LMFDB - Embedded newform 513.2.g.c.505.3

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			505.3
Character	$\chi$	$=$	513.505
Dual form			513.2.g.c.64.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19971 - 2.07797i) q^{2} +(-1.87863 + 3.25388i) q^{4} -0.719678 q^{5} +(1.65862 - 2.87282i) q^{7} +4.21641 q^{8} +(0.863408 + 1.49547i) q^{10} +(-0.550465 + 0.953433i) q^{11} +(2.37472 - 4.11314i) q^{13} -7.95949 q^{14} +(-1.30123 - 2.25380i) q^{16} +(3.13488 - 5.42977i) q^{17} +(-4.19132 + 1.19702i) q^{19} +(1.35201 - 2.34175i) q^{20} +2.64160 q^{22} +(-1.11407 + 1.92963i) q^{23} -4.48206 q^{25} -11.3960 q^{26} +(6.23187 + 10.7939i) q^{28} -5.94195 q^{29} +(-0.763210 - 1.32192i) q^{31} +(1.09420 - 1.89520i) q^{32} -15.0438 q^{34} +(-1.19367 + 2.06750i) q^{35} -3.69507 q^{37} +(7.51575 + 7.27334i) q^{38} -3.03446 q^{40} -5.68106 q^{41} +(-2.30746 - 3.99663i) q^{43} +(-2.06824 - 3.58229i) q^{44} +5.34627 q^{46} -0.283238 q^{47} +(-2.00206 - 3.46767i) q^{49} +(5.37720 + 9.31358i) q^{50} +(8.92245 + 15.4541i) q^{52} +(-1.90426 - 3.29828i) q^{53} +(0.396157 - 0.686164i) q^{55} +(6.99344 - 12.1130i) q^{56} +(7.12864 + 12.3472i) q^{58} +13.3719 q^{59} +11.8921 q^{61} +(-1.83127 + 3.17185i) q^{62} -10.4558 q^{64} +(-1.70904 + 2.96014i) q^{65} +(3.72296 - 6.44836i) q^{67} +(11.7785 + 20.4010i) q^{68} +5.72827 q^{70} +(-5.51472 + 9.55177i) q^{71} +(-5.22640 + 9.05239i) q^{73} +(4.43302 + 7.67822i) q^{74} +(3.97897 - 15.8868i) q^{76} +(1.82603 + 3.16277i) q^{77} +(-6.11654 - 10.5942i) q^{79} +(0.936469 + 1.62201i) q^{80} +(6.81565 + 11.8050i) q^{82} +(5.05059 - 8.74788i) q^{83} +(-2.25610 + 3.90769i) q^{85} +(-5.53657 + 9.58963i) q^{86} +(-2.32099 + 4.02007i) q^{88} +(-4.23637 - 7.33760i) q^{89} +(-7.87754 - 13.6443i) q^{91} +(-4.18585 - 7.25010i) q^{92} +(0.339804 + 0.588558i) q^{94} +(3.01640 - 0.861468i) q^{95} +(-6.16532 - 10.6786i) q^{97} +(-4.80380 + 8.32042i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.19971	−	2.07797i	−0.848326	−	1.46934i	−0.882701	−	0.469935i	$-0.844277\pi$
$2$	−1.19971	−	2.07797i	−0.848326	−	1.46934i	0.0343750	−	0.999409i	$-0.489056\pi$
$3$		0			0
$3$		0			0
$4$	−1.87863	+	3.25388i	−0.939314	+	1.62694i
$5$	−0.719678			−0.321850			−0.160925	−	0.986967i	$-0.551448\pi$
$5$	−0.719678			−0.321850			−0.160925	+	0.986967i	$0.551448\pi$
$6$		0			0
$7$	1.65862	−	2.87282i	0.626900	−	1.08582i	−0.361270	−	0.932461i	$-0.617657\pi$
$7$	1.65862	−	2.87282i	0.626900	−	1.08582i	0.988170	−	0.153362i	$-0.0490101\pi$
$8$	4.21641			1.49073
$9$		0			0
$10$	0.863408	+	1.49547i	0.273034	+	0.472908i
$11$	−0.550465	+	0.953433i	−0.165971	+	0.287471i	−0.937000	−	0.349330i	$-0.886409\pi$
$11$	−0.550465	+	0.953433i	−0.165971	+	0.287471i	0.771028	+	0.636801i	$0.219743\pi$
$12$		0			0
$13$	2.37472	−	4.11314i	0.658630	−	1.14078i	−0.322341	−	0.946624i	$-0.604470\pi$
$13$	2.37472	−	4.11314i	0.658630	−	1.14078i	0.980971	−	0.194157i	$-0.0621970\pi$
$14$	−7.95949			−2.12726
$15$		0			0
$16$	−1.30123	−	2.25380i	−0.325308	−	0.563451i
$17$	3.13488	−	5.42977i	0.760320	−	1.31691i	−0.182366	−	0.983231i	$-0.558376\pi$
$17$	3.13488	−	5.42977i	0.760320	−	1.31691i	0.942686	−	0.333682i	$-0.108291\pi$
$18$		0			0
$19$	−4.19132	+	1.19702i	−0.961554	+	0.274615i
$19$	−4.19132	+	1.19702i	−0.961554	+	0.274615i
$20$	1.35201	−	2.34175i	0.302318	−	0.523630i
$21$		0			0
$22$	2.64160			0.563191
$23$	−1.11407	+	1.92963i	−0.232300	+	0.402355i	−0.958485	−	0.285145i	$-0.907958\pi$
$23$	−1.11407	+	1.92963i	−0.232300	+	0.402355i	0.726185	+	0.687500i	$0.241292\pi$
$24$		0			0
$25$	−4.48206			−0.896413
$26$	−11.3960			−2.23493
$27$		0			0
$28$	6.23187	+	10.7939i	1.17771	+	2.03986i
$29$	−5.94195			−1.10339			−0.551696	−	0.834045i	$-0.686019\pi$
$29$	−5.94195			−1.10339			−0.551696	+	0.834045i	$0.686019\pi$
$30$		0			0
$31$	−0.763210	−	1.32192i	−0.137077	−	0.237424i	0.789312	−	0.613992i	$-0.210437\pi$
$31$	−0.763210	−	1.32192i	−0.137077	−	0.237424i	−0.926389	+	0.376568i	$0.877104\pi$
$32$	1.09420	−	1.89520i	0.193428	−	0.335028i
$33$		0			0
$34$	−15.0438			−2.58000
$35$	−1.19367	+	2.06750i	−0.201768	+	0.349472i
$36$		0			0
$37$	−3.69507			−0.607465			−0.303733	−	0.952757i	$-0.598233\pi$
$37$	−3.69507			−0.607465			−0.303733	+	0.952757i	$0.598233\pi$
$38$	7.51575	+	7.27334i	1.21922	+	1.17989i
$39$		0			0
$40$	−3.03446			−0.479790
$41$	−5.68106			−0.887232			−0.443616	−	0.896217i	$-0.646305\pi$
$41$	−5.68106			−0.887232			−0.443616	+	0.896217i	$0.646305\pi$
$42$		0			0
$43$	−2.30746	−	3.99663i	−0.351884	−	0.609480i	0.634696	−	0.772762i	$-0.281125\pi$
$43$	−2.30746	−	3.99663i	−0.351884	−	0.609480i	−0.986579	+	0.163282i	$0.947792\pi$
$44$	−2.06824	−	3.58229i	−0.311798	−	0.540051i
$45$		0			0
$46$	5.34627			0.788264
$47$	−0.283238			−0.0413144			−0.0206572	−	0.999787i	$-0.506576\pi$
$47$	−0.283238			−0.0413144			−0.0206572	+	0.999787i	$0.506576\pi$
$48$		0			0
$49$	−2.00206	−	3.46767i	−0.286008	−	0.495381i
$50$	5.37720	+	9.31358i	0.760450	+	1.31714i
$51$		0			0
$52$	8.92245	+	15.4541i	1.23732	+	2.14310i
$53$	−1.90426	−	3.29828i	−0.261570	−	0.453053i	0.705089	−	0.709119i	$-0.250907\pi$
$53$	−1.90426	−	3.29828i	−0.261570	−	0.453053i	−0.966659	+	0.256066i	$0.917574\pi$
$54$		0			0
$55$	0.396157	−	0.686164i	0.0534178	−	0.0925224i
$56$	6.99344	−	12.1130i	0.934537	−	1.61867i
$57$		0			0
$58$	7.12864	+	12.3472i	0.936037	+	1.62126i
$59$	13.3719			1.74087			0.870434	−	0.492286i	$-0.163839\pi$
$59$	13.3719			1.74087			0.870434	+	0.492286i	$0.163839\pi$
$60$		0			0
$61$	11.8921			1.52262			0.761311	−	0.648387i	$-0.224556\pi$
$61$	11.8921			1.52262			0.761311	+	0.648387i	$0.224556\pi$
$62$	−1.83127	+	3.17185i	−0.232571	+	0.402825i
$63$		0			0
$64$	−10.4558			−1.30698
$65$	−1.70904	+	2.96014i	−0.211980	+	0.367160i
$66$		0			0
$67$	3.72296	−	6.44836i	0.454832	−	0.787792i	−0.543847	−	0.839185i	$-0.683033\pi$
$67$	3.72296	−	6.44836i	0.454832	−	0.787792i	0.998679	+	0.0513926i	$0.0163660\pi$
$68$	11.7785	+	20.4010i	1.42836	+	2.47399i
$69$		0			0
$70$	5.72827			0.684659
$71$	−5.51472	+	9.55177i	−0.654477	+	1.13359i	0.327548	+	0.944834i	$0.393778\pi$
$71$	−5.51472	+	9.55177i	−0.654477	+	1.13359i	−0.982025	+	0.188752i	$0.939556\pi$
$72$		0			0
$73$	−5.22640	+	9.05239i	−0.611703	+	1.05950i	0.379250	+	0.925294i	$0.376182\pi$
$73$	−5.22640	+	9.05239i	−0.611703	+	1.05950i	−0.990953	+	0.134207i	$0.957151\pi$
$74$	4.43302	+	7.67822i	0.515329	+	0.892575i
$75$		0			0
$76$	3.97897	−	15.8868i	0.456419	−	1.82234i
$77$	1.82603	+	3.16277i	0.208095	+	0.360431i
$78$		0			0
$79$	−6.11654	−	10.5942i	−0.688164	−	1.19194i	−0.972431	−	0.233190i	$-0.925083\pi$
$79$	−6.11654	−	10.5942i	−0.688164	−	1.19194i	0.284267	−	0.958745i	$-0.408250\pi$
$80$	0.936469	+	1.62201i	0.104700	+	0.181346i
$81$		0			0
$82$	6.81565	+	11.8050i	0.752662	+	1.30365i
$83$	5.05059	−	8.74788i	0.554374	−	0.960205i	−0.443577	−	0.896236i	$-0.646291\pi$
$83$	5.05059	−	8.74788i	0.554374	−	0.960205i	0.997952	−	0.0639687i	$-0.0203758\pi$
$84$		0			0
$85$	−2.25610	+	3.90769i	−0.244709	+	0.423848i
$86$	−5.53657	+	9.58963i	−0.597024	+	1.03408i
$87$		0			0
$88$	−2.32099	+	4.02007i	−0.247418	+	0.428540i
$89$	−4.23637	−	7.33760i	−0.449054	−	0.777784i	0.549271	−	0.835644i	$-0.314906\pi$
$89$	−4.23637	−	7.33760i	−0.449054	−	0.777784i	−0.998325	+	0.0578602i	$0.981572\pi$
$90$		0			0
$91$	−7.87754	−	13.6443i	−0.825791	−	1.43031i
$92$	−4.18585	−	7.25010i	−0.436405	−	0.755876i
$93$		0			0
$94$	0.339804	+	0.588558i	0.0350481	+	0.0607051i
$95$	3.01640	−	0.861468i	0.309476	−	0.0883848i
$96$		0			0
$97$	−6.16532	−	10.6786i	−0.625993	−	1.08425i	−0.988348	−	0.152212i	$-0.951360\pi$
$97$	−6.16532	−	10.6786i	−0.625993	−	1.08425i	0.362355	−	0.932040i	$-0.381973\pi$
$98$	−4.80380	+	8.32042i	−0.485257	+	0.840489i
$99$		0			0
$100$	8.42013	−	14.5841i	0.842013	−	1.45841i
$101$	15.0234			1.49488			0.747441	−	0.664328i	$-0.231282\pi$
$101$	15.0234			1.49488			0.747441	+	0.664328i	$0.231282\pi$
$102$		0			0
$103$	0.947555	+	1.64121i	0.0933654	+	0.161714i	0.908925	−	0.416959i	$-0.136904\pi$
$103$	0.947555	+	1.64121i	0.0933654	+	0.161714i	−0.815560	+	0.578673i	$0.803571\pi$
$104$	10.0128	−	17.3427i	0.981837	−	1.70059i
$105$		0			0
$106$	−4.56914	+	7.91398i	−0.443794	+	0.768674i
$107$	2.81175			0.271822			0.135911	−	0.990721i	$-0.456604\pi$
$107$	2.81175			0.271822			0.135911	+	0.990721i	$0.456604\pi$
$108$		0			0
$109$	−1.58360	+	2.74287i	−0.151681	+	0.262719i	−0.931846	−	0.362855i	$-0.881802\pi$
$109$	−1.58360	+	2.74287i	−0.151681	+	0.262719i	0.780165	+	0.625574i	$0.215135\pi$
$110$	−1.90110			−0.181263
$111$		0			0
$112$	−8.63302			−0.815744
$113$	−6.93071	−	12.0043i	−0.651986	−	1.12927i	−0.982640	−	0.185522i	$-0.940603\pi$
$113$	−6.93071	−	12.0043i	−0.651986	−	1.12927i	0.330654	−	0.943752i	$-0.392731\pi$
$114$		0			0
$115$	0.801772	−	1.38871i	0.0747656	−	0.129498i
$116$	11.1627	−	19.3344i	1.03643	−	1.79515i
$117$		0			0
$118$	−16.0424	−	27.7863i	−1.47682	−	2.55793i
$119$	−10.3992	−	18.0119i	−0.953290	−	1.65115i
$120$		0			0
$121$	4.89398	+	8.47662i	0.444907	+	0.770602i
$122$	−14.2671	−	24.7113i	−1.29168	−	2.23726i
$123$		0			0
$124$	5.73515			0.515032
$125$	6.82403			0.610360
$126$		0			0
$127$	4.62043	+	8.00282i	0.409997	+	0.710136i	0.994889	−	0.100976i	$-0.0321964\pi$
$127$	4.62043	+	8.00282i	0.409997	+	0.710136i	−0.584892	+	0.811111i	$0.698863\pi$
$128$	10.3556	+	17.9364i	0.915315	+	1.58537i
$129$		0			0
$130$	8.20142			0.719312
$131$	7.26622			0.634853			0.317426	−	0.948283i	$-0.397181\pi$
$131$	7.26622			0.634853			0.317426	+	0.948283i	$0.397181\pi$
$132$		0			0
$133$	−3.51300	+	14.0263i	−0.304615	+	1.21623i
$134$	−17.8660			−1.54338
$135$		0			0
$136$	13.2179	−	22.8941i	1.13343	−	1.96316i
$137$	−18.4460			−1.57595			−0.787973	−	0.615710i	$-0.788869\pi$
$137$	−18.4460			−1.57595			−0.787973	+	0.615710i	$0.788869\pi$
$138$		0			0
$139$	−6.60178	+	11.4346i	−0.559956	+	0.969872i	0.437543	+	0.899197i	$0.355849\pi$
$139$	−6.60178	+	11.4346i	−0.559956	+	0.969872i	−0.997499	+	0.0706749i	$0.977485\pi$
$140$	−4.48494	−	7.76815i	−0.379047	−	0.656528i
$141$		0			0
$142$	26.4643			2.22084
$143$	2.61440	+	4.52828i	0.218627	+	0.378674i
$144$		0			0
$145$	4.27629			0.355127
$146$	25.0807			2.07570
$147$		0			0
$148$	6.94166	−	12.0233i	0.570601	−	0.988309i
$149$	2.47022			0.202369			0.101184	−	0.994868i	$-0.467737\pi$
$149$	2.47022			0.202369			0.101184	+	0.994868i	$0.467737\pi$
$150$		0			0
$151$	11.7861	−	20.4141i	0.959140	−	1.66128i	0.234542	−	0.972106i	$-0.424641\pi$
$151$	11.7861	−	20.4141i	0.959140	−	1.66128i	0.724597	−	0.689173i	$-0.242026\pi$
$152$	−17.6723	+	5.04713i	−1.43341	+	0.409376i
$153$		0			0
$154$	4.38142	−	7.58884i	0.353065	−	0.611526i
$155$	0.549265	+	0.951355i	0.0441181	+	0.0764147i
$156$		0			0
$157$	7.12368			0.568532			0.284266	−	0.958745i	$-0.408250\pi$
$157$	7.12368			0.568532			0.284266	+	0.958745i	$0.408250\pi$
$158$	−14.6762	+	25.4199i	−1.16758	+	2.02230i
$159$		0			0
$160$	−0.787469	+	1.36394i	−0.0622549	+	0.107829i
$161$	3.69565	+	6.40105i	0.291258	+	0.504473i
$162$		0			0
$163$	12.6404			0.990075			0.495038	−	0.868872i	$-0.335154\pi$
$163$	12.6404			0.990075			0.495038	+	0.868872i	$0.335154\pi$
$164$	10.6726	−	18.4855i	0.833390	−	1.44347i
$165$		0			0
$166$	−24.2371			−1.88116
$167$	3.84765	−	6.66432i	0.297740	−	0.515701i	−0.677878	−	0.735174i	$-0.737100\pi$
$167$	3.84765	−	6.66432i	0.297740	−	0.515701i	0.975619	+	0.219473i	$0.0704338\pi$
$168$		0			0
$169$	−4.77862	−	8.27682i	−0.367587	−	0.636679i
$170$	10.8267			0.830371
$171$		0			0
$172$	17.3394			1.32212
$173$	1.67994	+	2.90974i	0.127723	+	0.221223i	0.922794	−	0.385293i	$-0.125900\pi$
$173$	1.67994	+	2.90974i	0.127723	+	0.221223i	−0.795071	+	0.606517i	$0.792566\pi$
$174$		0			0
$175$	−7.43405	+	12.8762i	−0.561962	+	0.973346i
$176$	2.86513			0.215967
$177$		0			0
$178$	−10.1649	+	17.6060i	−0.761888	+	1.31963i
$179$	17.3530			1.29703			0.648514	−	0.761203i	$-0.275391\pi$
$179$	17.3530			1.29703			0.648514	+	0.761203i	$0.275391\pi$
$180$		0			0
$181$	−5.84752	−	10.1282i	−0.434643	−	0.752824i	0.562623	−	0.826713i	$-0.309792\pi$
$181$	−5.84752	−	10.1282i	−0.434643	−	0.752824i	−0.997266	+	0.0738895i	$0.976459\pi$
$182$	−18.9016	+	32.7385i	−1.40108	+	2.42674i
$183$		0			0
$184$	−4.69738	+	8.13610i	−0.346296	+	0.599801i
$185$	2.65926			0.195513
$186$		0			0
$187$	3.45128	+	5.97779i	0.252383	+	0.437139i
$188$	0.532098	−	0.921621i	0.0388072	−	0.0672161i
$189$		0			0
$190$	−5.40892	−	5.23446i	−0.392404	−	0.379748i
$191$	−1.22344	+	2.11906i	−0.0885251	+	0.153330i	−0.906888	−	0.421372i	$-0.861549\pi$
$191$	−1.22344	+	2.11906i	−0.0885251	+	0.153330i	0.818363	+	0.574702i	$0.194882\pi$
$192$		0			0
$193$	12.3613			0.889787			0.444894	−	0.895583i	$-0.353241\pi$
$193$	12.3613			0.889787			0.444894	+	0.895583i	$0.353241\pi$
$194$	−14.7932	+	25.6226i	−1.06209	+	1.83960i
$195$		0			0
$196$	15.0445			1.07461
$197$	5.54586			0.395126			0.197563	−	0.980290i	$-0.436697\pi$
$197$	5.54586			0.395126			0.197563	+	0.980290i	$0.436697\pi$
$198$		0			0
$199$	9.82630	+	17.0196i	0.696568	+	1.20649i	0.969649	+	0.244500i	$0.0786237\pi$
$199$	9.82630	+	17.0196i	0.696568	+	1.20649i	−0.273082	+	0.961991i	$0.588043\pi$
$200$	−18.8982			−1.33631
$201$		0			0
$202$	−18.0238	−	31.2181i	−1.26815	−	2.19650i
$203$	−9.85546	+	17.0702i	−0.691717	+	1.19809i
$204$		0			0
$205$	4.08853			0.285556
$206$	2.27359	−	3.93797i	0.158409	−	0.274372i
$207$		0			0
$208$	−12.3603			−0.857031
$209$	1.16589	−	4.65506i	0.0806466	−	0.321997i
$210$		0			0
$211$	1.34447			0.0925570			0.0462785	−	0.998929i	$-0.485264\pi$
$211$	1.34447			0.0925570			0.0462785	+	0.998929i	$0.485264\pi$
$212$	14.3096			0.982787
$213$		0			0
$214$	−3.37330	−	5.84272i	−0.230594	−	0.399400i
$215$	1.66062	+	2.87629i	0.113254	+	0.196161i
$216$		0			0
$217$	−5.06351			−0.343733
$218$	7.59946			0.514700
$219$		0			0
$220$	1.48846	+	2.57810i	0.100352	+	0.173815i
$221$	−14.8889	−	25.7884i	−1.00154	−	1.73472i
$222$		0			0
$223$	11.0676	+	19.1696i	0.741139	+	1.28369i	0.951977	+	0.306170i	$0.0990474\pi$
$223$	11.0676	+	19.1696i	0.741139	+	1.28369i	−0.210838	+	0.977521i	$0.567619\pi$
$224$	−3.62972	−	6.28686i	−0.242521	−	0.420058i
$225$		0			0
$226$	−16.6297	+	28.8036i	−1.10619	+	1.91598i
$227$	2.63704	−	4.56749i	0.175027	−	0.303155i	−0.765144	−	0.643859i	$-0.777332\pi$
$227$	2.63704	−	4.56749i	0.175027	−	0.303155i	0.940170	+	0.340704i	$0.110666\pi$
$228$		0			0
$229$	−8.36533	−	14.4892i	−0.552797	−	0.957472i	−0.998071	−	0.0620777i	$-0.980227\pi$
$229$	−8.36533	−	14.4892i	−0.552797	−	0.957472i	0.445275	−	0.895394i	$-0.353106\pi$
$230$	−3.84759			−0.253703
$231$		0			0
$232$	−25.0537			−1.64486
$233$	−0.652119	+	1.12950i	−0.0427217	+	0.0739962i	−0.886596	−	0.462545i	$-0.846936\pi$
$233$	−0.652119	+	1.12950i	−0.0427217	+	0.0739962i	0.843874	+	0.536542i	$0.180270\pi$
$234$		0			0
$235$	0.203840			0.0132970
$236$	−25.1207	+	43.5104i	−1.63522	+	2.83229i
$237$		0			0
$238$	−24.9520	+	43.2182i	−1.61740	+	2.80142i
$239$	9.60234	+	16.6317i	0.621124	+	1.07582i	0.989277	+	0.146053i	$0.0466570\pi$
$239$	9.60234	+	16.6317i	0.621124	+	1.07582i	−0.368153	+	0.929765i	$0.620010\pi$
$240$		0			0
$241$	1.79014			0.115313			0.0576566	−	0.998336i	$-0.481637\pi$
$241$	1.79014			0.115313			0.0576566	+	0.998336i	$0.481637\pi$
$242$	11.7427	−	20.3390i	0.754853	−	1.30744i
$243$		0			0
$244$	−22.3408	+	38.6953i	−1.43022	+	2.47722i
$245$	1.44084	+	2.49560i	0.0920517	+	0.159438i
$246$		0			0
$247$	−5.02971	+	20.0821i	−0.320033	+	1.27779i
$248$	−3.21801	−	5.57375i	−0.204344	−	0.353934i
$249$		0			0
$250$	−8.18689	−	14.1801i	−0.517784	−	0.896829i
$251$	3.17364	+	5.49691i	0.200319	+	0.346962i	0.948631	−	0.316384i	$-0.102469\pi$
$251$	3.17364	+	5.49691i	0.200319	+	0.346962i	−0.748312	+	0.663346i	$0.769136\pi$
$252$		0			0
$253$	−1.22651	−	2.12438i	−0.0771102	−	0.133559i
$254$	11.0864	−	19.2022i	0.695622	−	1.20485i
$255$		0			0
$256$	14.3917	−	24.9272i	0.899483	−	1.55795i
$257$	11.9228	−	20.6510i	0.743727	−	1.28817i	−0.207060	−	0.978328i	$-0.566390\pi$
$257$	11.9228	−	20.6510i	0.743727	−	1.28817i	0.950787	−	0.309845i	$-0.100277\pi$
$258$		0			0
$259$	−6.12872	+	10.6153i	−0.380820	+	0.659600i
$260$	−6.42129	−	11.1220i	−0.398231	−	0.689757i
$261$		0			0
$262$	−8.71739	−	15.0990i	−0.538562	−	0.932817i
$263$	2.26524	+	3.92351i	0.139681	+	0.241934i	0.927376	−	0.374131i	$-0.122059\pi$
$263$	2.26524	+	3.92351i	0.139681	+	0.241934i	−0.787695	+	0.616065i	$0.788726\pi$
$264$		0			0
$265$	1.37045	+	2.37370i	0.0841864	+	0.145815i
$266$	33.3608	−	9.52767i	2.04548	−	0.584179i
$267$		0			0
$268$	13.9881	+	24.2281i	0.854460	+	1.47997i
$269$	−2.41294	+	4.17933i	−0.147119	+	0.254818i	−0.930162	−	0.367150i	$-0.880333\pi$
$269$	−2.41294	+	4.17933i	−0.147119	+	0.254818i	0.783042	+	0.621968i	$0.213667\pi$
$270$		0			0
$271$	−1.69899	+	2.94273i	−0.103206	+	0.178758i	−0.913004	−	0.407951i	$-0.866243\pi$
$271$	−1.69899	+	2.94273i	−0.103206	+	0.178758i	0.809798	+	0.586709i	$0.199577\pi$
$272$	−16.3168			−0.989353
$273$		0			0
$274$	22.1299	+	38.3301i	1.33692	+	2.31561i
$275$	2.46722	−	4.27335i	0.148779	−	0.257692i
$276$		0			0
$277$	−7.98414	+	13.8289i	−0.479720	+	0.830900i	−0.999729	−	0.0232607i	$-0.992595\pi$
$277$	−7.98414	+	13.8289i	−0.479720	+	0.830900i	0.520009	+	0.854161i	$0.325929\pi$
$278$	31.6810			1.90010
$279$		0			0
$280$	−5.03302	+	8.71745i	−0.300781	+	0.520967i
$281$	−7.53948			−0.449768			−0.224884	−	0.974386i	$-0.572200\pi$
$281$	−7.53948			−0.449768			−0.224884	+	0.974386i	$0.572200\pi$
$282$		0			0
$283$	10.3238			0.613689			0.306844	−	0.951760i	$-0.400727\pi$
$283$	10.3238			0.613689			0.306844	+	0.951760i	$0.400727\pi$
$284$	−20.7202	−	35.8885i	−1.22952	−	2.12959i
$285$		0			0
$286$	6.27307	−	10.8653i	0.370934	−	0.642477i
$287$	−9.42273	+	16.3207i	−0.556206	+	0.963378i
$288$		0			0
$289$	−11.1549	−	19.3209i	−0.656172	−	1.13652i
$290$	−5.13033	−	8.88599i	−0.301263	−	0.521803i
$291$		0			0
$292$	−19.6369	−	34.0121i	−1.14916	−	1.99041i
$293$	3.88571	+	6.73025i	0.227006	+	0.393186i	0.956919	−	0.290354i	$-0.0937730\pi$
$293$	3.88571	+	6.73025i	0.227006	+	0.393186i	−0.729914	+	0.683539i	$0.760440\pi$
$294$		0			0
$295$	−9.62343			−0.560298
$296$	−15.5799			−0.905565
$297$		0			0
$298$	−2.96356	−	5.13304i	−0.171674	−	0.297349i
$299$	5.29122	+	9.16466i	0.305999	+	0.530006i
$300$		0			0
$301$	−15.3088			−0.882384
$302$	−56.5598			−3.25465
$303$		0			0
$304$	8.15173	+	7.88880i	0.467534	+	0.452454i
$305$	−8.55846			−0.490056
$306$		0			0
$307$	−4.92022	+	8.52206i	−0.280812	+	0.486380i	−0.971585	−	0.236692i	$-0.923937\pi$
$307$	−4.92022	+	8.52206i	−0.280812	+	0.486380i	0.690773	+	0.723071i	$0.257270\pi$
$308$	−13.7217			−0.781866
$309$		0			0
$310$	1.31792	−	2.28271i	0.0748530	−	0.129649i
$311$	12.6580	+	21.9243i	0.717769	+	1.24321i	0.961882	+	0.273466i	$0.0881701\pi$
$311$	12.6580	+	21.9243i	0.717769	+	1.24321i	−0.244112	+	0.969747i	$0.578497\pi$
$312$		0			0
$313$	−20.7713			−1.17406			−0.587030	−	0.809565i	$-0.699703\pi$
$313$	−20.7713			−1.17406			−0.587030	+	0.809565i	$0.699703\pi$
$314$	−8.54638	−	14.8028i	−0.482300	−	0.835369i
$315$		0			0
$316$	45.9628			2.58561
$317$	−8.78411			−0.493365			−0.246682	−	0.969096i	$-0.579340\pi$
$317$	−8.78411			−0.493365			−0.246682	+	0.969096i	$0.579340\pi$
$318$		0			0
$319$	3.27083	−	5.66525i	0.183132	−	0.317193i
$320$	7.52483			0.420651
$321$		0			0
$322$	8.86744	−	15.3589i	0.494163	−	0.855915i
$323$	−6.63974	+	26.5104i	−0.369445	+	1.47508i
$324$		0			0
$325$	−10.6437	+	18.4354i	−0.590404	+	1.02261i
$326$	−15.1649	−	26.2664i	−0.839907	−	1.45476i
$327$		0			0
$328$	−23.9537			−1.32262
$329$	−0.469784	+	0.813690i	−0.0259000	+	0.0448602i
$330$		0			0
$331$	9.59192	−	16.6137i	0.527219	−	0.913171i	−0.472277	−	0.881450i	$-0.656568\pi$
$331$	9.59192	−	16.6137i	0.527219	−	0.913171i	0.999497	−	0.0317208i	$-0.0100987\pi$
$332$	18.9764	+	32.8680i	1.04146	+	1.80387i
$333$		0			0
$334$	−18.4643			−1.01032
$335$	−2.67933	+	4.64074i	−0.146388	+	0.253551i
$336$		0			0
$337$	2.04230			0.111251			0.0556257	−	0.998452i	$-0.482285\pi$
$337$	2.04230			0.111251			0.0556257	+	0.998452i	$0.482285\pi$
$338$	−11.4660	+	19.8596i	−0.623666	+	1.08022i
$339$		0			0
$340$	−8.47676	−	14.6822i	−0.459717	−	0.796253i
$341$	1.68048			0.0910031
$342$		0			0
$343$	9.93808			0.536606
$344$	−9.72918	−	16.8514i	−0.524562	−	0.908569i
$345$		0			0
$346$	4.03089	−	6.98171i	0.216702	−	0.375339i
$347$	9.72894			0.522277			0.261138	−	0.965301i	$-0.415902\pi$
$347$	9.72894			0.522277			0.261138	+	0.965301i	$0.415902\pi$
$348$		0			0
$349$	7.61899	−	13.1965i	0.407835	−	0.706391i	−0.586812	−	0.809723i	$-0.699617\pi$
$349$	7.61899	−	13.1965i	0.407835	−	0.706391i	0.994647	+	0.103332i	$0.0329505\pi$
$350$	35.6750			1.90691
$351$		0			0
$352$	1.20463	+	2.08648i	0.0642071	+	0.111210i
$353$	13.3156	−	23.0632i	0.708716	−	1.22753i	−0.256618	−	0.966513i	$-0.582608\pi$
$353$	13.3156	−	23.0632i	0.708716	−	1.22753i	0.965334	−	0.261019i	$-0.0840585\pi$
$354$		0			0
$355$	3.96882	−	6.87420i	0.210643	−	0.364845i
$356$	31.8342			1.68721
$357$		0			0
$358$	−20.8187	−	36.0590i	−1.10030	−	1.90578i
$359$	5.98961	−	10.3743i	0.316119	−	0.547535i	−0.663555	−	0.748127i	$-0.730953\pi$
$359$	5.98961	−	10.3743i	0.316119	−	0.547535i	0.979675	+	0.200592i	$0.0642867\pi$
$360$		0			0
$361$	16.1343	−	10.0342i	0.849173	−	0.528114i
$362$	−14.0307	+	24.3019i	−0.737438	+	1.27728i
$363$		0			0
$364$	59.1959			3.10271
$365$	3.76132	−	6.51480i	0.196877	−	0.341000i
$366$		0			0
$367$	−1.60685			−0.0838768			−0.0419384	−	0.999120i	$-0.513353\pi$
$367$	−1.60685			−0.0838768			−0.0419384	+	0.999120i	$0.513353\pi$
$368$	5.79866			0.302276
$369$		0			0
$370$	−3.19035	−	5.52585i	−0.165858	−	0.287275i
$371$	−12.6338			−0.655914
$372$		0			0
$373$	4.06344	+	7.03808i	0.210397	+	0.364418i	0.951839	−	0.306599i	$-0.0991910\pi$
$373$	4.06344	+	7.03808i	0.210397	+	0.364418i	−0.741442	+	0.671017i	$0.765858\pi$
$374$	8.28110	−	14.3433i	0.428205	−	0.741673i
$375$		0			0
$376$	−1.19425			−0.0615885
$377$	−14.1105	+	24.4401i	−0.726727	+	1.25873i
$378$		0			0
$379$	33.1062			1.70055			0.850277	−	0.526336i	$-0.176435\pi$
$379$	33.1062			1.70055			0.850277	+	0.526336i	$0.176435\pi$
$380$	−2.86358	+	11.4334i	−0.146899	+	0.586520i
$381$		0			0
$382$	5.87112			0.300393
$383$	−19.6974			−1.00649			−0.503246	−	0.864143i	$-0.667861\pi$
$383$	−19.6974			−1.00649			−0.503246	+	0.864143i	$0.667861\pi$
$384$		0			0
$385$	−1.31415	−	2.27618i	−0.0669753	−	0.116005i
$386$	−14.8301	−	25.6864i	−0.754830	−	1.30740i
$387$		0			0
$388$	46.3294			2.35202
$389$	15.9471			0.808552			0.404276	−	0.914637i	$-0.367523\pi$
$389$	15.9471			0.808552			0.404276	+	0.914637i	$0.367523\pi$
$390$		0			0
$391$	6.98495	+	12.0983i	0.353244	+	0.611837i
$392$	−8.44150	−	14.6211i	−0.426360	−	0.738478i
$393$		0			0
$394$	−6.65345	−	11.5241i	−0.335196	−	0.580577i
$395$	4.40194	+	7.62438i	0.221486	+	0.383624i
$396$		0			0
$397$	−12.0149	+	20.8105i	−0.603012	+	1.04445i	0.389351	+	0.921090i	$0.372699\pi$
$397$	−12.0149	+	20.8105i	−0.603012	+	1.04445i	−0.992362	+	0.123357i	$0.960634\pi$
$398$	23.5775	−	40.8374i	1.18183	−	2.04699i
$399$		0			0
$400$	5.83221	+	10.1017i	0.291611	+	0.505084i
$401$	−3.78271			−0.188900			−0.0944498	−	0.995530i	$-0.530109\pi$
$401$	−3.78271			−0.188900			−0.0944498	+	0.995530i	$0.530109\pi$
$402$		0			0
$403$	−7.24965			−0.361131
$404$	−28.2234	+	48.8843i	−1.40416	+	2.43208i
$405$		0			0
$406$	47.2949			2.34721
$407$	2.03400	−	3.52300i	0.100822	−	0.174628i
$408$		0			0
$409$	13.5934	−	23.5444i	0.672148	−	1.16420i	−0.305145	−	0.952306i	$-0.598705\pi$
$409$	13.5934	−	23.5444i	0.672148	−	1.16420i	0.977294	−	0.211889i	$-0.0679617\pi$
$410$	−4.90507	−	8.49583i	−0.242244	−	0.419579i
$411$		0			0
$412$	−7.12041			−0.350798
$413$	22.1789	−	38.4149i	1.09135	−	1.89027i
$414$		0			0
$415$	−3.63480	+	6.29566i	−0.178425	+	0.309042i
$416$	−5.19683	−	9.00117i	−0.254795	−	0.441319i
$417$		0			0
$418$	−11.0718	+	3.16205i	−0.541539	+	0.154661i
$419$	−2.02350	−	3.50481i	−0.0988547	−	0.171221i	0.812356	−	0.583162i	$-0.198185\pi$
$419$	−2.02350	−	3.50481i	−0.0988547	−	0.171221i	−0.911211	+	0.411940i	$0.864851\pi$
$420$		0			0
$421$	3.32231	+	5.75442i	0.161920	+	0.280453i	0.935557	−	0.353175i	$-0.114898\pi$
$421$	3.32231	+	5.75442i	0.161920	+	0.280453i	−0.773637	+	0.633629i	$0.781565\pi$
$422$	−1.61298	−	2.79376i	−0.0785185	−	0.135998i
$423$		0			0
$424$	−8.02915	−	13.9069i	−0.389930	−	0.675379i
$425$	−14.0507	+	24.3366i	−0.681560	+	1.18050i
$426$		0			0
$427$	19.7244	−	34.1637i	0.954533	−	1.65330i
$428$	−5.28224	+	9.14910i	−0.255326	+	0.442238i
$429$		0			0
$430$	3.98455	−	6.90144i	0.192152	−	0.332817i
$431$	−8.57343	−	14.8496i	−0.412967	−	0.715281i	0.582245	−	0.813013i	$-0.302174\pi$
$431$	−8.57343	−	14.8496i	−0.412967	−	0.715281i	−0.995213	+	0.0977326i	$0.968841\pi$
$432$		0			0
$433$	−8.02098	−	13.8927i	−0.385464	−	0.667643i	0.606370	−	0.795183i	$-0.292625\pi$
$433$	−8.02098	−	13.8927i	−0.385464	−	0.667643i	−0.991833	+	0.127540i	$0.959292\pi$
$434$	6.07476	+	10.5218i	0.291598	+	0.505062i
$435$		0			0
$436$	−5.94998	−	10.3057i	−0.284952	−	0.493552i
$437$	2.35962	−	9.42124i	0.112876	−	0.450679i
$438$		0			0
$439$	−3.47970	−	6.02702i	−0.166077	−	0.287654i	0.770960	−	0.636883i	$-0.219777\pi$
$439$	−3.47970	−	6.02702i	−0.166077	−	0.287654i	−0.937037	+	0.349229i	$0.886443\pi$
$440$	1.67036	−	2.89315i	0.0796314	−	0.137926i
$441$		0			0
$442$	−35.7249	+	61.8774i	−1.69926	+	2.94321i
$443$	−2.43626			−0.115750			−0.0578751	−	0.998324i	$-0.518433\pi$
$443$	−2.43626			−0.115750			−0.0578751	+	0.998324i	$0.518433\pi$
$444$		0			0
$445$	3.04882	+	5.28071i	0.144528	+	0.250330i
$446$	26.5558	−	45.9961i	1.25746	−	2.17798i
$447$		0			0
$448$	−17.3423	+	30.0377i	−0.819345	+	1.41915i
$449$	−25.8086			−1.21798			−0.608991	−	0.793177i	$-0.708425\pi$
$449$	−25.8086			−1.21798			−0.608991	+	0.793177i	$0.708425\pi$
$450$		0			0
$451$	3.12722	−	5.41651i	0.147255	−	0.255053i
$452$	52.0809			2.44968
$453$		0			0
$454$	−12.6548			−0.593918
$455$	5.66929	+	9.81950i	0.265781	+	0.460345i
$456$		0			0
$457$	1.49509	−	2.58957i	0.0699372	−	0.121135i	−0.828936	−	0.559343i	$-0.811053\pi$
$457$	1.49509	−	2.58957i	0.0699372	−	0.121135i	0.898873	+	0.438208i	$0.144387\pi$
$458$	−20.0720	+	34.7657i	−0.937903	+	1.62450i
$459$		0			0
$460$	3.01246	+	5.21774i	0.140457	+	0.243278i
$461$	−7.06982	−	12.2453i	−0.329274	−	0.570320i	0.653094	−	0.757277i	$-0.273471\pi$
$461$	−7.06982	−	12.2453i	−0.329274	−	0.570320i	−0.982368	+	0.186957i	$0.940137\pi$
$462$		0			0
$463$	−13.8565	−	24.0001i	−0.643964	−	1.11538i	−0.984540	−	0.175161i	$-0.943955\pi$
$463$	−13.8565	−	24.0001i	−0.643964	−	1.11538i	0.340576	−	0.940217i	$-0.389378\pi$
$464$	7.73187	+	13.3920i	0.358943	+	0.621707i
$465$		0			0
$466$	3.12943			0.144968
$467$	−27.3728			−1.26666			−0.633330	−	0.773882i	$-0.718313\pi$
$467$	−27.3728			−1.26666			−0.633330	+	0.773882i	$0.718313\pi$
$468$		0			0
$469$	−12.3500	−	21.3908i	−0.570269	−	0.987734i
$470$	−0.244550	−	0.423572i	−0.0112802	−	0.0195379i
$471$		0			0
$472$	56.3813			2.59516
$473$	5.08069			0.233610
$474$		0			0
$475$	18.7858	−	5.36512i	0.861949	−	0.246168i
$476$	78.1446			3.58175
$477$		0			0
$478$	23.0401	−	39.9067i	1.05383	−	1.82529i
$479$	−32.3242			−1.47693			−0.738466	−	0.674291i	$-0.764449\pi$
$479$	−32.3242			−1.47693			−0.738466	+	0.674291i	$0.764449\pi$
$480$		0			0
$481$	−8.77476	+	15.1983i	−0.400095	+	0.692984i
$482$	−2.14766	−	3.71985i	−0.0978232	−	0.169435i
$483$		0			0
$484$	−36.7759			−1.67163
$485$	4.43704	+	7.68519i	0.201476	+	0.348966i
$486$		0			0
$487$	−20.0494			−0.908523			−0.454262	−	0.890868i	$-0.650097\pi$
$487$	−20.0494			−0.908523			−0.454262	+	0.890868i	$0.650097\pi$
$488$	50.1418			2.26981
$489$		0			0
$490$	3.45719	−	5.98802i	0.156180	−	0.270511i
$491$	4.69564			0.211911			0.105956	−	0.994371i	$-0.466210\pi$
$491$	4.69564			0.211911			0.105956	+	0.994371i	$0.466210\pi$
$492$		0			0
$493$	−18.6273	+	32.2634i	−0.838931	+	1.45307i
$494$	47.7641	−	13.6412i	2.14901	−	0.613746i
$495$		0			0
$496$	−1.98623	+	3.44025i	−0.0891843	+	0.154472i
$497$	18.2937	+	31.6856i	0.820583	+	1.42129i
$498$		0			0
$499$	21.1656			0.947503			0.473752	−	0.880658i	$-0.342899\pi$
$499$	21.1656			0.947503			0.473752	+	0.880658i	$0.342899\pi$
$500$	−12.8198	+	22.2046i	−0.573320	+	0.993019i
$501$		0			0
$502$	7.61493	−	13.1895i	0.339871	−	0.588674i
$503$	−12.8870	−	22.3210i	−0.574604	−	0.995243i	−0.996085	−	0.0884059i	$-0.971823\pi$
$503$	−12.8870	−	22.3210i	−0.574604	−	0.995243i	0.421481	−	0.906837i	$-0.361511\pi$
$504$		0			0
$505$	−10.8120			−0.481128
$506$	−2.94293	+	5.09730i	−0.130829	+	0.226603i
$507$		0			0
$508$	−34.7203			−1.54046
$509$	−13.5801	+	23.5215i	−0.601929	+	1.04257i	0.390599	+	0.920561i	$0.372268\pi$
$509$	−13.5801	+	23.5215i	−0.601929	+	1.04257i	−0.992529	+	0.122011i	$0.961066\pi$
$510$		0			0
$511$	17.3372	+	30.0290i	0.766954	+	1.32840i
$512$	−27.6414			−1.22159
$513$		0			0
$514$	−57.2161			−2.52369
$515$	−0.681934	−	1.18115i	−0.0300496	−	0.0520475i
$516$		0			0
$517$	0.155912	−	0.270048i	0.00685701	−	0.0118767i
$518$	29.4109			1.29224
$519$		0			0
$520$	−7.20600	+	12.4812i	−0.316004	+	0.547335i
$521$	−21.0677			−0.922994			−0.461497	−	0.887142i	$-0.652687\pi$
$521$	−21.0677			−0.922994			−0.461497	+	0.887142i	$0.652687\pi$
$522$		0			0
$523$	4.13511	+	7.16222i	0.180816	+	0.313182i	0.942159	−	0.335167i	$-0.108793\pi$
$523$	4.13511	+	7.16222i	0.180816	+	0.313182i	−0.761343	+	0.648350i	$0.775460\pi$
$524$	−13.6505	+	23.6434i	−0.596326	+	1.03287i
$525$		0			0
$526$	5.43528	−	9.41418i	0.236989	−	0.410478i
$527$	−9.57028			−0.416888
$528$		0			0
$529$	9.01769	+	15.6191i	0.392074	+	0.679091i
$530$	3.28831	−	5.69552i	0.142835	−	0.247397i
$531$		0			0
$532$	−39.0403	−	37.7811i	−1.69261	−	1.63802i
$533$	−13.4909	+	23.3670i	−0.584358	+	1.01214i
$534$		0			0
$535$	−2.02356			−0.0874859
$536$	15.6975	−	27.1889i	0.678030	−	1.17438i
$537$		0			0
$538$	11.5793			0.499221
$539$	4.40825			0.189877
$540$		0			0
$541$	−13.5852	−	23.5303i	−0.584074	−	1.01165i	−0.994990	−	0.0999732i	$-0.968124\pi$
$541$	−13.5852	−	23.5303i	−0.584074	−	1.01165i	0.410916	−	0.911673i	$-0.365209\pi$
$542$	8.15320			0.350210
$543$		0			0
$544$	−6.86035	−	11.8825i	−0.294135	−	0.509457i
$545$	1.13968	−	1.97398i	0.0488185	−	0.0845562i
$546$		0			0
$547$	18.8534			0.806113			0.403056	−	0.915175i	$-0.367948\pi$
$547$	18.8534			0.806113			0.403056	+	0.915175i	$0.367948\pi$
$548$	34.6531	−	60.0210i	1.48031	−	2.56397i
$549$		0			0
$550$	−11.8398			−0.504852
$551$	24.9046	−	7.11263i	1.06097	−	0.303008i
$552$		0			0
$553$	−40.5801			−1.72564
$554$	38.3147			1.62784
$555$		0			0
$556$	−24.8046	−	42.9628i	−1.05195	−	1.82203i
$557$	4.19140	+	7.25972i	0.177595	+	0.307604i	0.941056	−	0.338250i	$-0.109835\pi$
$557$	4.19140	+	7.25972i	0.177595	+	0.307604i	−0.763461	+	0.645854i	$0.776502\pi$
$558$		0			0
$559$	−21.9183			−0.927044
$560$	6.21300			0.262547
$561$		0			0
$562$	9.04522	+	15.6668i	0.381550	+	0.660863i
$563$	0.809051	+	1.40132i	0.0340974	+	0.0590585i	0.882571	−	0.470180i	$-0.155811\pi$
$563$	0.809051	+	1.40132i	0.0340974	+	0.0590585i	−0.848473	+	0.529239i	$0.822478\pi$
$564$		0			0
$565$	4.98788	+	8.63926i	0.209842	+	0.363457i
$566$	−12.3857	−	21.4526i	−0.520608	−	0.901720i
$567$		0			0
$568$	−23.2523	+	40.2742i	−0.975646	+	1.68987i
$569$	−5.07595	+	8.79180i	−0.212795	+	0.368571i	−0.952588	−	0.304263i	$-0.901590\pi$
$569$	−5.07595	+	8.79180i	−0.212795	+	0.368571i	0.739793	+	0.672834i	$0.234923\pi$
$570$		0			0
$571$	6.06347	+	10.5022i	0.253748	+	0.439505i	0.964555	−	0.263883i	$-0.0850031\pi$
$571$	6.06347	+	10.5022i	0.253748	+	0.439505i	−0.710806	+	0.703388i	$0.751670\pi$
$572$	−19.6460			−0.821439
$573$		0			0
$574$	45.2184			1.88738
$575$	4.99334	−	8.64871i	0.208236	−	0.360676i
$576$		0			0
$577$	42.8498			1.78386			0.891931	−	0.452171i	$-0.149350\pi$
$577$	42.8498			1.78386			0.891931	+	0.452171i	$0.149350\pi$
$578$	−26.7655	+	46.3591i	−1.11330	+	1.92829i
$579$		0			0
$580$	−8.03357	+	13.9145i	−0.333576	+	0.577770i
$581$	−16.7541	−	29.0189i	−0.695075	−	1.20391i
$582$		0			0
$583$	4.19291			0.173653
$584$	−22.0366	+	38.1686i	−0.911883	+	1.57943i
$585$		0			0
$586$	9.32349	−	16.1488i	0.385150	−	0.667099i
$587$	5.80566	+	10.0557i	0.239625	+	0.415043i	0.960607	−	0.277911i	$-0.0896422\pi$
$587$	5.80566	+	10.0557i	0.239625	+	0.415043i	−0.720982	+	0.692954i	$0.756309\pi$
$588$		0			0
$589$	4.78122	+	4.62700i	0.197007	+	0.190652i
$590$	11.5454	+	19.9972i	0.475315	+	0.823270i
$591$		0			0
$592$	4.80814	+	8.32795i	0.197613	+	0.342277i
$593$	−3.60159	−	6.23813i	−0.147899	−	0.256169i	0.782551	−	0.622586i	$-0.213918\pi$
$593$	−3.60159	−	6.23813i	−0.147899	−	0.256169i	−0.930451	+	0.366417i	$0.880585\pi$
$594$		0			0
$595$	7.48405	+	12.9628i	0.306816	+	0.531421i
$596$	−4.64063	+	8.03781i	−0.190088	+	0.329241i
$597$		0			0
$598$	12.6959	−	21.9899i	0.519174	−	0.899236i
$599$	−12.5193	+	21.6841i	−0.511525	+	0.885987i	0.488386	+	0.872628i	$0.337586\pi$
$599$	−12.5193	+	21.6841i	−0.511525	+	0.885987i	−0.999911	+	0.0133592i	$0.995748\pi$
$600$		0			0
$601$	−17.0803	+	29.5840i	−0.696720	+	1.20675i	0.272877	+	0.962049i	$0.412025\pi$
$601$	−17.0803	+	29.5840i	−0.696720	+	1.20675i	−0.969597	+	0.244706i	$0.921309\pi$
$602$	18.3662	+	31.8111i	0.748549	+	1.29653i
$603$		0			0
$604$	44.2834	+	76.7011i	1.80187	+	3.12093i
$605$	−3.52209	−	6.10044i	−0.143193	−	0.248018i
$606$		0			0
$607$	−0.908746	−	1.57399i	−0.0368849	−	0.0638865i	0.846994	−	0.531603i	$-0.178410\pi$
$607$	−0.908746	−	1.57399i	−0.0368849	−	0.0638865i	−0.883879	+	0.467717i	$0.845077\pi$
$608$	−2.31753	+	9.25318i	−0.0939882	+	0.375266i
$609$		0			0
$610$	10.2677	+	17.7842i	0.415727	+	0.720060i
$611$	−0.672611	+	1.16500i	−0.0272109	+	0.0471307i
$612$		0			0
$613$	−0.633570	+	1.09737i	−0.0255896	+	0.0443225i	−0.878537	−	0.477675i	$-0.841480\pi$
$613$	−0.633570	+	1.09737i	−0.0255896	+	0.0443225i	0.852947	+	0.521998i	$0.174813\pi$
$614$	23.6114			0.952879
$615$		0			0
$616$	7.69928	+	13.3355i	0.310213	+	0.537304i
$617$	15.6681	−	27.1379i	0.630774	−	1.09253i	−0.356620	−	0.934249i	$-0.616071\pi$
$617$	15.6681	−	27.1379i	0.630774	−	1.09253i	0.987394	−	0.158282i	$-0.0505957\pi$
$618$		0			0
$619$	6.71549	−	11.6316i	0.269918	−	0.467512i	−0.698922	−	0.715198i	$-0.746337\pi$
$619$	6.71549	−	11.6316i	0.269918	−	0.467512i	0.968840	+	0.247686i	$0.0796700\pi$
$620$	−4.12746			−0.165763
$621$		0			0
$622$	30.3720	−	52.6058i	1.21780	−	2.10930i
$623$	−28.1061			−1.12605
$624$		0			0
$625$	17.4992			0.699968
$626$	24.9196	+	43.1620i	0.995987	+	1.72510i
$627$		0			0
$628$	−13.3828	+	23.1796i	−0.534030	+	0.924967i
$629$	−11.5836	+	20.0634i	−0.461868	+	0.799978i
$630$		0			0
$631$	−0.634355	−	1.09874i	−0.0252533	−	0.0437400i	0.853123	−	0.521711i	$-0.174706\pi$
$631$	−0.634355	−	1.09874i	−0.0252533	−	0.0437400i	−0.878376	+	0.477971i	$0.841373\pi$
$632$	−25.7898	−	44.6693i	−1.02587	−	1.77685i
$633$		0			0
$634$	10.5384	+	18.2531i	0.418534	+	0.724923i
$635$	−3.32522	−	5.75946i	−0.131957	−	0.228557i
$636$		0			0
$637$	−19.0173			−0.753495
$638$	−15.6963			−0.621421
$639$		0			0
$640$	−7.45270	−	12.9085i	−0.294594	−	0.510252i
$641$	5.58707	+	9.67710i	0.220676	+	0.382222i	0.955013	−	0.296562i	$-0.0958403\pi$
$641$	5.58707	+	9.67710i	0.220676	+	0.382222i	−0.734337	+	0.678785i	$0.762507\pi$
$642$		0			0
$643$	−24.7361			−0.975497			−0.487749	−	0.872984i	$-0.662182\pi$
$643$	−24.7361			−0.975497			−0.487749	+	0.872984i	$0.662182\pi$
$644$	−27.7710			−1.09433
$645$		0			0
$646$	63.0535	−	18.0078i	2.48081	−	0.708506i
$647$	22.5664			0.887177			0.443589	−	0.896230i	$-0.353705\pi$
$647$	22.5664			0.887177			0.443589	+	0.896230i	$0.353705\pi$
$648$		0			0
$649$	−7.36073	+	12.7492i	−0.288934	+	0.500448i
$650$	51.0774			2.00342
$651$		0			0
$652$	−23.7467	+	41.1305i	−0.929992	+	1.61079i
$653$	−8.52063	−	14.7582i	−0.333438	−	0.577532i	0.649745	−	0.760152i	$-0.274875\pi$
$653$	−8.52063	−	14.7582i	−0.333438	−	0.577532i	−0.983184	+	0.182620i	$0.941542\pi$
$654$		0			0
$655$	−5.22934			−0.204327
$656$	7.39238	+	12.8040i	0.288624	+	0.499912i
$657$		0			0
$658$	2.25443			0.0878867
$659$	10.5917			0.412595			0.206297	−	0.978489i	$-0.433859\pi$
$659$	10.5917			0.412595			0.206297	+	0.978489i	$0.433859\pi$
$660$		0			0
$661$	6.09635	−	10.5592i	0.237120	−	0.410705i	−0.722766	−	0.691092i	$-0.757130\pi$
$661$	6.09635	−	10.5592i	0.237120	−	0.410705i	0.959887	+	0.280388i	$0.0904631\pi$
$662$	−46.0302			−1.78902
$663$		0			0
$664$	21.2954	−	36.8847i	0.826421	−	1.43140i
$665$	2.52823	−	10.0944i	0.0980404	−	0.391445i
$666$		0			0
$667$	6.61975	−	11.4658i	0.256318	−	0.443956i
$668$	14.4566	+	25.0396i	0.559343	+	0.968811i
$669$		0			0
$670$	12.8577			0.496738
$671$	−6.54616	+	11.3383i	−0.252712	+	0.437709i
$672$		0			0
$673$	8.59983	−	14.8953i	0.331499	−	0.574173i	−0.651307	−	0.758814i	$-0.725779\pi$
$673$	8.59983	−	14.8953i	0.331499	−	0.574173i	0.982806	+	0.184641i	$0.0591123\pi$
$674$	−2.45018	−	4.24384i	−0.0943774	−	0.163466i
$675$		0			0
$676$	35.9090			1.38112
$677$	−9.95754	+	17.2470i	−0.382699	+	0.662855i	−0.991447	−	0.130509i	$-0.958339\pi$
$677$	−9.95754	+	17.2470i	−0.382699	+	0.662855i	0.608748	+	0.793364i	$0.291672\pi$
$678$		0			0
$679$	−40.9038			−1.56974
$680$	−9.51266	+	16.4764i	−0.364794	+	0.631842i
$681$		0			0
$682$	−2.01610	−	3.49198i	−0.0772003	−	0.133715i
$683$	39.6556			1.51738			0.758689	−	0.651453i	$-0.225840\pi$
$683$	39.6556			1.51738			0.758689	+	0.651453i	$0.225840\pi$
$684$		0			0
$685$	13.2752			0.507218
$686$	−11.9229	−	20.6510i	−0.455217	−	0.788459i
$687$		0			0
$688$	−6.00508	+	10.4011i	−0.228941	+	0.396538i
$689$	−18.0884			−0.689112
$690$		0			0
$691$	−3.61123	+	6.25483i	−0.137378	+	0.237945i	−0.926503	−	0.376287i	$-0.877201\pi$
$691$	−3.61123	+	6.25483i	−0.137378	+	0.237945i	0.789126	+	0.614232i	$0.210534\pi$
$692$	−12.6239			−0.479889
$693$		0			0
$694$	−11.6719	−	20.2164i	−0.443061	−	0.767404i
$695$	4.75116	−	8.22925i	0.180222	−	0.312153i
$696$		0			0
$697$	−17.8094	+	30.8468i	−0.674580	+	1.16841i
$698$	−36.5624			−1.38391
$699$		0			0
$700$	−27.9316	−	48.3790i	−1.05572	−	1.82856i
$701$	0.929426	−	1.60981i	0.0351039	−	0.0608018i	−0.847940	−	0.530093i	$-0.822157\pi$
$701$	0.929426	−	1.60981i	0.0351039	−	0.0608018i	0.883044	+	0.469291i	$0.155490\pi$
$702$		0			0
$703$	15.4872	−	4.42306i	0.584111	−	0.166819i
$704$	5.75556	−	9.96892i	0.216921	−	0.375718i
$705$		0			0
$706$	−63.8995			−2.40489
$707$	24.9181	−	43.1595i	0.937142	−	1.62318i
$708$		0			0
$709$	−33.3284			−1.25167			−0.625836	−	0.779954i	$-0.715242\pi$
$709$	−33.3284			−1.25167			−0.625836	+	0.779954i	$0.715242\pi$
$710$	−19.0458			−0.714776
$711$		0			0
$712$	−17.8623	−	30.9384i	−0.669417	−	1.15946i
$713$	3.40108			0.127371
$714$		0			0
$715$	−1.88153	−	3.25890i	−0.0703652	−	0.121876i
$716$	−32.5999	+	56.4647i	−1.21832	+	2.11019i
$717$		0			0
$718$	−28.7433			−1.07269
$719$	−24.4759	+	42.3936i	−0.912799	+	1.58101i	−0.102706	+	0.994712i	$0.532750\pi$
$719$	−24.4759	+	42.3936i	−0.912799	+	1.58101i	−0.810093	+	0.586302i	$0.800583\pi$
$720$		0			0
$721$	6.28654			0.234123
$722$	−40.2072	−	21.4884i	−1.49636	−	0.799714i
$723$		0			0
$724$	43.9413			1.63307
$725$	26.6322			0.989095
$726$		0			0
$727$	13.8532	+	23.9944i	0.513785	+	0.889902i	0.999872	+	0.0159916i	$0.00509050\pi$
$727$	13.8532	+	23.9944i	0.513785	+	0.889902i	−0.486087	+	0.873910i	$0.661576\pi$
$728$	−33.2150	−	57.5300i	−1.23103	−	2.13220i
$729$		0			0
$730$	−18.0501			−0.668062
$731$	−28.9344			−1.07018
$732$		0			0
$733$	−12.9206	−	22.3791i	−0.477232	−	0.826591i	0.522427	−	0.852684i	$-0.325027\pi$
$733$	−12.9206	−	22.3791i	−0.477232	−	0.826591i	−0.999660	+	0.0260931i	$0.991693\pi$
$734$	1.92776	+	3.33898i	0.0711549	+	0.123244i
$735$		0			0
$736$	2.43802	+	4.22278i	0.0898668	+	0.155654i
$737$	4.09872	+	7.09918i	0.150978	+	0.261502i
$738$		0			0
$739$	12.4245	−	21.5199i	0.457044	−	0.791623i	−0.541759	−	0.840534i	$-0.682242\pi$
$739$	12.4245	−	21.5199i	0.457044	−	0.791623i	0.998803	+	0.0489105i	$0.0155749\pi$
$740$	−4.99576	+	8.65291i	−0.183648	+	0.318087i
$741$		0			0
$742$	15.1570	+	26.2526i	0.556429	+	0.963764i
$743$	8.28209			0.303841			0.151920	−	0.988393i	$-0.451454\pi$
$743$	8.28209			0.303841			0.151920	+	0.988393i	$0.451454\pi$
$744$		0			0
$745$	−1.77776			−0.0651323
$746$	9.74993	−	16.8874i	0.356970	−	0.618291i
$747$		0			0
$748$	−25.9347			−0.948266
$749$	4.66363	−	8.07765i	0.170405	−	0.295151i
$750$		0			0
$751$	9.42933	−	16.3321i	0.344081	−	0.595966i	−0.641105	−	0.767453i	$-0.721524\pi$
$751$	9.42933	−	16.3321i	0.344081	−	0.595966i	0.985186	+	0.171487i	$0.0548571\pi$
$752$	0.368558	+	0.638361i	0.0134399	+	0.0232786i
$753$		0			0
$754$	67.7142			2.46601
$755$	−8.48220	+	14.6916i	−0.308699	+	0.534682i
$756$		0			0
$757$	−2.76509	+	4.78927i	−0.100499	+	0.174069i	−0.911890	−	0.410434i	$-0.865377\pi$
$757$	−2.76509	+	4.78927i	−0.100499	+	0.174069i	0.811391	+	0.584503i	$0.198711\pi$
$758$	−39.7180	−	68.7937i	−1.44262	−	2.49870i
$759$		0			0
$760$	12.7184	−	3.63231i	0.461344	−	0.131758i
$761$	−9.58456	−	16.6009i	−0.347440	−	0.601784i	0.638354	−	0.769743i	$-0.279616\pi$
$761$	−9.58456	−	16.6009i	−0.347440	−	0.601784i	−0.985794	+	0.167959i	$0.946282\pi$
$762$		0			0
$763$	5.25318	+	9.09877i	0.190178	+	0.329398i
$764$	−4.59678	−	7.96186i	−0.166306	−	0.288050i
$765$		0			0
$766$	23.6313	+	40.9306i	0.853833	+	1.47888i
$767$	31.7545	−	55.0003i	1.14659	−	1.98595i
$768$		0			0
$769$	9.09700	−	15.7565i	0.328046	−	0.568192i	−0.654078	−	0.756427i	$-0.726943\pi$
$769$	9.09700	−	15.7565i	0.328046	−	0.568192i	0.982124	+	0.188235i	$0.0602765\pi$
$770$	−3.15321	+	5.46152i	−0.113634	+	0.196820i
$771$		0			0
$772$	−23.2223	+	40.2223i	−0.835790	+	1.44763i
$773$	−26.9898	−	46.7476i	−0.970754	−	1.68140i	−0.693288	−	0.720660i	$-0.743839\pi$
$773$	−26.9898	−	46.7476i	−0.970754	−	1.68140i	−0.277466	−	0.960736i	$-0.589495\pi$
$774$		0			0
$775$	3.42075	+	5.92492i	0.122877	+	0.212829i
$776$	−25.9955	−	45.0256i	−0.933185	−	1.61632i
$777$		0			0
$778$	−19.1320	−	33.1376i	−0.685916	−	1.18804i
$779$	23.8111	−	6.80034i	0.853122	−	0.243647i
$780$		0			0
$781$	−6.07131	−	10.5158i	−0.217249	−	0.376286i
$782$	16.7599	−	29.0290i	0.599333	−	1.03807i
$783$		0			0
$784$	−5.21029	+	9.02449i	−0.186082	+	0.322303i
$785$	−5.12676			−0.182982
$786$		0			0
$787$	3.16620	+	5.48402i	0.112863	+	0.195484i	0.916923	−	0.399063i	$-0.130665\pi$
$787$	3.16620	+	5.48402i	0.112863	+	0.195484i	−0.804061	+	0.594547i	$0.797331\pi$
$788$	−10.4186	+	18.0456i	−0.371148	+	0.642847i
$789$		0			0
$790$	10.5621	−	18.2942i	0.375784	−	0.650877i
$791$	−45.9817			−1.63492
$792$		0			0
$793$	28.2404	−	48.9137i	1.00284	−	1.73698i
$794$	57.6579			2.04620
$795$		0			0
$796$	−73.8398			−2.61718
$797$	21.3522	+	36.9831i	0.756334	+	1.31001i	0.944708	+	0.327912i	$0.106345\pi$
$797$	21.3522	+	36.9831i	0.756334	+	1.31001i	−0.188374	+	0.982097i	$0.560322\pi$
$798$		0			0
$799$	−0.887915	+	1.53791i	−0.0314122	+	0.0544075i
$800$	−4.90426	+	8.49442i	−0.173392	+	0.300323i
$801$		0			0
$802$	4.53817	+	7.86035i	0.160248	+	0.277558i
$803$	−5.75389	−	9.96603i	−0.203050	−	0.351694i
$804$		0			0
$805$	−2.65967	−	4.60669i	−0.0937412	−	0.162365i
$806$	8.69751	+	15.0645i	0.306357	+	0.530625i
$807$		0			0
$808$	63.3448			2.22846
$809$	50.3283			1.76945			0.884724	−	0.466115i	$-0.154347\pi$
$809$	50.3283			1.76945			0.884724	+	0.466115i	$0.154347\pi$
$810$		0			0
$811$	−17.0518	−	29.5346i	−0.598770	−	1.03710i	−0.993003	−	0.118089i	$-0.962323\pi$
$811$	−17.0518	−	29.5346i	−0.598770	−	1.03710i	0.394233	−	0.919011i	$-0.371010\pi$
$812$	−37.0295	−	64.1369i	−1.29948	−	2.25077i
$813$		0			0
$814$	−9.76089			−0.342119
$815$	−9.09704			−0.318656
$816$		0			0
$817$	14.4553	+	13.9891i	0.505728	+	0.489416i
$818$	−65.2326			−2.28080
$819$		0			0
$820$	−7.68084	+	13.3036i	−0.268226	+	0.464582i
$821$	42.1908			1.47247			0.736234	−	0.676727i	$-0.236602\pi$
$821$	42.1908			1.47247			0.736234	+	0.676727i	$0.236602\pi$
$822$		0			0
$823$	−8.41204	+	14.5701i	−0.293225	+	0.507881i	−0.974571	−	0.224081i	$-0.928062\pi$
$823$	−8.41204	+	14.5701i	−0.293225	+	0.507881i	0.681345	+	0.731962i	$0.261395\pi$
$824$	3.99528	+	6.92003i	0.139182	+	0.241071i
$825$		0			0
$826$	−106.433			−3.70328
$827$	−2.28586	−	3.95922i	−0.0794871	−	0.137676i	0.823542	−	0.567256i	$-0.191995\pi$
$827$	−2.28586	−	3.95922i	−0.0794871	−	0.137676i	−0.903029	+	0.429580i	$0.858662\pi$
$828$		0			0
$829$	11.6422			0.404351			0.202175	−	0.979349i	$-0.435199\pi$
$829$	11.6422			0.404351			0.202175	+	0.979349i	$0.435199\pi$
$830$	17.4429			0.605451
$831$		0			0
$832$	−24.8297	+	43.0063i	−0.860815	+	1.49097i
$833$	−25.1048			−0.869831
$834$		0			0
$835$	−2.76907	+	4.79617i	−0.0958276	+	0.165978i
$836$	12.9567	+	12.5388i	0.448117	+	0.433664i
$837$		0			0
$838$	−4.85525	+	8.40955i	−0.167722	+	0.290503i
$839$	−7.51748	−	13.0207i	−0.259532	−	0.449523i	0.706584	−	0.707629i	$-0.250235\pi$
$839$	−7.51748	−	13.0207i	−0.259532	−	0.449523i	−0.966117	+	0.258106i	$0.916902\pi$
$840$		0			0
$841$	6.30680			0.217476
$842$	7.97166	−	13.8073i	0.274721	−	0.475831i
$843$		0			0
$844$	−2.52576	+	4.37474i	−0.0869401	+	0.150585i
$845$	3.43907	+	5.95665i	0.118308	+	0.204915i
$846$		0			0
$847$	32.4690			1.11565
$848$	−4.95578	+	8.58366i	−0.170182	+	0.294764i
$849$		0			0
$850$	67.4274			2.31274
$851$	4.11656	−	7.13010i	0.141114	−	0.244417i
$852$		0			0
$853$	−21.9253	−	37.9758i	−0.750708	−	1.30027i	−0.947480	−	0.319816i	$-0.896379\pi$
$853$	−21.9253	−	37.9758i	−0.750708	−	1.30027i	0.196771	−	0.980449i	$-0.436954\pi$
$854$	−94.6548			−3.23902
$855$		0			0
$856$	11.8555			0.405213
$857$	1.38553	+	2.39980i	0.0473287	+	0.0819757i	0.888719	−	0.458452i	$-0.151596\pi$
$857$	1.38553	+	2.39980i	0.0473287	+	0.0819757i	−0.841391	+	0.540428i	$0.818263\pi$
$858$		0			0
$859$	−20.0995	+	34.8133i	−0.685785	+	1.18781i	0.287404	+	0.957809i	$0.407208\pi$
$859$	−20.0995	+	34.8133i	−0.685785	+	1.18781i	−0.973189	+	0.230005i	$0.926126\pi$
$860$	−12.4788			−0.425523
$861$		0			0
$862$	−20.5713	+	35.6306i	−0.700662	+	1.21358i
$863$	17.8546			0.607779			0.303890	−	0.952707i	$-0.401715\pi$
$863$	17.8546			0.607779			0.303890	+	0.952707i	$0.401715\pi$
$864$		0			0
$865$	−1.20901	−	2.09407i	−0.0411077	−	0.0712006i
$866$	−19.2458	+	33.3346i	−0.653998	+	1.13276i
$867$		0			0
$868$	9.51245	−	16.4760i	0.322874	−	0.559234i
$869$	13.4677			0.456862
$870$		0			0
$871$	−17.6820	−	30.6261i	−0.599132	−	1.03773i
$872$	−6.67710	+	11.5651i	−0.226115	+	0.391643i
$873$		0			0
$874$	−22.4079	+	6.39958i	−0.757958	+	0.216469i
$875$	11.3185	−	19.6042i	0.382635	−	0.662743i
$876$		0			0
$877$	−47.6522			−1.60910			−0.804550	−	0.593884i	$-0.797594\pi$
$877$	−47.6522			−1.60910			−0.804550	+	0.593884i	$0.797594\pi$
$878$	−8.34929	+	14.4614i	−0.281775	+	0.488049i
$879$		0			0
$880$	−2.06197			−0.0695091
$881$	40.8685			1.37689			0.688447	−	0.725287i	$-0.258293\pi$
$881$	40.8685			1.37689			0.688447	+	0.725287i	$0.258293\pi$
$882$		0			0
$883$	10.7098	+	18.5500i	0.360415	+	0.624257i	0.988029	−	0.154268i	$-0.0493018\pi$
$883$	10.7098	+	18.5500i	0.360415	+	0.624257i	−0.627614	+	0.778525i	$0.715968\pi$
$884$	111.883			3.76304
$885$		0			0
$886$	2.92281	+	5.06246i	0.0981939	+	0.170077i
$887$	−11.4299	+	19.7972i	−0.383779	+	0.664725i	−0.991599	−	0.129350i	$-0.958711\pi$
$887$	−11.4299	+	19.7972i	−0.383779	+	0.664725i	0.607820	+	0.794075i	$0.292044\pi$
$888$		0			0
$889$	30.6542			1.02811
$890$	7.31542	−	12.6707i	0.245214	−	0.424722i
$891$		0			0
$892$	−83.1674			−2.78465
$893$	1.18714	−	0.339041i	0.0397261	−	0.0113456i
$894$		0			0
$895$	−12.4886			−0.417448
$896$	68.7042			2.29525
$897$		0			0
$898$	30.9629	+	53.6293i	1.03325	+	1.78963i
$899$	4.53496	+	7.85477i	0.151249	+	0.261971i
$900$		0			0
$901$	−23.8785			−0.795508
$902$	−15.0071			−0.499681
$903$		0			0
$904$	−29.2227	−	50.6153i	−0.971934	−	1.68344i
$905$	4.20833	+	7.28905i	0.139890	+	0.242296i
$906$		0			0
$907$	13.3474	+	23.1184i	0.443193	+	0.767632i	0.997924	−	0.0643969i	$-0.0205124\pi$
$907$	13.3474	+	23.1184i	0.443193	+	0.767632i	−0.554732	+	0.832029i	$0.687179\pi$
$908$	9.90804	+	17.1612i	0.328810	+	0.569515i
$909$		0			0
$910$	13.6031	−	23.5612i	0.450937	−	0.781046i
$911$	4.63769	−	8.03271i	0.153653	−	0.266135i	−0.778915	−	0.627130i	$-0.784229\pi$
$911$	4.63769	−	8.03271i	0.153653	−	0.266135i	0.932568	+	0.360995i	$0.117563\pi$
$912$		0			0
$913$	5.56034	+	9.63080i	0.184021	+	0.318733i
$914$	−7.17471			−0.237318
$915$		0			0
$916$	62.8614			2.07700
$917$	12.0519	−	20.8745i	0.397989	−	0.689338i
$918$		0			0
$919$	−14.1549			−0.466926			−0.233463	−	0.972366i	$-0.575006\pi$
$919$	−14.1549			−0.466926			−0.233463	+	0.972366i	$0.575006\pi$
$920$	3.38060	−	5.85537i	0.111455	−	0.193046i
$921$		0			0
$922$	−16.9635	+	29.3817i	−0.558664	+	0.967635i
$923$	26.1919	+	45.3656i	0.862116	+	1.49323i
$924$		0			0
$925$	16.5615			0.544539
$926$	−33.2476	+	57.5865i	−1.09258	+	1.89241i
$927$		0			0
$928$	−6.50166	+	11.2612i	−0.213428	+	0.369667i
$929$	−4.14685	−	7.18256i	−0.136054	−	0.235652i	0.789946	−	0.613177i	$-0.210109\pi$
$929$	−4.14685	−	7.18256i	−0.136054	−	0.235652i	−0.926000	+	0.377525i	$0.876775\pi$
$930$		0			0
$931$	12.5421	+	12.1376i	0.411052	+	0.397794i
$932$	−2.45018	−	4.24383i	−0.0802583	−	0.139011i
$933$		0			0
$934$	32.8395	+	56.8797i	1.07454	+	1.86116i
$935$	−2.48381	−	4.30208i	−0.0812293	−	0.140693i
$936$		0			0
$937$	17.9166	+	31.0324i	0.585310	+	1.01379i	0.994837	+	0.101488i	$0.0323603\pi$
$937$	17.9166	+	31.0324i	0.585310	+	1.01379i	−0.409527	+	0.912298i	$0.634306\pi$
$938$	−29.6329	+	51.3256i	−0.967548	+	1.67584i
$939$		0			0
$940$	−0.382939	+	0.663270i	−0.0124901	+	0.0216335i
$941$	−21.7618	+	37.6926i	−0.709416	+	1.22874i	0.255659	+	0.966767i	$0.417708\pi$
$941$	−21.7618	+	37.6926i	−0.709416	+	1.22874i	−0.965074	+	0.261977i	$0.915626\pi$
$942$		0			0
$943$	6.32910	−	10.9623i	0.206104	−	0.356982i
$944$	−17.3999	−	30.1375i	−0.566319	−	0.980893i
$945$		0			0
$946$	−6.09537	−	10.5575i	−0.198178	−	0.343254i
$947$	19.3907	+	33.5856i	0.630112	+	1.09139i	0.987528	+	0.157441i	$0.0503245\pi$
$947$	19.3907	+	33.5856i	0.630112	+	1.09139i	−0.357416	+	0.933945i	$0.616342\pi$
$948$		0			0
$949$	24.8225	+	42.9938i	0.805772	+	1.39564i
$950$	−33.6861	−	32.5996i	−1.09292	−	1.05767i
$951$		0			0
$952$	−43.8472	−	75.9455i	−1.42109	−	2.46141i
$953$	−29.7666	+	51.5572i	−0.964234	+	1.67010i	−0.252576	+	0.967577i	$0.581278\pi$
$953$	−29.7666	+	51.5572i	−0.964234	+	1.67010i	−0.711658	+	0.702526i	$0.752055\pi$
$954$		0			0
$955$	0.880484	−	1.52504i	0.0284918	−	0.0493492i
$956$	−72.1569			−2.33372
$957$		0			0
$958$	38.7798	+	67.1687i	1.25292	+	2.17012i
$959$	−30.5949	+	52.9919i	−0.987961	+	1.71120i
$960$		0			0
$961$	14.3350	−	24.8290i	0.462420	−	0.800935i
$962$	42.1088			1.35764
$963$		0			0
$964$	−3.36301	+	5.82491i	−0.108315	+	0.187608i
$965$	−8.89617			−0.286378
$966$		0			0
$967$	25.5251			0.820831			0.410416	−	0.911899i	$-0.365384\pi$
$967$	25.5251			0.820831			0.410416	+	0.911899i	$0.365384\pi$
$968$	20.6350	+	35.7409i	0.663235	+	1.14876i
$969$		0			0
$970$	10.6464	−	18.4401i	0.341834	−	0.592075i
$971$	20.7913	−	36.0116i	0.667226	−	1.15567i	−0.311451	−	0.950262i	$-0.600815\pi$
$971$	20.7913	−	36.0116i	0.667226	−	1.15567i	0.978677	−	0.205406i	$-0.0658516\pi$
$972$		0			0
$973$	21.8997	+	37.9315i	0.702073	+	1.21603i
$974$	24.0535	+	41.6619i	0.770724	+	1.33493i
$975$		0			0
$976$	−15.4743	−	26.8024i	−0.495322	−	0.857923i
$977$	7.20968	+	12.4875i	0.230658	+	0.399511i	0.958002	−	0.286762i	$-0.0925788\pi$
$977$	7.20968	+	12.4875i	0.230658	+	0.399511i	−0.727344	+	0.686273i	$0.759245\pi$
$978$		0			0
$979$	9.32788			0.298120
$980$	−10.8272			−0.345862
$981$		0			0
$982$	−5.63343	−	9.75738i	−0.179770	−	0.311371i
$983$	−21.0814	−	36.5140i	−0.672391	−	1.16462i	−0.977224	−	0.212209i	$-0.931934\pi$
$983$	−21.0814	−	36.5140i	−0.672391	−	1.16462i	0.304833	−	0.952406i	$-0.401399\pi$
$984$		0			0
$985$	−3.99124			−0.127171
$986$	89.3897			2.84675
$987$		0			0
$988$	−55.8957	−	54.0928i	−1.77828	−	1.72092i
$989$	10.2827			0.326970
$990$		0			0
$991$	−7.13801	+	12.3634i	−0.226746	+	0.392736i	−0.956842	−	0.290609i	$-0.906142\pi$
$991$	−7.13801	+	12.3634i	−0.226746	+	0.392736i	0.730095	+	0.683345i	$0.239476\pi$
$992$	−3.34041			−0.106058
$993$		0			0
$994$	43.8944	−	76.0273i	1.39224	−	2.41144i
$995$	−7.07177	−	12.2487i	−0.224190	−	0.388309i
$996$		0			0
$997$	26.5129			0.839673			0.419836	−	0.907600i	$-0.362087\pi$
$997$	26.5129			0.839673			0.419836	+	0.907600i	$0.362087\pi$
$998$	−25.3927	−	43.9814i	−0.803792	−	1.39221i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.g.c.505.3		32
3.2	odd	2		171.2.g.c.106.14	✓	32
9.4	even	3		513.2.h.c.334.14		32
9.5	odd	6		171.2.h.c.49.3	yes	32
19.7	even	3		513.2.h.c.235.14		32
57.26	odd	6		171.2.h.c.7.3	yes	32
171.121	even	3	inner	513.2.g.c.64.3		32
171.140	odd	6		171.2.g.c.121.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.14	✓	32	3.2	odd	2
171.2.g.c.121.14	yes	32	171.140	odd	6
171.2.h.c.7.3	yes	32	57.26	odd	6
171.2.h.c.49.3	yes	32	9.5	odd	6
513.2.g.c.64.3		32	171.121	even	3	inner
513.2.g.c.505.3		32	1.1	even	1	trivial
513.2.h.c.235.14		32	19.7	even	3
513.2.h.c.334.14		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)

\(f(q)\)	\(=\)	\(q+(-1.19971 - 2.07797i) q^{2} +(-1.87863 + 3.25388i) q^{4} -0.719678 q^{5} +(1.65862 - 2.87282i) q^{7} +4.21641 q^{8} +(0.863408 + 1.49547i) q^{10} +(-0.550465 + 0.953433i) q^{11} +(2.37472 - 4.11314i) q^{13} -7.95949 q^{14} +(-1.30123 - 2.25380i) q^{16} +(3.13488 - 5.42977i) q^{17} +(-4.19132 + 1.19702i) q^{19} +(1.35201 - 2.34175i) q^{20} +2.64160 q^{22} +(-1.11407 + 1.92963i) q^{23} -4.48206 q^{25} -11.3960 q^{26} +(6.23187 + 10.7939i) q^{28} -5.94195 q^{29} +(-0.763210 - 1.32192i) q^{31} +(1.09420 - 1.89520i) q^{32} -15.0438 q^{34} +(-1.19367 + 2.06750i) q^{35} -3.69507 q^{37} +(7.51575 + 7.27334i) q^{38} -3.03446 q^{40} -5.68106 q^{41} +(-2.30746 - 3.99663i) q^{43} +(-2.06824 - 3.58229i) q^{44} +5.34627 q^{46} -0.283238 q^{47} +(-2.00206 - 3.46767i) q^{49} +(5.37720 + 9.31358i) q^{50} +(8.92245 + 15.4541i) q^{52} +(-1.90426 - 3.29828i) q^{53} +(0.396157 - 0.686164i) q^{55} +(6.99344 - 12.1130i) q^{56} +(7.12864 + 12.3472i) q^{58} +13.3719 q^{59} +11.8921 q^{61} +(-1.83127 + 3.17185i) q^{62} -10.4558 q^{64} +(-1.70904 + 2.96014i) q^{65} +(3.72296 - 6.44836i) q^{67} +(11.7785 + 20.4010i) q^{68} +5.72827 q^{70} +(-5.51472 + 9.55177i) q^{71} +(-5.22640 + 9.05239i) q^{73} +(4.43302 + 7.67822i) q^{74} +(3.97897 - 15.8868i) q^{76} +(1.82603 + 3.16277i) q^{77} +(-6.11654 - 10.5942i) q^{79} +(0.936469 + 1.62201i) q^{80} +(6.81565 + 11.8050i) q^{82} +(5.05059 - 8.74788i) q^{83} +(-2.25610 + 3.90769i) q^{85} +(-5.53657 + 9.58963i) q^{86} +(-2.32099 + 4.02007i) q^{88} +(-4.23637 - 7.33760i) q^{89} +(-7.87754 - 13.6443i) q^{91} +(-4.18585 - 7.25010i) q^{92} +(0.339804 + 0.588558i) q^{94} +(3.01640 - 0.861468i) q^{95} +(-6.16532 - 10.6786i) q^{97} +(-4.80380 + 8.32042i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 17 q^{4} + 6 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} - 4 q^{13} + 2 q^{14} - 11 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} + 16 q^{22} - 5 q^{23} + 18 q^{25} + 4 q^{26} - 10 q^{28}+ \cdots - 18 q^{98}+O(q^{100}) \) 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

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