LMFDB - Embedded newform 324.2.l.a.179.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,2,Mod(35,324)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("324.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.4
Character	$\chi$	$=$	324.179
Dual form			324.2.l.a.143.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.960112 + 1.03836i) q^{2} +(-0.156370 - 1.99388i) q^{4} +(-2.23728 - 0.394492i) q^{5} +(0.842213 + 1.00371i) q^{7} +(2.22049 + 1.75198i) q^{8} +(2.55766 - 1.94434i) q^{10} +(0.469629 + 2.66340i) q^{11} +(-4.27030 + 1.55426i) q^{13} +(-1.85083 - 0.0891568i) q^{14} +(-3.95110 + 0.623564i) q^{16} +(-4.20783 - 2.42939i) q^{17} +(-5.44971 + 3.14639i) q^{19} +(-0.436727 + 4.52254i) q^{20} +(-3.21645 - 2.06952i) q^{22} +(1.94350 + 1.63079i) q^{23} +(0.151321 + 0.0550764i) q^{25} +(2.48609 - 5.92636i) q^{26} +(1.86958 - 1.83622i) q^{28} +(-1.68452 + 4.62818i) q^{29} +(1.87889 - 2.23918i) q^{31} +(3.14601 - 4.70134i) q^{32} +(6.56256 - 2.03674i) q^{34} +(-1.48831 - 2.57783i) q^{35} +(-3.86074 + 6.68701i) q^{37} +(1.96525 - 8.67963i) q^{38} +(-4.27671 - 4.79563i) q^{40} +(-1.35861 - 3.73275i) q^{41} +(8.37644 - 1.47699i) q^{43} +(5.23705 - 1.35286i) q^{44} +(-3.55932 + 0.452305i) q^{46} +(-9.17264 + 7.69676i) q^{47} +(0.917425 - 5.20298i) q^{49} +(-0.202474 + 0.104246i) q^{50} +(3.76675 + 8.27142i) q^{52} +3.84281i q^{53} -6.14402i q^{55} +(0.111646 + 3.70427i) q^{56} +(-3.18837 - 6.19270i) q^{58} +(1.99002 - 11.2860i) q^{59} +(0.0301227 - 0.0252759i) q^{61} +(0.521117 + 4.10082i) q^{62} +(1.86114 + 7.78050i) q^{64} +(10.1670 - 1.79271i) q^{65} +(4.08179 + 11.2146i) q^{67} +(-4.18593 + 8.76978i) q^{68} +(4.10565 + 0.929606i) q^{70} +(-1.22570 + 2.12297i) q^{71} +(3.09175 + 5.35507i) q^{73} +(-3.23675 - 10.4291i) q^{74} +(7.12569 + 10.3741i) q^{76} +(-2.27775 + 2.71452i) q^{77} +(2.06018 - 5.66029i) q^{79} +(9.08569 + 0.163591i) q^{80} +(5.18035 + 2.17314i) q^{82} +(8.97051 + 3.26500i) q^{83} +(8.45570 + 7.09518i) q^{85} +(-6.50867 + 10.1158i) q^{86} +(-3.62341 + 6.73682i) q^{88} +(5.99050 - 3.45862i) q^{89} +(-5.15653 - 2.97713i) q^{91} +(2.94769 - 4.13011i) q^{92} +(0.814780 - 16.9142i) q^{94} +(13.4337 - 4.88948i) q^{95} +(-1.52040 - 8.62260i) q^{97} +(4.52172 + 5.94806i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.960112	+	1.03836i	−0.678902	+	0.734229i
$2$	−0.960112	+	1.03836i	−0.678902	+	0.734229i
$3$		0			0
$3$		0			0
$4$	−0.156370	−	1.99388i	−0.0781849	−	0.996939i
$5$	−2.23728	−	0.394492i	−1.00054	−	0.176422i	−0.350696	−	0.936489i	$-0.614055\pi$
$5$	−2.23728	−	0.394492i	−1.00054	−	0.176422i	−0.649845	+	0.760067i	$0.725166\pi$
$6$		0			0
$7$	0.842213	+	1.00371i	0.318327	+	0.379367i	0.901352	−	0.433087i	$-0.142576\pi$
$7$	0.842213	+	1.00371i	0.318327	+	0.379367i	−0.583025	+	0.812454i	$0.698131\pi$
$8$	2.22049	+	1.75198i	0.785061	+	0.619418i
$9$		0			0
$10$	2.55766	−	1.94434i	0.808803	−	0.614853i
$11$	0.469629	+	2.66340i	0.141598	+	0.803044i	0.970036	+	0.242963i	$0.0781192\pi$
$11$	0.469629	+	2.66340i	0.141598	+	0.803044i	−0.828437	+	0.560082i	$0.810770\pi$
$12$		0			0
$13$	−4.27030	+	1.55426i	−1.18437	+	0.431075i	−0.857743	−	0.514079i	$-0.828134\pi$
$13$	−4.27030	+	1.55426i	−1.18437	+	0.431075i	−0.326625	+	0.945154i	$0.605912\pi$
$14$	−1.85083	−	0.0891568i	−0.494655	−	0.0238282i
$15$		0			0
$16$	−3.95110	+	0.623564i	−0.987774	+	0.155891i
$17$	−4.20783	−	2.42939i	−1.02055	−	0.589214i	−0.106286	−	0.994336i	$-0.533896\pi$
$17$	−4.20783	−	2.42939i	−1.02055	−	0.589214i	−0.914263	+	0.405122i	$0.867229\pi$
$18$		0			0
$19$	−5.44971	+	3.14639i	−1.25025	+	0.721832i	−0.971159	−	0.238433i	$-0.923366\pi$
$19$	−5.44971	+	3.14639i	−1.25025	+	0.721832i	−0.279090	+	0.960265i	$0.590033\pi$
$20$	−0.436727	+	4.52254i	−0.0976551	+	1.01127i
$21$		0			0
$22$	−3.21645	−	2.06952i	−0.685750	−	0.441223i
$23$	1.94350	+	1.63079i	0.405248	+	0.340043i	0.822518	−	0.568739i	$-0.192569\pi$
$23$	1.94350	+	1.63079i	0.405248	+	0.340043i	−0.417270	+	0.908782i	$0.637013\pi$
$24$		0			0
$25$	0.151321	+	0.0550764i	0.0302642	+	0.0110153i
$26$	2.48609	−	5.92636i	0.487562	−	1.16226i
$27$		0			0
$28$	1.86958	−	1.83622i	0.353317	−	0.347013i
$29$	−1.68452	+	4.62818i	−0.312807	+	0.859431i	0.679280	+	0.733879i	$0.262292\pi$
$29$	−1.68452	+	4.62818i	−0.312807	+	0.859431i	−0.992087	+	0.125552i	$0.959930\pi$
$30$		0			0
$31$	1.87889	−	2.23918i	0.337459	−	0.402168i	−0.570452	−	0.821331i	$-0.693232\pi$
$31$	1.87889	−	2.23918i	0.337459	−	0.402168i	0.907911	+	0.419163i	$0.137676\pi$
$32$	3.14601	−	4.70134i	0.556142	−	0.831087i
$33$		0			0
$34$	6.56256	−	2.03674i	1.12547	−	0.349298i
$35$	−1.48831	−	2.57783i	−0.251570	−	0.435732i
$36$		0			0
$37$	−3.86074	+	6.68701i	−0.634703	+	1.09934i	0.351876	+	0.936047i	$0.385544\pi$
$37$	−3.86074	+	6.68701i	−0.634703	+	1.09934i	−0.986578	+	0.163290i	$0.947789\pi$
$38$	1.96525	−	8.67963i	0.318806	−	1.40802i
$39$		0			0
$40$	−4.27671	−	4.79563i	−0.676207	−	0.758255i
$41$	−1.35861	−	3.73275i	−0.212179	−	0.582958i	0.787254	−	0.616629i	$-0.211502\pi$
$41$	−1.35861	−	3.73275i	−0.212179	−	0.582958i	−0.999433	+	0.0336714i	$0.989280\pi$
$42$		0			0
$43$	8.37644	−	1.47699i	1.27739	−	0.225239i	0.506521	−	0.862228i	$-0.330931\pi$
$43$	8.37644	−	1.47699i	1.27739	−	0.225239i	0.770873	+	0.636988i	$0.219820\pi$
$44$	5.23705	−	1.35286i	0.789515	−	0.203951i
$45$		0			0
$46$	−3.55932	+	0.452305i	−0.524793	+	0.0666887i
$47$	−9.17264	+	7.69676i	−1.33797	+	1.12269i	−0.355824	+	0.934553i	$0.615800\pi$
$47$	−9.17264	+	7.69676i	−1.33797	+	1.12269i	−0.982143	+	0.188135i	$0.939756\pi$
$48$		0			0
$49$	0.917425	−	5.20298i	0.131061	−	0.743282i
$50$	−0.202474	+	0.104246i	−0.0286342	+	0.0147426i
$51$		0			0
$52$	3.76675	+	8.27142i	0.522355	+	1.14704i
$53$			3.84281i			0.527851i	0.964543	+	0.263925i	$0.0850173\pi$
$53$			3.84281i			0.527851i	−0.964543	+	0.263925i	$0.914983\pi$
$54$		0			0
$55$		−	6.14402i		−	0.828460i
$56$	0.111646	+	3.70427i	0.0149193	+	0.495004i
$57$		0			0
$58$	−3.18837	−	6.19270i	−0.418654	−	0.813142i
$59$	1.99002	−	11.2860i	0.259079	−	1.46931i	−0.526303	−	0.850297i	$-0.676422\pi$
$59$	1.99002	−	11.2860i	0.259079	−	1.46931i	0.785382	−	0.619011i	$-0.212466\pi$
$60$		0			0
$61$	0.0301227	−	0.0252759i	0.00385681	−	0.00323625i	−0.640857	−	0.767660i	$-0.721421\pi$
$61$	0.0301227	−	0.0252759i	0.00385681	−	0.00323625i	0.644714	+	0.764424i	$0.276976\pi$
$62$	0.521117	+	4.10082i	0.0661820	+	0.520805i
$63$		0			0
$64$	1.86114	+	7.78050i	0.232643	+	0.972562i
$65$	10.1670	−	1.79271i	1.26106	−	0.222359i
$66$		0			0
$67$	4.08179	+	11.2146i	0.498670	+	1.37008i	0.892561	+	0.450927i	$0.148907\pi$
$67$	4.08179	+	11.2146i	0.498670	+	1.37008i	−0.393891	+	0.919157i	$0.628871\pi$
$68$	−4.18593	+	8.76978i	−0.507619	+	1.06349i
$69$		0			0
$70$	4.10565	+	0.929606i	0.490719	+	0.111109i
$71$	−1.22570	+	2.12297i	−0.145463	+	0.251950i	−0.929546	−	0.368707i	$-0.879801\pi$
$71$	−1.22570	+	2.12297i	−0.145463	+	0.251950i	0.784082	+	0.620657i	$0.213134\pi$
$72$		0			0
$73$	3.09175	+	5.35507i	0.361862	+	0.626764i	0.988267	−	0.152734i	$-0.0488077\pi$
$73$	3.09175	+	5.35507i	0.361862	+	0.626764i	−0.626405	+	0.779498i	$0.715474\pi$
$74$	−3.23675	−	10.4291i	−0.376265	−	1.21236i
$75$		0			0
$76$	7.12569	+	10.3741i	0.817372	+	1.18999i
$77$	−2.27775	+	2.71452i	−0.259574	+	0.309348i
$78$		0			0
$79$	2.06018	−	5.66029i	0.231788	−	0.636833i	−0.768206	−	0.640203i	$-0.778850\pi$
$79$	2.06018	−	5.66029i	0.231788	−	0.636833i	0.999994	+	0.00336970i	$0.00107261\pi$
$80$	9.08569	+	0.163591i	1.01581	+	0.0182900i
$81$		0			0
$82$	5.18035	+	2.17314i	0.572074	+	0.239983i
$83$	8.97051	+	3.26500i	0.984641	+	0.358380i	0.783643	−	0.621211i	$-0.213359\pi$
$83$	8.97051	+	3.26500i	0.984641	+	0.358380i	0.200998	+	0.979592i	$0.435581\pi$
$84$		0			0
$85$	8.45570	+	7.09518i	0.917150	+	0.769580i
$86$	−6.50867	+	10.1158i	−0.701848	+	1.09082i
$87$		0			0
$88$	−3.62341	+	6.73682i	−0.386257	+	0.718148i
$89$	5.99050	−	3.45862i	0.634991	−	0.366613i	−0.147691	−	0.989034i	$-0.547184\pi$
$89$	5.99050	−	3.45862i	0.634991	−	0.366613i	0.782683	+	0.622421i	$0.213851\pi$
$90$		0			0
$91$	−5.15653	−	2.97713i	−0.540552	−	0.312088i
$92$	2.94769	−	4.13011i	0.307318	−	0.430593i
$93$		0			0
$94$	0.814780	−	16.9142i	0.0840382	−	1.74457i
$95$	13.4337	−	4.88948i	1.37827	−	0.501650i
$96$		0			0
$97$	−1.52040	−	8.62260i	−0.154373	−	0.875493i	−0.959357	−	0.282196i	$-0.908937\pi$
$97$	−1.52040	−	8.62260i	−0.154373	−	0.875493i	0.804984	−	0.593297i	$-0.202174\pi$
$98$	4.52172	+	5.94806i	0.456762	+	0.600844i
$99$		0			0
$100$	0.0861535	−	0.310328i	0.00861535	−	0.0310328i
$101$	−1.41538	−	1.68678i	−0.140835	−	0.167841i	0.691016	−	0.722839i	$-0.257163\pi$
$101$	−1.41538	−	1.68678i	−0.140835	−	0.167841i	−0.831851	+	0.554998i	$0.812719\pi$
$102$		0			0
$103$	1.93720	+	0.341580i	0.190878	+	0.0336569i	0.268270	−	0.963344i	$-0.413548\pi$
$103$	1.93720	+	0.341580i	0.190878	+	0.0336569i	−0.0773920	+	0.997001i	$0.524659\pi$
$104$	−12.2052	−	4.03025i	−1.19682	−	0.395199i
$105$		0			0
$106$	−3.99021	−	3.68953i	−0.387563	−	0.358359i
$107$	−4.06709			−0.393180			−0.196590	−	0.980486i	$-0.562987\pi$
$107$	−4.06709			−0.393180			−0.196590	+	0.980486i	$0.562987\pi$
$108$		0			0
$109$	−1.81021			−0.173387			−0.0866934	−	0.996235i	$-0.527630\pi$
$109$	−1.81021			−0.173387			−0.0866934	+	0.996235i	$0.527630\pi$
$110$	6.37969	+	5.89895i	0.608279	+	0.562443i
$111$		0			0
$112$	−3.95354	−	3.44058i	−0.373575	−	0.325105i
$113$	−3.45706	−	0.609573i	−0.325213	−	0.0573438i	0.00865836	−	0.999963i	$-0.497244\pi$
$113$	−3.45706	−	0.609573i	−0.325213	−	0.0573438i	−0.333871	+	0.942619i	$0.608355\pi$
$114$		0			0
$115$	−3.70481	−	4.41522i	−0.345475	−	0.411722i
$116$	9.49143	+	2.63502i	0.881257	+	0.244655i
$117$		0			0
$118$	9.80822	+	12.9021i	0.902920	+	1.18774i
$119$	−1.10548	−	6.26951i	−0.101340	−	0.574725i
$120$		0			0
$121$	3.46349	−	1.26061i	0.314862	−	0.114601i
$122$	−0.00267571	+	0.0555458i	−0.000242248	+	0.00502888i
$123$		0			0
$124$	−4.75845	−	3.39614i	−0.427321	−	0.304983i
$125$	9.52032	+	5.49656i	0.851523	+	0.491627i
$126$		0			0
$127$	−9.71588	+	5.60947i	−0.862145	+	0.497760i	−0.864730	−	0.502237i	$-0.832511\pi$
$127$	−9.71588	+	5.60947i	−0.862145	+	0.497760i	0.00258477	+	0.999997i	$0.499177\pi$
$128$	−9.86584	−	5.53762i	−0.872025	−	0.489461i
$129$		0			0
$130$	−7.89997	+	12.2782i	−0.692873	+	1.07687i
$131$	−3.93034	−	3.29795i	−0.343396	−	0.288143i	0.454736	−	0.890626i	$-0.349734\pi$
$131$	−3.93034	−	3.29795i	−0.343396	−	0.288143i	−0.798132	+	0.602483i	$0.794178\pi$
$132$		0			0
$133$	−7.74788	−	2.82000i	−0.671827	−	0.244525i
$134$	−15.5638	−	6.52894i	−1.34450	−	0.564015i
$135$		0			0
$136$	−5.08720	−	12.7665i	−0.436224	−	1.09472i
$137$	0.618497	−	1.69931i	0.0528418	−	0.145182i	−0.910464	−	0.413589i	$-0.864275\pi$
$137$	0.618497	−	1.69931i	0.0528418	−	0.145182i	0.963306	+	0.268407i	$0.0864973\pi$
$138$		0			0
$139$	−8.35679	+	9.95924i	−0.708814	+	0.844732i	−0.993493	−	0.113891i	$-0.963668\pi$
$139$	−8.35679	+	9.95924i	−0.708814	+	0.844732i	0.284679	+	0.958623i	$0.408113\pi$
$140$	−4.90714	+	3.37060i	−0.414729	+	0.284868i
$141$		0			0
$142$	−1.02759	−	3.31100i	−0.0862336	−	0.277853i
$143$	−6.14507	−	10.6436i	−0.513877	−	0.890061i
$144$		0			0
$145$	5.59452	−	9.68999i	0.464599	−	0.804710i
$146$	−8.52891	−	1.93113i	−0.705858	−	0.159821i
$147$		0			0
$148$	13.9368	+	6.65221i	1.14560	+	0.546808i
$149$	0.880225	+	2.41840i	0.0721108	+	0.198123i	0.970512	−	0.241053i	$-0.0774928\pi$
$149$	0.880225	+	2.41840i	0.0721108	+	0.198123i	−0.898401	+	0.439176i	$0.855271\pi$
$150$		0			0
$151$	−5.17039	+	0.911679i	−0.420760	+	0.0741914i	−0.380020	−	0.924978i	$-0.624083\pi$
$151$	−5.17039	+	0.911679i	−0.420760	+	0.0741914i	−0.0407405	+	0.999170i	$0.512972\pi$
$152$	−17.6134	−	2.56125i	−1.42864	−	0.207744i
$153$		0			0
$154$	−0.631743	−	4.97136i	−0.0509073	−	0.400604i
$155$	−5.08694	+	4.26845i	−0.408593	+	0.342850i
$156$		0			0
$157$	3.62805	−	20.5757i	0.289550	−	1.64212i	−0.399015	−	0.916945i	$-0.630648\pi$
$157$	3.62805	−	20.5757i	0.289550	−	1.64212i	0.688565	−	0.725175i	$-0.258241\pi$
$158$	3.89940	+	7.57372i	0.310220	+	0.602533i
$159$		0			0
$160$	−8.89315	+	9.27712i	−0.703065	+	0.733421i
$161$			3.32418i			0.261982i
$162$		0			0
$163$		−	3.28308i		−	0.257151i	−0.991700	−	0.128575i	$-0.958960\pi$
$163$		−	3.28308i		−	0.257151i	0.991700	−	0.128575i	$-0.0410404\pi$
$164$	−7.23021	+	3.29259i	−0.564584	+	0.257108i
$165$		0			0
$166$	−12.0029	+	6.17983i	−0.931608	+	0.479647i
$167$	−3.32534	+	18.8590i	−0.257323	+	1.45935i	0.532717	+	0.846294i	$0.321171\pi$
$167$	−3.32534	+	18.8590i	−0.257323	+	1.45935i	−0.790039	+	0.613056i	$0.789940\pi$
$168$		0			0
$169$	5.86116	−	4.91809i	0.450858	−	0.378315i
$170$	−15.4857	+	1.96787i	−1.18770	+	0.150929i
$171$		0			0
$172$	−4.25476	−	16.4706i	−0.324423	−	1.25587i
$173$	8.60928	−	1.51805i	0.654551	−	0.115415i	0.163497	−	0.986544i	$-0.447723\pi$
$173$	8.60928	−	1.51805i	0.654551	−	0.115415i	0.491055	+	0.871129i	$0.336612\pi$
$174$		0			0
$175$	0.0721639	+	0.198269i	0.00545508	+	0.0149877i
$176$	−3.51635	−	10.2305i	−0.265055	−	0.771153i
$177$		0			0
$178$	−2.16027	+	9.54093i	−0.161919	+	0.715123i
$179$	3.03371	−	5.25454i	0.226750	−	0.392743i	−0.730093	−	0.683348i	$-0.760523\pi$
$179$	3.03371	−	5.25454i	0.226750	−	0.392743i	0.956843	+	0.290605i	$0.0938565\pi$
$180$		0			0
$181$	−8.01419	−	13.8810i	−0.595690	−	1.03177i	−0.993449	−	0.114276i	$-0.963545\pi$
$181$	−8.01419	−	13.8810i	−0.595690	−	1.03177i	0.397759	−	0.917490i	$-0.369788\pi$
$182$	8.04217	−	2.49595i	0.596125	−	0.185012i
$183$		0			0
$184$	1.45841	+	7.02612i	0.107515	+	0.517972i
$185$	11.2755	−	13.4377i	0.828993	−	0.987956i
$186$		0			0
$187$	4.49432	−	12.3480i	0.328657	−	0.902977i
$188$	16.7807	+	17.0856i	1.22386	+	1.24609i
$189$		0			0
$190$	−7.82087	+	18.6435i	−0.567385	+	1.35254i
$191$	10.9918	+	4.00067i	0.795335	+	0.289478i	0.707552	−	0.706661i	$-0.249799\pi$
$191$	10.9918	+	4.00067i	0.795335	+	0.289478i	0.0877833	+	0.996140i	$0.472022\pi$
$192$		0			0
$193$	13.4605	+	11.2947i	0.968907	+	0.813010i	0.982379	−	0.186900i	$-0.0598439\pi$
$193$	13.4605	+	11.2947i	0.968907	+	0.813010i	−0.0134718	+	0.999909i	$0.504288\pi$
$194$	10.4131	+	6.69995i	0.747616	+	0.481028i
$195$		0			0
$196$	−10.5176	−	1.01565i	−0.751254	−	0.0725461i
$197$	−19.9607	+	11.5243i	−1.42214	+	0.821074i	−0.996482	−	0.0838089i	$-0.973291\pi$
$197$	−19.9607	+	11.5243i	−1.42214	+	0.821074i	−0.425660	+	0.904883i	$0.639958\pi$
$198$		0			0
$199$	−2.70763	−	1.56325i	−0.191939	−	0.110816i	0.400951	−	0.916099i	$-0.368680\pi$
$199$	−2.70763	−	1.56325i	−0.191939	−	0.110816i	−0.592890	+	0.805284i	$0.702013\pi$
$200$	0.239514	+	0.387408i	0.0169362	+	0.0273939i
$201$		0			0
$202$	3.11040	+	0.149832i	0.218847	+	0.0105421i
$203$	−6.06408	+	2.20714i	−0.425615	+	0.154911i
$204$		0			0
$205$	1.56705	+	8.88716i	0.109447	+	0.620706i
$206$	−2.21461	+	1.68355i	−0.154299	+	0.117298i
$207$		0			0
$208$	15.9032	−	8.80385i	1.10269	−	0.610437i
$209$	−10.9394	−	13.0371i	−0.756696	−	0.901795i
$210$		0			0
$211$	−12.6580	−	2.23195i	−0.871414	−	0.153654i	−0.279978	−	0.960006i	$-0.590327\pi$
$211$	−12.6580	−	2.23195i	−0.871414	−	0.153654i	−0.591435	+	0.806353i	$0.701438\pi$
$212$	7.66210	−	0.600900i	0.526235	−	0.0412700i
$213$		0			0
$214$	3.90486	−	4.22309i	0.266931	−	0.288685i
$215$	−19.3231			−1.31782
$216$		0			0
$217$	3.82992			0.259992
$218$	1.73801	−	1.87965i	0.117713	−	0.127306i
$219$		0			0
$220$	−12.2504	+	0.960739i	−0.825924	+	0.0647730i
$221$	21.7446	+	3.83416i	1.46270	+	0.257914i
$222$		0			0
$223$	6.64592	+	7.92030i	0.445044	+	0.530382i	0.941200	−	0.337851i	$-0.109700\pi$
$223$	6.64592	+	7.92030i	0.445044	+	0.530382i	−0.496156	+	0.868233i	$0.665256\pi$
$224$	7.36840	−	0.801844i	0.492322	−	0.0535754i
$225$		0			0
$226$	3.95212	−	3.00440i	0.262891	−	0.199850i
$227$	0.0166779	+	0.0945849i	0.00110695	+	0.00627782i	0.985356	−	0.170508i	$-0.0545410\pi$
$227$	0.0166779	+	0.0945849i	0.00110695	+	0.00627782i	−0.984249	+	0.176786i	$0.943430\pi$
$228$		0			0
$229$	−25.2522	+	9.19106i	−1.66871	+	0.607363i	−0.991696	−	0.128603i	$-0.958951\pi$
$229$	−25.2522	+	9.19106i	−1.66871	+	0.607363i	−0.677019	+	0.735966i	$0.736728\pi$
$230$	8.14161	+	0.392192i	0.536842	+	0.0258604i
$231$		0			0
$232$	−11.8489	+	7.32558i	−0.777920	+	0.480948i
$233$	−6.26494	−	3.61706i	−0.410430	−	0.236962i	0.280545	−	0.959841i	$-0.409485\pi$
$233$	−6.26494	−	3.61706i	−0.410430	−	0.236962i	−0.690974	+	0.722879i	$0.742818\pi$
$234$		0			0
$235$	23.5581	−	13.6013i	1.53676	−	0.887248i
$236$	−22.8140	−	2.20307i	−1.48507	−	0.143408i
$237$		0			0
$238$	7.57138	+	4.87154i	0.490779	+	0.315775i
$239$	9.77252	+	8.20012i	0.632132	+	0.530421i	0.901591	−	0.432590i	$-0.142400\pi$
$239$	9.77252	+	8.20012i	0.632132	+	0.530421i	−0.269459	+	0.963012i	$0.586845\pi$
$240$		0			0
$241$	7.11615	+	2.59007i	0.458391	+	0.166841i	0.560886	−	0.827893i	$-0.310460\pi$
$241$	7.11615	+	2.59007i	0.458391	+	0.166841i	−0.102495	+	0.994733i	$0.532683\pi$
$242$	−2.01638	+	4.80666i	−0.129618	+	0.308984i
$243$		0			0
$244$	−0.0551074	−	0.0561085i	−0.00352789	−	0.00359198i
$245$	−4.10507	+	11.2786i	−0.262263	+	0.720562i
$246$		0			0
$247$	18.3816	−	21.9063i	1.16959	−	1.39387i
$248$	8.09505	−	1.68029i	0.514036	−	0.106698i
$249$		0			0
$250$	−14.8480	+	4.60818i	−0.939068	+	0.291447i
$251$	5.95007	+	10.3058i	0.375565	+	0.650498i	0.990411	−	0.138149i	$-0.0441153\pi$
$251$	5.95007	+	10.3058i	0.375565	+	0.650498i	−0.614846	+	0.788647i	$0.710782\pi$
$252$		0			0
$253$	−3.43072	+	5.94217i	−0.215687	+	0.373581i
$254$	3.50371	−	15.4743i	0.219842	−	0.970942i
$255$		0			0
$256$	15.2223	−	4.92753i	0.951396	−	0.307970i
$257$	1.86711	+	5.12985i	0.116467	+	0.319991i	0.984205	−	0.177031i	$-0.0566492\pi$
$257$	1.86711	+	5.12985i	0.116467	+	0.319991i	−0.867738	+	0.497022i	$0.834427\pi$
$258$		0			0
$259$	−9.96339	+	1.75681i	−0.619095	+	0.109163i
$260$	−5.16426	−	19.9914i	−0.320274	−	1.23981i
$261$		0			0
$262$	7.19802	−	0.914698i	0.444695	−	0.0565102i
$263$	15.6031	−	13.0925i	0.962128	−	0.807321i	−0.0191703	−	0.999816i	$-0.506102\pi$
$263$	15.6031	−	13.0925i	0.962128	−	0.807321i	0.981298	+	0.192495i	$0.0616580\pi$
$264$		0			0
$265$	1.51596	−	8.59743i	0.0931247	−	0.528136i
$266$	10.3670	−	5.33755i	0.635642	−	0.327266i
$267$		0			0
$268$	21.7223	−	9.89221i	1.32690	−	0.604263i
$269$		−	9.12305i		−	0.556242i	−0.960546	−	0.278121i	$-0.910288\pi$
$269$		−	9.12305i		−	0.556242i	0.960546	−	0.278121i	$-0.0897116\pi$
$270$		0			0
$271$			21.2629i			1.29163i	0.763495	+	0.645813i	$0.223482\pi$
$271$			21.2629i			1.29163i	−0.763495	+	0.645813i	$0.776518\pi$
$272$	18.1404	+	6.97491i	1.09992	+	0.422916i
$273$		0			0
$274$	1.17066	+	2.27374i	0.0707222	+	0.137362i
$275$	−0.0756255	+	0.428894i	−0.00456039	+	0.0258633i
$276$		0			0
$277$	−19.5527	+	16.4067i	−1.17481	+	0.985783i	−0.174811	+	0.984602i	$0.555931\pi$
$277$	−19.5527	+	16.4067i	−1.17481	+	0.985783i	−0.999999	+	0.00118043i	$0.999624\pi$
$278$	−2.31779	−	18.2393i	−0.139012	−	1.09392i
$279$		0			0
$280$	1.21152	−	8.33152i	0.0724023	−	0.497903i
$281$	−12.1392	+	2.14046i	−0.724162	+	0.127689i	−0.523566	−	0.851985i	$-0.675399\pi$
$281$	−12.1392	+	2.14046i	−0.724162	+	0.127689i	−0.200595	+	0.979674i	$0.564288\pi$
$282$		0			0
$283$	5.71416	+	15.6995i	0.339672	+	0.933240i	0.985488	+	0.169747i	$0.0542951\pi$
$283$	5.71416	+	15.6995i	0.339672	+	0.933240i	−0.645816	+	0.763493i	$0.723483\pi$
$284$	4.42460	+	2.11192i	0.262552	+	0.125319i
$285$		0			0
$286$	16.9518	+	3.83825i	1.00238	+	0.226960i
$287$	2.60236	−	4.50743i	0.153613	−	0.266065i
$288$		0			0
$289$	3.30388	+	5.72249i	0.194346	+	0.336617i
$290$	4.69030	+	15.1126i	0.275424	+	0.887441i
$291$		0			0
$292$	10.1939	−	7.00195i	0.596553	−	0.409758i
$293$	−8.56800	+	10.2109i	−0.500548	+	0.596530i	−0.955867	−	0.293798i	$-0.905081\pi$
$293$	−8.56800	+	10.2109i	−0.500548	+	0.596530i	0.455319	+	0.890328i	$0.349525\pi$
$294$		0			0
$295$	−8.90446	+	24.4648i	−0.518437	+	1.42440i
$296$	−20.2882	+	8.08448i	−1.17923	+	0.469901i
$297$		0			0
$298$	−3.35627	−	1.40794i	−0.194424	−	0.0815601i
$299$	−10.8340	−	3.94325i	−0.626546	−	0.228044i
$300$		0			0
$301$	8.53722	+	7.16358i	0.492077	+	0.412902i
$302$	4.01750	−	6.24402i	0.231181	−	0.359303i
$303$		0			0
$304$	19.5703	−	15.8299i	1.12244	−	0.907909i
$305$	−0.0773639	+	0.0446661i	−0.00442984	+	0.00255757i
$306$		0			0
$307$	18.8505	+	10.8833i	1.07585	+	0.621144i	0.929775	−	0.368129i	$-0.120002\pi$
$307$	18.8505	+	10.8833i	1.07585	+	0.621144i	0.146078	+	0.989273i	$0.453335\pi$
$308$	5.76859	+	4.11709i	0.328696	+	0.234593i
$309$		0			0
$310$	0.451859	−	9.38025i	0.0256639	−	0.532763i
$311$	−13.4052	+	4.87909i	−0.760139	+	0.276668i	−0.692866	−	0.721067i	$-0.743652\pi$
$311$	−13.4052	+	4.87909i	−0.760139	+	0.276668i	−0.0672731	+	0.997735i	$0.521430\pi$
$312$		0			0
$313$	3.69449	+	20.9525i	0.208825	+	1.18430i	0.891307	+	0.453401i	$0.149789\pi$
$313$	3.69449	+	20.9525i	0.208825	+	1.18430i	−0.682482	+	0.730902i	$0.739099\pi$
$314$	17.8816	+	23.5222i	1.00912	+	1.32743i
$315$		0			0
$316$	−11.6081	−	3.22265i	−0.653006	−	0.181288i
$317$	4.33285	+	5.16369i	0.243357	+	0.290022i	0.873873	−	0.486155i	$-0.161601\pi$
$317$	4.33285	+	5.16369i	0.243357	+	0.290022i	−0.630516	+	0.776177i	$0.717156\pi$
$318$		0			0
$319$	−13.1178	−	2.31302i	−0.734454	−	0.129504i
$320$	−1.09455	−	18.1413i	−0.0611870	−	1.01413i
$321$		0			0
$322$	−3.45169	−	3.19159i	−0.192355	−	0.177860i
$323$	30.5753			1.70125
$324$		0			0
$325$	−0.731790			−0.0405924
$326$	3.40901	+	3.15213i	0.188808	+	0.174580i
$327$		0			0
$328$	3.52292	−	10.6688i	0.194521	−	0.589085i
$329$	−15.4506	−	2.72437i	−0.851822	−	0.150199i
$330$		0			0
$331$	−15.5537	−	18.5362i	−0.854910	−	1.01884i	−0.999569	−	0.0293609i	$-0.990653\pi$
$331$	−15.5537	−	18.5362i	−0.854910	−	1.01884i	0.144658	−	0.989482i	$-0.453792\pi$
$332$	5.10729	−	18.3966i	0.280299	−	1.00965i
$333$		0			0
$334$	−16.3896	−	21.5596i	−0.896800	−	1.17969i
$335$	−4.70801	−	26.7004i	−0.257226	−	1.45880i
$336$		0			0
$337$	−20.5343	+	7.47387i	−1.11857	+	0.407127i	−0.834131	−	0.551566i	$-0.814031\pi$
$337$	−20.5343	+	7.47387i	−1.11857	+	0.407127i	−0.284442	+	0.958693i	$0.591808\pi$
$338$	−0.520630	+	10.8079i	−0.0283185	+	0.587872i
$339$		0			0
$340$	12.8247	−	17.9691i	0.695517	−	0.974512i
$341$	6.84620	+	3.95266i	0.370743	+	0.214048i
$342$		0			0
$343$	13.9379	−	8.04707i	0.752577	−	0.434501i
$344$	21.1874	+	11.3957i	1.14235	+	0.614415i
$345$		0			0
$346$	−6.68960	+	10.3970i	−0.359635	+	0.558946i
$347$	−9.92193	−	8.32549i	−0.532637	−	0.446936i	0.336374	−	0.941729i	$-0.390799\pi$
$347$	−9.92193	−	8.32549i	−0.532637	−	0.446936i	−0.869011	+	0.494793i	$0.835244\pi$
$348$		0			0
$349$	3.63433	+	1.32279i	0.194541	+	0.0708071i	0.437453	−	0.899241i	$-0.355881\pi$
$349$	3.63433	+	1.32279i	0.194541	+	0.0708071i	−0.242912	+	0.970048i	$0.578103\pi$
$350$	−0.275159	−	0.115428i	−0.0147079	−	0.00616990i
$351$		0			0
$352$	13.9990	+	6.17120i	0.746149	+	0.328926i
$353$	1.04065	−	2.85915i	0.0553880	−	0.152177i	−0.908913	−	0.416986i	$-0.863086\pi$
$353$	1.04065	−	2.85915i	0.0553880	−	0.152177i	0.964301	+	0.264808i	$0.0853087\pi$
$354$		0			0
$355$	3.57972	−	4.26614i	0.189992	−	0.226423i
$356$	−7.83279	−	11.4035i	−0.415137	−	0.604384i
$357$		0			0
$358$	2.54339	+	8.19503i	0.134422	+	0.433121i
$359$	8.27544	+	14.3335i	0.436761	+	0.756492i	0.997438	−	0.0715425i	$-0.0227922\pi$
$359$	8.27544	+	14.3335i	0.436761	+	0.756492i	−0.560676	+	0.828035i	$0.689459\pi$
$360$		0			0
$361$	10.2995	−	17.8393i	0.542082	−	0.938913i
$362$	22.1079	+	5.00571i	1.16197	+	0.263094i
$363$		0			0
$364$	−5.12970	+	10.7470i	−0.268869	+	0.563297i
$365$	−4.80457	−	13.2005i	−0.251483	−	0.690944i
$366$		0			0
$367$	2.17336	−	0.383223i	0.113449	−	0.0200041i	−0.116636	−	0.993175i	$-0.537211\pi$
$367$	2.17336	−	0.383223i	0.113449	−	0.0200041i	0.230084	+	0.973171i	$0.426100\pi$
$368$	−8.69586	−	5.23151i	−0.453303	−	0.272711i
$369$		0			0
$370$	3.12731	+	24.6097i	0.162581	+	1.27940i
$371$	−3.85707	+	3.23647i	−0.200249	+	0.168029i
$372$		0			0
$373$	−1.82112	+	10.3281i	−0.0942938	+	0.534767i	0.900668	+	0.434509i	$0.143078\pi$
$373$	−1.82112	+	10.3281i	−0.0942938	+	0.534767i	−0.994961	+	0.100258i	$0.968033\pi$
$374$	8.50662	+	16.5222i	0.439867	+	0.854342i
$375$		0			0
$376$	−33.8523	+	1.02030i	−1.74580	+	0.0526181i
$377$		−	22.3819i		−	1.15273i
$378$		0			0
$379$			3.08694i			0.158565i	0.996852	+	0.0792826i	$0.0252630\pi$
$379$			3.08694i			0.158565i	−0.996852	+	0.0792826i	$0.974737\pi$
$380$	−11.8497	−	26.0207i	−0.607874	−	1.33483i
$381$		0			0
$382$	−14.7074	+	7.57227i	−0.752498	+	0.387431i
$383$	2.78976	−	15.8215i	0.142550	−	0.808442i	−0.826752	−	0.562567i	$-0.809814\pi$
$383$	2.78976	−	15.8215i	0.142550	−	0.808442i	0.969302	−	0.245875i	$-0.0790752\pi$
$384$		0			0
$385$	6.16682	−	5.17458i	0.314290	−	0.263721i
$386$	−24.6515	+	3.13262i	−1.25473	+	0.159446i
$387$		0			0
$388$	−16.9547	+	4.37980i	−0.860743	+	0.222351i
$389$	−17.3835	+	3.06519i	−0.881381	+	0.155411i	−0.595982	−	0.802998i	$-0.703237\pi$
$389$	−17.3835	+	3.06519i	−0.881381	+	0.155411i	−0.285399	+	0.958409i	$0.592126\pi$
$390$		0			0
$391$	−4.21609	−	11.5836i	−0.213217	−	0.585808i
$392$	11.1526	−	9.94584i	0.563293	−	0.502341i
$393$		0			0
$394$	7.19816	−	31.7910i	0.362638	−	1.60161i
$395$	−6.84213	+	11.8509i	−0.344265	+	0.596285i
$396$		0			0
$397$	6.73828	+	11.6710i	0.338185	+	0.585753i	0.984091	−	0.177663i	$-0.0568538\pi$
$397$	6.73828	+	11.6710i	0.338185	+	0.585753i	−0.645907	+	0.763416i	$0.723520\pi$
$398$	4.22284	−	1.31059i	0.211672	−	0.0656939i
$399$		0			0
$400$	−0.632228	−	0.123254i	−0.0316114	−	0.00616268i
$401$	−4.34436	+	5.17741i	−0.216947	+	0.258547i	−0.863531	−	0.504295i	$-0.831752\pi$
$401$	−4.34436	+	5.17741i	−0.216947	+	0.258547i	0.646584	+	0.762842i	$0.276197\pi$
$402$		0			0
$403$	−4.54317	+	12.4823i	−0.226311	+	0.621785i
$404$	−3.14191	+	3.08585i	−0.156316	+	0.153527i
$405$		0			0
$406$	3.53039	−	8.41578i	0.175210	−	0.417668i
$407$	−19.6233	−	7.14229i	−0.972689	−	0.354030i
$408$		0			0
$409$	14.4348	+	12.1122i	0.713756	+	0.598912i	0.925650	−	0.378381i	$-0.123519\pi$
$409$	14.4348	+	12.1122i	0.713756	+	0.598912i	−0.211895	+	0.977293i	$0.567963\pi$
$410$	−10.7326	−	6.90552i	−0.530045	−	0.341039i
$411$		0			0
$412$	0.378150	−	3.91595i	0.0186301	−	0.192925i
$413$	13.0039	−	7.50779i	0.639879	−	0.369434i
$414$		0			0
$415$	−18.7815	−	10.8435i	−0.921947	−	0.532287i
$416$	−6.12731	+	24.9659i	−0.300416	+	1.22405i
$417$		0			0
$418$	24.0402	+	1.15805i	1.17585	+	0.0566420i
$419$	−17.9428	+	6.53066i	−0.876565	+	0.319043i	−0.740823	−	0.671701i	$-0.765564\pi$
$419$	−17.9428	+	6.53066i	−0.876565	+	0.319043i	−0.135742	+	0.990744i	$0.543342\pi$
$420$		0			0
$421$	−3.91452	−	22.2004i	−0.190782	−	1.08198i	−0.918298	−	0.395889i	$-0.870436\pi$
$421$	−3.91452	−	22.2004i	−0.190782	−	1.08198i	0.727516	−	0.686091i	$-0.240675\pi$
$422$	14.4707	−	11.0006i	0.704421	−	0.535502i
$423$		0			0
$424$	−6.73252	+	8.53292i	−0.326960	+	0.414395i
$425$	−0.502931	−	0.599370i	−0.0243957	−	0.0290737i
$426$		0			0
$427$	0.0507394	+	0.00894673i	0.00245545	+	0.000432962i
$428$	0.635970	+	8.10928i	0.0307408	+	0.391977i
$429$		0			0
$430$	18.5523	−	20.0642i	0.894672	−	0.967584i
$431$	10.8059			0.520500			0.260250	−	0.965541i	$-0.416195\pi$
$431$	10.8059			0.520500			0.260250	+	0.965541i	$0.416195\pi$
$432$		0			0
$433$	−37.5914			−1.80653			−0.903264	−	0.429084i	$-0.858836\pi$
$433$	−37.5914			−1.80653			−0.903264	+	0.429084i	$0.858836\pi$
$434$	−3.67715	+	3.97682i	−0.176509	+	0.190893i
$435$		0			0
$436$	0.283062	+	3.60934i	0.0135562	+	0.172856i
$437$	−15.7226	−	2.77232i	−0.752114	−	0.132618i
$438$		0			0
$439$	20.5267	+	24.4627i	0.979685	+	1.16754i	0.985862	+	0.167562i	$0.0535893\pi$
$439$	20.5267	+	24.4627i	0.979685	+	1.16754i	−0.00617703	+	0.999981i	$0.501966\pi$
$440$	10.7642	−	13.6427i	0.513163	−	0.650392i
$441$		0			0
$442$	−24.8585	+	18.8974i	−1.18240	+	0.898859i
$443$	6.52594	+	37.0104i	0.310057	+	1.75842i	0.598691	+	0.800980i	$0.295688\pi$
$443$	6.52594	+	37.0104i	0.310057	+	1.75842i	−0.288634	+	0.957439i	$0.593201\pi$
$444$		0			0
$445$	−14.7668	+	5.37468i	−0.700013	+	0.254784i
$446$	−14.6049	−	0.703538i	−0.691563	−	0.0333135i
$447$		0			0
$448$	−6.24189	+	8.42089i	−0.294902	+	0.397850i
$449$	6.99926	+	4.04102i	0.330315	+	0.190708i	0.655981	−	0.754777i	$-0.272255\pi$
$449$	6.99926	+	4.04102i	0.330315	+	0.190708i	−0.325666	+	0.945485i	$0.605588\pi$
$450$		0			0
$451$	9.30376	−	5.37153i	0.438097	−	0.252935i
$452$	−0.674834	+	6.98827i	−0.0317415	+	0.328701i
$453$		0			0
$454$	−0.114226	−	0.0734946i	−0.00536087	−	0.00344927i
$455$	10.3621	+	8.69487i	0.485785	+	0.407622i
$456$		0			0
$457$	2.32495	+	0.846211i	0.108756	+	0.0395841i	0.395825	−	0.918326i	$-0.370459\pi$
$457$	2.32495	+	0.846211i	0.108756	+	0.0395841i	−0.287069	+	0.957910i	$0.592681\pi$
$458$	14.7014	−	35.0453i	0.686950	−	1.63756i
$459$		0			0
$460$	−8.22409	+	8.07735i	−0.383450	+	0.376608i
$461$	3.09034	−	8.49063i	0.143931	−	0.395448i	−0.846690	−	0.532087i	$-0.821408\pi$
$461$	3.09034	−	8.49063i	0.143931	−	0.395448i	0.990621	+	0.136639i	$0.0436301\pi$
$462$		0			0
$463$	0.896443	−	1.06834i	0.0416612	−	0.0496499i	−0.744811	−	0.667275i	$-0.767461\pi$
$463$	0.896443	−	1.06834i	0.0416612	−	0.0496499i	0.786473	+	0.617625i	$0.211905\pi$
$464$	3.76973	−	19.3368i	0.175005	−	0.897688i
$465$		0			0
$466$	9.77085	−	3.03246i	0.452626	−	0.140476i
$467$	10.5492	+	18.2717i	0.488158	+	0.845515i	0.999907	−	0.0136203i	$-0.00433561\pi$
$467$	10.5492	+	18.2717i	0.488158	+	0.845515i	−0.511749	+	0.859135i	$0.671002\pi$
$468$		0			0
$469$	−7.81850	+	13.5420i	−0.361025	+	0.625313i
$470$	−8.49542	+	37.5204i	−0.391865	+	1.73069i
$471$		0			0
$472$	24.1916	−	21.5739i	1.11351	−	0.993019i
$473$	7.86763	+	21.6161i	0.361754	+	0.993911i
$474$		0			0
$475$	−0.997948	+	0.175965i	−0.0457890	+	0.00807383i
$476$	−12.3278	+	3.18456i	−0.565042	+	0.145964i
$477$		0			0
$478$	−17.8974	+	2.27433i	−0.818606	+	0.104025i
$479$	11.1877	−	9.38756i	0.511177	−	0.428928i	−0.350366	−	0.936613i	$-0.613943\pi$
$479$	11.1877	−	9.38756i	0.511177	−	0.428928i	0.861543	+	0.507684i	$0.169498\pi$
$480$		0			0
$481$	6.09318	−	34.5561i	0.277825	−	1.57562i
$482$	−9.52171	+	4.90235i	−0.433702	+	0.223296i
$483$		0			0
$484$	−3.05508	−	6.70865i	−0.138867	−	0.304939i
$485$			19.8909i			0.903201i
$486$		0			0
$487$			0.282541i			0.0128032i	0.999980	+	0.00640158i	$0.00203770\pi$
$487$			0.282541i			0.0128032i	−0.999980	+	0.00640158i	$0.997962\pi$
$488$	0.111170	−	0.00335064i	0.00503242	−	0.000151676i
$489$		0			0
$490$	−7.76987	−	15.0912i	−0.351007	−	0.681752i
$491$	−2.69135	+	15.2634i	−0.121459	+	0.688829i	0.861889	+	0.507097i	$0.169281\pi$
$491$	−2.69135	+	15.2634i	−0.121459	+	0.688829i	−0.983348	+	0.181732i	$0.941830\pi$
$492$		0			0
$493$	18.3318	−	15.3822i	0.825624	−	0.692781i
$494$	5.09819	+	40.1191i	0.229379	+	1.80505i
$495$		0			0
$496$	−6.02742	+	10.0188i	−0.270639	+	0.449858i
$497$	−3.16314	+	0.557747i	−0.141886	+	0.0250184i
$498$		0			0
$499$	−13.9873	−	38.4299i	−0.626159	−	1.72036i	−0.691385	−	0.722487i	$-0.742999\pi$
$499$	−13.9873	−	38.4299i	−0.626159	−	1.72036i	0.0652259	−	0.997871i	$-0.479223\pi$
$500$	9.47078	−	19.8419i	0.423546	−	0.887355i
$501$		0			0
$502$	−16.4139	−	3.71645i	−0.732587	−	0.165873i
$503$	−9.96192	+	17.2546i	−0.444180	+	0.769343i	−0.997995	−	0.0632975i	$-0.979838\pi$
$503$	−9.96192	+	17.2546i	−0.444180	+	0.769343i	0.553815	+	0.832640i	$0.313172\pi$
$504$		0			0
$505$	2.50117	+	4.33215i	0.111301	+	0.192778i
$506$	−2.87623	−	9.26746i	−0.127864	−	0.411989i
$507$		0			0
$508$	12.7039	+	18.4951i	0.563643	+	0.820589i
$509$	−18.1997	+	21.6895i	−0.806686	+	0.961371i	−0.999804	−	0.0198048i	$-0.993696\pi$
$509$	−18.1997	+	21.6895i	−0.806686	+	0.961371i	0.193118	+	0.981176i	$0.438140\pi$
$510$		0			0
$511$	−2.77103	+	7.61334i	−0.122583	+	0.336794i
$512$	−9.49862	+	20.5372i	−0.419783	+	0.907624i
$513$		0			0
$514$	−7.11925	−	2.98650i	−0.314017	−	0.131729i
$515$	−4.19929	−	1.52842i	−0.185043	−	0.0673502i
$516$		0			0
$517$	−24.8073	−	20.8158i	−1.09102	−	0.915476i
$518$	7.74177	−	12.0323i	0.340154	−	0.528669i
$519$		0			0
$520$	25.7165	+	13.8316i	1.12774	+	0.606558i
$521$	18.4642	−	10.6603i	0.808931	−	0.467036i	−0.0376537	−	0.999291i	$-0.511988\pi$
$521$	18.4642	−	10.6603i	0.808931	−	0.467036i	0.846584	+	0.532255i	$0.178655\pi$
$522$		0			0
$523$	17.0213	+	9.82725i	0.744289	+	0.429716i	0.823627	−	0.567132i	$-0.191947\pi$
$523$	17.0213	+	9.82725i	0.744289	+	0.429716i	−0.0793376	+	0.996848i	$0.525281\pi$
$524$	−5.96112	+	8.35232i	−0.260413	+	0.364873i
$525$		0			0
$526$	−1.38598	+	28.7719i	−0.0604315	+	1.25451i
$527$	−13.3459	+	4.85751i	−0.581356	+	0.211596i
$528$		0			0
$529$	−2.87619	−	16.3117i	−0.125052	−	0.709205i
$530$	7.47171	+	9.82861i	0.324551	+	0.426927i
$531$		0			0
$532$	−4.41120	+	15.8893i	−0.191250	+	0.688888i
$533$	11.6034	+	13.8283i	0.502597	+	0.598972i
$534$		0			0
$535$	9.09921	+	1.60444i	0.393393	+	0.0693658i
$536$	−10.5842	+	32.0531i	−0.457168	+	1.38449i
$537$		0			0
$538$	9.47298	+	8.75915i	0.408409	+	0.377634i
$539$	14.2884			0.615447
$540$		0			0
$541$	41.1619			1.76969			0.884844	−	0.465888i	$-0.154265\pi$
$541$	41.1619			1.76969			0.884844	+	0.465888i	$0.154265\pi$
$542$	−22.0784	−	20.4147i	−0.948350	−	0.876888i
$543$		0			0
$544$	−24.6593	+	12.1395i	−1.05726	+	0.520478i
$545$	4.04994	+	0.714115i	0.173481	+	0.0305893i
$546$		0			0
$547$	−4.66923	−	5.56458i	−0.199642	−	0.237924i	0.656930	−	0.753952i	$-0.271855\pi$
$547$	−4.66923	−	5.56458i	−0.199642	−	0.237924i	−0.856572	+	0.516027i	$0.827410\pi$
$548$	−3.48492	−	0.967487i	−0.148869	−	0.0413290i
$549$		0			0
$550$	−0.372736	−	0.490312i	−0.0158935	−	0.0209070i
$551$	−5.38192	−	30.5224i	−0.229277	−	1.30030i
$552$		0			0
$553$	7.41641	−	2.69935i	0.315378	−	0.114788i
$554$	1.73681	−	36.0550i	0.0737902	−	1.53183i
$555$		0			0
$556$	21.1643	+	15.1051i	0.897564	+	0.640599i
$557$	−32.2123	−	18.5978i	−1.36488	−	0.788012i	−0.374609	−	0.927183i	$-0.622223\pi$
$557$	−32.2123	−	18.5978i	−1.36488	−	0.788012i	−0.990268	+	0.139170i	$0.955556\pi$
$558$		0			0
$559$	−33.4743	+	19.3264i	−1.41581	+	0.817419i
$560$	7.48789	+	9.25718i	0.316421	+	0.391187i
$561$		0			0
$562$	9.43239	−	14.6599i	0.397881	−	0.618389i
$563$	−34.0010	−	28.5303i	−1.43297	−	1.20241i	−0.943929	−	0.330148i	$-0.892901\pi$
$563$	−34.0010	−	28.5303i	−1.43297	−	1.20241i	−0.489044	−	0.872259i	$-0.662654\pi$
$564$		0			0
$565$	7.49393	+	2.72757i	0.315272	+	0.114750i
$566$	−21.7879	−	9.13997i	−0.915816	−	0.384181i
$567$		0			0
$568$	−6.44104	+	2.56663i	−0.270260	+	0.107694i
$569$	10.0872	−	27.7143i	0.422877	−	1.16184i	−0.527176	−	0.849756i	$-0.676749\pi$
$569$	10.0872	−	27.7143i	0.422877	−	1.16184i	0.950053	−	0.312089i	$-0.101029\pi$
$570$		0			0
$571$	8.42058	−	10.0353i	0.352390	−	0.419962i	−0.560508	−	0.828149i	$-0.689394\pi$
$571$	8.42058	−	10.0353i	0.352390	−	0.419962i	0.912899	+	0.408187i	$0.133839\pi$
$572$	−20.2611	+	13.9169i	−0.847159	+	0.581893i
$573$		0			0
$574$	2.18176	+	7.02982i	0.0910647	+	0.293419i
$575$	0.204274	+	0.353814i	0.00851883	+	0.0147550i
$576$		0			0
$577$	2.02124	−	3.50090i	0.0841455	−	0.145744i	−0.820881	−	0.571099i	$-0.806517\pi$
$577$	2.02124	−	3.50090i	0.0841455	−	0.145744i	0.905027	+	0.425355i	$0.139851\pi$
$578$	−9.11409	−	2.06363i	−0.379096	−	0.0858355i
$579$		0			0
$580$	−20.1955	−	9.63956i	−0.838571	−	0.400261i
$581$	4.27797	+	11.7536i	0.177480	+	0.487622i
$582$		0			0
$583$	−10.2349	+	1.80469i	−0.423888	+	0.0747428i
$584$	−2.51677	+	17.3076i	−0.104145	+	0.716192i
$585$		0			0
$586$	−2.37637	−	18.7003i	−0.0981667	−	0.772502i
$587$	5.57370	−	4.67689i	0.230051	−	0.193036i	−0.520474	−	0.853877i	$-0.674245\pi$
$587$	5.57370	−	4.67689i	0.230051	−	0.193036i	0.750525	+	0.660842i	$0.229800\pi$
$588$		0			0
$589$	−3.19409	+	18.1146i	−0.131610	+	0.746399i
$590$	−16.8539	−	32.7349i	−0.693864	−	1.34768i
$591$		0			0
$592$	11.0844	−	28.8284i	0.455566	−	1.18484i
$593$			2.93118i			0.120369i	0.998187	+	0.0601846i	$0.0191689\pi$
$593$			2.93118i			0.120369i	−0.998187	+	0.0601846i	$0.980831\pi$
$594$		0			0
$595$			14.4627i			0.592914i
$596$	4.68435	−	2.13322i	0.191878	−	0.0873803i
$597$		0			0
$598$	14.4964	−	7.46359i	0.592800	−	0.305209i
$599$	−0.235737	+	1.33693i	−0.00963195	+	0.0546255i	−0.989245	−	0.146269i	$-0.953274\pi$
$599$	−0.235737	+	1.33693i	−0.00963195	+	0.0546255i	0.979613	+	0.200894i	$0.0643847\pi$
$600$		0			0
$601$	5.92810	−	4.97426i	0.241812	−	0.202904i	−0.513825	−	0.857895i	$-0.671772\pi$
$601$	5.92810	−	4.97426i	0.241812	−	0.202904i	0.755637	+	0.654991i	$0.227327\pi$
$602$	−15.6350	+	1.98684i	−0.637236	+	0.0809777i
$603$		0			0
$604$	2.62627	+	10.1666i	0.106861	+	0.413672i
$605$	−8.24608	+	1.45401i	−0.335251	+	0.0591138i
$606$		0			0
$607$	−3.90767	−	10.7362i	−0.158607	−	0.435770i	0.834780	−	0.550584i	$-0.185595\pi$
$607$	−3.90767	−	10.7362i	−0.158607	−	0.435770i	−0.993387	+	0.114814i	$0.963373\pi$
$608$	−2.35260	+	35.5195i	−0.0954106	+	1.44051i
$609$		0			0
$610$	0.0278987	−	0.123216i	0.00112958	−	0.00498886i
$611$	27.2072	−	47.1242i	1.10068	−	1.90644i
$612$		0			0
$613$	−12.0261	−	20.8298i	−0.485729	−	0.841307i	0.514137	−	0.857708i	$-0.328112\pi$
$613$	−12.0261	−	20.8298i	−0.485729	−	0.841307i	−0.999865	+	0.0164015i	$0.994779\pi$
$614$	−29.3993	+	9.12430i	−1.18646	+	0.368227i
$615$		0			0
$616$	−9.81350	+	2.03699i	−0.395397	+	0.0820726i
$617$	31.0148	−	36.9620i	1.24861	−	1.48803i	0.441923	−	0.897053i	$-0.354296\pi$
$617$	31.0148	−	36.9620i	1.24861	−	1.48803i	0.806685	−	0.590981i	$-0.201259\pi$
$618$		0			0
$619$	1.54241	−	4.23775i	0.0619949	−	0.170329i	−0.904828	−	0.425777i	$-0.860001\pi$
$619$	1.54241	−	4.23775i	0.0619949	−	0.170329i	0.966823	+	0.255448i	$0.0822229\pi$
$620$	9.30621	+	9.47528i	0.373747	+	0.380537i
$621$		0			0
$622$	7.80425	−	18.6038i	0.312922	−	0.745946i
$623$	8.51673	+	3.09983i	0.341215	+	0.124192i
$624$		0			0
$625$	−19.7480	−	16.5706i	−0.789921	−	0.662823i
$626$	−25.3033	−	16.2805i	−1.01132	−	0.650700i
$627$		0			0
$628$	−41.5927	−	4.01647i	−1.65973	−	0.160275i
$629$	32.4907	−	18.7585i	1.29549	−	0.747951i
$630$		0			0
$631$	−9.73065	−	5.61799i	−0.387371	−	0.223649i	0.293649	−	0.955913i	$-0.405130\pi$
$631$	−9.73065	−	5.61799i	−0.387371	−	0.223649i	−0.681020	+	0.732264i	$0.738464\pi$
$632$	14.4913	−	8.95923i	0.576434	−	0.356379i
$633$		0			0
$634$	−9.52178	−	0.458676i	−0.378158	−	0.0182164i
$635$	23.9500	−	8.71709i	0.950427	−	0.345927i
$636$		0			0
$637$	4.16911	+	23.6442i	0.165186	+	0.936817i
$638$	14.9963	−	11.4002i	0.593708	−	0.451337i
$639$		0			0
$640$	19.8881	+	16.2812i	0.786145	+	0.643570i
$641$	26.0352	+	31.0276i	1.02833	+	1.22551i	0.973895	+	0.226998i	$0.0728910\pi$
$641$	26.0352	+	31.0276i	1.02833	+	1.22551i	0.0544338	+	0.998517i	$0.482665\pi$
$642$		0			0
$643$	−31.7725	−	5.60234i	−1.25298	−	0.220935i	−0.492512	−	0.870306i	$-0.663921\pi$
$643$	−31.7725	−	5.60234i	−1.25298	−	0.220935i	−0.760472	+	0.649371i	$0.775032\pi$
$644$	6.62802	−	0.519802i	0.261180	−	0.0204831i
$645$		0			0
$646$	−29.3557	+	31.7480i	−1.15498	+	1.24911i
$647$	−7.00490			−0.275391			−0.137696	−	0.990475i	$-0.543970\pi$
$647$	−7.00490			−0.275391			−0.137696	+	0.990475i	$0.543970\pi$
$648$		0			0
$649$	30.9936			1.21660
$650$	0.702600	−	0.759859i	0.0275582	−	0.0298041i
$651$		0			0
$652$	−6.54607	+	0.513375i	−0.256364	+	0.0201053i
$653$	34.5742	+	6.09636i	1.35299	+	0.238569i	0.802689	−	0.596397i	$-0.203402\pi$
$653$	34.5742	+	6.09636i	1.35299	+	0.238569i	0.550302	+	0.834966i	$0.314513\pi$
$654$		0			0
$655$	7.49225	+	8.92892i	0.292746	+	0.348882i
$656$	7.69561	+	13.9013i	0.300463	+	0.542754i
$657$		0			0
$658$	17.6632	−	13.4276i	0.688584	−	0.523462i
$659$	1.55544	+	8.82132i	0.0605912	+	0.343630i	1.00000		0.000830029i	$0.000264206\pi$
$659$	1.55544	+	8.82132i	0.0605912	+	0.343630i	−0.939408	+	0.342800i	$0.888625\pi$
$660$		0			0
$661$	33.4732	−	12.1833i	1.30196	−	0.473874i	0.404324	−	0.914616i	$-0.367507\pi$
$661$	33.4732	−	12.1833i	1.30196	−	0.473874i	0.897634	+	0.440742i	$0.145285\pi$
$662$	34.1805	+	1.64652i	1.32846	+	0.0639938i
$663$		0			0
$664$	14.1987	+	22.9660i	0.551017	+	0.891255i
$665$	16.2217	+	9.36560i	0.629050	+	0.363182i
$666$		0			0
$667$	−10.8214	+	6.24776i	−0.419008	+	0.241914i
$668$	38.1224	+	3.68136i	1.47500	+	0.142436i
$669$		0			0
$670$	32.2448	+	20.7468i	1.24573	+	0.801520i
$671$	0.0814663	+	0.0683583i	0.00314497	+	0.00263894i
$672$		0			0
$673$	3.17294	+	1.15485i	0.122308	+	0.0445164i	0.402449	−	0.915442i	$-0.368159\pi$
$673$	3.17294	+	1.15485i	0.122308	+	0.0445164i	−0.280141	+	0.959959i	$0.590381\pi$
$674$	11.9547	−	28.4977i	0.460477	−	1.09769i
$675$		0			0
$676$	−10.7226	−	10.9174i	−0.412407	−	0.419900i
$677$	−0.395252	+	1.08595i	−0.0151908	+	0.0417363i	−0.947056	−	0.321068i	$-0.895958\pi$
$677$	−0.395252	+	1.08595i	−0.0151908	+	0.0417363i	0.931865	+	0.362804i	$0.118181\pi$
$678$		0			0
$679$	7.37410	−	8.78811i	0.282992	−	0.337257i
$680$	6.34520	+	30.5690i	0.243327	+	1.17227i
$681$		0			0
$682$	−10.6774	+	3.31381i	−0.408858	+	0.126892i
$683$	−21.5897	−	37.3945i	−0.826107	−	1.43086i	−0.901070	−	0.433673i	$-0.857217\pi$
$683$	−21.5897	−	37.3945i	−0.826107	−	1.43086i	0.0749630	−	0.997186i	$-0.476116\pi$
$684$		0			0
$685$	−2.05411	+	3.55783i	−0.0784836	+	0.135938i
$686$	−5.02625	+	22.1986i	−0.191903	+	0.847548i
$687$		0			0
$688$	−32.1751	+	11.0590i	−1.22666	+	0.421620i
$689$	−5.97274	−	16.4100i	−0.227543	−	0.625170i
$690$		0			0
$691$	−12.6458	+	2.22980i	−0.481070	+	0.0848255i	−0.408924	−	0.912569i	$-0.634096\pi$
$691$	−12.6458	+	2.22980i	−0.481070	+	0.0848255i	−0.0721458	+	0.997394i	$0.522985\pi$
$692$	−4.37303	−	16.9285i	−0.166238	−	0.643524i
$693$		0			0
$694$	18.1710	−	2.30910i	0.689761	−	0.0876523i
$695$	22.6253	−	18.9849i	0.858227	−	0.720138i
$696$		0			0
$697$	−3.35151	+	19.0074i	−0.126948	+	0.719956i
$698$	−4.86288	+	2.50370i	−0.184063	+	0.0947666i
$699$		0			0
$700$	0.384039	−	0.174889i	0.0145153	−	0.00661019i
$701$		−	3.10248i		−	0.117179i	−0.998282	−	0.0585896i	$-0.981340\pi$
$701$		−	3.10248i		−	0.117179i	0.998282	−	0.0585896i	$-0.0186603\pi$
$702$		0			0
$703$		−	48.5896i		−	1.83259i
$704$	−19.8485	+	8.61091i	−0.748069	+	0.324536i
$705$		0			0
$706$	1.96968	+	3.82567i	0.0741300	+	0.143981i
$707$	0.500991	−	2.84126i	0.0188417	−	0.106857i
$708$		0			0
$709$	7.39499	−	6.20513i	0.277725	−	0.233039i	−0.493276	−	0.869873i	$-0.664201\pi$
$709$	7.39499	−	6.20513i	0.277725	−	0.233039i	0.771001	+	0.636834i	$0.219756\pi$
$710$	0.992846	+	7.81299i	0.0372609	+	0.293216i
$711$		0			0
$712$	19.3613	+	2.81540i	0.725594	+	0.105512i
$713$	7.30325	−	1.28776i	0.273509	−	0.0482270i
$714$		0			0
$715$	9.54942	+	26.2368i	0.357128	+	0.981201i
$716$	−10.9513	−	5.22720i	−0.409269	−	0.195350i
$717$		0			0
$718$	−22.8286	−	5.16889i	−0.851957	−	0.192901i
$719$	−20.9190	+	36.2327i	−0.780146	+	1.35125i	0.151711	+	0.988425i	$0.451522\pi$
$719$	−20.9190	+	36.2327i	−0.780146	+	1.35125i	−0.931856	+	0.362827i	$0.881812\pi$
$720$		0			0
$721$	1.28869	+	2.23207i	0.0479931	+	0.0831266i
$722$	8.63488	+	27.8224i	0.321357	+	1.03544i
$723$		0			0
$724$	−26.4238	+	18.1499i	−0.982033	+	0.674535i
$725$	−0.509807	+	0.607564i	−0.0189337	+	0.0225644i
$726$		0			0
$727$	−0.167774	+	0.460954i	−0.00622238	+	0.0170958i	−0.942765	−	0.333458i	$-0.891784\pi$
$727$	−0.167774	+	0.460954i	−0.00622238	+	0.0170958i	0.936543	+	0.350554i	$0.114007\pi$
$728$	−6.23417	−	15.6448i	−0.231054	−	0.579835i
$729$		0			0
$730$	18.3197	+	7.68506i	0.678043	+	0.284437i
$731$	−38.8348	−	14.1347i	−1.43636	−	0.522791i
$732$		0			0
$733$	22.4492	+	18.8371i	0.829179	+	0.695764i	0.955102	−	0.296276i	$-0.0957448\pi$
$733$	22.4492	+	18.8371i	0.829179	+	0.695764i	−0.125923	+	0.992040i	$0.540189\pi$
$734$	−1.68875	+	2.62466i	−0.0623330	+	0.0968781i
$735$		0			0
$736$	13.7812	−	4.00657i	0.507981	−	0.147684i
$737$	−27.9521	+	16.1381i	−1.02963	+	0.594456i
$738$		0			0
$739$	34.8536	+	20.1228i	1.28211	+	0.740227i	0.977234	−	0.212164i	$-0.0680512\pi$
$739$	34.8536	+	20.1228i	1.28211	+	0.740227i	0.304877	+	0.952392i	$0.401384\pi$
$740$	−28.5562	−	20.3808i	−1.04975	−	0.749212i
$741$		0			0
$742$	0.342613	−	7.11239i	0.0125777	−	0.261104i
$743$	36.9693	−	13.4557i	1.35627	−	0.493643i	0.441373	−	0.897324i	$-0.354491\pi$
$743$	36.9693	−	13.4557i	1.35627	−	0.493643i	0.914900	+	0.403680i	$0.132269\pi$
$744$		0			0
$745$	−1.01527	−	5.75787i	−0.0371965	−	0.210952i
$746$	−8.97574	−	11.8071i	−0.328625	−	0.432287i
$747$		0			0
$748$	−25.3232	−	7.03026i	−0.925909	−	0.257052i
$749$	−3.42536	−	4.08218i	−0.125160	−	0.149160i
$750$		0			0
$751$	27.0058	+	4.76186i	0.985457	+	0.173763i	0.643079	−	0.765800i	$-0.277657\pi$
$751$	27.0058	+	4.76186i	0.985457	+	0.173763i	0.342378	+	0.939562i	$0.388768\pi$
$752$	31.4426	−	36.1304i	1.14659	−	1.31754i
$753$		0			0
$754$	23.2404	+	21.4891i	0.846365	+	0.782588i
$755$	11.9272			0.434077
$756$		0			0
$757$	−13.2822			−0.482750			−0.241375	−	0.970432i	$-0.577598\pi$
$757$	−13.2822			−0.482750			−0.241375	+	0.970432i	$0.577598\pi$
$758$	−3.20534	−	2.96380i	−0.116423	−	0.107650i
$759$		0			0
$760$	38.3957	+	12.6786i	1.39276	+	0.459900i
$761$	−12.6761	−	2.23515i	−0.459510	−	0.0810240i	−0.0608985	−	0.998144i	$-0.519397\pi$
$761$	−12.6761	−	2.23515i	−0.459510	−	0.0810240i	−0.398611	+	0.917120i	$0.630508\pi$
$762$		0			0
$763$	−1.52458	−	1.81693i	−0.0551937	−	0.0657772i
$764$	6.25807	−	22.5418i	0.226409	−	0.815534i
$765$		0			0
$766$	13.7499	+	18.0872i	0.496804	+	0.653517i
$767$	9.04337	+	51.2875i	0.326537	+	1.85188i
$768$		0			0
$769$	−27.3171	+	9.94262i	−0.985080	+	0.358540i	−0.783813	−	0.620996i	$-0.786728\pi$
$769$	−27.3171	+	9.94262i	−0.985080	+	0.358540i	−0.201267	+	0.979536i	$0.564506\pi$
$770$	−0.547781	+	11.3715i	−0.0197407	+	0.409802i
$771$		0			0
$772$	20.4154	−	28.6047i	0.734767	−	1.02951i
$773$	−4.16046	−	2.40204i	−0.149641	−	0.0863954i	0.423310	−	0.905985i	$-0.360868\pi$
$773$	−4.16046	−	2.40204i	−0.149641	−	0.0863954i	−0.572951	+	0.819590i	$0.694202\pi$
$774$		0			0
$775$	0.407642	−	0.235352i	0.0146429	−	0.00845410i
$776$	11.7306	−	21.8101i	0.421104	−	0.782937i
$777$		0			0
$778$	13.5074	−	20.9932i	0.484264	−	0.752644i
$779$	19.1487	+	16.0677i	0.686074	+	0.575685i
$780$		0			0
$781$	−6.22993	−	2.26751i	−0.222924	−	0.0811378i
$782$	16.0758	+	6.74375i	0.574870	+	0.241156i
$783$		0			0
$784$	−0.380445	+	21.1295i	−0.0135873	+	0.754626i
$785$	−16.2339	+	44.6023i	−0.579413	+	1.59192i
$786$		0			0
$787$	−25.7907	+	30.7362i	−0.919339	+	1.09563i	0.0757975	+	0.997123i	$0.475850\pi$
$787$	−25.7907	+	30.7362i	−0.919339	+	1.09563i	−0.995137	+	0.0985027i	$0.968595\pi$
$788$	26.0993	+	37.9972i	0.929751	+	1.35359i
$789$		0			0
$790$	−5.73627	−	18.4828i	−0.204087	−	0.657588i
$791$	−2.29975	−	3.98328i	−0.0817696	−	0.141629i
$792$		0			0
$793$	−0.0893474	+	0.154754i	−0.00317282	+	0.00549548i
$794$	−18.5882	−	4.20877i	−0.659671	−	0.149364i
$795$		0			0
$796$	−2.69354	+	5.64313i	−0.0954699	+	0.200015i
$797$	−10.6320	−	29.2112i	−0.376605	−	1.03471i	−0.972754	−	0.231839i	$-0.925526\pi$
$797$	−10.6320	−	29.2112i	−0.376605	−	1.03471i	0.596150	−	0.802873i	$-0.296697\pi$
$798$		0			0
$799$	57.2954	−	10.1027i	2.02696	−	0.357408i
$800$	0.734991	−	0.538141i	0.0259859	−	0.0190262i
$801$		0			0
$802$	−1.20492	−	9.48189i	−0.0425473	−	0.334817i
$803$	−12.8107	+	10.7495i	−0.452080	+	0.379340i
$804$		0			0
$805$	1.31136	−	7.43712i	0.0462195	−	0.262124i
$806$	−8.59908	−	16.7018i	−0.302890	−	0.588296i
$807$		0			0
$808$	−0.187626	−	6.22519i	−0.00660066	−	0.219001i
$809$			26.7938i			0.942021i	0.882128	+	0.471010i	$0.156111\pi$
$809$			26.7938i			0.942021i	−0.882128	+	0.471010i	$0.843889\pi$
$810$		0			0
$811$		−	22.6335i		−	0.794769i	−0.917652	−	0.397384i	$-0.869918\pi$
$811$		−	22.6335i		−	0.794769i	0.917652	−	0.397384i	$-0.130082\pi$
$812$	5.34901	+	11.7459i	0.187714	+	0.412200i
$813$		0			0
$814$	26.2568	−	13.5186i	0.920300	−	0.473825i
$815$	−1.29515	+	7.34517i	−0.0453672	+	0.257290i
$816$		0			0
$817$	−41.0019	+	34.4047i	−1.43448	+	1.20367i
$818$	−26.4359	+	3.35937i	−0.924309	+	0.117458i
$819$		0			0
$820$	17.4749	−	4.51418i	0.610249	−	0.157642i
$821$	12.6018	−	2.22203i	0.439805	−	0.0775495i	0.0506388	−	0.998717i	$-0.483874\pi$
$821$	12.6018	−	2.22203i	0.439805	−	0.0775495i	0.389166	+	0.921168i	$0.372763\pi$
$822$		0			0
$823$	8.87992	+	24.3974i	0.309534	+	0.850439i	0.992747	+	0.120220i	$0.0383599\pi$
$823$	8.87992	+	24.3974i	0.309534	+	0.850439i	−0.683213	+	0.730219i	$0.739418\pi$
$824$	3.70308	+	4.15240i	0.129003	+	0.144656i
$825$		0			0
$826$	−4.68941	+	20.7110i	−0.163165	+	0.720627i
$827$	9.69134	−	16.7859i	0.337001	−	0.583703i	−0.646866	−	0.762603i	$-0.723921\pi$
$827$	9.69134	−	16.7859i	0.337001	−	0.583703i	0.983867	+	0.178901i	$0.0572542\pi$
$828$		0			0
$829$	−15.3678	−	26.6178i	−0.533745	−	0.924474i	−0.999223	−	0.0394143i	$-0.987451\pi$
$829$	−15.3678	−	26.6178i	−0.533745	−	0.924474i	0.465478	−	0.885060i	$-0.345883\pi$
$830$	29.2918	−	9.09092i	1.01673	−	0.315550i
$831$		0			0
$832$	−20.0406	−	30.3324i	−0.694782	−	1.05159i
$833$	−16.5004	+	19.6645i	−0.571706	+	0.681333i
$834$		0			0
$835$	14.8794	−	40.8809i	0.514924	−	1.41474i
$836$	−24.2838	+	23.8505i	−0.839872	+	0.824886i
$837$		0			0
$838$	10.4460	−	24.9012i	0.360850	−	0.860199i
$839$	−10.2752	−	3.73987i	−0.354740	−	0.129115i	0.158502	−	0.987359i	$-0.449333\pi$
$839$	−10.2752	−	3.73987i	−0.354740	−	0.129115i	−0.513242	+	0.858244i	$0.671556\pi$
$840$		0			0
$841$	3.63286	+	3.04833i	0.125271	+	0.105115i
$842$	26.8103	+	17.2502i	0.923944	+	0.594480i
$843$		0			0
$844$	−2.47090	+	25.5875i	−0.0850520	+	0.880760i
$845$	−15.0532	+	8.69096i	−0.517845	+	0.298978i
$846$		0			0
$847$	4.18228	+	2.41464i	0.143705	+	0.0829680i
$848$	−2.39624	−	15.1833i	−0.0822872	−	0.521397i
$849$		0			0
$850$	1.10523	+	0.0532404i	0.0379091	+	0.00182613i
$851$	−18.4085	+	6.70013i	−0.631034	+	0.229677i
$852$		0			0
$853$	1.11668	+	6.33302i	0.0382345	+	0.216838i	0.997939	−	0.0641734i	$-0.0204411\pi$
$853$	1.11668	+	6.33302i	0.0382345	+	0.216838i	−0.959704	+	0.281012i	$0.909330\pi$
$854$	−0.0580054	+	0.0440958i	−0.00198490	+	0.00150893i
$855$		0			0
$856$	−9.03093	−	7.12545i	−0.308671	−	0.243543i
$857$	2.04068	+	2.43199i	0.0697083	+	0.0830751i	0.799772	−	0.600304i	$-0.204954\pi$
$857$	2.04068	+	2.43199i	0.0697083	+	0.0830751i	−0.730063	+	0.683380i	$0.760509\pi$
$858$		0			0
$859$	27.9109	+	4.92145i	0.952309	+	0.167918i	0.628156	−	0.778087i	$-0.283810\pi$
$859$	27.9109	+	4.92145i	0.952309	+	0.167918i	0.324152	+	0.946005i	$0.394921\pi$
$860$	3.02154	+	38.5278i	0.103034	+	1.31379i
$861$		0			0
$862$	−10.3748	+	11.2203i	−0.353368	+	0.382166i
$863$	−53.5310			−1.82222			−0.911108	−	0.412168i	$-0.864772\pi$
$863$	−53.5310			−1.82222			−0.911108	+	0.412168i	$0.864772\pi$
$864$		0			0
$865$	−19.8602			−0.675267
$866$	36.0920	−	39.0333i	1.22646	−	1.32641i
$867$		0			0
$868$	−0.598883	−	7.63638i	−0.0203274	−	0.259196i
$869$	16.0431	+	2.82884i	0.544226	+	0.0959617i
$870$		0			0
$871$	−34.8609	−	41.5456i	−1.18122	−	1.40772i
$872$	−4.01956	−	3.17145i	−0.136119	−	0.107399i
$873$		0			0
$874$	17.9741	−	13.6639i	0.607984	−	0.462190i
$875$	2.50119	+	14.1849i	0.0845555	+	0.479538i
$876$		0			0
$877$	28.0872	−	10.2229i	0.948439	−	0.345204i	0.178946	−	0.983859i	$-0.442731\pi$
$877$	28.0872	−	10.2229i	0.948439	−	0.345204i	0.769493	+	0.638655i	$0.220509\pi$
$878$	−45.1090	−	2.17296i	−1.52235	−	0.0733337i
$879$		0			0
$880$	3.83119	+	24.2756i	0.129149	+	0.818331i
$881$	−14.9002	−	8.60262i	−0.502000	−	0.289830i	0.227539	−	0.973769i	$-0.426932\pi$
$881$	−14.9002	−	8.60262i	−0.502000	−	0.289830i	−0.729539	+	0.683939i	$0.760265\pi$
$882$		0			0
$883$	19.9228	−	11.5024i	0.670455	−	0.387088i	−0.125794	−	0.992056i	$-0.540148\pi$
$883$	19.9228	−	11.5024i	0.670455	−	0.387088i	0.796249	+	0.604969i	$0.206814\pi$
$884$	4.24465	−	43.9556i	0.142763	−	1.47839i
$885$		0			0
$886$	−44.6957	−	28.7579i	−1.50158	−	0.966141i
$887$	21.8640	+	18.3460i	0.734120	+	0.616000i	0.931251	−	0.364377i	$-0.118718\pi$
$887$	21.8640	+	18.3460i	0.734120	+	0.616000i	−0.197132	+	0.980377i	$0.563163\pi$
$888$		0			0
$889$	−13.8131	−	5.02757i	−0.463278	−	0.168619i
$890$	8.59695	−	20.4935i	0.288170	−	0.686944i
$891$		0			0
$892$	14.7529	−	14.4896i	0.493963	−	0.485149i
$893$	25.7712	−	70.8058i	0.862401	−	2.36943i
$894$		0			0
$895$	−8.86013	+	10.5591i	−0.296162	+	0.352952i
$896$	−2.75097	−	14.5663i	−0.0919036	−	0.486626i
$897$		0			0
$898$	−10.9161	+	3.38789i	−0.364275	+	0.113055i
$899$	7.19828	+	12.4678i	0.240076	+	0.415824i
$900$		0			0
$901$	9.33569	−	16.1699i	0.311017	−	0.538697i
$902$	−3.35509	+	14.8179i	−0.111712	+	0.493382i
$903$		0			0
$904$	−6.60840	−	7.41024i	−0.219792	−	0.246461i
$905$	12.4540	+	34.2172i	0.413986	+	1.13742i
$906$		0			0
$907$	−57.4172	+	10.1242i	−1.90651	+	0.336169i	−0.996858	−	0.0792103i	$-0.974760\pi$
$907$	−57.4172	+	10.1242i	−1.90651	+	0.336169i	−0.909649	+	0.415379i	$0.863649\pi$
$908$	0.185983	−	0.0480439i	0.00617206	−	0.00159439i
$909$		0			0
$910$	−18.9772	+	2.41155i	−0.629088	+	0.0799422i
$911$	3.02058	−	2.53457i	0.100076	−	0.0839741i	−0.591377	−	0.806395i	$-0.701415\pi$
$911$	3.02058	−	2.53457i	0.100076	−	0.0839741i	0.691453	+	0.722421i	$0.256971\pi$
$912$		0			0
$913$	−4.48318	+	25.4254i	−0.148372	+	0.841457i
$914$	−3.11088	+	1.60167i	−0.102899	+	0.0529784i
$915$		0			0
$916$	22.2745	+	48.9127i	0.735972	+	1.61612i
$917$		−	6.72250i		−	0.221997i
$918$		0			0
$919$			6.45794i			0.213028i	0.994311	+	0.106514i	$0.0339689\pi$
$919$			6.45794i			0.213028i	−0.994311	+	0.106514i	$0.966031\pi$
$920$	−0.491119	−	16.2947i	−0.0161917	−	0.537220i
$921$		0			0
$922$	5.84924	+	11.3608i	0.192634	+	0.374149i
$923$	1.93444	−	10.9708i	0.0636729	−	0.361107i
$924$		0			0
$925$	−0.952508	+	0.799249i	−0.0313183	+	0.0262792i
$926$	0.248631	+	1.95655i	0.00817054	+	0.0642963i
$927$		0			0
$928$	16.4591	+	22.4798i	0.540297	+	0.737936i
$929$	−56.1170	+	9.89493i	−1.84114	+	0.324642i	−0.982258	−	0.187535i	$-0.939950\pi$
$929$	−56.1170	+	9.89493i	−1.84114	+	0.324642i	−0.858880	+	0.512177i	$0.828839\pi$
$930$		0			0
$931$	11.3709	+	31.2413i	0.372666	+	1.02389i
$932$	−6.23234	+	13.0571i	−0.204147	+	0.427700i
$933$		0			0
$934$	−29.1010	−	6.58908i	−0.952213	−	0.215601i
$935$	−14.9262	+	25.8530i	−0.488140	+	0.845483i
$936$		0			0
$937$	9.57464	+	16.5838i	0.312790	+	0.541768i	0.978965	−	0.204027i	$-0.0654031\pi$
$937$	9.57464	+	16.5838i	0.312790	+	0.541768i	−0.666175	+	0.745795i	$0.732070\pi$
$938$	−6.55483	−	21.1203i	−0.214023	−	0.689601i
$939$		0			0
$940$	−30.8030	−	44.8451i	−1.00468	−	1.46268i
$941$	12.0148	−	14.3187i	0.391671	−	0.466775i	−0.533791	−	0.845617i	$-0.679233\pi$
$941$	12.0148	−	14.3187i	0.391671	−	0.466775i	0.925462	+	0.378841i	$0.123677\pi$
$942$		0			0
$943$	3.44687	−	9.47021i	0.112246	−	0.308392i
$944$	−0.825237	+	45.8329i	−0.0268592	+	1.49173i
$945$		0			0
$946$	−29.9991	−	12.5845i	−0.975354	−	0.409158i
$947$	26.7426	+	9.73349i	0.869016	+	0.316296i	0.737769	−	0.675054i	$-0.235880\pi$
$947$	26.7426	+	9.73349i	0.869016	+	0.316296i	0.131247	+	0.991350i	$0.458102\pi$
$948$		0			0
$949$	−21.5259	−	18.0624i	−0.698761	−	0.586330i
$950$	0.775427	−	1.20517i	0.0251582	−	0.0391009i
$951$		0			0
$952$	8.52933	−	15.8582i	0.276437	−	0.513966i
$953$	−39.0891	+	22.5681i	−1.26622	+	0.731052i	−0.974270	−	0.225382i	$-0.927637\pi$
$953$	−39.0891	+	22.5681i	−1.26622	+	0.731052i	−0.291949	+	0.956434i	$0.594304\pi$
$954$		0			0
$955$	−23.0134	−	13.2868i	−0.744695	−	0.429950i
$956$	14.8219	−	20.7675i	0.479375	−	0.671668i
$957$		0			0
$958$	−0.993768	+	20.6299i	−0.0321072	+	0.666521i
$959$	2.22652	−	0.810386i	0.0718980	−	0.0261687i
$960$		0			0
$961$	3.89942	+	22.1147i	0.125788	+	0.713377i
$962$	30.0315	+	39.5047i	0.968253	+	1.27368i
$963$		0			0
$964$	4.05152	−	14.5937i	0.130491	−	0.470032i
$965$	−25.6592	−	30.5794i	−0.825998	−	0.984386i
$966$		0			0
$967$	9.02769	+	1.59182i	0.290311	+	0.0511896i	0.316907	−	0.948457i	$-0.397356\pi$
$967$	9.02769	+	1.59182i	0.290311	+	0.0511896i	−0.0265962	+	0.999646i	$0.508467\pi$
$968$	9.89919	+	3.26879i	0.318172	+	0.105063i
$969$		0			0
$970$	−20.6539	−	19.0975i	−0.663156	−	0.613185i
$971$	−10.7197			−0.344010			−0.172005	−	0.985096i	$-0.555025\pi$
$971$	−10.7197			−0.344010			−0.172005	+	0.985096i	$0.555025\pi$
$972$		0			0
$973$	−17.0344			−0.546098
$974$	−0.293379	−	0.271271i	−0.00940046	−	0.00869209i
$975$		0			0
$976$	−0.103256	+	0.118651i	−0.00330516	+	0.00379793i
$977$	−49.0395	−	8.64698i	−1.56891	−	0.276641i	−0.679475	−	0.733699i	$-0.737792\pi$
$977$	−49.0395	−	8.64698i	−1.56891	−	0.276641i	−0.889437	+	0.457057i	$0.848903\pi$
$978$		0			0
$979$	12.0250	+	14.3308i	0.384320	+	0.458015i
$980$	23.1300	+	6.42138i	0.738862	+	0.205123i
$981$		0			0
$982$	−13.2649	−	17.4492i	−0.423299	−	0.556826i
$983$	−0.315908	−	1.79160i	−0.0100759	−	0.0571433i	0.979355	−	0.202147i	$-0.0647918\pi$
$983$	−0.315908	−	1.79160i	−0.0100759	−	0.0571433i	−0.989431	+	0.145003i	$0.953681\pi$
$984$		0			0
$985$	49.2039	−	17.9088i	1.56777	−	0.570620i
$986$	−1.62836	+	33.8036i	−0.0518577	+	1.07653i
$987$		0			0
$988$	−46.5528	−	33.2251i	−1.48104	−	1.05703i
$989$	18.6883	+	10.7897i	0.594252	+	0.343092i
$990$		0			0
$991$	−48.8792	+	28.2204i	−1.55270	+	0.896451i	−0.554777	+	0.831999i	$0.687196\pi$
$991$	−48.8792	+	28.2204i	−1.55270	+	0.896451i	−0.997921	+	0.0644516i	$0.979470\pi$
$992$	−4.61611	−	15.8778i	−0.146562	−	0.504121i
$993$		0			0
$994$	2.45783	−	3.81997i	0.0779577	−	0.121162i
$995$	5.44102	+	4.56556i	0.172492	+	0.144738i
$996$		0			0
$997$	−11.0934	−	4.03767i	−0.351331	−	0.127874i	0.160325	−	0.987064i	$-0.448746\pi$
$997$	−11.0934	−	4.03767i	−0.351331	−	0.127874i	−0.511657	+	0.859190i	$0.670968\pi$
$998$	53.3333	+	22.3731i	1.68824	+	0.708209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.179.4		96
3.2	odd	2		108.2.l.a.23.13	yes	96
4.3	odd	2	inner	324.2.l.a.179.9		96
9.2	odd	6		972.2.l.c.215.2		96
9.4	even	3		972.2.l.a.863.7		96
9.5	odd	6		972.2.l.d.863.10		96
9.7	even	3		972.2.l.b.215.15		96
12.11	even	2		108.2.l.a.23.8	✓	96
27.2	odd	18		972.2.l.a.107.2		96
27.7	even	9		108.2.l.a.47.8	yes	96
27.11	odd	18		972.2.l.b.755.13		96
27.16	even	9		972.2.l.c.755.4		96
27.20	odd	18	inner	324.2.l.a.143.9		96
27.25	even	9		972.2.l.d.107.15		96
36.7	odd	6		972.2.l.b.215.13		96
36.11	even	6		972.2.l.c.215.4		96
36.23	even	6		972.2.l.d.863.15		96
36.31	odd	6		972.2.l.a.863.2		96
108.7	odd	18		108.2.l.a.47.13	yes	96
108.11	even	18		972.2.l.b.755.15		96
108.43	odd	18		972.2.l.c.755.2		96
108.47	even	18	inner	324.2.l.a.143.4		96
108.79	odd	18		972.2.l.d.107.10		96
108.83	even	18		972.2.l.a.107.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.8	✓	96	12.11	even	2
108.2.l.a.23.13	yes	96	3.2	odd	2
108.2.l.a.47.8	yes	96	27.7	even	9
108.2.l.a.47.13	yes	96	108.7	odd	18
324.2.l.a.143.4		96	108.47	even	18	inner
324.2.l.a.143.9		96	27.20	odd	18	inner
324.2.l.a.179.4		96	1.1	even	1	trivial
324.2.l.a.179.9		96	4.3	odd	2	inner
972.2.l.a.107.2		96	27.2	odd	18
972.2.l.a.107.7		96	108.83	even	18
972.2.l.a.863.2		96	36.31	odd	6
972.2.l.a.863.7		96	9.4	even	3
972.2.l.b.215.13		96	36.7	odd	6
972.2.l.b.215.15		96	9.7	even	3
972.2.l.b.755.13		96	27.11	odd	18
972.2.l.b.755.15		96	108.11	even	18
972.2.l.c.215.2		96	9.2	odd	6
972.2.l.c.215.4		96	36.11	even	6
972.2.l.c.755.2		96	108.43	odd	18
972.2.l.c.755.4		96	27.16	even	9
972.2.l.d.107.10		96	108.79	odd	18
972.2.l.d.107.15		96	27.25	even	9
972.2.l.d.863.10		96	9.5	odd	6
972.2.l.d.863.15		96	36.23	even	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.960112 + 1.03836i) q^{2} +(-0.156370 - 1.99388i) q^{4} +(-2.23728 - 0.394492i) q^{5} +(0.842213 + 1.00371i) q^{7} +(2.22049 + 1.75198i) q^{8} +(2.55766 - 1.94434i) q^{10} +(0.469629 + 2.66340i) q^{11} +(-4.27030 + 1.55426i) q^{13} +(-1.85083 - 0.0891568i) q^{14} +(-3.95110 + 0.623564i) q^{16} +(-4.20783 - 2.42939i) q^{17} +(-5.44971 + 3.14639i) q^{19} +(-0.436727 + 4.52254i) q^{20} +(-3.21645 - 2.06952i) q^{22} +(1.94350 + 1.63079i) q^{23} +(0.151321 + 0.0550764i) q^{25} +(2.48609 - 5.92636i) q^{26} +(1.86958 - 1.83622i) q^{28} +(-1.68452 + 4.62818i) q^{29} +(1.87889 - 2.23918i) q^{31} +(3.14601 - 4.70134i) q^{32} +(6.56256 - 2.03674i) q^{34} +(-1.48831 - 2.57783i) q^{35} +(-3.86074 + 6.68701i) q^{37} +(1.96525 - 8.67963i) q^{38} +(-4.27671 - 4.79563i) q^{40} +(-1.35861 - 3.73275i) q^{41} +(8.37644 - 1.47699i) q^{43} +(5.23705 - 1.35286i) q^{44} +(-3.55932 + 0.452305i) q^{46} +(-9.17264 + 7.69676i) q^{47} +(0.917425 - 5.20298i) q^{49} +(-0.202474 + 0.104246i) q^{50} +(3.76675 + 8.27142i) q^{52} +3.84281i q^{53} -6.14402i q^{55} +(0.111646 + 3.70427i) q^{56} +(-3.18837 - 6.19270i) q^{58} +(1.99002 - 11.2860i) q^{59} +(0.0301227 - 0.0252759i) q^{61} +(0.521117 + 4.10082i) q^{62} +(1.86114 + 7.78050i) q^{64} +(10.1670 - 1.79271i) q^{65} +(4.08179 + 11.2146i) q^{67} +(-4.18593 + 8.76978i) q^{68} +(4.10565 + 0.929606i) q^{70} +(-1.22570 + 2.12297i) q^{71} +(3.09175 + 5.35507i) q^{73} +(-3.23675 - 10.4291i) q^{74} +(7.12569 + 10.3741i) q^{76} +(-2.27775 + 2.71452i) q^{77} +(2.06018 - 5.66029i) q^{79} +(9.08569 + 0.163591i) q^{80} +(5.18035 + 2.17314i) q^{82} +(8.97051 + 3.26500i) q^{83} +(8.45570 + 7.09518i) q^{85} +(-6.50867 + 10.1158i) q^{86} +(-3.62341 + 6.73682i) q^{88} +(5.99050 - 3.45862i) q^{89} +(-5.15653 - 2.97713i) q^{91} +(2.94769 - 4.13011i) q^{92} +(0.814780 - 16.9142i) q^{94} +(13.4337 - 4.88948i) q^{95} +(-1.52040 - 8.62260i) q^{97} +(4.52172 + 5.94806i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

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