LMFDB - Embedded newform 936.2.q.g.313.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(313,936)] 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("936.313"); S:= CuspForms(chi, 2); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [22,0,0,0,-3,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			313.6
Character	$\chi$	$=$	936.313
Dual form			936.2.q.g.625.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.215114 + 1.71864i) q^{3} +(-1.80041 - 3.11840i) q^{5} +(-2.42567 + 4.20138i) q^{7} +(-2.90745 - 0.739406i) q^{9} +(2.96999 - 5.14417i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(5.74669 - 2.42344i) q^{15} +3.14211 q^{17} +4.53444 q^{19} +(-6.69887 - 5.07263i) q^{21} +(2.40410 + 4.16402i) q^{23} +(-3.98293 + 6.89863i) q^{25} +(1.89621 - 4.83781i) q^{27} +(0.967295 - 1.67540i) q^{29} +(2.30944 + 4.00007i) q^{31} +(8.20210 + 6.21093i) q^{33} +17.4688 q^{35} +10.7700 q^{37} +(1.59594 - 0.673027i) q^{39} +(0.389576 + 0.674766i) q^{41} +(-0.164787 + 0.285420i) q^{43} +(2.92884 + 10.3978i) q^{45} +(2.01335 - 3.48722i) q^{47} +(-8.26774 - 14.3202i) q^{49} +(-0.675911 + 5.40016i) q^{51} -6.03880 q^{53} -21.3888 q^{55} +(-0.975419 + 7.79307i) q^{57} +(-1.75266 - 3.03569i) q^{59} +(2.77604 - 4.80825i) q^{61} +(10.1590 - 10.4218i) q^{63} +(-1.80041 + 3.11840i) q^{65} +(-2.91273 - 5.04500i) q^{67} +(-7.67361 + 3.23604i) q^{69} +3.18402 q^{71} +11.7545 q^{73} +(-10.9995 - 8.32921i) q^{75} +(14.4084 + 24.9561i) q^{77} +(1.97184 - 3.41532i) q^{79} +(7.90656 + 4.29958i) q^{81} +(-1.28229 + 2.22100i) q^{83} +(-5.65708 - 9.79835i) q^{85} +(2.67134 + 2.02283i) q^{87} +11.4418 q^{89} +4.85134 q^{91} +(-7.37147 + 3.10863i) q^{93} +(-8.16383 - 14.1402i) q^{95} +(2.58047 - 4.46950i) q^{97} +(-12.4387 + 12.7604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) $ 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Character values

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

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

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
$3$	−0.215114	+	1.71864i	−0.124196	+	0.992258i
$3$	−0.215114	+	1.71864i	−0.124196	+	0.992258i
$4$		0			0
$5$	−1.80041	−	3.11840i	−0.805166	−	1.39459i	−0.916179	−	0.400770i	$-0.868743\pi$
$5$	−1.80041	−	3.11840i	−0.805166	−	1.39459i	0.111013	−	0.993819i	$-0.464591\pi$
$6$		0			0
$7$	−2.42567	+	4.20138i	−0.916817	+	1.58797i	−0.112598	+	0.993641i	$0.535917\pi$
$7$	−2.42567	+	4.20138i	−0.916817	+	1.58797i	−0.804219	+	0.594333i	$0.797416\pi$
$8$		0			0
$9$	−2.90745	−	0.739406i	−0.969151	−	0.246469i
$10$		0			0
$11$	2.96999	−	5.14417i	0.895486	−	1.55103i	0.0622837	−	0.998058i	$-0.480162\pi$
$11$	2.96999	−	5.14417i	0.895486	−	1.55103i	0.833202	−	0.552969i	$-0.186505\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$		0			0
$15$	5.74669	−	2.42344i	1.48379	−	0.625730i
$16$		0			0
$17$	3.14211			0.762074			0.381037	−	0.924560i	$-0.375567\pi$
$17$	3.14211			0.762074			0.381037	+	0.924560i	$0.375567\pi$
$18$		0			0
$19$	4.53444			1.04027			0.520136	−	0.854084i	$-0.325881\pi$
$19$	4.53444			1.04027			0.520136	+	0.854084i	$0.325881\pi$
$20$		0			0
$21$	−6.69887	−	5.07263i	−1.46181	−	1.10694i
$22$		0			0
$23$	2.40410	+	4.16402i	0.501289	+	0.868258i	0.999999	+	0.00148934i	$0.000474070\pi$
$23$	2.40410	+	4.16402i	0.501289	+	0.868258i	−0.498710	+	0.866769i	$0.666193\pi$
$24$		0			0
$25$	−3.98293	+	6.89863i	−0.796585	+	1.37973i
$26$		0			0
$27$	1.89621	−	4.83781i	0.364925	−	0.931037i
$28$		0			0
$29$	0.967295	−	1.67540i	0.179622	−	0.311115i	−0.762129	−	0.647425i	$-0.775846\pi$
$29$	0.967295	−	1.67540i	0.179622	−	0.311115i	0.941751	+	0.336310i	$0.109179\pi$
$30$		0			0
$31$	2.30944	+	4.00007i	0.414787	+	0.718433i	0.995406	−	0.0957427i	$-0.0305226\pi$
$31$	2.30944	+	4.00007i	0.414787	+	0.718433i	−0.580619	+	0.814176i	$0.697189\pi$
$32$		0			0
$33$	8.20210	+	6.21093i	1.42780	+	1.08118i
$34$		0			0
$35$	17.4688			2.95276
$36$		0			0
$37$	10.7700			1.77058			0.885290	−	0.465039i	$-0.153960\pi$
$37$	10.7700			1.77058			0.885290	+	0.465039i	$0.153960\pi$
$38$		0			0
$39$	1.59594	−	0.673027i	0.255555	−	0.107770i
$40$		0			0
$41$	0.389576	+	0.674766i	0.0608416	+	0.105381i	0.894842	−	0.446383i	$-0.147288\pi$
$41$	0.389576	+	0.674766i	0.0608416	+	0.105381i	−0.834000	+	0.551764i	$0.813955\pi$
$42$		0			0
$43$	−0.164787	+	0.285420i	−0.0251298	+	0.0435261i	−0.878317	−	0.478079i	$-0.841333\pi$
$43$	−0.164787	+	0.285420i	−0.0251298	+	0.0435261i	0.853187	+	0.521605i	$0.174667\pi$
$44$		0			0
$45$	2.92884	+	10.3978i	0.436605	+	1.55001i
$46$		0			0
$47$	2.01335	−	3.48722i	0.293677	−	0.508663i	−0.680999	−	0.732284i	$-0.738454\pi$
$47$	2.01335	−	3.48722i	0.293677	−	0.508663i	0.974676	+	0.223621i	$0.0717877\pi$
$48$		0			0
$49$	−8.26774	−	14.3202i	−1.18111	−	2.04574i
$50$		0			0
$51$	−0.675911	+	5.40016i	−0.0946465	+	0.756174i
$52$		0			0
$53$	−6.03880			−0.829493			−0.414747	−	0.909937i	$-0.636130\pi$
$53$	−6.03880			−0.829493			−0.414747	+	0.909937i	$0.636130\pi$
$54$		0			0
$55$	−21.3888			−2.88406
$56$		0			0
$57$	−0.975419	+	7.79307i	−0.129197	+	1.03222i
$58$		0			0
$59$	−1.75266	−	3.03569i	−0.228176	−	0.395213i	0.729091	−	0.684417i	$-0.239943\pi$
$59$	−1.75266	−	3.03569i	−0.228176	−	0.395213i	−0.957268	+	0.289203i	$0.906610\pi$
$60$		0			0
$61$	2.77604	−	4.80825i	0.355436	−	0.615633i	−0.631757	−	0.775167i	$-0.717666\pi$
$61$	2.77604	−	4.80825i	0.355436	−	0.615633i	0.987192	+	0.159534i	$0.0509991\pi$
$62$		0			0
$63$	10.1590	−	10.4218i	1.27992	−	1.31302i
$64$		0			0
$65$	−1.80041	+	3.11840i	−0.223313	+	0.386789i
$66$		0			0
$67$	−2.91273	−	5.04500i	−0.355847	−	0.616345i	0.631415	−	0.775445i	$-0.282474\pi$
$67$	−2.91273	−	5.04500i	−0.355847	−	0.616345i	−0.987263	+	0.159099i	$0.949141\pi$
$68$		0			0
$69$	−7.67361	+	3.23604i	−0.923794	+	0.389574i
$70$		0			0
$71$	3.18402			0.377873			0.188937	−	0.981989i	$-0.439496\pi$
$71$	3.18402			0.377873			0.188937	+	0.981989i	$0.439496\pi$
$72$		0			0
$73$	11.7545			1.37576			0.687879	−	0.725826i	$-0.258542\pi$
$73$	11.7545			1.37576			0.687879	+	0.725826i	$0.258542\pi$
$74$		0			0
$75$	−10.9995	−	8.32921i	−1.27011	−	0.961774i
$76$		0			0
$77$	14.4084	+	24.9561i	1.64199	+	2.84402i
$78$		0			0
$79$	1.97184	−	3.41532i	0.221849	−	0.384254i	−0.733520	−	0.679667i	$-0.762124\pi$
$79$	1.97184	−	3.41532i	0.221849	−	0.384254i	0.955369	+	0.295414i	$0.0954575\pi$
$80$		0			0
$81$	7.90656	+	4.29958i	0.878506	+	0.477731i
$82$		0			0
$83$	−1.28229	+	2.22100i	−0.140750	+	0.243786i	−0.927779	−	0.373130i	$-0.878285\pi$
$83$	−1.28229	+	2.22100i	−0.140750	+	0.243786i	0.787029	+	0.616916i	$0.211618\pi$
$84$		0			0
$85$	−5.65708	−	9.79835i	−0.613596	−	1.06278i
$86$		0			0
$87$	2.67134	+	2.02283i	0.286398	+	0.216871i
$88$		0			0
$89$	11.4418			1.21282			0.606412	−	0.795150i	$-0.292608\pi$
$89$	11.4418			1.21282			0.606412	+	0.795150i	$0.292608\pi$
$90$		0			0
$91$	4.85134			0.508559
$92$		0			0
$93$	−7.37147	+	3.10863i	−0.764386	+	0.322350i
$94$		0			0
$95$	−8.16383	−	14.1402i	−0.837591	−	1.45075i
$96$		0			0
$97$	2.58047	−	4.46950i	0.262007	−	0.453809i	−0.704768	−	0.709437i	$-0.748949\pi$
$97$	2.58047	−	4.46950i	0.262007	−	0.453809i	0.966775	+	0.255629i	$0.0822824\pi$
$98$		0			0
$99$	−12.4387	+	12.7604i	−1.25014	+	1.28247i
$100$		0			0
$101$	−5.09235	+	8.82021i	−0.506708	+	0.877644i	0.493262	+	0.869881i	$0.335804\pi$
$101$	−5.09235	+	8.82021i	−0.506708	+	0.877644i	−0.999970	+	0.00776297i	$0.997529\pi$
$102$		0			0
$103$	−1.59094	−	2.75559i	−0.156760	−	0.271516i	0.776938	−	0.629577i	$-0.216772\pi$
$103$	−1.59094	−	2.75559i	−0.156760	−	0.271516i	−0.933698	+	0.358060i	$0.883438\pi$
$104$		0			0
$105$	−3.75777	+	30.0225i	−0.366721	+	2.92990i
$106$		0			0
$107$	16.4926			1.59440			0.797201	−	0.603714i	$-0.206313\pi$
$107$	16.4926			1.59440			0.797201	+	0.603714i	$0.206313\pi$
$108$		0			0
$109$	−6.31192			−0.604572			−0.302286	−	0.953217i	$-0.597750\pi$
$109$	−6.31192			−0.604572			−0.302286	+	0.953217i	$0.597750\pi$
$110$		0			0
$111$	−2.31678	+	18.5098i	−0.219899	+	1.75687i
$112$		0			0
$113$	−4.06899	−	7.04770i	−0.382779	−	0.662992i	0.608680	−	0.793416i	$-0.291699\pi$
$113$	−4.06899	−	7.04770i	−0.382779	−	0.662992i	−0.991458	+	0.130424i	$0.958366\pi$
$114$		0			0
$115$	8.65671	−	14.9939i	0.807242	−	1.39818i
$116$		0			0
$117$	0.813382	+	2.88763i	0.0751972	+	0.266962i
$118$		0			0
$119$	−7.62173	+	13.2012i	−0.698682	+	1.21015i
$120$		0			0
$121$	−12.1417	−	21.0300i	−1.10379	−	1.91182i
$122$		0			0
$123$	−1.24348	+	0.524390i	−0.112121	+	0.0472827i
$124$		0			0
$125$	10.6795			0.955201
$126$		0			0
$127$	9.41029			0.835028			0.417514	−	0.908671i	$-0.362901\pi$
$127$	9.41029			0.835028			0.417514	+	0.908671i	$0.362901\pi$
$128$		0			0
$129$	−0.455086	−	0.344608i	−0.0400681	−	0.0303410i
$130$		0			0
$131$	−9.18147	−	15.9028i	−0.802189	−	1.38943i	−0.918173	−	0.396180i	$-0.870336\pi$
$131$	−9.18147	−	15.9028i	−0.802189	−	1.38943i	0.115984	−	0.993251i	$-0.462998\pi$
$132$		0			0
$133$	−10.9990	+	19.0509i	−0.953738	+	1.65192i
$134$		0			0
$135$	−18.5001	+	2.79690i	−1.59224	+	0.240719i
$136$		0			0
$137$	3.72459	−	6.45117i	0.318213	−	0.551161i	−0.661902	−	0.749590i	$-0.730251\pi$
$137$	3.72459	−	6.45117i	0.318213	−	0.551161i	0.980115	+	0.198429i	$0.0635840\pi$
$138$		0			0
$139$	11.5014	+	19.9210i	0.975537	+	1.68968i	0.678151	+	0.734923i	$0.262782\pi$
$139$	11.5014	+	19.9210i	0.975537	+	1.68968i	0.297387	+	0.954757i	$0.403885\pi$
$140$		0			0
$141$	5.56018	+	4.21037i	0.468251	+	0.354577i
$142$		0			0
$143$	−5.93998			−0.496726
$144$		0			0
$145$	−6.96610			−0.578503
$146$		0			0
$147$	26.3897	−	11.1288i	2.17659	−	0.917890i
$148$		0			0
$149$	−2.82412	−	4.89152i	−0.231361	−	0.400729i	0.726848	−	0.686799i	$-0.240985\pi$
$149$	−2.82412	−	4.89152i	−0.231361	−	0.400729i	−0.958209	+	0.286069i	$0.907651\pi$
$150$		0			0
$151$	−5.96305	+	10.3283i	−0.485266	+	0.840506i	−0.999857	−	0.0169303i	$-0.994611\pi$
$151$	−5.96305	+	10.3283i	−0.485266	+	0.840506i	0.514590	+	0.857436i	$0.327944\pi$
$152$		0			0
$153$	−9.13554	−	2.32330i	−0.738565	−	0.187827i
$154$		0			0
$155$	8.31586	−	14.4035i	0.667946	−	1.15692i
$156$		0			0
$157$	−4.04029	−	6.99798i	−0.322450	−	0.558500i	0.658543	−	0.752543i	$-0.271173\pi$
$157$	−4.04029	−	6.99798i	−0.322450	−	0.558500i	−0.980993	+	0.194043i	$0.937840\pi$
$158$		0			0
$159$	1.29903	−	10.3785i	0.103020	−	0.823071i
$160$		0			0
$161$	−23.3262			−1.83836
$162$		0			0
$163$	12.7054			0.995160			0.497580	−	0.867418i	$-0.334222\pi$
$163$	12.7054			0.995160			0.497580	+	0.867418i	$0.334222\pi$
$164$		0			0
$165$	4.60101	−	36.7596i	0.358188	−	2.86173i
$166$		0			0
$167$	6.13446	+	10.6252i	0.474699	+	0.822202i	0.999580	−	0.0289730i	$-0.00922368\pi$
$167$	6.13446	+	10.6252i	0.474699	+	0.822202i	−0.524881	+	0.851175i	$0.675890\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$	−13.1837	−	3.35279i	−1.00818	−	0.256394i
$172$		0			0
$173$	−6.38764	+	11.0637i	−0.485643	+	0.841159i	−0.999864	−	0.0164990i	$-0.994748\pi$
$173$	−6.38764	+	11.0637i	−0.485643	+	0.841159i	0.514221	+	0.857658i	$0.328081\pi$
$174$		0			0
$175$	−19.3225	−	33.4676i	−1.46065	−	2.52991i
$176$		0			0
$177$	5.59428	−	2.35917i	0.420492	−	0.177326i
$178$		0			0
$179$	−5.65209			−0.422457			−0.211229	−	0.977437i	$-0.567746\pi$
$179$	−5.65209			−0.422457			−0.211229	+	0.977437i	$0.567746\pi$
$180$		0			0
$181$	−11.9835			−0.890723			−0.445362	−	0.895351i	$-0.646925\pi$
$181$	−11.9835			−0.890723			−0.445362	+	0.895351i	$0.646925\pi$
$182$		0			0
$183$	7.66649	+	5.80534i	0.566723	+	0.429143i
$184$		0			0
$185$	−19.3904	−	33.5852i	−1.42561	−	2.46923i
$186$		0			0
$187$	9.33204	−	16.1636i	0.682427	−	1.18200i
$188$		0			0
$189$	15.7259	+	19.7016i	1.14389	+	1.43308i
$190$		0			0
$191$	6.69583	−	11.5975i	0.484493	−	0.839167i	−0.515348	−	0.856981i	$-0.672337\pi$
$191$	6.69583	−	11.5975i	0.484493	−	0.839167i	0.999841	+	0.0178139i	$0.00567065\pi$
$192$		0			0
$193$	−0.00315107	−	0.00545781i	−0.000226819	−	0.000392862i	0.865912	−	0.500196i	$-0.166739\pi$
$193$	−0.00315107	−	0.00545781i	−0.000226819	−	0.000392862i	−0.866139	+	0.499804i	$0.833406\pi$
$194$		0			0
$195$	−4.97211	−	3.76506i	−0.356060	−	0.269622i
$196$		0			0
$197$	9.67863			0.689574			0.344787	−	0.938681i	$-0.387951\pi$
$197$	9.67863			0.689574			0.344787	+	0.938681i	$0.387951\pi$
$198$		0			0
$199$	−26.2710			−1.86230			−0.931149	−	0.364638i	$-0.881193\pi$
$199$	−26.2710			−1.86230			−0.931149	+	0.364638i	$0.881193\pi$
$200$		0			0
$201$	9.29712	−	3.92070i	0.655768	−	0.276545i
$202$		0			0
$203$	4.69268	+	8.12795i	0.329361	+	0.570470i
$204$		0			0
$205$	1.40279	−	2.42971i	0.0979752	−	0.169698i
$206$		0			0
$207$	−3.91090	−	13.8843i	−0.271826	−	0.965025i
$208$		0			0
$209$	13.4672	−	23.3259i	0.931548	−	1.61349i
$210$		0			0
$211$	−0.764674	−	1.32445i	−0.0526424	−	0.0911792i	0.838503	−	0.544896i	$-0.183431\pi$
$211$	−0.764674	−	1.32445i	−0.0526424	−	0.0911792i	−0.891146	+	0.453717i	$0.850098\pi$
$212$		0			0
$213$	−0.684925	+	5.47218i	−0.0469303	+	0.374948i
$214$		0			0
$215$	1.18674			0.0809347
$216$		0			0
$217$	−22.4077			−1.52114
$218$		0			0
$219$	−2.52855	+	20.2017i	−0.170863	+	1.36511i
$220$		0			0
$221$	−1.57106	−	2.72115i	−0.105681	−	0.183044i
$222$		0			0
$223$	−6.79374	+	11.7671i	−0.454943	+	0.787984i	−0.998685	−	0.0512684i	$-0.983674\pi$
$223$	−6.79374	+	11.7671i	−0.454943	+	0.787984i	0.543742	+	0.839252i	$0.317007\pi$
$224$		0			0
$225$	16.6811	−	17.1124i	1.11207	−	1.14083i
$226$		0			0
$227$	7.46880	−	12.9363i	0.495722	−	0.858615i	−0.504266	−	0.863548i	$-0.668237\pi$
$227$	7.46880	−	12.9363i	0.495722	−	0.858615i	0.999988	+	0.00493317i	$0.00157028\pi$
$228$		0			0
$229$	1.41828	+	2.45653i	0.0937225	+	0.162332i	0.909075	−	0.416633i	$-0.136790\pi$
$229$	1.41828	+	2.45653i	0.0937225	+	0.162332i	−0.815352	+	0.578965i	$0.803457\pi$
$230$		0			0
$231$	−45.9901	+	19.3945i	−3.02593	+	1.27607i
$232$		0			0
$233$	−12.7200			−0.833312			−0.416656	−	0.909064i	$-0.636798\pi$
$233$	−12.7200			−0.833312			−0.416656	+	0.909064i	$0.636798\pi$
$234$		0			0
$235$	−14.4994			−0.945834
$236$		0			0
$237$	5.44554	+	4.12356i	0.353726	+	0.267854i
$238$		0			0
$239$	−1.06154	−	1.83865i	−0.0686655	−	0.118932i	0.829649	−	0.558286i	$-0.188541\pi$
$239$	−1.06154	−	1.83865i	−0.0686655	−	0.118932i	−0.898314	+	0.439354i	$0.855207\pi$
$240$		0			0
$241$	1.66094	−	2.87684i	0.106991	−	0.185313i	−0.807559	−	0.589787i	$-0.799212\pi$
$241$	1.66094	−	2.87684i	0.106991	−	0.185313i	0.914550	+	0.404473i	$0.132545\pi$
$242$		0			0
$243$	−9.09023	+	12.6636i	−0.583139	+	0.812373i
$244$		0			0
$245$	−29.7706	+	51.5642i	−1.90197	+	3.29432i
$246$		0			0
$247$	−2.26722	−	3.92694i	−0.144260	−	0.249865i
$248$		0			0
$249$	−3.54125	−	2.68157i	−0.224418	−	0.169937i
$250$		0			0
$251$	14.9517			0.943746			0.471873	−	0.881667i	$-0.343578\pi$
$251$	14.9517			0.943746			0.471873	+	0.881667i	$0.343578\pi$
$252$		0			0
$253$	28.5606			1.79559
$254$		0			0
$255$	18.0568	−	7.61473i	1.13076	−	0.476853i
$256$		0			0
$257$	5.01395	+	8.68441i	0.312761	+	0.541719i	0.978959	−	0.204057i	$-0.0654126\pi$
$257$	5.01395	+	8.68441i	0.312761	+	0.541719i	−0.666198	+	0.745775i	$0.732079\pi$
$258$		0			0
$259$	−26.1245	+	45.2490i	−1.62330	+	2.81163i
$260$		0			0
$261$	−4.05117	+	4.15593i	−0.250761	+	0.257246i
$262$		0			0
$263$	2.40234	−	4.16098i	0.148135	−	0.256577i	−0.782403	−	0.622772i	$-0.786006\pi$
$263$	2.40234	−	4.16098i	0.148135	−	0.256577i	0.930538	+	0.366195i	$0.119340\pi$
$264$		0			0
$265$	10.8723	+	18.8314i	0.667880	+	1.15680i
$266$		0			0
$267$	−2.46128	+	19.6643i	−0.150628	+	1.20343i
$268$		0			0
$269$	−10.4507			−0.637190			−0.318595	−	0.947891i	$-0.603211\pi$
$269$	−10.4507			−0.637190			−0.318595	+	0.947891i	$0.603211\pi$
$270$		0			0
$271$	12.4552			0.756596			0.378298	−	0.925684i	$-0.376509\pi$
$271$	12.4552			0.756596			0.378298	+	0.925684i	$0.376509\pi$
$272$		0			0
$273$	−1.04359	+	8.33771i	−0.0631609	+	0.504621i
$274$		0			0
$275$	23.6585	+	40.9777i	1.42666	+	2.47105i
$276$		0			0
$277$	6.23063	−	10.7918i	0.374362	−	0.648414i	−0.615869	−	0.787848i	$-0.711195\pi$
$277$	6.23063	−	10.7918i	0.374362	−	0.648414i	0.990231	+	0.139434i	$0.0445283\pi$
$278$		0			0
$279$	−3.75691	−	13.3376i	−0.224920	−	0.798502i
$280$		0			0
$281$	15.0408	−	26.0515i	0.897261	−	1.55410i	0.0662788	−	0.997801i	$-0.478887\pi$
$281$	15.0408	−	26.0515i	0.897261	−	1.55410i	0.830982	−	0.556300i	$-0.187779\pi$
$282$		0			0
$283$	10.8709	+	18.8289i	0.646207	+	1.11926i	0.984021	+	0.178050i	$0.0569790\pi$
$283$	10.8709	+	18.8289i	0.646207	+	1.11926i	−0.337814	+	0.941213i	$0.609688\pi$
$284$		0			0
$285$	26.0580	−	10.9890i	1.54354	−	0.650929i
$286$		0			0
$287$	−3.77993			−0.223122
$288$		0			0
$289$	−7.12713			−0.419243
$290$		0			0
$291$	7.12637	+	5.39634i	0.417755	+	0.316339i
$292$		0			0
$293$	0.200069	+	0.346530i	0.0116882	+	0.0202445i	0.871810	−	0.489844i	$-0.162946\pi$
$293$	0.200069	+	0.346530i	0.0116882	+	0.0202445i	−0.860122	+	0.510088i	$0.829613\pi$
$294$		0			0
$295$	−6.31099	+	10.9310i	−0.367440	+	0.636425i
$296$		0			0
$297$	−19.2548	−	24.1227i	−1.11728	−	1.39974i
$298$		0			0
$299$	2.40410	−	4.16402i	0.139033	−	0.240812i
$300$		0			0
$301$	−0.799438	−	1.38467i	−0.0460789	−	0.0798109i
$302$		0			0
$303$	−14.0633	−	10.6493i	−0.807918	−	0.611785i
$304$		0			0
$305$	−19.9920			−1.14474
$306$		0			0
$307$	−23.5084			−1.34169			−0.670847	−	0.741596i	$-0.734069\pi$
$307$	−23.5084			−1.34169			−0.670847	+	0.741596i	$0.734069\pi$
$308$		0			0
$309$	5.07810	−	2.14149i	0.288883	−	0.121825i
$310$		0			0
$311$	8.79013	+	15.2249i	0.498442	+	0.863328i	0.999998	−	0.00179754i	$-0.000572174\pi$
$311$	8.79013	+	15.2249i	0.498442	+	0.863328i	−0.501556	+	0.865125i	$0.667239\pi$
$312$		0			0
$313$	−15.4108	+	26.6924i	−0.871073	+	1.50874i	−0.0101841	+	0.999948i	$0.503242\pi$
$313$	−15.4108	+	26.6924i	−0.871073	+	1.50874i	−0.860888	+	0.508794i	$0.830092\pi$
$314$		0			0
$315$	−50.7896	−	12.9165i	−2.86167	−	0.727763i
$316$		0			0
$317$	1.02914	−	1.78252i	0.0578021	−	0.100116i	−0.835676	−	0.549222i	$-0.814924\pi$
$317$	1.02914	−	1.78252i	0.0578021	−	0.100116i	0.893479	+	0.449106i	$0.148257\pi$
$318$		0			0
$319$	−5.74571	−	9.95187i	−0.321698	−	0.557198i
$320$		0			0
$321$	−3.54779	+	28.3449i	−0.198018	+	1.58206i
$322$		0			0
$323$	14.2477			0.792764
$324$		0			0
$325$	7.96585			0.441866
$326$		0			0
$327$	1.35778	−	10.8479i	0.0750854	−	0.599891i
$328$		0			0
$329$	9.76743	+	16.9177i	0.538496	+	0.932702i
$330$		0			0
$331$	−2.56919	+	4.44997i	−0.141216	+	0.244593i	−0.927955	−	0.372693i	$-0.878434\pi$
$331$	−2.56919	+	4.44997i	−0.141216	+	0.244593i	0.786739	+	0.617286i	$0.211768\pi$
$332$		0			0
$333$	−31.3133	−	7.96342i	−1.71596	−	0.436393i
$334$		0			0
$335$	−10.4882	+	18.1661i	−0.573032	+	0.992521i
$336$		0			0
$337$	10.6912	+	18.5177i	0.582388	+	1.00873i	0.995196	+	0.0979071i	$0.0312148\pi$
$337$	10.6912	+	18.5177i	0.582388	+	1.00873i	−0.412808	+	0.910818i	$0.635452\pi$
$338$		0			0
$339$	12.9878	−	5.47708i	0.705398	−	0.297474i
$340$		0			0
$341$	27.4360			1.48575
$342$		0			0
$343$	46.2599			2.49780
$344$		0			0
$345$	23.9069	+	18.1032i	1.28710	+	0.974641i
$346$		0			0
$347$	−7.80180	−	13.5131i	−0.418822	−	0.725422i	0.576999	−	0.816745i	$-0.304224\pi$
$347$	−7.80180	−	13.5131i	−0.418822	−	0.725422i	−0.995821	+	0.0913233i	$0.970890\pi$
$348$		0			0
$349$	−11.5993	+	20.0905i	−0.620895	+	1.07542i	0.368425	+	0.929658i	$0.379897\pi$
$349$	−11.5993	+	20.0905i	−0.620895	+	1.07542i	−0.989319	+	0.145764i	$0.953436\pi$
$350$		0			0
$351$	−5.13777	+	0.776743i	−0.274234	+	0.0414594i
$352$		0			0
$353$	−8.36520	+	14.4889i	−0.445235	+	0.771169i	−0.998069	−	0.0621226i	$-0.980213\pi$
$353$	−8.36520	+	14.4889i	−0.445235	+	0.771169i	0.552834	+	0.833291i	$0.313546\pi$
$354$		0			0
$355$	−5.73252	−	9.92902i	−0.304251	−	0.526978i
$356$		0			0
$357$	−21.0486	−	15.9388i	−1.11401	−	0.843569i
$358$		0			0
$359$	−13.8608			−0.731543			−0.365772	−	0.930705i	$-0.619195\pi$
$359$	−13.8608			−0.731543			−0.365772	+	0.930705i	$0.619195\pi$
$360$		0			0
$361$	1.56113			0.0821647
$362$		0			0
$363$	38.7549	−	16.3434i	2.03410	−	0.857804i
$364$		0			0
$365$	−21.1628	−	36.6551i	−1.10771	−	1.91862i
$366$		0			0
$367$	3.39093	−	5.87326i	0.177005	−	0.306582i	−0.763848	−	0.645396i	$-0.776692\pi$
$367$	3.39093	−	5.87326i	0.177005	−	0.306582i	0.940853	+	0.338814i	$0.110026\pi$
$368$		0			0
$369$	−0.633748	−	2.24990i	−0.0329916	−	0.117125i
$370$		0			0
$371$	14.6481	−	25.3713i	0.760494	−	1.31721i
$372$		0			0
$373$	−14.4619	−	25.0488i	−0.748811	−	1.29698i	−0.948393	−	0.317097i	$-0.897292\pi$
$373$	−14.4619	−	25.0488i	−0.748811	−	1.29698i	0.199582	−	0.979881i	$-0.436041\pi$
$374$		0			0
$375$	−2.29730	+	18.3542i	−0.118632	+	0.947806i
$376$		0			0
$377$	−1.93459			−0.0996364
$378$		0			0
$379$	4.07463			0.209300			0.104650	−	0.994509i	$-0.466628\pi$
$379$	4.07463			0.209300			0.104650	+	0.994509i	$0.466628\pi$
$380$		0			0
$381$	−2.02428	+	16.1729i	−0.103707	+	0.828563i
$382$		0			0
$383$	17.9208	+	31.0398i	0.915711	+	1.58606i	0.805857	+	0.592110i	$0.201705\pi$
$383$	17.9208	+	31.0398i	0.915711	+	1.58606i	0.109853	+	0.993948i	$0.464962\pi$
$384$		0			0
$385$	51.8821	−	89.8624i	2.64415	−	4.57981i
$386$		0			0
$387$	0.690152	−	0.708000i	0.0350824	−	0.0359896i
$388$		0			0
$389$	13.2149	−	22.8888i	0.670020	−	1.16051i	−0.307878	−	0.951426i	$-0.599619\pi$
$389$	13.2149	−	22.8888i	0.670020	−	1.16051i	0.977898	−	0.209083i	$-0.0670478\pi$
$390$		0			0
$391$	7.55395	+	13.0838i	0.382020	+	0.661677i
$392$		0			0
$393$	29.3062	−	12.3587i	1.47830	−	0.623416i
$394$		0			0
$395$	−14.2004			−0.714501
$396$		0			0
$397$	12.0428			0.604413			0.302206	−	0.953243i	$-0.402277\pi$
$397$	12.0428			0.604413			0.302206	+	0.953243i	$0.402277\pi$
$398$		0			0
$399$	−30.3756	−	23.0015i	−1.52068	−	1.15152i
$400$		0			0
$401$	−7.35012	−	12.7308i	−0.367047	−	0.635744i	0.622055	−	0.782973i	$-0.286298\pi$
$401$	−7.35012	−	12.7308i	−0.367047	−	0.635744i	−0.989102	+	0.147229i	$0.952965\pi$
$402$		0			0
$403$	2.30944	−	4.00007i	0.115041	−	0.199257i
$404$		0			0
$405$	−0.827241	−	32.3968i	−0.0411059	−	1.60981i
$406$		0			0
$407$	31.9869	−	55.4029i	1.58553	−	2.74622i
$408$		0			0
$409$	5.45923	+	9.45566i	0.269941	+	0.467552i	0.968846	−	0.247662i	$-0.0796623\pi$
$409$	5.45923	+	9.45566i	0.269941	+	0.467552i	−0.698905	+	0.715214i	$0.746329\pi$
$410$		0			0
$411$	10.2860	+	7.78896i	0.507373	+	0.384201i
$412$		0			0
$413$	17.0055			0.836784
$414$		0			0
$415$	9.23459			0.453308
$416$		0			0
$417$	−36.7112	+	15.4815i	−1.79776	+	0.758133i
$418$		0			0
$419$	13.9845	+	24.2219i	0.683187	+	1.18332i	0.974003	+	0.226536i	$0.0727401\pi$
$419$	13.9845	+	24.2219i	0.683187	+	1.18332i	−0.290815	+	0.956779i	$0.593927\pi$
$420$		0			0
$421$	4.71722	−	8.17046i	0.229903	−	0.398204i	−0.727876	−	0.685709i	$-0.759492\pi$
$421$	4.71722	−	8.17046i	0.229903	−	0.398204i	0.957779	+	0.287505i	$0.0928257\pi$
$422$		0			0
$423$	−8.43218	+	8.65024i	−0.409987	+	0.420589i
$424$		0			0
$425$	−12.5148	+	21.6763i	−0.607057	+	1.05145i
$426$		0			0
$427$	13.4675	+	23.3264i	0.651739	+	1.12885i
$428$		0			0
$429$	1.27777	−	10.2087i	0.0616914	−	0.492880i
$430$		0			0
$431$	8.51693			0.410246			0.205123	−	0.978736i	$-0.434241\pi$
$431$	8.51693			0.410246			0.205123	+	0.978736i	$0.434241\pi$
$432$		0			0
$433$	21.6386			1.03989			0.519943	−	0.854201i	$-0.325953\pi$
$433$	21.6386			1.03989			0.519943	+	0.854201i	$0.325953\pi$
$434$		0			0
$435$	1.49850	−	11.9722i	0.0718477	−	0.574024i
$436$		0			0
$437$	10.9012	+	18.8815i	0.521477	+	0.903224i
$438$		0			0
$439$	17.4828	−	30.2811i	0.834409	−	1.44524i	−0.0601023	−	0.998192i	$-0.519143\pi$
$439$	17.4828	−	30.2811i	0.834409	−	1.44524i	0.894511	−	0.447046i	$-0.147524\pi$
$440$		0			0
$441$	13.4497	+	47.7484i	0.640460	+	2.27373i
$442$		0			0
$443$	−16.7585	+	29.0265i	−0.796219	+	1.37909i	0.125844	+	0.992050i	$0.459836\pi$
$443$	−16.7585	+	29.0265i	−0.796219	+	1.37909i	−0.922062	+	0.387041i	$0.873497\pi$
$444$		0			0
$445$	−20.5998	−	35.6799i	−0.976525	−	1.69139i
$446$		0			0
$447$	9.01428	−	3.80142i	0.426361	−	0.179801i
$448$		0			0
$449$	−6.27418			−0.296097			−0.148048	−	0.988980i	$-0.547299\pi$
$449$	−6.27418			−0.296097			−0.148048	+	0.988980i	$0.547299\pi$
$450$		0			0
$451$	4.62815			0.217931
$452$		0			0
$453$	−16.4679	−	12.4701i	−0.773730	−	0.585897i
$454$		0			0
$455$	−8.73438	−	15.1284i	−0.409474	−	0.709230i
$456$		0			0
$457$	−8.38237	+	14.5187i	−0.392111	+	0.679155i	−0.992728	−	0.120381i	$-0.961588\pi$
$457$	−8.38237	+	14.5187i	−0.392111	+	0.679155i	0.600617	+	0.799537i	$0.294922\pi$
$458$		0			0
$459$	5.95809	−	15.2009i	0.278100	−	0.709519i
$460$		0			0
$461$	17.3348	−	30.0248i	0.807362	−	1.39839i	−0.107323	−	0.994224i	$-0.534228\pi$
$461$	17.3348	−	30.0248i	0.807362	−	1.39839i	0.914685	−	0.404168i	$-0.132439\pi$
$462$		0			0
$463$	16.1627	+	27.9946i	0.751143	+	1.30102i	0.947269	+	0.320439i	$0.103830\pi$
$463$	16.1627	+	27.9946i	0.751143	+	1.30102i	−0.196126	+	0.980579i	$0.562836\pi$
$464$		0			0
$465$	22.9656	+	17.3904i	1.06500	+	0.806458i
$466$		0			0
$467$	−8.51171			−0.393875			−0.196937	−	0.980416i	$-0.563100\pi$
$467$	−8.51171			−0.393875			−0.196937	+	0.980416i	$0.563100\pi$
$468$		0			0
$469$	28.2613			1.30499
$470$		0			0
$471$	12.8961	−	5.43844i	0.594223	−	0.250590i
$472$		0			0
$473$	0.978833	+	1.69539i	0.0450068	+	0.0779540i
$474$		0			0
$475$	−18.0603	+	31.2814i	−0.828665	+	1.43529i
$476$		0			0
$477$	17.5575	+	4.46513i	0.803904	+	0.204444i
$478$		0			0
$479$	0.650570	−	1.12682i	0.0297253	−	0.0514857i	−0.850780	−	0.525522i	$-0.823870\pi$
$479$	0.650570	−	1.12682i	0.0297253	−	0.0514857i	0.880505	+	0.474036i	$0.157203\pi$
$480$		0			0
$481$	−5.38501	−	9.32711i	−0.245535	−	0.425280i
$482$		0			0
$483$	5.01778	−	40.0894i	0.228317	−	1.82413i
$484$		0			0
$485$	−18.5835			−0.843835
$486$		0			0
$487$	−26.7805			−1.21354			−0.606771	−	0.794877i	$-0.707536\pi$
$487$	−26.7805			−1.21354			−0.606771	+	0.794877i	$0.707536\pi$
$488$		0			0
$489$	−2.73310	+	21.8359i	−0.123595	+	0.987456i
$490$		0			0
$491$	15.9518	+	27.6293i	0.719895	+	1.24690i	0.961041	+	0.276406i	$0.0891435\pi$
$491$	15.9518	+	27.6293i	0.719895	+	1.24690i	−0.241146	+	0.970489i	$0.577523\pi$
$492$		0			0
$493$	3.03935	−	5.26431i	0.136885	−	0.237092i
$494$		0			0
$495$	62.1868	+	15.8150i	2.79509	+	0.710830i
$496$		0			0
$497$	−7.72337	+	13.3773i	−0.346440	+	0.600052i
$498$		0			0
$499$	−3.26459	−	5.65444i	−0.146143	−	0.253127i	0.783656	−	0.621195i	$-0.213353\pi$
$499$	−3.26459	−	5.65444i	−0.146143	−	0.253127i	−0.929799	+	0.368068i	$0.880019\pi$
$500$		0			0
$501$	−19.5805	+	8.25731i	−0.874792	+	0.368909i
$502$		0			0
$503$	−36.4117			−1.62352			−0.811758	−	0.583994i	$-0.801489\pi$
$503$	−36.4117			−1.62352			−0.811758	+	0.583994i	$0.801489\pi$
$504$		0			0
$505$	36.6732			1.63194
$506$		0			0
$507$	−1.38083	−	1.04561i	−0.0613248	−	0.0464374i
$508$		0			0
$509$	1.36812	+	2.36966i	0.0606410	+	0.105033i	0.894752	−	0.446563i	$-0.147352\pi$
$509$	1.36812	+	2.36966i	0.0606410	+	0.105033i	−0.834111	+	0.551596i	$0.814019\pi$
$510$		0			0
$511$	−28.5125	+	49.3851i	−1.26132	+	2.18467i
$512$		0			0
$513$	8.59823	−	21.9367i	0.379621	−	0.968531i
$514$		0			0
$515$	−5.72868	+	9.92236i	−0.252436	+	0.437231i
$516$		0			0
$517$	−11.9592	−	20.7140i	−0.525967	−	0.911001i
$518$		0			0
$519$	−17.6405	−	13.3580i	−0.774332	−	0.586352i
$520$		0			0
$521$	−33.7588			−1.47900			−0.739500	−	0.673157i	$-0.764938\pi$
$521$	−33.7588			−1.47900			−0.739500	+	0.673157i	$0.764938\pi$
$522$		0			0
$523$	18.0617			0.789782			0.394891	−	0.918728i	$-0.370782\pi$
$523$	18.0617			0.789782			0.394891	+	0.918728i	$0.370782\pi$
$524$		0			0
$525$	61.6753	−	26.0091i	2.69173	−	1.13513i
$526$		0			0
$527$	7.25652	+	12.5687i	0.316099	+	0.547499i
$528$		0			0
$529$	−0.0593818	+	0.102852i	−0.00258182	+	0.00447184i
$530$		0			0
$531$	2.85116	+	10.1221i	0.123730	+	0.439260i
$532$		0			0
$533$	0.389576	−	0.674766i	0.0168744	−	0.0292274i
$534$		0			0
$535$	−29.6934	−	51.4305i	−1.28376	−	2.22354i
$536$		0			0
$537$	1.21584	−	9.71392i	0.0524675	−	0.419187i
$538$		0			0
$539$	−98.2205			−4.23066
$540$		0			0
$541$	9.82851			0.422561			0.211280	−	0.977426i	$-0.432237\pi$
$541$	9.82851			0.422561			0.211280	+	0.977426i	$0.432237\pi$
$542$		0			0
$543$	2.57780	−	20.5953i	0.110624	−	0.883827i
$544$		0			0
$545$	11.3640	+	19.6831i	0.486781	+	0.843129i
$546$		0			0
$547$	−6.09142	+	10.5506i	−0.260450	+	0.451113i	−0.966362	−	0.257187i	$-0.917204\pi$
$547$	−6.09142	+	10.5506i	−0.260450	+	0.451113i	0.705911	+	0.708300i	$0.250538\pi$
$548$		0			0
$549$	−11.6265	+	11.9271i	−0.496205	+	0.509037i
$550$		0			0
$551$	4.38614	−	7.59702i	0.186856	−	0.323644i
$552$		0			0
$553$	9.56605	+	16.5689i	0.406790	+	0.704581i
$554$		0			0
$555$	61.8920	−	26.1005i	2.62717	−	1.10791i
$556$		0			0
$557$	9.07479			0.384511			0.192256	−	0.981345i	$-0.438420\pi$
$557$	9.07479			0.384511			0.192256	+	0.981345i	$0.438420\pi$
$558$		0			0
$559$	0.329574			0.0139395
$560$		0			0
$561$	25.7719	+	19.5154i	1.08809	+	0.823942i
$562$		0			0
$563$	−16.3055	−	28.2419i	−0.687193	−	1.19025i	−0.972742	−	0.231889i	$-0.925509\pi$
$563$	−16.3055	−	28.2419i	−0.687193	−	1.19025i	0.285549	−	0.958364i	$-0.407824\pi$
$564$		0			0
$565$	−14.6517	+	25.3775i	−0.616401	+	1.06764i
$566$		0			0
$567$	−37.2429	+	22.7891i	−1.56405	+	0.957053i
$568$		0			0
$569$	10.2251	−	17.7105i	0.428660	−	0.742461i	−0.568094	−	0.822964i	$-0.692319\pi$
$569$	10.2251	−	17.7105i	0.428660	−	0.742461i	0.996754	+	0.0805022i	$0.0256524\pi$
$570$		0			0
$571$	12.7365	+	22.0603i	0.533007	+	0.923195i	0.999257	+	0.0385419i	$0.0122713\pi$
$571$	12.7365	+	22.0603i	0.533007	+	0.923195i	−0.466250	+	0.884653i	$0.654395\pi$
$572$		0			0
$573$	18.4916	+	14.0025i	0.772498	+	0.584963i
$574$		0			0
$575$	−38.3014			−1.59728
$576$		0			0
$577$	42.2188			1.75759			0.878795	−	0.477199i	$-0.158348\pi$
$577$	42.2188			1.75759			0.878795	+	0.477199i	$0.158348\pi$
$578$		0			0
$579$	0.0100579	−	0.00424151i	0.000417990	−	0.000176271i
$580$		0			0
$581$	−6.22083	−	10.7748i	−0.258084	−	0.447014i
$582$		0			0
$583$	−17.9352	+	31.0647i	−0.742800	+	1.28657i
$584$		0			0
$585$	7.54036	−	7.73535i	0.311755	−	0.319818i
$586$		0			0
$587$	−13.3873	+	23.1875i	−0.552555	+	0.957053i	0.445535	+	0.895265i	$0.353014\pi$
$587$	−13.3873	+	23.1875i	−0.552555	+	0.957053i	−0.998089	+	0.0617879i	$0.980320\pi$
$588$		0			0
$589$	10.4720	+	18.1380i	0.431492	+	0.747365i
$590$		0			0
$591$	−2.08200	+	16.6341i	−0.0856422	+	0.684235i
$592$		0			0
$593$	4.74780			0.194969			0.0974844	−	0.995237i	$-0.468920\pi$
$593$	4.74780			0.194969			0.0974844	+	0.995237i	$0.468920\pi$
$594$		0			0
$595$	54.8888			2.25022
$596$		0			0
$597$	5.65124	−	45.1503i	0.231290	−	1.84788i
$598$		0			0
$599$	17.9972	+	31.1721i	0.735347	+	1.27366i	0.954571	+	0.297984i	$0.0963141\pi$
$599$	17.9972	+	31.1721i	0.735347	+	1.27366i	−0.219224	+	0.975675i	$0.570353\pi$
$600$		0			0
$601$	2.62645	−	4.54915i	0.107135	−	0.185564i	−0.807473	−	0.589904i	$-0.799166\pi$
$601$	2.62645	−	4.54915i	0.107135	−	0.185564i	0.914609	+	0.404340i	$0.132499\pi$
$602$		0			0
$603$	4.73833	+	16.8218i	0.192960	+	0.685037i
$604$		0			0
$605$	−43.7199	+	75.7252i	−1.77747	+	3.07867i
$606$		0			0
$607$	0.624003	+	1.08081i	0.0253275	+	0.0438685i	0.878411	−	0.477905i	$-0.158604\pi$
$607$	0.624003	+	1.08081i	0.0253275	+	0.0438685i	−0.853084	+	0.521774i	$0.825270\pi$
$608$		0			0
$609$	−14.9785	+	6.31659i	−0.606959	+	0.255961i
$610$		0			0
$611$	−4.02669			−0.162903
$612$		0			0
$613$	−18.4731			−0.746120			−0.373060	−	0.927807i	$-0.621692\pi$
$613$	−18.4731			−0.746120			−0.373060	+	0.927807i	$0.621692\pi$
$614$		0			0
$615$	3.87403	+	2.93356i	0.156216	+	0.118292i
$616$		0			0
$617$	−18.0419	−	31.2495i	−0.726340	−	1.25806i	−0.958420	−	0.285361i	$-0.907886\pi$
$617$	−18.0419	−	31.2495i	−0.726340	−	1.25806i	0.232080	−	0.972697i	$-0.425447\pi$
$618$		0			0
$619$	22.2098	−	38.4685i	0.892688	−	1.54618i	0.0560473	−	0.998428i	$-0.482150\pi$
$619$	22.2098	−	38.4685i	0.892688	−	1.54618i	0.836640	−	0.547752i	$-0.184516\pi$
$620$		0			0
$621$	24.7034	−	3.73473i	0.991314	−	0.149870i
$622$		0			0
$623$	−27.7539	+	48.0712i	−1.11194	+	1.92593i
$624$		0			0
$625$	0.687235	+	1.19033i	0.0274894	+	0.0476131i
$626$		0			0
$627$	37.1919	+	28.1631i	1.48530	+	1.12472i
$628$		0			0
$629$	33.8406			1.34931
$630$		0			0
$631$	27.2686			1.08555			0.542773	−	0.839880i	$-0.317375\pi$
$631$	27.2686			1.08555			0.542773	+	0.839880i	$0.317375\pi$
$632$		0			0
$633$	2.44075	−	1.02929i	0.0970113	−	0.0409107i
$634$		0			0
$635$	−16.9423	−	29.3450i	−0.672336	−	1.16452i
$636$		0			0
$637$	−8.26774	+	14.3202i	−0.327580	+	0.567385i
$638$		0			0
$639$	−9.25737	−	2.35428i	−0.366216	−	0.0931339i
$640$		0			0
$641$	−10.1339	+	17.5524i	−0.400265	+	0.693280i	−0.993758	−	0.111560i	$-0.964415\pi$
$641$	−10.1339	+	17.5524i	−0.400265	+	0.693280i	0.593492	+	0.804840i	$0.297749\pi$
$642$		0			0
$643$	−10.0914	−	17.4789i	−0.397967	−	0.689299i	0.595508	−	0.803349i	$-0.296951\pi$
$643$	−10.0914	−	17.4789i	−0.397967	−	0.689299i	−0.993475	+	0.114051i	$0.963617\pi$
$644$		0			0
$645$	−0.255283	+	2.03957i	−0.0100518	+	0.0803081i
$646$		0			0
$647$	−9.41833			−0.370273			−0.185136	−	0.982713i	$-0.559273\pi$
$647$	−9.41833			−0.370273			−0.185136	+	0.982713i	$0.559273\pi$
$648$		0			0
$649$	−20.8215			−0.817315
$650$		0			0
$651$	4.82021	−	38.5109i	0.188919	−	1.50936i
$652$		0			0
$653$	−23.8178	−	41.2537i	−0.932063	−	1.61438i	−0.779790	−	0.626042i	$-0.784674\pi$
$653$	−23.8178	−	41.2537i	−0.932063	−	1.61438i	−0.152273	−	0.988338i	$-0.548659\pi$
$654$		0			0
$655$	−33.0607	+	57.2629i	−1.29179	+	2.23745i
$656$		0			0
$657$	−34.1756	−	8.69133i	−1.33332	−	0.339081i
$658$		0			0
$659$	−10.5791	+	18.3235i	−0.412102	+	0.713781i	−0.995119	−	0.0986782i	$-0.968539\pi$
$659$	−10.5791	+	18.3235i	−0.412102	+	0.713781i	0.583017	+	0.812460i	$0.301872\pi$
$660$		0			0
$661$	−11.3505	−	19.6596i	−0.441482	−	0.764669i	0.556318	−	0.830969i	$-0.312214\pi$
$661$	−11.3505	−	19.6596i	−0.441482	−	0.764669i	−0.997800	+	0.0663009i	$0.978880\pi$
$662$		0			0
$663$	5.01463	−	2.11473i	0.194752	−	0.0821291i
$664$		0			0
$665$	79.2110			3.07167
$666$		0			0
$667$	9.30189			0.360171
$668$		0			0
$669$	−18.7620	−	14.2073i	−0.725381	−	0.549285i
$670$		0			0
$671$	−16.4896	−	28.5609i	−0.636576	−	1.10258i
$672$		0			0
$673$	4.80850	−	8.32857i	0.185354	−	0.321043i	−0.758342	−	0.651857i	$-0.773990\pi$
$673$	4.80850	−	8.32857i	0.185354	−	0.321043i	0.943696	+	0.330815i	$0.107323\pi$
$674$		0			0
$675$	25.8218	+	32.3499i	0.993882	+	1.24515i
$676$		0			0
$677$	2.82985	−	4.90145i	0.108760	−	0.188378i	−0.806508	−	0.591223i	$-0.798645\pi$
$677$	2.82985	−	4.90145i	0.108760	−	0.188378i	0.915268	+	0.402845i	$0.131979\pi$
$678$		0			0
$679$	12.5187	+	21.6830i	0.480424	+	0.832119i
$680$		0			0
$681$	20.6263	+	15.6190i	0.790401	+	0.598520i
$682$		0			0
$683$	33.6477			1.28749			0.643747	−	0.765239i	$-0.277379\pi$
$683$	33.6477			1.28749			0.643747	+	0.765239i	$0.277379\pi$
$684$		0			0
$685$	−26.8231			−1.02486
$686$		0			0
$687$	−4.52698	+	1.90908i	−0.172715	+	0.0728359i
$688$		0			0
$689$	3.01940	+	5.22976i	0.115030	+	0.199238i
$690$		0			0
$691$	−4.26302	+	7.38378i	−0.162173	+	0.280892i	−0.935648	−	0.352935i	$-0.885184\pi$
$691$	−4.26302	+	7.38378i	−0.162173	+	0.280892i	0.773475	+	0.633827i	$0.218517\pi$
$692$		0			0
$693$	−23.4391	−	83.2125i	−0.890378	−	3.16098i
$694$		0			0
$695$	41.4144	−	71.7319i	1.57094	−	2.72095i
$696$		0			0
$697$	1.22409	+	2.12019i	0.0463658	+	0.0803079i
$698$		0			0
$699$	2.73624	−	21.8610i	0.103494	−	0.826861i
$700$		0			0
$701$	13.9968			0.528651			0.264326	−	0.964434i	$-0.414851\pi$
$701$	13.9968			0.528651			0.264326	+	0.964434i	$0.414851\pi$
$702$		0			0
$703$	48.8360			1.84188
$704$		0			0
$705$	3.11901	−	24.9192i	0.117469	−	0.938511i
$706$		0			0
$707$	−24.7047	−	42.7898i	−0.929117	−	1.60928i
$708$		0			0
$709$	−8.16793	+	14.1473i	−0.306753	+	0.531312i	−0.977650	−	0.210238i	$-0.932576\pi$
$709$	−8.16793	+	14.1473i	−0.306753	+	0.531312i	0.670897	+	0.741551i	$0.265909\pi$
$710$		0			0
$711$	−8.25833	+	8.47190i	−0.309712	+	0.317721i
$712$		0			0
$713$	−11.1042	+	19.2331i	−0.415857	+	0.720285i
$714$		0			0
$715$	10.6944	+	18.5232i	0.399947	+	0.692729i
$716$		0			0
$717$	3.38832	−	1.42889i	0.126539	−	0.0533630i
$718$		0			0
$719$	17.1133			0.638219			0.319110	−	0.947718i	$-0.396616\pi$
$719$	17.1133			0.638219			0.319110	+	0.947718i	$0.396616\pi$
$720$		0			0
$721$	15.4364			0.574881
$722$		0			0
$723$	4.58696	+	3.47341i	0.170591	+	0.129177i
$724$		0			0
$725$	7.70533	+	13.3460i	0.286169	+	0.495659i
$726$		0			0
$727$	−3.23624	+	5.60534i	−0.120026	+	0.207890i	−0.919778	−	0.392440i	$-0.871631\pi$
$727$	−3.23624	+	5.60534i	−0.120026	+	0.207890i	0.799752	+	0.600331i	$0.204964\pi$
$728$		0			0
$729$	−19.8088	−	18.3470i	−0.733660	−	0.679517i
$730$		0			0
$731$	−0.517780	+	0.896821i	−0.0191508	+	0.0331701i
$732$		0			0
$733$	24.1525	+	41.8334i	0.892093	+	1.54515i	0.837361	+	0.546650i	$0.184097\pi$
$733$	24.1525	+	41.8334i	0.892093	+	1.54515i	0.0547322	+	0.998501i	$0.482569\pi$
$734$		0			0
$735$	−82.2163	−	62.2571i	−3.03259	−	2.29639i
$736$		0			0
$737$	−34.6032			−1.27462
$738$		0			0
$739$	−18.1182			−0.666488			−0.333244	−	0.942841i	$-0.608143\pi$
$739$	−18.1182			−0.666488			−0.333244	+	0.942841i	$0.608143\pi$
$740$		0			0
$741$	7.23671	−	3.05180i	0.265847	−	0.112111i
$742$		0			0
$743$	−18.4567	−	31.9680i	−0.677112	−	1.17279i	−0.975847	−	0.218457i	$-0.929898\pi$
$743$	−18.4567	−	31.9680i	−0.677112	−	1.17279i	0.298734	−	0.954336i	$-0.403436\pi$
$744$		0			0
$745$	−10.1691	+	17.6135i	−0.372568	+	0.645307i
$746$		0			0
$747$	5.37042	−	5.50930i	0.196493	−	0.201575i
$748$		0			0
$749$	−40.0057	+	69.2918i	−1.46177	+	2.53187i
$750$		0			0
$751$	−22.5544	−	39.0654i	−0.823023	−	1.42552i	−0.903421	−	0.428755i	$-0.858952\pi$
$751$	−22.5544	−	39.0654i	−0.823023	−	1.42552i	0.0803976	−	0.996763i	$-0.474381\pi$
$752$		0			0
$753$	−3.21632	+	25.6967i	−0.117209	+	0.936439i
$754$		0			0
$755$	42.9437			1.56288
$756$		0			0
$757$	−14.8646			−0.540263			−0.270132	−	0.962823i	$-0.587067\pi$
$757$	−14.8646			−0.540263			−0.270132	+	0.962823i	$0.587067\pi$
$758$		0			0
$759$	−6.14377	+	49.0854i	−0.223005	+	1.78169i
$760$		0			0
$761$	2.24075	+	3.88109i	0.0812271	+	0.140689i	0.903777	−	0.428003i	$-0.140783\pi$
$761$	2.24075	+	3.88109i	0.0812271	+	0.140689i	−0.822550	+	0.568693i	$0.807449\pi$
$762$		0			0
$763$	15.3106	−	26.5188i	0.554282	−	0.960044i
$764$		0			0
$765$	9.20273	+	32.6711i	0.332725	+	1.18123i
$766$		0			0
$767$	−1.75266	+	3.03569i	−0.0632848	+	0.109612i
$768$		0			0
$769$	2.08442	+	3.61031i	0.0751659	+	0.130191i	0.901158	−	0.433490i	$-0.142718\pi$
$769$	2.08442	+	3.61031i	0.0751659	+	0.130191i	−0.825992	+	0.563681i	$0.809385\pi$
$770$		0			0
$771$	−16.0040	+	6.74904i	−0.576368	+	0.243061i
$772$		0			0
$773$	33.3000			1.19772			0.598858	−	0.800855i	$-0.295621\pi$
$773$	33.3000			1.19772			0.598858	+	0.800855i	$0.295621\pi$
$774$		0			0
$775$	−36.7933			−1.32165
$776$		0			0
$777$	−72.1470	−	54.6323i	−2.58826	−	1.95992i
$778$		0			0
$779$	1.76651	+	3.05968i	0.0632918	+	0.109625i
$780$		0			0
$781$	9.45650	−	16.3791i	0.338380	−	0.586091i
$782$		0			0
$783$	−6.27110	−	7.85650i	−0.224111	−	0.280768i
$784$		0			0
$785$	−14.5483	+	25.1984i	−0.519252	+	0.899370i
$786$		0			0
$787$	−6.82197	−	11.8160i	−0.243177	−	0.421195i	0.718441	−	0.695588i	$-0.244856\pi$
$787$	−6.82197	−	11.8160i	−0.243177	−	0.421195i	−0.961617	+	0.274394i	$0.911523\pi$
$788$		0			0
$789$	6.63445	+	5.02385i	0.236193	+	0.178854i
$790$		0			0
$791$	39.4801			1.40375
$792$		0			0
$793$	−5.55209			−0.197160
$794$		0			0
$795$	−34.7031	+	14.6347i	−1.23079	+	0.519039i
$796$		0			0
$797$	16.4935	+	28.5676i	0.584230	+	1.01192i	0.994971	+	0.100164i	$0.0319367\pi$
$797$	16.4935	+	28.5676i	0.584230	+	1.01192i	−0.410741	+	0.911752i	$0.634730\pi$
$798$		0			0
$799$	6.32616	−	10.9572i	0.223803	−	0.387639i
$800$		0			0
$801$	−33.2664	−	8.46011i	−1.17541	−	0.298923i
$802$		0			0
$803$	34.9107	−	60.4671i	1.23197	−	2.13384i
$804$		0			0
$805$	41.9966	+	72.7403i	1.48019	+	2.56376i
$806$		0			0
$807$	2.24809	−	17.9610i	0.0791364	−	0.632257i
$808$		0			0
$809$	−30.2406			−1.06320			−0.531601	−	0.846995i	$-0.678410\pi$
$809$	−30.2406			−1.06320			−0.531601	+	0.846995i	$0.678410\pi$
$810$		0			0
$811$	−38.3497			−1.34664			−0.673320	−	0.739351i	$-0.735132\pi$
$811$	−38.3497			−1.34664			−0.673320	+	0.739351i	$0.735132\pi$
$812$		0			0
$813$	−2.67927	+	21.4059i	−0.0939662	+	0.750739i
$814$		0			0
$815$	−22.8748	−	39.6203i	−0.801270	−	1.38784i
$816$		0			0
$817$	−0.747217	+	1.29422i	−0.0261418	+	0.0452790i
$818$		0			0
$819$	−14.1050	−	3.58711i	−0.492870	−	0.125344i
$820$		0			0
$821$	15.5824	−	26.9896i	0.543831	−	0.941942i	−0.454849	−	0.890569i	$-0.650307\pi$
$821$	15.5824	−	26.9896i	0.543831	−	0.941942i	0.998680	−	0.0513735i	$-0.0163599\pi$
$822$		0			0
$823$	1.44096	+	2.49581i	0.0502287	+	0.0869986i	0.890047	−	0.455870i	$-0.150672\pi$
$823$	1.44096	+	2.49581i	0.0502287	+	0.0869986i	−0.839818	+	0.542868i	$0.817338\pi$
$824$		0			0
$825$	−75.5153	+	31.8456i	−2.62910	+	1.10872i
$826$		0			0
$827$	−22.9312			−0.797396			−0.398698	−	0.917082i	$-0.630538\pi$
$827$	−22.9312			−0.797396			−0.398698	+	0.917082i	$0.630538\pi$
$828$		0			0
$829$	−44.0256			−1.52907			−0.764536	−	0.644581i	$-0.777032\pi$
$829$	−44.0256			−1.52907			−0.764536	+	0.644581i	$0.777032\pi$
$830$		0			0
$831$	17.2069	+	13.0297i	0.596900	+	0.451994i
$832$		0			0
$833$	−25.9782	−	44.9955i	−0.900091	−	1.55900i
$834$		0			0
$835$	22.0890	−	38.2593i	0.764423	−	1.32402i
$836$		0			0
$837$	23.7307	−	3.58768i	0.820254	−	0.124008i
$838$		0			0
$839$	−3.75434	+	6.50270i	−0.129614	+	0.224498i	−0.923527	−	0.383533i	$-0.874707\pi$
$839$	−3.75434	+	6.50270i	−0.129614	+	0.224498i	0.793913	+	0.608031i	$0.208040\pi$
$840$		0			0
$841$	12.6287	+	21.8735i	0.435472	+	0.754259i
$842$		0			0
$843$	41.5376	+	31.4538i	1.43063	+	1.08333i
$844$		0			0
$845$	3.60081			0.123872
$846$		0			0
$847$	117.807			4.04789
$848$		0			0
$849$	−34.6986	+	14.6328i	−1.19085	+	0.502196i
$850$		0			0
$851$	25.8922	+	44.8466i	0.887573	+	1.53732i
$852$		0			0
$853$	−17.4967	+	30.3052i	−0.599076	+	1.03763i	0.393882	+	0.919161i	$0.371132\pi$
$853$	−17.4967	+	30.3052i	−0.599076	+	1.03763i	−0.992958	+	0.118469i	$0.962201\pi$
$854$		0			0
$855$	13.2806	+	47.1483i	0.454188	+	1.61244i
$856$		0			0
$857$	1.94529	−	3.36935i	0.0664500	−	0.115095i	−0.830886	−	0.556442i	$-0.812166\pi$
$857$	1.94529	−	3.36935i	0.0664500	−	0.115095i	0.897336	+	0.441347i	$0.145499\pi$
$858$		0			0
$859$	−7.39306	−	12.8052i	−0.252248	−	0.436906i	0.711896	−	0.702285i	$-0.247837\pi$
$859$	−7.39306	−	12.8052i	−0.252248	−	0.436906i	−0.964144	+	0.265378i	$0.914503\pi$
$860$		0			0
$861$	0.813115	−	6.49635i	0.0277109	−	0.221395i
$862$		0			0
$863$	−39.4680			−1.34351			−0.671753	−	0.740775i	$-0.734459\pi$
$863$	−39.4680			−1.34351			−0.671753	+	0.740775i	$0.734459\pi$
$864$		0			0
$865$	46.0014			1.56409
$866$		0			0
$867$	1.53314	−	12.2490i	0.0520682	−	0.415997i
$868$		0			0
$869$	−11.7127	−	20.2869i	−0.397325	−	0.688188i
$870$		0			0
$871$	−2.91273	+	5.04500i	−0.0986942	+	0.170943i
$872$		0			0
$873$	−10.8074	+	11.0868i	−0.365774	+	0.375233i
$874$		0			0
$875$	−25.9049	+	44.8686i	−0.875745	+	1.51683i
$876$		0			0
$877$	−15.9102	−	27.5573i	−0.537249	−	0.930543i	−0.999051	−	0.0435599i	$-0.986130\pi$
$877$	−15.9102	−	27.5573i	−0.537249	−	0.930543i	0.461801	−	0.886983i	$-0.347203\pi$
$878$		0			0
$879$	−0.638598	+	0.269304i	−0.0215394	+	0.00908339i
$880$		0			0
$881$	−0.104015			−0.00350437			−0.00175218	−	0.999998i	$-0.500558\pi$
$881$	−0.104015			−0.00350437			−0.00175218	+	0.999998i	$0.500558\pi$
$882$		0			0
$883$	−37.7445			−1.27020			−0.635102	−	0.772428i	$-0.719042\pi$
$883$	−37.7445			−1.27020			−0.635102	+	0.772428i	$0.719042\pi$
$884$		0			0
$885$	−17.4288	−	13.1977i	−0.585863	−	0.443636i
$886$		0			0
$887$	14.0832	+	24.3928i	0.472867	+	0.819031i	0.999518	−	0.0310515i	$-0.00988559\pi$
$887$	14.0832	+	24.3928i	0.472867	+	0.819031i	−0.526650	+	0.850082i	$0.676552\pi$
$888$		0			0
$889$	−22.8262	+	39.5362i	−0.765568	+	1.32600i
$890$		0			0
$891$	45.6002	−	27.9030i	1.52766	−	0.934786i
$892$		0			0
$893$	9.12939	−	15.8126i	0.305504	−	0.529148i
$894$		0			0
$895$	10.1761	+	17.6255i	0.340148	+	0.589154i
$896$		0			0
$897$	6.63930	+	5.02752i	0.221680	+	0.167864i
$898$		0			0
$899$	8.93563			0.298020
$900$		0			0
$901$	−18.9746			−0.632136
$902$		0			0
$903$	2.55172	−	1.07609i	0.0849158	−	0.0358099i
$904$		0			0
$905$	21.5751	+	37.3691i	0.717180	+	1.24219i
$906$		0			0
$907$	18.1360	−	31.4125i	0.602197	−	1.04304i	−0.390291	−	0.920692i	$-0.627626\pi$
$907$	18.1360	−	31.4125i	0.602197	−	1.04304i	0.992488	−	0.122344i	$-0.0390411\pi$
$908$		0			0
$909$	21.3275	−	21.8790i	0.707388	−	0.725682i
$910$		0			0
$911$	−4.43178	+	7.67607i	−0.146831	+	0.254319i	−0.930055	−	0.367421i	$-0.880241\pi$
$911$	−4.43178	+	7.67607i	−0.146831	+	0.254319i	0.783223	+	0.621740i	$0.213574\pi$
$912$		0			0
$913$	7.61679	+	13.1927i	0.252079	+	0.436614i
$914$		0			0
$915$	4.30056	−	34.3591i	0.142172	−	1.13588i
$916$		0			0
$917$	89.0848			2.94184
$918$		0			0
$919$	17.7678			0.586106			0.293053	−	0.956096i	$-0.405329\pi$
$919$	17.7678			0.586106			0.293053	+	0.956096i	$0.405329\pi$
$920$		0			0
$921$	5.05697	−	40.4024i	0.166633	−	1.33131i
$922$		0			0
$923$	−1.59201	−	2.75744i	−0.0524016	−	0.0907622i
$924$		0			0
$925$	−42.8962	+	74.2984i	−1.41042	+	2.44292i
$926$		0			0
$927$	2.58808	+	9.18810i	0.0850038	+	0.301777i
$928$		0			0
$929$	−17.7193	+	30.6908i	−0.581352	+	1.00693i	0.413967	+	0.910292i	$0.364143\pi$
$929$	−17.7193	+	30.6908i	−0.581352	+	1.00693i	−0.995319	+	0.0966396i	$0.969191\pi$
$930$		0			0
$931$	−37.4896	−	64.9339i	−1.22867	−	2.12812i
$932$		0			0
$933$	−28.0571	+	11.8320i	−0.918548	+	0.387362i
$934$		0			0
$935$	−67.2059			−2.19787
$936$		0			0
$937$	26.0877			0.852248			0.426124	−	0.904665i	$-0.359879\pi$
$937$	26.0877			0.852248			0.426124	+	0.904665i	$0.359879\pi$
$938$		0			0
$939$	−42.5595	−	32.2276i	−1.38888	−	1.05171i
$940$		0			0
$941$	−10.2832	−	17.8111i	−0.335223	−	0.580624i	0.648304	−	0.761381i	$-0.275478\pi$
$941$	−10.2832	−	17.8111i	−0.335223	−	0.580624i	−0.983528	+	0.180757i	$0.942145\pi$
$942$		0			0
$943$	−1.87316	+	3.24441i	−0.0609985	+	0.105652i
$944$		0			0
$945$	33.1244	−	84.5105i	1.07754	−	2.74913i
$946$		0			0
$947$	−11.2111	+	19.4182i	−0.364311	+	0.631006i	−0.988665	−	0.150136i	$-0.952029\pi$
$947$	−11.2111	+	19.4182i	−0.364311	+	0.631006i	0.624354	+	0.781141i	$0.285362\pi$
$948$		0			0
$949$	−5.87724	−	10.1797i	−0.190783	−	0.330446i
$950$		0			0
$951$	2.84213	+	2.15216i	0.0921623	+	0.0697886i
$952$		0			0
$953$	−15.5106			−0.502438			−0.251219	−	0.967930i	$-0.580832\pi$
$953$	−15.5106			−0.502438			−0.251219	+	0.967930i	$0.580832\pi$
$954$		0			0
$955$	−48.2209			−1.56039
$956$		0			0
$957$	18.3397	−	7.73404i	0.592837	−	0.250006i
$958$		0			0
$959$	18.0692	+	31.2968i	0.583486	+	1.01063i
$960$		0			0
$961$	4.83299	−	8.37098i	0.155903	−	0.270031i
$962$		0			0
$963$	−47.9515	−	12.1947i	−1.54522	−	0.392970i
$964$		0			0
$965$	−0.0113464	+	0.0196526i	−0.000365254	+	0.000632638i
$966$		0			0
$967$	−6.61051	−	11.4497i	−0.212580	−	0.368199i	0.739942	−	0.672671i	$-0.234853\pi$
$967$	−6.61051	−	11.4497i	−0.212580	−	0.368199i	−0.952521	+	0.304473i	$0.901520\pi$
$968$		0			0
$969$	−3.06488	+	24.4867i	−0.0984580	+	0.786626i
$970$		0			0
$971$	22.0317			0.707031			0.353515	−	0.935429i	$-0.384986\pi$
$971$	22.0317			0.707031			0.353515	+	0.935429i	$0.384986\pi$
$972$		0			0
$973$	−111.595			−3.57756
$974$		0			0
$975$	−1.71356	+	13.6904i	−0.0548779	+	0.438445i
$976$		0			0
$977$	−23.8551	−	41.3182i	−0.763192	−	1.32189i	−0.941197	−	0.337858i	$-0.890298\pi$
$977$	−23.8551	−	41.3182i	−0.763192	−	1.32189i	0.178005	−	0.984030i	$-0.443036\pi$
$978$		0			0
$979$	33.9819	−	58.8584i	1.08607	−	1.88112i
$980$		0			0
$981$	18.3516	+	4.66707i	0.585921	+	0.149008i
$982$		0			0
$983$	−19.5800	+	33.9135i	−0.624504	+	1.08167i	0.364132	+	0.931347i	$0.381366\pi$
$983$	−19.5800	+	33.9135i	−0.624504	+	1.08167i	−0.988637	+	0.150326i	$0.951968\pi$
$984$		0			0
$985$	−17.4255	−	30.1818i	−0.555221	−	0.961672i
$986$		0			0
$987$	−31.1765	+	13.1475i	−0.992359	+	0.418489i
$988$		0			0
$989$	−1.58466			−0.0503892
$990$		0			0
$991$	−46.7781			−1.48596			−0.742978	−	0.669316i	$-0.766587\pi$
$991$	−46.7781			−1.48596			−0.742978	+	0.669316i	$0.766587\pi$
$992$		0			0
$993$	−7.09523	−	5.37277i	−0.225160	−	0.170500i
$994$		0			0
$995$	47.2984	+	81.9232i	1.49946	+	2.59714i
$996$		0			0
$997$	11.2351	−	19.4598i	0.355819	−	0.616297i	−0.631439	−	0.775426i	$-0.717535\pi$
$997$	11.2351	−	19.4598i	0.355819	−	0.616297i	0.987258	+	0.159129i	$0.0508686\pi$
$998$		0			0
$999$	20.4222	−	52.1033i	0.646129	−	1.64848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.g.313.6	✓	22
3.2	odd	2		2808.2.q.g.937.10		22
9.2	odd	6		8424.2.a.be.1.2		11
9.4	even	3	inner	936.2.q.g.625.6	yes	22
9.5	odd	6		2808.2.q.g.1873.10		22
9.7	even	3		8424.2.a.bf.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.g.313.6	✓	22	1.1	even	1	trivial
936.2.q.g.625.6	yes	22	9.4	even	3	inner
2808.2.q.g.937.10		22	3.2	odd	2
2808.2.q.g.1873.10		22	9.5	odd	6
8424.2.a.be.1.2		11	9.2	odd	6
8424.2.a.bf.1.10		11	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.215114 + 1.71864i) q^{3} +(-1.80041 - 3.11840i) q^{5} +(-2.42567 + 4.20138i) q^{7} +(-2.90745 - 0.739406i) q^{9} +(2.96999 - 5.14417i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(5.74669 - 2.42344i) q^{15} +3.14211 q^{17} +4.53444 q^{19} +(-6.69887 - 5.07263i) q^{21} +(2.40410 + 4.16402i) q^{23} +(-3.98293 + 6.89863i) q^{25} +(1.89621 - 4.83781i) q^{27} +(0.967295 - 1.67540i) q^{29} +(2.30944 + 4.00007i) q^{31} +(8.20210 + 6.21093i) q^{33} +17.4688 q^{35} +10.7700 q^{37} +(1.59594 - 0.673027i) q^{39} +(0.389576 + 0.674766i) q^{41} +(-0.164787 + 0.285420i) q^{43} +(2.92884 + 10.3978i) q^{45} +(2.01335 - 3.48722i) q^{47} +(-8.26774 - 14.3202i) q^{49} +(-0.675911 + 5.40016i) q^{51} -6.03880 q^{53} -21.3888 q^{55} +(-0.975419 + 7.79307i) q^{57} +(-1.75266 - 3.03569i) q^{59} +(2.77604 - 4.80825i) q^{61} +(10.1590 - 10.4218i) q^{63} +(-1.80041 + 3.11840i) q^{65} +(-2.91273 - 5.04500i) q^{67} +(-7.67361 + 3.23604i) q^{69} +3.18402 q^{71} +11.7545 q^{73} +(-10.9995 - 8.32921i) q^{75} +(14.4084 + 24.9561i) q^{77} +(1.97184 - 3.41532i) q^{79} +(7.90656 + 4.29958i) q^{81} +(-1.28229 + 2.22100i) q^{83} +(-5.65708 - 9.79835i) q^{85} +(2.67134 + 2.02283i) q^{87} +11.4418 q^{89} +4.85134 q^{91} +(-7.37147 + 3.10863i) q^{93} +(-8.16383 - 14.1402i) q^{95} +(2.58047 - 4.46950i) q^{97} +(-12.4387 + 12.7604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} - 4 q^{7} - 4 q^{9} + 5 q^{11} - 11 q^{13} + 5 q^{15} + 8 q^{17} + 10 q^{19} + 4 q^{21} + 9 q^{23} - 24 q^{25} - 12 q^{27} - 16 q^{29} - q^{31} + 9 q^{33} + 18 q^{37} + 3 q^{39} - 6 q^{41}+ \cdots - 109 q^{99}+O(q^{100}) \) 22 * q - 3 * q^5 - 4 * q^7 - 4 * q^9 + 5 * q^11 - 11 * q^13 + 5 * q^15 + 8 * q^17 + 10 * q^19 + 4 * q^21 + 9 * q^23 - 24 * q^25 - 12 * q^27 - 16 * q^29 - q^31 + 9 * q^33 + 18 * q^37 + 3 * q^39 - 6 * q^41 - 7 * q^43 - 21 * q^45 + 21 * q^47 - 27 * q^49 - 11 * q^51 + 32 * q^53 + 34 * q^55 + 2 * q^57 + 11 * q^59 - 2 * q^61 - 27 * q^63 - 3 * q^65 - 18 * q^67 + 7 * q^69 - 30 * q^71 + 18 * q^73 + 62 * q^75 - 9 * q^77 - 30 * q^79 + 4 * q^81 - 16 * q^83 - 32 * q^85 + 33 * q^87 + 26 * q^89 + 8 * q^91 + 20 * q^95 - 10 * q^97 - 109 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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