LMFDB - Embedded newform 368.2.m.d.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [368,2,Mod(49,368)] 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("368.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(368, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.m (of order $11$, degree $10$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.93849479438$
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:	no (minimal twist has level 92)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			177.1
Root			$2.26168 - 0.664090i$ of defining polynomial
Character	$\chi$	$=$	368.177
Dual form			368.2.m.d.289.1

$q$-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 $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$	$1$

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	$-0.920036\pi$
$3$	−1.98297	+	1.27438i	−1.14487	+	0.735764i	−0.176259	+	0.984344i	$0.556400\pi$
$4$		0			0
$5$	−0.105327	−	0.230633i	−0.0471035	−	0.103142i	0.884617	−	0.466318i	$-0.154420\pi$
$5$	−0.105327	−	0.230633i	−0.0471035	−	0.103142i	−0.931721	+	0.363176i	$0.881692\pi$
$6$		0			0
$7$	3.93129	−	1.15433i	1.48589	−	0.436297i	0.564663	−	0.825322i	$-0.309006\pi$
$7$	3.93129	−	1.15433i	1.48589	−	0.436297i	0.921227	+	0.389025i	$0.127188\pi$
$8$		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	$-0.317520\pi$
$11$	−1.21513	−	1.40234i	−0.366376	−	0.422820i	−0.908766	+	0.417307i	$0.862974\pi$
$12$		0			0
$13$	2.00683	+	0.589258i	0.556594	+	0.163431i	0.547919	−	0.836532i	$-0.315420\pi$
$13$	2.00683	+	0.589258i	0.556594	+	0.163431i	0.00867553	+	0.999962i	$0.497238\pi$
$14$		0			0
$15$	0.502775	+	0.323114i	0.129816	+	0.0834276i
$16$		0			0
$17$	−0.898799	+	6.25129i	−0.217991	+	1.51616i	0.527449	+	0.849587i	$0.323149\pi$
$17$	−0.898799	+	6.25129i	−0.217991	+	1.51616i	−0.745440	+	0.666573i	$0.767760\pi$
$18$		0			0
$19$	0.956723	+	6.65416i	0.219487	+	1.52657i	0.739937	+	0.672676i	$0.234855\pi$
$19$	0.956723	+	6.65416i	0.219487	+	1.52657i	−0.520450	+	0.853892i	$0.674236\pi$
$20$		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	0.857747	+	0.514072i	$0.171864\pi$
$29$	−0.592832	+	4.12324i	−0.110086	+	0.765666i	−0.967833	+	0.251593i	$0.919045\pi$
$30$		0			0
$31$	5.71804	+	3.67476i	1.02699	+	0.660006i	0.941736	−	0.336353i	$-0.109194\pi$
$31$	5.71804	+	3.67476i	1.02699	+	0.660006i	0.0852536	+	0.996359i	$0.472830\pi$
$32$		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	−0.835594	−	0.549348i	$-0.814876\pi$
$37$	0.771131	−	1.68854i	0.126773	−	0.277594i	0.962367	+	0.271753i	$0.0876035\pi$
$38$		0			0
$39$	−4.73043	+	1.38898i	−0.757475	+	0.222415i
$40$		0			0
$41$	−1.82023	−	3.98575i	−0.284272	−	0.622469i	0.712594	−	0.701577i	$-0.247520\pi$
$41$	−1.82023	−	3.98575i	−0.284272	−	0.622469i	−0.996866	+	0.0791076i	$0.974793\pi$
$42$		0			0
$43$	−1.87245	+	1.20335i	−0.285546	+	0.183510i	−0.675571	−	0.737295i	$-0.736103\pi$
$43$	−1.87245	+	1.20335i	−0.285546	+	0.183510i	0.390025	+	0.920804i	$0.372466\pi$
$44$		0			0
$45$	−0.648122			−0.0966163
$46$		0			0
$47$	−13.6462			−1.99050			−0.995249	−	0.0973620i	$-0.968960\pi$
$47$	−13.6462			−1.99050			−0.995249	+	0.0973620i	$0.968960\pi$
$48$		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	0.263740	−	0.964594i	$-0.415044\pi$
$53$	7.33188	−	2.15283i	1.00711	−	0.295714i	0.743371	+	0.668880i	$0.233226\pi$
$54$		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	$-0.168338\pi$
$59$	10.1156	+	2.97021i	1.31694	+	0.386689i	0.453553	+	0.891229i	$0.350156\pi$
$60$		0			0
$61$	−4.37602	−	2.81230i	−0.560292	−	0.360078i	0.229637	−	0.973276i	$-0.426246\pi$
$61$	−4.37602	−	2.81230i	−0.560292	−	0.360078i	−0.789929	+	0.613199i	$0.789883\pi$
$62$		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	$-0.698589\pi$
$67$	2.47443	−	2.85565i	0.302300	−	0.348873i	0.886493	+	0.462742i	$0.153134\pi$
$68$		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	$-0.749247\pi$
$71$	0.813338	−	0.938643i	0.0965255	−	0.111396i	0.801957	+	0.597382i	$0.203792\pi$
$72$		0			0
$73$	0.676249	+	4.70342i	0.0791490	+	0.550493i	0.990356	+	0.138545i	$0.0442426\pi$
$73$	0.676249	+	4.70342i	0.0791490	+	0.550493i	−0.911207	+	0.411948i	$0.864848\pi$
$74$		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	$-0.475577\pi$
$79$	−3.53674	−	1.03848i	−0.397914	−	0.116838i	−0.474566	+	0.880220i	$0.657395\pi$
$80$		0			0
$81$	6.63660	+	7.65905i	0.737400	+	0.851005i
$82$		0			0
$83$	4.20174	−	9.20053i	0.461201	−	1.00989i	−0.526011	−	0.850478i	$-0.676313\pi$
$83$	4.20174	−	9.20053i	0.461201	−	1.00989i	0.987212	−	0.159411i	$-0.0509596\pi$
$84$		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	0.203694	−	0.979035i	$-0.434705\pi$
$89$	11.1215	−	7.14733i	1.17887	−	0.757616i	0.975179	+	0.221419i	$0.0710688\pi$
$90$		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	0.667871	−	0.744277i	$-0.267206\pi$
$97$	−3.26961	−	7.15944i	−0.331978	−	0.726931i	−0.999850	+	0.0173456i	$0.994478\pi$
$98$		0			0
$99$	−4.55110	+	1.33632i	−0.457402	+	0.134305i
$100$		0			0
$101$	−4.69596	+	10.2827i	−0.467266	+	1.02317i	0.518505	+	0.855075i	$0.326489\pi$
$101$	−4.69596	+	10.2827i	−0.467266	+	1.02317i	−0.985771	+	0.168095i	$0.946239\pi$
$102$		0			0
$103$	1.62818	+	1.87902i	0.160430	+	0.185146i	0.830273	−	0.557356i	$-0.188184\pi$
$103$	1.62818	+	1.87902i	0.160430	+	0.185146i	−0.669844	+	0.742502i	$0.733639\pi$
$104$		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	$-0.572274\pi$
$107$	−12.4637	−	8.00992i	−1.20491	−	0.774348i	−0.979799	+	0.199985i	$0.935911\pi$
$108$		0			0
$109$	−0.108111	+	0.751927i	−0.0103551	+	0.0720216i	−0.994344	−	0.106210i	$-0.966128\pi$
$109$	−0.108111	+	0.751927i	−0.0103551	+	0.0720216i	0.983989	+	0.178231i	$0.0570376\pi$
$110$		0			0
$111$	0.622710	+	4.33105i	0.0591051	+	0.411085i
$112$		0			0
$113$	−5.42962	+	6.26611i	−0.510776	+	0.589466i	−0.951297	−	0.308276i	$-0.900248\pi$
$113$	−5.42962	+	6.26611i	−0.510776	+	0.589466i	0.440522	+	0.897742i	$0.354794\pi$
$114$		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	−0.995825	−	0.0912821i	$-0.970904\pi$
$127$	−10.6435	−	12.2832i	−0.944457	−	1.08996i	0.0513677	−	0.998680i	$-0.483642\pi$
$128$		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	$-0.639523\pi$
$131$	−3.34138	+	0.981117i	−0.291938	+	0.0857206i	0.132484	+	0.991185i	$0.457705\pi$
$132$		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	$-0.428730\pi$
$139$	5.23554			0.444073			0.222036	+	0.975038i	$0.428730\pi$
$140$		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	0.792799	−	0.609483i	$-0.208623\pi$
$149$	0.936158	+	1.08038i	0.0766931	+	0.0885085i	−0.716106	+	0.697991i	$0.754077\pi$
$150$		0			0
$151$	−0.363307	−	0.106676i	−0.0295655	−	0.00868121i	0.266916	−	0.963720i	$-0.413995\pi$
$151$	−0.363307	−	0.106676i	−0.0295655	−	0.00868121i	−0.296482	+	0.955038i	$0.595813\pi$
$152$		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	0.936877	+	0.349659i	$0.113703\pi$
$157$	1.70984	+	11.8922i	0.136460	+	0.949103i	−0.800417	+	0.599444i	$0.795388\pi$
$158$		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	$-0.588951\pi$
$163$	9.12665	−	10.5327i	0.714854	−	0.824986i	0.990678	+	0.136223i	$0.0434962\pi$
$164$		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	$-0.998349\pi$
$167$	−0.504578	+	3.50942i	−0.0390455	+	0.271567i	0.960941	+	0.276753i	$0.0892584\pi$
$168$		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	−0.993938	−	0.109943i	$-0.964933\pi$
$173$	−12.6441	−	14.5920i	−0.961310	−	1.10941i	0.0326280	−	0.999468i	$-0.489612\pi$
$174$		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	−0.999919	−	0.0127402i	$-0.995945\pi$
$179$	−4.74609	−	10.3925i	−0.354740	−	0.776771i	0.645179	−	0.764031i	$-0.276783\pi$
$180$		0			0
$181$	5.55530	−	3.57017i	0.412922	−	0.265369i	−0.317645	−	0.948210i	$-0.602892\pi$
$181$	5.55530	−	3.57017i	0.412922	−	0.265369i	0.730567	+	0.682841i	$0.239256\pi$
$182$		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	$-0.634730\pi$
$191$	−3.63954	+	1.06867i	−0.263348	+	0.0773260i	0.147393	+	0.989078i	$0.452912\pi$
$192$		0			0
$193$	−7.36527	+	16.1277i	−0.530163	+	1.16090i	0.435283	+	0.900294i	$0.356648\pi$
$193$	−7.36527	+	16.1277i	−0.530163	+	1.16090i	−0.965446	+	0.260602i	$0.916079\pi$
$194$		0			0
$195$	0.818585	+	0.944698i	0.0586201	+	0.0676512i
$196$		0			0
$197$	−11.5068	−	3.37869i	−0.819822	−	0.240722i	−0.155183	−	0.987886i	$-0.549597\pi$
$197$	−11.5068	−	3.37869i	−0.819822	−	0.240722i	−0.664640	+	0.747164i	$0.731415\pi$
$198$		0			0
$199$	7.24476	+	4.65593i	0.513568	+	0.330050i	0.771623	−	0.636080i	$-0.219445\pi$
$199$	7.24476	+	4.65593i	0.513568	+	0.330050i	−0.258055	+	0.966130i	$0.583082\pi$
$200$		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	$-0.0808354\pi$
$211$	−0.458612	−	3.18971i	−0.0315721	−	0.219589i	−0.999499	+	0.0316421i	$0.989926\pi$
$212$		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	$-0.703952\pi$
$223$	−9.96439	+	2.92581i	−0.667265	+	0.195927i	−0.0694802	+	0.997583i	$0.522134\pi$
$224$		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	$-0.737492\pi$
$227$	−4.41116	+	2.83488i	−0.292779	+	0.188158i	0.386003	+	0.922498i	$0.373856\pi$
$228$		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	−0.861089	−	0.508455i	$-0.830217\pi$
$233$	−11.5443	+	7.41906i	−0.756291	+	0.486039i	0.104798	+	0.994494i	$0.466580\pi$
$234$		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	$-0.928616\pi$
$239$	−2.60385	+	5.70164i	−0.168429	+	0.368808i	0.806530	+	0.591194i	$0.201343\pi$
$240$		0			0
$241$	−7.71902	−	8.90823i	−0.497226	−	0.573829i	0.450556	−	0.892748i	$-0.351226\pi$
$241$	−7.71902	−	8.90823i	−0.497226	−	0.573829i	−0.947782	+	0.318919i	$0.896680\pi$
$242$		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	$-0.798390\pi$
$251$	−1.67105	+	1.92850i	−0.105476	+	0.121726i	0.700557	+	0.713597i	$0.252935\pi$
$252$		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	0.987905	−	0.155060i	$-0.0495570\pi$
$257$	−0.0588063	−	0.409007i	−0.00366823	−	0.0255131i	−0.991573	+	0.129546i	$0.958648\pi$
$258$		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	$-0.317643\pi$
$263$	8.81824	+	2.58927i	0.543756	+	0.159661i	0.00169242	+	0.999999i	$0.499461\pi$
$264$		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	0.455936	−	0.890013i	$-0.349305\pi$
$269$	21.6606	−	6.36013i	1.32067	−	0.387784i	0.864735	+	0.502229i	$0.167487\pi$
$270$		0			0
$271$	11.5194	+	25.2240i	0.699756	+	1.53225i	0.840267	+	0.542172i	$0.182398\pi$
$271$	11.5194	+	25.2240i	0.699756	+	1.53225i	−0.140511	+	0.990079i	$0.544875\pi$
$272$		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	0.997393	+	0.0721659i	$0.0229911\pi$
$281$	6.68475	+	14.6376i	0.398779	+	0.873204i	−0.598614	+	0.801038i	$0.704282\pi$
$282$		0			0
$283$	−13.9357	+	4.09188i	−0.828388	+	0.243237i	−0.668325	−	0.743870i	$-0.732988\pi$
$283$	−13.9357	+	4.09188i	−0.828388	+	0.243237i	−0.160064	+	0.987107i	$0.551170\pi$
$284$		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	−0.477127	−	0.878834i	$-0.658322\pi$
$293$	3.90734	−	27.1762i	0.228269	−	1.58765i	0.705396	−	0.708813i	$-0.250769\pi$
$294$		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	$-0.518619\pi$
$307$	−17.3606	−	11.1570i	−0.990821	−	0.636762i	−0.932361	+	0.361528i	$0.882255\pi$
$308$		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	$-0.354151\pi$
$311$	−8.96468	−	10.3458i	−0.508340	−	0.586656i	−0.950673	+	0.310195i	$0.899606\pi$
$312$		0			0
$313$	14.0820	−	30.8353i	0.795963	−	1.74292i	0.137231	−	0.990539i	$-0.456180\pi$
$313$	14.0820	−	30.8353i	0.795963	−	1.74292i	0.658733	−	0.752377i	$-0.271093\pi$
$314$		0			0
$315$	−2.54796	+	0.748148i	−0.143561	+	0.0421533i
$316$		0			0
$317$	−5.69742	−	12.4756i	−0.319999	−	0.700700i	0.679456	−	0.733716i	$-0.262216\pi$
$317$	−5.69742	−	12.4756i	−0.319999	−	0.700700i	−0.999455	+	0.0330163i	$0.989489\pi$
$318$		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	$-0.764822\pi$
$331$	4.61740	−	10.1107i	0.253796	−	0.555735i	0.993050	+	0.117691i	$0.0375493\pi$
$332$		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	0.367258	−	0.930119i	$-0.380297\pi$
$337$	−5.98904	−	3.84892i	−0.326244	−	0.209664i	−0.693502	+	0.720455i	$0.743933\pi$
$338$		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	$-0.569722\pi$
$347$	14.5262	−	16.7641i	0.779805	−	0.899943i	0.997095	+	0.0761639i	$0.0242672\pi$
$348$		0			0
$349$	3.20623	+	22.2998i	0.171625	+	1.19368i	0.875450	+	0.483308i	$0.160565\pi$
$349$	3.20623	+	22.2998i	0.171625	+	1.19368i	−0.703825	+	0.710373i	$0.748526\pi$
$350$		0			0
$351$	0.311362	−	2.16557i	0.0166193	−	0.115589i
$352$		0			0
$353$	−0.0989141	−	0.0635682i	−0.00526467	−	0.00338340i	0.538006	−	0.842941i	$-0.319178\pi$
$353$	−0.0989141	−	0.0635682i	−0.00526467	−	0.00338340i	−0.543271	+	0.839558i	$0.682814\pi$
$354$		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	−0.617634	−	0.786466i	$-0.711909\pi$
$359$	7.22273	−	15.8156i	0.381201	−	0.834714i	0.998835	−	0.0482488i	$-0.0153640\pi$
$360$		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	$-0.324257\pi$
$367$	20.0955			1.04898			0.524488	+	0.851418i	$0.324257\pi$
$368$		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	−0.961503	−	0.274795i	$-0.911390\pi$
$373$	−10.4200	−	22.8167i	−0.539528	−	1.18140i	0.421974	−	0.906608i	$-0.361337\pi$
$374$		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	$-0.404569\pi$
$379$	−13.4789	−	15.5555i	−0.692366	−	0.799033i	−0.987700	+	0.156361i	$0.950024\pi$
$380$		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	$-0.247357\pi$
$383$	7.26607	+	4.66962i	0.371279	+	0.238606i	−0.341674	+	0.939819i	$0.610994\pi$
$384$		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	−0.665088	−	0.746765i	$-0.731606\pi$
$389$	3.32783	−	3.84052i	0.168728	−	0.194722i	0.833816	+	0.552043i	$0.186151\pi$
$390$		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	0.730965	+	0.682415i	$0.239070\pi$
$397$	−3.24076	+	22.5400i	−0.162649	+	1.13125i	−0.893614	+	0.448836i	$0.851839\pi$
$398$		0			0
$399$	−54.6194	−	35.1018i	−2.73439	−	1.75729i
$400$		0			0
$401$	−3.39941	−	0.998156i	−0.169758	−	0.0498456i	0.195749	−	0.980654i	$-0.437286\pi$
$401$	−3.39941	−	0.998156i	−0.169758	−	0.0498456i	−0.365507	+	0.930809i	$0.619104\pi$
$402$		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	−0.984633	−	0.174634i	$-0.944126\pi$
$409$	−9.54188	−	20.8938i	−0.471815	−	1.03313i	0.512818	−	0.858497i	$-0.328602\pi$
$410$		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	0.995346	+	0.0963651i	$0.0307216\pi$
$419$	8.52270	+	18.6621i	0.416361	+	0.911703i	−0.578985	+	0.815338i	$0.696551\pi$
$420$		0			0
$421$	−5.28793	+	1.55268i	−0.257718	+	0.0756728i	−0.408039	−	0.912964i	$-0.633787\pi$
$421$	−5.28793	+	1.55268i	−0.257718	+	0.0756728i	0.150321	+	0.988637i	$0.451969\pi$
$422$		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	0.885814	+	0.464041i	$0.153601\pi$
$431$	−1.96921	+	13.6962i	−0.0948537	+	0.659722i	−0.980668	+	0.195681i	$0.937308\pi$
$432$		0			0
$433$	−2.73014	−	18.9885i	−0.131202	−	0.912530i	−0.943991	−	0.329972i	$-0.892961\pi$
$433$	−2.73014	−	18.9885i	−0.131202	−	0.912530i	0.812789	−	0.582558i	$-0.197948\pi$
$434$		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	−0.186536	+	0.982448i	$0.559726\pi$
$439$	−23.7272	+	27.3827i	−1.13244	+	1.30690i	−0.945901	+	0.324455i	$0.894819\pi$
$440$		0			0
$441$	−3.56061	−	24.7646i	−0.169553	−	1.17927i
$442$		0			0
$443$	2.26323	−	15.7411i	0.107529	−	0.747883i	−0.862704	−	0.505710i	$-0.831231\pi$
$443$	2.26323	−	15.7411i	0.107529	−	0.747883i	0.970233	−	0.242173i	$-0.0778603\pi$
$444$		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	0.975895	−	0.218238i	$-0.0700311\pi$
$449$	13.1586	+	15.1859i	0.620994	+	0.716665i	−0.354901	+	0.934904i	$0.615486\pi$
$450$		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	−0.363412	−	0.931628i	$-0.618388\pi$
$457$	7.12001	−	4.57575i	0.333060	−	0.214045i	0.696472	+	0.717584i	$0.254752\pi$
$458$		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	$-0.842962\pi$
$463$	−17.5549	+	11.2819i	−0.815848	+	0.524313i	0.0649042	+	0.997891i	$0.479326\pi$
$464$		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	$-0.454446\pi$
$467$	17.2389	−	5.06180i	0.797722	−	0.234232i	0.655097	+	0.755544i	$0.272628\pi$
$468$		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	−0.995248	−	0.0973698i	$-0.968957\pi$
$479$	−1.48271	−	10.3125i	−0.0677468	−	0.471189i	0.927501	−	0.373819i	$-0.121952\pi$
$480$		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	−0.990433	−	0.137996i	$-0.955934\pi$
$487$	−1.74332	−	12.1251i	−0.0789974	−	0.549439i	0.911435	−	0.411443i	$-0.134975\pi$
$488$		0			0
$489$	−4.67523	+	32.5169i	−0.211421	+	1.47047i
$490$		0			0
$491$	32.7547	+	21.0501i	1.47820	+	0.949979i	0.997318	+	0.0731926i	$0.0233188\pi$
$491$	32.7547	+	21.0501i	1.47820	+	0.949979i	0.480879	+	0.876787i	$0.340318\pi$
$492$		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	$-0.480540\pi$
$499$	14.5673	−	4.27736i	0.652124	−	0.191481i	0.591028	+	0.806651i	$0.298722\pi$
$500$		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	$-0.529900\pi$
$503$	17.3335	−	11.1396i	0.772864	−	0.496689i	0.866658	+	0.498902i	$0.166263\pi$
$504$		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	−0.982582	−	0.185831i	$-0.940502\pi$
$509$	−27.5633	+	17.7139i	−1.22172	+	0.785154i	−0.239141	+	0.970985i	$0.576866\pi$
$510$		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	0.990035	−	0.140819i	$-0.0449737\pi$
$521$	29.0617	+	18.6768i	1.27322	+	0.818247i	0.283182	+	0.959066i	$0.408610\pi$
$522$		0			0
$523$	−3.25825	+	22.6616i	−0.142473	+	0.990924i	0.785655	+	0.618665i	$0.212326\pi$
$523$	−3.25825	+	22.6616i	−0.142473	+	0.990924i	−0.928129	+	0.372260i	$0.878583\pi$
$524$		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	0.271760	−	0.962365i	$-0.412394\pi$
$541$	−16.7348	−	19.3130i	−0.719485	−	0.830330i	−0.991245	+	0.132035i	$0.957849\pi$
$542$		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	−0.898492	−	0.438990i	$-0.855336\pi$
$547$	−15.0121	−	32.8719i	−0.641872	−	1.40550i	0.256620	−	0.966512i	$-0.417391\pi$
$548$		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	0.981232	−	0.192832i	$-0.0617673\pi$
$557$	4.55328	+	9.97029i	0.192929	+	0.422455i	−0.788303	+	0.615287i	$0.789040\pi$
$558$		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	0.994597	+	0.103811i	$0.0331039\pi$
$563$	22.6790	+	26.1730i	0.955806	+	1.10306i	−0.0387911	+	0.999247i	$0.512351\pi$
$564$		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	−0.796162	−	0.605084i	$-0.793140\pi$
$569$	3.29710	−	22.9318i	0.138222	−	0.961353i	0.934383	−	0.356269i	$-0.115951\pi$
$570$		0			0
$571$	−0.681807	−	4.74207i	−0.0285327	−	0.198450i	0.970569	−	0.240823i	$-0.0774172\pi$
$571$	−0.681807	−	4.74207i	−0.0285327	−	0.198450i	−0.999102	+	0.0423732i	$0.986508\pi$
$572$		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	−0.801882	−	0.597482i	$-0.796168\pi$
$577$	−2.31471	+	2.67131i	−0.0963624	+	0.111208i	0.705520	+	0.708690i	$0.250713\pi$
$578$		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	$-0.173932\pi$
$587$	5.29262	+	6.10801i	0.218450	+	0.252105i	−0.635938	+	0.771740i	$0.719387\pi$
$588$		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	0.695086	−	0.718927i	$-0.255366\pi$
$593$	−7.38894	−	16.1795i	−0.303427	−	0.664413i	−0.998513	+	0.0545138i	$0.982639\pi$
$594$		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	$-0.344059\pi$
$599$	23.0324			0.941079			0.470540	+	0.882379i	$0.344059\pi$
$600$		0			0
$601$	−24.4283	+	15.6991i	−0.996451	+	0.640380i	−0.933852	−	0.357659i	$-0.883575\pi$
$601$	−24.4283	+	15.6991i	−0.996451	+	0.640380i	−0.0625985	+	0.998039i	$0.519939\pi$
$602$		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	$-0.769512\pi$
$607$	5.96499	−	13.0615i	0.242111	−	0.530150i	0.991208	+	0.132310i	$0.0422396\pi$
$608$		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	0.999995	+	0.00311388i	$0.000991180\pi$
$613$	35.1140	+	22.5664i	1.41824	+	0.911448i	0.418245	+	0.908334i	$0.362645\pi$
$614$		0			0
$615$	0.372684	−	2.59207i	0.0150281	−	0.104522i
$616$		0			0
$617$	−2.90999	−	20.2394i	−0.117152	−	0.814807i	−0.960667	−	0.277703i	$-0.910427\pi$
$617$	−2.90999	−	20.2394i	−0.117152	−	0.814807i	0.843516	−	0.537105i	$-0.180482\pi$
$618$		0			0
$619$	−25.9815	+	29.9842i	−1.04428	+	1.20517i	−0.0660169	+	0.997819i	$0.521029\pi$
$619$	−25.9815	+	29.9842i	−1.04428	+	1.20517i	−0.978267	+	0.207349i	$0.933516\pi$
$620$		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	$-0.434910\pi$
$631$	−3.90579	−	1.14684i	−0.155487	−	0.0456551i	−0.358550	+	0.933511i	$0.616729\pi$
$632$		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	0.715059	−	0.699064i	$-0.246400\pi$
$641$	41.7239	−	26.8143i	1.64800	−	1.05910i	0.932937	−	0.360038i	$-0.117236\pi$
$642$		0			0
$643$	40.9629			1.61542			0.807711	−	0.589579i	$-0.200706\pi$
$643$	40.9629			1.61542			0.807711	+	0.589579i	$0.200706\pi$
$644$		0			0
$645$	−1.33024			−0.0523782
$646$		0			0
$647$	14.4760	−	9.30313i	0.569108	−	0.365744i	−0.224219	−	0.974539i	$-0.571983\pi$
$647$	14.4760	−	9.30313i	0.569108	−	0.365744i	0.793328	+	0.608795i	$0.208347\pi$
$648$		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	−0.986582	−	0.163267i	$-0.947797\pi$
$653$	−5.54824	+	12.1490i	−0.217119	+	0.475425i	0.769463	+	0.638692i	$0.220524\pi$
$654$		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	$-0.478063\pi$
$659$	−20.7936	−	13.3633i	−0.810006	−	0.520559i	−0.878867	+	0.477067i	$0.841700\pi$
$660$		0			0
$661$	−0.145017	+	1.00862i	−0.00564051	+	0.0392306i	−0.992447	−	0.122672i	$-0.960854\pi$
$661$	−0.145017	+	1.00862i	−0.00564051	+	0.0392306i	0.986807	+	0.161902i	$0.0517629\pi$
$662$		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	−0.991996	−	0.126268i	$-0.959700\pi$
$673$	−0.119569	+	0.831623i	−0.00460906	+	0.0320567i	0.987387	+	0.158325i	$0.0506092\pi$
$674$		0			0
$675$	−4.34333	−	2.79129i	−0.167175	−	0.107437i
$676$		0			0
$677$	−16.8545	−	4.94892i	−0.647771	−	0.190203i	−0.0586892	−	0.998276i	$-0.518692\pi$
$677$	−16.8545	−	4.94892i	−0.647771	−	0.190203i	−0.589081	+	0.808074i	$0.700510\pi$
$678$		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	$-0.736129\pi$
$683$	−22.0946	+	6.48756i	−0.845427	+	0.248240i	−0.169795	+	0.985479i	$0.554311\pi$
$684$		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	$-0.480901\pi$
$691$	3.15260			0.119931			0.0599654	+	0.998200i	$0.480901\pi$
$692$		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	0.543478	−	0.839423i	$-0.317107\pi$
$701$	−9.65715	−	11.1450i	−0.364746	−	0.420939i	−0.908224	+	0.418484i	$0.862562\pi$
$702$		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	0.465444	+	0.885077i	$0.345894\pi$
$709$	7.14161	+	49.6710i	0.268209	+	1.86543i	−0.197236	+	0.980356i	$0.563196\pi$
$710$		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	0.924274	+	0.381729i	$0.124671\pi$
$719$	−1.87983	+	13.0745i	−0.0701058	+	0.487597i	−0.994380	+	0.105868i	$0.966238\pi$
$720$		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	0.627930	+	0.778270i	$0.283902\pi$
$727$	−10.0155	+	21.9308i	−0.371454	+	0.813370i	−0.999384	+	0.0351003i	$0.988825\pi$
$728$		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	−0.771922	−	0.635717i	$-0.780705\pi$
$733$	−13.9247	+	8.94889i	−0.514322	+	0.330535i	0.257600	+	0.966252i	$0.417068\pi$
$734$		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	$-0.976007\pi$
$739$	−36.5060	+	23.4610i	−1.34290	+	0.863027i	−0.345735	+	0.938332i	$0.612370\pi$
$740$		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	$-0.530601\pi$
$743$	9.85124	−	2.89259i	0.361407	−	0.106119i	0.457395	+	0.889264i	$0.348783\pi$
$744$		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	$-0.254308\pi$
$751$	9.19040	+	5.90631i	0.335362	+	0.215524i	−0.362111	+	0.932135i	$0.617944\pi$
$752$		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	−0.451021	+	0.892513i	$0.648940\pi$
$757$	−34.9495	+	40.3339i	−1.27026	+	1.46596i	−0.819242	+	0.573448i	$0.805605\pi$
$758$		0			0
$759$	17.3189	+	11.8347i	0.628636	+	0.429572i
$760$		0			0
$761$	−21.0945	+	24.3444i	−0.764675	+	0.882482i	−0.995904	−	0.0904170i	$-0.971180\pi$
$761$	−21.0945	+	24.3444i	−0.764675	+	0.882482i	0.231229	+	0.972899i	$0.425725\pi$
$762$		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	0.201602	−	0.979468i	$-0.435385\pi$
$769$	−4.39089	−	1.28928i	−0.158340	−	0.0464927i	−0.359942	+	0.932975i	$0.617203\pi$
$770$		0			0
$771$	0.637841	+	0.736108i	0.0229713	+	0.0265103i
$772$		0			0
$773$	−5.12581	+	11.2240i	−0.184363	+	0.403698i	−0.979135	−	0.203209i	$-0.934863\pi$
$773$	−5.12581	+	11.2240i	−0.184363	+	0.403698i	0.794773	+	0.606907i	$0.207590\pi$
$774$		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	−0.944994	−	0.327087i	$-0.893933\pi$
$787$	−16.0845	−	35.2201i	−0.573350	−	1.25546i	0.371644	−	0.928375i	$-0.378794\pi$
$788$		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	0.843730	−	0.536768i	$-0.180355\pi$
$797$	19.9303	+	12.8084i	0.705967	+	0.453698i	−0.137763	+	0.990465i	$0.543991\pi$
$798$		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	−0.781714	−	0.623637i	$-0.785655\pi$
$809$	−5.89803	−	41.0217i	−0.207364	−	1.44225i	0.574351	−	0.818609i	$-0.305255\pi$
$810$		0			0
$811$	3.74221	−	26.0276i	0.131407	−	0.913954i	−0.812316	−	0.583217i	$-0.801794\pi$
$811$	3.74221	−	26.0276i	0.131407	−	0.913954i	0.943723	−	0.330737i	$-0.107297\pi$
$812$		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	0.0467895	−	0.998905i	$-0.485101\pi$
$821$	17.9426	−	5.26841i	0.626200	−	0.183869i	0.579411	+	0.815036i	$0.303283\pi$
$822$		0			0
$823$	−9.67159	−	21.1778i	−0.337130	−	0.738212i	0.662814	−	0.748784i	$-0.269362\pi$
$823$	−9.67159	−	21.1778i	−0.337130	−	0.738212i	−0.999944	+	0.0105718i	$0.996635\pi$
$824$		0			0
$825$	18.1611	−	11.6714i	0.632287	−	0.406346i
$826$		0			0
$827$	28.7698			1.00042			0.500212	−	0.865903i	$-0.333255\pi$
$827$	28.7698			1.00042			0.500212	+	0.865903i	$0.333255\pi$
$828$		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	$-0.350003\pi$
$839$	−14.2675	−	16.4655i	−0.492567	−	0.568453i	−0.946550	+	0.322558i	$0.895457\pi$
$840$		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	−0.783845	−	0.620957i	$-0.786744\pi$
$853$	−1.68392	+	1.94334i	−0.0576562	+	0.0665388i	0.726189	+	0.687495i	$0.241290\pi$
$854$		0			0
$855$	−0.620073	−	4.31270i	−0.0212060	−	0.147491i
$856$		0			0
$857$	3.47499	−	24.1691i	0.118703	−	0.825600i	−0.840283	−	0.542148i	$-0.817611\pi$
$857$	3.47499	−	24.1691i	0.118703	−	0.825600i	0.958986	−	0.283452i	$-0.0914796\pi$
$858$		0			0
$859$	−18.5782	−	11.9395i	−0.633882	−	0.407371i	0.183863	−	0.982952i	$-0.441140\pi$
$859$	−18.5782	−	11.9395i	−0.633882	−	0.407371i	−0.817745	+	0.575581i	$0.804776\pi$
$860$		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	$-0.134437\pi$
$863$	11.0631	+	12.7675i	0.376592	+	0.434611i	−0.535538	+	0.844511i	$0.679891\pi$
$864$		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	−0.350873	−	0.936423i	$-0.614115\pi$
$877$	10.5180	−	6.75953i	0.355169	−	0.228253i	0.706042	+	0.708170i	$0.250479\pi$
$878$		0			0
$879$	26.8846	+	58.8690i	0.906795	+	1.98560i
$880$		0			0
$881$	−38.0568	+	11.1745i	−1.28217	+	0.376478i	−0.850700	−	0.525652i	$-0.823822\pi$
$881$	−38.0568	+	11.1745i	−1.28217	+	0.376478i	−0.431466	+	0.902129i	$0.642003\pi$
$882$		0			0
$883$	−2.54042	+	5.56274i	−0.0854919	+	0.187201i	−0.947549	−	0.319609i	$-0.896448\pi$
$883$	−2.54042	+	5.56274i	−0.0854919	+	0.187201i	0.862058	+	0.506810i	$0.169176\pi$
$884$		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	$-0.552208\pi$
$887$	−24.8394	−	7.29352i	−0.834027	−	0.244892i	−0.670746	+	0.741687i	$0.734026\pi$
$888$		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	$-0.573240\pi$
$907$	−28.4997	−	8.36827i	−0.946317	−	0.277864i	−0.718253	+	0.695782i	$0.755058\pi$
$908$		0			0
$909$	18.9231	+	21.8384i	0.627639	+	0.724334i
$910$		0			0
$911$	21.4746	−	47.0228i	0.711485	−	1.55794i	−0.113980	−	0.993483i	$-0.536360\pi$
$911$	21.4746	−	47.0228i	0.711485	−	1.55794i	0.825465	−	0.564453i	$-0.190913\pi$
$912$		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	$-0.693228\pi$
$919$	−34.5860			−1.14089			−0.570443	+	0.821337i	$0.693228\pi$
$920$		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	−0.495947	−	0.868353i	$-0.665179\pi$
$929$	14.7852	−	32.3751i	0.485087	−	1.06219i	0.981033	−	0.193839i	$-0.0620939\pi$
$930$		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	−0.991811	−	0.127715i	$-0.959236\pi$
$937$	−0.128379	+	0.892894i	−0.00419395	+	0.0291696i	0.987617	+	0.156884i	$0.0501449\pi$
$938$		0			0
$939$	11.3716	+	79.0915i	0.371100	+	2.58105i
$940$		0			0
$941$	−14.7349	+	17.0050i	−0.480344	+	0.554346i	−0.943260	−	0.332056i	$-0.892258\pi$
$941$	−14.7349	+	17.0050i	−0.480344	+	0.554346i	0.462916	+	0.886402i	$0.346803\pi$
$942$		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	0.971567	+	0.236765i	$0.0760870\pi$
$947$	3.26381	+	22.7003i	0.106060	+	0.737660i	−0.865508	+	0.500896i	$0.833004\pi$
$948$		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	0.363681	−	0.931523i	$-0.381520\pi$
$953$	5.12485	+	1.50479i	0.166010	+	0.0487450i	−0.197671	+	0.980268i	$0.563338\pi$
$954$		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	$-0.599622\pi$
$967$	−19.1486			−0.615777			−0.307889	+	0.951422i	$0.599622\pi$
$968$		0			0
$969$	84.1910	−	54.1063i	2.70461	−	1.73814i
$970$		0			0
$971$	−12.4461	−	27.2532i	−0.399414	−	0.874596i	−0.997329	−	0.0730359i	$-0.976731\pi$
$971$	−12.4461	−	27.2532i	−0.399414	−	0.874596i	0.597915	−	0.801560i	$-0.295996\pi$
$972$		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	0.999696	+	0.0246378i	$0.00784324\pi$
$977$	27.5628	+	31.8092i	0.881812	+	1.01767i	−0.117885	+	0.993027i	$0.537611\pi$
$978$		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	−0.595713	−	0.803197i	$-0.703130\pi$
$983$	6.33817	−	44.0829i	0.202156	−	1.40603i	0.797869	−	0.602830i	$-0.205960\pi$
$984$		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	$-0.880912\pi$
$991$	−13.7448	+	15.8624i	−0.436619	+	0.503885i	0.494209	+	0.869343i	$0.335458\pi$
$992$		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	−0.251822	−	0.967774i	$-0.581030\pi$
$997$	−39.0508	−	25.0964i	−1.23675	−	0.794811i	−0.984928	+	0.172962i	$0.944666\pi$
$998$		0			0
$999$	−1.86309	−	0.547053i	−0.0589456	−	0.0173080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.d.177.1		20
4.3	odd	2		92.2.e.a.85.2	yes	20
12.11	even	2		828.2.q.a.361.2		20
23.6	even	11		8464.2.a.ce.1.2		10
23.13	even	11	inner	368.2.m.d.289.1		20
23.17	odd	22		8464.2.a.cd.1.2		10
92.59	odd	22		92.2.e.a.13.2	✓	20
92.63	even	22		2116.2.a.i.1.9		10
92.75	odd	22		2116.2.a.j.1.9		10
276.59	even	22		828.2.q.a.289.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.e.a.13.2	✓	20	92.59	odd	22
92.2.e.a.85.2	yes	20	4.3	odd	2
368.2.m.d.177.1		20	1.1	even	1	trivial
368.2.m.d.289.1		20	23.13	even	11	inner
828.2.q.a.289.2		20	276.59	even	22
828.2.q.a.361.2		20	12.11	even	2
2116.2.a.i.1.9		10	92.63	even	22
2116.2.a.j.1.9		10	92.75	odd	22
8464.2.a.cd.1.2		10	23.17	odd	22
8464.2.a.ce.1.2		10	23.6	even	11

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\), degree \(10\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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