381i	−0.972992	+	0.230837i	$0.925854\pi$
$588$		0			0
$589$	−19.6235	+	10.3649i	−0.808573	+	0.427077i
$590$	−2.64619	−	4.58333i	−0.108942	−	0.188693i
$591$		0			0
$592$	12.9596	+	22.4466i	0.532635	+	0.922551i
$593$	−7.23610	−	12.5333i	−0.297151	−	0.514681i	0.678332	−	0.734756i	$-0.262703\pi$
$593$	−7.23610	−	12.5333i	−0.297151	−	0.514681i	−0.975483	+	0.220075i	$0.929370\pi$
$594$		0			0
$595$	−4.65367	−	8.06040i	−0.190782	−	0.330444i
$596$	−1.12153	+	1.94255i	−0.0459397	+	0.0795698i
$597$		0			0
$598$	6.48723	−	11.2362i	0.265283	−	0.459483i
$599$	−6.04520	+	10.4706i	−0.247000	+	0.427817i	−0.962692	−	0.270599i	$-0.912778\pi$
$599$	−6.04520	+	10.4706i	−0.247000	+	0.427817i	0.715692	+	0.698416i	$0.246111\pi$
$600$		0			0
$601$	−14.0237	+	24.2898i	−0.572040	+	0.990803i	0.424316	+	0.905514i	$0.360515\pi$
$601$	−14.0237	+	24.2898i	−0.572040	+	0.990803i	−0.996356	+	0.0852884i	$0.972819\pi$
$602$	7.18556	+	12.4458i	0.292862	+	0.507251i
$603$		0			0
$604$	−0.176420	−	0.305569i	−0.00717843	−	0.0124334i
$605$	−4.92942	−	8.53800i	−0.200409	−	0.347119i
$606$		0			0
$607$	10.3136	+	17.8637i	0.418616	+	0.725063i	0.995800	−	0.0915501i	$-0.0291822\pi$
$607$	10.3136	+	17.8637i	0.418616	+	0.725063i	−0.577185	+	0.816613i	$0.695849\pi$
$608$	9.74956	+	6.12956i	0.395397	+	0.248586i
$609$		0			0
$610$	3.86947	+	6.70212i	0.156670	+	0.271361i
$611$	−18.7390	+	32.4569i	−0.758099	+	1.31307i
$612$		0			0
$613$	−6.15798	+	10.6659i	−0.248718	+	0.430793i	−0.963170	−	0.268891i	$-0.913343\pi$
$613$	−6.15798	+	10.6659i	−0.248718	+	0.430793i	0.714452	+	0.699684i	$0.246676\pi$
$614$	−19.0820			−0.770088
$615$		0			0
$616$	26.6386	+	46.1393i	1.07330	+	1.85901i
$617$	−18.2282	+	31.5722i	−0.733840	+	1.27105i	0.221390	+	0.975185i	$0.428941\pi$
$617$	−18.2282	+	31.5722i	−0.733840	+	1.27105i	−0.955230	+	0.295863i	$0.904393\pi$
$618$		0			0
$619$	19.8664	−	34.4097i	0.798500	−	1.38304i	−0.122093	−	0.992519i	$-0.538961\pi$
$619$	19.8664	−	34.4097i	0.798500	−	1.38304i	0.920593	−	0.390523i	$-0.127706\pi$
$620$	−1.34297			−0.0539352
$621$		0			0
$622$	−7.45555	+	12.9134i	−0.298940	+	0.517780i
$623$	7.27375			0.291417
$624$		0			0
$625$	20.5295			0.821182
$626$	−4.73383	−	8.19923i	−0.189202	−	0.327707i
$627$		0			0
$628$	1.29474	−	2.24255i	0.0516657	−	0.0894875i
$629$	−23.9569	+	41.4946i	−0.955225	+	1.65450i
$630$		0			0
$631$	−14.0414	−	24.3204i	−0.558980	−	0.968181i	−0.997582	−	0.0694998i	$-0.977860\pi$
$631$	−14.0414	−	24.3204i	−0.558980	−	0.968181i	0.438602	−	0.898681i	$-0.355474\pi$
$632$	−1.73891	−	3.01188i	−0.0691702	−	0.119806i
$633$		0			0
$634$	−5.87339	−	10.1730i	−0.233262	−	0.404022i
$635$	−2.89472	−	5.01380i	−0.114873	−	0.198967i
$636$		0			0
$637$	12.3964			0.491165
$638$	−36.4477			−1.44298
$639$		0			0
$640$	−1.56666	−	2.71353i	−0.0619277	−	0.107262i
$641$	−14.0612	−	24.3547i	−0.555384	−	0.961953i	−0.997874	−	0.0651798i	$-0.979238\pi$
$641$	−14.0612	−	24.3547i	−0.555384	−	0.961953i	0.442489	−	0.896774i	$-0.354095\pi$
$642$		0			0
$643$	19.8509			0.782844			0.391422	−	0.920211i	$-0.371983\pi$
$643$	19.8509			0.782844			0.391422	+	0.920211i	$0.371983\pi$
$644$	4.62930			0.182420
$645$		0			0
$646$	1.05337	−	27.9591i	0.0414444	−	1.10004i
$647$	22.5967			0.888369			0.444184	−	0.895935i	$-0.353494\pi$
$647$	22.5967			0.888369			0.444184	+	0.895935i	$0.353494\pi$
$648$		0			0
$649$	−20.8992	+	36.1986i	−0.820367	+	1.42092i
$650$	−20.4128			−0.800658
$651$		0			0
$652$	−2.40166	+	4.15980i	−0.0940564	+	0.162911i
$653$	20.4974	+	35.5026i	0.802127	+	1.38932i	0.918214	+	0.396085i	$0.129632\pi$
$653$	20.4974	+	35.5026i	0.802127	+	1.38932i	−0.116087	+	0.993239i	$0.537035\pi$
$654$		0			0
$655$	0.310767			0.0121427
$656$	−2.40667	−	4.16847i	−0.0939646	−	0.162751i
$657$		0			0
$658$	42.5489			1.65873
$659$	−35.3313			−1.37631			−0.688156	−	0.725563i	$-0.741579\pi$
$659$	−35.3313			−1.37631			−0.688156	+	0.725563i	$0.741579\pi$
$660$		0			0
$661$	22.3643	−	38.7362i	0.869872	−	1.50666i	0.00774569	−	0.999970i	$-0.497534\pi$
$661$	22.3643	−	38.7362i	0.869872	−	1.50666i	0.862127	−	0.506693i	$-0.169132\pi$
$662$	−11.9425			−0.464158
$663$		0			0
$664$	−3.49653	+	6.05617i	−0.135692	+	0.235025i
$665$	6.60071	+	4.14988i	0.255965	+	0.160925i
$666$		0			0
$667$	−8.20546	+	14.2123i	−0.317717	+	0.550301i
$668$	3.43024	+	5.94134i	0.132720	+	0.229877i
$669$		0			0
$670$	1.61426			0.0623644
$671$	30.5606	−	52.9325i	1.17978	−	2.04344i
$672$		0			0
$673$	−10.6195	+	18.3935i	−0.409351	+	0.709017i	−0.994817	−	0.101680i	$-0.967578\pi$
$673$	−10.6195	+	18.3935i	−0.409351	+	0.709017i	0.585466	+	0.810697i	$0.300912\pi$
$674$	18.7308	+	32.4427i	0.721483	+	1.24965i
$675$		0			0
$676$	0.278435			0.0107090
$677$	8.69327	−	15.0572i	0.334109	−	0.578694i	−0.649204	−	0.760614i	$-0.724898\pi$
$677$	8.69327	−	15.0572i	0.334109	−	0.578694i	0.983313	+	0.181920i	$0.0582312\pi$
$678$		0			0
$679$	26.5352			1.01833
$680$	4.38682	−	7.59819i	0.168227	−	0.291377i
$681$		0			0
$682$	−16.8746	−	29.2277i	−0.646163	−	1.11919i
$683$	−30.4671			−1.16579			−0.582896	−	0.812547i	$-0.698080\pi$
$683$	−30.4671			−1.16579			−0.582896	+	0.812547i	$0.698080\pi$
$684$		0			0
$685$	−9.50489			−0.363163
$686$	6.96554	+	12.0647i	0.265946	+	0.460631i
$687$		0			0
$688$	−5.05556	+	8.75649i	−0.192742	+	0.333838i
$689$	3.96095			0.150900
$690$		0			0
$691$	3.54990	−	6.14860i	0.135044	−	0.233904i	−0.790570	−	0.612372i	$-0.790216\pi$
$691$	3.54990	−	6.14860i	0.135044	−	0.233904i	0.925614	+	0.378468i	$0.123549\pi$
$692$	1.95834			0.0744448
$693$		0			0
$694$	−5.08265	−	8.80341i	−0.192935	−	0.334173i
$695$	−0.400551	+	0.693775i	−0.0151938	+	0.0263164i
$696$		0			0
$697$	4.44894	−	7.70578i	0.168515	−	0.291877i
$698$	−0.299886			−0.0113509
$699$		0			0
$700$	−3.64166	−	6.30754i	−0.137642	−	0.238402i
$701$	7.28494	−	12.6179i	0.275148	−	0.476571i	−0.695024	−	0.718986i	$-0.744606\pi$
$701$	7.28494	−	12.6179i	0.275148	−	0.476571i	0.970173	+	0.242416i	$0.0779397\pi$
$702$		0			0
$703$	1.51114	−	40.1094i	0.0569938	−	1.51276i
$704$	−23.8820	+	41.3648i	−0.900086	+	1.55899i
$705$		0			0
$706$	13.2730			0.499535
$707$	8.81204	−	15.2629i	0.331411	−	0.574020i
$708$		0			0
$709$	−12.3443			−0.463601			−0.231800	−	0.972763i	$-0.574462\pi$
$709$	−12.3443			−0.463601			−0.231800	+	0.972763i	$0.574462\pi$
$710$	−0.690942			−0.0259306
$711$		0			0
$712$	3.42833	+	5.93804i	0.128482	+	0.222537i
$713$	−15.1959			−0.569092
$714$		0			0
$715$	−5.22195	−	9.04469i	−0.195290	−	0.338252i
$716$	−0.469006	+	0.812343i	−0.0175276	+	0.0303587i
$717$		0			0
$718$	−20.5880			−0.768337
$719$	−6.57335	+	11.3854i	−0.245144	+	0.424603i	−0.962172	−	0.272442i	$-0.912169\pi$
$719$	−6.57335	+	11.3854i	−0.245144	+	0.424603i	0.717028	+	0.697045i	$0.245502\pi$
$720$		0			0
$721$	−45.0057			−1.67610
$722$	10.1586	+	21.1224i	0.378063	+	0.786093i
$723$		0			0
$724$	0.598603			0.0222469
$725$	25.8194			0.958910
$726$		0			0
$727$	2.51780	+	4.36095i	0.0933800	+	0.161739i	0.908931	−	0.416946i	$-0.136900\pi$
$727$	2.51780	+	4.36095i	0.0933800	+	0.161739i	−0.815551	+	0.578685i	$0.803566\pi$
$728$	17.4692	+	30.2575i	0.647451	+	1.12142i
$729$		0			0
$730$	8.14498			0.301459
$731$	−18.6913			−0.691323
$732$		0			0
$733$	21.5362	+	37.3019i	0.795459	+	1.37778i	0.922547	+	0.385884i	$0.126104\pi$
$733$	21.5362	+	37.3019i	0.795459	+	1.37778i	−0.127088	+	0.991891i	$0.540563\pi$
$734$	9.35663	+	16.2062i	0.345359	+	0.598180i
$735$		0			0
$736$	3.94278	+	6.82909i	0.145333	+	0.251724i
$737$	−6.37462	−	11.0412i	−0.234812	−	0.406706i
$738$		0			0
$739$	−5.54488	+	9.60401i	−0.203972	+	0.353289i	−0.949805	−	0.312844i	$-0.898718\pi$
$739$	−5.54488	+	9.60401i	−0.203972	+	0.353289i	0.745833	+	0.666133i	$0.232052\pi$
$740$	1.21446	−	2.10351i	0.0446445	−	0.0773265i
$741$		0			0
$742$	−2.24844	−	3.89441i	−0.0825428	−	0.142968i
$743$	6.01014			0.220491			0.110245	−	0.993904i	$-0.464836\pi$
$743$	6.01014			0.220491			0.110245	+	0.993904i	$0.464836\pi$
$744$		0			0
$745$	−2.58680			−0.0947732
$746$	−18.9984	+	32.9062i	−0.695580	+	1.20478i
$747$		0			0
$748$	−13.3721			−0.488934
$749$	−25.6221	+	44.3788i	−0.936212	+	1.62157i
$750$		0			0
$751$	1.75857	−	3.04593i	0.0641711	−	0.111148i	−0.832155	−	0.554543i	$-0.812893\pi$
$751$	1.75857	−	3.04593i	0.0641711	−	0.111148i	0.896326	+	0.443396i	$0.146226\pi$
$752$	14.9681	+	25.9255i	0.545831	+	0.945407i
$753$		0			0
$754$	−23.9018			−0.870453
$755$	0.203456	−	0.352396i	0.00740453	−	0.0128250i
$756$		0			0
$757$	−14.2947	+	24.7592i	−0.519551	+	0.899888i	0.480191	+	0.877164i	$0.340567\pi$
$757$	−14.2947	+	24.7592i	−0.519551	+	0.899888i	−0.999742	+	0.0227241i	$0.992766\pi$
$758$	−13.6951	−	23.7205i	−0.497427	−	0.861569i
$759$		0			0
$760$	−0.276709	+	7.34455i	−0.0100373	+	0.266415i
$761$	10.3023	+	17.8440i	0.373457	+	0.646846i	0.990095	−	0.140401i	$-0.0448391\pi$
$761$	10.3023	+	17.8440i	0.373457	+	0.646846i	−0.616638	+	0.787247i	$0.711506\pi$
$762$		0			0
$763$	−12.3142	−	21.3288i	−0.445803	−	0.772153i
$764$	3.99451	+	6.91870i	0.144516	+	0.250310i
$765$		0			0
$766$	1.91665	+	3.31974i	0.0692515	+	0.119947i
$767$	−13.7054	+	23.7385i	−0.494874	+	0.857147i
$768$		0			0
$769$	13.5687	−	23.5017i	0.489300	−	0.847493i	−0.510624	−	0.859804i	$-0.670586\pi$
$769$	13.5687	−	23.5017i	0.489300	−	0.847493i	0.999924	+	0.0123111i	$0.00391885\pi$
$770$	−5.92850	+	10.2685i	−0.213648	+	0.370050i
$771$		0			0
$772$	5.91619	−	10.2471i	0.212928	−	0.368803i
$773$	−24.5515	−	42.5244i	−0.883056	−	1.52950i	−0.847926	−	0.530115i	$-0.822149\pi$
$773$	−24.5515	−	42.5244i	−0.883056	−	1.52950i	−0.0351305	−	0.999383i	$-0.511185\pi$
$774$		0			0
$775$	11.9540	+	20.7049i	0.429399	+	0.743740i
$776$	12.5068	+	21.6624i	0.448968	+	0.777635i
$777$		0			0
$778$	−0.674767	−	1.16873i	−0.0241916	−	0.0419010i
$779$	−0.280628	+	7.44855i	−0.0100545	+	0.266872i
$780$		0			0
$781$	2.72849	+	4.72588i	0.0976329	+	0.169105i
$782$	9.57900	−	16.5913i	0.342544	−	0.593304i
$783$		0			0
$784$	4.95094	−	8.57528i	0.176819	−	0.306260i
$785$	2.98631			0.106586
$786$		0			0
$787$	13.5510	+	23.4710i	0.483040	+	0.836650i	0.999810	−	0.0194740i	$-0.00619914\pi$
$787$	13.5510	+	23.4710i	0.483040	+	0.836650i	−0.516770	+	0.856124i	$0.672866\pi$
$788$	−0.724246	+	1.25443i	−0.0258002	+	0.0446872i
$789$		0			0
$790$	0.387001	−	0.670305i	0.0137689	−	0.0238484i
$791$	−14.6960			−0.522529
$792$		0			0
$793$	20.0412	−	34.7124i	0.711684	−	1.23267i
$794$	40.9625			1.45371
$795$		0			0
$796$	8.44223			0.299227
$797$	13.1487	+	22.7743i	0.465752	+	0.806707i	0.999235	−	0.0391042i	$-0.0124504\pi$
$797$	13.1487	+	22.7743i	0.465752	+	0.806707i	−0.533483	+	0.845811i	$0.679117\pi$
$798$		0			0
$799$	−27.6699	+	47.9256i	−0.978890	+	1.69549i
$800$	6.20320	−	10.7443i	0.219316	−	0.379867i
$801$		0			0
$802$	6.60390	+	11.4383i	0.233192	+	0.403900i
$803$	−32.1640	−	55.7097i	−1.13504	−	1.96595i
$804$		0			0
$805$	2.66937	+	4.62348i	0.0940828	+	0.162956i
$806$	−11.0661	−	19.1671i	−0.389788	−	0.675132i
$807$		0			0
$808$	16.6135			0.584460
$809$	−5.16978			−0.181760			−0.0908799	−	0.995862i	$-0.528968\pi$
$809$	−5.16978			−0.181760			−0.0908799	+	0.995862i	$0.528968\pi$
$810$		0			0
$811$	−17.7354	−	30.7187i	−0.622775	−	1.07868i	−0.988967	−	0.148139i	$-0.952672\pi$
$811$	−17.7354	−	30.7187i	−0.622775	−	1.07868i	0.366191	−	0.930540i	$-0.380662\pi$
$812$	−4.26409	−	7.38563i	−0.149640	−	0.259185i
$813$		0			0
$814$	61.0394			2.13943
$815$	−5.53943			−0.194038
$816$		0			0
$817$	13.8453	−	7.31287i	0.484384	−	0.255845i
$818$	−13.8571			−0.484502
$819$		0			0
$820$	−0.225532	+	0.390634i	−0.00787593	+	0.0136415i
$821$	18.4619			0.644325			0.322162	−	0.946684i	$-0.395590\pi$
$821$	18.4619			0.644325			0.322162	+	0.946684i	$0.395590\pi$
$822$		0			0
$823$	−25.6857	+	44.4889i	−0.895347	+	1.55079i	−0.0619727	+	0.998078i	$0.519739\pi$
$823$	−25.6857	+	44.4889i	−0.895347	+	1.55079i	−0.833374	+	0.552709i	$0.813594\pi$
$824$	−21.2125	−	36.7410i	−0.738971	−	1.27993i
$825$		0			0
$826$	31.1196			1.08279
$827$	13.9591	+	24.1779i	0.485406	+	0.840748i	0.999859	−	0.0167707i	$-0.00533852\pi$
$827$	13.9591	+	24.1779i	0.485406	+	0.840748i	−0.514454	+	0.857518i	$0.672005\pi$
$828$		0			0
$829$	12.7112			0.441480			0.220740	−	0.975333i	$-0.429153\pi$
$829$	12.7112			0.441480			0.220740	+	0.975333i	$0.429153\pi$
$830$	−1.55633			−0.0540210
$831$		0			0
$832$	−15.6614	+	27.1264i	−0.542963	+	0.940439i
$833$	18.3045			0.634213
$834$		0			0
$835$	−3.95591	+	6.85184i	−0.136900	+	0.237118i
$836$	9.90518	−	5.23178i	0.342578	−	0.180945i
$837$		0			0
$838$	4.08869	−	7.08181i	0.141241	−	0.244637i
$839$	15.7790	+	27.3300i	0.544752	+	0.943537i	0.998623	+	0.0524699i	$0.0167094\pi$
$839$	15.7790	+	27.3300i	0.544752	+	0.943537i	−0.453871	+	0.891067i	$0.649957\pi$
$840$		0			0
$841$	1.23252			0.0425008
$842$	8.74006	−	15.1382i	0.301202	−	0.521698i
$843$		0			0
$844$	−1.94378	+	3.36673i	−0.0669077	+	0.115888i
$845$	0.160552	+	0.278084i	0.00552316	+	0.00956639i
$846$		0			0
$847$	57.9708			1.99190
$848$	1.58194	−	2.74000i	0.0543240	−	0.0940919i
$849$		0			0
$850$	−30.1415			−1.03384
$851$	13.7418	−	23.8015i	0.471062	−	0.815904i
$852$		0			0
$853$	2.65771	+	4.60329i	0.0909982	+	0.157614i	0.907931	−	0.419119i	$-0.137661\pi$
$853$	2.65771	+	4.60329i	0.0909982	+	0.157614i	−0.816933	+	0.576732i	$0.804328\pi$
$854$	−45.5057			−1.55717
$855$		0			0
$856$	−48.3057			−1.65106
$857$	3.55373	+	6.15525i	0.121393	+	0.210259i	0.920317	−	0.391173i	$-0.127930\pi$
$857$	3.55373	+	6.15525i	0.121393	+	0.210259i	−0.798924	+	0.601432i	$0.794597\pi$
$858$		0			0
$859$	−1.94186	+	3.36340i	−0.0662554	+	0.114758i	−0.897250	−	0.441523i	$-0.854439\pi$
$859$	−1.94186	+	3.36340i	−0.0662554	+	0.114758i	0.830995	+	0.556280i	$0.187772\pi$
$860$	0.947529			0.0323105
$861$		0			0
$862$	−7.58042	+	13.1297i	−0.258190	+	0.447198i
$863$	−48.2914			−1.64386			−0.821929	−	0.569589i	$-0.807102\pi$
$863$	−48.2914			−1.64386			−0.821929	+	0.569589i	$0.807102\pi$
$864$		0			0
$865$	1.12922	+	1.95587i	0.0383948	+	0.0665017i
$866$	7.90376	−	13.6897i	0.268581	−	0.465195i
$867$		0			0
$868$	3.94840	−	6.83883i	0.134018	−	0.232125i
$869$	−6.11296			−0.207368
$870$		0			0
$871$	−4.18038	−	7.24063i	−0.141647	−	0.245339i
$872$	11.6080	−	20.1057i	0.393098	−	0.680865i
$873$		0			0
$874$	−0.604219	+	16.0375i	−0.0204380	+	0.542475i
$875$	8.67154	−	15.0195i	0.293151	−	0.507753i
$876$		0			0
$877$	−19.1298			−0.645968			−0.322984	−	0.946404i	$-0.604686\pi$
$877$	−19.1298			−0.645968			−0.322984	+	0.946404i	$0.604686\pi$
$878$	−4.03679	+	6.99192i	−0.136235	+	0.235966i
$879$		0			0
$880$	−8.34226			−0.281217
$881$	−2.13502			−0.0719308			−0.0359654	−	0.999353i	$-0.511451\pi$
$881$	−2.13502			−0.0719308			−0.0359654	+	0.999353i	$0.511451\pi$
$882$		0			0
$883$	−12.2593	−	21.2338i	−0.412559	−	0.714573i	0.582610	−	0.812752i	$-0.302032\pi$
$883$	−12.2593	−	21.2338i	−0.412559	−	0.714573i	−0.995169	+	0.0981790i	$0.968698\pi$
$884$	−8.76925			−0.294942
$885$		0			0
$886$	2.85484	+	4.94473i	0.0959103	+	0.166122i
$887$	−16.7546	+	29.0199i	−0.562565	+	0.974391i	0.434706	+	0.900572i	$0.356852\pi$
$887$	−16.7546	+	29.0199i	−0.562565	+	0.974391i	−0.997272	+	0.0738192i	$0.976481\pi$
$888$		0			0
$889$	34.0424			1.14174
$890$	−0.762985	+	1.32153i	−0.0255753	+	0.0442978i
$891$		0			0
$892$	2.77759			0.0930005
$893$	1.74535	−	46.3258i	0.0584058	−	1.55023i
$894$		0			0
$895$	−1.08176			−0.0361593
$896$	18.4242			0.615509
$897$		0			0
$898$	10.2681	+	17.7848i	0.342650	+	0.593488i
$899$	13.9971	+	24.2437i	0.466830	+	0.808574i
$900$		0			0
$901$	5.84871			0.194849
$902$	−11.3354			−0.377426
$903$		0			0
$904$	−6.92663	−	11.9973i	−0.230376	−	0.399024i
$905$	0.345169	+	0.597850i	0.0114738	+	0.0198732i
$906$		0			0
$907$	8.38206	+	14.5181i	0.278322	+	0.482067i	0.970968	−	0.239210i	$-0.0768886\pi$
$907$	8.38206	+	14.5181i	0.278322	+	0.482067i	−0.692646	+	0.721278i	$0.743555\pi$
$908$	−2.81602	−	4.87750i	−0.0934530	−	0.161865i
$909$		0			0
$910$	−3.88782	+	6.73390i	−0.128880	+	0.223227i
$911$	−24.6760	+	42.7400i	−0.817551	+	1.41604i	0.0899306	+	0.995948i	$0.471335\pi$
$911$	−24.6760	+	42.7400i	−0.817551	+	1.41604i	−0.907482	+	0.420092i	$0.861998\pi$
$912$		0			0
$913$	6.14585	+	10.6449i	0.203398	+	0.352295i
$914$	−47.5494			−1.57279
$915$		0			0
$916$	12.0733			0.398913
$917$	−0.913669	+	1.58252i	−0.0301720	+	0.0522595i
$918$		0			0
$919$	26.1970			0.864158			0.432079	−	0.901836i	$-0.357780\pi$
$919$	26.1970			0.864158			0.432079	+	0.901836i	$0.357780\pi$
$920$	−2.51630	+	4.35835i	−0.0829599	+	0.143691i
$921$		0			0
$922$	−6.30556	+	10.9215i	−0.207662	+	0.359682i
$923$	1.78930	+	3.09916i	0.0588955	+	0.102010i
$924$		0			0
$925$	−43.2402			−1.42173
$926$	5.56576	−	9.64018i	0.182902	−	0.316796i
$927$		0			0
$928$	7.26346	−	12.5807i	0.238435	−	0.412981i
$929$	29.7479	+	51.5249i	0.975998	+	1.69048i	0.676603	+	0.736348i	$0.263451\pi$
$929$	29.7479	+	51.5249i	0.975998	+	1.69048i	0.299394	+	0.954129i	$0.403215\pi$
$930$		0			0
$931$	−13.5587	+	7.16153i	−0.444370	+	0.234710i
$932$	−4.32406	−	7.48950i	−0.141639	−	0.245327i
$933$		0			0
$934$	−19.1309	−	33.1357i	−0.625982	−	1.08423i
$935$	−7.71070	−	13.3553i	−0.252167	−	0.436766i
$936$		0			0
$937$	−7.96252	−	13.7915i	−0.260124	−	0.450548i	0.706150	−	0.708062i	$-0.250430\pi$
$937$	−7.96252	−	13.7915i	−0.260124	−	0.450548i	−0.966275	+	0.257513i	$0.917097\pi$
$938$	−4.74600	+	8.22031i	−0.154962	+	0.268403i
$939$		0			0
$940$	1.40268	−	2.42952i	0.0457505	−	0.0792422i
$941$	15.7672	−	27.3095i	0.513995	−	0.890265i	−0.485874	−	0.874029i	$-0.661498\pi$
$941$	15.7672	−	27.3095i	0.513995	−	0.890265i	0.999868	−	0.0162356i	$-0.00516817\pi$
$942$		0			0
$943$	−2.55193	+	4.42007i	−0.0831022	+	0.143937i
$944$	10.9474	+	18.9615i	0.356309	+	0.617145i
$945$		0			0
$946$	11.9058	+	20.6215i	0.387091	+	0.670461i
$947$	−24.1650	−	41.8550i	−0.785257	−	1.36010i	−0.928846	−	0.370467i	$-0.879198\pi$
$947$	−24.1650	−	41.8550i	−0.785257	−	1.36010i	0.143589	−	0.989637i	$-0.454136\pi$
$948$		0			0
$949$	−21.0927	−	36.5336i	−0.684698	−	1.18593i
$950$	22.3268	−	11.7927i	0.724376	−	0.382605i
$951$		0			0
$952$	25.7949	+	44.6780i	0.836016	+	1.44802i
$953$	−24.6011	+	42.6103i	−0.796907	+	1.38028i	0.124715	+	0.992193i	$0.460198\pi$
$953$	−24.6011	+	42.6103i	−0.796907	+	1.38028i	−0.921621	+	0.388090i	$0.873135\pi$
$954$		0			0
$955$	−4.60666	+	7.97898i	−0.149068	+	0.258194i
$956$	3.97782			0.128652
$957$		0			0
$958$	−21.6544	−	37.5065i	−0.699622	−	1.21178i
$959$	27.9448	−	48.4018i	0.902384	−	1.56298i
$960$		0			0
$961$	2.53914	−	4.39792i	0.0819078	−	0.141869i
$962$	40.0287			1.29058
$963$		0			0
$964$	4.73148	−	8.19516i	0.152391	−	0.263948i
$965$	13.6457			0.439270
$966$		0			0
$967$	9.18223			0.295280			0.147640	−	0.989041i	$-0.452832\pi$
$967$	9.18223			0.295280			0.147640	+	0.989041i	$0.452832\pi$
$968$	27.3233	+	47.3253i	0.878204	+	1.52109i
$969$		0			0
$970$	−2.78343	+	4.82104i	−0.0893705	+	0.154794i
$971$	18.6062	−	32.2269i	0.597101	−	1.03421i	−0.396146	−	0.918188i	$-0.629653\pi$
$971$	18.6062	−	32.2269i	0.597101	−	1.03421i	0.993247	−	0.116021i	$-0.0370141\pi$
$972$		0			0
$973$	−2.35527	−	4.07945i	−0.0755066	−	0.130781i
$974$	−14.7320	−	25.5166i	−0.472044	−	0.817605i
$975$		0			0
$976$	−16.0083	−	27.7271i	−0.512412	−	0.887524i
$977$	−21.1242	−	36.5882i	−0.675823	−	1.17056i	−0.976228	−	0.216748i	$-0.930455\pi$
$977$	−21.1242	−	36.5882i	−0.675823	−	1.17056i	0.300405	−	0.953812i	$-0.402878\pi$
$978$		0			0
$979$	12.0519			0.385181
$980$	−0.927920			−0.0296413
$981$		0			0
$982$	22.1230	+	38.3182i	0.705973	+	1.22278i
$983$	−24.4308	−	42.3155i	−0.779223	−	1.34965i	−0.932390	−	0.361453i	$-0.882281\pi$
$983$	−24.4308	−	42.3155i	−0.779223	−	1.34965i	0.153167	−	0.988200i	$-0.451053\pi$
$984$		0			0
$985$	−1.67047			−0.0532256
$986$	−35.2933			−1.12397
$987$		0			0
$988$	6.49567	−	3.43092i	0.206655	−	0.109152i
$989$	10.7214			0.340921
$990$		0			0
$991$	−23.9926	+	41.5564i	−0.762150	+	1.32008i	0.179590	+	0.983742i	$0.442523\pi$
$991$	−23.9926	+	41.5564i	−0.762150	+	1.32008i	−0.941740	+	0.336342i	$0.890810\pi$
$992$	13.4514			0.427083
$993$		0			0
$994$	2.03140	−	3.51849i	0.0644321	−	0.111600i
$995$	4.86799	+	8.43161i	0.154326	+	0.267300i
$996$		0			0
$997$	−4.41967			−0.139972			−0.0699862	−	0.997548i	$-0.522296\pi$
$997$	−4.41967			−0.139972			−0.0699862	+	0.997548i	$0.522296\pi$
$998$	17.2049	+	29.7998i	0.544613	+	0.943297i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.g.c.505.6		32
3.2	odd	2		171.2.g.c.106.11	✓	32
9.4	even	3		513.2.h.c.334.11		32
9.5	odd	6		171.2.h.c.49.6	yes	32
19.7	even	3		513.2.h.c.235.11		32
57.26	odd	6		171.2.h.c.7.6	yes	32
171.121	even	3	inner	513.2.g.c.64.6		32
171.140	odd	6		171.2.g.c.121.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.11	✓	32	3.2	odd	2
171.2.g.c.121.11	yes	32	171.140	odd	6
171.2.h.c.7.6	yes	32	57.26	odd	6
171.2.h.c.49.6	yes	32	9.5	odd	6
513.2.g.c.64.6		32	171.121	even	3	inner
513.2.g.c.505.6		32	1.1	even	1	trivial
513.2.h.c.235.11		32	19.7	even	3
513.2.h.c.334.11		32	9.4	even	3

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.616796 - 1.06832i) q^{2} +(0.239126 - 0.414178i) q^{4} +0.551543 q^{5} +(-1.62156 + 2.80862i) q^{7} -3.05715 q^{8} +(-0.340189 - 0.589225i) q^{10} +(-2.68677 + 4.65363i) q^{11} +(-1.76195 + 3.05178i) q^{13} +4.00069 q^{14} +(1.40739 + 2.43766i) q^{16} +(-2.60168 + 4.50624i) q^{17} +(0.164107 - 4.35581i) q^{19} +(0.131888 - 0.228437i) q^{20} +6.62876 q^{22} +(1.49233 - 2.58480i) q^{23} -4.69580 q^{25} +4.34704 q^{26} +(0.775514 + 1.34323i) q^{28} -5.49841 q^{29} +(-2.54567 - 4.40923i) q^{31} +(-1.32101 + 2.28806i) q^{32} +6.41881 q^{34} +(-0.894360 + 1.54908i) q^{35} +9.20826 q^{37} +(-4.75463 + 2.51133i) q^{38} -1.68615 q^{40} -1.71003 q^{41} +(1.79608 + 3.11091i) q^{43} +(1.28495 + 2.22561i) q^{44} -3.68186 q^{46} +10.6354 q^{47} +(-1.75891 - 3.04653i) q^{49} +(2.89635 + 5.01663i) q^{50} +(0.842653 + 1.45952i) q^{52} +(-0.562013 - 0.973435i) q^{53} +(-1.48187 + 2.56668i) q^{55} +(4.95735 - 8.58639i) q^{56} +(3.39140 + 5.87407i) q^{58} +7.77857 q^{59} -11.3745 q^{61} +(-3.14032 + 5.43919i) q^{62} +8.88872 q^{64} +(-0.971789 + 1.68319i) q^{65} +(-1.18630 + 2.05473i) q^{67} +(1.24426 + 2.15512i) q^{68} +2.20655 q^{70} +(0.507763 - 0.879471i) q^{71} +(-5.98562 + 10.3674i) q^{73} +(-5.67962 - 9.83738i) q^{74} +(-1.76484 - 1.10956i) q^{76} +(-8.71353 - 15.0923i) q^{77} +(0.568802 + 0.985193i) q^{79} +(0.776234 + 1.34448i) q^{80} +(1.05474 + 1.82686i) q^{82} +(1.14372 - 1.98099i) q^{83} +(-1.43494 + 2.48538i) q^{85} +(2.21563 - 3.83759i) q^{86} +(8.21387 - 14.2268i) q^{88} +(-1.12141 - 1.94234i) q^{89} +(-5.71420 - 9.89729i) q^{91} +(-0.713711 - 1.23618i) q^{92} +(-6.55987 - 11.3620i) q^{94} +(0.0905122 - 2.40242i) q^{95} +(-4.09100 - 7.08582i) q^{97} +(-2.16978 + 3.75817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) 32 * q - q^2 - 17 * q^4 + 6 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 - 4 * q^13 + 2 * q^14 - 11 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 + 16 * q^22 - 5 * q^23 + 18 * q^25 + 4 * q^26 - 10 * q^28 + 20 * q^29 - 10 * q^31 - 17 * q^32 + 26 * q^34 + 3 * q^35 + 2 * q^37 - 38 * q^38 - 24 * q^40 + 12 * q^41 + 7 * q^43 - 20 * q^44 - 18 * q^47 - 13 * q^49 - q^50 + 19 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 + 74 * q^59 + 24 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 - 11 * q^67 + 2 * q^68 - 48 * q^70 - 9 * q^71 - 10 * q^73 - 6 * q^74 + 29 * q^76 - 46 * q^77 - 8 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 - 27 * q^85 - 17 * q^86 + 9 * q^88 - 30 * q^89 - q^91 + 17 * q^92 - 18 * q^94 + 6 * q^95 - 18 * q^98

Introduction

L-functions

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