LMFDB - Embedded newform 92.2.e.a.13.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [92,2,Mod(9,92)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(92, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("92.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$92 = 2^{2} \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	92.e (of order $11$ , degree $10$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} - 9 x^{19} + 51 x^{18} - 200 x^{17} + 633 x^{16} - 1688 x^{15} + 3957 x^{14} - 8161 x^{13} + \cdots + 529$ x^20 - 9x^19 + 51x^18 - 200x^17 + 633x^16 - 1688x^15 + 3957x^14 - 8161x^13 + 14788x^12 - 23925x^11 + 35080x^10 - 43945x^9 + 57269x^8 - 57348x^7 + 52821x^6 - 34986x^5 + 26231x^4 + 96928x^3 + 49370x^2 + 8165*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.2
Root			$2.26168 + 0.664090i$ of defining polynomial
Character	$\chi$	$=$	92.13
Dual form			92.2.e.a.85.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98297 + 1.27438i) q^{3} +(-0.105327 + 0.230633i) q^{5} +(-3.93129 - 1.15433i) q^{7} +(1.06190 + 2.32523i) q^{9} +(1.21513 - 1.40234i) q^{11} +(2.00683 - 0.589258i) q^{13} +(-0.502775 + 0.323114i) q^{15} +(-0.898799 - 6.25129i) q^{17} +(-0.956723 + 6.65416i) q^{19} +(-6.32460 - 7.29897i) q^{21} +(-4.56155 + 1.48062i) q^{23} +(3.23221 + 3.73016i) q^{25} +(0.148866 - 1.03539i) q^{27} +(-0.592832 - 4.12324i) q^{29} +(-5.71804 + 3.67476i) q^{31} +(4.19668 - 1.23226i) q^{33} +(0.680298 - 0.785105i) q^{35} +(0.771131 + 1.68854i) q^{37} +(4.73043 + 1.38898i) q^{39} +(-1.82023 + 3.98575i) q^{41} +(1.87245 + 1.20335i) q^{43} -0.648122 q^{45} +13.6462 q^{47} +(8.23382 + 5.29155i) q^{49} +(6.18422 - 13.5416i) q^{51} +(7.33188 + 2.15283i) q^{53} +(0.195440 + 0.427953i) q^{55} +(-10.3771 + 11.9758i) q^{57} +(-10.1156 + 2.97021i) q^{59} +(-4.37602 + 2.81230i) q^{61} +(-1.49054 - 10.3669i) q^{63} +(-0.0754701 + 0.524906i) q^{65} +(-2.47443 - 2.85565i) q^{67} +(-10.9323 - 2.87713i) q^{69} +(-0.813338 - 0.938643i) q^{71} +(0.676249 - 4.70342i) q^{73} +(1.65573 + 11.5159i) q^{75} +(-6.39580 + 4.11033i) q^{77} +(3.53674 - 1.03848i) q^{79} +(6.63660 - 7.65905i) q^{81} +(-4.20174 - 9.20053i) q^{83} +(1.53642 + 0.451134i) q^{85} +(4.07900 - 8.93176i) q^{87} +(11.1215 + 7.14733i) q^{89} -8.56964 q^{91} -16.0218 q^{93} +(-1.43390 - 0.921513i) q^{95} +(-3.26961 + 7.15944i) q^{97} +(4.55110 + 1.33632i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 2 q^{3} + 2 q^{5} + 2 q^{7} - 4 q^{9} - 2 q^{11} + 6 q^{13} - 17 q^{15} - 9 q^{17} - 11 q^{19} - 47 q^{21} - 22 q^{23} - 16 q^{25} - 19 q^{27} - q^{29} - 13 q^{31} - 5 q^{33} + 14 q^{35} + 34 q^{37}+ \cdots - q^{99}+O(q^{100})$ 20 * q + 2 * q^3 + 2 * q^5 + 2 * q^7 - 4 * q^9 - 2 * q^11 + 6 * q^13 - 17 * q^15 - 9 * q^17 - 11 * q^19 - 47 * q^21 - 22 * q^23 - 16 * q^25 - 19 * q^27 - q^29 - 13 * q^31 - 5 * q^33 + 14 * q^35 + 34 * q^37 + 30 * q^39 + 28 * q^41 + 44 * q^43 + 78 * q^45 + 26 * q^47 + 60 * q^49 + 62 * q^51 + 14 * q^53 + 26 * q^55 + 3 * q^57 - 10 * q^59 - 56 * q^61 - 27 * q^63 - 87 * q^65 - 44 * q^67 - 51 * q^69 - 37 * q^71 - 12 * q^73 - 53 * q^75 - 47 * q^77 - 6 * q^79 - 10 * q^81 - 25 * q^83 + 8 * q^85 + 48 * q^87 + 10 * q^89 + 26 * q^91 - 14 * q^93 + 29 * q^95 - q^97 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$ .

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$		0			0
$2$		0			0
$3$	1.98297	+	1.27438i	1.14487	+	0.735764i	0.968611	−	0.248580i	$-0.0799639\pi$
$3$	1.98297	+	1.27438i	1.14487	+	0.735764i	0.176259	+	0.984344i	$0.443600\pi$
$4$		0			0
$5$	−0.105327	+	0.230633i	−0.0471035	+	0.103142i	−0.931721	−	0.363176i	$-0.881692\pi$
$5$	−0.105327	+	0.230633i	−0.0471035	+	0.103142i	0.884617	+	0.466318i	$0.154420\pi$
$6$		0			0
$7$	−3.93129	−	1.15433i	−1.48589	−	0.436297i	−0.564663	−	0.825322i	$-0.690994\pi$
$7$	−3.93129	−	1.15433i	−1.48589	−	0.436297i	−0.921227	+	0.389025i	$0.872812\pi$
$8$		0			0
$9$	1.06190	+	2.32523i	0.353966	+	0.775077i
$10$		0			0
$11$	1.21513	−	1.40234i	0.366376	−	0.422820i	−0.542390	−	0.840127i	$-0.682480\pi$
$11$	1.21513	−	1.40234i	0.366376	−	0.422820i	0.908766	+	0.417307i	$0.137026\pi$
$12$		0			0
$13$	2.00683	−	0.589258i	0.556594	−	0.163431i	0.00867553	−	0.999962i	$-0.497238\pi$
$13$	2.00683	−	0.589258i	0.556594	−	0.163431i	0.547919	+	0.836532i	$0.315420\pi$
$14$		0			0
$15$	−0.502775	+	0.323114i	−0.129816	+	0.0834276i
$16$		0			0
$17$	−0.898799	−	6.25129i	−0.217991	−	1.51616i	−0.745440	−	0.666573i	$-0.767760\pi$
$17$	−0.898799	−	6.25129i	−0.217991	−	1.51616i	0.527449	−	0.849587i	$-0.323149\pi$
$18$		0			0
$19$	−0.956723	+	6.65416i	−0.219487	+	1.52657i	0.520450	+	0.853892i	$0.325764\pi$
$19$	−0.956723	+	6.65416i	−0.219487	+	1.52657i	−0.739937	+	0.672676i	$0.765145\pi$
$20$		0			0
$21$	−6.32460	−	7.29897i	−1.38014	−	1.59277i
$22$		0			0
$23$	−4.56155	+	1.48062i	−0.951150	+	0.308730i
$23$	−4.56155	+	1.48062i	−0.951150	+	0.308730i
$24$		0			0
$25$	3.23221	+	3.73016i	0.646441	+	0.746033i
$26$		0			0
$27$	0.148866	−	1.03539i	0.0286493	−	0.199261i
$28$		0			0
$29$	−0.592832	−	4.12324i	−0.110086	−	0.765666i	−0.967833	−	0.251593i	$-0.919045\pi$
$29$	−0.592832	−	4.12324i	−0.110086	−	0.765666i	0.857747	−	0.514072i	$-0.171864\pi$
$30$		0			0
$31$	−5.71804	+	3.67476i	−1.02699	+	0.660006i	−0.941736	−	0.336353i	$-0.890806\pi$
$31$	−5.71804	+	3.67476i	−1.02699	+	0.660006i	−0.0852536	+	0.996359i	$0.527170\pi$
$32$		0			0
$33$	4.19668	−	1.23226i	0.730549	−	0.214508i
$34$		0			0
$35$	0.680298	−	0.785105i	0.114991	−	0.132707i
$36$		0			0
$37$	0.771131	+	1.68854i	0.126773	+	0.277594i	0.962367	−	0.271753i	$-0.0876035\pi$
$37$	0.771131	+	1.68854i	0.126773	+	0.277594i	−0.835594	+	0.549348i	$0.814876\pi$
$38$		0			0
$39$	4.73043	+	1.38898i	0.757475	+	0.222415i
$40$		0			0
$41$	−1.82023	+	3.98575i	−0.284272	+	0.622469i	−0.996866	−	0.0791076i	$-0.974793\pi$
$41$	−1.82023	+	3.98575i	−0.284272	+	0.622469i	0.712594	+	0.701577i	$0.247520\pi$
$42$		0			0
$43$	1.87245	+	1.20335i	0.285546	+	0.183510i	0.675571	−	0.737295i	$-0.263897\pi$
$43$	1.87245	+	1.20335i	0.285546	+	0.183510i	−0.390025	+	0.920804i	$0.627534\pi$
$44$		0			0
$45$	−0.648122			−0.0966163
$46$		0			0
$47$	13.6462			1.99050			0.995249	−	0.0973620i	$-0.0310405\pi$
$47$	13.6462			1.99050			0.995249	+	0.0973620i	$0.0310405\pi$
$48$		0			0
$49$	8.23382	+	5.29155i	1.17626	+	0.755936i
$50$		0			0
$51$	6.18422	−	13.5416i	0.865964	−	1.89620i
$52$		0			0
$53$	7.33188	+	2.15283i	1.00711	+	0.295714i	0.743371	−	0.668880i	$-0.233226\pi$
$53$	7.33188	+	2.15283i	1.00711	+	0.295714i	0.263740	+	0.964594i	$0.415044\pi$
$54$		0			0
$55$	0.195440	+	0.427953i	0.0263531	+	0.0577052i
$56$		0			0
$57$	−10.3771	+	11.9758i	−1.37448	+	1.58623i
$58$		0			0
$59$	−10.1156	+	2.97021i	−1.31694	+	0.386689i	−0.863388	−	0.504541i	$-0.831662\pi$
$59$	−10.1156	+	2.97021i	−1.31694	+	0.386689i	−0.453553	+	0.891229i	$0.649844\pi$
$60$		0			0
$61$	−4.37602	+	2.81230i	−0.560292	+	0.360078i	−0.789929	−	0.613199i	$-0.789883\pi$
$61$	−4.37602	+	2.81230i	−0.560292	+	0.360078i	0.229637	+	0.973276i	$0.426246\pi$
$62$		0			0
$63$	−1.49054	−	10.3669i	−0.187791	−	1.30611i
$64$		0			0
$65$	−0.0754701	+	0.524906i	−0.00936092	+	0.0651066i
$66$		0			0
$67$	−2.47443	−	2.85565i	−0.302300	−	0.348873i	0.584193	−	0.811615i	$-0.301411\pi$
$67$	−2.47443	−	2.85565i	−0.302300	−	0.348873i	−0.886493	+	0.462742i	$0.846866\pi$
$68$		0			0
$69$	−10.9323	−	2.87713i	−1.31610	−	0.346366i
$70$		0			0
$71$	−0.813338	−	0.938643i	−0.0965255	−	0.111396i	0.705432	−	0.708778i	$-0.250753\pi$
$71$	−0.813338	−	0.938643i	−0.0965255	−	0.111396i	−0.801957	+	0.597382i	$0.796208\pi$
$72$		0			0
$73$	0.676249	−	4.70342i	0.0791490	−	0.550493i	−0.911207	−	0.411948i	$-0.864848\pi$
$73$	0.676249	−	4.70342i	0.0791490	−	0.550493i	0.990356	−	0.138545i	$-0.0442426\pi$
$74$		0			0
$75$	1.65573	+	11.5159i	0.191188	+	1.32974i
$76$		0			0
$77$	−6.39580	+	4.11033i	−0.728869	+	0.468416i
$78$		0			0
$79$	3.53674	−	1.03848i	0.397914	−	0.116838i	−0.0766520	−	0.997058i	$-0.524423\pi$
$79$	3.53674	−	1.03848i	0.397914	−	0.116838i	0.474566	+	0.880220i	$0.342605\pi$
$80$		0			0
$81$	6.63660	−	7.65905i	0.737400	−	0.851005i
$82$		0			0
$83$	−4.20174	−	9.20053i	−0.461201	−	1.00989i	−0.987212	−	0.159411i	$-0.949040\pi$
$83$	−4.20174	−	9.20053i	−0.461201	−	1.00989i	0.526011	−	0.850478i	$-0.323687\pi$
$84$		0			0
$85$	1.53642	+	0.451134i	0.166648	+	0.0489324i
$86$		0			0
$87$	4.07900	−	8.93176i	0.437315	−	0.957586i
$88$		0			0
$89$	11.1215	+	7.14733i	1.17887	+	0.757616i	0.975179	−	0.221419i	$-0.0710688\pi$
$89$	11.1215	+	7.14733i	1.17887	+	0.757616i	0.203694	+	0.979035i	$0.434705\pi$
$90$		0			0
$91$	−8.56964			−0.898342
$92$		0			0
$93$	−16.0218			−1.66138
$94$		0			0
$95$	−1.43390	−	0.921513i	−0.147115	−	0.0945452i
$96$		0			0
$97$	−3.26961	+	7.15944i	−0.331978	+	0.726931i	−0.999850	−	0.0173456i	$-0.994478\pi$
$97$	−3.26961	+	7.15944i	−0.331978	+	0.726931i	0.667871	+	0.744277i	$0.267206\pi$
$98$		0			0
$99$	4.55110	+	1.33632i	0.457402	+	0.134305i
$100$		0			0
$101$	−4.69596	−	10.2827i	−0.467266	−	1.02317i	−0.985771	−	0.168095i	$-0.946239\pi$
$101$	−4.69596	−	10.2827i	−0.467266	−	1.02317i	0.518505	−	0.855075i	$-0.326489\pi$
$102$		0			0
$103$	−1.62818	+	1.87902i	−0.160430	+	0.185146i	−0.830273	−	0.557356i	$-0.811816\pi$
$103$	−1.62818	+	1.87902i	−0.160430	+	0.185146i	0.669844	+	0.742502i	$0.266361\pi$
$104$		0			0
$105$	2.34954	−	0.689886i	0.229291	−	0.0673260i
$106$		0			0
$107$	12.4637	−	8.00992i	1.20491	−	0.774348i	0.225111	−	0.974333i	$-0.427726\pi$
$107$	12.4637	−	8.00992i	1.20491	−	0.774348i	0.979799	+	0.199985i	$0.0640893\pi$
$108$		0			0
$109$	−0.108111	−	0.751927i	−0.0103551	−	0.0720216i	0.983989	−	0.178231i	$-0.0570376\pi$
$109$	−0.108111	−	0.751927i	−0.0103551	−	0.0720216i	−0.994344	+	0.106210i	$0.966128\pi$
$110$		0			0
$111$	−0.622710	+	4.33105i	−0.0591051	+	0.411085i
$112$		0			0
$113$	−5.42962	−	6.26611i	−0.510776	−	0.589466i	0.440522	−	0.897742i	$-0.354794\pi$
$113$	−5.42962	−	6.26611i	−0.510776	−	0.589466i	−0.951297	+	0.308276i	$0.900248\pi$
$114$		0			0
$115$	0.138974	−	1.20799i	0.0129594	−	0.112646i
$116$		0			0
$117$	3.50121	+	4.04061i	0.323687	+	0.373554i
$118$		0			0
$119$	−3.68262	+	25.6132i	−0.337585	+	2.34795i
$120$		0			0
$121$	1.07546	+	7.47999i	0.0977692	+	0.679999i
$122$		0			0
$123$	−8.68882	+	5.58397i	−0.783445	+	0.503489i
$124$		0			0
$125$	−2.41711	+	0.709729i	−0.216193	+	0.0634801i
$126$		0			0
$127$	10.6435	−	12.2832i	0.944457	−	1.08996i	−0.0513677	−	0.998680i	$-0.516358\pi$
$127$	10.6435	−	12.2832i	0.944457	−	1.08996i	0.995825	−	0.0912821i	$-0.0290965\pi$
$128$		0			0
$129$	2.17950	+	4.77243i	0.191894	+	0.420189i
$130$		0			0
$131$	3.34138	+	0.981117i	0.291938	+	0.0857206i	0.424422	−	0.905464i	$-0.360477\pi$
$131$	3.34138	+	0.981117i	0.291938	+	0.0857206i	−0.132484	+	0.991185i	$0.542295\pi$
$132$		0			0
$133$	11.4423	−	25.0551i	0.992170	−	2.17255i
$134$		0			0
$135$	0.223115	+	0.143388i	0.0192027	+	0.0123408i
$136$		0			0
$137$	−16.4760			−1.40764			−0.703820	−	0.710379i	$-0.748524\pi$
$137$	−16.4760			−1.40764			−0.703820	+	0.710379i	$0.748524\pi$
$138$		0			0
$139$	−5.23554			−0.444073			−0.222036	−	0.975038i	$-0.571270\pi$
$139$	−5.23554			−0.444073			−0.222036	+	0.975038i	$0.571270\pi$
$140$		0			0
$141$	27.0600	+	17.3904i	2.27886	+	1.46454i
$142$		0			0
$143$	1.61222	−	3.53027i	0.134821	−	0.295216i
$144$		0			0
$145$	1.01340	+	0.297560i	0.0841580	+	0.0247110i
$146$		0			0
$147$	9.58400	+	20.9860i	0.790475	+	1.73090i
$148$		0			0
$149$	0.936158	−	1.08038i	0.0766931	−	0.0885085i	−0.716106	−	0.697991i	$-0.754077\pi$
$149$	0.936158	−	1.08038i	0.0766931	−	0.0885085i	0.792799	+	0.609483i	$0.208623\pi$
$150$		0			0
$151$	0.363307	−	0.106676i	0.0295655	−	0.00868121i	−0.266916	−	0.963720i	$-0.586005\pi$
$151$	0.363307	−	0.106676i	0.0295655	−	0.00868121i	0.296482	+	0.955038i	$0.404187\pi$
$152$		0			0
$153$	13.5812	−	8.72814i	1.09798	−	0.705628i
$154$		0			0
$155$	−0.245260	−	1.70582i	−0.0196997	−	0.137015i
$156$		0			0
$157$	1.70984	−	11.8922i	0.136460	−	0.949103i	−0.800417	−	0.599444i	$-0.795388\pi$
$157$	1.70984	−	11.8922i	0.136460	−	0.949103i	0.936877	−	0.349659i	$-0.113703\pi$
$158$		0			0
$159$	11.7954	+	13.6126i	0.935435	+	1.07955i
$160$		0			0
$161$	19.6419	−	0.555191i	1.54800	−	0.0437551i
$162$		0			0
$163$	−9.12665	−	10.5327i	−0.714854	−	0.824986i	0.275824	−	0.961208i	$-0.411049\pi$
$163$	−9.12665	−	10.5327i	−0.714854	−	0.824986i	−0.990678	+	0.136223i	$0.956504\pi$
$164$		0			0
$165$	−0.157823	+	1.09768i	−0.0122865	+	0.0854546i
$166$		0			0
$167$	0.504578	+	3.50942i	0.0390455	+	0.271567i	0.999987	−	0.00518587i	$-0.00165072\pi$
$167$	0.504578	+	3.50942i	0.0390455	+	0.271567i	−0.960941	+	0.276753i	$0.910742\pi$
$168$		0			0
$169$	−7.25616	+	4.66325i	−0.558166	+	0.358711i
$170$		0			0
$171$	−16.4884	+	4.84143i	−1.26090	+	0.370233i
$172$		0			0
$173$	−12.6441	+	14.5920i	−0.961310	+	1.10941i	0.0326280	+	0.999468i	$0.489612\pi$
$173$	−12.6441	+	14.5920i	−0.961310	+	1.10941i	−0.993938	+	0.109943i	$0.964933\pi$
$174$		0			0
$175$	−8.40090	−	18.3954i	−0.635049	−	1.39056i
$176$		0			0
$177$	−23.8442	−	7.00128i	−1.79224	−	0.526249i
$178$		0			0
$179$	4.74609	−	10.3925i	0.354740	−	0.776771i	−0.645179	−	0.764031i	$-0.723217\pi$
$179$	4.74609	−	10.3925i	0.354740	−	0.776771i	0.999919	−	0.0127402i	$-0.00405544\pi$
$180$		0			0
$181$	5.55530	+	3.57017i	0.412922	+	0.265369i	0.730567	−	0.682841i	$-0.239256\pi$
$181$	5.55530	+	3.57017i	0.412922	+	0.265369i	−0.317645	+	0.948210i	$0.602892\pi$
$182$		0			0
$183$	−12.2615			−0.906394
$184$		0			0
$185$	−0.470654			−0.0346032
$186$		0			0
$187$	−9.85856	−	6.33571i	−0.720929	−	0.463313i
$188$		0			0
$189$	−1.78042	+	3.89857i	−0.129506	+	0.283580i
$190$		0			0
$191$	3.63954	+	1.06867i	0.263348	+	0.0773260i	0.410741	−	0.911752i	$-0.365270\pi$
$191$	3.63954	+	1.06867i	0.263348	+	0.0773260i	−0.147393	+	0.989078i	$0.547088\pi$
$192$		0			0
$193$	−7.36527	−	16.1277i	−0.530163	−	1.16090i	−0.965446	−	0.260602i	$-0.916079\pi$
$193$	−7.36527	−	16.1277i	−0.530163	−	1.16090i	0.435283	−	0.900294i	$-0.356648\pi$
$194$		0			0
$195$	−0.818585	+	0.944698i	−0.0586201	+	0.0676512i
$196$		0			0
$197$	−11.5068	+	3.37869i	−0.819822	+	0.240722i	−0.664640	−	0.747164i	$-0.731415\pi$
$197$	−11.5068	+	3.37869i	−0.819822	+	0.240722i	−0.155183	+	0.987886i	$0.549597\pi$
$198$		0			0
$199$	−7.24476	+	4.65593i	−0.513568	+	0.330050i	−0.771623	−	0.636080i	$-0.780555\pi$
$199$	−7.24476	+	4.65593i	−0.513568	+	0.330050i	0.258055	+	0.966130i	$0.416918\pi$
$200$		0			0
$201$	−1.26756	−	8.81604i	−0.0894064	−	0.621835i
$202$		0			0
$203$	−2.42899	+	16.8940i	−0.170481	+	1.18572i
$204$		0			0
$205$	−0.727527	−	0.839611i	−0.0508127	−	0.0586410i
$206$		0			0
$207$	−8.28667	−	9.03440i	−0.575964	−	0.627934i
$208$		0			0
$209$	8.16882	+	9.42732i	0.565049	+	0.652101i
$210$		0			0
$211$	0.458612	−	3.18971i	0.0315721	−	0.219589i	−0.967927	−	0.251231i	$-0.919165\pi$
$211$	0.458612	−	3.18971i	0.0315721	−	0.219589i	0.999499	+	0.0316421i	$0.0100737\pi$
$212$		0			0
$213$	−0.416642	−	2.89781i	−0.0285478	−	0.198554i
$214$		0			0
$215$	−0.474752	+	0.305105i	−0.0323778	+	0.0208080i
$216$		0			0
$217$	26.7212	−	7.84604i	1.81395	−	0.532624i
$218$		0			0
$219$	7.33493	−	8.46496i	0.495649	−	0.572009i
$220$		0			0
$221$	−5.48736	−	12.0156i	−0.369120	−	0.808260i
$222$		0			0
$223$	9.96439	+	2.92581i	0.667265	+	0.195927i	0.597785	−	0.801657i	$-0.296048\pi$
$223$	9.96439	+	2.92581i	0.667265	+	0.195927i	0.0694802	+	0.997583i	$0.477866\pi$
$224$		0			0
$225$	−5.24122	+	11.4767i	−0.349415	+	0.765112i
$226$		0			0
$227$	4.41116	+	2.83488i	0.292779	+	0.188158i	0.678782	−	0.734340i	$-0.262508\pi$
$227$	4.41116	+	2.83488i	0.292779	+	0.188158i	−0.386003	+	0.922498i	$0.626144\pi$
$228$		0			0
$229$	15.6825			1.03633			0.518163	−	0.855282i	$-0.326616\pi$
$229$	15.6825			1.03633			0.518163	+	0.855282i	$0.326616\pi$
$230$		0			0
$231$	−17.9208			−1.17910
$232$		0			0
$233$	−11.5443	−	7.41906i	−0.756291	−	0.486039i	0.104798	−	0.994494i	$-0.466580\pi$
$233$	−11.5443	−	7.41906i	−0.756291	−	0.486039i	−0.861089	+	0.508455i	$0.830217\pi$
$234$		0			0
$235$	−1.43731	+	3.14726i	−0.0937595	+	0.205305i
$236$		0			0
$237$	8.33669	+	2.44787i	0.541526	+	0.159006i
$238$		0			0
$239$	2.60385	+	5.70164i	0.168429	+	0.368808i	0.974959	−	0.222385i	$-0.0713842\pi$
$239$	2.60385	+	5.70164i	0.168429	+	0.368808i	−0.806530	+	0.591194i	$0.798657\pi$
$240$		0			0
$241$	−7.71902	+	8.90823i	−0.497226	+	0.573829i	−0.947782	−	0.318919i	$-0.896680\pi$
$241$	−7.71902	+	8.90823i	−0.497226	+	0.573829i	0.450556	+	0.892748i	$0.351226\pi$
$242$		0			0
$243$	19.9098	−	5.84603i	1.27721	−	0.375023i
$244$		0			0
$245$	−2.08765	+	1.34165i	−0.133375	+	0.0857149i
$246$		0			0
$247$	2.00104	+	13.9175i	0.127323	+	0.885550i
$248$		0			0
$249$	3.39303	−	23.5990i	0.215024	−	1.49553i
$250$		0			0
$251$	1.67105	+	1.92850i	0.105476	+	0.121726i	0.806033	−	0.591871i	$-0.201610\pi$
$251$	1.67105	+	1.92850i	0.105476	+	0.121726i	−0.700557	+	0.713597i	$0.747065\pi$
$252$		0			0
$253$	−3.46656	+	8.19597i	−0.217941	+	0.515276i
$254$		0			0
$255$	2.47177	+	2.85257i	0.154788	+	0.178635i
$256$		0			0
$257$	−0.0588063	+	0.409007i	−0.00366823	+	0.0255131i	−0.991573	−	0.129546i	$-0.958648\pi$
$257$	−0.0588063	+	0.409007i	−0.00366823	+	0.0255131i	0.987905	+	0.155060i	$0.0495570\pi$
$258$		0			0
$259$	−1.08240	−	7.52829i	−0.0672574	−	0.467785i
$260$		0			0
$261$	8.95795	−	5.75692i	0.554483	−	0.356345i
$262$		0			0
$263$	−8.81824	+	2.58927i	−0.543756	+	0.159661i	−0.542064	−	0.840337i	$-0.682357\pi$
$263$	−8.81824	+	2.58927i	−0.543756	+	0.159661i	−0.00169242	+	0.999999i	$0.500539\pi$
$264$		0			0
$265$	−1.26876	+	1.46422i	−0.0779391	+	0.0899465i
$266$		0			0
$267$	12.9452	+	28.3460i	0.792231	+	1.73474i
$268$		0			0
$269$	21.6606	+	6.36013i	1.32067	+	0.387784i	0.864735	−	0.502229i	$-0.167487\pi$
$269$	21.6606	+	6.36013i	1.32067	+	0.387784i	0.455936	+	0.890013i	$0.349305\pi$
$270$		0			0
$271$	−11.5194	+	25.2240i	−0.699756	+	1.53225i	0.140511	+	0.990079i	$0.455125\pi$
$271$	−11.5194	+	25.2240i	−0.699756	+	1.53225i	−0.840267	+	0.542172i	$0.817602\pi$
$272$		0			0
$273$	−16.9934	−	10.9210i	−1.02849	−	0.660968i
$274$		0			0
$275$	9.15850			0.552278
$276$		0			0
$277$	14.7388			0.885569			0.442784	−	0.896628i	$-0.353991\pi$
$277$	14.7388			0.885569			0.442784	+	0.896628i	$0.353991\pi$
$278$		0			0
$279$	−14.6166	−	9.39353i	−0.875074	−	0.562376i
$280$		0			0
$281$	6.68475	−	14.6376i	0.398779	−	0.873204i	−0.598614	−	0.801038i	$-0.704282\pi$
$281$	6.68475	−	14.6376i	0.398779	−	0.873204i	0.997393	−	0.0721659i	$-0.0229911\pi$
$282$		0			0
$283$	13.9357	+	4.09188i	0.828388	+	0.243237i	0.668325	−	0.743870i	$-0.267012\pi$
$283$	13.9357	+	4.09188i	0.828388	+	0.243237i	0.160064	+	0.987107i	$0.448830\pi$
$284$		0			0
$285$	−1.66903	−	3.65467i	−0.0988649	−	0.216484i
$286$		0			0
$287$	11.7567	−	13.5680i	0.693978	−	0.800893i
$288$		0			0
$289$	−21.9594	+	6.44785i	−1.29173	+	0.379285i
$290$		0			0
$291$	−15.6074	+	10.0303i	−0.914922	+	0.587985i
$292$		0			0
$293$	3.90734	+	27.1762i	0.228269	+	1.58765i	0.705396	+	0.708813i	$0.250769\pi$
$293$	3.90734	+	27.1762i	0.228269	+	1.58765i	−0.477127	+	0.878834i	$0.658322\pi$
$294$		0			0
$295$	0.380414	−	2.64584i	0.0221486	−	0.154047i
$296$		0			0
$297$	−1.27107	−	1.46689i	−0.0737550	−	0.0851178i
$298$		0			0
$299$	−8.28180	+	5.65928i	−0.478949	+	0.327284i
$300$		0			0
$301$	−5.97210	−	6.89217i	−0.344226	−	0.397258i
$302$		0			0
$303$	3.79213	−	26.3748i	0.217852	−	1.51519i
$304$		0			0
$305$	−0.187698	−	1.30547i	−0.0107475	−	0.0747508i
$306$		0			0
$307$	17.3606	−	11.1570i	0.990821	−	0.636762i	0.0584598	−	0.998290i	$-0.481381\pi$
$307$	17.3606	−	11.1570i	0.990821	−	0.636762i	0.932361	+	0.361528i	$0.117745\pi$
$308$		0			0
$309$	−5.62324	+	1.65113i	−0.319895	+	0.0939296i
$310$		0			0
$311$	8.96468	−	10.3458i	0.508340	−	0.586656i	−0.442333	−	0.896851i	$-0.645849\pi$
$311$	8.96468	−	10.3458i	0.508340	−	0.586656i	0.950673	+	0.310195i	$0.100394\pi$
$312$		0			0
$313$	14.0820	+	30.8353i	0.795963	+	1.74292i	0.658733	+	0.752377i	$0.271093\pi$
$313$	14.0820	+	30.8353i	0.795963	+	1.74292i	0.137231	+	0.990539i	$0.456180\pi$
$314$		0			0
$315$	2.54796	+	0.748148i	0.143561	+	0.0421533i
$316$		0			0
$317$	−5.69742	+	12.4756i	−0.319999	+	0.700700i	−0.999455	−	0.0330163i	$-0.989489\pi$
$317$	−5.69742	+	12.4756i	−0.319999	+	0.700700i	0.679456	+	0.733716i	$0.262216\pi$
$318$		0			0
$319$	−6.50253	−	4.17892i	−0.364072	−	0.233975i
$320$		0			0
$321$	34.9228			1.94920
$322$		0			0
$323$	42.4569			2.36237
$324$		0			0
$325$	8.68452	+	5.58120i	0.481730	+	0.309589i
$326$		0			0
$327$	0.743860	−	1.62883i	0.0411356	−	0.0900743i
$328$		0			0
$329$	−53.6471	−	15.7522i	−2.95766	−	0.868447i
$330$		0			0
$331$	−4.61740	−	10.1107i	−0.253796	−	0.555735i	0.739255	−	0.673426i	$-0.235178\pi$
$331$	−4.61740	−	10.1107i	−0.253796	−	0.555735i	−0.993050	+	0.117691i	$0.962451\pi$
$332$		0			0
$333$	−3.10738	+	3.58611i	−0.170284	+	0.196518i
$334$		0			0
$335$	0.919231	−	0.269911i	0.0502229	−	0.0147468i
$336$		0			0
$337$	−5.98904	+	3.84892i	−0.326244	+	0.209664i	−0.693502	−	0.720455i	$-0.743933\pi$
$337$	−5.98904	+	3.84892i	−0.326244	+	0.209664i	0.367258	+	0.930119i	$0.380297\pi$
$338$		0			0
$339$	−2.78138	−	19.3449i	−0.151064	−	1.05067i
$340$		0			0
$341$	−1.79492	+	12.4839i	−0.0972002	+	0.676042i
$342$		0			0
$343$	−7.47940	−	8.63169i	−0.403850	−	0.466067i
$344$		0			0
$345$	1.81503	−	2.21832i	0.0977177	−	0.119430i
$346$		0			0
$347$	−14.5262	−	16.7641i	−0.779805	−	0.899943i	0.217290	−	0.976107i	$-0.430278\pi$
$347$	−14.5262	−	16.7641i	−0.779805	−	0.899943i	−0.997095	+	0.0761639i	$0.975733\pi$
$348$		0			0
$349$	3.20623	−	22.2998i	0.171625	−	1.19368i	−0.703825	−	0.710373i	$-0.748526\pi$
$349$	3.20623	−	22.2998i	0.171625	−	1.19368i	0.875450	−	0.483308i	$-0.160565\pi$
$350$		0			0
$351$	−0.311362	−	2.16557i	−0.0166193	−	0.115589i
$352$		0			0
$353$	−0.0989141	+	0.0635682i	−0.00526467	+	0.00338340i	−0.543271	−	0.839558i	$-0.682814\pi$
$353$	−0.0989141	+	0.0635682i	−0.00526467	+	0.00338340i	0.538006	+	0.842941i	$0.319178\pi$
$354$		0			0
$355$	0.302148	−	0.0887188i	0.0160364	−	0.00470871i
$356$		0			0
$357$	−39.9434	+	46.0972i	−2.11403	+	2.43972i
$358$		0			0
$359$	−7.22273	−	15.8156i	−0.381201	−	0.834714i	−0.998835	−	0.0482488i	$-0.984636\pi$
$359$	−7.22273	−	15.8156i	−0.381201	−	0.834714i	0.617634	−	0.786466i	$-0.288091\pi$
$360$		0			0
$361$	−25.1321	−	7.37945i	−1.32274	−	0.388392i
$362$		0			0
$363$	−7.39974	+	16.2032i	−0.388386	+	0.850446i
$364$		0			0
$365$	1.01354	+	0.651361i	0.0530510	+	0.0340938i
$366$		0			0
$367$	−20.0955			−1.04898			−0.524488	−	0.851418i	$-0.675743\pi$
$367$	−20.0955			−1.04898			−0.524488	+	0.851418i	$0.675743\pi$
$368$		0			0
$369$	−11.2007			−0.583084
$370$		0			0
$371$	−26.3387	−	16.9268i	−1.36744	−	0.878798i
$372$		0			0
$373$	−10.4200	+	22.8167i	−0.539528	+	1.18140i	0.421974	+	0.906608i	$0.361337\pi$
$373$	−10.4200	+	22.8167i	−0.539528	+	1.18140i	−0.961503	+	0.274795i	$0.911390\pi$
$374$		0			0
$375$	−5.69754	−	1.67295i	−0.294220	−	0.0863907i
$376$		0			0
$377$	−3.61936	−	7.92530i	−0.186407	−	0.408174i
$378$		0			0
$379$	13.4789	−	15.5555i	0.692366	−	0.799033i	−0.295334	−	0.955394i	$-0.595431\pi$
$379$	13.4789	−	15.5555i	0.692366	−	0.799033i	0.987700	+	0.156361i	$0.0499764\pi$
$380$		0			0
$381$	36.7593	−	10.7935i	1.88324	−	0.552968i
$382$		0			0
$383$	−7.26607	+	4.66962i	−0.371279	+	0.238606i	−0.712953	−	0.701212i	$-0.752643\pi$
$383$	−7.26607	+	4.66962i	−0.371279	+	0.238606i	0.341674	+	0.939819i	$0.389006\pi$
$384$		0			0
$385$	−0.274331	−	1.90801i	−0.0139812	−	0.0972413i
$386$		0			0
$387$	−0.809719	+	5.63172i	−0.0411603	+	0.286276i
$388$		0			0
$389$	3.32783	+	3.84052i	0.168728	+	0.194722i	0.833816	−	0.552043i	$-0.186151\pi$
$389$	3.32783	+	3.84052i	0.168728	+	0.194722i	−0.665088	+	0.746765i	$0.731606\pi$
$390$		0			0
$391$	13.3557	+	27.1848i	0.675426	+	1.37479i
$392$		0			0
$393$	5.37555	+	6.20372i	0.271161	+	0.312936i
$394$		0			0
$395$	−0.133005	+	0.925070i	−0.00669221	+	0.0465453i
$396$		0			0
$397$	−3.24076	−	22.5400i	−0.162649	−	1.13125i	−0.893614	−	0.448836i	$-0.851839\pi$
$397$	−3.24076	−	22.5400i	−0.162649	−	1.13125i	0.730965	−	0.682415i	$-0.239070\pi$
$398$		0			0
$399$	54.6194	−	35.1018i	2.73439	−	1.75729i
$400$		0			0
$401$	−3.39941	+	0.998156i	−0.169758	+	0.0498456i	−0.365507	−	0.930809i	$-0.619104\pi$
$401$	−3.39941	+	0.998156i	−0.169758	+	0.0498456i	0.195749	+	0.980654i	$0.437286\pi$
$402$		0			0
$403$	−9.30974	+	10.7440i	−0.463751	+	0.535197i
$404$		0			0
$405$	1.06742	+	2.33732i	0.0530405	+	0.116143i
$406$		0			0
$407$	3.30493	+	0.970414i	0.163819	+	0.0481016i
$408$		0			0
$409$	−9.54188	+	20.8938i	−0.471815	+	1.03313i	0.512818	+	0.858497i	$0.328602\pi$
$409$	−9.54188	+	20.8938i	−0.471815	+	1.03313i	−0.984633	+	0.174634i	$0.944126\pi$
$410$		0			0
$411$	−32.6715	−	20.9967i	−1.61157	−	1.03569i
$412$		0			0
$413$	43.1961			2.12554
$414$		0			0
$415$	2.56450			0.125886
$416$		0			0
$417$	−10.3819	−	6.67207i	−0.508406	−	0.326733i
$418$		0			0
$419$	−8.52270	+	18.6621i	−0.416361	+	0.911703i	0.578985	+	0.815338i	$0.303449\pi$
$419$	−8.52270	+	18.6621i	−0.416361	+	0.911703i	−0.995346	+	0.0963651i	$0.969278\pi$
$420$		0			0
$421$	−5.28793	−	1.55268i	−0.257718	−	0.0756728i	0.150321	−	0.988637i	$-0.451969\pi$
$421$	−5.28793	−	1.55268i	−0.257718	−	0.0756728i	−0.408039	+	0.912964i	$0.633787\pi$
$422$		0			0
$423$	14.4908	+	31.7305i	0.704568	+	1.54279i
$424$		0			0
$425$	20.4132	−	23.5581i	0.990187	−	1.14274i
$426$		0			0
$427$	20.4497	−	6.00459i	0.989633	−	0.290582i
$428$		0			0
$429$	7.69591	−	4.94586i	0.371562	−	0.238788i
$430$		0			0
$431$	1.96921	+	13.6962i	0.0948537	+	0.659722i	0.980668	+	0.195681i	$0.0626918\pi$
$431$	1.96921	+	13.6962i	0.0948537	+	0.659722i	−0.885814	+	0.464041i	$0.846399\pi$
$432$		0			0
$433$	−2.73014	+	18.9885i	−0.131202	+	0.912530i	0.812789	+	0.582558i	$0.197948\pi$
$433$	−2.73014	+	18.9885i	−0.131202	+	0.912530i	−0.943991	+	0.329972i	$0.892961\pi$
$434$		0			0
$435$	1.63033	+	1.88151i	0.0781685	+	0.0902113i
$436$		0			0
$437$	−5.48811	−	31.7698i	−0.262532	−	1.51976i
$438$		0			0
$439$	23.7272	+	27.3827i	1.13244	+	1.30690i	0.945901	+	0.324455i	$0.105181\pi$
$439$	23.7272	+	27.3827i	1.13244	+	1.30690i	0.186536	+	0.982448i	$0.440274\pi$
$440$		0			0
$441$	−3.56061	+	24.7646i	−0.169553	+	1.17927i
$442$		0			0
$443$	−2.26323	−	15.7411i	−0.107529	−	0.747883i	−0.970233	−	0.242173i	$-0.922140\pi$
$443$	−2.26323	−	15.7411i	−0.107529	−	0.747883i	0.862704	−	0.505710i	$-0.168769\pi$
$444$		0			0
$445$	−2.81980	+	1.81218i	−0.133671	+	0.0859054i
$446$		0			0
$447$	3.23320	−	0.949353i	0.152925	−	0.0449028i
$448$		0			0
$449$	13.1586	−	15.1859i	0.620994	−	0.716665i	−0.354901	−	0.934904i	$-0.615486\pi$
$449$	13.1586	−	15.1859i	0.620994	−	0.716665i	0.975895	+	0.218238i	$0.0700311\pi$
$450$		0			0
$451$	3.37754	+	7.39578i	0.159042	+	0.348253i
$452$		0			0
$453$	0.856374	+	0.251454i	0.0402360	+	0.0118143i
$454$		0			0
$455$	0.902612	−	1.97644i	0.0423151	−	0.0926571i
$456$		0			0
$457$	7.12001	+	4.57575i	0.333060	+	0.214045i	0.696472	−	0.717584i	$-0.254752\pi$
$457$	7.12001	+	4.57575i	0.333060	+	0.214045i	−0.363412	+	0.931628i	$0.618388\pi$
$458$		0			0
$459$	−6.60631			−0.308356
$460$		0			0
$461$	5.29967			0.246830			0.123415	−	0.992355i	$-0.460615\pi$
$461$	5.29967			0.246830			0.123415	+	0.992355i	$0.460615\pi$
$462$		0			0
$463$	17.5549	+	11.2819i	0.815848	+	0.524313i	0.880752	−	0.473578i	$-0.157038\pi$
$463$	17.5549	+	11.2819i	0.815848	+	0.524313i	−0.0649042	+	0.997891i	$0.520674\pi$
$464$		0			0
$465$	1.68752	−	3.69515i	0.0782568	−	0.171358i
$466$		0			0
$467$	−17.2389	−	5.06180i	−0.797722	−	0.234232i	−0.142625	−	0.989777i	$-0.545554\pi$
$467$	−17.2389	−	5.06180i	−0.797722	−	0.234232i	−0.655097	+	0.755544i	$0.727372\pi$
$468$		0			0
$469$	6.43135	+	14.0827i	0.296972	+	0.650279i
$470$		0			0
$471$	18.5458	−	21.4030i	0.854545	−	0.986198i
$472$		0			0
$473$	3.96278	−	1.16358i	0.182209	−	0.0535013i
$474$		0			0
$475$	−27.9134	+	17.9389i	−1.28076	+	0.823092i
$476$		0			0
$477$	2.77986	+	19.3344i	0.127281	+	0.885261i
$478$		0			0
$479$	1.48271	−	10.3125i	0.0677468	−	0.471189i	−0.927501	−	0.373819i	$-0.878048\pi$
$479$	1.48271	−	10.3125i	0.0677468	−	0.471189i	0.995248	−	0.0973698i	$-0.0310429\pi$
$480$		0			0
$481$	2.54251	+	2.93422i	0.115929	+	0.133789i
$482$		0			0
$483$	39.6570	+	23.9304i	1.80445	+	1.08887i
$484$		0			0
$485$	−1.30683	−	1.50816i	−0.0593400	−	0.0684821i
$486$		0			0
$487$	1.74332	−	12.1251i	0.0789974	−	0.549439i	−0.911435	−	0.411443i	$-0.865025\pi$
$487$	1.74332	−	12.1251i	0.0789974	−	0.549439i	0.990433	−	0.137996i	$-0.0440661\pi$
$488$		0			0
$489$	−4.67523	−	32.5169i	−0.211421	−	1.47047i
$490$		0			0
$491$	−32.7547	+	21.0501i	−1.47820	+	0.949979i	−0.480879	+	0.876787i	$0.659682\pi$
$491$	−32.7547	+	21.0501i	−1.47820	+	0.949979i	−0.997318	+	0.0731926i	$0.976681\pi$
$492$		0			0
$493$	−25.2427	+	7.41192i	−1.13687	+	0.333816i
$494$		0			0
$495$	−0.787553	+	0.908884i	−0.0353979	+	0.0408513i
$496$		0			0
$497$	2.11397	+	4.62894i	0.0948244	+	0.207636i
$498$		0			0
$499$	−14.5673	−	4.27736i	−0.652124	−	0.191481i	−0.0610959	−	0.998132i	$-0.519460\pi$
$499$	−14.5673	−	4.27736i	−0.652124	−	0.191481i	−0.591028	+	0.806651i	$0.701278\pi$
$500$		0			0
$501$	−3.47177	+	7.60211i	−0.155107	+	0.339637i
$502$		0			0
$503$	−17.3335	−	11.1396i	−0.772864	−	0.496689i	0.0937945	−	0.995592i	$-0.470100\pi$
$503$	−17.3335	−	11.1396i	−0.772864	−	0.496689i	−0.866658	+	0.498902i	$0.833737\pi$
$504$		0			0
$505$	2.86615			0.127542
$506$		0			0
$507$	−20.3315			−0.902955
$508$		0			0
$509$	−27.5633	−	17.7139i	−1.22172	−	0.785154i	−0.239141	−	0.970985i	$-0.576866\pi$
$509$	−27.5633	−	17.7139i	−1.22172	−	0.785154i	−0.982582	+	0.185831i	$0.940502\pi$
$510$		0			0
$511$	−8.08784	+	17.7099i	−0.357785	+	0.783440i
$512$		0			0
$513$	6.74721	+	1.98116i	0.297897	+	0.0874704i
$514$		0			0
$515$	−0.261874	−	0.573425i	−0.0115396	−	0.0252681i
$516$		0			0
$517$	16.5819	−	19.1365i	0.729270	−	0.841623i
$518$		0			0
$519$	−43.6686	+	12.8223i	−1.91684	+	0.562835i
$520$		0			0
$521$	29.0617	−	18.6768i	1.27322	−	0.818247i	0.283182	−	0.959066i	$-0.408610\pi$
$521$	29.0617	−	18.6768i	1.27322	−	0.818247i	0.990035	+	0.140819i	$0.0449737\pi$
$522$		0			0
$523$	3.25825	+	22.6616i	0.142473	+	0.990924i	0.928129	+	0.372260i	$0.121417\pi$
$523$	3.25825	+	22.6616i	0.142473	+	0.990924i	−0.785655	+	0.618665i	$0.787674\pi$
$524$		0			0
$525$	6.78397	−	47.1836i	0.296077	−	2.05926i
$526$		0			0
$527$	28.1113	+	32.4422i	1.22455	+	1.41320i
$528$		0			0
$529$	18.6155	−	13.5078i	0.809372	−	0.587297i
$530$		0			0
$531$	−17.6482	−	20.3671i	−0.765865	−	0.883855i
$532$		0			0
$533$	−1.30426	+	9.07130i	−0.0564936	+	0.392922i
$534$		0			0
$535$	0.534596	+	3.71820i	0.0231126	+	0.160752i
$536$		0			0
$537$	22.6554	−	14.5597i	0.977651	−	0.628298i
$538$		0			0
$539$	17.4257	−	5.11665i	0.750578	−	0.220390i
$540$		0			0
$541$	−16.7348	+	19.3130i	−0.719485	+	0.830330i	−0.991245	−	0.132035i	$-0.957849\pi$
$541$	−16.7348	+	19.3130i	−0.719485	+	0.830330i	0.271760	+	0.962365i	$0.412394\pi$
$542$		0			0
$543$	6.46625	+	14.1591i	0.277494	+	0.607626i
$544$		0			0
$545$	0.184806	+	0.0542641i	0.00791624	+	0.00232442i
$546$		0			0
$547$	15.0121	−	32.8719i	0.641872	−	1.40550i	−0.256620	−	0.966512i	$-0.582609\pi$
$547$	15.0121	−	32.8719i	0.641872	−	1.40550i	0.898492	−	0.438990i	$-0.144664\pi$
$548$		0			0
$549$	−11.1861	−	7.18888i	−0.477412	−	0.306814i
$550$		0			0
$551$	28.0038			1.19300
$552$		0			0
$553$	−15.1027			−0.642233
$554$		0			0
$555$	−0.933295	−	0.599793i	−0.0396162	−	0.0254598i
$556$		0			0
$557$	4.55328	−	9.97029i	0.192929	−	0.422455i	−0.788303	−	0.615287i	$-0.789040\pi$
$557$	4.55328	−	9.97029i	0.192929	−	0.422455i	0.981232	+	0.192832i	$0.0617673\pi$
$558$		0			0
$559$	4.46678	+	1.31156i	0.188925	+	0.0554733i
$560$		0			0
$561$	−11.4752	−	25.1271i	−0.484482	−	1.06087i
$562$		0			0
$563$	−22.6790	+	26.1730i	−0.955806	+	1.10306i	0.0387911	+	0.999247i	$0.487649\pi$
$563$	−22.6790	+	26.1730i	−0.955806	+	1.10306i	−0.994597	+	0.103811i	$0.966896\pi$
$564$		0			0
$565$	2.01706	−	0.592262i	0.0848583	−	0.0249166i
$566$		0			0
$567$	−34.9315	+	22.4491i	−1.46699	+	0.942775i
$568$		0			0
$569$	3.29710	+	22.9318i	0.138222	+	0.961353i	0.934383	+	0.356269i	$0.115951\pi$
$569$	3.29710	+	22.9318i	0.138222	+	0.961353i	−0.796162	+	0.605084i	$0.793140\pi$
$570$		0			0
$571$	0.681807	−	4.74207i	0.0285327	−	0.198450i	−0.970569	−	0.240823i	$-0.922583\pi$
$571$	0.681807	−	4.74207i	0.0285327	−	0.198450i	0.999102	+	0.0423732i	$0.0134918\pi$
$572$		0			0
$573$	5.85523	+	6.75730i	0.244606	+	0.282290i
$574$		0			0
$575$	−20.2668	−	12.2297i	−0.845185	−	0.510013i
$576$		0			0
$577$	−2.31471	−	2.67131i	−0.0963624	−	0.111208i	0.705520	−	0.708690i	$-0.250713\pi$
$577$	−2.31471	−	2.67131i	−0.0963624	−	0.111208i	−0.801882	+	0.597482i	$0.796168\pi$
$578$		0			0
$579$	5.94767	−	41.3669i	0.247177	−	1.71915i
$580$		0			0
$581$	5.89781	+	41.0202i	0.244682	+	1.70180i
$582$		0			0
$583$	11.9282	−	7.66578i	0.494015	−	0.317484i
$584$		0			0
$585$	−1.30067	+	0.381911i	−0.0537761	+	0.0157901i
$586$		0			0
$587$	−5.29262	+	6.10801i	−0.218450	+	0.252105i	−0.854388	−	0.519635i	$-0.826068\pi$
$587$	−5.29262	+	6.10801i	−0.218450	+	0.252105i	0.635938	+	0.771740i	$0.280613\pi$
$588$		0			0
$589$	−18.9818	−	41.5644i	−0.782133	−	1.71263i
$590$		0			0
$591$	−27.1233	−	7.96413i	−1.11570	−	0.327601i
$592$		0			0
$593$	−7.38894	+	16.1795i	−0.303427	+	0.664413i	−0.998513	−	0.0545138i	$-0.982639\pi$
$593$	−7.38894	+	16.1795i	−0.303427	+	0.664413i	0.695086	+	0.718927i	$0.255366\pi$
$594$		0			0
$595$	−5.51937	−	3.54708i	−0.226272	−	0.145416i
$596$		0			0
$597$	−20.2996			−0.830807
$598$		0			0
$599$	−23.0324			−0.941079			−0.470540	−	0.882379i	$-0.655941\pi$
$599$	−23.0324			−0.941079			−0.470540	+	0.882379i	$0.655941\pi$
$600$		0			0
$601$	−24.4283	−	15.6991i	−0.996451	−	0.640380i	−0.0625985	−	0.998039i	$-0.519939\pi$
$601$	−24.4283	−	15.6991i	−0.996451	−	0.640380i	−0.933852	+	0.357659i	$0.883575\pi$
$602$		0			0
$603$	4.01244	−	8.78603i	0.163399	−	0.357795i
$604$		0			0
$605$	−1.83841	−	0.539806i	−0.0747420	−	0.0219462i
$606$		0			0
$607$	−5.96499	−	13.0615i	−0.242111	−	0.530150i	0.749097	−	0.662460i	$-0.230488\pi$
$607$	−5.96499	−	13.0615i	−0.242111	−	0.530150i	−0.991208	+	0.132310i	$0.957760\pi$
$608$		0			0
$609$	−26.3460	+	30.4049i	−1.06759	+	1.23207i
$610$		0			0
$611$	27.3855	−	8.04112i	1.10790	−	0.325309i
$612$		0			0
$613$	35.1140	−	22.5664i	1.41824	−	0.911448i	0.418245	−	0.908334i	$-0.362645\pi$
$613$	35.1140	−	22.5664i	1.41824	−	0.911448i	0.999995	−	0.00311388i	$-0.000991180\pi$
$614$		0			0
$615$	−0.372684	−	2.59207i	−0.0150281	−	0.104522i
$616$		0			0
$617$	−2.90999	+	20.2394i	−0.117152	+	0.814807i	0.843516	+	0.537105i	$0.180482\pi$
$617$	−2.90999	+	20.2394i	−0.117152	+	0.814807i	−0.960667	+	0.277703i	$0.910427\pi$
$618$		0			0
$619$	25.9815	+	29.9842i	1.04428	+	1.20517i	0.978267	+	0.207349i	$0.0664837\pi$
$619$	25.9815	+	29.9842i	1.04428	+	1.20517i	0.0660169	+	0.997819i	$0.478971\pi$
$620$		0			0
$621$	0.853951	+	4.94339i	0.0342679	+	0.198372i
$622$		0			0
$623$	−35.4714	−	40.9361i	−1.42113	−	1.64007i
$624$		0			0
$625$	−3.42123	+	23.7952i	−0.136849	+	0.951806i
$626$		0			0
$627$	4.18457	+	29.1043i	0.167116	+	1.16231i
$628$		0			0
$629$	9.86246	−	6.33822i	0.393242	−	0.252721i
$630$		0			0
$631$	3.90579	−	1.14684i	0.155487	−	0.0456551i	−0.203063	−	0.979166i	$-0.565090\pi$
$631$	3.90579	−	1.14684i	0.155487	−	0.0456551i	0.358550	+	0.933511i	$0.383271\pi$
$632$		0			0
$633$	4.97432	−	5.74068i	0.197712	−	0.228171i
$634$		0			0
$635$	1.71188	+	3.74850i	0.0679339	+	0.148755i
$636$		0			0
$637$	19.6420	+	5.76740i	0.778243	+	0.228513i
$638$		0			0
$639$	1.31888	−	2.88794i	0.0521740	−	0.114245i
$640$		0			0
$641$	41.7239	+	26.8143i	1.64800	+	1.05910i	0.932937	+	0.360038i	$0.117236\pi$
$641$	41.7239	+	26.8143i	1.64800	+	1.05910i	0.715059	+	0.699064i	$0.246400\pi$
$642$		0			0
$643$	−40.9629			−1.61542			−0.807711	−	0.589579i	$-0.799294\pi$
$643$	−40.9629			−1.61542			−0.807711	+	0.589579i	$0.799294\pi$
$644$		0			0
$645$	−1.33024			−0.0523782
$646$		0			0
$647$	−14.4760	−	9.30313i	−0.569108	−	0.365744i	0.224219	−	0.974539i	$-0.428017\pi$
$647$	−14.4760	−	9.30313i	−0.569108	−	0.365744i	−0.793328	+	0.608795i	$0.791653\pi$
$648$		0			0
$649$	−8.12656	+	17.7947i	−0.318995	+	0.698502i
$650$		0			0
$651$	62.9862	+	18.4944i	2.46863	+	0.724854i
$652$		0			0
$653$	−5.54824	−	12.1490i	−0.217119	−	0.475425i	0.769463	−	0.638692i	$-0.220524\pi$
$653$	−5.54824	−	12.1490i	−0.217119	−	0.475425i	−0.986582	+	0.163267i	$0.947797\pi$
$654$		0			0
$655$	−0.578215	+	0.667295i	−0.0225927	+	0.0260734i
$656$		0			0
$657$	11.6546	−	3.42211i	0.454691	−	0.133509i
$658$		0			0
$659$	20.7936	−	13.3633i	0.810006	−	0.520559i	−0.0688612	−	0.997626i	$-0.521937\pi$
$659$	20.7936	−	13.3633i	0.810006	−	0.520559i	0.878867	+	0.477067i	$0.158300\pi$
$660$		0			0
$661$	−0.145017	−	1.00862i	−0.00564051	−	0.0392306i	0.986807	−	0.161902i	$-0.0517629\pi$
$661$	−0.145017	−	1.00862i	−0.00564051	−	0.0392306i	−0.992447	+	0.122672i	$0.960854\pi$
$662$		0			0
$663$	4.43120	−	30.8197i	0.172094	−	1.19694i
$664$		0			0
$665$	4.57336	+	5.27794i	0.177347	+	0.204670i
$666$		0			0
$667$	8.80916	+	17.9306i	0.341092	+	0.694276i
$668$		0			0
$669$	16.0305	+	18.5002i	0.619776	+	0.715260i
$670$		0			0
$671$	−1.37365	+	9.55396i	−0.0530292	+	0.368826i
$672$		0			0
$673$	−0.119569	−	0.831623i	−0.00460906	−	0.0320567i	0.987387	−	0.158325i	$-0.0506092\pi$
$673$	−0.119569	−	0.831623i	−0.00460906	−	0.0320567i	−0.991996	+	0.126268i	$0.959700\pi$
$674$		0			0
$675$	4.34333	−	2.79129i	0.167175	−	0.107437i
$676$		0			0
$677$	−16.8545	+	4.94892i	−0.647771	+	0.190203i	−0.589081	−	0.808074i	$-0.700510\pi$
$677$	−16.8545	+	4.94892i	−0.647771	+	0.190203i	−0.0586892	+	0.998276i	$0.518692\pi$
$678$		0			0
$679$	21.1182	−	24.3717i	0.810441	−	0.935299i
$680$		0			0
$681$	5.13451	+	11.2430i	0.196755	+	0.430833i
$682$		0			0
$683$	22.0946	+	6.48756i	0.845427	+	0.248240i	0.675631	−	0.737240i	$-0.263871\pi$
$683$	22.0946	+	6.48756i	0.845427	+	0.248240i	0.169795	+	0.985479i	$0.445689\pi$
$684$		0			0
$685$	1.73536	−	3.79991i	0.0663048	−	0.145187i
$686$		0			0
$687$	31.0979	+	19.9854i	1.18646	+	0.762492i
$688$		0			0
$689$	15.9824			0.608881
$690$		0			0
$691$	−3.15260			−0.119931			−0.0599654	−	0.998200i	$-0.519099\pi$
$691$	−3.15260			−0.119931			−0.0599654	+	0.998200i	$0.519099\pi$
$692$		0			0
$693$	−16.3491	−	10.5070i	−0.621053	−	0.399126i
$694$		0			0
$695$	0.551442	−	1.20749i	0.0209174	−	0.0458027i
$696$		0			0
$697$	26.5521	+	7.79639i	1.00573	+	0.295309i
$698$		0			0
$699$	−13.4373	−	29.4236i	−0.508246	−	1.11290i
$700$		0			0
$701$	−9.65715	+	11.1450i	−0.364746	+	0.420939i	−0.908224	−	0.418484i	$-0.862562\pi$
$701$	−9.65715	+	11.1450i	−0.364746	+	0.420939i	0.543478	+	0.839423i	$0.317107\pi$
$702$		0			0
$703$	−11.9736	+	3.51576i	−0.451592	+	0.132599i
$704$		0			0
$705$	−6.86095	+	4.40926i	−0.258398	+	0.166062i
$706$		0			0
$707$	6.59153	+	45.8451i	0.247900	+	1.72418i
$708$		0			0
$709$	7.14161	−	49.6710i	0.268209	−	1.86543i	−0.197236	−	0.980356i	$-0.563196\pi$
$709$	7.14161	−	49.6710i	0.268209	−	1.86543i	0.465444	−	0.885077i	$-0.345894\pi$
$710$		0			0
$711$	6.17036	+	7.12098i	0.231407	+	0.267058i
$712$		0			0
$713$	20.6422	−	25.2288i	0.773057	−	0.944827i
$714$		0			0
$715$	0.644389	+	0.743664i	0.0240988	+	0.0278115i
$716$		0			0
$717$	−2.10269	+	14.6245i	−0.0785263	+	0.546162i
$718$		0			0
$719$	1.87983	+	13.0745i	0.0701058	+	0.487597i	0.994380	+	0.105868i	$0.0337621\pi$
$719$	1.87983	+	13.0745i	0.0701058	+	0.487597i	−0.924274	+	0.381729i	$0.875329\pi$
$720$		0			0
$721$	8.56989	−	5.50753i	0.319159	−	0.205111i
$722$		0			0
$723$	−26.6591	+	7.82782i	−0.991463	+	0.291120i
$724$		0			0
$725$	13.4642	−	15.5385i	0.500048	−	0.577086i
$726$		0			0
$727$	10.0155	+	21.9308i	0.371454	+	0.813370i	0.999384	+	0.0351003i	$0.0111751\pi$
$727$	10.0155	+	21.9308i	0.371454	+	0.813370i	−0.627930	+	0.778270i	$0.716098\pi$
$728$		0			0
$729$	17.7590	+	5.21452i	0.657742	+	0.193131i
$730$		0			0
$731$	5.83954	−	12.7868i	0.215983	−	0.472937i
$732$		0			0
$733$	−13.9247	−	8.94889i	−0.514322	−	0.330535i	0.257600	−	0.966252i	$-0.417068\pi$
$733$	−13.9247	−	8.94889i	−0.514322	−	0.330535i	−0.771922	+	0.635717i	$0.780705\pi$
$734$		0			0
$735$	−5.84953			−0.215763
$736$		0			0
$737$	−7.01133			−0.258266
$738$		0			0
$739$	36.5060	+	23.4610i	1.34290	+	0.863027i	0.997161	−	0.0753055i	$-0.0239932\pi$
$739$	36.5060	+	23.4610i	1.34290	+	0.863027i	0.345735	+	0.938332i	$0.387630\pi$
$740$		0			0
$741$	−13.7682	+	30.1482i	−0.505787	+	1.10752i
$742$		0			0
$743$	−9.85124	−	2.89259i	−0.361407	−	0.106119i	0.0959876	−	0.995383i	$-0.469399\pi$
$743$	−9.85124	−	2.89259i	−0.361407	−	0.106119i	−0.457395	+	0.889264i	$0.651217\pi$
$744$		0			0
$745$	0.150570	+	0.329703i	0.00551646	+	0.0120794i
$746$		0			0
$747$	16.9315	−	19.5400i	0.619492	−	0.714932i
$748$		0			0
$749$	−58.2445	+	17.1021i	−2.12821	+	0.624898i
$750$		0			0
$751$	−9.19040	+	5.90631i	−0.335362	+	0.215524i	−0.697473	−	0.716611i	$-0.745692\pi$
$751$	−9.19040	+	5.90631i	−0.335362	+	0.215524i	0.362111	+	0.932135i	$0.382056\pi$
$752$		0			0
$753$	0.856016	+	5.95372i	0.0311949	+	0.216966i
$754$		0			0
$755$	−0.0136627	+	0.0950265i	−0.000497238	+	0.00345837i
$756$		0			0
$757$	−34.9495	−	40.3339i	−1.27026	−	1.46596i	−0.819242	−	0.573448i	$-0.805605\pi$
$757$	−34.9495	−	40.3339i	−1.27026	−	1.46596i	−0.451021	−	0.892513i	$-0.648940\pi$
$758$		0			0
$759$	−17.3189	+	11.8347i	−0.628636	+	0.429572i
$760$		0			0
$761$	−21.0945	−	24.3444i	−0.764675	−	0.882482i	0.231229	−	0.972899i	$-0.425725\pi$
$761$	−21.0945	−	24.3444i	−0.764675	−	0.882482i	−0.995904	+	0.0904170i	$0.971180\pi$
$762$		0			0
$763$	−0.442958	+	3.08084i	−0.0160362	+	0.111534i
$764$		0			0
$765$	0.582531	+	4.05159i	0.0210615	+	0.146486i
$766$		0			0
$767$	−18.5501	+	11.9214i	−0.669805	+	0.430457i
$768$		0			0
$769$	−4.39089	+	1.28928i	−0.158340	+	0.0464927i	−0.359942	−	0.932975i	$-0.617203\pi$
$769$	−4.39089	+	1.28928i	−0.158340	+	0.0464927i	0.201602	+	0.979468i	$0.435385\pi$
$770$		0			0
$771$	−0.637841	+	0.736108i	−0.0229713	+	0.0265103i
$772$		0			0
$773$	−5.12581	−	11.2240i	−0.184363	−	0.403698i	0.794773	−	0.606907i	$-0.207590\pi$
$773$	−5.12581	−	11.2240i	−0.184363	−	0.403698i	−0.979135	+	0.203209i	$0.934863\pi$
$774$		0			0
$775$	−32.1893	−	9.45164i	−1.15627	−	0.339513i
$776$		0			0
$777$	7.44752	−	16.3078i	0.267178	−	0.585039i
$778$		0			0
$779$	−24.7803	−	15.9253i	−0.887847	−	0.570585i
$780$		0			0
$781$	−2.30460			−0.0824652
$782$		0			0
$783$	−4.35740			−0.155721
$784$		0			0
$785$	2.56265	+	1.64692i	0.0914650	+	0.0587810i
$786$		0			0
$787$	16.0845	−	35.2201i	0.573350	−	1.25546i	−0.371644	−	0.928375i	$-0.621206\pi$
$787$	16.0845	−	35.2201i	0.573350	−	1.25546i	0.944994	−	0.327087i	$-0.106067\pi$
$788$		0			0
$789$	−20.7861	−	6.10334i	−0.740004	−	0.217285i
$790$		0			0
$791$	14.1123	+	30.9015i	0.501774	+	1.09873i
$792$		0			0
$793$	−7.12476	+	8.22241i	−0.253008	+	0.291986i
$794$		0			0
$795$	−4.38189	+	1.28664i	−0.155410	+	0.0456324i
$796$		0			0
$797$	19.9303	−	12.8084i	0.705967	−	0.453698i	−0.137763	−	0.990465i	$-0.543991\pi$
$797$	19.9303	−	12.8084i	0.705967	−	0.453698i	0.843730	+	0.536768i	$0.180355\pi$
$798$		0			0
$799$	−12.2652	−	85.3061i	−0.433910	−	3.01791i
$800$		0			0
$801$	−4.80934	+	33.4497i	−0.169930	+	1.18189i
$802$		0			0
$803$	−5.77404	−	6.66360i	−0.203761	−	0.235153i
$804$		0			0
$805$	−1.94077	+	4.58856i	−0.0684033	+	0.161726i
$806$		0			0
$807$	34.8472	+	40.2158i	1.22668	+	1.41566i
$808$		0			0
$809$	−5.89803	+	41.0217i	−0.207364	+	1.44225i	0.574351	+	0.818609i	$0.305255\pi$
$809$	−5.89803	+	41.0217i	−0.207364	+	1.44225i	−0.781714	+	0.623637i	$0.785655\pi$
$810$		0			0
$811$	−3.74221	−	26.0276i	−0.131407	−	0.913954i	−0.943723	−	0.330737i	$-0.892703\pi$
$811$	−3.74221	−	26.0276i	−0.131407	−	0.913954i	0.812316	−	0.583217i	$-0.198206\pi$
$812$		0			0
$813$	−54.9878	+	35.3385i	−1.92851	+	1.23937i
$814$		0			0
$815$	3.39047	−	0.995533i	0.118763	−	0.0348720i
$816$		0			0
$817$	−9.79872	+	11.3083i	−0.342814	+	0.395628i
$818$		0			0
$819$	−9.10007	−	19.9264i	−0.317982	−	0.696284i
$820$		0			0
$821$	17.9426	+	5.26841i	0.626200	+	0.183869i	0.579411	−	0.815036i	$-0.303283\pi$
$821$	17.9426	+	5.26841i	0.626200	+	0.183869i	0.0467895	+	0.998905i	$0.485101\pi$
$822$		0			0
$823$	9.67159	−	21.1778i	0.337130	−	0.738212i	−0.662814	−	0.748784i	$-0.730638\pi$
$823$	9.67159	−	21.1778i	0.337130	−	0.738212i	0.999944	+	0.0105718i	$0.00336519\pi$
$824$		0			0
$825$	18.1611	+	11.6714i	0.632287	+	0.406346i
$826$		0			0
$827$	−28.7698			−1.00042			−0.500212	−	0.865903i	$-0.666745\pi$
$827$	−28.7698			−1.00042			−0.500212	+	0.865903i	$0.666745\pi$
$828$		0			0
$829$	−22.8006			−0.791899			−0.395949	−	0.918272i	$-0.629584\pi$
$829$	−22.8006			−0.791899			−0.395949	+	0.918272i	$0.629584\pi$
$830$		0			0
$831$	29.2267	+	18.7828i	1.01386	+	0.651569i
$832$		0			0
$833$	25.6785	−	56.2280i	0.889706	−	1.94819i
$834$		0			0
$835$	−0.862535	−	0.253263i	−0.0298492	−	0.00876453i
$836$		0			0
$837$	2.95358	+	6.46743i	0.102091	+	0.223547i
$838$		0			0
$839$	14.2675	−	16.4655i	0.492567	−	0.568453i	−0.453982	−	0.891011i	$-0.649997\pi$
$839$	14.2675	−	16.4655i	0.492567	−	0.568453i	0.946550	+	0.322558i	$0.104543\pi$
$840$		0			0
$841$	11.1757	−	3.28147i	0.385368	−	0.113154i
$842$		0			0
$843$	31.9095	−	20.5070i	1.09902	−	0.706298i
$844$		0			0
$845$	−0.311233	−	2.16468i	−0.0107068	−	0.0744671i
$846$		0			0
$847$	4.40644	−	30.6475i	0.151407	−	1.05306i
$848$		0			0
$849$	22.4194	+	25.8734i	0.769433	+	0.887973i
$850$		0			0
$851$	−6.01763	−	6.56062i	−0.206282	−	0.224895i
$852$		0			0
$853$	−1.68392	−	1.94334i	−0.0576562	−	0.0665388i	0.726189	−	0.687495i	$-0.241290\pi$
$853$	−1.68392	−	1.94334i	−0.0576562	−	0.0665388i	−0.783845	+	0.620957i	$0.786744\pi$
$854$		0			0
$855$	0.620073	−	4.31270i	0.0212060	−	0.147491i
$856$		0			0
$857$	3.47499	+	24.1691i	0.118703	+	0.825600i	0.958986	+	0.283452i	$0.0914796\pi$
$857$	3.47499	+	24.1691i	0.118703	+	0.825600i	−0.840283	+	0.542148i	$0.817611\pi$
$858$		0			0
$859$	18.5782	−	11.9395i	0.633882	−	0.407371i	−0.183863	−	0.982952i	$-0.558860\pi$
$859$	18.5782	−	11.9395i	0.633882	−	0.407371i	0.817745	+	0.575581i	$0.195224\pi$
$860$		0			0
$861$	40.6041	−	11.9224i	1.38378	−	0.406315i
$862$		0			0
$863$	−11.0631	+	12.7675i	−0.376592	+	0.434611i	−0.912130	−	0.409900i	$-0.865563\pi$
$863$	−11.0631	+	12.7675i	−0.376592	+	0.434611i	0.535538	+	0.844511i	$0.320109\pi$
$864$		0			0
$865$	−2.03365	−	4.45307i	−0.0691461	−	0.151409i
$866$		0			0
$867$	−51.7619	−	15.1987i	−1.75793	−	0.516173i
$868$		0			0
$869$	2.84130	−	6.22159i	0.0963846	−	0.211053i
$870$		0			0
$871$	−6.64848	−	4.27272i	−0.225275	−	0.144775i
$872$		0			0
$873$	−20.1193			−0.680936
$874$		0			0
$875$	10.3217			0.348935
$876$		0			0
$877$	10.5180	+	6.75953i	0.355169	+	0.228253i	0.706042	−	0.708170i	$-0.250479\pi$
$877$	10.5180	+	6.75953i	0.355169	+	0.228253i	−0.350873	+	0.936423i	$0.614115\pi$
$878$		0			0
$879$	−26.8846	+	58.8690i	−0.906795	+	1.98560i
$880$		0			0
$881$	−38.0568	−	11.1745i	−1.28217	−	0.376478i	−0.431466	−	0.902129i	$-0.642003\pi$
$881$	−38.0568	−	11.1745i	−1.28217	−	0.376478i	−0.850700	+	0.525652i	$0.823822\pi$
$882$		0			0
$883$	2.54042	+	5.56274i	0.0854919	+	0.187201i	0.947549	−	0.319609i	$-0.103552\pi$
$883$	2.54042	+	5.56274i	0.0854919	+	0.187201i	−0.862058	+	0.506810i	$0.830824\pi$
$884$		0			0
$885$	4.12616	−	4.76184i	0.138699	−	0.160067i
$886$		0			0
$887$	24.8394	−	7.29352i	0.834027	−	0.244892i	0.163281	−	0.986580i	$-0.447792\pi$
$887$	24.8394	−	7.29352i	0.834027	−	0.244892i	0.670746	+	0.741687i	$0.265974\pi$
$888$		0			0
$889$	−56.0217	+	36.0029i	−1.87891	+	1.20750i
$890$		0			0
$891$	−2.67622	−	18.6135i	−0.0896566	−	0.623575i
$892$		0			0
$893$	−13.0556	+	90.8037i	−0.436889	+	3.03863i
$894$		0			0
$895$	1.89696	+	2.18921i	0.0634085	+	0.0731774i
$896$		0			0
$897$	−23.6347	+	0.668047i	−0.789138	+	0.0223054i
$898$		0			0
$899$	18.5417	+	21.3983i	0.618401	+	0.713673i
$900$		0			0
$901$	6.86809	−	47.7686i	0.228809	−	1.59140i
$902$		0			0
$903$	−3.05927	−	21.2777i	−0.101806	−	0.708078i
$904$		0			0
$905$	−1.40852	+	0.905202i	−0.0468208	+	0.0300899i
$906$		0			0
$907$	28.4997	−	8.36827i	0.946317	−	0.277864i	0.228064	−	0.973646i	$-0.426760\pi$
$907$	28.4997	−	8.36827i	0.946317	−	0.277864i	0.718253	+	0.695782i	$0.244942\pi$
$908$		0			0
$909$	18.9231	−	21.8384i	0.627639	−	0.724334i
$910$		0			0
$911$	−21.4746	−	47.0228i	−0.711485	−	1.55794i	−0.825465	−	0.564453i	$-0.809087\pi$
$911$	−21.4746	−	47.0228i	−0.711485	−	1.55794i	0.113980	−	0.993483i	$-0.463640\pi$
$912$		0			0
$913$	−18.0079	−	5.28759i	−0.595974	−	0.174994i
$914$		0			0
$915$	1.29146	−	2.82790i	0.0426944	−	0.0934876i
$916$		0			0
$917$	−12.0034	−	7.71412i	−0.396387	−	0.254743i
$918$		0			0
$919$	34.5860			1.14089			0.570443	−	0.821337i	$-0.306772\pi$
$919$	34.5860			1.14089			0.570443	+	0.821337i	$0.306772\pi$
$920$		0			0
$921$	48.6438			1.60287
$922$		0			0
$923$	−2.18533	−	1.40443i	−0.0719312	−	0.0462274i
$924$		0			0
$925$	−3.80608	+	8.33415i	−0.125143	+	0.274025i
$926$		0			0
$927$	−6.09813	−	1.79057i	−0.200289	−	0.0588101i
$928$		0			0
$929$	14.7852	+	32.3751i	0.485087	+	1.06219i	0.981033	+	0.193839i	$0.0620939\pi$
$929$	14.7852	+	32.3751i	0.485087	+	1.06219i	−0.495947	+	0.868353i	$0.665179\pi$
$930$		0			0
$931$	−43.0883	+	49.7266i	−1.41216	+	1.62972i
$932$		0			0
$933$	30.9612	−	9.09103i	1.01362	−	0.297627i
$934$		0			0
$935$	2.49960	−	1.60639i	0.0817455	−	0.0525347i
$936$		0			0
$937$	−0.128379	−	0.892894i	−0.00419395	−	0.0291696i	0.987617	−	0.156884i	$-0.0501449\pi$
$937$	−0.128379	−	0.892894i	−0.00419395	−	0.0291696i	−0.991811	+	0.127715i	$0.959236\pi$
$938$		0			0
$939$	−11.3716	+	79.0915i	−0.371100	+	2.58105i
$940$		0			0
$941$	−14.7349	−	17.0050i	−0.480344	−	0.554346i	0.462916	−	0.886402i	$-0.346803\pi$
$941$	−14.7349	−	17.0050i	−0.480344	−	0.554346i	−0.943260	+	0.332056i	$0.892258\pi$
$942$		0			0
$943$	2.40171	−	20.8763i	0.0782105	−	0.679824i
$944$		0			0
$945$	−0.711615	−	0.821248i	−0.0231489	−	0.0267152i
$946$		0			0
$947$	−3.26381	+	22.7003i	−0.106060	+	0.737660i	0.865508	+	0.500896i	$0.166996\pi$
$947$	−3.26381	+	22.7003i	−0.106060	+	0.737660i	−0.971567	+	0.236765i	$0.923913\pi$
$948$		0			0
$949$	−1.41441	−	9.83744i	−0.0459137	−	0.319337i
$950$		0			0
$951$	−27.1965	+	17.4781i	−0.881907	+	0.566767i
$952$		0			0
$953$	5.12485	−	1.50479i	0.166010	−	0.0487450i	−0.197671	−	0.980268i	$-0.563338\pi$
$953$	5.12485	−	1.50479i	0.166010	−	0.0487450i	0.363681	+	0.931523i	$0.381520\pi$
$954$		0			0
$955$	−0.629811	+	0.726841i	−0.0203802	+	0.0235200i
$956$		0			0
$957$	−7.56881	−	16.5734i	−0.244665	−	0.535742i
$958$		0			0
$959$	64.7720	+	19.0188i	2.09160	+	0.614148i
$960$		0			0
$961$	6.31422	−	13.8262i	0.203684	−	0.446007i
$962$		0			0
$963$	31.8601	+	20.4752i	1.02668	+	0.659805i
$964$		0			0
$965$	4.49534			0.144710
$966$		0			0
$967$	19.1486			0.615777			0.307889	−	0.951422i	$-0.400378\pi$
$967$	19.1486			0.615777			0.307889	+	0.951422i	$0.400378\pi$
$968$		0			0
$969$	84.1910	+	54.1063i	2.70461	+	1.73814i
$970$		0			0
$971$	12.4461	−	27.2532i	0.399414	−	0.874596i	−0.597915	−	0.801560i	$-0.704004\pi$
$971$	12.4461	−	27.2532i	0.399414	−	0.874596i	0.997329	−	0.0730359i	$-0.0232688\pi$
$972$		0			0
$973$	20.5824	+	6.04355i	0.659843	+	0.193747i
$974$		0			0
$975$	10.1086	+	22.1347i	0.323734	+	0.708879i
$976$		0			0
$977$	27.5628	−	31.8092i	0.881812	−	1.01767i	−0.117885	−	0.993027i	$-0.537611\pi$
$977$	27.5628	−	31.8092i	0.881812	−	1.01767i	0.999696	−	0.0246378i	$-0.00784324\pi$
$978$		0			0
$979$	23.5370	−	6.91109i	0.752246	−	0.220879i
$980$		0			0
$981$	1.63360	−	1.04985i	0.0521569	−	0.0335192i
$982$		0			0
$983$	−6.33817	−	44.0829i	−0.202156	−	1.40603i	−0.797869	−	0.602830i	$-0.794040\pi$
$983$	−6.33817	−	44.0829i	−0.202156	−	1.40603i	0.595713	−	0.803197i	$-0.296870\pi$
$984$		0			0
$985$	0.432731	−	3.00971i	0.0137879	−	0.0958972i
$986$		0			0
$987$	−86.3065	−	99.6030i	−2.74717	−	3.17040i
$988$		0			0
$989$	−10.3230	−	2.71677i	−0.328252	−	0.0863883i
$990$		0			0
$991$	13.7448	+	15.8624i	0.436619	+	0.503885i	0.930828	−	0.365458i	$-0.119088\pi$
$991$	13.7448	+	15.8624i	0.436619	+	0.503885i	−0.494209	+	0.869343i	$0.664542\pi$
$992$		0			0
$993$	3.72869	−	25.9336i	0.118326	−	0.822978i
$994$		0			0
$995$	−0.310745	−	2.16128i	−0.00985127	−	0.0685171i
$996$		0			0
$997$	−39.0508	+	25.0964i	−1.23675	+	0.794811i	−0.984928	−	0.172962i	$-0.944666\pi$
$997$	−39.0508	+	25.0964i	−1.23675	+	0.794811i	−0.251822	+	0.967774i	$0.581030\pi$
$998$		0			0
$999$	1.86309	−	0.547053i	0.0589456	−	0.0173080i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.e.a.13.2	✓	20
3.2	odd	2		828.2.q.a.289.2		20
4.3	odd	2		368.2.m.d.289.1		20
23.4	even	11		2116.2.a.j.1.9		10
23.16	even	11	inner	92.2.e.a.85.2	yes	20
23.19	odd	22		2116.2.a.i.1.9		10
69.62	odd	22		828.2.q.a.361.2		20
92.19	even	22		8464.2.a.cd.1.2		10
92.27	odd	22		8464.2.a.ce.1.2		10
92.39	odd	22		368.2.m.d.177.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.13.2	✓	20	1.1	even	1	trivial
92.2.e.a.85.2	yes	20	23.16	even	11	inner
368.2.m.d.177.1		20	92.39	odd	22
368.2.m.d.289.1		20	4.3	odd	2
828.2.q.a.289.2		20	3.2	odd	2
828.2.q.a.361.2		20	69.62	odd	22
2116.2.a.i.1.9		10	23.19	odd	22
2116.2.a.j.1.9		10	23.4	even	11
8464.2.a.cd.1.2		10	92.19	even	22
8464.2.a.ce.1.2		10	92.27	odd	22

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	92.2.e.a.13.2

Level	$92$
Weight	$2$
Character	92.13
Analytic conductor	$0.735$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$