LMFDB - Embedded newform 936.2.s.f.529.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(529,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.529"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-3,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.19
Character	$\chi$	$=$	936.529
Dual form			936.2.s.f.913.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.64850 + 0.531456i) q^{3} +(-1.09120 - 1.89001i) q^{5} +1.62444 q^{7} +(2.43511 + 1.75221i) q^{9} +(-1.74498 - 3.02239i) q^{11} +(2.69679 - 2.39318i) q^{13} +(-0.794383 - 3.69561i) q^{15} +(-3.55485 - 6.15718i) q^{17} +(-0.0426269 - 0.0738319i) q^{19} +(2.67788 + 0.863317i) q^{21} -1.90847 q^{23} +(0.118572 - 0.205372i) q^{25} +(3.08305 + 4.18268i) q^{27} +(3.15239 + 5.46010i) q^{29} +(2.99631 + 5.18976i) q^{31} +(-1.27033 - 5.90980i) q^{33} +(-1.77258 - 3.07020i) q^{35} +(2.50439 - 4.33773i) q^{37} +(5.71753 - 2.51193i) q^{39} +11.0342 q^{41} -3.50171 q^{43} +(0.654515 - 6.51439i) q^{45} +(-1.46942 + 2.54511i) q^{47} -4.36121 q^{49} +(-2.58790 - 12.0394i) q^{51} -13.8893 q^{53} +(-3.80824 + 6.59606i) q^{55} +(-0.0310320 - 0.144366i) q^{57} +(7.53673 - 13.0540i) q^{59} +0.0516412 q^{61} +(3.95568 + 2.84636i) q^{63} +(-7.46587 - 2.48553i) q^{65} +13.6301 q^{67} +(-3.14612 - 1.01427i) q^{69} +(6.20338 + 10.7446i) q^{71} +2.16817 q^{73} +(0.304611 - 0.275540i) q^{75} +(-2.83461 - 4.90968i) q^{77} +(1.05985 - 1.83572i) q^{79} +(2.85950 + 8.53365i) q^{81} +(-1.31415 + 2.27618i) q^{83} +(-7.75810 + 13.4374i) q^{85} +(2.29491 + 10.6763i) q^{87} +(-2.44105 + 4.22802i) q^{89} +(4.38077 - 3.88757i) q^{91} +(2.18129 + 10.1477i) q^{93} +(-0.0930288 + 0.161131i) q^{95} -9.56568 q^{97} +(1.04666 - 10.4174i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.64850	+	0.531456i	0.951762	+	0.306836i
$3$	1.64850	+	0.531456i	0.951762	+	0.306836i
$4$		0			0
$5$	−1.09120	−	1.89001i	−0.487999	−	0.845239i	0.511906	−	0.859042i	$-0.328940\pi$
$5$	−1.09120	−	1.89001i	−0.487999	−	0.845239i	−0.999905	+	0.0138028i	$0.995606\pi$
$6$		0			0
$7$	1.62444			0.613979			0.306989	−	0.951713i	$-0.400678\pi$
$7$	1.62444			0.613979			0.306989	+	0.951713i	$0.400678\pi$
$8$		0			0
$9$	2.43511	+	1.75221i	0.811703	+	0.584071i
$10$		0			0
$11$	−1.74498	−	3.02239i	−0.526131	−	0.911286i	−0.999537	−	0.0304412i	$-0.990309\pi$
$11$	−1.74498	−	3.02239i	−0.526131	−	0.911286i	0.473405	−	0.880845i	$-0.343025\pi$
$12$		0			0
$13$	2.69679	−	2.39318i	0.747956	−	0.663749i
$13$	2.69679	−	2.39318i	0.747956	−	0.663749i
$14$		0			0
$15$	−0.794383	−	3.69561i	−0.205109	−	0.954202i
$16$		0			0
$17$	−3.55485	−	6.15718i	−0.862178	−	1.49334i	−0.869822	−	0.493365i	$-0.835767\pi$
$17$	−3.55485	−	6.15718i	−0.862178	−	1.49334i	0.00764447	−	0.999971i	$-0.497567\pi$
$18$		0			0
$19$	−0.0426269	−	0.0738319i	−0.00977928	−	0.0169382i	0.861094	−	0.508445i	$-0.169780\pi$
$19$	−0.0426269	−	0.0738319i	−0.00977928	−	0.0169382i	−0.870874	+	0.491507i	$0.836446\pi$
$20$		0			0
$21$	2.67788	+	0.863317i	0.584362	+	0.188391i
$22$		0			0
$23$	−1.90847			−0.397945			−0.198972	−	0.980005i	$-0.563760\pi$
$23$	−1.90847			−0.397945			−0.198972	+	0.980005i	$0.563760\pi$
$24$		0			0
$25$	0.118572	−	0.205372i	0.0237143	−	0.0410744i
$26$		0			0
$27$	3.08305	+	4.18268i	0.593334	+	0.804957i
$28$		0			0
$29$	3.15239	+	5.46010i	0.585384	+	1.01391i	0.994827	+	0.101579i	$0.0323894\pi$
$29$	3.15239	+	5.46010i	0.585384	+	1.01391i	−0.409444	+	0.912335i	$0.634277\pi$
$30$		0			0
$31$	2.99631	+	5.18976i	0.538153	+	0.932109i	0.999004	+	0.0446308i	$0.0142112\pi$
$31$	2.99631	+	5.18976i	0.538153	+	0.932109i	−0.460850	+	0.887478i	$0.652456\pi$
$32$		0			0
$33$	−1.27033	−	5.90980i	−0.221136	−	1.02876i
$34$		0			0
$35$	−1.77258	−	3.07020i	−0.299621	−	0.518959i
$36$		0			0
$37$	2.50439	−	4.33773i	0.411719	−	0.713119i	−0.583359	−	0.812215i	$-0.698262\pi$
$37$	2.50439	−	4.33773i	0.411719	−	0.713119i	0.995078	+	0.0990961i	$0.0315951\pi$
$38$		0			0
$39$	5.71753	−	2.51193i	0.915538	−	0.402231i
$40$		0			0
$41$	11.0342			1.72325			0.861624	−	0.507548i	$-0.169448\pi$
$41$	11.0342			1.72325			0.861624	+	0.507548i	$0.169448\pi$
$42$		0			0
$43$	−3.50171			−0.534006			−0.267003	−	0.963696i	$-0.586033\pi$
$43$	−3.50171			−0.534006			−0.267003	+	0.963696i	$0.586033\pi$
$44$		0			0
$45$	0.654515	−	6.51439i	0.0975693	−	0.971108i
$46$		0			0
$47$	−1.46942	+	2.54511i	−0.214337	+	0.371242i	−0.953067	−	0.302759i	$-0.902092\pi$
$47$	−1.46942	+	2.54511i	−0.214337	+	0.371242i	0.738731	+	0.674001i	$0.235426\pi$
$48$		0			0
$49$	−4.36121			−0.623030
$50$		0			0
$51$	−2.58790	−	12.0394i	−0.362378	−	1.68585i
$52$		0			0
$53$	−13.8893			−1.90784			−0.953920	−	0.300060i	$-0.902993\pi$
$53$	−13.8893			−1.90784			−0.953920	+	0.300060i	$0.902993\pi$
$54$		0			0
$55$	−3.80824	+	6.59606i	−0.513503	+	0.889413i
$56$		0			0
$57$	−0.0310320	−	0.144366i	−0.00411029	−	0.0191218i
$58$		0			0
$59$	7.53673	−	13.0540i	0.981198	−	1.69949i	0.323454	−	0.946244i	$-0.395156\pi$
$59$	7.53673	−	13.0540i	0.981198	−	1.69949i	0.657745	−	0.753241i	$-0.271511\pi$
$60$		0			0
$61$	0.0516412			0.00661198			0.00330599	−	0.999995i	$-0.498948\pi$
$61$	0.0516412			0.00661198			0.00330599	+	0.999995i	$0.498948\pi$
$62$		0			0
$63$	3.95568	+	2.84636i	0.498368	+	0.358607i
$64$		0			0
$65$	−7.46587	−	2.48553i	−0.926028	−	0.308292i
$66$		0			0
$67$	13.6301			1.66518			0.832592	−	0.553887i	$-0.186856\pi$
$67$	13.6301			1.66518			0.832592	+	0.553887i	$0.186856\pi$
$68$		0			0
$69$	−3.14612	−	1.01427i	−0.378749	−	0.122104i
$70$		0			0
$71$	6.20338	+	10.7446i	0.736205	+	1.27514i	0.954193	+	0.299193i	$0.0967175\pi$
$71$	6.20338	+	10.7446i	0.736205	+	1.27514i	−0.217987	+	0.975952i	$0.569949\pi$
$72$		0			0
$73$	2.16817			0.253766			0.126883	−	0.991918i	$-0.459503\pi$
$73$	2.16817			0.253766			0.126883	+	0.991918i	$0.459503\pi$
$74$		0			0
$75$	0.304611	−	0.275540i	0.0351735	−	0.0318166i
$76$		0			0
$77$	−2.83461	−	4.90968i	−0.323033	−	0.559510i
$78$		0			0
$79$	1.05985	−	1.83572i	0.119243	−	0.206535i	−0.800225	−	0.599700i	$-0.795287\pi$
$79$	1.05985	−	1.83572i	0.119243	−	0.206535i	0.919468	+	0.393165i	$0.128620\pi$
$80$		0			0
$81$	2.85950	+	8.53365i	0.317723	+	0.948184i
$82$		0			0
$83$	−1.31415	+	2.27618i	−0.144247	+	0.249843i	−0.929092	−	0.369849i	$-0.879409\pi$
$83$	−1.31415	+	2.27618i	−0.144247	+	0.249843i	0.784845	+	0.619692i	$0.212743\pi$
$84$		0			0
$85$	−7.75810	+	13.4374i	−0.841484	+	1.45749i
$86$		0			0
$87$	2.29491	+	10.6763i	0.246040	+	1.14462i
$88$		0			0
$89$	−2.44105	+	4.22802i	−0.258751	+	0.448170i	−0.965908	−	0.258887i	$-0.916644\pi$
$89$	−2.44105	+	4.22802i	−0.258751	+	0.448170i	0.707157	+	0.707057i	$0.249978\pi$
$90$		0			0
$91$	4.38077	−	3.88757i	0.459229	−	0.407528i
$92$		0			0
$93$	2.18129	+	10.1477i	0.226189	+	1.05227i
$94$		0			0
$95$	−0.0930288	+	0.161131i	−0.00954455	+	0.0165317i
$96$		0			0
$97$	−9.56568			−0.971248			−0.485624	−	0.874168i	$-0.661408\pi$
$97$	−9.56568			−0.971248			−0.485624	+	0.874168i	$0.661408\pi$
$98$		0			0
$99$	1.04666	−	10.4174i	0.105193	−	1.04699i
$100$		0			0
$101$	0.247149	+	0.428074i	0.0245922	+	0.0425950i	0.878060	−	0.478551i	$-0.158838\pi$
$101$	0.247149	+	0.428074i	0.0245922	+	0.0425950i	−0.853467	+	0.521146i	$0.825505\pi$
$102$		0			0
$103$	6.42380	+	11.1263i	0.632956	+	1.09631i	0.986944	+	0.161062i	$0.0514918\pi$
$103$	6.42380	+	11.1263i	0.632956	+	1.09631i	−0.353989	+	0.935250i	$0.615175\pi$
$104$		0			0
$105$	−1.29042	−	6.00328i	−0.125932	−	0.585860i
$106$		0			0
$107$	5.63470	−	9.75958i	0.544727	−	0.943494i	−0.453897	−	0.891054i	$-0.649967\pi$
$107$	5.63470	−	9.75958i	0.544727	−	0.943494i	0.998624	−	0.0524402i	$-0.0166999\pi$
$108$		0			0
$109$	−8.17104			−0.782643			−0.391322	−	0.920254i	$-0.627982\pi$
$109$	−8.17104			−0.782643			−0.391322	+	0.920254i	$0.627982\pi$
$110$		0			0
$111$	6.43380	−	5.81978i	0.610670	−	0.552389i
$112$		0			0
$113$	−5.74694	+	9.95399i	−0.540626	+	0.936392i	0.458242	+	0.888828i	$0.348479\pi$
$113$	−5.74694	+	9.95399i	−0.540626	+	0.936392i	−0.998868	+	0.0475648i	$0.984854\pi$
$114$		0			0
$115$	2.08252	+	3.60704i	0.194196	+	0.336358i
$116$		0			0
$117$	10.7603	−	1.10230i	0.994794	−	0.101908i
$118$		0			0
$119$	−5.77463	−	10.0019i	−0.529359	−	0.916877i
$120$		0			0
$121$	−0.589908	+	1.02175i	−0.0536280	+	0.0928863i
$122$		0			0
$123$	18.1898	+	5.86418i	1.64012	+	0.528755i
$124$		0			0
$125$	−11.4295			−1.02229
$126$		0			0
$127$	−9.03929	+	15.6565i	−0.802107	+	1.38929i	0.116120	+	0.993235i	$0.462954\pi$
$127$	−9.03929	+	15.6565i	−0.802107	+	1.38929i	−0.918227	+	0.396055i	$0.870379\pi$
$128$		0			0
$129$	−5.77257	−	1.86101i	−0.508246	−	0.163852i
$130$		0			0
$131$	4.32214	+	7.48616i	0.377627	+	0.654069i	0.990716	−	0.135945i	$-0.0434069\pi$
$131$	4.32214	+	7.48616i	0.377627	+	0.654069i	−0.613090	+	0.790013i	$0.710074\pi$
$132$		0			0
$133$	−0.0692446	−	0.119935i	−0.00600427	−	0.0103997i
$134$		0			0
$135$	4.54108	−	10.3911i	0.390834	−	0.894327i
$136$		0			0
$137$	−4.88291			−0.417175			−0.208588	−	0.978004i	$-0.566887\pi$
$137$	−4.88291			−0.417175			−0.208588	+	0.978004i	$0.566887\pi$
$138$		0			0
$139$	−8.44513	+	14.6274i	−0.716307	+	1.24068i	0.246146	+	0.969233i	$0.420836\pi$
$139$	−8.44513	+	14.6274i	−0.716307	+	1.24068i	−0.962453	+	0.271447i	$0.912498\pi$
$140$		0			0
$141$	−3.77495	+	3.41468i	−0.317908	+	0.287568i
$142$		0			0
$143$	−11.9390	−	3.97471i	−0.998388	−	0.332382i
$144$		0			0
$145$	6.87976	−	11.9161i	0.571333	−	0.989578i
$146$		0			0
$147$	−7.18945	−	2.31779i	−0.592976	−	0.191168i
$148$		0			0
$149$	−0.949804	+	1.64511i	−0.0778110	+	0.134773i	−0.902305	−	0.431098i	$-0.858126\pi$
$149$	−0.949804	+	1.64511i	−0.0778110	+	0.134773i	0.824494	+	0.565870i	$0.191460\pi$
$150$		0			0
$151$	0.337746	−	0.584993i	0.0274853	−	0.0476060i	−0.851956	−	0.523614i	$-0.824583\pi$
$151$	0.337746	−	0.584993i	0.0274853	−	0.0476060i	0.879441	+	0.476008i	$0.157917\pi$
$152$		0			0
$153$	2.13224	−	21.2223i	0.172382	−	1.71572i
$154$		0			0
$155$	6.53914	−	11.3261i	0.525236	−	0.909736i
$156$		0			0
$157$	4.74281	+	8.21479i	0.378518	+	0.655612i	0.990847	−	0.134991i	$-0.0431006\pi$
$157$	4.74281	+	8.21479i	0.378518	+	0.655612i	−0.612329	+	0.790603i	$0.709767\pi$
$158$		0			0
$159$	−22.8965	−	7.38155i	−1.81581	−	0.585395i
$160$		0			0
$161$	−3.10019			−0.244330
$162$		0			0
$163$	0.374266	+	0.648248i	0.0293148	+	0.0507747i	0.880311	−	0.474398i	$-0.157334\pi$
$163$	0.374266	+	0.648248i	0.0293148	+	0.0507747i	−0.850996	+	0.525172i	$0.824001\pi$
$164$		0			0
$165$	−9.78340	+	8.84970i	−0.761637	+	0.688948i
$166$		0			0
$167$	8.88147			0.687269			0.343635	−	0.939103i	$-0.388342\pi$
$167$	8.88147			0.687269			0.343635	+	0.939103i	$0.388342\pi$
$168$		0			0
$169$	1.54537	−	12.9078i	0.118875	−	0.992909i
$170$		0			0
$171$	0.0255681	−	0.254480i	0.00195524	−	0.0194606i
$172$		0			0
$173$	12.6011			0.958040			0.479020	−	0.877804i	$-0.340992\pi$
$173$	12.6011			0.958040			0.479020	+	0.877804i	$0.340992\pi$
$174$		0			0
$175$	0.192612	−	0.333614i	0.0145601	−	0.0252188i
$176$		0			0
$177$	19.3619	−	17.5141i	1.45533	−	1.31644i
$178$		0			0
$179$	0.552989	−	0.957806i	0.0413324	−	0.0715898i	−0.844619	−	0.535368i	$-0.820173\pi$
$179$	0.552989	−	0.957806i	0.0413324	−	0.0715898i	0.885952	+	0.463778i	$0.153506\pi$
$180$		0			0
$181$	−13.0578			−0.970581			−0.485291	−	0.874353i	$-0.661286\pi$
$181$	−13.0578			−0.970581			−0.485291	+	0.874353i	$0.661286\pi$
$182$		0			0
$183$	0.0851306	+	0.0274451i	0.00629303	+	0.00202880i
$184$		0			0
$185$	−10.9311			−0.803674
$186$		0			0
$187$	−12.4063	+	21.4883i	−0.907237	+	1.57138i
$188$		0			0
$189$	5.00822	+	6.79449i	0.364294	+	0.494226i
$190$		0			0
$191$	−15.8117			−1.14409			−0.572047	−	0.820221i	$-0.693851\pi$
$191$	−15.8117			−1.14409			−0.572047	+	0.820221i	$0.693851\pi$
$192$		0			0
$193$	−0.0877797			−0.00631852			−0.00315926	−	0.999995i	$-0.501006\pi$
$193$	−0.0877797			−0.00631852			−0.00315926	+	0.999995i	$0.501006\pi$
$194$		0			0
$195$	−10.9865	−	8.06519i	−0.786763	−	0.577560i
$196$		0			0
$197$	1.65641	−	2.86899i	0.118014	−	0.204407i	−0.800966	−	0.598709i	$-0.795680\pi$
$197$	1.65641	−	2.86899i	0.118014	−	0.204407i	0.918981	+	0.394302i	$0.129014\pi$
$198$		0			0
$199$	10.0424	+	17.3940i	0.711890	+	1.23303i	0.964147	+	0.265369i	$0.0854939\pi$
$199$	10.0424	+	17.3940i	0.711890	+	1.23303i	−0.252257	+	0.967660i	$0.581173\pi$
$200$		0			0
$201$	22.4693	+	7.24381i	1.58486	+	0.510939i
$202$		0			0
$203$	5.12085	+	8.86957i	0.359413	+	0.622522i
$204$		0			0
$205$	−12.0405	−	20.8547i	−0.840943	−	1.45656i
$206$		0			0
$207$	−4.64734	−	3.34405i	−0.323013	−	0.232428i
$208$		0			0
$209$	−0.148766	+	0.257670i	−0.0102904	+	0.0178234i
$210$		0			0
$211$	7.95799			0.547851			0.273925	−	0.961751i	$-0.411678\pi$
$211$	7.95799			0.547851			0.273925	+	0.961751i	$0.411678\pi$
$212$		0			0
$213$	4.51600	+	21.0092i	0.309431	+	1.43953i
$214$		0			0
$215$	3.82106	+	6.61827i	0.260594	+	0.451362i
$216$		0			0
$217$	4.86731	+	8.43043i	0.330415	+	0.572295i
$218$		0			0
$219$	3.57424	+	1.15229i	0.241525	+	0.0778646i
$220$		0			0
$221$	−24.3219	−	8.09724i	−1.63607	−	0.544679i
$222$		0			0
$223$	−8.59514	−	14.8872i	−0.575573	−	0.996922i	−0.995979	−	0.0895857i	$-0.971446\pi$
$223$	−8.59514	−	14.8872i	−0.575573	−	0.996922i	0.420406	−	0.907336i	$-0.361888\pi$
$224$		0			0
$225$	0.648590	−	0.292340i	0.0432393	−	0.0194894i
$226$		0			0
$227$	6.56551			0.435768			0.217884	−	0.975975i	$-0.430085\pi$
$227$	6.56551			0.435768			0.217884	+	0.975975i	$0.430085\pi$
$228$		0			0
$229$	3.57171	+	6.18638i	0.236025	+	0.408808i	0.959570	−	0.281470i	$-0.0908218\pi$
$229$	3.57171	+	6.18638i	0.236025	+	0.408808i	−0.723545	+	0.690277i	$0.757489\pi$
$230$		0			0
$231$	−2.06357	−	9.60009i	−0.135773	−	0.631639i
$232$		0			0
$233$	−26.7650			−1.75344			−0.876718	−	0.481005i	$-0.840272\pi$
$233$	−26.7650			−1.75344			−0.876718	+	0.481005i	$0.840272\pi$
$234$		0			0
$235$	6.41371			0.418384
$236$		0			0
$237$	2.72278	−	2.46292i	0.176863	−	0.159984i
$238$		0			0
$239$	−4.47336	−	7.74809i	−0.289358	−	0.501182i	0.684299	−	0.729202i	$-0.260108\pi$
$239$	−4.47336	−	7.74809i	−0.289358	−	0.501182i	−0.973657	+	0.228019i	$0.926775\pi$
$240$		0			0
$241$	4.80610			0.309588			0.154794	−	0.987947i	$-0.450529\pi$
$241$	4.80610			0.309588			0.154794	+	0.987947i	$0.450529\pi$
$242$		0			0
$243$	0.178629	+	15.5874i	0.0114591	+	0.999934i
$244$		0			0
$245$	4.75894	+	8.24273i	0.304038	+	0.526609i
$246$		0			0
$247$	−0.291649	−	0.0970955i	−0.0185572	−	0.00617804i
$248$		0			0
$249$	−3.37607	+	3.05387i	−0.213950	+	0.193531i
$250$		0			0
$251$	−3.00361	−	5.20240i	−0.189586	−	0.328372i	0.755526	−	0.655118i	$-0.227381\pi$
$251$	−3.00361	−	5.20240i	−0.189586	−	0.328372i	−0.945112	+	0.326746i	$0.894048\pi$
$252$		0			0
$253$	3.33025	+	5.76816i	0.209371	+	0.362641i
$254$		0			0
$255$	−19.9306	+	18.0285i	−1.24810	+	1.12899i
$256$		0			0
$257$	−24.8057			−1.54734			−0.773670	−	0.633589i	$-0.781581\pi$
$257$	−24.8057			−1.54734			−0.773670	+	0.633589i	$0.781581\pi$
$258$		0			0
$259$	4.06822	−	7.04637i	0.252787	−	0.437840i
$260$		0			0
$261$	−1.89084	+	18.8196i	−0.117040	+	1.16490i
$262$		0			0
$263$	13.4369	+	23.2734i	0.828555	+	1.43510i	0.899171	+	0.437597i	$0.144170\pi$
$263$	13.4369	+	23.2734i	0.828555	+	1.43510i	−0.0706160	+	0.997504i	$0.522496\pi$
$264$		0			0
$265$	15.1560	+	26.2509i	0.931024	+	1.61258i
$266$		0			0
$267$	−6.27109	+	5.67259i	−0.383784	+	0.347157i
$268$		0			0
$269$	2.24037	+	3.88044i	0.136598	+	0.236594i	0.926207	−	0.377016i	$-0.123050\pi$
$269$	2.24037	+	3.88044i	0.136598	+	0.236594i	−0.789609	+	0.613611i	$0.789717\pi$
$270$		0			0
$271$	−8.87915	+	15.3791i	−0.539370	+	0.934216i	0.459568	+	0.888142i	$0.348004\pi$
$271$	−8.87915	+	15.3791i	−0.539370	+	0.934216i	−0.998938	+	0.0460733i	$0.985329\pi$
$272$		0			0
$273$	9.28777	−	4.08047i	0.562121	−	0.246961i
$274$		0			0
$275$	−0.827620			−0.0499073
$276$		0			0
$277$	29.1347			1.75053			0.875267	−	0.483641i	$-0.160686\pi$
$277$	29.1347			1.75053			0.875267	+	0.483641i	$0.160686\pi$
$278$		0			0
$279$	−1.79722	+	17.8878i	−0.107597	+	1.07091i
$280$		0			0
$281$	−11.5323	+	19.9746i	−0.687962	+	1.19158i	0.284535	+	0.958666i	$0.408161\pi$
$281$	−11.5323	+	19.9746i	−0.687962	+	1.19158i	−0.972496	+	0.232919i	$0.925172\pi$
$282$		0			0
$283$	0.481154			0.0286017			0.0143008	−	0.999898i	$-0.495448\pi$
$283$	0.481154			0.0286017			0.0143008	+	0.999898i	$0.495448\pi$
$284$		0			0
$285$	−0.238992	+	0.216183i	−0.0141567	+	0.0128056i
$286$		0			0
$287$	17.9243			1.05804
$288$		0			0
$289$	−16.7739	+	29.0533i	−0.986701	+	1.70902i
$290$		0			0
$291$	−15.7690	−	5.08374i	−0.924397	−	0.298014i
$292$		0			0
$293$	7.51118	−	13.0098i	0.438808	−	0.760038i	−0.558790	−	0.829309i	$-0.688734\pi$
$293$	7.51118	−	13.0098i	0.438808	−	0.760038i	0.997598	+	0.0692715i	$0.0220675\pi$
$294$		0			0
$295$	−32.8963			−1.91529
$296$		0			0
$297$	7.26183	−	16.6169i	0.421374	−	0.964209i
$298$		0			0
$299$	−5.14676	+	4.56733i	−0.297645	+	0.264135i
$300$		0			0
$301$	−5.68830			−0.327868
$302$		0			0
$303$	0.179922	+	0.837029i	0.0103363	+	0.0480861i
$304$		0			0
$305$	−0.0563508	−	0.0976025i	−0.00322664	−	0.00558870i
$306$		0			0
$307$	−19.2835			−1.10057			−0.550283	−	0.834978i	$-0.685480\pi$
$307$	−19.2835			−1.10057			−0.550283	+	0.834978i	$0.685480\pi$
$308$		0			0
$309$	4.67647	+	21.7558i	0.266035	+	1.23764i
$310$		0			0
$311$	2.34648	+	4.06422i	0.133056	+	0.230461i	0.924853	−	0.380324i	$-0.124187\pi$
$311$	2.34648	+	4.06422i	0.133056	+	0.230461i	−0.791797	+	0.610785i	$0.790854\pi$
$312$		0			0
$313$	5.97393	−	10.3471i	0.337666	−	0.584855i	−0.646327	−	0.763060i	$-0.723696\pi$
$313$	5.97393	−	10.3471i	0.337666	−	0.584855i	0.983993	+	0.178205i	$0.0570292\pi$
$314$		0			0
$315$	1.06322	−	10.5822i	0.0599055	−	0.596240i
$316$		0			0
$317$	0.834451	−	1.44531i	0.0468674	−	0.0811768i	−0.841640	−	0.540039i	$-0.818409\pi$
$317$	0.834451	−	1.44531i	0.0468674	−	0.0811768i	0.888507	+	0.458862i	$0.151743\pi$
$318$		0			0
$319$	11.0017	−	19.0555i	0.615977	−	1.06690i
$320$		0			0
$321$	14.4756	−	13.0941i	0.807949	−	0.730840i
$322$		0			0
$323$	−0.303064	+	0.524923i	−0.0168630	+	0.0292075i
$324$		0			0
$325$	−0.171729	−	0.837609i	−0.00952583	−	0.0464622i
$326$		0			0
$327$	−13.4700	−	4.34255i	−0.744890	−	0.240144i
$328$		0			0
$329$	−2.38697	+	4.13436i	−0.131598	+	0.227935i
$330$		0			0
$331$	24.5403			1.34886			0.674430	−	0.738339i	$-0.264390\pi$
$331$	24.5403			1.34886			0.674430	+	0.738339i	$0.264390\pi$
$332$		0			0
$333$	13.6991	−	6.17462i	0.750705	−	0.338367i
$334$		0			0
$335$	−14.8732	−	25.7611i	−0.812608	−	1.40748i
$336$		0			0
$337$	−7.09634	−	12.2912i	−0.386562	−	0.669545i	0.605422	−	0.795904i	$-0.293004\pi$
$337$	−7.09634	−	12.2912i	−0.386562	−	0.669545i	−0.991985	+	0.126359i	$0.959671\pi$
$338$		0			0
$339$	−14.7639	+	13.3549i	−0.801867	+	0.725339i
$340$		0			0
$341$	10.4570	−	18.1121i	0.566278	−	0.980823i
$342$		0			0
$343$	−18.4556			−0.996506
$344$		0			0
$345$	1.51606	+	7.05298i	0.0816219	+	0.379720i
$346$		0			0
$347$	10.9540	−	18.9729i	0.588042	−	1.01852i	−0.406447	−	0.913674i	$-0.633232\pi$
$347$	10.9540	−	18.9729i	0.588042	−	1.01852i	0.994489	−	0.104844i	$-0.0334343\pi$
$348$		0			0
$349$	−9.65509	−	16.7231i	−0.516825	−	0.895168i	−0.999809	−	0.0195384i	$-0.993780\pi$
$349$	−9.65509	−	16.7231i	−0.516825	−	0.895168i	0.482984	−	0.875629i	$-0.339553\pi$
$350$		0			0
$351$	18.3243	+	3.90151i	0.978076	+	0.208247i
$352$		0			0
$353$	15.1041	+	26.1610i	0.803908	+	1.39241i	0.917026	+	0.398828i	$0.130583\pi$
$353$	15.1041	+	26.1610i	0.803908	+	1.39241i	−0.113118	+	0.993582i	$0.536084\pi$
$354$		0			0
$355$	13.5382	−	23.4489i	0.718535	−	1.24454i
$356$		0			0
$357$	−4.20388	−	19.5572i	−0.222493	−	1.03508i
$358$		0			0
$359$	4.42088			0.233325			0.116662	−	0.993172i	$-0.462780\pi$
$359$	4.42088			0.233325			0.116662	+	0.993172i	$0.462780\pi$
$360$		0			0
$361$	9.49637	−	16.4482i	0.499809	−	0.865694i
$362$		0			0
$363$	−1.51548	+	1.37085i	−0.0795420	+	0.0719507i
$364$		0			0
$365$	−2.36591	−	4.09788i	−0.123837	−	0.214493i
$366$		0			0
$367$	−9.39687	−	16.2759i	−0.490513	−	0.849593i	0.509428	−	0.860513i	$-0.329857\pi$
$367$	−9.39687	−	16.2759i	−0.490513	−	0.849593i	−0.999940	+	0.0109207i	$0.996524\pi$
$368$		0			0
$369$	26.8694	+	19.3342i	1.39876	+	1.00650i
$370$		0			0
$371$	−22.5623			−1.17137
$372$		0			0
$373$	4.49251	−	7.78126i	0.232614	−	0.402899i	−0.725963	−	0.687734i	$-0.758606\pi$
$373$	4.49251	−	7.78126i	0.232614	−	0.402899i	0.958576	+	0.284835i	$0.0919389\pi$
$374$		0			0
$375$	−18.8416	−	6.07429i	−0.972975	−	0.313675i
$376$		0			0
$377$	21.5683	+	7.18051i	1.11083	+	0.369815i
$378$		0			0
$379$	3.07943	−	5.33373i	0.158180	−	0.273975i	−0.776033	−	0.630693i	$-0.782771\pi$
$379$	3.07943	−	5.33373i	0.158180	−	0.273975i	0.934212	+	0.356717i	$0.116104\pi$
$380$		0			0
$381$	−23.2220	+	21.0058i	−1.18970	+	1.07616i
$382$		0			0
$383$	−8.93512	+	15.4761i	−0.456563	+	0.790791i	−0.998777	−	0.0494499i	$-0.984253\pi$
$383$	−8.93512	+	15.4761i	−0.456563	+	0.790791i	0.542213	+	0.840241i	$0.317587\pi$
$384$		0			0
$385$	−6.18624	+	10.7149i	−0.315280	+	0.546081i
$386$		0			0
$387$	−8.52704	−	6.13574i	−0.433454	−	0.311897i
$388$		0			0
$389$	9.77128	−	16.9244i	0.495424	−	0.858099i	−0.504563	−	0.863375i	$-0.668346\pi$
$389$	9.77128	−	16.9244i	0.495424	−	0.858099i	0.999986	+	0.00527638i	$0.00167953\pi$
$390$		0			0
$391$	6.78434	+	11.7508i	0.343099	+	0.594265i
$392$		0			0
$393$	3.14648	+	14.6380i	0.158719	+	0.738387i
$394$		0			0
$395$	−4.62605			−0.232762
$396$		0			0
$397$	10.9910	+	19.0370i	0.551623	+	0.955439i	0.998158	+	0.0606729i	$0.0193246\pi$
$397$	10.9910	+	19.0370i	0.551623	+	0.955439i	−0.446535	+	0.894766i	$0.647342\pi$
$398$		0			0
$399$	−0.0504095	−	0.234514i	−0.00252363	−	0.0117404i
$400$		0			0
$401$	19.7203			0.984784			0.492392	−	0.870374i	$-0.336123\pi$
$401$	19.7203			0.984784			0.492392	+	0.870374i	$0.336123\pi$
$402$		0			0
$403$	20.5005	+	6.82500i	1.02120	+	0.339977i
$404$		0			0
$405$	13.0084	−	14.7164i	0.646393	−	0.731264i
$406$		0			0
$407$	−17.4804			−0.866473
$408$		0			0
$409$	17.5244	−	30.3531i	0.866524	−	1.50086i	0.000997339	−	1.00000i	$-0.499683\pi$
$409$	17.5244	−	30.3531i	0.866524	−	1.50086i	0.865526	−	0.500863i	$-0.166984\pi$
$410$		0			0
$411$	−8.04948	−	2.59505i	−0.397052	−	0.128005i
$412$		0			0
$413$	12.2429	−	21.2054i	0.602435	−	1.04345i
$414$		0			0
$415$	5.73600			0.281569
$416$		0			0
$417$	−21.6956	+	19.6251i	−1.06244	+	0.961043i
$418$		0			0
$419$	31.8872			1.55779			0.778896	−	0.627153i	$-0.215780\pi$
$419$	31.8872			1.55779			0.778896	+	0.627153i	$0.215780\pi$
$420$		0			0
$421$	−0.817750	+	1.41638i	−0.0398547	+	0.0690304i	−0.885265	−	0.465088i	$-0.846023\pi$
$421$	−0.817750	+	1.41638i	−0.0398547	+	0.0690304i	0.845410	+	0.534118i	$0.179356\pi$
$422$		0			0
$423$	−8.03776	+	3.62288i	−0.390809	+	0.176150i
$424$		0			0
$425$	−1.68602			−0.0817838
$426$		0			0
$427$	0.0838878			0.00405962
$428$		0			0
$429$	−17.5690	−	12.8974i	−0.848241	−	0.622691i
$430$		0			0
$431$	9.96045	−	17.2520i	0.479778	−	0.831000i	−0.519953	−	0.854195i	$-0.674051\pi$
$431$	9.96045	−	17.2520i	0.479778	−	0.831000i	0.999731	+	0.0231952i	$0.00738392\pi$
$432$		0			0
$433$	−9.34496	−	16.1859i	−0.449090	−	0.777847i	0.549237	−	0.835667i	$-0.314918\pi$
$433$	−9.34496	−	16.1859i	−0.449090	−	0.777847i	−0.998327	+	0.0578197i	$0.981585\pi$
$434$		0			0
$435$	17.6742	−	15.9874i	0.847412	−	0.766537i
$436$		0			0
$437$	0.0813523	+	0.140906i	0.00389161	+	0.00674047i
$438$		0			0
$439$	3.53370	+	6.12055i	0.168654	+	0.292118i	0.937947	−	0.346779i	$-0.112725\pi$
$439$	3.53370	+	6.12055i	0.168654	+	0.292118i	−0.769293	+	0.638897i	$0.779391\pi$
$440$		0			0
$441$	−10.6200	−	7.64176i	−0.505715	−	0.363894i
$442$		0			0
$443$	3.32667	−	5.76196i	0.158055	−	0.273759i	−0.776112	−	0.630595i	$-0.782811\pi$
$443$	3.32667	−	5.76196i	0.158055	−	0.273759i	0.934167	+	0.356836i	$0.116144\pi$
$444$		0			0
$445$	10.6547			0.505081
$446$		0			0
$447$	−2.44006	+	2.20718i	−0.115411	+	0.104396i
$448$		0			0
$449$	13.9833	+	24.2198i	0.659913	+	1.14300i	0.980638	+	0.195830i	$0.0627402\pi$
$449$	13.9833	+	24.2198i	0.659913	+	1.14300i	−0.320725	+	0.947172i	$0.603926\pi$
$450$		0			0
$451$	−19.2544	−	33.3496i	−0.906654	−	1.57037i
$452$		0			0
$453$	0.867672	−	0.784863i	0.0407668	−	0.0368761i
$454$		0			0
$455$	−12.1278	−	4.03759i	−0.568562	−	0.189285i
$456$		0			0
$457$	−18.8730	−	32.6889i	−0.882840	−	1.52912i	−0.848169	−	0.529725i	$-0.822295\pi$
$457$	−18.8730	−	32.6889i	−0.882840	−	1.52912i	−0.0346709	−	0.999399i	$-0.511038\pi$
$458$		0			0
$459$	14.7937	−	33.8517i	0.690511	−	1.58006i
$460$		0			0
$461$	13.8811			0.646508			0.323254	−	0.946312i	$-0.395223\pi$
$461$	13.8811			0.646508			0.323254	+	0.946312i	$0.395223\pi$
$462$		0			0
$463$	18.9410	+	32.8067i	0.880262	+	1.52466i	0.851050	+	0.525085i	$0.175966\pi$
$463$	18.9410	+	32.8067i	0.880262	+	1.52466i	0.0292116	+	0.999573i	$0.490700\pi$
$464$		0			0
$465$	16.7991	−	15.1958i	0.779040	−	0.704691i
$466$		0			0
$467$	−3.86318			−0.178767			−0.0893834	−	0.995997i	$-0.528490\pi$
$467$	−3.86318			−0.178767			−0.0893834	+	0.995997i	$0.528490\pi$
$468$		0			0
$469$	22.1412			1.02239
$470$		0			0
$471$	3.45272	+	16.0627i	0.159093	+	0.740129i
$472$		0			0
$473$	6.11041	+	10.5835i	0.280957	+	0.486632i
$474$		0			0
$475$	−0.0202173			−0.000927635
$476$		0			0
$477$	−33.8219	−	24.3370i	−1.54860	−	1.11431i
$478$		0			0
$479$	8.64276	+	14.9697i	0.394898	+	0.683983i	0.993088	−	0.117371i	$-0.0374467\pi$
$479$	8.64276	+	14.9697i	0.394898	+	0.683983i	−0.598191	+	0.801354i	$0.704113\pi$
$480$		0			0
$481$	−3.62715	−	17.6914i	−0.165384	−	0.806659i
$482$		0			0
$483$	−5.11067	−	1.64762i	−0.232544	−	0.0749692i
$484$		0			0
$485$	10.4381	+	18.0793i	0.473968	+	0.820936i
$486$		0			0
$487$	−21.2463	−	36.7996i	−0.962760	−	1.66755i	−0.715516	−	0.698596i	$-0.753808\pi$
$487$	−21.2463	−	36.7996i	−0.962760	−	1.66755i	−0.247244	−	0.968953i	$-0.579525\pi$
$488$		0			0
$489$	0.272462	+	1.26754i	0.0123212	+	0.0573203i
$490$		0			0
$491$	−18.6850			−0.843242			−0.421621	−	0.906772i	$-0.638539\pi$
$491$	−18.6850			−0.843242			−0.421621	+	0.906772i	$0.638539\pi$
$492$		0			0
$493$	22.4125	−	38.8196i	1.00941	−	1.74835i
$494$		0			0
$495$	−20.8312	+	9.38928i	−0.936292	+	0.422017i
$496$		0			0
$497$	10.0770	+	17.4538i	0.452015	+	0.782912i
$498$		0			0
$499$	−10.3656	−	17.9537i	−0.464028	−	0.803720i	0.535129	−	0.844770i	$-0.320263\pi$
$499$	−10.3656	−	17.9537i	−0.464028	−	0.803720i	−0.999157	+	0.0410501i	$0.986930\pi$
$500$		0			0
$501$	14.6411	+	4.72012i	0.654117	+	0.210879i
$502$		0			0
$503$	11.4265	+	19.7913i	0.509482	+	0.882449i	0.999940	+	0.0109836i	$0.00349625\pi$
$503$	11.4265	+	19.7913i	0.509482	+	0.882449i	−0.490458	+	0.871465i	$0.663170\pi$
$504$		0			0
$505$	0.539377	−	0.934228i	0.0240019	−	0.0415726i
$506$		0			0
$507$	9.40749	−	20.4572i	0.417801	−	0.908538i
$508$		0			0
$509$	−5.63217			−0.249641			−0.124821	−	0.992179i	$-0.539836\pi$
$509$	−5.63217			−0.249641			−0.124821	+	0.992179i	$0.539836\pi$
$510$		0			0
$511$	3.52206			0.155807
$512$		0			0
$513$	0.177394	−	0.405922i	0.00783214	−	0.0179219i
$514$		0			0
$515$	14.0193	−	24.2821i	0.617763	−	1.07000i
$516$		0			0
$517$	10.2564			0.451077
$518$		0			0
$519$	20.7728	+	6.69691i	0.911826	+	0.293962i
$520$		0			0
$521$	9.68917			0.424490			0.212245	−	0.977216i	$-0.431922\pi$
$521$	9.68917			0.424490			0.212245	+	0.977216i	$0.431922\pi$
$522$		0			0
$523$	−6.14028	+	10.6353i	−0.268496	+	0.465048i	−0.968474	−	0.249116i	$-0.919860\pi$
$523$	−6.14028	+	10.6353i	−0.268496	+	0.465048i	0.699978	+	0.714164i	$0.253193\pi$
$524$		0			0
$525$	0.494822	−	0.447597i	0.0215958	−	0.0195347i
$526$		0			0
$527$	21.3029	−	36.8977i	0.927968	−	1.60729i
$528$		0			0
$529$	−19.3577			−0.841640
$530$		0			0
$531$	41.2261	−	18.5819i	1.78906	−	0.806387i
$532$		0			0
$533$	29.7569	−	26.4068i	1.28891	−	1.14380i
$534$		0			0
$535$	−24.5943			−1.06330
$536$		0			0
$537$	1.42064	−	1.28505i	0.0613049	−	0.0554541i
$538$		0			0
$539$	7.61022	+	13.1813i	0.327795	+	0.567758i
$540$		0			0
$541$	−0.713140			−0.0306603			−0.0153301	−	0.999882i	$-0.504880\pi$
$541$	−0.713140			−0.0306603			−0.0153301	+	0.999882i	$0.504880\pi$
$542$		0			0
$543$	−21.5258	−	6.93967i	−0.923763	−	0.297810i
$544$		0			0
$545$	8.91622	+	15.4434i	0.381929	+	0.661520i
$546$		0			0
$547$	−5.31715	+	9.20958i	−0.227345	+	0.393773i	−0.957020	−	0.290021i	$-0.906338\pi$
$547$	−5.31715	+	9.20958i	−0.227345	+	0.393773i	0.729675	+	0.683794i	$0.239671\pi$
$548$		0			0
$549$	0.125752	+	0.0904864i	0.00536696	+	0.00386186i
$550$		0			0
$551$	0.268753	−	0.465494i	0.0114493	−	0.0198307i
$552$		0			0
$553$	1.72167	−	2.98201i	0.0732126	−	0.126808i
$554$		0			0
$555$	−18.0200	−	5.80943i	−0.764907	−	0.246596i
$556$		0			0
$557$	3.33305	−	5.77301i	0.141226	−	0.244610i	−0.786733	−	0.617294i	$-0.788229\pi$
$557$	3.33305	−	5.77301i	0.141226	−	0.244610i	0.927958	+	0.372684i	$0.121562\pi$
$558$		0			0
$559$	−9.44338	+	8.38022i	−0.399412	+	0.354446i
$560$		0			0
$561$	−31.8719	+	28.8301i	−1.34563	+	1.21721i
$562$		0			0
$563$	−12.4797	+	21.6155i	−0.525957	+	0.910984i	0.473586	+	0.880748i	$0.342959\pi$
$563$	−12.4797	+	21.6155i	−0.525957	+	0.910984i	−0.999543	+	0.0302367i	$0.990374\pi$
$564$		0			0
$565$	25.0842			1.05530
$566$		0			0
$567$	4.64508	+	13.8624i	0.195075	+	0.582165i
$568$		0			0
$569$	−5.05096	−	8.74852i	−0.211747	−	0.366757i	0.740514	−	0.672041i	$-0.234582\pi$
$569$	−5.05096	−	8.74852i	−0.211747	−	0.366757i	−0.952261	+	0.305284i	$0.901249\pi$
$570$		0			0
$571$	12.9636	+	22.4536i	0.542510	+	0.939655i	0.998759	+	0.0498029i	$0.0158593\pi$
$571$	12.9636	+	22.4536i	0.542510	+	0.939655i	−0.456249	+	0.889852i	$0.650807\pi$
$572$		0			0
$573$	−26.0656	−	8.40323i	−1.08891	−	0.351050i
$574$		0			0
$575$	−0.226291	+	0.391947i	−0.00943698	+	0.0163453i
$576$		0			0
$577$	−35.4367			−1.47525			−0.737624	−	0.675212i	$-0.764052\pi$
$577$	−35.4367			−1.47525			−0.737624	+	0.675212i	$0.764052\pi$
$578$		0			0
$579$	−0.144705	−	0.0466511i	−0.00601373	−	0.00193875i
$580$		0			0
$581$	−2.13475	+	3.69750i	−0.0885645	+	0.153398i
$582$		0			0
$583$	24.2365	+	41.9789i	1.00377	+	1.73859i
$584$		0			0
$585$	−13.8250	−	19.1343i	−0.571595	−	0.791107i
$586$		0			0
$587$	−5.26118	−	9.11264i	−0.217152	−	0.376119i	0.736784	−	0.676128i	$-0.236343\pi$
$587$	−5.26118	−	9.11264i	−0.217152	−	0.376119i	−0.953936	+	0.300009i	$0.903010\pi$
$588$		0			0
$589$	0.255447	−	0.442447i	0.0105255	−	0.0182307i
$590$		0			0
$591$	4.25534	−	3.84922i	0.175041	−	0.158336i
$592$		0			0
$593$	41.5379			1.70576			0.852878	−	0.522111i	$-0.174855\pi$
$593$	41.5379			1.70576			0.852878	+	0.522111i	$0.174855\pi$
$594$		0			0
$595$	−12.6025	+	21.8282i	−0.516653	+	0.894870i
$596$		0			0
$597$	7.31081	+	34.0112i	0.299212	+	1.39198i
$598$		0			0
$599$	6.98319	+	12.0952i	0.285325	+	0.494198i	0.972688	−	0.232116i	$-0.0745650\pi$
$599$	6.98319	+	12.0952i	0.285325	+	0.494198i	−0.687363	+	0.726314i	$0.741232\pi$
$600$		0			0
$601$	−3.52866	−	6.11182i	−0.143937	−	0.249306i	0.785039	−	0.619447i	$-0.212643\pi$
$601$	−3.52866	−	6.11182i	−0.143937	−	0.249306i	−0.928976	+	0.370140i	$0.879310\pi$
$602$		0			0
$603$	33.1908	+	23.8829i	1.35163	+	0.972585i
$604$		0			0
$605$	2.57482			0.104682
$606$		0			0
$607$	12.1093	−	20.9740i	0.491503	−	0.851308i	−0.508449	−	0.861092i	$-0.669781\pi$
$607$	12.1093	−	20.9740i	0.491503	−	0.851308i	0.999952	+	0.00978374i	$0.00311431\pi$
$608$		0			0
$609$	3.72793	+	17.3430i	0.151064	+	0.702774i
$610$		0			0
$611$	2.12818	+	10.3802i	0.0860971	+	0.419938i
$612$		0			0
$613$	−2.26070	+	3.91565i	−0.0913090	+	0.158152i	−0.908062	−	0.418835i	$-0.862438\pi$
$613$	−2.26070	+	3.91565i	−0.0913090	+	0.158152i	0.816753	+	0.576987i	$0.195772\pi$
$614$		0			0
$615$	−8.76535	−	40.7780i	−0.353453	−	1.64433i
$616$		0			0
$617$	−1.76830	+	3.06278i	−0.0711890	+	0.123303i	−0.899423	−	0.437080i	$-0.856013\pi$
$617$	−1.76830	+	3.06278i	−0.0711890	+	0.123303i	0.828234	+	0.560383i	$0.189346\pi$
$618$		0			0
$619$	7.35242	−	12.7348i	0.295519	−	0.511854i	−0.679587	−	0.733595i	$-0.737841\pi$
$619$	7.35242	−	12.7348i	0.295519	−	0.511854i	0.975105	+	0.221742i	$0.0711742\pi$
$620$		0			0
$621$	−5.88393	−	7.98253i	−0.236114	−	0.320328i
$622$		0			0
$623$	−3.96533	+	6.86815i	−0.158868	+	0.275167i
$624$		0			0
$625$	11.8790	+	20.5751i	0.475161	+	0.823003i
$626$		0			0
$627$	−0.382182	+	0.345707i	−0.0152629	+	0.0138062i
$628$		0			0
$629$	−35.6109			−1.41990
$630$		0			0
$631$	−2.32952	−	4.03485i	−0.0927367	−	0.160625i	0.815925	−	0.578158i	$-0.196228\pi$
$631$	−2.32952	−	4.03485i	−0.0927367	−	0.160625i	−0.908662	+	0.417533i	$0.862895\pi$
$632$		0			0
$633$	13.1188	+	4.22933i	0.521424	+	0.168101i
$634$		0			0
$635$	39.4546			1.56571
$636$		0			0
$637$	−11.7613	+	10.4372i	−0.465999	+	0.413535i
$638$		0			0
$639$	−3.72086	+	37.0338i	−0.147195	+	1.46503i
$640$		0			0
$641$	−7.79332			−0.307818			−0.153909	−	0.988085i	$-0.549186\pi$
$641$	−7.79332			−0.307818			−0.153909	+	0.988085i	$0.549186\pi$
$642$		0			0
$643$	12.5629	−	21.7596i	0.495433	−	0.858115i	−0.504553	−	0.863381i	$-0.668343\pi$
$643$	12.5629	−	21.7596i	0.495433	−	0.858115i	0.999986	+	0.00526553i	$0.00167608\pi$
$644$		0			0
$645$	2.78170	+	12.9409i	0.109529	+	0.509549i
$646$		0			0
$647$	0.711209	−	1.23185i	0.0279605	−	0.0484290i	−0.851707	−	0.524019i	$-0.824432\pi$
$647$	0.711209	−	1.23185i	0.0279605	−	0.0484290i	0.879667	+	0.475590i	$0.157765\pi$
$648$		0			0
$649$	−52.6057			−2.06496
$650$		0			0
$651$	3.54336	+	16.4843i	0.138875	+	0.646072i
$652$		0			0
$653$	5.66303			0.221611			0.110806	−	0.993842i	$-0.464657\pi$
$653$	5.66303			0.221611			0.110806	+	0.993842i	$0.464657\pi$
$654$		0			0
$655$	9.43262	−	16.3378i	0.368563	−	0.638369i
$656$		0			0
$657$	5.27974	+	3.79910i	0.205982	+	0.148217i
$658$		0			0
$659$	−1.25551			−0.0489077			−0.0244538	−	0.999701i	$-0.507785\pi$
$659$	−1.25551			−0.0489077			−0.0244538	+	0.999701i	$0.507785\pi$
$660$		0			0
$661$	−15.2540			−0.593314			−0.296657	−	0.954984i	$-0.595872\pi$
$661$	−15.2540			−0.593314			−0.296657	+	0.954984i	$0.595872\pi$
$662$		0			0
$663$	−35.7914	−	26.2744i	−1.39002	−	1.02041i
$664$		0			0
$665$	−0.151119	+	0.261746i	−0.00586015	+	0.0101501i
$666$		0			0
$667$	−6.01625	−	10.4205i	−0.232950	−	0.403482i
$668$		0			0
$669$	−6.25718	−	29.1095i	−0.241917	−	1.12544i
$670$		0			0
$671$	−0.0901129	−	0.156080i	−0.00347877	−	0.00602540i
$672$		0			0
$673$	20.0909	+	34.7985i	0.774449	+	1.34138i	0.935104	+	0.354374i	$0.115306\pi$
$673$	20.0909	+	34.7985i	0.774449	+	1.34138i	−0.160655	+	0.987011i	$0.551361\pi$
$674$		0			0
$675$	1.22457	−	0.137226i	0.0471336	−	0.00528183i
$676$		0			0
$677$	−15.9810	+	27.6799i	−0.614200	+	1.06383i	0.376324	+	0.926488i	$0.377188\pi$
$677$	−15.9810	+	27.6799i	−0.614200	+	1.06383i	−0.990524	+	0.137338i	$0.956145\pi$
$678$		0			0
$679$	−15.5388			−0.596326
$680$		0			0
$681$	10.8232	+	3.48928i	0.414748	+	0.133710i
$682$		0			0
$683$	6.83432	+	11.8374i	0.261508	+	0.452945i	0.966643	−	0.256128i	$-0.0824468\pi$
$683$	6.83432	+	11.8374i	0.261508	+	0.452945i	−0.705135	+	0.709073i	$0.749114\pi$
$684$		0			0
$685$	5.32823	+	9.22876i	0.203581	+	0.352613i
$686$		0			0
$687$	2.60017	+	12.0965i	0.0992028	+	0.461509i
$688$		0			0
$689$	−37.4565	+	33.2396i	−1.42698	+	1.26633i
$690$		0			0
$691$	−1.95001	−	3.37752i	−0.0741819	−	0.128487i	0.826548	−	0.562866i	$-0.190301\pi$
$691$	−1.95001	−	3.37752i	−0.0741819	−	0.128487i	−0.900730	+	0.434379i	$0.856968\pi$
$692$		0			0
$693$	1.70023	−	16.9224i	0.0645865	−	0.642831i
$694$		0			0
$695$	36.8613			1.39823
$696$		0			0
$697$	−39.2248	−	67.9394i	−1.48575	−	2.57339i
$698$		0			0
$699$	−44.1222	−	14.2245i	−1.66885	−	0.538018i
$700$		0			0
$701$	12.5312			0.473295			0.236648	−	0.971596i	$-0.423951\pi$
$701$	12.5312			0.473295			0.236648	+	0.971596i	$0.423951\pi$
$702$		0			0
$703$	−0.427017			−0.0161053
$704$		0			0
$705$	10.5730	+	3.40861i	0.398202	+	0.128376i
$706$		0			0
$707$	0.401477	+	0.695379i	0.0150991	+	0.0261524i
$708$		0			0
$709$	−6.79651			−0.255248			−0.127624	−	0.991823i	$-0.540735\pi$
$709$	−6.79651			−0.255248			−0.127624	+	0.991823i	$0.540735\pi$
$710$		0			0
$711$	5.79743	−	2.61309i	0.217421	−	0.0979986i
$712$		0			0
$713$	−5.71838	−	9.90453i	−0.214155	−	0.370928i
$714$		0			0
$715$	5.51554	+	26.9020i	0.206270	+	1.00608i
$716$		0			0
$717$	−3.25657	−	15.1501i	−0.121619	−	0.565792i
$718$		0			0
$719$	17.5386	+	30.3777i	0.654078	+	1.13290i	0.982124	+	0.188235i	$0.0602766\pi$
$719$	17.5386	+	30.3777i	0.654078	+	1.13290i	−0.328046	+	0.944662i	$0.606390\pi$
$720$		0			0
$721$	10.4350	+	18.0740i	0.388622	+	0.673112i
$722$		0			0
$723$	7.92286	+	2.55423i	0.294654	+	0.0949929i
$724$		0			0
$725$	1.49513			0.0555279
$726$		0			0
$727$	19.3818	−	33.5702i	0.718830	−	1.24505i	−0.242633	−	0.970118i	$-0.578011\pi$
$727$	19.3818	−	33.5702i	0.718830	−	1.24505i	0.961464	−	0.274932i	$-0.0886555\pi$
$728$		0			0
$729$	−7.98957	+	25.7908i	−0.295910	+	0.955216i
$730$		0			0
$731$	12.4481	+	21.5607i	0.460408	+	0.797450i
$732$		0			0
$733$	17.4070	+	30.1498i	0.642943	+	1.11361i	0.984773	+	0.173848i	$0.0556200\pi$
$733$	17.4070	+	30.1498i	0.642943	+	1.11361i	−0.341830	+	0.939762i	$0.611047\pi$
$734$		0			0
$735$	3.46447	+	16.1173i	0.127789	+	0.594496i
$736$		0			0
$737$	−23.7843	−	41.1956i	−0.876105	−	1.51746i
$738$		0			0
$739$	2.48110	−	4.29740i	0.0912689	−	0.158082i	−0.816776	−	0.576954i	$-0.804241\pi$
$739$	2.48110	−	4.29740i	0.0912689	−	0.158082i	0.908045	+	0.418872i	$0.137574\pi$
$740$		0			0
$741$	−0.429181	−	0.315061i	−0.0157664	−	0.0115740i
$742$		0			0
$743$	−33.9452			−1.24533			−0.622665	−	0.782489i	$-0.713950\pi$
$743$	−33.9452			−1.24533			−0.622665	+	0.782489i	$0.713950\pi$
$744$		0			0
$745$	4.14570			0.151887
$746$		0			0
$747$	−7.18845	+	3.24007i	−0.263012	+	0.118548i
$748$		0			0
$749$	9.15320	−	15.8538i	0.334451	−	0.579286i
$750$		0			0
$751$	−29.1366			−1.06321			−0.531605	−	0.846992i	$-0.678411\pi$
$751$	−29.1366			−1.06321			−0.531605	+	0.846992i	$0.678411\pi$
$752$		0			0
$753$	−2.18660	−	10.1724i	−0.0796841	−	0.370704i
$754$		0			0
$755$	−1.47419			−0.0536513
$756$		0			0
$757$	25.5034	−	44.1732i	0.926937	−	1.60550i	0.138521	−	0.990359i	$-0.455765\pi$
$757$	25.5034	−	44.1732i	0.926937	−	1.60550i	0.788416	−	0.615143i	$-0.210902\pi$
$758$		0			0
$759$	2.42439	+	11.2787i	0.0879999	+	0.409391i
$760$		0			0
$761$	−11.0223	+	19.0912i	−0.399557	+	0.692054i	−0.993671	−	0.112327i	$-0.964170\pi$
$761$	−11.0223	+	19.0912i	−0.399557	+	0.692054i	0.594114	+	0.804381i	$0.297503\pi$
$762$		0			0
$763$	−13.2733			−0.480527
$764$		0			0
$765$	−42.4370	+	19.1277i	−1.53431	+	0.691565i
$766$		0			0
$767$	−10.9156	−	53.2406i	−0.394139	−	1.92241i
$768$		0			0
$769$	11.0164			0.397262			0.198631	−	0.980074i	$-0.436350\pi$
$769$	11.0164			0.397262			0.198631	+	0.980074i	$0.436350\pi$
$770$		0			0
$771$	−40.8923	−	13.1832i	−1.47270	−	0.474780i
$772$		0			0
$773$	−23.4470	−	40.6114i	−0.843329	−	1.46069i	−0.887064	−	0.461646i	$-0.847259\pi$
$773$	−23.4470	−	40.6114i	−0.843329	−	1.46069i	0.0437347	−	0.999043i	$-0.486074\pi$
$774$		0			0
$775$	1.42111			0.0510477
$776$		0			0
$777$	10.4513	−	9.45385i	0.374938	−	0.339155i
$778$		0			0
$779$	−0.470352	−	0.814674i	−0.0168521	−	0.0291887i
$780$		0			0
$781$	21.6495	−	37.4981i	0.774681	−	1.34179i
$782$		0			0
$783$	−13.1188	+	30.0192i	−0.468829	+	1.07280i
$784$		0			0
$785$	10.3507	−	17.9279i	0.369432	−	0.639875i
$786$		0			0
$787$	8.80158	−	15.2448i	0.313742	−	0.543418i	−0.665427	−	0.746463i	$-0.731751\pi$
$787$	8.80158	−	15.2448i	0.313742	−	0.543418i	0.979169	+	0.203045i	$0.0650839\pi$
$788$		0			0
$789$	9.78195	+	45.5074i	0.348247	+	1.62011i
$790$		0			0
$791$	−9.33553	+	16.1696i	−0.331933	+	0.574925i
$792$		0			0
$793$	0.139266	−	0.123587i	0.00494547	−	0.00438869i
$794$		0			0
$795$	11.0334	+	51.3294i	0.391315	+	1.82047i
$796$		0			0
$797$	−11.5238	+	19.9597i	−0.408192	+	0.707010i	−0.994687	−	0.102943i	$-0.967174\pi$
$797$	−11.5238	+	19.9597i	−0.408192	+	0.707010i	0.586495	+	0.809953i	$0.300507\pi$
$798$		0			0
$799$	20.8942			0.739185
$800$		0			0
$801$	−13.3526	+	6.01846i	−0.471792	+	0.212652i
$802$		0			0
$803$	−3.78342	−	6.55308i	−0.133514	−	0.231253i
$804$		0			0
$805$	3.38293	+	5.85940i	0.119233	+	0.206517i
$806$		0			0
$807$	1.63097	+	7.58756i	0.0574129	+	0.267095i
$808$		0			0
$809$	10.9443	−	18.9560i	0.384780	−	0.666458i	−0.606959	−	0.794733i	$-0.707611\pi$
$809$	10.9443	−	18.9560i	0.384780	−	0.666458i	0.991739	+	0.128275i	$0.0409441\pi$
$810$		0			0
$811$	−3.39855			−0.119339			−0.0596696	−	0.998218i	$-0.519005\pi$
$811$	−3.39855			−0.119339			−0.0596696	+	0.998218i	$0.519005\pi$
$812$		0			0
$813$	−22.8106	+	20.6336i	−0.800003	+	0.723653i
$814$		0			0
$815$	0.816797	−	1.41473i	0.0286112	−	0.0495560i
$816$		0			0
$817$	0.149267	+	0.258538i	0.00522219	+	0.00904510i
$818$		0			0
$819$	17.4795	−	1.79062i	0.610783	−	0.0625692i
$820$		0			0
$821$	17.9437	+	31.0794i	0.626239	+	1.08468i	0.988300	+	0.152523i	$0.0487397\pi$
$821$	17.9437	+	31.0794i	0.626239	+	1.08468i	−0.362061	+	0.932154i	$0.617927\pi$
$822$		0			0
$823$	7.29045	−	12.6274i	0.254129	−	0.440164i	−0.710530	−	0.703667i	$-0.751545\pi$
$823$	7.29045	−	12.6274i	0.254129	−	0.440164i	0.964659	+	0.263503i	$0.0848779\pi$
$824$		0			0
$825$	−1.36433	−	0.439844i	−0.0474999	−	0.0153134i
$826$		0			0
$827$	−22.7590			−0.791407			−0.395703	−	0.918378i	$-0.629499\pi$
$827$	−22.7590			−0.791407			−0.395703	+	0.918378i	$0.629499\pi$
$828$		0			0
$829$	14.1801	−	24.5607i	0.492496	−	0.853029i	−0.507466	−	0.861672i	$-0.669418\pi$
$829$	14.1801	−	24.5607i	0.492496	−	0.853029i	0.999963	+	0.00864285i	$0.00275114\pi$
$830$		0			0
$831$	48.0285	+	15.4838i	1.66609	+	0.537127i
$832$		0			0
$833$	15.5034	+	26.8528i	0.537163	+	0.930393i
$834$		0			0
$835$	−9.69145	−	16.7861i	−0.335387	−	0.580907i
$836$		0			0
$837$	−12.4693	+	28.5329i	−0.431003	+	0.986242i
$838$		0			0
$839$	5.69149			0.196492			0.0982460	−	0.995162i	$-0.468677\pi$
$839$	5.69149			0.196492			0.0982460	+	0.995162i	$0.468677\pi$
$840$		0			0
$841$	−5.37510	+	9.30994i	−0.185348	+	0.321032i
$842$		0			0
$843$	−29.6267	+	26.7992i	−1.02040	+	0.923013i
$844$		0			0
$845$	−26.0822	+	11.1642i	−0.897256	+	0.384061i
$846$		0			0
$847$	−0.958267	+	1.65977i	−0.0329264	+	0.0570303i
$848$		0			0
$849$	0.793183	+	0.255713i	0.0272220	+	0.00877603i
$850$		0			0
$851$	−4.77957	+	8.27845i	−0.163841	+	0.283782i
$852$		0			0
$853$	−27.2515	+	47.2010i	−0.933073	+	1.61613i	−0.155039	+	0.987908i	$0.549550\pi$
$853$	−27.2515	+	47.2010i	−0.933073	+	1.61613i	−0.778034	+	0.628222i	$0.783783\pi$
$854$		0			0
$855$	−0.508870	+	0.229364i	−0.0174030	+	0.00784409i
$856$		0			0
$857$	12.8776	−	22.3046i	0.439889	−	0.761910i	−0.557791	−	0.829981i	$-0.688351\pi$
$857$	12.8776	−	22.3046i	0.439889	−	0.761910i	0.997680	+	0.0680709i	$0.0216844\pi$
$858$		0			0
$859$	−23.5398	−	40.7721i	−0.803167	−	1.39113i	−0.917522	−	0.397686i	$-0.869813\pi$
$859$	−23.5398	−	40.7721i	−0.803167	−	1.39113i	0.114355	−	0.993440i	$-0.463520\pi$
$860$		0			0
$861$	29.5482	+	9.52598i	1.00700	+	0.324645i
$862$		0			0
$863$	−30.1155			−1.02514			−0.512572	−	0.858644i	$-0.671307\pi$
$863$	−30.1155			−1.02514			−0.512572	+	0.858644i	$0.671307\pi$
$864$		0			0
$865$	−13.7502	−	23.8161i	−0.467522	−	0.809773i
$866$		0			0
$867$	−43.0924	+	38.9798i	−1.46349	+	1.32382i
$868$		0			0
$869$	−7.39770			−0.250950
$870$		0			0
$871$	36.7576	−	32.6193i	1.24548	−	1.10526i
$872$		0			0
$873$	−23.2935	−	16.7611i	−0.788365	−	0.567278i
$874$		0			0
$875$	−18.5665			−0.627663
$876$		0			0
$877$	3.22324	−	5.58281i	0.108841	−	0.188518i	−0.806460	−	0.591289i	$-0.798619\pi$
$877$	3.22324	−	5.58281i	0.108841	−	0.188518i	0.915301	+	0.402771i	$0.131953\pi$
$878$		0			0
$879$	19.2963	−	17.4547i	0.650848	−	0.588733i
$880$		0			0
$881$	−4.32579	+	7.49249i	−0.145740	+	0.252429i	−0.929649	−	0.368447i	$-0.879890\pi$
$881$	−4.32579	+	7.49249i	−0.145740	+	0.252429i	0.783909	+	0.620876i	$0.213223\pi$
$882$		0			0
$883$	52.3558			1.76191			0.880957	−	0.473197i	$-0.156900\pi$
$883$	52.3558			1.76191			0.880957	+	0.473197i	$0.156900\pi$
$884$		0			0
$885$	−54.2295	−	17.4829i	−1.82290	−	0.587682i
$886$		0			0
$887$	−5.05784			−0.169826			−0.0849128	−	0.996388i	$-0.527061\pi$
$887$	−5.05784			−0.169826			−0.0849128	+	0.996388i	$0.527061\pi$
$888$		0			0
$889$	−14.6837	+	25.4330i	−0.492477	+	0.852995i
$890$		0			0
$891$	20.8023	−	23.5336i	0.696903	−	0.788405i
$892$		0			0
$893$	0.250547			0.00838423
$894$		0			0
$895$	−2.41368			−0.0806806
$896$		0			0
$897$	−10.9118	+	4.79396i	−0.364333	+	0.160066i
$898$		0			0
$899$	−18.8911	+	32.7203i	−0.630052	+	1.09128i
$900$		0			0
$901$	49.3743	+	85.5189i	1.64490	+	2.84905i
$902$		0			0
$903$	−9.37717	−	3.02308i	−0.312053	−	0.100602i
$904$		0			0
$905$	14.2487	+	24.6795i	0.473643	+	0.820373i
$906$		0			0
$907$	−29.2462	−	50.6560i	−0.971105	−	1.68200i	−0.692231	−	0.721676i	$-0.743372\pi$
$907$	−29.2462	−	50.6560i	−0.971105	−	1.68200i	−0.278874	−	0.960328i	$-0.589961\pi$
$908$		0			0
$909$	−0.148243	+	1.47546i	−0.00491691	+	0.0489380i
$910$		0			0
$911$	−25.2747	+	43.7770i	−0.837387	+	1.45040i	0.0546846	+	0.998504i	$0.482585\pi$
$911$	−25.2747	+	43.7770i	−0.837387	+	1.45040i	−0.892072	+	0.451894i	$0.850749\pi$
$912$		0			0
$913$	9.17267			0.303571
$914$		0			0
$915$	−0.0410229	−	0.190846i	−0.00135617	−	0.00630917i
$916$		0			0
$917$	7.02103	+	12.1608i	0.231855	+	0.401584i
$918$		0			0
$919$	22.2003	+	38.4520i	0.732319	+	1.26841i	0.955889	+	0.293727i	$0.0948955\pi$
$919$	22.2003	+	38.4520i	0.732319	+	1.26841i	−0.223570	+	0.974688i	$0.571771\pi$
$920$		0			0
$921$	−31.7888	−	10.2483i	−1.04748	−	0.337694i
$922$		0			0
$923$	42.4429	+	14.1300i	1.39702	+	0.465096i
$924$		0			0
$925$	−0.593899	−	1.02866i	−0.0195273	−	0.0338222i
$926$		0			0
$927$	−3.85308	+	38.3497i	−0.126552	+	1.25957i
$928$		0			0
$929$	6.16875			0.202390			0.101195	−	0.994867i	$-0.467733\pi$
$929$	6.16875			0.202390			0.101195	+	0.994867i	$0.467733\pi$
$930$		0			0
$931$	0.185905	+	0.321996i	0.00609278	+	0.0105530i
$932$		0			0
$933$	1.70821	+	7.94691i	0.0559244	+	0.260170i
$934$		0			0
$935$	54.1509			1.77092
$936$		0			0
$937$	−41.0909			−1.34238			−0.671190	−	0.741285i	$-0.734217\pi$
$937$	−41.0909			−1.34238			−0.671190	+	0.741285i	$0.734217\pi$
$938$		0			0
$939$	15.3471	−	13.8824i	0.500833	−	0.453035i
$940$		0			0
$941$	−19.2328	−	33.3122i	−0.626971	−	1.08595i	−0.988156	−	0.153452i	$-0.950961\pi$
$941$	−19.2328	−	33.3122i	−0.626971	−	1.08595i	0.361185	−	0.932494i	$-0.382372\pi$
$942$		0			0
$943$	−21.0584			−0.685757
$944$		0			0
$945$	7.37670	−	16.8797i	0.239964	−	0.549098i
$946$		0			0
$947$	−23.0226	−	39.8763i	−0.748135	−	1.29581i	−0.948716	−	0.316130i	$-0.897616\pi$
$947$	−23.0226	−	39.8763i	−0.748135	−	1.29581i	0.200581	−	0.979677i	$-0.435717\pi$
$948$		0			0
$949$	5.84712	−	5.18883i	0.189805	−	0.168437i
$950$		0			0
$951$	2.14371	−	1.93912i	0.0695147	−	0.0628804i
$952$		0			0
$953$	20.1025	+	34.8185i	0.651183	+	1.12788i	0.982836	+	0.184480i	$0.0590603\pi$
$953$	20.1025	+	34.8185i	0.651183	+	1.12788i	−0.331653	+	0.943401i	$0.607606\pi$
$954$		0			0
$955$	17.2537	+	29.8843i	0.558317	+	0.967033i
$956$		0			0
$957$	28.2635	−	25.5661i	0.913629	−	0.826434i
$958$		0			0
$959$	−7.93198			−0.256137
$960$		0			0
$961$	−2.45575	+	4.25348i	−0.0792177	+	0.137209i
$962$		0			0
$963$	30.8220	−	13.8924i	0.993223	−	0.447678i
$964$		0			0
$965$	0.0957851	+	0.165905i	0.00308343	+	0.00534066i
$966$		0			0
$967$	24.9108	+	43.1467i	0.801077	+	1.38751i	0.918908	+	0.394472i	$0.129072\pi$
$967$	24.9108	+	43.1467i	0.801077	+	1.38751i	−0.117831	+	0.993034i	$0.537594\pi$
$968$		0			0
$969$	−0.778576	+	0.704270i	−0.0250114	+	0.0226244i
$970$		0			0
$971$	12.8328	+	22.2270i	0.411823	+	0.713299i	0.995089	−	0.0989825i	$-0.0315588\pi$
$971$	12.8328	+	22.2270i	0.411823	+	0.713299i	−0.583266	+	0.812281i	$0.698225\pi$
$972$		0			0
$973$	−13.7186	+	23.7613i	−0.439797	+	0.761751i
$974$		0			0
$975$	0.162056	−	1.47206i	0.00518996	−	0.0471438i
$976$		0			0
$977$	46.2016			1.47812			0.739060	−	0.673639i	$-0.235270\pi$
$977$	46.2016			1.47812			0.739060	+	0.673639i	$0.235270\pi$
$978$		0			0
$979$	17.0383			0.544548
$980$		0			0
$981$	−19.8974	−	14.3174i	−0.635274	−	0.457119i
$982$		0			0
$983$	−3.29093	+	5.70005i	−0.104964	+	0.181803i	−0.913724	−	0.406336i	$-0.866806\pi$
$983$	−3.29093	+	5.70005i	−0.104964	+	0.181803i	0.808759	+	0.588140i	$0.200139\pi$
$984$		0			0
$985$	−7.22990			−0.230364
$986$		0			0
$987$	−6.13216	+	5.54692i	−0.195189	+	0.176561i
$988$		0			0
$989$	6.68292			0.212505
$990$		0			0
$991$	12.7671	−	22.1132i	0.405560	−	0.702450i	−0.588827	−	0.808259i	$-0.700410\pi$
$991$	12.7671	−	22.1132i	0.405560	−	0.702450i	0.994386	+	0.105809i	$0.0337433\pi$
$992$		0			0
$993$	40.4548	+	13.0421i	1.28379	+	0.413879i
$994$		0			0
$995$	21.9166	−	37.9607i	0.694803	−	1.20343i
$996$		0			0
$997$	−32.0279			−1.01433			−0.507166	−	0.861848i	$-0.669307\pi$
$997$	−32.0279			−1.01433			−0.507166	+	0.861848i	$0.669307\pi$
$998$		0			0
$999$	25.8645	−	2.89840i	0.818316	−	0.0917013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.s.f.529.19	yes	40
3.2	odd	2		2808.2.s.f.1153.16		40
9.4	even	3		936.2.r.f.841.6	yes	40
9.5	odd	6		2808.2.r.f.2089.16		40
13.3	even	3		936.2.r.f.601.6	✓	40
39.29	odd	6		2808.2.r.f.289.16		40
117.68	odd	6		2808.2.s.f.1225.16		40
117.94	even	3	inner	936.2.s.f.913.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.6	✓	40	13.3	even	3
936.2.r.f.841.6	yes	40	9.4	even	3
936.2.s.f.529.19	yes	40	1.1	even	1	trivial
936.2.s.f.913.19	yes	40	117.94	even	3	inner
2808.2.r.f.289.16		40	39.29	odd	6
2808.2.r.f.2089.16		40	9.5	odd	6
2808.2.s.f.1153.16		40	3.2	odd	2
2808.2.s.f.1225.16		40	117.68	odd	6

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64850 + 0.531456i) q^{3} +(-1.09120 - 1.89001i) q^{5} +1.62444 q^{7} +(2.43511 + 1.75221i) q^{9} +(-1.74498 - 3.02239i) q^{11} +(2.69679 - 2.39318i) q^{13} +(-0.794383 - 3.69561i) q^{15} +(-3.55485 - 6.15718i) q^{17} +(-0.0426269 - 0.0738319i) q^{19} +(2.67788 + 0.863317i) q^{21} -1.90847 q^{23} +(0.118572 - 0.205372i) q^{25} +(3.08305 + 4.18268i) q^{27} +(3.15239 + 5.46010i) q^{29} +(2.99631 + 5.18976i) q^{31} +(-1.27033 - 5.90980i) q^{33} +(-1.77258 - 3.07020i) q^{35} +(2.50439 - 4.33773i) q^{37} +(5.71753 - 2.51193i) q^{39} +11.0342 q^{41} -3.50171 q^{43} +(0.654515 - 6.51439i) q^{45} +(-1.46942 + 2.54511i) q^{47} -4.36121 q^{49} +(-2.58790 - 12.0394i) q^{51} -13.8893 q^{53} +(-3.80824 + 6.59606i) q^{55} +(-0.0310320 - 0.144366i) q^{57} +(7.53673 - 13.0540i) q^{59} +0.0516412 q^{61} +(3.95568 + 2.84636i) q^{63} +(-7.46587 - 2.48553i) q^{65} +13.6301 q^{67} +(-3.14612 - 1.01427i) q^{69} +(6.20338 + 10.7446i) q^{71} +2.16817 q^{73} +(0.304611 - 0.275540i) q^{75} +(-2.83461 - 4.90968i) q^{77} +(1.05985 - 1.83572i) q^{79} +(2.85950 + 8.53365i) q^{81} +(-1.31415 + 2.27618i) q^{83} +(-7.75810 + 13.4374i) q^{85} +(2.29491 + 10.6763i) q^{87} +(-2.44105 + 4.22802i) q^{89} +(4.38077 - 3.88757i) q^{91} +(2.18129 + 10.1477i) q^{93} +(-0.0930288 + 0.161131i) q^{95} -9.56568 q^{97} +(1.04666 - 10.4174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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